Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.178885 | 0.0894427 | − | 0.995992i | \(-0.471491\pi\) | ||||
0.0894427 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.0000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.0000 | 1.40809 | 0.704043 | − | 0.710158i | \(-0.251376\pi\) | ||||
0.704043 | + | 0.710158i | \(0.251376\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.00000 | −0.103280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 70.0000 | 0.998676 | 0.499338 | − | 0.866407i | \(-0.333577\pi\) | ||||
0.499338 | + | 0.866407i | \(0.333577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −92.0000 | −1.11086 | −0.555428 | − | 0.831565i | \(-0.687445\pi\) | ||||
−0.555428 | + | 0.831565i | \(0.687445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16.0000 | −0.145054 | −0.0725268 | − | 0.997366i | \(-0.523106\pi\) | ||||
−0.0725268 | + | 0.997366i | \(0.523106\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −121.000 | −0.968000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −122.000 | −0.781201 | −0.390601 | − | 0.920560i | \(-0.627733\pi\) | ||||
−0.390601 | + | 0.920560i | \(0.627733\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 64.0000 | 0.370798 | 0.185399 | − | 0.982663i | \(-0.440642\pi\) | ||||
0.185399 | + | 0.982663i | \(0.440642\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 36.0000 | 0.189903 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −306.000 | −1.35962 | −0.679812 | − | 0.733386i | \(-0.737939\pi\) | ||||
−0.679812 | + | 0.733386i | \(0.737939\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −198.000 | −0.812958 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −50.0000 | −0.190456 | −0.0952279 | − | 0.995455i | \(-0.530358\pi\) | ||||
−0.0952279 | + | 0.995455i | \(0.530358\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20.0000 | −0.0709296 | −0.0354648 | − | 0.999371i | \(-0.511291\pi\) | ||||
−0.0354648 | + | 0.999371i | \(0.511291\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.0000 | 0.0596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −176.000 | −0.546218 | −0.273109 | − | 0.961983i | \(-0.588052\pi\) | ||||
−0.273109 | + | 0.961983i | \(0.588052\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −210.000 | −0.576586 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 526.000 | 1.36324 | 0.681619 | − | 0.731707i | \(-0.261276\pi\) | ||||
0.681619 | + | 0.731707i | \(0.261276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.0000 | −0.0588393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 276.000 | 0.641353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 540.000 | 1.19156 | 0.595780 | − | 0.803148i | \(-0.296843\pi\) | ||||
0.595780 | + | 0.803148i | \(0.296843\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 818.000 | 1.71695 | 0.858477 | − | 0.512852i | \(-0.171411\pi\) | ||||
0.858477 | + | 0.512852i | \(0.171411\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 132.000 | 0.251886 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 228.000 | 0.415741 | 0.207870 | − | 0.978156i | \(-0.433347\pi\) | ||||
0.207870 | + | 0.978156i | \(0.433347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48.0000 | 0.0837467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −864.000 | −1.44420 | −0.722098 | − | 0.691791i | \(-0.756822\pi\) | ||||
−0.722098 | + | 0.691791i | \(0.756822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −106.000 | −0.169950 | −0.0849751 | − | 0.996383i | \(-0.527081\pi\) | ||||
−0.0849751 | + | 0.996383i | \(0.527081\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 363.000 | 0.558875 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −736.000 | −1.04818 | −0.524092 | − | 0.851662i | \(-0.675595\pi\) | ||||
−0.524092 | + | 0.851662i | \(0.675595\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −588.000 | −0.777607 | −0.388804 | − | 0.921321i | \(-0.627112\pi\) | ||||
−0.388804 | + | 0.921321i | \(0.627112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 140.000 | 0.178649 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 366.000 | 0.451027 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −146.000 | −0.173887 | −0.0869436 | − | 0.996213i | \(-0.527710\pi\) | ||||
−0.0869436 | + | 0.996213i | \(0.527710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −192.000 | −0.214080 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −184.000 | −0.198716 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1214.00 | 1.27075 | 0.635376 | − | 0.772203i | \(-0.280845\pi\) | ||||
0.635376 | + | 0.772203i | \(0.280845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −108.000 | −0.109640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −846.000 | −0.833467 | −0.416733 | − | 0.909029i | \(-0.636825\pi\) | ||||
−0.416733 | + | 0.909029i | \(0.636825\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −168.000 | −0.160714 | −0.0803570 | − | 0.996766i | \(-0.525606\pi\) | ||||
−0.0803570 | + | 0.996766i | \(0.525606\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 708.000 | 0.639672 | 0.319836 | − | 0.947473i | \(-0.396372\pi\) | ||||
0.319836 | + | 0.947473i | \(0.396372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 646.000 | 0.567666 | 0.283833 | − | 0.958874i | \(-0.408394\pi\) | ||||
0.283833 | + | 0.958874i | \(0.408394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 918.000 | 0.784979 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1938.00 | 1.61338 | 0.806689 | − | 0.590976i | \(-0.201257\pi\) | ||||
0.806689 | + | 0.590976i | \(0.201257\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −32.0000 | −0.0259480 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 594.000 | 0.469362 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 150.000 | 0.109960 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −492.000 | −0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −224.000 | −0.156510 | −0.0782551 | − | 0.996933i | \(-0.524935\pi\) | ||||
