Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,4,Mod(125,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.125");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.i (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.7369626429\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 125.16 | ||
Character | \(\chi\) | \(=\) | 504.125 |
Dual form | 504.4.i.b.125.14 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45064 | + | 1.41222i | −0.866432 | + | 0.499296i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.01126 | − | 6.92169i | 0.501408 | − | 0.865211i | ||||
\(5\) | 21.1851i | 1.89485i | 0.319975 | + | 0.947426i | \(0.396326\pi\) | ||||
−0.319975 | + | 0.947426i | \(0.603674\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.58217 | − | 16.8971i | 0.409399 | − | 0.912356i | ||||
\(8\) | −0.0551907 | + | 22.6273i | −0.00243911 | + | 0.999997i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −29.9180 | − | 51.9170i | −0.946092 | − | 1.64176i | ||||
\(11\) | −34.6846 | −0.950708 | −0.475354 | − | 0.879795i | \(-0.657680\pi\) | ||||
−0.475354 | + | 0.879795i | \(0.657680\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.0348 | 0.854128 | 0.427064 | − | 0.904221i | \(-0.359548\pi\) | ||||
0.427064 | + | 0.904221i | \(0.359548\pi\) | |||||||
\(14\) | 5.28124 | + | 52.1163i | 0.100819 | + | 0.994905i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −31.8196 | − | 55.5294i | −0.497181 | − | 0.867647i | ||||
\(17\) | −76.5612 | −1.09228 | −0.546142 | − | 0.837693i | \(-0.683904\pi\) | ||||
−0.546142 | + | 0.837693i | \(0.683904\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.05838 | 0.0369285 | 0.0184642 | − | 0.999830i | \(-0.494122\pi\) | ||||
0.0184642 | + | 0.999830i | \(0.494122\pi\) | |||||||
\(20\) | 146.637 | + | 84.9789i | 1.63945 | + | 0.950093i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 84.9993 | − | 48.9823i | 0.823723 | − | 0.474684i | ||||
\(23\) | − | 181.651i | − | 1.64682i | −0.567445 | − | 0.823411i | \(-0.692068\pi\) | ||
0.567445 | − | 0.823411i | \(-0.307932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −323.808 | −2.59046 | ||||||||
\(26\) | −98.1109 | + | 56.5380i | −0.740043 | + | 0.426462i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −86.5422 | − | 120.260i | −0.584105 | − | 0.811678i | ||||
\(29\) | −79.6686 | −0.510141 | −0.255070 | − | 0.966922i | \(-0.582099\pi\) | ||||
−0.255070 | + | 0.966922i | \(0.582099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 25.5766i | − | 0.148183i | −0.997251 | − | 0.0740917i | \(-0.976394\pi\) | ||
0.997251 | − | 0.0740917i | \(-0.0236058\pi\) | |||||||
\(32\) | 156.398 | + | 91.1462i | 0.863986 | + | 0.503516i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 187.624 | − | 108.121i | 0.946389 | − | 0.545373i | ||||
\(35\) | 357.966 | + | 160.629i | 1.72878 | + | 0.775750i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 162.762i | 0.723185i | 0.932336 | + | 0.361593i | \(0.117767\pi\) | ||||
−0.932336 | + | 0.361593i | \(0.882233\pi\) | |||||||
\(38\) | −7.49499 | + | 4.31911i | −0.0319960 | + | 0.0184382i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −479.362 | − | 1.16922i | −1.89485 | − | 0.00462175i | ||||
\(41\) | 191.358 | 0.728905 | 0.364452 | − | 0.931222i | \(-0.381256\pi\) | ||||
0.364452 | + | 0.931222i | \(0.381256\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 385.956i | 1.36878i | 0.729115 | + | 0.684392i | \(0.239932\pi\) | ||||
−0.729115 | + | 0.684392i | \(0.760068\pi\) | |||||||
\(44\) | −139.129 | + | 240.076i | −0.476692 | + | 0.822563i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 256.532 | + | 445.162i | 0.822252 | + | 1.42686i | ||||
\(47\) | −199.255 | −0.618391 | −0.309195 | − | 0.950999i | \(-0.600060\pi\) | ||||
−0.309195 | + | 0.950999i | \(0.600060\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −228.021 | − | 256.233i | −0.664786 | − | 0.747034i | ||||
\(50\) | 793.537 | − | 457.289i | 2.24446 | − | 1.29341i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 160.590 | − | 277.109i | 0.428266 | − | 0.739001i | ||||
\(53\) | −490.879 | −1.27222 | −0.636108 | − | 0.771600i | \(-0.719457\pi\) | ||||
−0.636108 | + | 0.771600i | \(0.719457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 734.795i | − | 1.80145i | ||||||
\(56\) | 381.917 | + | 172.497i | 0.911354 | + | 0.411623i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 195.239 | − | 112.510i | 0.442002 | − | 0.254711i | ||||
\(59\) | − | 811.088i | − | 1.78974i | −0.446327 | − | 0.894870i | \(-0.647268\pi\) | ||
0.446327 | − | 0.894870i | \(-0.352732\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −165.593 | −0.347575 | −0.173787 | − | 0.984783i | \(-0.555601\pi\) | ||||
−0.173787 | + | 0.984783i | \(0.555601\pi\) | |||||||
\(62\) | 36.1198 | + | 62.6789i | 0.0739874 | + | 0.128391i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −511.994 | − | 2.49764i | −0.999988 | − | 0.00487820i | ||||
\(65\) | 848.141i | 1.61845i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 632.062i | − | 1.15252i | −0.817268 | − | 0.576258i | \(-0.804512\pi\) | ||
0.817268 | − | 0.576258i | \(-0.195488\pi\) | |||||||
\(68\) | −307.107 | + | 529.933i | −0.547679 | + | 0.945056i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1104.09 | + | 111.884i | −1.88520 | + | 0.191038i | ||||
\(71\) | − | 618.163i | − | 1.03327i | −0.856205 | − | 0.516637i | \(-0.827184\pi\) | ||
0.856205 | − | 0.516637i | \(-0.172816\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 279.677i | 0.448407i | 0.974542 | + | 0.224203i | \(0.0719780\pi\) | ||||
−0.974542 | + | 0.224203i | \(0.928022\pi\) | |||||||
\(74\) | −229.856 | − | 398.870i | −0.361083 | − | 0.626591i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.2680 | − | 21.1692i | 0.0185162 | − | 0.0319509i | ||||
\(77\) | −262.984 | + | 586.067i | −0.389218 | + | 0.867384i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 598.872 | 0.852891 | 0.426445 | − | 0.904513i | \(-0.359766\pi\) | ||||
0.426445 | + | 0.904513i | \(0.359766\pi\) | |||||||
\(80\) | 1176.40 | − | 674.101i | 1.64406 | − | 0.942084i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −468.949 | + | 270.240i | −0.631546 | + | 0.363939i | ||||
\(83\) | − | 52.2938i | − | 0.0691565i | −0.999402 | − | 0.0345783i | \(-0.988991\pi\) | ||
0.999402 | − | 0.0345783i | \(-0.0110088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1621.96i | − | 2.06972i | ||||||
\(86\) | −545.055 | − | 945.838i | −0.683428 | − | 1.18596i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.91426 | − | 784.819i | 0.00231888 | − | 0.950705i | ||||
\(89\) | 1287.23 | 1.53310 | 0.766552 | − | 0.642183i | \(-0.221971\pi\) | ||||
0.766552 | + | 0.642183i | \(0.221971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 303.551 | − | 676.471i | 0.349679 | − | 0.779268i | ||||
\(92\) | −1257.33 | − | 728.651i | −1.42485 | − | 0.825729i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 488.303 | − | 281.393i | 0.535793 | − | 0.308760i | ||||
\(95\) | 64.7921i | 0.0699740i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1821.05i | − | 1.90618i | −0.302681 | − | 0.953092i | \(-0.597882\pi\) | ||
0.302681 | − | 0.953092i | \(-0.402118\pi\) | |||||||
\(98\) | 920.656 | + | 305.917i | 0.948982 | + | 0.315329i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1298.88 | + | 2241.30i | −1.29888 | + | 2.24130i | ||||
\(101\) | − | 1598.46i | − | 1.57478i | −0.616453 | − | 0.787392i | \(-0.711431\pi\) | ||
0.616453 | − | 0.787392i | \(-0.288569\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 598.346i | − | 0.572396i | −0.958171 | − | 0.286198i | \(-0.907608\pi\) | ||
0.958171 | − | 0.286198i | \(-0.0923915\pi\) | |||||||
\(104\) | −2.20955 | + | 905.882i | −0.00208331 | + | 0.854125i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1202.97 | − | 693.230i | 1.10229 | − | 0.635212i | ||||
\(107\) | −692.414 | −0.625591 | −0.312795 | − | 0.949821i | \(-0.601265\pi\) | ||||
−0.312795 | + | 0.949821i | \(0.601265\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1210.00i | 1.06327i | 0.846972 | + | 0.531637i | \(0.178423\pi\) | ||||
−0.846972 | + | 0.531637i | \(0.821577\pi\) | |||||||
\(110\) | 1037.69 | + | 1800.72i | 0.899457 | + | 1.56083i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1179.55 | + | 116.624i | −0.995148 | + | 0.0983924i | ||||
