Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8712,2,Mod(1,8712)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8712, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8712.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8712.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: | \(69.5656702409\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.62158000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 14x^{4} + 22x^{3} + 38x^{2} - 60x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 792) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.90351\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8712.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.07994 | 0.930177 | 0.465088 | − | 0.885264i | \(-0.346023\pi\) | ||||
0.465088 | + | 0.885264i | \(0.346023\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39055 | −0.525578 | −0.262789 | − | 0.964853i | \(-0.584642\pi\) | ||||
−0.262789 | + | 0.964853i | \(0.584642\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.79180 | 1.60636 | 0.803178 | − | 0.595739i | \(-0.203141\pi\) | ||||
0.803178 | + | 0.595739i | \(0.203141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.23340 | −1.75436 | −0.877179 | − | 0.480164i | \(-0.840577\pi\) | ||||
−0.877179 | + | 0.480164i | \(0.840577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.44752 | 1.93799 | 0.968997 | − | 0.247073i | \(-0.0794687\pi\) | ||||
0.968997 | + | 0.247073i | \(0.0794687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.19197 | −0.457057 | −0.228528 | − | 0.973537i | \(-0.573391\pi\) | ||||
−0.228528 | + | 0.973537i | \(0.573391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.673854 | −0.134771 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.03317 | −1.30603 | −0.653014 | − | 0.757346i | \(-0.726496\pi\) | ||||
−0.653014 | + | 0.757346i | \(0.726496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.55706 | −0.459261 | −0.229631 | − | 0.973278i | \(-0.573752\pi\) | ||||
−0.229631 | + | 0.973278i | \(0.573752\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.89226 | −0.488881 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.57290 | −1.40938 | −0.704688 | − | 0.709517i | \(-0.748913\pi\) | ||||
−0.704688 | + | 0.709517i | \(0.748913\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.07188 | 0.167399 | 0.0836995 | − | 0.996491i | \(-0.473326\pi\) | ||||
0.0836995 | + | 0.996491i | \(0.473326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.59881 | −1.15881 | −0.579404 | − | 0.815040i | \(-0.696715\pi\) | ||||
−0.579404 | + | 0.815040i | \(0.696715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.7784 | −1.57220 | −0.786098 | − | 0.618102i | \(-0.787902\pi\) | ||||
−0.786098 | + | 0.618102i | \(0.787902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.06637 | −0.723768 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.550965 | 0.0756808 | 0.0378404 | − | 0.999284i | \(-0.487952\pi\) | ||||
0.0378404 | + | 0.999284i | \(0.487952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4911 | −1.36582 | −0.682912 | − | 0.730500i | \(-0.739287\pi\) | ||||
−0.682912 | + | 0.730500i | \(0.739287\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5902 | −1.35594 | −0.677970 | − | 0.735090i | \(-0.737140\pi\) | ||||
−0.677970 | + | 0.735090i | \(0.737140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0466 | 1.49420 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.71154 | 0.331267 | 0.165634 | − | 0.986187i | \(-0.447033\pi\) | ||||
0.165634 | + | 0.986187i | \(0.447033\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.01881 | 0.239589 | 0.119795 | − | 0.992799i | \(-0.461776\pi\) | ||||
0.119795 | + | 0.992799i | \(0.461776\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.302349 | −0.0353873 | −0.0176936 | − | 0.999843i | \(-0.505632\pi\) | ||||
−0.0176936 | + | 0.999843i | \(0.505632\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.91851 | 0.553375 | 0.276688 | − | 0.960960i | \(-0.410763\pi\) | ||||
0.276688 | + | 0.960960i | \(0.410763\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6654 | 1.17068 | 0.585339 | − | 0.810789i | \(-0.300961\pi\) | ||||
0.585339 | + | 0.810789i | \(0.300961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.0450 | −1.63186 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.07002 | −0.431421 | −0.215710 | − | 0.976457i | \(-0.569207\pi\) | ||||
−0.215710 | + | 0.976457i | \(0.569207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.05378 | −0.844266 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.5703 | 1.80268 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.17377 | −0.119178 | −0.0595889 | − | 0.998223i | \(-0.518979\pi\) | ||||
