Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), degree \(2\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 16x^{14} + 174x^{12} + 1012x^{10} + 4243x^{8} + 9708x^{6} + 15858x^{4} + 12150x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 171) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1889.2 | ||
Root | \(-1.13921 + 1.97317i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1889 |
Dual form | 2736.2.dc.c.449.2 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.90154 | − | 1.67520i | −1.29761 | − | 0.749174i | −0.317617 | − | 0.948219i | \(-0.602883\pi\) |
−0.979990 | + | 0.199045i | \(0.936216\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.54697 | −1.34063 | −0.670314 | − | 0.742078i | \(-0.733841\pi\) | ||||
−0.670314 | + | 0.742078i | \(0.733841\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.251548i | − | 0.0758445i | −0.999281 | − | 0.0379223i | \(-0.987926\pi\) | ||
0.999281 | − | 0.0379223i | \(-0.0120739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.29049 | + | 2.47712i | −1.18997 | + | 0.687028i | −0.958299 | − | 0.285766i | \(-0.907752\pi\) |
−0.231669 | + | 0.972795i | \(0.574419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.11939 | + | 1.80098i | 0.756562 | + | 0.436801i | 0.828060 | − | 0.560639i | \(-0.189445\pi\) |
−0.0714979 | + | 0.997441i | \(0.522778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.15959 | + | 1.30301i | −0.954275 | + | 0.298931i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.89208 | + | 2.24709i | −0.811555 | + | 0.468552i | −0.847496 | − | 0.530802i | \(-0.821891\pi\) |
0.0359405 | + | 0.999354i | \(0.488557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.11262 | + | 5.39122i | 0.622524 | + | 1.07824i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.27843 | + | 3.94635i | 0.423093 | + | 0.732819i | 0.996240 | − | 0.0866337i | \(-0.0276110\pi\) |
−0.573147 | + | 0.819452i | \(0.694278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.28544i | − | 0.949294i | −0.880176 | − | 0.474647i | \(-0.842576\pi\) | ||
0.880176 | − | 0.474647i | \(-0.157424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.2917 | + | 5.94190i | 1.73961 | + | 1.00436i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.47474i | − | 1.06444i | −0.846606 | − | 0.532220i | \(-0.821358\pi\) | ||
0.846606 | − | 0.532220i | \(-0.178642\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.96212 | + | 8.59464i | −0.774953 | + | 1.34226i | 0.159868 | + | 0.987138i | \(0.448893\pi\) |
−0.934821 | + | 0.355119i | \(0.884440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.38610 | − | 5.86490i | 0.516376 | − | 0.894389i | −0.483443 | − | 0.875376i | \(-0.660614\pi\) |
0.999819 | − | 0.0190137i | \(-0.00605261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.96412 | − | 5.17544i | 1.30755 | − | 0.754915i | 0.325865 | − | 0.945416i | \(-0.394345\pi\) |
0.981687 | + | 0.190501i | \(0.0610113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.58098 | 0.797283 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.217847 | − | 0.377322i | −0.0299236 | − | 0.0518291i | 0.850676 | − | 0.525691i | \(-0.176193\pi\) |
−0.880599 | + | 0.473862i | \(0.842860\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.421394 | + | 0.729876i | −0.0568207 | + | 0.0984164i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.06058 | + | 3.56903i | −0.268265 | + | 0.464648i | −0.968414 | − | 0.249349i | \(-0.919783\pi\) |
0.700149 | + | 0.713997i | \(0.253117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.46836 | − | 11.2035i | −0.828189 | − | 1.43447i | −0.899458 | − | 0.437008i | \(-0.856038\pi\) |
0.0712687 | − | 0.997457i | \(-0.477295\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.5987 | 2.05882 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.273084 | + | 0.157665i | −0.0333625 | + | 0.0192618i | −0.516588 | − | 0.856234i | \(-0.672798\pi\) |
0.483226 | + | 0.875496i | \(0.339465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.10993 | − | 7.11860i | 0.487759 | − | 0.844823i | −0.512142 | − | 0.858901i | \(-0.671148\pi\) |
0.999901 | + | 0.0140778i | \(0.00448125\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.356142 | − | 0.616857i | 0.0416833 | − | 0.0721976i | −0.844431 | − | 0.535664i | \(-0.820061\pi\) |
0.886114 | + | 0.463467i | \(0.153395\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.892232i | 0.101679i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.57733 | + | 4.37477i | 0.852516 | + | 0.492200i | 0.861499 | − | 0.507759i | \(-0.169526\pi\) |
−0.00898288 | + | 0.999960i | \(0.502859\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.31440i | 0.144274i | 0.997395 | + | 0.0721369i | \(0.0229819\pi\) | ||||
−0.997395 | + | 0.0721369i | \(0.977018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.03401 | − | 10.4512i | −0.654481 | − | 1.13359i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.20839 | − | 2.09299i | −0.128089 | − | 0.221857i | 0.794847 | − | 0.606810i | \(-0.207551\pi\) |
−0.922936 | + | 0.384953i | \(0.874218\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.2182 | − | 8.78625i | 1.59530 | − | 0.921049i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.2520 | + | 3.18743i | 1.46223 | + | 0.327023i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.36417 | + | 5.40640i | 0.950787 | + | 0.548937i | 0.893325 | − | 0.449410i | \(-0.148366\pi\) |
0.0574618 | + | 0.998348i | \(0.481699\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.40904 | − | 3.12291i | 0.538220 | − | 0.310741i | −0.206137 | − | 0.978523i | \(-0.566089\pi\) |
0.744357 | + | 0.667782i | \(0.232756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.38110i | − | 0.431683i | −0.976428 | − | 0.215841i | \(-0.930751\pi\) | ||
