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: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + 2205 x^{5} - 6840 x^{4} - 3579 x^{3} + 3559 x^{2} + 1839 x - 180 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(0.914750\) 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 | ||||||||
\(5\) | 3.65794 | 1.63588 | 0.817940 | − | 0.575304i | \(-0.195116\pi\) | ||||
0.817940 | + | 0.575304i | \(0.195116\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.914750 | 0.345743 | 0.172872 | − | 0.984944i | \(-0.444695\pi\) | ||||
0.172872 | + | 0.984944i | \(0.444695\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.65794 | 1.15674 | ||||||||
\(11\) | −4.42842 | −1.33522 | −0.667609 | − | 0.744512i | \(-0.732682\pi\) | ||||
−0.667609 | + | 0.744512i | \(0.732682\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0.914750 | 0.244477 | ||||||||
\(15\) | −3.65794 | −0.944475 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.23101 | 1.26871 | 0.634354 | − | 0.773043i | \(-0.281266\pi\) | ||||
0.634354 | + | 0.773043i | \(0.281266\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.71880 | 0.394319 | 0.197159 | − | 0.980371i | \(-0.436828\pi\) | ||||
0.197159 | + | 0.980371i | \(0.436828\pi\) | |||||||
\(20\) | 3.65794 | 0.817940 | ||||||||
\(21\) | −0.914750 | −0.199615 | ||||||||
\(22\) | −4.42842 | −0.944141 | ||||||||
\(23\) | 1.96141 | 0.408981 | 0.204491 | − | 0.978869i | \(-0.434446\pi\) | ||||
0.204491 | + | 0.978869i | \(0.434446\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 8.38051 | 1.67610 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.914750 | 0.172872 | ||||||||
\(29\) | 0.973442 | 0.180764 | 0.0903818 | − | 0.995907i | \(-0.471191\pi\) | ||||
0.0903818 | + | 0.995907i | \(0.471191\pi\) | |||||||
\(30\) | −3.65794 | −0.667845 | ||||||||
\(31\) | 1.71880 | 0.308705 | 0.154352 | − | 0.988016i | \(-0.450671\pi\) | ||||
0.154352 | + | 0.988016i | \(0.450671\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.42842 | 0.770888 | ||||||||
\(34\) | 5.23101 | 0.897112 | ||||||||
\(35\) | 3.34610 | 0.565594 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 7.31297 | 1.20224 | 0.601122 | − | 0.799157i | \(-0.294720\pi\) | ||||
0.601122 | + | 0.799157i | \(0.294720\pi\) | |||||||
\(38\) | 1.71880 | 0.278826 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 3.65794 | 0.578371 | ||||||||
\(41\) | −6.72972 | −1.05101 | −0.525503 | − | 0.850792i | \(-0.676123\pi\) | ||||
−0.525503 | + | 0.850792i | \(0.676123\pi\) | |||||||
\(42\) | −0.914750 | −0.141149 | ||||||||
\(43\) | −1.19832 | −0.182742 | −0.0913709 | − | 0.995817i | \(-0.529125\pi\) | ||||
−0.0913709 | + | 0.995817i | \(0.529125\pi\) | |||||||
\(44\) | −4.42842 | −0.667609 | ||||||||
\(45\) | 3.65794 | 0.545293 | ||||||||
\(46\) | 1.96141 | 0.289194 | ||||||||
\(47\) | 0.170842 | 0.0249199 | 0.0124599 | − | 0.999922i | \(-0.496034\pi\) | ||||
0.0124599 | + | 0.999922i | \(0.496034\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.16323 | −0.880462 | ||||||||
\(50\) | 8.38051 | 1.18518 | ||||||||
\(51\) | −5.23101 | −0.732489 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −4.21836 | −0.579436 | −0.289718 | − | 0.957112i | \(-0.593561\pi\) | ||||
−0.289718 | + | 0.957112i | \(0.593561\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −16.1989 | −2.18425 | ||||||||
\(56\) | 0.914750 | 0.122239 | ||||||||
\(57\) | −1.71880 | −0.227660 | ||||||||
\(58\) | 0.973442 | 0.127819 | ||||||||
\(59\) | 0.893529 | 0.116328 | 0.0581638 | − | 0.998307i | \(-0.481475\pi\) | ||||
0.0581638 | + | 0.998307i | \(0.481475\pi\) | |||||||
\(60\) | −3.65794 | −0.472238 | ||||||||
\(61\) | 1.22151 | 0.156398 | 0.0781990 | − | 0.996938i | \(-0.475083\pi\) | ||||
0.0781990 | + | 0.996938i | \(0.475083\pi\) | |||||||
\(62\) | 1.71880 | 0.218287 | ||||||||
\(63\) | 0.914750 | 0.115248 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.65794 | 0.453711 | ||||||||
\(66\) | 4.42842 | 0.545100 | ||||||||
\(67\) | 6.26257 | 0.765095 | 0.382548 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382548 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(68\) | 5.23101 | 0.634354 | ||||||||
\(69\) | −1.96141 | −0.236126 | ||||||||
\(70\) | 3.34610 | 0.399935 | ||||||||
\(71\) | 8.89499 | 1.05564 | 0.527821 | − | 0.849356i | \(-0.323009\pi\) | ||||
0.527821 | + | 0.849356i | \(0.323009\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 10.4828 | 1.22692 | 0.613459 | − | 0.789727i | \(-0.289778\pi\) | ||||
0.613459 | + | 0.789727i | \(0.289778\pi\) | |||||||
\(74\) | 7.31297 | 0.850116 | ||||||||
\(75\) | −8.38051 | −0.967698 | ||||||||
\(76\) | 1.71880 | 0.197159 | ||||||||
\(77\) | −4.05089 | −0.461642 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −15.7891 | −1.77641 | −0.888205 | − | 0.459448i | \(-0.848047\pi\) | ||||
−0.888205 | + | 0.459448i | \(0.848047\pi\) | |||||||
\(80\) | 3.65794 | 0.408970 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.72972 | −0.743173 | ||||||||
\(83\) | 6.55258 | 0.719240 | 0.359620 | − | 0.933099i | \(-0.382906\pi\) | ||||
0.359620 | + | 0.933099i | \(0.382906\pi\) | |||||||
\(84\) | −0.914750 | −0.0998074 | ||||||||
\(85\) | 19.1347 | 2.07545 | ||||||||
\(86\) | −1.19832 | −0.129218 | ||||||||
\(87\) | −0.973442 | −0.104364 | ||||||||
\(88\) | −4.42842 | −0.472071 | ||||||||
\(89\) | −5.81526 | −0.616417 | −0.308208 | − | 0.951319i | \(-0.599729\pi\) | ||||
−0.308208 | + | 0.951319i | \(0.599729\pi\) | |||||||
\(90\) | 3.65794 | 0.385580 | ||||||||
\(91\) | 0.914750 | 0.0958919 | ||||||||
\(92\) | 1.96141 | 0.204491 | ||||||||
\(93\) | −1.71880 | −0.178231 | ||||||||
\(94\) | 0.170842 | 0.0176210 | ||||||||
\(95\) | 6.28725 | 0.645058 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 14.4016 | 1.46226 | 0.731128 | − | 0.682240i | \(-0.238994\pi\) | ||||
0.731128 | + | 0.682240i | \(0.238994\pi\) | |||||||
\(98\) | −6.16323 | −0.622580 | ||||||||
\(99\) | −4.42842 | −0.445072 | ||||||||
\(100\) | 8.38051 | 0.838051 | ||||||||
\(101\) | −5.12273 | −0.509731 | −0.254865 | − | 0.966977i | \(-0.582031\pi\) | ||||
−0.254865 | + | 0.966977i | \(0.582031\pi\) | |||||||
\(102\) | −5.23101 | −0.517948 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −3.34610 | −0.326546 | ||||||||
\(106\) | −4.21836 | −0.409723 | ||||||||
\(107\) | −7.37919 | −0.713373 | −0.356687 | − | 0.934224i | \(-0.616094\pi\) | ||||
−0.356687 | + | 0.934224i | \(0.616094\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 9.79616 | 0.938302 | 0.469151 | − | 0.883118i | \(-0.344560\pi\) | ||||
0.469151 | + | 0.883118i | \(0.344560\pi\) | |||||||
\(110\) | −16.1989 | −1.54450 | ||||||||
\(111\) | −7.31297 | −0.694116 | ||||||||
\(112\) | 0.914750 | 0.0864358 | ||||||||
\(113\) | 0.0993838 | 0.00934924 | 0.00467462 | − | 0.999989i | \(-0.498512\pi\) | ||||
0.00467462 | + | 0.999989i | \(0.498512\pi\) | |||||||
\(114\) | −1.71880 | −0.160980 | ||||||||
\(115\) | 7.17470 | 0.669044 | ||||||||
\(116\) | 0.973442 | 0.0903818 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0.893529 | 0.0822560 | ||||||||