−0.0595889 | + | 0.998223i | \(0.518979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.5486 | 1.34814 | 0.674068 | − | 0.738670i | \(-0.264546\pi\) | ||||
0.674068 | + | 0.738670i | \(0.264546\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.29833 | 0.916191 | 0.458096 | − | 0.888903i | \(-0.348532\pi\) | ||||
0.458096 | + | 0.888903i | \(0.348532\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.0108 | −1.25781 | −0.628903 | − | 0.777484i | \(-0.716496\pi\) | ||||
−0.628903 | + | 0.777484i | \(0.716496\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.97205 | 0.667801 | 0.333901 | − | 0.942608i | \(-0.391635\pi\) | ||||
0.333901 | + | 0.942608i | \(0.391635\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.27484 | 0.213999 | 0.106999 | − | 0.994259i | \(-0.465876\pi\) | ||||
0.106999 | + | 0.994259i | \(0.465876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.55916 | −0.425144 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0584 | 0.922052 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8013 | −1.05554 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.15906 | −0.280321 | −0.140161 | − | 0.990129i | \(-0.544762\pi\) | ||||
−0.140161 | + | 0.990129i | \(0.544762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.1519 | 1.67331 | 0.836655 | − | 0.547730i | \(-0.184508\pi\) | ||||
0.836655 | + | 0.547730i | \(0.184508\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7467 | −1.01857 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.61239 | −0.821242 | −0.410621 | − | 0.911806i | \(-0.634688\pi\) | ||||
−0.410621 | + | 0.911806i | \(0.634688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.4601 | 1.22649 | 0.613244 | − | 0.789894i | \(-0.289864\pi\) | ||||
0.613244 | + | 0.789894i | \(0.289864\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.6286 | −1.21484 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.06471 | −0.742610 | −0.371305 | − | 0.928511i | \(-0.621090\pi\) | ||||
−0.371305 | + | 0.928511i | \(0.621090\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.46141 | −0.281685 | −0.140843 | − | 0.990032i | \(-0.544981\pi\) | ||||
−0.140843 | + | 0.990032i | \(0.544981\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.31852 | −0.427194 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2040 | −1.37303 | −0.686514 | − | 0.727116i | \(-0.740860\pi\) | ||||
−0.686514 | + | 0.727116i | \(0.740860\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.04804 | 0.240219 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.53727 | −0.120408 | −0.0602040 | − | 0.998186i | \(-0.519175\pi\) | ||||
−0.0602040 | + | 0.998186i | \(0.519175\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.9812 | 1.46881 | 0.734404 | − | 0.678712i | \(-0.237462\pi\) | ||||
0.734404 | + | 0.678712i | \(0.237462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.5449 | 1.58038 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.9353 | −1.21154 | −0.605769 | − | 0.795641i | \(-0.707134\pi\) | ||||
−0.605769 | + | 0.795641i | \(0.707134\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.937027 | 0.0708326 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.63638 | −0.496027 | −0.248013 | − | 0.968757i | \(-0.579778\pi\) | ||||
−0.248013 | + | 0.968757i | \(0.579778\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.85656 | −0.732632 | −0.366316 | − | 0.930490i | \(-0.619381\pi\) | ||||
−0.366316 | + | 0.930490i | \(0.619381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.8311 | −1.31097 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.25837 | −0.452840 | −0.226420 | − | 0.974030i | \(-0.572702\pi\) | ||||
−0.226420 | + | 0.974030i | \(0.572702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8818 | 1.07121 | 0.535607 | − | 0.844467i | \(-0.320083\pi\) | ||||
0.535607 | + | 0.844467i | \(0.320083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.6099 | −0.898416 | −0.449208 | − | 0.893427i | \(-0.648294\pi\) | ||||
−0.449208 | + | 0.893427i | \(0.648294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3905 | 1.44544 | 0.722721 | − | 0.691140i | \(-0.242891\pi\) | ||||
0.722721 | + | 0.691140i | \(0.242891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.77997 | 0.686420 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.22944 | 0.155711 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.05700 | 0.554667 | 0.277333 | − | 0.960774i | \(-0.410549\pi\) | ||||
0.277333 | + | 0.960774i | \(0.410549\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.8051 | −1.07790 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.55572 | 0.241378 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.8944 | −2.81812 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.42920 | 0.296601 | 0.148301 | − | 0.988942i | \(-0.452620\pi\) | ||||
