Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.461844.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 14x^{2} - 12x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.352593\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.647407 | −0.244697 | −0.122348 | − | 0.992487i | \(-0.539043\pi\) | ||||
−0.122348 | + | 0.992487i | \(0.539043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.502467 | 0.151500 | 0.0757498 | − | 0.997127i | \(-0.475865\pi\) | ||||
0.0757498 | + | 0.997127i | \(0.475865\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.73074 | 1.14737 | 0.573686 | − | 0.819075i | \(-0.305513\pi\) | ||||
0.573686 | + | 0.819075i | \(0.305513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.58086 | −1.50975 | −0.754877 | − | 0.655867i | \(-0.772303\pi\) | ||||
−0.754877 | + | 0.655867i | \(0.772303\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.647407 | 0.141276 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.85013 | −0.594292 | −0.297146 | − | 0.954832i | \(-0.596035\pi\) | ||||
−0.297146 | + | 0.954832i | \(0.596035\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.294814 | 0.0547456 | 0.0273728 | − | 0.999625i | \(-0.491286\pi\) | ||||
0.0273728 | + | 0.999625i | \(0.491286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.20272 | 0.395620 | 0.197810 | − | 0.980240i | \(-0.436617\pi\) | ||||
0.197810 | + | 0.980240i | \(0.436617\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.502467 | −0.0874683 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.28605 | −1.19782 | −0.598910 | − | 0.800817i | \(-0.704399\pi\) | ||||
−0.598910 | + | 0.800817i | \(0.704399\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.58580 | 1.18470 | 0.592351 | − | 0.805680i | \(-0.298200\pi\) | ||||
0.592351 | + | 0.805680i | \(0.298200\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.444688 | −0.0678143 | −0.0339072 | − | 0.999425i | \(-0.510795\pi\) | ||||
−0.0339072 | + | 0.999425i | \(0.510795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.07840 | −1.17836 | −0.589178 | − | 0.808004i | \(-0.700548\pi\) | ||||
−0.589178 | + | 0.808004i | \(0.700548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58086 | −0.940123 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.73074 | −0.662436 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.7220 | 1.74750 | 0.873749 | − | 0.486377i | \(-0.161682\pi\) | ||||
0.873749 | + | 0.486377i | \(0.161682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.58086 | 0.871657 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8141 | 1.40787 | 0.703936 | − | 0.710263i | \(-0.251424\pi\) | ||||
0.703936 | + | 0.710263i | \(0.251424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4359 | 1.46422 | 0.732110 | − | 0.681186i | \(-0.238536\pi\) | ||||
0.732110 | + | 0.681186i | \(0.238536\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.647407 | −0.0815656 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.63864 | 1.05538 | 0.527689 | − | 0.849438i | \(-0.323059\pi\) | ||||
0.527689 | + | 0.849438i | \(0.323059\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.85013 | 0.343115 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.58086 | −0.306292 | −0.153146 | − | 0.988204i | \(-0.548941\pi\) | ||||
−0.153146 | + | 0.988204i | \(0.548941\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.6114 | −1.24196 | −0.620982 | − | 0.783825i | \(-0.713266\pi\) | ||||
−0.620982 | + | 0.783825i | \(0.713266\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.325301 | −0.0370715 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.28605 | 0.594727 | 0.297364 | − | 0.954764i | \(-0.403893\pi\) | ||||
0.297364 | + | 0.954764i | \(0.403893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.35259 | −0.587523 | −0.293762 | − | 0.955879i | \(-0.594907\pi\) | ||||
−0.293762 | + | 0.955879i | \(0.594907\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.294814 | −0.0316074 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.99507 | 0.529476 | 0.264738 | − | 0.964320i | \(-0.414715\pi\) | ||||
0.264738 | + | 0.964320i | \(0.414715\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.647407 | 0.0678667 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.20272 | −0.228411 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.29481 | 0.131468 | 0.0657342 | − | 0.997837i | \(-0.479061\pi\) | ||||
0.0657342 | + | 0.997837i | \(0.479061\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.502467 | 0.0504999 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.28605 | −0.426478 | −0.213239 | − | 0.977000i | \(-0.568401\pi\) | ||||
−0.213239 | + | 0.977000i | \(0.568401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.25556 | −0.714912 | −0.357456 | − | 0.933930i | \(-0.616356\pi\) | ||||
−0.357456 | + | 0.933930i | \(0.616356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.1362 | −0.979901 | −0.489951 | − | 0.871750i | \(-0.662985\pi\) | ||||
−0.489951 | + | 0.871750i | \(0.662985\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4527 | 1.67167 | 0.835833 | − | 0.548983i | \(-0.184985\pi\) | ||||
0.835833 | + | 0.548983i | \(0.184985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.28605 | 0.691561 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.8669 | −1.49263 | −0.746317 | − | 0.665591i | \(-0.768180\pi\) | ||||
