Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(73\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19612 | −1.55289 | −0.776445 | − | 0.630186i | \(-0.782979\pi\) | ||||
−0.776445 | + | 0.630186i | \(0.782979\pi\) | |||||||
\(3\) | 2.45439 | 1.41704 | 0.708522 | − | 0.705689i | \(-0.249362\pi\) | ||||
0.708522 | + | 0.705689i | \(0.249362\pi\) | |||||||
\(4\) | 2.82293 | 1.41146 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −5.39013 | −2.20051 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.80725 | −0.638959 | ||||||||
\(9\) | 3.02403 | 1.00801 | ||||||||
\(10\) | −2.19612 | −0.694473 | ||||||||
\(11\) | −4.94555 | −1.49114 | −0.745570 | − | 0.666427i | \(-0.767823\pi\) | ||||
−0.745570 | + | 0.666427i | \(0.767823\pi\) | |||||||
\(12\) | 6.92857 | 2.00011 | ||||||||
\(13\) | −5.58880 | −1.55005 | −0.775027 | − | 0.631928i | \(-0.782264\pi\) | ||||
−0.775027 | + | 0.631928i | \(0.782264\pi\) | |||||||
\(14\) | −2.19612 | −0.586937 | ||||||||
\(15\) | 2.45439 | 0.633721 | ||||||||
\(16\) | −1.67693 | −0.419232 | ||||||||
\(17\) | −1.65223 | −0.400724 | −0.200362 | − | 0.979722i | \(-0.564212\pi\) | ||||
−0.200362 | + | 0.979722i | \(0.564212\pi\) | |||||||
\(18\) | −6.64113 | −1.56533 | ||||||||
\(19\) | −6.19834 | −1.42200 | −0.710999 | − | 0.703193i | \(-0.751757\pi\) | ||||
−0.710999 | + | 0.703193i | \(0.751757\pi\) | |||||||
\(20\) | 2.82293 | 0.631226 | ||||||||
\(21\) | 2.45439 | 0.535592 | ||||||||
\(22\) | 10.8610 | 2.31558 | ||||||||
\(23\) | 7.68759 | 1.60297 | 0.801486 | − | 0.598013i | \(-0.204043\pi\) | ||||
0.801486 | + | 0.598013i | \(0.204043\pi\) | |||||||
\(24\) | −4.43569 | −0.905432 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 12.2737 | 2.40706 | ||||||||
\(27\) | 0.0589907 | 0.0113528 | ||||||||
\(28\) | 2.82293 | 0.533483 | ||||||||
\(29\) | −4.21500 | −0.782705 | −0.391353 | − | 0.920241i | \(-0.627993\pi\) | ||||
−0.391353 | + | 0.920241i | \(0.627993\pi\) | |||||||
\(30\) | −5.39013 | −0.984098 | ||||||||
\(31\) | 5.11417 | 0.918531 | 0.459266 | − | 0.888299i | \(-0.348113\pi\) | ||||
0.459266 | + | 0.888299i | \(0.348113\pi\) | |||||||
\(32\) | 7.29723 | 1.28998 | ||||||||
\(33\) | −12.1383 | −2.11301 | ||||||||
\(34\) | 3.62848 | 0.622280 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 8.53664 | 1.42277 | ||||||||
\(37\) | 4.28782 | 0.704914 | 0.352457 | − | 0.935828i | \(-0.385346\pi\) | ||||
0.352457 | + | 0.935828i | \(0.385346\pi\) | |||||||
\(38\) | 13.6123 | 2.20820 | ||||||||
\(39\) | −13.7171 | −2.19649 | ||||||||
\(40\) | −1.80725 | −0.285751 | ||||||||
\(41\) | 0.661754 | 0.103349 | 0.0516743 | − | 0.998664i | \(-0.483544\pi\) | ||||
0.0516743 | + | 0.998664i | \(0.483544\pi\) | |||||||
\(42\) | −5.39013 | −0.831715 | ||||||||
\(43\) | 11.9278 | 1.81897 | 0.909485 | − | 0.415736i | \(-0.136476\pi\) | ||||
0.909485 | + | 0.415736i | \(0.136476\pi\) | |||||||
\(44\) | −13.9609 | −2.10469 | ||||||||
\(45\) | 3.02403 | 0.450796 | ||||||||
\(46\) | −16.8828 | −2.48924 | ||||||||
\(47\) | 9.56527 | 1.39524 | 0.697619 | − | 0.716469i | \(-0.254243\pi\) | ||||
0.697619 | + | 0.716469i | \(0.254243\pi\) | |||||||
\(48\) | −4.11584 | −0.594071 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.19612 | −0.310578 | ||||||||
\(51\) | −4.05521 | −0.567843 | ||||||||
\(52\) | −15.7768 | −2.18785 | ||||||||
\(53\) | 4.84349 | 0.665304 | 0.332652 | − | 0.943050i | \(-0.392057\pi\) | ||||
0.332652 | + | 0.943050i | \(0.392057\pi\) | |||||||
\(54\) | −0.129550 | −0.0176296 | ||||||||
\(55\) | −4.94555 | −0.666858 | ||||||||
\(56\) | −1.80725 | −0.241504 | ||||||||
\(57\) | −15.2132 | −2.01503 | ||||||||
\(58\) | 9.25663 | 1.21545 | ||||||||
\(59\) | −2.63539 | −0.343098 | −0.171549 | − | 0.985176i | \(-0.554877\pi\) | ||||
−0.171549 | + | 0.985176i | \(0.554877\pi\) | |||||||
\(60\) | 6.92857 | 0.894475 | ||||||||
\(61\) | −5.46300 | −0.699465 | −0.349733 | − | 0.936850i | \(-0.613728\pi\) | ||||
−0.349733 | + | 0.936850i | \(0.613728\pi\) | |||||||
\(62\) | −11.2313 | −1.42638 | ||||||||
\(63\) | 3.02403 | 0.380993 | ||||||||
\(64\) | −12.6717 | −1.58396 | ||||||||
\(65\) | −5.58880 | −0.693206 | ||||||||
\(66\) | 26.6572 | 3.28127 | ||||||||
\(67\) | −2.39421 | −0.292499 | −0.146249 | − | 0.989248i | \(-0.546720\pi\) | ||||
−0.146249 | + | 0.989248i | \(0.546720\pi\) | |||||||
\(68\) | −4.66412 | −0.565608 | ||||||||
\(69\) | 18.8683 | 2.27148 | ||||||||
\(70\) | −2.19612 | −0.262486 | ||||||||
\(71\) | 7.36214 | 0.873725 | 0.436863 | − | 0.899528i | \(-0.356090\pi\) | ||||
0.436863 | + | 0.899528i | \(0.356090\pi\) | |||||||
\(72\) | −5.46518 | −0.644078 | ||||||||
\(73\) | −1.58835 | −0.185902 | −0.0929511 | − | 0.995671i | \(-0.529630\pi\) | ||||
−0.0929511 | + | 0.995671i | \(0.529630\pi\) | |||||||
\(74\) | −9.41656 | −1.09465 | ||||||||
\(75\) | 2.45439 | 0.283409 | ||||||||
\(76\) | −17.4975 | −2.00710 | ||||||||
\(77\) | −4.94555 | −0.563598 | ||||||||
\(78\) | 30.1244 | 3.41091 | ||||||||
\(79\) | −3.65057 | −0.410721 | −0.205360 | − | 0.978686i | \(-0.565837\pi\) | ||||
−0.205360 | + | 0.978686i | \(0.565837\pi\) | |||||||
\(80\) | −1.67693 | −0.187486 | ||||||||
\(81\) | −8.92732 | −0.991924 | ||||||||
\(82\) | −1.45329 | −0.160489 | ||||||||
\(83\) | −7.40723 | −0.813049 | −0.406525 | − | 0.913640i | \(-0.633259\pi\) | ||||
−0.406525 | + | 0.913640i | \(0.633259\pi\) | |||||||
\(84\) | 6.92857 | 0.755969 | ||||||||
\(85\) | −1.65223 | −0.179209 | ||||||||
\(86\) | −26.1948 | −2.82466 | ||||||||
\(87\) | −10.3453 | −1.10913 | ||||||||
\(88\) | 8.93784 | 0.952777 | ||||||||
\(89\) | 13.4338 | 1.42398 | 0.711988 | − | 0.702192i | \(-0.247795\pi\) | ||||
0.711988 | + | 0.702192i | \(0.247795\pi\) | |||||||
\(90\) | −6.64113 | −0.700037 | ||||||||
\(91\) | −5.58880 | −0.585866 | ||||||||
\(92\) | 21.7015 | 2.26254 | ||||||||
\(93\) | 12.5522 | 1.30160 | ||||||||
\(94\) | −21.0065 | −2.16665 | ||||||||
\(95\) | −6.19834 | −0.635937 | ||||||||
\(96\) | 17.9103 | 1.82796 | ||||||||
\(97\) | 4.86127 | 0.493587 | 0.246794 | − | 0.969068i | \(-0.420623\pi\) | ||||
0.246794 | + | 0.969068i | \(0.420623\pi\) | |||||||
\(98\) | −2.19612 | −0.221841 | ||||||||
\(99\) | −14.9555 | −1.50309 | ||||||||
\(100\) | 2.82293 | 0.282293 | ||||||||
\(101\) | 6.02446 | 0.599456 | 0.299728 | − | 0.954025i | \(-0.403104\pi\) | ||||
0.299728 | + | 0.954025i | \(0.403104\pi\) | |||||||
\(102\) | 8.90572 | 0.881798 | ||||||||
\(103\) | 13.6572 | 1.34568 | 0.672840 | − | 0.739788i | \(-0.265074\pi\) | ||||
0.672840 | + | 0.739788i | \(0.265074\pi\) | |||||||
\(104\) | 10.1004 | 0.990421 | ||||||||
\(105\) | 2.45439 | 0.239524 | ||||||||
\(106\) | −10.6369 | −1.03314 | ||||||||
\(107\) | −10.8007 | −1.04414 | −0.522069 | − | 0.852903i | \(-0.674840\pi\) | ||||
−0.522069 | + | 0.852903i | \(0.674840\pi\) | |||||||
\(108\) | 0.166526 | 0.0160240 | ||||||||
\(109\) | 16.4942 | 1.57986 | 0.789928 | − | 0.613200i | \(-0.210118\pi\) | ||||
0.789928 | + | 0.613200i | \(0.210118\pi\) | |||||||
\(110\) | 10.8610 | 1.03556 | ||||||||
\(111\) | 10.5240 | 0.998893 | ||||||||
\(112\) | −1.67693 | −0.158455 | ||||||||
