Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 386x^{10} + 54793x^{8} + 3447408x^{6} + 90154296x^{4} + 707138208x^{2} + 525876624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.8 | ||
Root | \(9.31944i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.e.673.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 8.40898i | − 0.752122i | −0.926595 | − | 0.376061i | \(-0.877278\pi\) | ||||
0.926595 | − | 0.376061i | \(-0.122722\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.3001i | 1.15945i | 0.814811 | + | 0.579726i | \(0.196840\pi\) | ||||
−0.814811 | + | 0.579726i | \(0.803160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.41890i | 0.200949i | 0.994940 | + | 0.100474i | \(0.0320360\pi\) | ||||
−0.994940 | + | 0.100474i | \(0.967964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.2269 | 0.434238 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 107.603 | 1.53516 | 0.767578 | − | 0.640956i | \(-0.221462\pi\) | ||||
0.767578 | + | 0.640956i | \(0.221462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 124.796i | − 1.50685i | −0.657534 | − | 0.753425i | \(-0.728400\pi\) | ||||
0.657534 | − | 0.753425i | \(-0.271600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −55.2983 | −0.501326 | −0.250663 | − | 0.968074i | \(-0.580649\pi\) | ||||
−0.250663 | + | 0.968074i | \(0.580649\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 54.2890 | 0.434312 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 47.1557i | 0.301951i | 0.988537 | + | 0.150976i | \(0.0482415\pi\) | ||||
−0.988537 | + | 0.150976i | \(0.951758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −318.539 | −1.84553 | −0.922763 | − | 0.385368i | \(-0.874074\pi\) | ||||
−0.922763 | + | 0.385368i | \(0.874074\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −126.900 | −0.669410 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 58.8629i | 0.284275i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 88.8183i | − 0.394639i | −0.980339 | − | 0.197319i | \(-0.936776\pi\) | ||||
0.980339 | − | 0.197319i | \(-0.0632236\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −28.2567 | −0.116018 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 105.791 | 0.402969 | 0.201484 | − | 0.979492i | \(-0.435423\pi\) | ||||
0.201484 | + | 0.979492i | \(0.435423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 202.714i | − 0.718922i | −0.933160 | − | 0.359461i | \(-0.882961\pi\) | ||||
0.933160 | − | 0.359461i | \(-0.117039\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 75.6808i | 0.250707i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −176.014 | −0.546261 | −0.273131 | − | 0.961977i | \(-0.588059\pi\) | ||||
−0.273131 | + | 0.961977i | \(0.588059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 322.810i | 0.886322i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 393.735i | − 1.02045i | −0.860042 | − | 0.510223i | \(-0.829563\pi\) | ||||
0.860042 | − | 0.510223i | \(-0.170437\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 355.701 | 0.872050 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 374.388 | 0.869980 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 898.392i | 1.98238i | 0.132434 | + | 0.991192i | \(0.457721\pi\) | ||||
−0.132434 | + | 0.991192i | \(0.542279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 904.556i | 1.89863i | 0.314324 | + | 0.949316i | \(0.398222\pi\) | ||||
−0.314324 | + | 0.949316i | \(0.601778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 79.2034 | 0.151138 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 67.0601i | 0.122279i | 0.998129 | + | 0.0611395i | \(0.0194735\pi\) | ||||
−0.998129 | + | 0.0611395i | \(0.980527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 165.895i | − 0.289441i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 620.245 | 1.03675 | 0.518377 | − | 0.855152i | \(-0.326536\pi\) | ||||
0.518377 | + | 0.855152i | \(0.326536\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 481.892 | 0.772620 | 0.386310 | − | 0.922369i | \(-0.373750\pi\) | ||||
0.386310 | + | 0.922369i | \(0.373750\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 162.867i | 0.250750i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 296.101i | − 0.438232i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 375.551 | 0.534845 | 0.267422 | − | 0.963579i | \(-0.413828\pi\) | ||||
0.267422 | + | 0.963579i | \(0.413828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 976.706i | − 1.29166i | −0.763483 | − | 0.645828i | \(-0.776512\pi\) | ||||
0.763483 | − | 0.645828i | \(-0.223488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 904.835i | − 1.15462i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −141.467 | −0.174332 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1187.44 | 1.41426 | 0.707128 | − | 0.707086i | \(-0.249991\pi\) | ||||
0.707128 | + | 0.707086i | \(0.249991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 65.9323i | − 0.0759515i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 955.617i | − 1.06551i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1049.41 | −1.13334 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 599.694 | 0.627729 | 0.313864 | − | 0.949468i | \(-0.398376\pi\) | ||||
0.313864 | + | 0.949468i | \(0.398376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 380.701i | − 0.386484i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 727.366i | 0.716591i | 0.933608 | + | 0.358295i | \(0.116642\pi\) | ||||
−0.933608 | + | 0.358295i | \(0.883358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 890.145 | 0.851539 | 0.425770 | − | 0.904832i | \(-0.360003\pi\) | ||||
0.425770 | + | 0.904832i | \(0.360003\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −176.589 | −0.164127 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 729.014i | − 0.658658i | −0.944215 | − | 0.329329i | \(-0.893177\pi\) | ||||
0.944215 | − | 0.329329i | \(-0.106823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1123.45i | − 0.987216i | −0.869685 | − | 0.493608i | \(-0.835678\pi\) | ||||
0.869685 | − | 0.493608i | \(-0.164322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 266.455 | 0.227845 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 397.884 | 0.331237 | 0.165619 | − | 0.986190i | \(-0.447038\pi\) | ||||
