Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,4,Mod(53,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("120.53");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.08022920069\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(64\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 53.11 | ||
Character | \(\chi\) | \(=\) | 120.53 |
Dual form | 120.4.w.c.77.11 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49705 | + | 1.32844i | −0.882839 | + | 0.469675i | ||||
\(3\) | 0.0934179 | + | 5.19531i | 0.0179783 | + | 0.999838i | ||||
\(4\) | 4.47048 | − | 6.63436i | 0.558811 | − | 0.829295i | ||||
\(5\) | 5.77473 | − | 9.57353i | 0.516507 | − | 0.856283i | ||||
\(6\) | −7.13494 | − | 12.8488i | −0.485471 | − | 0.874253i | ||||
\(7\) | −15.4977 | + | 15.4977i | −0.836799 | + | 0.836799i | −0.988436 | − | 0.151637i | \(-0.951546\pi\) |
0.151637 | + | 0.988436i | \(0.451546\pi\) | |||||||
\(8\) | −2.34964 | + | 22.5051i | −0.103841 | + | 0.994594i | ||||
\(9\) | −26.9825 | + | 0.970671i | −0.999354 | + | 0.0359508i | ||||
\(10\) | −1.70189 | + | 31.5769i | −0.0538184 | + | 0.998551i | ||||
\(11\) | 24.0882 | 0.660259 | 0.330130 | − | 0.943936i | \(-0.392908\pi\) | ||||
0.330130 | + | 0.943936i | \(0.392908\pi\) | |||||||
\(12\) | 34.8852 | + | 22.6058i | 0.839208 | + | 0.543811i | ||||
\(13\) | −64.6828 | + | 64.6828i | −1.37998 | + | 1.37998i | −0.535360 | + | 0.844624i | \(0.679824\pi\) |
−0.844624 | + | 0.535360i | \(0.820176\pi\) | |||||||
\(14\) | 18.1107 | − | 59.2864i | 0.345736 | − | 1.13178i | ||||
\(15\) | 50.2770 | + | 29.1072i | 0.865430 | + | 0.501029i | ||||
\(16\) | −24.0295 | − | 59.3176i | −0.375461 | − | 0.926838i | ||||
\(17\) | −69.5236 | − | 69.5236i | −0.991880 | − | 0.991880i | 0.00808721 | − | 0.999967i | \(-0.497426\pi\) |
−0.999967 | + | 0.00808721i | \(0.997426\pi\) | |||||||
\(18\) | 66.0872 | − | 38.2686i | 0.865383 | − | 0.501110i | ||||
\(19\) | −0.230558 | −0.00278387 | −0.00139194 | − | 0.999999i | \(-0.500443\pi\) | ||||
−0.00139194 | + | 0.999999i | \(0.500443\pi\) | |||||||
\(20\) | −37.6984 | − | 81.1100i | −0.421481 | − | 0.906837i | ||||
\(21\) | −81.9634 | − | 79.0678i | −0.851708 | − | 0.821620i | ||||
\(22\) | −60.1493 | + | 31.9997i | −0.582903 | + | 0.310107i | ||||
\(23\) | −23.1362 | + | 23.1362i | −0.209749 | + | 0.209749i | −0.804161 | − | 0.594412i | \(-0.797385\pi\) |
0.594412 | + | 0.804161i | \(0.297385\pi\) | |||||||
\(24\) | −117.140 | − | 10.1048i | −0.996300 | − | 0.0859427i | ||||
\(25\) | −58.3050 | − | 110.569i | −0.466440 | − | 0.884553i | ||||
\(26\) | 75.5887 | − | 247.443i | 0.570160 | − | 1.86645i | ||||
\(27\) | −7.56359 | − | 140.092i | −0.0539116 | − | 0.998546i | ||||
\(28\) | 33.5352 | + | 172.100i | 0.226341 | + | 1.16157i | ||||
\(29\) | 110.723i | 0.708991i | 0.935058 | + | 0.354496i | \(0.115347\pi\) | ||||
−0.935058 | + | 0.354496i | \(0.884653\pi\) | |||||||
\(30\) | −164.211 | − | 5.89199i | −0.999357 | − | 0.0358575i | ||||
\(31\) | −210.319 | −1.21853 | −0.609266 | − | 0.792966i | \(-0.708536\pi\) | ||||
−0.609266 | + | 0.792966i | \(0.708536\pi\) | |||||||
\(32\) | 138.803 | + | 116.197i | 0.766785 | + | 0.641904i | ||||
\(33\) | 2.25027 | + | 125.146i | 0.0118703 | + | 0.660153i | ||||
\(34\) | 265.962 | + | 81.2457i | 1.34153 | + | 0.409809i | ||||
\(35\) | 58.8729 | + | 237.863i | 0.284324 | + | 1.14875i | ||||
\(36\) | −114.185 | + | 183.351i | −0.528636 | + | 0.848849i | ||||
\(37\) | 16.5677 | + | 16.5677i | 0.0736140 | + | 0.0736140i | 0.742955 | − | 0.669341i | \(-0.233424\pi\) |
−0.669341 | + | 0.742955i | \(0.733424\pi\) | |||||||
\(38\) | 0.575714 | − | 0.306283i | 0.00245771 | − | 0.00130752i | ||||
\(39\) | −342.090 | − | 330.005i | −1.40457 | − | 1.35495i | ||||
\(40\) | 201.885 | + | 152.455i | 0.798019 | + | 0.602632i | ||||
\(41\) | − | 28.8516i | − | 0.109899i | −0.998489 | − | 0.0549495i | \(-0.982500\pi\) | ||
0.998489 | − | 0.0549495i | \(-0.0174998\pi\) | |||||||
\(42\) | 309.703 | + | 88.5525i | 1.13782 | + | 0.325332i | ||||
\(43\) | 66.7330 | − | 66.7330i | 0.236667 | − | 0.236667i | −0.578801 | − | 0.815469i | \(-0.696479\pi\) |
0.815469 | + | 0.578801i | \(0.196479\pi\) | |||||||
\(44\) | 107.686 | − | 159.810i | 0.368960 | − | 0.547550i | ||||
\(45\) | −146.524 | + | 263.924i | −0.485390 | + | 0.874298i | ||||
\(46\) | 27.0371 | − | 88.5073i | 0.0866609 | − | 0.283689i | ||||
\(47\) | 171.055 | + | 171.055i | 0.530872 | + | 0.530872i | 0.920832 | − | 0.389960i | \(-0.127511\pi\) |
−0.389960 | + | 0.920832i | \(0.627511\pi\) | |||||||
\(48\) | 305.929 | − | 130.382i | 0.919938 | − | 0.392064i | ||||
\(49\) | − | 137.360i | − | 0.400466i | ||||||
\(50\) | 292.475 | + | 198.641i | 0.827244 | + | 0.561843i | ||||
\(51\) | 354.702 | − | 367.692i | 0.973887 | − | 1.00955i | ||||
\(52\) | 139.966 | + | 718.293i | 0.373265 | + | 1.91556i | ||||
\(53\) | −375.292 | − | 375.292i | −0.972647 | − | 0.972647i | 0.0269890 | − | 0.999636i | \(-0.491408\pi\) |
−0.999636 | + | 0.0269890i | \(0.991408\pi\) | |||||||
\(54\) | 204.991 | + | 339.769i | 0.516587 | + | 0.856234i | ||||
\(55\) | 139.103 | − | 230.609i | 0.341029 | − | 0.565369i | ||||
\(56\) | −312.364 | − | 385.192i | −0.745382 | − | 0.919169i | ||||
\(57\) | −0.0215382 | − | 1.19782i | −5.00493e−5 | − | 0.00278342i | ||||
\(58\) | −147.089 | − | 276.481i | −0.332996 | − | 0.625925i | ||||
\(59\) | 713.261i | 1.57388i | 0.617032 | + | 0.786938i | \(0.288335\pi\) | ||||
−0.617032 | + | 0.786938i | \(0.711665\pi\) | |||||||
\(60\) | 417.870 | − | 203.432i | 0.899113 | − | 0.437717i | ||||
\(61\) | 699.712i | 1.46867i | 0.678786 | + | 0.734336i | \(0.262506\pi\) | ||||
−0.678786 | + | 0.734336i | \(0.737494\pi\) | |||||||
\(62\) | 525.177 | − | 279.397i | 1.07577 | − | 0.572314i | ||||
\(63\) | 403.125 | − | 433.212i | 0.806175 | − | 0.866342i | ||||
\(64\) | −500.958 | − | 105.758i | −0.978434 | − | 0.206558i | ||||
\(65\) | 245.717 | + | 992.769i | 0.468884 | + | 1.89443i | ||||
\(66\) | −171.868 | − | 309.505i | −0.320537 | − | 0.577234i | ||||
\(67\) | 401.278 | + | 401.278i | 0.731700 | + | 0.731700i | 0.970956 | − | 0.239257i | \(-0.0769037\pi\) |
−0.239257 | + | 0.970956i | \(0.576904\pi\) | |||||||
\(68\) | −772.049 | + | 150.441i | −1.37683 | + | 0.268288i | ||||
\(69\) | −122.361 | − | 118.038i | −0.213486 | − | 0.205944i | ||||
\(70\) | −462.996 | − | 515.747i | −0.790551 | − | 0.880622i | ||||
\(71\) | − | 534.168i | − | 0.892875i | −0.894815 | − | 0.446438i | \(-0.852693\pi\) | ||
0.894815 | − | 0.446438i | \(-0.147307\pi\) | |||||||
\(72\) | 41.5544 | − | 609.525i | 0.0680171 | − | 0.997684i | ||||
\(73\) | 124.152 | + | 124.152i | 0.199054 | + | 0.199054i | 0.799594 | − | 0.600541i | \(-0.205048\pi\) |
−0.600541 | + | 0.799594i | \(0.705048\pi\) | |||||||
\(74\) | −63.3797 | − | 19.3611i | −0.0995641 | − | 0.0304147i | ||||
\(75\) | 568.994 | − | 313.242i | 0.876024 | − | 0.482267i | ||||
\(76\) | −1.03071 | + | 1.52960i | −0.00155566 | + | 0.00230865i | ||||
\(77\) | −373.312 | + | 373.312i | −0.552505 | + | 0.552505i | ||||
\(78\) | 1292.61 | + | 369.591i | 1.87640 | + | 0.536512i | ||||
\(79\) | 647.639i | 0.922342i | 0.887311 | + | 0.461171i | \(0.152571\pi\) | ||||
−0.887311 | + | 0.461171i | \(0.847429\pi\) | |||||||
\(80\) | −706.643 | − | 112.496i | −0.987564 | − | 0.157218i | ||||
\(81\) | 727.116 | − | 52.3823i | 0.997415 | − | 0.0718551i | ||||
\(82\) | 38.3276 | + | 72.0437i | 0.0516168 | + | 0.0970231i | ||||
\(83\) | −29.7418 | − | 29.7418i | −0.0393324 | − | 0.0393324i | 0.687167 | − | 0.726499i | \(-0.258854\pi\) |
−0.726499 | + | 0.687167i | \(0.758854\pi\) | |||||||
\(84\) | −890.981 | + | 190.303i | −1.15731 | + | 0.247188i | ||||
\(85\) | −1067.07 | + | 264.107i | −1.36164 | + | 0.337016i | ||||
\(86\) | −77.9845 | + | 255.286i | −0.0977824 | + | 0.320096i | ||||
\(87\) | −575.241 | + | 10.3435i | −0.708877 | + | 0.0127465i | ||||
\(88\) | −56.5986 | + | 542.106i | −0.0685617 | + | 0.656690i | ||||
\(89\) | −250.355 | −0.298175 | −0.149087 | − | 0.988824i | \(-0.547634\pi\) | ||||
−0.149087 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(90\) | 15.2705 | − | 853.678i | 0.0178850 | − | 0.999840i | ||||
\(91\) | − | 2004.88i | − | 2.30954i | ||||||
\(92\) | 50.0639 | + | 256.924i | 0.0567339 | + | 0.291154i | ||||
\(93\) | −19.6476 | − | 1092.68i | −0.0219071 | − | 1.21833i | ||||
\(94\) | −654.370 | − | 199.896i | −0.718012 | − | 0.219337i | ||||
\(95\) | −1.33141 | + | 2.20725i | −0.00143789 | + | 0.00238378i | ||||
\(96\) | −590.713 | + | 731.979i | −0.628015 | + | 0.778201i | ||||
\(97\) | −209.767 | + | 209.767i | −0.219573 | + | 0.219573i | −0.808318 | − | 0.588746i | \(-0.799622\pi\) |
0.588746 | + | 0.808318i | \(0.299622\pi\) | |||||||
\(98\) | 182.475 | + | 342.994i | 0.188089 | + | 0.353548i | ||||
\(99\) | −649.960 | + | 23.3817i | −0.659833 | + | 0.0237368i | ||||
\(100\) | −994.207 | − | 107.481i | −0.994207 | − | 0.107481i | ||||
\(101\) | −107.008 | −0.105423 | −0.0527115 | − | 0.998610i | \(-0.516786\pi\) | ||||
−0.0527115 | + | 0.998610i | \(0.516786\pi\) | |||||||
\(102\) | −397.251 | + | 1389.35i | −0.385625 | + | 1.34868i | ||||
\(103\) | 371.193 | + | 371.193i | 0.355095 | + | 0.355095i | 0.862001 | − | 0.506906i | \(-0.169211\pi\) |
−0.506906 | + | 0.862001i | \(0.669211\pi\) | |||||||
\(104\) | −1303.71 | − | 1607.67i | −1.22923 | − | 1.51582i | ||||
\(105\) | −1230.27 | + | 328.084i | −1.14345 | + | 0.304930i | ||||
\(106\) | 1435.67 | + | 438.568i | 1.31552 | + | 0.401863i | ||||
\(107\) | 868.693 | − | 868.693i | 0.784858 | − | 0.784858i | −0.195789 | − | 0.980646i | \(-0.562727\pi\) |
0.980646 | + | 0.195789i | \(0.0627266\pi\) | |||||||
\(108\) | −963.235 | − | 576.100i | −0.858216 | − | 0.513289i | ||||
\(109\) | 1296.69 | 1.13945 | 0.569725 | − | 0.821835i | \(-0.307050\pi\) | ||||
0.569725 | + | 0.821835i | \(0.307050\pi\) | |||||||
\(110\) | −40.9953 | + | 760.631i | −0.0355341 | + | 0.659302i | ||||
\(111\) | −84.5269 | + | 87.6223i | −0.0722787 | + | 0.0749256i | ||||
\(112\) | 1291.69 | + | 546.886i | 1.08976 | + | 0.461392i | ||||
\(113\) | 1121.02 | − | 1121.02i | 0.933243 | − | 0.933243i | −0.0646636 | − | 0.997907i | \(-0.520597\pi\) |
0.997907 | + | 0.0646636i | \(0.0205974\pi\) | |||||||
