Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 55 x^{16} + 288 x^{15} + 1222 x^{14} - 6888 x^{13} - 13745 x^{12} + 88434 x^{11} + \cdots - 115488 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.83157\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.83157 | −0.819101 | −0.409550 | − | 0.912287i | \(-0.634314\pi\) | ||||
−0.409550 | + | 0.912287i | \(0.634314\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.10909 | −1.17513 | −0.587563 | − | 0.809178i | \(-0.699913\pi\) | ||||
−0.587563 | + | 0.809178i | \(0.699913\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.83870 | 1.45892 | 0.729462 | − | 0.684022i | \(-0.239771\pi\) | ||||
0.729462 | + | 0.684022i | \(0.239771\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.03048 | −1.11785 | −0.558927 | − | 0.829217i | \(-0.688787\pi\) | ||||
−0.558927 | + | 0.829217i | \(0.688787\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.83157 | −0.472908 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.45134 | −1.07961 | −0.539804 | − | 0.841790i | \(-0.681502\pi\) | ||||
−0.539804 | + | 0.841790i | \(0.681502\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.14088 | −0.720568 | −0.360284 | − | 0.932843i | \(-0.617320\pi\) | ||||
−0.360284 | + | 0.932843i | \(0.617320\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.10909 | −0.678460 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.64537 | −0.329074 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.50715 | 1.70754 | 0.853768 | − | 0.520654i | \(-0.174312\pi\) | ||||
0.853768 | + | 0.520654i | \(0.174312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.83870 | 0.842310 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.69451 | 0.962547 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.88709 | 0.803433 | 0.401716 | − | 0.915764i | \(-0.368414\pi\) | ||||
0.401716 | + | 0.915764i | \(0.368414\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.03048 | −0.645393 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.35449 | 1.30475 | 0.652376 | − | 0.757895i | \(-0.273772\pi\) | ||||
0.652376 | + | 0.757895i | \(0.273772\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.8921 | −1.96603 | −0.983013 | − | 0.183535i | \(-0.941246\pi\) | ||||
−0.983013 | + | 0.183535i | \(0.941246\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.83157 | −0.273034 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.49782 | −0.947804 | −0.473902 | − | 0.880578i | \(-0.657155\pi\) | ||||
−0.473902 | + | 0.880578i | \(0.657155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.66646 | 0.380923 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.45134 | −0.623312 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.97722 | 0.546313 | 0.273157 | − | 0.961970i | \(-0.411932\pi\) | ||||
0.273157 | + | 0.961970i | \(0.411932\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.86240 | −1.19501 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.14088 | −0.416020 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.69780 | 1.13236 | 0.566178 | − | 0.824283i | \(-0.308421\pi\) | ||||
0.566178 | + | 0.824283i | \(0.308421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6082 | −1.61432 | −0.807158 | − | 0.590336i | \(-0.798995\pi\) | ||||
−0.807158 | + | 0.590336i | \(0.798995\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.10909 | −0.391709 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.38209 | 0.915635 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9816 | 1.46378 | 0.731891 | − | 0.681422i | \(-0.238638\pi\) | ||||
0.731891 | + | 0.681422i | \(0.238638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1914 | −1.32818 | −0.664090 | − | 0.747653i | \(-0.731181\pi\) | ||||
−0.664090 | + | 0.747653i | \(0.731181\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.9336 | −1.51376 | −0.756879 | − | 0.653555i | \(-0.773277\pi\) | ||||
−0.756879 | + | 0.653555i | \(0.773277\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.64537 | −0.189991 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.0440 | −1.71442 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.60254 | 0.180300 | 0.0901499 | − | 0.995928i | \(-0.471265\pi\) | ||||
0.0901499 | + | 0.995928i | \(0.471265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.42371 | 0.595330 | 0.297665 | − | 0.954670i | \(-0.403792\pi\) | ||||
0.297665 | + | 0.954670i | \(0.403792\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.15292 | 0.884309 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.27276 | 0.664911 | 0.332455 | − | 0.943119i | \(-0.392123\pi\) | ||||
0.332455 | + | 0.943119i | \(0.392123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.5311 | 1.31362 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.50715 | 0.985846 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.75273 | 0.590218 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00312 | 0.406455 | 0.203228 | − | 0.979132i | \(-0.434857\pi\) | ||||
0.203228 | + | 0.979132i | \(0.434857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.83870 | 0.486308 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.9721 | −1.78829 | −0.894143 | − | 0.447781i | \(-0.852214\pi\) | ||||
−0.894143 | + | 0.447781i | \(0.852214\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2667 | 1.60280 | 0.801401 | − | 0.598127i | \(-0.204088\pi\) | ||||
0.801401 | + | 0.598127i | \(0.204088\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.69451 | 0.555727 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.9817 | 1.64168 | 0.820842 | − | 0.571156i | \(-0.193505\pi\) | ||||
0.820842 | + | 0.571156i | \(0.193505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.05063 | 0.387980 | 0.193990 | − | 0.981004i | \(-0.437857\pi\) | ||||
0.193990 | + | 0.981004i | \(0.437857\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.88709 | 0.463862 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.20069 | 0.583312 | 0.291656 | − | 0.956523i | \(-0.405794\pi\) | ||||
