Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,4,Mod(1,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1280.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.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: | \(75.5224448073\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 21x^{4} + 38x^{3} + 93x^{2} - 108x - 60 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.46129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1 |
$q$-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 | ||||||||
\(3\) | −6.25785 | −1.20432 | −0.602161 | − | 0.798374i | \(-0.705694\pi\) | ||||
−0.602161 | + | 0.798374i | \(0.705694\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 34.6280 | 1.86973 | 0.934867 | − | 0.354998i | \(-0.115518\pi\) | ||||
0.934867 | + | 0.354998i | \(0.115518\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 12.1606 | 0.450394 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.91595 | 0.216977 | 0.108489 | − | 0.994098i | \(-0.465399\pi\) | ||||
0.108489 | + | 0.994098i | \(0.465399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.0346 | −0.235420 | −0.117710 | − | 0.993048i | \(-0.537555\pi\) | ||||
−0.117710 | + | 0.993048i | \(0.537555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.2892 | −0.538590 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 57.6152 | 0.821985 | 0.410992 | − | 0.911639i | \(-0.365182\pi\) | ||||
0.410992 | + | 0.911639i | \(0.365182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −141.133 | −1.70411 | −0.852055 | − | 0.523453i | \(-0.824644\pi\) | ||||
−0.852055 | + | 0.523453i | \(0.824644\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −216.696 | −2.25176 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −129.328 | −1.17247 | −0.586233 | − | 0.810143i | \(-0.699390\pi\) | ||||
−0.586233 | + | 0.810143i | \(0.699390\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 92.8625 | 0.661903 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −89.1664 | −0.570958 | −0.285479 | − | 0.958385i | \(-0.592153\pi\) | ||||
−0.285479 | + | 0.958385i | \(0.592153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −78.3307 | −0.453826 | −0.226913 | − | 0.973915i | \(-0.572863\pi\) | ||||
−0.226913 | + | 0.973915i | \(0.572863\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −49.5368 | −0.261310 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 173.140 | 0.836171 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −249.332 | −1.10783 | −0.553917 | − | 0.832572i | \(-0.686868\pi\) | ||||
−0.553917 | + | 0.832572i | \(0.686868\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 69.0530 | 0.283521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −91.8705 | −0.349946 | −0.174973 | − | 0.984573i | \(-0.555984\pi\) | ||||
−0.174973 | + | 0.984573i | \(0.555984\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −194.184 | −0.688668 | −0.344334 | − | 0.938847i | \(-0.611895\pi\) | ||||
−0.344334 | + | 0.938847i | \(0.611895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 60.8031 | 0.201422 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −72.6149 | −0.225361 | −0.112680 | − | 0.993631i | \(-0.535944\pi\) | ||||
−0.112680 | + | 0.993631i | \(0.535944\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 856.096 | 2.49591 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −360.547 | −0.989935 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 456.782 | 1.18385 | 0.591923 | − | 0.805995i | \(-0.298369\pi\) | ||||
0.591923 | + | 0.805995i | \(0.298369\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 39.5797 | 0.0970351 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 883.187 | 2.05230 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −341.098 | −0.752664 | −0.376332 | − | 0.926485i | \(-0.622815\pi\) | ||||
−0.376332 | + | 0.926485i | \(0.622815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −217.067 | −0.455616 | −0.227808 | − | 0.973706i | \(-0.573156\pi\) | ||||
−0.227808 | + | 0.973706i | \(0.573156\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 421.098 | 0.842117 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −55.1731 | −0.105283 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 529.237 | 0.965024 | 0.482512 | − | 0.875889i | \(-0.339724\pi\) | ||||
0.482512 | + | 0.875889i | \(0.339724\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 809.314 | 1.41203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −381.540 | −0.637754 | −0.318877 | − | 0.947796i | \(-0.603306\pi\) | ||||
−0.318877 | + | 0.947796i | \(0.603306\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 876.902 | 1.40594 | 0.702970 | − | 0.711220i | \(-0.251857\pi\) | ||||
0.702970 | + | 0.711220i | \(0.251857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −156.446 | −0.240865 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 274.113 | 0.405690 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −203.950 | −0.290458 | −0.145229 | − | 0.989398i | \(-0.546392\pi\) | ||||
−0.145229 | + | 0.989398i | \(0.546392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −909.456 | −1.24754 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −996.654 | −1.31804 | −0.659018 | − | 0.752127i | \(-0.729028\pi\) | ||||
−0.659018 | + | 0.752127i | \(0.729028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 288.076 | 0.367603 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 557.989 | 0.687618 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −172.456 | −0.205396 | −0.102698 | − | 0.994713i | \(-0.532748\pi\) | ||||
−0.102698 | + | 0.994713i | \(0.532748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −382.107 | −0.440172 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 490.182 | 0.546553 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −705.664 | −0.762101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1058.49 | 1.10797 | 0.553984 | − | 0.832527i | \(-0.313107\pi\) | ||||
0.553984 | + | 0.832527i | \(0.313107\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 96.2629 | 0.0977251 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 689.992 | 0.679770 | 0.339885 | − | 0.940467i | \(-0.389612\pi\) | ||||
0.339885 | + | 0.940467i | \(0.389612\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1289.96 | −1.23402 | −0.617009 | − | 0.786956i | \(-0.711656\pi\) | ||||
−0.617009 | + | 0.786956i | \(0.711656\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1083.48 | −1.00702 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1843.74 | −1.66580 | −0.832902 | − | 0.553420i | \(-0.813322\pi\) | ||||
−0.832902 | + | 0.553420i | \(0.813322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 340.598 | 0.299297 | 0.149648 | − | 0.988739i | \(-0.452186\pi\) | ||||
