Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(71.7463225670\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3221.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.44437\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-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 | ||||||||
\(3\) | 10.3081 | 1.98379 | 0.991897 | − | 0.127047i | \(-0.0405499\pi\) | ||||
0.991897 | + | 0.127047i | \(0.0405499\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −14.1468 | −1.26533 | −0.632663 | − | 0.774427i | \(-0.718038\pi\) | ||||
−0.632663 | + | 0.774427i | \(0.718038\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.06119 | −0.219283 | −0.109642 | − | 0.993971i | \(-0.534970\pi\) | ||||
−0.109642 | + | 0.993971i | \(0.534970\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 79.2568 | 2.93544 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.53059 | 0.151594 | 0.0757971 | − | 0.997123i | \(-0.475850\pi\) | ||||
0.0757971 | + | 0.997123i | \(0.475850\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.6697 | 0.974345 | 0.487172 | − | 0.873306i | \(-0.338028\pi\) | ||||
0.487172 | + | 0.873306i | \(0.338028\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −145.826 | −2.51015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −92.8486 | −1.32465 | −0.662326 | − | 0.749216i | \(-0.730431\pi\) | ||||
−0.662326 | + | 0.749216i | \(0.730431\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −41.8631 | −0.435013 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −57.0689 | −0.517378 | −0.258689 | − | 0.965961i | \(-0.583290\pi\) | ||||
−0.258689 | + | 0.965961i | \(0.583290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 75.1314 | 0.601051 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 538.668 | 3.83951 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 290.147 | 1.85790 | 0.928948 | − | 0.370209i | \(-0.120714\pi\) | ||||
0.928948 | + | 0.370209i | \(0.120714\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 163.494 | 0.947240 | 0.473620 | − | 0.880729i | \(-0.342947\pi\) | ||||
0.473620 | + | 0.880729i | \(0.342947\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 57.0099 | 0.300732 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 57.4527 | 0.277465 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 81.3659 | 0.361526 | 0.180763 | − | 0.983527i | \(-0.442143\pi\) | ||||
0.180763 | + | 0.983527i | \(0.442143\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 470.767 | 1.93290 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 73.1997 | 0.278826 | 0.139413 | − | 0.990234i | \(-0.455478\pi\) | ||||
0.139413 | + | 0.990234i | \(0.455478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 346.600 | 1.22921 | 0.614605 | − | 0.788835i | \(-0.289315\pi\) | ||||
0.614605 | + | 0.788835i | \(0.289315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1121.23 | −3.71428 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 503.383 | 1.56225 | 0.781127 | − | 0.624372i | \(-0.214645\pi\) | ||||
0.781127 | + | 0.624372i | \(0.214645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −326.507 | −0.951915 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −957.092 | −2.62784 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 164.243 | 0.425670 | 0.212835 | − | 0.977088i | \(-0.431730\pi\) | ||||
0.212835 | + | 0.977088i | \(0.431730\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −78.2401 | −0.191816 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −195.854 | −0.455113 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 763.585 | 1.68492 | 0.842460 | − | 0.538759i | \(-0.181107\pi\) | ||||
0.842460 | + | 0.538759i | \(0.181107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −545.832 | −1.14568 | −0.572841 | − | 0.819666i | \(-0.694159\pi\) | ||||
−0.572841 | + | 0.819666i | \(0.694159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −321.877 | −0.643693 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −646.079 | −1.23286 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 510.800 | 0.931406 | 0.465703 | − | 0.884941i | \(-0.345801\pi\) | ||||
0.465703 | + | 0.884941i | \(0.345801\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −588.272 | −1.02637 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −294.139 | −0.491659 | −0.245830 | − | 0.969313i | \(-0.579060\pi\) | ||||
−0.245830 | + | 0.969313i | \(0.579060\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −172.903 | −0.277217 | −0.138608 | − | 0.990347i | \(-0.544263\pi\) | ||||
−0.138608 | + | 0.990347i | \(0.544263\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 774.461 | 1.19236 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22.4608 | −0.0332421 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −973.626 | −1.38660 | −0.693300 | − | 0.720649i | \(-0.743844\pi\) | ||||
−0.693300 | + | 0.720649i | \(0.743844\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3412.70 | 4.68135 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −510.932 | −0.675688 | −0.337844 | − | 0.941202i | \(-0.609698\pi\) | ||||
−0.337844 | + | 0.941202i | \(0.609698\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1313.51 | 1.67612 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2990.87 | 3.68568 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 845.158 | 1.00659 | 0.503295 | − | 0.864114i | \(-0.332121\pi\) | ||||
0.503295 | + | 0.864114i | \(0.332121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −185.473 | −0.213658 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1685.31 | 1.87913 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 268.789 | 0.290286 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −863.606 | −0.903979 | −0.451989 | − | 0.892023i | \(-0.649286\pi\) | ||||
−0.451989 | + | 0.892023i | \(0.649286\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 438.337 | 0.444995 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1016.53 | 1.00147 | 0.500735 | − | 0.865600i | \(-0.333063\pi\) | ||||
0.500735 | + | 0.865600i | \(0.333063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −185.045 | −0.177020 | −0.0885100 | − | 0.996075i | \(-0.528211\pi\) | ||||
−0.0885100 | + | 0.996075i | \(0.528211\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 592.228 | 0.550434 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 396.796 | 0.358502 | 0.179251 | − | 0.983803i | \(-0.442633\pi\) | ||||
0.179251 | + | 0.983803i | \(0.442633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1355.57 | −1.19119 | −0.595595 | − | 0.803285i | \(-0.703084\pi\) | ||||
