Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(26,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.26");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.s (of order \(6\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.11 | ||
Character | \(\chi\) | \(=\) | 105.101 |
Dual form | 105.4.s.a.26.11 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48940 | − | 0.859905i | 0.526582 | − | 0.304022i | −0.213041 | − | 0.977043i | \(-0.568337\pi\) |
0.739624 | + | 0.673021i | \(0.235004\pi\) | |||||||
\(3\) | −4.11977 | − | 3.16663i | −0.792849 | − | 0.609418i | ||||
\(4\) | −2.52113 | + | 4.36672i | −0.315141 | + | 0.545840i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | −8.85898 | − | 1.17376i | −0.602777 | − | 0.0798646i | ||||
\(7\) | 2.28179 | + | 18.3792i | 0.123205 | + | 0.992381i | ||||
\(8\) | 22.4302i | 0.991284i | ||||||||
\(9\) | 6.94494 | + | 26.0915i | 0.257220 | + | 0.966353i | ||||
\(10\) | −7.44700 | − | 4.29953i | −0.235495 | − | 0.135963i | ||||
\(11\) | 49.7733 | + | 28.7366i | 1.36429 | + | 0.787674i | 0.990192 | − | 0.139714i | \(-0.0446183\pi\) |
0.374100 | + | 0.927388i | \(0.377952\pi\) | |||||||
\(12\) | 24.2142 | − | 10.0064i | 0.582504 | − | 0.240716i | ||||
\(13\) | − | 44.6643i | − | 0.952896i | −0.879203 | − | 0.476448i | \(-0.841924\pi\) | ||
0.879203 | − | 0.476448i | \(-0.158076\pi\) | |||||||
\(14\) | 19.2028 | + | 25.4118i | 0.366584 | + | 0.485113i | ||||
\(15\) | −3.41248 | + | 25.7557i | −0.0587400 | + | 0.443339i | ||||
\(16\) | −0.881158 | − | 1.52621i | −0.0137681 | − | 0.0238470i | ||||
\(17\) | −54.8920 | + | 95.0758i | −0.783134 | + | 1.35643i | 0.146974 | + | 0.989140i | \(0.453047\pi\) |
−0.930108 | + | 0.367287i | \(0.880287\pi\) | |||||||
\(18\) | 32.7800 | + | 32.8887i | 0.429241 | + | 0.430664i | ||||
\(19\) | −79.5306 | + | 45.9170i | −0.960293 | + | 0.554426i | −0.896263 | − | 0.443522i | \(-0.853729\pi\) |
−0.0640300 | + | 0.997948i | \(0.520395\pi\) | |||||||
\(20\) | 25.2113 | 0.281870 | ||||||||
\(21\) | 48.7995 | − | 82.9434i | 0.507091 | − | 0.861892i | ||||
\(22\) | 98.8431 | 0.957883 | ||||||||
\(23\) | −27.1329 | + | 15.6652i | −0.245983 | + | 0.142018i | −0.617923 | − | 0.786238i | \(-0.712026\pi\) |
0.371941 | + | 0.928257i | \(0.378693\pi\) | |||||||
\(24\) | 71.0281 | − | 92.4072i | 0.604106 | − | 0.785939i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −38.4071 | − | 66.5230i | −0.289702 | − | 0.501778i | ||||
\(27\) | 54.0106 | − | 129.483i | 0.384976 | − | 0.922927i | ||||
\(28\) | −86.0093 | − | 36.3722i | −0.580508 | − | 0.245489i | ||||
\(29\) | 183.561i | 1.17539i | 0.809082 | + | 0.587696i | \(0.199965\pi\) | ||||
−0.809082 | + | 0.587696i | \(0.800035\pi\) | |||||||
\(30\) | 17.0649 | + | 41.2949i | 0.103854 | + | 0.251313i | ||||
\(31\) | 123.493 | + | 71.2990i | 0.715486 | + | 0.413086i | 0.813089 | − | 0.582139i | \(-0.197784\pi\) |
−0.0976027 | + | 0.995225i | \(0.531117\pi\) | |||||||
\(32\) | −158.026 | − | 91.2362i | −0.872977 | − | 0.504014i | ||||
\(33\) | −114.056 | − | 276.002i | −0.601655 | − | 1.45593i | ||||
\(34\) | 188.808i | 0.952361i | ||||||||
\(35\) | 73.8796 | − | 55.8283i | 0.356798 | − | 0.269620i | ||||
\(36\) | −131.443 | − | 35.4534i | −0.608534 | − | 0.164136i | ||||
\(37\) | −114.912 | − | 199.033i | −0.510579 | − | 0.884349i | −0.999925 | − | 0.0122589i | \(-0.996098\pi\) |
0.489346 | − | 0.872090i | \(-0.337236\pi\) | |||||||
\(38\) | −78.9686 | + | 136.778i | −0.337116 | + | 0.583901i | ||||
\(39\) | −141.435 | + | 184.006i | −0.580711 | + | 0.755503i | ||||
\(40\) | 97.1256 | − | 56.0755i | 0.383923 | − | 0.221658i | ||||
\(41\) | 185.753 | 0.707555 | 0.353778 | − | 0.935330i | \(-0.384897\pi\) | ||||
0.353778 | + | 0.935330i | \(0.384897\pi\) | |||||||
\(42\) | 1.35845 | − | 165.499i | 0.00499080 | − | 0.608024i | ||||
\(43\) | −22.3617 | −0.0793054 | −0.0396527 | − | 0.999214i | \(-0.512625\pi\) | ||||
−0.0396527 | + | 0.999214i | \(0.512625\pi\) | |||||||
\(44\) | −250.969 | + | 144.897i | −0.859888 | + | 0.496457i | ||||
