Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
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: | \( x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} - 760 x^{4} - 742 x^{3} + 366 x^{2} + 236 x - 47 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.73913\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 | \(-0.0801961\pi\) | ||||
0.968430 | + | 0.249287i | \(0.0801961\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.50285 | 2.75142 | ||||||||
\(5\) | 0.604616 | 0.270392 | 0.135196 | − | 0.990819i | \(-0.456834\pi\) | ||||
0.135196 | + | 0.990819i | \(0.456834\pi\) | |||||||
\(6\) | −2.73913 | −1.11825 | ||||||||
\(7\) | −1.91298 | −0.723040 | −0.361520 | − | 0.932364i | \(-0.617742\pi\) | ||||
−0.361520 | + | 0.932364i | \(0.617742\pi\) | |||||||
\(8\) | 9.59477 | 3.39226 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.65612 | 0.523712 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −5.50285 | −1.58854 | ||||||||
\(13\) | 0.176875 | 0.0490563 | 0.0245282 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245282 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(14\) | −5.23991 | −1.40043 | ||||||||
\(15\) | −0.604616 | −0.156111 | ||||||||
\(16\) | 15.2757 | 3.81891 | ||||||||
\(17\) | 2.74225 | 0.665093 | 0.332546 | − | 0.943087i | \(-0.392092\pi\) | ||||
0.332546 | + | 0.943087i | \(0.392092\pi\) | |||||||
\(18\) | 2.73913 | 0.645620 | ||||||||
\(19\) | 3.64728 | 0.836745 | 0.418372 | − | 0.908276i | \(-0.362601\pi\) | ||||
0.418372 | + | 0.908276i | \(0.362601\pi\) | |||||||
\(20\) | 3.32711 | 0.743964 | ||||||||
\(21\) | 1.91298 | 0.417447 | ||||||||
\(22\) | 2.73913 | 0.583985 | ||||||||
\(23\) | 1.61899 | 0.337582 | 0.168791 | − | 0.985652i | \(-0.446014\pi\) | ||||
0.168791 | + | 0.985652i | \(0.446014\pi\) | |||||||
\(24\) | −9.59477 | −1.95852 | ||||||||
\(25\) | −4.63444 | −0.926888 | ||||||||
\(26\) | 0.484484 | 0.0950152 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −10.5269 | −1.98939 | ||||||||
\(29\) | −7.55848 | −1.40357 | −0.701787 | − | 0.712387i | \(-0.747614\pi\) | ||||
−0.701787 | + | 0.712387i | \(0.747614\pi\) | |||||||
\(30\) | −1.65612 | −0.302365 | ||||||||
\(31\) | 7.88196 | 1.41564 | 0.707821 | − | 0.706392i | \(-0.249678\pi\) | ||||
0.707821 | + | 0.706392i | \(0.249678\pi\) | |||||||
\(32\) | 22.6525 | 4.00443 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 7.51138 | 1.28819 | ||||||||
\(35\) | −1.15662 | −0.195504 | ||||||||
\(36\) | 5.50285 | 0.917142 | ||||||||
\(37\) | 8.43648 | 1.38695 | 0.693475 | − | 0.720481i | \(-0.256079\pi\) | ||||
0.693475 | + | 0.720481i | \(0.256079\pi\) | |||||||
\(38\) | 9.99040 | 1.62066 | ||||||||
\(39\) | −0.176875 | −0.0283227 | ||||||||
\(40\) | 5.80115 | 0.917242 | ||||||||
\(41\) | 8.93210 | 1.39496 | 0.697480 | − | 0.716604i | \(-0.254305\pi\) | ||||
0.697480 | + | 0.716604i | \(0.254305\pi\) | |||||||
\(42\) | 5.23991 | 0.808536 | ||||||||
\(43\) | −4.51816 | −0.689013 | −0.344507 | − | 0.938784i | \(-0.611954\pi\) | ||||
−0.344507 | + | 0.938784i | \(0.611954\pi\) | |||||||
\(44\) | 5.50285 | 0.829586 | ||||||||
\(45\) | 0.604616 | 0.0901308 | ||||||||
\(46\) | 4.43462 | 0.653848 | ||||||||
\(47\) | −2.48579 | −0.362590 | −0.181295 | − | 0.983429i | \(-0.558029\pi\) | ||||
−0.181295 | + | 0.983429i | \(0.558029\pi\) | |||||||
\(48\) | −15.2757 | −2.20485 | ||||||||
\(49\) | −3.34050 | −0.477214 | ||||||||
\(50\) | −12.6943 | −1.79525 | ||||||||
\(51\) | −2.74225 | −0.383991 | ||||||||
\(52\) | 0.973317 | 0.134975 | ||||||||
\(53\) | −7.57327 | −1.04027 | −0.520135 | − | 0.854084i | \(-0.674118\pi\) | ||||
−0.520135 | + | 0.854084i | \(0.674118\pi\) | |||||||
\(54\) | −2.73913 | −0.372749 | ||||||||
\(55\) | 0.604616 | 0.0815264 | ||||||||
\(56\) | −18.3546 | −2.45274 | ||||||||
\(57\) | −3.64728 | −0.483095 | ||||||||
\(58\) | −20.7037 | −2.71852 | ||||||||
\(59\) | 1.33758 | 0.174138 | 0.0870692 | − | 0.996202i | \(-0.472250\pi\) | ||||
0.0870692 | + | 0.996202i | \(0.472250\pi\) | |||||||
\(60\) | −3.32711 | −0.429528 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 21.5897 | 2.74190 | ||||||||
\(63\) | −1.91298 | −0.241013 | ||||||||
\(64\) | 31.4969 | 3.93711 | ||||||||
\(65\) | 0.106941 | 0.0132645 | ||||||||
\(66\) | −2.73913 | −0.337164 | ||||||||
\(67\) | −5.50196 | −0.672171 | −0.336086 | − | 0.941831i | \(-0.609103\pi\) | ||||
−0.336086 | + | 0.941831i | \(0.609103\pi\) | |||||||
\(68\) | 15.0902 | 1.82995 | ||||||||
\(69\) | −1.61899 | −0.194903 | ||||||||
\(70\) | −3.16813 | −0.378665 | ||||||||
\(71\) | 0.330471 | 0.0392197 | 0.0196098 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196098 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(72\) | 9.59477 | 1.13075 | ||||||||
\(73\) | −1.75560 | −0.205477 | −0.102739 | − | 0.994708i | \(-0.532761\pi\) | ||||
−0.102739 | + | 0.994708i | \(0.532761\pi\) | |||||||
\(74\) | 23.1086 | 2.68633 | ||||||||
\(75\) | 4.63444 | 0.535139 | ||||||||
\(76\) | 20.0705 | 2.30224 | ||||||||
\(77\) | −1.91298 | −0.218005 | ||||||||
\(78\) | −0.484484 | −0.0548570 | ||||||||
\(79\) | −12.9780 | −1.46014 | −0.730070 | − | 0.683372i | \(-0.760513\pi\) | ||||
−0.730070 | + | 0.683372i | \(0.760513\pi\) | |||||||
\(80\) | 9.23590 | 1.03260 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 24.4662 | 2.70184 | ||||||||
\(83\) | 12.9300 | 1.41925 | 0.709625 | − | 0.704580i | \(-0.248864\pi\) | ||||
0.709625 | + | 0.704580i | \(0.248864\pi\) | |||||||
\(84\) | 10.5269 | 1.14857 | ||||||||
\(85\) | 1.65801 | 0.179836 | ||||||||
\(86\) | −12.3759 | −1.33452 | ||||||||
\(87\) | 7.55848 | 0.810354 | ||||||||
\(88\) | 9.59477 | 1.02281 | ||||||||
\(89\) | −4.11061 | −0.435724 | −0.217862 | − | 0.975980i | \(-0.569908\pi\) | ||||
−0.217862 | + | 0.975980i | \(0.569908\pi\) | |||||||
\(90\) | 1.65612 | 0.174571 | ||||||||
\(91\) | −0.338359 | −0.0354697 | ||||||||
\(92\) | 8.90903 | 0.928831 | ||||||||
\(93\) | −7.88196 | −0.817321 | ||||||||
\(94\) | −6.80891 | −0.702285 | ||||||||
\(95\) | 2.20521 | 0.226249 | ||||||||
\(96\) | −22.6525 | −2.31196 | ||||||||
\(97\) | −12.7524 | −1.29481 | −0.647404 | − | 0.762147i | \(-0.724145\pi\) | ||||
−0.647404 | + | 0.762147i | \(0.724145\pi\) | |||||||
\(98\) | −9.15006 | −0.924296 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −25.5026 | −2.55026 | ||||||||
\(101\) | −10.0353 | −0.998553 | −0.499276 | − | 0.866443i | \(-0.666401\pi\) | ||||
−0.499276 | + | 0.866443i | \(0.666401\pi\) | |||||||
\(102\) | −7.51138 | −0.743737 | ||||||||
\(103\) | −6.05237 | −0.596357 | −0.298179 | − | 0.954510i | \(-0.596379\pi\) | ||||
−0.298179 | + | 0.954510i | \(0.596379\pi\) | |||||||
\(104\) | 1.69708 | 0.166412 | ||||||||
\(105\) | 1.15662 | 0.112875 | ||||||||
\(106\) | −20.7442 | −2.01485 | ||||||||
\(107\) | 12.2595 | 1.18517 | 0.592587 | − | 0.805506i | \(-0.298107\pi\) | ||||
0.592587 | + | 0.805506i | \(0.298107\pi\) | |||||||
\(108\) | −5.50285 | −0.529512 | ||||||||
\(109\) | −1.38440 | −0.132602 | −0.0663008 | − | 0.997800i | \(-0.521120\pi\) | ||||
−0.0663008 | + | 0.997800i | \(0.521120\pi\) | |||||||
\(110\) | 1.65612 | 0.157905 | ||||||||
\(111\) | −8.43648 | −0.800756 | ||||||||
