Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,4,Mod(1,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.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: | \(11.5643743611\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 6.08276 | 1.17063 | 0.585314 | − | 0.810807i | \(-0.300971\pi\) | ||||
0.585314 | + | 0.810807i | \(0.300971\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.1655 | −1.71422 | −0.857108 | − | 0.515136i | \(-0.827741\pi\) | ||||
−0.857108 | + | 0.515136i | \(0.827741\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 10.0000 | 0.370370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.5793 | −0.728543 | −0.364271 | − | 0.931293i | \(-0.618682\pi\) | ||||
−0.364271 | + | 0.931293i | \(0.618682\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.3311 | 0.220409 | 0.110205 | − | 0.993909i | \(-0.464849\pi\) | ||||
0.110205 | + | 0.993909i | \(0.464849\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −116.579 | −2.00671 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −101.331 | −1.44567 | −0.722835 | − | 0.691021i | \(-0.757161\pi\) | ||||
−0.722835 | + | 0.691021i | \(0.757161\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −93.7517 | −1.13201 | −0.566003 | − | 0.824403i | \(-0.691511\pi\) | ||||
−0.566003 | + | 0.824403i | \(0.691511\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.57934 | −0.0777789 | −0.0388895 | − | 0.999244i | \(-0.512382\pi\) | ||||
−0.0388895 | + | 0.999244i | \(0.512382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 242.317 | 1.93854 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −103.407 | −0.737062 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.3174 | 0.335003 | 0.167502 | − | 0.985872i | \(-0.446430\pi\) | ||||
0.167502 | + | 0.985872i | \(0.446430\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −55.4207 | −0.321092 | −0.160546 | − | 0.987028i | \(-0.551325\pi\) | ||||
−0.160546 | + | 0.987028i | \(0.551325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −161.676 | −0.852853 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 428.476 | 1.90381 | 0.951906 | − | 0.306391i | \(-0.0991215\pi\) | ||||
0.951906 | + | 0.306391i | \(0.0991215\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 62.8413 | 0.258017 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −137.007 | −0.521875 | −0.260938 | − | 0.965356i | \(-0.584032\pi\) | ||||
−0.260938 | + | 0.965356i | \(0.584032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −172.000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −191.655 | −0.634895 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −49.2414 | −0.152821 | −0.0764107 | − | 0.997076i | \(-0.524346\pi\) | ||||
−0.0764107 | + | 0.997076i | \(0.524346\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −616.373 | −1.69234 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −474.476 | −1.22970 | −0.614852 | − | 0.788643i | \(-0.710784\pi\) | ||||
−0.614852 | + | 0.788643i | \(0.710784\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 509.407 | 1.24888 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −570.269 | −1.32516 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 197.062 | 0.434836 | 0.217418 | − | 0.976079i | \(-0.430237\pi\) | ||||
0.217418 | + | 0.976079i | \(0.430237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −401.124 | −0.841946 | −0.420973 | − | 0.907073i | \(-0.638311\pi\) | ||||
−0.420973 | + | 0.907073i | \(0.638311\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −198.000 | −0.377829 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 125.421 | 0.228695 | 0.114348 | − | 0.993441i | \(-0.463522\pi\) | ||||
0.114348 | + | 0.993441i | \(0.463522\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −52.1861 | −0.0910502 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 788.635 | 1.31822 | 0.659111 | − | 0.752046i | \(-0.270933\pi\) | ||||
0.659111 | + | 0.752046i | \(0.270933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 604.655 | 0.969446 | 0.484723 | − | 0.874668i | \(-0.338920\pi\) | ||||
0.484723 | + | 0.874668i | \(0.338920\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1473.96 | 2.26931 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 783.007 | 1.11513 | 0.557565 | − | 0.830134i | \(-0.311736\pi\) | ||||
0.557565 | + | 0.830134i | \(0.311736\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −899.000 | −1.23320 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −339.283 | −0.448689 | −0.224344 | − | 0.974510i | \(-0.572024\pi\) | ||||
−0.224344 | + | 0.974510i | \(0.572024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1942.06 | 2.47819 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 318.234 | 0.392164 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 511.966 | 0.609756 | 0.304878 | − | 0.952391i | \(-0.401384\pi\) | ||||
0.304878 | + | 0.952391i | \(0.401384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −337.111 | −0.375879 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1796.80 | 1.94050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −672.290 | −0.703719 | −0.351859 | − | 0.936053i | \(-0.614450\pi\) | ||||
−0.351859 | + | 0.936053i | \(0.614450\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −265.793 | −0.269831 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 133.773 | 0.131791 | 0.0658955 | − | 0.997827i | \(-0.479010\pi\) | ||||
0.0658955 | + | 0.997827i | \(0.479010\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1160.74 | 1.11040 | 0.555202 | − | 0.831716i | \(-0.312641\pi\) | ||||
0.555202 | + | 0.831716i | \(0.312641\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1308.79 | −1.18248 | −0.591239 | − | 0.806497i | \(-0.701361\pi\) | ||||
−0.591239 | + | 0.806497i | \(0.701361\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1045.84 | −0.919022 | −0.459511 | − | 0.888172i | \(-0.651975\pi\) | ||||
−0.459511 | + | 0.888172i | \(0.651975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2606.32 | 2.22866 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −117.587 | −0.0978905 | −0.0489453 | − | 0.998801i | \(-0.515586\pi\) | ||||