\(119\) | 4.78507 | 0.438647 | ||||||||
\(120\) | −3.65794 | −0.333923 | ||||||||
\(121\) | 8.61086 | 0.782806 | ||||||||
\(122\) | 1.22151 | 0.110590 | ||||||||
\(123\) | 6.72972 | 0.606798 | ||||||||
\(124\) | 1.71880 | 0.154352 | ||||||||
\(125\) | 12.3657 | 1.10602 | ||||||||
\(126\) | 0.914750 | 0.0814924 | ||||||||
\(127\) | 5.04372 | 0.447558 | 0.223779 | − | 0.974640i | \(-0.428161\pi\) | ||||
0.223779 | + | 0.974640i | \(0.428161\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.19832 | 0.105506 | ||||||||
\(130\) | 3.65794 | 0.320822 | ||||||||
\(131\) | −2.24919 | −0.196513 | −0.0982564 | − | 0.995161i | \(-0.531327\pi\) | ||||
−0.0982564 | + | 0.995161i | \(0.531327\pi\) | |||||||
\(132\) | 4.42842 | 0.385444 | ||||||||
\(133\) | 1.57227 | 0.136333 | ||||||||
\(134\) | 6.26257 | 0.541004 | ||||||||
\(135\) | −3.65794 | −0.314825 | ||||||||
\(136\) | 5.23101 | 0.448556 | ||||||||
\(137\) | 4.58596 | 0.391805 | 0.195902 | − | 0.980623i | \(-0.437236\pi\) | ||||
0.195902 | + | 0.980623i | \(0.437236\pi\) | |||||||
\(138\) | −1.96141 | −0.166966 | ||||||||
\(139\) | −16.5435 | −1.40320 | −0.701602 | − | 0.712569i | \(-0.747532\pi\) | ||||
−0.701602 | + | 0.712569i | \(0.747532\pi\) | |||||||
\(140\) | 3.34610 | 0.282797 | ||||||||
\(141\) | −0.170842 | −0.0143875 | ||||||||
\(142\) | 8.89499 | 0.746451 | ||||||||
\(143\) | −4.42842 | −0.370323 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.56079 | 0.295707 | ||||||||
\(146\) | 10.4828 | 0.867562 | ||||||||
\(147\) | 6.16323 | 0.508335 | ||||||||
\(148\) | 7.31297 | 0.601122 | ||||||||
\(149\) | 17.8038 | 1.45855 | 0.729273 | − | 0.684222i | \(-0.239858\pi\) | ||||
0.729273 | + | 0.684222i | \(0.239858\pi\) | |||||||
\(150\) | −8.38051 | −0.684266 | ||||||||
\(151\) | 18.2792 | 1.48754 | 0.743771 | − | 0.668434i | \(-0.233035\pi\) | ||||
0.743771 | + | 0.668434i | \(0.233035\pi\) | |||||||
\(152\) | 1.71880 | 0.139413 | ||||||||
\(153\) | 5.23101 | 0.422902 | ||||||||
\(154\) | −4.05089 | −0.326430 | ||||||||
\(155\) | 6.28725 | 0.505004 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | −7.83062 | −0.624951 | −0.312476 | − | 0.949926i | \(-0.601158\pi\) | ||||
−0.312476 | + | 0.949926i | \(0.601158\pi\) | |||||||
\(158\) | −15.7891 | −1.25611 | ||||||||
\(159\) | 4.21836 | 0.334537 | ||||||||
\(160\) | 3.65794 | 0.289185 | ||||||||
\(161\) | 1.79420 | 0.141402 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −4.97429 | −0.389616 | −0.194808 | − | 0.980841i | \(-0.562408\pi\) | ||||
−0.194808 | + | 0.980841i | \(0.562408\pi\) | |||||||
\(164\) | −6.72972 | −0.525503 | ||||||||
\(165\) | 16.1989 | 1.26108 | ||||||||
\(166\) | 6.55258 | 0.508579 | ||||||||
\(167\) | 0.527598 | 0.0408268 | 0.0204134 | − | 0.999792i | \(-0.493502\pi\) | ||||
0.0204134 | + | 0.999792i | \(0.493502\pi\) | |||||||
\(168\) | −0.914750 | −0.0705745 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 19.1347 | 1.46757 | ||||||||
\(171\) | 1.71880 | 0.131440 | ||||||||
\(172\) | −1.19832 | −0.0913709 | ||||||||
\(173\) | 1.10173 | 0.0837629 | 0.0418814 | − | 0.999123i | \(-0.486665\pi\) | ||||
0.0418814 | + | 0.999123i | \(0.486665\pi\) | |||||||
\(174\) | −0.973442 | −0.0737964 | ||||||||
\(175\) | 7.66607 | 0.579500 | ||||||||
\(176\) | −4.42842 | −0.333804 | ||||||||
\(177\) | −0.893529 | −0.0671617 | ||||||||
\(178\) | −5.81526 | −0.435872 | ||||||||
\(179\) | 21.9135 | 1.63789 | 0.818945 | − | 0.573872i | \(-0.194559\pi\) | ||||
0.818945 | + | 0.573872i | \(0.194559\pi\) | |||||||
\(180\) | 3.65794 | 0.272647 | ||||||||
\(181\) | 8.70219 | 0.646829 | 0.323414 | − | 0.946257i | \(-0.395169\pi\) | ||||
0.323414 | + | 0.946257i | \(0.395169\pi\) | |||||||
\(182\) | 0.914750 | 0.0678058 | ||||||||
\(183\) | −1.22151 | −0.0902964 | ||||||||
\(184\) | 1.96141 | 0.144597 | ||||||||
\(185\) | 26.7504 | 1.96673 | ||||||||
\(186\) | −1.71880 | −0.126028 | ||||||||
\(187\) | −23.1651 | −1.69400 | ||||||||
\(188\) | 0.170842 | 0.0124599 | ||||||||
\(189\) | −0.914750 | −0.0665383 | ||||||||
\(190\) | 6.28725 | 0.456125 | ||||||||
\(191\) | −12.1667 | −0.880354 | −0.440177 | − | 0.897911i | \(-0.645084\pi\) | ||||
−0.440177 | + | 0.897911i | \(0.645084\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −7.71466 | −0.555314 | −0.277657 | − | 0.960680i | \(-0.589558\pi\) | ||||
−0.277657 | + | 0.960680i | \(0.589558\pi\) | |||||||
\(194\) | 14.4016 | 1.03397 | ||||||||
\(195\) | −3.65794 | −0.261950 | ||||||||
\(196\) | −6.16323 | −0.440231 | ||||||||
\(197\) | −4.95515 | −0.353040 | −0.176520 | − | 0.984297i | \(-0.556484\pi\) | ||||
−0.176520 | + | 0.984297i | \(0.556484\pi\) | |||||||
\(198\) | −4.42842 | −0.314714 | ||||||||
\(199\) | −0.902701 | −0.0639908 | −0.0319954 | − | 0.999488i | \(-0.510186\pi\) | ||||
−0.0319954 | + | 0.999488i | \(0.510186\pi\) | |||||||
\(200\) | 8.38051 | 0.592591 | ||||||||
\(201\) | −6.26257 | −0.441728 | ||||||||
\(202\) | −5.12273 | −0.360434 | ||||||||
\(203\) | 0.890456 | 0.0624977 | ||||||||
\(204\) | −5.23101 | −0.366244 | ||||||||
\(205\) | −24.6169 | −1.71932 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 1.96141 | 0.136327 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −7.61154 | −0.526501 | ||||||||
\(210\) | −3.34610 | −0.230903 | ||||||||
\(211\) | −24.4435 | −1.68276 | −0.841380 | − | 0.540445i | \(-0.818256\pi\) | ||||
−0.841380 | + | 0.540445i | \(0.818256\pi\) | |||||||
\(212\) | −4.21836 | −0.289718 | ||||||||
\(213\) | −8.89499 | −0.609475 | ||||||||
\(214\) | −7.37919 | −0.504431 | ||||||||
\(215\) | −4.38337 | −0.298943 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 1.57227 | 0.106733 | ||||||||
\(218\) | 9.79616 | 0.663480 | ||||||||
\(219\) | −10.4828 | −0.708361 | ||||||||
\(220\) | −16.1989 | −1.09213 | ||||||||
\(221\) | 5.23101 | 0.351876 | ||||||||
\(222\) | −7.31297 | −0.490814 | ||||||||
\(223\) | −1.85778 | −0.124406 | −0.0622031 | − | 0.998064i | \(-0.519813\pi\) | ||||
−0.0622031 | + | 0.998064i | \(0.519813\pi\) | |||||||
\(224\) | 0.914750 | 0.0611193 | ||||||||
\(225\) | 8.38051 | 0.558701 | ||||||||
\(226\) | 0.0993838 | 0.00661091 | ||||||||
\(227\) | 18.9743 | 1.25937 | 0.629684 | − | 0.776852i | \(-0.283185\pi\) | ||||
0.629684 | + | 0.776852i | \(0.283185\pi\) | |||||||
\(228\) | −1.71880 | −0.113830 | ||||||||
\(229\) | 4.58595 | 0.303048 | 0.151524 | − | 0.988454i | \(-0.451582\pi\) | ||||
0.151524 | + | 0.988454i | \(0.451582\pi\) | |||||||
\(230\) | 7.17470 | 0.473086 | ||||||||
\(231\) | 4.05089 | 0.266529 | ||||||||
\(232\) | 0.973442 | 0.0639096 | ||||||||
\(233\) | 6.46254 | 0.423375 | 0.211687 | − | 0.977337i | \(-0.432104\pi\) | ||||
0.211687 | + | 0.977337i | \(0.432104\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 0.624929 | 0.0407659 | ||||||||
\(236\) | 0.893529 | 0.0581638 | ||||||||
\(237\) | 15.7891 | 1.02561 | ||||||||
\(238\) | 4.78507 | 0.310170 | ||||||||
\(239\) | −27.2859 | −1.76498 | −0.882489 | − | 0.470333i | \(-0.844134\pi\) | ||||
−0.882489 | + | 0.470333i | \(0.844134\pi\) | |||||||
\(240\) | −3.65794 | −0.236119 | ||||||||
