Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} - 2790 x^{3} - 352 x^{2} + 1768 x + 768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.37328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.83399 | −1.71461 | −0.857307 | − | 0.514806i | \(-0.827864\pi\) | ||||
−0.857307 | + | 0.514806i | \(0.827864\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −3.29790 | −1.24649 | −0.623244 | − | 0.782028i | \(-0.714186\pi\) | ||||
−0.623244 | + | 0.782028i | \(0.714186\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.83399 | 1.21241 | ||||||||
\(11\) | −1.08694 | −0.327724 | −0.163862 | − | 0.986483i | \(-0.552395\pi\) | ||||
−0.163862 | + | 0.986483i | \(0.552395\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.29790 | 0.881400 | ||||||||
\(15\) | −3.83399 | −0.989933 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.28528 | −1.28187 | −0.640934 | − | 0.767596i | \(-0.721453\pi\) | ||||
−0.640934 | + | 0.767596i | \(0.721453\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 7.52849 | 1.72715 | 0.863577 | − | 0.504218i | \(-0.168219\pi\) | ||||
0.863577 | + | 0.504218i | \(0.168219\pi\) | |||||||
\(20\) | −3.83399 | −0.857307 | ||||||||
\(21\) | −3.29790 | −0.719660 | ||||||||
\(22\) | 1.08694 | 0.231736 | ||||||||
\(23\) | −4.86940 | −1.01534 | −0.507670 | − | 0.861551i | \(-0.669493\pi\) | ||||
−0.507670 | + | 0.861551i | \(0.669493\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 9.69950 | 1.93990 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −3.29790 | −0.623244 | ||||||||
\(29\) | −8.02922 | −1.49099 | −0.745494 | − | 0.666512i | \(-0.767787\pi\) | ||||
−0.745494 | + | 0.666512i | \(0.767787\pi\) | |||||||
\(30\) | 3.83399 | 0.699988 | ||||||||
\(31\) | 3.95486 | 0.710314 | 0.355157 | − | 0.934807i | \(-0.384427\pi\) | ||||
0.355157 | + | 0.934807i | \(0.384427\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.08694 | −0.189212 | ||||||||
\(34\) | 5.28528 | 0.906418 | ||||||||
\(35\) | 12.6441 | 2.13724 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.95146 | 0.649616 | 0.324808 | − | 0.945780i | \(-0.394700\pi\) | ||||
0.324808 | + | 0.945780i | \(0.394700\pi\) | |||||||
\(38\) | −7.52849 | −1.22128 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 3.83399 | 0.606207 | ||||||||
\(41\) | 5.35805 | 0.836787 | 0.418393 | − | 0.908266i | \(-0.362593\pi\) | ||||
0.418393 | + | 0.908266i | \(0.362593\pi\) | |||||||
\(42\) | 3.29790 | 0.508876 | ||||||||
\(43\) | 11.4696 | 1.74910 | 0.874549 | − | 0.484938i | \(-0.161158\pi\) | ||||
0.874549 | + | 0.484938i | \(0.161158\pi\) | |||||||
\(44\) | −1.08694 | −0.163862 | ||||||||
\(45\) | −3.83399 | −0.571538 | ||||||||
\(46\) | 4.86940 | 0.717954 | ||||||||
\(47\) | 11.5592 | 1.68608 | 0.843038 | − | 0.537854i | \(-0.180765\pi\) | ||||
0.843038 | + | 0.537854i | \(0.180765\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 3.87612 | 0.553731 | ||||||||
\(50\) | −9.69950 | −1.37172 | ||||||||
\(51\) | −5.28528 | −0.740087 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 1.82123 | 0.250166 | 0.125083 | − | 0.992146i | \(-0.460080\pi\) | ||||
0.125083 | + | 0.992146i | \(0.460080\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.16732 | 0.561921 | ||||||||
\(56\) | 3.29790 | 0.440700 | ||||||||
\(57\) | 7.52849 | 0.997172 | ||||||||
\(58\) | 8.02922 | 1.05429 | ||||||||
\(59\) | 10.3370 | 1.34577 | 0.672883 | − | 0.739749i | \(-0.265056\pi\) | ||||
0.672883 | + | 0.739749i | \(0.265056\pi\) | |||||||
\(60\) | −3.83399 | −0.494966 | ||||||||
\(61\) | −14.8682 | −1.90368 | −0.951839 | − | 0.306597i | \(-0.900810\pi\) | ||||
−0.951839 | + | 0.306597i | \(0.900810\pi\) | |||||||
\(62\) | −3.95486 | −0.502268 | ||||||||
\(63\) | −3.29790 | −0.415496 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.83399 | −0.475548 | ||||||||
\(66\) | 1.08694 | 0.133793 | ||||||||
\(67\) | 9.36012 | 1.14352 | 0.571761 | − | 0.820421i | \(-0.306261\pi\) | ||||
0.571761 | + | 0.820421i | \(0.306261\pi\) | |||||||
\(68\) | −5.28528 | −0.640934 | ||||||||
\(69\) | −4.86940 | −0.586207 | ||||||||
\(70\) | −12.6441 | −1.51126 | ||||||||
\(71\) | −9.48805 | −1.12602 | −0.563012 | − | 0.826449i | \(-0.690358\pi\) | ||||
−0.563012 | + | 0.826449i | \(0.690358\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −5.79522 | −0.678279 | −0.339140 | − | 0.940736i | \(-0.610136\pi\) | ||||
−0.339140 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(74\) | −3.95146 | −0.459348 | ||||||||
\(75\) | 9.69950 | 1.12000 | ||||||||
\(76\) | 7.52849 | 0.863577 | ||||||||
\(77\) | 3.58461 | 0.408504 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 6.22766 | 0.700666 | 0.350333 | − | 0.936625i | \(-0.386068\pi\) | ||||
0.350333 | + | 0.936625i | \(0.386068\pi\) | |||||||
\(80\) | −3.83399 | −0.428653 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.35805 | −0.591697 | ||||||||
\(83\) | 2.49468 | 0.273827 | 0.136913 | − | 0.990583i | \(-0.456282\pi\) | ||||
0.136913 | + | 0.990583i | \(0.456282\pi\) | |||||||
\(84\) | −3.29790 | −0.359830 | ||||||||
\(85\) | 20.2637 | 2.19791 | ||||||||
\(86\) | −11.4696 | −1.23680 | ||||||||
\(87\) | −8.02922 | −0.860823 | ||||||||
\(88\) | 1.08694 | 0.115868 | ||||||||
\(89\) | 5.79834 | 0.614623 | 0.307311 | − | 0.951609i | \(-0.400571\pi\) | ||||
0.307311 | + | 0.951609i | \(0.400571\pi\) | |||||||
\(90\) | 3.83399 | 0.404138 | ||||||||
\(91\) | −3.29790 | −0.345713 | ||||||||
\(92\) | −4.86940 | −0.507670 | ||||||||
\(93\) | 3.95486 | 0.410100 | ||||||||
\(94\) | −11.5592 | −1.19224 | ||||||||
\(95\) | −28.8642 | −2.96140 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −5.65476 | −0.574153 | −0.287077 | − | 0.957908i | \(-0.592683\pi\) | ||||
−0.287077 | + | 0.957908i | \(0.592683\pi\) | |||||||
\(98\) | −3.87612 | −0.391547 | ||||||||
\(99\) | −1.08694 | −0.109241 | ||||||||
\(100\) | 9.69950 | 0.969950 | ||||||||
\(101\) | −9.00487 | −0.896018 | −0.448009 | − | 0.894029i | \(-0.647867\pi\) | ||||
−0.448009 | + | 0.894029i | \(0.647867\pi\) | |||||||
\(102\) | 5.28528 | 0.523320 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 12.6441 | 1.23394 | ||||||||
\(106\) | −1.82123 | −0.176894 | ||||||||
\(107\) | 12.8287 | 1.24019 | 0.620097 | − | 0.784525i | \(-0.287093\pi\) | ||||
0.620097 | + | 0.784525i | \(0.287093\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −18.0578 | −1.72962 | −0.864812 | − | 0.502095i | \(-0.832563\pi\) | ||||
−0.864812 | + | 0.502095i | \(0.832563\pi\) | |||||||
\(110\) | −4.16732 | −0.397338 | ||||||||
\(111\) | 3.95146 | 0.375056 | ||||||||
\(112\) | −3.29790 | −0.311622 | ||||||||
\(113\) | −10.4337 | −0.981521 | −0.490761 | − | 0.871294i | \(-0.663281\pi\) | ||||
−0.490761 | + | 0.871294i | \(0.663281\pi\) | |||||||
\(114\) | −7.52849 | −0.705107 | ||||||||
\(115\) | 18.6693 | 1.74092 | ||||||||
\(116\) | −8.02922 | −0.745494 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −10.3370 | −0.951600 | ||||||||
\(119\) | 17.4303 | 1.59783 | ||||||||
\(120\) | 3.83399 | 0.349994 | ||||||||
