Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.73913\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73913 | −1.93686 | −0.968430 | − | 0.249287i | \(-0.919804\pi\) | ||||
−0.968430 | + | 0.249287i | \(0.919804\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.50285 | 2.75142 | ||||||||
\(5\) | −0.604616 | −0.270392 | −0.135196 | − | 0.990819i | \(-0.543166\pi\) | ||||
−0.135196 | + | 0.990819i | \(0.543166\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.91298 | −0.723040 | −0.361520 | − | 0.932364i | \(-0.617742\pi\) | ||||
−0.361520 | + | 0.932364i | \(0.617742\pi\) | |||||||
\(8\) | −9.59477 | −3.39226 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.65612 | 0.523712 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.176875 | 0.0490563 | 0.0245282 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245282 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(14\) | 5.23991 | 1.40043 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.2757 | 3.81891 | ||||||||
\(17\) | −2.74225 | −0.665093 | −0.332546 | − | 0.943087i | \(-0.607908\pi\) | ||||
−0.332546 | + | 0.943087i | \(0.607908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.64728 | 0.836745 | 0.418372 | − | 0.908276i | \(-0.362601\pi\) | ||||
0.418372 | + | 0.908276i | \(0.362601\pi\) | |||||||
\(20\) | −3.32711 | −0.743964 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.73913 | 0.583985 | ||||||||
\(23\) | −1.61899 | −0.337582 | −0.168791 | − | 0.985652i | \(-0.553986\pi\) | ||||
−0.168791 | + | 0.985652i | \(0.553986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.63444 | −0.926888 | ||||||||
\(26\) | −0.484484 | −0.0950152 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.5269 | −1.98939 | ||||||||
\(29\) | 7.55848 | 1.40357 | 0.701787 | − | 0.712387i | \(-0.252386\pi\) | ||||
0.701787 | + | 0.712387i | \(0.252386\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.88196 | 1.41564 | 0.707821 | − | 0.706392i | \(-0.249678\pi\) | ||||
0.707821 | + | 0.706392i | \(0.249678\pi\) | |||||||
\(32\) | −22.6525 | −4.00443 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.51138 | 1.28819 | ||||||||
\(35\) | 1.15662 | 0.195504 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.43648 | 1.38695 | 0.693475 | − | 0.720481i | \(-0.256079\pi\) | ||||
0.693475 | + | 0.720481i | \(0.256079\pi\) | |||||||
\(38\) | −9.99040 | −1.62066 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.80115 | 0.917242 | ||||||||
\(41\) | −8.93210 | −1.39496 | −0.697480 | − | 0.716604i | \(-0.745695\pi\) | ||||
−0.697480 | + | 0.716604i | \(0.745695\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.51816 | −0.689013 | −0.344507 | − | 0.938784i | \(-0.611954\pi\) | ||||
−0.344507 | + | 0.938784i | \(0.611954\pi\) | |||||||
\(44\) | −5.50285 | −0.829586 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.43462 | 0.653848 | ||||||||
\(47\) | 2.48579 | 0.362590 | 0.181295 | − | 0.983429i | \(-0.441971\pi\) | ||||
0.181295 | + | 0.983429i | \(0.441971\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.34050 | −0.477214 | ||||||||
\(50\) | 12.6943 | 1.79525 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.973317 | 0.134975 | ||||||||
\(53\) | 7.57327 | 1.04027 | 0.520135 | − | 0.854084i | \(-0.325882\pi\) | ||||
0.520135 | + | 0.854084i | \(0.325882\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.604616 | 0.0815264 | ||||||||
\(56\) | 18.3546 | 2.45274 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −20.7037 | −2.71852 | ||||||||
\(59\) | −1.33758 | −0.174138 | −0.0870692 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870692 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −21.5897 | −2.74190 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 31.4969 | 3.93711 | ||||||||
\(65\) | −0.106941 | −0.0132645 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50196 | −0.672171 | −0.336086 | − | 0.941831i | \(-0.609103\pi\) | ||||
−0.336086 | + | 0.941831i | \(0.609103\pi\) | |||||||
\(68\) | −15.0902 | −1.82995 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.16813 | −0.378665 | ||||||||
\(71\) | −0.330471 | −0.0392197 | −0.0196098 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196098 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.75560 | −0.205477 | −0.102739 | − | 0.994708i | \(-0.532761\pi\) | ||||
−0.102739 | + | 0.994708i | \(0.532761\pi\) | |||||||
\(74\) | −23.1086 | −2.68633 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.0705 | 2.30224 | ||||||||
\(77\) | 1.91298 | 0.218005 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9780 | −1.46014 | −0.730070 | − | 0.683372i | \(-0.760513\pi\) | ||||
−0.730070 | + | 0.683372i | \(0.760513\pi\) | |||||||
\(80\) | −9.23590 | −1.03260 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 24.4662 | 2.70184 | ||||||||
\(83\) | −12.9300 | −1.41925 | −0.709625 | − | 0.704580i | \(-0.751136\pi\) | ||||
−0.709625 | + | 0.704580i | \(0.751136\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.65801 | 0.179836 | ||||||||
\(86\) | 12.3759 | 1.33452 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.59477 | 1.02281 | ||||||||
\(89\) | 4.11061 | 0.435724 | 0.217862 | − | 0.975980i | \(-0.430092\pi\) | ||||
0.217862 | + | 0.975980i | \(0.430092\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.338359 | −0.0354697 | ||||||||
\(92\) | −8.90903 | −0.928831 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.80891 | −0.702285 | ||||||||
\(95\) | −2.20521 | −0.226249 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7524 | −1.29481 | −0.647404 | − | 0.762147i | \(-0.724145\pi\) | ||||
−0.647404 | + | 0.762147i | \(0.724145\pi\) | |||||||
\(98\) | 9.15006 | 0.924296 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −25.5026 | −2.55026 | ||||||||
\(101\) | 10.0353 | 0.998553 | 0.499276 | − | 0.866443i | \(-0.333599\pi\) | ||||
0.499276 | + | 0.866443i | \(0.333599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.05237 | −0.596357 | −0.298179 | − | 0.954510i | \(-0.596379\pi\) | ||||
−0.298179 | + | 0.954510i | \(0.596379\pi\) | |||||||
\(104\) | −1.69708 | −0.166412 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.7442 | −2.01485 | ||||||||
\(107\) | −12.2595 | −1.18517 | −0.592587 | − | 0.805506i | \(-0.701893\pi\) | ||||
−0.592587 | + | 0.805506i | \(0.701893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.38440 | −0.132602 | −0.0663008 | − | 0.997800i | \(-0.521120\pi\) | ||||
−0.0663008 | + | 0.997800i | \(0.521120\pi\) | |||||||
\(110\) | −1.65612 | −0.157905 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −29.2221 | −2.76123 | ||||||||
