Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(124,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.124");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.b (of order \(2\), degree \(1\), 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1632160000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 12x^{6} + 46x^{4} + 65x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 124.5 | ||
Root | \(1.46673i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.124 |
Dual form | 375.2.b.c.124.4 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0935099i | 0.0661215i | 0.999453 | + | 0.0330607i | \(0.0105255\pi\) | ||||
−0.999453 | + | 0.0330607i | \(0.989475\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 1.99126 | 0.995628 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0935099 | 0.0381753 | ||||||||
\(7\) | 2.93346i | 1.10875i | 0.832269 | + | 0.554373i | \(0.187042\pi\) | ||||
−0.832269 | + | 0.554373i | \(0.812958\pi\) | |||||||
\(8\) | 0.373222i | 0.131954i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.04905 | 1.52235 | 0.761173 | − | 0.648549i | \(-0.224624\pi\) | ||||
0.761173 | + | 0.648549i | \(0.224624\pi\) | |||||||
\(12\) | − 1.99126i | − 0.574826i | ||||||||
\(13\) | 3.69740i | 1.02547i | 0.858546 | + | 0.512737i | \(0.171368\pi\) | ||||
−0.858546 | + | 0.512737i | \(0.828632\pi\) | |||||||
\(14\) | −0.274308 | −0.0733119 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.94761 | 0.986903 | ||||||||
\(17\) | − 2.85410i | − 0.692221i | −0.938194 | − | 0.346111i | \(-0.887502\pi\) | ||||
0.938194 | − | 0.346111i | \(-0.112498\pi\) | |||||||
\(18\) | − 0.0935099i | − 0.0220405i | ||||||||
\(19\) | −4.43101 | −1.01654 | −0.508272 | − | 0.861196i | \(-0.669716\pi\) | ||||
−0.508272 | + | 0.861196i | \(0.669716\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.93346 | 0.640134 | ||||||||
\(22\) | 0.472136i | 0.100660i | ||||||||
\(23\) | − 8.36448i | − 1.74411i | −0.489404 | − | 0.872057i | \(-0.662786\pi\) | ||||
0.489404 | − | 0.872057i | \(-0.337214\pi\) | |||||||
\(24\) | 0.373222 | 0.0761836 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.345743 | −0.0678058 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 5.84128i | 1.10390i | ||||||||
\(29\) | −1.88442 | −0.349927 | −0.174964 | − | 0.984575i | \(-0.555981\pi\) | ||||
−0.174964 | + | 0.984575i | \(0.555981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.266381 | 0.0478435 | 0.0239218 | − | 0.999714i | \(-0.492385\pi\) | ||||
0.0239218 | + | 0.999714i | \(0.492385\pi\) | |||||||
\(32\) | 1.11558i | 0.197209i | ||||||||
\(33\) | − 5.04905i | − 0.878926i | ||||||||
\(34\) | 0.266887 | 0.0457707 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.99126 | −0.331876 | ||||||||
\(37\) | − 8.35655i | − 1.37381i | −0.726748 | − | 0.686904i | \(-0.758969\pi\) | ||||
0.726748 | − | 0.686904i | \(-0.241031\pi\) | |||||||
\(38\) | − 0.414344i | − 0.0672154i | ||||||||
\(39\) | 3.69740 | 0.592057 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.169532 | −0.0264764 | −0.0132382 | − | 0.999912i | \(-0.504214\pi\) | ||||
−0.0132382 | + | 0.999912i | \(0.504214\pi\) | |||||||
\(42\) | 0.274308i | 0.0423266i | ||||||||
\(43\) | 9.59262i | 1.46286i | 0.681916 | + | 0.731430i | \(0.261147\pi\) | ||||
−0.681916 | + | 0.731430i | \(0.738853\pi\) | |||||||
\(44\) | 10.0539 | 1.51569 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.782161 | 0.115323 | ||||||||
\(47\) | 2.43101i | 0.354600i | 0.984157 | + | 0.177300i | \(0.0567363\pi\) | ||||
−0.984157 | + | 0.177300i | \(0.943264\pi\) | |||||||
\(48\) | − 3.94761i | − 0.569789i | ||||||||
\(49\) | −1.60521 | −0.229316 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.85410 | −0.399654 | ||||||||
\(52\) | 7.36246i | 1.02099i | ||||||||
\(53\) | 7.24889i | 0.995712i | 0.867260 | + | 0.497856i | \(0.165879\pi\) | ||||
−0.867260 | + | 0.497856i | \(0.834121\pi\) | |||||||
\(54\) | −0.0935099 | −0.0127251 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.09483 | −0.146303 | ||||||||
\(57\) | 4.43101i | 0.586902i | ||||||||
\(58\) | − 0.176211i | − 0.0231377i | ||||||||
\(59\) | −5.89522 | −0.767493 | −0.383746 | − | 0.923439i | \(-0.625366\pi\) | ||||
−0.383746 | + | 0.923439i | \(0.625366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.48496 | −0.830314 | −0.415157 | − | 0.909750i | \(-0.636273\pi\) | ||||
−0.415157 | + | 0.909750i | \(0.636273\pi\) | |||||||
\(62\) | 0.0249093i | 0.00316348i | ||||||||
\(63\) | − 2.93346i | − 0.369582i | ||||||||
\(64\) | 7.79091 | 0.973863 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.472136 | 0.0581159 | ||||||||
\(67\) | − 8.55942i | − 1.04570i | −0.852425 | − | 0.522850i | \(-0.824869\pi\) | ||||
0.852425 | − | 0.522850i | \(-0.175131\pi\) | |||||||
\(68\) | − 5.68325i | − 0.689195i | ||||||||
\(69\) | −8.36448 | −1.00696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.2676 | −1.93061 | −0.965306 | − | 0.261121i | \(-0.915908\pi\) | ||||
−0.965306 | + | 0.261121i | \(0.915908\pi\) | |||||||
\(72\) | − 0.373222i | − 0.0439846i | ||||||||
\(73\) | 1.81298i | 0.212193i | 0.994356 | + | 0.106097i | \(0.0338353\pi\) | ||||
−0.994356 | + | 0.106097i | \(0.966165\pi\) | |||||||
\(74\) | 0.781420 | 0.0908383 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.82328 | −1.01210 | ||||||||
\(77\) | 14.8112i | 1.68789i | ||||||||
\(78\) | 0.345743i | 0.0391477i | ||||||||
\(79\) | −2.67198 | −0.300621 | −0.150311 | − | 0.988639i | \(-0.548027\pi\) | ||||
−0.150311 | + | 0.988639i | \(0.548027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.0158529i | − 0.00175066i | ||||||||
\(83\) | − 12.9032i | − 1.41630i | −0.706060 | − | 0.708152i | \(-0.749529\pi\) | ||||
0.706060 | − | 0.708152i | \(-0.250471\pi\) | |||||||
\(84\) | 5.84128 | 0.637336 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.897005 | −0.0967265 | ||||||||
\(87\) | 1.88442i | 0.202031i | ||||||||
\(88\) | 1.88442i | 0.200879i | ||||||||
\(89\) | −12.6309 | −1.33887 | −0.669434 | − | 0.742871i | \(-0.733463\pi\) | ||||
−0.669434 | + | 0.742871i | \(0.733463\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.8462 | −1.13699 | ||||||||
\(92\) | − 16.6558i | − 1.73649i | ||||||||
\(93\) | − 0.266381i | − 0.0276225i | ||||||||
\(94\) | −0.227324 | −0.0234467 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.11558 | 0.113859 | ||||||||
\(97\) | − 6.89032i | − 0.699606i | −0.936823 | − | 0.349803i | \(-0.886248\pi\) | ||||
0.936823 | − | 0.349803i | \(-0.113752\pi\) | |||||||
\(98\) | − 0.150103i | − 0.0151627i | ||||||||
\(99\) | −5.04905 | −0.507448 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.77964 | 0.973110 | 0.486555 | − | 0.873650i | \(-0.338253\pi\) | ||||
0.486555 | + | 0.873650i | \(0.338253\pi\) | |||||||
\(102\) | − 0.266887i | − 0.0264257i | ||||||||
\(103\) | 14.8620i | 1.46440i | 0.681090 | + | 0.732200i | \(0.261506\pi\) | ||||
−0.681090 | + | 0.732200i | \(0.738494\pi\) | |||||||
\(104\) | −1.37995 | −0.135315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.677843 | −0.0658380 | ||||||||
\(107\) | 3.63552i | 0.351459i | 0.984438 | + | 0.175730i | \(0.0562284\pi\) | ||||
−0.984438 | + | 0.175730i | \(0.943772\pi\) | |||||||
\(108\) | 1.99126i | 0.191609i | ||||||||
