Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [464,4,Mod(1,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, 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("464.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 464.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: | \(27.3768862427\) |
Analytic rank: | \(0\) |
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: | \( x^{6} - 40x^{4} - 88x^{3} - 8x^{2} + 48x - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(7.22553\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 464.1 |
$q$-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 | ||||||||
\(3\) | 9.88017 | 1.90144 | 0.950719 | − | 0.310053i | \(-0.100347\pi\) | ||||
0.950719 | + | 0.310053i | \(0.100347\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.64112 | 0.236229 | 0.118114 | − | 0.993000i | \(-0.462315\pi\) | ||||
0.118114 | + | 0.993000i | \(0.462315\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.30580 | −0.178496 | −0.0892482 | − | 0.996009i | \(-0.528446\pi\) | ||||
−0.0892482 | + | 0.996009i | \(0.528446\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 70.6177 | 2.61547 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.3440 | 0.776913 | 0.388457 | − | 0.921467i | \(-0.373008\pi\) | ||||
0.388457 | + | 0.921467i | \(0.373008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 85.7400 | 1.82923 | 0.914615 | − | 0.404325i | \(-0.132494\pi\) | ||||
0.914615 | + | 0.404325i | \(0.132494\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.0947 | 0.449175 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −111.092 | −1.58492 | −0.792462 | − | 0.609922i | \(-0.791201\pi\) | ||||
−0.792462 | + | 0.609922i | \(0.791201\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −99.8826 | −1.20603 | −0.603017 | − | 0.797729i | \(-0.706035\pi\) | ||||
−0.603017 | + | 0.797729i | \(0.706035\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −32.6619 | −0.339400 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 110.105 | 0.998196 | 0.499098 | − | 0.866546i | \(-0.333665\pi\) | ||||
0.499098 | + | 0.866546i | \(0.333665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −118.024 | −0.944196 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 430.950 | 3.07172 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 60.0577 | 0.347957 | 0.173979 | − | 0.984749i | \(-0.444338\pi\) | ||||
0.173979 | + | 0.984749i | \(0.444338\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 280.044 | 1.47725 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.73102 | −0.0421660 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 119.286 | 0.530014 | 0.265007 | − | 0.964247i | \(-0.414626\pi\) | ||||
0.265007 | + | 0.964247i | \(0.414626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 847.126 | 3.47817 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −285.212 | −1.08641 | −0.543204 | − | 0.839601i | \(-0.682789\pi\) | ||||
−0.543204 | + | 0.839601i | \(0.682789\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 249.574 | 0.885110 | 0.442555 | − | 0.896741i | \(-0.354072\pi\) | ||||
0.442555 | + | 0.896741i | \(0.354072\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 186.510 | 0.617850 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 226.276 | 0.702251 | 0.351125 | − | 0.936328i | \(-0.385799\pi\) | ||||
0.351125 | + | 0.936328i | \(0.385799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −332.072 | −0.968139 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1097.60 | −3.01363 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 387.165 | 1.00342 | 0.501709 | − | 0.865036i | \(-0.332705\pi\) | ||||
0.501709 | + | 0.865036i | \(0.332705\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 74.8600 | 0.183529 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −986.857 | −2.29320 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −164.811 | −0.363670 | −0.181835 | − | 0.983329i | \(-0.558204\pi\) | ||||
−0.181835 | + | 0.983329i | \(0.558204\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 188.155 | 0.394932 | 0.197466 | − | 0.980310i | \(-0.436729\pi\) | ||||
0.197466 | + | 0.980310i | \(0.436729\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −233.448 | −0.466852 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 226.450 | 0.432117 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 903.648 | 1.64773 | 0.823867 | − | 0.566783i | \(-0.191812\pi\) | ||||
0.823867 | + | 0.566783i | \(0.191812\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1087.86 | 1.89801 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −820.374 | −1.37127 | −0.685637 | − | 0.727943i | \(-0.740476\pi\) | ||||
−0.685637 | + | 0.727943i | \(0.740476\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −394.228 | −0.632066 | −0.316033 | − | 0.948748i | \(-0.602351\pi\) | ||||
−0.316033 | + | 0.948748i | \(0.602351\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1166.10 | −1.79533 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −93.6997 | −0.138676 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −605.439 | −0.862243 | −0.431122 | − | 0.902294i | \(-0.641882\pi\) | ||||
−0.431122 | + | 0.902294i | \(0.641882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2351.18 | 3.22521 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 504.986 | 0.667824 | 0.333912 | − | 0.942604i | \(-0.391631\pi\) | ||||
0.333912 | + | 0.942604i | \(0.391631\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −293.406 | −0.374405 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −286.525 | −0.353088 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −930.620 | −1.10838 | −0.554189 | − | 0.832391i | \(-0.686971\pi\) | ||||
−0.554189 | + | 0.832391i | \(0.686971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −283.439 | −0.326511 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 593.380 | 0.661620 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −263.802 | −0.284900 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2577 | 0.0128307 | 0.00641535 | − | 0.999979i | \(-0.497958\pi\) | ||||
0.00641535 | + | 0.999979i | \(0.497958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2001.59 | 2.03199 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1165.44 | −1.14818 | −0.574089 | − | 0.818793i | \(-0.694644\pi\) | ||||
−0.574089 | + | 0.818793i | \(0.694644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 216.871 | 0.207465 | 0.103733 | − | 0.994605i | \(-0.466921\pi\) | ||||
