Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.08636 | −0.627211 | −0.313606 | − | 0.949553i | \(-0.601537\pi\) | ||||
−0.313606 | + | 0.949553i | \(0.601537\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0864029 | −0.0386406 | −0.0193203 | − | 0.999813i | \(-0.506150\pi\) | ||||
−0.0193203 | + | 0.999813i | \(0.506150\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.643099 | −0.243069 | −0.121534 | − | 0.992587i | \(-0.538781\pi\) | ||||
−0.121534 | + | 0.992587i | \(0.538781\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.81982 | −0.606606 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.53359 | −1.36693 | −0.683464 | − | 0.729984i | \(-0.739528\pi\) | ||||
−0.683464 | + | 0.729984i | \(0.739528\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.55688 | 1.26385 | 0.631926 | − | 0.775029i | \(-0.282265\pi\) | ||||
0.631926 | + | 0.775029i | \(0.282265\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0938648 | 0.0242358 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.52956 | 0.613509 | 0.306754 | − | 0.951789i | \(-0.400757\pi\) | ||||
0.306754 | + | 0.951789i | \(0.400757\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.06564 | 0.932722 | 0.466361 | − | 0.884595i | \(-0.345565\pi\) | ||||
0.466361 | + | 0.884595i | \(0.345565\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.698638 | 0.152455 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0799297 | 0.0166665 | 0.00833324 | − | 0.999965i | \(-0.497347\pi\) | ||||
0.00833324 | + | 0.999965i | \(0.497347\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99253 | −0.998507 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.23607 | 1.00768 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.92904 | −0.915299 | −0.457649 | − | 0.889133i | \(-0.651309\pi\) | ||||
−0.457649 | + | 0.889133i | \(0.651309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.43721 | 0.976551 | 0.488276 | − | 0.872689i | \(-0.337626\pi\) | ||||
0.488276 | + | 0.872689i | \(0.337626\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.92512 | 0.857353 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0555656 | 0.00939231 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.43701 | −0.236243 | −0.118122 | − | 0.992999i | \(-0.537687\pi\) | ||||
−0.118122 | + | 0.992999i | \(0.537687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.95042 | −0.792702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.75696 | −0.742913 | −0.371456 | − | 0.928450i | \(-0.621141\pi\) | ||||
−0.371456 | + | 0.928450i | \(0.621141\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.56498 | 0.238657 | 0.119328 | − | 0.992855i | \(-0.461926\pi\) | ||||
0.119328 | + | 0.992855i | \(0.461926\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.157238 | 0.0234396 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.54900 | 0.809404 | 0.404702 | − | 0.914449i | \(-0.367375\pi\) | ||||
0.404702 | + | 0.914449i | \(0.367375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58642 | −0.940918 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.74802 | −0.384800 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.8813 | −1.76939 | −0.884693 | − | 0.466174i | \(-0.845632\pi\) | ||||
−0.884693 | + | 0.466174i | \(0.845632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.391715 | 0.0528189 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.41676 | −0.585014 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.90937 | −0.899524 | −0.449762 | − | 0.893149i | \(-0.648491\pi\) | ||||
−0.449762 | + | 0.893149i | \(0.648491\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.25651 | −0.929101 | −0.464550 | − | 0.885547i | \(-0.653784\pi\) | ||||
−0.464550 | + | 0.885547i | \(0.653784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.17032 | 0.147447 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.393728 | −0.0488359 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.62308 | −0.198290 | −0.0991452 | − | 0.995073i | \(-0.531611\pi\) | ||||
−0.0991452 | + | 0.995073i | \(0.531611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0868325 | −0.0104534 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.50057 | 0.652797 | 0.326399 | − | 0.945232i | \(-0.394165\pi\) | ||||
0.326399 | + | 0.945232i | \(0.394165\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0785 | −1.29664 | −0.648318 | − | 0.761370i | \(-0.724527\pi\) | ||||
−0.648318 | + | 0.761370i | \(0.724527\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.42370 | 0.626275 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.91555 | 0.332257 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.91385 | 1.00289 | 0.501443 | − | 0.865191i | \(-0.332803\pi\) | ||||
0.501443 | + | 0.865191i | \(0.332803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.228807 | −0.0254231 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.11686 | 0.122591 | 0.0612955 | − | 0.998120i | \(-0.480477\pi\) | ||||
0.0612955 | + | 0.998120i | \(0.480477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.218562 | −0.0237063 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.35472 | 0.574086 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.69683 | 0.285863 | 0.142932 | − | 0.989733i | \(-0.454347\pi\) | ||||
0.142932 | + | 0.989733i | \(0.454347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.93053 | −0.307203 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.90677 | −0.612504 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.351283 | −0.0360409 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3347 | 1.15087 | 0.575433 | − | 0.817849i | \(-0.304834\pi\) | ||||
0.575433 | + | 0.817849i | \(0.304834\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.25031 | 0.829187 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.0514 | 1.59717 | 0.798586 | − | 0.601881i | \(-0.205582\pi\) | ||||
0.798586 | + | 0.601881i | \(0.205582\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.46182 | −0.144037 | −0.0720187 | − | 0.997403i | \(-0.522944\pi\) | ||||
−0.0720187 | + | 0.997403i | \(0.522944\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0603644 | −0.00589096 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.83803 | 0.661057 | 0.330529 | − | 0.943796i | \(-0.392773\pi\) | ||||
0.330529 | + | 0.943796i | \(0.392773\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.2483 | 1.84365 | 0.921825 | − | 0.387607i | \(-0.126698\pi\) | ||||