0.976428 | − | 0.215841i | \(-0.0692494\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.98108 | −0.191519 | −0.0957593 | − | 0.995405i | \(-0.530528\pi\) | ||||
−0.0957593 | + | 0.995405i | \(0.530528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.897781 | − | 0.518334i | −0.0859918 | − | 0.0496474i | 0.456387 | − | 0.889781i | \(-0.349143\pi\) |
−0.542379 | + | 0.840134i | \(0.682476\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.32954 | 0.125073 | 0.0625364 | − | 0.998043i | \(-0.480081\pi\) | ||||
0.0625364 | + | 0.998043i | \(0.480081\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.0574 | 1.40411 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0644 | − | 6.38801i | −1.01427 | − | 0.585588i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9367 | 0.994248 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.10505i | − | 0.367167i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.10729 | + | 4.10340i | −0.630670 | + | 0.364118i | −0.781012 | − | 0.624517i | \(-0.785296\pi\) |
0.150341 | + | 0.988634i | \(0.451963\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.70643 | + | 2.71726i | 0.411203 | + | 0.237408i | 0.691307 | − | 0.722562i | \(-0.257035\pi\) |
−0.280103 | + | 0.959970i | \(0.590369\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.7539 | − | 4.62173i | 1.27933 | − | 0.400755i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8941 | − | 6.86706i | 1.01618 | − | 0.586692i | 0.103185 | − | 0.994662i | \(-0.467097\pi\) |
0.912995 | + | 0.407970i | \(0.133763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.17422 | + | 2.03381i | 0.0995959 | + | 0.172505i | 0.911517 | − | 0.411261i | \(-0.134912\pi\) |
−0.811922 | + | 0.583767i | \(0.801578\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.623113 | + | 1.07926i | 0.0521073 | + | 0.0902525i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 15.2673i | − | 1.26788i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.31058 | + | 4.79812i | 0.680829 | + | 0.393077i | 0.800167 | − | 0.599777i | \(-0.204744\pi\) |
−0.119338 | + | 0.992854i | \(0.538077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.06053i | − | 0.574577i | −0.957844 | − | 0.287289i | \(-0.907246\pi\) | ||
0.957844 | − | 0.287289i | \(-0.0927539\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.85420 | + | 15.3359i | −0.711186 | + | 1.23181i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.17492 | + | 14.1594i | −0.652429 | + | 1.13004i | 0.330102 | + | 0.943945i | \(0.392917\pi\) |
−0.982532 | + | 0.186096i | \(0.940417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.8051 | − | 7.97037i | 1.08799 | − | 0.628153i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3119 | −0.964340 | −0.482170 | − | 0.876078i | \(-0.660151\pi\) | ||||
−0.482170 | + | 0.876078i | \(0.660151\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.623113 | − | 1.07926i | −0.0482179 | − | 0.0835159i | 0.840909 | − | 0.541176i | \(-0.182021\pi\) |
−0.889127 | + | 0.457660i | \(0.848688\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.77221 | − | 9.99776i | 0.444016 | − | 0.769058i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.24623 | − | 2.15853i | 0.0947488 | − | 0.164110i | −0.814755 | − | 0.579805i | \(-0.803129\pi\) |
0.909504 | + | 0.415696i | \(0.136462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.0404 | − | 19.1225i | −0.834573 | − | 1.44552i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.0722 | 1.57501 | 0.787507 | − | 0.616306i | \(-0.211372\pi\) | ||||
0.787507 | + | 0.616306i | \(0.211372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4387 | + | 10.6456i | −1.37054 | + | 0.791280i | −0.990996 | − | 0.133894i | \(-0.957252\pi\) |
−0.379542 | + | 0.925174i | \(0.623918\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8465 | + | 18.7867i | −0.797452 | + | 1.38123i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.453032 | − | 0.784675i | 0.0331290 | − | 0.0573811i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1888i | 0.737237i | 0.929581 | + | 0.368618i | \(0.120169\pi\) | ||||
−0.929581 | + | 0.368618i | \(0.879831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.93139 | − | 5.15654i | −0.642896 | − | 0.371176i | 0.142833 | − | 0.989747i | \(-0.454379\pi\) |
−0.785729 | + | 0.618571i | \(0.787712\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 14.3901i | − | 1.02525i | −0.858613 | − | 0.512625i | \(-0.828673\pi\) | ||
0.858613 | − | 0.512625i | \(-0.171327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.3022 | + | 19.5759i | 0.801189 | + | 1.38770i | 0.918834 | + | 0.394645i | \(0.129132\pi\) |
−0.117644 | + | 0.993056i | \(0.537534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.08150 | − | 13.9976i | −0.567210 | − | 0.982437i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.7956 | − | 16.6251i | 2.01117 | − | 1.16115i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.327769 | + | 1.04633i | 0.0226723 | + | 0.0723765i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.09839 | + | 4.67561i | 0.557516 | + | 0.321882i | 0.752148 | − | 0.658994i | \(-0.229018\pi\) |
−0.194632 | + | 0.980876i | \(0.562351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.6498 | + | 11.3448i | −1.34011 | + | 0.773711i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.7473i | 1.27265i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.8449 | −1.20038 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.63200 | + | 1.51959i | 0.176252 | + | 0.101759i | 0.585530 | − | 0.810650i | \(-0.300886\pi\) |
−0.409279 | + | 0.912409i | \(0.634220\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.35592 | −0.156368 | −0.0781841 | − | 0.996939i | \(-0.524912\pi\) | ||||
−0.0781841 | + | 0.996939i | \(0.524912\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.15801 | −0.208687 | −0.104344 | − | 0.994541i | \(-0.533274\pi\) | ||||
