Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,4,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, 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("2025.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.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: | \(119.478867762\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 64 x^{10} + 241 x^{9} + 1452 x^{8} - 5130 x^{7} - 13834 x^{6} + 45247 x^{5} + 52669 x^{4} - 144610 x^{3} - 96816 x^{2} + 143136 x + 73008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 225) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.38827\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38827 | −0.490828 | −0.245414 | − | 0.969418i | \(-0.578924\pi\) | ||||
−0.245414 | + | 0.969418i | \(0.578924\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.07270 | −0.759088 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.4332 | −1.42726 | −0.713631 | − | 0.700522i | \(-0.752950\pi\) | ||||
−0.713631 | + | 0.700522i | \(0.752950\pi\) | |||||||
\(8\) | 19.5367 | 0.863410 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −62.0909 | −1.70192 | −0.850959 | − | 0.525232i | \(-0.823979\pi\) | ||||
−0.850959 | + | 0.525232i | \(0.823979\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.6621 | 1.08086 | 0.540428 | − | 0.841390i | \(-0.318262\pi\) | ||||
0.540428 | + | 0.841390i | \(0.318262\pi\) | |||||||
\(14\) | 36.6965 | 0.700540 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 21.4593 | 0.335302 | ||||||||
\(17\) | 40.9457 | 0.584165 | 0.292082 | − | 0.956393i | \(-0.405652\pi\) | ||||
0.292082 | + | 0.956393i | \(0.405652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −139.322 | −1.68224 | −0.841120 | − | 0.540849i | \(-0.818103\pi\) | ||||
−0.841120 | + | 0.540849i | \(0.818103\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 86.1990 | 0.835349 | ||||||||
\(23\) | 60.7057 | 0.550348 | 0.275174 | − | 0.961394i | \(-0.411265\pi\) | ||||
0.275174 | + | 0.961394i | \(0.411265\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −70.3328 | −0.530515 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 160.521 | 1.08342 | ||||||||
\(29\) | 175.339 | 1.12274 | 0.561372 | − | 0.827563i | \(-0.310274\pi\) | ||||
0.561372 | + | 0.827563i | \(0.310274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.9611 | 0.0808865 | 0.0404432 | − | 0.999182i | \(-0.487123\pi\) | ||||
0.0404432 | + | 0.999182i | \(0.487123\pi\) | |||||||
\(32\) | −186.085 | −1.02799 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −56.8438 | −0.286725 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −144.558 | −0.642303 | −0.321152 | − | 0.947028i | \(-0.604070\pi\) | ||||
−0.321152 | + | 0.947028i | \(0.604070\pi\) | |||||||
\(38\) | 193.416 | 0.825691 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 414.449 | 1.57868 | 0.789342 | − | 0.613953i | \(-0.210422\pi\) | ||||
0.789342 | + | 0.613953i | \(0.210422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 191.900 | 0.680570 | 0.340285 | − | 0.940322i | \(-0.389476\pi\) | ||||
0.340285 | + | 0.940322i | \(0.389476\pi\) | |||||||
\(44\) | 377.059 | 1.29191 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −84.2759 | −0.270126 | ||||||||
\(47\) | −201.541 | −0.625485 | −0.312742 | − | 0.949838i | \(-0.601248\pi\) | ||||
−0.312742 | + | 0.949838i | \(0.601248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 355.716 | 1.03707 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −307.656 | −0.820465 | ||||||||
\(53\) | 114.667 | 0.297185 | 0.148592 | − | 0.988899i | \(-0.452526\pi\) | ||||
0.148592 | + | 0.988899i | \(0.452526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −516.419 | −1.23231 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −243.418 | −0.551075 | ||||||||
\(59\) | 313.338 | 0.691410 | 0.345705 | − | 0.938343i | \(-0.387640\pi\) | ||||
0.345705 | + | 0.938343i | \(0.387640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −382.137 | −0.802093 | −0.401046 | − | 0.916058i | \(-0.631353\pi\) | ||||
−0.401046 | + | 0.916058i | \(0.631353\pi\) | |||||||
\(62\) | −19.3817 | −0.0397013 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 86.6623 | 0.169262 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 321.266 | 0.585805 | 0.292903 | − | 0.956142i | \(-0.405379\pi\) | ||||
0.292903 | + | 0.956142i | \(0.405379\pi\) | |||||||
\(68\) | −248.651 | −0.443432 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 373.813 | 0.624837 | 0.312418 | − | 0.949945i | \(-0.398861\pi\) | ||||
0.312418 | + | 0.949945i | \(0.398861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 716.432 | 1.14866 | 0.574329 | − | 0.818624i | \(-0.305263\pi\) | ||||
0.574329 | + | 0.818624i | \(0.305263\pi\) | |||||||
\(74\) | 200.686 | 0.315261 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 846.058 | 1.27697 | ||||||||
\(77\) | 1641.26 | 2.42908 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 609.015 | 0.867336 | 0.433668 | − | 0.901073i | \(-0.357219\pi\) | ||||
0.433668 | + | 0.901073i | \(0.357219\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −575.368 | −0.774863 | ||||||||
\(83\) | −222.116 | −0.293740 | −0.146870 | − | 0.989156i | \(-0.546920\pi\) | ||||
−0.146870 | + | 0.989156i | \(0.546920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −266.410 | −0.334043 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1213.05 | −1.46945 | ||||||||
\(89\) | 175.854 | 0.209443 | 0.104722 | − | 0.994502i | \(-0.466605\pi\) | ||||
0.104722 | + | 0.994502i | \(0.466605\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1339.16 | −1.54266 | ||||||||
\(92\) | −368.647 | −0.417762 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 279.794 | 0.307006 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 546.993 | 0.572564 | 0.286282 | − | 0.958145i | \(-0.407581\pi\) | ||||
0.286282 | + | 0.958145i | \(0.407581\pi\) | |||||||
\(98\) | −493.831 | −0.509025 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1864.39 | −1.83677 | −0.918385 | − | 0.395689i | \(-0.870506\pi\) | ||||
−0.918385 | + | 0.395689i | \(0.870506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1521.04 | −1.45507 | −0.727535 | − | 0.686071i | \(-0.759334\pi\) | ||||