\(109\) | 4.62293 | 0.442797 | 0.221398 | − | 0.975183i | \(-0.428938\pi\) | ||||
0.221398 | + | 0.975183i | \(0.428938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.35655 | −0.793169 | ||||||||
\(112\) | 11.5802i | 1.09422i | ||||||||
\(113\) | − 0.776757i | − 0.0730712i | −0.999332 | − | 0.0365356i | \(-0.988368\pi\) | ||||
0.999332 | − | 0.0365356i | \(-0.0116322\pi\) | |||||||
\(114\) | −0.414344 | −0.0388068 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.75235 | −0.348397 | ||||||||
\(117\) | − 3.69740i | − 0.341824i | ||||||||
\(118\) | − 0.551262i | − 0.0507478i | ||||||||
\(119\) | 8.37240 | 0.767497 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.4929 | 1.31754 | ||||||||
\(122\) | − 0.606408i | − 0.0549016i | ||||||||
\(123\) | 0.169532i | 0.0152861i | ||||||||
\(124\) | 0.530434 | 0.0476343 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.274308 | 0.0244373 | ||||||||
\(127\) | 6.26763i | 0.556162i | 0.960558 | + | 0.278081i | \(0.0896984\pi\) | ||||
−0.960558 | + | 0.278081i | \(0.910302\pi\) | |||||||
\(128\) | 2.95970i | 0.261603i | ||||||||
\(129\) | 9.59262 | 0.844583 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.1346 | −1.40968 | −0.704841 | − | 0.709365i | \(-0.748982\pi\) | ||||
−0.704841 | + | 0.709365i | \(0.748982\pi\) | |||||||
\(132\) | − 10.0539i | − 0.875084i | ||||||||
\(133\) | − 12.9982i | − 1.12709i | ||||||||
\(134\) | 0.800391 | 0.0691432 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.06521 | 0.0913413 | ||||||||
\(137\) | − 17.9650i | − 1.53486i | −0.641135 | − | 0.767428i | \(-0.721536\pi\) | ||||
0.641135 | − | 0.767428i | \(-0.278464\pi\) | |||||||
\(138\) | − 0.782161i | − 0.0665820i | ||||||||
\(139\) | −8.83661 | −0.749512 | −0.374756 | − | 0.927124i | \(-0.622273\pi\) | ||||
−0.374756 | + | 0.927124i | \(0.622273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.43101 | 0.204728 | ||||||||
\(142\) | − 1.52118i | − 0.127655i | ||||||||
\(143\) | 18.6683i | 1.56112i | ||||||||
\(144\) | −3.94761 | −0.328968 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.169532 | −0.0140305 | ||||||||
\(147\) | 1.60521i | 0.132395i | ||||||||
\(148\) | − 16.6400i | − 1.36780i | ||||||||
\(149\) | 17.3881 | 1.42449 | 0.712245 | − | 0.701931i | \(-0.247679\pi\) | ||||
0.712245 | + | 0.701931i | \(0.247679\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.96378 | 0.241189 | 0.120594 | − | 0.992702i | \(-0.461520\pi\) | ||||
0.120594 | + | 0.992702i | \(0.461520\pi\) | |||||||
\(152\) | − 1.65375i | − 0.134137i | ||||||||
\(153\) | 2.85410i | 0.230740i | ||||||||
\(154\) | −1.38499 | −0.111606 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.36246 | 0.589469 | ||||||||
\(157\) | 3.06654i | 0.244736i | 0.992485 | + | 0.122368i | \(0.0390489\pi\) | ||||
−0.992485 | + | 0.122368i | \(0.960951\pi\) | |||||||
\(158\) | − 0.249857i | − 0.0198775i | ||||||||
\(159\) | 7.24889 | 0.574875 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.5369 | 1.93378 | ||||||||
\(162\) | 0.0935099i | 0.00734683i | ||||||||
\(163\) | − 10.1803i | − 0.797386i | −0.917085 | − | 0.398693i | \(-0.869464\pi\) | ||||
0.917085 | − | 0.398693i | \(-0.130536\pi\) | |||||||
\(164\) | −0.337581 | −0.0263606 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.20657 | 0.0936482 | ||||||||
\(167\) | 20.2373i | 1.56601i | 0.622015 | + | 0.783005i | \(0.286314\pi\) | ||||
−0.622015 | + | 0.783005i | \(0.713686\pi\) | |||||||
\(168\) | 1.09483i | 0.0844682i | ||||||||
\(169\) | −0.670734 | −0.0515950 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.43101 | 0.338848 | ||||||||
\(172\) | 19.1014i | 1.45647i | ||||||||
\(173\) | 5.07734i | 0.386023i | 0.981196 | + | 0.193012i | \(0.0618255\pi\) | ||||
−0.981196 | + | 0.193012i | \(0.938174\pi\) | |||||||
\(174\) | −0.176211 | −0.0133586 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.9317 | 1.50241 | ||||||||
\(177\) | 5.89522i | 0.443112i | ||||||||
\(178\) | − 1.18111i | − 0.0885280i | ||||||||
\(179\) | −12.3216 | −0.920958 | −0.460479 | − | 0.887671i | \(-0.652322\pi\) | ||||
−0.460479 | + | 0.887671i | \(0.652322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.4243 | 1.36947 | 0.684735 | − | 0.728792i | \(-0.259918\pi\) | ||||
0.684735 | + | 0.728792i | \(0.259918\pi\) | |||||||
\(182\) | − 1.01422i | − 0.0751793i | ||||||||
\(183\) | 6.48496i | 0.479382i | ||||||||
\(184\) | 3.12181 | 0.230143 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.0249093 | 0.00182644 | ||||||||
\(187\) | − 14.4105i | − 1.05380i | ||||||||
\(188\) | 4.84077i | 0.353050i | ||||||||
\(189\) | −2.93346 | −0.213378 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.60847 | 0.116385 | 0.0581925 | − | 0.998305i | \(-0.481466\pi\) | ||||
0.0581925 | + | 0.998305i | \(0.481466\pi\) | |||||||
\(192\) | − 7.79091i | − 0.562260i | ||||||||
\(193\) | − 15.3167i | − 1.10252i | −0.834334 | − | 0.551259i | \(-0.814148\pi\) | ||||
0.834334 | − | 0.551259i | \(-0.185852\pi\) | |||||||
\(194\) | 0.644314 | 0.0462590 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.19638 | −0.228313 | ||||||||
\(197\) | − 5.48496i | − 0.390787i | −0.980725 | − | 0.195394i | \(-0.937402\pi\) | ||||
0.980725 | − | 0.195394i | \(-0.0625984\pi\) | |||||||
\(198\) | − 0.472136i | − 0.0335532i | ||||||||
\(199\) | −12.0885 | −0.856933 | −0.428467 | − | 0.903558i | \(-0.640946\pi\) | ||||
−0.428467 | + | 0.903558i | \(0.640946\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.55942 | −0.603735 | ||||||||
\(202\) | 0.914493i | 0.0643435i | ||||||||
\(203\) | − 5.52786i | − 0.387980i | ||||||||
\(204\) | −5.68325 | −0.397907 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.38975 | −0.0968282 | ||||||||
\(207\) | 8.36448i | 0.581371i | ||||||||
\(208\) | 14.5959i | 1.01204i | ||||||||
\(209\) | −22.3724 | −1.54753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.26148 | −0.362215 | −0.181108 | − | 0.983463i | \(-0.557968\pi\) | ||||
−0.181108 | + | 0.983463i | \(0.557968\pi\) | |||||||
\(212\) | 14.4344i | 0.991359i | ||||||||
\(213\) | 16.2676i | 1.11464i | ||||||||
\(214\) | −0.339957 | −0.0232390 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.373222 | −0.0253945 | ||||||||
\(217\) | 0.781420i | 0.0530463i | ||||||||
\(218\) | 0.432290i | 0.0292784i | ||||||||
\(219\) | 1.81298 | 0.122510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.5527 | 0.709854 | ||||||||
\(222\) | − 0.781420i | − 0.0524455i | ||||||||
\(223\) | − 1.41228i | − 0.0945732i | −0.998881 | − | 0.0472866i | \(-0.984943\pi\) | ||||
0.998881 | − | 0.0472866i | \(-0.0150574\pi\) | |||||||
\(224\) | −3.27253 | −0.218655 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.0726345 | 0.00483157 | ||||||||
\(227\) | − 19.5656i | − 1.29861i | −0.760527 | − | 0.649306i | \(-0.775059\pi\) | ||||
0.760527 | − | 0.649306i | \(-0.224941\pi\) | |||||||
\(228\) | 8.82328i | 0.584336i | ||||||||
\(229\) | 21.3735 | 1.41240 | 0.706200 | − | 0.708012i | \(-0.250408\pi\) | ||||
0.706200 | + | 0.708012i | \(0.250408\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.8112 | 0.974505 | ||||||||
\(232\) | − 0.703305i | − 0.0461742i | ||||||||
\(233\) | 3.15382i | 0.206614i | 0.994650 | + | 0.103307i | \(0.0329424\pi\) | ||||
