Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + 229 x^{12} - 14020 x^{11} + 3356 x^{10} + 23404 x^{9} - 9429 x^{8} - 21252 x^{7} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.66148\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66148 | −1.88195 | −0.940974 | − | 0.338480i | \(-0.890087\pi\) | ||||
−0.940974 | + | 0.338480i | \(0.890087\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.08345 | 2.54173 | ||||||||
\(5\) | 2.46126 | 1.10071 | 0.550353 | − | 0.834932i | \(-0.314493\pi\) | ||||
0.550353 | + | 0.834932i | \(0.314493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.08484 | −1.92189 | −0.960944 | − | 0.276744i | \(-0.910744\pi\) | ||||
−0.960944 | + | 0.276744i | \(0.910744\pi\) | |||||||
\(8\) | −8.20653 | −2.90145 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.55057 | −2.07147 | ||||||||
\(11\) | 0.841814 | 0.253816 | 0.126908 | − | 0.991914i | \(-0.459495\pi\) | ||||
0.126908 | + | 0.991914i | \(0.459495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.31476 | −1.19670 | −0.598350 | − | 0.801235i | \(-0.704177\pi\) | ||||
−0.598350 | + | 0.801235i | \(0.704177\pi\) | |||||||
\(14\) | 13.5332 | 3.61689 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.6746 | 2.91865 | ||||||||
\(17\) | 0.607296 | 0.147291 | 0.0736454 | − | 0.997284i | \(-0.476537\pi\) | ||||
0.0736454 | + | 0.997284i | \(0.476537\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.12670 | −1.63498 | −0.817489 | − | 0.575944i | \(-0.804635\pi\) | ||||
−0.817489 | + | 0.575944i | \(0.804635\pi\) | |||||||
\(20\) | 12.5117 | 2.79770 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.24047 | −0.477669 | ||||||||
\(23\) | −6.45037 | −1.34499 | −0.672497 | − | 0.740100i | \(-0.734778\pi\) | ||||
−0.672497 | + | 0.740100i | \(0.734778\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.05778 | 0.211555 | ||||||||
\(26\) | 11.4836 | 2.25213 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −25.8485 | −4.88491 | ||||||||
\(29\) | 0.953320 | 0.177027 | 0.0885136 | − | 0.996075i | \(-0.471788\pi\) | ||||
0.0885136 | + | 0.996075i | \(0.471788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.79400 | 0.322212 | 0.161106 | − | 0.986937i | \(-0.448494\pi\) | ||||
0.161106 | + | 0.986937i | \(0.448494\pi\) | |||||||
\(32\) | −14.6586 | −2.59129 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.61630 | −0.277194 | ||||||||
\(35\) | −12.5151 | −2.11543 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.38489 | −0.720872 | −0.360436 | − | 0.932784i | \(-0.617372\pi\) | ||||
−0.360436 | + | 0.932784i | \(0.617372\pi\) | |||||||
\(38\) | 18.9675 | 3.07694 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −20.1984 | −3.19364 | ||||||||
\(41\) | 9.65928 | 1.50853 | 0.754263 | − | 0.656572i | \(-0.227994\pi\) | ||||
0.754263 | + | 0.656572i | \(0.227994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.60860 | 0.855303 | 0.427652 | − | 0.903944i | \(-0.359341\pi\) | ||||
0.427652 | + | 0.903944i | \(0.359341\pi\) | |||||||
\(44\) | 4.27932 | 0.645132 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.1675 | 2.53121 | ||||||||
\(47\) | 5.73361 | 0.836332 | 0.418166 | − | 0.908371i | \(-0.362673\pi\) | ||||
0.418166 | + | 0.908371i | \(0.362673\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.8556 | 2.69365 | ||||||||
\(50\) | −2.81525 | −0.398136 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −21.9339 | −3.04168 | ||||||||
\(53\) | −0.509397 | −0.0699711 | −0.0349855 | − | 0.999388i | \(-0.511139\pi\) | ||||
−0.0349855 | + | 0.999388i | \(0.511139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.07192 | 0.279377 | ||||||||
\(56\) | 41.7289 | 5.57626 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.53724 | −0.333156 | ||||||||
\(59\) | 10.9292 | 1.42286 | 0.711432 | − | 0.702755i | \(-0.248047\pi\) | ||||
0.711432 | + | 0.702755i | \(0.248047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9561 | 1.40278 | 0.701390 | − | 0.712778i | \(-0.252563\pi\) | ||||
0.701390 | + | 0.712778i | \(0.252563\pi\) | |||||||
\(62\) | −4.77468 | −0.606385 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 15.6642 | 1.95803 | ||||||||
\(65\) | −10.6197 | −1.31722 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.55272 | 0.311864 | 0.155932 | − | 0.987768i | \(-0.450162\pi\) | ||||
0.155932 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(68\) | 3.08716 | 0.374373 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 33.3086 | 3.98114 | ||||||||
\(71\) | −4.53464 | −0.538162 | −0.269081 | − | 0.963117i | \(-0.586720\pi\) | ||||
−0.269081 | + | 0.963117i | \(0.586720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.87319 | 1.03853 | 0.519264 | − | 0.854614i | \(-0.326206\pi\) | ||||
0.519264 | + | 0.854614i | \(0.326206\pi\) | |||||||
\(74\) | 11.6703 | 1.35664 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −36.2283 | −4.15567 | ||||||||
\(77\) | −4.28048 | −0.487806 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.69076 | −0.190226 | −0.0951128 | − | 0.995466i | \(-0.530321\pi\) | ||||
−0.0951128 | + | 0.995466i | \(0.530321\pi\) | |||||||
\(80\) | 28.7341 | 3.21257 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −25.7079 | −2.83897 | ||||||||
\(83\) | 10.0976 | 1.10836 | 0.554179 | − | 0.832398i | \(-0.313032\pi\) | ||||
0.554179 | + | 0.832398i | \(0.313032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.49471 | 0.162124 | ||||||||
\(86\) | −14.9271 | −1.60964 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.90837 | −0.736435 | ||||||||
\(89\) | 13.6428 | 1.44614 | 0.723068 | − | 0.690777i | \(-0.242731\pi\) | ||||
0.723068 | + | 0.690777i | \(0.242731\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.9399 | 2.29992 | ||||||||
\(92\) | −32.7901 | −3.41861 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.2599 | −1.57393 | ||||||||
\(95\) | −17.5406 | −1.79963 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.1354 | 1.63830 | 0.819149 | − | 0.573581i | \(-0.194446\pi\) | ||||
0.819149 | + | 0.573581i | \(0.194446\pi\) | |||||||
\(98\) | −50.1836 | −5.06931 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.37716 | 0.537716 | ||||||||
\(101\) | −12.4874 | −1.24254 | −0.621272 | − | 0.783595i | \(-0.713384\pi\) | ||||
−0.621272 | + | 0.783595i | \(0.713384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4503 | −1.22677 | −0.613384 | − | 0.789785i | \(-0.710192\pi\) | ||||
−0.613384 | + | 0.789785i | \(0.710192\pi\) | |||||||
\(104\) | 35.4093 | 3.47216 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.35575 | 0.131682 | ||||||||
\(107\) | −3.48642 | −0.337045 | −0.168522 | − | 0.985698i | \(-0.553900\pi\) | ||||