\(45\) | 95.6173 | − | 95.3013i | 0.316751 | − | 0.315704i | ||||
\(46\) | −26.9412 | + | 46.6635i | −0.0863535 | + | 0.149569i | ||||
\(47\) | −116.516 | − | 201.811i | −0.361608 | − | 0.626323i | 0.626618 | − | 0.779326i | \(-0.284439\pi\) |
−0.988226 | + | 0.153004i | \(0.951105\pi\) | |||||||
\(48\) | −1.20277 | + | 9.07793i | −0.00361678 | + | 0.0272976i | ||||
\(49\) | −332.587 | + | 83.8749i | −0.969641 | + | 0.244533i | ||||
\(50\) | 42.9953i | 0.121609i | ||||||||
\(51\) | 527.212 | − | 217.867i | 1.44754 | − | 0.598187i | ||||
\(52\) | 195.036 | + | 112.604i | 0.520128 | + | 0.300296i | ||||
\(53\) | 400.091 | + | 230.993i | 1.03692 | + | 0.598666i | 0.918959 | − | 0.394352i | \(-0.129031\pi\) |
0.117961 | + | 0.993018i | \(0.462364\pi\) | |||||||
\(54\) | −30.8998 | − | 239.296i | −0.0778690 | − | 0.603038i | ||||
\(55\) | − | 287.366i | − | 0.704517i | ||||||
\(56\) | −412.248 | + | 51.1811i | −0.983732 | + | 0.122131i | ||||
\(57\) | 473.050 | + | 62.6764i | 1.09924 | + | 0.145644i | ||||
\(58\) | 157.845 | + | 273.395i | 0.357346 | + | 0.618941i | ||||
\(59\) | 229.693 | − | 397.840i | 0.506839 | − | 0.877872i | −0.493129 | − | 0.869956i | \(-0.664147\pi\) |
0.999969 | − | 0.00791551i | \(-0.00251961\pi\) | |||||||
\(60\) | −103.864 | − | 79.8347i | −0.223481 | − | 0.171777i | ||||
\(61\) | −248.601 | + | 143.530i | −0.521804 | + | 0.301264i | −0.737673 | − | 0.675159i | \(-0.764075\pi\) |
0.215868 | + | 0.976423i | \(0.430742\pi\) | |||||||
\(62\) | 245.241 | 0.502350 | ||||||||
\(63\) | −463.693 | + | 187.178i | −0.927300 | + | 0.374320i | ||||
\(64\) | −299.720 | −0.585390 | ||||||||
\(65\) | −193.402 | + | 111.661i | −0.369055 | + | 0.213074i | ||||
\(66\) | −407.210 | − | 312.999i | −0.759457 | − | 0.583751i | ||||
\(67\) | 416.027 | − | 720.580i | 0.758594 | − | 1.31392i | −0.184973 | − | 0.982744i | \(-0.559220\pi\) |
0.943568 | − | 0.331180i | \(-0.107447\pi\) | |||||||
\(68\) | −276.779 | − | 479.396i | −0.493595 | − | 0.854931i | ||||
\(69\) | 161.387 | + | 21.3829i | 0.281576 | + | 0.0373072i | ||||
\(70\) | 62.0292 | − | 146.680i | 0.105913 | − | 0.250452i | ||||
\(71\) | 471.261i | 0.787723i | 0.919170 | + | 0.393862i | \(0.128861\pi\) | ||||
−0.919170 | + | 0.393862i | \(0.871139\pi\) | |||||||
\(72\) | −585.238 | + | 155.776i | −0.957930 | + | 0.254978i | ||||
\(73\) | 469.038 | + | 270.799i | 0.752010 | + | 0.434173i | 0.826420 | − | 0.563054i | \(-0.190374\pi\) |
−0.0744096 | + | 0.997228i | \(0.523707\pi\) | |||||||
\(74\) | −342.300 | − | 197.627i | −0.537724 | − | 0.310455i | ||||
\(75\) | 120.057 | − | 49.6127i | 0.184839 | − | 0.0763838i | ||||
\(76\) | − | 463.050i | − | 0.698888i | ||||||
\(77\) | −414.583 | + | 980.362i | −0.613585 | + | 1.45094i | ||||
\(78\) | −52.4254 | + | 395.680i | −0.0761026 | + | 0.574384i | ||||
\(79\) | −175.522 | − | 304.014i | −0.249972 | − | 0.432965i | 0.713546 | − | 0.700609i | \(-0.247088\pi\) |
−0.963518 | + | 0.267644i | \(0.913755\pi\) | |||||||
\(80\) | −4.40579 | + | 7.63105i | −0.00615728 | + | 0.0106647i | ||||
\(81\) | −632.536 | + | 362.408i | −0.867676 | + | 0.497131i | ||||
\(82\) | 276.661 | − | 159.730i | 0.372586 | − | 0.215113i | ||||
\(83\) | 866.597 | 1.14604 | 0.573020 | − | 0.819541i | \(-0.305772\pi\) | ||||
0.573020 | + | 0.819541i | \(0.305772\pi\) | |||||||
\(84\) | 239.161 | + | 422.204i | 0.310650 | + | 0.548408i | ||||
\(85\) | 548.920 | 0.700456 | ||||||||
\(86\) | −33.3055 | + | 19.2290i | −0.0417608 | + | 0.0241106i | ||||
\(87\) | 581.269 | − | 756.228i | 0.716305 | − | 0.931909i | ||||
\(88\) | −644.568 | + | 1116.43i | −0.780809 | + | 1.35240i | ||||
\(89\) | 519.613 | + | 899.995i | 0.618863 | + | 1.07190i | 0.989694 | + | 0.143202i | \(0.0457398\pi\) |
−0.370830 | + | 0.928701i | \(0.620927\pi\) | |||||||
\(90\) | 60.4622 | − | 224.164i | 0.0708142 | − | 0.262543i | ||||
\(91\) | 820.892 | − | 101.915i | 0.945636 | − | 0.117402i | ||||
\(92\) | − | 157.976i | − | 0.179023i | ||||||
\(93\) | −282.987 | − | 684.793i | −0.315531 | − | 0.763545i | ||||
\(94\) | −347.077 | − | 200.385i | −0.380832 | − | 0.219874i | ||||