−0.994650 | + | 0.103307i | \(0.967058\pi\) | |||||||
\(234\) | 0.345743 | 0.0226019 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.7389 | −0.764137 | ||||||||
\(237\) | 2.67198i | 0.173564i | ||||||||
\(238\) | 0.782903i | 0.0507480i | ||||||||
\(239\) | 19.2725 | 1.24664 | 0.623318 | − | 0.781968i | \(-0.285784\pi\) | ||||
0.623318 | + | 0.781968i | \(0.285784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7210 | 1.46359 | 0.731795 | − | 0.681525i | \(-0.238683\pi\) | ||||
0.731795 | + | 0.681525i | \(0.238683\pi\) | |||||||
\(242\) | 1.35523i | 0.0871174i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −12.9132 | −0.826684 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0158529 | −0.00101074 | ||||||||
\(247\) | − 16.3832i | − 1.04244i | ||||||||
\(248\) | 0.0994194i | 0.00631314i | ||||||||
\(249\) | −12.9032 | −0.817704 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.14124 | 0.513870 | 0.256935 | − | 0.966429i | \(-0.417287\pi\) | ||||
0.256935 | + | 0.966429i | \(0.417287\pi\) | |||||||
\(252\) | − 5.84128i | − 0.367966i | ||||||||
\(253\) | − 42.2327i | − 2.65514i | ||||||||
\(254\) | −0.586085 | −0.0367743 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.3051 | 0.956566 | ||||||||
\(257\) | 22.6653i | 1.41382i | 0.707302 | + | 0.706911i | \(0.249912\pi\) | ||||
−0.707302 | + | 0.706911i | \(0.750088\pi\) | |||||||
\(258\) | 0.897005i | 0.0558451i | ||||||||
\(259\) | 24.5136 | 1.52320 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.88442 | 0.116642 | ||||||||
\(262\) | − 1.50874i | − 0.0932103i | ||||||||
\(263\) | 6.81500i | 0.420231i | 0.977677 | + | 0.210115i | \(0.0673840\pi\) | ||||
−0.977677 | + | 0.210115i | \(0.932616\pi\) | |||||||
\(264\) | 1.88442 | 0.115978 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.21546 | 0.0745248 | ||||||||
\(267\) | 12.6309i | 0.772996i | ||||||||
\(268\) | − 17.0440i | − 1.04113i | ||||||||
\(269\) | 20.1089 | 1.22606 | 0.613031 | − | 0.790059i | \(-0.289950\pi\) | ||||
0.613031 | + | 0.790059i | \(0.289950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8366 | −1.02275 | −0.511376 | − | 0.859357i | \(-0.670864\pi\) | ||||
−0.511376 | + | 0.859357i | \(0.670864\pi\) | |||||||
\(272\) | − 11.2669i | − 0.683155i | ||||||||
\(273\) | 10.8462i | 0.656440i | ||||||||
\(274\) | 1.67991 | 0.101487 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −16.6558 | −1.00256 | ||||||||
\(277\) | − 25.7015i | − 1.54425i | −0.635468 | − | 0.772127i | \(-0.719193\pi\) | ||||
0.635468 | − | 0.772127i | \(-0.280807\pi\) | |||||||
\(278\) | − 0.826311i | − 0.0495588i | ||||||||
\(279\) | −0.266381 | −0.0159478 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.7097 | −1.65302 | −0.826511 | − | 0.562921i | \(-0.809677\pi\) | ||||
−0.826511 | + | 0.562921i | \(0.809677\pi\) | |||||||
\(282\) | 0.227324i | 0.0135369i | ||||||||
\(283\) | − 11.6466i | − 0.692317i | −0.938176 | − | 0.346158i | \(-0.887486\pi\) | ||||
0.938176 | − | 0.346158i | \(-0.112514\pi\) | |||||||
\(284\) | −32.3930 | −1.92217 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.74567 | −0.103224 | ||||||||
\(287\) | − 0.497315i | − 0.0293556i | ||||||||
\(288\) | − 1.11558i | − 0.0657365i | ||||||||
\(289\) | 8.85410 | 0.520830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.89032 | −0.403918 | ||||||||
\(292\) | 3.61011i | 0.211266i | ||||||||
\(293\) | 7.72593i | 0.451354i | 0.974202 | + | 0.225677i | \(0.0724593\pi\) | ||||
−0.974202 | + | 0.225677i | \(0.927541\pi\) | |||||||
\(294\) | −0.150103 | −0.00875418 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.11885 | 0.181279 | ||||||||
\(297\) | 5.04905i | 0.292975i | ||||||||
\(298\) | 1.62596i | 0.0941894i | ||||||||
\(299\) | 30.9268 | 1.78854 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.1396 | −1.62194 | ||||||||
\(302\) | 0.277142i | 0.0159478i | ||||||||
\(303\) | − 9.77964i | − 0.561826i | ||||||||
\(304\) | −17.4919 | −1.00323 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.266887 | −0.0152569 | ||||||||
\(307\) | − 12.3674i | − 0.705842i | −0.935653 | − | 0.352921i | \(-0.885188\pi\) | ||||
0.935653 | − | 0.352921i | \(-0.114812\pi\) | |||||||
\(308\) | 29.4929i | 1.68051i | ||||||||
\(309\) | 14.8620 | 0.845471 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.53276 | −0.257029 | −0.128515 | − | 0.991708i | \(-0.541021\pi\) | ||||
−0.128515 | + | 0.991708i | \(0.541021\pi\) | |||||||
\(312\) | 1.37995i | 0.0781242i | ||||||||
\(313\) | − 2.33090i | − 0.131750i | −0.997828 | − | 0.0658752i | \(-0.979016\pi\) | ||||
0.997828 | − | 0.0658752i | \(-0.0209839\pi\) | |||||||
\(314\) | −0.286751 | −0.0161823 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.32060 | −0.299307 | ||||||||
\(317\) | 7.86693i | 0.441851i | 0.975291 | + | 0.220925i | \(0.0709077\pi\) | ||||
−0.975291 | + | 0.220925i | \(0.929092\pi\) | |||||||
\(318\) | 0.677843i | 0.0380116i | ||||||||
\(319\) | −9.51450 | −0.532710 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.63552 | 0.202915 | ||||||||
\(322\) | 2.29444i | 0.127864i | ||||||||
\(323\) | 12.6466i | 0.703674i | ||||||||
\(324\) | 1.99126 | 0.110625 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.951962 | 0.0527243 | ||||||||
\(327\) | − 4.62293i | − 0.255649i | ||||||||
\(328\) | − 0.0632729i | − 0.00349366i | ||||||||
\(329\) | −7.13129 | −0.393161 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.3744 | −1.11988 | −0.559940 | − | 0.828533i | \(-0.689176\pi\) | ||||
−0.559940 | + | 0.828533i | \(0.689176\pi\) | |||||||
\(332\) | − 25.6935i | − 1.41011i | ||||||||
\(333\) | 8.35655i | 0.457936i | ||||||||
\(334\) | −1.89239 | −0.103547 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 11.5802 | 0.631750 | ||||||||
\(337\) | 17.0141i | 0.926816i | 0.886145 | + | 0.463408i | \(0.153373\pi\) | ||||
−0.886145 | + | 0.463408i | \(0.846627\pi\) | |||||||
\(338\) | − 0.0627203i | − 0.00341153i | ||||||||
\(339\) | −0.776757 | −0.0421877 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.34497 | 0.0728344 | ||||||||
\(342\) | 0.414344i | 0.0224051i | ||||||||
\(343\) | 15.8254i | 0.854493i | ||||||||
\(344\) | −3.58018 | −0.193030 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.474782 | −0.0255244 | ||||||||
\(347\) | 33.7908i | 1.81399i | 0.421145 | + | 0.906993i | \(0.361628\pi\) | ||||
−0.421145 | + | 0.906993i | \(0.638372\pi\) | |||||||
\(348\) | 3.75235i | 0.201147i | ||||||||
\(349\) | −18.8798 | −1.01061 | −0.505305 | − | 0.862941i | \(-0.668620\pi\) | ||||
−0.505305 | + | 0.862941i | \(0.668620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.69740 | −0.197352 | ||||||||
\(352\) | 5.63264i | 0.300221i | ||||||||
\(353\) | − 14.2330i | − 0.757548i | −0.925489 | − | 0.378774i | \(-0.876346\pi\) | ||||
0.925489 | − | 0.378774i | \(-0.123654\pi\) | |||||||
\(354\) | −0.551262 | −0.0292992 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −25.1513 | −1.33301 | ||||||||
\(357\) | − 8.37240i | − 0.443115i | ||||||||
\(358\) | − 1.15219i | − 0.0608951i | ||||||||
\(359\) | −11.1014 | −0.585907 | −0.292954 | − | 0.956127i | \(-0.594638\pi\) | ||||
−0.292954 | + | 0.956127i | \(0.594638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.633887 | 0.0333625 | ||||||||