0.103733 | + | 0.994605i | \(0.466921\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −86.2639 | −0.0801761 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1868.17 | 1.68787 | 0.843937 | − | 0.536443i | \(-0.180232\pi\) | ||||
0.843937 | + | 0.536443i | \(0.180232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −624.737 | −0.548981 | −0.274490 | − | 0.961590i | \(-0.588509\pi\) | ||||
−0.274490 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1178.57 | 1.00779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1181.43 | −0.983537 | −0.491769 | − | 0.870726i | \(-0.663649\pi\) | ||||
−0.491769 | + | 0.870726i | \(0.663649\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 290.801 | 0.235803 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6054.76 | 4.78430 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 367.247 | 0.282903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −527.616 | −0.396406 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2817.95 | −2.06574 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −641.857 | −0.459275 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1693.76 | −1.18344 | −0.591720 | − | 0.806144i | \(-0.701551\pi\) | ||||
−0.591720 | + | 0.806144i | \(0.701551\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2465.84 | 1.68298 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 195.314 | 0.130265 | 0.0651323 | − | 0.997877i | \(-0.479253\pi\) | ||||
0.0651323 | + | 0.997877i | \(0.479253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 330.192 | 0.215273 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1138.19 | 0.725628 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −319.479 | −0.199233 | −0.0996164 | − | 0.995026i | \(-0.531762\pi\) | ||||
−0.0996164 | + | 0.995026i | \(0.531762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1096.70 | 0.669213 | 0.334607 | − | 0.942358i | \(-0.391397\pi\) | ||||
0.334607 | + | 0.942358i | \(0.391397\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2235.65 | 1.33529 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2430.22 | 1.42115 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −76.5925 | −0.0438666 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3280.92 | −1.84086 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1194.25 | 0.656625 | 0.328312 | − | 0.944569i | \(-0.393520\pi\) | ||||
0.328312 | + | 0.944569i | \(0.393520\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2259.35 | −1.21764 | −0.608819 | − | 0.793309i | \(-0.708357\pi\) | ||||
−0.608819 | + | 0.793309i | \(0.708357\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7845.04 | −4.14532 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 158.620 | 0.0821976 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2592.33 | −1.31777 | −0.658887 | − | 0.752242i | \(-0.728972\pi\) | ||||
−0.658887 | + | 0.752242i | \(0.728972\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3825.25 | 1.90794 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −363.986 | −0.178174 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −498.162 | −0.239381 | −0.119690 | − | 0.992811i | \(-0.538190\pi\) | ||||
−0.119690 | + | 0.992811i | \(0.538190\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 739.629 | 0.348970 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −551.442 | −0.255520 | −0.127760 | − | 0.991805i | \(-0.540779\pi\) | ||||
−0.127760 | + | 0.991805i | \(0.540779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5154.35 | 2.34609 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7053.48 | −3.15434 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2539.86 | 1.11620 | 0.558099 | − | 0.829774i | \(-0.311531\pi\) | ||||
0.558099 | + | 0.829774i | \(0.311531\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 390.165 | 0.168536 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1628.36 | −0.691496 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −739.618 | −0.308836 | −0.154418 | − | 0.988006i | \(-0.549350\pi\) | ||||
−0.154418 | + | 0.988006i | \(0.549350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4127.70 | −1.69508 | −0.847539 | − | 0.530733i | \(-0.821917\pi\) | ||||
−0.847539 | + | 0.530733i | \(0.821917\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1859.01 | 0.750938 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 315.049 | 0.125205 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3148.79 | −1.23135 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1424.63 | −0.548290 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1630.27 | 0.617605 | 0.308802 | − | 0.951126i | \(-0.400072\pi\) | ||||
0.308802 | + | 0.951126i | \(0.400072\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −210.636 | −0.0785592 | −0.0392796 | − | 0.999228i | \(-0.512506\pi\) | ||||
−0.0392796 | + | 0.999228i | \(0.512506\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2237.36 | 0.821645 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4418.37 | −1.59795 | −0.798974 | − | 0.601366i | \(-0.794623\pi\) | ||||
−0.798974 | + | 0.601366i | \(0.794623\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1436.52 | 0.511721 | 0.255860 | − | 0.966714i | \(-0.417641\pi\) | ||||
0.255860 | + | 0.966714i | \(0.417641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8928.19 | 3.13307 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 95.8682 | 0.0331460 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −753.280 | −0.256641 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7775.37 | 2.61075 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2831.07 | −0.936983 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3571.25 | −1.16519 | −0.582595 | − | 0.812763i | \(-0.697963\pi\) | ||||
−0.582595 | + | 0.812763i | \(0.697963\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8105.43 | −2.60739 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 659.156 | 0.209089 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −198.539 | −0.0621092 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3895.03 | −1.20184 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9525.00 | −2.89919 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6382.81 | 1.91670 | 0.958351 | − | 0.285594i | \(-0.0921909\pi\) | ||||
0.958351 | + | 0.285594i | \(0.0921909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8334.61 | −2.46952 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4565.57 | −1.33492 | −0.667462 | − | 0.744644i | \(-0.732619\pi\) | ||||
−0.667462 | + | 0.744644i | \(0.732619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5084.23 | 1.46714 | 0.733570 | − | 0.679614i | \(-0.237853\pi\) | ||||