\(113\) | −2.95170 | −0.277673 | −0.138836 | − | 0.990315i | \(-0.544336\pi\) | ||||
−0.138836 | + | 0.990315i | \(0.544336\pi\) | |||||||
\(114\) | 33.4099 | 3.12912 | ||||||||
\(115\) | 7.68759 | 0.716871 | ||||||||
\(116\) | −11.8986 | −1.10476 | ||||||||
\(117\) | −16.9007 | −1.56247 | ||||||||
\(118\) | 5.78762 | 0.532793 | ||||||||
\(119\) | −1.65223 | −0.151459 | ||||||||
\(120\) | −4.43569 | −0.404922 | ||||||||
\(121\) | 13.4585 | 1.22350 | ||||||||
\(122\) | 11.9974 | 1.08619 | ||||||||
\(123\) | 1.62420 | 0.146449 | ||||||||
\(124\) | 14.4369 | 1.29647 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −6.64113 | −0.591639 | ||||||||
\(127\) | 20.8814 | 1.85293 | 0.926464 | − | 0.376383i | \(-0.122832\pi\) | ||||
0.926464 | + | 0.376383i | \(0.122832\pi\) | |||||||
\(128\) | 13.2341 | 1.16974 | ||||||||
\(129\) | 29.2755 | 2.57756 | ||||||||
\(130\) | 12.2737 | 1.07647 | ||||||||
\(131\) | −21.0653 | −1.84049 | −0.920244 | − | 0.391345i | \(-0.872010\pi\) | ||||
−0.920244 | + | 0.391345i | \(0.872010\pi\) | |||||||
\(132\) | −34.2656 | −2.98244 | ||||||||
\(133\) | −6.19834 | −0.537465 | ||||||||
\(134\) | 5.25796 | 0.454218 | ||||||||
\(135\) | 0.0589907 | 0.00507711 | ||||||||
\(136\) | 2.98599 | 0.256046 | ||||||||
\(137\) | 1.87977 | 0.160599 | 0.0802997 | − | 0.996771i | \(-0.474412\pi\) | ||||
0.0802997 | + | 0.996771i | \(0.474412\pi\) | |||||||
\(138\) | −41.4371 | −3.52736 | ||||||||
\(139\) | 7.48345 | 0.634738 | 0.317369 | − | 0.948302i | \(-0.397201\pi\) | ||||
0.317369 | + | 0.948302i | \(0.397201\pi\) | |||||||
\(140\) | 2.82293 | 0.238581 | ||||||||
\(141\) | 23.4769 | 1.97711 | ||||||||
\(142\) | −16.1681 | −1.35680 | ||||||||
\(143\) | 27.6397 | 2.31135 | ||||||||
\(144\) | −5.07109 | −0.422591 | ||||||||
\(145\) | −4.21500 | −0.350036 | ||||||||
\(146\) | 3.48820 | 0.288686 | ||||||||
\(147\) | 2.45439 | 0.202435 | ||||||||
\(148\) | 12.1042 | 0.994961 | ||||||||
\(149\) | 6.61991 | 0.542324 | 0.271162 | − | 0.962534i | \(-0.412592\pi\) | ||||
0.271162 | + | 0.962534i | \(0.412592\pi\) | |||||||
\(150\) | −5.39013 | −0.440102 | ||||||||
\(151\) | −3.76214 | −0.306158 | −0.153079 | − | 0.988214i | \(-0.548919\pi\) | ||||
−0.153079 | + | 0.988214i | \(0.548919\pi\) | |||||||
\(152\) | 11.2019 | 0.908598 | ||||||||
\(153\) | −4.99639 | −0.403934 | ||||||||
\(154\) | 10.8610 | 0.875205 | ||||||||
\(155\) | 5.11417 | 0.410780 | ||||||||
\(156\) | −38.7224 | −3.10027 | ||||||||
\(157\) | −9.63194 | −0.768712 | −0.384356 | − | 0.923185i | \(-0.625576\pi\) | ||||
−0.384356 | + | 0.923185i | \(0.625576\pi\) | |||||||
\(158\) | 8.01707 | 0.637804 | ||||||||
\(159\) | 11.8878 | 0.942764 | ||||||||
\(160\) | 7.29723 | 0.576897 | ||||||||
\(161\) | 7.68759 | 0.605867 | ||||||||
\(162\) | 19.6054 | 1.54035 | ||||||||
\(163\) | 17.9989 | 1.40978 | 0.704891 | − | 0.709316i | \(-0.250996\pi\) | ||||
0.704891 | + | 0.709316i | \(0.250996\pi\) | |||||||
\(164\) | 1.86808 | 0.145873 | ||||||||
\(165\) | −12.1383 | −0.944967 | ||||||||
\(166\) | 16.2671 | 1.26258 | ||||||||
\(167\) | 15.6341 | 1.20980 | 0.604902 | − | 0.796300i | \(-0.293212\pi\) | ||||
0.604902 | + | 0.796300i | \(0.293212\pi\) | |||||||
\(168\) | −4.43569 | −0.342221 | ||||||||
\(169\) | 18.2347 | 1.40267 | ||||||||
\(170\) | 3.62848 | 0.278292 | ||||||||
\(171\) | −18.7440 | −1.43339 | ||||||||
\(172\) | 33.6713 | 2.56741 | ||||||||
\(173\) | 3.07918 | 0.234106 | 0.117053 | − | 0.993126i | \(-0.462655\pi\) | ||||
0.117053 | + | 0.993126i | \(0.462655\pi\) | |||||||
\(174\) | 22.7194 | 1.72235 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 8.29334 | 0.625134 | ||||||||
\(177\) | −6.46827 | −0.486185 | ||||||||
\(178\) | −29.5021 | −2.21128 | ||||||||
\(179\) | −7.11863 | −0.532072 | −0.266036 | − | 0.963963i | \(-0.585714\pi\) | ||||
−0.266036 | + | 0.963963i | \(0.585714\pi\) | |||||||
\(180\) | 8.53664 | 0.636283 | ||||||||
\(181\) | −17.8518 | −1.32692 | −0.663459 | − | 0.748213i | \(-0.730912\pi\) | ||||
−0.663459 | + | 0.748213i | \(0.730912\pi\) | |||||||
\(182\) | 12.2737 | 0.909784 | ||||||||
\(183\) | −13.4083 | −0.991173 | ||||||||
\(184\) | −13.8934 | −1.02423 | ||||||||
\(185\) | 4.28782 | 0.315247 | ||||||||
\(186\) | −27.5660 | −2.02124 | ||||||||
\(187\) | 8.17118 | 0.597536 | ||||||||
\(188\) | 27.0021 | 1.96933 | ||||||||
\(189\) | 0.0589907 | 0.00429094 | ||||||||
\(190\) | 13.6123 | 0.987539 | ||||||||
\(191\) | 6.12249 | 0.443008 | 0.221504 | − | 0.975159i | \(-0.428903\pi\) | ||||
0.221504 | + | 0.975159i | \(0.428903\pi\) | |||||||
\(192\) | −31.1013 | −2.24455 | ||||||||
\(193\) | −22.6276 | −1.62877 | −0.814384 | − | 0.580326i | \(-0.802925\pi\) | ||||
−0.814384 | + | 0.580326i | \(0.802925\pi\) | |||||||
\(194\) | −10.6759 | −0.766487 | ||||||||
\(195\) | −13.7171 | −0.982302 | ||||||||
\(196\) | 2.82293 | 0.201638 | ||||||||
\(197\) | −6.01958 | −0.428877 | −0.214439 | − | 0.976737i | \(-0.568792\pi\) | ||||
−0.214439 | + | 0.976737i | \(0.568792\pi\) | |||||||
\(198\) | 32.8441 | 2.33413 | ||||||||
\(199\) | 9.65352 | 0.684320 | 0.342160 | − | 0.939642i | \(-0.388842\pi\) | ||||
0.342160 | + | 0.939642i | \(0.388842\pi\) | |||||||
\(200\) | −1.80725 | −0.127792 | ||||||||
\(201\) | −5.87632 | −0.414483 | ||||||||
\(202\) | −13.2304 | −0.930889 | ||||||||
\(203\) | −4.21500 | −0.295835 | ||||||||
\(204\) | −11.4476 | −0.801491 | ||||||||
\(205\) | 0.661754 | 0.0462189 | ||||||||
\(206\) | −29.9927 | −2.08969 | ||||||||
\(207\) | 23.2475 | 1.61581 | ||||||||
\(208\) | 9.37203 | 0.649833 | ||||||||
\(209\) | 30.6542 | 2.12040 | ||||||||
\(210\) | −5.39013 | −0.371954 | ||||||||
\(211\) | 26.4355 | 1.81989 | 0.909947 | − | 0.414725i | \(-0.136122\pi\) | ||||
0.909947 | + | 0.414725i | \(0.136122\pi\) | |||||||
\(212\) | 13.6728 | 0.939053 | ||||||||
\(213\) | 18.0696 | 1.23811 | ||||||||
\(214\) | 23.7195 | 1.62143 | ||||||||
\(215\) | 11.9278 | 0.813468 | ||||||||
\(216\) | −0.106611 | −0.00725394 | ||||||||
\(217\) | 5.11417 | 0.347172 | ||||||||
\(218\) | −36.2231 | −2.45334 | ||||||||
\(219\) | −3.89843 | −0.263432 | ||||||||
\(220\) | −13.9609 | −0.941247 | ||||||||
\(221\) | 9.23397 | 0.621144 | ||||||||
\(222\) | −23.1119 | −1.55117 | ||||||||
\(223\) | 21.2564 | 1.42344 | 0.711718 | − | 0.702465i | \(-0.247917\pi\) | ||||
0.711718 | + | 0.702465i | \(0.247917\pi\) | |||||||
\(224\) | 7.29723 | 0.487567 | ||||||||
\(225\) | 3.02403 | 0.201602 | ||||||||
\(226\) | 6.48228 | 0.431195 | ||||||||
\(227\) | −7.51651 | −0.498888 | −0.249444 | − | 0.968389i | \(-0.580248\pi\) | ||||
−0.249444 | + | 0.968389i | \(0.580248\pi\) | |||||||
\(228\) | −42.9457 | −2.84415 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −16.8828 | −1.11322 | ||||||||
\(231\) | −12.1383 | −0.798643 | ||||||||
\(232\) | 7.61755 | 0.500116 | ||||||||
\(233\) | 14.6716 | 0.961169 | 0.480584 | − | 0.876949i | \(-0.340425\pi\) | ||||
0.480584 | + | 0.876949i | \(0.340425\pi\) | |||||||
\(234\) | 37.1160 | 2.42635 | ||||||||
\(235\) | 9.56527 | 0.623970 | ||||||||
\(236\) | −7.43951 | −0.484271 | ||||||||
\(237\) | −8.95992 | −0.582009 | ||||||||
