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 | 53.43 | ||
Character | \(\chi\) | \(=\) | 120.53 |
Dual form | 120.4.w.c.77.43 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.32844 | − | 2.49705i | 0.469675 | − | 0.882839i | ||||
\(3\) | −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 | ||||
\(6\) | −13.0970 | − | 6.66840i | −0.891141 | − | 0.453727i | ||||
\(7\) | −15.4977 | + | 15.4977i | −0.836799 | + | 0.836799i | −0.988436 | − | 0.151637i | \(-0.951546\pi\) |
0.151637 | + | 0.988436i | \(0.451546\pi\) | |||||||
\(8\) | −22.5051 | + | 2.34964i | −0.994594 | + | 0.103841i | ||||
\(9\) | −26.9825 | + | 0.970671i | −0.999354 | + | 0.0359508i | ||||
\(10\) | 16.2342 | + | 27.1376i | 0.513369 | + | 0.858168i | ||||
\(11\) | −24.0882 | −0.660259 | −0.330130 | − | 0.943936i | \(-0.607092\pi\) | ||||
−0.330130 | + | 0.943936i | \(0.607092\pi\) | |||||||
\(12\) | −34.0500 | + | 23.8453i | −0.819115 | + | 0.573630i | ||||
\(13\) | 64.6828 | − | 64.6828i | 1.37998 | − | 1.37998i | 0.535360 | − | 0.844624i | \(-0.320176\pi\) |
0.844624 | − | 0.535360i | \(-0.179824\pi\) | |||||||
\(14\) | 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 | \(0.997426\pi\) | |||||||
\(18\) | −33.4209 | + | 68.6662i | −0.437633 | + | 0.899154i | ||||
\(19\) | 0.230558 | 0.00278387 | 0.00139194 | − | 0.999999i | \(-0.499557\pi\) | ||||
0.00139194 | + | 0.999999i | \(0.499557\pi\) | |||||||
\(20\) | 89.3301 | − | 4.48668i | 0.998741 | − | 0.0501626i | ||||
\(21\) | 81.9634 | + | 79.0678i | 0.851708 | + | 0.821620i | ||||
\(22\) | −31.9997 | + | 60.1493i | −0.310107 | + | 0.582903i | ||||
\(23\) | −23.1362 | + | 23.1362i | −0.209749 | + | 0.209749i | −0.804161 | − | 0.594412i | \(-0.797385\pi\) |
0.594412 | + | 0.804161i | \(0.297385\pi\) | |||||||
\(24\) | 14.3095 | + | 116.701i | 0.121705 | + | 0.992566i | ||||
\(25\) | −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 | ||||
\(28\) | 172.100 | + | 33.5352i | 1.16157 | + | 0.226341i | ||||
\(29\) | − | 110.723i | − | 0.708991i | −0.935058 | − | 0.354496i | \(-0.884653\pi\) | ||
0.935058 | − | 0.354496i | \(-0.115347\pi\) | |||||||
\(30\) | 139.472 | − | 86.8767i | 0.848800 | − | 0.528715i | ||||
\(31\) | −210.319 | −1.21853 | −0.609266 | − | 0.792966i | \(-0.708536\pi\) | ||||
−0.609266 | + | 0.792966i | \(0.708536\pi\) | |||||||
\(32\) | 116.197 | + | 138.803i | 0.641904 | + | 0.766785i | ||||
\(33\) | 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 | ||||
\(36\) | 127.065 | + | 174.673i | 0.588263 | + | 0.808670i | ||||
\(37\) | −16.5677 | − | 16.5677i | −0.0736140 | − | 0.0736140i | 0.669341 | − | 0.742955i | \(-0.266576\pi\) |
−0.742955 | + | 0.669341i | \(0.766576\pi\) | |||||||
\(38\) | 0.306283 | − | 0.575714i | 0.00130752 | − | 0.00245771i | ||||
\(39\) | −342.090 | − | 330.005i | −1.40457 | − | 1.35495i | ||||
\(40\) | 107.466 | − | 229.022i | 0.424798 | − | 0.905288i | ||||
\(41\) | − | 28.8516i | − | 0.109899i | −0.998489 | − | 0.0549495i | \(-0.982500\pi\) | ||
0.998489 | − | 0.0549495i | \(-0.0174998\pi\) | |||||||
\(42\) | 306.320 | − | 99.6294i | 1.12538 | − | 0.366027i | ||||
\(43\) | −66.7330 | + | 66.7330i | −0.236667 | + | 0.236667i | −0.815469 | − | 0.578801i | \(-0.803521\pi\) |
0.578801 | + | 0.815469i | \(0.303521\pi\) | |||||||
\(44\) | 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 | \(0.627511\pi\) | |||||||
\(48\) | 310.418 | + | 119.300i | 0.933438 | + | 0.358738i | ||||
\(49\) | − | 137.360i | − | 0.400466i | ||||||
\(50\) | −353.551 | − | 1.29426i | −0.999993 | − | 0.00366073i | ||||
\(51\) | −354.702 | + | 367.692i | −0.973887 | + | 1.00955i | ||||
\(52\) | −718.293 | − | 139.966i | −1.91556 | − | 0.373265i | ||||
\(53\) | 375.292 | + | 375.292i | 0.972647 | + | 0.972647i | 0.999636 | − | 0.0269890i | \(-0.00859192\pi\) |
−0.0269890 | + | 0.999636i | \(0.508592\pi\) | |||||||
\(54\) | 359.864 | + | 167.218i | 0.906876 | + | 0.421397i | ||||
\(55\) | 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 | ||||
\(58\) | −276.481 | − | 147.089i | −0.625925 | − | 0.332996i | ||||
\(59\) | − | 713.261i | − | 1.57388i | −0.617032 | − | 0.786938i | \(-0.711665\pi\) | ||
0.617032 | − | 0.786938i | \(-0.288335\pi\) | |||||||
\(60\) | −31.6548 | − | 463.679i | −0.0681102 | − | 0.997678i | ||||
\(61\) | − | 699.712i | − | 1.46867i | −0.678786 | − | 0.734336i | \(-0.737494\pi\) | ||
0.678786 | − | 0.734336i | \(-0.262506\pi\) | |||||||
\(62\) | −279.397 | + | 525.177i | −0.572314 | + | 1.07577i | ||||
\(63\) | 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 | ||||
\(66\) | 315.484 | + | 160.630i | 0.588384 | + | 0.299578i | ||||
\(67\) | −401.278 | − | 401.278i | −0.731700 | − | 0.731700i | 0.239257 | − | 0.970956i | \(-0.423096\pi\) |
−0.970956 | + | 0.239257i | \(0.923096\pi\) | |||||||
\(68\) | −150.441 | + | 772.049i | −0.268288 | + | 1.37683i | ||||
\(69\) | 122.361 | + | 118.038i | 0.213486 | + | 0.205944i | ||||
\(70\) | −672.165 | − | 168.979i | −1.14770 | − | 0.288527i | ||||
\(71\) | − | 534.168i | − | 0.892875i | −0.894815 | − | 0.446438i | \(-0.852693\pi\) | ||
0.894815 | − | 0.446438i | \(-0.147307\pi\) | |||||||
\(72\) | 604.964 | − | 85.2444i | 0.990218 | − | 0.139530i | ||||
\(73\) | 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 | ||||
\(78\) | −1278.48 | + | 415.822i | −1.85590 | + | 0.603623i | ||||
\(79\) | 647.639i | 0.922342i | 0.887311 | + | 0.461171i | \(0.152571\pi\) | ||||
−0.887311 | + | 0.461171i | \(0.847429\pi\) | |||||||
\(80\) | −429.115 | − | 572.591i | −0.599707 | − | 0.800220i | ||||
\(81\) | 727.116 | − | 52.3823i | 0.997415 | − | 0.0718551i | ||||
\(82\) | −72.0437 | − | 38.3276i | −0.0970231 | − | 0.0516168i | ||||
\(83\) | 29.7418 | + | 29.7418i | 0.0393324 | + | 0.0393324i | 0.726499 | − | 0.687167i | \(-0.241146\pi\) |
−0.687167 | + | 0.726499i | \(0.741146\pi\) | |||||||
\(84\) | 158.149 | − | 897.246i | 0.205422 | − | 1.16545i | ||||
\(85\) | 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 | ||||
\(88\) | 542.106 | − | 56.5986i | 0.656690 | − | 0.0685617i | ||||
\(89\) | −250.355 | −0.298175 | −0.149087 | − | 0.988824i | \(-0.547634\pi\) | ||||
−0.149087 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(90\) | −464.381 | − | 716.485i | −0.543889 | − | 0.839157i | ||||
\(91\) | 2004.88i | 2.30954i | ||||||||
\(92\) | 256.924 | + | 50.0639i | 0.291154 | + | 0.0567339i | ||||
\(93\) | 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 | ||||
\(96\) | 710.270 | − | 616.647i | 0.755121 | − | 0.655586i | ||||
\(97\) | −209.767 | + | 209.767i | −0.219573 | + | 0.219573i | −0.808318 | − | 0.588746i | \(-0.799622\pi\) |
0.588746 | + | 0.808318i | \(0.299622\pi\) | |||||||
\(98\) | −342.994 | − | 182.475i | −0.353548 | − | 0.188089i | ||||
\(99\) | 649.960 | − | 23.3817i | 0.659833 | − | 0.0237368i | ||||
\(100\) | −472.904 | + | 881.114i | −0.472904 | + | 0.881114i | ||||
\(101\) | 107.008 | 0.105423 | 0.0527115 | − | 0.998610i | \(-0.483214\pi\) | ||||
0.0527115 | + | 0.998610i | \(0.483214\pi\) | |||||||
\(102\) | 446.942 | + | 1374.17i | 0.433862 | + | 1.33395i | ||||
\(103\) | 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 | −0.980646 | − | 0.195789i | \(-0.937273\pi\) |
0.195789 | + | 0.980646i | \(0.437273\pi\) | |||||||
\(108\) | 895.609 | − | 676.459i | 0.797963 | − | 0.602707i | ||||
\(109\) | −1296.69 | −1.13945 | −0.569725 | − | 0.821835i | \(-0.692950\pi\) | ||||
−0.569725 | + | 0.821835i | \(0.692950\pi\) | |||||||
\(110\) | −391.051 | − | 653.696i | −0.338957 | − | 0.566613i | ||||
\(111\) | −84.5269 | + | 87.6223i | −0.0722787 | + | 0.0749256i | ||||
\(112\) | −546.886 | − | 1291.69i | −0.461392 | − | 1.08976i | ||||
\(113\) | 1121.02 | − | 1121.02i | 0.933243 | − | 0.933243i | −0.0646636 | − | 0.997907i | \(-0.520597\pi\) |
0.997907 | + | 0.0646636i | \(0.0205974\pi\) | |||||||
\(114\) | −3.01963 | − | 1.53745i | −0.00248082 | − | 0.00126312i | ||||
