Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5586,2,Mod(1,5586)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5586, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5586.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5586.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: | \(44.6044345691\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 22x^{6} + 60x^{5} + 87x^{4} - 176x^{3} - 40x^{2} + 64x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.514116\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5586.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.93854 | 1.76137 | 0.880685 | − | 0.473702i | \(-0.157083\pi\) | ||||
0.880685 | + | 0.473702i | \(0.157083\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.93854 | 1.24548 | ||||||||
\(11\) | 1.27293 | 0.383803 | 0.191901 | − | 0.981414i | \(-0.438535\pi\) | ||||
0.191901 | + | 0.981414i | \(0.438535\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.94914 | 1.64999 | 0.824997 | − | 0.565137i | \(-0.191177\pi\) | ||||
0.824997 | + | 0.565137i | \(0.191177\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.93854 | −1.01693 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.05310 | −0.740486 | −0.370243 | − | 0.928935i | \(-0.620726\pi\) | ||||
−0.370243 | + | 0.928935i | \(0.620726\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.93854 | 0.880685 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.27293 | 0.271390 | ||||||||
\(23\) | −0.148774 | −0.0310216 | −0.0155108 | − | 0.999880i | \(-0.504937\pi\) | ||||
−0.0155108 | + | 0.999880i | \(0.504937\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 10.5121 | 2.10242 | ||||||||
\(26\) | 5.94914 | 1.16672 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.60877 | −1.22722 | −0.613609 | − | 0.789610i | \(-0.710283\pi\) | ||||
−0.613609 | + | 0.789610i | \(0.710283\pi\) | |||||||
\(30\) | −3.93854 | −0.719076 | ||||||||
\(31\) | 8.01988 | 1.44041 | 0.720206 | − | 0.693760i | \(-0.244047\pi\) | ||||
0.720206 | + | 0.693760i | \(0.244047\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.27293 | −0.221589 | ||||||||
\(34\) | −3.05310 | −0.523603 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.14824 | 1.01076 | 0.505382 | − | 0.862896i | \(-0.331352\pi\) | ||||
0.505382 | + | 0.862896i | \(0.331352\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −5.94914 | −0.952624 | ||||||||
\(40\) | 3.93854 | 0.622738 | ||||||||
\(41\) | −6.28274 | −0.981198 | −0.490599 | − | 0.871385i | \(-0.663222\pi\) | ||||
−0.490599 | + | 0.871385i | \(0.663222\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.91174 | 1.20653 | 0.603264 | − | 0.797541i | \(-0.293866\pi\) | ||||
0.603264 | + | 0.797541i | \(0.293866\pi\) | |||||||
\(44\) | 1.27293 | 0.191901 | ||||||||
\(45\) | 3.93854 | 0.587123 | ||||||||
\(46\) | −0.148774 | −0.0219356 | ||||||||
\(47\) | −8.22182 | −1.19928 | −0.599638 | − | 0.800272i | \(-0.704689\pi\) | ||||
−0.599638 | + | 0.800272i | \(0.704689\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.5121 | 1.48664 | ||||||||
\(51\) | 3.05310 | 0.427520 | ||||||||
\(52\) | 5.94914 | 0.824997 | ||||||||
\(53\) | 11.3312 | 1.55646 | 0.778232 | − | 0.627977i | \(-0.216117\pi\) | ||||
0.778232 | + | 0.627977i | \(0.216117\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 5.01349 | 0.676019 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −6.60877 | −0.867774 | ||||||||
\(59\) | −1.84029 | −0.239585 | −0.119793 | − | 0.992799i | \(-0.538223\pi\) | ||||
−0.119793 | + | 0.992799i | \(0.538223\pi\) | |||||||
\(60\) | −3.93854 | −0.508464 | ||||||||
\(61\) | −12.1881 | −1.56053 | −0.780266 | − | 0.625448i | \(-0.784916\pi\) | ||||
−0.780266 | + | 0.625448i | \(0.784916\pi\) | |||||||
\(62\) | 8.01988 | 1.01853 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 23.4309 | 2.90625 | ||||||||
\(66\) | −1.27293 | −0.156687 | ||||||||
\(67\) | 2.61205 | 0.319112 | 0.159556 | − | 0.987189i | \(-0.448994\pi\) | ||||
0.159556 | + | 0.987189i | \(0.448994\pi\) | |||||||
\(68\) | −3.05310 | −0.370243 | ||||||||
\(69\) | 0.148774 | 0.0179103 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.8117 | −1.52047 | −0.760236 | − | 0.649647i | \(-0.774917\pi\) | ||||
−0.760236 | + | 0.649647i | \(0.774917\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 16.2859 | 1.90612 | 0.953059 | − | 0.302784i | \(-0.0979162\pi\) | ||||
0.953059 | + | 0.302784i | \(0.0979162\pi\) | |||||||
\(74\) | 6.14824 | 0.714718 | ||||||||
\(75\) | −10.5121 | −1.21384 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.94914 | −0.673607 | ||||||||
\(79\) | 7.44674 | 0.837824 | 0.418912 | − | 0.908027i | \(-0.362412\pi\) | ||||
0.418912 | + | 0.908027i | \(0.362412\pi\) | |||||||
\(80\) | 3.93854 | 0.440343 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.28274 | −0.693812 | ||||||||
\(83\) | −12.1746 | −1.33634 | −0.668170 | − | 0.744009i | \(-0.732922\pi\) | ||||
−0.668170 | + | 0.744009i | \(0.732922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0248 | −1.30427 | ||||||||
\(86\) | 7.91174 | 0.853144 | ||||||||
\(87\) | 6.60877 | 0.708534 | ||||||||
\(88\) | 1.27293 | 0.135695 | ||||||||
\(89\) | 5.40934 | 0.573389 | 0.286694 | − | 0.958022i | \(-0.407444\pi\) | ||||
0.286694 | + | 0.958022i | \(0.407444\pi\) | |||||||
\(90\) | 3.93854 | 0.415159 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.148774 | −0.0155108 | ||||||||
\(93\) | −8.01988 | −0.831623 | ||||||||
\(94\) | −8.22182 | −0.848016 | ||||||||
\(95\) | −3.93854 | −0.404086 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −11.2277 | −1.14000 | −0.570002 | − | 0.821643i | \(-0.693058\pi\) | ||||
−0.570002 | + | 0.821643i | \(0.693058\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.27293 | 0.127934 | ||||||||
\(100\) | 10.5121 | 1.05121 | ||||||||
\(101\) | −4.38789 | −0.436612 | −0.218306 | − | 0.975880i | \(-0.570053\pi\) | ||||
−0.218306 | + | 0.975880i | \(0.570053\pi\) | |||||||
\(102\) | 3.05310 | 0.302302 | ||||||||
\(103\) | −6.48370 | −0.638858 | −0.319429 | − | 0.947610i | \(-0.603491\pi\) | ||||
−0.319429 | + | 0.947610i | \(0.603491\pi\) | |||||||
\(104\) | 5.94914 | 0.583361 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.3312 | 1.10059 | ||||||||
\(107\) | 4.09675 | 0.396047 | 0.198024 | − | 0.980197i | \(-0.436548\pi\) | ||||
0.198024 | + | 0.980197i | \(0.436548\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 5.93860 | 0.568815 | 0.284407 | − | 0.958704i | \(-0.408203\pi\) | ||||
0.284407 | + | 0.958704i | \(0.408203\pi\) | |||||||
\(110\) | 5.01349 | 0.478017 | ||||||||
\(111\) | −6.14824 | −0.583565 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.83385 | 0.360658 | 0.180329 | − | 0.983606i | \(-0.442284\pi\) | ||||
0.180329 | + | 0.983606i | \(0.442284\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | −0.585954 | −0.0546405 | ||||||||