−0.727535 | + | 0.686071i | \(0.759334\pi\) | |||||||
\(104\) | 989.772 | 0.933222 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −159.190 | −0.145867 | ||||||||
\(107\) | 1042.82 | 0.942179 | 0.471090 | − | 0.882085i | \(-0.343861\pi\) | ||||
0.471090 | + | 0.882085i | \(0.343861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 995.777 | 0.875029 | 0.437515 | − | 0.899211i | \(-0.355859\pi\) | ||||
0.437515 | + | 0.899211i | \(0.355859\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −567.239 | −0.478563 | ||||||||
\(113\) | −1760.65 | −1.46573 | −0.732866 | − | 0.680373i | \(-0.761818\pi\) | ||||
−0.732866 | + | 0.680373i | \(0.761818\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1064.78 | −0.852262 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −434.999 | −0.339363 | ||||||||
\(119\) | −1082.33 | −0.833756 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2524.28 | 1.89653 | ||||||||
\(122\) | 530.510 | 0.393690 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −84.7813 | −0.0613999 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −156.362 | −0.109251 | −0.0546257 | − | 0.998507i | \(-0.517397\pi\) | ||||
−0.0546257 | + | 0.998507i | \(0.517397\pi\) | |||||||
\(128\) | 1368.37 | 0.944907 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 221.921 | 0.148010 | 0.0740050 | − | 0.997258i | \(-0.476422\pi\) | ||||
0.0740050 | + | 0.997258i | \(0.476422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3682.72 | 2.40100 | ||||||||
\(134\) | −446.005 | −0.287530 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 799.946 | 0.504374 | ||||||||
\(137\) | −1326.33 | −0.827126 | −0.413563 | − | 0.910476i | \(-0.635716\pi\) | ||||
−0.413563 | + | 0.910476i | \(0.635716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 853.570 | 0.520855 | 0.260428 | − | 0.965493i | \(-0.416136\pi\) | ||||
0.260428 | + | 0.965493i | \(0.416136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −518.954 | −0.306687 | ||||||||
\(143\) | −3145.65 | −1.83953 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −994.603 | −0.563794 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 877.859 | 0.487565 | ||||||||
\(149\) | 299.702 | 0.164782 | 0.0823911 | − | 0.996600i | \(-0.473744\pi\) | ||||
0.0823911 | + | 0.996600i | \(0.473744\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2892.42 | 1.55882 | 0.779411 | − | 0.626513i | \(-0.215518\pi\) | ||||
0.779411 | + | 0.626513i | \(0.215518\pi\) | |||||||
\(152\) | −2721.89 | −1.45246 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2278.52 | −1.19226 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1223.70 | 0.622049 | 0.311025 | − | 0.950402i | \(-0.399328\pi\) | ||||
0.311025 | + | 0.950402i | \(0.399328\pi\) | |||||||
\(158\) | −845.478 | −0.425713 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1604.65 | −0.785490 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1015.65 | 0.488047 | 0.244023 | − | 0.969769i | \(-0.421533\pi\) | ||||
0.244023 | + | 0.969769i | \(0.421533\pi\) | |||||||
\(164\) | −2516.83 | −1.19836 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 308.357 | 0.144176 | ||||||||
\(167\) | −3580.19 | −1.65894 | −0.829472 | − | 0.558549i | \(-0.811358\pi\) | ||||
−0.829472 | + | 0.558549i | \(0.811358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 369.648 | 0.168251 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1165.35 | −0.516613 | ||||||||
\(173\) | −3273.54 | −1.43863 | −0.719314 | − | 0.694685i | \(-0.755544\pi\) | ||||
−0.719314 | + | 0.694685i | \(0.755544\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1332.43 | −0.570656 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −244.133 | −0.102801 | ||||||||
\(179\) | −401.667 | −0.167720 | −0.0838602 | − | 0.996478i | \(-0.526725\pi\) | ||||
−0.0838602 | + | 0.996478i | \(0.526725\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1575.07 | −0.646816 | −0.323408 | − | 0.946260i | \(-0.604829\pi\) | ||||
−0.323408 | + | 0.946260i | \(0.604829\pi\) | |||||||
\(182\) | 1859.12 | 0.757183 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1185.99 | 0.475176 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2542.36 | −0.994201 | ||||||||
\(188\) | 1223.90 | 0.474798 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1152.15 | 0.436476 | 0.218238 | − | 0.975896i | \(-0.429969\pi\) | ||||
0.218238 | + | 0.975896i | \(0.429969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3515.12 | 1.31101 | 0.655503 | − | 0.755193i | \(-0.272457\pi\) | ||||
0.655503 | + | 0.755193i | \(0.272457\pi\) | |||||||
\(194\) | −759.375 | −0.281031 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2160.16 | −0.787230 | ||||||||
\(197\) | 2854.38 | 1.03232 | 0.516158 | − | 0.856493i | \(-0.327362\pi\) | ||||
0.516158 | + | 0.856493i | \(0.327362\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2961.76 | 1.05504 | 0.527521 | − | 0.849542i | \(-0.323122\pi\) | ||||
0.527521 | + | 0.849542i | \(0.323122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2588.28 | 0.901538 | ||||||||
\(203\) | −4634.77 | −1.60245 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2111.61 | 0.714189 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1087.17 | 0.362413 | ||||||||
\(209\) | 8650.60 | 2.86303 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4802.41 | −1.56688 | −0.783440 | − | 0.621467i | \(-0.786537\pi\) | ||||
−0.783440 | + | 0.621467i | \(0.786537\pi\) | |||||||
\(212\) | −696.341 | −0.225589 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1447.72 | −0.462448 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −369.036 | −0.115446 | ||||||||
\(218\) | −1382.41 | −0.429489 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2074.40 | 0.631398 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2114.30 | −0.634906 | −0.317453 | − | 0.948274i | \(-0.602828\pi\) | ||||
−0.317453 | + | 0.948274i | \(0.602828\pi\) | |||||||
\(224\) | 4918.84 | 1.46720 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2444.26 | 0.719422 | ||||||||
\(227\) | −3769.35 | −1.10212 | −0.551058 | − | 0.834467i | \(-0.685776\pi\) | ||||
−0.551058 | + | 0.834467i | \(0.685776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1373.72 | −0.396412 | −0.198206 | − | 0.980160i | \(-0.563511\pi\) | ||||