0.149648 | + | 0.988739i | \(0.452186\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1560.28 | 1.33419 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 157.831 | 0.131393 | 0.0656967 | − | 0.997840i | \(-0.479073\pi\) | ||||
0.0656967 | + | 0.997840i | \(0.479073\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −646.639 | −0.524343 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −134.188 | −0.106031 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1995.10 | 1.53689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1268.34 | −0.952921 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 574.912 | 0.421447 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 494.704 | 0.345652 | 0.172826 | − | 0.984952i | \(-0.444710\pi\) | ||||
0.172826 | + | 0.984952i | \(0.444710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1215.17 | 0.829379 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −488.783 | −0.325993 | −0.162997 | − | 0.986627i | \(-0.552116\pi\) | ||||
−0.162997 | + | 0.986627i | \(0.552116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4887.14 | −3.18623 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 464.312 | 0.296012 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1532.13 | 0.955464 | 0.477732 | − | 0.878506i | \(-0.341459\pi\) | ||||
0.477732 | + | 0.878506i | \(0.341459\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −755.095 | −0.460765 | −0.230382 | − | 0.973100i | \(-0.573998\pi\) | ||||
−0.230382 | + | 0.973100i | \(0.573998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 454.413 | 0.271407 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −87.3495 | −0.0510807 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −445.832 | −0.255340 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5357.32 | −3.00588 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1446.67 | 0.795410 | 0.397705 | − | 0.917513i | \(-0.369807\pi\) | ||||
0.397705 | + | 0.917513i | \(0.369807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1230.20 | 0.662998 | 0.331499 | − | 0.943456i | \(-0.392446\pi\) | ||||
0.331499 | + | 0.943456i | \(0.392446\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 700.637 | 0.370217 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −391.654 | −0.202957 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1773.74 | −0.901657 | −0.450828 | − | 0.892611i | \(-0.648871\pi\) | ||||
−0.450828 | + | 0.892611i | \(0.648871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2858.47 | −1.42573 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4478.36 | −2.19220 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1711.28 | −0.822319 | −0.411159 | − | 0.911563i | \(-0.634876\pi\) | ||||
−0.411159 | + | 0.911563i | \(0.634876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −247.684 | −0.116862 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3913.26 | −1.81328 | −0.906638 | − | 0.421909i | \(-0.861360\pi\) | ||||
−0.906638 | + | 0.421909i | \(0.861360\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2075.24 | −0.944578 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1716.26 | −0.767520 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3985.34 | −1.75144 | −0.875722 | − | 0.482815i | \(-0.839614\pi\) | ||||
−0.875722 | + | 0.482815i | \(0.839614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 865.699 | 0.373947 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2134.54 | 0.906450 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 884.734 | 0.369431 | 0.184715 | − | 0.982792i | \(-0.440864\pi\) | ||||
0.184715 | + | 0.982792i | \(0.440864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2810.77 | −1.15427 | −0.577134 | − | 0.816649i | \(-0.695829\pi\) | ||||
−0.577134 | + | 0.816649i | \(0.695829\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1358.37 | 0.548709 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1246.66 | −0.495439 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 456.079 | 0.178352 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3215.64 | 1.23758 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −749.321 | −0.283869 | −0.141935 | − | 0.989876i | \(-0.545332\pi\) | ||||
−0.141935 | + | 0.989876i | \(0.545332\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3969.83 | −1.48060 | −0.740298 | − | 0.672279i | \(-0.765315\pi\) | ||||
−0.740298 | + | 0.672279i | \(0.765315\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 345.265 | 0.126795 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2243.20 | 0.811275 | 0.405638 | − | 0.914034i | \(-0.367049\pi\) | ||||
0.405638 | + | 0.914034i | \(0.367049\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 672.030 | 0.239392 | 0.119696 | − | 0.992811i | \(-0.461808\pi\) | ||||
0.119696 | + | 0.992811i | \(0.461808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3311.89 | −1.16220 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3087.65 | −1.06754 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −459.353 | −0.156500 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1572.71 | −0.528071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1117.20 | −0.369753 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1935.07 | −0.631356 | −0.315678 | − | 0.948866i | \(-0.602232\pi\) | ||||
−0.315678 | + | 0.948866i | \(0.602232\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2387.62 | 0.768061 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −970.918 | −0.307982 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2712.43 | −0.848535 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5487.52 | −1.69321 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −635.762 | −0.193511 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2492.56 | 0.748494 | 0.374247 | − | 0.927329i | \(-0.377901\pi\) | ||||
0.374247 | + | 0.927329i | \(0.377901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 304.016 | 0.0900787 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3155.27 | 0.922567 | 0.461283 | − | 0.887253i | \(-0.347389\pi\) | ||||
0.461283 | + | 0.887253i | \(0.347389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2299.43 | 0.663539 | 0.331770 | − | 0.943360i | \(-0.392354\pi\) | ||||
0.331770 | + | 0.943360i | \(0.392354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1715.36 | −0.488581 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −741.991 | −0.208624 | −0.104312 | − | 0.994545i | \(-0.533264\pi\) | ||||
−0.104312 | + | 0.994545i | \(0.533264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −363.074 | −0.100785 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1276.29 | 0.349806 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5786.01 | 1.56597 | 0.782984 | − | 0.622042i | \(-0.213697\pi\) | ||||
