Nuclear magnetic shielding constants of Dirac one-electron atoms in some low-lying discrete energy eigenstates

Nuclear magnetic shielding constants of Dirac one-electron atoms
in some low-lying discrete energy eigenstates

Patrycja Stefańska pstefanska@mif.pg.gda.pl Atomic and Optical Physics Division, Department of Atomic, Molecular and Optical Physics,
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology,
Narutowicza 11/12, 80–233 Gdańsk, Poland
February 12, 2018

We present tabulated data for the nuclear magnetic shielding constants () of the Dirac one-electron atoms with a pointlike, motionless and spinless nucleus of charge . Utilizing the exact general analytical formula for derived by us [P. Stefańska, Phys. Rev. A. 94 (2016) 012508/1-15], valid for an arbitrary discrete energy eigenstate, we have computed the numerical values of the magnetic shielding factors for the ground state and for the first and the second set of excited states, i.e.: 2s, 2p, 2p, 3s, 3p, 3p, 3d, and 3d, of the relativistic hydrogenic ions with the nuclear charge numbers from the range . The comparisons of our results with the numerical values reported by other authors for some atomic states are also presented.

journal: Atomic Data and Nuclear Data Tables\biboptions

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Keywords: Hydrogenlike atom, Shielding constant, Magnetic field, Screening factor, Nuclear magnetic resonance

Published as: At. Data Nucl. Data Tables 120 (2018) 352–372

*[1ex] doi: 10.1016/j.adt.2017.05.005

*[5ex]

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Introduction

When an atom or a molecule is placed in an external magnetic field, then electrons circling around their nuclei will begin to interact with the perturbing field. In this way, an additional magnetic field, oriented opposite to the external field, is generated in the system. Consequently, the strength of the magnetic field “effectively sensed” by the nucleus decreases. This phenomenon is called nuclear magnetic shielding. The changes that occur in the location of the nucleus can be fully characterized by the magnetic shielding constant (or the nuclear screening factor). This physical quantity – of course, depending on the electron density – is directly related to the chemical shift, by which the position of the signal in the NMR (Nuclear Magnetic Resonance) spectrum is determined. This makes the magnetic shielding constant () one of the most important atomic parameters currently used in chemistry and medicine.

There are many experimental results for the magnetic screening constants for many-electron atoms and molecules. But relativistic theoretical investigations of that quantity for such complex systems are quite complicated – very often they come down to performing numerical calculations, which almost always require access to specialized software. The numerical values for for some closed-shell atoms and ions were reported, among others, in Refs. [1, 2, 3]. However, for the simplest systems, like one-electron atoms, the purely analytical relativistic calculations for the magnetic shielding constant (and also for another properties of the atom) are possible, and this was suggested already in 1969 by Hegstrom in Ref. [4]. One of such a technique which allows one to derive analytically the formula for the shielding factor () is the one based on the perturbation theory combined with the Sturmian expansion of the first-order generalized Dirac–Coulomb Green function, proposed in Ref. [5]. Using the method presented in that article, some time ago we have found the closed-form expression for for the ground state of relativistic hydrogenlike atom [6], in agreement with corresponding formulas derived earlier by other authors in completely different ways. (For other applications of the technique proposed by Szmytkowski in Ref. [5] to some electromagnetic properties of the ground state of Dirac one-electron atoms, see Refs. [7, 8, 9, 10, 11, 12, 13, 14, 15].).

Quite recently, we have shown that the usefulness of the aforementioned method goes beyond the study of the atomic ground state. In Refs. [17, 18, 19, 16, 20] we have considered an arbitrary discrete energy eigenstate of relativistic hydrogenlike atom, in order to obtain analytical expressions (and further – the numerical values) for some properties illustrating the influence of the external electromagnetic perturbations on the atom. In particular, in Ref. [16] one can find a detailed derivation of the formula for the magnetic shielding constant of Dirac one-electron atom being in an arbitrary energy eigenstate. The quantum state of the electron is generally characterized by the set of quantum numbers , in which denotes the radial quantum number, the Dirac quantum number is an integer different form zero, whereas is the magnetic quantum number. The final closed-form expression for the shielding factor for such a state we have arrived at in Ref. [16] reads as follows:

(1)

where

(2)

with

(3)

and

(4)

In Ref. [16] we have proved analytically that the above result is valid for an arbitrary atomic state. However, in the aforementioned article, there are no tables with the numerical values of the relativistic shielding factors of hydrogenic ions. This kind of data may be useful – among others – to those who deal with the spectroscopic methods, for example, the NMR technique. This fact, as well as the lack of sufficiently large data sets in the literature, prompted us to carry out numerical calculations for the magnetic shielding constant for one-electron atoms ions with the nuclear charge numbers from the whole range . Our results will be discussed briefly in the next section.

Discussion of results

Numerical results presented in this work has been computed with the help of the exact analytical formula given in Eqs. (1)–(4). In Table 1 we have included the values of the magnetic shielding factors for the ground state (1s) of Dirac one-electron atoms. Tables 25 contain the results for states belonging to the first set of excited state, i.e.: 2s, 2p, and 2p. The second excited atomic states (i.e.: 3s, 3p, 3p, 3d, and 3d) are presented in Tables 614. For the excited states, all possible values of the magnetic quantum number were considered. The Reader should observe that for the states with , there is a restriction for the nuclear charge number, i.e.: (see Tables 13, 6, and 7); a detailed explanation of this limitation can be found just follow Eq. (3.17) in Ref. [16].

The value of the inverse of the fine-structure constant we have used during creating Tables 114 was , and was taken from the newest CODATA 2014 report on Recommended Values of the Fundamental Physical Constants [21]. However, in order to make the most accurate comparison of our exact results with the numerical results reported earlier by other authors for some atomic states [22, 23], we have performed two additional tables with the values of obtained using (from CODATA 1986) [24].

States with zero radial quantum number have been considered in Table 15, where we have confronted our results with the values published by Moore in Ref. [22]. Actually, to be able to compare these numbers, we had to add the corresponding numerical components provided by her for a given atomic state. The resulting sums of the three ingredients for each state (the lower entries in Table 15) appear to be in a pretty good agreement with our exact results (the upper entries therein).

In contrast to the values of the screening constants presented in Tables 115 (where they were given in units of ), the numbers included in Table 16 should be multiplied only by the commonly used factor of . We have rescaled in this way a part of the data from Tables 1 and 35 (i.e. for states 1s, 2p, and 2p), because we wanted to compare them with the corresponding numerical values provided by Pyper and Zhang [23]. The agreement between their results and ours is also very good, and this has been shown in Table 16. The value of the magnetic shielding factor for the ground state of relativistic hydrogen atom () can be found – among others – in the paper by Feiock and Johnson [25]. Their result, which is (not shown in Table 16), also agrees with our result for this case.

Acknowledgments

I am indebted to Professor A. Rutkowski for his suggestion to publish present results. I also thank Professor R. Szmytkowski for technical assistance in carrying out the calculations.

