Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4005,2,Mod(1,4005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4005, 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("4005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4005 = 3^{2} \cdot 5 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4005.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: | \(31.9800860095\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 5 x^{16} - 15 x^{15} + 105 x^{14} + 45 x^{13} - 849 x^{12} + 320 x^{11} + 3371 x^{10} - 2456 x^{9} - 7002 x^{8} + 6279 x^{7} + 7299 x^{6} - 7119 x^{5} - 3066 x^{4} + \cdots + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.59605\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59605 | −1.12858 | −0.564288 | − | 0.825578i | \(-0.690849\pi\) | ||||
−0.564288 | + | 0.825578i | \(0.690849\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.547372 | 0.273686 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.65189 | 0.624357 | 0.312179 | − | 0.950023i | \(-0.398941\pi\) | ||||
0.312179 | + | 0.950023i | \(0.398941\pi\) | |||||||
\(8\) | 2.31847 | 0.819701 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.59605 | −0.504715 | ||||||||
\(11\) | −0.312701 | −0.0942830 | −0.0471415 | − | 0.998888i | \(-0.515011\pi\) | ||||
−0.0471415 | + | 0.998888i | \(0.515011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.26577 | −1.18311 | −0.591556 | − | 0.806264i | \(-0.701486\pi\) | ||||
−0.591556 | + | 0.806264i | \(0.701486\pi\) | |||||||
\(14\) | −2.63650 | −0.704635 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.79513 | −1.19878 | ||||||||
\(17\) | 3.29407 | 0.798929 | 0.399465 | − | 0.916749i | \(-0.369196\pi\) | ||||
0.399465 | + | 0.916749i | \(0.369196\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.57815 | 0.591467 | 0.295734 | − | 0.955270i | \(-0.404436\pi\) | ||||
0.295734 | + | 0.955270i | \(0.404436\pi\) | |||||||
\(20\) | 0.547372 | 0.122396 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.499086 | 0.106406 | ||||||||
\(23\) | −5.06311 | −1.05573 | −0.527866 | − | 0.849328i | \(-0.677008\pi\) | ||||
−0.527866 | + | 0.849328i | \(0.677008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.80838 | 1.33523 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.904200 | 0.170878 | ||||||||
\(29\) | −5.30438 | −0.984999 | −0.492499 | − | 0.870313i | \(-0.663917\pi\) | ||||
−0.492499 | + | 0.870313i | \(0.663917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.85629 | 1.23143 | 0.615713 | − | 0.787971i | \(-0.288868\pi\) | ||||
0.615713 | + | 0.787971i | \(0.288868\pi\) | |||||||
\(32\) | 3.01633 | 0.533216 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.25750 | −0.901653 | ||||||||
\(35\) | 1.65189 | 0.279221 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.86431 | 1.62168 | 0.810841 | − | 0.585266i | \(-0.199010\pi\) | ||||
0.810841 | + | 0.585266i | \(0.199010\pi\) | |||||||
\(38\) | −4.11485 | −0.667516 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.31847 | 0.366582 | ||||||||
\(41\) | −4.30603 | −0.672488 | −0.336244 | − | 0.941775i | \(-0.609157\pi\) | ||||
−0.336244 | + | 0.941775i | \(0.609157\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.15263 | 0.175774 | 0.0878868 | − | 0.996130i | \(-0.471989\pi\) | ||||
0.0878868 | + | 0.996130i | \(0.471989\pi\) | |||||||
\(44\) | −0.171164 | −0.0258039 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.08097 | 1.19147 | ||||||||
\(47\) | −8.26666 | −1.20582 | −0.602908 | − | 0.797810i | \(-0.705992\pi\) | ||||
−0.602908 | + | 0.797810i | \(0.705992\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.27125 | −0.610178 | ||||||||
\(50\) | −1.59605 | −0.225715 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.33496 | −0.323801 | ||||||||
\(53\) | 6.28163 | 0.862848 | 0.431424 | − | 0.902149i | \(-0.358011\pi\) | ||||
0.431424 | + | 0.902149i | \(0.358011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.312701 | −0.0421646 | ||||||||
\(56\) | 3.82986 | 0.511786 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.46605 | 1.11165 | ||||||||
\(59\) | 5.37742 | 0.700081 | 0.350040 | − | 0.936735i | \(-0.386168\pi\) | ||||
0.350040 | + | 0.936735i | \(0.386168\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7981 | 1.51059 | 0.755297 | − | 0.655383i | \(-0.227493\pi\) | ||||
0.755297 | + | 0.655383i | \(0.227493\pi\) | |||||||
\(62\) | −10.9430 | −1.38976 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.77605 | 0.597006 | ||||||||
\(65\) | −4.26577 | −0.529104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.735092 | 0.0898058 | 0.0449029 | − | 0.998991i | \(-0.485702\pi\) | ||||
0.0449029 | + | 0.998991i | \(0.485702\pi\) | |||||||
\(68\) | 1.80308 | 0.218656 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.63650 | −0.315122 | ||||||||
\(71\) | 3.08726 | 0.366390 | 0.183195 | − | 0.983077i | \(-0.441356\pi\) | ||||
0.183195 | + | 0.983077i | \(0.441356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.86570 | 0.569487 | 0.284743 | − | 0.958604i | \(-0.408092\pi\) | ||||
0.284743 | + | 0.958604i | \(0.408092\pi\) | |||||||
\(74\) | −15.7439 | −1.83019 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.41120 | 0.161876 | ||||||||
\(77\) | −0.516549 | −0.0588663 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4024 | 1.17036 | 0.585182 | − | 0.810902i | \(-0.301023\pi\) | ||||
0.585182 | + | 0.810902i | \(0.301023\pi\) | |||||||
\(80\) | −4.79513 | −0.536112 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.87263 | 0.758955 | ||||||||
\(83\) | 6.74042 | 0.739858 | 0.369929 | − | 0.929060i | \(-0.379382\pi\) | ||||
0.369929 | + | 0.929060i | \(0.379382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.29407 | 0.357292 | ||||||||
\(86\) | −1.83965 | −0.198374 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.724987 | −0.0772839 | ||||||||
\(89\) | −1.00000 | −0.106000 | ||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.04660 | −0.738685 | ||||||||
\(92\) | −2.77140 | −0.288939 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.1940 | 1.36086 | ||||||||
\(95\) | 2.57815 | 0.264512 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.83568 | 0.490989 | 0.245495 | − | 0.969398i | \(-0.421050\pi\) | ||||
0.245495 | + | 0.969398i | \(0.421050\pi\) | |||||||
\(98\) | 6.81712 | 0.688633 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.547372 | 0.0547372 | ||||||||
\(101\) | −17.9368 | −1.78478 | −0.892389 | − | 0.451268i | \(-0.850972\pi\) | ||||
−0.892389 | + | 0.451268i | \(0.850972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1543 | −1.19759 | −0.598797 | − | 0.800901i | \(-0.704354\pi\) | ||||
−0.598797 | + | 0.800901i | \(0.704354\pi\) | |||||||
