Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5239,2,Mod(1,5239)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5239, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5239.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5239 = 13^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5239.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: | \(41.8336256189\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 17 x^{14} + 80 x^{13} + 98 x^{12} - 628 x^{11} - 158 x^{10} + 2458 x^{9} - 510 x^{8} - 5030 x^{7} + 2318 x^{6} + 5112 x^{5} - 3154 x^{4} - 2086 x^{3} + \cdots - 147 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 403) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.44015\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5239.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.44015 | −1.01834 | −0.509170 | − | 0.860666i | \(-0.670048\pi\) | ||||
−0.509170 | + | 0.860666i | \(0.670048\pi\) | |||||||
\(3\) | −2.79139 | −1.61161 | −0.805804 | − | 0.592182i | \(-0.798267\pi\) | ||||
−0.805804 | + | 0.592182i | \(0.798267\pi\) | |||||||
\(4\) | 0.0740342 | 0.0370171 | ||||||||
\(5\) | 2.61757 | 1.17061 | 0.585306 | − | 0.810813i | \(-0.300975\pi\) | ||||
0.585306 | + | 0.810813i | \(0.300975\pi\) | |||||||
\(6\) | 4.02002 | 1.64117 | ||||||||
\(7\) | 4.99660 | 1.88854 | 0.944269 | − | 0.329173i | \(-0.106770\pi\) | ||||
0.944269 | + | 0.329173i | \(0.106770\pi\) | |||||||
\(8\) | 2.77368 | 0.980644 | ||||||||
\(9\) | 4.79185 | 1.59728 | ||||||||
\(10\) | −3.76969 | −1.19208 | ||||||||
\(11\) | 0.0546038 | 0.0164637 | 0.00823183 | − | 0.999966i | \(-0.497380\pi\) | ||||
0.00823183 | + | 0.999966i | \(0.497380\pi\) | |||||||
\(12\) | −0.206658 | −0.0596571 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.19586 | −1.92318 | ||||||||
\(15\) | −7.30664 | −1.88657 | ||||||||
\(16\) | −4.14259 | −1.03565 | ||||||||
\(17\) | 5.08006 | 1.23209 | 0.616047 | − | 0.787709i | \(-0.288733\pi\) | ||||
0.616047 | + | 0.787709i | \(0.288733\pi\) | |||||||
\(18\) | −6.90098 | −1.62658 | ||||||||
\(19\) | −1.17518 | −0.269604 | −0.134802 | − | 0.990873i | \(-0.543040\pi\) | ||||
−0.134802 | + | 0.990873i | \(0.543040\pi\) | |||||||
\(20\) | 0.193789 | 0.0433326 | ||||||||
\(21\) | −13.9475 | −3.04359 | ||||||||
\(22\) | −0.0786376 | −0.0167656 | ||||||||
\(23\) | 7.81207 | 1.62893 | 0.814464 | − | 0.580213i | \(-0.197031\pi\) | ||||
0.814464 | + | 0.580213i | \(0.197031\pi\) | |||||||
\(24\) | −7.74242 | −1.58041 | ||||||||
\(25\) | 1.85165 | 0.370331 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00174 | −0.962586 | ||||||||
\(28\) | 0.369920 | 0.0699082 | ||||||||
\(29\) | −7.02474 | −1.30446 | −0.652231 | − | 0.758020i | \(-0.726167\pi\) | ||||
−0.652231 | + | 0.758020i | \(0.726167\pi\) | |||||||
\(30\) | 10.5227 | 1.92117 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0.418588 | 0.0739966 | ||||||||
\(33\) | −0.152420 | −0.0265330 | ||||||||
\(34\) | −7.31605 | −1.25469 | ||||||||
\(35\) | 13.0789 | 2.21075 | ||||||||
\(36\) | 0.354761 | 0.0591268 | ||||||||
\(37\) | 6.75099 | 1.10986 | 0.554928 | − | 0.831899i | \(-0.312746\pi\) | ||||
0.554928 | + | 0.831899i | \(0.312746\pi\) | |||||||
\(38\) | 1.69243 | 0.274549 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.26030 | 1.14795 | ||||||||
\(41\) | 1.55918 | 0.243503 | 0.121751 | − | 0.992561i | \(-0.461149\pi\) | ||||
0.121751 | + | 0.992561i | \(0.461149\pi\) | |||||||
\(42\) | 20.0864 | 3.09941 | ||||||||
\(43\) | 3.02644 | 0.461528 | 0.230764 | − | 0.973010i | \(-0.425877\pi\) | ||||
0.230764 | + | 0.973010i | \(0.425877\pi\) | |||||||
\(44\) | 0.00404255 | 0.000609437 0 | ||||||||
\(45\) | 12.5430 | 1.86980 | ||||||||
\(46\) | −11.2506 | −1.65880 | ||||||||
\(47\) | 0.191499 | 0.0279330 | 0.0139665 | − | 0.999902i | \(-0.495554\pi\) | ||||
0.0139665 | + | 0.999902i | \(0.495554\pi\) | |||||||
\(48\) | 11.5636 | 1.66906 | ||||||||
\(49\) | 17.9661 | 2.56658 | ||||||||
\(50\) | −2.66666 | −0.377123 | ||||||||
\(51\) | −14.1804 | −1.98565 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.59226 | 1.18024 | 0.590119 | − | 0.807317i | \(-0.299081\pi\) | ||||
0.590119 | + | 0.807317i | \(0.299081\pi\) | |||||||
\(54\) | 7.20326 | 0.980240 | ||||||||
\(55\) | 0.142929 | 0.0192725 | ||||||||
\(56\) | 13.8590 | 1.85199 | ||||||||
\(57\) | 3.28038 | 0.434497 | ||||||||
\(58\) | 10.1167 | 1.32839 | ||||||||
\(59\) | −2.91407 | −0.379379 | −0.189690 | − | 0.981844i | \(-0.560748\pi\) | ||||
−0.189690 | + | 0.981844i | \(0.560748\pi\) | |||||||
\(60\) | −0.540942 | −0.0698353 | ||||||||
\(61\) | 5.96368 | 0.763571 | 0.381786 | − | 0.924251i | \(-0.375309\pi\) | ||||
0.381786 | + | 0.924251i | \(0.375309\pi\) | |||||||
\(62\) | 1.44015 | 0.182899 | ||||||||
\(63\) | 23.9430 | 3.01653 | ||||||||
\(64\) | 7.68234 | 0.960293 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.219508 | 0.0270196 | ||||||||
\(67\) | −1.50321 | −0.183646 | −0.0918231 | − | 0.995775i | \(-0.529269\pi\) | ||||
−0.0918231 | + | 0.995775i | \(0.529269\pi\) | |||||||
\(68\) | 0.376098 | 0.0456086 | ||||||||
\(69\) | −21.8065 | −2.62520 | ||||||||
\(70\) | −18.8357 | −2.25129 | ||||||||
\(71\) | −1.44037 | −0.170940 | −0.0854701 | − | 0.996341i | \(-0.527239\pi\) | ||||
−0.0854701 | + | 0.996341i | \(0.527239\pi\) | |||||||
\(72\) | 13.2911 | 1.56637 | ||||||||
\(73\) | 13.9550 | 1.63331 | 0.816656 | − | 0.577124i | \(-0.195825\pi\) | ||||
0.816656 | + | 0.577124i | \(0.195825\pi\) | |||||||
\(74\) | −9.72244 | −1.13021 | ||||||||
\(75\) | −5.16869 | −0.596829 | ||||||||
\(76\) | −0.0870034 | −0.00997997 | ||||||||
\(77\) | 0.272833 | 0.0310922 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.10819 | 0.124681 | 0.0623404 | − | 0.998055i | \(-0.480144\pi\) | ||||
0.0623404 | + | 0.998055i | \(0.480144\pi\) | |||||||
\(80\) | −10.8435 | −1.21234 | ||||||||
\(81\) | −0.413740 | −0.0459711 | ||||||||
\(82\) | −2.24545 | −0.247969 | ||||||||
\(83\) | −1.74923 | −0.192003 | −0.0960015 | − | 0.995381i | \(-0.530605\pi\) | ||||
−0.0960015 | + | 0.995381i | \(0.530605\pi\) | |||||||
\(84\) | −1.03259 | −0.112665 | ||||||||
\(85\) | 13.2974 | 1.44230 | ||||||||
\(86\) | −4.35854 | −0.469993 | ||||||||
\(87\) | 19.6088 | 2.10228 | ||||||||
\(88\) | 0.151453 | 0.0161450 | ||||||||
\(89\) | 2.35995 | 0.250154 | 0.125077 | − | 0.992147i | \(-0.460082\pi\) | ||||
0.125077 | + | 0.992147i | \(0.460082\pi\) | |||||||
\(90\) | −18.0638 | −1.90409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.578360 | 0.0602982 | ||||||||
\(93\) | 2.79139 | 0.289453 | ||||||||
\(94\) | −0.275787 | −0.0284453 | ||||||||
\(95\) | −3.07611 | −0.315602 | ||||||||
\(96\) | −1.16844 | −0.119254 | ||||||||
\(97\) | 12.1357 | 1.23220 | 0.616098 | − | 0.787670i | \(-0.288713\pi\) | ||||
0.616098 | + | 0.787670i | \(0.288713\pi\) | |||||||
\(98\) | −25.8738 | −2.61365 | ||||||||
\(99\) | 0.261653 | 0.0262971 | ||||||||
\(100\) | 0.137086 | 0.0137086 | ||||||||
\(101\) | −11.6128 | −1.15552 | −0.577758 | − | 0.816208i | \(-0.696072\pi\) | ||||
−0.577758 | + | 0.816208i | \(0.696072\pi\) | |||||||
\(102\) | 20.4219 | 2.02207 | ||||||||
\(103\) | 12.7238 | 1.25371 | 0.626857 | − | 0.779134i | \(-0.284341\pi\) | ||||