−0.198206 | + | 0.980160i | \(0.563511\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3425.55 | 0.969389 | ||||||||
\(233\) | −3045.69 | −0.856352 | −0.428176 | − | 0.903695i | \(-0.640844\pi\) | ||||
−0.428176 | + | 0.903695i | \(0.640844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1902.81 | −0.524840 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1502.57 | 0.409231 | ||||||||
\(239\) | 3032.36 | 0.820699 | 0.410349 | − | 0.911928i | \(-0.365407\pi\) | ||||
0.410349 | + | 0.911928i | \(0.365407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2529.56 | −0.676113 | −0.338057 | − | 0.941126i | \(-0.609770\pi\) | ||||
−0.338057 | + | 0.941126i | \(0.609770\pi\) | |||||||
\(242\) | −3504.38 | −0.930868 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2320.61 | 0.608859 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7058.32 | −1.81826 | ||||||||
\(248\) | 272.753 | 0.0698382 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2473.85 | −0.622104 | −0.311052 | − | 0.950393i | \(-0.600681\pi\) | ||||
−0.311052 | + | 0.950393i | \(0.600681\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3769.27 | −0.936647 | ||||||||
\(254\) | 217.073 | 0.0536236 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2592.97 | −0.633049 | ||||||||
\(257\) | −4504.78 | −1.09339 | −0.546694 | − | 0.837333i | \(-0.684114\pi\) | ||||
−0.546694 | + | 0.837333i | \(0.684114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3821.14 | 0.916735 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −308.086 | −0.0726475 | ||||||||
\(263\) | −4193.64 | −0.983235 | −0.491617 | − | 0.870811i | \(-0.663594\pi\) | ||||
−0.491617 | + | 0.870811i | \(0.663594\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5112.62 | −1.17848 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1950.96 | −0.444677 | ||||||||
\(269\) | 4727.04 | 1.07142 | 0.535711 | − | 0.844401i | \(-0.320044\pi\) | ||||
0.535711 | + | 0.844401i | \(0.320044\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4692.61 | 1.05187 | 0.525933 | − | 0.850526i | \(-0.323716\pi\) | ||||
0.525933 | + | 0.850526i | \(0.323716\pi\) | |||||||
\(272\) | 878.668 | 0.195872 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1841.31 | 0.405977 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2865.79 | −0.621619 | −0.310809 | − | 0.950472i | \(-0.600600\pi\) | ||||
−0.310809 | + | 0.950472i | \(0.600600\pi\) | |||||||
\(278\) | −1184.99 | −0.255650 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8407.98 | 1.78498 | 0.892488 | − | 0.451071i | \(-0.148958\pi\) | ||||
0.892488 | + | 0.451071i | \(0.148958\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8549.38 | −1.79579 | −0.897893 | − | 0.440213i | \(-0.854903\pi\) | ||||
−0.897893 | + | 0.440213i | \(0.854903\pi\) | |||||||
\(284\) | −2270.05 | −0.474306 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4367.02 | 0.902893 | ||||||||
\(287\) | −10955.2 | −2.25320 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3236.45 | −0.658752 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4350.68 | −0.871933 | ||||||||
\(293\) | 5122.05 | 1.02128 | 0.510638 | − | 0.859796i | \(-0.329409\pi\) | ||||
0.510638 | + | 0.859796i | \(0.329409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2824.20 | −0.554571 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −416.068 | −0.0808797 | ||||||||
\(299\) | 3075.48 | 0.594847 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5072.55 | −0.971352 | ||||||||
\(302\) | −4015.47 | −0.765114 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2989.75 | −0.564058 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5427.96 | 1.00909 | 0.504544 | − | 0.863386i | \(-0.331661\pi\) | ||||
0.504544 | + | 0.863386i | \(0.331661\pi\) | |||||||
\(308\) | −9966.90 | −1.84389 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10418.0 | −1.89952 | −0.949758 | − | 0.312985i | \(-0.898671\pi\) | ||||
−0.949758 | + | 0.312985i | \(0.898671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −612.798 | −0.110663 | −0.0553313 | − | 0.998468i | \(-0.517621\pi\) | ||||
−0.0553313 | + | 0.998468i | \(0.517621\pi\) | |||||||
\(314\) | −1698.83 | −0.305319 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3698.37 | −0.658384 | ||||||||
\(317\) | −3945.19 | −0.699004 | −0.349502 | − | 0.936936i | \(-0.613649\pi\) | ||||
−0.349502 | + | 0.936936i | \(0.613649\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10886.9 | −1.91082 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2227.69 | 0.385541 | ||||||||
\(323\) | −5704.62 | −0.982705 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1409.99 | −0.239547 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8096.98 | 1.36305 | ||||||||
\(329\) | 5327.38 | 0.892730 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1569.58 | −0.260641 | −0.130320 | − | 0.991472i | \(-0.541601\pi\) | ||||
−0.130320 | + | 0.991472i | \(0.541601\pi\) | |||||||
\(332\) | 1348.84 | 0.222974 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4970.28 | 0.814256 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −162.355 | −0.0262435 | −0.0131217 | − | 0.999914i | \(-0.504177\pi\) | ||||
−0.0131217 | + | 0.999914i | \(0.504177\pi\) | |||||||
\(338\) | −513.172 | −0.0825825 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −866.854 | −0.137662 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −336.135 | −0.0529142 | ||||||||
\(344\) | 3749.11 | 0.587611 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4544.57 | 0.706120 | ||||||||
\(347\) | 2240.16 | 0.346566 | 0.173283 | − | 0.984872i | \(-0.444563\pi\) | ||||
0.173283 | + | 0.984872i | \(0.444563\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6442.75 | 0.988174 | 0.494087 | − | 0.869413i | \(-0.335503\pi\) | ||||
0.494087 | + | 0.869413i | \(0.335503\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11554.2 | 1.74955 | ||||||||
\(353\) | −6723.97 | −1.01383 | −0.506914 | − | 0.861997i | \(-0.669214\pi\) | ||||
−0.506914 | + | 0.861997i | \(0.669214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1067.91 | −0.158986 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 557.622 | 0.0823219 | ||||||||
