Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(40,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.40");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.g (of order \(10\), degree \(4\), not minimal) |
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: | no |
Analytic conductor: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 118.2 | ||
Root | \(-1.29715 + 0.104262i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.118 |
Dual form | 363.3.g.g.40.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.797149 | − | 1.09718i | −0.398574 | − | 0.548591i | 0.561811 | − | 0.827266i | \(-0.310105\pi\) |
−0.960385 | + | 0.278675i | \(0.910105\pi\) | |||||||
\(3\) | −0.535233 | − | 1.64728i | −0.178411 | − | 0.549093i | ||||
\(4\) | 0.667707 | − | 2.05499i | 0.166927 | − | 0.513748i | ||||
\(5\) | −1.85613 | − | 1.34856i | −0.371226 | − | 0.269711i | 0.386493 | − | 0.922292i | \(-0.373686\pi\) |
−0.757719 | + | 0.652581i | \(0.773686\pi\) | |||||||
\(6\) | −1.38070 | + | 1.90037i | −0.230117 | + | 0.316729i | ||||
\(7\) | −9.29312 | − | 3.01952i | −1.32759 | − | 0.431360i | −0.442494 | − | 0.896771i | \(-0.645906\pi\) |
−0.885094 | + | 0.465412i | \(0.845906\pi\) | |||||||
\(8\) | −7.94622 | + | 2.58188i | −0.993277 | + | 0.322735i | ||||
\(9\) | −2.42705 | + | 1.76336i | −0.269672 | + | 0.195928i | ||||
\(10\) | 3.11151i | 0.311151i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.74252 | −0.311877 | ||||||||
\(13\) | 9.04570 | + | 12.4503i | 0.695823 | + | 0.957719i | 0.999987 | + | 0.00509895i | \(0.00162305\pi\) |
−0.304164 | + | 0.952620i | \(0.598377\pi\) | |||||||
\(14\) | 4.09504 | + | 12.6032i | 0.292503 | + | 0.900232i | ||||
\(15\) | −1.22799 | + | 3.77935i | −0.0818658 | + | 0.251957i | ||||
\(16\) | 2.17479 | + | 1.58008i | 0.135924 | + | 0.0987547i | ||||
\(17\) | −6.94586 | + | 9.56015i | −0.408580 | + | 0.562362i | −0.962871 | − | 0.269961i | \(-0.912989\pi\) |
0.554292 | + | 0.832323i | \(0.312989\pi\) | |||||||
\(18\) | 3.86944 | + | 1.25726i | 0.214969 | + | 0.0698477i | ||||
\(19\) | 11.4934 | − | 3.73442i | 0.604914 | − | 0.196548i | 0.00948292 | − | 0.999955i | \(-0.496981\pi\) |
0.595431 | + | 0.803407i | \(0.296981\pi\) | |||||||
\(20\) | −4.01063 | + | 2.91389i | −0.200531 | + | 0.145695i | ||||
\(21\) | 16.9245i | 0.805929i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.6610 | 0.724390 | 0.362195 | − | 0.932102i | \(-0.382027\pi\) | ||||
0.362195 | + | 0.932102i | \(0.382027\pi\) | |||||||
\(24\) | 8.50616 | + | 11.7077i | 0.354423 | + | 0.487822i | ||||
\(25\) | −6.09881 | − | 18.7702i | −0.243953 | − | 0.750809i | ||||
\(26\) | 6.44951 | − | 19.8496i | 0.248058 | − | 0.763444i | ||||
\(27\) | 4.20378 | + | 3.05422i | 0.155695 | + | 0.113119i | ||||
\(28\) | −12.4102 | + | 17.0811i | −0.443220 | + | 0.610041i | ||||
\(29\) | −25.2435 | − | 8.20211i | −0.870466 | − | 0.282831i | −0.160473 | − | 0.987040i | \(-0.551302\pi\) |
−0.709993 | + | 0.704209i | \(0.751302\pi\) | |||||||
\(30\) | 5.12553 | − | 1.66538i | 0.170851 | − | 0.0555128i | ||||
\(31\) | −3.36662 | + | 2.44599i | −0.108601 | + | 0.0789031i | −0.640760 | − | 0.767741i | \(-0.721381\pi\) |
0.532159 | + | 0.846644i | \(0.321381\pi\) | |||||||
\(32\) | 29.7749i | 0.930466i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 16.0261 | 0.471356 | ||||||||
\(35\) | 13.1772 | + | 18.1369i | 0.376493 | + | 0.518198i | ||||
\(36\) | 2.00312 | + | 6.16498i | 0.0556423 | + | 0.171249i | ||||
\(37\) | 20.8036 | − | 64.0270i | 0.562260 | − | 1.73046i | −0.113693 | − | 0.993516i | \(-0.536268\pi\) |
0.675954 | − | 0.736944i | \(-0.263732\pi\) | |||||||
\(38\) | −13.2593 | − | 9.63341i | −0.348928 | − | 0.253511i | ||||
\(39\) | 15.6676 | − | 21.5646i | 0.401734 | − | 0.552939i | ||||
\(40\) | 18.2310 | + | 5.92362i | 0.455776 | + | 0.148090i | ||||
\(41\) | −17.1641 | + | 5.57695i | −0.418636 | + | 0.136023i | −0.510758 | − | 0.859725i | \(-0.670635\pi\) |
0.0921216 | + | 0.995748i | \(0.470635\pi\) | |||||||
\(42\) | 18.5692 | − | 13.4913i | 0.442125 | − | 0.321223i | ||||
\(43\) | 46.3735i | 1.07845i | 0.842160 | + | 0.539227i | \(0.181284\pi\) | ||||
−0.842160 | + | 0.539227i | \(0.818716\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.88291 | 0.152954 | ||||||||
\(46\) | −13.2813 | − | 18.2801i | −0.288723 | − | 0.397394i | ||||
\(47\) | 18.8238 | + | 57.9336i | 0.400505 | + | 1.23263i | 0.924590 | + | 0.380963i | \(0.124407\pi\) |
−0.524085 | + | 0.851666i | \(0.675593\pi\) | |||||||
\(48\) | 1.43881 | − | 4.42819i | 0.0299751 | − | 0.0922539i | ||||
\(49\) | 37.6028 | + | 27.3200i | 0.767404 | + | 0.557551i | ||||
\(50\) | −15.7327 | + | 21.6542i | −0.314653 | + | 0.433083i | ||||
\(51\) | 19.4659 | + | 6.32485i | 0.381684 | + | 0.124017i | ||||
\(52\) | 31.6252 | − | 10.2757i | 0.608178 | − | 0.197609i | ||||
\(53\) | −81.8850 | + | 59.4929i | −1.54500 | + | 1.12251i | −0.597900 | + | 0.801571i | \(0.703998\pi\) |
−0.947100 | + | 0.320937i | \(0.896002\pi\) | |||||||
\(54\) | − | 7.04697i | − | 0.130500i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 81.6412 | 1.45788 | ||||||||
\(57\) | −12.3033 | − | 16.9340i | −0.215847 | − | 0.297087i | ||||
\(58\) | 11.1236 | + | 34.2350i | 0.191787 | + | 0.590259i | ||||
\(59\) | −30.0654 | + | 92.5318i | −0.509583 | + | 1.56834i | 0.283344 | + | 0.959018i | \(0.408556\pi\) |
−0.792927 | + | 0.609317i | \(0.791444\pi\) | |||||||
\(60\) | 6.94661 | + | 5.04701i | 0.115777 | + | 0.0841168i | ||||
\(61\) | −0.739825 | + | 1.01828i | −0.0121283 | + | 0.0166931i | −0.815038 | − | 0.579407i | \(-0.803284\pi\) |
0.802910 | + | 0.596101i | \(0.203284\pi\) | |||||||
\(62\) | 5.36740 | + | 1.74397i | 0.0865710 | + | 0.0281286i | ||||
\(63\) | 27.8794 | − | 9.05855i | 0.442530 | − | 0.143787i | ||||
\(64\) | 41.3676 | − | 30.0553i | 0.646369 | − | 0.469615i | ||||
\(65\) | − | 35.3081i | − | 0.543202i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −55.1168 | −0.822638 | −0.411319 | − | 0.911491i | \(-0.634932\pi\) | ||||
−0.411319 | + | 0.911491i | \(0.634932\pi\) | |||||||
\(68\) | 15.0082 | + | 20.6571i | 0.220709 | + | 0.303780i | ||||
\(69\) | −8.91750 | − | 27.4453i | −0.129239 | − | 0.397757i | ||||
\(70\) | 9.39527 | − | 28.9157i | 0.134218 | − | 0.413081i | ||||
\(71\) | 12.0997 | + | 8.79093i | 0.170418 | + | 0.123816i | 0.669725 | − | 0.742609i | \(-0.266412\pi\) |
−0.499307 | + | 0.866425i | \(0.666412\pi\) | |||||||
\(72\) | 14.7331 | − | 20.2784i | 0.204626 | − | 0.281644i | ||||
\(73\) | −72.1677 | − | 23.4487i | −0.988598 | − | 0.321215i | −0.230298 | − | 0.973120i | \(-0.573970\pi\) |
−0.758300 | + | 0.651905i | \(0.773970\pi\) | |||||||
\(74\) | −86.8328 | + | 28.2137i | −1.17342 | + | 0.381266i | ||||
\(75\) | −27.6555 | + | 20.0929i | −0.368740 | + | 0.267905i | ||||
\(76\) | − | 26.1123i | − | 0.343582i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −36.1497 | −0.463458 | ||||||||
\(79\) | −17.1751 | − | 23.6395i | −0.217407 | − | 0.299235i | 0.686358 | − | 0.727264i | \(-0.259208\pi\) |
−0.903765 | + | 0.428029i | \(0.859208\pi\) | |||||||
\(80\) | −1.90587 | − | 5.86565i | −0.0238233 | − | 0.0733206i | ||||
\(81\) | 2.78115 | − | 8.55951i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 19.8013 | + | 14.3865i | 0.241479 | + | 0.175445i | ||||
\(83\) | 3.74556 | − | 5.15531i | 0.0451272 | − | 0.0621122i | −0.785857 | − | 0.618408i | \(-0.787778\pi\) |
0.830984 | + | 0.556296i | \(0.187778\pi\) | |||||||
\(84\) | 34.7797 | + | 11.3006i | 0.414044 | + | 0.134531i | ||||
\(85\) | 25.7848 | − | 8.37800i | 0.303351 | − | 0.0985647i | ||||
\(86\) | 50.8802 | − | 36.9666i | 0.591630 | − | 0.429844i | ||||
\(87\) | 45.9731i | 0.528427i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.95503 | −0.0444385 | −0.0222193 | − | 0.999753i | \(-0.507073\pi\) | ||||
−0.0222193 | + | 0.999753i | \(0.507073\pi\) | |||||||
\(90\) | −5.48670 | − | 7.55180i | −0.0609634 | − | 0.0839089i | ||||
\(91\) | −46.4688 | − | 143.016i | −0.510646 | − | 1.57161i | ||||
\(92\) | 11.1247 | − | 34.2382i | 0.120920 | − | 0.372154i | ||||
\(93\) | 5.83116 | + | 4.23659i | 0.0627007 | + | 0.0455547i | ||||
\(94\) | 48.5583 | − | 66.8347i | 0.516577 | − | 0.711008i | ||||
\(95\) | −26.3692 | − | 8.56789i | −0.277571 | − | 0.0901883i | ||||
\(96\) | 49.0475 | − | 15.9365i | 0.510912 | − | 0.166005i | ||||
\(97\) | 26.8066 | − | 19.4762i | 0.276357 | − | 0.200785i | −0.440970 | − | 0.897522i | \(-0.645365\pi\) |
0.717327 | + | 0.696737i | \(0.245365\pi\) | |||||||
\(98\) | − | 63.0352i | − | 0.643216i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −42.6449 | −0.426449 | ||||||||
\(101\) | −57.0618 | − | 78.5388i | −0.564968 | − | 0.777612i | 0.426979 | − | 0.904261i | \(-0.359578\pi\) |
−0.991948 | + | 0.126649i | \(0.959578\pi\) | |||||||
\(102\) | −8.57770 | − | 26.3994i | −0.0840951 | − | 0.258818i | ||||
\(103\) | −57.4944 | + | 176.949i | −0.558198 | + | 1.71796i | 0.129148 | + | 0.991625i | \(0.458776\pi\) |
−0.687346 | + | 0.726330i | \(0.741224\pi\) | |||||||
\(104\) | −104.024 | − | 75.5782i | −1.00024 | − | 0.726713i | ||||
\(105\) | 22.8237 | − | 31.4141i | 0.217368 | − | 0.299182i | ||||
\(106\) | 130.549 | + | 42.4180i | 1.23160 | + | 0.400169i | ||||
\(107\) | −182.491 | + | 59.2950i | −1.70553 | + | 0.554159i | −0.989578 | − | 0.143995i | \(-0.954005\pi\) |
−0.715947 | + | 0.698154i | \(0.754005\pi\) | |||||||
\(108\) | 9.08329 | − | 6.59940i | 0.0841046 | − | 0.0611056i | ||||
\(109\) | − | 113.760i | − | 1.04367i | −0.853047 | − | 0.521834i | \(-0.825248\pi\) | ||
0.853047 | − | 0.521834i | \(-0.174752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −116.605 | −1.05050 | ||||||||
\(112\) | −15.4395 | − | 21.2506i | −0.137853 | − | 0.189738i | ||||
\(113\) | 5.06119 | + | 15.5768i | 0.0447893 | + | 0.137847i | 0.970950 | − | 0.239281i | \(-0.0769116\pi\) |