\(115\) | −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 | ||||
\(118\) | −1781.05 | − | 947.526i | −1.38948 | − | 0.739210i | ||||
\(119\) | 2154.92 | 1.66001 | ||||||||
\(120\) | −1199.88 | − | 536.927i | −0.912779 | − | 0.408454i | ||||
\(121\) | −750.761 | −0.564058 | ||||||||
\(122\) | −1747.21 | − | 929.527i | −1.29660 | − | 0.689798i | ||||
\(123\) | −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 | ||||
\(126\) | −546.221 | − | 1582.12i | −0.386201 | − | 1.11862i | ||||
\(127\) | −1017.88 | + | 1017.88i | −0.711197 | + | 0.711197i | −0.966786 | − | 0.255588i | \(-0.917731\pi\) |
0.255588 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(128\) | 401.411 | − | 1391.41i | 0.277188 | − | 0.960816i | ||||
\(129\) | 352.933 | + | 340.465i | 0.240884 | + | 0.232374i | ||||
\(130\) | 2805.41 | + | 705.268i | 1.89270 | + | 0.475816i | ||||
\(131\) | 139.067 | 0.0927508 | 0.0463754 | − | 0.998924i | \(-0.485233\pi\) | ||||
0.0463754 | + | 0.998924i | \(0.485233\pi\) | |||||||
\(132\) | 820.201 | − | 574.390i | 0.540828 | − | 0.378744i | ||||
\(133\) | −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 | \(0.677573\pi\) | |||||||
\(138\) | 457.297 | − | 148.734i | 0.282085 | − | 0.0917471i | ||||
\(139\) | −2280.35 | −1.39149 | −0.695743 | − | 0.718291i | \(-0.744925\pi\) | ||||
−0.695743 | + | 0.718291i | \(0.744925\pi\) | |||||||
\(140\) | −1314.88 | + | 1453.95i | −0.793770 | + | 0.877722i | ||||
\(141\) | 872.706 | − | 904.665i | 0.521242 | − | 0.540330i | ||||
\(142\) | −1333.84 | − | 709.612i | −0.788265 | − | 0.419361i | ||||
\(143\) | −1558.09 | + | 1558.09i | −0.911147 | + | 0.911147i | ||||
\(144\) | 590.800 | − | 1623.87i | 0.341898 | − | 0.939737i | ||||
\(145\) | 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 | ||||
\(148\) | −35.8506 | + | 183.982i | −0.0199115 | + | 0.102184i | ||||
\(149\) | − | 2215.59i | − | 1.21817i | −0.793103 | − | 0.609087i | \(-0.791536\pi\) | ||
0.793103 | − | 0.609087i | \(-0.208464\pi\) | |||||||
\(150\) | 26.3039 | + | 1836.93i | 0.0143180 | + | 0.999897i | ||||
\(151\) | 1552.95 | 0.836936 | 0.418468 | − | 0.908231i | \(-0.362567\pi\) | ||||
0.418468 | + | 0.908231i | \(0.362567\pi\) | |||||||
\(152\) | −5.18873 | + | 0.541729i | −0.00276882 | + | 0.000289079i | ||||
\(153\) | 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 | ||||
\(156\) | −660.064 | + | 3744.83i | −0.338766 | + | 1.92196i | ||||
\(157\) | 1466.03 | + | 1466.03i | 0.745235 | + | 0.745235i | 0.973580 | − | 0.228345i | \(-0.0733314\pi\) |
−0.228345 | + | 0.973580i | \(0.573331\pi\) | |||||||
\(158\) | 1617.18 | + | 860.350i | 0.814280 | + | 0.433201i | ||||
\(159\) | 1914.70 | − | 1984.82i | 0.955003 | − | 0.989976i | ||||
\(160\) | −1999.84 | + | 310.867i | −0.988133 | + | 0.153601i | ||||
\(161\) | − | 717.118i | − | 0.351036i | ||||||
\(162\) | 835.130 | − | 1885.23i | 0.405025 | − | 0.914306i | ||||
\(163\) | 2451.50 | − | 2451.50i | 1.17801 | − | 1.17801i | 0.197766 | − | 0.980249i | \(-0.436632\pi\) |
0.980249 | − | 0.197766i | \(-0.0633685\pi\) | |||||||
\(164\) | −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 | \(0.691511\pi\) | |||||||
\(168\) | −2030.37 | − | 1586.84i | −0.932421 | − | 0.728736i | ||||
\(169\) | − | 6170.74i | − | 2.80871i | ||||||
\(170\) | 758.050 | − | 3015.37i | 0.341999 | − | 1.36040i | ||||
\(171\) | −6.22104 | + | 0.223796i | −0.00278207 | + | 0.000100082i | ||||
\(172\) | 741.060 | + | 144.402i | 0.328519 | + | 0.0640148i | ||||
\(173\) | −697.593 | − | 697.593i | −0.306572 | − | 0.306572i | 0.537006 | − | 0.843578i | \(-0.319555\pi\) |
−0.843578 | + | 0.537006i | \(0.819555\pi\) | |||||||
\(174\) | −738.346 | + | 1450.14i | −0.321689 | + | 0.631811i | ||||
\(175\) | 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 | ||||
\(178\) | −332.582 | + | 625.148i | −0.140045 | + | 0.263240i | ||||
\(179\) | 403.165i | 0.168346i | 0.996451 | + | 0.0841731i | \(0.0268249\pi\) | ||||
−0.996451 | + | 0.0841731i | \(0.973175\pi\) | |||||||
\(180\) | −2406.00 | + | 207.772i | −0.996292 | + | 0.0860357i | ||||
\(181\) | 2079.83i | 0.854102i | 0.904228 | + | 0.427051i | \(0.140448\pi\) | ||||
−0.904228 | + | 0.427051i | \(0.859552\pi\) | |||||||
\(182\) | 5006.27 | + | 2663.36i | 2.03895 | + | 1.08473i | ||||
\(183\) | −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 | ||||
\(186\) | 2754.56 | + | 1402.49i | 1.08588 | + | 0.552881i | ||||
\(187\) | 1674.70 | + | 1674.70i | 0.654898 | + | 0.654898i | ||||
\(188\) | 370.143 | − | 1899.54i | 0.143593 | − | 0.736906i | ||||
\(189\) | −2288.33 | − | 2053.89i | −0.880696 | − | 0.790469i | ||||
\(190\) | 3.74292 | + | 6.25680i | 0.00142916 | + | 0.00238903i | ||||
\(191\) | − | 1633.99i | − | 0.619013i | −0.950897 | − | 0.309506i | \(-0.899836\pi\) | ||
0.950897 | − | 0.309506i | \(-0.100164\pi\) | |||||||
\(192\) | −596.244 | − | 2592.76i | −0.224116 | − | 0.974563i | ||||
\(193\) | −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 | −0.698984 | − | 0.715138i | \(-0.746364\pi\) |
0.715138 | + | 0.698984i | \(0.246364\pi\) | |||||||
\(198\) | 805.049 | − | 1654.04i | 0.288951 | − | 0.593675i | ||||
\(199\) | 3949.02i | 1.40673i | 0.710831 | + | 0.703363i | \(0.248319\pi\) | ||||
−0.710831 | + | 0.703363i | \(0.751681\pi\) | |||||||
\(200\) | 1571.96 | + | 2351.37i | 0.555771 | + | 0.831335i | ||||
\(201\) | −2047.28 | + | 2122.25i | −0.718427 | + | 0.744736i | ||||
\(202\) | 142.154 | − | 267.205i | 0.0495145 | − | 0.0930715i | ||||
\(203\) | 1715.96 | + | 1715.96i | 0.593284 | + | 0.593284i | ||||
\(204\) | 4025.09 | + | 709.463i | 1.38144 | + | 0.243492i | ||||
\(205\) | 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 | ||||
\(208\) | 2282.53 | + | 5391.13i | 0.760891 | + | 1.79715i | ||||
\(209\) | −5.55372 | −0.00183808 | ||||||||
\(210\) | −815.108 | + | 3507.89i | −0.267847 | + | 1.15270i | ||||
\(211\) | − | 1517.04i | − | 0.494963i | −0.968893 | − | 0.247481i | \(-0.920397\pi\) | ||
0.968893 | − | 0.247481i | \(-0.0796029\pi\) | |||||||
\(212\) | 812.085 | − | 4167.56i | 0.263086 | − | 1.35014i | ||||
\(213\) | −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 | ||||
\(216\) | −499.386 | − | 3135.01i | −0.157310 | − | 0.987549i | ||||
\(217\) | 3259.48 | − | 3259.48i | 1.01967 | − | 1.01967i | ||||
\(218\) | −1722.57 | + | 3237.89i | −0.535171 | + | 1.00595i | ||||
\(219\) | 633.411 | − | 656.607i | 0.195443 | − | 0.202600i | ||||
\(220\) | −2151.80 | + | 108.076i | −0.659428 | + | 0.0331203i | ||||
\(221\) | −8993.97 | −2.73756 | ||||||||
\(222\) | 106.508 | + | 327.469i | 0.0321998 | + | 0.0990012i | ||||
\(223\) | −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 | −0.544091 | − | 0.839026i | \(-0.683125\pi\) |
0.839026 | + | 0.544091i | \(0.183125\pi\) | |||||||
\(228\) | −7.85049 | + | 5.49773i | −0.00228031 | + | 0.00159691i | ||||
\(229\) | 186.732 | 0.0538848 | 0.0269424 | − | 0.999637i | \(-0.491423\pi\) | ||||
0.0269424 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(230\) | −1003.46 | − | 252.265i | −0.287679 | − | 0.0723212i | ||||
\(231\) | −1974.35 | − | 1904.60i | −0.562348 | − | 0.542482i | ||||
\(232\) | 260.160 | + | 2491.83i | 0.0736221 | + | 0.705159i | ||||
\(233\) | −3814.45 | + | 3814.45i | −1.07250 | + | 1.07250i | −0.0753429 | + | 0.997158i | \(0.524005\pi\) |
−0.997158 | + | 0.0753429i | \(0.975995\pi\) | |||||||
\(234\) | 2279.76 | + | 6603.28i | 0.636892 | + | 1.84474i | ||||
\(235\) | −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 | ||||
\(238\) | 2862.68 | − | 5380.93i | 0.779665 | − | 1.46552i | ||||
\(239\) | −3294.18 | −0.891561 | −0.445780 | − | 0.895142i | \(-0.647074\pi\) | ||||
−0.445780 | + | 0.895142i | \(0.647074\pi\) | |||||||
\(240\) | −2934.70 | + | 2282.88i | −0.789309 | + | 0.613996i | ||||
\(241\) | −3900.68 | −1.04259 | −0.521296 | − | 0.853376i | \(-0.674551\pi\) | ||||
