Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,3,Mod(17,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.h (of order \(2\), degree \(1\), not 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: | \(7.84743161358\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.33808912384.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 11x^{6} - 18x^{5} + 47x^{4} - 28x^{3} - 44x^{2} + 48x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(1.15139 + 0.593052i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.17 |
Dual form | 288.3.h.a.17.2 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.67101 | −1.53420 | −0.767101 | − | 0.641526i | \(-0.778302\pi\) | ||||
−0.767101 | + | 0.641526i | \(0.778302\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.21110 | 1.03016 | 0.515079 | − | 0.857143i | \(-0.327763\pi\) | ||||
0.515079 | + | 0.857143i | \(0.327763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.05164 | 0.550149 | 0.275075 | − | 0.961423i | \(-0.411297\pi\) | ||||
0.275075 | + | 0.961423i | \(0.411297\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.29014i | − 0.176164i | −0.996113 | − | 0.0880821i | \(-0.971926\pi\) | ||||
0.996113 | − | 0.0880821i | \(-0.0280738\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 21.8103i | − 1.28296i | −0.767140 | − | 0.641479i | \(-0.778321\pi\) | ||||
0.767140 | − | 0.641479i | \(-0.221679\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 34.8355i | − 1.83345i | −0.399523 | − | 0.916723i | \(-0.630824\pi\) | ||||
0.399523 | − | 0.916723i | \(-0.369176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 21.5117i | − 0.935293i | −0.883915 | − | 0.467647i | \(-0.845102\pi\) | ||||
0.883915 | − | 0.467647i | \(-0.154898\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 33.8444 | 1.35378 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.9098 | −0.376198 | −0.188099 | − | 0.982150i | \(-0.560233\pi\) | ||||
−0.188099 | + | 0.982150i | \(0.560233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 37.6333 | 1.21398 | 0.606989 | − | 0.794710i | \(-0.292377\pi\) | ||||
0.606989 | + | 0.794710i | \(0.292377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −55.3164 | −1.58047 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 34.8355i | − 0.941499i | −0.882267 | − | 0.470750i | \(-0.843983\pi\) | ||||
0.882267 | − | 0.470750i | \(-0.156017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13.3250i | 0.325000i | 0.986709 | + | 0.162500i | \(0.0519558\pi\) | ||||
−0.986709 | + | 0.162500i | \(0.948044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 60.5104i | 1.40722i | 0.710587 | + | 0.703609i | \(0.248430\pi\) | ||||
−0.710587 | + | 0.703609i | \(0.751570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.34701i | 0.0712129i | 0.999366 | + | 0.0356065i | \(0.0113363\pi\) | ||||
−0.999366 | + | 0.0356065i | \(0.988664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.0612245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 35.1163 | 0.662572 | 0.331286 | − | 0.943530i | \(-0.392518\pi\) | ||||
0.331286 | + | 0.943530i | \(0.392518\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −46.4222 | −0.844040 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 37.1615 | 0.629856 | 0.314928 | − | 0.949116i | \(-0.398020\pi\) | ||||
0.314928 | + | 0.949116i | \(0.398020\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 25.6749i | − 0.420901i | −0.977605 | − | 0.210450i | \(-0.932507\pi\) | ||||
0.977605 | − | 0.210450i | \(-0.0674930\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.5677i | 0.270272i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 25.6749i | − 0.383208i | −0.981472 | − | 0.191604i | \(-0.938631\pi\) | ||||
0.981472 | − | 0.191604i | \(-0.0613689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 37.2881i | − 0.525185i | −0.964907 | − | 0.262592i | \(-0.915423\pi\) | ||||
0.964907 | − | 0.262592i | \(-0.0845775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −77.6888 | −1.06423 | −0.532115 | − | 0.846672i | \(-0.678603\pi\) | ||||
−0.532115 | + | 0.846672i | \(0.678603\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 43.6390 | 0.566740 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −31.3221 | −0.396483 | −0.198241 | − | 0.980153i | \(-0.563523\pi\) | ||||
−0.198241 | + | 0.980153i | \(0.563523\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 55.3164 | 0.666463 | 0.333232 | − | 0.942845i | \(-0.391861\pi\) | ||||
0.333232 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 167.307i | 1.96832i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 5.43682i | − 0.0610878i | −0.999533 | − | 0.0305439i | \(-0.990276\pi\) | ||||
0.999533 | − | 0.0305439i | \(-0.00972394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 16.5144i | − 0.181477i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 267.223i | 2.81288i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.8444 | −0.544788 | −0.272394 | − | 0.962186i | \(-0.587815\pi\) | ||||
−0.272394 | + | 0.962186i | \(0.587815\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −90.0069 | −0.891158 | −0.445579 | − | 0.895243i | \(-0.647002\pi\) | ||||
−0.445579 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −119.211 | −1.15739 | −0.578695 | − | 0.815544i | \(-0.696438\pi\) | ||||
