Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, 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("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.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: | \(21.5196833447\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 22x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.29554\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.29554 | −1.62319 | −0.811597 | − | 0.584217i | \(-0.801402\pi\) | ||||
−0.811597 | + | 0.584217i | \(0.801402\pi\) | |||||||
\(3\) | −0.293572 | −0.169494 | −0.0847470 | − | 0.996403i | \(-0.527008\pi\) | ||||
−0.0847470 | + | 0.996403i | \(0.527008\pi\) | |||||||
\(4\) | 3.26952 | 1.63476 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.673908 | 0.275122 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.91425 | −1.03034 | ||||||||
\(9\) | −2.91382 | −0.971272 | ||||||||
\(10\) | −2.29554 | −0.725915 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.959841 | −0.277082 | ||||||||
\(13\) | −1.45308 | −0.403013 | −0.201507 | − | 0.979487i | \(-0.564584\pi\) | ||||
−0.201507 | + | 0.979487i | \(0.564584\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.293572 | −0.0758000 | ||||||||
\(16\) | 0.150739 | 0.0376847 | ||||||||
\(17\) | −1.37718 | −0.334016 | −0.167008 | − | 0.985956i | \(-0.553411\pi\) | ||||
−0.167008 | + | 0.985956i | \(0.553411\pi\) | |||||||
\(18\) | 6.68879 | 1.57656 | ||||||||
\(19\) | −3.61374 | −0.829050 | −0.414525 | − | 0.910038i | \(-0.636052\pi\) | ||||
−0.414525 | + | 0.910038i | \(0.636052\pi\) | |||||||
\(20\) | 3.26952 | 0.731088 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.29554 | 0.489412 | ||||||||
\(23\) | −5.58209 | −1.16395 | −0.581973 | − | 0.813208i | \(-0.697719\pi\) | ||||
−0.581973 | + | 0.813208i | \(0.697719\pi\) | |||||||
\(24\) | 0.855542 | 0.174637 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.33562 | 0.654169 | ||||||||
\(27\) | 1.73613 | 0.334119 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.104098 | 0.0193304 | 0.00966522 | − | 0.999953i | \(-0.496923\pi\) | ||||
0.00966522 | + | 0.999953i | \(0.496923\pi\) | |||||||
\(30\) | 0.673908 | 0.123038 | ||||||||
\(31\) | −6.72703 | −1.20821 | −0.604105 | − | 0.796905i | \(-0.706469\pi\) | ||||
−0.604105 | + | 0.796905i | \(0.706469\pi\) | |||||||
\(32\) | 5.48247 | 0.969173 | ||||||||
\(33\) | 0.293572 | 0.0511043 | ||||||||
\(34\) | 3.16139 | 0.542173 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.52679 | −1.58780 | ||||||||
\(37\) | 0.435179 | 0.0715430 | 0.0357715 | − | 0.999360i | \(-0.488611\pi\) | ||||
0.0357715 | + | 0.999360i | \(0.488611\pi\) | |||||||
\(38\) | 8.29551 | 1.34571 | ||||||||
\(39\) | 0.426585 | 0.0683083 | ||||||||
\(40\) | −2.91425 | −0.460783 | ||||||||
\(41\) | 1.22902 | 0.191940 | 0.0959702 | − | 0.995384i | \(-0.469405\pi\) | ||||
0.0959702 | + | 0.995384i | \(0.469405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.44836 | 0.678368 | 0.339184 | − | 0.940720i | \(-0.389849\pi\) | ||||
0.339184 | + | 0.940720i | \(0.389849\pi\) | |||||||
\(44\) | −3.26952 | −0.492899 | ||||||||
\(45\) | −2.91382 | −0.434366 | ||||||||
\(46\) | 12.8139 | 1.88931 | ||||||||
\(47\) | −0.126494 | −0.0184511 | −0.00922555 | − | 0.999957i | \(-0.502937\pi\) | ||||
−0.00922555 | + | 0.999957i | \(0.502937\pi\) | |||||||
\(48\) | −0.0442527 | −0.00638733 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.29554 | −0.324639 | ||||||||
\(51\) | 0.404303 | 0.0566137 | ||||||||
\(52\) | −4.75089 | −0.658831 | ||||||||
\(53\) | 8.05754 | 1.10679 | 0.553394 | − | 0.832920i | \(-0.313332\pi\) | ||||
0.553394 | + | 0.832920i | \(0.313332\pi\) | |||||||
\(54\) | −3.98537 | −0.542340 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.06089 | 0.140519 | ||||||||
\(58\) | −0.238961 | −0.0313771 | ||||||||
\(59\) | 11.3961 | 1.48365 | 0.741826 | − | 0.670593i | \(-0.233960\pi\) | ||||
0.741826 | + | 0.670593i | \(0.233960\pi\) | |||||||
\(60\) | −0.959841 | −0.123915 | ||||||||
\(61\) | 5.32148 | 0.681346 | 0.340673 | − | 0.940182i | \(-0.389345\pi\) | ||||
0.340673 | + | 0.940182i | \(0.389345\pi\) | |||||||
\(62\) | 15.4422 | 1.96116 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8867 | −1.61084 | ||||||||
\(65\) | −1.45308 | −0.180233 | ||||||||
\(66\) | −0.673908 | −0.0829523 | ||||||||
\(67\) | 9.34121 | 1.14121 | 0.570605 | − | 0.821224i | \(-0.306709\pi\) | ||||
0.570605 | + | 0.821224i | \(0.306709\pi\) | |||||||
\(68\) | −4.50273 | −0.546037 | ||||||||
\(69\) | 1.63875 | 0.197282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.97924 | −0.828283 | −0.414141 | − | 0.910213i | \(-0.635918\pi\) | ||||
−0.414141 | + | 0.910213i | \(0.635918\pi\) | |||||||
\(72\) | 8.49158 | 1.00074 | ||||||||
\(73\) | 14.7242 | 1.72334 | 0.861671 | − | 0.507468i | \(-0.169418\pi\) | ||||
0.861671 | + | 0.507468i | \(0.169418\pi\) | |||||||
\(74\) | −0.998973 | −0.116128 | ||||||||
\(75\) | −0.293572 | −0.0338988 | ||||||||
\(76\) | −11.8152 | −1.35530 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.979245 | −0.110878 | ||||||||
\(79\) | −7.63740 | −0.859275 | −0.429637 | − | 0.903002i | \(-0.641359\pi\) | ||||
−0.429637 | + | 0.903002i | \(0.641359\pi\) | |||||||
\(80\) | 0.150739 | 0.0168531 | ||||||||
\(81\) | 8.23177 | 0.914641 | ||||||||
\(82\) | −2.82126 | −0.311557 | ||||||||
\(83\) | 8.19774 | 0.899818 | 0.449909 | − | 0.893074i | \(-0.351456\pi\) | ||||
0.449909 | + | 0.893074i | \(0.351456\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.37718 | −0.149377 | ||||||||
\(86\) | −10.2114 | −1.10112 | ||||||||
\(87\) | −0.0305602 | −0.00327639 | ||||||||
\(88\) | 2.91425 | 0.310660 | ||||||||
\(89\) | −3.74462 | −0.396929 | −0.198464 | − | 0.980108i | \(-0.563595\pi\) | ||||
−0.198464 | + | 0.980108i | \(0.563595\pi\) | |||||||
\(90\) | 6.68879 | 0.705061 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −18.2508 | −1.90278 | ||||||||
\(93\) | 1.97487 | 0.204784 | ||||||||
\(94\) | 0.290373 | 0.0299497 | ||||||||
\(95\) | −3.61374 | −0.370762 | ||||||||
\(96\) | −1.60950 | −0.164269 | ||||||||
\(97\) | −1.39488 | −0.141629 | −0.0708144 | − | 0.997490i | \(-0.522560\pi\) | ||||
−0.0708144 | + | 0.997490i | \(0.522560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.91382 | 0.292849 | ||||||||
\(100\) | 3.26952 | 0.326952 | ||||||||
\(101\) | 6.33566 | 0.630422 | 0.315211 | − | 0.949022i | \(-0.397925\pi\) | ||||
0.315211 | + | 0.949022i | \(0.397925\pi\) | |||||||
\(102\) | −0.928095 | −0.0918951 | ||||||||
\(103\) | −11.4060 | −1.12386 | −0.561932 | − | 0.827184i | \(-0.689942\pi\) | ||||
−0.561932 | + | 0.827184i | \(0.689942\pi\) | |||||||
\(104\) | 4.23465 | 0.415242 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.4964 | −1.79653 | ||||||||
\(107\) | 12.3939 | 1.19816 | 0.599080 | − | 0.800689i | \(-0.295533\pi\) | ||||
0.599080 | + | 0.800689i | \(0.295533\pi\) | |||||||
\(108\) | 5.67632 | 0.546204 | ||||||||
\(109\) | −14.7889 | −1.41652 | −0.708260 | − | 0.705951i | \(-0.750520\pi\) | ||||