−0.0782551 | + | 0.996933i | \(0.524935\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 60.0000 | 0.0409512 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2588.00 | −1.72607 | −0.863033 | − | 0.505148i | \(-0.831438\pi\) | ||||
−0.863033 | + | 0.505148i | \(0.831438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −54.0000 | −0.0344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 490.000 | 0.305573 | 0.152787 | − | 0.988259i | \(-0.451175\pi\) | ||||
0.152787 | + | 0.988259i | \(0.451175\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1716.00 | −1.04712 | −0.523558 | − | 0.851990i | \(-0.675396\pi\) | ||||
−0.523558 | + | 0.851990i | \(0.675396\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 528.000 | 0.315359 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −792.000 | −0.463149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −244.000 | −0.139745 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2386.00 | −1.31187 | −0.655935 | − | 0.754817i | \(-0.727726\pi\) | ||||
−0.655935 | + | 0.754817i | \(0.727726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 104.000 | 0.0560490 | 0.0280245 | − | 0.999607i | \(-0.491078\pi\) | ||||
0.0280245 | + | 0.999607i | \(0.491078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 630.000 | 0.332892 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 128.000 | 0.0663304 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1566.00 | −0.796054 | −0.398027 | − | 0.917374i | \(-0.630305\pi\) | ||||
−0.398027 | + | 0.917374i | \(0.630305\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1578.00 | −0.787066 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1076.00 | 0.517048 | 0.258524 | − | 0.966005i | \(-0.416764\pi\) | ||||
0.258524 | + | 0.966005i | \(0.416764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 72.0000 | 0.0339709 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2760.00 | −1.27889 | −0.639447 | − | 0.768835i | \(-0.720837\pi\) | ||||
−0.639447 | + | 0.768835i | \(0.720837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2159.00 | 0.982704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −828.000 | −0.370285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1558.00 | −0.684697 | −0.342348 | − | 0.939573i | \(-0.611222\pi\) | ||||
−0.342348 | + | 0.939573i | \(0.611222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1620.00 | −0.687947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3452.00 | 1.44142 | 0.720711 | − | 0.693235i | \(-0.243815\pi\) | ||||
0.720711 | + | 0.693235i | \(0.243815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1162.00 | 0.477187 | 0.238593 | − | 0.971120i | \(-0.423314\pi\) | ||||
0.238593 | + | 0.971120i | \(0.423314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2454.00 | −0.991284 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −612.000 | −0.243217 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −840.000 | −0.328486 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1928.00 | −0.730394 | −0.365197 | − | 0.930930i | \(-0.618998\pi\) | ||||
−0.365197 | + | 0.930930i | \(0.618998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −318.000 | −0.118602 | −0.0593009 | − | 0.998240i | \(-0.518887\pi\) | ||||
−0.0593009 | + | 0.998240i | \(0.518887\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −396.000 | −0.145426 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4062.00 | 1.46906 | 0.734532 | − | 0.678574i | \(-0.237402\pi\) | ||||
0.734532 | + | 0.678574i | \(0.237402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5480.00 | 1.95209 | 0.976047 | − | 0.217558i | \(-0.0698090\pi\) | ||||
0.976047 | + | 0.217558i | \(0.0698090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −684.000 | −0.240028 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −100.000 | −0.0340698 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −144.000 | −0.0483512 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1104.00 | 0.365384 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4892.00 | −1.59611 | −0.798055 | − | 0.602585i | \(-0.794138\pi\) | ||||
−0.798055 | + | 0.602585i | \(0.794138\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2592.00 | 0.833807 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −40.0000 | −0.0126883 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 318.000 | 0.0981208 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4620.00 | 1.40622 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4320.00 | 1.29726 | 0.648629 | − | 0.761105i | \(-0.275343\pi\) | ||||
0.648629 | + | 0.761105i | \(0.275343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1089.00 | −0.322667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5516.00 | −1.61282 | −0.806409 | − | 0.591358i | \(-0.798592\pi\) | ||||
−0.806409 | + | 0.591358i | \(0.798592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1670.00 | −0.481907 | −0.240954 | − | 0.970537i | \(-0.577460\pi\) | ||||
−0.240954 | + | 0.970537i | \(0.577460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3926.00 | −1.10387 | −0.551933 | − | 0.833888i | \(-0.686110\pi\) | ||||
−0.551933 | + | 0.833888i | \(0.686110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −352.000 | −0.0977104 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2208.00 | 0.605169 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3640.00 | −0.985155 | −0.492577 | − | 0.870269i | \(-0.663945\pi\) | ||||
−0.492577 | + | 0.870269i | \(0.663945\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5650.00 | −1.51016 | −0.755080 | − | 0.655633i | \(-0.772402\pi\) | ||||