−0.0489453 | + | 0.998801i | \(0.515586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 164.428 | 0.133330 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 103.311 | 0.0816330 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −624.539 | −0.469225 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −833.380 | −0.610922 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2248.45 | −1.60886 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1788.63 | −1.24973 | −0.624865 | − | 0.780733i | \(-0.714846\pi\) | ||||
−0.624865 | + | 0.780733i | \(0.714846\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1046.24 | −0.714077 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1949.28 | −1.30007 | −0.650037 | − | 0.759903i | \(-0.725247\pi\) | ||||
−0.650037 | + | 0.759903i | \(0.725247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1981.85 | 1.26348 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −571.539 | −0.356422 | −0.178211 | − | 0.983992i | \(-0.557031\pi\) | ||||
−0.178211 | + | 0.983992i | \(0.557031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1176.58 | 0.717958 | 0.358979 | − | 0.933346i | \(-0.383125\pi\) | ||||
0.358979 | + | 0.933346i | \(0.383125\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −299.524 | −0.178897 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −274.592 | −0.160577 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1002.69 | −0.574268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1773.33 | 0.975014 | 0.487507 | − | 0.873119i | \(-0.337906\pi\) | ||||
0.487507 | + | 0.873119i | \(0.337906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −503.007 | −0.271087 | −0.135544 | − | 0.990771i | \(-0.543278\pi\) | ||||
−0.135544 | + | 0.990771i | \(0.543278\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1013.31 | −0.535433 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1062.17 | 0.550421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2336.31 | 1.18763 | 0.593815 | − | 0.804601i | \(-0.297621\pi\) | ||||
0.593815 | + | 0.804601i | \(0.297621\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2886.12 | −1.43953 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1736.59 | −0.834482 | −0.417241 | − | 0.908796i | \(-0.637003\pi\) | ||||
−0.417241 | + | 0.908796i | \(0.637003\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3098.60 | 1.46197 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 668.331 | 0.309683 | 0.154841 | − | 0.987939i | \(-0.450513\pi\) | ||||
0.154841 | + | 0.987939i | \(0.450513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2090.27 | −0.951420 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −937.517 | −0.419262 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2145.23 | −0.942769 | −0.471385 | − | 0.881928i | \(-0.656246\pi\) | ||||
−0.471385 | + | 0.881928i | \(0.656246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1198.68 | 0.509031 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3767.55 | 1.57318 | 0.786591 | − | 0.617474i | \(-0.211844\pi\) | ||||
0.786591 | + | 0.617474i | \(0.211844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1752.51 | −0.719686 | −0.359843 | − | 0.933013i | \(-0.617170\pi\) | ||||
−0.359843 | + | 0.933013i | \(0.617170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2439.94 | −0.985606 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8211.97 | −3.26355 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2693.31 | 1.05323 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2011.12 | −0.761882 | −0.380941 | − | 0.924599i | \(-0.624400\pi\) | ||||
−0.380941 | + | 0.924599i | \(0.624400\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1579.95 | −0.589261 | −0.294631 | − | 0.955611i | \(-0.595197\pi\) | ||||
−0.294631 | + | 0.955611i | \(0.595197\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1204.39 | −0.442297 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.4132 | −0.00955262 | −0.00477631 | − | 0.999989i | \(-0.501520\pi\) | ||||
−0.00477631 | + | 0.999989i | \(0.501520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −57.5462 | −0.0204992 | −0.0102496 | − | 0.999947i | \(-0.503263\pi\) | ||||
−0.0102496 | + | 0.999947i | \(0.503263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 762.904 | 0.267717 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2625.81 | 0.894607 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −85.7934 | −0.0288070 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2491.86 | 0.824715 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1193.90 | −0.389534 | −0.194767 | − | 0.980850i | \(-0.562395\pi\) | ||||
−0.194767 | + | 0.980850i | \(0.562395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4797.08 | 1.54315 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3296.47 | 1.04566 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3677.97 | 1.13486 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1046.86 | −0.318639 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2921.66 | −0.877348 | −0.438674 | − | 0.898646i | \(-0.644552\pi\) | ||||
−0.438674 | + | 0.898646i | \(0.644552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2423.17 | 0.717977 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3112.34 | −0.910016 | −0.455008 | − | 0.890487i | \(-0.650364\pi\) | ||||
−0.455008 | + | 0.890487i | \(0.650364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5335.31 | −1.53959 | −0.769797 | − | 0.638289i | \(-0.779643\pi\) | ||||
−0.769797 | + | 0.638289i | \(0.779643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5238.08 | −1.47278 | −0.736390 | − | 0.676557i | \(-0.763471\pi\) | ||||
−0.736390 | + | 0.676557i | \(0.763471\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 943.738 | 0.261969 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4762.85 | 1.30540 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4181.05 | 1.13159 | 0.565794 | − | 0.824547i | \(-0.308570\pi\) | ||||
0.565794 | + | 0.824547i | \(0.308570\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5464.88 | 1.46068 | 0.730340 | − | 0.683084i | \(-0.239362\pi\) | ||||