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(114\) | −8.77212 | + | 26.9978i | −0.0769484 | + | 0.236823i | ||||
\(115\) | −30.9249 | − | 22.4683i | −0.268912 | − | 0.195376i | ||||
\(116\) | −33.7106 | + | 46.3986i | −0.290608 | + | 0.399988i | ||||
\(117\) | −43.9088 | − | 14.2668i | −0.375289 | − | 0.121939i | ||||
\(118\) | 125.491 | − | 40.7744i | 1.06348 | − | 0.345546i | ||||
\(119\) | 93.4157 | − | 67.8705i | 0.785006 | − | 0.570340i | ||||
\(120\) | − | 33.2021i | − | 0.276684i | ||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.70699 | 0.0139917 | ||||||||
\(123\) | 18.3736 | + | 25.2891i | 0.149379 | + | 0.205602i | ||||
\(124\) | 2.77858 | + | 8.55159i | 0.0224079 | + | 0.0689645i | ||||
\(125\) | −31.7170 | + | 97.6148i | −0.253736 | + | 0.780919i | ||||
\(126\) | −32.1629 | − | 23.3677i | −0.255261 | − | 0.185458i | ||||
\(127\) | −3.28438 | + | 4.52055i | −0.0258612 | + | 0.0355949i | −0.821752 | − | 0.569846i | \(-0.807003\pi\) |
0.795891 | + | 0.605440i | \(0.207003\pi\) | |||||||
\(128\) | 47.3181 | + | 15.3746i | 0.369673 | + | 0.120114i | ||||
\(129\) | 76.3901 | − | 24.8207i | 0.592172 | − | 0.192408i | ||||
\(130\) | −38.7394 | + | 28.1458i | −0.297995 | + | 0.216506i | ||||
\(131\) | − | 225.713i | − | 1.72300i | −0.507758 | − | 0.861500i | \(-0.669526\pi\) | ||
0.507758 | − | 0.861500i | \(-0.330474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −118.085 | −0.887860 | ||||||||
\(134\) | 43.9363 | + | 60.4731i | 0.327883 | + | 0.451292i | ||||
\(135\) | −3.68396 | − | 11.3381i | −0.0272886 | − | 0.0839857i | ||||
\(136\) | 30.5101 | − | 93.9004i | 0.224339 | − | 0.690444i | ||||
\(137\) | −42.3519 | − | 30.7705i | −0.309138 | − | 0.224602i | 0.422388 | − | 0.906415i | \(-0.361192\pi\) |
−0.731527 | + | 0.681813i | \(0.761192\pi\) | |||||||
\(138\) | −23.0038 | + | 31.6621i | −0.166695 | + | 0.229435i | ||||
\(139\) | 26.6923 | + | 8.67286i | 0.192031 | + | 0.0623947i | 0.403454 | − | 0.915000i | \(-0.367810\pi\) |
−0.211423 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(140\) | 46.0698 | − | 14.9690i | 0.329070 | − | 0.106921i | ||||
\(141\) | 85.3576 | − | 62.0159i | 0.605373 | − | 0.439829i | ||||
\(142\) | − | 20.2832i | − | 0.142840i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.06456 | −0.0560039 | ||||||||
\(145\) | 35.7942 | + | 49.2665i | 0.246857 | + | 0.339769i | ||||
\(146\) | 31.8009 | + | 97.8731i | 0.217814 | + | 0.670364i | ||||
\(147\) | 24.8774 | − | 76.5648i | 0.169234 | − | 0.520849i | ||||
\(148\) | −117.684 | − | 85.5026i | −0.795164 | − | 0.577720i | ||||
\(149\) | −6.60805 | + | 9.09520i | −0.0443493 | + | 0.0610416i | −0.830616 | − | 0.556846i | \(-0.812011\pi\) |
0.786266 | + | 0.617888i | \(0.212011\pi\) | |||||||
\(150\) | 44.0911 | + | 14.3261i | 0.293941 | + | 0.0955071i | ||||
\(151\) | −96.2142 | + | 31.2619i | −0.637180 | + | 0.207032i | −0.609753 | − | 0.792592i | \(-0.708731\pi\) |
−0.0274269 | + | 0.999624i | \(0.508731\pi\) | |||||||
\(152\) | −81.6869 | + | 59.3490i | −0.537414 | + | 0.390454i | ||||
\(153\) | − | 35.4510i | − | 0.231706i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.54745 | 0.0615965 | ||||||||
\(156\) | −33.8538 | − | 46.5957i | −0.217011 | − | 0.298690i | ||||
\(157\) | 5.89355 | + | 18.1385i | 0.0375385 | + | 0.115532i | 0.968070 | − | 0.250681i | \(-0.0806544\pi\) |
−0.930531 | + | 0.366212i | \(0.880654\pi\) | |||||||
\(158\) | −12.2457 | + | 37.6885i | −0.0775046 | + | 0.238535i | ||||
\(159\) | 141.829 | + | 103.045i | 0.892006 | + | 0.648080i | ||||
\(160\) | 40.1532 | − | 55.2661i | 0.250957 | − | 0.345413i | ||||
\(161\) | −154.832 | − | 50.3081i | −0.961692 | − | 0.312473i | ||||
\(162\) | −11.6083 | + | 3.77177i | −0.0716563 | + | 0.0232826i | ||||
\(163\) | 11.6917 | − | 8.49453i | 0.0717283 | − | 0.0521137i | −0.551343 | − | 0.834278i | \(-0.685885\pi\) |
0.623072 | + | 0.782165i | \(0.285885\pi\) | |||||||
\(164\) | 38.9958i | 0.237779i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.64208 | −0.0520607 | ||||||||
\(167\) | −77.5183 | − | 106.695i | −0.464182 | − | 0.638891i | 0.511188 | − | 0.859469i | \(-0.329206\pi\) |
−0.975369 | + | 0.220578i | \(0.929206\pi\) | |||||||
\(168\) | −43.6971 | − | 134.486i | −0.260102 | − | 0.800511i | ||||
\(169\) | −20.9624 | + | 64.5157i | −0.124038 | + | 0.381750i | ||||
\(170\) | −29.7465 | − | 21.6121i | −0.174980 | − | 0.127130i | ||||
\(171\) | −21.3099 | + | 29.3305i | −0.124619 | + | 0.171523i | ||||
\(172\) | 95.2973 | + | 30.9640i | 0.554054 | + | 0.180023i | ||||
\(173\) | −33.4129 | + | 10.8565i | −0.193138 | + | 0.0627544i | −0.403989 | − | 0.914764i | \(-0.632377\pi\) |
0.210851 | + | 0.977518i | \(0.432377\pi\) | |||||||
\(174\) | 50.4408 | − | 36.6474i | 0.289890 | − | 0.210617i | ||||
\(175\) | 192.849i | 1.10200i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 168.518 | 0.952077 | ||||||||
\(178\) | 3.15275 | + | 4.33938i | 0.0177121 | + | 0.0243786i | ||||
\(179\) | −55.9219 | − | 172.110i | −0.312413 | − | 0.961507i | −0.976806 | − | 0.214124i | \(-0.931310\pi\) |
0.664394 | − | 0.747383i | \(-0.268690\pi\) | |||||||
\(180\) | 4.59577 | − | 14.1443i | 0.0255321 | − | 0.0785796i | ||||
\(181\) | −16.4744 | − | 11.9693i | −0.0910186 | − | 0.0661289i | 0.541345 | − | 0.840800i | \(-0.317915\pi\) |
−0.632364 | + | 0.774672i | \(0.717915\pi\) | |||||||
\(182\) | −119.872 | + | 164.990i | −0.658638 | + | 0.906538i | ||||
\(183\) | 2.07337 | + | 0.673679i | 0.0113299 | + | 0.00368131i | ||||
\(184\) | −132.392 | + | 43.0167i | −0.719520 | + | 0.233786i | ||||
\(185\) | −124.958 | + | 90.7876i | −0.675451 | + | 0.490744i | ||||
\(186\) | − | 9.77503i | − | 0.0525539i | ||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 131.622 | 0.700116 | ||||||||
\(189\) | −29.8439 | − | 41.0766i | −0.157904 | − | 0.217337i | ||||
\(190\) | 11.6197 | + | 35.7617i | 0.0611562 | + | 0.188220i | ||||
\(191\) | 18.4023 | − | 56.6363i | 0.0963469 | − | 0.296525i | −0.891255 | − | 0.453502i | \(-0.850175\pi\) |
0.987602 | + | 0.156976i | \(0.0501746\pi\) | |||||||
\(192\) | −71.6508 | − | 52.0574i | −0.373181 | − | 0.271132i | ||||
\(193\) | 145.812 | − | 200.693i | 0.755502 | − | 1.03986i | −0.242073 | − | 0.970258i | \(-0.577827\pi\) |
0.997575 | − | 0.0696010i | \(-0.0221726\pi\) | |||||||
\(194\) | −42.7378 | − | 13.8863i | −0.220298 | − | 0.0715791i | ||||
\(195\) | −58.1623 | + | 18.8981i | −0.298268 | + | 0.0969132i | ||||
\(196\) | 81.2501 | − | 59.0316i | 0.414541 | − | 0.301182i | ||||
\(197\) | 166.342i | 0.844374i | 0.906509 | + | 0.422187i | \(0.138737\pi\) | ||||
−0.906509 | + | 0.422187i | \(0.861263\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 97.9933 | 0.492429 | 0.246214 | − | 0.969215i | \(-0.420813\pi\) | ||||
0.246214 | + | 0.969215i | \(0.420813\pi\) | |||||||
\(200\) | 96.9250 | + | 133.406i | 0.484625 | + | 0.667029i | ||||
\(201\) | 29.5003 | + | 90.7926i | 0.146768 | + | 0.451705i | ||||
\(202\) | −40.6846 | + | 125.214i | −0.201409 | + | 0.619872i | ||||
\(203\) | 209.825 | + | 152.446i | 1.03362 | + | 0.750968i | ||||
\(204\) | 25.9950 | − | 35.7791i | 0.127427 | − | 0.175388i | ||||
\(205\) | 39.3796 | + | 12.7952i | 0.192096 | + | 0.0624157i | ||||
\(206\) | 239.977 | − | 77.9733i | 1.16494 | − | 0.378511i | ||||
\(207\) | −40.4370 | + | 29.3792i | −0.195348 | + | 0.141929i | ||||
\(208\) | 41.3698i | 0.198893i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −52.6608 | −0.250766 | ||||||||
\(211\) | 6.82048 | + | 9.38759i | 0.0323246 | + | 0.0444910i | 0.824873 | − | 0.565318i | \(-0.191246\pi\) |
−0.792549 | + | 0.609808i | \(0.791246\pi\) | |||||||
\(212\) | 67.5823 | + | 207.997i | 0.318784 | + | 0.981118i | ||||
\(213\) | 8.00496 | − | 24.6367i | 0.0375820 | − | 0.115665i | ||||
\(214\) | 210.530 | + | 152.959i | 0.983785 | + | 0.714762i | ||||
\(215\) | 62.5374 | − | 86.0753i | 0.290872 | − | 0.400350i | ||||
\(216\) | −41.2898 | − | 13.4159i | −0.191156 | − | 0.0621104i | ||||
\(217\) | 38.6722 | − | 12.5653i | 0.178213 | − | 0.0579048i | ||||
\(218\) | −124.815 | + | 90.6835i | −0.572547 | + | 0.415979i | ||||
\(219\) | 131.431i | 0.600140i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −181.857 | −0.822884 | ||||||||
\(222\) | 92.9516 | + | 127.937i | 0.418701 | + | 0.576292i | ||||
\(223\) | 96.3872 | + | 296.649i | 0.432229 | + | 1.33027i | 0.895899 | + | 0.444257i | \(0.146532\pi\) |
−0.463670 | + | 0.886008i | \(0.653468\pi\) | |||||||
\(224\) | 89.9058 | − | 276.702i | 0.401365 | − | 1.23528i | ||||
\(225\) | 47.9007 | + | 34.8019i | 0.212892 | + | 0.154675i | ||||
\(226\) | 13.0560 | − | 17.9700i | 0.0577699 | − | 0.0795135i | ||||
\(227\) | −9.06939 | − | 2.94682i | −0.0399533 | − | 0.0129816i | 0.288972 | − | 0.957337i | \(-0.406686\pi\) |
−0.328925 | + | 0.944356i | \(0.606686\pi\) | |||||||
\(228\) | −43.0142 | + | 13.9761i | −0.188659 | + | 0.0612989i | ||||
\(229\) | −162.466 | + | 118.038i | −0.709458 | + | 0.515451i | −0.882999 | − | 0.469376i | \(-0.844479\pi\) |
0.173541 | + | 0.984827i | \(0.444479\pi\) | |||||||
\(230\) | 51.8408i | 0.225395i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 221.767 | 0.955893 | ||||||||
\(233\) | −141.241 | − | 194.402i | −0.606185 | − | 0.834341i | 0.390072 | − | 0.920784i | \(-0.372450\pi\) |
−0.996257 | + | 0.0864428i | \(0.972450\pi\) | |||||||
\(234\) | 19.3485 | + | 59.5487i | 0.0826860 | + | 0.254481i | ||||
\(235\) | 43.1874 | − | 132.917i | 0.183776 | − | 0.565605i | ||||
\(236\) | 170.077 | + | 123.568i | 0.720666 | + | 0.523595i | ||||
\(237\) | −29.7482 | + | 40.9449i | −0.125520 | + | 0.172763i | ||||
\(238\) | −148.932 | − | 48.3911i | −0.625767 | − | 0.203324i | ||||
\(239\) | 76.7469 | − | 24.9366i | 0.321117 | − | 0.104337i | −0.144023 | − | 0.989574i | \(-0.546004\pi\) |