−0.708260 | + | 0.705951i | \(0.750520\pi\) | |||||||
\(110\) | 2.29554 | 0.218872 | ||||||||
\(111\) | −0.127756 | −0.0121261 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.64437 | 0.907266 | 0.453633 | − | 0.891189i | \(-0.350128\pi\) | ||||
0.453633 | + | 0.891189i | \(0.350128\pi\) | |||||||
\(114\) | −2.43533 | −0.228090 | ||||||||
\(115\) | −5.58209 | −0.520533 | ||||||||
\(116\) | 0.340350 | 0.0316007 | ||||||||
\(117\) | 4.23402 | 0.391435 | ||||||||
\(118\) | −26.1604 | −2.40826 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.855542 | 0.0781000 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −12.2157 | −1.10596 | ||||||||
\(123\) | −0.360805 | −0.0325327 | ||||||||
\(124\) | −21.9942 | −1.97514 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.268275 | 0.0238055 | 0.0119028 | − | 0.999929i | \(-0.496211\pi\) | ||||
0.0119028 | + | 0.999929i | \(0.496211\pi\) | |||||||
\(128\) | 18.6171 | 1.64554 | ||||||||
\(129\) | −1.30591 | −0.114979 | ||||||||
\(130\) | 3.33562 | 0.292553 | ||||||||
\(131\) | 10.5415 | 0.921019 | 0.460509 | − | 0.887655i | \(-0.347667\pi\) | ||||
0.460509 | + | 0.887655i | \(0.347667\pi\) | |||||||
\(132\) | 0.959841 | 0.0835434 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −21.4432 | −1.85241 | ||||||||
\(135\) | 1.73613 | 0.149422 | ||||||||
\(136\) | 4.01345 | 0.344151 | ||||||||
\(137\) | −4.98272 | −0.425703 | −0.212851 | − | 0.977085i | \(-0.568275\pi\) | ||||
−0.212851 | + | 0.977085i | \(0.568275\pi\) | |||||||
\(138\) | −3.76182 | −0.320227 | ||||||||
\(139\) | 5.80701 | 0.492544 | 0.246272 | − | 0.969201i | \(-0.420794\pi\) | ||||
0.246272 | + | 0.969201i | \(0.420794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.0371352 | 0.00312735 | ||||||||
\(142\) | 16.0211 | 1.34446 | ||||||||
\(143\) | 1.45308 | 0.121513 | ||||||||
\(144\) | −0.439225 | −0.0366021 | ||||||||
\(145\) | 0.104098 | 0.00864484 | ||||||||
\(146\) | −33.8001 | −2.79732 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.42283 | 0.116956 | ||||||||
\(149\) | −8.28793 | −0.678974 | −0.339487 | − | 0.940611i | \(-0.610253\pi\) | ||||
−0.339487 | + | 0.940611i | \(0.610253\pi\) | |||||||
\(150\) | 0.673908 | 0.0550243 | ||||||||
\(151\) | −2.40230 | −0.195496 | −0.0977480 | − | 0.995211i | \(-0.531164\pi\) | ||||
−0.0977480 | + | 0.995211i | \(0.531164\pi\) | |||||||
\(152\) | 10.5313 | 0.854205 | ||||||||
\(153\) | 4.01286 | 0.324420 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.72703 | −0.540328 | ||||||||
\(156\) | 1.39473 | 0.111668 | ||||||||
\(157\) | −16.0405 | −1.28017 | −0.640085 | − | 0.768304i | \(-0.721101\pi\) | ||||
−0.640085 | + | 0.768304i | \(0.721101\pi\) | |||||||
\(158\) | 17.5320 | 1.39477 | ||||||||
\(159\) | −2.36547 | −0.187594 | ||||||||
\(160\) | 5.48247 | 0.433427 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −18.8964 | −1.48464 | ||||||||
\(163\) | −3.93239 | −0.308008 | −0.154004 | − | 0.988070i | \(-0.549217\pi\) | ||||
−0.154004 | + | 0.988070i | \(0.549217\pi\) | |||||||
\(164\) | 4.01830 | 0.313777 | ||||||||
\(165\) | 0.293572 | 0.0228546 | ||||||||
\(166\) | −18.8183 | −1.46058 | ||||||||
\(167\) | 12.2979 | 0.951642 | 0.475821 | − | 0.879542i | \(-0.342151\pi\) | ||||
0.475821 | + | 0.879542i | \(0.342151\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8885 | −0.837580 | ||||||||
\(170\) | 3.16139 | 0.242467 | ||||||||
\(171\) | 10.5298 | 0.805233 | ||||||||
\(172\) | 14.5440 | 1.10897 | ||||||||
\(173\) | 11.3383 | 0.862033 | 0.431017 | − | 0.902344i | \(-0.358155\pi\) | ||||
0.431017 | + | 0.902344i | \(0.358155\pi\) | |||||||
\(174\) | 0.0701522 | 0.00531822 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.150739 | −0.0113624 | ||||||||
\(177\) | −3.34559 | −0.251470 | ||||||||
\(178\) | 8.59594 | 0.644293 | ||||||||
\(179\) | −25.3377 | −1.89383 | −0.946913 | − | 0.321488i | \(-0.895817\pi\) | ||||
−0.946913 | + | 0.321488i | \(0.895817\pi\) | |||||||
\(180\) | −9.52679 | −0.710085 | ||||||||
\(181\) | 3.52411 | 0.261945 | 0.130972 | − | 0.991386i | \(-0.458190\pi\) | ||||
0.130972 | + | 0.991386i | \(0.458190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.56224 | −0.115484 | ||||||||
\(184\) | 16.2676 | 1.19926 | ||||||||
\(185\) | 0.435179 | 0.0319950 | ||||||||
\(186\) | −4.53340 | −0.332405 | ||||||||
\(187\) | 1.37718 | 0.100710 | ||||||||
\(188\) | −0.413576 | −0.0301632 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.29551 | 0.601819 | ||||||||
\(191\) | 10.3942 | 0.752100 | 0.376050 | − | 0.926599i | \(-0.377282\pi\) | ||||
0.376050 | + | 0.926599i | \(0.377282\pi\) | |||||||
\(192\) | 3.78318 | 0.273028 | ||||||||
\(193\) | 6.33141 | 0.455745 | 0.227872 | − | 0.973691i | \(-0.426823\pi\) | ||||
0.227872 | + | 0.973691i | \(0.426823\pi\) | |||||||
\(194\) | 3.20201 | 0.229891 | ||||||||
\(195\) | 0.426585 | 0.0305484 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.7530 | 1.83483 | 0.917413 | − | 0.397937i | \(-0.130274\pi\) | ||||
0.917413 | + | 0.397937i | \(0.130274\pi\) | |||||||
\(198\) | −6.68879 | −0.475352 | ||||||||
\(199\) | −8.00340 | −0.567346 | −0.283673 | − | 0.958921i | \(-0.591553\pi\) | ||||
−0.283673 | + | 0.958921i | \(0.591553\pi\) | |||||||
\(200\) | −2.91425 | −0.206068 | ||||||||
\(201\) | −2.74232 | −0.193428 | ||||||||
\(202\) | −14.5438 | −1.02330 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.32188 | 0.0925499 | ||||||||
\(205\) | 1.22902 | 0.0858383 | ||||||||
\(206\) | 26.1829 | 1.82425 | ||||||||
\(207\) | 16.2652 | 1.13051 | ||||||||
\(208\) | −0.219036 | −0.0151874 | ||||||||
\(209\) | 3.61374 | 0.249968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.5161 | 0.861643 | 0.430821 | − | 0.902437i | \(-0.358224\pi\) | ||||
0.430821 | + | 0.902437i | \(0.358224\pi\) | |||||||
\(212\) | 26.3443 | 1.80933 | ||||||||
\(213\) | 2.04891 | 0.140389 | ||||||||
\(214\) | −28.4507 | −1.94485 | ||||||||
\(215\) | 4.44836 | 0.303375 | ||||||||
\(216\) | −5.05952 | −0.344257 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 33.9486 | 2.29929 | ||||||||
\(219\) | −4.32263 | −0.292096 | ||||||||
\(220\) | −3.26952 | −0.220431 | ||||||||
\(221\) | 2.00116 | 0.134613 | ||||||||
\(222\) | 0.293271 | 0.0196830 | ||||||||
\(223\) | −17.1800 | −1.15046 | −0.575229 | − | 0.817992i | \(-0.695087\pi\) | ||||
−0.575229 | + | 0.817992i | \(0.695087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.91382 | −0.194254 | ||||||||
\(226\) | −22.1391 | −1.47267 | ||||||||
\(227\) | 21.9004 | 1.45358 | 0.726789 | − | 0.686861i | \(-0.241012\pi\) | ||||
0.726789 | + | 0.686861i | \(0.241012\pi\) | |||||||
\(228\) | 3.46862 | 0.229715 | ||||||||
\(229\) | 12.9430 | 0.855296 | 0.427648 | − | 0.903945i | \(-0.359342\pi\) | ||||
0.427648 | + | 0.903945i | \(0.359342\pi\) | |||||||
\(230\) | 12.8139 | 0.844926 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.303366 | −0.0199170 | ||||||||
\(233\) | −2.46926 | −0.161767 | −0.0808833 | − | 0.996724i | \(-0.525774\pi\) | ||||