−0.746317 | + | 0.665591i | \(0.768180\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.06271 | −0.280758 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7475 | −0.977048 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.58580 | −0.683988 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.99124 | −0.886579 | −0.443289 | − | 0.896379i | \(-0.646189\pi\) | ||||
−0.443289 | + | 0.896379i | \(0.646189\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.444688 | 0.0391526 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.2811 | 1.42249 | 0.711244 | − | 0.702945i | \(-0.248132\pi\) | ||||
0.711244 | + | 0.702945i | \(0.248132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.26050 | 0.369432 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.73567 | −0.404596 | −0.202298 | − | 0.979324i | \(-0.564841\pi\) | ||||
−0.202298 | + | 0.979324i | \(0.564841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.4615 | −1.48106 | −0.740532 | − | 0.672022i | \(-0.765426\pi\) | ||||
−0.740532 | + | 0.672022i | \(0.765426\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.07840 | 0.680324 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.502467 | −0.0420184 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.58086 | 0.542781 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.29481 | 0.433768 | 0.216884 | − | 0.976197i | \(-0.430411\pi\) | ||||
0.216884 | + | 0.976197i | \(0.430411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5143 | 1.50667 | 0.753337 | − | 0.657635i | \(-0.228443\pi\) | ||||
0.753337 | + | 0.657635i | \(0.228443\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.73074 | 0.382458 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5809 | 1.40311 | 0.701553 | − | 0.712617i | \(-0.252490\pi\) | ||||
0.701553 | + | 0.712617i | \(0.252490\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.7220 | −1.00892 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.84519 | 0.145421 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0119 | 0.784189 | 0.392094 | − | 0.919925i | \(-0.371751\pi\) | ||||
0.392094 | + | 0.919925i | \(0.371751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.69642 | 0.672949 | 0.336475 | − | 0.941693i | \(-0.390765\pi\) | ||||
0.336475 | + | 0.941693i | \(0.390765\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.58086 | −0.503251 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0069 | −1.36904 | −0.684520 | − | 0.728994i | \(-0.739988\pi\) | ||||
−0.684520 | + | 0.728994i | \(0.739988\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.8141 | −0.812835 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.73457 | −0.204391 | −0.102196 | − | 0.994764i | \(-0.532587\pi\) | ||||
−0.102196 | + | 0.994764i | \(0.532587\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.8757 | 1.25436 | 0.627180 | − | 0.778875i | \(-0.284209\pi\) | ||||
0.627180 | + | 0.778875i | \(0.284209\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4359 | −0.845368 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.37704 | 0.173826 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.647407 | 0.0470919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5896 | 0.910954 | 0.455477 | − | 0.890248i | \(-0.349469\pi\) | ||||
0.455477 | + | 0.890248i | \(0.349469\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0728 | 1.44487 | 0.722437 | − | 0.691437i | \(-0.243022\pi\) | ||||
0.722437 | + | 0.691437i | \(0.243022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.6163 | 1.11261 | 0.556307 | − | 0.830977i | \(-0.312218\pi\) | ||||
0.556307 | + | 0.830977i | \(0.312218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7307 | −1.11512 | −0.557561 | − | 0.830136i | \(-0.688263\pi\) | ||||
−0.557561 | + | 0.830136i | \(0.688263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.63864 | −0.609323 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.190865 | −0.0133961 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.85013 | −0.198097 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.30667 | −0.228727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.85013 | 0.471582 | 0.235791 | − | 0.971804i | \(-0.424232\pi\) | ||||
0.235791 | + | 0.971804i | \(0.424232\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.58086 | 0.176838 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.42606 | −0.0968070 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.6114 | 0.717049 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.73074 | −0.318224 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.15974 | 0.0776621 | 0.0388311 | − | 0.999246i | \(-0.487637\pi\) | ||||
0.0388311 | + | 0.999246i | \(0.487637\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.1207 | 1.73369 | 0.866847 | − | 0.498574i | \(-0.166143\pi\) | ||||
0.866847 | + | 0.498574i | \(0.166143\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.02062 | −0.265690 | −0.132845 | − | 0.991137i | \(-0.542411\pi\) | ||||
−0.132845 | + | 0.991137i | \(0.542411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.325301 | 0.0214032 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.99507 | −0.458262 | −0.229131 | − | 0.973396i | \(-0.573588\pi\) | ||||
−0.229131 | + | 0.973396i | \(0.573588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.28605 | −0.343366 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.4037 | −0.996382 | −0.498191 | − | 0.867067i | \(-0.666002\pi\) | ||||
