Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
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 | \(\chi\) | \(=\) | 2205.1 |
$q$-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 | \(0.845080\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 17.0000 | 2.12500 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −45.0000 | −1.98874 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −25.0000 | −0.790569 | ||||||||
\(11\) | −12.0000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.0000 | −0.640039 | −0.320019 | − | 0.947411i | \(-0.603689\pi\) | ||||
−0.320019 | + | 0.947411i | \(0.603689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | −134.000 | −1.91175 | −0.955876 | − | 0.293771i | \(-0.905090\pi\) | ||||
−0.955876 | + | 0.293771i | \(0.905090\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 92.0000 | 1.11086 | 0.555428 | − | 0.831565i | \(-0.312555\pi\) | ||||
0.555428 | + | 0.831565i | \(0.312555\pi\) | |||||||
\(20\) | 85.0000 | 0.950329 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 60.0000 | 0.581456 | ||||||||
\(23\) | −112.000 | −1.01537 | −0.507687 | − | 0.861541i | \(-0.669499\pi\) | ||||
−0.507687 | + | 0.861541i | \(0.669499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 150.000 | 1.13144 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 58.0000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 224.000 | 1.29779 | 0.648897 | − | 0.760877i | \(-0.275231\pi\) | ||||
0.648897 | + | 0.760877i | \(0.275231\pi\) | |||||||
\(32\) | −85.0000 | −0.469563 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 670.000 | 3.37953 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −146.000 | −0.648710 | −0.324355 | − | 0.945936i | \(-0.605147\pi\) | ||||
−0.324355 | + | 0.945936i | \(0.605147\pi\) | |||||||
\(38\) | −460.000 | −1.96373 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −225.000 | −0.889391 | ||||||||
\(41\) | 18.0000 | 0.0685641 | 0.0342820 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342820 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 340.000 | 1.20580 | 0.602901 | − | 0.797816i | \(-0.294011\pi\) | ||||
0.602901 | + | 0.797816i | \(0.294011\pi\) | |||||||
\(44\) | −204.000 | −0.698958 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 560.000 | 1.79495 | ||||||||
\(47\) | 208.000 | 0.645530 | 0.322765 | − | 0.946479i | \(-0.395388\pi\) | ||||
0.322765 | + | 0.946479i | \(0.395388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −125.000 | −0.353553 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −510.000 | −1.36008 | ||||||||
\(53\) | 754.000 | 1.95415 | 0.977074 | − | 0.212899i | \(-0.0682905\pi\) | ||||
0.977074 | + | 0.212899i | \(0.0682905\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −60.0000 | −0.147098 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −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 | \(-0.771650\pi\) | ||||
−0.753529 | + | 0.657415i | \(0.771650\pi\) | |||||||
\(62\) | −1120.00 | −2.29420 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −287.000 | −0.560547 | ||||||||
\(65\) | −150.000 | −0.286234 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 412.000 | 0.751251 | 0.375625 | − | 0.926772i | \(-0.377428\pi\) | ||||
0.375625 | + | 0.926772i | \(0.377428\pi\) | |||||||
\(68\) | −2278.00 | −4.06247 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 960.000 | 1.60466 | 0.802331 | − | 0.596879i | \(-0.203593\pi\) | ||||
0.802331 | + | 0.596879i | \(0.203593\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −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 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 896.000 | 1.27605 | 0.638025 | − | 0.770016i | \(-0.279752\pi\) | ||||
0.638025 | + | 0.770016i | \(0.279752\pi\) | |||||||
\(80\) | 445.000 | 0.621906 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −90.0000 | −0.121205 | ||||||||
\(83\) | 436.000 | 0.576593 | 0.288296 | − | 0.957541i | \(-0.406911\pi\) | ||||
0.288296 | + | 0.957541i | \(0.406911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −670.000 | −0.854961 | ||||||||
\(86\) | −1700.00 | −2.13158 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1904.00 | −2.15767 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1040.00 | −1.14115 | ||||||||
\(95\) | 460.000 | 0.496790 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 702.000 | 0.734818 | 0.367409 | − | 0.930060i | \(-0.380245\pi\) | ||||
0.367409 | + | 0.930060i | \(0.380245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 425.000 | 0.425000 | ||||||||
\(101\) | 46.0000 | 0.0453185 | 0.0226593 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226593 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −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 | \(0.607277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −378.000 | −0.332164 | −0.166082 | − | 0.986112i | \(-0.553112\pi\) | ||||
−0.166082 | + | 0.986112i | \(0.553112\pi\) | |||||||
\(110\) | 300.000 | 0.260035 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1458.00 | −1.21378 | −0.606890 | − | 0.794786i | \(-0.707583\pi\) | ||||
−0.606890 | + | 0.794786i | \(0.707583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −560.000 | −0.454089 | ||||||||
