Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(1,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, 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("405.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 2x^{6} - 44x^{5} + 74x^{4} + 479x^{3} - 460x^{2} - 1200x + 288 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.225250\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.225250 | −0.0796378 | −0.0398189 | − | 0.999207i | \(-0.512678\pi\) | ||||
−0.0398189 | + | 0.999207i | \(0.512678\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.94926 | −0.993658 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.1940 | −1.68432 | −0.842159 | − | 0.539229i | \(-0.818716\pi\) | ||||
−0.842159 | + | 0.539229i | \(0.818716\pi\) | |||||||
\(8\) | 3.59257 | 0.158771 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.12625 | 0.0356151 | ||||||||
\(11\) | 18.1285 | 0.496904 | 0.248452 | − | 0.968644i | \(-0.420078\pi\) | ||||
0.248452 | + | 0.968644i | \(0.420078\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −50.1562 | −1.07006 | −0.535032 | − | 0.844832i | \(-0.679700\pi\) | ||||
−0.535032 | + | 0.844832i | \(0.679700\pi\) | |||||||
\(14\) | 7.02645 | 0.134136 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 62.7849 | 0.981014 | ||||||||
\(17\) | −131.631 | −1.87795 | −0.938977 | − | 0.343981i | \(-0.888224\pi\) | ||||
−0.938977 | + | 0.343981i | \(0.888224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.2428 | 0.280646 | 0.140323 | − | 0.990106i | \(-0.455186\pi\) | ||||
0.140323 | + | 0.990106i | \(0.455186\pi\) | |||||||
\(20\) | 39.7463 | 0.444377 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.08344 | −0.0395723 | ||||||||
\(23\) | −32.9856 | −0.299043 | −0.149521 | − | 0.988759i | \(-0.547773\pi\) | ||||
−0.149521 | + | 0.988759i | \(0.547773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 11.2977 | 0.0852176 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 247.969 | 1.67364 | ||||||||
\(29\) | 125.817 | 0.805645 | 0.402823 | − | 0.915278i | \(-0.368029\pi\) | ||||
0.402823 | + | 0.915278i | \(0.368029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 125.113 | 0.724868 | 0.362434 | − | 0.932009i | \(-0.381946\pi\) | ||||
0.362434 | + | 0.932009i | \(0.381946\pi\) | |||||||
\(32\) | −42.8828 | −0.236896 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 29.6499 | 0.149556 | ||||||||
\(35\) | 155.970 | 0.753250 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 99.9894 | 0.444274 | 0.222137 | − | 0.975015i | \(-0.428697\pi\) | ||||
0.222137 | + | 0.975015i | \(0.428697\pi\) | |||||||
\(38\) | −5.23544 | −0.0223500 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −17.9628 | −0.0710044 | ||||||||
\(41\) | 245.326 | 0.934473 | 0.467237 | − | 0.884132i | \(-0.345250\pi\) | ||||
0.467237 | + | 0.884132i | \(0.345250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 139.176 | 0.493586 | 0.246793 | − | 0.969068i | \(-0.420623\pi\) | ||||
0.246793 | + | 0.969068i | \(0.420623\pi\) | |||||||
\(44\) | −144.108 | −0.493752 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.43001 | 0.0238151 | ||||||||
\(47\) | −472.961 | −1.46784 | −0.733919 | − | 0.679237i | \(-0.762311\pi\) | ||||
−0.733919 | + | 0.679237i | \(0.762311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 630.067 | 1.83693 | ||||||||
\(50\) | −5.63125 | −0.0159276 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 398.705 | 1.06328 | ||||||||
\(53\) | 421.529 | 1.09248 | 0.546240 | − | 0.837628i | \(-0.316059\pi\) | ||||
0.546240 | + | 0.837628i | \(0.316059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −90.6424 | −0.222222 | ||||||||
\(56\) | −112.067 | −0.267420 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −28.3404 | −0.0641598 | ||||||||
\(59\) | −742.413 | −1.63820 | −0.819101 | − | 0.573649i | \(-0.805527\pi\) | ||||
−0.819101 | + | 0.573649i | \(0.805527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.97736 | 0.0188432 | 0.00942158 | − | 0.999956i | \(-0.497001\pi\) | ||||
0.00942158 | + | 0.999956i | \(0.497001\pi\) | |||||||
\(62\) | −28.1816 | −0.0577269 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −492.620 | −0.962148 | ||||||||
\(65\) | 250.781 | 0.478547 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 588.906 | 1.07383 | 0.536913 | − | 0.843638i | \(-0.319590\pi\) | ||||
0.536913 | + | 0.843638i | \(0.319590\pi\) | |||||||
\(68\) | 1046.37 | 1.86604 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −35.1322 | −0.0599872 | ||||||||
\(71\) | −48.5526 | −0.0811568 | −0.0405784 | − | 0.999176i | \(-0.512920\pi\) | ||||
−0.0405784 | + | 0.999176i | \(0.512920\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 409.800 | 0.657034 | 0.328517 | − | 0.944498i | \(-0.393451\pi\) | ||||
0.328517 | + | 0.944498i | \(0.393451\pi\) | |||||||
\(74\) | −22.5226 | −0.0353811 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −184.763 | −0.278866 | ||||||||
\(77\) | −565.500 | −0.836944 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 530.527 | 0.755556 | 0.377778 | − | 0.925896i | \(-0.376688\pi\) | ||||
0.377778 | + | 0.925896i | \(0.376688\pi\) | |||||||
\(80\) | −313.924 | −0.438723 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −55.2595 | −0.0744195 | ||||||||
\(83\) | −294.590 | −0.389584 | −0.194792 | − | 0.980845i | \(-0.562403\pi\) | ||||
−0.194792 | + | 0.980845i | \(0.562403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 658.155 | 0.839846 | ||||||||
\(86\) | −31.3495 | −0.0393081 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 65.1278 | 0.0788937 | ||||||||
\(89\) | 852.817 | 1.01571 | 0.507856 | − | 0.861442i | \(-0.330438\pi\) | ||||
0.507856 | + | 0.861442i | \(0.330438\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1564.57 | 1.80233 | ||||||||
\(92\) | 262.211 | 0.297146 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 106.534 | 0.116896 | ||||||||
\(95\) | −116.214 | −0.125509 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −388.091 | −0.406233 | −0.203117 | − | 0.979155i | \(-0.565107\pi\) | ||||
−0.203117 | + | 0.979155i | \(0.565107\pi\) | |||||||
\(98\) | −141.922 | −0.146289 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −198.732 | −0.198732 | ||||||||
\(101\) | −1079.99 | −1.06399 | −0.531997 | − | 0.846746i | \(-0.678558\pi\) | ||||
−0.531997 | + | 0.846746i | \(0.678558\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −594.997 | −0.569192 | −0.284596 | − | 0.958648i | \(-0.591859\pi\) | ||||
−0.284596 | + | 0.958648i | \(0.591859\pi\) | |||||||
\(104\) | −180.190 | −0.169895 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −94.9494 | −0.0870028 | ||||||||
\(107\) | −498.693 | −0.450565 | −0.225282 | − | 0.974293i | \(-0.572330\pi\) | ||||
−0.225282 | + | 0.974293i | \(0.572330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −959.301 | −0.842976 | −0.421488 | − | 0.906834i | \(-0.638492\pi\) | ||||