0.921825 | + | 0.387607i | \(0.126698\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.56111 | 0.148174 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.9421 | −1.31156 | −0.655781 | − | 0.754951i | \(-0.727661\pi\) | ||||
−0.655781 | + | 0.754951i | \(0.727661\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.00690615 | −0.000644002 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.29269 | −0.766660 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.62676 | −0.149125 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.55343 | 0.868494 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.16778 | 0.465963 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.863384 | 0.0772234 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.37287 | 0.654236 | 0.327118 | − | 0.944983i | \(-0.393922\pi\) | ||||
0.327118 | + | 0.944983i | \(0.393922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.70013 | −0.149688 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.87682 | −0.251349 | −0.125675 | − | 0.992072i | \(-0.540110\pi\) | ||||
−0.125675 | + | 0.992072i | \(0.540110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.61461 | −0.226715 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.452411 | −0.0389374 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.58750 | 0.477373 | 0.238686 | − | 0.971097i | \(-0.423283\pi\) | ||||
0.238686 | + | 0.971097i | \(0.423283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.53750 | 0.554503 | 0.277252 | − | 0.960797i | \(-0.410576\pi\) | ||||
0.277252 | + | 0.960797i | \(0.410576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.02822 | −0.507668 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −20.6590 | −1.72759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.425883 | 0.0353677 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.15524 | 0.590154 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.88365 | −0.563930 | −0.281965 | − | 0.959425i | \(-0.590986\pi\) | ||||
−0.281965 | + | 0.959425i | \(0.590986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.1390 | 1.55751 | 0.778754 | − | 0.627329i | \(-0.215852\pi\) | ||||
0.778754 | + | 0.627329i | \(0.215852\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.60334 | −0.372158 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.469790 | −0.0377345 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.944598 | −0.0753872 | −0.0376936 | − | 0.999289i | \(-0.512001\pi\) | ||||
−0.0376936 | + | 0.999289i | \(0.512001\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.9938 | 1.10978 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0514027 | −0.00405110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.1266 | 1.18481 | 0.592404 | − | 0.805641i | \(-0.298179\pi\) | ||||
0.592404 | + | 0.805641i | \(0.298179\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.425545 | −0.0331286 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.0445 | −1.78323 | −0.891617 | − | 0.452791i | \(-0.850428\pi\) | ||||
−0.891617 | + | 0.452791i | \(0.850428\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.76516 | 0.597320 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.39872 | −0.565795 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1542 | 1.15215 | 0.576077 | − | 0.817395i | \(-0.304583\pi\) | ||||
0.576077 | + | 0.817395i | \(0.304583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.21069 | 0.242706 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.50608 | 0.564191 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.6301 | 0.944018 | 0.472009 | − | 0.881594i | \(-0.343529\pi\) | ||||
0.472009 | + | 0.881594i | \(0.343529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.4885 | 0.928260 | 0.464130 | − | 0.885767i | \(-0.346367\pi\) | ||||
0.464130 | + | 0.885767i | \(0.346367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.88319 | 0.582742 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.124162 | 0.00912856 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.4680 | −0.838623 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.36731 | −0.244936 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.4480 | 1.91371 | 0.956857 | − | 0.290560i | \(-0.0938416\pi\) | ||||
0.956857 | + | 0.290560i | \(0.0938416\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.15147 | 0.370811 | 0.185405 | − | 0.982662i | \(-0.440640\pi\) | ||||
0.185405 | + | 0.982662i | \(0.440640\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.427731 | 0.0306304 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.71102 | −0.193152 | −0.0965760 | − | 0.995326i | \(-0.530789\pi\) | ||||
−0.0965760 | + | 0.995326i | \(0.530789\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.4862 | −1.52312 | −0.761558 | − | 0.648097i | \(-0.775565\pi\) | ||||
−0.761558 | + | 0.648097i | \(0.775565\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.76325 | 0.124370 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.16986 | 0.222480 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.411015 | 0.0287066 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.145457 | −0.0101100 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.4319 | −1.27496 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.2749 | 1.67116 | 0.835578 | − | 0.549372i | \(-0.185133\pi\) | ||||
0.835578 | + | 0.549372i | \(0.185133\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.97560 | −0.409442 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.135218 | −0.00922182 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.49666 | −0.237369 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0352 | 0.813265 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.5269 | 0.775384 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.65697 | 0.110959 | 0.0554796 | − | 0.998460i | \(-0.482331\pi\) | ||||
0.0554796 | + | 0.998460i | \(0.482331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.08550 | 0.605700 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.8621 | −1.31829 | −0.659146 | − | 0.752015i | \(-0.729082\pi\) | ||||
−0.659146 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2503 | 1.47034 | 0.735171 | − | 0.677881i | \(-0.237102\pi\) | ||||