\(113\) | 738.014i | 0.614394i | 0.951646 | + | 0.307197i | \(0.0993911\pi\) | ||||
−0.951646 | + | 0.307197i | \(0.900609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3848.30 | 3.12049 | ||||||||
\(116\) | −319.571 | + | 551.441i | −0.255788 | + | 0.441379i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1145.44 | + | 1987.68i | 0.893609 | + | 1.55069i | ||||
\(119\) | −580.500 | + | 1293.66i | −0.447179 | + | 0.996551i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −127.982 | −0.0961547 | ||||||||
\(122\) | 405.809 | − | 233.854i | 0.301150 | − | 0.173542i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −177.033 | − | 102.594i | −0.128210 | − | 0.0743003i | ||||
\(125\) | − | 4211.77i | − | 3.01369i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −166.510 | −0.116341 | −0.0581707 | − | 0.998307i | \(-0.518527\pi\) | ||||
−0.0581707 | + | 0.998307i | \(0.518527\pi\) | |||||||
\(128\) | 1258.24 | − | 716.928i | 0.868857 | − | 0.495063i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1197.76 | − | 2078.49i | −0.808083 | − | 1.40227i | ||||
\(131\) | − | 414.302i | − | 0.276319i | −0.990410 | − | 0.138159i | \(-0.955881\pi\) | ||
0.990410 | − | 0.138159i | \(-0.0441186\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.1892 | − | 51.6777i | 0.0151185 | − | 0.0336919i | ||||
\(134\) | 892.611 | + | 1548.95i | 0.575447 | + | 0.998577i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.22547 | − | 1732.38i | 0.00266420 | − | 1.09228i | ||||
\(137\) | − | 2462.32i | − | 1.53555i | −0.640722 | − | 0.767773i | \(-0.721365\pi\) | ||
0.640722 | − | 0.767773i | \(-0.278635\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −332.412 | −0.202840 | −0.101420 | − | 0.994844i | \(-0.532339\pi\) | ||||
−0.101420 | + | 0.994844i | \(0.532339\pi\) | |||||||
\(140\) | 2547.72 | − | 1833.40i | 1.53801 | − | 1.10679i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 872.983 | + | 1514.89i | 0.515909 | + | 0.895261i | ||||
\(143\) | −1388.59 | −0.812026 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1687.79i | − | 0.966641i | ||||||
\(146\) | −394.966 | − | 685.387i | −0.223888 | − | 0.388514i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1126.59 | + | 652.879i | 0.625708 | + | 0.362611i | ||||
\(149\) | 812.037 | 0.446474 | 0.223237 | − | 0.974764i | \(-0.428338\pi\) | ||||
0.223237 | + | 0.974764i | \(0.428338\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −893.543 | −0.481559 | −0.240780 | − | 0.970580i | \(-0.577403\pi\) | ||||
−0.240780 | + | 0.970580i | \(0.577403\pi\) | |||||||
\(152\) | −0.168794 | + | 69.2031i | −9.00724e−5 | + | 0.0369283i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −183.178 | − | 1807.63i | −0.0958498 | − | 0.945864i | ||||
\(155\) | 541.842 | 0.280786 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 894.542 | 0.454728 | 0.227364 | − | 0.973810i | \(-0.426989\pi\) | ||||
0.227364 | + | 0.973810i | \(0.426989\pi\) | |||||||
\(158\) | −1467.62 | + | 845.740i | −0.738971 | + | 0.425845i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1930.94 | + | 3313.31i | −0.954089 | + | 1.63713i | ||||
\(161\) | −3069.37 | − | 1377.31i | −1.50249 | − | 0.674207i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1039.42i | 0.499473i | 0.968314 | + | 0.249736i | \(0.0803439\pi\) | ||||
−0.968314 | + | 0.249736i | \(0.919656\pi\) | |||||||
\(164\) | 767.587 | − | 1324.52i | 0.365478 | − | 0.630657i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 73.8504 | + | 128.153i | 0.0345295 | + | 0.0599194i | ||||
\(167\) | 2025.47 | 0.938537 | 0.469269 | − | 0.883055i | \(-0.344518\pi\) | ||||
0.469269 | + | 0.883055i | \(0.344518\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −594.214 | −0.270466 | ||||||||
\(170\) | 2290.56 | + | 3974.83i | 1.03340 | + | 1.79327i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2671.46 | + | 1548.17i | 1.18429 | + | 0.686318i | ||||
\(173\) | − | 678.349i | − | 0.298115i | −0.988829 | − | 0.149058i | \(-0.952376\pi\) | ||
0.988829 | − | 0.149058i | \(-0.0476240\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2455.17 | + | 5471.41i | −1.06053 | + | 2.36342i | ||||
\(176\) | 1103.65 | + | 1926.01i | 0.472674 | + | 0.824879i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3154.54 | + | 1817.85i | −1.32833 | + | 0.765472i | ||||
\(179\) | −3481.81 | −1.45387 | −0.726936 | − | 0.686706i | \(-0.759056\pi\) | ||||
−0.726936 | + | 0.686706i | \(0.759056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1541.69 | −0.633109 | −0.316555 | − | 0.948574i | \(-0.602526\pi\) | ||||
−0.316555 | + | 0.948574i | \(0.602526\pi\) | |||||||
\(182\) | 211.434 | + | 2086.47i | 0.0861127 | + | 0.849776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4110.29 | + | 10.0255i | 1.64682 | + | 0.00401678i | ||||
\(185\) | −3448.12 | −1.37033 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2655.49 | 1.03844 | ||||||||
\(188\) | −799.265 | + | 1379.18i | −0.310066 | + | 0.535039i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −91.5008 | − | 158.782i | −0.0349377 | − | 0.0606277i | ||||
\(191\) | 3772.38i | 1.42911i | 0.699580 | + | 0.714554i | \(0.253370\pi\) | ||||
−0.699580 | + | 0.714554i | \(0.746630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1514.61 | 0.564891 | 0.282445 | − | 0.959283i | \(-0.408854\pi\) | ||||
0.282445 | + | 0.959283i | \(0.408854\pi\) | |||||||
\(194\) | 2571.73 | + | 4462.74i | 0.951749 | + | 1.65158i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2688.22 | + | 550.478i | −0.979671 | + | 0.200611i | ||||
\(197\) | −3631.15 | −1.31324 | −0.656621 | − | 0.754220i | \(-0.728015\pi\) | ||||
−0.656621 | + | 0.754220i | \(0.728015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2271.88i | 0.809293i | 0.914473 | + | 0.404646i | \(0.132605\pi\) | ||||
−0.914473 | + | 0.404646i | \(0.867395\pi\) | |||||||
\(200\) | 17.8712 | − | 7326.92i | 0.00631842 | − | 2.59046i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2257.39 | + | 3917.26i | 0.786283 | + | 1.36444i | ||||
\(203\) | −604.060 | + | 1346.16i | −0.208851 | + | 0.465430i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4053.94i | 1.38117i | ||||||||
\(206\) | 844.997 | + | 1466.33i | 0.285795 | + | 0.495942i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1273.89 | − | 2223.11i | −0.424656 | − | 0.741081i | ||||
\(209\) | −106.079 | −0.0351082 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5972.67i | − | 1.94870i | −0.225037 | − | 0.974350i | \(-0.572250\pi\) | ||
0.225037 | − | 0.974350i | \(-0.427750\pi\) | |||||||
\(212\) | −1969.05 | + | 3397.71i | −0.637899 | + | 1.10074i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1696.86 | − | 977.842i | 0.542032 | − | 0.312355i | ||||
\(215\) | −8176.50 | −2.59364 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −432.169 | − | 193.926i | −0.135196 | − | 0.0606661i | ||||
\(218\) | −1708.79 | − | 2965.27i | −0.530888 | − | 0.921254i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5086.03 | − | 2947.46i | −1.55864 | − | 0.903261i | ||||
\(221\) | −3065.11 | −0.932950 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 404.511i | − | 0.121471i | −0.998154 | − | 0.0607356i | \(-0.980655\pi\) | ||
0.998154 | − | 0.0607356i | \(-0.0193446\pi\) | |||||||
\(224\) | 2725.94 | − | 1951.58i | 0.813101 | − | 0.582123i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1042.24 | − | 1808.61i | −0.306764 | − | 0.532330i | ||||
\(227\) | 3627.98i | 1.06078i | 0.847754 | + | 0.530390i | \(0.177955\pi\) | ||||
−0.847754 | + | 0.530390i | \(0.822045\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5078.24 | −1.46541 | −0.732707 | − | 0.680544i | \(-0.761743\pi\) | ||||
−0.732707 | + | 0.680544i | \(0.761743\pi\) | |||||||
\(230\) | −9430.79 | + | 5434.65i | −2.70369 | + | 1.55805i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.39696 | − | 1802.69i | 0.00124429 | − | 0.510139i | ||||
\(233\) | − | 1456.59i | − | 0.409548i | −0.978809 | − | 0.204774i | \(-0.934354\pi\) | ||
0.978809 | − | 0.204774i | \(-0.0656459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4221.24i | − | 1.17176i | ||||||
\(236\) | −5614.10 | − | 3253.48i | −1.54850 | − | 0.897389i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −404.339 | − | 3990.09i | −0.110123 | − | 1.08672i | ||||
\(239\) | 5261.69i | 1.42406i | 0.702149 | + | 0.712030i | \(0.252224\pi\) | ||||
