Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,6,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(85.1638083207\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(7.96013\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.96013 | 1.05361 | 0.526806 | − | 0.849985i | \(-0.323389\pi\) | ||||
0.526806 | + | 0.849985i | \(0.323389\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.52316 | 0.110099 | ||||||||
\(5\) | −65.6425 | −1.17425 | −0.587125 | − | 0.809496i | \(-0.699740\pi\) | ||||
−0.587125 | + | 0.809496i | \(0.699740\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 119.026 | 0.918111 | 0.459055 | − | 0.888408i | \(-0.348188\pi\) | ||||
0.459055 | + | 0.888408i | \(0.348188\pi\) | |||||||
\(8\) | −169.726 | −0.937611 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −391.238 | −1.23720 | ||||||||
\(11\) | −237.620 | −0.592109 | −0.296054 | − | 0.955171i | \(-0.595671\pi\) | ||||
−0.296054 | + | 0.955171i | \(0.595671\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 999.008 | 1.63950 | 0.819749 | − | 0.572723i | \(-0.194113\pi\) | ||||
0.819749 | + | 0.572723i | \(0.194113\pi\) | |||||||
\(14\) | 709.408 | 0.967333 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1124.33 | −1.09798 | ||||||||
\(17\) | 1276.40 | 1.07118 | 0.535592 | − | 0.844477i | \(-0.320088\pi\) | ||||
0.535592 | + | 0.844477i | \(0.320088\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1426.51 | 0.906546 | 0.453273 | − | 0.891372i | \(-0.350256\pi\) | ||||
0.453273 | + | 0.891372i | \(0.350256\pi\) | |||||||
\(20\) | −231.269 | −0.129283 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1416.25 | −0.623853 | ||||||||
\(23\) | −546.573 | −0.215441 | −0.107721 | − | 0.994181i | \(-0.534355\pi\) | ||||
−0.107721 | + | 0.994181i | \(0.534355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1183.94 | 0.378862 | ||||||||
\(26\) | 5954.22 | 1.72739 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 419.346 | 0.101083 | ||||||||
\(29\) | 1547.67 | 0.341731 | 0.170865 | − | 0.985294i | \(-0.445344\pi\) | ||||
0.170865 | + | 0.985294i | \(0.445344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7569.31 | −1.41466 | −0.707330 | − | 0.706883i | \(-0.750101\pi\) | ||||
−0.707330 | + | 0.706883i | \(0.750101\pi\) | |||||||
\(32\) | −1269.92 | −0.219231 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7607.51 | 1.12861 | ||||||||
\(35\) | −7813.14 | −1.07809 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1012.21 | −0.121554 | −0.0607769 | − | 0.998151i | \(-0.519358\pi\) | ||||
−0.0607769 | + | 0.998151i | \(0.519358\pi\) | |||||||
\(38\) | 8502.16 | 0.955148 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11141.2 | 1.10099 | ||||||||
\(41\) | −13264.9 | −1.23237 | −0.616187 | − | 0.787600i | \(-0.711324\pi\) | ||||
−0.616187 | + | 0.787600i | \(0.711324\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21794.0 | −1.79749 | −0.898743 | − | 0.438476i | \(-0.855518\pi\) | ||||
−0.898743 | + | 0.438476i | \(0.855518\pi\) | |||||||
\(44\) | −837.174 | −0.0651905 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3257.65 | −0.226992 | ||||||||
\(47\) | −23038.8 | −1.52130 | −0.760650 | − | 0.649163i | \(-0.775119\pi\) | ||||
−0.760650 | + | 0.649163i | \(0.775119\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2639.91 | −0.157072 | ||||||||
\(50\) | 7056.46 | 0.399174 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3519.67 | 0.180507 | ||||||||
\(53\) | −19051.5 | −0.931624 | −0.465812 | − | 0.884884i | \(-0.654238\pi\) | ||||
−0.465812 | + | 0.884884i | \(0.654238\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15598.0 | 0.695283 | ||||||||
\(56\) | −20201.7 | −0.860831 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9224.33 | 0.360052 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7235.44 | −0.248966 | −0.124483 | − | 0.992222i | \(-0.539727\pi\) | ||||
−0.124483 | + | 0.992222i | \(0.539727\pi\) | |||||||
\(62\) | −45114.1 | −1.49050 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 28409.6 | 0.866992 | ||||||||
\(65\) | −65577.4 | −1.92518 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69873.8 | 1.90164 | 0.950818 | − | 0.309752i | \(-0.100246\pi\) | ||||
0.950818 | + | 0.309752i | \(0.100246\pi\) | |||||||
\(68\) | 4496.96 | 0.117936 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −46567.3 | −1.13589 | ||||||||
\(71\) | −17826.0 | −0.419671 | −0.209836 | − | 0.977737i | \(-0.567293\pi\) | ||||
−0.209836 | + | 0.977737i | \(0.567293\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9089.91 | 0.199642 | 0.0998212 | − | 0.995005i | \(-0.468173\pi\) | ||||
0.0998212 | + | 0.995005i | \(0.468173\pi\) | |||||||
\(74\) | −6032.93 | −0.128071 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5025.81 | 0.0998096 | ||||||||
\(77\) | −28282.9 | −0.543622 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31488.7 | 0.567658 | 0.283829 | − | 0.958875i | \(-0.408395\pi\) | ||||
0.283829 | + | 0.958875i | \(0.408395\pi\) | |||||||
\(80\) | 73803.8 | 1.28930 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −79060.3 | −1.29845 | ||||||||
\(83\) | 102025. | 1.62560 | 0.812798 | − | 0.582546i | \(-0.197944\pi\) | ||||
0.812798 | + | 0.582546i | \(0.197944\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −83786.1 | −1.25784 | ||||||||
\(86\) | −129895. | −1.89385 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 40330.2 | 0.555168 | ||||||||
\(89\) | −104185. | −1.39422 | −0.697111 | − | 0.716963i | \(-0.745532\pi\) | ||||
−0.697111 | + | 0.716963i | \(0.745532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 118908. | 1.50524 | ||||||||
\(92\) | −1925.67 | −0.0237198 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −137314. | −1.60286 | ||||||||
\(95\) | −93639.5 | −1.06451 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −117345. | −1.26629 | −0.633147 | − | 0.774032i | \(-0.718237\pi\) | ||||
−0.633147 | + | 0.774032i | \(0.718237\pi\) | |||||||
\(98\) | −15734.2 | −0.165493 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4171.22 | 0.0417122 | ||||||||
\(101\) | −109234. | −1.06550 | −0.532751 | − | 0.846272i | \(-0.678842\pi\) | ||||
−0.532751 | + | 0.846272i | \(0.678842\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −162469. | −1.50896 | −0.754481 | − | 0.656322i | \(-0.772111\pi\) | ||||
−0.754481 | + | 0.656322i | \(0.772111\pi\) | |||||||
\(104\) | −169557. | −1.53721 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −113550. | −0.981570 | ||||||||
\(107\) | 9555.85 | 0.0806882 | 0.0403441 | − | 0.999186i | \(-0.487155\pi\) | ||||
0.0403441 | + | 0.999186i | \(0.487155\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −80849.6 | −0.651796 | −0.325898 | − | 0.945405i | \(-0.605667\pi\) | ||||
−0.325898 | + | 0.945405i | \(0.605667\pi\) | |||||||