\(241\) | 24.0349 | 1.54823 | 0.774113 | − | 0.633048i | \(-0.218196\pi\) | ||||
0.774113 | + | 0.633048i | \(0.218196\pi\) | |||||||
\(242\) | 8.61086 | 0.553527 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.22151 | 0.0781990 | ||||||||
\(245\) | −22.5447 | −1.44033 | ||||||||
\(246\) | 6.72972 | 0.429071 | ||||||||
\(247\) | 1.71880 | 0.109364 | ||||||||
\(248\) | 1.71880 | 0.109144 | ||||||||
\(249\) | −6.55258 | −0.415253 | ||||||||
\(250\) | 12.3657 | 0.782075 | ||||||||
\(251\) | −20.2541 | −1.27843 | −0.639215 | − | 0.769028i | \(-0.720740\pi\) | ||||
−0.639215 | + | 0.769028i | \(0.720740\pi\) | |||||||
\(252\) | 0.914750 | 0.0576238 | ||||||||
\(253\) | −8.68592 | −0.546079 | ||||||||
\(254\) | 5.04372 | 0.316471 | ||||||||
\(255\) | −19.1347 | −1.19826 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.81242 | −0.175434 | −0.0877171 | − | 0.996145i | \(-0.527957\pi\) | ||||
−0.0877171 | + | 0.996145i | \(0.527957\pi\) | |||||||
\(258\) | 1.19832 | 0.0746040 | ||||||||
\(259\) | 6.68954 | 0.415668 | ||||||||
\(260\) | 3.65794 | 0.226856 | ||||||||
\(261\) | 0.973442 | 0.0602545 | ||||||||
\(262\) | −2.24919 | −0.138955 | ||||||||
\(263\) | −4.00949 | −0.247236 | −0.123618 | − | 0.992330i | \(-0.539450\pi\) | ||||
−0.123618 | + | 0.992330i | \(0.539450\pi\) | |||||||
\(264\) | 4.42842 | 0.272550 | ||||||||
\(265\) | −15.4305 | −0.947887 | ||||||||
\(266\) | 1.57227 | 0.0964020 | ||||||||
\(267\) | 5.81526 | 0.355888 | ||||||||
\(268\) | 6.26257 | 0.382548 | ||||||||
\(269\) | −18.8430 | −1.14888 | −0.574438 | − | 0.818548i | \(-0.694779\pi\) | ||||
−0.574438 | + | 0.818548i | \(0.694779\pi\) | |||||||
\(270\) | −3.65794 | −0.222615 | ||||||||
\(271\) | −19.0394 | −1.15656 | −0.578281 | − | 0.815837i | \(-0.696276\pi\) | ||||
−0.578281 | + | 0.815837i | \(0.696276\pi\) | |||||||
\(272\) | 5.23101 | 0.317177 | ||||||||
\(273\) | −0.914750 | −0.0553632 | ||||||||
\(274\) | 4.58596 | 0.277048 | ||||||||
\(275\) | −37.1124 | −2.23796 | ||||||||
\(276\) | −1.96141 | −0.118063 | ||||||||
\(277\) | 25.1167 | 1.50911 | 0.754557 | − | 0.656235i | \(-0.227852\pi\) | ||||
0.754557 | + | 0.656235i | \(0.227852\pi\) | |||||||
\(278\) | −16.5435 | −0.992215 | ||||||||
\(279\) | 1.71880 | 0.102902 | ||||||||
\(280\) | 3.34610 | 0.199968 | ||||||||
\(281\) | −25.7761 | −1.53767 | −0.768837 | − | 0.639445i | \(-0.779164\pi\) | ||||
−0.768837 | + | 0.639445i | \(0.779164\pi\) | |||||||
\(282\) | −0.170842 | −0.0101735 | ||||||||
\(283\) | 28.5628 | 1.69788 | 0.848940 | − | 0.528489i | \(-0.177241\pi\) | ||||
0.848940 | + | 0.528489i | \(0.177241\pi\) | |||||||
\(284\) | 8.89499 | 0.527821 | ||||||||
\(285\) | −6.28725 | −0.372425 | ||||||||
\(286\) | −4.42842 | −0.261858 | ||||||||
\(287\) | −6.15601 | −0.363378 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 10.3635 | 0.609619 | ||||||||
\(290\) | 3.56079 | 0.209097 | ||||||||
\(291\) | −14.4016 | −0.844234 | ||||||||
\(292\) | 10.4828 | 0.613459 | ||||||||
\(293\) | 29.7590 | 1.73854 | 0.869270 | − | 0.494338i | \(-0.164590\pi\) | ||||
0.869270 | + | 0.494338i | \(0.164590\pi\) | |||||||
\(294\) | 6.16323 | 0.359447 | ||||||||
\(295\) | 3.26847 | 0.190298 | ||||||||
\(296\) | 7.31297 | 0.425058 | ||||||||
\(297\) | 4.42842 | 0.256963 | ||||||||
\(298\) | 17.8038 | 1.03135 | ||||||||
\(299\) | 1.96141 | 0.113431 | ||||||||
\(300\) | −8.38051 | −0.483849 | ||||||||
\(301\) | −1.09616 | −0.0631817 | ||||||||
\(302\) | 18.2792 | 1.05185 | ||||||||
\(303\) | 5.12273 | 0.294293 | ||||||||
\(304\) | 1.71880 | 0.0985797 | ||||||||
\(305\) | 4.46820 | 0.255848 | ||||||||
\(306\) | 5.23101 | 0.299037 | ||||||||
\(307\) | −11.9130 | −0.679912 | −0.339956 | − | 0.940441i | \(-0.610412\pi\) | ||||
−0.339956 | + | 0.940441i | \(0.610412\pi\) | |||||||
\(308\) | −4.05089 | −0.230821 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 6.28725 | 0.357092 | ||||||||
\(311\) | −17.0556 | −0.967132 | −0.483566 | − | 0.875308i | \(-0.660659\pi\) | ||||
−0.483566 | + | 0.875308i | \(0.660659\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 29.1954 | 1.65022 | 0.825110 | − | 0.564972i | \(-0.191113\pi\) | ||||
0.825110 | + | 0.564972i | \(0.191113\pi\) | |||||||
\(314\) | −7.83062 | −0.441907 | ||||||||
\(315\) | 3.34610 | 0.188531 | ||||||||
\(316\) | −15.7891 | −0.888205 | ||||||||
\(317\) | −11.2339 | −0.630957 | −0.315478 | − | 0.948933i | \(-0.602165\pi\) | ||||
−0.315478 | + | 0.948933i | \(0.602165\pi\) | |||||||
\(318\) | 4.21836 | 0.236554 | ||||||||
\(319\) | −4.31080 | −0.241359 | ||||||||
\(320\) | 3.65794 | 0.204485 | ||||||||
\(321\) | 7.37919 | 0.411866 | ||||||||
\(322\) | 1.79420 | 0.0999867 | ||||||||
\(323\) | 8.99105 | 0.500275 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 8.38051 | 0.464867 | ||||||||
\(326\) | −4.97429 | −0.275500 | ||||||||
\(327\) | −9.79616 | −0.541729 | ||||||||
\(328\) | −6.72972 | −0.371587 | ||||||||
\(329\) | 0.156278 | 0.00861587 | ||||||||
\(330\) | 16.1989 | 0.891718 | ||||||||
\(331\) | −36.0555 | −1.98179 | −0.990895 | − | 0.134639i | \(-0.957012\pi\) | ||||
−0.990895 | + | 0.134639i | \(0.957012\pi\) | |||||||
\(332\) | 6.55258 | 0.359620 | ||||||||
\(333\) | 7.31297 | 0.400748 | ||||||||
\(334\) | 0.527598 | 0.0288689 | ||||||||
\(335\) | 22.9081 | 1.25160 | ||||||||
\(336\) | −0.914750 | −0.0499037 | ||||||||
\(337\) | −19.4420 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −0.0993838 | −0.00539779 | ||||||||
\(340\) | 19.1347 | 1.03773 | ||||||||
\(341\) | −7.61154 | −0.412188 | ||||||||
\(342\) | 1.71880 | 0.0929418 | ||||||||
\(343\) | −12.0411 | −0.650157 | ||||||||
\(344\) | −1.19832 | −0.0646090 | ||||||||
\(345\) | −7.17470 | −0.386273 | ||||||||
\(346\) | 1.10173 | 0.0592293 | ||||||||
\(347\) | 4.24821 | 0.228056 | 0.114028 | − | 0.993478i | \(-0.463625\pi\) | ||||
0.114028 | + | 0.993478i | \(0.463625\pi\) | |||||||
\(348\) | −0.973442 | −0.0521819 | ||||||||
\(349\) | 13.2219 | 0.707751 | 0.353875 | − | 0.935293i | \(-0.384864\pi\) | ||||
0.353875 | + | 0.935293i | \(0.384864\pi\) | |||||||
\(350\) | 7.66607 | 0.409769 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −4.42842 | −0.236035 | ||||||||
\(353\) | 28.2177 | 1.50188 | 0.750938 | − | 0.660373i | \(-0.229602\pi\) | ||||
0.750938 | + | 0.660373i | \(0.229602\pi\) | |||||||
\(354\) | −0.893529 | −0.0474905 | ||||||||
\(355\) | 32.5373 | 1.72690 | ||||||||
\(356\) | −5.81526 | −0.308208 | ||||||||
\(357\) | −4.78507 | −0.253253 | ||||||||
\(358\) | 21.9135 | 1.15816 | ||||||||
\(359\) | 19.9685 | 1.05389 | 0.526947 | − | 0.849898i | \(-0.323336\pi\) | ||||
0.526947 | + | 0.849898i | \(0.323336\pi\) | |||||||
\(360\) | 3.65794 | 0.192790 | ||||||||
\(361\) | −16.0457 | −0.844513 | ||||||||
\(362\) | 8.70219 | 0.457377 | ||||||||
\(363\) | −8.61086 | −0.451953 | ||||||||
\(364\) | 0.914750 | 0.0479459 | ||||||||
\(365\) | 38.3454 | 2.00709 | ||||||||
\(366\) | −1.22151 | −0.0638492 | ||||||||
\(367\) | −9.37152 | −0.489189 | −0.244595 | − | 0.969625i | \(-0.578655\pi\) | ||||
−0.244595 | + | 0.969625i | \(0.578655\pi\) | |||||||