\(116\) | −6.60877 | −0.613609 | ||||||||
\(117\) | 5.94914 | 0.549998 | ||||||||
\(118\) | −1.84029 | −0.169412 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.93854 | −0.359538 | ||||||||
\(121\) | −9.37965 | −0.852695 | ||||||||
\(122\) | −12.1881 | −1.10346 | ||||||||
\(123\) | 6.28274 | 0.566495 | ||||||||
\(124\) | 8.01988 | 0.720206 | ||||||||
\(125\) | 21.7097 | 1.94178 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4576 | −1.37164 | −0.685821 | − | 0.727771i | \(-0.740557\pi\) | ||||
−0.685821 | + | 0.727771i | \(0.740557\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.91174 | −0.696589 | ||||||||
\(130\) | 23.4309 | 2.05503 | ||||||||
\(131\) | 5.76015 | 0.503267 | 0.251633 | − | 0.967823i | \(-0.419032\pi\) | ||||
0.251633 | + | 0.967823i | \(0.419032\pi\) | |||||||
\(132\) | −1.27293 | −0.110794 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.61205 | 0.225646 | ||||||||
\(135\) | −3.93854 | −0.338976 | ||||||||
\(136\) | −3.05310 | −0.261801 | ||||||||
\(137\) | 16.2798 | 1.39088 | 0.695440 | − | 0.718584i | \(-0.255209\pi\) | ||||
0.695440 | + | 0.718584i | \(0.255209\pi\) | |||||||
\(138\) | 0.148774 | 0.0126645 | ||||||||
\(139\) | −8.24825 | −0.699608 | −0.349804 | − | 0.936823i | \(-0.613752\pi\) | ||||
−0.349804 | + | 0.936823i | \(0.613752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.22182 | 0.692402 | ||||||||
\(142\) | −12.8117 | −1.07514 | ||||||||
\(143\) | 7.57283 | 0.633272 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −26.0289 | −2.16158 | ||||||||
\(146\) | 16.2859 | 1.34783 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.14824 | 0.505382 | ||||||||
\(149\) | −5.92450 | −0.485354 | −0.242677 | − | 0.970107i | \(-0.578026\pi\) | ||||
−0.242677 | + | 0.970107i | \(0.578026\pi\) | |||||||
\(150\) | −10.5121 | −0.858311 | ||||||||
\(151\) | −1.09856 | −0.0893992 | −0.0446996 | − | 0.999000i | \(-0.514233\pi\) | ||||
−0.0446996 | + | 0.999000i | \(0.514233\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −3.05310 | −0.246829 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31.5866 | 2.53710 | ||||||||
\(156\) | −5.94914 | −0.476312 | ||||||||
\(157\) | 8.29607 | 0.662098 | 0.331049 | − | 0.943613i | \(-0.392597\pi\) | ||||
0.331049 | + | 0.943613i | \(0.392597\pi\) | |||||||
\(158\) | 7.44674 | 0.592431 | ||||||||
\(159\) | −11.3312 | −0.898625 | ||||||||
\(160\) | 3.93854 | 0.311369 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 12.5954 | 0.986550 | 0.493275 | − | 0.869873i | \(-0.335800\pi\) | ||||
0.493275 | + | 0.869873i | \(0.335800\pi\) | |||||||
\(164\) | −6.28274 | −0.490599 | ||||||||
\(165\) | −5.01349 | −0.390300 | ||||||||
\(166\) | −12.1746 | −0.944935 | ||||||||
\(167\) | −9.65057 | −0.746784 | −0.373392 | − | 0.927674i | \(-0.621805\pi\) | ||||
−0.373392 | + | 0.927674i | \(0.621805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.3922 | 1.72248 | ||||||||
\(170\) | −12.0248 | −0.922258 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 7.91174 | 0.603264 | ||||||||
\(173\) | −14.1088 | −1.07267 | −0.536335 | − | 0.844005i | \(-0.680192\pi\) | ||||
−0.536335 | + | 0.844005i | \(0.680192\pi\) | |||||||
\(174\) | 6.60877 | 0.501009 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.27293 | 0.0959507 | ||||||||
\(177\) | 1.84029 | 0.138325 | ||||||||
\(178\) | 5.40934 | 0.405447 | ||||||||
\(179\) | −12.4256 | −0.928731 | −0.464365 | − | 0.885644i | \(-0.653718\pi\) | ||||
−0.464365 | + | 0.885644i | \(0.653718\pi\) | |||||||
\(180\) | 3.93854 | 0.293562 | ||||||||
\(181\) | 12.3729 | 0.919671 | 0.459836 | − | 0.888004i | \(-0.347908\pi\) | ||||
0.459836 | + | 0.888004i | \(0.347908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.1881 | 0.900973 | ||||||||
\(184\) | −0.148774 | −0.0109678 | ||||||||
\(185\) | 24.2151 | 1.78033 | ||||||||
\(186\) | −8.01988 | −0.588046 | ||||||||
\(187\) | −3.88638 | −0.284201 | ||||||||
\(188\) | −8.22182 | −0.599638 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.93854 | −0.285732 | ||||||||
\(191\) | −4.07435 | −0.294810 | −0.147405 | − | 0.989076i | \(-0.547092\pi\) | ||||
−0.147405 | + | 0.989076i | \(0.547092\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −4.50280 | −0.324119 | −0.162059 | − | 0.986781i | \(-0.551814\pi\) | ||||
−0.162059 | + | 0.986781i | \(0.551814\pi\) | |||||||
\(194\) | −11.2277 | −0.806105 | ||||||||
\(195\) | −23.4309 | −1.67792 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.322407 | 0.0229706 | 0.0114853 | − | 0.999934i | \(-0.496344\pi\) | ||||
0.0114853 | + | 0.999934i | \(0.496344\pi\) | |||||||
\(198\) | 1.27293 | 0.0904632 | ||||||||
\(199\) | −22.6125 | −1.60296 | −0.801478 | − | 0.598024i | \(-0.795953\pi\) | ||||
−0.801478 | + | 0.598024i | \(0.795953\pi\) | |||||||
\(200\) | 10.5121 | 0.743319 | ||||||||
\(201\) | −2.61205 | −0.184239 | ||||||||
\(202\) | −4.38789 | −0.308731 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.05310 | 0.213760 | ||||||||
\(205\) | −24.7448 | −1.72825 | ||||||||
\(206\) | −6.48370 | −0.451741 | ||||||||
\(207\) | −0.148774 | −0.0103405 | ||||||||
\(208\) | 5.94914 | 0.412498 | ||||||||
\(209\) | −1.27293 | −0.0880504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.346997 | 0.0238882 | 0.0119441 | − | 0.999929i | \(-0.496198\pi\) | ||||
0.0119441 | + | 0.999929i | \(0.496198\pi\) | |||||||
\(212\) | 11.3312 | 0.778232 | ||||||||
\(213\) | 12.8117 | 0.877844 | ||||||||
\(214\) | 4.09675 | 0.280048 | ||||||||
\(215\) | 31.1607 | 2.12514 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.93860 | 0.402213 | ||||||||
\(219\) | −16.2859 | −1.10050 | ||||||||
\(220\) | 5.01349 | 0.338009 | ||||||||
\(221\) | −18.1633 | −1.22180 | ||||||||
\(222\) | −6.14824 | −0.412643 | ||||||||
\(223\) | 2.29672 | 0.153800 | 0.0769000 | − | 0.997039i | \(-0.475498\pi\) | ||||
0.0769000 | + | 0.997039i | \(0.475498\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.5121 | 0.700808 | ||||||||
\(226\) | 3.83385 | 0.255024 | ||||||||
\(227\) | −15.3728 | −1.02033 | −0.510166 | − | 0.860076i | \(-0.670416\pi\) | ||||
−0.510166 | + | 0.860076i | \(0.670416\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 11.7178 | 0.774336 | 0.387168 | − | 0.922009i | \(-0.373453\pi\) | ||||
0.387168 | + | 0.922009i | \(0.373453\pi\) | |||||||
\(230\) | −0.585954 | −0.0386367 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.60877 | −0.433887 | ||||||||
\(233\) | 13.7683 | 0.901989 | 0.450995 | − | 0.892527i | \(-0.351069\pi\) | ||||
0.450995 | + | 0.892527i | \(0.351069\pi\) | |||||||
\(234\) | 5.94914 | 0.388907 | ||||||||
\(235\) | −32.3820 | −2.11237 | ||||||||
\(236\) | −1.84029 | −0.119793 | ||||||||
\(237\) | −7.44674 | −0.483718 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.3226 | 1.76735 | 0.883676 | − | 0.468100i | \(-0.155061\pi\) | ||||