−0.0808833 | + | 0.996724i | \(0.525774\pi\) | |||||||
\(234\) | −9.71938 | −0.635376 | ||||||||
\(235\) | −0.126494 | −0.00825158 | ||||||||
\(236\) | 37.2600 | 2.42542 | ||||||||
\(237\) | 2.24213 | 0.145642 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.2734 | −0.987957 | −0.493978 | − | 0.869474i | \(-0.664458\pi\) | ||||
−0.493978 | + | 0.869474i | \(0.664458\pi\) | |||||||
\(240\) | −0.0442527 | −0.00285650 | ||||||||
\(241\) | −4.64559 | −0.299248 | −0.149624 | − | 0.988743i | \(-0.547806\pi\) | ||||
−0.149624 | + | 0.988743i | \(0.547806\pi\) | |||||||
\(242\) | −2.29554 | −0.147563 | ||||||||
\(243\) | −7.62501 | −0.489145 | ||||||||
\(244\) | 17.3987 | 1.11384 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.828245 | 0.0528070 | ||||||||
\(247\) | 5.25108 | 0.334118 | ||||||||
\(248\) | 19.6042 | 1.24487 | ||||||||
\(249\) | −2.40663 | −0.152514 | ||||||||
\(250\) | −2.29554 | −0.145183 | ||||||||
\(251\) | 25.2788 | 1.59558 | 0.797791 | − | 0.602935i | \(-0.206002\pi\) | ||||
0.797791 | + | 0.602935i | \(0.206002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.58209 | 0.350943 | ||||||||
\(254\) | −0.615837 | −0.0386410 | ||||||||
\(255\) | 0.404303 | 0.0253184 | ||||||||
\(256\) | −16.9630 | −1.06019 | ||||||||
\(257\) | 30.7280 | 1.91676 | 0.958378 | − | 0.285501i | \(-0.0921600\pi\) | ||||
0.958378 | + | 0.285501i | \(0.0921600\pi\) | |||||||
\(258\) | 2.99778 | 0.186634 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.75089 | −0.294638 | ||||||||
\(261\) | −0.303321 | −0.0187751 | ||||||||
\(262\) | −24.1986 | −1.49499 | ||||||||
\(263\) | −17.7003 | −1.09145 | −0.545725 | − | 0.837965i | \(-0.683746\pi\) | ||||
−0.545725 | + | 0.837965i | \(0.683746\pi\) | |||||||
\(264\) | −0.855542 | −0.0526550 | ||||||||
\(265\) | 8.05754 | 0.494971 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.09932 | 0.0672770 | ||||||||
\(268\) | 30.5413 | 1.86561 | ||||||||
\(269\) | 18.4815 | 1.12683 | 0.563417 | − | 0.826173i | \(-0.309486\pi\) | ||||
0.563417 | + | 0.826173i | \(0.309486\pi\) | |||||||
\(270\) | −3.98537 | −0.242542 | ||||||||
\(271\) | 27.4033 | 1.66463 | 0.832316 | − | 0.554302i | \(-0.187015\pi\) | ||||
0.832316 | + | 0.554302i | \(0.187015\pi\) | |||||||
\(272\) | −0.207595 | −0.0125873 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.4381 | 0.690999 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 5.35792 | 0.322509 | ||||||||
\(277\) | −9.27239 | −0.557124 | −0.278562 | − | 0.960418i | \(-0.589858\pi\) | ||||
−0.278562 | + | 0.960418i | \(0.589858\pi\) | |||||||
\(278\) | −13.3302 | −0.799495 | ||||||||
\(279\) | 19.6013 | 1.17350 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8183 | 1.36122 | 0.680612 | − | 0.732644i | \(-0.261714\pi\) | ||||
0.680612 | + | 0.732644i | \(0.261714\pi\) | |||||||
\(282\) | −0.0852456 | −0.00507630 | ||||||||
\(283\) | 22.9802 | 1.36603 | 0.683015 | − | 0.730404i | \(-0.260668\pi\) | ||||
0.683015 | + | 0.730404i | \(0.260668\pi\) | |||||||
\(284\) | −22.8188 | −1.35405 | ||||||||
\(285\) | 1.06089 | 0.0628420 | ||||||||
\(286\) | −3.33562 | −0.197239 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −15.9749 | −0.941330 | ||||||||
\(289\) | −15.1034 | −0.888433 | ||||||||
\(290\) | −0.238961 | −0.0140323 | ||||||||
\(291\) | 0.409499 | 0.0240052 | ||||||||
\(292\) | 48.1412 | 2.81725 | ||||||||
\(293\) | 7.46806 | 0.436289 | 0.218144 | − | 0.975917i | \(-0.430000\pi\) | ||||
0.218144 | + | 0.975917i | \(0.430000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.3961 | 0.663509 | ||||||||
\(296\) | −1.26822 | −0.0737138 | ||||||||
\(297\) | −1.73613 | −0.100741 | ||||||||
\(298\) | 19.0253 | 1.10211 | ||||||||
\(299\) | 8.11125 | 0.469086 | ||||||||
\(300\) | −0.959841 | −0.0554165 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.51458 | 0.317328 | ||||||||
\(303\) | −1.85997 | −0.106853 | ||||||||
\(304\) | −0.544732 | −0.0312425 | ||||||||
\(305\) | 5.32148 | 0.304707 | ||||||||
\(306\) | −9.21169 | −0.526597 | ||||||||
\(307\) | −15.3016 | −0.873311 | −0.436655 | − | 0.899629i | \(-0.643837\pi\) | ||||
−0.436655 | + | 0.899629i | \(0.643837\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.34847 | 0.190488 | ||||||||
\(310\) | 15.4422 | 0.877058 | ||||||||
\(311\) | −22.5435 | −1.27833 | −0.639163 | − | 0.769072i | \(-0.720719\pi\) | ||||
−0.639163 | + | 0.769072i | \(0.720719\pi\) | |||||||
\(312\) | −1.24318 | −0.0703809 | ||||||||
\(313\) | 8.51249 | 0.481154 | 0.240577 | − | 0.970630i | \(-0.422663\pi\) | ||||
0.240577 | + | 0.970630i | \(0.422663\pi\) | |||||||
\(314\) | 36.8217 | 2.07797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.9707 | −1.40471 | ||||||||
\(317\) | −19.7133 | −1.10721 | −0.553605 | − | 0.832779i | \(-0.686748\pi\) | ||||
−0.553605 | + | 0.832779i | \(0.686748\pi\) | |||||||
\(318\) | 5.43004 | 0.304501 | ||||||||
\(319\) | −0.104098 | −0.00582835 | ||||||||
\(320\) | −12.8867 | −0.720390 | ||||||||
\(321\) | −3.63849 | −0.203081 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.97679 | 0.276916 | ||||||||
\(324\) | 26.9140 | 1.49522 | ||||||||
\(325\) | −1.45308 | −0.0806026 | ||||||||
\(326\) | 9.02697 | 0.499957 | ||||||||
\(327\) | 4.34161 | 0.240092 | ||||||||
\(328\) | −3.58166 | −0.197764 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.673908 | −0.0370974 | ||||||||
\(331\) | 14.8302 | 0.815140 | 0.407570 | − | 0.913174i | \(-0.366376\pi\) | ||||
0.407570 | + | 0.913174i | \(0.366376\pi\) | |||||||
\(332\) | 26.8027 | 1.47099 | ||||||||
\(333\) | −1.26803 | −0.0694877 | ||||||||
\(334\) | −28.2304 | −1.54470 | ||||||||
\(335\) | 9.34121 | 0.510365 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.99144 | 0.326374 | 0.163187 | − | 0.986595i | \(-0.447823\pi\) | ||||
0.163187 | + | 0.986595i | \(0.447823\pi\) | |||||||
\(338\) | 24.9951 | 1.35956 | ||||||||
\(339\) | −2.83132 | −0.153776 | ||||||||
\(340\) | −4.50273 | −0.244195 | ||||||||
\(341\) | 6.72703 | 0.364289 | ||||||||
\(342\) | −24.1716 | −1.30705 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.9636 | −0.698951 | ||||||||
\(345\) | 1.63875 | 0.0882272 | ||||||||
\(346\) | −26.0275 | −1.39925 | ||||||||
\(347\) | −11.7269 | −0.629535 | −0.314767 | − | 0.949169i | \(-0.601926\pi\) | ||||
−0.314767 | + | 0.949169i | \(0.601926\pi\) | |||||||
\(348\) | −0.0999172 | −0.00535612 | ||||||||
\(349\) | 27.8798 | 1.49237 | 0.746186 | − | 0.665738i | \(-0.231883\pi\) | ||||
0.746186 | + | 0.665738i | \(0.231883\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.52275 | −0.134654 | ||||||||
\(352\) | −5.48247 | −0.292217 | ||||||||
\(353\) | 22.0207 | 1.17204 | 0.586021 | − | 0.810296i | \(-0.300693\pi\) | ||||
0.586021 | + | 0.810296i | \(0.300693\pi\) | |||||||
\(354\) | 7.67995 | 0.408185 | ||||||||
\(355\) | −6.97924 | −0.370419 | ||||||||
\(356\) | −12.2431 | −0.648884 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 58.1638 | 3.07405 | ||||||||
\(359\) | −17.8613 | −0.942682 | −0.471341 | − | 0.881951i | \(-0.656230\pi\) | ||||