0.148301 | + | 0.988942i | \(0.452620\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.6801 | −1.43896 | −0.719479 | − | 0.694515i | \(-0.755619\pi\) | ||||
−0.719479 | + | 0.694515i | \(0.755619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.92281 | −0.457472 | −0.228736 | − | 0.973488i | \(-0.573459\pi\) | ||||
−0.228736 | + | 0.973488i | \(0.573459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.27854 | −0.280297 | −0.140148 | − | 0.990131i | \(-0.544758\pi\) | ||||
−0.140148 | + | 0.990131i | \(0.544758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4185 | −1.46242 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.3560 | −0.863926 | −0.431963 | − | 0.901891i | \(-0.642179\pi\) | ||||
−0.431963 | + | 0.901891i | \(0.642179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0451 | −0.647061 | −0.323531 | − | 0.946218i | \(-0.604870\pi\) | ||||
−0.323531 | + | 0.946218i | \(0.604870\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.5377 | −0.673232 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 48.9263 | 3.11311 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.6697 | −1.30466 | −0.652330 | − | 0.757935i | \(-0.726209\pi\) | ||||
−0.652330 | + | 0.757935i | \(0.726209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.4903 | −0.779124 | −0.389562 | − | 0.921000i | \(-0.627374\pi\) | ||||
−0.389562 | + | 0.921000i | \(0.627374\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.9210 | 0.740737 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.6796 | 1.02851 | 0.514254 | − | 0.857638i | \(-0.328069\pi\) | ||||
0.514254 | + | 0.857638i | \(0.328069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.14597 | 0.0703966 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.6211 | 1.37923 | 0.689615 | − | 0.724176i | \(-0.257780\pi\) | ||||
0.689615 | + | 0.724176i | \(0.257780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.39992 | −0.267276 | −0.133638 | − | 0.991030i | \(-0.542666\pi\) | ||||
−0.133638 | + | 0.991030i | \(0.542666\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8092 | −0.889800 | −0.444900 | − | 0.895580i | \(-0.646761\pi\) | ||||
−0.444900 | + | 0.895580i | \(0.646761\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.6414 | −1.52964 | −0.764818 | − | 0.644246i | \(-0.777171\pi\) | ||||
−0.764818 | + | 0.644246i | \(0.777171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4934 | 0.920988 | 0.460494 | − | 0.887663i | \(-0.347672\pi\) | ||||
0.460494 | + | 0.887663i | \(0.347672\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.49050 | −0.0879812 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.3221 | 2.07777 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.0055 | 0.642949 | 0.321474 | − | 0.946918i | \(-0.395822\pi\) | ||||
0.321474 | + | 0.946918i | \(0.395822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.8208 | −1.27046 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.6954 | −0.734196 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5665 | 0.609044 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.0270 | −1.26126 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.25608 | 0.528272 | 0.264136 | − | 0.964485i | \(-0.414913\pi\) | ||||
0.264136 | + | 0.964485i | \(0.414913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.57301 | 0.542836 | 0.271418 | − | 0.962462i | \(-0.412507\pi\) | ||||
0.271418 | + | 0.962462i | \(0.412507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50665 | −0.311254 | −0.155627 | − | 0.987816i | \(-0.549740\pi\) | ||||
−0.155627 | + | 0.987816i | \(0.549740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.3576 | 0.862568 | 0.431284 | − | 0.902216i | \(-0.358061\pi\) | ||||
0.431284 | + | 0.902216i | \(0.358061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −61.1043 | −3.39993 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.90283 | −0.216490 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.9879 | 0.826312 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1054 | −1.05013 | −0.525064 | − | 0.851063i | \(-0.675959\pi\) | ||||
−0.525064 | + | 0.851063i | \(0.675959\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.63984 | 0.308137 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0067 | −1.03536 | −0.517680 | − | 0.855574i | \(-0.673204\pi\) | ||||
−0.517680 | + | 0.855574i | \(0.673204\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7789 | 0.905975 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.4727 | −1.47481 | −0.737406 | − | 0.675450i | \(-0.763949\pi\) | ||||
−0.737406 | + | 0.675450i | \(0.763949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.31972 | −0.177700 | −0.0888502 | − | 0.996045i | \(-0.528319\pi\) | ||||