0.730340 | + | 0.683084i | \(0.239362\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2676.42 | −0.706552 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −968.554 | −0.249504 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2063.78 | −0.525248 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5718.95 | −1.43816 | −0.719078 | − | 0.694930i | \(-0.755436\pi\) | ||||
−0.719078 | + | 0.694930i | \(0.755436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 228.033 | 0.0566653 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11813.1 | 2.90104 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1018.28 | 0.247154 | 0.123577 | − | 0.992335i | \(-0.460563\pi\) | ||||
0.123577 | + | 0.992335i | \(0.460563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 523.174 | 0.124075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8224.31 | −1.92826 | −0.964130 | − | 0.265430i | \(-0.914486\pi\) | ||||
−0.964130 | + | 0.265430i | \(0.914486\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9093.58 | 2.10798 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3114.17 | 0.713797 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5867.88 | −1.33000 | −0.665002 | − | 0.746841i | \(-0.731569\pi\) | ||||
−0.665002 | + | 0.746841i | \(0.731569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6216.77 | 1.39351 | 0.696757 | − | 0.717307i | \(-0.254626\pi\) | ||||
0.696757 | + | 0.717307i | \(0.254626\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6440.63 | −1.41231 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1477.52 | 0.320490 | 0.160245 | − | 0.987077i | \(-0.448772\pi\) | ||||
0.160245 | + | 0.987077i | \(0.448772\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −554.207 | −0.118923 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3611.93 | −0.766797 | −0.383398 | − | 0.923583i | \(-0.625246\pi\) | ||||
−0.383398 | + | 0.923583i | \(0.625246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7628.07 | −1.60227 | −0.801134 | − | 0.598485i | \(-0.795770\pi\) | ||||
−0.801134 | + | 0.598485i | \(0.795770\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10929.5 | 2.27161 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5354.98 | 1.08996 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4089.38 | −0.823793 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5393.67 | −1.07543 | −0.537716 | − | 0.843126i | \(-0.680713\pi\) | ||||
−0.537716 | + | 0.843126i | \(0.680713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3776.80 | −0.745403 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2748.49 | 0.536981 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −88.6336 | −0.0171432 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 813.708 | 0.154278 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7687.76 | 1.44328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8054.16 | 1.49731 | 0.748656 | − | 0.662958i | \(-0.230699\pi\) | ||||
0.748656 | + | 0.662958i | \(0.230699\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7060.54 | 1.29987 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2284.61 | 0.416554 | 0.208277 | − | 0.978070i | \(-0.433215\pi\) | ||||
0.208277 | + | 0.978070i | \(0.433215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8336.13 | 1.50539 | 0.752694 | − | 0.658371i | \(-0.228754\pi\) | ||||
0.752694 | + | 0.658371i | \(0.228754\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10416.2 | −1.84552 | −0.922762 | − | 0.385369i | \(-0.874074\pi\) | ||||
−0.922762 | + | 0.385369i | \(0.874074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1390.56 | −0.244064 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7961.03 | −1.38424 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9499.96 | 1.63651 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2503.39 | 0.427272 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6361.60 | −1.07583 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6943.88 | 1.15308 | 0.576541 | − | 0.817068i | \(-0.304402\pi\) | ||||
0.576541 | + | 0.817068i | \(0.304402\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4284.76 | 0.705115 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2403.75 | −0.392033 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4951.93 | 0.800442 | 0.400221 | − | 0.916419i | \(-0.368933\pi\) | ||||
0.400221 | + | 0.916419i | \(0.368933\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −715.252 | −0.114593 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1473.04 | 0.233929 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1000.17 | 0.156080 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7275.35 | 1.12554 | 0.562769 | − | 0.826614i | \(-0.309736\pi\) | ||||
0.562769 | + | 0.826614i | \(0.309736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3433.29 | 0.526589 | 0.263294 | − | 0.964716i | \(-0.415191\pi\) | ||||
0.263294 | + | 0.964716i | \(0.415191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1068.30 | −0.162455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6159.09 | 0.928655 | 0.464328 | − | 0.885664i | \(-0.346296\pi\) | ||||
0.464328 | + | 0.885664i | \(0.346296\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15114.6 | −2.25972 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8006.62 | 1.17708 | 0.588542 | − | 0.808466i | \(-0.299702\pi\) | ||||
0.588542 | + | 0.808466i | \(0.299702\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1930.38 | 0.281438 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3798.92 | −0.549288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11588.5 | −1.66184 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1184.49 | 0.168474 | 0.0842372 | − | 0.996446i | \(-0.473155\pi\) | ||||
0.0842372 | + | 0.996446i | \(0.473155\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1370.07 | −0.193287 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −944.218 | −0.131072 | −0.0655359 | − | 0.997850i | \(-0.520876\pi\) | ||||