−0.104344 | + | 0.994541i | \(0.533274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.4642 | + | 11.8150i | 1.34065 | + | 0.774026i | 0.986903 | − | 0.161314i | \(-0.0515731\pi\) |
0.353750 | + | 0.935340i | \(0.384906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.6797 | −2.26225 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.5878i | 1.33171i | 0.746080 | + | 0.665857i | \(0.231934\pi\) | ||||
−0.746080 | + | 0.665857i | \(0.768066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.12835 | − | 1.80615i | 0.201515 | − | 0.116345i | −0.395847 | − | 0.918316i | \(-0.629549\pi\) |
0.597362 | + | 0.801972i | \(0.296216\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.1934 | − | 9.34928i | −1.03456 | − | 0.597304i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.6190 | − | 15.8943i | 0.930183 | − | 1.01133i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.28043 | − | 3.62601i | 0.396417 | − | 0.228872i | −0.288520 | − | 0.957474i | \(-0.593163\pi\) |
0.684937 | + | 0.728602i | \(0.259830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.565252 | + | 0.979044i | 0.0355371 | + | 0.0615520i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.40905 | − | 16.2970i | −0.586920 | − | 1.01658i | −0.994633 | − | 0.103466i | \(-0.967007\pi\) |
0.407713 | − | 0.913110i | \(-0.366326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.9657i | 1.42702i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.21963 | + | 3.01355i | 0.321856 | + | 0.185824i | 0.652220 | − | 0.758030i | \(-0.273838\pi\) |
−0.330364 | + | 0.943854i | \(0.607171\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.45975i | 0.0896718i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.29557 | + | 5.70810i | −0.200935 | + | 0.348029i | −0.948830 | − | 0.315788i | \(-0.897731\pi\) |
0.747895 | + | 0.663817i | \(0.231065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4497 | + | 18.0994i | −0.634773 | + | 1.09946i | 0.351790 | + | 0.936079i | \(0.385573\pi\) |
−0.986563 | + | 0.163380i | \(0.947760\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.35615 | − | 0.782973i | 0.0817788 | − | 0.0472150i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8223 | −1.55151 | −0.775755 | − | 0.631034i | \(-0.782631\pi\) | ||||
−0.775755 | + | 0.631034i | \(0.782631\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.43948 | + | 16.3497i | 0.563112 | + | 0.975338i | 0.997223 | + | 0.0744789i | \(0.0237293\pi\) |
−0.434111 | + | 0.900860i | \(0.642937\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.38245 | − | 14.5188i | 0.498285 | − | 0.863055i | −0.501713 | − | 0.865034i | \(-0.667297\pi\) |
0.999998 | + | 0.00197917i | \(0.000629990\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.6005 | − | 30.4849i | 1.03892 | − | 1.79947i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.01295 | − | 3.48654i | −0.118409 | − | 0.205091i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.0683 | 1.63977 | 0.819885 | − | 0.572529i | \(-0.194037\pi\) | ||||
0.819885 | + | 0.572529i | \(0.194037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.9577 | − | 6.90378i | 0.696204 | − | 0.401954i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.1326 | − | 19.2823i | 0.643816 | − | 1.11512i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0104 | + | 20.8026i | −0.692268 | + | 1.19904i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.3433i | 2.48183i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.6261 | − | 11.3311i | −1.12012 | − | 0.646703i | −0.178690 | − | 0.983905i | \(-0.557186\pi\) |
−0.941432 | + | 0.337203i | \(0.890519\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8544i | 1.01243i | 0.862407 | + | 0.506216i | \(0.168956\pi\) | ||||
−0.862407 | + | 0.506216i | \(0.831044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.18630 | + | 12.4470i | 0.406193 | + | 0.703548i | 0.994460 | − | 0.105120i | \(-0.0335226\pi\) |
−0.588266 | + | 0.808667i | \(0.700189\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.89586 | − | 15.4081i | −0.499641 | − | 0.865404i | 0.500359 | − | 0.865818i | \(-0.333201\pi\) |
−1.00000 | 0.000414314i | \(0.999868\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.992696 | − | 0.573133i | 0.0555803 | − | 0.0320893i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3220 | − | 3.42674i | −0.852542 | − | 0.190669i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.7093 | − | 15.4206i | −1.48157 | − | 0.855383i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.7955 | + | 18.3571i | −1.75294 | + | 1.01206i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 27.4202i | − | 1.50715i | −0.657361 | − | 0.753575i | \(-0.728327\pi\) | ||
0.657361 | − | 0.753575i | \(-0.271673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.05648 | 0.0577219 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.9188 | − | 8.61340i | −0.812681 | − | 0.469202i | 0.0352050 | − | 0.999380i | \(-0.488792\pi\) |
−0.847886 | + | 0.530179i | \(0.822125\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.32954 | −0.0719987 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.03321 | 0.271768 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.28635 | − | 4.20677i | −0.391152 | − | 0.225832i | 0.291507 | − | 0.956569i | \(-0.405843\pi\) |
−0.682659 | + | 0.730737i | \(0.739177\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5389 | −0.617661 | −0.308831 | − | 0.951117i | \(-0.599938\pi\) | ||||
−0.308831 | + | 0.951117i | \(0.599938\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0544i | 0.641592i | 0.947148 | + | 0.320796i | \(0.103950\pi\) | ||||
−0.947148 | + | 0.320796i | \(0.896050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.8502 | + | 13.7699i | −1.26584 | + | 0.730833i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.7710 | + | 16.0336i | 1.46570 | + | 0.846220i | 0.999265 | − | 0.0383367i | \(-0.0122060\pi\) |