−0.498191 | + | 0.867067i | \(0.666002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.14987 | 0.331733 | 0.165866 | − | 0.986148i | \(-0.446958\pi\) | ||||
0.165866 | + | 0.986148i | \(0.446958\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.58086 | 0.418730 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.35259 | 0.339207 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.5858 | 1.11001 | 0.555003 | − | 0.831848i | \(-0.312717\pi\) | ||||
0.555003 | + | 0.831848i | \(0.312717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.43209 | −0.0900350 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.3421 | 0.957013 | 0.478507 | − | 0.878084i | \(-0.341178\pi\) | ||||
0.478507 | + | 0.878084i | \(0.341178\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.71704 | 0.293103 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.294814 | 0.0182485 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.0168 | −1.29595 | −0.647975 | − | 0.761661i | \(-0.724384\pi\) | ||||
−0.647975 | + | 0.761661i | \(0.724384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.99507 | −0.305693 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.57210 | −0.339737 | −0.169868 | − | 0.985467i | \(-0.554334\pi\) | ||||
−0.169868 | + | 0.985467i | \(0.554334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50939 | −0.334671 | −0.167336 | − | 0.985900i | \(-0.553516\pi\) | ||||
−0.167336 | + | 0.985900i | \(0.553516\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.647407 | −0.0391829 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.5672 | 1.77652 | 0.888259 | − | 0.459342i | \(-0.151915\pi\) | ||||
0.888259 | + | 0.459342i | \(0.151915\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.20272 | 0.131873 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.14111 | −0.306693 | −0.153346 | − | 0.988172i | \(-0.549005\pi\) | ||||
−0.153346 | + | 0.988172i | \(0.549005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.3509 | −0.853070 | −0.426535 | − | 0.904471i | \(-0.640266\pi\) | ||||
−0.426535 | + | 0.904471i | \(0.640266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.91110 | −0.289893 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.37989 | 0.316464 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.29481 | −0.0759033 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.4516 | 0.902693 | 0.451346 | − | 0.892349i | \(-0.350944\pi\) | ||||
0.451346 | + | 0.892349i | \(0.350944\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.502467 | −0.0291561 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.85013 | 0.164827 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.287894 | 0.0165940 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.28605 | 0.246227 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12432 | 0.121241 | 0.0606207 | − | 0.998161i | \(-0.480692\pi\) | ||||
0.0606207 | + | 0.998161i | \(0.480692\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.25556 | 0.412755 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.6331 | 1.85045 | 0.925226 | − | 0.379417i | \(-0.123875\pi\) | ||||
0.925226 | + | 0.379417i | \(0.123875\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7318 | −1.05879 | −0.529393 | − | 0.848377i | \(-0.677580\pi\) | ||||
−0.529393 | + | 0.848377i | \(0.677580\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.3452 | −1.47969 | −0.739846 | − | 0.672776i | \(-0.765102\pi\) | ||||
−0.739846 | + | 0.672776i | \(0.765102\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.148134 | 0.00829393 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.1362 | 0.565746 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.1323 | −1.73225 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.4527 | −0.965137 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.23001 | 0.288340 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.3116 | 1.33629 | 0.668143 | − | 0.744033i | \(-0.267089\pi\) | ||||
0.668143 | + | 0.744033i | \(0.267089\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.28605 | −0.399273 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.72382 | 0.0939024 | 0.0469512 | − | 0.998897i | \(-0.485049\pi\) | ||||
0.0469512 | + | 0.998897i | \(0.485049\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.8669 | 0.861772 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.10679 | 0.0599362 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.79235 | 0.474742 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.44086 | −0.184715 | −0.0923575 | − | 0.995726i | \(-0.529440\pi\) | ||||
−0.0923575 | + | 0.995726i | \(0.529440\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.2059 | 0.653368 | 0.326684 | − | 0.945134i | \(-0.394069\pi\) | ||||
0.326684 | + | 0.945134i | \(0.394069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.3967 | 0.872707 | 0.436353 | − | 0.899775i | \(-0.356270\pi\) | ||||
0.436353 | + | 0.899775i | \(0.356270\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.06271 | 0.162096 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.511231 | 0.0269817 | 0.0134909 | − | 0.999909i | \(-0.495706\pi\) | ||||
0.0134909 | + | 0.999909i | \(0.495706\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.3078 | 1.27936 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7475 | 0.564099 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.3028 | 0.851001 | 0.425501 | − | 0.904958i | \(-0.360098\pi\) | ||||