\(113\) | −12.6874 | −1.19353 | −0.596765 | − | 0.802416i | \(-0.703548\pi\) | ||||
−0.596765 | + | 0.802416i | \(0.703548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.978864 | 0.0912795 | ||||||||
\(116\) | 41.5931 | 3.86183 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.66382 | 0.337282 | ||||||||
\(119\) | 5.24587 | 0.480888 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.73913 | 0.247989 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 43.3732 | 3.89503 | ||||||||
\(125\) | 5.82513 | 0.521016 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.42636 | 0.658983 | 0.329491 | − | 0.944159i | \(-0.393123\pi\) | ||||
0.329491 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(128\) | −40.9692 | −3.62120 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.292927 | 0.0256914 | ||||||||
\(131\) | 7.69981 | 0.672735 | 0.336368 | − | 0.941731i | \(-0.390802\pi\) | ||||
0.336368 | + | 0.941731i | \(0.390802\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.97719 | −0.604999 | ||||||||
\(134\) | 15.0706 | 1.30190 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 26.3112 | 2.25617 | ||||||||
\(137\) | 15.9210 | 1.36022 | 0.680112 | − | 0.733108i | \(-0.261931\pi\) | ||||
0.680112 | + | 0.733108i | \(0.261931\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.40561 | −0.204041 | −0.102021 | − | 0.994782i | \(-0.532531\pi\) | ||||
−0.102021 | + | 0.994782i | \(0.532531\pi\) | |||||||
\(140\) | 6.36470 | 0.537916 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.905204 | 0.0759630 | ||||||||
\(143\) | −0.176875 | −0.0147910 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.56997 | −0.379516 | ||||||||
\(146\) | 4.80881 | 0.397980 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 46.4247 | 3.81609 | ||||||||
\(149\) | 14.5339 | 1.19066 | 0.595331 | − | 0.803480i | \(-0.297021\pi\) | ||||
0.595331 | + | 0.803480i | \(0.297021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.9430 | −0.890525 | −0.445262 | − | 0.895400i | \(-0.646890\pi\) | ||||
−0.445262 | + | 0.895400i | \(0.646890\pi\) | |||||||
\(152\) | −34.9949 | −2.83846 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.23991 | −0.422244 | ||||||||
\(155\) | −4.76556 | −0.382779 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.6497 | 1.32879 | 0.664394 | − | 0.747383i | \(-0.268690\pi\) | ||||
0.664394 | + | 0.747383i | \(0.268690\pi\) | |||||||
\(158\) | 35.5485 | 2.82809 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.6961 | 1.08277 | ||||||||
\(161\) | 3.09709 | 0.244085 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.05976 | −0.161333 | −0.0806666 | − | 0.996741i | \(-0.525705\pi\) | ||||
−0.0806666 | + | 0.996741i | \(0.525705\pi\) | |||||||
\(164\) | −49.1520 | −3.83813 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.4169 | 2.74889 | ||||||||
\(167\) | 15.3296 | 1.18624 | 0.593121 | − | 0.805113i | \(-0.297895\pi\) | ||||
0.593121 | + | 0.805113i | \(0.297895\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9687 | −0.997593 | ||||||||
\(170\) | −4.54150 | −0.348317 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −24.8628 | −1.89577 | ||||||||
\(173\) | −13.0360 | −0.991105 | −0.495553 | − | 0.868578i | \(-0.665034\pi\) | ||||
−0.495553 | + | 0.868578i | \(0.665034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.86560 | 0.670177 | ||||||||
\(176\) | −15.2757 | −1.15145 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.2595 | −0.843936 | ||||||||
\(179\) | 11.6608 | 0.871571 | 0.435786 | − | 0.900050i | \(-0.356471\pi\) | ||||
0.435786 | + | 0.900050i | \(0.356471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.58234 | −0.712250 | −0.356125 | − | 0.934438i | \(-0.615902\pi\) | ||||
−0.356125 | + | 0.934438i | \(0.615902\pi\) | |||||||
\(182\) | 0.926810 | 0.0686997 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.5338 | 1.14517 | ||||||||
\(185\) | −5.10083 | −0.375021 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.74225 | 0.200533 | ||||||||
\(188\) | 13.6789 | 0.997638 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.04035 | 0.438213 | ||||||||
\(191\) | 18.4200 | 1.33283 | 0.666414 | − | 0.745582i | \(-0.267828\pi\) | ||||
0.666414 | + | 0.745582i | \(0.267828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.40862 | −0.389321 | −0.194661 | − | 0.980871i | \(-0.562361\pi\) | ||||
−0.194661 | + | 0.980871i | \(0.562361\pi\) | |||||||
\(194\) | 34.9305 | 2.50786 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.3822 | −1.31302 | ||||||||
\(197\) | 2.86614 | 0.204204 | 0.102102 | − | 0.994774i | \(-0.467443\pi\) | ||||
0.102102 | + | 0.994774i | \(0.467443\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.9550 | 0.847469 | 0.423735 | − | 0.905786i | \(-0.360719\pi\) | ||||
0.423735 | + | 0.905786i | \(0.360719\pi\) | |||||||
\(200\) | 44.4664 | 3.14425 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −27.4881 | −1.93406 | ||||||||
\(203\) | −14.4592 | −1.01484 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.40049 | 0.377187 | ||||||||
\(206\) | 16.5782 | 1.15506 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.70188 | 0.187342 | ||||||||
\(209\) | −3.64728 | −0.252288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3432 | 1.67585 | 0.837927 | − | 0.545783i | \(-0.183768\pi\) | ||||
0.837927 | + | 0.545783i | \(0.183768\pi\) | |||||||
\(212\) | 41.6746 | 2.86222 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 33.5805 | 2.29552 | ||||||||
\(215\) | 2.73175 | 0.186304 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.0781 | −1.02357 | ||||||||
\(218\) | 3.79206 | 0.256831 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.32711 | 0.224314 | ||||||||
\(221\) | −0.485035 | −0.0326270 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.7257 | 1.05307 | 0.526535 | − | 0.850154i | \(-0.323491\pi\) | ||||
0.526535 | + | 0.850154i | \(0.323491\pi\) | |||||||
\(224\) | 43.3338 | 2.89536 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 34.7525 | 2.31170 | ||||||||
\(227\) | 0.677571 | 0.0449720 | 0.0224860 | − | 0.999747i | \(-0.492842\pi\) | ||||
0.0224860 | + | 0.999747i | \(0.492842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4531 | 0.889006 | 0.444503 | − | 0.895777i | \(-0.353380\pi\) | ||||
0.444503 | + | 0.895777i | \(0.353380\pi\) | |||||||
\(230\) | −2.68124 | −0.176796 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −72.5218 | −4.76129 | ||||||||
\(233\) | 12.1025 | 0.792862 | 0.396431 | − | 0.918064i | \(-0.370249\pi\) | ||||
0.396431 | + | 0.918064i | \(0.370249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.50295 | −0.0980415 | ||||||||