−0.421488 | + | 0.906834i | \(0.638492\pi\) | |||||||
\(110\) | 20.4172 | 0.0176973 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1958.51 | −1.65234 | ||||||||
\(113\) | 1728.79 | 1.43921 | 0.719607 | − | 0.694382i | \(-0.244322\pi\) | ||||
0.719607 | + | 0.694382i | \(0.244322\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 164.928 | 0.133736 | ||||||||
\(116\) | −1000.16 | −0.800536 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 167.228 | 0.130463 | ||||||||
\(119\) | 4106.10 | 3.16307 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1002.36 | −0.753087 | ||||||||
\(122\) | −2.02215 | −0.00150063 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −994.554 | −0.720271 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1019.95 | 0.712647 | 0.356324 | − | 0.934363i | \(-0.384030\pi\) | ||||
0.356324 | + | 0.934363i | \(0.384030\pi\) | |||||||
\(128\) | 454.025 | 0.313520 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −56.4884 | −0.0381105 | ||||||||
\(131\) | −1702.39 | −1.13541 | −0.567705 | − | 0.823232i | \(-0.692169\pi\) | ||||
−0.567705 | + | 0.823232i | \(0.692169\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −725.037 | −0.472697 | ||||||||
\(134\) | −132.651 | −0.0855172 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −472.893 | −0.298164 | ||||||||
\(137\) | −1049.68 | −0.654599 | −0.327300 | − | 0.944921i | \(-0.606139\pi\) | ||||
−0.327300 | + | 0.944921i | \(0.606139\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1434.82 | 0.875540 | 0.437770 | − | 0.899087i | \(-0.355768\pi\) | ||||
0.437770 | + | 0.899087i | \(0.355768\pi\) | |||||||
\(140\) | −1239.85 | −0.748473 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.9365 | 0.00646316 | ||||||||
\(143\) | −909.256 | −0.531719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −629.087 | −0.360295 | ||||||||
\(146\) | −92.3075 | −0.0523248 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −794.842 | −0.441457 | ||||||||
\(149\) | 1218.46 | 0.669935 | 0.334968 | − | 0.942230i | \(-0.391275\pi\) | ||||
0.334968 | + | 0.942230i | \(0.391275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1609.50 | 0.867414 | 0.433707 | − | 0.901054i | \(-0.357205\pi\) | ||||
0.433707 | + | 0.901054i | \(0.357205\pi\) | |||||||
\(152\) | 83.5014 | 0.0445583 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 127.379 | 0.0666524 | ||||||||
\(155\) | −625.563 | −0.324171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1286.34 | 0.653890 | 0.326945 | − | 0.945043i | \(-0.393981\pi\) | ||||
0.326945 | + | 0.945043i | \(0.393981\pi\) | |||||||
\(158\) | −119.501 | −0.0601708 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 214.414 | 0.105943 | ||||||||
\(161\) | 1028.95 | 0.503683 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1416.84 | 0.680830 | 0.340415 | − | 0.940275i | \(-0.389432\pi\) | ||||
0.340415 | + | 0.940275i | \(0.389432\pi\) | |||||||
\(164\) | −1950.16 | −0.928547 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 66.3563 | 0.0310256 | ||||||||
\(167\) | 894.975 | 0.414702 | 0.207351 | − | 0.978267i | \(-0.433516\pi\) | ||||
0.207351 | + | 0.978267i | \(0.433516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 318.645 | 0.145037 | ||||||||
\(170\) | −148.249 | −0.0668835 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1106.35 | −0.490456 | ||||||||
\(173\) | −1735.10 | −0.762526 | −0.381263 | − | 0.924467i | \(-0.624511\pi\) | ||||
−0.381263 | + | 0.924467i | \(0.624511\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −779.850 | −0.336864 | ||||||||
\(176\) | 1138.19 | 0.487469 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −192.097 | −0.0808892 | ||||||||
\(179\) | 2133.37 | 0.890815 | 0.445408 | − | 0.895328i | \(-0.353059\pi\) | ||||
0.445408 | + | 0.895328i | \(0.353059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3611.98 | −1.48330 | −0.741648 | − | 0.670789i | \(-0.765955\pi\) | ||||
−0.741648 | + | 0.670789i | \(0.765955\pi\) | |||||||
\(182\) | −352.420 | −0.143534 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −118.503 | −0.0474792 | ||||||||
\(185\) | −499.947 | −0.198686 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2386.27 | −0.933162 | ||||||||
\(188\) | 3759.69 | 1.45853 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 26.1772 | 0.00999523 | ||||||||
\(191\) | −596.990 | −0.226160 | −0.113080 | − | 0.993586i | \(-0.536072\pi\) | ||||
−0.113080 | + | 0.993586i | \(0.536072\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1207.74 | −0.450442 | −0.225221 | − | 0.974308i | \(-0.572310\pi\) | ||||
−0.225221 | + | 0.974308i | \(0.572310\pi\) | |||||||
\(194\) | 87.4173 | 0.0323515 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5008.57 | −1.82528 | ||||||||
\(197\) | −3268.56 | −1.18211 | −0.591054 | − | 0.806632i | \(-0.701288\pi\) | ||||
−0.591054 | + | 0.806632i | \(0.701288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2109.88 | −0.751585 | −0.375793 | − | 0.926704i | \(-0.622629\pi\) | ||||
−0.375793 | + | 0.926704i | \(0.622629\pi\) | |||||||
\(200\) | 89.8142 | 0.0317541 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 243.268 | 0.0847342 | ||||||||
\(203\) | −3924.75 | −1.35696 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1226.63 | −0.417909 | ||||||||
\(206\) | 134.023 | 0.0453292 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3149.05 | −1.04975 | ||||||||
\(209\) | 421.357 | 0.139454 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 658.642 | 0.214895 | 0.107447 | − | 0.994211i | \(-0.465732\pi\) | ||||
0.107447 | + | 0.994211i | \(0.465732\pi\) | |||||||
\(212\) | −3350.85 | −1.08555 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 112.330 | 0.0358820 | ||||||||
\(215\) | −695.882 | −0.220738 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3902.77 | −1.22091 | ||||||||
\(218\) | 216.082 | 0.0671328 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 720.540 | 0.220813 | ||||||||
\(221\) | 6602.11 | 2.00953 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1218.79 | 0.365993 | 0.182997 | − | 0.983114i | \(-0.441420\pi\) | ||||
0.182997 | + | 0.983114i | \(0.441420\pi\) | |||||||
\(224\) | 1337.69 | 0.399009 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −389.410 | −0.114616 | ||||||||
\(227\) | −1525.57 | −0.446060 | −0.223030 | − | 0.974812i | \(-0.571595\pi\) | ||||
−0.223030 | + | 0.974812i | \(0.571595\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6182.65 | −1.78411 | −0.892055 | − | 0.451927i | \(-0.850737\pi\) | ||||
−0.892055 | + | 0.451927i | \(0.850737\pi\) | |||||||
\(230\) | −37.1500 | −0.0106504 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 452.008 | 0.127913 | ||||||||
\(233\) | −2013.82 | −0.566222 | −0.283111 | − | 0.959087i | \(-0.591367\pi\) | ||||
−0.283111 | + | 0.959087i | \(0.591367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2364.80 | 0.656438 | ||||||||