0.425501 | + | 0.904958i | \(0.360098\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.58580 | 0.394901 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.23630 | −0.427607 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.3372 | 1.67435 | 0.837177 | − | 0.546932i | \(-0.184204\pi\) | ||||
0.837177 | + | 0.546932i | \(0.184204\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.294814 | −0.0151837 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.36445 | 0.481019 | 0.240510 | − | 0.970647i | \(-0.422685\pi\) | ||||
0.240510 | + | 0.970647i | \(0.422685\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.99124 | 0.511867 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.0423 | 0.513140 | 0.256570 | − | 0.966526i | \(-0.417408\pi\) | ||||
0.256570 | + | 0.966526i | \(0.417408\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.444688 | −0.0226048 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.8974 | 1.82007 | 0.910035 | − | 0.414531i | \(-0.136054\pi\) | ||||
0.910035 | + | 0.414531i | \(0.136054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.4832 | −0.681875 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.2811 | −0.821274 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 39.2979 | 1.97231 | 0.986153 | − | 0.165840i | \(-0.0530336\pi\) | ||||
0.986153 | + | 0.165840i | \(0.0530336\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.26050 | −0.213292 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.69333 | −0.134499 | −0.0672493 | − | 0.997736i | \(-0.521422\pi\) | ||||
−0.0672493 | + | 0.997736i | \(0.521422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.20272 | −0.109725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.66100 | −0.181469 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8963 | 1.28049 | 0.640245 | − | 0.768171i | \(-0.278833\pi\) | ||||
0.640245 | + | 0.768171i | \(0.278833\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.73567 | 0.233594 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.00110 | −0.344502 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.4615 | 0.855092 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.0374 | −0.930038 | −0.465019 | − | 0.885301i | \(-0.653953\pi\) | ||||
−0.465019 | + | 0.885301i | \(0.653953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.5721 | 1.10010 | 0.550048 | − | 0.835133i | \(-0.314609\pi\) | ||||
0.550048 | + | 0.835133i | \(0.314609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.07840 | −0.392785 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.40370 | −0.358290 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.502467 | 0.0242593 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.75246 | −0.469760 | −0.234880 | − | 0.972024i | \(-0.575470\pi\) | ||||
−0.234880 | + | 0.972024i | \(0.575470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.14604 | 0.391474 | 0.195737 | − | 0.980656i | \(-0.437290\pi\) | ||||
0.195737 | + | 0.980656i | \(0.437290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.7563 | 0.897235 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.870744 | 0.0415583 | 0.0207792 | − | 0.999784i | \(-0.493385\pi\) | ||||
0.0207792 | + | 0.999784i | \(0.493385\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.58086 | −0.313374 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.3470 | −1.58436 | −0.792182 | − | 0.610284i | \(-0.791055\pi\) | ||||
−0.792182 | + | 0.610284i | \(0.791055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.29481 | −0.250436 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.0641 | 1.79635 | 0.898177 | − | 0.439634i | \(-0.144892\pi\) | ||||
0.898177 | + | 0.439634i | \(0.144892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.81161 | 0.179482 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.5143 | −0.869879 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0938351 | 0.00438942 | 0.00219471 | − | 0.999998i | \(-0.499301\pi\) | ||||
0.00219471 | + | 0.999998i | \(0.499301\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.73074 | −0.220812 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.1617 | −1.45135 | −0.725673 | − | 0.688040i | \(-0.758472\pi\) | ||||
−0.725673 | + | 0.688040i | \(0.758472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7748 | 0.779592 | 0.389796 | − | 0.920901i | \(-0.372546\pi\) | ||||
0.389796 | + | 0.920901i | \(0.372546\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.7594 | −1.14573 | −0.572864 | − | 0.819651i | \(-0.694168\pi\) | ||||
−0.572864 | + | 0.819651i | \(0.694168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.59272 | −0.258248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.5809 | −0.810083 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.223441 | −0.0102738 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.7220 | 0.582499 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.8130 | 0.768204 | 0.384102 | − | 0.923291i | \(-0.374511\pi\) | ||||
0.384102 | + | 0.923291i | \(0.374511\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.28605 | 0.332215 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.84519 | −0.0839591 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.78741 | −0.262253 | −0.131126 | − | 0.991366i | \(-0.541859\pi\) | ||||
