Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.00000 | −1.76777 | −0.883883 | − | 0.467707i | \(-0.845080\pi\) | ||||
−0.883883 | + | 0.467707i | \(0.845080\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −15.0000 | −1.02062 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −45.0000 | −1.98874 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 51.0000 | 1.22687 | ||||||||
\(13\) | −30.0000 | −0.640039 | −0.320019 | − | 0.947411i | \(-0.603689\pi\) | ||||
−0.320019 | + | 0.947411i | \(0.603689\pi\) | |||||||
\(14\) | 35.0000 | 0.668153 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | 134.000 | 1.91175 | 0.955876 | − | 0.293771i | \(-0.0949105\pi\) | ||||
0.955876 | + | 0.293771i | \(0.0949105\pi\) | |||||||
\(18\) | −45.0000 | −0.589256 | ||||||||
\(19\) | −92.0000 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −60.0000 | −0.581456 | ||||||||
\(23\) | −112.000 | −1.01537 | −0.507687 | − | 0.861541i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861541i | \(0.669499\pi\) | |||||||
\(24\) | −135.000 | −1.14820 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 150.000 | 1.13144 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −119.000 | −0.803175 | ||||||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −224.000 | −1.29779 | −0.648897 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | −85.0000 | −0.469563 | ||||||||
\(33\) | 36.0000 | 0.189903 | ||||||||
\(34\) | −670.000 | −3.37953 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 153.000 | 0.708333 | ||||||||
\(37\) | 146.000 | 0.648710 | 0.324355 | − | 0.945936i | \(-0.394853\pi\) | ||||
0.324355 | + | 0.945936i | \(0.394853\pi\) | |||||||
\(38\) | 460.000 | 1.96373 | ||||||||
\(39\) | −90.0000 | −0.369527 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.0000 | 0.0685641 | 0.0342820 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342820 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(42\) | 105.000 | 0.385758 | ||||||||
\(43\) | −340.000 | −1.20580 | −0.602901 | − | 0.797816i | \(-0.705989\pi\) | ||||
−0.602901 | + | 0.797816i | \(0.705989\pi\) | |||||||
\(44\) | 204.000 | 0.698958 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 560.000 | 1.79495 | ||||||||
\(47\) | −208.000 | −0.645530 | −0.322765 | − | 0.946479i | \(-0.604612\pi\) | ||||
−0.322765 | + | 0.946479i | \(0.604612\pi\) | |||||||
\(48\) | 267.000 | 0.802878 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 402.000 | 1.10375 | ||||||||
\(52\) | −510.000 | −1.36008 | ||||||||
\(53\) | 754.000 | 1.95415 | 0.977074 | − | 0.212899i | \(-0.0682905\pi\) | ||||
0.977074 | + | 0.212899i | \(0.0682905\pi\) | |||||||
\(54\) | −135.000 | −0.340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 315.000 | 0.751672 | ||||||||
\(57\) | −276.000 | −0.641353 | ||||||||
\(58\) | 290.000 | 0.656532 | ||||||||
\(59\) | 380.000 | 0.838505 | 0.419252 | − | 0.907870i | \(-0.362292\pi\) | ||||
0.419252 | + | 0.907870i | \(0.362292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 718.000 | 1.50706 | 0.753529 | − | 0.657415i | \(-0.228350\pi\) | ||||
0.753529 | + | 0.657415i | \(0.228350\pi\) | |||||||
\(62\) | 1120.00 | 2.29420 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −180.000 | −0.335704 | ||||||||
\(67\) | −412.000 | −0.751251 | −0.375625 | − | 0.926772i | \(-0.622572\pi\) | ||||
−0.375625 | + | 0.926772i | \(0.622572\pi\) | |||||||
\(68\) | 2278.00 | 4.06247 | ||||||||
\(69\) | −336.000 | −0.586227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −960.000 | −1.60466 | −0.802331 | − | 0.596879i | \(-0.796407\pi\) | ||||
−0.802331 | + | 0.596879i | \(0.796407\pi\) | |||||||
\(72\) | −405.000 | −0.662913 | ||||||||
\(73\) | −1066.00 | −1.70912 | −0.854561 | − | 0.519352i | \(-0.826174\pi\) | ||||
−0.854561 | + | 0.519352i | \(0.826174\pi\) | |||||||
\(74\) | −730.000 | −1.14677 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1564.00 | −2.36057 | ||||||||
\(77\) | −84.0000 | −0.124321 | ||||||||
\(78\) | 450.000 | 0.653237 | ||||||||
\(79\) | 896.000 | 1.27605 | 0.638025 | − | 0.770016i | \(-0.279752\pi\) | ||||
0.638025 | + | 0.770016i | \(0.279752\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −90.0000 | −0.121205 | ||||||||
\(83\) | −436.000 | −0.576593 | −0.288296 | − | 0.957541i | \(-0.593089\pi\) | ||||
−0.288296 | + | 0.957541i | \(0.593089\pi\) | |||||||
\(84\) | −357.000 | −0.463713 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1700.00 | 2.13158 | ||||||||
\(87\) | −174.000 | −0.214423 | ||||||||
\(88\) | −540.000 | −0.654139 | ||||||||
\(89\) | −1038.00 | −1.23627 | −0.618134 | − | 0.786073i | \(-0.712111\pi\) | ||||
−0.618134 | + | 0.786073i | \(0.712111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 210.000 | 0.241912 | ||||||||
\(92\) | −1904.00 | −2.15767 | ||||||||
\(93\) | −672.000 | −0.749281 | ||||||||
\(94\) | 1040.00 | 1.14115 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −255.000 | −0.271102 | ||||||||
\(97\) | 702.000 | 0.734818 | 0.367409 | − | 0.930060i | \(-0.380245\pi\) | ||||
0.367409 | + | 0.930060i | \(0.380245\pi\) | |||||||
\(98\) | −245.000 | −0.252538 | ||||||||
\(99\) | 108.000 | 0.109640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 46.0000 | 0.0453185 | 0.0226593 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226593 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(102\) | −2010.00 | −1.95117 | ||||||||
\(103\) | −1880.00 | −1.79847 | −0.899233 | − | 0.437471i | \(-0.855874\pi\) | ||||
−0.899233 | + | 0.437471i | \(0.855874\pi\) | |||||||
\(104\) | 1350.00 | 1.27287 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3770.00 | −3.45448 | ||||||||
\(107\) | −732.000 | −0.661356 | −0.330678 | − | 0.943744i | \(-0.607277\pi\) | ||||
−0.330678 | + | 0.943744i | \(0.607277\pi\) | |||||||
\(108\) | 459.000 | 0.408956 | ||||||||
\(109\) | −378.000 | −0.332164 | −0.166082 | − | 0.986112i | \(-0.553112\pi\) | ||||
−0.166082 | + | 0.986112i | \(0.553112\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 438.000 | 0.374533 | ||||||||
\(112\) | −623.000 | −0.525607 | ||||||||
\(113\) | −1458.00 | −1.21378 | −0.606890 | − | 0.794786i | \(-0.707583\pi\) | ||||
−0.606890 | + | 0.794786i | \(0.707583\pi\) | |||||||
\(114\) | 1380.00 | 1.13376 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −986.000 | −0.789205 | ||||||||
\(117\) | −270.000 | −0.213346 | ||||||||
\(118\) | −1900.00 | −1.48228 | ||||||||
\(119\) | −938.000 | −0.722574 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | −3590.00 | −2.66413 | ||||||||
\(123\) | 54.0000 | 0.0395855 | ||||||||
\(124\) | −3808.00 | −2.75781 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 315.000 | 0.222718 | ||||||||
\(127\) | −608.000 | −0.424813 | −0.212407 | − | 0.977181i | \(-0.568130\pi\) | ||||
−0.212407 | + | 0.977181i | \(0.568130\pi\) | |||||||