−0.521296 | + | 0.853376i | \(0.674551\pi\) | |||||||
\(242\) | −997.342 | + | 1874.68i | −0.264924 | + | 0.497972i | ||||
\(243\) | −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 | ||||
\(246\) | −192.394 | + | 377.870i | −0.0498641 | + | 0.0979354i | ||||
\(247\) | 14.9131 | − | 14.9131i | 0.00384170 | − | 0.00384170i | ||||
\(248\) | 4733.26 | − | 494.176i | 1.21194 | − | 0.126533i | ||||
\(249\) | 151.740 | − | 157.296i | 0.0386189 | − | 0.0400331i | ||||
\(250\) | 2054.05 | − | 3377.26i | 0.519639 | − | 0.854386i | ||||
\(251\) | 934.348 | 0.234962 | 0.117481 | − | 0.993075i | \(-0.462518\pi\) | ||||
0.117481 | + | 0.993075i | \(0.462518\pi\) | |||||||
\(252\) | −4676.25 | − | 737.813i | −1.16895 | − | 0.184436i | ||||
\(253\) | 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 | \(0.887641\pi\) | |||||||
\(258\) | 1319.01 | − | 429.002i | 0.318286 | − | 0.103521i | ||||
\(259\) | 513.525 | 0.123200 | ||||||||
\(260\) | 5487.91 | − | 6068.34i | 1.30902 | − | 1.44747i | ||||
\(261\) | 107.476 | + | 2987.59i | 0.0254888 | + | 0.708533i | ||||
\(262\) | 184.743 | − | 347.257i | 0.0435627 | − | 0.0818841i | ||||
\(263\) | −3531.42 | + | 3531.42i | −0.827972 | + | 0.827972i | −0.987236 | − | 0.159264i | \(-0.949088\pi\) |
0.159264 | + | 0.987236i | \(0.449088\pi\) | |||||||
\(264\) | −344.690 | − | 2811.12i | −0.0803568 | − | 0.655351i | ||||
\(265\) | −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 | ||||
\(268\) | −868.316 | + | 4456.13i | −0.197914 | + | 1.01568i | ||||
\(269\) | 2818.14i | 0.638754i | 0.947628 | + | 0.319377i | \(0.103474\pi\) | ||||
−0.947628 | + | 0.319377i | \(0.896526\pi\) | |||||||
\(270\) | −3678.98 | + | 2479.54i | −0.829243 | + | 0.558888i | ||||
\(271\) | −2634.55 | −0.590544 | −0.295272 | − | 0.955413i | \(-0.595410\pi\) | ||||
−0.295272 | + | 0.955413i | \(0.595410\pi\) | |||||||
\(272\) | 5794.60 | − | 2453.36i | 1.29172 | − | 0.546899i | ||||
\(273\) | 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 | ||||
\(276\) | 236.096 | − | 1339.48i | 0.0514903 | − | 0.292127i | ||||
\(277\) | 1406.39 | + | 1406.39i | 0.305061 | + | 0.305061i | 0.842990 | − | 0.537929i | \(-0.180793\pi\) |
−0.537929 | + | 0.842990i | \(0.680793\pi\) | |||||||
\(278\) | −3029.31 | + | 5694.14i | −0.653546 | + | 1.22846i | ||||
\(279\) | 5674.95 | − | 204.151i | 1.21774 | − | 0.0438071i | ||||
\(280\) | 1883.83 | + | 5214.81i | 0.402074 | + | 1.11302i | ||||
\(281\) | − | 3886.21i | − | 0.825024i | −0.910952 | − | 0.412512i | \(-0.864651\pi\) | ||
0.910952 | − | 0.412512i | \(-0.135349\pi\) | |||||||
\(282\) | −1099.65 | − | 3380.98i | −0.232210 | − | 0.713952i | ||||
\(283\) | 1661.83 | − | 1661.83i | 0.349065 | − | 0.349065i | −0.510696 | − | 0.859761i | \(-0.670612\pi\) |
0.859761 | + | 0.510696i | \(0.170612\pi\) | |||||||
\(284\) | −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 | ||||
\(288\) | −3270.02 | − | 3632.47i | −0.669056 | − | 0.743212i | ||||
\(289\) | 4754.08i | 0.967652i | ||||||||
\(290\) | 3004.76 | − | 1797.50i | 0.608434 | − | 0.363974i | ||||
\(291\) | 1109.40 | + | 1070.21i | 0.223485 | + | 0.215590i | ||||
\(292\) | 268.650 | − | 1378.69i | 0.0538409 | − | 0.276307i | ||||
\(293\) | 2067.70 | + | 2067.70i | 0.412273 | + | 0.412273i | 0.882530 | − | 0.470257i | \(-0.155839\pi\) |
−0.470257 | + | 0.882530i | \(0.655839\pi\) | |||||||
\(294\) | −915.972 | + | 1799.01i | −0.181703 | + | 0.356872i | ||||
\(295\) | 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 | ||||
\(298\) | −5532.43 | − | 2943.28i | −1.07545 | − | 0.572146i | ||||
\(299\) | 2993.03i | 0.578901i | ||||||||
\(300\) | 4621.84 | + | 2374.57i | 0.889474 | + | 0.456986i | ||||
\(301\) | − | 2068.42i | − | 0.396086i | ||||||
\(302\) | 2063.01 | − | 3877.79i | 0.393088 | − | 0.738880i | ||||
\(303\) | −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 | ||||
\(306\) | 7097.47 | − | 2450.38i | 1.32593 | − | 0.457774i | ||||
\(307\) | −2153.93 | − | 2153.93i | −0.400428 | − | 0.400428i | 0.477956 | − | 0.878384i | \(-0.341378\pi\) |
−0.878384 | + | 0.477956i | \(0.841378\pi\) | |||||||
\(308\) | −4145.57 | − | 807.802i | −0.766935 | − | 0.149444i | ||||
\(309\) | 1893.79 | − | 1963.14i | 0.348653 | − | 0.361421i | ||||
\(310\) | −3414.36 | − | 5707.57i | −0.625557 | − | 1.04570i | ||||
\(311\) | − | 1366.14i | − | 0.249089i | −0.992214 | − | 0.124545i | \(-0.960253\pi\) | ||
0.992214 | − | 0.124545i | \(-0.0397470\pi\) | |||||||
\(312\) | 8474.16 | + | 6623.00i | 1.53768 | + | 1.20177i | ||||
\(313\) | 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 | −0.863303 | − | 0.504687i | \(-0.831608\pi\) |
0.504687 | + | 0.863303i | \(0.331608\pi\) | |||||||
\(318\) | −2412.61 | − | 7417.80i | −0.425449 | − | 1.30808i | ||||
\(319\) | 2667.11i | 0.468118i | ||||||||
\(320\) | −1880.42 | + | 5406.66i | −0.328496 | + | 0.944505i | ||||
\(321\) | 4594.29 | + | 4431.98i | 0.798841 | + | 0.770620i | ||||
\(322\) | −1790.68 | − | 952.649i | −0.309908 | − | 0.164873i | ||||
\(323\) | −16.0292 | − | 16.0292i | −0.00276127 | − | 0.00276127i | ||||
\(324\) | −3598.08 | − | 4589.77i | −0.616955 | − | 0.786998i | ||||
\(325\) | −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 | ||||
\(328\) | 67.7909 | + | 649.307i | 0.0114120 | + | 0.109305i | ||||
\(329\) | −5301.94 | −0.888466 | ||||||||
\(330\) | −3359.62 | + | 2092.70i | −0.560428 | + | 0.349089i | ||||
\(331\) | − | 5796.56i | − | 0.962562i | −0.876566 | − | 0.481281i | \(-0.840172\pi\) | ||
0.876566 | − | 0.481281i | \(-0.159828\pi\) | |||||||
\(332\) | 64.3576 | − | 330.278i | 0.0106388 | − | 0.0545975i | ||||
\(333\) | 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 | ||||
\(336\) | −6659.66 | + | 2961.91i | −1.08129 | + | 0.480909i | ||||
\(337\) | 6068.78 | − | 6068.78i | 0.980972 | − | 0.980972i | −0.0188504 | − | 0.999822i | \(-0.506001\pi\) |
0.999822 | + | 0.0188504i | \(0.00600062\pi\) | |||||||
\(338\) | −15408.6 | − | 8197.47i | −2.47964 | − | 1.31918i | ||||
\(339\) | −5928.76 | − | 5719.32i | −0.949871 | − | 0.916315i | ||||
\(340\) | −6522.49 | − | 5898.63i | −1.04039 | − | 0.940876i | ||||
\(341\) | 5066.21 | 0.804547 | ||||||||
\(342\) | −7.70546 | + | 15.8315i | −0.00121831 | + | 0.00250313i | ||||
\(343\) | −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 | −0.818758 | − | 0.574139i | \(-0.805337\pi\) |
0.574139 | + | 0.818758i | \(0.305337\pi\) | |||||||
\(348\) | 2640.23 | + | 3770.12i | 0.406698 | + | 0.580745i | ||||
\(349\) | 1671.59 | 0.256384 | 0.128192 | − | 0.991749i | \(-0.459083\pi\) | ||||
0.128192 | + | 0.991749i | \(0.459083\pi\) | |||||||
\(350\) | 5499.30 | − | 5459.18i | 0.839857 | − | 0.833730i | ||||
\(351\) | 9550.79 | + | 8572.32i | 1.45237 | + | 1.30358i | ||||
\(352\) | −2798.97 | − | 3343.51i | −0.423823 | − | 0.506277i | ||||
\(353\) | 8700.46 | − | 8700.46i | 1.31184 | − | 1.31184i | 0.391777 | − | 0.920060i | \(-0.371860\pi\) |
0.920060 | − | 0.391777i | \(-0.128140\pi\) | |||||||
\(354\) | −4756.31 | + | 9341.61i | −0.714111 | + | 1.40255i | ||||
\(355\) | 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 | ||||
\(358\) | 1006.72 | + | 535.582i | 0.148623 | + | 0.0790681i | ||||
\(359\) | 3722.45 | 0.547252 | 0.273626 | − | 0.961836i | \(-0.411777\pi\) | ||||
0.273626 | + | 0.961836i | \(0.411777\pi\) | |||||||
\(360\) | −2677.41 | + | 6283.90i | −0.391978 | + | 0.919975i | ||||
\(361\) | −6858.95 | −0.999992 | ||||||||
\(362\) | 5193.43 | + | 2762.93i | 0.754035 | + | 0.401150i | ||||
\(363\) | 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 | ||||
\(366\) | −4665.96 | + | 9164.16i | −0.666376 | + | 1.30879i | ||||
\(367\) | −4883.48 | + | 4883.48i | −0.694593 | + | 0.694593i | −0.963239 | − | 0.268646i | \(-0.913424\pi\) |
0.268646 | + | 0.963239i | \(0.413424\pi\) | |||||||
\(368\) | −816.433 | − | 1928.34i | −0.115651 | − | 0.273156i | ||||
\(369\) | 28.0054 | + | 778.489i | 0.00395095 | + | 0.109828i | ||||