−0.0655359 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13676.8 | −1.88338 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 540.493 | 0.0738377 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2906.32 | −0.393898 | −0.196949 | − | 0.980414i | \(-0.563103\pi\) | ||||
−0.196949 | + | 0.980414i | \(0.563103\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10879.8 | −1.46297 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1146.84 | −0.153005 | −0.0765023 | − | 0.997069i | \(-0.524375\pi\) | ||||
−0.0765023 | + | 0.997069i | \(0.524375\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1720.00 | −0.225924 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5589.49 | −0.728530 | −0.364265 | − | 0.931295i | \(-0.618680\pi\) | ||||
−0.364265 | + | 0.931295i | \(0.618680\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 869.353 | 0.112443 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11857.0 | −1.52190 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15006.7 | −1.91157 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3154.10 | 0.398740 | 0.199370 | − | 0.979924i | \(-0.436110\pi\) | ||||
0.199370 | + | 0.979924i | \(0.436110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6391.76 | −0.795983 | −0.397992 | − | 0.917389i | \(-0.630293\pi\) | ||||
−0.397992 | + | 0.917389i | \(0.630293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −572.554 | −0.0707715 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17229.8 | 2.11397 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11388.6 | −1.38701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 196.630 | 0.0237720 | 0.0118860 | − | 0.999929i | \(-0.496216\pi\) | ||||
0.0118860 | + | 0.999929i | \(0.496216\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3476.53 | −0.417238 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6502.54 | 0.769150 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7156.86 | 0.840462 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15699.9 | −1.83052 | −0.915262 | − | 0.402858i | \(-0.868017\pi\) | ||||
−0.915262 | + | 0.402858i | \(0.868017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8097.20 | −0.937372 | −0.468686 | − | 0.883365i | \(-0.655272\pi\) | ||||
−0.468686 | + | 0.883365i | \(0.655272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −492.414 | −0.0566005 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24554.3 | −2.80249 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1670.28 | −0.187976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11578.4 | 1.29399 | 0.646995 | − | 0.762494i | \(-0.276026\pi\) | ||||
0.646995 | + | 0.762494i | \(0.276026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7270.25 | −0.806896 | −0.403448 | − | 0.915003i | \(-0.632188\pi\) | ||||
−0.403448 | + | 0.915003i | \(0.632188\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6099.12 | −0.672254 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 804.328 | 0.0880462 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4127.39 | −0.448723 | −0.224362 | − | 0.974506i | \(-0.572030\pi\) | ||||
−0.224362 | + | 0.974506i | \(0.572030\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −190.439 | −0.0204244 | −0.0102122 | − | 0.999948i | \(-0.503251\pi\) | ||||
−0.0102122 | + | 0.999948i | \(0.503251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9812.09 | −1.04525 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10786.8 | 1.14138 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17175.2 | 1.80523 | 0.902613 | − | 0.430454i | \(-0.141646\pi\) | ||||
0.902613 | + | 0.430454i | \(0.141646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3641.55 | 0.380208 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3059.67 | −0.317342 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3505.80 | −0.358850 | −0.179425 | − | 0.983772i | \(-0.557424\pi\) | ||||
−0.179425 | + | 0.983772i | \(0.557424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10478.3 | 1.06555 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5983.80 | 0.604541 | 0.302270 | − | 0.953222i | \(-0.402255\pi\) | ||||
0.302270 | + | 0.953222i | \(0.402255\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14057.4 | 1.41102 | 0.705510 | − | 0.708700i | \(-0.250718\pi\) | ||||
0.705510 | + | 0.708700i | \(0.250718\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6460.90 | 0.644338 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18773.8 | 1.86027 | 0.930137 | − | 0.367211i | \(-0.119687\pi\) | ||||
0.930137 | + | 0.367211i | \(0.119687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14211.2 | 1.39027 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4571.65 | 0.444407 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22717.7 | −2.19444 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4744.76 | −0.455446 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 263.773 | 0.0251610 | 0.0125805 | − | 0.999921i | \(-0.495995\pi\) | ||||
0.0125805 | + | 0.999921i | \(0.495995\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4426.61 | 0.419617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12884.8 | 1.20633 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12654.9 | 1.17751 | 0.588757 | − | 0.808310i | \(-0.299617\pi\) | ||||
0.588757 | + | 0.808310i | \(0.299617\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10563.3 | −0.976868 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19041.6 | 1.75017 | 0.875087 | − | 0.483965i | \(-0.160804\pi\) | ||||
0.875087 | + | 0.483965i | \(0.160804\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5301.37 | −0.484304 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5094.07 | 0.462548 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17999.4 | −1.61476 | −0.807378 | − | 0.590035i | \(-0.799114\pi\) | ||||
−0.807378 | + | 0.590035i | \(0.799114\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4065.30 | 0.362523 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15245.1 | 1.35139 | 0.675693 | − | 0.737183i | \(-0.263845\pi\) | ||||