0.735171 | + | 0.677881i | \(0.237102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.16734 | −0.208396 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9240 | 0.846682 | 0.423341 | − | 0.905970i | \(-0.360857\pi\) | ||||
0.423341 | + | 0.905970i | \(0.360857\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.479450 | −0.0312758 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.68366 | −0.629021 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.5055 | 1.32639 | 0.663196 | − | 0.748446i | \(-0.269200\pi\) | ||||
0.663196 | + | 0.748446i | \(0.269200\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9383 | 0.769016 | 0.384508 | − | 0.923122i | \(-0.374371\pi\) | ||||
0.384508 | + | 0.923122i | \(0.374371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4596 | −0.991736 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.569086 | 0.0363576 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.5266 | 1.17882 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.21331 | −0.0768905 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.6715 | −1.49413 | −0.747066 | − | 0.664750i | \(-0.768538\pi\) | ||||
−0.747066 | + | 0.664750i | \(0.768538\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.362368 | −0.0227819 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.237437 | 0.0148689 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.08886 | 0.317434 | 0.158717 | − | 0.987324i | \(-0.449264\pi\) | ||||
0.158717 | + | 0.987324i | \(0.449264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.924140 | 0.0574233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.96995 | 0.555226 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.1800 | −0.997703 | −0.498852 | − | 0.866687i | \(-0.666245\pi\) | ||||
−0.498852 | + | 0.866687i | \(0.666245\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.11298 | 0.0683701 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.92973 | −0.179297 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.3752 | 1.60813 | 0.804063 | − | 0.594544i | \(-0.202667\pi\) | ||||
0.804063 | + | 0.594544i | \(0.202667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.7424 | 1.07777 | 0.538887 | − | 0.842378i | \(-0.318845\pi\) | ||||
0.538887 | + | 0.842378i | \(0.318845\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.18361 | 0.192681 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.6341 | 1.36489 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.52925 | 0.272136 | 0.136068 | − | 0.990700i | \(-0.456553\pi\) | ||||
0.136068 | + | 0.990700i | \(0.456553\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.89473 | −0.592382 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.0818 | −1.67522 | −0.837610 | − | 0.546268i | \(-0.816048\pi\) | ||||
−0.837610 | + | 0.546268i | \(0.816048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.06552 | 0.538889 | 0.269445 | − | 0.963016i | \(-0.413160\pi\) | ||||
0.269445 | + | 0.963016i | \(0.413160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.381621 | 0.0226052 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.05920 | 0.180579 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.6013 | −0.623607 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.3136 | −0.721836 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.04959 | 0.470262 | 0.235131 | − | 0.971964i | \(-0.424448\pi\) | ||||
0.235131 | + | 0.971964i | \(0.424448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.596990 | 0.0347581 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.7382 | −1.37743 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.364230 | 0.0210640 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00643 | −0.0580099 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.4376 | −1.00176 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.626983 | 0.0359010 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.7127 | −0.611409 | −0.305704 | − | 0.952126i | \(-0.598892\pi\) | ||||
−0.305704 | + | 0.952126i | \(0.598892\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.58807 | 0.0903419 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.9805 | 0.792760 | 0.396380 | − | 0.918087i | \(-0.370266\pi\) | ||||
0.396380 | + | 0.918087i | \(0.370266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.56354 | 0.314470 | 0.157235 | − | 0.987561i | \(-0.449742\pi\) | ||||
0.157235 | + | 0.987561i | \(0.449742\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.101119 | −0.00569743 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.26371 | 0.351805 | 0.175903 | − | 0.984408i | \(-0.443716\pi\) | ||||
0.175903 | + | 0.984408i | \(0.443716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.3462 | 1.25115 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.42858 | −0.414623 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.2843 | 0.572233 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.7504 | −1.26196 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.9106 | −1.15636 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.56855 | −0.196741 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.6294 | −1.40872 | −0.704361 | − | 0.709842i | \(-0.748766\pi\) | ||||
−0.704361 | + | 0.709842i | \(0.748766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.61510 | 0.143306 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.140239 | 0.00766205 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.0011 | 1.36189 | 0.680947 | − | 0.732332i | \(-0.261568\pi\) | ||||
0.680947 | + | 0.732332i | \(0.261568\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.1462 | 0.822627 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.6501 | −1.33488 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.73742 | 0.471776 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.00750258 | 0.000403925 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.8856 | −0.745416 | −0.372708 | − | 0.927949i | \(-0.621571\pi\) | ||||
−0.372708 | + | 0.927949i | \(0.621571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.7614 | −1.43250 | −0.716252 | − | 0.697842i | \(-0.754144\pi\) | ||||
−0.716252 | + | 0.697842i | \(0.754144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.8601 | 1.27356 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.94995 | −0.476358 | −0.238179 | − | 0.971221i | \(-0.576550\pi\) | ||||