\(370\) | 180.646 | − | 718.573i | 0.0253820 | − | 0.100964i | ||||
\(371\) | −11632.3 | −1.62782 | ||||||||
\(372\) | 7161.37 | − | 5015.14i | 0.998117 | − | 0.698986i | ||||
\(373\) | 5585.36 | − | 5585.36i | 0.775332 | − | 0.775332i | −0.203701 | − | 0.979033i | \(-0.565297\pi\) |
0.979033 | + | 0.203701i | \(0.0652971\pi\) | |||||||
\(374\) | 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 | ||||
\(378\) | −8168.58 | + | 2985.59i | −1.11150 | + | 0.406249i | ||||
\(379\) | −12771.6 | −1.73096 | −0.865480 | − | 0.500944i | \(-0.832986\pi\) | ||||
−0.865480 | + | 0.500944i | \(0.832986\pi\) | |||||||
\(380\) | 20.5958 | − | 1.03444i | 0.00278037 | − | 0.000139646i | ||||
\(381\) | 5383.28 | + | 5193.11i | 0.723869 | + | 0.698296i | ||||
\(382\) | −4080.15 | − | 2170.66i | −0.546489 | − | 0.290735i | ||||
\(383\) | 1175.44 | − | 1175.44i | 0.156821 | − | 0.156821i | −0.624335 | − | 0.781156i | \(-0.714630\pi\) |
0.781156 | + | 0.624335i | \(0.214630\pi\) | |||||||
\(384\) | −7266.31 | − | 1955.48i | −0.965644 | − | 0.259870i | ||||
\(385\) | 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 | ||||
\(388\) | 2329.43 | + | 453.909i | 0.304790 | + | 0.0593911i | ||||
\(389\) | − | 2725.23i | − | 0.355205i | −0.984102 | − | 0.177603i | \(-0.943166\pi\) | ||
0.984102 | − | 0.177603i | \(-0.0568342\pi\) | |||||||
\(390\) | 3402.01 | − | 14640.9i | 0.441712 | − | 1.90095i | ||||
\(391\) | 3217.03 | 0.416092 | ||||||||
\(392\) | 322.747 | + | 3091.30i | 0.0415847 | + | 0.398301i | ||||
\(393\) | −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 | ||||
\(396\) | −3060.76 | − | 4207.54i | −0.388406 | − | 0.533932i | ||||
\(397\) | 4427.98 | + | 4427.98i | 0.559783 | + | 0.559783i | 0.929246 | − | 0.369462i | \(-0.120458\pi\) |
−0.369462 | + | 0.929246i | \(0.620458\pi\) | |||||||
\(398\) | 9860.89 | + | 5246.04i | 1.24191 | + | 0.660705i | ||||
\(399\) | 18.8973 | + | 18.2297i | 0.00237105 | + | 0.00228729i | ||||
\(400\) | 7959.74 | − | 801.592i | 0.994967 | − | 0.100199i | ||||
\(401\) | 5621.50i | 0.700061i | 0.936738 | + | 0.350030i | \(0.113829\pi\) | ||||
−0.936738 | + | 0.350030i | \(0.886171\pi\) | |||||||
\(402\) | 2579.67 | + | 7931.43i | 0.320055 | + | 0.984040i | ||||
\(403\) | −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 | ||||
\(408\) | 7118.66 | − | 9108.36i | 0.863790 | − | 1.10522i | ||||
\(409\) | − | 9555.77i | − | 1.15526i | −0.816298 | − | 0.577631i | \(-0.803977\pi\) | ||
0.816298 | − | 0.577631i | \(-0.196023\pi\) | |||||||
\(410\) | 782.963 | − | 468.381i | 0.0943117 | − | 0.0564187i | ||||
\(411\) | 2609.90 | − | 2705.47i | 0.313228 | − | 0.324699i | ||||
\(412\) | 803.217 | − | 4122.04i | 0.0960477 | − | 0.492909i | ||||
\(413\) | 11053.9 | + | 11053.9i | 1.31702 | + | 1.31702i | ||||
\(414\) | −815.441 | − | 2361.91i | −0.0968037 | − | 0.280390i | ||||
\(415\) | −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 | ||||
\(418\) | −7.37779 | + | 13.8679i | −0.000863300 | + | 0.00162273i | ||||
\(419\) | 14436.1i | 1.68317i | 0.540121 | + | 0.841587i | \(0.318379\pi\) | ||||
−0.540121 | + | 0.841587i | \(0.681621\pi\) | |||||||
\(420\) | 7676.55 | + | 6695.40i | 0.891851 | + | 0.777862i | ||||
\(421\) | − | 6067.89i | − | 0.702449i | −0.936291 | − | 0.351224i | \(-0.885765\pi\) | ||
0.936291 | − | 0.351224i | \(-0.114235\pi\) | |||||||
\(422\) | −3788.11 | − | 2015.30i | −0.436973 | − | 0.232472i | ||||
\(423\) | −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 | ||||
\(426\) | −3562.05 | + | 6996.02i | −0.405122 | + | 0.795677i | ||||
\(427\) | 10844.0 | + | 10844.0i | 1.22898 | + | 1.22898i | ||||
\(428\) | 9646.71 | + | 1879.75i | 1.08947 | + | 0.212292i | ||||
\(429\) | 8240.32 | + | 7949.21i | 0.927381 | + | 0.894619i | ||||
\(430\) | −2894.33 | − | 727.622i | −0.324598 | − | 0.0816024i | ||||
\(431\) | − | 8129.78i | − | 0.908579i | −0.890854 | − | 0.454289i | \(-0.849893\pi\) | ||
0.890854 | − | 0.454289i | \(-0.150107\pi\) | |||||||
\(432\) | −8491.68 | − | 2917.69i | −0.945732 | − | 0.324948i | ||||
\(433\) | 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 | ||||
\(438\) | −798.129 | − | 2453.92i | −0.0870687 | − | 0.267701i | ||||
\(439\) | 4452.71i | 0.484092i | 0.970265 | + | 0.242046i | \(0.0778185\pi\) | ||||
−0.970265 | + | 0.242046i | \(0.922181\pi\) | |||||||
\(440\) | −2588.67 | + | 5516.71i | −0.280477 | + | 0.597725i | ||||
\(441\) | 133.331 | + | 3706.32i | 0.0143971 | + | 0.400208i | ||||
\(442\) | −11948.0 | + | 22458.4i | −1.28576 | + | 2.41682i | ||||
\(443\) | −11176.9 | − | 11176.9i | −1.19872 | − | 1.19872i | −0.974552 | − | 0.224164i | \(-0.928035\pi\) |
−0.224164 | − | 0.974552i | \(-0.571965\pi\) | |||||||
\(444\) | 959.194 | + | 169.068i | 0.102526 | + | 0.0180712i | ||||
\(445\) | 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 | ||||
\(448\) | −6124.71 | + | 9402.73i | −0.645905 | + | 0.991601i | ||||
\(449\) | −5163.70 | −0.542740 | −0.271370 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271370 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(450\) | 9540.96 | − | 308.259i | 0.999478 | − | 0.0322922i | ||||
\(451\) | 694.981i | 0.0725618i | ||||||||
\(452\) | −12448.7 | − | 2425.75i | −1.29544 | − | 0.252428i | ||||
\(453\) | −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 | ||||
\(456\) | 3.29917 | + | 26.9065i | 0.000338811 | + | 0.00276318i | ||||
\(457\) | 5030.18 | − | 5030.18i | 0.514884 | − | 0.514884i | −0.401135 | − | 0.916019i | \(-0.631384\pi\) |
0.916019 | + | 0.401135i | \(0.131384\pi\) | |||||||
\(458\) | 248.063 | − | 466.280i | 0.0253084 | − | 0.0475716i | ||||
\(459\) | 9213.86 | − | 10265.6i | 0.936964 | − | 1.04391i | ||||
\(460\) | −1962.95 | + | 2170.56i | −0.198964 | + | 0.220007i | ||||
\(461\) | 1788.64 | 0.180705 | 0.0903526 | − | 0.995910i | \(-0.471201\pi\) | ||||
0.0903526 | + | 0.995910i | \(0.471201\pi\) | |||||||
\(462\) | −7378.68 | + | 2399.89i | −0.743046 | + | 0.241673i | ||||
\(463\) | −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 | −0.275514 | − | 0.961297i | \(-0.588848\pi\) |
0.961297 | + | 0.275514i | \(0.0888479\pi\) | |||||||
\(468\) | 19517.2 | + | 3079.41i | 1.92774 | + | 0.304157i | ||||
\(469\) | 12437.8 | 1.22457 | ||||||||
\(470\) | −1865.10 | + | 7418.98i | −0.183044 | + | 0.728110i | ||||
\(471\) | 7479.53 | − | 7753.44i | 0.731717 | − | 0.758513i | ||||
\(472\) | 1675.91 | + | 16052.0i | 0.163432 | + | 1.56537i | ||||
\(473\) | 1607.48 | − | 1607.48i | 0.156262 | − | 0.156262i | ||||
\(474\) | 4318.72 | − | 8482.15i | 0.418492 | − | 0.821937i | ||||
\(475\) | −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 | ||||
\(478\) | −4376.13 | + | 8225.73i | −0.418744 | + | 0.787105i | ||||
\(479\) | 942.693 | 0.0899222 | 0.0449611 | − | 0.998989i | \(-0.485684\pi\) | ||||
0.0449611 | + | 0.998989i | \(0.485684\pi\) | |||||||
\(480\) | 1801.87 | + | 10360.8i | 0.171341 | + | 0.985212i | ||||
\(481\) | −2143.30 | −0.203172 | ||||||||
\(482\) | −5181.83 | + | 9740.18i | −0.489680 | + | 0.920442i | ||||
\(483\) | −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 | ||||
\(486\) | −9872.37 | − | 4162.65i | −0.921440 | − | 0.388521i | ||||
\(487\) | 11981.9 | − | 11981.9i | 1.11489 | − | 1.11489i | 0.122413 | − | 0.992479i | \(-0.460937\pi\) |
0.992479 | − | 0.122413i | \(-0.0390633\pi\) | |||||||
\(488\) | 1644.07 | + | 15747.1i | 0.152508 | + | 1.46073i | ||||
\(489\) | −12965.3 | − | 12507.3i | −1.19900 | − | 1.15665i | ||||
\(490\) | 3727.63 | − | 2229.92i | 0.343667 | − | 0.205587i | ||||
\(491\) | 16182.0 | 1.48734 | 0.743670 | − | 0.668547i | \(-0.233083\pi\) | ||||
0.743670 | + | 0.668547i | \(0.233083\pi\) | |||||||
\(492\) | 687.975 | + | 982.395i | 0.0630413 | + | 0.0900199i | ||||
\(493\) | −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 | ||||
\(498\) | −191.199 | − | 587.860i | −0.0172045 | − | 0.0528968i | ||||