−0.702149 | + | 0.712030i | \(0.747776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4776.22i | 1.27661i | 0.769783 | + | 0.638306i | \(0.220365\pi\) | ||||
−0.769783 | + | 0.638306i | \(0.779635\pi\) | |||||||
\(242\) | 313.637 | − | 180.739i | 0.0833114 | − | 0.0480096i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −664.238 | + | 1146.19i | −0.174276 | + | 0.300725i | ||||
\(245\) | 5428.31 | − | 4830.66i | 1.41552 | − | 1.25967i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 122.442 | 0.0315416 | ||||||||
\(248\) | 578.730 | + | 1.41159i | 0.148183 | + | 0.000361435i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5947.95 | + | 10321.5i | 1.50472 | + | 2.61116i | ||||
\(251\) | 2707.08i | 0.680754i | 0.940289 | + | 0.340377i | \(0.110555\pi\) | ||||
−0.940289 | + | 0.340377i | \(0.889445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6300.50i | 1.56565i | ||||||||
\(254\) | 408.056 | − | 235.149i | 0.100802 | − | 0.0580888i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2071.03 | + | 3533.84i | −0.505622 | + | 0.862755i | ||||
\(257\) | 6235.13 | 1.51337 | 0.756686 | − | 0.653778i | \(-0.226817\pi\) | ||||
0.756686 | + | 0.653778i | \(0.226817\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2750.19 | + | 1234.09i | 0.659802 | + | 0.296071i | ||||
\(260\) | 5870.57 | + | 3402.11i | 1.40030 | + | 0.811501i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 585.087 | + | 1015.31i | 0.137965 | + | 0.239411i | ||||
\(263\) | − | 401.960i | − | 0.0942431i | −0.998889 | − | 0.0471215i | \(-0.984995\pi\) | ||
0.998889 | − | 0.0471215i | \(-0.0150048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10399.3i | − | 2.41066i | ||||||
\(266\) | 16.1521 | + | 159.391i | 0.00372311 | + | 0.0367403i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4374.93 | − | 2535.36i | −0.997170 | − | 0.577881i | ||||
\(269\) | 3612.69i | 0.818847i | 0.912345 | + | 0.409423i | \(0.134270\pi\) | ||||
−0.912345 | + | 0.409423i | \(0.865730\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2392.24i | − | 0.536229i | −0.963387 | − | 0.268115i | \(-0.913599\pi\) | ||
0.963387 | − | 0.268115i | \(-0.0864006\pi\) | |||||||
\(272\) | 2436.15 | + | 4251.40i | 0.543063 | + | 0.947717i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3477.34 | + | 6034.25i | 0.766692 | + | 1.33045i | ||||
\(275\) | 11231.1 | 2.46277 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7905.15i | − | 1.71471i | −0.514726 | − | 0.857355i | \(-0.672106\pi\) | ||
0.514726 | − | 0.857355i | \(-0.327894\pi\) | |||||||
\(278\) | 814.622 | − | 469.439i | 0.175747 | − | 0.101277i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3654.36 | + | 8090.95i | −0.779964 | + | 1.72688i | ||||
\(281\) | 6507.60i | 1.38153i | 0.723078 | + | 0.690767i | \(0.242727\pi\) | ||||
−0.723078 | + | 0.690767i | \(0.757273\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2385.57 | 0.501086 | 0.250543 | − | 0.968106i | \(-0.419391\pi\) | ||||
0.250543 | + | 0.968106i | \(0.419391\pi\) | |||||||
\(284\) | −4278.73 | − | 2479.61i | −0.894000 | − | 0.518091i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3402.93 | − | 1961.00i | 0.703565 | − | 0.405441i | ||||
\(287\) | 1450.91 | − | 3233.39i | 0.298413 | − | 0.665020i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 948.621 | 0.193084 | ||||||||
\(290\) | 2383.53 | + | 4136.15i | 0.482640 | + | 0.837529i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1935.84 | + | 1121.86i | 0.387967 | + | 0.224835i | ||||
\(293\) | − | 4825.82i | − | 0.962210i | −0.876663 | − | 0.481105i | \(-0.840236\pi\) | ||
0.876663 | − | 0.481105i | \(-0.159764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17183.0 | 3.39129 | ||||||||
\(296\) | −3682.87 | − | 8.98293i | −0.723183 | − | 0.00176393i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1990.01 | + | 1146.78i | −0.386839 | + | 0.222923i | ||||
\(299\) | − | 7272.38i | − | 1.40660i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6521.52 | + | 2926.38i | 1.24882 | + | 0.560378i | ||||
\(302\) | 2189.75 | − | 1261.88i | 0.417238 | − | 0.240441i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −97.3164 | − | 169.830i | −0.0183601 | − | 0.0320409i | ||||
\(305\) | − | 3508.11i | − | 0.658602i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 414.961 | 0.0771435 | 0.0385718 | − | 0.999256i | \(-0.487719\pi\) | ||||
0.0385718 | + | 0.999256i | \(0.487719\pi\) | |||||||
\(308\) | 3001.68 | + | 4171.16i | 0.555313 | + | 0.771669i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1327.86 | + | 765.201i | −0.243282 | + | 0.140195i | ||||
\(311\) | −9767.89 | −1.78099 | −0.890493 | − | 0.454998i | \(-0.849640\pi\) | ||||
−0.890493 | + | 0.454998i | \(0.849640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7636.60i | 1.37906i | 0.724257 | + | 0.689531i | \(0.242183\pi\) | ||||
−0.724257 | + | 0.689531i | \(0.757817\pi\) | |||||||
\(314\) | −2192.20 | + | 1263.29i | −0.393990 | + | 0.227044i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2402.23 | − | 4145.21i | 0.427646 | − | 0.737931i | ||||
\(317\) | −2580.26 | −0.457168 | −0.228584 | − | 0.973524i | \(-0.573409\pi\) | ||||
−0.228584 | + | 0.973524i | \(0.573409\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2763.27 | 0.484995 | ||||||||
\(320\) | 52.9127 | − | 10846.6i | 0.00924346 | − | 1.89483i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9466.99 | − | 959.345i | 1.63843 | − | 0.166032i | ||||
\(323\) | −234.153 | −0.0403364 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12963.6 | −2.21259 | ||||||||
\(326\) | −1467.90 | − | 2547.25i | −0.249385 | − | 0.432759i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.5612 | + | 4329.92i | −0.00177788 | + | 0.728903i | ||||
\(329\) | −1510.79 | + | 3366.83i | −0.253168 | + | 0.564192i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3338.88i | 0.554445i | 0.960806 | + | 0.277223i | \(0.0894140\pi\) | ||||
−0.960806 | + | 0.277223i | \(0.910586\pi\) | |||||||
\(332\) | −361.961 | − | 209.764i | −0.0598350 | − | 0.0346756i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4963.70 | + | 2860.42i | −0.813178 | + | 0.468608i | ||||
\(335\) | 13390.3 | 2.18385 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 619.770 | 0.100181 | 0.0500906 | − | 0.998745i | \(-0.484049\pi\) | ||||
0.0500906 | + | 0.998745i | \(0.484049\pi\) | |||||||
\(338\) | 1456.20 | − | 839.162i | 0.234340 | − | 0.135043i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11226.7 | − | 6506.09i | −1.79074 | − | 1.03777i | ||||
\(341\) | 887.112i | 0.140879i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6058.48 | + | 1910.09i | −0.953723 | + | 0.300686i | ||||
\(344\) | −8733.15 | − | 21.3011i | −1.36878 | − | 0.00333861i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 957.979 | + | 1662.39i | 0.148848 | + | 0.258296i | ||||
\(347\) | 5312.40 | 0.821858 | 0.410929 | − | 0.911667i | \(-0.365204\pi\) | ||||
0.410929 | + | 0.911667i | \(0.365204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8996.20 | −1.37982 | −0.689908 | − | 0.723897i | \(-0.742349\pi\) | ||||
−0.689908 | + | 0.723897i | \(0.742349\pi\) | |||||||
\(350\) | −1710.11 | − | 16875.7i | −0.261169 | − | 2.57727i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5424.60 | − | 3161.37i | −0.821398 | − | 0.478697i | ||||
\(353\) | 11852.7 | 1.78713 | 0.893566 | − | 0.448932i | \(-0.148195\pi\) | ||||
0.893566 | + | 0.448932i | \(0.148195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13095.8 | 1.95790 | ||||||||
\(356\) | 5163.42 | − | 8909.81i | 0.768709 | − | 1.32646i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8532.67 | − | 4917.09i | 1.25968 | − | 0.725912i | ||||
\(359\) | − | 9168.52i | − | 1.34790i | −0.738777 | − | 0.673950i | \(-0.764596\pi\) | ||
0.738777 | − | 0.673950i | \(-0.235404\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6849.65 | −0.998636 | ||||||||
\(362\) | 3778.12 | − | 2177.21i | 0.548546 | − | 0.316109i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3464.70 | − | 4814.58i | −0.498900 | − | 0.693277i | ||||
\(365\) | −5924.98 | −0.849665 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4679.82i | 0.665625i | 0.942993 | + | 0.332813i | \(0.107998\pi\) | ||||
−0.942993 | + | 0.332813i | \(0.892002\pi\) | |||||||