−0.595595 | + | 0.803285i | \(0.703084\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 838.727 | 0.717193 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1915.38 | 1.59455 | 0.797275 | − | 0.603616i | \(-0.206274\pi\) | ||||
0.797275 | + | 0.603616i | \(0.206274\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 807.341 | 0.654652 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3619.63 | 2.86013 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 377.075 | 0.290474 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1300.41 | −0.977019 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 754.549 | 0.553134 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 705.481 | 0.504801 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 985.870 | 0.688833 | 0.344417 | − | 0.938817i | \(-0.388077\pi\) | ||||
0.344417 | + | 0.938817i | \(0.388077\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3572.79 | 2.43850 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2296.18 | −1.53144 | −0.765718 | − | 0.643176i | \(-0.777616\pi\) | ||||
−0.765718 | + | 0.643176i | \(0.777616\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 77.1626 | 0.0503071 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7620.41 | −4.85823 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1344.91 | 0.838712 | 0.419356 | − | 0.907822i | \(-0.362256\pi\) | ||||
0.419356 | + | 0.907822i | \(0.362256\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −402.094 | −0.245361 | −0.122681 | − | 0.992446i | \(-0.539149\pi\) | ||||
−0.122681 | + | 0.992446i | \(0.539149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5188.92 | 3.09919 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 252.580 | 0.147705 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4104.65 | −2.35085 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3365.66 | −1.88840 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 738.796 | 0.406205 | 0.203102 | − | 0.979158i | \(-0.434898\pi\) | ||||
0.203102 | + | 0.979158i | \(0.434898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 819.258 | 0.441525 | 0.220762 | − | 0.975328i | \(-0.429145\pi\) | ||||
0.220762 | + | 0.975328i | \(0.429145\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7358.88 | −3.88843 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2312.92 | −1.19857 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1469.33 | 0.746913 | 0.373456 | − | 0.927648i | \(-0.378173\pi\) | ||||
0.373456 | + | 0.927648i | \(0.378173\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1693.03 | 0.844442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 231.767 | 0.113452 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 582.247 | 0.279786 | 0.139893 | − | 0.990167i | \(-0.455324\pi\) | ||||
0.139893 | + | 0.990167i | \(0.455324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −806.506 | −0.380524 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2401.31 | 1.11269 | 0.556345 | − | 0.830952i | \(-0.312203\pi\) | ||||
0.556345 | + | 0.830952i | \(0.312203\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −111.282 | −0.0506519 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1505.88 | −0.673435 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1104.21 | −0.485269 | −0.242635 | − | 0.970118i | \(-0.578012\pi\) | ||||
−0.242635 | + | 0.970118i | \(0.578012\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −305.122 | −0.131801 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7871.10 | 3.34253 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 822.030 | 0.343248 | 0.171624 | − | 0.985163i | \(-0.445099\pi\) | ||||
0.171624 | + | 0.985163i | \(0.445099\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −151.476 | −0.0622052 | −0.0311026 | − | 0.999516i | \(-0.509902\pi\) | ||||
−0.0311026 | + | 0.999516i | \(0.509902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5626.49 | −2.27280 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1151.07 | −0.457449 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −513.508 | −0.200810 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2187.63 | −0.841940 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 477.884 | 0.181039 | 0.0905195 | − | 0.995895i | \(-0.471147\pi\) | ||||
0.0905195 | + | 0.995895i | \(0.471147\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2169.48 | −0.809134 | −0.404567 | − | 0.914508i | \(-0.632578\pi\) | ||||
−0.404567 | + | 0.914508i | \(0.632578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6659.84 | −2.44575 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1444.93 | −0.522574 | −0.261287 | − | 0.965261i | \(-0.584147\pi\) | ||||
−0.261287 | + | 0.965261i | \(0.584147\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1490.17 | 0.530830 | 0.265415 | − | 0.964134i | \(-0.414491\pi\) | ||||
0.265415 | + | 0.964134i | \(0.414491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5265.38 | 1.84772 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1178.34 | −0.407406 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1035.54 | −0.352806 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4523.10 | −1.51873 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −105.081 | −0.0347781 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2270.00 | 0.740630 | 0.370315 | − | 0.928906i | \(-0.379250\pi\) | ||||
0.370315 | + | 0.928906i | \(0.379250\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3032.01 | −0.975351 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4903.28 | −1.55535 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −663.981 | −0.207714 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1782.30 | −0.549941 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4240.36 | −1.29067 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2380.30 | 0.714783 | 0.357392 | − | 0.933955i | \(-0.383666\pi\) | ||||
0.357392 | + | 0.933955i | \(0.383666\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5954.67 | 1.76435 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1972.94 | 0.576865 | 0.288432 | − | 0.957500i | \(-0.406866\pi\) | ||||
0.288432 | + | 0.957500i | \(0.406866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.4526 | −0.00619053 | −0.00309526 | − | 0.999995i | \(-0.500985\pi\) | ||||
−0.00309526 | + | 0.999995i | \(0.500985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −231.528 | −0.0659455 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1711.23 | 0.481143 | 0.240571 | − | 0.970631i | \(-0.422665\pi\) | ||||