−0.578695 | + | 0.815544i | \(0.696438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 24.2066 | 0.226230 | 0.113115 | − | 0.993582i | \(-0.463917\pi\) | ||||
0.113115 | + | 0.993582i | \(0.463917\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 132.472i | 1.21533i | 0.794192 | + | 0.607667i | \(0.207895\pi\) | ||||
−0.794192 | + | 0.607667i | \(0.792105\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 160.560i | 1.42089i | 0.703754 | + | 0.710444i | \(0.251506\pi\) | ||||
−0.703754 | + | 0.710444i | \(0.748494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 165.017i | 1.43493i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 157.276i | − 1.32165i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −84.3776 | −0.697336 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −67.8456 | −0.542765 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 146.478 | 1.15337 | 0.576684 | − | 0.816967i | \(-0.304346\pi\) | ||||
0.576684 | + | 0.816967i | \(0.304346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 184.956 | 1.41188 | 0.705939 | − | 0.708273i | \(-0.250525\pi\) | ||||
0.705939 | + | 0.708273i | \(0.250525\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 251.202i | − 1.88874i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 133.313i | − 0.973089i | −0.873656 | − | 0.486544i | \(-0.838257\pi\) | ||||
0.873656 | − | 0.486544i | \(-0.161743\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 165.017i | − 1.18717i | −0.804771 | − | 0.593586i | \(-0.797712\pi\) | ||||
0.804771 | − | 0.593586i | \(-0.202288\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 13.8591i | − 0.0969166i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 83.6888 | 0.577164 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 228.937 | 1.53649 | 0.768244 | − | 0.640157i | \(-0.221131\pi\) | ||||
0.768244 | + | 0.640157i | \(0.221131\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −162.478 | −1.07601 | −0.538006 | − | 0.842941i | \(-0.680822\pi\) | ||||
−0.538006 | + | 0.842941i | \(0.680822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −288.686 | −1.86249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 113.667i | − 0.723993i | −0.932179 | − | 0.361997i | \(-0.882095\pi\) | ||||
0.932179 | − | 0.361997i | \(-0.117905\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 155.123i | − 0.963499i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 111.860i | 0.686259i | 0.939288 | + | 0.343130i | \(0.111487\pi\) | ||||
−0.939288 | + | 0.343130i | \(0.888513\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 151.541i | − 0.907430i | −0.891147 | − | 0.453715i | \(-0.850098\pi\) | ||||
0.891147 | − | 0.453715i | \(-0.149902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.755 | 0.968966 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 98.0198 | 0.566588 | 0.283294 | − | 0.959033i | \(-0.408573\pi\) | ||||
0.283294 | + | 0.959033i | \(0.408573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 244.056 | 1.39460 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −222.117 | −1.24088 | −0.620440 | − | 0.784254i | \(-0.713046\pi\) | ||||
−0.620440 | + | 0.784254i | \(0.713046\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 118.731i | 0.655971i | 0.944683 | + | 0.327985i | \(0.106370\pi\) | ||||
−0.944683 | + | 0.327985i | \(0.893630\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 267.223i | 1.44445i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 131.988i | − 0.705818i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 151.541i | 0.793408i | 0.917947 | + | 0.396704i | \(0.129846\pi\) | ||||
−0.917947 | + | 0.396704i | \(0.870154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 113.378 | 0.587449 | 0.293724 | − | 0.955890i | \(-0.405105\pi\) | ||||
0.293724 | + | 0.955890i | \(0.405105\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −319.454 | −1.62159 | −0.810796 | − | 0.585329i | \(-0.800965\pi\) | ||||
−0.810796 | + | 0.585329i | \(0.800965\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 41.0109 | 0.206085 | 0.103043 | − | 0.994677i | \(-0.467142\pi\) | ||||
0.103043 | + | 0.994677i | \(0.467142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −78.6713 | −0.387544 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 102.216i | − 0.498616i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 210.812i | − 1.00867i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 95.3459i | − 0.451876i | −0.974142 | − | 0.225938i | \(-0.927455\pi\) | ||||
0.974142 | − | 0.225938i | \(-0.0725447\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 464.176i | − 2.15896i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 271.378 | 1.25059 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −49.9485 | −0.226011 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 268.167 | 1.20254 | 0.601270 | − | 0.799046i | \(-0.294662\pi\) | ||||
0.601270 | + | 0.799046i | \(0.294662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 65.7164 | 0.289499 | 0.144750 | − | 0.989468i | \(-0.453762\pi\) | ||||
0.144750 | + | 0.989468i | \(0.453762\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 155.373i | − 0.678484i | −0.940699 | − | 0.339242i | \(-0.889829\pi\) | ||||