\(236\) | −7.36052 | −0.479129 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.3691 | −0.931413 | ||||||||
\(239\) | 7.34142 | 0.474877 | 0.237438 | − | 0.971403i | \(-0.423692\pi\) | ||||
0.237438 | + | 0.971403i | \(0.423692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.9723 | −1.73744 | −0.868719 | − | 0.495306i | \(-0.835056\pi\) | ||||
−0.868719 | + | 0.495306i | \(0.835056\pi\) | |||||||
\(242\) | −2.73913 | −0.176078 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.50285 | −0.352284 | ||||||||
\(245\) | 2.01972 | 0.129035 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.645114 | 0.0410476 | ||||||||
\(248\) | −75.6256 | −4.80223 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.9558 | −1.00913 | ||||||||
\(251\) | 17.0405 | 1.07559 | 0.537794 | − | 0.843076i | \(-0.319258\pi\) | ||||
0.537794 | + | 0.843076i | \(0.319258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61899 | 0.101785 | ||||||||
\(254\) | −20.3418 | −1.27636 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 49.2263 | 3.07664 | ||||||||
\(257\) | −13.6010 | −0.848410 | −0.424205 | − | 0.905566i | \(-0.639446\pi\) | ||||
−0.424205 | + | 0.905566i | \(0.639446\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.1388 | −1.00282 | ||||||||
\(260\) | −0.588483 | −0.0364961 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.0908 | −1.30299 | ||||||||
\(263\) | −18.2508 | −1.12539 | −0.562696 | − | 0.826664i | \(-0.690236\pi\) | ||||
−0.562696 | + | 0.826664i | \(0.690236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.57892 | −0.281281 | ||||||||
\(266\) | 19.1115 | 1.17180 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −30.2764 | −1.84943 | ||||||||
\(269\) | 9.66539 | 0.589309 | 0.294655 | − | 0.955604i | \(-0.404795\pi\) | ||||
0.294655 | + | 0.955604i | \(0.404795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.1115 | 1.82914 | 0.914571 | − | 0.404425i | \(-0.132528\pi\) | ||||
0.914571 | + | 0.404425i | \(0.132528\pi\) | |||||||
\(272\) | −41.8896 | −2.53993 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −43.6098 | −2.63456 | ||||||||
\(275\) | 4.63444 | 0.279467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.89926 | −0.354452 | −0.177226 | − | 0.984170i | \(-0.556712\pi\) | ||||
−0.177226 | + | 0.984170i | \(0.556712\pi\) | |||||||
\(278\) | 6.58929 | 0.395199 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.0975 | −0.663202 | ||||||||
\(281\) | −6.40992 | −0.382384 | −0.191192 | − | 0.981553i | \(-0.561235\pi\) | ||||
−0.191192 | + | 0.981553i | \(0.561235\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.51457 | 0.149476 | 0.0747380 | − | 0.997203i | \(-0.476188\pi\) | ||||
0.0747380 | + | 0.997203i | \(0.476188\pi\) | |||||||
\(284\) | −1.81853 | −0.107910 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.484484 | 0.0286482 | ||||||||
\(287\) | 17.0870 | 1.00861 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.48008 | −0.557652 | ||||||||
\(290\) | 12.5178 | 0.735068 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.66079 | −0.565355 | ||||||||
\(293\) | 12.3742 | 0.722908 | 0.361454 | − | 0.932390i | \(-0.382280\pi\) | ||||
0.361454 | + | 0.932390i | \(0.382280\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.808724 | 0.0470857 | ||||||||
\(296\) | −80.9461 | −4.70490 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −39.8102 | −2.30615 | ||||||||
\(299\) | −0.286358 | −0.0165605 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.64317 | 0.498184 | ||||||||
\(302\) | 29.9742 | 1.72482 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 55.7146 | 3.19545 | ||||||||
\(305\) | 0.604616 | 0.0346202 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.2440 | 1.21246 | 0.606230 | − | 0.795290i | \(-0.292681\pi\) | ||||
0.606230 | + | 0.795290i | \(0.292681\pi\) | |||||||
\(308\) | 10.5269 | 0.599823 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.0535 | 0.741389 | ||||||||
\(311\) | −26.4545 | −1.50010 | −0.750049 | − | 0.661383i | \(-0.769970\pi\) | ||||
−0.750049 | + | 0.661383i | \(0.769970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.7427 | 1.73768 | 0.868841 | − | 0.495090i | \(-0.164865\pi\) | ||||
0.868841 | + | 0.495090i | \(0.164865\pi\) | |||||||
\(314\) | −45.6056 | −2.57367 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −71.4160 | −4.01747 | ||||||||
\(317\) | 21.9554 | 1.23314 | 0.616569 | − | 0.787301i | \(-0.288522\pi\) | ||||
0.616569 | + | 0.787301i | \(0.288522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.55848 | −0.423193 | ||||||||
\(320\) | −19.0435 | −1.06457 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.48334 | −0.472758 | ||||||||
\(323\) | −10.0018 | −0.556513 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.819717 | −0.0454697 | ||||||||
\(326\) | 5.64197 | 0.312480 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 85.7015 | 4.73207 | ||||||||
\(329\) | −4.75527 | −0.262167 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8159 | −0.869318 | −0.434659 | − | 0.900595i | \(-0.643131\pi\) | ||||
−0.434659 | + | 0.900595i | \(0.643131\pi\) | |||||||
\(332\) | −71.1517 | −3.90496 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −41.9899 | −2.29759 | ||||||||
\(335\) | 3.32657 | 0.181750 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.1532 | −1.80597 | −0.902986 | − | 0.429671i | \(-0.858630\pi\) | ||||
−0.902986 | + | 0.429671i | \(0.858630\pi\) | |||||||
\(338\) | 35.5230 | 1.93220 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.12376 | 0.494805 | ||||||||
\(341\) | −7.88196 | −0.426832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7812 | 1.06808 | ||||||||
\(344\) | 43.3507 | 2.33732 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 35.7072 | 1.91963 | ||||||||
\(347\) | −23.0402 | −1.23686 | −0.618430 | − | 0.785840i | \(-0.712231\pi\) | ||||
−0.618430 | + | 0.785840i | \(0.712231\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.7544 | −1.75330 | −0.876651 | − | 0.481127i | \(-0.840227\pi\) | ||||
−0.876651 | + | 0.481127i | \(0.840227\pi\) | |||||||
\(350\) | −24.2841 | −1.29804 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.6525 | 1.20738 | ||||||||
\(353\) | −0.349353 | −0.0185942 | −0.00929708 | − | 0.999957i | \(-0.502959\pi\) | ||||
−0.00929708 | + | 0.999957i | \(0.502959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.199808 | 0.0106047 | ||||||||
\(356\) | 22.6201 | 1.19886 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.9406 | −1.68811 | ||||||||
\(359\) | −29.2479 | −1.54365 | −0.771823 | − | 0.635838i | \(-0.780655\pi\) | ||||
−0.771823 | + | 0.635838i | \(0.780655\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.69731 | −0.299859 | ||||||||