\(112\) | −29.2221 | −2.76123 | ||||||||
\(113\) | 12.6874 | 1.19353 | 0.596765 | − | 0.802416i | \(-0.296452\pi\) | ||||
0.596765 | + | 0.802416i | \(0.296452\pi\) | |||||||
\(114\) | −9.99040 | −0.935686 | ||||||||
\(115\) | 0.978864 | 0.0912795 | ||||||||
\(116\) | −41.5931 | −3.86183 | ||||||||
\(117\) | 0.176875 | 0.0163521 | ||||||||
\(118\) | 3.66382 | 0.337282 | ||||||||
\(119\) | −5.24587 | −0.480888 | ||||||||
\(120\) | −5.80115 | −0.529570 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.73913 | −0.247989 | ||||||||
\(123\) | −8.93210 | −0.805381 | ||||||||
\(124\) | 43.3732 | 3.89503 | ||||||||
\(125\) | −5.82513 | −0.521016 | ||||||||
\(126\) | −5.23991 | −0.466809 | ||||||||
\(127\) | 7.42636 | 0.658983 | 0.329491 | − | 0.944159i | \(-0.393123\pi\) | ||||
0.329491 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(128\) | 40.9692 | 3.62120 | ||||||||
\(129\) | 4.51816 | 0.397802 | ||||||||
\(130\) | 0.292927 | 0.0256914 | ||||||||
\(131\) | −7.69981 | −0.672735 | −0.336368 | − | 0.941731i | \(-0.609198\pi\) | ||||
−0.336368 | + | 0.941731i | \(0.609198\pi\) | |||||||
\(132\) | −5.50285 | −0.478962 | ||||||||
\(133\) | −6.97719 | −0.604999 | ||||||||
\(134\) | −15.0706 | −1.30190 | ||||||||
\(135\) | −0.604616 | −0.0520370 | ||||||||
\(136\) | 26.3112 | 2.25617 | ||||||||
\(137\) | −15.9210 | −1.36022 | −0.680112 | − | 0.733108i | \(-0.738069\pi\) | ||||
−0.680112 | + | 0.733108i | \(0.738069\pi\) | |||||||
\(138\) | −4.43462 | −0.377500 | ||||||||
\(139\) | −2.40561 | −0.204041 | −0.102021 | − | 0.994782i | \(-0.532531\pi\) | ||||
−0.102021 | + | 0.994782i | \(0.532531\pi\) | |||||||
\(140\) | −6.36470 | −0.537916 | ||||||||
\(141\) | 2.48579 | 0.209341 | ||||||||
\(142\) | 0.905204 | 0.0759630 | ||||||||
\(143\) | 0.176875 | 0.0147910 | ||||||||
\(144\) | 15.2757 | 1.27297 | ||||||||
\(145\) | −4.56997 | −0.379516 | ||||||||
\(146\) | −4.80881 | −0.397980 | ||||||||
\(147\) | 3.34050 | 0.275519 | ||||||||
\(148\) | 46.4247 | 3.81609 | ||||||||
\(149\) | −14.5339 | −1.19066 | −0.595331 | − | 0.803480i | \(-0.702979\pi\) | ||||
−0.595331 | + | 0.803480i | \(0.702979\pi\) | |||||||
\(150\) | 12.6943 | 1.03649 | ||||||||
\(151\) | −10.9430 | −0.890525 | −0.445262 | − | 0.895400i | \(-0.646890\pi\) | ||||
−0.445262 | + | 0.895400i | \(0.646890\pi\) | |||||||
\(152\) | 34.9949 | 2.83846 | ||||||||
\(153\) | 2.74225 | 0.221698 | ||||||||
\(154\) | −5.23991 | −0.422244 | ||||||||
\(155\) | 4.76556 | 0.382779 | ||||||||
\(156\) | −0.973317 | −0.0779277 | ||||||||
\(157\) | 16.6497 | 1.32879 | 0.664394 | − | 0.747383i | \(-0.268690\pi\) | ||||
0.664394 | + | 0.747383i | \(0.268690\pi\) | |||||||
\(158\) | −35.5485 | −2.82809 | ||||||||
\(159\) | 7.57327 | 0.600600 | ||||||||
\(160\) | 13.6961 | 1.08277 | ||||||||
\(161\) | −3.09709 | −0.244085 | ||||||||
\(162\) | 2.73913 | 0.215207 | ||||||||
\(163\) | −2.05976 | −0.161333 | −0.0806666 | − | 0.996741i | \(-0.525705\pi\) | ||||
−0.0806666 | + | 0.996741i | \(0.525705\pi\) | |||||||
\(164\) | 49.1520 | 3.83813 | ||||||||
\(165\) | −0.604616 | −0.0470693 | ||||||||
\(166\) | 35.4169 | 2.74889 | ||||||||
\(167\) | −15.3296 | −1.18624 | −0.593121 | − | 0.805113i | \(-0.702105\pi\) | ||||
−0.593121 | + | 0.805113i | \(0.702105\pi\) | |||||||
\(168\) | 18.3546 | 1.41609 | ||||||||
\(169\) | −12.9687 | −0.997593 | ||||||||
\(170\) | 4.54150 | 0.348317 | ||||||||
\(171\) | 3.64728 | 0.278915 | ||||||||
\(172\) | −24.8628 | −1.89577 | ||||||||
\(173\) | 13.0360 | 0.991105 | 0.495553 | − | 0.868578i | \(-0.334966\pi\) | ||||
0.495553 | + | 0.868578i | \(0.334966\pi\) | |||||||
\(174\) | 20.7037 | 1.56954 | ||||||||
\(175\) | 8.86560 | 0.670177 | ||||||||
\(176\) | 15.2757 | 1.15145 | ||||||||
\(177\) | −1.33758 | −0.100539 | ||||||||
\(178\) | −11.2595 | −0.843936 | ||||||||
\(179\) | −11.6608 | −0.871571 | −0.435786 | − | 0.900050i | \(-0.643529\pi\) | ||||
−0.435786 | + | 0.900050i | \(0.643529\pi\) | |||||||
\(180\) | 3.32711 | 0.247988 | ||||||||
\(181\) | −9.58234 | −0.712250 | −0.356125 | − | 0.934438i | \(-0.615902\pi\) | ||||
−0.356125 | + | 0.934438i | \(0.615902\pi\) | |||||||
\(182\) | −0.926810 | −0.0686997 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 15.5338 | 1.14517 | ||||||||
\(185\) | 5.10083 | 0.375021 | ||||||||
\(186\) | −21.5897 | −1.58304 | ||||||||
\(187\) | 2.74225 | 0.200533 | ||||||||
\(188\) | −13.6789 | −0.997638 | ||||||||
\(189\) | 1.91298 | 0.139149 | ||||||||
\(190\) | 6.04035 | 0.438213 | ||||||||
\(191\) | −18.4200 | −1.33283 | −0.666414 | − | 0.745582i | \(-0.732172\pi\) | ||||
−0.666414 | + | 0.745582i | \(0.732172\pi\) | |||||||
\(192\) | −31.4969 | −2.27309 | ||||||||
\(193\) | −5.40862 | −0.389321 | −0.194661 | − | 0.980871i | \(-0.562361\pi\) | ||||
−0.194661 | + | 0.980871i | \(0.562361\pi\) | |||||||
\(194\) | −34.9305 | −2.50786 | ||||||||
\(195\) | −0.106941 | −0.00765824 | ||||||||
\(196\) | −18.3822 | −1.31302 | ||||||||
\(197\) | −2.86614 | −0.204204 | −0.102102 | − | 0.994774i | \(-0.532557\pi\) | ||||
−0.102102 | + | 0.994774i | \(0.532557\pi\) | |||||||
\(198\) | 2.73913 | 0.194662 | ||||||||
\(199\) | 11.9550 | 0.847469 | 0.423735 | − | 0.905786i | \(-0.360719\pi\) | ||||
0.423735 | + | 0.905786i | \(0.360719\pi\) | |||||||
\(200\) | −44.4664 | −3.14425 | ||||||||
\(201\) | 5.50196 | 0.388078 | ||||||||
\(202\) | −27.4881 | −1.93406 | ||||||||
\(203\) | 14.4592 | 1.01484 | ||||||||
\(204\) | −15.0902 | −1.05652 | ||||||||
\(205\) | 5.40049 | 0.377187 | ||||||||
\(206\) | −16.5782 | −1.15506 | ||||||||
\(207\) | 1.61899 | 0.112527 | ||||||||
\(208\) | 2.70188 | 0.187342 | ||||||||
\(209\) | 3.64728 | 0.252288 | ||||||||
\(210\) | 3.16813 | 0.218622 | ||||||||
\(211\) | 24.3432 | 1.67585 | 0.837927 | − | 0.545783i | \(-0.183768\pi\) | ||||
0.837927 | + | 0.545783i | \(0.183768\pi\) | |||||||
\(212\) | −41.6746 | −2.86222 | ||||||||
\(213\) | −0.330471 | −0.0226435 | ||||||||
\(214\) | 33.5805 | 2.29552 | ||||||||
\(215\) | −2.73175 | −0.186304 | ||||||||
\(216\) | −9.59477 | −0.652841 | ||||||||
\(217\) | −15.0781 | −1.02357 | ||||||||
\(218\) | −3.79206 | −0.256831 | ||||||||
\(219\) | 1.75560 | 0.118632 | ||||||||
\(220\) | 3.32711 | 0.224314 | ||||||||
\(221\) | 0.485035 | 0.0326270 | ||||||||
\(222\) | −23.1086 | −1.55095 | ||||||||
\(223\) | 15.7257 | 1.05307 | 0.526535 | − | 0.850154i | \(-0.323491\pi\) | ||||
0.526535 | + | 0.850154i | \(0.323491\pi\) | |||||||
\(224\) | −43.3338 | −2.89536 | ||||||||
\(225\) | −4.63444 | −0.308963 | ||||||||
\(226\) | 34.7525 | 2.31170 | ||||||||
\(227\) | −0.677571 | −0.0449720 | −0.0224860 | − | 0.999747i | \(-0.507158\pi\) | ||||
−0.0224860 | + | 0.999747i | \(0.507158\pi\) | |||||||
\(228\) | −20.0705 | −1.32920 | ||||||||
\(229\) | 13.4531 | 0.889006 | 0.444503 | − | 0.895777i | \(-0.353380\pi\) | ||||
0.444503 | + | 0.895777i | \(0.353380\pi\) | |||||||
\(230\) | 2.68124 | 0.176796 | ||||||||
\(231\) | 1.91298 | 0.125865 | ||||||||
\(232\) | −72.5218 | −4.76129 | ||||||||
\(233\) | −12.1025 | −0.792862 | −0.396431 | − | 0.918064i | \(-0.629751\pi\) | ||||
−0.396431 | + | 0.918064i | \(0.629751\pi\) | |||||||
\(234\) | 0.484484 | 0.0316717 | ||||||||