\(238\) | 3.62848 | 0.235200 | ||||||||
\(239\) | 26.4836 | 1.71308 | 0.856539 | − | 0.516082i | \(-0.172610\pi\) | ||||
0.856539 | + | 0.516082i | \(0.172610\pi\) | |||||||
\(240\) | −4.11584 | −0.265676 | ||||||||
\(241\) | −7.09957 | −0.457323 | −0.228662 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228662 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(242\) | −29.5564 | −1.89996 | ||||||||
\(243\) | −22.0881 | −1.41695 | ||||||||
\(244\) | −15.4217 | −0.987271 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −3.56694 | −0.227420 | ||||||||
\(247\) | 34.6413 | 2.20417 | ||||||||
\(248\) | −9.24257 | −0.586904 | ||||||||
\(249\) | −18.1802 | −1.15213 | ||||||||
\(250\) | −2.19612 | −0.138895 | ||||||||
\(251\) | −4.15242 | −0.262098 | −0.131049 | − | 0.991376i | \(-0.541835\pi\) | ||||
−0.131049 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(252\) | 8.53664 | 0.537757 | ||||||||
\(253\) | −38.0194 | −2.39026 | ||||||||
\(254\) | −45.8581 | −2.87739 | ||||||||
\(255\) | −4.05521 | −0.253947 | ||||||||
\(256\) | −3.72020 | −0.232512 | ||||||||
\(257\) | −17.0809 | −1.06547 | −0.532737 | − | 0.846281i | \(-0.678837\pi\) | ||||
−0.532737 | + | 0.846281i | \(0.678837\pi\) | |||||||
\(258\) | −64.2923 | −4.00267 | ||||||||
\(259\) | 4.28782 | 0.266432 | ||||||||
\(260\) | −15.7768 | −0.978435 | ||||||||
\(261\) | −12.7463 | −0.788976 | ||||||||
\(262\) | 46.2620 | 2.85807 | ||||||||
\(263\) | 10.9980 | 0.678168 | 0.339084 | − | 0.940756i | \(-0.389883\pi\) | ||||
0.339084 | + | 0.940756i | \(0.389883\pi\) | |||||||
\(264\) | 21.9370 | 1.35013 | ||||||||
\(265\) | 4.84349 | 0.297533 | ||||||||
\(266\) | 13.6123 | 0.834623 | ||||||||
\(267\) | 32.9717 | 2.01783 | ||||||||
\(268\) | −6.75867 | −0.412852 | ||||||||
\(269\) | 9.37029 | 0.571317 | 0.285658 | − | 0.958332i | \(-0.407788\pi\) | ||||
0.285658 | + | 0.958332i | \(0.407788\pi\) | |||||||
\(270\) | −0.129550 | −0.00788418 | ||||||||
\(271\) | −22.6637 | −1.37672 | −0.688360 | − | 0.725369i | \(-0.741669\pi\) | ||||
−0.688360 | + | 0.725369i | \(0.741669\pi\) | |||||||
\(272\) | 2.77067 | 0.167997 | ||||||||
\(273\) | −13.7171 | −0.830197 | ||||||||
\(274\) | −4.12819 | −0.249393 | ||||||||
\(275\) | −4.94555 | −0.298228 | ||||||||
\(276\) | 53.2640 | 3.20612 | ||||||||
\(277\) | 32.4158 | 1.94767 | 0.973837 | − | 0.227248i | \(-0.0729728\pi\) | ||||
0.973837 | + | 0.227248i | \(0.0729728\pi\) | |||||||
\(278\) | −16.4345 | −0.985677 | ||||||||
\(279\) | 15.4654 | 0.925890 | ||||||||
\(280\) | −1.80725 | −0.108004 | ||||||||
\(281\) | −28.6772 | −1.71074 | −0.855368 | − | 0.518021i | \(-0.826669\pi\) | ||||
−0.855368 | + | 0.518021i | \(0.826669\pi\) | |||||||
\(282\) | −51.5581 | −3.07024 | ||||||||
\(283\) | 21.4890 | 1.27739 | 0.638694 | − | 0.769461i | \(-0.279475\pi\) | ||||
0.638694 | + | 0.769461i | \(0.279475\pi\) | |||||||
\(284\) | 20.7828 | 1.23323 | ||||||||
\(285\) | −15.2132 | −0.901150 | ||||||||
\(286\) | −60.7000 | −3.58927 | ||||||||
\(287\) | 0.661754 | 0.0390621 | ||||||||
\(288\) | 22.0671 | 1.30032 | ||||||||
\(289\) | −14.2701 | −0.839420 | ||||||||
\(290\) | 9.25663 | 0.543568 | ||||||||
\(291\) | 11.9315 | 0.699435 | ||||||||
\(292\) | −4.48380 | −0.262394 | ||||||||
\(293\) | −24.4590 | −1.42891 | −0.714455 | − | 0.699681i | \(-0.753325\pi\) | ||||
−0.714455 | + | 0.699681i | \(0.753325\pi\) | |||||||
\(294\) | −5.39013 | −0.314359 | ||||||||
\(295\) | −2.63539 | −0.153438 | ||||||||
\(296\) | −7.74916 | −0.450411 | ||||||||
\(297\) | −0.291741 | −0.0169286 | ||||||||
\(298\) | −14.5381 | −0.842169 | ||||||||
\(299\) | −42.9644 | −2.48469 | ||||||||
\(300\) | 6.92857 | 0.400021 | ||||||||
\(301\) | 11.9278 | 0.687506 | ||||||||
\(302\) | 8.26209 | 0.475430 | ||||||||
\(303\) | 14.7864 | 0.849455 | ||||||||
\(304\) | 10.3942 | 0.596148 | ||||||||
\(305\) | −5.46300 | −0.312810 | ||||||||
\(306\) | 10.9727 | 0.627265 | ||||||||
\(307\) | −3.49370 | −0.199396 | −0.0996980 | − | 0.995018i | \(-0.531788\pi\) | ||||
−0.0996980 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(308\) | −13.9609 | −0.795499 | ||||||||
\(309\) | 33.5200 | 1.90689 | ||||||||
\(310\) | −11.2313 | −0.637895 | ||||||||
\(311\) | 21.8624 | 1.23970 | 0.619850 | − | 0.784720i | \(-0.287193\pi\) | ||||
0.619850 | + | 0.784720i | \(0.287193\pi\) | |||||||
\(312\) | 24.7902 | 1.40347 | ||||||||
\(313\) | −21.4076 | −1.21003 | −0.605015 | − | 0.796214i | \(-0.706833\pi\) | ||||
−0.605015 | + | 0.796214i | \(0.706833\pi\) | |||||||
\(314\) | 21.1529 | 1.19372 | ||||||||
\(315\) | 3.02403 | 0.170385 | ||||||||
\(316\) | −10.3053 | −0.579718 | ||||||||
\(317\) | 28.1015 | 1.57834 | 0.789169 | − | 0.614176i | \(-0.210512\pi\) | ||||
0.789169 | + | 0.614176i | \(0.210512\pi\) | |||||||
\(318\) | −26.1070 | −1.46401 | ||||||||
\(319\) | 20.8455 | 1.16712 | ||||||||
\(320\) | −12.6717 | −0.708370 | ||||||||
\(321\) | −26.5090 | −1.47959 | ||||||||
\(322\) | −16.8828 | −0.940844 | ||||||||
\(323\) | 10.2411 | 0.569829 | ||||||||
\(324\) | −25.2012 | −1.40007 | ||||||||
\(325\) | −5.58880 | −0.310011 | ||||||||
\(326\) | −39.5276 | −2.18923 | ||||||||
\(327\) | 40.4831 | 2.23872 | ||||||||
\(328\) | −1.19595 | −0.0660355 | ||||||||
\(329\) | 9.56527 | 0.527351 | ||||||||
\(330\) | 26.6572 | 1.46743 | ||||||||
\(331\) | 18.2913 | 1.00538 | 0.502690 | − | 0.864467i | \(-0.332344\pi\) | ||||
0.502690 | + | 0.864467i | \(0.332344\pi\) | |||||||
\(332\) | −20.9101 | −1.14759 | ||||||||
\(333\) | 12.9665 | 0.710561 | ||||||||
\(334\) | −34.3344 | −1.87869 | ||||||||
\(335\) | −2.39421 | −0.130809 | ||||||||
\(336\) | −4.11584 | −0.224538 | ||||||||
\(337\) | 13.8736 | 0.755745 | 0.377872 | − | 0.925858i | \(-0.376656\pi\) | ||||
0.377872 | + | 0.925858i | \(0.376656\pi\) | |||||||
\(338\) | −40.0455 | −2.17819 | ||||||||
\(339\) | −7.24463 | −0.393474 | ||||||||
\(340\) | −4.66412 | −0.252947 | ||||||||
\(341\) | −25.2924 | −1.36966 | ||||||||
\(342\) | 41.1640 | 2.22590 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −21.5565 | −1.16225 | ||||||||
\(345\) | 18.8683 | 1.01584 | ||||||||
\(346\) | −6.76224 | −0.363540 | ||||||||
\(347\) | −4.43945 | −0.238322 | −0.119161 | − | 0.992875i | \(-0.538021\pi\) | ||||
−0.119161 | + | 0.992875i | \(0.538021\pi\) | |||||||
\(348\) | −29.2039 | −1.56549 | ||||||||
\(349\) | 12.5880 | 0.673818 | 0.336909 | − | 0.941537i | \(-0.390618\pi\) | ||||
0.336909 | + | 0.941537i | \(0.390618\pi\) | |||||||
\(350\) | −2.19612 | −0.117387 | ||||||||
\(351\) | −0.329687 | −0.0175974 | ||||||||
\(352\) | −36.0888 | −1.92354 | ||||||||
\(353\) | 31.2812 | 1.66493 | 0.832465 | − | 0.554077i | \(-0.186929\pi\) | ||||
0.832465 | + | 0.554077i | \(0.186929\pi\) | |||||||
\(354\) | 14.2051 | 0.754991 | ||||||||
\(355\) | 7.36214 | 0.390742 | ||||||||
\(356\) | 37.9225 | 2.00989 | ||||||||
\(357\) | −4.05521 | −0.214625 | ||||||||
\(358\) | 15.6333 | 0.826248 | ||||||||
\(359\) | −23.8120 | −1.25675 | −0.628375 | − | 0.777911i | \(-0.716279\pi\) | ||||
−0.628375 | + | 0.777911i | \(0.716279\pi\) | |||||||
\(360\) | −5.46518 | −0.288040 | ||||||||
\(361\) | 19.4195 | 1.02208 | ||||||||