−0.238179 | + | 0.971221i | \(0.576550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.475265 | −0.0252244 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.76725 | 0.0935327 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.1713 | 1.75071 | 0.875356 | − | 0.483479i | \(-0.160627\pi\) | ||||
0.875356 | + | 0.483479i | \(0.160627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47058 | −0.130030 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.3785 | −0.544729 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.957212 | 0.0501027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7634 | 0.561844 | 0.280922 | − | 0.959731i | \(-0.409360\pi\) | ||||
0.280922 | + | 0.959731i | \(0.409360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.65680 | 0.450655 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.28397 | 0.430082 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.4079 | −1.31557 | −0.657786 | − | 0.753205i | \(-0.728507\pi\) | ||||
−0.657786 | + | 0.753205i | \(0.728507\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.937947 | −0.0484354 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.4610 | −1.15680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.795661 | −0.0408703 | −0.0204352 | − | 0.999791i | \(-0.506505\pi\) | ||||
−0.0204352 | + | 0.999791i | \(0.506505\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.00960 | −0.410344 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2933 | 1.34352 | 0.671762 | − | 0.740767i | \(-0.265538\pi\) | ||||
0.671762 | + | 0.740767i | \(0.265538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.251912 | −0.0128386 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.84797 | −0.144770 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.8254 | 1.05589 | 0.527946 | − | 0.849278i | \(-0.322962\pi\) | ||||
0.527946 | + | 0.849278i | \(0.322962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.202187 | 0.0102250 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.12527 | 0.157649 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.770182 | −0.0387521 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.5081 | −1.07946 | −0.539730 | − | 0.841838i | \(-0.681474\pi\) | ||||
−0.539730 | + | 0.841838i | \(0.681474\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.84041 | 0.142198 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.2060 | 0.509662 | 0.254831 | − | 0.966986i | \(-0.417980\pi\) | ||||
0.254831 | + | 0.966986i | \(0.417980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.7767 | 1.23422 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.0197696 | 0.000982361 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.51482 | 0.322927 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0291 | 0.940929 | 0.470465 | − | 0.882419i | \(-0.344086\pi\) | ||||
0.470465 | + | 0.882419i | \(0.344086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.07005 | −0.299413 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.44341 | 0.218646 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0964998 | −0.00473699 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.10209 | −0.347791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.7730 | −0.819415 | −0.409707 | − | 0.912217i | \(-0.634369\pi\) | ||||
−0.409707 | + | 0.912217i | \(0.634369\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.9413 | −0.679458 | −0.339729 | − | 0.940523i | \(-0.610335\pi\) | ||||
−0.339729 | + | 0.940523i | \(0.610335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.0982 | −0.490990 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.6289 | −0.612593 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.66665 | 0.225835 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.4432 | 1.08357 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.42592 | −0.0686842 | −0.0343421 | − | 0.999410i | \(-0.510934\pi\) | ||||
−0.0343421 | + | 0.999410i | \(0.510934\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.39205 | −0.211069 | −0.105534 | − | 0.994416i | \(-0.533655\pi\) | ||||
−0.105534 | + | 0.994416i | \(0.533655\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.462663 | −0.0221830 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.324965 | 0.0155452 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.163858 | −0.00782052 | −0.00391026 | − | 0.999992i | \(-0.501245\pi\) | ||||
−0.00391026 | + | 0.999992i | \(0.501245\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.9861 | 0.570766 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.0145 | 1.18847 | 0.594236 | − | 0.804290i | \(-0.297454\pi\) | ||||
0.594236 | + | 0.804290i | \(0.297454\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.233014 | −0.0110459 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.47813 | 0.353703 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.0945 | 1.32586 | 0.662932 | − | 0.748680i | \(-0.269312\pi\) | ||||
0.662932 | + | 0.748680i | \(0.269312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.5661 | 1.01551 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.7919 | −0.976887 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.253206 | 0.0118705 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.60049 | 0.121646 | 0.0608228 | − | 0.998149i | \(-0.480628\pi\) | ||||
0.0608228 | + | 0.998149i | \(0.480628\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.2450 | 0.618222 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.4245 | −1.23071 | −0.615356 | − | 0.788249i | \(-0.710988\pi\) | ||||
−0.615356 | + | 0.788249i | \(0.710988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.2995 | 0.850450 | 0.425225 | − | 0.905088i | \(-0.360195\pi\) | ||||
0.425225 | + | 0.905088i | \(0.360195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.510362 | 0.0236675 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.59517 | −0.305188 | −0.152594 | − | 0.988289i | \(-0.548763\pi\) | ||||
−0.152594 | + | 0.988289i | \(0.548763\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.04380 | 0.0481982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.02618 | 0.0472837 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.09496 | −0.326226 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.2978 | −0.931329 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.4417 | 1.07332 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.8696 | 0.542336 | 0.271168 | − | 0.962532i | \(-0.412590\pi\) | ||||