0.782984 | + | 0.622042i | \(0.213697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 265.054 | 0.0708449 | 0.0354224 | − | 0.999372i | \(-0.488722\pi\) | ||||
0.0354224 | + | 0.999372i | \(0.488722\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3183.95 | 0.840537 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4280.48 | 1.11620 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1557.35 | 0.401181 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6236.91 | 1.58734 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1762.02 | −0.443098 | −0.221549 | − | 0.975149i | \(-0.571111\pi\) | ||||
−0.221549 | + | 0.975149i | \(0.571111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1023.75 | −0.254398 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1802.74 | −0.442713 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1507.84 | −0.365980 | −0.182990 | − | 0.983115i | \(-0.558578\pi\) | ||||
−0.182990 | + | 0.983115i | \(0.558578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8633.85 | −2.07136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1084.32 | −0.257156 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2772.54 | −0.650046 | −0.325023 | − | 0.945706i | \(-0.605372\pi\) | ||||
−0.325023 | + | 0.945706i | \(0.605372\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2283.91 | 0.529432 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1079.20 | 0.247364 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5166.61 | 1.17106 | 0.585528 | − | 0.810652i | \(-0.300887\pi\) | ||||
0.585528 | + | 0.810652i | \(0.300887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1458.79 | −0.326994 | −0.163497 | − | 0.986544i | \(-0.552277\pi\) | ||||
−0.163497 | + | 0.986544i | \(0.552277\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2391.16 | 0.530109 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 197.899 | 0.0433954 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1994.60 | −0.432650 | −0.216325 | − | 0.976321i | \(-0.569407\pi\) | ||||
−0.216325 | + | 0.976321i | \(0.569407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −952.551 | −0.204400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 311.583 | 0.0661477 | 0.0330739 | − | 0.999453i | \(-0.489470\pi\) | ||||
0.0330739 | + | 0.999453i | \(0.489470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6072.33 | −1.27549 | −0.637743 | − | 0.770249i | \(-0.720132\pi\) | ||||
−0.637743 | + | 0.770249i | \(0.720132\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4415.93 | 0.917815 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3181.29 | −0.654305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1593.49 | −0.324341 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6623.84 | −1.33435 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2321.06 | −0.462791 | −0.231395 | − | 0.972860i | \(-0.574329\pi\) | ||||
−0.231395 | + | 0.972860i | \(0.574329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1705.49 | −0.336602 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 735.095 | 0.143618 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1427.08 | 0.276021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6724.19 | −1.28763 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4317.86 | −0.818662 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1085.34 | −0.203758 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2499.43 | 0.464658 | 0.232329 | − | 0.972637i | \(-0.425365\pi\) | ||||
0.232329 | + | 0.972637i | \(0.425365\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8072.39 | 1.48616 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3052.83 | 0.556624 | 0.278312 | − | 0.960491i | \(-0.410225\pi\) | ||||
0.278312 | + | 0.960491i | \(0.410225\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6179.23 | −1.11588 | −0.557941 | − | 0.829881i | \(-0.688408\pi\) | ||||
−0.557941 | + | 0.829881i | \(0.688408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2105.49 | 0.376606 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3116.20 | 0.552124 | 0.276062 | − | 0.961140i | \(-0.410971\pi\) | ||||
0.276062 | + | 0.961140i | \(0.410971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −705.836 | −0.123885 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11537.8 | 2.00617 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8131.39 | −1.40075 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −275.866 | −0.0470839 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2131.41 | −0.360450 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2514.51 | −0.421365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4157.26 | 0.690343 | 0.345171 | − | 0.938540i | \(-0.387821\pi\) | ||||
0.345171 | + | 0.938540i | \(0.387821\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3032.03 | −0.498962 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2646.19 | 0.431572 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8123.42 | −1.31309 | −0.656544 | − | 0.754287i | \(-0.727983\pi\) | ||||
−0.656544 | + | 0.754287i | \(0.727983\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −987.679 | −0.158240 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −620.062 | −0.0984699 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17767.5 | 2.79695 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4046.57 | 0.631478 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4620.55 | −0.714824 | −0.357412 | − | 0.933947i | \(-0.616341\pi\) | ||||
−0.357412 | + | 0.933947i | \(0.616341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5560.98 | 0.852929 | 0.426465 | − | 0.904504i | \(-0.359759\pi\) | ||||
0.426465 | + | 0.904504i | \(0.359759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1024.70 | −0.155825 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12031.8 | 1.81413 | 0.907066 | − | 0.420989i | \(-0.138317\pi\) | ||||
0.907066 | + | 0.420989i | \(0.138317\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1907.70 | −0.285212 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12485.0 | −1.85092 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1533.24 | −0.225408 | −0.112704 | − | 0.993629i | \(-0.535951\pi\) | ||||
−0.112704 | + | 0.993629i | \(0.535951\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13059.5 | 1.90399 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7937.06 | 1.14762 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4384.51 | 0.628755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5480.04 | −0.779444 | −0.389722 | − | 0.920933i | \(-0.627429\pi\) | ||||