−0.0888502 | + | 0.996045i | \(0.528319\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1782 | 0.594956 | 0.297478 | − | 0.954729i | \(-0.403855\pi\) | ||||
0.297478 | + | 0.954729i | \(0.403855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.19901 | 0.222860 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.590367 | 0.0311584 | 0.0155792 | − | 0.999879i | \(-0.495041\pi\) | ||||
0.0155792 | + | 0.999879i | \(0.495041\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.3606 | 2.75582 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.628867 | −0.0329164 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.6794 | −1.60145 | −0.800726 | − | 0.599030i | \(-0.795553\pi\) | ||||
−0.800726 | + | 0.599030i | \(0.795553\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.766144 | −0.0397762 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.85036 | 0.458254 | 0.229127 | − | 0.973396i | \(-0.426413\pi\) | ||||
0.229127 | + | 0.973396i | \(0.426413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.7347 | −2.09795 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6542 | −1.16367 | −0.581834 | − | 0.813308i | \(-0.697665\pi\) | ||||
−0.581834 | + | 0.813308i | \(0.697665\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.26423 | 0.320087 | 0.160044 | − | 0.987110i | \(-0.448837\pi\) | ||||
0.160044 | + | 0.987110i | \(0.448837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.6929 | −1.60689 | −0.803447 | − | 0.595377i | \(-0.797003\pi\) | ||||
−0.803447 | + | 0.595377i | \(0.797003\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8554 | 0.801841 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.2302 | 0.514737 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.24531 | −0.162877 | −0.0814386 | − | 0.996678i | \(-0.525951\pi\) | ||||
−0.0814386 | + | 0.996678i | \(0.525951\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.8348 | 1.04044 | 0.520220 | − | 0.854032i | \(-0.325850\pi\) | ||||
0.520220 | + | 0.854032i | \(0.325850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.8100 | −0.737737 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6722 | −0.676046 | −0.338023 | − | 0.941138i | \(-0.609758\pi\) | ||||
−0.338023 | + | 0.941138i | \(0.609758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.5884 | 0.717848 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.1834 | 1.08894 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.05402 | 0.0514924 | 0.0257462 | − | 0.999669i | \(-0.491804\pi\) | ||||
0.0257462 | + | 0.999669i | \(0.491804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.7281 | 0.961487 | 0.480744 | − | 0.876861i | \(-0.340367\pi\) | ||||
0.480744 | + | 0.876861i | \(0.340367\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.87426 | 0.236436 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.7262 | 0.712653 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.80184 | 0.327633 | 0.163817 | − | 0.986491i | \(-0.447619\pi\) | ||||
0.163817 | + | 0.986491i | \(0.447619\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.36860 | −0.209942 | −0.104971 | − | 0.994475i | \(-0.533475\pi\) | ||||
−0.104971 | + | 0.994475i | \(0.533475\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.5167 | −0.885773 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.269843 | 0.0128789 | 0.00643944 | − | 0.999979i | \(-0.497950\pi\) | ||||
0.00643944 | + | 0.999979i | \(0.497950\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.6718 | −1.26721 | −0.633607 | − | 0.773655i | \(-0.718426\pi\) | ||||
−0.633607 | + | 0.773655i | \(0.718426\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.46538 | −0.401298 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.49052 | −0.164728 | −0.0823639 | − | 0.996602i | \(-0.526247\pi\) | ||||
−0.0823639 | + | 0.996602i | \(0.526247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.7514 | −0.785317 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.5942 | −1.43113 | −0.715567 | − | 0.698544i | \(-0.753832\pi\) | ||||
−0.715567 | + | 0.698544i | \(0.753832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.8689 | 1.34456 | 0.672280 | − | 0.740297i | \(-0.265315\pi\) | ||||
0.672280 | + | 0.740297i | \(0.265315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.46908 | −0.347118 | −0.173559 | − | 0.984824i | \(-0.555527\pi\) | ||||
−0.173559 | + | 0.984824i | \(0.555527\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.52200 | −0.301802 | −0.150901 | − | 0.988549i | \(-0.548218\pi\) | ||||
−0.150901 | + | 0.988549i | \(0.548218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.77053 | −0.174107 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.69239 | −0.261185 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.9726 | 0.866882 | 0.433441 | − | 0.901182i | \(-0.357299\pi\) | ||||
