Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.526440\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.3400 | −1.72982 | −0.864909 | − | 0.501928i | \(-0.832624\pi\) | ||||
−0.864909 | + | 0.501928i | \(0.832624\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.84136 | −0.261409 | −0.130704 | − | 0.991421i | \(-0.541724\pi\) | ||||
−0.130704 | + | 0.991421i | \(0.541724\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −61.0728 | −1.67401 | −0.837006 | − | 0.547194i | \(-0.815696\pi\) | ||||
−0.837006 | + | 0.547194i | \(0.815696\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −58.0199 | −0.998711 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −41.7885 | −0.596188 | −0.298094 | − | 0.954537i | \(-0.596351\pi\) | ||||
−0.298094 | + | 0.954537i | \(0.596351\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −107.561 | −1.29875 | −0.649374 | − | 0.760469i | \(-0.724969\pi\) | ||||
−0.649374 | + | 0.760469i | \(0.724969\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.5241 | −0.150925 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.5138 | −0.258502 | −0.129251 | − | 0.991612i | \(-0.541257\pi\) | ||||
−0.129251 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 249.034 | 1.99227 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 89.8886 | 0.575583 | 0.287791 | − | 0.957693i | \(-0.407079\pi\) | ||||
0.287791 | + | 0.957693i | \(0.407079\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −183.108 | −1.06087 | −0.530437 | − | 0.847724i | \(-0.677972\pi\) | ||||
−0.530437 | + | 0.847724i | \(0.677972\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −183.218 | −0.966491 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 93.6318 | 0.452190 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −418.029 | −1.85739 | −0.928696 | − | 0.370843i | \(-0.879069\pi\) | ||||
−0.928696 | + | 0.370843i | \(0.879069\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −142.674 | −0.543460 | −0.271730 | − | 0.962373i | \(-0.587596\pi\) | ||||
−0.271730 | + | 0.962373i | \(0.587596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −71.0935 | −0.252132 | −0.126066 | − | 0.992022i | \(-0.540235\pi\) | ||||
−0.126066 | + | 0.992022i | \(0.540235\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −174.060 | −0.576606 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −323.711 | −1.00464 | −0.502321 | − | 0.864681i | \(-0.667520\pi\) | ||||
−0.502321 | + | 0.864681i | \(0.667520\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −319.561 | −0.931665 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −125.365 | −0.344209 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25.1047 | 0.0650641 | 0.0325321 | − | 0.999471i | \(-0.489643\pi\) | ||||
0.0325321 | + | 0.999471i | \(0.489643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1181.15 | 2.89574 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −322.683 | −0.749832 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −684.508 | −1.51043 | −0.755215 | − | 0.655477i | \(-0.772467\pi\) | ||||
−0.755215 | + | 0.655477i | \(0.772467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −308.125 | −0.646744 | −0.323372 | − | 0.946272i | \(-0.604816\pi\) | ||||
−0.323372 | + | 0.946272i | \(0.604816\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −43.5723 | −0.0871363 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 251.420 | 0.479765 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 672.808 | 1.22681 | 0.613407 | − | 0.789767i | \(-0.289798\pi\) | ||||
0.613407 | + | 0.789767i | \(0.289798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −85.5413 | −0.149246 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 326.837 | 0.546315 | 0.273158 | − | 0.961969i | \(-0.411932\pi\) | ||||
0.273158 | + | 0.961969i | \(0.411932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 24.3058 | 0.0389695 | 0.0194847 | − | 0.999810i | \(-0.493797\pi\) | ||||
0.0194847 | + | 0.999810i | \(0.493797\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 747.103 | 1.15024 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 295.675 | 0.437602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −166.810 | −0.237565 | −0.118783 | − | 0.992920i | \(-0.537899\pi\) | ||||
−0.118783 | + | 0.992920i | \(0.537899\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −201.093 | −0.265938 | −0.132969 | − | 0.991120i | \(-0.542451\pi\) | ||||
−0.132969 | + | 0.991120i | \(0.542451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 808.188 | 1.03130 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 269.666 | 0.332313 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 108.834 | 0.129622 | 0.0648109 | − | 0.997898i | \(-0.479356\pi\) | ||||
0.0648109 | + | 0.997898i | \(0.479356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 62.9377 | 0.0725018 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −549.323 | −0.612496 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2080.23 | 2.24660 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1157.95 | 1.21208 | 0.606041 | − | 0.795434i | \(-0.292757\pi\) | ||||
0.606041 | + | 0.795434i | \(0.292757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −549.655 | −0.558004 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1702.75 | −1.67752 | −0.838761 | − | 0.544500i | \(-0.816719\pi\) | ||||
−0.838761 | + | 0.544500i | \(0.816719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1455.14 | 1.39203 | 0.696015 | − | 0.718027i | \(-0.254955\pi\) | ||||
0.696015 | + | 0.718027i | \(0.254955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 280.895 | 0.261072 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −822.762 | −0.743359 | −0.371679 | − | 0.928361i | \(-0.621218\pi\) | ||||
−0.371679 | + | 0.928361i | \(0.621218\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −457.264 | −0.401816 | −0.200908 | − | 0.979610i | \(-0.564389\pi\) | ||||
−0.200908 | + | 0.979610i | \(0.564389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1254.09 | −1.07237 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −381.693 | −0.317758 | −0.158879 | − | 0.987298i | \(-0.550788\pi\) | ||||
−0.158879 | + | 0.987298i | \(0.550788\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 551.456 | 0.447161 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 202.313 | 0.155849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2398.88 | 1.80232 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −428.021 | −0.313767 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2398.82 | −1.71645 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1129.09 | 0.788905 | 0.394452 | − | 0.918916i | \(-0.370934\pi\) | ||||