\(110\) | 92966.1 | 0.732559 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −133824. | −1.00806 | ||||||||
\(113\) | 131306. | 0.967359 | 0.483679 | − | 0.875245i | \(-0.339300\pi\) | ||||
0.483679 | + | 0.875245i | \(0.339300\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 35878.5 | 0.252982 | ||||||||
\(116\) | 5452.70 | 0.0376241 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20747.2 | 0.137169 | ||||||||
\(119\) | 151924. | 0.983466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −104588. | −0.649407 | ||||||||
\(122\) | −43124.1 | −0.262314 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −26667.9 | −0.155752 | ||||||||
\(125\) | 127416. | 0.729371 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −234331. | −1.28920 | −0.644600 | − | 0.764520i | \(-0.722976\pi\) | ||||
−0.644600 | + | 0.764520i | \(0.722976\pi\) | |||||||
\(128\) | 209963. | 1.13270 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −390850. | −2.02839 | ||||||||
\(131\) | −135156. | −0.688108 | −0.344054 | − | 0.938950i | \(-0.611800\pi\) | ||||
−0.344054 | + | 0.938950i | \(0.611800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 169791. | 0.832309 | ||||||||
\(134\) | 416457. | 2.00359 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −216638. | −1.00435 | ||||||||
\(137\) | 133343. | 0.606971 | 0.303486 | − | 0.952836i | \(-0.401850\pi\) | ||||
0.303486 | + | 0.952836i | \(0.401850\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 197409. | 0.866622 | 0.433311 | − | 0.901244i | \(-0.357345\pi\) | ||||
0.433311 | + | 0.901244i | \(0.357345\pi\) | |||||||
\(140\) | −27527.0 | −0.118697 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −106246. | −0.442171 | ||||||||
\(143\) | −237384. | −0.970761 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −101593. | −0.401277 | ||||||||
\(146\) | 54177.1 | 0.210346 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3566.20 | −0.0133829 | ||||||||
\(149\) | −94205.2 | −0.347624 | −0.173812 | − | 0.984779i | \(-0.555608\pi\) | ||||
−0.173812 | + | 0.984779i | \(0.555608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −32019.8 | −0.114281 | −0.0571407 | − | 0.998366i | \(-0.518198\pi\) | ||||
−0.0571407 | + | 0.998366i | \(0.518198\pi\) | |||||||
\(152\) | −242115. | −0.849987 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −168570. | −0.572766 | ||||||||
\(155\) | 496869. | 1.66116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 487099. | 1.57713 | 0.788565 | − | 0.614951i | \(-0.210824\pi\) | ||||
0.788565 | + | 0.614951i | \(0.210824\pi\) | |||||||
\(158\) | 187677. | 0.598091 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 83361.0 | 0.257432 | ||||||||
\(161\) | −65056.2 | −0.197799 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 349125. | 1.02923 | 0.514615 | − | 0.857421i | \(-0.327935\pi\) | ||||
0.514615 | + | 0.857421i | \(0.327935\pi\) | |||||||
\(164\) | −46734.2 | −0.135683 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 608084. | 1.71275 | ||||||||
\(167\) | −68091.2 | −0.188930 | −0.0944648 | − | 0.995528i | \(-0.530114\pi\) | ||||
−0.0944648 | + | 0.995528i | \(0.530114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 626725. | 1.68795 | ||||||||
\(170\) | −499376. | −1.32527 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −76783.7 | −0.197901 | ||||||||
\(173\) | −15052.9 | −0.0382388 | −0.0191194 | − | 0.999817i | \(-0.506086\pi\) | ||||
−0.0191194 | + | 0.999817i | \(0.506086\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 140920. | 0.347837 | ||||||||
\(176\) | 267163. | 0.650122 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −620959. | −1.46897 | ||||||||
\(179\) | −716413. | −1.67121 | −0.835604 | − | 0.549332i | \(-0.814882\pi\) | ||||
−0.835604 | + | 0.549332i | \(0.814882\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −702418. | −1.59367 | −0.796837 | − | 0.604194i | \(-0.793495\pi\) | ||||
−0.796837 | + | 0.604194i | \(0.793495\pi\) | |||||||
\(182\) | 708704. | 1.58594 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 92767.5 | 0.202000 | ||||||||
\(185\) | 66444.3 | 0.142734 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −303298. | −0.634258 | ||||||||
\(188\) | −81169.3 | −0.167493 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −558104. | −1.12158 | ||||||||
\(191\) | 28509.8 | 0.0565472 | 0.0282736 | − | 0.999600i | \(-0.490999\pi\) | ||||
0.0282736 | + | 0.999600i | \(0.490999\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −310039. | −0.599133 | −0.299567 | − | 0.954075i | \(-0.596842\pi\) | ||||
−0.299567 | + | 0.954075i | \(0.596842\pi\) | |||||||
\(194\) | −699390. | −1.33418 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9300.85 | −0.0172935 | ||||||||
\(197\) | −664034. | −1.21906 | −0.609530 | − | 0.792763i | \(-0.708642\pi\) | ||||
−0.609530 | + | 0.792763i | \(0.708642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 326015. | 0.583586 | 0.291793 | − | 0.956481i | \(-0.405748\pi\) | ||||
0.291793 | + | 0.956481i | \(0.405748\pi\) | |||||||
\(200\) | −200946. | −0.355225 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −651048. | −1.12263 | ||||||||
\(203\) | 184213. | 0.313747 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 870739. | 1.44712 | ||||||||
\(206\) | −968338. | −1.58986 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.12321e6 | −1.80013 | ||||||||
\(209\) | −338967. | −0.536774 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −775314. | −1.19887 | −0.599434 | − | 0.800424i | \(-0.704608\pi\) | ||||
−0.599434 | + | 0.800424i | \(0.704608\pi\) | |||||||
\(212\) | −67121.7 | −0.102571 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 56954.1 | 0.0850141 | ||||||||
\(215\) | 1.43061e6 | 2.11070 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −900942. | −1.29882 | ||||||||
\(218\) | −481874. | −0.686740 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 54954.2 | 0.0765499 | ||||||||
\(221\) | 1.27513e6 | 1.75620 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −855406. | −1.15189 | −0.575944 | − | 0.817489i | \(-0.695365\pi\) | ||||
−0.575944 | + | 0.817489i | \(0.695365\pi\) | |||||||
\(224\) | −151153. | −0.201279 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 782599. | 1.01922 | ||||||||
\(227\) | −255022. | −0.328483 | −0.164241 | − | 0.986420i | \(-0.552518\pi\) | ||||
−0.164241 | + | 0.986420i | \(0.552518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 504531. | 0.635769 | 0.317884 | − | 0.948129i | \(-0.397028\pi\) | ||||
0.317884 | + | 0.948129i | \(0.397028\pi\) | |||||||
\(230\) | 213840. | 0.266545 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −262680. | −0.320410 | ||||||||
\(233\) | −315787. | −0.381070 | −0.190535 | − | 0.981680i | \(-0.561022\pi\) | ||||