0.940699 | − | 0.339242i | \(-0.110171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 285.451i | − 1.22511i | −0.790427 | − | 0.612556i | \(-0.790141\pi\) | ||||
0.790427 | − | 0.612556i | \(-0.209859\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 25.6749i | − 0.109255i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 421.153i | 1.76214i | 0.472982 | + | 0.881072i | \(0.343178\pi\) | ||||
−0.472982 | + | 0.881072i | \(0.656822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −191.600 | −0.795019 | −0.397510 | − | 0.917598i | \(-0.630126\pi\) | ||||
−0.397510 | + | 0.917598i | \(0.630126\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.0130 | −0.0939307 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −79.7779 | −0.322988 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 483.190 | 1.92506 | 0.962529 | − | 0.271178i | \(-0.0874131\pi\) | ||||
0.962529 | + | 0.271178i | \(0.0874131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 130.181i | − 0.514551i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 21.2132i | − 0.0825416i | −0.999148 | − | 0.0412708i | \(-0.986859\pi\) | ||||
0.999148 | − | 0.0412708i | \(-0.0131406\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 251.202i | − 0.969893i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 246.670i | − 0.937910i | −0.883222 | − | 0.468955i | \(-0.844631\pi\) | ||||
0.883222 | − | 0.468955i | \(-0.155369\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −269.378 | −1.01652 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −241.040 | −0.896060 | −0.448030 | − | 0.894019i | \(-0.647874\pi\) | ||||
−0.448030 | + | 0.894019i | \(0.647874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −61.7443 | −0.227839 | −0.113919 | − | 0.993490i | \(-0.536341\pi\) | ||||
−0.113919 | + | 0.993490i | \(0.536341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 204.814 | 0.744779 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 379.093i | 1.36857i | 0.729215 | + | 0.684284i | \(0.239885\pi\) | ||||
−0.729215 | + | 0.684284i | \(0.760115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 301.227i | 1.07198i | 0.844223 | + | 0.535992i | \(0.180062\pi\) | ||||
−0.844223 | + | 0.535992i | \(0.819938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 399.705i | 1.41238i | 0.708020 | + | 0.706192i | \(0.249588\pi\) | ||||
−0.708020 | + | 0.706192i | \(0.750412\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 96.0880i | 0.334801i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −186.689 | −0.645982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 258.085 | 0.880838 | 0.440419 | − | 0.897792i | \(-0.354830\pi\) | ||||
0.440419 | + | 0.897792i | \(0.354830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −285.066 | −0.966327 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −49.2648 | −0.164765 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 436.347i | 1.44966i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 196.953i | 0.645747i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 286.038i | − 0.931719i | −0.884859 | − | 0.465859i | \(-0.845745\pi\) | ||||
0.884859 | − | 0.465859i | \(-0.154255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 464.647i | 1.49404i | 0.664800 | + | 0.747021i | \(0.268517\pi\) | ||||
−0.664800 | + | 0.747021i | \(0.731483\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 158.000 | 0.504792 | 0.252396 | − | 0.967624i | \(-0.418781\pi\) | ||||
0.252396 | + | 0.967624i | \(0.418781\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.6388 | 0.0903433 | 0.0451717 | − | 0.998979i | \(-0.485617\pi\) | ||||
0.0451717 | + | 0.998979i | \(0.485617\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −66.0219 | −0.206965 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −759.772 | −2.35224 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 77.5083i | − 0.238487i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.1356i | 0.0733605i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 428.993i | 1.29605i | 0.761619 | + | 0.648026i | \(0.224405\pi\) | ||||
−0.761619 | + | 0.648026i | \(0.775595\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 196.953i | 0.587919i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 290.755 | 0.862775 | 0.431388 | − | 0.902167i | \(-0.358024\pi\) | ||||
0.431388 | + | 0.902167i | \(0.358024\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 227.743 | 0.667869 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −331.711 | −0.967087 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 179.756 | 0.518029 | 0.259014 | − | 0.965873i | \(-0.416602\pi\) | ||||
0.259014 | + | 0.965873i | \(0.416602\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 225.527i | 0.646210i | 0.946363 | + | 0.323105i | \(0.104727\pi\) | ||||
−0.946363 | + | 0.323105i | \(0.895273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 133.784i | 0.378992i | 0.981881 | + | 0.189496i | \(0.0606854\pi\) | ||||
−0.981881 | + | 0.189496i | \(0.939315\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 286.038i | 0.805740i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 239.018i | − 0.665787i | −0.942964 | − | 0.332894i | \(-0.891975\pi\) | ||||