0.883676 | + | 0.468100i | \(0.155061\pi\) | |||||||
\(240\) | −3.93854 | −0.254232 | ||||||||
\(241\) | 29.4781 | 1.89885 | 0.949427 | − | 0.313988i | \(-0.101665\pi\) | ||||
0.949427 | + | 0.313988i | \(0.101665\pi\) | |||||||
\(242\) | −9.37965 | −0.602947 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.1881 | −0.780266 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.28274 | 0.400573 | ||||||||
\(247\) | −5.94914 | −0.378534 | ||||||||
\(248\) | 8.01988 | 0.509263 | ||||||||
\(249\) | 12.1746 | 0.771536 | ||||||||
\(250\) | 21.7097 | 1.37304 | ||||||||
\(251\) | −22.6060 | −1.42688 | −0.713440 | − | 0.700716i | \(-0.752864\pi\) | ||||
−0.713440 | + | 0.700716i | \(0.752864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.189379 | −0.0119062 | ||||||||
\(254\) | −15.4576 | −0.969897 | ||||||||
\(255\) | 12.0248 | 0.753021 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.9880 | −1.62109 | −0.810543 | − | 0.585679i | \(-0.800828\pi\) | ||||
−0.810543 | + | 0.585679i | \(0.800828\pi\) | |||||||
\(258\) | −7.91174 | −0.492563 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 23.4309 | 1.45312 | ||||||||
\(261\) | −6.60877 | −0.409072 | ||||||||
\(262\) | 5.76015 | 0.355863 | ||||||||
\(263\) | 6.16848 | 0.380365 | 0.190182 | − | 0.981749i | \(-0.439092\pi\) | ||||
0.190182 | + | 0.981749i | \(0.439092\pi\) | |||||||
\(264\) | −1.27293 | −0.0783434 | ||||||||
\(265\) | 44.6285 | 2.74151 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.40934 | −0.331046 | ||||||||
\(268\) | 2.61205 | 0.159556 | ||||||||
\(269\) | −10.1268 | −0.617442 | −0.308721 | − | 0.951153i | \(-0.599901\pi\) | ||||
−0.308721 | + | 0.951153i | \(0.599901\pi\) | |||||||
\(270\) | −3.93854 | −0.239692 | ||||||||
\(271\) | −10.9731 | −0.666568 | −0.333284 | − | 0.942826i | \(-0.608157\pi\) | ||||
−0.333284 | + | 0.942826i | \(0.608157\pi\) | |||||||
\(272\) | −3.05310 | −0.185122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.2798 | 0.983501 | ||||||||
\(275\) | 13.3812 | 0.806916 | ||||||||
\(276\) | 0.148774 | 0.00895516 | ||||||||
\(277\) | 2.90574 | 0.174589 | 0.0872946 | − | 0.996183i | \(-0.472178\pi\) | ||||
0.0872946 | + | 0.996183i | \(0.472178\pi\) | |||||||
\(278\) | −8.24825 | −0.494697 | ||||||||
\(279\) | 8.01988 | 0.480138 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5310 | 0.807191 | 0.403595 | − | 0.914938i | \(-0.367760\pi\) | ||||
0.403595 | + | 0.914938i | \(0.367760\pi\) | |||||||
\(282\) | 8.22182 | 0.489602 | ||||||||
\(283\) | −15.3969 | −0.915252 | −0.457626 | − | 0.889145i | \(-0.651300\pi\) | ||||
−0.457626 | + | 0.889145i | \(0.651300\pi\) | |||||||
\(284\) | −12.8117 | −0.760236 | ||||||||
\(285\) | 3.93854 | 0.233299 | ||||||||
\(286\) | 7.57283 | 0.447791 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −7.67857 | −0.451680 | ||||||||
\(290\) | −26.0289 | −1.52847 | ||||||||
\(291\) | 11.2277 | 0.658182 | ||||||||
\(292\) | 16.2859 | 0.953059 | ||||||||
\(293\) | 14.5720 | 0.851307 | 0.425654 | − | 0.904886i | \(-0.360044\pi\) | ||||
0.425654 | + | 0.904886i | \(0.360044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.24806 | −0.421998 | ||||||||
\(296\) | 6.14824 | 0.357359 | ||||||||
\(297\) | −1.27293 | −0.0738629 | ||||||||
\(298\) | −5.92450 | −0.343197 | ||||||||
\(299\) | −0.885079 | −0.0511854 | ||||||||
\(300\) | −10.5121 | −0.606918 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.09856 | −0.0632148 | ||||||||
\(303\) | 4.38789 | 0.252078 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −48.0035 | −2.74867 | ||||||||
\(306\) | −3.05310 | −0.174534 | ||||||||
\(307\) | 26.2382 | 1.49749 | 0.748745 | − | 0.662858i | \(-0.230657\pi\) | ||||
0.748745 | + | 0.662858i | \(0.230657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.48370 | 0.368845 | ||||||||
\(310\) | 31.5866 | 1.79400 | ||||||||
\(311\) | −7.89074 | −0.447443 | −0.223721 | − | 0.974653i | \(-0.571821\pi\) | ||||
−0.223721 | + | 0.974653i | \(0.571821\pi\) | |||||||
\(312\) | −5.94914 | −0.336804 | ||||||||
\(313\) | 17.3496 | 0.980655 | 0.490327 | − | 0.871538i | \(-0.336877\pi\) | ||||
0.490327 | + | 0.871538i | \(0.336877\pi\) | |||||||
\(314\) | 8.29607 | 0.468174 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.44674 | 0.418912 | ||||||||
\(317\) | 31.0193 | 1.74222 | 0.871108 | − | 0.491092i | \(-0.163402\pi\) | ||||
0.871108 | + | 0.491092i | \(0.163402\pi\) | |||||||
\(318\) | −11.3312 | −0.635424 | ||||||||
\(319\) | −8.41250 | −0.471009 | ||||||||
\(320\) | 3.93854 | 0.220171 | ||||||||
\(321\) | −4.09675 | −0.228658 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.05310 | 0.169879 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 62.5381 | 3.46899 | ||||||||
\(326\) | 12.5954 | 0.697597 | ||||||||
\(327\) | −5.93860 | −0.328405 | ||||||||
\(328\) | −6.28274 | −0.346906 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.01349 | −0.275983 | ||||||||
\(331\) | −27.7615 | −1.52591 | −0.762954 | − | 0.646453i | \(-0.776252\pi\) | ||||
−0.762954 | + | 0.646453i | \(0.776252\pi\) | |||||||
\(332\) | −12.1746 | −0.668170 | ||||||||
\(333\) | 6.14824 | 0.336921 | ||||||||
\(334\) | −9.65057 | −0.528056 | ||||||||
\(335\) | 10.2877 | 0.562075 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.9053 | −0.648523 | −0.324261 | − | 0.945968i | \(-0.605116\pi\) | ||||
−0.324261 | + | 0.945968i | \(0.605116\pi\) | |||||||
\(338\) | 22.3922 | 1.21798 | ||||||||
\(339\) | −3.83385 | −0.208226 | ||||||||
\(340\) | −12.0248 | −0.652135 | ||||||||
\(341\) | 10.2087 | 0.552834 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.91174 | 0.426572 | ||||||||
\(345\) | 0.585954 | 0.0315467 | ||||||||
\(346\) | −14.1088 | −0.758493 | ||||||||
\(347\) | 18.8103 | 1.00979 | 0.504895 | − | 0.863181i | \(-0.331531\pi\) | ||||
0.504895 | + | 0.863181i | \(0.331531\pi\) | |||||||
\(348\) | 6.60877 | 0.354267 | ||||||||
\(349\) | 8.76894 | 0.469391 | 0.234695 | − | 0.972069i | \(-0.424591\pi\) | ||||
0.234695 | + | 0.972069i | \(0.424591\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.94914 | −0.317541 | ||||||||
\(352\) | 1.27293 | 0.0678474 | ||||||||
\(353\) | 29.8162 | 1.58696 | 0.793478 | − | 0.608599i | \(-0.208268\pi\) | ||||
0.793478 | + | 0.608599i | \(0.208268\pi\) | |||||||
\(354\) | 1.84029 | 0.0978103 | ||||||||
\(355\) | −50.4595 | −2.67811 | ||||||||
\(356\) | 5.40934 | 0.286694 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.4256 | −0.656712 | ||||||||
\(359\) | 17.1263 | 0.903890 | 0.451945 | − | 0.892046i | \(-0.350730\pi\) | ||||
0.451945 | + | 0.892046i | \(0.350730\pi\) | |||||||
\(360\) | 3.93854 | 0.207579 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 12.3729 | 0.650306 | ||||||||
\(363\) | 9.37965 | 0.492304 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 64.1426 | 3.35738 | ||||||||