−0.190535 | + | 0.981680i | \(0.561022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.51232e6 | 1.78638 | ||||||||
\(236\) | 12264.1 | 0.0143336 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 905488. | 1.03619 | ||||||||
\(239\) | 1.31913e6 | 1.49380 | 0.746901 | − | 0.664935i | \(-0.231541\pi\) | ||||
0.746901 | + | 0.664935i | \(0.231541\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −101157. | −0.112190 | −0.0560950 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560950 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(242\) | −623356. | −0.684223 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −25491.6 | −0.0274109 | ||||||||
\(245\) | 173291. | 0.184442 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.42509e6 | 1.48628 | ||||||||
\(248\) | 1.28471e6 | 1.32640 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 759415. | 0.768474 | ||||||||
\(251\) | −1.78020e6 | −1.78354 | −0.891771 | − | 0.452487i | \(-0.850537\pi\) | ||||
−0.891771 | + | 0.452487i | \(0.850537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 129877. | 0.127565 | ||||||||
\(254\) | −1.39664e6 | −1.35832 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 342297. | 0.326440 | ||||||||
\(257\) | 381509. | 0.360307 | 0.180153 | − | 0.983639i | \(-0.442341\pi\) | ||||
0.180153 | + | 0.983639i | \(0.442341\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −120479. | −0.111600 | ||||||||
\(260\) | −231040. | −0.211960 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −805547. | −0.724999 | ||||||||
\(263\) | 225601. | 0.201118 | 0.100559 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100559 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.25059e6 | 1.09396 | ||||||||
\(266\) | 1.01197e6 | 0.876931 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 246177. | 0.209368 | ||||||||
\(269\) | 562259. | 0.473757 | 0.236879 | − | 0.971539i | \(-0.423876\pi\) | ||||
0.236879 | + | 0.971539i | \(0.423876\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.36135e6 | −1.12602 | −0.563012 | − | 0.826449i | \(-0.690358\pi\) | ||||
−0.563012 | + | 0.826449i | \(0.690358\pi\) | |||||||
\(272\) | −1.43509e6 | −1.17614 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 794741. | 0.639512 | ||||||||
\(275\) | −281329. | −0.224327 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.03987e6 | −1.59736 | −0.798681 | − | 0.601755i | \(-0.794468\pi\) | ||||
−0.798681 | + | 0.601755i | \(0.794468\pi\) | |||||||
\(278\) | 1.17658e6 | 0.913083 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.32609e6 | 1.01083 | ||||||||
\(281\) | 667020. | 0.503933 | 0.251967 | − | 0.967736i | \(-0.418923\pi\) | ||||
0.251967 | + | 0.967736i | \(0.418923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.41041e6 | 1.04684 | 0.523418 | − | 0.852076i | \(-0.324657\pi\) | ||||
0.523418 | + | 0.852076i | \(0.324657\pi\) | |||||||
\(284\) | −62804.0 | −0.0462053 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.41484e6 | −1.02281 | ||||||||
\(287\) | −1.57886e6 | −1.13146 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 209339. | 0.147437 | ||||||||
\(290\) | −605508. | −0.422790 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 32025.2 | 0.0219804 | ||||||||
\(293\) | −928970. | −0.632168 | −0.316084 | − | 0.948731i | \(-0.602368\pi\) | ||||
−0.316084 | + | 0.948731i | \(0.602368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −228502. | −0.152874 | ||||||||
\(296\) | 171799. | 0.113970 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −561475. | −0.366261 | ||||||||
\(299\) | −546031. | −0.353215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.59404e6 | −1.65029 | ||||||||
\(302\) | −190842. | −0.120408 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.60386e6 | −0.995366 | ||||||||
\(305\) | 474952. | 0.292348 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −756619. | −0.458175 | −0.229087 | − | 0.973406i | \(-0.573574\pi\) | ||||
−0.229087 | + | 0.973406i | \(0.573574\pi\) | |||||||
\(308\) | −99645.1 | −0.0598521 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.96140e6 | 1.75022 | ||||||||
\(311\) | 1.45073e6 | 0.850521 | 0.425260 | − | 0.905071i | \(-0.360182\pi\) | ||||
0.425260 | + | 0.905071i | \(0.360182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −401791. | −0.231814 | −0.115907 | − | 0.993260i | \(-0.536977\pi\) | ||||
−0.115907 | + | 0.993260i | \(0.536977\pi\) | |||||||
\(314\) | 2.90317e6 | 1.66168 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 110940. | 0.0624985 | ||||||||
\(317\) | 1.81917e6 | 1.01678 | 0.508388 | − | 0.861128i | \(-0.330241\pi\) | ||||
0.508388 | + | 0.861128i | \(0.330241\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −367758. | −0.202342 | ||||||||
\(320\) | −1.86488e6 | −1.01807 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −387743. | −0.208403 | ||||||||
\(323\) | 1.82079e6 | 0.971078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.18277e6 | 0.621143 | ||||||||
\(326\) | 2.08083e6 | 1.08441 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.25139e6 | 1.15549 | ||||||||
\(329\) | −2.74220e6 | −1.39672 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.27514e6 | 1.64309 | 0.821543 | − | 0.570147i | \(-0.193114\pi\) | ||||
0.821543 | + | 0.570147i | \(0.193114\pi\) | |||||||
\(332\) | 359451. | 0.178976 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −405833. | −0.199059 | ||||||||
\(335\) | −4.58669e6 | −2.23299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.40437e6 | 0.673606 | 0.336803 | − | 0.941575i | \(-0.390654\pi\) | ||||
0.336803 | + | 0.941575i | \(0.390654\pi\) | |||||||
\(338\) | 3.73536e6 | 1.77845 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −295192. | −0.138486 | ||||||||
\(341\) | 1.79862e6 | 0.837633 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.31468e6 | −1.06232 | ||||||||
\(344\) | 3.69900e6 | 1.68534 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −89717.1 | −0.0402888 | ||||||||
\(347\) | −4.10924e6 | −1.83205 | −0.916025 | − | 0.401120i | \(-0.868621\pi\) | ||||
−0.916025 | + | 0.401120i | \(0.868621\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 65008.4 | 0.0285697 | 0.0142849 | − | 0.999898i | \(-0.495453\pi\) | ||||
0.0142849 | + | 0.999898i | \(0.495453\pi\) | |||||||
\(350\) | 839899. | 0.366486 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 301759. | 0.129809 | ||||||||
\(353\) | −2.87105e6 | −1.22632 | −0.613160 | − | 0.789959i | \(-0.710102\pi\) | ||||
−0.613160 | + | 0.789959i | \(0.710102\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.17015e6 | 0.492799 | ||||||||
\(356\) | −367062. | −0.153502 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.26991e6 | −1.76081 | ||||||||
\(359\) | 2.59406e6 | 1.06229 | 0.531146 | − | 0.847281i | \(-0.321762\pi\) | ||||