0.291656 | + | 0.956523i | \(0.405794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.83157 | 0.170794 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.03048 | −0.372618 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.8396 | 1.26868 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4130 | 1.12846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.35449 | 0.753299 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1714 | 1.08865 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.95054 | −0.705496 | −0.352748 | − | 0.935718i | \(-0.614753\pi\) | ||||
−0.352748 | + | 0.935718i | \(0.614753\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.8921 | −1.13509 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3744 | −0.993789 | −0.496894 | − | 0.867811i | \(-0.665526\pi\) | ||||
−0.496894 | + | 0.867811i | \(0.665526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.76530 | 0.846759 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.83157 | −0.157636 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.6828 | 1.42531 | 0.712654 | − | 0.701515i | \(-0.247493\pi\) | ||||
0.712654 | + | 0.701515i | \(0.247493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.7097 | 1.67176 | 0.835879 | − | 0.548914i | \(-0.184959\pi\) | ||||
0.835879 | + | 0.548914i | \(0.184959\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.49782 | −0.547215 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −19.5023 | −1.63086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.83157 | −0.152103 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.66646 | 0.219926 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.6042 | 1.85181 | 0.925903 | − | 0.377760i | \(-0.123306\pi\) | ||||
0.925903 | + | 0.377760i | \(0.123306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2717 | 0.998654 | 0.499327 | − | 0.866413i | \(-0.333581\pi\) | ||||
0.499327 | + | 0.866413i | \(0.333581\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.45134 | −0.359870 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.4130 | −1.39864 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0414 | −1.59948 | −0.799739 | − | 0.600348i | \(-0.795029\pi\) | ||||
−0.799739 | + | 0.600348i | \(0.795029\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.97722 | 0.315414 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.10909 | 0.245031 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3286 | 1.12230 | 0.561151 | − | 0.827713i | \(-0.310359\pi\) | ||||
0.561151 | + | 0.827713i | \(0.310359\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.86240 | −0.689937 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.3476 | 0.800719 | 0.400360 | − | 0.916358i | \(-0.368885\pi\) | ||||
0.400360 | + | 0.916358i | \(0.368885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.24477 | 0.249598 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.14088 | −0.240189 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.38817 | −0.105540 | −0.0527701 | − | 0.998607i | \(-0.516805\pi\) | ||||
−0.0527701 | + | 0.998607i | \(0.516805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.11560 | 0.386703 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.69780 | 0.653767 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.03157 | 0.376077 | 0.188038 | − | 0.982162i | \(-0.439787\pi\) | ||||
0.188038 | + | 0.982162i | \(0.439787\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0046 | −1.11529 | −0.557643 | − | 0.830081i | \(-0.688294\pi\) | ||||
−0.557643 | + | 0.830081i | \(0.688294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.6082 | −0.932026 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.95103 | −0.658093 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.5387 | −1.57507 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.10909 | −0.226153 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.4952 | 1.41062 | 0.705312 | − | 0.708897i | \(-0.250807\pi\) | ||||
0.705312 | + | 0.708897i | \(0.250807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.47403 | −0.106103 | −0.0530515 | − | 0.998592i | \(-0.516895\pi\) | ||||
−0.0530515 | + | 0.998592i | \(0.516895\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.38209 | 0.528642 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.60174 | −0.684096 | −0.342048 | − | 0.939682i | \(-0.611121\pi\) | ||||
−0.342048 | + | 0.939682i | \(0.611121\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.91035 | −0.135421 | −0.0677105 | − | 0.997705i | \(-0.521569\pi\) | ||||
−0.0677105 | + | 0.997705i | \(0.521569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.9816 | 0.845115 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.10909 | −0.218216 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3018 | −1.06872 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.1978 | −1.05125 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.08821 | 0.625658 | 0.312829 | − | 0.949809i | \(-0.398723\pi\) | ||||
0.312829 | + | 0.949809i | \(0.398723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.1914 | −0.766825 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 23.6127 | 1.61037 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.5586 | −2.00657 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.9336 | −0.873969 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9410 | 1.20684 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0320 | 1.60930 | 0.804652 | − | 0.593747i | \(-0.202352\pi\) | ||||
0.804652 | + | 0.593747i | \(0.202352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.64537 | −0.109691 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.46998 | 0.562172 | 0.281086 | − | 0.959683i | \(-0.409305\pi\) | ||||
0.281086 | + | 0.959683i | \(0.409305\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.15444 | −0.604942 | −0.302471 | − | 0.953159i | \(-0.597812\pi\) | ||||
−0.302471 | + | 0.953159i | \(0.597812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.0440 | −0.989821 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.65199 | 0.304762 | 0.152381 | − | 0.988322i | \(-0.451306\pi\) | ||||
0.152381 | + | 0.988322i | \(0.451306\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.9012 | 0.776347 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.60254 | 0.104096 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9170 | −1.41770 | −0.708848 | − | 0.705361i | \(-0.750785\pi\) | ||||