\(235\) | −1.50295 | −0.0980415 | ||||||||
\(236\) | 7.36052 | 0.479129 | ||||||||
\(237\) | 12.9780 | 0.843012 | ||||||||
\(238\) | −14.3691 | −0.931413 | ||||||||
\(239\) | −7.34142 | −0.474877 | −0.237438 | − | 0.971403i | \(-0.576308\pi\) | ||||
−0.237438 | + | 0.971403i | \(0.576308\pi\) | |||||||
\(240\) | −9.23590 | −0.596175 | ||||||||
\(241\) | −26.9723 | −1.73744 | −0.868719 | − | 0.495306i | \(-0.835056\pi\) | ||||
−0.868719 | + | 0.495306i | \(0.835056\pi\) | |||||||
\(242\) | 2.73913 | 0.176078 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.50285 | −0.352284 | ||||||||
\(245\) | −2.01972 | −0.129035 | ||||||||
\(246\) | −24.4662 | −1.55991 | ||||||||
\(247\) | 0.645114 | 0.0410476 | ||||||||
\(248\) | 75.6256 | 4.80223 | ||||||||
\(249\) | −12.9300 | −0.819404 | ||||||||
\(250\) | −15.9558 | −1.00913 | ||||||||
\(251\) | −17.0405 | −1.07559 | −0.537794 | − | 0.843076i | \(-0.680742\pi\) | ||||
−0.537794 | + | 0.843076i | \(0.680742\pi\) | |||||||
\(252\) | −10.5269 | −0.663130 | ||||||||
\(253\) | 1.61899 | 0.101785 | ||||||||
\(254\) | 20.3418 | 1.27636 | ||||||||
\(255\) | −1.65801 | −0.103828 | ||||||||
\(256\) | 49.2263 | 3.07664 | ||||||||
\(257\) | 13.6010 | 0.848410 | 0.424205 | − | 0.905566i | \(-0.360554\pi\) | ||||
0.424205 | + | 0.905566i | \(0.360554\pi\) | |||||||
\(258\) | 12.3759 | 0.770487 | ||||||||
\(259\) | −16.1388 | −1.00282 | ||||||||
\(260\) | 0.588483 | 0.0364961 | ||||||||
\(261\) | −7.55848 | −0.467858 | ||||||||
\(262\) | −21.0908 | −1.30299 | ||||||||
\(263\) | 18.2508 | 1.12539 | 0.562696 | − | 0.826664i | \(-0.309764\pi\) | ||||
0.562696 | + | 0.826664i | \(0.309764\pi\) | |||||||
\(264\) | −9.59477 | −0.590517 | ||||||||
\(265\) | −4.57892 | −0.281281 | ||||||||
\(266\) | −19.1115 | −1.17180 | ||||||||
\(267\) | 4.11061 | 0.251565 | ||||||||
\(268\) | −30.2764 | −1.84943 | ||||||||
\(269\) | −9.66539 | −0.589309 | −0.294655 | − | 0.955604i | \(-0.595205\pi\) | ||||
−0.294655 | + | 0.955604i | \(0.595205\pi\) | |||||||
\(270\) | −1.65612 | −0.100788 | ||||||||
\(271\) | 30.1115 | 1.82914 | 0.914571 | − | 0.404425i | \(-0.132528\pi\) | ||||
0.914571 | + | 0.404425i | \(0.132528\pi\) | |||||||
\(272\) | 41.8896 | 2.53993 | ||||||||
\(273\) | 0.338359 | 0.0204784 | ||||||||
\(274\) | −43.6098 | −2.63456 | ||||||||
\(275\) | −4.63444 | −0.279467 | ||||||||
\(276\) | −8.90903 | −0.536261 | ||||||||
\(277\) | −5.89926 | −0.354452 | −0.177226 | − | 0.984170i | \(-0.556712\pi\) | ||||
−0.177226 | + | 0.984170i | \(0.556712\pi\) | |||||||
\(278\) | −6.58929 | −0.395199 | ||||||||
\(279\) | 7.88196 | 0.471881 | ||||||||
\(280\) | −11.0975 | −0.663202 | ||||||||
\(281\) | 6.40992 | 0.382384 | 0.191192 | − | 0.981553i | \(-0.438765\pi\) | ||||
0.191192 | + | 0.981553i | \(0.438765\pi\) | |||||||
\(282\) | 6.80891 | 0.405464 | ||||||||
\(283\) | 2.51457 | 0.149476 | 0.0747380 | − | 0.997203i | \(-0.476188\pi\) | ||||
0.0747380 | + | 0.997203i | \(0.476188\pi\) | |||||||
\(284\) | 1.81853 | 0.107910 | ||||||||
\(285\) | −2.20521 | −0.130625 | ||||||||
\(286\) | 0.484484 | 0.0286482 | ||||||||
\(287\) | −17.0870 | −1.00861 | ||||||||
\(288\) | 22.6525 | 1.33481 | ||||||||
\(289\) | −9.48008 | −0.557652 | ||||||||
\(290\) | −12.5178 | −0.735068 | ||||||||
\(291\) | 12.7524 | 0.747558 | ||||||||
\(292\) | −9.66079 | −0.565355 | ||||||||
\(293\) | −12.3742 | −0.722908 | −0.361454 | − | 0.932390i | \(-0.617720\pi\) | ||||
−0.361454 | + | 0.932390i | \(0.617720\pi\) | |||||||
\(294\) | 9.15006 | 0.533642 | ||||||||
\(295\) | 0.808724 | 0.0470857 | ||||||||
\(296\) | 80.9461 | 4.70490 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −39.8102 | −2.30615 | ||||||||
\(299\) | 0.286358 | 0.0165605 | ||||||||
\(300\) | 25.5026 | 1.47239 | ||||||||
\(301\) | 8.64317 | 0.498184 | ||||||||
\(302\) | −29.9742 | −1.72482 | ||||||||
\(303\) | 10.0353 | 0.576515 | ||||||||
\(304\) | 55.7146 | 3.19545 | ||||||||
\(305\) | −0.604616 | −0.0346202 | ||||||||
\(306\) | 7.51138 | 0.429397 | ||||||||
\(307\) | 21.2440 | 1.21246 | 0.606230 | − | 0.795290i | \(-0.292681\pi\) | ||||
0.606230 | + | 0.795290i | \(0.292681\pi\) | |||||||
\(308\) | −10.5269 | −0.599823 | ||||||||
\(309\) | 6.05237 | 0.344307 | ||||||||
\(310\) | 13.0535 | 0.741389 | ||||||||
\(311\) | 26.4545 | 1.50010 | 0.750049 | − | 0.661383i | \(-0.230030\pi\) | ||||
0.750049 | + | 0.661383i | \(0.230030\pi\) | |||||||
\(312\) | −1.69708 | −0.0960780 | ||||||||
\(313\) | 30.7427 | 1.73768 | 0.868841 | − | 0.495090i | \(-0.164865\pi\) | ||||
0.868841 | + | 0.495090i | \(0.164865\pi\) | |||||||
\(314\) | 45.6056 | 2.57367 | ||||||||
\(315\) | −1.15662 | −0.0651681 | ||||||||
\(316\) | −71.4160 | −4.01747 | ||||||||
\(317\) | −21.9554 | −1.23314 | −0.616569 | − | 0.787301i | \(-0.711478\pi\) | ||||
−0.616569 | + | 0.787301i | \(0.711478\pi\) | |||||||
\(318\) | 20.7442 | 1.16328 | ||||||||
\(319\) | −7.55848 | −0.423193 | ||||||||
\(320\) | 19.0435 | 1.06457 | ||||||||
\(321\) | −12.2595 | −0.684261 | ||||||||
\(322\) | −8.48334 | −0.472758 | ||||||||
\(323\) | 10.0018 | 0.556513 | ||||||||
\(324\) | 5.50285 | 0.305714 | ||||||||
\(325\) | −0.819717 | −0.0454697 | ||||||||
\(326\) | −5.64197 | −0.312480 | ||||||||
\(327\) | 1.38440 | 0.0765575 | ||||||||
\(328\) | 85.7015 | 4.73207 | ||||||||
\(329\) | 4.75527 | 0.262167 | ||||||||
\(330\) | −1.65612 | −0.0911666 | ||||||||
\(331\) | −15.8159 | −0.869318 | −0.434659 | − | 0.900595i | \(-0.643131\pi\) | ||||
−0.434659 | + | 0.900595i | \(0.643131\pi\) | |||||||
\(332\) | 71.1517 | 3.90496 | ||||||||
\(333\) | 8.43648 | 0.462316 | ||||||||
\(334\) | −41.9899 | −2.29759 | ||||||||
\(335\) | −3.32657 | −0.181750 | ||||||||
\(336\) | 29.2221 | 1.59419 | ||||||||
\(337\) | −33.1532 | −1.80597 | −0.902986 | − | 0.429671i | \(-0.858630\pi\) | ||||
−0.902986 | + | 0.429671i | \(0.858630\pi\) | |||||||
\(338\) | −35.5230 | −1.93220 | ||||||||
\(339\) | −12.6874 | −0.689085 | ||||||||
\(340\) | 9.12376 | 0.494805 | ||||||||
\(341\) | 7.88196 | 0.426832 | ||||||||
\(342\) | 9.99040 | 0.540219 | ||||||||
\(343\) | 19.7812 | 1.06808 | ||||||||
\(344\) | −43.3507 | −2.33732 | ||||||||
\(345\) | −0.978864 | −0.0527003 | ||||||||
\(346\) | 35.7072 | 1.91963 | ||||||||
\(347\) | 23.0402 | 1.23686 | 0.618430 | − | 0.785840i | \(-0.287769\pi\) | ||||
0.618430 | + | 0.785840i | \(0.287769\pi\) | |||||||
\(348\) | 41.5931 | 2.22963 | ||||||||
\(349\) | −32.7544 | −1.75330 | −0.876651 | − | 0.481127i | \(-0.840227\pi\) | ||||
−0.876651 | + | 0.481127i | \(0.840227\pi\) | |||||||
\(350\) | 24.2841 | 1.29804 | ||||||||
\(351\) | −0.176875 | −0.00944089 | ||||||||
\(352\) | 22.6525 | 1.20738 | ||||||||
\(353\) | 0.349353 | 0.0185942 | 0.00929708 | − | 0.999957i | \(-0.497041\pi\) | ||||
0.00929708 | + | 0.999957i | \(0.497041\pi\) | |||||||
\(354\) | −3.66382 | −0.194730 | ||||||||
\(355\) | 0.199808 | 0.0106047 | ||||||||
\(356\) | −22.6201 | −1.19886 | ||||||||
\(357\) | 5.24587 | 0.277641 | ||||||||
\(358\) | −31.9406 | −1.68811 | ||||||||
\(359\) | 29.2479 | 1.54365 | 0.771823 | − | 0.635838i | \(-0.219345\pi\) | ||||
0.771823 | + | 0.635838i | \(0.219345\pi\) | |||||||
\(360\) | 5.80115 | 0.305747 | ||||||||