\(499\) | 18027.6 | 1.61729 | 0.808646 | − | 0.588296i | \(-0.200201\pi\) | ||||
0.808646 | + | 0.588296i | \(0.200201\pi\) | |||||||
\(500\) | −5704.48 | − | 9615.55i | −0.510224 | − | 0.860041i | ||||
\(501\) | 2845.10 | − | 2949.29i | 0.253712 | − | 0.263003i | ||||
\(502\) | 1241.23 | − | 2333.11i | 0.110356 | − | 0.207434i | ||||
\(503\) | −10877.7 | + | 10877.7i | −0.964241 | + | 0.964241i | −0.999382 | − | 0.0351416i | \(-0.988812\pi\) |
0.0351416 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(504\) | −8054.48 | + | 10696.7i | −0.711855 | + | 0.945372i | ||||
\(505\) | −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 | ||||
\(508\) | 11303.4 | + | 2202.56i | 0.987217 | + | 0.192368i | ||||
\(509\) | − | 12313.1i | − | 1.07223i | −0.844144 | − | 0.536116i | \(-0.819891\pi\) | ||
0.844144 | − | 0.536116i | \(-0.180109\pi\) | |||||||
\(510\) | −15736.6 | − | 3656.62i | −1.36633 | − | 0.317486i | ||||
\(511\) | −3848.16 | −0.333136 | ||||||||
\(512\) | −11025.6 | + | 3557.17i | −0.951696 | + | 0.307043i | ||||
\(513\) | 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 | ||||
\(516\) | 680.986 | − | 3863.53i | 0.0580983 | − | 0.329617i | ||||
\(517\) | −4120.41 | − | 4120.41i | −0.350513 | − | 0.350513i | ||||
\(518\) | 682.188 | − | 1282.30i | 0.0578641 | − | 0.108766i | ||||
\(519\) | −3559.05 | + | 3689.38i | −0.301011 | + | 0.312034i | ||||
\(520\) | −7862.55 | − | 21765.0i | −0.663068 | − | 1.83550i | ||||
\(521\) | 14943.2i | 1.25657i | 0.777982 | + | 0.628287i | \(0.216243\pi\) | ||||
−0.777982 | + | 0.628287i | \(0.783757\pi\) | |||||||
\(522\) | 7602.92 | + | 3700.47i | 0.637492 | + | 0.310278i | ||||
\(523\) | 12402.4 | − | 12402.4i | 1.03694 | − | 1.03694i | 0.0376438 | − | 0.999291i | \(-0.488015\pi\) |
0.999291 | − | 0.0376438i | \(-0.0119852\pi\) | |||||||
\(524\) | −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 | ||||
\(528\) | −7477.41 | − | 2873.71i | −0.616311 | − | 0.236860i | ||||
\(529\) | 11096.4i | 0.912011i | ||||||||
\(530\) | −4091.99 | + | 16277.1i | −0.335367 | + | 1.33402i | ||||
\(531\) | 692.342 | + | 19245.6i | 0.0565821 | + | 1.57286i | ||||
\(532\) | 39.6790 | + | 7.73181i | 0.00323365 | + | 0.000630106i | ||||
\(533\) | −1866.20 | − | 1866.20i | −0.151659 | − | 0.151659i | ||||
\(534\) | 3278.91 | + | 1669.47i | 0.265716 | + | 0.135290i | ||||
\(535\) | −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 | ||||
\(538\) | 7037.02 | + | 3743.73i | 0.563917 | + | 0.300007i | ||||
\(539\) | 3308.75i | 0.264412i | ||||||||
\(540\) | 1304.21 | + | 12480.5i | 0.103933 | + | 0.994584i | ||||
\(541\) | − | 6136.90i | − | 0.487701i | −0.969813 | − | 0.243850i | \(-0.921589\pi\) | ||
0.969813 | − | 0.243850i | \(-0.0784106\pi\) | |||||||
\(542\) | −3499.84 | + | 6578.59i | −0.277364 | + | 0.521355i | ||||
\(543\) | 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 | ||||
\(546\) | 13369.3 | − | 26257.9i | 1.04790 | − | 2.05812i | ||||
\(547\) | −11284.3 | − | 11284.3i | −0.882052 | − | 0.882052i | 0.111691 | − | 0.993743i | \(-0.464373\pi\) |
−0.993743 | + | 0.111691i | \(0.964373\pi\) | |||||||
\(548\) | 1106.94 | − | 5680.74i | 0.0862887 | − | 0.442827i | ||||
\(549\) | 679.190 | + | 18880.0i | 0.0527999 | + | 1.46772i | ||||
\(550\) | 8516.39 | + | 31.1765i | 0.660255 | + | 0.00241703i | ||||
\(551\) | − | 25.5281i | − | 0.00197374i | ||||||
\(552\) | −3031.10 | − | 2368.96i | −0.233717 | − | 0.182662i | ||||
\(553\) | −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 | −0.757974 | − | 0.652285i | \(-0.773810\pi\) |
0.652285 | + | 0.757974i | \(0.273810\pi\) | |||||||
\(558\) | 7029.07 | − | 14441.8i | 0.533269 | − | 1.09565i | ||||
\(559\) | 8632.96i | 0.653194i | ||||||||
\(560\) | 15524.2 | + | 2223.55i | 1.17146 | + | 0.167789i | ||||
\(561\) | 8544.13 | − | 8857.02i | 0.643018 | − | 0.666566i | ||||
\(562\) | −9704.05 | − | 5162.60i | −0.728364 | − | 0.387493i | ||||
\(563\) | −10269.7 | − | 10269.7i | −0.768770 | − | 0.768770i | 0.209120 | − | 0.977890i | \(-0.432940\pi\) |
−0.977890 | + | 0.209120i | \(0.932940\pi\) | |||||||
\(564\) | −9903.30 | − | 1745.56i | −0.739369 | − | 0.130321i | ||||
\(565\) | 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 | ||||
\(568\) | 1255.11 | + | 12021.5i | 0.0927167 | + | 0.888048i | ||||
\(569\) | −16770.0 | −1.23556 | −0.617780 | − | 0.786351i | \(-0.711968\pi\) | ||||
−0.617780 | + | 0.786351i | \(0.711968\pi\) | |||||||
\(570\) | 32.1564 | − | 20.0301i | 0.00236295 | − | 0.00147188i | ||||
\(571\) | − | 3312.29i | − | 0.242758i | −0.992606 | − | 0.121379i | \(-0.961268\pi\) | ||
0.992606 | − | 0.121379i | \(-0.0387316\pi\) | |||||||
\(572\) | 17302.4 | + | 3371.52i | 1.26477 | + | 0.246451i | ||||
\(573\) | −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 | ||||
\(576\) | −13414.5 | + | 3339.88i | −0.970376 | + | 0.241600i | ||||
\(577\) | −323.244 | + | 323.244i | −0.0233220 | + | 0.0233220i | −0.718672 | − | 0.695350i | \(-0.755250\pi\) |
0.695350 | + | 0.718672i | \(0.255250\pi\) | |||||||
\(578\) | 11871.1 | + | 6315.51i | 0.854281 | + | 0.454482i | ||||
\(579\) | −7462.50 | + | 7735.78i | −0.535632 | + | 0.555247i | ||||
\(580\) | −496.779 | − | 9890.90i | −0.0355649 | − | 0.708099i | ||||
\(581\) | −921.861 | −0.0658266 | ||||||||
\(582\) | 4146.13 | − | 1348.51i | 0.295297 | − | 0.0960441i | ||||
\(583\) | −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 | −0.167639 | − | 0.985848i | \(-0.553614\pi\) |
0.985848 | + | 0.167639i | \(0.0536143\pi\) | |||||||
\(588\) | 3275.39 | + | 4677.10i | 0.229719 | + | 0.328028i | ||||
\(589\) | −48.4908 | −0.00339224 | ||||||||
\(590\) | 19356.2 | − | 11579.2i | 1.35065 | − | 0.807980i | ||||
\(591\) | −236.228 | − | 227.883i | −0.0164418 | − | 0.0158610i | ||||
\(592\) | 1380.87 | − | 584.644i | 0.0958675 | − | 0.0405891i | ||||
\(593\) | 962.627 | − | 962.627i | 0.0666616 | − | 0.0666616i | −0.672990 | − | 0.739652i | \(-0.734990\pi\) |
0.739652 | + | 0.672990i | \(0.234990\pi\) | |||||||
\(594\) | −8668.47 | − | 4027.96i | −0.598774 | − | 0.278231i | ||||
\(595\) | −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 | ||||
\(598\) | 7473.74 | + | 3976.07i | 0.511077 | + | 0.271895i | ||||
\(599\) | 8514.50 | 0.580790 | 0.290395 | − | 0.956907i | \(-0.406213\pi\) | ||||
0.290395 | + | 0.956907i | \(0.406213\pi\) | |||||||
\(600\) | 12069.3 | − | 8386.47i | 0.821209 | − | 0.570627i | ||||
\(601\) | 9858.11 | 0.669086 | 0.334543 | − | 0.942381i | \(-0.391418\pi\) | ||||
0.334543 | + | 0.942381i | \(0.391418\pi\) | |||||||
\(602\) | −5164.95 | − | 2747.78i | −0.349680 | − | 0.186032i | ||||
\(603\) | 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 | ||||
\(606\) | −1401.49 | − | 713.574i | −0.0939467 | − | 0.0478333i | ||||
\(607\) | 16619.7 | − | 16619.7i | 1.11132 | − | 1.11132i | 0.118352 | − | 0.992972i | \(-0.462239\pi\) |
0.992972 | − | 0.118352i | \(-0.0377612\pi\) | |||||||
\(608\) | 26.7902 | + | 32.0021i | 0.00178698 | + | 0.00213463i | ||||
\(609\) | 8754.63 | − | 9075.23i | 0.582521 | − | 0.603854i | ||||
\(610\) | 18988.5 | − | 11359.2i | 1.26037 | − | 0.753971i | ||||
\(611\) | 22128.7 | 1.46519 | ||||||||
\(612\) | 3309.87 | − | 20977.9i | 0.218617 | − | 1.38559i | ||||
\(613\) | −15827.0 | + | 15827.0i | −1.04282 | + | 1.04282i | −0.0437762 | + | 0.999041i | \(0.513939\pi\) |
−0.999041 | + | 0.0437762i | \(0.986061\pi\) | |||||||
\(614\) | −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 | \(0.835446\pi\) | |||||||
\(618\) | −2386.27 | − | 7336.80i | −0.155323 | − | 0.477555i | ||||
\(619\) | 8459.52 | 0.549300 | 0.274650 | − | 0.961544i | \(-0.411438\pi\) | ||||
0.274650 | + | 0.961544i | \(0.411438\pi\) | |||||||
\(620\) | −18787.9 | + | 943.636i | −1.21700 | + | 0.0611248i | ||||
\(621\) | −3416.19 | − | 3066.21i | −0.220752 | − | 0.198136i | ||||
\(622\) | −3411.32 | − | 1814.84i | −0.219906 | − | 0.116991i | ||||
