Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(129,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.129");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 128) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.129 |
Dual form | 256.4.b.h.129.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 4.92820i | − 0.948433i | −0.880408 | − | 0.474217i | \(-0.842731\pi\) | ||||
0.880408 | − | 0.474217i | \(-0.157269\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.8564i | 1.41824i | 0.705088 | + | 0.709120i | \(0.250908\pi\) | ||||
−0.705088 | + | 0.709120i | \(0.749092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.8564 | −0.964155 | −0.482078 | − | 0.876128i | \(-0.660118\pi\) | ||||
−0.482078 | + | 0.876128i | \(0.660118\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.71281 | 0.100475 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 52.9282i | − 1.45077i | −0.688344 | − | 0.725384i | \(-0.741662\pi\) | ||||
0.688344 | − | 0.725384i | \(-0.258338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 8.43078i | − 0.179868i | −0.995948 | − | 0.0899338i | \(-0.971334\pi\) | ||||
0.995948 | − | 0.0899338i | \(-0.0286655\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 78.1436 | 1.34511 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 129.138 | 1.84239 | 0.921196 | − | 0.389098i | \(-0.127213\pi\) | ||||
0.921196 | + | 0.389098i | \(0.127213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 50.4974i | 0.609732i | 0.952395 | + | 0.304866i | \(0.0986116\pi\) | ||||
−0.952395 | + | 0.304866i | \(0.901388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 88.0000i | 0.914437i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 128.708 | 1.16684 | 0.583422 | − | 0.812169i | \(-0.301713\pi\) | ||||
0.583422 | + | 0.812169i | \(0.301713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −126.426 | −1.01141 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 146.431i | − 1.04373i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 111.282i | − 0.712571i | −0.934377 | − | 0.356285i | \(-0.884043\pi\) | ||||
0.934377 | − | 0.356285i | \(-0.115957\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 302.851 | 1.75464 | 0.877318 | − | 0.479910i | \(-0.159331\pi\) | ||||
0.877318 | + | 0.479910i | \(0.159331\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −260.841 | −1.37596 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 283.138i | − 1.36740i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 182.995i | − 0.813086i | −0.913632 | − | 0.406543i | \(-0.866734\pi\) | ||||
0.913632 | − | 0.406543i | \(-0.133266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −41.5486 | −0.170592 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 94.5744 | 0.360245 | 0.180122 | − | 0.983644i | \(-0.442351\pi\) | ||||
0.180122 | + | 0.983644i | \(0.442351\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 184.641i | − 0.654825i | −0.944881 | − | 0.327413i | \(-0.893823\pi\) | ||||
0.944881 | − | 0.327413i | \(-0.106177\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 43.0155i | 0.142497i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −296.841 | −0.921249 | −0.460624 | − | 0.887595i | \(-0.652375\pi\) | ||||
−0.460624 | + | 0.887595i | \(0.652375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.1487 | −0.0704045 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 636.420i | − 1.74739i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 102.995i | − 0.266933i | −0.991053 | − | 0.133466i | \(-0.957389\pi\) | ||||
0.991053 | − | 0.133466i | \(-0.0426108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 839.251 | 2.05754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 248.862 | 0.578290 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 93.3693i | 0.206028i | 0.994680 | + | 0.103014i | \(0.0328486\pi\) | ||||
−0.994680 | + | 0.103014i | \(0.967151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 338.974i | 0.711495i | 0.934582 | + | 0.355748i | \(0.115774\pi\) | ||||
−0.934582 | + | 0.355748i | \(0.884226\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −48.4411 | −0.0968731 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 133.682 | 0.255095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 489.041i | 0.891729i | 0.895100 | + | 0.445865i | \(0.147104\pi\) | ||||
−0.895100 | + | 0.445865i | \(0.852896\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 634.297i | − 1.10667i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −86.9845 | −0.145397 | −0.0726983 | − | 0.997354i | \(-0.523161\pi\) | ||||
−0.0726983 | + | 0.997354i | \(0.523161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 154.267 | 0.247336 | 0.123668 | − | 0.992324i | \(-0.460534\pi\) | ||||
0.123668 | + | 0.992324i | \(0.460534\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 623.051i | 0.959250i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 945.108i | 1.39877i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 449.415 | 0.640040 | 0.320020 | − | 0.947411i | \(-0.396310\pi\) | ||||
0.320020 | + | 0.947411i | \(0.396310\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −648.395 | −0.889430 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 383.933i | 0.507737i | 0.967239 | + | 0.253868i | \(0.0817030\pi\) | ||||
−0.967239 | + | 0.253868i | \(0.918297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2047.67i | 2.61295i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −548.420 | −0.675826 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 517.672 | 0.616551 | 0.308276 | − | 0.951297i | \(-0.400248\pi\) | ||||
0.308276 | + | 0.951297i | \(0.400248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 150.543i | 0.173420i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1492.51i | − 1.66415i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −800.708 | −0.864746 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1739.39 | 1.82071 | 0.910355 | − | 0.413829i | \(-0.135809\pi\) | ||||
0.910355 | + | 0.413829i | \(0.135809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 143.584i | − 0.145765i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1158.99i | − 1.14182i | −0.821011 | − | 0.570912i | \(-0.806590\pi\) | ||||
0.821011 | − | 0.570912i | \(-0.193410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1635.01 | −1.56410 | −0.782048 | − | 0.623218i | \(-0.785825\pi\) | ||||
−0.782048 | + | 0.623218i | \(0.785825\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1395.36 | −1.29689 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 282.589i | − 0.255317i | −0.991818 | − | 0.127659i | \(-0.959254\pi\) | ||||