\(359\) | −13327.2 | −1.95929 | −0.979643 | − | 0.200746i | \(-0.935663\pi\) | ||||
−0.979643 | + | 0.200746i | \(0.935663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12551.5 | 1.82993 | ||||||||
\(362\) | 2186.62 | 0.317476 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8132.34 | 1.17102 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 180.672 | 0.0256975 | 0.0128487 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128487 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(368\) | 1302.70 | 0.184533 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3031.03 | −0.424160 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9876.50 | 1.37101 | 0.685504 | − | 0.728069i | \(-0.259582\pi\) | ||||
0.685504 | + | 0.728069i | \(0.259582\pi\) | |||||||
\(374\) | 3529.48 | 0.487982 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3937.45 | −0.540050 | ||||||||
\(377\) | 8883.03 | 1.21353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7885.55 | −1.06874 | −0.534371 | − | 0.845250i | \(-0.679452\pi\) | ||||
−0.534371 | + | 0.845250i | \(0.679452\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1599.50 | −0.214235 | ||||||||
\(383\) | −5056.75 | −0.674642 | −0.337321 | − | 0.941390i | \(-0.609521\pi\) | ||||
−0.337321 | + | 0.941390i | \(0.609521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4879.95 | −0.643479 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3321.73 | −0.434627 | ||||||||
\(389\) | −143.433 | −0.0186950 | −0.00934748 | − | 0.999956i | \(-0.502975\pi\) | ||||
−0.00934748 | + | 0.999956i | \(0.502975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2485.64 | 0.321494 | ||||||||
\(392\) | 6949.54 | 0.895420 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3962.66 | −0.506690 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4718.38 | −0.596496 | −0.298248 | − | 0.954488i | \(-0.596402\pi\) | ||||
−0.298248 | + | 0.954488i | \(0.596402\pi\) | |||||||
\(398\) | −4111.72 | −0.517844 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8004.58 | −0.996832 | −0.498416 | − | 0.866938i | \(-0.666085\pi\) | ||||
−0.498416 | + | 0.866938i | \(0.666085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 707.297 | 0.0874267 | ||||||||
\(404\) | 11321.9 | 1.39427 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6434.32 | 0.786528 | ||||||||
\(407\) | 8975.75 | 1.09315 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14396.5 | −1.74049 | −0.870245 | − | 0.492618i | \(-0.836040\pi\) | ||||
−0.870245 | + | 0.492618i | \(0.836040\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9236.80 | 1.10453 | ||||||||
\(413\) | −8282.55 | −0.986822 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9427.47 | −1.11110 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12009.4 | −1.40526 | ||||||||
\(419\) | −7082.65 | −0.825799 | −0.412900 | − | 0.910777i | \(-0.635484\pi\) | ||||
−0.412900 | + | 0.910777i | \(0.635484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11764.3 | 1.36189 | 0.680946 | − | 0.732333i | \(-0.261569\pi\) | ||||
0.680946 | + | 0.732333i | \(0.261569\pi\) | |||||||
\(422\) | 6667.06 | 0.769069 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2240.23 | 0.256592 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10101.1 | 1.14480 | ||||||||
\(428\) | −6332.73 | −0.715197 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11183.1 | −1.24981 | −0.624906 | − | 0.780700i | \(-0.714863\pi\) | ||||
−0.624906 | + | 0.780700i | \(0.714863\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2138.50 | 0.237344 | 0.118672 | − | 0.992934i | \(-0.462136\pi\) | ||||
0.118672 | + | 0.992934i | \(0.462136\pi\) | |||||||
\(434\) | 512.322 | 0.0566642 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6047.06 | −0.664224 | ||||||||
\(437\) | −8457.61 | −0.925817 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3478.39 | −0.378166 | −0.189083 | − | 0.981961i | \(-0.560551\pi\) | ||||
−0.189083 | + | 0.981961i | \(0.560551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2879.83 | −0.309908 | ||||||||
\(443\) | 11835.2 | 1.26932 | 0.634658 | − | 0.772793i | \(-0.281141\pi\) | ||||
0.634658 | + | 0.772793i | \(0.281141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2935.23 | 0.311630 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2290.77 | −0.241582 | ||||||||
\(449\) | 11395.8 | 1.19778 | 0.598890 | − | 0.800832i | \(-0.295609\pi\) | ||||
0.598890 | + | 0.800832i | \(0.295609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25733.5 | −2.68679 | ||||||||
\(452\) | 10691.9 | 1.11262 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5232.88 | 0.540950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3548.95 | −0.363267 | −0.181633 | − | 0.983366i | \(-0.558138\pi\) | ||||
−0.181633 | + | 0.983366i | \(0.558138\pi\) | |||||||
\(458\) | 1907.10 | 0.194570 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 782.186 | 0.0790239 | 0.0395120 | − | 0.999219i | \(-0.487420\pi\) | ||||
0.0395120 | + | 0.999219i | \(0.487420\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −483.665 | −0.0485483 | −0.0242741 | − | 0.999705i | \(-0.507727\pi\) | ||||
−0.0242741 | + | 0.999705i | \(0.507727\pi\) | |||||||
\(464\) | 3762.65 | 0.376458 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4228.25 | 0.420322 | ||||||||
\(467\) | −1463.20 | −0.144987 | −0.0724934 | − | 0.997369i | \(-0.523096\pi\) | ||||
−0.0724934 | + | 0.997369i | \(0.523096\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8492.11 | −0.836097 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6121.61 | 0.596970 | ||||||||
\(473\) | −11915.3 | −1.15828 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6572.66 | 0.632894 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4209.74 | −0.402822 | ||||||||
\(479\) | −2813.55 | −0.268380 | −0.134190 | − | 0.990956i | \(-0.542843\pi\) | ||||
−0.134190 | + | 0.990956i | \(0.542843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7323.62 | −0.694238 | ||||||||
\(482\) | 3511.72 | 0.331855 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15329.2 | −1.43963 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −763.032 | −0.0709985 | −0.0354993 | − | 0.999370i | \(-0.511302\pi\) | ||||