\(368\) | −10087.0 | + | 5780.07i | −1.42886 | + | 0.818769i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8450.10 | − | 4869.51i | 1.18730 | − | 0.684199i | ||||
\(371\) | −3721.93 | + | 8294.42i | −0.520844 | + | 1.16071i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3237.88i | − | 0.449467i | −0.974420 | − | 0.224734i | \(-0.927849\pi\) | ||
0.974420 | − | 0.224734i | \(-0.0721512\pi\) | |||||||
\(374\) | −6507.65 | + | 3750.14i | −0.899740 | + | 0.518490i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.9970 | − | 4508.62i | 0.00150832 | − | 0.618389i | ||||
\(377\) | −3189.52 | −0.435725 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2473.40i | 0.335224i | 0.985853 | + | 0.167612i | \(0.0536055\pi\) | ||||
−0.985853 | + | 0.167612i | \(0.946394\pi\) | |||||||
\(380\) | 448.471 | + | 259.898i | 0.0605423 | + | 0.0350855i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5327.43 | − | 9244.73i | −0.713547 | − | 1.23822i | ||||
\(383\) | −8396.19 | −1.12017 | −0.560085 | − | 0.828435i | \(-0.689232\pi\) | ||||
−0.560085 | + | 0.828435i | \(0.689232\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12415.9 | − | 5571.34i | −1.64356 | − | 0.737511i | ||||
\(386\) | −3711.76 | + | 2138.96i | −0.489439 | + | 0.282048i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12604.8 | − | 7304.71i | −1.64925 | − | 0.955775i | ||||
\(389\) | −1094.01 | −0.142593 | −0.0712966 | − | 0.997455i | \(-0.522714\pi\) | ||||
−0.0712966 | + | 0.997455i | \(0.522714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13907.4i | 1.79880i | ||||||||
\(392\) | 5810.45 | − | 5145.38i | 0.748653 | − | 0.662962i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8898.64 | − | 5127.99i | 1.13783 | − | 0.655696i | ||||
\(395\) | 12687.2i | 1.61610i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9534.52 | −1.20535 | −0.602675 | − | 0.797987i | \(-0.705899\pi\) | ||||
−0.602675 | + | 0.797987i | \(0.705899\pi\) | |||||||
\(398\) | −3208.40 | − | 5567.56i | −0.404076 | − | 0.701197i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10303.4 | + | 17980.9i | 1.28793 | + | 2.24761i | ||||
\(401\) | 2554.19i | 0.318081i | 0.987272 | + | 0.159040i | \(0.0508400\pi\) | ||||
−0.987272 | + | 0.159040i | \(0.949160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1023.95i | − | 0.126568i | ||||||
\(404\) | −11064.1 | − | 6411.86i | −1.36252 | − | 0.789609i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −420.749 | − | 4152.03i | −0.0514321 | − | 0.507541i | ||||
\(407\) | − | 5645.32i | − | 0.687538i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5080.09i | − | 0.614167i | −0.951683 | − | 0.307084i | \(-0.900647\pi\) | ||
0.951683 | − | 0.307084i | \(-0.0993532\pi\) | |||||||
\(410\) | −5725.06 | − | 9934.73i | −0.689611 | − | 1.19669i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4141.57 | − | 2400.12i | −0.495243 | − | 0.287004i | ||||
\(413\) | −13705.0 | − | 6149.80i | −1.63288 | − | 0.732717i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1107.85 | 0.131041 | ||||||||
\(416\) | 6261.37 | + | 3649.02i | 0.737954 | + | 0.430067i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 259.960 | − | 149.806i | 0.0304188 | − | 0.0175294i | ||||
\(419\) | 9210.28i | 1.07387i | 0.843623 | + | 0.536935i | \(0.180418\pi\) | ||||
−0.843623 | + | 0.536935i | \(0.819582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9284.04i | − | 1.07477i | −0.843338 | − | 0.537383i | \(-0.819413\pi\) | ||
0.843338 | − | 0.537383i | \(-0.180587\pi\) | |||||||
\(422\) | 8434.74 | + | 14636.9i | 0.972978 | + | 1.68842i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 27.0920 | − | 11107.3i | 0.00310307 | − | 1.27221i | ||||
\(425\) | 24791.1 | 2.82952 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1255.56 | + | 2798.04i | −0.142297 | + | 0.317112i | ||||
\(428\) | −2777.45 | + | 4792.68i | −0.313676 | + | 0.541268i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20037.7 | − | 11547.0i | 2.24721 | − | 1.29499i | ||||
\(431\) | − | 14348.9i | − | 1.60363i | −0.597574 | − | 0.801814i | \(-0.703869\pi\) | ||
0.597574 | − | 0.801814i | \(-0.296131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7019.84i | − | 0.779104i | −0.921004 | − | 0.389552i | \(-0.872630\pi\) | ||
0.921004 | − | 0.389552i | \(-0.127370\pi\) | |||||||
\(434\) | 1332.96 | − | 135.076i | 0.147428 | − | 0.0149398i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8375.24 | + | 4853.62i | 0.919957 | + | 0.533134i | ||||
\(437\) | − | 555.559i | − | 0.0608146i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13744.5i | − | 1.49428i | −0.664667 | − | 0.747139i | \(-0.731427\pi\) | ||
0.664667 | − | 0.747139i | \(-0.268573\pi\) | |||||||
\(440\) | 16626.5 | + | 40.5539i | 1.80145 | + | 0.00439393i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7511.49 | − | 4328.62i | 0.808337 | − | 0.465818i | ||||
\(443\) | 4282.17 | 0.459259 | 0.229630 | − | 0.973278i | \(-0.426249\pi\) | ||||
0.229630 | + | 0.973278i | \(0.426249\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27270.1i | 2.90500i | ||||||||
\(446\) | 571.259 | + | 991.311i | 0.0606500 | + | 0.105246i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3924.23 | + | 8632.26i | −0.413844 | + | 0.910348i | ||||
\(449\) | − | 239.688i | − | 0.0251929i | −0.999921 | − | 0.0125964i | \(-0.995990\pi\) | ||
0.999921 | − | 0.0125964i | \(-0.00400967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6637.17 | −0.692975 | ||||||||
\(452\) | 5108.30 | + | 2960.37i | 0.531581 | + | 0.308062i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5123.51 | − | 8890.86i | −0.529643 | − | 0.919094i | ||||
\(455\) | 14331.1 | + | 6430.75i | 1.47660 | + | 0.662589i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4705.34 | −0.481633 | −0.240817 | − | 0.970571i | \(-0.577415\pi\) | ||||
−0.240817 | + | 0.970571i | \(0.577415\pi\) | |||||||
\(458\) | 12444.9 | − | 7171.61i | 1.26968 | − | 0.731675i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15436.5 | − | 26636.7i | 1.56463 | − | 2.69988i | ||||
\(461\) | 8816.96i | 0.890774i | 0.895338 | + | 0.445387i | \(0.146934\pi\) | ||||
−0.895338 | + | 0.445387i | \(0.853066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13333.2 | −1.33833 | −0.669166 | − | 0.743113i | \(-0.733349\pi\) | ||||
−0.669166 | + | 0.743113i | \(0.733349\pi\) | |||||||
\(464\) | 2535.02 | + | 4423.95i | 0.253632 | + | 0.442622i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2057.03 | + | 3569.59i | 0.204485 | + | 0.354845i | ||||
\(467\) | 6893.25i | 0.683044i | 0.939874 | + | 0.341522i | \(0.110942\pi\) | ||||
−0.939874 | + | 0.341522i | \(0.889058\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10680.0 | − | 4792.40i | −1.05151 | − | 0.471839i | ||||
\(470\) | 5961.33 | + | 10344.7i | 0.585054 | + | 1.01525i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18352.8 | + | 44.7645i | 1.78973 | + | 0.00436536i | ||||
\(473\) | − | 13386.7i | − | 1.30131i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −990.328 | −0.0956619 | ||||||||
\(476\) | 6625.78 | + | 9207.25i | 0.638008 | + | 0.886583i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7430.67 | − | 12894.5i | −0.711027 | − | 1.23385i | ||||
\(479\) | 6071.06 | 0.579110 | 0.289555 | − | 0.957161i | \(-0.406493\pi\) | ||||
0.289555 | + | 0.957161i | \(0.406493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6516.13i | 0.617692i | ||||||||
\(482\) | −6745.09 | − | 11704.8i | −0.637407 | − | 1.10610i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −513.369 | + | 885.851i | −0.0482127 | + | 0.0831941i | ||||
\(485\) | 38579.2 | 3.61194 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10085.1 | −0.938397 | −0.469198 | − | 0.883093i | \(-0.655457\pi\) | ||||
−0.469198 | + | 0.883093i | \(0.655457\pi\) | |||||||
\(488\) | 9.13920 | − | 3746.94i | 0.000847771 | − | 0.347573i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6480.88 | + | 19504.2i | −0.597503 | + | 1.79818i | ||||
\(491\) | −11027.2 | −1.01354 | −0.506772 | − | 0.862080i | \(-0.669161\pi\) | ||||
−0.506772 | + | 0.862080i | \(0.669161\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6099.52 | 0.557218 | ||||||||
\(494\) | −300.060 | + | 172.915i | −0.0273287 | + | 0.0157486i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1420.25 | + | 813.836i | −0.128571 | + | 0.0736740i | ||||