0.626857 | + | 0.779134i | \(0.284341\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −36.5084 | −3.56286 | ||||||||
\(106\) | −12.3741 | −1.20188 | ||||||||
\(107\) | −2.95463 | −0.285635 | −0.142817 | − | 0.989749i | \(-0.545616\pi\) | ||||
−0.142817 | + | 0.989749i | \(0.545616\pi\) | |||||||
\(108\) | −0.370300 | −0.0356321 | ||||||||
\(109\) | −19.9084 | −1.90688 | −0.953439 | − | 0.301587i | \(-0.902484\pi\) | ||||
−0.953439 | + | 0.301587i | \(0.902484\pi\) | |||||||
\(110\) | −0.205839 | −0.0196260 | ||||||||
\(111\) | −18.8446 | −1.78865 | ||||||||
\(112\) | −20.6989 | −1.95586 | ||||||||
\(113\) | 0.926163 | 0.0871261 | 0.0435630 | − | 0.999051i | \(-0.486129\pi\) | ||||
0.0435630 | + | 0.999051i | \(0.486129\pi\) | |||||||
\(114\) | −4.72424 | −0.442465 | ||||||||
\(115\) | 20.4486 | 1.90684 | ||||||||
\(116\) | −0.520071 | −0.0482874 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.19670 | 0.386337 | ||||||||
\(119\) | 25.3830 | 2.32686 | ||||||||
\(120\) | −20.2663 | −1.85005 | ||||||||
\(121\) | −10.9970 | −0.999729 | ||||||||
\(122\) | −8.58860 | −0.777575 | ||||||||
\(123\) | −4.35227 | −0.392431 | ||||||||
\(124\) | −0.0740342 | −0.00664847 | ||||||||
\(125\) | −8.24100 | −0.737098 | ||||||||
\(126\) | −34.4815 | −3.07185 | ||||||||
\(127\) | −16.3194 | −1.44812 | −0.724058 | − | 0.689739i | \(-0.757725\pi\) | ||||
−0.724058 | + | 0.689739i | \(0.757725\pi\) | |||||||
\(128\) | −11.9009 | −1.05190 | ||||||||
\(129\) | −8.44798 | −0.743803 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1689 | 1.32532 | 0.662658 | − | 0.748922i | \(-0.269428\pi\) | ||||
0.662658 | + | 0.748922i | \(0.269428\pi\) | |||||||
\(132\) | −0.0112843 | −0.000982174 0 | ||||||||
\(133\) | −5.87190 | −0.509158 | ||||||||
\(134\) | 2.16485 | 0.187014 | ||||||||
\(135\) | −13.0924 | −1.12681 | ||||||||
\(136\) | 14.0905 | 1.20825 | ||||||||
\(137\) | −11.4877 | −0.981463 | −0.490732 | − | 0.871311i | \(-0.663270\pi\) | ||||
−0.490732 | + | 0.871311i | \(0.663270\pi\) | |||||||
\(138\) | 31.4047 | 2.67334 | ||||||||
\(139\) | −6.64791 | −0.563869 | −0.281934 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281934 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(140\) | 0.968289 | 0.0818354 | ||||||||
\(141\) | −0.534548 | −0.0450170 | ||||||||
\(142\) | 2.07435 | 0.174075 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −19.8506 | −1.65422 | ||||||||
\(145\) | −18.3877 | −1.52702 | ||||||||
\(146\) | −20.0973 | −1.66327 | ||||||||
\(147\) | −50.1502 | −4.13632 | ||||||||
\(148\) | 0.499804 | 0.0410836 | ||||||||
\(149\) | 1.35792 | 0.111245 | 0.0556224 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556224 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(150\) | 7.44369 | 0.607775 | ||||||||
\(151\) | 12.4451 | 1.01277 | 0.506384 | − | 0.862308i | \(-0.330982\pi\) | ||||
0.506384 | + | 0.862308i | \(0.330982\pi\) | |||||||
\(152\) | −3.25957 | −0.264386 | ||||||||
\(153\) | 24.3429 | 1.96800 | ||||||||
\(154\) | −0.392921 | −0.0316625 | ||||||||
\(155\) | −2.61757 | −0.210248 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5894 | 1.24417 | 0.622086 | − | 0.782949i | \(-0.286286\pi\) | ||||
0.622086 | + | 0.782949i | \(0.286286\pi\) | |||||||
\(158\) | −1.59596 | −0.126968 | ||||||||
\(159\) | −23.9843 | −1.90208 | ||||||||
\(160\) | 1.09568 | 0.0866213 | ||||||||
\(161\) | 39.0338 | 3.07630 | ||||||||
\(162\) | 0.595848 | 0.0468143 | ||||||||
\(163\) | −2.52440 | −0.197726 | −0.0988632 | − | 0.995101i | \(-0.531521\pi\) | ||||
−0.0988632 | + | 0.995101i | \(0.531521\pi\) | |||||||
\(164\) | 0.115433 | 0.00901377 | ||||||||
\(165\) | −0.398970 | −0.0310598 | ||||||||
\(166\) | 2.51916 | 0.195524 | ||||||||
\(167\) | 9.92382 | 0.767928 | 0.383964 | − | 0.923348i | \(-0.374559\pi\) | ||||
0.383964 | + | 0.923348i | \(0.374559\pi\) | |||||||
\(168\) | −38.6858 | −2.98468 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −19.1502 | −1.46876 | ||||||||
\(171\) | −5.63127 | −0.430634 | ||||||||
\(172\) | 0.224060 | 0.0170844 | ||||||||
\(173\) | 20.3536 | 1.54745 | 0.773726 | − | 0.633520i | \(-0.218391\pi\) | ||||
0.773726 | + | 0.633520i | \(0.218391\pi\) | |||||||
\(174\) | −28.2396 | −2.14084 | ||||||||
\(175\) | 9.25199 | 0.699385 | ||||||||
\(176\) | −0.226201 | −0.0170505 | ||||||||
\(177\) | 8.13429 | 0.611411 | ||||||||
\(178\) | −3.39869 | −0.254742 | ||||||||
\(179\) | −4.85781 | −0.363090 | −0.181545 | − | 0.983383i | \(-0.558110\pi\) | ||||
−0.181545 | + | 0.983383i | \(0.558110\pi\) | |||||||
\(180\) | 0.928610 | 0.0692145 | ||||||||
\(181\) | −6.82673 | −0.507427 | −0.253713 | − | 0.967279i | \(-0.581652\pi\) | ||||
−0.253713 | + | 0.967279i | \(0.581652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.6469 | −1.23058 | ||||||||
\(184\) | 21.6682 | 1.59740 | ||||||||
\(185\) | 17.6712 | 1.29921 | ||||||||
\(186\) | −4.02002 | −0.294762 | ||||||||
\(187\) | 0.277390 | 0.0202848 | ||||||||
\(188\) | 0.0141775 | 0.00103400 | ||||||||
\(189\) | −24.9917 | −1.81788 | ||||||||
\(190\) | 4.43006 | 0.321390 | ||||||||
\(191\) | −13.8071 | −0.999043 | −0.499522 | − | 0.866301i | \(-0.666491\pi\) | ||||
−0.499522 | + | 0.866301i | \(0.666491\pi\) | |||||||
\(192\) | −21.4444 | −1.54762 | ||||||||
\(193\) | 8.92165 | 0.642194 | 0.321097 | − | 0.947046i | \(-0.395948\pi\) | ||||
0.321097 | + | 0.947046i | \(0.395948\pi\) | |||||||
\(194\) | −17.4773 | −1.25479 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.33010 | 0.0950073 | ||||||||
\(197\) | 8.13765 | 0.579783 | 0.289892 | − | 0.957059i | \(-0.406381\pi\) | ||||
0.289892 | + | 0.957059i | \(0.406381\pi\) | |||||||
\(198\) | −0.376820 | −0.0267794 | ||||||||
\(199\) | −12.4940 | −0.885678 | −0.442839 | − | 0.896601i | \(-0.646029\pi\) | ||||
−0.442839 | + | 0.896601i | \(0.646029\pi\) | |||||||
\(200\) | 5.13590 | 0.363163 | ||||||||
\(201\) | 4.19604 | 0.295966 | ||||||||
\(202\) | 16.7242 | 1.17671 | ||||||||
\(203\) | −35.0999 | −2.46353 | ||||||||
\(204\) | −1.04984 | −0.0735032 | ||||||||
\(205\) | 4.08126 | 0.285047 | ||||||||
\(206\) | −18.3242 | −1.27671 | ||||||||
\(207\) | 37.4342 | 2.60186 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0641691 | −0.00443867 | ||||||||
\(210\) | 52.5776 | 3.62820 | ||||||||
\(211\) | −20.8611 | −1.43614 | −0.718068 | − | 0.695973i | \(-0.754973\pi\) | ||||
−0.718068 | + | 0.695973i | \(0.754973\pi\) | |||||||
\(212\) | 0.636121 | 0.0436890 | ||||||||
\(213\) | 4.02063 | 0.275489 | ||||||||
\(214\) | 4.25511 | 0.290873 | ||||||||
\(215\) | 7.92192 | 0.540270 | ||||||||
\(216\) | −13.8732 | −0.943954 | ||||||||
\(217\) | −4.99660 | −0.339192 | ||||||||
\(218\) | 28.6711 | 1.94185 | ||||||||
\(219\) | −38.9539 | −2.63226 | ||||||||
\(220\) | 0.0105816 | 0.000713414 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 27.1391 | 1.82146 | ||||||||
\(223\) | −18.6577 | −1.24941 | −0.624707 | − | 0.780859i | \(-0.714782\pi\) | ||||
−0.624707 | + | 0.780859i | \(0.714782\pi\) | |||||||
\(224\) | 2.09152 | 0.139746 | ||||||||
\(225\) | 8.87285 | 0.591523 | ||||||||
\(226\) | −1.33381 | −0.0887240 | ||||||||
\(227\) | −27.9915 | −1.85786 | −0.928932 | − | 0.370251i | \(-0.879272\pi\) | ||||