\(116\) | 986.000 | 0.789205 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1900.00 | −1.48228 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 3590.00 | 2.66413 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3808.00 | 2.75781 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 608.000 | 0.424813 | 0.212407 | − | 0.977181i | \(-0.431870\pi\) | ||||
0.212407 | + | 0.977181i | \(0.431870\pi\) | |||||||
\(128\) | 2115.00 | 1.46048 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 750.000 | 0.505995 | ||||||||
\(131\) | −956.000 | −0.637604 | −0.318802 | − | 0.947821i | \(-0.603280\pi\) | ||||
−0.318802 | + | 0.947821i | \(0.603280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −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 | \(0.462795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −396.000 | −0.241642 | −0.120821 | − | 0.992674i | \(-0.538553\pi\) | ||||
−0.120821 | + | 0.992674i | \(0.538553\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4800.00 | −2.83667 | ||||||||
\(143\) | 360.000 | 0.210522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 290.000 | 0.166091 | ||||||||
\(146\) | 5330.00 | 3.02133 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2482.00 | −1.37851 | ||||||||
\(149\) | 1874.00 | 1.03036 | 0.515181 | − | 0.857081i | \(-0.327725\pi\) | ||||
0.515181 | + | 0.857081i | \(0.327725\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1120.00 | 0.580391 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1918.00 | −0.974988 | −0.487494 | − | 0.873126i | \(-0.662089\pi\) | ||||
−0.487494 | + | 0.873126i | \(0.662089\pi\) | |||||||
\(158\) | −4480.00 | −2.25576 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −425.000 | −0.209995 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2316.00 | 1.11290 | 0.556451 | − | 0.830880i | \(-0.312163\pi\) | ||||
0.556451 | + | 0.830880i | \(0.312163\pi\) | |||||||
\(164\) | 306.000 | 0.145699 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2180.00 | −1.01928 | ||||||||
\(167\) | −1736.00 | −0.804405 | −0.402203 | − | 0.915551i | \(-0.631755\pi\) | ||||
−0.402203 | + | 0.915551i | \(0.631755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1297.00 | −0.590350 | ||||||||
\(170\) | 3350.00 | 1.51137 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5780.00 | 2.56233 | ||||||||
\(173\) | −2442.00 | −1.07319 | −0.536595 | − | 0.843840i | \(-0.680290\pi\) | ||||
−0.536595 | + | 0.843840i | \(0.680290\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1068.00 | −0.457406 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5190.00 | 2.18543 | ||||||||
\(179\) | 4092.00 | 1.70866 | 0.854331 | − | 0.519730i | \(-0.173967\pi\) | ||||
0.854331 | + | 0.519730i | \(0.173967\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1270.00 | −0.521538 | −0.260769 | − | 0.965401i | \(-0.583976\pi\) | ||||
−0.260769 | + | 0.965401i | \(0.583976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5040.00 | 2.01931 | ||||||||
\(185\) | −730.000 | −0.290112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1608.00 | 0.628816 | ||||||||
\(188\) | 3536.00 | 1.37175 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2300.00 | −0.878208 | ||||||||
\(191\) | −4904.00 | −1.85781 | −0.928903 | − | 0.370323i | \(-0.879247\pi\) | ||||
−0.928903 | + | 0.370323i | \(0.879247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2178.00 | 0.812310 | 0.406155 | − | 0.913804i | \(-0.366869\pi\) | ||||
0.406155 | + | 0.913804i | \(0.366869\pi\) | |||||||
\(194\) | −3510.00 | −1.29899 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2850.00 | 1.03073 | 0.515366 | − | 0.856970i | \(-0.327656\pi\) | ||||
0.515366 | + | 0.856970i | \(0.327656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1144.00 | 0.407518 | 0.203759 | − | 0.979021i | \(-0.434684\pi\) | ||||
0.203759 | + | 0.979021i | \(0.434684\pi\) | |||||||
\(200\) | −1125.00 | −0.397748 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −230.000 | −0.0801126 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 90.0000 | 0.0306628 | ||||||||
\(206\) | 9400.00 | 3.17927 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3660.00 | 1.16912 | ||||||||
\(215\) | 1700.00 | 0.539251 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1890.00 | 0.587188 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1020.00 | −0.312584 | ||||||||
\(221\) | 4020.00 | 1.22359 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1632.00 | 0.490075 | 0.245038 | − | 0.969514i | \(-0.421200\pi\) | ||||
0.245038 | + | 0.969514i | \(0.421200\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7290.00 | 2.14568 | ||||||||
\(227\) | 4084.00 | 1.19412 | 0.597059 | − | 0.802198i | \(-0.296336\pi\) | ||||
0.597059 | + | 0.802198i | \(0.296336\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3386.00 | 0.977088 | 0.488544 | − | 0.872539i | \(-0.337528\pi\) | ||||
0.488544 | + | 0.872539i | \(0.337528\pi\) | |||||||
\(230\) | 2800.00 | 0.802724 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2610.00 | −0.738599 | ||||||||
\(233\) | −5322.00 | −1.49638 | −0.748188 | − | 0.663486i | \(-0.769076\pi\) | ||||
−0.748188 | + | 0.663486i | \(0.769076\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1040.00 | 0.288690 | ||||||||
\(236\) | 6460.00 | 1.78182 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3736.00 | −1.01114 | −0.505569 | − | 0.862786i | \(-0.668717\pi\) | ||||