−0.131126 | + | 0.991366i | \(0.541859\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.0119 | −0.452752 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.650602 | −0.0293612 | −0.0146806 | − | 0.999892i | \(-0.504673\pi\) | ||||
−0.0146806 | + | 0.999892i | \(0.504673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.39469 | 0.0628136 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.67087 | 0.0749487 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.5300 | −1.41148 | −0.705738 | − | 0.708472i | \(-0.749385\pi\) | ||||
−0.705738 | + | 0.708472i | \(0.749385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.69642 | −0.388527 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.61135 | −0.116434 | −0.0582172 | − | 0.998304i | \(-0.518542\pi\) | ||||
−0.0582172 | + | 0.998304i | \(0.518542\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.27037 | −0.100632 | −0.0503161 | − | 0.998733i | \(-0.516023\pi\) | ||||
−0.0503161 | + | 0.998733i | \(0.516023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.86986 | 0.303905 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.58086 | 0.290552 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.05913 | −0.178520 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.0069 | 0.790416 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.87185 | 0.125818 | 0.0629090 | − | 0.998019i | \(-0.479962\pi\) | ||||
0.0629090 | + | 0.998019i | \(0.479962\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.1469 | −0.618602 | −0.309301 | − | 0.950964i | \(-0.600095\pi\) | ||||
−0.309301 | + | 0.950964i | \(0.600095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.4205 | 0.453924 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.8768 | −0.646817 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8141 | 0.469291 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.58580 | −0.328577 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.73457 | 0.118005 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.30667 | −0.142428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5504 | 0.625570 | 0.312785 | − | 0.949824i | \(-0.398738\pi\) | ||||
0.312785 | + | 0.949824i | \(0.398738\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.8757 | −0.724205 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5378 | −0.578834 | −0.289417 | − | 0.957203i | \(-0.593461\pi\) | ||||
−0.289417 | + | 0.957203i | \(0.593461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.4359 | 0.488073 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.94013 | −0.0826524 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.42223 | −0.145528 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.20098 | 0.135630 | 0.0678149 | − | 0.997698i | \(-0.478397\pi\) | ||||
0.0678149 | + | 0.997698i | \(0.478397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.444688 | 0.0188083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.37704 | −0.100359 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.0088 | −0.590399 | −0.295200 | − | 0.955436i | \(-0.595386\pi\) | ||||
−0.295200 | + | 0.955436i | \(0.595386\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.647407 | −0.0271885 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.0571 | 1.17622 | 0.588108 | − | 0.808782i | \(-0.299873\pi\) | ||||
0.588108 | + | 0.808782i | \(0.299873\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.4733 | 1.81930 | 0.909651 | − | 0.415373i | \(-0.136349\pi\) | ||||
0.909651 | + | 0.415373i | \(0.136349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.5896 | −0.525939 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.6281 | 1.73300 | 0.866501 | − | 0.499175i | \(-0.166364\pi\) | ||||
0.866501 | + | 0.499175i | \(0.166364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.0728 | −0.834198 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.46531 | 0.143765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.39237 | 0.264745 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.2489 | 1.70252 | 0.851262 | − | 0.524741i | \(-0.175838\pi\) | ||||
0.851262 | + | 0.524741i | \(0.175838\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4958 | −0.597289 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.6163 | −0.642368 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.5416 | −0.843543 | −0.421771 | − | 0.906702i | \(-0.638592\pi\) | ||||
−0.421771 | + | 0.906702i | \(0.638592\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.7307 | 0.643816 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0316 | 0.573315 | 0.286658 | − | 0.958033i | \(-0.407456\pi\) | ||||
0.286658 | + | 0.958033i | \(0.407456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.6610 | −0.598035 | −0.299017 | − | 0.954248i | \(-0.596659\pi\) | ||||
−0.299017 | + | 0.954248i | \(0.596659\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.63864 | 0.351793 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.8875 | −0.888388 | −0.444194 | − | 0.895931i | \(-0.646510\pi\) | ||||
−0.444194 | + | 0.895931i | \(0.646510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.190865 | 0.00773423 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.07840 | 0.326817 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.0099 | 0.969749 | 0.484875 | − | 0.874584i | \(-0.338865\pi\) | ||||
0.484875 | + | 0.874584i | \(0.338865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.21468 | −0.0891595 | −0.0445798 | − | 0.999006i | \(-0.514195\pi\) | ||||