0.165619 | + | 0.986190i | \(0.447038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 465.003i | 0.377058i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 84.7701i | − 0.0669829i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −753.223 | −0.580234 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −458.303 | −0.344330 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 317.372i | 0.232654i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1507.64i | − 1.07878i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2718.70 | 1.89957 | 0.949784 | − | 0.312905i | \(-0.101302\pi\) | ||||
0.949784 | + | 0.312905i | \(0.101302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 608.143 | 0.415070 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 305.953i | 0.204055i | 0.994782 | + | 0.102028i | \(0.0325330\pi\) | ||||
−0.994782 | + | 0.102028i | \(0.967467\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 873.571i | 0.569536i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −227.043 | −0.144746 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 422.151 | 0.263261 | 0.131631 | − | 0.991299i | \(-0.457979\pi\) | ||||
0.131631 | + | 0.991299i | \(0.457979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1681.97i | 1.02635i | 0.858284 | + | 0.513176i | \(0.171531\pi\) | ||||
−0.858284 | + | 0.513176i | \(0.828469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 528.042i | − 0.315384i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −398.421 | −0.232990 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 396.531 | 0.227104 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 536.114i | − 0.294766i | −0.989079 | − | 0.147383i | \(-0.952915\pi\) | ||||
0.989079 | − | 0.147383i | \(-0.0470850\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −148.402 | −0.0799789 | −0.0399894 | − | 0.999200i | \(-0.512732\pi\) | ||||
−0.0399894 | + | 0.999200i | \(0.512732\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −968.430 | −0.511718 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2678.59i | 1.38806i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1115.22i | 0.566906i | 0.958986 | + | 0.283453i | \(0.0914800\pi\) | ||||
−0.958986 | + | 0.283453i | \(0.908520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1181.20 | 0.589154 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 387.088 | 0.189483 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2519.03i | 1.21046i | 0.796050 | + | 0.605231i | \(0.206919\pi\) | ||||
−0.796050 | + | 0.605231i | \(0.793081\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1067.10i | 0.503478i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3077.29 | 1.42592 | 0.712958 | − | 0.701206i | \(-0.247355\pi\) | ||||
0.712958 | + | 0.701206i | \(0.247355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2108.28 | 0.959620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1123.16i | 0.502283i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4020.80i | − 1.76703i | −0.468406 | − | 0.883513i | \(-0.655172\pi\) | ||||
0.468406 | − | 0.883513i | \(-0.344828\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −380.023 | −0.164155 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2695.18 | −1.14453 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1912.07i | 0.798408i | 0.916862 | + | 0.399204i | \(0.130713\pi\) | ||||
−0.916862 | + | 0.399204i | \(0.869287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1165.84i | − 0.478765i | −0.970925 | − | 0.239383i | \(-0.923055\pi\) | ||||
0.970925 | − | 0.239383i | \(-0.0769450\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2713.67 | −1.09618 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −746.872 | −0.296817 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4551.64i | 1.77994i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4062.94 | 1.53918 | 0.769592 | − | 0.638536i | \(-0.220460\pi\) | ||||
0.769592 | + | 0.638536i | \(0.220460\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3782.90 | 1.41088 | 0.705438 | − | 0.708772i | \(-0.250750\pi\) | ||||
0.705438 | + | 0.708772i | \(0.250750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 237.610i | 0.0872596i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1109.48i | 0.401254i | 0.979668 | + | 0.200627i | \(0.0642980\pi\) | ||||
−0.979668 | + | 0.200627i | \(0.935702\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5309.30 | 1.89129 | 0.945644 | − | 0.325204i | \(-0.105433\pi\) | ||||
0.945644 | + | 0.325204i | \(0.105433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −201.180 | −0.0705978 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 330.090i | − 0.114127i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 889.592i | − 0.303082i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 497.685 | 0.167109 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5278.89 | 1.74712 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3106.33i | − 1.01350i | −0.862093 | − | 0.506751i | \(-0.830846\pi\) | ||||
0.862093 | − | 0.506751i | \(-0.169154\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1860.73i | 0.598570i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1704.62 | −0.540717 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2229.77 | 0.697543 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1445.68i | 0.446072i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1013.51i | 0.308488i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5998.73 | −1.80137 | −0.900683 | − | 0.434476i | \(-0.856933\pi\) | ||||
−0.900683 | + | 0.434476i | \(0.856933\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −488.601 | −0.144771 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3581.68i | 1.04725i | 0.851950 | + | 0.523623i | \(0.175420\pi\) | ||||
−0.851950 | + | 0.523623i | \(0.824580\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 272.597i | 0.0786626i | 0.999226 | + | 0.0393313i | \(0.0125228\pi\) | ||||
−0.999226 | + | 0.0393313i | \(0.987477\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 888.303 | 0.253013 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3776.00 | 1.06169 | 0.530845 | − | 0.847469i | \(-0.321875\pi\) | ||||
0.530845 | + | 0.847469i | \(0.321875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1480.10i | 0.410855i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1126.65i | 0.308793i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3897.69 | −1.05490 | −0.527449 | − | 0.849587i | \(-0.676852\pi\) | ||||
−0.527449 | + | 0.849587i | \(0.676852\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3216.40 | −0.859695 | −0.429847 | − | 0.902902i | \(-0.641433\pi\) | ||||