\(497\) | −10445.1 | − | 4687.01i | −0.942713 | − | 0.423021i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3102.73i | 0.278352i | 0.990268 | + | 0.139176i | \(0.0444453\pi\) | ||||
−0.990268 | + | 0.139176i | \(0.955555\pi\) | |||||||
\(500\) | −29152.5 | − | 16894.5i | −2.60748 | − | 1.51109i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3822.99 | − | 6634.07i | −0.339898 | − | 0.589827i | ||||
\(503\) | −5879.25 | −0.521158 | −0.260579 | − | 0.965452i | \(-0.583913\pi\) | ||||
−0.260579 | + | 0.965452i | \(0.583913\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33863.6 | 2.98398 | ||||||||
\(506\) | −8897.70 | − | 15440.2i | −0.781721 | − | 1.35653i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −667.915 | + | 1152.53i | −0.0583345 | + | 0.100660i | ||||
\(509\) | 20971.1i | 1.82618i | 0.407756 | + | 0.913091i | \(0.366311\pi\) | ||||
−0.407756 | + | 0.913091i | \(0.633689\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4725.72 | + | 2120.56i | 0.409107 | + | 0.183577i | ||||
\(512\) | 84.7722 | − | 11584.9i | 0.00731726 | − | 0.999973i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15280.1 | + | 8805.39i | −1.31123 | + | 0.755621i | ||||
\(515\) | 12676.0 | 1.08461 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6911.08 | 0.587909 | ||||||||
\(518\) | −8482.54 | + | 859.584i | −0.719500 | + | 0.0729111i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −19191.2 | − | 46.8095i | −1.61844 | − | 0.00394756i | ||||
\(521\) | 18346.9 | 1.54278 | 0.771392 | − | 0.636360i | \(-0.219561\pi\) | ||||
0.771392 | + | 0.636360i | \(0.219561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2876.39 | 0.240489 | 0.120245 | − | 0.992744i | \(-0.461632\pi\) | ||||
0.120245 | + | 0.992744i | \(0.461632\pi\) | |||||||
\(524\) | −2867.67 | − | 1661.87i | −0.239074 | − | 0.138548i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 567.657 | + | 985.059i | 0.0470552 | + | 0.0816552i | ||||
\(527\) | 1958.17i | 0.161858i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20830.2 | −1.71202 | ||||||||
\(530\) | 14686.2 | + | 25485.0i | 1.20363 | + | 2.08867i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −264.679 | − | 367.801i | −0.0215701 | − | 0.0299740i | ||||
\(533\) | 7660.98 | 0.622578 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14668.9i | − | 1.18540i | ||||||
\(536\) | 14301.9 | + | 34.8839i | 1.15251 | + | 0.00281111i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5101.92 | − | 8853.40i | −0.408847 | − | 0.709475i | ||||
\(539\) | 7908.82 | + | 8887.32i | 0.632017 | + | 0.710211i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14029.6i | 1.11493i | 0.830200 | + | 0.557465i | \(0.188226\pi\) | ||||
−0.830200 | + | 0.557465i | \(0.811774\pi\) | |||||||
\(542\) | 3378.37 | + | 5862.51i | 0.267737 | + | 0.464606i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −11974.0 | − | 6978.26i | −0.943718 | − | 0.549983i | ||||
\(545\) | −25633.9 | −2.01475 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2660.42i | 0.207955i | 0.994580 | + | 0.103977i | \(0.0331570\pi\) | ||||
−0.994580 | + | 0.103977i | \(0.966843\pi\) | |||||||
\(548\) | −17043.4 | − | 9876.99i | −1.32857 | − | 0.769934i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −27523.5 | + | 15860.9i | −2.13383 | + | 1.22965i | ||||
\(551\) | −243.657 | −0.0188387 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4540.75 | − | 10119.2i | 0.349172 | − | 0.778140i | ||||
\(554\) | 11163.8 | + | 19372.7i | 0.856147 | + | 1.48568i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1333.39 | + | 2300.85i | −0.101706 | + | 0.175500i | ||||
\(557\) | −8706.57 | −0.662315 | −0.331157 | − | 0.943576i | \(-0.607439\pi\) | ||||
−0.331157 | + | 0.943576i | \(0.607439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15451.7i | 1.16912i | ||||||||
\(560\) | −2470.69 | − | 24988.8i | −0.186439 | − | 1.88566i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9190.17 | − | 15947.8i | −0.689794 | − | 1.19700i | ||||
\(563\) | − | 25257.4i | − | 1.89071i | −0.326041 | − | 0.945356i | \(-0.605715\pi\) | ||
0.326041 | − | 0.945356i | \(-0.394285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15634.9 | −1.16419 | ||||||||
\(566\) | −5846.16 | + | 3368.95i | −0.434156 | + | 0.250190i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13987.4 | + | 34.1168i | 1.03327 | + | 0.00252026i | ||||
\(569\) | − | 18513.7i | − | 1.36403i | −0.731336 | − | 0.682017i | \(-0.761103\pi\) | ||
0.731336 | − | 0.682017i | \(-0.238897\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15952.0i | − | 1.16913i | −0.811348 | − | 0.584564i | \(-0.801266\pi\) | ||
0.811348 | − | 0.584564i | \(-0.198734\pi\) | |||||||
\(572\) | −5569.99 | + | 9611.39i | −0.407156 | + | 0.702574i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1010.61 | + | 9972.87i | 0.0734878 | + | 0.725191i | ||||
\(575\) | 58820.2i | 4.26604i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17649.3i | − | 1.27339i | −0.771114 | − | 0.636697i | \(-0.780300\pi\) | ||
0.771114 | − | 0.636697i | \(-0.219700\pi\) | |||||||
\(578\) | −2324.73 | + | 1339.66i | −0.167294 | + | 0.0964059i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11682.3 | − | 6770.15i | −0.836349 | − | 0.484681i | ||||
\(581\) | −883.612 | − | 396.500i | −0.0630953 | − | 0.0283126i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17025.9 | 1.20951 | ||||||||
\(584\) | −6328.35 | − | 15.4356i | −0.448406 | − | 0.00109371i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6815.13 | + | 11826.4i | 0.480428 | + | 0.833690i | ||||
\(587\) | 20281.0i | 1.42604i | 0.701142 | + | 0.713021i | \(0.252674\pi\) | ||||
−0.701142 | + | 0.713021i | \(0.747326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 78.2229i | − | 0.00547219i | ||||||
\(590\) | −42109.2 | + | 24266.2i | −2.93832 | + | 1.69326i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9038.06 | − | 5179.01i | 0.627469 | − | 0.359554i | ||||
\(593\) | −2821.24 | −0.195370 | −0.0976852 | − | 0.995217i | \(-0.531144\pi\) | ||||
−0.0976852 | + | 0.995217i | \(0.531144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27406.3 | − | 12297.9i | −1.88832 | − | 0.847339i | ||||
\(596\) | 3257.29 | − | 5620.67i | 0.223865 | − | 0.386294i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10270.2 | + | 17822.0i | 0.702308 | + | 1.21872i | ||||
\(599\) | 10804.1i | 0.736965i | 0.929635 | + | 0.368483i | \(0.120123\pi\) | ||||
−0.929635 | + | 0.368483i | \(0.879877\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20731.4i | 1.40707i | 0.710660 | + | 0.703536i | \(0.248396\pi\) | ||||
−0.710660 | + | 0.703536i | \(0.751604\pi\) | |||||||
\(602\) | −20114.6 | + | 2038.33i | −1.36181 | + | 0.138000i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3584.23 | + | 6184.82i | −0.241457 | + | 0.416651i | ||||
\(605\) | − | 2711.31i | − | 0.182199i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1910.79i | 0.127770i | 0.997957 | + | 0.0638852i | \(0.0203492\pi\) | ||||
−0.997957 | + | 0.0638852i | \(0.979651\pi\) | |||||||
\(608\) | 478.325 | + | 278.760i | 0.0319057 | + | 0.0185941i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4954.23 | + | 8597.11i | 0.328837 | + | 0.570634i | ||||
\(611\) | −7977.15 | −0.528185 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 7113.05i | − | 0.468668i | −0.972156 | − | 0.234334i | \(-0.924709\pi\) | ||
0.972156 | − | 0.234334i | \(-0.0752909\pi\) | |||||||
\(614\) | −1016.92 | + | 586.016i | −0.0668396 | + | 0.0385174i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13246.6 | − | 5982.98i | −0.866432 | − | 0.391333i | ||||
\(617\) | 8852.59i | 0.577621i | 0.957386 | + | 0.288810i | \(0.0932597\pi\) | ||||
−0.957386 | + | 0.288810i | \(0.906740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1652.28 | −0.107287 | −0.0536437 | − | 0.998560i | \(-0.517084\pi\) | ||||
−0.0536437 | + | 0.998560i | \(0.517084\pi\) | |||||||
\(620\) | 2173.47 | − | 3750.46i | 0.140788 | − | 0.242939i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23937.6 | − | 13794.4i | 1.54310 | − | 0.889238i | ||||
\(623\) | 9760.00 | − | 21750.4i | 0.627650 | − | 1.39874i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 48750.6 | 3.12004 | ||||||||
\(626\) | −10784.6 | − | 18714.5i | −0.688559 | − | 1.19486i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3588.24 | − | 6191.74i | 0.228004 | − | 0.393435i | ||||