\(114\) | 1.64502 | + | 2.96240i | 0.00135149 | + | 0.00243381i | ||||
\(115\) | 87.8899 | + | 355.100i | 0.0712676 | + | 0.287942i | ||||
\(116\) | 734.577 | + | 494.986i | 0.587963 | + | 0.396192i | ||||
\(117\) | 1682.52 | − | 1808.09i | 1.32948 | − | 1.42870i | ||||
\(118\) | −947.526 | − | 1781.05i | −0.739210 | − | 1.38948i | ||||
\(119\) | 2154.92 | 1.66001 | ||||||||
\(120\) | −773.193 | + | 1063.10i | −0.588188 | + | 0.808724i | ||||
\(121\) | −750.761 | −0.564058 | ||||||||
\(122\) | −929.527 | − | 1747.21i | −0.689798 | − | 1.29660i | ||||
\(123\) | 149.893 | − | 2.69525i | 0.109881 | − | 0.00197579i | ||||
\(124\) | −940.230 | + | 1395.34i | −0.680928 | + | 1.01052i | ||||
\(125\) | −1395.23 | − | 80.3216i | −0.998347 | − | 0.0574735i | ||||
\(126\) | −431.126 | + | 1617.28i | −0.304824 | + | 1.14348i | ||||
\(127\) | −1017.88 | + | 1017.88i | −0.711197 | + | 0.711197i | −0.966786 | − | 0.255588i | \(-0.917731\pi\) |
0.255588 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(128\) | 1391.41 | − | 401.411i | 0.960816 | − | 0.277188i | ||||
\(129\) | 352.933 | + | 340.465i | 0.240884 | + | 0.232374i | ||||
\(130\) | −1932.40 | − | 2152.57i | −1.30372 | − | 1.45225i | ||||
\(131\) | −139.067 | −0.0927508 | −0.0463754 | − | 0.998924i | \(-0.514767\pi\) | ||||
−0.0463754 | + | 0.998924i | \(0.514767\pi\) | |||||||
\(132\) | 840.320 | + | 544.532i | 0.554095 | + | 0.359056i | ||||
\(133\) | 3.57313 | − | 3.57313i | 0.00232954 | − | 0.00232954i | ||||
\(134\) | −1535.08 | − | 468.935i | −0.989635 | − | 0.302312i | ||||
\(135\) | −1384.85 | − | 736.584i | −0.882883 | − | 0.469593i | ||||
\(136\) | 1727.99 | − | 1401.28i | 1.08952 | − | 0.883521i | ||||
\(137\) | 511.555 | + | 511.555i | 0.319015 | + | 0.319015i | 0.848389 | − | 0.529374i | \(-0.177573\pi\) |
−0.529374 | + | 0.848389i | \(0.677573\pi\) | |||||||
\(138\) | 462.349 | + | 132.198i | 0.285201 | + | 0.0815466i | ||||
\(139\) | 2280.35 | 1.39149 | 0.695743 | − | 0.718291i | \(-0.255075\pi\) | ||||
0.695743 | + | 0.718291i | \(0.255075\pi\) | |||||||
\(140\) | 1841.26 | + | 672.781i | 1.11154 | + | 0.406145i | ||||
\(141\) | −872.706 | + | 904.665i | −0.521242 | + | 0.540330i | ||||
\(142\) | 709.612 | + | 1333.84i | 0.419361 | + | 0.788265i | ||||
\(143\) | −1558.09 | + | 1558.09i | −0.911147 | + | 0.911147i | ||||
\(144\) | 705.956 | + | 1577.22i | 0.408539 | + | 0.912741i | ||||
\(145\) | 1060.01 | + | 639.395i | 0.607097 | + | 0.366199i | ||||
\(146\) | −474.943 | − | 145.085i | −0.269223 | − | 0.0822418i | ||||
\(147\) | 713.628 | − | 12.8319i | 0.400402 | − | 0.00719970i | ||||
\(148\) | 183.982 | − | 35.8506i | 0.102184 | − | 0.0199115i | ||||
\(149\) | 2215.59i | 1.21817i | 0.793103 | + | 0.609087i | \(0.208464\pi\) | ||||
−0.793103 | + | 0.609087i | \(0.791536\pi\) | |||||||
\(150\) | −1004.68 | + | 1538.06i | −0.546879 | + | 0.837211i | ||||
\(151\) | 1552.95 | 0.836936 | 0.418468 | − | 0.908231i | \(-0.362567\pi\) | ||||
0.418468 | + | 0.908231i | \(0.362567\pi\) | |||||||
\(152\) | 0.541729 | − | 5.18873i | 0.000289079 | − | 0.00276882i | ||||
\(153\) | 1943.41 | + | 1808.44i | 1.02690 | + | 0.955580i | ||||
\(154\) | 436.254 | − | 1428.10i | 0.228275 | − | 0.747270i | ||||
\(155\) | −1214.54 | + | 2013.50i | −0.629381 | + | 1.04341i | ||||
\(156\) | −3718.68 | + | 794.267i | −1.90854 | + | 0.407643i | ||||
\(157\) | −1466.03 | − | 1466.03i | −0.745235 | − | 0.745235i | 0.228345 | − | 0.973580i | \(-0.426669\pi\) |
−0.973580 | + | 0.228345i | \(0.926669\pi\) | |||||||
\(158\) | −860.350 | − | 1617.18i | −0.433201 | − | 0.814280i | ||||
\(159\) | 1914.70 | − | 1984.82i | 0.955003 | − | 0.989976i | ||||
\(160\) | 1913.97 | − | 657.827i | 0.945702 | − | 0.325036i | ||||
\(161\) | − | 717.118i | − | 0.351036i | ||||||
\(162\) | −1746.05 | + | 1096.73i | −0.846809 | + | 0.531898i | ||||
\(163\) | −2451.50 | + | 2451.50i | −1.17801 | + | 1.17801i | −0.197766 | + | 0.980249i | \(0.563368\pi\) |
−0.980249 | + | 0.197766i | \(0.936632\pi\) | |||||||
\(164\) | −191.412 | − | 128.980i | −0.0911387 | − | 0.0614127i | ||||
\(165\) | 1211.08 | + | 701.138i | 0.571408 | + | 0.330809i | ||||
\(166\) | 113.777 | + | 34.7564i | 0.0531976 | + | 0.0162507i | ||||
\(167\) | 557.655 | + | 557.655i | 0.258399 | + | 0.258399i | 0.824403 | − | 0.566004i | \(-0.191511\pi\) |
−0.566004 | + | 0.824403i | \(0.691511\pi\) | |||||||
\(168\) | 1972.01 | − | 1658.81i | 0.905620 | − | 0.761786i | ||||
\(169\) | − | 6170.74i | − | 2.80871i | ||||||
\(170\) | 2313.67 | − | 2077.02i | 1.04382 | − | 0.937061i | ||||
\(171\) | 6.22104 | − | 0.223796i | 0.00278207 | − | 0.000100082i | ||||
\(172\) | −144.402 | − | 741.060i | −0.0640148 | − | 0.328519i | ||||
\(173\) | 697.593 | + | 697.593i | 0.306572 | + | 0.306572i | 0.843578 | − | 0.537006i | \(-0.180445\pi\) |
−0.537006 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(174\) | 1422.66 | − | 790.002i | 0.619838 | − | 0.344195i | ||||
\(175\) | 2617.17 | + | 809.975i | 1.13051 | + | 0.349876i | ||||
\(176\) | −578.827 | − | 1428.85i | −0.247902 | − | 0.611953i | ||||
\(177\) | −3705.61 | + | 66.6314i | −1.57362 | + | 0.0282956i | ||||
\(178\) | 625.148 | − | 332.582i | 0.263240 | − | 0.140045i | ||||
\(179\) | − | 403.165i | − | 0.168346i | −0.996451 | − | 0.0841731i | \(-0.973175\pi\) | ||
0.996451 | − | 0.0841731i | \(-0.0268249\pi\) | |||||||
\(180\) | 1095.93 | + | 2151.96i | 0.453810 | + | 0.891098i | ||||
\(181\) | − | 2079.83i | − | 0.854102i | −0.904228 | − | 0.427051i | \(-0.859552\pi\) | ||
0.904228 | − | 0.427051i | \(-0.140448\pi\) | |||||||
\(182\) | 2663.36 | + | 5006.27i | 1.08473 | + | 2.03895i | ||||
\(183\) | −3635.22 | + | 65.3657i | −1.46843 | + | 0.0264042i | ||||
\(184\) | −466.320 | − | 575.044i | −0.186835 | − | 0.230396i | ||||
\(185\) | 254.286 | − | 62.9376i | 0.101057 | − | 0.0250122i | ||||
\(186\) | 1500.62 | + | 2702.36i | 0.591562 | + | 1.06530i | ||||
\(187\) | −1674.70 | − | 1674.70i | −0.654898 | − | 0.654898i | ||||
\(188\) | 1899.54 | − | 370.143i | 0.736906 | − | 0.143593i | ||||
\(189\) | 2288.33 | + | 2053.89i | 0.880696 | + | 0.790469i | ||||
\(190\) | 0.392384 | − | 7.28032i | 0.000149824 | − | 0.00277984i | ||||
\(191\) | − | 1633.99i | − | 0.619013i | −0.950897 | − | 0.309506i | \(-0.899836\pi\) | ||
0.950897 | − | 0.309506i | \(-0.100164\pi\) | |||||||
\(192\) | 502.647 | − | 2612.51i | 0.188935 | − | 0.981990i | ||||
\(193\) | −1462.69 | − | 1462.69i | −0.545527 | − | 0.545527i | 0.379616 | − | 0.925144i | \(-0.376056\pi\) |
−0.925144 | + | 0.379616i | \(0.876056\pi\) | |||||||
\(194\) | 245.134 | − | 802.460i | 0.0907197 | − | 0.296976i | ||||
\(195\) | −5134.79 | + | 1369.32i | −1.88569 | + | 0.502867i | ||||
\(196\) | −911.296 | − | 614.066i | −0.332105 | − | 0.223785i | ||||
\(197\) | −44.6663 | + | 44.6663i | −0.0161540 | + | 0.0161540i | −0.715138 | − | 0.698984i | \(-0.753636\pi\) |
0.698984 | + | 0.715138i | \(0.253636\pi\) | |||||||
\(198\) | 1591.92 | − | 921.819i | 0.571378 | − | 0.330863i | ||||
\(199\) | 3949.02i | 1.40673i | 0.710831 | + | 0.703363i | \(0.248319\pi\) | ||||
−0.710831 | + | 0.703363i | \(0.751681\pi\) | |||||||
\(200\) | 2625.36 | − | 1052.36i | 0.928206 | − | 0.372066i | ||||
\(201\) | −2047.28 | + | 2122.25i | −0.718427 | + | 0.744736i | ||||
\(202\) | 267.205 | − | 142.154i | 0.0930715 | − | 0.0495145i | ||||
\(203\) | −1715.96 | − | 1715.96i | −0.593284 | − | 0.593284i | ||||
\(204\) | −853.710 | − | 3996.98i | −0.292998 | − | 1.37179i | ||||
\(205\) | −276.211 | − | 166.610i | −0.0941046 | − | 0.0567636i | ||||
\(206\) | −1420.00 | − | 433.778i | −0.480271 | − | 0.146712i | ||||
\(207\) | 601.816 | − | 646.731i | 0.202073 | − | 0.217154i | ||||
\(208\) | 5391.13 | + | 2282.53i | 1.79715 | + | 0.760891i | ||||
\(209\) | −5.55372 | −0.00183808 | ||||||||
\(210\) | 2636.21 | − | 2453.59i | 0.866267 | − | 0.806256i | ||||
\(211\) | 1517.04i | 0.494963i | 0.968893 | + | 0.247481i | \(0.0796029\pi\) | ||||
−0.968893 | + | 0.247481i | \(0.920397\pi\) | |||||||
\(212\) | −4167.56 | + | 812.085i | −1.35014 | + | 0.263086i | ||||
\(213\) | 2775.17 | − | 49.9009i | 0.892731 | − | 0.0160524i | ||||
\(214\) | −1015.16 | + | 3323.18i | −0.324275 | + | 1.06153i | ||||
\(215\) | −253.506 | − | 1024.24i | −0.0804136 | − | 0.324894i | ||||
\(216\) | 3170.56 | + | 158.947i | 0.998746 | + | 0.0500694i | ||||
\(217\) | 3259.48 | − | 3259.48i | 1.01967 | − | 1.01967i | ||||
\(218\) | −3237.89 | + | 1722.57i | −1.00595 | + | 0.535171i | ||||
\(219\) | −633.411 | + | 656.607i | −0.195443 | + | 0.202600i | ||||
\(220\) | −908.086 | − | 1953.79i | −0.278287 | − | 0.598748i | ||||
\(221\) | 8993.97 | 2.73756 | ||||||||
\(222\) | 94.6664 | − | 331.086i | 0.0286198 | − | 0.100095i | ||||
\(223\) | −1184.11 | − | 1184.11i | −0.355577 | − | 0.355577i | 0.506603 | − | 0.862180i | \(-0.330901\pi\) |
−0.862180 | + | 0.506603i | \(0.830901\pi\) | |||||||
\(224\) | −3951.92 | + | 350.339i | −1.17879 | + | 0.104500i | ||||
\(225\) | 1680.54 | + | 2926.84i | 0.497939 | + | 0.867212i | ||||
\(226\) | −1310.03 | + | 4288.44i | −0.385583 | + | 1.26223i | ||||
\(227\) | −1008.71 | + | 1008.71i | −0.294935 | + | 0.294935i | −0.839026 | − | 0.544091i | \(-0.816875\pi\) |
0.544091 | + | 0.839026i | \(0.316875\pi\) | |||||||
\(228\) | −8.04306 | − | 5.21195i | −0.00233625 | − | 0.00151390i | ||||
\(229\) | −186.732 | −0.0538848 | −0.0269424 | − | 0.999637i | \(-0.508577\pi\) | ||||
−0.0269424 | + | 0.999637i | \(0.508577\pi\) | |||||||
\(230\) | −691.195 | − | 769.946i | −0.198157 | − | 0.220734i | ||||
\(231\) | −1974.35 | − | 1904.60i | −0.562348 | − | 0.542482i | ||||
\(232\) | −2491.83 | − | 260.160i | −0.705159 | − | 0.0736221i | ||||
\(233\) | −3814.45 | + | 3814.45i | −1.07250 | + | 1.07250i | −0.0753429 | + | 0.997158i | \(0.524005\pi\) |
−0.997158 | + | 0.0753429i | \(0.975995\pi\) | |||||||
\(234\) | −1799.39 | + | 6750.03i | −0.502691 | + | 1.88574i | ||||
\(235\) | 2625.40 | − | 649.805i | 0.728776 | − | 0.180377i | ||||
\(236\) | 4732.03 | + | 3188.62i | 1.30521 | + | 0.879499i | ||||
\(237\) | −3364.69 | + | 60.5011i | −0.922193 | + | 0.0165821i | ||||
\(238\) | −5380.93 | + | 2862.68i | −1.46552 | + | 0.779665i | ||||
\(239\) | −3294.18 | −0.891561 | −0.445780 | − | 0.895142i | \(-0.647074\pi\) | ||||