\(128\) | 2115.00 | 1.46048 | ||||||||
\(129\) | −1020.00 | −0.696170 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −956.000 | −0.637604 | −0.318802 | − | 0.947821i | \(-0.603280\pi\) | ||||
−0.318802 | + | 0.947821i | \(0.603280\pi\) | |||||||
\(132\) | 612.000 | 0.403544 | ||||||||
\(133\) | 644.000 | 0.419864 | ||||||||
\(134\) | 2060.00 | 1.32804 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6030.00 | −3.80197 | ||||||||
\(137\) | 374.000 | 0.233233 | 0.116617 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116617 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(138\) | 1680.00 | 1.03631 | ||||||||
\(139\) | 396.000 | 0.241642 | 0.120821 | − | 0.992674i | \(-0.461447\pi\) | ||||
0.120821 | + | 0.992674i | \(0.461447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −624.000 | −0.372697 | ||||||||
\(142\) | 4800.00 | 2.83667 | ||||||||
\(143\) | −360.000 | −0.210522 | ||||||||
\(144\) | 801.000 | 0.463542 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5330.00 | 3.02133 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 2482.00 | 1.37851 | ||||||||
\(149\) | −1874.00 | −1.03036 | −0.515181 | − | 0.857081i | \(-0.672275\pi\) | ||||
−0.515181 | + | 0.857081i | \(0.672275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1096.00 | −0.590670 | −0.295335 | − | 0.955394i | \(-0.595431\pi\) | ||||
−0.295335 | + | 0.955394i | \(0.595431\pi\) | |||||||
\(152\) | 4140.00 | 2.20920 | ||||||||
\(153\) | 1206.00 | 0.637250 | ||||||||
\(154\) | 420.000 | 0.219770 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1530.00 | −0.785244 | ||||||||
\(157\) | −1918.00 | −0.974988 | −0.487494 | − | 0.873126i | \(-0.662089\pi\) | ||||
−0.487494 | + | 0.873126i | \(0.662089\pi\) | |||||||
\(158\) | −4480.00 | −2.25576 | ||||||||
\(159\) | 2262.00 | 1.12823 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 784.000 | 0.383776 | ||||||||
\(162\) | −405.000 | −0.196419 | ||||||||
\(163\) | −2316.00 | −1.11290 | −0.556451 | − | 0.830880i | \(-0.687837\pi\) | ||||
−0.556451 | + | 0.830880i | \(0.687837\pi\) | |||||||
\(164\) | 306.000 | 0.145699 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2180.00 | 1.01928 | ||||||||
\(167\) | 1736.00 | 0.804405 | 0.402203 | − | 0.915551i | \(-0.368245\pi\) | ||||
0.402203 | + | 0.915551i | \(0.368245\pi\) | |||||||
\(168\) | 945.000 | 0.433978 | ||||||||
\(169\) | −1297.00 | −0.590350 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −828.000 | −0.370285 | ||||||||
\(172\) | −5780.00 | −2.56233 | ||||||||
\(173\) | 2442.00 | 1.07319 | 0.536595 | − | 0.843840i | \(-0.319710\pi\) | ||||
0.536595 | + | 0.843840i | \(0.319710\pi\) | |||||||
\(174\) | 870.000 | 0.379049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1068.00 | 0.457406 | ||||||||
\(177\) | 1140.00 | 0.484111 | ||||||||
\(178\) | 5190.00 | 2.18543 | ||||||||
\(179\) | −4092.00 | −1.70866 | −0.854331 | − | 0.519730i | \(-0.826033\pi\) | ||||
−0.854331 | + | 0.519730i | \(0.826033\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1270.00 | 0.521538 | 0.260769 | − | 0.965401i | \(-0.416024\pi\) | ||||
0.260769 | + | 0.965401i | \(0.416024\pi\) | |||||||
\(182\) | −1050.00 | −0.427644 | ||||||||
\(183\) | 2154.00 | 0.870100 | ||||||||
\(184\) | 5040.00 | 2.01931 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3360.00 | 1.32455 | ||||||||
\(187\) | 1608.00 | 0.628816 | ||||||||
\(188\) | −3536.00 | −1.37175 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4904.00 | 1.85781 | 0.928903 | − | 0.370323i | \(-0.120753\pi\) | ||||
0.928903 | + | 0.370323i | \(0.120753\pi\) | |||||||
\(192\) | −861.000 | −0.323632 | ||||||||
\(193\) | −2178.00 | −0.812310 | −0.406155 | − | 0.913804i | \(-0.633131\pi\) | ||||
−0.406155 | + | 0.913804i | \(0.633131\pi\) | |||||||
\(194\) | −3510.00 | −1.29899 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 833.000 | 0.303571 | ||||||||
\(197\) | 2850.00 | 1.03073 | 0.515366 | − | 0.856970i | \(-0.327656\pi\) | ||||
0.515366 | + | 0.856970i | \(0.327656\pi\) | |||||||
\(198\) | −540.000 | −0.193819 | ||||||||
\(199\) | −1144.00 | −0.407518 | −0.203759 | − | 0.979021i | \(-0.565316\pi\) | ||||
−0.203759 | + | 0.979021i | \(0.565316\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1236.00 | −0.433735 | ||||||||
\(202\) | −230.000 | −0.0801126 | ||||||||
\(203\) | 406.000 | 0.140372 | ||||||||
\(204\) | 6834.00 | 2.34547 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9400.00 | 3.17927 | ||||||||
\(207\) | −1008.00 | −0.338458 | ||||||||
\(208\) | −2670.00 | −0.890054 | ||||||||
\(209\) | −1104.00 | −0.365384 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 412.000 | 0.134423 | 0.0672115 | − | 0.997739i | \(-0.478590\pi\) | ||||
0.0672115 | + | 0.997739i | \(0.478590\pi\) | |||||||
\(212\) | 12818.0 | 4.15257 | ||||||||
\(213\) | −2880.00 | −0.926452 | ||||||||
\(214\) | 3660.00 | 1.16912 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1215.00 | −0.382733 | ||||||||
\(217\) | 1568.00 | 0.490520 | ||||||||
\(218\) | 1890.00 | 0.587188 | ||||||||
\(219\) | −3198.00 | −0.986762 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4020.00 | −1.22359 | ||||||||
\(222\) | −2190.00 | −0.662086 | ||||||||
\(223\) | 1632.00 | 0.490075 | 0.245038 | − | 0.969514i | \(-0.421200\pi\) | ||||
0.245038 | + | 0.969514i | \(0.421200\pi\) | |||||||
\(224\) | 595.000 | 0.177478 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7290.00 | 2.14568 | ||||||||
\(227\) | −4084.00 | −1.19412 | −0.597059 | − | 0.802198i | \(-0.703664\pi\) | ||||
−0.597059 | + | 0.802198i | \(0.703664\pi\) | |||||||
\(228\) | −4692.00 | −1.36287 | ||||||||
\(229\) | −3386.00 | −0.977088 | −0.488544 | − | 0.872539i | \(-0.662472\pi\) | ||||
−0.488544 | + | 0.872539i | \(0.662472\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −252.000 | −0.0717765 | ||||||||
\(232\) | 2610.00 | 0.738599 | ||||||||
\(233\) | −5322.00 | −1.49638 | −0.748188 | − | 0.663486i | \(-0.769076\pi\) | ||||
−0.748188 | + | 0.663486i | \(0.769076\pi\) | |||||||
\(234\) | 1350.00 | 0.377146 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6460.00 | 1.78182 | ||||||||
\(237\) | 2688.00 | 0.736727 | ||||||||
\(238\) | 4690.00 | 1.27734 | ||||||||
\(239\) | 3736.00 | 1.01114 | 0.505569 | − | 0.862786i | \(-0.331283\pi\) | ||||
0.505569 | + | 0.862786i | \(0.331283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 210.000 | 0.0561298 | 0.0280649 | − | 0.999606i | \(-0.491065\pi\) | ||||
0.0280649 | + | 0.999606i | \(0.491065\pi\) | |||||||
\(242\) | 5935.00 | 1.57651 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 12206.0 | 3.20250 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −270.000 | −0.0699779 | ||||||||
\(247\) | 2760.00 | 0.710990 | ||||||||
\(248\) | 10080.0 | 2.58097 | ||||||||