−0.389722 | + | 0.920933i | \(0.627429\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1117.20 | −0.157613 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15817.4 | 2.21348 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6225.70 | −0.864221 | −0.432111 | − | 0.901821i | \(-0.642231\pi\) | ||||
−0.432111 | + | 0.901821i | \(0.642231\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −782.231 | −0.107718 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 983.917 | 0.134415 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11172.0 | 1.51416 | 0.757078 | − | 0.653325i | \(-0.226626\pi\) | ||||
0.757078 | + | 0.653325i | \(0.226626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3095.78 | −0.416277 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7621.03 | 1.01675 | 0.508376 | − | 0.861135i | \(-0.330246\pi\) | ||||
0.508376 | + | 0.861135i | \(0.330246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1370.57 | 0.181430 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2361.40 | −0.310172 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5546.31 | −0.722903 | −0.361451 | − | 0.932391i | \(-0.617719\pi\) | ||||
−0.361451 | + | 0.932391i | \(0.617719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7451.25 | −0.963749 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3058.73 | 0.392601 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1019.75 | −0.129897 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11025.2 | −1.39380 | −0.696900 | − | 0.717169i | \(-0.745438\pi\) | ||||
−0.696900 | + | 0.717169i | \(0.745438\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30583.0 | 3.83725 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10522.3 | 1.31037 | 0.655186 | − | 0.755467i | \(-0.272590\pi\) | ||||
0.655186 | + | 0.755467i | \(0.272590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 864.350 | 0.106840 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4547.28 | −0.557916 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1973.70 | −0.240375 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2320.17 | −0.280502 | −0.140251 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140251 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9587.82 | −1.15069 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11811.5 | −1.40728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4983.27 | −0.589444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4725.27 | 0.554910 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9212.17 | 1.07409 | 0.537045 | − | 0.843554i | \(-0.319541\pi\) | ||||
0.537045 | + | 0.843554i | \(0.319541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6967.70 | −0.806615 | −0.403308 | − | 0.915064i | \(-0.632140\pi\) | ||||
−0.403308 | + | 0.915064i | \(0.632140\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −883.042 | −0.101501 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1440.38 | 0.164397 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7516.59 | −0.851882 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 546.620 | 0.0615176 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11247.1 | −1.25697 | −0.628486 | − | 0.777821i | \(-0.716325\pi\) | ||||
−0.628486 | + | 0.777821i | \(0.716325\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2589.27 | 0.287372 | 0.143686 | − | 0.989623i | \(-0.454104\pi\) | ||||
0.143686 | + | 0.989623i | \(0.454104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2789.95 | 0.307512 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18252.4 | 1.99801 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4220.01 | −0.458793 | −0.229396 | − | 0.973333i | \(-0.573675\pi\) | ||||
−0.229396 | + | 0.973333i | \(0.573675\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10410.7 | 1.12414 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9764.04 | 1.04719 | 0.523593 | − | 0.851969i | \(-0.324591\pi\) | ||||
0.523593 | + | 0.851969i | \(0.324591\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −862.279 | −0.0918560 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9053.06 | −0.957931 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17159.3 | −1.80355 | −0.901777 | − | 0.432202i | \(-0.857737\pi\) | ||||
−0.901777 | + | 0.432202i | \(0.857737\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −727.242 | −0.0759302 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7698.43 | −0.798463 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1910.53 | −0.196851 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13027.3 | −1.33346 | −0.666730 | − | 0.745299i | \(-0.732307\pi\) | ||||
−0.666730 | + | 0.745299i | \(0.732307\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5350.29 | 0.544075 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −313.396 | −0.0316623 | −0.0158312 | − | 0.999875i | \(-0.505039\pi\) | ||||
−0.0158312 | + | 0.999875i | \(0.505039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12166.5 | −1.22123 | −0.610613 | − | 0.791930i | \(-0.709077\pi\) | ||||
−0.610613 | + | 0.791930i | \(0.709077\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2450.91 | 0.244426 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1844.42 | −0.182761 | −0.0913806 | − | 0.995816i | \(-0.529128\pi\) | ||||
−0.0913806 | + | 0.995816i | \(0.529128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18326.4 | 1.80434 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11099.8 | 1.08589 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1537.15 | −0.149425 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3528.32 | −0.340822 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5554.75 | 0.533196 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16355.9 | −1.56017 | −0.780084 | − | 0.625675i | \(-0.784824\pi\) | ||||
−0.780084 | + | 0.625675i | \(0.784824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2751.28 | 0.260806 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28024.9 | 2.64012 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5292.43 | 0.495499 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11824.6 | −1.10025 | −0.550126 | − | 0.835082i | \(-0.685420\pi\) | ||||
−0.550126 | + | 0.835082i | \(0.685420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10708.9 | 0.990337 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7931.40 | 0.729000 | 0.364500 | − | 0.931203i | \(-0.381240\pi\) | ||||
0.364500 | + | 0.931203i | \(0.381240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5137.34 | −0.469319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 481.315 | 0.0437040 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13212.0 | −1.19243 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2734.69 | 0.245333 | 0.122667 | − | 0.992448i | \(-0.460855\pi\) | ||||
