PHOTOCHEMICAL GENERATION & HYDRATION OF ISOMERIC ...

PHOTOCHEMICAL GENERATION & HYDRATION OF ISOMERIC NAPHTHAQUINONE

METHIDES

by

FARES A. EL-KATRI

(Under the Direction of Vladimir Popik)

ABSTRACT

The ortho-quinone methides (o-QMs) are potentially very important intermediates in organic and

biochemistry. This work is a contribution to the chemistry of the o-QMs. Different ways to

produce o-QMs are explored. The focus in this work is on the photogeneration of the ortho-

naphthaquinone methide isomers with possible spectroscopic and kinetic investigation for their

hydration back to their synthetic precursors.

INDEX WORDS: o-quinone methides, methides, o-naphthaquinone methides

http://www.chem.uga.edu/phonebook/cgi/expand.cfm?ln=Popik&fn=Vladimir&id=1&sortvar=LastName,FirstName


METHIDES

by

FARES A. EL-KATRI

B.S., Mansoura University, Egypt, 1986

Dip. Chem., Bielefeld University, Germany, 1994

A Thesis Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment

of the Requirements for the Degree

MASTER OF SCIENCE

ATHENS, GEORGIA

2006

© 2006

FARES A. EL-KATRI

All Rights Reserved


METHIDES

by

FARES A. EL-KATRI

Major Professor: Vladimir Popik

Committee: Nigel G Adams John L Stickney

Electronic Version Approved: Maureen Grasso Dean of the Graduate School The University of Georgia May 2006


http://www.chem.uga.edu/phonebook/cgi/expand.cfm?ln=Adams&fn=Nigel&id=1&sortvar=LastName,FirstName

ACKNOWLEDGEMENTS

I would like to thank my advisor Dr. Vladimir Popik, his research group and my

committee members for their support.

iv


TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS........................................................................................................... iv

LIST OF TABLES......................................................................................................................... vi

LIST OF FIGURES & SCHEMES............................................................................................... vii

CHAPTER

1 INTRODUCTION .........................................................................................................1

2 O-QUINONE METHIDES CHEMICAL PROPERTIES .............................................6

3 O-QUINONE METHIDES GENERATION ...............................................................23

4 O-QUINONE METHIDES PRECURSORS…………………………………………32

5 FLASH PHOTOLYSIS………………………………………….…………………...35

5 EXPERIMENTAL…………………………………………………………………...41

6 SPECTRA....................................................................................................................46

APPENDIX……………………………………………………………………………................73

REFERENCES ..........................................................................................................................…94

v

LIST OF TABLES

Page

Table 1: Calculated Resonance Energies for Naphthaquinone Methides (96-98)……………….20

Table 2: Chemical Reactivity Indices for Naphthaquinone Methides (96-98) ..............................21

Table 3: Chemical Reactivity Indices for Naphthaquinone Methides (96-98) ..............................22

vi

LIST OF FIGURES & SCHEMES

Page

Scheme 1: Ortho-quinone methide and its resonance structure…………………………………...1

Scheme 2a: alkylation sites on purine and pyrimidine nucleobases……….………………….….2

Scheme 2b: Possible reactive orientations between an o-quinone methide and dG, and dA…….2

Scheme 2c: DNA cross-linking through tandem quinone methide generation induced by

fluoride……………………………………………….……………………………………………3

Scheme 3: o-QMs reactivity…………………..……………………………………….………….4

Scheme 4: Photogeneration of o-naphthaquinone methides intermediates…………………..…..5

Scheme 5: Diels-Alder [2+4] intermolecular cycloadditions……………………………………..6




Scheme 9: Reduction of o-QMs………………………………………………………………….10

Scheme 10: Reduction of o-Quinone Methides Mechanism.........................................................11

Scheme 11: Reactions of o-QMs with nucleophiles………………………………………..……11

Scheme 12: Reactions of o-QMs with nucleophiles…………………………………………..…12

Scheme 13: Reactions of o-QMs with nucleophiles……………………………………………..12

Scheme 14: Formation of lactones …………….……………………...…………………………13

Scheme 15: formation of furans and phenanthrapyran-2-one …………………………...………15

vii

Scheme 16: electrocyclic rearrangements………………………………………………………..16

Scheme 17: Sigmatropic shift……………………..…….……………………………….………16

Scheme 18: o-QMs interaction with radiation ……………………………………….………….17

Scheme 19: o-QMs interaction with radiation………………………………...…………………17

Scheme 20: 2 o-QMs interaction with radiation…………………………………………………18

Scheme 21: o-Naphthaquinone Methides………………………………………………….……19

Scheme 22: nucleophilic addition and/or dimerization………………………………….………20

Scheme 23: Tautomerization……………………………………………………………….……25

Scheme 24: Oxidation……………………………………………………………………………26

Scheme 25: Thermolysis…………………………………………………………………………27

Scheme 26: Photolysis…………………………………………………………………...………28

Scheme 27: Using an acid……………………………………………………………..…………29

Scheme 28: Using a base……………………………………………………...…………………30

Scheme 29: Olefination…………………………………………………………………..………31

Scheme 30: o-QMs Preprecursors…………………………………………………….…………32

Scheme 31: o-QMs Isomers……………………………………………………………...………32

Scheme 32: preparation of 3-(hydroxymethyl)-2-naphthol (2)……………………….…………33

Scheme 33: photogeneration of the o-naphthaquinone methide (5)…………………………..…33

Scheme 34: preparation of 2-(Hydroxymethyl)-1-naphthol (6)……………………………….…34

Scheme 35: photogeneration of the o-naphthaquinone methide (6)………………………..……34

Scheme 36: decomposition to methylenedinaphthol……………………………………….……34

Figure 1 Flash photolysis set-up………………………………………...……………….………35

Figure 2 Kinetic mode…………………………………………………………………...………36

viii

Figure 3 Spectral Slicing…………………………………………………………………………37

Figure 4 Spectral mode…………………………………………………………………..………37

Figure 5: Kinetic Slicing……………………………………………...…………………….……37

Figure 6: UV-vis spectra…………………………………………………………………………38

Figure 7: Fluorescence Spectrum………………………………………………………...………39

Scheme 37: Dehydration reaction……………………………………………………..…………39

Scheme 38: Hydration reaction…………………………………………………..………………40

Scheme 39: The kinetic reaction…………………………………………………………………40

Figure 8: Spex Flurolog fluorescence spectrophotometer………………………………………45

ix

CHAPTER 1

INTRODUCTION

Ortho-Quinone methides (o-QMs) exist widely as reactive intermediates in

organic and biochemistry.3-7 The therapeutic benefits of antitumor and antibiotic drugs

such as mitomycin C and that of vitamins E and K depend on such compounds to produce

transient electrophilic o-QMs intermediates.1

The o-QM 1 is an example of strongly resonance-stabilized zwitterion 2 (scheme

1). This high resonance stabilization leads to a high kinetic stability and consequently

very important biological activities due to their high electrophile selectivities toward

DNA (scheme 2) and proteins.2, 8

O

1

O

2

Scheme 1: o-quinone methide and its resonance structure

1

N

NN

N

R

NH2

N

NHN

N

R

O

NH2N

N

NH2

O

R

N

NH

O

O

RdA dG dC dT

Scheme 2a: alkylation sites on purine and pyrimidine nucleobases

N

NN

N

R

NH2

dA

O

N

NN

N

R

NH2

O

N

NHN

N

R

O

NH2

dG

O

N

NN

N

R

O

NH2

O

H

3

4

Scheme 2b: possible reactive orientations between an o-QM and dG, and dA

2

OSi(Me)2tBu

BrBr+HF

-Si(Me)2tBu

O

BrBr

-Br

O

Br+DNA

-Br

O

DNA

+DNA

O

DNADNA

5 6

7 8

9

Scheme 2c: DNA cross-linking through tandem o-QM generation induced by fluoride

In general the o-QMs 1 and 18 undergo nucleophilic reactions (by reacting with

HX 10-12 to give the products 13-15, where X=-OH, -OCH3, -OCH2CF3) and a hetero-

Diels-Alder cycloaddition by reacting with an alkene 16 to give the product (17) due to

the presence of two different highly functioning groups (scheme 3).172 Consequently, it

has been suggested that o-QMs would have a very high synthetic potential. However, o-

QMs are still outside the synthetic scope. 6

3

O

1

OH

X

13-15

O

R2

R1O OEt

R218

16 17

HX10-12

Scheme 3: o-QMs reactivity

o-QMs can be photochemically generated by the photolysis of their precursors.

Consider the irradiation of the 3-(Hydroxymethyl)-2-naphthol (19) in its electronic

ground state S0 to give the corresponding o-QM (21) through the intermediate (20)

(scheme 4).

The intermediate 20 is the first electronic excited state S1,of the 3-(Hydroxymethyl)-2-

naphthol (19) where one electron is promoted from the HOMO to the LUMO causing

disturbance to the molecular electronic structure (and consequently leading to a chemical

reaction). The electronic density distribution in S1 is different from that in S0.

Accordingly, the marked proton in S1 is more acidic than in S097-104 and a rearrangement

step involving an excited state intramolecular proton transfer (ESIPT)105-155, 171 leading to

the o-QM 20 takes place.

The hydration of 21 back to 19 and the ESIPT direct kinetic measurements are possible

using time resolved spectroscopy.

4

O

OH

O

OH

O OH

OH

19 20

21 19

HH

hυ

S0S1

H2O-H2O

Scheme 4: photogeneration of o-naphthaquinone methide intermediates

The ESIPT is pH dependent. The ESIPT rate dependency on pH (the rate profile)

could be investigated in aqueous buffered solutions. Isotope substitution of the marked H

in 19 and 20 with D by using D2O in their aqueous solutions as a solvent would make the

investigation of the kinetic isotope effect KIE possible, where: KIE=KH/KD.9-10, 171, 173-177

5

CHAPTER 2

O-QUINONE METHIDES CHEMICAL PROPERTIES

2.1 Reactivity

The o-QMs are highly reactive intermediates.6 The o-QM 1 has been

characterized only spectroscopically at -100˚C. The reactivity of such intermediates can

be illustrated by their reactions in organic and bioorganic chemistry.

2.1.1. Diels-Alder [2+4] intermolecular cycloadditions:11-17

o-QMs like 1 react with alkenes like ethene 2 to produce the chroman 3 (scheme

5).

+

OO

1 2 3 Scheme 5: Diels-Alder [2+4] intermolecular cycloadditions

The o-QMs E (4) and Z (5) react with olefins (6) to give the trans-products (7)

and (8) which are thermodynamically favored and the cis-form (9) which is kinetically

favored (scheme 6). Where, the product form depends on the transition state orientation,

the starting o-QM geometry and the products stability. Heating C60 (10) for 48h with (11)

6

gives the [2+4] adduct (12), in 31% yield, where; heating 11 gives the o-QM 1 first.

While; the same reaction could be done using microwave/800w in 4 min. in 27% yield

(scheme 7). The chroman (16) is produced by heating vinylphenol (13), which undergoes

1,5-sigmatropic shift to give Z o-QM (14), that equilibrates to the more stable E o-QM

(15) and that reacts with vinylphenol (13) to give the product (scheme 8).

R3

O

R1

R3

R2

R3

endo

exo

O

R1R2

R3

trans-2,4-disubstituted chroman

R3

R3 O

R2

R1

R3

exo

endocis-2,4-disubstituted chroman

O

R1

R2 EO

R2

R1

Z

O

R2

R1 Z

O

R1 R2E

45

6 6

7

8

9

5

4

6

6

Scheme 6: Diels-Alder [2+4] intermolecular cycloadditions

7

+

O

O

10

11

12

OH

OH

Δ

Δ1

Scheme 7: Diels-Alder [2+4] intermolecular cycloadditions 2.1.2. Reduction of o-QMs:17-23

The phenolic ketones side-chain oxygen reductive removal is seen in the

reduction of 17-19 to give 20 (85, 29% yield), 21 (90% yield), and 22-26 (87%-95%)

respectively (scheme 9), where; these reactions takes place through the reduction of o-

QMs intermediates. As an example, in the last reaction the keton is reduced to benzylic

alcohol 27 (followed by carbonate migration 28), which decomposes to the o-QM (29).

8

Hydride addition to 29 gives 30. Protonation of 30 gives the phenolic adducts 22-26

(scheme 10).

OH

90oC12h

O

Z

O

EOH

O

13

14

15

13

16OH

Scheme 8: Diels-Alder [2+4] intermolecular cycloadditions

2.1.3. Reactions of o-QMs with nucleophiles: 14, 18, 21, 23-34

Oxidation of 31 with Ag2O gives the o-QM 32, which; undergoes; conjugate

additions with amines, thiols, alcohols, and DNA bases to give 33-36 (scheme 11).

Heating the phenol 11 gives the o-quinone methide (1), which reacts with N,N-

carbonyldiimidazole 37 (X=O) or N,N-thionyldiimidazole 38 (X=S) to produce benzylic

imidazoles 39 and 40 (scheme 12).

9

The β-naphthol Mannich base 41 gives the o-QM 42, which reacts with aniline

derivatives 43 to give the 1-4 addition product 44, which by heating gives the polycyclic

heteroatomic compounds 45-47 through intramolecular cyclization (scheme 13).

Y

X

OH

NMe3

Y

X

OH

LAH

AcHN OAc

n-Pr

O

NaBH4

aq. C2H5OH

AcHN OAc

n-Pr

K

L

M

R

J

O

NaBH4 / THF

H2O

K

L

M

OH

R

17

18

19

20

21

22-26

Scheme 9: Reduction of o-QMs

Where,

22: R=-CH3, K=J=-OCO2Me, L=M=H, 94% yield

23: R=-CH3, K=M=H, L=J=-OCO2Me, 98% yield

24: R=-CH3, K=L=H, M=J=-OCO2Me, 92% yield

25: R=-CH3, K=M=J=-OCO2Me, L=H, 87% yield

26: R=-Ph, K=J=OCO2Me, L=M=H, 95% yield

10

M J

L

K

O R

NaBH4

M J

L

K

O R

K

L

M O

J R

-CO2

-OMe-M O

L

K

H- H+

R

22-26

M O

L

K

R

19 28

30

27

29

Scheme 10: Reduction of o-QMs Mechanism

OAc

OH

Ag2O

NuH

OAc

O Nu

33: Nu=-NHPh

35: Nu=-OEt

H

34: Nu=-SBu

36: Nu=-Adenosine

OAc

31

O

32

33-36

Scheme 11: Reactions of o-QMs with nucleophiles

11

N

N

X

N

N

O

N

N

X

N

N

O

OH

OH

OHN

N

OHN

N

11

39

40

37

38

OΔ

1


OH NMe2

H2N

R'

RO R'

OH

R

NH2

N

N

N

HN

N

41 42 43

44

47

4645


12

2.1.4 Formation of γ-lactone, furan, and δ-lactone drevatives: 35-36

Condensation of the phenol 48 with the aldehyde 49 upon the addition of an acid

gives the o-hydroxybenzyl alcohol 50, which gives the o-QM 51 under acidic conditions.

The o-QM 51 undergoes Pd mediated carbonylation to give 52 which gives the lactones

53-55 by reductive elimination in yields ≈ 50% (scheme 14).

R1 R1 R

R2

R1

R1

O

R

R2

R1

R1

OPd

O

R

O O

O

O

O

O

O

O

O

O

O

O

O

Pd - CO g, 80 - 160 oC51 52

R2

R1 OH

RCHO

CF3CO2H

R2

R1 OH

OH H+

48

49

50

555453

Scheme 14: Formation of lactones

13

The o-QM 56 reacts with 1 equivalent of nonstabilized phosphonium ylides 57 to

produce the o-QM intermediate 58 that reacts with another equivalent of 57 to produce

the intermediate 59, which undergoes SN2 displacement to give 60. Oxidation of 60 with

NBS gives the corresponding furan 61 (scheme 15).

The o-QM 56 also reacts with 1 equivalent ester stabilized phosphonium ylides 62

to give the o-QM intermediate 63 which reacts again with another equivalent of 62 to

give the intermediate 65. Elimination of PPh3 and ROH from 64 leads to the production

of 63 and phenanthrapyran-2-one 66 (scheme 15).

2.1.5 Electrocyclic Rearrangements: 6, 21, 23, 37-41

Oxidation of 67 and 68 leads to the o-QMs 69 and 72, which undergo

electrocyclic rearrangements 2π+2π+2π to produce 71 in 90% yield and 74 in 80% yield

respectively (scheme 16). The addition of Grignard reagent 75 to 76 or 77 gives the o-

QM 78, which reacts with 75 to give 79. The compound 78 also undergoes sigmatropic

shift (in the absence of the nucleophile) to give 80. (scheme 17).