−0.755080 | + | 0.655633i | \(0.772402\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6072.00 | −1.56418 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1764.00 | 0.448952 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4652.00 | 1.16985 | 0.584924 | − | 0.811088i | \(-0.301124\pi\) | ||||
0.584924 | + | 0.811088i | \(0.301124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 192.000 | 0.0477112 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −420.000 | −0.103143 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6006.00 | 1.45776 | 0.728879 | − | 0.684642i | \(-0.240042\pi\) | ||||
0.728879 | + | 0.684642i | \(0.240042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1098.00 | −0.260400 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5040.00 | −1.18167 | −0.590836 | − | 0.806792i | \(-0.701202\pi\) | ||||
−0.590836 | + | 0.806792i | \(0.701202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1052.00 | 0.243864 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 438.000 | 0.100394 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5478.00 | −1.24163 | −0.620817 | − | 0.783956i | \(-0.713199\pi\) | ||||
−0.620817 | + | 0.783956i | \(0.713199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2176.00 | −0.487759 | −0.243879 | − | 0.969806i | \(-0.578420\pi\) | ||||
−0.243879 | + | 0.969806i | \(0.578420\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1452.00 | 0.318396 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4658.00 | −1.01037 | −0.505184 | − | 0.863011i | \(-0.668575\pi\) | ||||
−0.505184 | + | 0.863011i | \(0.668575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 576.000 | 0.123599 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4614.00 | −0.979531 | −0.489765 | − | 0.871854i | \(-0.662918\pi\) | ||||
−0.489765 | + | 0.871854i | \(0.662918\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1244.00 | 0.261301 | 0.130650 | − | 0.991429i | \(-0.458293\pi\) | ||||
0.130650 | + | 0.991429i | \(0.458293\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 552.000 | 0.114729 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.00264604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3642.00 | −0.733669 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6354.00 | 1.26691 | 0.633455 | − | 0.773780i | \(-0.281636\pi\) | ||||
0.633455 | + | 0.773780i | \(0.281636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1080.00 | 0.213153 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 324.000 | 0.0633010 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1056.00 | −0.204248 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2538.00 | 0.481202 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1636.00 | 0.307138 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3740.00 | −0.695287 | −0.347643 | − | 0.937627i | \(-0.613018\pi\) | ||||
−0.347643 | + | 0.937627i | \(0.613018\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 504.000 | 0.0927882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2184.00 | −0.398210 | −0.199105 | − | 0.979978i | \(-0.563803\pi\) | ||||
−0.199105 | + | 0.979978i | \(0.563803\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4442.00 | −0.802162 | −0.401081 | − | 0.916043i | \(-0.631365\pi\) | ||||
−0.401081 | + | 0.916043i | \(0.631365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4314.00 | −0.764348 | −0.382174 | − | 0.924090i | \(-0.624825\pi\) | ||||
−0.382174 | + | 0.924090i | \(0.624825\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1464.00 | 0.256954 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2124.00 | −0.369315 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6440.00 | −1.10938 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7986.00 | −1.36303 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1938.00 | −0.327742 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7988.00 | −1.32647 | −0.663233 | − | 0.748413i | \(-0.730816\pi\) | ||||
−0.663233 | + | 0.748413i | \(0.730816\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2754.00 | −0.453208 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 456.000 | 0.0743700 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10606.0 | −1.71438 | −0.857189 | − | 0.515001i | \(-0.827791\pi\) | ||||
−0.857189 | + | 0.515001i | \(0.827791\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5814.00 | −0.931484 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −768.000 | −0.121963 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 96.0000 | 0.0149811 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8340.00 | 1.29024 | 0.645122 | − | 0.764080i | \(-0.276807\pi\) | ||||
0.645122 | + | 0.764080i | \(0.276807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10498.0 | 1.61016 | 0.805079 | − | 0.593168i | \(-0.202123\pi\) | ||||
0.805079 | + | 0.593168i | \(0.202123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1782.00 | −0.270986 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7878.00 | 1.18783 | 0.593914 | − | 0.804528i | \(-0.297582\pi\) | ||||
0.593914 | + | 0.804528i | \(0.297582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1728.00 | −0.258346 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11856.0 | −1.74300 | −0.871498 | − | 0.490399i | \(-0.836851\pi\) | ||||
−0.871498 | + | 0.490399i | \(0.836851\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1605.00 | 0.233999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3561.00 | 0.514887 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −212.000 | −0.0304016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5488.00 | −0.780576 | −0.390288 | − | 0.920693i | \(-0.627625\pi\) | ||||