0.465140 | + | 0.885237i | \(0.346004\pi\) | |||||||
\(240\) | −8.64228 | + | 6.27898i | −0.0360095 | + | 0.0261624i | ||||
\(241\) | 153.259i | 0.635928i | 0.948103 | + | 0.317964i | \(0.102999\pi\) | ||||
−0.948103 | + | 0.317964i | \(0.897001\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 1.59857 | + | 2.20025i | 0.00655153 | + | 0.00901741i | ||||
\(245\) | −32.9530 | − | 101.419i | −0.134502 | − | 0.413955i | ||||
\(246\) | 13.1002 | − | 40.3183i | 0.0532529 | − | 0.163895i | ||||
\(247\) | 150.460 | + | 109.316i | 0.609151 | + | 0.442574i | ||||
\(248\) | 20.4366 | − | 28.1286i | 0.0824058 | − | 0.113422i | ||||
\(249\) | −10.4970 | − | 3.41068i | −0.0421566 | − | 0.0136975i | ||||
\(250\) | 132.384 | − | 43.0143i | 0.529537 | − | 0.172057i | ||||
\(251\) | 285.085 | − | 207.126i | 1.13580 | − | 0.825205i | 0.149269 | − | 0.988797i | \(-0.452308\pi\) |
0.986528 | + | 0.163592i | \(0.0523080\pi\) | |||||||
\(252\) | − | 63.3403i | − | 0.251351i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 7.57800 | 0.0298347 | ||||||||
\(255\) | −27.6018 | − | 37.9906i | −0.108242 | − | 0.148983i | ||||
\(256\) | −84.0550 | − | 258.695i | −0.328340 | − | 1.01053i | ||||
\(257\) | 40.0671 | − | 123.314i | 0.155903 | − | 0.479820i | −0.842348 | − | 0.538934i | \(-0.818827\pi\) |
0.998251 | + | 0.0591134i | \(0.0188274\pi\) | |||||||
\(258\) | −88.1271 | − | 64.0281i | −0.341578 | − | 0.248171i | ||||
\(259\) | −386.661 | + | 532.194i | −1.49290 | + | 2.05480i | ||||
\(260\) | −72.5579 | − | 23.5755i | −0.279069 | − | 0.0906749i | ||||
\(261\) | 75.7305 | − | 24.6063i | 0.290155 | − | 0.0942771i | ||||
\(262\) | −247.648 | + | 179.927i | −0.945221 | + | 0.686744i | ||||
\(263\) | 180.174i | 0.685072i | 0.939505 | + | 0.342536i | \(0.111286\pi\) | ||||
−0.939505 | + | 0.342536i | \(0.888714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 232.219 | 0.876297 | ||||||||
\(266\) | 94.1316 | + | 129.561i | 0.353878 | + | 0.487071i | ||||
\(267\) | 2.11686 | + | 6.51503i | 0.00792832 | + | 0.0244009i | ||||
\(268\) | −36.8019 | + | 113.265i | −0.137320 | + | 0.422629i | ||||
\(269\) | −272.236 | − | 197.791i | −1.01203 | − | 0.735282i | −0.0473956 | − | 0.998876i | \(-0.515092\pi\) |
−0.964634 | + | 0.263594i | \(0.915092\pi\) | |||||||
\(270\) | −9.50325 | + | 13.0801i | −0.0351972 | + | 0.0484448i | ||||
\(271\) | −208.731 | − | 67.8209i | −0.770226 | − | 0.250261i | −0.102564 | − | 0.994726i | \(-0.532705\pi\) |
−0.667662 | + | 0.744465i | \(0.732705\pi\) | |||||||
\(272\) | −30.2115 | + | 9.81632i | −0.111072 | + | 0.0360894i | ||||
\(273\) | −210.716 | + | 153.094i | −0.771853 | + | 0.560784i | ||||
\(274\) | 70.9964i | 0.259111i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −62.3541 | −0.225921 | ||||||||
\(277\) | 143.905 | + | 198.069i | 0.519514 | + | 0.715050i | 0.985487 | − | 0.169749i | \(-0.0542957\pi\) |
−0.465973 | + | 0.884799i | \(0.654296\pi\) | |||||||
\(278\) | −11.7621 | − | 36.1999i | −0.0423095 | − | 0.130215i | ||||
\(279\) | 3.85781 | − | 11.8731i | 0.0138273 | − | 0.0425559i | ||||
\(280\) | −151.537 | − | 110.098i | −0.541202 | − | 0.393207i | ||||
\(281\) | 202.927 | − | 279.305i | 0.722160 | − | 0.993968i | −0.277290 | − | 0.960786i | \(-0.589436\pi\) |
0.999449 | − | 0.0331812i | \(-0.0105638\pi\) | |||||||
\(282\) | −136.085 | − | 44.2168i | −0.482572 | − | 0.156797i | ||||
\(283\) | −221.203 | + | 71.8731i | −0.781634 | + | 0.253968i | −0.672538 | − | 0.740063i | \(-0.734796\pi\) |
−0.109097 | + | 0.994031i | \(0.534796\pi\) | |||||||
\(284\) | 26.1443 | − | 18.9950i | 0.0920576 | − | 0.0668837i | ||||
\(285\) | 48.0233i | 0.168503i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 176.348 | 0.614452 | ||||||||
\(288\) | −52.5037 | − | 72.2652i | −0.182305 | − | 0.250921i | ||||
\(289\) | 46.1544 | + | 142.048i | 0.159704 | + | 0.491517i | ||||
\(290\) | 25.5210 | − | 78.5455i | 0.0880033 | − | 0.270846i | ||||
\(291\) | −46.4304 | − | 33.7337i | −0.159555 | − | 0.115923i | ||||
\(292\) | −96.3738 | + | 132.647i | −0.330047 | + | 0.454271i | ||||
\(293\) | 507.607 | + | 164.931i | 1.73245 | + | 0.562906i | 0.993799 | − | 0.111187i | \(-0.0354654\pi\) |
0.738646 | + | 0.674093i | \(0.235465\pi\) | |||||||
\(294\) | −103.836 | + | 33.7385i | −0.353185 | + | 0.114757i | ||||
\(295\) | 180.590 | − | 131.206i | 0.612168 | − | 0.444766i | ||||
\(296\) | 562.485i | 1.90029i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.2467 | 0.0511633 | ||||||||
\(299\) | 150.710 | + | 207.435i | 0.504048 | + | 0.693762i | ||||
\(300\) | 22.8250 | + | 70.2480i | 0.0760832 | + | 0.234160i | ||||
\(301\) | 140.026 | − | 430.955i | 0.465202 | − | 1.43174i | ||||
\(302\) | 110.997 | + | 80.6440i | 0.367540 | + | 0.267033i | ||||
\(303\) | −98.8339 | + | 136.033i | −0.326184 | + | 0.448954i | ||||
\(304\) | 30.8963 | + | 10.0388i | 0.101633 | + | 0.0330224i | ||||
\(305\) | 2.74642 | − | 0.892367i | 0.00900466 | − | 0.00292579i | ||||
\(306\) | −38.8962 | + | 28.2597i | −0.127112 | + | 0.0923520i | ||||
\(307\) | − | 142.846i | − | 0.465296i | −0.972561 | − | 0.232648i | \(-0.925261\pi\) | ||
0.972561 | − | 0.232648i | \(-0.0747389\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 322.258 | 1.04291 | ||||||||
\(310\) | −7.61074 | − | 10.4753i | −0.0245508 | − | 0.0337912i | ||||
\(311\) | −14.1841 | − | 43.6540i | −0.0456079 | − | 0.140367i | 0.925659 | − | 0.378358i | \(-0.123511\pi\) |
−0.971267 | + | 0.237991i | \(0.923511\pi\) | |||||||
\(312\) | −68.8210 | + | 211.809i | −0.220580 | + | 0.678876i | ||||
\(313\) | −288.424 | − | 209.552i | −0.921482 | − | 0.669496i | 0.0224108 | − | 0.999749i | \(-0.492866\pi\) |
−0.943892 | + | 0.330253i | \(0.892866\pi\) | |||||||
\(314\) | 15.2032 | − | 20.9254i | 0.0484177 | − | 0.0666413i | ||||
\(315\) | −63.9637 | − | 20.7831i | −0.203059 | − | 0.0659780i | ||||
\(316\) | −60.0471 | + | 19.5105i | −0.190022 | + | 0.0617420i | ||||
\(317\) | 50.0448 | − | 36.3597i | 0.157870 | − | 0.114699i | −0.506046 | − | 0.862507i | \(-0.668893\pi\) |
0.663916 | + | 0.747807i | \(0.268893\pi\) | |||||||
\(318\) | − | 237.754i | − | 0.747655i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −117.315 | −0.366609 | ||||||||
\(321\) | 195.351 | + | 268.877i | 0.608569 | + | 0.837624i | ||||
\(322\) | 68.2274 | + | 209.982i | 0.211886 | + | 0.652119i | ||||
\(323\) | −44.1296 | + | 135.817i | −0.136624 | + | 0.420486i | ||||
\(324\) | −15.7327 | − | 11.4305i | −0.0485578 | − | 0.0352793i | ||||
\(325\) | 178.528 | − | 245.722i | 0.549316 | − | 0.756068i | ||||
\(326\) | −18.6401 | − | 6.05653i | −0.0571781 | − | 0.0185783i | ||||
\(327\) | −187.394 | + | 60.8880i | −0.573071 | + | 0.186202i | ||||
\(328\) | 121.991 | − | 88.6313i | 0.371922 | − | 0.270217i | ||||
\(329\) | − | 595.222i | − | 1.80919i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −339.961 | −1.02707 | −0.513536 | − | 0.858068i | \(-0.671665\pi\) | ||||
−0.513536 | + | 0.858068i | \(0.671665\pi\) | |||||||
\(332\) | −8.09320 | − | 11.1393i | −0.0243771 | − | 0.0335522i | ||||
\(333\) | 62.4109 | + | 192.081i | 0.187420 | + | 0.576820i | ||||
\(334\) | −55.2699 | + | 170.103i | −0.165479 | + | 0.509291i | ||||
\(335\) | 102.304 | + | 74.3281i | 0.305385 | + | 0.221875i | ||||
\(336\) | −26.7420 | + | 36.8072i | −0.0795893 | + | 0.109545i | ||||
\(337\) | −284.575 | − | 92.4640i | −0.844436 | − | 0.274374i | −0.145322 | − | 0.989384i | \(-0.546422\pi\) |
−0.699114 | + | 0.715010i | \(0.746422\pi\) | |||||||
\(338\) | 87.4956 | − | 28.4290i | 0.258863 | − | 0.0841096i | ||||
\(339\) | 22.9503 | − | 16.6744i | 0.0677001 | − | 0.0491870i | ||||
\(340\) | − | 58.5817i | − | 0.172299i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 49.1680 | 0.143766 | ||||||||
\(343\) | 14.4759 | + | 19.9243i | 0.0422037 | + | 0.0580884i | ||||
\(344\) | −119.731 | − | 368.494i | −0.348055 | − | 1.07120i | ||||
\(345\) | −20.4595 | + | 62.9677i | −0.0593028 | + | 0.182515i | ||||
\(346\) | 38.5466 | + | 28.0058i | 0.111406 | + | 0.0809415i | ||||
\(347\) | −125.224 | + | 172.357i | −0.360877 | + | 0.496705i | −0.950393 | − | 0.311052i | \(-0.899319\pi\) |
0.589516 | + | 0.807757i | \(0.299319\pi\) | |||||||
\(348\) | 94.4744 | + | 30.6966i | 0.271478 | + | 0.0882086i | ||||
\(349\) | −71.2895 | + | 23.1634i | −0.204268 | + | 0.0663707i | −0.409364 | − | 0.912371i | \(-0.634249\pi\) |
0.205096 | + | 0.978742i | \(0.434249\pi\) | |||||||
\(350\) | 211.591 | − | 153.730i | 0.604545 | − | 0.439228i | ||||
\(351\) | 79.9660i | 0.227823i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −372.860 | −1.05626 | −0.528130 | − | 0.849164i | \(-0.677107\pi\) | ||||
−0.528130 | + | 0.849164i | \(0.677107\pi\) | |||||||
\(354\) | −134.334 | − | 184.894i | −0.379473 | − | 0.522300i | ||||
\(355\) | −10.6035 | − | 32.6342i | −0.0298690 | − | 0.0919274i | ||||
\(356\) | −2.64080 | + | 8.12755i | −0.00741798 | + | 0.0228302i | ||||
\(357\) | −161.801 | − | 117.555i | −0.453223 | − | 0.329286i | ||||
\(358\) | −144.258 | + | 198.554i | −0.402954 | + | 0.554619i | ||||
\(359\) | 252.527 | + | 82.0510i | 0.703418 | + | 0.228554i | 0.638819 | − | 0.769357i | \(-0.279423\pi\) |
0.0645988 | + | 0.997911i | \(0.479423\pi\) | |||||||
\(360\) | −54.6931 | + | 17.7709i | −0.151925 | + | 0.0493635i | ||||
\(361\) | −173.904 | + | 126.348i | −0.481728 | + | 0.349996i | ||||
\(362\) | 27.6167i | 0.0762892i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −324.925 | −0.892651 | ||||||||
\(365\) | 102.331 | + | 140.846i | 0.280358 | + | 0.385880i | ||||
\(366\) | −0.913638 | − | 2.81189i | −0.00249628 | − | 0.00768275i | ||||
\(367\) | 30.7482 | − | 94.6332i | 0.0837826 | − | 0.257856i | −0.900386 | − | 0.435092i | \(-0.856716\pi\) |
0.984168 | + | 0.177236i | \(0.0567157\pi\) | |||||||