2.1.6 o-QMs interaction with radiation: 41-45

The 4-Phenyl-3-chromanone 81 photoisomerizes to 4-Phenyldihydrocoumarin 85.

Where, the chromanone 81 undergoes enol tautomerization to 82. The compound 82

undergoes photochemical ring opening to the o-QM 83, which undergoes ring closure by

heating or photolysis to give 1- hydroxy-5-phenyl-2 oxabenzobicyclo[3.1.0]hex-3-ene

(84) and that undergoes ring opening to the observed dihydrocoumarin 85 (scheme 18).

14

O

O

PPh3

R

O

R

PPh3

R

OPPh3

R

R

OO

R

R

NBS R

R

5657 5758 59

60 61

O

O

CO2R

CH

Ph3P CO2R56 63Ph3P CO2R 6262

O

O

CO2R

CO2R

PPh3

-PPh3

OH

CO2R

O

OR

-ROH64 65

O

O

RO2C 66

Scheme 15: Formation of furans and phenanthrapyran-2-one

15

Ph

O

O

Ph

O

O

O

O

Ph

O

O

O

Ph

O O

O

O O

O

O O

O

697170

O

O

HO

Ag2O

Na BH4

Δ

O O

HO

Ag2O7372 74

67

68

Scheme 16: electrocyclic rearrangements

Y

X

OCOB

OBOC

O

Y

X

OCOB O

Y

X

OH

H

Y

X

OH

Y

X

2CH3 M

gBr

CH 3MgBr

O

2CH3 M

gBr

Sigmatropic Shift76

75

75

7577

78

79

80

Scheme 17: sigmatropic shift

16

O

Ph

OH

PhPh

O

OH

OOH

Ph

hυ

83

84

hυ

or Δ

Δ (?)82

O

O

81

O

Ph

O

85

Scheme 18: o-QMs interaction with radiation

The compound 86 isomerizes to 87, which by photolysis gives the biradical 88

and that rearranges in 89 to the cycloheptatrien 90 (scheme 19). Photolysis 91 at 433nm

gives the carbene 92, which by radiation at 313 nm gives the Z o-QM intermediate 93.

Irradiating 89 at 313nm for 20h gives 94. While, irradiating 93 at 366-340 nm produces

95 (scheme 20).

X

Y

Z

O

Ph

CORX

Y

Z

O

COR

Ph

ROC

X

Y O

Z

O

ROC

O

ROC

hυ86 8788

89 90

17


O NN

Cl

O

Cl

O

H

Cl

433 nm 313 nm

366

313 nm

-340 nm

Cl

O

OCl

91 92

93

95

94


18

2.2. O-QMs Stability:

The stability of o-naphthaquinone methides 96-98 (scheme 21) depends on their

structure (the structure is a function of conjugation, electronic and steric effects of

substituents).

O O

96

O

97

O

98

O O

Figure 21: o-naphthaquinone methides

The stability of naphthaquinone methides 96-98 was investigated in terms of

thermodynamic and kinetic stabilities.46-47

1. Thermodynamic stability: the calculated aromatic stabilization (the

aromaticity) using HMO of 4n-π-electron species 96-98 is correlated with

their thermodynamic stability (equation 1), where;

19

Aromatic Stability Hueckel Energu − The Localized structure Energy/The Number of Electrons The resonance Energy/Electron≡ The Thermodynamic Stability equation 1

Accordingly the compounds 96-98 are considered as non aromatic crossconjugated

enones because their resonance energy per electron (REPE) in table 1 are very low

(<0.030β).

Table 1: Calculated Resonance Energies for Naphthaquinone Methides (96-98)47

Compound HMO E(β) REPE(β)

1,2-Naphthaquinone Methide 16.0268 0.0472

2,1- Naphthaquinone Methide 16.0248 0.0470


2. kinetic stability: was investigated in terms of the ability of 96-98 to undergo

the following nucleophilic addition and/or dimerization reactions (scheme 22).

O

+ NuNu

O

O

2

O

O

Scheme 22: nucleophilic addition and/or dimerization

20

The possibility of the previous reactions to take place can be evaluated using the

frontier orbital theory by calculating the reactivity indices for the compounds 96-98 (table

2) following Klopman 90-92 procedures, where; according to the perturbation theory, the

covalent interaction between 2 centers i and j is described by the following general

expression (equation 2):

ΔEij 2moccn

unocc − munoccn

occ.cimcjnHij/n − m equation 2

Where, ci and cj are the expansion coefficients for the reacting centers i and j, εm and εm

are the energies for the unoccupied and occupied orbitals respectively. Hij is the

resonance integral between the atomic orbitals. According to equation 2 , a σ-bond will

be formed between 2 centers i and j, which afford the highest Δ Eij value, i.e. the

maximum overlap stabilization.

Table 2: Chemical Reactivity Indices for Naphthaquinone Methides (96-98)47

Compound ΔEi(β-1) ΔEij(β-1)

1,2-Naphthaquinone Methide 1.3277 0.387



The stability index P (table 3) represents the overall stability of the o-naphthaquinone

methides (96-98) as a combination of the thermodynamic, the kinetic and the perturbation

terms (equation 3), where; C is a normalization constant, and ΔEi is the perturbation

indices.

P CREPE/ΔEi.ΔEij equation 3

21

Table 3: Chemical Reactivity Indices for o-naphthaquinone methides (96-98)47

Compound P Stability Reference

1,2-Naphthaquinone Methide 40.2 Moderately stable 193

2,1- Naphthaquinone Methide 35.2 Not known 47

2,3- Naphthaquinone Methide 11.9 Not stable 47

22

CHAPTER 3

O-QUINONE METHIDES GENERATION

3.1. Tautomerization:12-38

Coenzyme Qn (1) and vitamin K1 (2) tautomerize to produce o-QMs 3 and 4

(scheme 23).

3.2. Oxidation:13-14, 48-54

The compounds 5-9 undergo oxidation to the o-QMs 10-12, 15-16. The epoxide

13 equilibrates with the o-QM 15. While, the epoxy intermediate 14 leads to the o-QM 16

(scheme 24).

3.3. Thermolysis:11, 14, 15, 30, 31, 36, 54-72

It is the most common method to generate the o-QMs, where the precursors 17-29

(17: R=-H, -CH3; R2=-H, 18: R=S, R2=2(-CF3), 20: R2=Ph, R4=-OCH(CH3)2, 22: X=-Cl,

-Br, 23: R=R2=-H, X=halogen, 25: R=-H, -Ph, R2=-H, 26: R=Ph) are shown to give the

o-QMs 30-42 (30=36=40=42: A=B=C=D=R2=R3=-H, 32=35=37=39=41:

A=B=C=D=R3=-H, 31: A=B=C=D=H, R2=2-CF3, 33: A=-Ph, B=-OCH(CH3)2, C=-OH,

D=-H, R2=R3=-H, 34: A=B=C=D=R3=-H, R2=CN, 38: A=B=C=D=R3=-H, R2=C4H8CN)

respectively as intermediates (scheme 25).

23

3.4. Photolysis:6, 9, 10, 39, 40, 42-44, 50, 73-83

Radiation of 17, 19, 23-24, 43-45 gives 50 (R1=-H, R2=-H or -Ph), 51=52=53

(R1=R2=-H), 54 (R1=-CH3, R2=-Ph), 55 (R1=-H, R2=-Ph), and 56 (R1=R2=-H)

respectively (scheme 26), where 46 and 49 are starting materials and 47-48 are

intermediates.

3.5. Using an acid:84-89

The compounds 17, 26, 58-60 lead to the o-QMs 63-67 through acid facilitation,

where; Halogenation of the THP protected phenol 61 under free radical conditions using

NBS/AlBN gives 58. The compound 58 reacts with 1 equivalent of tetrachlorocatechol

TCC, which cleaves the THP group producing 66. The salicylic aldehyde 62 is used to

synthesize the o-TMS and o-MOM aryl ether benzyl alcohols 59 and 60. Treating 59 or

60 with acid cleaves the TMS or the MOM groups to afford the o-QM 67 (scheme 27).

3.6. Using a base:12, 21-23, 26-28, 38, 156-169

The compounds 68-78 produce the o-QMs 81-91 through base facilitation

(scheme 28), where compound 79 reacts with NaBH4 to give the precursor 70, the

compound 80 reacts with CH2(OCH3)2 to give the precursor 72, and the compound 92

reacts with Nuc-M+ to give the precursor 78.

3.7. Olefination:170-171

Phosphorous ylides 93 react with phenanthraquinone 94 to produce the o-QMs 95.

Also the o-quinone 96 reacts with ynamine 97 to give the o-QM 98 (scheme 29).

24

OO

O

O O

O

n

Coenzyme Qn

Vitamin K1

OH

OO

O

n

HO O

1

2

3

4

Scheme 23: Tautomerization

25

O

HOK3Fe(CN)6

O

O

5 10

O

HO O

O

6 11K3Fe(CN)6

t-Bu

t-Bu

OH

Ag2O7

t-Bu

t-Bu

O

12

O

R1 R2

O

X

R1

R2

O O

X

R1

R2

O

DMDO

OO

OO

O

O OO

O

O2 -MeOH9 14 16

8 13 15

X

Scheme 24: Oxidation

26

N

HOR

R2

X

HO

R2

O

N

HO R2

X

HO

R2

O

R

O

R2

O

OR

OH

R2

O

O

R

R

R2

O

O

N

OR2

RRS

OH

R2

OH

OR

O

R2

R

R

R1

ON3

Δ

O

R3

R2

A

B

C

D

ΔMe2NRΔ

X-

Δ

Δ

Δ

Δ

Δ

N2

Me2NH

RO2

Δ

Δ

Δ

Δ

ROH

Δ

R2CO

N

R

17

18

19

20

21

2223

24

25

26

27

28

29

30-42

Scheme 25: Thermolysis

27

OH

R2

OR

NMe2

R2

OH

OH

R2

Me3N

R2HO

O

R2

O

N

N

Ph

OH

N2

OH

O

O

Cl

NN

O

Cl

R1

R2

O254nm

, RT

Φ=0.25

>300

nm, 0

o CΦ=

0.98

254nm

Φ=0.98

254nm, ESIPT

Φ=0.13

1,5-σ tropic shift254

nm300 nm

300 nm254 nm

433 n

m

313 nm

50-56

17

19

23

24

46

47

4849

43

44

45

Scheme 26: Photolysis

28

X

R2

OH

OMOM

X

R2

OH

OTMS

XH

OH

OH

(1) -H+

(2) -R2

HClCH3OH/Δ

SR

OH

R2

OR

OH

R2

A: LiClO4/CH3NO2 , or MgBr2, or cat. BF3.Et2O

B: TiCl3, or BF3.Et2O, or AlCl3, or TFA/20-70oC

C: LiClO4/CH3NO2 or H3O+ , or Benzene, cat. BF3.Et2O

D: 1 eq. TCC/Δ

63=64=65 (R1=R3=H), 66 (R1=X, R2=H, R3=Y)

O

BO PhR2

Y

X OTHPNBSAlBN

Y

X

OTHP

Br

O

R2

R3

R1

63-66

A

B

C

D

2617

57 61

58

X

R2

O

62

59

60

67

Scheme 27: Using an acid

29

O

YX

O

XY

O

O

RR2

O

O

X

Y

RO

OR2

HO

AcO

O2N

OH

O2N

OHX

Y

OHX

Cl

CF3 OH

R2-IMe3N+

Y

Br

OAc

OTMSY

Br

O

X

Y

OMe3Si

AcO

Y

X

AcO

OY

X

O OR2

NaB

H 4

HO OHR2

Nuc

- M+

A

B

C

D

O

NaO

H

KO t-Bu

Base

CH2

(OCH

3) 2

Bas

e

pH=10.4

NaSH

F-

NuH

MOC(O)R2

81 (A=B=H, C=ONa, D=Y, E=X)

82 (A=R2 , B=C=D=E=H)

83 (A=R, B=C=H, D=Y, E=X)

84 = 87 (A=B=C=D=E=H)

85 (A=B=D=E=H, C=NO 2)

86 (B=D=H, A=CF 3, C=Y, E=X)

88 (A=B=D=E=H, C=Y)

89 (A=B=C=D=H, E=Y)

90 (A=B=H, C=OH, D=Y, E=X)

91 (A=D=E=H, B=Y, C=X)

68

69

70

71

72

73 74

75

76

77

78

79

80

81-91

92

E

Scheme 28: Using a base

30

O O

PPh3R

N

94

+ 97

O

O

t-Bu t-Bu

O

R

95

O

N

O

98

93

96

Scheme 29: Olefination

31

CHAPTER 4

O-QUINONE METHIDES PRECURSORS

In this work we focused on o-hydroxymethyl naphthol isomers 1-3 (scheme 30) as

possible precursors for the photogeneration of o-naphthaquinone methide isomers 4-6

(scheme 31). Accordingly, 2-(hydroxymethyl)-1-naphthol (1) and 3-(hydroxymethyl)-2-

naphthol (2) were synthesized.

HO

OHOH HO

OH

231

OH

Scheme 30: o-QMs Preprecursors.

O

OO

564

Scheme 31: o-QMs isomers

32

4.1. 3-(hydroxymethyl)-2-naphthol 2: was prepared by the reduction of 2-hydroxy-

3-naphthoic acid methyl ester 7 using lithium aluminum hydride (scheme 32).93, 95, 96

3-(hydroxymethyl)-2-naphthol 2 is known to be used to synthesize a wide range

of photochromic molecules to investigate photochromism.94 It is used here as a possible

precursor for the photogeneration of the o-naphthaquinone methide 5 (scheme 33).

4.2. 2-(Hydroxymethyl)-1-naphthol (1): was prepared by the reduction of 1-

hydroxy-2-naphthoic acid 8 with lithium aluminum hydride (scheme 34).

2-(Hydroxymethyl)-1-naphthol 1 is used here as a possible precursor for the

photogeneration of the o-naphthaquinone methide 4 (scheme 35).

HO

O

O

1.1 R: LiAlH4, S: THF, 30 min., RT; 3h, RT; RT 00C

1.2 R: HCl, S: (C2H5)2O, S: H2O, pH=4

HO

HO

88%

7 2

Scheme 32: preparation of 3-(hydroxymethyl)-2-naphthol 2

OH

OH

O

hυ

2 5

Scheme 33: photogeneration of the o-naphthaquinone methide 5

33

COOH1.1 R: LiAlH4, S: THF, 1h, RT; 4h, RT; RT 00C

1.2 R: HCl, S: (C2H5)2O, S: H2O, pH=4

OH OH

OH

18

Scheme 34: preparation of 2-(Hydroxymethyl)-1-naphthol 1

hυ

OH OH O

41

Scheme 35 photogeneration of the o-naphthaquinone methide 4

2-(Hydroxymethyl)-1-naphthol 1 is not stable, it probably undergoes decomposition to

the bisnaphthol 9 (scheme 36).

OH OH

1

OH OH

9

Scheme 36: decomposition to methylenedinaphthol

34

CHAPTER 5

FLASH PHOTOLYSIS

1. An Overview

Flash photolysis is a very important tool for studying the initial physicochemical

effects of light on matter. It was introduced in 1949 by Sir George Porter (Nobel Prize in

Chemistry 1967). It involves irradiating the investigated sample with a very high intense

pulse of radiation of very short duration (figure 1). Before the excitation pulse takes

place, consider the sample absorption is Ao(λ) and the monitoring light intensity is Iin(λ).

After the excitation pulse takes place, the sample absorption changes with time according

to equation 1 and the monitoring light intensity at the detector is given by equation 2.

Consequently, the spectrum ∆ A(λ,t) is given by equation 3.178-180

MONO-CHROMATOR

MONITORING

LAMP

FLASH LAMP/PULSED LASER

EXCITATION

SAMPLE

SIGNALRECORDER

PHOTO-DETECTOR

I=I(t, λmon)

λmon

Figure 1: Flash photolysis set-up

35

The transient species are electronically excited states (singlet or triplet), free radicals, or

ions. The duration of the excitation pulse determines the time resolution applied in the

process (fs-s). When “Timing is Everything” kinetics takes place.

A(λ, t)=A0(λ)+ΔA(λ, t) 1

Iout(λ, t)= Iin(λ).10-A(λ, t) 2

ΔA(λ, t)=-log(Iout(λ, t)/ I0(λ))

=-log(1+(Δ Iout(λ, t)/ I0(λ))) 3

2. Laser Flash Photolysis Modes181-184

There are two modes of operation of the laser flash photolysis spectrometer: Kinetic

mode (figure 2) and Spectral mode (figure 4).

2.1. Kinetic Mode: For measuring the laser induced transient absorption and/or

emission kinetics and the associated spectra. Where the time resolved (ns-s) absorption

and/or emission spectrum (figure 3) is produced by automatic scanning through a pre-

defined spectral range (200-2500 nm).