\(104\) | −9.89004 | −0.969799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0258 | −0.973790 | ||||||||
\(107\) | 2.47111 | 0.238891 | 0.119446 | − | 0.992841i | \(-0.461888\pi\) | ||||
0.119446 | + | 0.992841i | \(0.461888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6997 | 1.02485 | 0.512425 | − | 0.858732i | \(-0.328747\pi\) | ||||
0.512425 | + | 0.858732i | \(0.328747\pi\) | |||||||
\(110\) | 0.499086 | 0.0475860 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.92104 | −0.748468 | ||||||||
\(113\) | 17.1698 | 1.61520 | 0.807599 | − | 0.589732i | \(-0.200767\pi\) | ||||
0.807599 | + | 0.589732i | \(0.200767\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.06311 | −0.472138 | ||||||||
\(116\) | −2.90347 | −0.269580 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.58263 | −0.790095 | ||||||||
\(119\) | 5.44145 | 0.498817 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9022 | −0.991111 | ||||||||
\(122\) | −18.8304 | −1.70482 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.75294 | 0.337024 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.530525 | −0.0470765 | −0.0235382 | − | 0.999723i | \(-0.507493\pi\) | ||||
−0.0235382 | + | 0.999723i | \(0.507493\pi\) | |||||||
\(128\) | −13.6555 | −1.20698 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.80838 | 0.597134 | ||||||||
\(131\) | −3.01167 | −0.263131 | −0.131565 | − | 0.991308i | \(-0.542000\pi\) | ||||
−0.131565 | + | 0.991308i | \(0.542000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.25882 | 0.369287 | ||||||||
\(134\) | −1.17324 | −0.101353 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.63719 | 0.654883 | ||||||||
\(137\) | −11.0835 | −0.946925 | −0.473463 | − | 0.880814i | \(-0.656996\pi\) | ||||
−0.473463 | + | 0.880814i | \(0.656996\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.13255 | 0.435337 | 0.217669 | − | 0.976023i | \(-0.430155\pi\) | ||||
0.217669 | + | 0.976023i | \(0.430155\pi\) | |||||||
\(140\) | 0.904200 | 0.0764188 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.92742 | −0.413500 | ||||||||
\(143\) | 1.33391 | 0.111547 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.30438 | −0.440505 | ||||||||
\(146\) | −7.76589 | −0.642710 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.39944 | 0.443831 | ||||||||
\(149\) | −1.19416 | −0.0978294 | −0.0489147 | − | 0.998803i | \(-0.515576\pi\) | ||||
−0.0489147 | + | 0.998803i | \(0.515576\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.29569 | −0.105442 | −0.0527208 | − | 0.998609i | \(-0.516789\pi\) | ||||
−0.0527208 | + | 0.998609i | \(0.516789\pi\) | |||||||
\(152\) | 5.97734 | 0.484826 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.824438 | 0.0664351 | ||||||||
\(155\) | 6.85629 | 0.550710 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.1427 | 1.52775 | 0.763876 | − | 0.645363i | \(-0.223294\pi\) | ||||
0.763876 | + | 0.645363i | \(0.223294\pi\) | |||||||
\(158\) | −16.6028 | −1.32084 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.01633 | 0.238462 | ||||||||
\(161\) | −8.36373 | −0.659154 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.1277 | −1.65485 | −0.827424 | − | 0.561578i | \(-0.810195\pi\) | ||||
−0.827424 | + | 0.561578i | \(0.810195\pi\) | |||||||
\(164\) | −2.35700 | −0.184050 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.7580 | −0.834986 | ||||||||
\(167\) | 11.5765 | 0.895813 | 0.447906 | − | 0.894080i | \(-0.352170\pi\) | ||||
0.447906 | + | 0.894080i | \(0.352170\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.19681 | 0.399754 | ||||||||
\(170\) | −5.25750 | −0.403232 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.630914 | 0.0481068 | ||||||||
\(173\) | −16.3647 | −1.24419 | −0.622093 | − | 0.782943i | \(-0.713718\pi\) | ||||
−0.622093 | + | 0.782943i | \(0.713718\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.65189 | 0.124871 | ||||||||
\(176\) | 1.49944 | 0.113025 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.59605 | 0.119629 | ||||||||
\(179\) | −14.5100 | −1.08452 | −0.542262 | − | 0.840209i | \(-0.682432\pi\) | ||||
−0.542262 | + | 0.840209i | \(0.682432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.6306 | −1.53346 | −0.766731 | − | 0.641968i | \(-0.778118\pi\) | ||||
−0.766731 | + | 0.641968i | \(0.778118\pi\) | |||||||
\(182\) | 11.2467 | 0.833662 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.7387 | −0.865385 | ||||||||
\(185\) | 9.86431 | 0.725238 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.03006 | −0.0753254 | ||||||||
\(188\) | −4.52494 | −0.330015 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.11485 | −0.298522 | ||||||||
\(191\) | 19.7013 | 1.42554 | 0.712768 | − | 0.701400i | \(-0.247441\pi\) | ||||
0.712768 | + | 0.701400i | \(0.247441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.5596 | 1.33595 | 0.667975 | − | 0.744184i | \(-0.267161\pi\) | ||||
0.667975 | + | 0.744184i | \(0.267161\pi\) | |||||||
\(194\) | −7.71799 | −0.554119 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.33796 | −0.166997 | ||||||||
\(197\) | 13.1125 | 0.934229 | 0.467115 | − | 0.884197i | \(-0.345294\pi\) | ||||
0.467115 | + | 0.884197i | \(0.345294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.3651 | 1.58542 | 0.792711 | − | 0.609598i | \(-0.208669\pi\) | ||||
0.792711 | + | 0.609598i | \(0.208669\pi\) | |||||||
\(200\) | 2.31847 | 0.163940 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 28.6280 | 2.01426 | ||||||||
\(203\) | −8.76227 | −0.614991 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.30603 | −0.300746 | ||||||||
\(206\) | 19.3988 | 1.35158 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.4549 | 1.41829 | ||||||||
\(209\) | −0.806189 | −0.0557653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.5062 | −1.20518 | −0.602589 | − | 0.798051i | \(-0.705864\pi\) | ||||
−0.602589 | + | 0.798051i | \(0.705864\pi\) | |||||||
\(212\) | 3.43838 | 0.236149 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.94401 | −0.269607 | ||||||||
\(215\) | 1.15263 | 0.0786084 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3259 | 0.768850 | ||||||||
\(218\) | −17.0773 | −1.15662 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.171164 | −0.0115399 | ||||||||
\(221\) | −14.0517 | −0.945223 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.4098 | 1.50067 | 0.750336 | − | 0.661057i | \(-0.229892\pi\) | ||||
0.750336 | + | 0.661057i | \(0.229892\pi\) | |||||||
\(224\) | 4.98265 | 0.332917 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −27.4038 | −1.82288 | ||||||||
\(227\) | 27.4458 | 1.82164 | 0.910821 | − | 0.412801i | \(-0.135449\pi\) | ||||
0.910821 | + | 0.412801i | \(0.135449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.7472 | 1.76750 | 0.883751 | − | 0.467958i | \(-0.155010\pi\) | ||||