0.991818 | − | 0.127659i | \(-0.0407462\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1004.98i | − 0.883120i | −0.897232 | − | 0.441560i | \(-0.854425\pi\) | ||||
0.897232 | − | 0.441560i | \(-0.145575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −901.836 | −0.771157 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −567.108 | −0.472115 | −0.236057 | − | 0.971739i | \(-0.575855\pi\) | ||||
−0.236057 | + | 0.971739i | \(0.575855\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2040.84i | 1.65486i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 22.8711i | − 0.0180721i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2305.95 | −1.77635 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1470.39 | −1.10473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 466.082i | − 0.341668i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 22.6053i | − 0.0161750i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 496.616 | 0.346988 | 0.173494 | − | 0.984835i | \(-0.444494\pi\) | ||||
0.173494 | + | 0.984835i | \(0.444494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −909.948 | −0.621058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1658.72i | 1.10628i | 0.833087 | + | 0.553142i | \(0.186571\pi\) | ||||
−0.833087 | + | 0.553142i | \(0.813429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 901.703i | − 0.587876i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2321.87 | 1.48025 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 432.872 | 0.269947 | 0.134974 | − | 0.990849i | \(-0.456905\pi\) | ||||
0.134974 | + | 0.990849i | \(0.456905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 146.148i | 0.0891809i | 0.999005 | + | 0.0445904i | \(0.0141983\pi\) | ||||
−0.999005 | + | 0.0445904i | \(0.985802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1462.89i | 0.873743i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −446.226 | −0.260946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1764.53 | 1.01060 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 119.010i | 0.0667740i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3556.29i | 1.95532i | 0.210198 | + | 0.977659i | \(0.432589\pi\) | ||||
−0.210198 | + | 0.977659i | \(0.567411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1320.32 | −0.711562 | −0.355781 | − | 0.934569i | \(-0.615785\pi\) | ||||
−0.355781 | + | 0.934569i | \(0.615785\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 350.328 | 0.185114 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4802.13i | 2.48849i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2040.43i | − 1.03722i | −0.855010 | − | 0.518612i | \(-0.826449\pi\) | ||||
0.855010 | − | 0.518612i | \(-0.173551\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −507.580 | −0.253168 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2298.26 | −1.12502 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 2392.21i | − 1.14952i | −0.818321 | − | 0.574762i | \(-0.805095\pi\) | ||||
0.818321 | − | 0.574762i | \(-0.194905\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 4136.00i | − 1.95144i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2068.34 | 0.958400 | 0.479200 | − | 0.877706i | \(-0.340927\pi\) | ||||
0.479200 | + | 0.877706i | \(0.340927\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2125.92 | 0.967648 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 136.990i | 0.0612625i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2441.87i | 1.07313i | 0.843859 | + | 0.536566i | \(0.180279\pi\) | ||||
−0.843859 | + | 0.536566i | \(0.819721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2257.51 | 0.975152 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 460.143 | 0.195404 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2430.84i | − 1.01502i | −0.861645 | − | 0.507512i | \(-0.830565\pi\) | ||||
0.861645 | − | 0.507512i | \(-0.169435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1928.96i | 0.792148i | 0.918219 | + | 0.396074i | \(0.129628\pi\) | ||||
−0.918219 | + | 0.396074i | \(0.870372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1670.53 | 0.674806 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2901.64 | 1.15315 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6835.07i | − 2.67288i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2614.73i | 1.00631i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4087.34 | −1.54843 | −0.774214 | − | 0.632924i | \(-0.781855\pi\) | ||||
−0.774214 | + | 0.632924i | \(0.781855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1156.52 | −0.431339 | −0.215669 | − | 0.976466i | \(-0.569193\pi\) | ||||
−0.215669 | + | 0.976466i | \(0.569193\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 658.811i | − 0.241941i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2658.44i | − 0.961452i | −0.876871 | − | 0.480726i | \(-0.840373\pi\) | ||||
0.876871 | − | 0.480726i | \(-0.159627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −742.369 | −0.264448 | −0.132224 | − | 0.991220i | \(-0.542212\pi\) | ||||
−0.132224 | + | 0.991220i | \(0.542212\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2410.09 | 0.845745 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1987.10i | 0.687029i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1499.61i | 0.510914i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 349.160 | 0.117238 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2672.74 | 0.884580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3838.30i | − 1.25232i | −0.779694 | − | 0.626160i | \(-0.784626\pi\) | ||||
0.779694 | − | 0.626160i | \(-0.215374\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 428.677i | 0.137899i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2927.74 | 0.928700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5407.84 | −1.69174 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 760.257i | − 0.234582i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1088.74i | − 0.331387i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3418.34 | 1.02650 | 0.513249 | − | 0.858240i | \(-0.328442\pi\) | ||||
0.513249 | + | 0.858240i | \(0.328442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −342.969 | −0.101620 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 515.729i | 0.150793i | 0.997154 | + | 0.0753967i | \(0.0240223\pi\) | ||||
−0.997154 | + | 0.0753967i | \(0.975978\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1595.26i | 0.460340i | 0.973150 | + | 0.230170i | \(0.0739282\pi\) | ||||
−0.973150 | + | 0.230170i | \(0.926072\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4657.68 | 1.32664 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5251.27 | −1.47649 | −0.738245 | − | 0.674533i | \(-0.764345\pi\) | ||||