References

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Explanation of Tables

In all the tables we have used the following notation:


Magnetic dipole shielding constant
Nuclear charge number
Fine structure constant
Magnetic quantum number;
The atomic states are referred to as , according to the following guidelines:
Principal quantum number
Note that for the radial quantum number , is the negative integer!
Dirac quantum number;
Total angular momentum quantum number;
States with the orbital angular momentum quantum number
States with the orbital angular momentum quantum number
States with the orbital angular momentum quantum number
1 3.333 811 647 331(1) 41 1.746 602 974 210(1) 81 7.817 869 668 184(1)
2 6.670 494 089 568(1) 42 1.811 496 081 836(1) 82 8.174 063 737 041(1)
3 1.001 292 267 930(0) 43 1.878 357 035 573(1) 83 8.552 930 762 593(1)
4 1.336 398 189 894(0) 44 1.947 283 571 199(1) 84 8.956 539 142 795(1)
5 1.672 656 996 173(0) 45 2.018 378 683 624(1) 85 9.387 209 193 087(1)
6 2.010 360 345 643(0) 46 2.091 751 011 580(1) 86 9.847 552 267 330(1)
7 2.349 802 205 046(0) 47 2.167 515 254 880(1) 87 1.034 051 735 170(2)
8 2.691 279 326 667(0) 48 2.245 792 627 529(1) 88 1.086 944 684 530(2)
9 3.035 091 734 955(0) 49 2.326 711 350 387(1) 89 1.143 814 370 449(2)
10 3.381 543 223 662(0) 50 2.410 407 187 488(1) 90 1.205 095 273 710(2)
11 3.730 941 865 202(0) 51 2.497 024 030 612(1) 91 1.271 285 963 977(2)
12 4.083 600 533 933(0) 52 2.586 714 537 291(1) 92 1.342 961 245 207(2)
13 4.439 837 445 187(0) 53 2.679 640 828 022(1) 93 1.420 787 155 992(2)
14 4.799 976 711 934(0) 54 2.775 975 249 240(1) 94 1.505 539 637 316(2)
15 5.164 348 921 084(0) 55 2.875 901 209 373(1) 95 1.598 127 955 178(2)
16 5.533 291 731 519(0) 56 2.979 614 096 288(1) 96 1.699 624 349 813(2)
17 5.907 150 496 098(0) 57 3.087 322 285 525(1) 97 1.811 301 927 131(2)
18 6.286 278 909 991(0) 58 3.199 248 249 922(1) 98 1.934 683 588 841(2)
19 6.671 039 687 874(0) 59 3.315 629 782 747(1) 99 2.071 605 935 952(2)
20 7.061 805 272 665(0) 60 3.436 721 348 028(1) 100 2.224 303 767 330(2)
21 7.458 958 578 693(0) 61 3.562 795 573 774(1) 101 2.395 523 341 337(2)
22 7.862 893 772 380(0) 62 3.694 144 905 961(1) 102 2.588 676 489 615(2)
23 8.274 017 093 771(0) 63 3.831 083 443 758(1) 103 2.808 053 844 970(2)
24 8.692 747 722 474(0) 64 3.973 948 979 521(1) 104 3.059 125 404 493(2)
25 9.119 518 691 881(0) 65 4.123 105 270 560(1) 105 3.348 973 163 289(2)
26 9.554 777 855 843(0) 66 4.278 944 573 894(1) 106 3.686 928 794 988(2)
27 9.998 988 912 301(0) 67 4.441 890 480 008(1) 107 4.085 539 365 807(2)
28 1.045 263 248 880(1) 68 4.612 401 087 408(1) 108 4.562 076 240 559(2)
29 1.091 620 729 515(1) 69 4.790 972 566 522(1) 109 5.140 980 242 816(2)
30 1.139 023 134 915(1) 70 4.978 143 169 555(1) 110 5.857 998 577 753(2)
31 1.187 524 328 142(1) 71 5.174 497 752 454(1) 111 6.767 556 412 750(2)
32 1.237 180 372 659(1) 72 5.380 672 886 556(1) 112 7.956 754 800 431(2)
33 1.288 049 680 794(1) 73 5.597 362 651 196(1) 113 9.574 166 598 994(2)
34 1.340 193 172 405(1) 74 5.825 325 214 966(1) 114 1.189 558 089 718(3)
35 1.393 674 444 622(1) 75 6.065 390 333 183(1) 115 1.549 704 391 322(3)
36 1.448 559 953 664(1) 76 6.318 467 913 180(1) 116 2.181 580 134 554(3)
37 1.504 919 209 807(1) 77 6.585 557 828 282(1) 117 3.571 862 766 845(3)
38 1.562 824 986 692(1) 78 6.867 761 197 138(1) 118 9.084 394 854 718(3)
39 1.622 353 546 292(1) 79 7.166 293 388 930(1)
40 1.683 584 880 967(1) 80 7.482 499 069 208(1)
Table 1: (continued)
1 8.334 039 107 064(2) 41 3.997 600 222 359(0) 81 1.571 351 017 454(1)
2 1.667 231 453 748(1) 42 4.130 373 857 431(0) 82 1.641 605 092 176(1)
3 2.501 907 102 596(1) 43 4.266 391 434 659(0) 83 1.716 707 475 740(1)
4 3.337 857 016 011(1) 44 4.405 831 332 584(0) 84 1.797 140 369 287(1)
5 4.175 509 888 277(1) 45 4.548 882 753 481(0) 85 1.883 447 735 330(1)
6 5.015 297 808 566(1) 46 4.695 746 564 523(0) 86 1.976 245 167 495(1)
7 5.857 657 132 582(1) 47 4.846 636 213 933(0) 87 2.076 231 677 664(1)
8 6.703 029 369 684(1) 48 5.001 778 729 970(0) 88 2.184 203 844 590(1)
9 7.551 862 088 762(1) 49 5.161 415 811 537(0) 89 2.301 072 888 914(1)
10 8.404 609 846 285(1) 50 5.325 805 020 255(0) 90 2.427 885 398 357(1)
11 9.261 735 140 035(1) 51 5.495 221 085 057(0) 91 2.565 848 637 678(1)
12 1.012 370 939 221(0) 52 5.669 957 331 700(0) 92 2.716 361 660 258(1)
13 1.099 101 396 575(0) 53 5.850 327 251 216(0) 93 2.881 053 819 696(1)
14 1.186 414 121 797(0) 54 6.036 666 223 042(0) 94 3.061 832 801 062(1)
15 1.274 359 559 565(0) 55 6.229 333 410 669(0) 95 3.260 945 011 467(1)
16 1.362 989 477 637(0) 56 6.428 713 849 971(0) 96 3.481 052 176 147(1)
17 1.452 357 086 056(0) 57 6.635 220 753 092(0) 97 3.725 329 411 875(1)
18 1.542 517 161 970(0) 58 6.849 298 053 857(0) 98 3.997 592 096 977(1)