\(366\) | 12.1881 | 0.637084 | ||||||||
\(367\) | −24.3662 | −1.27190 | −0.635952 | − | 0.771728i | \(-0.719393\pi\) | ||||
−0.635952 | + | 0.771728i | \(0.719393\pi\) | |||||||
\(368\) | −0.148774 | −0.00775540 | ||||||||
\(369\) | −6.28274 | −0.327066 | ||||||||
\(370\) | 24.2151 | 1.25888 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.01988 | −0.415811 | ||||||||
\(373\) | 24.1414 | 1.24999 | 0.624997 | − | 0.780627i | \(-0.285100\pi\) | ||||
0.624997 | + | 0.780627i | \(0.285100\pi\) | |||||||
\(374\) | −3.88638 | −0.200960 | ||||||||
\(375\) | −21.7097 | −1.12109 | ||||||||
\(376\) | −8.22182 | −0.424008 | ||||||||
\(377\) | −39.3165 | −2.02490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.51695 | 0.437486 | 0.218743 | − | 0.975782i | \(-0.429804\pi\) | ||||
0.218743 | + | 0.975782i | \(0.429804\pi\) | |||||||
\(380\) | −3.93854 | −0.202043 | ||||||||
\(381\) | 15.4576 | 0.791917 | ||||||||
\(382\) | −4.07435 | −0.208462 | ||||||||
\(383\) | 17.3654 | 0.887331 | 0.443665 | − | 0.896193i | \(-0.353678\pi\) | ||||
0.443665 | + | 0.896193i | \(0.353678\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.50280 | −0.229187 | ||||||||
\(387\) | 7.91174 | 0.402176 | ||||||||
\(388\) | −11.2277 | −0.570002 | ||||||||
\(389\) | −22.5117 | −1.14139 | −0.570694 | − | 0.821163i | \(-0.693326\pi\) | ||||
−0.570694 | + | 0.821163i | \(0.693326\pi\) | |||||||
\(390\) | −23.4309 | −1.18647 | ||||||||
\(391\) | 0.454223 | 0.0229711 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.76015 | −0.290561 | ||||||||
\(394\) | 0.322407 | 0.0162426 | ||||||||
\(395\) | 29.3293 | 1.47572 | ||||||||
\(396\) | 1.27293 | 0.0639671 | ||||||||
\(397\) | −33.8779 | −1.70028 | −0.850140 | − | 0.526556i | \(-0.823483\pi\) | ||||
−0.850140 | + | 0.526556i | \(0.823483\pi\) | |||||||
\(398\) | −22.6125 | −1.13346 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.5121 | 0.525606 | ||||||||
\(401\) | 33.1403 | 1.65495 | 0.827474 | − | 0.561504i | \(-0.189777\pi\) | ||||
0.827474 | + | 0.561504i | \(0.189777\pi\) | |||||||
\(402\) | −2.61205 | −0.130277 | ||||||||
\(403\) | 47.7114 | 2.37667 | ||||||||
\(404\) | −4.38789 | −0.218306 | ||||||||
\(405\) | 3.93854 | 0.195708 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.82627 | 0.387934 | ||||||||
\(408\) | 3.05310 | 0.151151 | ||||||||
\(409\) | 28.2927 | 1.39899 | 0.699493 | − | 0.714639i | \(-0.253409\pi\) | ||||
0.699493 | + | 0.714639i | \(0.253409\pi\) | |||||||
\(410\) | −24.7448 | −1.22206 | ||||||||
\(411\) | −16.2798 | −0.803025 | ||||||||
\(412\) | −6.48370 | −0.319429 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.148774 | −0.00731186 | ||||||||
\(415\) | −47.9503 | −2.35379 | ||||||||
\(416\) | 5.94914 | 0.291680 | ||||||||
\(417\) | 8.24825 | 0.403919 | ||||||||
\(418\) | −1.27293 | −0.0622610 | ||||||||
\(419\) | −24.5157 | −1.19767 | −0.598836 | − | 0.800872i | \(-0.704370\pi\) | ||||
−0.598836 | + | 0.800872i | \(0.704370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.4678 | −1.77733 | −0.888667 | − | 0.458553i | \(-0.848368\pi\) | ||||
−0.888667 | + | 0.458553i | \(0.848368\pi\) | |||||||
\(422\) | 0.346997 | 0.0168915 | ||||||||
\(423\) | −8.22182 | −0.399758 | ||||||||
\(424\) | 11.3312 | 0.550293 | ||||||||
\(425\) | −32.0946 | −1.55682 | ||||||||
\(426\) | 12.8117 | 0.620730 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.09675 | 0.198024 | ||||||||
\(429\) | −7.57283 | −0.365620 | ||||||||
\(430\) | 31.1607 | 1.50270 | ||||||||
\(431\) | 7.38080 | 0.355521 | 0.177760 | − | 0.984074i | \(-0.443115\pi\) | ||||
0.177760 | + | 0.984074i | \(0.443115\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 11.4859 | 0.551975 | 0.275988 | − | 0.961161i | \(-0.410995\pi\) | ||||
0.275988 | + | 0.961161i | \(0.410995\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.0289 | 1.24799 | ||||||||
\(436\) | 5.93860 | 0.284407 | ||||||||
\(437\) | 0.148774 | 0.00711684 | ||||||||
\(438\) | −16.2859 | −0.778169 | ||||||||
\(439\) | 22.2521 | 1.06204 | 0.531018 | − | 0.847360i | \(-0.321809\pi\) | ||||
0.531018 | + | 0.847360i | \(0.321809\pi\) | |||||||
\(440\) | 5.01349 | 0.239009 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.1633 | −0.863941 | ||||||||
\(443\) | −22.7804 | −1.08233 | −0.541165 | − | 0.840917i | \(-0.682016\pi\) | ||||
−0.541165 | + | 0.840917i | \(0.682016\pi\) | |||||||
\(444\) | −6.14824 | −0.291782 | ||||||||
\(445\) | 21.3049 | 1.00995 | ||||||||
\(446\) | 2.29672 | 0.108753 | ||||||||
\(447\) | 5.92450 | 0.280219 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.19585 | −0.386786 | −0.193393 | − | 0.981121i | \(-0.561949\pi\) | ||||
−0.193393 | + | 0.981121i | \(0.561949\pi\) | |||||||
\(450\) | 10.5121 | 0.495546 | ||||||||
\(451\) | −7.99748 | −0.376587 | ||||||||
\(452\) | 3.83385 | 0.180329 | ||||||||
\(453\) | 1.09856 | 0.0516146 | ||||||||
\(454\) | −15.3728 | −0.721483 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −17.9078 | −0.837691 | −0.418846 | − | 0.908058i | \(-0.637565\pi\) | ||||
−0.418846 | + | 0.908058i | \(0.637565\pi\) | |||||||
\(458\) | 11.7178 | 0.547539 | ||||||||
\(459\) | 3.05310 | 0.142507 | ||||||||
\(460\) | −0.585954 | −0.0273203 | ||||||||
\(461\) | 10.8937 | 0.507372 | 0.253686 | − | 0.967287i | \(-0.418357\pi\) | ||||
0.253686 | + | 0.967287i | \(0.418357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.6911 | −1.84460 | −0.922300 | − | 0.386475i | \(-0.873693\pi\) | ||||
−0.922300 | + | 0.386475i | \(0.873693\pi\) | |||||||
\(464\) | −6.60877 | −0.306804 | ||||||||
\(465\) | −31.5866 | −1.46480 | ||||||||
\(466\) | 13.7683 | 0.637803 | ||||||||
\(467\) | −32.0868 | −1.48480 | −0.742400 | − | 0.669956i | \(-0.766313\pi\) | ||||
−0.742400 | + | 0.669956i | \(0.766313\pi\) | |||||||
\(468\) | 5.94914 | 0.274999 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −32.3820 | −1.49367 | ||||||||
\(471\) | −8.29607 | −0.382263 | ||||||||
\(472\) | −1.84029 | −0.0847062 | ||||||||
\(473\) | 10.0711 | 0.463069 | ||||||||
\(474\) | −7.44674 | −0.342040 | ||||||||
\(475\) | −10.5121 | −0.482329 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3312 | 0.518821 | ||||||||
\(478\) | 27.3226 | 1.24971 | ||||||||
\(479\) | 21.5125 | 0.982933 | 0.491466 | − | 0.870897i | \(-0.336461\pi\) | ||||
0.491466 | + | 0.870897i | \(0.336461\pi\) | |||||||
\(480\) | −3.93854 | −0.179769 | ||||||||
\(481\) | 36.5767 | 1.66775 | ||||||||
\(482\) | 29.4781 | 1.34269 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.37965 | −0.426348 | ||||||||
\(485\) | −44.2209 | −2.00797 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −22.7496 | −1.03088 | −0.515441 | − | 0.856925i | \(-0.672372\pi\) | ||||
−0.515441 | + | 0.856925i | \(0.672372\pi\) | |||||||
\(488\) | −12.1881 | −0.551731 | ||||||||