\(362\) | 26.2473 | 1.37953 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.86194 | −0.0975921 | ||||||||
\(365\) | 1.06146 | 0.0555594 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9617 | −0.728795 | −0.364397 | − | 0.931244i | \(-0.618725\pi\) | ||||
−0.364397 | + | 0.931244i | \(0.618725\pi\) | |||||||
\(368\) | −24.7311 | −1.28920 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.9719 | 0.726362 | ||||||||
\(371\) | −14.4875 | −0.752156 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.7140 | 0.710084 | 0.355042 | − | 0.934850i | \(-0.384467\pi\) | ||||
0.355042 | + | 0.934850i | \(0.384467\pi\) | |||||||
\(374\) | −7.51138 | −0.388404 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.8506 | −1.23000 | ||||||||
\(377\) | 1.33691 | 0.0688541 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.6378 | 1.77922 | 0.889612 | − | 0.456717i | \(-0.150975\pi\) | ||||
0.889612 | + | 0.456717i | \(0.150975\pi\) | |||||||
\(380\) | −12.1349 | −0.622508 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −50.4550 | −2.58150 | ||||||||
\(383\) | −7.28622 | −0.372308 | −0.186154 | − | 0.982521i | \(-0.559602\pi\) | ||||
−0.186154 | + | 0.982521i | \(0.559602\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.15662 | −0.0589468 | ||||||||
\(386\) | 14.8149 | 0.754060 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −70.1744 | −3.56257 | ||||||||
\(389\) | 30.6669 | 1.55487 | 0.777437 | − | 0.628960i | \(-0.216519\pi\) | ||||
0.777437 | + | 0.628960i | \(0.216519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.43966 | 0.224523 | ||||||||
\(392\) | 32.0513 | 1.61883 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.85074 | −0.395514 | ||||||||
\(395\) | 7.84671 | 0.394811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12627 | −0.0565257 | −0.0282628 | − | 0.999601i | \(-0.508998\pi\) | ||||
−0.0282628 | + | 0.999601i | \(0.508998\pi\) | |||||||
\(398\) | −32.7464 | −1.64143 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −70.7941 | −3.53970 | ||||||||
\(401\) | 9.38421 | 0.468625 | 0.234312 | − | 0.972161i | \(-0.424716\pi\) | ||||
0.234312 | + | 0.972161i | \(0.424716\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.39412 | 0.0694462 | ||||||||
\(404\) | 55.2229 | 2.74744 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 39.6058 | 1.96560 | ||||||||
\(407\) | −8.43648 | −0.418181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.3783 | 1.69990 | 0.849948 | − | 0.526867i | \(-0.176633\pi\) | ||||
0.849948 | + | 0.526867i | \(0.176633\pi\) | |||||||
\(410\) | −14.7927 | −0.730558 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −33.3053 | −1.64083 | ||||||||
\(413\) | 2.55877 | 0.125909 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.81767 | 0.383754 | ||||||||
\(416\) | −4.00666 | −0.196443 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.99040 | 0.488646 | ||||||||
\(419\) | 1.53252 | 0.0748685 | 0.0374343 | − | 0.999299i | \(-0.488082\pi\) | ||||
0.0374343 | + | 0.999299i | \(0.488082\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4022 | 0.653185 | 0.326593 | − | 0.945165i | \(-0.394100\pi\) | ||||
0.326593 | + | 0.945165i | \(0.394100\pi\) | |||||||
\(422\) | −66.6792 | −3.24589 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −72.6638 | −3.52887 | ||||||||
\(425\) | 12.7088 | 0.616466 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.91298 | 0.0925757 | ||||||||
\(428\) | −67.4624 | −3.26092 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.48263 | −0.360845 | ||||||||
\(431\) | 4.01874 | 0.193576 | 0.0967880 | − | 0.995305i | \(-0.469143\pi\) | ||||
0.0967880 | + | 0.995305i | \(0.469143\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.2933 | 0.927175 | 0.463587 | − | 0.886051i | \(-0.346562\pi\) | ||||
0.463587 | + | 0.886051i | \(0.346562\pi\) | |||||||
\(434\) | 41.3008 | 1.98250 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.61815 | −0.364843 | ||||||||
\(437\) | −5.90490 | −0.282470 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.1285 | −1.10386 | −0.551930 | − | 0.833890i | \(-0.686109\pi\) | ||||
−0.551930 | + | 0.833890i | \(0.686109\pi\) | |||||||
\(440\) | −5.80115 | −0.276559 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.32858 | 0.0631939 | ||||||||
\(443\) | 18.3618 | 0.872398 | 0.436199 | − | 0.899850i | \(-0.356324\pi\) | ||||
0.436199 | + | 0.899850i | \(0.356324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.48534 | −0.117816 | ||||||||
\(446\) | −43.0747 | −2.03965 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −60.2530 | −2.84669 | ||||||||
\(449\) | 12.2717 | 0.579135 | 0.289568 | − | 0.957158i | \(-0.406488\pi\) | ||||
0.289568 | + | 0.957158i | \(0.406488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.93210 | 0.420596 | ||||||||
\(452\) | −69.8168 | −3.28391 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.85596 | −0.0871044 | ||||||||
\(455\) | 0.204577 | 0.00959073 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9930 | 0.841679 | 0.420840 | − | 0.907135i | \(-0.361736\pi\) | ||||
0.420840 | + | 0.907135i | \(0.361736\pi\) | |||||||
\(458\) | −36.8498 | −1.72188 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.38654 | 0.251149 | ||||||||
\(461\) | 1.26483 | 0.0589088 | 0.0294544 | − | 0.999566i | \(-0.490623\pi\) | ||||
0.0294544 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3872 | −0.482732 | −0.241366 | − | 0.970434i | \(-0.577595\pi\) | ||||
−0.241366 | + | 0.970434i | \(0.577595\pi\) | |||||||
\(464\) | 115.461 | 5.36012 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.1504 | −1.53566 | ||||||||
\(467\) | −10.9780 | −0.507999 | −0.253999 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.253999 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.5252 | 0.486006 | ||||||||
\(470\) | 4.11677 | 0.189893 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.8338 | 0.590724 | ||||||||
\(473\) | 4.51816 | 0.207745 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9031 | −0.775568 | ||||||||
\(476\) | 28.8672 | 1.32313 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.1091 | −0.919770 | ||||||||
\(479\) | 17.8446 | 0.815339 | 0.407670 | − | 0.913130i | \(-0.366342\pi\) | ||||
0.407670 | + | 0.913130i | \(0.366342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.49220 | 0.0680386 | ||||||||
\(482\) | 73.8807 | 3.36517 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.50285 | 0.250130 | ||||||||
\(485\) | 7.71029 | 0.350106 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.6964 | −0.892531 | −0.446266 | − | 0.894901i | \(-0.647246\pi\) | ||||