2.2. Spectral Mode: For measuring laser induced time resolved transient absorption

and/or emission spectra and the associated kinetics. Where spectrally resolved absorption

kinetics is produced by automatically stepping the gate delay through a pre-defined time

range (figure 5).

Figure 2: Kinetic mode

36

Figure 3: Spectral Slicing

Figure 4: Spectral mode

Figure 5: Kinetic Slicing

37

3. Absorption and Emission Studies

3.1. UV-vis Absorption: spectra for 3-(Hydroxymethyl) -2-naphthol (9x10-6M) in

acetonitrile were taken (see the experimental section, also the appendix for the details) in

different solvents (figure 6).

0.00E+00

1.00E+04

2.00E+04

3.00E+04

4.00E+04

5.00E+04

6.00E+04

7.00E+04

8.00E+04

220 240 260 280 300 320 340

wavelength(nm)

mol

ar a

bsor

btiv

ity(L

/mol

.cm

)

In THF

In Hexane

In Ethanol

In Acetonitrile

Figure 6: UV-vis spectra

3.2. Fluorescence Emission: spectrum for 3-(Hydroxymethyl) -2-naphthol (9x10-6M)

in acetonitrile was measured at the absorption excitation wavelength 228 nm in the range

325-400nm (figure 7).

38

0200400600800

10001200140016001800

300 400 500 600 700 800

Intensity

Wavelength (nm)

Figure 7: Fluorescence Spectrum.

4. The Photogeneration Process: on 3-(Hydroxymethyl) -2-naphthol would have 2

reactions. The first is the photodehydration reaction from 1 at the absorption excitation

wavelength 228 nm or ≈275 nm to produce 2 (scheme 37). The second is the hydration

reaction of 2 back to the starting material 1 (scheme 38).

OH

OH O

hυ 228 nm/275 nm

1 2

λmax=228 nm/275 nm λmax=395.5 nm46

-H2O

Scheme 37: Dehydration reaction

39

OH

OH O

hυ 228 nm/275 nm

1 2

λmax=228 nm/275 nm λmax=395.5 nm46

+H2O

Figure 38: Hydration reaction

The kinetics of the second reaction could be studied (This experiment was not

done because there is no Flash Photolysis Experimental set-up available at the UGA, and

also because the radiation wavelength for the process is in the deep UV which also was

not available by our contact source). The kinetics of reaction 2 will be studied. Where,

the hydration rate could be measured for a series of buffered solution (in H2O and D2O)

at different pH values. The goal is to fit the hydration rate profile. The predicted

nanosecond absorption kinetics is considered to go according to the following reaction

(scheme 39), unless the kinetics data proves to be otherwise.

OH

OHO

+H2Ok0

Scheme 39: The kinetic reaction

However, flash photolysis studies were not done because there is no flash photolysis

availability at the UGA.

40

CHAPTER 6

EXPERIMENTAL

6.1. Physical characterization

1H NMR and 13C NMR spectra were recorded on a Varian Mercury Plus 400 MHz

spectrometer using tetramethylsilane (TMS) as an internal standard using acetone-d 6 as

solvent.

Chemical shifts were reported in ppm (δ) downfield from TMS (δ 0.00) and splitting

patterns were designated as s, singlet; d, doublet; t, triplet; q, quartet; m, multiplet and b,

broad. UV/VIS spectra were recorded using the MeasureNet UV-vis Spectrometer with

High 1 nm resolution in the general chemistry lab.

The fluorescence spectrum was taken using the Spex Flurolog fluorescence

spectrophotometer in the megalab (figure 8).185-192. Electron bombardment mass spectra

were performed using Hewlett Packard MSD GC/MS.

6.2. Chemicals and reagents:

All chemicals were purchased from commercial sources and used without further

purification. Anhydrous THF for synthesis was obtained by distillation over sodium.

41

6.3. Synthesis:

6.3.1. 3-(Hydroxymethyl)-2-naphthol: 93, 95, 96

A solution of methyl 3-hydroxy-2-naphthoate (1.88 g, 9.31 mmol) in anhydrous THF (30

mL) was added at room temperature to a suspension of LAH (0.71 g, 19 mmol) in dry

THF (50 mL) over 30 min and the mixture stirred at room temperature for 3 h. The

reaction was quenched by pouring the suspension into cold, wet diethyl ether, then the

mixture was treated with aqueous 10% HCl at 0 °C. The ether layer was separated, and

the aqueous layer was extracted with diethyl ether. The combined organic layers were

dried over anhydrous MgSO4, filtered, and evaporated to give a pale yellow solid, 1.423

g (88%). The powder was dissolved in the minimum amount of boiling ethanol, filtered

and put in a beaker in a container over 50 ml benzene. Crystals of the product were

extracted after 48 h for analysis: mp 185-188 °C (Literature value is 186-188).96

1H-NMR (acetone-d6) δ= 4.51 (t, 1H), 4.88 (d, 1H), 7.186 (s, 1H), 7.27(t, 1H), 7.357 (t,

1H), 7.655 (d, 1H), 7.769 (d, 1H), 7.97 (d, 1H, H-4), 9.195 (s, 1H, OH).

13C-NMR (acetone-d6) δ=60.919 (C-9), 109.007, 123.176, 125.850, 125.982, 126.209,

127.711, 128.766, 131.008, 134.370, 153.887 (C-2).

MS m/z 174 (M+, 35), 156 (46), 129 (13.4), 128 (100), 127 (21), 115 (12.5), 64 (8.3), 63

(7.1), 51 (7.1).

6.3.2. 2-(Hydroxymethyl)-1-naphthol:

A solution of 1-hydroxy-2-naphthoic acid (3.76 g, 20 mmol) in anhydrous THF (60 mL)

was added at room temperature to a suspension of LAH (2.24 g, 60 mmol) in dry THF

42

(100 mL) over 30 min and the mixture stirred at room temperature for 3 h. The reaction

was quenched by pouring the suspension into cold, wet diethyl ether and 200mL of

distilled water was added to the mixture. The pH of the aqueous medium was reported to

be 11.5.

On the other hand, 10mL of 38% HCl was added to 700 ml of distilled water (to give

0.54% HCl). Then the mixture was treated with 485mL of aqueous 0.54% HCl at 0 °C

until pH=4. The ether layer was partially separated with a yellow color, and the aqueous

layer was extracted with diethyl ether. The combined organic layers were dried over

anhydrous MgSO4, filtered and collected in flask number 1.

The rest of the mixture was then further treated with 0.54% HCl until a complete

separation of the ether layer. The combined organic layers were dried over anhydrous

MgSO4, filtered and collected in flask number 2.

Flask 1 have been collected under conditions of pH=4

Flask 2 have been collected under conditions of a lower pH

The dry organic layer in flask 1 was evaporated to give a white solid, 0.289 g (%).which

was characterized with NMR (fraction 2.1) The solid is not stable and undergo chemical

transformation to a yellow solid, which is still in the phase of characterization (fraction

2.2).

The dry organic layer in flask 2 was extracted in 2mL THF and put open in a closed

container over petrol ether. Needle crystals were extracted for analysis (fraction 2.3),

0.407g.

43

Fraction 2.1 1H-NMR (acetone-d6) δ=4.719 (t, 1H), 5.279 (d, 1H), 7.132 (d, 1H), 7.363

(m, 1H), 7.46 (m, 1H), 7.715 (d, 1H), 7.783 (d, 1H), 7.804 (1H, H-4), 8.808 (s, 1H, OH).

Fraction 2.1 13C-NMR (acetone-d6) δ= 57.68 1 (C-9), 116.861, 118.883, 122.751,

122.846, 126.473, 128.517, 128.986, 129.279, 133.154, 153.975 (C-2). The NMR-spectra

confirm to be 2-(Hydroxymethyl)-1-naphthol.

6.4. UV-vis Spectra: The UV-vis absorbance spectra for 9x10-6M 3-(Hydroxymethyl)

-2-naphthol were measured in HPLC grade ethanol, tetrahydrofurane, acetonitrile, and

hexane (see figure 6 in chapter 5). 0.01566 g of 3-(Hydroxymethyl) -2-naphthol was

dissolved in 100 ml ethanol (9x10-6M). One ml of that solution was diluted in 100 ml of

tetrahydrofurane, acetonitrile, and hexane to give solutions in the concentrations of

9x10-6M. The blank sample for each solution was prepared by dissolving 1 ml of ethanol

in 100 ml of the previous considered solvent. UV-vis spectra were then taken.

6.5. Fluorescence Spectrum: for 3-(Hydroxymethyl) -2-naphthol (9x10-6M) in

acetonitrile was taken (see figure 7 in chapter 5). One ml of ethanol was dissolved in 100

ml of acetonitrile to prepare the blank sample for that measurement. The emission

fluorescence spectra is recorded between 325 – 800 nm with the excitation wavelength

set at 228 nm. The experiment labeled “3511b.exp” on the Spex fluorimeter is used to set

up the correct parameters for this step.

44

450 WX

e Lamp

excitationm

onochromator

microm

eterslit controls

(1) - (4) = Start-up S

equence for Spectrofl uorimeter C

omponents

sample

compartm

ent

emission

monochrom

ator

Xe Lamp

Pow

er Supply

PM

T

Figure 3

(1)

(4)

(3)(2)

G1

G2

G3

Figure 8 Spex Flurolog fluorescence spectrophotometer

45

CHAPTER 6

SPECTRA

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67 67

68

]

69

70 70

71

72 72

73

APPENDIX

UV-vis/Fluorescence

1=Wavelength/nm/ UV-vis

2=Absorbance/ Ethanol

3=Absorbance/ THF

4=Absorbance/ Acetonitrile

5=Absorbance/ Hexane

6=Wavelength/nm/ Fluorescence

7= Emission/in acetonitrile

8= molar absorbtivity/Ethanol

9= molar absorbtivity/THF

10= molar absorbtivity/ Acetonitrile

11= molar absorbtivity/ Hexane

1 2 3 4 5 6 7 8 9 10 11

202.6 0.11 0.176 0.133 0.18 203 12 12444.4 19555.6 14777.8 19555.56203.4 0.11 0.114 0.148 0.19 204 9 11888.9 12666.7 16444.4 20777.78204.1 0.1 0.105 0.168 0.17 205 18 11111.1 11666.7 18666.7 18555.56204.9 0.13 0.138 0.161 0.16 206 13 13888.9 15333.3 17888.9 18000205.6 0.14 0.067 0.171 0.17 207 9 15333.3 7444.44 19000 18555.56206.4 0.15 0.035 0.176 0.19 208 10 16555.6 3888.89 19555.6 21555.56207.2 0.13 0.16 0.181 0.18 209 15 14333.3 17777.8 20111.1 19555.56207.9 0.16 0.097 0.185 0.2 210 11 17333.3 10777.8 20555.6 21888.89208.7 0.18 0.067 0.195 0.19 211 20 19777.8 7444.44 21666.7 21444.44209.4 0.18 0.125 0.198 0.19 212 12 20333.3 13888.9 22000 21111.11210.2 0.19 0.166 0.204 0.21 213 19 21555.6 18444.4 22666.7 22888.89210.9 0.18 0.183 0.215 0.21 214 13 20000 20333.3 23888.9 23222.22211.7 0.21 0.202 0.23 0.22 215 15 23000 22444.4 25555.6 24111.11212.4 0.23 0.204 0.232 0.23 216 12 25000 22666.7 25777.8 25333.33213.2 0.22 0.193 0.247 0.23 217 10 24666.7 21444.4 27444.4 25555.56

74

214 0.24 0.212 0.253 0.25 218 8 26333.3 23555.6 28111.1 27555.56214.7 0.25 0.222 0.266 0.26 219 7 28000 24666.7 29555.6 29000215.5 0.26 0.225 0.284 0.27 220 8 28444.4 25000 31555.6 30333.33216.2 0.28 0.252 0.294 0.29 221 5 31333.3 28000 32666.7 32111.11

217 0.29 0.268 0.324 0.31 222 10 32111.1 29777.8 36000 34111.11217.7 0.32 0.278 0.351 0.31 223 15 35333.3 30888.9 39000 34666.67218.5 0.33 0.325 0.365 0.35 224 10 36777.8 36111.1 40555.6 38666.67219.2 0.35 0.316 0.388 0.36 225 10 39000 35111.1 43111.1 40111.11

220 0.38 0.346 0.42 0.38 226 7 42222.2 38444.4 46666.7 42555.56220.7 0.4 0.355 0.444 0.41 227 9 44666.7 39444.4 49333.3 45888.89221.5 0.43 0.381 0.471 0.45 228 12 47666.7 42333.3 52333.3 49777.78222.2 0.46 0.429 0.505 0.47 229 14 50888.9 47666.7 56111.1 51888.89

223 0.49 0.441 0.522 0.51 230 10 54222.2 49000 58000 56555.56223.8 0.51 0.462 0.552 0.53 231 4 57000 51333.3 61333.3 59111.11224.5 0.56 0.505 0.577 0.56 232 15 61888.9 56111.1 64111.1 62111.11225.3 0.58 0.517 0.597 0.59 233 11 64000 57444.4 66333.3 65222.22

226 0.59 0.541 0.611 0.6 234 9 65777.8 60111.1 67888.9 67000226.8 0.62 0.58 0.627 0.63 235 7 68555.6 64444.4 69666.7 69666.67227.5 0.63 0.598 0.629 0.64 236 12 70111.1 66444.4 69888.9 71222.22228.3 0.65 0.62 0.629 0.65 237 8 72333.3 68888.9 69888.9 72111.11

229 0.65 0.641 0.626 0.66 238 10 72000 71222.2 69555.6 73111.11229.8 0.65 0.637 0.613 0.66 239 12 72111.1 70777.8 68111.1 72888.89230.5 0.63 0.643 0.593 0.65 240 7 70111.1 71444.4 65888.9 72555.56231.3 0.62 0.646 0.574 0.64 241 8 69111.1 71777.8 63777.8 70888.89

232 0.6 0.641 0.538 0.61 242 11 66111.1 71222.2 59777.8 68111.11232.8 0.56 0.641 0.502 0.58 243 12 61666.7 71222.2 55777.8 64000233.5 0.51 0.608 0.455 0.53 244 9 57000 67555.6 50555.6 59333.33234.3 0.47 0.578 0.404 0.48 245 6 51777.8 64222.2 44888.9 52888.89

235 0.41 0.538 0.357 0.42 246 10 45666.7 59777.8 39666.7 46555.56235.8 0.36 0.483 0.31 0.36 247 8 39444.4 53666.7 34444.4 40333.33236.5 0.3 0.429 0.264 0.31 248 10 33666.7 47666.7 29333.3 34666.67237.3 0.26 0.375 0.227 0.27 249 13 28333.3 41666.7 25222.2 29888.89

238 0.22 0.322 0.192 0.23 250 8 24111.1 35777.8 21333.3 25666.67238.8 0.18 0.281 0.17 0.21 251 9 20333.3 31222.2 18888.9 22777.78239.5 0.16 0.249 0.146 0.18 252 7 17444.4 27666.7 16222.2 20000240.3 0.13 0.226 0.124 0.16 253 6 14888.9 25111.1 13777.8 17888.89

241 0.11 0.198 0.107 0.15 254 6 12666.7 22000 11888.9 16222.22241.8 0.09 0.181 0.092 0.14 255 8 10444.4 20111.1 10222.2 15000242.6 0.08 0.161 0.081 0.12 256 15 8777.78 17888.9 9000 13777.78243.3 0.07 0.145 0.068 0.11 257 11 7222.22 16111.1 7555.56 12666.67244.1 0.06 0.138 0.063 0.11 258 10 6111.11 15333.3 7000 11777.78244.8 0.05 0.132 0.054 0.11 259 14 5444.44 14666.7 6000 11666.67245.6 0.05 0.127 0.051 0.1 260 7 5000 14111.1 5666.67 11444.44246.3 0.04 0.128 0.047 0.1 261 12 4444.44 14222.2 5222.22 11444.44

247 0.04 0.129 0.046 0.1 262 12 4222.22 14333.3 5111.11 11555.56247.8 0.04 0.128 0.043 0.1 263 11 4111.11 14222.2 4777.78 11333.33248.5 0.04 0.132 0.041 0.1 264 12 3888.89 14666.7 4555.56 11555.56249.3 0.04 0.136 0.039 0.11 265 9 4000 15111.1 4333.33 11888.89

250 0.03 0.139 0.038 0.11 266 7 3777.78 15444.4 4222.22 12333.33

75

250.8 0.04 0.146 0.04 0.11 267 8 3888.89 16222.2 4444.44 12555.56251.5 0.03 0.148 0.038 0.12 268 7 3666.67 16444.4 4222.22 12888.89252.3 0.04 0.155 0.038 0.12 269 14 3888.89 17222.2 4222.22 13444.44