−0.168522 | + | 0.985698i | \(0.553900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.59512 | −0.631698 | −0.315849 | − | 0.948809i | \(-0.602289\pi\) | ||||
−0.315849 | + | 0.948809i | \(0.602289\pi\) | |||||||
\(110\) | −5.51436 | −0.525773 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −59.3633 | −5.60931 | ||||||||
\(113\) | 14.2622 | 1.34168 | 0.670838 | − | 0.741604i | \(-0.265934\pi\) | ||||
0.670838 | + | 0.741604i | \(0.265934\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8760 | −1.48044 | ||||||||
\(116\) | 4.84616 | 0.449955 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.0879 | −2.67776 | ||||||||
\(119\) | −3.08800 | −0.283076 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2913 | −0.935577 | ||||||||
\(122\) | −29.1593 | −2.63996 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.11970 | 0.818974 | ||||||||
\(125\) | −9.70282 | −0.867846 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.2640 | 1.44320 | 0.721599 | − | 0.692311i | \(-0.243407\pi\) | ||||
0.721599 | + | 0.692311i | \(0.243407\pi\) | |||||||
\(128\) | −12.3728 | −1.09361 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 28.2642 | 2.47893 | ||||||||
\(131\) | −21.0513 | −1.83926 | −0.919631 | − | 0.392783i | \(-0.871512\pi\) | ||||
−0.919631 | + | 0.392783i | \(0.871512\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 36.2381 | 3.14224 | ||||||||
\(134\) | −6.79399 | −0.586912 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.98379 | −0.427357 | ||||||||
\(137\) | 14.5332 | 1.24166 | 0.620830 | − | 0.783946i | \(-0.286796\pi\) | ||||
0.620830 | + | 0.783946i | \(0.286796\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.13395 | −0.605094 | −0.302547 | − | 0.953134i | \(-0.597837\pi\) | ||||
−0.302547 | + | 0.953134i | \(0.597837\pi\) | |||||||
\(140\) | −63.6198 | −5.37685 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.0688 | 1.01279 | ||||||||
\(143\) | −3.63223 | −0.303742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.34636 | 0.194855 | ||||||||
\(146\) | −23.6158 | −1.95446 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −22.2904 | −1.83226 | ||||||||
\(149\) | 5.29154 | 0.433500 | 0.216750 | − | 0.976227i | \(-0.430454\pi\) | ||||
0.216750 | + | 0.976227i | \(0.430454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.990912 | −0.0806393 | −0.0403196 | − | 0.999187i | \(-0.512838\pi\) | ||||
−0.0403196 | + | 0.999187i | \(0.512838\pi\) | |||||||
\(152\) | 58.4855 | 4.74380 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.3924 | 0.918026 | ||||||||
\(155\) | 4.41549 | 0.354660 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.80762 | −0.543307 | −0.271654 | − | 0.962395i | \(-0.587570\pi\) | ||||
−0.271654 | + | 0.962395i | \(0.587570\pi\) | |||||||
\(158\) | 4.49992 | 0.357995 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −36.0784 | −2.85225 | ||||||||
\(161\) | 32.7990 | 2.58493 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.21737 | 0.565308 | 0.282654 | − | 0.959222i | \(-0.408785\pi\) | ||||
0.282654 | + | 0.959222i | \(0.408785\pi\) | |||||||
\(164\) | 49.1025 | 3.83426 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.8746 | −2.08587 | ||||||||
\(167\) | 3.13902 | 0.242904 | 0.121452 | − | 0.992597i | \(-0.461245\pi\) | ||||
0.121452 | + | 0.992597i | \(0.461245\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.61719 | 0.432091 | ||||||||
\(170\) | −3.97813 | −0.305109 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 28.5110 | 2.17395 | ||||||||
\(173\) | −15.5000 | −1.17844 | −0.589222 | − | 0.807971i | \(-0.700566\pi\) | ||||
−0.589222 | + | 0.807971i | \(0.700566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.37862 | −0.406585 | ||||||||
\(176\) | 9.82782 | 0.740800 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −36.3100 | −2.72155 | ||||||||
\(179\) | 16.9058 | 1.26360 | 0.631799 | − | 0.775133i | \(-0.282317\pi\) | ||||
0.631799 | + | 0.775133i | \(0.282317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.63874 | −0.419125 | −0.209562 | − | 0.977795i | \(-0.567204\pi\) | ||||
−0.209562 | + | 0.977795i | \(0.567204\pi\) | |||||||
\(182\) | −58.3924 | −4.32833 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 52.9351 | 3.90243 | ||||||||
\(185\) | −10.7923 | −0.793468 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.511230 | 0.0373848 | ||||||||
\(188\) | 29.1465 | 2.12573 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 46.6840 | 3.38681 | ||||||||
\(191\) | 9.41280 | 0.681087 | 0.340543 | − | 0.940229i | \(-0.389389\pi\) | ||||
0.340543 | + | 0.940229i | \(0.389389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0149 | −1.36873 | −0.684363 | − | 0.729142i | \(-0.739920\pi\) | ||||
−0.684363 | + | 0.729142i | \(0.739920\pi\) | |||||||
\(194\) | −42.9439 | −3.08319 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 95.8513 | 6.84652 | ||||||||
\(197\) | 5.53908 | 0.394643 | 0.197321 | − | 0.980339i | \(-0.436776\pi\) | ||||
0.197321 | + | 0.980339i | \(0.436776\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.1741 | −0.933884 | −0.466942 | − | 0.884288i | \(-0.654644\pi\) | ||||
−0.466942 | + | 0.884288i | \(0.654644\pi\) | |||||||
\(200\) | −8.68068 | −0.613817 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 33.2350 | 2.33840 | ||||||||
\(203\) | −4.84748 | −0.340226 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.7740 | 1.66045 | ||||||||
\(206\) | 33.1363 | 2.30871 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −50.3731 | −3.49274 | ||||||||
\(209\) | −5.99936 | −0.414984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4645 | 0.789250 | 0.394625 | − | 0.918842i | \(-0.370875\pi\) | ||||
0.394625 | + | 0.918842i | \(0.370875\pi\) | |||||||
\(212\) | −2.58950 | −0.177847 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.27902 | 0.634301 | ||||||||
\(215\) | 13.8042 | 0.941438 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.12219 | −0.619254 | ||||||||
\(218\) | 17.5527 | 1.18882 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.5325 | 0.710101 | ||||||||
\(221\) | −2.62034 | −0.176263 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.94910 | 0.331416 | 0.165708 | − | 0.986175i | \(-0.447009\pi\) | ||||
0.165708 | + | 0.986175i | \(0.447009\pi\) | |||||||
\(224\) | 74.5363 | 4.98017 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.9586 | −2.52497 | ||||||||
\(227\) | −27.3319 | −1.81408 | −0.907039 | − | 0.421046i | \(-0.861663\pi\) | ||||
−0.907039 | + | 0.421046i | \(0.861663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1182 | 1.13121 | 0.565603 | − | 0.824678i | \(-0.308644\pi\) | ||||
0.565603 | + | 0.824678i | \(0.308644\pi\) | |||||||