0.240571 | + | 0.970631i | \(0.422665\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7121.24 | −1.97676 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10036.2 | −2.75073 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2193.99 | −0.593796 | −0.296898 | − | 0.954909i | \(-0.595952\pi\) | ||||
−0.296898 | + | 0.954909i | \(0.595952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 726.890 | 0.194287 | 0.0971434 | − | 0.995270i | \(-0.469029\pi\) | ||||
0.0971434 | + | 0.995270i | \(0.469029\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20634.4 | 5.44732 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4619.02 | 1.20448 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −867.724 | −0.223530 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5266.74 | −1.34043 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3168.49 | −0.796785 | −0.398393 | − | 0.917215i | \(-0.630432\pi\) | ||||
−0.398393 | + | 0.917215i | \(0.630432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −315.625 | −0.0784315 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13539.8 | 3.32507 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4341.53 | 1.05376 | 0.526881 | − | 0.849939i | \(-0.323361\pi\) | ||||
0.526881 | + | 0.849939i | \(0.323361\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −330.442 | −0.0792767 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22996.1 | 5.45374 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6418.23 | −1.50481 | −0.752405 | − | 0.658701i | \(-0.771106\pi\) | ||||
−0.752405 | + | 0.658701i | \(0.771106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2323.51 | −0.538612 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8711.97 | 1.99687 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6476.36 | −1.46792 | −0.733961 | − | 0.679192i | \(-0.762330\pi\) | ||||
−0.733961 | + | 0.679192i | \(0.762330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6832.73 | −1.53158 | −0.765791 | − | 0.643090i | \(-0.777652\pi\) | ||||
−0.765791 | + | 0.643090i | \(0.777652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1911.87 | −0.423853 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 415.521 | 0.0911158 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3243.37 | 0.703521 | 0.351761 | − | 0.936090i | \(-0.385583\pi\) | ||||
0.351761 | + | 0.936090i | \(0.385583\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12958.0 | 2.78056 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4524.91 | 0.960618 | 0.480309 | − | 0.877099i | \(-0.340524\pi\) | ||||
0.480309 | + | 0.877099i | \(0.340524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 363.865 | 0.0764293 | 0.0382147 | − | 0.999270i | \(-0.487833\pi\) | ||||
0.0382147 | + | 0.999270i | \(0.487833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2770.70 | 0.575867 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −297.278 | −0.0611420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3707.85 | 0.754703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8902.13 | −1.79331 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4565.73 | 0.910350 | 0.455175 | − | 0.890402i | \(-0.349577\pi\) | ||||
0.455175 | + | 0.890402i | \(0.349577\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10802.3 | −2.13197 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2979.15 | 0.582047 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2606.32 | −0.504104 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1407.61 | −0.269546 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10478.5 | 1.98671 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7721.77 | 1.44966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8554.23 | −1.59028 | −0.795139 | − | 0.606427i | \(-0.792602\pi\) | ||||
−0.795139 | + | 0.606427i | \(0.792602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1907.46 | −0.351171 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2620.19 | 0.477740 | 0.238870 | − | 0.971052i | \(-0.423223\pi\) | ||||
0.238870 | + | 0.971052i | \(0.423223\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5233.04 | −0.945013 | −0.472507 | − | 0.881327i | \(-0.656651\pi\) | ||||
−0.472507 | + | 0.881327i | \(0.656651\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4553.52 | 0.814481 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8199.12 | −1.45271 | −0.726354 | − | 0.687320i | \(-0.758787\pi\) | ||||
−0.726354 | + | 0.687320i | \(0.758787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1604.69 | 0.281646 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4090.21 | 0.711194 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1764.12 | 0.303896 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3431.22 | 0.585631 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13973.3 | −2.36307 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2044.33 | −0.342576 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4942.10 | −0.820672 | −0.410336 | − | 0.911934i | \(-0.634589\pi\) | ||||
−0.410336 | + | 0.911934i | \(0.634589\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6448.80 | 1.06124 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7226.18 | −1.17853 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11622.4 | −1.87868 | −0.939339 | − | 0.342991i | \(-0.888560\pi\) | ||||
−0.939339 | + | 0.342991i | \(0.888560\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19744.0 | 3.16326 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 904.221 | 0.143596 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2718.99 | 0.428023 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8322.15 | 1.29869 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6401.72 | 0.990382 | 0.495191 | − | 0.868784i | \(-0.335098\pi\) | ||||
0.495191 | + | 0.868784i | \(0.335098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9713.15 | 1.48978 | 0.744890 | − | 0.667188i | \(-0.232502\pi\) | ||||
0.744890 | + | 0.667188i | \(0.232502\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24600.8 | 3.74100 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10674.0 | −1.60941 | −0.804705 | − | 0.593675i | \(-0.797677\pi\) | ||||
−0.804705 | + | 0.593675i | \(0.797677\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4161.11 | 0.622110 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3886.93 | 0.576241 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4991.30 | −0.733791 | −0.366895 | − | 0.930262i | \(-0.619579\pi\) | ||||