\(368\) | 1.96141 | 0.102245 | ||||||||
\(369\) | −6.72972 | −0.350335 | ||||||||
\(370\) | 26.7504 | 1.39069 | ||||||||
\(371\) | −3.85874 | −0.200336 | ||||||||
\(372\) | −1.71880 | −0.0891154 | ||||||||
\(373\) | 10.9714 | 0.568076 | 0.284038 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284038 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(374\) | −23.1651 | −1.19784 | ||||||||
\(375\) | −12.3657 | −0.638561 | ||||||||
\(376\) | 0.170842 | 0.00881050 | ||||||||
\(377\) | 0.973442 | 0.0501348 | ||||||||
\(378\) | −0.914750 | −0.0470497 | ||||||||
\(379\) | −4.03145 | −0.207081 | −0.103541 | − | 0.994625i | \(-0.533017\pi\) | ||||
−0.103541 | + | 0.994625i | \(0.533017\pi\) | |||||||
\(380\) | 6.28725 | 0.322529 | ||||||||
\(381\) | −5.04372 | −0.258397 | ||||||||
\(382\) | −12.1667 | −0.622505 | ||||||||
\(383\) | 12.2886 | 0.627919 | 0.313959 | − | 0.949436i | \(-0.398344\pi\) | ||||
0.313959 | + | 0.949436i | \(0.398344\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −14.8179 | −0.755191 | ||||||||
\(386\) | −7.71466 | −0.392666 | ||||||||
\(387\) | −1.19832 | −0.0609139 | ||||||||
\(388\) | 14.4016 | 0.731128 | ||||||||
\(389\) | −7.96737 | −0.403962 | −0.201981 | − | 0.979389i | \(-0.564738\pi\) | ||||
−0.201981 | + | 0.979389i | \(0.564738\pi\) | |||||||
\(390\) | −3.65794 | −0.185227 | ||||||||
\(391\) | 10.2601 | 0.518878 | ||||||||
\(392\) | −6.16323 | −0.311290 | ||||||||
\(393\) | 2.24919 | 0.113457 | ||||||||
\(394\) | −4.95515 | −0.249637 | ||||||||
\(395\) | −57.7555 | −2.90599 | ||||||||
\(396\) | −4.42842 | −0.222536 | ||||||||
\(397\) | −8.42629 | −0.422904 | −0.211452 | − | 0.977388i | \(-0.567819\pi\) | ||||
−0.211452 | + | 0.977388i | \(0.567819\pi\) | |||||||
\(398\) | −0.902701 | −0.0452483 | ||||||||
\(399\) | −1.57227 | −0.0787119 | ||||||||
\(400\) | 8.38051 | 0.419025 | ||||||||
\(401\) | 14.5861 | 0.728396 | 0.364198 | − | 0.931322i | \(-0.381343\pi\) | ||||
0.364198 | + | 0.931322i | \(0.381343\pi\) | |||||||
\(402\) | −6.26257 | −0.312349 | ||||||||
\(403\) | 1.71880 | 0.0856193 | ||||||||
\(404\) | −5.12273 | −0.254865 | ||||||||
\(405\) | 3.65794 | 0.181764 | ||||||||
\(406\) | 0.890456 | 0.0441926 | ||||||||
\(407\) | −32.3849 | −1.60526 | ||||||||
\(408\) | −5.23101 | −0.258974 | ||||||||
\(409\) | −8.12621 | −0.401815 | −0.200908 | − | 0.979610i | \(-0.564389\pi\) | ||||
−0.200908 | + | 0.979610i | \(0.564389\pi\) | |||||||
\(410\) | −24.6169 | −1.21574 | ||||||||
\(411\) | −4.58596 | −0.226209 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | 0.817355 | 0.0402194 | ||||||||
\(414\) | 1.96141 | 0.0963978 | ||||||||
\(415\) | 23.9689 | 1.17659 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 16.5435 | 0.810141 | ||||||||
\(418\) | −7.61154 | −0.372293 | ||||||||
\(419\) | 35.1857 | 1.71893 | 0.859467 | − | 0.511191i | \(-0.170796\pi\) | ||||
0.859467 | + | 0.511191i | \(0.170796\pi\) | |||||||
\(420\) | −3.34610 | −0.163273 | ||||||||
\(421\) | −18.3372 | −0.893701 | −0.446850 | − | 0.894609i | \(-0.647454\pi\) | ||||
−0.446850 | + | 0.894609i | \(0.647454\pi\) | |||||||
\(422\) | −24.4435 | −1.18989 | ||||||||
\(423\) | 0.170842 | 0.00830662 | ||||||||
\(424\) | −4.21836 | −0.204861 | ||||||||
\(425\) | 43.8386 | 2.12648 | ||||||||
\(426\) | −8.89499 | −0.430964 | ||||||||
\(427\) | 1.11737 | 0.0540735 | ||||||||
\(428\) | −7.37919 | −0.356687 | ||||||||
\(429\) | 4.42842 | 0.213806 | ||||||||
\(430\) | −4.38337 | −0.211385 | ||||||||
\(431\) | 10.2701 | 0.494693 | 0.247346 | − | 0.968927i | \(-0.420441\pi\) | ||||
0.247346 | + | 0.968927i | \(0.420441\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 19.5716 | 0.940553 | 0.470277 | − | 0.882519i | \(-0.344154\pi\) | ||||
0.470277 | + | 0.882519i | \(0.344154\pi\) | |||||||
\(434\) | 1.57227 | 0.0754713 | ||||||||
\(435\) | −3.56079 | −0.170727 | ||||||||
\(436\) | 9.79616 | 0.469151 | ||||||||
\(437\) | 3.37126 | 0.161269 | ||||||||
\(438\) | −10.4828 | −0.500887 | ||||||||
\(439\) | −36.2242 | −1.72889 | −0.864443 | − | 0.502731i | \(-0.832328\pi\) | ||||
−0.864443 | + | 0.502731i | \(0.832328\pi\) | |||||||
\(440\) | −16.1989 | −0.772251 | ||||||||
\(441\) | −6.16323 | −0.293487 | ||||||||
\(442\) | 5.23101 | 0.248814 | ||||||||
\(443\) | −19.4044 | −0.921930 | −0.460965 | − | 0.887418i | \(-0.652497\pi\) | ||||
−0.460965 | + | 0.887418i | \(0.652497\pi\) | |||||||
\(444\) | −7.31297 | −0.347058 | ||||||||
\(445\) | −21.2719 | −1.00838 | ||||||||
\(446\) | −1.85778 | −0.0879685 | ||||||||
\(447\) | −17.8038 | −0.842092 | ||||||||
\(448\) | 0.914750 | 0.0432179 | ||||||||
\(449\) | −15.8186 | −0.746527 | −0.373263 | − | 0.927725i | \(-0.621761\pi\) | ||||
−0.373263 | + | 0.927725i | \(0.621761\pi\) | |||||||
\(450\) | 8.38051 | 0.395061 | ||||||||
\(451\) | 29.8020 | 1.40332 | ||||||||
\(452\) | 0.0993838 | 0.00467462 | ||||||||
\(453\) | −18.2792 | −0.858833 | ||||||||
\(454\) | 18.9743 | 0.890507 | ||||||||
\(455\) | 3.34610 | 0.156868 | ||||||||
\(456\) | −1.71880 | −0.0804900 | ||||||||
\(457\) | −4.13162 | −0.193269 | −0.0966346 | − | 0.995320i | \(-0.530808\pi\) | ||||
−0.0966346 | + | 0.995320i | \(0.530808\pi\) | |||||||
\(458\) | 4.58595 | 0.214287 | ||||||||
\(459\) | −5.23101 | −0.244163 | ||||||||
\(460\) | 7.17470 | 0.334522 | ||||||||
\(461\) | −7.23501 | −0.336968 | −0.168484 | − | 0.985704i | \(-0.553887\pi\) | ||||
−0.168484 | + | 0.985704i | \(0.553887\pi\) | |||||||
\(462\) | 4.05089 | 0.188465 | ||||||||
\(463\) | 2.76102 | 0.128315 | 0.0641577 | − | 0.997940i | \(-0.479564\pi\) | ||||
0.0641577 | + | 0.997940i | \(0.479564\pi\) | |||||||
\(464\) | 0.973442 | 0.0451909 | ||||||||
\(465\) | −6.28725 | −0.291564 | ||||||||
\(466\) | 6.46254 | 0.299371 | ||||||||
\(467\) | 25.9191 | 1.19939 | 0.599697 | − | 0.800227i | \(-0.295288\pi\) | ||||
0.599697 | + | 0.800227i | \(0.295288\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 5.72869 | 0.264526 | ||||||||
\(470\) | 0.624929 | 0.0288258 | ||||||||
\(471\) | 7.83062 | 0.360816 | ||||||||
\(472\) | 0.893529 | 0.0411280 | ||||||||
\(473\) | 5.30665 | 0.244000 | ||||||||
\(474\) | 15.7891 | 0.725216 | ||||||||
\(475\) | 14.4044 | 0.660919 | ||||||||
\(476\) | 4.78507 | 0.219323 | ||||||||
\(477\) | −4.21836 | −0.193145 | ||||||||
\(478\) | −27.2859 | −1.24803 | ||||||||
\(479\) | −18.8215 | −0.859977 | −0.429988 | − | 0.902834i | \(-0.641482\pi\) | ||||
−0.429988 | + | 0.902834i | \(0.641482\pi\) | |||||||
\(480\) | −3.65794 | −0.166961 | ||||||||
\(481\) | 7.31297 | 0.333443 | ||||||||
\(482\) | 24.0349 | 1.09476 | ||||||||
\(483\) | −1.79420 | −0.0816388 | ||||||||
\(484\) | 8.61086 | 0.391403 | ||||||||
\(485\) | 52.6800 | 2.39207 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 29.4004 | 1.33226 | 0.666129 | − | 0.745837i | \(-0.267950\pi\) | ||||
0.666129 | + | 0.745837i | \(0.267950\pi\) | |||||||
\(488\) | 1.22151 | 0.0552950 | ||||||||
\(489\) | 4.97429 | 0.224945 | ||||||||
\(490\) | −22.5447 | −1.01847 | ||||||||
\(491\) | 7.82617 | 0.353190 | 0.176595 | − | 0.984284i | \(-0.443492\pi\) | ||||