−0.505569 | + | 0.862786i | \(0.668717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −210.000 | −0.0561298 | −0.0280649 | − | 0.999606i | \(-0.508935\pi\) | ||||
−0.0280649 | + | 0.999606i | \(0.508935\pi\) | |||||||
\(242\) | 5935.00 | 1.57651 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12206.0 | −3.20250 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2760.00 | −0.710990 | ||||||||
\(248\) | −10080.0 | −2.58097 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −625.000 | −0.158114 | ||||||||
\(251\) | −4212.00 | −1.05920 | −0.529600 | − | 0.848248i | \(-0.677658\pi\) | ||||
−0.529600 | + | 0.848248i | \(0.677658\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | \(-0.286089\pi\) | ||||
0.622569 | + | 0.782565i | \(0.286089\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2550.00 | −0.608247 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4780.00 | 1.12714 | ||||||||
\(263\) | −848.000 | −0.198821 | −0.0994105 | − | 0.995047i | \(-0.531696\pi\) | ||||
−0.0994105 | + | 0.995047i | \(0.531696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3770.00 | 0.873922 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(-0.530872\pi\) | ||||
−0.0968344 | + | 0.995301i | \(0.530872\pi\) | |||||||
\(272\) | −11926.0 | −2.65853 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1870.00 | −0.412302 | ||||||||
\(275\) | −300.000 | −0.0657843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8530.00 | −1.85025 | −0.925123 | − | 0.379668i | \(-0.876038\pi\) | ||||
−0.925123 | + | 0.379668i | \(0.876038\pi\) | |||||||
\(278\) | 1980.00 | 0.427167 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5382.00 | 1.14257 | 0.571287 | − | 0.820750i | \(-0.306444\pi\) | ||||
0.571287 | + | 0.820750i | \(0.306444\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −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 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13043.0 | 2.65479 | ||||||||
\(290\) | −1450.00 | −0.293610 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −18122.0 | −3.63188 | ||||||||
\(293\) | −818.000 | −0.163099 | −0.0815496 | − | 0.996669i | \(-0.525987\pi\) | ||||
−0.0815496 | + | 0.996669i | \(0.525987\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1900.00 | 0.374991 | ||||||||
\(296\) | 6570.00 | 1.29011 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9370.00 | −1.82144 | ||||||||
\(299\) | 3360.00 | 0.649879 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5480.00 | 1.04417 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8188.00 | 1.54478 | ||||||||
\(305\) | −3590.00 | −0.673976 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2268.00 | 0.421634 | 0.210817 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210817 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5600.00 | −1.02600 | ||||||||
\(311\) | 6648.00 | 1.21213 | 0.606067 | − | 0.795414i | \(-0.292746\pi\) | ||||
0.606067 | + | 0.795414i | \(0.292746\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −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 | \(0.526368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −696.000 | −0.122158 | ||||||||
\(320\) | −1435.00 | −0.250684 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12328.0 | −2.12368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −750.000 | −0.128008 | ||||||||
\(326\) | −11580.0 | −1.96735 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −810.000 | −0.136356 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8680.00 | 1.42200 | ||||||||
\(335\) | 2060.00 | 0.335970 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6062.00 | −0.979876 | −0.489938 | − | 0.871757i | \(-0.662981\pi\) | ||||
−0.489938 | + | 0.871757i | \(0.662981\pi\) | |||||||
\(338\) | 6485.00 | 1.04360 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11390.0 | −1.81679 | ||||||||
\(341\) | −2688.00 | −0.426872 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −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 | \(0.536620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −254.000 | −0.0389579 | −0.0194790 | − | 0.999810i | \(-0.506201\pi\) | ||||
−0.0194790 | + | 0.999810i | \(0.506201\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1020.00 | 0.154449 | ||||||||
\(353\) | −10950.0 | −1.65102 | −0.825509 | − | 0.564388i | \(-0.809112\pi\) | ||||
−0.825509 | + | 0.564388i | \(0.809112\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4800.00 | 0.717627 | ||||||||
\(356\) | −17646.0 | −2.62707 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20460.0 | −3.02052 | ||||||||
\(359\) | −11376.0 | −1.67243 | −0.836215 | − | 0.548402i | \(-0.815236\pi\) | ||||
−0.836215 | + | 0.548402i | \(0.815236\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 6350.00 | 0.921957 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5330.00 | −0.764342 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1136.00 | 0.161577 | 0.0807884 | − | 0.996731i | \(-0.474256\pi\) | ||||
0.0807884 | + | 0.996731i | \(0.474256\pi\) | |||||||
\(368\) | −9968.00 | −1.41201 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3650.00 | 0.512850 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8242.00 | −1.14411 | −0.572057 | − | 0.820214i | \(-0.693854\pi\) | ||||