−0.708848 | + | 0.705361i | \(0.750785\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.6679 | 1.13809 | 0.569044 | − | 0.822307i | \(-0.307313\pi\) | ||||
0.569044 | + | 0.822307i | \(0.307313\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.88380 | −0.312014 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.6593 | 0.805490 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.42371 | 0.343714 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.6382 | 1.30267 | 0.651337 | − | 0.758789i | \(-0.274208\pi\) | ||||
0.651337 | + | 0.758789i | \(0.274208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.83870 | −0.304207 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.15292 | 0.510556 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.94398 | 0.370775 | 0.185388 | − | 0.982665i | \(-0.440646\pi\) | ||||
0.185388 | + | 0.982665i | \(0.440646\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.1944 | −0.944136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.6177 | −0.839705 | −0.419853 | − | 0.907592i | \(-0.637918\pi\) | ||||
−0.419853 | + | 0.907592i | \(0.637918\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.28454 | −0.447486 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.27276 | 0.383886 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4974 | −0.883923 | −0.441962 | − | 0.897034i | \(-0.645717\pi\) | ||||
−0.441962 | + | 0.897034i | \(0.645717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.79087 | −0.351770 | −0.175885 | − | 0.984411i | \(-0.556279\pi\) | ||||
−0.175885 | + | 0.984411i | \(0.556279\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.5311 | 0.758419 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.96145 | −0.480093 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.7006 | 1.72445 | 0.862227 | − | 0.506522i | \(-0.169069\pi\) | ||||
0.862227 | + | 0.506522i | \(0.169069\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.50715 | 0.569178 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.20665 | 0.489568 | 0.244784 | − | 0.969578i | \(-0.421283\pi\) | ||||
0.244784 | + | 0.969578i | \(0.421283\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0977388 | −0.00580997 | −0.00290499 | − | 0.999996i | \(-0.500925\pi\) | ||||
−0.00290499 | + | 0.999996i | \(0.500925\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.75273 | 0.340762 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.9749 | −1.53325 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.81444 | 0.165555 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00312 | 0.234667 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.0168 | −1.28623 | −0.643117 | − | 0.765768i | \(-0.722359\pi\) | ||||
−0.643117 | + | 0.765768i | \(0.722359\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.9306 | −0.927515 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.83870 | 0.280770 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.03048 | 0.233089 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 40.0827 | 2.31033 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.9721 | −1.03247 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.0928 | 1.32229 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.4854 | −1.28331 | −0.641655 | − | 0.766993i | \(-0.721752\pi\) | ||||
−0.641655 | + | 0.766993i | \(0.721752\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.2667 | 0.925379 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.6844 | −0.946083 | −0.473042 | − | 0.881040i | \(-0.656844\pi\) | ||||
−0.473042 | + | 0.881040i | \(0.656844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.1953 | −0.745842 | −0.372921 | − | 0.927863i | \(-0.621644\pi\) | ||||
−0.372921 | + | 0.927863i | \(0.621644\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.69451 | 0.320849 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0287 | 0.675599 | 0.337800 | − | 0.941218i | \(-0.390317\pi\) | ||||
0.337800 | + | 0.941218i | \(0.390317\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.83870 | 0.270915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.9817 | 0.947826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9811 | 0.777931 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.63163 | 0.367856 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.05063 | 0.224000 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.2023 | 1.11379 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.846716 | −0.0465397 | −0.0232699 | − | 0.999729i | \(-0.507408\pi\) | ||||
−0.0232699 | + | 0.999729i | \(0.507408\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.88709 | 0.267811 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.9450 | −1.19898 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3107 | 1.10640 | 0.553198 | − | 0.833050i | \(-0.313407\pi\) | ||||
0.553198 | + | 0.833050i | \(0.313407\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.20069 | 0.336775 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 46.0023 | 2.49116 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4734 | 0.727494 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.83157 | 0.0986082 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.24008 | −0.388668 | −0.194334 | − | 0.980935i | \(-0.562254\pi\) | ||||
−0.194334 | + | 0.980935i | \(0.562254\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.49870 | 0.240810 | 0.120405 | − | 0.992725i | \(-0.461581\pi\) | ||||
0.120405 | + | 0.992725i | \(0.461581\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.03048 | −0.215131 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.0463 | −1.06696 | −0.533480 | − | 0.845813i | \(-0.679116\pi\) | ||||
−0.533480 | + | 0.845813i | \(0.679116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.4978 | 1.08791 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.8396 | 0.732471 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.94647 | −0.102731 | −0.0513653 | − | 0.998680i | \(-0.516357\pi\) | ||||
−0.0513653 | + | 0.998680i | \(0.516357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.13486 | −0.480782 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.4130 | 0.651515 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.6887 | 1.23992 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.8526 | 1.87149 | 0.935746 | − | 0.352675i | \(-0.114728\pi\) | ||||