\(362\) | 1.72286i | 0.0905514i | ||||||||
\(363\) | − 14.4929i | − 0.760679i | ||||||||
\(364\) | −21.5975 | −1.13202 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.606408 | −0.0316975 | ||||||||
\(367\) | 32.1387i | 1.67763i | 0.544420 | + | 0.838813i | \(0.316750\pi\) | ||||
−0.544420 | + | 0.838813i | \(0.683250\pi\) | |||||||
\(368\) | − 33.0197i | − 1.72127i | ||||||||
\(369\) | 0.169532 | 0.00882546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.2644 | −1.10399 | ||||||||
\(372\) | − 0.530434i | − 0.0275017i | ||||||||
\(373\) | 15.4754i | 0.801286i | 0.916234 | + | 0.400643i | \(0.131213\pi\) | ||||
−0.916234 | + | 0.400643i | \(0.868787\pi\) | |||||||
\(374\) | 1.34752 | 0.0696788 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.907308 | −0.0467908 | ||||||||
\(377\) | − 6.96743i | − 0.358841i | ||||||||
\(378\) | − 0.274308i | − 0.0141089i | ||||||||
\(379\) | 23.4164 | 1.20282 | 0.601410 | − | 0.798941i | \(-0.294606\pi\) | ||||
0.601410 | + | 0.798941i | \(0.294606\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.26763 | 0.321100 | ||||||||
\(382\) | 0.150408i | 0.00769555i | ||||||||
\(383\) | 2.64042i | 0.134919i | 0.997722 | + | 0.0674596i | \(0.0214894\pi\) | ||||
−0.997722 | + | 0.0674596i | \(0.978511\pi\) | |||||||
\(384\) | 2.95970 | 0.151036 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.43226 | 0.0729002 | ||||||||
\(387\) | − 9.59262i | − 0.487620i | ||||||||
\(388\) | − 13.7204i | − 0.696548i | ||||||||
\(389\) | 3.98415 | 0.202004 | 0.101002 | − | 0.994886i | \(-0.467795\pi\) | ||||
0.101002 | + | 0.994886i | \(0.467795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.8731 | −1.20731 | ||||||||
\(392\) | − 0.599099i | − 0.0302591i | ||||||||
\(393\) | 16.1346i | 0.813881i | ||||||||
\(394\) | 0.512898 | 0.0258394 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −10.0539 | −0.505230 | ||||||||
\(397\) | − 7.25768i | − 0.364253i | −0.983275 | − | 0.182126i | \(-0.941702\pi\) | ||||
0.983275 | − | 0.182126i | \(-0.0582980\pi\) | |||||||
\(398\) | − 1.13040i | − 0.0566617i | ||||||||
\(399\) | −12.9982 | −0.650725 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.83373 | 0.241385 | 0.120693 | − | 0.992690i | \(-0.461488\pi\) | ||||
0.120693 | + | 0.992690i | \(0.461488\pi\) | |||||||
\(402\) | − 0.800391i | − 0.0399199i | ||||||||
\(403\) | 0.984918i | 0.0490622i | ||||||||
\(404\) | 19.4738 | 0.968856 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.516910 | 0.0256538 | ||||||||
\(407\) | − 42.1926i | − 2.09141i | ||||||||
\(408\) | − 1.06521i | − 0.0527359i | ||||||||
\(409\) | −15.1508 | −0.749159 | −0.374579 | − | 0.927195i | \(-0.622213\pi\) | ||||
−0.374579 | + | 0.927195i | \(0.622213\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.9650 | −0.886149 | ||||||||
\(412\) | 29.5941i | 1.45800i | ||||||||
\(413\) | − 17.2934i | − 0.850954i | ||||||||
\(414\) | −0.782161 | −0.0384411 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.12476 | −0.202233 | ||||||||
\(417\) | 8.83661i | 0.432731i | ||||||||
\(418\) | − 2.09204i | − 0.102325i | ||||||||
\(419\) | −16.2070 | −0.791764 | −0.395882 | − | 0.918301i | \(-0.629561\pi\) | ||||
−0.395882 | + | 0.918301i | \(0.629561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.4085 | 0.604752 | 0.302376 | − | 0.953189i | \(-0.402220\pi\) | ||||
0.302376 | + | 0.953189i | \(0.402220\pi\) | |||||||
\(422\) | − 0.492001i | − 0.0239502i | ||||||||
\(423\) | − 2.43101i | − 0.118200i | ||||||||
\(424\) | −2.70545 | −0.131388 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.52118 | −0.0737016 | ||||||||
\(427\) | − 19.0234i | − 0.920607i | ||||||||
\(428\) | 7.23926i | 0.349923i | ||||||||
\(429\) | 18.6683 | 0.901315 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.68255 | −0.0810457 | −0.0405229 | − | 0.999179i | \(-0.512902\pi\) | ||||
−0.0405229 | + | 0.999179i | \(0.512902\pi\) | |||||||
\(432\) | 3.94761i | 0.189930i | ||||||||
\(433\) | 14.9052i | 0.716297i | 0.933665 | + | 0.358148i | \(0.116592\pi\) | ||||
−0.933665 | + | 0.358148i | \(0.883408\pi\) | |||||||
\(434\) | −0.0730705 | −0.00350750 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.20544 | 0.440861 | ||||||||
\(437\) | 37.0631i | 1.77297i | ||||||||
\(438\) | 0.169532i | 0.00810053i | ||||||||
\(439\) | 22.0631 | 1.05302 | 0.526508 | − | 0.850170i | \(-0.323501\pi\) | ||||
0.526508 | + | 0.850170i | \(0.323501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.60521 | 0.0764385 | ||||||||
\(442\) | 0.986786i | 0.0469366i | ||||||||
\(443\) | − 20.0061i | − 0.950521i | −0.879845 | − | 0.475260i | \(-0.842354\pi\) | ||||
0.879845 | − | 0.475260i | \(-0.157646\pi\) | |||||||
\(444\) | −16.6400 | −0.789701 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.132062 | 0.00625332 | ||||||||
\(447\) | − 17.3881i | − 0.822429i | ||||||||
\(448\) | 22.8543i | 1.07977i | ||||||||
\(449\) | 16.5517 | 0.781125 | 0.390562 | − | 0.920576i | \(-0.372281\pi\) | ||||
0.390562 | + | 0.920576i | \(0.372281\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.855973 | −0.0403062 | ||||||||
\(452\) | − 1.54672i | − 0.0727517i | ||||||||
\(453\) | − 2.96378i | − 0.139250i | ||||||||
\(454\) | 1.82957 | 0.0858662 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.65375 | −0.0774440 | ||||||||
\(457\) | 9.29771i | 0.434928i | 0.976068 | + | 0.217464i | \(0.0697785\pi\) | ||||
−0.976068 | + | 0.217464i | \(0.930221\pi\) | |||||||
\(458\) | 1.99863i | 0.0933900i | ||||||||
\(459\) | 2.85410 | 0.133218 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8179 | 0.876436 | 0.438218 | − | 0.898869i | \(-0.355610\pi\) | ||||
0.438218 | + | 0.898869i | \(0.355610\pi\) | |||||||
\(462\) | 1.38499i | 0.0644357i | ||||||||
\(463\) | 7.50533i | 0.348802i | 0.984675 | + | 0.174401i | \(0.0557990\pi\) | ||||
−0.984675 | + | 0.174401i | \(0.944201\pi\) | |||||||
\(464\) | −7.43894 | −0.345344 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.294914 | −0.0136616 | ||||||||
\(467\) | − 4.50749i | − 0.208582i | −0.994547 | − | 0.104291i | \(-0.966743\pi\) | ||||
0.994547 | − | 0.104291i | \(-0.0332573\pi\) | |||||||
\(468\) | − 7.36246i | − 0.340330i | ||||||||
\(469\) | 25.1088 | 1.15941 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.06654 | 0.141299 | ||||||||
\(472\) | − 2.20023i | − 0.101274i | ||||||||
\(473\) | 48.4336i | 2.22698i | ||||||||
\(474\) | −0.249857 | −0.0114763 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 16.6716 | 0.764142 | ||||||||
\(477\) | − 7.24889i | − 0.331904i | ||||||||
\(478\) | 1.80217i | 0.0824294i | ||||||||
\(479\) | −21.3291 | −0.974552 | −0.487276 | − | 0.873248i | \(-0.662009\pi\) | ||||
−0.487276 | + | 0.873248i | \(0.662009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.8975 | 1.40880 | ||||||||
\(482\) | 2.12464i | 0.0967747i | ||||||||
\(483\) | − 24.5369i | − 1.11647i | ||||||||
\(484\) | 28.8590 | 1.31177 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.0935099 | 0.00424169 | ||||||||
\(487\) | − 18.5203i | − 0.839236i | −0.907701 | − | 0.419618i | \(-0.862164\pi\) | ||||
0.907701 | − | 0.419618i | \(-0.137836\pi\) | |||||||
\(488\) | − 2.42033i | − 0.109563i | ||||||||
\(489\) | −10.1803 | −0.460371 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.44369 | 0.426188 | 0.213094 | − | 0.977032i | \(-0.431646\pi\) | ||||