\(629\) | − | 12461.2i | − | 0.789923i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7993.10 | 0.504279 | 0.252140 | − | 0.967691i | \(-0.418866\pi\) | ||||
0.252140 | + | 0.967691i | \(0.418866\pi\) | |||||||
\(632\) | −33.0521 | + | 13550.9i | −0.00208029 | + | 0.852888i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6323.30 | − | 3643.91i | 0.396104 | − | 0.228262i | ||||
\(635\) | − | 3527.53i | − | 0.220450i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9128.80 | − | 10258.2i | −0.567812 | − | 0.638062i | ||||
\(638\) | −6771.77 | + | 3902.35i | −0.420215 | + | 0.242156i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15188.2 | + | 26655.9i | 0.938071 | + | 1.64636i | ||||
\(641\) | − | 4622.24i | − | 0.284817i | −0.989808 | − | 0.142408i | \(-0.954515\pi\) | ||
0.989808 | − | 0.142408i | \(-0.0454846\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4207.35 | −0.258043 | −0.129022 | − | 0.991642i | \(-0.541184\pi\) | ||||
−0.129022 | + | 0.991642i | \(0.541184\pi\) | |||||||
\(644\) | −21845.4 | + | 15720.5i | −1.33669 | + | 0.961917i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 573.825 | − | 330.676i | 0.0349487 | − | 0.0201398i | ||||
\(647\) | 13738.8 | 0.834822 | 0.417411 | − | 0.908718i | \(-0.362938\pi\) | ||||
0.417411 | + | 0.908718i | \(0.362938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28132.2i | 1.70152i | ||||||||
\(650\) | 31769.1 | − | 18307.5i | 1.91706 | − | 1.10474i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7194.58 | + | 4169.40i | 0.432149 | + | 0.250439i | ||||
\(653\) | −1083.79 | −0.0649492 | −0.0324746 | − | 0.999473i | \(-0.510339\pi\) | ||||
−0.0324746 | + | 0.999473i | \(0.510339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8777.03 | 0.523583 | ||||||||
\(656\) | −6088.93 | − | 10626.0i | −0.362398 | − | 0.632432i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1052.32 | − | 10384.4i | −0.0623458 | − | 0.615240i | ||||
\(659\) | −13466.6 | −0.796030 | −0.398015 | − | 0.917379i | \(-0.630301\pi\) | ||||
−0.398015 | + | 0.917379i | \(0.630301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8956.78 | 0.527048 | 0.263524 | − | 0.964653i | \(-0.415115\pi\) | ||||
0.263524 | + | 0.964653i | \(0.415115\pi\) | |||||||
\(662\) | −4715.24 | − | 8182.39i | −0.276832 | − | 0.480389i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1183.27 | + | 2.88613i | 0.0691563 | + | 0.000168680i | ||||
\(665\) | 1094.80 | + | 491.264i | 0.0638411 | + | 0.0286472i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14471.9i | 0.840111i | ||||||||
\(668\) | 8124.70 | − | 14019.7i | 0.470590 | − | 0.812033i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −32814.7 | + | 18910.0i | −1.89216 | + | 1.09039i | ||||
\(671\) | 5743.53 | 0.330442 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15097.9 | −0.864755 | −0.432377 | − | 0.901693i | \(-0.642325\pi\) | ||||
−0.432377 | + | 0.901693i | \(0.642325\pi\) | |||||||
\(674\) | −1518.83 | + | 875.253i | −0.0868001 | + | 0.0500200i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2383.55 | + | 4112.96i | −0.135614 | + | 0.234010i | ||||
\(677\) | 6316.41i | 0.358581i | 0.983796 | + | 0.179290i | \(0.0573802\pi\) | ||||
−0.983796 | + | 0.179290i | \(0.942620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30770.4 | − | 13807.5i | −1.73912 | − | 0.780389i | ||||
\(680\) | 36700.6 | + | 89.5169i | 2.06971 | + | 0.00504826i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1252.80 | − | 2173.99i | −0.0703404 | − | 0.122062i | ||||
\(683\) | 7973.40 | 0.446696 | 0.223348 | − | 0.974739i | \(-0.428301\pi\) | ||||
0.223348 | + | 0.974739i | \(0.428301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 52164.4 | 2.90963 | ||||||||
\(686\) | 12149.7 | − | 13236.9i | 0.676205 | − | 0.736714i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 21431.9 | − | 12280.9i | 1.18762 | − | 0.680533i | ||||
\(689\) | −19652.3 | −1.08664 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21774.4 | −1.19875 | −0.599377 | − | 0.800467i | \(-0.704585\pi\) | ||||
−0.599377 | + | 0.800467i | \(0.704585\pi\) | |||||||
\(692\) | −4695.32 | − | 2721.04i | −0.257933 | − | 0.149477i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13018.8 | + | 7502.29i | −0.712084 | + | 0.410350i | ||||
\(695\) | − | 7042.18i | − | 0.384353i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14650.6 | −0.796171 | ||||||||
\(698\) | 22046.4 | − | 12704.6i | 1.19552 | − | 0.688936i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28023.1 | + | 38941.1i | 1.51310 | + | 2.10262i | ||||
\(701\) | −20650.6 | −1.11264 | −0.556320 | − | 0.830968i | \(-0.687787\pi\) | ||||
−0.556320 | + | 0.830968i | \(0.687787\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 497.787i | 0.0267061i | ||||||||
\(704\) | 17758.3 | + | 86.6294i | 0.950697 | + | 0.00463774i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29046.8 | + | 16738.7i | −1.54843 | + | 0.892307i | ||||
\(707\) | −27009.4 | − | 12119.8i | −1.43676 | − | 0.644714i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2585.40i | − | 0.136949i | −0.997653 | − | 0.0684745i | \(-0.978187\pi\) | ||
0.997653 | − | 0.0684745i | \(-0.0218132\pi\) | |||||||
\(710\) | −32093.2 | + | 18494.2i | −1.69639 | + | 0.977571i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −71.0431 | + | 29126.6i | −0.00373940 | + | 1.53310i | ||||
\(713\) | −4646.02 | −0.244032 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 29417.4i | − | 1.53867i | ||||||
\(716\) | −13966.5 | + | 24100.0i | −0.728982 | + | 1.25791i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12948.0 | + | 22468.7i | 0.673000 | + | 1.16786i | ||||
\(719\) | −28992.4 | −1.50380 | −0.751901 | − | 0.659276i | \(-0.770863\pi\) | ||||
−0.751901 | + | 0.659276i | \(0.770863\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10110.3 | − | 4536.76i | −0.522229 | − | 0.234338i | ||||
\(722\) | 16786.0 | − | 9673.22i | 0.865250 | − | 0.498615i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6184.11 | + | 10671.1i | −0.317446 | + | 0.547773i | ||||
\(725\) | 25797.3 | 1.32150 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26205.1i | 1.33685i | 0.743779 | + | 0.668426i | \(0.233032\pi\) | ||||
−0.743779 | + | 0.668426i | \(0.766968\pi\) | |||||||
\(728\) | 15290.0 | + | 6905.88i | 0.778413 | + | 0.351578i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14520.0 | − | 8367.38i | 0.736176 | − | 0.424234i | ||||
\(731\) | − | 29549.2i | − | 1.49510i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26682.9 | 1.34455 | 0.672275 | − | 0.740302i | \(-0.265317\pi\) | ||||
0.672275 | + | 0.740302i | \(0.265317\pi\) | |||||||
\(734\) | −6608.94 | − | 11468.5i | −0.332344 | − | 0.576719i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16556.8 | − | 28409.9i | 0.829202 | − | 1.42283i | ||||
\(737\) | 21922.8i | 1.09571i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37027.6i | 1.84314i | 0.388207 | + | 0.921572i | \(0.373095\pi\) | ||||
−0.388207 | + | 0.921572i | \(0.626905\pi\) | |||||||
\(740\) | −13831.3 | + | 23866.8i | −0.687093 | + | 1.18562i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2592.45 | − | 25582.8i | −0.128264 | − | 1.26573i | ||||
\(743\) | − | 21843.7i | − | 1.07856i | −0.842127 | − | 0.539279i | \(-0.818697\pi\) | ||
0.842127 | − | 0.539279i | \(-0.181303\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17203.1i | 0.846002i | ||||||||
\(746\) | 4572.61 | + | 7934.88i | 0.224417 | + | 0.389432i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10651.9 | − | 18380.5i | 0.520683 | − | 0.898472i | ||||
\(749\) | −5250.00 | + | 11699.8i | −0.256116 | + | 0.570761i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8792.87 | −0.427239 | −0.213619 | − | 0.976917i | \(-0.568525\pi\) | ||||
−0.213619 | + | 0.976917i | \(0.568525\pi\) | |||||||
\(752\) | 6340.22 | + | 11064.5i | 0.307452 | + | 0.536545i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7816.35 | − | 4504.30i | 0.377526 | − | 0.217556i | ||||
\(755\) | − | 18929.8i | − | 0.912484i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8034.47i | 0.385757i | 0.981223 | + | 0.192878i | \(0.0617823\pi\) | ||||
−0.981223 | + | 0.192878i | \(0.938218\pi\) | |||||||
\(758\) | −3492.98 | − | 6061.40i | −0.167376 | − | 0.290449i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1466.07 | − | 3.57592i | −0.0699738 | − | 0.000170674i | ||||