−0.429847 | + | 0.902902i | \(0.641433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 412.040i | − 0.107446i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1175.44 | 0.302800 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2930.12 | 0.745738 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2656.75i | − 0.668097i | −0.942556 | − | 0.334049i | \(-0.891585\pi\) | ||||
0.942556 | − | 0.334049i | \(-0.108415\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2339.13i | − 0.581264i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2714.50 | 0.666623 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5167.55 | −1.25425 | −0.627126 | − | 0.778918i | \(-0.715769\pi\) | ||||
−0.627126 | + | 0.778918i | \(0.715769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 621.728i | 0.149159i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 424.401i | − 0.100650i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 64.3415 | 0.0150854 | 0.00754271 | − | 0.999972i | \(-0.497599\pi\) | ||||
0.00754271 | + | 0.999972i | \(0.497599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3310.91 | −0.767500 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3562.33i | 0.816521i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4208.58i | − 0.953908i | −0.878928 | − | 0.476954i | \(-0.841741\pi\) | ||||
0.878928 | − | 0.476954i | \(-0.158259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −767.619 | −0.172065 | −0.0860324 | − | 0.996292i | \(-0.527419\pi\) | ||||
−0.0860324 | + | 0.996292i | \(0.527419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 197.797 | 0.0438506 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2296.43i | 0.503564i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2572.37i | 0.557974i | 0.960295 | + | 0.278987i | \(0.0899987\pi\) | ||||
−0.960295 | + | 0.278987i | \(0.910001\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2866.85 | 0.615175 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6947.17 | 1.47485 | 0.737426 | − | 0.675428i | \(-0.236041\pi\) | ||||
0.737426 | + | 0.675428i | \(0.236041\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1351.64i | 0.283910i | 0.989873 | + | 0.141955i | \(0.0453388\pi\) | ||||
−0.989873 | + | 0.141955i | \(0.954661\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 3148.22i | − 0.654331i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −740.535 | −0.152308 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6665.48 | 1.35670 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1799.08i | 0.362419i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1261.75i | 0.251578i | 0.992057 | + | 0.125789i | \(0.0401463\pi\) | ||||
−0.992057 | + | 0.125789i | \(0.959854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7554.56 | 1.49099 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1142.10 | 0.223137 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 520.849i | − 0.100741i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1419.00i | 0.271727i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2182.10 | −0.413724 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7606.39 | 1.42800 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9167.14i | 1.70422i | 0.523361 | + | 0.852111i | \(0.324678\pi\) | ||||
−0.523361 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2670.43i | 0.491637i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2425.05 | 0.442161 | 0.221081 | − | 0.975256i | \(-0.429042\pi\) | ||||
0.221081 | + | 0.975256i | \(0.429042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3837.73 | −0.693039 | −0.346520 | − | 0.938043i | \(-0.612637\pi\) | ||||
−0.346520 | + | 0.938043i | \(0.612637\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 529.766i | − 0.0947585i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5810.18i | 1.02944i | 0.857359 | + | 0.514719i | \(0.172104\pi\) | ||||
−0.857359 | + | 0.514719i | \(0.827896\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1994.69 | −0.350098 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2187.04 | 0.380277 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 13428.5i | − 2.31325i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 511.343i | 0.0872745i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3370.34 | 0.569969 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1232.10 | 0.206467 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5253.39i | 0.872364i | 0.899858 | + | 0.436182i | \(0.143670\pi\) | ||||
−0.899858 | + | 0.436182i | \(0.856330\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 799.365i | 0.131546i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 563.907 | 0.0919688 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5689.30 | −0.919632 | −0.459816 | − | 0.888014i | \(-0.652085\pi\) | ||||
−0.459816 | + | 0.888014i | \(0.652085\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1193.65i | 0.191240i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 13474.2i | − 2.13980i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1395.01 | −0.217695 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 9445.38i | − 1.46125i | −0.682777 | − | 0.730626i | \(-0.739228\pi\) | ||||
0.682777 | − | 0.730626i | \(-0.260772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 9480.35i | − 1.45407i | −0.686599 | − | 0.727037i | \(-0.740897\pi\) | ||||
0.686599 | − | 0.727037i | \(-0.259103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 254.310 | 0.0386726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6172.70 | 0.930708 | 0.465354 | − | 0.885125i | \(-0.345927\pi\) | ||||
0.465354 | + | 0.885125i | \(0.345927\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5215.63i | − 0.779766i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2259.67i | − 0.334998i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7209.01 | −1.05982 | −0.529912 | − | 0.848052i | \(-0.677775\pi\) | ||||
−0.529912 | + | 0.848052i | \(0.677775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8715.02 | −1.27060 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 1374.91i | − 0.198799i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4052.22i | − 0.581104i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3196.42 | −0.454638 | −0.227319 | − | 0.973820i | \(-0.572996\pi\) | ||||