\(236\) | 5901.64 | 1.62781 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −924.898 | −0.251900 | ||||||||
\(239\) | 5086.31 | 1.37659 | 0.688297 | − | 0.725429i | \(-0.258359\pi\) | ||||
0.688297 | + | 0.725429i | \(0.258359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3286.83 | 0.878519 | 0.439259 | − | 0.898360i | \(-0.355241\pi\) | ||||
0.439259 | + | 0.898360i | \(0.355241\pi\) | |||||||
\(242\) | 225.781 | 0.0599742 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −71.3634 | −0.0187237 | ||||||||
\(245\) | −3150.33 | −0.821500 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1165.77 | −0.300309 | ||||||||
\(248\) | 449.476 | 0.115088 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 28.1562 | 0.00712303 | ||||||||
\(251\) | 3480.55 | 0.875260 | 0.437630 | − | 0.899155i | \(-0.355818\pi\) | ||||
0.437630 | + | 0.899155i | \(0.355818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −597.979 | −0.148595 | ||||||||
\(254\) | −229.744 | −0.0567537 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3838.69 | 0.937180 | ||||||||
\(257\) | −6794.98 | −1.64926 | −0.824628 | − | 0.565675i | \(-0.808616\pi\) | ||||
−0.824628 | + | 0.565675i | \(0.808616\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3119.07 | −0.748300 | ||||||||
\(260\) | −1993.52 | −0.475512 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 383.464 | 0.0904216 | ||||||||
\(263\) | 5364.24 | 1.25769 | 0.628846 | − | 0.777530i | \(-0.283528\pi\) | ||||
0.628846 | + | 0.777530i | \(0.283528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2107.65 | −0.488572 | ||||||||
\(266\) | 163.314 | 0.0376445 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4681.37 | −1.06702 | ||||||||
\(269\) | 48.4985 | 0.0109926 | 0.00549629 | − | 0.999985i | \(-0.498250\pi\) | ||||
0.00549629 | + | 0.999985i | \(0.498250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7643.16 | 1.71324 | 0.856622 | − | 0.515945i | \(-0.172559\pi\) | ||||
0.856622 | + | 0.515945i | \(0.172559\pi\) | |||||||
\(272\) | −8264.43 | −1.84230 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 236.440 | 0.0521309 | ||||||||
\(275\) | 453.212 | 0.0993807 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5146.02 | 1.11623 | 0.558113 | − | 0.829765i | \(-0.311526\pi\) | ||||
0.558113 | + | 0.829765i | \(0.311526\pi\) | |||||||
\(278\) | −323.193 | −0.0697261 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 560.333 | 0.119594 | ||||||||
\(281\) | 5854.74 | 1.24293 | 0.621467 | − | 0.783440i | \(-0.286537\pi\) | ||||
0.621467 | + | 0.783440i | \(0.286537\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9393.84 | 1.97317 | 0.986583 | − | 0.163260i | \(-0.0522009\pi\) | ||||
0.986583 | + | 0.163260i | \(0.0522009\pi\) | |||||||
\(284\) | 385.957 | 0.0806421 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 204.810 | 0.0423449 | ||||||||
\(287\) | −7652.69 | −1.57395 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12413.7 | 2.52671 | ||||||||
\(290\) | 141.702 | 0.0286932 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3257.61 | −0.652867 | ||||||||
\(293\) | −1780.58 | −0.355026 | −0.177513 | − | 0.984118i | \(-0.556805\pi\) | ||||
−0.177513 | + | 0.984118i | \(0.556805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3712.07 | 0.732627 | ||||||||
\(296\) | 359.219 | 0.0705377 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −274.458 | −0.0533522 | ||||||||
\(299\) | 1654.43 | 0.319995 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4341.47 | −0.831356 | ||||||||
\(302\) | −362.540 | −0.0690790 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1459.30 | 0.275317 | ||||||||
\(305\) | −44.8868 | −0.00842692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8480.18 | 1.57651 | 0.788256 | − | 0.615347i | \(-0.210984\pi\) | ||||
0.788256 | + | 0.615347i | \(0.210984\pi\) | |||||||
\(308\) | 4495.31 | 0.831636 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 140.908 | 0.0258163 | ||||||||
\(311\) | −6810.79 | −1.24182 | −0.620908 | − | 0.783884i | \(-0.713236\pi\) | ||||
−0.620908 | + | 0.783884i | \(0.713236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8046.81 | 1.45314 | 0.726570 | − | 0.687093i | \(-0.241113\pi\) | ||||
0.726570 | + | 0.687093i | \(0.241113\pi\) | |||||||
\(314\) | −289.747 | −0.0520744 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4217.30 | −0.750764 | ||||||||
\(317\) | 1566.22 | 0.277501 | 0.138751 | − | 0.990327i | \(-0.455691\pi\) | ||||
0.138751 | + | 0.990327i | \(0.455691\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2280.88 | 0.400328 | ||||||||
\(320\) | 2463.10 | 0.430286 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −231.772 | −0.0401122 | ||||||||
\(323\) | −3059.47 | −0.527039 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1253.91 | −0.214013 | ||||||||
\(326\) | −319.142 | −0.0542198 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 881.349 | 0.148367 | ||||||||
\(329\) | 14753.5 | 2.47231 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2442.56 | 0.405605 | 0.202802 | − | 0.979220i | \(-0.434995\pi\) | ||||
0.202802 | + | 0.979220i | \(0.434995\pi\) | |||||||
\(332\) | 2341.77 | 0.387113 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −201.593 | −0.0330260 | ||||||||
\(335\) | −2944.53 | −0.480229 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9472.98 | 1.53123 | 0.765617 | − | 0.643296i | \(-0.222434\pi\) | ||||
0.765617 | + | 0.643296i | \(0.222434\pi\) | |||||||
\(338\) | −71.7748 | −0.0115504 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5231.85 | −0.834520 | ||||||||
\(341\) | 2268.10 | 0.360190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8954.76 | −1.40966 | ||||||||
\(344\) | 500.001 | 0.0783670 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 390.830 | 0.0607259 | ||||||||
\(347\) | −3312.47 | −0.512457 | −0.256229 | − | 0.966616i | \(-0.582480\pi\) | ||||
−0.256229 | + | 0.966616i | \(0.582480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5668.95 | 0.869490 | 0.434745 | − | 0.900554i | \(-0.356838\pi\) | ||||
0.434745 | + | 0.900554i | \(0.356838\pi\) | |||||||
\(350\) | 175.661 | 0.0268271 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −777.400 | −0.117715 | ||||||||
\(353\) | −1739.08 | −0.262215 | −0.131108 | − | 0.991368i | \(-0.541853\pi\) | ||||
−0.131108 | + | 0.991368i | \(0.541853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 242.763 | 0.0362944 | ||||||||
\(356\) | −6779.27 | −1.00927 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −480.542 | −0.0709426 | ||||||||
\(359\) | 8624.58 | 1.26793 | 0.633966 | − | 0.773361i | \(-0.281426\pi\) | ||||
0.633966 | + | 0.773361i | \(0.281426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6318.77 | −0.921238 | ||||||||
\(362\) | 813.598 | 0.118126 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12437.2 | −1.79090 | ||||||||