−0.445780 | + | 0.895142i | \(0.647074\pi\) | |||||||
\(240\) | 518.437 | − | 3681.74i | 0.139437 | − | 0.990231i | ||||
\(241\) | −3900.68 | −1.04259 | −0.521296 | − | 0.853376i | \(-0.674551\pi\) | ||||
−0.521296 | + | 0.853376i | \(0.674551\pi\) | |||||||
\(242\) | 1874.68 | − | 997.342i | 0.497972 | − | 0.264924i | ||||
\(243\) | 340.068 | + | 3772.70i | 0.0897753 | + | 0.995962i | ||||
\(244\) | 4642.14 | + | 3128.05i | 1.21796 | + | 0.820709i | ||||
\(245\) | −1315.02 | − | 793.217i | −0.342912 | − | 0.206844i | ||||
\(246\) | −370.709 | + | 205.854i | −0.0960794 | + | 0.0533528i | ||||
\(247\) | 14.9131 | − | 14.9131i | 0.00384170 | − | 0.00384170i | ||||
\(248\) | 494.176 | − | 4733.26i | 0.126533 | − | 1.21194i | ||||
\(249\) | 151.740 | − | 157.296i | 0.0386189 | − | 0.0400331i | ||||
\(250\) | 3590.66 | − | 1652.92i | 0.908374 | − | 0.418159i | ||||
\(251\) | −934.348 | −0.234962 | −0.117481 | − | 0.993075i | \(-0.537482\pi\) | ||||
−0.117481 | + | 0.993075i | \(0.537482\pi\) | |||||||
\(252\) | −1071.92 | − | 4611.15i | −0.267954 | − | 1.15268i | ||||
\(253\) | −557.308 | + | 557.308i | −0.138489 | + | 0.138489i | ||||
\(254\) | 1189.50 | − | 3893.88i | 0.293841 | − | 0.961905i | ||||
\(255\) | −1471.80 | − | 5519.07i | −0.361442 | − | 1.35536i | ||||
\(256\) | −2941.16 | + | 2850.75i | −0.718057 | + | 0.695984i | ||||
\(257\) | −2441.71 | − | 2441.71i | −0.592645 | − | 0.592645i | 0.345700 | − | 0.938345i | \(-0.387641\pi\) |
−0.938345 | + | 0.345700i | \(0.887641\pi\) | |||||||
\(258\) | −1333.58 | − | 381.306i | −0.321802 | − | 0.0920118i | ||||
\(259\) | −513.525 | −0.123200 | ||||||||
\(260\) | 7684.86 | + | 2807.98i | 1.83306 | + | 0.669783i | ||||
\(261\) | −107.476 | − | 2987.59i | −0.0254888 | − | 0.708533i | ||||
\(262\) | 347.257 | − | 184.743i | 0.0818841 | − | 0.0435627i | ||||
\(263\) | −3531.42 | + | 3531.42i | −0.827972 | + | 0.827972i | −0.987236 | − | 0.159264i | \(-0.949088\pi\) |
0.159264 | + | 0.987236i | \(0.449088\pi\) | |||||||
\(264\) | −2821.70 | − | 243.405i | −0.657816 | − | 0.0567445i | ||||
\(265\) | −5760.07 | + | 1425.66i | −1.33524 | + | 0.330481i | ||||
\(266\) | −4.17557 | + | 13.6690i | −0.000962484 | + | 0.00315074i | ||||
\(267\) | −23.3876 | − | 1300.67i | −0.00536067 | − | 0.298127i | ||||
\(268\) | 4456.13 | − | 868.316i | 1.01568 | − | 0.197914i | ||||
\(269\) | − | 2818.14i | − | 0.638754i | −0.947628 | − | 0.319377i | \(-0.896526\pi\) | ||
0.947628 | − | 0.319377i | \(-0.103474\pi\) | |||||||
\(270\) | 4436.55 | − | 0.414082i | 1.00000 | − | 9.33341e-5i | ||||
\(271\) | −2634.55 | −0.590544 | −0.295272 | − | 0.955413i | \(-0.595410\pi\) | ||||
−0.295272 | + | 0.955413i | \(0.595410\pi\) | |||||||
\(272\) | −2453.36 | + | 5794.60i | −0.546899 | + | 1.29172i | ||||
\(273\) | 10416.0 | − | 187.291i | 2.30917 | − | 0.0415216i | ||||
\(274\) | −1956.95 | − | 597.805i | −0.431472 | − | 0.131806i | ||||
\(275\) | −1404.46 | − | 2663.41i | −0.307971 | − | 0.584034i | ||||
\(276\) | −1330.12 | + | 284.099i | −0.290087 | + | 0.0619592i | ||||
\(277\) | −1406.39 | − | 1406.39i | −0.305061 | − | 0.305061i | 0.537929 | − | 0.842990i | \(-0.319207\pi\) |
−0.842990 | + | 0.537929i | \(0.819207\pi\) | |||||||
\(278\) | −5694.14 | + | 3029.31i | −1.22846 | + | 0.653546i | ||||
\(279\) | 5674.95 | − | 204.151i | 1.21774 | − | 0.0438071i | ||||
\(280\) | −5491.47 | + | 766.045i | −1.17206 | + | 0.163500i | ||||
\(281\) | − | 3886.21i | − | 0.825024i | −0.910952 | − | 0.412512i | \(-0.864651\pi\) | ||
0.910952 | − | 0.412512i | \(-0.135349\pi\) | |||||||
\(282\) | 977.392 | − | 3418.33i | 0.206393 | − | 0.721839i | ||||
\(283\) | −1661.83 | + | 1661.83i | −0.349065 | + | 0.349065i | −0.859761 | − | 0.510696i | \(-0.829388\pi\) |
0.510696 | + | 0.859761i | \(0.329388\pi\) | |||||||
\(284\) | −3543.87 | − | 2387.99i | −0.740457 | − | 0.498948i | ||||
\(285\) | −11.5918 | − | 6.71089i | −0.00240925 | − | 0.00139480i | ||||
\(286\) | 1820.79 | − | 5960.46i | 0.376453 | − | 1.23234i | ||||
\(287\) | 447.134 | + | 447.134i | 0.0919634 | + | 0.0919634i | ||||
\(288\) | −3858.04 | − | 3000.56i | −0.789366 | − | 0.613923i | ||||
\(289\) | 4754.08i | 0.967652i | ||||||||
\(290\) | −3496.30 | − | 188.438i | −0.707964 | − | 0.0381568i | ||||
\(291\) | −1109.40 | − | 1070.21i | −0.223485 | − | 0.215590i | ||||
\(292\) | 1378.69 | − | 268.650i | 0.276307 | − | 0.0538409i | ||||
\(293\) | −2067.70 | − | 2067.70i | −0.412273 | − | 0.412273i | 0.470257 | − | 0.882530i | \(-0.344161\pi\) |
−0.882530 | + | 0.470257i | \(0.844161\pi\) | |||||||
\(294\) | −1764.92 | + | 980.055i | −0.350109 | + | 0.194415i | ||||
\(295\) | 6828.43 | + | 4118.89i | 1.34768 | + | 0.812919i | ||||
\(296\) | −411.787 | + | 333.930i | −0.0808602 | + | 0.0655720i | ||||
\(297\) | −182.193 | − | 3374.56i | −0.0355957 | − | 0.659299i | ||||
\(298\) | −2943.28 | − | 5532.43i | −0.572146 | − | 1.07545i | ||||
\(299\) | − | 2993.03i | − | 0.578901i | ||||||
\(300\) | 465.520 | − | 5175.26i | 0.0895893 | − | 0.995979i | ||||
\(301\) | 2068.42i | 0.396086i | ||||||||
\(302\) | −3877.79 | + | 2063.01i | −0.738880 | + | 0.393088i | ||||
\(303\) | −9.99649 | − | 555.941i | −0.00189532 | − | 0.105406i | ||||
\(304\) | 5.54020 | + | 13.6762i | 0.00104524 | + | 0.00258020i | ||||
\(305\) | 6698.72 | + | 4040.65i | 1.25760 | + | 0.758580i | ||||
\(306\) | −7255.19 | − | 1934.05i | −1.35540 | − | 0.361315i | ||||
\(307\) | 2153.93 | + | 2153.93i | 0.400428 | + | 0.400428i | 0.878384 | − | 0.477956i | \(-0.158622\pi\) |
−0.477956 | + | 0.878384i | \(0.658622\pi\) | |||||||
\(308\) | 807.802 | + | 4145.57i | 0.149444 | + | 0.766935i | ||||
\(309\) | −1893.79 | + | 1963.14i | −0.348653 | + | 0.361421i | ||||
\(310\) | 357.940 | − | 6641.25i | 0.0655795 | − | 1.21677i | ||||
\(311\) | − | 1366.14i | − | 0.249089i | −0.992214 | − | 0.124545i | \(-0.960253\pi\) | ||
0.992214 | − | 0.124545i | \(-0.0397470\pi\) | |||||||
\(312\) | 8230.58 | − | 6923.37i | 1.49348 | − | 1.25628i | ||||
\(313\) | 76.9542 | + | 76.9542i | 0.0138968 | + | 0.0138968i | 0.714021 | − | 0.700124i | \(-0.246872\pi\) |
−0.700124 | + | 0.714021i | \(0.746872\pi\) | |||||||
\(314\) | 5608.28 | + | 1713.21i | 1.00794 | + | 0.307905i | ||||
\(315\) | −1819.43 | − | 6361.01i | −0.325438 | − | 1.13779i | ||||
\(316\) | 4296.67 | + | 2895.26i | 0.764894 | + | 0.515415i | ||||
\(317\) | 2024.04 | − | 2024.04i | 0.358616 | − | 0.358616i | −0.504687 | − | 0.863303i | \(-0.668392\pi\) |
0.863303 | + | 0.504687i | \(0.168392\pi\) | |||||||
\(318\) | −2144.38 | + | 7499.75i | −0.378147 | + | 1.32253i | ||||
\(319\) | 2667.11i | 0.468118i | ||||||||
\(320\) | −3905.38 | + | 4185.22i | −0.682241 | + | 0.731127i | ||||
\(321\) | 4594.29 | + | 4431.98i | 0.798841 | + | 0.770620i | ||||
\(322\) | 952.649 | + | 1790.68i | 0.164873 | + | 0.309908i | ||||
\(323\) | 16.0292 | + | 16.0292i | 0.00276127 | + | 0.00276127i | ||||
\(324\) | 2903.04 | − | 5058.12i | 0.497777 | − | 0.867305i | ||||
\(325\) | 10923.3 | + | 3380.59i | 1.86435 | + | 0.576989i | ||||
\(326\) | 2864.84 | − | 9378.19i | 0.486714 | − | 1.59328i | ||||
\(327\) | 121.134 | + | 6736.69i | 0.0204854 | + | 1.13927i | ||||
\(328\) | 649.307 | + | 67.7909i | 0.109305 | + | 0.0114120i | ||||
\(329\) | −5301.94 | −0.888466 | ||||||||
\(330\) | −3955.54 | − | 141.927i | −0.659835 | − | 0.0236752i | ||||
\(331\) | 5796.56i | 0.962562i | 0.876566 | + | 0.481281i | \(0.159828\pi\) | ||||
−0.876566 | + | 0.481281i | \(0.840172\pi\) | |||||||
\(332\) | −330.278 | + | 64.3576i | −0.0545975 | + | 0.0106388i | ||||
\(333\) | −463.122 | − | 430.958i | −0.0762129 | − | 0.0709200i | ||||
\(334\) | −2133.30 | − | 651.678i | −0.349488 | − | 0.106761i | ||||
\(335\) | 6158.92 | − | 1524.38i | 1.00447 | − | 0.248613i | ||||
\(336\) | −2720.58 | + | 6761.84i | −0.441725 | + | 1.09788i | ||||
\(337\) | 6068.78 | − | 6068.78i | 0.980972 | − | 0.980972i | −0.0188504 | − | 0.999822i | \(-0.506001\pi\) |
0.999822 | + | 0.0188504i | \(0.00600062\pi\) | |||||||
\(338\) | 8197.47 | + | 15408.6i | 1.31918 | + | 2.47964i | ||||
\(339\) | 5928.76 | + | 5719.32i | 0.949871 | + | 0.916315i | ||||
\(340\) | −3018.13 | + | 8259.99i | −0.481415 | + | 1.31753i | ||||
\(341\) | −5066.21 | −0.804547 | ||||||||
\(342\) | −15.2369 | + | 8.82312i | −0.00240912 | + | 0.00139503i | ||||
\(343\) | −3186.96 | − | 3186.96i | −0.501689 | − | 0.501689i | ||||
\(344\) | 1345.03 | + | 1658.63i | 0.210812 | + | 0.259963i | ||||
\(345\) | −1836.65 | + | 489.788i | −0.286614 | + | 0.0764328i | ||||
\(346\) | −2668.63 | − | 815.210i | −0.414643 | − | 0.126665i | ||||
\(347\) | 1581.19 | − | 1581.19i | 0.244618 | − | 0.244618i | −0.574139 | − | 0.818758i | \(-0.694663\pi\) |
0.818758 | + | 0.574139i | \(0.194663\pi\) | |||||||
\(348\) | −2502.98 | + | 3862.60i | −0.385557 | + | 0.594991i | ||||
\(349\) | −1671.59 | −0.256384 | −0.128192 | − | 0.991749i | \(-0.540917\pi\) | ||||
−0.128192 | + | 0.991749i | \(0.540917\pi\) | |||||||
\(350\) | −7611.19 | + | 1454.21i | −1.16239 | + | 0.222088i | ||||
\(351\) | 9550.79 | + | 8572.32i | 1.45237 | + | 1.30358i | ||||
\(352\) | 3343.51 | + | 2798.97i | 0.506277 | + | 0.423823i | ||||
\(353\) | 8700.46 | − | 8700.46i | 1.31184 | − | 1.31184i | 0.391777 | − | 0.920060i | \(-0.371860\pi\) |
0.920060 | − | 0.391777i | \(-0.128140\pi\) | |||||||
\(354\) | 9164.58 | − | 5089.08i | 1.37597 | − | 0.764071i | ||||
\(355\) | −5113.88 | − | 3084.68i | −0.764553 | − | 0.461177i | ||||
\(356\) | −1119.21 | + | 1660.94i | −0.166623 | + | 0.247275i | ||||
\(357\) | 201.308 | + | 11195.5i | 0.0298441 | + | 1.65974i | ||||
\(358\) | 535.582 | + | 1006.72i | 0.0790681 | + | 0.148623i | ||||
\(359\) | 3722.45 | 0.547252 | 0.273626 | − | 0.961836i | \(-0.411777\pi\) | ||||
0.273626 | + | 0.961836i | \(0.411777\pi\) | |||||||
\(360\) | −5595.35 | − | 3917.67i | −0.819168 | − | 0.573553i | ||||
\(361\) | −6858.95 | −0.999992 | ||||||||
\(362\) | 2762.93 | + | 5193.43i | 0.401150 | + | 0.754035i | ||||
\(363\) | −70.1345 | − | 3900.44i | −0.0101408 | − | 0.563966i | ||||
\(364\) | −13301.1 | − | 8962.77i | −1.91529 | − | 1.29059i | ||||
\(365\) | 1905.52 | − | 471.630i | 0.273259 | − | 0.0676335i | ||||
\(366\) | 8990.49 | − | 4992.40i | 1.28399 | − | 0.712998i | ||||