−0.227319 | + | 0.973820i | \(0.572996\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −952.116 | −0.134323 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2756.14i | 0.385692i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11311.7i | 1.57023i | 0.619347 | + | 0.785117i | \(0.287397\pi\) | ||||
−0.619347 | + | 0.785117i | \(0.712603\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4522.91 | 0.622833 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −444.155 | −0.0606767 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1601.01i | 0.216987i | 0.994097 | + | 0.108494i | \(0.0346027\pi\) | ||||
−0.994097 | + | 0.108494i | \(0.965397\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8156.09i | 1.09672i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5392.30 | 0.719408 | 0.359704 | − | 0.933066i | \(-0.382878\pi\) | ||||
0.359704 | + | 0.933066i | \(0.382878\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2489.91 | −0.329604 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1824.43i | 0.239641i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 3958.04i | − 0.515888i | −0.966160 | − | 0.257944i | \(-0.916955\pi\) | ||||
0.966160 | − | 0.257944i | \(-0.0830450\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5950.28 | −0.769613 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −917.858 | −0.117811 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 3158.00i | − 0.402269i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 924.331i | − 0.116854i | −0.998292 | − | 0.0584268i | \(-0.981392\pi\) | ||||
0.998292 | − | 0.0584268i | \(-0.0186084\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2620.71 | −0.328822 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5168.91 | −0.643698 | −0.321849 | − | 0.946791i | \(-0.604304\pi\) | ||||
−0.321849 | + | 0.946791i | \(0.604304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3000.29i | − 0.370856i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 681.128i | − 0.0835691i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3757.03 | 0.457565 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10204.9 | −1.23374 | −0.616868 | − | 0.787067i | \(-0.711599\pi\) | ||||
−0.616868 | + | 0.787067i | \(0.711599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1266.45i | 0.151994i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 6288.74i | − 0.749271i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8213.10 | −0.971483 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5045.91 | −0.592564 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 1698.81i | − 0.198072i | −0.995084 | − | 0.0990361i | \(-0.968424\pi\) | ||||
0.995084 | − | 0.0990361i | \(-0.0315759\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 978.378i | − 0.113262i | −0.998395 | − | 0.0566309i | \(-0.981964\pi\) | ||||
0.998395 | − | 0.0566309i | \(-0.0180358\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1584.13 | 0.182087 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5841.68 | 0.666737 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6331.89i | − 0.717615i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1195.26i | − 0.134517i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5647.32 | −0.631141 | −0.315571 | − | 0.948902i | \(-0.602196\pi\) | ||||
−0.315571 | + | 0.948902i | \(0.602196\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4698.41 | 0.521458 | 0.260729 | − | 0.965412i | \(-0.416037\pi\) | ||||
0.260729 | + | 0.965412i | \(0.416037\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1189.59i | 0.131119i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6901.00i | 0.755423i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11114.9 | 1.20840 | 0.604199 | − | 0.796833i | \(-0.293493\pi\) | ||||
0.604199 | + | 0.796833i | \(0.293493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8622.15i | − 0.924720i | −0.886692 | − | 0.462360i | \(-0.847003\pi\) | ||||
0.886692 | − | 0.462360i | \(-0.152997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 9985.19i | − 1.06369i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1608.34 | 0.170183 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14647.9 | 1.53959 | 0.769797 | − | 0.638288i | \(-0.220357\pi\) | ||||
0.769797 | + | 0.638288i | \(0.220357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4474.96i | 0.467223i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 445.207i | − 0.0461758i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −554.424 | −0.0571248 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1697.97 | 0.173802 | 0.0869011 | − | 0.996217i | \(-0.472304\pi\) | ||||
0.0869011 | + | 0.996217i | \(0.472304\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2905.29i | − 0.295441i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1444.97i | 0.145985i | 0.997333 | + | 0.0729923i | \(0.0232549\pi\) | ||||
−0.997333 | + | 0.0729923i | \(0.976745\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5328.42 | 0.534844 | 0.267422 | − | 0.963580i | \(-0.413828\pi\) | ||||
0.267422 | + | 0.963580i | \(0.413828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8035.77 | −0.801397 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3489.64i | − 0.345785i | −0.984941 | − | 0.172892i | \(-0.944689\pi\) | ||||
0.984941 | − | 0.172892i | \(-0.0553113\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 469.421i | − 0.0462171i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3345.66 | −0.327303 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8574.85 | 0.833556 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 6775.05i | − 0.654443i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3543.61i | 0.340149i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7492.93 | −0.714740 | −0.357370 | − | 0.933963i | \(-0.616327\pi\) | ||||
−0.357370 | + | 0.933963i | \(0.616327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 836.571 | 0.0793022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1161.26i | 0.109398i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 5042.81i | − 0.472129i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4445.02 | −0.413600 | −0.206800 | − | 0.978383i | \(-0.566305\pi\) | ||||
−0.206800 | + | 0.978383i | \(0.566305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7557.08 | −0.698861 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 7213.35i | − 0.663001i | −0.943455 | − | 0.331501i | \(-0.892445\pi\) | ||||