19 1.633 526 180 598(0) 59 7.071 423 224 280(0) 99 4.302 461 842 982(1)
20 1.725 442 452 936(0) 60 7.302 110 395 887(0) 100 4.645 586 300 011(1)
21 1.818 326 270 827(0) 61 7.541 913 824 393(0) 101 5.033 934 212 128(1)
22 1.912 240 060 086(0) 62 7.791 431 741 840(0) 102 5.476 197 434 780(1)
23 2.007 248 542 403(0) 63 8.051 310 646 855(0) 103 5.983 347 838 958(1)
24 2.103 418 906 810(0) 64 8.322 250 091 266(0) 104 6.569 423 189 190(1)
25 2.200 820 991 594(0) 65 8.605 008 030 248(0) 105 7.252 659 472 489(1)
26 2.299 527 477 552(0) 66 8.900 406 813 608(0) 106 8.057 161 366 631(1)
27 2.399 614 093 624(0) 67 9.209 339 908 149(0) 107 9.015 433 969 588(1)
28 2.501 159 835 993(0) 68 9.532 779 455 591(0) 108 1.017 234 117 123(2)
29 2.604 247 201 842(0) 69 9.871 784 787 734(0) 109 1.159 152 367 476(2)
30 2.708 962 439 094(0) 70 1.022 751 204 100(1) 110 1.336 626 242 678(2)
31 2.815 395 813 536(0) 71 1.060 122 503 690(1) 111 1.563 884 307 016(2)
32 2.923 641 894 917(0) 72 1.099 430 762 400(1) 112 1.863 733 718 839(2)
33 3.033 799 863 705(0) 73 1.140 827 771 213(1) 113 2.275 128 203 952(2)
34 3.145 973 840 398(0) 74 1.184 480 327 146(1) 114 2.870 448 942 588(2)
35 3.260 273 239 442(0) 75 1.230 572 062 005(1) 115 3.800 992 106 755(2)
36 3.376 813 150 031(0) 76 1.279 305 538 535(1) 116 5.444 431 551 858(2)
37 3.495 714 746 272(0) 77 1.330 904 660 023(1) 117 9.080 005 674 542(2)
38 3.617 105 729 484(0) 78 1.385 617 448 619(1) 118 2.355 074 407 820(3)
39 3.741 120 805 656(0) 79 1.443 719 258 992(1)
40 3.867 902 201 437(0) 80 1.505 516 507 875(1)
Table 2: (continued)
1 2.782 118 900 586(3) 41 7.073 605 130 669(1) 81 4.268 987 601 923(1)
2 1.391 156 693 555(3) 42 6.920 391 087 899(1) 82 4.253 568 075 818(1)
3 9.275 458 812 054(2) 43 6.774 808 572 768(1) 83 4.240 611 438 939(1)
4 6.957 729 597 111(2) 44 6.636 351 171 133(1) 84 4.230 218 908 270(1)
5 5.567 352 419 207(2) 45 6.504 558 340 066(1) 85 4.222 510 517 120(1)
6 4.640 651 768 925(2) 46 6.379 010 482 398(1) 86 4.217 627 714 061(1)
7 3.978 909 669 943(2) 47 6.259 324 655 342(1) 87 4.215 736 488 486(1)
8 3.482 767 222 004(2) 48 6.145 150 821 268(1) 88 4.217 031 142 058(1)
9 3.097 025 115 434(2) 49 6.036 168 563 751(1) 89 4.221 738 857 880(1)
10 2.788 563 837 135(2) 50 5.932 084 204 416(1) 90 4.230 125 261 997(1)
11 2.536 307 400 749(2) 51 5.832 628 266 254(1) 91 4.242 501 228 544(1)
12 2.326 205 211 906(2) 52 5.737 553 237 555(1) 92 4.259 231 255 729(1)
13 2.148 529 995 819(2) 53 5.646 631 597 617(1) 93 4.280 743 842 405(1)
14 1.996 333 756 060(2) 54 5.559 654 071 244(1) 94 4.307 544 434 970(1)
15 1.864 521 349 974(2) 55 5.476 428 083 960(1) 95 4.340 231 707 680(1)
16 1.749 271 473 459(2) 56 5.396 776 394 033(1) 96 4.379 518 209 652(1)
17 1.647 662 004 198(2) 57 5.320 535 880 893(1) 97 4.426 256 794 431(1)
18 1.557 420 230 630(2) 58 5.247 556 472 517(1) 98 4.481 474 797 271(1)
19 1.476 751 956 119(2) 59 5.177 700 196 926(1) 99 4.546 418 726 240(1)
20 1.404 221 872 018(2) 60 5.110 840 345 139(1) 100 4.622 613 420 492(1)
21 1.338 668 110 010(2) 61 5.046 860 734 826(1) 101 4.711 941 421 401(1)
22 1.279 140 098 492(2) 62 4.985 655 065 612(1) 102 4.816 751 062 641(1)
23 1.224 852 630 502(2) 63 4.927 126 358 438(1) 103 4.940 006 131 445(1)
24 1.175 151 414 807(2) 64 4.871 186 472 732(1) 104 5.085 496 966 089(1)
25 1.129 486 894 895(2) 65 4.817 755 696 354(1) 105 5.258 144 484 154(1)
26 1.087 394 109 900(2) 66 4.766 762 404 386(1) 106 5.464 448 525 148(1)
27 1.048 477 031 051(2) 67 4.718 142 783 913(1) 107 5.713 167 113 854(1)
28 1.012 396 254 761(2) 68 4.671 840 622 963(1) 108 6.016 378 170 848(1)
29 9.788 592 421 701(1) 69 4.627 807 162 767(1) 109 6.391 200 505 719(1)
30 9.476 125 109 579(1) 70 4.586 001 013 568(1) 110 6.862 706 229 409(1)
31 9.184 353 386 252(1) 71 4.546 388 135 254(1) 111 7.469 111 353 803(1)
32 8.911 346 466 148(1) 72 4.508 941 885 265(1) 112 8.271 633 642 451(1)
33 8.655 408 148 122(1) 73 4.473 643 137 479(1) 113 9.374 773 835 554(1)
34 8.415 042 348 935(1) 74 4.440 480 477 216(1) 114 1.097 262 326 270(2)
35 8.188 924 547 711(1) 75 4.409 450 479 113(1) 115 1.347 075 187 532(2)
36 7.975 877 992 212(1) 76 4.380 558 076 535(1) 116 1.788 133 909 961(2)
37 7.774 853 766 263(1) 77 4.353 817 033 378(1) 117 2.763 233 894 940(2)
38 7.584 914 007 315(1) 78 4.329 250 531 831(1) 118 6.641 887 213 111(2)
39 7.405 217 708 967(1) 79 4.306 891 892 840(1)
40 7.235 008 656 373(1) 80 4.286 785 449 937(1)
Table 3: (continued)
1 2.781 968 897 415(3) 47 5.514 965 913 733(1) 93 2.165 593 616 341(1)
2 1.390 856 668 182(3) 48 5.382 867 430 870(1) 94 2.124 047 243 592(1)
3 9.270 957 955 406(2) 49 5.255 790 538 763(1) 95 2.083 138 472 906(1)
4 6.951 727 565 491(2) 50 5.133 432 930 687(1) 96 2.042 845 685 127(1)
5 5.559 848 448 573(2) 51 5.015 515 982 506(1) 97 2.003 148 109 115(1)