0.733570 | + | 0.679614i | \(0.237853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −925.769 | −0.263684 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5743.69 | −1.61494 | −0.807471 | − | 0.589907i | \(-0.799164\pi\) | ||||
−0.807471 | + | 0.589907i | \(0.799164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 597.623 | 0.165892 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5981.84 | −1.63950 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5554.14 | −1.50321 | −0.751605 | − | 0.659614i | \(-0.770720\pi\) | ||||
−0.751605 | + | 0.659614i | \(0.770720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2222.62 | −0.594073 | −0.297036 | − | 0.954866i | \(-0.595998\pi\) | ||||
−0.297036 | + | 0.954866i | \(0.595998\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11594.4 | 3.06082 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −877.041 | −0.228702 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8563.93 | −2.20611 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4989.34 | 1.26983 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4973.67 | −1.25074 | −0.625369 | − | 0.780329i | \(-0.715052\pi\) | ||||
−0.625369 | + | 0.780329i | \(0.715052\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3120.82 | 0.775512 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2898.90 | −0.711908 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0797 | 0.00366011 | 0.00183005 | − | 0.999998i | \(-0.499417\pi\) | ||||
0.00183005 | + | 0.999998i | \(0.499417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −394.336 | −0.0946056 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2047.91 | −0.485680 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3238.30 | −0.759248 | −0.379624 | − | 0.925141i | \(-0.623947\pi\) | ||||
−0.379624 | + | 0.925141i | \(0.623947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1022.55 | 0.237037 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9194.68 | −2.10751 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4147.30 | 0.940020 | 0.470010 | − | 0.882661i | \(-0.344250\pi\) | ||||
0.470010 | + | 0.882661i | \(0.344250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1309.45 | −0.293519 | −0.146759 | − | 0.989172i | \(-0.546884\pi\) | ||||
−0.146759 | + | 0.989172i | \(0.546884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2800.43 | −0.620841 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3345.29 | −0.733558 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6746.76 | 1.46344 | 0.731721 | − | 0.681604i | \(-0.238717\pi\) | ||||
0.731721 | + | 0.681604i | \(0.238717\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4241.13 | 0.910072 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2896.25 | 0.614861 | 0.307430 | − | 0.951571i | \(-0.400531\pi\) | ||||
0.307430 | + | 0.951571i | \(0.400531\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8577.44 | 1.80168 | 0.900841 | − | 0.434150i | \(-0.142951\pi\) | ||||
0.900841 | + | 0.434150i | \(0.142951\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2606.41 | −0.541720 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 942.856 | 0.193920 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7428.36 | 1.51198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 121.108 | 0.0243968 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8204.00 | −1.63578 | −0.817888 | − | 0.575377i | \(-0.804855\pi\) | ||||
−0.817888 | + | 0.575377i | \(0.804855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −435.285 | −0.0859093 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12214.9 | 2.38646 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9440.41 | 1.82593 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −825.044 | −0.157989 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11514.8 | −2.18319 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 496.941 | 0.0932943 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2506.45 | 0.465963 | 0.232981 | − | 0.972481i | \(-0.425152\pi\) | ||||
0.232981 | + | 0.972481i | \(0.425152\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2142.72 | 0.394482 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6501.50 | 1.18542 | 0.592711 | − | 0.805415i | \(-0.298058\pi\) | ||||
0.592711 | + | 0.805415i | \(0.298058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7244.35 | 1.30823 | 0.654113 | − | 0.756397i | \(-0.273042\pi\) | ||||
0.654113 | + | 0.756397i | \(0.273042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −616.564 | −0.110284 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8069.20 | 1.42969 | 0.714845 | − | 0.699283i | \(-0.246497\pi\) | ||||
0.714845 | + | 0.699283i | \(0.246497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −821.977 | −0.144269 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18457.8 | 3.20939 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11096.1 | 1.91147 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10119.4 | −1.72715 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6172.50 | −1.04385 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −748.024 | −0.125349 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6351.97 | −1.05479 | −0.527396 | − | 0.849620i | \(-0.676832\pi\) | ||||
−0.527396 | + | 0.849620i | \(0.676832\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8423.71 | 1.38624 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2386.64 | 0.389242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1126.41 | −0.182076 | −0.0910381 | − | 0.995847i | \(-0.529019\pi\) | ||||
−0.0910381 | + | 0.995847i | \(0.529019\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11672.7 | −1.87014 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1702.28 | 0.270333 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2231.65 | 0.351306 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2873.16 | 0.448365 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5208.09 | −0.805720 | −0.402860 | − | 0.915262i | \(-0.631984\pi\) | ||||
−0.402860 | + | 0.915262i | \(0.631984\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9644.73 | 1.47928 | 0.739642 | − | 0.673000i | \(-0.234995\pi\) | ||||
0.739642 | + | 0.673000i | \(0.234995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36949.6 | 5.61888 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3082.55 | 0.464780 | 0.232390 | − | 0.972623i | \(-0.425345\pi\) | ||||