\(362\) | 39.2047 | 2.06056 | ||||||||
\(363\) | 33.0324 | 1.73375 | ||||||||
\(364\) | −15.7768 | −0.826928 | ||||||||
\(365\) | −1.58835 | −0.0831380 | ||||||||
\(366\) | 29.4463 | 1.53918 | ||||||||
\(367\) | 12.2720 | 0.640594 | 0.320297 | − | 0.947317i | \(-0.396217\pi\) | ||||
0.320297 | + | 0.947317i | \(0.396217\pi\) | |||||||
\(368\) | −12.8915 | −0.672018 | ||||||||
\(369\) | 2.00117 | 0.104177 | ||||||||
\(370\) | −9.41656 | −0.489544 | ||||||||
\(371\) | 4.84349 | 0.251461 | ||||||||
\(372\) | 35.4339 | 1.83716 | ||||||||
\(373\) | 13.6385 | 0.706172 | 0.353086 | − | 0.935591i | \(-0.385132\pi\) | ||||
0.353086 | + | 0.935591i | \(0.385132\pi\) | |||||||
\(374\) | −17.9449 | −0.927907 | ||||||||
\(375\) | 2.45439 | 0.126744 | ||||||||
\(376\) | −17.2868 | −0.891500 | ||||||||
\(377\) | 23.5568 | 1.21324 | ||||||||
\(378\) | −0.129550 | −0.00666335 | ||||||||
\(379\) | 34.3728 | 1.76561 | 0.882807 | − | 0.469736i | \(-0.155651\pi\) | ||||
0.882807 | + | 0.469736i | \(0.155651\pi\) | |||||||
\(380\) | −17.4975 | −0.897602 | ||||||||
\(381\) | 51.2512 | 2.62568 | ||||||||
\(382\) | −13.4457 | −0.687942 | ||||||||
\(383\) | −28.7891 | −1.47105 | −0.735526 | − | 0.677496i | \(-0.763065\pi\) | ||||
−0.735526 | + | 0.677496i | \(0.763065\pi\) | |||||||
\(384\) | 32.4816 | 1.65757 | ||||||||
\(385\) | −4.94555 | −0.252049 | ||||||||
\(386\) | 49.6928 | 2.52930 | ||||||||
\(387\) | 36.0700 | 1.83354 | ||||||||
\(388\) | 13.7230 | 0.696681 | ||||||||
\(389\) | −13.0171 | −0.659995 | −0.329997 | − | 0.943982i | \(-0.607048\pi\) | ||||
−0.329997 | + | 0.943982i | \(0.607048\pi\) | |||||||
\(390\) | 30.1244 | 1.52541 | ||||||||
\(391\) | −12.7016 | −0.642350 | ||||||||
\(392\) | −1.80725 | −0.0912798 | ||||||||
\(393\) | −51.7026 | −2.60805 | ||||||||
\(394\) | 13.2197 | 0.665999 | ||||||||
\(395\) | −3.65057 | −0.183680 | ||||||||
\(396\) | −42.2184 | −2.12155 | ||||||||
\(397\) | 26.6535 | 1.33770 | 0.668850 | − | 0.743397i | \(-0.266787\pi\) | ||||
0.668850 | + | 0.743397i | \(0.266787\pi\) | |||||||
\(398\) | −21.2002 | −1.06267 | ||||||||
\(399\) | −15.2132 | −0.761611 | ||||||||
\(400\) | −1.67693 | −0.0838465 | ||||||||
\(401\) | 4.22919 | 0.211196 | 0.105598 | − | 0.994409i | \(-0.466324\pi\) | ||||
0.105598 | + | 0.994409i | \(0.466324\pi\) | |||||||
\(402\) | 12.9051 | 0.643647 | ||||||||
\(403\) | −28.5821 | −1.42377 | ||||||||
\(404\) | 17.0066 | 0.846111 | ||||||||
\(405\) | −8.92732 | −0.443602 | ||||||||
\(406\) | 9.25663 | 0.459399 | ||||||||
\(407\) | −21.2057 | −1.05113 | ||||||||
\(408\) | 7.32878 | 0.362828 | ||||||||
\(409\) | 20.3143 | 1.00448 | 0.502240 | − | 0.864728i | \(-0.332510\pi\) | ||||
0.502240 | + | 0.864728i | \(0.332510\pi\) | |||||||
\(410\) | −1.45329 | −0.0717728 | ||||||||
\(411\) | 4.61368 | 0.227576 | ||||||||
\(412\) | 38.5532 | 1.89938 | ||||||||
\(413\) | −2.63539 | −0.129679 | ||||||||
\(414\) | −51.0543 | −2.50918 | ||||||||
\(415\) | −7.40723 | −0.363607 | ||||||||
\(416\) | −40.7828 | −1.99954 | ||||||||
\(417\) | 18.3673 | 0.899451 | ||||||||
\(418\) | −67.3203 | −3.29274 | ||||||||
\(419\) | −21.2343 | −1.03736 | −0.518682 | − | 0.854967i | \(-0.673577\pi\) | ||||
−0.518682 | + | 0.854967i | \(0.673577\pi\) | |||||||
\(420\) | 6.92857 | 0.338080 | ||||||||
\(421\) | −6.97438 | −0.339910 | −0.169955 | − | 0.985452i | \(-0.554362\pi\) | ||||
−0.169955 | + | 0.985452i | \(0.554362\pi\) | |||||||
\(422\) | −58.0554 | −2.82609 | ||||||||
\(423\) | 28.9257 | 1.40642 | ||||||||
\(424\) | −8.75338 | −0.425102 | ||||||||
\(425\) | −1.65223 | −0.0801448 | ||||||||
\(426\) | −39.6829 | −1.92264 | ||||||||
\(427\) | −5.46300 | −0.264373 | ||||||||
\(428\) | −30.4895 | −1.47376 | ||||||||
\(429\) | 67.8387 | 3.27528 | ||||||||
\(430\) | −26.1948 | −1.26323 | ||||||||
\(431\) | 7.07766 | 0.340919 | 0.170459 | − | 0.985365i | \(-0.445475\pi\) | ||||
0.170459 | + | 0.985365i | \(0.445475\pi\) | |||||||
\(432\) | −0.0989232 | −0.00475944 | ||||||||
\(433\) | 4.58340 | 0.220264 | 0.110132 | − | 0.993917i | \(-0.464873\pi\) | ||||
0.110132 | + | 0.993917i | \(0.464873\pi\) | |||||||
\(434\) | −11.2313 | −0.539120 | ||||||||
\(435\) | −10.3453 | −0.496017 | ||||||||
\(436\) | 46.5619 | 2.22991 | ||||||||
\(437\) | −47.6503 | −2.27942 | ||||||||
\(438\) | 8.56141 | 0.409080 | ||||||||
\(439\) | 13.1942 | 0.629727 | 0.314863 | − | 0.949137i | \(-0.398041\pi\) | ||||
0.314863 | + | 0.949137i | \(0.398041\pi\) | |||||||
\(440\) | 8.93784 | 0.426095 | ||||||||
\(441\) | 3.02403 | 0.144002 | ||||||||
\(442\) | −20.2789 | −0.964568 | ||||||||
\(443\) | −15.0463 | −0.714870 | −0.357435 | − | 0.933938i | \(-0.616349\pi\) | ||||
−0.357435 | + | 0.933938i | \(0.616349\pi\) | |||||||
\(444\) | 29.7085 | 1.40990 | ||||||||
\(445\) | 13.4338 | 0.636821 | ||||||||
\(446\) | −46.6816 | −2.21044 | ||||||||
\(447\) | 16.2478 | 0.768497 | ||||||||
\(448\) | −12.6717 | −0.598682 | ||||||||
\(449\) | 9.93890 | 0.469046 | 0.234523 | − | 0.972111i | \(-0.424647\pi\) | ||||
0.234523 | + | 0.972111i | \(0.424647\pi\) | |||||||
\(450\) | −6.64113 | −0.313066 | ||||||||
\(451\) | −3.27274 | −0.154107 | ||||||||
\(452\) | −8.33244 | −0.391925 | ||||||||
\(453\) | −9.23375 | −0.433840 | ||||||||
\(454\) | 16.5071 | 0.774718 | ||||||||
\(455\) | −5.58880 | −0.262007 | ||||||||
\(456\) | 27.4940 | 1.28752 | ||||||||
\(457\) | −2.94162 | −0.137603 | −0.0688016 | − | 0.997630i | \(-0.521918\pi\) | ||||
−0.0688016 | + | 0.997630i | \(0.521918\pi\) | |||||||
\(458\) | −2.19612 | −0.102618 | ||||||||
\(459\) | −0.0974660 | −0.00454932 | ||||||||
\(460\) | 21.7015 | 1.01184 | ||||||||
\(461\) | 12.7864 | 0.595521 | 0.297760 | − | 0.954641i | \(-0.403760\pi\) | ||||
0.297760 | + | 0.954641i | \(0.403760\pi\) | |||||||
\(462\) | 26.6572 | 1.24020 | ||||||||
\(463\) | 2.34334 | 0.108904 | 0.0544521 | − | 0.998516i | \(-0.482659\pi\) | ||||
0.0544521 | + | 0.998516i | \(0.482659\pi\) | |||||||
\(464\) | 7.06825 | 0.328135 | ||||||||
\(465\) | 12.5522 | 0.582093 | ||||||||
\(466\) | −32.2206 | −1.49259 | ||||||||
\(467\) | −25.8535 | −1.19636 | −0.598179 | − | 0.801362i | \(-0.704109\pi\) | ||||
−0.598179 | + | 0.801362i | \(0.704109\pi\) | |||||||
\(468\) | −47.7096 | −2.20538 | ||||||||
\(469\) | −2.39421 | −0.110554 | ||||||||
\(470\) | −21.0065 | −0.968956 | ||||||||
\(471\) | −23.6405 | −1.08930 | ||||||||
\(472\) | 4.76280 | 0.219226 | ||||||||
\(473\) | −58.9895 | −2.71234 | ||||||||
\(474\) | 19.6770 | 0.903796 | ||||||||
\(475\) | −6.19834 | −0.284400 | ||||||||
\(476\) | −4.66412 | −0.213780 | ||||||||
\(477\) | 14.6469 | 0.670634 | ||||||||
\(478\) | −58.1610 | −2.66022 | ||||||||
\(479\) | −10.5695 | −0.482935 | −0.241467 | − | 0.970409i | \(-0.577629\pi\) | ||||
−0.241467 | + | 0.970409i | \(0.577629\pi\) | |||||||
\(480\) | 17.9103 | 0.817488 | ||||||||
\(481\) | −23.9638 | −1.09266 | ||||||||
\(482\) | 15.5915 | 0.710173 | ||||||||
\(483\) | 18.8683 | 0.858539 | ||||||||
\(484\) | 37.9924 | 1.72693 | ||||||||
\(485\) | 4.86127 | 0.220739 | ||||||||
\(486\) | 48.5080 | 2.20037 | ||||||||
\(487\) | −26.2342 | −1.18879 | −0.594393 | − | 0.804175i | \(-0.702608\pi\) | ||||