0.271168 | + | 0.962532i | \(0.412590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.54828 | −0.298576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0558419 | 0.00254089 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.979353 | −0.0444701 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.2560 | 1.32571 | 0.662857 | − | 0.748746i | \(-0.269344\pi\) | ||||
0.662857 | + | 0.748746i | \(0.269344\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.4330 | −0.743125 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.9712 | 0.630513 | 0.315256 | − | 0.949007i | \(-0.397910\pi\) | ||||
0.315256 | + | 0.949007i | \(0.397910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.4683 | −0.561544 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.712851 | −0.0320403 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.53741 | −0.158674 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.22901 | −0.413147 | −0.206574 | − | 0.978431i | \(-0.566231\pi\) | ||||
−0.206574 | + | 0.978431i | \(0.566231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.0346 | 1.11846 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.1056 | 1.74363 | 0.871817 | − | 0.489833i | \(-0.162942\pi\) | ||||
0.871817 | + | 0.489833i | \(0.162942\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.38689 | −0.0617156 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.43577 | −0.374646 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.4622 | −0.906970 | −0.453485 | − | 0.891264i | \(-0.649819\pi\) | ||||
−0.453485 | + | 0.891264i | \(0.649819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.12455 | 0.315172 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.2880 | 0.939886 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.126306 | 0.00556569 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.1569 | −1.10640 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.4630 | −0.722644 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2992 | −0.451216 | −0.225608 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225608 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.3558 | 1.58973 | 0.794864 | − | 0.606788i | \(-0.207542\pi\) | ||||
0.794864 | + | 0.606788i | \(0.207542\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.48798 | −0.152228 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.7538 | 0.599123 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9936 | −0.999722 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5738 | 0.545656 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.6769 | −0.938931 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.590826 | −0.0255436 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.7209 | −0.592099 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.8601 | 1.28617 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.6247 | 1.31666 | 0.658330 | − | 0.752730i | \(-0.271263\pi\) | ||||
0.658330 | + | 0.752730i | \(0.271263\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.5670 | −0.582215 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.66311 | −0.0712396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.5797 | 0.666140 | 0.333070 | − | 0.942902i | \(-0.391916\pi\) | ||||
0.333070 | + | 0.942902i | \(0.391916\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.2055 | 0.563598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.0397 | −0.853719 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.73249 | −0.243770 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.134885 | −0.00572554 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.1697 | −1.02410 | −0.512052 | − | 0.858955i | \(-0.671114\pi\) | ||||
−0.512052 | + | 0.858955i | \(0.671114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.13141 | 0.301626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.4584 | 0.525994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.0486 | 0.929239 | 0.464619 | − | 0.885510i | \(-0.346191\pi\) | ||||
0.464619 | + | 0.885510i | \(0.346191\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.20464 | 0.0506795 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.147146 | 0.00617955 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3055 | 1.10278 | 0.551392 | − | 0.834246i | \(-0.314097\pi\) | ||||
0.551392 | + | 0.834246i | \(0.314097\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −47.5564 | −1.99017 | −0.995086 | − | 0.0990110i | \(-0.968432\pi\) | ||||
−0.995086 | + | 0.0990110i | \(0.968432\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.7321 | −1.20030 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.399052 | −0.0166416 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.1394 | 1.42124 | 0.710620 | − | 0.703576i | \(-0.248414\pi\) | ||||
0.710620 | + | 0.703576i | \(0.248414\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.59636 | −0.232577 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.718250 | −0.0297980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 58.3986 | 2.41862 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.716513 | 0.0296242 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.89205 | 0.0780934 | 0.0390467 | − | 0.999237i | \(-0.487568\pi\) | ||||
0.0390467 | + | 0.999237i | \(0.487568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.1057 | 0.910850 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.94514 | 0.121147 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1452 | 0.786197 | 0.393099 | − | 0.919496i | \(-0.371403\pi\) | ||||
0.393099 | + | 0.919496i | \(0.371403\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.140557 | 0.00576226 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.3418 | 0.955315 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.6458 | −1.70160 | −0.850801 | − | 0.525488i | \(-0.823883\pi\) | ||||
−0.850801 | + | 0.525488i | \(0.823883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.2507 | 1.60107 | 0.800536 | − | 0.599285i | \(-0.204548\pi\) | ||||
0.800536 | + | 0.599285i | \(0.204548\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.95371 | 0.120284 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.825444 | −0.0335591 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.8704 | 1.25299 | 0.626496 | − | 0.779425i | \(-0.284489\pi\) | ||||
0.626496 | + | 0.779425i | \(0.284489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.44361 | −0.139542 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.2861 | 1.02297 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5488 | 0.628009 | 0.314004 | − | 0.949422i | \(-0.398329\pi\) | ||||