−0.738245 | + | 0.674533i | \(0.764345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 4706.83i | − 1.30655i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2214.81i | − 0.607035i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2029.27 | 0.549216 | 0.274608 | − | 0.961556i | \(-0.411452\pi\) | ||||
0.274608 | + | 0.961556i | \(0.411452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4615.72 | −1.23371 | −0.616856 | − | 0.787076i | \(-0.711594\pi\) | ||||
−0.616856 | + | 0.787076i | \(0.711594\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 758.210i | − 0.200161i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 382.912i | − 0.0998505i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 425.733 | 0.109671 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1892.10 | 0.481554 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2702.52i | 0.679607i | 0.940496 | + | 0.339804i | \(0.110361\pi\) | ||||
−0.940496 | + | 0.339804i | \(0.889639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6812.27i | − 1.69282i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10091.3 | 2.47821 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 991.785 | 0.240723 | 0.120362 | − | 0.992730i | \(-0.461595\pi\) | ||||
0.120362 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3267.63i | 0.783941i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 301.887i | − 0.0715952i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7430.74 | −1.74220 | −0.871101 | − | 0.491105i | \(-0.836593\pi\) | ||||
−0.871101 | + | 0.491105i | \(0.836593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1633.13 | 0.378575 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2551.19i | − 0.584758i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3281.50i | − 0.743778i | −0.928277 | − | 0.371889i | \(-0.878710\pi\) | ||||
0.928277 | − | 0.371889i | \(-0.121290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 221.518 | 0.0496542 | 0.0248271 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248271 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 741.909 | 0.164477 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6691.48i | 1.46731i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1106.28i | 0.239963i | 0.992776 | + | 0.119982i | \(0.0382835\pi\) | ||||
−0.992776 | + | 0.119982i | \(0.961716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 821.579 | 0.176296 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2372.52 | 0.503676 | 0.251838 | − | 0.967769i | \(-0.418965\pi\) | ||||
0.251838 | + | 0.967769i | \(0.418965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2549.89i | − 0.535602i | −0.963474 | − | 0.267801i | \(-0.913703\pi\) | ||||
0.963474 | − | 0.267801i | \(-0.0862970\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3946.05i | 0.820154i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1688.76 | −0.347332 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11763.7 | 2.39441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 8572.09i | − 1.72682i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 130.319i | 0.0259840i | 0.999916 | + | 0.0129920i | \(0.00413560\pi\) | ||||
−0.999916 | + | 0.0129920i | \(0.995864\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1480.50 | −0.292197 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7750.32 | −1.51421 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1085.11i | − 0.209877i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3297.03i | 0.631353i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5711.76 | −1.08294 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5374.91 | −1.00907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 62.1182i | − 0.0115481i | −0.999983 | − | 0.00577406i | \(-0.998162\pi\) | ||||
0.999983 | − | 0.00577406i | \(-0.00183795\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8057.64i | 1.48344i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −593.837 | −0.108275 | −0.0541373 | − | 0.998533i | \(-0.517241\pi\) | ||||
−0.0541373 | + | 0.998533i | \(0.517241\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3669.69 | −0.662694 | −0.331347 | − | 0.943509i | \(-0.607503\pi\) | ||||
−0.331347 | + | 0.943509i | \(0.607503\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 768.102i | − 0.137389i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 374.339i | − 0.0663249i | −0.999450 | − | 0.0331625i | \(-0.989442\pi\) | ||||
0.999450 | − | 0.0331625i | \(-0.0105579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5889.96 | −1.03378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1392.66 | −0.242151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6521.16i | 1.12337i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1065.87i | 0.181919i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4952.77 | −0.837580 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5300.51 | 0.888227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5871.13i | 0.974945i | 0.873138 | + | 0.487472i | \(0.162081\pi\) | ||||
−0.873138 | + | 0.487472i | \(0.837919\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 496.431i | − 0.0816944i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7754.43 | −1.26469 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1047.83 | 0.169373 | 0.0846865 | − | 0.996408i | \(-0.473011\pi\) | ||||
0.0846865 | + | 0.996408i | \(0.473011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2794.82i | 0.447769i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 16029.4i | − 2.54557i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6555.96 | 1.03204 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10057.7 | 1.56953 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3921.88i | 0.606737i | 0.952873 | + | 0.303368i | \(0.0981113\pi\) | ||||
−0.952873 | + | 0.303368i | \(0.901889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11604.9i | 1.77993i | 0.456027 | + | 0.889966i | \(0.349272\pi\) | ||||
−0.456027 | + | 0.889966i | \(0.650728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1234.53 | −0.187733 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1530.22 | −0.230724 | −0.115362 | − | 0.993324i | \(-0.536803\pi\) | ||||
−0.115362 | + | 0.993324i | \(0.536803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1379.26i | − 0.206207i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11364.2i | 1.68475i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10764.0 | −1.58246 | −0.791231 | − | 0.611518i | \(-0.790559\pi\) | ||||