\(368\) | 36.2341 | + | 26.3256i | 0.0984622 | + | 0.0715370i | ||||
\(369\) | 31.8240 | − | 43.8019i | 0.0862438 | − | 0.118704i | ||||
\(370\) | 199.221 | + | 64.7308i | 0.538435 | + | 0.174948i | ||||
\(371\) | 940.607 | − | 305.622i | 2.53533 | − | 0.823779i | ||||
\(372\) | 12.5997 | − | 9.15419i | 0.0338701 | − | 0.0246080i | ||||
\(373\) | − | 469.949i | − | 1.25992i | −0.776629 | − | 0.629959i | \(-0.783072\pi\) | ||
0.776629 | − | 0.629959i | \(-0.216928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 177.775 | 0.474066 | ||||||||
\(376\) | −299.155 | − | 411.752i | −0.795626 | − | 1.09508i | ||||
\(377\) | −126.226 | − | 388.484i | −0.334817 | − | 1.03046i | ||||
\(378\) | −21.2785 | + | 65.4884i | −0.0562922 | + | 0.173250i | ||||
\(379\) | −233.514 | − | 169.658i | −0.616131 | − | 0.447645i | 0.235437 | − | 0.971890i | \(-0.424348\pi\) |
−0.851568 | + | 0.524244i | \(0.824348\pi\) | |||||||
\(380\) | −35.2139 | + | 48.4677i | −0.0926681 | + | 0.127547i | ||||
\(381\) | 9.20452 | + | 2.99073i | 0.0241588 | + | 0.00784968i | ||||
\(382\) | −76.8097 | + | 24.9570i | −0.201072 | + | 0.0653324i | ||||
\(383\) | 159.146 | − | 115.626i | 0.415524 | − | 0.301896i | −0.360311 | − | 0.932832i | \(-0.617329\pi\) |
0.775834 | + | 0.630937i | \(0.217329\pi\) | |||||||
\(384\) | − | 86.1752i | − | 0.224414i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −336.430 | −0.871581 | ||||||||
\(387\) | −81.7731 | − | 112.551i | −0.211300 | − | 0.290829i | ||||
\(388\) | −22.1244 | − | 68.0918i | −0.0570216 | − | 0.175494i | ||||
\(389\) | −138.683 | + | 426.822i | −0.356511 | + | 1.09723i | 0.598617 | + | 0.801035i | \(0.295717\pi\) |
−0.955128 | + | 0.296193i | \(0.904283\pi\) | |||||||
\(390\) | 67.0986 | + | 48.7500i | 0.172048 | + | 0.125000i | ||||
\(391\) | −115.725 | + | 159.281i | −0.295971 | + | 0.407369i | ||||
\(392\) | −369.337 | − | 120.005i | −0.942186 | − | 0.306135i | ||||
\(393\) | −371.812 | + | 120.809i | −0.946086 | + | 0.307402i | ||||
\(394\) | 182.507 | − | 132.599i | 0.463216 | − | 0.336546i | ||||
\(395\) | 67.0397i | 0.169721i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 608.594 | 1.53298 | 0.766491 | − | 0.642255i | \(-0.222001\pi\) | ||||
0.766491 | + | 0.642255i | \(0.222001\pi\) | |||||||
\(398\) | −78.1152 | − | 107.516i | −0.196269 | − | 0.270142i | ||||
\(399\) | 63.2032 | + | 194.519i | 0.158404 | + | 0.487517i | ||||
\(400\) | 16.3947 | − | 50.4578i | 0.0409869 | − | 0.126145i | ||||
\(401\) | 209.678 | + | 152.340i | 0.522888 | + | 0.379900i | 0.817691 | − | 0.575658i | \(-0.195254\pi\) |
−0.294803 | + | 0.955558i | \(0.595254\pi\) | |||||||
\(402\) | 76.0998 | − | 104.742i | 0.189303 | − | 0.260553i | ||||
\(403\) | −60.9069 | − | 19.7899i | −0.151134 | − | 0.0491064i | ||||
\(404\) | −199.497 | + | 64.8206i | −0.493805 | + | 0.160447i | ||||
\(405\) | −16.7052 | + | 12.1370i | −0.0412473 | + | 0.0299679i | ||||
\(406\) | − | 351.738i | − | 0.866350i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −171.010 | −0.419142 | ||||||||
\(409\) | −154.101 | − | 212.102i | −0.376776 | − | 0.518588i | 0.577951 | − | 0.816072i | \(-0.303853\pi\) |
−0.954727 | + | 0.297484i | \(0.903853\pi\) | |||||||
\(410\) | −17.3527 | − | 53.4063i | −0.0423238 | − | 0.130259i | ||||
\(411\) | −28.0194 | + | 86.2348i | −0.0681737 | + | 0.209817i | ||||
\(412\) | 325.240 | + | 236.301i | 0.789418 | + | 0.573546i | ||||
\(413\) | 558.803 | − | 769.126i | 1.35303 | − | 1.86229i | ||||
\(414\) | 64.4687 | + | 20.9471i | 0.155721 | + | 0.0505970i | ||||
\(415\) | −13.9045 | + | 4.51784i | −0.0335048 | + | 0.0108864i | ||||
\(416\) | −370.708 | + | 269.335i | −0.891124 | + | 0.647440i | ||||
\(417\) | − | 48.6117i | − | 0.116575i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −650.465 | −1.55242 | −0.776211 | − | 0.630473i | \(-0.782861\pi\) | ||||
−0.776211 | + | 0.630473i | \(0.782861\pi\) | |||||||
\(420\) | −49.3162 | − | 67.8779i | −0.117419 | − | 0.161614i | ||||
\(421\) | −194.344 | − | 598.129i | −0.461624 | − | 1.42073i | −0.863179 | − | 0.504899i | \(-0.831530\pi\) |
0.401554 | − | 0.915835i | \(-0.368470\pi\) | |||||||
\(422\) | 4.86295 | − | 14.9666i | 0.0115236 | − | 0.0354659i | ||||
\(423\) | −147.844 | − | 107.415i | −0.349512 | − | 0.253935i | ||||
\(424\) | 497.072 | − | 684.161i | 1.17234 | − | 1.61359i | ||||
\(425\) | 221.808 | + | 72.0696i | 0.521900 | + | 0.169576i | ||||
\(426\) | −33.4121 | + | 10.8563i | −0.0784322 | + | 0.0254842i | ||||
\(427\) | 9.95000 | − | 7.22910i | 0.0233021 | − | 0.0169300i | ||||
\(428\) | 414.610i | 0.968715i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −144.292 | −0.335562 | ||||||||
\(431\) | −346.219 | − | 476.530i | −0.803292 | − | 1.10564i | −0.992324 | − | 0.123666i | \(-0.960535\pi\) |
0.189031 | − | 0.981971i | \(-0.439465\pi\) | |||||||
\(432\) | 4.31642 | + | 13.2846i | 0.00999171 | + | 0.0307513i | ||||
\(433\) | −48.2393 | + | 148.465i | −0.111407 | + | 0.342876i | −0.991181 | − | 0.132517i | \(-0.957694\pi\) |
0.879774 | + | 0.475393i | \(0.157694\pi\) | |||||||
\(434\) | −44.6139 | − | 32.4139i | −0.102797 | − | 0.0746864i | ||||
\(435\) | 61.9974 | − | 85.3321i | 0.142523 | − | 0.196166i | ||||
\(436\) | −233.776 | − | 75.9583i | −0.536182 | − | 0.174216i | ||||
\(437\) | 191.491 | − | 62.2190i | 0.438193 | − | 0.142378i | ||||
\(438\) | 144.203 | − | 104.770i | 0.329231 | − | 0.239201i | ||||
\(439\) | 209.017i | 0.476121i | 0.971250 | + | 0.238060i | \(0.0765116\pi\) | ||||
−0.971250 | + | 0.238060i | \(0.923488\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −139.439 | −0.316188 | ||||||||
\(442\) | 144.967 | + | 199.530i | 0.327980 | + | 0.451426i | ||||
\(443\) | 105.799 | + | 325.617i | 0.238825 | + | 0.735028i | 0.996591 | + | 0.0825012i | \(0.0262908\pi\) |
−0.757766 | + | 0.652526i | \(0.773709\pi\) | |||||||
\(444\) | −77.8581 | + | 239.623i | −0.175356 | + | 0.539691i | ||||
\(445\) | 7.34105 | + | 5.33358i | 0.0164967 | + | 0.0119856i | ||||
\(446\) | 248.643 | − | 342.228i | 0.557496 | − | 0.767327i | ||||
\(447\) | 18.5192 | + | 6.01724i | 0.0414299 | + | 0.0134614i | ||||
\(448\) | −475.187 | + | 154.398i | −1.06068 | + | 0.344637i | ||||
\(449\) | −46.5303 | + | 33.8062i | −0.103631 | + | 0.0752923i | −0.638394 | − | 0.769710i | \(-0.720401\pi\) |
0.534763 | + | 0.845002i | \(0.320401\pi\) | |||||||
\(450\) | − | 80.2981i | − | 0.178440i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 35.3895 | 0.0782954 | ||||||||
\(453\) | 102.994 | + | 141.759i | 0.227360 | + | 0.312934i | ||||
\(454\) | 3.99645 | + | 12.2998i | 0.00880276 | + | 0.0270921i | ||||
\(455\) | −106.613 | + | 328.123i | −0.234315 | + | 0.721148i | ||||
\(456\) | 141.486 | + | 102.795i | 0.310276 | + | 0.225429i | ||||
\(457\) | −375.925 | + | 517.417i | −0.822593 | + | 1.13220i | 0.166663 | + | 0.986014i | \(0.446701\pi\) |
−0.989257 | + | 0.146189i | \(0.953299\pi\) | |||||||
\(458\) | 259.019 | + | 84.1603i | 0.565543 | + | 0.183756i | ||||
\(459\) | −58.3976 | + | 18.9745i | −0.127228 | + | 0.0413389i | ||||
\(460\) | −66.8209 | + | 48.5483i | −0.145263 | + | 0.105540i | ||||
\(461\) | − | 492.084i | − | 1.06743i | −0.845666 | − | 0.533713i | \(-0.820796\pi\) | ||
0.845666 | − | 0.533713i | \(-0.179204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 366.054 | 0.790614 | 0.395307 | − | 0.918549i | \(-0.370638\pi\) | ||||
0.395307 | + | 0.918549i | \(0.370638\pi\) | |||||||
\(464\) | −41.9393 | − | 57.7245i | −0.0903864 | − | 0.124406i | ||||
\(465\) | −5.11011 | − | 15.7273i | −0.0109895 | − | 0.0338222i | ||||
\(466\) | −100.704 | + | 309.934i | −0.216102 | + | 0.665094i | ||||
\(467\) | −263.332 | − | 191.322i | −0.563881 | − | 0.409683i | 0.268996 | − | 0.963141i | \(-0.413308\pi\) |
−0.832877 | + | 0.553458i | \(0.813308\pi\) | |||||||
\(468\) | −58.6364 | + | 80.7061i | −0.125292 | + | 0.172449i | ||||
\(469\) | 512.207 | + | 166.426i | 1.09213 | + | 0.354853i | ||||
\(470\) | −180.261 | + | 58.5703i | −0.383534 | + | 0.124618i | ||||
\(471\) | 26.7247 | − | 19.4166i | 0.0567404 | − | 0.0412243i | ||||
\(472\) | − | 812.903i | − | 1.72225i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 68.6377 | 0.144805 | ||||||||
\(475\) | −140.192 | − | 192.957i | −0.295140 | − | 0.406226i | ||||
\(476\) | −77.0990 | − | 237.286i | −0.161973 | − | 0.498500i | ||||
\(477\) | 93.8319 | − | 288.785i | 0.196713 | − | 0.605419i | ||||
\(478\) | −88.5387 | − | 64.3271i | −0.185227 | − | 0.134576i | ||||
\(479\) | −193.072 | + | 265.741i | −0.403074 | + | 0.554783i | −0.961512 | − | 0.274763i | \(-0.911401\pi\) |
0.558438 | + | 0.829546i | \(0.311401\pi\) | |||||||
\(480\) | −112.530 | − | 36.5632i | −0.234437 | − | 0.0761733i | ||||
\(481\) | 985.342 | − | 320.157i | 2.04853 | − | 0.665607i | ||||
\(482\) | 168.152 | − | 122.170i | 0.348864 | − | 0.253465i | ||||
\(483\) | 281.979i | 0.583807i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −76.0213 | −0.156745 | ||||||||
\(486\) | 12.4263 | + | 17.1034i | 0.0255686 | + | 0.0351921i | ||||
\(487\) | 99.5938 | + | 306.518i | 0.204505 | + | 0.629401i | 0.999733 | + | 0.0230911i | \(0.00735078\pi\) |
−0.795229 | + | 0.606310i | \(0.792649\pi\) | |||||||
\(488\) | 3.24973 | − | 10.0016i | 0.00665928 | − | 0.0204951i | ||||
\(489\) | −20.2506 | − | 14.7129i | −0.0414123 | − | 0.0300878i | ||||
\(490\) | −85.0066 | + | 117.001i | −0.173483 | + | 0.238779i | ||||
\(491\) | 735.903 | + | 239.109i | 1.49878 | + | 0.486985i | 0.939663 | − | 0.342101i | \(-0.111139\pi\) |
0.559121 | + | 0.829086i | \(0.311139\pi\) | |||||||
\(492\) | 64.2370 | − | 20.8719i | 0.130563 | − | 0.0424225i | ||||
\(493\) | 253.751 | − | 184.361i | 0.514708 | − | 0.373957i | ||||
\(494\) | − | 252.223i | − | 0.510573i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.1865 | −0.0225535 | ||||||||