0.394452 | + | 0.918916i | \(0.370934\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −213.281 | −0.145568 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −852.761 | −0.568749 | −0.284374 | − | 0.958713i | \(-0.591786\pi\) | ||||
−0.284374 | + | 0.958713i | \(0.591786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 520.742 | 0.339504 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −522.179 | −0.332904 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −488.903 | −0.304889 | −0.152445 | − | 0.988312i | \(-0.548715\pi\) | ||||
−0.152445 | + | 0.988312i | \(0.548715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 407.123 | 0.248430 | 0.124215 | − | 0.992255i | \(-0.460359\pi\) | ||||
0.124215 | + | 0.992255i | \(0.460359\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −971.134 | −0.580030 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 793.946 | 0.464287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1738.44 | −0.995654 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −958.684 | −0.537897 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1717.63 | −0.944388 | −0.472194 | − | 0.881495i | \(-0.656538\pi\) | ||||
−0.472194 | + | 0.881495i | \(0.656538\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1341.79 | −0.723133 | −0.361567 | − | 0.932346i | \(-0.617758\pi\) | ||||
−0.361567 | + | 0.932346i | \(0.617758\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −376.096 | −0.198729 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3541.30 | 1.83512 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 760.546 | 0.386612 | 0.193306 | − | 0.981138i | \(-0.438079\pi\) | ||||
0.193306 | + | 0.981138i | \(0.438079\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 75.3142 | 0.0375648 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 138.046 | 0.0675746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2712.09 | 1.30323 | 0.651616 | − | 0.758549i | \(-0.274091\pi\) | ||||
0.651616 | + | 0.758549i | \(0.274091\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3543.44 | 1.67185 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1551.69 | −0.719004 | −0.359502 | − | 0.933144i | \(-0.617053\pi\) | ||||
−0.359502 | + | 0.933144i | \(0.617053\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −968.050 | −0.432916 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3970.26 | 1.74482 | 0.872409 | − | 0.488777i | \(-0.162557\pi\) | ||||
0.872409 | + | 0.488777i | \(0.162557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1205.66 | −0.520798 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2053.52 | −0.872047 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2690.95 | −1.12364 | −0.561818 | − | 0.827261i | \(-0.689898\pi\) | ||||
−0.561818 | + | 0.827261i | \(0.689898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4371.10 | 1.79503 | 0.897517 | − | 0.440980i | \(-0.145369\pi\) | ||||
0.897517 | + | 0.440980i | \(0.145369\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −924.375 | −0.373398 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8084.66 | 3.21295 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2552.14 | 0.998026 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −130.717 | −0.0503082 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1408.47 | −0.533578 | −0.266789 | − | 0.963755i | \(-0.585963\pi\) | ||||
−0.266789 | + | 0.963755i | \(0.585963\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4131.69 | −1.54096 | −0.770481 | − | 0.637463i | \(-0.779984\pi\) | ||||
−0.770481 | + | 0.637463i | \(0.779984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 754.259 | 0.276993 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3401.23 | 1.23009 | 0.615045 | − | 0.788492i | \(-0.289138\pi\) | ||||
0.615045 | + | 0.788492i | \(0.289138\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3520.74 | 1.25416 | 0.627081 | − | 0.778954i | \(-0.284249\pi\) | ||||
0.627081 | + | 0.778954i | \(0.284249\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2018.42 | 0.708302 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −435.183 | −0.150463 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2759.30 | 0.940088 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −256.624 | −0.0861672 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6569.05 | 2.17412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2245.22 | −0.732545 | −0.366272 | − | 0.930508i | \(-0.619366\pi\) | ||||
−0.366272 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 980.510 | 0.315415 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1374.95 | 0.436142 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 886.490 | 0.277322 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 72.9173 | 0.0224990 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 543.250 | 0.165353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3431.26 | −1.03038 | −0.515188 | − | 0.857077i | \(-0.672278\pi\) | ||||
−0.515188 | + | 0.857077i | \(0.672278\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2241.31 | 0.664091 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4757.91 | −1.39116 | −0.695581 | − | 0.718448i | \(-0.744853\pi\) | ||||
−0.695581 | + | 0.718448i | \(0.744853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4368.93 | 1.26073 | 0.630364 | − | 0.776300i | \(-0.282906\pi\) | ||||
0.630364 | + | 0.776300i | \(0.282906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 887.026 | 0.252649 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3642.00 | −1.02401 | −0.512007 | − | 0.858981i | \(-0.671098\pi\) | ||||
−0.512007 | + | 0.858981i | \(0.671098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6260.57 | 1.73785 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −500.431 | −0.137158 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2236.17 | −0.605213 | −0.302606 | − | 0.953116i | \(-0.597857\pi\) | ||||
−0.302606 | + | 0.953116i | \(0.597857\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6538.78 | 1.74772 | 0.873858 | − | 0.486181i | \(-0.161610\pi\) | ||||