0.213094 | + | 0.977032i | \(0.431646\pi\) | |||||||
\(492\) | 0.337581i | 0.0152193i | ||||||||
\(493\) | 5.37831i | 0.242227i | ||||||||
\(494\) | 1.53199 | 0.0689276 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.05157 | 0.0472169 | ||||||||
\(497\) | − 47.7205i | − 2.14056i | ||||||||
\(498\) | − 1.20657i | − 0.0540678i | ||||||||
\(499\) | 24.5706 | 1.09993 | 0.549966 | − | 0.835187i | \(-0.314641\pi\) | ||||
0.549966 | + | 0.835187i | \(0.314641\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.2373 | 0.904137 | ||||||||
\(502\) | 0.761286i | 0.0339779i | ||||||||
\(503\) | − 25.7970i | − 1.15023i | −0.818072 | − | 0.575115i | \(-0.804957\pi\) | ||||
0.818072 | − | 0.575115i | \(-0.195043\pi\) | |||||||
\(504\) | 1.09483 | 0.0487677 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.94917 | 0.175562 | ||||||||
\(507\) | 0.670734i | 0.0297884i | ||||||||
\(508\) | 12.4805i | 0.553730i | ||||||||
\(509\) | 27.4970 | 1.21878 | 0.609392 | − | 0.792869i | \(-0.291414\pi\) | ||||
0.609392 | + | 0.792869i | \(0.291414\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.31831 | −0.235268 | ||||||||
\(512\) | 7.35057i | 0.324852i | ||||||||
\(513\) | − 4.43101i | − 0.195634i | ||||||||
\(514\) | −2.11943 | −0.0934840 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 19.1014 | 0.840890 | ||||||||
\(517\) | 12.2743i | 0.539823i | ||||||||
\(518\) | 2.29227i | 0.100716i | ||||||||
\(519\) | 5.07734 | 0.222871 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.23443 | −0.404568 | −0.202284 | − | 0.979327i | \(-0.564836\pi\) | ||||
−0.202284 | + | 0.979327i | \(0.564836\pi\) | |||||||
\(522\) | 0.176211i | 0.00771257i | ||||||||
\(523\) | 34.1612i | 1.49377i | 0.664956 | + | 0.746883i | \(0.268450\pi\) | ||||
−0.664956 | + | 0.746883i | \(0.731550\pi\) | |||||||
\(524\) | −32.1280 | −1.40352 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.637270 | −0.0277863 | ||||||||
\(527\) | − 0.760280i | − 0.0331183i | ||||||||
\(528\) | − 19.9317i | − 0.867415i | ||||||||
\(529\) | −46.9645 | −2.04193 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.89522 | 0.255831 | ||||||||
\(532\) | − 25.8828i | − 1.12216i | ||||||||
\(533\) | − 0.626825i | − 0.0271508i | ||||||||
\(534\) | −1.18111 | −0.0511116 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.19456 | 0.137984 | ||||||||
\(537\) | 12.3216i | 0.531715i | ||||||||
\(538\) | 1.88038i | 0.0810690i | ||||||||
\(539\) | −8.10478 | −0.349097 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.4858 | 0.708781 | 0.354391 | − | 0.935098i | \(-0.384688\pi\) | ||||
0.354391 | + | 0.935098i | \(0.384688\pi\) | |||||||
\(542\) | − 1.57439i | − 0.0676258i | ||||||||
\(543\) | − 18.4243i | − 0.790664i | ||||||||
\(544\) | 3.18399 | 0.136513 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.01422 | −0.0434048 | ||||||||
\(547\) | 17.6399i | 0.754227i | 0.926167 | + | 0.377114i | \(0.123083\pi\) | ||||
−0.926167 | + | 0.377114i | \(0.876917\pi\) | |||||||
\(548\) | − 35.7730i | − 1.52815i | ||||||||
\(549\) | 6.48496 | 0.276771 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.34987 | 0.355716 | ||||||||
\(552\) | − 3.12181i | − 0.132873i | ||||||||
\(553\) | − 7.83816i | − 0.333312i | ||||||||
\(554\) | 2.40335 | 0.102108 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.5960 | −0.746235 | ||||||||
\(557\) | 23.9964i | 1.01676i | 0.861132 | + | 0.508381i | \(0.169756\pi\) | ||||
−0.861132 | + | 0.508381i | \(0.830244\pi\) | |||||||
\(558\) | − 0.0249093i | − 0.00105449i | ||||||||
\(559\) | −35.4677 | −1.50012 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4105 | −0.608412 | ||||||||
\(562\) | − 2.59113i | − 0.109300i | ||||||||
\(563\) | − 3.56884i | − 0.150409i | −0.997168 | − | 0.0752043i | \(-0.976039\pi\) | ||||
0.997168 | − | 0.0752043i | \(-0.0239609\pi\) | |||||||
\(564\) | 4.84077 | 0.203833 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.08907 | 0.0457770 | ||||||||
\(567\) | 2.93346i | 0.123194i | ||||||||
\(568\) | − 6.07144i | − 0.254752i | ||||||||
\(569\) | 11.4585 | 0.480367 | 0.240183 | − | 0.970728i | \(-0.422792\pi\) | ||||
0.240183 | + | 0.970728i | \(0.422792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.5027 | 1.48574 | 0.742871 | − | 0.669435i | \(-0.233464\pi\) | ||||
0.742871 | + | 0.669435i | \(0.233464\pi\) | |||||||
\(572\) | 37.1734i | 1.55430i | ||||||||
\(573\) | − 1.60847i | − 0.0671949i | ||||||||
\(574\) | 0.0465038 | 0.00194103 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.79091 | −0.324621 | ||||||||
\(577\) | 0.225114i | 0.00937161i | 0.999989 | + | 0.00468581i | \(0.00149154\pi\) | ||||
−0.999989 | + | 0.00468581i | \(0.998508\pi\) | |||||||
\(578\) | 0.827946i | 0.0344380i | ||||||||
\(579\) | −15.3167 | −0.636539 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.8509 | 1.57032 | ||||||||
\(582\) | − 0.644314i | − 0.0267077i | ||||||||
\(583\) | 36.6000i | 1.51582i | ||||||||
\(584\) | −0.676644 | −0.0279997 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.722451 | −0.0298442 | ||||||||
\(587\) | − 13.8981i | − 0.573636i | −0.957985 | − | 0.286818i | \(-0.907402\pi\) | ||||
0.957985 | − | 0.286818i | \(-0.0925975\pi\) | |||||||
\(588\) | 3.19638i | 0.131817i | ||||||||
\(589\) | −1.18034 | −0.0486351 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.48496 | −0.225621 | ||||||||
\(592\) | − 32.9884i | − 1.35582i | ||||||||
\(593\) | − 9.45488i | − 0.388266i | −0.980975 | − | 0.194133i | \(-0.937811\pi\) | ||||
0.980975 | − | 0.194133i | \(-0.0621893\pi\) | |||||||
\(594\) | −0.472136 | −0.0193720 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34.6242 | 1.41826 | ||||||||
\(597\) | 12.0885i | 0.494751i | ||||||||
\(598\) | 2.89196i | 0.118261i | ||||||||
\(599\) | −8.07648 | −0.329996 | −0.164998 | − | 0.986294i | \(-0.552762\pi\) | ||||
−0.164998 | + | 0.986294i | \(0.552762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.6038 | 1.16677 | 0.583387 | − | 0.812194i | \(-0.301727\pi\) | ||||
0.583387 | + | 0.812194i | \(0.301727\pi\) | |||||||
\(602\) | − 2.63133i | − 0.107245i | ||||||||
\(603\) | 8.55942i | 0.348567i | ||||||||
\(604\) | 5.90164 | 0.240134 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.914493 | 0.0371487 | ||||||||
\(607\) | − 1.42208i | − 0.0577203i | −0.999583 | − | 0.0288602i | \(-0.990812\pi\) | ||||
0.999583 | − | 0.0288602i | \(-0.00918775\pi\) | |||||||
\(608\) | − 4.94317i | − 0.200472i | ||||||||
\(609\) | −5.52786 | −0.224000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.98842 | −0.363633 | ||||||||
\(612\) | 5.68325i | 0.229732i | ||||||||
\(613\) | 14.7556i | 0.595974i | 0.954570 | + | 0.297987i | \(0.0963152\pi\) | ||||
−0.954570 | + | 0.297987i | \(0.903685\pi\) | |||||||
\(614\) | 1.15647 | 0.0466714 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.52786 | −0.222724 | ||||||||
\(617\) | 31.3519i | 1.26218i | 0.775710 | + | 0.631090i | \(0.217392\pi\) | ||||
−0.775710 | + | 0.631090i | \(0.782608\pi\) | |||||||
\(618\) | 1.38975i | 0.0559038i | ||||||||
\(619\) | −12.6563 | −0.508699 | −0.254349 | − | 0.967112i | \(-0.581861\pi\) | ||||