\(623\) | 3879.93 | − | 3879.93i | 0.249512 | − | 0.249512i | ||||
\(624\) | 27795.4 | − | 12362.1i | 1.78318 | − | 0.793077i | ||||
\(625\) | −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 | ||||
\(628\) | 3172.31 | − | 16280.0i | 0.201575 | − | 1.03447i | ||||
\(629\) | 2303.70i | 0.146033i | ||||||||
\(630\) | 18300.7 | + | 3907.04i | 1.15733 | + | 0.247080i | ||||
\(631\) | 2376.36 | 0.149923 | 0.0749615 | − | 0.997186i | \(-0.476117\pi\) | ||||
0.0749615 | + | 0.997186i | \(0.476117\pi\) | |||||||
\(632\) | −1521.72 | − | 14575.2i | −0.0957766 | − | 0.917356i | ||||
\(633\) | −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 | ||||
\(636\) | −21727.6 | − | 3829.71i | −1.35465 | − | 0.238770i | ||||
\(637\) | −8884.83 | − | 8884.83i | −0.552637 | − | 0.552637i | ||||
\(638\) | 6659.91 | + | 3543.11i | 0.413273 | + | 0.219863i | ||||
\(639\) | 518.502 | + | 14413.2i | 0.0320995 | + | 0.892298i | ||||
\(640\) | 11002.7 | + | 11877.9i | 0.679560 | + | 0.733620i | ||||
\(641\) | − | 24800.9i | − | 1.52820i | −0.645097 | − | 0.764100i | \(-0.723183\pi\) | ||
0.645097 | − | 0.764100i | \(-0.276817\pi\) | |||||||
\(642\) | 17170.1 | − | 5584.51i | 1.05553 | − | 0.343307i | ||||
\(643\) | 8206.68 | − | 8206.68i | 0.503328 | − | 0.503328i | −0.409143 | − | 0.912470i | \(-0.634172\pi\) |
0.912470 | + | 0.409143i | \(0.134172\pi\) | |||||||
\(644\) | −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 | \(0.388218\pi\) | |||||||
\(648\) | −16240.7 | + | 2887.33i | −0.984562 | + | 0.175039i | ||||
\(649\) | 17181.1i | 1.03917i | ||||||||
\(650\) | −22952.4 | + | 22785.0i | −1.38503 | + | 1.37492i | ||||
\(651\) | −17238.5 | − | 16629.5i | −1.03783 | − | 1.00117i | ||||
\(652\) | −27223.6 | − | 5304.75i | −1.63521 | − | 0.318635i | ||||
\(653\) | −11411.3 | − | 11411.3i | −0.683858 | − | 0.683858i | 0.277010 | − | 0.960867i | \(-0.410657\pi\) |
−0.960867 | + | 0.277010i | \(0.910657\pi\) | |||||||
\(654\) | 16982.8 | + | 8646.83i | 1.01541 | + | 0.517000i | ||||
\(655\) | −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 | ||||
\(658\) | −7043.32 | + | 13239.2i | −0.417291 | + | 0.784373i | ||||
\(659\) | 9185.31i | 0.542958i | 0.962444 | + | 0.271479i | \(0.0875127\pi\) | ||||
−0.962444 | + | 0.271479i | \(0.912487\pi\) | |||||||
\(660\) | 762.505 | + | 11169.2i | 0.0449704 | + | 0.658726i | ||||
\(661\) | 867.859i | 0.0510678i | 0.999674 | + | 0.0255339i | \(0.00812857\pi\) | ||||
−0.999674 | + | 0.0255339i | \(0.991871\pi\) | |||||||
\(662\) | −14474.3 | − | 7700.40i | −0.849787 | − | 0.452091i | ||||
\(663\) | 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 | ||||
\(666\) | 1691.35 | − | 583.934i | 0.0984063 | − | 0.0339744i | ||||
\(667\) | 2561.71 | + | 2561.71i | 0.148710 | + | 0.148710i | ||||
\(668\) | 1206.70 | − | 6192.67i | 0.0698930 | − | 0.358685i | ||||
\(669\) | −6041.19 | + | 6262.43i | −0.349127 | + | 0.361912i | ||||
\(670\) | 4375.33 | − | 17404.1i | 0.252289 | − | 1.00355i | ||||
\(671\) | 16854.8i | 0.969704i | ||||||||
\(672\) | −1450.94 | + | 20564.2i | −0.0832906 | + | 1.18048i | ||||
\(673\) | 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 | −0.991732 | − | 0.128325i | \(-0.959040\pi\) |
0.128325 | + | 0.991732i | \(0.459040\pi\) | |||||||
\(678\) | −22157.4 | + | 7206.62i | −1.25509 | + | 0.408213i | ||||
\(679\) | − | 6501.82i | − | 0.367477i | ||||||
\(680\) | −23393.9 | + | 8450.97i | −1.31929 | + | 0.476588i | ||||
\(681\) | −5334.78 | − | 5146.31i | −0.300190 | − | 0.289585i | ||||
\(682\) | 6730.16 | − | 12650.6i | 0.377876 | − | 0.710286i | ||||
\(683\) | 18772.1 | + | 18772.1i | 1.05167 | + | 1.05167i | 0.998590 | + | 0.0530848i | \(0.0169054\pi\) |
0.0530848 | + | 0.998590i | \(0.483095\pi\) | |||||||
\(684\) | 29.2958 | + | 40.2722i | 0.00163765 | + | 0.00225123i | ||||
\(685\) | −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 | ||||
\(688\) | −2354.88 | − | 5562.01i | −0.130493 | − | 0.308211i | ||||
\(689\) | 48549.9 | 2.68447 | ||||||||
\(690\) | −1216.86 | + | 5236.85i | −0.0671375 | + | 0.288932i | ||||
\(691\) | − | 7733.79i | − | 0.425770i | −0.977077 | − | 0.212885i | \(-0.931714\pi\) | ||
0.977077 | − | 0.212885i | \(-0.0682860\pi\) | |||||||
\(692\) | −1509.51 | + | 7746.66i | −0.0829231 | + | 0.425555i | ||||
\(693\) | −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 | ||||
\(696\) | 12921.5 | − | 1584.39i | 0.703721 | − | 0.0862877i | ||||
\(697\) | −2005.87 | + | 2005.87i | −0.109007 | + | 0.109007i | ||||
\(698\) | 2220.61 | − | 4174.03i | 0.120417 | − | 0.226346i | ||||
\(699\) | 20173.6 | + | 19460.9i | 1.09161 | + | 1.05305i | ||||
\(700\) | −6326.34 | − | 20984.2i | −0.341590 | − | 1.13304i | ||||
\(701\) | 9004.44 | 0.485154 | 0.242577 | − | 0.970132i | \(-0.422007\pi\) | ||||
0.242577 | + | 0.970132i | \(0.422007\pi\) | |||||||
\(702\) | 34093.1 | − | 12460.9i | 1.83300 | − | 0.669954i | ||||
\(703\) | −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 | ||||
\(708\) | 17008.0 | + | 24286.5i | 0.902822 | + | 1.28919i | ||||
\(709\) | −21498.3 | −1.13877 | −0.569384 | − | 0.822071i | \(-0.692818\pi\) | ||||
−0.569384 | + | 0.822071i | \(0.692818\pi\) | |||||||
\(710\) | 14496.1 | − | 8671.78i | 0.766237 | − | 0.458375i | ||||
\(711\) | −628.644 | − | 17474.9i | −0.0331589 | − | 0.921746i | ||||
\(712\) | 5634.26 | − | 588.245i | 0.296563 | − | 0.0309627i | ||||
\(713\) | 4865.99 | − | 4865.99i | 0.255586 | − | 0.255586i | ||||
\(714\) | −28223.1 | − | 14369.9i | −1.47930 | − | 0.753191i | ||||
\(715\) | −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 | ||||
\(718\) | 4945.06 | − | 9295.14i | 0.257031 | − | 0.483136i | ||||
\(719\) | −36837.8 | −1.91074 | −0.955368 | − | 0.295417i | \(-0.904541\pi\) | ||||
−0.955368 | + | 0.295417i | \(0.904541\pi\) | |||||||
\(720\) | 12134.4 | + | 15033.4i | 0.628088 | + | 0.778143i | ||||
\(721\) | −11505.3 | −0.594286 | ||||||||
\(722\) | −9111.71 | + | 17127.1i | −0.469671 | + | 0.882832i | ||||
\(723\) | 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 | ||||
\(726\) | 9832.74 | + | 5006.37i | 0.502655 | + | 0.255928i | ||||
\(727\) | −18920.8 | + | 18920.8i | −0.965247 | + | 0.965247i | −0.999416 | − | 0.0341694i | \(-0.989121\pi\) |
0.0341694 | + | 0.999416i | \(0.489121\pi\) | |||||||
\(728\) | −4710.75 | − | 45119.9i | −0.239824 | − | 2.29705i | ||||
\(729\) | −19568.6 | + | 2119.20i | −0.994187 | + | 0.107666i | ||||
\(730\) | −1353.69 | + | 5384.70i | −0.0686333 | + | 0.273009i | ||||
\(731\) | 9279.04 | 0.469491 | ||||||||
\(732\) | 16684.9 | + | 23825.2i | 0.842473 | + | 1.20301i | ||||
\(733\) | 9773.14 | − | 9773.14i | 0.492468 | − | 0.492468i | −0.416615 | − | 0.909083i | \(-0.636784\pi\) |
0.909083 | + | 0.416615i | \(0.136784\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | 1981.13 | + | 964.246i | 0.0988161 | + | 0.0480954i | ||||
\(739\) | 1238.92 | 0.0616706 | 0.0308353 | − | 0.999524i | \(-0.490183\pi\) | ||||
0.0308353 | + | 0.999524i | \(0.490183\pi\) | |||||||
\(740\) | −1554.33 | − | 1405.66i | −0.0772140 | − | 0.0698287i | ||||
\(741\) | −78.8716 | − | 76.0853i | −0.00391015 | − | 0.00377201i | ||||
\(742\) | −15452.9 | + | 29046.5i | −0.764547 | + | 1.43710i | ||||
\(743\) | 25273.4 | − | 25273.4i | 1.24790 | − | 1.24790i | 0.291259 | − | 0.956644i | \(-0.405926\pi\) |
0.956644 | − | 0.291259i | \(-0.0940740\pi\) | |||||||
\(744\) | −3009.57 | − | 24544.6i | −0.148301 | − | 1.20947i | ||||
\(745\) | 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 | ||||
\(748\) | 3623.84 | − | 18597.3i | 0.177140 | − | 0.909068i | ||||
\(749\) | − | 26925.6i | − | 1.31354i | ||||||
\(750\) | −17737.8 | − | 10355.9i | −0.863590 | − | 0.504194i | ||||
\(751\) | −7222.12 | −0.350917 | −0.175459 | − | 0.984487i | \(-0.556141\pi\) | ||||
−0.175459 | + | 0.984487i | \(0.556141\pi\) | |||||||
\(752\) | −14257.0 | + | 6036.22i | −0.691354 | + | 0.292710i | ||||