0.883751 | + | 0.467958i | \(0.155010\pi\) | |||||||
\(230\) | 8.08097 | 0.532844 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.2980 | −0.807405 | ||||||||
\(233\) | 3.78149 | 0.247734 | 0.123867 | − | 0.992299i | \(-0.460470\pi\) | ||||
0.123867 | + | 0.992299i | \(0.460470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.26666 | −0.539258 | ||||||||
\(236\) | 2.94345 | 0.191602 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.68483 | −0.562954 | ||||||||
\(239\) | −20.3619 | −1.31710 | −0.658550 | − | 0.752537i | \(-0.728830\pi\) | ||||
−0.658550 | + | 0.752537i | \(0.728830\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.45826 | −0.158350 | −0.0791752 | − | 0.996861i | \(-0.525229\pi\) | ||||
−0.0791752 | + | 0.996861i | \(0.525229\pi\) | |||||||
\(242\) | 17.4005 | 1.11854 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.45795 | 0.413428 | ||||||||
\(245\) | −4.27125 | −0.272880 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9978 | −0.699772 | ||||||||
\(248\) | 15.8961 | 1.00940 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.59605 | −0.100943 | ||||||||
\(251\) | −20.7248 | −1.30814 | −0.654070 | − | 0.756434i | \(-0.726940\pi\) | ||||
−0.654070 | + | 0.756434i | \(0.726940\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.58324 | 0.0995376 | ||||||||
\(254\) | 0.846743 | 0.0531294 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.2427 | 0.765168 | ||||||||
\(257\) | 11.2294 | 0.700473 | 0.350237 | − | 0.936661i | \(-0.386101\pi\) | ||||
0.350237 | + | 0.936661i | \(0.386101\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.2948 | 1.01251 | ||||||||
\(260\) | −2.33496 | −0.144808 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.80677 | 0.296963 | ||||||||
\(263\) | 2.14224 | 0.132096 | 0.0660480 | − | 0.997816i | \(-0.478961\pi\) | ||||
0.0660480 | + | 0.997816i | \(0.478961\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.28163 | 0.385877 | ||||||||
\(266\) | −6.79729 | −0.416768 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.402369 | 0.0245786 | ||||||||
\(269\) | 12.2972 | 0.749774 | 0.374887 | − | 0.927070i | \(-0.377681\pi\) | ||||
0.374887 | + | 0.927070i | \(0.377681\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.67702 | 0.405600 | 0.202800 | − | 0.979220i | \(-0.434996\pi\) | ||||
0.202800 | + | 0.979220i | \(0.434996\pi\) | |||||||
\(272\) | −15.7955 | −0.957742 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.6898 | 1.06868 | ||||||||
\(275\) | −0.312701 | −0.0188566 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.65816 | 0.580303 | 0.290151 | − | 0.956981i | \(-0.406294\pi\) | ||||
0.290151 | + | 0.956981i | \(0.406294\pi\) | |||||||
\(278\) | −8.19180 | −0.491312 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.82986 | 0.228878 | ||||||||
\(281\) | 19.0745 | 1.13789 | 0.568944 | − | 0.822376i | \(-0.307352\pi\) | ||||
0.568944 | + | 0.822376i | \(0.307352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.01850 | 0.179431 | 0.0897156 | − | 0.995967i | \(-0.471404\pi\) | ||||
0.0897156 | + | 0.995967i | \(0.471404\pi\) | |||||||
\(284\) | 1.68988 | 0.100276 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.12899 | −0.125890 | ||||||||
\(287\) | −7.11310 | −0.419873 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.14910 | −0.361712 | ||||||||
\(290\) | 8.46605 | 0.497144 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.66334 | 0.155860 | ||||||||
\(293\) | −22.7079 | −1.32661 | −0.663305 | − | 0.748349i | \(-0.730847\pi\) | ||||
−0.663305 | + | 0.748349i | \(0.730847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.37742 | 0.313086 | ||||||||
\(296\) | 22.8701 | 1.32930 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.90594 | 0.110408 | ||||||||
\(299\) | 21.5981 | 1.24905 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.90401 | 0.109746 | ||||||||
\(302\) | 2.06798 | 0.118999 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.3625 | −0.709040 | ||||||||
\(305\) | 11.7981 | 0.675558 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4280 | 1.28003 | 0.640016 | − | 0.768362i | \(-0.278928\pi\) | ||||
0.640016 | + | 0.768362i | \(0.278928\pi\) | |||||||
\(308\) | −0.282744 | −0.0161109 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.9430 | −0.621519 | ||||||||
\(311\) | 2.80828 | 0.159243 | 0.0796213 | − | 0.996825i | \(-0.474629\pi\) | ||||
0.0796213 | + | 0.996825i | \(0.474629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.0478 | 1.35926 | 0.679631 | − | 0.733554i | \(-0.262140\pi\) | ||||
0.679631 | + | 0.733554i | \(0.262140\pi\) | |||||||
\(314\) | −30.5527 | −1.72419 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.69399 | 0.320312 | ||||||||
\(317\) | −0.567561 | −0.0318774 | −0.0159387 | − | 0.999873i | \(-0.505074\pi\) | ||||
−0.0159387 | + | 0.999873i | \(0.505074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.65869 | 0.0928686 | ||||||||
\(320\) | 4.77605 | 0.266989 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.3489 | 0.743906 | ||||||||
\(323\) | 8.49259 | 0.472540 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.26577 | −0.236622 | ||||||||
\(326\) | 33.7208 | 1.86762 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.98337 | −0.551239 | ||||||||
\(329\) | −13.6557 | −0.752860 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8342 | 1.20012 | 0.600059 | − | 0.799956i | \(-0.295144\pi\) | ||||
0.600059 | + | 0.799956i | \(0.295144\pi\) | |||||||
\(332\) | 3.68952 | 0.202489 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.4766 | −1.01099 | ||||||||
\(335\) | 0.735092 | 0.0401624 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.8567 | 1.46298 | 0.731490 | − | 0.681852i | \(-0.238825\pi\) | ||||
0.731490 | + | 0.681852i | \(0.238825\pi\) | |||||||
\(338\) | −8.29436 | −0.451153 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.80308 | 0.0977858 | ||||||||
\(341\) | −2.14397 | −0.116102 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.6189 | −1.00533 | ||||||||
\(344\) | 2.67232 | 0.144082 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26.1189 | 1.40416 | ||||||||
\(347\) | 19.1660 | 1.02889 | 0.514443 | − | 0.857525i | \(-0.327999\pi\) | ||||
0.514443 | + | 0.857525i | \(0.327999\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8496 | −0.901937 | −0.450968 | − | 0.892540i | \(-0.648921\pi\) | ||||
−0.450968 | + | 0.892540i | \(0.648921\pi\) | |||||||
\(350\) | −2.63650 | −0.140927 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.943209 | −0.0502732 | ||||||||
\(353\) | 20.7985 | 1.10699 | 0.553497 | − | 0.832851i | \(-0.313293\pi\) | ||||