6 4.631 644 902 110(2) 52 4.901 782 474 997(1) 98 1.964 025 777 215(1)
7 3.968 398 755 243(2) 53 4.791 994 574 013(1) 99 1.925 459 483 366(1)
8 3.470 750 911 465(2) 54 4.685 932 035 049(1) 100 1.887 430 743 694(1)
9 3.083 501 862 844(2) 55 4.583 390 603 666(1) 101 1.849 921 759 375(1)
10 2.773 531 895 705(2) 56 4.484 180 587 267(1) 102 1.812 915 381 648(1)
11 2.519 764 820 488(2) 57 4.388 125 577 208(1) 103 1.776 395 078 803(1)
12 2.308 149 836 664(2) 58 4.295 061 303 080(1) 104 1.740 344 905 021(1)
13 2.128 959 460 006(2) 59 4.204 834 603 487(1) 105 1.704 749 470 934(1)
14 1.975 245 481 015(2) 60 4.117 302 499 730(1) 106 1.669 593 915 801(1)
15 1.841 912 539 984(2) 61 4.032 331 360 582(1) 107 1.634 863 881 172(1)
16 1.725 139 111 401(2) 62 3.949 796 147 874(1) 108 1.600 545 485 961(1)
17 1.622 002 846 802(2) 63 3.869 579 733 915(1) 109 1.566 625 302 816(1)
18 1.530 230 803 335(2) 64 3.791 572 282 875(1) 110 1.533 090 335 718(1)
19 1.448 028 547 513(2) 65 3.715 670 689 259(1) 111 1.499 927 998 718(1)
20 1.373 960 527 835(2) 66 3.641 778 067 406(1) 112 1.467 126 095 735(1)
21 1.306 864 626 665(2) 67 3.569 803 286 684(1) 113 1.434 672 801 357(1)
22 1.245 790 016 129(2) 68 3.499 660 547 672(1) 114 1.402 556 642 568(1)
23 1.189 951 225 530(2) 69 3.431 268 995 185(1) 115 1.370 766 481 354(1)
24 1.138 693 691 896(2) 70 3.364 552 364 433(1) 116 1.339 291 498 115(1)
25 1.091 467 578 399(2) 71 3.299 438 657 067(1) 117 1.308 121 175 841(1)
26 1.047 807 634 676(2) 72 3.235 859 844 203(1) 118 1.277 245 285 008(1)
27 1.007 317 532 629(2) 73 3.173 751 593 817(1) 119 1.246 653 869 129(1)
28 9.696 575 588 466(1) 74 3.113 053 020 237(1) 120 1.216 337 230 938(1)
29 9.345 348 534 052(1) 75 3.053 706 453 634(1) 121 1.186 285 919 145(1)
30 9.016 956 009 213(1) 76 2.995 657 227 701(1) 122 1.156 490 715 746(1)
31 8.709 187 330 046(1) 77 2.938 853 483 843(1) 123 1.126 942 623 829(1)
32 8.420 108 115 013(1) 78 2.883 245 990 403(1) 124 1.097 632 855 862(1)
33 8.148 018 420 549(1) 79 2.828 787 975 591(1) 125 1.068 552 822 412(1)
34 7.891 418 264 493(1) 80 2.775 434 972 921(1) 126 1.039 694 121 284(1)
35 7.648 979 059 765(1) 81 2.723 144 678 065(1) 127 1.011 048 527 031(1)
36 7.419 519 809 088(1) 82 2.671 876 816 148(1) 128 9.826 079 808 224(0)
37 7.201 987 160 001(1) 83 2.621 593 018 616(1) 129 9.543 645 806 388(0)
38 6.995 438 609 077(1) 84 2.572 256 708 861(1) 130 9.263 105 717 640(0)
39 6.799 028 290 080(1) 85 2.523 832 995 892(1) 131 8.984 383 375 590(0)
40 6.611 994 893 890(1) 86 2.476 288 575 390(1) 132 8.707 403 904 875(0)
41 6.433 651 356 224(1) 87 2.429 591 637 556(1) 133 8.432 093 633 740(0)
42 6.263 376 018 530(1) 88 2.383 711 781 208(1) 134 8.158 380 008 720(0)
43 6.100 605 022 221(1) 89 2.338 619 933 633(1) 135 7.886 191 511 223(0)
44 5.944 825 740 051(1) 90 2.294 288 275 746(1) 136 7.615 457 575 802(0)
45 5.795 571 083 286(1) 91 2.250 690 172 150(1) 137 7.346 108 509 931(0)
46 5.652 414 551 403(1) 92 2.207 800 105 715(1)
Table 4: (continued)
1 1.000 028 534 293(1) 47 5.006 732 203 585(0) 93 1.194 851 329 368(1)
2 2.000 228 284 951(1) 48 5.127 227 928 174(0) 94 1.214 396 435 565(1)
3 3.000 770 521 391(1) 49 5.248 650 771 844(0) 95 1.234 202 117 158(1)
4 4.001 826 619 163(1) 50 5.371 024 936 168(0) 96 1.254 274 039 325(1)
5 5.003 568 113 104(1) 51 5.494 374 957 625(0) 97 1.274 617 999 639(1)
6 6.006 166 750 591(1) 52 5.618 725 718 030(0) 98 1.295 239 932 296(1)
7 7.009 794 544 924(1) 53 5.744 102 455 240(0) 99 1.316 145 912 505(1)
8 8.014 623 828 881(1) 54 5.870 530 774 109(0) 100 1.337 342 161 028(1)
9 9.020 827 308 481(1) 55 5.998 036 657 744(0) 101 1.358 835 048 900(1)
10 1.002 857 811 697(0) 56 6.126 646 479 032(0) 102 1.380 631 102 320(1)
11 1.103 804 986 909(0) 57 6.256 387 012 479(0) 103 1.402 737 007 727(1)
12 1.204 941 671 566(0) 58 6.387 285 446 364(0) 104 1.425 159 617 068(1)
13 1.306 285 339 846(0) 59 6.519 369 395 201(0) 105 1.447 905 953 270(1)
14 1.407 853 530 555(0) 60 6.652 666 912 562(0) 106 1.470 983 215 919(1)
15 1.509 663 852 696(0) 61 6.787 206 504 222(0) 107 1.494 398 787 160(1)
16 1.611 733 991 085(0) 62 6.923 017 141 690(0) 108 1.518 160 237 830(1)
17 1.714 081 712 011(0) 63 7.060 128 276 102(0) 109 1.542 275 333 825(1)
18 1.816 724 868 958(0) 64 7.198 569 852 506(0) 110 1.566 752 042 724(1)
19 1.919 681 408 371(0) 65 7.338 372 324 559(0) 111 1.591 598 540 679(1)
20 2.022 969 375 495(0) 66 7.479 566 669 634(0) 112 1.616 823 219 571(1)
21 2.126 606 920 262(0) 67 7.622 184 404 374(0) 113 1.642 434 694 463(1)
22 2.230 612 303 263(0) 68 7.766 257 600 692(0) 114 1.668 441 811 354(1)
23 2.335 003 901 781(0) 69 7.911 818 902 242(0) 115 1.694 853 655 251(1)
24 2.439 800 215 902(0) 70 8.058 901 541 383(0) 116 1.721 679 558 568(1)
25 2.545 019 874 708(0) 71 8.207 539 356 645(0) 117 1.748 929 109 879(1)