−0.390288 | + | 0.920693i | \(0.627625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −450.000 | −0.0634853 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7570.00 | −1.05083 | −0.525415 | − | 0.850846i | \(-0.676090\pi\) | ||||
−0.525415 | + | 0.850846i | \(0.676090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1476.00 | 0.203254 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8052.00 | −1.10000 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13596.0 | 1.84269 | 0.921345 | − | 0.388746i | \(-0.127092\pi\) | ||||
0.921345 | + | 0.388746i | \(0.127092\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 672.000 | 0.0903612 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8592.00 | −1.14629 | −0.573147 | − | 0.819452i | \(-0.694278\pi\) | ||||
−0.573147 | + | 0.819452i | \(0.694278\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −180.000 | −0.0236432 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −610.000 | −0.0795070 | −0.0397535 | − | 0.999210i | \(-0.512657\pi\) | ||||
−0.0397535 | + | 0.999210i | \(0.512657\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1120.00 | −0.144861 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7764.00 | 0.996545 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1472.00 | −0.187505 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −910.000 | −0.115042 | −0.0575209 | − | 0.998344i | \(-0.518320\pi\) | ||||
−0.0575209 | + | 0.998344i | \(0.518320\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8094.00 | −1.00797 | −0.503984 | − | 0.863713i | \(-0.668133\pi\) | ||||
−0.503984 | + | 0.863713i | \(0.668133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4224.00 | 0.522115 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 162.000 | 0.0198762 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3672.00 | 0.447210 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10122.0 | −1.22372 | −0.611859 | − | 0.790967i | \(-0.709578\pi\) | ||||
−0.611859 | + | 0.790967i | \(0.709578\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1470.00 | −0.176423 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1176.00 | −0.139103 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5148.00 | 0.604553 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4228.00 | 0.492963 | 0.246481 | − | 0.969148i | \(-0.420726\pi\) | ||||
0.246481 | + | 0.969148i | \(0.420726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9218.00 | −1.06712 | −0.533560 | − | 0.845762i | \(-0.679146\pi\) | ||||
−0.533560 | + | 0.845762i | \(0.679146\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1584.00 | −0.182073 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8470.00 | −0.966718 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2376.00 | 0.267399 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9192.00 | −1.02729 | −0.513646 | − | 0.858002i | \(-0.671706\pi\) | ||||
−0.513646 | + | 0.858002i | \(0.671706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3614.00 | 0.401103 | 0.200552 | − | 0.979683i | \(-0.435727\pi\) | ||||
0.200552 | + | 0.979683i | \(0.435727\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 732.000 | 0.0806821 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1472.00 | 0.161133 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4344.00 | −0.472273 | −0.236136 | − | 0.971720i | \(-0.575881\pi\) | ||||
−0.236136 | + | 0.971720i | \(0.575881\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10876.0 | −1.16644 | −0.583222 | − | 0.812313i | \(-0.698208\pi\) | ||||
−0.583222 | + | 0.812313i | \(0.698208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −292.000 | −0.0311059 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7158.00 | 0.757409 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15550.0 | −1.63441 | −0.817205 | − | 0.576347i | \(-0.804478\pi\) | ||||
−0.817205 | + | 0.576347i | \(0.804478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 600.000 | 0.0626450 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −312.000 | −0.0323599 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7834.00 | 0.801880 | 0.400940 | − | 0.916104i | \(-0.368684\pi\) | ||||
0.400940 | + | 0.916104i | \(0.368684\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1890.00 | −0.192195 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15990.0 | −1.61546 | −0.807732 | − | 0.589550i | \(-0.799305\pi\) | ||||
−0.807732 | + | 0.589550i | \(0.799305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12448.0 | 1.24948 | 0.624738 | − | 0.780834i | \(-0.285206\pi\) | ||||
0.624738 | + | 0.780834i | \(0.285206\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −384.000 | −0.0382959 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13860.0 | 1.37337 | 0.686686 | − | 0.726955i | \(-0.259065\pi\) | ||||
0.686686 | + | 0.726955i | \(0.259065\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4698.00 | 0.459602 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 240.000 | 0.0233303 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11132.0 | 1.07531 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4734.00 | 0.454413 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14368.0 | −1.37054 | −0.685272 | − | 0.728287i | \(-0.740317\pi\) | ||||
−0.685272 | + | 0.728287i | \(0.740317\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20196.0 | −1.91447 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2428.00 | 0.227319 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17240.0 | 1.60415 | 0.802073 | − | 0.597226i | \(-0.203731\pi\) | ||||
0.802073 | + | 0.597226i | \(0.203731\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3228.00 | −0.298518 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18156.0 | −1.66878 | −0.834388 | − | 0.551178i | \(-0.814179\pi\) | ||||