\(489\) | −12.5954 | −0.569585 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.4966 | −1.19577 | −0.597887 | − | 0.801581i | \(-0.703993\pi\) | ||||
−0.597887 | + | 0.801581i | \(0.703993\pi\) | |||||||
\(492\) | 6.28274 | 0.283248 | ||||||||
\(493\) | 20.1772 | 0.908737 | ||||||||
\(494\) | −5.94914 | −0.267664 | ||||||||
\(495\) | 5.01349 | 0.225340 | ||||||||
\(496\) | 8.01988 | 0.360103 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.1746 | 0.545558 | ||||||||
\(499\) | 20.4302 | 0.914580 | 0.457290 | − | 0.889318i | \(-0.348820\pi\) | ||||
0.457290 | + | 0.889318i | \(0.348820\pi\) | |||||||
\(500\) | 21.7097 | 0.970889 | ||||||||
\(501\) | 9.65057 | 0.431156 | ||||||||
\(502\) | −22.6060 | −1.00896 | ||||||||
\(503\) | 0.0114171 | 0.000509063 0 | 0.000254532 | − | 1.00000i | \(-0.499919\pi\) | ||||
0.000254532 | 1.00000i | \(0.499919\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.2819 | −0.769035 | ||||||||
\(506\) | −0.189379 | −0.00841894 | ||||||||
\(507\) | −22.3922 | −0.994474 | ||||||||
\(508\) | −15.4576 | −0.685821 | ||||||||
\(509\) | −17.0678 | −0.756518 | −0.378259 | − | 0.925700i | \(-0.623477\pi\) | ||||
−0.378259 | + | 0.925700i | \(0.623477\pi\) | |||||||
\(510\) | 12.0248 | 0.532466 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −25.9880 | −1.14628 | ||||||||
\(515\) | −25.5363 | −1.12527 | ||||||||
\(516\) | −7.91174 | −0.348295 | ||||||||
\(517\) | −10.4658 | −0.460285 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1088 | 0.619307 | ||||||||
\(520\) | 23.4309 | 1.02751 | ||||||||
\(521\) | −6.84370 | −0.299828 | −0.149914 | − | 0.988699i | \(-0.547900\pi\) | ||||
−0.149914 | + | 0.988699i | \(0.547900\pi\) | |||||||
\(522\) | −6.60877 | −0.289258 | ||||||||
\(523\) | 10.9826 | 0.480237 | 0.240119 | − | 0.970744i | \(-0.422814\pi\) | ||||
0.240119 | + | 0.970744i | \(0.422814\pi\) | |||||||
\(524\) | 5.76015 | 0.251633 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.16848 | 0.268958 | ||||||||
\(527\) | −24.4855 | −1.06661 | ||||||||
\(528\) | −1.27293 | −0.0553972 | ||||||||
\(529\) | −22.9779 | −0.999038 | ||||||||
\(530\) | 44.6285 | 1.93854 | ||||||||
\(531\) | −1.84029 | −0.0798618 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.3769 | −1.61897 | ||||||||
\(534\) | −5.40934 | −0.234085 | ||||||||
\(535\) | 16.1352 | 0.697586 | ||||||||
\(536\) | 2.61205 | 0.112823 | ||||||||
\(537\) | 12.4256 | 0.536203 | ||||||||
\(538\) | −10.1268 | −0.436597 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.93854 | −0.169488 | ||||||||
\(541\) | 18.7473 | 0.806011 | 0.403006 | − | 0.915197i | \(-0.367965\pi\) | ||||
0.403006 | + | 0.915197i | \(0.367965\pi\) | |||||||
\(542\) | −10.9731 | −0.471335 | ||||||||
\(543\) | −12.3729 | −0.530973 | ||||||||
\(544\) | −3.05310 | −0.130901 | ||||||||
\(545\) | 23.3894 | 1.00189 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.12794 | −0.219255 | −0.109628 | − | 0.993973i | \(-0.534966\pi\) | ||||
−0.109628 | + | 0.993973i | \(0.534966\pi\) | |||||||
\(548\) | 16.2798 | 0.695440 | ||||||||
\(549\) | −12.1881 | −0.520177 | ||||||||
\(550\) | 13.3812 | 0.570576 | ||||||||
\(551\) | 6.60877 | 0.281543 | ||||||||
\(552\) | 0.148774 | 0.00633226 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.90574 | 0.123453 | ||||||||
\(555\) | −24.2151 | −1.02787 | ||||||||
\(556\) | −8.24825 | −0.349804 | ||||||||
\(557\) | −19.8712 | −0.841970 | −0.420985 | − | 0.907068i | \(-0.638316\pi\) | ||||
−0.420985 | + | 0.907068i | \(0.638316\pi\) | |||||||
\(558\) | 8.01988 | 0.339509 | ||||||||
\(559\) | 47.0680 | 1.99076 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.88638 | 0.164083 | ||||||||
\(562\) | 13.5310 | 0.570770 | ||||||||
\(563\) | 5.45760 | 0.230010 | 0.115005 | − | 0.993365i | \(-0.463312\pi\) | ||||
0.115005 | + | 0.993365i | \(0.463312\pi\) | |||||||
\(564\) | 8.22182 | 0.346201 | ||||||||
\(565\) | 15.0998 | 0.635252 | ||||||||
\(566\) | −15.3969 | −0.647181 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.8117 | −0.537568 | ||||||||
\(569\) | 5.92409 | 0.248351 | 0.124175 | − | 0.992260i | \(-0.460371\pi\) | ||||
0.124175 | + | 0.992260i | \(0.460371\pi\) | |||||||
\(570\) | 3.93854 | 0.164967 | ||||||||
\(571\) | 22.8266 | 0.955265 | 0.477633 | − | 0.878560i | \(-0.341495\pi\) | ||||
0.477633 | + | 0.878560i | \(0.341495\pi\) | |||||||
\(572\) | 7.57283 | 0.316636 | ||||||||
\(573\) | 4.07435 | 0.170208 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.56393 | −0.0652206 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −12.2583 | −0.510320 | −0.255160 | − | 0.966899i | \(-0.582128\pi\) | ||||
−0.255160 | + | 0.966899i | \(0.582128\pi\) | |||||||
\(578\) | −7.67857 | −0.319386 | ||||||||
\(579\) | 4.50280 | 0.187130 | ||||||||
\(580\) | −26.0289 | −1.08079 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 11.2277 | 0.465405 | ||||||||
\(583\) | 14.4239 | 0.597375 | ||||||||
\(584\) | 16.2859 | 0.673915 | ||||||||
\(585\) | 23.4309 | 0.968750 | ||||||||
\(586\) | 14.5720 | 0.601965 | ||||||||
\(587\) | 43.2598 | 1.78552 | 0.892762 | − | 0.450528i | \(-0.148764\pi\) | ||||
0.892762 | + | 0.450528i | \(0.148764\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.01988 | −0.330453 | ||||||||
\(590\) | −7.24806 | −0.298398 | ||||||||
\(591\) | −0.322407 | −0.0132621 | ||||||||
\(592\) | 6.14824 | 0.252691 | ||||||||
\(593\) | −18.4196 | −0.756403 | −0.378201 | − | 0.925723i | \(-0.623457\pi\) | ||||
−0.378201 | + | 0.925723i | \(0.623457\pi\) | |||||||
\(594\) | −1.27293 | −0.0522289 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.92450 | −0.242677 | ||||||||
\(597\) | 22.6125 | 0.925467 | ||||||||
\(598\) | −0.885079 | −0.0361936 | ||||||||
\(599\) | −6.36854 | −0.260212 | −0.130106 | − | 0.991500i | \(-0.541532\pi\) | ||||
−0.130106 | + | 0.991500i | \(0.541532\pi\) | |||||||
\(600\) | −10.5121 | −0.429156 | ||||||||
\(601\) | 26.8167 | 1.09388 | 0.546939 | − | 0.837173i | \(-0.315793\pi\) | ||||
0.546939 | + | 0.837173i | \(0.315793\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.61205 | 0.106371 | ||||||||
\(604\) | −1.09856 | −0.0446996 | ||||||||
\(605\) | −36.9422 | −1.50191 | ||||||||
\(606\) | 4.38789 | 0.178246 | ||||||||
\(607\) | 45.5076 | 1.84710 | 0.923549 | − | 0.383482i | \(-0.125275\pi\) | ||||
0.923549 | + | 0.383482i | \(0.125275\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −48.0035 | −1.94361 | ||||||||
\(611\) | −48.9127 | −1.97880 | ||||||||
\(612\) | −3.05310 | −0.123414 | ||||||||
\(613\) | −4.94269 | −0.199633 | −0.0998167 | − | 0.995006i | \(-0.531826\pi\) | ||||
−0.0998167 | + | 0.995006i | \(0.531826\pi\) | |||||||
\(614\) | 26.2382 | 1.05889 | ||||||||
\(615\) | 24.7448 | 0.997808 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.7247 | −1.67977 | −0.839887 | − | 0.542762i | \(-0.817379\pi\) | ||||
−0.839887 | + | 0.542762i | \(0.817379\pi\) | |||||||