26 2.650 681 642 553(0) 72 8.357 766 810 726(0) 118 1.776 612 163 038(1)
27 2.756 804 425 433(0) 73 8.509 619 009 031(0) 119 1.804 738 846 673(1)
28 2.863 407 277 441(0) 74 8.663 131 718 786(0) 120 1.833 319 574 096(1)
29 2.970 509 407 327(0) 75 8.818 341 388 736(0) 121 1.862 365 053 620(1)
30 3.078 130 185 159(0) 76 8.975 285 169 462(0) 122 1.891 886 299 335(1)
31 3.186 289 149 091(0) 77 9.134 000 934 331(0) 123 1.921 894 642 340(1)
32 3.295 006 012 245(0) 78 9.294 527 301 111(0) 124 1.952 401 742 466(1)
33 3.404 300 669 711(0) 79 9.456 903 654 276(0) 125 1.983 419 600 518(1)
34 3.514 193 205 667(0) 80 9.621 170 168 023(0) 126 2.014 960 571 055(1)
35 3.624 703 900 634(0) 81 9.787 367 830 040(0) 127 2.047 037 375 737(1)
36 3.735 853 238 857(0) 82 9.955 538 466 039(0) 128 2.079 663 117 281(1)
37 3.847 661 915 832(0) 83 1.012 572 476 510(1) 129 2.112 851 294 034(1)
38 3.960 150 845 976(0) 84 1.029 797 030 587(1) 130 2.146 615 815 223(1)
39 4.073 341 170 449(0) 85 1.047 231 958 359(1) 131 2.180 971 016 896(1)
40 4.187 254 265 134(0) 86 1.064 881 803 806(1) 132 2.215 931 678 605(1)
41 4.301 911 748 780(0) 87 1.082 751 208 257(1) 133 2.251 513 040 866(1)
42 4.417 335 491 320(0) 88 1.100 844 913 376(1) 134 2.287 730 823 434(1)
43 4.533 547 622 359(0) 89 1.119 167 764 254(1) 135 2.324 601 244 454(1)
44 4.650 570 539 855(0) 90 1.137 724 712 608(1) 136 2.362 141 040 512(1)
45 4.768 426 918 985(0) 91 1.156 520 820 089(1) 137 2.400 367 487 661(1)
46 4.887 139 721 218(0) 92 1.175 561 261 705(1)
Table 5: (continued)
1 3.703 923 474 808(2) 41 1.698 307 552 238(0) 81 5.725 125 585 478(0)
2 7.409 166 080 451(2) 42 1.750 586 151 557(0) 82 5.948 718 328 129(0)
3 1.111 704 947 074(1) 43 1.803 857 232 510(0) 83 6.186 797 501 693(0)
4 1.482 890 035 448(1) 44 1.858 174 655 865(0) 84 6.440 797 647 070(0)
5 1.854 605 304 549(1) 45 1.913 595 512 887(0) 85 6.712 336 790 020(0)
6 2.226 985 204 001(1) 46 1.970 180 375 848(0) 86 7.003 245 748 591(0)
7 2.600 165 463 054(1) 47 2.027 993 570 833(0) 87 7.315 603 132 682(0)
8 2.974 283 356 588(1) 48 2.087 103 475 176(0) 88 7.651 777 353 963(0)
9 3.349 477 976 707(1) 49 2.147 582 842 152(0) 89 8.014 477 322 932(0)
10 3.725 890 510 936(1) 50 2.209 509 155 821(0) 90 8.406 813 981 412(0)
11 4.103 664 528 074(1) 51 2.272 965 019 336(0) 91 8.832 375 444 528(0)
12 4.482 946 272 799(1) 52 2.338 038 580 388(0) 92 9.295 319 363 853(0)
13 4.863 884 970 172(1) 53 2.404 823 997 949(0) 93 9.800 487 255 876(0)
14 5.246 633 141 248(1) 54 2.473 421 955 003(0) 94 1.035 354 708 691(1)
15 5.631 346 931 066(1) 55 2.543 940 222 552(0) 95 1.096 117 254 246(1)
16 6.018 186 450 373(1) 56 2.616 494 280 894(0) 96 1.163 127 039 630(1)
17 6.407 316 132 504(1) 57 2.691 208 004 969(0) 97 1.237 327 162 567(1)
18 6.798 905 106 957(1) 58 2.768 214 421 486(0) 98 1.319 850 799 508(1)
19 7.193 127 591 287(1) 59 2.847 656 546 617(0) 99 1.412 070 469 260(1)
20 7.590 163 303 074(1) 60 2.929 688 314 272(0) 100 1.515 663 274 100(1)
21 7.990 197 893 839(1) 61 3.014 475 606 402(0) 101 1.632 698 474 256(1)
22 8.393 423 406 928(1) 62 3.102 197 398 437(0) 102 1.765 756 807 248(1)
23 8.800 038 761 551(1) 63 3.193 047 034 904(0) 103 1.918 095 774 939(1)
24 9.210 250 265 322(1) 64 3.287 233 652 513(0) 104 2.093 882 885 492(1)
25 9.624 272 157 863(1) 65 3.384 983 770 672(0) 105 2.298 531 714 264(1)
26 1.004 232 718 823(0) 66 3.486 543 072 483(0) 106 2.539 197 671 391(1)
27 1.046 464 722 914(0) 67 3.592 178 402 917(0) 107 2.825 529 369 226(1)
28 1.089 147 393 139(0) 68 3.702 180 015 200(0) 108 3.170 843 377 905(1)
29 1.132 305 942 176(0) 69 3.816 864 101 559(0) 109 3.594 028 934 195(1)
30 1.175 966 704 866(0) 70 3.936 575 650 516(0) 110 4.122 771 915 489(1)
31 1.220 157 217 942(0) 71 4.061 691 680 195(0) 111 4.799 301 658 298(1)
32 1.264 906 305 410(0) 72 4.192 624 905 734(0) 112 5.691 306 540 264(1)
33 1.310 244 170 078(0) 73 4.329 827 909 268(0) 113 6.914 393 412 568(1)
34 1.356 202 491 797(0) 74 4.473 797 893 488(0) 114 8.683 371 886 153(1)
35 1.402 814 533 026(0) 75 4.625 082 114 826(0) 115 1.144 724 698 887(2)
36 1.450 115 252 398(0) 76 4.784 284 110 729(0) 116 1.632 684 158 293(2)
37 1.498 141 427 021(0) 77 4.952 070 857 746(0) 117 2.711 853 575 923(2)
38 1.546 931 784 343(0) 78 5.129 181 024 556(0) 118 7.006 562 986 455(2)
39 1.596 527 144 476(0) 79 5.316 434 517 645(0)
40 1.646 970 573 984(0) 80 5.514 743 558 845(0)
Table 6: (continued)
1 2.782 082 890 470(3) 41 6.910 908 149 276(1) 81 3.768 455 123 575(1)
2 1.391 084 662 008(3) 42 6.752 836 629 589(1) 82 3.735 948 908 009(1)
3 9.274 378 055 773(2) 43 6.602 317 513 960(1) 83 3.704 927 797 438(1)
4 6.956 288 059 806(2) 44 6.458 840 370 844(1) 84 3.675 401 178 243(1)
5 5.565 549 646 388(2) 45 6.321 940 416 759(1) 85 3.647 385 858 656(1)