\(230\) | 42.2536 | 2.78612 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.82346 | −0.513635 | ||||||||
\(233\) | 5.09654 | 0.333886 | 0.166943 | − | 0.985967i | \(-0.446610\pi\) | ||||
0.166943 | + | 0.985967i | \(0.446610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.1119 | 0.920557 | ||||||||
\(236\) | 55.5582 | 3.61653 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.21863 | 0.532735 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.20240 | −0.206285 | −0.103142 | − | 0.994667i | \(-0.532890\pi\) | ||||
−0.103142 | + | 0.994667i | \(0.532890\pi\) | |||||||
\(242\) | 27.3902 | 1.76071 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 55.6946 | 3.56548 | ||||||||
\(245\) | 46.4083 | 2.96492 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.7500 | 1.95658 | ||||||||
\(248\) | −14.7225 | −0.934880 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 25.8238 | 1.63324 | ||||||||
\(251\) | −10.7171 | −0.676455 | −0.338228 | − | 0.941064i | \(-0.609827\pi\) | ||||
−0.338228 | + | 0.941064i | \(0.609827\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.43000 | −0.341381 | ||||||||
\(254\) | −43.2863 | −2.71602 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.60154 | 0.100096 | ||||||||
\(257\) | 28.7630 | 1.79418 | 0.897092 | − | 0.441843i | \(-0.145675\pi\) | ||||
0.897092 | + | 0.441843i | \(0.145675\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.2964 | 1.38543 | ||||||||
\(260\) | −53.9849 | −3.34800 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 56.0276 | 3.46139 | ||||||||
\(263\) | 17.0337 | 1.05034 | 0.525170 | − | 0.850997i | \(-0.324002\pi\) | ||||
0.525170 | + | 0.850997i | \(0.324002\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.25376 | −0.0770177 | ||||||||
\(266\) | −96.4469 | −5.91354 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.9766 | 0.792673 | ||||||||
\(269\) | −30.6001 | −1.86572 | −0.932861 | − | 0.360235i | \(-0.882696\pi\) | ||||
−0.932861 | + | 0.360235i | \(0.882696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.8062 | 1.87134 | 0.935672 | − | 0.352871i | \(-0.114795\pi\) | ||||
0.935672 | + | 0.352871i | \(0.114795\pi\) | |||||||
\(272\) | 7.08992 | 0.429890 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −38.6799 | −2.33674 | ||||||||
\(275\) | 0.890451 | 0.0536962 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.08078 | 0.0649377 | 0.0324688 | − | 0.999473i | \(-0.489663\pi\) | ||||
0.0324688 | + | 0.999473i | \(0.489663\pi\) | |||||||
\(278\) | 18.9868 | 1.13875 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 102.705 | 6.13782 | ||||||||
\(281\) | 31.0662 | 1.85325 | 0.926627 | − | 0.375981i | \(-0.122694\pi\) | ||||
0.926627 | + | 0.375981i | \(0.122694\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3082 | −1.08831 | −0.544154 | − | 0.838985i | \(-0.683149\pi\) | ||||
−0.544154 | + | 0.838985i | \(0.683149\pi\) | |||||||
\(284\) | −23.0516 | −1.36786 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.66708 | 0.571627 | ||||||||
\(287\) | −49.1159 | −2.89922 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6312 | −0.978305 | ||||||||
\(290\) | −6.24479 | −0.366707 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 45.1064 | 2.63965 | ||||||||
\(293\) | 13.8274 | 0.807803 | 0.403901 | − | 0.914802i | \(-0.367654\pi\) | ||||
0.403901 | + | 0.914802i | \(0.367654\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.8996 | 1.56616 | ||||||||
\(296\) | 35.9848 | 2.09157 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.0833 | −0.815824 | ||||||||
\(299\) | 27.8318 | 1.60955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.5188 | −1.64380 | ||||||||
\(302\) | 2.63729 | 0.151759 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −83.2013 | −4.77192 | ||||||||
\(305\) | 26.9657 | 1.54405 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.4835 | 0.940764 | 0.470382 | − | 0.882463i | \(-0.344116\pi\) | ||||
0.470382 | + | 0.882463i | \(0.344116\pi\) | |||||||
\(308\) | −21.7596 | −1.23987 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.7517 | −0.667452 | ||||||||
\(311\) | −7.93968 | −0.450218 | −0.225109 | − | 0.974334i | \(-0.572274\pi\) | ||||
−0.225109 | + | 0.974334i | \(0.572274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.0730 | −1.36069 | −0.680344 | − | 0.732893i | \(-0.738170\pi\) | ||||
−0.680344 | + | 0.732893i | \(0.738170\pi\) | |||||||
\(314\) | 18.1183 | 1.02248 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.59491 | −0.483502 | ||||||||
\(317\) | 2.33927 | 0.131386 | 0.0656932 | − | 0.997840i | \(-0.479074\pi\) | ||||
0.0656932 | + | 0.997840i | \(0.479074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.802518 | 0.0449324 | ||||||||
\(320\) | 38.5536 | 2.15521 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −87.2939 | −4.86470 | ||||||||
\(323\) | −4.32802 | −0.240817 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.56406 | −0.253168 | ||||||||
\(326\) | −19.2088 | −1.06388 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −79.2692 | −4.37691 | ||||||||
\(329\) | −29.1544 | −1.60734 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.4068 | −1.06669 | −0.533347 | − | 0.845896i | \(-0.679066\pi\) | ||||
−0.533347 | + | 0.845896i | \(0.679066\pi\) | |||||||
\(332\) | 51.3308 | 2.81714 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.35441 | −0.457133 | ||||||||
\(335\) | 6.28289 | 0.343271 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.36874 | 0.183507 | 0.0917534 | − | 0.995782i | \(-0.470753\pi\) | ||||
0.0917534 | + | 0.995782i | \(0.470753\pi\) | |||||||
\(338\) | −14.9500 | −0.813173 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.59828 | 0.412075 | ||||||||
\(341\) | 1.51021 | 0.0817826 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −60.2835 | −3.25500 | ||||||||
\(344\) | −46.0271 | −2.48162 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 41.2529 | 2.21777 | ||||||||
\(347\) | 14.5068 | 0.778767 | 0.389383 | − | 0.921076i | \(-0.372688\pi\) | ||||
0.389383 | + | 0.921076i | \(0.372688\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.09523 | 0.379799 | 0.189900 | − | 0.981804i | \(-0.439184\pi\) | ||||
0.189900 | + | 0.981804i | \(0.439184\pi\) | |||||||
\(350\) | 14.3151 | 0.765172 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.3398 | −0.657712 | ||||||||
\(353\) | −9.42842 | −0.501824 | −0.250912 | − | 0.968010i | \(-0.580730\pi\) | ||||
−0.250912 | + | 0.968010i | \(0.580730\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.1609 | −0.592359 | ||||||||
\(356\) | 69.3526 | 3.67568 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −44.9943 | −2.37802 | ||||||||