0.232390 | + | 0.972623i | \(0.425345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2166.71 | −0.323935 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3628.46 | 0.537923 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5668.89 | −0.833405 | −0.416702 | − | 0.909043i | \(-0.636814\pi\) | ||||
−0.416702 | + | 0.909043i | \(0.636814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3117.53 | 0.454517 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5212.94 | −0.753742 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1041.20 | −0.149312 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12831.6 | 1.82507 | 0.912537 | − | 0.408994i | \(-0.134120\pi\) | ||||
0.912537 | + | 0.408994i | \(0.134120\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20141.0 | −2.84147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1279.89 | −0.179107 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5541.65 | 0.769265 | 0.384632 | − | 0.923070i | \(-0.374328\pi\) | ||||
0.384632 | + | 0.923070i | \(0.374328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6341.65 | −0.873284 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2486.46 | −0.339680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11614.1 | −1.57408 | −0.787039 | − | 0.616903i | \(-0.788387\pi\) | ||||
−0.787039 | + | 0.616903i | \(0.788387\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16734.6 | −2.25024 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2733.89 | −0.364739 | −0.182370 | − | 0.983230i | \(-0.558377\pi\) | ||||
−0.182370 | + | 0.983230i | \(0.558377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −247.472 | −0.0327593 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17624.4 | 2.31498 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8079.05 | −1.05302 | −0.526509 | − | 0.850169i | \(-0.676499\pi\) | ||||
−0.526509 | + | 0.850169i | \(0.676499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12231.8 | −1.58206 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1929.73 | 0.247690 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1599.04 | −0.203687 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4371.33 | −0.552622 | −0.276311 | − | 0.961068i | \(-0.589112\pi\) | ||||
−0.276311 | + | 0.961068i | \(0.589112\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3262.35 | 0.409328 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15230.3 | −1.89667 | −0.948337 | − | 0.317265i | \(-0.897236\pi\) | ||||
−0.948337 | + | 0.317265i | \(0.897236\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5149.35 | 0.636494 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6209.74 | 0.761888 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3381.05 | 0.411775 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −382.195 | −0.0462061 | −0.0231031 | − | 0.999733i | \(-0.507355\pi\) | ||||
−0.0231031 | + | 0.999733i | \(0.507355\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3156.50 | −0.378829 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 544.831 | 0.0649138 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1333.73 | 0.157759 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10835.6 | 1.27247 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5109.88 | 0.595785 | 0.297893 | − | 0.954599i | \(-0.403716\pi\) | ||||
0.297893 | + | 0.954599i | \(0.403716\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9354.78 | 1.08295 | 0.541477 | − | 0.840715i | \(-0.317865\pi\) | ||||
0.541477 | + | 0.840715i | \(0.317865\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15979.1 | 1.83672 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13111.5 | 1.49648 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −622.004 | −0.0704939 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24010.9 | 2.70224 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3609.19 | 0.403361 | 0.201680 | − | 0.979451i | \(-0.435360\pi\) | ||||
0.201680 | + | 0.979451i | \(0.435360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3781.22 | −0.419662 | −0.209831 | − | 0.977738i | \(-0.567291\pi\) | ||||
−0.209831 | + | 0.977738i | \(0.567291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −756.746 | −0.0834097 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10997.6 | −1.20386 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1990.19 | 0.216370 | 0.108185 | − | 0.994131i | \(-0.465496\pi\) | ||||
0.108185 | + | 0.994131i | \(0.465496\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −23450.1 | −2.53214 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2859.89 | 0.306721 | 0.153361 | − | 0.988170i | \(-0.450990\pi\) | ||||
0.153361 | + | 0.988170i | \(0.450990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2457.88 | −0.261831 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11799.4 | 1.24853 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1177.30 | −0.123742 | −0.0618709 | − | 0.998084i | \(-0.519707\pi\) | ||||
−0.0618709 | + | 0.998084i | \(0.519707\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8084.07 | −0.844044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22322.8 | −2.31527 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −748.597 | −0.0771314 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 427.683 | 0.0437772 | 0.0218886 | − | 0.999760i | \(-0.493032\pi\) | ||||
0.0218886 | + | 0.999760i | \(0.493032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −47874.9 | −4.86843 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12610.0 | 1.27399 | 0.636994 | − | 0.770869i | \(-0.280178\pi\) | ||||
0.636994 | + | 0.770869i | \(0.280178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4584.31 | 0.460153 | 0.230076 | − | 0.973173i | \(-0.426102\pi\) | ||||
0.230076 | + | 0.973173i | \(0.426102\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1567.19 | 0.156294 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 315.535 | 0.0312660 | 0.0156330 | − | 0.999878i | \(-0.495024\pi\) | ||||
0.0156330 | + | 0.999878i | \(0.495024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2987.28 | −0.294115 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25612.6 | −2.50566 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7073.95 | 0.687654 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11788.6 | 1.13873 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27340.7 | 2.62441 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9507.29 | 0.906888 | 0.453444 | − | 0.891285i | \(-0.350195\pi\) | ||||