0.122667 | + | 0.992448i | \(0.460855\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24488.6 | 2.18377 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7297.64 | −0.646890 | −0.323445 | − | 0.946247i | \(-0.604841\pi\) | ||||
−0.323445 | + | 0.946247i | \(0.604841\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3449.96 | 0.304002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12986.5 | 1.13758 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10972.4 | 0.955486 | 0.477743 | − | 0.878500i | \(-0.341455\pi\) | ||||
0.477743 | + | 0.878500i | \(0.341455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30365.3 | 2.62873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13105.9 | −1.12796 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6449.81 | −0.551869 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −574.815 | −0.0488982 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24939.7 | 2.10931 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7693.43 | −0.646939 | −0.323470 | − | 0.946239i | \(-0.604849\pi\) | ||||
−0.323470 | + | 0.946239i | \(0.604849\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14535.3 | −1.21527 | −0.607634 | − | 0.794217i | \(-0.707881\pi\) | ||||
−0.607634 | + | 0.794217i | \(0.707881\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5417.41 | −0.450353 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4513.04 | −0.373038 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4558.69 | 0.374676 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4147.97 | −0.338995 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1013.76 | 0.0823840 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9218.70 | −0.744970 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5536.53 | −0.444914 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6776.81 | 0.541555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19131.8 | 1.52040 | 0.760202 | − | 0.649686i | \(-0.225100\pi\) | ||||
0.760202 | + | 0.649686i | \(0.225100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17589.3 | 1.39011 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1702.99 | 0.133850 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7142.78 | 0.558324 | 0.279162 | − | 0.960244i | \(-0.409943\pi\) | ||||
0.279162 | + | 0.960244i | \(0.409943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2639.67 | −0.205207 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12584.3 | 0.972974 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7062.39 | −0.543080 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7801.40 | 0.596668 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11347.8 | 0.863236 | 0.431618 | − | 0.902057i | \(-0.357943\pi\) | ||||
0.431618 | + | 0.902057i | \(0.357943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2142.74 | 0.162126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2854.07 | −0.214793 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8802.19 | −0.658913 | −0.329456 | − | 0.944171i | \(-0.606865\pi\) | ||||
−0.329456 | + | 0.944171i | \(0.606865\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 789.153 | 0.0587609 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31492.6 | −2.33257 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16714.7 | −1.23149 | −0.615744 | − | 0.787946i | \(-0.711145\pi\) | ||||
−0.615744 | + | 0.787946i | \(0.711145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17386.8 | 1.27428 | 0.637142 | − | 0.770746i | \(-0.280116\pi\) | ||||
0.637142 | + | 0.770746i | \(0.280116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4689.14 | 0.341870 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3233.20 | −0.234493 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2260.52 | 0.163097 | 0.0815483 | − | 0.996669i | \(-0.474014\pi\) | ||||
0.0815483 | + | 0.996669i | \(0.474014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24842.6 | 1.78311 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34512.1 | −2.46438 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3615.86 | 0.256867 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −670.940 | −0.0474187 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25591.0 | 1.79941 | 0.899705 | − | 0.436498i | \(-0.143781\pi\) | ||||
0.899705 | + | 0.436498i | \(0.143781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11055.0 | 0.773369 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14037.6 | −0.977037 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10053.7 | −0.696218 | −0.348109 | − | 0.937454i | \(-0.613176\pi\) | ||||
−0.348109 | + | 0.937454i | \(0.613176\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9975.49 | 0.687320 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4205.46 | −0.288305 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7086.68 | 0.483395 | 0.241698 | − | 0.970352i | \(-0.422296\pi\) | ||||
0.241698 | + | 0.970352i | \(0.422296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6673.11 | −0.452915 | −0.226458 | − | 0.974021i | \(-0.572714\pi\) | ||||
−0.226458 | + | 0.974021i | \(0.572714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6435.86 | 0.434641 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6341.69 | −0.426159 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15205.6 | −1.01677 | −0.508383 | − | 0.861131i | \(-0.669757\pi\) | ||||
−0.508383 | + | 0.861131i | \(0.669757\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19322.0 | 1.28566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 801.278 | 0.0530544 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8147.64 | 0.536836 | 0.268418 | − | 0.963303i | \(-0.413499\pi\) | ||||
0.268418 | + | 0.963303i | \(0.413499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2874.56 | 0.188477 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −449.110 | −0.0293039 | −0.0146519 | − | 0.999893i | \(-0.504664\pi\) | ||||
−0.0146519 | + | 0.999893i | \(0.504664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27800.4 | −1.80516 | −0.902579 | − | 0.430524i | \(-0.858329\pi\) | ||||
−0.902579 | + | 0.430524i | \(0.858329\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12009.7 | −0.776059 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5971.79 | −0.384037 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6991.26 | 0.445302 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14365.3 | −0.910623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14793.5 | −0.933315 | −0.466657 | − | 0.884438i | \(-0.654542\pi\) | ||||
−0.466657 | + | 0.884438i | \(0.654542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12109.4 | 0.760356 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2473.52 | 0.154580 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9446.70 | −0.587585 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4639.77 | −0.287240 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13853.8 | −0.853655 | −0.426828 | − | 0.904333i | \(-0.640369\pi\) | ||||