\(497\) | −85.8994 | − | 118.230i | −0.172836 | − | 0.237888i | ||||
\(498\) | 4.62553 | + | 14.2359i | 0.00928821 | + | 0.0285862i | ||||
\(499\) | −15.7914 | + | 48.6010i | −0.0316462 | + | 0.0973969i | −0.965632 | − | 0.259913i | \(-0.916306\pi\) |
0.933986 | + | 0.357310i | \(0.116306\pi\) | |||||||
\(500\) | 179.420 | + | 130.356i | 0.358840 | + | 0.260713i | ||||
\(501\) | −134.266 | + | 184.801i | −0.267995 | + | 0.368864i | ||||
\(502\) | −454.510 | − | 147.679i | −0.905399 | − | 0.294182i | ||||
\(503\) | −395.326 | + | 128.449i | −0.785936 | + | 0.255366i | −0.674373 | − | 0.738391i | \(-0.735586\pi\) |
−0.111564 | + | 0.993757i | \(0.535586\pi\) | |||||||
\(504\) | −198.147 | + | 143.962i | −0.393150 | + | 0.285640i | ||||
\(505\) | 222.729i | 0.441048i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 117.495 | 0.231746 | ||||||||
\(508\) | 7.09670 | + | 9.76777i | 0.0139699 | + | 0.0192279i | ||||
\(509\) | 103.330 | + | 318.018i | 0.203006 | + | 0.624789i | 0.999789 | + | 0.0205238i | \(0.00653339\pi\) |
−0.796783 | + | 0.604266i | \(0.793467\pi\) | |||||||
\(510\) | −19.6798 | + | 60.5683i | −0.0385879 | + | 0.118761i | ||||
\(511\) | 599.859 | + | 435.823i | 1.17389 | + | 0.852883i | ||||
\(512\) | −99.8537 | + | 137.437i | −0.195027 | + | 0.268431i | ||||
\(513\) | 59.7212 | + | 19.4046i | 0.116416 | + | 0.0378257i | ||||
\(514\) | −167.237 | + | 54.3386i | −0.325364 | + | 0.105717i | ||||
\(515\) | 345.343 | − | 250.907i | 0.670570 | − | 0.487197i | ||||
\(516\) | − | 173.554i | − | 0.336345i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 892.140 | 1.72228 | ||||||||
\(519\) | 35.7674 | + | 49.2296i | 0.0689160 | + | 0.0948547i | ||||
\(520\) | 91.1614 | + | 280.566i | 0.175310 | + | 0.539550i | ||||
\(521\) | 267.754 | − | 824.063i | 0.513924 | − | 1.58169i | −0.271308 | − | 0.962492i | \(-0.587456\pi\) |
0.785232 | − | 0.619202i | \(-0.212544\pi\) | |||||||
\(522\) | −87.3661 | − | 63.4752i | −0.167368 | − | 0.121600i | ||||
\(523\) | 256.726 | − | 353.353i | 0.490872 | − | 0.675627i | −0.489676 | − | 0.871904i | \(-0.662885\pi\) |
0.980549 | + | 0.196277i | \(0.0628851\pi\) | |||||||
\(524\) | −463.838 | − | 150.710i | −0.885188 | − | 0.287615i | ||||
\(525\) | 317.677 | − | 103.219i | 0.605098 | − | 0.196608i | ||||
\(526\) | 197.683 | − | 143.625i | 0.375824 | − | 0.273052i | ||||
\(527\) | − | 49.1749i | − | 0.0933111i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −251.412 | −0.475259 | ||||||||
\(530\) | −185.113 | − | 254.786i | −0.349270 | − | 0.480729i | ||||
\(531\) | −90.1962 | − | 277.595i | −0.169861 | − | 0.522778i | ||||
\(532\) | −78.8465 | + | 242.664i | −0.148208 | + | 0.456136i | ||||
\(533\) | −224.696 | − | 163.251i | −0.421569 | − | 0.306288i | ||||
\(534\) | 5.46072 | − | 7.51603i | 0.0102261 | − | 0.0140750i | ||||
\(535\) | 418.690 | + | 136.041i | 0.782598 | + | 0.254282i | ||||
\(536\) | 437.970 | − | 142.305i | 0.817108 | − | 0.265494i | ||||
\(537\) | −253.581 | + | 184.238i | −0.472219 | + | 0.343087i | ||||
\(538\) | 456.361i | 0.848255i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −25.7594 | −0.0477027 | ||||||||
\(541\) | 456.249 | + | 627.973i | 0.843343 | + | 1.16076i | 0.985290 | + | 0.170888i | \(0.0546638\pi\) |
−0.141947 | + | 0.989874i | \(0.545336\pi\) | |||||||
\(542\) | 91.9780 | + | 283.079i | 0.169701 | + | 0.522286i | ||||
\(543\) | −10.8992 | + | 33.5442i | −0.0200722 | + | 0.0617758i | ||||
\(544\) | −284.652 | − | 206.812i | −0.523258 | − | 0.380169i | ||||
\(545\) | −153.412 | + | 211.153i | −0.281489 | + | 0.387437i | ||||
\(546\) | 335.944 | + | 109.155i | 0.615282 | + | 0.199917i | ||||
\(547\) | −754.421 | + | 245.126i | −1.37920 | + | 0.448128i | −0.902405 | − | 0.430888i | \(-0.858200\pi\) |
−0.476792 | + | 0.879016i | \(0.658200\pi\) | |||||||
\(548\) | −91.5118 | + | 66.4872i | −0.166992 | + | 0.121327i | ||||
\(549\) | − | 3.77600i | − | 0.00687795i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −320.763 | −0.582147 | ||||||||
\(552\) | 141.721 | + | 195.062i | 0.256741 | + | 0.353373i | ||||
\(553\) | 88.2306 | + | 271.546i | 0.159549 | + | 0.491041i | ||||
\(554\) | 102.603 | − | 315.781i | 0.185205 | − | 0.570001i | ||||
\(555\) | 216.434 | + | 157.249i | 0.389972 | + | 0.283331i | ||||
\(556\) | 35.6453 | − | 49.0616i | 0.0641103 | − | 0.0882402i | ||||
\(557\) | −632.587 | − | 205.540i | −1.13570 | − | 0.369013i | −0.319963 | − | 0.947430i | \(-0.603671\pi\) |
−0.815741 | + | 0.578417i | \(0.803671\pi\) | |||||||
\(558\) | −16.1022 | + | 5.23192i | −0.0288570 | + | 0.00937620i | ||||
\(559\) | −577.367 | + | 419.481i | −1.03286 | + | 0.750414i | ||||
\(560\) | 60.2650i | 0.107616i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −468.211 | −0.833116 | ||||||||
\(563\) | 232.286 | + | 319.715i | 0.412587 | + | 0.567877i | 0.963847 | − | 0.266457i | \(-0.0858529\pi\) |
−0.551260 | + | 0.834333i | \(0.685853\pi\) | |||||||
\(564\) | −70.4483 | − | 216.818i | −0.124908 | − | 0.384429i | ||||
\(565\) | 11.6119 | − | 35.7378i | 0.0205521 | − | 0.0632527i | ||||
\(566\) | 255.189 | + | 185.406i | 0.450864 | + | 0.327572i | ||||
\(567\) | −51.6912 | + | 71.1468i | −0.0911661 | + | 0.125479i | ||||
\(568\) | −118.844 | − | 38.6147i | −0.209232 | − | 0.0679836i | ||||
\(569\) | −50.4513 | + | 16.3926i | −0.0886667 | + | 0.0288096i | −0.353014 | − | 0.935618i | \(-0.614843\pi\) |
0.264348 | + | 0.964427i | \(0.414843\pi\) | |||||||
\(570\) | 52.6903 | − | 38.2817i | 0.0924391 | − | 0.0671609i | ||||
\(571\) | 878.429i | 1.53840i | 0.639005 | + | 0.769202i | \(0.279346\pi\) | ||||
−0.639005 | + | 0.769202i | \(0.720654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −103.145 | −0.180009 | ||||||||
\(574\) | −140.575 | − | 193.485i | −0.244905 | − | 0.337082i | ||||
\(575\) | −101.612 | − | 312.730i | −0.176717 | − | 0.543878i | ||||
\(576\) | −47.4031 | + | 145.892i | −0.0822970 | + | 0.253284i | ||||
\(577\) | −875.781 | − | 636.292i | −1.51782 | − | 1.10276i | −0.962556 | − | 0.271083i | \(-0.912618\pi\) |
−0.555262 | − | 0.831676i | \(-0.687382\pi\) | |||||||
\(578\) | 119.061 | − | 163.873i | 0.205988 | − | 0.283518i | ||||
\(579\) | −408.640 | − | 132.775i | −0.705769 | − | 0.229318i | ||||
\(580\) | 125.142 | − | 40.6612i | 0.215763 | − | 0.0701055i | ||||
\(581\) | −50.3745 | + | 36.5992i | −0.0867030 | + | 0.0629934i | ||||
\(582\) | 77.8334i | 0.133734i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 634.002 | 1.08562 | ||||||||
\(585\) | 62.2608 | + | 85.6946i | 0.106429 | + | 0.146486i | ||||
\(586\) | −223.678 | − | 688.411i | −0.381704 | − | 1.17476i | ||||
\(587\) | 4.71454 | − | 14.5099i | 0.00803159 | − | 0.0247187i | −0.946960 | − | 0.321350i | \(-0.895863\pi\) |
0.954992 | + | 0.296632i | \(0.0958633\pi\) | |||||||
\(588\) | −140.729 | − | 102.246i | −0.239336 | − | 0.173887i | ||||
\(589\) | −29.5594 | + | 40.6851i | −0.0501858 | + | 0.0690748i | ||||
\(590\) | −287.914 | − | 93.5488i | −0.487989 | − | 0.158557i | ||||
\(591\) | 274.011 | − | 89.0316i | 0.463640 | − | 0.150646i | ||||
\(592\) | 146.411 | − | 106.374i | 0.247316 | − | 0.179686i | ||||
\(593\) | − | 214.000i | − | 0.360877i | −0.983586 | − | 0.180439i | \(-0.942248\pi\) | ||
0.983586 | − | 0.180439i | \(-0.0577517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −264.919 | −0.445242 | ||||||||
\(596\) | 14.2783 | + | 19.6524i | 0.0239569 | + | 0.0329739i | ||||
\(597\) | −52.4492 | − | 161.422i | −0.0878547 | − | 0.270389i | ||||
\(598\) | 107.455 | − | 330.713i | 0.179691 | − | 0.553032i | ||||
\(599\) | −504.698 | − | 366.685i | −0.842568 | − | 0.612161i | 0.0805191 | − | 0.996753i | \(-0.474342\pi\) |
−0.923087 | + | 0.384592i | \(0.874342\pi\) | |||||||
\(600\) | 167.879 | − | 231.066i | 0.279798 | − | 0.385109i | ||||
\(601\) | 384.201 | + | 124.834i | 0.639269 | + | 0.207711i | 0.610677 | − | 0.791880i | \(-0.290897\pi\) |
0.0285926 | + | 0.999591i | \(0.490897\pi\) | |||||||
\(602\) | −584.457 | + | 189.902i | −0.970859 | + | 0.315451i | ||||
\(603\) | 133.771 | − | 97.1904i | 0.221843 | − | 0.161178i | ||||
\(604\) | 218.593i | 0.361909i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 228.038 | 0.376301 | ||||||||
\(607\) | 216.040 | + | 297.354i | 0.355915 | + | 0.489875i | 0.949005 | − | 0.315261i | \(-0.102092\pi\) |
−0.593090 | + | 0.805136i | \(0.702092\pi\) | |||||||
\(608\) | 111.192 | + | 342.214i | 0.182881 | + | 0.562851i | ||||
\(609\) | 138.817 | − | 427.234i | 0.227942 | − | 0.701533i | ||||
\(610\) | −3.16840 | − | 2.30197i | −0.00519409 | − | 0.00377373i | ||||
\(611\) | −551.019 | + | 758.412i | −0.901831 | + | 1.24126i | ||||
\(612\) | −72.8515 | − | 23.6709i | −0.119038 | − | 0.0386779i | ||||
\(613\) | 463.347 | − | 150.551i | 0.755868 | − | 0.245597i | 0.0943640 | − | 0.995538i | \(-0.469918\pi\) |
0.661504 | + | 0.749941i | \(0.269918\pi\) | |||||||
\(614\) | −156.728 | + | 113.869i | −0.255257 | + | 0.185455i | ||||
\(615\) | − | 71.7176i | − | 0.116614i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 455.862 | 0.738836 | 0.369418 | − | 0.929263i | \(-0.379557\pi\) | ||||
0.369418 | + | 0.929263i | \(0.379557\pi\) | |||||||
\(618\) | −256.887 | − | 353.575i | −0.415675 | − | 0.572128i | ||||
\(619\) | 176.858 | + | 544.313i | 0.285715 | + | 0.879342i | 0.986183 | + | 0.165658i | \(0.0529747\pi\) |
−0.700468 | + | 0.713684i | \(0.747025\pi\) | |||||||
\(620\) | 6.37491 | − | 19.6199i | 0.0102821 | − | 0.0316451i | ||||
\(621\) | 70.0390 | + | 50.8863i | 0.112784 | + | 0.0819425i | ||||
\(622\) | −36.5896 | + | 50.3612i | −0.0588257 | + | 0.0809666i | ||||
\(623\) | 36.7546 | + | 11.9423i | 0.0589961 | + | 0.0191690i | ||||
\(624\) | 68.1475 | − | 22.1425i | 0.109211 | − | 0.0354847i | ||||
\(625\) | −208.662 | + | 151.602i | −0.333860 | + | 0.242563i | ||||