0.314004 | + | 0.949422i | \(0.398329\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.446511 | −0.0180051 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.93307 | −0.399890 | −0.199945 | − | 0.979807i | \(-0.564076\pi\) | ||||
−0.199945 | + | 0.979807i | \(0.564076\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.08575 | 0.164220 | 0.0821100 | − | 0.996623i | \(-0.473834\pi\) | ||||
0.0821100 | + | 0.996623i | \(0.473834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.418517 | 0.0167945 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73433 | −0.0694844 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8881 | 0.995523 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 20.0238 | 0.799672 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.63501 | −0.144937 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1626 | 0.523995 | 0.261997 | − | 0.965069i | \(-0.415619\pi\) | ||||
0.261997 | + | 0.965069i | \(0.415619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.3714 | −1.04817 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.637037 | −0.0252801 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.0135 | −1.18918 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.0100 | −0.395991 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3850 | −0.489176 | −0.244588 | − | 0.969627i | \(-0.578653\pi\) | ||||
−0.244588 | + | 0.969627i | \(0.578653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6135 | −0.891788 | −0.445894 | − | 0.895086i | \(-0.647114\pi\) | ||||
−0.445894 | + | 0.895086i | \(0.647114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.146896 | 0.00578403 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.93742 | −0.390680 | −0.195340 | − | 0.980736i | \(-0.562581\pi\) | ||||
−0.195340 | + | 0.980736i | \(0.562581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.3243 | 1.22958 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.79864 | 0.148880 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.1952 | −0.555500 | −0.277750 | − | 0.960653i | \(-0.589589\pi\) | ||||
−0.277750 | + | 0.960653i | \(0.589589\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.248566 | 0.00971227 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.1608 | 0.786547 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.0553 | −1.63824 | −0.819120 | − | 0.573622i | \(-0.805538\pi\) | ||||
−0.819120 | + | 0.573622i | \(0.805538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.6652 | −1.73728 | −0.868638 | − | 0.495447i | \(-0.835004\pi\) | ||||
−0.868638 | + | 0.495447i | \(0.835004\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.5224 | −0.486330 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.225910 | 0.00876041 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.393976 | −0.0152548 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.80007 | −0.0695949 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.8980 | 1.27001 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.03801 | 0.194201 | 0.0971005 | − | 0.995275i | \(-0.469043\pi\) | ||||
0.0971005 | + | 0.995275i | \(0.469043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −26.1412 | −1.00618 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.0307 | 1.23104 | 0.615521 | − | 0.788121i | \(-0.288946\pi\) | ||||
0.615521 | + | 0.788121i | \(0.288946\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.28935 | −0.279739 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.5774 | 0.826848 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.5034 | 1.85593 | 0.927965 | − | 0.372667i | \(-0.121557\pi\) | ||||
0.927965 | + | 0.372667i | \(0.121557\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.482776 | −0.0184459 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.1719 | −0.922216 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −58.6986 | −2.23624 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.6212 | 0.822507 | 0.411254 | − | 0.911521i | \(-0.365091\pi\) | ||||
0.411254 | + | 0.911521i | \(0.365091\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.30577 | −0.201549 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.564859 | −0.0214263 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0330 | −0.455784 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0402 | −0.531049 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.6093 | 0.627323 | 0.313662 | − | 0.949535i | \(-0.398444\pi\) | ||||
0.313662 | + | 0.949535i | \(0.398444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.84237 | −0.220349 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.520856 | 0.0196166 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.3226 | −0.388222 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0103 | −0.939283 | −0.469642 | − | 0.882857i | \(-0.655617\pi\) | ||||
−0.469642 | + | 0.882857i | \(0.655617\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.2216 | −0.608357 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.434594 | 0.0162757 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.78500 | 0.0667552 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.2764 | −0.831928 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.2422 | −1.23972 | −0.619862 | − | 0.784711i | \(-0.712811\pi\) | ||||
−0.619862 | + | 0.784711i | \(0.712811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.940095 | 0.0350110 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.9693 | −0.482335 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.6084 | 0.913932 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.42728 | 0.127111 | 0.0635554 | − | 0.997978i | \(-0.479756\pi\) | ||||
0.0635554 | + | 0.997978i | \(0.479756\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.4812 | 0.647451 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.95870 | 0.146418 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3373 | 0.381815 | 0.190908 | − | 0.981608i | \(-0.438857\pi\) | ||||
0.190908 | + | 0.981608i | \(0.438857\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.618233 | −0.0228039 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.35836 | 0.271049 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.7360 | −1.60886 | −0.804428 | − | 0.594050i | \(-0.797528\pi\) | ||||