0.873858 | + | 0.486181i | \(0.161610\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6180.30 | 1.61161 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1398.29 | 0.360208 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −603.280 | −0.153539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2507.12 | 0.630470 | 0.315235 | − | 0.949014i | \(-0.397917\pi\) | ||||
0.315235 | + | 0.949014i | \(0.397917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1741.42 | 0.432735 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2424.56 | 0.595420 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −808.131 | −0.196147 | −0.0980735 | − | 0.995179i | \(-0.531268\pi\) | ||||
−0.0980735 | + | 0.995179i | \(0.531268\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2023.83 | 0.485539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 808.998 | 0.191861 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2940.70 | −0.689472 | −0.344736 | − | 0.938700i | \(-0.612032\pi\) | ||||
−0.344736 | + | 0.938700i | \(0.612032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −485.525 | −0.112549 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 326.501 | 0.0748371 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7111.50 | −1.61188 | −0.805940 | − | 0.591997i | \(-0.798340\pi\) | ||||
−0.805940 | + | 0.591997i | \(0.798340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2034.96 | −0.456145 | −0.228072 | − | 0.973644i | \(-0.573242\pi\) | ||||
−0.228072 | + | 0.973644i | \(0.573242\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 188.813 | 0.0418589 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15209.2 | −3.33509 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2723.20 | −0.590689 | −0.295345 | − | 0.955391i | \(-0.595434\pi\) | ||||
−0.295345 | + | 0.955391i | \(0.595434\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1647.97 | −0.353625 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3265.56 | 0.693263 | 0.346632 | − | 0.938001i | \(-0.387325\pi\) | ||||
0.346632 | + | 0.938001i | \(0.387325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1144.02 | 0.240299 | 0.120150 | − | 0.992756i | \(-0.461663\pi\) | ||||
0.120150 | + | 0.992756i | \(0.461663\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6240.68 | 1.29707 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 690.735 | 0.142065 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3166.72 | −0.644560 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3473.85 | 0.699796 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1677.35 | 0.334444 | 0.167222 | − | 0.985919i | \(-0.446520\pi\) | ||||
0.167222 | + | 0.985919i | \(0.446520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13238.4 | 2.61277 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1648.96 | −0.322164 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 370.679 | 0.0716954 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 344.190 | 0.0659095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5108.24 | −0.968518 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5959.13 | 1.11875 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7207.70 | 1.33995 | 0.669975 | − | 0.742383i | \(-0.266305\pi\) | ||||
0.669975 | + | 0.742383i | \(0.266305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4365.42 | 0.803689 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −412.963 | −0.0752958 | −0.0376479 | − | 0.999291i | \(-0.511987\pi\) | ||||
−0.0376479 | + | 0.999291i | \(0.511987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2936.39 | 0.530270 | 0.265135 | − | 0.964211i | \(-0.414583\pi\) | ||||
0.265135 | + | 0.964211i | \(0.414583\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 842.686 | 0.150730 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −377.956 | −0.0669657 | −0.0334828 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334828 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5489.75 | −0.963533 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2468.28 | −0.429178 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4494.81 | 0.774298 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3237.44 | −0.552557 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1371.79 | −0.231989 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1567.20 | 0.262622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4428.17 | −0.735330 | −0.367665 | − | 0.929958i | \(-0.619843\pi\) | ||||
−0.367665 | + | 0.929958i | \(0.619843\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3762.26 | −0.619130 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13012.1 | −2.12217 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1768.76 | −0.285907 | −0.142953 | − | 0.989729i | \(-0.545660\pi\) | ||||
−0.142953 | + | 0.989729i | \(0.545660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1145.08 | −0.183458 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11182.9 | 1.77592 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3207.70 | 0.504955 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1654.37 | 0.258168 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2412.97 | 0.373300 | 0.186650 | − | 0.982426i | \(-0.440237\pi\) | ||||
0.186650 | + | 0.982426i | \(0.440237\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9967.45 | 1.52878 | 0.764392 | − | 0.644752i | \(-0.223039\pi\) | ||||
0.764392 | + | 0.644752i | \(0.223039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4516.30 | 0.680959 | 0.340479 | − | 0.940252i | \(-0.389411\pi\) | ||||
0.340479 | + | 0.940252i | \(0.389411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6321.01 | −0.945027 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 606.939 | 0.0899794 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12159.8 | −1.78767 | −0.893833 | − | 0.448400i | \(-0.851994\pi\) | ||||
−0.893833 | + | 0.448400i | \(0.851994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4710.38 | 0.686745 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7196.65 | 1.04057 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −470.072 | −0.0674102 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2674.25 | 0.380367 | 0.190183 | − | 0.981749i | \(-0.439092\pi\) | ||||
0.190183 | + | 0.981749i | \(0.439092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1284.06 | −0.181153 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −121.541 | −0.0170083 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9601.74 | −1.33287 | −0.666433 | − | 0.745564i | \(-0.732180\pi\) | ||||