253 0.04 0.159 0.039 0.13 270 10 4000 17666.7 4333.33 14111.11253.8 0.04 0.166 0.04 0.13 271 9 4111.11 18444.4 4444.44 14333.33254.5 0.04 0.173 0.038 0.13 272 14 4111.11 19222.2 4222.22 14888.89255.3 0.04 0.178 0.04 0.14 273 5 4444.44 19777.8 4444.44 15444.44

256 0.04 0.18 0.038 0.14 274 13 4444.44 20000 4222.22 15555.56256.8 0.04 0.19 0.039 0.14 275 16 4444.44 21111.1 4333.33 16000257.5 0.04 0.195 0.039 0.15 276 11 4444.44 21666.7 4333.33 16555.56258.3 0.04 0.197 0.037 0.15 277 14 4444.44 21888.9 4111.11 16666.67

259 0.04 0.205 0.035 0.15 278 6 4555.56 22777.8 3888.89 17000259.8 0.04 0.21 0.038 0.16 279 13 4666.67 23333.3 4222.22 17444.44260.5 0.04 0.217 0.036 0.16 280 8 4666.67 24111.1 4000 18000261.3 0.04 0.22 0.038 0.17 281 7 4777.78 24444.4 4222.22 18444.44

262 0.05 0.228 0.038 0.17 282 13 5000 25333.3 4222.22 18888.89262.8 0.05 0.231 0.039 0.18 283 7 5111.11 25666.7 4333.33 19444.44263.5 0.05 0.238 0.039 0.18 284 16 5222.22 26444.4 4333.33 19777.78264.3 0.05 0.243 0.041 0.18 285 13 5333.33 27000 4555.56 20444.44

265 0.05 0.249 0.04 0.19 286 14 5444.44 27666.7 4444.44 20888.89265.7 0.05 0.252 0.041 0.19 287 8 5666.67 28000 4555.56 21111.11266.5 0.05 0.256 0.041 0.19 288 10 5666.67 28444.4 4555.56 21444.44267.2 0.05 0.259 0.039 0.19 289 10 5666.67 28777.8 4333.33 21444.44

268 0.05 0.266 0.039 0.2 290 8 5333.33 29555.6 4333.33 21777.78268.7 0.05 0.264 0.039 0.2 291 14 5333.33 29333.3 4333.33 21777.78269.5 0.05 0.268 0.037 0.2 292 6 5333.33 29777.8 4111.11 22000270.2 0.05 0.271 0.036 0.2 293 6 5222.22 30111.1 4000 22333.33

271 0.05 0.271 0.037 0.2 294 10 5222.22 30111.1 4111.11 22222.22271.7 0.05 0.275 0.038 0.21 295 13 5333.33 30555.6 4222.22 22777.78272.5 0.05 0.277 0.039 0.21 296 7 5444.44 30777.8 4333.33 23000273.2 0.05 0.277 0.038 0.21 297 14 5666.67 30777.8 4222.22 23000273.9 0.05 0.282 0.04 0.21 298 12 5777.78 31333.3 4444.44 23444.44274.7 0.05 0.284 0.041 0.21 299 9 5888.89 31555.6 4555.56 23666.67275.4 0.05 0.283 0.042 0.22 300 11 6000 31444.4 4666.67 24000276.2 0.05 0.287 0.044 0.22 301 12 6000 31888.9 4888.89 23888.89276.9 0.06 0.288 0.043 0.21 302 12 6111.11 32000 4777.78 23777.78277.7 0.06 0.287 0.041 0.21 303 10 6111.11 31888.9 4555.56 23666.67278.4 0.05 0.287 0.042 0.21 304 11 5888.89 31888.9 4666.67 23555.56279.2 0.05 0.283 0.039 0.21 305 11 5333.33 31444.4 4333.33 23333.33279.9 0.05 0.28 0.036 0.21 306 10 5222.22 31111.1 4000 23000280.6 0.04 0.278 0.035 0.2 307 14 4777.78 30888.9 3888.89 22666.67281.4 0.04 0.275 0.032 0.2 308 12 4555.56 30555.6 3555.56 22333.33282.1 0.04 0.269 0.032 0.2 309 7 4666.67 29888.9 3555.56 22000282.9 0.04 0.267 0.034 0.2 310 18 4222.22 29666.7 3777.78 21888.89283.6 0.04 0.263 0.033 0.2 311 11 4555.56 29222.2 3666.67 21666.67284.4 0.04 0.261 0.034 0.19 312 13 4666.67 29000 3777.78 21555.56285.1 0.04 0.258 0.036 0.19 313 7 4666.67 28666.7 4000 21333.33285.9 0.04 0.256 0.036 0.19 314 7 4666.67 28444.4 4000 21222.22286.6 0.04 0.253 0.036 0.19 315 10 4666.67 28111.1 4000 21222.22

76

287.3 0.04 0.252 0.036 0.19 316 11 4777.78 28000 4000 20888.89288.1 0.04 0.246 0.036 0.19 317 13 4555.56 27333.3 4000 20777.78288.8 0.04 0.243 0.036 0.18 318 14 4555.56 27000 4000 20333.33289.6 0.04 0.238 0.037 0.18 319 16 4222.22 26444.4 4111.11 19888.89290.3 0.04 0.231 0.031 0.17 320 11 3888.89 25666.7 3444.44 19222.22

291 0.03 0.225 0.03 0.17 321 16 3666.67 25000 3333.33 18555.56291.8 0.03 0.217 0.028 0.16 322 30 3333.33 24111.1 3111.11 18111.11292.5 0.03 0.21 0.028 0.16 323 20 3111.11 23333.3 3111.11 17444.44293.3 0.03 0.202 0.026 0.15 324 42 3000 22444.4 2888.89 16888.89

294 0.03 0.196 0.025 0.15 325 58 2888.89 21777.8 2777.78 16444.44294.8 0.02 0.188 0.026 0.14 326 88 2555.56 20888.9 2888.89 16000295.5 0.02 0.181 0.024 0.14 327 116 2666.67 20111.1 2666.67 15444.44296.2 0.02 0.177 0.025 0.14 328 126 2333.33 19666.7 2777.78 15111.11

297 0.02 0.17 0.025 0.13 329 212 2555.56 18888.9 2777.78 14777.78297.7 0.02 0.167 0.025 0.13 330 268 2444.44 18555.6 2777.78 14111.11298.5 0.02 0.16 0.026 0.12 331 376 2555.56 17777.8 2888.89 13777.78299.2 0.02 0.156 0.026 0.12 332 445 2555.56 17333.3 2888.89 13555.56299.9 0.02 0.152 0.026 0.12 333 574 2555.56 16888.9 2888.89 13111.11300.7 0.02 0.145 0.029 0.12 334 714 2555.56 16111.1 3222.22 12777.78301.4 0.02 0.139 0.028 0.11 335 805 2555.56 15444.4 3111.11 12555.56302.2 0.02 0.135 0.028 0.11 336 899 2555.56 15000 3111.11 12222.22302.9 0.03 0.132 0.03 0.11 337 ### 2777.78 14666.7 3333.33 12000303.6 0.03 0.126 0.029 0.11 338 ### 2777.78 14000 3222.22 11777.78304.4 0.03 0.121 0.029 0.1 339 ### 2777.78 13444.4 3222.22 11111.11305.1 0.02 0.115 0.031 0.1 340 ### 2666.67 12777.8 3444.44 10888.89305.9 0.03 0.108 0.031 0.1 341 ### 2777.78 12000 3444.44 10555.56306.6 0.03 0.107 0.031 0.09 342 ### 3000 11888.9 3444.44 10222.22307.3 0.03 0.102 0.033 0.09 343 ### 2888.89 11333.3 3666.67 9888.889308.1 0.03 0.095 0.033 0.09 344 ### 3000 10555.6 3666.67 9444.444308.8 0.03 0.092 0.033 0.08 345 ### 3000 10222.2 3666.67 9000309.6 0.03 0.088 0.036 0.08 346 ### 3111.11 9777.78 4000 8777.778310.3 0.03 0.083 0.034 0.08 347 ### 3111.11 9222.22 3777.78 8555.556

311 0.03 0.081 0.036 0.07 348 ### 3111.11 9000 4000 8000311.8 0.03 0.077 0.036 0.07 349 ### 3222.22 8555.56 4000 7777.778312.5 0.03 0.075 0.037 0.07 350 ### 3111.11 8333.33 4111.11 7888.889313.2 0.03 0.071 0.037 0.07 351 ### 3444.44 7888.89 4111.11 7444.444

314 0.03 0.068 0.038 0.07 352 ### 3555.56 7555.56 4222.22 7333.333314.7 0.03 0.066 0.039 0.06 353 ### 3333.33 7333.33 4333.33 7000315.5 0.03 0.063 0.04 0.06 354 ### 3444.44 7000 4444.44 6888.889316.2 0.03 0.059 0.04 0.06 355 ### 3666.67 6555.56 4444.44 6666.667316.9 0.03 0.056 0.041 0.06 356 ### 3777.78 6222.22 4555.56 6666.667317.7 0.03 0.054 0.04 0.06 357 ### 3666.67 6000 4444.44 6444.444318.4 0.03 0.052 0.041 0.06 358 ### 3555.56 5777.78 4555.56 6222.222319.1 0.03 0.05 0.041 0.05 359 ### 3555.56 5555.56 4555.56 6000319.9 0.03 0.047 0.04 0.05 360 ### 3666.67 5222.22 4444.44 6000320.6 0.03 0.045 0.04 0.05 361 ### 3555.56 5000 4444.44 5888.889321.4 0.03 0.045 0.04 0.05 362 ### 3666.67 5000 4444.44 5666.667322.1 0.03 0.044 0.041 0.05 363 ### 3666.67 4888.89 4555.56 5333.333322.8 0.03 0.042 0.041 0.05 364 ### 3777.78 4666.67 4555.56 5111.111

77

323.6 0.03 0.041 0.041 0.05 365 ### 3555.56 4555.56 4555.56 5000324.3 0.04 0.039 0.041 0.05 366 ### 3888.89 4333.33 4555.56 5000

325 0.03 0.039 0.041 0.04 367 ### 3777.78 4333.33 4555.56 4888.889325.8 0.03 0.038 0.041 0.04 368 ### 3666.67 4222.22 4555.56 4777.778326.5 0.04 0.038 0.042 0.04 369 ### 3888.89 4222.22 4666.67 4666.667327.2 0.04 0.038 0.043 0.04 370 ### 3888.89 4222.22 4777.78 4444.444

328 0.04 0.04 0.043 0.04 371 952 3888.89 4444.44 4777.78 4555.556328.7 0.04 0.039 0.04 0.04 372 ### 3888.89 4333.33 4444.44 4666.667329.4 0.04 0.037 0.041 0.04 373 951 4000 4111.11 4555.56 4555.556330.2 0.04 0.037 0.043 0.04 374 902 4000 4111.11 4777.78 4666.667330.9 0.04 0.036 0.041 0.04 375 831 4000 4000 4555.56 4666.667331.7 0.03 0.036 0.041 0.04 376 872 3777.78 4000 4555.56 4444.444332.4 0.03 0.033 0.04 0.04 377 755 3666.67 3666.67 4444.44 4555.556333.1 0.03 0.032 0.038 0.04 378 762 3555.56 3555.56 4222.22 4555.556333.9 0.03 0.031 0.038 0.04 379 732 3222.22 3444.44 4222.22 4444.444334.6 0.03 0.03 0.037 0.04 380 679 3222.22 3333.33 4111.11 4555.556335.3 0.03 0.027 0.035 0.04 381 634 3000 3000 3888.89 4333.333336.1 0.03 0.026 0.033 0.04 382 599 3111.11 2888.89 3666.67 4000336.8 0.03 0.025 0.032 0.04 383 612 2777.78 2777.78 3555.56 3888.889337.5 0.02 0.024 0.031 0.03 384 551 2555.56 2666.67 3444.44 3666.667338.3 0.02 0.023 0.03 0.03 385 546 2666.67 2555.56 3333.33 3444.444

339 0.02 0.02 0.028 0.03 386 487 2333.33 2222.22 3111.11 3333.333339.7 0.02 0.02 0.027 0.03 387 520 2222.22 2222.22 3000 3111.111340.5 0.02 0.019 0.029 0.03 388 447 2000 2111.11 3222.22 2888.889341.2 0.02 0.018 0.027 0.03 389 434 2000 2000 3000 2777.778341.9 0.02 0.017 0.025 0.02 390 394 1888.89 1888.89 2777.78 2555.556342.7 0.02 0.016 0.025 0.02 391 376 1888.89 1777.78 2777.78 2444.444343.4 0.02 0.015 0.024 0.02 392 376 1777.78 1666.67 2666.67 2333.333344.1 0.01 0.015 0.025 0.02 393 353 1555.56 1666.67 2777.78 2222.222344.8 0.02 0.013 0.026 0.02 394 338 1666.67 1444.44 2888.89 2333.333345.6 0.02 0.015 0.024 0.02 395 332 1777.78 1666.67 2666.67 2222.222346.3 0.01 0.015 0.023 0.02 396 292 1444.44 1666.67 2555.56 2111.111

347 0.01 0.014 0.025 0.02 397 252 1555.56 1555.56 2777.78 2222.222347.8 0.02 0.014 0.024 0.02 398 264 1666.67 1555.56 2666.67 2111.111348.5 0.01 0.014 0.024 0.02 399 269 1444.44 1555.56 2666.67 2111.111349.2 0.01 0.015 0.024 0.02 400 259 1555.56 1666.67 2666.67 2111.111

350 0.01 0.012 0.024 0.02 401 194 1444.44 1333.33 2666.67 2222.222350.7 0.01 0.013 0.022 0.02 402 218 1444.44 1444.44 2444.44 2111.111351.4 0.01 0.012 0.023 0.02 403 212 1222.22 1333.33 2555.56 1888.889352.2 0.01 0.013 0.022 0.02 404 218 1333.33 1444.44 2444.44 2000352.9 0.01 0.012 0.02 0.02 405 180 1111.11 1333.33 2222.22 1888.889353.6 0.01 0.013 0.023 0.02 406 180 1333.33 1444.44 2555.56 1777.778354.4 0.01 0.012 0.022 0.02 407 167 1555.56 1333.33 2444.44 1888.889355.1 0.01 0.012 0.023 0.02 408 171 1111.11 1333.33 2555.56 1888.889355.8 0.01 0.013 0.019 0.02 409 153 1111.11 1444.44 2111.11 2111.111356.5 0.01 0.011 0.022 0.02 410 139 1333.33 1222.22 2444.44 1666.667357.3 0.01 0.011 0.021 0.02 411 128 1333.33 1222.22 2333.33 1777.778

358 0.01 0.011 0.021 0.02 412 121 1444.44 1222.22 2333.33 1777.778358.7 0.01 0.011 0.02 0.02 413 130 1333.33 1222.22 2222.22 1777.778

78

359.5 0.01 0.01 0.021 0.02 414 114 1333.33 1111.11 2333.33 1666.667360.2 0.01 0.01 0.022 0.02 415 107 1222.22 1111.11 2444.44 1777.778360.9 0.01 0.01 0.02 0.02 416 105 1333.33 1111.11 2222.22 1888.889361.6 0.01 0.011 0.021 0.02 417 103 1111.11 1222.22 2333.33 1666.667362.4 0.01 0.011 0.021 0.02 418 93 1111.11 1222.22 2333.33 1888.889363.1 0.01 0.01 0.021 0.01 419 93 1333.33 1111.11 2333.33 1555.556363.8 0.01 0.01 0.021 0.02 420 89 1000 1111.11 2333.33 1666.667364.6 0.01 0.011 0.02 0.02 421 79 1111.11 1222.22 2222.22 1777.778365.3 0.01 0.009 0.019 0.01 422 86 1111.11 1000 2111.11 1444.444

366 0.01 0.01 0.02 0.01 423 69 1333.33 1111.11 2222.22 1444.444366.7 0.01 0.009 0.021 0.01 424 59 1111.11 1000 2333.33 1555.556367.5 0.01 0.009 0.019 0.02 425 62 1000 1000 2111.11 1666.667368.2 0.01 0.01 0.019 0.01 426 59 1222.22 1111.11 2111.11 1444.444368.9 0.01 0.008 0.017 0.02 427 52 1222.22 888.889 1888.89 1666.667369.7 0.01 0.009 0.019 0.01 428 47 1111.11 1000 2111.11 1555.556370.4 0.01 0.01 0.018 0.01 429 35 1111.11 1111.11 2000 1333.333371.1 0.01 0.01 0.019 0.01 430 54 1222.22 1111.11 2111.11 1555.556371.8 0.01 0.009 0.02 0.02 431 41 888.889 1000 2222.22 1666.667372.6 0.01 0.01 0.019 0.01 432 31 1222.22 1111.11 2111.11 1555.556373.3 0.01 0.009 0.019 0.01 433 36 1222.22 1000 2111.11 1444.444