\(618\) | 6.48370 | 0.260813 | ||||||||
\(619\) | −28.8296 | −1.15876 | −0.579380 | − | 0.815058i | \(-0.696705\pi\) | ||||
−0.579380 | + | 0.815058i | \(0.696705\pi\) | |||||||
\(620\) | 31.5866 | 1.26855 | ||||||||
\(621\) | 0.148774 | 0.00597011 | ||||||||
\(622\) | −7.89074 | −0.316390 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.94914 | −0.238156 | ||||||||
\(625\) | 32.9441 | 1.31777 | ||||||||
\(626\) | 17.3496 | 0.693428 | ||||||||
\(627\) | 1.27293 | 0.0508359 | ||||||||
\(628\) | 8.29607 | 0.331049 | ||||||||
\(629\) | −18.7712 | −0.748457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.8512 | −0.750455 | −0.375228 | − | 0.926933i | \(-0.622435\pi\) | ||||
−0.375228 | + | 0.926933i | \(0.622435\pi\) | |||||||
\(632\) | 7.44674 | 0.296215 | ||||||||
\(633\) | −0.346997 | −0.0137919 | ||||||||
\(634\) | 31.0193 | 1.23193 | ||||||||
\(635\) | −60.8805 | −2.41597 | ||||||||
\(636\) | −11.3312 | −0.449312 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.41250 | −0.333054 | ||||||||
\(639\) | −12.8117 | −0.506824 | ||||||||
\(640\) | 3.93854 | 0.155685 | ||||||||
\(641\) | −12.1065 | −0.478178 | −0.239089 | − | 0.970998i | \(-0.576849\pi\) | ||||
−0.239089 | + | 0.970998i | \(0.576849\pi\) | |||||||
\(642\) | −4.09675 | −0.161686 | ||||||||
\(643\) | −40.2074 | −1.58563 | −0.792813 | − | 0.609465i | \(-0.791384\pi\) | ||||
−0.792813 | + | 0.609465i | \(0.791384\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.1607 | −1.22695 | ||||||||
\(646\) | 3.05310 | 0.120123 | ||||||||
\(647\) | 18.0855 | 0.711016 | 0.355508 | − | 0.934673i | \(-0.384308\pi\) | ||||
0.355508 | + | 0.934673i | \(0.384308\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.34256 | −0.0919535 | ||||||||
\(650\) | 62.5381 | 2.45294 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.5954 | 0.493275 | ||||||||
\(653\) | −42.2280 | −1.65251 | −0.826255 | − | 0.563296i | \(-0.809533\pi\) | ||||
−0.826255 | + | 0.563296i | \(0.809533\pi\) | |||||||
\(654\) | −5.93860 | −0.232218 | ||||||||
\(655\) | 22.6866 | 0.886439 | ||||||||
\(656\) | −6.28274 | −0.245300 | ||||||||
\(657\) | 16.2859 | 0.635373 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.2743 | 1.68573 | 0.842864 | − | 0.538126i | \(-0.180868\pi\) | ||||
0.842864 | + | 0.538126i | \(0.180868\pi\) | |||||||
\(660\) | −5.01349 | −0.195150 | ||||||||
\(661\) | 38.8777 | 1.51217 | 0.756083 | − | 0.654476i | \(-0.227111\pi\) | ||||
0.756083 | + | 0.654476i | \(0.227111\pi\) | |||||||
\(662\) | −27.7615 | −1.07898 | ||||||||
\(663\) | 18.1633 | 0.705405 | ||||||||
\(664\) | −12.1746 | −0.472467 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.14824 | 0.238239 | ||||||||
\(667\) | 0.983215 | 0.0380702 | ||||||||
\(668\) | −9.65057 | −0.373392 | ||||||||
\(669\) | −2.29672 | −0.0887965 | ||||||||
\(670\) | 10.2877 | 0.397447 | ||||||||
\(671\) | −15.5146 | −0.598936 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.3534 | −0.514737 | −0.257369 | − | 0.966313i | \(-0.582855\pi\) | ||||
−0.257369 | + | 0.966313i | \(0.582855\pi\) | |||||||
\(674\) | −11.9053 | −0.458575 | ||||||||
\(675\) | −10.5121 | −0.404612 | ||||||||
\(676\) | 22.3922 | 0.861239 | ||||||||
\(677\) | 12.3254 | 0.473704 | 0.236852 | − | 0.971546i | \(-0.423884\pi\) | ||||
0.236852 | + | 0.971546i | \(0.423884\pi\) | |||||||
\(678\) | −3.83385 | −0.147238 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −12.0248 | −0.461129 | ||||||||
\(681\) | 15.3728 | 0.589089 | ||||||||
\(682\) | 10.2087 | 0.390913 | ||||||||
\(683\) | −14.1727 | −0.542305 | −0.271152 | − | 0.962536i | \(-0.587405\pi\) | ||||
−0.271152 | + | 0.962536i | \(0.587405\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 64.1189 | 2.44986 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.7178 | −0.447063 | ||||||||
\(688\) | 7.91174 | 0.301632 | ||||||||
\(689\) | 67.4110 | 2.56816 | ||||||||
\(690\) | 0.585954 | 0.0223069 | ||||||||
\(691\) | −41.6858 | −1.58580 | −0.792902 | − | 0.609350i | \(-0.791431\pi\) | ||||
−0.792902 | + | 0.609350i | \(0.791431\pi\) | |||||||
\(692\) | −14.1088 | −0.536335 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.8103 | 0.714029 | ||||||||
\(695\) | −32.4861 | −1.23227 | ||||||||
\(696\) | 6.60877 | 0.250505 | ||||||||
\(697\) | 19.1818 | 0.726564 | ||||||||
\(698\) | 8.76894 | 0.331909 | ||||||||
\(699\) | −13.7683 | −0.520764 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.0286 | −0.643162 | −0.321581 | − | 0.946882i | \(-0.604214\pi\) | ||||
−0.321581 | + | 0.946882i | \(0.604214\pi\) | |||||||
\(702\) | −5.94914 | −0.224536 | ||||||||
\(703\) | −6.14824 | −0.231885 | ||||||||
\(704\) | 1.27293 | 0.0479753 | ||||||||
\(705\) | 32.3820 | 1.21958 | ||||||||
\(706\) | 29.8162 | 1.12215 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.84029 | 0.0691623 | ||||||||
\(709\) | 32.3459 | 1.21478 | 0.607388 | − | 0.794405i | \(-0.292217\pi\) | ||||
0.607388 | + | 0.794405i | \(0.292217\pi\) | |||||||
\(710\) | −50.4595 | −1.89371 | ||||||||
\(711\) | 7.44674 | 0.279275 | ||||||||
\(712\) | 5.40934 | 0.202724 | ||||||||
\(713\) | −1.19315 | −0.0446839 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.8259 | 1.11543 | ||||||||
\(716\) | −12.4256 | −0.464365 | ||||||||
\(717\) | −27.3226 | −1.02038 | ||||||||
\(718\) | 17.1263 | 0.639146 | ||||||||
\(719\) | 6.79180 | 0.253291 | 0.126646 | − | 0.991948i | \(-0.459579\pi\) | ||||
0.126646 | + | 0.991948i | \(0.459579\pi\) | |||||||
\(720\) | 3.93854 | 0.146781 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −29.4781 | −1.09630 | ||||||||
\(724\) | 12.3729 | 0.459836 | ||||||||
\(725\) | −69.4722 | −2.58013 | ||||||||
\(726\) | 9.37965 | 0.348111 | ||||||||
\(727\) | 35.1033 | 1.30191 | 0.650955 | − | 0.759116i | \(-0.274368\pi\) | ||||
0.650955 | + | 0.759116i | \(0.274368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 64.1426 | 2.37403 | ||||||||
\(731\) | −24.1553 | −0.893417 | ||||||||
\(732\) | 12.1881 | 0.450487 | ||||||||
\(733\) | −18.2408 | −0.673737 | −0.336869 | − | 0.941552i | \(-0.609368\pi\) | ||||
−0.336869 | + | 0.941552i | \(0.609368\pi\) | |||||||
\(734\) | −24.3662 | −0.899373 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.148774 | −0.00548390 | ||||||||
\(737\) | 3.32495 | 0.122476 | ||||||||
\(738\) | −6.28274 | −0.231271 | ||||||||
\(739\) | 2.59627 | 0.0955054 | 0.0477527 | − | 0.998859i | \(-0.484794\pi\) | ||||
0.0477527 | + | 0.998859i | \(0.484794\pi\) | |||||||
\(740\) | 24.2151 | 0.890165 | ||||||||
\(741\) | 5.94914 | 0.218547 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.38432 | 0.197531 | 0.0987657 | − | 0.995111i | \(-0.468511\pi\) | ||||
0.0987657 | + | 0.995111i | \(0.468511\pi\) | |||||||
\(744\) | −8.01988 | −0.294023 | ||||||||
\(745\) | −23.3339 | −0.854889 | ||||||||
\(746\) | 24.1414 | 0.883879 | ||||||||
\(747\) | −12.1746 | −0.445447 | ||||||||