\(249\) | −1308.00 | −0.332896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4212.00 | −1.05920 | −0.529600 | − | 0.848248i | \(-0.677658\pi\) | ||||
−0.529600 | + | 0.848248i | \(0.677658\pi\) | |||||||
\(252\) | −1071.00 | −0.267725 | ||||||||
\(253\) | −1344.00 | −0.333978 | ||||||||
\(254\) | 3040.00 | 0.750971 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | −5130.00 | −1.24514 | −0.622569 | − | 0.782565i | \(-0.713911\pi\) | ||||
−0.622569 | + | 0.782565i | \(0.713911\pi\) | |||||||
\(258\) | 5100.00 | 1.23067 | ||||||||
\(259\) | −1022.00 | −0.245189 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −522.000 | −0.123797 | ||||||||
\(262\) | 4780.00 | 1.12714 | ||||||||
\(263\) | −848.000 | −0.198821 | −0.0994105 | − | 0.995047i | \(-0.531696\pi\) | ||||
−0.0994105 | + | 0.995047i | \(0.531696\pi\) | |||||||
\(264\) | −1620.00 | −0.377667 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3220.00 | −0.742221 | ||||||||
\(267\) | −3114.00 | −0.713759 | ||||||||
\(268\) | −7004.00 | −1.59641 | ||||||||
\(269\) | −1274.00 | −0.288763 | −0.144381 | − | 0.989522i | \(-0.546119\pi\) | ||||
−0.144381 | + | 0.989522i | \(0.546119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 864.000 | 0.193669 | 0.0968344 | − | 0.995301i | \(-0.469128\pi\) | ||||
0.0968344 | + | 0.995301i | \(0.469128\pi\) | |||||||
\(272\) | 11926.0 | 2.65853 | ||||||||
\(273\) | 630.000 | 0.139668 | ||||||||
\(274\) | −1870.00 | −0.412302 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5712.00 | −1.24573 | ||||||||
\(277\) | 8530.00 | 1.85025 | 0.925123 | − | 0.379668i | \(-0.123962\pi\) | ||||
0.925123 | + | 0.379668i | \(0.123962\pi\) | |||||||
\(278\) | −1980.00 | −0.427167 | ||||||||
\(279\) | −2016.00 | −0.432598 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5382.00 | −1.14257 | −0.571287 | − | 0.820750i | \(-0.693556\pi\) | ||||
−0.571287 | + | 0.820750i | \(0.693556\pi\) | |||||||
\(282\) | 3120.00 | 0.658841 | ||||||||
\(283\) | −6236.00 | −1.30986 | −0.654932 | − | 0.755687i | \(-0.727303\pi\) | ||||
−0.654932 | + | 0.755687i | \(0.727303\pi\) | |||||||
\(284\) | −16320.0 | −3.40991 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1800.00 | 0.372155 | ||||||||
\(287\) | −126.000 | −0.0259148 | ||||||||
\(288\) | −765.000 | −0.156521 | ||||||||
\(289\) | 13043.0 | 2.65479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2106.00 | 0.424247 | ||||||||
\(292\) | −18122.0 | −3.63188 | ||||||||
\(293\) | 818.000 | 0.163099 | 0.0815496 | − | 0.996669i | \(-0.474013\pi\) | ||||
0.0815496 | + | 0.996669i | \(0.474013\pi\) | |||||||
\(294\) | −735.000 | −0.145803 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6570.00 | −1.29011 | ||||||||
\(297\) | 324.000 | 0.0633010 | ||||||||
\(298\) | 9370.00 | 1.82144 | ||||||||
\(299\) | 3360.00 | 0.649879 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2380.00 | 0.455751 | ||||||||
\(302\) | 5480.00 | 1.04417 | ||||||||
\(303\) | 138.000 | 0.0261647 | ||||||||
\(304\) | −8188.00 | −1.54478 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6030.00 | −1.12651 | ||||||||
\(307\) | 2268.00 | 0.421634 | 0.210817 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210817 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(308\) | −1428.00 | −0.264181 | ||||||||
\(309\) | −5640.00 | −1.03834 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6648.00 | 1.21213 | 0.606067 | − | 0.795414i | \(-0.292746\pi\) | ||||
0.606067 | + | 0.795414i | \(0.292746\pi\) | |||||||
\(312\) | 4050.00 | 0.734891 | ||||||||
\(313\) | −9818.00 | −1.77299 | −0.886495 | − | 0.462737i | \(-0.846867\pi\) | ||||
−0.886495 | + | 0.462737i | \(0.846867\pi\) | |||||||
\(314\) | 9590.00 | 1.72355 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15232.0 | 2.71160 | ||||||||
\(317\) | −934.000 | −0.165485 | −0.0827424 | − | 0.996571i | \(-0.526368\pi\) | ||||
−0.0827424 | + | 0.996571i | \(0.526368\pi\) | |||||||
\(318\) | −11310.0 | −1.99444 | ||||||||
\(319\) | −696.000 | −0.122158 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2196.00 | −0.381834 | ||||||||
\(322\) | −3920.00 | −0.678426 | ||||||||
\(323\) | −12328.0 | −2.12368 | ||||||||
\(324\) | 1377.00 | 0.236111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11580.0 | 1.96735 | ||||||||
\(327\) | −1134.00 | −0.191775 | ||||||||
\(328\) | −810.000 | −0.136356 | ||||||||
\(329\) | 1456.00 | 0.243987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2292.00 | 0.380603 | 0.190302 | − | 0.981726i | \(-0.439053\pi\) | ||||
0.190302 | + | 0.981726i | \(0.439053\pi\) | |||||||
\(332\) | −7412.00 | −1.22526 | ||||||||
\(333\) | 1314.00 | 0.216237 | ||||||||
\(334\) | −8680.00 | −1.42200 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1869.00 | −0.303459 | ||||||||
\(337\) | 6062.00 | 0.979876 | 0.489938 | − | 0.871757i | \(-0.337019\pi\) | ||||
0.489938 | + | 0.871757i | \(0.337019\pi\) | |||||||
\(338\) | 6485.00 | 1.04360 | ||||||||
\(339\) | −4374.00 | −0.700776 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2688.00 | −0.426872 | ||||||||
\(342\) | 4140.00 | 0.654578 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 15300.0 | 2.39803 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12210.0 | −1.89715 | ||||||||
\(347\) | −1484.00 | −0.229583 | −0.114791 | − | 0.993390i | \(-0.536620\pi\) | ||||
−0.114791 | + | 0.993390i | \(0.536620\pi\) | |||||||
\(348\) | −2958.00 | −0.455648 | ||||||||
\(349\) | 254.000 | 0.0389579 | 0.0194790 | − | 0.999810i | \(-0.493799\pi\) | ||||
0.0194790 | + | 0.999810i | \(0.493799\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −810.000 | −0.123176 | ||||||||
\(352\) | −1020.00 | −0.154449 | ||||||||
\(353\) | 10950.0 | 1.65102 | 0.825509 | − | 0.564388i | \(-0.190888\pi\) | ||||
0.825509 | + | 0.564388i | \(0.190888\pi\) | |||||||
\(354\) | −5700.00 | −0.855795 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17646.0 | −2.62707 | ||||||||
\(357\) | −2814.00 | −0.417178 | ||||||||
\(358\) | 20460.0 | 3.02052 | ||||||||
\(359\) | 11376.0 | 1.67243 | 0.836215 | − | 0.548402i | \(-0.184764\pi\) | ||||
0.836215 | + | 0.548402i | \(0.184764\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | −6350.00 | −0.921957 | ||||||||
\(363\) | −3561.00 | −0.514887 | ||||||||
\(364\) | 3570.00 | 0.514063 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −10770.0 | −1.53813 | ||||||||
\(367\) | 1136.00 | 0.161577 | 0.0807884 | − | 0.996731i | \(-0.474256\pi\) | ||||
0.0807884 | + | 0.996731i | \(0.474256\pi\) | |||||||
\(368\) | −9968.00 | −1.41201 | ||||||||
\(369\) | 162.000 | 0.0228547 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5278.00 | −0.738599 | ||||||||
\(372\) | −11424.0 | −1.59222 | ||||||||
\(373\) | 8242.00 | 1.14411 | 0.572057 | − | 0.820214i | \(-0.306146\pi\) | ||||
0.572057 | + | 0.820214i | \(0.306146\pi\) | |||||||