−0.791231 | + | 0.611518i | \(0.790559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4309.01 | 0.628227 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7246.40i | 1.04776i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2446.11i | 0.350782i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10713.0 | 1.52374 | 0.761869 | − | 0.647731i | \(-0.224282\pi\) | ||||
0.761869 | + | 0.647731i | \(0.224282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 256.563 | 0.0361954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1839.12i | 0.257365i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 9186.32i | − 1.27520i | −0.770368 | − | 0.637600i | \(-0.779927\pi\) | ||||
0.770368 | − | 0.637600i | \(-0.220073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −111.404 | −0.0153409 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −938.194 | −0.128168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14201.0i | 1.92468i | 0.271842 | + | 0.962342i | \(0.412367\pi\) | ||||
−0.271842 | + | 0.962342i | \(0.587633\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2447.42i | − 0.329095i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9691.24 | −1.29295 | −0.646474 | − | 0.762936i | \(-0.723757\pi\) | ||||
−0.646474 | + | 0.762936i | \(0.723757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14986.0 | −1.98379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 500.897i | − 0.0657933i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6358.79i | 0.828801i | 0.910095 | + | 0.414400i | \(0.136009\pi\) | ||||
−0.910095 | + | 0.414400i | \(0.863991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16621.1 | 2.14978 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8174.52 | 1.04924 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7126.11i | 0.907731i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 13034.2i | − 1.64778i | −0.566752 | − | 0.823888i | \(-0.691800\pi\) | ||||
0.566752 | − | 0.823888i | \(-0.308200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4443.77 | −0.557561 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6705.06 | 0.834999 | 0.417499 | − | 0.908677i | \(-0.362907\pi\) | ||||
0.417499 | + | 0.908677i | \(0.362907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2553.27i | − 0.315602i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 10281.2i | − 1.26143i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9685.59 | −1.17960 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10967.8 | −1.32598 | −0.662988 | − | 0.748630i | \(-0.730712\pi\) | ||||
−0.662988 | + | 0.748630i | \(0.730712\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 2133.28i | − 0.256027i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1667.24i | − 0.198643i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6087.80 | −0.720093 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 720.249 | 0.0845821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13686.0i | 1.59571i | 0.602849 | + | 0.797856i | \(0.294032\pi\) | ||||
−0.602849 | + | 0.797856i | \(0.705968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 8552.92i | − 0.990128i | −0.868857 | − | 0.495064i | \(-0.835145\pi\) | ||||
0.868857 | − | 0.495064i | \(-0.164855\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −805.274 | −0.0925621 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16326.4 | −1.86340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6052.86i | − 0.685992i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2199.09i | 0.247490i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12187.6 | −1.36208 | −0.681039 | − | 0.732247i | \(-0.738472\pi\) | ||||
−0.681039 | + | 0.732247i | \(0.738472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8906.35 | −0.988480 | −0.494240 | − | 0.869326i | \(-0.664554\pi\) | ||||
−0.494240 | + | 0.869326i | \(0.664554\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 8695.98i | − 0.958483i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6499.41i | 0.711462i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4655.21 | −0.506107 | −0.253054 | − | 0.967452i | \(-0.581435\pi\) | ||||
−0.253054 | + | 0.967452i | \(0.581435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −65.5110 | −0.00707386 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10008.8i | − 1.07343i | −0.843763 | − | 0.536716i | \(-0.819665\pi\) | ||||
0.843763 | − | 0.536716i | \(-0.180335\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8208.41i | 0.874418i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17526.1 | 1.85449 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3373.71 | −0.354600 | −0.177300 | − | 0.984157i | \(-0.556736\pi\) | ||||
−0.177300 | + | 0.984157i | \(0.556736\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5005.65i | − 0.522632i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6506.79i | 0.674869i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2387.08 | −0.245952 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13600.4 | 1.39212 | 0.696060 | − | 0.717984i | \(-0.254935\pi\) | ||||
0.696060 | + | 0.717984i | \(0.254935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 18909.8i | − 1.92295i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3559.45i | 0.359609i | 0.983702 | + | 0.179805i | \(0.0575466\pi\) | ||||
−0.983702 | + | 0.179805i | \(0.942453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8019.14 | 0.804926 | 0.402463 | − | 0.915436i | \(-0.368154\pi\) | ||||
0.402463 | + | 0.915436i | \(0.368154\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23665.9 | 2.36017 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2066.14i | − 0.204731i | −0.994747 | − | 0.102365i | \(-0.967359\pi\) | ||||
0.994747 | − | 0.102365i | \(-0.0326411\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 8732.51i | − 0.859765i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10055.7 | −0.983737 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9772.72 | −0.950000 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 6384.17i | − 0.616686i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 279.406i | − 0.0268199i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3679.26 | 0.350960 | 0.175480 | − | 0.984483i | \(-0.443852\pi\) | ||||
0.175480 | + | 0.984483i | \(0.443852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1542.79 | −0.146248 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11326.3i | 1.06700i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27580.5i | 2.58220i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10884.4 | 1.01277 | 0.506386 | − | 0.862307i | \(-0.330981\pi\) | ||||
0.506386 | + | 0.862307i | \(0.330981\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11789.3 | −1.09025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14548.9i | 1.33723i | 0.743608 | + | 0.668616i | \(0.233113\pi\) | ||||