\(361\) | −5.69731 | −0.299859 | ||||||||
\(362\) | −26.2473 | −1.37953 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −1.86194 | −0.0975921 | ||||||||
\(365\) | −1.06146 | −0.0555594 | ||||||||
\(366\) | 2.73913 | 0.143177 | ||||||||
\(367\) | −13.9617 | −0.728795 | −0.364397 | − | 0.931244i | \(-0.618725\pi\) | ||||
−0.364397 | + | 0.931244i | \(0.618725\pi\) | |||||||
\(368\) | 24.7311 | 1.28920 | ||||||||
\(369\) | 8.93210 | 0.464987 | ||||||||
\(370\) | 13.9719 | 0.726362 | ||||||||
\(371\) | 14.4875 | 0.752156 | ||||||||
\(372\) | −43.3732 | −2.24880 | ||||||||
\(373\) | 13.7140 | 0.710084 | 0.355042 | − | 0.934850i | \(-0.384467\pi\) | ||||
0.355042 | + | 0.934850i | \(0.384467\pi\) | |||||||
\(374\) | 7.51138 | 0.388404 | ||||||||
\(375\) | 5.82513 | 0.300809 | ||||||||
\(376\) | −23.8506 | −1.23000 | ||||||||
\(377\) | −1.33691 | −0.0688541 | ||||||||
\(378\) | 5.23991 | 0.269512 | ||||||||
\(379\) | 34.6378 | 1.77922 | 0.889612 | − | 0.456717i | \(-0.150975\pi\) | ||||
0.889612 | + | 0.456717i | \(0.150975\pi\) | |||||||
\(380\) | 12.1349 | 0.622508 | ||||||||
\(381\) | −7.42636 | −0.380464 | ||||||||
\(382\) | −50.4550 | −2.58150 | ||||||||
\(383\) | 7.28622 | 0.372308 | 0.186154 | − | 0.982521i | \(-0.440398\pi\) | ||||
0.186154 | + | 0.982521i | \(0.440398\pi\) | |||||||
\(384\) | −40.9692 | −2.09070 | ||||||||
\(385\) | −1.15662 | −0.0589468 | ||||||||
\(386\) | −14.8149 | −0.754060 | ||||||||
\(387\) | −4.51816 | −0.229671 | ||||||||
\(388\) | −70.1744 | −3.56257 | ||||||||
\(389\) | −30.6669 | −1.55487 | −0.777437 | − | 0.628960i | \(-0.783481\pi\) | ||||
−0.777437 | + | 0.628960i | \(0.783481\pi\) | |||||||
\(390\) | −0.292927 | −0.0148329 | ||||||||
\(391\) | 4.43966 | 0.224523 | ||||||||
\(392\) | −32.0513 | −1.61883 | ||||||||
\(393\) | 7.69981 | 0.388404 | ||||||||
\(394\) | −7.85074 | −0.395514 | ||||||||
\(395\) | −7.84671 | −0.394811 | ||||||||
\(396\) | 5.50285 | 0.276529 | ||||||||
\(397\) | −1.12627 | −0.0565257 | −0.0282628 | − | 0.999601i | \(-0.508998\pi\) | ||||
−0.0282628 | + | 0.999601i | \(0.508998\pi\) | |||||||
\(398\) | 32.7464 | 1.64143 | ||||||||
\(399\) | 6.97719 | 0.349297 | ||||||||
\(400\) | −70.7941 | −3.53970 | ||||||||
\(401\) | −9.38421 | −0.468625 | −0.234312 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234312 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(402\) | 15.0706 | 0.751653 | ||||||||
\(403\) | 1.39412 | 0.0694462 | ||||||||
\(404\) | −55.2229 | −2.74744 | ||||||||
\(405\) | 0.604616 | 0.0300436 | ||||||||
\(406\) | 39.6058 | 1.96560 | ||||||||
\(407\) | 8.43648 | 0.418181 | ||||||||
\(408\) | −26.3112 | −1.30260 | ||||||||
\(409\) | 34.3783 | 1.69990 | 0.849948 | − | 0.526867i | \(-0.176633\pi\) | ||||
0.849948 | + | 0.526867i | \(0.176633\pi\) | |||||||
\(410\) | 14.7927 | 0.730558 | ||||||||
\(411\) | 15.9210 | 0.785326 | ||||||||
\(412\) | −33.3053 | −1.64083 | ||||||||
\(413\) | −2.55877 | −0.125909 | ||||||||
\(414\) | 4.43462 | 0.217949 | ||||||||
\(415\) | 7.81767 | 0.383754 | ||||||||
\(416\) | 4.00666 | 0.196443 | ||||||||
\(417\) | 2.40561 | 0.117803 | ||||||||
\(418\) | 9.99040 | 0.488646 | ||||||||
\(419\) | −1.53252 | −0.0748685 | −0.0374343 | − | 0.999299i | \(-0.511918\pi\) | ||||
−0.0374343 | + | 0.999299i | \(0.511918\pi\) | |||||||
\(420\) | 6.36470 | 0.310566 | ||||||||
\(421\) | 13.4022 | 0.653185 | 0.326593 | − | 0.945165i | \(-0.394100\pi\) | ||||
0.326593 | + | 0.945165i | \(0.394100\pi\) | |||||||
\(422\) | 66.6792 | 3.24589 | ||||||||
\(423\) | −2.48579 | −0.120863 | ||||||||
\(424\) | −72.6638 | −3.52887 | ||||||||
\(425\) | −12.7088 | −0.616466 | ||||||||
\(426\) | −0.905204 | −0.0438573 | ||||||||
\(427\) | 1.91298 | 0.0925757 | ||||||||
\(428\) | 67.4624 | 3.26092 | ||||||||
\(429\) | −0.176875 | −0.00853961 | ||||||||
\(430\) | −7.48263 | −0.360845 | ||||||||
\(431\) | −4.01874 | −0.193576 | −0.0967880 | − | 0.995305i | \(-0.530857\pi\) | ||||
−0.0967880 | + | 0.995305i | \(0.530857\pi\) | |||||||
\(432\) | −15.2757 | −0.734950 | ||||||||
\(433\) | 19.2933 | 0.927175 | 0.463587 | − | 0.886051i | \(-0.346562\pi\) | ||||
0.463587 | + | 0.886051i | \(0.346562\pi\) | |||||||
\(434\) | −41.3008 | −1.98250 | ||||||||
\(435\) | 4.56997 | 0.219113 | ||||||||
\(436\) | −7.61815 | −0.364843 | ||||||||
\(437\) | 5.90490 | 0.282470 | ||||||||
\(438\) | 4.80881 | 0.229774 | ||||||||
\(439\) | −23.1285 | −1.10386 | −0.551930 | − | 0.833890i | \(-0.686109\pi\) | ||||
−0.551930 | + | 0.833890i | \(0.686109\pi\) | |||||||
\(440\) | 5.80115 | 0.276559 | ||||||||
\(441\) | −3.34050 | −0.159071 | ||||||||
\(442\) | 1.32858 | 0.0631939 | ||||||||
\(443\) | −18.3618 | −0.872398 | −0.436199 | − | 0.899850i | \(-0.643676\pi\) | ||||
−0.436199 | + | 0.899850i | \(0.643676\pi\) | |||||||
\(444\) | −46.4247 | −2.20322 | ||||||||
\(445\) | −2.48534 | −0.117816 | ||||||||
\(446\) | 43.0747 | 2.03965 | ||||||||
\(447\) | 14.5339 | 0.687429 | ||||||||
\(448\) | −60.2530 | −2.84669 | ||||||||
\(449\) | −12.2717 | −0.579135 | −0.289568 | − | 0.957158i | \(-0.593512\pi\) | ||||
−0.289568 | + | 0.957158i | \(0.593512\pi\) | |||||||
\(450\) | −12.6943 | −0.598417 | ||||||||
\(451\) | 8.93210 | 0.420596 | ||||||||
\(452\) | 69.8168 | 3.28391 | ||||||||
\(453\) | 10.9430 | 0.514145 | ||||||||
\(454\) | −1.85596 | −0.0871044 | ||||||||
\(455\) | −0.204577 | −0.00959073 | ||||||||
\(456\) | −34.9949 | −1.63878 | ||||||||
\(457\) | 17.9930 | 0.841679 | 0.420840 | − | 0.907135i | \(-0.361736\pi\) | ||||
0.420840 | + | 0.907135i | \(0.361736\pi\) | |||||||
\(458\) | 36.8498 | 1.72188 | ||||||||
\(459\) | −2.74225 | −0.127997 | ||||||||
\(460\) | 5.38654 | 0.251149 | ||||||||
\(461\) | −1.26483 | −0.0589088 | −0.0294544 | − | 0.999566i | \(-0.509377\pi\) | ||||
−0.0294544 | + | 0.999566i | \(0.509377\pi\) | |||||||
\(462\) | 5.23991 | 0.243783 | ||||||||
\(463\) | −10.3872 | −0.482732 | −0.241366 | − | 0.970434i | \(-0.577595\pi\) | ||||
−0.241366 | + | 0.970434i | \(0.577595\pi\) | |||||||
\(464\) | −115.461 | −5.36012 | ||||||||
\(465\) | −4.76556 | −0.220997 | ||||||||
\(466\) | −33.1504 | −1.53566 | ||||||||
\(467\) | 10.9780 | 0.507999 | 0.253999 | − | 0.967204i | \(-0.418254\pi\) | ||||
0.253999 | + | 0.967204i | \(0.418254\pi\) | |||||||
\(468\) | 0.973317 | 0.0449916 | ||||||||
\(469\) | 10.5252 | 0.486006 | ||||||||
\(470\) | −4.11677 | −0.189893 | ||||||||
\(471\) | −16.6497 | −0.767176 | ||||||||
\(472\) | 12.8338 | 0.590724 | ||||||||
\(473\) | −4.51816 | −0.207745 | ||||||||
\(474\) | 35.5485 | 1.63280 | ||||||||
\(475\) | −16.9031 | −0.775568 | ||||||||
\(476\) | −28.8672 | −1.32313 | ||||||||
\(477\) | −7.57327 | −0.346756 | ||||||||
\(478\) | −20.1091 | −0.919770 | ||||||||
\(479\) | −17.8446 | −0.815339 | −0.407670 | − | 0.913130i | \(-0.633658\pi\) | ||||
−0.407670 | + | 0.913130i | \(0.633658\pi\) | |||||||
\(480\) | −13.6961 | −0.625137 | ||||||||
\(481\) | 1.49220 | 0.0680386 | ||||||||
\(482\) | −73.8807 | −3.36517 | ||||||||
\(483\) | 3.09709 | 0.140923 | ||||||||
\(484\) | 5.50285 | 0.250130 | ||||||||
\(485\) | −7.71029 | −0.350106 | ||||||||
\(486\) | −2.73913 | −0.124250 | ||||||||