\(365\) | −2049.00 | −0.293835 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6109.17 | −0.868927 | −0.434463 | − | 0.900689i | \(-0.643062\pi\) | ||||
−0.434463 | + | 0.900689i | \(0.643062\pi\) | |||||||
\(368\) | −2071.00 | −0.293365 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 112.613 | 0.0158229 | ||||||||
\(371\) | −13149.2 | −1.84009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6555.33 | 0.909979 | 0.454990 | − | 0.890497i | \(-0.349643\pi\) | ||||
0.454990 | + | 0.890497i | \(0.349643\pi\) | |||||||
\(374\) | 537.507 | 0.0743150 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1699.14 | −0.233050 | ||||||||
\(377\) | −6310.52 | −0.862092 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5032.40 | 0.682050 | 0.341025 | − | 0.940054i | \(-0.389226\pi\) | ||||
0.341025 | + | 0.940054i | \(0.389226\pi\) | |||||||
\(380\) | 923.816 | 0.124713 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 134.472 | 0.0180109 | ||||||||
\(383\) | 3662.99 | 0.488695 | 0.244347 | − | 0.969688i | \(-0.421426\pi\) | ||||
0.244347 | + | 0.969688i | \(0.421426\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2827.50 | 0.374293 | ||||||||
\(386\) | 272.044 | 0.0358722 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3085.03 | 0.403657 | ||||||||
\(389\) | −4870.96 | −0.634878 | −0.317439 | − | 0.948279i | \(-0.602823\pi\) | ||||
−0.317439 | + | 0.948279i | \(0.602823\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4341.93 | 0.561588 | ||||||||
\(392\) | 2263.56 | 0.291650 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 736.243 | 0.0941406 | ||||||||
\(395\) | −2652.63 | −0.337895 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3744.62 | −0.473393 | −0.236696 | − | 0.971584i | \(-0.576065\pi\) | ||||
−0.236696 | + | 0.971584i | \(0.576065\pi\) | |||||||
\(398\) | 475.250 | 0.0598546 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1569.62 | 0.196203 | ||||||||
\(401\) | −1800.87 | −0.224267 | −0.112134 | − | 0.993693i | \(-0.535768\pi\) | ||||
−0.112134 | + | 0.993693i | \(0.535768\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6275.18 | −0.775655 | ||||||||
\(404\) | 8585.16 | 1.05725 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 884.049 | 0.108066 | ||||||||
\(407\) | 1812.66 | 0.220762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15932.0 | 1.92613 | 0.963064 | − | 0.269274i | \(-0.0867837\pi\) | ||||
0.963064 | + | 0.269274i | \(0.0867837\pi\) | |||||||
\(410\) | 276.298 | 0.0332814 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4729.79 | 0.565582 | ||||||||
\(413\) | 23158.8 | 2.75926 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1472.95 | 0.174227 | ||||||||
\(416\) | 2150.84 | 0.253494 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −94.9106 | −0.0111058 | ||||||||
\(419\) | −3447.75 | −0.401989 | −0.200995 | − | 0.979592i | \(-0.564417\pi\) | ||||
−0.200995 | + | 0.979592i | \(0.564417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5615.98 | 0.650133 | 0.325066 | − | 0.945691i | \(-0.394613\pi\) | ||||
0.325066 | + | 0.945691i | \(0.394613\pi\) | |||||||
\(422\) | −148.359 | −0.0171137 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1514.37 | 0.173454 | ||||||||
\(425\) | −3290.77 | −0.375591 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −280.040 | −0.0317379 | ||||||||
\(428\) | 3964.24 | 0.447707 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 156.747 | 0.0175791 | ||||||||
\(431\) | −3534.04 | −0.394962 | −0.197481 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197481 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6674.80 | 0.740809 | 0.370405 | − | 0.928871i | \(-0.379219\pi\) | ||||
0.370405 | + | 0.928871i | \(0.379219\pi\) | |||||||
\(434\) | 879.098 | 0.0972305 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7625.74 | 0.837630 | ||||||||
\(437\) | −766.679 | −0.0839250 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6543.52 | −0.711401 | −0.355700 | − | 0.934600i | \(-0.615758\pi\) | ||||
−0.355700 | + | 0.934600i | \(0.615758\pi\) | |||||||
\(440\) | −325.639 | −0.0352823 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1487.12 | −0.160035 | ||||||||
\(443\) | 14309.7 | 1.53471 | 0.767353 | − | 0.641225i | \(-0.221573\pi\) | ||||
0.767353 | + | 0.641225i | \(0.221573\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4264.09 | −0.454241 | ||||||||
\(446\) | −274.533 | −0.0291469 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15366.8 | 1.62056 | ||||||||
\(449\) | −14587.4 | −1.53324 | −0.766618 | − | 0.642104i | \(-0.778062\pi\) | ||||
−0.766618 | + | 0.642104i | \(0.778062\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4447.38 | 0.464343 | ||||||||
\(452\) | −13742.6 | −1.43009 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 343.634 | 0.0355232 | ||||||||
\(455\) | −7822.87 | −0.806026 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2025.77 | 0.207356 | 0.103678 | − | 0.994611i | \(-0.466939\pi\) | ||||
0.103678 | + | 0.994611i | \(0.466939\pi\) | |||||||
\(458\) | 1392.64 | 0.142083 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1311.06 | −0.132888 | ||||||||
\(461\) | −3556.19 | −0.359280 | −0.179640 | − | 0.983732i | \(-0.557493\pi\) | ||||
−0.179640 | + | 0.983732i | \(0.557493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10282.7 | −1.03213 | −0.516066 | − | 0.856549i | \(-0.672604\pi\) | ||||
−0.516066 | + | 0.856549i | \(0.672604\pi\) | |||||||
\(464\) | 7899.43 | 0.790349 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 453.613 | 0.0450927 | ||||||||
\(467\) | 8217.44 | 0.814256 | 0.407128 | − | 0.913371i | \(-0.366530\pi\) | ||||
0.407128 | + | 0.913371i | \(0.366530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18370.3 | −1.80866 | ||||||||
\(470\) | −532.672 | −0.0522773 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2667.17 | −0.260098 | ||||||||
\(473\) | 2523.06 | 0.245265 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 581.070 | 0.0561291 | ||||||||
\(476\) | −32640.5 | −3.14301 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1145.69 | −0.109629 | ||||||||
\(479\) | 13685.2 | 1.30541 | 0.652705 | − | 0.757612i | \(-0.273634\pi\) | ||||
0.652705 | + | 0.757612i | \(0.273634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5015.09 | −0.475402 | ||||||||
\(482\) | −740.357 | −0.0699633 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7968.01 | 0.748310 | ||||||||
\(485\) | 1940.45 | 0.181673 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3239.59 | −0.301437 | −0.150718 | − | 0.988577i | \(-0.548159\pi\) | ||||
−0.150718 | + | 0.988577i | \(0.548159\pi\) | |||||||
\(488\) | 32.2518 | 0.00299174 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 709.612 | 0.0654225 | ||||||||
\(491\) | 11128.1 | 1.02282 | 0.511409 | − | 0.859338i | \(-0.329124\pi\) | ||||