−0.743608 | + | 0.668616i | \(0.766887\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 14370.8i | − 1.31284i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2276.73 | 0.206730 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1553.23 | 0.140185 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8461.92i | 0.759134i | 0.925164 | + | 0.379567i | \(0.123927\pi\) | ||||
−0.925164 | + | 0.379567i | \(0.876073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 10193.2i | − 0.908978i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −983.702 | −0.0871990 | −0.0435995 | − | 0.999049i | \(-0.513883\pi\) | ||||
−0.0435995 | + | 0.999049i | \(0.513883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18377.5 | 1.61938 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 10477.0i | − 0.917749i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 14472.5i | − 1.26028i | −0.776481 | − | 0.630140i | \(-0.782997\pi\) | ||||
0.776481 | − | 0.630140i | \(-0.217003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2754.65 | −0.238470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7394.38 | 0.636393 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 25925.3i | − 2.21826i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15711.3i | 1.33652i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12034.0 | 1.01779 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10761.8 | 0.904959 | 0.452480 | − | 0.891775i | \(-0.350540\pi\) | ||||
0.452480 | + | 0.891775i | \(0.350540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1516.67i | 0.126806i | 0.997988 | + | 0.0634029i | \(0.0201953\pi\) | ||||
−0.997988 | + | 0.0634029i | \(0.979805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 11125.5i | − 0.924866i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39109.7 | 3.23273 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4398.66 | 0.361524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 253.293i | 0.0207006i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 797.336i | − 0.0647963i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4480.85 | 0.362101 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11979.7 | −0.962682 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1278.15i | 0.102141i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22541.9i | 1.79141i | 0.444652 | + | 0.895704i | \(0.353327\pi\) | ||||
−0.444652 | + | 0.895704i | \(0.646673\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9506.33 | 0.751299 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15935.4 | 1.25248 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 10202.0i | − 0.797448i | −0.917071 | − | 0.398724i | \(-0.869453\pi\) | ||||
0.917071 | − | 0.398724i | \(-0.130547\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 919.574i | 0.0714872i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5619.46 | 0.434477 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8024.94 | −0.617098 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 14299.9i | − 1.09369i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7139.06i | 0.543073i | 0.962428 | + | 0.271536i | \(0.0875317\pi\) | ||||
−0.962428 | + | 0.271536i | \(0.912468\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1556.67 | −0.117782 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33684.6 | −2.53505 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19558.0i | 1.46407i | 0.681268 | + | 0.732034i | \(0.261429\pi\) | ||||
−0.681268 | + | 0.732034i | \(0.738571\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 8992.29i | − 0.669572i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11578.0 | 0.857549 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5835.86 | 0.429969 | 0.214984 | − | 0.976617i | \(-0.431030\pi\) | ||||
0.214984 | + | 0.976617i | \(0.431030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9820.65i | 0.719757i | 0.932999 | + | 0.359879i | \(0.117182\pi\) | ||||
−0.932999 | + | 0.359879i | \(0.882818\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20143.3i | 1.46858i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16271.9 | −1.18015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 451.231 | 0.0325563 | 0.0162782 | − | 0.999868i | \(-0.494818\pi\) | ||||
0.0162782 | + | 0.999868i | \(0.494818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5699.58i | 0.409096i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6855.67i | − 0.489537i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5451.33 | −0.387257 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 362.654 | 0.0256306 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 24775.7i | − 1.74208i | −0.491209 | − | 0.871042i | \(-0.663445\pi\) | ||||
0.491209 | − | 0.871042i | \(-0.336555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15293.2i | 1.06986i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13101.3 | −0.911873 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4207.64 | −0.291378 | −0.145689 | − | 0.989330i | \(-0.546540\pi\) | ||||
−0.145689 | + | 0.989330i | \(0.546540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 36564.1i | − 2.51929i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3658.54i | 0.250811i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1916.32 | 0.130715 | 0.0653577 | − | 0.997862i | \(-0.479181\pi\) | ||||
0.0653577 | + | 0.997862i | \(0.479181\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19361.1 | 1.31407 | 0.657034 | − | 0.753861i | \(-0.271811\pi\) | ||||
0.657034 | + | 0.753861i | \(0.271811\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1326.68i | 0.0895961i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 23315.2i | − 1.56677i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6097.02 | −0.407694 | −0.203847 | − | 0.979003i | \(-0.565345\pi\) | ||||
−0.203847 | + | 0.979003i | \(0.565345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9792.82 | 0.651601 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2502.60i | 0.165703i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13837.7i | − 0.911743i | −0.890046 | − | 0.455872i | \(-0.849328\pi\) | ||||
0.890046 | − | 0.455872i | \(-0.150672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7390.38 | 0.484567 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11959.1 | −0.780318 | −0.390159 | − | 0.920747i | \(-0.627580\pi\) | ||||
−0.390159 | + | 0.920747i | \(0.627580\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8385.02i | 0.544463i | 0.962232 | + | 0.272231i | \(0.0877616\pi\) | ||||