0.531146 | + | 0.847281i | \(0.321762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −441179. | −0.178175 | ||||||||
\(362\) | −4.18651e6 | −1.67911 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 418930. | 0.165725 | ||||||||
\(365\) | −596685. | −0.234430 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.69904e6 | 0.658472 | 0.329236 | − | 0.944248i | \(-0.393209\pi\) | ||||
0.329236 | + | 0.944248i | \(0.393209\pi\) | |||||||
\(368\) | 614528. | 0.236550 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 396017. | 0.150387 | ||||||||
\(371\) | −2.26762e6 | −0.855334 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.30896e6 | 0.487142 | 0.243571 | − | 0.969883i | \(-0.421681\pi\) | ||||
0.243571 | + | 0.969883i | \(0.421681\pi\) | |||||||
\(374\) | −1.80770e6 | −0.668262 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.91027e6 | 1.42639 | ||||||||
\(377\) | 1.54614e6 | 0.560266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.85503e6 | −1.02097 | −0.510485 | − | 0.859887i | \(-0.670534\pi\) | ||||
−0.510485 | + | 0.859887i | \(0.670534\pi\) | |||||||
\(380\) | −329907. | −0.117201 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 169922. | 0.0595788 | ||||||||
\(383\) | 1.29291e6 | 0.450371 | 0.225186 | − | 0.974316i | \(-0.427701\pi\) | ||||
0.225186 | + | 0.974316i | \(0.427701\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.85656e6 | 0.638347 | ||||||||
\(386\) | −1.84788e6 | −0.631254 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −413425. | −0.139417 | ||||||||
\(389\) | 514685. | 0.172452 | 0.0862259 | − | 0.996276i | \(-0.472519\pi\) | ||||
0.0862259 | + | 0.996276i | \(0.472519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −697646. | −0.230777 | ||||||||
\(392\) | 448061. | 0.147273 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.95773e6 | −1.28442 | ||||||||
\(395\) | −2.06700e6 | −0.666572 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.92612e6 | −1.25022 | −0.625112 | − | 0.780535i | \(-0.714947\pi\) | ||||
−0.625112 | + | 0.780535i | \(0.714947\pi\) | |||||||
\(398\) | 1.94309e6 | 0.614873 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.33114e6 | −0.415982 | ||||||||
\(401\) | 2.41292e6 | 0.749346 | 0.374673 | − | 0.927157i | \(-0.377755\pi\) | ||||
0.374673 | + | 0.927157i | \(0.377755\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.56181e6 | −2.31933 | ||||||||
\(404\) | −384849. | −0.117310 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.09793e6 | 0.330567 | ||||||||
\(407\) | 240523. | 0.0719730 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.67029e6 | 1.08491 | 0.542454 | − | 0.840086i | \(-0.317495\pi\) | ||||
0.542454 | + | 0.840086i | \(0.317495\pi\) | |||||||
\(410\) | 5.18972e6 | 1.52470 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −572405. | −0.166135 | ||||||||
\(413\) | 414328. | 0.119528 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.69720e6 | −1.90885 | ||||||||
\(416\) | −1.26866e6 | −0.359429 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.02029e6 | −0.565551 | ||||||||
\(419\) | 1.90475e6 | 0.530034 | 0.265017 | − | 0.964244i | \(-0.414622\pi\) | ||||
0.265017 | + | 0.964244i | \(0.414622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.91363e6 | 1.35113 | 0.675565 | − | 0.737300i | \(-0.263900\pi\) | ||||
0.675565 | + | 0.737300i | \(0.263900\pi\) | |||||||
\(422\) | −4.62097e6 | −1.26314 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.23354e6 | 0.873500 | ||||||||
\(425\) | 1.51118e6 | 0.405831 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −861202. | −0.228578 | ||||||||
\(428\) | 33666.8 | 0.00888367 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.52664e6 | 2.22386 | ||||||||
\(431\) | 3.65588e6 | 0.947979 | 0.473990 | − | 0.880530i | \(-0.342813\pi\) | ||||
0.473990 | + | 0.880530i | \(0.342813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.06298e6 | −1.29774 | −0.648869 | − | 0.760900i | \(-0.724758\pi\) | ||||
−0.648869 | + | 0.760900i | \(0.724758\pi\) | |||||||
\(434\) | −5.36973e6 | −1.36845 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −284846. | −0.0717619 | ||||||||
\(437\) | −779690. | −0.195307 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.94551e6 | −0.977108 | −0.488554 | − | 0.872534i | \(-0.662475\pi\) | ||||
−0.488554 | + | 0.872534i | \(0.662475\pi\) | |||||||
\(440\) | −2.64738e6 | −0.651905 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.59996e6 | 1.85036 | ||||||||
\(443\) | 3.37423e6 | 0.816894 | 0.408447 | − | 0.912782i | \(-0.366070\pi\) | ||||
0.408447 | + | 0.912782i | \(0.366070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.83900e6 | 1.63716 | ||||||||
\(446\) | −5.09833e6 | −1.21364 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.38147e6 | 0.795995 | ||||||||
\(449\) | 5.64111e6 | 1.32053 | 0.660266 | − | 0.751032i | \(-0.270444\pi\) | ||||
0.660266 | + | 0.751032i | \(0.270444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.15200e6 | 0.729700 | ||||||||
\(452\) | 462611. | 0.106505 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.51996e6 | −0.346094 | ||||||||
\(455\) | −7.80539e6 | −1.76753 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −134096. | −0.0300348 | −0.0150174 | − | 0.999887i | \(-0.504780\pi\) | ||||
−0.0150174 | + | 0.999887i | \(0.504780\pi\) | |||||||
\(458\) | 3.00707e6 | 0.669854 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 126406. | 0.0278530 | ||||||||
\(461\) | −4.00954e6 | −0.878703 | −0.439351 | − | 0.898315i | \(-0.644792\pi\) | ||||
−0.439351 | + | 0.898315i | \(0.644792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.02971e6 | 1.74079 | 0.870397 | − | 0.492351i | \(-0.163862\pi\) | ||||
0.870397 | + | 0.492351i | \(0.163862\pi\) | |||||||
\(464\) | −1.74009e6 | −0.375212 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.88213e6 | −0.401500 | ||||||||
\(467\) | 1.17884e6 | 0.250129 | 0.125065 | − | 0.992149i | \(-0.460086\pi\) | ||||
0.125065 | + | 0.992149i | \(0.460086\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.31677e6 | 1.74591 | ||||||||
\(470\) | 9.01365e6 | 1.88216 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −590815. | −0.122067 | ||||||||
\(473\) | 5.17869e6 | 1.06431 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.68890e6 | 0.343456 | ||||||||
\(476\) | 535254. | 0.108278 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.86219e6 | 1.57389 | ||||||||
\(479\) | 7.03708e6 | 1.40137 | 0.700686 | − | 0.713470i | \(-0.252877\pi\) | ||||
0.700686 | + | 0.713470i | \(0.252877\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.01121e6 | −0.199287 | ||||||||
\(482\) | −602910. | −0.118205 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −368479. | −0.0714990 | ||||||||
\(485\) | 7.70281e6 | 1.48694 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.74859e6 | −0.334093 | −0.167046 | − | 0.985949i | \(-0.553423\pi\) | ||||