0.433441 | + | 0.901182i | \(0.357299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.6525 | −2.26396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.44136 | −0.110857 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.6822 | 0.937199 | 0.468599 | − | 0.883411i | \(-0.344759\pi\) | ||||
0.468599 | + | 0.883411i | \(0.344759\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.2184 | 0.731925 | 0.365963 | − | 0.930630i | \(-0.380740\pi\) | ||||
0.365963 | + | 0.930630i | \(0.380740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 50.8738 | 2.29124 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.80726 | −0.125923 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.8935 | 1.20392 | 0.601958 | − | 0.798527i | \(-0.294387\pi\) | ||||
0.601958 | + | 0.798527i | \(0.294387\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.561440 | 0.0250334 | 0.0125167 | − | 0.999922i | \(-0.496016\pi\) | ||||
0.0125167 | + | 0.999922i | \(0.496016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.1802 | 1.25400 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.50788 | −0.332781 | −0.166391 | − | 0.986060i | \(-0.553211\pi\) | ||||
−0.166391 | + | 0.986060i | \(0.553211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.420431 | 0.0185988 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.3399 | 0.852220 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.60817 | −0.158077 | −0.0790384 | − | 0.996872i | \(-0.525185\pi\) | ||||
−0.0790384 | + | 0.996872i | \(0.525185\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.3913 | 0.673013 | 0.336506 | − | 0.941681i | \(-0.390755\pi\) | ||||
0.336506 | + | 0.941681i | \(0.390755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.4962 | 0.805708 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1953 | −0.791099 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.20809 | 0.268902 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.0618 | −1.16998 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.85837 | −0.337858 | −0.168929 | − | 0.985628i | \(-0.554031\pi\) | ||||
−0.168929 | + | 0.985628i | \(0.554031\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.5014 | 0.621173 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.7441 | 1.48555 | 0.742775 | − | 0.669541i | \(-0.233509\pi\) | ||||
0.742775 | + | 0.669541i | \(0.233509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.4129 | −2.53107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.83942 | −0.290842 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.1420 | −0.599214 | −0.299607 | − | 0.954063i | \(-0.596856\pi\) | ||||
−0.299607 | + | 0.954063i | \(0.596856\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.0108 | −1.86146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.6519 | 0.870373 | 0.435187 | − | 0.900340i | \(-0.356682\pi\) | ||||
0.435187 | + | 0.900340i | \(0.356682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.73152 | 0.199057 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.0737 | −0.799611 | −0.399805 | − | 0.916600i | \(-0.630922\pi\) | ||||
−0.399805 | + | 0.916600i | \(0.630922\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.33635 | 0.139622 | 0.0698110 | − | 0.997560i | \(-0.477760\pi\) | ||||
0.0698110 | + | 0.997560i | \(0.477760\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.47707 | 0.0615979 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.54116 | −0.230682 | −0.115341 | − | 0.993326i | \(-0.536796\pi\) | ||||
−0.115341 | + | 0.993326i | \(0.536796\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.8307 | −0.615283 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.5147 | 0.764183 | 0.382092 | − | 0.924124i | \(-0.375204\pi\) | ||||
0.382092 | + | 0.924124i | \(0.375204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.6008 | −0.890045 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.4582 | 1.62035 | 0.810177 | − | 0.586186i | \(-0.199371\pi\) | ||||
0.810177 | + | 0.586186i | \(0.199371\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.9209 | 0.857672 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.3132 | −1.52457 | −0.762287 | − | 0.647239i | \(-0.775924\pi\) | ||||
−0.762287 | + | 0.647239i | \(0.775924\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.5132 | 1.36703 | 0.683516 | − | 0.729935i | \(-0.260450\pi\) | ||||
0.683516 | + | 0.729935i | \(0.260450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5608 | −0.631591 | −0.315796 | − | 0.948827i | \(-0.602271\pi\) | ||||
−0.315796 | + | 0.948827i | \(0.602271\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.4265 | −2.52551 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.9534 | −1.08864 | −0.544319 | − | 0.838878i | \(-0.683212\pi\) | ||||