−0.446266 | + | 0.894901i | \(0.647246\pi\) | |||||||
\(488\) | 9.59477 | 0.434335 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.53227 | −0.249923 | ||||||||
\(491\) | 17.3750 | 0.784124 | 0.392062 | − | 0.919939i | \(-0.371762\pi\) | ||||
0.392062 | + | 0.919939i | \(0.371762\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.7272 | −0.933507 | ||||||||
\(494\) | −1.76705 | −0.0795034 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 120.402 | 5.40621 | ||||||||
\(497\) | 0.632185 | 0.0283574 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.1532 | 1.12601 | 0.563005 | − | 0.826454i | \(-0.309645\pi\) | ||||
0.563005 | + | 0.826454i | \(0.309645\pi\) | |||||||
\(500\) | 32.0548 | 1.43354 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −46.6763 | −2.08326 | ||||||||
\(503\) | −18.0309 | −0.803958 | −0.401979 | − | 0.915649i | \(-0.631678\pi\) | ||||
−0.401979 | + | 0.915649i | \(0.631678\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.06752 | −0.270001 | ||||||||
\(506\) | −4.43462 | −0.197143 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 40.8661 | 1.81314 | ||||||||
\(509\) | 35.8893 | 1.59077 | 0.795383 | − | 0.606108i | \(-0.207270\pi\) | ||||
0.795383 | + | 0.606108i | \(0.207270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.35843 | 0.148568 | ||||||||
\(512\) | −52.8990 | −2.33783 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 37.2551 | 1.64325 | ||||||||
\(515\) | 3.65936 | 0.161250 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.48579 | −0.109325 | ||||||||
\(518\) | 44.2065 | 1.94232 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.02608 | 0.0449965 | ||||||||
\(521\) | −6.16062 | −0.269902 | −0.134951 | − | 0.990852i | \(-0.543088\pi\) | ||||
−0.134951 | + | 0.990852i | \(0.543088\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.39141 | −0.104569 | −0.0522846 | − | 0.998632i | \(-0.516650\pi\) | ||||
−0.0522846 | + | 0.998632i | \(0.516650\pi\) | |||||||
\(524\) | 42.3709 | 1.85098 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.9914 | 2.17973 | ||||||||
\(527\) | −21.6143 | −0.941533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3789 | −0.886039 | ||||||||
\(530\) | 12.5423 | 0.544801 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −38.3944 | −1.66461 | ||||||||
\(533\) | −1.57987 | −0.0684316 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.41231 | 0.320462 | ||||||||
\(536\) | 52.7900 | 2.28018 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.4748 | −1.14141 | ||||||||
\(539\) | 3.34050 | 0.143885 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.9269 | 1.32965 | 0.664827 | − | 0.746998i | \(-0.268505\pi\) | ||||
0.664827 | + | 0.746998i | \(0.268505\pi\) | |||||||
\(542\) | −82.4793 | −3.54279 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 62.1188 | 2.66332 | ||||||||
\(545\) | 0.837031 | 0.0358545 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.4601 | 1.34514 | 0.672569 | − | 0.740035i | \(-0.265191\pi\) | ||||
0.672569 | + | 0.740035i | \(0.265191\pi\) | |||||||
\(548\) | 87.6109 | 3.74255 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.6943 | −0.541289 | ||||||||
\(551\) | 27.5679 | 1.17443 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.8267 | 1.05574 | ||||||||
\(554\) | 16.1589 | 0.686524 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.2377 | −0.561404 | ||||||||
\(557\) | 43.3173 | 1.83541 | 0.917706 | − | 0.397261i | \(-0.130039\pi\) | ||||
0.917706 | + | 0.397261i | \(0.130039\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.799150 | −0.0338005 | ||||||||
\(560\) | 17.6681 | 0.746614 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.5576 | 0.740623 | ||||||||
\(563\) | 12.7937 | 0.539192 | 0.269596 | − | 0.962974i | \(-0.413110\pi\) | ||||
0.269596 | + | 0.962974i | \(0.413110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.67100 | 0.322721 | ||||||||
\(566\) | −6.88775 | −0.289514 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.17079 | 0.133044 | ||||||||
\(569\) | −16.2156 | −0.679791 | −0.339896 | − | 0.940463i | \(-0.610392\pi\) | ||||
−0.339896 | + | 0.940463i | \(0.610392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.4511 | 0.646607 | 0.323303 | − | 0.946295i | \(-0.395207\pi\) | ||||
0.323303 | + | 0.946295i | \(0.395207\pi\) | |||||||
\(572\) | −0.973317 | −0.0406964 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −46.8035 | −1.95354 | ||||||||
\(575\) | 7.50309 | 0.312900 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7967 | −0.574365 | −0.287182 | − | 0.957876i | \(-0.592719\pi\) | ||||
−0.287182 | + | 0.957876i | \(0.592719\pi\) | |||||||
\(578\) | 25.9672 | 1.08009 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25.1479 | −1.04421 | ||||||||
\(581\) | 24.7348 | 1.02617 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.57327 | −0.313653 | ||||||||
\(584\) | 16.8445 | 0.697032 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −33.8946 | −1.40017 | ||||||||
\(587\) | 0.731957 | 0.0302111 | 0.0151056 | − | 0.999886i | \(-0.495192\pi\) | ||||
0.0151056 | + | 0.999886i | \(0.495192\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.7478 | 1.18453 | ||||||||
\(590\) | −2.21520 | −0.0911984 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 128.873 | 5.29664 | ||||||||
\(593\) | −16.9597 | −0.696450 | −0.348225 | − | 0.937411i | \(-0.613215\pi\) | ||||
−0.348225 | + | 0.937411i | \(0.613215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.17174 | −0.130029 | ||||||||
\(596\) | 79.9778 | 3.27602 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.784373 | 0.0320754 | ||||||||
\(599\) | 11.3334 | 0.463070 | 0.231535 | − | 0.972827i | \(-0.425625\pi\) | ||||
0.231535 | + | 0.972827i | \(0.425625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.8868 | 1.54543 | 0.772717 | − | 0.634750i | \(-0.218897\pi\) | ||||
0.772717 | + | 0.634750i | \(0.218897\pi\) | |||||||
\(602\) | −23.6748 | −0.964912 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −60.2174 | −2.45021 | ||||||||
\(605\) | −0.604616 | −0.0245811 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.55272 | −0.387733 | −0.193866 | − | 0.981028i | \(-0.562103\pi\) | ||||
−0.193866 | + | 0.981028i | \(0.562103\pi\) | |||||||
\(608\) | −82.6201 | −3.35069 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.65612 | −0.0670545 | ||||||||
\(611\) | 0.439674 | 0.0177873 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.7337 | 0.756646 | 0.378323 | − | 0.925674i | \(-0.376501\pi\) | ||||
0.378323 | + | 0.925674i | \(0.376501\pi\) | |||||||
\(614\) | −58.1902 | −2.34836 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.3546 | −0.739529 | ||||||||