−0.366895 | + | 0.930262i | \(0.619579\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13404.8 | −1.93820 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2446.03 | 0.350770 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7742.21 | −1.10120 | −0.550599 | − | 0.834770i | \(-0.685601\pi\) | ||||
−0.550599 | + | 0.834770i | \(0.685601\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5801.57 | 0.818477 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −667.022 | −0.0933425 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1644.48 | 0.228279 | 0.114139 | − | 0.993465i | \(-0.463589\pi\) | ||||
0.114139 | + | 0.993465i | \(0.463589\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7272.16 | 1.00142 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13250.9 | 1.81023 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1385.48 | 0.187776 | 0.0938881 | − | 0.995583i | \(-0.470070\pi\) | ||||
0.0938881 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10162.4 | 1.36650 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6651.19 | −0.887363 | −0.443682 | − | 0.896185i | \(-0.646328\pi\) | ||||
−0.443682 | + | 0.896185i | \(0.646328\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 317.748 | 0.0420621 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27470.4 | 3.60827 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9322.00 | −1.21502 | −0.607512 | − | 0.794311i | \(-0.707832\pi\) | ||||
−0.607512 | + | 0.794311i | \(0.707832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5298.76 | 0.685345 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23669.2 | −3.03805 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13773.7 | 1.75450 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11403.0 | −1.44157 | −0.720783 | − | 0.693160i | \(-0.756218\pi\) | ||||
−0.720783 | + | 0.693160i | \(0.756218\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 795.399 | 0.0997989 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3794.17 | 0.472498 | 0.236249 | − | 0.971693i | \(-0.424082\pi\) | ||||
0.236249 | + | 0.971693i | \(0.424082\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7466.73 | 0.922939 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −48278.8 | −5.92343 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 450.002 | 0.0548053 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3210.32 | 0.388118 | 0.194059 | − | 0.980990i | \(-0.437835\pi\) | ||||
0.194059 | + | 0.980990i | \(0.437835\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13863.5 | 1.66383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3101.06 | −0.369475 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7228.05 | 0.854966 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4144.83 | −0.486746 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5646.89 | −0.658398 | −0.329199 | − | 0.944261i | \(-0.606779\pi\) | ||||
−0.329199 | + | 0.944261i | \(0.606779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1912.56 | 0.221407 | 0.110704 | − | 0.993853i | \(-0.464690\pi\) | ||||
0.110704 | + | 0.993853i | \(0.464690\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 39896.5 | 4.58590 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6975.84 | −0.796183 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2216.73 | 0.251229 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2603.62 | 0.293016 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4568.25 | −0.510545 | −0.255273 | − | 0.966869i | \(-0.582165\pi\) | ||||
−0.255273 | + | 0.966869i | \(0.582165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7432.60 | 0.824915 | 0.412458 | − | 0.910977i | \(-0.364671\pi\) | ||||
0.412458 | + | 0.910977i | \(0.364671\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −42311.1 | −4.66359 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1084.31 | 0.118695 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5937.86 | −0.645555 | −0.322777 | − | 0.946475i | \(-0.604617\pi\) | ||||
−0.322777 | + | 0.946475i | \(0.604617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25877.9 | −2.79428 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11714.5 | −1.25638 | −0.628188 | − | 0.778062i | \(-0.716203\pi\) | ||||
−0.628188 | + | 0.778062i | \(0.716203\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11956.3 | −1.27367 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7615.57 | 0.805826 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2007.87 | 0.211040 | 0.105520 | − | 0.994417i | \(-0.466349\pi\) | ||||
0.105520 | + | 0.994417i | \(0.466349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 404.838 | 0.0422684 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8444.98 | 0.875894 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2623.85 | 0.270347 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1447.39 | 0.148153 | 0.0740764 | − | 0.997253i | \(-0.476399\pi\) | ||||
0.0740764 | + | 0.997253i | \(0.476399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −50014.5 | −5.08601 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2893.39 | 0.292318 | 0.146159 | − | 0.989261i | \(-0.453309\pi\) | ||||
0.146159 | + | 0.989261i | \(0.453309\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13259.1 | −1.33089 | −0.665445 | − | 0.746447i | \(-0.731758\pi\) | ||||
−0.665445 | + | 0.746447i | \(0.731758\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −23841.8 | −2.37771 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4031.59 | −0.399486 | −0.199743 | − | 0.979848i | \(-0.564011\pi\) | ||||
−0.199743 | + | 0.979848i | \(0.564011\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2074.46 | −0.204242 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15146.0 | 1.48172 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1916.91 | 0.186341 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1427.50 | −0.137891 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13017.4 | 1.24953 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8616.81 | −0.821946 | −0.410973 | − | 0.911647i | \(-0.634811\pi\) | ||||
−0.410973 | + | 0.911647i | \(0.634811\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3715.95 | 0.352251 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2389.08 | 0.225066 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12217.2 | 1.14383 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10149.9 | −0.944429 | −0.472215 | − | 0.881484i | \(-0.656545\pi\) | ||||