−0.666433 | + | 0.745564i | \(0.732180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7196.45 | −0.990995 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1168.55 | −0.159638 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9019.65 | 1.22245 | 0.611225 | − | 0.791457i | \(-0.290677\pi\) | ||||
0.611225 | + | 0.791457i | \(0.290677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3387.28 | 0.455474 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4015.34 | 0.535703 | 0.267852 | − | 0.963460i | \(-0.413686\pi\) | ||||
0.267852 | + | 0.963460i | \(0.413686\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5718.35 | −0.756972 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −639.842 | −0.0840439 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2725.35 | 0.355221 | 0.177610 | − | 0.984101i | \(-0.443163\pi\) | ||||
0.177610 | + | 0.984101i | \(0.443163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1191.55 | 0.154115 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2558.28 | −0.328367 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3226.11 | 0.410945 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4391.59 | 0.555182 | 0.277591 | − | 0.960699i | \(-0.410464\pi\) | ||||
0.277591 | + | 0.960699i | \(0.410464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1562.23 | 0.196013 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3762.48 | 0.468552 | 0.234276 | − | 0.972170i | \(-0.424728\pi\) | ||||
0.234276 | + | 0.972170i | \(0.424728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2380.40 | 0.294234 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1566.54 | −0.192202 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25530.2 | 3.10930 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6797.81 | −0.821833 | −0.410917 | − | 0.911673i | \(-0.634791\pi\) | ||||
−0.410917 | + | 0.911673i | \(0.634791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1466.71 | −0.176028 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3313.95 | 0.394840 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3889.14 | 0.460025 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1221.37 | 0.143431 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12594.2 | −1.46841 | −0.734207 | − | 0.678925i | \(-0.762446\pi\) | ||||
−0.734207 | + | 0.678925i | \(0.762446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6888.04 | −0.797393 | −0.398697 | − | 0.917083i | \(-0.630537\pi\) | ||||
−0.398697 | + | 0.917083i | \(0.630537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2913.40 | −0.334881 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10406.8 | −1.18777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1491.74 | 0.169065 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2381.84 | 0.268056 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7384.53 | 0.825291 | 0.412645 | − | 0.910892i | \(-0.364605\pi\) | ||||
0.412645 | + | 0.910892i | \(0.364605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9068.33 | 1.00646 | 0.503229 | − | 0.864153i | \(-0.332145\pi\) | ||||
0.503229 | + | 0.864153i | \(0.332145\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5215.33 | −0.574841 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3066.97 | 0.335728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16875.4 | −1.83466 | −0.917331 | − | 0.398125i | \(-0.869661\pi\) | ||||
−0.917331 | + | 0.398125i | \(0.869661\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2876.05 | −0.310555 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6766.18 | −0.725668 | −0.362834 | − | 0.931854i | \(-0.618191\pi\) | ||||
−0.362834 | + | 0.931854i | \(0.618191\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2104.84 | −0.224222 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5152.90 | −0.545243 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 140.944 | 0.0148141 | 0.00740706 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740706 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8713.47 | 0.909759 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4025.36 | −0.417501 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1217.21 | −0.125415 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17733.1 | −1.81514 | −0.907571 | − | 0.419898i | \(-0.862066\pi\) | ||||
−0.907571 | + | 0.419898i | \(0.862066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1128.29 | −0.114736 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2293.37 | −0.231699 | −0.115849 | − | 0.993267i | \(-0.536959\pi\) | ||||
−0.115849 | + | 0.993267i | \(0.536959\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13770.9 | −1.38226 | −0.691129 | − | 0.722731i | \(-0.742887\pi\) | ||||
−0.691129 | + | 0.722731i | \(0.742887\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10623.9 | 1.05951 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3477.37 | −0.344568 | −0.172284 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172284 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3257.31 | −0.320700 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2281.64 | 0.223211 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4341.88 | 0.422072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26786.4 | −2.58746 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 225.943 | 0.0216880 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3137.39 | 0.299271 | 0.149636 | − | 0.988741i | \(-0.452190\pi\) | ||||
0.149636 | + | 0.988741i | \(0.452190\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5434.37 | 0.515148 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 414.137 | 0.0390142 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22394.7 | −2.09668 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5996.52 | −0.557964 | −0.278982 | − | 0.960296i | \(-0.589997\pi\) | ||||
−0.278982 | + | 0.960296i | \(0.589997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8136.26 | 0.752422 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9401.49 | −0.864121 | −0.432060 | − | 0.901845i | \(-0.642213\pi\) | ||||
−0.432060 | + | 0.901845i | \(0.642213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3756.31 | −0.343156 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10630.3 | 0.965246 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1582.34 | −0.142812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5052.33 | −0.453253 | −0.226626 | − | 0.973982i | \(-0.572770\pi\) | ||||