374 0.01 0.01 0.016 0.01 434 45 1000 1111.11 1777.78 1555.556374.7 0.01 0.01 0.017 0.01 435 39 1000 1111.11 1888.89 1555.556375.5 0.01 0.009 0.018 0.01 436 47 1000 1000 2000 1333.333376.2 0.01 0.01 0.018 0.01 437 37 1000 1111.11 2000 1333.333376.9 0.01 0.007 0.018 0.01 438 34 888.889 777.778 2000 1555.556377.6 0.01 0.008 0.017 0.01 439 24 1000 888.889 1888.89 1333.333378.4 0.01 0.008 0.019 0.01 440 20 888.889 888.889 2111.11 1444.444379.1 0.01 0.007 0.018 0.01 441 24 1222.22 777.778 2000 1555.556379.8 0.01 0.008 0.016 0.01 442 34 1111.11 888.889 1777.78 1333.333380.5 0.01 0.008 0.018 0.01 443 33 1000 888.889 2000 1444.444381.3 0.01 0.008 0.019 0.01 444 14 1000 888.889 2111.11 1444.444

382 0.01 0.008 0.019 0.01 445 20 1000 888.889 2111.11 1333.333382.7 0.01 0.008 0.017 0.01 446 24 666.667 888.889 1888.89 1333.333383.4 0.01 0.008 0.018 0.01 447 30 1111.11 888.889 2000 1333.333384.2 0.01 0.008 0.017 0.01 448 20 1111.11 888.889 1888.89 1333.333384.9 0.01 0.008 0.017 0.01 449 26 1000 888.889 1888.89 1222.222385.6 0.01 0.006 0.017 0.01 450 36 1000 666.667 1888.89 1222.222386.3 0.01 0.008 0.016 0.01 451 24 1000 888.889 1777.78 1222.222387.1 0.01 0.007 0.016 0.01 452 12 777.778 777.778 1777.78 1222.222387.8 0.01 0.008 0.017 0.01 453 21 1000 888.889 1888.89 1333.333388.5 0.01 0.007 0.017 0.01 454 20 888.889 777.778 1888.89 1333.333389.2 0.01 0.008 0.017 0.01 455 21 1111.11 888.889 1888.89 1333.333

390 0.01 0.008 0.017 0.01 456 33 1000 888.889 1888.89 1222.222390.7 0.01 0.009 0.017 0.01 457 25 1000 1000 1888.89 1333.333391.4 0.01 0.007 0.016 0.01 458 36 1000 777.778 1777.78 1222.222392.1 0.01 0.009 0.017 0.01 459 26 1000 1000 1888.89 1444.444392.9 0.01 0.007 0.018 0.01 460 16 1000 777.778 2000 1333.333393.6 0.01 0.008 0.016 0.01 461 25 666.667 888.889 1777.78 1222.222394.3 0.01 0.007 0.016 0.01 462 24 888.889 777.778 1777.78 1111.111

79

395 0.01 0.005 0.016 0.01 463 19 777.778 555.556 1777.78 1111.111395.7 0.01 0.007 0.016 0.01 464 19 1000 777.778 1777.78 1222.222396.5 0.01 0.005 0.017 0.01 465 25 888.889 555.556 1888.89 1222.222397.2 0.01 0.006 0.015 0.01 466 11 888.889 666.667 1666.67 1222.222397.9 0.01 0.007 0.016 0.01 467 20 777.778 777.778 1777.78 1111.111398.6 0.01 0.006 0.016 0.01 468 17 1111.11 666.667 1777.78 1333.333399.3 0.01 0.006 0.014 0.01 469 17 1000 666.667 1555.56 1222.222400.1 0.01 0.007 0.014 0.01 470 13 888.889 777.778 1555.56 1222.222400.8 0.01 0.007 0.016 0.01 471 18 777.778 777.778 1777.78 1000401.5 0.01 0.006 0.017 0.01 472 21 1000 666.667 1888.89 1222.222402.2 0.01 0.005 0.016 0.01 473 16 1000 555.556 1777.78 1222.222

403 0.01 0.004 0.014 0.01 474 8 888.889 444.444 1555.56 1111.111403.7 0.01 0.007 0.014 0.01 475 22 666.667 777.778 1555.56 1333.333404.4 0.01 0.005 0.015 0.01 476 9 888.889 555.556 1666.67 1444.444405.1 0.01 0.007 0.013 0.01 477 20 777.778 777.778 1444.44 1222.222405.8 0.01 0.006 0.016 0.01 478 11 777.778 666.667 1777.78 1111.111406.6 0.01 0.006 0.014 0.01 479 11 1000 666.667 1555.56 1222.222407.3 0.01 0.006 0.013 0.01 480 10 555.556 666.667 1444.44 1222.222

408 0.01 0.005 0.014 0.01 481 11 888.889 555.556 1555.56 1111.111408.7 0.01 0.006 0.014 0.01 482 12 888.889 666.667 1555.56 1111.111409.4 0.01 0.005 0.016 0.01 483 21 888.889 555.556 1777.78 888.8889410.2 0.01 0.007 0.014 0.01 484 14 888.889 777.778 1555.56 1111.111410.9 0.01 0.006 0.014 0.01 485 18 1000 666.667 1555.56 1222.222411.6 0.01 0.005 0.014 0.01 486 12 777.778 555.556 1555.56 1111.111412.3 0.01 0.007 0.014 0.01 487 13 1111.11 777.778 1555.56 1111.111

413 0.01 0.005 0.014 0.01 488 13 777.778 555.556 1555.56 1000413.7 0.01 0.006 0.014 0.01 489 10 888.889 666.667 1555.56 1000414.5 0.01 0.006 0.013 0.01 490 8 888.889 666.667 1444.44 1111.111415.2 0.01 0.005 0.014 0.01 491 15 555.556 555.556 1555.56 888.8889415.9 0.01 0.004 0.014 0.01 492 14 1111.11 444.444 1555.56 1111.111416.6 0.01 0.005 0.013 0.01 493 13 888.889 555.556 1444.44 1000417.3 0.01 0.004 0.015 0.01 494 10 777.778 444.444 1666.67 1000418.1 0.01 0.006 0.014 0.01 495 17 777.778 666.667 1555.56 1000418.8 0.01 0.005 0.014 0.01 496 7 666.667 555.556 1555.56 1111.111419.5 0.01 0.005 0.012 0.01 497 12 777.778 555.556 1333.33 1222.222420.2 0.01 0.004 0.014 0.01 498 19 888.889 444.444 1555.56 1111.111420.9 0.01 0.007 0.015 0.01 499 11 777.778 777.778 1666.67 1222.222421.6 0.01 0.005 0.013 0.01 500 13 666.667 555.556 1444.44 1222.222422.4 0.01 0.004 0.014 0.01 501 14 777.778 444.444 1555.56 1000423.1 0.01 0.005 0.012 0.01 502 14 777.778 555.556 1333.33 1000423.8 0.01 0.005 0.015 0.01 503 8 1000 555.556 1666.67 1000424.5 0.01 0.006 0.015 0.01 504 6 888.889 666.667 1666.67 1222.222425.2 0.01 0.005 0.013 0.01 505 9 777.778 555.556 1444.44 1111.111425.9 0.01 0.007 0.013 0.01 506 11 666.667 777.778 1444.44 888.8889426.6 0.01 0.004 0.012 0.01 507 4 666.667 444.444 1333.33 1000427.4 0.01 0.003 0.012 0.01 508 21 888.889 333.333 1333.33 1000428.1 0.01 0.004 0.014 0.01 509 15 666.667 444.444 1555.56 888.8889428.8 0.01 0.005 0.013 0.01 510 11 777.778 555.556 1444.44 1000429.5 0.01 0.006 0.013 0.01 511 16 1000 666.667 1444.44 777.7778

80

430.2 0.01 0.004 0.015 0.01 512 13 555.556 444.444 1666.67 888.8889430.9 0.01 0.004 0.013 0.01 513 23 777.778 444.444 1444.44 777.7778431.7 0.01 0.004 0.014 0.01 514 14 777.778 444.444 1555.56 888.8889432.4 0.01 0.003 0.014 0.01 515 10 777.778 333.333 1555.56 888.8889433.1 0.01 0.005 0.014 0.01 516 13 888.889 555.556 1555.56 1000433.8 0.01 0.004 0.013 0.01 517 10 1000 444.444 1444.44 1111.111434.5 0.01 0.003 0.016 0.01 518 9 1000 333.333 1777.78 666.6667435.2 0.01 0.004 0.012 0.01 519 10 777.778 444.444 1333.33 1000435.9 0.01 0.006 0.012 0.01 520 11 777.778 666.667 1333.33 888.8889436.6 0.01 0.004 0.011 0.01 521 7 888.889 444.444 1222.22 555.5556437.4 0.01 0.006 0.012 0.01 522 7 777.778 666.667 1333.33 888.8889438.1 0.01 0.005 0.012 0.01 523 7 777.778 555.556 1333.33 888.8889438.8 0.01 0.004 0.014 0.01 524 8 777.778 444.444 1555.56 888.8889439.5 0.01 0.006 0.011 0.01 525 14 666.667 666.667 1222.22 1000440.2 0.01 0.004 0.014 0.01 526 8 888.889 444.444 1555.56 1000440.9 0.01 0.006 0.011 0.01 527 11 1000 666.667 1222.22 888.8889441.6 0.01 0.005 0.013 0.01 528 10 1000 555.556 1444.44 1000442.4 0.01 0.005 0.012 0.01 529 8 777.778 555.556 1333.33 1111.111443.1 0.01 0.006 0.012 0.01 530 12 666.667 666.667 1333.33 777.7778443.8 0.01 0.002 0.01 0.01 531 10 666.667 222.222 1111.11 777.7778444.5 0.01 0.002 0.013 0.01 532 13 888.889 222.222 1444.44 1000445.2 0.01 0.005 0.011 0.01 533 7 777.778 555.556 1222.22 888.8889445.9 0.01 0.004 0.01 0.01 534 9 888.889 444.444 1111.11 1000446.6 0.01 0.003 0.012 0.01 535 6 888.889 333.333 1333.33 888.8889447.3 0.01 0.003 0.013 0.01 536 7 888.889 333.333 1444.44 1000

448 0.01 0.002 0.012 0.01 537 11 777.778 222.222 1333.33 1000448.8 0.01 0.004 0.012 0.01 538 6 777.778 444.444 1333.33 555.5556449.5 0.01 0.003 0.012 0.01 539 15 777.778 333.333 1333.33 777.7778450.2 0.01 0.005 0.012 0.01 540 8 777.778 555.556 1333.33 1111.111450.9 0.01 0.004 0.013 0.01 541 11 777.778 444.444 1444.44 1000451.6 0.01 0.004 0.012 0.01 542 11 777.778 444.444 1333.33 888.8889452.3 0.01 0.005 0.009 0.01 543 3 666.667 555.556 1000 1000

453 0.01 0.003 0.011 0.01 544 11 555.556 333.333 1222.22 777.7778453.7 0.01 0.005 0.012 0.01 545 7 666.667 555.556 1333.33 666.6667454.4 0.01 0.003 0.009 0.01 546 7 555.556 333.333 1000 1000455.1 0.01 0.004 0.012 0.01 547 9 888.889 444.444 1333.33 888.8889455.9 0.01 0.005 0.012 0.01 548 11 777.778 555.556 1333.33 888.8889456.6 0.01 0.004 0.011 0.01 549 11 666.667 444.444 1222.22 888.8889457.3 0.01 0.005 0.009 0.01 550 8 888.889 555.556 1000 888.8889

458 0.01 0.003 0.01 0.01 551 10 666.667 333.333 1111.11 888.8889458.7 0.01 0.003 0.011 0.01 552 7 555.556 333.333 1222.22 777.7778459.4 0.01 0.003 0.013 0.01 553 11 888.889 333.333 1444.44 666.6667460.1 0.01 0.006 0.012 0.01 554 12 666.667 666.667 1333.33 888.8889460.8 0.01 0.004 0.01 0.01 555 13 555.556 444.444 1111.11 1000461.5 0.01 0.003 0.011 0.01 556 10 777.778 333.333 1222.22 777.7778462.2 0.01 0.003 0.012 0.01 557 8 777.778 333.333 1333.33 777.7778462.9 0.01 0.004 0.01 0.01 558 13 666.667 444.444 1111.11 1000463.6 0.01 0.003 0.011 0.01 559 12 555.556 333.333 1222.22 888.8889464.4 0.01 0.003 0.011 0.01 560 8 777.778 333.333 1222.22 555.5556

81

465.1 0.01 0.002 0.012 0.01 561 11 777.778 222.222 1333.33 1000465.8 0.01 0.004 0.009 0.01 562 7 888.889 444.444 1000 666.6667466.5 0.01 0.005 0.011 0.01 563 11 666.667 555.556 1222.22 555.5556467.2 0.01 0.002 0.01 0.01 564 14 777.778 222.222 1111.11 777.7778467.9 0.01 0.003 0.011 0.01 565 6 666.667 333.333 1222.22 666.6667468.6 0.01 0.003 0.009 0.01 566 8 666.667 333.333 1000 666.6667469.3 0 0.002 0.012 0.01 567 13 444.444 222.222 1333.33 888.8889

470 0.01 0.004 0.008 0.01 568 12 777.778 444.444 888.889 666.6667470.7 0.01 0.004 0.013 0.01 569 11 555.556 444.444 1444.44 1000471.4 0.01 0.003 0.012 0.01 570 17 888.889 333.333 1333.33 777.7778472.1 0.01 0.002 0.009 0.01 571 10 666.667 222.222 1000 666.6667472.8 0.01 0.002 0.013 0.01 572 8 777.778 222.222 1444.44 666.6667473.5 0 0.002 0.01 0.01 573 11 444.444 222.222 1111.11 666.6667474.2 0.01 0.004 0.011 0.01 574 14 777.778 444.444 1222.22 666.6667474.9 0.01 0.003 0.011 0.01 575 12 888.889 333.333 1222.22 888.8889475.6 0.01 0.006 0.009 0.01 576 6 777.778 666.667 1000 888.8889476.4 0.01 0.005 0.009 0.01 577 7 1000 555.556 1000 888.8889477.1 0.01 0.004 0.012 0.01 578 8 666.667 444.444 1333.33 666.6667477.8 0.01 0.003 0.008 0.01 579 12 888.889 333.333 888.889 666.6667478.5 0.01 0.006 0.009 0.01 580 4 666.667 666.667 1000 666.6667479.2 0.01 0.002 0.009 0.01 581 17 666.667 222.222 1000 888.8889479.9 0.01 0.006 0.009 0.01 582 11 777.778 666.667 1000 555.5556480.6 0.01 0.006 0.01 0.01 583 12 555.556 666.667 1111.11 777.7778481.3 0.01 0.002 0.012 0.01 584 11 555.556 222.222 1333.33 777.7778

482 0.01 0.002 0.011 0.01 585 7 666.667 222.222 1222.22 666.6667482.7 0.01 0.005 0.009 0.01 586 3 888.889 555.556 1000 777.7778483.4 0.01 0.002 0.009 0.01 587 9 888.889 222.222 1000 555.5556484.1 0.01 0.003 0.008 0.01 588 8 777.778 333.333 888.889 777.7778484.8 0.01 0.004 0.01 0.01 589 11 555.556 444.444 1111.11 888.8889485.5 0.01 0.003 0.01 0.01 590 6 888.889 333.333 1111.11 777.7778486.2 0.01 0.004 0.01 0.01 591 14 666.667 444.444 1111.11 888.8889486.9 0.01 0.005 0.011 0.01 592 10 666.667 555.556 1222.22 777.7778487.6 0.01 0.005 0.01 0.01 593 12 555.556 555.556 1111.11 666.6667488.3 0.01 0.004 0.01 0.01 594 11 666.667 444.444 1111.11 888.8889

489 0.01 0.003 0.011 0.01 595 11 666.667 333.333 1222.22 555.5556489.7 0.01 0.004 0.009 0.01 596 9 666.667 444.444 1000 777.7778490.4 0.01 0.003 0.008 0.01 597 15 555.556 333.333 888.889 777.7778491.1 0.01 0.005 0.009 0.01 598 15 777.778 555.556 1000 666.6667491.8 0.01 0.004 0.009 0.01 599 11 666.667 444.444 1000 777.7778492.5 0.01 0.004 0.01 0.01 600 17 777.778 444.444 1111.11 777.7778493.2 0.01 0.003 0.008 0.01 601 3 1000 333.333 888.889 666.6667493.9 0.01 0.003 0.009 0.01 602 9 777.778 333.333 1000 666.6667494.6 0.01 0.004 0.008 0.01 603 12 777.778 444.444 888.889 666.6667495.3 0.01 0.001 0.009 0.01 604 22 777.778 111.111 1000 666.6667