\(367\) | −4883.48 | + | 4883.48i | −0.694593 | + | 0.694593i | −0.963239 | − | 0.268646i | \(-0.913424\pi\) |
0.268646 | + | 0.963239i | \(0.413424\pi\) | |||||||
\(368\) | 1928.34 | + | 816.433i | 0.273156 | + | 0.115651i | ||||
\(369\) | 28.0054 | + | 778.489i | 0.00395095 | + | 0.109828i | ||||
\(370\) | −551.355 | + | 494.962i | −0.0774691 | + | 0.0695456i | ||||
\(371\) | 11632.3 | 1.62782 | ||||||||
\(372\) | −7337.04 | − | 4754.44i | −1.02260 | − | 0.662651i | ||||
\(373\) | −5585.36 | + | 5585.36i | −0.775332 | + | 0.775332i | −0.979033 | − | 0.203701i | \(-0.934703\pi\) |
0.203701 | + | 0.979033i | \(0.434703\pi\) | |||||||
\(374\) | 6406.53 | + | 1957.06i | 0.885759 | + | 0.270580i | ||||
\(375\) | 286.956 | − | 7256.17i | 0.0395156 | − | 0.999219i | ||||
\(376\) | −4251.53 | + | 3447.70i | −0.583128 | + | 0.472876i | ||||
\(377\) | −7161.88 | − | 7161.88i | −0.978397 | − | 0.978397i | ||||
\(378\) | −8442.54 | − | 2088.75i | −1.14878 | − | 0.284217i | ||||
\(379\) | 12771.6 | 1.73096 | 0.865480 | − | 0.500944i | \(-0.167014\pi\) | ||||
0.865480 | + | 0.500944i | \(0.167014\pi\) | |||||||
\(380\) | 8.69168 | + | 18.7005i | 0.00117335 | + | 0.00252452i | ||||
\(381\) | −5383.28 | − | 5193.11i | −0.723869 | − | 0.698296i | ||||
\(382\) | 2170.66 | + | 4080.15i | 0.290735 | + | 0.546489i | ||||
\(383\) | 1175.44 | − | 1175.44i | 0.156821 | − | 0.156821i | −0.624335 | − | 0.781156i | \(-0.714630\pi\) |
0.781156 | + | 0.624335i | \(0.214630\pi\) | |||||||
\(384\) | 2215.44 | + | 7191.31i | 0.294417 | + | 0.955677i | ||||
\(385\) | 1418.14 | + | 5729.69i | 0.187727 | + | 0.758473i | ||||
\(386\) | 5595.51 | + | 1709.31i | 0.737834 | + | 0.225392i | ||||
\(387\) | −1735.85 | + | 1865.40i | −0.228006 | + | 0.245023i | ||||
\(388\) | 453.909 | + | 2329.43i | 0.0593911 | + | 0.304790i | ||||
\(389\) | 2725.23i | 0.355205i | 0.984102 | + | 0.177603i | \(0.0568342\pi\) | ||||
−0.984102 | + | 0.177603i | \(0.943166\pi\) | |||||||
\(390\) | 11002.7 | − | 10240.5i | 1.42858 | − | 1.32961i | ||||
\(391\) | 3217.03 | 0.416092 | ||||||||
\(392\) | 3091.30 | + | 322.747i | 0.398301 | + | 0.0415847i | ||||
\(393\) | −12.9914 | − | 722.497i | −0.00166750 | − | 0.0927358i | ||||
\(394\) | 52.1973 | − | 170.870i | 0.00667426 | − | 0.0218485i | ||||
\(395\) | 6200.19 | + | 3739.94i | 0.789786 | + | 0.476397i | ||||
\(396\) | −2750.51 | + | 4416.60i | −0.349037 | + | 0.560460i | ||||
\(397\) | −4427.98 | − | 4427.98i | −0.559783 | − | 0.559783i | 0.369462 | − | 0.929246i | \(-0.379542\pi\) |
−0.929246 | + | 0.369462i | \(0.879542\pi\) | |||||||
\(398\) | −5246.04 | − | 9860.89i | −0.660705 | − | 1.24191i | ||||
\(399\) | 18.8973 | + | 18.2297i | 0.00237105 | + | 0.00228729i | ||||
\(400\) | −5157.65 | + | 6115.44i | −0.644707 | + | 0.764430i | ||||
\(401\) | 5621.50i | 0.700061i | 0.936738 | + | 0.350030i | \(0.113829\pi\) | ||||
−0.936738 | + | 0.350030i | \(0.886171\pi\) | |||||||
\(402\) | 2292.86 | − | 8019.05i | 0.284471 | − | 0.994910i | ||||
\(403\) | 13604.1 | − | 13604.1i | 1.68155 | − | 1.68155i | ||||
\(404\) | −478.379 | + | 709.932i | −0.0589115 | + | 0.0874268i | ||||
\(405\) | 3697.41 | − | 7263.56i | 0.453644 | − | 0.891183i | ||||
\(406\) | 6564.37 | + | 2005.28i | 0.802425 | + | 0.245124i | ||||
\(407\) | 399.086 | + | 399.086i | 0.0486044 | + | 0.0486044i | ||||
\(408\) | 7441.51 | + | 8846.55i | 0.902965 | + | 1.07346i | ||||
\(409\) | − | 9555.77i | − | 1.15526i | −0.816298 | − | 0.577631i | \(-0.803977\pi\) | ||
0.816298 | − | 0.577631i | \(-0.196023\pi\) | |||||||
\(410\) | 911.044 | + | 49.1021i | 0.109740 | + | 0.00591459i | ||||
\(411\) | −2609.90 | + | 2705.47i | −0.313228 | + | 0.324699i | ||||
\(412\) | 4122.04 | − | 803.217i | 0.492909 | − | 0.0960477i | ||||
\(413\) | −11053.9 | − | 11053.9i | −1.31702 | − | 1.31702i | ||||
\(414\) | −643.618 | + | 2414.40i | −0.0764060 | + | 0.286621i | ||||
\(415\) | −456.485 | + | 112.983i | −0.0539951 | + | 0.0133642i | ||||
\(416\) | −16494.1 | + | 1462.21i | −1.94397 | + | 0.172333i | ||||
\(417\) | 213.025 | + | 11847.1i | 0.0250165 | + | 1.39126i | ||||
\(418\) | 13.8679 | − | 7.37779i | 0.00162273 | − | 0.000863300i | ||||
\(419\) | − | 14436.1i | − | 1.68317i | −0.540121 | − | 0.841587i | \(-0.681621\pi\) | ||
0.540121 | − | 0.841587i | \(-0.318379\pi\) | |||||||
\(420\) | −3323.30 | + | 9628.78i | −0.386096 | + | 1.11866i | ||||
\(421\) | 6067.89i | 0.702449i | 0.936291 | + | 0.351224i | \(0.114235\pi\) | ||||
−0.936291 | + | 0.351224i | \(0.885765\pi\) | |||||||
\(422\) | −2015.30 | − | 3788.11i | −0.232472 | − | 0.436973i | ||||
\(423\) | −4781.54 | − | 4449.47i | −0.549614 | − | 0.511443i | ||||
\(424\) | 9327.78 | − | 7564.17i | 1.06839 | − | 0.866388i | ||||
\(425\) | −3633.59 | + | 11740.7i | −0.414718 | + | 1.34002i | ||||
\(426\) | −6863.44 | + | 3811.26i | −0.780598 | + | 0.433465i | ||||
\(427\) | −10844.0 | − | 10844.0i | −1.22898 | − | 1.22898i | ||||
\(428\) | −1879.75 | − | 9646.71i | −0.212292 | − | 1.08947i | ||||
\(429\) | −8240.32 | − | 7949.21i | −0.927381 | − | 0.894619i | ||||
\(430\) | 1993.65 | + | 2220.80i | 0.223587 | + | 0.249061i | ||||
\(431\) | − | 8129.78i | − | 0.908579i | −0.890854 | − | 0.454289i | \(-0.849893\pi\) | ||
0.890854 | − | 0.454289i | \(-0.150107\pi\) | |||||||
\(432\) | −8128.18 | + | 3815.00i | −0.905248 | + | 0.424883i | ||||
\(433\) | 12678.1 | + | 12678.1i | 1.40709 | + | 1.40709i | 0.774440 | + | 0.632648i | \(0.218032\pi\) |
0.632648 | + | 0.774440i | \(0.281968\pi\) | |||||||
\(434\) | −3809.04 | + | 12469.1i | −0.421290 | + | 1.37911i | ||||
\(435\) | −3222.84 | + | 5566.82i | −0.355226 | + | 0.613583i | ||||
\(436\) | 5796.82 | − | 8602.69i | 0.636737 | − | 0.944941i | ||||
\(437\) | 5.33423 | − | 5.33423i | 0.000583915 | − | 0.000583915i | ||||
\(438\) | 709.393 | − | 2481.03i | 0.0773883 | − | 0.270658i | ||||
\(439\) | 4452.71i | 0.484092i | 0.970265 | + | 0.242046i | \(0.0778185\pi\) | ||||
−0.970265 | + | 0.242046i | \(0.922181\pi\) | |||||||
\(440\) | 4863.03 | + | 3672.37i | 0.526900 | + | 0.397893i | ||||
\(441\) | 133.331 | + | 3706.32i | 0.0143971 | + | 0.400208i | ||||
\(442\) | −22458.4 | + | 11948.0i | −2.41682 | + | 1.28576i | ||||
\(443\) | 11176.9 | + | 11176.9i | 1.19872 | + | 1.19872i | 0.974552 | + | 0.224164i | \(0.0719650\pi\) |
0.224164 | + | 0.974552i | \(0.428035\pi\) | |||||||
\(444\) | 203.442 | + | 952.496i | 0.0217454 | + | 0.101810i | ||||
\(445\) | −1445.73 | + | 2396.78i | −0.154010 | + | 0.255322i | ||||
\(446\) | 4529.79 | + | 1383.75i | 0.480923 | + | 0.146912i | ||||
\(447\) | −11510.7 | + | 206.976i | −1.21798 | + | 0.0219007i | ||||
\(448\) | 9402.73 | − | 6124.71i | 0.991601 | − | 0.645905i | ||||
\(449\) | −5163.70 | −0.542740 | −0.271370 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271370 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(450\) | −8084.53 | − | 5075.95i | −0.846908 | − | 0.531739i | ||||
\(451\) | − | 694.981i | − | 0.0725618i | ||||||
\(452\) | −2425.75 | − | 12448.7i | −0.252428 | − | 1.29544i | ||||
\(453\) | 145.073 | + | 8068.07i | 0.0150467 | + | 0.836801i | ||||
\(454\) | 1178.78 | − | 3858.79i | 0.121856 | − | 0.398904i | ||||
\(455\) | −19193.7 | − | 11577.6i | −1.97762 | − | 1.19289i | ||||
\(456\) | 27.0077 | + | 2.32973i | 0.00277357 | + | 0.000239254i | ||||
\(457\) | 5030.18 | − | 5030.18i | 0.514884 | − | 0.514884i | −0.401135 | − | 0.916019i | \(-0.631384\pi\) |
0.916019 | + | 0.401135i | \(0.131384\pi\) | |||||||
\(458\) | 466.280 | − | 248.063i | 0.0475716 | − | 0.0253084i | ||||
\(459\) | −9213.86 | + | 10265.6i | −0.936964 | + | 1.04391i | ||||
\(460\) | 2748.78 | + | 1004.38i | 0.278614 | + | 0.101803i | ||||
\(461\) | −1788.64 | −0.180705 | −0.0903526 | − | 0.995910i | \(-0.528799\pi\) | ||||
−0.0903526 | + | 0.995910i | \(0.528799\pi\) | |||||||
\(462\) | 7460.18 | + | 2133.07i | 0.751254 | + | 0.214804i | ||||
\(463\) | −10105.4 | − | 10105.4i | −1.01433 | − | 1.01433i | −0.999896 | − | 0.0144371i | \(-0.995404\pi\) |
−0.0144371 | − | 0.999896i | \(-0.504596\pi\) | |||||||
\(464\) | 6567.83 | − | 2660.62i | 0.657120 | − | 0.266199i | ||||
\(465\) | −10574.2 | − | 6121.81i | −1.05455 | − | 0.610520i | ||||
\(466\) | 4457.58 | − | 14592.1i | 0.443119 | − | 1.45057i | ||||
\(467\) | −6920.90 | + | 6920.90i | −0.685784 | + | 0.685784i | −0.961297 | − | 0.275514i | \(-0.911152\pi\) |
0.275514 | + | 0.961297i | \(0.411152\pi\) | |||||||
\(468\) | −4473.86 | − | 19245.5i | −0.441889 | − | 1.90091i | ||||
\(469\) | −12437.8 | −1.22457 | ||||||||
\(470\) | −5692.52 | + | 5110.29i | −0.558673 | + | 0.501532i | ||||
\(471\) | 7479.53 | − | 7753.44i | 0.731717 | − | 0.758513i | ||||
\(472\) | −16052.0 | − | 1675.91i | −1.56537 | − | 0.163432i | ||||
\(473\) | 1607.48 | − | 1607.48i | 0.156262 | − | 0.156262i | ||||
\(474\) | 8321.41 | − | 4620.86i | 0.806360 | − | 0.447771i | ||||
\(475\) | 13.4427 | + | 25.4926i | 0.00129851 | + | 0.00246248i | ||||
\(476\) | 9633.53 | − | 14296.5i | 0.927631 | − | 1.37664i | ||||
\(477\) | 10490.6 | + | 9762.04i | 1.00699 | + | 0.937051i | ||||
\(478\) | 8225.73 | − | 4376.13i | 0.787105 | − | 0.418744i | ||||
\(479\) | 942.693 | 0.0899222 | 0.0449611 | − | 0.998989i | \(-0.485684\pi\) | ||||
0.0449611 | + | 0.998989i | \(0.485684\pi\) | |||||||
\(480\) | 3596.42 | + | 9882.20i | 0.341986 | + | 0.939705i | ||||
\(481\) | −2143.30 | −0.203172 | ||||||||
\(482\) | 9740.18 | − | 5181.83i | 0.920442 | − | 0.489680i | ||||
\(483\) | 3725.65 | − | 66.9916i | 0.350979 | − | 0.00631103i | ||||
\(484\) | −3356.26 | + | 4980.82i | −0.315201 | + | 0.467770i | ||||
\(485\) | 796.862 | + | 3219.55i | 0.0746054 | + | 0.301428i | ||||
\(486\) | −5860.98 | − | 8968.85i | −0.547036 | − | 0.837109i | ||||
\(487\) | 11981.9 | − | 11981.9i | 1.11489 | − | 1.11489i | 0.122413 | − | 0.992479i | \(-0.460937\pi\) |
0.992479 | − | 0.122413i | \(-0.0390633\pi\) | |||||||
\(488\) | −15747.1 | − | 1644.07i | −1.46073 | − | 0.152508i | ||||
\(489\) | −12965.3 | − | 12507.3i | −1.19900 | − | 1.15665i | ||||
\(490\) | 4337.41 | + | 233.771i | 0.399886 | + | 0.0215525i | ||||
\(491\) | −16182.0 | −1.48734 | −0.743670 | − | 0.668547i | \(-0.766917\pi\) | ||||
−0.743670 | + | 0.668547i | \(0.766917\pi\) | |||||||
\(492\) | 652.213 | − | 1006.49i | 0.0597642 | − | 0.0922280i | ||||