\(121\) | −9.81856 | −0.892597 | ||||||||
\(122\) | 14.8682 | 1.34610 | ||||||||
\(123\) | 5.35805 | 0.483119 | ||||||||
\(124\) | 3.95486 | 0.355157 | ||||||||
\(125\) | −18.0179 | −1.61157 | ||||||||
\(126\) | 3.29790 | 0.293800 | ||||||||
\(127\) | −9.93819 | −0.881871 | −0.440936 | − | 0.897539i | \(-0.645353\pi\) | ||||
−0.440936 | + | 0.897539i | \(0.645353\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.4696 | 1.00984 | ||||||||
\(130\) | 3.83399 | 0.336263 | ||||||||
\(131\) | −13.4253 | −1.17297 | −0.586486 | − | 0.809959i | \(-0.699489\pi\) | ||||
−0.586486 | + | 0.809959i | \(0.699489\pi\) | |||||||
\(132\) | −1.08694 | −0.0946059 | ||||||||
\(133\) | −24.8282 | −2.15287 | ||||||||
\(134\) | −9.36012 | −0.808591 | ||||||||
\(135\) | −3.83399 | −0.329978 | ||||||||
\(136\) | 5.28528 | 0.453209 | ||||||||
\(137\) | 18.7763 | 1.60416 | 0.802082 | − | 0.597214i | \(-0.203726\pi\) | ||||
0.802082 | + | 0.597214i | \(0.203726\pi\) | |||||||
\(138\) | 4.86940 | 0.414511 | ||||||||
\(139\) | −0.112175 | −0.00951457 | −0.00475728 | − | 0.999989i | \(-0.501514\pi\) | ||||
−0.00475728 | + | 0.999989i | \(0.501514\pi\) | |||||||
\(140\) | 12.6441 | 1.06862 | ||||||||
\(141\) | 11.5592 | 0.973457 | ||||||||
\(142\) | 9.48805 | 0.796219 | ||||||||
\(143\) | −1.08694 | −0.0908944 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 30.7840 | 2.55647 | ||||||||
\(146\) | 5.79522 | 0.479616 | ||||||||
\(147\) | 3.87612 | 0.319697 | ||||||||
\(148\) | 3.95146 | 0.324808 | ||||||||
\(149\) | −3.20558 | −0.262612 | −0.131306 | − | 0.991342i | \(-0.541917\pi\) | ||||
−0.131306 | + | 0.991342i | \(0.541917\pi\) | |||||||
\(150\) | −9.69950 | −0.791961 | ||||||||
\(151\) | 9.10079 | 0.740612 | 0.370306 | − | 0.928910i | \(-0.379253\pi\) | ||||
0.370306 | + | 0.928910i | \(0.379253\pi\) | |||||||
\(152\) | −7.52849 | −0.610641 | ||||||||
\(153\) | −5.28528 | −0.427289 | ||||||||
\(154\) | −3.58461 | −0.288856 | ||||||||
\(155\) | −15.1629 | −1.21791 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −14.3195 | −1.14282 | −0.571410 | − | 0.820665i | \(-0.693603\pi\) | ||||
−0.571410 | + | 0.820665i | \(0.693603\pi\) | |||||||
\(158\) | −6.22766 | −0.495446 | ||||||||
\(159\) | 1.82123 | 0.144433 | ||||||||
\(160\) | 3.83399 | 0.303104 | ||||||||
\(161\) | 16.0588 | 1.26561 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −14.6517 | −1.14761 | −0.573804 | − | 0.818993i | \(-0.694533\pi\) | ||||
−0.573804 | + | 0.818993i | \(0.694533\pi\) | |||||||
\(164\) | 5.35805 | 0.418393 | ||||||||
\(165\) | 4.16732 | 0.324425 | ||||||||
\(166\) | −2.49468 | −0.193625 | ||||||||
\(167\) | 3.44383 | 0.266492 | 0.133246 | − | 0.991083i | \(-0.457460\pi\) | ||||
0.133246 | + | 0.991083i | \(0.457460\pi\) | |||||||
\(168\) | 3.29790 | 0.254438 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −20.2637 | −1.55416 | ||||||||
\(171\) | 7.52849 | 0.575718 | ||||||||
\(172\) | 11.4696 | 0.874549 | ||||||||
\(173\) | −4.14641 | −0.315246 | −0.157623 | − | 0.987499i | \(-0.550383\pi\) | ||||
−0.157623 | + | 0.987499i | \(0.550383\pi\) | |||||||
\(174\) | 8.02922 | 0.608694 | ||||||||
\(175\) | −31.9879 | −2.41806 | ||||||||
\(176\) | −1.08694 | −0.0819311 | ||||||||
\(177\) | 10.3370 | 0.776978 | ||||||||
\(178\) | −5.79834 | −0.434604 | ||||||||
\(179\) | 7.84629 | 0.586459 | 0.293230 | − | 0.956042i | \(-0.405270\pi\) | ||||
0.293230 | + | 0.956042i | \(0.405270\pi\) | |||||||
\(180\) | −3.83399 | −0.285769 | ||||||||
\(181\) | 4.55624 | 0.338663 | 0.169331 | − | 0.985559i | \(-0.445839\pi\) | ||||
0.169331 | + | 0.985559i | \(0.445839\pi\) | |||||||
\(182\) | 3.29790 | 0.244456 | ||||||||
\(183\) | −14.8682 | −1.09909 | ||||||||
\(184\) | 4.86940 | 0.358977 | ||||||||
\(185\) | −15.1499 | −1.11384 | ||||||||
\(186\) | −3.95486 | −0.289985 | ||||||||
\(187\) | 5.74477 | 0.420099 | ||||||||
\(188\) | 11.5592 | 0.843038 | ||||||||
\(189\) | −3.29790 | −0.239887 | ||||||||
\(190\) | 28.8642 | 2.09403 | ||||||||
\(191\) | 5.88806 | 0.426045 | 0.213023 | − | 0.977047i | \(-0.431669\pi\) | ||||
0.213023 | + | 0.977047i | \(0.431669\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 3.69894 | 0.266256 | 0.133128 | − | 0.991099i | \(-0.457498\pi\) | ||||
0.133128 | + | 0.991099i | \(0.457498\pi\) | |||||||
\(194\) | 5.65476 | 0.405988 | ||||||||
\(195\) | −3.83399 | −0.274558 | ||||||||
\(196\) | 3.87612 | 0.276865 | ||||||||
\(197\) | 5.26650 | 0.375223 | 0.187611 | − | 0.982243i | \(-0.439925\pi\) | ||||
0.187611 | + | 0.982243i | \(0.439925\pi\) | |||||||
\(198\) | 1.08694 | 0.0772454 | ||||||||
\(199\) | 14.3971 | 1.02059 | 0.510293 | − | 0.860001i | \(-0.329537\pi\) | ||||
0.510293 | + | 0.860001i | \(0.329537\pi\) | |||||||
\(200\) | −9.69950 | −0.685858 | ||||||||
\(201\) | 9.36012 | 0.660212 | ||||||||
\(202\) | 9.00487 | 0.633581 | ||||||||
\(203\) | 26.4795 | 1.85850 | ||||||||
\(204\) | −5.28528 | −0.370043 | ||||||||
\(205\) | −20.5427 | −1.43477 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −4.86940 | −0.338447 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −8.18301 | −0.566030 | ||||||||
\(210\) | −12.6441 | −0.872526 | ||||||||
\(211\) | 10.4702 | 0.720795 | 0.360398 | − | 0.932799i | \(-0.382641\pi\) | ||||
0.360398 | + | 0.932799i | \(0.382641\pi\) | |||||||
\(212\) | 1.82123 | 0.125083 | ||||||||
\(213\) | −9.48805 | −0.650110 | ||||||||
\(214\) | −12.8287 | −0.876950 | ||||||||
\(215\) | −43.9744 | −2.99903 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −13.0427 | −0.885398 | ||||||||
\(218\) | 18.0578 | 1.22303 | ||||||||
\(219\) | −5.79522 | −0.391605 | ||||||||
\(220\) | 4.16732 | 0.280960 | ||||||||
\(221\) | −5.28528 | −0.355526 | ||||||||
\(222\) | −3.95146 | −0.265205 | ||||||||
\(223\) | 15.9747 | 1.06975 | 0.534873 | − | 0.844932i | \(-0.320359\pi\) | ||||
0.534873 | + | 0.844932i | \(0.320359\pi\) | |||||||
\(224\) | 3.29790 | 0.220350 | ||||||||
\(225\) | 9.69950 | 0.646633 | ||||||||
\(226\) | 10.4337 | 0.694040 | ||||||||
\(227\) | 4.41065 | 0.292745 | 0.146373 | − | 0.989230i | \(-0.453240\pi\) | ||||
0.146373 | + | 0.989230i | \(0.453240\pi\) | |||||||
\(228\) | 7.52849 | 0.498586 | ||||||||
\(229\) | −7.15661 | −0.472922 | −0.236461 | − | 0.971641i | \(-0.575988\pi\) | ||||
−0.236461 | + | 0.971641i | \(0.575988\pi\) | |||||||
\(230\) | −18.6693 | −1.23101 | ||||||||
\(231\) | 3.58461 | 0.235850 | ||||||||
\(232\) | 8.02922 | 0.527144 | ||||||||
\(233\) | 24.7436 | 1.62101 | 0.810503 | − | 0.585735i | \(-0.199194\pi\) | ||||
0.810503 | + | 0.585735i | \(0.199194\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −44.3177 | −2.89097 | ||||||||
\(236\) | 10.3370 | 0.672883 | ||||||||
\(237\) | 6.22766 | 0.404530 | ||||||||
\(238\) | −17.4303 | −1.12984 | ||||||||
\(239\) | −3.79838 | −0.245697 | −0.122848 | − | 0.992425i | \(-0.539203\pi\) | ||||
−0.122848 | + | 0.992425i | \(0.539203\pi\) | |||||||
\(240\) | −3.83399 | −0.247483 | ||||||||
\(241\) | −21.6703 | −1.39591 | −0.697954 | − | 0.716143i | \(-0.745906\pi\) | ||||