−0.426828 | + | 0.904333i | \(0.640369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4978.60 | −0.305345 | −0.152672 | − | 0.988277i | \(-0.548788\pi\) | ||||
−0.152672 | + | 0.988277i | \(0.548788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6075.86 | 0.370910 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1903.39 | 0.115657 | 0.0578284 | − | 0.998327i | \(-0.481582\pi\) | ||||
0.0578284 | + | 0.998327i | \(0.481582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2700.11 | −0.163311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16974.0 | 1.02191 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10877.0 | 0.651839 | 0.325920 | − | 0.945397i | \(-0.394326\pi\) | ||||
0.325920 | + | 0.945397i | \(0.394326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2443.91 | −0.145789 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10663.7 | 0.633226 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30611.3 | −1.80948 | −0.904739 | − | 0.425965i | \(-0.859935\pi\) | ||||
−0.904739 | + | 0.425965i | \(0.859935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16098.8 | 0.947310 | 0.473655 | − | 0.880710i | \(-0.342934\pi\) | ||||
0.473655 | + | 0.880710i | \(0.342934\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3978.50 | 0.233050 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24435.7 | −1.42493 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11531.7 | 0.669429 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15598.0 | −0.901428 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1718.29 | −0.0988583 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23837.8 | −1.36535 | −0.682673 | − | 0.730724i | \(-0.739183\pi\) | ||||
−0.682673 | + | 0.730724i | \(0.739183\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2321.56 | 0.132381 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25235.3 | −1.43260 | −0.716302 | − | 0.697791i | \(-0.754167\pi\) | ||||
−0.716302 | + | 0.697791i | \(0.754167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36653.2 | 2.07161 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19745.2 | −1.11107 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19975.3 | 1.11909 | 0.559543 | − | 0.828802i | \(-0.310977\pi\) | ||||
0.559543 | + | 0.828802i | \(0.310977\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7660.64 | 0.427297 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14389.5 | −0.799115 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5040.42 | −0.278700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13772.3 | 0.758209 | 0.379104 | − | 0.925354i | \(-0.376232\pi\) | ||||
0.379104 | + | 0.925354i | \(0.376232\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3333.39 | 0.182720 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3775.48 | −0.206060 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5293.14 | −0.287650 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4643.26 | 0.251251 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6347.90 | −0.342021 | −0.171011 | − | 0.985269i | \(-0.554703\pi\) | ||||
−0.171011 | + | 0.985269i | \(0.554703\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35188.9 | 1.88787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2272.06 | 0.121377 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23893.0 | 1.27099 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17910.5 | −0.948719 | −0.474360 | − | 0.880331i | \(-0.657320\pi\) | ||||
−0.474360 | + | 0.880331i | \(0.657320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2480.16 | −0.130821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10130.3 | 0.532096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −436.748 | −0.0228440 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −36208.0 | −1.88593 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36601.6 | 1.89849 | 0.949243 | − | 0.314545i | \(-0.101852\pi\) | ||||
0.949243 | + | 0.314545i | \(0.101852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44668.8 | −2.30728 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1658.67 | −0.0853201 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2229.16 | −0.114192 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2644.18 | −0.134893 | −0.0674466 | − | 0.997723i | \(-0.521485\pi\) | ||||
−0.0674466 | + | 0.997723i | \(0.521485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4630.66 | 0.235262 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11187.9 | −0.566075 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33452.1 | 1.68565 | 0.842825 | − | 0.538188i | \(-0.180891\pi\) | ||||
0.842825 | + | 0.538188i | \(0.180891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −26786.6 | −1.34427 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4189.42 | 0.209388 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25834.9 | 1.28600 | 0.642999 | − | 0.765867i | \(-0.277690\pi\) | ||||
0.642999 | + | 0.765867i | \(0.277690\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9745.64 | −0.483151 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7625.09 | −0.376497 | −0.188249 | − | 0.982121i | \(-0.560281\pi\) | ||||
−0.188249 | + | 0.982121i | \(0.560281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7233.37 | 0.355718 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12119.9 | −0.593635 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −63845.0 | −3.11461 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25362.7 | 1.23235 | 0.616177 | − | 0.787607i | \(-0.288680\pi\) | ||||
0.616177 | + | 0.787607i | \(0.288680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11026.4 | 0.533633 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6151.02 | 0.296502 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38948.0 | 1.87000 | 0.935000 | − | 0.354648i | \(-0.115399\pi\) | ||||
0.935000 | + | 0.354648i | \(0.115399\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6406.48 | 0.306378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13722.2 | 0.653654 | 0.326827 | − | 0.945084i | \(-0.394021\pi\) | ||||
0.326827 | + | 0.945084i | \(0.394021\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11794.2 | 0.559606 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3503.19 | 0.165566 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3763.89 | 0.177192 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18689.5 | 0.876414 | 0.438207 | − | 0.898874i | \(-0.355614\pi\) | ||||