0.942964 | − | 0.332894i | \(-0.108025\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −852.511 | −2.36153 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 595.952 | 1.63274 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 188.389 | 0.513320 | 0.256660 | − | 0.966502i | \(-0.417378\pi\) | ||||
0.256660 | + | 0.966502i | \(0.417378\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 253.227 | 0.682554 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 561.108i | − 1.50431i | −0.658985 | − | 0.752156i | \(-0.729014\pi\) | ||||
0.658985 | − | 0.752156i | \(-0.270986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.9848i | 0.0662727i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 328.227i | 0.866034i | 0.901386 | + | 0.433017i | \(0.142551\pi\) | ||||
−0.901386 | + | 0.433017i | \(0.857449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 204.118i | − 0.532945i | −0.963843 | − | 0.266472i | \(-0.914142\pi\) | ||||
0.963843 | − | 0.266472i | \(-0.0858581\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −334.755 | −0.869494 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −60.1746 | −0.154690 | −0.0773452 | − | 0.997004i | \(-0.524644\pi\) | ||||
−0.0773452 | + | 0.997004i | \(0.524644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −469.177 | −1.19994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 240.272 | 0.608285 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 592.203i | − 1.49170i | −0.666116 | − | 0.745848i | \(-0.732045\pi\) | ||||
0.666116 | − | 0.745848i | \(-0.267955\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 653.178i | 1.62887i | 0.580254 | + | 0.814436i | \(0.302953\pi\) | ||||
−0.580254 | + | 0.814436i | \(0.697047\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 86.1854i | − 0.213859i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 210.812i | − 0.517965i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 355.156 | 0.868351 | 0.434176 | − | 0.900828i | \(-0.357040\pi\) | ||||
0.434176 | + | 0.900828i | \(0.357040\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 267.976 | 0.648851 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −424.333 | −1.02249 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 299.085 | 0.713808 | 0.356904 | − | 0.934141i | \(-0.383832\pi\) | ||||
0.356904 | + | 0.934141i | \(0.383832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 769.638i | 1.82812i | 0.405582 | + | 0.914059i | \(0.367069\pi\) | ||||
−0.405582 | + | 0.914059i | \(0.632931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 738.156i | − 1.73684i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 185.145i | − 0.433594i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 411.583i | 0.954948i | 0.878646 | + | 0.477474i | \(0.158448\pi\) | ||||
−0.878646 | + | 0.477474i | \(0.841552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 516.133 | 1.19199 | 0.595996 | − | 0.802987i | \(-0.296757\pi\) | ||||
0.595996 | + | 0.802987i | \(0.296757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −749.372 | −1.71481 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 865.788 | 1.97218 | 0.986091 | − | 0.166205i | \(-0.0531513\pi\) | ||||
0.986091 | + | 0.166205i | \(0.0531513\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −546.261 | −1.23310 | −0.616548 | − | 0.787318i | \(-0.711469\pi\) | ||||
−0.616548 | + | 0.787318i | \(0.711469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 41.7059i | 0.0937211i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 428.978i | − 0.955407i | −0.878521 | − | 0.477704i | \(-0.841469\pi\) | ||||
0.878521 | − | 0.477704i | \(-0.158531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 80.6382i | 0.178799i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 126.682i | 0.278422i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 75.5997 | 0.165426 | 0.0827130 | − | 0.996573i | \(-0.473642\pi\) | ||||
0.0827130 | + | 0.996573i | \(0.473642\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −771.365 | −1.67324 | −0.836622 | − | 0.547781i | \(-0.815473\pi\) | ||||
−0.836622 | + | 0.547781i | \(0.815473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 468.278 | 1.01140 | 0.505699 | − | 0.862710i | \(-0.331235\pi\) | ||||
0.505699 | + | 0.862710i | \(0.331235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −452.842 | −0.969682 | −0.484841 | − | 0.874602i | \(-0.661123\pi\) | ||||
−0.484841 | + | 0.874602i | \(0.661123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 185.145i | − 0.394765i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 366.187i | 0.774180i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 1178.99i | − 2.48208i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 467.523i | − 0.976040i | −0.872832 | − | 0.488020i | \(-0.837719\pi\) | ||||
0.872832 | − | 0.488020i | \(-0.162281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −79.7779 | −0.165859 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 405.370 | 0.835815 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 863.766 | 1.77365 | 0.886824 | − | 0.462108i | \(-0.152907\pi\) | ||||
0.886824 | + | 0.462108i | \(0.152907\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −149.498 | −0.304476 | −0.152238 | − | 0.988344i | \(-0.548648\pi\) | ||||