−0.928932 | + | 0.370251i | \(0.879272\pi\) | |||||||
\(228\) | 0.242860 | 0.0160838 | ||||||||
\(229\) | −9.20943 | −0.608576 | −0.304288 | − | 0.952580i | \(-0.598419\pi\) | ||||
−0.304288 | + | 0.952580i | \(0.598419\pi\) | |||||||
\(230\) | −29.4491 | −1.94181 | ||||||||
\(231\) | −0.761584 | −0.0501085 | ||||||||
\(232\) | −19.4844 | −1.27921 | ||||||||
\(233\) | −19.5339 | −1.27971 | −0.639854 | − | 0.768497i | \(-0.721005\pi\) | ||||
−0.639854 | + | 0.768497i | \(0.721005\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.501261 | 0.0326987 | ||||||||
\(236\) | −0.215741 | −0.0140435 | ||||||||
\(237\) | −3.09338 | −0.200937 | ||||||||
\(238\) | −36.5554 | −2.36953 | ||||||||
\(239\) | −16.9297 | −1.09509 | −0.547546 | − | 0.836776i | \(-0.684438\pi\) | ||||
−0.547546 | + | 0.836776i | \(0.684438\pi\) | |||||||
\(240\) | 30.2684 | 1.95382 | ||||||||
\(241\) | 14.6063 | 0.940875 | 0.470438 | − | 0.882433i | \(-0.344096\pi\) | ||||
0.470438 | + | 0.882433i | \(0.344096\pi\) | |||||||
\(242\) | 15.8374 | 1.01806 | ||||||||
\(243\) | 16.1601 | 1.03667 | ||||||||
\(244\) | 0.441516 | 0.0282652 | ||||||||
\(245\) | 47.0273 | 3.00447 | ||||||||
\(246\) | 6.26793 | 0.399629 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.77368 | −0.176129 | ||||||||
\(249\) | 4.88278 | 0.309434 | ||||||||
\(250\) | 11.8683 | 0.750616 | ||||||||
\(251\) | 28.9232 | 1.82561 | 0.912807 | − | 0.408391i | \(-0.133910\pi\) | ||||
0.912807 | + | 0.408391i | \(0.133910\pi\) | |||||||
\(252\) | 1.77260 | 0.111663 | ||||||||
\(253\) | 0.426568 | 0.0268181 | ||||||||
\(254\) | 23.5025 | 1.47468 | ||||||||
\(255\) | −37.1182 | −2.32443 | ||||||||
\(256\) | 1.77442 | 0.110901 | ||||||||
\(257\) | 19.4544 | 1.21353 | 0.606767 | − | 0.794880i | \(-0.292466\pi\) | ||||
0.606767 | + | 0.794880i | \(0.292466\pi\) | |||||||
\(258\) | 12.1664 | 0.757445 | ||||||||
\(259\) | 33.7320 | 2.09601 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33.6615 | −2.08359 | ||||||||
\(262\) | −21.8456 | −1.34962 | ||||||||
\(263\) | 20.2310 | 1.24750 | 0.623750 | − | 0.781624i | \(-0.285608\pi\) | ||||
0.623750 | + | 0.781624i | \(0.285608\pi\) | |||||||
\(264\) | −0.422765 | −0.0260194 | ||||||||
\(265\) | 22.4908 | 1.38160 | ||||||||
\(266\) | 8.45642 | 0.518496 | ||||||||
\(267\) | −6.58754 | −0.403151 | ||||||||
\(268\) | −0.111289 | −0.00679805 | ||||||||
\(269\) | −8.30420 | −0.506316 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(270\) | 18.8550 | 1.14748 | ||||||||
\(271\) | −14.7486 | −0.895912 | −0.447956 | − | 0.894056i | \(-0.647848\pi\) | ||||
−0.447956 | + | 0.894056i | \(0.647848\pi\) | |||||||
\(272\) | −21.0446 | −1.27601 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5441 | 0.999464 | ||||||||
\(275\) | 0.101107 | 0.00609700 | ||||||||
\(276\) | −1.61443 | −0.0971772 | ||||||||
\(277\) | 15.4228 | 0.926664 | 0.463332 | − | 0.886185i | \(-0.346654\pi\) | ||||
0.463332 | + | 0.886185i | \(0.346654\pi\) | |||||||
\(278\) | 9.57400 | 0.574210 | ||||||||
\(279\) | −4.79185 | −0.286880 | ||||||||
\(280\) | 36.2768 | 2.16795 | ||||||||
\(281\) | 17.2595 | 1.02962 | 0.514808 | − | 0.857306i | \(-0.327863\pi\) | ||||
0.514808 | + | 0.857306i | \(0.327863\pi\) | |||||||
\(282\) | 0.769829 | 0.0458427 | ||||||||
\(283\) | −12.2230 | −0.726583 | −0.363291 | − | 0.931676i | \(-0.618347\pi\) | ||||
−0.363291 | + | 0.931676i | \(0.618347\pi\) | |||||||
\(284\) | −0.106636 | −0.00632771 | ||||||||
\(285\) | 8.58661 | 0.508627 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.79060 | 0.459865 | ||||||||
\(288\) | 2.00581 | 0.118194 | ||||||||
\(289\) | 8.80698 | 0.518057 | ||||||||
\(290\) | 26.4811 | 1.55502 | ||||||||
\(291\) | −33.8755 | −1.98582 | ||||||||
\(292\) | 1.03315 | 0.0604605 | ||||||||
\(293\) | −11.5516 | −0.674850 | −0.337425 | − | 0.941352i | \(-0.609556\pi\) | ||||
−0.337425 | + | 0.941352i | \(0.609556\pi\) | |||||||
\(294\) | 72.2239 | 4.21218 | ||||||||
\(295\) | −7.62776 | −0.444106 | ||||||||
\(296\) | 18.7251 | 1.08837 | ||||||||
\(297\) | −0.273114 | −0.0158477 | ||||||||
\(298\) | −1.95560 | −0.113285 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.382660 | −0.0220929 | ||||||||
\(301\) | 15.1219 | 0.871614 | ||||||||
\(302\) | −17.9228 | −1.03134 | ||||||||
\(303\) | 32.4158 | 1.86224 | ||||||||
\(304\) | 4.86828 | 0.279215 | ||||||||
\(305\) | 15.6103 | 0.893845 | ||||||||
\(306\) | −35.0574 | −2.00410 | ||||||||
\(307\) | −22.1226 | −1.26260 | −0.631302 | − | 0.775537i | \(-0.717479\pi\) | ||||
−0.631302 | + | 0.775537i | \(0.717479\pi\) | |||||||
\(308\) | 0.0201990 | 0.00115095 | ||||||||
\(309\) | −35.5171 | −2.02050 | ||||||||
\(310\) | 3.76969 | 0.214104 | ||||||||
\(311\) | 17.1273 | 0.971203 | 0.485601 | − | 0.874180i | \(-0.338601\pi\) | ||||
0.485601 | + | 0.874180i | \(0.338601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.9822 | −1.63817 | −0.819086 | − | 0.573670i | \(-0.805519\pi\) | ||||
−0.819086 | + | 0.573670i | \(0.805519\pi\) | |||||||
\(314\) | −22.4511 | −1.26699 | ||||||||
\(315\) | 62.6723 | 3.53118 | ||||||||
\(316\) | 0.0820438 | 0.00461532 | ||||||||
\(317\) | 6.22426 | 0.349590 | 0.174795 | − | 0.984605i | \(-0.444074\pi\) | ||||
0.174795 | + | 0.984605i | \(0.444074\pi\) | |||||||
\(318\) | 34.5410 | 1.93697 | ||||||||
\(319\) | −0.383577 | −0.0214762 | ||||||||
\(320\) | 20.1090 | 1.12413 | ||||||||
\(321\) | 8.24751 | 0.460331 | ||||||||
\(322\) | −56.2146 | −3.13272 | ||||||||
\(323\) | −5.96997 | −0.332178 | ||||||||
\(324\) | −0.0306309 | −0.00170172 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.63552 | 0.201353 | ||||||||
\(327\) | 55.5720 | 3.07314 | ||||||||
\(328\) | 4.32467 | 0.238790 | ||||||||
\(329\) | 0.956844 | 0.0527525 | ||||||||
\(330\) | 0.574577 | 0.0316294 | ||||||||
\(331\) | 5.28437 | 0.290455 | 0.145228 | − | 0.989398i | \(-0.453609\pi\) | ||||
0.145228 | + | 0.989398i | \(0.453609\pi\) | |||||||
\(332\) | −0.129503 | −0.00710740 | ||||||||
\(333\) | 32.3497 | 1.77275 | ||||||||
\(334\) | −14.2918 | −0.782012 | ||||||||
\(335\) | −3.93475 | −0.214978 | ||||||||
\(336\) | 57.7786 | 3.15208 | ||||||||
\(337\) | 7.23845 | 0.394304 | 0.197152 | − | 0.980373i | \(-0.436831\pi\) | ||||
0.197152 | + | 0.980373i | \(0.436831\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.58528 | −0.140413 | ||||||||
\(340\) | 0.984462 | 0.0533899 | ||||||||
\(341\) | −0.0546038 | −0.00295696 | ||||||||
\(342\) | 8.10988 | 0.438532 | ||||||||
\(343\) | 54.7930 | 2.95855 | ||||||||
\(344\) | 8.39439 | 0.452595 | ||||||||
\(345\) | −57.0800 | −3.07308 | ||||||||
\(346\) | −29.3122 | −1.57583 | ||||||||
\(347\) | 33.0880 | 1.77626 | 0.888128 | − | 0.459597i | \(-0.152006\pi\) | ||||
0.888128 | + | 0.459597i | \(0.152006\pi\) | |||||||
\(348\) | 1.45172 | 0.0778204 | ||||||||
\(349\) | −6.94086 | −0.371536 | −0.185768 | − | 0.982594i | \(-0.559477\pi\) | ||||
−0.185768 | + | 0.982594i | \(0.559477\pi\) | |||||||
\(350\) | −13.3243 | −0.712211 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0228565 | 0.00121825 | ||||||||
\(353\) | 30.0813 | 1.60107 | 0.800534 | − | 0.599288i | \(-0.204550\pi\) | ||||
0.800534 | + | 0.599288i | \(0.204550\pi\) | |||||||