−0.472215 | + | 0.881484i | \(0.656545\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6001.85 | 0.555037 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5982.00 | 0.549825 | 0.274912 | − | 0.961469i | \(-0.411351\pi\) | ||||
0.274912 | + | 0.961469i | \(0.411351\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26939.8 | −2.46107 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6201.06 | −0.563064 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1194.55 | 0.107813 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2022.13 | −0.181409 | −0.0907044 | − | 0.995878i | \(-0.528912\pi\) | ||||
−0.0907044 | + | 0.995878i | \(0.528912\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24752.9 | 2.20735 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1621.54 | −0.143739 | −0.0718697 | − | 0.997414i | \(-0.522897\pi\) | ||||
−0.0718697 | + | 0.997414i | \(0.522897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14380.6 | −1.26719 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1147.11 | −0.100483 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1108.58 | 0.0965358 | 0.0482679 | − | 0.998834i | \(-0.484630\pi\) | ||||
0.0482679 | + | 0.998834i | \(0.484630\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 702.193 | 0.0607890 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10234.7 | −0.880843 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2617.80 | 0.223988 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2784.01 | 0.236829 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11382.3 | −0.962674 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5249.04 | 0.441391 | 0.220696 | − | 0.975343i | \(-0.429167\pi\) | ||||
0.220696 | + | 0.975343i | \(0.429167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6191.33 | −0.517645 | −0.258822 | − | 0.965925i | \(-0.583334\pi\) | ||||
−0.258822 | + | 0.965925i | \(0.583334\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3145.23 | −0.261465 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15180.2 | −1.25476 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8910.14 | −0.732320 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 60519.3 | 4.94597 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3343.01 | 0.271673 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5613.38 | −0.453622 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8473.56 | 0.680933 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1805.78 | −0.144305 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16975.2 | 1.34903 | 0.674513 | − | 0.738263i | \(-0.264354\pi\) | ||||
0.674513 | + | 0.738263i | \(0.264354\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1561.43 | −0.123402 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19176.9 | 1.50724 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16676.3 | −1.30352 | −0.651762 | − | 0.758424i | \(-0.725970\pi\) | ||||
−0.651762 | + | 0.758424i | \(0.725970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −43260.9 | −3.36308 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5512.80 | −0.426231 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3954.08 | 0.304059 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11865.3 | −0.907484 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12448.6 | 0.946973 | 0.473486 | − | 0.880801i | \(-0.342995\pi\) | ||||
0.473486 | + | 0.880801i | \(0.342995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15829.1 | 1.19768 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5293.28 | −0.398365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12829.5 | −0.960386 | −0.480193 | − | 0.877163i | \(-0.659433\pi\) | ||||
−0.480193 | + | 0.877163i | \(0.659433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27096.5 | −2.01763 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13859.6 | −1.02654 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −916.141 | −0.0674985 | −0.0337492 | − | 0.999430i | \(-0.510745\pi\) | ||||
−0.0337492 | + | 0.999430i | \(0.510745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1247.99 | −0.0914654 | −0.0457327 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457327 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4926.07 | 0.359144 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4287.66 | −0.310970 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12669.4 | 0.914095 | 0.457047 | − | 0.889442i | \(-0.348907\pi\) | ||||
0.457047 | + | 0.889442i | \(0.348907\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22363.2 | −1.60516 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2074.99 | 0.148167 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 908.362 | 0.0645292 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −51206.1 | −3.61899 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20350.0 | 1.43089 | 0.715446 | − | 0.698668i | \(-0.246223\pi\) | ||||
0.715446 | + | 0.698668i | \(0.246223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3106.39 | −0.217312 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14894.5 | −1.03668 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2306.21 | 0.159705 | 0.0798523 | − | 0.996807i | \(-0.474555\pi\) | ||||
0.0798523 | + | 0.996807i | \(0.474555\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5334.40 | −0.367545 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15360.8 | 1.05306 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21458.5 | −1.46372 | −0.731861 | − | 0.681454i | \(-0.761348\pi\) | ||||
−0.731861 | + | 0.681454i | \(0.761348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8415.81 | 0.571195 | 0.285598 | − | 0.958350i | \(-0.407808\pi\) | ||||
0.285598 | + | 0.958350i | \(0.407808\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40484.4 | 2.73408 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18396.6 | 1.23625 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3515.81 | −0.235095 | −0.117547 | − | 0.993067i | \(-0.537503\pi\) | ||||
−0.117547 | + | 0.993067i | \(0.537503\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12146.5 | −0.808209 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22989.3 | 1.52217 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16618.5 | −1.09497 | −0.547484 | − | 0.836816i | \(-0.684414\pi\) | ||||
−0.547484 | + | 0.836816i | \(0.684414\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10674.4 | −0.699895 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29469.3 | 1.92284 | 0.961419 | − | 0.275088i | \(-0.0887069\pi\) | ||||