\(617\) | 2.88614 | 0.116192 | 0.0580958 | − | 0.998311i | \(-0.481497\pi\) | ||||
0.0580958 | + | 0.998311i | \(0.481497\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.4797 | 1.14470 | 0.572348 | − | 0.820011i | \(-0.306033\pi\) | ||||
0.572348 | + | 0.820011i | \(0.306033\pi\) | |||||||
\(620\) | −26.2241 | −1.05319 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 72.4624 | 2.90548 | ||||||||
\(623\) | −7.86353 | −0.315046 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.6502 | 0.786009 | ||||||||
\(626\) | −84.2085 | −3.36565 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 91.6205 | 3.65606 | ||||||||
\(629\) | −23.1349 | −0.922450 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.8981 | 0.752322 | 0.376161 | − | 0.926554i | \(-0.377244\pi\) | ||||
0.376161 | + | 0.926554i | \(0.377244\pi\) | |||||||
\(632\) | 124.521 | 4.95318 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −60.1388 | −2.38842 | ||||||||
\(635\) | −4.49009 | −0.178184 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.590850 | −0.0234103 | ||||||||
\(638\) | 20.7037 | 0.819666 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.7706 | 0.979145 | ||||||||
\(641\) | −29.7753 | −1.17605 | −0.588026 | − | 0.808842i | \(-0.700095\pi\) | ||||
−0.588026 | + | 0.808842i | \(0.700095\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.68829 | −0.0665798 | −0.0332899 | − | 0.999446i | \(-0.510598\pi\) | ||||
−0.0332899 | + | 0.999446i | \(0.510598\pi\) | |||||||
\(644\) | 17.0428 | 0.671581 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.3961 | 1.07789 | ||||||||
\(647\) | 31.7652 | 1.24882 | 0.624409 | − | 0.781098i | \(-0.285340\pi\) | ||||
0.624409 | + | 0.781098i | \(0.285340\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.33758 | 0.0525047 | ||||||||
\(650\) | 2.24531 | 0.0880684 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.3346 | −0.443896 | ||||||||
\(653\) | 12.0681 | 0.472261 | 0.236130 | − | 0.971721i | \(-0.424121\pi\) | ||||
0.236130 | + | 0.971721i | \(0.424121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.65542 | −0.181902 | ||||||||
\(656\) | −136.444 | −5.32723 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.0253 | 0.507780 | ||||||||
\(659\) | −17.5896 | −0.685192 | −0.342596 | − | 0.939483i | \(-0.611306\pi\) | ||||
−0.342596 | + | 0.939483i | \(0.611306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.9318 | 0.736361 | 0.368181 | − | 0.929754i | \(-0.379981\pi\) | ||||
0.368181 | + | 0.929754i | \(0.379981\pi\) | |||||||
\(662\) | 43.3217 | 1.68375 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 124.060 | 4.81447 | ||||||||
\(665\) | 4.21852 | 0.163587 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.2371 | −0.473821 | ||||||||
\(668\) | 84.3567 | 3.26386 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.11192 | −0.352024 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.3060 | 1.90061 | 0.950303 | − | 0.311325i | \(-0.100773\pi\) | ||||
0.950303 | + | 0.311325i | \(0.100773\pi\) | |||||||
\(674\) | 90.8111 | 3.49791 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −71.3649 | −2.74480 | ||||||||
\(677\) | −6.96645 | −0.267742 | −0.133871 | − | 0.990999i | \(-0.542741\pi\) | ||||
−0.133871 | + | 0.990999i | \(0.542741\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.3951 | 0.936198 | ||||||||
\(680\) | −15.9082 | −0.610051 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21.5897 | 0.826714 | ||||||||
\(683\) | −17.4032 | −0.665913 | −0.332957 | − | 0.942942i | \(-0.608046\pi\) | ||||
−0.332957 | + | 0.942942i | \(0.608046\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.62609 | −0.367794 | ||||||||
\(686\) | −54.1833 | −2.06873 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −69.0179 | −2.63128 | ||||||||
\(689\) | 1.33952 | 0.0510318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.3254 | −0.621048 | −0.310524 | − | 0.950566i | \(-0.600505\pi\) | ||||
−0.310524 | + | 0.950566i | \(0.600505\pi\) | |||||||
\(692\) | −71.7349 | −2.72695 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 63.1100 | 2.39562 | ||||||||
\(695\) | 1.45447 | 0.0551712 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.4940 | 0.927778 | ||||||||
\(698\) | 89.7186 | 3.39590 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 48.7861 | 1.84394 | ||||||||
\(701\) | 1.25848 | 0.0475322 | 0.0237661 | − | 0.999718i | \(-0.492434\pi\) | ||||
0.0237661 | + | 0.999718i | \(0.492434\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.7703 | 1.16052 | ||||||||
\(704\) | −31.4969 | −1.18708 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.956923 | 0.0360143 | ||||||||
\(707\) | −19.1974 | −0.721993 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.8435 | 1.68413 | 0.842067 | − | 0.539373i | \(-0.181339\pi\) | ||||
0.842067 | + | 0.539373i | \(0.181339\pi\) | |||||||
\(710\) | −0.547301 | −0.0205398 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −39.4404 | −1.47809 | ||||||||
\(713\) | −12.7608 | −0.477895 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.106941 | 0.00399938 | ||||||||
\(716\) | 64.1678 | 2.39806 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 80.1139 | 2.98982 | ||||||||
\(719\) | −39.7590 | −1.48276 | −0.741381 | − | 0.671085i | \(-0.765829\pi\) | ||||
−0.741381 | + | 0.671085i | \(0.765829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5781 | 0.431190 | ||||||||
\(722\) | 15.6057 | 0.580784 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −52.7302 | −1.95970 | ||||||||
\(725\) | −35.0293 | −1.30096 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.6673 | 1.47118 | 0.735589 | − | 0.677428i | \(-0.236905\pi\) | ||||
0.735589 | + | 0.677428i | \(0.236905\pi\) | |||||||
\(728\) | 3.24648 | 0.120322 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.90748 | −0.107611 | ||||||||
\(731\) | 12.3899 | 0.458258 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.45224 | −0.164447 | −0.0822235 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822235 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(734\) | 38.2430 | 1.41157 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.6741 | 1.35182 | ||||||||
\(737\) | 5.50196 | 0.202667 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.8922 | −1.24674 | −0.623372 | − | 0.781926i | \(-0.714238\pi\) | ||||
−0.623372 | + | 0.781926i | \(0.714238\pi\) | |||||||
\(740\) | −28.0691 | −1.03184 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 39.6833 | 1.45682 | ||||||||
\(743\) | 9.90914 | 0.363531 | 0.181766 | − | 0.983342i | \(-0.441819\pi\) | ||||