−0.0354993 | + | 0.999370i | \(0.511302\pi\) | |||||||
\(488\) | −7465.72 | −0.692535 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6818.64 | 0.626723 | 0.313362 | − | 0.949634i | \(-0.398545\pi\) | ||||
0.313362 | + | 0.949634i | \(0.398545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7179.38 | 0.655868 | ||||||||
\(494\) | 9798.87 | 0.892453 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 299.595 | 0.0271214 | ||||||||
\(497\) | −9881.08 | −0.891805 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15367.3 | 1.37863 | 0.689315 | − | 0.724462i | \(-0.257911\pi\) | ||||
0.689315 | + | 0.724462i | \(0.257911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3434.38 | 0.305346 | ||||||||
\(503\) | −10126.5 | −0.897652 | −0.448826 | − | 0.893619i | \(-0.648158\pi\) | ||||
−0.448826 | + | 0.893619i | \(0.648158\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5232.77 | 0.459733 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 949.542 | 0.0829313 | ||||||||
\(509\) | 379.594 | 0.0330554 | 0.0165277 | − | 0.999863i | \(-0.494739\pi\) | ||||
0.0165277 | + | 0.999863i | \(0.494739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18937.6 | −1.63944 | ||||||||
\(512\) | −7347.22 | −0.634188 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6253.86 | 0.536665 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12513.9 | 1.06452 | ||||||||
\(518\) | −5304.78 | −0.449959 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −175.365 | −0.0147464 | −0.00737320 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737320 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6412.16 | −0.536107 | −0.268054 | − | 0.963404i | \(-0.586380\pi\) | ||||
−0.268054 | + | 0.963404i | \(0.586380\pi\) | |||||||
\(524\) | −1347.66 | −0.112353 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5821.91 | 0.482599 | ||||||||
\(527\) | 571.646 | 0.0472510 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8481.82 | −0.697117 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22364.1 | −1.82257 | ||||||||
\(533\) | 20996.9 | 1.70633 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6276.50 | 0.505790 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6562.41 | −0.525884 | ||||||||
\(539\) | −22086.7 | −1.76502 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3097.02 | −0.246120 | −0.123060 | − | 0.992399i | \(-0.539271\pi\) | ||||
−0.123060 | + | 0.992399i | \(0.539271\pi\) | |||||||
\(542\) | −6514.62 | −0.516286 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7619.40 | −0.600513 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19366.9 | −1.51384 | −0.756918 | − | 0.653510i | \(-0.773296\pi\) | ||||
−0.756918 | + | 0.653510i | \(0.773296\pi\) | |||||||
\(548\) | 8054.42 | 0.627861 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24428.5 | −1.88873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16098.2 | −1.23791 | ||||||||
\(554\) | 3978.49 | 0.305108 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5183.47 | −0.395375 | ||||||||
\(557\) | 2285.09 | 0.173828 | 0.0869142 | − | 0.996216i | \(-0.472299\pi\) | ||||
0.0869142 | + | 0.996216i | \(0.472299\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9722.07 | 0.735599 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11672.6 | −0.876117 | ||||||||
\(563\) | −9294.62 | −0.695775 | −0.347888 | − | 0.937536i | \(-0.613101\pi\) | ||||
−0.347888 | + | 0.937536i | \(0.613101\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11868.9 | 0.881423 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7303.08 | 0.539490 | ||||||||
\(569\) | 4799.80 | 0.353635 | 0.176817 | − | 0.984244i | \(-0.443420\pi\) | ||||
0.176817 | + | 0.984244i | \(0.443420\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7340.74 | 0.538005 | 0.269002 | − | 0.963140i | \(-0.413306\pi\) | ||||
0.269002 | + | 0.963140i | \(0.413306\pi\) | |||||||
\(572\) | 19102.6 | 1.39636 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15208.8 | 1.10593 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4603.40 | −0.332136 | −0.166068 | − | 0.986114i | \(-0.553107\pi\) | ||||
−0.166068 | + | 0.986114i | \(0.553107\pi\) | |||||||
\(578\) | 4493.07 | 0.323334 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5871.24 | 0.419243 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7119.80 | −0.505784 | ||||||||
\(584\) | 13996.8 | 0.991763 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7110.80 | −0.501271 | ||||||||
\(587\) | −26036.4 | −1.83073 | −0.915364 | − | 0.402628i | \(-0.868097\pi\) | ||||
−0.915364 | + | 0.402628i | \(0.868097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1945.08 | −0.136070 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3102.12 | −0.215366 | ||||||||
\(593\) | 9879.23 | 0.684134 | 0.342067 | − | 0.939676i | \(-0.388873\pi\) | ||||
0.342067 | + | 0.939676i | \(0.388873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1820.00 | −0.125084 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4269.60 | −0.291968 | ||||||||
\(599\) | 10145.0 | 0.692011 | 0.346005 | − | 0.938233i | \(-0.387538\pi\) | ||||
0.346005 | + | 0.938233i | \(0.387538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11375.1 | −0.772047 | −0.386023 | − | 0.922489i | \(-0.626152\pi\) | ||||
−0.386023 | + | 0.922489i | \(0.626152\pi\) | |||||||
\(602\) | 7042.08 | 0.476767 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17564.8 | −1.18328 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 136.064 | 0.00909827 | 0.00454914 | − | 0.999990i | \(-0.498552\pi\) | ||||
0.00454914 | + | 0.999990i | \(0.498552\pi\) | |||||||
\(608\) | 25925.7 | 1.72932 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10210.5 | −0.676059 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16261.8 | 1.07146 | 0.535731 | − | 0.844389i | \(-0.320036\pi\) | ||||
0.535731 | + | 0.844389i | \(0.320036\pi\) | |||||||
\(614\) | −7535.48 | −0.495289 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 32064.9 | 2.09729 | ||||||||
\(617\) | −25423.1 | −1.65883 | −0.829413 | − | 0.558636i | \(-0.811325\pi\) | ||||
−0.829413 | + | 0.558636i | \(0.811325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14794.0 | 0.960618 | 0.480309 | − | 0.877099i | \(-0.340525\pi\) | ||||