−0.152238 | + | 0.988344i | \(0.548648\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 237.945i | 0.482647i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 268.889i | − 0.541023i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 205.400i | 0.411622i | 0.978592 | + | 0.205811i | \(0.0659833\pi\) | ||||
−0.978592 | + | 0.205811i | \(0.934017\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 349.923i | 0.695673i | 0.937555 | + | 0.347836i | \(0.113084\pi\) | ||||
−0.937555 | + | 0.347836i | \(0.886916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 690.444 | 1.36722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −529.468 | −1.04021 | −0.520106 | − | 0.854102i | \(-0.674108\pi\) | ||||
−0.520106 | + | 0.854102i | \(0.674108\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −560.222 | −1.09632 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 914.470 | 1.77567 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2549i | 0.0391777i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 367.318i | − 0.705026i | −0.935807 | − | 0.352513i | \(-0.885327\pi\) | ||||
0.935807 | − | 0.352513i | \(-0.114673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 577.495i | − 1.10420i | −0.833779 | − | 0.552099i | \(-0.813827\pi\) | ||||
0.833779 | − | 0.552099i | \(-0.186173\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 820.793i | − 1.55748i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 66.2447 | 0.125226 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.5161 | 0.0572534 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −185.689 | −0.347082 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.1549 | 0.0336826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 326.777i | 0.604023i | 0.953304 | + | 0.302012i | \(0.0976582\pi\) | ||||
−0.953304 | + | 0.302012i | \(0.902342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 1016.19i | − 1.86457i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 273.137i | − 0.499336i | −0.968332 | − | 0.249668i | \(-0.919679\pi\) | ||||
0.968332 | − | 0.249668i | \(-0.0803214\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 380.046i | 0.689739i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −225.867 | −0.408440 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −93.2457 | −0.167407 | −0.0837035 | − | 0.996491i | \(-0.526675\pi\) | ||||
−0.0837035 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 138.577 | 0.247902 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.3615 | 0.0752424 | 0.0376212 | − | 0.999292i | \(-0.488022\pi\) | ||||
0.0376212 | + | 0.999292i | \(0.488022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1231.66i | − 2.17993i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1055.57i | 1.85513i | 0.373663 | + | 0.927564i | \(0.378102\pi\) | ||||
−0.373663 | + | 0.927564i | \(0.621898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.9344i | 0.0384141i | 0.999816 | + | 0.0192070i | \(0.00611417\pi\) | ||||
−0.999816 | + | 0.0192070i | \(0.993886\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 728.052i | − 1.26618i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 161.378 | 0.279684 | 0.139842 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139842 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 398.893 | 0.686562 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 212.511 | 0.364513 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −481.396 | −0.820096 | −0.410048 | − | 0.912064i | \(-0.634488\pi\) | ||||
−0.410048 | + | 0.912064i | \(0.634488\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1310.97i | − 2.22576i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 321.781i | 0.542632i | 0.962490 | + | 0.271316i | \(0.0874588\pi\) | ||||
−0.962490 | + | 0.271316i | \(0.912541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1206.47i | 2.02768i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 35.8419i | − 0.0598362i | −0.999552 | − | 0.0299181i | \(-0.990475\pi\) | ||||
0.999552 | − | 0.0299181i | \(-0.00952464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 147.867 | 0.246035 | 0.123018 | − | 0.992404i | \(-0.460743\pi\) | ||||
0.123018 | + | 0.992404i | \(0.460743\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 647.262 | 1.06985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 636.611 | 1.04878 | 0.524391 | − | 0.851478i | \(-0.324293\pi\) | ||||
0.524391 | + | 0.851478i | \(0.324293\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.66510 | 0.0125452 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 870.887i | 1.42070i | 0.703850 | + | 0.710348i | \(0.251463\pi\) | ||||
−0.703850 | + | 0.710348i | \(0.748537\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1126.69i | − 1.82607i | −0.407876 | − | 0.913037i | \(-0.633730\pi\) | ||||
0.407876 | − | 0.913037i | \(-0.366270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 311.713i | 0.503575i | 0.967783 | + | 0.251787i | \(0.0810183\pi\) | ||||