−0.697954 | + | 0.716143i | \(0.745906\pi\) | |||||||
\(242\) | 9.81856 | 0.631161 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.8682 | −0.951839 | ||||||||
\(245\) | −14.8610 | −0.949435 | ||||||||
\(246\) | −5.35805 | −0.341617 | ||||||||
\(247\) | 7.52849 | 0.479026 | ||||||||
\(248\) | −3.95486 | −0.251134 | ||||||||
\(249\) | 2.49468 | 0.158094 | ||||||||
\(250\) | 18.0179 | 1.13955 | ||||||||
\(251\) | −15.8714 | −1.00179 | −0.500897 | − | 0.865507i | \(-0.666996\pi\) | ||||
−0.500897 | + | 0.865507i | \(0.666996\pi\) | |||||||
\(252\) | −3.29790 | −0.207748 | ||||||||
\(253\) | 5.29275 | 0.332752 | ||||||||
\(254\) | 9.93819 | 0.623577 | ||||||||
\(255\) | 20.2637 | 1.26896 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.3680 | −1.20814 | −0.604072 | − | 0.796930i | \(-0.706456\pi\) | ||||
−0.604072 | + | 0.796930i | \(0.706456\pi\) | |||||||
\(258\) | −11.4696 | −0.714066 | ||||||||
\(259\) | −13.0315 | −0.809738 | ||||||||
\(260\) | −3.83399 | −0.237774 | ||||||||
\(261\) | −8.02922 | −0.496996 | ||||||||
\(262\) | 13.4253 | 0.829417 | ||||||||
\(263\) | 2.61834 | 0.161454 | 0.0807269 | − | 0.996736i | \(-0.474276\pi\) | ||||
0.0807269 | + | 0.996736i | \(0.474276\pi\) | |||||||
\(264\) | 1.08694 | 0.0668965 | ||||||||
\(265\) | −6.98260 | −0.428938 | ||||||||
\(266\) | 24.8282 | 1.52231 | ||||||||
\(267\) | 5.79834 | 0.354853 | ||||||||
\(268\) | 9.36012 | 0.571761 | ||||||||
\(269\) | 22.0924 | 1.34700 | 0.673498 | − | 0.739189i | \(-0.264791\pi\) | ||||
0.673498 | + | 0.739189i | \(0.264791\pi\) | |||||||
\(270\) | 3.83399 | 0.233329 | ||||||||
\(271\) | −13.7745 | −0.836741 | −0.418370 | − | 0.908277i | \(-0.637399\pi\) | ||||
−0.418370 | + | 0.908277i | \(0.637399\pi\) | |||||||
\(272\) | −5.28528 | −0.320467 | ||||||||
\(273\) | −3.29790 | −0.199598 | ||||||||
\(274\) | −18.7763 | −1.13432 | ||||||||
\(275\) | −10.5428 | −0.635753 | ||||||||
\(276\) | −4.86940 | −0.293104 | ||||||||
\(277\) | 5.22578 | 0.313987 | 0.156993 | − | 0.987600i | \(-0.449820\pi\) | ||||
0.156993 | + | 0.987600i | \(0.449820\pi\) | |||||||
\(278\) | 0.112175 | 0.00672782 | ||||||||
\(279\) | 3.95486 | 0.236771 | ||||||||
\(280\) | −12.6441 | −0.755630 | ||||||||
\(281\) | −10.2219 | −0.609784 | −0.304892 | − | 0.952387i | \(-0.598620\pi\) | ||||
−0.304892 | + | 0.952387i | \(0.598620\pi\) | |||||||
\(282\) | −11.5592 | −0.688338 | ||||||||
\(283\) | −12.3497 | −0.734116 | −0.367058 | − | 0.930198i | \(-0.619635\pi\) | ||||
−0.367058 | + | 0.930198i | \(0.619635\pi\) | |||||||
\(284\) | −9.48805 | −0.563012 | ||||||||
\(285\) | −28.8642 | −1.70977 | ||||||||
\(286\) | 1.08694 | 0.0642721 | ||||||||
\(287\) | −17.6703 | −1.04304 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 10.9342 | 0.643185 | ||||||||
\(290\) | −30.7840 | −1.80770 | ||||||||
\(291\) | −5.65476 | −0.331488 | ||||||||
\(292\) | −5.79522 | −0.339140 | ||||||||
\(293\) | −6.42954 | −0.375618 | −0.187809 | − | 0.982206i | \(-0.560139\pi\) | ||||
−0.187809 | + | 0.982206i | \(0.560139\pi\) | |||||||
\(294\) | −3.87612 | −0.226060 | ||||||||
\(295\) | −39.6321 | −2.30747 | ||||||||
\(296\) | −3.95146 | −0.229674 | ||||||||
\(297\) | −1.08694 | −0.0630706 | ||||||||
\(298\) | 3.20558 | 0.185694 | ||||||||
\(299\) | −4.86940 | −0.281605 | ||||||||
\(300\) | 9.69950 | 0.560001 | ||||||||
\(301\) | −37.8255 | −2.18023 | ||||||||
\(302\) | −9.10079 | −0.523692 | ||||||||
\(303\) | −9.00487 | −0.517316 | ||||||||
\(304\) | 7.52849 | 0.431788 | ||||||||
\(305\) | 57.0046 | 3.26407 | ||||||||
\(306\) | 5.28528 | 0.302139 | ||||||||
\(307\) | 14.6133 | 0.834026 | 0.417013 | − | 0.908901i | \(-0.363077\pi\) | ||||
0.417013 | + | 0.908901i | \(0.363077\pi\) | |||||||
\(308\) | 3.58461 | 0.204252 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 15.1629 | 0.861195 | ||||||||
\(311\) | −11.9468 | −0.677438 | −0.338719 | − | 0.940888i | \(-0.609994\pi\) | ||||
−0.338719 | + | 0.940888i | \(0.609994\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −7.08127 | −0.400257 | −0.200128 | − | 0.979770i | \(-0.564136\pi\) | ||||
−0.200128 | + | 0.979770i | \(0.564136\pi\) | |||||||
\(314\) | 14.3195 | 0.808096 | ||||||||
\(315\) | 12.6441 | 0.712415 | ||||||||
\(316\) | 6.22766 | 0.350333 | ||||||||
\(317\) | −23.8099 | −1.33730 | −0.668648 | − | 0.743579i | \(-0.733127\pi\) | ||||
−0.668648 | + | 0.743579i | \(0.733127\pi\) | |||||||
\(318\) | −1.82123 | −0.102130 | ||||||||
\(319\) | 8.72727 | 0.488634 | ||||||||
\(320\) | −3.83399 | −0.214327 | ||||||||
\(321\) | 12.8287 | 0.716027 | ||||||||
\(322\) | −16.0588 | −0.894921 | ||||||||
\(323\) | −39.7901 | −2.21398 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 9.69950 | 0.538032 | ||||||||
\(326\) | 14.6517 | 0.811481 | ||||||||
\(327\) | −18.0578 | −0.998599 | ||||||||
\(328\) | −5.35805 | −0.295849 | ||||||||
\(329\) | −38.1209 | −2.10167 | ||||||||
\(330\) | −4.16732 | −0.229403 | ||||||||
\(331\) | −35.9491 | −1.97594 | −0.987969 | − | 0.154650i | \(-0.950575\pi\) | ||||
−0.987969 | + | 0.154650i | \(0.950575\pi\) | |||||||
\(332\) | 2.49468 | 0.136913 | ||||||||
\(333\) | 3.95146 | 0.216539 | ||||||||
\(334\) | −3.44383 | −0.188438 | ||||||||
\(335\) | −35.8866 | −1.96070 | ||||||||
\(336\) | −3.29790 | −0.179915 | ||||||||
\(337\) | 0.991712 | 0.0540220 | 0.0270110 | − | 0.999635i | \(-0.491401\pi\) | ||||
0.0270110 | + | 0.999635i | \(0.491401\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −10.4337 | −0.566681 | ||||||||
\(340\) | 20.2637 | 1.09895 | ||||||||
\(341\) | −4.29869 | −0.232787 | ||||||||
\(342\) | −7.52849 | −0.407094 | ||||||||
\(343\) | 10.3022 | 0.556269 | ||||||||
\(344\) | −11.4696 | −0.618399 | ||||||||
\(345\) | 18.6693 | 1.00512 | ||||||||
\(346\) | 4.14641 | 0.222912 | ||||||||
\(347\) | −18.9111 | −1.01520 | −0.507600 | − | 0.861593i | \(-0.669467\pi\) | ||||
−0.507600 | + | 0.861593i | \(0.669467\pi\) | |||||||
\(348\) | −8.02922 | −0.430411 | ||||||||
\(349\) | −28.2832 | −1.51397 | −0.756984 | − | 0.653434i | \(-0.773328\pi\) | ||||
−0.756984 | + | 0.653434i | \(0.773328\pi\) | |||||||
\(350\) | 31.9879 | 1.70983 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 1.08694 | 0.0579340 | ||||||||
\(353\) | 15.5041 | 0.825198 | 0.412599 | − | 0.910913i | \(-0.364621\pi\) | ||||
0.412599 | + | 0.910913i | \(0.364621\pi\) | |||||||
\(354\) | −10.3370 | −0.549407 | ||||||||
\(355\) | 36.3771 | 1.93070 | ||||||||
\(356\) | 5.79834 | 0.307311 | ||||||||
\(357\) | 17.4303 | 0.922509 | ||||||||
\(358\) | −7.84629 | −0.414689 | ||||||||
\(359\) | 9.62071 | 0.507761 | 0.253881 | − | 0.967236i | \(-0.418293\pi\) | ||||
0.253881 | + | 0.967236i | \(0.418293\pi\) | |||||||
\(360\) | 3.83399 | 0.202069 | ||||||||
\(361\) | 37.6781 | 1.98306 | ||||||||
\(362\) | −4.55624 | −0.239471 | ||||||||
\(363\) | −9.81856 | −0.515341 | ||||||||
\(364\) | −3.29790 | −0.172857 | ||||||||
\(365\) | 22.2188 | 1.16299 | ||||||||
\(366\) | 14.8682 | 0.777174 | ||||||||
\(367\) | 24.2108 | 1.26379 | 0.631896 | − | 0.775053i | \(-0.282277\pi\) | ||||