\(359\) | −20.1249 | −1.06215 | −0.531077 | − | 0.847324i | \(-0.678212\pi\) | ||||
−0.531077 | + | 0.847324i | \(0.678212\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.7899 | 1.67315 | ||||||||
\(362\) | 15.0074 | 0.788770 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 111.530 | 5.84577 | ||||||||
\(365\) | 21.8392 | 1.14311 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.3115 | −1.06025 | −0.530126 | − | 0.847919i | \(-0.677855\pi\) | ||||
−0.530126 | + | 0.847919i | \(0.677855\pi\) | |||||||
\(368\) | −75.3053 | −3.92556 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 28.7235 | 1.49327 | ||||||||
\(371\) | 2.59020 | 0.134477 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0769 | 0.728875 | 0.364438 | − | 0.931228i | \(-0.381261\pi\) | ||||
0.364438 | + | 0.931228i | \(0.381261\pi\) | |||||||
\(374\) | −1.36063 | −0.0703562 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −47.0530 | −2.42657 | ||||||||
\(377\) | −4.11335 | −0.211848 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.4329 | −1.66597 | −0.832983 | − | 0.553299i | \(-0.813369\pi\) | ||||
−0.832983 | + | 0.553299i | \(0.813369\pi\) | |||||||
\(380\) | −89.1670 | −4.57417 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25.0520 | −1.28177 | ||||||||
\(383\) | 28.8970 | 1.47657 | 0.738283 | − | 0.674491i | \(-0.235637\pi\) | ||||
0.738283 | + | 0.674491i | \(0.235637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5354 | −0.536932 | ||||||||
\(386\) | 50.6078 | 2.57587 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 82.0233 | 4.16410 | ||||||||
\(389\) | 26.1348 | 1.32509 | 0.662543 | − | 0.749024i | \(-0.269477\pi\) | ||||
0.662543 | + | 0.749024i | \(0.269477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.91728 | −0.198105 | ||||||||
\(392\) | −154.739 | −7.81549 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.7421 | −0.742697 | ||||||||
\(395\) | −4.16140 | −0.209383 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.8466 | −0.945882 | −0.472941 | − | 0.881094i | \(-0.656808\pi\) | ||||
−0.472941 | + | 0.881094i | \(0.656808\pi\) | |||||||
\(398\) | 35.0624 | 1.75752 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.3491 | 0.617455 | ||||||||
\(401\) | 28.8908 | 1.44274 | 0.721370 | − | 0.692550i | \(-0.243513\pi\) | ||||
0.721370 | + | 0.692550i | \(0.243513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.74068 | −0.385591 | ||||||||
\(404\) | −63.4792 | −3.15821 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.9014 | 0.640288 | ||||||||
\(407\) | −3.69126 | −0.182969 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.0306 | −1.43547 | −0.717736 | − | 0.696316i | \(-0.754821\pi\) | ||||
−0.717736 | + | 0.696316i | \(0.754821\pi\) | |||||||
\(410\) | −63.2738 | −3.12487 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −63.2907 | −3.11811 | ||||||||
\(413\) | −55.5733 | −2.73459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.8528 | 1.21998 | ||||||||
\(416\) | 63.2482 | 3.10100 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.9671 | 0.780978 | ||||||||
\(419\) | 6.92669 | 0.338391 | 0.169195 | − | 0.985583i | \(-0.445883\pi\) | ||||
0.169195 | + | 0.985583i | \(0.445883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.8865 | 1.55405 | 0.777027 | − | 0.629467i | \(-0.216727\pi\) | ||||
0.777027 | + | 0.629467i | \(0.216727\pi\) | |||||||
\(422\) | −30.5125 | −1.48533 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.18039 | 0.203017 | ||||||||
\(425\) | 0.642383 | 0.0311602 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −55.7098 | −2.69599 | ||||||||
\(428\) | −17.7231 | −0.856676 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.7395 | −1.77174 | ||||||||
\(431\) | 0.380253 | 0.0183161 | 0.00915807 | − | 0.999958i | \(-0.497085\pi\) | ||||
0.00915807 | + | 0.999958i | \(0.497085\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.4837 | 0.696042 | 0.348021 | − | 0.937487i | \(-0.386854\pi\) | ||||
0.348021 | + | 0.937487i | \(0.386854\pi\) | |||||||
\(434\) | 24.2785 | 1.16540 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −33.5260 | −1.60560 | ||||||||
\(437\) | 45.9698 | 2.19904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.62838 | −0.220900 | −0.110450 | − | 0.993882i | \(-0.535229\pi\) | ||||
−0.110450 | + | 0.993882i | \(0.535229\pi\) | |||||||
\(440\) | −17.0033 | −0.810599 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.97396 | 0.331718 | ||||||||
\(443\) | −25.3781 | −1.20575 | −0.602874 | − | 0.797837i | \(-0.705978\pi\) | ||||
−0.602874 | + | 0.797837i | \(0.705978\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.5785 | 1.59177 | ||||||||
\(446\) | −13.1719 | −0.623707 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −79.6500 | −3.76311 | ||||||||
\(449\) | 7.89535 | 0.372605 | 0.186302 | − | 0.982492i | \(-0.440350\pi\) | ||||
0.186302 | + | 0.982492i | \(0.440350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.13132 | 0.382889 | ||||||||
\(452\) | 72.5013 | 3.41018 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 72.7431 | 3.41400 | ||||||||
\(455\) | 53.9996 | 2.53154 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6158 | 1.15148 | 0.575740 | − | 0.817633i | \(-0.304714\pi\) | ||||
0.575740 | + | 0.817633i | \(0.304714\pi\) | |||||||
\(458\) | −45.5598 | −2.12887 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −80.7049 | −3.76288 | ||||||||
\(461\) | 26.5949 | 1.23865 | 0.619324 | − | 0.785136i | \(-0.287407\pi\) | ||||
0.619324 | + | 0.785136i | \(0.287407\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5795 | 0.956412 | 0.478206 | − | 0.878248i | \(-0.341287\pi\) | ||||
0.478206 | + | 0.878248i | \(0.341287\pi\) | |||||||
\(464\) | 11.1296 | 0.516680 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.5643 | −0.628355 | ||||||||
\(467\) | −4.02325 | −0.186174 | −0.0930869 | − | 0.995658i | \(-0.529673\pi\) | ||||
−0.0930869 | + | 0.995658i | \(0.529673\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.9801 | −0.599367 | ||||||||
\(470\) | −37.5584 | −1.73244 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −89.6911 | −4.12837 | ||||||||
\(473\) | 4.72139 | 0.217090 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.53846 | −0.345888 | ||||||||
\(476\) | −15.6977 | −0.719502 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.66148 | −0.121733 | ||||||||
\(479\) | −11.1649 | −0.510138 | −0.255069 | − | 0.966923i | \(-0.582098\pi\) | ||||
−0.255069 | + | 0.966923i | \(0.582098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9198 | 0.862667 | ||||||||
\(482\) | 8.52310 | 0.388217 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −52.3156 | −2.37798 | ||||||||