\(753\) | −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 | ||||
\(756\) | −3396.32 | + | 24363.5i | −0.163390 | + | 1.17208i | ||||
\(757\) | 15785.6 | + | 15785.6i | 0.757908 | + | 0.757908i | 0.975941 | − | 0.218034i | \(-0.0699642\pi\) |
−0.218034 | + | 0.975941i | \(0.569964\pi\) | |||||||
\(758\) | −16966.3 | + | 31891.3i | −0.812989 | + | 1.52816i | ||||
\(759\) | −2947.45 | − | 2843.33i | −0.140956 | − | 0.135977i | ||||
\(760\) | 24.7772 | − | 52.8028i | 0.00118259 | − | 0.00252021i | ||||
\(761\) | 19069.0i | 0.908344i | 0.890914 | + | 0.454172i | \(0.150065\pi\) | ||||
−0.890914 | + | 0.454172i | \(0.849935\pi\) | |||||||
\(762\) | 20118.8 | − | 6543.57i | 0.956467 | − | 0.311087i | ||||
\(763\) | 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 | ||||
\(768\) | −14535.8 | + | 15546.6i | −0.682962 | + | 0.730454i | ||||
\(769\) | 24492.5i | 1.14853i | 0.818668 | + | 0.574267i | \(0.194713\pi\) | ||||
−0.818668 | + | 0.574267i | \(0.805287\pi\) | |||||||
\(770\) | 16191.2 | + | 4070.40i | 0.757781 | + | 0.190503i | ||||
\(771\) | −12457.3 | + | 12913.5i | −0.581894 | + | 0.603203i | ||||
\(772\) | −3165.08 | + | 16243.0i | −0.147557 | + | 0.757250i | ||||
\(773\) | −5285.07 | − | 5285.07i | −0.245913 | − | 0.245913i | 0.573378 | − | 0.819291i | \(-0.305633\pi\) |
−0.819291 | + | 0.573378i | \(0.805633\pi\) | |||||||
\(774\) | −2352.02 | − | 6812.58i | −0.109227 | − | 0.316373i | ||||
\(775\) | 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 | ||||
\(778\) | −6805.04 | − | 3620.31i | −0.313589 | − | 0.166831i | ||||
\(779\) | − | 6.65196i | − | 0.000305945i | ||||||
\(780\) | −32039.6 | − | 27944.5i | −1.47077 | − | 1.28279i | ||||
\(781\) | 12867.1i | 0.589529i | ||||||||
\(782\) | 4273.63 | − | 8033.06i | 0.195428 | − | 0.367342i | ||||
\(783\) | 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 | ||||
\(786\) | −1821.37 | − | 927.356i | −0.0826540 | − | 0.0420836i | ||||
\(787\) | −1754.94 | − | 1754.94i | −0.0794877 | − | 0.0794877i | 0.666245 | − | 0.745733i | \(-0.267900\pi\) |
−0.745733 | + | 0.666245i | \(0.767900\pi\) | |||||||
\(788\) | −496.012 | − | 96.6524i | −0.0224235 | − | 0.00436942i | ||||
\(789\) | 18676.7 | + | 18016.9i | 0.842724 | + | 0.812953i | ||||
\(790\) | −17575.4 | + | 10513.9i | −0.791525 | + | 0.473502i | ||||
\(791\) | 34746.5i | 1.56188i | ||||||||
\(792\) | −14572.5 | + | 2053.38i | −0.653801 | + | 0.0921259i | ||||
\(793\) | −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 | −0.272921 | − | 0.962036i | \(-0.587990\pi\) |
0.962036 | + | 0.272921i | \(0.0879897\pi\) | |||||||
\(798\) | 70.6244 | − | 22.9703i | 0.00313293 | − | 0.00101897i | ||||
\(799\) | − | 23784.8i | − | 1.05312i | ||||||
\(800\) | 8572.44 | − | 20940.7i | 0.378852 | − | 0.925457i | ||||
\(801\) | 6755.21 | − | 243.012i | 0.297982 | − | 0.0107196i | ||||
\(802\) | 14037.1 | + | 7467.84i | 0.618041 | + | 0.328801i | ||||
\(803\) | −2990.60 | − | 2990.60i | −0.131427 | − | 0.131427i | ||||
\(804\) | 23232.1 | + | 4094.89i | 1.01907 | + | 0.179621i | ||||
\(805\) | 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 | ||||
\(808\) | −2408.23 | + | 251.431i | −0.104853 | + | 0.0109472i | ||||
\(809\) | −1929.99 | −0.0838749 | −0.0419374 | − | 0.999120i | \(-0.513353\pi\) | ||||
−0.0419374 | + | 0.999120i | \(0.513353\pi\) | |||||||
\(810\) | 13225.6 | + | 18881.8i | 0.573706 | + | 0.819061i | ||||
\(811\) | 14596.0i | 0.631980i | 0.948763 | + | 0.315990i | \(0.102337\pi\) | ||||
−0.948763 | + | 0.315990i | \(0.897663\pi\) | |||||||
\(812\) | 3713.12 | − | 19055.4i | 0.160474 | − | 0.823540i | ||||
\(813\) | 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 | ||||
\(816\) | −13287.3 | − | 29875.6i | −0.570034 | − | 1.28168i | ||||
\(817\) | −15.3858 | + | 15.3858i | −0.000658852 | + | 0.000658852i | ||||
\(818\) | −23861.2 | − | 12694.3i | −1.01991 | − | 0.542598i | ||||
\(819\) | −1946.07 | − | 54096.6i | −0.0830297 | − | 2.30805i | ||||
\(820\) | −129.448 | − | 2577.31i | −0.00551282 | − | 0.109761i | ||||
\(821\) | −33180.4 | −1.41048 | −0.705240 | − | 0.708968i | \(-0.749161\pi\) | ||||
−0.705240 | + | 0.708968i | \(0.749161\pi\) | |||||||
\(822\) | −3288.60 | − | 10111.1i | −0.139541 | − | 0.429033i | ||||
\(823\) | 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 | −0.111295 | − | 0.993787i | \(-0.535500\pi\) |
0.993787 | + | 0.111295i | \(0.0355000\pi\) | |||||||
\(828\) | −6981.06 | − | 1101.46i | −0.293005 | − | 0.0462301i | ||||
\(829\) | −44941.5 | −1.88285 | −0.941425 | − | 0.337223i | \(-0.890512\pi\) | ||||
−0.941425 | + | 0.337223i | \(0.890512\pi\) | |||||||
\(830\) | −324.289 | + | 1289.96i | −0.0135617 | + | 0.0539458i | ||||
\(831\) | 7175.27 | − | 7438.03i | 0.299527 | − | 0.310496i | ||||
\(832\) | 25562.7 | − | 39244.1i | 1.06518 | − | 1.63527i | ||||
\(833\) | −9549.77 | + | 9549.77i | −0.397215 | + | 0.397215i | ||||
\(834\) | 29865.8 | + | 15206.3i | 1.24001 | + | 0.631355i | ||||
\(835\) | −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 | ||||
\(838\) | 36047.6 | + | 19177.5i | 1.48597 | + | 0.790545i | ||||
\(839\) | 18984.0 | 0.781169 | 0.390585 | − | 0.920567i | \(-0.372273\pi\) | ||||
0.390585 | + | 0.920567i | \(0.372273\pi\) | |||||||
\(840\) | 26916.6 | − | 10274.3i | 1.10561 | − | 0.422019i | ||||
\(841\) | 12129.4 | 0.497331 | ||||||||
\(842\) | −15151.8 | − | 8060.84i | −0.620149 | − | 0.329923i | ||||
\(843\) | −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 | ||||
\(846\) | −17462.5 | + | 6028.88i | −0.709662 | + | 0.245009i | ||||
\(847\) | 11635.1 | − | 11635.1i | 0.472003 | − | 0.472003i | ||||
\(848\) | −31279.5 | + | 13243.3i | −1.26668 | + | 0.536295i | ||||
\(849\) | −8788.96 | − | 8478.47i | −0.355284 | − | 0.342733i | ||||
\(850\) | 24490.2 | + | 24670.1i | 0.988242 | + | 0.995504i | ||||
\(851\) | 766.629 | 0.0308810 | ||||||||
\(852\) | 12737.4 | + | 18188.4i | 0.512180 | + | 0.731367i | ||||
\(853\) | 15050.4 | − | 15050.4i | 0.604123 | − | 0.604123i | −0.337281 | − | 0.941404i | \(-0.609507\pi\) |
0.941404 | + | 0.337281i | \(0.109507\pi\) | |||||||
\(854\) | 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 | \(0.804463\pi\) | |||||||
\(858\) | 30796.3 | − | 10016.4i | 1.22537 | − | 0.398548i | ||||
\(859\) | −18659.4 | −0.741152 | −0.370576 | − | 0.928802i | \(-0.620840\pi\) | ||||
−0.370576 | + | 0.928802i | \(0.620840\pi\) | |||||||
\(860\) | −5661.86 | + | 6260.68i | −0.224497 | + | 0.248241i | ||||
\(861\) | 2281.23 | − | 2364.77i | 0.0902952 | − | 0.0936018i | ||||
\(862\) | −20300.4 | − | 10799.9i | −0.802129 | − | 0.426737i | ||||
\(863\) | 20846.2 | − | 20846.2i | 0.822265 | − | 0.822265i | −0.164168 | − | 0.986432i | \(-0.552494\pi\) |
0.986432 | + | 0.164168i | \(0.0524938\pi\) | |||||||
\(864\) | −18566.3 | + | 17328.1i | −0.731064 | + | 0.682309i | ||||
\(865\) | 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 | ||||
\(868\) | −36196.0 | − | 7053.11i | −1.41541 | − | 0.275804i | ||||
\(869\) | − | 15600.4i | − | 0.608985i | ||||||
\(870\) | −9619.25 | − | 15442.8i | −0.374854 | − | 0.601792i | ||||
\(871\) | −51911.6 | −2.01947 | ||||||||
\(872\) | 29182.1 | − | 3046.75i | 1.13329 | − | 0.118321i | ||||
\(873\) | 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 | ||||
\(876\) | −7187.83 | − | 1266.93i | −0.277231 | − | 0.0488647i | ||||
\(877\) | 17713.5 | + | 17713.5i | 0.682034 | + | 0.682034i | 0.960458 | − | 0.278424i | \(-0.0898121\pi\) |
−0.278424 | + | 0.960458i | \(0.589812\pi\) | |||||||
\(878\) | 11118.6 | + | 5915.17i | 0.427376 | + | 0.227366i | ||||
\(879\) | 10549.2 | − | 10935.5i | 0.404795 | − | 0.419619i | ||||
\(880\) | 10336.6 | + | 13792.7i | 0.395962 | + | 0.528353i | ||||
\(881\) | 9604.82i | 0.367304i | 0.982991 | + | 0.183652i | \(0.0587919\pi\) | ||||
−0.982991 | + | 0.183652i | \(0.941208\pi\) | |||||||