0.181766 | + | 0.983342i | \(0.441819\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.78742 | −0.321946 | ||||||||
\(746\) | −37.5645 | −1.37533 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.0902 | 0.551751 | ||||||||
\(749\) | 23.4523 | 0.856928 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.30472 | 0.120591 | 0.0602955 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602955 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(752\) | 37.9720 | 1.38470 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.66196 | −0.133361 | ||||||||
\(755\) | 6.61628 | 0.240791 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.4977 | 0.490583 | 0.245292 | − | 0.969449i | \(-0.421116\pi\) | ||||
0.245292 | + | 0.969449i | \(0.421116\pi\) | |||||||
\(758\) | −94.8776 | −3.44611 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 21.1584 | 0.767497 | ||||||||
\(761\) | 28.0515 | 1.01687 | 0.508433 | − | 0.861101i | \(-0.330225\pi\) | ||||
0.508433 | + | 0.861101i | \(0.330225\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.64834 | 0.0958762 | ||||||||
\(764\) | 101.363 | 3.66718 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.9579 | 0.721109 | ||||||||
\(767\) | −0.236585 | −0.00854259 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.0212 | −1.04653 | −0.523266 | − | 0.852170i | \(-0.675286\pi\) | ||||
−0.523266 | + | 0.852170i | \(0.675286\pi\) | |||||||
\(770\) | 3.16813 | 0.114172 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −29.7628 | −1.07119 | ||||||||
\(773\) | 18.5820 | 0.668350 | 0.334175 | − | 0.942511i | \(-0.391542\pi\) | ||||
0.334175 | + | 0.942511i | \(0.391542\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.5285 | −1.31214 | ||||||||
\(776\) | 122.356 | 4.39233 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −84.0008 | −3.01157 | ||||||||
\(779\) | −32.5779 | −1.16723 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.330471 | 0.0118252 | ||||||||
\(782\) | −12.1608 | −0.434870 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −51.0282 | −1.82244 | ||||||||
\(785\) | −10.0666 | −0.359294 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2557 | 1.22108 | 0.610541 | − | 0.791985i | \(-0.290952\pi\) | ||||
0.610541 | + | 0.791985i | \(0.290952\pi\) | |||||||
\(788\) | 15.7719 | 0.561852 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.4932 | −0.764693 | ||||||||
\(791\) | 24.2708 | 0.862969 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.176875 | −0.00628102 | ||||||||
\(794\) | 3.08499 | 0.109482 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 65.7867 | 2.33175 | ||||||||
\(797\) | 11.0127 | 0.390088 | 0.195044 | − | 0.980794i | \(-0.437515\pi\) | ||||
0.195044 | + | 0.980794i | \(0.437515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.81665 | −0.241156 | ||||||||
\(800\) | 104.982 | 3.71166 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25.7046 | −0.907660 | ||||||||
\(803\) | 1.75560 | 0.0619537 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.87255 | −0.0659987 | ||||||||
\(806\) | −3.81869 | −0.134507 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −96.2867 | −3.38735 | ||||||||
\(809\) | −45.2337 | −1.59033 | −0.795165 | − | 0.606392i | \(-0.792616\pi\) | ||||
−0.795165 | + | 0.606392i | \(0.792616\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.9688 | 1.15769 | 0.578846 | − | 0.815437i | \(-0.303503\pi\) | ||||
0.578846 | + | 0.815437i | \(0.303503\pi\) | |||||||
\(812\) | −79.5670 | −2.79225 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.1086 | 0.809958 | ||||||||
\(815\) | 1.24537 | 0.0436232 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.4790 | −0.576528 | ||||||||
\(818\) | −94.1666 | −3.29246 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29.7181 | 1.03780 | ||||||||
\(821\) | −17.6348 | −0.615460 | −0.307730 | − | 0.951474i | \(-0.599569\pi\) | ||||
−0.307730 | + | 0.951474i | \(0.599569\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.60202 | −0.230132 | −0.115066 | − | 0.993358i | \(-0.536708\pi\) | ||||
−0.115066 | + | 0.993358i | \(0.536708\pi\) | |||||||
\(824\) | 58.0711 | 2.02300 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.00882 | −0.243868 | ||||||||
\(827\) | 0.843089 | 0.0293171 | 0.0146585 | − | 0.999893i | \(-0.495334\pi\) | ||||
0.0146585 | + | 0.999893i | \(0.495334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.4340 | −1.40433 | −0.702166 | − | 0.712014i | \(-0.747783\pi\) | ||||
−0.702166 | + | 0.712014i | \(0.747783\pi\) | |||||||
\(830\) | −21.4136 | −0.743278 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.57102 | 0.193140 | ||||||||
\(833\) | 9.16047 | 0.317391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.26854 | −0.320751 | ||||||||
\(836\) | −20.0705 | −0.694151 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.19778 | −0.145010 | ||||||||
\(839\) | −49.0996 | −1.69511 | −0.847553 | − | 0.530710i | \(-0.821925\pi\) | ||||
−0.847553 | + | 0.530710i | \(0.821925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1305 | 0.970019 | ||||||||
\(842\) | −36.7105 | −1.26513 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 133.957 | 4.61098 | ||||||||
\(845\) | 7.84109 | 0.269742 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.91298 | −0.0657309 | ||||||||
\(848\) | 115.687 | 3.97270 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −34.8110 | −1.19401 | ||||||||
\(851\) | −13.6585 | −0.468209 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0517 | 1.20015 | 0.600074 | − | 0.799944i | \(-0.295138\pi\) | ||||
0.600074 | + | 0.799944i | \(0.295138\pi\) | |||||||
\(854\) | −5.23991 | −0.179306 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 117.627 | 4.02042 | ||||||||
\(857\) | −51.8553 | −1.77134 | −0.885672 | − | 0.464311i | \(-0.846302\pi\) | ||||
−0.885672 | + | 0.464311i | \(0.846302\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.2016 | −1.06458 | −0.532292 | − | 0.846561i | \(-0.678669\pi\) | ||||
−0.532292 | + | 0.846561i | \(0.678669\pi\) | |||||||
\(860\) | 15.0324 | 0.512601 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.0079 | −0.374929 | ||||||||
\(863\) | 21.2847 | 0.724539 | 0.362269 | − | 0.932073i | \(-0.382002\pi\) | ||||
0.362269 | + | 0.932073i | \(0.382002\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.88174 | 0.267987 | ||||||||
\(866\) | −52.8468 | −1.79581 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −82.9723 | −2.81626 | ||||||||
\(869\) | 12.9780 | 0.440249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.973159 | −0.0329742 | ||||||||
\(872\) | 13.2830 | 0.449819 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.1743 | 0.547104 | ||||||||