−0.167046 | + | 0.985949i | \(0.553423\pi\) | |||||||
\(488\) | 1.22804e6 | 0.233433 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.03284e6 | 0.194330 | ||||||||
\(491\) | −5.71036e6 | −1.06896 | −0.534478 | − | 0.845183i | \(-0.679492\pi\) | ||||
−0.534478 | + | 0.845183i | \(0.679492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.97545e6 | 0.366057 | ||||||||
\(494\) | 8.49373e6 | 1.56596 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.51040e6 | 1.55327 | ||||||||
\(497\) | −2.12176e6 | −0.385305 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.18564e6 | −0.572724 | −0.286362 | − | 0.958121i | \(-0.592446\pi\) | ||||
−0.286362 | + | 0.958121i | \(0.592446\pi\) | |||||||
\(500\) | 448907. | 0.0803029 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.06102e7 | −1.87916 | ||||||||
\(503\) | −7.57762e6 | −1.33541 | −0.667703 | − | 0.744428i | \(-0.732722\pi\) | ||||
−0.667703 | + | 0.744428i | \(0.732722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.17039e6 | 1.25116 | ||||||||
\(506\) | 774083. | 0.134404 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −825586. | −0.141939 | ||||||||
\(509\) | 6.23348e6 | 1.06644 | 0.533220 | − | 0.845977i | \(-0.320982\pi\) | ||||
0.533220 | + | 0.845977i | \(0.320982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.08193e6 | 0.183294 | ||||||||
\(512\) | −4.67867e6 | −0.788764 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.27385e6 | 0.379624 | ||||||||
\(515\) | 1.06649e7 | 1.77190 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.47448e6 | 0.900775 | ||||||||
\(518\) | −718073. | −0.117583 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.11302e7 | 1.80507 | ||||||||
\(521\) | 4.48711e6 | 0.724224 | 0.362112 | − | 0.932135i | \(-0.382056\pi\) | ||||
0.362112 | + | 0.932135i | \(0.382056\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.66955e6 | −1.06621 | −0.533104 | − | 0.846050i | \(-0.678975\pi\) | ||||
−0.533104 | + | 0.846050i | \(0.678975\pi\) | |||||||
\(524\) | −476176. | −0.0757599 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.34461e6 | 0.211901 | ||||||||
\(527\) | −9.66147e6 | −1.51536 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.13760e6 | −0.953585 | ||||||||
\(530\) | 7.45369e6 | 1.15261 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 598200. | 0.0916363 | ||||||||
\(533\) | −1.32517e7 | −2.02048 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −627270. | −0.0947481 | ||||||||
\(536\) | −1.18594e7 | −1.78299 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.35114e6 | 0.499157 | ||||||||
\(539\) | 627297. | 0.0930039 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.56886e6 | −0.818038 | −0.409019 | − | 0.912526i | \(-0.634129\pi\) | ||||
−0.409019 | + | 0.912526i | \(0.634129\pi\) | |||||||
\(542\) | −8.11385e6 | −1.18639 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.62093e6 | −0.234837 | ||||||||
\(545\) | 5.30717e6 | 0.765371 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.15071e7 | 1.64437 | 0.822184 | − | 0.569222i | \(-0.192756\pi\) | ||||
0.822184 | + | 0.569222i | \(0.192756\pi\) | |||||||
\(548\) | 469788. | 0.0668268 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.67676e6 | −0.236354 | ||||||||
\(551\) | 2.20776e6 | 0.309794 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.74796e6 | 0.521173 | ||||||||
\(554\) | −1.21579e7 | −1.68300 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 695503. | 0.0954140 | ||||||||
\(557\) | −3.88277e6 | −0.530277 | −0.265139 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265139 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.17724e7 | −2.94697 | ||||||||
\(560\) | 8.78454e6 | 1.18372 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.97553e6 | 0.530950 | ||||||||
\(563\) | −981269. | −0.130472 | −0.0652360 | − | 0.997870i | \(-0.520780\pi\) | ||||
−0.0652360 | + | 0.997870i | \(0.520780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.61924e6 | −1.13592 | ||||||||
\(566\) | 8.40621e6 | 1.10296 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.02554e6 | 0.393488 | ||||||||
\(569\) | 8.63190e6 | 1.11770 | 0.558850 | − | 0.829268i | \(-0.311243\pi\) | ||||
0.558850 | + | 0.829268i | \(0.311243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.06342e7 | 1.36494 | 0.682469 | − | 0.730915i | \(-0.260906\pi\) | ||||
0.682469 | + | 0.730915i | \(0.260906\pi\) | |||||||
\(572\) | −836344. | −0.106880 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.41019e6 | −1.19212 | ||||||||
\(575\) | −647112. | −0.0816225 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.83248e6 | 0.479225 | 0.239613 | − | 0.970869i | \(-0.422980\pi\) | ||||
0.239613 | + | 0.970869i | \(0.422980\pi\) | |||||||
\(578\) | 1.24769e6 | 0.155341 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −357929. | −0.0441801 | ||||||||
\(581\) | 1.21436e7 | 1.49248 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.52703e6 | 0.551622 | ||||||||
\(584\) | −1.54279e6 | −0.187187 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.53678e6 | −0.666060 | ||||||||
\(587\) | 3.74170e6 | 0.448202 | 0.224101 | − | 0.974566i | \(-0.428055\pi\) | ||||
0.224101 | + | 0.974566i | \(0.428055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.07977e7 | −1.28245 | ||||||||
\(590\) | −1.36190e6 | −0.161070 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.13806e6 | 0.133463 | ||||||||
\(593\) | 411565. | 0.0480620 | 0.0240310 | − | 0.999711i | \(-0.492350\pi\) | ||||
0.0240310 | + | 0.999711i | \(0.492350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.97269e6 | −1.15483 | ||||||||
\(596\) | −331900. | −0.0382729 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.25442e6 | −0.372152 | ||||||||
\(599\) | −6.06004e6 | −0.690094 | −0.345047 | − | 0.938585i | \(-0.612137\pi\) | ||||
−0.345047 | + | 0.938585i | \(0.612137\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.69768e6 | 0.756376 | 0.378188 | − | 0.925729i | \(-0.376547\pi\) | ||||
0.378188 | + | 0.925729i | \(0.376547\pi\) | |||||||
\(602\) | −1.54608e7 | −1.73877 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −112811. | −0.0125822 | ||||||||
\(605\) | 6.86540e6 | 0.762566 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.00236e6 | −0.110421 | −0.0552106 | − | 0.998475i | \(-0.517583\pi\) | ||||
−0.0552106 | + | 0.998475i | \(0.517583\pi\) | |||||||
\(608\) | −1.81155e6 | −0.198743 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.83078e6 | 0.308022 | ||||||||
\(611\) | −2.30159e7 | −2.49417 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.24680e7 | −1.34013 | −0.670064 | − | 0.742303i | \(-0.733733\pi\) | ||||
−0.670064 | + | 0.742303i | \(0.733733\pi\) | |||||||