\(761\) | −27879.9 | −1.32805 | −0.664024 | − | 0.747711i | \(-0.731153\pi\) | ||||
−0.664024 | + | 0.747711i | \(0.731153\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20445.4 | + | 9174.41i | 0.970084 | + | 0.435303i | ||||
\(764\) | 26111.2 | + | 15132.0i | 1.23648 | + | 0.716566i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20576.0 | − | 11857.3i | 0.970551 | − | 0.559296i | ||||
\(767\) | − | 32471.7i | − | 1.52867i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19306.7i | 0.905355i | 0.891674 | + | 0.452677i | \(0.149531\pi\) | ||||
−0.891674 | + | 0.452677i | \(0.850469\pi\) | |||||||
\(770\) | 38294.8 | − | 3880.63i | 1.79227 | − | 0.181621i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6075.49 | − | 10483.7i | 0.283241 | − | 0.488750i | ||||
\(773\) | − | 6350.02i | − | 0.295465i | −0.989027 | − | 0.147732i | \(-0.952803\pi\) | ||
0.989027 | − | 0.147732i | \(-0.0471975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8281.90i | 0.383864i | ||||||||
\(776\) | 41205.6 | + | 100.505i | 1.90618 | + | 0.00464938i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2681.03 | − | 1544.99i | 0.123547 | − | 0.0711962i | ||||
\(779\) | 585.246 | 0.0269173 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21440.7i | 0.982341i | ||||||||
\(782\) | −19640.4 | − | 34082.1i | −0.898132 | − | 1.55854i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6972.90 | + | 20815.1i | −0.317643 | + | 0.948210i | ||||
\(785\) | 18951.0i | 0.861642i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22291.3 | 1.00965 | 0.504827 | − | 0.863221i | \(-0.331556\pi\) | ||||
0.504827 | + | 0.863221i | \(0.331556\pi\) | |||||||
\(788\) | −14565.5 | + | 25133.7i | −0.658470 | + | 1.13623i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17917.1 | − | 31091.6i | −0.806913 | − | 1.40024i | ||||
\(791\) | 12470.3 | + | 5595.75i | 0.560546 | + | 0.251532i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6629.50 | −0.296873 | ||||||||
\(794\) | 23365.7 | − | 13464.9i | 1.04435 | − | 0.601826i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15725.2 | + | 9113.10i | 0.700209 | + | 0.405786i | ||||
\(797\) | − | 1865.27i | − | 0.0828998i | −0.999141 | − | 0.0414499i | \(-0.986802\pi\) | ||
0.999141 | − | 0.0414499i | \(-0.0131977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15255.2 | 0.675458 | ||||||||
\(800\) | −50643.0 | − | 29513.9i | −2.23812 | − | 1.30434i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3607.09 | − | 6259.41i | −0.158816 | − | 0.275595i | ||||
\(803\) | − | 9700.47i | − | 0.426304i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29178.5 | − | 65025.0i | 1.27752 | − | 2.84699i | ||||
\(806\) | 1446.05 | + | 2509.34i | 0.0631946 | + | 0.109662i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 36169.0 | + | 88.2203i | 1.57478 | + | 0.00384107i | ||||
\(809\) | 18548.4i | 0.806089i | 0.915180 | + | 0.403045i | \(0.132048\pi\) | ||||
−0.915180 | + | 0.403045i | \(0.867952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17430.4 | 0.754704 | 0.377352 | − | 0.926070i | \(-0.376835\pi\) | ||||
0.377352 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(812\) | 6894.69 | + | 9580.94i | 0.297976 | + | 0.414070i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7972.44 | + | 13834.6i | 0.343285 | + | 0.595705i | ||||
\(815\) | −22020.3 | −0.946427 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1180.40i | 0.0505470i | ||||||||
\(818\) | 7174.22 | + | 12449.5i | 0.306651 | + | 0.532134i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28060.1 | + | 16261.4i | 1.19500 | + | 0.692527i | ||||
\(821\) | −22238.3 | −0.945335 | −0.472668 | − | 0.881241i | \(-0.656709\pi\) | ||||
−0.472668 | + | 0.881241i | \(0.656709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13685.2 | −0.579630 | −0.289815 | − | 0.957083i | \(-0.593594\pi\) | ||||
−0.289815 | + | 0.957083i | \(0.593594\pi\) | |||||||
\(824\) | 13539.0 | + | 33.0231i | 0.572394 | + | 0.00139613i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 42270.9 | − | 4283.55i | 1.78062 | − | 0.180441i | ||||
\(827\) | 19942.6 | 0.838539 | 0.419270 | − | 0.907862i | \(-0.362286\pi\) | ||||
0.419270 | + | 0.907862i | \(0.362286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18891.1 | −0.791455 | −0.395728 | − | 0.918368i | \(-0.629508\pi\) | ||||
−0.395728 | + | 0.918368i | \(0.629508\pi\) | |||||||
\(830\) | −2714.94 | + | 1564.53i | −0.113538 | + | 0.0654284i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20497.6 | − | 99.9924i | −0.854117 | − | 0.00416660i | ||||
\(833\) | 17457.6 | + | 19617.5i | 0.726135 | + | 0.815973i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42909.8i | 1.77839i | ||||||||
\(836\) | −425.509 | + | 734.243i | −0.0176035 | + | 0.0303760i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13007.0 | − | 22571.1i | −0.536179 | − | 0.930436i | ||||
\(839\) | −33269.2 | −1.36899 | −0.684494 | − | 0.729018i | \(-0.739977\pi\) | ||||
−0.684494 | + | 0.729018i | \(0.739977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18041.9 | −0.739756 | ||||||||
\(842\) | 13111.1 | + | 22751.8i | 0.536626 | + | 0.931211i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −41341.0 | − | 23957.9i | −1.68604 | − | 0.977093i | ||||
\(845\) | − | 12588.5i | − | 0.512493i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −970.380 | + | 2162.52i | −0.0393656 | + | 0.0877272i | ||||
\(848\) | 15619.6 | + | 27258.2i | 0.632522 | + | 1.10383i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −60754.1 | + | 35010.6i | −2.45159 | + | 1.41277i | ||||
\(851\) | 29565.9 | 1.19096 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17794.2 | −0.714256 | −0.357128 | − | 0.934055i | \(-0.616244\pi\) | ||||
−0.357128 | + | 0.934055i | \(0.616244\pi\) | |||||||
\(854\) | −874.539 | − | 8630.11i | −0.0350423 | − | 0.345804i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 38.2148 | − | 15667.5i | 0.00152588 | − | 0.625589i | ||||
\(857\) | −2452.81 | −0.0977671 | −0.0488835 | − | 0.998804i | \(-0.515566\pi\) | ||||
−0.0488835 | + | 0.998804i | \(0.515566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3783.50 | −0.150281 | −0.0751404 | − | 0.997173i | \(-0.523941\pi\) | ||||
−0.0751404 | + | 0.997173i | \(0.523941\pi\) | |||||||
\(860\) | −32798.1 | + | 56595.2i | −1.30047 | + | 2.24405i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20263.9 | + | 35164.0i | 0.800684 | + | 1.38943i | ||||
\(863\) | − | 39332.7i | − | 1.55145i | −0.631070 | − | 0.775726i | \(-0.717384\pi\) | ||
0.631070 | − | 0.775726i | \(-0.282616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14370.9 | 0.564884 | ||||||||
\(866\) | 9913.57 | + | 17203.1i | 0.389003 | + | 0.675040i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3075.84 | + | 2213.45i | −0.120277 | + | 0.0865547i | ||||
\(869\) | −20771.6 | −0.810850 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 25304.5i | − | 0.984396i | ||||||
\(872\) | −27379.1 | − | 66.7807i | −1.06327 | − | 0.00259344i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 784.572 | + | 1361.47i | 0.0303645 | + | 0.0526917i | ||||
\(875\) | −71166.5 | − | 31934.3i | −2.74956 | − | 1.23380i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 21948.9i | − | 0.845110i | −0.906337 | − | 0.422555i | \(-0.861133\pi\) | ||
0.906337 | − | 0.422555i | \(-0.138867\pi\) | |||||||
\(878\) | 19410.3 | + | 33682.8i | 0.746087 | + | 1.29469i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −40802.7 | + | 23380.9i | −1.56302 | + | 0.895647i | ||||
\(881\) | 2497.58 | 0.0955114 | 0.0477557 | − | 0.998859i | \(-0.484793\pi\) | ||||
0.0477557 | + | 0.998859i | \(0.484793\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 31080.3i | − | 1.18452i | −0.805746 | − | 0.592261i | \(-0.798235\pi\) | ||
0.805746 | − | 0.592261i | \(-0.201765\pi\) | |||||||
\(884\) | −12295.0 | + | 21215.8i | −0.467788 | + | 0.807199i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10494.0 | + | 6047.37i | −0.397917 | + | 0.229306i | ||||
\(887\) | −5232.45 | −0.198071 | −0.0990353 | − | 0.995084i | \(-0.531576\pi\) | ||||
−0.0990353 | + | 0.995084i | \(0.531576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1262.51 | + | 2813.53i | −0.0476300 | + | 0.106145i | ||||