−0.544319 | + | 0.838878i | \(0.683212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.1595 | −0.570040 | −0.285020 | − | 0.958522i | \(-0.592000\pi\) | ||||
−0.285020 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.7923 | −0.916098 | −0.458049 | − | 0.888927i | \(-0.651452\pi\) | ||||
−0.458049 | + | 0.888927i | \(0.651452\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.65956 | 0.226745 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.1767 | −0.847066 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 62.0112 | 2.47255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.60859 | 0.143656 | 0.0718278 | − | 0.997417i | \(-0.477117\pi\) | ||||
0.0718278 | + | 0.997417i | \(0.477117\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.57065 | −0.260748 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.3434 | −1.16263 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.4830 | 1.95446 | 0.977230 | − | 0.212183i | \(-0.0680572\pi\) | ||||
0.977230 | + | 0.212183i | \(0.0680572\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.4709 | 1.87207 | 0.936034 | − | 0.351908i | \(-0.114467\pi\) | ||||
0.936034 | + | 0.351908i | \(0.114467\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.6658 | −1.00903 | −0.504514 | − | 0.863404i | \(-0.668328\pi\) | ||||
−0.504514 | + | 0.863404i | \(0.668328\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.11555 | 0.0436547 | 0.0218273 | − | 0.999762i | \(-0.493052\pi\) | ||||
0.0218273 | + | 0.999762i | \(0.493052\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.8348 | 1.55647 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.5988 | −1.03614 | −0.518071 | − | 0.855338i | \(-0.673350\pi\) | ||||
−0.518071 | + | 0.855338i | \(0.673350\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.45103 | 0.250916 | 0.125458 | − | 0.992099i | \(-0.459960\pi\) | ||||
0.125458 | + | 0.992099i | \(0.459960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −24.4324 | −0.947448 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.4165 | 0.596929 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.48012 | −0.249790 | −0.124895 | − | 0.992170i | \(-0.539859\pi\) | ||||
−0.124895 | + | 0.992170i | \(0.539859\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.48486 | −0.210800 | −0.105400 | − | 0.994430i | \(-0.533612\pi\) | ||||
−0.105400 | + | 0.994430i | \(0.533612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.63218 | 0.0626373 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.9800 | −0.458402 | −0.229201 | − | 0.973379i | \(-0.573611\pi\) | ||||
−0.229201 | + | 0.973379i | \(0.573611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.9932 | −0.763901 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.19108 | 0.121570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.9522 | −0.949226 | −0.474613 | − | 0.880195i | \(-0.657412\pi\) | ||||
−0.474613 | + | 0.880195i | \(0.657412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.0761 | 1.14085 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.75331 | −0.293678 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.1665 | 0.610600 | 0.305300 | − | 0.952256i | \(-0.401243\pi\) | ||||
0.305300 | + | 0.952256i | \(0.401243\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −72.4197 | −2.73136 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.8400 | −0.708550 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.3518 | −1.13989 | −0.569943 | − | 0.821684i | \(-0.693035\pi\) | ||||
−0.569943 | + | 0.821684i | \(0.693035\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.60499 | 0.209908 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.6654 | 1.40468 | 0.702341 | − | 0.711840i | \(-0.252138\pi\) | ||||
0.702341 | + | 0.711840i | \(0.252138\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9298 | −0.481530 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.73933 | 0.176014 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.4997 | 1.76167 | 0.880833 | − | 0.473428i | \(-0.156984\pi\) | ||||
0.880833 | + | 0.473428i | \(0.156984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.9653 | 2.03296 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.1572 | 0.596781 | 0.298391 | − | 0.954444i | \(-0.403550\pi\) | ||||
0.298391 | + | 0.954444i | \(0.403550\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.4917 | 1.85737 | 0.928684 | − | 0.370871i | \(-0.120941\pi\) | ||||
0.928684 | + | 0.370871i | \(0.120941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.2859 | 0.780902 | 0.390451 | − | 0.920624i | \(-0.372319\pi\) | ||||
0.390451 | + | 0.920624i | \(0.372319\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.8540 | −0.690759 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0922 | 0.661075 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.79656 | 0.175029 | 0.0875145 | − | 0.996163i | \(-0.472108\pi\) | ||||