0.961419 | + | 0.275088i | \(0.0887069\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29408.3 | −1.90957 | −0.954783 | − | 0.297304i | \(-0.903912\pi\) | ||||
−0.954783 | + | 0.297304i | \(0.903912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30741.2 | −1.98647 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3432.34 | −0.220729 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19371.7 | −1.23979 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1083.19 | −0.0689926 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7554.70 | −0.478896 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1315.79 | 0.0830124 | 0.0415062 | − | 0.999138i | \(-0.486784\pi\) | ||||
0.0415062 | + | 0.999138i | \(0.486784\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23399.3 | 1.46926 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13946.9 | −0.871599 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14911.5 | −0.927493 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23312.5 | −1.44324 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28499.5 | −1.75610 | −0.878052 | − | 0.478565i | \(-0.841157\pi\) | ||||
−0.878052 | + | 0.478565i | \(0.841157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19337.7 | −1.18601 | −0.593006 | − | 0.805198i | \(-0.702059\pi\) | ||||
−0.593006 | + | 0.805198i | \(0.702059\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −50543.5 | −3.08550 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23409.8 | 1.42246 | 0.711232 | − | 0.702957i | \(-0.248137\pi\) | ||||
0.711232 | + | 0.702957i | \(0.248137\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4223.08 | 0.255424 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6844.38 | −0.412062 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11324.7 | −0.678665 | −0.339332 | − | 0.940667i | \(-0.610201\pi\) | ||||
−0.339332 | + | 0.940667i | \(0.610201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32483.5 | 1.93777 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13703.8 | −0.813752 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6171.58 | 0.364811 | 0.182406 | − | 0.983223i | \(-0.441612\pi\) | ||||
0.182406 | + | 0.983223i | \(0.441612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10178.3 | 0.598926 | 0.299463 | − | 0.954108i | \(-0.403193\pi\) | ||||
0.299463 | + | 0.954108i | \(0.403193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −43710.0 | −2.56042 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1091.60 | −0.0636549 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16558.4 | −0.961234 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24536.3 | 1.41798 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3018.78 | −0.173679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1615.15 | −0.0925106 | −0.0462553 | − | 0.998930i | \(-0.514729\pi\) | ||||
−0.0462553 | + | 0.998930i | \(0.514729\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 40470.8 | 2.30774 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33333.2 | −1.89232 | −0.946158 | − | 0.323706i | \(-0.895071\pi\) | ||||
−0.946158 | + | 0.323706i | \(0.895071\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3507.27 | 0.198228 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20337.2 | 1.14438 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11254.4 | −0.630507 | −0.315253 | − | 0.949008i | \(-0.602089\pi\) | ||||
−0.315253 | + | 0.949008i | \(0.602089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19026.2 | −1.06124 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −221.136 | −0.0122807 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7500.93 | 0.414750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15873.6 | 0.873891 | 0.436945 | − | 0.899488i | \(-0.356060\pi\) | ||||
0.436945 | + | 0.899488i | \(0.356060\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1780.17 | −0.0975801 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5688.34 | 0.310462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6796.49 | −0.369348 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17639.5 | 0.954487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14151.8 | 0.762494 | 0.381247 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381247 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1545.95 | −0.0829398 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −73406.5 | −3.92148 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4128.32 | −0.219606 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26805.8 | 1.41991 | 0.709953 | − | 0.704249i | \(-0.248716\pi\) | ||||
0.709953 | + | 0.704249i | \(0.248716\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −77166.4 | −4.07028 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9330.44 | −0.490081 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3573.20 | −0.186895 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22615.8 | −1.17797 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −254.907 | −0.0132217 | −0.00661087 | − | 0.999978i | \(-0.502104\pi\) | ||||
−0.00661087 | + | 0.999978i | \(0.502104\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 751.504 | 0.0388176 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7492.85 | 0.385425 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21799.2 | 1.11669 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10874.1 | 0.554745 | 0.277373 | − | 0.960762i | \(-0.410536\pi\) | ||||
0.277373 | + | 0.960762i | \(0.410536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 120559. | 6.12502 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32181.3 | −1.62828 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14048.2 | 0.707888 | 0.353944 | − | 0.935267i | \(-0.384840\pi\) | ||||
0.353944 | + | 0.935267i | \(0.384840\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 47613.3 | 2.38945 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2825.03 | 0.141196 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 334.036 | 0.0166275 | 0.00831374 | − | 0.999965i | \(-0.497354\pi\) | ||||
0.00831374 | + | 0.999965i | \(0.497354\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8944.57 | −0.443437 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10340.4 | 0.510571 | 0.255286 | − | 0.966866i | \(-0.417831\pi\) | ||||