\(487\) | −19.6964 | −0.892531 | −0.446266 | − | 0.894901i | \(-0.647246\pi\) | ||||
−0.446266 | + | 0.894901i | \(0.647246\pi\) | |||||||
\(488\) | −9.59477 | −0.434335 | ||||||||
\(489\) | 2.05976 | 0.0931457 | ||||||||
\(490\) | −5.53227 | −0.249923 | ||||||||
\(491\) | −17.3750 | −0.784124 | −0.392062 | − | 0.919939i | \(-0.628238\pi\) | ||||
−0.392062 | + | 0.919939i | \(0.628238\pi\) | |||||||
\(492\) | −49.1520 | −2.21594 | ||||||||
\(493\) | −20.7272 | −0.933507 | ||||||||
\(494\) | 1.76705 | 0.0795034 | ||||||||
\(495\) | 0.604616 | 0.0271755 | ||||||||
\(496\) | 120.402 | 5.40621 | ||||||||
\(497\) | −0.632185 | −0.0283574 | ||||||||
\(498\) | −35.4169 | −1.58707 | ||||||||
\(499\) | 25.1532 | 1.12601 | 0.563005 | − | 0.826454i | \(-0.309645\pi\) | ||||
0.563005 | + | 0.826454i | \(0.309645\pi\) | |||||||
\(500\) | −32.0548 | −1.43354 | ||||||||
\(501\) | 15.3296 | 0.684878 | ||||||||
\(502\) | −46.6763 | −2.08326 | ||||||||
\(503\) | 18.0309 | 0.803958 | 0.401979 | − | 0.915649i | \(-0.368322\pi\) | ||||
0.401979 | + | 0.915649i | \(0.368322\pi\) | |||||||
\(504\) | −18.3546 | −0.817580 | ||||||||
\(505\) | −6.06752 | −0.270001 | ||||||||
\(506\) | 4.43462 | 0.197143 | ||||||||
\(507\) | 12.9687 | 0.575961 | ||||||||
\(508\) | 40.8661 | 1.81314 | ||||||||
\(509\) | −35.8893 | −1.59077 | −0.795383 | − | 0.606108i | \(-0.792730\pi\) | ||||
−0.795383 | + | 0.606108i | \(0.792730\pi\) | |||||||
\(510\) | −4.54150 | −0.201101 | ||||||||
\(511\) | 3.35843 | 0.148568 | ||||||||
\(512\) | 52.8990 | 2.33783 | ||||||||
\(513\) | −3.64728 | −0.161032 | ||||||||
\(514\) | 37.2551 | 1.64325 | ||||||||
\(515\) | −3.65936 | −0.161250 | ||||||||
\(516\) | 24.8628 | 1.09452 | ||||||||
\(517\) | −2.48579 | −0.109325 | ||||||||
\(518\) | −44.2065 | −1.94232 | ||||||||
\(519\) | −13.0360 | −0.572215 | ||||||||
\(520\) | 1.02608 | 0.0449965 | ||||||||
\(521\) | 6.16062 | 0.269902 | 0.134951 | − | 0.990852i | \(-0.456912\pi\) | ||||
0.134951 | + | 0.990852i | \(0.456912\pi\) | |||||||
\(522\) | −20.7037 | −0.906175 | ||||||||
\(523\) | −2.39141 | −0.104569 | −0.0522846 | − | 0.998632i | \(-0.516650\pi\) | ||||
−0.0522846 | + | 0.998632i | \(0.516650\pi\) | |||||||
\(524\) | −42.3709 | −1.85098 | ||||||||
\(525\) | −8.86560 | −0.386927 | ||||||||
\(526\) | 49.9914 | 2.17973 | ||||||||
\(527\) | 21.6143 | 0.941533 | ||||||||
\(528\) | −15.2757 | −0.664787 | ||||||||
\(529\) | −20.3789 | −0.886039 | ||||||||
\(530\) | −12.5423 | −0.544801 | ||||||||
\(531\) | 1.33758 | 0.0580462 | ||||||||
\(532\) | −38.3944 | −1.66461 | ||||||||
\(533\) | 1.57987 | 0.0684316 | ||||||||
\(534\) | 11.2595 | 0.487247 | ||||||||
\(535\) | 7.41231 | 0.320462 | ||||||||
\(536\) | −52.7900 | −2.28018 | ||||||||
\(537\) | 11.6608 | 0.503202 | ||||||||
\(538\) | −26.4748 | −1.14141 | ||||||||
\(539\) | −3.34050 | −0.143885 | ||||||||
\(540\) | −3.32711 | −0.143176 | ||||||||
\(541\) | 30.9269 | 1.32965 | 0.664827 | − | 0.746998i | \(-0.268505\pi\) | ||||
0.664827 | + | 0.746998i | \(0.268505\pi\) | |||||||
\(542\) | 82.4793 | 3.54279 | ||||||||
\(543\) | 9.58234 | 0.411217 | ||||||||
\(544\) | 62.1188 | 2.66332 | ||||||||
\(545\) | −0.837031 | −0.0358545 | ||||||||
\(546\) | 0.926810 | 0.0396638 | ||||||||
\(547\) | 31.4601 | 1.34514 | 0.672569 | − | 0.740035i | \(-0.265191\pi\) | ||||
0.672569 | + | 0.740035i | \(0.265191\pi\) | |||||||
\(548\) | −87.6109 | −3.74255 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | −12.6943 | −0.541289 | ||||||||
\(551\) | −27.5679 | −1.17443 | ||||||||
\(552\) | −15.5338 | −0.661162 | ||||||||
\(553\) | 24.8267 | 1.05574 | ||||||||
\(554\) | −16.1589 | −0.686524 | ||||||||
\(555\) | −5.10083 | −0.216518 | ||||||||
\(556\) | −13.2377 | −0.561404 | ||||||||
\(557\) | −43.3173 | −1.83541 | −0.917706 | − | 0.397261i | \(-0.869961\pi\) | ||||
−0.917706 | + | 0.397261i | \(0.869961\pi\) | |||||||
\(558\) | 21.5897 | 0.913967 | ||||||||
\(559\) | −0.799150 | −0.0338005 | ||||||||
\(560\) | −17.6681 | −0.746614 | ||||||||
\(561\) | −2.74225 | −0.115778 | ||||||||
\(562\) | 17.5576 | 0.740623 | ||||||||
\(563\) | −12.7937 | −0.539192 | −0.269596 | − | 0.962974i | \(-0.586890\pi\) | ||||
−0.269596 | + | 0.962974i | \(0.586890\pi\) | |||||||
\(564\) | 13.6789 | 0.575987 | ||||||||
\(565\) | 7.67100 | 0.322721 | ||||||||
\(566\) | 6.88775 | 0.289514 | ||||||||
\(567\) | −1.91298 | −0.0803377 | ||||||||
\(568\) | 3.17079 | 0.133044 | ||||||||
\(569\) | 16.2156 | 0.679791 | 0.339896 | − | 0.940463i | \(-0.389608\pi\) | ||||
0.339896 | + | 0.940463i | \(0.389608\pi\) | |||||||
\(570\) | −6.04035 | −0.253003 | ||||||||
\(571\) | 15.4511 | 0.646607 | 0.323303 | − | 0.946295i | \(-0.395207\pi\) | ||||
0.323303 | + | 0.946295i | \(0.395207\pi\) | |||||||
\(572\) | 0.973317 | 0.0406964 | ||||||||
\(573\) | 18.4200 | 0.769509 | ||||||||
\(574\) | −46.8035 | −1.95354 | ||||||||
\(575\) | −7.50309 | −0.312900 | ||||||||
\(576\) | 31.4969 | 1.31237 | ||||||||
\(577\) | −13.7967 | −0.574365 | −0.287182 | − | 0.957876i | \(-0.592719\pi\) | ||||
−0.287182 | + | 0.957876i | \(0.592719\pi\) | |||||||
\(578\) | −25.9672 | −1.08009 | ||||||||
\(579\) | 5.40862 | 0.224775 | ||||||||
\(580\) | −25.1479 | −1.04421 | ||||||||
\(581\) | −24.7348 | −1.02617 | ||||||||
\(582\) | 34.9305 | 1.44791 | ||||||||
\(583\) | −7.57327 | −0.313653 | ||||||||
\(584\) | −16.8445 | −0.697032 | ||||||||
\(585\) | 0.106941 | 0.00442148 | ||||||||
\(586\) | −33.8946 | −1.40017 | ||||||||
\(587\) | −0.731957 | −0.0302111 | −0.0151056 | − | 0.999886i | \(-0.504808\pi\) | ||||
−0.0151056 | + | 0.999886i | \(0.504808\pi\) | |||||||
\(588\) | 18.3822 | 0.758071 | ||||||||
\(589\) | 28.7478 | 1.18453 | ||||||||
\(590\) | 2.21520 | 0.0911984 | ||||||||
\(591\) | 2.86614 | 0.117897 | ||||||||
\(592\) | 128.873 | 5.29664 | ||||||||
\(593\) | 16.9597 | 0.696450 | 0.348225 | − | 0.937411i | \(-0.386785\pi\) | ||||
0.348225 | + | 0.937411i | \(0.386785\pi\) | |||||||
\(594\) | −2.73913 | −0.112388 | ||||||||
\(595\) | −3.17174 | −0.130029 | ||||||||
\(596\) | −79.9778 | −3.27602 | ||||||||
\(597\) | −11.9550 | −0.489287 | ||||||||
\(598\) | 0.784373 | 0.0320754 | ||||||||
\(599\) | −11.3334 | −0.463070 | −0.231535 | − | 0.972827i | \(-0.574375\pi\) | ||||
−0.231535 | + | 0.972827i | \(0.574375\pi\) | |||||||
\(600\) | 44.4664 | 1.81533 | ||||||||
\(601\) | 37.8868 | 1.54543 | 0.772717 | − | 0.634750i | \(-0.218897\pi\) | ||||
0.772717 | + | 0.634750i | \(0.218897\pi\) | |||||||
\(602\) | 23.6748 | 0.964912 | ||||||||
\(603\) | −5.50196 | −0.224057 | ||||||||
\(604\) | −60.2174 | −2.45021 | ||||||||
\(605\) | 0.604616 | 0.0245811 | ||||||||
\(606\) | 27.4881 | 1.11663 | ||||||||
\(607\) | −9.55272 | −0.387733 | −0.193866 | − | 0.981028i | \(-0.562103\pi\) | ||||
−0.193866 | + | 0.981028i | \(0.562103\pi\) | |||||||
\(608\) | 82.6201 | 3.35069 | ||||||||
\(609\) | −14.4592 | −0.585918 | ||||||||
\(610\) | −1.65612 | −0.0670545 | ||||||||
\(611\) | −0.439674 | −0.0177873 | ||||||||
\(612\) | 15.0902 | 0.609984 | ||||||||
\(613\) | 18.7337 | 0.756646 | 0.378323 | − | 0.925674i | \(-0.376501\pi\) | ||||
0.378323 | + | 0.925674i | \(0.376501\pi\) | |||||||
\(614\) | 58.1902 | 2.34836 | ||||||||