−0.471341 | + | 0.881951i | \(0.656230\pi\) | |||||||
\(360\) | 8.49158 | 0.447546 | ||||||||
\(361\) | −5.94086 | −0.312677 | ||||||||
\(362\) | −8.08975 | −0.425188 | ||||||||
\(363\) | −0.293572 | −0.0154085 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.7242 | 0.770702 | ||||||||
\(366\) | 3.58619 | 0.187453 | ||||||||
\(367\) | 4.37925 | 0.228595 | 0.114298 | − | 0.993447i | \(-0.463538\pi\) | ||||
0.114298 | + | 0.993447i | \(0.463538\pi\) | |||||||
\(368\) | −0.841439 | −0.0438630 | ||||||||
\(369\) | −3.58113 | −0.186426 | ||||||||
\(370\) | −0.998973 | −0.0519341 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.45688 | 0.334774 | ||||||||
\(373\) | −7.46212 | −0.386374 | −0.193187 | − | 0.981162i | \(-0.561882\pi\) | ||||
−0.193187 | + | 0.981162i | \(0.561882\pi\) | |||||||
\(374\) | −3.16139 | −0.163471 | ||||||||
\(375\) | −0.293572 | −0.0151600 | ||||||||
\(376\) | 0.368636 | 0.0190110 | ||||||||
\(377\) | −0.151263 | −0.00779042 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.4780 | −0.589588 | −0.294794 | − | 0.955561i | \(-0.595251\pi\) | ||||
−0.294794 | + | 0.955561i | \(0.595251\pi\) | |||||||
\(380\) | −11.8152 | −0.606108 | ||||||||
\(381\) | −0.0787580 | −0.00403489 | ||||||||
\(382\) | −23.8604 | −1.22081 | ||||||||
\(383\) | 24.7310 | 1.26369 | 0.631847 | − | 0.775093i | \(-0.282297\pi\) | ||||
0.631847 | + | 0.775093i | \(0.282297\pi\) | |||||||
\(384\) | −5.46547 | −0.278908 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.5340 | −0.739763 | ||||||||
\(387\) | −12.9617 | −0.658880 | ||||||||
\(388\) | −4.56060 | −0.231529 | ||||||||
\(389\) | −28.4414 | −1.44204 | −0.721019 | − | 0.692916i | \(-0.756326\pi\) | ||||
−0.721019 | + | 0.692916i | \(0.756326\pi\) | |||||||
\(390\) | −0.979245 | −0.0495860 | ||||||||
\(391\) | 7.68757 | 0.388777 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.09470 | −0.156107 | ||||||||
\(394\) | −59.1172 | −2.97828 | ||||||||
\(395\) | −7.63740 | −0.384279 | ||||||||
\(396\) | 9.52679 | 0.478739 | ||||||||
\(397\) | 23.1144 | 1.16008 | 0.580038 | − | 0.814589i | \(-0.303038\pi\) | ||||
0.580038 | + | 0.814589i | \(0.303038\pi\) | |||||||
\(398\) | 18.3722 | 0.920913 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.150739 | 0.00753695 | ||||||||
\(401\) | 2.84597 | 0.142121 | 0.0710606 | − | 0.997472i | \(-0.477362\pi\) | ||||
0.0710606 | + | 0.997472i | \(0.477362\pi\) | |||||||
\(402\) | 6.29512 | 0.313972 | ||||||||
\(403\) | 9.77494 | 0.486925 | ||||||||
\(404\) | 20.7146 | 1.03059 | ||||||||
\(405\) | 8.23177 | 0.409040 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.435179 | −0.0215710 | ||||||||
\(408\) | −1.17824 | −0.0583315 | ||||||||
\(409\) | −27.0904 | −1.33953 | −0.669767 | − | 0.742571i | \(-0.733606\pi\) | ||||
−0.669767 | + | 0.742571i | \(0.733606\pi\) | |||||||
\(410\) | −2.82126 | −0.139332 | ||||||||
\(411\) | 1.46279 | 0.0721540 | ||||||||
\(412\) | −37.2921 | −1.83725 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −37.3375 | −1.83504 | ||||||||
\(415\) | 8.19774 | 0.402411 | ||||||||
\(416\) | −7.96649 | −0.390589 | ||||||||
\(417\) | −1.70478 | −0.0834833 | ||||||||
\(418\) | −8.29551 | −0.405747 | ||||||||
\(419\) | 7.34341 | 0.358749 | 0.179375 | − | 0.983781i | \(-0.442593\pi\) | ||||
0.179375 | + | 0.983781i | \(0.442593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.3775 | 1.57798 | 0.788991 | − | 0.614404i | \(-0.210604\pi\) | ||||
0.788991 | + | 0.614404i | \(0.210604\pi\) | |||||||
\(422\) | −28.7312 | −1.39861 | ||||||||
\(423\) | 0.368581 | 0.0179210 | ||||||||
\(424\) | −23.4817 | −1.14037 | ||||||||
\(425\) | −1.37718 | −0.0668032 | ||||||||
\(426\) | −4.70336 | −0.227879 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 40.5220 | 1.95871 | ||||||||
\(429\) | −0.426585 | −0.0205957 | ||||||||
\(430\) | −10.2114 | −0.492437 | ||||||||
\(431\) | 35.9538 | 1.73183 | 0.865916 | − | 0.500190i | \(-0.166736\pi\) | ||||
0.865916 | + | 0.500190i | \(0.166736\pi\) | |||||||
\(432\) | 0.261703 | 0.0125912 | ||||||||
\(433\) | −15.9908 | −0.768468 | −0.384234 | − | 0.923236i | \(-0.625534\pi\) | ||||
−0.384234 | + | 0.923236i | \(0.625534\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0305602 | −0.00146525 | ||||||||
\(436\) | −48.3527 | −2.31567 | ||||||||
\(437\) | 20.1723 | 0.964970 | ||||||||
\(438\) | 9.92278 | 0.474129 | ||||||||
\(439\) | 17.5823 | 0.839157 | 0.419578 | − | 0.907719i | \(-0.362178\pi\) | ||||
0.419578 | + | 0.907719i | \(0.362178\pi\) | |||||||
\(440\) | 2.91425 | 0.138931 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.59376 | −0.218503 | ||||||||
\(443\) | 4.62095 | 0.219548 | 0.109774 | − | 0.993957i | \(-0.464987\pi\) | ||||
0.109774 | + | 0.993957i | \(0.464987\pi\) | |||||||
\(444\) | −0.417703 | −0.0198233 | ||||||||
\(445\) | −3.74462 | −0.177512 | ||||||||
\(446\) | 39.4375 | 1.86742 | ||||||||
\(447\) | 2.43311 | 0.115082 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.2318 | 0.671642 | 0.335821 | − | 0.941926i | \(-0.390986\pi\) | ||||
0.335821 | + | 0.941926i | \(0.390986\pi\) | |||||||
\(450\) | 6.68879 | 0.315313 | ||||||||
\(451\) | −1.22902 | −0.0578722 | ||||||||
\(452\) | 31.5325 | 1.48316 | ||||||||
\(453\) | 0.705247 | 0.0331354 | ||||||||
\(454\) | −50.2732 | −2.35944 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.09171 | −0.144783 | ||||||||
\(457\) | −39.2810 | −1.83749 | −0.918745 | − | 0.394852i | \(-0.870796\pi\) | ||||
−0.918745 | + | 0.394852i | \(0.870796\pi\) | |||||||
\(458\) | −29.7112 | −1.38831 | ||||||||
\(459\) | −2.39097 | −0.111601 | ||||||||
\(460\) | −18.2508 | −0.850947 | ||||||||
\(461\) | 2.04093 | 0.0950556 | 0.0475278 | − | 0.998870i | \(-0.484866\pi\) | ||||
0.0475278 | + | 0.998870i | \(0.484866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.9813 | 0.835660 | 0.417830 | − | 0.908525i | \(-0.362791\pi\) | ||||
0.417830 | + | 0.908525i | \(0.362791\pi\) | |||||||
\(464\) | 0.0156916 | 0.000728462 0 | ||||||||
\(465\) | 1.97487 | 0.0915823 | ||||||||
\(466\) | 5.66829 | 0.262579 | ||||||||
\(467\) | −8.06125 | −0.373030 | −0.186515 | − | 0.982452i | \(-0.559719\pi\) | ||||
−0.186515 | + | 0.982452i | \(0.559719\pi\) | |||||||
\(468\) | 13.8432 | 0.639904 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.290373 | 0.0133939 | ||||||||
\(471\) | 4.70904 | 0.216981 | ||||||||
\(472\) | −33.2112 | −1.52867 | ||||||||
\(473\) | −4.44836 | −0.204536 | ||||||||
\(474\) | −5.14690 | −0.236405 | ||||||||
\(475\) | −3.61374 | −0.165810 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.4782 | −1.07499 | ||||||||
\(478\) | 35.0609 | 1.60365 | ||||||||
\(479\) | 15.0626 | 0.688226 | 0.344113 | − | 0.938928i | \(-0.388180\pi\) | ||||
0.344113 | + | 0.938928i | \(0.388180\pi\) | |||||||
\(480\) | −1.60950 | −0.0734633 | ||||||||
\(481\) | −0.632352 | −0.0288328 | ||||||||
\(482\) | 10.6641 | 0.485739 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.26952 | 0.148615 | ||||||||
\(485\) | −1.39488 | −0.0633383 | ||||||||