−0.572057 | + | 0.820214i | \(0.693854\pi\) | |||||||
\(374\) | −8040.00 | −1.11160 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9360.00 | −1.28379 | ||||||||
\(377\) | −1740.00 | −0.237704 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3620.00 | 0.490625 | 0.245313 | − | 0.969444i | \(-0.421109\pi\) | ||||
0.245313 | + | 0.969444i | \(0.421109\pi\) | |||||||
\(380\) | 7820.00 | 1.05568 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24520.0 | 3.28417 | ||||||||
\(383\) | −8464.00 | −1.12922 | −0.564609 | − | 0.825359i | \(-0.690973\pi\) | ||||
−0.564609 | + | 0.825359i | \(0.690973\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10890.0 | −1.43598 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11934.0 | 1.56149 | ||||||||
\(389\) | −3678.00 | −0.479388 | −0.239694 | − | 0.970848i | \(-0.577047\pi\) | ||||
−0.239694 | + | 0.970848i | \(0.577047\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15008.0 | 1.94114 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14250.0 | −1.82209 | ||||||||
\(395\) | 4480.00 | 0.570666 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12590.0 | −1.59162 | −0.795811 | − | 0.605545i | \(-0.792955\pi\) | ||||
−0.795811 | + | 0.605545i | \(0.792955\pi\) | |||||||
\(398\) | −5720.00 | −0.720396 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2225.00 | 0.278125 | ||||||||
\(401\) | −2850.00 | −0.354918 | −0.177459 | − | 0.984128i | \(-0.556788\pi\) | ||||
−0.177459 | + | 0.984128i | \(0.556788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6720.00 | −0.830638 | ||||||||
\(404\) | 782.000 | 0.0963019 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1752.00 | 0.213374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1226.00 | −0.148220 | −0.0741098 | − | 0.997250i | \(-0.523612\pi\) | ||||
−0.0741098 | + | 0.997250i | \(0.523612\pi\) | |||||||
\(410\) | −450.000 | −0.0542047 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31960.0 | −3.82174 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2180.00 | 0.257860 | ||||||||
\(416\) | 2550.00 | 0.300539 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −33930.0 | −3.88629 | ||||||||
\(425\) | −3350.00 | −0.382350 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12444.0 | −1.40538 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8500.00 | −0.953271 | ||||||||
\(431\) | 4984.00 | 0.557009 | 0.278504 | − | 0.960435i | \(-0.410161\pi\) | ||||
0.278504 | + | 0.960435i | \(0.410161\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1694.00 | 0.188010 | 0.0940051 | − | 0.995572i | \(-0.470033\pi\) | ||||
0.0940051 | + | 0.995572i | \(0.470033\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6426.00 | −0.705848 | ||||||||
\(437\) | −10304.0 | −1.12793 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13864.0 | −1.50727 | −0.753636 | − | 0.657292i | \(-0.771702\pi\) | ||||
−0.753636 | + | 0.657292i | \(0.771702\pi\) | |||||||
\(440\) | 2700.00 | 0.292540 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −20100.0 | −2.16303 | ||||||||
\(443\) | 4644.00 | 0.498066 | 0.249033 | − | 0.968495i | \(-0.419887\pi\) | ||||
0.249033 | + | 0.968495i | \(0.419887\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5190.00 | −0.552875 | ||||||||
\(446\) | −8160.00 | −0.866339 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4926.00 | 0.517756 | 0.258878 | − | 0.965910i | \(-0.416647\pi\) | ||||
0.258878 | + | 0.965910i | \(0.416647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −216.000 | −0.0225522 | ||||||||
\(452\) | −24786.0 | −2.57928 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20420.0 | −2.11092 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14694.0 | −1.50406 | −0.752031 | − | 0.659128i | \(-0.770926\pi\) | ||||
−0.752031 | + | 0.659128i | \(0.770926\pi\) | |||||||
\(458\) | −16930.0 | −1.72726 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9520.00 | −0.964940 | ||||||||
\(461\) | 2006.00 | 0.202665 | 0.101333 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101333 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4896.00 | 0.491439 | 0.245720 | − | 0.969341i | \(-0.420976\pi\) | ||||
0.245720 | + | 0.969341i | \(0.420976\pi\) | |||||||
\(464\) | 5162.00 | 0.516465 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26610.0 | 2.64525 | ||||||||
\(467\) | 2660.00 | 0.263576 | 0.131788 | − | 0.991278i | \(-0.457928\pi\) | ||||
0.131788 | + | 0.991278i | \(0.457928\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5200.00 | −0.510336 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −17100.0 | −1.66757 | ||||||||
\(473\) | −4080.00 | −0.396614 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2300.00 | 0.222171 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20179.0 | −1.89510 | ||||||||
\(485\) | 3510.00 | 0.328620 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6424.00 | −0.597740 | −0.298870 | − | 0.954294i | \(-0.596610\pi\) | ||||
−0.298870 | + | 0.954294i | \(0.596610\pi\) | |||||||
\(488\) | 32310.0 | 2.99714 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18900.0 | 1.73716 | 0.868579 | − | 0.495550i | \(-0.165033\pi\) | ||||
0.868579 | + | 0.495550i | \(0.165033\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7772.00 | −0.710007 | ||||||||