0.553497 | + | 0.832851i | \(0.313293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.08726 | 0.163855 | ||||||||
\(356\) | −0.547372 | −0.0290106 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.1586 | 1.22397 | ||||||||
\(359\) | 24.1169 | 1.27284 | 0.636419 | − | 0.771343i | \(-0.280415\pi\) | ||||
0.636419 | + | 0.771343i | \(0.280415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3532 | −0.650167 | ||||||||
\(362\) | 32.9275 | 1.73063 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.85711 | −0.202167 | ||||||||
\(365\) | 4.86570 | 0.254682 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.78328 | 0.0930864 | 0.0465432 | − | 0.998916i | \(-0.485179\pi\) | ||||
0.0465432 | + | 0.998916i | \(0.485179\pi\) | |||||||
\(368\) | 24.2783 | 1.26559 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.7439 | −0.818487 | ||||||||
\(371\) | 10.3766 | 0.538725 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.80838 | 0.248968 | 0.124484 | − | 0.992222i | \(-0.460272\pi\) | ||||
0.124484 | + | 0.992222i | \(0.460272\pi\) | |||||||
\(374\) | 1.64403 | 0.0850105 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.1660 | −0.988410 | ||||||||
\(377\) | 22.6273 | 1.16536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.9770 | 0.769319 | 0.384659 | − | 0.923059i | \(-0.374319\pi\) | ||||
0.384659 | + | 0.923059i | \(0.374319\pi\) | |||||||
\(380\) | 1.41120 | 0.0723932 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −31.4442 | −1.60883 | ||||||||
\(383\) | 16.5874 | 0.847579 | 0.423789 | − | 0.905761i | \(-0.360700\pi\) | ||||
0.423789 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.516549 | −0.0263258 | ||||||||
\(386\) | −29.6220 | −1.50772 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.64692 | 0.134377 | ||||||||
\(389\) | 4.03093 | 0.204376 | 0.102188 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102188 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.6782 | −0.843455 | ||||||||
\(392\) | −9.90274 | −0.500164 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.9282 | −1.05435 | ||||||||
\(395\) | 10.4024 | 0.523402 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.69116 | 0.185254 | 0.0926270 | − | 0.995701i | \(-0.470474\pi\) | ||||
0.0926270 | + | 0.995701i | \(0.470474\pi\) | |||||||
\(398\) | −35.6958 | −1.78927 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.79513 | −0.239756 | ||||||||
\(401\) | −20.7374 | −1.03558 | −0.517788 | − | 0.855509i | \(-0.673244\pi\) | ||||
−0.517788 | + | 0.855509i | \(0.673244\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.2474 | −1.45691 | ||||||||
\(404\) | −9.81809 | −0.488468 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.9850 | 0.694065 | ||||||||
\(407\) | −3.08458 | −0.152897 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.59295 | 0.177660 | 0.0888300 | − | 0.996047i | \(-0.471687\pi\) | ||||
0.0888300 | + | 0.996047i | \(0.471687\pi\) | |||||||
\(410\) | 6.87263 | 0.339415 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.65289 | −0.327765 | ||||||||
\(413\) | 8.88293 | 0.437101 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.74042 | 0.330874 | ||||||||
\(416\) | −12.8670 | −0.630854 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.28672 | 0.0629354 | ||||||||
\(419\) | −17.8945 | −0.874204 | −0.437102 | − | 0.899412i | \(-0.643995\pi\) | ||||
−0.437102 | + | 0.899412i | \(0.643995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.0678 | −0.734362 | −0.367181 | − | 0.930150i | \(-0.619677\pi\) | ||||
−0.367181 | + | 0.930150i | \(0.619677\pi\) | |||||||
\(422\) | 27.9408 | 1.36014 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.5637 | 0.707278 | ||||||||
\(425\) | 3.29407 | 0.159786 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.4892 | 0.943150 | ||||||||
\(428\) | 1.35262 | 0.0653811 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.83965 | −0.0887156 | ||||||||
\(431\) | 21.4719 | 1.03426 | 0.517132 | − | 0.855905i | \(-0.326999\pi\) | ||||
0.517132 | + | 0.855905i | \(0.326999\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.12381 | −0.102064 | −0.0510319 | − | 0.998697i | \(-0.516251\pi\) | ||||
−0.0510319 | + | 0.998697i | \(0.516251\pi\) | |||||||
\(434\) | −18.0766 | −0.867706 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.85674 | 0.280487 | ||||||||
\(437\) | −13.0534 | −0.624431 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.5896 | −1.84178 | −0.920891 | − | 0.389819i | \(-0.872538\pi\) | ||||
−0.920891 | + | 0.389819i | \(0.872538\pi\) | |||||||
\(440\) | −0.724987 | −0.0345624 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.4273 | 1.06676 | ||||||||
\(443\) | −18.5685 | −0.882217 | −0.441108 | − | 0.897454i | \(-0.645415\pi\) | ||||
−0.441108 | + | 0.897454i | \(0.645415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | −0.0474045 | ||||||||
\(446\) | −35.7671 | −1.69362 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.88953 | 0.372745 | ||||||||
\(449\) | 36.0323 | 1.70047 | 0.850236 | − | 0.526402i | \(-0.176459\pi\) | ||||
0.850236 | + | 0.526402i | \(0.176459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.34650 | 0.0634042 | ||||||||
\(452\) | 9.39826 | 0.442057 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −43.8049 | −2.05586 | ||||||||
\(455\) | −7.04660 | −0.330350 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.4574 | 0.489175 | 0.244588 | − | 0.969627i | \(-0.421347\pi\) | ||||
0.244588 | + | 0.969627i | \(0.421347\pi\) | |||||||
\(458\) | −42.6898 | −1.99476 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.77140 | −0.129217 | ||||||||
\(461\) | 0.185494 | 0.00863930 | 0.00431965 | − | 0.999991i | \(-0.498625\pi\) | ||||
0.00431965 | + | 0.999991i | \(0.498625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.19924 | −0.334577 | −0.167288 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167288 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(464\) | 25.4352 | 1.18080 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.03544 | −0.279587 | ||||||||
\(467\) | 18.1602 | 0.840354 | 0.420177 | − | 0.907442i | \(-0.361968\pi\) | ||||
0.420177 | + | 0.907442i | \(0.361968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.21429 | 0.0560709 | ||||||||
\(470\) | 13.1940 | 0.608594 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.4674 | 0.573857 | ||||||||
\(473\) | −0.360427 | −0.0165725 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.57815 | 0.118293 | ||||||||
\(476\) | 2.97850 | 0.136519 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 32.4985 | 1.48645 | ||||||||
\(479\) | −14.5331 | −0.664035 | −0.332018 | − | 0.943273i | \(-0.607729\pi\) | ||||
−0.332018 | + | 0.943273i | \(0.607729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.0789 | −1.91863 | ||||||||