\(615\) | −5.40049 | −0.217769 | ||||||||
\(616\) | −18.3546 | −0.739529 | ||||||||
\(617\) | −2.88614 | −0.116192 | −0.0580958 | − | 0.998311i | \(-0.518503\pi\) | ||||
−0.0580958 | + | 0.998311i | \(0.518503\pi\) | |||||||
\(618\) | 16.5782 | 0.666874 | ||||||||
\(619\) | 28.4797 | 1.14470 | 0.572348 | − | 0.820011i | \(-0.306033\pi\) | ||||
0.572348 | + | 0.820011i | \(0.306033\pi\) | |||||||
\(620\) | 26.2241 | 1.05319 | ||||||||
\(621\) | −1.61899 | −0.0649676 | ||||||||
\(622\) | 72.4624 | 2.90548 | ||||||||
\(623\) | 7.86353 | 0.315046 | ||||||||
\(624\) | −2.70188 | −0.108162 | ||||||||
\(625\) | 19.6502 | 0.786009 | ||||||||
\(626\) | 84.2085 | 3.36565 | ||||||||
\(627\) | −3.64728 | −0.145659 | ||||||||
\(628\) | 91.6205 | 3.65606 | ||||||||
\(629\) | 23.1349 | 0.922450 | ||||||||
\(630\) | −3.16813 | −0.126222 | ||||||||
\(631\) | 18.8981 | 0.752322 | 0.376161 | − | 0.926554i | \(-0.377244\pi\) | ||||
0.376161 | + | 0.926554i | \(0.377244\pi\) | |||||||
\(632\) | −124.521 | −4.95318 | ||||||||
\(633\) | −24.3432 | −0.967554 | ||||||||
\(634\) | −60.1388 | −2.38842 | ||||||||
\(635\) | 4.49009 | 0.178184 | ||||||||
\(636\) | 41.6746 | 1.65250 | ||||||||
\(637\) | −0.590850 | −0.0234103 | ||||||||
\(638\) | −20.7037 | −0.819666 | ||||||||
\(639\) | 0.330471 | 0.0130732 | ||||||||
\(640\) | 24.7706 | 0.979145 | ||||||||
\(641\) | 29.7753 | 1.17605 | 0.588026 | − | 0.808842i | \(-0.299905\pi\) | ||||
0.588026 | + | 0.808842i | \(0.299905\pi\) | |||||||
\(642\) | −33.5805 | −1.32532 | ||||||||
\(643\) | −1.68829 | −0.0665798 | −0.0332899 | − | 0.999446i | \(-0.510598\pi\) | ||||
−0.0332899 | + | 0.999446i | \(0.510598\pi\) | |||||||
\(644\) | −17.0428 | −0.671581 | ||||||||
\(645\) | 2.73175 | 0.107563 | ||||||||
\(646\) | 27.3961 | 1.07789 | ||||||||
\(647\) | −31.7652 | −1.24882 | −0.624409 | − | 0.781098i | \(-0.714660\pi\) | ||||
−0.624409 | + | 0.781098i | \(0.714660\pi\) | |||||||
\(648\) | 9.59477 | 0.376918 | ||||||||
\(649\) | 1.33758 | 0.0525047 | ||||||||
\(650\) | −2.24531 | −0.0880684 | ||||||||
\(651\) | 15.0781 | 0.590956 | ||||||||
\(652\) | −11.3346 | −0.443896 | ||||||||
\(653\) | −12.0681 | −0.472261 | −0.236130 | − | 0.971721i | \(-0.575879\pi\) | ||||
−0.236130 | + | 0.971721i | \(0.575879\pi\) | |||||||
\(654\) | 3.79206 | 0.148281 | ||||||||
\(655\) | −4.65542 | −0.181902 | ||||||||
\(656\) | 136.444 | 5.32723 | ||||||||
\(657\) | −1.75560 | −0.0684924 | ||||||||
\(658\) | 13.0253 | 0.507780 | ||||||||
\(659\) | 17.5896 | 0.685192 | 0.342596 | − | 0.939483i | \(-0.388694\pi\) | ||||
0.342596 | + | 0.939483i | \(0.388694\pi\) | |||||||
\(660\) | −3.32711 | −0.129508 | ||||||||
\(661\) | 18.9318 | 0.736361 | 0.368181 | − | 0.929754i | \(-0.379981\pi\) | ||||
0.368181 | + | 0.929754i | \(0.379981\pi\) | |||||||
\(662\) | −43.3217 | −1.68375 | ||||||||
\(663\) | −0.485035 | −0.0188372 | ||||||||
\(664\) | 124.060 | 4.81447 | ||||||||
\(665\) | −4.21852 | −0.163587 | ||||||||
\(666\) | 23.1086 | 0.895442 | ||||||||
\(667\) | −12.2371 | −0.473821 | ||||||||
\(668\) | −84.3567 | −3.26386 | ||||||||
\(669\) | −15.7257 | −0.607990 | ||||||||
\(670\) | −9.11192 | −0.352024 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 43.3338 | 1.67164 | ||||||||
\(673\) | 49.3060 | 1.90061 | 0.950303 | − | 0.311325i | \(-0.100773\pi\) | ||||
0.950303 | + | 0.311325i | \(0.100773\pi\) | |||||||
\(674\) | −90.8111 | −3.49791 | ||||||||
\(675\) | 4.63444 | 0.178380 | ||||||||
\(676\) | −71.3649 | −2.74480 | ||||||||
\(677\) | 6.96645 | 0.267742 | 0.133871 | − | 0.990999i | \(-0.457259\pi\) | ||||
0.133871 | + | 0.990999i | \(0.457259\pi\) | |||||||
\(678\) | −34.7525 | −1.33466 | ||||||||
\(679\) | 24.3951 | 0.936198 | ||||||||
\(680\) | 15.9082 | 0.610051 | ||||||||
\(681\) | 0.677571 | 0.0259646 | ||||||||
\(682\) | 21.5897 | 0.826714 | ||||||||
\(683\) | 17.4032 | 0.665913 | 0.332957 | − | 0.942942i | \(-0.391954\pi\) | ||||
0.332957 | + | 0.942942i | \(0.391954\pi\) | |||||||
\(684\) | 20.0705 | 0.767413 | ||||||||
\(685\) | −9.62609 | −0.367794 | ||||||||
\(686\) | 54.1833 | 2.06873 | ||||||||
\(687\) | −13.4531 | −0.513268 | ||||||||
\(688\) | −69.0179 | −2.63128 | ||||||||
\(689\) | −1.33952 | −0.0510318 | ||||||||
\(690\) | −2.68124 | −0.102073 | ||||||||
\(691\) | −16.3254 | −0.621048 | −0.310524 | − | 0.950566i | \(-0.600505\pi\) | ||||
−0.310524 | + | 0.950566i | \(0.600505\pi\) | |||||||
\(692\) | 71.7349 | 2.72695 | ||||||||
\(693\) | −1.91298 | −0.0726682 | ||||||||
\(694\) | 63.1100 | 2.39562 | ||||||||
\(695\) | −1.45447 | −0.0551712 | ||||||||
\(696\) | 72.5218 | 2.74893 | ||||||||
\(697\) | 24.4940 | 0.927778 | ||||||||
\(698\) | −89.7186 | −3.39590 | ||||||||
\(699\) | 12.1025 | 0.457759 | ||||||||
\(700\) | 48.7861 | 1.84394 | ||||||||
\(701\) | −1.25848 | −0.0475322 | −0.0237661 | − | 0.999718i | \(-0.507566\pi\) | ||||
−0.0237661 | + | 0.999718i | \(0.507566\pi\) | |||||||
\(702\) | −0.484484 | −0.0182857 | ||||||||
\(703\) | 30.7703 | 1.16052 | ||||||||
\(704\) | 31.4969 | 1.18708 | ||||||||
\(705\) | 1.50295 | 0.0566043 | ||||||||
\(706\) | 0.956923 | 0.0360143 | ||||||||
\(707\) | 19.1974 | 0.721993 | ||||||||
\(708\) | −7.36052 | −0.276625 | ||||||||
\(709\) | 44.8435 | 1.68413 | 0.842067 | − | 0.539373i | \(-0.181339\pi\) | ||||
0.842067 | + | 0.539373i | \(0.181339\pi\) | |||||||
\(710\) | 0.547301 | 0.0205398 | ||||||||
\(711\) | −12.9780 | −0.486713 | ||||||||
\(712\) | −39.4404 | −1.47809 | ||||||||
\(713\) | 12.7608 | 0.477895 | ||||||||
\(714\) | 14.3691 | 0.537752 | ||||||||
\(715\) | 0.106941 | 0.00399938 | ||||||||
\(716\) | −64.1678 | −2.39806 | ||||||||
\(717\) | 7.34142 | 0.274170 | ||||||||
\(718\) | 80.1139 | 2.98982 | ||||||||
\(719\) | 39.7590 | 1.48276 | 0.741381 | − | 0.671085i | \(-0.234171\pi\) | ||||
0.741381 | + | 0.671085i | \(0.234171\pi\) | |||||||
\(720\) | 9.23590 | 0.344202 | ||||||||
\(721\) | 11.5781 | 0.431190 | ||||||||
\(722\) | −15.6057 | −0.580784 | ||||||||
\(723\) | 26.9723 | 1.00311 | ||||||||
\(724\) | −52.7302 | −1.95970 | ||||||||
\(725\) | 35.0293 | 1.30096 | ||||||||
\(726\) | −2.73913 | −0.101659 | ||||||||
\(727\) | 39.6673 | 1.47118 | 0.735589 | − | 0.677428i | \(-0.236905\pi\) | ||||
0.735589 | + | 0.677428i | \(0.236905\pi\) | |||||||
\(728\) | −3.24648 | −0.120322 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.90748 | −0.107611 | ||||||||
\(731\) | −12.3899 | −0.458258 | ||||||||
\(732\) | 5.50285 | 0.203391 | ||||||||
\(733\) | −4.45224 | −0.164447 | −0.0822235 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822235 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(734\) | −38.2430 | −1.41157 | ||||||||
\(735\) | 2.01972 | 0.0744984 | ||||||||
\(736\) | 36.6741 | 1.35182 | ||||||||
\(737\) | −5.50196 | −0.202667 | ||||||||
\(738\) | 24.4662 | 0.900614 | ||||||||
\(739\) | −33.8922 | −1.24674 | −0.623372 | − | 0.781926i | \(-0.714238\pi\) | ||||
−0.623372 | + | 0.781926i | \(0.714238\pi\) | |||||||
\(740\) | 28.0691 | 1.03184 | ||||||||
\(741\) | −0.645114 | −0.0236988 | ||||||||
\(742\) | 39.6833 | 1.45682 | ||||||||
\(743\) | −9.90914 | −0.363531 | −0.181766 | − | 0.983342i | \(-0.558181\pi\) | ||||