0.943455 | − | 0.331501i | \(-0.107555\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5074.11i | 0.463542i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3201.31 | −0.290683 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4341.71 | −0.391856 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13727.6i | 1.23153i | 0.787931 | + | 0.615763i | \(0.211152\pi\) | ||||
−0.787931 | + | 0.615763i | \(0.788848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9231.88i | 0.823253i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8699.38 | −0.771146 | −0.385573 | − | 0.922677i | \(-0.625996\pi\) | ||||
−0.385573 | + | 0.922677i | \(0.625996\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6116.41 | 0.538964 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6324.85i | 0.554037i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12917.9i | 1.12491i | 0.826829 | + | 0.562453i | \(0.190142\pi\) | ||||
−0.826829 | + | 0.562453i | \(0.809858\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3373.25 | −0.292023 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3369.49 | −0.289993 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 7485.21i | − 0.640462i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7445.42i | − 0.633364i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12062.4 | 1.02019 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9852.45 | 0.828490 | 0.414245 | − | 0.910165i | \(-0.364046\pi\) | ||||
0.414245 | + | 0.910165i | \(0.364046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 14109.6i | − 1.17967i | −0.807523 | − | 0.589835i | \(-0.799193\pi\) | ||||
0.807523 | − | 0.589835i | \(-0.200807\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1140.07i | − 0.0947747i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34275.9 | −2.83317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9109.10 | −0.748672 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 8085.53i | − 0.660795i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 996.432i | 0.0809761i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6130.27 | −0.495392 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5736.22 | −0.460961 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2072.71i | 0.165636i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1338.43i | 0.106366i | 0.998585 | + | 0.0531828i | \(0.0169366\pi\) | ||||
−0.998585 | + | 0.0531828i | \(0.983063\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3497.53 | 0.276415 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9447.03 | −0.742507 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 12462.6i | − 0.974151i | −0.873360 | − | 0.487076i | \(-0.838064\pi\) | ||||
0.873360 | − | 0.487076i | \(-0.161936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8141.00i | − 0.632877i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5884.84 | 0.454995 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2628.85 | −0.202152 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 2240.61i | − 0.171367i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17426.2i | 1.32562i | 0.748787 | + | 0.662811i | \(0.230637\pi\) | ||||
−0.748787 | + | 0.662811i | \(0.769363\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1909.35 | 0.144466 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13654.9 | −1.02765 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 20585.9i | − 1.54102i | −0.637429 | − | 0.770509i | \(-0.720002\pi\) | ||||
0.637429 | − | 0.770509i | \(-0.279998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 3345.80i | − 0.249131i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4334.40 | −0.319345 | −0.159672 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159672 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14014.8i | 1.02715i | 0.858046 | + | 0.513573i | \(0.171679\pi\) | ||||
−0.858046 | + | 0.513573i | \(0.828321\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12188.8i | 0.888648i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3002.09 | −0.217732 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 782.119 | 0.0564299 | 0.0282150 | − | 0.999602i | \(-0.491018\pi\) | ||||
0.0282150 | + | 0.999602i | \(0.491018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11348.7i | 0.814569i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6836.94i | 0.488200i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16655.0 | 1.18316 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −712.830 | −0.0503793 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 11299.3i | − 0.794500i | −0.917710 | − | 0.397250i | \(-0.869965\pi\) | ||||
0.917710 | − | 0.397250i | \(-0.130035\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39752.4i | 2.78093i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3328.44 | −0.231664 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16620.0 | −1.15093 | −0.575464 | − | 0.817827i | \(-0.695179\pi\) | ||||
−0.575464 | + | 0.817827i | \(0.695179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6333.84i | 0.436407i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15927.9i | 1.09194i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2792.53 | −0.190484 | −0.0952419 | − | 0.995454i | \(-0.530362\pi\) | ||||
−0.0952419 | + | 0.995454i | \(0.530362\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25010.4 | −1.69750 | −0.848748 | − | 0.528798i | \(-0.822643\pi\) | ||||
−0.848748 | + | 0.528798i | \(0.822643\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 603.541i | − 0.0407597i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3853.86i | 0.258978i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13307.9 | −0.889868 | −0.444934 | − | 0.895563i | \(-0.646773\pi\) | ||||
−0.444934 | + | 0.895563i | \(0.646773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 990.269 | 0.0658912 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1657.86i | − 0.109770i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28351.9i | 1.86806i | 0.357192 | + | 0.934031i | \(0.383734\pi\) | ||||
−0.357192 | + | 0.934031i | \(0.616266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2668.78 | 0.174984 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23107.5 | −1.50774 | −0.753868 | − | 0.657026i | \(-0.771814\pi\) | ||||
−0.753868 | + | 0.657026i | \(0.771814\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 792.761i | − 0.0514762i | −0.999669 | − | 0.0257381i | \(-0.991806\pi\) | ||||