\(485\) | 39.7132 | 1.80329 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.4989 | 0.928894 | 0.464447 | − | 0.885601i | \(-0.346253\pi\) | ||||
0.464447 | + | 0.885601i | \(0.346253\pi\) | |||||||
\(488\) | −89.9113 | −4.07009 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −123.515 | −5.57982 | ||||||||
\(491\) | 18.7828 | 0.847657 | 0.423828 | − | 0.905743i | \(-0.360686\pi\) | ||||
0.423828 | + | 0.905743i | \(0.360686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.578947 | 0.0260745 | ||||||||
\(494\) | −81.8405 | −3.68218 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.9442 | 0.940422 | ||||||||
\(497\) | 23.0579 | 1.03429 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.8795 | 1.29283 | 0.646413 | − | 0.762988i | \(-0.276269\pi\) | ||||
0.646413 | + | 0.762988i | \(0.276269\pi\) | |||||||
\(500\) | −49.3238 | −2.20583 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.5232 | 1.27305 | ||||||||
\(503\) | 4.25152 | 0.189566 | 0.0947828 | − | 0.995498i | \(-0.469784\pi\) | ||||
0.0947828 | + | 0.995498i | \(0.469784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.7347 | −1.36768 | ||||||||
\(506\) | 14.4518 | 0.642462 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 82.6774 | 3.66822 | ||||||||
\(509\) | 32.0917 | 1.42244 | 0.711219 | − | 0.702970i | \(-0.248143\pi\) | ||||
0.711219 | + | 0.702970i | \(0.248143\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −45.1187 | −1.99593 | ||||||||
\(512\) | 20.4832 | 0.905238 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −76.5519 | −3.37656 | ||||||||
\(515\) | −30.6434 | −1.35031 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.82663 | 0.212275 | ||||||||
\(518\) | −59.3415 | −2.60731 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 87.1512 | 3.82183 | ||||||||
\(521\) | −19.6524 | −0.860986 | −0.430493 | − | 0.902594i | \(-0.641660\pi\) | ||||
−0.430493 | + | 0.902594i | \(0.641660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.99001 | −0.218198 | −0.109099 | − | 0.994031i | \(-0.534797\pi\) | ||||
−0.109099 | + | 0.994031i | \(0.534797\pi\) | |||||||
\(524\) | −107.013 | −4.67490 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.3347 | −1.97668 | ||||||||
\(527\) | 1.08949 | 0.0474588 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.6072 | 0.809009 | ||||||||
\(530\) | 3.33684 | 0.144943 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 184.215 | 7.98672 | ||||||||
\(533\) | −41.6775 | −1.80525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.58097 | −0.370988 | ||||||||
\(536\) | −20.9490 | −0.904857 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 81.4415 | 3.51119 | ||||||||
\(539\) | 15.8729 | 0.683692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.40609 | −0.0604526 | −0.0302263 | − | 0.999543i | \(-0.509623\pi\) | ||||
−0.0302263 | + | 0.999543i | \(0.509623\pi\) | |||||||
\(542\) | −81.9900 | −3.52177 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.90208 | −0.381673 | ||||||||
\(545\) | −16.2323 | −0.695314 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.50342 | 0.149795 | 0.0748977 | − | 0.997191i | \(-0.476137\pi\) | ||||
0.0748977 | + | 0.997191i | \(0.476137\pi\) | |||||||
\(548\) | 73.8791 | 3.15596 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.36991 | −0.101053 | ||||||||
\(551\) | −6.79403 | −0.289436 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.59725 | 0.365592 | ||||||||
\(554\) | −2.87647 | −0.122209 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −36.2651 | −1.53798 | ||||||||
\(557\) | −29.7433 | −1.26026 | −0.630131 | − | 0.776489i | \(-0.716999\pi\) | ||||
−0.630131 | + | 0.776489i | \(0.716999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.1998 | −1.02354 | ||||||||
\(560\) | −146.108 | −6.17420 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −82.6819 | −3.48773 | ||||||||
\(563\) | 17.7864 | 0.749609 | 0.374805 | − | 0.927104i | \(-0.377710\pi\) | ||||
0.374805 | + | 0.927104i | \(0.377710\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.1030 | 1.47679 | ||||||||
\(566\) | 48.7268 | 2.04814 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 37.2137 | 1.56145 | ||||||||
\(569\) | 18.0597 | 0.757101 | 0.378551 | − | 0.925581i | \(-0.376423\pi\) | ||||
0.378551 | + | 0.925581i | \(0.376423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.80579 | −0.284813 | −0.142407 | − | 0.989808i | \(-0.545484\pi\) | ||||
−0.142407 | + | 0.989808i | \(0.545484\pi\) | |||||||
\(572\) | −18.4643 | −0.772029 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 130.721 | 5.45618 | ||||||||
\(575\) | −6.82305 | −0.284541 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.745890 | −0.0310518 | −0.0155259 | − | 0.999879i | \(-0.504942\pi\) | ||||
−0.0155259 | + | 0.999879i | \(0.504942\pi\) | |||||||
\(578\) | 44.2635 | 1.84112 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.9276 | 0.495268 | ||||||||
\(581\) | −51.3447 | −2.13014 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.428817 | −0.0177598 | ||||||||
\(584\) | −72.8181 | −3.01324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.8012 | −1.52024 | ||||||||
\(587\) | 23.8937 | 0.986199 | 0.493099 | − | 0.869973i | \(-0.335864\pi\) | ||||
0.493099 | + | 0.869973i | \(0.335864\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.7853 | −0.526809 | ||||||||
\(590\) | −71.5927 | −2.94742 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −51.1918 | −2.10397 | ||||||||
\(593\) | −40.9714 | −1.68249 | −0.841247 | − | 0.540650i | \(-0.818178\pi\) | ||||
−0.841247 | + | 0.540650i | \(0.818178\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.60035 | −0.311584 | ||||||||
\(596\) | 26.8993 | 1.10184 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −74.0737 | −3.02910 | ||||||||
\(599\) | −25.0423 | −1.02320 | −0.511601 | − | 0.859223i | \(-0.670947\pi\) | ||||
−0.511601 | + | 0.859223i | \(0.670947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.5737 | 1.49187 | 0.745937 | − | 0.666017i | \(-0.232002\pi\) | ||||
0.745937 | + | 0.666017i | \(0.232002\pi\) | |||||||
\(602\) | 75.9021 | 3.09354 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.03725 | −0.204963 | ||||||||
\(605\) | −25.3296 | −1.02980 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.60649 | −0.146383 | −0.0731915 | − | 0.997318i | \(-0.523318\pi\) | ||||
−0.0731915 | + | 0.997318i | \(0.523318\pi\) | |||||||
\(608\) | 104.467 | 4.23670 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −71.7685 | −2.90582 | ||||||||
\(611\) | −24.7392 | −1.00084 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2711 | 1.22264 | 0.611319 | − | 0.791384i | \(-0.290639\pi\) | ||||