−0.834388 | + | 0.551178i | \(0.814179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8540.00 | −0.780167 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −216.000 | −0.0196131 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1084.00 | −0.0972475 | −0.0486238 | − | 0.998817i | \(-0.515484\pi\) | ||||
−0.0486238 | + | 0.998817i | \(0.515484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8280.00 | 0.738369 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1048.00 | −0.0928986 | −0.0464493 | − | 0.998921i | \(-0.514791\pi\) | ||||
−0.0464493 | + | 0.998921i | \(0.514791\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1692.00 | −0.149095 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6477.00 | −0.567364 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5046.00 | −0.439411 | −0.219705 | − | 0.975566i | \(-0.570510\pi\) | ||||
−0.219705 | + | 0.975566i | \(0.570510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2484.00 | 0.213784 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −336.000 | −0.0287494 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2112.00 | 0.179663 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4674.00 | 0.395310 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3390.00 | 0.285064 | 0.142532 | − | 0.989790i | \(-0.454476\pi\) | ||||
0.142532 | + | 0.989790i | \(0.454476\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13052.0 | 1.09125 | 0.545625 | − | 0.838029i | \(-0.316292\pi\) | ||||
0.545625 | + | 0.838029i | \(0.316292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4480.00 | 0.370307 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11911.0 | −0.978959 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4860.00 | 0.397187 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3300.00 | −0.268178 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1416.00 | 0.114428 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10356.0 | −0.832206 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16966.0 | 1.34829 | 0.674145 | − | 0.738599i | \(-0.264512\pi\) | ||||
0.674145 | + | 0.738599i | \(0.264512\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3486.00 | −0.275504 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1292.00 | 0.101547 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11348.0 | 0.887030 | 0.443515 | − | 0.896267i | \(-0.353731\pi\) | ||||
0.443515 | + | 0.896267i | \(0.353731\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7362.00 | 0.572318 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11224.0 | 0.867801 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1836.00 | 0.140421 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16118.0 | 1.22611 | 0.613053 | − | 0.790041i | \(-0.289941\pi\) | ||||
0.613053 | + | 0.790041i | \(0.289941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1320.00 | −0.0998749 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2520.00 | 0.189651 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15244.0 | −1.14113 | −0.570567 | − | 0.821251i | \(-0.693276\pi\) | ||||
−0.570567 | + | 0.821251i | \(0.693276\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3876.00 | 0.288610 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18918.0 | −1.39382 | −0.696910 | − | 0.717158i | \(-0.745442\pi\) | ||||
−0.696910 | + | 0.717158i | \(0.745442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19372.0 | 1.41978 | 0.709889 | − | 0.704314i | \(-0.248745\pi\) | ||||
0.709889 | + | 0.704314i | \(0.248745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5784.00 | 0.421693 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1936.00 | 0.140412 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7230.00 | 0.521644 | 0.260822 | − | 0.965387i | \(-0.416006\pi\) | ||||
0.260822 | + | 0.965387i | \(0.416006\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 954.000 | 0.0684748 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6312.00 | −0.448399 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1188.00 | 0.0839620 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7396.00 | −0.520044 | −0.260022 | − | 0.965603i | \(-0.583730\pi\) | ||||
−0.260022 | + | 0.965603i | \(0.583730\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5888.00 | −0.411903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12186.0 | −0.848164 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −714.000 | −0.0494443 | −0.0247221 | − | 0.999694i | \(-0.507870\pi\) | ||||
−0.0247221 | + | 0.999694i | \(0.507870\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16440.0 | −1.12704 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11536.0 | 0.786892 | 0.393446 | − | 0.919348i | \(-0.371283\pi\) | ||||
0.393446 | + | 0.919348i | \(0.371283\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4138.00 | −0.280853 | −0.140426 | − | 0.990091i | \(-0.544847\pi\) | ||||
−0.140426 | + | 0.990091i | \(0.544847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2052.00 | 0.138580 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2374.00 | −0.159532 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6848.00 | −0.457911 | −0.228955 | − | 0.973437i | \(-0.573531\pi\) | ||||
−0.228955 | + | 0.973437i | \(0.573531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11616.0 | −0.769121 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12722.0 | −0.838233 | −0.419116 | − | 0.907932i | \(-0.637660\pi\) | ||||
−0.419116 | + | 0.907932i | \(0.637660\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 300.000 | 0.0196702 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24726.0 | −1.61334 | −0.806670 | − | 0.591002i | \(-0.798733\pi\) | ||||
−0.806670 | + | 0.591002i | \(0.798733\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23964.0 | 1.55605 | 0.778025 | − | 0.628234i | \(-0.216222\pi\) | ||||