0.255286 | + | 0.966866i | \(0.417831\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10451.6 | −0.513981 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40494.9 | −1.98344 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1611.46 | −0.0786135 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31144.7 | 1.51330 | 0.756648 | − | 0.653822i | \(-0.226836\pi\) | ||||
0.756648 | + | 0.653822i | \(0.226836\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −32661.0 | −1.58066 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11589.9 | −0.558673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1688.02 | 0.0810465 | 0.0405233 | − | 0.999179i | \(-0.487098\pi\) | ||||
0.0405233 | + | 0.999179i | \(0.487098\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3253.49 | −0.155592 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11804.3 | 0.562296 | 0.281148 | − | 0.959664i | \(-0.409285\pi\) | ||||
0.281148 | + | 0.959664i | \(0.409285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5505.21 | 0.261208 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 104104. | 4.92013 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34872.7 | 1.64169 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20685.2 | 0.969995 | 0.484998 | − | 0.874516i | \(-0.338821\pi\) | ||||
0.484998 | + | 0.874516i | \(0.338821\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 44752.9 | 2.09045 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24226.8 | 1.12727 | 0.563634 | − | 0.826024i | \(-0.309403\pi\) | ||||
0.563634 | + | 0.826024i | \(0.309403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12283.6 | 0.569340 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3406.23 | −0.157269 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1390.79 | −0.0639671 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1626.76 | −0.0745327 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 156293. | 7.13340 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20786.3 | −0.945089 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2974.74 | 0.134737 | 0.0673685 | − | 0.997728i | \(-0.478540\pi\) | ||||
0.0673685 | + | 0.997728i | \(0.478540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −66159.7 | −2.98523 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7778.73 | −0.349659 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24928.0 | −1.11629 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23951.0 | −1.06849 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3979.23 | 0.176853 | 0.0884264 | − | 0.996083i | \(-0.471816\pi\) | ||||
0.0884264 | + | 0.996083i | \(0.471816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46738.4 | −2.06944 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 66984.5 | 2.95478 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −956.259 | −0.0420245 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3278.76 | −0.143554 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −66759.0 | −2.91205 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27125.7 | 1.17885 | 0.589425 | − | 0.807823i | \(-0.299354\pi\) | ||||
0.589425 | + | 0.807823i | \(0.299354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8095.42 | −0.350516 | −0.175258 | − | 0.984523i | \(-0.556076\pi\) | ||||
−0.175258 | + | 0.984523i | \(0.556076\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −70432.4 | −3.03834 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8236.91 | −0.354020 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6585.41 | −0.282000 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14700.0 | −0.627179 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19575.6 | 0.832148 | 0.416074 | − | 0.909331i | \(-0.363406\pi\) | ||||
0.416074 | + | 0.909331i | \(0.363406\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −857.808 | −0.0363321 | −0.0181660 | − | 0.999835i | \(-0.505783\pi\) | ||||
−0.0181660 | + | 0.999835i | \(0.505783\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4283.23 | 0.180755 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33329.2 | 1.40142 | 0.700708 | − | 0.713448i | \(-0.252867\pi\) | ||||
0.700708 | + | 0.713448i | \(0.252867\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37545.6 | 1.57299 | 0.786497 | − | 0.617594i | \(-0.211893\pi\) | ||||
0.786497 | + | 0.617594i | \(0.211893\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33433.0 | 1.39564 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30315.7 | 1.26096 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33970.8 | −1.40791 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 88069.1 | 3.63693 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8699.05 | −0.357955 | −0.178978 | − | 0.983853i | \(-0.557279\pi\) | ||||
−0.178978 | + | 0.983853i | \(0.557279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59796.5 | 2.45178 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46643.2 | 1.90567 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1574.28 | 0.0640911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5281.22 | 0.214244 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3750.75 | 0.151620 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4643.46 | −0.187046 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39492.9 | 1.58524 | 0.792621 | − | 0.609715i | \(-0.208716\pi\) | ||||
0.792621 | + | 0.609715i | \(0.208716\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21303.3 | 0.852115 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −49878.9 | −1.98813 | −0.994067 | − | 0.108774i | \(-0.965308\pi\) | ||||
−0.994067 | + | 0.108774i | \(0.965308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21676.4 | 0.860988 | 0.430494 | − | 0.902593i | \(-0.358339\pi\) | ||||
0.430494 | + | 0.902593i | \(0.358339\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3064.37 | −0.121293 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19826.9 | −0.782058 | −0.391029 | − | 0.920378i | \(-0.627881\pi\) | ||||
−0.391029 | + | 0.920378i | \(0.627881\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15621.0 | 0.614024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38220.9 | 1.49717 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5384.73 | −0.210201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23328.1 | 0.907511 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −68446.7 | −2.65357 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2865.09 | −0.110694 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28960.6 | 1.11509 | 0.557543 | − | 0.830148i | \(-0.311744\pi\) | ||||