\(374\) | −8040.00 | −1.11160 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9360.00 | 1.28379 | ||||||||
\(377\) | 1740.00 | 0.237704 | ||||||||
\(378\) | 945.000 | 0.128586 | ||||||||
\(379\) | 3620.00 | 0.490625 | 0.245313 | − | 0.969444i | \(-0.421109\pi\) | ||||
0.245313 | + | 0.969444i | \(0.421109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1824.00 | −0.245266 | ||||||||
\(382\) | −24520.0 | −3.28417 | ||||||||
\(383\) | 8464.00 | 1.12922 | 0.564609 | − | 0.825359i | \(-0.309027\pi\) | ||||
0.564609 | + | 0.825359i | \(0.309027\pi\) | |||||||
\(384\) | 6345.00 | 0.843208 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10890.0 | 1.43598 | ||||||||
\(387\) | −3060.00 | −0.401934 | ||||||||
\(388\) | 11934.0 | 1.56149 | ||||||||
\(389\) | 3678.00 | 0.479388 | 0.239694 | − | 0.970848i | \(-0.422953\pi\) | ||||
0.239694 | + | 0.970848i | \(0.422953\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15008.0 | −1.94114 | ||||||||
\(392\) | −2205.00 | −0.284105 | ||||||||
\(393\) | −2868.00 | −0.368121 | ||||||||
\(394\) | −14250.0 | −1.82209 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1836.00 | 0.232986 | ||||||||
\(397\) | −12590.0 | −1.59162 | −0.795811 | − | 0.605545i | \(-0.792955\pi\) | ||||
−0.795811 | + | 0.605545i | \(0.792955\pi\) | |||||||
\(398\) | 5720.00 | 0.720396 | ||||||||
\(399\) | 1932.00 | 0.242408 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2850.00 | 0.354918 | 0.177459 | − | 0.984128i | \(-0.443212\pi\) | ||||
0.177459 | + | 0.984128i | \(0.443212\pi\) | |||||||
\(402\) | 6180.00 | 0.766742 | ||||||||
\(403\) | 6720.00 | 0.830638 | ||||||||
\(404\) | 782.000 | 0.0963019 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2030.00 | −0.248146 | ||||||||
\(407\) | 1752.00 | 0.213374 | ||||||||
\(408\) | −18090.0 | −2.19507 | ||||||||
\(409\) | 1226.00 | 0.148220 | 0.0741098 | − | 0.997250i | \(-0.476388\pi\) | ||||
0.0741098 | + | 0.997250i | \(0.476388\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1122.00 | 0.134657 | ||||||||
\(412\) | −31960.0 | −3.82174 | ||||||||
\(413\) | −2660.00 | −0.316925 | ||||||||
\(414\) | 5040.00 | 0.598315 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2550.00 | 0.300539 | ||||||||
\(417\) | 1188.00 | 0.139512 | ||||||||
\(418\) | 5520.00 | 0.645914 | ||||||||
\(419\) | 612.000 | 0.0713560 | 0.0356780 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356780 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5182.00 | 0.599894 | 0.299947 | − | 0.953956i | \(-0.403031\pi\) | ||||
0.299947 | + | 0.953956i | \(0.403031\pi\) | |||||||
\(422\) | −2060.00 | −0.237629 | ||||||||
\(423\) | −1872.00 | −0.215177 | ||||||||
\(424\) | −33930.0 | −3.88629 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14400.0 | 1.63775 | ||||||||
\(427\) | −5026.00 | −0.569614 | ||||||||
\(428\) | −12444.0 | −1.40538 | ||||||||
\(429\) | −1080.00 | −0.121545 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4984.00 | −0.557009 | −0.278504 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278504 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(432\) | 2403.00 | 0.267626 | ||||||||
\(433\) | 1694.00 | 0.188010 | 0.0940051 | − | 0.995572i | \(-0.470033\pi\) | ||||
0.0940051 | + | 0.995572i | \(0.470033\pi\) | |||||||
\(434\) | −7840.00 | −0.867125 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6426.00 | −0.705848 | ||||||||
\(437\) | 10304.0 | 1.12793 | ||||||||
\(438\) | 15990.0 | 1.74436 | ||||||||
\(439\) | 13864.0 | 1.50727 | 0.753636 | − | 0.657292i | \(-0.228298\pi\) | ||||
0.753636 | + | 0.657292i | \(0.228298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 20100.0 | 2.16303 | ||||||||
\(443\) | 4644.00 | 0.498066 | 0.249033 | − | 0.968495i | \(-0.419887\pi\) | ||||
0.249033 | + | 0.968495i | \(0.419887\pi\) | |||||||
\(444\) | 7446.00 | 0.795882 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8160.00 | −0.866339 | ||||||||
\(447\) | −5622.00 | −0.594880 | ||||||||
\(448\) | 2009.00 | 0.211867 | ||||||||
\(449\) | −4926.00 | −0.517756 | −0.258878 | − | 0.965910i | \(-0.583353\pi\) | ||||
−0.258878 | + | 0.965910i | \(0.583353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 216.000 | 0.0225522 | ||||||||
\(452\) | −24786.0 | −2.57928 | ||||||||
\(453\) | −3288.00 | −0.341024 | ||||||||
\(454\) | 20420.0 | 2.11092 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12420.0 | 1.27548 | ||||||||
\(457\) | 14694.0 | 1.50406 | 0.752031 | − | 0.659128i | \(-0.229074\pi\) | ||||
0.752031 | + | 0.659128i | \(0.229074\pi\) | |||||||
\(458\) | 16930.0 | 1.72726 | ||||||||
\(459\) | 3618.00 | 0.367917 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2006.00 | 0.202665 | 0.101333 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101333 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(462\) | 1260.00 | 0.126884 | ||||||||
\(463\) | −4896.00 | −0.491439 | −0.245720 | − | 0.969341i | \(-0.579024\pi\) | ||||
−0.245720 | + | 0.969341i | \(0.579024\pi\) | |||||||
\(464\) | −5162.00 | −0.516465 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26610.0 | 2.64525 | ||||||||
\(467\) | −2660.00 | −0.263576 | −0.131788 | − | 0.991278i | \(-0.542072\pi\) | ||||
−0.131788 | + | 0.991278i | \(0.542072\pi\) | |||||||
\(468\) | −4590.00 | −0.453361 | ||||||||
\(469\) | 2884.00 | 0.283946 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5754.00 | −0.562909 | ||||||||
\(472\) | −17100.0 | −1.66757 | ||||||||
\(473\) | −4080.00 | −0.396614 | ||||||||
\(474\) | −13440.0 | −1.30236 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −15946.0 | −1.53547 | ||||||||
\(477\) | 6786.00 | 0.651383 | ||||||||
\(478\) | −18680.0 | −1.78745 | ||||||||
\(479\) | −5600.00 | −0.534176 | −0.267088 | − | 0.963672i | \(-0.586062\pi\) | ||||
−0.267088 | + | 0.963672i | \(0.586062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4380.00 | −0.415199 | ||||||||
\(482\) | −1050.00 | −0.0992245 | ||||||||
\(483\) | 2352.00 | 0.221573 | ||||||||
\(484\) | −20179.0 | −1.89510 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1215.00 | −0.113402 | ||||||||
\(487\) | 6424.00 | 0.597740 | 0.298870 | − | 0.954294i | \(-0.403390\pi\) | ||||
0.298870 | + | 0.954294i | \(0.403390\pi\) | |||||||
\(488\) | −32310.0 | −2.99714 | ||||||||
\(489\) | −6948.00 | −0.642535 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18900.0 | −1.73716 | −0.868579 | − | 0.495550i | \(-0.834967\pi\) | ||||
−0.868579 | + | 0.495550i | \(0.834967\pi\) | |||||||
\(492\) | 918.000 | 0.0841192 | ||||||||
\(493\) | −7772.00 | −0.710007 | ||||||||
\(494\) | −13800.0 | −1.25687 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19936.0 | −1.80474 | ||||||||
\(497\) | 6720.00 | 0.606505 | ||||||||
\(498\) | 6540.00 | 0.588483 | ||||||||
\(499\) | −15364.0 | −1.37833 | −0.689165 | − | 0.724604i | \(-0.742023\pi\) | ||||