0.176595 | + | 0.984284i | \(0.443492\pi\) | |||||||
\(492\) | 6.72972 | 0.303399 | ||||||||
\(493\) | 5.09209 | 0.229336 | ||||||||
\(494\) | 1.71880 | 0.0773323 | ||||||||
\(495\) | −16.1989 | −0.728085 | ||||||||
\(496\) | 1.71880 | 0.0771762 | ||||||||
\(497\) | 8.13669 | 0.364981 | ||||||||
\(498\) | −6.55258 | −0.293628 | ||||||||
\(499\) | −26.4365 | −1.18346 | −0.591730 | − | 0.806137i | \(-0.701555\pi\) | ||||
−0.591730 | + | 0.806137i | \(0.701555\pi\) | |||||||
\(500\) | 12.3657 | 0.553010 | ||||||||
\(501\) | −0.527598 | −0.0235713 | ||||||||
\(502\) | −20.2541 | −0.903986 | ||||||||
\(503\) | −17.1437 | −0.764401 | −0.382201 | − | 0.924079i | \(-0.624834\pi\) | ||||
−0.382201 | + | 0.924079i | \(0.624834\pi\) | |||||||
\(504\) | 0.914750 | 0.0407462 | ||||||||
\(505\) | −18.7386 | −0.833858 | ||||||||
\(506\) | −8.68592 | −0.386136 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 5.04372 | 0.223779 | ||||||||
\(509\) | 29.4586 | 1.30573 | 0.652866 | − | 0.757474i | \(-0.273567\pi\) | ||||
0.652866 | + | 0.757474i | \(0.273567\pi\) | |||||||
\(510\) | −19.1347 | −0.847300 | ||||||||
\(511\) | 9.58913 | 0.424198 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.71880 | −0.0758867 | ||||||||
\(514\) | −2.81242 | −0.124051 | ||||||||
\(515\) | 3.65794 | 0.161188 | ||||||||
\(516\) | 1.19832 | 0.0527530 | ||||||||
\(517\) | −0.756559 | −0.0332734 | ||||||||
\(518\) | 6.68954 | 0.293922 | ||||||||
\(519\) | −1.10173 | −0.0483605 | ||||||||
\(520\) | 3.65794 | 0.160411 | ||||||||
\(521\) | −15.2884 | −0.669799 | −0.334899 | − | 0.942254i | \(-0.608702\pi\) | ||||
−0.334899 | + | 0.942254i | \(0.608702\pi\) | |||||||
\(522\) | 0.973442 | 0.0426064 | ||||||||
\(523\) | 22.7942 | 0.996720 | 0.498360 | − | 0.866970i | \(-0.333936\pi\) | ||||
0.498360 | + | 0.866970i | \(0.333936\pi\) | |||||||
\(524\) | −2.24919 | −0.0982564 | ||||||||
\(525\) | −7.66607 | −0.334575 | ||||||||
\(526\) | −4.00949 | −0.174822 | ||||||||
\(527\) | 8.99105 | 0.391656 | ||||||||
\(528\) | 4.42842 | 0.192722 | ||||||||
\(529\) | −19.1529 | −0.832734 | ||||||||
\(530\) | −15.4305 | −0.670257 | ||||||||
\(531\) | 0.893529 | 0.0387758 | ||||||||
\(532\) | 1.57227 | 0.0681665 | ||||||||
\(533\) | −6.72972 | −0.291497 | ||||||||
\(534\) | 5.81526 | 0.251651 | ||||||||
\(535\) | −26.9926 | −1.16699 | ||||||||
\(536\) | 6.26257 | 0.270502 | ||||||||
\(537\) | −21.9135 | −0.945636 | ||||||||
\(538\) | −18.8430 | −0.812378 | ||||||||
\(539\) | 27.2934 | 1.17561 | ||||||||
\(540\) | −3.65794 | −0.157413 | ||||||||
\(541\) | 12.4956 | 0.537228 | 0.268614 | − | 0.963248i | \(-0.413434\pi\) | ||||
0.268614 | + | 0.963248i | \(0.413434\pi\) | |||||||
\(542\) | −19.0394 | −0.817814 | ||||||||
\(543\) | −8.70219 | −0.373447 | ||||||||
\(544\) | 5.23101 | 0.224278 | ||||||||
\(545\) | 35.8338 | 1.53495 | ||||||||
\(546\) | −0.914750 | −0.0391477 | ||||||||
\(547\) | −12.6299 | −0.540016 | −0.270008 | − | 0.962858i | \(-0.587026\pi\) | ||||
−0.270008 | + | 0.962858i | \(0.587026\pi\) | |||||||
\(548\) | 4.58596 | 0.195902 | ||||||||
\(549\) | 1.22151 | 0.0521327 | ||||||||
\(550\) | −37.1124 | −1.58248 | ||||||||
\(551\) | 1.67315 | 0.0712785 | ||||||||
\(552\) | −1.96141 | −0.0834830 | ||||||||
\(553\) | −14.4431 | −0.614181 | ||||||||
\(554\) | 25.1167 | 1.06710 | ||||||||
\(555\) | −26.7504 | −1.13549 | ||||||||
\(556\) | −16.5435 | −0.701602 | ||||||||
\(557\) | 12.9474 | 0.548600 | 0.274300 | − | 0.961644i | \(-0.411554\pi\) | ||||
0.274300 | + | 0.961644i | \(0.411554\pi\) | |||||||
\(558\) | 1.71880 | 0.0727624 | ||||||||
\(559\) | −1.19832 | −0.0506834 | ||||||||
\(560\) | 3.34610 | 0.141398 | ||||||||
\(561\) | 23.1651 | 0.978032 | ||||||||
\(562\) | −25.7761 | −1.08730 | ||||||||
\(563\) | −5.91159 | −0.249144 | −0.124572 | − | 0.992211i | \(-0.539756\pi\) | ||||
−0.124572 | + | 0.992211i | \(0.539756\pi\) | |||||||
\(564\) | −0.170842 | −0.00719375 | ||||||||
\(565\) | 0.363540 | 0.0152942 | ||||||||
\(566\) | 28.5628 | 1.20058 | ||||||||
\(567\) | 0.914750 | 0.0384159 | ||||||||
\(568\) | 8.89499 | 0.373226 | ||||||||
\(569\) | −2.74793 | −0.115199 | −0.0575995 | − | 0.998340i | \(-0.518345\pi\) | ||||
−0.0575995 | + | 0.998340i | \(0.518345\pi\) | |||||||
\(570\) | −6.28725 | −0.263344 | ||||||||
\(571\) | 15.9042 | 0.665569 | 0.332784 | − | 0.943003i | \(-0.392012\pi\) | ||||
0.332784 | + | 0.943003i | \(0.392012\pi\) | |||||||
\(572\) | −4.42842 | −0.185161 | ||||||||
\(573\) | 12.1667 | 0.508273 | ||||||||
\(574\) | −6.15601 | −0.256947 | ||||||||
\(575\) | 16.4376 | 0.685494 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.3737 | −1.22285 | −0.611423 | − | 0.791304i | \(-0.709402\pi\) | ||||
−0.611423 | + | 0.791304i | \(0.709402\pi\) | |||||||
\(578\) | 10.3635 | 0.431065 | ||||||||
\(579\) | 7.71466 | 0.320610 | ||||||||
\(580\) | 3.56079 | 0.147854 | ||||||||
\(581\) | 5.99398 | 0.248672 | ||||||||
\(582\) | −14.4016 | −0.596963 | ||||||||
\(583\) | 18.6806 | 0.773673 | ||||||||
\(584\) | 10.4828 | 0.433781 | ||||||||
\(585\) | 3.65794 | 0.151237 | ||||||||
\(586\) | 29.7590 | 1.22933 | ||||||||
\(587\) | −27.8661 | −1.15016 | −0.575079 | − | 0.818098i | \(-0.695029\pi\) | ||||
−0.575079 | + | 0.818098i | \(0.695029\pi\) | |||||||
\(588\) | 6.16323 | 0.254167 | ||||||||
\(589\) | 2.95426 | 0.121728 | ||||||||
\(590\) | 3.26847 | 0.134561 | ||||||||
\(591\) | 4.95515 | 0.203828 | ||||||||
\(592\) | 7.31297 | 0.300561 | ||||||||
\(593\) | 35.4100 | 1.45412 | 0.727058 | − | 0.686576i | \(-0.240887\pi\) | ||||
0.727058 | + | 0.686576i | \(0.240887\pi\) | |||||||
\(594\) | 4.42842 | 0.181700 | ||||||||
\(595\) | 17.5035 | 0.717573 | ||||||||
\(596\) | 17.8038 | 0.729273 | ||||||||
\(597\) | 0.902701 | 0.0369451 | ||||||||
\(598\) | 1.96141 | 0.0802079 | ||||||||
\(599\) | −10.7617 | −0.439713 | −0.219856 | − | 0.975532i | \(-0.570559\pi\) | ||||
−0.219856 | + | 0.975532i | \(0.570559\pi\) | |||||||
\(600\) | −8.38051 | −0.342133 | ||||||||
\(601\) | 21.4956 | 0.876824 | 0.438412 | − | 0.898774i | \(-0.355541\pi\) | ||||
0.438412 | + | 0.898774i | \(0.355541\pi\) | |||||||
\(602\) | −1.09616 | −0.0446762 | ||||||||
\(603\) | 6.26257 | 0.255032 | ||||||||
\(604\) | 18.2792 | 0.743771 | ||||||||
\(605\) | 31.4980 | 1.28058 | ||||||||
\(606\) | 5.12273 | 0.208097 | ||||||||
\(607\) | 27.6113 | 1.12071 | 0.560354 | − | 0.828253i | \(-0.310665\pi\) | ||||
0.560354 | + | 0.828253i | \(0.310665\pi\) | |||||||
\(608\) | 1.71880 | 0.0697064 | ||||||||
\(609\) | −0.890456 | −0.0360831 | ||||||||
\(610\) | 4.46820 | 0.180912 | ||||||||
\(611\) | 0.170842 | 0.00691153 | ||||||||
\(612\) | 5.23101 | 0.211451 | ||||||||
\(613\) | 7.24980 | 0.292817 | 0.146408 | − | 0.989224i | \(-0.453229\pi\) | ||||
0.146408 | + | 0.989224i | \(0.453229\pi\) | |||||||
\(614\) | −11.9130 | −0.480770 | ||||||||
\(615\) | 24.6169 | 0.992649 | ||||||||
\(616\) | −4.05089 | −0.163215 | ||||||||
\(617\) | 15.1433 | 0.609646 | 0.304823 | − | 0.952409i | \(-0.401403\pi\) | ||||