\(354\) | −11.7146 | −0.622624 | ||||||||
\(355\) | −3.77026 | −0.200105 | ||||||||
\(356\) | 0.174717 | 0.00925999 | ||||||||
\(357\) | −70.8539 | −3.74999 | ||||||||
\(358\) | 6.99598 | 0.369749 | ||||||||
\(359\) | −3.73997 | −0.197388 | −0.0986940 | − | 0.995118i | \(-0.531466\pi\) | ||||
−0.0986940 | + | 0.995118i | \(0.531466\pi\) | |||||||
\(360\) | 34.7902 | 1.83361 | ||||||||
\(361\) | −17.6190 | −0.927314 | ||||||||
\(362\) | 9.83152 | 0.516733 | ||||||||
\(363\) | 30.6969 | 1.61117 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.5282 | 1.91197 | ||||||||
\(366\) | 23.9741 | 1.25315 | ||||||||
\(367\) | 4.57778 | 0.238958 | 0.119479 | − | 0.992837i | \(-0.461878\pi\) | ||||
0.119479 | + | 0.992837i | \(0.461878\pi\) | |||||||
\(368\) | −32.3622 | −1.68700 | ||||||||
\(369\) | 7.47135 | 0.388943 | ||||||||
\(370\) | −25.4491 | −1.32304 | ||||||||
\(371\) | 42.9321 | 2.22892 | ||||||||
\(372\) | 0.206658 | 0.0107147 | ||||||||
\(373\) | −11.9473 | −0.618607 | −0.309303 | − | 0.950963i | \(-0.600096\pi\) | ||||
−0.309303 | + | 0.950963i | \(0.600096\pi\) | |||||||
\(374\) | −0.399484 | −0.0206568 | ||||||||
\(375\) | 23.0038 | 1.18791 | ||||||||
\(376\) | 0.531157 | 0.0273923 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 35.9919 | 1.85122 | ||||||||
\(379\) | −0.620093 | −0.0318521 | −0.0159260 | − | 0.999873i | \(-0.505070\pi\) | ||||
−0.0159260 | + | 0.999873i | \(0.505070\pi\) | |||||||
\(380\) | −0.227737 | −0.0116827 | ||||||||
\(381\) | 45.5539 | 2.33380 | ||||||||
\(382\) | 19.8842 | 1.01737 | ||||||||
\(383\) | −27.8945 | −1.42534 | −0.712671 | − | 0.701498i | \(-0.752515\pi\) | ||||
−0.712671 | + | 0.701498i | \(0.752515\pi\) | |||||||
\(384\) | 33.2201 | 1.69525 | ||||||||
\(385\) | 0.714160 | 0.0363969 | ||||||||
\(386\) | −12.8485 | −0.653972 | ||||||||
\(387\) | 14.5023 | 0.737191 | ||||||||
\(388\) | 0.898459 | 0.0456123 | ||||||||
\(389\) | −12.8614 | −0.652097 | −0.326048 | − | 0.945353i | \(-0.605717\pi\) | ||||
−0.326048 | + | 0.945353i | \(0.605717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.6858 | 2.00699 | ||||||||
\(392\) | 49.8321 | 2.51690 | ||||||||
\(393\) | −42.3424 | −2.13589 | ||||||||
\(394\) | −11.7194 | −0.590417 | ||||||||
\(395\) | 2.90075 | 0.145953 | ||||||||
\(396\) | 0.0193713 | 0.000973443 0 | ||||||||
\(397\) | −24.6396 | −1.23663 | −0.618314 | − | 0.785931i | \(-0.712184\pi\) | ||||
−0.618314 | + | 0.785931i | \(0.712184\pi\) | |||||||
\(398\) | 17.9933 | 0.901922 | ||||||||
\(399\) | 16.3907 | 0.820564 | ||||||||
\(400\) | −7.67064 | −0.383532 | ||||||||
\(401\) | 20.3020 | 1.01383 | 0.506917 | − | 0.861995i | \(-0.330785\pi\) | ||||
0.506917 | + | 0.861995i | \(0.330785\pi\) | |||||||
\(402\) | −6.04293 | −0.301394 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.859744 | −0.0427739 | ||||||||
\(405\) | −1.08299 | −0.0538143 | ||||||||
\(406\) | 50.5491 | 2.50871 | ||||||||
\(407\) | 0.368629 | 0.0182723 | ||||||||
\(408\) | −39.3319 | −1.94722 | ||||||||
\(409\) | 7.67595 | 0.379551 | 0.189776 | − | 0.981827i | \(-0.439224\pi\) | ||||
0.189776 | + | 0.981827i | \(0.439224\pi\) | |||||||
\(410\) | −5.87762 | −0.290275 | ||||||||
\(411\) | 32.0667 | 1.58174 | ||||||||
\(412\) | 0.941997 | 0.0464089 | ||||||||
\(413\) | −14.5604 | −0.716472 | ||||||||
\(414\) | −53.9110 | −2.64958 | ||||||||
\(415\) | −4.57873 | −0.224761 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.5569 | 0.908736 | ||||||||
\(418\) | 0.0924132 | 0.00452008 | ||||||||
\(419\) | −24.4074 | −1.19238 | −0.596189 | − | 0.802844i | \(-0.703319\pi\) | ||||
−0.596189 | + | 0.802844i | \(0.703319\pi\) | |||||||
\(420\) | −2.70287 | −0.131887 | ||||||||
\(421\) | −7.83588 | −0.381898 | −0.190949 | − | 0.981600i | \(-0.561156\pi\) | ||||
−0.190949 | + | 0.981600i | \(0.561156\pi\) | |||||||
\(422\) | 30.0431 | 1.46248 | ||||||||
\(423\) | 0.917633 | 0.0446169 | ||||||||
\(424\) | 23.8322 | 1.15739 | ||||||||
\(425\) | 9.40651 | 0.456283 | ||||||||
\(426\) | −5.79031 | −0.280541 | ||||||||
\(427\) | 29.7982 | 1.44203 | ||||||||
\(428\) | −0.218744 | −0.0105734 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.4088 | −0.550179 | ||||||||
\(431\) | −7.77841 | −0.374673 | −0.187337 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187337 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(432\) | 20.7202 | 0.996899 | ||||||||
\(433\) | −26.6655 | −1.28146 | −0.640732 | − | 0.767765i | \(-0.721369\pi\) | ||||
−0.640732 | + | 0.767765i | \(0.721369\pi\) | |||||||
\(434\) | 7.19586 | 0.345413 | ||||||||
\(435\) | 51.3273 | 2.46096 | ||||||||
\(436\) | −1.47390 | −0.0705871 | ||||||||
\(437\) | −9.18057 | −0.439166 | ||||||||
\(438\) | 56.0995 | 2.68054 | ||||||||
\(439\) | −14.4283 | −0.688626 | −0.344313 | − | 0.938855i | \(-0.611888\pi\) | ||||
−0.344313 | + | 0.938855i | \(0.611888\pi\) | |||||||
\(440\) | 0.396439 | 0.0188995 | ||||||||
\(441\) | 86.0906 | 4.09955 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.19341 | 0.246746 | 0.123373 | − | 0.992360i | \(-0.460629\pi\) | ||||
0.123373 | + | 0.992360i | \(0.460629\pi\) | |||||||
\(444\) | −1.39515 | −0.0662108 | ||||||||
\(445\) | 6.17733 | 0.292834 | ||||||||
\(446\) | 26.8699 | 1.27233 | ||||||||
\(447\) | −3.79047 | −0.179283 | ||||||||
\(448\) | 38.3856 | 1.81355 | ||||||||
\(449\) | 14.9729 | 0.706615 | 0.353308 | − | 0.935507i | \(-0.385057\pi\) | ||||
0.353308 | + | 0.935507i | \(0.385057\pi\) | |||||||
\(450\) | −12.7782 | −0.602372 | ||||||||
\(451\) | 0.0851371 | 0.00400895 | ||||||||
\(452\) | 0.0685677 | 0.00322516 | ||||||||
\(453\) | −34.7391 | −1.63218 | ||||||||
\(454\) | 40.3120 | 1.89194 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.09872 | 0.426087 | ||||||||
\(457\) | 42.0543 | 1.96722 | 0.983609 | − | 0.180316i | \(-0.0577121\pi\) | ||||
0.983609 | + | 0.180316i | \(0.0577121\pi\) | |||||||
\(458\) | 13.2630 | 0.619738 | ||||||||
\(459\) | −25.4091 | −1.18600 | ||||||||
\(460\) | 1.51390 | 0.0705858 | ||||||||
\(461\) | 9.31370 | 0.433782 | 0.216891 | − | 0.976196i | \(-0.430408\pi\) | ||||
0.216891 | + | 0.976196i | \(0.430408\pi\) | |||||||
\(462\) | 1.09680 | 0.0510275 | ||||||||
\(463\) | 10.3203 | 0.479625 | 0.239813 | − | 0.970819i | \(-0.422914\pi\) | ||||
0.239813 | + | 0.970819i | \(0.422914\pi\) | |||||||
\(464\) | 29.1006 | 1.35096 | ||||||||
\(465\) | 7.30664 | 0.338838 | ||||||||
\(466\) | 28.1318 | 1.30318 | ||||||||
\(467\) | 0.661824 | 0.0306255 | 0.0153128 | − | 0.999883i | \(-0.495126\pi\) | ||||
0.0153128 | + | 0.999883i | \(0.495126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.51094 | −0.346823 | ||||||||
\(470\) | −0.721891 | −0.0332984 | ||||||||
\(471\) | −43.5161 | −2.00512 | ||||||||
\(472\) | −8.08269 | −0.372036 | ||||||||
\(473\) | 0.165255 | 0.00759844 | ||||||||
\(474\) | 4.45493 | 0.204622 | ||||||||
\(475\) | −2.17602 | −0.0998428 | ||||||||
\(476\) | 1.87921 | 0.0861336 | ||||||||
\(477\) | 41.1728 | 1.88517 | ||||||||
\(478\) | 24.3813 | 1.11518 | ||||||||
\(479\) | −3.63440 | −0.166060 | −0.0830300 | − | 0.996547i | \(-0.526460\pi\) | ||||
−0.0830300 | + | 0.996547i | \(0.526460\pi\) | |||||||
\(480\) | −3.05847 | −0.139600 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −21.0353 | −0.958131 | ||||||||