\(482\) | 3.92350 | 0.178710 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.96756 | −0.271253 | ||||||||
\(485\) | 4.83568 | 0.219577 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.5099 | 1.02002 | 0.510011 | − | 0.860168i | \(-0.329641\pi\) | ||||
0.510011 | + | 0.860168i | \(0.329641\pi\) | |||||||
\(488\) | 27.3535 | 1.23824 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.81712 | 0.307966 | ||||||||
\(491\) | −14.0158 | −0.632524 | −0.316262 | − | 0.948672i | \(-0.602428\pi\) | ||||
−0.316262 | + | 0.948672i | \(0.602428\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.4730 | −0.786944 | ||||||||
\(494\) | 17.5530 | 0.789746 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −32.8768 | −1.47621 | ||||||||
\(497\) | 5.09983 | 0.228758 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.7705 | 0.974583 | 0.487292 | − | 0.873239i | \(-0.337985\pi\) | ||||
0.487292 | + | 0.873239i | \(0.337985\pi\) | |||||||
\(500\) | 0.547372 | 0.0244792 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 33.0779 | 1.47634 | ||||||||
\(503\) | 21.0760 | 0.939731 | 0.469865 | − | 0.882738i | \(-0.344302\pi\) | ||||
0.469865 | + | 0.882738i | \(0.344302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.9368 | −0.798177 | ||||||||
\(506\) | −2.52693 | −0.112336 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.290394 | −0.0128842 | ||||||||
\(509\) | −13.1967 | −0.584934 | −0.292467 | − | 0.956276i | \(-0.594476\pi\) | ||||
−0.292467 | + | 0.956276i | \(0.594476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.03761 | 0.355563 | ||||||||
\(512\) | 7.77101 | 0.343433 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.9227 | −0.790538 | ||||||||
\(515\) | −12.1543 | −0.535581 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.58500 | 0.113688 | ||||||||
\(518\) | −26.0073 | −1.14269 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.89004 | −0.433707 | ||||||||
\(521\) | −31.6444 | −1.38637 | −0.693183 | − | 0.720762i | \(-0.743792\pi\) | ||||
−0.693183 | + | 0.720762i | \(0.743792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.5164 | 0.853393 | 0.426696 | − | 0.904395i | \(-0.359677\pi\) | ||||
0.426696 | + | 0.904395i | \(0.359677\pi\) | |||||||
\(524\) | −1.64850 | −0.0720151 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.41911 | −0.149080 | ||||||||
\(527\) | 22.5851 | 0.983822 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.63511 | 0.114570 | ||||||||
\(530\) | −10.0258 | −0.435492 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.33116 | 0.101069 | ||||||||
\(533\) | 18.3685 | 0.795629 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.47111 | 0.106835 | ||||||||
\(536\) | 1.70429 | 0.0736139 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.6269 | −0.846178 | ||||||||
\(539\) | 1.33562 | 0.0575294 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.8616 | −0.724938 | −0.362469 | − | 0.931996i | \(-0.618066\pi\) | ||||
−0.362469 | + | 0.931996i | \(0.618066\pi\) | |||||||
\(542\) | −10.6569 | −0.457751 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.93599 | 0.426002 | ||||||||
\(545\) | 10.6997 | 0.458327 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.59443 | −0.153687 | −0.0768433 | − | 0.997043i | \(-0.524484\pi\) | ||||
−0.0768433 | + | 0.997043i | \(0.524484\pi\) | |||||||
\(548\) | −6.06678 | −0.259160 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.499086 | 0.0212811 | ||||||||
\(551\) | −13.6755 | −0.582594 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1837 | 0.730725 | ||||||||
\(554\) | −15.4149 | −0.654916 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.80941 | 0.119146 | ||||||||
\(557\) | −0.0100663 | −0.000426524 0 | −0.000213262 | − | 1.00000i | \(-0.500068\pi\) | ||||
−0.000213262 | 1.00000i | \(0.500068\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.91684 | −0.207960 | ||||||||
\(560\) | −7.92104 | −0.334725 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.4438 | −1.28419 | ||||||||
\(563\) | 37.8978 | 1.59720 | 0.798601 | − | 0.601861i | \(-0.205574\pi\) | ||||
0.798601 | + | 0.601861i | \(0.205574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.1698 | 0.722339 | ||||||||
\(566\) | −4.81768 | −0.202502 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.15771 | 0.300331 | ||||||||
\(569\) | 23.1594 | 0.970891 | 0.485446 | − | 0.874267i | \(-0.338657\pi\) | ||||
0.485446 | + | 0.874267i | \(0.338657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.5298 | −1.02654 | −0.513271 | − | 0.858227i | \(-0.671566\pi\) | ||||
−0.513271 | + | 0.858227i | \(0.671566\pi\) | |||||||
\(572\) | 0.730146 | 0.0305289 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.3528 | 0.473859 | ||||||||
\(575\) | −5.06311 | −0.211146 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.7052 | −0.487292 | −0.243646 | − | 0.969864i | \(-0.578343\pi\) | ||||
−0.243646 | + | 0.969864i | \(0.578343\pi\) | |||||||
\(578\) | 9.81427 | 0.408220 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.90347 | −0.120560 | ||||||||
\(581\) | 11.1345 | 0.461935 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.96427 | −0.0813519 | ||||||||
\(584\) | 11.2810 | 0.466809 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.2429 | 1.49718 | ||||||||
\(587\) | 6.12814 | 0.252936 | 0.126468 | − | 0.991971i | \(-0.459636\pi\) | ||||
0.126468 | + | 0.991971i | \(0.459636\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.6765 | 0.728348 | ||||||||
\(590\) | −8.58263 | −0.353341 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −47.3006 | −1.94404 | ||||||||
\(593\) | 18.5032 | 0.759837 | 0.379918 | − | 0.925020i | \(-0.375952\pi\) | ||||
0.379918 | + | 0.925020i | \(0.375952\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.44145 | 0.223078 | ||||||||
\(596\) | −0.653649 | −0.0267745 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −34.4716 | −1.40965 | ||||||||
\(599\) | −45.8000 | −1.87134 | −0.935668 | − | 0.352882i | \(-0.885202\pi\) | ||||
−0.935668 | + | 0.352882i | \(0.885202\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.5468 | −1.44998 | −0.724991 | − | 0.688758i | \(-0.758156\pi\) | ||||
−0.724991 | + | 0.688758i | \(0.758156\pi\) | |||||||
\(602\) | −3.03890 | −0.123856 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.709224 | −0.0288579 | ||||||||
\(605\) | −10.9022 | −0.443238 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.3881 | −1.31459 | −0.657297 | − | 0.753632i | \(-0.728300\pi\) | ||||
−0.657297 | + | 0.753632i | \(0.728300\pi\) | |||||||
\(608\) | 7.77653 | 0.315380 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.8304 | −0.762419 | ||||||||