0.304823 | + | 0.952409i | \(0.401403\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | 34.2081 | 1.37494 | 0.687471 | − | 0.726212i | \(-0.258721\pi\) | ||||
0.687471 | + | 0.726212i | \(0.258721\pi\) | |||||||
\(620\) | 6.28725 | 0.252502 | ||||||||
\(621\) | −1.96141 | −0.0787085 | ||||||||
\(622\) | −17.0556 | −0.683866 | ||||||||
\(623\) | −5.31951 | −0.213122 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 3.33038 | 0.133215 | ||||||||
\(626\) | 29.1954 | 1.16688 | ||||||||
\(627\) | 7.61154 | 0.303976 | ||||||||
\(628\) | −7.83062 | −0.312476 | ||||||||
\(629\) | 38.2543 | 1.52530 | ||||||||
\(630\) | 3.34610 | 0.133312 | ||||||||
\(631\) | 37.1474 | 1.47881 | 0.739407 | − | 0.673259i | \(-0.235106\pi\) | ||||
0.739407 | + | 0.673259i | \(0.235106\pi\) | |||||||
\(632\) | −15.7891 | −0.628056 | ||||||||
\(633\) | 24.4435 | 0.971542 | ||||||||
\(634\) | −11.2339 | −0.446154 | ||||||||
\(635\) | 18.4496 | 0.732150 | ||||||||
\(636\) | 4.21836 | 0.167269 | ||||||||
\(637\) | −6.16323 | −0.244196 | ||||||||
\(638\) | −4.31080 | −0.170666 | ||||||||
\(639\) | 8.89499 | 0.351880 | ||||||||
\(640\) | 3.65794 | 0.144593 | ||||||||
\(641\) | −3.59215 | −0.141881 | −0.0709407 | − | 0.997481i | \(-0.522600\pi\) | ||||
−0.0709407 | + | 0.997481i | \(0.522600\pi\) | |||||||
\(642\) | 7.37919 | 0.291233 | ||||||||
\(643\) | −4.96575 | −0.195830 | −0.0979151 | − | 0.995195i | \(-0.531217\pi\) | ||||
−0.0979151 | + | 0.995195i | \(0.531217\pi\) | |||||||
\(644\) | 1.79420 | 0.0707012 | ||||||||
\(645\) | 4.38337 | 0.172595 | ||||||||
\(646\) | 8.99105 | 0.353748 | ||||||||
\(647\) | −31.2408 | −1.22820 | −0.614101 | − | 0.789227i | \(-0.710481\pi\) | ||||
−0.614101 | + | 0.789227i | \(0.710481\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.95692 | −0.155323 | ||||||||
\(650\) | 8.38051 | 0.328711 | ||||||||
\(651\) | −1.57227 | −0.0616221 | ||||||||
\(652\) | −4.97429 | −0.194808 | ||||||||
\(653\) | −7.76229 | −0.303762 | −0.151881 | − | 0.988399i | \(-0.548533\pi\) | ||||
−0.151881 | + | 0.988399i | \(0.548533\pi\) | |||||||
\(654\) | −9.79616 | −0.383060 | ||||||||
\(655\) | −8.22740 | −0.321471 | ||||||||
\(656\) | −6.72972 | −0.262751 | ||||||||
\(657\) | 10.4828 | 0.408973 | ||||||||
\(658\) | 0.156278 | 0.00609234 | ||||||||
\(659\) | 38.8977 | 1.51524 | 0.757620 | − | 0.652696i | \(-0.226362\pi\) | ||||
0.757620 | + | 0.652696i | \(0.226362\pi\) | |||||||
\(660\) | 16.1989 | 0.630540 | ||||||||
\(661\) | −23.0813 | −0.897760 | −0.448880 | − | 0.893592i | \(-0.648177\pi\) | ||||
−0.448880 | + | 0.893592i | \(0.648177\pi\) | |||||||
\(662\) | −36.0555 | −1.40134 | ||||||||
\(663\) | −5.23101 | −0.203156 | ||||||||
\(664\) | 6.55258 | 0.254290 | ||||||||
\(665\) | 5.75126 | 0.223024 | ||||||||
\(666\) | 7.31297 | 0.283372 | ||||||||
\(667\) | 1.90931 | 0.0739289 | ||||||||
\(668\) | 0.527598 | 0.0204134 | ||||||||
\(669\) | 1.85778 | 0.0718260 | ||||||||
\(670\) | 22.9081 | 0.885017 | ||||||||
\(671\) | −5.40934 | −0.208825 | ||||||||
\(672\) | −0.914750 | −0.0352873 | ||||||||
\(673\) | −22.0362 | −0.849433 | −0.424717 | − | 0.905326i | \(-0.639626\pi\) | ||||
−0.424717 | + | 0.905326i | \(0.639626\pi\) | |||||||
\(674\) | −19.4420 | −0.748877 | ||||||||
\(675\) | −8.38051 | −0.322566 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −3.39656 | −0.130540 | −0.0652702 | − | 0.997868i | \(-0.520791\pi\) | ||||
−0.0652702 | + | 0.997868i | \(0.520791\pi\) | |||||||
\(678\) | −0.0993838 | −0.00381681 | ||||||||
\(679\) | 13.1738 | 0.505565 | ||||||||
\(680\) | 19.1347 | 0.733783 | ||||||||
\(681\) | −18.9743 | −0.727096 | ||||||||
\(682\) | −7.61154 | −0.291461 | ||||||||
\(683\) | −19.6276 | −0.751029 | −0.375515 | − | 0.926817i | \(-0.622534\pi\) | ||||
−0.375515 | + | 0.926817i | \(0.622534\pi\) | |||||||
\(684\) | 1.71880 | 0.0657198 | ||||||||
\(685\) | 16.7751 | 0.640945 | ||||||||
\(686\) | −12.0411 | −0.459730 | ||||||||
\(687\) | −4.58595 | −0.174965 | ||||||||
\(688\) | −1.19832 | −0.0456854 | ||||||||
\(689\) | −4.21836 | −0.160707 | ||||||||
\(690\) | −7.17470 | −0.273136 | ||||||||
\(691\) | −12.1157 | −0.460904 | −0.230452 | − | 0.973084i | \(-0.574020\pi\) | ||||
−0.230452 | + | 0.973084i | \(0.574020\pi\) | |||||||
\(692\) | 1.10173 | 0.0418814 | ||||||||
\(693\) | −4.05089 | −0.153881 | ||||||||
\(694\) | 4.24821 | 0.161260 | ||||||||
\(695\) | −60.5152 | −2.29547 | ||||||||
\(696\) | −0.973442 | −0.0368982 | ||||||||
\(697\) | −35.2033 | −1.33342 | ||||||||
\(698\) | 13.2219 | 0.500455 | ||||||||
\(699\) | −6.46254 | −0.244436 | ||||||||
\(700\) | 7.66607 | 0.289750 | ||||||||
\(701\) | −6.28294 | −0.237303 | −0.118652 | − | 0.992936i | \(-0.537857\pi\) | ||||
−0.118652 | + | 0.992936i | \(0.537857\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 12.5695 | 0.474068 | ||||||||
\(704\) | −4.42842 | −0.166902 | ||||||||
\(705\) | −0.624929 | −0.0235362 | ||||||||
\(706\) | 28.2177 | 1.06199 | ||||||||
\(707\) | −4.68602 | −0.176236 | ||||||||
\(708\) | −0.893529 | −0.0335809 | ||||||||
\(709\) | −30.3734 | −1.14070 | −0.570349 | − | 0.821403i | \(-0.693192\pi\) | ||||
−0.570349 | + | 0.821403i | \(0.693192\pi\) | |||||||
\(710\) | 32.5373 | 1.22110 | ||||||||
\(711\) | −15.7891 | −0.592137 | ||||||||
\(712\) | −5.81526 | −0.217936 | ||||||||
\(713\) | 3.37126 | 0.126255 | ||||||||
\(714\) | −4.78507 | −0.179077 | ||||||||
\(715\) | −16.1989 | −0.605803 | ||||||||
\(716\) | 21.9135 | 0.818945 | ||||||||
\(717\) | 27.2859 | 1.01901 | ||||||||
\(718\) | 19.9685 | 0.745216 | ||||||||
\(719\) | −41.3809 | −1.54325 | −0.771623 | − | 0.636080i | \(-0.780555\pi\) | ||||
−0.771623 | + | 0.636080i | \(0.780555\pi\) | |||||||
\(720\) | 3.65794 | 0.136323 | ||||||||
\(721\) | 0.914750 | 0.0340671 | ||||||||
\(722\) | −16.0457 | −0.597161 | ||||||||
\(723\) | −24.0349 | −0.893868 | ||||||||
\(724\) | 8.70219 | 0.323414 | ||||||||
\(725\) | 8.15794 | 0.302978 | ||||||||
\(726\) | −8.61086 | −0.319579 | ||||||||
\(727\) | 40.7346 | 1.51076 | 0.755381 | − | 0.655285i | \(-0.227452\pi\) | ||||
0.755381 | + | 0.655285i | \(0.227452\pi\) | |||||||
\(728\) | 0.914750 | 0.0339029 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 38.3454 | 1.41923 | ||||||||
\(731\) | −6.26842 | −0.231846 | ||||||||
\(732\) | −1.22151 | −0.0451482 | ||||||||
\(733\) | −1.14253 | −0.0422003 | −0.0211001 | − | 0.999777i | \(-0.506717\pi\) | ||||
−0.0211001 | + | 0.999777i | \(0.506717\pi\) | |||||||
\(734\) | −9.37152 | −0.345909 | ||||||||
\(735\) | 22.5447 | 0.831575 | ||||||||
\(736\) | 1.96141 | 0.0722984 | ||||||||
\(737\) | −27.7333 | −1.02157 | ||||||||
\(738\) | −6.72972 | −0.247724 | ||||||||
\(739\) | −6.08169 | −0.223719 | −0.111859 | − | 0.993724i | \(-0.535681\pi\) | ||||
−0.111859 | + | 0.993724i | \(0.535681\pi\) | |||||||
\(740\) | 26.7504 | 0.983364 | ||||||||
\(741\) | −1.71880 | −0.0631416 | ||||||||
\(742\) | −3.85874 | −0.141659 | ||||||||
\(743\) | −2.05578 | −0.0754191 | −0.0377096 | − | 0.999289i | \(-0.512006\pi\) | ||||
−0.0377096 | + | 0.999289i | \(0.512006\pi\) | |||||||
\(744\) | −1.71880 | −0.0630141 | ||||||||