\(748\) | −3.88638 | −0.142100 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −21.7097 | −0.792728 | ||||||||
\(751\) | 52.2522 | 1.90671 | 0.953356 | − | 0.301850i | \(-0.0976041\pi\) | ||||
0.953356 | + | 0.301850i | \(0.0976041\pi\) | |||||||
\(752\) | −8.22182 | −0.299819 | ||||||||
\(753\) | 22.6060 | 0.823810 | ||||||||
\(754\) | −39.3165 | −1.43182 | ||||||||
\(755\) | −4.32671 | −0.157465 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.2585 | −0.518233 | −0.259116 | − | 0.965846i | \(-0.583431\pi\) | ||||
−0.259116 | + | 0.965846i | \(0.583431\pi\) | |||||||
\(758\) | 8.51695 | 0.309349 | ||||||||
\(759\) | 0.189379 | 0.00687403 | ||||||||
\(760\) | −3.93854 | −0.142866 | ||||||||
\(761\) | −4.51447 | −0.163649 | −0.0818247 | − | 0.996647i | \(-0.526075\pi\) | ||||
−0.0818247 | + | 0.996647i | \(0.526075\pi\) | |||||||
\(762\) | 15.4576 | 0.559970 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.07435 | −0.147405 | ||||||||
\(765\) | −12.0248 | −0.434757 | ||||||||
\(766\) | 17.3654 | 0.627437 | ||||||||
\(767\) | −10.9481 | −0.395314 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −16.9779 | −0.612239 | −0.306120 | − | 0.951993i | \(-0.599031\pi\) | ||||
−0.306120 | + | 0.951993i | \(0.599031\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.9880 | 0.935935 | ||||||||
\(772\) | −4.50280 | −0.162059 | ||||||||
\(773\) | −39.7267 | −1.42887 | −0.714435 | − | 0.699702i | \(-0.753316\pi\) | ||||
−0.714435 | + | 0.699702i | \(0.753316\pi\) | |||||||
\(774\) | 7.91174 | 0.284381 | ||||||||
\(775\) | 84.3060 | 3.02836 | ||||||||
\(776\) | −11.2277 | −0.403052 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.5117 | −0.807083 | ||||||||
\(779\) | 6.28274 | 0.225102 | ||||||||
\(780\) | −23.4309 | −0.838962 | ||||||||
\(781\) | −16.3084 | −0.583561 | ||||||||
\(782\) | 0.454223 | 0.0162430 | ||||||||
\(783\) | 6.60877 | 0.236178 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.6744 | 1.16620 | ||||||||
\(786\) | −5.76015 | −0.205458 | ||||||||
\(787\) | 54.3699 | 1.93808 | 0.969039 | − | 0.246908i | \(-0.0794144\pi\) | ||||
0.969039 | + | 0.246908i | \(0.0794144\pi\) | |||||||
\(788\) | 0.322407 | 0.0114853 | ||||||||
\(789\) | −6.16848 | −0.219604 | ||||||||
\(790\) | 29.3293 | 1.04349 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.27293 | 0.0452316 | ||||||||
\(793\) | −72.5089 | −2.57487 | ||||||||
\(794\) | −33.8779 | −1.20228 | ||||||||
\(795\) | −44.6285 | −1.58281 | ||||||||
\(796\) | −22.6125 | −0.801478 | ||||||||
\(797\) | −17.4243 | −0.617201 | −0.308600 | − | 0.951192i | \(-0.599861\pi\) | ||||
−0.308600 | + | 0.951192i | \(0.599861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1020 | 0.888046 | ||||||||
\(800\) | 10.5121 | 0.371660 | ||||||||
\(801\) | 5.40934 | 0.191130 | ||||||||
\(802\) | 33.1403 | 1.17022 | ||||||||
\(803\) | 20.7308 | 0.731573 | ||||||||
\(804\) | −2.61205 | −0.0921197 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 47.7114 | 1.68056 | ||||||||
\(807\) | 10.1268 | 0.356480 | ||||||||
\(808\) | −4.38789 | −0.154366 | ||||||||
\(809\) | 31.2970 | 1.10034 | 0.550172 | − | 0.835051i | \(-0.314562\pi\) | ||||
0.550172 | + | 0.835051i | \(0.314562\pi\) | |||||||
\(810\) | 3.93854 | 0.138386 | ||||||||
\(811\) | −12.7410 | −0.447398 | −0.223699 | − | 0.974658i | \(-0.571813\pi\) | ||||
−0.223699 | + | 0.974658i | \(0.571813\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.9731 | 0.384843 | ||||||||
\(814\) | 7.82627 | 0.274311 | ||||||||
\(815\) | 49.6077 | 1.73768 | ||||||||
\(816\) | 3.05310 | 0.106880 | ||||||||
\(817\) | −7.91174 | −0.276797 | ||||||||
\(818\) | 28.2927 | 0.989233 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.7448 | −0.864127 | ||||||||
\(821\) | −0.210997 | −0.00736386 | −0.00368193 | − | 0.999993i | \(-0.501172\pi\) | ||||
−0.00368193 | + | 0.999993i | \(0.501172\pi\) | |||||||
\(822\) | −16.2798 | −0.567825 | ||||||||
\(823\) | −26.1195 | −0.910468 | −0.455234 | − | 0.890372i | \(-0.650444\pi\) | ||||
−0.455234 | + | 0.890372i | \(0.650444\pi\) | |||||||
\(824\) | −6.48370 | −0.225870 | ||||||||
\(825\) | −13.3812 | −0.465873 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.9617 | −0.659364 | −0.329682 | − | 0.944092i | \(-0.606942\pi\) | ||||
−0.329682 | + | 0.944092i | \(0.606942\pi\) | |||||||
\(828\) | −0.148774 | −0.00517027 | ||||||||
\(829\) | −7.91930 | −0.275049 | −0.137524 | − | 0.990498i | \(-0.543915\pi\) | ||||
−0.137524 | + | 0.990498i | \(0.543915\pi\) | |||||||
\(830\) | −47.9503 | −1.66438 | ||||||||
\(831\) | −2.90574 | −0.100799 | ||||||||
\(832\) | 5.94914 | 0.206249 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.24825 | 0.285614 | ||||||||
\(835\) | −38.0092 | −1.31536 | ||||||||
\(836\) | −1.27293 | −0.0440252 | ||||||||
\(837\) | −8.01988 | −0.277208 | ||||||||
\(838\) | −24.5157 | −0.846882 | ||||||||
\(839\) | −1.11414 | −0.0384644 | −0.0192322 | − | 0.999815i | \(-0.506122\pi\) | ||||
−0.0192322 | + | 0.999815i | \(0.506122\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.6758 | 0.506062 | ||||||||
\(842\) | −36.4678 | −1.25676 | ||||||||
\(843\) | −13.5310 | −0.466032 | ||||||||
\(844\) | 0.346997 | 0.0119441 | ||||||||
\(845\) | 88.1928 | 3.03392 | ||||||||
\(846\) | −8.22182 | −0.282672 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.3312 | 0.389116 | ||||||||
\(849\) | 15.3969 | 0.528421 | ||||||||
\(850\) | −32.0946 | −1.10084 | ||||||||
\(851\) | −0.914700 | −0.0313555 | ||||||||
\(852\) | 12.8117 | 0.438922 | ||||||||
\(853\) | −32.7675 | −1.12194 | −0.560969 | − | 0.827837i | \(-0.689571\pi\) | ||||
−0.560969 | + | 0.827837i | \(0.689571\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.93854 | −0.134695 | ||||||||
\(856\) | 4.09675 | 0.140024 | ||||||||
\(857\) | 19.0262 | 0.649921 | 0.324960 | − | 0.945728i | \(-0.394649\pi\) | ||||
0.324960 | + | 0.945728i | \(0.394649\pi\) | |||||||
\(858\) | −7.57283 | −0.258532 | ||||||||
\(859\) | −4.70887 | −0.160664 | −0.0803322 | − | 0.996768i | \(-0.525598\pi\) | ||||
−0.0803322 | + | 0.996768i | \(0.525598\pi\) | |||||||
\(860\) | 31.1607 | 1.06257 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.38080 | 0.251391 | ||||||||
\(863\) | 3.17462 | 0.108065 | 0.0540326 | − | 0.998539i | \(-0.482793\pi\) | ||||
0.0540326 | + | 0.998539i | \(0.482793\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −55.5680 | −1.88937 | ||||||||
\(866\) | 11.4859 | 0.390306 | ||||||||
\(867\) | 7.67857 | 0.260778 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.47918 | 0.321559 | ||||||||
\(870\) | 26.0289 | 0.882463 | ||||||||
\(871\) | 15.5394 | 0.526533 | ||||||||
\(872\) | 5.93860 | 0.201106 | ||||||||
\(873\) | −11.2277 | −0.380001 | ||||||||
\(874\) | 0.148774 | 0.00503237 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.2859 | −0.550249 | ||||||||