496 0.01 0.002 0.01 0.01 605 11 666.667 222.222 1111.11 666.6667496.7 0.01 0.003 0.009 0.01 606 10 777.778 333.333 1000 777.7778497.4 0.01 0.002 0.009 0.01 607 15 666.667 222.222 1000 666.6667498.1 0.01 0.002 0.011 0.01 608 18 666.667 222.222 1222.22 666.6667498.8 0 0.003 0.009 0.01 609 9 444.444 333.333 1000 666.6667

82

499.5 0.01 0.001 0.01 0.01 610 17 777.778 111.111 1111.11 666.6667500.2 0.01 0.004 0.011 0 611 11 666.667 444.444 1222.22 444.4444500.9 0.01 0.003 0.012 0.01 612 9 555.556 333.333 1333.33 555.5556501.6 0.01 0.003 0.009 0.01 613 12 666.667 333.333 1000 666.6667502.3 0.01 0.004 0.009 0.01 614 14 666.667 444.444 1000 777.7778

503 0.01 0.003 0.008 0.01 615 12 666.667 333.333 888.889 555.5556503.7 0.01 0.004 0.009 0.01 616 12 666.667 444.444 1000 555.5556504.4 0.01 0.004 0.009 0.01 617 12 777.778 444.444 1000 555.5556505.1 0.01 0.002 0.009 0.01 618 10 777.778 222.222 1000 666.6667505.8 0.01 0.003 0.009 0.01 619 13 777.778 333.333 1000 777.7778506.5 0.01 0.006 0.009 0.01 620 18 888.889 666.667 1000 666.6667507.2 0.01 0.001 0.007 0.01 621 9 888.889 111.111 777.778 666.6667507.9 0.01 0.002 0.009 0.01 622 9 777.778 222.222 1000 777.7778508.6 0.01 0.004 0.009 0.01 623 22 666.667 444.444 1000 555.5556509.3 0.01 0.003 0.009 0.01 624 7 555.556 333.333 1000 555.5556

510 0.01 0.004 0.009 0.01 625 13 666.667 444.444 1000 666.6667510.7 0.01 0.003 0.009 0.01 626 3 777.778 333.333 1000 777.7778511.4 0.01 0.003 0.01 0.01 627 14 555.556 333.333 1111.11 555.5556512.1 0.01 0.003 0.007 0 628 14 555.556 333.333 777.778 444.4444512.8 0.01 0.003 0.008 0.01 629 14 777.778 333.333 888.889 666.6667513.5 0.01 0.002 0.008 0.01 630 14 666.667 222.222 888.889 666.6667514.2 0.01 0.003 0.009 0.01 631 10 666.667 333.333 1000 666.6667514.9 0.01 0.003 0.007 0.01 632 14 555.556 333.333 777.778 666.6667515.6 0.01 0.002 0.009 0.01 633 7 777.778 222.222 1000 777.7778516.3 0.01 0.003 0.01 0.01 634 10 555.556 333.333 1111.11 555.5556516.9 0.01 0.004 0.008 0.01 635 8 666.667 444.444 888.889 666.6667517.6 0.01 0.002 0.009 0.01 636 9 777.778 222.222 1000 777.7778518.3 0.01 0.004 0.009 0.01 637 12 888.889 444.444 1000 888.8889

519 0.01 0.003 0.007 0.01 638 7 777.778 333.333 777.778 777.7778519.7 0.01 0.003 0.008 0.01 639 9 888.889 333.333 888.889 666.6667520.4 0.01 0.001 0.008 0.01 640 19 777.778 111.111 888.889 666.6667521.1 0.01 0.002 0.011 0.01 641 13 555.556 222.222 1222.22 666.6667521.8 0.01 0.003 0.01 0.01 642 11 888.889 333.333 1111.11 666.6667522.5 0.01 0.002 0.008 0 643 12 777.778 222.222 888.889 444.4444523.2 0.01 0.002 0.008 0.01 644 15 666.667 222.222 888.889 666.6667523.9 0.01 0.002 0.009 0.01 645 14 666.667 222.222 1000 555.5556524.6 0.01 0.005 0.008 0.01 646 11 555.556 555.556 888.889 666.6667525.3 0.01 0.002 0.008 0.01 647 14 777.778 222.222 888.889 666.6667

526 0.01 0.002 0.008 0.01 648 11 777.778 222.222 888.889 666.6667526.7 0.01 0.002 0.008 0 649 17 666.667 222.222 888.889 444.4444527.4 0.01 0.003 0.007 0.01 650 17 666.667 333.333 777.778 666.6667

528 0.01 0.003 0.005 0 651 12 777.778 333.333 555.556 444.4444528.7 0.01 0.002 0.009 0.01 652 14 888.889 222.222 1000 777.7778529.4 0.01 0.003 0.008 0.01 653 14 555.556 333.333 888.889 666.6667530.1 0 0.003 0.008 0.01 654 15 333.333 333.333 888.889 555.5556530.8 0.01 0.002 0.007 0.01 655 17 777.778 222.222 777.778 888.8889531.5 0.01 0.002 0.008 0.01 656 15 555.556 222.222 888.889 666.6667532.2 0.01 0.003 0.009 0.01 657 18 666.667 333.333 1000 555.5556532.9 0.01 0.004 0.008 0.01 658 27 555.556 444.444 888.889 666.6667

83

533.6 0.01 0.001 0.007 0.01 659 27 666.667 111.111 777.778 555.5556534.3 0.01 0.002 0.008 0.01 660 26 777.778 222.222 888.889 555.5556

535 0.01 0.002 0.009 0.01 661 30 777.778 222.222 1000 666.6667535.7 0.01 0.002 0.006 0.01 662 56 666.667 222.222 666.667 666.6667536.3 0.01 0.003 0.01 0 663 35 666.667 333.333 1111.11 333.3333

537 0.01 0.005 0.008 0.01 664 32 888.889 555.556 888.889 666.6667537.7 0.01 0.003 0.008 0.01 665 41 666.667 333.333 888.889 666.6667538.4 0.01 0.003 0.009 0 666 50 555.556 333.333 1000 444.4444539.1 0.01 0.004 0.006 0.01 667 50 666.667 444.444 666.667 555.5556539.8 0.01 0.003 0.007 0.01 668 68 666.667 333.333 777.778 777.7778540.5 0.01 0.003 0.006 0.01 669 56 666.667 333.333 666.667 555.5556541.2 0 0.001 0.007 0 670 62 444.444 111.111 777.778 444.4444541.9 0.01 0.003 0.007 0 671 63 666.667 333.333 777.778 444.4444542.5 0.01 0.003 0.005 0 672 65 888.889 333.333 555.556 333.3333543.2 0.01 0.002 0.008 0.01 673 87 1000 222.222 888.889 555.5556543.9 0.01 0.001 0.006 0.01 674 92 666.667 111.111 666.667 666.6667544.6 0.01 0.003 0.007 0.01 675 70 666.667 333.333 777.778 555.5556545.3 0.01 0.004 0.008 0.01 676 92 666.667 444.444 888.889 555.5556

546 0.01 0.003 0.007 0 677 83 888.889 333.333 777.778 444.4444546.7 0.01 0.002 0.007 0.01 678 84 666.667 222.222 777.778 555.5556547.4 0.01 0.001 0.006 0 679 74 777.778 111.111 666.667 444.4444548.1 0.01 0.003 0.008 0 680 80 888.889 333.333 888.889 333.3333548.7 0.01 0.003 0.007 0 681 81 888.889 333.333 777.778 444.4444549.4 0.01 0.003 0.008 0 682 64 777.778 333.333 888.889 444.4444550.1 0.01 0.004 0.008 0.01 683 68 666.667 444.444 888.889 555.5556550.8 0.01 0.002 0.006 0.01 684 92 777.778 222.222 666.667 555.5556551.5 0.01 0.002 0.008 0.01 685 74 666.667 222.222 888.889 555.5556552.2 0.01 0.002 0.007 0.01 686 91 777.778 222.222 777.778 666.6667552.9 0.01 0.004 0.007 0.01 687 70 555.556 444.444 777.778 555.5556553.5 0.01 0.002 0.007 0.01 688 71 666.667 222.222 777.778 666.6667554.2 0.01 0.002 0.007 0.01 689 69 666.667 222.222 777.778 555.5556554.9 0.01 0.004 0.007 0.01 690 61 666.667 444.444 777.778 555.5556555.6 0.01 0.002 0.006 0 691 69 666.667 222.222 666.667 444.4444556.3 0.01 0.003 0.008 0 692 62 888.889 333.333 888.889 444.4444

557 0.01 0.002 0.006 0.01 693 60 777.778 222.222 666.667 777.7778557.7 0.01 0.002 0.006 0 694 66 666.667 222.222 666.667 444.4444558.3 0.01 0.001 0.006 0.01 695 62 666.667 111.111 666.667 555.5556

559 0.01 0.001 0.007 0.01 696 68 555.556 111.111 777.778 666.6667559.7 0.01 0.002 0.007 0.01 697 72 888.889 222.222 777.778 555.5556560.4 0.01 0.002 0.007 0.01 698 45 666.667 222.222 777.778 555.5556561.1 0.01 0.001 0.007 0.01 699 64 666.667 111.111 777.778 666.6667561.8 0.01 0 0.006 0.01 700 50 666.667 0 666.667 666.6667562.5 0.01 0.001 0.007 0 701 49 777.778 111.111 777.778 333.3333563.1 0.01 0 0.008 0.01 702 63 888.889 0 888.889 666.6667563.8 0.01 0.003 0.007 0.01 703 54 666.667 333.333 777.778 666.6667564.5 0.01 0.002 0.007 0.01 704 49 666.667 222.222 777.778 555.5556565.2 0.01 0.001 0.007 0 705 52 777.778 111.111 777.778 444.4444565.9 0.01 0.003 0.008 0 706 57 888.889 333.333 888.889 333.3333566.6 0.01 0.001 0.006 0.01 707 52 666.667 111.111 666.667 555.5556

84

567.2 0.01 0.003 0.007 0.01 708 49 666.667 333.333 777.778 666.6667567.9 0.01 0.002 0.004 0 709 73 666.667 222.222 444.444 444.4444568.6 0.01 0.002 0.007 0.01 710 61 777.778 222.222 777.778 555.5556569.3 0.01 0.003 0.005 0.01 711 66 777.778 333.333 555.556 777.7778

570 0.01 0.003 0.006 0 712 68 666.667 333.333 666.667 444.4444570.6 0.01 0.002 0.004 0.01 713 52 777.778 222.222 444.444 555.5556571.3 0.01 0.002 0.007 0.01 714 56 777.778 222.222 777.778 777.7778

572 0.01 0.001 0.007 0 715 68 555.556 111.111 777.778 444.4444572.7 0.01 0.002 0.007 0.01 716 55 555.556 222.222 777.778 555.5556573.4 0.01 0 0.007 0 717 66 555.556 0 777.778 444.4444574.1 0.01 0 0.007 0 718 76 777.778 0 777.778 444.4444574.7 0.01 0.003 0.007 0 719 61 555.556 333.333 777.778 333.3333575.4 0.01 0.002 0.007 0.01 720 74 666.667 222.222 777.778 555.5556576.1 0.01 0.002 0.008 0 721 56 555.556 222.222 888.889 222.2222576.8 0.01 0.004 0.006 0.01 722 63 666.667 444.444 666.667 555.5556577.5 0.01 0 0.006 0.01 723 43 777.778 0 666.667 555.5556578.1 0.01 0.001 0.007 0 724 51 555.556 111.111 777.778 444.4444578.8 0.01 0.001 0.007 0.01 725 59 666.667 111.111 777.778 555.5556579.5 0.01 0.002 0.006 0 726 49 666.667 222.222 666.667 444.4444580.2 0.01 0.001 0.007 0 727 59 555.556 111.111 777.778 333.3333580.9 0 0.003 0.006 0.01 728 67 444.444 333.333 666.667 555.5556581.5 0.01 0.002 0.005 0 729 60 666.667 222.222 555.556 444.4444582.2 0.01 0.002 0.006 0 730 58 666.667 222.222 666.667 333.3333582.9 0.01 0.001 0.005 0.01 731 52 666.667 111.111 555.556 555.5556583.6 0.01 0.001 0.007 0 732 48 666.667 111.111 777.778 444.4444584.2 0.01 0.004 0.005 0 733 46 666.667 444.444 555.556 333.3333584.9 0.01 0.003 0.006 0 734 41 666.667 333.333 666.667 444.4444585.6 0.01 0.002 0.005 0 735 71 777.778 222.222 555.556 444.4444586.3 0 0.002 0.005 0 736 54 444.444 222.222 555.556 444.4444

587 0.01 0.002 0.006 0 737 58 555.556 222.222 666.667 444.4444587.6 0.01 0.003 0.006 0.01 738 53 666.667 333.333 666.667 555.5556588.3 0.01 0.003 0.008 0 739 45 666.667 333.333 888.889 222.2222

589 0.01 0.002 0.006 0 740 39 666.667 222.222 666.667 444.4444589.7 0.01 0.003 0.005 0 741 43 555.556 333.333 555.556 333.3333590.3 0.01 0.002 0.006 0.01 742 58 666.667 222.222 666.667 555.5556

591 0.01 0.002 0.007 0.01 743 37 555.556 222.222 777.778 555.5556591.7 0.01 0.002 0.006 0 744 46 666.667 222.222 666.667 444.4444592.4 0.01 0.002 0.007 0 745 35 777.778 222.222 777.778 444.4444

593 0.01 0.001 0.006 0.01 746 29 555.556 111.111 666.667 555.5556593.7 0.01 0.001 0.006 0 747 40 666.667 111.111 666.667 333.3333594.4 0.01 0.002 0.007 0.01 748 42 666.667 222.222 777.778 666.6667595.1 0.01 0.001 0.007 0 749 34 666.667 111.111 777.778 444.4444595.8 0.01 0.002 0.007 0 750 51 777.778 222.222 777.778 333.3333596.4 0.01 0.001 0.005 0 751 48 555.556 111.111 555.556 333.3333597.1 0.01 0.002 0.007 0 752 40 777.778 222.222 777.778 333.3333597.8 0.01 0.002 0.006 0 753 25 666.667 222.222 666.667 333.3333598.5 0.01 0.002 0.006 0 754 24 666.667 222.222 666.667 333.3333599.1 0.01 0.002 0.007 0 755 27 666.667 222.222 777.778 444.4444599.8 0.01 0.001 0.007 0 756 44 666.667 111.111 777.778 333.3333

85

600.5 0.01 0.003 0.006 0.01 757 29 666.667 333.333 666.667 555.5556601.1 0.01 0.002 0.007 0 758 32 777.778 222.222 777.778 444.4444601.8 0 0.001 0.007 0 759 27 444.444 111.111 777.778 444.4444602.5 0 0.002 0.006 0 760 24 333.333 222.222 666.667 444.4444603.2 0.01 0.003 0.007 0 761 38 555.556 333.333 777.778 222.2222603.8 0.01 0.002 0.006 0 762 27 555.556 222.222 666.667 333.3333604.5 0.01 0.002 0.006 0.01 763 22 666.667 222.222 666.667 555.5556605.2 0.01 0.003 0.005 0.01 764 22 555.556 333.333 555.556 555.5556605.9 0.01 0.002 0.006 0 765 26 777.778 222.222 666.667 222.2222606.5 0.01 0.002 0.005 0.01 766 21 666.667 222.222 555.556 555.5556607.2 0.01 0.003 0.006 0 767 17 666.667 333.333 666.667 333.3333607.9 0.01 0.003 0.006 0.01 768 10 666.667 333.333 666.667 555.5556608.5 0.01 0.002 0.008 0.01 769 20 777.778 222.222 888.889 666.6667609.2 0.01 0.001 0.005 0 770 20 666.667 111.111 555.556 444.4444609.9 0.01 0.002 0.006 0 771 26 777.778 222.222 666.667 444.4444610.6 0.01 0.001 0.006 0 772 12 666.667 111.111 666.667 444.4444611.2 0.01 0.002 0.005 0 773 13 555.556 222.222 555.556 111.1111611.9 0.01 0.003 0.006 0 774 15 777.778 333.333 666.667 444.4444612.6 0.01 0.002 0.006 0 775 21 666.667 222.222 666.667 222.2222613.2 0.01 0.001 0.006 0 776 19 777.778 111.111 666.667 333.3333613.9 0.01 0.003 0.004 0 777 12 666.667 333.333 444.444 333.3333614.6 0.01 0.002 0.005 0.01 778 9 666.667 222.222 555.556 555.5556615.3 0.01 0.003 0.005 0 779 19 555.556 333.333 555.556 444.4444615.9 0.01 0.003 0.004 0 780 11 777.778 333.333 444.444 333.3333616.6 0 0.002 0.004 0 781 23 444.444 222.222 444.444 333.3333617.3 0.01 0.003 0.004 0.01 782 13 666.667 333.333 444.444 666.6667617.9 0.01 0.001 0.005 0.01 783 8 666.667 111.111 555.556 666.6667618.6 0.01 0.001 0.007 0 784 14 666.667 111.111 777.778 444.4444619.3 0.01 0.002 0.006 0 785 9 666.667 222.222 666.667 444.4444619.9 0.01 0.002 0.007 0.01 786 9 777.778 222.222 777.778 555.5556620.6 0.01 0.003 0.005 0 787 14 777.778 333.333 555.556 444.4444621.3 0.01 0.002 0.008 0 788 9 555.556 222.222 888.889 444.4444621.9 0.01 0 0.006 0 789 6 555.556 0 666.667 222.2222622.6 0.01 0.002 0.006 0 790 9 555.556 222.222 666.667 222.2222623.3 0.01 0.004 0.005 0 791 11 555.556 444.444 555.556 333.3333