−0.181766 | + | 0.983342i | \(0.558181\pi\) | |||||||
\(744\) | −75.6256 | −2.77257 | ||||||||
\(745\) | −8.78742 | −0.321946 | ||||||||
\(746\) | 37.5645 | 1.37533 | ||||||||
\(747\) | 12.9300 | 0.473083 | ||||||||
\(748\) | 15.0902 | 0.551751 | ||||||||
\(749\) | −23.4523 | −0.856928 | ||||||||
\(750\) | 15.9558 | 0.582624 | ||||||||
\(751\) | 3.30472 | 0.120591 | 0.0602955 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602955 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(752\) | −37.9720 | −1.38470 | ||||||||
\(753\) | 17.0405 | 0.620991 | ||||||||
\(754\) | −3.66196 | −0.133361 | ||||||||
\(755\) | −6.61628 | −0.240791 | ||||||||
\(756\) | 10.5269 | 0.382858 | ||||||||
\(757\) | 13.4977 | 0.490583 | 0.245292 | − | 0.969449i | \(-0.421116\pi\) | ||||
0.245292 | + | 0.969449i | \(0.421116\pi\) | |||||||
\(758\) | 94.8776 | 3.44611 | ||||||||
\(759\) | −1.61899 | −0.0587654 | ||||||||
\(760\) | 21.1584 | 0.767497 | ||||||||
\(761\) | −28.0515 | −1.01687 | −0.508433 | − | 0.861101i | \(-0.669775\pi\) | ||||
−0.508433 | + | 0.861101i | \(0.669775\pi\) | |||||||
\(762\) | −20.3418 | −0.736905 | ||||||||
\(763\) | 2.64834 | 0.0958762 | ||||||||
\(764\) | −101.363 | −3.66718 | ||||||||
\(765\) | 1.65801 | 0.0599453 | ||||||||
\(766\) | 19.9579 | 0.721109 | ||||||||
\(767\) | 0.236585 | 0.00854259 | ||||||||
\(768\) | −49.2263 | −1.77630 | ||||||||
\(769\) | −29.0212 | −1.04653 | −0.523266 | − | 0.852170i | \(-0.675286\pi\) | ||||
−0.523266 | + | 0.852170i | \(0.675286\pi\) | |||||||
\(770\) | −3.16813 | −0.114172 | ||||||||
\(771\) | −13.6010 | −0.489830 | ||||||||
\(772\) | −29.7628 | −1.07119 | ||||||||
\(773\) | −18.5820 | −0.668350 | −0.334175 | − | 0.942511i | \(-0.608458\pi\) | ||||
−0.334175 | + | 0.942511i | \(0.608458\pi\) | |||||||
\(774\) | −12.3759 | −0.444841 | ||||||||
\(775\) | −36.5285 | −1.31214 | ||||||||
\(776\) | −122.356 | −4.39233 | ||||||||
\(777\) | 16.1388 | 0.578978 | ||||||||
\(778\) | −84.0008 | −3.01157 | ||||||||
\(779\) | 32.5779 | 1.16723 | ||||||||
\(780\) | −0.588483 | −0.0210711 | ||||||||
\(781\) | 0.330471 | 0.0118252 | ||||||||
\(782\) | 12.1608 | 0.434870 | ||||||||
\(783\) | 7.55848 | 0.270118 | ||||||||
\(784\) | −51.0282 | −1.82244 | ||||||||
\(785\) | 10.0666 | 0.359294 | ||||||||
\(786\) | 21.0908 | 0.752284 | ||||||||
\(787\) | 34.2557 | 1.22108 | 0.610541 | − | 0.791985i | \(-0.290952\pi\) | ||||
0.610541 | + | 0.791985i | \(0.290952\pi\) | |||||||
\(788\) | −15.7719 | −0.561852 | ||||||||
\(789\) | −18.2508 | −0.649746 | ||||||||
\(790\) | −21.4932 | −0.764693 | ||||||||
\(791\) | −24.2708 | −0.862969 | ||||||||
\(792\) | 9.59477 | 0.340935 | ||||||||
\(793\) | −0.176875 | −0.00628102 | ||||||||
\(794\) | −3.08499 | −0.109482 | ||||||||
\(795\) | 4.57892 | 0.162398 | ||||||||
\(796\) | 65.7867 | 2.33175 | ||||||||
\(797\) | −11.0127 | −0.390088 | −0.195044 | − | 0.980794i | \(-0.562485\pi\) | ||||
−0.195044 | + | 0.980794i | \(0.562485\pi\) | |||||||
\(798\) | 19.1115 | 0.676538 | ||||||||
\(799\) | −6.81665 | −0.241156 | ||||||||
\(800\) | −104.982 | −3.71166 | ||||||||
\(801\) | −4.11061 | −0.145241 | ||||||||
\(802\) | −25.7046 | −0.907660 | ||||||||
\(803\) | −1.75560 | −0.0619537 | ||||||||
\(804\) | 30.2764 | 1.06777 | ||||||||
\(805\) | −1.87255 | −0.0659987 | ||||||||
\(806\) | 3.81869 | 0.134507 | ||||||||
\(807\) | 9.66539 | 0.340238 | ||||||||
\(808\) | −96.2867 | −3.38735 | ||||||||
\(809\) | 45.2337 | 1.59033 | 0.795165 | − | 0.606392i | \(-0.207384\pi\) | ||||
0.795165 | + | 0.606392i | \(0.207384\pi\) | |||||||
\(810\) | 1.65612 | 0.0581902 | ||||||||
\(811\) | 32.9688 | 1.15769 | 0.578846 | − | 0.815437i | \(-0.303503\pi\) | ||||
0.578846 | + | 0.815437i | \(0.303503\pi\) | |||||||
\(812\) | 79.5670 | 2.79225 | ||||||||
\(813\) | −30.1115 | −1.05606 | ||||||||
\(814\) | 23.1086 | 0.809958 | ||||||||
\(815\) | −1.24537 | −0.0436232 | ||||||||
\(816\) | −41.8896 | −1.46643 | ||||||||
\(817\) | −16.4790 | −0.576528 | ||||||||
\(818\) | 94.1666 | 3.29246 | ||||||||
\(819\) | −0.338359 | −0.0118232 | ||||||||
\(820\) | 29.7181 | 1.03780 | ||||||||
\(821\) | 17.6348 | 0.615460 | 0.307730 | − | 0.951474i | \(-0.400431\pi\) | ||||
0.307730 | + | 0.951474i | \(0.400431\pi\) | |||||||
\(822\) | 43.6098 | 1.52107 | ||||||||
\(823\) | −6.60202 | −0.230132 | −0.115066 | − | 0.993358i | \(-0.536708\pi\) | ||||
−0.115066 | + | 0.993358i | \(0.536708\pi\) | |||||||
\(824\) | −58.0711 | −2.02300 | ||||||||
\(825\) | 4.63444 | 0.161350 | ||||||||
\(826\) | −7.00882 | −0.243868 | ||||||||
\(827\) | −0.843089 | −0.0293171 | −0.0146585 | − | 0.999893i | \(-0.504666\pi\) | ||||
−0.0146585 | + | 0.999893i | \(0.504666\pi\) | |||||||
\(828\) | 8.90903 | 0.309610 | ||||||||
\(829\) | −40.4340 | −1.40433 | −0.702166 | − | 0.712014i | \(-0.747783\pi\) | ||||
−0.702166 | + | 0.712014i | \(0.747783\pi\) | |||||||
\(830\) | 21.4136 | 0.743278 | ||||||||
\(831\) | 5.89926 | 0.204643 | ||||||||
\(832\) | 5.57102 | 0.193140 | ||||||||
\(833\) | −9.16047 | −0.317391 | ||||||||
\(834\) | 6.58929 | 0.228168 | ||||||||
\(835\) | −9.26854 | −0.320751 | ||||||||
\(836\) | 20.0705 | 0.694151 | ||||||||
\(837\) | −7.88196 | −0.272440 | ||||||||
\(838\) | −4.19778 | −0.145010 | ||||||||
\(839\) | 49.0996 | 1.69511 | 0.847553 | − | 0.530710i | \(-0.178075\pi\) | ||||
0.847553 | + | 0.530710i | \(0.178075\pi\) | |||||||
\(840\) | 11.0975 | 0.382900 | ||||||||
\(841\) | 28.1305 | 0.970019 | ||||||||
\(842\) | 36.7105 | 1.26513 | ||||||||
\(843\) | −6.40992 | −0.220769 | ||||||||
\(844\) | 133.957 | 4.61098 | ||||||||
\(845\) | −7.84109 | −0.269742 | ||||||||
\(846\) | −6.80891 | −0.234095 | ||||||||
\(847\) | −1.91298 | −0.0657309 | ||||||||
\(848\) | −115.687 | −3.97270 | ||||||||
\(849\) | −2.51457 | −0.0863000 | ||||||||
\(850\) | −34.8110 | −1.19401 | ||||||||
\(851\) | 13.6585 | 0.468209 | ||||||||
\(852\) | −1.81853 | −0.0623019 | ||||||||
\(853\) | 35.0517 | 1.20015 | 0.600074 | − | 0.799944i | \(-0.295138\pi\) | ||||
0.600074 | + | 0.799944i | \(0.295138\pi\) | |||||||
\(854\) | 5.23991 | 0.179306 | ||||||||
\(855\) | 2.20521 | 0.0754164 | ||||||||
\(856\) | 117.627 | 4.02042 | ||||||||
\(857\) | 51.8553 | 1.77134 | 0.885672 | − | 0.464311i | \(-0.153698\pi\) | ||||
0.885672 | + | 0.464311i | \(0.153698\pi\) | |||||||
\(858\) | −0.484484 | −0.0165400 | ||||||||
\(859\) | −31.2016 | −1.06458 | −0.532292 | − | 0.846561i | \(-0.678669\pi\) | ||||
−0.532292 | + | 0.846561i | \(0.678669\pi\) | |||||||
\(860\) | −15.0324 | −0.512601 | ||||||||
\(861\) | 17.0870 | 0.582322 | ||||||||
\(862\) | −11.0079 | −0.374929 | ||||||||
\(863\) | −21.2847 | −0.724539 | −0.362269 | − | 0.932073i | \(-0.617998\pi\) | ||||
−0.362269 | + | 0.932073i | \(0.617998\pi\) | |||||||
\(864\) | −22.6525 | −0.770654 | ||||||||
\(865\) | 7.88174 | 0.267987 | ||||||||
\(866\) | 52.8468 | 1.79581 | ||||||||
\(867\) | 9.48008 | 0.321960 | ||||||||
\(868\) | −82.9723 | −2.81626 | ||||||||
\(869\) | −12.9780 | −0.440249 | ||||||||
\(870\) | 12.5178 | 0.424392 | ||||||||
\(871\) | −0.973159 | −0.0329742 | ||||||||
\(872\) | −13.2830 | −0.449819 | ||||||||
\(873\) | −12.7524 | −0.431603 | ||||||||
\(874\) | 16.1743 | 0.547104 | ||||||||