0.999669 | − | 0.0257381i | \(-0.00819359\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1493.05i | 0.0964802i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8312.10 | −0.534538 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5891.58 | −0.377061 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15836.7i | 1.00870i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 9557.15i | − 0.605832i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24342.8 | 1.53577 | 0.767884 | − | 0.640589i | \(-0.221310\pi\) | ||||
0.767884 | + | 0.640589i | \(0.221310\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9319.00 | 0.585145 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 22861.5i | − 1.42871i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 461.526i | 0.0287070i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5582.20 | −0.345585 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8587.39 | 0.529144 | 0.264572 | − | 0.964366i | \(-0.414769\pi\) | ||||
0.264572 | + | 0.964366i | \(0.414769\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21410.4i | 1.31313i | 0.754269 | + | 0.656565i | \(0.227991\pi\) | ||||
−0.754269 | + | 0.656565i | \(0.772009\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 5113.86i | − 0.312183i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17879.1 | 1.08640 | 0.543200 | − | 0.839603i | \(-0.317212\pi\) | ||||
0.543200 | + | 0.839603i | \(0.317212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −38002.1 | −2.29848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6689.32i | 0.402727i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 27765.7i | − 1.66394i | −0.554819 | − | 0.831971i | \(-0.687212\pi\) | ||||
0.554819 | − | 0.831971i | \(-0.312788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2572.75 | 0.153474 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4337.03 | −0.257540 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 13334.8i | − 0.788240i | −0.919059 | − | 0.394120i | \(-0.871049\pi\) | ||||
0.919059 | − | 0.394120i | \(-0.128951\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21256.8i | 1.25082i | 0.780295 | + | 0.625412i | \(0.215069\pi\) | ||||
−0.780295 | + | 0.625412i | \(0.784931\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3040.52 | −0.178105 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7345.85 | 0.428360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2607.63i | − 0.151376i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 17996.2i | − 1.04002i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38262.8 | −2.20137 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8963.29 | 0.513387 | 0.256693 | − | 0.966493i | \(-0.417367\pi\) | ||||
0.256693 | + | 0.966493i | \(0.417367\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1465.80i | − 0.0835834i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 25166.0i | − 1.42867i | −0.699805 | − | 0.714334i | \(-0.746730\pi\) | ||||
0.699805 | − | 0.714334i | \(-0.253270\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4197.86 | −0.237259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10745.1 | −0.604627 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 791.146i | 0.0443226i | 0.999754 | + | 0.0221613i | \(0.00705475\pi\) | ||||
−0.999754 | + | 0.0221613i | \(0.992945\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 3549.86i | − 0.198005i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −817.792 | −0.0454159 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3708.55 | 0.205057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2389.97i | 0.131576i | 0.997834 | + | 0.0657878i | \(0.0209561\pi\) | ||||
−0.997834 | + | 0.0657878i | \(0.979044\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2664.91i | 0.146077i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14143.7 | 0.771941 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11383.4 | 0.618620 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11328.0i | 0.612967i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6711.69i | 0.361622i | 0.983518 | + | 0.180811i | \(0.0578722\pi\) | ||||
−0.983518 | + | 0.180811i | \(0.942128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11084.2 | −0.594662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4440.29 | −0.237207 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 5091.56i | − 0.270846i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 15903.4i | − 0.842405i | −0.906967 | − | 0.421202i | \(-0.861608\pi\) | ||||
0.906967 | − | 0.421202i | \(-0.138392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3379.96 | −0.178282 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17614.7 | 0.925210 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3350.31i | 0.175237i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 11693.1i | − 0.609046i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35162.7 | −1.82385 | −0.911924 | − | 0.410360i | \(-0.865403\pi\) | ||||
−0.911924 | + | 0.410360i | \(0.865403\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6231.01 | −0.321852 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 9649.19i | − 0.496345i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2560.04i | 0.131141i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8519.06 | 0.434600 | 0.217300 | − | 0.976105i | \(-0.430275\pi\) | ||||
0.217300 | + | 0.976105i | \(0.430275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 21812.7i | − 1.10366i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16085.0i | − 0.810524i | −0.914201 | − | 0.405262i | \(-0.867180\pi\) | ||||
0.914201 | − | 0.405262i | \(-0.132820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1236.12 | 0.0620340 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2836.65 | −0.141777 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 24279.1i | − 1.20855i | −0.796775 | − | 0.604276i | \(-0.793462\pi\) | ||||
0.796775 | − | 0.604276i | \(-0.206538\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3526.32i | 0.174821i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16834.0 | 0.831195 | 0.415598 | − | 0.909549i | \(-0.363572\pi\) | ||||
0.415598 | + | 0.909549i | \(0.363572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4508.18 | −0.221700 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8790.35i | 0.430552i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5103.10i | 0.248949i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30640.0 | 1.48877 | 0.744386 | − | 0.667749i | \(-0.232742\pi\) | ||||