−0.594393 | + | 0.804175i | \(0.702608\pi\) | |||||||
\(488\) | 9.87300 | 0.446930 | ||||||||
\(489\) | 44.1763 | 1.99772 | ||||||||
\(490\) | −2.19612 | −0.0992104 | ||||||||
\(491\) | −16.8697 | −0.761321 | −0.380660 | − | 0.924715i | \(-0.624303\pi\) | ||||
−0.380660 | + | 0.924715i | \(0.624303\pi\) | |||||||
\(492\) | 4.58501 | 0.206708 | ||||||||
\(493\) | 6.96413 | 0.313649 | ||||||||
\(494\) | −76.0764 | −3.42284 | ||||||||
\(495\) | −14.9555 | −0.672201 | ||||||||
\(496\) | −8.57610 | −0.385078 | ||||||||
\(497\) | 7.36214 | 0.330237 | ||||||||
\(498\) | 39.9259 | 1.78912 | ||||||||
\(499\) | 12.7637 | 0.571383 | 0.285692 | − | 0.958322i | \(-0.407777\pi\) | ||||
0.285692 | + | 0.958322i | \(0.407777\pi\) | |||||||
\(500\) | 2.82293 | 0.126245 | ||||||||
\(501\) | 38.3722 | 1.71435 | ||||||||
\(502\) | 9.11919 | 0.407009 | ||||||||
\(503\) | 11.4691 | 0.511380 | 0.255690 | − | 0.966759i | \(-0.417697\pi\) | ||||
0.255690 | + | 0.966759i | \(0.417697\pi\) | |||||||
\(504\) | −5.46518 | −0.243439 | ||||||||
\(505\) | 6.02446 | 0.268085 | ||||||||
\(506\) | 83.4949 | 3.71180 | ||||||||
\(507\) | 44.7551 | 1.98764 | ||||||||
\(508\) | 58.9468 | 2.61534 | ||||||||
\(509\) | −5.63743 | −0.249875 | −0.124937 | − | 0.992165i | \(-0.539873\pi\) | ||||
−0.124937 | + | 0.992165i | \(0.539873\pi\) | |||||||
\(510\) | 8.90572 | 0.394352 | ||||||||
\(511\) | −1.58835 | −0.0702645 | ||||||||
\(512\) | −18.2982 | −0.808674 | ||||||||
\(513\) | −0.365644 | −0.0161436 | ||||||||
\(514\) | 37.5116 | 1.65456 | ||||||||
\(515\) | 13.6572 | 0.601806 | ||||||||
\(516\) | 82.6425 | 3.63813 | ||||||||
\(517\) | −47.3056 | −2.08050 | ||||||||
\(518\) | −9.41656 | −0.413740 | ||||||||
\(519\) | 7.55751 | 0.331738 | ||||||||
\(520\) | 10.1004 | 0.442930 | ||||||||
\(521\) | −26.3700 | −1.15529 | −0.577646 | − | 0.816287i | \(-0.696029\pi\) | ||||
−0.577646 | + | 0.816287i | \(0.696029\pi\) | |||||||
\(522\) | 27.9924 | 1.22519 | ||||||||
\(523\) | −27.4718 | −1.20126 | −0.600628 | − | 0.799528i | \(-0.705083\pi\) | ||||
−0.600628 | + | 0.799528i | \(0.705083\pi\) | |||||||
\(524\) | −59.4660 | −2.59778 | ||||||||
\(525\) | 2.45439 | 0.107118 | ||||||||
\(526\) | −24.1530 | −1.05312 | ||||||||
\(527\) | −8.44977 | −0.368078 | ||||||||
\(528\) | 20.3551 | 0.885842 | ||||||||
\(529\) | 36.0990 | 1.56952 | ||||||||
\(530\) | −10.6369 | −0.462036 | ||||||||
\(531\) | −7.96950 | −0.345847 | ||||||||
\(532\) | −17.4975 | −0.758612 | ||||||||
\(533\) | −3.69841 | −0.160196 | ||||||||
\(534\) | −72.4097 | −3.13347 | ||||||||
\(535\) | −10.8007 | −0.466953 | ||||||||
\(536\) | 4.32692 | 0.186895 | ||||||||
\(537\) | −17.4719 | −0.753968 | ||||||||
\(538\) | −20.5782 | −0.887191 | ||||||||
\(539\) | −4.94555 | −0.213020 | ||||||||
\(540\) | 0.166526 | 0.00716616 | ||||||||
\(541\) | 13.8575 | 0.595778 | 0.297889 | − | 0.954600i | \(-0.403717\pi\) | ||||
0.297889 | + | 0.954600i | \(0.403717\pi\) | |||||||
\(542\) | 49.7721 | 2.13789 | ||||||||
\(543\) | −43.8154 | −1.88030 | ||||||||
\(544\) | −12.0567 | −0.516926 | ||||||||
\(545\) | 16.4942 | 0.706533 | ||||||||
\(546\) | 30.1244 | 1.28920 | ||||||||
\(547\) | 45.6047 | 1.94992 | 0.974958 | − | 0.222390i | \(-0.0713859\pi\) | ||||
0.974958 | + | 0.222390i | \(0.0713859\pi\) | |||||||
\(548\) | 5.30645 | 0.226680 | ||||||||
\(549\) | −16.5203 | −0.705069 | ||||||||
\(550\) | 10.8610 | 0.463115 | ||||||||
\(551\) | 26.1260 | 1.11301 | ||||||||
\(552\) | −34.0998 | −1.45138 | ||||||||
\(553\) | −3.65057 | −0.155238 | ||||||||
\(554\) | −71.1888 | −3.02452 | ||||||||
\(555\) | 10.5240 | 0.446719 | ||||||||
\(556\) | 21.1252 | 0.895910 | ||||||||
\(557\) | 17.9103 | 0.758885 | 0.379443 | − | 0.925215i | \(-0.376116\pi\) | ||||
0.379443 | + | 0.925215i | \(0.376116\pi\) | |||||||
\(558\) | −33.9639 | −1.43780 | ||||||||
\(559\) | −66.6620 | −2.81950 | ||||||||
\(560\) | −1.67693 | −0.0708632 | ||||||||
\(561\) | 20.0553 | 0.846734 | ||||||||
\(562\) | 62.9784 | 2.65658 | ||||||||
\(563\) | 0.0718832 | 0.00302951 | 0.00151476 | − | 0.999999i | \(-0.499518\pi\) | ||||
0.00151476 | + | 0.999999i | \(0.499518\pi\) | |||||||
\(564\) | 66.2737 | 2.79063 | ||||||||
\(565\) | −2.95170 | −0.124179 | ||||||||
\(566\) | −47.1923 | −1.98364 | ||||||||
\(567\) | −8.92732 | −0.374912 | ||||||||
\(568\) | −13.3052 | −0.558274 | ||||||||
\(569\) | 13.2603 | 0.555901 | 0.277951 | − | 0.960595i | \(-0.410345\pi\) | ||||
0.277951 | + | 0.960595i | \(0.410345\pi\) | |||||||
\(570\) | 33.4099 | 1.39939 | ||||||||
\(571\) | 19.0584 | 0.797568 | 0.398784 | − | 0.917045i | \(-0.369432\pi\) | ||||
0.398784 | + | 0.917045i | \(0.369432\pi\) | |||||||
\(572\) | 78.0249 | 3.26239 | ||||||||
\(573\) | 15.0270 | 0.627761 | ||||||||
\(574\) | −1.45329 | −0.0606591 | ||||||||
\(575\) | 7.68759 | 0.320594 | ||||||||
\(576\) | −38.3197 | −1.59665 | ||||||||
\(577\) | −35.3975 | −1.47362 | −0.736810 | − | 0.676100i | \(-0.763669\pi\) | ||||
−0.736810 | + | 0.676100i | \(0.763669\pi\) | |||||||
\(578\) | 31.3389 | 1.30353 | ||||||||
\(579\) | −55.5369 | −2.30803 | ||||||||
\(580\) | −11.8986 | −0.494064 | ||||||||
\(581\) | −7.40723 | −0.307304 | ||||||||
\(582\) | −26.2029 | −1.08614 | ||||||||
\(583\) | −23.9537 | −0.992061 | ||||||||
\(584\) | 2.87054 | 0.118784 | ||||||||
\(585\) | −16.9007 | −0.698759 | ||||||||
\(586\) | 53.7148 | 2.21894 | ||||||||
\(587\) | −8.53373 | −0.352225 | −0.176112 | − | 0.984370i | \(-0.556352\pi\) | ||||
−0.176112 | + | 0.984370i | \(0.556352\pi\) | |||||||
\(588\) | 6.92857 | 0.285729 | ||||||||
\(589\) | −31.6994 | −1.30615 | ||||||||
\(590\) | 5.78762 | 0.238272 | ||||||||
\(591\) | −14.7744 | −0.607737 | ||||||||
\(592\) | −7.19038 | −0.295523 | ||||||||
\(593\) | 30.4940 | 1.25224 | 0.626119 | − | 0.779728i | \(-0.284643\pi\) | ||||
0.626119 | + | 0.779728i | \(0.284643\pi\) | |||||||
\(594\) | 0.640698 | 0.0262882 | ||||||||
\(595\) | −1.65223 | −0.0677347 | ||||||||
\(596\) | 18.6875 | 0.765471 | ||||||||
\(597\) | 23.6935 | 0.969710 | ||||||||
\(598\) | 94.3548 | 3.85846 | ||||||||
\(599\) | 39.6689 | 1.62083 | 0.810413 | − | 0.585858i | \(-0.199243\pi\) | ||||
0.810413 | + | 0.585858i | \(0.199243\pi\) | |||||||
\(600\) | −4.43569 | −0.181086 | ||||||||
\(601\) | −45.0305 | −1.83683 | −0.918417 | − | 0.395614i | \(-0.870532\pi\) | ||||
−0.918417 | + | 0.395614i | \(0.870532\pi\) | |||||||
\(602\) | −26.1948 | −1.06762 | ||||||||
\(603\) | −7.24016 | −0.294842 | ||||||||
\(604\) | −10.6202 | −0.432132 | ||||||||
\(605\) | 13.4585 | 0.547165 | ||||||||
\(606\) | −32.4726 | −1.31911 | ||||||||
\(607\) | −30.8199 | −1.25094 | −0.625471 | − | 0.780247i | \(-0.715093\pi\) | ||||
−0.625471 | + | 0.780247i | \(0.715093\pi\) | |||||||
\(608\) | −45.2307 | −1.83435 | ||||||||
\(609\) | −10.3453 | −0.419211 | ||||||||
\(610\) | 11.9974 | 0.485760 | ||||||||
\(611\) | −53.4584 | −2.16270 | ||||||||
\(612\) | −14.1045 | −0.570139 | ||||||||
\(613\) | 6.52482 | 0.263535 | 0.131767 | − | 0.991281i | \(-0.457935\pi\) | ||||
0.131767 | + | 0.991281i | \(0.457935\pi\) | |||||||