0.631896 | + | 0.775053i | \(0.282277\pi\) | |||||||
\(368\) | −4.86940 | −0.253835 | ||||||||
\(369\) | 5.35805 | 0.278929 | ||||||||
\(370\) | 15.1499 | 0.787604 | ||||||||
\(371\) | −6.00624 | −0.311828 | ||||||||
\(372\) | 3.95486 | 0.205050 | ||||||||
\(373\) | −1.14257 | −0.0591598 | −0.0295799 | − | 0.999562i | \(-0.509417\pi\) | ||||
−0.0295799 | + | 0.999562i | \(0.509417\pi\) | |||||||
\(374\) | −5.74477 | −0.297055 | ||||||||
\(375\) | −18.0179 | −0.930438 | ||||||||
\(376\) | −11.5592 | −0.596118 | ||||||||
\(377\) | −8.02922 | −0.413526 | ||||||||
\(378\) | 3.29790 | 0.169625 | ||||||||
\(379\) | −8.84686 | −0.454433 | −0.227216 | − | 0.973844i | \(-0.572962\pi\) | ||||
−0.227216 | + | 0.973844i | \(0.572962\pi\) | |||||||
\(380\) | −28.8642 | −1.48070 | ||||||||
\(381\) | −9.93819 | −0.509149 | ||||||||
\(382\) | −5.88806 | −0.301259 | ||||||||
\(383\) | −3.54043 | −0.180908 | −0.0904538 | − | 0.995901i | \(-0.528832\pi\) | ||||
−0.0904538 | + | 0.995901i | \(0.528832\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −13.7434 | −0.700427 | ||||||||
\(386\) | −3.69894 | −0.188271 | ||||||||
\(387\) | 11.4696 | 0.583032 | ||||||||
\(388\) | −5.65476 | −0.287077 | ||||||||
\(389\) | 15.8087 | 0.801534 | 0.400767 | − | 0.916180i | \(-0.368744\pi\) | ||||
0.400767 | + | 0.916180i | \(0.368744\pi\) | |||||||
\(390\) | 3.83399 | 0.194142 | ||||||||
\(391\) | 25.7361 | 1.30153 | ||||||||
\(392\) | −3.87612 | −0.195773 | ||||||||
\(393\) | −13.4253 | −0.677216 | ||||||||
\(394\) | −5.26650 | −0.265323 | ||||||||
\(395\) | −23.8768 | −1.20137 | ||||||||
\(396\) | −1.08694 | −0.0546207 | ||||||||
\(397\) | 36.8850 | 1.85120 | 0.925602 | − | 0.378499i | \(-0.123560\pi\) | ||||
0.925602 | + | 0.378499i | \(0.123560\pi\) | |||||||
\(398\) | −14.3971 | −0.721663 | ||||||||
\(399\) | −24.8282 | −1.24296 | ||||||||
\(400\) | 9.69950 | 0.484975 | ||||||||
\(401\) | 21.5806 | 1.07769 | 0.538843 | − | 0.842406i | \(-0.318862\pi\) | ||||
0.538843 | + | 0.842406i | \(0.318862\pi\) | |||||||
\(402\) | −9.36012 | −0.466840 | ||||||||
\(403\) | 3.95486 | 0.197006 | ||||||||
\(404\) | −9.00487 | −0.448009 | ||||||||
\(405\) | −3.83399 | −0.190513 | ||||||||
\(406\) | −26.4795 | −1.31416 | ||||||||
\(407\) | −4.29500 | −0.212895 | ||||||||
\(408\) | 5.28528 | 0.261660 | ||||||||
\(409\) | −39.4851 | −1.95241 | −0.976207 | − | 0.216840i | \(-0.930425\pi\) | ||||
−0.976207 | + | 0.216840i | \(0.930425\pi\) | |||||||
\(410\) | 20.5427 | 1.01453 | ||||||||
\(411\) | 18.7763 | 0.926165 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −34.0904 | −1.67748 | ||||||||
\(414\) | 4.86940 | 0.239318 | ||||||||
\(415\) | −9.56459 | −0.469507 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −0.112175 | −0.00549324 | ||||||||
\(418\) | 8.18301 | 0.400244 | ||||||||
\(419\) | −16.1944 | −0.791147 | −0.395574 | − | 0.918434i | \(-0.629454\pi\) | ||||
−0.395574 | + | 0.918434i | \(0.629454\pi\) | |||||||
\(420\) | 12.6441 | 0.616969 | ||||||||
\(421\) | −16.4463 | −0.801544 | −0.400772 | − | 0.916178i | \(-0.631258\pi\) | ||||
−0.400772 | + | 0.916178i | \(0.631258\pi\) | |||||||
\(422\) | −10.4702 | −0.509679 | ||||||||
\(423\) | 11.5592 | 0.562025 | ||||||||
\(424\) | −1.82123 | −0.0884469 | ||||||||
\(425\) | −51.2646 | −2.48670 | ||||||||
\(426\) | 9.48805 | 0.459697 | ||||||||
\(427\) | 49.0338 | 2.37291 | ||||||||
\(428\) | 12.8287 | 0.620097 | ||||||||
\(429\) | −1.08694 | −0.0524779 | ||||||||
\(430\) | 43.9744 | 2.12063 | ||||||||
\(431\) | 7.93853 | 0.382386 | 0.191193 | − | 0.981553i | \(-0.438764\pi\) | ||||
0.191193 | + | 0.981553i | \(0.438764\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 40.9214 | 1.96656 | 0.983278 | − | 0.182108i | \(-0.0582921\pi\) | ||||
0.983278 | + | 0.182108i | \(0.0582921\pi\) | |||||||
\(434\) | 13.0427 | 0.626071 | ||||||||
\(435\) | 30.7840 | 1.47598 | ||||||||
\(436\) | −18.0578 | −0.864812 | ||||||||
\(437\) | −36.6592 | −1.75365 | ||||||||
\(438\) | 5.79522 | 0.276906 | ||||||||
\(439\) | −26.1722 | −1.24913 | −0.624565 | − | 0.780973i | \(-0.714724\pi\) | ||||
−0.624565 | + | 0.780973i | \(0.714724\pi\) | |||||||
\(440\) | −4.16732 | −0.198669 | ||||||||
\(441\) | 3.87612 | 0.184577 | ||||||||
\(442\) | 5.28528 | 0.251395 | ||||||||
\(443\) | −8.73740 | −0.415126 | −0.207563 | − | 0.978222i | \(-0.566553\pi\) | ||||
−0.207563 | + | 0.978222i | \(0.566553\pi\) | |||||||
\(444\) | 3.95146 | 0.187528 | ||||||||
\(445\) | −22.2308 | −1.05384 | ||||||||
\(446\) | −15.9747 | −0.756425 | ||||||||
\(447\) | −3.20558 | −0.151619 | ||||||||
\(448\) | −3.29790 | −0.155811 | ||||||||
\(449\) | −27.0573 | −1.27692 | −0.638458 | − | 0.769657i | \(-0.720427\pi\) | ||||
−0.638458 | + | 0.769657i | \(0.720427\pi\) | |||||||
\(450\) | −9.69950 | −0.457239 | ||||||||
\(451\) | −5.82387 | −0.274235 | ||||||||
\(452\) | −10.4337 | −0.490761 | ||||||||
\(453\) | 9.10079 | 0.427593 | ||||||||
\(454\) | −4.41065 | −0.207002 | ||||||||
\(455\) | 12.6441 | 0.592765 | ||||||||
\(456\) | −7.52849 | −0.352554 | ||||||||
\(457\) | −12.4155 | −0.580771 | −0.290385 | − | 0.956910i | \(-0.593783\pi\) | ||||
−0.290385 | + | 0.956910i | \(0.593783\pi\) | |||||||
\(458\) | 7.15661 | 0.334406 | ||||||||
\(459\) | −5.28528 | −0.246696 | ||||||||
\(460\) | 18.6693 | 0.870459 | ||||||||
\(461\) | −25.3222 | −1.17937 | −0.589687 | − | 0.807632i | \(-0.700749\pi\) | ||||
−0.589687 | + | 0.807632i | \(0.700749\pi\) | |||||||
\(462\) | −3.58461 | −0.166771 | ||||||||
\(463\) | −11.0274 | −0.512487 | −0.256244 | − | 0.966612i | \(-0.582485\pi\) | ||||
−0.256244 | + | 0.966612i | \(0.582485\pi\) | |||||||
\(464\) | −8.02922 | −0.372747 | ||||||||
\(465\) | −15.1629 | −0.703163 | ||||||||
\(466\) | −24.7436 | −1.14622 | ||||||||
\(467\) | −0.314734 | −0.0145641 | −0.00728207 | − | 0.999973i | \(-0.502318\pi\) | ||||
−0.00728207 | + | 0.999973i | \(0.502318\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −30.8687 | −1.42538 | ||||||||
\(470\) | 44.3177 | 2.04422 | ||||||||
\(471\) | −14.3195 | −0.659808 | ||||||||
\(472\) | −10.3370 | −0.475800 | ||||||||
\(473\) | −12.4668 | −0.573222 | ||||||||
\(474\) | −6.22766 | −0.286046 | ||||||||
\(475\) | 73.0226 | 3.35050 | ||||||||
\(476\) | 17.4303 | 0.798916 | ||||||||
\(477\) | 1.82123 | 0.0833886 | ||||||||
\(478\) | 3.79838 | 0.173734 | ||||||||
\(479\) | −30.3516 | −1.38680 | −0.693401 | − | 0.720552i | \(-0.743888\pi\) | ||||
−0.693401 | + | 0.720552i | \(0.743888\pi\) | |||||||
\(480\) | 3.83399 | 0.174997 | ||||||||
\(481\) | 3.95146 | 0.180171 | ||||||||
\(482\) | 21.6703 | 0.987056 | ||||||||
\(483\) | 16.0588 | 0.730700 | ||||||||
\(484\) | −9.81856 | −0.446298 | ||||||||
\(485\) | 21.6803 | 0.984451 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 22.7338 | 1.03017 | 0.515083 | − | 0.857140i | \(-0.327761\pi\) | ||||
0.515083 | + | 0.857140i | \(0.327761\pi\) | |||||||
\(488\) | 14.8682 | 0.673052 | ||||||||
\(489\) | −14.6517 | −0.662571 | ||||||||
\(490\) | 14.8610 | 0.671352 | ||||||||