\(95\) | 397.653 | + | 229.585i | 0.429456 | + | 0.247947i | ||||
\(96\) | 362.118 | + | 876.281i | 0.384985 | + | 0.931615i | ||||
\(97\) | − | 323.548i | − | 0.338674i | −0.985558 | − | 0.169337i | \(-0.945837\pi\) | ||
0.985558 | − | 0.169337i | \(-0.0541626\pi\) | |||||||
\(98\) | −423.230 | + | 410.916i | −0.436252 | + | 0.423559i | ||||
\(99\) | −404.110 | + | 1498.24i | −0.410248 | + | 1.52099i | ||||
\(100\) | −63.0281 | − | 109.168i | −0.0630281 | − | 0.109168i | ||||
\(101\) | −87.3093 | + | 151.224i | −0.0860158 | + | 0.148984i | −0.905824 | − | 0.423655i | \(-0.860747\pi\) |
0.819808 | + | 0.572639i | \(0.194080\pi\) | |||||||
\(102\) | 597.884 | − | 777.844i | 0.580385 | − | 0.755079i | ||||
\(103\) | −907.603 | + | 524.005i | −0.868241 | + | 0.501279i | −0.866763 | − | 0.498720i | \(-0.833804\pi\) |
−0.00147739 | + | 0.999999i | \(0.500470\pi\) | |||||||
\(104\) | 1001.83 | 0.944590 | ||||||||
\(105\) | −481.154 | − | 3.94942i | −0.447199 | − | 0.00367071i | ||||
\(106\) | 794.528 | 0.728032 | ||||||||
\(107\) | 1345.17 | − | 776.636i | 1.21535 | − | 0.701684i | 0.251432 | − | 0.967875i | \(-0.419098\pi\) |
0.963920 | + | 0.266190i | \(0.0857650\pi\) | |||||||
\(108\) | 429.248 | + | 562.292i | 0.382449 | + | 0.500987i | ||||
\(109\) | −274.721 | + | 475.830i | −0.241408 | + | 0.418131i | −0.961116 | − | 0.276146i | \(-0.910943\pi\) |
0.719708 | + | 0.694277i | \(0.244276\pi\) | |||||||
\(110\) | −247.108 | − | 428.003i | −0.214189 | − | 0.370986i | ||||
\(111\) | −156.854 | + | 1183.85i | −0.134126 | + | 1.01231i | ||||
\(112\) | 26.0398 | − | 19.6774i | 0.0219690 | − | 0.0166013i | ||||
\(113\) | 1141.04i | 0.949913i | 0.880009 | + | 0.474957i | \(0.157536\pi\) | ||||
−0.880009 | + | 0.474957i | \(0.842464\pi\) | |||||||
\(114\) | 758.456 | − | 313.428i | 0.623122 | − | 0.257502i | ||||
\(115\) | 135.665 | + | 78.3260i | 0.110007 | + | 0.0635125i | ||||
\(116\) | −801.558 | − | 462.780i | −0.641576 | − | 0.370414i | ||||
\(117\) | 1165.36 | − | 310.191i | 0.920833 | − | 0.245104i | ||||
\(118\) | − | 790.058i | − | 0.616362i | ||||||
\(119\) | −1872.66 | − | 791.926i | −1.44258 | − | 0.610048i | ||||
\(120\) | −577.705 | − | 76.5427i | −0.439475 | − | 0.0582280i | ||||
\(121\) | 986.087 | + | 1707.95i | 0.740862 | + | 1.28321i | ||||
\(122\) | −246.844 | + | 427.546i | −0.183182 | + | 0.317280i | ||||
\(123\) | −765.259 | − | 588.211i | −0.560985 | − | 0.431197i | ||||
\(124\) | −622.685 | + | 359.507i | −0.450958 | + | 0.260361i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −529.670 | + | 677.515i | −0.374498 | + | 0.479030i | ||||
\(127\) | −1279.98 | −0.894329 | −0.447165 | − | 0.894452i | \(-0.647566\pi\) | ||||
−0.447165 | + | 0.894452i | \(0.647566\pi\) | |||||||
\(128\) | 817.804 | − | 472.159i | 0.564722 | − | 0.326042i | ||||
\(129\) | 92.1251 | + | 70.8112i | 0.0628772 | + | 0.0483301i | ||||
\(130\) | −192.035 | + | 332.615i | −0.129559 | + | 0.224402i | ||||
\(131\) | −1165.86 | − | 2019.33i | −0.777569 | − | 1.34679i | −0.933339 | − | 0.358995i | \(-0.883119\pi\) |
0.155771 | − | 0.987793i | \(-0.450214\pi\) | |||||||
\(132\) | 1492.77 | + | 197.784i | 0.984311 | + | 0.130416i | ||||
\(133\) | −1025.39 | − | 1356.93i | −0.668515 | − | 0.884669i | ||||
\(134\) | − | 1430.98i | − | 0.922519i | ||||||
\(135\) | −695.704 | + | 89.8349i | −0.443531 | + | 0.0572722i | ||||
\(136\) | −2132.57 | − | 1231.24i | −1.34460 | − | 0.776308i | ||||
\(137\) | −1548.79 | − | 894.195i | −0.965855 | − | 0.557637i | −0.0678852 | − | 0.997693i | \(-0.521625\pi\) |
−0.897970 | + | 0.440056i | \(0.854959\pi\) | |||||||
\(138\) | 258.757 | − | 106.930i | 0.159615 | − | 0.0659600i | ||||
\(139\) | 1312.40i | 0.800839i | 0.916332 | + | 0.400419i | \(0.131136\pi\) | ||||
−0.916332 | + | 0.400419i | \(0.868864\pi\) | |||||||
\(140\) | 57.5269 | + | 463.362i | 0.0347279 | + | 0.279723i | ||||
\(141\) | −159.043 | + | 1200.38i | −0.0949918 | + | 0.716949i | ||||
\(142\) | 405.239 | + | 701.895i | 0.239485 | + | 0.414801i | ||||