\(486\) | 17.5036 | 0.793977 | ||||||||
\(487\) | −40.3416 | −1.82805 | −0.914025 | − | 0.405657i | \(-0.867043\pi\) | ||||
−0.914025 | + | 0.405657i | \(0.867043\pi\) | |||||||
\(488\) | −15.5081 | −0.702020 | ||||||||
\(489\) | 1.15444 | 0.0522055 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3021 | −0.645444 | −0.322722 | − | 0.946494i | \(-0.604598\pi\) | ||||
−0.322722 | + | 0.946494i | \(0.604598\pi\) | |||||||
\(492\) | −1.17966 | −0.0531833 | ||||||||
\(493\) | −0.143361 | −0.00645668 | ||||||||
\(494\) | −12.0541 | −0.542339 | ||||||||
\(495\) | 2.91382 | 0.130966 | ||||||||
\(496\) | −1.01403 | −0.0455311 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.52452 | 0.247560 | ||||||||
\(499\) | 24.6179 | 1.10205 | 0.551025 | − | 0.834489i | \(-0.314237\pi\) | ||||
0.551025 | + | 0.834489i | \(0.314237\pi\) | |||||||
\(500\) | 3.26952 | 0.146218 | ||||||||
\(501\) | −3.61033 | −0.161298 | ||||||||
\(502\) | −58.0285 | −2.58994 | ||||||||
\(503\) | 6.42927 | 0.286667 | 0.143333 | − | 0.989674i | \(-0.454218\pi\) | ||||
0.143333 | + | 0.989674i | \(0.454218\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.33566 | 0.281933 | ||||||||
\(506\) | −12.8139 | −0.569649 | ||||||||
\(507\) | 3.19657 | 0.141965 | ||||||||
\(508\) | 0.877131 | 0.0389164 | ||||||||
\(509\) | −34.7891 | −1.54200 | −0.771001 | − | 0.636834i | \(-0.780244\pi\) | ||||
−0.771001 | + | 0.636834i | \(0.780244\pi\) | |||||||
\(510\) | −0.928095 | −0.0410967 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.70500 | 0.0753512 | ||||||||
\(513\) | −6.27393 | −0.277001 | ||||||||
\(514\) | −70.5374 | −3.11127 | ||||||||
\(515\) | −11.4060 | −0.502607 | ||||||||
\(516\) | −4.26971 | −0.187964 | ||||||||
\(517\) | 0.126494 | 0.00556322 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.32860 | −0.146109 | ||||||||
\(520\) | 4.23465 | 0.185702 | ||||||||
\(521\) | −12.8010 | −0.560821 | −0.280410 | − | 0.959880i | \(-0.590471\pi\) | ||||
−0.280410 | + | 0.959880i | \(0.590471\pi\) | |||||||
\(522\) | 0.696287 | 0.0304757 | ||||||||
\(523\) | 2.71397 | 0.118674 | 0.0593368 | − | 0.998238i | \(-0.481101\pi\) | ||||
0.0593368 | + | 0.998238i | \(0.481101\pi\) | |||||||
\(524\) | 34.4658 | 1.50565 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 40.6319 | 1.77163 | ||||||||
\(527\) | 9.26435 | 0.403562 | ||||||||
\(528\) | 0.0442527 | 0.00192585 | ||||||||
\(529\) | 8.15976 | 0.354772 | ||||||||
\(530\) | −18.4964 | −0.803434 | ||||||||
\(531\) | −33.2063 | −1.44103 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.78587 | −0.0773545 | ||||||||
\(534\) | −2.52353 | −0.109204 | ||||||||
\(535\) | 12.3939 | 0.535833 | ||||||||
\(536\) | −27.2226 | −1.17584 | ||||||||
\(537\) | 7.43844 | 0.320992 | ||||||||
\(538\) | −42.4250 | −1.82907 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.67632 | 0.244270 | ||||||||
\(541\) | 18.3714 | 0.789848 | 0.394924 | − | 0.918714i | \(-0.370771\pi\) | ||||
0.394924 | + | 0.918714i | \(0.370771\pi\) | |||||||
\(542\) | −62.9055 | −2.70202 | ||||||||
\(543\) | −1.03458 | −0.0443981 | ||||||||
\(544\) | −7.55037 | −0.323719 | ||||||||
\(545\) | −14.7889 | −0.633487 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.58542 | 0.324329 | 0.162165 | − | 0.986764i | \(-0.448152\pi\) | ||||
0.162165 | + | 0.986764i | \(0.448152\pi\) | |||||||
\(548\) | −16.2911 | −0.695923 | ||||||||
\(549\) | −15.5058 | −0.661772 | ||||||||
\(550\) | 2.29554 | 0.0978823 | ||||||||
\(551\) | −0.376182 | −0.0160259 | ||||||||
\(552\) | −4.77572 | −0.203268 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 21.2852 | 0.904321 | ||||||||
\(555\) | −0.127756 | −0.00542296 | ||||||||
\(556\) | 18.9862 | 0.805193 | ||||||||
\(557\) | 24.4867 | 1.03754 | 0.518768 | − | 0.854915i | \(-0.326391\pi\) | ||||
0.518768 | + | 0.854915i | \(0.326391\pi\) | |||||||
\(558\) | −44.9957 | −1.90482 | ||||||||
\(559\) | −6.46384 | −0.273391 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.404303 | −0.0170697 | ||||||||
\(562\) | −52.3804 | −2.20953 | ||||||||
\(563\) | −5.29195 | −0.223029 | −0.111514 | − | 0.993763i | \(-0.535570\pi\) | ||||
−0.111514 | + | 0.993763i | \(0.535570\pi\) | |||||||
\(564\) | 0.121415 | 0.00511247 | ||||||||
\(565\) | 9.64437 | 0.405741 | ||||||||
\(566\) | −52.7521 | −2.21733 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.3392 | 0.853415 | ||||||||
\(569\) | 38.2666 | 1.60422 | 0.802111 | − | 0.597176i | \(-0.203710\pi\) | ||||
0.802111 | + | 0.597176i | \(0.203710\pi\) | |||||||
\(570\) | −2.43533 | −0.102005 | ||||||||
\(571\) | −28.8958 | −1.20925 | −0.604627 | − | 0.796509i | \(-0.706678\pi\) | ||||
−0.604627 | + | 0.796509i | \(0.706678\pi\) | |||||||
\(572\) | 4.75089 | 0.198645 | ||||||||
\(573\) | −3.05146 | −0.127476 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.58209 | −0.232789 | ||||||||
\(576\) | 37.5495 | 1.56456 | ||||||||
\(577\) | 26.4403 | 1.10073 | 0.550363 | − | 0.834925i | \(-0.314489\pi\) | ||||
0.550363 | + | 0.834925i | \(0.314489\pi\) | |||||||
\(578\) | 34.6704 | 1.44210 | ||||||||
\(579\) | −1.85873 | −0.0772460 | ||||||||
\(580\) | 0.340350 | 0.0141322 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.940022 | −0.0389652 | ||||||||
\(583\) | −8.05754 | −0.333709 | ||||||||
\(584\) | −42.9101 | −1.77563 | ||||||||
\(585\) | 4.23402 | 0.175055 | ||||||||
\(586\) | −17.1433 | −0.708182 | ||||||||
\(587\) | −29.7315 | −1.22715 | −0.613576 | − | 0.789636i | \(-0.710269\pi\) | ||||
−0.613576 | + | 0.789636i | \(0.710269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.3098 | 1.00167 | ||||||||
\(590\) | −26.1604 | −1.07700 | ||||||||
\(591\) | −7.56036 | −0.310992 | ||||||||
\(592\) | 0.0655984 | 0.00269608 | ||||||||
\(593\) | −6.72955 | −0.276349 | −0.138175 | − | 0.990408i | \(-0.544124\pi\) | ||||
−0.138175 | + | 0.990408i | \(0.544124\pi\) | |||||||
\(594\) | 3.98537 | 0.163522 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.0976 | −1.10996 | ||||||||
\(597\) | 2.34957 | 0.0961617 | ||||||||
\(598\) | −18.6197 | −0.761418 | ||||||||
\(599\) | 15.2411 | 0.622736 | 0.311368 | − | 0.950289i | \(-0.399213\pi\) | ||||
0.311368 | + | 0.950289i | \(0.399213\pi\) | |||||||
\(600\) | 0.855542 | 0.0349274 | ||||||||
\(601\) | 20.2186 | 0.824736 | 0.412368 | − | 0.911017i | \(-0.364702\pi\) | ||||
0.412368 | + | 0.911017i | \(0.364702\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.2186 | −1.10843 | ||||||||
\(604\) | −7.85436 | −0.319590 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 4.26965 | 0.173443 | ||||||||
\(607\) | −40.0956 | −1.62743 | −0.813715 | − | 0.581264i | \(-0.802559\pi\) | ||||
−0.813715 | + | 0.581264i | \(0.802559\pi\) | |||||||
\(608\) | −19.8122 | −0.803492 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.2157 | −0.494599 | ||||||||
\(611\) | 0.183807 | 0.00743604 | ||||||||
\(612\) | 13.1201 | 0.530350 | ||||||||
\(613\) | −10.0274 | −0.405002 | −0.202501 | − | 0.979282i | \(-0.564907\pi\) | ||||
−0.202501 | + | 0.979282i | \(0.564907\pi\) | |||||||