0.611319 | + | 0.791384i | \(0.290639\pi\) | |||||||
\(614\) | −43.8705 | −1.77047 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 35.1279 | 1.41534 | ||||||||
\(617\) | −44.0450 | −1.77319 | −0.886593 | − | 0.462551i | \(-0.846934\pi\) | ||||
−0.886593 | + | 0.462551i | \(0.846934\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.1839 | 1.85629 | 0.928144 | − | 0.372221i | \(-0.121404\pi\) | ||||
0.928144 | + | 0.372221i | \(0.121404\pi\) | |||||||
\(620\) | 22.4459 | 0.901450 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.1313 | 0.847286 | ||||||||
\(623\) | −69.3715 | −2.77931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1700 | −1.16680 | ||||||||
\(626\) | 64.0698 | 2.56074 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −34.6062 | −1.38094 | ||||||||
\(629\) | −2.66292 | −0.106178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.9537 | −0.515678 | −0.257839 | − | 0.966188i | \(-0.583010\pi\) | ||||
−0.257839 | + | 0.966188i | \(0.583010\pi\) | |||||||
\(632\) | 13.8753 | 0.551930 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.22590 | −0.247262 | ||||||||
\(635\) | 40.0299 | 1.58854 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −81.3573 | −3.22349 | ||||||||
\(638\) | −2.13588 | −0.0845604 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −30.4527 | −1.20375 | ||||||||
\(641\) | 33.2322 | 1.31259 | 0.656297 | − | 0.754502i | \(-0.272122\pi\) | ||||
0.656297 | + | 0.754502i | \(0.272122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.4401 | 1.12157 | 0.560784 | − | 0.827962i | \(-0.310500\pi\) | ||||
0.560784 | + | 0.827962i | \(0.310500\pi\) | |||||||
\(644\) | 166.732 | 6.57018 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.5189 | 0.453205 | ||||||||
\(647\) | 37.1337 | 1.45988 | 0.729938 | − | 0.683513i | \(-0.239549\pi\) | ||||
0.729938 | + | 0.683513i | \(0.239549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.20037 | 0.361146 | ||||||||
\(650\) | 12.1471 | 0.476449 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 36.6891 | 1.43686 | ||||||||
\(653\) | 5.54976 | 0.217179 | 0.108590 | − | 0.994087i | \(-0.465367\pi\) | ||||
0.108590 | + | 0.994087i | \(0.465367\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −51.8127 | −2.02449 | ||||||||
\(656\) | 112.768 | 4.40286 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 77.5938 | 3.02492 | ||||||||
\(659\) | −26.9825 | −1.05109 | −0.525545 | − | 0.850766i | \(-0.676138\pi\) | ||||
−0.525545 | + | 0.850766i | \(0.676138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.9018 | 0.774089 | 0.387044 | − | 0.922061i | \(-0.373496\pi\) | ||||
0.387044 | + | 0.922061i | \(0.373496\pi\) | |||||||
\(662\) | 51.6508 | 2.00746 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −82.8665 | −3.21584 | ||||||||
\(665\) | 89.1913 | 3.45869 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.14927 | −0.238101 | ||||||||
\(668\) | 15.9570 | 0.617396 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.7218 | −0.646018 | ||||||||
\(671\) | 9.22296 | 0.356048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.01717 | −0.193398 | −0.0966988 | − | 0.995314i | \(-0.530828\pi\) | ||||
−0.0966988 | + | 0.995314i | \(0.530828\pi\) | |||||||
\(674\) | −8.96581 | −0.345350 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.5547 | 1.09826 | ||||||||
\(677\) | 23.7408 | 0.912431 | 0.456216 | − | 0.889869i | \(-0.349205\pi\) | ||||
0.456216 | + | 0.889869i | \(0.349205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −82.0457 | −3.14862 | ||||||||
\(680\) | −12.2664 | −0.470394 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.01939 | −0.153910 | ||||||||
\(683\) | −34.8003 | −1.33160 | −0.665799 | − | 0.746132i | \(-0.731909\pi\) | ||||
−0.665799 | + | 0.746132i | \(0.731909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.7700 | 1.36670 | ||||||||
\(686\) | 160.443 | 6.12575 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 65.4780 | 2.49633 | ||||||||
\(689\) | 2.19793 | 0.0837344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4812 | 0.398724 | 0.199362 | − | 0.979926i | \(-0.436113\pi\) | ||||
0.199362 | + | 0.979926i | \(0.436113\pi\) | |||||||
\(692\) | −78.7936 | −2.99528 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −38.6095 | −1.46560 | ||||||||
\(695\) | −17.5585 | −0.666031 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.86604 | 0.222192 | ||||||||
\(698\) | −18.8838 | −0.714762 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −27.3420 | −1.03343 | ||||||||
\(701\) | −3.42304 | −0.129286 | −0.0646432 | − | 0.997908i | \(-0.520591\pi\) | ||||
−0.0646432 | + | 0.997908i | \(0.520591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.2498 | 1.17861 | ||||||||
\(704\) | 13.1864 | 0.496979 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.0935 | 0.944406 | ||||||||
\(707\) | 63.4965 | 2.38803 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.4436 | −1.89445 | −0.947225 | − | 0.320571i | \(-0.896125\pi\) | ||||
−0.947225 | + | 0.320571i | \(0.896125\pi\) | |||||||
\(710\) | 29.7045 | 1.11479 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −111.960 | −4.19589 | ||||||||
\(713\) | −11.5719 | −0.433373 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.93984 | −0.334331 | ||||||||
\(716\) | 85.9397 | 3.21172 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 53.5620 | 1.99892 | ||||||||
\(719\) | −9.37934 | −0.349791 | −0.174895 | − | 0.984587i | \(-0.555959\pi\) | ||||
−0.174895 | + | 0.984587i | \(0.555959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 63.3079 | 2.35771 | ||||||||
\(722\) | −84.6081 | −3.14879 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.6643 | −1.06530 | ||||||||
\(725\) | 1.00840 | 0.0374510 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.55094 | −0.168785 | −0.0843926 | − | 0.996433i | \(-0.526895\pi\) | ||||
−0.0843926 | + | 0.996433i | \(0.526895\pi\) | |||||||
\(728\) | −180.050 | −6.67311 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −58.1244 | −2.15128 | ||||||||
\(731\) | 3.40608 | 0.125978 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.9913 | −1.66179 | −0.830896 | − | 0.556427i | \(-0.812172\pi\) | ||||
−0.830896 | + | 0.556427i | \(0.812172\pi\) | |||||||
\(734\) | 54.0585 | 1.99534 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 94.5530 | 3.48527 | ||||||||
\(737\) | 2.14891 | 0.0791562 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.7428 | −1.05732 | −0.528660 | − | 0.848834i | \(-0.677305\pi\) | ||||
−0.528660 | + | 0.848834i | \(0.677305\pi\) | |||||||
\(740\) | −54.8623 | −2.01678 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.89376 | −0.253078 | ||||||||