\(626\) | 483.497i | 0.772360i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 41.2096 | 0.0656204 | ||||||||
\(629\) | 467.609 | + | 643.608i | 0.743416 | + | 1.02322i | ||||
\(630\) | 28.1858 | + | 86.7470i | 0.0447394 | + | 0.137694i | ||||
\(631\) | 69.2314 | − | 213.072i | 0.109717 | − | 0.337674i | −0.881092 | − | 0.472946i | \(-0.843191\pi\) |
0.990809 | + | 0.135272i | \(0.0431907\pi\) | |||||||
\(632\) | 197.512 | + | 143.501i | 0.312519 | + | 0.227058i | ||||
\(633\) | 11.8134 | − | 16.2598i | 0.0186626 | − | 0.0256869i | ||||
\(634\) | −79.7863 | − | 25.9241i | −0.125846 | − | 0.0408898i | ||||
\(635\) | 12.1925 | − | 3.96157i | 0.0192007 | − | 0.00623869i | ||||
\(636\) | 306.457 | − | 222.654i | 0.481850 | − | 0.350084i | ||||
\(637\) | 715.296i | 1.12291i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −44.8681 | −0.0702161 | ||||||||
\(640\) | −67.0951 | − | 92.3485i | −0.104836 | − | 0.144295i | ||||
\(641\) | −146.522 | − | 450.950i | −0.228584 | − | 0.703510i | −0.997908 | − | 0.0646506i | \(-0.979407\pi\) |
0.769324 | − | 0.638859i | \(-0.220593\pi\) | |||||||
\(642\) | 139.283 | − | 428.670i | 0.216952 | − | 0.667711i | ||||
\(643\) | 669.515 | + | 486.431i | 1.04124 | + | 0.756503i | 0.970527 | − | 0.240994i | \(-0.0774734\pi\) |
0.0707105 | + | 0.997497i | \(0.477473\pi\) | |||||||
\(644\) | −206.766 | + | 284.588i | −0.321065 | + | 0.441907i | ||||
\(645\) | −175.262 | − | 56.9461i | −0.271724 | − | 0.0882885i | ||||
\(646\) | 184.194 | − | 59.8482i | 0.285130 | − | 0.0926442i | ||||
\(647\) | −400.770 | + | 291.176i | −0.619428 | + | 0.450041i | −0.852722 | − | 0.522366i | \(-0.825050\pi\) |
0.233294 | + | 0.972406i | \(0.425050\pi\) | |||||||
\(648\) | 75.1963i | 0.116044i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −411.915 | −0.633715 | ||||||||
\(651\) | −41.3972 | − | 56.9784i | −0.0635902 | − | 0.0875244i | ||||
\(652\) | −9.64954 | − | 29.6982i | −0.0147999 | − | 0.0455494i | ||||
\(653\) | −207.539 | + | 638.739i | −0.317824 | + | 0.978160i | 0.656753 | + | 0.754106i | \(0.271929\pi\) |
−0.974577 | + | 0.224055i | \(0.928071\pi\) | |||||||
\(654\) | 216.186 | + | 157.068i | 0.330560 | + | 0.240166i | ||||
\(655\) | −304.387 | + | 418.953i | −0.464713 | + | 0.639622i | ||||
\(656\) | −46.1402 | − | 14.9919i | −0.0703357 | − | 0.0228535i | ||||
\(657\) | 216.503 | − | 70.3461i | 0.329533 | − | 0.107072i | ||||
\(658\) | −653.067 | + | 474.481i | −0.992503 | + | 0.721095i | ||||
\(659\) | 59.3106i | 0.0900009i | 0.998987 | + | 0.0450004i | \(0.0143289\pi\) | ||||
−0.998987 | + | 0.0450004i | \(0.985671\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 604.118 | 0.913946 | 0.456973 | − | 0.889481i | \(-0.348934\pi\) | ||||
0.456973 | + | 0.889481i | \(0.348934\pi\) | |||||||
\(662\) | 271.000 | + | 372.999i | 0.409365 | + | 0.563442i | ||||
\(663\) | 97.3361 | + | 299.570i | 0.146812 | + | 0.451839i | ||||
\(664\) | −16.4526 | + | 50.6358i | −0.0247780 | + | 0.0762588i | ||||
\(665\) | 219.182 | + | 159.245i | 0.329597 | + | 0.239466i | ||||
\(666\) | 160.997 | − | 221.593i | 0.241737 | − | 0.332723i | ||||
\(667\) | −420.581 | − | 136.655i | −0.630557 | − | 0.204880i | ||||
\(668\) | −271.017 | + | 88.0587i | −0.405714 | + | 0.131824i | ||||
\(669\) | 437.074 | − | 317.553i | 0.653325 | − | 0.474668i | ||||
\(670\) | − | 171.496i | − | 0.255965i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −503.925 | −0.749889 | ||||||||
\(673\) | −59.3383 | − | 81.6721i | −0.0881698 | − | 0.121355i | 0.762653 | − | 0.646807i | \(-0.223896\pi\) |
−0.850823 | + | 0.525452i | \(0.823896\pi\) | |||||||
\(674\) | 125.399 | + | 385.938i | 0.186052 | + | 0.572608i | ||||
\(675\) | 31.6904 | − | 97.5329i | 0.0469487 | − | 0.144493i | ||||
\(676\) | 118.583 | + | 86.1552i | 0.175418 | + | 0.127449i | ||||
\(677\) | −118.346 | + | 162.890i | −0.174810 | + | 0.240605i | −0.887427 | − | 0.460948i | \(-0.847510\pi\) |
0.712617 | + | 0.701553i | \(0.247510\pi\) | |||||||
\(678\) | −36.5897 | − | 11.8887i | −0.0539671 | − | 0.0175350i | ||||
\(679\) | −307.926 | + | 100.051i | −0.453499 | + | 0.147351i | ||||
\(680\) | −183.261 | + | 133.147i | −0.269501 | + | 0.195804i | ||||
\(681\) | 16.5170i | 0.0242541i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 381.312 | 0.558290 | 0.279145 | − | 0.960249i | \(-0.409949\pi\) | ||||
0.279145 | + | 0.960249i | \(0.409949\pi\) | |||||||
\(684\) | 46.0452 | + | 63.3758i | 0.0673176 | + | 0.0926547i | ||||
\(685\) | 37.1149 | + | 114.228i | 0.0541824 | + | 0.166756i | ||||
\(686\) | 10.3212 | − | 31.7653i | 0.0150454 | − | 0.0463051i | ||||
\(687\) | 281.399 | + | 204.448i | 0.409605 | + | 0.297596i | ||||
\(688\) | −73.2737 | + | 100.853i | −0.106503 | + | 0.146588i | ||||
\(689\) | −1481.42 | − | 481.341i | −2.15009 | − | 0.698608i | ||||
\(690\) | 85.3962 | − | 27.7469i | 0.123763 | − | 0.0402129i | ||||
\(691\) | 925.277 | − | 672.253i | 1.33904 | − | 0.972870i | 0.339561 | − | 0.940584i | \(-0.389721\pi\) |
0.999479 | − | 0.0322856i | \(-0.0102786\pi\) | |||||||
\(692\) | 75.9123i | 0.109700i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 288.929 | 0.416324 | ||||||||
\(695\) | −37.8486 | − | 52.0941i | −0.0544584 | − | 0.0749555i | ||||
\(696\) | −118.697 | − | 365.312i | −0.170542 | − | 0.524874i | ||||
\(697\) | 65.9028 | − | 202.828i | 0.0945521 | − | 0.291001i | ||||
\(698\) | 82.2428 | + | 59.7529i | 0.117826 | + | 0.0856058i | ||||
\(699\) | −244.637 | + | 336.713i | −0.349981 | + | 0.481707i | ||||
\(700\) | 396.304 | + | 128.767i | 0.566149 | + | 0.183953i | ||||
\(701\) | −490.012 | + | 159.214i | −0.699018 | + | 0.227125i | −0.636903 | − | 0.770944i | \(-0.719785\pi\) |
−0.0621155 | + | 0.998069i | \(0.519785\pi\) | |||||||
\(702\) | 87.7372 | − | 63.7448i | 0.124982 | − | 0.0908046i | ||||
\(703\) | − | 813.575i | − | 1.15729i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −242.067 | −0.343357 | ||||||||
\(706\) | 297.225 | + | 409.095i | 0.420998 | + | 0.579454i | ||||
\(707\) | 293.133 | + | 902.170i | 0.414615 | + | 1.27605i | ||||
\(708\) | 112.520 | − | 346.302i | 0.158927 | − | 0.489128i | ||||
\(709\) | 723.855 | + | 525.911i | 1.02095 | + | 0.741765i | 0.966478 | − | 0.256751i | \(-0.0826519\pi\) |
0.0544737 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(710\) | −27.3531 | + | 37.6483i | −0.0385255 | + | 0.0530258i | ||||
\(711\) | 83.3699 | + | 27.0885i | 0.117257 | + | 0.0380992i | ||||
\(712\) | 31.4275 | − | 10.2114i | 0.0441398 | − | 0.0143419i | ||||
\(713\) | −56.0912 | + | 40.7526i | −0.0786693 | + | 0.0571566i | ||||
\(714\) | 271.234i | 0.379879i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −391.024 | −0.546122 | ||||||||
\(717\) | −82.1550 | − | 113.077i | −0.114582 | − | 0.157708i | ||||
\(718\) | −111.277 | − | 342.475i | −0.154982 | − | 0.476984i | ||||
\(719\) | 48.3966 | − | 148.950i | 0.0673110 | − | 0.207162i | −0.911744 | − | 0.410760i | \(-0.865263\pi\) |
0.979055 | + | 0.203598i | \(0.0652635\pi\) | |||||||
\(720\) | 14.9689 | + | 10.8755i | 0.0207901 | + | 0.0151049i | ||||
\(721\) | 1068.60 | − | 1470.81i | 1.48211 | − | 2.03995i | ||||
\(722\) | 277.254 | + | 90.0854i | 0.384009 | + | 0.124772i | ||||
\(723\) | 252.460 | − | 82.0291i | 0.349183 | − | 0.113457i | ||||
\(724\) | −35.5969 | + | 25.8627i | −0.0491670 | + | 0.0357219i | ||||
\(725\) | 523.849i | 0.722551i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.5853 | 0.0393195 | 0.0196598 | − | 0.999807i | \(-0.493742\pi\) | ||||
0.0196598 | + | 0.999807i | \(0.493742\pi\) | |||||||
\(728\) | 738.502 | + | 1016.46i | 1.01443 | + | 1.39624i | ||||
\(729\) | 8.34346 | + | 25.6785i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 72.9609 | − | 224.550i | 0.0999464 | − | 0.307603i | ||||
\(731\) | −443.338 | − | 322.104i | −0.606482 | − | 0.440635i | ||||
\(732\) | 2.76881 | − | 3.81094i | 0.00378253 | − | 0.00520621i | ||||
\(733\) | 513.352 | + | 166.798i | 0.700344 | + | 0.227556i | 0.637481 | − | 0.770466i | \(-0.279977\pi\) |
0.0628638 | + | 0.998022i | \(0.479977\pi\) | |||||||
\(734\) | −128.341 | + | 41.7004i | −0.174851 | + | 0.0568126i | ||||
\(735\) | −149.428 | + | 108.566i | −0.203303 | + | 0.147708i | ||||
\(736\) | 496.079i | 0.674020i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −73.4271 | −0.0994947 | ||||||||
\(739\) | −208.533 | − | 287.022i | −0.282183 | − | 0.388392i | 0.644272 | − | 0.764796i | \(-0.277160\pi\) |
−0.926455 | + | 0.376404i | \(0.877160\pi\) | |||||||
\(740\) | 103.132 | + | 317.408i | 0.139368 | + | 0.428930i | ||||
\(741\) | 99.5422 | − | 306.359i | 0.134335 | − | 0.413441i | ||||
\(742\) | −1085.13 | − | 788.391i | −1.46243 | − | 1.06252i | ||||
\(743\) | −506.927 | + | 697.725i | −0.682271 | + | 0.939065i | −0.999958 | − | 0.00913029i | \(-0.997094\pi\) |
0.317688 | + | 0.948195i | \(0.397094\pi\) | |||||||
\(744\) | −57.2740 | − | 18.6095i | −0.0769812 | − | 0.0250127i | ||||
\(745\) | 24.5308 | − | 7.97053i | 0.0329272 | − | 0.0106987i | ||||
\(746\) | −515.619 | + | 374.619i | −0.691179 | + | 0.502171i | ||||
\(747\) | 19.1170i | 0.0255916i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1874.96 | 2.50328 | ||||||||
\(750\) | −141.713 | − | 195.051i | −0.188951 | − | 0.260068i | ||||
\(751\) | 5.75038 | + | 17.6979i | 0.00765697 | + | 0.0235657i | 0.954812 | − | 0.297210i | \(-0.0960563\pi\) |
−0.947155 | + | 0.320776i | \(0.896056\pi\) | |||||||
\(752\) | −50.6017 | + | 155.736i | −0.0672895 | + | 0.207096i | ||||
\(753\) | −493.782 | − | 358.753i | −0.655753 | − | 0.476432i | ||||
\(754\) | −325.617 | + | 448.173i | −0.431852 | + | 0.594394i | ||||
\(755\) | 220.744 | + | 71.7242i | 0.292377 | + | 0.0949989i | ||||
\(756\) | −104.339 | + | 33.9019i | −0.138015 | + | 0.0448437i | ||||