6 4.638 487 191 071(2) 46 6.191 193 574 145(1) 86 3.620 906 878 910(1)
7 3.976 382 601 559(2) 47 6.066 212 161 873(1) 87 3.595 998 504 140(1)
8 3.479 876 860 479(2) 48 5.946 641 126 318(1) 88 3.572 705 440 162(1)
9 3.093 770 539 701(2) 49 5.832 154 735 956(1) 89 3.551 084 323 375(1)
10 2.784 944 006 127(2) 50 5.722 453 674 811(1) 90 3.531 205 550 596(1)
11 2.532 321 151 645(2) 51 5.617 262 480 245(1) 91 3.513 155 533 989(1)
12 2.321 851 258 161(2) 52 5.516 327 278 985(1) 92 3.497 039 492 050(1)
13 2.143 806 924 971(2) 53 5.419 413 782 287(1) 93 3.482 984 922 609(1)
14 1.991 240 027 311(2) 54 5.326 305 506 963(1) 94 3.471 145 951 425(1)
15 1.859 055 291 532(2) 55 5.236 802 193 870(1) 95 3.461 708 815 888(1)
16 1.743 431 279 627(2) 56 5.150 718 399 566(1) 96 3.454 898 835 331(1)
17 1.641 445 732 216(2) 57 5.067 882 240 303(1) 97 3.450 989 349 864(1)
18 1.550 825 797 236(2) 58 4.988 134 270 460(1) 98 3.450 313 296 775(1)
19 1.469 777 133 836(2) 59 4.911 326 479 992(1) 99 3.453 278 366 550(1)
20 1.396 864 285 149(2) 60 4.837 321 397 631(1) 100 3.460 387 085 178(1)
21 1.330 925 230 312(2) 61 4.765 991 288 379(1) 101 3.472 263 780 408(1)
22 1.271 009 240 538(2) 62 4.697 217 435 415(1) 102 3.489 691 330 579(1)
23 1.216 330 946 687(2) 63 4.630 889 497 914(1) 103 3.513 662 076 432(1)
24 1.166 235 889 998(2) 64 4.566 904 937 439(1) 104 3.545 449 667 254(1)
25 1.120 174 340 699(2) 65 4.505 168 506 668(1) 105 3.586 712 578 046(1)
26 1.077 681 158 524(2) 66 4.445 591 795 079(1) 106 3.639 646 816 218(1)
27 1.038 360 128 725(2) 67 4.388 092 827 129(1) 107 3.707 217 347 249(1)
28 1.001 871 654 717(2) 68 4.332 595 709 156(1) 108 3.793 519 906 978(1)
29 9.679 229 971 192(1) 69 4.279 030 321 984(1) 109 3.904 367 600 688(1)
30 9.362 604 650 627(1) 70 4.227 332 056 852(1) 110 4.048 283 752 422(1)
31 9.066 631 189 104(1) 71 4.177 441 592 928(1) 111 4.238 271 612 142(1)
32 8.789 376 537 916(1) 72 4.129 304 715 310(1) 112 4.495 175 649 644(1)
33 8.529 142 134 710(1) 73 4.082 872 173 044(1) 113 4.854 597 436 902(1)
34 8.284 429 430 218(1) 74 4.038 099 577 366(1) 114 5.382 687 229 570(1)
35 8.053 911 325 475(1) 75 3.994 947 341 072(1) 115 6.217 710 776 460(1)
36 7.836 408 370 333(1) 76 3.953 380 660 727(1) 116 7.704 800 767 952(1)
37 7.630 868 822 552(1) 77 3.913 369 544 286(1) 117 1.101 294 081 066(2)
38 7.436 351 856 396(1) 78 3.874 888 887 715(1) 118 2.422 288 410 147(2)
39 7.252 013 355 511(1) 79 3.837 918 605 407(1)
40 7.077 093 837 929(1) 80 3.802 443 820 582(1)
Table 7: (continued)
1 2.782 016 222 669(3) 47 5.739 014 103 697(1) 93 2.619 661 547 266(1)
2 1.390 951 319 594(3) 48 5.611 756 338 335(1) 94 2.583 348 334 573(1)
3 9.272 377 749 217(2) 49 5.489 525 051 725(1) 95 2.547 686 251 175(1)
4 6.953 620 666 150(2) 50 5.372 018 064 047(1) 96 2.512 653 963 211(1)
5 5.562 214 892 304(2) 51 5.258 956 879 768(1) 97 2.478 230 991 076(1)
6 4.634 484 734 216(2) 52 5.150 084 410 021(1) 98 2.444 397 665 079(1)
7 3.971 712 030 117(2) 53 5.045 162 952 819(1) 99 2.411 135 083 748(1)
8 3.474 537 692 607(2) 54 4.943 972 397 676(1) 100 2.378 425 074 608(1)
9 3.087 762 222 882(2) 55 4.846 308 626 081(1) 101 2.346 250 157 263(1)
10 2.778 265 916 417(2) 56 4.751 982 083 340(1) 102 2.314 593 508 609(1)
11 2.524 972 592 825(2) 57 4.660 816 500 732(1) 103 2.283 438 930 047(1)
12 2.313 831 460 779(2) 58 4.572 647 749 860(1) 104 2.252 770 816 546(1)
13 2.135 115 045 286(2) 59 4.487 322 813 483(1) 105 2.222 574 127 442(1)
14 1.981 875 146 112(2) 60 4.404 698 859 264(1) 106 2.192 834 358 849(1)
15 1.849 016 412 854(2) 61 4.324 642 404 609(1) 107 2.163 537 517 581(1)
16 1.732 717 329 342(2) 62 4.247 028 562 317(1) 108 2.134 670 096 479(1)
17 1.630 055 556 498(2) 63 4.171 740 358 065(1) 109 2.106 219 051 055(1)
18 1.538 758 160 899(2) 64 4.098 668 111 863(1) 110 2.078 171 777 368(1)
19 1.457 030 718 536(2) 65 4.027 708 876 595(1) 111 2.050 516 091 047(1)
20 1.383 437 687 439(2) 66 3.958 765 927 589(1) 112 2.023 240 207 397(1)
21 1.316 816 959 554(2) 67 3.891 748 297 888(1) 113 1.996 332 722 501(1)
22 1.256 217 716 650(2) 68 3.826 570 354 511(1) 114 1.969 782 595 276(1)
23 1.200 854 497 732(2) 69 3.763 151 411 544(1) 115 1.943 579 130 410(1)
24 1.150 072 749 592(2) 70 3.701 415 376 394(1) 116 1.917 711 962 119(1)
25 1.103 322 645 236(2) 71 3.641 290 425 908(1) 117 1.892 171 038 690(1)
26 1.060 138 944 201(2) 72 3.582 708 709 478(1) 118 1.866 946 607 742(1)
27 1.020 125 328 369(2) 73 3.525 606 076 537(1) 119 1.842 029 202 171(1)
28 9.829 420 943 764(1) 74 3.469 921 826 121(1) 120 1.817 409 626 731(1)
29 9.482 963 924 340(1) 75 3.415 598 476 471(1) 121 1.793 078 945 215(1)
30 9.159 344 173 736(1) 76 3.362 581 552 792(1) 122 1.769 028 468 193(1)
31 8.856 351 111 072(1) 77 3.310 819 391 544(1) 123 1.745 249 741 272(1)
32 8.572 050 458 736(1) 78 3.260 262 959 771(1) 124 1.721 734 533 856(1)