\(614\) | −4.50955e6 | −0.482739 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.80033e6 | 0.509705 | ||||||||
\(617\) | 7.98964e6 | 0.844917 | 0.422459 | − | 0.906382i | \(-0.361167\pi\) | ||||
0.422459 | + | 0.906382i | \(0.361167\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.83016e6 | −0.926279 | −0.463140 | − | 0.886285i | \(-0.653277\pi\) | ||||
−0.463140 | + | 0.886285i | \(0.653277\pi\) | |||||||
\(620\) | 1.75055e6 | 0.182892 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.64653e6 | 0.896119 | ||||||||
\(623\) | −1.24007e7 | −1.28005 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.20637e7 | −1.23533 | ||||||||
\(626\) | −2.39473e6 | −0.244242 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.71613e6 | 0.173640 | ||||||||
\(629\) | −1.29199e6 | −0.130207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.18563e6 | −0.818425 | −0.409212 | − | 0.912439i | \(-0.634196\pi\) | ||||
−0.409212 | + | 0.912439i | \(0.634196\pi\) | |||||||
\(632\) | −5.34444e6 | −0.532242 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.08425e7 | 1.07129 | ||||||||
\(635\) | 1.53821e7 | 1.51384 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.63730e6 | −0.257520 | ||||||||
\(638\) | −2.19189e6 | −0.213190 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.37825e7 | −1.33008 | ||||||||
\(641\) | 1.08929e7 | 1.04713 | 0.523564 | − | 0.851986i | \(-0.324602\pi\) | ||||
0.523564 | + | 0.851986i | \(0.324602\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.87772e6 | 0.465254 | 0.232627 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232627 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(644\) | −229204. | −0.0217774 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.08522e7 | 1.02314 | ||||||||
\(647\) | 5.09261e6 | 0.478277 | 0.239138 | − | 0.970985i | \(-0.423135\pi\) | ||||
0.239138 | + | 0.970985i | \(0.423135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −827156. | −0.0770860 | ||||||||
\(650\) | 7.04946e6 | 0.654444 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.23002e6 | 0.113317 | ||||||||
\(653\) | 1.57557e7 | 1.44595 | 0.722976 | − | 0.690873i | \(-0.242774\pi\) | ||||
0.722976 | + | 0.690873i | \(0.242774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.87198e6 | 0.808011 | ||||||||
\(656\) | 1.49141e7 | 1.35312 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.63439e7 | −1.47160 | ||||||||
\(659\) | −1.52866e7 | −1.37119 | −0.685596 | − | 0.727983i | \(-0.740458\pi\) | ||||
−0.685596 | + | 0.727983i | \(0.740458\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.43781e6 | −0.662127 | −0.331064 | − | 0.943608i | \(-0.607408\pi\) | ||||
−0.331064 | + | 0.943608i | \(0.607408\pi\) | |||||||
\(662\) | 1.95203e7 | 1.73117 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.73163e7 | −1.52418 | ||||||||
\(665\) | −1.11455e7 | −0.977339 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −845916. | −0.0736229 | ||||||||
\(668\) | −239896. | −0.0208009 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.73373e7 | −2.35271 | ||||||||
\(671\) | 1.71929e6 | 0.147415 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.00568e7 | −1.70697 | −0.853483 | − | 0.521121i | \(-0.825514\pi\) | ||||
−0.853483 | + | 0.521121i | \(0.825514\pi\) | |||||||
\(674\) | 8.37021e6 | 0.709719 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.20805e6 | 0.185841 | ||||||||
\(677\) | −2.08686e6 | −0.174993 | −0.0874965 | − | 0.996165i | \(-0.527887\pi\) | ||||
−0.0874965 | + | 0.996165i | \(0.527887\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.39670e7 | −1.16260 | ||||||||
\(680\) | 1.42207e7 | 1.17936 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.07200e7 | 0.882540 | ||||||||
\(683\) | −5.45861e6 | −0.447745 | −0.223872 | − | 0.974618i | \(-0.571870\pi\) | ||||
−0.223872 | + | 0.974618i | \(0.571870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.75296e6 | −0.712736 | ||||||||
\(686\) | −1.37958e7 | −1.11927 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.45036e7 | 1.97360 | ||||||||
\(689\) | −1.90326e7 | −1.52739 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 655073. | 0.0521908 | 0.0260954 | − | 0.999659i | \(-0.491693\pi\) | ||||
0.0260954 | + | 0.999659i | \(0.491693\pi\) | |||||||
\(692\) | −53033.7 | −0.00421004 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.44916e7 | −1.93027 | ||||||||
\(695\) | −1.29584e7 | −1.01763 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.69313e7 | −1.32010 | ||||||||
\(698\) | 387459. | 0.0301014 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 496482. | 0.0382965 | ||||||||
\(701\) | 2.15464e7 | 1.65607 | 0.828037 | − | 0.560674i | \(-0.189458\pi\) | ||||
0.828037 | + | 0.560674i | \(0.189458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.44393e6 | −0.110194 | ||||||||
\(704\) | −6.75069e6 | −0.513354 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.71118e7 | −1.29207 | ||||||||
\(707\) | −1.30016e7 | −0.978248 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.65045e7 | 1.23307 | 0.616533 | − | 0.787329i | \(-0.288537\pi\) | ||||
0.616533 | + | 0.787329i | \(0.288537\pi\) | |||||||
\(710\) | 6.97423e6 | 0.519219 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.76829e7 | 1.30724 | ||||||||
\(713\) | 4.13719e6 | 0.304776 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.55825e7 | 1.13992 | ||||||||
\(716\) | −2.52404e6 | −0.183998 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.54609e7 | 1.11924 | ||||||||
\(719\) | −3.65458e6 | −0.263642 | −0.131821 | − | 0.991274i | \(-0.542082\pi\) | ||||
−0.131821 | + | 0.991274i | \(0.542082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.93380e7 | −1.38539 | ||||||||
\(722\) | −2.62948e6 | −0.187727 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.47473e6 | −0.175462 | ||||||||
\(725\) | 1.83236e6 | 0.129469 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.40192e7 | 0.983757 | 0.491878 | − | 0.870664i | \(-0.336310\pi\) | ||||
0.491878 | + | 0.870664i | \(0.336310\pi\) | |||||||
\(728\) | −2.01817e7 | −1.41133 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.55632e6 | −0.246998 | ||||||||
\(731\) | −2.78178e7 | −1.92544 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.41229e7 | −1.65833 | −0.829163 | − | 0.559007i | \(-0.811183\pi\) | ||||
−0.829163 | + | 0.559007i | \(0.811183\pi\) | |||||||
\(734\) | 1.01265e7 | 0.693774 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 694106. | 0.0472315 | ||||||||
\(737\) | −1.66034e7 | −1.12597 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00291e7 | −0.675537 | −0.337768 | − | 0.941229i | \(-0.609672\pi\) | ||||
−0.337768 | + | 0.941229i | \(0.609672\pi\) | |||||||
\(740\) | 234094. | 0.0157149 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.35153e7 | −0.901190 | ||||||||