0.0875145 | + | 0.996163i | \(0.472108\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.19952 | −0.262017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.2400 | −1.02640 | −0.513200 | − | 0.858269i | \(-0.671540\pi\) | ||||
−0.513200 | + | 0.858269i | \(0.671540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.78628 | 0.354752 | 0.177376 | − | 0.984143i | \(-0.443239\pi\) | ||||
0.177376 | + | 0.984143i | \(0.443239\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.69498 | −0.350982 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −60.7623 | −2.19400 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.4358 | 1.67452 | 0.837259 | − | 0.546807i | \(-0.184157\pi\) | ||||
0.837259 | + | 0.546807i | \(0.184157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.8843 | −1.75825 | −0.879123 | − | 0.476595i | \(-0.841871\pi\) | ||||
−0.879123 | + | 0.476595i | \(0.841871\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.72308 | 0.0618950 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.05470 | 0.324418 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −35.7833 | −1.27716 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.29963 | 0.117619 | 0.0588096 | − | 0.998269i | \(-0.481270\pi\) | ||||
0.0588096 | + | 0.998269i | \(0.481270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.16327 | −0.112473 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −61.3365 | −2.17812 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.7072 | −1.08770 | −0.543852 | − | 0.839181i | \(-0.683035\pi\) | ||||
−0.543852 | + | 0.839181i | \(0.683035\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 77.9647 | 2.75819 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.33974 | 0.223446 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.0909 | −0.741518 | −0.370759 | − | 0.928729i | \(-0.620902\pi\) | ||||
−0.370759 | + | 0.928729i | \(0.620902\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.2483 | 1.58888 | 0.794441 | − | 0.607342i | \(-0.207764\pi\) | ||||
0.794441 | + | 0.607342i | \(0.207764\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.19742 | −0.112001 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64.1911 | −2.24576 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.29830 | 0.254713 | 0.127356 | − | 0.991857i | \(-0.459351\pi\) | ||||
0.127356 | + | 0.991857i | \(0.459351\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.8711 | −1.07610 | −0.538050 | − | 0.842913i | \(-0.680839\pi\) | ||||
−0.538050 | + | 0.842913i | \(0.680839\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.0220 | −1.18306 | −0.591530 | − | 0.806283i | \(-0.701476\pi\) | ||||
−0.591530 | + | 0.806283i | \(0.701476\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.5040 | 1.51096 | 0.755478 | − | 0.655174i | \(-0.227405\pi\) | ||||
0.755478 | + | 0.655174i | \(0.227405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.6471 | 1.26975 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.4797 | 1.36625 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.8583 | 1.13439 | 0.567197 | − | 0.823582i | \(-0.308028\pi\) | ||||
0.567197 | + | 0.823582i | \(0.308028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.4655 | 0.705708 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.7322 | 1.47003 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.7915 | 0.644165 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.5423 | 0.395201 | 0.197600 | − | 0.980283i | \(-0.436685\pi\) | ||||
0.197600 | + | 0.980283i | \(0.436685\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.54480 | −0.291885 | −0.145942 | − | 0.989293i | \(-0.546621\pi\) | ||||
−0.145942 | + | 0.989293i | \(0.546621\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.4781 | 1.89289 | 0.946443 | − | 0.322869i | \(-0.104647\pi\) | ||||
0.946443 | + | 0.322869i | \(0.104647\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.751023 | −0.0255651 | −0.0127826 | − | 0.999918i | \(-0.504069\pi\) | ||||
−0.0127826 | + | 0.999918i | \(0.504069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.1444 | −1.12694 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.7047 | 0.532133 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.4102 | 0.554768 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.93104 | 0.234045 | 0.117022 | − | 0.993129i | \(-0.462665\pi\) | ||||
0.117022 | + | 0.993129i | \(0.462665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.45456 | −0.183769 | −0.0918844 | − | 0.995770i | \(-0.529289\pi\) | ||||
−0.0918844 | + | 0.995770i | \(0.529289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.1936 | −1.52088 | −0.760442 | − | 0.649406i | \(-0.775018\pi\) | ||||