−0.226626 | + | 0.973982i | \(0.572770\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4655.08 | −0.415117 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8184.02 | −0.725462 | −0.362731 | − | 0.931894i | \(-0.618156\pi\) | ||||
−0.362731 | + | 0.931894i | \(0.618156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32931.1 | 2.90181 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6039.12 | −0.525892 | −0.262946 | − | 0.964811i | \(-0.584694\pi\) | ||||
−0.262946 | + | 0.964811i | \(0.584694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −117.673 | −0.0101870 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2904.15 | −0.249944 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28142.3 | −2.40796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19770.0 | 1.68178 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11910.8 | 1.00737 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14602.5 | −1.22792 | −0.613960 | − | 0.789337i | \(-0.710424\pi\) | ||||
−0.613960 | + | 0.789337i | \(0.710424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8910.70 | 0.745005 | 0.372502 | − | 0.928031i | \(-0.378500\pi\) | ||||
0.372502 | + | 0.928031i | \(0.378500\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3616.99 | −0.300683 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7651.79 | 0.632481 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11354.0 | −0.933177 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6160.57 | −0.503477 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1854.76 | 0.150729 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15912.2 | 1.28588 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8072.84 | −0.648731 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19516.5 | 1.55962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13313.6 | 1.05803 | 0.529017 | − | 0.848611i | \(-0.322561\pi\) | ||||
0.529017 | + | 0.848611i | \(0.322561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13113.3 | 1.03636 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8843.47 | 0.695069 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4116.94 | −0.321806 | −0.160903 | − | 0.986970i | \(-0.551441\pi\) | ||||
−0.160903 | + | 0.986970i | \(0.551441\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2773.12 | −0.215581 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9668.52 | −0.747537 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 807.590 | 0.0621016 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24254.0 | 1.85500 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6888.37 | 0.524003 | 0.262002 | − | 0.965067i | \(-0.415617\pi\) | ||||
0.262002 | + | 0.965067i | \(0.415617\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 924.216 | 0.0699288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7656.42 | 0.576211 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10537.1 | 0.788782 | 0.394391 | − | 0.918943i | \(-0.370955\pi\) | ||||
0.394391 | + | 0.918943i | \(0.370955\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7381.92 | 0.549664 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −392.150 | −0.0290454 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26930.1 | 1.98413 | 0.992065 | − | 0.125722i | \(-0.0401248\pi\) | ||||
0.992065 | + | 0.125722i | \(0.0401248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3125.60 | −0.229076 | −0.114538 | − | 0.993419i | \(-0.536539\pi\) | ||||
−0.114538 | + | 0.993419i | \(0.536539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4225.42 | −0.308062 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7100.91 | −0.515006 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4787.13 | 0.345391 | 0.172696 | − | 0.984975i | \(-0.444752\pi\) | ||||
0.172696 | + | 0.984975i | \(0.444752\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12395.1 | −0.889675 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 973.566 | 0.0695186 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1533.22 | −0.108918 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2262.78 | 0.159922 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18380.8 | 1.29243 | 0.646214 | − | 0.763156i | \(-0.276351\pi\) | ||||
0.646214 | + | 0.763156i | \(0.276351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19695.3 | 1.37781 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10203.7 | 0.710193 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13831.7 | −0.957843 | −0.478922 | − | 0.877858i | \(-0.658972\pi\) | ||||
−0.478922 | + | 0.877858i | \(0.658972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3912.73 | −0.269590 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10562.2 | 0.724091 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12248.6 | −0.835502 | −0.417751 | − | 0.908562i | \(-0.637182\pi\) | ||||
−0.417751 | + | 0.908562i | \(0.637182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9719.56 | 0.659682 | 0.329841 | − | 0.944036i | \(-0.393005\pi\) | ||||
0.329841 | + | 0.944036i | \(0.393005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6055.27 | 0.408938 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −46394.3 | −3.11768 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1607.83 | −0.107512 | −0.0537560 | − | 0.998554i | \(-0.517119\pi\) | ||||
−0.0537560 | + | 0.998554i | \(0.517119\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1305.55 | −0.0868696 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4208.25 | 0.278638 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14731.1 | −0.970610 | −0.485305 | − | 0.874345i | \(-0.661291\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8277.91 | 0.542760 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27951.8 | 1.82382 | 0.911909 | − | 0.410392i | \(-0.134608\pi\) | ||||
0.911909 | + | 0.410392i | \(0.134608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16200.2 | 1.05192 | 0.525961 | − | 0.850509i | \(-0.323706\pi\) | ||||
0.525961 | + | 0.850509i | \(0.323706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −769.872 | −0.0497486 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −526.903 | −0.0338843 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15263.8 | 0.976880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19707.2 | 1.25523 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17468.8 | 1.10735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12731.8 | −0.803239 | −0.401619 | − | 0.915807i | \(-0.631553\pi\) | ||||