−0.254349 | + | 0.967112i | \(0.581861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.36448 | 0.335655 | ||||||||
\(622\) | − 0.423858i | − 0.0169952i | ||||||||
\(623\) | − 37.0522i | − 1.48446i | ||||||||
\(624\) | 14.5959 | 0.584303 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.217962 | 0.00871153 | ||||||||
\(627\) | 22.3724i | 0.893468i | ||||||||
\(628\) | 6.10626i | 0.243666i | ||||||||
\(629\) | −23.8504 | −0.950980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0741 | 0.759327 | 0.379663 | − | 0.925125i | \(-0.376040\pi\) | ||||
0.379663 | + | 0.925125i | \(0.376040\pi\) | |||||||
\(632\) | − 0.997242i | − 0.0396682i | ||||||||
\(633\) | 5.26148i | 0.209125i | ||||||||
\(634\) | −0.735636 | −0.0292158 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14.4344 | 0.572361 | ||||||||
\(637\) | − 5.93509i | − 0.235157i | ||||||||
\(638\) | − 0.889700i | − 0.0352236i | ||||||||
\(639\) | 16.2676 | 0.643537 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.58594 | −0.141636 | −0.0708180 | − | 0.997489i | \(-0.522561\pi\) | ||||
−0.0708180 | + | 0.997489i | \(0.522561\pi\) | |||||||
\(642\) | 0.339957i | 0.0134170i | ||||||||
\(643\) | 37.6409i | 1.48441i | 0.670172 | + | 0.742206i | \(0.266220\pi\) | ||||
−0.670172 | + | 0.742206i | \(0.733780\pi\) | |||||||
\(644\) | 48.8592 | 1.92532 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.18258 | −0.0465280 | ||||||||
\(647\) | − 2.21935i | − 0.0872517i | −0.999048 | − | 0.0436258i | \(-0.986109\pi\) | ||||
0.999048 | − | 0.0436258i | \(-0.0138909\pi\) | |||||||
\(648\) | 0.373222i | 0.0146615i | ||||||||
\(649\) | −29.7653 | −1.16839 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.781420 | 0.0306263 | ||||||||
\(652\) | − 20.2717i | − 0.793900i | ||||||||
\(653\) | − 3.13494i | − 0.122680i | −0.998117 | − | 0.0613399i | \(-0.980463\pi\) | ||||
0.998117 | − | 0.0613399i | \(-0.0195374\pi\) | |||||||
\(654\) | 0.432290 | 0.0169039 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.669245 | −0.0261296 | ||||||||
\(657\) | − 1.81298i | − 0.0707311i | ||||||||
\(658\) | − 0.666846i | − 0.0259964i | ||||||||
\(659\) | 21.6691 | 0.844108 | 0.422054 | − | 0.906571i | \(-0.361309\pi\) | ||||
0.422054 | + | 0.906571i | \(0.361309\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.9730 | −0.854649 | −0.427324 | − | 0.904098i | \(-0.640544\pi\) | ||||
−0.427324 | + | 0.904098i | \(0.640544\pi\) | |||||||
\(662\) | − 1.90521i | − 0.0740481i | ||||||||
\(663\) | − 10.5527i | − 0.409835i | ||||||||
\(664\) | 4.81574 | 0.186887 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.781420 | −0.0302794 | ||||||||
\(667\) | 15.7622i | 0.610313i | ||||||||
\(668\) | 40.2977i | 1.55916i | ||||||||
\(669\) | −1.41228 | −0.0546019 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.7429 | −1.26402 | ||||||||
\(672\) | 3.27253i | 0.126240i | ||||||||
\(673\) | − 32.7911i | − 1.26400i | −0.774967 | − | 0.632001i | \(-0.782234\pi\) | ||||
0.774967 | − | 0.632001i | \(-0.217766\pi\) | |||||||
\(674\) | −1.59098 | −0.0612824 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.33560 | −0.0513694 | ||||||||
\(677\) | − 25.8289i | − 0.992686i | −0.868126 | − | 0.496343i | \(-0.834676\pi\) | ||||
0.868126 | − | 0.496343i | \(-0.165324\pi\) | |||||||
\(678\) | − 0.0726345i | − 0.00278951i | ||||||||
\(679\) | 20.2125 | 0.775685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.5656 | −0.749754 | ||||||||
\(682\) | 0.125768i | 0.00481592i | ||||||||
\(683\) | − 23.4044i | − 0.895543i | −0.894148 | − | 0.447771i | \(-0.852218\pi\) | ||||
0.894148 | − | 0.447771i | \(-0.147782\pi\) | |||||||
\(684\) | 8.82328 | 0.337367 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.47983 | −0.0565003 | ||||||||
\(687\) | − 21.3735i | − 0.815450i | ||||||||
\(688\) | 37.8679i | 1.44370i | ||||||||
\(689\) | −26.8020 | −1.02108 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.91799 | 0.377298 | 0.188649 | − | 0.982045i | \(-0.439589\pi\) | ||||
0.188649 | + | 0.982045i | \(0.439589\pi\) | |||||||
\(692\) | 10.1103i | 0.384336i | ||||||||
\(693\) | − 14.8112i | − 0.562631i | ||||||||
\(694\) | −3.15978 | −0.119943 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.703305 | −0.0266587 | ||||||||
\(697\) | 0.483860i | 0.0183275i | ||||||||
\(698\) | − 1.76544i | − 0.0668230i | ||||||||
\(699\) | 3.15382 | 0.119289 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.6906 | −1.38578 | −0.692892 | − | 0.721042i | \(-0.743664\pi\) | ||||
−0.692892 | + | 0.721042i | \(0.743664\pi\) | |||||||
\(702\) | − 0.345743i | − 0.0130492i | ||||||||
\(703\) | 37.0280i | 1.39654i | ||||||||
\(704\) | 39.3367 | 1.48256 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.33093 | 0.0500902 | ||||||||
\(707\) | 28.6882i | 1.07893i | ||||||||
\(708\) | 11.7389i | 0.441175i | ||||||||
\(709\) | 33.0393 | 1.24082 | 0.620409 | − | 0.784278i | \(-0.286967\pi\) | ||||
0.620409 | + | 0.784278i | \(0.286967\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.67198 | 0.100207 | ||||||||
\(712\) | − 4.71411i | − 0.176669i | ||||||||
\(713\) | − 2.22814i | − 0.0834446i | ||||||||
\(714\) | 0.782903 | 0.0292994 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.5354 | −0.916931 | ||||||||
\(717\) | − 19.2725i | − 0.719746i | ||||||||
\(718\) | − 1.03809i | − 0.0387411i | ||||||||
\(719\) | −30.0339 | −1.12008 | −0.560038 | − | 0.828467i | \(-0.689213\pi\) | ||||
−0.560038 | + | 0.828467i | \(0.689213\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.5972 | −1.62365 | ||||||||
\(722\) | 0.0592747i | 0.00220598i | ||||||||
\(723\) | − 22.7210i | − 0.845004i | ||||||||
\(724\) | 36.6876 | 1.36348 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.35523 | 0.0502972 | ||||||||
\(727\) | 29.5053i | 1.09429i | 0.837037 | + | 0.547146i | \(0.184286\pi\) | ||||
−0.837037 | + | 0.547146i | \(0.815714\pi\) | |||||||
\(728\) | − 4.04803i | − 0.150030i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.3783 | 1.01262 | ||||||||
\(732\) | 12.9132i | 0.477286i | ||||||||
\(733\) | − 39.2642i | − 1.45026i | −0.688614 | − | 0.725128i | \(-0.741780\pi\) | ||||
0.688614 | − | 0.725128i | \(-0.258220\pi\) | |||||||
\(734\) | −3.00528 | −0.110927 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.33128 | 0.343956 | ||||||||
\(737\) | − 43.2169i | − 1.59192i | ||||||||
\(738\) | 0.0158529i | 0 0.000583553i | ||||||||
\(739\) | −7.12841 | −0.262223 | −0.131111 | − | 0.991368i | \(-0.541855\pi\) | ||||
−0.131111 | + | 0.991368i | \(0.541855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.3832 | −0.601852 | ||||||||
\(742\) | − 1.98843i | − 0.0729975i | ||||||||
\(743\) | 10.2060i | 0.374421i | 0.982320 | + | 0.187211i | \(0.0599447\pi\) | ||||
−0.982320 | + | 0.187211i | \(0.940055\pi\) | |||||||
\(744\) | 0.0994194 | 0.00364489 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.44710 | −0.0529822 | ||||||||
\(747\) | 12.9032i | 0.472102i | ||||||||
\(748\) | − 28.6950i | − 1.04919i | ||||||||
\(749\) | −10.6647 | −0.389679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.89220 | 0.215009 | 0.107505 | − | 0.994205i | \(-0.465714\pi\) | ||||
0.107505 | + | 0.994205i | \(0.465714\pi\) | |||||||
\(752\) | 9.59670i | 0.349956i | ||||||||
\(753\) | − 8.14124i | − 0.296683i | ||||||||