0.675693 | + | 0.737183i | \(0.263845\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2563.83 | −0.225918 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12714.6 | −1.11376 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4807.85 | 0.418672 | 0.209336 | − | 0.977844i | \(-0.432870\pi\) | ||||
0.209336 | + | 0.977844i | \(0.432870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9694.58 | 0.834359 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22246.3 | −1.90347 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1308.80 | 0.111337 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13048.9 | −1.10363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −300.226 | −0.0252460 | −0.0126230 | − | 0.999920i | \(-0.504018\pi\) | ||||
−0.0126230 | + | 0.999920i | \(0.504018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 795.488 | 0.0665091 | 0.0332546 | − | 0.999447i | \(-0.489413\pi\) | ||||
0.0332546 | + | 0.999447i | \(0.489413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5615.83 | 0.464193 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12093.4 | −0.993950 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1970.62 | 0.161050 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1415.42 | −0.115026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25083.6 | 2.02702 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22917.1 | 1.84161 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18669.7 | −1.48368 | −0.741841 | − | 0.670576i | \(-0.766047\pi\) | ||||
−0.741841 | + | 0.670576i | \(0.766047\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10660.1 | −0.842485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20044.1 | 1.57540 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3264.72 | −0.255191 | −0.127596 | − | 0.991826i | \(-0.540726\pi\) | ||||
−0.127596 | + | 0.991826i | \(0.540726\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4011.24 | −0.311832 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4904.84 | −0.379226 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −49951.5 | −3.82040 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13404.7 | 1.01970 | 0.509852 | − | 0.860262i | \(-0.329700\pi\) | ||||
0.509852 | + | 0.860262i | \(0.329700\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1776.94 | −0.134448 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16382.8 | 1.23294 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9299.00 | 0.696103 | 0.348051 | − | 0.937475i | \(-0.386843\pi\) | ||||
0.348051 | + | 0.937475i | \(0.386843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2253.61 | 0.167806 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20197.8 | 1.48811 | 0.744055 | − | 0.668119i | \(-0.232900\pi\) | ||||
0.744055 | + | 0.668119i | \(0.232900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9413.56 | −0.689922 | −0.344961 | − | 0.938617i | \(-0.612108\pi\) | ||||
−0.344961 | + | 0.938617i | \(0.612108\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12233.2 | −0.891880 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2078.92 | −0.150777 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7737.70 | 0.558275 | 0.279138 | − | 0.960251i | \(-0.409951\pi\) | ||||
0.279138 | + | 0.960251i | \(0.409951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9610.47 | −0.689806 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12611.3 | 0.895892 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1980.00 | −0.139937 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16755.0 | 1.17811 | 0.589057 | − | 0.808091i | \(-0.299499\pi\) | ||||
0.589057 | + | 0.808091i | \(0.299499\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5195.78 | 0.363478 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −160.666 | −0.0111826 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11772.9 | −0.815270 | −0.407635 | − | 0.913145i | \(-0.633646\pi\) | ||||
−0.407635 | + | 0.913145i | \(0.633646\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −350.040 | −0.0239970 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25259.3 | −1.72299 | −0.861493 | − | 0.507769i | \(-0.830470\pi\) | ||||
−0.861493 | + | 0.507769i | \(0.830470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 187.801 | 0.0127464 | 0.00637319 | − | 0.999980i | \(-0.497971\pi\) | ||||
0.00637319 | + | 0.999980i | \(0.497971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1254.21 | 0.0847019 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11969.6 | 0.804354 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17655.3 | 1.18057 | 0.590284 | − | 0.807196i | \(-0.299016\pi\) | ||||
0.590284 | + | 0.807196i | \(0.299016\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −508.716 | −0.0336832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1004.93 | −0.0662130 | −0.0331065 | − | 0.999452i | \(-0.510540\pi\) | ||||
−0.0331065 | + | 0.999452i | \(0.510540\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15972.2 | 1.04725 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8416.05 | 0.549137 | 0.274568 | − | 0.961568i | \(-0.411465\pi\) | ||||
0.274568 | + | 0.961568i | \(0.411465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6285.24 | 0.408118 | 0.204059 | − | 0.978959i | \(-0.434587\pi\) | ||||
0.204059 | + | 0.978959i | \(0.434587\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 887.163 | 0.0573279 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12803.0 | 0.819394 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15157.4 | 0.965435 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43417.9 | −2.75228 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15928.9 | 1.00495 | 0.502473 | − | 0.864593i | \(-0.332424\pi\) | ||||
0.502473 | + | 0.864593i | \(0.332424\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7262.24 | −0.456000 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34280.1 | 2.14231 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7886.35 | 0.488230 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12683.0 | −0.781513 | −0.390756 | − | 0.920494i | \(-0.627787\pi\) | ||||