\(143\) | 1283.50 | − | 2223.09i | 0.750571 | − | 1.30003i | ||||
\(144\) | 33.7016 | − | 33.5902i | 0.0195032 | − | 0.0194388i | ||||
\(145\) | 794.842 | − | 458.902i | 0.455228 | − | 0.262826i | ||||
\(146\) | 931.447 | 0.527994 | ||||||||
\(147\) | 1635.78 | + | 707.634i | 0.917802 | + | 0.397038i | ||||
\(148\) | 1158.83 | 0.643617 | ||||||||
\(149\) | 745.637 | − | 430.494i | 0.409966 | − | 0.236694i | −0.280809 | − | 0.959764i | \(-0.590603\pi\) |
0.690775 | + | 0.723070i | \(0.257269\pi\) | |||||||
\(150\) | 136.150 | − | 177.130i | 0.0741107 | − | 0.0964176i | ||||
\(151\) | 1587.96 | − | 2750.43i | 0.855805 | − | 1.48230i | −0.0200921 | − | 0.999798i | \(-0.506396\pi\) |
0.875897 | − | 0.482499i | \(-0.160271\pi\) | |||||||
\(152\) | −1029.93 | − | 1783.89i | −0.549593 | − | 0.951924i | ||||
\(153\) | −2861.89 | − | 771.921i | −1.51222 | − | 0.407883i | ||||
\(154\) | 225.540 | + | 1816.65i | 0.118016 | + | 0.950585i | ||||
\(155\) | − | 712.990i | − | 0.369476i | ||||||
\(156\) | −446.928 | − | 1081.51i | −0.229378 | − | 0.555065i | ||||
\(157\) | −1015.83 | − | 586.490i | −0.516382 | − | 0.298134i | 0.219071 | − | 0.975709i | \(-0.429697\pi\) |
−0.735453 | + | 0.677575i | \(0.763031\pi\) | |||||||
\(158\) | −522.846 | − | 301.865i | −0.263262 | − | 0.151994i | ||||
\(159\) | −916.814 | − | 2218.58i | −0.457284 | − | 1.10657i | ||||
\(160\) | 912.362i | 0.450804i | ||||||||
\(161\) | −349.825 | − | 462.936i | −0.171243 | − | 0.226611i | ||||
\(162\) | −630.461 | + | 1083.69i | −0.305764 | + | 0.525573i | ||||
\(163\) | −425.656 | − | 737.258i | −0.204540 | − | 0.354273i | 0.745446 | − | 0.666566i | \(-0.232236\pi\) |
−0.949986 | + | 0.312293i | \(0.898903\pi\) | |||||||
\(164\) | −468.307 | + | 811.132i | −0.222979 | + | 0.386212i | ||||
\(165\) | −909.982 | + | 1183.88i | −0.429345 | + | 0.558576i | ||||
\(166\) | 1290.71 | − | 745.191i | 0.603485 | − | 0.348422i | ||||
\(167\) | 1963.71 | 0.909921 | 0.454960 | − | 0.890512i | \(-0.349653\pi\) | ||||
0.454960 | + | 0.890512i | \(0.349653\pi\) | |||||||
\(168\) | 1860.44 | + | 1094.58i | 0.854380 | + | 0.502672i | ||||
\(169\) | 202.102 | 0.0919899 | ||||||||
\(170\) | 817.562 | − | 472.019i | 0.368848 | − | 0.212954i | ||||
\(171\) | −1750.38 | − | 1756.18i | −0.782778 | − | 0.785373i | ||||
\(172\) | 56.3767 | − | 97.6473i | 0.0249923 | − | 0.0432880i | ||||
\(173\) | 97.2325 | + | 168.412i | 0.0427309 | + | 0.0740121i | 0.886600 | − | 0.462537i | \(-0.153061\pi\) |
−0.843869 | + | 0.536549i | \(0.819728\pi\) | |||||||
\(174\) | 215.457 | − | 1626.16i | 0.0938723 | − | 0.708500i | ||||
\(175\) | −426.443 | − | 180.337i | −0.184206 | − | 0.0778983i | ||||
\(176\) | − | 101.286i | − | 0.0433791i | ||||||
\(177\) | −2206.10 | + | 911.657i | −0.936838 | + | 0.387143i | ||||
\(178\) | 1547.82 | + | 893.635i | 0.651765 | + | 0.376297i | ||||
\(179\) | 4101.34 | + | 2367.91i | 1.71256 | + | 0.988749i | 0.931075 | + | 0.364828i | \(0.118872\pi\) |
0.781488 | + | 0.623921i | \(0.214461\pi\) | |||||||
\(180\) | 175.091 | + | 657.800i | 0.0725028 | + | 0.272386i | ||||
\(181\) | 2963.89i | 1.21715i | 0.793497 | + | 0.608575i | \(0.208258\pi\) | ||||
−0.793497 | + | 0.608575i | \(0.791742\pi\) | |||||||
\(182\) | 1135.00 | − | 857.681i | 0.462262 | − | 0.349316i | ||||
\(183\) | 1478.68 | + | 195.917i | 0.597308 | + | 0.0791399i | ||||
\(184\) | −351.374 | − | 608.597i | −0.140780 | − | 0.243839i | ||||
\(185\) | −574.560 | + | 995.167i | −0.228338 | + | 0.395493i | ||||
\(186\) | −1010.34 | − | 776.588i | −0.398288 | − | 0.306141i | ||||
\(187\) | −5464.31 | + | 3154.82i | −2.13685 | + | 1.23371i | ||||
\(188\) | 1175.00 | 0.455829 | ||||||||
\(189\) | 2503.03 | + | 697.216i | 0.963326 | + | 0.268333i | ||||
\(190\) | 789.686 | 0.301525 | ||||||||
\(191\) | −553.249 | + | 319.418i | −0.209590 | + | 0.121007i | −0.601121 | − | 0.799158i | \(-0.705279\pi\) |
0.391531 | + | 0.920165i | \(0.371946\pi\) | |||||||
\(192\) | 1234.77 | + | 949.100i | 0.464126 | + | 0.356747i | ||||
\(193\) | 787.552 | − | 1364.08i | 0.293727 | − | 0.508749i | −0.680961 | − | 0.732319i | \(-0.738438\pi\) |