\(494\) | 13800.0 | 1.25687 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19936.0 | 1.80474 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15364.0 | −1.37833 | −0.689165 | − | 0.724604i | \(-0.742023\pi\) | ||||
−0.689165 | + | 0.724604i | \(0.742023\pi\) | |||||||
\(500\) | 2125.00 | 0.190066 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21060.0 | 1.87242 | ||||||||
\(503\) | 2216.00 | 0.196435 | 0.0982173 | − | 0.995165i | \(-0.468686\pi\) | ||||
0.0982173 | + | 0.995165i | \(0.468686\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 230.000 | 0.0202671 | ||||||||
\(506\) | −6720.00 | −0.590396 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24475.0 | 2.11260 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25650.0 | −2.20111 | ||||||||
\(515\) | −9400.00 | −0.804298 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2496.00 | −0.212329 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6750.00 | 0.569244 | ||||||||
\(521\) | −4702.00 | −0.395390 | −0.197695 | − | 0.980264i | \(-0.563346\pi\) | ||||
−0.197695 | + | 0.980264i | \(0.563346\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 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 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | −18850.0 | −1.54489 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −540.000 | −0.0438837 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3660.00 | −0.295767 | ||||||||
\(536\) | −18540.0 | −1.49404 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6370.00 | 0.510465 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 11390.0 | 0.897688 | ||||||||
\(545\) | −1890.00 | −0.148548 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19284.0 | −1.50736 | −0.753679 | − | 0.657243i | \(-0.771722\pi\) | ||||
−0.753679 | + | 0.657243i | \(0.771722\pi\) | |||||||
\(548\) | 6358.00 | 0.495621 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1500.00 | 0.116291 | ||||||||
\(551\) | 5336.00 | 0.412561 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 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 | \(0.231159\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10200.0 | −0.771760 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26910.0 | −2.01980 | ||||||||
\(563\) | −25612.0 | −1.91726 | −0.958630 | − | 0.284656i | \(-0.908121\pi\) | ||||
−0.958630 | + | 0.284656i | \(0.908121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7290.00 | −0.542819 | ||||||||
\(566\) | 31180.0 | 2.31554 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43200.0 | −3.19125 | ||||||||
\(569\) | −7002.00 | −0.515886 | −0.257943 | − | 0.966160i | \(-0.583045\pi\) | ||||
−0.257943 | + | 0.966160i | \(0.583045\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2800.00 | −0.203075 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6014.00 | 0.433910 | 0.216955 | − | 0.976182i | \(-0.430388\pi\) | ||||
0.216955 | + | 0.976182i | \(0.430388\pi\) | |||||||
\(578\) | −65215.0 | −4.69306 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4930.00 | 0.352943 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −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 | \(-0.635528\pi\) | ||||
−0.413025 | + | 0.910719i | \(0.635528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20608.0 | 1.44166 | ||||||||
\(590\) | −9500.00 | −0.662896 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12994.0 | −0.902112 | ||||||||
\(593\) | −9462.00 | −0.655241 | −0.327620 | − | 0.944809i | \(-0.606247\pi\) | ||||
−0.327620 | + | 0.944809i | \(0.606247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 31858.0 | 2.18952 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16800.0 | −1.14883 | ||||||||
\(599\) | −2320.00 | −0.158251 | −0.0791257 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791257 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4650.00 | −0.315603 | −0.157802 | − | 0.987471i | \(-0.550441\pi\) | ||||
−0.157802 | + | 0.987471i | \(0.550441\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18632.0 | −1.25517 | ||||||||
\(605\) | −5935.00 | −0.398830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14656.0 | 0.980014 | 0.490007 | − | 0.871718i | \(-0.336994\pi\) | ||||
0.490007 | + | 0.871718i | \(0.336994\pi\) | |||||||
\(608\) | −7820.00 | −0.521617 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17950.0 | 1.19143 | ||||||||
\(611\) | −6240.00 | −0.413164 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29166.0 | 1.92170 | 0.960851 | − | 0.277065i | \(-0.0893616\pi\) | ||||
0.960851 | + | 0.277065i | \(0.0893616\pi\) | |||||||
\(614\) | −11340.0 | −0.745350 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28554.0 | −1.86311 | −0.931557 | − | 0.363597i | \(-0.881549\pi\) | ||||
−0.931557 | + | 0.363597i | \(0.881549\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3876.00 | 0.251679 | 0.125840 | − | 0.992051i | \(-0.459837\pi\) | ||||
0.125840 | + | 0.992051i | \(0.459837\pi\) | |||||||
\(620\) | 19040.0 | 1.23333 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −33240.0 | −2.14277 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 49090.0 | 3.13423 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4670.00 | 0.292538 | ||||||||
\(635\) | 3040.00 | 0.189982 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3480.00 | 0.215948 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10575.0 | 0.653146 | ||||||||