0.935746 | + | 0.352675i | \(0.114728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.35449 | 0.434918 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.3655 | −0.641987 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.6842 | 1.79588 | 0.897940 | − | 0.440117i | \(-0.145063\pi\) | ||||
0.897940 | + | 0.440117i | \(0.145063\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.1714 | 0.628530 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.03048 | −0.207580 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.7325 | 1.21906 | 0.609529 | − | 0.792764i | \(-0.291359\pi\) | ||||
0.609529 | + | 0.792764i | \(0.291359\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.95054 | −0.407319 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.4865 | −1.14900 | −0.574502 | − | 0.818503i | \(-0.694804\pi\) | ||||
−0.574502 | + | 0.818503i | \(0.694804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.5540 | 1.40428 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.8921 | −0.655342 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.64191 | 0.184652 | 0.0923261 | − | 0.995729i | \(-0.470570\pi\) | ||||
0.0923261 | + | 0.995729i | \(0.470570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.45134 | 0.225114 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.3744 | −0.573764 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.93516 | −0.147684 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3873 | 1.27415 | 0.637077 | − | 0.770800i | \(-0.280143\pi\) | ||||
0.637077 | + | 0.770800i | \(0.280143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.76530 | 0.488876 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9834 | 0.997922 | 0.498961 | − | 0.866625i | \(-0.333715\pi\) | ||||
0.498961 | + | 0.866625i | \(0.333715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38.3184 | −1.90877 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.83157 | −0.0910112 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.6472 | 1.17215 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.0045 | 0.840821 | 0.420410 | − | 0.907334i | \(-0.361886\pi\) | ||||
0.420410 | + | 0.907334i | \(0.361886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.6828 | 0.822902 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −27.0423 | −1.33066 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.93388 | −0.487635 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.7097 | 0.965190 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.9932 | 1.61182 | 0.805912 | − | 0.592035i | \(-0.201675\pi\) | ||||
0.805912 | + | 0.592035i | \(0.201675\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.1890 | 1.76374 | 0.881871 | − | 0.471491i | \(-0.156284\pi\) | ||||
0.881871 | + | 0.471491i | \(0.156284\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.49782 | −0.315935 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.32410 | 0.355271 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.2001 | 1.89703 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.5023 | −0.941579 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.5089 | −1.80674 | −0.903369 | − | 0.428863i | \(-0.858914\pi\) | ||||
−0.903369 | + | 0.428863i | \(0.858914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.895806 | 0.0430497 | 0.0215248 | − | 0.999768i | \(-0.493148\pi\) | ||||
0.0215248 | + | 0.999768i | \(0.493148\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.83157 | −0.0878168 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.14088 | 0.150249 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.5024 | 1.16944 | 0.584718 | − | 0.811237i | \(-0.301205\pi\) | ||||
0.584718 | + | 0.811237i | \(0.301205\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.66646 | 0.126974 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.2559 | −1.38999 | −0.694994 | − | 0.719015i | \(-0.744593\pi\) | ||||
−0.694994 | + | 0.719015i | \(0.744593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.4890 | −0.544629 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.6042 | 1.06914 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.320562 | 0.0151283 | 0.00756413 | − | 0.999971i | \(-0.497592\pi\) | ||||
0.00756413 | + | 0.999971i | \(0.497592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.4249 | 1.90353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.2717 | 0.576573 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.9516 | −1.07599 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.3928 | 0.720047 | 0.360024 | − | 0.932943i | \(-0.382769\pi\) | ||||
0.360024 | + | 0.932943i | \(0.382769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.45134 | −0.207771 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.6362 | 1.10085 | 0.550424 | − | 0.834885i | \(-0.314466\pi\) | ||||
0.550424 | + | 0.834885i | \(0.314466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6247 | 0.679668 | 0.339834 | − | 0.940485i | \(-0.389629\pi\) | ||||
0.339834 | + | 0.940485i | \(0.389629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.4130 | −0.807507 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.9948 | −1.34172 | −0.670859 | − | 0.741585i | \(-0.734075\pi\) | ||||
−0.670859 | + | 0.741585i | \(0.734075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −37.2518 | −1.72013 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.0414 | −0.923459 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −62.3810 | −2.86828 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.16791 | 0.237120 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.97722 | 0.182104 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.13630 | −0.143301 | −0.0716507 | − | 0.997430i | \(-0.522827\pi\) | ||||
−0.0716507 | + | 0.997430i | \(0.522827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.6973 | −0.898121 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.10909 | 0.141469 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.33198 | −0.332928 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.0683 | 0.773437 | 0.386719 | − | 0.922198i | \(-0.373608\pi\) | ||||