\(754\) | 0.651524 | 0.0237271 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.84128 | −0.212445 | ||||||||
\(757\) | 28.9643i | 1.05272i | 0.850261 | + | 0.526362i | \(0.176444\pi\) | ||||
−0.850261 | + | 0.526362i | \(0.823556\pi\) | |||||||
\(758\) | 2.18967i | 0.0795322i | ||||||||
\(759\) | −42.2327 | −1.53295 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.8720 | 0.865358 | 0.432679 | − | 0.901548i | \(-0.357568\pi\) | ||||
0.432679 | + | 0.901548i | \(0.357568\pi\) | |||||||
\(762\) | 0.586085i | 0.0212316i | ||||||||
\(763\) | 13.5612i | 0.490949i | ||||||||
\(764\) | 3.20288 | 0.115876 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.246905 | −0.00892106 | ||||||||
\(767\) | − 21.7970i | − 0.787043i | ||||||||
\(768\) | − 15.3051i | − 0.552273i | ||||||||
\(769\) | −32.1167 | −1.15816 | −0.579079 | − | 0.815272i | \(-0.696588\pi\) | ||||
−0.579079 | + | 0.815272i | \(0.696588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.6653 | 0.816271 | ||||||||
\(772\) | − 30.4994i | − 1.09770i | ||||||||
\(773\) | 22.9098i | 0.824009i | 0.911182 | + | 0.412005i | \(0.135171\pi\) | ||||
−0.911182 | + | 0.412005i | \(0.864829\pi\) | |||||||
\(774\) | 0.897005 | 0.0322422 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.57162 | 0.0923158 | ||||||||
\(777\) | − 24.5136i | − 0.879422i | ||||||||
\(778\) | 0.372557i | 0.0133568i | ||||||||
\(779\) | 0.751197 | 0.0269144 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −82.1360 | −2.93906 | ||||||||
\(782\) | − 2.23237i | − 0.0798293i | ||||||||
\(783\) | − 1.88442i | − 0.0673435i | ||||||||
\(784\) | −6.33674 | −0.226312 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.50874 | −0.0538150 | ||||||||
\(787\) | 0.790593i | 0.0281816i | 0.999901 | + | 0.0140908i | \(0.00448539\pi\) | ||||
−0.999901 | + | 0.0140908i | \(0.995515\pi\) | |||||||
\(788\) | − 10.9220i | − 0.389079i | ||||||||
\(789\) | 6.81500 | 0.242620 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.27859 | 0.0810173 | ||||||||
\(792\) | − 1.88442i | − 0.0669598i | ||||||||
\(793\) | − 23.9775i | − 0.851465i | ||||||||
\(794\) | 0.678665 | 0.0240849 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.0714 | −0.853187 | ||||||||
\(797\) | − 31.1524i | − 1.10348i | −0.834018 | − | 0.551738i | \(-0.813965\pi\) | ||||
0.834018 | − | 0.551738i | \(-0.186035\pi\) | |||||||
\(798\) | − 1.21546i | − 0.0430269i | ||||||||
\(799\) | 6.93836 | 0.245462 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.6309 | 0.446289 | ||||||||
\(802\) | 0.452002i | 0.0159607i | ||||||||
\(803\) | 9.15382i | 0.323031i | ||||||||
\(804\) | −17.0440 | −0.601096 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.0920995 | −0.00324407 | ||||||||
\(807\) | − 20.1089i | − 0.707867i | ||||||||
\(808\) | 3.64998i | 0.128406i | ||||||||
\(809\) | 0.120629 | 0.00424110 | 0.00212055 | − | 0.999998i | \(-0.499325\pi\) | ||||
0.00212055 | + | 0.999998i | \(0.499325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.55313 | 0.0545379 | 0.0272689 | − | 0.999628i | \(-0.491319\pi\) | ||||
0.0272689 | + | 0.999628i | \(0.491319\pi\) | |||||||
\(812\) | − 11.0074i | − 0.386284i | ||||||||
\(813\) | 16.8366i | 0.590486i | ||||||||
\(814\) | 3.94543 | 0.138287 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −11.2669 | −0.394420 | ||||||||
\(817\) | − 42.5050i | − 1.48706i | ||||||||
\(818\) | − 1.41675i | − 0.0495355i | ||||||||
\(819\) | 10.8462 | 0.378996 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.6965 | −0.512912 | −0.256456 | − | 0.966556i | \(-0.582555\pi\) | ||||
−0.256456 | + | 0.966556i | \(0.582555\pi\) | |||||||
\(822\) | − 1.67991i | − 0.0585935i | ||||||||
\(823\) | − 9.71652i | − 0.338697i | −0.985556 | − | 0.169348i | \(-0.945834\pi\) | ||||
0.985556 | − | 0.169348i | \(-0.0541663\pi\) | |||||||
\(824\) | −5.54683 | −0.193233 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.61711 | 0.0562663 | ||||||||
\(827\) | 32.6997i | 1.13708i | 0.822656 | + | 0.568539i | \(0.192491\pi\) | ||||
−0.822656 | + | 0.568539i | \(0.807509\pi\) | |||||||
\(828\) | 16.6558i | 0.578830i | ||||||||
\(829\) | 37.5623 | 1.30459 | 0.652296 | − | 0.757964i | \(-0.273806\pi\) | ||||
0.652296 | + | 0.757964i | \(0.273806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.7015 | −0.891576 | ||||||||
\(832\) | 28.8061i | 0.998670i | ||||||||
\(833\) | 4.58143i | 0.158737i | ||||||||
\(834\) | −0.826311 | −0.0286128 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −44.5492 | −1.54077 | ||||||||
\(837\) | 0.266381i | 0.00920749i | ||||||||
\(838\) | − 1.51551i | − 0.0523526i | ||||||||
\(839\) | −23.6116 | −0.815163 | −0.407581 | − | 0.913169i | \(-0.633628\pi\) | ||||
−0.407581 | + | 0.913169i | \(0.633628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.4490 | −0.877551 | ||||||||
\(842\) | 1.16032i | 0.0399871i | ||||||||
\(843\) | 27.7097i | 0.954372i | ||||||||
\(844\) | −10.4770 | −0.360632 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.227324 | 0.00781556 | ||||||||
\(847\) | 42.5144i | 1.46081i | ||||||||
\(848\) | 28.6158i | 0.982671i | ||||||||
\(849\) | −11.6466 | −0.399709 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −69.8982 | −2.39608 | ||||||||
\(852\) | 32.3930i | 1.10977i | ||||||||
\(853\) | 1.72305i | 0.0589960i | 0.999565 | + | 0.0294980i | \(0.00939086\pi\) | ||||
−0.999565 | + | 0.0294980i | \(0.990609\pi\) | |||||||
\(854\) | 1.77888 | 0.0608719 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.35686 | −0.0463764 | ||||||||
\(857\) | 25.9461i | 0.886303i | 0.896447 | + | 0.443152i | \(0.146140\pi\) | ||||
−0.896447 | + | 0.443152i | \(0.853860\pi\) | |||||||
\(858\) | 1.74567i | 0.0595963i | ||||||||
\(859\) | −33.1188 | −1.13000 | −0.565000 | − | 0.825091i | \(-0.691124\pi\) | ||||
−0.565000 | + | 0.825091i | \(0.691124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.497315 | −0.0169484 | ||||||||
\(862\) | − 0.157335i | − 0.00535886i | ||||||||
\(863\) | 29.3696i | 0.999753i | 0.866097 | + | 0.499877i | \(0.166621\pi\) | ||||
−0.866097 | + | 0.499877i | \(0.833379\pi\) | |||||||
\(864\) | −1.11558 | −0.0379530 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.39378 | −0.0473626 | ||||||||
\(867\) | − 8.85410i | − 0.300701i | ||||||||
\(868\) | 1.55601i | 0.0528143i | ||||||||
\(869\) | −13.4910 | −0.457649 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6476 | 1.07234 | ||||||||
\(872\) | 1.72538i | 0.0584287i | ||||||||
\(873\) | 6.89032i | 0.233202i | ||||||||
\(874\) | −3.46577 | −0.117231 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.61011 | 0.121974 | ||||||||
\(877\) | 51.6306i | 1.74344i | 0.490004 | + | 0.871720i | \(0.336995\pi\) | ||||
−0.490004 | + | 0.871720i | \(0.663005\pi\) | |||||||
\(878\) | 2.06312i | 0.0696269i | ||||||||
\(879\) | 7.72593 | 0.260589 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.6132 | −0.593405 | −0.296702 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296702 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(882\) | 0.150103i | 0.00505423i | ||||||||
\(883\) | − 1.65829i | − 0.0558059i | −0.999611 | − | 0.0279030i | \(-0.991117\pi\) | ||||
0.999611 | − | 0.0279030i | \(-0.00888294\pi\) | |||||||