624 0.01 0.001 0.005 0 792 10 666.667 111.111 555.556 444.4444624.6 0.01 0.002 0.005 0 793 10 666.667 222.222 555.556 222.2222625.3 0.01 0.001 0.006 0 794 10 777.778 111.111 666.667 444.4444

626 0.01 0.001 0.004 0 795 7 666.667 111.111 444.444 444.4444626.6 0.01 0.003 0.006 0 796 12 555.556 333.333 666.667 222.2222627.3 0.01 0.003 0.006 0 797 8 666.667 333.333 666.667 333.3333

628 0 0.002 0.004 0 798 11 444.444 222.222 444.444 444.4444628.6 0.01 0.002 0.005 0 799 12 666.667 222.222 555.556 333.3333629.3 0.01 0.002 0.005 0 800 9 555.556 222.222 555.556 444.4444

630 0.01 0.002 0.005 0 � 555.556 222.222 555.556 222.2222630.6 0.01 0.002 0.006 0 666.667 222.222 666.667 222.2222631.3 0.01 0.002 0.005 0 666.667 222.222 555.556 333.3333631.9 0.01 0 0.005 0 555.556 0 555.556 444.4444632.6 0.01 0.003 0.005 0 555.556 333.333 555.556 333.3333

86

633.3 0.01 0.003 0.006 0 555.556 333.333 666.667 333.3333633.9 0.01 0.002 0.004 0 555.556 222.222 444.444 222.2222634.6 0.01 0.001 0.005 0 555.556 111.111 555.556 333.3333635.3 0.01 0 0.004 0 666.667 0 444.444 222.2222635.9 0.01 0.001 0.005 0.01 666.667 111.111 555.556 555.5556636.6 0.01 0.003 0.006 0 666.667 333.333 666.667 444.4444637.3 0.01 0.003 0.005 0 555.556 333.333 555.556 444.4444637.9 0.01 0.001 0.005 0 666.667 111.111 555.556 444.4444638.6 0.01 0.001 0.005 0 777.778 111.111 555.556 222.2222639.3 0.01 0.004 0.004 0 777.778 444.444 444.444 333.3333639.9 0.01 0.002 0.005 0 888.889 222.222 555.556 444.4444640.6 0.01 0.002 0.006 0 555.556 222.222 666.667 222.2222641.2 0.01 0.001 0.005 0 666.667 111.111 555.556 333.3333641.9 0.01 0.002 0.005 0 777.778 222.222 555.556 333.3333642.6 0.01 0.003 0.005 0 555.556 333.333 555.556 444.4444643.2 0.01 0.001 0.005 0 666.667 111.111 555.556 333.3333643.9 0.01 0 0.004 0 555.556 0 444.444 333.3333644.6 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333645.2 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333645.9 0 0.002 0.005 0 444.444 222.222 555.556 444.4444646.5 0 0 0.006 0 444.444 0 666.667 444.4444647.2 0.01 0.002 0.006 0 777.778 222.222 666.667 333.3333647.9 0.01 0.001 0.005 0 555.556 111.111 555.556 222.2222648.5 0.01 0.002 0.005 0 555.556 222.222 555.556 333.3333649.2 0.01 0.002 0.005 0 666.667 222.222 555.556 444.4444649.8 0.01 0 0.004 0 666.667 0 444.444 444.4444650.5 0.01 0.001 0.005 0 666.667 111.111 555.556 333.3333651.2 0.01 0.002 0.003 0 666.667 222.222 333.333 222.2222651.8 0.01 0.002 0.005 0 888.889 222.222 555.556 333.3333652.5 0.01 0.002 0.004 0 666.667 222.222 444.444 222.2222653.1 0.01 0.002 0.004 0 666.667 222.222 444.444 444.4444653.8 0.01 0.003 0.005 0 777.778 333.333 555.556 333.3333654.5 0.01 0.002 0.005 0 666.667 222.222 555.556 333.3333655.1 0.01 0.002 0.005 0 666.667 222.222 555.556 333.3333655.8 0 0.002 0.006 0 444.444 222.222 666.667 333.3333656.4 0.01 0.001 0.005 0 555.556 111.111 555.556 444.4444657.1 0.01 0.002 0.005 0 555.556 222.222 555.556 222.2222657.8 0.01 0.002 0.005 0 777.778 222.222 555.556 333.3333658.4 0.01 0.002 0.005 0 666.667 222.222 555.556 111.1111659.1 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333659.7 0.01 0.003 0.004 0 666.667 333.333 444.444 444.4444660.4 0.01 0.001 0.004 0 777.778 111.111 444.444 222.2222

661 0.01 0.001 0.004 0 1000 111.111 444.444 111.1111661.7 0.01 0.001 0.005 0 666.667 111.111 555.556 333.3333662.4 0.01 0.001 0.004 0 777.778 111.111 444.444 222.2222

663 0.01 0.001 0.005 0 666.667 111.111 555.556 222.2222663.7 0 0.001 0.005 0 444.444 111.111 555.556 444.4444664.3 0.01 0.001 0.004 0 777.778 111.111 444.444 222.2222

665 0.01 0.001 0.004 0 555.556 111.111 444.444 333.3333

87

665.6 0.01 0 0.006 0 666.667 0 666.667 333.3333666.3 0.01 0.001 0.005 0 555.556 111.111 555.556 444.4444666.9 0.01 0.002 0.005 0.01 666.667 222.222 555.556 555.5556667.6 0.01 0.001 0.005 0.01 555.556 111.111 555.556 666.6667668.3 0.01 0 0.005 0.01 555.556 0 555.556 555.5556668.9 0.01 0.001 0.005 0 555.556 111.111 555.556 333.3333669.6 0.01 0.002 0.005 0 666.667 222.222 555.556 333.3333670.2 0.01 0.001 0.005 0.01 666.667 111.111 555.556 666.6667670.9 0.01 0.001 0.005 0 666.667 111.111 555.556 444.4444671.5 0 0.001 0.005 0 444.444 111.111 555.556 444.4444672.2 0.01 0.002 0.005 0 555.556 222.222 555.556 444.4444672.8 0.01 0.001 0.005 0 777.778 111.111 555.556 333.3333673.5 0.01 0.002 0.006 0.01 666.667 222.222 666.667 555.5556674.1 0.01 0.003 0.004 0 666.667 333.333 444.444 333.3333674.8 0.01 0.003 0.005 0 888.889 333.333 555.556 222.2222675.5 0.01 0.001 0.003 0 666.667 111.111 333.333 333.3333676.1 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333676.8 0.01 0.002 0.006 0 666.667 222.222 666.667 333.3333677.4 0.01 0 0.005 0.01 777.778 0 555.556 555.5556678.1 0.01 0.002 0.004 0 777.778 222.222 444.444 444.4444678.7 0.01 0.002 0.004 0 555.556 222.222 444.444 333.3333679.4 0.01 0.001 0.004 0 888.889 111.111 444.444 333.3333

680 0.01 0.001 0.005 0 777.778 111.111 555.556 333.3333680.7 0.01 0.001 0.004 0 777.778 111.111 444.444 111.1111681.3 0.01 0.001 0.005 0 555.556 111.111 555.556 222.2222

682 0.01 0.001 0.005 0 777.778 111.111 555.556 0682.6 0.01 0.001 0.006 0 888.889 111.111 666.667 222.2222683.3 0.01 0 0.004 0 888.889 0 444.444 222.2222683.9 0.01 0.002 0.007 0 777.778 222.222 777.778 444.4444684.6 0.01 0.002 0.005 0 555.556 222.222 555.556 444.4444685.2 0.01 0.003 0.005 0 777.778 333.333 555.556 333.3333685.9 0.01 0.002 0.005 0 555.556 222.222 555.556 444.4444686.5 0.01 0.001 0.003 0 666.667 111.111 333.333 444.4444687.2 0 0.002 0.003 0 444.444 222.222 333.333 111.1111687.8 0.01 0.001 0.006 0 777.778 111.111 666.667 333.3333688.5 0.01 0 0.003 0 555.556 0 333.333 222.2222689.1 0 0.002 0.004 0 444.444 222.222 444.444 333.3333689.8 0 0 0.004 0 444.444 0 444.444 111.1111690.4 0 0.002 0.005 0 444.444 222.222 555.556 444.4444691.1 0.01 0 0.006 0 555.556 0 666.667 333.3333691.7 0.01 0.001 0.003 0 666.667 111.111 333.333 333.3333692.4 0.01 0.003 0.005 0 555.556 333.333 555.556 333.3333

693 0.01 0.001 0.004 0 555.556 111.111 444.444 333.3333693.7 0.01 0.001 0.005 0 555.556 111.111 555.556 444.4444694.3 0.01 0.002 0.006 0 666.667 222.222 666.667 222.2222

695 0.01 0.002 0.003 0 555.556 222.222 333.333 333.3333695.6 0.01 0.001 0.004 0.01 777.778 111.111 444.444 555.5556696.2 0.01 0 0.005 0 777.778 0 555.556 333.3333696.9 0.01 0.001 0.006 0 777.778 111.111 666.667 444.4444

88

697.5 0.01 0.001 0.004 0 555.556 111.111 444.444 444.4444698.2 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333698.8 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333699.5 0 0.003 0.005 0 444.444 333.333 555.556 333.3333700.1 0.01 0.001 0.004 0 888.889 111.111 444.444 444.4444700.8 0.01 0 0.002 0 777.778 0 222.222 222.2222701.4 0.01 0 0.003 0 666.667 0 333.333 444.4444702.1 0.01 0.002 0.003 0 888.889 222.222 333.333 111.1111702.7 0.01 0.002 0.004 0 666.667 222.222 444.444 222.2222703.3 0.01 -0 0.004 -0 666.667 -111.111 444.444 -111.111

704 0.01 0.002 0.005 0 777.778 222.222 555.556 333.3333704.6 0.01 0.002 0.004 0 666.667 222.222 444.444 222.2222705.3 0.01 0.002 0.003 0 555.556 222.222 333.333 222.2222705.9 0 0.001 0.006 0 444.444 111.111 666.667 111.1111706.6 0.01 0.001 0.004 0 555.556 111.111 444.444 222.2222707.2 0.01 0.001 0.002 0 888.889 111.111 222.222 111.1111707.9 0.01 0.001 0.003 0 666.667 111.111 333.333 222.2222708.5 0.01 0 0.005 0 777.778 0 555.556 111.1111709.1 0.01 0.002 0.005 0 666.667 222.222 555.556 111.1111709.8 0 0.001 0.003 0 444.444 111.111 333.333 0710.4 0 0.002 0.003 0 444.444 222.222 333.333 333.3333711.1 0.01 0.002 0.005 0 666.667 222.222 555.556 333.3333711.7 0.01 0.001 0.004 0 666.667 111.111 444.444 111.1111712.3 0.01 0.001 0.005 0 666.667 111.111 555.556 0

713 0.01 0 0.004 0 555.556 0 444.444 111.1111713.6 0.01 0.001 0.006 0 555.556 111.111 666.667 111.1111714.3 0.01 0.003 0.006 0 666.667 333.333 666.667 222.2222714.9 0.01 0.002 0.004 0 666.667 222.222 444.444 333.3333715.6 0.01 0 0.003 0 777.778 0 333.333 333.3333716.2 0.01 0 0.004 0 666.667 0 444.444 222.2222716.8 0.01 0 0.004 0 555.556 0 444.444 0717.5 0 0.001 0.005 0 444.444 111.111 555.556 111.1111718.1 0 0.001 0.004 0 333.333 111.111 444.444 111.1111718.8 0.01 0.001 0.005 0 666.667 111.111 555.556 333.3333719.4 0.01 0.002 0.004 0 777.778 222.222 444.444 222.2222

720 0.01 0 0.004 0 888.889 0 444.444 333.3333720.7 0.01 0.002 0.003 0 666.667 222.222 333.333 111.1111721.3 0.01 0.002 0.003 0 666.667 222.222 333.333 222.2222

722 0.01 0 0.002 0 777.778 0 222.222 111.1111722.6 0.01 -0 0.004 0 666.667 -111.111 444.444 222.2222723.2 0.01 -0 0.004 0 555.556 -111.111 444.444 222.2222723.9 0 0 0.005 0 444.444 0 555.556 333.3333724.5 0.01 -0 0.004 0 555.556 -111.111 444.444 222.2222725.1 0.01 0 0.004 0 555.556 0 444.444 333.3333725.8 0 0 0.003 0 444.444 0 333.333 333.3333726.4 0 0.001 0.005 0 333.333 111.111 555.556 333.3333727.1 0.01 0.001 0.004 0 555.556 111.111 444.444 222.2222727.7 0.01 0.001 0.003 0 666.667 111.111 333.333 222.2222728.3 0.01 0 0.004 0 555.556 0 444.444 222.2222

89

729 0.01 0 0.005 0 666.667 0 555.556 333.3333729.6 0.01 0.002 0.003 0 888.889 222.222 333.333 333.3333730.2 0.01 0.002 0.005 0 666.667 222.222 555.556 444.4444730.9 0.01 0.001 0.006 0 666.667 111.111 666.667 333.3333731.5 0 0 0.005 0 444.444 0 555.556 333.3333732.1 0.01 0.001 0.005 0 555.556 111.111 555.556 333.3333732.8 0.01 0 0.005 0 555.556 0 555.556 111.1111733.4 0.01 0.002 0.005 0 666.667 222.222 555.556 222.2222734.1 0.01 0.003 0.006 0 555.556 333.333 666.667 444.4444734.7 0.01 0.002 0.004 0 555.556 222.222 444.444 333.3333735.3 0.01 0 0.004 0 666.667 0 444.444 444.4444

736 0.01 0 0.006 0 666.667 0 666.667 444.4444736.6 0.01 0.002 0.006 0 666.667 222.222 666.667 333.3333737.2 0.01 0.001 0.004 0 777.778 111.111 444.444 333.3333737.9 0.01 0 0.005 0 555.556 0 555.556 222.2222738.5 0 0.001 0.005 0 444.444 111.111 555.556 444.4444739.1 0.01 0 0.005 0 666.667 0 555.556 111.1111739.8 0 0 0.004 0 444.444 0 444.444 444.4444740.4 0.01 0 0.005 0 666.667 0 555.556 111.1111

741 0.01 0.001 0.005 0 888.889 111.111 555.556 444.4444741.7 0.01 0.001 0.005 0 777.778 111.111 555.556 333.3333742.3 0.01 0.001 0.005 0 666.667 111.111 555.556 222.2222742.9 0.01 0 0.005 0 555.556 0 555.556 333.3333743.6 0.01 0.002 0.007 0 555.556 222.222 777.778 111.1111744.2 0 -0 0.004 0 444.444 -111.111 444.444 444.4444744.8 0 0.002 0.006 0 333.333 222.222 666.667 333.3333745.4 0 0.001 0.004 0 444.444 111.111 444.444 444.4444746.1 0.01 -0 0.003 0 777.778 -111.111 333.333 222.2222746.7 0.01 0 0.002 0 555.556 0 222.222 333.3333747.3 0 0 0.004 0 444.444 0 444.444 333.3333