\(611\) | 35.2637 | 1.42662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.42107 | 0.380513 | 0.190257 | − | 0.981734i | \(-0.439068\pi\) | ||||
0.190257 | + | 0.981734i | \(0.439068\pi\) | |||||||
\(614\) | −35.7961 | −1.44461 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.19760 | −0.0482528 | ||||||||
\(617\) | 32.5296 | 1.30959 | 0.654796 | − | 0.755805i | \(-0.272754\pi\) | ||||
0.654796 | + | 0.755805i | \(0.272754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.60286 | 0.144811 | 0.0724056 | − | 0.997375i | \(-0.476932\pi\) | ||||
0.0724056 | + | 0.997375i | \(0.476932\pi\) | |||||||
\(620\) | 3.75294 | 0.150722 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.48214 | −0.179718 | ||||||||
\(623\) | −1.65189 | −0.0661817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −38.3815 | −1.53403 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.4782 | 0.418124 | ||||||||
\(629\) | 32.4937 | 1.29561 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.77736 | 0.269802 | 0.134901 | − | 0.990859i | \(-0.456928\pi\) | ||||
0.134901 | + | 0.990859i | \(0.456928\pi\) | |||||||
\(632\) | 24.1176 | 0.959348 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.905855 | 0.0359761 | ||||||||
\(635\) | −0.530525 | −0.0210532 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.2202 | 0.721909 | ||||||||
\(638\) | −2.64734 | −0.104809 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.6555 | −0.539780 | ||||||||
\(641\) | 12.3607 | 0.488220 | 0.244110 | − | 0.969748i | \(-0.421504\pi\) | ||||
0.244110 | + | 0.969748i | \(0.421504\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7782 | −0.543360 | −0.271680 | − | 0.962388i | \(-0.587579\pi\) | ||||
−0.271680 | + | 0.962388i | \(0.587579\pi\) | |||||||
\(644\) | −4.57807 | −0.180401 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.5546 | −0.533298 | ||||||||
\(647\) | 15.0963 | 0.593499 | 0.296749 | − | 0.954955i | \(-0.404097\pi\) | ||||
0.296749 | + | 0.954955i | \(0.404097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.68153 | −0.0660057 | ||||||||
\(650\) | 6.80838 | 0.267047 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.5647 | −0.452908 | ||||||||
\(653\) | −8.93166 | −0.349523 | −0.174761 | − | 0.984611i | \(-0.555915\pi\) | ||||
−0.174761 | + | 0.984611i | \(0.555915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.01167 | −0.117676 | ||||||||
\(656\) | 20.6479 | 0.806167 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.7951 | 0.849661 | ||||||||
\(659\) | 23.2632 | 0.906205 | 0.453103 | − | 0.891458i | \(-0.350317\pi\) | ||||
0.453103 | + | 0.891458i | \(0.350317\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.4474 | 1.26206 | 0.631028 | − | 0.775760i | \(-0.282633\pi\) | ||||
0.631028 | + | 0.775760i | \(0.282633\pi\) | |||||||
\(662\) | −34.8485 | −1.35443 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.6274 | 0.606462 | ||||||||
\(665\) | 4.25882 | 0.165150 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8567 | 1.03989 | ||||||||
\(668\) | 6.33662 | 0.245171 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.17324 | −0.0453263 | ||||||||
\(671\) | −3.68928 | −0.142423 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.30803 | 0.358798 | 0.179399 | − | 0.983776i | \(-0.442585\pi\) | ||||
0.179399 | + | 0.983776i | \(0.442585\pi\) | |||||||
\(674\) | −42.8647 | −1.65109 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.84458 | 0.109407 | ||||||||
\(677\) | −13.4553 | −0.517127 | −0.258564 | − | 0.965994i | \(-0.583249\pi\) | ||||
−0.258564 | + | 0.965994i | \(0.583249\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.98803 | 0.306553 | ||||||||
\(680\) | 7.63719 | 0.292873 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.42188 | 0.131031 | ||||||||
\(683\) | −5.46981 | −0.209296 | −0.104648 | − | 0.994509i | \(-0.533372\pi\) | ||||
−0.104648 | + | 0.994509i | \(0.533372\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.0835 | −0.423478 | ||||||||
\(686\) | 29.7167 | 1.13459 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.52698 | −0.210714 | ||||||||
\(689\) | −26.7960 | −1.02085 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.5511 | 1.65676 | 0.828382 | − | 0.560164i | \(-0.189262\pi\) | ||||
0.828382 | + | 0.560164i | \(0.189262\pi\) | |||||||
\(692\) | −8.95758 | −0.340516 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.5899 | −1.16118 | ||||||||
\(695\) | 5.13255 | 0.194689 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.1843 | −0.537270 | ||||||||
\(698\) | 26.8927 | 1.01790 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.904200 | 0.0341755 | ||||||||
\(701\) | 2.98694 | 0.112815 | 0.0564075 | − | 0.998408i | \(-0.482035\pi\) | ||||
0.0564075 | + | 0.998408i | \(0.482035\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4316 | 0.959172 | ||||||||
\(704\) | −1.49348 | −0.0562875 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.1954 | −1.24933 | ||||||||
\(707\) | −29.6297 | −1.11434 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.1866 | 0.720568 | 0.360284 | − | 0.932843i | \(-0.382680\pi\) | ||||
0.360284 | + | 0.932843i | \(0.382680\pi\) | |||||||
\(710\) | −4.92742 | −0.184923 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.31847 | −0.0868882 | ||||||||
\(713\) | −34.7142 | −1.30006 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.33391 | 0.0498855 | ||||||||
\(716\) | −7.94234 | −0.296819 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.4917 | −1.43650 | ||||||||
\(719\) | 43.3314 | 1.61599 | 0.807994 | − | 0.589190i | \(-0.200553\pi\) | ||||
0.807994 | + | 0.589190i | \(0.200553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.0775 | −0.747727 | ||||||||
\(722\) | 19.7163 | 0.733763 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.2926 | −0.419687 | ||||||||
\(725\) | −5.30438 | −0.197000 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.6380 | 1.43300 | 0.716502 | − | 0.697585i | \(-0.245742\pi\) | ||||
0.716502 | + | 0.697585i | \(0.245742\pi\) | |||||||
\(728\) | −16.3373 | −0.605501 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.76589 | −0.287428 | ||||||||
\(731\) | 3.79683 | 0.140431 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.6371 | 0.983865 | 0.491932 | − | 0.870633i | \(-0.336291\pi\) | ||||
0.491932 | + | 0.870633i | \(0.336291\pi\) | |||||||
\(734\) | −2.84620 | −0.105055 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.2720 | −0.562933 | ||||||||
\(737\) | −0.229864 | −0.00846716 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.8083 | 0.618304 | 0.309152 | − | 0.951013i | \(-0.399955\pi\) | ||||
0.309152 | + | 0.951013i | \(0.399955\pi\) | |||||||
\(740\) | 5.39944 | 0.198487 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.5615 | −0.607993 | ||||||||