0.453444 | + | 0.891285i | \(0.350195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10227.6 | 0.969518 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3596.24 | −0.338788 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 32.3740 | 0.00303098 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2848.85 | −0.265079 | −0.132540 | − | 0.991178i | \(-0.542313\pi\) | ||||
−0.132540 | + | 0.991178i | \(0.542313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4921.92 | −0.455168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16581.9 | −1.52409 | −0.762046 | − | 0.647522i | \(-0.775805\pi\) | ||||
−0.762046 | + | 0.647522i | \(0.775805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3221.66 | 0.294313 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5286.44 | 0.480015 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2711.99 | 0.244768 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14103.9 | 1.26528 | 0.632642 | − | 0.774444i | \(-0.281970\pi\) | ||||
0.632642 | + | 0.774444i | \(0.281970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5448.34 | −0.485856 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1773.92 | 0.157247 | 0.0786236 | − | 0.996904i | \(-0.474947\pi\) | ||||
0.0786236 | + | 0.996904i | \(0.474947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3078.08 | −0.271233 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 50925.8 | 4.46094 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14432.9 | −1.25683 | −0.628414 | − | 0.777879i | \(-0.716296\pi\) | ||||
−0.628414 | + | 0.777879i | \(0.716296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1303.24 | 0.112822 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −43044.4 | −3.70459 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 572.782 | 0.0490093 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6413.58 | 0.545588 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25094.3 | 2.12238 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1855.69 | 0.156044 | 0.0780222 | − | 0.996952i | \(-0.475140\pi\) | ||||
0.0780222 | + | 0.996952i | \(0.475140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10294.0 | −0.860660 | −0.430330 | − | 0.902672i | \(-0.641603\pi\) | ||||
−0.430330 | + | 0.902672i | \(0.641603\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3854.90 | 0.320460 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6671.91 | −0.551486 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −43.8612 | −0.00360493 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11638.5 | −0.951167 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24454.1 | −1.98729 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4934.05 | 0.398725 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7307.55 | −0.587233 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9412.25 | −0.752160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4340.91 | −0.344973 | −0.172486 | − | 0.985012i | \(-0.555180\pi\) | ||||
−0.172486 | + | 0.985012i | \(0.555180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40782.3 | −3.22309 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1650.00 | −0.129685 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18868.8 | 1.47490 | 0.737452 | − | 0.675399i | \(-0.236029\pi\) | ||||
0.737452 | + | 0.675399i | \(0.236029\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13287.1 | 1.03293 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2896.60 | 0.223955 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2001.46 | 0.153907 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3112.74 | 0.238069 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6986.62 | 0.531477 | 0.265738 | − | 0.964045i | \(-0.414384\pi\) | ||||
0.265738 | + | 0.964045i | \(0.414384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21398.5 | 1.61907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31110.5 | −2.34133 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19006.3 | 1.42277 | 0.711386 | − | 0.702802i | \(-0.248068\pi\) | ||||
0.711386 | + | 0.702802i | \(0.248068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3120.30 | −0.232340 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7772.53 | −0.575689 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5475.13 | −0.403391 | −0.201696 | − | 0.979448i | \(-0.564645\pi\) | ||||
−0.201696 | + | 0.979448i | \(0.564645\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1264.86 | −0.0927016 | −0.0463508 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463508 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16107.4 | 1.17434 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12995.1 | −0.942492 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27670.3 | 1.99642 | 0.998208 | − | 0.0598463i | \(-0.0190611\pi\) | ||||
0.998208 | + | 0.0598463i | \(0.0190611\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2081.12 | −0.149375 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1669.38 | −0.119204 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10973.8 | 0.779569 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15991.3 | 1.13019 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6872.78 | −0.483254 | −0.241627 | − | 0.970369i | \(-0.577681\pi\) | ||||
−0.241627 | + | 0.970369i | \(0.577681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5998.72 | −0.419648 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43654.2 | −3.03840 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4896.40 | −0.339074 | −0.169537 | − | 0.985524i | \(-0.554227\pi\) | ||||
−0.169537 | + | 0.985524i | \(0.554227\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 969.943 | 0.0668299 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14193.1 | 0.973006 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11189.9 | 0.763282 | 0.381641 | − | 0.924311i | \(-0.375359\pi\) | ||||
0.381641 | + | 0.924311i | \(0.375359\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6271.18 | −0.425635 | −0.212818 | − | 0.977092i | \(-0.568264\pi\) | ||||
−0.212818 | + | 0.977092i | \(0.568264\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 63813.5 | 4.30960 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1393.50 | −0.0936426 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22094.6 | 1.47742 | 0.738710 | − | 0.674024i | \(-0.235436\pi\) | ||||
0.738710 | + | 0.674024i | \(0.235436\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 947.194 | 0.0630250 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19400.9 | 1.28458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26196.1 | 1.72602 | 0.863009 | − | 0.505189i | \(-0.168577\pi\) | ||||