\(614\) | 7.67258 | 0.309640 | ||||||||
\(615\) | 1.62420 | 0.0654942 | ||||||||
\(616\) | 8.93784 | 0.360116 | ||||||||
\(617\) | −36.0035 | −1.44945 | −0.724723 | − | 0.689040i | \(-0.758032\pi\) | ||||
−0.724723 | + | 0.689040i | \(0.758032\pi\) | |||||||
\(618\) | −73.6138 | −2.96118 | ||||||||
\(619\) | 19.2311 | 0.772964 | 0.386482 | − | 0.922297i | \(-0.373690\pi\) | ||||
0.386482 | + | 0.922297i | \(0.373690\pi\) | |||||||
\(620\) | 14.4369 | 0.579801 | ||||||||
\(621\) | 0.453496 | 0.0181982 | ||||||||
\(622\) | −48.0123 | −1.92512 | ||||||||
\(623\) | 13.4338 | 0.538212 | ||||||||
\(624\) | 23.0026 | 0.920842 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 47.0136 | 1.87904 | ||||||||
\(627\) | 75.2375 | 3.00470 | ||||||||
\(628\) | −27.1903 | −1.08501 | ||||||||
\(629\) | −7.08446 | −0.282476 | ||||||||
\(630\) | −6.64113 | −0.264589 | ||||||||
\(631\) | −44.6267 | −1.77656 | −0.888280 | − | 0.459303i | \(-0.848099\pi\) | ||||
−0.888280 | + | 0.459303i | \(0.848099\pi\) | |||||||
\(632\) | 6.59748 | 0.262434 | ||||||||
\(633\) | 64.8830 | 2.57887 | ||||||||
\(634\) | −61.7142 | −2.45098 | ||||||||
\(635\) | 20.8814 | 0.828655 | ||||||||
\(636\) | 33.5584 | 1.33068 | ||||||||
\(637\) | −5.58880 | −0.221436 | ||||||||
\(638\) | −45.7791 | −1.81241 | ||||||||
\(639\) | 22.2634 | 0.880725 | ||||||||
\(640\) | 13.2341 | 0.523124 | ||||||||
\(641\) | 40.5712 | 1.60247 | 0.801233 | − | 0.598352i | \(-0.204178\pi\) | ||||
0.801233 | + | 0.598352i | \(0.204178\pi\) | |||||||
\(642\) | 58.2169 | 2.29764 | ||||||||
\(643\) | −5.29777 | −0.208924 | −0.104462 | − | 0.994529i | \(-0.533312\pi\) | ||||
−0.104462 | + | 0.994529i | \(0.533312\pi\) | |||||||
\(644\) | 21.7015 | 0.855159 | ||||||||
\(645\) | 29.2755 | 1.15272 | ||||||||
\(646\) | −22.4906 | −0.884881 | ||||||||
\(647\) | −6.63540 | −0.260864 | −0.130432 | − | 0.991457i | \(-0.541636\pi\) | ||||
−0.130432 | + | 0.991457i | \(0.541636\pi\) | |||||||
\(648\) | 16.1339 | 0.633799 | ||||||||
\(649\) | 13.0334 | 0.511607 | ||||||||
\(650\) | 12.2737 | 0.481413 | ||||||||
\(651\) | 12.5522 | 0.491958 | ||||||||
\(652\) | 50.8096 | 1.98986 | ||||||||
\(653\) | −48.2227 | −1.88710 | −0.943550 | − | 0.331231i | \(-0.892536\pi\) | ||||
−0.943550 | + | 0.331231i | \(0.892536\pi\) | |||||||
\(654\) | −88.9057 | −3.47649 | ||||||||
\(655\) | −21.0653 | −0.823091 | ||||||||
\(656\) | −1.10971 | −0.0433271 | ||||||||
\(657\) | −4.80322 | −0.187392 | ||||||||
\(658\) | −21.0065 | −0.818917 | ||||||||
\(659\) | −44.4986 | −1.73342 | −0.866710 | − | 0.498813i | \(-0.833769\pi\) | ||||
−0.866710 | + | 0.498813i | \(0.833769\pi\) | |||||||
\(660\) | −34.2656 | −1.33379 | ||||||||
\(661\) | 9.27332 | 0.360691 | 0.180345 | − | 0.983603i | \(-0.442278\pi\) | ||||
0.180345 | + | 0.983603i | \(0.442278\pi\) | |||||||
\(662\) | −40.1698 | −1.56124 | ||||||||
\(663\) | 22.6638 | 0.880188 | ||||||||
\(664\) | 13.3867 | 0.519505 | ||||||||
\(665\) | −6.19834 | −0.240361 | ||||||||
\(666\) | −28.4760 | −1.10342 | ||||||||
\(667\) | −32.4032 | −1.25466 | ||||||||
\(668\) | 44.1340 | 1.70760 | ||||||||
\(669\) | 52.1716 | 2.01707 | ||||||||
\(670\) | 5.25796 | 0.203133 | ||||||||
\(671\) | 27.0175 | 1.04300 | ||||||||
\(672\) | 17.9103 | 0.690903 | ||||||||
\(673\) | −17.9728 | −0.692802 | −0.346401 | − | 0.938087i | \(-0.612596\pi\) | ||||
−0.346401 | + | 0.938087i | \(0.612596\pi\) | |||||||
\(674\) | −30.4681 | −1.17359 | ||||||||
\(675\) | 0.0589907 | 0.00227055 | ||||||||
\(676\) | 51.4753 | 1.97982 | ||||||||
\(677\) | 1.40251 | 0.0539027 | 0.0269514 | − | 0.999637i | \(-0.491420\pi\) | ||||
0.0269514 | + | 0.999637i | \(0.491420\pi\) | |||||||
\(678\) | 15.9100 | 0.611022 | ||||||||
\(679\) | 4.86127 | 0.186559 | ||||||||
\(680\) | 2.98599 | 0.114507 | ||||||||
\(681\) | −18.4484 | −0.706946 | ||||||||
\(682\) | 55.5450 | 2.12693 | ||||||||
\(683\) | 8.22770 | 0.314824 | 0.157412 | − | 0.987533i | \(-0.449685\pi\) | ||||
0.157412 | + | 0.987533i | \(0.449685\pi\) | |||||||
\(684\) | −52.9130 | −2.02318 | ||||||||
\(685\) | 1.87977 | 0.0718222 | ||||||||
\(686\) | −2.19612 | −0.0838481 | ||||||||
\(687\) | 2.45439 | 0.0936409 | ||||||||
\(688\) | −20.0021 | −0.762572 | ||||||||
\(689\) | −27.0693 | −1.03126 | ||||||||
\(690\) | −41.4371 | −1.57748 | ||||||||
\(691\) | 47.0264 | 1.78897 | 0.894485 | − | 0.447098i | \(-0.147543\pi\) | ||||
0.894485 | + | 0.447098i | \(0.147543\pi\) | |||||||
\(692\) | 8.69231 | 0.330432 | ||||||||
\(693\) | −14.9555 | −0.568113 | ||||||||
\(694\) | 9.74956 | 0.370088 | ||||||||
\(695\) | 7.48345 | 0.283863 | ||||||||
\(696\) | 18.6964 | 0.708687 | ||||||||
\(697\) | −1.09337 | −0.0414143 | ||||||||
\(698\) | −27.6446 | −1.04637 | ||||||||
\(699\) | 36.0098 | 1.36202 | ||||||||
\(700\) | 2.82293 | 0.106697 | ||||||||
\(701\) | −25.0204 | −0.945007 | −0.472504 | − | 0.881329i | \(-0.656650\pi\) | ||||
−0.472504 | + | 0.881329i | \(0.656650\pi\) | |||||||
\(702\) | 0.724031 | 0.0273268 | ||||||||
\(703\) | −26.5774 | −1.00239 | ||||||||
\(704\) | 62.6686 | 2.36191 | ||||||||
\(705\) | 23.4769 | 0.884192 | ||||||||
\(706\) | −68.6972 | −2.58545 | ||||||||
\(707\) | 6.02446 | 0.226573 | ||||||||
\(708\) | −18.2595 | −0.686233 | ||||||||
\(709\) | 16.2255 | 0.609362 | 0.304681 | − | 0.952454i | \(-0.401450\pi\) | ||||
0.304681 | + | 0.952454i | \(0.401450\pi\) | |||||||
\(710\) | −16.1681 | −0.606779 | ||||||||
\(711\) | −11.0394 | −0.414012 | ||||||||
\(712\) | −24.2781 | −0.909862 | ||||||||
\(713\) | 39.3156 | 1.47238 | ||||||||
\(714\) | 8.90572 | 0.333288 | ||||||||
\(715\) | 27.6397 | 1.03367 | ||||||||
\(716\) | −20.0954 | −0.751000 | ||||||||
\(717\) | 65.0010 | 2.42751 | ||||||||
\(718\) | 52.2939 | 1.95159 | ||||||||
\(719\) | −15.4971 | −0.577946 | −0.288973 | − | 0.957337i | \(-0.593314\pi\) | ||||
−0.288973 | + | 0.957337i | \(0.593314\pi\) | |||||||
\(720\) | −5.07109 | −0.188989 | ||||||||
\(721\) | 13.6572 | 0.508619 | ||||||||
\(722\) | −42.6474 | −1.58717 | ||||||||
\(723\) | −17.4251 | −0.648047 | ||||||||
\(724\) | −50.3945 | −1.87290 | ||||||||
\(725\) | −4.21500 | −0.156541 | ||||||||
\(726\) | −72.5430 | −2.69232 | ||||||||
\(727\) | −27.6644 | −1.02602 | −0.513008 | − | 0.858384i | \(-0.671469\pi\) | ||||
−0.513008 | + | 0.858384i | \(0.671469\pi\) | |||||||
\(728\) | 10.1004 | 0.374344 | ||||||||
\(729\) | −27.4309 | −1.01596 | ||||||||
\(730\) | 3.48820 | 0.129104 | ||||||||
\(731\) | −19.7074 | −0.728905 | ||||||||
\(732\) | −37.8508 | −1.39901 | ||||||||
\(733\) | −1.98455 | −0.0733010 | −0.0366505 | − | 0.999328i | \(-0.511669\pi\) | ||||
−0.0366505 | + | 0.999328i | \(0.511669\pi\) | |||||||
\(734\) | −26.9508 | −0.994772 | ||||||||
\(735\) | 2.45439 | 0.0905316 | ||||||||
\(736\) | 56.0981 | 2.06780 | ||||||||
\(737\) | 11.8407 | 0.436157 | ||||||||
\(738\) | −4.39480 | −0.161775 | ||||||||
\(739\) | 35.2231 | 1.29570 | 0.647852 | − | 0.761766i | \(-0.275667\pi\) | ||||
0.647852 | + | 0.761766i | \(0.275667\pi\) | |||||||
\(740\) | 12.1042 | 0.444960 | ||||||||
\(741\) | 85.0233 | 3.12341 | ||||||||
\(742\) | −10.6369 | −0.390491 | ||||||||