0.386719 | + | 0.922198i | \(0.373608\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.3286 | 0.647962 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.15595 | 0.368073 | 0.184036 | − | 0.982919i | \(-0.441084\pi\) | ||||
0.184036 | + | 0.982919i | \(0.441084\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.45134 | −0.200478 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.86240 | −0.398335 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.7952 | 1.56078 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9606 | −0.580195 | −0.290098 | − | 0.956997i | \(-0.593688\pi\) | ||||
−0.290098 | + | 0.956997i | \(0.593688\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.3476 | 0.462295 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.9798 | −1.06921 | −0.534604 | − | 0.845103i | \(-0.679539\pi\) | ||||
−0.534604 | + | 0.845103i | \(0.679539\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.9170 | 1.46479 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.24477 | 0.144105 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.9181 | −1.37042 | −0.685209 | − | 0.728346i | \(-0.740289\pi\) | ||||
−0.685209 | + | 0.728346i | \(0.740289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.2116 | 1.77886 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.14088 | −0.138673 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.7935 | −1.31286 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.4410 | −1.38277 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.38817 | −0.0609337 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.0628 | 0.484672 | 0.242336 | − | 0.970192i | \(-0.422086\pi\) | ||||
0.242336 | + | 0.970192i | \(0.422086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.79862 | −0.122375 | −0.0611876 | − | 0.998126i | \(-0.519489\pi\) | ||||
−0.0611876 | + | 0.998126i | \(0.519489\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.11560 | 0.223263 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.3196 | −1.84347 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.69780 | 0.377452 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.6726 | −1.45852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31.1031 | −1.34470 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.03157 | 0.217128 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.9022 | 0.555737 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.1977 | −1.12633 | −0.563164 | − | 0.826345i | \(-0.690416\pi\) | ||||
−0.563164 | + | 0.826345i | \(0.690416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0046 | −0.643910 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.41899 | −0.317795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.9076 | −1.02221 | −0.511107 | − | 0.859517i | \(-0.670764\pi\) | ||||
−0.511107 | + | 0.859517i | \(0.670764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.6082 | −0.538105 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.14088 | −0.133806 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.98244 | −0.211875 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.95103 | −0.379950 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.4004 | 1.49996 | 0.749981 | − | 0.661459i | \(-0.230062\pi\) | ||||
0.749981 | + | 0.661459i | \(0.230062\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.9613 | 2.19773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.5387 | −0.909365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.8707 | −0.795306 | −0.397653 | − | 0.917536i | \(-0.630175\pi\) | ||||
−0.397653 | + | 0.917536i | \(0.630175\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3570 | −0.477791 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.10909 | −0.130570 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.91386 | −0.206000 | −0.103000 | − | 0.994681i | \(-0.532844\pi\) | ||||
−0.103000 | + | 0.994681i | \(0.532844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.9641 | −1.54690 | −0.773450 | − | 0.633857i | \(-0.781471\pi\) | ||||
−0.773450 | + | 0.633857i | \(0.781471\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.4952 | 0.814424 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.64537 | 0.0686166 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.5606 | −0.897579 | −0.448790 | − | 0.893637i | \(-0.648145\pi\) | ||||
−0.448790 | + | 0.893637i | \(0.648145\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.47403 | −0.0612586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.8628 | −0.699588 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.2446 | 0.797029 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.38209 | 0.305212 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.54546 | −0.105062 | −0.0525312 | − | 0.998619i | \(-0.516729\pi\) | ||||
−0.0525312 | + | 0.998619i | \(0.516729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.8608 | −1.23039 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.60174 | −0.394963 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.1345 | 1.27854 | 0.639271 | − | 0.768981i | \(-0.279236\pi\) | ||||
0.639271 | + | 0.768981i | \(0.279236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25.3482 | −1.03917 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.91035 | −0.0781854 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.6912 | 1.09057 | 0.545286 | − | 0.838250i | \(-0.316421\pi\) | ||||
0.545286 | + | 0.838250i | \(0.316421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2438 | 0.703390 | 0.351695 | − | 0.936115i | \(-0.385605\pi\) | ||||
0.351695 | + | 0.936115i | \(0.385605\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9816 | 0.487927 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.7353 | −0.924320 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.7673 | −0.964685 | −0.482343 | − | 0.875983i | \(-0.660214\pi\) | ||||
−0.482343 | + | 0.875983i | \(0.660214\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.10909 | −0.125987 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.1893 | 1.05951 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.5084 | −1.67651 | −0.838255 | − | 0.545279i | \(-0.816424\pi\) | ||||