\(491\) | −37.6519 | −1.69921 | −0.849604 | − | 0.527422i | \(-0.823159\pi\) | ||||
−0.849604 | + | 0.527422i | \(0.823159\pi\) | |||||||
\(492\) | 5.35805 | 0.241559 | ||||||||
\(493\) | 42.4367 | 1.91125 | ||||||||
\(494\) | −7.52849 | −0.338723 | ||||||||
\(495\) | 4.16732 | 0.187307 | ||||||||
\(496\) | 3.95486 | 0.177579 | ||||||||
\(497\) | 31.2906 | 1.40357 | ||||||||
\(498\) | −2.49468 | −0.111789 | ||||||||
\(499\) | −37.8361 | −1.69378 | −0.846889 | − | 0.531770i | \(-0.821527\pi\) | ||||
−0.846889 | + | 0.531770i | \(0.821527\pi\) | |||||||
\(500\) | −18.0179 | −0.805783 | ||||||||
\(501\) | 3.44383 | 0.153859 | ||||||||
\(502\) | 15.8714 | 0.708375 | ||||||||
\(503\) | 18.3213 | 0.816905 | 0.408452 | − | 0.912780i | \(-0.366069\pi\) | ||||
0.408452 | + | 0.912780i | \(0.366069\pi\) | |||||||
\(504\) | 3.29790 | 0.146900 | ||||||||
\(505\) | 34.5246 | 1.53633 | ||||||||
\(506\) | −5.29275 | −0.235291 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −9.93819 | −0.440936 | ||||||||
\(509\) | 31.1958 | 1.38273 | 0.691364 | − | 0.722507i | \(-0.257010\pi\) | ||||
0.691364 | + | 0.722507i | \(0.257010\pi\) | |||||||
\(510\) | −20.2637 | −0.897292 | ||||||||
\(511\) | 19.1120 | 0.845467 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.52849 | 0.332391 | ||||||||
\(514\) | 19.3680 | 0.854286 | ||||||||
\(515\) | 3.83399 | 0.168946 | ||||||||
\(516\) | 11.4696 | 0.504921 | ||||||||
\(517\) | −12.5641 | −0.552568 | ||||||||
\(518\) | 13.0315 | 0.572571 | ||||||||
\(519\) | −4.14641 | −0.182007 | ||||||||
\(520\) | 3.83399 | 0.168132 | ||||||||
\(521\) | −39.7366 | −1.74089 | −0.870446 | − | 0.492264i | \(-0.836170\pi\) | ||||
−0.870446 | + | 0.492264i | \(0.836170\pi\) | |||||||
\(522\) | 8.02922 | 0.351429 | ||||||||
\(523\) | −15.5654 | −0.680626 | −0.340313 | − | 0.940312i | \(-0.610533\pi\) | ||||
−0.340313 | + | 0.940312i | \(0.610533\pi\) | |||||||
\(524\) | −13.4253 | −0.586486 | ||||||||
\(525\) | −31.9879 | −1.39607 | ||||||||
\(526\) | −2.61834 | −0.114165 | ||||||||
\(527\) | −20.9025 | −0.910529 | ||||||||
\(528\) | −1.08694 | −0.0473030 | ||||||||
\(529\) | 0.711092 | 0.0309170 | ||||||||
\(530\) | 6.98260 | 0.303305 | ||||||||
\(531\) | 10.3370 | 0.448589 | ||||||||
\(532\) | −24.8282 | −1.07644 | ||||||||
\(533\) | 5.35805 | 0.232083 | ||||||||
\(534\) | −5.79834 | −0.250919 | ||||||||
\(535\) | −49.1850 | −2.12645 | ||||||||
\(536\) | −9.36012 | −0.404296 | ||||||||
\(537\) | 7.84629 | 0.338592 | ||||||||
\(538\) | −22.0924 | −0.952469 | ||||||||
\(539\) | −4.21310 | −0.181471 | ||||||||
\(540\) | −3.83399 | −0.164989 | ||||||||
\(541\) | 36.4563 | 1.56738 | 0.783689 | − | 0.621153i | \(-0.213336\pi\) | ||||
0.783689 | + | 0.621153i | \(0.213336\pi\) | |||||||
\(542\) | 13.7745 | 0.591665 | ||||||||
\(543\) | 4.55624 | 0.195527 | ||||||||
\(544\) | 5.28528 | 0.226604 | ||||||||
\(545\) | 69.2335 | 2.96564 | ||||||||
\(546\) | 3.29790 | 0.141137 | ||||||||
\(547\) | 23.1673 | 0.990562 | 0.495281 | − | 0.868733i | \(-0.335065\pi\) | ||||
0.495281 | + | 0.868733i | \(0.335065\pi\) | |||||||
\(548\) | 18.7763 | 0.802082 | ||||||||
\(549\) | −14.8682 | −0.634560 | ||||||||
\(550\) | 10.5428 | 0.449545 | ||||||||
\(551\) | −60.4479 | −2.57517 | ||||||||
\(552\) | 4.86940 | 0.207256 | ||||||||
\(553\) | −20.5382 | −0.873372 | ||||||||
\(554\) | −5.22578 | −0.222022 | ||||||||
\(555\) | −15.1499 | −0.643076 | ||||||||
\(556\) | −0.112175 | −0.00475728 | ||||||||
\(557\) | −9.59679 | −0.406629 | −0.203315 | − | 0.979113i | \(-0.565171\pi\) | ||||
−0.203315 | + | 0.979113i | \(0.565171\pi\) | |||||||
\(558\) | −3.95486 | −0.167423 | ||||||||
\(559\) | 11.4696 | 0.485112 | ||||||||
\(560\) | 12.6441 | 0.534311 | ||||||||
\(561\) | 5.74477 | 0.242545 | ||||||||
\(562\) | 10.2219 | 0.431183 | ||||||||
\(563\) | −23.4170 | −0.986911 | −0.493455 | − | 0.869771i | \(-0.664266\pi\) | ||||
−0.493455 | + | 0.869771i | \(0.664266\pi\) | |||||||
\(564\) | 11.5592 | 0.486728 | ||||||||
\(565\) | 40.0028 | 1.68293 | ||||||||
\(566\) | 12.3497 | 0.519098 | ||||||||
\(567\) | −3.29790 | −0.138499 | ||||||||
\(568\) | 9.48805 | 0.398110 | ||||||||
\(569\) | −26.6193 | −1.11594 | −0.557969 | − | 0.829862i | \(-0.688419\pi\) | ||||
−0.557969 | + | 0.829862i | \(0.688419\pi\) | |||||||
\(570\) | 28.8642 | 1.20899 | ||||||||
\(571\) | 0.0404241 | 0.00169170 | 0.000845848 | − | 1.00000i | \(-0.499731\pi\) | ||||
0.000845848 | 1.00000i | \(0.499731\pi\) | ||||||||
\(572\) | −1.08694 | −0.0454472 | ||||||||
\(573\) | 5.88806 | 0.245977 | ||||||||
\(574\) | 17.6703 | 0.737543 | ||||||||
\(575\) | −47.2308 | −1.96966 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −38.2566 | −1.59264 | −0.796321 | − | 0.604875i | \(-0.793223\pi\) | ||||
−0.796321 | + | 0.604875i | \(0.793223\pi\) | |||||||
\(578\) | −10.9342 | −0.454801 | ||||||||
\(579\) | 3.69894 | 0.153723 | ||||||||
\(580\) | 30.7840 | 1.27823 | ||||||||
\(581\) | −8.22719 | −0.341322 | ||||||||
\(582\) | 5.65476 | 0.234397 | ||||||||
\(583\) | −1.97957 | −0.0819854 | ||||||||
\(584\) | 5.79522 | 0.239808 | ||||||||
\(585\) | −3.83399 | −0.158516 | ||||||||
\(586\) | 6.42954 | 0.265602 | ||||||||
\(587\) | −16.9963 | −0.701512 | −0.350756 | − | 0.936467i | \(-0.614075\pi\) | ||||
−0.350756 | + | 0.936467i | \(0.614075\pi\) | |||||||
\(588\) | 3.87612 | 0.159848 | ||||||||
\(589\) | 29.7741 | 1.22682 | ||||||||
\(590\) | 39.6321 | 1.63163 | ||||||||
\(591\) | 5.26650 | 0.216635 | ||||||||
\(592\) | 3.95146 | 0.162404 | ||||||||
\(593\) | −0.753800 | −0.0309548 | −0.0154774 | − | 0.999880i | \(-0.504927\pi\) | ||||
−0.0154774 | + | 0.999880i | \(0.504927\pi\) | |||||||
\(594\) | 1.08694 | 0.0445977 | ||||||||
\(595\) | −66.8276 | −2.73967 | ||||||||
\(596\) | −3.20558 | −0.131306 | ||||||||
\(597\) | 14.3971 | 0.589235 | ||||||||
\(598\) | 4.86940 | 0.199125 | ||||||||
\(599\) | 16.7987 | 0.686378 | 0.343189 | − | 0.939266i | \(-0.388493\pi\) | ||||
0.343189 | + | 0.939266i | \(0.388493\pi\) | |||||||
\(600\) | −9.69950 | −0.395980 | ||||||||
\(601\) | 4.34433 | 0.177209 | 0.0886046 | − | 0.996067i | \(-0.471759\pi\) | ||||
0.0886046 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(602\) | 37.8255 | 1.54165 | ||||||||
\(603\) | 9.36012 | 0.381174 | ||||||||
\(604\) | 9.10079 | 0.370306 | ||||||||
\(605\) | 37.6443 | 1.53046 | ||||||||
\(606\) | 9.00487 | 0.365798 | ||||||||
\(607\) | 27.4366 | 1.11362 | 0.556808 | − | 0.830641i | \(-0.312026\pi\) | ||||
0.556808 | + | 0.830641i | \(0.312026\pi\) | |||||||
\(608\) | −7.52849 | −0.305320 | ||||||||
\(609\) | 26.4795 | 1.07300 | ||||||||
\(610\) | −57.0046 | −2.30805 | ||||||||
\(611\) | 11.5592 | 0.467633 | ||||||||
\(612\) | −5.28528 | −0.213645 | ||||||||
\(613\) | −31.6726 | −1.27925 | −0.639623 | − | 0.768689i | \(-0.720910\pi\) | ||||
−0.639623 | + | 0.768689i | \(0.720910\pi\) | |||||||
\(614\) | −14.6133 | −0.589745 | ||||||||
\(615\) | −20.5427 | −0.828362 | ||||||||
\(616\) | −3.58461 | −0.144428 | ||||||||
\(617\) | −13.1275 | −0.528495 | −0.264247 | − | 0.964455i | \(-0.585124\pi\) | ||||