0.974688 | + | 0.223570i | \(0.0717712\pi\) | |||||||
\(194\) | −278.221 | − | 481.893i | −0.102964 | − | 0.178340i | ||||
\(195\) | 1150.36 | + | 152.416i | 0.422456 | + | 0.0559730i | ||||
\(196\) | 472.235 | − | 1663.77i | 0.172097 | − | 0.606331i | ||||
\(197\) | − | 325.944i | − | 0.117881i | −0.998261 | − | 0.0589405i | \(-0.981228\pi\) | ||
0.998261 | − | 0.0589405i | \(-0.0187722\pi\) | |||||||
\(198\) | 686.460 | + | 2578.97i | 0.246387 | + | 0.925653i | ||||
\(199\) | −526.526 | − | 303.990i | −0.187560 | − | 0.108288i | 0.403280 | − | 0.915077i | \(-0.367870\pi\) |
−0.590840 | + | 0.806789i | \(0.701203\pi\) | |||||||
\(200\) | −485.628 | − | 280.378i | −0.171695 | − | 0.0991284i | ||||
\(201\) | −3995.74 | + | 1651.22i | −1.40218 | + | 0.579443i | ||||
\(202\) | 300.311i | 0.104603i | ||||||||
\(203\) | −3373.69 | + | 418.848i | −1.16644 | + | 0.144815i | ||||
\(204\) | −377.802 | + | 2851.46i | −0.129664 | + | 0.978637i | ||||
\(205\) | −464.383 | − | 804.335i | −0.158214 | − | 0.274035i | ||||
\(206\) | −901.189 | + | 1560.91i | −0.304800 | + | 0.527929i | ||||
\(207\) | −597.166 | − | 599.145i | −0.200512 | − | 0.201176i | ||||
\(208\) | −68.1671 | + | 39.3563i | −0.0227237 | + | 0.0131196i | ||||
\(209\) | −5278.00 | −1.74683 | ||||||||
\(210\) | −720.027 | + | 407.865i | −0.236603 | + | 0.134025i | ||||
\(211\) | 3315.33 | 1.08169 | 0.540846 | − | 0.841122i | \(-0.318104\pi\) | ||||
0.540846 | + | 0.841122i | \(0.318104\pi\) | |||||||
\(212\) | −2017.36 | + | 1164.72i | −0.653551 | + | 0.377328i | ||||
\(213\) | 1492.31 | − | 1941.48i | 0.480052 | − | 0.624546i | ||||
\(214\) | 1335.67 | − | 2313.44i | 0.426656 | − | 0.738989i | ||||
\(215\) | 55.9043 | + | 96.8291i | 0.0177332 | + | 0.0307148i | ||||
\(216\) | 2904.33 | + | 1211.47i | 0.914883 | + | 0.381620i | ||||
\(217\) | −1028.63 | + | 2432.40i | −0.321787 | + | 0.760930i | ||||
\(218\) | 944.935i | 0.293574i | ||||||||
\(219\) | −1074.81 | − | 2600.90i | −0.331638 | − | 0.802522i | ||||
\(220\) | 1254.85 | + | 724.486i | 0.384554 | + | 0.222022i | ||||
\(221\) | 4246.49 | + | 2451.71i | 1.29253 | + | 0.746245i | ||||
\(222\) | 784.385 | + | 1898.11i | 0.237137 | + | 0.573842i | ||||
\(223\) | − | 4592.55i | − | 1.37910i | −0.724236 | − | 0.689552i | \(-0.757808\pi\) | ||
0.724236 | − | 0.689552i | \(-0.242192\pi\) | |||||||
\(224\) | 1316.26 | − | 3112.56i | 0.392618 | − | 0.928424i | ||||
\(225\) | −651.710 | − | 175.782i | −0.193099 | − | 0.0520834i | ||||
\(226\) | 981.188 | + | 1699.47i | 0.288795 | + | 0.500207i | ||||
\(227\) | −2428.78 | + | 4206.77i | −0.710149 | + | 1.23001i | 0.254652 | + | 0.967033i | \(0.418039\pi\) |
−0.964801 | + | 0.262982i | \(0.915294\pi\) | |||||||
\(228\) | −1466.31 | + | 1907.66i | −0.425915 | + | 0.554113i | ||||
\(229\) | 4633.45 | − | 2675.12i | 1.33706 | − | 0.771953i | 0.350691 | − | 0.936491i | \(-0.385947\pi\) |
0.986371 | + | 0.164539i | \(0.0526135\pi\) | |||||||
\(230\) | 269.412 | 0.0772369 | ||||||||
\(231\) | 4812.42 | − | 2726.03i | 1.37071 | − | 0.776450i | ||||
\(232\) | −4117.31 | −1.16515 | ||||||||
\(233\) | 1126.35 | − | 650.300i | 0.316694 | − | 0.182844i | −0.333224 | − | 0.942848i | \(-0.608136\pi\) |
0.649918 | + | 0.760004i | \(0.274803\pi\) | |||||||
\(234\) | 1468.95 | − | 1464.10i | 0.410377 | − | 0.409021i | ||||
\(235\) | −582.578 | + | 1009.06i | −0.161716 | + | 0.280100i | ||||
\(236\) | 1158.17 | + | 2006.01i | 0.319451 | + | 0.553306i | ||||
\(237\) | −239.587 | + | 1808.28i | −0.0656660 | + | 0.495613i | ||||
\(238\) | −3470.13 | + | 430.820i | −0.945105 | + | 0.117336i | ||||
\(239\) | 1750.92i | 0.473882i | 0.971524 | + | 0.236941i | \(0.0761448\pi\) | ||||
−0.971524 | + | 0.236941i | \(0.923855\pi\) | |||||||
\(240\) | 42.3155 | − | 17.4867i | 0.0113811 | − | 0.00470316i | ||||
\(241\) | 1844.54 | + | 1064.95i | 0.493018 | + | 0.284644i | 0.725825 | − | 0.687879i | \(-0.241458\pi\) |
−0.232808 | + | 0.972523i | \(0.574791\pi\) | |||||||
\(242\) | 2937.36 | + | 1695.88i | 0.780249 | + | 0.450477i | ||||