\(743\) | −4.51165e6 | −0.299822 | −0.149911 | − | 0.988699i | \(-0.547899\pi\) | ||||
−0.149911 | + | 0.988699i | \(0.547899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.18387e6 | 0.408197 | ||||||||
\(746\) | 7.80160e6 | 0.513259 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.06857e6 | −0.0698310 | ||||||||
\(749\) | 1.13739e6 | 0.0740807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.58055e7 | 1.02260 | 0.511302 | − | 0.859401i | \(-0.329163\pi\) | ||||
0.511302 | + | 0.859401i | \(0.329163\pi\) | |||||||
\(752\) | 2.59031e7 | 1.67035 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.21518e6 | 0.590304 | ||||||||
\(755\) | 2.10186e6 | 0.134195 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.71419e6 | 0.489272 | 0.244636 | − | 0.969615i | \(-0.421331\pi\) | ||||
0.244636 | + | 0.969615i | \(0.421331\pi\) | |||||||
\(758\) | −1.70163e7 | −1.07571 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.58930e7 | 0.998097 | ||||||||
\(761\) | 1.26944e7 | 0.794603 | 0.397302 | − | 0.917688i | \(-0.369947\pi\) | ||||
0.397302 | + | 0.917688i | \(0.369947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.62316e6 | −0.598421 | ||||||||
\(764\) | 100445. | 0.00622578 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.70590e6 | 0.474517 | ||||||||
\(767\) | 3.47755e6 | 0.213444 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.29528e6 | −0.200944 | −0.100472 | − | 0.994940i | \(-0.532035\pi\) | ||||
−0.100472 | + | 0.994940i | \(0.532035\pi\) | |||||||
\(770\) | 1.10653e7 | 0.672571 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.09232e6 | −0.0659639 | ||||||||
\(773\) | 5.51865e6 | 0.332188 | 0.166094 | − | 0.986110i | \(-0.446884\pi\) | ||||
0.166094 | + | 0.986110i | \(0.446884\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.96164e6 | −0.535961 | ||||||||
\(776\) | 1.99164e7 | 1.18729 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.06759e6 | 0.181697 | ||||||||
\(779\) | −1.89224e7 | −1.11720 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.23583e6 | 0.248491 | ||||||||
\(782\) | −4.15806e6 | −0.243150 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.96813e6 | 0.172462 | ||||||||
\(785\) | −3.19744e7 | −1.85194 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.63062e7 | 0.938459 | 0.469230 | − | 0.883076i | \(-0.344532\pi\) | ||||
0.469230 | + | 0.883076i | \(0.344532\pi\) | |||||||
\(788\) | −2.33950e6 | −0.134217 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.23196e7 | −0.702309 | ||||||||
\(791\) | 1.56287e7 | 0.888143 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.22826e6 | −0.408179 | ||||||||
\(794\) | −2.34002e7 | −1.31725 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.14860e6 | 0.0642521 | ||||||||
\(797\) | −3.19084e7 | −1.77934 | −0.889671 | − | 0.456602i | \(-0.849066\pi\) | ||||
−0.889671 | + | 0.456602i | \(0.849066\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.94067e7 | −1.62959 | ||||||||
\(800\) | −1.50352e6 | −0.0830584 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.43813e7 | 0.789520 | ||||||||
\(803\) | −2.15995e6 | −0.118210 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.27045e6 | 0.232265 | ||||||||
\(806\) | −4.50694e7 | −2.44368 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.85398e7 | 0.999025 | ||||||||
\(809\) | −1.70126e7 | −0.913900 | −0.456950 | − | 0.889492i | \(-0.651058\pi\) | ||||
−0.456950 | + | 0.889492i | \(0.651058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.05241e7 | 0.561865 | 0.280932 | − | 0.959728i | \(-0.409356\pi\) | ||||
0.280932 | + | 0.959728i | \(0.409356\pi\) | |||||||
\(812\) | 649010. | 0.0345431 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.43355e6 | 0.0758317 | ||||||||
\(815\) | −2.29175e7 | −1.20857 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.10892e7 | −1.62950 | ||||||||
\(818\) | 2.18754e7 | 1.14307 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.06775e6 | 0.159326 | ||||||||
\(821\) | −3.31358e7 | −1.71569 | −0.857847 | − | 0.513906i | \(-0.828198\pi\) | ||||
−0.857847 | + | 0.513906i | \(0.828198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.83322e7 | 1.45808 | 0.729039 | − | 0.684472i | \(-0.239967\pi\) | ||||
0.729039 | + | 0.684472i | \(0.239967\pi\) | |||||||
\(824\) | 2.75752e7 | 1.41482 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.46945e6 | 0.125936 | ||||||||
\(827\) | −8.10406e6 | −0.412039 | −0.206020 | − | 0.978548i | \(-0.566051\pi\) | ||||
−0.206020 | + | 0.978548i | \(0.566051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.88681e7 | −1.45892 | −0.729461 | − | 0.684022i | \(-0.760229\pi\) | ||||
−0.729461 | + | 0.684022i | \(0.760229\pi\) | |||||||
\(830\) | −3.99162e7 | −2.01119 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.83814e7 | 1.42143 | ||||||||
\(833\) | −3.36959e6 | −0.168253 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.46968e6 | 0.221851 | ||||||||
\(836\) | −1.19423e6 | −0.0590981 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.13526e7 | 0.558450 | ||||||||
\(839\) | 3.01221e7 | 1.47734 | 0.738671 | − | 0.674066i | \(-0.235454\pi\) | ||||
0.738671 | + | 0.674066i | \(0.235454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.81159e7 | −0.883220 | ||||||||
\(842\) | 2.92859e7 | 1.42357 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.73156e6 | −0.131994 | ||||||||
\(845\) | −4.11398e7 | −1.98208 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.24486e7 | −0.596228 | ||||||||
\(848\) | 2.14202e7 | 1.02290 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.00686e6 | 0.427589 | ||||||||
\(851\) | 553249. | 0.0261877 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.03837e7 | −1.42977 | −0.714887 | − | 0.699240i | \(-0.753522\pi\) | ||||
−0.714887 | + | 0.699240i | \(0.753522\pi\) | |||||||
\(854\) | −5.13288e6 | −0.240833 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.62187e6 | −0.0756541 | ||||||||
\(857\) | 3.42703e7 | 1.59392 | 0.796958 | − | 0.604035i | \(-0.206441\pi\) | ||||
0.796958 | + | 0.604035i | \(0.206441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.21405e6 | −0.333577 | −0.166789 | − | 0.985993i | \(-0.553340\pi\) | ||||
−0.166789 | + | 0.985993i | \(0.553340\pi\) | |||||||
\(860\) | 5.04028e6 | 0.232385 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.17895e7 | 0.998802 | ||||||||
\(863\) | 3.87581e7 | 1.77148 | 0.885739 | − | 0.464184i | \(-0.153652\pi\) | ||||
0.885739 | + | 0.464184i | \(0.153652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 988108. | 0.0449019 | ||||||||
\(866\) | −3.01761e7 | −1.36731 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.17416e6 | −0.142998 | ||||||||
\(869\) | −7.48235e6 | −0.336115 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.98045e7 | 3.11773 | ||||||||