\(493\) | 7697.87 | − | 7697.87i | 0.703234 | − | 0.703234i | ||||
\(494\) | −17.4276 | + | 57.0500i | −0.00158725 | + | 0.00519596i | ||||
\(495\) | −3529.50 | + | 6357.43i | −0.320483 | + | 0.577263i | ||||
\(496\) | 5053.88 | + | 12475.7i | 0.457512 | + | 1.12938i | ||||
\(497\) | 8278.40 | + | 8278.40i | 0.747157 | + | 0.747157i | ||||
\(498\) | −169.942 | + | 594.353i | −0.0152917 | + | 0.0534812i | ||||
\(499\) | −18027.6 | −1.61729 | −0.808646 | − | 0.588296i | \(-0.799799\pi\) | ||||
−0.808646 | + | 0.588296i | \(0.799799\pi\) | |||||||
\(500\) | −6770.25 | + | 8897.40i | −0.605549 | + | 0.795808i | ||||
\(501\) | −2845.10 | + | 2949.29i | −0.253712 | + | 0.263003i | ||||
\(502\) | 2333.11 | − | 1241.23i | 0.207434 | − | 0.110356i | ||||
\(503\) | −10877.7 | + | 10877.7i | −0.964241 | + | 0.964241i | −0.999382 | − | 0.0351416i | \(-0.988812\pi\) |
0.0351416 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(504\) | 8802.27 | + | 10090.3i | 0.777945 | + | 0.891778i | ||||
\(505\) | −617.944 | + | 1024.45i | −0.0544517 | + | 0.0902719i | ||||
\(506\) | 651.273 | − | 2131.98i | 0.0572186 | − | 0.187308i | ||||
\(507\) | 32058.9 | − | 576.458i | 2.80826 | − | 0.0504958i | ||||
\(508\) | 2202.56 | + | 11303.4i | 0.192368 | + | 0.987217i | ||||
\(509\) | 12313.1i | 1.07223i | 0.844144 | + | 0.536116i | \(0.180109\pi\) | ||||
−0.844144 | + | 0.536116i | \(0.819891\pi\) | |||||||
\(510\) | 11006.9 | + | 11826.2i | 0.955676 | + | 1.02681i | ||||
\(511\) | −3848.16 | −0.333136 | ||||||||
\(512\) | 3557.17 | − | 11025.6i | 0.307043 | − | 0.951696i | ||||
\(513\) | 1.74385 | + | 32.2993i | 0.000150083 | + | 0.00277983i | ||||
\(514\) | 9340.73 | + | 2853.39i | 0.801560 | + | 0.244860i | ||||
\(515\) | 5697.17 | − | 1410.09i | 0.487470 | − | 0.120652i | ||||
\(516\) | 3836.55 | − | 819.442i | 0.327315 | − | 0.0699107i | ||||
\(517\) | 4120.41 | + | 4120.41i | 0.350513 | + | 0.350513i | ||||
\(518\) | 1282.30 | − | 682.188i | 0.108766 | − | 0.0578641i | ||||
\(519\) | −3559.05 | + | 3689.38i | −0.301011 | + | 0.312034i | ||||
\(520\) | −22919.7 | + | 3197.24i | −1.93288 | + | 0.269631i | ||||
\(521\) | 14943.2i | 1.25657i | 0.777982 | + | 0.628287i | \(0.216243\pi\) | ||||
−0.777982 | + | 0.628287i | \(0.783757\pi\) | |||||||
\(522\) | 4237.21 | + | 7317.37i | 0.355283 | + | 0.613549i | ||||
\(523\) | −12402.4 | + | 12402.4i | −1.03694 | + | 1.03694i | −0.0376438 | + | 0.999291i | \(0.511985\pi\) |
−0.999291 | + | 0.0376438i | \(0.988015\pi\) | |||||||
\(524\) | −621.698 | + | 922.622i | −0.0518301 | + | 0.0769178i | ||||
\(525\) | −3963.58 | + | 13672.7i | −0.329495 | + | 1.13662i | ||||
\(526\) | 4126.84 | − | 13509.4i | 0.342089 | − | 1.11984i | ||||
\(527\) | 14622.2 | + | 14622.2i | 1.20864 | + | 1.20864i | ||||
\(528\) | 7369.26 | − | 3140.67i | 0.607398 | − | 0.258864i | ||||
\(529\) | 11096.4i | 0.912011i | ||||||||
\(530\) | 12489.3 | − | 11211.9i | 1.02358 | − | 0.918891i | ||||
\(531\) | −692.342 | − | 19245.6i | −0.0565821 | − | 1.57286i | ||||
\(532\) | −7.73181 | − | 39.6790i | −0.000630106 | − | 0.00323365i | ||||
\(533\) | 1866.20 | + | 1866.20i | 0.151659 | + | 0.151659i | ||||
\(534\) | 1786.27 | + | 3216.77i | 0.144755 | + | 0.260680i | ||||
\(535\) | −3299.99 | − | 13332.9i | −0.266675 | − | 1.07744i | ||||
\(536\) | −9973.65 | + | 8087.93i | −0.803724 | + | 0.651764i | ||||
\(537\) | 2094.57 | − | 37.6629i | 0.168319 | − | 0.00302658i | ||||
\(538\) | 3743.73 | + | 7037.02i | 0.300007 | + | 0.563917i | ||||
\(539\) | − | 3308.75i | − | 0.264412i | ||||||
\(540\) | −11077.7 | + | 5894.74i | −0.882795 | + | 0.469758i | ||||
\(541\) | 6136.90i | 0.487701i | 0.969813 | + | 0.243850i | \(0.0784106\pi\) | ||||
−0.969813 | + | 0.243850i | \(0.921589\pi\) | |||||||
\(542\) | 6578.59 | − | 3499.84i | 0.521355 | − | 0.277364i | ||||
\(543\) | 10805.4 | − | 194.293i | 0.853964 | − | 0.0153553i | ||||
\(544\) | −1571.64 | − | 17728.5i | −0.123867 | − | 1.39725i | ||||
\(545\) | 7488.02 | − | 12413.9i | 0.588535 | − | 0.975692i | ||||
\(546\) | −25760.3 | + | 14304.7i | −2.01912 | + | 1.12121i | ||||
\(547\) | 11284.3 | + | 11284.3i | 0.882052 | + | 0.882052i | 0.993743 | − | 0.111691i | \(-0.0356268\pi\) |
−0.111691 | + | 0.993743i | \(0.535627\pi\) | |||||||
\(548\) | 5680.74 | − | 1106.94i | 0.442827 | − | 0.0862887i | ||||
\(549\) | −679.190 | − | 18880.0i | −0.0527999 | − | 1.46772i | ||||
\(550\) | 7045.18 | + | 4784.91i | 0.546196 | + | 0.370962i | ||||
\(551\) | − | 25.5281i | − | 0.00197374i | ||||||
\(552\) | 2943.97 | − | 2476.40i | 0.227000 | − | 0.190947i | ||||
\(553\) | −10036.9 | − | 10036.9i | −0.771816 | − | 0.771816i | ||||
\(554\) | 5380.14 | + | 1643.52i | 0.412600 | + | 0.126040i | ||||
\(555\) | 350.735 | + | 1315.22i | 0.0268250 | + | 0.100591i | ||||
\(556\) | 10194.3 | − | 15128.7i | 0.777577 | − | 1.15395i | ||||
\(557\) | 1389.34 | − | 1389.34i | 0.105688 | − | 0.105688i | −0.652285 | − | 0.757974i | \(-0.726190\pi\) |
0.757974 | + | 0.652285i | \(0.226190\pi\) | |||||||
\(558\) | −13899.4 | + | 8048.62i | −1.05450 | + | 0.610619i | ||||
\(559\) | 8632.96i | 0.653194i | ||||||||
\(560\) | 12694.8 | − | 9207.94i | 0.957953 | − | 0.694833i | ||||
\(561\) | 8544.13 | − | 8857.02i | 0.643018 | − | 0.666566i | ||||
\(562\) | 5162.60 | + | 9704.05i | 0.387493 | + | 0.728364i | ||||
\(563\) | 10269.7 | + | 10269.7i | 0.768770 | + | 0.768770i | 0.977890 | − | 0.209120i | \(-0.0670599\pi\) |
−0.209120 | + | 0.977890i | \(0.567060\pi\) | |||||||
\(564\) | 2100.46 | + | 9834.14i | 0.156818 | + | 0.734206i | ||||
\(565\) | −4258.53 | − | 17205.7i | −0.317093 | − | 1.28115i | ||||
\(566\) | 1942.02 | − | 6357.30i | 0.144221 | − | 0.472116i | ||||
\(567\) | −10456.8 | + | 12080.5i | −0.774508 | + | 0.894765i | ||||
\(568\) | 12021.5 | + | 1255.11i | 0.888048 | + | 0.0927167i | ||||
\(569\) | −16770.0 | −1.23556 | −0.617780 | − | 0.786351i | \(-0.711968\pi\) | ||||
−0.617780 | + | 0.786351i | \(0.711968\pi\) | |||||||
\(570\) | 37.8602 | + | 1.35844i | 0.00278208 | + | 9.98228e-5i | ||||
\(571\) | 3312.29i | 0.242758i | 0.992606 | + | 0.121379i | \(0.0387316\pi\) | ||||
−0.992606 | + | 0.121379i | \(0.961268\pi\) | |||||||
\(572\) | 3371.52 | + | 17302.4i | 0.246451 | + | 1.26477i | ||||
\(573\) | 8489.09 | − | 152.644i | 0.618913 | − | 0.0111288i | ||||
\(574\) | −1710.51 | − | 522.523i | −0.124382 | − | 0.0379960i | ||||
\(575\) | 3907.11 | + | 1209.19i | 0.283370 | + | 0.0876988i | ||||
\(576\) | 13619.8 | + | 2367.35i | 0.985228 | + | 0.171249i | ||||
\(577\) | −323.244 | + | 323.244i | −0.0233220 | + | 0.0233220i | −0.718672 | − | 0.695350i | \(-0.755250\pi\) |
0.695350 | + | 0.718672i | \(0.255250\pi\) | |||||||
\(578\) | −6315.51 | − | 11871.1i | −0.454482 | − | 0.854281i | ||||
\(579\) | 7462.50 | − | 7735.78i | 0.535632 | − | 0.555247i | ||||
\(580\) | 8980.74 | − | 4174.09i | 0.642940 | − | 0.298827i | ||||
\(581\) | 921.861 | 0.0658266 | ||||||||
\(582\) | 4191.93 | + | 1198.59i | 0.298559 | + | 0.0853659i | ||||
\(583\) | −9040.09 | − | 9040.09i | −0.642199 | − | 0.642199i | ||||
\(584\) | −3085.77 | + | 2502.34i | −0.218647 | + | 0.177308i | ||||
\(585\) | −7593.73 | − | 26548.9i | −0.536687 | − | 1.87635i | ||||
\(586\) | 7909.94 | + | 2416.32i | 0.557605 | + | 0.170337i | ||||
\(587\) | −11636.5 | + | 11636.5i | −0.818209 | + | 0.818209i | −0.985848 | − | 0.167639i | \(-0.946386\pi\) |
0.167639 | + | 0.985848i | \(0.446386\pi\) | |||||||
\(588\) | 3105.13 | − | 4791.83i | 0.217778 | − | 0.336075i | ||||
\(589\) | 48.4908 | 0.00339224 | ||||||||
\(590\) | −22522.6 | − | 1213.89i | −1.57160 | − | 0.0847035i | ||||
\(591\) | −236.228 | − | 227.883i | −0.0164418 | − | 0.0158610i | ||||
\(592\) | 584.644 | − | 1380.87i | 0.0405891 | − | 0.0958675i | ||||
\(593\) | 962.627 | − | 962.627i | 0.0666616 | − | 0.0666616i | −0.672990 | − | 0.739652i | \(-0.734990\pi\) |
0.739652 | + | 0.672990i | \(0.234990\pi\) | |||||||
\(594\) | 4937.85 | + | 8184.40i | 0.341082 | + | 0.565337i | ||||
\(595\) | 12444.1 | − | 20630.2i | 0.857407 | − | 1.42144i | ||||
\(596\) | 14699.0 | + | 9904.75i | 1.01023 | + | 0.680729i | ||||
\(597\) | −20516.4 | + | 368.909i | −1.40650 | + | 0.0252905i | ||||
\(598\) | 3976.07 | + | 7473.74i | 0.271895 | + | 0.511077i | ||||
\(599\) | 8514.50 | 0.580790 | 0.290395 | − | 0.956907i | \(-0.406213\pi\) | ||||
0.290395 | + | 0.956907i | \(0.406213\pi\) | |||||||
\(600\) | 5712.60 | + | 13541.3i | 0.388693 | + | 0.921367i | ||||
\(601\) | 9858.11 | 0.669086 | 0.334543 | − | 0.942381i | \(-0.391418\pi\) | ||||
0.334543 | + | 0.942381i | \(0.391418\pi\) | |||||||
\(602\) | −2747.78 | − | 5164.95i | −0.186032 | − | 0.349680i | ||||
\(603\) | −11217.0 | − | 10438.0i | −0.757532 | − | 0.704922i | ||||
\(604\) | 6942.44 | − | 10302.8i | 0.467689 | − | 0.694067i | ||||
\(605\) | −4335.44 | + | 7187.43i | −0.291340 | + | 0.482993i | ||||
\(606\) | 763.497 | + | 1374.93i | 0.0511798 | + | 0.0921663i | ||||
\(607\) | 16619.7 | − | 16619.7i | 1.11132 | − | 1.11132i | 0.118352 | − | 0.992972i | \(-0.462239\pi\) |
0.992972 | − | 0.118352i | \(-0.0377612\pi\) | |||||||
\(608\) | −32.0021 | − | 26.7902i | −0.00213463 | − | 0.00178698i | ||||
\(609\) | 8754.63 | − | 9075.23i | 0.582521 | − | 0.603854i | ||||
\(610\) | −22094.8 | − | 1190.83i | −1.46654 | − | 0.0790416i | ||||
\(611\) | −22128.7 | −1.46519 | ||||||||
\(612\) | 20685.8 | − | 4808.68i | 1.36630 | − | 0.317613i | ||||
\(613\) | 15827.0 | − | 15827.0i | 1.04282 | − | 1.04282i | 0.0437762 | − | 0.999041i | \(-0.486061\pi\) |
0.999041 | − | 0.0437762i | \(-0.0139388\pi\) | |||||||
\(614\) | −8239.83 | − | 2517.09i | −0.541584 | − | 0.165442i | ||||
\(615\) | 839.788 | − | 1450.57i | 0.0550626 | − | 0.0951099i | ||||
\(616\) | −7524.27 | − | 9278.57i | −0.492145 | − | 0.606890i | ||||
\(617\) | −5748.54 | − | 5748.54i | −0.375085 | − | 0.375085i | 0.494240 | − | 0.869325i | \(-0.335446\pi\) |
−0.869325 | + | 0.494240i | \(0.835446\pi\) | |||||||
\(618\) | 2120.96 | − | 7417.84i | 0.138054 | − | 0.482831i | ||||
\(619\) | −8459.52 | −0.549300 | −0.274650 | − | 0.961544i | \(-0.588562\pi\) | ||||
−0.274650 | + | 0.961544i | \(0.588562\pi\) | |||||||
\(620\) | 7928.71 | + | 17059.0i | 0.513588 | + | 1.10501i | ||||
\(621\) | 3416.19 | + | 3066.21i | 0.220752 | + | 0.198136i | ||||