0.480309 | + | 0.877099i | \(0.340525\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14463.0 | 0.932336 | ||||||||
\(623\) | −4648.39 | −0.298930 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 850.730 | 0.0543163 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7431.15 | −0.472190 | ||||||||
\(629\) | −5919.04 | −0.375211 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25793.0 | −1.62726 | −0.813632 | − | 0.581381i | \(-0.802513\pi\) | ||||
−0.813632 | + | 0.581381i | \(0.802513\pi\) | |||||||
\(632\) | 11898.2 | 0.748866 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5477.00 | 0.343091 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18021.3 | 1.12093 | ||||||||
\(638\) | 15114.0 | 0.937884 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1300.58 | −0.0801399 | −0.0400700 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400700 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3758.25 | −0.230499 | −0.115250 | − | 0.993337i | \(-0.536767\pi\) | ||||
−0.115250 | + | 0.993337i | \(0.536767\pi\) | |||||||
\(644\) | 9744.54 | 0.596256 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7919.57 | 0.482339 | ||||||||
\(647\) | −22398.4 | −1.36101 | −0.680505 | − | 0.732743i | \(-0.738240\pi\) | ||||
−0.680505 | + | 0.732743i | \(0.738240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19455.4 | −1.17672 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6167.72 | −0.370470 | ||||||||
\(653\) | 20852.4 | 1.24964 | 0.624822 | − | 0.780767i | \(-0.285171\pi\) | ||||
0.624822 | + | 0.780767i | \(0.285171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8893.80 | 0.529336 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7395.86 | −0.438177 | ||||||||
\(659\) | −2275.07 | −0.134483 | −0.0672414 | − | 0.997737i | \(-0.521420\pi\) | ||||
−0.0672414 | + | 0.997737i | \(0.521420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1840.62 | 0.108308 | 0.0541542 | − | 0.998533i | \(-0.482754\pi\) | ||||
0.0541542 | + | 0.998533i | \(0.482754\pi\) | |||||||
\(662\) | 2179.01 | 0.127930 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4339.42 | −0.253618 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10644.1 | 0.617900 | ||||||||
\(668\) | 21741.4 | 1.25928 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23727.2 | 1.36510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31183.1 | 1.78606 | 0.893030 | − | 0.449996i | \(-0.148575\pi\) | ||||
0.893030 | + | 0.449996i | \(0.148575\pi\) | |||||||
\(674\) | 225.393 | 0.0128810 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2244.76 | −0.127718 | ||||||||
\(677\) | −16071.3 | −0.912362 | −0.456181 | − | 0.889887i | \(-0.650783\pi\) | ||||
−0.456181 | + | 0.889887i | \(0.650783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14458.8 | −0.817199 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1203.43 | 0.0675684 | ||||||||
\(683\) | −2603.13 | −0.145836 | −0.0729180 | − | 0.997338i | \(-0.523231\pi\) | ||||
−0.0729180 | + | 0.997338i | \(0.523231\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 466.647 | 0.0259718 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4118.05 | 0.228197 | ||||||||
\(689\) | 5809.30 | 0.321214 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31931.3 | 1.75792 | 0.878961 | − | 0.476894i | \(-0.158237\pi\) | ||||
0.878961 | + | 0.476894i | \(0.158237\pi\) | |||||||
\(692\) | 19879.2 | 1.09205 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3109.96 | −0.170104 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16969.9 | 0.922212 | ||||||||
\(698\) | −8944.29 | −0.485023 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28906.8 | 1.55748 | 0.778740 | − | 0.627347i | \(-0.215859\pi\) | ||||
0.778740 | + | 0.627347i | \(0.215859\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20140.1 | 1.08051 | ||||||||
\(704\) | −5380.94 | −0.288071 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9334.70 | 0.497615 | ||||||||
\(707\) | 49281.9 | 2.62155 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4665.85 | 0.247151 | 0.123575 | − | 0.992335i | \(-0.460564\pi\) | ||||
0.123575 | + | 0.992335i | \(0.460564\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3435.61 | 0.180836 | ||||||||
\(713\) | 847.515 | 0.0445157 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2439.20 | 0.127315 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18501.8 | 0.961673 | ||||||||
\(719\) | −11419.5 | −0.592318 | −0.296159 | − | 0.955139i | \(-0.595706\pi\) | ||||
−0.296159 | + | 0.955139i | \(0.595706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40205.9 | 2.07676 | ||||||||
\(722\) | −17424.9 | −0.898182 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9564.90 | 0.490990 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21207.8 | 1.08192 | 0.540960 | − | 0.841049i | \(-0.318061\pi\) | ||||
0.540960 | + | 0.841049i | \(0.318061\pi\) | |||||||
\(728\) | −26162.9 | −1.33195 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7857.50 | 0.397565 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5089.94 | −0.256482 | −0.128241 | − | 0.991743i | \(-0.540933\pi\) | ||||
−0.128241 | + | 0.991743i | \(0.540933\pi\) | |||||||
\(734\) | −250.821 | −0.0126130 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11296.4 | −0.565750 | ||||||||
\(737\) | −19947.7 | −0.996992 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22403.1 | 1.11517 | 0.557586 | − | 0.830119i | \(-0.311728\pi\) | ||||
0.557586 | + | 0.830119i | \(0.311728\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4207.90 | 0.208190 | ||||||||
\(743\) | 9518.12 | 0.469968 | 0.234984 | − | 0.971999i | \(-0.424496\pi\) | ||||
0.234984 | + | 0.971999i | \(0.424496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13711.3 | −0.672929 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15439.0 | 0.754685 | ||||||||
\(749\) | −27565.1 | −1.34474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7550.19 | −0.366858 | −0.183429 | − | 0.983033i | \(-0.558720\pi\) | ||||
−0.183429 | + | 0.983033i | \(0.558720\pi\) | |||||||