\(614\) | 35.1256 | 1.41755 | ||||||||
\(615\) | −0.360805 | −0.0145491 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.1046 | −1.25222 | −0.626112 | − | 0.779733i | \(-0.715355\pi\) | ||||
−0.626112 | + | 0.779733i | \(0.715355\pi\) | |||||||
\(618\) | −7.68657 | −0.309199 | ||||||||
\(619\) | −15.6172 | −0.627710 | −0.313855 | − | 0.949471i | \(-0.601621\pi\) | ||||
−0.313855 | + | 0.949471i | \(0.601621\pi\) | |||||||
\(620\) | −21.9942 | −0.883308 | ||||||||
\(621\) | −9.69125 | −0.388896 | ||||||||
\(622\) | 51.7496 | 2.07497 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.0643030 | 0.00257418 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −19.5408 | −0.781007 | ||||||||
\(627\) | −1.06089 | −0.0423680 | ||||||||
\(628\) | −52.4448 | −2.09277 | ||||||||
\(629\) | −0.599321 | −0.0238965 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.02267 | −0.160140 | −0.0800699 | − | 0.996789i | \(-0.525514\pi\) | ||||
−0.0800699 | + | 0.996789i | \(0.525514\pi\) | |||||||
\(632\) | 22.2573 | 0.885347 | ||||||||
\(633\) | −3.67437 | −0.146043 | ||||||||
\(634\) | 45.2528 | 1.79722 | ||||||||
\(635\) | 0.268275 | 0.0106462 | ||||||||
\(636\) | −7.73395 | −0.306671 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.238961 | 0.00946054 | ||||||||
\(639\) | 20.3362 | 0.804488 | ||||||||
\(640\) | 18.6171 | 0.735906 | ||||||||
\(641\) | 27.6129 | 1.09064 | 0.545321 | − | 0.838227i | \(-0.316408\pi\) | ||||
0.545321 | + | 0.838227i | \(0.316408\pi\) | |||||||
\(642\) | 8.35232 | 0.329640 | ||||||||
\(643\) | −30.9004 | −1.21859 | −0.609296 | − | 0.792942i | \(-0.708548\pi\) | ||||
−0.609296 | + | 0.792942i | \(0.708548\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.30591 | −0.0514203 | ||||||||
\(646\) | −11.4244 | −0.449488 | ||||||||
\(647\) | 42.4760 | 1.66990 | 0.834952 | − | 0.550323i | \(-0.185495\pi\) | ||||
0.834952 | + | 0.550323i | \(0.185495\pi\) | |||||||
\(648\) | −23.9894 | −0.942393 | ||||||||
\(649\) | −11.3961 | −0.447338 | ||||||||
\(650\) | 3.33562 | 0.130834 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.8570 | −0.503520 | ||||||||
\(653\) | 38.7082 | 1.51477 | 0.757385 | − | 0.652969i | \(-0.226477\pi\) | ||||
0.757385 | + | 0.652969i | \(0.226477\pi\) | |||||||
\(654\) | −9.96636 | −0.389716 | ||||||||
\(655\) | 10.5415 | 0.411892 | ||||||||
\(656\) | 0.185261 | 0.00723322 | ||||||||
\(657\) | −42.9037 | −1.67383 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.7649 | −0.575160 | −0.287580 | − | 0.957757i | \(-0.592851\pi\) | ||||
−0.287580 | + | 0.957757i | \(0.592851\pi\) | |||||||
\(660\) | 0.959841 | 0.0373618 | ||||||||
\(661\) | −28.2032 | −1.09698 | −0.548489 | − | 0.836158i | \(-0.684797\pi\) | ||||
−0.548489 | + | 0.836158i | \(0.684797\pi\) | |||||||
\(662\) | −34.0433 | −1.32313 | ||||||||
\(663\) | −0.587486 | −0.0228161 | ||||||||
\(664\) | −23.8902 | −0.927121 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.91082 | 0.112792 | ||||||||
\(667\) | −0.581083 | −0.0224996 | ||||||||
\(668\) | 40.2084 | 1.55571 | ||||||||
\(669\) | 5.04357 | 0.194996 | ||||||||
\(670\) | −21.4432 | −0.828422 | ||||||||
\(671\) | −5.32148 | −0.205434 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9087 | 0.459048 | 0.229524 | − | 0.973303i | \(-0.426283\pi\) | ||||
0.229524 | + | 0.973303i | \(0.426283\pi\) | |||||||
\(674\) | −13.7536 | −0.529769 | ||||||||
\(675\) | 1.73613 | 0.0668237 | ||||||||
\(676\) | −35.6004 | −1.36924 | ||||||||
\(677\) | 10.1493 | 0.390069 | 0.195035 | − | 0.980796i | \(-0.437518\pi\) | ||||
0.195035 | + | 0.980796i | \(0.437518\pi\) | |||||||
\(678\) | 6.49941 | 0.249608 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.01345 | 0.153909 | ||||||||
\(681\) | −6.42933 | −0.246373 | ||||||||
\(682\) | −15.4422 | −0.591312 | ||||||||
\(683\) | 6.84024 | 0.261735 | 0.130867 | − | 0.991400i | \(-0.458224\pi\) | ||||
0.130867 | + | 0.991400i | \(0.458224\pi\) | |||||||
\(684\) | 34.4274 | 1.31636 | ||||||||
\(685\) | −4.98272 | −0.190380 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.79970 | −0.144967 | ||||||||
\(688\) | 0.670540 | 0.0255641 | ||||||||
\(689\) | −11.7083 | −0.446050 | ||||||||
\(690\) | −3.76182 | −0.143210 | ||||||||
\(691\) | 25.7899 | 0.981094 | 0.490547 | − | 0.871415i | \(-0.336797\pi\) | ||||
0.490547 | + | 0.871415i | \(0.336797\pi\) | |||||||
\(692\) | 37.0708 | 1.40922 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.9197 | 1.02186 | ||||||||
\(695\) | 5.80701 | 0.220272 | ||||||||
\(696\) | 0.0890599 | 0.00337581 | ||||||||
\(697\) | −1.69258 | −0.0641111 | ||||||||
\(698\) | −63.9993 | −2.42241 | ||||||||
\(699\) | 0.724906 | 0.0274184 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.6370 | −0.968298 | −0.484149 | − | 0.874986i | \(-0.660871\pi\) | ||||
−0.484149 | + | 0.874986i | \(0.660871\pi\) | |||||||
\(702\) | 5.79107 | 0.218570 | ||||||||
\(703\) | −1.57263 | −0.0593127 | ||||||||
\(704\) | 12.8867 | 0.485687 | ||||||||
\(705\) | 0.0371352 | 0.00139859 | ||||||||
\(706\) | −50.5495 | −1.90245 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −10.9385 | −0.411094 | ||||||||
\(709\) | 35.1596 | 1.32045 | 0.660223 | − | 0.751069i | \(-0.270462\pi\) | ||||
0.660223 | + | 0.751069i | \(0.270462\pi\) | |||||||
\(710\) | 16.0211 | 0.601263 | ||||||||
\(711\) | 22.2540 | 0.834589 | ||||||||
\(712\) | 10.9128 | 0.408973 | ||||||||
\(713\) | 37.5509 | 1.40629 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.45308 | 0.0543423 | ||||||||
\(716\) | −82.8421 | −3.09596 | ||||||||
\(717\) | 4.48386 | 0.167453 | ||||||||
\(718\) | 41.0013 | 1.53016 | ||||||||
\(719\) | −44.8159 | −1.67135 | −0.835676 | − | 0.549222i | \(-0.814924\pi\) | ||||
−0.835676 | + | 0.549222i | \(0.814924\pi\) | |||||||
\(720\) | −0.439225 | −0.0163690 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.6375 | 0.507535 | ||||||||
\(723\) | 1.36381 | 0.0507208 | ||||||||
\(724\) | 11.5222 | 0.428217 | ||||||||
\(725\) | 0.104098 | 0.00386609 | ||||||||
\(726\) | 0.673908 | 0.0250111 | ||||||||
\(727\) | −39.1944 | −1.45364 | −0.726819 | − | 0.686829i | \(-0.759002\pi\) | ||||
−0.726819 | + | 0.686829i | \(0.759002\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.4568 | −0.831734 | ||||||||
\(730\) | −33.8001 | −1.25100 | ||||||||
\(731\) | −6.12620 | −0.226586 | ||||||||
\(732\) | −5.10778 | −0.188789 | ||||||||
\(733\) | 18.2423 | 0.673796 | 0.336898 | − | 0.941541i | \(-0.390622\pi\) | ||||
0.336898 | + | 0.941541i | \(0.390622\pi\) | |||||||
\(734\) | −10.0528 | −0.371055 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.6037 | −1.12807 | ||||||||
\(737\) | −9.34121 | −0.344088 | ||||||||
\(738\) | 8.22065 | 0.302606 | ||||||||
\(739\) | −46.9095 | −1.72559 | −0.862797 | − | 0.505550i | \(-0.831290\pi\) | ||||
−0.862797 | + | 0.505550i | \(0.831290\pi\) | |||||||
\(740\) | 1.42283 | 0.0523042 | ||||||||
\(741\) | −1.54157 | −0.0566310 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.95770 | 0.365312 | 0.182656 | − | 0.983177i | \(-0.441530\pi\) | ||||