0.778025 | + | 0.628234i | \(0.216222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 432.000 | 0.0279156 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14141.0 | 0.905024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3312.00 | −0.210955 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21420.0 | −1.35782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17224.0 | 1.08665 | 0.543325 | − | 0.839522i | \(-0.317165\pi\) | ||||
0.543325 | + | 0.839522i | \(0.317165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14676.0 | 0.921514 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −448.000 | −0.0279974 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7776.00 | −0.481399 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18190.0 | −1.12085 | −0.560423 | − | 0.828207i | \(-0.689361\pi\) | ||||
−0.560423 | + | 0.828207i | \(0.689361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14116.0 | 0.865755 | 0.432878 | − | 0.901453i | \(-0.357498\pi\) | ||||
0.432878 | + | 0.901453i | \(0.357498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 120.000 | 0.00732557 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4056.00 | 0.246457 | 0.123229 | − | 0.992378i | \(-0.460675\pi\) | ||||
0.123229 | + | 0.992378i | \(0.460675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6480.00 | −0.391930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16490.0 | −0.988214 | −0.494107 | − | 0.869401i | \(-0.664505\pi\) | ||||
−0.494107 | + | 0.869401i | \(0.664505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5176.00 | −0.308768 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −954.000 | −0.0566501 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4988.00 | 0.294848 | 0.147424 | − | 0.989073i | \(-0.452902\pi\) | ||||
0.147424 | + | 0.989073i | \(0.452902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4982.00 | −0.293158 | −0.146579 | − | 0.989199i | \(-0.546826\pi\) | ||||
−0.146579 | + | 0.989199i | \(0.546826\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13860.0 | −0.811882 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1952.00 | 0.113316 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12960.0 | −0.748972 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9816.00 | −0.564743 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16190.0 | −0.927309 | −0.463654 | − | 0.886016i | \(-0.653462\pi\) | ||||
−0.463654 | + | 0.886016i | \(0.653462\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3267.00 | 0.186292 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23202.0 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16548.0 | 0.931161 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13452.0 | −0.753626 | −0.376813 | − | 0.926289i | \(-0.622980\pi\) | ||||
−0.376813 | + | 0.926289i | \(0.622980\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 980.000 | 0.0546626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5010.00 | 0.278229 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34716.0 | 1.91956 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31220.0 | 1.71876 | 0.859381 | − | 0.511336i | \(-0.170849\pi\) | ||||
0.859381 | + | 0.511336i | \(0.170849\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3432.00 | −0.187314 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3500.00 | −0.190204 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11778.0 | 0.637317 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33542.0 | 1.80722 | 0.903612 | − | 0.428352i | \(-0.140906\pi\) | ||||
0.903612 | + | 0.428352i | \(0.140906\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28152.0 | 1.51035 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1056.00 | 0.0564131 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28562.0 | −1.51293 | −0.756466 | − | 0.654033i | \(-0.773076\pi\) | ||||
−0.756466 | + | 0.654033i | \(0.773076\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6624.00 | −0.349394 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1024.00 | −0.0537856 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1584.00 | −0.0828507 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10920.0 | 0.568779 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1248.00 | 0.0647323 | 0.0323662 | − | 0.999476i | \(-0.489696\pi\) | ||||
0.0323662 | + | 0.999476i | \(0.489696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16950.0 | 0.871891 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14762.0 | 0.756203 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4216.00 | −0.215079 | −0.107540 | − | 0.994201i | \(-0.534297\pi\) | ||||
−0.107540 | + | 0.994201i | \(0.534297\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1400.00 | −0.0708357 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12670.0 | −0.638441 | −0.319220 | − | 0.947680i | \(-0.603421\pi\) | ||||
−0.319220 | + | 0.947680i | \(0.603421\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2736.00 | −0.136746 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25996.0 | −1.29402 | −0.647008 | − | 0.762483i | \(-0.723980\pi\) | ||||
−0.647008 | + | 0.762483i | \(0.723980\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18216.0 | 0.903079 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24368.0 | 1.20320 | 0.601598 | − | 0.798799i | \(-0.294531\pi\) | ||||
0.601598 | + | 0.798799i | \(0.294531\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4772.00 | −0.234675 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5292.00 | −0.259202 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17600.0 | −0.855171 | −0.427585 | − | 0.903975i | \(-0.640636\pi\) | ||||
−0.427585 | + | 0.903975i | \(0.640636\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13956.0 | −0.675412 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 208.000 | 0.0100264 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17182.0 | 0.824954 | 0.412477 | − | 0.910968i | \(-0.364664\pi\) | ||||