−0.401619 | + | 0.915807i | \(0.631553\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6735.65 | −0.422935 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21836.6 | −1.36466 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4154.30 | 0.258397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2941.53 | 0.182105 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11556.9 | −0.712119 | −0.356059 | − | 0.934463i | \(-0.615880\pi\) | ||||
−0.356059 | + | 0.934463i | \(0.615880\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9181.25 | −0.563100 | −0.281550 | − | 0.959547i | \(-0.590848\pi\) | ||||
−0.281550 | + | 0.959547i | \(0.590848\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4124.84 | 0.251807 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5244.11 | −0.318651 | −0.159326 | − | 0.987226i | \(-0.550932\pi\) | ||||
−0.159326 | + | 0.987226i | \(0.550932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41804.8 | 2.52848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2659.47 | 0.160112 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16421.4 | 0.984106 | 0.492053 | − | 0.870565i | \(-0.336247\pi\) | ||||
0.492053 | + | 0.870565i | \(0.336247\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16492.4 | 0.983832 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 218.752 | 0.0129898 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1838.11 | 0.108653 | 0.0543266 | − | 0.998523i | \(-0.482699\pi\) | ||||
0.0543266 | + | 0.998523i | \(0.482699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5500.93 | 0.323694 | 0.161847 | − | 0.986816i | \(-0.448255\pi\) | ||||
0.161847 | + | 0.986816i | \(0.448255\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1629.75 | 0.0954665 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10071.1 | −0.587281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2563.07 | −0.148789 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10293.8 | −0.594888 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18818.0 | 1.08266 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25986.7 | −1.48843 | −0.744216 | − | 0.667939i | \(-0.767177\pi\) | ||||
−0.744216 | + | 0.667939i | \(0.767177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6723.92 | 0.383413 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11691.3 | 0.663714 | 0.331857 | − | 0.943330i | \(-0.392325\pi\) | ||||
0.331857 | + | 0.943330i | \(0.392325\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5606.05 | −0.316849 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14273.7 | −0.803188 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11111.5 | −0.622501 | −0.311251 | − | 0.950328i | \(-0.600748\pi\) | ||||
−0.311251 | + | 0.950328i | \(0.600748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9455.37 | 0.527403 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13106.8 | 0.727882 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −326.361 | −0.0180455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7542.55 | −0.415242 | −0.207621 | − | 0.978209i | \(-0.566572\pi\) | ||||
−0.207621 | + | 0.978209i | \(0.566572\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2661.08 | 0.145867 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7873.75 | −0.429738 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5962.11 | 0.324005 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10926.0 | −0.591215 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8231.17 | 0.443491 | 0.221745 | − | 0.975105i | \(-0.428825\pi\) | ||||
0.221745 | + | 0.975105i | \(0.428825\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44963.6 | 2.41228 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18781.7 | 1.00335 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8243.61 | 0.438519 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28044.6 | −1.48553 | −0.742764 | − | 0.669554i | \(-0.766485\pi\) | ||||
−0.742764 | + | 0.669554i | \(0.766485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1501.29 | −0.0791884 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5221.09 | 0.274238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15354.9 | −0.803133 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6708.51 | −0.349420 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29686.4 | −1.53980 | −0.769901 | − | 0.638163i | \(-0.779694\pi\) | ||||
−0.769901 | + | 0.638163i | \(0.779694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7044.86 | −0.363889 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19616.3 | 1.00904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22385.3 | 1.14672 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27654.5 | 1.41080 | 0.705398 | − | 0.708812i | \(-0.250768\pi\) | ||||
0.705398 | + | 0.708812i | \(0.250768\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2970.89 | 0.150318 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13077.5 | 0.658975 | 0.329488 | − | 0.944160i | \(-0.393124\pi\) | ||||
0.329488 | + | 0.944160i | \(0.393124\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18540.9 | 0.930465 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41090.3 | −2.05370 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4218.33 | −0.209978 | −0.104989 | − | 0.994473i | \(-0.533481\pi\) | ||||
−0.104989 | + | 0.994473i | \(0.533481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4194.88 | 0.207966 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7725.54 | −0.381457 | −0.190728 | − | 0.981643i | \(-0.561085\pi\) | ||||
−0.190728 | + | 0.981643i | \(0.561085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33218.9 | 1.63362 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1809.84 | −0.0886460 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3983.29 | 0.194321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7506.12 | −0.364717 | −0.182358 | − | 0.983232i | \(-0.558373\pi\) | ||||
−0.182358 | + | 0.983232i | \(0.558373\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7521.35 | 0.364002 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25950.1 | 1.25089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2741.62 | 0.131632 | 0.0658162 | − | 0.997832i | \(-0.479035\pi\) | ||||
0.0658162 | + | 0.997832i | \(0.479035\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5224.25 | 0.249839 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29740.0 | 1.41666 | 0.708328 | − | 0.705883i | \(-0.249450\pi\) | ||||