\(875\) | −11.1434 | −0.376715 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.4130 | 1.90493 | 0.952465 | − | 0.304647i | \(-0.0985386\pi\) | ||||
0.952465 | + | 0.304647i | \(0.0985386\pi\) | |||||||
\(878\) | 63.3519 | 2.13802 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.23590 | 0.311342 | ||||||||
\(881\) | 13.2697 | 0.447067 | 0.223534 | − | 0.974696i | \(-0.428241\pi\) | ||||
0.223534 | + | 0.974696i | \(0.428241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.1064 | −1.01316 | −0.506581 | − | 0.862192i | \(-0.669091\pi\) | ||||
−0.506581 | + | 0.862192i | \(0.669091\pi\) | |||||||
\(884\) | −2.66908 | −0.0897707 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50.2955 | −1.68971 | ||||||||
\(887\) | −7.10163 | −0.238449 | −0.119225 | − | 0.992867i | \(-0.538041\pi\) | ||||
−0.119225 | + | 0.992867i | \(0.538041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.2065 | −0.476471 | ||||||||
\(890\) | 6.80768 | 0.228194 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 86.5360 | 2.89744 | ||||||||
\(893\) | 9.06638 | 0.303395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.05032 | −0.235666 | ||||||||
\(896\) | 78.3734 | 2.61827 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.6137 | −1.12170 | ||||||||
\(899\) | 59.5756 | 1.98696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.7678 | −0.691875 | ||||||||
\(902\) | −24.4662 | −0.814636 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 121.733 | 4.04877 | ||||||||
\(905\) | 5.79363 | 0.192587 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.7879 | 0.823069 | 0.411535 | − | 0.911394i | \(-0.364993\pi\) | ||||
0.411535 | + | 0.911394i | \(0.364993\pi\) | |||||||
\(908\) | 3.72857 | 0.123737 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.560364 | −0.0185759 | ||||||||
\(911\) | −41.3254 | −1.36917 | −0.684586 | − | 0.728932i | \(-0.740017\pi\) | ||||
−0.684586 | + | 0.728932i | \(0.740017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9300 | 0.427920 | ||||||||
\(914\) | −49.2853 | −1.63021 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 74.0304 | 2.44603 | ||||||||
\(917\) | −14.7296 | −0.486414 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.7229 | 1.21138 | 0.605688 | − | 0.795702i | \(-0.292898\pi\) | ||||
0.605688 | + | 0.795702i | \(0.292898\pi\) | |||||||
\(920\) | −9.39197 | −0.309644 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.46453 | −0.114098 | ||||||||
\(923\) | −0.0584521 | −0.00192397 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.0984 | −1.28555 | ||||||||
\(926\) | 28.4518 | 0.934984 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −171.218 | −5.62052 | ||||||||
\(929\) | −1.56310 | −0.0512837 | −0.0256418 | − | 0.999671i | \(-0.508163\pi\) | ||||
−0.0256418 | + | 0.999671i | \(0.508163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.1837 | −0.399306 | ||||||||
\(932\) | 66.5983 | 2.18150 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.0701 | 0.983923 | ||||||||
\(935\) | −1.65801 | −0.0542226 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.58638 | 0.117162 | 0.0585810 | − | 0.998283i | \(-0.481342\pi\) | ||||
0.0585810 | + | 0.998283i | \(0.481342\pi\) | |||||||
\(938\) | −28.8298 | −0.941326 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.27049 | −0.269754 | ||||||||
\(941\) | 41.9408 | 1.36723 | 0.683616 | − | 0.729842i | \(-0.260407\pi\) | ||||
0.683616 | + | 0.729842i | \(0.260407\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.4609 | 0.470913 | ||||||||
\(944\) | −20.4325 | −0.665020 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.3759 | −0.402374 | ||||||||
\(947\) | −53.9167 | −1.75206 | −0.876028 | − | 0.482260i | \(-0.839816\pi\) | ||||
−0.876028 | + | 0.482260i | \(0.839816\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.310521 | −0.0100799 | ||||||||
\(950\) | 46.2999 | 1.50217 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −50.3329 | −1.63130 | ||||||||
\(953\) | −6.24884 | −0.202420 | −0.101210 | − | 0.994865i | \(-0.532271\pi\) | ||||
−0.101210 | + | 0.994865i | \(0.532271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.1371 | −0.360387 | ||||||||
\(956\) | 40.3987 | 1.30659 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −48.8786 | −1.57920 | ||||||||
\(959\) | −30.4566 | −0.983496 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.1253 | 1.00404 | ||||||||
\(962\) | −4.08734 | −0.131781 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −148.424 | −4.78043 | ||||||||
\(965\) | 3.27014 | 0.105269 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.7133 | −0.376674 | −0.188337 | − | 0.982104i | \(-0.560310\pi\) | ||||
−0.188337 | + | 0.982104i | \(0.560310\pi\) | |||||||
\(968\) | −9.59477 | −0.308388 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.1195 | −0.678107 | ||||||||
\(971\) | 20.8971 | 0.670620 | 0.335310 | − | 0.942108i | \(-0.391159\pi\) | ||||
0.335310 | + | 0.942108i | \(0.391159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.60189 | 0.147530 | ||||||||
\(974\) | 53.9512 | 1.72871 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.2757 | −0.488962 | ||||||||
\(977\) | −15.7320 | −0.503311 | −0.251655 | − | 0.967817i | \(-0.580975\pi\) | ||||
−0.251655 | + | 0.967817i | \(0.580975\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.11061 | −0.131376 | ||||||||
\(980\) | 11.1142 | 0.355030 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −47.5925 | −1.51874 | ||||||||
\(983\) | 40.6563 | 1.29674 | 0.648368 | − | 0.761327i | \(-0.275452\pi\) | ||||
0.648368 | + | 0.761327i | \(0.275452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.73291 | −0.0552152 | ||||||||
\(986\) | 56.7746 | 1.80807 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.54996 | 0.112939 | ||||||||
\(989\) | 7.31484 | 0.232598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9691 | 0.443742 | 0.221871 | − | 0.975076i | \(-0.428784\pi\) | ||||
0.221871 | + | 0.975076i | \(0.428784\pi\) | |||||||
\(992\) | −178.546 | −5.66885 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.73164 | −0.0549243 | ||||||||
\(995\) | −7.22820 | −0.229149 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.2639 | −0.356731 | −0.178365 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178365 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(998\) | −68.8978 | −2.18092 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6039.2.a.i.1.1 | 13 | ||
3.2 | odd | 2 | 2013.2.a.e.1.13 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.13 | ✓ | 13 | 3.2 | odd | 2 | ||
6039.2.a.i.1.1 | 13 | 1.1 | even | 1 | trivial |