\(743\) | 17.5762 | 0.644808 | 0.322404 | − | 0.946602i | \(-0.395509\pi\) | ||||
0.322404 | + | 0.946602i | \(0.395509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.0238 | 0.477156 | ||||||||
\(746\) | −37.4654 | −1.37171 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.59881 | 0.0950220 | ||||||||
\(749\) | 17.7279 | 0.647762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.6670 | −0.425734 | −0.212867 | − | 0.977081i | \(-0.568280\pi\) | ||||
−0.212867 | + | 0.977081i | \(0.568280\pi\) | |||||||
\(752\) | 66.9375 | 2.44096 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.9476 | 0.398688 | ||||||||
\(755\) | −2.43889 | −0.0887602 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.2970 | 1.46462 | 0.732309 | − | 0.680972i | \(-0.238443\pi\) | ||||
0.732309 | + | 0.680972i | \(0.238443\pi\) | |||||||
\(758\) | 86.3194 | 3.13526 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 143.948 | 5.22154 | ||||||||
\(761\) | 1.07339 | 0.0389104 | 0.0194552 | − | 0.999811i | \(-0.493807\pi\) | ||||
0.0194552 | + | 0.999811i | \(0.493807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.5351 | 1.21405 | ||||||||
\(764\) | 47.8495 | 1.73114 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −76.9086 | −2.77882 | ||||||||
\(767\) | −47.1570 | −1.70274 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.2765 | −1.92120 | −0.960600 | − | 0.277935i | \(-0.910350\pi\) | ||||
−0.960600 | + | 0.277935i | \(0.910350\pi\) | |||||||
\(770\) | 28.0396 | 1.01048 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −96.6616 | −3.47893 | ||||||||
\(773\) | −6.87421 | −0.247248 | −0.123624 | − | 0.992329i | \(-0.539452\pi\) | ||||
−0.123624 | + | 0.992329i | \(0.539452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.89765 | 0.0681656 | ||||||||
\(776\) | −132.415 | −4.75344 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −69.5571 | −2.49374 | ||||||||
\(779\) | −68.8389 | −2.46641 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.81732 | −0.136594 | ||||||||
\(782\) | 10.4257 | 0.372824 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 220.131 | 7.86181 | ||||||||
\(785\) | −16.7553 | −0.598022 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.4891 | 1.08682 | 0.543410 | − | 0.839467i | \(-0.317133\pi\) | ||||
0.543410 | + | 0.839467i | \(0.317133\pi\) | |||||||
\(788\) | 28.1576 | 1.00307 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.0755 | 0.394047 | ||||||||
\(791\) | −72.5210 | −2.57855 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.2728 | −1.67871 | ||||||||
\(794\) | 50.1597 | 1.78010 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −66.9697 | −2.37368 | ||||||||
\(797\) | 16.2226 | 0.574633 | 0.287316 | − | 0.957836i | \(-0.407237\pi\) | ||||
0.287316 | + | 0.957836i | \(0.407237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.48199 | 0.123184 | ||||||||
\(800\) | −15.5055 | −0.548201 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −76.8922 | −2.71516 | ||||||||
\(803\) | 7.46957 | 0.263595 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 80.7268 | 2.84525 | ||||||||
\(806\) | 20.6016 | 0.725661 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 102.478 | 3.60518 | ||||||||
\(809\) | 29.3350 | 1.03136 | 0.515681 | − | 0.856781i | \(-0.327539\pi\) | ||||
0.515681 | + | 0.856781i | \(0.327539\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.7325 | 0.376867 | 0.188434 | − | 0.982086i | \(-0.439659\pi\) | ||||
0.188434 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(812\) | −24.6419 | −0.864762 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.82420 | 0.344338 | ||||||||
\(815\) | 17.7638 | 0.622238 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.9708 | −1.39840 | ||||||||
\(818\) | 77.2643 | 2.70148 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 120.854 | 4.22040 | ||||||||
\(821\) | 2.60579 | 0.0909428 | 0.0454714 | − | 0.998966i | \(-0.485521\pi\) | ||||
0.0454714 | + | 0.998966i | \(0.485521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0974 | −0.630837 | −0.315418 | − | 0.948953i | \(-0.602145\pi\) | ||||
−0.315418 | + | 0.948953i | \(0.602145\pi\) | |||||||
\(824\) | 102.174 | 3.55940 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 147.907 | 5.14635 | ||||||||
\(827\) | −33.0633 | −1.14972 | −0.574862 | − | 0.818250i | \(-0.694944\pi\) | ||||
−0.574862 | + | 0.818250i | \(0.694944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.0572 | −1.14813 | −0.574063 | − | 0.818811i | \(-0.694633\pi\) | ||||
−0.574063 | + | 0.818811i | \(0.694633\pi\) | |||||||
\(830\) | −66.1452 | −2.29593 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −67.5874 | −2.34317 | ||||||||
\(833\) | 11.4509 | 0.396750 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.72592 | 0.267366 | ||||||||
\(836\) | −30.4974 | −1.05478 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.4352 | −0.636834 | ||||||||
\(839\) | 13.8010 | 0.476462 | 0.238231 | − | 0.971209i | \(-0.423432\pi\) | ||||
0.238231 | + | 0.971209i | \(0.423432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0912 | −0.968661 | ||||||||
\(842\) | −84.8652 | −2.92465 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 58.2793 | 2.00606 | ||||||||
\(845\) | 13.8253 | 0.475606 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 52.3298 | 1.79807 | ||||||||
\(848\) | −5.94700 | −0.204221 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.70969 | −0.0586418 | ||||||||
\(851\) | 28.2841 | 0.969568 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4019 | −0.664310 | −0.332155 | − | 0.943225i | \(-0.607776\pi\) | ||||
−0.332155 | + | 0.943225i | \(0.607776\pi\) | |||||||
\(854\) | 148.270 | 5.07370 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.6114 | 0.977918 | ||||||||
\(857\) | −7.72283 | −0.263807 | −0.131903 | − | 0.991263i | \(-0.542109\pi\) | ||||
−0.131903 | + | 0.991263i | \(0.542109\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.9600 | −0.919865 | −0.459932 | − | 0.887954i | \(-0.652126\pi\) | ||||
−0.459932 | + | 0.887954i | \(0.652126\pi\) | |||||||
\(860\) | 70.1729 | 2.39288 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.01203 | −0.0344700 | ||||||||
\(863\) | −37.1997 | −1.26629 | −0.633146 | − | 0.774032i | \(-0.718237\pi\) | ||||
−0.633146 | + | 0.774032i | \(0.718237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.1495 | −1.29712 | ||||||||
\(866\) | −38.5480 | −1.30991 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −46.3722 | −1.57397 | ||||||||
\(869\) | −1.42331 | −0.0482824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.0144 | −0.373208 | ||||||||