−0.689165 | + | 0.724604i | \(0.742023\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5208.00 | 0.464424 | ||||||||
\(502\) | 21060.0 | 1.87242 | ||||||||
\(503\) | −2216.00 | −0.196435 | −0.0982173 | − | 0.995165i | \(-0.531314\pi\) | ||||
−0.0982173 | + | 0.995165i | \(0.531314\pi\) | |||||||
\(504\) | 2835.00 | 0.250557 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6720.00 | 0.590396 | ||||||||
\(507\) | −3891.00 | −0.340839 | ||||||||
\(508\) | −10336.0 | −0.902728 | ||||||||
\(509\) | −3754.00 | −0.326902 | −0.163451 | − | 0.986551i | \(-0.552263\pi\) | ||||
−0.163451 | + | 0.986551i | \(0.552263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7462.00 | 0.645987 | ||||||||
\(512\) | 24475.0 | 2.11260 | ||||||||
\(513\) | −2484.00 | −0.213784 | ||||||||
\(514\) | 25650.0 | 2.20111 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −17340.0 | −1.47936 | ||||||||
\(517\) | −2496.00 | −0.212329 | ||||||||
\(518\) | 5110.00 | 0.433437 | ||||||||
\(519\) | 7326.00 | 0.619606 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4702.00 | −0.395390 | −0.197695 | − | 0.980264i | \(-0.563346\pi\) | ||||
−0.197695 | + | 0.980264i | \(0.563346\pi\) | |||||||
\(522\) | 2610.00 | 0.218844 | ||||||||
\(523\) | 22660.0 | 1.89456 | 0.947278 | − | 0.320413i | \(-0.103822\pi\) | ||||
0.947278 | + | 0.320413i | \(0.103822\pi\) | |||||||
\(524\) | −16252.0 | −1.35491 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4240.00 | 0.351469 | ||||||||
\(527\) | −30016.0 | −2.48106 | ||||||||
\(528\) | 3204.00 | 0.264084 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3420.00 | 0.279502 | ||||||||
\(532\) | 10948.0 | 0.892211 | ||||||||
\(533\) | −540.000 | −0.0438837 | ||||||||
\(534\) | 15570.0 | 1.26176 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18540.0 | 1.49404 | ||||||||
\(537\) | −12276.0 | −0.986496 | ||||||||
\(538\) | 6370.00 | 0.510465 | ||||||||
\(539\) | 588.000 | 0.0469888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8634.00 | −0.686145 | −0.343073 | − | 0.939309i | \(-0.611468\pi\) | ||||
−0.343073 | + | 0.939309i | \(0.611468\pi\) | |||||||
\(542\) | −4320.00 | −0.342361 | ||||||||
\(543\) | 3810.00 | 0.301110 | ||||||||
\(544\) | −11390.0 | −0.897688 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3150.00 | −0.246900 | ||||||||
\(547\) | 19284.0 | 1.50736 | 0.753679 | − | 0.657243i | \(-0.228278\pi\) | ||||
0.753679 | + | 0.657243i | \(0.228278\pi\) | |||||||
\(548\) | 6358.00 | 0.495621 | ||||||||
\(549\) | 6462.00 | 0.502352 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5336.00 | 0.412561 | ||||||||
\(552\) | 15120.0 | 1.16585 | ||||||||
\(553\) | −6272.00 | −0.482301 | ||||||||
\(554\) | −42650.0 | −3.27080 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6732.00 | 0.513490 | ||||||||
\(557\) | 19658.0 | 1.49540 | 0.747699 | − | 0.664038i | \(-0.231159\pi\) | ||||
0.747699 | + | 0.664038i | \(0.231159\pi\) | |||||||
\(558\) | 10080.0 | 0.764732 | ||||||||
\(559\) | 10200.0 | 0.771760 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4824.00 | 0.363047 | ||||||||
\(562\) | 26910.0 | 2.01980 | ||||||||
\(563\) | 25612.0 | 1.91726 | 0.958630 | − | 0.284656i | \(-0.0918793\pi\) | ||||
0.958630 | + | 0.284656i | \(0.0918793\pi\) | |||||||
\(564\) | −10608.0 | −0.791981 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 31180.0 | 2.31554 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 43200.0 | 3.19125 | ||||||||
\(569\) | 7002.00 | 0.515886 | 0.257943 | − | 0.966160i | \(-0.416955\pi\) | ||||
0.257943 | + | 0.966160i | \(0.416955\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4524.00 | −0.331565 | −0.165782 | − | 0.986162i | \(-0.553015\pi\) | ||||
−0.165782 | + | 0.986162i | \(0.553015\pi\) | |||||||
\(572\) | −6120.00 | −0.447360 | ||||||||
\(573\) | 14712.0 | 1.07260 | ||||||||
\(574\) | 630.000 | 0.0458113 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2583.00 | −0.186849 | ||||||||
\(577\) | 6014.00 | 0.433910 | 0.216955 | − | 0.976182i | \(-0.430388\pi\) | ||||
0.216955 | + | 0.976182i | \(0.430388\pi\) | |||||||
\(578\) | −65215.0 | −4.69306 | ||||||||
\(579\) | −6534.00 | −0.468988 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3052.00 | 0.217932 | ||||||||
\(582\) | −10530.0 | −0.749970 | ||||||||
\(583\) | 9048.00 | 0.642761 | ||||||||
\(584\) | 47970.0 | 3.39899 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4090.00 | −0.288321 | ||||||||
\(587\) | 11748.0 | 0.826051 | 0.413025 | − | 0.910719i | \(-0.364472\pi\) | ||||
0.413025 | + | 0.910719i | \(0.364472\pi\) | |||||||
\(588\) | 2499.00 | 0.175267 | ||||||||
\(589\) | 20608.0 | 1.44166 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8550.00 | 0.595093 | ||||||||
\(592\) | 12994.0 | 0.902112 | ||||||||
\(593\) | 9462.00 | 0.655241 | 0.327620 | − | 0.944809i | \(-0.393753\pi\) | ||||
0.327620 | + | 0.944809i | \(0.393753\pi\) | |||||||
\(594\) | −1620.00 | −0.111901 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31858.0 | −2.18952 | ||||||||
\(597\) | −3432.00 | −0.235280 | ||||||||
\(598\) | −16800.0 | −1.14883 | ||||||||
\(599\) | 2320.00 | 0.158251 | 0.0791257 | − | 0.996865i | \(-0.474787\pi\) | ||||
0.0791257 | + | 0.996865i | \(0.474787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4650.00 | 0.315603 | 0.157802 | − | 0.987471i | \(-0.449559\pi\) | ||||
0.157802 | + | 0.987471i | \(0.449559\pi\) | |||||||
\(602\) | −11900.0 | −0.805661 | ||||||||
\(603\) | −3708.00 | −0.250417 | ||||||||
\(604\) | −18632.0 | −1.25517 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −690.000 | −0.0462530 | ||||||||
\(607\) | 14656.0 | 0.980014 | 0.490007 | − | 0.871718i | \(-0.336994\pi\) | ||||
0.490007 | + | 0.871718i | \(0.336994\pi\) | |||||||
\(608\) | 7820.00 | 0.521617 | ||||||||
\(609\) | 1218.00 | 0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6240.00 | 0.413164 | ||||||||
\(612\) | 20502.0 | 1.35416 | ||||||||
\(613\) | −29166.0 | −1.92170 | −0.960851 | − | 0.277065i | \(-0.910638\pi\) | ||||
−0.960851 | + | 0.277065i | \(0.910638\pi\) | |||||||
\(614\) | −11340.0 | −0.745350 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3780.00 | 0.247241 | ||||||||
\(617\) | −28554.0 | −1.86311 | −0.931557 | − | 0.363597i | \(-0.881549\pi\) | ||||
−0.931557 | + | 0.363597i | \(0.881549\pi\) | |||||||
\(618\) | 28200.0 | 1.83555 | ||||||||
\(619\) | −3876.00 | −0.251679 | −0.125840 | − | 0.992051i | \(-0.540163\pi\) | ||||
−0.125840 | + | 0.992051i | \(0.540163\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3024.00 | −0.195409 | ||||||||
\(622\) | −33240.0 | −2.14277 | ||||||||
\(623\) | 7266.00 | 0.467265 | ||||||||
\(624\) | −8010.00 | −0.513873 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 49090.0 | 3.13423 | ||||||||
\(627\) | −3312.00 | −0.210955 | ||||||||
\(628\) | −32606.0 | −2.07185 | ||||||||