748 0 -0 0.003 0 444.444 -111.111 333.333 444.4444748.6 0.01 0 0.002 0 555.556 0 222.222 333.3333749.2 0.01 -0 0.003 0 777.778 -111.111 333.333 222.2222749.9 0.01 0.001 0.003 0 666.667 111.111 333.333 222.2222750.5 0.01 0 0.003 0 555.556 0 333.333 222.2222751.1 0.01 0.002 0.003 -0 555.556 222.222 333.333 -111.111751.7 0 0.002 0.004 0 444.444 222.222 444.444 333.3333752.4 0.01 0.002 0.006 0 666.667 222.222 666.667 333.3333

753 0.01 0.002 0.004 0 777.778 222.222 444.444 222.2222753.6 0.01 0.002 0.003 0 777.778 222.222 333.333 333.3333754.3 0.01 0.001 0.004 0 555.556 111.111 444.444 444.4444754.9 0.01 0.002 0.001 0 888.889 222.222 111.111 444.4444755.5 0.01 0.001 0.003 0 555.556 111.111 333.333 444.4444756.1 0 0.001 0.003 0 444.444 111.111 333.333 333.3333756.8 0.01 0.001 0.001 0 777.778 111.111 111.111 333.3333757.4 0.01 0.001 0.003 0 666.667 111.111 333.333 222.2222

758 0.01 0 0.003 0 555.556 0 333.333 222.2222758.7 0.01 0.001 0.004 0 777.778 111.111 444.444 222.2222759.3 0.01 -0 0.002 0 555.556 -111.111 222.222 444.4444

90

759.9 0.01 0.002 0.004 0 777.778 222.222 444.444 111.1111760.5 0.01 0.002 0.004 -0 555.556 222.222 444.444 -111.111761.2 0.01 0 0.004 -0 888.889 0 444.444 -222.222761.8 0.01 0.001 0.005 0 777.778 111.111 555.556 0762.4 0.01 0.002 0.003 0 1000 222.222 333.333 0

763 0.01 0.001 0.004 0 555.556 111.111 444.444 111.1111763.7 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333764.3 0.01 0 0.003 0 555.556 0 333.333 222.2222764.9 0 0.001 0.003 0 444.444 111.111 333.333 111.1111765.5 0.01 0 0.003 0 666.667 0 333.333 444.4444766.2 0.01 -0 0.004 0 555.556 -111.111 444.444 333.3333766.8 0.01 0.001 0.002 0 555.556 111.111 222.222 444.4444767.4 0.01 0.001 0.002 0.01 555.556 111.111 222.222 555.5556

768 0.01 0 0.004 0 777.778 0 444.444 333.3333768.7 0.01 -0 0.002 0 777.778 -111.111 222.222 111.1111769.3 0.01 0 0.005 0 1222.22 0 555.556 111.1111769.9 0.01 0 0.005 0 888.889 0 555.556 111.1111770.5 0.01 0.001 0.004 0 666.667 111.111 444.444 111.1111771.2 0.01 0 0.003 0 555.556 0 333.333 333.3333771.8 0.01 -0 0.004 0 666.667 -111.111 444.444 444.4444772.4 0 0.002 0.004 0 444.444 222.222 444.444 333.3333

773 0 0.001 0.004 0 444.444 111.111 444.444 111.1111773.6 0 0.002 0.002 0 444.444 222.222 222.222 0774.3 0 0.001 0.003 0 333.333 111.111 333.333 111.1111774.9 0 0.002 0.004 0 444.444 222.222 444.444 444.4444775.5 0 0.001 0.004 0 444.444 111.111 444.444 333.3333776.1 0.01 0.002 0.003 0 555.556 222.222 333.333 222.2222776.7 0.01 0 0.004 0 666.667 0 444.444 222.2222777.4 0.01 0 0.004 0 666.667 0 444.444 222.2222

778 0.01 0.002 0.001 0 777.778 222.222 111.111 333.3333778.6 0.01 0.001 0.001 0 666.667 111.111 111.111 222.2222779.2 0.01 0.002 0.003 0 666.667 222.222 333.333 0779.8 0.01 0.002 0.005 0.01 666.667 222.222 555.556 666.6667780.5 0.01 0.001 0.005 0.01 666.667 111.111 555.556 555.5556781.1 0.01 0 0.004 0 555.556 0 444.444 222.2222781.7 0.01 0.002 0.003 0 666.667 222.222 333.333 444.4444782.3 0.01 0.001 0.004 0 777.778 111.111 444.444 222.2222782.9 0.01 0.003 0.002 0 555.556 333.333 222.222 444.4444783.6 0.01 0.001 0.004 0 666.667 111.111 444.444 333.3333784.2 0.01 0.003 0.003 0 777.778 333.333 333.333 444.4444784.8 0.01 0 0.005 0 555.556 0 555.556 222.2222785.4 0.01 0.002 0.005 0 555.556 222.222 555.556 111.1111

786 0.01 0.001 0.003 0 555.556 111.111 333.333 222.2222786.7 0.01 0.003 0.004 0 555.556 333.333 444.444 333.3333787.3 0.01 0.002 0.004 0.01 1000 222.222 444.444 555.5556787.9 0.01 0 0.003 0 666.667 0 333.333 111.1111788.5 0.01 0.002 0.004 0 888.889 222.222 444.444 333.3333789.1 0.01 0.002 0.004 0 666.667 222.222 444.444 222.2222789.7 0.01 0.001 0.003 0 777.778 111.111 333.333 222.2222

91

790.4 0.01 0.002 0.003 0 777.778 222.222 333.333 444.4444791 0.01 0.001 0.005 0 666.667 111.111 555.556 333.3333

791.6 0.01 0.001 0.003 0 777.778 111.111 333.333 444.4444792.2 0.01 0.001 0.003 -0 666.667 111.111 333.333 -111.111792.8 0.01 -0 0.005 0 555.556 -111.111 555.556 333.3333793.4 0.01 0 0.006 0 555.556 0 666.667 222.2222

794 0.01 0.001 0.005 0 888.889 111.111 555.556 444.4444794.7 0.01 0.001 0.004 0 777.778 111.111 444.444 333.3333795.3 0.01 -0 0.003 0.01 888.889 -222.222 333.333 555.5556795.9 0.01 0 0.002 0 555.556 0 222.222 222.2222796.5 0.01 0 0.003 0 777.778 0 333.333 444.4444797.1 0.01 -0 0.003 0.01 777.778 -111.111 333.333 666.6667797.7 0.01 0.001 0.005 0 777.778 111.111 555.556 333.3333798.3 0 0.001 0.002 0 444.444 111.111 222.222 222.2222

799 0 0.002 0 0 444.444 222.222 0 222.2222799.6 0.01 0.001 0.001 0 555.556 111.111 111.111 333.3333800.2 0 -0 0.002 0.01 333.333 -222.222 222.222 555.5556800.8 0 -0 0 0 333.333 -111.111 0 111.1111801.4 0.01 0 0.002 0 555.556 0 222.222 222.2222

802 0 0.001 0.001 0.01 444.444 111.111 111.111 555.5556802.6 0.01 0 0.004 0 777.778 0 444.444 444.4444803.2 0.01 0.004 0.004 0 888.889 444.444 444.444 444.4444803.9 0.01 0 0.005 0 777.778 0 555.556 333.3333804.5 0.01 0.003 0.004 0 666.667 333.333 444.444 222.2222805.1 0.01 0 0.003 0 555.556 0 333.333 111.1111805.7 0 0 0.004 0 444.444 0 444.444 222.2222806.3 0.01 -0 0.004 0 555.556 -111.111 444.444 333.3333806.9 0 0 0.001 0 444.444 0 111.111 111.1111807.5 0 0 0.003 0 444.444 0 333.333 444.4444808.1 0 0 0.004 0 444.444 0 444.444 333.3333808.7 0.01 0 0.004 0 666.667 0 444.444 333.3333809.4 0.01 0 0.004 0 777.778 0 444.444 333.3333

810 0 0.002 0.004 0 222.222 222.222 444.444 444.4444810.6 0.01 0.002 0.003 0.01 777.778 222.222 333.333 666.6667811.2 0.01 0.002 0.006 -0 777.778 222.222 666.667 -111.111811.8 0.01 0 0.001 0 888.889 0 111.111 444.4444812.4 0.01 0.003 0.001 0 555.556 333.333 111.111 444.4444

813 0.01 0.002 0.002 0 888.889 222.222 222.222 333.3333813.6 0.01 0.001 0.002 0 888.889 111.111 222.222 111.1111814.2 0 0 0.004 0 444.444 0 444.444 333.3333814.8 0.01 0.001 0.005 0 555.556 111.111 555.556 333.3333815.4 0.01 -0 0 0 666.667 -222.222 0 333.3333

816 0.01 -0 0.002 0 777.778 -222.222 222.222 333.3333816.7 0.01 0 0.003 0 666.667 0 333.333 333.3333817.3 0.01 0.001 0.004 0 666.667 111.111 444.444 444.4444817.9 0 0.002 0.003 0 333.333 222.222 333.333 222.2222818.5 0 0.001 0.005 0 444.444 111.111 555.556 444.4444819.1 0 0.004 0.006 0 444.444 444.444 666.667 333.3333819.7 0 0.003 0 0 444.444 333.333 0 333.3333

92

820.3 0.01 0.001 0 0 666.667 111.111 0 333.3333820.9 0.01 0.003 0.002 0 888.889 333.333 222.222 444.4444821.5 0.01 0.002 0.001 0.01 777.778 222.222 111.111 666.6667822.1 0 0.003 0.004 0 333.333 333.333 444.444 222.2222822.7 0.01 0.001 0.001 0.01 555.556 111.111 111.111 555.5556823.3 0.01 0 0.002 0 666.667 0 222.222 444.4444823.9 0.01 0.003 0 0.01 666.667 333.333 0 777.7778824.5 0.01 0 0 0 666.667 0 0 111.1111825.1 0.01 0.002 0.004 0 777.778 222.222 444.444 111.1111825.7 0.01 0.003 0.004 0 555.556 333.333 444.444 444.4444826.3 0.01 0 0.005 0 666.667 0 555.556 444.4444826.9 0.01 0 0.002 0 666.667 0 222.222 444.4444827.5 0 0 0.002 0 444.444 0 222.222 0828.1 0.01 -0 0.002 0 555.556 -222.222 222.222 222.2222828.7 0.01 0.002 0.007 0 555.556 222.222 777.778 111.1111829.3 0.01 0.003 0.006 0 777.778 333.333 666.667 444.4444

830 0.01 -0 0.003 0 1111.11 -222.222 333.333 222.2222830.6 0.01 0.003 0.003 0.01 555.556 333.333 333.333 666.6667831.2 0.01 0 0.002 0.01 555.556 0 222.222 555.5556831.8 0.01 -0 0.005 0 666.667 -222.222 555.556 333.3333832.4 0.01 0.002 0.002 0 777.778 222.222 222.222 222.2222

833 0.01 0.002 0.002 0 777.778 222.222 222.222 222.2222833.6 0 0 0 0 444.444 0 0 222.2222834.2 0.01 0.002 0.003 0 777.778 222.222 333.333 444.4444834.8 0.01 0.004 0.001 0 777.778 444.444 111.111 333.3333835.4 0.01 0.002 0.003 0.01 888.889 222.222 333.333 555.5556

836 0.01 0.002 0.001 0 666.667 222.222 111.111 222.2222836.6 0.01 0.001 0.003 0 777.778 111.111 333.333 333.3333837.2 0.01 0.003 0.002 0.01 555.556 333.333 222.222 666.6667837.8 0.01 0 0.003 0 666.667 0 333.333 444.4444838.4 0 -0 0.004 -0 444.444 -111.111 444.444 -111.111

839 0.01 -0 0 0 555.556 -222.222 0 333.3333839.6 0.01 0.002 0.003 0 666.667 222.222 333.333 333.3333840.2 0.01 0.001 0.004 0.01 666.667 111.111 444.444 555.5556840.8 0.01 0.001 0.001 0.01 555.556 111.111 111.111 555.5556841.4 0.01 0.004 0.003 0.01 777.778 444.444 333.333 555.5556841.9 0 0 0.003 0 222.222 0 333.333 333.3333842.5 0 0 0.002 0 444.444 0 222.222 111.1111843.1 0.01 0.002 0.003 0 777.778 222.222 333.333 333.3333843.7 0.01 0.001 -0 0 555.556 111.111 -111.111 111.1111844.3 0 0.001 0.005 0 444.444 111.111 555.556 111.1111844.9 0.01 0.002 0.003 0 777.778 222.222 333.333 111.1111845.5 0.01 0.001 0.006 0 666.667 111.111 666.667 444.4444846.1 0.01 0.002 0.006 0 888.889 222.222 666.667 333.3333846.7 0.01 0.001 0.005 0 666.667 111.111 555.556 444.4444847.3 0.01 -0 0.005 0 666.667 -111.111 555.556 111.1111847.9 0 -0 0.001 0.01 333.333 -333.333 111.111 555.5556848.5 0.01 0.003 0.002 0 777.778 333.333 222.222 333.3333849.1 0.01 0.001 0.003 0 1222.22 111.111 333.333 111.1111

93

849.7 0.01 0 0.005 0 777.778 0 555.556 111.1111850.3 0.01 0.001 0.005 0 666.667 111.111 555.556 111.1111850.9 0 -0 0.005 0.01 333.333 -111.111 555.556 666.6667851.5 0.01 0.004 0.002 0 555.556 444.444 222.222 111.1111852.1 0.01 0.001 0.005 0 777.778 111.111 555.556 111.1111852.7 0.01 0.002 0.002 0 666.667 222.222 222.222 222.2222853.3 0 0 0.004 0 222.222 0 444.444 222.2222853.9 0.01 0 0.004 0 555.556 0 444.444 222.2222854.5 0.01 0.004 0.004 0 666.667 444.444 444.444 444.4444

855 0 0.001 0.004 0 222.222 111.111 444.444 0855.6 0.01 0.004 -0 0 666.667 444.444 -111.111 111.1111856.2 0.01 0 0.003 0 666.667 0 333.333 444.4444856.8 0 0.002 0.004 0 444.444 222.222 444.444 222.2222857.4 0.01 0.004 0.002 0.01 777.778 444.444 222.222 777.7778

858 0.01 -0 0.002 0 888.889 -111.111 222.222 222.2222858.6 0.01 -0 0.002 0 555.556 -111.111 222.222 0859.2 0 -0 0.002 0 444.444 -111.111 222.222 333.3333859.8 0.01 -0 0.001 -0 666.667 -111.111 111.111 -222.222860.4 0 0.003 0.003 0 222.222 333.333 333.333 222.2222

861 0 -0 0.009 0 333.333 -333.333 1000 222.2222861.5 0.01 -0 0.002 0 888.889 -111.111 222.222 333.3333862.1 0.01 0.002 0.004 0 888.889 222.222 444.444 111.1111862.7 0 -0 0.004 0 444.444 -111.111 444.444 444.4444863.3 0 0.003 0.002 0 0 333.333 222.222 111.1111863.9 0 0.001 0.004 0 444.444 111.111 444.444 222.2222864.5 0.01 0.003 0.001 0 666.667 333.333 111.111 333.3333865.1 0.01 -0 0.003 0 1222.22 -222.222 333.333 333.3333865.7 0.01 0.004 0.002 0 777.778 444.444 222.222 111.1111866.3 0.01 0.002 0.002 0 1111.11 222.222 222.222 333.3333866.9 0 0.004 0.002 0 333.333 444.444 222.222 444.4444867.4 0 0.001 0.003 0 444.444 111.111 333.333 0

868 0.01 0.001 0.003 0.01 888.889 111.111 333.333 555.5556868.6 0 0.003 0.004 -0 444.444 333.333 444.444 -222.222869.2 0.01 0.001 0.005 0 555.556 111.111 555.556 444.4444869.8 0.01 0.002 0.001 0 777.778 222.222 111.111 444.4444870.4 0 0.004 0.006 -0 444.444 444.444 666.667 -222.222

871 0 0.002 0.002 0 444.444 222.222 222.222 222.2222871.6 0.01 0.002 0.004 -0 555.556 222.222 444.444 -111.111872.1 0.01 0.003 -0 0 888.889 333.333 -111.111 111.1111872.7 0 0.003 0.005 0 444.444 333.333 555.556 111.1111873.3 0.01 0.002 0.005 0 555.556 222.222 555.556 111.1111873.9 0.01 -0 0.003 -0 555.556 -111.111 333.333 -222.222874.5 0.01 -0 0.001 0 555.556 -111.111 111.111 333.3333875.1 0.01 -0 0.005 0 555.556 -111.111 555.556 0875.7 0.01 0.002 0.008 0.01 666.667 222.222 888.889 555.5556876.2 0.01 0.003 0.002 0.01 666.667 333.333 222.222 555.5556876.8 0.01 -0 0.002 0 666.667 -222.222 222.222 222.2222

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