−0.962232 | + | 0.272231i | \(0.912238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 18846.8i | − 1.21787i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9243.75 | −0.594451 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15444.8 | −0.988465 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 13171.8i | − 0.838965i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 23631.7i | − 1.49802i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13592.1 | 0.857513 | 0.428757 | − | 0.903420i | \(-0.358952\pi\) | ||||
0.428757 | + | 0.903420i | \(0.358952\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18915.9 | −1.18774 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7874.54i | 0.492113i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 203.593i | 0.0126635i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −235.973 | −0.0146087 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18123.4 | −1.11674 | −0.558371 | − | 0.829591i | \(-0.688573\pi\) | ||||
−0.558371 | + | 0.829591i | \(0.688573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 25042.1i | − 1.53587i | −0.640528 | − | 0.767935i | \(-0.721284\pi\) | ||||
0.640528 | − | 0.767935i | \(-0.278716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 14428.5i | − 0.880809i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6022.08 | −0.365923 | −0.182962 | − | 0.983120i | \(-0.558568\pi\) | ||||
−0.182962 | + | 0.983120i | \(0.558568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4941.87 | 0.298899 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26650.9i | 1.60450i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14093.8i | 0.844617i | 0.906452 | + | 0.422308i | \(0.138780\pi\) | ||||
−0.906452 | + | 0.422308i | \(0.861220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26301.4 | −1.56898 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 418.496 | 0.0248510 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17240.7i | 1.01912i | 0.860434 | + | 0.509562i | \(0.170193\pi\) | ||||
−0.860434 | + | 0.509562i | \(0.829807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20209.5i | 1.18920i | 0.804023 | + | 0.594598i | \(0.202689\pi\) | ||||
−0.804023 | + | 0.594598i | \(0.797311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5365.52 | −0.314298 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14297.8 | 0.833749 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 14322.8i | − 0.831459i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 16846.3i | − 0.973564i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17941.3 | 1.03221 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6838.55 | 0.391689 | 0.195845 | − | 0.980635i | \(-0.437255\pi\) | ||||
0.195845 | + | 0.980635i | \(0.437255\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18512.6i | 1.05563i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 187.425i | − 0.0106401i | −0.999986 | − | 0.00532003i | \(-0.998307\pi\) | ||||
0.999986 | − | 0.00532003i | \(-0.00169343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31059.3 | −1.75545 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2541.62 | 0.143018 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23476.0i | 1.31520i | 0.753367 | + | 0.657601i | \(0.228429\pi\) | ||||
−0.753367 | + | 0.657601i | \(0.771571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6863.79i | 0.382850i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7861.77 | 0.436602 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −868.327 | −0.0480125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6309.92i | 0.347382i | 0.984800 | + | 0.173691i | \(0.0555694\pi\) | ||||
−0.984800 | + | 0.173691i | \(0.944431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2563.90i | 0.140540i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2317.39 | −0.126480 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12213.2 | 0.663712 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25879.3i | 1.40035i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24920.4i | 1.34270i | 0.741142 | + | 0.671348i | \(0.234284\pi\) | ||||
−0.741142 | + | 0.671348i | \(0.765716\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9240.77 | 0.495764 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23196.2 | −1.23918 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20695.5i | 1.10090i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14478.9i | 0.766949i | 0.923551 | + | 0.383474i | \(0.125273\pi\) | ||||
−0.923551 | + | 0.383474i | \(0.874727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1219.18 | 0.0643077 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38979.3 | 2.04738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 7075.54i | − 0.370084i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 10000.7i | − 0.520895i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6411.30 | −0.332547 | −0.166273 | − | 0.986080i | \(-0.553173\pi\) | ||||
−0.166273 | + | 0.986080i | \(0.553173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29195.3 | 1.50803 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22747.2i | 1.17009i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14068.9i | 0.720698i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20626.3 | 1.05225 | 0.526126 | − | 0.850407i | \(-0.323644\pi\) | ||||
0.526126 | + | 0.850407i | \(0.323644\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21243.3 | −1.07927 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 23844.3i | − 1.20645i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 5732.29i | − 0.288850i | −0.989516 | − | 0.144425i | \(-0.953867\pi\) | ||||
0.989516 | − | 0.144425i | \(-0.0461332\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1887.07 | −0.0947015 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25884.1 | 1.29369 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36336.0i | 1.80872i | 0.426773 | + | 0.904359i | \(0.359650\pi\) | ||||
−0.426773 | + | 0.904359i | \(0.640350\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 2098.10i | − 0.104016i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4363.83 | −0.215469 | −0.107734 | − | 0.994180i | \(-0.534360\pi\) | ||||
−0.107734 | + | 0.994180i | \(0.534360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −56389.9 | −2.77311 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1041.54i | 0.0510146i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5046.03i | 0.246166i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16162.7 | −0.785334 | −0.392667 | − | 0.919681i | \(-0.628448\pi\) | ||||
−0.392667 | + | 0.919681i | \(0.628448\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13318.6 | 0.644562 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 20935.5i | − 1.00917i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4411.92i | 0.211828i | 0.994375 | + | 0.105914i | \(0.0337769\pi\) | ||||