\(629\) | 19564.0 | 1.24017 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2904.00 | 0.183211 | 0.0916057 | − | 0.995795i | \(-0.470800\pi\) | ||||
0.0916057 | + | 0.995795i | \(0.470800\pi\) | |||||||
\(632\) | −40320.0 | −2.53773 | ||||||||
\(633\) | 1236.00 | 0.0776091 | ||||||||
\(634\) | 4670.00 | 0.292538 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 38454.0 | 2.39748 | ||||||||
\(637\) | −1470.00 | −0.0914341 | ||||||||
\(638\) | 3480.00 | 0.215948 | ||||||||
\(639\) | −8640.00 | −0.534888 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9330.00 | 0.574903 | 0.287452 | − | 0.957795i | \(-0.407192\pi\) | ||||
0.287452 | + | 0.957795i | \(0.407192\pi\) | |||||||
\(642\) | 10980.0 | 0.674994 | ||||||||
\(643\) | 18332.0 | 1.12433 | 0.562164 | − | 0.827025i | \(-0.309969\pi\) | ||||
0.562164 | + | 0.827025i | \(0.309969\pi\) | |||||||
\(644\) | 13328.0 | 0.815523 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 61640.0 | 3.75417 | ||||||||
\(647\) | 2088.00 | 0.126874 | 0.0634372 | − | 0.997986i | \(-0.479794\pi\) | ||||
0.0634372 | + | 0.997986i | \(0.479794\pi\) | |||||||
\(648\) | −3645.00 | −0.220971 | ||||||||
\(649\) | 4560.00 | 0.275802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4704.00 | 0.283202 | ||||||||
\(652\) | −39372.0 | −2.36492 | ||||||||
\(653\) | −22.0000 | −0.00131842 | −0.000659209 | − | 1.00000i | \(-0.500210\pi\) | ||||
−0.000659209 | 1.00000i | \(0.500210\pi\) | ||||||||
\(654\) | 5670.00 | 0.339013 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1602.00 | 0.0953469 | ||||||||
\(657\) | −9594.00 | −0.569707 | ||||||||
\(658\) | −7280.00 | −0.431313 | ||||||||
\(659\) | 16260.0 | 0.961153 | 0.480576 | − | 0.876953i | \(-0.340427\pi\) | ||||
0.480576 | + | 0.876953i | \(0.340427\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23818.0 | −1.40153 | −0.700766 | − | 0.713391i | \(-0.747158\pi\) | ||||
−0.700766 | + | 0.713391i | \(0.747158\pi\) | |||||||
\(662\) | −11460.0 | −0.672818 | ||||||||
\(663\) | −12060.0 | −0.706443 | ||||||||
\(664\) | 19620.0 | 1.14669 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6570.00 | −0.382256 | ||||||||
\(667\) | 6496.00 | 0.377101 | ||||||||
\(668\) | 29512.0 | 1.70936 | ||||||||
\(669\) | 4896.00 | 0.282945 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8616.00 | 0.495703 | ||||||||
\(672\) | 1785.00 | 0.102467 | ||||||||
\(673\) | −31106.0 | −1.78165 | −0.890823 | − | 0.454350i | \(-0.849872\pi\) | ||||
−0.890823 | + | 0.454350i | \(0.849872\pi\) | |||||||
\(674\) | −30310.0 | −1.73219 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22049.0 | −1.25449 | ||||||||
\(677\) | 1090.00 | 0.0618790 | 0.0309395 | − | 0.999521i | \(-0.490150\pi\) | ||||
0.0309395 | + | 0.999521i | \(0.490150\pi\) | |||||||
\(678\) | 21870.0 | 1.23881 | ||||||||
\(679\) | −4914.00 | −0.277735 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12252.0 | −0.689424 | ||||||||
\(682\) | 13440.0 | 0.754610 | ||||||||
\(683\) | 12372.0 | 0.693121 | 0.346560 | − | 0.938028i | \(-0.387350\pi\) | ||||
0.346560 | + | 0.938028i | \(0.387350\pi\) | |||||||
\(684\) | −14076.0 | −0.786856 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1715.00 | 0.0954504 | ||||||||
\(687\) | −10158.0 | −0.564122 | ||||||||
\(688\) | −30260.0 | −1.67682 | ||||||||
\(689\) | −22620.0 | −1.25073 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3252.00 | 0.179033 | 0.0895166 | − | 0.995985i | \(-0.471468\pi\) | ||||
0.0895166 | + | 0.995985i | \(0.471468\pi\) | |||||||
\(692\) | 41514.0 | 2.28053 | ||||||||
\(693\) | −756.000 | −0.0414402 | ||||||||
\(694\) | 7420.00 | 0.405849 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7830.00 | 0.426430 | ||||||||
\(697\) | 2412.00 | 0.131077 | ||||||||
\(698\) | −1270.00 | −0.0688685 | ||||||||
\(699\) | −15966.0 | −0.863934 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5434.00 | −0.292781 | −0.146390 | − | 0.989227i | \(-0.546766\pi\) | ||||
−0.146390 | + | 0.989227i | \(0.546766\pi\) | |||||||
\(702\) | 4050.00 | 0.217746 | ||||||||
\(703\) | −13432.0 | −0.720622 | ||||||||
\(704\) | −3444.00 | −0.184376 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −54750.0 | −2.91862 | ||||||||
\(707\) | −322.000 | −0.0171288 | ||||||||
\(708\) | 19380.0 | 1.02874 | ||||||||
\(709\) | −5330.00 | −0.282331 | −0.141165 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141165 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8064.00 | 0.425350 | ||||||||
\(712\) | 46710.0 | 2.45861 | ||||||||
\(713\) | 25088.0 | 1.31775 | ||||||||
\(714\) | 14070.0 | 0.737474 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −69564.0 | −3.63091 | ||||||||
\(717\) | 11208.0 | 0.583780 | ||||||||
\(718\) | −56880.0 | −2.95647 | ||||||||
\(719\) | −7520.00 | −0.390054 | −0.195027 | − | 0.980798i | \(-0.562479\pi\) | ||||
−0.195027 | + | 0.980798i | \(0.562479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13160.0 | 0.679756 | ||||||||
\(722\) | −8025.00 | −0.413656 | ||||||||
\(723\) | 630.000 | 0.0324066 | ||||||||
\(724\) | 21590.0 | 1.10827 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17805.0 | 0.910200 | ||||||||
\(727\) | −19336.0 | −0.986427 | −0.493214 | − | 0.869908i | \(-0.664178\pi\) | ||||
−0.493214 | + | 0.869908i | \(0.664178\pi\) | |||||||
\(728\) | −9450.00 | −0.481099 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45560.0 | −2.30519 | ||||||||
\(732\) | 36618.0 | 1.84896 | ||||||||
\(733\) | 22498.0 | 1.13367 | 0.566837 | − | 0.823830i | \(-0.308167\pi\) | ||||
0.566837 | + | 0.823830i | \(0.308167\pi\) | |||||||
\(734\) | −5680.00 | −0.285630 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9520.00 | 0.476782 | ||||||||
\(737\) | −4944.00 | −0.247103 | ||||||||
\(738\) | −810.000 | −0.0404018 | ||||||||
\(739\) | −18292.0 | −0.910531 | −0.455265 | − | 0.890356i | \(-0.650456\pi\) | ||||
−0.455265 | + | 0.890356i | \(0.650456\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8280.00 | 0.410490 | ||||||||
\(742\) | 26390.0 | 1.30567 | ||||||||
\(743\) | −17904.0 | −0.884030 | −0.442015 | − | 0.897008i | \(-0.645736\pi\) | ||||
−0.442015 | + | 0.897008i | \(0.645736\pi\) | |||||||
\(744\) | 30240.0 | 1.49012 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −41210.0 | −2.02253 | ||||||||
\(747\) | −3924.00 | −0.192198 | ||||||||
\(748\) | 27336.0 | 1.33623 | ||||||||
\(749\) | 5124.00 | 0.249969 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5408.00 | 0.262771 | 0.131385 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131385 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(752\) | −18512.0 | −0.897690 | ||||||||
\(753\) | −12636.0 | −0.611529 | ||||||||
\(754\) | −8700.00 | −0.420206 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3213.00 | −0.154571 | ||||||||
\(757\) | −8318.00 | −0.399370 | −0.199685 | − | 0.979860i | \(-0.563992\pi\) | ||||