\(757\) | −508.936 | + | 369.763i | −0.672306 | + | 0.488459i | −0.870796 | − | 0.491644i | \(-0.836396\pi\) |
0.198490 | + | 0.980103i | \(0.436396\pi\) | |||||||
\(758\) | 391.449i | 0.516424i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 231.657 | 0.304812 | ||||||||
\(761\) | −554.797 | − | 763.612i | −0.729036 | − | 1.00343i | −0.999175 | − | 0.0406109i | \(-0.987070\pi\) |
0.270139 | − | 0.962821i | \(-0.412930\pi\) | |||||||
\(762\) | −4.05600 | − | 12.4831i | −0.00532283 | − | 0.0163820i | ||||
\(763\) | −343.500 | + | 1057.18i | −0.450196 | + | 1.38556i | ||||
\(764\) | −104.100 | − | 75.6330i | −0.136256 | − | 0.0989961i | ||||
\(765\) | −47.8077 | + | 65.8016i | −0.0624937 | + | 0.0860152i | ||||
\(766\) | −253.725 | − | 82.4404i | −0.331234 | − | 0.107624i | ||||
\(767\) | −1424.02 | + | 462.691i | −1.85660 | + | 0.603247i | ||||
\(768\) | −381.153 | + | 276.924i | −0.496293 | + | 0.360578i | ||||
\(769\) | 332.508i | 0.432390i | 0.976350 | + | 0.216195i | \(0.0693646\pi\) | ||||
−0.976350 | + | 0.216195i | \(0.930635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −224.577 | −0.291281 | ||||||||
\(772\) | −315.062 | − | 433.646i | −0.408112 | − | 0.561718i | ||||
\(773\) | −285.513 | − | 878.717i | −0.369356 | − | 1.13676i | −0.947208 | − | 0.320620i | \(-0.896109\pi\) |
0.577851 | − | 0.816142i | \(-0.303891\pi\) | |||||||
\(774\) | −58.3035 | + | 179.440i | −0.0753275 | + | 0.231834i | ||||
\(775\) | 66.4443 | + | 48.2746i | 0.0857345 | + | 0.0622898i | ||||
\(776\) | −162.726 | + | 223.973i | −0.209699 | + | 0.288625i | ||||
\(777\) | 1083.63 | + | 352.091i | 1.39463 | + | 0.453142i | ||||
\(778\) | 578.852 | − | 188.080i | 0.744025 | − | 0.241749i | ||||
\(779\) | −176.446 | + | 128.196i | −0.226504 | + | 0.164565i | ||||
\(780\) | 132.141i | 0.169412i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 267.010 | 0.341445 | ||||||||
\(783\) | −81.0670 | − | 111.579i | −0.103534 | − | 0.142502i | ||||
\(784\) | 38.6104 | + | 118.830i | 0.0492479 | + | 0.151570i | ||||
\(785\) | 13.5216 | − | 41.6152i | 0.0172250 | − | 0.0530130i | ||||
\(786\) | 428.939 | + | 311.642i | 0.545724 | + | 0.396492i | ||||
\(787\) | 756.922 | − | 1041.81i | 0.961781 | − | 1.32378i | 0.0156903 | − | 0.999877i | \(-0.495005\pi\) |
0.946091 | − | 0.323901i | \(-0.104995\pi\) | |||||||
\(788\) | 341.831 | + | 111.068i | 0.433796 | + | 0.140949i | ||||
\(789\) | 296.796 | − | 96.4350i | 0.376168 | − | 0.122224i | ||||
\(790\) | 73.5547 | − | 53.4406i | 0.0931073 | − | 0.0676464i | ||||
\(791\) | − | 160.039i | − | 0.202325i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.3702 | −0.0244265 | ||||||||
\(794\) | −485.140 | − | 667.738i | −0.611007 | − | 0.840979i | ||||
\(795\) | −124.291 | − | 382.529i | −0.156341 | − | 0.481169i | ||||
\(796\) | 65.4308 | − | 201.375i | 0.0821996 | − | 0.252984i | ||||
\(797\) | 176.574 | + | 128.288i | 0.221548 | + | 0.160964i | 0.693023 | − | 0.720915i | \(-0.256278\pi\) |
−0.471475 | + | 0.881879i | \(0.656278\pi\) | |||||||
\(798\) | 163.041 | − | 224.406i | 0.204312 | − | 0.281211i | ||||
\(799\) | −684.601 | − | 222.440i | −0.856822 | − | 0.278398i | ||||
\(800\) | 558.881 | − | 181.592i | 0.698602 | − | 0.226989i | ||||
\(801\) | 9.59906 | − | 6.97412i | 0.0119838 | − | 0.00870677i | ||||
\(802\) | − | 351.492i | − | 0.438270i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 206.276 | 0.256562 | ||||||||
\(805\) | 219.546 | + | 302.179i | 0.272728 | + | 0.375377i | ||||
\(806\) | 26.8388 | + | 82.6014i | 0.0332988 | + | 0.102483i | ||||
\(807\) | −180.107 | + | 554.313i | −0.223181 | + | 0.686881i | ||||
\(808\) | 656.203 | + | 476.760i | 0.812133 | + | 0.590049i | ||||
\(809\) | 453.078 | − | 623.608i | 0.560047 | − | 0.770838i | −0.431286 | − | 0.902215i | \(-0.641940\pi\) |
0.991332 | + | 0.131377i | \(0.0419399\pi\) | |||||||
\(810\) | 26.6330 | + | 8.65359i | 0.0328803 | + | 0.0106834i | ||||
\(811\) | 1503.40 | − | 488.486i | 1.85377 | − | 0.602325i | 0.857654 | − | 0.514227i | \(-0.171921\pi\) |
0.996112 | − | 0.0880985i | \(-0.0280790\pi\) | |||||||
\(812\) | 453.378 | − | 329.398i | 0.558347 | − | 0.405663i | ||||
\(813\) | 380.138i | 0.467575i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.1567 | −0.0406831 | ||||||||
\(816\) | 32.3404 | + | 44.5128i | 0.0396329 | + | 0.0545500i | ||||
\(817\) | 173.178 | + | 532.988i | 0.211968 | + | 0.652372i | ||||
\(818\) | −109.873 | + | 338.154i | −0.134319 | + | 0.413392i | ||||
\(819\) | 364.971 | + | 265.167i | 0.445630 | + | 0.323769i | ||||
\(820\) | 52.5881 | − | 72.3813i | 0.0641319 | − | 0.0882699i | ||||
\(821\) | 189.117 | + | 61.4477i | 0.230349 | + | 0.0748450i | 0.421917 | − | 0.906634i | \(-0.361357\pi\) |
−0.191568 | + | 0.981479i | \(0.561357\pi\) | |||||||
\(822\) | 116.951 | − | 37.9996i | 0.142276 | − | 0.0462283i | ||||
\(823\) | −108.723 | + | 78.9920i | −0.132106 | + | 0.0959806i | −0.651876 | − | 0.758326i | \(-0.726018\pi\) |
0.519770 | + | 0.854306i | \(0.326018\pi\) | |||||||
\(824\) | − | 1554.52i | − | 1.88656i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1289.32 | −1.56092 | ||||||||
\(827\) | −702.436 | − | 966.820i | −0.849378 | − | 1.16907i | −0.983999 | − | 0.178172i | \(-0.942982\pi\) |
0.134621 | − | 0.990897i | \(-0.457018\pi\) | |||||||
\(828\) | 33.3740 | + | 102.715i | 0.0403067 | + | 0.124051i | ||||
\(829\) | 441.399 | − | 1358.49i | 0.532448 | − | 1.63870i | −0.216653 | − | 0.976249i | \(-0.569514\pi\) |
0.749101 | − | 0.662456i | \(-0.230486\pi\) | |||||||
\(830\) | 16.0408 | + | 11.6543i | 0.0193263 | + | 0.0140414i | ||||
\(831\) | 249.251 | − | 343.065i | 0.299942 | − | 0.412834i | ||||
\(832\) | 748.398 | + | 243.169i | 0.899517 | + | 0.292271i | ||||
\(833\) | −522.367 | + | 169.727i | −0.627091 | + | 0.203754i | ||||
\(834\) | −53.3358 | + | 38.7507i | −0.0639518 | + | 0.0464637i | ||||
\(835\) | 302.577i | 0.362368i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.6231 | −0.0258341 | ||||||||
\(838\) | 518.517 | + | 713.678i | 0.618756 | + | 0.851644i | ||||
\(839\) | 294.589 | + | 906.652i | 0.351119 | + | 1.08063i | 0.958226 | + | 0.286014i | \(0.0923303\pi\) |
−0.607106 | + | 0.794621i | \(0.707670\pi\) | |||||||
\(840\) | −100.254 | + | 308.551i | −0.119350 | + | 0.367323i | ||||
\(841\) | −110.423 | − | 80.2273i | −0.131300 | − | 0.0953951i | ||||
\(842\) | −501.335 | + | 690.028i | −0.595410 | + | 0.819511i | ||||
\(843\) | −568.706 | − | 184.784i | −0.674622 | − | 0.219198i | ||||
\(844\) | 23.8455 | − | 7.74788i | 0.0282530 | − | 0.00917995i | ||||
\(845\) | 125.912 | − | 91.4805i | 0.149008 | − | 0.108261i | ||||
\(846\) | 247.837i | 0.292951i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −272.086 | −0.320856 | ||||||||
\(849\) | 236.790 | + | 325.913i | 0.278904 | + | 0.383879i | ||||
\(850\) | −97.7402 | − | 300.813i | −0.114988 | − | 0.353898i | ||||
\(851\) | 346.609 | − | 1066.75i | 0.407296 | − | 1.25353i | ||||
\(852\) | −45.2833 | − | 32.9003i | −0.0531495 | − | 0.0386153i | ||||
\(853\) | −572.858 | + | 788.472i | −0.671581 | + | 0.924352i | −0.999795 | − | 0.0202516i | \(-0.993553\pi\) |
0.328214 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(854\) | −15.8633 | − | 5.15429i | −0.0185753 | − | 0.00603547i | ||||
\(855\) | 79.1077 | − | 25.7037i | 0.0925237 | − | 0.0300628i | ||||
\(856\) | 1297.02 | − | 942.342i | 1.51521 | − | 1.10087i | ||||
\(857\) | − | 1571.80i | − | 1.83407i | −0.398805 | − | 0.917036i | \(-0.630575\pi\) | ||
0.398805 | − | 0.917036i | \(-0.369425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −740.779 | −0.862373 | −0.431187 | − | 0.902263i | \(-0.641905\pi\) | ||||
−0.431187 | + | 0.902263i | \(0.641905\pi\) | |||||||
\(860\) | −135.127 | − | 185.987i | −0.157125 | − | 0.216264i | ||||
\(861\) | −94.3871 | − | 290.494i | −0.109625 | − | 0.337391i | ||||
\(862\) | −246.851 | + | 759.730i | −0.286370 | + | 0.881357i | ||||
\(863\) | −275.883 | − | 200.441i | −0.319679 | − | 0.232260i | 0.416360 | − | 0.909200i | \(-0.363306\pi\) |
−0.736038 | + | 0.676940i | \(0.763306\pi\) | |||||||
\(864\) | −90.9391 | + | 125.167i | −0.105254 | + | 0.144869i | ||||
\(865\) | 76.6593 | + | 24.9081i | 0.0886235 | + | 0.0287955i | ||||
\(866\) | 201.347 | − | 65.4216i | 0.232502 | − | 0.0755446i | ||||
\(867\) | 209.290 | − | 152.058i | 0.241396 | − | 0.175384i | ||||
\(868\) | − | 87.8610i | − | 0.101222i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −143.046 | −0.164421 | ||||||||
\(871\) | −498.570 | − | 686.223i | −0.572411 | − | 0.787856i | ||||
\(872\) | 293.714 | + | 903.960i | 0.336829 | + | 1.03665i | ||||
\(873\) | −30.7177 | + | 94.5393i | −0.0351863 | + | 0.108292i | ||||
\(874\) | −220.912 | − | 160.502i | −0.252760 | − | 0.183641i | ||||
\(875\) | 589.500 | − | 811.377i | 0.673714 | − | 0.927288i | ||||
\(876\) | 270.089 | + | 87.7573i | 0.308321 | + | 0.100180i | ||||
\(877\) | −973.335 | + | 316.256i | −1.10985 | + | 0.360611i | −0.805884 | − | 0.592073i | \(-0.798310\pi\) |
−0.303962 | + | 0.952684i | \(0.598310\pi\) | |||||||
\(878\) | 229.330 | − | 166.618i | 0.261195 | − | 0.189770i | ||||
\(879\) | − | 924.446i | − | 1.05170i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1023.93 | −1.16224 | −0.581121 | − | 0.813817i | \(-0.697386\pi\) | ||||
−0.581121 | + | 0.813817i | \(0.697386\pi\) | |||||||
\(882\) | 111.153 | + | 152.990i | 0.126024 | + | 0.173458i | ||||
\(883\) | −515.168 | − | 1585.52i | −0.583429 | − | 1.79561i | −0.605489 | − | 0.795854i | \(-0.707022\pi\) |
0.0220600 | − | 0.999757i | \(-0.492978\pi\) | |||||||
\(884\) | −121.427 | + | 373.715i | −0.137361 | + | 0.422755i | ||||
\(885\) | −312.790 | − | 227.256i | −0.353436 | − | 0.256786i | ||||
\(886\) | 272.923 | − | 375.647i | 0.308040 | − | 0.423980i | ||||
\(887\) | 660.220 | + | 214.519i | 0.744329 | + | 0.241847i | 0.656539 | − | 0.754292i | \(-0.272020\pi\) |