33 8.304 742 378 030(1) 79 3.210 865 688 131(1) 125 1.698 474 828 351(1)
34 8.052 926 992 630(1) 80 3.162 583 316 438(1) 126 1.675 462 809 811(1)
35 7.815 275 822 307(1) 81 3.115 373 750 624(1) 127 1.652 690 855 982(1)
36 7.590 607 977 682(1) 82 3.069 196 930 148(1) 128 1.630 151 527 713(1)
37 7.377 870 215 282(1) 83 3.024 014 704 980(1) 129 1.607 837 559 731(1)
38 7.176 120 141 789(1) 84 2.979 790 721 344(1) 130 1.585 741 851 724(1)
39 6.984 512 002 240(1) 85 2.936 490 315 510(1) 131 1.563 857 459 739(1)
40 6.802 284 599 995(1) 86 2.894 080 414 980(1) 132 1.542 177 587 854(1)
41 6.628 750 984 496(1) 87 2.852 529 446 464(1) 133 1.520 695 580 111(1)
42 6.463 289 612 200(1) 88 2.811 807 250 107(1) 134 1.499 404 912 687(1)
43 6.305 336 740 860(1) 89 2.771 884 999 488(1) 135 1.478 299 186 285(1)
44 6.154 379 860 940(1) 90 2.732 735 126 918(1) 136 1.457 372 118 729(1)
45 6.009 952 002 835(1) 91 2.694 331 253 645(1) 137 1.436 617 537 737(1)
46 5.871 626 786 613(1) 92 2.656 648 124 590(1)
Table 8: (continued)
1 4.444 542 008 200(2) 47 2.194 987 914 398(0) 93 5.083 238 724 003(0)
2 8.889 669 447 279(2) 48 2.246 579 299 652(0) 94 5.163 010 060 919(0)
3 1.333 596 798 990(1) 49 2.298 500 313 290(0) 95 5.243 811 083 108(0)
4 1.778 402 379 248(1) 50 2.350 760 108 989(0) 96 5.325 667 295 712(0)
5 2.223 442 373 750(1) 51 2.403 367 999 735(0) 97 5.408 604 900 878(0)
6 2.668 775 567 636(1) 52 2.456 333 463 074(0) 98 5.492 650 821 928(0)
7 3.114 460 867 302(1) 53 2.509 666 146 488(0) 99 5.577 832 728 494(0)
8 3.560 557 324 843(1) 54 2.563 375 872 945(0) 100 5.664 179 062 647(0)
9 4.007 124 162 612(1) 55 2.617 472 646 587(0) 101 5.751 719 066 073(0)
10 4.454 220 797 908(1) 56 2.671 966 658 592(0) 102 5.840 482 808 346(0)
11 4.901 906 867 805(1) 57 2.726 868 293 206(0) 103 5.930 501 216 344(0)
12 5.350 242 254 146(1) 58 2.782 188 133 950(0) 104 6.021 806 104 865(0)
13 5.799 287 108 724(1) 59 2.837 936 970 007(0) 105 6.114 430 208 506(0)
14 6.249 101 878 663(1) 60 2.894 125 802 809(0) 106 6.208 407 214 850(0)
15 6.699 747 332 021(1) 61 2.950 765 852 815(0) 107 6.303 771 799 040(0)
16 7.151 284 583 638(1) 62 3.007 868 566 502(0) 108 6.400 559 659 794(0)
17 7.603 775 121 240(1) 63 3.065 445 623 562(0) 109 6.498 807 556 946(0)
18 8.057 280 831 832(1) 64 3.123 508 944 337(0) 110 6.598 553 350 564(0)
19 8.511 864 028 389(1) 65 3.182 070 697 466(0) 111 6.699 836 041 752(0)
20 8.967 587 476 874(1) 66 3.241 143 307 798(0) 112 6.802 695 815 194(0)
21 9.424 514 423 596(1) 67 3.300 739 464 531(0) 113 6.907 174 083 538(0)
22 9.882 708 622 943(1) 68 3.360 872 129 636(0) 114 7.013 313 533 718(0)
23 1.034 223 436 550(0) 69 3.421 554 546 533(0) 115 7.121 158 175 290(0)
24 1.080 315 650 657(0) 70 3.482 800 249 064(0) 116 7.230 753 390 916(0)
25 1.126 554 049 517(0) 71 3.544 623 070 756(0) 117 7.342 145 989 073(0)
26 1.172 945 240 340(0) 72 3.607 037 154 384(0) 118 7.455 384 259 126(0)
27 1.219 495 895 642(0) 73 3.670 056 961 863(0) 119 7.570 518 028 870(0)
28 1.266 212 756 280(0) 74 3.733 697 284 465(0) 120 7.687 598 724 686(0)
29 1.313 102 634 554(0) 75 3.797 973 253 386(0) 121 7.806 679 434 429(0)
30 1.360 172 417 352(0) 76 3.862 900 350 665(0) 122 7.927 814 973 205(0)
31 1.407 429 069 364(0) 77 3.928 494 420 490(0) 123 8.051 061 952 193(0)
32 1.454 879 636 352(0) 78 3.994 771 680 880(0) 124 8.176 478 850 660(0)
33 1.502 531 248 486(0) 79 4.061 748 735 782(0) 125 8.304 126 091 351(0)
34 1.550 391 123 748(0) 80 4.129 442 587 592(0) 126 8.434 066 119 441(0)
35 1.598 466 571 404(0) 81 4.197 870 650 111(0) 127 8.566 363 485 232(0)
36 1.646 764 995 554(0) 82 4.267 050 761 964(0) 128 8.701 084 930 806(0)
37 1.695 293 898 752(0) 83 4.337 001 200 500(0) 129 8.838 299 480 853(0)
38 1.744 060 885 713(0) 84 4.407 740 696 188(0) 130 8.978 078 537 913(0)
39 1.793 073 667 098(0) 85 4.479 288 447 534(0) 131 9.120 495 982 258(0)
40 1.842 340 063 390(0) 86 4.551 664 136 542(0) 132 9.265 628 276 706(0)
41 1.891 868 008 857(0) 87 4.624 887 944 747(0) 133 9.413 554 576 624(0)
42 1.941 665 555 613(0) 88 4.698 980 569 824(0) 134 9.564 356 845 429(0)
43 1.991 740 877 772(0) 89 4.773 963 242 834(0) 135 9.718 119 975 899(0)
44 2.042 102 275 713(0) 90 4.849 857 746 095(0) 136 9.874 931 917 637(0)
45 2.092 758 180 441(0) 91 4.926 686 431 739(0) 137 1.003 488 381 104(1)
46 2.143 717 158 067(0) 92 5.004 472 240 959(0)
Table 9: (continued)
1 1.802 795 342 177(3) 47 3.951 137 250 530(1) 93 2.175 154 669 680(1)
2 9.014 341 164 174(2) 48 3.873 740 825 098(1) 94 2.157 344 556 779(1)
3 6.009 965 739 946(2) 49 3.799 609 803 823(1) 95 2.139 978 768 223(1)
4 4.507 899 541 760(2) 50 3.728 548 584 369(1) 96 2.123 043 947 913(1)
5 3.606 757 053 822(2) 51 3.660 376 914 457(1) 97 2.106 527 303 938(1)
6 3.006 076 442 268(2) 52 3.594 928 416 047(1) 98 2.090 416 580 185(1)