−0.199685 | + | 0.979860i | \(0.563992\pi\) | |||||||
\(758\) | −18100.0 | −0.867311 | ||||||||
\(759\) | −4032.00 | −0.192823 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6690.00 | 0.318676 | 0.159338 | − | 0.987224i | \(-0.449064\pi\) | ||||
0.159338 | + | 0.987224i | \(0.449064\pi\) | |||||||
\(762\) | 9120.00 | 0.433573 | ||||||||
\(763\) | 2646.00 | 0.125546 | ||||||||
\(764\) | 83368.0 | 3.94784 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42320.0 | −1.99619 | ||||||||
\(767\) | −11400.0 | −0.536676 | ||||||||
\(768\) | −24837.0 | −1.16696 | ||||||||
\(769\) | 9266.00 | 0.434513 | 0.217257 | − | 0.976115i | \(-0.430289\pi\) | ||||
0.217257 | + | 0.976115i | \(0.430289\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15390.0 | −0.718881 | ||||||||
\(772\) | −37026.0 | −1.72616 | ||||||||
\(773\) | −9678.00 | −0.450315 | −0.225157 | − | 0.974322i | \(-0.572290\pi\) | ||||
−0.225157 | + | 0.974322i | \(0.572290\pi\) | |||||||
\(774\) | 15300.0 | 0.710526 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −31590.0 | −1.46136 | ||||||||
\(777\) | −3066.00 | −0.141560 | ||||||||
\(778\) | −18390.0 | −0.847447 | ||||||||
\(779\) | −1656.00 | −0.0761648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11520.0 | −0.527808 | ||||||||
\(782\) | 75040.0 | 3.43149 | ||||||||
\(783\) | −1566.00 | −0.0714742 | ||||||||
\(784\) | 4361.00 | 0.198661 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14340.0 | 0.650752 | ||||||||
\(787\) | 6860.00 | 0.310715 | 0.155357 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155357 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(788\) | 48450.0 | 2.19030 | ||||||||
\(789\) | −2544.00 | −0.114789 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10206.0 | 0.458766 | ||||||||
\(792\) | −4860.00 | −0.218046 | ||||||||
\(793\) | −21540.0 | −0.964575 | ||||||||
\(794\) | 62950.0 | 2.81362 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19448.0 | −0.865975 | ||||||||
\(797\) | −10950.0 | −0.486661 | −0.243331 | − | 0.969943i | \(-0.578240\pi\) | ||||
−0.243331 | + | 0.969943i | \(0.578240\pi\) | |||||||
\(798\) | −9660.00 | −0.428522 | ||||||||
\(799\) | −27872.0 | −1.23409 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9342.00 | −0.412089 | ||||||||
\(802\) | −14250.0 | −0.627413 | ||||||||
\(803\) | −12792.0 | −0.562167 | ||||||||
\(804\) | −21012.0 | −0.921687 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33600.0 | −1.46837 | ||||||||
\(807\) | −3822.00 | −0.166717 | ||||||||
\(808\) | −2070.00 | −0.0901267 | ||||||||
\(809\) | 26010.0 | 1.13036 | 0.565181 | − | 0.824967i | \(-0.308806\pi\) | ||||
0.565181 | + | 0.824967i | \(0.308806\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14628.0 | −0.633364 | −0.316682 | − | 0.948532i | \(-0.602569\pi\) | ||||
−0.316682 | + | 0.948532i | \(0.602569\pi\) | |||||||
\(812\) | 6902.00 | 0.298292 | ||||||||
\(813\) | 2592.00 | 0.111815 | ||||||||
\(814\) | −8760.00 | −0.377196 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 35778.0 | 1.53490 | ||||||||
\(817\) | 31280.0 | 1.33947 | ||||||||
\(818\) | −6130.00 | −0.262018 | ||||||||
\(819\) | 1890.00 | 0.0806373 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8718.00 | 0.370597 | 0.185299 | − | 0.982682i | \(-0.440675\pi\) | ||||
0.185299 | + | 0.982682i | \(0.440675\pi\) | |||||||
\(822\) | −5610.00 | −0.238043 | ||||||||
\(823\) | 7432.00 | 0.314779 | 0.157390 | − | 0.987537i | \(-0.449692\pi\) | ||||
0.157390 | + | 0.987537i | \(0.449692\pi\) | |||||||
\(824\) | 84600.0 | 3.57668 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13300.0 | 0.560250 | ||||||||
\(827\) | −17388.0 | −0.731125 | −0.365562 | − | 0.930787i | \(-0.619123\pi\) | ||||
−0.365562 | + | 0.930787i | \(0.619123\pi\) | |||||||
\(828\) | −17136.0 | −0.719224 | ||||||||
\(829\) | 7902.00 | 0.331059 | 0.165529 | − | 0.986205i | \(-0.447067\pi\) | ||||
0.165529 | + | 0.986205i | \(0.447067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25590.0 | 1.06824 | ||||||||
\(832\) | 8610.00 | 0.358772 | ||||||||
\(833\) | 6566.00 | 0.273107 | ||||||||
\(834\) | −5940.00 | −0.246625 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −18768.0 | −0.776441 | ||||||||
\(837\) | −6048.00 | −0.249760 | ||||||||
\(838\) | −3060.00 | −0.126141 | ||||||||
\(839\) | −31848.0 | −1.31051 | −0.655253 | − | 0.755409i | \(-0.727438\pi\) | ||||
−0.655253 | + | 0.755409i | \(0.727438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | −25910.0 | −1.06047 | ||||||||
\(843\) | −16146.0 | −0.659665 | ||||||||
\(844\) | 7004.00 | 0.285649 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9360.00 | 0.380382 | ||||||||
\(847\) | 8309.00 | 0.337073 | ||||||||
\(848\) | 67106.0 | 2.71749 | ||||||||
\(849\) | −18708.0 | −0.756251 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16352.0 | −0.658683 | ||||||||
\(852\) | −48960.0 | −1.96871 | ||||||||
\(853\) | −30150.0 | −1.21022 | −0.605109 | − | 0.796142i | \(-0.706871\pi\) | ||||
−0.605109 | + | 0.796142i | \(0.706871\pi\) | |||||||
\(854\) | 25130.0 | 1.00694 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32940.0 | 1.31526 | ||||||||
\(857\) | 4350.00 | 0.173388 | 0.0866938 | − | 0.996235i | \(-0.472370\pi\) | ||||
0.0866938 | + | 0.996235i | \(0.472370\pi\) | |||||||
\(858\) | 5400.00 | 0.214864 | ||||||||
\(859\) | −30676.0 | −1.21845 | −0.609227 | − | 0.792996i | \(-0.708520\pi\) | ||||
−0.609227 | + | 0.792996i | \(0.708520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −378.000 | −0.0149619 | ||||||||
\(862\) | 24920.0 | 0.984662 | ||||||||
\(863\) | 23688.0 | 0.934356 | 0.467178 | − | 0.884163i | \(-0.345271\pi\) | ||||
0.467178 | + | 0.884163i | \(0.345271\pi\) | |||||||
\(864\) | −2295.00 | −0.0903675 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8470.00 | −0.332358 | ||||||||
\(867\) | 39129.0 | 1.53275 | ||||||||
\(868\) | 26656.0 | 1.04235 | ||||||||
\(869\) | 10752.0 | 0.419720 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12360.0 | 0.480830 | ||||||||
\(872\) | 17010.0 | 0.660586 | ||||||||
\(873\) | 6318.00 | 0.244939 | ||||||||
\(874\) | −51520.0 | −1.99392 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −54366.0 | −2.09687 | ||||||||
\(877\) | −31910.0 | −1.22865 | −0.614324 | − | 0.789054i | \(-0.710571\pi\) | ||||
−0.614324 | + | 0.789054i | \(0.710571\pi\) | |||||||
\(878\) | −69320.0 | −2.66451 | ||||||||
\(879\) | 2454.00 | 0.0941654 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50250.0 | 1.92164 | 0.960820 | − | 0.277172i | \(-0.0893971\pi\) | ||||
0.960820 | + | 0.277172i | \(0.0893971\pi\) | |||||||
\(882\) | −2205.00 | −0.0841794 | ||||||||
\(883\) | −5980.00 | −0.227908 | −0.113954 | − | 0.993486i | \(-0.536352\pi\) | ||||
−0.113954 | + | 0.993486i | \(0.536352\pi\) | |||||||