0.438207 | + | 0.898874i | \(0.355614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9435.86 | 0.440758 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6386.49 | −0.297162 | −0.148581 | − | 0.988900i | \(-0.547471\pi\) | ||||
−0.148581 | + | 0.988900i | \(0.547471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1958.27 | −0.0907653 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 54029.3 | 2.49458 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12965.9 | 0.596345 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3020.25 | −0.138378 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8280.21 | −0.377919 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8868.71 | −0.403233 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19410.3 | −0.879167 | −0.439583 | − | 0.898202i | \(-0.644874\pi\) | ||||
−0.439583 | + | 0.898202i | \(0.644874\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17350.1 | 0.782865 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5465.35 | 0.245671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2395.25 | 0.107261 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14292.3 | −0.637607 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30740.8 | 1.36624 | 0.683121 | − | 0.730305i | \(-0.260622\pi\) | ||||
0.683121 | + | 0.730305i | \(0.260622\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4183.72 | −0.185243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2097.17 | −0.0925092 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6941.51 | 0.305057 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22391.8 | −0.980382 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32331.9 | −1.41033 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31805.5 | −1.38223 | −0.691114 | − | 0.722746i | \(-0.742880\pi\) | ||||
−0.691114 | + | 0.722746i | \(0.742880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31014.7 | −1.34288 | −0.671439 | − | 0.741060i | \(-0.734323\pi\) | ||||
−0.671439 | + | 0.741060i | \(0.734323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9128.90 | 0.393806 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8556.41 | −0.367752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27405.7 | 1.17357 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4646.66 | −0.198251 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12021.4 | 0.511021 | 0.255511 | − | 0.966806i | \(-0.417756\pi\) | ||||
0.255511 | + | 0.966806i | \(0.417756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15489.0 | −0.656032 | −0.328016 | − | 0.944672i | \(-0.606380\pi\) | ||||
−0.328016 | + | 0.944672i | \(0.606380\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1238.42 | −0.0522621 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17097.2 | −0.718898 | −0.359449 | − | 0.933165i | \(-0.617035\pi\) | ||||
−0.359449 | + | 0.933165i | \(0.617035\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9885.97 | −0.414178 | −0.207089 | − | 0.978322i | \(-0.566399\pi\) | ||||
−0.207089 | + | 0.978322i | \(0.566399\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12481.9 | 0.521050 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 49324.2 | 2.05160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19566.3 | −0.810922 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7273.99 | −0.300389 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39204.3 | 1.61321 | 0.806606 | − | 0.591090i | \(-0.201302\pi\) | ||||
0.806606 | + | 0.591090i | \(0.201302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16438.4 | −0.674007 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1949.84 | −0.0796632 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10376.2 | −0.422428 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43920.0 | −1.78171 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37999.7 | 1.53610 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32245.5 | 1.29890 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45054.1 | 1.80847 | 0.904234 | − | 0.427038i | \(-0.140443\pi\) | ||||
0.904234 | + | 0.427038i | \(0.140443\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8581.31 | −0.343245 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48464.2 | 1.93174 | 0.965872 | − | 0.259021i | \(-0.0834000\pi\) | ||||
0.965872 | + | 0.259021i | \(0.0834000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1000.76 | −0.0397503 | −0.0198751 | − | 0.999802i | \(-0.506327\pi\) | ||||
−0.0198751 | + | 0.999802i | \(0.506327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19908.0 | 0.787995 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22485.5 | 0.886922 | 0.443461 | − | 0.896294i | \(-0.353750\pi\) | ||||
0.443461 | + | 0.896294i | \(0.353750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19926.7 | −0.783270 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9971.79 | 0.390611 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1614.46 | −0.0630228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5839.94 | −0.227186 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12871.9 | 0.499022 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4328.50 | 0.167234 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43726.2 | 1.68361 | 0.841806 | − | 0.539780i | \(-0.181493\pi\) | ||||
0.841806 | + | 0.539780i | \(0.181493\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14524.8 | 0.557349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20290.0 | 0.775923 | 0.387962 | − | 0.921675i | \(-0.373179\pi\) | ||||
0.387962 | + | 0.921675i | \(0.373179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14887.3 | −0.567382 | −0.283691 | − | 0.958916i | \(-0.591559\pi\) | ||||
−0.283691 | + | 0.958916i | \(0.591559\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10672.7 | 0.405377 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34359.3 | −1.30065 | −0.650323 | − | 0.759658i | \(-0.725367\pi\) | ||||
−0.650323 | + | 0.759658i | \(0.725367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17130.6 | 0.646278 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7199.21 | −0.270687 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10248.3 | 0.384040 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4423.67 | 0.165214 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8930.47 | −0.332419 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6984.47 | 0.259116 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26317.6 | 0.973103 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42078.9 | 1.55072 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14053.8 | −0.516205 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −53363.9 | −1.95360 | −0.976802 | − | 0.214144i | \(-0.931304\pi\) | ||||