−0.994375 | + | 0.105914i | \(0.966223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33572.2 | −1.60553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28281.8 | −1.34719 | −0.673597 | − | 0.739099i | \(-0.735251\pi\) | ||||
−0.673597 | + | 0.739099i | \(0.735251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17945.4i | 0.851465i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5554.95i | 0.262535i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 787.176 | 0.0370577 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15016.8 | −0.704186 | −0.352093 | − | 0.935965i | \(-0.614530\pi\) | ||||
−0.352093 | + | 0.935965i | \(0.614530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 4887.72i | − 0.228310i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8674.11i | 0.403604i | 0.979426 | + | 0.201802i | \(0.0646798\pi\) | ||||
−0.979426 | + | 0.201802i | \(0.935320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38288.2 | −1.77465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16103.5 | 0.743515 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4775.76i | 0.219653i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4603.94i | 0.210937i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16295.1 | −0.743729 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32353.9 | 1.47103 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23660.2i | 1.07166i | 0.844327 | + | 0.535829i | \(0.180001\pi\) | ||||
−0.844327 | + | 0.535829i | \(0.819999\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36620.2i | 1.65236i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10126.5 | 0.455192 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2857.82 | 0.127975 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 8048.39i | − 0.359053i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 35432.5i | − 1.57476i | −0.616468 | − | 0.787380i | \(-0.711437\pi\) | ||||
0.616468 | − | 0.787380i | \(-0.288563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38333.6 | −1.69730 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1404.35 | 0.0619477 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 8165.05i | − 0.358827i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 36442.1i | − 1.59555i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16171.9 | −0.705424 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14005.5 | 0.608664 | 0.304332 | − | 0.952566i | \(-0.401567\pi\) | ||||
0.304332 | + | 0.952566i | \(0.401567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 22580.8i | − 0.977706i | −0.872366 | − | 0.488853i | \(-0.837416\pi\) | ||||
0.872366 | − | 0.488853i | \(-0.162584\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1091.69i | − 0.0470937i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37931.8 | 1.63030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9323.90 | 0.399268 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 408.396i | 0.0174243i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21308.9i | 0.905827i | 0.891554 | + | 0.452914i | \(0.149615\pi\) | ||||
−0.891554 | + | 0.452914i | \(0.850385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13571.4 | −0.574810 | −0.287405 | − | 0.957809i | \(-0.592793\pi\) | ||||
−0.287405 | + | 0.957809i | \(0.592793\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32977.0 | 1.39165 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 19295.2i | − 0.811318i | −0.914025 | − | 0.405659i | \(-0.867042\pi\) | ||||
0.914025 | − | 0.405659i | \(-0.132958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 28752.7i | − 1.20461i | −0.798265 | − | 0.602306i | \(-0.794249\pi\) | ||||
0.798265 | − | 0.602306i | \(-0.205751\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5451.96 | 0.227589 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3118.53 | −0.129713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32796.4i | 1.35924i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 44346.7i | − 1.83136i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 566.927 | 0.0233284 | 0.0116642 | − | 0.999932i | \(-0.496287\pi\) | ||||
0.0116642 | + | 0.999932i | \(0.496287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12005.3 | 0.492243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 11692.3i | − 0.477703i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33709.5i | 1.37236i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26256.0 | 1.06513 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12566.4 | −0.507983 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 23552.8i | − 0.948744i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34698.1i | 1.39278i | 0.717665 | + | 0.696389i | \(0.245211\pi\) | ||||
−0.717665 | + | 0.696389i | \(0.754789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2172.17 | −0.0868850 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −37362.0 | −1.48922 | −0.744610 | − | 0.667500i | \(-0.767364\pi\) | ||||
−0.744610 | + | 0.667500i | \(0.767364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29572.2i | 1.17461i | 0.809366 | + | 0.587305i | \(0.199811\pi\) | ||||
−0.809366 | + | 0.587305i | \(0.800189\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8322.54i | 0.329421i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11636.5 | −0.458994 | −0.229497 | − | 0.973309i | \(-0.573708\pi\) | ||||
−0.229497 | + | 0.973309i | \(0.573708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38719.2 | −1.52196 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 57974.1i | − 2.27094i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 23786.7i | − 0.928550i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4123.00 | 0.160393 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4718.65 | 0.182935 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 403.649i | 0.0155952i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 19878.2i | − 0.765380i | −0.923877 | − | 0.382690i | \(-0.874998\pi\) | ||||
0.923877 | − | 0.382690i | \(-0.125002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 642.238 | 0.0246441 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36460.3 | −1.39430 | −0.697150 | − | 0.716926i | \(-0.745549\pi\) | ||||
−0.697150 | + | 0.716926i | \(0.745549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28119.9i | 1.07170i | 0.844314 | + | 0.535849i | \(0.180009\pi\) | ||||
−0.844314 | + | 0.535849i | \(0.819991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7296.21i | 0.277129i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41888.4 | 1.58565 | 0.792826 | − | 0.609448i | \(-0.208609\pi\) | ||||