\(743\) | 30.2622 | 1.11021 | 0.555107 | − | 0.831779i | \(-0.312677\pi\) | ||||
0.555107 | + | 0.831779i | \(0.312677\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.19416 | −0.0437506 | ||||||||
\(746\) | −7.67440 | −0.280980 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.563826 | −0.0206155 | ||||||||
\(749\) | 4.08201 | 0.149153 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5893 | −0.860787 | −0.430394 | − | 0.902641i | \(-0.641625\pi\) | ||||
−0.430394 | + | 0.902641i | \(0.641625\pi\) | |||||||
\(752\) | 39.6397 | 1.44551 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −36.1142 | −1.31520 | ||||||||
\(755\) | −1.29569 | −0.0471550 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.5701 | −1.65627 | −0.828137 | − | 0.560526i | \(-0.810599\pi\) | ||||
−0.828137 | + | 0.560526i | \(0.810599\pi\) | |||||||
\(758\) | −23.9041 | −0.868235 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.97734 | 0.216821 | ||||||||
\(761\) | −34.3822 | −1.24636 | −0.623178 | − | 0.782080i | \(-0.714159\pi\) | ||||
−0.623178 | + | 0.782080i | \(0.714159\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6748 | 0.639872 | ||||||||
\(764\) | 10.7839 | 0.390149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.4744 | −0.956558 | ||||||||
\(767\) | −22.9389 | −0.828274 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.77880 | −0.208389 | −0.104194 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104194 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(770\) | 0.824438 | 0.0297107 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.1590 | 0.365631 | ||||||||
\(773\) | −7.43120 | −0.267282 | −0.133641 | − | 0.991030i | \(-0.542667\pi\) | ||||
−0.133641 | + | 0.991030i | \(0.542667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.85629 | 0.246285 | ||||||||
\(776\) | 11.2114 | 0.402465 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.43356 | −0.230654 | ||||||||
\(779\) | −11.1016 | −0.397755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.965390 | −0.0345444 | ||||||||
\(782\) | 26.6193 | 0.951904 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.4812 | 0.731470 | ||||||||
\(785\) | 19.1427 | 0.683232 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.45412 | −0.230064 | −0.115032 | − | 0.993362i | \(-0.536697\pi\) | ||||
−0.115032 | + | 0.993362i | \(0.536697\pi\) | |||||||
\(788\) | 7.17743 | 0.255685 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.6028 | −0.590700 | ||||||||
\(791\) | 28.3627 | 1.00846 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.3280 | −1.78720 | ||||||||
\(794\) | −5.89127 | −0.209073 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.2420 | 0.433907 | ||||||||
\(797\) | 18.2999 | 0.648216 | 0.324108 | − | 0.946020i | \(-0.394936\pi\) | ||||
0.324108 | + | 0.946020i | \(0.394936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2310 | −0.963362 | ||||||||
\(800\) | 3.01633 | 0.106643 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 33.0979 | 1.16873 | ||||||||
\(803\) | −1.52151 | −0.0536929 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.36373 | −0.294783 | ||||||||
\(806\) | 46.6802 | 1.64424 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −41.5858 | −1.46298 | ||||||||
\(809\) | −48.0281 | −1.68858 | −0.844288 | − | 0.535889i | \(-0.819977\pi\) | ||||
−0.844288 | + | 0.535889i | \(0.819977\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2349 | 0.710543 | 0.355272 | − | 0.934763i | \(-0.384388\pi\) | ||||
0.355272 | + | 0.934763i | \(0.384388\pi\) | |||||||
\(812\) | −4.79622 | −0.168314 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.92314 | 0.172556 | ||||||||
\(815\) | −21.1277 | −0.740071 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.97164 | 0.103964 | ||||||||
\(818\) | −5.73452 | −0.200503 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.35700 | −0.0823099 | ||||||||
\(821\) | 18.6121 | 0.649566 | 0.324783 | − | 0.945788i | \(-0.394709\pi\) | ||||
0.324783 | + | 0.945788i | \(0.394709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.6408 | −1.38179 | −0.690896 | − | 0.722954i | \(-0.742784\pi\) | ||||
−0.690896 | + | 0.722954i | \(0.742784\pi\) | |||||||
\(824\) | −28.1792 | −0.981670 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.1776 | −0.493302 | ||||||||
\(827\) | 46.0444 | 1.60112 | 0.800561 | − | 0.599251i | \(-0.204535\pi\) | ||||
0.800561 | + | 0.599251i | \(0.204535\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.8796 | −0.794641 | −0.397320 | − | 0.917680i | \(-0.630060\pi\) | ||||
−0.397320 | + | 0.917680i | \(0.630060\pi\) | |||||||
\(830\) | −10.7580 | −0.373417 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.3735 | −0.706326 | ||||||||
\(833\) | −14.0698 | −0.487489 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.5765 | 0.400620 | ||||||||
\(836\) | −0.441285 | −0.0152622 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.5605 | 0.986607 | ||||||||
\(839\) | −51.4718 | −1.77700 | −0.888502 | − | 0.458872i | \(-0.848254\pi\) | ||||
−0.888502 | + | 0.458872i | \(0.848254\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.863551 | −0.0297776 | ||||||||
\(842\) | 24.0490 | 0.828784 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.58242 | −0.329840 | ||||||||
\(845\) | 5.19681 | 0.178776 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.0093 | −0.618807 | ||||||||
\(848\) | −30.1212 | −1.03437 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.25750 | −0.180331 | ||||||||
\(851\) | −49.9441 | −1.71206 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.3073 | −1.79097 | −0.895485 | − | 0.445093i | \(-0.853171\pi\) | ||||
−0.895485 | + | 0.445093i | \(0.853171\pi\) | |||||||
\(854\) | −31.1058 | −1.06442 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.72918 | 0.195819 | ||||||||
\(857\) | −44.2539 | −1.51169 | −0.755843 | − | 0.654753i | \(-0.772773\pi\) | ||||
−0.755843 | + | 0.654753i | \(0.772773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.9864 | 0.681928 | 0.340964 | − | 0.940076i | \(-0.389247\pi\) | ||||
0.340964 | + | 0.940076i | \(0.389247\pi\) | |||||||
\(860\) | 0.630914 | 0.0215140 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.2702 | −1.16725 | ||||||||
\(863\) | −43.4641 | −1.47953 | −0.739767 | − | 0.672863i | \(-0.765064\pi\) | ||||
−0.739767 | + | 0.672863i | \(0.765064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.3647 | −0.556417 | ||||||||
\(866\) | 3.38970 | 0.115187 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.19946 | 0.210423 | ||||||||
\(869\) | −3.25285 | −0.110345 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.13573 | −0.106250 | ||||||||