−0.264247 | + | 0.964455i | \(0.585124\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | 17.3610 | 0.697799 | 0.348899 | − | 0.937160i | \(-0.386555\pi\) | ||||
0.348899 | + | 0.937160i | \(0.386555\pi\) | |||||||
\(620\) | −15.1629 | −0.608957 | ||||||||
\(621\) | −4.86940 | −0.195402 | ||||||||
\(622\) | 11.9468 | 0.479021 | ||||||||
\(623\) | −19.1223 | −0.766120 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 20.5828 | 0.823313 | ||||||||
\(626\) | 7.08127 | 0.283024 | ||||||||
\(627\) | −8.18301 | −0.326798 | ||||||||
\(628\) | −14.3195 | −0.571410 | ||||||||
\(629\) | −20.8846 | −0.832722 | ||||||||
\(630\) | −12.6441 | −0.503753 | ||||||||
\(631\) | 18.9049 | 0.752592 | 0.376296 | − | 0.926499i | \(-0.377198\pi\) | ||||
0.376296 | + | 0.926499i | \(0.377198\pi\) | |||||||
\(632\) | −6.22766 | −0.247723 | ||||||||
\(633\) | 10.4702 | 0.416151 | ||||||||
\(634\) | 23.8099 | 0.945611 | ||||||||
\(635\) | 38.1029 | 1.51207 | ||||||||
\(636\) | 1.82123 | 0.0722166 | ||||||||
\(637\) | 3.87612 | 0.153577 | ||||||||
\(638\) | −8.72727 | −0.345516 | ||||||||
\(639\) | −9.48805 | −0.375341 | ||||||||
\(640\) | 3.83399 | 0.151552 | ||||||||
\(641\) | −8.94991 | −0.353500 | −0.176750 | − | 0.984256i | \(-0.556558\pi\) | ||||
−0.176750 | + | 0.984256i | \(0.556558\pi\) | |||||||
\(642\) | −12.8287 | −0.506307 | ||||||||
\(643\) | 42.0008 | 1.65635 | 0.828174 | − | 0.560471i | \(-0.189380\pi\) | ||||
0.828174 | + | 0.560471i | \(0.189380\pi\) | |||||||
\(644\) | 16.0588 | 0.632805 | ||||||||
\(645\) | −43.9744 | −1.73149 | ||||||||
\(646\) | 39.7901 | 1.56552 | ||||||||
\(647\) | −20.9806 | −0.824834 | −0.412417 | − | 0.910995i | \(-0.635315\pi\) | ||||
−0.412417 | + | 0.910995i | \(0.635315\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −11.2357 | −0.441040 | ||||||||
\(650\) | −9.69950 | −0.380446 | ||||||||
\(651\) | −13.0427 | −0.511185 | ||||||||
\(652\) | −14.6517 | −0.573804 | ||||||||
\(653\) | 43.9854 | 1.72128 | 0.860642 | − | 0.509211i | \(-0.170063\pi\) | ||||
0.860642 | + | 0.509211i | \(0.170063\pi\) | |||||||
\(654\) | 18.0578 | 0.706116 | ||||||||
\(655\) | 51.4724 | 2.01119 | ||||||||
\(656\) | 5.35805 | 0.209197 | ||||||||
\(657\) | −5.79522 | −0.226093 | ||||||||
\(658\) | 38.1209 | 1.48611 | ||||||||
\(659\) | 7.26503 | 0.283005 | 0.141503 | − | 0.989938i | \(-0.454807\pi\) | ||||
0.141503 | + | 0.989938i | \(0.454807\pi\) | |||||||
\(660\) | 4.16732 | 0.162213 | ||||||||
\(661\) | −13.2990 | −0.517273 | −0.258636 | − | 0.965975i | \(-0.583273\pi\) | ||||
−0.258636 | + | 0.965975i | \(0.583273\pi\) | |||||||
\(662\) | 35.9491 | 1.39720 | ||||||||
\(663\) | −5.28528 | −0.205263 | ||||||||
\(664\) | −2.49468 | −0.0968124 | ||||||||
\(665\) | 95.1910 | 3.69135 | ||||||||
\(666\) | −3.95146 | −0.153116 | ||||||||
\(667\) | 39.0975 | 1.51386 | ||||||||
\(668\) | 3.44383 | 0.133246 | ||||||||
\(669\) | 15.9747 | 0.617618 | ||||||||
\(670\) | 35.8866 | 1.38642 | ||||||||
\(671\) | 16.1608 | 0.623882 | ||||||||
\(672\) | 3.29790 | 0.127219 | ||||||||
\(673\) | −44.7188 | −1.72378 | −0.861891 | − | 0.507094i | \(-0.830720\pi\) | ||||
−0.861891 | + | 0.507094i | \(0.830720\pi\) | |||||||
\(674\) | −0.991712 | −0.0381993 | ||||||||
\(675\) | 9.69950 | 0.373334 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 12.3260 | 0.473728 | 0.236864 | − | 0.971543i | \(-0.423880\pi\) | ||||
0.236864 | + | 0.971543i | \(0.423880\pi\) | |||||||
\(678\) | 10.4337 | 0.400704 | ||||||||
\(679\) | 18.6488 | 0.715675 | ||||||||
\(680\) | −20.2637 | −0.777078 | ||||||||
\(681\) | 4.41065 | 0.169016 | ||||||||
\(682\) | 4.29869 | 0.164605 | ||||||||
\(683\) | 28.1431 | 1.07687 | 0.538433 | − | 0.842668i | \(-0.319017\pi\) | ||||
0.538433 | + | 0.842668i | \(0.319017\pi\) | |||||||
\(684\) | 7.52849 | 0.287859 | ||||||||
\(685\) | −71.9881 | −2.75052 | ||||||||
\(686\) | −10.3022 | −0.393341 | ||||||||
\(687\) | −7.15661 | −0.273042 | ||||||||
\(688\) | 11.4696 | 0.437274 | ||||||||
\(689\) | 1.82123 | 0.0693835 | ||||||||
\(690\) | −18.6693 | −0.710727 | ||||||||
\(691\) | −8.55552 | −0.325467 | −0.162734 | − | 0.986670i | \(-0.552031\pi\) | ||||
−0.162734 | + | 0.986670i | \(0.552031\pi\) | |||||||
\(692\) | −4.14641 | −0.157623 | ||||||||
\(693\) | 3.58461 | 0.136168 | ||||||||
\(694\) | 18.9111 | 0.717855 | ||||||||
\(695\) | 0.430079 | 0.0163138 | ||||||||
\(696\) | 8.02922 | 0.304347 | ||||||||
\(697\) | −28.3188 | −1.07265 | ||||||||
\(698\) | 28.2832 | 1.07054 | ||||||||
\(699\) | 24.7436 | 0.935888 | ||||||||
\(700\) | −31.9879 | −1.20903 | ||||||||
\(701\) | 5.05341 | 0.190865 | 0.0954323 | − | 0.995436i | \(-0.469577\pi\) | ||||
0.0954323 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 29.7485 | 1.12199 | ||||||||
\(704\) | −1.08694 | −0.0409656 | ||||||||
\(705\) | −44.3177 | −1.66910 | ||||||||
\(706\) | −15.5041 | −0.583503 | ||||||||
\(707\) | 29.6971 | 1.11688 | ||||||||
\(708\) | 10.3370 | 0.388489 | ||||||||
\(709\) | −24.1843 | −0.908259 | −0.454130 | − | 0.890936i | \(-0.650050\pi\) | ||||
−0.454130 | + | 0.890936i | \(0.650050\pi\) | |||||||
\(710\) | −36.3771 | −1.36521 | ||||||||
\(711\) | 6.22766 | 0.233555 | ||||||||
\(712\) | −5.79834 | −0.217302 | ||||||||
\(713\) | −19.2578 | −0.721211 | ||||||||
\(714\) | −17.4303 | −0.652312 | ||||||||
\(715\) | 4.16732 | 0.155849 | ||||||||
\(716\) | 7.84629 | 0.293230 | ||||||||
\(717\) | −3.79838 | −0.141853 | ||||||||
\(718\) | −9.62071 | −0.359042 | ||||||||
\(719\) | −25.7695 | −0.961039 | −0.480520 | − | 0.876984i | \(-0.659552\pi\) | ||||
−0.480520 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(720\) | −3.83399 | −0.142884 | ||||||||
\(721\) | 3.29790 | 0.122820 | ||||||||
\(722\) | −37.6781 | −1.40223 | ||||||||
\(723\) | −21.6703 | −0.805928 | ||||||||
\(724\) | 4.55624 | 0.169331 | ||||||||
\(725\) | −77.8794 | −2.89237 | ||||||||
\(726\) | 9.81856 | 0.364401 | ||||||||
\(727\) | 37.5268 | 1.39179 | 0.695897 | − | 0.718142i | \(-0.255007\pi\) | ||||
0.695897 | + | 0.718142i | \(0.255007\pi\) | |||||||
\(728\) | 3.29790 | 0.122228 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −22.2188 | −0.822356 | ||||||||
\(731\) | −60.6200 | −2.24211 | ||||||||
\(732\) | −14.8682 | −0.549545 | ||||||||
\(733\) | 29.6385 | 1.09472 | 0.547361 | − | 0.836896i | \(-0.315632\pi\) | ||||
0.547361 | + | 0.836896i | \(0.315632\pi\) | |||||||
\(734\) | −24.2108 | −0.893636 | ||||||||
\(735\) | −14.8610 | −0.548156 | ||||||||
\(736\) | 4.86940 | 0.179489 | ||||||||
\(737\) | −10.1739 | −0.374760 | ||||||||
\(738\) | −5.35805 | −0.197232 | ||||||||
\(739\) | −5.64072 | −0.207497 | −0.103749 | − | 0.994604i | \(-0.533084\pi\) | ||||
−0.103749 | + | 0.994604i | \(0.533084\pi\) | |||||||
\(740\) | −15.1499 | −0.556920 | ||||||||
\(741\) | 7.52849 | 0.276566 | ||||||||
\(742\) | 6.00624 | 0.220496 | ||||||||
\(743\) | 22.3300 | 0.819210 | 0.409605 | − | 0.912263i | \(-0.365667\pi\) | ||||
0.409605 | + | 0.912263i | \(0.365667\pi\) | |||||||
\(744\) | −3.95486 | −0.144992 | ||||||||