0.182656 | + | 0.983177i | \(0.441530\pi\) | |||||||
\(744\) | −5.75526 | −0.210998 | ||||||||
\(745\) | −8.28793 | −0.303646 | ||||||||
\(746\) | 17.1296 | 0.627160 | ||||||||
\(747\) | −23.8867 | −0.873968 | ||||||||
\(748\) | 4.50273 | 0.164636 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.673908 | 0.0246076 | ||||||||
\(751\) | 8.46961 | 0.309060 | 0.154530 | − | 0.987988i | \(-0.450614\pi\) | ||||
0.154530 | + | 0.987988i | \(0.450614\pi\) | |||||||
\(752\) | −0.0190676 | −0.000695325 0 | ||||||||
\(753\) | −7.42114 | −0.270441 | ||||||||
\(754\) | 0.347230 | 0.0126454 | ||||||||
\(755\) | −2.40230 | −0.0874285 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.4472 | 0.743167 | 0.371584 | − | 0.928399i | \(-0.378815\pi\) | ||||
0.371584 | + | 0.928399i | \(0.378815\pi\) | |||||||
\(758\) | 26.3484 | 0.957016 | ||||||||
\(759\) | −1.63875 | −0.0594827 | ||||||||
\(760\) | 10.5313 | 0.382012 | ||||||||
\(761\) | 52.8243 | 1.91488 | 0.957439 | − | 0.288635i | \(-0.0932015\pi\) | ||||
0.957439 | + | 0.288635i | \(0.0932015\pi\) | |||||||
\(762\) | 0.180792 | 0.00654942 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 33.9842 | 1.22951 | ||||||||
\(765\) | 4.01286 | 0.145085 | ||||||||
\(766\) | −56.7711 | −2.05122 | ||||||||
\(767\) | −16.5596 | −0.597931 | ||||||||
\(768\) | 4.97985 | 0.179695 | ||||||||
\(769\) | 15.4979 | 0.558870 | 0.279435 | − | 0.960165i | \(-0.409853\pi\) | ||||
0.279435 | + | 0.960165i | \(0.409853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.02087 | −0.324879 | ||||||||
\(772\) | 20.7007 | 0.745035 | ||||||||
\(773\) | −25.4616 | −0.915790 | −0.457895 | − | 0.889006i | \(-0.651396\pi\) | ||||
−0.457895 | + | 0.889006i | \(0.651396\pi\) | |||||||
\(774\) | 29.7541 | 1.06949 | ||||||||
\(775\) | −6.72703 | −0.241642 | ||||||||
\(776\) | 4.06503 | 0.145926 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 65.2885 | 2.34071 | ||||||||
\(779\) | −4.44136 | −0.159128 | ||||||||
\(780\) | 1.39473 | 0.0499394 | ||||||||
\(781\) | 6.97924 | 0.249737 | ||||||||
\(782\) | −17.6471 | −0.631061 | ||||||||
\(783\) | 0.180727 | 0.00645866 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.0405 | −0.572510 | ||||||||
\(786\) | 7.10403 | 0.253392 | ||||||||
\(787\) | −31.9072 | −1.13737 | −0.568684 | − | 0.822556i | \(-0.692547\pi\) | ||||
−0.568684 | + | 0.822556i | \(0.692547\pi\) | |||||||
\(788\) | 84.2001 | 2.99950 | ||||||||
\(789\) | 5.19632 | 0.184994 | ||||||||
\(790\) | 17.5320 | 0.623760 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8.49158 | −0.301735 | ||||||||
\(793\) | −7.73256 | −0.274591 | ||||||||
\(794\) | −53.0600 | −1.88303 | ||||||||
\(795\) | −2.36547 | −0.0838945 | ||||||||
\(796\) | −26.1673 | −0.927475 | ||||||||
\(797\) | −28.8682 | −1.02256 | −0.511281 | − | 0.859413i | \(-0.670829\pi\) | ||||
−0.511281 | + | 0.859413i | \(0.670829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.174206 | 0.00616296 | ||||||||
\(800\) | 5.48247 | 0.193835 | ||||||||
\(801\) | 10.9111 | 0.385526 | ||||||||
\(802\) | −6.53306 | −0.230690 | ||||||||
\(803\) | −14.7242 | −0.519607 | ||||||||
\(804\) | −8.96608 | −0.316209 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −22.4388 | −0.790374 | ||||||||
\(807\) | −5.42564 | −0.190992 | ||||||||
\(808\) | −18.4637 | −0.649551 | ||||||||
\(809\) | 37.4007 | 1.31494 | 0.657469 | − | 0.753482i | \(-0.271627\pi\) | ||||
0.657469 | + | 0.753482i | \(0.271627\pi\) | |||||||
\(810\) | −18.8964 | −0.663951 | ||||||||
\(811\) | −28.2722 | −0.992771 | −0.496386 | − | 0.868102i | \(-0.665340\pi\) | ||||
−0.496386 | + | 0.868102i | \(0.665340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.04484 | −0.282145 | ||||||||
\(814\) | 0.998973 | 0.0350140 | ||||||||
\(815\) | −3.93239 | −0.137745 | ||||||||
\(816\) | 0.0609441 | 0.00213347 | ||||||||
\(817\) | −16.0752 | −0.562401 | ||||||||
\(818\) | 62.1872 | 2.17433 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.01830 | 0.140325 | ||||||||
\(821\) | −11.4769 | −0.400548 | −0.200274 | − | 0.979740i | \(-0.564183\pi\) | ||||
−0.200274 | + | 0.979740i | \(0.564183\pi\) | |||||||
\(822\) | −3.35790 | −0.117120 | ||||||||
\(823\) | −28.5492 | −0.995164 | −0.497582 | − | 0.867417i | \(-0.665779\pi\) | ||||
−0.497582 | + | 0.867417i | \(0.665779\pi\) | |||||||
\(824\) | 33.2398 | 1.15796 | ||||||||
\(825\) | 0.293572 | 0.0102209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.3199 | 1.26297 | 0.631483 | − | 0.775390i | \(-0.282446\pi\) | ||||
0.631483 | + | 0.775390i | \(0.282446\pi\) | |||||||
\(828\) | 53.1794 | 1.84811 | ||||||||
\(829\) | 29.2920 | 1.01735 | 0.508677 | − | 0.860957i | \(-0.330135\pi\) | ||||
0.508677 | + | 0.860957i | \(0.330135\pi\) | |||||||
\(830\) | −18.8183 | −0.653192 | ||||||||
\(831\) | 2.72212 | 0.0944291 | ||||||||
\(832\) | 18.7255 | 0.649190 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.91339 | 0.135510 | ||||||||
\(835\) | 12.2979 | 0.425587 | ||||||||
\(836\) | 11.8152 | 0.408638 | ||||||||
\(837\) | −11.6790 | −0.403686 | ||||||||
\(838\) | −16.8571 | −0.582320 | ||||||||
\(839\) | −3.32507 | −0.114794 | −0.0573971 | − | 0.998351i | \(-0.518280\pi\) | ||||
−0.0573971 | + | 0.998351i | \(0.518280\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9892 | −0.999626 | ||||||||
\(842\) | −74.3240 | −2.56137 | ||||||||
\(843\) | −6.69881 | −0.230719 | ||||||||
\(844\) | 40.9216 | 1.40858 | ||||||||
\(845\) | −10.8885 | −0.374577 | ||||||||
\(846\) | −0.846095 | −0.0290893 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.21458 | 0.0417090 | ||||||||
\(849\) | −6.74634 | −0.231534 | ||||||||
\(850\) | 3.16139 | 0.108435 | ||||||||
\(851\) | −2.42921 | −0.0832722 | ||||||||
\(852\) | 6.69896 | 0.229503 | ||||||||
\(853\) | 27.1154 | 0.928415 | 0.464208 | − | 0.885726i | \(-0.346339\pi\) | ||||
0.464208 | + | 0.885726i | \(0.346339\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.5298 | 0.360111 | ||||||||
\(856\) | −36.1188 | −1.23451 | ||||||||
\(857\) | 55.1107 | 1.88255 | 0.941273 | − | 0.337648i | \(-0.109631\pi\) | ||||
0.941273 | + | 0.337648i | \(0.109631\pi\) | |||||||
\(858\) | 0.979245 | 0.0334309 | ||||||||
\(859\) | 23.9506 | 0.817185 | 0.408592 | − | 0.912717i | \(-0.366020\pi\) | ||||
0.408592 | + | 0.912717i | \(0.366020\pi\) | |||||||
\(860\) | 14.5440 | 0.495946 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −82.5335 | −2.81110 | ||||||||
\(863\) | 0.309183 | 0.0105247 | 0.00526235 | − | 0.999986i | \(-0.498325\pi\) | ||||
0.00526235 | + | 0.999986i | \(0.498325\pi\) | |||||||
\(864\) | 9.51829 | 0.323819 | ||||||||
\(865\) | 11.3383 | 0.385513 | ||||||||
\(866\) | 36.7075 | 1.24737 | ||||||||
\(867\) | 4.43393 | 0.150584 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.63740 | 0.259081 | ||||||||
\(870\) | 0.0701522 | 0.00237838 | ||||||||
\(871\) | −13.5736 | −0.459923 | ||||||||
\(872\) | 43.0986 | 1.45950 | ||||||||
\(873\) | 4.06443 | 0.137560 | ||||||||