0.511409 | + | 0.859338i | \(0.329124\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16561.5 | −1.51296 | ||||||||
\(494\) | 262.590 | 0.0239159 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7855.18 | 0.711105 | ||||||||
\(497\) | 1514.55 | 0.136694 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5427.22 | −0.486885 | −0.243443 | − | 0.969915i | \(-0.578277\pi\) | ||||
−0.243443 | + | 0.969915i | \(0.578277\pi\) | |||||||
\(500\) | 993.658 | 0.0888755 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −783.993 | −0.0697038 | ||||||||
\(503\) | −9600.22 | −0.850999 | −0.425500 | − | 0.904959i | \(-0.639902\pi\) | ||||
−0.425500 | + | 0.904959i | \(0.639902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5399.97 | 0.475833 | ||||||||
\(506\) | 134.695 | 0.0118338 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8107.87 | −0.708127 | ||||||||
\(509\) | −18939.9 | −1.64930 | −0.824652 | − | 0.565641i | \(-0.808629\pi\) | ||||
−0.824652 | + | 0.565641i | \(0.808629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12783.3 | −1.10666 | ||||||||
\(512\) | −4496.87 | −0.388155 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1530.57 | 0.131343 | ||||||||
\(515\) | 2974.98 | 0.254550 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8574.06 | −0.729375 | ||||||||
\(518\) | 702.570 | 0.0595930 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 900.948 | 0.0759792 | ||||||||
\(521\) | 19292.6 | 1.62231 | 0.811155 | − | 0.584831i | \(-0.198839\pi\) | ||||
0.811155 | + | 0.584831i | \(0.198839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17967.5 | 1.50223 | 0.751114 | − | 0.660172i | \(-0.229517\pi\) | ||||
0.751114 | + | 0.660172i | \(0.229517\pi\) | |||||||
\(524\) | 13532.8 | 1.12821 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1208.29 | −0.100160 | ||||||||
\(527\) | −16468.7 | −1.36127 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11078.9 | −0.910574 | ||||||||
\(530\) | 474.747 | 0.0389088 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5763.51 | 0.469699 | ||||||||
\(533\) | −12304.6 | −0.999946 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2493.46 | 0.201499 | ||||||||
\(536\) | 2115.69 | 0.170492 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.9243 | −0.000875426 0 | ||||||||
\(539\) | 11422.1 | 0.912777 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8299.36 | −0.659552 | −0.329776 | − | 0.944059i | \(-0.606973\pi\) | ||||
−0.329776 | + | 0.944059i | \(0.606973\pi\) | |||||||
\(542\) | −1721.62 | −0.136439 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5644.71 | 0.444880 | ||||||||
\(545\) | 4796.50 | 0.376990 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 84.7210 | 0.00662232 | 0.00331116 | − | 0.999995i | \(-0.498946\pi\) | ||||
0.00331116 | + | 0.999995i | \(0.498946\pi\) | |||||||
\(548\) | 8344.17 | 0.650448 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −102.086 | −0.00791447 | ||||||||
\(551\) | 2924.35 | 0.226101 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16549.3 | −1.27260 | ||||||||
\(554\) | −1159.14 | −0.0888938 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11405.8 | −0.869987 | ||||||||
\(557\) | −20914.0 | −1.59094 | −0.795469 | − | 0.605994i | \(-0.792776\pi\) | ||||
−0.795469 | + | 0.605994i | \(0.792776\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6980.56 | −0.528169 | ||||||||
\(560\) | 9792.56 | 0.738949 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1318.78 | −0.0989846 | ||||||||
\(563\) | 11041.0 | 0.826503 | 0.413252 | − | 0.910617i | \(-0.364393\pi\) | ||||
0.413252 | + | 0.910617i | \(0.364393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8643.96 | −0.643636 | ||||||||
\(566\) | −2115.96 | −0.157139 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −174.429 | −0.0128853 | ||||||||
\(569\) | −6014.62 | −0.443139 | −0.221569 | − | 0.975145i | \(-0.571118\pi\) | ||||
−0.221569 | + | 0.975145i | \(0.571118\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21937.3 | −1.60779 | −0.803896 | − | 0.594770i | \(-0.797243\pi\) | ||||
−0.803896 | + | 0.594770i | \(0.797243\pi\) | |||||||
\(572\) | 7227.91 | 0.528346 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1723.77 | 0.125346 | ||||||||
\(575\) | −824.641 | −0.0598085 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 473.507 | 0.0341635 | 0.0170818 | − | 0.999854i | \(-0.494562\pi\) | ||||
0.0170818 | + | 0.999854i | \(0.494562\pi\) | |||||||
\(578\) | −2796.19 | −0.201222 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5000.78 | 0.358010 | ||||||||
\(581\) | 9189.44 | 0.656183 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7641.68 | 0.542858 | ||||||||
\(584\) | 1472.24 | 0.104318 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 401.076 | 0.0282735 | ||||||||
\(587\) | 13020.3 | 0.915514 | 0.457757 | − | 0.889077i | \(-0.348653\pi\) | ||||
0.457757 | + | 0.889077i | \(0.348653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2907.97 | 0.203431 | ||||||||
\(590\) | −836.142 | −0.0583448 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6277.82 | 0.435839 | ||||||||
\(593\) | −12887.3 | −0.892441 | −0.446220 | − | 0.894923i | \(-0.647230\pi\) | ||||
−0.446220 | + | 0.894923i | \(0.647230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20530.5 | −1.41457 | ||||||||
\(596\) | −9685.88 | −0.665686 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −372.661 | −0.0254837 | ||||||||
\(599\) | −8674.48 | −0.591702 | −0.295851 | − | 0.955234i | \(-0.595603\pi\) | ||||
−0.295851 | + | 0.955234i | \(0.595603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10935.7 | 0.742225 | 0.371112 | − | 0.928588i | \(-0.378976\pi\) | ||||
0.371112 | + | 0.928588i | \(0.378976\pi\) | |||||||
\(602\) | 977.916 | 0.0662074 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12794.4 | −0.861913 | ||||||||
\(605\) | 5011.79 | 0.336791 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21670.4 | 1.44905 | 0.724527 | − | 0.689246i | \(-0.242058\pi\) | ||||
0.724527 | + | 0.689246i | \(0.242058\pi\) | |||||||
\(608\) | −996.718 | −0.0664840 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.1107 | 0.000671102 0 | ||||||||
\(611\) | 23721.9 | 1.57068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15571.2 | −1.02596 | −0.512982 | − | 0.858399i | \(-0.671459\pi\) | ||||
−0.512982 | + | 0.858399i | \(0.671459\pi\) | |||||||
\(614\) | −1910.16 | −0.125550 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2031.60 | −0.132882 | ||||||||
\(617\) | 9726.54 | 0.634645 | 0.317322 | − | 0.948318i | \(-0.397216\pi\) | ||||
0.317322 | + | 0.948318i | \(0.397216\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6297.59 | 0.408920 | 0.204460 | − | 0.978875i | \(-0.434456\pi\) | ||||
0.204460 | + | 0.978875i | \(0.434456\pi\) | |||||||
\(620\) | 4972.77 | 0.322115 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1534.13 | 0.0988955 | ||||||||