0.792826 | + | 0.609448i | \(0.208609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8867.77 | −0.334551 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34318.4i | 1.29036i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 14989.7i | − 0.561715i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38544.3 | 1.43955 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5347.62 | −0.199055 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 33701.9i | − 1.25030i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 13300.6i | − 0.491795i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16248.4 | 0.598796 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30586.4 | −1.12346 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12575.3i | 0.460371i | 0.973147 | + | 0.230185i | \(0.0739333\pi\) | ||||
−0.973147 | + | 0.230185i | \(0.926067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 3144.14i | − 0.114724i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39814.7 | −1.44799 | −0.723995 | − | 0.689805i | \(-0.757696\pi\) | ||||
−0.723995 | + | 0.689805i | \(0.757696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20320.9 | 0.736609 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26488.7i | 0.957036i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 29618.8i | − 1.06663i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8987.93 | −0.322616 | −0.161308 | − | 0.986904i | \(-0.551571\pi\) | ||||
−0.161308 | + | 0.986904i | \(0.551571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −306.131 | −0.0109526 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 733.348i | 0.0261521i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23135.2i | 0.822359i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4435.46 | −0.157152 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 234.252 | 0.00827293 | 0.00413647 | − | 0.999991i | \(-0.498683\pi\) | ||||
0.00413647 | + | 0.999991i | \(0.498683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1219.45i | − 0.0429279i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2926.55i | 0.102691i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 108380. | 3.79079 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17624.6 | −0.614483 | −0.307241 | − | 0.951632i | \(-0.599406\pi\) | ||||
−0.307241 | + | 0.951632i | \(0.599406\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18085.0i | 0.628521i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30532.1i | 1.05772i | 0.848708 | + | 0.528861i | \(0.177381\pi\) | ||||
−0.848708 | + | 0.528861i | \(0.822619\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12172.4 | 0.420349 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −41460.2 | −1.42720 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 42092.8i | − 1.44438i | −0.691692 | − | 0.722192i | \(-0.743135\pi\) | ||||
0.691692 | − | 0.722192i | \(-0.256865\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1300.59i | − 0.0444877i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1844.82 | −0.0629048 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48641.0 | 1.65334 | 0.826672 | − | 0.562683i | \(-0.190231\pi\) | ||||
0.826672 | + | 0.562683i | \(0.190231\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 64810.6i | − 2.19604i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29026.9i | 0.980467i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7729.54 | −0.260271 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61927.9 | 2.07874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 766.612i | − 0.0256529i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 18338.3i | − 0.611742i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53000.5 | 1.76254 | 0.881272 | − | 0.472609i | \(-0.156688\pi\) | ||||
0.881272 | + | 0.472609i | \(0.156688\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 32137.6 | 1.06544 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 26286.3i | − 0.868761i | −0.900729 | − | 0.434381i | \(-0.856967\pi\) | ||||
0.900729 | − | 0.434381i | \(-0.143033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2609.68i | − 0.0859842i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5252.81 | 0.172538 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30508.0 | −0.999014 | −0.499507 | − | 0.866310i | \(-0.666486\pi\) | ||||
−0.499507 | + | 0.866310i | \(0.666486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 27399.4i | − 0.894473i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 2726.34i | − 0.0887311i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37044.3 | −1.20196 | −0.600982 | − | 0.799263i | \(-0.705224\pi\) | ||||
−0.600982 | + | 0.799263i | \(0.705224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42153.3 | 1.36357 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 26122.0i | − 0.842424i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 23764.7i | − 0.764079i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47803.5 | 1.53232 | 0.766160 | − | 0.642650i | \(-0.222165\pi\) | ||||
0.766160 | + | 0.642650i | \(0.222165\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28934.1 | 0.924670 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 11771.3i | − 0.375051i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 13478.1i | − 0.428140i | −0.976818 | − | 0.214070i | \(-0.931328\pi\) | ||||
0.976818 | − | 0.214070i | \(-0.0686720\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26796.1 | −0.848639 |
(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 | 256.4.b.h.129.2 | 4 | ||
4.3 | odd | 2 | 256.4.b.i.129.3 | 4 | |||
8.3 | odd | 2 | 256.4.b.i.129.2 | 4 | |||
8.5 | even | 2 | inner | 256.4.b.h.129.3 | 4 | ||
16.3 | odd | 4 | 128.4.a.h.1.1 | yes | 2 | ||
16.5 | even | 4 | 128.4.a.g.1.1 | yes | 2 | ||
16.11 | odd | 4 | 128.4.a.e.1.2 | ✓ | 2 | ||
16.13 | even | 4 | 128.4.a.f.1.2 | yes | 2 | ||
48.5 | odd | 4 | 1152.4.a.t.1.2 | 2 | |||
48.11 | even | 4 | 1152.4.a.s.1.2 | 2 | |||
48.29 | odd | 4 | 1152.4.a.r.1.1 | 2 | |||
48.35 | even | 4 | 1152.4.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.a.e.1.2 | ✓ | 2 | 16.11 | odd | 4 | ||
128.4.a.f.1.2 | yes | 2 | 16.13 | even | 4 | ||
128.4.a.g.1.1 | yes | 2 | 16.5 | even | 4 | ||
128.4.a.h.1.1 | yes | 2 | 16.3 | odd | 4 | ||
256.4.b.h.129.2 | 4 | 1.1 | even | 1 | trivial | ||
256.4.b.h.129.3 | 4 | 8.5 | even | 2 | inner | ||
256.4.b.i.129.2 | 4 | 8.3 | odd | 2 | |||
256.4.b.i.129.3 | 4 | 4.3 | odd | 2 | |||
1152.4.a.q.1.1 | 2 | 48.35 | even | 4 | |||
1152.4.a.r.1.1 | 2 | 48.29 | odd | 4 | |||
1152.4.a.s.1.2 | 2 | 48.11 | even | 4 | |||
1152.4.a.t.1.2 | 2 | 48.5 | odd | 4 |