\(875\) | 11.1434 | 0.376715 | ||||||||
\(876\) | 9.66079 | 0.326408 | ||||||||
\(877\) | 56.4130 | 1.90493 | 0.952465 | − | 0.304647i | \(-0.0985386\pi\) | ||||
0.952465 | + | 0.304647i | \(0.0985386\pi\) | |||||||
\(878\) | −63.3519 | −2.13802 | ||||||||
\(879\) | 12.3742 | 0.417371 | ||||||||
\(880\) | 9.23590 | 0.311342 | ||||||||
\(881\) | −13.2697 | −0.447067 | −0.223534 | − | 0.974696i | \(-0.571759\pi\) | ||||
−0.223534 | + | 0.974696i | \(0.571759\pi\) | |||||||
\(882\) | −9.15006 | −0.308099 | ||||||||
\(883\) | −30.1064 | −1.01316 | −0.506581 | − | 0.862192i | \(-0.669091\pi\) | ||||
−0.506581 | + | 0.862192i | \(0.669091\pi\) | |||||||
\(884\) | 2.66908 | 0.0897707 | ||||||||
\(885\) | −0.808724 | −0.0271850 | ||||||||
\(886\) | −50.2955 | −1.68971 | ||||||||
\(887\) | 7.10163 | 0.238449 | 0.119225 | − | 0.992867i | \(-0.461959\pi\) | ||||
0.119225 | + | 0.992867i | \(0.461959\pi\) | |||||||
\(888\) | −80.9461 | −2.71637 | ||||||||
\(889\) | −14.2065 | −0.476471 | ||||||||
\(890\) | −6.80768 | −0.228194 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 86.5360 | 2.89744 | ||||||||
\(893\) | −9.06638 | −0.303395 | ||||||||
\(894\) | 39.8102 | 1.33145 | ||||||||
\(895\) | −7.05032 | −0.235666 | ||||||||
\(896\) | −78.3734 | −2.61827 | ||||||||
\(897\) | −0.286358 | −0.00956122 | ||||||||
\(898\) | −33.6137 | −1.12170 | ||||||||
\(899\) | −59.5756 | −1.98696 | ||||||||
\(900\) | −25.5026 | −0.850087 | ||||||||
\(901\) | −20.7678 | −0.691875 | ||||||||
\(902\) | 24.4662 | 0.814636 | ||||||||
\(903\) | −8.64317 | −0.287627 | ||||||||
\(904\) | 121.733 | 4.04877 | ||||||||
\(905\) | −5.79363 | −0.192587 | ||||||||
\(906\) | 29.9742 | 0.995826 | ||||||||
\(907\) | 24.7879 | 0.823069 | 0.411535 | − | 0.911394i | \(-0.364993\pi\) | ||||
0.411535 | + | 0.911394i | \(0.364993\pi\) | |||||||
\(908\) | −3.72857 | −0.123737 | ||||||||
\(909\) | −10.0353 | −0.332851 | ||||||||
\(910\) | −0.560364 | −0.0185759 | ||||||||
\(911\) | 41.3254 | 1.36917 | 0.684586 | − | 0.728932i | \(-0.259983\pi\) | ||||
0.684586 | + | 0.728932i | \(0.259983\pi\) | |||||||
\(912\) | −55.7146 | −1.84490 | ||||||||
\(913\) | 12.9300 | 0.427920 | ||||||||
\(914\) | 49.2853 | 1.63021 | ||||||||
\(915\) | 0.604616 | 0.0199880 | ||||||||
\(916\) | 74.0304 | 2.44603 | ||||||||
\(917\) | 14.7296 | 0.486414 | ||||||||
\(918\) | −7.51138 | −0.247912 | ||||||||
\(919\) | 36.7229 | 1.21138 | 0.605688 | − | 0.795702i | \(-0.292898\pi\) | ||||
0.605688 | + | 0.795702i | \(0.292898\pi\) | |||||||
\(920\) | 9.39197 | 0.309644 | ||||||||
\(921\) | −21.2440 | −0.700014 | ||||||||
\(922\) | −3.46453 | −0.114098 | ||||||||
\(923\) | 0.0584521 | 0.00192397 | ||||||||
\(924\) | 10.5269 | 0.346308 | ||||||||
\(925\) | −39.0984 | −1.28555 | ||||||||
\(926\) | −28.4518 | −0.934984 | ||||||||
\(927\) | −6.05237 | −0.198786 | ||||||||
\(928\) | −171.218 | −5.62052 | ||||||||
\(929\) | 1.56310 | 0.0512837 | 0.0256418 | − | 0.999671i | \(-0.491837\pi\) | ||||
0.0256418 | + | 0.999671i | \(0.491837\pi\) | |||||||
\(930\) | −13.0535 | −0.428041 | ||||||||
\(931\) | −12.1837 | −0.399306 | ||||||||
\(932\) | −66.5983 | −2.18150 | ||||||||
\(933\) | −26.4545 | −0.866081 | ||||||||
\(934\) | 30.0701 | 0.983923 | ||||||||
\(935\) | 1.65801 | 0.0542226 | ||||||||
\(936\) | 1.69708 | 0.0554706 | ||||||||
\(937\) | 3.58638 | 0.117162 | 0.0585810 | − | 0.998283i | \(-0.481342\pi\) | ||||
0.0585810 | + | 0.998283i | \(0.481342\pi\) | |||||||
\(938\) | 28.8298 | 0.941326 | ||||||||
\(939\) | −30.7427 | −1.00325 | ||||||||
\(940\) | −8.27049 | −0.269754 | ||||||||
\(941\) | −41.9408 | −1.36723 | −0.683616 | − | 0.729842i | \(-0.739593\pi\) | ||||
−0.683616 | + | 0.729842i | \(0.739593\pi\) | |||||||
\(942\) | −45.6056 | −1.48591 | ||||||||
\(943\) | 14.4609 | 0.470913 | ||||||||
\(944\) | 20.4325 | 0.665020 | ||||||||
\(945\) | 1.15662 | 0.0376248 | ||||||||
\(946\) | −12.3759 | −0.402374 | ||||||||
\(947\) | 53.9167 | 1.75206 | 0.876028 | − | 0.482260i | \(-0.160184\pi\) | ||||
0.876028 | + | 0.482260i | \(0.160184\pi\) | |||||||
\(948\) | 71.4160 | 2.31948 | ||||||||
\(949\) | −0.310521 | −0.0100799 | ||||||||
\(950\) | −46.2999 | −1.50217 | ||||||||
\(951\) | 21.9554 | 0.711953 | ||||||||
\(952\) | −50.3329 | −1.63130 | ||||||||
\(953\) | 6.24884 | 0.202420 | 0.101210 | − | 0.994865i | \(-0.467729\pi\) | ||||
0.101210 | + | 0.994865i | \(0.467729\pi\) | |||||||
\(954\) | −20.7442 | −0.671618 | ||||||||
\(955\) | −11.1371 | −0.360387 | ||||||||
\(956\) | −40.3987 | −1.30659 | ||||||||
\(957\) | 7.55848 | 0.244331 | ||||||||
\(958\) | −48.8786 | −1.57920 | ||||||||
\(959\) | 30.4566 | 0.983496 | ||||||||
\(960\) | −19.0435 | −0.614627 | ||||||||
\(961\) | 31.1253 | 1.00404 | ||||||||
\(962\) | 4.08734 | 0.131781 | ||||||||
\(963\) | 12.2595 | 0.395058 | ||||||||
\(964\) | −148.424 | −4.78043 | ||||||||
\(965\) | −3.27014 | −0.105269 | ||||||||
\(966\) | 8.48334 | 0.272947 | ||||||||
\(967\) | −11.7133 | −0.376674 | −0.188337 | − | 0.982104i | \(-0.560310\pi\) | ||||
−0.188337 | + | 0.982104i | \(0.560310\pi\) | |||||||
\(968\) | 9.59477 | 0.308388 | ||||||||
\(969\) | −10.0018 | −0.321303 | ||||||||
\(970\) | −21.1195 | −0.678107 | ||||||||
\(971\) | −20.8971 | −0.670620 | −0.335310 | − | 0.942108i | \(-0.608841\pi\) | ||||
−0.335310 | + | 0.942108i | \(0.608841\pi\) | |||||||
\(972\) | −5.50285 | −0.176504 | ||||||||
\(973\) | 4.60189 | 0.147530 | ||||||||
\(974\) | −53.9512 | −1.72871 | ||||||||
\(975\) | 0.819717 | 0.0262519 | ||||||||
\(976\) | −15.2757 | −0.488962 | ||||||||
\(977\) | 15.7320 | 0.503311 | 0.251655 | − | 0.967817i | \(-0.419025\pi\) | ||||
0.251655 | + | 0.967817i | \(0.419025\pi\) | |||||||
\(978\) | 5.64197 | 0.180410 | ||||||||
\(979\) | −4.11061 | −0.131376 | ||||||||
\(980\) | −11.1142 | −0.355030 | ||||||||
\(981\) | −1.38440 | −0.0442005 | ||||||||
\(982\) | −47.5925 | −1.51874 | ||||||||
\(983\) | −40.6563 | −1.29674 | −0.648368 | − | 0.761327i | \(-0.724548\pi\) | ||||
−0.648368 | + | 0.761327i | \(0.724548\pi\) | |||||||
\(984\) | −85.7015 | −2.73206 | ||||||||
\(985\) | −1.73291 | −0.0552152 | ||||||||
\(986\) | −56.7746 | −1.80807 | ||||||||
\(987\) | −4.75527 | −0.151362 | ||||||||
\(988\) | 3.54996 | 0.112939 | ||||||||
\(989\) | −7.31484 | −0.232598 | ||||||||
\(990\) | 1.65612 | 0.0526350 | ||||||||
\(991\) | 13.9691 | 0.443742 | 0.221871 | − | 0.975076i | \(-0.428784\pi\) | ||||
0.221871 | + | 0.975076i | \(0.428784\pi\) | |||||||
\(992\) | 178.546 | 5.66885 | ||||||||
\(993\) | 15.8159 | 0.501901 | ||||||||
\(994\) | −1.73164 | −0.0549243 | ||||||||
\(995\) | 7.22820 | 0.229149 | ||||||||
\(996\) | −71.1517 | −2.25453 | ||||||||
\(997\) | −11.2639 | −0.356731 | −0.178365 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178365 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(998\) | 68.8978 | 2.18092 | ||||||||
\(999\) | −8.43648 | −0.266919 |
(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 | 2013.2.a.e.1.13 | ✓ | 13 | |
3.2 | odd | 2 | 6039.2.a.i.1.1 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.e.1.13 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6039.2.a.i.1.1 | 13 | 3.2 | odd | 2 |