Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
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([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.b (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: | \(79.2985670477\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.1 | ||
Root | \(-2.44949i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.c.895.2 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.44949i | − | 0.219089i | −0.993982 | − | 0.109545i | \(-0.965061\pi\) | ||
0.993982 | − | 0.109545i | \(-0.0349392\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.0000 | − | 7.34847i | −0.917914 | − | 0.396780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 56.3383i | − | 1.54424i | −0.635478 | − | 0.772119i | \(-0.719197\pi\) | ||
0.635478 | − | 0.772119i | \(-0.280803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 73.4847i | 1.56777i | 0.620907 | + | 0.783884i | \(0.286764\pi\) | ||||
−0.620907 | + | 0.783884i | \(0.713236\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7.34847i | − | 0.126491i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 51.4393i | 0.733874i | 0.930246 | + | 0.366937i | \(0.119594\pi\) | ||||
−0.930246 | + | 0.366937i | \(0.880406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.0000 | 0.120745 | 0.0603726 | − | 0.998176i | \(-0.480771\pi\) | ||||
0.0603726 | + | 0.998176i | \(0.480771\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −51.0000 | − | 22.0454i | −0.529958 | − | 0.229081i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 115.126i | − | 1.04371i | −0.853033 | − | 0.521857i | \(-0.825239\pi\) | ||
0.853033 | − | 0.521857i | \(-0.174761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 119.000 | 0.952000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −126.000 | −0.806814 | −0.403407 | − | 0.915021i | \(-0.632174\pi\) | ||||
−0.403407 | + | 0.915021i | \(0.632174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −0.0463498 | −0.0231749 | − | 0.999731i | \(-0.507377\pi\) | ||||
−0.0231749 | + | 0.999731i | \(0.507377\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 169.015i | − | 0.891567i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −18.0000 | + | 41.6413i | −0.0869302 | + | 0.201105i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −244.000 | −1.08414 | −0.542072 | − | 0.840332i | \(-0.682360\pi\) | ||||
−0.542072 | + | 0.840332i | \(0.682360\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 220.454i | 0.905151i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 369.873i | − | 1.40889i | −0.709759 | − | 0.704445i | \(-0.751196\pi\) | ||
0.709759 | − | 0.704445i | \(-0.248804\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 161.666i | − | 0.573346i | −0.958028 | − | 0.286673i | \(-0.907451\pi\) | ||
0.958028 | − | 0.286673i | \(-0.0925493\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 22.0454i | − | 0.0730297i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 180.000 | 0.558632 | 0.279316 | − | 0.960199i | \(-0.409892\pi\) | ||||
0.279316 | + | 0.960199i | \(0.409892\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 235.000 | + | 249.848i | 0.685131 | + | 0.728420i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 154.318i | 0.423702i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −594.000 | −1.53947 | −0.769737 | − | 0.638361i | \(-0.779613\pi\) | ||||
−0.769737 | + | 0.638361i | \(0.779613\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −138.000 | −0.338326 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.0000 | 0.0697122 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −540.000 | −1.19156 | −0.595780 | − | 0.803148i | \(-0.703157\pi\) | ||||
−0.595780 | + | 0.803148i | \(0.703157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 352.727i | 0.740361i | 0.928960 | + | 0.370180i | \(0.120704\pi\) | ||||
−0.928960 | + | 0.370180i | \(0.879296\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −153.000 | − | 66.1362i | −0.305971 | − | 0.132260i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 180.000 | 0.343481 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1058.18i | 1.92951i | 0.263149 | + | 0.964755i | \(0.415239\pi\) | ||||
−0.263149 | + | 0.964755i | \(0.584761\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 345.378i | − | 0.602589i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 178.813i | − | 0.298890i | −0.988770 | − | 0.149445i | \(-0.952251\pi\) | ||
0.988770 | − | 0.149445i | \(-0.0477486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 661.362i | − | 1.06036i | −0.847884 | − | 0.530182i | \(-0.822124\pi\) | ||
0.847884 | − | 0.530182i | \(-0.177876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 357.000 | 0.549637 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −414.000 | + | 957.750i | −0.612723 | + | 1.41748i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1028.79i | 1.46516i | 0.680682 | + | 0.732579i | \(0.261683\pi\) | ||||
−0.680682 | + | 0.732579i | \(0.738317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −864.000 | −1.14261 | −0.571303 | − | 0.820739i | \(-0.693562\pi\) | ||||
−0.571303 | + | 0.820739i | \(0.693562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 126.000 | 0.160784 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −378.000 | −0.465814 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1290.88i | 1.53745i | 0.639579 | + | 0.768725i | \(0.279109\pi\) | ||||
−0.639579 | + | 0.768725i | \(0.720891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 540.000 | − | 1249.24i | 0.622059 | − | 1.43908i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.0000 | −0.0267600 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 24.4949i | − | 0.0264539i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 808.332i | 0.846120i | 0.906102 | + | 0.423060i | \(0.139044\pi\) | ||||
−0.906102 | + | 0.423060i | \(0.860956\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 507.044i | − | 0.514746i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 36.7423i | − | 0.0361980i | −0.999836 | − | 0.0180990i | \(-0.994239\pi\) | ||
0.999836 | − | 0.0180990i | \(-0.00576141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1376.00 | −1.31632 | −0.658162 | − | 0.752877i | \(-0.728666\pi\) | ||||
−0.658162 | + | 0.752877i | \(0.728666\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −54.0000 | + | 124.924i | −0.0501891 | + | 0.116108i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1183.10i | 1.06892i | 0.845192 | + | 0.534462i | \(0.179486\pi\) | ||||
−0.845192 | + | 0.534462i | \(0.820514\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −602.000 | −0.529001 | −0.264501 | − | 0.964386i | \(-0.585207\pi\) | ||||
−0.264501 | + | 0.964386i | \(0.585207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −732.000 | −0.625931 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2106.00 | −1.75324 | −0.876619 | − | 0.481186i | \(-0.840206\pi\) | ||||
−0.876619 | + | 0.481186i | \(0.840206\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −282.000 | −0.228666 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 661.362i | 0.522589i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 378.000 | − | 874.468i | 0.291187 | − | 0.673633i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1843.00 | −1.38467 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1109.62i | − | 0.813422i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 597.675i | − | 0.427662i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1028.79i | − | 0.718819i | −0.933180 | − | 0.359409i | \(-0.882978\pi\) | ||
0.933180 | − | 0.359409i | \(-0.117022\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 484.999i | − | 0.331022i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −576.000 | −0.384163 | −0.192082 | − | 0.981379i | \(-0.561524\pi\) | ||||
−0.192082 | + | 0.981379i | \(0.561524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −170.000 | − | 73.4847i | −0.110834 | − | 0.0479093i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 66.1362i | − | 0.0421637i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1674.00 | −1.04394 | −0.521969 | − | 0.852965i | \(-0.674802\pi\) | ||||
−0.521969 | + | 0.852965i | \(0.674802\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 308.000 | 0.187944 | 0.0939720 | − | 0.995575i | \(-0.470044\pi\) | ||||
0.0939720 | + | 0.995575i | \(0.470044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 540.000 | 0.322526 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4140.00 | 2.42101 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 308.636i | 0.176764i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 705.000 | + | 749.544i | 0.395561 | + | 0.420553i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 522.000 | 0.287006 | 0.143503 | − | 0.989650i | \(-0.454163\pi\) | ||||
0.143503 | + | 0.989650i | \(0.454163\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1366.82i | 0.736622i | 0.929703 | + | 0.368311i | \(0.120064\pi\) | ||||
−0.929703 | + | 0.368311i | \(0.879936\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 462.954i | 0.244625i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.5959i | 0.0101547i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2880.60i | − | 1.46431i | −0.681137 | − | 0.732156i | \(-0.738514\pi\) | ||
0.681137 | − | 0.732156i | \(-0.261486\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1782.00 | −0.888816 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −846.000 | + | 1957.14i | −0.414125 | + | 0.958040i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 293.939i | 0.141246i | 0.997503 | + | 0.0706229i | \(0.0224987\pi\) | ||||
−0.997503 | + | 0.0706229i | \(0.977501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −414.000 | −0.195332 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3564.00 | 1.65144 | 0.825720 | − | 0.564080i | \(-0.190769\pi\) | ||||
0.825720 | + | 0.564080i | \(0.190769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3203.00 | −1.45790 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 90.0000 | 0.0402484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1383.96i | 0.608212i | 0.952638 | + | 0.304106i | \(0.0983577\pi\) | ||||
−0.952638 | + | 0.304106i | \(0.901642\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2023.00 | − | 874.468i | −0.873854 | − | 0.377735i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1620.00 | −0.687947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 139.621i | 0.0583003i | 0.999575 | + | 0.0291502i | \(0.00928010\pi\) | ||||
−0.999575 | + | 0.0291502i | \(0.990720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3101.05i | 1.27348i | 0.771079 | + | 0.636739i | \(0.219717\pi\) | ||||
−0.771079 | + | 0.636739i | \(0.780283\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1058.18i | 0.427447i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 597.675i | 0.237524i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2898.00 | 1.13328 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −459.000 | − | 198.409i | −0.176653 | − | 0.0763604i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 673.610i | − | 0.255187i | −0.991827 | − | 0.127593i | \(-0.959275\pi\) | ||
0.991827 | − | 0.127593i | \(-0.0407253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2144.00 | −0.799630 | −0.399815 | − | 0.916596i | \(-0.630926\pi\) | ||||
−0.399815 | + | 0.916596i | \(0.630926\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 540.000 | 0.198309 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −234.000 | −0.0846285 | −0.0423142 | − | 0.999104i | \(-0.513473\pi\) | ||||
−0.0423142 | + | 0.999104i | \(0.513473\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2654.00 | 0.945412 | 0.472706 | − | 0.881220i | \(-0.343277\pi\) | ||||
0.472706 | + | 0.881220i | \(0.343277\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3174.54i | 1.11400i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2142.00 | + | 925.907i | 0.740586 | + | 0.320128i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −906.000 | −0.308672 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1036.13i | − | 0.347905i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 563.383i | − | 0.186459i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2307.42i | − | 0.752840i | −0.926449 | − | 0.376420i | \(-0.877155\pi\) | ||
0.926449 | − | 0.376420i | \(-0.122845\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 536.438i | − | 0.172564i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −396.000 | −0.125614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 136.000 | + | 58.7878i | 0.0425451 | + | 0.0183907i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1984.09i | − | 0.612202i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3780.00 | −1.15054 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −838.000 | −0.251644 | −0.125822 | − | 0.992053i | \(-0.540157\pi\) | ||||
−0.125822 | + | 0.992053i | \(0.540157\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1071.00 | 0.317333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4860.00 | −1.42101 | −0.710506 | − | 0.703692i | \(-0.751534\pi\) | ||||
−0.710506 | + | 0.703692i | \(0.751534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.6969i | − | 0.00424105i | −0.999998 | − | 0.00212053i | \(-0.999325\pi\) | ||
0.999998 | − | 0.00212053i | \(-0.000674985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1242.00 | + | 2873.25i | −0.353756 | + | 0.818381i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1458.00 | 0.409943 | 0.204972 | − | 0.978768i | \(-0.434290\pi\) | ||||
0.204972 | + | 0.978768i | \(0.434290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 440.908i | − | 0.122390i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3086.36i | 0.845909i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3211.28i | − | 0.869123i | −0.900642 | − | 0.434562i | \(-0.856903\pi\) | ||
0.900642 | − | 0.434562i | \(-0.143097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 808.332i | 0.216055i | 0.994148 | + | 0.108027i | \(0.0344534\pi\) | ||||
−0.994148 | + | 0.108027i | \(0.965547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 612.000 | − | 575.630i | 0.159589 | − | 0.150105i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 734.847i | 0.189300i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2592.00 | −0.659684 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 576.000 | 0.144848 | 0.0724239 | − | 0.997374i | \(-0.476927\pi\) | ||||
0.0724239 | + | 0.997374i | \(0.476927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6486.00 | −1.61174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 378.000 | 0.0928285 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4436.03i | − | 1.07670i | −0.842722 | − | 0.538350i | \(-0.819048\pi\) | ||
0.842722 | − | 0.538350i | \(-0.180952\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4148.00 | + | 1793.03i | 0.995151 | + | 0.430167i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1134.00 | −0.268938 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5420.72i | − | 1.27094i | −0.772128 | − | 0.635468i | \(-0.780807\pi\) | ||
0.772128 | − | 0.635468i | \(-0.219193\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1455.00i | 0.337282i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3872.64i | 0.887648i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6233.95i | 1.41298i | 0.707725 | + | 0.706488i | \(0.249722\pi\) | ||||
−0.707725 | + | 0.706488i | \(0.750278\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5024.00 | −1.12615 | −0.563074 | − | 0.826406i | \(-0.690382\pi\) | ||||
−0.563074 | + | 0.826406i | \(0.690382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1620.00 | − | 3747.72i | 0.359146 | − | 0.830851i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 6704.25i | − | 1.47012i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4024.00 | −0.872847 | −0.436424 | − | 0.899741i | \(-0.643755\pi\) | ||||
−0.436424 | + | 0.899741i | \(0.643755\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −72.0000 | −0.0154499 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 630.000 | 0.133746 | 0.0668730 | − | 0.997761i | \(-0.478698\pi\) | ||||
0.0668730 | + | 0.997761i | \(0.478698\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9002.00 | −1.89086 | −0.945430 | − | 0.325825i | \(-0.894358\pi\) | ||||
−0.945430 | + | 0.325825i | \(0.894358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 73.4847i | − | 0.0152732i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2718.00 | + | 6287.84i | −0.559019 | + | 1.29324i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2267.00 | 0.461429 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2424.99i | 0.488508i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9148.84i | − | 1.82417i | −0.410004 | − | 0.912084i | \(-0.634473\pi\) | ||
0.410004 | − | 0.912084i | \(-0.365527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1322.72i | 0.261058i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1521.13i | − | 0.297189i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8460.00 | 1.63630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1188.00 | + | 2748.33i | −0.227492 | + | 0.526282i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 110.227i | − | 0.0208989i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 864.000 | 0.162205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5246.00 | −0.975261 | −0.487630 | − | 0.873050i | \(-0.662139\pi\) | ||||
−0.487630 | + | 0.873050i | \(0.662139\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4128.00 | −0.759980 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8136.00 | 1.48344 | 0.741721 | − | 0.670709i | \(-0.234010\pi\) | ||||
0.741721 | + | 0.670709i | \(0.234010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 499.696i | 0.0902380i | 0.998982 | + | 0.0451190i | \(0.0143667\pi\) | ||||
−0.998982 | + | 0.0451190i | \(0.985633\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −162.000 | + | 374.772i | −0.0289767 | + | 0.0670349i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8838.00 | −1.56590 | −0.782952 | − | 0.622082i | \(-0.786287\pi\) | ||||
−0.782952 | + | 0.622082i | \(0.786287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7098.62i | 1.24591i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3549.31i | 0.617144i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 514.393i | 0.0886117i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8744.68i | 1.49252i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1806.00 | −0.305419 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3060.00 | − | 1322.72i | −0.512776 | − | 0.221654i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9068.01i | 1.50581i | 0.658129 | + | 0.752905i | \(0.271348\pi\) | ||||
−0.658129 | + | 0.752905i | \(0.728652\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2196.00 | −0.361382 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2592.00 | 0.422735 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7982.00 | 1.29023 | 0.645115 | − | 0.764086i | \(-0.276810\pi\) | ||||
0.645115 | + | 0.764086i | \(0.276810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6318.00 | −1.01223 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 450.706i | 0.0715751i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2159.00 | − | 5974.31i | −0.339869 | − | 0.940473i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −846.000 | −0.132021 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 4308.65i | − | 0.666572i | −0.942826 | − | 0.333286i | \(-0.891842\pi\) | ||
0.942826 | − | 0.333286i | \(-0.108158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4291.51i | 0.658221i | 0.944291 | + | 0.329110i | \(0.106749\pi\) | ||||
−0.944291 | + | 0.329110i | \(0.893251\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1984.09i | 0.301717i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6258.45i | 0.943636i | 0.881696 | + | 0.471818i | \(0.156402\pi\) | ||||
−0.881696 | + | 0.471818i | \(0.843598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −438.000 | −0.0654835 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1134.00 | − | 2623.40i | 0.168117 | − | 0.388922i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8605.06i | − | 1.26506i | −0.774535 | − | 0.632531i | \(-0.782016\pi\) | ||
0.774535 | − | 0.632531i | \(-0.217984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6759.00 | −0.985421 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5529.00 | −0.799441 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1620.00 | −0.232314 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5570.00 | 0.792239 | 0.396119 | − | 0.918199i | \(-0.370357\pi\) | ||||
0.396119 | + | 0.918199i | \(0.370357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 3328.86i | − | 0.469630i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10098.0 | + | 4364.99i | 1.41311 | + | 0.610833i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7282.00 | 1.01085 | 0.505426 | − | 0.862870i | \(-0.331335\pi\) | ||||
0.505426 | + | 0.862870i | \(0.331335\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1793.03i | − | 0.246911i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9259.07i | − | 1.26490i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 984.695i | − | 0.133457i | −0.997771 | − | 0.0667287i | \(-0.978744\pi\) | ||
0.997771 | − | 0.0667287i | \(-0.0212562\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3086.36i | − | 0.415010i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11628.0 | −1.55134 | −0.775670 | − | 0.631139i | \(-0.782588\pi\) | ||||
−0.775670 | + | 0.631139i | \(0.782588\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2346.00 | + | 1014.09i | 0.310554 | + | 0.134241i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 1455.00i | − | 0.191115i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4518.00 | 0.588873 | 0.294437 | − | 0.955671i | \(-0.404868\pi\) | ||||
0.294437 | + | 0.955671i | \(0.404868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5922.00 | 0.765955 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1728.00 | −0.221797 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2520.00 | 0.321000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7260.29i | − | 0.917842i | −0.888477 | − | 0.458921i | \(-0.848236\pi\) | ||
0.888477 | − | 0.458921i | \(-0.151764\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −510.000 | − | 220.454i | −0.0639898 | − | 0.0276604i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10062.0 | 1.25305 | 0.626524 | − | 0.779402i | \(-0.284477\pi\) | ||||
0.626524 | + | 0.779402i | \(0.284477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 587.878i | − | 0.0726657i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 198.409i | − | 0.0243432i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13746.5i | 1.67418i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6804.68i | 0.822665i | 0.911485 | + | 0.411332i | \(0.134936\pi\) | ||||
−0.911485 | + | 0.411332i | \(0.865064\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5022.00 | −0.602718 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9180.00 | + | 3968.17i | 1.09375 | + | 0.472787i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2116.36i | 0.250332i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 924.000 | 0.108510 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12564.0 | 1.46490 | 0.732448 | − | 0.680823i | \(-0.238378\pi\) | ||||
0.732448 | + | 0.680823i | \(0.238378\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3752.00 | 0.434350 | 0.217175 | − | 0.976133i | \(-0.430316\pi\) | ||||
0.217175 | + | 0.976133i | \(0.430316\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1620.00 | 0.186211 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6121.27i | 0.698648i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2592.00 | − | 5996.35i | 0.293760 | − | 0.679587i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12420.0 | 1.39777 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6086.98i | 0.680278i | 0.940375 | + | 0.340139i | \(0.110474\pi\) | ||||
−0.940375 | + | 0.340139i | \(0.889526\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3321.51i | 0.368641i | 0.982866 | + | 0.184320i | \(0.0590084\pi\) | ||||
−0.982866 | + | 0.184320i | \(0.940992\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 925.907i | 0.102055i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1151.26i | − | 0.126023i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14506.0 | −1.57707 | −0.788535 | − | 0.614990i | \(-0.789160\pi\) | ||||
−0.788535 | + | 0.614990i | \(0.789160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2115.00 | + | 2248.63i | 0.228377 | + | 0.242807i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11858.0i | − | 1.27176i | −0.771788 | − | 0.635880i | \(-0.780637\pi\) | ||
0.771788 | − | 0.635880i | \(-0.219363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3162.00 | 0.336839 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1566.00 | 0.165703 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7866.00 | −0.826769 | −0.413385 | − | 0.910556i | \(-0.635654\pi\) | ||||
−0.413385 | + | 0.910556i | \(0.635654\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20838.0 | −2.17566 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4100.45i | 0.425289i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3060.00 | − | 1322.72i | −0.315286 | − | 0.136286i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6058.00 | −0.620090 | −0.310045 | − | 0.950722i | \(-0.600344\pi\) | ||||
−0.310045 | + | 0.950722i | \(0.600344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1388.86i | 0.141234i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10481.4i | 1.05893i | 0.848332 | + | 0.529464i | \(0.177607\pi\) | ||||
−0.848332 | + | 0.529464i | \(0.822393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13726.9i | − | 1.37785i | −0.724832 | − | 0.688926i | \(-0.758083\pi\) | ||
0.724832 | − | 0.688926i | \(-0.241917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 58.7878i | 0.00586283i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14472.0 | 1.43401 | 0.717007 | − | 0.697066i | \(-0.245512\pi\) | ||||
0.717007 | + | 0.697066i | \(0.245512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7776.00 | − | 17989.1i | 0.765591 | − | 1.77112i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8641.80i | − | 0.845421i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9108.00 | −0.885383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1190.00 | 0.114949 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5346.00 | −0.513158 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3816.00 | 0.364003 | 0.182002 | − | 0.983298i | \(-0.441742\pi\) | ||||
0.182002 | + | 0.983298i | \(0.441742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 17930.3i | − | 1.69969i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2538.00 | + | 5871.43i | −0.239095 | + | 0.553125i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1980.00 | 0.185376 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14799.8i | − | 1.37709i | −0.725193 | − | 0.688546i | \(-0.758249\pi\) | ||
0.725193 | − | 0.688546i | \(-0.241751\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 881.816i | 0.0815483i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1349.67i | 0.124052i | 0.998075 | + | 0.0620262i | \(0.0197562\pi\) | ||||
−0.998075 | + | 0.0620262i | \(0.980244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6481.35i | − | 0.592100i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1242.00 | −0.112775 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1314.00 | + | 3039.82i | −0.118593 | + | 0.274355i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2689.54i | 0.241283i | 0.992696 | + | 0.120642i | \(0.0384952\pi\) | ||||
−0.992696 | + | 0.120642i | \(0.961505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10692.0 | 0.953460 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7596.00 | 0.673338 | 0.336669 | − | 0.941623i | \(-0.390700\pi\) | ||||
0.336669 | + | 0.941623i | \(0.390700\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −90.0000 | −0.00793059 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9609.00 | −0.841717 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 19671.9i | − | 1.71304i | −0.516110 | − | 0.856522i | \(-0.672621\pi\) | ||
0.516110 | − | 0.856522i | \(-0.327379\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4860.00 | + | 11243.2i | −0.420731 | + | 0.973323i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 270.000 | 0.0232374 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3370.50i | 0.288392i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10140.9i | − | 0.862661i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4151.89i | 0.351151i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10393.2i | 0.873961i | 0.899471 | + | 0.436981i | \(0.143952\pi\) | ||||
−0.899471 | + | 0.436981i | \(0.856048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17956.0 | −1.50126 | −0.750632 | − | 0.660721i | \(-0.770251\pi\) | ||||
−0.750632 | + | 0.660721i | \(0.770251\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6069.00 | − | 2623.40i | −0.504520 | − | 0.218085i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 411.514i | − | 0.0340149i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1087.00 | −0.0893400 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4860.00 | −0.397187 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27180.0 | 2.20881 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2898.00 | 0.234190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 418.863i | 0.0336597i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14076.0 | − | 13239.5i | 1.12485 | − | 1.05801i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14192.0 | 1.12784 | 0.563920 | − | 0.825829i | \(-0.309293\pi\) | ||||
0.563920 | + | 0.825829i | \(0.309293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9303.16i | 0.735243i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1474.59i | 0.115898i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2733.63i | − | 0.213678i | −0.994276 | − | 0.106839i | \(-0.965927\pi\) | ||
0.994276 | − | 0.106839i | \(-0.0340729\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3174.54i | 0.246787i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1260.00 | −0.0974189 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7560.00 | − | 17489.4i | 0.581345 | − | 1.34489i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1793.03i | 0.137135i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16254.0 | −1.23645 | −0.618226 | − | 0.786000i | \(-0.712148\pi\) | ||||
−0.618226 | + | 0.786000i | \(0.712148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11880.0 | 0.898874 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8694.00 | 0.654298 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3672.00 | 0.274878 | 0.137439 | − | 0.990510i | \(-0.456113\pi\) | ||||
0.137439 | + | 0.990510i | \(0.456113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5158.63i | 0.384115i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1377.00 | − | 595.226i | −0.101990 | − | 0.0440867i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11466.0 | 0.844780 | 0.422390 | − | 0.906414i | \(-0.361191\pi\) | ||||
0.422390 | + | 0.906414i | \(0.361191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20869.7i | 1.52954i | 0.644303 | + | 0.764770i | \(0.277148\pi\) | ||||
−0.644303 | + | 0.764770i | \(0.722852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2020.83i | − | 0.147332i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 13700.0i | − | 0.993616i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19752.7i | − | 1.42516i | −0.701593 | − | 0.712578i | \(-0.747527\pi\) | ||
0.701593 | − | 0.712578i | \(-0.252473\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6432.00 | −0.461666 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14688.0 | + | 6349.08i | 1.04881 | + | 0.453363i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33464.9i | 2.37732i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1620.00 | 0.114494 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18720.0 | 1.31628 | 0.658141 | − | 0.752895i | \(-0.271343\pi\) | ||||
0.658141 | + | 0.752895i | \(0.271343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −80.0000 | −0.00559651 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −702.000 | −0.0488603 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1643.61i | − | 0.113819i | −0.998379 | − | 0.0569097i | \(-0.981875\pi\) | ||
0.998379 | − | 0.0569097i | \(-0.0181247\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2142.00 | − | 925.907i | −0.147586 | − | 0.0637958i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7962.00 | 0.545834 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10099.2i | 0.688888i | 0.938807 | + | 0.344444i | \(0.111933\pi\) | ||||
−0.938807 | + | 0.344444i | \(0.888067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7466.04i | 0.506733i | 0.967370 | + | 0.253366i | \(0.0815378\pi\) | ||||
−0.967370 | + | 0.253366i | \(0.918462\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9523.62i | 0.643170i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4514.41i | 0.303367i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7198.00 | −0.481314 | −0.240657 | − | 0.970610i | \(-0.577363\pi\) | ||||
−0.240657 | + | 0.970610i | \(0.577363\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6426.00 | + | 2777.72i | 0.427577 | + | 0.184826i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13227.2i | 0.875805i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5662.00 | 0.373060 | 0.186530 | − | 0.982449i | \(-0.440276\pi\) | ||||
0.186530 | + | 0.982449i | \(0.440276\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2718.00 | −0.178212 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3546.00 | −0.231372 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8180.00 | 0.531150 | 0.265575 | − | 0.964090i | \(-0.414438\pi\) | ||||
0.265575 | + | 0.964090i | \(0.414438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 3108.40i | − | 0.200863i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9486.00 | − | 21945.0i | 0.610030 | − | 1.41125i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13411.0 | 0.858304 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1690.15i | − | 0.107652i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 12551.2i | − | 0.795626i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2410.30i | 0.152064i | 0.997105 | + | 0.0760320i | \(0.0242251\pi\) | ||||
−0.997105 | + | 0.0760320i | \(0.975775\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6922.26i | − | 0.434653i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2520.00 | −0.157485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18360.0 | + | 17268.9i | −1.14199 | + | 1.07413i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 1609.31i | − | 0.0996299i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26010.0 | 1.60270 | 0.801352 | − | 0.598193i | \(-0.204114\pi\) | ||||
0.801352 | + | 0.598193i | \(0.204114\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4582.00 | 0.281021 | 0.140510 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140510 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1188.00 | −0.0725232 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5832.00 | 0.354373 | 0.177187 | − | 0.984177i | \(-0.443300\pi\) | ||||
0.177187 | + | 0.984177i | \(0.443300\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30422.7i | 1.84005i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 408.000 | + | 176.363i | 0.0245634 | + | 0.0106179i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21474.0 | −1.28690 | −0.643448 | − | 0.765490i | \(-0.722497\pi\) | ||||
−0.643448 | + | 0.765490i | \(0.722497\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1410.91i | 0.0841659i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5952.26i | − | 0.353455i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27936.4i | − | 1.65136i | −0.564136 | − | 0.825682i | \(-0.690791\pi\) | ||
0.564136 | − | 0.825682i | \(-0.309209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 18430.0i | − | 1.08448i | −0.840223 | − | 0.542241i | \(-0.817576\pi\) | ||
0.840223 | − | 0.542241i | \(-0.182424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11340.0 | −0.664267 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −180.000 | + | 416.413i | −0.0104964 | + | 0.0242824i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14505.9i | 0.842084i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2514.00 | −0.145287 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19872.0 | 1.14329 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14344.0 | 0.821576 | 0.410788 | − | 0.911731i | \(-0.365254\pi\) | ||||
0.410788 | + | 0.911731i | \(0.365254\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3213.00 | 0.183212 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26599.0i | 1.51002i | 0.655714 | + | 0.755010i | \(0.272368\pi\) | ||||
−0.655714 | + | 0.755010i | \(0.727632\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5940.00 | − | 13741.6i | 0.335724 | − | 0.776665i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14580.0 | −0.820421 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 27407.3i | − | 1.53545i | −0.640779 | − | 0.767725i | \(-0.721389\pi\) | ||
0.640779 | − | 0.767725i | \(-0.278611\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4100.45i | 0.228715i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 44.0908i | − | 0.00244857i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 43649.9i | − | 2.41354i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6716.00 | 0.369738 | 0.184869 | − | 0.982763i | \(-0.440814\pi\) | ||||
0.184869 | + | 0.982763i | \(0.440814\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3726.00 | + | 8619.75i | −0.204241 | + | 0.472493i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 754.443i | − | 0.0411765i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19026.0 | 1.03395 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4374.00 | 0.236681 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12546.0 | 0.675971 | 0.337986 | − | 0.941151i | \(-0.390254\pi\) | ||||
0.337986 | + | 0.941151i | \(0.390254\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2440.00 | −0.130905 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1322.72i | − | 0.0706620i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −270.000 | + | 624.620i | −0.0143627 | + | 0.0332267i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24562.0 | 1.30105 | 0.650526 | − | 0.759484i | \(-0.274549\pi\) | ||||
0.650526 | + | 0.759484i | \(0.274549\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9259.07i | 0.488386i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 921.008i | 0.0483759i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 10140.9i | − | 0.530416i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 9633.84i | − | 0.501789i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7704.00 | 0.399598 | 0.199799 | − | 0.979837i | \(-0.435971\pi\) | ||||
0.199799 | + | 0.979837i | \(0.435971\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23392.0 | + | 10111.5i | 1.20827 | + | 0.522291i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2424.99i | 0.124739i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14994.0 | −0.768087 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22160.0 | −1.13049 | −0.565247 | − | 0.824922i | \(-0.691219\pi\) | ||||
−0.565247 | + | 0.824922i | \(0.691219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8316.00 | 0.420764 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17004.4i | 0.856849i | 0.903578 | + | 0.428424i | \(0.140931\pi\) | ||||
−0.903578 | + | 0.428424i | \(0.859069\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1836.00 | − | 1726.89i | 0.0921386 | − | 0.0866630i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 59616.0 | 2.97962 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 18371.2i | − | 0.914472i | −0.889345 | − | 0.457236i | \(-0.848840\pi\) | ||
0.889345 | − | 0.457236i | \(-0.151160\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2204.54i | 0.109293i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23532.2i | − | 1.16193i | −0.813928 | − | 0.580965i | \(-0.802675\pi\) | ||
0.813928 | − | 0.580965i | \(-0.197325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1278.63i | − | 0.0628799i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7776.00 | −0.380869 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8694.00 | − | 20112.8i | 0.424128 | − | 0.981181i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 10831.6i | − | 0.526301i | −0.964755 | − | 0.263151i | \(-0.915238\pi\) | ||
0.964755 | − | 0.263151i | \(-0.0847616\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1728.00 | 0.0836279 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3348.00 | 0.161386 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12206.0 | −0.586043 | −0.293022 | − | 0.956106i | \(-0.594661\pi\) | ||||
−0.293022 | + | 0.956106i | \(0.594661\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19458.0 | −0.930541 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 23640.0i | − | 1.12608i | −0.826428 | − | 0.563042i | \(-0.809631\pi\) | ||
0.826428 | − | 0.563042i | \(-0.190369\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10234.0 | + | 4423.78i | 0.485578 | + | 0.209897i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1134.00 | 0.0535946 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 39681.7i | − | 1.86809i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27718.4i | − | 1.29981i | −0.760017 | − | 0.649904i | \(-0.774809\pi\) | ||
0.760017 | − | 0.649904i | \(-0.225191\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 13308.1i | − | 0.621633i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 40272.1i | − | 1.87385i | −0.349532 | − | 0.936925i | \(-0.613659\pi\) | ||
0.349532 | − | 0.936925i | \(-0.386341\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −952.000 | −0.0441250 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12444.0 | + | 5379.08i | 0.574551 | + | 0.248357i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3698.73i | − | 0.170116i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10074.0 | −0.461557 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3402.00 | −0.155271 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7056.00 | −0.320815 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12188.0 | 0.552040 | 0.276020 | − | 0.961152i | \(-0.410984\pi\) | ||||
0.276020 | + | 0.961152i | \(0.410984\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 16262.2i | − | 0.733775i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35802.0 | + | 15475.9i | 1.60932 | + | 0.695650i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25920.0 | −1.16071 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4364.99i | 0.194730i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9109.65i | 0.404869i | 0.979296 | + | 0.202434i | \(0.0648853\pi\) | ||||
−0.979296 | + | 0.202434i | \(0.935115\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9259.07i | 0.409965i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11617.9i | 0.512484i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37260.0 | −1.63746 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4794.00 | + | 2072.27i | 0.209896 | + | 0.0907303i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18701.9i | 0.815782i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19710.0 | −0.856572 | −0.428286 | − | 0.903643i | \(-0.640882\pi\) | ||||
−0.428286 | + | 0.903643i | \(0.640882\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8164.00 | −0.353486 | −0.176743 | − | 0.984257i | \(-0.556556\pi\) | ||||
−0.176743 | + | 0.984257i | \(0.556556\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15072.0 | −0.650182 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 720.000 | 0.0309454 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1616.66i | − | 0.0692287i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4860.00 | − | 11243.2i | 0.207353 | − | 0.479692i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17226.0 | −0.732267 | −0.366134 | − | 0.930562i | \(-0.619319\pi\) | ||||
−0.366134 | + | 0.930562i | \(0.619319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16636.9i | 0.704650i | 0.935878 | + | 0.352325i | \(0.114609\pi\) | ||||
−0.935878 | + | 0.352325i | \(0.885391\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 20112.8i | − | 0.848771i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39517.6i | 1.66162i | 0.556554 | + | 0.830811i | \(0.312123\pi\) | ||||
−0.556554 | + | 0.830811i | \(0.687877\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38873.4i | 1.62862i | 0.580428 | + | 0.814312i | \(0.302885\pi\) | ||||
−0.580428 | + | 0.814312i | \(0.697115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12072.0 | −0.503939 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12852.0 | + | 12088.2i | −0.534568 | + | 0.502800i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 8729.98i | − | 0.361813i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −216.000 | −0.00892001 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33804.0 | 1.39099 | 0.695497 | − | 0.718529i | \(-0.255184\pi\) | ||||
0.695497 | + | 0.718529i | \(0.255184\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8513.00 | −0.349051 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1890.00 | 0.0772183 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7845.72i | 0.319409i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31331.0 | + | 13543.2i | 1.27101 | + | 0.549411i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27006.0 | −1.09169 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28090.7i | 1.13154i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6260.90i | − | 0.251312i | −0.992074 | − | 0.125656i | \(-0.959896\pi\) | ||
0.992074 | − | 0.125656i | \(-0.0401035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 220.454i | − | 0.00881798i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12240.1i | 0.487881i | 0.969790 | + | 0.243940i | \(0.0784401\pi\) | ||||
−0.969790 | + | 0.243940i | \(0.921560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40382.0 | −1.60398 | −0.801988 | − | 0.597340i | \(-0.796224\pi\) | ||||
−0.801988 | + | 0.597340i | \(0.796224\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8154.00 | + | 18863.5i | −0.322750 | + | 0.746652i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9369.30i | 0.369565i | 0.982779 | + | 0.184783i | \(0.0591581\pi\) | ||||
−0.982779 | + | 0.184783i | \(0.940842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3390.00 | 0.133253 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6801.00 | 0.266406 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57960.0 | 2.26255 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −77760.0 | −3.02503 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7274.98i | 0.282040i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4392.00 | + | 10160.5i | −0.169688 | + | 0.392557i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −578.000 | −0.0222550 | −0.0111275 | − | 0.999938i | \(-0.503542\pi\) | ||||
−0.0111275 | + | 0.999938i | \(0.503542\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 27446.5i | − | 1.05318i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11902.1i | 0.455154i | 0.973760 | + | 0.227577i | \(0.0730804\pi\) | ||||
−0.973760 | + | 0.227577i | \(0.926920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46633.4i | 1.77728i | 0.458605 | + | 0.888640i | \(0.348349\pi\) | ||||
−0.458605 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3968.17i | 0.150722i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23724.0 | 0.898054 | 0.449027 | − | 0.893518i | \(-0.351771\pi\) | ||||
0.449027 | + | 0.893518i | \(0.351771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7560.00 | + | 17489.4i | −0.285213 | + | 0.659813i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4563.40i | − | 0.171582i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1800.00 | 0.0674521 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 342.000 | 0.0127730 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25380.0 | 0.944720 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1008.00 | 0.0373956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 30554.9i | − | 1.12978i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3564.00 | + | 8244.98i | −0.131343 | + | 0.303849i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7596.00 | 0.279005 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 25998.9i | − | 0.951796i | −0.879501 | − | 0.475898i | \(-0.842123\pi\) | ||
0.879501 | − | 0.475898i | \(-0.157877\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 330.681i | − | 0.0120660i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45126.9i | 1.64119i | 0.571511 | + | 0.820594i | \(0.306357\pi\) | ||||
−0.571511 | + | 0.820594i | \(0.693643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48676.3i | 1.76446i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2592.00 | 0.0936490 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9792.00 | + | 4232.72i | 0.352628 | + | 0.152428i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35316.7i | − | 1.26767i | −0.773467 | − | 0.633837i | \(-0.781479\pi\) | ||
0.773467 | − | 0.633837i | \(-0.218521\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15738.0 | −0.563067 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13140.0 | 0.468590 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29036.0 | −1.03211 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12384.0 | −0.438774 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27064.4i | 0.955818i | 0.878409 | + | 0.477909i | \(0.158605\pi\) | ||||
−0.878409 | + | 0.477909i | \(0.841395\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2350.00 | + | 2498.48i | 0.0827263 | + | 0.0879531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24408.0 | 0.856465 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7098.62i | − | 0.248288i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13286.0i | − | 0.463219i | −0.972809 | − | 0.231609i | \(-0.925601\pi\) | ||
0.972809 | − | 0.231609i | \(-0.0743991\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1499.09i | 0.0520989i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 8850.01i | − | 0.306591i | −0.988180 | − | 0.153295i | \(-0.951011\pi\) | ||
0.988180 | − | 0.153295i | \(-0.0489886\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42582.0 | −1.47048 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −486.000 | + | 1124.32i | −0.0167297 | + | 0.0387026i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3397.44i | − | 0.116581i | −0.998300 | − | 0.0582904i | \(-0.981435\pi\) | ||
0.998300 | − | 0.0582904i | \(-0.0185649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48600.0 | 1.66241 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26514.0 | −0.904075 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41346.0 | −1.40538 | −0.702691 | − | 0.711496i | \(-0.748018\pi\) | ||||
−0.702691 | + | 0.711496i | \(0.748018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1650.00 | −0.0559086 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21295.9i | 0.719329i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28458.0 | + | 12301.3i | 0.958245 | + | 0.414214i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29727.0 | −0.997852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10647.9i | 0.356308i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5251.71i | 0.175190i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43561.7i | 1.44866i | 0.689455 | + | 0.724328i | \(0.257850\pi\) | ||||
−0.689455 | + | 0.724328i | \(0.742150\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1543.18i | 0.0511600i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54252.0 | −1.79303 | −0.896514 | − | 0.443016i | \(-0.853908\pi\) | ||||
−0.896514 | + | 0.443016i | \(0.853908\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5236.00 | − | 2263.33i | −0.172516 | − | 0.0745724i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26234.0i | 0.861704i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13734.0 | 0.449733 | 0.224867 | − | 0.974390i | \(-0.427805\pi\) | ||||
0.224867 | + | 0.974390i | \(0.427805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72726.0 | 2.37419 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5418.00 | −0.176334 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17172.0 | −0.557174 | −0.278587 | − | 0.960411i | \(-0.589866\pi\) | ||||
−0.278587 | + | 0.960411i | \(0.589866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 573.181i | 0.0185412i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9180.00 | − | 3968.17i | −0.296051 | − | 0.127972i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18612.0 | −0.598410 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13712.2i | 0.439540i | 0.975552 | + | 0.219770i | \(0.0705306\pi\) | ||||
−0.975552 | + | 0.219770i | \(0.929469\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27204.0i | 0.869380i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 6500.95i | − | 0.207129i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14461.8i | 0.459388i | 0.973263 | + | 0.229694i | \(0.0737725\pi\) | ||||
−0.973263 | + | 0.229694i | \(0.926228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6588.00 | −0.208644 |
(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.b.c.895.1 | 2 | ||
4.3 | odd | 2 | 1344.4.b.b.895.1 | 2 | |||
7.6 | odd | 2 | 1344.4.b.b.895.2 | 2 | |||
8.3 | odd | 2 | 336.4.b.d.223.2 | yes | 2 | ||
8.5 | even | 2 | 336.4.b.a.223.2 | yes | 2 | ||
24.5 | odd | 2 | 1008.4.b.a.559.1 | 2 | |||
24.11 | even | 2 | 1008.4.b.f.559.1 | 2 | |||
28.27 | even | 2 | inner | 1344.4.b.c.895.2 | 2 | ||
56.13 | odd | 2 | 336.4.b.d.223.1 | yes | 2 | ||
56.27 | even | 2 | 336.4.b.a.223.1 | ✓ | 2 | ||
168.83 | odd | 2 | 1008.4.b.a.559.2 | 2 | |||
168.125 | even | 2 | 1008.4.b.f.559.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.b.a.223.1 | ✓ | 2 | 56.27 | even | 2 | ||
336.4.b.a.223.2 | yes | 2 | 8.5 | even | 2 | ||
336.4.b.d.223.1 | yes | 2 | 56.13 | odd | 2 | ||
336.4.b.d.223.2 | yes | 2 | 8.3 | odd | 2 | ||
1008.4.b.a.559.1 | 2 | 24.5 | odd | 2 | |||
1008.4.b.a.559.2 | 2 | 168.83 | odd | 2 | |||
1008.4.b.f.559.1 | 2 | 24.11 | even | 2 | |||
1008.4.b.f.559.2 | 2 | 168.125 | even | 2 | |||
1344.4.b.b.895.1 | 2 | 4.3 | odd | 2 | |||
1344.4.b.b.895.2 | 2 | 7.6 | odd | 2 | |||
1344.4.b.c.895.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.b.c.895.2 | 2 | 28.27 | even | 2 | inner |