\(890\) | −38511.4 | − | 66829.2i | −1.45046 | − | 2.51699i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2799.90 | − | 1622.60i | −0.105098 | − | 0.0609066i | ||||
\(893\) | −609.399 | −0.0228362 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 73762.5i | − | 2.75487i | ||||||
\(896\) | −2573.80 | − | 26696.4i | −0.0959649 | − | 0.995385i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 338.493 | + | 587.389i | 0.0125787 | + | 0.0218279i | ||||
\(899\) | 2037.65i | 0.0755944i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37582.3 | 1.38962 | ||||||||
\(902\) | 16265.3 | − | 9373.15i | 0.600416 | − | 0.346000i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16699.3 | − | 40.7315i | −0.614392 | − | 0.00149857i | ||||
\(905\) | − | 32660.8i | − | 1.19965i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19181.1i | 0.702202i | 0.936338 | + | 0.351101i | \(0.114193\pi\) | ||||
−0.936338 | + | 0.351101i | \(0.885807\pi\) | |||||||
\(908\) | 25111.7 | + | 14552.8i | 0.917799 | + | 0.531883i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −44202.0 | + | 4479.24i | −1.61020 | + | 0.163171i | ||||
\(911\) | 11163.6i | 0.405999i | 0.979179 | + | 0.203000i | \(0.0650690\pi\) | ||||
−0.979179 | + | 0.203000i | \(0.934931\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1813.79i | 0.0657476i | ||||||||
\(914\) | 11531.1 | − | 6644.98i | 0.417302 | − | 0.240477i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20370.2 | + | 35150.0i | −0.734770 | + | 1.26789i | ||||
\(917\) | −7000.49 | − | 3141.31i | −0.252101 | − | 0.113125i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16868.9 | 0.605497 | 0.302749 | − | 0.953070i | \(-0.402096\pi\) | ||||
0.302749 | + | 0.953070i | \(0.402096\pi\) | |||||||
\(920\) | −212.390 | + | 87076.8i | −0.00761120 | + | 3.12048i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12451.5 | − | 21607.2i | −0.444760 | − | 0.771795i | ||||
\(923\) | − | 24748.0i | − | 0.882548i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 52703.5i | − | 1.87339i | ||||||
\(926\) | 32674.9 | − | 18829.5i | 1.15957 | − | 0.668224i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12460.0 | − | 7261.49i | −0.440754 | − | 0.256864i | ||||
\(929\) | −2289.19 | −0.0808460 | −0.0404230 | − | 0.999183i | \(-0.512871\pi\) | ||||
−0.0404230 | + | 0.999183i | \(0.512871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −697.377 | − | 783.657i | −0.0245495 | − | 0.0275868i | ||||
\(932\) | −10082.1 | − | 5842.78i | −0.354345 | − | 0.205350i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9734.80 | − | 16892.9i | −0.341041 | − | 0.591811i | ||||
\(935\) | 56256.8i | 1.96770i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27738.4i | 0.967100i | 0.875317 | + | 0.483550i | \(0.160653\pi\) | ||||
−0.875317 | + | 0.483550i | \(0.839347\pi\) | |||||||
\(938\) | 32940.7 | − | 3338.07i | 1.14664 | − | 0.116196i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −29218.1 | − | 16932.5i | −1.01382 | − | 0.587529i | ||||
\(941\) | 17456.0i | 0.604729i | 0.953192 | + | 0.302365i | \(0.0977760\pi\) | ||||
−0.953192 | + | 0.302365i | \(0.902224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 34760.4i | − | 1.20038i | ||||||
\(944\) | −45039.2 | + | 25808.5i | −1.55286 | + | 0.889824i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18905.0 | + | 32806.0i | 0.649740 | + | 1.12750i | ||||
\(947\) | 27608.2 | 0.947357 | 0.473679 | − | 0.880698i | \(-0.342926\pi\) | ||||
0.473679 | + | 0.880698i | \(0.342926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11196.8i | 0.382997i | ||||||||
\(950\) | 2426.94 | − | 1398.56i | 0.0828845 | − | 0.0477636i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −29240.1 | − | 13206.6i | −0.995458 | − | 0.449609i | ||||
\(953\) | 29064.4i | 0.987922i | 0.869484 | + | 0.493961i | \(0.164451\pi\) | ||||
−0.869484 | + | 0.493961i | \(0.835549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −79918.1 | −2.70795 | ||||||||
\(956\) | 36419.8 | + | 21106.0i | 1.23211 | + | 0.714035i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14878.0 | + | 8573.68i | −0.501759 | + | 0.289147i | ||||
\(959\) | −41605.9 | − | 18669.7i | −1.40096 | − | 0.628650i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29136.8 | 0.978042 | ||||||||
\(962\) | −9202.22 | − | 15968.7i | −0.308411 | − | 0.535188i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 33059.5 | + | 19158.7i | 1.10454 | + | 0.640103i | ||||
\(965\) | 32087.1i | 1.07038i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9916.78 | 0.329785 | 0.164892 | − | 0.986312i | \(-0.447272\pi\) | ||||
0.164892 | + | 0.986312i | \(0.447272\pi\) | |||||||
\(968\) | 7.06340 | − | 2895.89i | 0.000234531 | − | 0.0961544i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −94543.6 | + | 54482.3i | −3.12950 | + | 1.80342i | ||||
\(971\) | − | 44197.3i | − | 1.46072i | −0.683063 | − | 0.730359i | \(-0.739353\pi\) | ||
0.683063 | − | 0.730359i | \(-0.260647\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2520.40 | + | 5616.79i | −0.0830426 | + | 0.185063i | ||||
\(974\) | 24714.9 | − | 14242.4i | 0.813057 | − | 0.468538i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5269.11 | + | 9195.30i | 0.172807 | + | 0.301572i | ||||
\(977\) | 23220.3i | 0.760373i | 0.924910 | + | 0.380186i | \(0.124140\pi\) | ||||
−0.924910 | + | 0.380186i | \(0.875860\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −44647.0 | −1.45753 | ||||||||
\(980\) | −11661.9 | − | 56950.1i | −0.380129 | − | 1.85633i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27023.7 | − | 15572.8i | 0.878166 | − | 0.506058i | ||||
\(983\) | 54837.1 | 1.77928 | 0.889640 | − | 0.456663i | \(-0.150955\pi\) | ||||
0.889640 | + | 0.456663i | \(0.150955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 76926.3i | − | 2.48840i | ||||||
\(986\) | −14947.7 | + | 8613.88i | −0.482792 | + | 0.278217i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 491.146 | − | 847.503i | 0.0158152 | − | 0.0272902i | ||||
\(989\) | 70109.3 | 2.25414 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18645.4 | 0.597670 | 0.298835 | − | 0.954305i | \(-0.403402\pi\) | ||||
0.298835 | + | 0.954305i | \(0.403402\pi\) | |||||||
\(992\) | 2331.21 | − | 4000.13i | 0.0746128 | − | 0.128028i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32216.4 | − | 3264.67i | 1.02801 | − | 0.104174i | ||||
\(995\) | −48130.0 | −1.53349 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38576.5 | 1.22541 | 0.612703 | − | 0.790313i | \(-0.290082\pi\) | ||||
0.612703 | + | 0.790313i | \(0.290082\pi\) | |||||||
\(998\) | −4381.75 | − | 7603.68i | −0.138980 | − | 0.241173i | ||||
\(999\) | 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 | 504.4.i.b.125.16 | yes | 88 | |
3.2 | odd | 2 | inner | 504.4.i.b.125.74 | yes | 88 | |
4.3 | odd | 2 | 2016.4.i.b.881.10 | 88 | |||
7.6 | odd | 2 | inner | 504.4.i.b.125.15 | yes | 88 | |
8.3 | odd | 2 | 2016.4.i.b.881.79 | 88 | |||
8.5 | even | 2 | inner | 504.4.i.b.125.75 | yes | 88 | |
12.11 | even | 2 | 2016.4.i.b.881.53 | 88 | |||
21.20 | even | 2 | inner | 504.4.i.b.125.73 | yes | 88 | |
24.5 | odd | 2 | inner | 504.4.i.b.125.13 | ✓ | 88 | |
24.11 | even | 2 | 2016.4.i.b.881.36 | 88 | |||
28.27 | even | 2 | 2016.4.i.b.881.35 | 88 | |||
56.13 | odd | 2 | inner | 504.4.i.b.125.76 | yes | 88 | |
56.27 | even | 2 | 2016.4.i.b.881.54 | 88 | |||
84.83 | odd | 2 | 2016.4.i.b.881.80 | 88 | |||
168.83 | odd | 2 | 2016.4.i.b.881.9 | 88 | |||
168.125 | even | 2 | inner | 504.4.i.b.125.14 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.4.i.b.125.13 | ✓ | 88 | 24.5 | odd | 2 | inner | |
504.4.i.b.125.14 | yes | 88 | 168.125 | even | 2 | inner | |
504.4.i.b.125.15 | yes | 88 | 7.6 | odd | 2 | inner | |
504.4.i.b.125.16 | yes | 88 | 1.1 | even | 1 | trivial | |
504.4.i.b.125.73 | yes | 88 | 21.20 | even | 2 | inner | |
504.4.i.b.125.74 | yes | 88 | 3.2 | odd | 2 | inner | |
504.4.i.b.125.75 | yes | 88 | 8.5 | even | 2 | inner | |
504.4.i.b.125.76 | yes | 88 | 56.13 | odd | 2 | inner | |
2016.4.i.b.881.9 | 88 | 168.83 | odd | 2 | |||
2016.4.i.b.881.10 | 88 | 4.3 | odd | 2 | |||
2016.4.i.b.881.35 | 88 | 28.27 | even | 2 | |||
2016.4.i.b.881.36 | 88 | 24.11 | even | 2 | |||
2016.4.i.b.881.53 | 88 | 12.11 | even | 2 | |||
2016.4.i.b.881.54 | 88 | 56.27 | even | 2 | |||
2016.4.i.b.881.79 | 88 | 8.3 | odd | 2 | |||
2016.4.i.b.881.80 | 88 | 84.83 | odd | 2 |