\(243\) | 3753.51 | + | 509.966i | 0.990896 | + | 0.134627i | ||||
\(244\) | − | 1447.43i | − | 0.379762i | ||||||
\(245\) | 1194.66 | + | 1230.46i | 0.311526 | + | 0.320861i | ||||
\(246\) | −1645.58 | − | 218.031i | −0.426498 | − | 0.0565086i | ||||
\(247\) | 2050.85 | + | 3552.18i | 0.528310 | + | 0.915059i | ||||
\(248\) | −1599.25 | + | 2769.98i | −0.409486 | + | 0.709250i | ||||
\(249\) | −3570.18 | − | 2744.19i | −0.908638 | − | 0.698418i | ||||
\(250\) | 186.175 | − | 107.488i | 0.0470990 | − | 0.0271926i | ||||
\(251\) | −414.788 | −0.104308 | −0.0521538 | − | 0.998639i | \(-0.516609\pi\) | ||||
−0.0521538 | + | 0.998639i | \(0.516609\pi\) | |||||||
\(252\) | 351.677 | − | 2496.72i | 0.0879110 | − | 0.624120i | ||||
\(253\) | −1800.66 | −0.447457 | ||||||||
\(254\) | −1906.40 | + | 1100.66i | −0.470938 | + | 0.271896i | ||||
\(255\) | −2261.42 | − | 1738.23i | −0.555356 | − | 0.426870i | ||||
\(256\) | 2010.90 | − | 3482.99i | 0.490943 | − | 0.850338i | ||||
\(257\) | −221.421 | − | 383.512i | −0.0537426 | − | 0.0930848i | 0.837903 | − | 0.545820i | \(-0.183782\pi\) |
−0.891645 | + | 0.452735i | \(0.850448\pi\) | |||||||
\(258\) | 198.102 | + | 26.2474i | 0.0478034 | + | 0.00633369i | ||||
\(259\) | 3395.86 | − | 2566.14i | 0.814705 | − | 0.615645i | ||||
\(260\) | − | 1126.04i | − | 0.268593i | ||||||
\(261\) | −4789.38 | + | 1274.82i | −1.13584 | + | 0.302335i | ||||
\(262\) | −3472.86 | − | 2005.06i | −0.818908 | − | 0.472797i | ||||
\(263\) | 4312.97 | + | 2490.09i | 1.01121 | + | 0.583824i | 0.911546 | − | 0.411197i | \(-0.134889\pi\) |
0.0996661 | + | 0.995021i | \(0.468223\pi\) | |||||||
\(264\) | 6190.77 | − | 2558.30i | 1.44324 | − | 0.596411i | ||||
\(265\) | − | 2309.93i | − | 0.535463i | ||||||
\(266\) | −2694.05 | − | 1139.28i | −0.620987 | − | 0.262607i | ||||
\(267\) | 709.268 | − | 5353.19i | 0.162571 | − | 1.22700i | ||||
\(268\) | 2097.71 | + | 3633.35i | 0.478128 | + | 0.828142i | ||||
\(269\) | −693.992 | + | 1202.03i | −0.157299 | + | 0.272450i | −0.933894 | − | 0.357551i | \(-0.883612\pi\) |
0.776595 | + | 0.630000i | \(0.216945\pi\) | |||||||
\(270\) | −958.932 | + | 732.040i | −0.216144 | + | 0.165002i | ||||
\(271\) | 571.186 | − | 329.774i | 0.128033 | − | 0.0739201i | −0.434615 | − | 0.900616i | \(-0.643116\pi\) |
0.562649 | + | 0.826696i | \(0.309782\pi\) | |||||||
\(272\) | 193.474 | 0.0431290 | ||||||||
\(273\) | −3704.61 | − | 2179.59i | −0.821293 | − | 0.483205i | ||||
\(274\) | −3075.69 | −0.678136 | ||||||||
\(275\) | −1244.33 | + | 718.416i | −0.272858 | + | 0.157535i | ||||
\(276\) | −500.250 | + | 650.823i | −0.109100 | + | 0.141938i | ||||
\(277\) | −2718.43 | + | 4708.45i | −0.589655 | + | 1.02131i | 0.404622 | + | 0.914484i | \(0.367403\pi\) |
−0.994277 | + | 0.106829i | \(0.965930\pi\) | |||||||
\(278\) | 1128.54 | + | 1954.69i | 0.243473 | + | 0.421707i | ||||
\(279\) | −1002.64 | + | 3717.30i | −0.215150 | + | 0.797666i | ||||
\(280\) | 1252.24 | + | 1657.13i | 0.267270 | + | 0.353688i | ||||
\(281\) | − | 3329.00i | − | 0.706732i | −0.935485 | − | 0.353366i | \(-0.885037\pi\) | ||
0.935485 | − | 0.353366i | \(-0.114963\pi\) | |||||||
\(282\) | 795.331 | + | 1924.60i | 0.167948 | + | 0.406413i | ||||
\(283\) | 5532.85 | + | 3194.39i | 1.16217 | + | 0.670979i | 0.951823 | − | 0.306648i | \(-0.0992075\pi\) |
0.210346 | + | 0.977627i | \(0.432541\pi\) | |||||||
\(284\) | −2057.86 | − | 1188.11i | −0.429971 | − | 0.248244i | ||||
\(285\) | −911.227 | − | 2205.06i | −0.189391 | − | 0.458303i | ||||
\(286\) | − | 4414.76i | − | 0.912762i | ||||||
\(287\) | 423.850 | + | 3413.99i | 0.0871745 | + | 0.702165i | ||||
\(288\) | 1283.01 | − | 4756.76i | 0.262508 | − | 0.973247i | ||||
\(289\) | −3569.77 | − | 6183.02i | −0.726596 | − | 1.25850i | ||||
\(290\) | 789.225 | − | 1366.98i | 0.159810 | − | 0.276799i | ||||
\(291\) | −1024.56 | + | 1332.94i | −0.206394 | + | 0.268517i | ||||
\(292\) | −2365.01 | + | 1365.44i | −0.473978 | + | 0.273651i | ||||
\(293\) | −6510.06 | −1.29803 | −0.649013 | − | 0.760777i | \(-0.724818\pi\) | ||||