−0.838255 | + | 0.545279i | \(0.816424\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.3018 | −0.617028 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.1306 | 0.931202 | 0.465601 | − | 0.884995i | \(-0.345838\pi\) | ||||
0.465601 | + | 0.884995i | \(0.345838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.4359 | 1.42429 | 0.712146 | − | 0.702032i | \(-0.247724\pi\) | ||||
0.712146 | + | 0.702032i | \(0.247724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.5026 | −0.781354 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.0659 | −0.562637 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.1978 | −0.606941 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.7541 | −0.867393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.3568 | 1.48715 | 0.743576 | − | 0.668651i | \(-0.233128\pi\) | ||||
0.743576 | + | 0.668651i | \(0.233128\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.08821 | 0.361224 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.5619 | 0.577873 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.7471 | −0.425816 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.1914 | −0.442726 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.95954 | −0.195890 | −0.0979451 | − | 0.995192i | \(-0.531227\pi\) | ||||
−0.0979451 | + | 0.995192i | \(0.531227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.01098 | −0.276486 | −0.138243 | − | 0.990398i | \(-0.544146\pi\) | ||||
−0.138243 | + | 0.990398i | \(0.544146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.6127 | 0.929750 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.9377 | 1.45217 | 0.726086 | − | 0.687604i | \(-0.241338\pi\) | ||||
0.726086 | + | 0.687604i | \(0.241338\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.0860 | 1.65202 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.5586 | −1.15849 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.7151 | −1.31937 | −0.659686 | − | 0.751541i | \(-0.729311\pi\) | ||||
−0.659686 | + | 0.751541i | \(0.729311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.8330 | 0.814013 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.9336 | −0.504586 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.80164 | −0.148091 | −0.0740455 | − | 0.997255i | \(-0.523591\pi\) | ||||
−0.0740455 | + | 0.997255i | \(0.523591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.1948 | 1.29113 | 0.645564 | − | 0.763706i | \(-0.276622\pi\) | ||||
0.645564 | + | 0.763706i | \(0.276622\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.9410 | 0.696772 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.8858 | −0.693581 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0320 | 0.929132 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −61.0074 | −2.35516 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3365 | 1.16939 | 0.584693 | − | 0.811255i | \(-0.301215\pi\) | ||||
0.584693 | + | 0.811255i | \(0.301215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.64537 | −0.0633303 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.9494 | 0.882016 | 0.441008 | − | 0.897503i | \(-0.354621\pi\) | ||||
0.441008 | + | 0.897503i | \(0.354621\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.4461 | −0.477636 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.46998 | 0.324570 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.74528 | −0.143309 | −0.0716547 | − | 0.997430i | \(-0.522828\pi\) | ||||
−0.0716547 | + | 0.997430i | \(0.522828\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.5557 | −1.16747 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.15444 | −0.349264 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.0301 | −0.610698 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2703 | 0.618950 | 0.309475 | − | 0.950908i | \(-0.399847\pi\) | ||||
0.309475 | + | 0.950908i | \(0.399847\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.0440 | −0.571473 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.0997 | −1.36934 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.1887 | −1.40862 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.65199 | 0.175954 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.24727 | −0.122648 | −0.0613239 | − | 0.998118i | \(-0.519532\pi\) | ||||
−0.0613239 | + | 0.998118i | \(0.519532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.3498 | −0.578928 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.9012 | 0.448224 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 55.8768 | 2.10146 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8398 | 1.42110 | 0.710552 | − | 0.703645i | \(-0.248445\pi\) | ||||
0.710552 | + | 0.703645i | \(0.248445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.60254 | 0.0600999 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.50715 | −0.356046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.7197 | 1.33584 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.9170 | −0.818507 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.70119 | 0.138031 | 0.0690155 | − | 0.997616i | \(-0.478014\pi\) | ||||
0.0690155 | + | 0.997616i | \(0.478014\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.5746 | −1.88350 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.6679 | 0.657076 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.64537 | −0.0611075 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.7573 | −0.806932 | −0.403466 | − | 0.914995i | \(-0.632195\pi\) | ||||
−0.403466 | + | 0.914995i | \(0.632195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 57.3871 | 2.12254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.28425 | 0.158243 | 0.0791213 | − | 0.996865i | \(-0.474789\pi\) | ||||
0.0791213 | + | 0.996865i | \(0.474789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.88380 | −0.180142 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 57.9752 | 2.13555 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.4991 | 0.386215 | 0.193107 | − | 0.981178i | \(-0.438143\pi\) | ||||
0.193107 | + | 0.981178i | \(0.438143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.6593 | 0.465050 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.4932 | −1.30212 | −0.651060 | − | 0.759026i | \(-0.725675\pi\) | ||||