\(483\) | −108.959 | −4.95778 | ||||||||
\(484\) | −0.814156 | −0.0370071 | ||||||||
\(485\) | 31.7661 | 1.44242 | ||||||||
\(486\) | −23.2730 | −1.05569 | ||||||||
\(487\) | −31.1232 | −1.41033 | −0.705163 | − | 0.709045i | \(-0.749126\pi\) | ||||
−0.705163 | + | 0.709045i | \(0.749126\pi\) | |||||||
\(488\) | 16.5413 | 0.748792 | ||||||||
\(489\) | 7.04659 | 0.318658 | ||||||||
\(490\) | −67.7265 | −3.05957 | ||||||||
\(491\) | −17.9607 | −0.810555 | −0.405277 | − | 0.914194i | \(-0.632825\pi\) | ||||
−0.405277 | + | 0.914194i | \(0.632825\pi\) | |||||||
\(492\) | −0.322217 | −0.0145267 | ||||||||
\(493\) | −35.6861 | −1.60722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.684894 | 0.0307837 | ||||||||
\(496\) | 4.14259 | 0.186008 | ||||||||
\(497\) | −7.19695 | −0.322827 | ||||||||
\(498\) | −7.03194 | −0.315109 | ||||||||
\(499\) | 8.12403 | 0.363681 | 0.181841 | − | 0.983328i | \(-0.441794\pi\) | ||||
0.181841 | + | 0.983328i | \(0.441794\pi\) | |||||||
\(500\) | −0.610116 | −0.0272852 | ||||||||
\(501\) | −27.7012 | −1.23760 | ||||||||
\(502\) | −41.6537 | −1.85910 | ||||||||
\(503\) | −38.6811 | −1.72471 | −0.862354 | − | 0.506307i | \(-0.831010\pi\) | ||||
−0.862354 | + | 0.506307i | \(0.831010\pi\) | |||||||
\(504\) | 66.4102 | 2.95814 | ||||||||
\(505\) | −30.3973 | −1.35266 | ||||||||
\(506\) | −0.614323 | −0.0273100 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.20820 | −0.0536051 | ||||||||
\(509\) | −16.1272 | −0.714826 | −0.357413 | − | 0.933946i | \(-0.616341\pi\) | ||||
−0.357413 | + | 0.933946i | \(0.616341\pi\) | |||||||
\(510\) | 53.4558 | 2.36706 | ||||||||
\(511\) | 69.7278 | 3.08458 | ||||||||
\(512\) | 21.2464 | 0.938967 | ||||||||
\(513\) | 5.87794 | 0.259517 | ||||||||
\(514\) | −28.0173 | −1.23579 | ||||||||
\(515\) | 33.3054 | 1.46761 | ||||||||
\(516\) | −0.625439 | −0.0275334 | ||||||||
\(517\) | 0.0104566 | 0.000459879 0 | ||||||||
\(518\) | −48.5792 | −2.13445 | ||||||||
\(519\) | −56.8147 | −2.49389 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.58342 | 0.244614 | 0.122307 | − | 0.992492i | \(-0.460971\pi\) | ||||
0.122307 | + | 0.992492i | \(0.460971\pi\) | |||||||
\(522\) | 48.4776 | 2.12181 | ||||||||
\(523\) | −24.8140 | −1.08504 | −0.542520 | − | 0.840043i | \(-0.682530\pi\) | ||||
−0.542520 | + | 0.840043i | \(0.682530\pi\) | |||||||
\(524\) | 1.12302 | 0.0490594 | ||||||||
\(525\) | −25.8259 | −1.12713 | ||||||||
\(526\) | −29.1358 | −1.27038 | ||||||||
\(527\) | −5.08006 | −0.221291 | ||||||||
\(528\) | 0.631414 | 0.0274788 | ||||||||
\(529\) | 38.0284 | 1.65341 | ||||||||
\(530\) | −32.3901 | −1.40694 | ||||||||
\(531\) | −13.9638 | −0.605976 | ||||||||
\(532\) | −0.434721 | −0.0188476 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.48705 | 0.410545 | ||||||||
\(535\) | −7.73394 | −0.334367 | ||||||||
\(536\) | −4.16942 | −0.180092 | ||||||||
\(537\) | 13.5600 | 0.585159 | ||||||||
\(538\) | 11.9593 | 0.515602 | ||||||||
\(539\) | 0.981014 | 0.0422553 | ||||||||
\(540\) | −0.969285 | −0.0417114 | ||||||||
\(541\) | 30.2928 | 1.30239 | 0.651195 | − | 0.758911i | \(-0.274268\pi\) | ||||
0.651195 | + | 0.758911i | \(0.274268\pi\) | |||||||
\(542\) | 21.2402 | 0.912344 | ||||||||
\(543\) | 19.0560 | 0.817773 | ||||||||
\(544\) | 2.12645 | 0.0911709 | ||||||||
\(545\) | −52.1115 | −2.23221 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.782832 | −0.0334715 | −0.0167357 | − | 0.999860i | \(-0.505327\pi\) | ||||
−0.0167357 | + | 0.999860i | \(0.505327\pi\) | |||||||
\(548\) | −0.850485 | −0.0363309 | ||||||||
\(549\) | 28.5770 | 1.21964 | ||||||||
\(550\) | −0.145610 | −0.00620882 | ||||||||
\(551\) | 8.25532 | 0.351688 | ||||||||
\(552\) | −60.4843 | −2.57438 | ||||||||
\(553\) | 5.53717 | 0.235465 | ||||||||
\(554\) | −22.2111 | −0.943659 | ||||||||
\(555\) | −49.3271 | −2.09382 | ||||||||
\(556\) | −0.492173 | −0.0208728 | ||||||||
\(557\) | 12.1105 | 0.513140 | 0.256570 | − | 0.966526i | \(-0.417408\pi\) | ||||
0.256570 | + | 0.966526i | \(0.417408\pi\) | |||||||
\(558\) | 6.90098 | 0.292142 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −54.1807 | −2.28955 | ||||||||
\(561\) | −0.774304 | −0.0326911 | ||||||||
\(562\) | −24.8563 | −1.04850 | ||||||||
\(563\) | −11.9218 | −0.502446 | −0.251223 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251223 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(564\) | −0.0395748 | −0.00166640 | ||||||||
\(565\) | 2.42429 | 0.101991 | ||||||||
\(566\) | 17.6030 | 0.739908 | ||||||||
\(567\) | −2.06730 | −0.0868183 | ||||||||
\(568\) | −3.99512 | −0.167632 | ||||||||
\(569\) | 14.4513 | 0.605831 | 0.302916 | − | 0.953017i | \(-0.402040\pi\) | ||||
0.302916 | + | 0.953017i | \(0.402040\pi\) | |||||||
\(570\) | −12.3660 | −0.517955 | ||||||||
\(571\) | 22.3002 | 0.933233 | 0.466616 | − | 0.884460i | \(-0.345473\pi\) | ||||
0.466616 | + | 0.884460i | \(0.345473\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.5408 | 1.61007 | ||||||||
\(574\) | −11.2196 | −0.468299 | ||||||||
\(575\) | 14.4653 | 0.603243 | ||||||||
\(576\) | 36.8126 | 1.53386 | ||||||||
\(577\) | −34.1283 | −1.42078 | −0.710390 | − | 0.703808i | \(-0.751481\pi\) | ||||
−0.710390 | + | 0.703808i | \(0.751481\pi\) | |||||||
\(578\) | −12.6834 | −0.527559 | ||||||||
\(579\) | −24.9038 | −1.03497 | ||||||||
\(580\) | −1.36132 | −0.0565258 | ||||||||
\(581\) | −8.74022 | −0.362605 | ||||||||
\(582\) | 48.7858 | 2.02224 | ||||||||
\(583\) | 0.469169 | 0.0194310 | ||||||||
\(584\) | 38.7068 | 1.60170 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.6360 | 0.687227 | ||||||||
\(587\) | −17.1675 | −0.708579 | −0.354290 | − | 0.935136i | \(-0.615277\pi\) | ||||
−0.354290 | + | 0.935136i | \(0.615277\pi\) | |||||||
\(588\) | −3.71283 | −0.153115 | ||||||||
\(589\) | 1.17518 | 0.0484224 | ||||||||
\(590\) | 10.9851 | 0.452251 | ||||||||
\(591\) | −22.7153 | −0.934384 | ||||||||
\(592\) | −27.9666 | −1.14942 | ||||||||
\(593\) | 23.3023 | 0.956909 | 0.478455 | − | 0.878112i | \(-0.341197\pi\) | ||||
0.478455 | + | 0.878112i | \(0.341197\pi\) | |||||||
\(594\) | 0.393325 | 0.0161383 | ||||||||
\(595\) | 66.4418 | 2.72385 | ||||||||
\(596\) | 0.100532 | 0.00411796 | ||||||||
\(597\) | 34.8757 | 1.42737 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.7509 | −0.520986 | −0.260493 | − | 0.965476i | \(-0.583885\pi\) | ||||
−0.260493 | + | 0.965476i | \(0.583885\pi\) | |||||||
\(600\) | −14.3363 | −0.585277 | ||||||||
\(601\) | 21.0313 | 0.857886 | 0.428943 | − | 0.903332i | \(-0.358886\pi\) | ||||
0.428943 | + | 0.903332i | \(0.358886\pi\) | |||||||
\(602\) | −21.7779 | −0.887600 | ||||||||
\(603\) | −7.20315 | −0.293335 | ||||||||
\(604\) | 0.921363 | 0.0374897 | ||||||||
\(605\) | −28.7854 | −1.17029 | ||||||||
\(606\) | −46.6837 | −1.89639 | ||||||||
\(607\) | −28.5285 | −1.15793 | −0.578967 | − | 0.815351i | \(-0.696544\pi\) | ||||
−0.578967 | + | 0.815351i | \(0.696544\pi\) | |||||||
\(608\) | −0.491915 | −0.0199498 | ||||||||
\(609\) | 97.9773 | 3.97024 | ||||||||
\(610\) | −22.4812 | −0.910238 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.80220 | 0.0728498 | ||||||||