\(884\) | −68340.0 | −2.60014 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23220.0 | −0.880464 | ||||||||
\(887\) | 24568.0 | 0.930003 | 0.465002 | − | 0.885310i | \(-0.346054\pi\) | ||||
0.465002 | + | 0.885310i | \(0.346054\pi\) | |||||||
\(888\) | −19710.0 | −0.744847 | ||||||||
\(889\) | 4256.00 | 0.160564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 972.000 | 0.0365468 | ||||||||
\(892\) | 27744.0 | 1.04141 | ||||||||
\(893\) | 19136.0 | 0.717091 | ||||||||
\(894\) | 28110.0 | 1.05161 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −14805.0 | −0.552009 | ||||||||
\(897\) | 10080.0 | 0.375208 | ||||||||
\(898\) | 24630.0 | 0.915271 | ||||||||
\(899\) | 12992.0 | 0.481988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 101036. | 3.73585 | ||||||||
\(902\) | −1080.00 | −0.0398670 | ||||||||
\(903\) | 7140.00 | 0.263128 | ||||||||
\(904\) | 65610.0 | 2.41389 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16440.0 | 0.602850 | ||||||||
\(907\) | −13252.0 | −0.485144 | −0.242572 | − | 0.970133i | \(-0.577991\pi\) | ||||
−0.242572 | + | 0.970133i | \(0.577991\pi\) | |||||||
\(908\) | −69428.0 | −2.53750 | ||||||||
\(909\) | 414.000 | 0.0151062 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6744.00 | −0.245267 | −0.122634 | − | 0.992452i | \(-0.539134\pi\) | ||||
−0.122634 | + | 0.992452i | \(0.539134\pi\) | |||||||
\(912\) | −24564.0 | −0.891881 | ||||||||
\(913\) | −5232.00 | −0.189654 | ||||||||
\(914\) | −73470.0 | −2.65883 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −57562.0 | −2.07631 | ||||||||
\(917\) | 6692.00 | 0.240992 | ||||||||
\(918\) | −18090.0 | −0.650391 | ||||||||
\(919\) | −45336.0 | −1.62731 | −0.813654 | − | 0.581349i | \(-0.802525\pi\) | ||||
−0.813654 | + | 0.581349i | \(0.802525\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6804.00 | 0.243430 | ||||||||
\(922\) | −10030.0 | −0.358265 | ||||||||
\(923\) | 28800.0 | 1.02705 | ||||||||
\(924\) | −4284.00 | −0.152525 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24480.0 | 0.868750 | ||||||||
\(927\) | −16920.0 | −0.599488 | ||||||||
\(928\) | 4930.00 | 0.174391 | ||||||||
\(929\) | 30074.0 | 1.06211 | 0.531053 | − | 0.847339i | \(-0.321797\pi\) | ||||
0.531053 | + | 0.847339i | \(0.321797\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4508.00 | −0.158694 | ||||||||
\(932\) | −90474.0 | −3.17980 | ||||||||
\(933\) | 19944.0 | 0.699826 | ||||||||
\(934\) | 13300.0 | 0.465941 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12150.0 | 0.424290 | ||||||||
\(937\) | −21754.0 | −0.758455 | −0.379227 | − | 0.925303i | \(-0.623810\pi\) | ||||
−0.379227 | + | 0.925303i | \(0.623810\pi\) | |||||||
\(938\) | −14420.0 | −0.501951 | ||||||||
\(939\) | −29454.0 | −1.02364 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14550.0 | 0.504056 | 0.252028 | − | 0.967720i | \(-0.418903\pi\) | ||||
0.252028 | + | 0.967720i | \(0.418903\pi\) | |||||||
\(942\) | 28770.0 | 0.995093 | ||||||||
\(943\) | −2016.00 | −0.0696182 | ||||||||
\(944\) | 33820.0 | 1.16605 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20400.0 | 0.701122 | ||||||||
\(947\) | −46660.0 | −1.60110 | −0.800552 | − | 0.599263i | \(-0.795460\pi\) | ||||
−0.800552 | + | 0.599263i | \(0.795460\pi\) | |||||||
\(948\) | 45696.0 | 1.56555 | ||||||||
\(949\) | 31980.0 | 1.09390 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2802.00 | −0.0955427 | ||||||||
\(952\) | 42210.0 | 1.43701 | ||||||||
\(953\) | −20810.0 | −0.707347 | −0.353674 | − | 0.935369i | \(-0.615068\pi\) | ||||
−0.353674 | + | 0.935369i | \(0.615068\pi\) | |||||||
\(954\) | −33930.0 | −1.15149 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 63512.0 | 2.14867 | ||||||||
\(957\) | −2088.00 | −0.0705282 | ||||||||
\(958\) | 28000.0 | 0.944300 | ||||||||
\(959\) | −2618.00 | −0.0881539 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 21900.0 | 0.733975 | ||||||||
\(963\) | −6588.00 | −0.220452 | ||||||||
\(964\) | 3570.00 | 0.119276 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11760.0 | −0.391689 | ||||||||
\(967\) | −2776.00 | −0.0923166 | −0.0461583 | − | 0.998934i | \(-0.514698\pi\) | ||||
−0.0461583 | + | 0.998934i | \(0.514698\pi\) | |||||||
\(968\) | 53415.0 | 1.77358 | ||||||||
\(969\) | −36984.0 | −1.22611 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27292.0 | 0.902000 | 0.451000 | − | 0.892524i | \(-0.351067\pi\) | ||||
0.451000 | + | 0.892524i | \(0.351067\pi\) | |||||||
\(972\) | 4131.00 | 0.136319 | ||||||||
\(973\) | −2772.00 | −0.0913322 | ||||||||
\(974\) | −32120.0 | −1.05666 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 63902.0 | 2.09575 | ||||||||
\(977\) | 62.0000 | 0.00203025 | 0.00101513 | − | 0.999999i | \(-0.499677\pi\) | ||||
0.00101513 | + | 0.999999i | \(0.499677\pi\) | |||||||
\(978\) | 34740.0 | 1.13585 | ||||||||
\(979\) | −12456.0 | −0.406635 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3402.00 | −0.110721 | ||||||||
\(982\) | 94500.0 | 3.07089 | ||||||||
\(983\) | −37912.0 | −1.23012 | −0.615058 | − | 0.788481i | \(-0.710868\pi\) | ||||
−0.615058 | + | 0.788481i | \(0.710868\pi\) | |||||||
\(984\) | −2430.00 | −0.0787252 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 38860.0 | 1.25513 | ||||||||
\(987\) | 4368.00 | 0.140866 | ||||||||
\(988\) | 46920.0 | 1.51085 | ||||||||
\(989\) | 38080.0 | 1.22434 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10656.0 | 0.341573 | 0.170787 | − | 0.985308i | \(-0.445369\pi\) | ||||
0.170787 | + | 0.985308i | \(0.445369\pi\) | |||||||
\(992\) | 19040.0 | 0.609396 | ||||||||
\(993\) | 6876.00 | 0.219741 | ||||||||
\(994\) | −33600.0 | −1.07216 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −22236.0 | −0.707404 | ||||||||
\(997\) | 29434.0 | 0.934989 | 0.467495 | − | 0.883996i | \(-0.345157\pi\) | ||||
0.467495 | + | 0.883996i | \(0.345157\pi\) | |||||||
\(998\) | 76820.0 | 2.43657 | ||||||||
\(999\) | 3942.00 | 0.124844 |
(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 | 525.4.a.a.1.1 | 1 | ||
3.2 | odd | 2 | 1575.4.a.l.1.1 | 1 | |||
5.2 | odd | 4 | 525.4.d.a.274.1 | 2 | |||
5.3 | odd | 4 | 525.4.d.a.274.2 | 2 | |||
5.4 | even | 2 | 105.4.a.b.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 315.4.a.a.1.1 | 1 | |||
20.19 | odd | 2 | 1680.4.a.u.1.1 | 1 | |||
35.34 | odd | 2 | 735.4.a.j.1.1 | 1 | |||
105.104 | even | 2 | 2205.4.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.b.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
315.4.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
525.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
525.4.d.a.274.1 | 2 | 5.2 | odd | 4 | |||
525.4.d.a.274.2 | 2 | 5.3 | odd | 4 | |||
735.4.a.j.1.1 | 1 | 35.34 | odd | 2 | |||
1575.4.a.l.1.1 | 1 | 3.2 | odd | 2 | |||
1680.4.a.u.1.1 | 1 | 20.19 | odd | 2 | |||
2205.4.a.b.1.1 | 1 | 105.104 | even | 2 |