−0.651060 | + | 0.759026i | \(0.725675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −41.4010 | −1.51682 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.42371 | 0.198443 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.7977 | −1.92919 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.7618 | 1.23199 | 0.615993 | − | 0.787752i | \(-0.288755\pi\) | ||||
0.615993 | + | 0.787752i | \(0.288755\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.6382 | 0.752099 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.4764 | −0.817999 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.5938 | −1.36637 | −0.683185 | − | 0.730246i | \(-0.739406\pi\) | ||||
−0.683185 | + | 0.730246i | \(0.739406\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.83870 | −0.175634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.0023 | 1.01508 | 0.507542 | − | 0.861627i | \(-0.330554\pi\) | ||||
0.507542 | + | 0.861627i | \(0.330554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.5938 | −0.455925 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.15292 | 0.294770 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35.0563 | −1.26581 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.22693 | −0.152427 | −0.0762135 | − | 0.997092i | \(-0.524283\pi\) | ||||
−0.0762135 | + | 0.997092i | \(0.524283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.94398 | 0.214067 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.2902 | −1.37720 | −0.688602 | − | 0.725139i | \(-0.741775\pi\) | ||||
−0.688602 | + | 0.725139i | \(0.741775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.6428 | −0.561905 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.1944 | −0.545097 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.2405 | −0.940163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.1520 | −1.93771 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.7071 | 1.31013 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.7226 | −1.30902 | −0.654509 | − | 0.756054i | \(-0.727125\pi\) | ||||
−0.654509 | + | 0.756054i | \(0.727125\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.6177 | −0.484804 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.2785 | −0.685465 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 50.8171 | 1.80457 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.28454 | −0.258356 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.04095 | −0.249403 | −0.124702 | − | 0.992194i | \(-0.539797\pi\) | ||||
−0.124702 | + | 0.992194i | \(0.539797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.9240 | 1.02326 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.27276 | 0.221637 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −62.5816 | −2.20846 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.69451 | −0.200705 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4974 | −0.510333 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.8928 | −1.05098 | −0.525488 | − | 0.850801i | \(-0.676117\pi\) | ||||
−0.525488 | + | 0.850801i | \(0.676117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1299 | 0.952659 | 0.476330 | − | 0.879267i | \(-0.341967\pi\) | ||||
0.476330 | + | 0.879267i | \(0.341967\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.79087 | −0.203095 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.2438 | −0.919279 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.4926 | 1.41666 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.5311 | 0.437873 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.81157 | −0.0981246 | −0.0490623 | − | 0.998796i | \(-0.515623\pi\) | ||||
−0.0490623 | + | 0.998796i | \(0.515623\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.4840 | −0.748883 | −0.374442 | − | 0.927250i | \(-0.622166\pi\) | ||||
−0.374442 | + | 0.927250i | \(0.622166\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.96145 | −0.277182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2327 | 1.22516 | 0.612580 | − | 0.790409i | \(-0.290132\pi\) | ||||
0.612580 | + | 0.790409i | \(0.290132\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.8597 | 1.21073 | 0.605363 | − | 0.795949i | \(-0.293028\pi\) | ||||
0.605363 | + | 0.795949i | \(0.293028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.7006 | 0.995614 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.8693 | −0.411248 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.9523 | −0.655870 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.50715 | 0.328615 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.7081 | 0.887543 | 0.443772 | − | 0.896140i | \(-0.353640\pi\) | ||||
0.443772 | + | 0.896140i | \(0.353640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.20665 | 0.282652 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.94301 | −0.204446 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.5933 | −1.32608 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.0977388 | −0.00335439 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.88709 | −0.167527 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.0372 | 0.446387 | 0.223193 | − | 0.974774i | \(-0.428352\pi\) | ||||
0.223193 | + | 0.974774i | \(0.428352\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.75273 | 0.196739 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.3866 | −1.03799 | −0.518994 | − | 0.854778i | \(-0.673693\pi\) | ||||
−0.518994 | + | 0.854778i | \(0.673693\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.07450 | 0.104901 | 0.0524503 | − | 0.998624i | \(-0.483297\pi\) | ||||
0.0524503 | + | 0.998624i | \(0.483297\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.9749 | −0.885222 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.7487 | 1.82963 | 0.914813 | − | 0.403877i | \(-0.132338\pi\) | ||||
0.914813 | + | 0.403877i | \(0.132338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.54252 | 0.0864481 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.81444 | 0.0955833 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.75421 | 0.263044 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.2915 | −1.63629 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.00312 | 0.135485 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.8421 | −1.27930 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.9284 | −1.55089 | −0.775446 | − | 0.631414i | \(-0.782475\pi\) | ||||