0.863009 | + | 0.505189i | \(0.168577\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7442.53 | −0.487987 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1836.57 | 0.119834 | 0.0599169 | − | 0.998203i | \(-0.480916\pi\) | ||||
0.0599169 | + | 0.998203i | \(0.480916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4634.79 | 0.300950 | 0.150475 | − | 0.988614i | \(-0.451920\pi\) | ||||
0.150475 | + | 0.988614i | \(0.451920\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 47449.8 | 3.06617 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3076.45 | 0.197841 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13057.8 | 0.835702 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27971.5 | −1.78162 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13251.7 | −0.840031 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16556.8 | 1.04456 | 0.522278 | − | 0.852775i | \(-0.325082\pi\) | ||||
0.522278 | + | 0.852775i | \(0.325082\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35284.6 | −2.21554 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4473.42 | −0.279563 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28471.8 | −1.77095 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −57932.9 | −3.58653 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1437.66 | −0.0885866 | −0.0442933 | − | 0.999019i | \(-0.514104\pi\) | ||||
−0.0442933 | + | 0.999019i | \(0.514104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9284.85 | 0.569454 | 0.284727 | − | 0.958609i | \(-0.408097\pi\) | ||||
0.284727 | + | 0.958609i | \(0.408097\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6512.57 | 0.397569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14249.5 | −0.865852 | −0.432926 | − | 0.901430i | \(-0.642519\pi\) | ||||
−0.432926 | + | 0.901430i | \(0.642519\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4671.40 | −0.282540 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1961.60 | −0.118097 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11031.1 | −0.661071 | −0.330535 | − | 0.943794i | \(-0.607229\pi\) | ||||
−0.330535 | + | 0.943794i | \(0.607229\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 515.847 | 0.0307723 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27839.4 | −1.65315 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23429.9 | 1.38497 | 0.692487 | − | 0.721430i | \(-0.256515\pi\) | ||||
0.692487 | + | 0.721430i | \(0.256515\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20939.6 | 1.23216 | 0.616079 | − | 0.787684i | \(-0.288720\pi\) | ||||
0.616079 | + | 0.787684i | \(0.288720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −94108.6 | −5.51263 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 872.077 | 0.0508537 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3193.05 | −0.185360 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 63063.2 | 3.64449 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5333.08 | 0.306828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10460.4 | 0.599138 | 0.299569 | − | 0.954075i | \(-0.403157\pi\) | ||||
0.299569 | + | 0.954075i | \(0.403157\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −50862.6 | −2.90030 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1898.28 | −0.107765 | −0.0538824 | − | 0.998547i | \(-0.517160\pi\) | ||||
−0.0538824 | + | 0.998547i | \(0.517160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −40.5214 | −0.00229024 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −45108.6 | −2.53827 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6001.01 | 0.336197 | 0.168098 | − | 0.985770i | \(-0.446237\pi\) | ||||
0.168098 | + | 0.985770i | \(0.446237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −843.781 | −0.0470646 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50233.0 | 2.78968 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33195.5 | 1.83548 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20066.6 | −1.10473 | −0.552367 | − | 0.833601i | \(-0.686275\pi\) | ||||
−0.552367 | + | 0.833601i | \(0.686275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6616.85 | −0.362704 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2896.51 | 0.158088 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31684.7 | 1.72187 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −56748.6 | −3.07071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7897.60 | −0.425518 | −0.212759 | − | 0.977105i | \(-0.568245\pi\) | ||||
−0.212759 | + | 0.977105i | \(0.568245\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11914.6 | −0.639215 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5904.61 | 0.315433 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3852.72 | 0.204946 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8805.89 | −0.466449 | −0.233224 | − | 0.972423i | \(-0.574928\pi\) | ||||
−0.233224 | + | 0.972423i | \(0.574928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42754.7 | −2.25517 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6612.66 | 0.347330 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6418.49 | 0.335718 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −54875.8 | −2.85826 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9315.54 | 0.483186 | 0.241593 | − | 0.970378i | \(-0.422330\pi\) | ||||
0.241593 | + | 0.970378i | \(0.422330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −716.932 | −0.0370318 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21959.9 | −1.12959 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3422.71 | 0.175333 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12393.7 | 0.632264 | 0.316132 | − | 0.948715i | \(-0.397616\pi\) | ||||
0.316132 | + | 0.948715i | \(0.397616\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 51072.7 | 2.59476 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27725.6 | −1.40283 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25018.2 | −1.26067 | −0.630333 | − | 0.776325i | \(-0.717082\pi\) | ||||
−0.630333 | + | 0.776325i | \(0.717082\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8665.31 | −0.434864 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25613.0 | 1.28015 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2887.04 | −0.143710 | −0.0718548 | − | 0.997415i | \(-0.522892\pi\) | ||||
−0.0718548 | + | 0.997415i | \(0.522892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −84613.1 | −4.19479 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34004.2 | −1.67899 | −0.839497 | − | 0.543365i | \(-0.817150\pi\) | ||||