\(623\) | −26602.8 | −1.71078 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −1812.54 | −0.115725 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10225.4 | −0.649743 | ||||||||
\(629\) | −13161.7 | −0.834327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5670.98 | −0.357778 | −0.178889 | − | 0.983869i | \(-0.557250\pi\) | ||||
−0.178889 | + | 0.983869i | \(0.557250\pi\) | |||||||
\(632\) | 1905.95 | 0.119960 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −352.792 | −0.0220996 | ||||||||
\(635\) | −5099.76 | −0.318705 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31601.8 | −1.96563 | ||||||||
\(638\) | −513.767 | −0.0318813 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2270.13 | −0.140210 | ||||||||
\(641\) | 21664.5 | 1.33494 | 0.667470 | − | 0.744637i | \(-0.267377\pi\) | ||||
0.667470 | + | 0.744637i | \(0.267377\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6223.72 | 0.381710 | 0.190855 | − | 0.981618i | \(-0.438874\pi\) | ||||
0.190855 | + | 0.981618i | \(0.438874\pi\) | |||||||
\(644\) | −8179.43 | −0.500488 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 689.146 | 0.0419723 | ||||||||
\(647\) | 20451.9 | 1.24273 | 0.621365 | − | 0.783521i | \(-0.286578\pi\) | ||||
0.621365 | + | 0.783521i | \(0.286578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13458.8 | −0.814029 | ||||||||
\(650\) | 282.442 | 0.0170435 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11262.8 | −0.676512 | ||||||||
\(653\) | 7448.44 | 0.446371 | 0.223185 | − | 0.974776i | \(-0.428354\pi\) | ||||
0.223185 | + | 0.974776i | \(0.428354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8511.96 | 0.507771 | ||||||||
\(656\) | 15402.7 | 0.916731 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3323.23 | −0.196889 | ||||||||
\(659\) | 826.370 | 0.0488480 | 0.0244240 | − | 0.999702i | \(-0.492225\pi\) | ||||
0.0244240 | + | 0.999702i | \(0.492225\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6258.22 | −0.368255 | −0.184127 | − | 0.982902i | \(-0.558946\pi\) | ||||
−0.184127 | + | 0.982902i | \(0.558946\pi\) | |||||||
\(662\) | −550.186 | −0.0323015 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1058.33 | −0.0618544 | ||||||||
\(665\) | 3625.18 | 0.211396 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4150.17 | −0.240922 | ||||||||
\(668\) | −7114.39 | −0.412072 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 663.255 | 0.0382444 | ||||||||
\(671\) | 162.746 | 0.00936324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10079.8 | −0.577337 | −0.288668 | − | 0.957429i | \(-0.593213\pi\) | ||||
−0.288668 | + | 0.957429i | \(0.593213\pi\) | |||||||
\(674\) | −2133.79 | −0.121944 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2532.99 | −0.144117 | ||||||||
\(677\) | −25710.4 | −1.45958 | −0.729788 | − | 0.683674i | \(-0.760381\pi\) | ||||
−0.729788 | + | 0.683674i | \(0.760381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12106.1 | 0.684226 | ||||||||
\(680\) | 2364.47 | 0.133343 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −510.890 | −0.0286847 | ||||||||
\(683\) | −32091.0 | −1.79784 | −0.898922 | − | 0.438109i | \(-0.855648\pi\) | ||||
−0.898922 | + | 0.438109i | \(0.855648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5248.39 | 0.292746 | ||||||||
\(686\) | 2017.06 | 0.112262 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8738.17 | 0.484215 | ||||||||
\(689\) | −21142.3 | −1.16902 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10565.7 | 0.581679 | 0.290839 | − | 0.956772i | \(-0.406066\pi\) | ||||
0.290839 | + | 0.956772i | \(0.406066\pi\) | |||||||
\(692\) | 13792.7 | 0.757690 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 746.133 | 0.0408110 | ||||||||
\(695\) | −7174.11 | −0.391553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32292.4 | −1.75490 | ||||||||
\(698\) | −1276.93 | −0.0692443 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6199.24 | 0.334727 | ||||||||
\(701\) | 13081.8 | 0.704837 | 0.352419 | − | 0.935842i | \(-0.385359\pi\) | ||||
0.352419 | + | 0.935842i | \(0.385359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2324.04 | 0.124684 | ||||||||
\(704\) | −8930.44 | −0.478095 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 391.728 | 0.0208823 | ||||||||
\(707\) | 33689.4 | 1.79211 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28221.2 | −1.49488 | −0.747440 | − | 0.664329i | \(-0.768717\pi\) | ||||
−0.747440 | + | 0.664329i | \(0.768717\pi\) | |||||||
\(710\) | −54.6823 | −0.00289041 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3063.80 | 0.161265 | ||||||||
\(713\) | −4126.92 | −0.216766 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4546.28 | 0.237792 | ||||||||
\(716\) | −16958.8 | −0.885165 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1942.68 | −0.100975 | ||||||||
\(719\) | −11471.4 | −0.595010 | −0.297505 | − | 0.954720i | \(-0.596154\pi\) | ||||
−0.297505 | + | 0.954720i | \(0.596154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18560.3 | 0.958701 | ||||||||
\(722\) | 1423.30 | 0.0733654 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28712.6 | 1.47389 | ||||||||
\(725\) | 3145.44 | 0.161129 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21659.3 | 1.10495 | 0.552475 | − | 0.833530i | \(-0.313684\pi\) | ||||
0.552475 | + | 0.833530i | \(0.313684\pi\) | |||||||
\(728\) | 5620.84 | 0.286157 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 461.537 | 0.0234004 | ||||||||
\(731\) | −18319.9 | −0.926932 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5681.72 | 0.286302 | 0.143151 | − | 0.989701i | \(-0.454277\pi\) | ||||
0.143151 | + | 0.989701i | \(0.454277\pi\) | |||||||
\(734\) | 1376.09 | 0.0691995 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1414.52 | 0.0708421 | ||||||||
\(737\) | 10676.0 | 0.533588 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 261.324 | 0.0130080 | 0.00650402 | − | 0.999979i | \(-0.497930\pi\) | ||||
0.00650402 | + | 0.999979i | \(0.497930\pi\) | |||||||
\(740\) | 3974.21 | 0.197425 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2961.85 | 0.146540 | ||||||||
\(743\) | −16405.9 | −0.810061 | −0.405031 | − | 0.914303i | \(-0.632739\pi\) | ||||
−0.405031 | + | 0.914303i | \(0.632739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6092.31 | −0.299604 | ||||||||
\(746\) | −1476.59 | −0.0724688 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18969.1 | 0.927244 | ||||||||
\(749\) | 15556.2 | 0.758895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21474.6 | 1.04343 | 0.521716 | − | 0.853119i | \(-0.325292\pi\) | ||||
0.521716 | + | 0.853119i | \(0.325292\pi\) | |||||||
\(752\) | −29694.8 | −1.43997 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1421.44 | 0.0686551 | ||||||||
\(755\) | −8047.51 | −0.387919 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13643.2 | −0.655046 | −0.327523 | − | 0.944843i | \(-0.606214\pi\) | ||||