\(872\) | 1.37222e7 | 0.611131 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.64706e6 | −0.205778 | ||||||||
\(875\) | 1.51657e7 | 0.669644 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.06345e6 | −0.178400 | −0.0892002 | − | 0.996014i | \(-0.528431\pi\) | ||||
−0.0892002 | + | 0.996014i | \(0.528431\pi\) | |||||||
\(878\) | −2.35158e7 | −1.02949 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.75373e7 | −0.763405 | ||||||||
\(881\) | 4.47103e7 | 1.94074 | 0.970372 | − | 0.241616i | \(-0.0776775\pi\) | ||||
0.970372 | + | 0.241616i | \(0.0776775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.18489e6 | −0.266950 | −0.133475 | − | 0.991052i | \(-0.542614\pi\) | ||||
−0.133475 | + | 0.991052i | \(0.542614\pi\) | |||||||
\(884\) | 4.49250e6 | 0.193356 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.01109e7 | 0.860690 | ||||||||
\(887\) | −4.16533e7 | −1.77763 | −0.888813 | − | 0.458270i | \(-0.848469\pi\) | ||||
−0.888813 | + | 0.458270i | \(0.848469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.78914e7 | −1.18363 | ||||||||
\(890\) | 4.07613e7 | 1.72494 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.01374e6 | −0.126822 | ||||||||
\(893\) | −3.28650e7 | −1.37913 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.70272e7 | 1.96242 | ||||||||
\(896\) | 2.49909e7 | 1.03995 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.36218e7 | 1.39133 | ||||||||
\(899\) | −1.17148e7 | −0.483433 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.43174e7 | −0.997941 | ||||||||
\(902\) | 1.87863e7 | 0.768821 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.22860e7 | −0.907006 | ||||||||
\(905\) | 4.61085e7 | 1.87137 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.48069e7 | 1.00128 | 0.500639 | − | 0.865656i | \(-0.333098\pi\) | ||||
0.500639 | + | 0.865656i | \(0.333098\pi\) | |||||||
\(908\) | −898483. | −0.0361656 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.65212e7 | −1.86229 | ||||||||
\(911\) | −2.87038e7 | −1.14589 | −0.572946 | − | 0.819593i | \(-0.694200\pi\) | ||||
−0.572946 | + | 0.819593i | \(0.694200\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.42432e7 | −0.962529 | ||||||||
\(914\) | −799228. | −0.0316450 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.77754e6 | 0.0699974 | ||||||||
\(917\) | −1.60870e7 | −0.631760 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.98850e7 | 1.55783 | 0.778917 | − | 0.627127i | \(-0.215769\pi\) | ||||
0.778917 | + | 0.627127i | \(0.215769\pi\) | |||||||
\(920\) | −6.08950e6 | −0.237198 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.38974e7 | −0.925812 | ||||||||
\(923\) | −1.78084e7 | −0.688050 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.19840e6 | −0.0460521 | ||||||||
\(926\) | 4.78581e7 | 1.83412 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.96542e6 | −0.0749180 | ||||||||
\(929\) | 3.09058e7 | 1.17490 | 0.587451 | − | 0.809260i | \(-0.300132\pi\) | ||||
0.587451 | + | 0.809260i | \(0.300132\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.76585e6 | −0.142393 | ||||||||
\(932\) | −1.11257e6 | −0.0419553 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.02606e6 | 0.263539 | ||||||||
\(935\) | 1.99093e7 | 0.744777 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.92068e7 | −1.45886 | −0.729428 | − | 0.684058i | \(-0.760214\pi\) | ||||
−0.729428 | + | 0.684058i | \(0.760214\pi\) | |||||||
\(938\) | 4.95690e7 | 1.83951 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.32816e6 | 0.196679 | ||||||||
\(941\) | 4.21602e7 | 1.55213 | 0.776066 | − | 0.630652i | \(-0.217212\pi\) | ||||
0.776066 | + | 0.630652i | \(0.217212\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.25021e6 | 0.265504 | ||||||||
\(944\) | −3.91379e6 | −0.142944 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.08657e7 | 1.12137 | ||||||||
\(947\) | −5.32912e7 | −1.93099 | −0.965497 | − | 0.260416i | \(-0.916140\pi\) | ||||
−0.965497 | + | 0.260416i | \(0.916140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.08090e6 | 0.327313 | ||||||||
\(950\) | 1.00661e7 | 0.361869 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.57854e7 | −0.922109 | ||||||||
\(953\) | −3.66273e7 | −1.30639 | −0.653194 | − | 0.757190i | \(-0.726572\pi\) | ||||
−0.653194 | + | 0.757190i | \(0.726572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.87146e6 | −0.0664005 | ||||||||
\(956\) | 4.64751e6 | 0.164466 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.19419e7 | 1.47650 | ||||||||
\(959\) | 1.58712e7 | 0.557267 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.86654e7 | 1.00127 | ||||||||
\(962\) | −6.02695e6 | −0.209971 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −356393. | −0.0123520 | ||||||||
\(965\) | 2.03518e7 | 0.703532 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.44677e7 | −1.18535 | −0.592675 | − | 0.805442i | \(-0.701928\pi\) | ||||
−0.592675 | + | 0.805442i | \(0.701928\pi\) | |||||||
\(968\) | 1.77512e7 | 0.608891 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.59098e7 | 1.56666 | ||||||||
\(971\) | −9.21316e6 | −0.313589 | −0.156794 | − | 0.987631i | \(-0.550116\pi\) | ||||
−0.156794 | + | 0.987631i | \(0.550116\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.34967e7 | 0.795655 | ||||||||
\(974\) | −1.04219e7 | −0.352004 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.13501e6 | 0.273359 | ||||||||
\(977\) | −3.66542e6 | −0.122854 | −0.0614268 | − | 0.998112i | \(-0.519565\pi\) | ||||
−0.0614268 | + | 0.998112i | \(0.519565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.47566e7 | 0.825531 | ||||||||
\(980\) | 610531. | 0.0203069 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.40345e7 | −1.12626 | ||||||||
\(983\) | 7.59961e6 | 0.250846 | 0.125423 | − | 0.992103i | \(-0.459971\pi\) | ||||
0.125423 | + | 0.992103i | \(0.459971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.35889e7 | 1.43148 | ||||||||
\(986\) | 1.17739e7 | 0.385682 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.02083e6 | 0.163638 | ||||||||
\(989\) | 1.19120e7 | 0.387252 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.53749e7 | 1.14422 | 0.572112 | − | 0.820175i | \(-0.306124\pi\) | ||||
0.572112 | + | 0.820175i | \(0.306124\pi\) | |||||||
\(992\) | 9.61245e6 | 0.310138 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.26459e7 | −0.405962 | ||||||||
\(995\) | −2.14005e7 | −0.685276 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.58278e7 | 1.14152 | 0.570759 | − | 0.821118i | \(-0.306649\pi\) | ||||
0.570759 | + | 0.821118i | \(0.306649\pi\) | |||||||
\(998\) | −1.89868e7 | −0.603429 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.6.a.c.1.10 | 12 | ||
3.2 | odd | 2 | 177.6.a.c.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.c.1.3 | ✓ | 12 | 3.2 | odd | 2 | ||
531.6.a.c.1.10 | 12 | 1.1 | even | 1 | trivial |