\(622\) | 1814.84 | + | 3411.32i | 0.116991 | + | 0.219906i | ||||
\(623\) | 3879.93 | − | 3879.93i | 0.249512 | − | 0.249512i | ||||
\(624\) | −11354.9 | + | 28221.8i | −0.728458 | + | 1.81054i | ||||
\(625\) | −8826.05 | + | 12893.5i | −0.564867 | + | 0.825182i | ||||
\(626\) | −294.387 | − | 89.9291i | −0.0187957 | − | 0.00574168i | ||||
\(627\) | −0.518817 | − | 28.8533i | −3.30455e−5 | − | 0.00183778i | ||||
\(628\) | −16280.0 | + | 3172.31i | −1.03447 | + | 0.201575i | ||||
\(629\) | − | 2303.70i | − | 0.146033i | ||||||
\(630\) | 12993.4 | + | 13466.7i | 0.821699 | + | 0.851632i | ||||
\(631\) | 2376.36 | 0.149923 | 0.0749615 | − | 0.997186i | \(-0.476117\pi\) | ||||
0.0749615 | + | 0.997186i | \(0.476117\pi\) | |||||||
\(632\) | −14575.2 | − | 1521.72i | −0.917356 | − | 0.0957766i | ||||
\(633\) | −7881.49 | + | 141.719i | −0.494883 | + | 0.00889859i | ||||
\(634\) | −2365.30 | + | 7742.93i | −0.148167 | + | 0.485033i | ||||
\(635\) | 3866.72 | + | 15622.7i | 0.241647 | + | 0.976325i | ||||
\(636\) | −4608.36 | − | 21575.9i | −0.287317 | − | 1.34519i | ||||
\(637\) | 8884.83 | + | 8884.83i | 0.552637 | + | 0.552637i | ||||
\(638\) | −3543.11 | − | 6659.91i | −0.219863 | − | 0.413273i | ||||
\(639\) | 518.502 | + | 14413.2i | 0.0320995 | + | 0.892298i | ||||
\(640\) | 4192.09 | − | 15638.7i | 0.258917 | − | 0.965900i | ||||
\(641\) | − | 24800.9i | − | 1.52820i | −0.645097 | − | 0.764100i | \(-0.723183\pi\) | ||
0.645097 | − | 0.764100i | \(-0.276817\pi\) | |||||||
\(642\) | −17359.8 | − | 4963.63i | −1.06719 | − | 0.305138i | ||||
\(643\) | −8206.68 | + | 8206.68i | −0.503328 | + | 0.503328i | −0.912470 | − | 0.409143i | \(-0.865828\pi\) |
0.409143 | + | 0.912470i | \(0.365828\pi\) | |||||||
\(644\) | −4757.62 | − | 3205.86i | −0.291112 | − | 0.196163i | ||||
\(645\) | 5297.54 | − | 1412.72i | 0.323396 | − | 0.0862417i | ||||
\(646\) | −61.3196 | − | 18.7318i | −0.00373466 | − | 0.00114086i | ||||
\(647\) | 21114.1 | + | 21114.1i | 1.28297 | + | 1.28297i | 0.938970 | + | 0.343999i | \(0.111782\pi\) |
0.343999 | + | 0.938970i | \(0.388218\pi\) | |||||||
\(648\) | −529.594 | + | 16486.9i | −0.0321056 | + | 0.999484i | ||||
\(649\) | 17181.1i | 1.03917i | ||||||||
\(650\) | −31766.8 | + | 6069.42i | −1.91692 | + | 0.366250i | ||||
\(651\) | 17238.5 | + | 16629.5i | 1.03783 | + | 1.00117i | ||||
\(652\) | 5304.75 | + | 27223.6i | 0.318635 | + | 1.63521i | ||||
\(653\) | 11411.3 | + | 11411.3i | 0.683858 | + | 0.683858i | 0.960867 | − | 0.277010i | \(-0.0893434\pi\) |
−0.277010 | + | 0.960867i | \(0.589343\pi\) | |||||||
\(654\) | −9251.78 | − | 16660.9i | −0.553170 | − | 0.996168i | ||||
\(655\) | −803.075 | + | 1331.36i | −0.0479065 | + | 0.0794209i | ||||
\(656\) | −1711.41 | + | 693.290i | −0.101859 | + | 0.0412628i | ||||
\(657\) | −3470.45 | − | 3229.43i | −0.206081 | − | 0.191769i | ||||
\(658\) | 13239.2 | − | 7043.32i | 0.784373 | − | 0.417291i | ||||
\(659\) | − | 9185.31i | − | 0.542958i | −0.962444 | − | 0.271479i | \(-0.912487\pi\) | ||
0.962444 | − | 0.271479i | \(-0.0875127\pi\) | |||||||
\(660\) | 10065.7 | − | 4900.31i | 0.593648 | − | 0.289007i | ||||
\(661\) | − | 867.859i | − | 0.0510678i | −0.999674 | − | 0.0255339i | \(-0.991871\pi\) | ||
0.999674 | − | 0.0255339i | \(-0.00812857\pi\) | |||||||
\(662\) | −7700.40 | − | 14474.3i | −0.452091 | − | 0.849787i | ||||
\(663\) | 840.198 | + | 46726.5i | 0.0492166 | + | 2.73711i | ||||
\(664\) | 739.224 | − | 599.459i | 0.0432040 | − | 0.0350354i | ||||
\(665\) | −13.5736 | − | 54.8413i | −0.000791522 | − | 0.00319798i | ||||
\(666\) | 1728.94 | + | 460.892i | 0.100593 | + | 0.0268156i | ||||
\(667\) | −2561.71 | − | 2561.71i | −0.148710 | − | 0.148710i | ||||
\(668\) | 6192.67 | − | 1206.70i | 0.358685 | − | 0.0698930i | ||||
\(669\) | 6041.19 | − | 6262.43i | 0.349127 | − | 0.361912i | ||||
\(670\) | −13354.1 | + | 11988.2i | −0.770018 | + | 0.691260i | ||||
\(671\) | 16854.8i | 0.969704i | ||||||||
\(672\) | −2189.30 | − | 20498.7i | −0.125676 | − | 1.17672i | ||||
\(673\) | 21033.6 | + | 21033.6i | 1.20474 | + | 1.20474i | 0.972710 | + | 0.232025i | \(0.0745352\pi\) |
0.232025 | + | 0.972710i | \(0.425465\pi\) | |||||||
\(674\) | −7092.01 | + | 23216.1i | −0.405303 | + | 1.32678i | ||||
\(675\) | −15048.9 | + | 9004.37i | −0.858120 | + | 0.513449i | ||||
\(676\) | −40938.9 | − | 27586.2i | −2.32925 | − | 1.56954i | ||||
\(677\) | 15208.9 | − | 15208.9i | 0.863407 | − | 0.863407i | −0.128325 | − | 0.991732i | \(-0.540960\pi\) |
0.991732 | + | 0.128325i | \(0.0409602\pi\) | |||||||
\(678\) | −22402.2 | − | 6405.38i | −1.26895 | − | 0.362828i | ||||
\(679\) | − | 6501.82i | − | 0.367477i | ||||||
\(680\) | −3436.52 | − | 24635.0i | −0.193801 | − | 1.38928i | ||||
\(681\) | −5334.78 | − | 5146.31i | −0.300190 | − | 0.289585i | ||||
\(682\) | 12650.6 | − | 6730.16i | 0.710286 | − | 0.377876i | ||||
\(683\) | −18772.1 | − | 18772.1i | −1.05167 | − | 1.05167i | −0.998590 | − | 0.0530848i | \(-0.983095\pi\) |
−0.0530848 | − | 0.998590i | \(-0.516905\pi\) | |||||||
\(684\) | 26.3263 | − | 42.2731i | 0.00147166 | − | 0.00236309i | ||||
\(685\) | 7851.47 | − | 1943.30i | 0.437941 | − | 0.108393i | ||||
\(686\) | 12191.7 | + | 3724.29i | 0.678542 | + | 0.207280i | ||||
\(687\) | −17.4442 | − | 970.133i | −0.000968757 | − | 0.0538761i | ||||
\(688\) | −5562.01 | − | 2354.88i | −0.308211 | − | 0.130493i | ||||
\(689\) | 48549.9 | 2.68447 | ||||||||
\(690\) | 3935.54 | − | 3662.90i | 0.217135 | − | 0.202093i | ||||
\(691\) | 7733.79i | 0.425770i | 0.977077 | + | 0.212885i | \(0.0682860\pi\) | ||||
−0.977077 | + | 0.212885i | \(0.931714\pi\) | |||||||
\(692\) | 7746.66 | − | 1509.51i | 0.425555 | − | 0.0829231i | ||||
\(693\) | 9710.55 | − | 10435.3i | 0.532285 | − | 0.572010i | ||||
\(694\) | −1847.78 | + | 6048.81i | −0.101068 | + | 0.330850i | ||||
\(695\) | 13168.4 | − | 21831.0i | 0.718713 | − | 1.19151i | ||||
\(696\) | 1118.83 | − | 12970.1i | 0.0609326 | − | 0.706368i | ||||
\(697\) | −2005.87 | + | 2005.87i | −0.109007 | + | 0.109007i | ||||
\(698\) | 4174.03 | − | 2220.61i | 0.226346 | − | 0.120417i | ||||
\(699\) | −20173.6 | − | 19460.9i | −1.09161 | − | 1.05305i | ||||
\(700\) | 17073.7 | − | 13742.3i | 0.921892 | − | 0.742012i | ||||
\(701\) | −9004.44 | −0.485154 | −0.242577 | − | 0.970132i | \(-0.577993\pi\) | ||||
−0.242577 | + | 0.970132i | \(0.577993\pi\) | |||||||
\(702\) | −35236.6 | − | 8717.81i | −1.89447 | − | 0.468708i | ||||
\(703\) | −3.81982 | − | 3.81982i | −0.000204932 | − | 0.000204932i | ||||
\(704\) | −12067.2 | − | 2547.51i | −0.646020 | − | 0.136382i | ||||
\(705\) | 3621.20 | + | 13579.1i | 0.193450 | + | 0.725415i | ||||
\(706\) | −10167.4 | + | 33283.5i | −0.542004 | + | 1.77428i | ||||
\(707\) | 1658.39 | − | 1658.39i | 0.0882179 | − | 0.0882179i | ||||
\(708\) | −16123.8 | + | 24882.3i | −0.855891 | + | 1.32081i | ||||
\(709\) | 21498.3 | 1.13877 | 0.569384 | − | 0.822071i | \(-0.307182\pi\) | ||||
0.569384 | + | 0.822071i | \(0.307182\pi\) | |||||||
\(710\) | 16867.4 | + | 909.095i | 0.891581 | + | 0.0480531i | ||||
\(711\) | −628.644 | − | 17474.9i | −0.0331589 | − | 0.921746i | ||||
\(712\) | 588.245 | − | 5634.26i | 0.0309627 | − | 0.296563i | ||||
\(713\) | 4865.99 | − | 4865.99i | 0.255586 | − | 0.255586i | ||||
\(714\) | −15375.2 | − | 27688.2i | −0.805887 | − | 1.45127i | ||||
\(715\) | 5918.88 | + | 23914.0i | 0.309585 | + | 1.25081i | ||||
\(716\) | −2674.74 | − | 1802.34i | −0.139609 | − | 0.0940737i | ||||
\(717\) | −307.736 | − | 17114.3i | −0.0160287 | − | 0.891416i | ||||
\(718\) | −9295.14 | + | 4945.06i | −0.483136 | + | 0.257031i | ||||
\(719\) | −36837.8 | −1.91074 | −0.955368 | − | 0.295417i | \(-0.904541\pi\) | ||||
−0.955368 | + | 0.295417i | \(0.904541\pi\) | |||||||
\(720\) | 19176.2 | + | 2349.50i | 0.992578 | + | 0.121612i | ||||
\(721\) | −11505.3 | −0.594286 | ||||||||
\(722\) | 17127.1 | − | 9111.71i | 0.882832 | − | 0.469671i | ||||
\(723\) | −364.393 | − | 20265.2i | −0.0187440 | − | 1.04242i | ||||
\(724\) | −13798.3 | − | 9297.84i | −0.708303 | − | 0.477281i | ||||
\(725\) | 12242.5 | − | 6455.71i | 0.627140 | − | 0.330702i | ||||
\(726\) | 5356.63 | + | 9646.40i | 0.273834 | + | 0.493129i | ||||
\(727\) | −18920.8 | + | 18920.8i | −0.965247 | + | 0.965247i | −0.999416 | − | 0.0341694i | \(-0.989121\pi\) |
0.0341694 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(728\) | 45119.9 | + | 4710.75i | 2.29705 | + | 0.239824i | ||||
\(729\) | −19568.6 | + | 2119.20i | −0.994187 | + | 0.107666i | ||||
\(730\) | −4131.64 | + | 3709.05i | −0.209478 | + | 0.188052i | ||||
\(731\) | −9279.04 | −0.469491 | ||||||||
\(732\) | −15817.5 | + | 24409.6i | −0.798680 | + | 1.23252i | ||||
\(733\) | −9773.14 | + | 9773.14i | −0.492468 | + | 0.492468i | −0.909083 | − | 0.416615i | \(-0.863216\pi\) |
0.416615 | + | 0.909083i | \(0.363216\pi\) | |||||||
\(734\) | 5706.86 | − | 18681.7i | 0.286981 | − | 0.939447i | ||||
\(735\) | 3998.16 | − | 6906.04i | 0.200645 | − | 0.346576i | ||||
\(736\) | −5899.73 | + | 523.013i | −0.295471 | + | 0.0261936i | ||||
\(737\) | 9666.04 | + | 9666.04i | 0.483112 | + | 0.483112i | ||||
\(738\) | −1104.11 | − | 1906.72i | −0.0550715 | − | 0.0951047i | ||||
\(739\) | −1238.92 | −0.0616706 | −0.0308353 | − | 0.999524i | \(-0.509817\pi\) | ||||
−0.0308353 | + | 0.999524i | \(0.509817\pi\) | |||||||
\(740\) | 719.231 | − | 1968.39i | 0.0357290 | − | 0.0977829i | ||||
\(741\) | 78.8716 | + | 76.0853i | 0.00391015 | + | 0.00377201i | ||||
\(742\) | −29046.5 | + | 15452.9i | −1.43710 | + | 0.764547i | ||||
\(743\) | 25273.4 | − | 25273.4i | 1.24790 | − | 1.24790i | 0.291259 | − | 0.956644i | \(-0.405926\pi\) |
0.956644 | − | 0.291259i | \(-0.0940740\pi\) | |||||||
\(744\) | 24636.9 | + | 2125.23i | 1.21402 | + | 0.104724i | ||||
\(745\) | 21211.0 | + | 12794.4i | 1.04310 | + | 0.629196i | ||||
\(746\) | 6527.07 | − | 21366.7i | 0.320339 | − | 1.04865i | ||||
\(747\) | 831.379 | + | 773.640i | 0.0407210 | + | 0.0378929i | ||||
\(748\) | −18597.3 | + | 3623.84i | −0.909068 | + | 0.177140i | ||||
\(749\) | 26925.6i | 1.31354i | ||||||||
\(750\) | 8922.86 | + | 18500.2i | 0.434422 | + | 0.900709i | ||||
\(751\) | −7222.12 | −0.350917 | −0.175459 | − | 0.984487i | \(-0.556141\pi\) | ||||