0.708328 | + | 0.705883i | \(0.249450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2213.78 | 0.105038 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7273.69 | 0.343766 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8898.60 | 0.418918 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19896.3 | −0.933004 | −0.466502 | − | 0.884520i | \(-0.654486\pi\) | ||||
−0.466502 | + | 0.884520i | \(0.654486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2424.39 | −0.113246 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13601.3 | 0.632866 | 0.316433 | − | 0.948615i | \(-0.397515\pi\) | ||||
0.316433 | + | 0.948615i | \(0.397515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −45600.1 | −2.11355 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6071.48 | 0.280326 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15346.1 | 0.705818 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19960.8 | −0.914539 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2426.99 | 0.110771 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14708.9 | −0.668770 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1498.29 | −0.0678631 | −0.0339315 | − | 0.999424i | \(-0.510803\pi\) | ||||
−0.0339315 | + | 0.999424i | \(0.510803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8822.09 | −0.398067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1847.91 | 0.0830647 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4005.62 | 0.179374 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1456.57 | −0.0649803 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3713.30 | 0.165034 | 0.0825168 | − | 0.996590i | \(-0.473704\pi\) | ||||
0.0825168 | + | 0.996590i | \(0.473704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13527.4 | 0.598955 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 979.502 | 0.0432072 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1484.42 | −0.0652354 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2669.80 | −0.116892 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21334.5 | −0.930620 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34527.6 | −1.50053 | −0.750263 | − | 0.661139i | \(-0.770073\pi\) | ||||
−0.750263 | + | 0.661139i | \(0.770073\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37279.2 | −1.61412 | −0.807059 | − | 0.590471i | \(-0.798942\pi\) | ||||
−0.807059 | + | 0.590471i | \(0.798942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6104.89 | −0.263355 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −52451.6 | −2.25436 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7646.90 | 0.327455 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 566.439 | 0.0241673 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13877.9 | −0.589943 | −0.294972 | − | 0.955506i | \(-0.595310\pi\) | ||||
−0.294972 | + | 0.955506i | \(0.595310\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18945.1 | −0.802410 | −0.401205 | − | 0.915988i | \(-0.631408\pi\) | ||||
−0.401205 | + | 0.915988i | \(0.631408\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −45627.6 | −1.92552 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7804.75 | −0.328171 | −0.164086 | − | 0.986446i | \(-0.552467\pi\) | ||||
−0.164086 | + | 0.986446i | \(0.552467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5784.85 | −0.242360 | −0.121180 | − | 0.992631i | \(-0.538668\pi\) | ||||
−0.121180 | + | 0.992631i | \(0.538668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8169.59 | −0.341035 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13354.0 | 0.555448 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30009.7 | 1.24375 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4943.91 | −0.204165 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5011.42 | 0.206214 | 0.103107 | − | 0.994670i | \(-0.467122\pi\) | ||||
0.103107 | + | 0.994670i | \(0.467122\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16309.0 | −0.668704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9796.68 | 0.400256 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3268.45 | −0.133063 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11613.9 | −0.471142 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3432.05 | 0.138737 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11919.6 | 0.480138 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22059.0 | 0.885446 | 0.442723 | − | 0.896659i | \(-0.354013\pi\) | ||||
0.442723 | + | 0.896659i | \(0.354013\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18722.0 | 0.748866 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13956.2 | 0.556283 | 0.278141 | − | 0.960540i | \(-0.410282\pi\) | ||||
0.278141 | + | 0.960540i | \(0.410282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12498.5 | 0.496442 | 0.248221 | − | 0.968703i | \(-0.420154\pi\) | ||||
0.248221 | + | 0.968703i | \(0.420154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2072.20 | 0.0820215 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38631.2 | 1.52378 | 0.761890 | − | 0.647707i | \(-0.224272\pi\) | ||||
0.761890 | + | 0.647707i | \(0.224272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −76784.7 | −3.01822 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9500.17 | −0.372137 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10187.6 | 0.397687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8746.51 | −0.340257 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10421.5 | 0.404027 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11613.5 | 0.448696 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 856.756 | 0.0329881 | 0.0164941 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164941 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5032.06 | 0.193091 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33638.6 | 1.28640 | 0.643198 | − | 0.765700i | \(-0.277607\pi\) | ||||
0.643198 | + | 0.765700i | \(0.277607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31109.1 | −1.18562 | −0.592811 | − | 0.805342i | \(-0.701982\pi\) | ||||
−0.592811 | + | 0.805342i | \(0.701982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 39715.1 | 1.50848 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26080.3 | −0.987248 | −0.493624 | − | 0.869675i | \(-0.664328\pi\) | ||||