−0.0445798 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.4348 | 0.499798 | 0.249899 | − | 0.968272i | \(-0.419603\pi\) | ||||
0.249899 | + | 0.968272i | \(0.419603\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.85013 | 0.114372 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.23384 | −0.129561 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.30667 | 0.132056 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.4684 | −1.37434 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4684 | 1.05369 | 0.526845 | − | 0.849961i | \(-0.323375\pi\) | ||||
0.526845 | + | 0.849961i | \(0.323375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.85013 | −0.272268 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.58086 | 0.260743 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.58086 | −0.102097 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.44852 | −0.254701 | −0.127351 | − | 0.991858i | \(-0.540647\pi\) | ||||
−0.127351 | + | 0.991858i | \(0.540647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.01863 | 0.0796071 | 0.0398035 | − | 0.999208i | \(-0.487327\pi\) | ||||
0.0398035 | + | 0.999208i | \(0.487327\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.142954 | −0.00562012 | −0.00281006 | − | 0.999996i | \(-0.500894\pi\) | ||||
−0.00281006 | + | 0.999996i | \(0.500894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.43371 | 0.213292 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.42606 | 0.0558915 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.1823 | 0.868062 | 0.434031 | − | 0.900898i | \(-0.357091\pi\) | ||||
0.434031 | + | 0.900898i | \(0.357091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.6114 | −0.413988 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.4989 | 1.11016 | 0.555079 | − | 0.831797i | \(-0.312688\pi\) | ||||
0.555079 | + | 0.831797i | \(0.312688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8680 | −0.850567 | −0.425284 | − | 0.905060i | \(-0.639826\pi\) | ||||
−0.425284 | + | 0.905060i | \(0.639826\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.73074 | 0.183727 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.840257 | −0.0325349 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.15974 | −0.0448382 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.74618 | 0.221829 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0679 | 0.388089 | 0.194044 | − | 0.980993i | \(-0.437839\pi\) | ||||
0.194044 | + | 0.980993i | \(0.437839\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.7003 | 1.06461 | 0.532304 | − | 0.846554i | \(-0.321326\pi\) | ||||
0.532304 | + | 0.846554i | \(0.321326\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.838272 | −0.0321699 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.1207 | −1.00095 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.73631 | −0.296022 | −0.148011 | − | 0.988986i | \(-0.547287\pi\) | ||||
−0.148011 | + | 0.988986i | \(0.547287\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.02062 | 0.153396 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.7220 | −0.484669 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.7115 | 1.77699 | 0.888494 | − | 0.458888i | \(-0.151752\pi\) | ||||
0.888494 | + | 0.458888i | \(0.151752\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.325301 | −0.0123572 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.8864 | 1.35930 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.99507 | 0.264578 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −39.7670 | −1.50198 | −0.750990 | − | 0.660313i | \(-0.770423\pi\) | ||||
−0.750990 | + | 0.660313i | \(0.770423\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.9485 | 1.80841 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.77482 | 0.104358 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.5988 | −1.33694 | −0.668470 | − | 0.743739i | \(-0.733050\pi\) | ||||
−0.668470 | + | 0.743739i | \(0.733050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.28605 | 0.198242 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.27803 | −0.235114 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.4037 | 0.575262 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.6995 | 1.44325 | 0.721624 | − | 0.692285i | \(-0.243396\pi\) | ||||
0.721624 | + | 0.692285i | \(0.243396\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.69730 | 0.174937 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.14987 | −0.191526 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8788 | 0.737263 | 0.368631 | − | 0.929576i | \(-0.379826\pi\) | ||||
0.368631 | + | 0.929576i | \(0.379826\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.10370 | −0.0778083 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.2693 | 0.527047 | 0.263524 | − | 0.964653i | \(-0.415115\pi\) | ||||
0.263524 | + | 0.964653i | \(0.415115\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.34063 | 0.159889 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.3801 | −0.455410 | −0.227705 | − | 0.973730i | \(-0.573122\pi\) | ||||
−0.227705 | + | 0.973730i | \(0.573122\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.58086 | −0.241754 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.23321 | 0.155301 | 0.0776506 | − | 0.996981i | \(-0.475258\pi\) | ||||