−0.804428 | + | 0.594050i | \(0.797528\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.1266 | −0.739370 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.3659 | −1.07733 | −0.538665 | − | 0.842520i | \(-0.681071\pi\) | ||||
−0.538665 | + | 0.842520i | \(0.681071\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.594767 | 0.0217906 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.03248 | −0.0743645 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.39753 | −0.160682 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.7158 | 0.937136 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.65366 | −0.0601830 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.3449 | 1.79347 | 0.896735 | − | 0.442568i | \(-0.145933\pi\) | ||||
0.896735 | + | 0.442568i | \(0.145933\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.393663 | 0.0142891 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.6088 | 0.457068 | 0.228534 | − | 0.973536i | \(-0.426607\pi\) | ||||
0.228534 | + | 0.973536i | \(0.426607\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.3785 | −0.448133 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.397742 | 0.0143804 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.4852 | −1.13686 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.02880 | 0.289526 | 0.144763 | − | 0.989466i | \(-0.453758\pi\) | ||||
0.144763 | + | 0.989466i | \(0.453758\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.52834 | −0.199098 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −45.3549 | −1.63130 | −0.815652 | − | 0.578543i | \(-0.803621\pi\) | ||||
−0.815652 | + | 0.578543i | \(0.803621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.1454 | −0.975093 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.00395 | −0.0360165 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.3401 | −0.692931 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.9373 | −0.892327 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25.8088 | −0.922330 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0816160 | 0.00291300 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.3514 | −0.404635 | −0.202318 | − | 0.979320i | \(-0.564847\pi\) | ||||
−0.202318 | + | 0.979320i | \(0.564847\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.5774 | 0.625771 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.96615 | 0.318800 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.0670 | −1.17424 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.20910 | −0.0428825 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.8609 | −1.62448 | −0.812238 | − | 0.583326i | \(-0.801751\pi\) | ||||
−0.812238 | + | 0.583326i | \(0.801751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.0365 | 0.496577 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.90774 | −0.173406 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.2252 | 1.77241 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.00444134 | 0.000156537 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.6531 | −1.00864 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5190 | 0.475302 | 0.237651 | − | 0.971351i | \(-0.423623\pi\) | ||||
0.237651 | + | 0.971351i | \(0.423623\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.7329 | −1.32498 | −0.662491 | − | 0.749070i | \(-0.730501\pi\) | ||||
−0.662491 | + | 0.749070i | \(0.730501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.2747 | −0.675992 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.30698 | −0.0457816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.36263 | 0.222600 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.33302 | 0.186351 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.6436 | 1.69767 | 0.848836 | − | 0.528656i | \(-0.177304\pi\) | ||||
0.848836 | + | 0.528656i | \(0.177304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.9530 | −1.39268 | −0.696338 | − | 0.717714i | \(-0.745188\pi\) | ||||
−0.696338 | + | 0.717714i | \(0.745188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.5888 | −0.856073 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.5132 | −0.365581 | −0.182790 | − | 0.983152i | \(-0.558513\pi\) | ||||
−0.182790 | + | 0.983152i | \(0.558513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.7750 | 0.756277 | 0.378139 | − | 0.925749i | \(-0.376564\pi\) | ||||
0.378139 | + | 0.925749i | \(0.376564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.92040 | −0.170687 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.6608 | −0.577261 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.99111 | 0.0689051 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 28.4696 | 0.984052 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.8305 | 0.650102 | 0.325051 | − | 0.945696i | \(-0.394619\pi\) | ||||
0.325051 | + | 0.945696i | \(0.394619\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.70461 | −0.162228 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.5070 | 1.05072 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.670932 | −0.0230808 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.14380 | −0.211104 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.84844 | −0.337998 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.114860 | −0.00393734 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.39978 | −0.116406 | −0.0582031 | − | 0.998305i | \(-0.518537\pi\) | ||||
−0.0582031 | + | 0.998305i | \(0.518537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.639271 | 0.0218626 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.7786 | 1.70040 | 0.850202 | − | 0.526457i | \(-0.176480\pi\) | ||||
0.850202 | + | 0.526457i | \(0.176480\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2516 | −0.486257 | −0.243128 | − | 0.969994i | \(-0.578174\pi\) | ||||
−0.243128 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.32340 | −0.113261 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.3168 | 0.385228 | 0.192614 | − | 0.981275i | \(-0.438303\pi\) | ||||
0.192614 | + | 0.981275i | \(0.438303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.30937 | −0.0445199 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.5169 | 0.391133 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.4117 | −1.37087 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.39617 | −0.250610 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.6271 | −0.698122 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.555242 | −0.0187706 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.5164 | −1.33437 | −0.667187 | − | 0.744890i | \(-0.732502\pi\) | ||||