\(745\) | 65.1253 | 2.38601 | ||||||||
\(746\) | 10.9714 | 0.401690 | ||||||||
\(747\) | 6.55258 | 0.239747 | ||||||||
\(748\) | −23.1651 | −0.847000 | ||||||||
\(749\) | −6.75012 | −0.246644 | ||||||||
\(750\) | −12.3657 | −0.451531 | ||||||||
\(751\) | −50.1829 | −1.83120 | −0.915600 | − | 0.402090i | \(-0.868284\pi\) | ||||
−0.915600 | + | 0.402090i | \(0.868284\pi\) | |||||||
\(752\) | 0.170842 | 0.00622997 | ||||||||
\(753\) | 20.2541 | 0.738101 | ||||||||
\(754\) | 0.973442 | 0.0354507 | ||||||||
\(755\) | 66.8643 | 2.43344 | ||||||||
\(756\) | −0.914750 | −0.0332691 | ||||||||
\(757\) | 17.5089 | 0.636371 | 0.318185 | − | 0.948029i | \(-0.396927\pi\) | ||||
0.318185 | + | 0.948029i | \(0.396927\pi\) | |||||||
\(758\) | −4.03145 | −0.146429 | ||||||||
\(759\) | 8.68592 | 0.315279 | ||||||||
\(760\) | 6.28725 | 0.228062 | ||||||||
\(761\) | −13.7120 | −0.497058 | −0.248529 | − | 0.968624i | \(-0.579947\pi\) | ||||
−0.248529 | + | 0.968624i | \(0.579947\pi\) | |||||||
\(762\) | −5.04372 | −0.182715 | ||||||||
\(763\) | 8.96104 | 0.324412 | ||||||||
\(764\) | −12.1667 | −0.440177 | ||||||||
\(765\) | 19.1347 | 0.691818 | ||||||||
\(766\) | 12.2886 | 0.444006 | ||||||||
\(767\) | 0.893529 | 0.0322635 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −15.2454 | −0.549761 | −0.274881 | − | 0.961478i | \(-0.588638\pi\) | ||||
−0.274881 | + | 0.961478i | \(0.588638\pi\) | |||||||
\(770\) | −14.8179 | −0.534001 | ||||||||
\(771\) | 2.81242 | 0.101287 | ||||||||
\(772\) | −7.71466 | −0.277657 | ||||||||
\(773\) | 18.1461 | 0.652670 | 0.326335 | − | 0.945254i | \(-0.394186\pi\) | ||||
0.326335 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(774\) | −1.19832 | −0.0430726 | ||||||||
\(775\) | 14.4044 | 0.517421 | ||||||||
\(776\) | 14.4016 | 0.516986 | ||||||||
\(777\) | −6.68954 | −0.239986 | ||||||||
\(778\) | −7.96737 | −0.285644 | ||||||||
\(779\) | −11.5670 | −0.414431 | ||||||||
\(780\) | −3.65794 | −0.130975 | ||||||||
\(781\) | −39.3907 | −1.40951 | ||||||||
\(782\) | 10.2601 | 0.366902 | ||||||||
\(783\) | −0.973442 | −0.0347880 | ||||||||
\(784\) | −6.16323 | −0.220115 | ||||||||
\(785\) | −28.6439 | −1.02234 | ||||||||
\(786\) | 2.24919 | 0.0802260 | ||||||||
\(787\) | −28.3674 | −1.01119 | −0.505595 | − | 0.862771i | \(-0.668727\pi\) | ||||
−0.505595 | + | 0.862771i | \(0.668727\pi\) | |||||||
\(788\) | −4.95515 | −0.176520 | ||||||||
\(789\) | 4.00949 | 0.142742 | ||||||||
\(790\) | −57.7555 | −2.05485 | ||||||||
\(791\) | 0.0909113 | 0.00323243 | ||||||||
\(792\) | −4.42842 | −0.157357 | ||||||||
\(793\) | 1.22151 | 0.0433770 | ||||||||
\(794\) | −8.42629 | −0.299038 | ||||||||
\(795\) | 15.4305 | 0.547263 | ||||||||
\(796\) | −0.902701 | −0.0319954 | ||||||||
\(797\) | −14.8175 | −0.524862 | −0.262431 | − | 0.964951i | \(-0.584524\pi\) | ||||
−0.262431 | + | 0.964951i | \(0.584524\pi\) | |||||||
\(798\) | −1.57227 | −0.0556577 | ||||||||
\(799\) | 0.893677 | 0.0316160 | ||||||||
\(800\) | 8.38051 | 0.296296 | ||||||||
\(801\) | −5.81526 | −0.205472 | ||||||||
\(802\) | 14.5861 | 0.515054 | ||||||||
\(803\) | −46.4222 | −1.63820 | ||||||||
\(804\) | −6.26257 | −0.220864 | ||||||||
\(805\) | 6.56306 | 0.231317 | ||||||||
\(806\) | 1.71880 | 0.0605420 | ||||||||
\(807\) | 18.8430 | 0.663304 | ||||||||
\(808\) | −5.12273 | −0.180217 | ||||||||
\(809\) | 23.8544 | 0.838674 | 0.419337 | − | 0.907831i | \(-0.362263\pi\) | ||||
0.419337 | + | 0.907831i | \(0.362263\pi\) | |||||||
\(810\) | 3.65794 | 0.128527 | ||||||||
\(811\) | −2.70581 | −0.0950140 | −0.0475070 | − | 0.998871i | \(-0.515128\pi\) | ||||
−0.0475070 | + | 0.998871i | \(0.515128\pi\) | |||||||
\(812\) | 0.890456 | 0.0312489 | ||||||||
\(813\) | 19.0394 | 0.667742 | ||||||||
\(814\) | −32.3849 | −1.13509 | ||||||||
\(815\) | −18.1956 | −0.637366 | ||||||||
\(816\) | −5.23101 | −0.183122 | ||||||||
\(817\) | −2.05966 | −0.0720585 | ||||||||
\(818\) | −8.12621 | −0.284126 | ||||||||
\(819\) | 0.914750 | 0.0319640 | ||||||||
\(820\) | −24.6169 | −0.859659 | ||||||||
\(821\) | −31.8825 | −1.11271 | −0.556354 | − | 0.830946i | \(-0.687800\pi\) | ||||
−0.556354 | + | 0.830946i | \(0.687800\pi\) | |||||||
\(822\) | −4.58596 | −0.159954 | ||||||||
\(823\) | 36.0459 | 1.25648 | 0.628241 | − | 0.778019i | \(-0.283775\pi\) | ||||
0.628241 | + | 0.778019i | \(0.283775\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 37.1124 | 1.29209 | ||||||||
\(826\) | 0.817355 | 0.0284394 | ||||||||
\(827\) | 9.92174 | 0.345013 | 0.172506 | − | 0.985008i | \(-0.444813\pi\) | ||||
0.172506 | + | 0.985008i | \(0.444813\pi\) | |||||||
\(828\) | 1.96141 | 0.0681636 | ||||||||
\(829\) | 14.8089 | 0.514336 | 0.257168 | − | 0.966367i | \(-0.417211\pi\) | ||||
0.257168 | + | 0.966367i | \(0.417211\pi\) | |||||||
\(830\) | 23.9689 | 0.831974 | ||||||||
\(831\) | −25.1167 | −0.871287 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −32.2400 | −1.11705 | ||||||||
\(834\) | 16.5435 | 0.572856 | ||||||||
\(835\) | 1.92992 | 0.0667877 | ||||||||
\(836\) | −7.61154 | −0.263251 | ||||||||
\(837\) | −1.71880 | −0.0594103 | ||||||||
\(838\) | 35.1857 | 1.21547 | ||||||||
\(839\) | −36.3475 | −1.25486 | −0.627428 | − | 0.778675i | \(-0.715892\pi\) | ||||
−0.627428 | + | 0.778675i | \(0.715892\pi\) | |||||||
\(840\) | −3.34610 | −0.115451 | ||||||||
\(841\) | −28.0524 | −0.967325 | ||||||||
\(842\) | −18.3372 | −0.631942 | ||||||||
\(843\) | 25.7761 | 0.887776 | ||||||||
\(844\) | −24.4435 | −0.841380 | ||||||||
\(845\) | 3.65794 | 0.125837 | ||||||||
\(846\) | 0.170842 | 0.00587367 | ||||||||
\(847\) | 7.87679 | 0.270650 | ||||||||
\(848\) | −4.21836 | −0.144859 | ||||||||
\(849\) | −28.5628 | −0.980271 | ||||||||
\(850\) | 43.8386 | 1.50365 | ||||||||
\(851\) | 14.3437 | 0.491696 | ||||||||
\(852\) | −8.89499 | −0.304737 | ||||||||
\(853\) | −0.600488 | −0.0205603 | −0.0102802 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102802 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(854\) | 1.11737 | 0.0382357 | ||||||||
\(855\) | 6.28725 | 0.215019 | ||||||||
\(856\) | −7.37919 | −0.252216 | ||||||||
\(857\) | −53.8982 | −1.84113 | −0.920565 | − | 0.390591i | \(-0.872271\pi\) | ||||
−0.920565 | + | 0.390591i | \(0.872271\pi\) | |||||||
\(858\) | 4.42842 | 0.151184 | ||||||||
\(859\) | 25.4380 | 0.867934 | 0.433967 | − | 0.900929i | \(-0.357113\pi\) | ||||
0.433967 | + | 0.900929i | \(0.357113\pi\) | |||||||
\(860\) | −4.38337 | −0.149472 | ||||||||
\(861\) | 6.15601 | 0.209796 | ||||||||
\(862\) | 10.2701 | 0.349800 | ||||||||
\(863\) | 5.04305 | 0.171667 | 0.0858337 | − | 0.996309i | \(-0.472645\pi\) | ||||
0.0858337 | + | 0.996309i | \(0.472645\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 4.03006 | 0.137026 | ||||||||
\(866\) | 19.5716 | 0.665072 | ||||||||
\(867\) | −10.3635 | −0.351963 | ||||||||
\(868\) | 1.57227 | 0.0533663 | ||||||||
\(869\) | 69.9206 | 2.37189 | ||||||||
\(870\) | −3.56079 | −0.120722 | ||||||||
\(871\) | 6.26257 | 0.212199 | ||||||||
\(872\) | 9.79616 | 0.331740 | ||||||||
\(873\) | 14.4016 | 0.487419 | ||||||||