0.0776506 | + | 0.996981i | \(0.475258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.35259 | −0.195841 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.56223 | 0.239779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.6418 | −0.753231 | −0.376616 | − | 0.926370i | \(-0.622912\pi\) | ||||
−0.376616 | + | 0.926370i | \(0.622912\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.5858 | −0.640862 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.7033 | −1.04324 | −0.521620 | − | 0.853178i | \(-0.674672\pi\) | ||||
−0.521620 | + | 0.853178i | \(0.674672\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.43209 | 0.0519817 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.53963 | −0.237061 | −0.118531 | − | 0.992950i | \(-0.537818\pi\) | ||||
−0.118531 | + | 0.992950i | \(0.537818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2990 | −0.409052 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.8141 | −0.390473 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.58690 | 0.273591 | 0.136795 | − | 0.990599i | \(-0.456320\pi\) | ||||
0.136795 | + | 0.990599i | \(0.456320\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.3421 | −0.552532 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.7151 | 0.745069 | 0.372534 | − | 0.928018i | \(-0.378489\pi\) | ||||
0.372534 | + | 0.928018i | \(0.378489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.71704 | −0.169223 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −49.9211 | −1.78861 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.29680 | −0.0464031 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.294814 | −0.0105358 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.0486 | −1.85533 | −0.927667 | − | 0.373410i | \(-0.878189\pi\) | ||||
−0.927667 | + | 0.373410i | \(0.878189\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.0168 | 0.748217 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.2724 | 0.365243 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.4359 | −0.406102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.1796 | −0.679377 | −0.339689 | − | 0.940538i | \(-0.610322\pi\) | ||||
−0.339689 | + | 0.940538i | \(0.610322\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.2168 | −1.35201 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.99507 | 0.176492 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.33186 | −0.188157 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.57210 | 0.196147 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.4803 | 1.49353 | 0.746763 | − | 0.665090i | \(-0.231607\pi\) | ||||
0.746763 | + | 0.665090i | \(0.231607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5094 | −0.755297 | −0.377648 | − | 0.925949i | \(-0.623267\pi\) | ||||
−0.377648 | + | 0.925949i | \(0.623267\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.50939 | 0.193223 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.92643 | 0.102383 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.647407 | 0.0226222 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.3067 | 0.743608 | 0.371804 | − | 0.928311i | \(-0.378739\pi\) | ||||
0.371804 | + | 0.928311i | \(0.378739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.24680 | −0.252608 | −0.126304 | − | 0.991992i | \(-0.540311\pi\) | ||||
−0.126304 | + | 0.991992i | \(0.540311\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.7076 | 1.51986 | 0.759932 | − | 0.650003i | \(-0.225232\pi\) | ||||
0.759932 | + | 0.650003i | \(0.225232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.3665 | −0.846285 | −0.423142 | − | 0.906063i | \(-0.639073\pi\) | ||||
−0.423142 | + | 0.906063i | \(0.639073\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.5672 | −1.02567 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −31.1323 | −1.07867 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.20272 | −0.0761371 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0553 | −0.623338 | −0.311669 | − | 0.950191i | \(-0.600888\pi\) | ||||
−0.311669 | + | 0.950191i | \(0.600888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9131 | −0.997003 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.14111 | 0.177069 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.95802 | 0.239081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.3509 | 0.492520 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.7662 | 0.711855 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.28679 | 0.215256 | 0.107628 | − | 0.994191i | \(-0.465675\pi\) | ||||
0.107628 | + | 0.994191i | \(0.465675\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.82074 | −0.164673 | −0.0823367 | − | 0.996605i | \(-0.526238\pi\) | ||||
−0.0823367 | + | 0.996605i | \(0.526238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.32420 | 0.249898 | 0.124949 | − | 0.992163i | \(-0.460123\pi\) | ||||
0.124949 | + | 0.992163i | \(0.460123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.91110 | 0.167370 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.0567 | 0.478495 | 0.239247 | − | 0.970959i | \(-0.423099\pi\) | ||||
0.239247 | + | 0.970959i | \(0.423099\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.37989 | −0.182710 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.65607 | 0.0901009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.63864 | −0.292709 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.29481 | 0.0438228 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6747 | 0.427994 | 0.213997 | − | 0.976834i | \(-0.431352\pi\) | ||||