0.744386 | + | 0.667749i | \(0.232742\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7970.24 | 0.385726 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1247.91i | 0.0601539i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25016.9i | 1.20113i | 0.799575 | + | 0.600566i | \(0.205058\pi\) | ||||
−0.799575 | + | 0.600566i | \(0.794942\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7017.38 | 0.335593 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31113.8 | 1.48210 | 0.741048 | − | 0.671452i | \(-0.234329\pi\) | ||||
0.741048 | + | 0.671452i | \(0.234329\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7864.12i | 0.373133i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8143.51i | 0.384875i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8461.86 | −0.398357 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25683.5 | −1.20438 | −0.602192 | − | 0.798351i | \(-0.705706\pi\) | ||||
−0.602192 | + | 0.798351i | \(0.705706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 15502.6i | − 0.724143i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 10195.1i | − 0.474375i | −0.971464 | − | 0.237187i | \(-0.923774\pi\) | ||||
0.971464 | − | 0.237187i | \(-0.0762255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17293.2 | −0.801534 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1865.18 | −0.0861173 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 13202.2i | − 0.607214i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26236.5i | 1.20207i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1273.20 | 0.0581106 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9377.87 | 0.426383 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34242.3i | − 1.55096i | −0.631372 | − | 0.775480i | \(-0.717508\pi\) | ||||
0.631372 | − | 0.775480i | \(-0.282492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 193.024i | 0.00870957i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2785.19 | −0.125196 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8519.92 | −0.381528 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 9932.72i | − 0.443116i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 20801.8i | − 0.924512i | −0.886746 | − | 0.462256i | \(-0.847040\pi\) | ||||
0.886746 | − | 0.462256i | \(-0.152960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18939.7 | −0.838596 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10687.0 | −0.471418 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20384.1i | 0.895815i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3255.02i | − 0.142515i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12625.7 | 0.550739 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15209.7 | −0.660993 | −0.330496 | − | 0.943807i | \(-0.607216\pi\) | ||||
−0.330496 | + | 0.943807i | \(0.607216\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 25337.6i | − 1.09707i | −0.836128 | − | 0.548534i | \(-0.815186\pi\) | ||||
0.836128 | − | 0.548534i | \(-0.184814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2302.86i | − 0.0993416i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21182.4 | 0.910416 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25297.9 | −1.08331 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 593.391i | 0.0253172i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 17766.3i | − 0.755237i | −0.925961 | − | 0.377618i | \(-0.876743\pi\) | ||||
0.925961 | − | 0.377618i | \(-0.123257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6605.85 | 0.279788 | 0.139894 | − | 0.990167i | \(-0.455324\pi\) | ||||
0.139894 | + | 0.990167i | \(0.455324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6889.30 | −0.290733 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11302.2i | 0.475229i | 0.971360 | + | 0.237614i | \(0.0763655\pi\) | ||||
−0.971360 | + | 0.237614i | \(0.923635\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30888.8i | 1.29410i | 0.762446 | + | 0.647051i | \(0.223998\pi\) | ||||
−0.762446 | + | 0.647051i | \(0.776002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7717.12 | −0.322147 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5272.56 | 0.219308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 25876.9i | − 1.07246i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8600.55i | 0.355172i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11316.7 | 0.465671 | 0.232835 | − | 0.972516i | \(-0.425200\pi\) | ||||
0.232835 | + | 0.972516i | \(0.425200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22165.3 | 0.908825 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20841.5i | 0.851506i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 17728.5i | − 0.721751i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3208.12 | 0.130144 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4054.91 | −0.163915 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4911.50i | 0.197843i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 13992.3i | − 0.561650i | −0.959759 | − | 0.280825i | \(-0.909392\pi\) | ||||
0.959759 | − | 0.280825i | \(-0.0906081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9444.66 | 0.377778 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30193.9 | 1.20350 | 0.601752 | − | 0.798683i | \(-0.294470\pi\) | ||||
0.601752 | + | 0.798683i | \(0.294470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19915.5i | 0.791047i | 0.918456 | + | 0.395523i | \(0.129437\pi\) | ||||
−0.918456 | + | 0.395523i | \(0.870563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 2221.60i | − 0.0879350i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34621.8 | −1.36563 | −0.682815 | − | 0.730591i | \(-0.739244\pi\) | ||||
−0.682815 | + | 0.730591i | \(0.739244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33810.8 | −1.32902 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19996.4i | 0.783292i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15885.8i | 0.620127i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −631.632 | −0.0245718 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5397.24 | −0.209243 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10553.5i | 0.407740i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 16375.7i | − 0.630521i | −0.949005 | − | 0.315260i | \(-0.897908\pi\) | ||||