0.412477 | + | 0.910968i | \(0.364664\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −576.000 | −0.0275461 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7038.00 | 0.335253 | 0.167626 | − | 0.985851i | \(-0.446390\pi\) | ||||
0.167626 | + | 0.985851i | \(0.446390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1260.00 | 0.0595495 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35640.0 | 1.67782 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18254.0 | 0.855990 | 0.427995 | − | 0.903781i | \(-0.359220\pi\) | ||||
0.427995 | + | 0.903781i | \(0.359220\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18018.0 | −0.841637 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2990.00 | −0.139124 | −0.0695620 | − | 0.997578i | \(-0.522160\pi\) | ||||
−0.0695620 | + | 0.997578i | \(0.522160\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7744.00 | −0.358933 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4600.00 | 0.211569 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10368.0 | 0.475027 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3294.00 | 0.150342 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3132.00 | −0.142402 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10804.0 | 0.489353 | 0.244677 | − | 0.969605i | \(-0.421318\pi\) | ||||
0.244677 | + | 0.969605i | \(0.421318\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15120.0 | 0.682239 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53988.0 | 2.41762 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3156.00 | −0.140795 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11238.0 | −0.499461 | −0.249730 | − | 0.968315i | \(-0.580342\pi\) | ||||
−0.249730 | + | 0.968315i | \(0.580342\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12320.0 | −0.545495 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1314.00 | −0.0579624 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1272.00 | 0.0559003 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16434.0 | 0.716858 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35034.0 | 1.52253 | 0.761267 | − | 0.648439i | \(-0.224578\pi\) | ||||
0.761267 | + | 0.648439i | \(0.224578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9252.00 | −0.400594 | −0.200297 | − | 0.979735i | \(-0.564191\pi\) | ||||
−0.200297 | + | 0.979735i | \(0.564191\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6528.00 | 0.281608 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2152.00 | 0.0924924 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1840.00 | 0.0787925 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18318.0 | 0.778688 | 0.389344 | − | 0.921092i | \(-0.372702\pi\) | ||||
0.389344 | + | 0.921092i | \(0.372702\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30200.0 | −1.27911 | −0.639554 | − | 0.768746i | \(-0.720881\pi\) | ||||
−0.639554 | + | 0.768746i | \(0.720881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4356.00 | −0.183826 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9612.00 | −0.404162 | −0.202081 | − | 0.979369i | \(-0.564770\pi\) | ||||
−0.202081 | + | 0.979369i | \(0.564770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3806.00 | −0.159455 | −0.0797273 | − | 0.996817i | \(-0.525405\pi\) | ||||
−0.0797273 | + | 0.996817i | \(0.525405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13974.0 | 0.583337 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5520.00 | −0.228775 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1728.00 | −0.0713601 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19176.0 | −0.789069 | −0.394535 | − | 0.918881i | \(-0.629094\pi\) | ||||
−0.394535 | + | 0.918881i | \(0.629094\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9505.00 | −0.389725 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13842.0 | 0.565532 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4318.00 | 0.175791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3732.00 | −0.150862 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4896.00 | 0.197218 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38234.0 | 1.53471 | 0.767355 | − | 0.641223i | \(-0.221573\pi\) | ||||
0.767355 | + | 0.641223i | \(0.221573\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1656.00 | −0.0662386 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34818.0 | −1.38782 | −0.693909 | − | 0.720063i | \(-0.744113\pi\) | ||||
−0.693909 | + | 0.720063i | \(0.744113\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15764.0 | −0.626148 | −0.313074 | − | 0.949729i | \(-0.601359\pi\) | ||||
−0.313074 | + | 0.949729i | \(0.601359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1832.00 | 0.0722619 | 0.0361309 | − | 0.999347i | \(-0.488497\pi\) | ||||
0.0361309 | + | 0.999347i | \(0.488497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3116.00 | −0.122482 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.0000 | 0.00152769 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8832.00 | 0.344770 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15048.0 | 0.585398 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10926.0 | 0.423584 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18374.0 | 0.707464 | 0.353732 | − | 0.935347i | \(-0.384912\pi\) | ||||
0.353732 | + | 0.935347i | \(0.384912\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19062.0 | −0.731451 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40490.0 | −1.54840 | −0.774201 | − | 0.632939i | \(-0.781848\pi\) | ||||
−0.774201 | + | 0.632939i | \(0.781848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 548.000 | 0.0208852 | 0.0104426 | − | 0.999945i | \(-0.496676\pi\) | ||||