−0.775446 | + | 0.631414i | \(0.782475\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.0168 | −0.742608 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.2828 | −1.25609 | −0.628045 | − | 0.778177i | \(-0.716144\pi\) | ||||
−0.628045 | + | 0.778177i | \(0.716144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.4023 | 0.350066 | 0.175033 | − | 0.984563i | \(-0.443997\pi\) | ||||
0.175033 | + | 0.984563i | \(0.443997\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.9306 | −0.535501 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.9270 | −0.937696 | −0.468848 | − | 0.883279i | \(-0.655331\pi\) | ||||
−0.468848 | + | 0.883279i | \(0.655331\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.7190 | 0.829048 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.83870 | 0.162103 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20.4089 | 0.682957 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.21564 | −0.308045 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.03048 | 0.134574 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.50715 | 0.317081 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.7040 | −0.589804 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 40.0827 | 1.33387 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.4820 | 0.913531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.1754 | −0.570301 | −0.285150 | − | 0.958483i | \(-0.592044\pi\) | ||||
−0.285150 | + | 0.958483i | \(0.592044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.9721 | −0.596096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3579 | −1.56904 | −0.784519 | − | 0.620105i | \(-0.787090\pi\) | ||||
−0.784519 | + | 0.620105i | \(0.787090\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.2437 | 0.868541 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.0928 | 0.763423 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35.3642 | 1.16783 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8387 | 0.654418 | 0.327209 | − | 0.944952i | \(-0.393892\pi\) | ||||
0.327209 | + | 0.944952i | \(0.393892\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.4854 | −0.740920 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.1069 | 1.48471 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.04107 | −0.264389 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.2667 | 0.534268 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.1487 | 0.529820 | 0.264910 | − | 0.964273i | \(-0.414658\pi\) | ||||
0.264910 | + | 0.964273i | \(0.414658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.37504 | −0.274481 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.6844 | −0.546221 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 39.4496 | 1.29014 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.6162 | 1.58822 | 0.794110 | − | 0.607774i | \(-0.207937\pi\) | ||||
0.794110 | + | 0.607774i | \(0.207937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.1953 | −0.430612 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.0398 | −0.327289 | −0.163644 | − | 0.986519i | \(-0.552325\pi\) | ||||
−0.163644 | + | 0.986519i | \(0.552325\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.35449 | −0.272060 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.69451 | 0.185242 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.37566 | −0.272172 | −0.136086 | − | 0.990697i | \(-0.543452\pi\) | ||||
−0.136086 | + | 0.990697i | \(0.543452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 52.1284 | 1.69216 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0287 | 0.390057 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.8507 | −1.19371 | −0.596856 | − | 0.802349i | \(-0.703584\pi\) | ||||
−0.596856 | + | 0.802349i | \(0.703584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.7067 | −1.15544 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.83870 | 0.156413 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −51.8684 | −1.67492 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.3860 | 1.91568 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.9817 | 0.547228 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.69978 | 0.0869091 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.7974 | 0.990377 | 0.495189 | − | 0.868786i | \(-0.335099\pi\) | ||||
0.495189 | + | 0.868786i | \(0.335099\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.9811 | 0.449139 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.1169 | 1.03068 | 0.515340 | − | 0.856986i | \(-0.327666\pi\) | ||||
0.515340 | + | 0.856986i | \(0.327666\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −61.2794 | −1.96453 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.63163 | 0.212382 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.0375 | −1.63283 | −0.816416 | − | 0.577464i | \(-0.804043\pi\) | ||||
−0.816416 | + | 0.577464i | \(0.804043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.3520 | 0.970054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.05063 | 0.129327 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.9284 | 0.444246 | 0.222123 | − | 0.975019i | \(-0.428701\pi\) | ||||
0.222123 | + | 0.975019i | \(0.428701\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5862 | 0.560344 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.2023 | 0.643047 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.8921 | 0.409945 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.2564 | −1.69174 | −0.845872 | − | 0.533386i | \(-0.820919\pi\) | ||||
−0.845872 | + | 0.533386i | \(0.820919\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.846716 | −0.0268697 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.49893 | 0.110924 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0378 | −0.697943 | −0.348971 | − | 0.937133i | \(-0.613469\pi\) | ||||
−0.348971 | + | 0.937133i | \(0.613469\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.88709 | 0.154621 |
(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 | 8004.2.a.k.1.7 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.k.1.7 | ✓ | 18 | 1.1 | even | 1 | trivial |