−0.327523 | + | 0.944843i | \(0.606214\pi\) | |||||||
\(758\) | −1133.55 | −0.0543170 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −417.507 | −0.0199271 | ||||||||
\(761\) | 26937.9 | 1.28318 | 0.641589 | − | 0.767048i | \(-0.278275\pi\) | ||||
0.641589 | + | 0.767048i | \(0.278275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29924.4 | 1.41984 | ||||||||
\(764\) | 4745.63 | 0.224726 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −825.088 | −0.0389186 | ||||||||
\(767\) | 37236.6 | 1.75298 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28885.4 | −1.35453 | −0.677265 | − | 0.735739i | \(-0.736835\pi\) | ||||
−0.677265 | + | 0.735739i | \(0.736835\pi\) | |||||||
\(770\) | −636.894 | −0.0298079 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9600.67 | 0.447585 | ||||||||
\(773\) | 3031.34 | 0.141048 | 0.0705238 | − | 0.997510i | \(-0.477533\pi\) | ||||
0.0705238 | + | 0.997510i | \(0.477533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3127.82 | 0.144974 | ||||||||
\(776\) | −1394.24 | −0.0644979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1097.18 | 0.0505603 | ||||||||
\(779\) | 5702.06 | 0.262256 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −880.185 | −0.0403271 | ||||||||
\(782\) | −978.019 | −0.0447236 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 39558.7 | 1.80205 | ||||||||
\(785\) | −6431.68 | −0.292429 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15154.8 | 0.686416 | 0.343208 | − | 0.939259i | \(-0.388486\pi\) | ||||
0.343208 | + | 0.939259i | \(0.388486\pi\) | |||||||
\(788\) | 25982.7 | 1.17461 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 597.505 | 0.0269092 | ||||||||
\(791\) | −53928.0 | −2.42409 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −450.270 | −0.0201634 | ||||||||
\(794\) | 843.474 | 0.0377000 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16772.0 | 0.746819 | ||||||||
\(797\) | 28380.6 | 1.26135 | 0.630673 | − | 0.776048i | \(-0.282779\pi\) | ||||
0.630673 | + | 0.776048i | \(0.282779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62256.3 | 2.75653 | ||||||||
\(800\) | −1072.07 | −0.0473793 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 405.646 | 0.0178602 | ||||||||
\(803\) | 7429.06 | 0.326483 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5144.77 | −0.225254 | ||||||||
\(806\) | 1413.48 | 0.0617715 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3879.95 | −0.168931 | ||||||||
\(809\) | −14569.6 | −0.633175 | −0.316588 | − | 0.948563i | \(-0.602537\pi\) | ||||
−0.316588 | + | 0.948563i | \(0.602537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27927.7 | 1.20921 | 0.604607 | − | 0.796524i | \(-0.293330\pi\) | ||||
0.604607 | + | 0.796524i | \(0.293330\pi\) | |||||||
\(812\) | 31198.9 | 1.34836 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −408.300 | −0.0175810 | ||||||||
\(815\) | −7084.19 | −0.304476 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3234.85 | 0.138523 | ||||||||
\(818\) | −3588.68 | −0.153393 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9750.79 | 0.415259 | ||||||||
\(821\) | 18044.1 | 0.767043 | 0.383521 | − | 0.923532i | \(-0.374711\pi\) | ||||
0.383521 | + | 0.923532i | \(0.374711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32252.8 | −1.36606 | −0.683028 | − | 0.730393i | \(-0.739337\pi\) | ||||
−0.683028 | + | 0.730393i | \(0.739337\pi\) | |||||||
\(824\) | −2137.57 | −0.0903710 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5216.53 | −0.219741 | ||||||||
\(827\) | 13569.5 | 0.570566 | 0.285283 | − | 0.958443i | \(-0.407912\pi\) | ||||
0.285283 | + | 0.958443i | \(0.407912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 742.559 | 0.0311099 | 0.0155550 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155550 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(830\) | −331.782 | −0.0138751 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24707.9 | 1.02956 | ||||||||
\(833\) | −82936.3 | −3.44967 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4474.87 | −0.185460 | ||||||||
\(836\) | −3349.48 | −0.138569 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 776.605 | 0.0320136 | ||||||||
\(839\) | −35504.7 | −1.46097 | −0.730487 | − | 0.682927i | \(-0.760707\pi\) | ||||
−0.730487 | + | 0.682927i | \(0.760707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8558.98 | −0.350936 | ||||||||
\(842\) | −1265.00 | −0.0517752 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5235.72 | −0.213532 | ||||||||
\(845\) | −1593.23 | −0.0648623 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31267.6 | 1.26844 | ||||||||
\(848\) | 26465.7 | 1.07174 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 741.246 | 0.0299112 | ||||||||
\(851\) | −3298.21 | −0.132857 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 375.048 | 0.0150544 | 0.00752719 | − | 0.999972i | \(-0.497604\pi\) | ||||
0.00752719 | + | 0.999972i | \(0.497604\pi\) | |||||||
\(854\) | 63.0790 | 0.00252754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1791.59 | −0.0715365 | ||||||||
\(857\) | 32194.8 | 1.28326 | 0.641629 | − | 0.767015i | \(-0.278259\pi\) | ||||
0.641629 | + | 0.767015i | \(0.278259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28137.5 | −1.11763 | −0.558813 | − | 0.829294i | \(-0.688743\pi\) | ||||
−0.558813 | + | 0.829294i | \(0.688743\pi\) | |||||||
\(860\) | 5531.75 | 0.219338 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 796.042 | 0.0314539 | ||||||||
\(863\) | 15724.6 | 0.620244 | 0.310122 | − | 0.950697i | \(-0.399630\pi\) | ||||
0.310122 | + | 0.950697i | \(0.399630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8675.48 | 0.341012 | ||||||||
\(866\) | −1503.50 | −0.0589964 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 31024.1 | 1.21317 | ||||||||
\(869\) | 9617.64 | 0.375438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29537.3 | −1.14906 | ||||||||
\(872\) | −3446.35 | −0.133840 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 172.694 | 0.00668361 | ||||||||
\(875\) | 3899.25 | 0.150650 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15280.5 | 0.588352 | 0.294176 | − | 0.955751i | \(-0.404955\pi\) | ||||
0.294176 | + | 0.955751i | \(0.404955\pi\) | |||||||
\(878\) | 1473.93 | 0.0566544 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5690.97 | −0.218003 | ||||||||
\(881\) | −24687.6 | −0.944092 | −0.472046 | − | 0.881574i | \(-0.656484\pi\) | ||||
−0.472046 | + | 0.881574i | \(0.656484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6562.59 | 0.250112 | 0.125056 | − | 0.992150i | \(-0.460089\pi\) | ||||
0.125056 | + | 0.992150i | \(0.460089\pi\) | |||||||
\(884\) | −52481.9 | −1.99678 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3223.26 | −0.122221 | ||||||||
\(887\) | 50511.1 | 1.91206 | 0.956030 | − | 0.293270i | \(-0.0947436\pi\) | ||||