−0.390756 | + | 0.920494i | \(0.627787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1461.21 | −0.0896179 | −0.0448090 | − | 0.998996i | \(-0.514268\pi\) | ||||
−0.0448090 | + | 0.998996i | \(0.514268\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20051.6 | 1.22408 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24001.4 | 1.45841 | 0.729206 | − | 0.684294i | \(-0.239890\pi\) | ||||
0.729206 | + | 0.684294i | \(0.239890\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5237.78 | −0.316797 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9097.14 | 0.545174 | 0.272587 | − | 0.962131i | \(-0.412121\pi\) | ||||
0.272587 | + | 0.962131i | \(0.412121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 37359.0 | 2.22861 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6046.55 | 0.359054 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15018.0 | −0.887738 | −0.443869 | − | 0.896092i | \(-0.646394\pi\) | ||||
−0.443869 | + | 0.896092i | \(0.646394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24497.2 | −1.44150 | −0.720748 | − | 0.693197i | \(-0.756202\pi\) | ||||
−0.720748 | + | 0.693197i | \(0.756202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6367.78 | −0.373008 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −448.848 | −0.0260562 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17771.7 | −1.02705 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10661.6 | 0.613394 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1378.86 | 0.0789762 | 0.0394881 | − | 0.999220i | \(-0.487427\pi\) | ||||
0.0394881 | + | 0.999220i | \(0.487427\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25057.3 | −1.42882 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12535.0 | −0.711607 | −0.355804 | − | 0.934561i | \(-0.615793\pi\) | ||||
−0.355804 | + | 0.934561i | \(0.615793\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18931.7 | −1.06529 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27054.1 | 1.51566 | 0.757830 | − | 0.652452i | \(-0.226259\pi\) | ||||
0.757830 | + | 0.652452i | \(0.226259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10953.8 | 0.610985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32453.4 | −1.80229 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4901.84 | −0.271038 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25843.5 | −1.42277 | −0.711385 | − | 0.702803i | \(-0.751932\pi\) | ||||
−0.711385 | + | 0.702803i | \(0.751932\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22549.8 | −1.23074 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13883.0 | 0.754459 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31862.0 | −1.72408 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29351.6 | −1.58145 | −0.790723 | − | 0.612174i | \(-0.790295\pi\) | ||||
−0.790723 | + | 0.612174i | \(0.790295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40170.4 | −2.15513 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5740.53 | 0.306668 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17013.4 | −0.901202 | −0.450601 | − | 0.892725i | \(-0.648790\pi\) | ||||
−0.450601 | + | 0.892725i | \(0.648790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7830.07 | 0.413011 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 475.473 | 0.0249742 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5262.71 | 0.275265 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25432.3 | 1.32467 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14546.5 | 0.754510 | 0.377255 | − | 0.926109i | \(-0.376868\pi\) | ||||
0.377255 | + | 0.926109i | \(0.376868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33241.5 | 1.70991 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12677.4 | 0.649416 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25023.9 | 1.27660 | 0.638298 | − | 0.769790i | \(-0.279639\pi\) | ||||
0.638298 | + | 0.769790i | \(0.279639\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7993.00 | 0.406086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17428.9 | 0.881850 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12899.2 | −0.649988 | −0.324994 | − | 0.945716i | \(-0.605362\pi\) | ||||
−0.324994 | + | 0.945716i | \(0.605362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3333.60 | −0.166614 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15253.3 | −0.759270 | −0.379635 | − | 0.925136i | \(-0.623950\pi\) | ||||
−0.379635 | + | 0.925136i | \(0.623950\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5891.48 | −0.292077 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7984.56 | −0.394247 | −0.197123 | − | 0.980379i | \(-0.563160\pi\) | ||||
−0.197123 | + | 0.980379i | \(0.563160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33986.8 | −1.67138 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3392.83 | −0.166181 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32781.6 | 1.59283 | 0.796416 | − | 0.604750i | \(-0.206727\pi\) | ||||
0.796416 | + | 0.604750i | \(0.206727\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −34787.0 | −1.68355 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9640.40 | 0.464702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16431.5 | −0.788920 | −0.394460 | − | 0.918913i | \(-0.629068\pi\) | ||||
−0.394460 | + | 0.918913i | \(0.629068\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1387.07 | 0.0663340 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33858.3 | −1.61283 | −0.806415 | − | 0.591350i | \(-0.798595\pi\) | ||||
−0.806415 | + | 0.591350i | \(0.798595\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19420.6 | 0.917849 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2035.86 | 0.0958418 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36173.6 | −1.69630 | −0.848149 | − | 0.529758i | \(-0.822283\pi\) | ||||
−0.848149 | + | 0.529758i | \(0.822283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6193.96 | 0.289326 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20812.8 | 0.968416 | 0.484208 | − | 0.874953i | \(-0.339108\pi\) | ||||