−0.839497 | + | 0.543365i | \(0.817150\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3154.17 | 0.155114 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 35660.9 | 1.74667 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6175.79 | −0.301279 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37460.2 | 1.82016 | 0.910081 | − | 0.414431i | \(-0.136019\pi\) | ||||
0.910081 | + | 0.414431i | \(0.136019\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −49140.7 | −2.37820 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5967.22 | −0.287641 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30483.5 | 1.46359 | 0.731797 | − | 0.681523i | \(-0.238682\pi\) | ||||
0.731797 | + | 0.681523i | \(0.238682\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 30834.2 | 1.47459 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19511.6 | 0.929430 | 0.464715 | − | 0.885460i | \(-0.346157\pi\) | ||||
0.464715 | + | 0.885460i | \(0.346157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2065.25 | 0.0979912 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20719.7 | −0.979244 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14130.9 | −0.665236 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17422.4 | −0.816995 | −0.408497 | − | 0.912760i | \(-0.633947\pi\) | ||||
−0.408497 | + | 0.912760i | \(0.633947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 148.990 | 0.00695947 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3685.78 | −0.171498 | −0.0857491 | − | 0.996317i | \(-0.527328\pi\) | ||||
−0.0857491 | + | 0.996317i | \(0.527328\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7088.28 | −0.328540 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3896.11 | −0.179887 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28487.8 | 1.31024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23252.7 | −1.06536 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12497.5 | −0.570403 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6846.65 | −0.311296 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7764.73 | 0.351694 | 0.175847 | − | 0.984418i | \(-0.443734\pi\) | ||||
0.175847 | + | 0.984418i | \(0.443734\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31994.9 | −1.44366 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3905.58 | 0.175558 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16132.4 | 0.722421 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10103.0 | 0.450710 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22754.0 | 1.01128 | 0.505639 | − | 0.862745i | \(-0.331257\pi\) | ||||
0.505639 | + | 0.862745i | \(0.331257\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25137.4 | −1.11301 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −65718.2 | −2.89893 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11174.0 | −0.491061 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −961.330 | −0.0420900 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40976.0 | 1.78739 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9866.29 | 0.428776 | 0.214388 | − | 0.976749i | \(-0.431224\pi\) | ||||
0.214388 | + | 0.976749i | \(0.431224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12456.6 | −0.539346 | −0.269673 | − | 0.962952i | \(-0.586916\pi\) | ||||
−0.269673 | + | 0.962952i | \(0.586916\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12937.6 | −0.558108 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1315.71 | −0.0565487 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24928.1 | −1.06747 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20015.8 | −0.853980 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22347.4 | 0.949976 | 0.474988 | − | 0.879992i | \(-0.342452\pi\) | ||||
0.474988 | + | 0.879992i | \(0.342452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37377.5 | 1.58311 | 0.791554 | − | 0.611100i | \(-0.209273\pi\) | ||||
0.791554 | + | 0.611100i | \(0.209273\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −33052.0 | −1.39482 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21218.3 | 0.892182 | 0.446091 | − | 0.894988i | \(-0.352816\pi\) | ||||
0.446091 | + | 0.894988i | \(0.352816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12922.1 | 0.541378 | 0.270689 | − | 0.962667i | \(-0.412749\pi\) | ||||
0.270689 | + | 0.962667i | \(0.412749\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 66659.1 | 2.78265 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36890.4 | 1.53443 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1456.42 | −0.0603613 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25881.9 | 1.06883 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25253.6 | −1.03915 | −0.519577 | − | 0.854423i | \(-0.673911\pi\) | ||||
−0.519577 | + | 0.854423i | \(0.673911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28615.4 | 1.16912 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13613.3 | 0.554213 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1744.19 | 0.0707571 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 84746.5 | 3.42579 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13134.0 | 0.529058 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23958.9 | 0.961707 | 0.480854 | − | 0.876801i | \(-0.340327\pi\) | ||||
0.480854 | + | 0.876801i | \(0.340327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18629.1 | −0.745147 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1289.87 | −0.0514133 | −0.0257066 | − | 0.999670i | \(-0.508184\pi\) | ||||
−0.0257066 | + | 0.999670i | \(0.508184\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12961.8 | −0.514843 | −0.257422 | − | 0.966299i | \(-0.582873\pi\) | ||||
−0.257422 | + | 0.966299i | \(0.582873\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9315.57 | 0.368727 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39133.0 | −1.54357 | −0.771785 | − | 0.635883i | \(-0.780636\pi\) | ||||
−0.771785 | + | 0.635883i | \(0.780636\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6708.09 | 0.263678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 73393.5 | 2.87494 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17160.6 | −0.669888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 77478.8 | 3.01409 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 865.609 | 0.0335583 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2121.85 | 0.0819790 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12957.8 | −0.498921 | −0.249460 | − | 0.968385i | \(-0.580253\pi\) | ||||