\(874\) | 3.37126 | 0.114034 | ||||||||
\(875\) | 11.3115 | 0.382399 | ||||||||
\(876\) | −10.4828 | −0.354181 | ||||||||
\(877\) | 20.2628 | 0.684226 | 0.342113 | − | 0.939659i | \(-0.388857\pi\) | ||||
0.342113 | + | 0.939659i | \(0.388857\pi\) | |||||||
\(878\) | −36.2242 | −1.22251 | ||||||||
\(879\) | −29.7590 | −1.00375 | ||||||||
\(880\) | −16.1989 | −0.546064 | ||||||||
\(881\) | 41.2377 | 1.38933 | 0.694667 | − | 0.719331i | \(-0.255552\pi\) | ||||
0.694667 | + | 0.719331i | \(0.255552\pi\) | |||||||
\(882\) | −6.16323 | −0.207527 | ||||||||
\(883\) | −3.22454 | −0.108514 | −0.0542571 | − | 0.998527i | \(-0.517279\pi\) | ||||
−0.0542571 | + | 0.998527i | \(0.517279\pi\) | |||||||
\(884\) | 5.23101 | 0.175938 | ||||||||
\(885\) | −3.26847 | −0.109869 | ||||||||
\(886\) | −19.4044 | −0.651903 | ||||||||
\(887\) | −9.07062 | −0.304562 | −0.152281 | − | 0.988337i | \(-0.548662\pi\) | ||||
−0.152281 | + | 0.988337i | \(0.548662\pi\) | |||||||
\(888\) | −7.31297 | −0.245407 | ||||||||
\(889\) | 4.61374 | 0.154740 | ||||||||
\(890\) | −21.2719 | −0.713035 | ||||||||
\(891\) | −4.42842 | −0.148357 | ||||||||
\(892\) | −1.85778 | −0.0622031 | ||||||||
\(893\) | 0.293643 | 0.00982637 | ||||||||
\(894\) | −17.8038 | −0.595449 | ||||||||
\(895\) | 80.1581 | 2.67939 | ||||||||
\(896\) | 0.914750 | 0.0305597 | ||||||||
\(897\) | −1.96141 | −0.0654894 | ||||||||
\(898\) | −15.8186 | −0.527874 | ||||||||
\(899\) | 1.67315 | 0.0558026 | ||||||||
\(900\) | 8.38051 | 0.279350 | ||||||||
\(901\) | −22.0663 | −0.735135 | ||||||||
\(902\) | 29.8020 | 0.992298 | ||||||||
\(903\) | 1.09616 | 0.0364780 | ||||||||
\(904\) | 0.0993838 | 0.00330545 | ||||||||
\(905\) | 31.8321 | 1.05813 | ||||||||
\(906\) | −18.2792 | −0.607287 | ||||||||
\(907\) | 10.8622 | 0.360675 | 0.180337 | − | 0.983605i | \(-0.442281\pi\) | ||||
0.180337 | + | 0.983605i | \(0.442281\pi\) | |||||||
\(908\) | 18.9743 | 0.629684 | ||||||||
\(909\) | −5.12273 | −0.169910 | ||||||||
\(910\) | 3.34610 | 0.110922 | ||||||||
\(911\) | −13.9020 | −0.460594 | −0.230297 | − | 0.973120i | \(-0.573970\pi\) | ||||
−0.230297 | + | 0.973120i | \(0.573970\pi\) | |||||||
\(912\) | −1.71880 | −0.0569150 | ||||||||
\(913\) | −29.0176 | −0.960341 | ||||||||
\(914\) | −4.13162 | −0.136662 | ||||||||
\(915\) | −4.46820 | −0.147714 | ||||||||
\(916\) | 4.58595 | 0.151524 | ||||||||
\(917\) | −2.05745 | −0.0679429 | ||||||||
\(918\) | −5.23101 | −0.172649 | ||||||||
\(919\) | 23.4193 | 0.772533 | 0.386267 | − | 0.922387i | \(-0.373765\pi\) | ||||
0.386267 | + | 0.922387i | \(0.373765\pi\) | |||||||
\(920\) | 7.17470 | 0.236543 | ||||||||
\(921\) | 11.9130 | 0.392547 | ||||||||
\(922\) | −7.23501 | −0.238272 | ||||||||
\(923\) | 8.89499 | 0.292782 | ||||||||
\(924\) | 4.05089 | 0.133265 | ||||||||
\(925\) | 61.2864 | 2.01508 | ||||||||
\(926\) | 2.76102 | 0.0907327 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 0.973442 | 0.0319548 | ||||||||
\(929\) | 23.4469 | 0.769269 | 0.384634 | − | 0.923069i | \(-0.374328\pi\) | ||||
0.384634 | + | 0.923069i | \(0.374328\pi\) | |||||||
\(930\) | −6.28725 | −0.206167 | ||||||||
\(931\) | −10.5933 | −0.347183 | ||||||||
\(932\) | 6.46254 | 0.211687 | ||||||||
\(933\) | 17.0556 | 0.558374 | ||||||||
\(934\) | 25.9191 | 0.848099 | ||||||||
\(935\) | −84.7365 | −2.77118 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 8.69746 | 0.284134 | 0.142067 | − | 0.989857i | \(-0.454625\pi\) | ||||
0.142067 | + | 0.989857i | \(0.454625\pi\) | |||||||
\(938\) | 5.72869 | 0.187048 | ||||||||
\(939\) | −29.1954 | −0.952755 | ||||||||
\(940\) | 0.624929 | 0.0203829 | ||||||||
\(941\) | −52.2988 | −1.70489 | −0.852446 | − | 0.522815i | \(-0.824882\pi\) | ||||
−0.852446 | + | 0.522815i | \(0.824882\pi\) | |||||||
\(942\) | 7.83062 | 0.255135 | ||||||||
\(943\) | −13.1997 | −0.429842 | ||||||||
\(944\) | 0.893529 | 0.0290819 | ||||||||
\(945\) | −3.34610 | −0.108849 | ||||||||
\(946\) | 5.30665 | 0.172534 | ||||||||
\(947\) | −45.7838 | −1.48777 | −0.743887 | − | 0.668306i | \(-0.767020\pi\) | ||||
−0.743887 | + | 0.668306i | \(0.767020\pi\) | |||||||
\(948\) | 15.7891 | 0.512805 | ||||||||
\(949\) | 10.4828 | 0.340286 | ||||||||
\(950\) | 14.4044 | 0.467340 | ||||||||
\(951\) | 11.2339 | 0.364283 | ||||||||
\(952\) | 4.78507 | 0.155085 | ||||||||
\(953\) | −38.2532 | −1.23914 | −0.619571 | − | 0.784941i | \(-0.712693\pi\) | ||||
−0.619571 | + | 0.784941i | \(0.712693\pi\) | |||||||
\(954\) | −4.21836 | −0.136574 | ||||||||
\(955\) | −44.5052 | −1.44015 | ||||||||
\(956\) | −27.2859 | −0.882489 | ||||||||
\(957\) | 4.31080 | 0.139348 | ||||||||
\(958\) | −18.8215 | −0.608096 | ||||||||
\(959\) | 4.19500 | 0.135464 | ||||||||
\(960\) | −3.65794 | −0.118059 | ||||||||
\(961\) | −28.0457 | −0.904701 | ||||||||
\(962\) | 7.31297 | 0.235780 | ||||||||
\(963\) | −7.37919 | −0.237791 | ||||||||
\(964\) | 24.0349 | 0.774113 | ||||||||
\(965\) | −28.2198 | −0.908426 | ||||||||
\(966\) | −1.79420 | −0.0577273 | ||||||||
\(967\) | −18.0188 | −0.579446 | −0.289723 | − | 0.957111i | \(-0.593563\pi\) | ||||
−0.289723 | + | 0.957111i | \(0.593563\pi\) | |||||||
\(968\) | 8.61086 | 0.276764 | ||||||||
\(969\) | −8.99105 | −0.288834 | ||||||||
\(970\) | 52.6800 | 1.69145 | ||||||||
\(971\) | −3.26308 | −0.104717 | −0.0523586 | − | 0.998628i | \(-0.516674\pi\) | ||||
−0.0523586 | + | 0.998628i | \(0.516674\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −15.1332 | −0.485148 | ||||||||
\(974\) | 29.4004 | 0.942048 | ||||||||
\(975\) | −8.38051 | −0.268391 | ||||||||
\(976\) | 1.22151 | 0.0390995 | ||||||||
\(977\) | −58.3105 | −1.86552 | −0.932759 | − | 0.360500i | \(-0.882606\pi\) | ||||
−0.932759 | + | 0.360500i | \(0.882606\pi\) | |||||||
\(978\) | 4.97429 | 0.159060 | ||||||||
\(979\) | 25.7524 | 0.823050 | ||||||||
\(980\) | −22.5447 | −0.720165 | ||||||||
\(981\) | 9.79616 | 0.312767 | ||||||||
\(982\) | 7.82617 | 0.249743 | ||||||||
\(983\) | 42.3991 | 1.35232 | 0.676161 | − | 0.736754i | \(-0.263642\pi\) | ||||
0.676161 | + | 0.736754i | \(0.263642\pi\) | |||||||
\(984\) | 6.72972 | 0.214536 | ||||||||
\(985\) | −18.1256 | −0.577531 | ||||||||
\(986\) | 5.09209 | 0.162165 | ||||||||
\(987\) | −0.156278 | −0.00497437 | ||||||||
\(988\) | 1.71880 | 0.0546822 | ||||||||
\(989\) | −2.35039 | −0.0747380 | ||||||||
\(990\) | −16.1989 | −0.514834 | ||||||||
\(991\) | −25.7734 | −0.818719 | −0.409360 | − | 0.912373i | \(-0.634248\pi\) | ||||
−0.409360 | + | 0.912373i | \(0.634248\pi\) | |||||||
\(992\) | 1.71880 | 0.0545718 | ||||||||
\(993\) | 36.0555 | 1.14419 | ||||||||
\(994\) | 8.13669 | 0.258080 | ||||||||
\(995\) | −3.30202 | −0.104681 | ||||||||
\(996\) | −6.55258 | −0.207627 | ||||||||
\(997\) | 30.7216 | 0.972962 | 0.486481 | − | 0.873691i | \(-0.338280\pi\) | ||||
0.486481 | + | 0.873691i | \(0.338280\pi\) | |||||||
\(998\) | −26.4365 | −0.836832 | ||||||||
\(999\) | −7.31297 | −0.231372 |
(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.y.1.13 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.y.1.13 | ✓ | 13 | 1.1 | even | 1 | trivial |