\(872\) | 54.1231 | 1.83284 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −122.348 | −4.13847 | ||||||||
\(875\) | 49.3372 | 1.66790 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.19507 | −0.107890 | −0.0539449 | − | 0.998544i | \(-0.517180\pi\) | ||||
−0.0539449 | + | 0.998544i | \(0.517180\pi\) | |||||||
\(878\) | 12.3183 | 0.415723 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 24.1888 | 0.815404 | ||||||||
\(881\) | 3.64187 | 0.122698 | 0.0613489 | − | 0.998116i | \(-0.480460\pi\) | ||||
0.0613489 | + | 0.998116i | \(0.480460\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.0188 | 1.68327 | 0.841633 | − | 0.540050i | \(-0.181595\pi\) | ||||
0.841633 | + | 0.540050i | \(0.181595\pi\) | |||||||
\(884\) | −13.3204 | −0.448012 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 67.5431 | 2.26915 | ||||||||
\(887\) | −11.3702 | −0.381775 | −0.190888 | − | 0.981612i | \(-0.561137\pi\) | ||||
−0.190888 | + | 0.981612i | \(0.561137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −82.6999 | −2.77366 | ||||||||
\(890\) | −89.3682 | −2.99563 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.1585 | 0.842369 | ||||||||
\(893\) | −40.8617 | −1.36739 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.6094 | 1.39085 | ||||||||
\(896\) | 62.9138 | 2.10180 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.0133 | −0.701222 | ||||||||
\(899\) | 1.71026 | 0.0570402 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.309355 | −0.0103061 | ||||||||
\(902\) | −21.6413 | −0.720576 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −117.043 | −3.89281 | ||||||||
\(905\) | −13.8784 | −0.461333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.2253 | 0.804389 | 0.402195 | − | 0.915554i | \(-0.368248\pi\) | ||||
0.402195 | + | 0.915554i | \(0.368248\pi\) | |||||||
\(908\) | −138.940 | −4.61089 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −143.719 | −4.76423 | ||||||||
\(911\) | −17.0859 | −0.566081 | −0.283040 | − | 0.959108i | \(-0.591343\pi\) | ||||
−0.283040 | + | 0.959108i | \(0.591343\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.50031 | 0.281319 | ||||||||
\(914\) | −65.5144 | −2.16702 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 87.0198 | 2.87521 | ||||||||
\(917\) | 107.042 | 3.53485 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2142 | 0.336935 | 0.168467 | − | 0.985707i | \(-0.446118\pi\) | ||||
0.168467 | + | 0.985707i | \(0.446118\pi\) | |||||||
\(920\) | 130.287 | 4.29543 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −70.7817 | −2.33107 | ||||||||
\(923\) | 19.5659 | 0.644019 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.63824 | −0.152504 | ||||||||
\(926\) | −54.7719 | −1.79992 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −13.9743 | −0.458729 | ||||||||
\(929\) | 4.19595 | 0.137665 | 0.0688324 | − | 0.997628i | \(-0.478073\pi\) | ||||
0.0688324 | + | 0.997628i | \(0.478073\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −134.378 | −4.40406 | ||||||||
\(932\) | 25.9080 | 0.848646 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.7078 | 0.350369 | ||||||||
\(935\) | 1.25827 | 0.0411497 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.6095 | 0.673284 | 0.336642 | − | 0.941633i | \(-0.390709\pi\) | ||||
0.336642 | + | 0.941633i | \(0.390709\pi\) | |||||||
\(938\) | 34.5463 | 1.12798 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 71.7370 | 2.33980 | ||||||||
\(941\) | −16.4231 | −0.535379 | −0.267689 | − | 0.963505i | \(-0.586260\pi\) | ||||
−0.267689 | + | 0.963505i | \(0.586260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.3059 | −2.02896 | ||||||||
\(944\) | 127.594 | 4.15284 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.5659 | −0.408552 | ||||||||
\(947\) | 46.2414 | 1.50264 | 0.751322 | − | 0.659936i | \(-0.229417\pi\) | ||||
0.751322 | + | 0.659936i | \(0.229417\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.2857 | −1.24281 | ||||||||
\(950\) | 20.0634 | 0.650944 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 25.3418 | 0.821331 | ||||||||
\(953\) | −17.1233 | −0.554678 | −0.277339 | − | 0.960772i | \(-0.589453\pi\) | ||||
−0.277339 | + | 0.960772i | \(0.589453\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.1673 | 0.749677 | ||||||||
\(956\) | 5.08345 | 0.164411 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.7151 | 0.960053 | ||||||||
\(959\) | −73.8992 | −2.38633 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.7816 | −0.896180 | ||||||||
\(962\) | −50.3545 | −1.62349 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.2792 | −0.524319 | ||||||||
\(965\) | −46.8006 | −1.50657 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.08972 | 0.292306 | 0.146153 | − | 0.989262i | \(-0.453311\pi\) | ||||
0.146153 | + | 0.989262i | \(0.453311\pi\) | |||||||
\(968\) | 84.4563 | 2.71453 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −105.696 | −3.39369 | ||||||||
\(971\) | −17.5375 | −0.562806 | −0.281403 | − | 0.959590i | \(-0.590800\pi\) | ||||
−0.281403 | + | 0.959590i | \(0.590800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.2750 | 1.16292 | ||||||||
\(974\) | −54.5573 | −1.74813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 127.907 | 4.09422 | ||||||||
\(977\) | 43.9565 | 1.40629 | 0.703147 | − | 0.711044i | \(-0.251777\pi\) | ||||
0.703147 | + | 0.711044i | \(0.251777\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.4847 | 0.367053 | ||||||||
\(980\) | 235.914 | 7.53601 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −49.9900 | −1.59525 | ||||||||
\(983\) | 0.659283 | 0.0210279 | 0.0105139 | − | 0.999945i | \(-0.496653\pi\) | ||||
0.0105139 | + | 0.999945i | \(0.496653\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.6331 | 0.434386 | ||||||||
\(986\) | −1.54085 | −0.0490708 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 156.316 | 4.97309 | ||||||||
\(989\) | −36.1775 | −1.15038 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6899 | 0.816067 | 0.408033 | − | 0.912967i | \(-0.366215\pi\) | ||||
0.408033 | + | 0.912967i | \(0.366215\pi\) | |||||||
\(992\) | −26.2974 | −0.834944 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −61.3680 | −1.94647 | ||||||||
\(995\) | −32.4247 | −1.02793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.2490 | 0.577953 | 0.288977 | − | 0.957336i | \(-0.406685\pi\) | ||||
0.288977 | + | 0.957336i | \(0.406685\pi\) | |||||||
\(998\) | −76.8621 | −2.43303 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.2.a.k.1.1 | yes | 20 | |
3.2 | odd | 2 | 2151.2.a.j.1.20 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.20 | ✓ | 20 | 3.2 | odd | 2 | ||
2151.2.a.k.1.1 | yes | 20 | 1.1 | even | 1 | trivial |