0.0104426 | + | 0.999945i | \(0.496676\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3240.00 | −0.123064 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1272.00 | −0.0481506 | −0.0240753 | − | 0.999710i | \(-0.507664\pi\) | ||||
−0.0240753 | + | 0.999710i | \(0.507664\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −972.000 | −0.0365468 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16192.0 | 0.606769 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6904.00 | 0.257849 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3168.00 | 0.117922 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7808.00 | −0.289668 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36820.0 | 1.36143 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2324.00 | 0.0853617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15100.0 | 0.552797 | 0.276399 | − | 0.961043i | \(-0.410859\pi\) | ||||
0.276399 | + | 0.961043i | \(0.410859\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7614.00 | −0.277822 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53192.0 | −1.93450 | −0.967250 | − | 0.253825i | \(-0.918311\pi\) | ||||
−0.967250 | + | 0.253825i | \(0.918311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7056.00 | 0.255772 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4908.00 | −0.177326 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53624.0 | 1.92480 | 0.962401 | − | 0.271634i | \(-0.0875639\pi\) | ||||
0.962401 | + | 0.271634i | \(0.0875639\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11220.0 | 0.401424 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −57024.0 | −2.03355 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37026.0 | 1.31612 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1512.00 | −0.0535713 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28966.0 | 1.02297 | 0.511487 | − | 0.859291i | \(-0.329095\pi\) | ||||
0.511487 | + | 0.859291i | \(0.329095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6552.00 | 0.229907 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1680.00 | −0.0587614 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50874.0 | −1.77373 | −0.886863 | − | 0.462033i | \(-0.847120\pi\) | ||||
−0.886863 | + | 0.462033i | \(0.847120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13326.0 | 0.463128 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16566.0 | −0.573896 | −0.286948 | − | 0.957946i | \(-0.592641\pi\) | ||||
−0.286948 | + | 0.957946i | \(0.592641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 800.000 | 0.0276263 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38428.0 | 1.31863 | 0.659315 | − | 0.751867i | \(-0.270846\pi\) | ||||
0.659315 | + | 0.751867i | \(0.270846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6996.00 | −0.239304 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12942.0 | 0.441297 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 746.000 | 0.0253571 | 0.0126785 | − | 0.999920i | \(-0.495964\pi\) | ||||
0.0126785 | + | 0.999920i | \(0.495964\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3856.00 | −0.130657 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4392.00 | −0.148352 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25695.0 | −0.862509 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6372.00 | 0.213224 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −636.000 | −0.0212161 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9432.00 | −0.313664 | −0.156832 | − | 0.987625i | \(-0.550128\pi\) | ||||
−0.156832 | + | 0.987625i | \(0.550128\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19320.0 | 0.640503 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3452.00 | 0.114089 | 0.0570443 | − | 0.998372i | \(-0.481832\pi\) | ||||
0.0570443 | + | 0.998372i | \(0.481832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23958.0 | 0.786944 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18078.0 | −0.591982 | −0.295991 | − | 0.955191i | \(-0.595650\pi\) | ||||
−0.295991 | + | 0.955191i | \(0.595650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1752.00 | 0.0571953 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5814.00 | 0.189222 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 792.000 | 0.0256977 | 0.0128489 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128489 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8124.00 | 0.262794 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 320.000 | 0.0102886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14976.0 | 0.480049 | 0.240024 | − | 0.970767i | \(-0.422845\pi\) | ||||
0.240024 | + | 0.970767i | \(0.422845\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23964.0 | 0.765835 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10960.0 | 0.349201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17114.0 | 0.543637 | 0.271818 | − | 0.962349i | \(-0.412375\pi\) | ||||
0.271818 | + | 0.962349i | \(0.412375\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8262.00 | 0.261660 |
(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 | 2352.4.a.k.1.1 | 1 | ||
4.3 | odd | 2 | 1176.4.a.l.1.1 | 1 | |||
7.6 | odd | 2 | 336.4.a.i.1.1 | 1 | |||
21.20 | even | 2 | 1008.4.a.k.1.1 | 1 | |||
28.27 | even | 2 | 168.4.a.b.1.1 | ✓ | 1 | ||
56.13 | odd | 2 | 1344.4.a.h.1.1 | 1 | |||
56.27 | even | 2 | 1344.4.a.u.1.1 | 1 | |||
84.83 | odd | 2 | 504.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.b.1.1 | ✓ | 1 | 28.27 | even | 2 | ||
336.4.a.i.1.1 | 1 | 7.6 | odd | 2 | |||
504.4.a.d.1.1 | 1 | 84.83 | odd | 2 | |||
1008.4.a.k.1.1 | 1 | 21.20 | even | 2 | |||
1176.4.a.l.1.1 | 1 | 4.3 | odd | 2 | |||
1344.4.a.h.1.1 | 1 | 56.13 | odd | 2 | |||
1344.4.a.u.1.1 | 1 | 56.27 | even | 2 | |||
2352.4.a.k.1.1 | 1 | 1.1 | even | 1 | trivial |