\(882\) | 9431.98 | + | 4590.70i | 0.360081 | + | 0.175257i | ||||
\(883\) | 7027.53 | − | 7027.53i | 0.267831 | − | 0.267831i | −0.560394 | − | 0.828226i | \(-0.689350\pi\) |
0.828226 | + | 0.560394i | \(0.189350\pi\) | |||||||
\(884\) | 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 | \(0.881199\pi\) | |||||||
\(888\) | 1696.40 | − | 2170.56i | 0.0641076 | − | 0.0820260i | ||||
\(889\) | − | 31549.6i | − | 1.19026i | ||||||
\(890\) | −4064.30 | − | 6794.04i | −0.153074 | − | 0.255884i | ||||
\(891\) | −17514.9 | + | 1261.79i | −0.658553 | + | 0.0474430i | ||||
\(892\) | −2562.26 | + | 13149.3i | −0.0961782 | + | 0.493579i | ||||
\(893\) | 39.4381 | + | 39.4381i | 0.00147788 | + | 0.00147788i | ||||
\(894\) | −14774.4 | + | 29017.6i | −0.552719 | + | 1.08557i | ||||
\(895\) | −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 | ||||
\(898\) | −6859.68 | + | 12894.0i | −0.254911 | + | 0.479152i | ||||
\(899\) | 23287.2i | 0.863928i | ||||||||
\(900\) | 11904.9 | − | 24233.7i | 0.440921 | − | 0.897546i | ||||
\(901\) | − | 52183.3i | − | 1.92950i | ||||||
\(902\) | 1735.40 | + | 923.242i | 0.0640604 | + | 0.0340805i | ||||
\(903\) | −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 | ||||
\(906\) | −20339.1 | − | 10355.7i | −0.745828 | − | 0.379741i | ||||
\(907\) | −345.391 | − | 345.391i | −0.0126445 | − | 0.0126445i | 0.700756 | − | 0.713401i | \(-0.252846\pi\) |
−0.713401 | + | 0.700756i | \(0.752846\pi\) | |||||||
\(908\) | −11201.5 | − | 2182.72i | −0.409401 | − | 0.0797754i | ||||
\(909\) | −2887.36 | + | 103.870i | −0.105355 | + | 0.00379004i | ||||
\(910\) | −54407.6 | + | 32547.5i | −1.98197 | + | 1.18565i | ||||
\(911\) | 23701.1i | 0.861966i | 0.902360 | + | 0.430983i | \(0.141833\pi\) | ||||
−0.902360 | + | 0.430983i | \(0.858167\pi\) | |||||||
\(912\) | 71.5694 | + | 27.5055i | 0.00259858 | + | 0.000998681i | ||||
\(913\) | −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 | ||||
\(918\) | −13393.5 | − | 36644.7i | −0.481538 | − | 1.31749i | ||||
\(919\) | − | 16350.4i | − | 0.586889i | −0.955976 | − | 0.293444i | \(-0.905198\pi\) | ||
0.955976 | − | 0.293444i | \(-0.0948016\pi\) | |||||||
\(920\) | 2812.33 | + | 7785.06i | 0.100782 | + | 0.278985i | ||||
\(921\) | −10989.1 | + | 11391.6i | −0.393164 | + | 0.407562i | ||||
\(922\) | 2376.10 | − | 4466.31i | 0.0848728 | − | 0.159534i | ||||
\(923\) | −34551.5 | − | 34551.5i | −1.23215 | − | 1.23215i | ||||
\(924\) | −3809.51 | + | 21613.0i | −0.135632 | + | 0.769498i | ||||
\(925\) | −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 | ||||
\(928\) | 15368.7 | − | 12865.7i | 0.543644 | − | 0.455105i | ||||
\(929\) | 23050.1 | 0.814047 | 0.407024 | − | 0.913418i | \(-0.366567\pi\) | ||||
0.407024 | + | 0.913418i | \(0.366567\pi\) | |||||||
\(930\) | −29333.7 | + | 18271.9i | −1.03429 | + | 0.644256i | ||||
\(931\) | − | 31.6694i | − | 0.00111485i | ||||||
\(932\) | 42358.8 | + | 8253.99i | 1.48874 | + | 0.290095i | ||||
\(933\) | −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 | ||||
\(936\) | 33616.9 | − | 44644.6i | 1.17394 | − | 1.55903i | ||||
\(937\) | −5420.55 | + | 5420.55i | −0.188988 | + | 0.188988i | −0.795258 | − | 0.606271i | \(-0.792665\pi\) |
0.606271 | + | 0.795258i | \(0.292665\pi\) | |||||||
\(938\) | 16522.9 | − | 31057.8i | 0.575151 | − | 1.08110i | ||||
\(939\) | 392.612 | − | 406.990i | 0.0136447 | − | 0.0141444i | ||||
\(940\) | 16047.9 | + | 14512.9i | 0.556833 | + | 0.503574i | ||||
\(941\) | −25394.9 | −0.879754 | −0.439877 | − | 0.898058i | \(-0.644978\pi\) | ||||
−0.439877 | + | 0.898058i | \(0.644978\pi\) | |||||||
\(942\) | −9424.58 | − | 28976.7i | −0.325976 | − | 1.00224i | ||||
\(943\) | 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 | \(0.531143\pi\) |
−0.995218 | + | 0.0976812i | \(0.968857\pi\) | |||||||
\(948\) | −15443.2 | − | 22052.1i | −0.529083 | − | 0.755504i | ||||
\(949\) | 16061.0 | 0.549381 | ||||||||
\(950\) | −81.5140 | − | 0.298403i | −0.00278386 | − | 1.01910e-5i | ||||
\(951\) | 10704.6 | + | 10326.4i | 0.365005 | + | 0.352111i | ||||
\(952\) | −48496.7 | + | 5063.29i | −1.65104 | + | 0.172376i | ||||
\(953\) | −32189.0 | + | 32189.0i | −1.09413 | + | 1.09413i | −0.0990432 | + | 0.995083i | \(0.531578\pi\) |
−0.995083 | + | 0.0990432i | \(0.968422\pi\) | |||||||
\(954\) | −38312.4 | + | 13227.2i | −1.30022 | + | 0.448897i | ||||
\(955\) | 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 | ||||
\(958\) | 1252.31 | − | 2353.95i | 0.0422342 | − | 0.0793869i | ||||
\(959\) | −15855.9 | −0.533903 | ||||||||
\(960\) | 28265.0 | + | 9264.30i | 0.950258 | + | 0.311462i | ||||
\(961\) | 14443.3 | 0.484820 | ||||||||
\(962\) | −2847.24 | + | 5351.91i | −0.0954250 | + | 0.179369i | ||||
\(963\) | 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 | ||||
\(966\) | −4782.03 | + | 9392.12i | −0.159275 | + | 0.312822i | ||||
\(967\) | 34684.1 | − | 34684.1i | 1.15343 | − | 1.15343i | 0.167566 | − | 0.985861i | \(-0.446409\pi\) |
0.985861 | − | 0.167566i | \(-0.0535908\pi\) | |||||||
\(968\) | 16895.9 | − | 1764.02i | 0.561008 | − | 0.0585721i | ||||
\(969\) | −81.7794 | + | 84.7743i | −0.00271118 | + | 0.00281047i | ||||
\(970\) | −9097.96 | − | 2287.19i | −0.301152 | − | 0.0757084i | ||||
\(971\) | 191.895 | 0.00634214 | 0.00317107 | − | 0.999995i | \(-0.498991\pi\) | ||||
0.00317107 | + | 0.999995i | \(0.498991\pi\) | |||||||
\(972\) | −23509.2 | + | 19121.9i | −0.775779 | + | 0.631004i | ||||
\(973\) | 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 | \(0.952942\pi\) | |||||||
\(978\) | −48455.0 | + | 15759.8i | −1.58427 | + | 0.515279i | ||||
\(979\) | 6030.59 | 0.196873 | ||||||||
\(980\) | −616.291 | − | 12270.4i | −0.0200884 | − | 0.399962i | ||||
\(981\) | 34987.9 | − | 1258.66i | 1.13871 | − | 0.0409641i | ||||
\(982\) | 21496.9 | − | 40407.2i | 0.698567 | − | 1.31308i | ||||
\(983\) | −29865.8 | + | 29865.8i | −0.969044 | + | 0.969044i | −0.999535 | − | 0.0304913i | \(-0.990293\pi\) |
0.0304913 | + | 0.999535i | \(0.490293\pi\) | |||||||
\(984\) | 3367.02 | − | 412.852i | 0.109082 | − | 0.0133752i | ||||
\(985\) | 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 | ||||
\(988\) | −165.608 | − | 32.2702i | −0.00533269 | − | 0.00103912i | ||||
\(989\) | − | 3087.90i | − | 0.0992815i | ||||||
\(990\) | 11186.1 | + | 17258.8i | 0.359108 | + | 0.554061i | ||||
\(991\) | 38515.4 | 1.23459 | 0.617296 | − | 0.786731i | \(-0.288228\pi\) | ||||
0.617296 | + | 0.786731i | \(0.288228\pi\) | |||||||
\(992\) | −24438.5 | − | 29192.9i | −0.782181 | − | 0.934352i | ||||
\(993\) | −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 | ||||
\(996\) | −1721.91 | − | 303.504i | −0.0547799 | − | 0.00965551i | ||||
\(997\) | −19278.3 | − | 19278.3i | −0.612387 | − | 0.612387i | 0.331180 | − | 0.943567i | \(-0.392553\pi\) |
−0.943567 | + | 0.331180i | \(0.892553\pi\) | |||||||
\(998\) | 23948.7 | − | 45015.9i | 0.759601 | − | 1.42781i | ||||
\(999\) | 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.53.43 | yes | 128 | |
3.2 | odd | 2 | inner | 120.4.w.c.53.22 | yes | 128 | |
5.2 | odd | 4 | inner | 120.4.w.c.77.54 | yes | 128 | |
8.5 | even | 2 | inner | 120.4.w.c.53.11 | ✓ | 128 | |
15.2 | even | 4 | inner | 120.4.w.c.77.11 | yes | 128 | |
24.5 | odd | 2 | inner | 120.4.w.c.53.54 | yes | 128 | |
40.37 | odd | 4 | inner | 120.4.w.c.77.22 | yes | 128 | |
120.77 | even | 4 | inner | 120.4.w.c.77.43 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.w.c.53.11 | ✓ | 128 | 8.5 | even | 2 | inner | |
120.4.w.c.53.22 | yes | 128 | 3.2 | odd | 2 | inner | |
120.4.w.c.53.43 | yes | 128 | 1.1 | even | 1 | trivial | |
120.4.w.c.53.54 | yes | 128 | 24.5 | odd | 2 | inner | |
120.4.w.c.77.11 | yes | 128 | 15.2 | even | 4 | inner | |
120.4.w.c.77.22 | yes | 128 | 40.37 | odd | 4 | inner | |
120.4.w.c.77.43 | yes | 128 | 120.77 | even | 4 | inner | |
120.4.w.c.77.54 | yes | 128 | 5.2 | odd | 4 | inner |