0.949005 | − | 0.315260i | \(-0.102092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3785.26 | −0.145249 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25301.9 | −0.967586 | −0.483793 | − | 0.875183i | \(-0.660741\pi\) | ||||
−0.483793 | + | 0.875183i | \(0.660741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20642.4i | 0.786718i | 0.919385 | + | 0.393359i | \(0.128687\pi\) | ||||
−0.919385 | + | 0.393359i | \(0.871313\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22663.7i | 0.860826i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13123.7 | −0.496788 | −0.248394 | − | 0.968659i | \(-0.579903\pi\) | ||||
−0.248394 | + | 0.968659i | \(0.579903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19030.9 | −0.717969 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3426.31i | 0.128828i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21965.8i | 0.823133i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16078.6 | 0.600500 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1562.55 | 0.0581627 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 15020.9i | − 0.557259i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 42367.2i | − 1.56654i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4257.00 | −0.156882 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9803.56 | −0.360090 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13064.4i | 0.478277i | 0.970985 | + | 0.239138i | \(0.0768650\pi\) | ||||
−0.970985 | + | 0.239138i | \(0.923135\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 6546.30i | − 0.238864i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52055.4 | 1.89316 | 0.946582 | − | 0.322462i | \(-0.104510\pi\) | ||||
0.946582 | + | 0.322462i | \(0.104510\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41314.8 | 1.49761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22819.2i | 0.824458i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2141.67i | − 0.0771256i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24860.3 | −0.892347 | −0.446173 | − | 0.894947i | \(-0.647214\pi\) | ||||
−0.446173 | + | 0.894947i | \(0.647214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27501.4 | −0.983933 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5842.03i | 0.208334i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4821.86i | − 0.171396i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8011.30 | −0.283846 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32081.0 | 1.13298 | 0.566492 | − | 0.824067i | \(-0.308300\pi\) | ||||
0.566492 | + | 0.824067i | \(0.308300\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6115.00i | − 0.215264i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7275.16i | 0.255282i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38274.6 | 1.33873 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50156.5 | 1.74871 | 0.874355 | − | 0.485287i | \(-0.161285\pi\) | ||||
0.874355 | + | 0.485287i | \(0.161285\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 11513.2i | − 0.400126i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 755.090i | − 0.0261586i | −0.999914 | − | 0.0130793i | \(-0.995837\pi\) | ||||
0.999914 | − | 0.0130793i | \(-0.00416339\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5850.05 | −0.202019 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1589.30 | 0.0547088 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 49944.3i | − 1.71380i | −0.515480 | − | 0.856902i | \(-0.672386\pi\) | ||||
0.515480 | − | 0.856902i | \(-0.327614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4538.90i | 0.155257i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17430.5 | −0.594347 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14174.2 | −0.481791 | −0.240895 | − | 0.970551i | \(-0.577441\pi\) | ||||
−0.240895 | + | 0.970551i | \(0.577441\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 34165.2i | − 1.15765i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5984.08i | − 0.202129i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2955.06 | −0.0995034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71676.1 | 2.40597 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6561.13i | 0.219553i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 31810.3i | − 1.06115i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39816.7 | 1.32411 | 0.662057 | − | 0.749453i | \(-0.269683\pi\) | ||||
0.662057 | + | 0.749453i | \(0.269683\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 40285.4 | 1.33555 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10300.1i | 0.340416i | 0.985408 | + | 0.170208i | \(0.0544440\pi\) | ||||
−0.985408 | + | 0.170208i | \(0.945556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 11773.8i | − 0.387924i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1534.03 | −0.0503879 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39564.3 | 1.29557 | 0.647786 | − | 0.761822i | \(-0.275695\pi\) | ||||
0.647786 | + | 0.761822i | \(0.275695\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50229.0i | 1.63976i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10111.0i | 0.329072i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4441.00 | −0.144095 | −0.0720477 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720477 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9329.59 | 0.301792 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3696.29i | 0.119204i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11209.8i | 0.360414i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31663.9 | −1.01497 | −0.507485 | − | 0.861661i | \(-0.669425\pi\) | ||||
−0.507485 | + | 0.861661i | \(0.669425\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15760.2 | −0.503660 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 44645.8i | − 1.42248i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18057.4i | 0.573605i | 0.957990 | + | 0.286803i | \(0.0925924\pi\) | ||||
−0.957990 | + | 0.286803i | \(0.907408\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2398.09 | −0.0759483 |
(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 | 1344.4.c.e.673.8 | yes | 12 | |
4.3 | odd | 2 | 1344.4.c.h.673.2 | yes | 12 | ||
8.3 | odd | 2 | 1344.4.c.h.673.11 | yes | 12 | ||
8.5 | even | 2 | inner | 1344.4.c.e.673.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.e.673.5 | ✓ | 12 | 8.5 | even | 2 | inner | |
1344.4.c.e.673.8 | yes | 12 | 1.1 | even | 1 | trivial | |
1344.4.c.h.673.2 | yes | 12 | 4.3 | odd | 2 | ||
1344.4.c.h.673.11 | yes | 12 | 8.3 | odd | 2 |