−0.649013 | + | 0.760777i | \(0.724818\pi\) | |||||||
\(294\) | 3044.83 | − | 352.667i | 0.604007 | − | 0.0699590i | ||||
\(295\) | −2296.93 | −0.453331 | ||||||||
\(296\) | 4464.36 | − | 2577.50i | 0.876641 | − | 0.506129i | ||||
\(297\) | 6409.19 | − | 4892.71i | 1.25219 | − | 0.955906i | ||||
\(298\) | 740.368 | − | 1282.35i | 0.143921 | − | 0.249278i | ||||
\(299\) | 699.675 | + | 1211.87i | 0.135329 | + | 0.234396i | ||||
\(300\) | −86.0330 | + | 649.333i | −0.0165571 | + | 0.124964i | ||||
\(301\) | −51.0248 | − | 410.990i | −0.00977084 | − | 0.0787011i | ||||
\(302\) | − | 5461.99i | − | 1.04074i | ||||||
\(303\) | 838.564 | − | 346.532i | 0.158991 | − | 0.0657021i | ||||
\(304\) | 140.158 | + | 80.9203i | 0.0264428 | + | 0.0152668i | ||||
\(305\) | 1243.00 | + | 717.649i | 0.233358 | + | 0.134729i | ||||
\(306\) | −4926.28 | + | 1311.26i | −0.920316 | + | 0.244966i | ||||
\(307\) | 2643.43i | 0.491428i | 0.969342 | + | 0.245714i | \(0.0790225\pi\) | ||||
−0.969342 | + | 0.245714i | \(0.920978\pi\) | |||||||
\(308\) | −3235.75 | − | 4281.98i | −0.598617 | − | 0.792171i | ||||
\(309\) | 5398.44 | + | 715.263i | 0.993872 | + | 0.131682i | ||||
\(310\) | −613.104 | − | 1061.93i | −0.112329 | − | 0.194559i | ||||
\(311\) | 1396.85 | − | 2419.42i | 0.254688 | − | 0.441133i | −0.710122 | − | 0.704078i | \(-0.751360\pi\) |
0.964811 | + | 0.262945i | \(0.0846937\pi\) | |||||||
\(312\) | −4127.30 | − | 3172.42i | −0.748918 | − | 0.575650i | ||||
\(313\) | −5645.67 | + | 3259.53i | −1.01953 | + | 0.588625i | −0.913967 | − | 0.405788i | \(-0.866997\pi\) |
−0.105561 | + | 0.994413i | \(0.533664\pi\) | |||||||
\(314\) | −2017.30 | −0.362557 | ||||||||
\(315\) | 1969.74 | + | 1539.91i | 0.352324 | + | 0.275441i | ||||
\(316\) | 1770.06 | 0.315106 | ||||||||
\(317\) | −2657.94 | + | 1534.56i | −0.470929 | + | 0.271891i | −0.716629 | − | 0.697455i | \(-0.754316\pi\) |
0.245699 | + | 0.969346i | \(0.420982\pi\) | |||||||
\(318\) | −3273.27 | − | 2515.97i | −0.577219 | − | 0.443675i | ||||
\(319\) | −5274.92 | + | 9136.43i | −0.925827 | + | 1.60358i | ||||
\(320\) | 749.299 | + | 1297.82i | 0.130897 | + | 0.226720i | ||||
\(321\) | −8001.11 | − | 1060.10i | −1.39121 | − | 0.184328i | ||||
\(322\) | −919.110 | − | 388.680i | −0.159068 | − | 0.0672679i | ||||
\(323\) | − | 10081.9i | − | 1.73676i | ||||||
\(324\) | 12.1664 | − | 3675.78i | 0.00208614 | − | 0.630278i | ||||
\(325\) | 967.010 | + | 558.304i | 0.165046 | + | 0.0952896i | ||||
\(326\) | −1267.94 | − | 732.048i | −0.215414 | − | 0.124369i | ||||
\(327\) | 2638.56 | − | 1090.37i | 0.446216 | − | 0.184396i | ||||
\(328\) | 4166.48i | 0.701388i | ||||||||
\(329\) | 3443.25 | − | 2601.95i | 0.576999 | − | 0.436019i | ||||
\(330\) | −337.300 | + | 2545.77i | −0.0562660 | + | 0.424667i | ||||
\(331\) | 3072.11 | + | 5321.04i | 0.510146 | + | 0.883598i | 0.999931 | + | 0.0117549i | \(0.00374179\pi\) |
−0.489785 | + | 0.871843i | \(0.662925\pi\) | |||||||
\(332\) | −2184.80 | + | 3784.19i | −0.361164 | + | 0.625555i | ||||
\(333\) | 4395.03 | − | 4380.51i | 0.723262 | − | 0.720872i | ||||
\(334\) | 2924.75 | − | 1688.61i | 0.479148 | − | 0.276636i | ||||
\(335\) | −4160.27 | −0.678507 | ||||||||
\(336\) | −169.589 | − | 1.39203i | −0.0275353 | − | 0.000226016i | ||||
\(337\) | 4494.84 | 0.726556 | 0.363278 | − | 0.931681i | \(-0.381658\pi\) | ||||
0.363278 | + | 0.931681i | \(0.381658\pi\) | |||||||
\(338\) | 301.010 | − | 173.788i | 0.0484403 | − | 0.0279670i | ||||
\(339\) | 3613.25 | − | 4700.83i | 0.578894 | − | 0.753138i | ||||
\(340\) | −1383.90 | + | 2396.98i | −0.220742 | + | 0.382337i | ||||
\(341\) | 4097.78 | + | 7097.57i | 0.650755 | + | 1.12714i | ||||
\(342\) | −4117.17 | − | 1110.50i | −0.650968 | − | 0.175581i | ||||
\(343\) | −2300.44 | − | 5921.28i | −0.362135 | − | 0.932126i | ||||
\(344\) | − | 501.578i | − | 0.0786142i | ||||||
\(345\) | −310.877 | − | 752.284i | −0.0485132 | − | 0.117396i | ||||
\(346\) | 289.636 | + | 167.221i | 0.0450027 | + | 0.0259823i | ||||