0.466432 | + | 0.884557i | \(0.345539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.6043 | − | 10.8400i | 0.821281 | − | 0.570524i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.06672 | + | 1.19322i | −0.108177 | + | 0.0624561i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47004 | + | 2.54618i | 0.0767354 | + | 0.132910i | 0.901840 | − | 0.432071i | \(-0.142217\pi\) |
−0.825104 | + | 0.564981i | \(0.808884\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.772695 | + | 1.33835i | 0.0401164 | + | 0.0694836i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.4374i | 1.16177i | 0.813987 | + | 0.580883i | \(0.197293\pi\) | ||||
−0.813987 | + | 0.580883i | \(0.802707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.5511 | − | 11.2879i | −1.00693 | − | 0.581354i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 9.54429i | − | 0.490257i | −0.969491 | − | 0.245129i | \(-0.921170\pi\) | ||
0.969491 | − | 0.245129i | \(-0.0788302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.61920 | − | 13.1968i | 0.389323 | − | 0.674327i | −0.603035 | − | 0.797714i | \(-0.706042\pi\) |
0.992359 | + | 0.123387i | \(0.0393756\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.49467 | − | 2.58885i | 0.0761755 | − | 0.131940i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.6174 | − | 9.01671i | 0.791833 | − | 0.457165i | −0.0487743 | − | 0.998810i | \(-0.515531\pi\) |
0.840608 | + | 0.541645i | \(0.182198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.1879 | −0.818656 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.6573 | − | 25.3872i | −0.737488 | − | 1.27737i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.09927 | − | 12.2963i | 0.356302 | − | 0.617133i | −0.631038 | − | 0.775752i | \(-0.717371\pi\) |
0.987340 | + | 0.158619i | \(0.0507041\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.24623 | − | 9.08674i | 0.261984 | − | 0.453770i | −0.704785 | − | 0.709421i | \(-0.748956\pi\) |
0.966769 | + | 0.255651i | \(0.0822898\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.0927 | + | 22.6772i | 0.652192 | + | 1.12963i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.62871 | −0.0807320 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.9650 | − | 6.33065i | 0.542185 | − | 0.313031i | −0.203779 | − | 0.979017i | \(-0.565322\pi\) |
0.745964 | + | 0.665986i | \(0.231989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.30881 | − | 12.6592i | 0.359643 | − | 0.622920i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.20188 | − | 3.81378i | 0.108086 | − | 0.187211i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.3392i | 1.33561i | 0.744338 | + | 0.667804i | \(0.232765\pi\) | ||||
−0.744338 | + | 0.667804i | \(0.767235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3913 | + | 12.9276i | 1.09129 | + | 0.630055i | 0.933919 | − | 0.357485i | \(-0.116366\pi\) |
0.157368 | + | 0.987540i | \(0.449699\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.4230i | 1.08768i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.9431 | + | 39.7386i | 1.11029 | + | 1.92308i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.09274 | + | 14.0170i | 0.389813 | + | 0.675176i | 0.992424 | − | 0.122859i | \(-0.0392062\pi\) |
−0.602611 | + | 0.798035i | \(0.705873\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.4504 | − | 8.34294i | 0.694442 | − | 0.400936i | −0.110832 | − | 0.993839i | \(-0.535352\pi\) |
0.805274 | + | 0.592903i | \(0.202018\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.2615 | − | 14.4184i | 0.634382 | − | 0.689726i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.2233 | + | 16.8721i | 1.39475 | + | 0.805261i | 0.993837 | − | 0.110854i | \(-0.0353587\pi\) |
0.400916 | + | 0.916115i | \(0.368692\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3770 | − | 9.45529i | 0.778096 | − | 0.449234i | −0.0576588 | − | 0.998336i | \(-0.518364\pi\) |
0.835755 | + | 0.549102i | \(0.185030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.09719i | 0.383844i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.0530 | −1.51267 | −0.756336 | − | 0.654183i | \(-0.773013\pi\) | ||||
−0.756336 | + | 0.654183i | \(0.773013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.16196 | + | 1.24821i | 0.101803 | + | 0.0587759i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −58.8751 | −2.76011 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5605 | 1.28922 | 0.644612 | − | 0.764510i | \(-0.277019\pi\) | ||||
0.644612 | + | 0.764510i | \(0.277019\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.4207 | − | 8.90317i | −0.718215 | − | 0.414662i | 0.0958800 | − | 0.995393i | \(-0.469433\pi\) |
−0.814096 | + | 0.580731i | \(0.802767\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.5005 | −1.46395 | −0.731977 | − | 0.681329i | \(-0.761402\pi\) | ||||
−0.731977 | + | 0.681329i | \(0.761402\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 34.7591i | − | 1.60846i | −0.594317 | − | 0.804231i | \(-0.702578\pi\) | ||
0.594317 | − | 0.804231i | \(-0.297422\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.968620 | − | 0.559233i | 0.0447267 | − | 0.0258230i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.47530 | − | 0.851767i | −0.0678345 | − | 0.0391643i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.9720 | − | 18.3695i | −0.916379 | − | 0.842849i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.62312 | − | 2.66916i | 0.211236 | − | 0.121957i | −0.390650 | − | 0.920539i | \(-0.627750\pi\) |
0.601886 | + | 0.798582i | \(0.294416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0387 | + | 27.7798i | 0.731301 | + | 1.26665i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.1137 | − | 31.3738i | −0.822499 | − | 1.42461i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 37.8144i | − | 1.71353i | −0.515705 | − | 0.856766i | \(-0.672470\pi\) | ||