\(613\) | 20.0076 | 0.808099 | 0.404050 | − | 0.914737i | \(-0.367602\pi\) | ||||
0.404050 | + | 0.914737i | \(0.367602\pi\) | |||||||
\(614\) | 31.8599 | 1.28576 | ||||||||
\(615\) | −11.3924 | −0.459385 | ||||||||
\(616\) | 0.756753 | 0.0304904 | ||||||||
\(617\) | 5.04682 | 0.203177 | 0.101589 | − | 0.994826i | \(-0.467607\pi\) | ||||
0.101589 | + | 0.994826i | \(0.467607\pi\) | |||||||
\(618\) | 51.1500 | 2.05755 | ||||||||
\(619\) | 27.5782 | 1.10846 | 0.554231 | − | 0.832363i | \(-0.313013\pi\) | ||||
0.554231 | + | 0.832363i | \(0.313013\pi\) | |||||||
\(620\) | −0.193789 | −0.00778277 | ||||||||
\(621\) | −39.0740 | −1.56798 | ||||||||
\(622\) | −24.6660 | −0.989015 | ||||||||
\(623\) | 11.7917 | 0.472426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8296 | −1.23319 | ||||||||
\(626\) | 41.7388 | 1.66822 | ||||||||
\(627\) | 0.179121 | 0.00715340 | ||||||||
\(628\) | 1.15415 | 0.0460556 | ||||||||
\(629\) | 34.2954 | 1.36745 | ||||||||
\(630\) | −90.2576 | −3.59595 | ||||||||
\(631\) | −46.3626 | −1.84566 | −0.922832 | − | 0.385202i | \(-0.874132\pi\) | ||||
−0.922832 | + | 0.385202i | \(0.874132\pi\) | |||||||
\(632\) | 3.07376 | 0.122268 | ||||||||
\(633\) | 58.2314 | 2.31449 | ||||||||
\(634\) | −8.96388 | −0.356001 | ||||||||
\(635\) | −42.7172 | −1.69518 | ||||||||
\(636\) | −1.77566 | −0.0704095 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.552409 | 0.0218701 | ||||||||
\(639\) | −6.90202 | −0.273040 | ||||||||
\(640\) | −31.1514 | −1.23137 | ||||||||
\(641\) | −16.3261 | −0.644843 | −0.322422 | − | 0.946596i | \(-0.604497\pi\) | ||||
−0.322422 | + | 0.946596i | \(0.604497\pi\) | |||||||
\(642\) | −11.8777 | −0.468774 | ||||||||
\(643\) | −6.80196 | −0.268243 | −0.134122 | − | 0.990965i | \(-0.542821\pi\) | ||||
−0.134122 | + | 0.990965i | \(0.542821\pi\) | |||||||
\(644\) | 2.88984 | 0.113876 | ||||||||
\(645\) | −22.1131 | −0.870704 | ||||||||
\(646\) | 8.59766 | 0.338270 | ||||||||
\(647\) | 12.7863 | 0.502681 | 0.251340 | − | 0.967899i | \(-0.419129\pi\) | ||||
0.251340 | + | 0.967899i | \(0.419129\pi\) | |||||||
\(648\) | −1.14758 | −0.0450813 | ||||||||
\(649\) | −0.159119 | −0.00624597 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.9475 | 0.546644 | ||||||||
\(652\) | −0.186892 | −0.00731926 | ||||||||
\(653\) | 31.3311 | 1.22608 | 0.613041 | − | 0.790051i | \(-0.289946\pi\) | ||||
0.613041 | + | 0.790051i | \(0.289946\pi\) | |||||||
\(654\) | −80.0321 | −3.12950 | ||||||||
\(655\) | 39.7057 | 1.55143 | ||||||||
\(656\) | −6.45904 | −0.252183 | ||||||||
\(657\) | 66.8704 | 2.60886 | ||||||||
\(658\) | −1.37800 | −0.0537200 | ||||||||
\(659\) | −18.7431 | −0.730127 | −0.365064 | − | 0.930983i | \(-0.618953\pi\) | ||||
−0.365064 | + | 0.930983i | \(0.618953\pi\) | |||||||
\(660\) | −0.0295374 | −0.00114974 | ||||||||
\(661\) | −13.7249 | −0.533836 | −0.266918 | − | 0.963719i | \(-0.586005\pi\) | ||||
−0.266918 | + | 0.963719i | \(0.586005\pi\) | |||||||
\(662\) | −7.61029 | −0.295782 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.85181 | −0.188287 | ||||||||
\(665\) | −15.3701 | −0.596026 | ||||||||
\(666\) | −46.5885 | −1.80527 | ||||||||
\(667\) | −54.8778 | −2.12488 | ||||||||
\(668\) | 0.734702 | 0.0284265 | ||||||||
\(669\) | 52.0810 | 2.01357 | ||||||||
\(670\) | 5.66663 | 0.218921 | ||||||||
\(671\) | 0.325639 | 0.0125712 | ||||||||
\(672\) | −5.83824 | −0.225215 | ||||||||
\(673\) | −15.0786 | −0.581237 | −0.290619 | − | 0.956839i | \(-0.593861\pi\) | ||||
−0.290619 | + | 0.956839i | \(0.593861\pi\) | |||||||
\(674\) | −10.4245 | −0.401535 | ||||||||
\(675\) | −9.26150 | −0.356475 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.8652 | −1.03251 | −0.516257 | − | 0.856434i | \(-0.672675\pi\) | ||||
−0.516257 | + | 0.856434i | \(0.672675\pi\) | |||||||
\(678\) | 3.72319 | 0.142988 | ||||||||
\(679\) | 60.6374 | 2.32705 | ||||||||
\(680\) | 36.8827 | 1.41439 | ||||||||
\(681\) | 78.1352 | 2.99415 | ||||||||
\(682\) | 0.0786376 | 0.00301119 | ||||||||
\(683\) | 10.6702 | 0.408285 | 0.204143 | − | 0.978941i | \(-0.434559\pi\) | ||||
0.204143 | + | 0.978941i | \(0.434559\pi\) | |||||||
\(684\) | −0.416907 | −0.0159408 | ||||||||
\(685\) | −30.0699 | −1.14891 | ||||||||
\(686\) | −78.9102 | −3.01281 | ||||||||
\(687\) | 25.7071 | 0.980787 | ||||||||
\(688\) | −12.5373 | −0.477980 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 82.2038 | 3.12945 | ||||||||
\(691\) | 0.654117 | 0.0248838 | 0.0124419 | − | 0.999923i | \(-0.496040\pi\) | ||||
0.0124419 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(692\) | 1.50686 | 0.0572822 | ||||||||
\(693\) | 1.30738 | 0.0496631 | ||||||||
\(694\) | −47.6517 | −1.80883 | ||||||||
\(695\) | −17.4014 | −0.660071 | ||||||||
\(696\) | 54.3885 | 2.06159 | ||||||||
\(697\) | 7.92072 | 0.300019 | ||||||||
\(698\) | 9.99588 | 0.378350 | ||||||||
\(699\) | 54.5267 | 2.06239 | ||||||||
\(700\) | 0.684964 | 0.0258892 | ||||||||
\(701\) | −20.2045 | −0.763112 | −0.381556 | − | 0.924346i | \(-0.624612\pi\) | ||||
−0.381556 | + | 0.924346i | \(0.624612\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.93361 | −0.299222 | ||||||||
\(704\) | 0.419485 | 0.0158099 | ||||||||
\(705\) | −1.39921 | −0.0526974 | ||||||||
\(706\) | −43.3216 | −1.63043 | ||||||||
\(707\) | −58.0246 | −2.18224 | ||||||||
\(708\) | 0.602216 | 0.0226327 | ||||||||
\(709\) | −48.7025 | −1.82906 | −0.914530 | − | 0.404518i | \(-0.867439\pi\) | ||||
−0.914530 | + | 0.404518i | \(0.867439\pi\) | |||||||
\(710\) | 5.42974 | 0.203775 | ||||||||
\(711\) | 5.31026 | 0.199150 | ||||||||
\(712\) | 6.54575 | 0.245313 | ||||||||
\(713\) | −7.81207 | −0.292564 | ||||||||
\(714\) | 102.040 | 3.81876 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.359644 | −0.0134405 | ||||||||
\(717\) | 47.2574 | 1.76486 | ||||||||
\(718\) | 5.38612 | 0.201008 | ||||||||
\(719\) | −16.7247 | −0.623725 | −0.311862 | − | 0.950127i | \(-0.600953\pi\) | ||||
−0.311862 | + | 0.950127i | \(0.600953\pi\) | |||||||
\(720\) | −51.9604 | −1.93645 | ||||||||
\(721\) | 63.5758 | 2.36769 | ||||||||
\(722\) | 25.3740 | 0.944321 | ||||||||
\(723\) | −40.7719 | −1.51632 | ||||||||
\(724\) | −0.505411 | −0.0187835 | ||||||||
\(725\) | −13.0074 | −0.483083 | ||||||||
\(726\) | −44.2082 | −1.64072 | ||||||||
\(727\) | 20.1667 | 0.747940 | 0.373970 | − | 0.927441i | \(-0.377996\pi\) | ||||
0.373970 | + | 0.927441i | \(0.377996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8680 | −1.62474 | ||||||||
\(730\) | −52.6062 | −1.94704 | ||||||||
\(731\) | 15.3745 | 0.568647 | ||||||||
\(732\) | −1.23244 | −0.0455524 | ||||||||
\(733\) | −6.69141 | −0.247153 | −0.123576 | − | 0.992335i | \(-0.539436\pi\) | ||||
−0.123576 | + | 0.992335i | \(0.539436\pi\) | |||||||
\(734\) | −6.59270 | −0.243341 | ||||||||
\(735\) | −131.272 | −4.84203 | ||||||||
\(736\) | 3.27004 | 0.120535 | ||||||||
\(737\) | −0.0820809 | −0.00302349 | ||||||||
\(738\) | −10.7599 | −0.396076 | ||||||||
\(739\) | 14.7948 | 0.544235 | 0.272118 | − | 0.962264i | \(-0.412276\pi\) | ||||
0.272118 | + | 0.962264i | \(0.412276\pi\) | |||||||
\(740\) | 1.30827 | 0.0480930 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −61.8287 | −2.26980 | ||||||||