\(884\) | 21.0132 | 0.706751 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.87077 | 0.0628498 | ||||||||
\(887\) | − 20.1490i | − 0.676538i | −0.941050 | − | 0.338269i | \(-0.890159\pi\) | ||||
0.941050 | − | 0.338269i | \(-0.109841\pi\) | |||||||
\(888\) | − 3.11885i | − 0.104662i | ||||||||
\(889\) | −18.3859 | −0.616642 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.04905 | 0.169149 | ||||||||
\(892\) | − 2.81221i | − 0.0941597i | ||||||||
\(893\) | − 10.7719i | − 0.360466i | ||||||||
\(894\) | 1.62596 | 0.0543803 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.68216 | −0.290051 | ||||||||
\(897\) | − 30.9268i | − 1.03262i | ||||||||
\(898\) | 1.54775i | 0.0516491i | ||||||||
\(899\) | −0.501973 | −0.0167417 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.6891 | 0.689253 | ||||||||
\(902\) | − 0.0800420i | − 0.00266511i | ||||||||
\(903\) | 28.1396i | 0.936427i | ||||||||
\(904\) | 0.289903 | 0.00964202 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.277142 | 0.00920744 | ||||||||
\(907\) | − 31.8504i | − 1.05758i | −0.848754 | − | 0.528788i | \(-0.822647\pi\) | ||||
0.848754 | − | 0.528788i | \(-0.177353\pi\) | |||||||
\(908\) | − 38.9601i | − 1.29293i | ||||||||
\(909\) | −9.77964 | −0.324370 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.7213 | 1.01784 | 0.508920 | − | 0.860814i | \(-0.330045\pi\) | ||||
0.508920 | + | 0.860814i | \(0.330045\pi\) | |||||||
\(912\) | 17.4919i | 0.579215i | ||||||||
\(913\) | − 65.1486i | − 2.15610i | ||||||||
\(914\) | −0.869427 | −0.0287581 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 42.5601 | 1.40623 | ||||||||
\(917\) | − 47.3301i | − 1.56298i | ||||||||
\(918\) | 0.266887i | 0.00880858i | ||||||||
\(919\) | 36.0752 | 1.19001 | 0.595005 | − | 0.803722i | \(-0.297150\pi\) | ||||
0.595005 | + | 0.803722i | \(0.297150\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.3674 | −0.407518 | ||||||||
\(922\) | 1.75966i | 0.0579512i | ||||||||
\(923\) | − 60.1479i | − 1.97979i | ||||||||
\(924\) | 29.4929 | 0.970245 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.701823 | −0.0230633 | ||||||||
\(927\) | − 14.8620i | − 0.488133i | ||||||||
\(928\) | − 2.10222i | − 0.0690089i | ||||||||
\(929\) | −13.7648 | −0.451608 | −0.225804 | − | 0.974173i | \(-0.572501\pi\) | ||||
−0.225804 | + | 0.974173i | \(0.572501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.11270 | 0.233109 | ||||||||
\(932\) | 6.28007i | 0.205711i | ||||||||
\(933\) | 4.53276i | 0.148396i | ||||||||
\(934\) | 0.421495 | 0.0137917 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.37995 | 0.0451050 | ||||||||
\(937\) | 40.1571i | 1.31187i | 0.754815 | + | 0.655937i | \(0.227726\pi\) | ||||
−0.754815 | + | 0.655937i | \(0.772274\pi\) | |||||||
\(938\) | 2.34792i | 0.0766622i | ||||||||
\(939\) | −2.33090 | −0.0760661 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.7005 | 0.446624 | 0.223312 | − | 0.974747i | \(-0.428313\pi\) | ||||
0.223312 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(942\) | 0.286751i | 0.00934287i | ||||||||
\(943\) | 1.41804i | 0.0461778i | ||||||||
\(944\) | −23.2721 | −0.757441 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.52902 | −0.147251 | ||||||||
\(947\) | 27.1382i | 0.881873i | 0.897538 | + | 0.440937i | \(0.145354\pi\) | ||||
−0.897538 | + | 0.440937i | \(0.854646\pi\) | |||||||
\(948\) | 5.32060i | 0.172805i | ||||||||
\(949\) | −6.70331 | −0.217598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.86693 | 0.255103 | ||||||||
\(952\) | 3.12476i | 0.101274i | ||||||||
\(953\) | 47.9437i | 1.55305i | 0.630086 | + | 0.776525i | \(0.283019\pi\) | ||||
−0.630086 | + | 0.776525i | \(0.716981\pi\) | |||||||
\(954\) | 0.677843 | 0.0219460 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 38.3765 | 1.24119 | ||||||||
\(957\) | 9.51450i | 0.307560i | ||||||||
\(958\) | − 1.99448i | − 0.0644388i | ||||||||
\(959\) | 52.6997 | 1.70176 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9290 | −0.997711 | ||||||||
\(962\) | 2.88922i | 0.0931522i | ||||||||
\(963\) | − 3.63552i | − 0.117153i | ||||||||
\(964\) | 45.2434 | 1.45719 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.29444 | 0.0738225 | ||||||||
\(967\) | − 2.33998i | − 0.0752487i | −0.999292 | − | 0.0376243i | \(-0.988021\pi\) | ||||
0.999292 | − | 0.0376243i | \(-0.0119790\pi\) | |||||||
\(968\) | 5.40906i | 0.173854i | ||||||||
\(969\) | 12.6466 | 0.406266 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.9343 | 1.63456 | 0.817280 | − | 0.576241i | \(-0.195481\pi\) | ||||
0.817280 | + | 0.576241i | \(0.195481\pi\) | |||||||
\(972\) | − 1.99126i | − 0.0638696i | ||||||||
\(973\) | − 25.9219i | − 0.831017i | ||||||||
\(974\) | 1.73183 | 0.0554915 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.6001 | −0.819440 | ||||||||
\(977\) | 58.0048i | 1.85574i | 0.372905 | + | 0.927870i | \(0.378362\pi\) | ||||
−0.372905 | + | 0.927870i | \(0.621638\pi\) | |||||||
\(978\) | − 0.951962i | − 0.0304404i | ||||||||
\(979\) | −63.7738 | −2.03822 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.62293 | −0.147599 | ||||||||
\(982\) | 0.883079i | 0.0281802i | ||||||||
\(983\) | − 35.2324i | − 1.12374i | −0.827226 | − | 0.561870i | \(-0.810082\pi\) | ||||
0.827226 | − | 0.561870i | \(-0.189918\pi\) | |||||||
\(984\) | −0.0632729 | −0.00201707 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.502926 | −0.0160164 | ||||||||
\(987\) | 7.13129i | 0.226992i | ||||||||
\(988\) | − 32.6232i | − 1.03788i | ||||||||
\(989\) | 80.2373 | 2.55140 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.7908 | −0.755741 | −0.377870 | − | 0.925859i | \(-0.623343\pi\) | ||||
−0.377870 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(992\) | 0.297171i | 0.00943519i | ||||||||
\(993\) | 20.3744i | 0.646563i | ||||||||
\(994\) | 4.46234 | 0.141537 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.6935 | −0.814129 | ||||||||
\(997\) | 8.78958i | 0.278369i | 0.990266 | + | 0.139184i | \(0.0444481\pi\) | ||||
−0.990266 | + | 0.139184i | \(0.955552\pi\) | |||||||
\(998\) | 2.29760i | 0.0727291i | ||||||||
\(999\) | 8.35655 | 0.264390 |
(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 | 375.2.b.c.124.5 | 8 | ||
3.2 | odd | 2 | 1125.2.b.g.874.4 | 8 | |||
4.3 | odd | 2 | 6000.2.f.o.1249.5 | 8 | |||
5.2 | odd | 4 | 375.2.a.e.1.3 | ✓ | 4 | ||
5.3 | odd | 4 | 375.2.a.f.1.2 | yes | 4 | ||
5.4 | even | 2 | inner | 375.2.b.c.124.4 | 8 | ||
15.2 | even | 4 | 1125.2.a.l.1.2 | 4 | |||
15.8 | even | 4 | 1125.2.a.h.1.3 | 4 | |||
15.14 | odd | 2 | 1125.2.b.g.874.5 | 8 | |||
20.3 | even | 4 | 6000.2.a.bg.1.1 | 4 | |||
20.7 | even | 4 | 6000.2.a.bh.1.4 | 4 | |||
20.19 | odd | 2 | 6000.2.f.o.1249.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
375.2.a.e.1.3 | ✓ | 4 | 5.2 | odd | 4 | ||
375.2.a.f.1.2 | yes | 4 | 5.3 | odd | 4 | ||
375.2.b.c.124.4 | 8 | 5.4 | even | 2 | inner | ||
375.2.b.c.124.5 | 8 | 1.1 | even | 1 | trivial | ||
1125.2.a.h.1.3 | 4 | 15.8 | even | 4 | |||
1125.2.a.l.1.2 | 4 | 15.2 | even | 4 | |||
1125.2.b.g.874.4 | 8 | 3.2 | odd | 2 | |||
1125.2.b.g.874.5 | 8 | 15.14 | odd | 2 | |||
6000.2.a.bg.1.1 | 4 | 20.3 | even | 4 | |||
6000.2.a.bh.1.4 | 4 | 20.7 | even | 4 | |||
6000.2.f.o.1249.4 | 8 | 20.19 | odd | 2 | |||
6000.2.f.o.1249.5 | 8 | 4.3 | odd | 2 |