−0.667187 | + | 0.744890i | \(0.732502\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.74477 | −0.294954 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.1496 | 1.15053 | 0.575265 | − | 0.817967i | \(-0.304899\pi\) | ||||
0.575265 | + | 0.817967i | \(0.304899\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.6502 | 0.762241 | 0.381121 | − | 0.924525i | \(-0.375538\pi\) | ||||
0.381121 | + | 0.924525i | \(0.375538\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.648547 | −0.0218007 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.49135 | 0.318688 | 0.159344 | − | 0.987223i | \(-0.449062\pi\) | ||||
0.159344 | + | 0.987223i | \(0.449062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.74148 | −0.159024 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.03732 | 0.0347515 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.5602 | 0.754949 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.09128 | −0.0364774 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.395685 | −0.0132115 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.8002 | −0.893836 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.5841 | −1.08553 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.09335 | 0.0363845 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.07904 | −0.0358685 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7746 | 0.756218 | 0.378109 | − | 0.925761i | \(-0.376575\pi\) | ||||
0.378109 | + | 0.925761i | \(0.376575\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −29.2106 | −0.968854 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.5037 | 0.348002 | 0.174001 | − | 0.984745i | \(-0.444330\pi\) | ||||
0.174001 | + | 0.984745i | \(0.444330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.06337 | −0.167573 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.681131 | −0.0225175 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.85008 | 0.0610951 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.97329 | −0.197041 | −0.0985204 | − | 0.995135i | \(-0.531411\pi\) | ||||
−0.0985204 | + | 0.995135i | \(0.531411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.6379 | 0.383482 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.0654 | 0.825038 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.17432 | 0.235890 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.66025 | 0.0873740 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.1852 | −1.18720 | −0.593600 | − | 0.804760i | \(-0.702294\pi\) | ||||
−0.593600 | + | 0.804760i | \(0.702294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.7780 | −0.877614 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15.1879 | −0.497228 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.990868 | 0.0324049 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.8861 | 1.85839 | 0.929193 | − | 0.369594i | \(-0.120503\pi\) | ||||
0.929193 | + | 0.369594i | \(0.120503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.04402 | −0.197239 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.0907 | −0.948328 | −0.474164 | − | 0.880436i | \(-0.657250\pi\) | ||||
−0.474164 | + | 0.880436i | \(0.657250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.380222 | −0.0123817 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.290945 | 0.00946445 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.58176 | −0.311366 | −0.155683 | − | 0.987807i | \(-0.549758\pi\) | ||||
−0.155683 | + | 0.987807i | \(0.549758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.4832 | −1.63876 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.80466 | −0.220656 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.2933 | −1.69395 | −0.846973 | − | 0.531636i | \(-0.821577\pi\) | ||||
−0.846973 | + | 0.531636i | \(0.821577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.28519 | −0.0739470 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.2761 | −0.784734 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.59332 | −0.116034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.43678 | −0.0463479 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.4440 | −0.401001 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.445102 | −0.0143283 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9187 | 0.351122 | 0.175561 | − | 0.984469i | \(-0.443826\pi\) | ||||
0.175561 | + | 0.984469i | \(0.443826\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.1725 | −0.358911 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.2093 | 0.584363 | 0.292182 | − | 0.956363i | \(-0.405619\pi\) | ||||
0.292182 | + | 0.956363i | \(0.405619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.20426 | −0.134782 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.7151 | 0.791518 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.4537 | −1.35821 | −0.679107 | − | 0.734039i | \(-0.737633\pi\) | ||||
−0.679107 | + | 0.734039i | \(0.737633\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.2263 | −0.390755 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35.0283 | −1.11837 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.3144 | 1.79615 | 0.898076 | − | 0.439841i | \(-0.144965\pi\) | ||||
0.898076 | + | 0.439841i | \(0.144965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.234240 | 0.00746350 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.87674 | 0.123398 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.125088 | 0.00397757 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6246 | 0.813992 | 0.406996 | − | 0.913430i | \(-0.366576\pi\) | ||||
0.406996 | + | 0.913430i | \(0.366576\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.8428 | 0.883566 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.85647 | 0.0588540 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.3571 | 1.62650 | 0.813248 | − | 0.581917i | \(-0.197697\pi\) | ||||
0.813248 | + | 0.581917i | \(0.197697\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.52428 | −0.238058 |
(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 | 6008.2.a.d.1.16 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.d.1.16 | ✓ | 49 | 1.1 | even | 1 | trivial |