0.213997 | + | 0.976834i | \(0.431352\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.4516 | −0.521170 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.0325 | −0.910747 | −0.455374 | − | 0.890300i | \(-0.650494\pi\) | ||||
−0.455374 | + | 0.890300i | \(0.650494\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.14693 | 0.274166 | 0.137083 | − | 0.990560i | \(-0.456227\pi\) | ||||
0.137083 | + | 0.990560i | \(0.456227\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.4173 | −0.887006 | −0.443503 | − | 0.896273i | \(-0.646264\pi\) | ||||
−0.443503 | + | 0.896273i | \(0.646264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.46840 | 0.216943 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.502467 | 0.0168333 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53.1628 | 1.77903 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.85013 | −0.0951629 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.649392 | 0.0216585 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.1843 | 2.00503 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.287894 | −0.00958052 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.12815 | −0.236686 | −0.118343 | − | 0.992973i | \(-0.537758\pi\) | ||||
−0.118343 | + | 0.992973i | \(0.537758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.28605 | −0.142159 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.1911 | 0.569567 | 0.284783 | − | 0.958592i | \(-0.408078\pi\) | ||||
0.284783 | + | 0.958592i | \(0.408078\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.68950 | −0.0890095 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.5405 | −0.348078 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.35888 | 0.110799 | 0.0553996 | − | 0.998464i | \(-0.482357\pi\) | ||||
0.0553996 | + | 0.998464i | \(0.482357\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.12432 | −0.0699988 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.58086 | 0.0849502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.25556 | −0.238304 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.75048 | 0.254285 | 0.127142 | − | 0.991884i | \(-0.459419\pi\) | ||||
0.127142 | + | 0.991884i | \(0.459419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43.3078 | 1.41935 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −32.6331 | −1.06836 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.75320 | 0.187949 | 0.0939744 | − | 0.995575i | \(-0.470043\pi\) | ||||
0.0939744 | + | 0.995575i | \(0.470043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.7318 | 0.611291 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.43209 | 0.0466850 | 0.0233425 | − | 0.999728i | \(-0.492569\pi\) | ||||
0.0233425 | + | 0.999728i | \(0.492569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.6205 | −0.704060 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.6830 | −1.51699 | −0.758496 | − | 0.651677i | \(-0.774066\pi\) | ||||
−0.758496 | + | 0.651677i | \(0.774066\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.6114 | 0.344459 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.3452 | 0.854301 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.1145 | −0.424819 | −0.212409 | − | 0.977181i | \(-0.568131\pi\) | ||||
−0.212409 | + | 0.977181i | \(0.568131\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.148134 | −0.00478850 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.06591 | 0.0990033 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.1480 | −0.843485 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.1362 | −0.326634 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4765 | 0.754954 | 0.377477 | − | 0.926019i | \(-0.376792\pi\) | ||||
0.377477 | + | 0.926019i | \(0.376792\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.1323 | 1.00012 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.3687 | 1.84105 | 0.920525 | − | 0.390683i | \(-0.127761\pi\) | ||||
0.920525 | + | 0.390683i | \(0.127761\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.3047 | 0.362411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.2961 | −1.67310 | −0.836550 | − | 0.547891i | \(-0.815431\pi\) | ||||
−0.836550 | + | 0.547891i | \(0.815431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50986 | 0.0802154 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4527 | 0.557222 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.5074 | −0.558399 | −0.279200 | − | 0.960233i | \(-0.590069\pi\) | ||||
−0.279200 | + | 0.960233i | \(0.590069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.23001 | −0.166473 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.26742 | 0.0403015 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.4527 | −1.57092 | −0.785459 | − | 0.618914i | \(-0.787573\pi\) | ||||
−0.785459 | + | 0.618914i | \(0.787573\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.3116 | −0.771505 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.0493 | 1.26837 | 0.634186 | − | 0.773180i | \(-0.281335\pi\) | ||||
0.634186 | + | 0.773180i | \(0.281335\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.28605 | 0.230520 |
(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 | 7800.2.a.bu.1.3 | ✓ | 4 | |
5.4 | even | 2 | 7800.2.a.bx.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bu.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7800.2.a.bx.1.2 | yes | 4 | 5.4 | even | 2 |