−0.493624 | + | 0.869675i | \(0.664328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5466.35 | −0.206227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4946.89 | −0.186001 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34818.8 | 1.30478 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52042.8 | 1.94369 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1112.04 | 0.0413934 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16459.3 | −0.610621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1049.09 | −0.0387905 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1032.57 | 0.0380529 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −84536.9 | −3.10508 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20169.0 | 0.738369 | 0.369184 | − | 0.929356i | \(-0.379637\pi\) | ||||
0.369184 | + | 0.929356i | \(0.379637\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15324.7 | −0.559174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19982.2 | −0.726716 | −0.363358 | − | 0.931650i | \(-0.618370\pi\) | ||||
−0.363358 | + | 0.931650i | \(0.618370\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12281.3 | 0.445184 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17877.4 | 0.645910 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4128.52 | 0.148676 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38513.1 | −1.38241 | −0.691203 | − | 0.722661i | \(-0.742919\pi\) | ||||
−0.691203 | + | 0.722661i | \(0.742919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21623.1 | 0.773621 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4248.88 | −0.151521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −104103. | −3.70043 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13096.3 | 0.464010 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23218.9 | 0.820009 | 0.410005 | − | 0.912083i | \(-0.365527\pi\) | ||||
0.410005 | + | 0.912083i | \(0.365527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34372.3 | 1.21000 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1238.89 | −0.0434721 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −49358.3 | −1.72640 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11112.9 | −0.387452 | −0.193726 | − | 0.981056i | \(-0.562057\pi\) | ||||
−0.193726 | + | 0.981056i | \(0.562057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8809.17 | 0.306152 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45570.4 | −1.57869 | −0.789347 | − | 0.613947i | \(-0.789581\pi\) | ||||
−0.789347 | + | 0.613947i | \(0.789581\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4068.16 | 0.140485 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2528.06 | 0.0870240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34903.9 | 1.19770 | 0.598852 | − | 0.800860i | \(-0.295624\pi\) | ||||
0.598852 | + | 0.800860i | \(0.295624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −315.975 | −0.0108082 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1133.87 | −0.0386626 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2886.52 | −0.0981151 | −0.0490575 | − | 0.998796i | \(-0.515622\pi\) | ||||
−0.0490575 | + | 0.998796i | \(0.515622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27239.8 | 0.922994 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16469.2 | −0.556296 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2366.96 | 0.0797008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3737.42 | 0.125455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7404.85 | −0.247786 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 79906.8 | 2.66559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11593.8 | −0.385556 | −0.192778 | − | 0.981242i | \(-0.561750\pi\) | ||||
−0.192778 | + | 0.981242i | \(0.561750\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13484.4 | 0.447041 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4952.12 | −0.163667 | −0.0818337 | − | 0.996646i | \(-0.526078\pi\) | ||||
−0.0818337 | + | 0.996646i | \(0.526078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1971.03 | −0.0649418 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9712.33 | −0.319019 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19650.1 | −0.643462 | −0.321731 | − | 0.946831i | \(-0.604265\pi\) | ||||
−0.321731 | + | 0.946831i | \(0.604265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6646.77 | −0.216988 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4115.38 | −0.133939 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56818.4 | −1.84357 | −0.921783 | − | 0.387707i | \(-0.873267\pi\) | ||||
−0.921783 | + | 0.387707i | \(0.873267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −65779.7 | −2.12783 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4701.61 | 0.151625 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2027.15 | 0.0651764 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19120.4 | 0.612897 | 0.306448 | − | 0.951887i | \(-0.400859\pi\) | ||||
0.306448 | + | 0.951887i | \(0.400859\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13284.5 | −0.424543 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −68090.9 | −2.16947 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38887.9 | −1.23530 | −0.617650 | − | 0.786453i | \(-0.711915\pi\) | ||||
−0.617650 | + | 0.786453i | \(0.711915\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11286.8 | −0.357455 |
(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 | 2496.4.a.bp.1.1 | 3 | ||
4.3 | odd | 2 | 2496.4.a.bl.1.1 | 3 | |||
8.3 | odd | 2 | 39.4.a.c.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 624.4.a.t.1.3 | 3 | |||
24.5 | odd | 2 | 1872.4.a.bk.1.1 | 3 | |||
24.11 | even | 2 | 117.4.a.f.1.2 | 3 | |||
40.19 | odd | 2 | 975.4.a.l.1.2 | 3 | |||
56.27 | even | 2 | 1911.4.a.k.1.2 | 3 | |||
104.51 | odd | 2 | 507.4.a.h.1.2 | 3 | |||
104.83 | even | 4 | 507.4.b.g.337.3 | 6 | |||
104.99 | even | 4 | 507.4.b.g.337.4 | 6 | |||
312.155 | even | 2 | 1521.4.a.u.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
117.4.a.f.1.2 | 3 | 24.11 | even | 2 | |||
507.4.a.h.1.2 | 3 | 104.51 | odd | 2 | |||
507.4.b.g.337.3 | 6 | 104.83 | even | 4 | |||
507.4.b.g.337.4 | 6 | 104.99 | even | 4 | |||
624.4.a.t.1.3 | 3 | 8.5 | even | 2 | |||
975.4.a.l.1.2 | 3 | 40.19 | odd | 2 | |||
1521.4.a.u.1.2 | 3 | 312.155 | even | 2 | |||
1872.4.a.bk.1.1 | 3 | 24.5 | odd | 2 | |||
1911.4.a.k.1.2 | 3 | 56.27 | even | 2 | |||
2496.4.a.bl.1.1 | 3 | 4.3 | odd | 2 | |||
2496.4.a.bp.1.1 | 3 | 1.1 | even | 1 | trivial |