−0.175459 | + | 0.984487i | \(0.556141\pi\) | |||||||
\(752\) | 6036.22 | − | 14257.0i | 0.292710 | − | 0.691354i | ||||
\(753\) | −87.2849 | − | 4854.23i | −0.00422422 | − | 0.234924i | ||||
\(754\) | 27397.7 | + | 8369.41i | 1.32330 | + | 0.404238i | ||||
\(755\) | 8967.87 | − | 14867.2i | 0.432284 | − | 0.716654i | ||||
\(756\) | 23856.2 | − | 5999.71i | 1.14767 | − | 0.288634i | ||||
\(757\) | −15785.6 | − | 15785.6i | −0.757908 | − | 0.757908i | 0.218034 | − | 0.975941i | \(-0.430036\pi\) |
−0.975941 | + | 0.218034i | \(0.930036\pi\) | |||||||
\(758\) | −31891.3 | + | 16966.3i | −1.52816 | + | 0.812989i | ||||
\(759\) | −2947.45 | − | 2843.33i | −0.140956 | − | 0.135977i | ||||
\(760\) | −46.5461 | − | 35.1498i | −0.00222159 | − | 0.00167765i | ||||
\(761\) | 19069.0i | 0.908344i | 0.890914 | + | 0.454172i | \(0.150065\pi\) | ||||
−0.890914 | + | 0.454172i | \(0.849935\pi\) | |||||||
\(762\) | 20341.0 | + | 5816.05i | 0.967032 | + | 0.276500i | ||||
\(763\) | −20095.7 | + | 20095.7i | −0.953491 | + | 0.953491i | ||||
\(764\) | −10840.5 | − | 7304.73i | −0.513344 | − | 0.345911i | ||||
\(765\) | 28535.8 | − | 8162.04i | 1.34865 | − | 0.385751i | ||||
\(766\) | −1373.63 | + | 4496.65i | −0.0647928 | + | 0.212102i | ||||
\(767\) | −46135.8 | − | 46135.8i | −2.17192 | − | 2.17192i | ||||
\(768\) | −15085.3 | − | 15014.0i | −0.708781 | − | 0.705429i | ||||
\(769\) | 24492.5i | 1.14853i | 0.818668 | + | 0.574267i | \(0.194713\pi\) | ||||
−0.818668 | + | 0.574267i | \(0.805287\pi\) | |||||||
\(770\) | −11152.7 | − | 12423.4i | −0.521969 | − | 0.581439i | ||||
\(771\) | 12457.3 | − | 12913.5i | 0.581894 | − | 0.603203i | ||||
\(772\) | −16243.0 | + | 3165.08i | −0.757250 | + | 0.147557i | ||||
\(773\) | 5285.07 | + | 5285.07i | 0.245913 | + | 0.245913i | 0.819291 | − | 0.573378i | \(-0.194367\pi\) |
−0.573378 | + | 0.819291i | \(0.694367\pi\) | |||||||
\(774\) | 1856.42 | − | 6963.97i | 0.0862115 | − | 0.323404i | ||||
\(775\) | 12262.7 | + | 23254.8i | 0.568372 | + | 1.07786i | ||||
\(776\) | −4227.94 | − | 5213.69i | −0.195585 | − | 0.241186i | ||||
\(777\) | −47.9724 | − | 2667.92i | −0.00221493 | − | 0.123180i | ||||
\(778\) | −3620.31 | − | 6805.04i | −0.166831 | − | 0.313589i | ||||
\(779\) | 6.65196i | 0.000305945i | ||||||||
\(780\) | −13870.4 | + | 40187.6i | −0.636719 | + | 1.84480i | ||||
\(781\) | − | 12867.1i | − | 0.589529i | ||||||
\(782\) | −8033.06 | + | 4273.63i | −0.367342 | + | 0.195428i | ||||
\(783\) | 15511.4 | − | 837.464i | 0.707960 | − | 0.0382229i | ||||
\(784\) | −8147.87 | + | 3300.70i | −0.371167 | + | 0.150360i | ||||
\(785\) | −22501.0 | + | 5569.16i | −1.02305 | + | 0.253213i | ||||
\(786\) | 992.236 | + | 1786.85i | 0.0450278 | + | 0.0810876i | ||||
\(787\) | 1754.94 | + | 1754.94i | 0.0794877 | + | 0.0794877i | 0.745733 | − | 0.666245i | \(-0.232100\pi\) |
−0.666245 | + | 0.745733i | \(0.732100\pi\) | |||||||
\(788\) | 96.6524 | + | 496.012i | 0.00436942 | + | 0.0224235i | ||||
\(789\) | −18676.7 | − | 18016.9i | −0.842724 | − | 0.812953i | ||||
\(790\) | −20450.5 | − | 1102.21i | −0.921006 | − | 0.0496390i | ||||
\(791\) | 34746.5i | 1.56188i | ||||||||
\(792\) | 1000.97 | − | 14682.3i | 0.0449089 | − | 0.658730i | ||||
\(793\) | −45259.4 | − | 45259.4i | −2.02674 | − | 2.02674i | ||||
\(794\) | 16939.2 | + | 5174.56i | 0.757115 | + | 0.231282i | ||||
\(795\) | −7944.84 | − | 29792.2i | −0.354433 | − | 1.32908i | ||||
\(796\) | 26199.2 | + | 17654.0i | 1.16659 | + | 0.786094i | ||||
\(797\) | −15505.3 | + | 15505.3i | −0.689116 | + | 0.689116i | −0.962036 | − | 0.272921i | \(-0.912010\pi\) |
0.272921 | + | 0.962036i | \(0.412010\pi\) | |||||||
\(798\) | −71.4046 | − | 20.4165i | −0.00316754 | − | 0.000905684i | ||||
\(799\) | − | 23784.8i | − | 1.05312i | ||||||
\(800\) | 4754.90 | − | 22122.2i | 0.210139 | − | 0.977672i | ||||
\(801\) | 6755.21 | − | 243.012i | 0.297982 | − | 0.0107196i | ||||
\(802\) | −7467.84 | − | 14037.1i | −0.328801 | − | 0.618041i | ||||
\(803\) | 2990.60 | + | 2990.60i | 0.131427 | + | 0.131427i | ||||
\(804\) | 4927.46 | + | 23069.9i | 0.216142 | + | 1.01195i | ||||
\(805\) | −6865.35 | − | 4141.16i | −0.300586 | − | 0.181313i | ||||
\(806\) | −15897.8 | + | 52042.2i | −0.694758 | + | 2.27433i | ||||
\(807\) | 14641.1 | − | 263.264i | 0.638651 | − | 0.0114837i | ||||
\(808\) | 251.431 | − | 2408.23i | 0.0109472 | − | 0.104853i | ||||
\(809\) | −1929.99 | −0.0838749 | −0.0419374 | − | 0.999120i | \(-0.513353\pi\) | ||||
−0.0419374 | + | 0.999120i | \(0.513353\pi\) | |||||||
\(810\) | 416.605 | + | 23049.2i | 0.0180716 | + | 0.999837i | ||||
\(811\) | − | 14596.0i | − | 0.631980i | −0.948763 | − | 0.315990i | \(-0.897663\pi\) | ||
0.948763 | − | 0.315990i | \(-0.102337\pi\) | |||||||
\(812\) | −19055.4 | + | 3713.12i | −0.823540 | + | 0.160474i | ||||
\(813\) | −246.114 | − | 13687.3i | −0.0106170 | − | 0.590448i | ||||
\(814\) | −1526.70 | − | 466.374i | −0.0657381 | − | 0.0200816i | ||||
\(815\) | 9312.77 | + | 37626.3i | 0.400260 | + | 1.61717i | ||||
\(816\) | −30333.9 | − | 12204.6i | −1.30135 | − | 0.523588i | ||||
\(817\) | −15.3858 | + | 15.3858i | −0.000658852 | + | 0.000658852i | ||||
\(818\) | 12694.3 | + | 23861.2i | 0.542598 | + | 1.01991i | ||||
\(819\) | 1946.07 | + | 54096.6i | 0.0830297 | + | 2.30805i | ||||
\(820\) | −2340.15 | + | 1087.66i | −0.0996604 | + | 0.0463204i | ||||
\(821\) | 33180.4 | 1.41048 | 0.705240 | − | 0.708968i | \(-0.250839\pi\) | ||||
0.705240 | + | 0.708968i | \(0.250839\pi\) | |||||||
\(822\) | 2922.97 | − | 10222.8i | 0.124027 | − | 0.433772i | ||||
\(823\) | 990.285 | + | 990.285i | 0.0419431 | + | 0.0419431i | 0.727767 | − | 0.685824i | \(-0.240558\pi\) |
−0.685824 | + | 0.727767i | \(0.740558\pi\) | |||||||
\(824\) | −9225.91 | + | 7481.56i | −0.390048 | + | 0.316302i | ||||
\(825\) | 13706.0 | − | 7545.42i | 0.578403 | − | 0.318422i | ||||
\(826\) | 42286.7 | + | 12917.7i | 1.78129 | + | 0.544145i | ||||
\(827\) | −20987.9 | + | 20987.9i | −0.882492 | + | 0.882492i | −0.993787 | − | 0.111295i | \(-0.964500\pi\) |
0.111295 | + | 0.993787i | \(0.464500\pi\) | |||||||
\(828\) | −1600.24 | − | 6883.87i | −0.0671645 | − | 0.288926i | ||||
\(829\) | 44941.5 | 1.88285 | 0.941425 | − | 0.337223i | \(-0.109488\pi\) | ||||
0.941425 | + | 0.337223i | \(0.109488\pi\) | |||||||
\(830\) | 989.772 | − | 888.538i | 0.0413922 | − | 0.0371586i | ||||
\(831\) | 7175.27 | − | 7438.03i | 0.299527 | − | 0.310496i | ||||
\(832\) | 39244.1 | − | 25562.7i | 1.63527 | − | 1.06518i | ||||
\(833\) | −9549.77 | + | 9549.77i | −0.397215 | + | 0.397215i | ||||
\(834\) | −16270.1 | − | 29299.8i | −0.675526 | − | 1.21651i | ||||
\(835\) | 8559.03 | − | 2118.42i | 0.354727 | − | 0.0877976i | ||||
\(836\) | −24.8278 | + | 36.8454i | −0.00102714 | + | 0.00152431i | ||||
\(837\) | 1590.77 | + | 29464.1i | 0.0656930 | + | 1.21676i | ||||
\(838\) | 19177.5 | + | 36047.6i | 0.790545 | + | 1.48597i | ||||
\(839\) | 18984.0 | 0.781169 | 0.390585 | − | 0.920567i | \(-0.372273\pi\) | ||||
0.390585 | + | 0.920567i | \(0.372273\pi\) | |||||||
\(840\) | −4492.84 | − | 28458.3i | −0.184545 | − | 1.16894i | ||||
\(841\) | 12129.4 | 0.497331 | ||||||||
\(842\) | −8060.84 | − | 15151.8i | −0.329923 | − | 0.620149i | ||||
\(843\) | 20190.1 | − | 363.042i | 0.824891 | − | 0.0148325i | ||||
\(844\) | 10064.6 | + | 6781.89i | 0.410470 | + | 0.276591i | ||||
\(845\) | −59075.8 | − | 35634.3i | −2.40505 | − | 1.45072i | ||||
\(846\) | 17850.6 | + | 4758.53i | 0.725433 | + | 0.193382i | ||||
\(847\) | 11635.1 | − | 11635.1i | 0.472003 | − | 0.472003i | ||||
\(848\) | −13243.3 | + | 31279.5i | −0.536295 | + | 1.26668i | ||||
\(849\) | −8788.96 | − | 8478.47i | −0.355284 | − | 0.342733i | ||||
\(850\) | −6523.65 | − | 34144.2i | −0.263246 | − | 1.37781i | ||||
\(851\) | −766.629 | −0.0308810 | ||||||||
\(852\) | 12075.3 | − | 18634.6i | 0.485555 | − | 0.749308i | ||||
\(853\) | −15050.4 | + | 15050.4i | −0.604123 | + | 0.604123i | −0.941404 | − | 0.337281i | \(-0.890493\pi\) |
0.337281 | + | 0.941404i | \(0.390493\pi\) | |||||||
\(854\) | 41483.4 | + | 12672.3i | 1.66222 | + | 0.507772i | ||||
\(855\) | 33.7823 | − | 60.8497i | 0.00135126 | − | 0.00243394i | ||||
\(856\) | 17508.9 | + | 21591.1i | 0.699114 | + | 0.862115i | ||||
\(857\) | −6041.10 | − | 6041.10i | −0.240793 | − | 0.240793i | 0.576385 | − | 0.817178i | \(-0.304463\pi\) |
−0.817178 | + | 0.576385i | \(0.804463\pi\) | |||||||
\(858\) | 31136.5 | + | 8902.77i | 1.23891 | + | 0.354237i | ||||
\(859\) | 18659.4 | 0.741152 | 0.370576 | − | 0.928802i | \(-0.379160\pi\) | ||||
0.370576 | + | 0.928802i | \(0.379160\pi\) | |||||||
\(860\) | −7928.44 | − | 2896.98i | −0.314369 | − | 0.114868i | ||||
\(861\) | −2281.23 | + | 2364.77i | −0.0902952 | + | 0.0936018i | ||||
\(862\) | 10799.9 | + | 20300.4i | 0.426737 | + | 0.802129i | ||||
\(863\) | 20846.2 | − | 20846.2i | 0.822265 | − | 0.822265i | −0.164168 | − | 0.986432i | \(-0.552494\pi\) |
0.986432 | + | 0.164168i | \(0.0524938\pi\) | |||||||
\(864\) | 15228.4 | − | 20324.1i | 0.599632 | − | 0.800276i | ||||
\(865\) | 10706.8 | − | 2650.02i | 0.420859 | − | 0.104166i | ||||
\(866\) | −48499.8 | − | 14815.6i | −1.90311 | − | 0.581358i | ||||
\(867\) | −24698.9 | + | 444.116i | −0.967496 | + | 0.0173967i | ||||
\(868\) | −7053.11 | − | 36196.0i | −0.275804 | − | 1.41541i | ||||
\(869\) | 15600.4i | 0.608985i | ||||||||
\(870\) | 652.379 | − | 18181.9i | 0.0254227 | − | 0.708535i | ||||
\(871\) | −51911.6 | −2.01947 | ||||||||
\(872\) | −3046.75 | + | 29182.1i | −0.118321 | + | 1.13329i | ||||
\(873\) | 5456.42 | − | 5863.65i | 0.211537 | − | 0.227325i | ||||
\(874\) | −6.23361 | + | 20.4061i | −0.000241253 | + | 0.000789754i | ||||
\(875\) | 22867.8 | − | 20378.1i | 0.883510 | − | 0.787322i | ||||
\(876\) | 1524.52 | + | 7137.63i | 0.0587998 | + | 0.275295i | ||||
\(877\) | −17713.5 | − | 17713.5i | −0.682034 | − | 0.682034i | 0.278424 | − | 0.960458i | \(-0.410188\pi\) |
−0.960458 | + | 0.278424i | \(0.910188\pi\) | |||||||
\(878\) | −5915.17 | − | 11118.6i | −0.227366 | − | 0.427376i | ||||
\(879\) | 10549.2 | − | 10935.5i | 0.404795 | − | 0.419619i | ||||
\(880\) | −17021.7 | − | 2709.82i | −0.652048 | − | 0.103804i | ||||
\(881\) | 9604.82i | 0.367304i | 0.982991 | + | 0.183652i | \(0.0587919\pi\) | ||||