−0.967783 | + | 0.251787i | \(0.918982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 39.2054i | − 0.0629301i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −325.666 | −0.521066 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −759.772 | −1.20790 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 203.278 | 0.322153 | 0.161076 | − | 0.986942i | \(-0.448503\pi\) | ||||
0.161076 | + | 0.986942i | \(0.448503\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1123.63 | −1.76950 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.87041i | − 0.0107856i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 586.490i | 0.914960i | 0.889220 | + | 0.457480i | \(0.151248\pi\) | ||||
−0.889220 | + | 0.457480i | \(0.848752\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.16054i | 0.0142466i | 0.999975 | + | 0.00712328i | \(0.00226743\pi\) | ||||
−0.999975 | + | 0.00712328i | \(0.997733\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 859.040i | 1.32773i | 0.747853 | + | 0.663864i | \(0.231085\pi\) | ||||
−0.747853 | + | 0.663864i | \(0.768915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 224.888 | 0.346515 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 131.775 | 0.201799 | 0.100899 | − | 0.994897i | \(-0.467828\pi\) | ||||
0.100899 | + | 0.994897i | \(0.467828\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1418.80 | −2.16611 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −305.137 | −0.463030 | −0.231515 | − | 0.972831i | \(-0.574368\pi\) | ||||
−0.231515 | + | 0.972831i | \(0.574368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 623.298i | 0.942962i | 0.881876 | + | 0.471481i | \(0.156280\pi\) | ||||
−0.881876 | + | 0.471481i | \(0.843720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1926.97i | 2.89771i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 234.688i | 0.351856i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 155.376i | − 0.231558i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −263.867 | −0.392076 | −0.196038 | − | 0.980596i | \(-0.562808\pi\) | ||||
−0.196038 | + | 0.980596i | \(0.562808\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 788.411 | 1.16457 | 0.582283 | − | 0.812986i | \(-0.302160\pi\) | ||||
0.582283 | + | 0.812986i | \(0.302160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −381.066 | −0.561217 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 905.773 | 1.32617 | 0.663084 | − | 0.748545i | \(-0.269247\pi\) | ||||
0.663084 | + | 0.748545i | \(0.269247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1022.65i | 1.49291i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 80.4211i | − 0.116721i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.8027i | 0.0662847i | 0.999451 | + | 0.0331423i | \(0.0105515\pi\) | ||||
−0.999451 | + | 0.0331423i | \(0.989449\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1265.85i | 1.82136i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 290.622 | 0.416962 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1019.73 | 1.45468 | 0.727339 | − | 0.686279i | \(-0.240757\pi\) | ||||
0.727339 | + | 0.686279i | \(0.240757\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1213.51 | −1.72619 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −649.049 | −0.918033 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 84.7350i | 0.119513i | 0.998213 | + | 0.0597567i | \(0.0190325\pi\) | ||||
−0.998213 | + | 0.0597567i | \(0.980968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 809.558i | − 1.13543i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 106.313i | 0.148690i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 646.311i | − 0.898903i | −0.893305 | − | 0.449451i | \(-0.851619\pi\) | ||||
0.893305 | − | 0.449451i | \(-0.148381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −859.643 | −1.19229 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −369.234 | −0.509288 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 648.789 | 0.892419 | 0.446210 | − | 0.894928i | \(-0.352774\pi\) | ||||
0.446210 | + | 0.894928i | \(0.352774\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1319.75 | 1.80540 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 696.353i | 0.950004i | 0.879985 | + | 0.475002i | \(0.157553\pi\) | ||||
−0.879985 | + | 0.475002i | \(0.842447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 155.376i | − 0.210822i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 740.833i | − 1.00248i | −0.865308 | − | 0.501240i | \(-0.832877\pi\) | ||||
0.865308 | − | 0.501240i | \(-0.167123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 111.377i | − 0.149901i | −0.997187 | − | 0.0749507i | \(-0.976120\pi\) | ||||
0.997187 | − | 0.0749507i | \(-0.0238800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1756.18 | −2.35728 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 174.556 | 0.233052 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −923.699 | −1.22996 | −0.614979 | − | 0.788543i | \(-0.710836\pi\) | ||||
−0.614979 | + | 0.788543i | \(0.710836\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1246.37 | 1.65082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1233.47i | − 1.62941i | −0.579873 | − | 0.814707i | \(-0.696898\pi\) | ||||
0.579873 | − | 0.814707i | \(-0.303102\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 179.070i | − 0.235309i | −0.993055 | − | 0.117654i | \(-0.962463\pi\) | ||||