\(752\) | −4324.93 | −0.209726 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12332.1 | −0.595633 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2455.82 | 0.117911 | 0.0589554 | − | 0.998261i | \(-0.481223\pi\) | ||||
0.0589554 | + | 0.998261i | \(0.481223\pi\) | |||||||
\(758\) | 10947.3 | 0.524569 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22130.3 | 1.05417 | 0.527086 | − | 0.849812i | \(-0.323285\pi\) | ||||
0.527086 | + | 0.849812i | \(0.323285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26321.6 | −1.24889 | ||||||||
\(764\) | −6996.69 | −0.331324 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7020.15 | 0.331134 | ||||||||
\(767\) | 15874.4 | 0.747315 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24572.2 | 1.15227 | 0.576136 | − | 0.817354i | \(-0.304560\pi\) | ||||
0.576136 | + | 0.817354i | \(0.304560\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21346.3 | −0.995168 | ||||||||
\(773\) | 4726.47 | 0.219922 | 0.109961 | − | 0.993936i | \(-0.464927\pi\) | ||||
0.109961 | + | 0.993936i | \(0.464927\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10686.5 | 0.494358 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 199.124 | 0.00917601 | ||||||||
\(779\) | −57741.7 | −2.65573 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23210.4 | −1.06342 | ||||||||
\(782\) | −3450.74 | −0.157798 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7633.43 | 0.347733 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8034.51 | −0.363913 | −0.181956 | − | 0.983307i | \(-0.558243\pi\) | ||||
−0.181956 | + | 0.983307i | \(0.558243\pi\) | |||||||
\(788\) | −17333.8 | −0.783618 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46539.6 | 2.09198 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19359.9 | −0.866948 | ||||||||
\(794\) | 6550.40 | 0.292777 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17985.9 | −0.800869 | ||||||||
\(797\) | −28316.0 | −1.25847 | −0.629237 | − | 0.777214i | \(-0.716632\pi\) | ||||
−0.629237 | + | 0.777214i | \(0.716632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8252.25 | −0.365386 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11112.5 | 0.489273 | ||||||||
\(803\) | −44483.9 | −1.95492 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −981.920 | −0.0429115 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36424.1 | −1.58588 | ||||||||
\(809\) | −25667.5 | −1.11548 | −0.557739 | − | 0.830016i | \(-0.688331\pi\) | ||||
−0.557739 | + | 0.830016i | \(0.688331\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7069.35 | −0.306089 | −0.153045 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153045 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(812\) | 28145.6 | 1.21640 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12460.8 | −0.536548 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26735.9 | −1.14488 | ||||||||
\(818\) | 19986.2 | 0.854282 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40718.4 | 1.73092 | 0.865458 | − | 0.500982i | \(-0.167028\pi\) | ||||
0.865458 | + | 0.500982i | \(0.167028\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27978.1 | 1.18500 | 0.592501 | − | 0.805570i | \(-0.298141\pi\) | ||||
0.592501 | + | 0.805570i | \(0.298141\pi\) | |||||||
\(824\) | −29716.1 | −1.25632 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11498.4 | 0.484360 | ||||||||
\(827\) | 33072.0 | 1.39060 | 0.695299 | − | 0.718720i | \(-0.255272\pi\) | ||||
0.695299 | + | 0.718720i | \(0.255272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8834.66 | 0.370133 | 0.185067 | − | 0.982726i | \(-0.440750\pi\) | ||||
0.185067 | + | 0.982726i | \(0.440750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4390.49 | 0.182948 | ||||||||
\(833\) | 14565.1 | 0.605822 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −52532.5 | −2.17329 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9832.64 | 0.405326 | ||||||||
\(839\) | 7157.16 | 0.294508 | 0.147254 | − | 0.989099i | \(-0.452956\pi\) | ||||
0.147254 | + | 0.989099i | \(0.452956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6354.70 | 0.260556 | ||||||||
\(842\) | −16332.0 | −0.668455 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29163.6 | 1.18940 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −66724.8 | −2.70684 | ||||||||
\(848\) | 2460.69 | 0.0996466 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8775.50 | −0.353490 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17887.7 | 0.718012 | 0.359006 | − | 0.933335i | \(-0.383116\pi\) | ||||
0.359006 | + | 0.933335i | \(0.383116\pi\) | |||||||
\(854\) | −14023.1 | −0.561898 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20373.3 | 0.813487 | ||||||||
\(857\) | 7275.68 | 0.290003 | 0.145001 | − | 0.989431i | \(-0.453681\pi\) | ||||
0.145001 | + | 0.989431i | \(0.453681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14124.1 | 0.561011 | 0.280505 | − | 0.959852i | \(-0.409498\pi\) | ||||
0.280505 | + | 0.959852i | \(0.409498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15525.1 | 0.613443 | ||||||||
\(863\) | 46912.8 | 1.85044 | 0.925221 | − | 0.379430i | \(-0.123880\pi\) | ||||
0.925221 | + | 0.379430i | \(0.123880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2968.82 | −0.116495 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2241.05 | 0.0876337 | ||||||||
\(869\) | −37814.3 | −1.47613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16276.0 | 0.633171 | ||||||||
\(872\) | 19454.2 | 0.755509 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11741.5 | 0.454417 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23062.3 | −0.887982 | −0.443991 | − | 0.896031i | \(-0.646438\pi\) | ||||
−0.443991 | + | 0.896031i | \(0.646438\pi\) | |||||||
\(878\) | 4828.96 | 0.185614 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22672.9 | 0.867047 | 0.433523 | − | 0.901142i | \(-0.357270\pi\) | ||||
0.433523 | + | 0.901142i | \(0.357270\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24676.9 | −0.940481 | −0.470241 | − | 0.882538i | \(-0.655833\pi\) | ||||
−0.470241 | + | 0.882538i | \(0.655833\pi\) | |||||||
\(884\) | −12597.2 | −0.479287 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16430.5 | −0.623016 | ||||||||