0.515705 | − | 0.856766i | \(-0.327530\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.95830 | + | 5.17208i | 0.404283 | + | 0.233413i | 0.688330 | − | 0.725398i | \(-0.258344\pi\) |
−0.284048 | + | 0.958810i | \(0.591677\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.4136i | 0.739231i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.5778 | + | 25.2495i | −0.653903 | + | 1.13259i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6603 | − | 27.1244i | 0.701051 | − | 1.21426i | −0.267047 | − | 0.963683i | \(-0.586048\pi\) |
0.968098 | − | 0.250572i | \(-0.0806187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.1154 | + | 11.0363i | −0.852315 | + | 0.492084i | −0.861431 | − | 0.507874i | \(-0.830432\pi\) |
0.00911608 | + | 0.999958i | \(0.497098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.9261 | −0.931198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.73681 | − | 9.93645i | −0.254280 | − | 0.440425i | 0.710420 | − | 0.703778i | \(-0.248505\pi\) |
−0.964700 | + | 0.263353i | \(0.915172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.26323 | + | 2.18797i | −0.0558818 | + | 0.0967901i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.33924 | + | 12.7119i | −0.323405 | + | 0.560155i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.30187 | − | 2.25490i | −0.0572562 | − | 0.0991706i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.0265 | 0.702133 | 0.351066 | − | 0.936351i | \(-0.385819\pi\) | ||||
0.351066 | + | 0.936351i | \(0.385819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1731 | − | 5.87344i | 0.444839 | − | 0.256828i | −0.260809 | − | 0.965390i | \(-0.583989\pi\) |
0.705648 | + | 0.708563i | \(0.250656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.51897 | − | 16.4873i | 0.414653 | − | 0.718200i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.40114 | + | 2.42684i | −0.0609189 | + | 0.105515i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 49.1670i | − | 2.12966i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.74819 | + | 3.31872i | 0.248516 | + | 0.143481i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.40388i | − | 0.0604695i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.5906 | + | 33.9319i | 0.842265 | + | 1.45885i | 0.887975 | + | 0.459891i | \(0.152111\pi\) |
−0.0457105 | + | 0.998955i | \(0.514555\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.73663 | + | 3.00793i | 0.0743891 | + | 0.128846i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.36275 | + | 4.82824i | −0.357565 | + | 0.206440i | −0.668012 | − | 0.744150i | \(-0.732855\pi\) |
0.310447 | + | 0.950591i | \(0.399521\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.6194 | − | 13.4464i | −0.622809 | − | 0.572835i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.8765 | − | 15.5172i | −1.14291 | − | 0.659858i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.1760 | − | 15.1127i | 1.10911 | − | 0.640346i | 0.170512 | − | 0.985356i | \(-0.445458\pi\) |
0.938599 | + | 0.345010i | \(0.112124\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.5511i | 1.41906i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.7803 | −1.67654 | −0.838269 | − | 0.545257i | \(-0.816432\pi\) | ||||
−0.838269 | + | 0.545257i | \(0.816432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.85772 | − | 2.22725i | −0.162295 | − | 0.0937013i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.7383 | −0.534018 | −0.267009 | − | 0.963694i | \(-0.586035\pi\) | ||||
−0.267009 | + | 0.963694i | \(0.586035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.21174 | 0.176256 | 0.0881280 | − | 0.996109i | \(-0.471912\pi\) | ||||
0.0881280 | + | 0.996109i | \(0.471912\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.2291 | − | 13.9887i | −1.01042 | − | 0.583369i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.82818 | −0.201000 | −0.100500 | − | 0.994937i | \(-0.532044\pi\) | ||||
−0.100500 | + | 0.994937i | \(0.532044\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.66212i | − | 0.193418i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0949144 | + | 0.0547989i | −0.00393095 | + | 0.00226954i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.4624 | − | 8.92722i | −0.638201 | − | 0.368466i | 0.145720 | − | 0.989326i | \(-0.453450\pi\) |
−0.783921 | + | 0.620860i | \(0.786784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.88698 | + | 21.9853i | 0.283773 | + | 0.905887i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4379 | − | 11.7998i | 0.839284 | − | 0.484561i | −0.0177369 | − | 0.999843i | \(-0.505646\pi\) |
0.857021 | + | 0.515282i | \(0.172313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.4025 | + | 37.0701i | 0.877415 | + | 1.51973i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.1857 | − | 40.1588i | −0.947342 | − | 1.64084i | −0.750992 | − | 0.660311i | \(-0.770424\pi\) |
−0.196350 | − | 0.980534i | \(-0.562909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.8985i | − | 0.852466i | −0.904613 | − | 0.426233i | \(-0.859840\pi\) | ||
0.904613 | − | 0.426233i | \(-0.140160\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.7333 | − | 18.3212i | −1.29014 | − | 0.744865i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.0730i | 1.91064i | 0.295580 | + | 0.955318i | \(0.404487\pi\) | ||||
−0.295580 | + | 0.955318i | \(0.595513\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.6403 | + | 44.4103i | −1.03730 | + | 1.79665i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.887781 | − | 1.53768i | 0.0358571 | − | 0.0621063i | −0.847540 | − | 0.530732i | \(-0.821917\pi\) |
0.883397 | + | 0.468625i | \(0.155251\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.39218 | + | 3.69052i | −0.257339 | + | 0.148575i | −0.623120 | − | 0.782126i | \(-0.714135\pi\) |