0.557543 | + | 0.830148i | \(0.311744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47063.9 | 1.80595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9612.36 | 0.367592 | 0.183796 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183796 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37634.8 | 1.43433 | 0.717164 | − | 0.696905i | \(-0.245440\pi\) | ||||
0.717164 | + | 0.696905i | \(0.245440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −111351. | −4.22939 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11501.8 | 0.435390 | 0.217695 | − | 0.976017i | \(-0.430146\pi\) | ||||
0.217695 | + | 0.976017i | \(0.430146\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4003.80 | −0.151050 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18874.3 | 0.709666 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9564.27 | −0.358406 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11629.1 | −0.434321 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26866.2 | −1.00004 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 47437.4 | 1.75987 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15249.7 | −0.563865 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14509.8 | −0.534723 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2142.90 | 0.0787099 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18651.0 | 0.682796 | 0.341398 | − | 0.939919i | \(-0.389100\pi\) | ||||
0.341398 | + | 0.939919i | \(0.389100\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 80566.9 | 2.93975 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42680.1 | 1.55220 | 0.776100 | − | 0.630610i | \(-0.217195\pi\) | ||||
0.776100 | + | 0.630610i | \(0.217195\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2825.76 | −0.102430 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 79596.7 | 2.87583 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9325.21 | 0.335819 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5918.21 | −0.212431 | −0.106215 | − | 0.994343i | \(-0.533873\pi\) | ||||
−0.106215 | + | 0.994343i | \(0.533873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −88177.8 | −3.15478 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13433.2 | −0.479046 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6113.13 | 0.217296 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14666.1 | −0.519631 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21425.2 | −0.756661 | −0.378331 | − | 0.925671i | \(-0.623502\pi\) | ||||
−0.378331 | + | 0.925671i | \(0.623502\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6203.63 | 0.218384 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27009.1 | 0.947738 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7264.48 | 0.254090 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26280.8 | −0.916283 | −0.458142 | − | 0.888879i | \(-0.651485\pi\) | ||||
−0.458142 | + | 0.888879i | \(0.651485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −53942.7 | −1.87471 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17105.3 | −0.592581 | −0.296290 | − | 0.955098i | \(-0.595750\pi\) | ||||
−0.296290 | + | 0.955098i | \(0.595750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4177.43 | −0.144258 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30947.9 | 1.06533 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30353.4 | −1.04155 | −0.520777 | − | 0.853692i | \(-0.674358\pi\) | ||||
−0.520777 | + | 0.853692i | \(0.674358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7896.44 | −0.270105 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −84517.3 | −2.88187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16580.1 | −0.563569 | −0.281784 | − | 0.959478i | \(-0.590926\pi\) | ||||
−0.281784 | + | 0.959478i | \(0.590926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6760.52 | −0.229074 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16541.3 | 0.558728 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5461.94 | −0.183916 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3060.60 | −0.102736 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31448.8 | 1.05236 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30691.2 | 1.02382 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1243.10 | 0.0413396 | 0.0206698 | − | 0.999786i | \(-0.493420\pi\) | ||||
0.0206698 | + | 0.999786i | \(0.493420\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18184.7 | 0.602867 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19859.0 | −0.656341 | −0.328170 | − | 0.944619i | \(-0.606432\pi\) | ||||
−0.328170 | + | 0.944619i | \(0.606432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1632.98 | 0.0538036 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 35369.4 | 1.16177 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21378.0 | 0.700043 | 0.350021 | − | 0.936742i | \(-0.386174\pi\) | ||||
0.350021 | + | 0.936742i | \(0.386174\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4674.23 | 0.152593 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −107438. | −3.49666 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37387.5 | −1.21310 | −0.606549 | − | 0.795046i | \(-0.707447\pi\) | ||||
−0.606549 | + | 0.795046i | \(0.707447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20441.1 | 0.661227 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21073.2 | −0.679601 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19780.1 | −0.635966 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56543.4 | −1.81247 | −0.906236 | − | 0.422771i | \(-0.861057\pi\) | ||||
−0.906236 | + | 0.422771i | \(0.861057\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −50943.7 | −1.62804 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21081.1 | −0.671674 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17828.4 | −0.566330 | −0.283165 | − | 0.959071i | \(-0.591384\pi\) | ||||
−0.283165 | + | 0.959071i | \(0.591384\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43829.2 | 1.38808 |
(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 | 1216.4.a.x.1.3 | 3 | ||
4.3 | odd | 2 | 1216.4.a.q.1.1 | 3 | |||
8.3 | odd | 2 | 304.4.a.j.1.3 | 3 | |||
8.5 | even | 2 | 152.4.a.b.1.1 | ✓ | 3 | ||
24.5 | odd | 2 | 1368.4.a.e.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.4.a.b.1.1 | ✓ | 3 | 8.5 | even | 2 | ||
304.4.a.j.1.3 | 3 | 8.3 | odd | 2 | |||
1216.4.a.q.1.1 | 3 | 4.3 | odd | 2 | |||
1216.4.a.x.1.3 | 3 | 1.1 | even | 1 | trivial | ||
1368.4.a.e.1.1 | 3 | 24.5 | odd | 2 |