\(745\) | 12.2902 | 0.450278 | ||||||||
\(746\) | 1.14257 | 0.0418323 | ||||||||
\(747\) | 2.49468 | 0.0912756 | ||||||||
\(748\) | 5.74477 | 0.210050 | ||||||||
\(749\) | −42.3076 | −1.54589 | ||||||||
\(750\) | 18.0179 | 0.657919 | ||||||||
\(751\) | −16.8612 | −0.615274 | −0.307637 | − | 0.951504i | \(-0.599538\pi\) | ||||
−0.307637 | + | 0.951504i | \(0.599538\pi\) | |||||||
\(752\) | 11.5592 | 0.421519 | ||||||||
\(753\) | −15.8714 | −0.578386 | ||||||||
\(754\) | 8.02922 | 0.292407 | ||||||||
\(755\) | −34.8924 | −1.26986 | ||||||||
\(756\) | −3.29790 | −0.119943 | ||||||||
\(757\) | 2.53666 | 0.0921966 | 0.0460983 | − | 0.998937i | \(-0.485321\pi\) | ||||
0.0460983 | + | 0.998937i | \(0.485321\pi\) | |||||||
\(758\) | 8.84686 | 0.321332 | ||||||||
\(759\) | 5.29275 | 0.192114 | ||||||||
\(760\) | 28.8642 | 1.04701 | ||||||||
\(761\) | 18.5717 | 0.673224 | 0.336612 | − | 0.941643i | \(-0.390719\pi\) | ||||
0.336612 | + | 0.941643i | \(0.390719\pi\) | |||||||
\(762\) | 9.93819 | 0.360023 | ||||||||
\(763\) | 59.5528 | 2.15596 | ||||||||
\(764\) | 5.88806 | 0.213023 | ||||||||
\(765\) | 20.2637 | 0.732636 | ||||||||
\(766\) | 3.54043 | 0.127921 | ||||||||
\(767\) | 10.3370 | 0.373248 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −13.3869 | −0.482745 | −0.241372 | − | 0.970433i | \(-0.577597\pi\) | ||||
−0.241372 | + | 0.970433i | \(0.577597\pi\) | |||||||
\(770\) | 13.7434 | 0.495277 | ||||||||
\(771\) | −19.3680 | −0.697522 | ||||||||
\(772\) | 3.69894 | 0.133128 | ||||||||
\(773\) | 25.0931 | 0.902537 | 0.451268 | − | 0.892388i | \(-0.350972\pi\) | ||||
0.451268 | + | 0.892388i | \(0.350972\pi\) | |||||||
\(774\) | −11.4696 | −0.412266 | ||||||||
\(775\) | 38.3602 | 1.37794 | ||||||||
\(776\) | 5.65476 | 0.202994 | ||||||||
\(777\) | −13.0315 | −0.467503 | ||||||||
\(778\) | −15.8087 | −0.566770 | ||||||||
\(779\) | 40.3380 | 1.44526 | ||||||||
\(780\) | −3.83399 | −0.137279 | ||||||||
\(781\) | 10.3129 | 0.369026 | ||||||||
\(782\) | −25.7361 | −0.920323 | ||||||||
\(783\) | −8.02922 | −0.286941 | ||||||||
\(784\) | 3.87612 | 0.138433 | ||||||||
\(785\) | 54.9009 | 1.95950 | ||||||||
\(786\) | 13.4253 | 0.478864 | ||||||||
\(787\) | 19.8191 | 0.706476 | 0.353238 | − | 0.935533i | \(-0.385081\pi\) | ||||
0.353238 | + | 0.935533i | \(0.385081\pi\) | |||||||
\(788\) | 5.26650 | 0.187611 | ||||||||
\(789\) | 2.61834 | 0.0932154 | ||||||||
\(790\) | 23.8768 | 0.849498 | ||||||||
\(791\) | 34.4093 | 1.22345 | ||||||||
\(792\) | 1.08694 | 0.0386227 | ||||||||
\(793\) | −14.8682 | −0.527985 | ||||||||
\(794\) | −36.8850 | −1.30900 | ||||||||
\(795\) | −6.98260 | −0.247647 | ||||||||
\(796\) | 14.3971 | 0.510293 | ||||||||
\(797\) | −53.8034 | −1.90581 | −0.952906 | − | 0.303265i | \(-0.901923\pi\) | ||||
−0.952906 | + | 0.303265i | \(0.901923\pi\) | |||||||
\(798\) | 24.8282 | 0.878907 | ||||||||
\(799\) | −61.0933 | −2.16133 | ||||||||
\(800\) | −9.69950 | −0.342929 | ||||||||
\(801\) | 5.79834 | 0.204874 | ||||||||
\(802\) | −21.5806 | −0.762039 | ||||||||
\(803\) | 6.29905 | 0.222289 | ||||||||
\(804\) | 9.36012 | 0.330106 | ||||||||
\(805\) | −61.5693 | −2.17003 | ||||||||
\(806\) | −3.95486 | −0.139304 | ||||||||
\(807\) | 22.0924 | 0.777688 | ||||||||
\(808\) | 9.00487 | 0.316790 | ||||||||
\(809\) | 23.8958 | 0.840130 | 0.420065 | − | 0.907494i | \(-0.362007\pi\) | ||||
0.420065 | + | 0.907494i | \(0.362007\pi\) | |||||||
\(810\) | 3.83399 | 0.134713 | ||||||||
\(811\) | −19.3621 | −0.679894 | −0.339947 | − | 0.940445i | \(-0.610409\pi\) | ||||
−0.339947 | + | 0.940445i | \(0.610409\pi\) | |||||||
\(812\) | 26.4795 | 0.929249 | ||||||||
\(813\) | −13.7745 | −0.483092 | ||||||||
\(814\) | 4.29500 | 0.150540 | ||||||||
\(815\) | 56.1744 | 1.96770 | ||||||||
\(816\) | −5.28528 | −0.185022 | ||||||||
\(817\) | 86.3487 | 3.02096 | ||||||||
\(818\) | 39.4851 | 1.38057 | ||||||||
\(819\) | −3.29790 | −0.115238 | ||||||||
\(820\) | −20.5427 | −0.717383 | ||||||||
\(821\) | −55.5460 | −1.93857 | −0.969284 | − | 0.245943i | \(-0.920902\pi\) | ||||
−0.969284 | + | 0.245943i | \(0.920902\pi\) | |||||||
\(822\) | −18.7763 | −0.654897 | ||||||||
\(823\) | −53.5826 | −1.86777 | −0.933886 | − | 0.357571i | \(-0.883605\pi\) | ||||
−0.933886 | + | 0.357571i | \(0.883605\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −10.5428 | −0.367052 | ||||||||
\(826\) | 34.0904 | 1.18616 | ||||||||
\(827\) | 48.1665 | 1.67491 | 0.837457 | − | 0.546504i | \(-0.184042\pi\) | ||||
0.837457 | + | 0.546504i | \(0.184042\pi\) | |||||||
\(828\) | −4.86940 | −0.169223 | ||||||||
\(829\) | 19.4417 | 0.675238 | 0.337619 | − | 0.941283i | \(-0.390379\pi\) | ||||
0.337619 | + | 0.941283i | \(0.390379\pi\) | |||||||
\(830\) | 9.56459 | 0.331992 | ||||||||
\(831\) | 5.22578 | 0.181280 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −20.4863 | −0.709810 | ||||||||
\(834\) | 0.112175 | 0.00388431 | ||||||||
\(835\) | −13.2036 | −0.456930 | ||||||||
\(836\) | −8.18301 | −0.283015 | ||||||||
\(837\) | 3.95486 | 0.136700 | ||||||||
\(838\) | 16.1944 | 0.559425 | ||||||||
\(839\) | −14.3329 | −0.494827 | −0.247414 | − | 0.968910i | \(-0.579581\pi\) | ||||
−0.247414 | + | 0.968910i | \(0.579581\pi\) | |||||||
\(840\) | −12.6441 | −0.436263 | ||||||||
\(841\) | 35.4684 | 1.22305 | ||||||||
\(842\) | 16.4463 | 0.566777 | ||||||||
\(843\) | −10.2219 | −0.352059 | ||||||||
\(844\) | 10.4702 | 0.360398 | ||||||||
\(845\) | −3.83399 | −0.131893 | ||||||||
\(846\) | −11.5592 | −0.397412 | ||||||||
\(847\) | 32.3806 | 1.11261 | ||||||||
\(848\) | 1.82123 | 0.0625414 | ||||||||
\(849\) | −12.3497 | −0.423842 | ||||||||
\(850\) | 51.2646 | 1.75836 | ||||||||
\(851\) | −19.2413 | −0.659582 | ||||||||
\(852\) | −9.48805 | −0.325055 | ||||||||
\(853\) | 9.66768 | 0.331015 | 0.165507 | − | 0.986209i | \(-0.447074\pi\) | ||||
0.165507 | + | 0.986209i | \(0.447074\pi\) | |||||||
\(854\) | −49.0338 | −1.67790 | ||||||||
\(855\) | −28.8642 | −0.987133 | ||||||||
\(856\) | −12.8287 | −0.438475 | ||||||||
\(857\) | −27.4062 | −0.936179 | −0.468089 | − | 0.883681i | \(-0.655057\pi\) | ||||
−0.468089 | + | 0.883681i | \(0.655057\pi\) | |||||||
\(858\) | 1.08694 | 0.0371075 | ||||||||
\(859\) | 36.9580 | 1.26099 | 0.630495 | − | 0.776193i | \(-0.282852\pi\) | ||||
0.630495 | + | 0.776193i | \(0.282852\pi\) | |||||||
\(860\) | −43.9744 | −1.49951 | ||||||||
\(861\) | −17.6703 | −0.602202 | ||||||||
\(862\) | −7.93853 | −0.270387 | ||||||||
\(863\) | 20.0855 | 0.683719 | 0.341859 | − | 0.939751i | \(-0.388943\pi\) | ||||
0.341859 | + | 0.939751i | \(0.388943\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 15.8973 | 0.540525 | ||||||||
\(866\) | −40.9214 | −1.39057 | ||||||||
\(867\) | 10.9342 | 0.371343 | ||||||||
\(868\) | −13.0427 | −0.442699 | ||||||||
\(869\) | −6.76908 | −0.229625 | ||||||||
\(870\) | −30.7840 | −1.04367 | ||||||||
\(871\) | 9.36012 | 0.317156 | ||||||||
\(872\) | 18.0578 | 0.611515 | ||||||||
\(873\) | −5.65476 | −0.191384 | ||||||||
\(874\) | 36.6592 | 1.24002 | ||||||||