0.365781 | + | 0.930701i | \(0.380802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.0914 | −1.00851 | −0.504254 | − | 0.863555i | \(-0.668232\pi\) | ||||
−0.504254 | + | 0.863555i | \(0.668232\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.28612 | + | 7.42377i | 0.171720 | + | 0.297427i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.68630 | − | 15.0451i | 0.347452 | − | 0.601804i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.6609 | − | 20.1972i | 0.464949 | − | 0.805316i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.73692 | + | 4.74048i | 0.108955 | + | 0.188715i | 0.915347 | − | 0.402666i | \(-0.131916\pi\) |
−0.806392 | + | 0.591381i | \(0.798583\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.4961 | 1.09115 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.9451 | + | 13.8247i | −0.948741 | + | 0.547756i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.6782 | + | 35.8157i | −0.816740 | + | 1.41464i | 0.0913319 | + | 0.995821i | \(0.470888\pi\) |
−0.908072 | + | 0.418815i | \(0.862446\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.1035 | + | 36.5523i | −0.832239 | + | 1.44148i | 0.0640194 | + | 0.997949i | \(0.479608\pi\) |
−0.896259 | + | 0.443532i | \(0.853725\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.7852i | 0.502639i | 0.967904 | + | 0.251319i | \(0.0808645\pi\) | ||||
−0.967904 | + | 0.251319i | \(0.919136\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.897781 | + | 0.518334i | 0.0352410 | + | 0.0203464i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 12.4197i | − | 0.486021i | −0.970024 | − | 0.243011i | \(-0.921865\pi\) | ||
0.970024 | − | 0.243011i | \(-0.0781350\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.10394 | − | 15.7685i | −0.355720 | − | 0.616126i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.38658 | + | 2.40162i | 0.0540133 | + | 0.0935538i | 0.891768 | − | 0.452493i | \(-0.149465\pi\) |
−0.837755 | + | 0.546047i | \(0.816132\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.90526 | − | 4.56411i | 0.307479 | − | 0.177523i | −0.338319 | − | 0.941032i | \(-0.609858\pi\) |
0.645798 | + | 0.763508i | \(0.276525\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −50.5514 | − | 11.3057i | −1.96030 | − | 0.438416i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.7356 | − | 10.2397i | −0.686727 | − | 0.396482i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.81822 | + | 1.62710i | −0.108796 | + | 0.0628136i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.33862i | − | 0.128694i | −0.997928 | − | 0.0643472i | \(-0.979503\pi\) | ||
0.997928 | − | 0.0643472i | \(-0.0204965\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.3794 | −1.74407 | −0.872037 | − | 0.489441i | \(-0.837201\pi\) | ||||
−0.872037 | + | 0.489441i | \(0.837201\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.2144 | − | 19.1763i | −1.27465 | − | 0.735921i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.7656 | −1.29201 | −0.646003 | − | 0.763335i | \(-0.723561\pi\) | ||||
−0.646003 | + | 0.763335i | \(0.723561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.0149 | −1.75814 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.86934 | + | 1.07926i | 0.0712161 | + | 0.0411167i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.6057 | 1.81101 | 0.905504 | − | 0.424338i | \(-0.139493\pi\) | ||||
0.905504 | + | 0.424338i | \(0.139493\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 7.86823i | − | 0.298459i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.9575 | + | 17.8733i | −1.17260 | + | 0.677001i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.81431 | + | 5.66630i | 0.370682 | + | 0.214013i | 0.673756 | − | 0.738954i | \(-0.264680\pi\) |
−0.303075 | + | 0.952967i | \(0.598013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.43664 | + | 26.9323i | 0.318194 | + | 1.01577i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.1857 | + | 11.0769i | −0.721553 | + | 0.416589i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.10276 | + | 14.0344i | 0.304306 | + | 0.527073i | 0.977106 | − | 0.212751i | \(-0.0682423\pi\) |
−0.672801 | + | 0.739824i | \(0.734909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.8769 | + | 20.5714i | 0.444793 | + | 0.770404i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 4.17537i | − | 0.156150i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.73659 | + | 3.88937i | 0.251232 | + | 0.145049i | 0.620328 | − | 0.784342i | \(-0.286999\pi\) |
−0.369096 | + | 0.929391i | \(0.620333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.5396i | 0.578726i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.1837 | + | 24.5670i | −0.526771 | + | 0.912394i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.7320 | + | 27.2486i | −0.583467 | + | 1.01059i | 0.411598 | + | 0.911366i | \(0.364971\pi\) |
−0.995065 | + | 0.0992290i | \(0.968362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.1251 | − | 12.1966i | 0.781341 | − | 0.451107i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.80147 | −0.325090 | −0.162545 | − | 0.986701i | \(-0.551970\pi\) | ||||
−0.162545 | + | 0.986701i | \(0.551970\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0396603 | + | 0.0686936i | 0.00146091 | + | 0.00253036i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.08996 | + | 5.35197i | −0.113666 | + | 0.196876i | −0.917246 | − | 0.398322i | \(-0.869593\pi\) |
0.803580 | + | 0.595197i | \(0.202926\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.3126 | − | 35.1825i | 0.745197 | − | 1.29072i | −0.204906 | − | 0.978782i | \(-0.565689\pi\) |
0.950103 | − | 0.311937i | \(-0.100978\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.0757 | − | 27.8438i | −0.588966 | − | 1.02012i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.02684 | 0.256755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4204 | − | 6.01624i | 0.380247 | − | 0.219536i | −0.297679 | − | 0.954666i | \(-0.596212\pi\) |