−0.982991 | + | 0.183652i | \(0.941208\pi\) | |||||||
\(882\) | −5256.57 | − | 9077.74i | −0.200678 | − | 0.346557i | ||||
\(883\) | −7027.53 | + | 7027.53i | −0.267831 | + | 0.267831i | −0.828226 | − | 0.560394i | \(-0.810650\pi\) |
0.560394 | + | 0.828226i | \(0.310650\pi\) | |||||||
\(884\) | 40207.4 | − | 59669.3i | 1.52978 | − | 2.27024i | ||||
\(885\) | −20761.0 | + | 35860.6i | −0.788558 | + | 1.36208i | ||||
\(886\) | −42757.1 | − | 13061.4i | −1.62128 | − | 0.495266i | ||||
\(887\) | −14966.3 | − | 14966.3i | −0.566538 | − | 0.566538i | 0.364619 | − | 0.931157i | \(-0.381199\pi\) |
−0.931157 | + | 0.364619i | \(0.881199\pi\) | |||||||
\(888\) | −1773.34 | − | 2108.17i | −0.0670151 | − | 0.0796683i | ||||
\(889\) | − | 31549.6i | − | 1.19026i | ||||||
\(890\) | 426.076 | − | 7905.44i | 0.0160473 | − | 0.297743i | ||||
\(891\) | 17514.9 | − | 1261.79i | 0.658553 | − | 0.0474430i | ||||
\(892\) | −13149.3 | + | 2562.26i | −0.493579 | + | 0.0961782i | ||||
\(893\) | −39.4381 | − | 39.4381i | −0.00147788 | − | 0.00147788i | ||||
\(894\) | 28467.7 | − | 15808.1i | 1.06499 | − | 0.591389i | ||||
\(895\) | −3859.72 | − | 2328.17i | −0.144152 | − | 0.0869521i | ||||
\(896\) | −15342.7 | + | 27784.7i | −0.572059 | + | 1.03596i | ||||
\(897\) | 15549.7 | − | 279.603i | 0.578807 | − | 0.0104076i | ||||
\(898\) | 12894.0 | − | 6859.68i | 0.479152 | − | 0.254911i | ||||
\(899\) | − | 23287.2i | − | 0.863928i | ||||||
\(900\) | 26930.6 | + | 1935.06i | 0.997428 | + | 0.0716689i | ||||
\(901\) | 52183.3i | 1.92950i | ||||||||
\(902\) | 923.242 | + | 1735.40i | 0.0340805 | + | 0.0640604i | ||||
\(903\) | −10746.1 | + | 193.228i | −0.396022 | + | 0.00712095i | ||||
\(904\) | 22594.6 | + | 27862.6i | 0.831290 | + | 1.02511i | ||||
\(905\) | −19911.3 | − | 12010.4i | −0.731353 | − | 0.441150i | ||||
\(906\) | −11080.2 | − | 19953.6i | −0.406308 | − | 0.731694i | ||||
\(907\) | 345.391 | + | 345.391i | 0.0126445 | + | 0.0126445i | 0.713401 | − | 0.700756i | \(-0.247154\pi\) |
−0.700756 | + | 0.713401i | \(0.747154\pi\) | |||||||
\(908\) | 2182.72 | + | 11201.5i | 0.0797754 | + | 0.409401i | ||||
\(909\) | 2887.36 | − | 103.870i | 0.105355 | − | 0.00379004i | ||||
\(910\) | 63307.9 | + | 3412.07i | 2.30619 | + | 0.124296i | ||||
\(911\) | 23701.1i | 0.861966i | 0.902360 | + | 0.430983i | \(0.141833\pi\) | ||||
−0.902360 | + | 0.430983i | \(0.858167\pi\) | |||||||
\(912\) | −70.5343 | + | 30.0607i | −0.00256099 | + | 0.00109146i | ||||
\(913\) | −716.425 | − | 716.425i | −0.0259696 | − | 0.0259696i | ||||
\(914\) | −5878.29 | + | 19242.9i | −0.212732 | + | 0.696388i | ||||
\(915\) | −20366.6 | + | 35179.4i | −0.735848 | + | 1.27103i | ||||
\(916\) | −834.784 | + | 1238.85i | −0.0301114 | + | 0.0446864i | ||||
\(917\) | 2155.23 | − | 2155.23i | 0.0776138 | − | 0.0776138i | ||||
\(918\) | 9370.25 | − | 37873.7i | 0.336889 | − | 1.36167i | ||||
\(919\) | − | 16350.4i | − | 0.586889i | −0.955976 | − | 0.293444i | \(-0.905198\pi\) | ||
0.955976 | − | 0.293444i | \(-0.0948016\pi\) | |||||||
\(920\) | −8198.08 | + | 1143.61i | −0.293785 | + | 0.0409823i | ||||
\(921\) | −10989.1 | + | 11391.6i | −0.393164 | + | 0.407562i | ||||
\(922\) | 4466.31 | − | 2376.10i | 0.159534 | − | 0.0848728i | ||||
\(923\) | 34551.5 | + | 34551.5i | 1.23215 | + | 1.23215i | ||||
\(924\) | −21462.1 | + | 4584.05i | −0.764124 | + | 0.163208i | ||||
\(925\) | 865.898 | − | 2797.86i | 0.0307790 | − | 0.0994520i | ||||
\(926\) | 38658.0 | + | 11809.2i | 1.37190 | + | 0.419086i | ||||
\(927\) | −10376.0 | − | 9655.43i | −0.367631 | − | 0.342099i | ||||
\(928\) | −12865.7 | + | 15368.7i | −0.455105 | + | 0.543644i | ||||
\(929\) | 23050.1 | 0.814047 | 0.407024 | − | 0.913418i | \(-0.366567\pi\) | ||||
0.407024 | + | 0.913418i | \(0.366567\pi\) | |||||||
\(930\) | 34536.8 | + | 1239.20i | 1.21775 | + | 0.0436935i | ||||
\(931\) | 31.6694i | 0.00111485i | ||||||||
\(932\) | 8253.99 | + | 42358.8i | 0.290095 | + | 1.48874i | ||||
\(933\) | 7097.52 | − | 127.622i | 0.249049 | − | 0.00447819i | ||||
\(934\) | 8087.79 | − | 26475.8i | 0.283341 | − | 0.927532i | ||||
\(935\) | −25703.7 | + | 6361.84i | −0.899038 | + | 0.222518i | ||||
\(936\) | 36738.0 | + | 42113.7i | 1.28293 | + | 1.47065i | ||||
\(937\) | −5420.55 | + | 5420.55i | −0.188988 | + | 0.188988i | −0.795258 | − | 0.606271i | \(-0.792665\pi\) |
0.606271 | + | 0.795258i | \(0.292665\pi\) | |||||||
\(938\) | 31057.8 | − | 16522.9i | 1.08110 | − | 0.575151i | ||||
\(939\) | −392.612 | + | 406.990i | −0.0136447 | + | 0.0141444i | ||||
\(940\) | 7425.77 | − | 20322.8i | 0.257662 | − | 0.705167i | ||||
\(941\) | 25394.9 | 0.879754 | 0.439877 | − | 0.898058i | \(-0.355022\pi\) | ||||
0.439877 | + | 0.898058i | \(0.355022\pi\) | |||||||
\(942\) | −8376.75 | + | 29296.8i | −0.289734 | + | 1.01331i | ||||
\(943\) | 667.515 | + | 667.515i | 0.0230512 | + | 0.0230512i | ||||
\(944\) | 42309.0 | − | 17139.3i | 1.45873 | − | 0.590930i | ||||
\(945\) | 32877.5 | − | 10046.7i | 1.13175 | − | 0.345841i | ||||
\(946\) | −1878.50 | + | 6149.38i | −0.0645617 | + | 0.211346i | ||||
\(947\) | 31849.7 | − | 31849.7i | 1.09290 | − | 1.09290i | 0.0976812 | − | 0.995218i | \(-0.468857\pi\) |
0.995218 | − | 0.0976812i | \(-0.0311425\pi\) | |||||||
\(948\) | −14640.4 | + | 22593.0i | −0.501580 | + | 0.774037i | ||||
\(949\) | −16061.0 | −0.549381 | ||||||||
\(950\) | −67.4324 | − | 45.7983i | −0.00230294 | − | 0.00156410i | ||||
\(951\) | 10704.6 | + | 10326.4i | 0.365005 | + | 0.352111i | ||||
\(952\) | −5063.29 | + | 48496.7i | −0.172376 | + | 1.65104i | ||||
\(953\) | −32189.0 | + | 32189.0i | −1.09413 | + | 1.09413i | −0.0990432 | + | 0.995083i | \(0.531578\pi\) |
−0.995083 | + | 0.0990432i | \(0.968422\pi\) | |||||||
\(954\) | −39163.8 | − | 10440.1i | −1.32912 | − | 0.354309i | ||||
\(955\) | −15643.1 | − | 9435.85i | −0.530050 | − | 0.319725i | ||||
\(956\) | −14726.6 | + | 21854.8i | −0.498213 | + | 0.739367i | ||||
\(957\) | −13856.5 | + | 249.156i | −0.468043 | + | 0.00841596i | ||||
\(958\) | −2353.95 | + | 1252.31i | −0.0793869 | + | 0.0422342i | ||||
\(959\) | −15855.9 | −0.533903 | ||||||||
\(960\) | −22108.3 | − | 19898.7i | −0.743275 | − | 0.668986i | ||||
\(961\) | 14443.3 | 0.484820 | ||||||||
\(962\) | 5351.91 | − | 2847.24i | 0.179369 | − | 0.0954250i | ||||
\(963\) | −22596.3 | + | 24282.8i | −0.756134 | + | 0.812566i | ||||
\(964\) | −17437.9 | + | 25878.5i | −0.582612 | + | 0.864617i | ||||
\(965\) | −22449.8 | + | 5556.47i | −0.748895 | + | 0.185357i | ||||
\(966\) | −9214.13 | + | 5116.59i | −0.306894 | + | 0.170418i | ||||
\(967\) | 34684.1 | − | 34684.1i | 1.15343 | − | 1.15343i | 0.167566 | − | 0.985861i | \(-0.446409\pi\) |
0.985861 | − | 0.167566i | \(-0.0535908\pi\) | |||||||
\(968\) | 1764.02 | − | 16895.9i | 0.0585721 | − | 0.561008i | ||||
\(969\) | −81.7794 | + | 84.7743i | −0.00271118 | + | 0.00281047i | ||||
\(970\) | −6266.79 | − | 6980.79i | −0.207438 | − | 0.231072i | ||||
\(971\) | −191.895 | −0.00634214 | −0.00317107 | − | 0.999995i | \(-0.501009\pi\) | ||||
−0.00317107 | + | 0.999995i | \(0.501009\pi\) | |||||||
\(972\) | 26549.7 | + | 14609.7i | 0.876114 | + | 0.482104i | ||||
\(973\) | −35340.2 | + | 35340.2i | −1.16439 | + | 1.16439i | ||||
\(974\) | −14002.1 | + | 45836.7i | −0.460634 | + | 1.50791i | ||||
\(975\) | −16542.8 | + | 57065.5i | −0.543378 | + | 1.87442i | ||||
\(976\) | 41505.3 | − | 16813.8i | 1.36122 | − | 0.551429i | ||||
\(977\) | −25706.8 | − | 25706.8i | −0.841794 | − | 0.841794i | 0.147298 | − | 0.989092i | \(-0.452942\pi\) |
−0.989092 | + | 0.147298i | \(0.952942\pi\) | |||||||
\(978\) | 48990.3 | + | 14007.6i | 1.60177 | + | 0.457990i | ||||
\(979\) | −6030.59 | −0.196873 | ||||||||
\(980\) | −11141.3 | + | 5178.26i | −0.363158 | + | 0.168789i | ||||
\(981\) | −34987.9 | + | 1258.66i | −1.13871 | + | 0.0409641i | ||||
\(982\) | 40407.2 | − | 21496.9i | 1.31308 | − | 0.698567i | ||||
\(983\) | −29865.8 | + | 29865.8i | −0.969044 | + | 0.969044i | −0.999535 | − | 0.0304913i | \(-0.990293\pi\) |
0.0304913 | + | 0.999535i | \(0.490293\pi\) | |||||||
\(984\) | −291.538 | + | 3379.69i | −0.00944501 | + | 0.109492i | ||||
\(985\) | 169.678 | + | 685.550i | 0.00548874 | + | 0.0221761i | ||||
\(986\) | −8995.77 | + | 29448.1i | −0.290551 | + | 0.951135i | ||||
\(987\) | −495.296 | − | 27545.2i | −0.0159731 | − | 0.888323i | ||||
\(988\) | −32.2702 | − | 165.608i | −0.00103912 | − | 0.00533269i | ||||
\(989\) | 3087.90i | 0.0992815i | ||||||||
\(990\) | 367.837 | − | 20563.5i | 0.0118087 | − | 0.660154i | ||||
\(991\) | 38515.4 | 1.23459 | 0.617296 | − | 0.786731i | \(-0.288228\pi\) | ||||
0.617296 | + | 0.786731i | \(0.288228\pi\) | |||||||
\(992\) | −29192.9 | − | 24438.5i | −0.934352 | − | 0.782181i | ||||
\(993\) | −30115.0 | + | 541.503i | −0.962406 | + | 0.0173052i | ||||
\(994\) | −31668.9 | − | 9674.18i | −1.01054 | − | 0.308699i | ||||
\(995\) | 37806.1 | + | 22804.5i | 1.20456 | + | 0.726585i | ||||
\(996\) | −365.212 | − | 1709.89i | −0.0116187 | − | 0.0543974i | ||||
\(997\) | 19278.3 | + | 19278.3i | 0.612387 | + | 0.612387i | 0.943567 | − | 0.331180i | \(-0.107447\pi\) |
−0.331180 | + | 0.943567i | \(0.607447\pi\) | |||||||
\(998\) | 45015.9 | − | 23948.7i | 1.42781 | − | 0.759601i | ||||
\(999\) | 2195.70 | − | 2446.32i | 0.0695383 | − | 0.0774756i |
(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 | 120.4.w.c.53.11 | ✓ | 128 | |
3.2 | odd | 2 | inner | 120.4.w.c.53.54 | yes | 128 | |
5.2 | odd | 4 | inner | 120.4.w.c.77.22 | yes | 128 | |
8.5 | even | 2 | inner | 120.4.w.c.53.43 | yes | 128 | |
15.2 | even | 4 | inner | 120.4.w.c.77.43 | yes | 128 | |
24.5 | odd | 2 | inner | 120.4.w.c.53.22 | yes | 128 | |
40.37 | odd | 4 | inner | 120.4.w.c.77.54 | yes | 128 | |
120.77 | even | 4 | inner | 120.4.w.c.77.11 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.w.c.53.11 | ✓ | 128 | 1.1 | even | 1 | trivial | |
120.4.w.c.53.22 | yes | 128 | 24.5 | odd | 2 | inner | |
120.4.w.c.53.43 | yes | 128 | 8.5 | even | 2 | inner | |
120.4.w.c.53.54 | yes | 128 | 3.2 | odd | 2 | inner | |
120.4.w.c.77.11 | yes | 128 | 120.77 | even | 4 | inner | |
120.4.w.c.77.22 | yes | 128 | 5.2 | odd | 4 | inner | |
120.4.w.c.77.43 | yes | 128 | 15.2 | even | 4 | inner | |
120.4.w.c.77.54 | yes | 128 | 40.37 | odd | 4 | inner |