\(874\) | −46.3063 | −1.56633 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.1329 | −0.477507 | ||||||||
\(877\) | −28.4555 | −0.960873 | −0.480437 | − | 0.877029i | \(-0.659522\pi\) | ||||
−0.480437 | + | 0.877029i | \(0.659522\pi\) | |||||||
\(878\) | −40.3609 | −1.36212 | ||||||||
\(879\) | −2.19241 | −0.0739483 | ||||||||
\(880\) | −0.150739 | −0.00508141 | ||||||||
\(881\) | 37.5430 | 1.26486 | 0.632428 | − | 0.774619i | \(-0.282059\pi\) | ||||
0.632428 | + | 0.774619i | \(0.282059\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.90495 | −0.0977592 | −0.0488796 | − | 0.998805i | \(-0.515565\pi\) | ||||
−0.0488796 | + | 0.998805i | \(0.515565\pi\) | |||||||
\(884\) | 6.54285 | 0.220060 | ||||||||
\(885\) | −3.34559 | −0.112461 | ||||||||
\(886\) | −10.6076 | −0.356370 | ||||||||
\(887\) | −56.7508 | −1.90550 | −0.952752 | − | 0.303749i | \(-0.901762\pi\) | ||||
−0.952752 | + | 0.303749i | \(0.901762\pi\) | |||||||
\(888\) | 0.372314 | 0.0124940 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.59594 | 0.288137 | ||||||||
\(891\) | −8.23177 | −0.275775 | ||||||||
\(892\) | −56.1705 | −1.88073 | ||||||||
\(893\) | 0.457118 | 0.0152969 | ||||||||
\(894\) | −5.58530 | −0.186800 | ||||||||
\(895\) | −25.3377 | −0.846945 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.38124 | −0.0795072 | ||||||||
\(898\) | −32.6698 | −1.09021 | ||||||||
\(899\) | −0.700268 | −0.0233552 | ||||||||
\(900\) | −9.52679 | −0.317560 | ||||||||
\(901\) | −11.0967 | −0.369685 | ||||||||
\(902\) | 2.82126 | 0.0939378 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.1061 | −0.934794 | ||||||||
\(905\) | 3.52411 | 0.117145 | ||||||||
\(906\) | −1.61893 | −0.0537852 | ||||||||
\(907\) | −2.60141 | −0.0863784 | −0.0431892 | − | 0.999067i | \(-0.513752\pi\) | ||||
−0.0431892 | + | 0.999067i | \(0.513752\pi\) | |||||||
\(908\) | 71.6037 | 2.37625 | ||||||||
\(909\) | −18.4610 | −0.612311 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.8906 | −0.625872 | −0.312936 | − | 0.949774i | \(-0.601313\pi\) | ||||
−0.312936 | + | 0.949774i | \(0.601313\pi\) | |||||||
\(912\) | 0.159918 | 0.00529542 | ||||||||
\(913\) | −8.19774 | −0.271305 | ||||||||
\(914\) | 90.1714 | 2.98260 | ||||||||
\(915\) | −1.56224 | −0.0516460 | ||||||||
\(916\) | 42.3174 | 1.39821 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.48858 | 0.181150 | ||||||||
\(919\) | 2.85576 | 0.0942028 | 0.0471014 | − | 0.998890i | \(-0.485002\pi\) | ||||
0.0471014 | + | 0.998890i | \(0.485002\pi\) | |||||||
\(920\) | 16.2676 | 0.536327 | ||||||||
\(921\) | 4.49214 | 0.148021 | ||||||||
\(922\) | −4.68505 | −0.154294 | ||||||||
\(923\) | 10.1414 | 0.333809 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.435179 | 0.0143086 | ||||||||
\(926\) | −41.2768 | −1.35644 | ||||||||
\(927\) | 33.2349 | 1.09158 | ||||||||
\(928\) | 0.570712 | 0.0187345 | ||||||||
\(929\) | −4.55208 | −0.149349 | −0.0746744 | − | 0.997208i | \(-0.523792\pi\) | ||||
−0.0746744 | + | 0.997208i | \(0.523792\pi\) | |||||||
\(930\) | −4.53340 | −0.148656 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8.07330 | −0.264450 | ||||||||
\(933\) | 6.61815 | 0.216668 | ||||||||
\(934\) | 18.5050 | 0.605501 | ||||||||
\(935\) | 1.37718 | 0.0450387 | ||||||||
\(936\) | −12.3390 | −0.403312 | ||||||||
\(937\) | 39.5112 | 1.29078 | 0.645388 | − | 0.763855i | \(-0.276696\pi\) | ||||
0.645388 | + | 0.763855i | \(0.276696\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.49903 | −0.0815527 | ||||||||
\(940\) | −0.413576 | −0.0134894 | ||||||||
\(941\) | −35.4567 | −1.15585 | −0.577927 | − | 0.816088i | \(-0.696138\pi\) | ||||
−0.577927 | + | 0.816088i | \(0.696138\pi\) | |||||||
\(942\) | −10.8098 | −0.352203 | ||||||||
\(943\) | −6.86049 | −0.223408 | ||||||||
\(944\) | 1.71784 | 0.0559110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.2114 | 0.332001 | ||||||||
\(947\) | 8.35366 | 0.271457 | 0.135729 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135729 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(948\) | 7.33069 | 0.238090 | ||||||||
\(949\) | −21.3956 | −0.694529 | ||||||||
\(950\) | 8.29551 | 0.269142 | ||||||||
\(951\) | 5.78728 | 0.187665 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.3306 | −0.367033 | −0.183517 | − | 0.983017i | \(-0.558748\pi\) | ||||
−0.183517 | + | 0.983017i | \(0.558748\pi\) | |||||||
\(954\) | 53.8952 | 1.74492 | ||||||||
\(955\) | 10.3942 | 0.336350 | ||||||||
\(956\) | −49.9369 | −1.61507 | ||||||||
\(957\) | 0.0305602 | 0.000987869 0 | ||||||||
\(958\) | −34.5768 | −1.11713 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.78318 | 0.122102 | ||||||||
\(961\) | 14.2529 | 0.459772 | ||||||||
\(962\) | 1.45159 | 0.0468012 | ||||||||
\(963\) | −36.1134 | −1.16374 | ||||||||
\(964\) | −15.1889 | −0.489200 | ||||||||
\(965\) | 6.33141 | 0.203815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.7910 | 0.829383 | 0.414692 | − | 0.909962i | \(-0.363889\pi\) | ||||
0.414692 | + | 0.909962i | \(0.363889\pi\) | |||||||
\(968\) | −2.91425 | −0.0936675 | ||||||||
\(969\) | −1.46105 | −0.0469356 | ||||||||
\(970\) | 3.20201 | 0.102810 | ||||||||
\(971\) | 25.8433 | 0.829349 | 0.414675 | − | 0.909970i | \(-0.363895\pi\) | ||||
0.414675 | + | 0.909970i | \(0.363895\pi\) | |||||||
\(972\) | −24.9302 | −0.799635 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 92.6058 | 2.96728 | ||||||||
\(975\) | 0.426585 | 0.0136617 | ||||||||
\(976\) | 0.802154 | 0.0256763 | ||||||||
\(977\) | 23.7974 | 0.761345 | 0.380673 | − | 0.924710i | \(-0.375692\pi\) | ||||
0.380673 | + | 0.924710i | \(0.375692\pi\) | |||||||
\(978\) | −2.65007 | −0.0847398 | ||||||||
\(979\) | 3.74462 | 0.119679 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.0922 | 1.37583 | ||||||||
\(982\) | 32.8311 | 1.04768 | ||||||||
\(983\) | −54.2199 | −1.72935 | −0.864674 | − | 0.502334i | \(-0.832475\pi\) | ||||
−0.864674 | + | 0.502334i | \(0.832475\pi\) | |||||||
\(984\) | 1.05148 | 0.0335198 | ||||||||
\(985\) | 25.7530 | 0.820559 | ||||||||
\(986\) | 0.329093 | 0.0104804 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.1685 | 0.546203 | ||||||||
\(989\) | −24.8311 | −0.789584 | ||||||||
\(990\) | −6.68879 | −0.212584 | ||||||||
\(991\) | −42.1179 | −1.33792 | −0.668959 | − | 0.743299i | \(-0.733260\pi\) | ||||
−0.668959 | + | 0.743299i | \(0.733260\pi\) | |||||||
\(992\) | −36.8807 | −1.17096 | ||||||||
\(993\) | −4.35372 | −0.138161 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00340 | −0.253725 | ||||||||
\(996\) | −7.86852 | −0.249324 | ||||||||
\(997\) | 20.6025 | 0.652487 | 0.326244 | − | 0.945286i | \(-0.394217\pi\) | ||||
0.326244 | + | 0.945286i | \(0.394217\pi\) | |||||||
\(998\) | −56.5116 | −1.78884 | ||||||||
\(999\) | 0.755528 | 0.0239038 |
(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 | 2695.2.a.x.1.1 | yes | 10 | |
7.6 | odd | 2 | 2695.2.a.w.1.1 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2695.2.a.w.1.1 | ✓ | 10 | 7.6 | odd | 2 | ||
2695.2.a.x.1.1 | yes | 10 | 1.1 | even | 1 | trivial |