−0.760442 | + | 0.649406i | \(0.775018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.7926 | −1.33611 | −0.668053 | − | 0.744114i | \(-0.732872\pi\) | ||||
−0.668053 | + | 0.744114i | \(0.732872\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.39283 | 0.147331 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −91.0510 | −3.04691 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.8033 | −0.461393 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9842 | 0.599808 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.98535 | −0.132771 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.5010 | −0.681478 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.25231 | 0.207605 | 0.103802 | − | 0.994598i | \(-0.466899\pi\) | ||||
0.103802 | + | 0.994598i | \(0.466899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.0042 | −1.55732 | −0.778659 | − | 0.627447i | \(-0.784100\pi\) | ||||
−0.778659 | + | 0.627447i | \(0.784100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.6317 | −0.879455 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.7422 | −1.21201 | −0.606007 | − | 0.795460i | \(-0.707230\pi\) | ||||
−0.606007 | + | 0.795460i | \(0.707230\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.6926 | 0.384866 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.77688 | 0.189943 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.1704 | 0.793005 | 0.396503 | − | 0.918034i | \(-0.370224\pi\) | ||||
0.396503 | + | 0.918034i | \(0.370224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.7983 | −1.40266 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.8459 | −0.811681 | −0.405840 | − | 0.913944i | \(-0.633021\pi\) | ||||
−0.405840 | + | 0.913944i | \(0.633021\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.36285 | −0.174824 | −0.0874120 | − | 0.996172i | \(-0.527860\pi\) | ||||
−0.0874120 | + | 0.996172i | \(0.527860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.34952 | −0.0765108 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.39581 | −0.0453576 | −0.0226788 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226788 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.75114 | −0.0568445 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.7702 | 0.834780 | 0.417390 | − | 0.908728i | \(-0.362945\pi\) | ||||
0.417390 | + | 0.908728i | \(0.362945\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.0170 | −0.421221 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.3665 | 0.431627 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.4615 | −0.789079 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30.9532 | 0.996420 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.4436 | −1.20410 | −0.602052 | − | 0.798457i | \(-0.705650\pi\) | ||||
−0.602052 | + | 0.798457i | \(0.705650\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.1236 | −1.25554 | −0.627768 | − | 0.778400i | \(-0.716031\pi\) | ||||
−0.627768 | + | 0.778400i | \(0.716031\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.1075 | −0.644615 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.3777 | 0.843896 | 0.421948 | − | 0.906620i | \(-0.361347\pi\) | ||||
0.421948 | + | 0.906620i | \(0.361347\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.7779 | −1.20493 | −0.602463 | − | 0.798147i | \(-0.705814\pi\) | ||||
−0.602463 | + | 0.798147i | \(0.705814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.2278 | −0.835686 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.6564 | 0.529641 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.8482 | −0.916393 | −0.458197 | − | 0.888851i | \(-0.651504\pi\) | ||||
−0.458197 | + | 0.888851i | \(0.651504\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.4109 | 1.34452 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0341 | −0.539474 | −0.269737 | − | 0.962934i | \(-0.586937\pi\) | ||||
−0.269737 | + | 0.962934i | \(0.586937\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8712.2.a.ch.1.6 | 6 | ||
3.2 | odd | 2 | 8712.2.a.cj.1.1 | 6 | |||
11.5 | even | 5 | 792.2.r.i.289.1 | yes | 12 | ||
11.9 | even | 5 | 792.2.r.i.433.1 | yes | 12 | ||
11.10 | odd | 2 | 8712.2.a.ci.1.6 | 6 | |||
33.5 | odd | 10 | 792.2.r.h.289.3 | ✓ | 12 | ||
33.20 | odd | 10 | 792.2.r.h.433.3 | yes | 12 | ||
33.32 | even | 2 | 8712.2.a.ck.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
792.2.r.h.289.3 | ✓ | 12 | 33.5 | odd | 10 | ||
792.2.r.h.433.3 | yes | 12 | 33.20 | odd | 10 | ||
792.2.r.i.289.1 | yes | 12 | 11.5 | even | 5 | ||
792.2.r.i.433.1 | yes | 12 | 11.9 | even | 5 | ||
8712.2.a.ch.1.6 | 6 | 1.1 | even | 1 | trivial | ||
8712.2.a.ci.1.6 | 6 | 11.10 | odd | 2 | |||
8712.2.a.cj.1.1 | 6 | 3.2 | odd | 2 | |||
8712.2.a.ck.1.1 | 6 | 33.32 | even | 2 |