\(641\) | −9330.00 | −0.574903 | −0.287452 | − | 0.957795i | \(-0.592808\pi\) | ||||
−0.287452 | + | 0.957795i | \(0.592808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18332.0 | 1.12433 | 0.562164 | − | 0.827025i | \(-0.309969\pi\) | ||||
0.562164 | + | 0.827025i | \(0.309969\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 61640.0 | 3.75417 | ||||||||
\(647\) | −2088.00 | −0.126874 | −0.0634372 | − | 0.997986i | \(-0.520206\pi\) | ||||
−0.0634372 | + | 0.997986i | \(0.520206\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4560.00 | −0.275802 | ||||||||
\(650\) | 3750.00 | 0.226288 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 39372.0 | 2.36492 | ||||||||
\(653\) | −22.0000 | −0.00131842 | −0.000659209 | − | 1.00000i | \(-0.500210\pi\) | ||||
−0.000659209 | 1.00000i | \(0.500210\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4780.00 | −0.285145 | ||||||||
\(656\) | 1602.00 | 0.0953469 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16260.0 | −0.961153 | −0.480576 | − | 0.876953i | \(-0.659573\pi\) | ||||
−0.480576 | + | 0.876953i | \(0.659573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23818.0 | 1.40153 | 0.700766 | − | 0.713391i | \(-0.252842\pi\) | ||||
0.700766 | + | 0.713391i | \(0.252842\pi\) | |||||||
\(662\) | −11460.0 | −0.672818 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19620.0 | −1.14669 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6496.00 | −0.377101 | ||||||||
\(668\) | −29512.0 | −1.70936 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10300.0 | −0.593916 | ||||||||
\(671\) | 8616.00 | 0.495703 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31106.0 | 1.78165 | 0.890823 | − | 0.454350i | \(-0.150128\pi\) | ||||
0.890823 | + | 0.454350i | \(0.150128\pi\) | |||||||
\(674\) | 30310.0 | 1.73219 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22049.0 | −1.25449 | ||||||||
\(677\) | −1090.00 | −0.0618790 | −0.0309395 | − | 0.999521i | \(-0.509850\pi\) | ||||
−0.0309395 | + | 0.999521i | \(0.509850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 30150.0 | 1.70029 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13440.0 | 0.754610 | ||||||||
\(683\) | 12372.0 | 0.693121 | 0.346560 | − | 0.938028i | \(-0.387350\pi\) | ||||
0.346560 | + | 0.938028i | \(0.387350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1870.00 | 0.104305 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30260.0 | 1.67682 | ||||||||
\(689\) | −22620.0 | −1.25073 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3252.00 | −0.179033 | −0.0895166 | − | 0.995985i | \(-0.528532\pi\) | ||||
−0.0895166 | + | 0.995985i | \(0.528532\pi\) | |||||||
\(692\) | −41514.0 | −2.28053 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7420.00 | 0.405849 | ||||||||
\(695\) | −1980.00 | −0.108066 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2412.00 | −0.131077 | ||||||||
\(698\) | 1270.00 | 0.0688685 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5434.00 | 0.292781 | 0.146390 | − | 0.989227i | \(-0.453234\pi\) | ||||
0.146390 | + | 0.989227i | \(0.453234\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13432.0 | −0.720622 | ||||||||
\(704\) | 3444.00 | 0.184376 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 54750.0 | 2.91862 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5330.00 | −0.282331 | −0.141165 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141165 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(710\) | −24000.0 | −1.26860 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 46710.0 | 2.45861 | ||||||||
\(713\) | −25088.0 | −1.31775 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1800.00 | 0.0941485 | ||||||||
\(716\) | 69564.0 | 3.63091 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8025.00 | −0.413656 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21590.0 | −1.10827 | ||||||||
\(725\) | 1450.00 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19336.0 | −0.986427 | −0.493214 | − | 0.869908i | \(-0.664178\pi\) | ||||
−0.493214 | + | 0.869908i | \(0.664178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26650.0 | 1.35118 | ||||||||
\(731\) | −45560.0 | −2.30519 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18292.0 | −0.910531 | −0.455265 | − | 0.890356i | \(-0.650456\pi\) | ||||
−0.455265 | + | 0.890356i | \(0.650456\pi\) | |||||||
\(740\) | −12410.0 | −0.616487 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17904.0 | −0.884030 | −0.442015 | − | 0.897008i | \(-0.645736\pi\) | ||||
−0.442015 | + | 0.897008i | \(0.645736\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9370.00 | 0.460792 | ||||||||
\(746\) | 41210.0 | 2.02253 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27336.0 | 1.33623 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8700.00 | 0.420206 | ||||||||
\(755\) | −5480.00 | −0.264156 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8318.00 | 0.399370 | 0.199685 | − | 0.979860i | \(-0.436008\pi\) | ||||
0.199685 | + | 0.979860i | \(0.436008\pi\) | |||||||
\(758\) | −18100.0 | −0.867311 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −20700.0 | −0.987984 | ||||||||
\(761\) | 6690.00 | 0.318676 | 0.159338 | − | 0.987224i | \(-0.449064\pi\) | ||||