\(743\) | −12.2435 | −0.449170 | −0.224585 | − | 0.974455i | \(-0.572103\pi\) | ||||
−0.224585 | + | 0.974455i | \(0.572103\pi\) | |||||||
\(744\) | 7.74242 | 0.283851 | ||||||||
\(745\) | 3.55444 | 0.130224 | ||||||||
\(746\) | 17.2059 | 0.629952 | ||||||||
\(747\) | −8.38205 | −0.306683 | ||||||||
\(748\) | 0.0205364 | 0.000750884 0 | ||||||||
\(749\) | −14.7631 | −0.539432 | ||||||||
\(750\) | −33.1290 | −1.20970 | ||||||||
\(751\) | −22.4866 | −0.820548 | −0.410274 | − | 0.911962i | \(-0.634567\pi\) | ||||
−0.410274 | + | 0.911962i | \(0.634567\pi\) | |||||||
\(752\) | −0.793301 | −0.0289287 | ||||||||
\(753\) | −80.7358 | −2.94218 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.5759 | 1.18556 | ||||||||
\(756\) | −1.85024 | −0.0672927 | ||||||||
\(757\) | 3.82393 | 0.138983 | 0.0694915 | − | 0.997583i | \(-0.477862\pi\) | ||||
0.0694915 | + | 0.997583i | \(0.477862\pi\) | |||||||
\(758\) | 0.893028 | 0.0324362 | ||||||||
\(759\) | −1.19072 | −0.0432203 | ||||||||
\(760\) | −8.53214 | −0.309493 | ||||||||
\(761\) | 33.7254 | 1.22254 | 0.611272 | − | 0.791420i | \(-0.290658\pi\) | ||||
0.611272 | + | 0.791420i | \(0.290658\pi\) | |||||||
\(762\) | −65.6045 | −2.37660 | ||||||||
\(763\) | −99.4743 | −3.60121 | ||||||||
\(764\) | −1.02219 | −0.0369817 | ||||||||
\(765\) | 63.7190 | 2.30377 | ||||||||
\(766\) | 40.1723 | 1.45148 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −4.95308 | −0.178729 | ||||||||
\(769\) | 12.5287 | 0.451795 | 0.225897 | − | 0.974151i | \(-0.427469\pi\) | ||||
0.225897 | + | 0.974151i | \(0.427469\pi\) | |||||||
\(770\) | −1.02850 | −0.0370645 | ||||||||
\(771\) | −54.3048 | −1.95574 | ||||||||
\(772\) | 0.660507 | 0.0237722 | ||||||||
\(773\) | 23.6248 | 0.849723 | 0.424862 | − | 0.905258i | \(-0.360323\pi\) | ||||
0.424862 | + | 0.905258i | \(0.360323\pi\) | |||||||
\(774\) | −20.8854 | −0.750711 | ||||||||
\(775\) | −1.85165 | −0.0665134 | ||||||||
\(776\) | 33.6606 | 1.20835 | ||||||||
\(777\) | −94.1592 | −3.37794 | ||||||||
\(778\) | 18.5223 | 0.664056 | ||||||||
\(779\) | −1.83231 | −0.0656494 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0786495 | −0.00281430 | ||||||||
\(782\) | −57.1535 | −2.04380 | ||||||||
\(783\) | 35.1359 | 1.25566 | ||||||||
\(784\) | −74.4260 | −2.65807 | ||||||||
\(785\) | 40.8063 | 1.45644 | ||||||||
\(786\) | 60.9794 | 2.17506 | ||||||||
\(787\) | 1.20685 | 0.0430194 | 0.0215097 | − | 0.999769i | \(-0.493153\pi\) | ||||
0.0215097 | + | 0.999769i | \(0.493153\pi\) | |||||||
\(788\) | 0.602464 | 0.0214619 | ||||||||
\(789\) | −56.4727 | −2.01048 | ||||||||
\(790\) | −4.17752 | −0.148630 | ||||||||
\(791\) | 4.62767 | 0.164541 | ||||||||
\(792\) | 0.725742 | 0.0257881 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 35.4848 | 1.25931 | ||||||||
\(795\) | −62.7806 | −2.22660 | ||||||||
\(796\) | −0.924985 | −0.0327852 | ||||||||
\(797\) | 28.1207 | 0.996085 | 0.498042 | − | 0.867153i | \(-0.334052\pi\) | ||||
0.498042 | + | 0.867153i | \(0.334052\pi\) | |||||||
\(798\) | −23.6051 | −0.835613 | ||||||||
\(799\) | 0.972825 | 0.0344161 | ||||||||
\(800\) | 0.775081 | 0.0274032 | ||||||||
\(801\) | 11.3085 | 0.399567 | ||||||||
\(802\) | −29.2380 | −1.03243 | ||||||||
\(803\) | 0.761997 | 0.0268903 | ||||||||
\(804\) | 0.310650 | 0.0109558 | ||||||||
\(805\) | 102.174 | 3.60115 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.1802 | 0.815983 | ||||||||
\(808\) | −32.2102 | −1.13315 | ||||||||
\(809\) | −32.4182 | −1.13976 | −0.569881 | − | 0.821727i | \(-0.693011\pi\) | ||||
−0.569881 | + | 0.821727i | \(0.693011\pi\) | |||||||
\(810\) | 1.55967 | 0.0548013 | ||||||||
\(811\) | 15.1013 | 0.530279 | 0.265139 | − | 0.964210i | \(-0.414582\pi\) | ||||
0.265139 | + | 0.964210i | \(0.414582\pi\) | |||||||
\(812\) | −2.59859 | −0.0911926 | ||||||||
\(813\) | 41.1690 | 1.44386 | ||||||||
\(814\) | −0.530882 | −0.0186074 | ||||||||
\(815\) | −6.60779 | −0.231461 | ||||||||
\(816\) | 58.7436 | 2.05644 | ||||||||
\(817\) | −3.55661 | −0.124430 | ||||||||
\(818\) | −11.0545 | −0.386513 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.302153 | 0.0105516 | ||||||||
\(821\) | 7.53751 | 0.263061 | 0.131531 | − | 0.991312i | \(-0.458011\pi\) | ||||
0.131531 | + | 0.991312i | \(0.458011\pi\) | |||||||
\(822\) | −46.1809 | −1.61074 | ||||||||
\(823\) | 20.7098 | 0.721897 | 0.360949 | − | 0.932586i | \(-0.382453\pi\) | ||||
0.360949 | + | 0.932586i | \(0.382453\pi\) | |||||||
\(824\) | 35.2918 | 1.22945 | ||||||||
\(825\) | −0.282230 | −0.00982598 | ||||||||
\(826\) | 20.9692 | 0.729613 | ||||||||
\(827\) | −22.6064 | −0.786101 | −0.393051 | − | 0.919517i | \(-0.628580\pi\) | ||||
−0.393051 | + | 0.919517i | \(0.628580\pi\) | |||||||
\(828\) | 2.77141 | 0.0963133 | ||||||||
\(829\) | −50.3014 | −1.74704 | −0.873520 | − | 0.486789i | \(-0.838168\pi\) | ||||
−0.873520 | + | 0.486789i | \(0.838168\pi\) | |||||||
\(830\) | 6.59406 | 0.228883 | ||||||||
\(831\) | −43.0509 | −1.49342 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 91.2686 | 3.16227 | ||||||||
\(834\) | −26.7247 | −0.925402 | ||||||||
\(835\) | 25.9763 | 0.898945 | ||||||||
\(836\) | −0.00475071 | −0.000164307 0 | ||||||||
\(837\) | 5.00174 | 0.172885 | ||||||||
\(838\) | 35.1503 | 1.21425 | ||||||||
\(839\) | 27.1797 | 0.938346 | 0.469173 | − | 0.883106i | \(-0.344552\pi\) | ||||
0.469173 | + | 0.883106i | \(0.344552\pi\) | |||||||
\(840\) | −101.263 | −3.49389 | ||||||||
\(841\) | 20.3470 | 0.701620 | ||||||||
\(842\) | 11.2849 | 0.388902 | ||||||||
\(843\) | −48.1779 | −1.65934 | ||||||||
\(844\) | −1.54443 | −0.0531616 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.32153 | −0.0454351 | ||||||||
\(847\) | −54.9478 | −1.88803 | ||||||||
\(848\) | −35.5942 | −1.22231 | ||||||||
\(849\) | 34.1192 | 1.17097 | ||||||||
\(850\) | −13.5468 | −0.464651 | ||||||||
\(851\) | 52.7392 | 1.80788 | ||||||||
\(852\) | 0.297664 | 0.0101978 | ||||||||
\(853\) | −7.69689 | −0.263536 | −0.131768 | − | 0.991281i | \(-0.542065\pi\) | ||||
−0.131768 | + | 0.991281i | \(0.542065\pi\) | |||||||
\(854\) | −42.9138 | −1.46848 | ||||||||
\(855\) | −14.7402 | −0.504105 | ||||||||
\(856\) | −8.19520 | −0.280106 | ||||||||
\(857\) | 53.2084 | 1.81756 | 0.908782 | − | 0.417272i | \(-0.137014\pi\) | ||||
0.908782 | + | 0.417272i | \(0.137014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.0111 | −0.955728 | −0.477864 | − | 0.878434i | \(-0.658589\pi\) | ||||
−0.477864 | + | 0.878434i | \(0.658589\pi\) | |||||||
\(860\) | 0.586493 | 0.0199992 | ||||||||
\(861\) | −21.7466 | −0.741122 | ||||||||
\(862\) | 11.2021 | 0.381545 | ||||||||
\(863\) | 19.3779 | 0.659630 | 0.329815 | − | 0.944046i | \(-0.393014\pi\) | ||||
0.329815 | + | 0.944046i | \(0.393014\pi\) | |||||||
\(864\) | −2.09367 | −0.0712281 | ||||||||
\(865\) | 53.2768 | 1.81146 | ||||||||
\(866\) | 38.4024 | 1.30497 | ||||||||
\(867\) | −24.5837 | −0.834906 | ||||||||
\(868\) | −0.369920 | −0.0125559 | ||||||||
\(869\) | 0.0605112 | 0.00205270 | ||||||||
\(870\) | −73.9190 | −2.50609 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −55.2195 | −1.86997 | ||||||||
\(873\) | 58.1525 | 1.96817 | ||||||||
\(874\) | 13.2214 | 0.447221 | ||||||||
\(875\) | −41.1770 | −1.39204 | ||||||||