0.484208 | + | 0.874953i | \(0.339108\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13429.4 | −0.622449 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12844.6 | 0.590766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20961.4 | −0.960381 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5409.98 | −0.246918 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44776.6 | −2.03586 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29722.2 | −1.34623 | −0.673114 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673114 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −50026.5 | −2.25728 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4144.04 | −0.185573 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 55314.1 | 2.46766 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6475.82 | 0.287811 | 0.143905 | − | 0.989591i | \(-0.454034\pi\) | ||||
0.143905 | + | 0.989591i | \(0.454034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4989.69 | 0.220929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5119.66 | 0.225835 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16071.3 | −0.706283 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35692.9 | −1.55694 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39418.9 | −1.71309 | −0.856547 | − | 0.516069i | \(-0.827395\pi\) | ||||
−0.856547 | + | 0.516069i | \(0.827395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38728.6 | 1.67688 | 0.838438 | − | 0.544997i | \(-0.183469\pi\) | ||||
0.838438 | + | 0.544997i | \(0.183469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37815.2 | 1.63129 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33282.7 | 1.43048 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16125.3 | 0.690517 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32010.0 | 1.36073 | 0.680363 | − | 0.732876i | \(-0.261822\pi\) | ||||
0.680363 | + | 0.732876i | \(0.261822\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10137.8 | 0.429384 | 0.214692 | − | 0.976682i | \(-0.431125\pi\) | ||||
0.214692 | + | 0.976682i | \(0.431125\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39176.9 | −1.65329 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9064.96 | 0.381160 | 0.190580 | − | 0.981672i | \(-0.438963\pi\) | ||||
0.190580 | + | 0.981672i | \(0.438963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19310.3 | 0.809017 | 0.404508 | − | 0.914534i | \(-0.367443\pi\) | ||||
0.404508 | + | 0.914534i | \(0.367443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8987.43 | 0.375175 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12808.9 | −0.530863 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5730.88 | 0.236665 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11458.4 | 0.471498 | 0.235749 | − | 0.971814i | \(-0.424246\pi\) | ||||
0.235749 | + | 0.971814i | \(0.424246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21651.9 | −0.887773 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21970.5 | −0.897634 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40061.1 | 1.63094 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −46399.8 | −1.87566 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3676.04 | −0.148076 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6203.94 | 0.249026 | 0.124513 | − | 0.992218i | \(-0.460263\pi\) | ||||
0.124513 | + | 0.992218i | \(0.460263\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17968.0 | 0.718705 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15577.8 | −0.620920 | −0.310460 | − | 0.950587i | \(-0.600483\pi\) | ||||
−0.310460 | + | 0.950587i | \(0.600483\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11893.7 | −0.472420 | −0.236210 | − | 0.971702i | \(-0.575905\pi\) | ||||
−0.236210 | + | 0.971702i | \(0.575905\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11673.6 | −0.460455 | −0.230227 | − | 0.973137i | \(-0.573947\pi\) | ||||
−0.230227 | + | 0.973137i | \(0.573947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41114.5 | 1.61611 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32573.1 | 1.27594 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20811.8 | −0.812420 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1295.73 | 0.0504065 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6722.90 | −0.260637 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3063.66 | −0.117962 | −0.0589808 | − | 0.998259i | \(-0.518785\pi\) | ||||
−0.0589808 | + | 0.998259i | \(0.518785\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32808.4 | −1.25893 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19236.9 | 0.735649 | 0.367825 | − | 0.929895i | \(-0.380103\pi\) | ||||
0.367825 | + | 0.929895i | \(0.380103\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35556.9 | −1.35514 | −0.677569 | − | 0.735459i | \(-0.736966\pi\) | ||||
−0.677569 | + | 0.735459i | \(0.736966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22973.4 | −0.872590 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23218.8 | 0.878928 | 0.439464 | − | 0.898260i | \(-0.355168\pi\) | ||||
0.439464 | + | 0.898260i | \(0.355168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23894.8 | 0.898436 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4616.47 | 0.172995 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −72207.0 | −2.69678 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −539.137 | −0.0200683 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2899.46 | −0.107567 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48079.2 | 1.77775 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33587.8 | 1.23370 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20516.7 | −0.751098 | −0.375549 | − | 0.926803i | \(-0.622546\pi\) | ||||
−0.375549 | + | 0.926803i | \(0.622546\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1337.73 | 0.0488115 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18247.6 | 0.663634 | 0.331817 | − | 0.943344i | \(-0.392338\pi\) | ||||
0.331817 | + | 0.943344i | \(0.392338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9017.92 | 0.326889 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 46762.8 | 1.68954 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27362.2 | −0.982149 | −0.491074 | − | 0.871118i | \(-0.663396\pi\) | ||||