\(877\) | −1.38358 | −0.0467201 | −0.0233601 | − | 0.999727i | \(-0.507436\pi\) | ||||
−0.0233601 | + | 0.999727i | \(0.507436\pi\) | |||||||
\(878\) | 22.2521 | 0.750974 | ||||||||
\(879\) | −14.5720 | −0.491503 | ||||||||
\(880\) | 5.01349 | 0.169005 | ||||||||
\(881\) | −0.922545 | −0.0310813 | −0.0155407 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155407 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.2691 | −1.92726 | −0.963630 | − | 0.267241i | \(-0.913888\pi\) | ||||
−0.963630 | + | 0.267241i | \(0.913888\pi\) | |||||||
\(884\) | −18.1633 | −0.610899 | ||||||||
\(885\) | 7.24806 | 0.243641 | ||||||||
\(886\) | −22.7804 | −0.765322 | ||||||||
\(887\) | −52.8038 | −1.77298 | −0.886488 | − | 0.462751i | \(-0.846862\pi\) | ||||
−0.886488 | + | 0.462751i | \(0.846862\pi\) | |||||||
\(888\) | −6.14824 | −0.206321 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21.3049 | 0.714143 | ||||||||
\(891\) | 1.27293 | 0.0426447 | ||||||||
\(892\) | 2.29672 | 0.0769000 | ||||||||
\(893\) | 8.22182 | 0.275133 | ||||||||
\(894\) | 5.92450 | 0.198145 | ||||||||
\(895\) | −48.9386 | −1.63584 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.885079 | 0.0295519 | ||||||||
\(898\) | −8.19585 | −0.273499 | ||||||||
\(899\) | −53.0015 | −1.76770 | ||||||||
\(900\) | 10.5121 | 0.350404 | ||||||||
\(901\) | −34.5954 | −1.15254 | ||||||||
\(902\) | −7.99748 | −0.266287 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.83385 | 0.127512 | ||||||||
\(905\) | 48.7313 | 1.61988 | ||||||||
\(906\) | 1.09856 | 0.0364971 | ||||||||
\(907\) | 35.0561 | 1.16402 | 0.582009 | − | 0.813182i | \(-0.302267\pi\) | ||||
0.582009 | + | 0.813182i | \(0.302267\pi\) | |||||||
\(908\) | −15.3728 | −0.510166 | ||||||||
\(909\) | −4.38789 | −0.145537 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.3448 | 0.773449 | 0.386724 | − | 0.922195i | \(-0.373606\pi\) | ||||
0.386724 | + | 0.922195i | \(0.373606\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | −15.4975 | −0.512891 | ||||||||
\(914\) | −17.9078 | −0.592337 | ||||||||
\(915\) | 48.0035 | 1.58695 | ||||||||
\(916\) | 11.7178 | 0.387168 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.05310 | 0.100767 | ||||||||
\(919\) | 2.68302 | 0.0885045 | 0.0442523 | − | 0.999020i | \(-0.485909\pi\) | ||||
0.0442523 | + | 0.999020i | \(0.485909\pi\) | |||||||
\(920\) | −0.585954 | −0.0193183 | ||||||||
\(921\) | −26.2382 | −0.864577 | ||||||||
\(922\) | 10.8937 | 0.358766 | ||||||||
\(923\) | −76.2187 | −2.50877 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 64.6310 | 2.12506 | ||||||||
\(926\) | −39.6911 | −1.30433 | ||||||||
\(927\) | −6.48370 | −0.212953 | ||||||||
\(928\) | −6.60877 | −0.216943 | ||||||||
\(929\) | −16.0004 | −0.524955 | −0.262478 | − | 0.964938i | \(-0.584540\pi\) | ||||
−0.262478 | + | 0.964938i | \(0.584540\pi\) | |||||||
\(930\) | −31.5866 | −1.03577 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.7683 | 0.450995 | ||||||||
\(933\) | 7.89074 | 0.258331 | ||||||||
\(934\) | −32.0868 | −1.04991 | ||||||||
\(935\) | −15.3067 | −0.500582 | ||||||||
\(936\) | 5.94914 | 0.194454 | ||||||||
\(937\) | −49.2753 | −1.60975 | −0.804876 | − | 0.593443i | \(-0.797768\pi\) | ||||
−0.804876 | + | 0.593443i | \(0.797768\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.3496 | −0.566181 | ||||||||
\(940\) | −32.3820 | −1.05618 | ||||||||
\(941\) | −12.9474 | −0.422074 | −0.211037 | − | 0.977478i | \(-0.567684\pi\) | ||||
−0.211037 | + | 0.977478i | \(0.567684\pi\) | |||||||
\(942\) | −8.29607 | −0.270301 | ||||||||
\(943\) | 0.934710 | 0.0304383 | ||||||||
\(944\) | −1.84029 | −0.0598963 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0711 | 0.327439 | ||||||||
\(947\) | −24.6036 | −0.799510 | −0.399755 | − | 0.916622i | \(-0.630905\pi\) | ||||
−0.399755 | + | 0.916622i | \(0.630905\pi\) | |||||||
\(948\) | −7.44674 | −0.241859 | ||||||||
\(949\) | 96.8869 | 3.14508 | ||||||||
\(950\) | −10.5121 | −0.341058 | ||||||||
\(951\) | −31.0193 | −1.00587 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.2606 | −1.07742 | −0.538708 | − | 0.842493i | \(-0.681087\pi\) | ||||
−0.538708 | + | 0.842493i | \(0.681087\pi\) | |||||||
\(954\) | 11.3312 | 0.366862 | ||||||||
\(955\) | −16.0470 | −0.519269 | ||||||||
\(956\) | 27.3226 | 0.883676 | ||||||||
\(957\) | 8.41250 | 0.271937 | ||||||||
\(958\) | 21.5125 | 0.695038 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.93854 | −0.127116 | ||||||||
\(961\) | 33.3184 | 1.07479 | ||||||||
\(962\) | 36.5767 | 1.17928 | ||||||||
\(963\) | 4.09675 | 0.132016 | ||||||||
\(964\) | 29.4781 | 0.949427 | ||||||||
\(965\) | −17.7345 | −0.570893 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.48135 | −0.0797949 | −0.0398974 | − | 0.999204i | \(-0.512703\pi\) | ||||
−0.0398974 | + | 0.999204i | \(0.512703\pi\) | |||||||
\(968\) | −9.37965 | −0.301473 | ||||||||
\(969\) | −3.05310 | −0.0980798 | ||||||||
\(970\) | −44.2209 | −1.41985 | ||||||||
\(971\) | −9.65888 | −0.309968 | −0.154984 | − | 0.987917i | \(-0.549533\pi\) | ||||
−0.154984 | + | 0.987917i | \(0.549533\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −22.7496 | −0.728944 | ||||||||
\(975\) | −62.5381 | −2.00282 | ||||||||
\(976\) | −12.1881 | −0.390133 | ||||||||
\(977\) | −34.6842 | −1.10965 | −0.554823 | − | 0.831968i | \(-0.687214\pi\) | ||||
−0.554823 | + | 0.831968i | \(0.687214\pi\) | |||||||
\(978\) | −12.5954 | −0.402758 | ||||||||
\(979\) | 6.88571 | 0.220068 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.93860 | 0.189605 | ||||||||
\(982\) | −26.4966 | −0.845539 | ||||||||
\(983\) | 2.51987 | 0.0803715 | 0.0401857 | − | 0.999192i | \(-0.487205\pi\) | ||||
0.0401857 | + | 0.999192i | \(0.487205\pi\) | |||||||
\(984\) | 6.28274 | 0.200286 | ||||||||
\(985\) | 1.26981 | 0.0404597 | ||||||||
\(986\) | 20.1772 | 0.642574 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.94914 | −0.189267 | ||||||||
\(989\) | −1.17706 | −0.0374284 | ||||||||
\(990\) | 5.01349 | 0.159339 | ||||||||
\(991\) | −40.5602 | −1.28844 | −0.644219 | − | 0.764841i | \(-0.722817\pi\) | ||||
−0.644219 | + | 0.764841i | \(0.722817\pi\) | |||||||
\(992\) | 8.01988 | 0.254631 | ||||||||
\(993\) | 27.7615 | 0.880983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −89.0603 | −2.82340 | ||||||||
\(996\) | 12.1746 | 0.385768 | ||||||||
\(997\) | 0.253401 | 0.00802530 | 0.00401265 | − | 0.999992i | \(-0.498723\pi\) | ||||
0.00401265 | + | 0.999992i | \(0.498723\pi\) | |||||||
\(998\) | 20.4302 | 0.646706 | ||||||||
\(999\) | −6.14824 | −0.194522 |
(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 | 5586.2.a.ce.1.8 | ✓ | 8 | |
7.6 | odd | 2 | 5586.2.a.cf.1.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5586.2.a.ce.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5586.2.a.cf.1.1 | yes | 8 | 7.6 | odd | 2 |