0.159338 | + | 0.987224i | \(0.449064\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −83368.0 | −3.94784 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42320.0 | 1.99619 | ||||||||
\(767\) | −11400.0 | −0.536676 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9266.00 | −0.434513 | −0.217257 | − | 0.976115i | \(-0.569711\pi\) | ||||
−0.217257 | + | 0.976115i | \(0.569711\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 37026.0 | 1.72616 | ||||||||
\(773\) | 9678.00 | 0.450315 | 0.225157 | − | 0.974322i | \(-0.427710\pi\) | ||||
0.225157 | + | 0.974322i | \(0.427710\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5600.00 | 0.259559 | ||||||||
\(776\) | −31590.0 | −1.46136 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18390.0 | 0.847447 | ||||||||
\(779\) | 1656.00 | 0.0761648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11520.0 | −0.527808 | ||||||||
\(782\) | −75040.0 | −3.43149 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9590.00 | −0.436028 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6860.00 | 0.310715 | 0.155357 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155357 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(788\) | 48450.0 | 2.19030 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22400.0 | −1.00881 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(-0.421760\pi\) | ||||
0.243331 | + | 0.969943i | \(0.421760\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27872.0 | −1.23409 | ||||||||
\(800\) | −2125.00 | −0.0939126 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14250.0 | 0.627413 | ||||||||
\(803\) | 12792.0 | 0.562167 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33600.0 | 1.46837 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2070.00 | −0.0901267 | ||||||||
\(809\) | −26010.0 | −1.13036 | −0.565181 | − | 0.824967i | \(-0.691194\pi\) | ||||
−0.565181 | + | 0.824967i | \(0.691194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14628.0 | 0.633364 | 0.316682 | − | 0.948532i | \(-0.397431\pi\) | ||||
0.316682 | + | 0.948532i | \(0.397431\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8760.00 | −0.377196 | ||||||||
\(815\) | 11580.0 | 0.497705 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31280.0 | 1.33947 | ||||||||
\(818\) | 6130.00 | 0.262018 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1530.00 | 0.0651584 | ||||||||
\(821\) | −8718.00 | −0.370597 | −0.185299 | − | 0.982682i | \(-0.559325\pi\) | ||||
−0.185299 | + | 0.982682i | \(0.559325\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7432.00 | −0.314779 | −0.157390 | − | 0.987537i | \(-0.550308\pi\) | ||||
−0.157390 | + | 0.987537i | \(0.550308\pi\) | |||||||
\(824\) | 84600.0 | 3.57668 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17388.0 | −0.731125 | −0.365562 | − | 0.930787i | \(-0.619123\pi\) | ||||
−0.365562 | + | 0.930787i | \(0.619123\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7902.00 | −0.331059 | −0.165529 | − | 0.986205i | \(-0.552933\pi\) | ||||
−0.165529 | + | 0.986205i | \(0.552933\pi\) | |||||||
\(830\) | −10900.0 | −0.455837 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8610.00 | 0.358772 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8680.00 | −0.359741 | ||||||||
\(836\) | −18768.0 | −0.776441 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7004.00 | 0.285649 | ||||||||
\(845\) | −6485.00 | −0.264013 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 67106.0 | 2.71749 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16750.0 | 0.675906 | ||||||||
\(851\) | 16352.0 | 0.658683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30150.0 | −1.21022 | −0.605109 | − | 0.796142i | \(-0.706871\pi\) | ||||
−0.605109 | + | 0.796142i | \(0.706871\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32940.0 | 1.31526 | ||||||||
\(857\) | −4350.00 | −0.173388 | −0.0866938 | − | 0.996235i | \(-0.527630\pi\) | ||||
−0.0866938 | + | 0.996235i | \(0.527630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30676.0 | 1.21845 | 0.609227 | − | 0.792996i | \(-0.291480\pi\) | ||||
0.609227 | + | 0.792996i | \(0.291480\pi\) | |||||||
\(860\) | 28900.0 | 1.14591 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24920.0 | −0.984662 | ||||||||
\(863\) | 23688.0 | 0.934356 | 0.467178 | − | 0.884163i | \(-0.345271\pi\) | ||||
0.467178 | + | 0.884163i | \(0.345271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12210.0 | −0.479945 | ||||||||
\(866\) | −8470.00 | −0.332358 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10752.0 | −0.419720 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12360.0 | −0.480830 | ||||||||
\(872\) | 17010.0 | 0.660586 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 51520.0 | 1.99392 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31910.0 | 1.22865 | 0.614324 | − | 0.789054i | \(-0.289429\pi\) | ||||
0.614324 | + | 0.789054i | \(0.289429\pi\) | |||||||
\(878\) | 69320.0 | 2.66451 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5340.00 | −0.204558 | ||||||||
\(881\) | 50250.0 | 1.92164 | 0.960820 | − | 0.277172i | \(-0.0893971\pi\) | ||||
0.960820 | + | 0.277172i | \(0.0893971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5980.00 | 0.227908 | 0.113954 | − | 0.993486i | \(-0.463648\pi\) | ||||