−0.491074 | + | 0.871118i | \(0.663396\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48991.5 | 1.75280 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8147.42 | 0.290548 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 103827. | 3.69061 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11607.4 | 0.411261 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43542.6 | 1.53777 | 0.768884 | − | 0.639389i | \(-0.220813\pi\) | ||||
0.768884 | + | 0.639389i | \(0.220813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13896.7 | 0.487629 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −51618.7 | −1.80547 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32990.1 | 1.15020 | 0.575101 | − | 0.818083i | \(-0.304963\pi\) | ||||
0.575101 | + | 0.818083i | \(0.304963\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 50706.7 | 1.76225 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17311.6 | −0.599726 | −0.299863 | − | 0.953982i | \(-0.596941\pi\) | ||||
−0.299863 | + | 0.953982i | \(0.596941\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1175.43 | 0.0405909 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1335.71 | −0.0458339 | −0.0229169 | − | 0.999737i | \(-0.507295\pi\) | ||||
−0.0229169 | + | 0.999737i | \(0.507295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6246.72 | 0.213675 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −63359.2 | −2.16042 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18877.6 | 0.641663 | 0.320831 | − | 0.947136i | \(-0.396038\pi\) | ||||
0.320831 | + | 0.947136i | \(0.396038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38544.1 | 1.30603 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8458.45 | −0.285708 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26719.6 | −0.896900 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13087.9 | −0.437955 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 30280.6 | 1.01012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39814.6 | −1.32405 | −0.662023 | − | 0.749483i | \(-0.730302\pi\) | ||||
−0.662023 | + | 0.749483i | \(0.730302\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 57786.0 | 1.91574 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22844.8 | −0.755021 | −0.377511 | − | 0.926005i | \(-0.623220\pi\) | ||||
−0.377511 | + | 0.926005i | \(0.623220\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15227.5 | 0.500176 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24396.6 | 0.798891 | 0.399446 | − | 0.916757i | \(-0.369203\pi\) | ||||
0.399446 | + | 0.916757i | \(0.369203\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13607.7 | −0.444233 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10458.4 | −0.340379 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32975.5 | 1.06994 | 0.534972 | − | 0.844870i | \(-0.320322\pi\) | ||||
0.534972 | + | 0.844870i | \(0.320322\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 506.224 | 0.0163753 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1475.65 | 0.0474447 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11877.1 | −0.380717 | −0.190358 | − | 0.981715i | \(-0.560965\pi\) | ||||
−0.190358 | + | 0.981715i | \(0.560965\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42238.0 | 1.34983 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1102.90 | 0.0351401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16386.3 | 0.520522 | 0.260261 | − | 0.965538i | \(-0.416191\pi\) | ||||
0.260261 | + | 0.965538i | \(0.416191\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44307.4 | −1.40323 |
(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 | 196.4.a.e.1.2 | 2 | ||
3.2 | odd | 2 | 1764.4.a.z.1.2 | 2 | |||
4.3 | odd | 2 | 784.4.a.u.1.1 | 2 | |||
7.2 | even | 3 | 28.4.e.a.25.1 | yes | 4 | ||
7.3 | odd | 6 | 196.4.e.g.177.2 | 4 | |||
7.4 | even | 3 | 28.4.e.a.9.1 | ✓ | 4 | ||
7.5 | odd | 6 | 196.4.e.g.165.2 | 4 | |||
7.6 | odd | 2 | 196.4.a.g.1.1 | 2 | |||
21.2 | odd | 6 | 252.4.k.c.109.1 | 4 | |||
21.5 | even | 6 | 1764.4.k.ba.361.2 | 4 | |||
21.11 | odd | 6 | 252.4.k.c.37.1 | 4 | |||
21.17 | even | 6 | 1764.4.k.ba.1549.2 | 4 | |||
21.20 | even | 2 | 1764.4.a.n.1.1 | 2 | |||
28.11 | odd | 6 | 112.4.i.d.65.2 | 4 | |||
28.23 | odd | 6 | 112.4.i.d.81.2 | 4 | |||
28.27 | even | 2 | 784.4.a.ba.1.2 | 2 | |||
35.2 | odd | 12 | 700.4.r.d.249.4 | 8 | |||
35.4 | even | 6 | 700.4.i.g.401.2 | 4 | |||
35.9 | even | 6 | 700.4.i.g.501.2 | 4 | |||
35.18 | odd | 12 | 700.4.r.d.149.4 | 8 | |||
35.23 | odd | 12 | 700.4.r.d.249.1 | 8 | |||
35.32 | odd | 12 | 700.4.r.d.149.1 | 8 | |||
56.11 | odd | 6 | 448.4.i.g.65.1 | 4 | |||
56.37 | even | 6 | 448.4.i.h.193.2 | 4 | |||
56.51 | odd | 6 | 448.4.i.g.193.1 | 4 | |||
56.53 | even | 6 | 448.4.i.h.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.e.a.9.1 | ✓ | 4 | 7.4 | even | 3 | ||
28.4.e.a.25.1 | yes | 4 | 7.2 | even | 3 | ||
112.4.i.d.65.2 | 4 | 28.11 | odd | 6 | |||
112.4.i.d.81.2 | 4 | 28.23 | odd | 6 | |||
196.4.a.e.1.2 | 2 | 1.1 | even | 1 | trivial | ||
196.4.a.g.1.1 | 2 | 7.6 | odd | 2 | |||
196.4.e.g.165.2 | 4 | 7.5 | odd | 6 | |||
196.4.e.g.177.2 | 4 | 7.3 | odd | 6 | |||
252.4.k.c.37.1 | 4 | 21.11 | odd | 6 | |||
252.4.k.c.109.1 | 4 | 21.2 | odd | 6 | |||
448.4.i.g.65.1 | 4 | 56.11 | odd | 6 | |||
448.4.i.g.193.1 | 4 | 56.51 | odd | 6 | |||
448.4.i.h.65.2 | 4 | 56.53 | even | 6 | |||
448.4.i.h.193.2 | 4 | 56.37 | even | 6 | |||
700.4.i.g.401.2 | 4 | 35.4 | even | 6 | |||
700.4.i.g.501.2 | 4 | 35.9 | even | 6 | |||
700.4.r.d.149.1 | 8 | 35.32 | odd | 12 | |||
700.4.r.d.149.4 | 8 | 35.18 | odd | 12 | |||
700.4.r.d.249.1 | 8 | 35.23 | odd | 12 | |||
700.4.r.d.249.4 | 8 | 35.2 | odd | 12 | |||
784.4.a.u.1.1 | 2 | 4.3 | odd | 2 | |||
784.4.a.ba.1.2 | 2 | 28.27 | even | 2 | |||
1764.4.a.n.1.1 | 2 | 21.20 | even | 2 | |||
1764.4.a.z.1.2 | 2 | 3.2 | odd | 2 | |||
1764.4.k.ba.361.2 | 4 | 21.5 | even | 6 | |||
1764.4.k.ba.1549.2 | 4 | 21.17 | even | 6 |