\(887\) | −8579.09 | −0.324755 | −0.162378 | − | 0.986729i | \(-0.551916\pi\) | ||||
−0.162378 | + | 0.986729i | \(0.551916\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4133.16 | 0.155930 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12839.5 | 0.481950 | ||||||||
\(893\) | 28079.0 | 1.05222 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −36170.5 | −1.34863 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15820.5 | −0.587904 | ||||||||
\(899\) | 2447.92 | 0.0908148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4695.15 | 0.173605 | ||||||||
\(902\) | 35725.1 | 1.31875 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34397.3 | −1.26553 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10650.0 | −0.389888 | −0.194944 | − | 0.980814i | \(-0.562453\pi\) | ||||
−0.194944 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(908\) | 22890.1 | 0.836603 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4222.07 | 0.153549 | 0.0767747 | − | 0.997048i | \(-0.475538\pi\) | ||||
0.0767747 | + | 0.997048i | \(0.475538\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13791.4 | 0.499921 | ||||||||
\(914\) | 4926.91 | 0.178302 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8342.22 | 0.300911 | ||||||||
\(917\) | −5866.09 | −0.211249 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5262.94 | −0.188910 | −0.0944550 | − | 0.995529i | \(-0.530111\pi\) | ||||
−0.0944550 | + | 0.995529i | \(0.530111\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1085.89 | −0.0387872 | ||||||||
\(923\) | 18938.1 | 0.675359 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 671.459 | 0.0238289 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32628.0 | −1.15417 | ||||||||
\(929\) | −9699.02 | −0.342535 | −0.171267 | − | 0.985225i | \(-0.554786\pi\) | ||||
−0.171267 | + | 0.985225i | \(0.554786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49559.0 | −1.74461 | ||||||||
\(932\) | 18495.6 | 0.650046 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2031.32 | 0.0711636 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26451.8 | 0.922243 | 0.461121 | − | 0.887337i | \(-0.347447\pi\) | ||||
0.461121 | + | 0.887337i | \(0.347447\pi\) | |||||||
\(938\) | 11789.4 | 0.410380 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −177.394 | −0.00614547 | −0.00307273 | − | 0.999995i | \(-0.500978\pi\) | ||||
−0.00307273 | + | 0.999995i | \(0.500978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25159.4 | 0.868826 | ||||||||
\(944\) | 6724.02 | 0.231831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16541.6 | 0.568514 | ||||||||
\(947\) | 41170.5 | 1.41274 | 0.706368 | − | 0.707845i | \(-0.250333\pi\) | ||||
0.706368 | + | 0.707845i | \(0.250333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36296.0 | 1.24154 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21145.2 | −0.719873 | ||||||||
\(953\) | −95.6454 | −0.00325106 | −0.00162553 | − | 0.999999i | \(-0.500517\pi\) | ||||
−0.00162553 | + | 0.999999i | \(0.500517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18414.6 | −0.622982 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3905.97 | 0.131729 | ||||||||
\(959\) | 35059.3 | 1.18052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29596.1 | −0.993457 | ||||||||
\(962\) | 10167.2 | 0.340752 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15361.3 | 0.513229 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38487.1 | −1.27990 | −0.639950 | − | 0.768417i | \(-0.721045\pi\) | ||||
−0.639950 | + | 0.768417i | \(0.721045\pi\) | |||||||
\(968\) | 49316.1 | 1.63748 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28964.1 | −0.957263 | −0.478632 | − | 0.878016i | \(-0.658867\pi\) | ||||
−0.478632 | + | 0.878016i | \(0.658867\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22562.6 | −0.743396 | ||||||||
\(974\) | 1059.30 | 0.0348481 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8200.41 | −0.268943 | ||||||||
\(977\) | −2029.70 | −0.0664647 | −0.0332323 | − | 0.999448i | \(-0.510580\pi\) | ||||
−0.0332323 | + | 0.999448i | \(0.510580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10918.9 | −0.356456 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9466.13 | −0.307613 | ||||||||
\(983\) | 44554.5 | 1.44564 | 0.722821 | − | 0.691035i | \(-0.242845\pi\) | ||||
0.722821 | + | 0.691035i | \(0.242845\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9966.93 | −0.321918 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 42863.1 | 1.38022 | ||||||||
\(989\) | 11649.4 | 0.374551 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3215.90 | −0.103084 | −0.0515420 | − | 0.998671i | \(-0.516414\pi\) | ||||
−0.0515420 | + | 0.998671i | \(0.516414\pi\) | |||||||
\(992\) | −2597.95 | −0.0831501 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13717.6 | 0.437723 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19664.3 | 0.624649 | 0.312325 | − | 0.949975i | \(-0.398892\pi\) | ||||
0.312325 | + | 0.949975i | \(0.398892\pi\) | |||||||
\(998\) | −21334.0 | −0.676671 | ||||||||
\(999\) | 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 | 2025.4.a.be.1.6 | 12 | ||
3.2 | odd | 2 | 2025.4.a.bi.1.7 | 12 | |||
5.4 | even | 2 | 2025.4.a.bj.1.7 | 12 | |||
9.2 | odd | 6 | 225.4.e.e.76.6 | ✓ | 24 | ||
9.5 | odd | 6 | 225.4.e.e.151.6 | yes | 24 | ||
15.14 | odd | 2 | 2025.4.a.bf.1.6 | 12 | |||
45.2 | even | 12 | 225.4.k.e.49.15 | 48 | |||
45.14 | odd | 6 | 225.4.e.f.151.7 | yes | 24 | ||
45.23 | even | 12 | 225.4.k.e.124.15 | 48 | |||
45.29 | odd | 6 | 225.4.e.f.76.7 | yes | 24 | ||
45.32 | even | 12 | 225.4.k.e.124.10 | 48 | |||
45.38 | even | 12 | 225.4.k.e.49.10 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.6 | ✓ | 24 | 9.2 | odd | 6 | ||
225.4.e.e.151.6 | yes | 24 | 9.5 | odd | 6 | ||
225.4.e.f.76.7 | yes | 24 | 45.29 | odd | 6 | ||
225.4.e.f.151.7 | yes | 24 | 45.14 | odd | 6 | ||
225.4.k.e.49.10 | 48 | 45.38 | even | 12 | |||
225.4.k.e.49.15 | 48 | 45.2 | even | 12 | |||
225.4.k.e.124.10 | 48 | 45.32 | even | 12 | |||
225.4.k.e.124.15 | 48 | 45.23 | even | 12 | |||
2025.4.a.be.1.6 | 12 | 1.1 | even | 1 | trivial | ||
2025.4.a.bf.1.6 | 12 | 15.14 | odd | 2 | |||
2025.4.a.bi.1.7 | 12 | 3.2 | odd | 2 | |||
2025.4.a.bj.1.7 | 12 | 5.4 | even | 2 |