7 2.577 088 353 792(2) 53 3.532 049 276 600(1) 99 2.074 700 029 684(1)
8 2.255 408 115 306(2) 54 3.471 597 085 764(1) 100 2.059 366 389 564(1)
9 2.005 266 467 157(2) 55 3.413 439 798 966(1) 101 2.044 404 857 517(1)
10 1.805 201 856 422(2) 56 3.357 454 812 058(1) 102 2.029 805 069 664(1)
11 1.641 556 933 857(2) 57 3.303 528 133 374(1) 103 2.015 557 079 718(1)
12 1.505 226 802 369(2) 58 3.251 553 641 437(1) 104 2.001 651 339 383(1)
13 1.389 908 073 897(2) 59 3.201 432 418 162(1) 105 1.988 078 679 875(1)
14 1.291 098 330 474(2) 60 3.153 072 148 750(1) 106 1.974 830 294 518(1)
15 1.205 495 800 880(2) 61 3.106 386 580 602(1) 107 1.961 897 722 333(1)
16 1.130 624 158 535(2) 62 3.061 295 034 613(1) 108 1.949 272 832 559(1)
17 1.064 589 743 680(2) 63 3.017 721 963 011(1) 109 1.936 947 810 045(1)
18 1.005 919 711 489(2) 64 2.975 596 548 653(1) 110 1.924 915 141 466(1)
19 9.534 512 913 077(1) 65 2.934 852 341 319(1) 111 1.913 167 602 301(1)
20 9.062 542 681 220(1) 66 2.895 426 927 075(1) 112 1.901 698 244 536(1)
21 8.635 756 121 769(1) 67 2.857 261 627 251(1) 113 1.890 500 385 045(1)
22 8.247 992 096 101(1) 68 2.820 301 223 984(1) 114 1.879 567 594 604(1)
23 7.894 160 981 382(1) 69 2.784 493 709 640(1) 115 1.868 893 687 509(1)
24 7.570 021 438 219(1) 70 2.749 790 057 713(1) 116 1.858 472 711 757(1)
25 7.272 010 754 079(1) 71 2.716 144 013 099(1) 117 1.848 298 939 758(1)
26 6.997 114 338 234(1) 72 2.683 511 899 850(1) 118 1.838 366 859 551(1)
27 6.742 764 217 836(1) 73 2.651 852 444 735(1) 119 1.828 671 166 493(1)
28 6.506 759 284 831(1) 74 2.621 126 615 118(1) 120 1.819 206 755 398(1)
29 6.287 202 043 529(1) 75 2.591 297 469 812(1) 121 1.809 968 713 096(1)
30 6.082 448 008 652(1) 76 2.562 330 021 713(1) 122 1.800 952 311 396(1)
31 5.891 064 897 319(1) 77 2.534 191 111 152(1) 123 1.792 153 000 426(1)
32 5.711 799 472 544(1) 78 2.506 849 288 987(1) 124 1.783 566 402 340(1)
33 5.543 550 415 181(1) 79 2.480 274 708 597(1) 125 1.775 188 305 360(1)
34 5.385 345 983 192(1) 80 2.454 439 025 968(1) 126 1.767 014 658 145(1)
35 5.236 325 500 747(1) 81 2.429 315 307 204(1) 127 1.759 041 564 473(1)
36 5.095 723 932 487(1) 82 2.404 877 942 805(1) 128 1.751 265 278 217(1)
37 4.962 858 959 259(1) 83 2.381 102 568 155(1) 129 1.743 682 198 598(1)
38 4.837 120 094 531(1) 84 2.357 965 989 698(1) 130 1.736 288 865 710(1)
39 4.717 959 475 207(1) 85 2.335 446 116 333(1) 131 1.729 081 956 308(1)
40 4.604 884 033 827(1) 86 2.313 521 895 613(1) 132 1.722 058 279 828(1)
41 4.497 448 816 301(1) 87 2.292 173 254 342(1) 133 1.715 214 774 659(1)
42 4.395 251 254 260(1) 88 2.271 381 043 244(1) 134 1.708 548 504 632(1)
43 4.297 926 236 616(1) 89 2.251 126 985 368(1) 135 1.702 056 655 731(1)
44 4.205 141 853 187(1) 90 2.231 393 627 942(1) 136 1.695 736 533 017(1)
45 4.116 595 705 847(1) 91 2.212 164 297 423(1) 137 1.689 585 557 753(1)
46 4.032 011 700 828(1) 92 2.193 423 057 473(1)
Table 10: (continued)
1 1.201 888 253 354(3) 47 2.756 044 695 895(1) 93 1.732 057 778 713(1)
2 6.010 054 646 848(2) 48 2.707 313 019 753(1) 94 1.724 582 439 587(1)
3 4.007 384 714 441(2) 49 2.660 776 483 764(1) 95 1.717 458 526 708(1)
4 3.006 254 364 150(2) 50 2.616 305 183 525(1) 96 1.710 678 455 982(1)
5 2.405 739 951 535(2) 51 2.573 779 456 173(1) 97 1.704 235 054 005(1)
6 2.005 533 620 160(2) 52 2.533 088 896 773(1) 98 1.698 121 540 307(1)
7 1.719 789 167 354(2) 53 2.494 131 486 101(1) 99 1.692 331 510 790(1)
8 1.505 583 510 670(2) 54 2.456 812 815 372(1) 100 1.686 858 922 295(1)
9 1.339 070 510 039(2) 55 2.421 045 395 594(1) 101 1.681 698 078 219(1)
10 1.205 942 496 647(2) 56 2.386 748 040 959(1) 102 1.676 843 615 111(1)
11 1.097 094 604 245(2) 57 2.353 845 317 178(1) 103 1.672 290 490 205(1)
12 1.006 456 934 815(2) 58 2.322 267 046 939(1) 104 1.668 033 969 813(1)
13 9.298 272 631 635(1) 59 2.291 947 865 689(1) 105 1.664 069 618 536(1)
14 8.642 040 109 841(1) 60 2.262 826 821 895(1) 106 1.660 393 289 254(1)
15 8.073 860 312 973(1) 61 2.234 847 016 658(1) 107 1.657 001 113 834(1)
16 7.577 224 737 343(1) 62 2.207 955 278 260(1) 108 1.653 889 494 537(1)
17 7.139 509 326 648(1) 63 2.182 101 867 747(1) 109 1.651 055 096 069(1)
18 6.750 895 459 555(1) 64 2.157 240 212 165(1) 110 1.648 494 838 258(1)
19 6.403 631 678 089(1) 65 2.133 326 662 469(1) 111 1.646 205 889 319(1)
20 6.091 516 897 556(1) 66 2.110 320 273 493(1) 112 1.644 185 659 678(1)
21 5.809 531 270 816(1) 67 2.088 182 603 672(1) 113 1.642 431 796 340(1)
22 5.553 567 725 985(1) 68 2.066 877 532 491(1) 114 1.640 942 177 763(1)
23 5.320 233 537 818(1) 69 2.046 371 093 862(1) 115 1.639 714 909 234(1)
24 5.106 701 506 295(1) 70 2.026 631 323 834(1) 116 1.638 748 318 713(1)
25 4.910 596 852 378(1) 71 2.007 628 121 236(1) 117 1.638 040 953 141(1)
26 4.729 910 214 796(1) 72 1.989 333 119 984(