\(872\) | 24.8070 | 0.840071 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.8339 | 0.704718 | ||||||||
\(875\) | 1.65189 | 0.0558442 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.561222 | −0.0189511 | −0.00947555 | − | 0.999955i | \(-0.503016\pi\) | ||||
−0.00947555 | + | 0.999955i | \(0.503016\pi\) | |||||||
\(878\) | 61.5909 | 2.07859 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.49944 | 0.0505462 | ||||||||
\(881\) | −38.9725 | −1.31302 | −0.656509 | − | 0.754318i | \(-0.727968\pi\) | ||||
−0.656509 | + | 0.754318i | \(0.727968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.0122 | 1.51478 | 0.757390 | − | 0.652963i | \(-0.226474\pi\) | ||||
0.757390 | + | 0.652963i | \(0.226474\pi\) | |||||||
\(884\) | −7.69153 | −0.258694 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 29.6362 | 0.995649 | ||||||||
\(887\) | −50.6113 | −1.69936 | −0.849681 | − | 0.527297i | \(-0.823206\pi\) | ||||
−0.849681 | + | 0.527297i | \(0.823206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.876371 | −0.0293925 | ||||||||
\(890\) | 1.59605 | 0.0534997 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.2665 | 0.410712 | ||||||||
\(893\) | −21.3127 | −0.713201 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.5100 | −0.485014 | ||||||||
\(896\) | −22.5574 | −0.753589 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −57.5094 | −1.91911 | ||||||||
\(899\) | −36.3684 | −1.21295 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.6921 | 0.689354 | ||||||||
\(902\) | −2.14908 | −0.0715565 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.8076 | 1.32398 | ||||||||
\(905\) | −20.6306 | −0.685785 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.0299 | −0.598672 | −0.299336 | − | 0.954148i | \(-0.596765\pi\) | ||||
−0.299336 | + | 0.954148i | \(0.596765\pi\) | |||||||
\(908\) | 15.0231 | 0.498558 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 11.2467 | 0.372825 | ||||||||
\(911\) | 12.8735 | 0.426517 | 0.213258 | − | 0.976996i | \(-0.431592\pi\) | ||||
0.213258 | + | 0.976996i | \(0.431592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.10774 | −0.0697560 | ||||||||
\(914\) | −16.6905 | −0.552072 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.6406 | 0.483740 | ||||||||
\(917\) | −4.97496 | −0.164288 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.98015 | 0.263241 | 0.131621 | − | 0.991300i | \(-0.457982\pi\) | ||||
0.131621 | + | 0.991300i | \(0.457982\pi\) | |||||||
\(920\) | −11.7387 | −0.387012 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.296057 | −0.00975011 | ||||||||
\(923\) | −13.1695 | −0.433481 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.86431 | 0.324336 | ||||||||
\(926\) | 11.4903 | 0.377596 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.9997 | −0.525217 | ||||||||
\(929\) | 59.0076 | 1.93598 | 0.967989 | − | 0.250994i | \(-0.0807575\pi\) | ||||
0.967989 | + | 0.250994i | \(0.0807575\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0119 | −0.360900 | ||||||||
\(932\) | 2.06988 | 0.0678012 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.9846 | −0.948404 | ||||||||
\(935\) | −1.03006 | −0.0336866 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.28011 | −0.0418194 | −0.0209097 | − | 0.999781i | \(-0.506656\pi\) | ||||
−0.0209097 | + | 0.999781i | \(0.506656\pi\) | |||||||
\(938\) | −1.93807 | −0.0632803 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.52494 | −0.147587 | ||||||||
\(941\) | 17.8453 | 0.581739 | 0.290870 | − | 0.956763i | \(-0.406055\pi\) | ||||
0.290870 | + | 0.956763i | \(0.406055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.8019 | 0.709967 | ||||||||
\(944\) | −25.7854 | −0.839244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.575260 | 0.0187033 | ||||||||
\(947\) | −37.6144 | −1.22230 | −0.611152 | − | 0.791513i | \(-0.709293\pi\) | ||||
−0.611152 | + | 0.791513i | \(0.709293\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.7560 | −0.673767 | ||||||||
\(950\) | −4.11485 | −0.133503 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.6158 | 0.408881 | ||||||||
\(953\) | −31.4840 | −1.01987 | −0.509933 | − | 0.860214i | \(-0.670330\pi\) | ||||
−0.509933 | + | 0.860214i | \(0.670330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7013 | 0.637519 | ||||||||
\(956\) | −11.1455 | −0.360471 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.1956 | 0.749415 | ||||||||
\(959\) | −18.3087 | −0.591220 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.0087 | 0.516410 | ||||||||
\(962\) | 67.1599 | 2.16532 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.34558 | −0.0433382 | ||||||||
\(965\) | 18.5596 | 0.597455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.5286 | 0.563681 | 0.281841 | − | 0.959461i | \(-0.409055\pi\) | ||||
0.281841 | + | 0.959461i | \(0.409055\pi\) | |||||||
\(968\) | −25.2764 | −0.812415 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.71799 | −0.247810 | ||||||||
\(971\) | −37.3269 | −1.19788 | −0.598939 | − | 0.800795i | \(-0.704411\pi\) | ||||
−0.598939 | + | 0.800795i | \(0.704411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.47843 | 0.271806 | ||||||||
\(974\) | −35.9269 | −1.15117 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −56.5734 | −1.81087 | ||||||||
\(977\) | 11.3776 | 0.364001 | 0.182000 | − | 0.983298i | \(-0.441743\pi\) | ||||
0.182000 | + | 0.983298i | \(0.441743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.312701 | 0.00999398 | ||||||||
\(980\) | −2.33796 | −0.0746834 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.3699 | 0.713852 | ||||||||
\(983\) | −17.9011 | −0.570958 | −0.285479 | − | 0.958385i | \(-0.592153\pi\) | ||||
−0.285479 | + | 0.958385i | \(0.592153\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1125 | 0.417800 | ||||||||
\(986\) | 27.8878 | 0.888127 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.01987 | −0.191518 | ||||||||
\(989\) | −5.83587 | −0.185570 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.1988 | −1.30872 | −0.654362 | − | 0.756181i | \(-0.727063\pi\) | ||||
−0.654362 | + | 0.756181i | \(0.727063\pi\) | |||||||
\(992\) | 20.6808 | 0.656616 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.13957 | −0.258171 | ||||||||
\(995\) | 22.3651 | 0.709022 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.0200 | −1.20411 | −0.602053 | − | 0.798456i | \(-0.705650\pi\) | ||||
−0.602053 | + | 0.798456i | \(0.705650\pi\) | |||||||
\(998\) | −34.7468 | −1.09989 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4005.2.a.x.1.3 | yes | 17 | |
3.2 | odd | 2 | 4005.2.a.w.1.15 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4005.2.a.w.1.15 | ✓ | 17 | 3.2 | odd | 2 | ||
4005.2.a.x.1.3 | yes | 17 | 1.1 | even | 1 | trivial |