0.677926 | + | 0.735130i | \(0.262879\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.8278 | + | 20.4864i | −0.430459 | + | 0.745576i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.43515 | − | 7.68190i | 0.161198 | − | 0.279204i | −0.774100 | − | 0.633063i | \(-0.781797\pi\) |
0.935299 | + | 0.353859i | \(0.115131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 10.3745i | − | 0.376076i | −0.982162 | − | 0.188038i | \(-0.939787\pi\) | ||
0.982162 | − | 0.188038i | \(-0.0602127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.18440 | + | 1.83851i | 0.115283 | + | 0.0665587i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 20.4172i | − | 0.737222i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.1749 | − | 29.7478i | −0.619343 | − | 1.07273i | −0.989606 | − | 0.143807i | \(-0.954066\pi\) |
0.370262 | − | 0.928927i | \(-0.379268\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.4831 | + | 45.8701i | 0.952531 | + | 1.64983i | 0.739920 | + | 0.672695i | \(0.234864\pi\) |
0.212612 | + | 0.977137i | \(0.431803\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.4950 | − | 16.4516i | 1.02357 | − | 0.590958i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.44147 | − | 42.2158i | 0.338276 | − | 1.51254i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.79067 | − | 1.03384i | −0.0640752 | − | 0.0369938i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.4397 | − | 27.3893i | 1.69319 | − | 0.977567i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.75236i | − | 0.0624648i | −0.999512 | − | 0.0312324i | \(-0.990057\pi\) | ||
0.999512 | − | 0.0312324i | \(-0.00994319\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.71584 | −0.167676 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.5049 | + | 32.0458i | 1.97104 | + | 1.13798i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.7424 | 1.54944 | 0.774718 | − | 0.632307i | \(-0.217892\pi\) | ||||
0.774718 | + | 0.632307i | \(0.217892\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.2834 | 1.31899 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.155169 | − | 0.0895868i | −0.00547579 | − | 0.00316145i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −53.4080 | −1.88238 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.97955i | 0.0695974i | 0.999394 | + | 0.0347987i | \(0.0110790\pi\) | ||||
−0.999394 | + | 0.0347987i | \(0.988921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.9304 | − | 10.3521i | 0.629620 | − | 0.363511i | −0.150985 | − | 0.988536i | \(-0.548244\pi\) |
0.780605 | + | 0.625025i | \(0.214911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.7234 | + | 20.6249i | 1.25134 | + | 0.722459i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.44277 | + | 28.8077i | −0.225404 | + | 1.00785i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.7618 | + | 13.1415i | −0.794392 | + | 0.458643i | −0.841507 | − | 0.540247i | \(-0.818331\pi\) |
0.0471143 | + | 0.998890i | \(0.484998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.16801 | − | 15.8795i | −0.319577 | − | 0.553523i | 0.660823 | − | 0.750542i | \(-0.270207\pi\) |
−0.980400 | + | 0.197019i | \(0.936874\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7899 | + | 44.6694i | 0.896803 | + | 1.55331i | 0.831557 | + | 0.555439i | \(0.187450\pi\) |
0.0652454 | + | 0.997869i | \(0.479217\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 30.7526i | − | 1.06808i | −0.845458 | − | 0.534042i | \(-0.820673\pi\) | ||
0.845458 | − | 0.534042i | \(-0.179327\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.4092 | + | 10.0512i | 0.603194 | + | 0.348254i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.17537i | 0.144495i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.2481 | + | 36.8028i | −0.733566 | + | 1.27057i | 0.221784 | + | 0.975096i | \(0.428812\pi\) |
−0.955350 | + | 0.295478i | \(0.904521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.11755 | − | 7.13180i | 0.141984 | − | 0.245924i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.4966 | + | 19.3393i | −1.15232 | + | 0.665291i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.7922 | −1.33292 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.5494 | + | 25.2002i | 0.498745 | + | 0.863852i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.296220 | + | 0.513068i | −0.0101424 | + | 0.0175671i | −0.871052 | − | 0.491191i | \(-0.836562\pi\) |
0.860910 | + | 0.508758i | \(0.169895\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.8976 | − | 24.0714i | 0.474734 | − | 0.822264i | −0.524847 | − | 0.851196i | \(-0.675878\pi\) |
0.999581 | + | 0.0289327i | \(0.00921085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.8549 | − | 20.5332i | −0.404483 | − | 0.700585i | 0.589778 | − | 0.807565i | \(-0.299215\pi\) |
−0.994261 | + | 0.106980i | \(0.965882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.2464 | −0.484954 | −0.242477 | − | 0.970157i | \(-0.577960\pi\) | ||||
−0.242477 | + | 0.970157i | \(0.577960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.23195 | + | 4.17537i | −0.245894 | + | 0.141967i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.10046 | − | 1.90606i | 0.0373307 | − | 0.0646587i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.781109 | − | 1.35292i | 0.0264669 | − | 0.0458420i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.5605i | 0.492234i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.5049 | − | 9.52910i | −0.557331 | − | 0.321775i | 0.194743 | − | 0.980854i | \(-0.437613\pi\) |
−0.752073 | + | 0.659079i | \(0.770946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0700i | 0.541411i | 0.962662 | + | 0.270706i | \(0.0872570\pi\) | ||||
−0.962662 | + | 0.270706i | \(0.912743\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.6274 | + | 23.6033i | 0.458598 | + | 0.794316i | 0.998887 | − | 0.0471641i | \(-0.0150184\pi\) |