0.993055 | − | 0.117654i | \(-0.0375375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 955.266i | 1.25199i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 85.1049i | − 0.110958i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −251.511 | −0.327062 | −0.163531 | − | 0.986538i | \(-0.552288\pi\) | ||||
−0.163531 | + | 0.986538i | \(0.552288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −184.110 | −0.238176 | −0.119088 | − | 0.992884i | \(-0.537997\pi\) | ||||
−0.119088 | + | 0.992884i | \(0.537997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1273.68 | 1.64345 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 464.183 | 0.595870 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 225.654i | − 0.288930i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 871.941i | 1.11075i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1351.36i | − 1.71710i | −0.512731 | − | 0.858550i | \(-0.671366\pi\) | ||||
0.512731 | − | 0.858550i | \(-0.328634\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1157.82i | 1.46374i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −58.7991 | −0.0741476 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1407.20 | −1.76562 | −0.882812 | − | 0.469727i | \(-0.844352\pi\) | ||||
−0.882812 | + | 0.469727i | \(0.844352\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 72.9992 | 0.0913632 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −470.145 | −0.585485 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1189.95i | 1.47820i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 741.991i | − 0.917171i | −0.888650 | − | 0.458585i | \(-0.848356\pi\) | ||||
0.888650 | − | 0.458585i | \(-0.151644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 716.837i | 0.883893i | 0.897041 | + | 0.441947i | \(0.145712\pi\) | ||||
−0.897041 | + | 0.441947i | \(0.854288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 858.082i | − 1.05286i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2107.91 | 2.58006 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 244.447 | 0.297743 | 0.148871 | − | 0.988857i | \(-0.452436\pi\) | ||||
0.148871 | + | 0.988857i | \(0.452436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −331.500 | −0.402795 | −0.201398 | − | 0.979510i | \(-0.564548\pi\) | ||||
−0.201398 | + | 0.979510i | \(0.564548\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 724.314 | 0.875833 | 0.437916 | − | 0.899016i | \(-0.355717\pi\) | ||||
0.437916 | + | 0.899016i | \(0.355717\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 77.5083i | 0.0934961i | 0.998907 | + | 0.0467481i | \(0.0148858\pi\) | ||||
−0.998907 | + | 0.0467481i | \(0.985114\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 65.4309i | − 0.0785485i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1162.47i | 1.39218i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 952.252i | 1.13498i | 0.823379 | + | 0.567492i | \(0.192086\pi\) | ||||
−0.823379 | + | 0.567492i | \(0.807914\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −721.977 | −0.858475 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1256.17 | −1.48659 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −608.456 | −0.718366 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −749.372 | −0.880578 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 282.424i | 0.331095i | 0.986202 | + | 0.165548i | \(0.0529392\pi\) | ||||
−0.986202 | + | 0.165548i | \(0.947061\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 539.665i | 0.629714i | 0.949139 | + | 0.314857i | \(0.101956\pi\) | ||||
−0.949139 | + | 0.314857i | \(0.898044\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.2837i | 0.0620299i | 0.999519 | + | 0.0310150i | \(0.00987395\pi\) | ||||
−0.999519 | + | 0.0310150i | \(0.990126\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 632.435i | 0.732834i | 0.930451 | + | 0.366417i | \(0.119416\pi\) | ||||
−0.930451 | + | 0.366417i | \(0.880584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −751.911 | −0.869261 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −189.550 | −0.218125 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −58.7991 | −0.0675075 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −489.241 | −0.559133 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 346.548i | 0.395152i | 0.980288 | + | 0.197576i | \(0.0633069\pi\) | ||||
−0.980288 | + | 0.197576i | \(0.936693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1394.26i | 1.58258i | 0.611438 | + | 0.791292i | \(0.290591\pi\) | ||||
−0.611438 | + | 0.791292i | \(0.709409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1714.29i | − 1.94144i | −0.240212 | − | 0.970720i | \(-0.577217\pi\) | ||||
0.240212 | − | 0.970720i | \(-0.422783\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1149.19i | − 1.29559i | −0.761815 | − | 0.647795i | \(-0.775691\pi\) | ||||
0.761815 | − | 0.647795i | \(-0.224309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1056.27 | 1.18815 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 116.595 | 0.130565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1703.87 | 1.90376 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −410.570 | −0.456696 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 765.897i | − 0.850052i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 910.785i | − 1.00639i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 507.952i | 0.560035i | 0.959995 | + | 0.280017i | \(0.0903402\pi\) | ||||