\(875\) | 59.4210 | 2.00880 | ||||||||
\(876\) | −5.79522 | −0.195802 | ||||||||
\(877\) | 17.9521 | 0.606199 | 0.303099 | − | 0.952959i | \(-0.401979\pi\) | ||||
0.303099 | + | 0.952959i | \(0.401979\pi\) | |||||||
\(878\) | 26.1722 | 0.883268 | ||||||||
\(879\) | −6.42954 | −0.216863 | ||||||||
\(880\) | 4.16732 | 0.140480 | ||||||||
\(881\) | 41.0166 | 1.38189 | 0.690943 | − | 0.722909i | \(-0.257196\pi\) | ||||
0.690943 | + | 0.722909i | \(0.257196\pi\) | |||||||
\(882\) | −3.87612 | −0.130516 | ||||||||
\(883\) | −8.43264 | −0.283781 | −0.141890 | − | 0.989882i | \(-0.545318\pi\) | ||||
−0.141890 | + | 0.989882i | \(0.545318\pi\) | |||||||
\(884\) | −5.28528 | −0.177763 | ||||||||
\(885\) | −39.6321 | −1.33222 | ||||||||
\(886\) | 8.73740 | 0.293539 | ||||||||
\(887\) | 36.9741 | 1.24147 | 0.620734 | − | 0.784021i | \(-0.286835\pi\) | ||||
0.620734 | + | 0.784021i | \(0.286835\pi\) | |||||||
\(888\) | −3.95146 | −0.132602 | ||||||||
\(889\) | 32.7751 | 1.09924 | ||||||||
\(890\) | 22.2308 | 0.745178 | ||||||||
\(891\) | −1.08694 | −0.0364138 | ||||||||
\(892\) | 15.9747 | 0.534873 | ||||||||
\(893\) | 87.0229 | 2.91211 | ||||||||
\(894\) | 3.20558 | 0.107211 | ||||||||
\(895\) | −30.0826 | −1.00555 | ||||||||
\(896\) | 3.29790 | 0.110175 | ||||||||
\(897\) | −4.86940 | −0.162585 | ||||||||
\(898\) | 27.0573 | 0.902915 | ||||||||
\(899\) | −31.7545 | −1.05907 | ||||||||
\(900\) | 9.69950 | 0.323317 | ||||||||
\(901\) | −9.62573 | −0.320679 | ||||||||
\(902\) | 5.82387 | 0.193914 | ||||||||
\(903\) | −37.8255 | −1.25875 | ||||||||
\(904\) | 10.4337 | 0.347020 | ||||||||
\(905\) | −17.4686 | −0.580676 | ||||||||
\(906\) | −9.10079 | −0.302354 | ||||||||
\(907\) | −33.5901 | −1.11534 | −0.557670 | − | 0.830063i | \(-0.688305\pi\) | ||||
−0.557670 | + | 0.830063i | \(0.688305\pi\) | |||||||
\(908\) | 4.41065 | 0.146373 | ||||||||
\(909\) | −9.00487 | −0.298673 | ||||||||
\(910\) | −12.6441 | −0.419148 | ||||||||
\(911\) | 4.69896 | 0.155683 | 0.0778417 | − | 0.996966i | \(-0.475197\pi\) | ||||
0.0778417 | + | 0.996966i | \(0.475197\pi\) | |||||||
\(912\) | 7.52849 | 0.249293 | ||||||||
\(913\) | −2.71157 | −0.0897397 | ||||||||
\(914\) | 12.4155 | 0.410667 | ||||||||
\(915\) | 57.0046 | 1.88451 | ||||||||
\(916\) | −7.15661 | −0.236461 | ||||||||
\(917\) | 44.2752 | 1.46209 | ||||||||
\(918\) | 5.28528 | 0.174440 | ||||||||
\(919\) | −1.61816 | −0.0533781 | −0.0266890 | − | 0.999644i | \(-0.508496\pi\) | ||||
−0.0266890 | + | 0.999644i | \(0.508496\pi\) | |||||||
\(920\) | −18.6693 | −0.615507 | ||||||||
\(921\) | 14.6133 | 0.481525 | ||||||||
\(922\) | 25.3222 | 0.833943 | ||||||||
\(923\) | −9.48805 | −0.312303 | ||||||||
\(924\) | 3.58461 | 0.117925 | ||||||||
\(925\) | 38.3272 | 1.26019 | ||||||||
\(926\) | 11.0274 | 0.362383 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 8.02922 | 0.263572 | ||||||||
\(929\) | −31.3272 | −1.02781 | −0.513905 | − | 0.857847i | \(-0.671802\pi\) | ||||
−0.513905 | + | 0.857847i | \(0.671802\pi\) | |||||||
\(930\) | 15.1629 | 0.497211 | ||||||||
\(931\) | 29.1813 | 0.956378 | ||||||||
\(932\) | 24.7436 | 0.810503 | ||||||||
\(933\) | −11.9468 | −0.391119 | ||||||||
\(934\) | 0.314734 | 0.0102984 | ||||||||
\(935\) | −22.0254 | −0.720308 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −17.5332 | −0.572785 | −0.286392 | − | 0.958112i | \(-0.592456\pi\) | ||||
−0.286392 | + | 0.958112i | \(0.592456\pi\) | |||||||
\(938\) | 30.8687 | 1.00790 | ||||||||
\(939\) | −7.08127 | −0.231088 | ||||||||
\(940\) | −44.3177 | −1.44548 | ||||||||
\(941\) | 26.9382 | 0.878161 | 0.439080 | − | 0.898448i | \(-0.355304\pi\) | ||||
0.439080 | + | 0.898448i | \(0.355304\pi\) | |||||||
\(942\) | 14.3195 | 0.466554 | ||||||||
\(943\) | −26.0905 | −0.849624 | ||||||||
\(944\) | 10.3370 | 0.336441 | ||||||||
\(945\) | 12.6441 | 0.411313 | ||||||||
\(946\) | 12.4668 | 0.405329 | ||||||||
\(947\) | 48.8593 | 1.58772 | 0.793858 | − | 0.608104i | \(-0.208069\pi\) | ||||
0.793858 | + | 0.608104i | \(0.208069\pi\) | |||||||
\(948\) | 6.22766 | 0.202265 | ||||||||
\(949\) | −5.79522 | −0.188121 | ||||||||
\(950\) | −73.0226 | −2.36916 | ||||||||
\(951\) | −23.8099 | −0.772088 | ||||||||
\(952\) | −17.4303 | −0.564919 | ||||||||
\(953\) | −24.9828 | −0.809274 | −0.404637 | − | 0.914477i | \(-0.632602\pi\) | ||||
−0.404637 | + | 0.914477i | \(0.632602\pi\) | |||||||
\(954\) | −1.82123 | −0.0589646 | ||||||||
\(955\) | −22.5748 | −0.730503 | ||||||||
\(956\) | −3.79838 | −0.122848 | ||||||||
\(957\) | 8.72727 | 0.282113 | ||||||||
\(958\) | 30.3516 | 0.980616 | ||||||||
\(959\) | −61.9222 | −1.99957 | ||||||||
\(960\) | −3.83399 | −0.123742 | ||||||||
\(961\) | −15.3591 | −0.495454 | ||||||||
\(962\) | −3.95146 | −0.127400 | ||||||||
\(963\) | 12.8287 | 0.413398 | ||||||||
\(964\) | −21.6703 | −0.697954 | ||||||||
\(965\) | −14.1817 | −0.456525 | ||||||||
\(966\) | −16.0588 | −0.516683 | ||||||||
\(967\) | −30.0342 | −0.965836 | −0.482918 | − | 0.875666i | \(-0.660423\pi\) | ||||
−0.482918 | + | 0.875666i | \(0.660423\pi\) | |||||||
\(968\) | 9.81856 | 0.315581 | ||||||||
\(969\) | −39.7901 | −1.27824 | ||||||||
\(970\) | −21.6803 | −0.696112 | ||||||||
\(971\) | 46.2170 | 1.48317 | 0.741587 | − | 0.670857i | \(-0.234073\pi\) | ||||
0.741587 | + | 0.670857i | \(0.234073\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0.369942 | 0.0118598 | ||||||||
\(974\) | −22.7338 | −0.728437 | ||||||||
\(975\) | 9.69950 | 0.310633 | ||||||||
\(976\) | −14.8682 | −0.475920 | ||||||||
\(977\) | 17.5927 | 0.562839 | 0.281419 | − | 0.959585i | \(-0.409195\pi\) | ||||
0.281419 | + | 0.959585i | \(0.409195\pi\) | |||||||
\(978\) | 14.6517 | 0.468509 | ||||||||
\(979\) | −6.30244 | −0.201427 | ||||||||
\(980\) | −14.8610 | −0.474717 | ||||||||
\(981\) | −18.0578 | −0.576542 | ||||||||
\(982\) | 37.6519 | 1.20152 | ||||||||
\(983\) | 17.4539 | 0.556694 | 0.278347 | − | 0.960481i | \(-0.410213\pi\) | ||||
0.278347 | + | 0.960481i | \(0.410213\pi\) | |||||||
\(984\) | −5.35805 | −0.170808 | ||||||||
\(985\) | −20.1917 | −0.643362 | ||||||||
\(986\) | −42.4367 | −1.35146 | ||||||||
\(987\) | −38.1209 | −1.21340 | ||||||||
\(988\) | 7.52849 | 0.239513 | ||||||||
\(989\) | −55.8501 | −1.77593 | ||||||||
\(990\) | −4.16732 | −0.132446 | ||||||||
\(991\) | −0.107141 | −0.00340343 | −0.00170172 | − | 0.999999i | \(-0.500542\pi\) | ||||
−0.00170172 | + | 0.999999i | \(0.500542\pi\) | |||||||
\(992\) | −3.95486 | −0.125567 | ||||||||
\(993\) | −35.9491 | −1.14081 | ||||||||
\(994\) | −31.2906 | −0.992477 | ||||||||
\(995\) | −55.1985 | −1.74991 | ||||||||
\(996\) | 2.49468 | 0.0790470 | ||||||||
\(997\) | −57.4384 | −1.81909 | −0.909546 | − | 0.415603i | \(-0.863570\pi\) | ||||
−0.909546 | + | 0.415603i | \(0.863570\pi\) | |||||||
\(998\) | 37.8361 | 1.19768 | ||||||||
\(999\) | 3.95146 | 0.125019 |
(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 | 8034.2.a.w.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.w.1.1 | ✓ | 12 | 1.1 | even | 1 | trivial |