\(743\) | 36.9688 | 1.35625 | 0.678127 | − | 0.734945i | \(-0.262792\pi\) | ||||
0.678127 | + | 0.734945i | \(0.262792\pi\) | |||||||
\(744\) | −22.6849 | −0.831668 | ||||||||
\(745\) | 6.61991 | 0.242535 | ||||||||
\(746\) | −29.9516 | −1.09661 | ||||||||
\(747\) | −22.3997 | −0.819563 | ||||||||
\(748\) | 23.0667 | 0.843400 | ||||||||
\(749\) | −10.8007 | −0.394647 | ||||||||
\(750\) | −5.39013 | −0.196820 | ||||||||
\(751\) | −0.0711650 | −0.00259685 | −0.00129842 | − | 0.999999i | \(-0.500413\pi\) | ||||
−0.00129842 | + | 0.999999i | \(0.500413\pi\) | |||||||
\(752\) | −16.0403 | −0.584929 | ||||||||
\(753\) | −10.1917 | −0.371405 | ||||||||
\(754\) | −51.7335 | −1.88402 | ||||||||
\(755\) | −3.76214 | −0.136918 | ||||||||
\(756\) | 0.166526 | 0.00605651 | ||||||||
\(757\) | −45.4618 | −1.65234 | −0.826169 | − | 0.563422i | \(-0.809485\pi\) | ||||
−0.826169 | + | 0.563422i | \(0.809485\pi\) | |||||||
\(758\) | −75.4867 | −2.74180 | ||||||||
\(759\) | −93.3144 | −3.38710 | ||||||||
\(760\) | 11.2019 | 0.406337 | ||||||||
\(761\) | −37.6826 | −1.36599 | −0.682997 | − | 0.730421i | \(-0.739324\pi\) | ||||
−0.682997 | + | 0.730421i | \(0.739324\pi\) | |||||||
\(762\) | −112.554 | −4.07739 | ||||||||
\(763\) | 16.4942 | 0.597129 | ||||||||
\(764\) | 17.2833 | 0.625290 | ||||||||
\(765\) | −4.99639 | −0.180645 | ||||||||
\(766\) | 63.2242 | 2.28438 | ||||||||
\(767\) | 14.7287 | 0.531821 | ||||||||
\(768\) | −9.13082 | −0.329480 | ||||||||
\(769\) | 3.73886 | 0.134827 | 0.0674133 | − | 0.997725i | \(-0.478525\pi\) | ||||
0.0674133 | + | 0.997725i | \(0.478525\pi\) | |||||||
\(770\) | 10.8610 | 0.391404 | ||||||||
\(771\) | −41.9231 | −1.50982 | ||||||||
\(772\) | −63.8760 | −2.29895 | ||||||||
\(773\) | −32.0112 | −1.15136 | −0.575682 | − | 0.817674i | \(-0.695263\pi\) | ||||
−0.575682 | + | 0.817674i | \(0.695263\pi\) | |||||||
\(774\) | −79.2140 | −2.84729 | ||||||||
\(775\) | 5.11417 | 0.183706 | ||||||||
\(776\) | −8.78553 | −0.315382 | ||||||||
\(777\) | 10.5240 | 0.377546 | ||||||||
\(778\) | 28.5871 | 1.02490 | ||||||||
\(779\) | −4.10178 | −0.146961 | ||||||||
\(780\) | −38.7224 | −1.38648 | ||||||||
\(781\) | −36.4098 | −1.30285 | ||||||||
\(782\) | 27.8943 | 0.997498 | ||||||||
\(783\) | −0.248645 | −0.00888586 | ||||||||
\(784\) | −1.67693 | −0.0598903 | ||||||||
\(785\) | −9.63194 | −0.343779 | ||||||||
\(786\) | 113.545 | 4.05001 | ||||||||
\(787\) | 15.7829 | 0.562599 | 0.281300 | − | 0.959620i | \(-0.409235\pi\) | ||||
0.281300 | + | 0.959620i | \(0.409235\pi\) | |||||||
\(788\) | −16.9928 | −0.605345 | ||||||||
\(789\) | 26.9935 | 0.960994 | ||||||||
\(790\) | 8.01707 | 0.285235 | ||||||||
\(791\) | −2.95170 | −0.104950 | ||||||||
\(792\) | 27.0283 | 0.960410 | ||||||||
\(793\) | 30.5316 | 1.08421 | ||||||||
\(794\) | −58.5342 | −2.07730 | ||||||||
\(795\) | 11.8878 | 0.421617 | ||||||||
\(796\) | 27.2512 | 0.965893 | ||||||||
\(797\) | 10.5919 | 0.375183 | 0.187592 | − | 0.982247i | \(-0.439932\pi\) | ||||
0.187592 | + | 0.982247i | \(0.439932\pi\) | |||||||
\(798\) | 33.4099 | 1.18270 | ||||||||
\(799\) | −15.8040 | −0.559106 | ||||||||
\(800\) | 7.29723 | 0.257996 | ||||||||
\(801\) | 40.6242 | 1.43538 | ||||||||
\(802\) | −9.28780 | −0.327964 | ||||||||
\(803\) | 7.85527 | 0.277206 | ||||||||
\(804\) | −16.5884 | −0.585029 | ||||||||
\(805\) | 7.68759 | 0.270952 | ||||||||
\(806\) | 62.7695 | 2.21096 | ||||||||
\(807\) | 22.9984 | 0.809580 | ||||||||
\(808\) | −10.8877 | −0.383028 | ||||||||
\(809\) | −22.3987 | −0.787498 | −0.393749 | − | 0.919218i | \(-0.628822\pi\) | ||||
−0.393749 | + | 0.919218i | \(0.628822\pi\) | |||||||
\(810\) | 19.6054 | 0.688865 | ||||||||
\(811\) | −28.2714 | −0.992742 | −0.496371 | − | 0.868110i | \(-0.665334\pi\) | ||||
−0.496371 | + | 0.868110i | \(0.665334\pi\) | |||||||
\(812\) | −11.8986 | −0.417560 | ||||||||
\(813\) | −55.6255 | −1.95087 | ||||||||
\(814\) | 46.5701 | 1.63228 | ||||||||
\(815\) | 17.9989 | 0.630473 | ||||||||
\(816\) | 6.80031 | 0.238058 | ||||||||
\(817\) | −73.9325 | −2.58657 | ||||||||
\(818\) | −44.6127 | −1.55985 | ||||||||
\(819\) | −16.9007 | −0.590559 | ||||||||
\(820\) | 1.86808 | 0.0652363 | ||||||||
\(821\) | 53.4893 | 1.86679 | 0.933394 | − | 0.358852i | \(-0.116832\pi\) | ||||
0.933394 | + | 0.358852i | \(0.116832\pi\) | |||||||
\(822\) | −10.1322 | −0.353401 | ||||||||
\(823\) | 44.2763 | 1.54338 | 0.771688 | − | 0.636001i | \(-0.219413\pi\) | ||||
0.771688 | + | 0.636001i | \(0.219413\pi\) | |||||||
\(824\) | −24.6819 | −0.859833 | ||||||||
\(825\) | −12.1383 | −0.422602 | ||||||||
\(826\) | 5.78762 | 0.201377 | ||||||||
\(827\) | −35.2492 | −1.22574 | −0.612868 | − | 0.790185i | \(-0.709984\pi\) | ||||
−0.612868 | + | 0.790185i | \(0.709984\pi\) | |||||||
\(828\) | 65.6261 | 2.28067 | ||||||||
\(829\) | 37.7323 | 1.31050 | 0.655248 | − | 0.755414i | \(-0.272564\pi\) | ||||
0.655248 | + | 0.755414i | \(0.272564\pi\) | |||||||
\(830\) | 16.2671 | 0.564641 | ||||||||
\(831\) | 79.5609 | 2.75994 | ||||||||
\(832\) | 70.8197 | 2.45523 | ||||||||
\(833\) | −1.65223 | −0.0572463 | ||||||||
\(834\) | −40.3368 | −1.39675 | ||||||||
\(835\) | 15.6341 | 0.541041 | ||||||||
\(836\) | 86.5347 | 2.99287 | ||||||||
\(837\) | 0.301688 | 0.0104279 | ||||||||
\(838\) | 46.6331 | 1.61091 | ||||||||
\(839\) | 42.0150 | 1.45052 | 0.725260 | − | 0.688476i | \(-0.241720\pi\) | ||||
0.725260 | + | 0.688476i | \(0.241720\pi\) | |||||||
\(840\) | −4.43569 | −0.153046 | ||||||||
\(841\) | −11.2338 | −0.387372 | ||||||||
\(842\) | 15.3165 | 0.527843 | ||||||||
\(843\) | −70.3850 | −2.42419 | ||||||||
\(844\) | 74.6255 | 2.56872 | ||||||||
\(845\) | 18.2347 | 0.627293 | ||||||||
\(846\) | −63.5243 | −2.18401 | ||||||||
\(847\) | 13.4585 | 0.462439 | ||||||||
\(848\) | −8.12218 | −0.278917 | ||||||||
\(849\) | 52.7424 | 1.81011 | ||||||||
\(850\) | 3.62848 | 0.124456 | ||||||||
\(851\) | 32.9630 | 1.12996 | ||||||||
\(852\) | 51.0091 | 1.74754 | ||||||||
\(853\) | 33.9468 | 1.16232 | 0.581158 | − | 0.813791i | \(-0.302600\pi\) | ||||
0.581158 | + | 0.813791i | \(0.302600\pi\) | |||||||
\(854\) | 11.9974 | 0.410542 | ||||||||
\(855\) | −18.7440 | −0.641032 | ||||||||
\(856\) | 19.5195 | 0.667161 | ||||||||
\(857\) | −15.4007 | −0.526079 | −0.263040 | − | 0.964785i | \(-0.584725\pi\) | ||||
−0.263040 | + | 0.964785i | \(0.584725\pi\) | |||||||
\(858\) | −148.982 | −5.08615 | ||||||||
\(859\) | 9.31017 | 0.317659 | 0.158829 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158829 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(860\) | 33.6713 | 1.14818 | ||||||||
\(861\) | 1.62420 | 0.0553527 | ||||||||
\(862\) | −15.5434 | −0.529409 | ||||||||
\(863\) | −56.1301 | −1.91069 | −0.955345 | − | 0.295493i | \(-0.904516\pi\) | ||||
−0.955345 | + | 0.295493i | \(0.904516\pi\) | |||||||
\(864\) | 0.430468 | 0.0146448 | ||||||||
\(865\) | 3.07918 | 0.104695 | ||||||||
\(866\) | −10.0657 | −0.342046 | ||||||||
\(867\) | −35.0245 | −1.18949 | ||||||||
\(868\) | 14.4369 | 0.490021 | ||||||||
\(869\) | 18.0541 | 0.612443 | ||||||||
\(870\) | 22.7194 | 0.770259 | ||||||||
\(871\) | 13.3807 | 0.453389 | ||||||||