−0.540289 | + | 0.841480i | \(0.681685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.46016 | − | 14.6534i | −0.284065 | − | 0.492014i | 0.688317 | − | 0.725410i | \(-0.258350\pi\) |
−0.972382 | + | 0.233395i | \(0.925016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.2093 | − | 14.5546i | 0.845494 | − | 0.488146i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.5434 | + | 33.2080i | −1.02210 | + | 1.11126i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −61.1419 | − | 35.3003i | −2.04375 | − | 1.17996i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 20.8582 | − | 12.0425i | 0.695660 | − | 0.401640i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.56935i | − | 0.0522826i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 71.3341 | 2.37123 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.16196 | − | 1.24821i | −0.0717868 | − | 0.0414461i | 0.463677 | − | 0.886004i | \(-0.346530\pi\) |
−0.535464 | + | 0.844558i | \(0.679863\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.0838 | 1.02985 | 0.514926 | − | 0.857235i | \(-0.327819\pi\) | ||||
0.514926 | + | 0.857235i | \(0.327819\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.330634 | 0.0109424 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.6936 | − | 9.63804i | −0.551270 | − | 0.318276i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.1750 | −0.434604 | −0.217302 | − | 0.976104i | \(-0.569726\pi\) | ||||
−0.217302 | + | 0.976104i | \(0.569726\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.7231i | 1.34042i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.9067 | − | 20.1534i | 1.14773 | − | 0.662640i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.08127 | − | 0.624270i | −0.0354752 | − | 0.0204816i | 0.482157 | − | 0.876085i | \(-0.339853\pi\) |
−0.517633 | + | 0.855603i | \(0.673187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.2146 | + | 7.27207i | −0.760827 | + | 0.238332i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.62898 | + | 1.51784i | −0.0859769 | + | 0.0496388i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.58551 | + | 4.47824i | 0.0844649 | + | 0.146298i | 0.905163 | − | 0.425064i | \(-0.139749\pi\) |
−0.820698 | + | 0.571362i | \(0.806415\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.7406 | − | 32.4597i | −0.610926 | − | 1.05816i | −0.991085 | − | 0.133234i | \(-0.957464\pi\) |
0.380159 | − | 0.924921i | \(-0.375869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 44.6014i | − | 1.45242i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.42574 | + | 2.55520i | 0.143817 | + | 0.0830328i | 0.570182 | − | 0.821518i | \(-0.306873\pi\) |
−0.426365 | + | 0.904551i | \(0.640206\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.52882i | 0.114550i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.30089 | + | 10.9135i | −0.204106 | + | 0.353522i | −0.949848 | − | 0.312713i | \(-0.898762\pi\) |
0.745742 | + | 0.666235i | \(0.232095\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.0683 | − | 29.5632i | 0.552319 | − | 0.956644i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −42.1880 | + | 24.3572i | −1.36232 | + | 0.786536i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.06408 | 0.0988412 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.2765 | + | 29.9238i | 0.556151 | + | 0.963282i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.11699 | + | 5.39879i | −0.100236 | + | 0.173613i | −0.911782 | − | 0.410675i | \(-0.865293\pi\) |
0.811546 | + | 0.584289i | \(0.198626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.10993 | − | 7.11860i | 0.131894 | − | 0.228447i | −0.792513 | − | 0.609855i | \(-0.791228\pi\) |
0.924407 | + | 0.381408i | \(0.124561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.16492 | − | 7.21385i | −0.133521 | − | 0.231265i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.0799 | −1.47423 | −0.737113 | − | 0.675769i | \(-0.763812\pi\) | ||||
−0.737113 | + | 0.675769i | \(0.763812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.526487 | + | 0.303968i | −0.0168266 | + | 0.00971485i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.60597 | − | 6.24572i | 0.115013 | − | 0.199208i | −0.802772 | − | 0.596286i | \(-0.796642\pi\) |
0.917785 | + | 0.397078i | \(0.129976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.1063 | + | 41.7534i | −0.768091 | + | 1.33037i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.4356i | 0.967795i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.3753 | + | 10.0316i | 0.551945 | + | 0.318665i | 0.749906 | − | 0.661544i | \(-0.230099\pi\) |
−0.197961 | + | 0.980210i | \(0.563432\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 75.7338i | − | 2.40092i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0129544 | − | 0.0224377i | −0.000410270 | − | 0.000710608i | 0.865820 | − | 0.500355i | \(-0.166797\pi\) |
−0.866230 | + | 0.499645i | \(0.833464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2736.2.dc.c.1889.2 | 16 | ||
3.2 | odd | 2 | inner | 2736.2.dc.c.1889.7 | 16 | ||
4.3 | odd | 2 | 171.2.m.a.8.7 | yes | 16 | ||
12.11 | even | 2 | 171.2.m.a.8.2 | ✓ | 16 | ||
19.12 | odd | 6 | inner | 2736.2.dc.c.449.7 | 16 | ||
57.50 | even | 6 | inner | 2736.2.dc.c.449.2 | 16 | ||
76.31 | even | 6 | 171.2.m.a.107.2 | yes | 16 | ||
228.107 | odd | 6 | 171.2.m.a.107.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.m.a.8.2 | ✓ | 16 | 12.11 | even | 2 | ||
171.2.m.a.8.7 | yes | 16 | 4.3 | odd | 2 | ||
171.2.m.a.107.2 | yes | 16 | 76.31 | even | 6 | ||
171.2.m.a.107.7 | yes | 16 | 228.107 | odd | 6 | ||
2736.2.dc.c.449.2 | 16 | 57.50 | even | 6 | inner | ||
2736.2.dc.c.449.7 | 16 | 19.12 | odd | 6 | inner | ||
2736.2.dc.c.1889.2 | 16 | 1.1 | even | 1 | trivial | ||
2736.2.dc.c.1889.7 | 16 | 3.2 | odd | 2 | inner |