0.956030 | + | 0.293270i | \(0.0947436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31816.4 | −1.20032 | ||||||||
\(890\) | 960.485 | 0.0361747 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9688.51 | −0.363672 | ||||||||
\(893\) | −10992.9 | −0.411943 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10666.9 | −0.398385 | ||||||||
\(896\) | −14162.9 | −0.528067 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3285.81 | 0.122104 | ||||||||
\(899\) | 15741.4 | 0.583986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55486.3 | −2.05163 | ||||||||
\(902\) | −1001.77 | −0.0369793 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6210.81 | 0.228505 | ||||||||
\(905\) | 18059.9 | 0.663350 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7017.44 | −0.256902 | −0.128451 | − | 0.991716i | \(-0.541001\pi\) | ||||
−0.128451 | + | 0.991716i | \(0.541001\pi\) | |||||||
\(908\) | 12127.2 | 0.443231 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1762.10 | 0.0641902 | ||||||||
\(911\) | −6124.59 | −0.222741 | −0.111370 | − | 0.993779i | \(-0.535524\pi\) | ||||
−0.111370 | + | 0.993779i | \(0.535524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5340.47 | −0.193586 | ||||||||
\(914\) | −456.305 | −0.0165134 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 49147.5 | 1.77279 | ||||||||
\(917\) | 53104.4 | 1.91239 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23780.7 | 0.853594 | 0.426797 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426797 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(920\) | 592.516 | 0.0212333 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 801.031 | 0.0286123 | ||||||||
\(923\) | 2435.22 | 0.0868430 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2499.74 | 0.0888549 | ||||||||
\(926\) | 2316.17 | 0.0821967 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5395.41 | −0.190854 | ||||||||
\(929\) | 10189.1 | 0.359842 | 0.179921 | − | 0.983681i | \(-0.442416\pi\) | ||||
0.179921 | + | 0.983681i | \(0.442416\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14644.5 | 0.515526 | ||||||||
\(932\) | 16008.4 | 0.562631 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1850.98 | −0.0648456 | ||||||||
\(935\) | 11931.3 | 0.417323 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3880.22 | −0.135284 | −0.0676421 | − | 0.997710i | \(-0.521548\pi\) | ||||
−0.0676421 | + | 0.997710i | \(0.521548\pi\) | |||||||
\(938\) | 4137.92 | 0.144038 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18798.4 | −0.652274 | ||||||||
\(941\) | −38673.9 | −1.33978 | −0.669890 | − | 0.742461i | \(-0.733659\pi\) | ||||
−0.669890 | + | 0.742461i | \(0.733659\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8092.22 | −0.279447 | ||||||||
\(944\) | −46612.3 | −1.60710 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −568.318 | −0.0195324 | ||||||||
\(947\) | −7754.88 | −0.266103 | −0.133052 | − | 0.991109i | \(-0.542478\pi\) | ||||
−0.133052 | + | 0.991109i | \(0.542478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20554.0 | −0.703069 | ||||||||
\(950\) | −130.886 | −0.00447000 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14751.4 | 0.502203 | ||||||||
\(953\) | −22527.9 | −0.765739 | −0.382870 | − | 0.923802i | \(-0.625064\pi\) | ||||
−0.382870 | + | 0.923802i | \(0.625064\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2984.95 | 0.101142 | ||||||||
\(956\) | −40432.4 | −1.36786 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3082.58 | −0.103960 | ||||||||
\(959\) | 32743.7 | 1.10255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14137.8 | −0.474567 | ||||||||
\(962\) | 1129.65 | 0.0378600 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −26127.8 | −0.872947 | ||||||||
\(965\) | 6038.72 | 0.201444 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5652.41 | −0.187972 | −0.0939861 | − | 0.995574i | \(-0.529961\pi\) | ||||
−0.0939861 | + | 0.995574i | \(0.529961\pi\) | |||||||
\(968\) | −3601.04 | −0.119568 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −437.087 | −0.0144680 | ||||||||
\(971\) | 19612.4 | 0.648188 | 0.324094 | − | 0.946025i | \(-0.394941\pi\) | ||||
0.324094 | + | 0.946025i | \(0.394941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44757.9 | −1.47469 | ||||||||
\(974\) | 729.716 | 0.0240058 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 563.642 | 0.0184854 | ||||||||
\(977\) | −27683.6 | −0.906528 | −0.453264 | − | 0.891376i | \(-0.649741\pi\) | ||||
−0.453264 | + | 0.891376i | \(0.649741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15460.3 | 0.504712 | ||||||||
\(980\) | 25042.8 | 0.816290 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2506.60 | −0.0814549 | ||||||||
\(983\) | −30616.4 | −0.993400 | −0.496700 | − | 0.867922i | \(-0.665455\pi\) | ||||
−0.496700 | + | 0.867922i | \(0.665455\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16342.8 | 0.528655 | ||||||||
\(986\) | 3730.47 | 0.120489 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9267.02 | 0.298404 | ||||||||
\(989\) | −4590.82 | −0.147603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14462.4 | −0.463587 | −0.231793 | − | 0.972765i | \(-0.574459\pi\) | ||||
−0.231793 | + | 0.972765i | \(0.574459\pi\) | |||||||
\(992\) | −5365.19 | −0.171719 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −341.152 | −0.0108860 | ||||||||
\(995\) | 10549.4 | 0.336119 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6897.26 | −0.219096 | −0.109548 | − | 0.993982i | \(-0.534940\pi\) | ||||
−0.109548 | + | 0.993982i | \(0.534940\pi\) | |||||||
\(998\) | 1222.48 | 0.0387745 | ||||||||
\(999\) | 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 | 405.4.a.m.1.4 | 7 | ||
3.2 | odd | 2 | 405.4.a.n.1.4 | 7 | |||
5.4 | even | 2 | 2025.4.a.bb.1.4 | 7 | |||
9.2 | odd | 6 | 135.4.e.c.91.4 | 14 | |||
9.4 | even | 3 | 45.4.e.c.16.4 | ✓ | 14 | ||
9.5 | odd | 6 | 135.4.e.c.46.4 | 14 | |||
9.7 | even | 3 | 45.4.e.c.31.4 | yes | 14 | ||
15.14 | odd | 2 | 2025.4.a.ba.1.4 | 7 | |||
45.4 | even | 6 | 225.4.e.d.151.4 | 14 | |||
45.7 | odd | 12 | 225.4.k.d.49.7 | 28 | |||
45.13 | odd | 12 | 225.4.k.d.124.7 | 28 | |||
45.22 | odd | 12 | 225.4.k.d.124.8 | 28 | |||
45.34 | even | 6 | 225.4.e.d.76.4 | 14 | |||
45.43 | odd | 12 | 225.4.k.d.49.8 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.4 | ✓ | 14 | 9.4 | even | 3 | ||
45.4.e.c.31.4 | yes | 14 | 9.7 | even | 3 | ||
135.4.e.c.46.4 | 14 | 9.5 | odd | 6 | |||
135.4.e.c.91.4 | 14 | 9.2 | odd | 6 | |||
225.4.e.d.76.4 | 14 | 45.34 | even | 6 | |||
225.4.e.d.151.4 | 14 | 45.4 | even | 6 | |||
225.4.k.d.49.7 | 28 | 45.7 | odd | 12 | |||
225.4.k.d.49.8 | 28 | 45.43 | odd | 12 | |||
225.4.k.d.124.7 | 28 | 45.13 | odd | 12 | |||
225.4.k.d.124.8 | 28 | 45.22 | odd | 12 | |||
405.4.a.m.1.4 | 7 | 1.1 | even | 1 | trivial | ||
405.4.a.n.1.4 | 7 | 3.2 | odd | 2 | |||
2025.4.a.ba.1.4 | 7 | 15.14 | odd | 2 | |||
2025.4.a.bb.1.4 | 7 | 5.4 | even | 2 |