−0.976802 | + | 0.214144i | \(0.931304\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8390.73 | 0.306164 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25213.9 | −0.916984 | −0.458492 | − | 0.888699i | \(-0.651610\pi\) | ||||
−0.458492 | + | 0.888699i | \(0.651610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7889.46 | −0.285984 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6791.86 | 0.245390 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16925.5 | −0.609521 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3747.02 | −0.134497 | −0.0672485 | − | 0.997736i | \(-0.521422\pi\) | ||||
−0.0672485 | + | 0.997736i | \(0.521422\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15641.1 | −0.559599 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4210.15 | 0.150140 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6233.29 | −0.221567 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15686.8 | −0.555794 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27726.7 | −0.979209 | −0.489604 | − | 0.871945i | \(-0.662859\pi\) | ||||
−0.489604 | + | 0.871945i | \(0.662859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −120823. | −4.25330 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19104.1 | −0.670355 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2280.40 | 0.0797614 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29333.2 | −1.02270 | −0.511352 | − | 0.859371i | \(-0.670855\pi\) | ||||
−0.511352 | + | 0.859371i | \(0.670855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38668.7 | 1.34388 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24218.4 | 0.838998 | 0.419499 | − | 0.907756i | \(-0.362206\pi\) | ||||
0.419499 | + | 0.907756i | \(0.362206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11881.4 | 0.410299 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16078.2 | 0.553464 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50824.6 | −1.74401 | −0.872005 | − | 0.489497i | \(-0.837180\pi\) | ||||
−0.872005 | + | 0.489497i | \(0.837180\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9676.28 | −0.330986 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19500.7 | −0.664935 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10155.1 | 0.345180 | 0.172590 | − | 0.984994i | \(-0.444786\pi\) | ||||
0.172590 | + | 0.984994i | \(0.444786\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3746.61 | −0.126950 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4417.01 | 0.149197 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53054.5 | 1.78646 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23655.3 | −0.794042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22421.0 | −0.750268 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19849.2 | −0.662142 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28225.7 | 0.938652 | 0.469326 | − | 0.883025i | \(-0.344497\pi\) | ||||
0.469326 | + | 0.883025i | \(0.344497\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 50885.0 | 1.68696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47631.4 | 1.57422 | 0.787109 | − | 0.616814i | \(-0.211577\pi\) | ||||
0.787109 | + | 0.616814i | \(0.211577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26147.4 | −0.861508 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1726.32 | 0.0567042 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13542.4 | 0.443460 | 0.221730 | − | 0.975108i | \(-0.428830\pi\) | ||||
0.221730 | + | 0.975108i | \(0.428830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1365.15 | −0.0445663 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4141.88 | 0.134801 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35108.5 | 1.13915 | 0.569576 | − | 0.821938i | \(-0.307107\pi\) | ||||
0.569576 | + | 0.821938i | \(0.307107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11216.0 | 0.362813 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15735.4 | 0.507460 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25113.4 | 0.807440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42816.1 | −1.37245 | −0.686225 | − | 0.727390i | \(-0.740733\pi\) | ||||
−0.686225 | + | 0.727390i | \(0.740733\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26015.5 | −0.831396 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3360.15 | 0.107059 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13029.0 | 0.413873 | 0.206936 | − | 0.978354i | \(-0.433651\pi\) | ||||
0.206936 | + | 0.978354i | \(0.433651\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23153.6 | −0.733280 |
(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 | 1280.4.a.bb.1.2 | 6 | ||
4.3 | odd | 2 | 1280.4.a.bd.1.5 | 6 | |||
8.3 | odd | 2 | 1280.4.a.ba.1.2 | 6 | |||
8.5 | even | 2 | 1280.4.a.bc.1.5 | 6 | |||
16.3 | odd | 4 | 160.4.d.a.81.10 | 12 | |||
16.5 | even | 4 | 40.4.d.a.21.2 | yes | 12 | ||
16.11 | odd | 4 | 160.4.d.a.81.3 | 12 | |||
16.13 | even | 4 | 40.4.d.a.21.1 | ✓ | 12 | ||
48.5 | odd | 4 | 360.4.k.c.181.11 | 12 | |||
48.11 | even | 4 | 1440.4.k.c.721.6 | 12 | |||
48.29 | odd | 4 | 360.4.k.c.181.12 | 12 | |||
48.35 | even | 4 | 1440.4.k.c.721.12 | 12 | |||
80.3 | even | 4 | 800.4.f.b.49.3 | 12 | |||
80.13 | odd | 4 | 200.4.f.c.149.4 | 12 | |||
80.19 | odd | 4 | 800.4.d.d.401.3 | 12 | |||
80.27 | even | 4 | 800.4.f.b.49.4 | 12 | |||
80.29 | even | 4 | 200.4.d.b.101.12 | 12 | |||
80.37 | odd | 4 | 200.4.f.c.149.3 | 12 | |||
80.43 | even | 4 | 800.4.f.c.49.9 | 12 | |||
80.53 | odd | 4 | 200.4.f.b.149.10 | 12 | |||
80.59 | odd | 4 | 800.4.d.d.401.10 | 12 | |||
80.67 | even | 4 | 800.4.f.c.49.10 | 12 | |||
80.69 | even | 4 | 200.4.d.b.101.11 | 12 | |||
80.77 | odd | 4 | 200.4.f.b.149.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.d.a.21.1 | ✓ | 12 | 16.13 | even | 4 | ||
40.4.d.a.21.2 | yes | 12 | 16.5 | even | 4 | ||
160.4.d.a.81.3 | 12 | 16.11 | odd | 4 | |||
160.4.d.a.81.10 | 12 | 16.3 | odd | 4 | |||
200.4.d.b.101.11 | 12 | 80.69 | even | 4 | |||
200.4.d.b.101.12 | 12 | 80.29 | even | 4 | |||
200.4.f.b.149.9 | 12 | 80.77 | odd | 4 | |||
200.4.f.b.149.10 | 12 | 80.53 | odd | 4 | |||
200.4.f.c.149.3 | 12 | 80.37 | odd | 4 | |||
200.4.f.c.149.4 | 12 | 80.13 | odd | 4 | |||
360.4.k.c.181.11 | 12 | 48.5 | odd | 4 | |||
360.4.k.c.181.12 | 12 | 48.29 | odd | 4 | |||
800.4.d.d.401.3 | 12 | 80.19 | odd | 4 | |||
800.4.d.d.401.10 | 12 | 80.59 | odd | 4 | |||
800.4.f.b.49.3 | 12 | 80.3 | even | 4 | |||
800.4.f.b.49.4 | 12 | 80.27 | even | 4 | |||
800.4.f.c.49.9 | 12 | 80.43 | even | 4 | |||
800.4.f.c.49.10 | 12 | 80.67 | even | 4 | |||
1280.4.a.ba.1.2 | 6 | 8.3 | odd | 2 | |||
1280.4.a.bb.1.2 | 6 | 1.1 | even | 1 | trivial | ||
1280.4.a.bc.1.5 | 6 | 8.5 | even | 2 | |||
1280.4.a.bd.1.5 | 6 | 4.3 | odd | 2 | |||
1440.4.k.c.721.6 | 12 | 48.11 | even | 4 | |||
1440.4.k.c.721.12 | 12 | 48.35 | even | 4 |