\(876\) | −2.88392 | −0.0974387 | ||||||||
\(877\) | 6.54713 | 0.221081 | 0.110540 | − | 0.993872i | \(-0.464742\pi\) | ||||
0.110540 | + | 0.993872i | \(0.464742\pi\) | |||||||
\(878\) | 20.7790 | 0.701256 | ||||||||
\(879\) | 32.2449 | 1.08759 | ||||||||
\(880\) | −0.592096 | −0.0199595 | ||||||||
\(881\) | 50.1477 | 1.68952 | 0.844760 | − | 0.535145i | \(-0.179743\pi\) | ||||
0.844760 | + | 0.535145i | \(0.179743\pi\) | |||||||
\(882\) | −123.983 | −4.17474 | ||||||||
\(883\) | 6.21470 | 0.209141 | 0.104571 | − | 0.994517i | \(-0.466653\pi\) | ||||
0.104571 | + | 0.994517i | \(0.466653\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.2920 | 0.715724 | ||||||||
\(886\) | −7.47929 | −0.251272 | ||||||||
\(887\) | −0.519213 | −0.0174335 | −0.00871673 | − | 0.999962i | \(-0.502775\pi\) | ||||
−0.00871673 | + | 0.999962i | \(0.502775\pi\) | |||||||
\(888\) | −52.2690 | −1.75403 | ||||||||
\(889\) | −81.5418 | −2.73482 | ||||||||
\(890\) | −8.89629 | −0.298204 | ||||||||
\(891\) | −0.0225918 | −0.000756853 0 | ||||||||
\(892\) | −1.38131 | −0.0462497 | ||||||||
\(893\) | −0.225045 | −0.00753085 | ||||||||
\(894\) | 5.45885 | 0.182571 | ||||||||
\(895\) | −12.7156 | −0.425037 | ||||||||
\(896\) | −59.4641 | −1.98656 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.5632 | −0.719575 | ||||||||
\(899\) | 7.02474 | 0.234288 | ||||||||
\(900\) | 0.656894 | 0.0218965 | ||||||||
\(901\) | 43.6492 | 1.45416 | ||||||||
\(902\) | −0.122610 | −0.00408247 | ||||||||
\(903\) | −42.2112 | −1.40470 | ||||||||
\(904\) | 2.56888 | 0.0854397 | ||||||||
\(905\) | −17.8694 | −0.593999 | ||||||||
\(906\) | 50.0295 | 1.66212 | ||||||||
\(907\) | 32.5497 | 1.08079 | 0.540397 | − | 0.841410i | \(-0.318274\pi\) | ||||
0.540397 | + | 0.841410i | \(0.318274\pi\) | |||||||
\(908\) | −2.07233 | −0.0687727 | ||||||||
\(909\) | −55.6468 | −1.84569 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.1736 | 0.403331 | 0.201665 | − | 0.979454i | \(-0.435365\pi\) | ||||
0.201665 | + | 0.979454i | \(0.435365\pi\) | |||||||
\(912\) | −13.5892 | −0.449985 | ||||||||
\(913\) | −0.0955146 | −0.00316107 | ||||||||
\(914\) | −60.5645 | −2.00330 | ||||||||
\(915\) | −43.5745 | −1.44053 | ||||||||
\(916\) | −0.681813 | −0.0225277 | ||||||||
\(917\) | 75.7932 | 2.50291 | ||||||||
\(918\) | 36.5930 | 1.20775 | ||||||||
\(919\) | 33.3627 | 1.10053 | 0.550266 | − | 0.834989i | \(-0.314526\pi\) | ||||
0.550266 | + | 0.834989i | \(0.314526\pi\) | |||||||
\(920\) | 56.7179 | 1.86993 | ||||||||
\(921\) | 61.7528 | 2.03482 | ||||||||
\(922\) | −13.4131 | −0.441738 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.0563833 | −0.00185487 | ||||||||
\(925\) | 12.5005 | 0.411014 | ||||||||
\(926\) | −14.8628 | −0.488422 | ||||||||
\(927\) | 60.9706 | 2.00254 | ||||||||
\(928\) | −2.94047 | −0.0965258 | ||||||||
\(929\) | −4.29919 | −0.141052 | −0.0705259 | − | 0.997510i | \(-0.522468\pi\) | ||||
−0.0705259 | + | 0.997510i | \(0.522468\pi\) | |||||||
\(930\) | −10.5227 | −0.345052 | ||||||||
\(931\) | −21.1133 | −0.691961 | ||||||||
\(932\) | −1.44618 | −0.0473711 | ||||||||
\(933\) | −47.8091 | −1.56520 | ||||||||
\(934\) | −0.953126 | −0.0311872 | ||||||||
\(935\) | 0.726087 | 0.0237456 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.4050 | 1.58132 | 0.790662 | − | 0.612253i | \(-0.209737\pi\) | ||||
0.790662 | + | 0.612253i | \(0.209737\pi\) | |||||||
\(938\) | 10.8169 | 0.353184 | ||||||||
\(939\) | 80.9006 | 2.64009 | ||||||||
\(940\) | 0.0371105 | 0.00121041 | ||||||||
\(941\) | −31.2320 | −1.01813 | −0.509067 | − | 0.860727i | \(-0.670010\pi\) | ||||
−0.509067 | + | 0.860727i | \(0.670010\pi\) | |||||||
\(942\) | 62.6698 | 2.04189 | ||||||||
\(943\) | 12.1804 | 0.396649 | ||||||||
\(944\) | 12.0718 | 0.392903 | ||||||||
\(945\) | −65.4175 | −2.12803 | ||||||||
\(946\) | −0.237992 | −0.00773780 | ||||||||
\(947\) | 27.4625 | 0.892410 | 0.446205 | − | 0.894931i | \(-0.352775\pi\) | ||||
0.446205 | + | 0.894931i | \(0.352775\pi\) | |||||||
\(948\) | −0.229016 | −0.00743809 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 3.13380 | 0.101674 | ||||||||
\(951\) | −17.3743 | −0.563401 | ||||||||
\(952\) | 70.4044 | 2.28182 | ||||||||
\(953\) | 39.5670 | 1.28170 | 0.640850 | − | 0.767666i | \(-0.278582\pi\) | ||||
0.640850 | + | 0.767666i | \(0.278582\pi\) | |||||||
\(954\) | −59.2950 | −1.91975 | ||||||||
\(955\) | −36.1409 | −1.16949 | ||||||||
\(956\) | −1.25338 | −0.0405371 | ||||||||
\(957\) | 1.07071 | 0.0346112 | ||||||||
\(958\) | 5.23409 | 0.169106 | ||||||||
\(959\) | −57.3997 | −1.85353 | ||||||||
\(960\) | −56.1322 | −1.81166 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.1581 | −0.456239 | ||||||||
\(964\) | 1.08137 | 0.0348285 | ||||||||
\(965\) | 23.3530 | 0.751760 | ||||||||
\(966\) | 156.917 | 5.04871 | ||||||||
\(967\) | 0.618915 | 0.0199030 | 0.00995149 | − | 0.999950i | \(-0.496832\pi\) | ||||
0.00995149 | + | 0.999950i | \(0.496832\pi\) | |||||||
\(968\) | −30.5022 | −0.980379 | ||||||||
\(969\) | 16.6645 | 0.535341 | ||||||||
\(970\) | −45.7479 | −1.46888 | ||||||||
\(971\) | 9.35978 | 0.300370 | 0.150185 | − | 0.988658i | \(-0.452013\pi\) | ||||
0.150185 | + | 0.988658i | \(0.452013\pi\) | |||||||
\(972\) | 1.19640 | 0.0383746 | ||||||||
\(973\) | −33.2170 | −1.06489 | ||||||||
\(974\) | 44.8221 | 1.43619 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.7051 | −0.790790 | ||||||||
\(977\) | −21.1557 | −0.676830 | −0.338415 | − | 0.940997i | \(-0.609891\pi\) | ||||
−0.338415 | + | 0.940997i | \(0.609891\pi\) | |||||||
\(978\) | −10.1481 | −0.324502 | ||||||||
\(979\) | 0.128862 | 0.00411846 | ||||||||
\(980\) | 3.48163 | 0.111217 | ||||||||
\(981\) | −95.3979 | −3.04582 | ||||||||
\(982\) | 25.8661 | 0.825421 | ||||||||
\(983\) | −18.5493 | −0.591630 | −0.295815 | − | 0.955245i | \(-0.595591\pi\) | ||||
−0.295815 | + | 0.955245i | \(0.595591\pi\) | |||||||
\(984\) | −12.0718 | −0.384836 | ||||||||
\(985\) | 21.3008 | 0.678701 | ||||||||
\(986\) | 51.3933 | 1.63670 | ||||||||
\(987\) | −2.67092 | −0.0850164 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.6428 | 0.751797 | ||||||||
\(990\) | −0.986350 | −0.0313483 | ||||||||
\(991\) | −32.6306 | −1.03654 | −0.518272 | − | 0.855216i | \(-0.673425\pi\) | ||||
−0.518272 | + | 0.855216i | \(0.673425\pi\) | |||||||
\(992\) | −0.418588 | −0.0132902 | ||||||||
\(993\) | −14.7507 | −0.468100 | ||||||||
\(994\) | 10.3647 | 0.328748 | ||||||||
\(995\) | −32.7039 | −1.03678 | ||||||||
\(996\) | 0.361493 | 0.0114543 | ||||||||
\(997\) | −12.4748 | −0.395082 | −0.197541 | − | 0.980295i | \(-0.563296\pi\) | ||||
−0.197541 | + | 0.980295i | \(0.563296\pi\) | |||||||
\(998\) | −11.6998 | −0.370351 | ||||||||
\(999\) | −33.7667 | −1.06833 |
(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 | 5239.2.a.l.1.4 | 16 | ||
13.5 | odd | 4 | 403.2.c.b.311.23 | yes | 32 | ||
13.8 | odd | 4 | 403.2.c.b.311.10 | ✓ | 32 | ||
13.12 | even | 2 | 5239.2.a.k.1.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.10 | ✓ | 32 | 13.8 | odd | 4 | ||
403.2.c.b.311.23 | yes | 32 | 13.5 | odd | 4 | ||
5239.2.a.k.1.13 | 16 | 13.12 | even | 2 | |||
5239.2.a.l.1.4 | 16 | 1.1 | even | 1 | trivial |