\(872\) | −29.8091 | −1.00946 | ||||||||
\(873\) | 14.7007 | 0.497542 | ||||||||
\(874\) | 104.646 | 3.53969 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −11.0050 | −0.371824 | ||||||||
\(877\) | 25.6779 | 0.867082 | 0.433541 | − | 0.901134i | \(-0.357264\pi\) | ||||
0.433541 | + | 0.901134i | \(0.357264\pi\) | |||||||
\(878\) | −28.9761 | −0.977895 | ||||||||
\(879\) | −60.0320 | −2.02483 | ||||||||
\(880\) | 8.29334 | 0.279569 | ||||||||
\(881\) | 5.02781 | 0.169391 | 0.0846955 | − | 0.996407i | \(-0.473008\pi\) | ||||
0.0846955 | + | 0.996407i | \(0.473008\pi\) | |||||||
\(882\) | −6.64113 | −0.223619 | ||||||||
\(883\) | −39.5017 | −1.32934 | −0.664670 | − | 0.747137i | \(-0.731428\pi\) | ||||
−0.664670 | + | 0.747137i | \(0.731428\pi\) | |||||||
\(884\) | 26.0668 | 0.876723 | ||||||||
\(885\) | −6.46827 | −0.217428 | ||||||||
\(886\) | 33.0434 | 1.11011 | ||||||||
\(887\) | 15.0545 | 0.505480 | 0.252740 | − | 0.967534i | \(-0.418668\pi\) | ||||
0.252740 | + | 0.967534i | \(0.418668\pi\) | |||||||
\(888\) | −19.0195 | −0.638252 | ||||||||
\(889\) | 20.8814 | 0.700341 | ||||||||
\(890\) | −29.5021 | −0.988913 | ||||||||
\(891\) | 44.1505 | 1.47910 | ||||||||
\(892\) | 60.0054 | 2.00913 | ||||||||
\(893\) | −59.2889 | −1.98403 | ||||||||
\(894\) | −35.6822 | −1.19339 | ||||||||
\(895\) | −7.11863 | −0.237950 | ||||||||
\(896\) | 13.2341 | 0.442120 | ||||||||
\(897\) | −105.451 | −3.52092 | ||||||||
\(898\) | −21.8270 | −0.728376 | ||||||||
\(899\) | −21.5562 | −0.718939 | ||||||||
\(900\) | 8.53664 | 0.284555 | ||||||||
\(901\) | −8.00254 | −0.266603 | ||||||||
\(902\) | 7.18732 | 0.239311 | ||||||||
\(903\) | 29.2755 | 0.974226 | ||||||||
\(904\) | 5.33446 | 0.177421 | ||||||||
\(905\) | −17.8518 | −0.593415 | ||||||||
\(906\) | 20.2784 | 0.673705 | ||||||||
\(907\) | −46.1079 | −1.53099 | −0.765493 | − | 0.643444i | \(-0.777505\pi\) | ||||
−0.765493 | + | 0.643444i | \(0.777505\pi\) | |||||||
\(908\) | −21.2186 | −0.704163 | ||||||||
\(909\) | 18.2182 | 0.604259 | ||||||||
\(910\) | 12.2737 | 0.406868 | ||||||||
\(911\) | 47.2701 | 1.56613 | 0.783064 | − | 0.621941i | \(-0.213656\pi\) | ||||
0.783064 | + | 0.621941i | \(0.213656\pi\) | |||||||
\(912\) | 25.5114 | 0.844767 | ||||||||
\(913\) | 36.6328 | 1.21237 | ||||||||
\(914\) | 6.46014 | 0.213682 | ||||||||
\(915\) | −13.4083 | −0.443266 | ||||||||
\(916\) | 2.82293 | 0.0932722 | ||||||||
\(917\) | −21.0653 | −0.695639 | ||||||||
\(918\) | 0.214047 | 0.00706459 | ||||||||
\(919\) | 4.03568 | 0.133125 | 0.0665625 | − | 0.997782i | \(-0.478797\pi\) | ||||
0.0665625 | + | 0.997782i | \(0.478797\pi\) | |||||||
\(920\) | −13.8934 | −0.458051 | ||||||||
\(921\) | −8.57491 | −0.282553 | ||||||||
\(922\) | −28.0804 | −0.924778 | ||||||||
\(923\) | −41.1455 | −1.35432 | ||||||||
\(924\) | −34.2656 | −1.12726 | ||||||||
\(925\) | 4.28782 | 0.140983 | ||||||||
\(926\) | −5.14625 | −0.169116 | ||||||||
\(927\) | 41.2997 | 1.35646 | ||||||||
\(928\) | −30.7578 | −1.00967 | ||||||||
\(929\) | −23.2005 | −0.761184 | −0.380592 | − | 0.924743i | \(-0.624280\pi\) | ||||
−0.380592 | + | 0.924743i | \(0.624280\pi\) | |||||||
\(930\) | −27.5660 | −0.903925 | ||||||||
\(931\) | −6.19834 | −0.203143 | ||||||||
\(932\) | 41.4169 | 1.35666 | ||||||||
\(933\) | 53.6588 | 1.75671 | ||||||||
\(934\) | 56.7774 | 1.85781 | ||||||||
\(935\) | 8.17118 | 0.267226 | ||||||||
\(936\) | 30.5438 | 0.998356 | ||||||||
\(937\) | 28.5313 | 0.932079 | 0.466039 | − | 0.884764i | \(-0.345681\pi\) | ||||
0.466039 | + | 0.884764i | \(0.345681\pi\) | |||||||
\(938\) | 5.25796 | 0.171678 | ||||||||
\(939\) | −52.5426 | −1.71466 | ||||||||
\(940\) | 27.0021 | 0.880711 | ||||||||
\(941\) | 40.6349 | 1.32466 | 0.662329 | − | 0.749213i | \(-0.269568\pi\) | ||||
0.662329 | + | 0.749213i | \(0.269568\pi\) | |||||||
\(942\) | 51.9174 | 1.69156 | ||||||||
\(943\) | 5.08729 | 0.165665 | ||||||||
\(944\) | 4.41936 | 0.143838 | ||||||||
\(945\) | 0.0589907 | 0.00191897 | ||||||||
\(946\) | 129.548 | 4.21196 | ||||||||
\(947\) | 52.2132 | 1.69670 | 0.848350 | − | 0.529435i | \(-0.177596\pi\) | ||||
0.848350 | + | 0.529435i | \(0.177596\pi\) | |||||||
\(948\) | −25.2932 | −0.821486 | ||||||||
\(949\) | 8.87697 | 0.288159 | ||||||||
\(950\) | 13.6123 | 0.441641 | ||||||||
\(951\) | 68.9721 | 2.23657 | ||||||||
\(952\) | 2.98599 | 0.0967763 | ||||||||
\(953\) | −25.8371 | −0.836945 | −0.418472 | − | 0.908230i | \(-0.637434\pi\) | ||||
−0.418472 | + | 0.908230i | \(0.637434\pi\) | |||||||
\(954\) | −32.1662 | −1.04142 | ||||||||
\(955\) | 6.12249 | 0.198119 | ||||||||
\(956\) | 74.7612 | 2.41795 | ||||||||
\(957\) | 51.1630 | 1.65386 | ||||||||
\(958\) | 23.2119 | 0.749944 | ||||||||
\(959\) | 1.87977 | 0.0607008 | ||||||||
\(960\) | −31.1013 | −1.00379 | ||||||||
\(961\) | −4.84531 | −0.156300 | ||||||||
\(962\) | 52.6273 | 1.69677 | ||||||||
\(963\) | −32.6615 | −1.05250 | ||||||||
\(964\) | −20.0416 | −0.645496 | ||||||||
\(965\) | −22.6276 | −0.728407 | ||||||||
\(966\) | −41.4371 | −1.33322 | ||||||||
\(967\) | 16.2900 | 0.523850 | 0.261925 | − | 0.965088i | \(-0.415643\pi\) | ||||
0.261925 | + | 0.965088i | \(0.415643\pi\) | |||||||
\(968\) | −24.3228 | −0.781765 | ||||||||
\(969\) | 25.1356 | 0.807472 | ||||||||
\(970\) | −10.6759 | −0.342783 | ||||||||
\(971\) | −1.49540 | −0.0479898 | −0.0239949 | − | 0.999712i | \(-0.507639\pi\) | ||||
−0.0239949 | + | 0.999712i | \(0.507639\pi\) | |||||||
\(972\) | −62.3531 | −1.99998 | ||||||||
\(973\) | 7.48345 | 0.239908 | ||||||||
\(974\) | 57.6134 | 1.84605 | ||||||||
\(975\) | −13.7171 | −0.439299 | ||||||||
\(976\) | 9.16107 | 0.293239 | ||||||||
\(977\) | 14.0931 | 0.450877 | 0.225439 | − | 0.974257i | \(-0.427618\pi\) | ||||
0.225439 | + | 0.974257i | \(0.427618\pi\) | |||||||
\(978\) | −97.0163 | −3.10224 | ||||||||
\(979\) | −66.4374 | −2.12335 | ||||||||
\(980\) | 2.82293 | 0.0901752 | ||||||||
\(981\) | 49.8789 | 1.59251 | ||||||||
\(982\) | 37.0479 | 1.18225 | ||||||||
\(983\) | 9.43406 | 0.300900 | 0.150450 | − | 0.988618i | \(-0.451928\pi\) | ||||
0.150450 | + | 0.988618i | \(0.451928\pi\) | |||||||
\(984\) | −2.93534 | −0.0935751 | ||||||||
\(985\) | −6.01958 | −0.191800 | ||||||||
\(986\) | −15.2941 | −0.487062 | ||||||||
\(987\) | 23.4769 | 0.747279 | ||||||||
\(988\) | 97.7900 | 3.11111 | ||||||||
\(989\) | 91.6959 | 2.91576 | ||||||||
\(990\) | 32.8441 | 1.04385 | ||||||||
\(991\) | 53.5621 | 1.70146 | 0.850728 | − | 0.525606i | \(-0.176162\pi\) | ||||
0.850728 | + | 0.525606i | \(0.176162\pi\) | |||||||
\(992\) | 37.3192 | 1.18489 | ||||||||
\(993\) | 44.8940 | 1.42467 | ||||||||
\(994\) | −16.1681 | −0.512822 | ||||||||
\(995\) | 9.65352 | 0.306037 | ||||||||
\(996\) | −51.3215 | −1.62618 | ||||||||
\(997\) | 30.0774 | 0.952561 | 0.476280 | − | 0.879294i | \(-0.341985\pi\) | ||||
0.476280 | + | 0.879294i | \(0.341985\pi\) | |||||||
\(998\) | −28.0307 | −0.887295 | ||||||||
\(999\) | 0.252942 | 0.00800272 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8015.2.a.o.1.11 | ✓ | 73 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.o.1.11 | ✓ | 73 | 1.1 | even | 1 | trivial |