0.113954 | + | 0.993486i | \(0.463648\pi\) | |||||||
\(884\) | 68340.0 | 2.60014 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23220.0 | −0.880464 | ||||||||
\(887\) | −24568.0 | −0.930003 | −0.465002 | − | 0.885310i | \(-0.653946\pi\) | ||||
−0.465002 | + | 0.885310i | \(0.653946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 25950.0 | 0.977355 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27744.0 | 1.04141 | ||||||||
\(893\) | 19136.0 | 0.717091 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20460.0 | 0.764137 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24630.0 | −0.915271 | ||||||||
\(899\) | 12992.0 | 0.481988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −101036. | −3.73585 | ||||||||
\(902\) | 1080.00 | 0.0398670 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 65610.0 | 2.41389 | ||||||||
\(905\) | −6350.00 | −0.233239 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13252.0 | 0.485144 | 0.242572 | − | 0.970133i | \(-0.422009\pi\) | ||||
0.242572 | + | 0.970133i | \(0.422009\pi\) | |||||||
\(908\) | 69428.0 | 2.53750 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6744.00 | 0.245267 | 0.122634 | − | 0.992452i | \(-0.460866\pi\) | ||||
0.122634 | + | 0.992452i | \(0.460866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5232.00 | −0.189654 | ||||||||
\(914\) | 73470.0 | 2.65883 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 57562.0 | 2.07631 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45336.0 | −1.62731 | −0.813654 | − | 0.581349i | \(-0.802525\pi\) | ||||
−0.813654 | + | 0.581349i | \(0.802525\pi\) | |||||||
\(920\) | 25200.0 | 0.903065 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10030.0 | −0.358265 | ||||||||
\(923\) | −28800.0 | −1.02705 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3650.00 | −0.129742 | ||||||||
\(926\) | −24480.0 | −0.868750 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −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 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −90474.0 | −3.17980 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13300.0 | −0.465941 | ||||||||
\(935\) | 8040.00 | 0.281215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21754.0 | −0.758455 | −0.379227 | − | 0.925303i | \(-0.623810\pi\) | ||||
−0.379227 | + | 0.925303i | \(0.623810\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 17680.0 | 0.613466 | ||||||||
\(941\) | 14550.0 | 0.504056 | 0.252028 | − | 0.967720i | \(-0.418903\pi\) | ||||
0.252028 | + | 0.967720i | \(0.418903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | \(0.795460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31980.0 | 1.09390 | ||||||||
\(950\) | −11500.0 | −0.392747 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20810.0 | −0.707347 | −0.353674 | − | 0.935369i | \(-0.615068\pi\) | ||||
−0.353674 | + | 0.935369i | \(0.615068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24520.0 | −0.830836 | ||||||||
\(956\) | −63512.0 | −2.14867 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28000.0 | 0.944300 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | −21900.0 | −0.733975 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3570.00 | −0.119276 | ||||||||
\(965\) | 10890.0 | 0.363276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2776.00 | 0.0923166 | 0.0461583 | − | 0.998934i | \(-0.485302\pi\) | ||||
0.0461583 | + | 0.998934i | \(0.485302\pi\) | |||||||
\(968\) | 53415.0 | 1.77358 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −17550.0 | −0.580924 | ||||||||
\(971\) | 27292.0 | 0.902000 | 0.451000 | − | 0.892524i | \(-0.351067\pi\) | ||||
0.451000 | + | 0.892524i | \(0.351067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | \(0.499677\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12456.0 | 0.406635 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −94500.0 | −3.07089 | ||||||||
\(983\) | 37912.0 | 1.23012 | 0.615058 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615058 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14250.0 | 0.460957 | ||||||||
\(986\) | 38860.0 | 1.25513 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5720.00 | 0.182247 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29434.0 | 0.934989 | 0.467495 | − | 0.883996i | \(-0.345157\pi\) | ||||
0.467495 | + | 0.883996i | \(0.345157\pi\) | |||||||
\(998\) | 76820.0 | 2.43657 | ||||||||
\(999\) | 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 | 2205.4.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 735.4.a.j.1.1 | 1 | |||
7.6 | odd | 2 | 315.4.a.a.1.1 | 1 | |||
21.20 | even | 2 | 105.4.a.b.1.1 | ✓ | 1 | ||
35.34 | odd | 2 | 1575.4.a.l.1.1 | 1 | |||
84.83 | odd | 2 | 1680.4.a.u.1.1 | 1 | |||
105.62 | odd | 4 | 525.4.d.a.274.2 | 2 | |||
105.83 | odd | 4 | 525.4.d.a.274.1 | 2 | |||
105.104 | even | 2 | 525.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.b.1.1 | ✓ | 1 | 21.20 | even | 2 | ||
315.4.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
525.4.a.a.1.1 | 1 | 105.104 | even | 2 | |||
525.4.d.a.274.1 | 2 | 105.83 | odd | 4 | |||
525.4.d.a.274.2 | 2 | 105.62 | odd | 4 | |||
735.4.a.j.1.1 | 1 | 3.2 | odd | 2 | |||
1575.4.a.l.1.1 | 1 | 35.34 | odd | 2 | |||
1680.4.a.u.1.1 | 1 | 84.83 | odd | 2 | |||
2205.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial |