Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), degree \(2\), 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.9948826238976.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 36x^{6} + 935x^{4} + 12996x^{2} + 130321 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.4 | ||
Root | \(-2.76295 - 3.37136i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.a.215.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44949 | − | 1.41421i | 0.866025 | − | 0.500000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.5357 | + | 18.2483i | 0.942338 | + | 1.63218i | 0.760996 | + | 0.648756i | \(0.224711\pi\) |
0.181341 | + | 0.983420i | \(0.441956\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.6274i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 51.6140 | + | 29.7993i | 1.63218 | + | 0.942338i | ||||
\(11\) | −13.4722 | − | 7.77817i | −0.369274 | − | 0.213201i | 0.303867 | − | 0.952714i | \(-0.401722\pi\) |
−0.673141 | + | 0.739514i | \(0.735055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 29.7993i | − | 0.635757i | −0.948131 | − | 0.317879i | \(-0.897030\pi\) | ||
0.948131 | − | 0.317879i | \(-0.102970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 32.0000 | + | 55.4256i | 0.500000 | + | 0.866025i | ||||
\(17\) | −31.6070 | + | 54.7449i | −0.450930 | + | 0.781034i | −0.998444 | − | 0.0557626i | \(-0.982241\pi\) |
0.547514 | + | 0.836797i | \(0.315574\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 77.4209 | − | 44.6990i | 0.934820 | − | 0.539719i | 0.0464872 | − | 0.998919i | \(-0.485197\pi\) |
0.888333 | + | 0.459200i | \(0.151864\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −44.0000 | −0.426401 | ||||||||
\(23\) | −67.3610 | + | 38.8909i | −0.610684 | + | 0.352579i | −0.773233 | − | 0.634122i | \(-0.781362\pi\) |
0.162549 | + | 0.986700i | \(0.448028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −159.500 | + | 276.262i | −1.27600 | + | 2.21010i | ||||
\(26\) | −42.1426 | − | 72.9932i | −0.317879 | − | 0.550582i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 125.865i | 0.805950i | 0.915211 | + | 0.402975i | \(0.132024\pi\) | ||||
−0.915211 | + | 0.402975i | \(0.867976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −206.456 | − | 119.197i | −1.19615 | − | 0.690596i | −0.236453 | − | 0.971643i | \(-0.575985\pi\) |
−0.959694 | + | 0.281047i | \(0.909318\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 178.796i | 0.901860i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 92.0000 | + | 159.349i | 0.408776 | + | 0.708021i | 0.994753 | − | 0.102307i | \(-0.0326224\pi\) |
−0.585977 | + | 0.810328i | \(0.699289\pi\) | |||||||
\(38\) | 126.428 | − | 218.979i | 0.539719 | − | 0.934820i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −412.912 | + | 238.395i | −1.63218 | + | 0.942338i | ||||
\(41\) | 105.357 | 0.401315 | 0.200658 | − | 0.979661i | \(-0.435692\pi\) | ||||
0.200658 | + | 0.979661i | \(0.435692\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −190.000 | −0.673831 | −0.336915 | − | 0.941535i | \(-0.609384\pi\) | ||||
−0.336915 | + | 0.941535i | \(0.609384\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −110.000 | + | 190.526i | −0.352579 | + | 0.610684i | ||||
\(47\) | 21.0713 | + | 36.4966i | 0.0653950 | + | 0.113268i | 0.896869 | − | 0.442296i | \(-0.145836\pi\) |
−0.831474 | + | 0.555563i | \(0.812503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 902.268i | 2.55200i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 309.860 | + | 178.898i | 0.803068 | + | 0.463652i | 0.844543 | − | 0.535488i | \(-0.179872\pi\) |
−0.0414748 | + | 0.999140i | \(0.513206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 327.793i | − | 0.803628i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 178.000 | + | 308.305i | 0.402975 | + | 0.697973i | ||||
\(59\) | 42.1426 | − | 72.9932i | 0.0929915 | − | 0.161066i | −0.815777 | − | 0.578366i | \(-0.803690\pi\) |
0.908769 | + | 0.417300i | \(0.137024\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 567.753 | − | 327.793i | 1.19169 | − | 0.688025i | 0.233004 | − | 0.972476i | \(-0.425144\pi\) |
0.958691 | + | 0.284450i | \(0.0918111\pi\) | |||||||
\(62\) | −674.282 | −1.38119 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 543.787 | − | 313.955i | 1.03767 | − | 0.599098i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −148.000 | + | 256.344i | −0.269867 | + | 0.467423i | −0.968827 | − | 0.247737i | \(-0.920313\pi\) |
0.698960 | + | 0.715160i | \(0.253646\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 329.512i | 0.550787i | 0.961332 | + | 0.275393i | \(0.0888081\pi\) | ||||
−0.961332 | + | 0.275393i | \(0.911192\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 696.788 | + | 402.291i | 1.11716 | + | 0.644994i | 0.940675 | − | 0.339308i | \(-0.110193\pi\) |
0.176488 | + | 0.984303i | \(0.443526\pi\) | |||||||
\(74\) | 450.706 | + | 260.215i | 0.708021 | + | 0.408776i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −418.000 | − | 723.997i | −0.595300 | − | 1.03109i | −0.993505 | − | 0.113793i | \(-0.963700\pi\) |
0.398205 | − | 0.917297i | \(-0.369633\pi\) | |||||||
\(80\) | −674.282 | + | 1167.89i | −0.942338 | + | 1.63218i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 258.070 | − | 148.997i | 0.347549 | − | 0.200658i | ||||
\(83\) | 1222.14 | 1.61623 | 0.808113 | − | 0.589027i | \(-0.200489\pi\) | ||||
0.808113 | + | 0.589027i | \(0.200489\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1332.00 | −1.69971 | ||||||||
\(86\) | −465.403 | + | 268.701i | −0.583555 | + | 0.336915i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 176.000 | − | 304.841i | 0.213201 | − | 0.369274i | ||||
\(89\) | 347.677 | + | 602.193i | 0.414086 | + | 0.717218i | 0.995332 | − | 0.0965100i | \(-0.0307680\pi\) |
−0.581246 | + | 0.813728i | \(0.697435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 103.228 | + | 59.5987i | 0.113268 | + | 0.0653950i | ||||
\(95\) | 1631.36 | + | 941.866i | 1.76183 | + | 1.01719i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 566.187i | 0.592656i | 0.955086 | + | 0.296328i | \(0.0957621\pi\) | ||||
−0.955086 | + | 0.296328i | \(0.904238\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 368.748 | − | 638.690i | 0.363285 | − | 0.629228i | −0.625214 | − | 0.780453i | \(-0.714988\pi\) |
0.988499 | + | 0.151225i | \(0.0483218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −567.753 | + | 327.793i | −0.543130 | + | 0.313576i | −0.746347 | − | 0.665557i | \(-0.768194\pi\) |
0.203216 | + | 0.979134i | \(0.434861\pi\) | |||||||
\(104\) | 674.282 | 0.635757 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1012.00 | 0.927303 | ||||||||
\(107\) | 1718.32 | − | 992.071i | 1.55249 | − | 0.896328i | 0.554547 | − | 0.832152i | \(-0.312891\pi\) |
0.997939 | − | 0.0641758i | \(-0.0204418\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 422.000 | − | 730.925i | 0.370828 | − | 0.642293i | −0.618865 | − | 0.785497i | \(-0.712407\pi\) |
0.989693 | + | 0.143204i | \(0.0457405\pi\) | |||||||
\(110\) | −463.569 | − | 802.925i | −0.401814 | − | 0.695962i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 575.585i | 0.479172i | 0.970875 | + | 0.239586i | \(0.0770118\pi\) | ||||
−0.970875 | + | 0.239586i | \(0.922988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1419.38 | − | 819.482i | −1.15094 | − | 0.664496i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 238.395i | − | 0.185983i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −544.500 | − | 943.102i | −0.409091 | − | 0.708566i | ||||
\(122\) | 927.138 | − | 1605.85i | 0.688025 | − | 1.19169i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4087.83 | −2.92502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −220.000 | −0.153715 | −0.0768577 | − | 0.997042i | \(-0.524489\pi\) | ||||
−0.0768577 | + | 0.997042i | \(0.524489\pi\) | |||||||
\(128\) | −1254.14 | + | 724.077i | −0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 888.000 | − | 1538.06i | 0.599098 | − | 1.03767i | ||||
\(131\) | −653.211 | − | 1131.39i | −0.435659 | − | 0.754583i | 0.561691 | − | 0.827347i | \(-0.310151\pi\) |
−0.997349 | + | 0.0727646i | \(0.976818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 837.214i | 0.539734i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1238.73 | − | 715.184i | −0.781034 | − | 0.450930i | ||||
\(137\) | −1358.24 | − | 784.181i | −0.847025 | − | 0.489030i | 0.0126208 | − | 0.999920i | \(-0.495983\pi\) |
−0.859646 | + | 0.510890i | \(0.829316\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 655.585i | − | 0.400043i | −0.979791 | − | 0.200022i | \(-0.935899\pi\) | ||
0.979791 | − | 0.200022i | \(-0.0641012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 466.000 | + | 807.136i | 0.275393 | + | 0.476995i | ||||
\(143\) | −231.784 | + | 401.462i | −0.135544 | + | 0.234769i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2296.82 | + | 1326.07i | −1.31545 | + | 0.759477i | ||||
\(146\) | 2275.70 | 1.28999 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1270.06 | − | 733.270i | 0.698305 | − | 0.403166i | −0.108411 | − | 0.994106i | \(-0.534576\pi\) |
0.806716 | + | 0.590940i | \(0.201243\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −985.000 | + | 1706.07i | −0.530849 | + | 0.919457i | 0.468503 | + | 0.883462i | \(0.344793\pi\) |
−0.999352 | + | 0.0359952i | \(0.988540\pi\) | |||||||
\(152\) | 1011.42 | + | 1751.84i | 0.539719 | + | 0.934820i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5023.29i | − | 2.60310i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2271.01 | + | 1311.17i | 1.15444 | + | 0.666515i | 0.949965 | − | 0.312358i | \(-0.101119\pi\) |
0.204473 | + | 0.978872i | \(0.434452\pi\) | |||||||
\(158\) | −2047.77 | − | 1182.28i | −1.03109 | − | 0.595300i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 668.000 | + | 1157.01i | 0.320993 | + | 0.555976i | 0.980693 | − | 0.195553i | \(-0.0626502\pi\) |
−0.659700 | + | 0.751529i | \(0.729317\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2993.61 | − | 1728.36i | 1.39969 | − | 0.808113i | ||||
\(167\) | 2317.84 | 1.07401 | 0.537006 | − | 0.843578i | \(-0.319555\pi\) | ||||
0.537006 | + | 0.843578i | \(0.319555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1309.00 | 0.595812 | ||||||||
\(170\) | −3262.72 | + | 1883.73i | −1.47200 | + | 0.849857i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 115.892 | + | 200.731i | 0.0509313 | + | 0.0882157i | 0.890367 | − | 0.455243i | \(-0.150448\pi\) |
−0.839436 | + | 0.543459i | \(0.817114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 995.606i | − | 0.426401i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1703.26 | + | 983.378i | 0.717218 | + | 0.414086i | ||||
\(179\) | −94.3054 | − | 54.4472i | −0.0393783 | − | 0.0227351i | 0.480182 | − | 0.877169i | \(-0.340571\pi\) |
−0.519560 | + | 0.854434i | \(0.673904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2592.54i | 1.06465i | 0.846539 | + | 0.532326i | \(0.178682\pi\) | ||||
−0.846539 | + | 0.532326i | \(0.821318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −880.000 | − | 1524.20i | −0.352579 | − | 0.610684i | ||||
\(185\) | −1938.56 | + | 3357.68i | −0.770410 | + | 1.33439i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 851.630 | − | 491.689i | 0.333034 | − | 0.192277i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5328.00 | 2.03439 | ||||||||
\(191\) | −1926.52 | + | 1112.28i | −0.729834 | + | 0.421370i | −0.818362 | − | 0.574704i | \(-0.805117\pi\) |
0.0885272 | + | 0.996074i | \(0.471784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1870.00 | + | 3238.94i | −0.697438 | + | 1.20800i | 0.271914 | + | 0.962322i | \(0.412343\pi\) |
−0.969352 | + | 0.245677i | \(0.920990\pi\) | |||||||
\(194\) | 800.710 | + | 1386.87i | 0.296328 | + | 0.513255i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1197.84i | − | 0.433211i | −0.976259 | − | 0.216605i | \(-0.930502\pi\) | ||
0.976259 | − | 0.216605i | \(-0.0694985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −696.788 | − | 402.291i | −0.248211 | − | 0.143305i | 0.370734 | − | 0.928739i | \(-0.379106\pi\) |
−0.618945 | + | 0.785434i | \(0.712440\pi\) | |||||||
\(200\) | −6251.10 | − | 3609.07i | −2.21010 | − | 1.27600i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 2085.95i | − | 0.726570i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1110.00 | + | 1922.58i | 0.378174 | + | 0.655017i | ||||
\(206\) | −927.138 | + | 1605.85i | −0.313576 | + | 0.543130i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1651.65 | − | 953.579i | 0.550582 | − | 0.317879i | ||||
\(209\) | −1390.71 | −0.460274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3590.00 | 1.17131 | 0.585654 | − | 0.810561i | \(-0.300838\pi\) | ||||
0.585654 | + | 0.810561i | \(0.300838\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2806.00 | − | 4860.13i | 0.896328 | − | 1.55249i | ||||
\(215\) | −2001.77 | − | 3467.17i | −0.634976 | − | 1.09981i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 2387.19i | − | 0.741656i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1631.36 | + | 941.866i | 0.496548 | + | 0.286682i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3009.73i | − | 0.903796i | −0.892070 | − | 0.451898i | \(-0.850747\pi\) | ||
0.892070 | − | 0.451898i | \(-0.149253\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 814.000 | + | 1409.89i | 0.239586 | + | 0.414975i | ||||
\(227\) | 1854.28 | − | 3211.70i | 0.542170 | − | 0.939066i | −0.456609 | − | 0.889667i | \(-0.650936\pi\) |
0.998779 | − | 0.0493984i | \(-0.0157304\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 283.877 | − | 163.896i | 0.0819175 | − | 0.0472951i | −0.458482 | − | 0.888704i | \(-0.651607\pi\) |
0.540399 | + | 0.841409i | \(0.318273\pi\) | |||||||
\(230\) | −4635.69 | −1.32899 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2848.00 | −0.805950 | ||||||||
\(233\) | 557.259 | − | 321.734i | 0.156683 | − | 0.0904612i | −0.419608 | − | 0.907705i | \(-0.637833\pi\) |
0.576292 | + | 0.817244i | \(0.304499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −444.000 | + | 769.031i | −0.123248 | + | 0.213472i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 646.296i | − | 0.174918i | −0.996168 | − | 0.0874590i | \(-0.972125\pi\) | ||
0.996168 | − | 0.0874590i | \(-0.0278747\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −335.491 | − | 193.696i | −0.0896716 | − | 0.0517719i | 0.454494 | − | 0.890750i | \(-0.349820\pi\) |
−0.544165 | + | 0.838978i | \(0.683154\pi\) | |||||||
\(242\) | −2667.49 | − | 1540.08i | −0.708566 | − | 0.409091i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1332.00 | − | 2307.09i | −0.343130 | − | 0.594319i | ||||
\(248\) | 2697.13 | − | 4671.56i | 0.690596 | − | 1.19615i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10013.1 | + | 5781.07i | −2.53314 | + | 1.46251i | ||||
\(251\) | 6194.96 | 1.55786 | 0.778930 | − | 0.627111i | \(-0.215763\pi\) | ||||
0.778930 | + | 0.627111i | \(0.215763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1210.00 | 0.300680 | ||||||||
\(254\) | −538.888 | + | 311.127i | −0.133121 | + | 0.0768577i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1780.53 | + | 3083.96i | 0.432164 | + | 0.748530i | 0.997059 | − | 0.0766326i | \(-0.0244169\pi\) |
−0.564895 | + | 0.825162i | \(0.691084\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3200.06 | − | 1847.56i | −0.754583 | − | 0.435659i | ||||
\(263\) | −520.517 | − | 300.520i | −0.122040 | − | 0.0704596i | 0.437737 | − | 0.899103i | \(-0.355780\pi\) |
−0.559777 | + | 0.828643i | \(0.689113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7539.23i | 1.74767i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2433.74 | − | 4215.35i | 0.551626 | − | 0.955445i | −0.446531 | − | 0.894768i | \(-0.647341\pi\) |
0.998157 | − | 0.0606768i | \(-0.0193259\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1548.42 | − | 893.980i | 0.347084 | − | 0.200389i | −0.316316 | − | 0.948654i | \(-0.602446\pi\) |
0.663400 | + | 0.748265i | \(0.269113\pi\) | |||||||
\(272\) | −4045.69 | −0.901860 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4436.00 | −0.978060 | ||||||||
\(275\) | 4297.63 | − | 2481.24i | 0.942388 | − | 0.544088i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 563.000 | − | 975.145i | 0.122121 | − | 0.211519i | −0.798483 | − | 0.602017i | \(-0.794364\pi\) |
0.920604 | + | 0.390498i | \(0.127697\pi\) | |||||||
\(278\) | −927.138 | − | 1605.85i | −0.200022 | − | 0.346448i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5075.61i | − | 1.07753i | −0.842456 | − | 0.538765i | \(-0.818891\pi\) | ||
0.842456 | − | 0.538765i | \(-0.181109\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6167.87 | − | 3561.02i | −1.29555 | − | 0.747988i | −0.315921 | − | 0.948786i | \(-0.602313\pi\) |
−0.979633 | + | 0.200797i | \(0.935647\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1311.17i | 0.271088i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 458.500 | + | 794.145i | 0.0933238 | + | 0.161642i | ||||
\(290\) | −3750.69 | + | 6496.39i | −0.759477 | + | 1.31545i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 231.784 | 0.0462150 | 0.0231075 | − | 0.999733i | \(-0.492644\pi\) | ||||
0.0231075 | + | 0.999733i | \(0.492644\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1776.00 | 0.350518 | ||||||||
\(296\) | −3605.65 | + | 2081.72i | −0.708021 | + | 0.408776i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2074.00 | − | 3592.27i | 0.403166 | − | 0.698305i | ||||
\(299\) | 1158.92 | + | 2007.31i | 0.224154 | + | 0.388247i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5572.00i | 1.06170i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4954.94 | + | 2860.74i | 0.934820 | + | 0.539719i | ||||
\(305\) | 11963.3 | + | 6907.02i | 2.24596 | + | 1.29670i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8850.40i | − | 1.64534i | −0.568520 | − | 0.822669i | \(-0.692484\pi\) | ||
0.568520 | − | 0.822669i | \(-0.307516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7104.00 | − | 12304.5i | −1.30155 | − | 2.25435i | ||||
\(311\) | −3244.98 | + | 5620.47i | −0.591659 | + | 1.02478i | 0.402350 | + | 0.915486i | \(0.368194\pi\) |
−0.994009 | + | 0.109298i | \(0.965140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9393.74 | − | 5423.48i | 1.69638 | − | 0.979403i | 0.747230 | − | 0.664566i | \(-0.231383\pi\) |
0.949146 | − | 0.314837i | \(-0.101950\pi\) | |||||||
\(314\) | 7417.10 | 1.33303 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1541.95 | − | 890.247i | 0.273201 | − | 0.157733i | −0.357140 | − | 0.934051i | \(-0.616248\pi\) |
0.630341 | + | 0.776318i | \(0.282915\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 979.000 | − | 1695.68i | 0.171829 | − | 0.297617i | ||||
\(320\) | −5394.25 | − | 9343.12i | −0.942338 | − | 1.63218i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5651.20i | 0.973502i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8232.43 | + | 4752.99i | 1.40509 | + | 0.811226i | ||||
\(326\) | 3272.52 | + | 1889.39i | 0.555976 | + | 0.320993i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2383.95i | 0.401315i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4763.00 | + | 8249.76i | 0.790931 | + | 1.36993i | 0.925391 | + | 0.379014i | \(0.123737\pi\) |
−0.134460 | + | 0.990919i | \(0.542930\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5677.53 | − | 3277.93i | 0.930122 | − | 0.537006i | ||||
\(335\) | −6237.11 | −1.01722 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8272.00 | −1.33711 | −0.668553 | − | 0.743665i | \(-0.733086\pi\) | ||||
−0.668553 | + | 0.743665i | \(0.733086\pi\) | |||||||
\(338\) | 3206.38 | − | 1851.21i | 0.515989 | − | 0.297906i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1854.28 | + | 3211.70i | 0.294471 | + | 0.510039i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4299.21i | − | 0.673831i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 567.753 | + | 327.793i | 0.0882157 | + | 0.0509313i | ||||
\(347\) | 8474.01 | + | 4892.47i | 1.31098 | + | 0.756892i | 0.982258 | − | 0.187536i | \(-0.0600500\pi\) |
0.328718 | + | 0.944428i | \(0.393383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6317.46i | − | 0.968956i | −0.874803 | − | 0.484478i | \(-0.839010\pi\) | ||
0.874803 | − | 0.484478i | \(-0.160990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2728.73 | + | 4726.31i | −0.411433 | + | 0.712623i | −0.995047 | − | 0.0994085i | \(-0.968305\pi\) |
0.583614 | + | 0.812031i | \(0.301638\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6013.03 | + | 3471.62i | −0.898981 | + | 0.519027i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −308.000 | −0.0454701 | ||||||||
\(359\) | 9390.12 | − | 5421.39i | 1.38048 | − | 0.797019i | 0.388262 | − | 0.921549i | \(-0.373076\pi\) |
0.992216 | + | 0.124530i | \(0.0397423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 566.500 | − | 981.207i | 0.0825922 | − | 0.143054i | ||||
\(362\) | 3666.41 | + | 6350.40i | 0.532326 | + | 0.922016i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16953.6i | 2.43121i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3225.87 | + | 1862.46i | 0.458826 | + | 0.264903i | 0.711550 | − | 0.702635i | \(-0.247993\pi\) |
−0.252724 | + | 0.967538i | \(0.581327\pi\) | |||||||
\(368\) | −4311.10 | − | 2489.02i | −0.610684 | − | 0.352579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10966.2i | 1.54082i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2101.00 | − | 3639.04i | −0.291651 | − | 0.505154i | 0.682550 | − | 0.730839i | \(-0.260871\pi\) |
−0.974200 | + | 0.225686i | \(0.927538\pi\) | |||||||
\(374\) | 1390.71 | − | 2408.77i | 0.192277 | − | 0.333034i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −825.823 | + | 476.789i | −0.113268 | + | 0.0653950i | ||||
\(377\) | 3750.69 | 0.512389 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2506.00 | −0.339643 | −0.169821 | − | 0.985475i | \(-0.554319\pi\) | ||||
−0.169821 | + | 0.985475i | \(0.554319\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3146.00 | + | 5449.03i | −0.421370 | + | 0.729834i | ||||
\(383\) | 6553.18 | + | 11350.4i | 0.874286 | + | 1.51431i | 0.857521 | + | 0.514449i | \(0.172004\pi\) |
0.0167654 | + | 0.999859i | \(0.494663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10578.3i | 1.39488i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4011.04 | − | 2315.77i | −0.522796 | − | 0.301837i | 0.215282 | − | 0.976552i | \(-0.430933\pi\) |
−0.738078 | + | 0.674715i | \(0.764266\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 4916.89i | − | 0.635953i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1694.00 | − | 2934.09i | −0.216605 | − | 0.375171i | ||||
\(395\) | 8807.81 | − | 15255.6i | 1.12195 | − | 1.94327i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6967.88 | + | 4022.91i | −0.880877 | + | 0.508574i | −0.870947 | − | 0.491376i | \(-0.836494\pi\) |
−0.00992932 | + | 0.999951i | \(0.503161\pi\) | |||||||
\(398\) | −2275.70 | −0.286610 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20416.0 | −2.55200 | ||||||||
\(401\) | −11736.7 | + | 6776.20i | −1.46161 | + | 0.843859i | −0.999086 | − | 0.0427492i | \(-0.986388\pi\) |
−0.462521 | + | 0.886608i | \(0.653055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3552.00 | + | 6152.24i | −0.439051 | + | 0.760459i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2862.37i | − | 0.348605i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8800.18 | − | 5080.79i | −1.06391 | − | 0.614251i | −0.137402 | − | 0.990515i | \(-0.543875\pi\) |
−0.926512 | + | 0.376264i | \(0.877208\pi\) | |||||||
\(410\) | 5437.87 | + | 3139.55i | 0.655017 | + | 0.378174i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12876.0 | + | 22301.9i | 1.52303 | + | 2.63797i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3406.52 | + | 1966.76i | −0.398609 | + | 0.230137i | ||||
\(419\) | −8934.23 | −1.04168 | −0.520842 | − | 0.853653i | \(-0.674382\pi\) | ||||
−0.520842 | + | 0.853653i | \(0.674382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5606.00 | 0.648978 | 0.324489 | − | 0.945889i | \(-0.394808\pi\) | ||||
0.324489 | + | 0.945889i | \(0.394808\pi\) | |||||||
\(422\) | 8793.67 | − | 5077.03i | 1.01438 | − | 0.585654i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4048.00 | + | 7011.34i | −0.463652 | + | 0.803068i | ||||
\(425\) | −10082.6 | − | 17463.6i | −1.15077 | − | 1.99320i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9806.65 | − | 5661.87i | −1.09981 | − | 0.634976i | ||||
\(431\) | 765.466 | + | 441.942i | 0.0855480 | + | 0.0493911i | 0.542164 | − | 0.840273i | \(-0.317605\pi\) |
−0.456616 | + | 0.889664i | \(0.650939\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1966.76i | 0.218282i | 0.994026 | + | 0.109141i | \(0.0348101\pi\) | ||||
−0.994026 | + | 0.109141i | \(0.965190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3476.77 | + | 6021.93i | −0.380586 | + | 0.659195i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 335.491 | − | 193.696i | 0.0364740 | − | 0.0210583i | −0.481652 | − | 0.876363i | \(-0.659963\pi\) |
0.518126 | + | 0.855304i | \(0.326630\pi\) | |||||||
\(440\) | 7417.10 | 0.803628 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5328.00 | 0.573365 | ||||||||
\(443\) | −2271.90 | + | 1311.68i | −0.243660 | + | 0.140677i | −0.616858 | − | 0.787075i | \(-0.711595\pi\) |
0.373198 | + | 0.927752i | \(0.378261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7326.00 | + | 12689.0i | −0.780417 | + | 1.35172i | ||||
\(446\) | −4256.40 | − | 7372.31i | −0.451898 | − | 0.782711i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5140.67i | 0.540319i | 0.962816 | + | 0.270159i | \(0.0870764\pi\) | ||||
−0.962816 | + | 0.270159i | \(0.912924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1419.38 | − | 819.482i | −0.148195 | − | 0.0855607i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 10489.4i | − | 1.08434i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1804.00 | − | 3124.62i | −0.184655 | − | 0.319833i | 0.758805 | − | 0.651318i | \(-0.225784\pi\) |
−0.943460 | + | 0.331485i | \(0.892450\pi\) | |||||||
\(458\) | 463.569 | − | 802.925i | 0.0472951 | − | 0.0819175i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1538.21 | 0.155404 | 0.0777021 | − | 0.996977i | \(-0.475242\pi\) | ||||
0.0777021 | + | 0.996977i | \(0.475242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1772.00 | 0.177866 | 0.0889329 | − | 0.996038i | \(-0.471654\pi\) | ||||
0.0889329 | + | 0.996038i | \(0.471654\pi\) | |||||||
\(464\) | −6976.15 | + | 4027.68i | −0.697973 | + | 0.402975i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 910.000 | − | 1576.17i | 0.0904612 | − | 0.156683i | ||||
\(467\) | −6384.61 | − | 11058.5i | −0.632643 | − | 1.09577i | −0.987009 | − | 0.160663i | \(-0.948637\pi\) |
0.354366 | − | 0.935107i | \(-0.384697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2511.64i | 0.246497i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1651.65 | + | 953.579i | 0.161066 | + | 0.0929915i | ||||
\(473\) | 2559.72 | + | 1477.85i | 0.248829 | + | 0.143661i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28518.0i | 2.75472i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −914.000 | − | 1583.09i | −0.0874590 | − | 0.151483i | ||||
\(479\) | −2317.84 | + | 4014.62i | −0.221096 | + | 0.382950i | −0.955141 | − | 0.296151i | \(-0.904297\pi\) |
0.734045 | + | 0.679101i | \(0.237630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4748.48 | − | 2741.54i | 0.450129 | − | 0.259882i | ||||
\(482\) | −1095.71 | −0.103544 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10331.9 | + | 5965.15i | −0.967319 | + | 0.558482i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −979.000 | + | 1695.68i | −0.0910939 | + | 0.157779i | −0.907972 | − | 0.419032i | \(-0.862370\pi\) |
0.816878 | + | 0.576811i | \(0.195703\pi\) | |||||||
\(488\) | 7417.10 | + | 12846.8i | 0.688025 | + | 1.19169i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7126.22i | 0.654994i | 0.944852 | + | 0.327497i | \(0.106205\pi\) | ||||
−0.944852 | + | 0.327497i | \(0.893795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6890.46 | − | 3978.21i | −0.629474 | − | 0.363427i | ||||
\(494\) | −6525.44 | − | 3767.46i | −0.594319 | − | 0.343130i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 15257.3i | − | 1.38119i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5155.00 | − | 8928.72i | −0.462464 | − | 0.801011i | 0.536619 | − | 0.843825i | \(-0.319701\pi\) |
−0.999083 | + | 0.0428136i | \(0.986368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15174.5 | − | 8761.00i | 1.34915 | − | 0.778930i | ||||
\(503\) | 126.428 | 0.0112070 | 0.00560352 | − | 0.999984i | \(-0.498216\pi\) | ||||
0.00560352 | + | 0.999984i | \(0.498216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15540.0 | 1.36935 | ||||||||
\(506\) | 2963.88 | − | 1711.20i | 0.260397 | − | 0.150340i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3550.52 | + | 6149.67i | 0.309182 | + | 0.535520i | 0.978184 | − | 0.207742i | \(-0.0666113\pi\) |
−0.669001 | + | 0.743261i | \(0.733278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11585.2i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8722.76 | + | 5036.09i | 0.748530 | + | 0.432164i | ||||
\(515\) | −11963.3 | − | 6907.02i | −1.02362 | − | 0.590990i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 655.585i | − | 0.0557691i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7104.00 | + | 12304.5i | 0.599098 | + | 1.03767i | ||||
\(521\) | −2244.09 | + | 3886.89i | −0.188705 | + | 0.326847i | −0.944819 | − | 0.327593i | \(-0.893762\pi\) |
0.756113 | + | 0.654441i | \(0.227096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8051.78 | + | 4648.70i | −0.673192 | + | 0.388668i | −0.797285 | − | 0.603603i | \(-0.793731\pi\) |
0.124093 | + | 0.992271i | \(0.460398\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1700.00 | −0.140919 | ||||||||
\(527\) | 13050.9 | − | 7534.93i | 1.07876 | − | 0.622821i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3058.50 | + | 5297.48i | −0.251377 | + | 0.435397i | ||||
\(530\) | 10662.1 | + | 18467.3i | 0.873833 | + | 1.51352i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3139.55i | − | 0.255139i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36207.2 | + | 20904.2i | 2.92593 | + | 1.68929i | ||||
\(536\) | −5800.39 | − | 3348.86i | −0.467423 | − | 0.269867i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 13767.3i | − | 1.10325i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7823.00 | + | 13549.8i | 0.621695 | + | 1.07681i | 0.989170 | + | 0.146774i | \(0.0468890\pi\) |
−0.367475 | + | 0.930033i | \(0.619778\pi\) | |||||||
\(542\) | 2528.56 | − | 4379.59i | 0.200389 | − | 0.347084i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17784.2 | 1.39778 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1880.00 | 0.146952 | 0.0734762 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734762 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7018.00 | − | 12155.5i | 0.544088 | − | 0.942388i | ||||
\(551\) | 5626.04 | + | 9744.59i | 0.434986 | + | 0.753418i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 3184.81i | − | 0.244241i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6063.71 | + | 3500.89i | 0.461271 | + | 0.266315i | 0.712578 | − | 0.701593i | \(-0.247527\pi\) |
−0.251308 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5661.87i | 0.428393i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7178.00 | − | 12432.7i | −0.538765 | − | 0.933168i | ||||
\(563\) | −4193.19 | + | 7262.82i | −0.313893 | + | 0.543679i | −0.979202 | − | 0.202890i | \(-0.934967\pi\) |
0.665308 | + | 0.746569i | \(0.268300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10503.4 | + | 6064.16i | −0.782094 | + | 0.451542i | ||||
\(566\) | −20144.2 | −1.49598 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7456.00 | −0.550787 | ||||||||
\(569\) | −15506.5 | + | 8952.68i | −1.14247 | + | 0.659606i | −0.947041 | − | 0.321112i | \(-0.895944\pi\) |
−0.195430 | + | 0.980718i | \(0.562610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12368.0 | − | 21422.0i | 0.906453 | − | 1.57002i | 0.0874983 | − | 0.996165i | \(-0.472113\pi\) |
0.818955 | − | 0.573858i | \(-0.194554\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 24812.4i | − | 1.79956i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15019.7 | − | 8671.60i | −1.08367 | − | 0.625656i | −0.151785 | − | 0.988414i | \(-0.548502\pi\) |
−0.931884 | + | 0.362757i | \(0.881835\pi\) | |||||||
\(578\) | 2246.18 | + | 1296.83i | 0.161642 | + | 0.0933238i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2783.00 | − | 4820.30i | −0.197702 | − | 0.342429i | ||||
\(584\) | −9102.80 | + | 15766.5i | −0.644994 | + | 1.11716i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 567.753 | − | 327.793i | 0.0400233 | − | 0.0231075i | ||||
\(587\) | −3329.27 | −0.234095 | −0.117047 | − | 0.993126i | \(-0.537343\pi\) | ||||
−0.117047 | + | 0.993126i | \(0.537343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21312.0 | −1.49091 | ||||||||
\(590\) | 4350.29 | − | 2511.64i | 0.303557 | − | 0.175259i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5888.00 | + | 10198.3i | −0.408776 | + | 0.708021i | ||||
\(593\) | −11283.7 | − | 19543.9i | −0.781392 | − | 1.35341i | −0.931131 | − | 0.364685i | \(-0.881177\pi\) |
0.149739 | − | 0.988726i | \(-0.452157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5677.53 | + | 3277.93i | 0.388247 | + | 0.224154i | ||||
\(599\) | −21838.4 | − | 12608.4i | −1.48964 | − | 0.860044i | −0.489709 | − | 0.871886i | \(-0.662897\pi\) |
−0.999930 | + | 0.0118422i | \(0.996230\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13290.5i | − | 0.902048i | −0.892512 | − | 0.451024i | \(-0.851059\pi\) | ||
0.892512 | − | 0.451024i | \(-0.148941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11473.3 | − | 19872.4i | 0.771003 | − | 1.33542i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15922.9 | − | 9193.09i | 1.06473 | − | 0.614722i | 0.137993 | − | 0.990433i | \(-0.455935\pi\) |
0.926737 | + | 0.375711i | \(0.122602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39072.0 | 2.59341 | ||||||||
\(611\) | 1087.57 | − | 627.911i | 0.0720107 | − | 0.0415754i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13277.0 | − | 22996.4i | 0.874801 | − | 1.51520i | 0.0178263 | − | 0.999841i | \(-0.494325\pi\) |
0.856975 | − | 0.515359i | \(-0.172341\pi\) | |||||||
\(614\) | −12516.4 | − | 21679.0i | −0.822669 | − | 1.42491i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 26475.5i | − | 1.72749i | −0.503927 | − | 0.863746i | \(-0.668112\pi\) | ||
0.503927 | − | 0.863746i | \(-0.331888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14193.8 | − | 8194.82i | −0.921645 | − | 0.532112i | −0.0374857 | − | 0.999297i | \(-0.511935\pi\) |
−0.884160 | + | 0.467185i | \(0.845268\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18356.4i | 1.18332i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23130.5 | − | 40063.2i | −1.48035 | − | 2.56404i | ||||
\(626\) | 15339.9 | − | 26569.5i | 0.979403 | − | 1.69638i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11631.4 | −0.737318 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24860.0 | 1.56840 | 0.784200 | − | 0.620508i | \(-0.213073\pi\) | ||||
0.784200 | + | 0.620508i | \(0.213073\pi\) | |||||||
\(632\) | 16382.2 | − | 9458.26i | 1.03109 | − | 0.595300i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2518.00 | − | 4361.30i | 0.157733 | − | 0.273201i | ||||
\(635\) | −2317.84 | − | 4014.62i | −0.144852 | − | 0.250890i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 5538.06i | − | 0.343658i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26426.3 | − | 15257.3i | −1.63218 | − | 0.942338i | ||||
\(641\) | 4571.97 | + | 2639.63i | 0.281719 | + | 0.162651i | 0.634201 | − | 0.773168i | \(-0.281329\pi\) |
−0.352482 | + | 0.935819i | \(0.614662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2652.14i | 0.162660i | 0.996687 | + | 0.0813299i | \(0.0259167\pi\) | ||||
−0.996687 | + | 0.0813299i | \(0.974083\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7992.00 | + | 13842.6i | 0.486751 | + | 0.843077i | ||||
\(647\) | −11504.9 | + | 19927.1i | −0.699081 | + | 1.21084i | 0.269704 | + | 0.962943i | \(0.413074\pi\) |
−0.968785 | + | 0.247901i | \(0.920259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1135.51 | + | 655.585i | −0.0686788 | + | 0.0396517i | ||||
\(650\) | 26887.0 | 1.62245 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5079.02 | + | 2932.37i | −0.304376 | + | 0.175731i | −0.644407 | − | 0.764683i | \(-0.722896\pi\) |
0.340031 | + | 0.940414i | \(0.389562\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13764.0 | − | 23839.9i | 0.821075 | − | 1.42214i | ||||
\(656\) | 3371.41 | + | 5839.45i | 0.200658 | + | 0.347549i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2759.13i | − | 0.163096i | −0.996669 | − | 0.0815482i | \(-0.974014\pi\) | ||
0.996669 | − | 0.0815482i | \(-0.0259864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18168.1 | − | 10489.4i | −1.06907 | − | 0.617230i | −0.141145 | − | 0.989989i | \(-0.545078\pi\) |
−0.927928 | + | 0.372759i | \(0.878412\pi\) | |||||||
\(662\) | 23333.8 | + | 13471.8i | 1.36993 | + | 0.790931i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 27653.8i | 1.61623i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4895.00 | − | 8478.39i | −0.284161 | − | 0.492181i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −15277.7 | + | 8820.60i | −0.880941 | + | 0.508611i | ||||
\(671\) | −10198.5 | −0.586750 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13636.0 | −0.781024 | −0.390512 | − | 0.920598i | \(-0.627702\pi\) | ||||
−0.390512 | + | 0.920598i | \(0.627702\pi\) | |||||||
\(674\) | −20262.2 | + | 11698.4i | −1.15797 | + | 0.668553i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4983.36 | + | 8631.44i | 0.282904 | + | 0.490005i | 0.972099 | − | 0.234572i | \(-0.0753688\pi\) |
−0.689194 | + | 0.724576i | \(0.742035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 30139.7i | − | 1.69971i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9084.06 | + | 5244.68i | 0.510039 | + | 0.294471i | ||||
\(683\) | −175.139 | − | 101.116i | −0.00981184 | − | 0.00566487i | 0.495086 | − | 0.868844i | \(-0.335137\pi\) |
−0.504898 | + | 0.863179i | \(0.668470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 33047.5i | − | 1.84333i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6080.00 | − | 10530.9i | −0.336915 | − | 0.583555i | ||||
\(689\) | 5331.04 | − | 9233.63i | 0.294770 | − | 0.510556i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17393.9 | + | 10042.4i | −0.957591 | + | 0.552865i | −0.895431 | − | 0.445201i | \(-0.853132\pi\) |
−0.0621600 | + | 0.998066i | \(0.519799\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27676.0 | 1.51378 | ||||||||
\(695\) | 11963.3 | − | 6907.02i | 0.652941 | − | 0.376976i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3330.00 | + | 5767.73i | −0.180965 | + | 0.313441i | ||||
\(698\) | −8934.23 | − | 15474.5i | −0.484478 | − | 0.839141i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22883.4i | 1.23294i | 0.787377 | + | 0.616472i | \(0.211439\pi\) | ||||
−0.787377 | + | 0.616472i | \(0.788561\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14245.5 | + | 8224.61i | 0.764264 | + | 0.441248i | ||||
\(704\) | 6897.76 | + | 3982.43i | 0.369274 | + | 0.213201i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15436.1i | 0.822866i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6106.00 | − | 10575.9i | −0.323435 | − | 0.560206i | 0.657759 | − | 0.753228i | \(-0.271504\pi\) |
−0.981194 | + | 0.193022i | \(0.938171\pi\) | |||||||
\(710\) | −9819.23 | + | 17007.4i | −0.519027 | + | 0.898981i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −13626.1 | + | 7867.02i | −0.717218 | + | 0.414086i | ||||
\(713\) | 18542.8 | 0.973957 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9768.00 | −0.510913 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15334.0 | − | 26559.3i | 0.797019 | − | 1.38048i | ||||
\(719\) | 14412.8 | + | 24963.7i | 0.747574 | + | 1.29484i | 0.948982 | + | 0.315329i | \(0.102115\pi\) |
−0.201408 | + | 0.979507i | \(0.564552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 3204.61i | − | 0.165184i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34771.7 | − | 20075.5i | −1.78123 | − | 1.02839i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 3277.93i | − | 0.167224i | −0.996498 | − | 0.0836118i | \(-0.973354\pi\) | ||
0.996498 | − | 0.0836118i | \(-0.0266456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23976.0 | + | 41527.7i | 1.21560 | + | 2.10549i | ||||
\(731\) | 6005.32 | − | 10401.5i | 0.303851 | − | 0.526285i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10503.4 | − | 6064.16i | 0.529268 | − | 0.305573i | −0.211450 | − | 0.977389i | \(-0.567819\pi\) |
0.740718 | + | 0.671816i | \(0.234485\pi\) | |||||||
\(734\) | 10535.7 | 0.529807 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3987.77 | − | 2302.34i | 0.199310 | − | 0.115072i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −880.000 | + | 1524.20i | −0.0438042 | + | 0.0758711i | −0.887096 | − | 0.461584i | \(-0.847281\pi\) |
0.843292 | + | 0.537456i | \(0.180614\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 22436.5i | − | 1.10783i | −0.832574 | − | 0.553913i | \(-0.813134\pi\) | ||
0.832574 | − | 0.553913i | \(-0.186866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26761.8 | + | 15451.0i | 1.31608 | + | 0.759838i | ||||
\(746\) | −10292.8 | − | 5942.53i | −0.505154 | − | 0.291651i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2561.00 | + | 4435.78i | 0.124437 | + | 0.215531i | 0.921513 | − | 0.388348i | \(-0.126954\pi\) |
−0.797076 | + | 0.603879i | \(0.793621\pi\) | |||||||
\(752\) | −1348.56 | + | 2335.78i | −0.0653950 | + | 0.113268i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9187.28 | − | 5304.28i | 0.443742 | − | 0.256194i | ||||
\(755\) | −41510.5 | −2.00095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18772.0 | −0.901295 | −0.450647 | − | 0.892702i | \(-0.648807\pi\) | ||||
−0.450647 | + | 0.892702i | \(0.648807\pi\) | |||||||
\(758\) | −6138.42 | + | 3544.02i | −0.294139 | + | 0.169821i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21312.0 | + | 36913.5i | −1.01719 | + | 1.76183i | ||||
\(761\) | 14486.5 | + | 25091.4i | 0.690061 | + | 1.19522i | 0.971818 | + | 0.235734i | \(0.0757495\pi\) |
−0.281757 | + | 0.959486i | \(0.590917\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32103.9 | + | 18535.2i | 1.51431 | + | 0.874286i | ||||
\(767\) | −2175.15 | − | 1255.82i | −0.102399 | − | 0.0591201i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 11740.9i | − | 0.550571i | −0.961363 | − | 0.275285i | \(-0.911228\pi\) | ||
0.961363 | − | 0.275285i | \(-0.0887724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6353.00 | − | 11003.7i | 0.295603 | − | 0.512000i | −0.679522 | − | 0.733655i | \(-0.737813\pi\) |
0.975125 | + | 0.221655i | \(0.0711460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 65859.4 | − | 38023.9i | 3.05257 | − | 1.76240i | ||||
\(776\) | −12811.4 | −0.592656 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13100.0 | −0.603673 | ||||||||
\(779\) | 8156.80 | − | 4709.33i | 0.375158 | − | 0.216597i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2563.00 | − | 4439.25i | 0.117428 | − | 0.203391i | ||||
\(782\) | −6953.53 | − | 12043.9i | −0.317977 | − | 0.550752i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55256.2i | 2.51233i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22813.4 | − | 13171.3i | −1.03330 | − | 0.596577i | −0.115373 | − | 0.993322i | \(-0.536806\pi\) |
−0.917929 | + | 0.396745i | \(0.870140\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 49824.5i | − | 2.24389i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9768.00 | − | 16918.7i | −0.437417 | − | 0.757629i | ||||
\(794\) | −11378.5 | + | 19708.2i | −0.508574 | + | 0.880877i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19448.8 | 0.864382 | 0.432191 | − | 0.901782i | \(-0.357741\pi\) | ||||
0.432191 | + | 0.901782i | \(0.357741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2664.00 | −0.117954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19166.0 | + | 33196.5i | −0.843859 | + | 1.46161i | ||||
\(803\) | −6258.18 | − | 10839.5i | −0.275027 | − | 0.476360i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20093.1i | 0.878103i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14451.9 | + | 8343.81i | 0.629228 | + | 0.363285i | ||||
\(809\) | −29958.5 | − | 17296.5i | −1.30196 | − | 0.751686i | −0.321219 | − | 0.947005i | \(-0.604092\pi\) |
−0.980740 | + | 0.195319i | \(0.937426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28607.4i | 1.23864i | 0.785137 | + | 0.619322i | \(0.212592\pi\) | ||||
−0.785137 | + | 0.619322i | \(0.787408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4048.00 | − | 7011.34i | −0.174303 | − | 0.301901i | ||||
\(815\) | −14075.6 | + | 24379.7i | −0.604967 | + | 1.04783i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14710.0 | + | 8492.81i | −0.629911 | + | 0.363679i | ||||
\(818\) | −28741.3 | −1.22850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24655.3 | + | 14234.8i | −1.04808 | + | 0.605112i | −0.922112 | − | 0.386922i | \(-0.873538\pi\) |
−0.125972 | + | 0.992034i | \(0.540205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11734.0 | + | 20323.9i | −0.496988 | + | 0.860809i | −0.999994 | − | 0.00347391i | \(-0.998894\pi\) |
0.503005 | + | 0.864283i | \(0.332228\pi\) | |||||||
\(824\) | −7417.10 | − | 12846.8i | −0.313576 | − | 0.543130i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 37447.0i | − | 1.57456i | −0.616598 | − | 0.787278i | \(-0.711489\pi\) | ||
0.616598 | − | 0.787278i | \(-0.288511\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9367.93 | + | 5408.58i | 0.392475 | + | 0.226596i | 0.683232 | − | 0.730201i | \(-0.260574\pi\) |
−0.290757 | + | 0.956797i | \(0.593907\pi\) | |||||||
\(830\) | 63079.3 | + | 36418.8i | 2.63797 | + | 1.52303i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15257.3i | 0.635757i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24420.0 | + | 42296.7i | 1.01208 | + | 1.75298i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21884.3 | + | 12634.9i | −0.902125 | + | 0.520842i | ||||
\(839\) | 42690.5 | 1.75666 | 0.878331 | − | 0.478054i | \(-0.158658\pi\) | ||||
0.878331 | + | 0.478054i | \(0.158658\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8547.00 | 0.350445 | ||||||||
\(842\) | 13731.8 | − | 7928.08i | 0.562031 | − | 0.324489i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13791.2 | + | 23887.0i | 0.561456 | + | 0.972471i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 22898.9i | 0.927303i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −49394.6 | − | 28518.0i | −1.99320 | − | 1.15077i | ||||
\(851\) | −12394.4 | − | 7155.92i | −0.499266 | − | 0.288251i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4589.10i | 0.184206i | 0.995749 | + | 0.0921030i | \(0.0293589\pi\) | ||||
−0.995749 | + | 0.0921030i | \(0.970641\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22448.0 | + | 38881.1i | 0.896328 | + | 1.55249i | ||||
\(857\) | 2391.59 | − | 4142.36i | 0.0953270 | − | 0.165111i | −0.814418 | − | 0.580279i | \(-0.802944\pi\) |
0.909745 | + | 0.415167i | \(0.136277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32078.1 | + | 18520.3i | −1.27414 | + | 0.735627i | −0.975765 | − | 0.218820i | \(-0.929779\pi\) |
−0.298379 | + | 0.954448i | \(0.596446\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2500.00 | 0.0987823 | ||||||||
\(863\) | 1034.91 | − | 597.505i | 0.0408212 | − | 0.0235682i | −0.479450 | − | 0.877569i | \(-0.659164\pi\) |
0.520272 | + | 0.854001i | \(0.325831\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2442.00 | + | 4229.67i | −0.0959890 | + | 0.166258i | ||||
\(866\) | 2781.41 | + | 4817.55i | 0.109141 | + | 0.189038i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13005.1i | 0.507673i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7638.86 | + | 4410.30i | 0.297168 | + | 0.171570i | ||||
\(872\) | 16539.0 | + | 9548.77i | 0.642293 | + | 0.370828i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 19667.6i | 0.761173i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17149.0 | − | 29702.9i | −0.660297 | − | 1.14367i | −0.980538 | − | 0.196332i | \(-0.937097\pi\) |
0.320240 | − | 0.947336i | \(-0.396236\pi\) | |||||||
\(878\) | 547.854 | − | 948.911i | 0.0210583 | − | 0.0364740i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18168.1 | − | 10489.4i | 0.695962 | − | 0.401814i | ||||
\(881\) | 21682.4 | 0.829169 | 0.414584 | − | 0.910011i | \(-0.363927\pi\) | ||||
0.414584 | + | 0.910011i | \(0.363927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16034.0 | 0.611084 | 0.305542 | − | 0.952179i | \(-0.401162\pi\) | ||||
0.305542 | + | 0.952179i | \(0.401162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3710.00 | + | 6425.91i | −0.140677 | + | 0.243660i | ||||
\(887\) | −23410.2 | − | 40547.7i | −0.886176 | − | 1.53490i | −0.844360 | − | 0.535777i | \(-0.820019\pi\) |
−0.0418168 | − | 0.999125i | \(-0.513315\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 41442.1i | 1.56083i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3262.72 | + | 1883.73i | 0.122265 | + | 0.0705898i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2294.55i | − | 0.0856964i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7270.00 | + | 12592.0i | 0.270159 | + | 0.467930i | ||||
\(899\) | 15002.8 | − | 25985.6i | 0.556586 | − | 0.964034i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19587.5 | + | 11308.8i | −0.724255 | + | 0.418149i | ||||
\(902\) | −4635.69 | −0.171121 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13024.0 | −0.479172 | ||||||||
\(905\) | −47309.4 | + | 27314.1i | −1.73770 | + | 1.00326i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25861.0 | + | 44792.6i | −0.946748 | + | 1.63982i | −0.194535 | + | 0.980896i | \(0.562320\pi\) |
−0.752213 | + | 0.658920i | \(0.771014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38564.2i | 1.40251i | 0.712909 | + | 0.701256i | \(0.247377\pi\) | ||||
−0.712909 | + | 0.701256i | \(0.752623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16464.9 | − | 9505.99i | −0.596831 | − | 0.344581i | ||||
\(914\) | −8837.76 | − | 5102.48i | −0.319833 | − | 0.184655i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15235.0 | − | 26387.8i | −0.546851 | − | 0.947174i | −0.998488 | − | 0.0549722i | \(-0.982493\pi\) |
0.451637 | − | 0.892202i | \(-0.350840\pi\) | |||||||
\(920\) | 18542.8 | − | 32117.0i | 0.664496 | − | 1.15094i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3767.82 | − | 2175.35i | 0.134584 | − | 0.0777021i | ||||
\(923\) | 9819.23 | 0.350167 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58696.0 | −2.08639 | ||||||||
\(926\) | 4340.50 | − | 2505.99i | 0.154036 | − | 0.0889329i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13222.2 | − | 22901.6i | −0.466962 | − | 0.808802i | 0.532326 | − | 0.846540i | \(-0.321318\pi\) |
−0.999288 | + | 0.0377376i | \(0.987985\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31278.1 | − | 18058.4i | −1.09577 | − | 0.632643i | ||||
\(935\) | 17945.0 | + | 10360.5i | 0.627661 | + | 0.362380i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19667.6i | 0.685711i | 0.939388 | + | 0.342855i | \(0.111394\pi\) | ||||
−0.939388 | + | 0.342855i | \(0.888606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1970.17 | − | 3412.43i | 0.0682525 | − | 0.118217i | −0.829880 | − | 0.557942i | \(-0.811591\pi\) |
0.898132 | + | 0.439726i | \(0.144924\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7096.92 | + | 4097.41i | −0.245077 | + | 0.141495i | ||||
\(944\) | 5394.25 | 0.185983 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8360.00 | 0.287322 | ||||||||
\(947\) | 45103.7 | − | 26040.6i | 1.54770 | − | 0.893565i | 0.549384 | − | 0.835570i | \(-0.314862\pi\) |
0.998317 | − | 0.0579954i | \(-0.0184709\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11988.0 | − | 20763.8i | 0.410060 | − | 0.710245i | ||||
\(950\) | 40330.5 | + | 69854.4i | 1.37736 | + | 2.38566i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15993.3i | 0.543626i | 0.962350 | + | 0.271813i | \(0.0876231\pi\) | ||||
−0.962350 | + | 0.271813i | \(0.912377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −40594.4 | − | 23437.2i | −1.37550 | − | 0.794146i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13111.7i | 0.442192i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13520.5 | + | 23418.2i | 0.453845 | + | 0.786083i | ||||
\(962\) | 7754.24 | − | 13430.7i | 0.259882 | − | 0.450129i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −78806.7 | −2.62889 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24772.0 | −0.823799 | −0.411900 | − | 0.911229i | \(-0.635135\pi\) | ||||
−0.411900 | + | 0.911229i | \(0.635135\pi\) | |||||||
\(968\) | 21340.0 | − | 12320.6i | 0.708566 | − | 0.409091i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16872.0 | + | 29223.2i | −0.558482 | + | 0.967319i | ||||
\(971\) | −27561.3 | − | 47737.5i | −0.910899 | − | 1.57772i | −0.812797 | − | 0.582548i | \(-0.802056\pi\) |
−0.0981028 | − | 0.995176i | \(-0.531277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5538.06i | 0.182188i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36336.2 | + | 20978.7i | 1.19169 | + | 0.688025i | ||||
\(977\) | 39109.8 | + | 22580.0i | 1.28069 | + | 0.739406i | 0.976974 | − | 0.213357i | \(-0.0684399\pi\) |
0.303714 | + | 0.952763i | \(0.401773\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 10817.2i | − | 0.353134i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10078.0 | + | 17455.6i | 0.327497 | + | 0.567241i | ||||
\(983\) | −16920.3 | + | 29306.7i | −0.549006 | + | 0.950906i | 0.449337 | + | 0.893362i | \(0.351660\pi\) |
−0.998343 | + | 0.0575434i | \(0.981673\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21858.5 | − | 12620.0i | 0.707076 | − | 0.408231i | ||||
\(986\) | −22504.2 | −0.726854 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12798.6 | − | 7389.27i | 0.411498 | − | 0.237578i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9191.00 | − | 15919.3i | 0.294613 | − | 0.510285i | −0.680282 | − | 0.732951i | \(-0.738143\pi\) |
0.974895 | + | 0.222666i | \(0.0714758\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 16953.6i | − | 0.540166i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33497.5 | + | 19339.8i | 1.06407 | + | 0.614340i | 0.926555 | − | 0.376160i | \(-0.122756\pi\) |
0.137513 | + | 0.990500i | \(0.456089\pi\) | |||||||
\(998\) | −25254.2 | − | 14580.5i | −0.801011 | − | 0.462464i | ||||
\(999\) | 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 | 441.4.p.a.80.4 | 8 | ||
3.2 | odd | 2 | inner | 441.4.p.a.80.1 | 8 | ||
7.2 | even | 3 | inner | 441.4.p.a.215.2 | 8 | ||
7.3 | odd | 6 | 63.4.c.b.62.4 | yes | 4 | ||
7.4 | even | 3 | 63.4.c.b.62.3 | yes | 4 | ||
7.5 | odd | 6 | inner | 441.4.p.a.215.1 | 8 | ||
7.6 | odd | 2 | inner | 441.4.p.a.80.3 | 8 | ||
21.2 | odd | 6 | inner | 441.4.p.a.215.3 | 8 | ||
21.5 | even | 6 | inner | 441.4.p.a.215.4 | 8 | ||
21.11 | odd | 6 | 63.4.c.b.62.2 | yes | 4 | ||
21.17 | even | 6 | 63.4.c.b.62.1 | ✓ | 4 | ||
21.20 | even | 2 | inner | 441.4.p.a.80.2 | 8 | ||
28.3 | even | 6 | 1008.4.k.b.881.4 | 4 | |||
28.11 | odd | 6 | 1008.4.k.b.881.1 | 4 | |||
84.11 | even | 6 | 1008.4.k.b.881.3 | 4 | |||
84.59 | odd | 6 | 1008.4.k.b.881.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.c.b.62.1 | ✓ | 4 | 21.17 | even | 6 | ||
63.4.c.b.62.2 | yes | 4 | 21.11 | odd | 6 | ||
63.4.c.b.62.3 | yes | 4 | 7.4 | even | 3 | ||
63.4.c.b.62.4 | yes | 4 | 7.3 | odd | 6 | ||
441.4.p.a.80.1 | 8 | 3.2 | odd | 2 | inner | ||
441.4.p.a.80.2 | 8 | 21.20 | even | 2 | inner | ||
441.4.p.a.80.3 | 8 | 7.6 | odd | 2 | inner | ||
441.4.p.a.80.4 | 8 | 1.1 | even | 1 | trivial | ||
441.4.p.a.215.1 | 8 | 7.5 | odd | 6 | inner | ||
441.4.p.a.215.2 | 8 | 7.2 | even | 3 | inner | ||
441.4.p.a.215.3 | 8 | 21.2 | odd | 6 | inner | ||
441.4.p.a.215.4 | 8 | 21.5 | even | 6 | inner | ||
1008.4.k.b.881.1 | 4 | 28.11 | odd | 6 | |||
1008.4.k.b.881.2 | 4 | 84.59 | odd | 6 | |||
1008.4.k.b.881.3 | 4 | 84.11 | even | 6 | |||
1008.4.k.b.881.4 | 4 | 28.3 | even | 6 |