−0.249460 | + | 0.968385i | \(0.580253\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −81056.8 | −3.11033 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33767.4 | −1.29132 | −0.645659 | − | 0.763626i | \(-0.723417\pi\) | ||||
−0.645659 | + | 0.763626i | \(0.723417\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34290.1 | 1.30686 | 0.653428 | − | 0.756989i | \(-0.273330\pi\) | ||||
0.653428 | + | 0.756989i | \(0.273330\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4300.68 | −0.163351 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10538.1 | −0.398911 | −0.199456 | − | 0.979907i | \(-0.563917\pi\) | ||||
−0.199456 | + | 0.979907i | \(0.563917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5599.23 | 0.211240 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 66641.9 | 2.50571 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22601.1 | −0.846938 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1953.42 | −0.0729560 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 93272.9 | 3.47190 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1741.67 | −0.0646141 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43010.8 | −1.59034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8151.57 | −0.300407 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10901.7 | −0.400427 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25835.0 | −0.945797 | −0.472899 | − | 0.881117i | \(-0.656792\pi\) | ||||
−0.472899 | + | 0.881117i | \(0.656792\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −82300.9 | −3.00302 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6732.30 | −0.244842 | −0.122421 | − | 0.992478i | \(-0.539066\pi\) | ||||
−0.122421 | + | 0.992478i | \(0.539066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14313.3 | 0.518841 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4909.86 | 0.177393 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −645.669 | −0.0232518 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16257.6 | −0.583557 | −0.291778 | − | 0.956486i | \(-0.594247\pi\) | ||||
−0.291778 | + | 0.956486i | \(0.594247\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24764.1 | 0.886000 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −70338.9 | −2.50838 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14078.7 | −0.500437 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15314.9 | 0.542619 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27354.8 | −0.966073 | −0.483037 | − | 0.875600i | \(-0.660466\pi\) | ||||
−0.483037 | + | 0.875600i | \(0.660466\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33168.2 | 1.16761 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 64235.9 | 2.25401 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8316.32 | −0.290880 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38897.4 | 1.35616 | 0.678080 | − | 0.734988i | \(-0.262812\pi\) | ||||
0.678080 | + | 0.734988i | \(0.262812\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 71575.4 | 2.48751 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36998.7 | 1.28175 | 0.640874 | − | 0.767646i | \(-0.278572\pi\) | ||||
0.640874 | + | 0.767646i | \(0.278572\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31403.4 | −1.08445 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3762.63 | −0.129522 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37594.0 | −1.29001 | −0.645006 | − | 0.764177i | \(-0.723145\pi\) | ||||
−0.645006 | + | 0.764177i | \(0.723145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33801.1 | −1.15620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 79725.0 | 2.71847 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49341.0 | 1.67714 | 0.838568 | − | 0.544797i | \(-0.183393\pi\) | ||||
0.838568 | + | 0.544797i | \(0.183393\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4305.75 | 0.145896 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8121.27 | −0.274319 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1056.13 | 0.0355624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26184.1 | −0.878926 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 131926. | 4.41458 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −556.315 | −0.0185579 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44067.6 | −1.46548 | −0.732740 | − | 0.680509i | \(-0.761759\pi\) | ||||
−0.732740 | + | 0.680509i | \(0.761759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 109632. | 3.63454 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51385.3 | 1.69828 | 0.849141 | − | 0.528166i | \(-0.177120\pi\) | ||||
0.849141 | + | 0.528166i | \(0.177120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3625.46 | −0.119452 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −99981.6 | −3.28407 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27297.1 | 0.893871 | 0.446935 | − | 0.894566i | \(-0.352515\pi\) | ||||
0.446935 | + | 0.894566i | \(0.352515\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26377.5 | −0.861113 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44117.4 | −1.43584 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3876.96 | 0.125794 | 0.0628972 | − | 0.998020i | \(-0.479966\pi\) | ||||
0.0628972 | + | 0.998020i | \(0.479966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11669.4 | −0.377481 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7390.60 | −0.238344 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27479.4 | 0.883514 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11942.6 | −0.382814 | −0.191407 | − | 0.981511i | \(-0.561305\pi\) | ||||
−0.191407 | + | 0.981511i | \(0.561305\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −62758.6 | −2.00562 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3794.03 | 0.120883 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60556.0 | 1.92360 | 0.961800 | − | 0.273755i | \(-0.0882656\pi\) | ||||
0.961800 | + | 0.273755i | \(0.0882656\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51406.3 | 1.62805 |
(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 | 464.4.a.n.1.6 | 6 | ||
4.3 | odd | 2 | 232.4.a.e.1.1 | ✓ | 6 | ||
8.3 | odd | 2 | 1856.4.a.bd.1.6 | 6 | |||
8.5 | even | 2 | 1856.4.a.bc.1.1 | 6 | |||
12.11 | even | 2 | 2088.4.a.l.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.e.1.1 | ✓ | 6 | 4.3 | odd | 2 | ||
464.4.a.n.1.6 | 6 | 1.1 | even | 1 | trivial | ||
1856.4.a.bc.1.1 | 6 | 8.5 | even | 2 | |||
1856.4.a.bd.1.6 | 6 | 8.3 | odd | 2 | |||
2088.4.a.l.1.3 | 6 | 12.11 | even | 2 |