−0.959995 | + | 0.280017i | \(0.909660\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1488.13i | − 1.63351i | −0.576984 | − | 0.816756i | \(-0.695770\pi\) | ||||
0.576984 | − | 0.816756i | \(-0.304230\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 334.755 | 0.366654 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1333.74 | 1.45446 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 335.790 | 0.365386 | 0.182693 | − | 0.983170i | \(-0.441519\pi\) | ||||
0.182693 | + | 0.983170i | \(0.441519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −85.3949 | −0.0925188 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 1178.99i | − 1.27458i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1685.87i | − 1.81471i | −0.420363 | − | 0.907356i | \(-0.638097\pi\) | ||||
0.420363 | − | 0.907356i | \(-0.361903\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 104.506i | − 0.112252i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1012.48i | 1.08287i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.7342 | −0.0530781 | −0.0265390 | − | 0.999648i | \(-0.508449\pi\) | ||||
−0.0265390 | + | 0.999648i | \(0.508449\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1689.50 | 1.79543 | 0.897715 | − | 0.440577i | \(-0.145226\pi\) | ||||
0.897715 | + | 0.440577i | \(0.145226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 286.644 | 0.303971 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1036.44 | −1.09445 | −0.547225 | − | 0.836986i | \(-0.684316\pi\) | ||||
−0.547225 | + | 0.836986i | \(0.684316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 177.918i | 0.187479i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 388.814i | − 0.407989i | −0.978972 | − | 0.203995i | \(-0.934608\pi\) | ||||
0.978972 | − | 0.203995i | \(-0.0653925\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1162.47i | − 1.21725i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 961.335i | − 1.00243i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 455.266 | 0.473742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −869.721 | −0.901265 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 201.899 | 0.208789 | 0.104395 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104395 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1500.54 | −1.54535 | −0.772676 | − | 0.634800i | \(-0.781082\pi\) | ||||
−0.772676 | + | 0.634800i | \(0.781082\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1189.95i | − 1.22297i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 866.378i | − 0.886774i | −0.896330 | − | 0.443387i | \(-0.853777\pi\) | ||||
0.896330 | − | 0.443387i | \(-0.146223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 32.9017i | − 0.0336074i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 613.800i | − 0.624415i | −0.950014 | − | 0.312207i | \(-0.898932\pi\) | ||||
0.950014 | − | 0.312207i | \(-0.101068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2450.53 | 2.48785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1301.68 | 1.31616 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1460.50 | −1.47376 | −0.736882 | − | 0.676022i | \(-0.763703\pi\) | ||||
−0.736882 | + | 0.676022i | \(0.763703\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −314.595 | −0.316176 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1378.84i | − 1.38299i | −0.722382 | − | 0.691494i | \(-0.756953\pi\) | ||||
0.722382 | − | 0.691494i | \(-0.243047\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 288.3.h.a.17.1 | 8 | ||
3.2 | odd | 2 | inner | 288.3.h.a.17.7 | 8 | ||
4.3 | odd | 2 | 72.3.h.a.53.4 | yes | 8 | ||
8.3 | odd | 2 | 72.3.h.a.53.6 | yes | 8 | ||
8.5 | even | 2 | inner | 288.3.h.a.17.8 | 8 | ||
12.11 | even | 2 | 72.3.h.a.53.5 | yes | 8 | ||
16.3 | odd | 4 | 2304.3.e.n.1025.8 | 8 | |||
16.5 | even | 4 | 2304.3.e.o.1025.1 | 8 | |||
16.11 | odd | 4 | 2304.3.e.n.1025.1 | 8 | |||
16.13 | even | 4 | 2304.3.e.o.1025.8 | 8 | |||
24.5 | odd | 2 | inner | 288.3.h.a.17.2 | 8 | ||
24.11 | even | 2 | 72.3.h.a.53.3 | ✓ | 8 | ||
48.5 | odd | 4 | 2304.3.e.o.1025.7 | 8 | |||
48.11 | even | 4 | 2304.3.e.n.1025.7 | 8 | |||
48.29 | odd | 4 | 2304.3.e.o.1025.2 | 8 | |||
48.35 | even | 4 | 2304.3.e.n.1025.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.h.a.53.3 | ✓ | 8 | 24.11 | even | 2 | ||
72.3.h.a.53.4 | yes | 8 | 4.3 | odd | 2 | ||
72.3.h.a.53.5 | yes | 8 | 12.11 | even | 2 | ||
72.3.h.a.53.6 | yes | 8 | 8.3 | odd | 2 | ||
288.3.h.a.17.1 | 8 | 1.1 | even | 1 | trivial | ||
288.3.h.a.17.2 | 8 | 24.5 | odd | 2 | inner | ||
288.3.h.a.17.7 | 8 | 3.2 | odd | 2 | inner | ||
288.3.h.a.17.8 | 8 | 8.5 | even | 2 | inner | ||
2304.3.e.n.1025.1 | 8 | 16.11 | odd | 4 | |||
2304.3.e.n.1025.2 | 8 | 48.35 | even | 4 | |||
2304.3.e.n.1025.7 | 8 | 48.11 | even | 4 | |||
2304.3.e.n.1025.8 | 8 | 16.3 | odd | 4 | |||
2304.3.e.o.1025.1 | 8 | 16.5 | even | 4 | |||
2304.3.e.o.1025.2 | 8 | 48.29 | odd | 4 | |||
2304.3.e.o.1025.7 | 8 | 48.5 | odd | 4 | |||
2304.3.e.o.1025.8 | 8 | 16.13 | even | 4 |