0.0877899 | + | 0.996139i | \(0.472020\pi\) | |||||||
\(888\) | 926.569 | − | 301.061i | 1.04343 | − | 0.339032i | ||||
\(889\) | 44.1720 | − | 32.0928i | 0.0496873 | − | 0.0360999i | ||||
\(890\) | − | 12.3061i | − | 0.0138271i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 673.970 | 0.755572 | ||||||||
\(893\) | 432.696 | + | 595.555i | 0.484542 | + | 0.666915i | ||||
\(894\) | −8.16053 | − | 25.1155i | −0.00912810 | − | 0.0280934i | ||||
\(895\) | −128.302 | + | 394.872i | −0.143354 | + | 0.441198i | ||||
\(896\) | −393.309 | − | 285.756i | −0.438961 | − | 0.318924i | ||||
\(897\) | 261.038 | − | 359.288i | 0.291012 | − | 0.400544i | ||||
\(898\) | 74.1831 | + | 24.1036i | 0.0826093 | + | 0.0268414i | ||||
\(899\) | 105.048 | − | 34.1321i | 0.116849 | − | 0.0379667i | ||||
\(900\) | 103.501 | − | 75.1981i | 0.115001 | − | 0.0835534i | ||||
\(901\) | − | 1196.06i | − | 1.32748i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −784.849 | −0.869157 | ||||||||
\(904\) | −80.4347 | − | 110.709i | −0.0889764 | − | 0.122466i | ||||
\(905\) | 14.4372 | + | 44.4332i | 0.0159527 | + | 0.0490975i | ||||
\(906\) | 73.4339 | − | 226.006i | 0.0810528 | − | 0.249455i | ||||
\(907\) | 653.260 | + | 474.621i | 0.720243 | + | 0.523287i | 0.886462 | − | 0.462802i | \(-0.153156\pi\) |
−0.166219 | + | 0.986089i | \(0.553156\pi\) | |||||||
\(908\) | −12.1114 | + | 16.6699i | −0.0133385 | + | 0.0183589i | ||||
\(909\) | 276.984 | + | 89.9975i | 0.304713 | + | 0.0990071i | ||||
\(910\) | 444.997 | − | 144.588i | 0.489007 | − | 0.158888i | ||||
\(911\) | 740.106 | − | 537.719i | 0.812411 | − | 0.590251i | −0.102118 | − | 0.994772i | \(-0.532562\pi\) |
0.914529 | + | 0.404521i | \(0.132562\pi\) | |||||||
\(912\) | − | 56.2679i | − | 0.0616972i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 867.368 | 0.948981 | ||||||||
\(915\) | −2.93995 | − | 4.04650i | −0.00321306 | − | 0.00442240i | ||||
\(916\) | 134.088 | + | 412.681i | 0.146384 | + | 0.450525i | ||||
\(917\) | −681.544 | + | 2097.58i | −0.743233 | + | 2.28743i | ||||
\(918\) | 67.3701 | + | 48.9473i | 0.0733879 | + | 0.0533195i | ||||
\(919\) | −593.922 | + | 817.464i | −0.646270 | + | 0.889514i | −0.998930 | − | 0.0462371i | \(-0.985277\pi\) |
0.352661 | + | 0.935751i | \(0.385277\pi\) | |||||||
\(920\) | 303.747 | + | 98.6933i | 0.330159 | + | 0.107275i | ||||
\(921\) | −235.307 | + | 76.4558i | −0.255490 | + | 0.0830139i | ||||
\(922\) | −539.905 | + | 392.264i | −0.585580 | + | 0.425449i | ||||
\(923\) | 230.165i | 0.249367i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1328.68 | −1.43641 | ||||||||
\(926\) | −291.800 | − | 401.628i | −0.315118 | − | 0.433723i | ||||
\(927\) | −172.483 | − | 530.848i | −0.186066 | − | 0.572652i | ||||
\(928\) | 244.217 | − | 751.623i | 0.263165 | − | 0.809938i | ||||
\(929\) | 200.314 | + | 145.537i | 0.215623 | + | 0.156660i | 0.690354 | − | 0.723471i | \(-0.257455\pi\) |
−0.474731 | + | 0.880131i | \(0.657455\pi\) | |||||||
\(930\) | −13.1822 | + | 18.1437i | −0.0141744 | + | 0.0195094i | ||||
\(931\) | 534.207 | + | 173.574i | 0.573799 | + | 0.186439i | ||||
\(932\) | −493.801 | + | 160.446i | −0.529830 | + | 0.172152i | ||||
\(933\) | −64.3186 | + | 46.7302i | −0.0689374 | + | 0.0500859i | ||||
\(934\) | 441.436i | 0.472629i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 385.744 | 0.412120 | ||||||||
\(937\) | −754.932 | − | 1039.07i | −0.805690 | − | 1.10894i | −0.991974 | − | 0.126441i | \(-0.959644\pi\) |
0.186284 | − | 0.982496i | \(-0.440356\pi\) | |||||||
\(938\) | −225.705 | − | 694.650i | −0.240624 | − | 0.740565i | ||||
\(939\) | −190.817 | + | 587.273i | −0.203213 | + | 0.625424i | ||||
\(940\) | −244.307 | − | 177.499i | −0.259901 | − | 0.188829i | ||||
\(941\) | 1029.50 | − | 1416.98i | 1.09404 | − | 1.50582i | 0.250993 | − | 0.967989i | \(-0.419243\pi\) |
0.843051 | − | 0.537833i | \(-0.180757\pi\) | |||||||
\(942\) | −42.6071 | − | 13.8439i | −0.0452305 | − | 0.0146963i | ||||
\(943\) | −285.970 | + | 92.9174i | −0.303256 | + | 0.0985338i | ||||
\(944\) | −211.593 | + | 153.731i | −0.224145 | + | 0.162851i | ||||
\(945\) | 116.490i | 0.123270i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −87.2570 | −0.0921405 | −0.0460702 | − | 0.998938i | \(-0.514670\pi\) | ||||
−0.0460702 | + | 0.998938i | \(0.514670\pi\) | |||||||
\(948\) | 64.2783 | + | 88.4716i | 0.0678042 | + | 0.0933244i | ||||
\(949\) | −360.863 | − | 1110.62i | −0.380256 | − | 1.17031i | ||||
\(950\) | −99.9555 | + | 307.631i | −0.105216 | + | 0.323823i | ||||
\(951\) | −86.6801 | − | 62.9768i | −0.0911463 | − | 0.0662216i | ||||
\(952\) | −567.068 | + | 780.502i | −0.595660 | + | 0.819855i | ||||
\(953\) | −1227.56 | − | 398.859i | −1.28810 | − | 0.418529i | −0.416675 | − | 0.909056i | \(-0.636805\pi\) |
−0.871426 | + | 0.490526i | \(0.836805\pi\) | |||||||
\(954\) | −391.647 | + | 127.254i | −0.410532 | + | 0.133390i | ||||
\(955\) | −110.534 | + | 80.3079i | −0.115743 | + | 0.0840920i | ||||
\(956\) | − | 174.365i | − | 0.182390i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 445.474 | 0.465004 | ||||||||
\(959\) | 300.670 | + | 413.836i | 0.313524 | + | 0.431529i | ||||
\(960\) | 62.7909 | + | 193.250i | 0.0654072 | + | 0.201303i | ||||
\(961\) | −291.614 | + | 897.496i | −0.303449 | + | 0.933919i | ||||
\(962\) | −1136.73 | − | 825.886i | −1.18164 | − | 0.858509i | ||||
\(963\) | 338.357 | − | 465.709i | 0.351358 | − | 0.483602i | ||||
\(964\) | 314.945 | + | 102.332i | 0.326707 | + | 0.106153i | ||||
\(965\) | −541.291 | + | 175.876i | −0.560924 | + | 0.182255i | ||||
\(966\) | 309.382 | − | 224.779i | 0.320271 | − | 0.232690i | ||||
\(967\) | − | 321.693i | − | 0.332671i | −0.986069 | − | 0.166336i | \(-0.946806\pi\) | ||
0.986069 | − | 0.166336i | \(-0.0531935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 247.348 | 0.255261 | ||||||||
\(970\) | 60.6003 | + | 83.4091i | 0.0624745 | + | 0.0859888i | ||||
\(971\) | 38.6437 | + | 118.933i | 0.0397979 | + | 0.122485i | 0.968982 | − | 0.247133i | \(-0.0794885\pi\) |
−0.929184 | + | 0.369618i | \(0.879488\pi\) | |||||||
\(972\) | −10.4085 | + | 32.0342i | −0.0107084 | + | 0.0329570i | ||||
\(973\) | −221.867 | − | 161.196i | −0.228024 | − | 0.165669i | ||||
\(974\) | 256.915 | − | 353.613i | 0.263773 | − | 0.363052i | ||||
\(975\) | −500.327 | − | 162.566i | −0.513156 | − | 0.166734i | ||||
\(976\) | −3.21792 | + | 1.04557i | −0.00329705 | + | 0.00107128i | ||||
\(977\) | −1140.11 | + | 828.336i | −1.16695 | + | 0.847836i | −0.990640 | − | 0.136499i | \(-0.956415\pi\) |
−0.176307 | + | 0.984335i | \(0.556415\pi\) | |||||||
\(978\) | 33.9470i | 0.0347107i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −230.418 | −0.235121 | ||||||||
\(981\) | 200.599 | + | 276.101i | 0.204484 | + | 0.281448i | ||||
\(982\) | −324.278 | − | 998.025i | −0.330222 | − | 1.01632i | ||||
\(983\) | 5.70955 | − | 17.5722i | 0.00580829 | − | 0.0178761i | −0.948110 | − | 0.317941i | \(-0.897008\pi\) |
0.953919 | + | 0.300065i | \(0.0970085\pi\) | |||||||
\(984\) | −211.294 | − | 153.514i | −0.214729 | − | 0.156010i | ||||
\(985\) | 224.321 | − | 308.752i | 0.227737 | − | 0.313454i | ||||
\(986\) | −404.555 | − | 131.448i | −0.410299 | − | 0.133314i | ||||
\(987\) | −980.497 | + | 318.583i | −0.993411 | + | 0.322779i | ||||
\(988\) | 325.107 | − | 236.204i | 0.329055 | − | 0.239073i | ||||
\(989\) | 772.628i | 0.781222i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −212.736 | −0.214668 | −0.107334 | − | 0.994223i | \(-0.534231\pi\) | ||||
−0.107334 | + | 0.994223i | \(0.534231\pi\) | |||||||
\(992\) | −72.8292 | − | 100.241i | −0.0734166 | − | 0.101049i | ||||
\(993\) | 181.958 | + | 560.010i | 0.183241 | + | 0.563958i | ||||
\(994\) | −61.2456 | + | 188.494i | −0.0616153 | + | 0.189632i | ||||
\(995\) | −181.888 | − | 132.150i | −0.182802 | − | 0.132814i | ||||
\(996\) | −14.0178 | + | 19.2939i | −0.0140741 | + | 0.0193714i | ||||
\(997\) | −334.094 | − | 108.554i | −0.335099 | − | 0.108880i | 0.136634 | − | 0.990622i | \(-0.456372\pi\) |
−0.471733 | + | 0.881741i | \(0.656372\pi\) | |||||||
\(998\) | 65.9123 | − | 21.4162i | 0.0660444 | − | 0.0214591i | ||||
\(999\) | 283.007 | − | 205.616i | 0.283290 | − | 0.205822i |
(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 | 363.3.g.g.118.2 | 16 | ||
11.2 | odd | 10 | 363.3.c.e.241.6 | 16 | |||
11.3 | even | 5 | 363.3.g.f.94.2 | 16 | |||
11.4 | even | 5 | 363.3.g.a.40.3 | 16 | |||
11.5 | even | 5 | 33.3.g.a.13.3 | ✓ | 16 | ||
11.6 | odd | 10 | 363.3.g.f.112.2 | 16 | |||
11.7 | odd | 10 | inner | 363.3.g.g.40.2 | 16 | ||
11.8 | odd | 10 | 33.3.g.a.28.3 | yes | 16 | ||
11.9 | even | 5 | 363.3.c.e.241.11 | 16 | |||
11.10 | odd | 2 | 363.3.g.a.118.3 | 16 | |||
33.2 | even | 10 | 1089.3.c.m.604.11 | 16 | |||
33.5 | odd | 10 | 99.3.k.c.46.2 | 16 | |||
33.8 | even | 10 | 99.3.k.c.28.2 | 16 | |||
33.20 | odd | 10 | 1089.3.c.m.604.6 | 16 | |||
44.19 | even | 10 | 528.3.bf.b.193.2 | 16 | |||
44.27 | odd | 10 | 528.3.bf.b.145.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.13.3 | ✓ | 16 | 11.5 | even | 5 | ||
33.3.g.a.28.3 | yes | 16 | 11.8 | odd | 10 | ||
99.3.k.c.28.2 | 16 | 33.8 | even | 10 | |||
99.3.k.c.46.2 | 16 | 33.5 | odd | 10 | |||
363.3.c.e.241.6 | 16 | 11.2 | odd | 10 | |||
363.3.c.e.241.11 | 16 | 11.9 | even | 5 | |||
363.3.g.a.40.3 | 16 | 11.4 | even | 5 | |||
363.3.g.a.118.3 | 16 | 11.10 | odd | 2 | |||
363.3.g.f.94.2 | 16 | 11.3 | even | 5 | |||
363.3.g.f.112.2 | 16 | 11.6 | odd | 10 | |||
363.3.g.g.40.2 | 16 | 11.7 | odd | 10 | inner | ||
363.3.g.g.118.2 | 16 | 1.1 | even | 1 | trivial | ||
528.3.bf.b.145.2 | 16 | 44.27 | odd | 10 | |||
528.3.bf.b.193.2 | 16 | 44.19 | even | 10 | |||
1089.3.c.m.604.6 | 16 | 33.20 | odd | 10 | |||
1089.3.c.m.604.11 | 16 | 33.2 | even | 10 |