\(347\) | 3001.05 | + | 1732.66i | 0.464279 | + | 0.268051i | 0.713842 | − | 0.700307i | \(-0.246954\pi\) |
−0.249563 | + | 0.968359i | \(0.580287\pi\) | |||||||
\(348\) | 1836.78 | + | 4444.78i | 0.282936 | + | 0.684670i | ||||
\(349\) | 4800.19i | 0.736241i | 0.929778 | + | 0.368121i | \(0.119999\pi\) | ||||
−0.929778 | + | 0.368121i | \(0.880001\pi\) | |||||||
\(350\) | −790.217 | + | 98.1063i | −0.120682 | + | 0.0149829i | ||||
\(351\) | −5783.27 | − | 2412.34i | −0.879453 | − | 0.366842i | ||||
\(352\) | −5243.64 | − | 9082.26i | −0.793997 | − | 1.37524i | ||||
\(353\) | −3971.17 | + | 6878.27i | −0.598765 | + | 1.03709i | 0.394238 | + | 0.919008i | \(0.371009\pi\) |
−0.993004 | + | 0.118084i | \(0.962325\pi\) | |||||||
\(354\) | −2501.82 | + | 3254.85i | −0.375622 | + | 0.488682i | ||||
\(355\) | 2040.62 | − | 1178.15i | 0.305084 | − | 0.176140i | ||||
\(356\) | −5240.03 | −0.780116 | ||||||||
\(357\) | 5207.21 | + | 9192.58i | 0.771974 | + | 1.36281i | ||||
\(358\) | 8144.72 | 1.20241 | ||||||||
\(359\) | 9607.02 | − | 5546.61i | 1.41236 | − | 0.815429i | 0.416754 | − | 0.909019i | \(-0.363168\pi\) |
0.995611 | + | 0.0935901i | \(0.0298343\pi\) | |||||||
\(360\) | 2137.63 | + | 2144.71i | 0.312952 | + | 0.313990i | ||||
\(361\) | 787.245 | − | 1363.55i | 0.114776 | − | 0.198797i | ||||
\(362\) | 2548.66 | + | 4414.41i | 0.370041 | + | 0.640929i | ||||
\(363\) | 1346.00 | − | 10158.9i | 0.194619 | − | 1.46889i | ||||
\(364\) | −1624.54 | + | 3841.54i | −0.233926 | + | 0.553164i | ||||
\(365\) | − | 2707.99i | − | 0.388336i | ||||||
\(366\) | 2370.82 | − | 979.728i | 0.338592 | − | 0.139921i | ||||
\(367\) | −3691.36 | − | 2131.21i | −0.525034 | − | 0.303128i | 0.213958 | − | 0.976843i | \(-0.431364\pi\) |
−0.738992 | + | 0.673715i | \(0.764698\pi\) | |||||||
\(368\) | 47.8168 | + | 27.6070i | 0.00677343 | + | 0.00391064i | ||||
\(369\) | 1290.05 | + | 4846.58i | 0.181997 | + | 0.683748i | ||||
\(370\) | 1976.27i | 0.277679i | ||||||||
\(371\) | −3332.53 | + | 7880.42i | −0.466351 | + | 1.10278i | ||||
\(372\) | 3703.74 | + | 490.725i | 0.516210 | + | 0.0683949i | ||||
\(373\) | −1046.28 | − | 1812.22i | −0.145240 | − | 0.251563i | 0.784223 | − | 0.620480i | \(-0.213062\pi\) |
−0.929462 | + | 0.368917i | \(0.879729\pi\) | |||||||
\(374\) | −5425.70 | + | 9397.58i | −0.750150 | + | 1.29930i | ||||
\(375\) | −514.971 | − | 395.828i | −0.0709146 | − | 0.0545080i | ||||
\(376\) | 4526.66 | − | 2613.47i | 0.620864 | − | 0.358456i | ||||
\(377\) | 8198.61 | 1.12003 | ||||||||
\(378\) | 4327.55 | − | 1113.94i | 0.588850 | − | 0.151573i | ||||
\(379\) | −7320.18 | −0.992117 | −0.496059 | − | 0.868289i | \(-0.665220\pi\) | ||||
−0.496059 | + | 0.868289i | \(0.665220\pi\) | |||||||
\(380\) | −2005.07 | + | 1157.63i | −0.270678 | + | 0.156276i | ||||
\(381\) | 5273.22 | + | 4053.22i | 0.709068 | + | 0.545020i | ||||
\(382\) | −549.339 | + | 951.483i | −0.0735776 | + | 0.127440i | ||||
\(383\) | −1594.48 | − | 2761.73i | −0.212727 | − | 0.368453i | 0.739840 | − | 0.672783i | \(-0.234901\pi\) |
−0.952567 | + | 0.304329i | \(0.901568\pi\) | |||||||
\(384\) | −4864.31 | − | 644.494i | −0.646435 | − | 0.0856490i | ||||
\(385\) | 5281.55 | − | 655.710i | 0.699150 | − | 0.0868003i | ||||
\(386\) | − | 2708.88i | − | 0.357198i | ||||||
\(387\) | −155.301 | − | 583.451i | −0.0203989 | − | 0.0766370i | ||||
\(388\) | 1412.84 | + | 815.706i | 0.184862 | + | 0.106730i | ||||
\(389\) | 5822.56 | + | 3361.65i | 0.758908 | + | 0.438156i | 0.828904 | − | 0.559391i | \(-0.188965\pi\) |
−0.0699955 | + | 0.997547i | \(0.522298\pi\) | |||||||
\(390\) | 1844.41 | − | 762.191i | 0.239475 | − | 0.0989617i | ||||
\(391\) | − | 3439.58i | − | 0.444877i | ||||||
\(392\) | −1881.33 | − | 7459.99i | −0.242402 | − | 0.961190i | ||||
\(393\) | −1591.39 | + | 12011.0i | −0.204262 | + | 1.54166i | ||||
\(394\) | −280.281 | − | 485.461i | −0.0358385 | − | 0.0620740i | ||||
\(395\) | −877.612 | + | 1520.07i | −0.111791 | + | 0.193628i | ||||
\(396\) | −5523.56 | − | 5541.87i | −0.700933 | − | 0.703257i | ||||
\(397\) | 10725.6 | − | 6192.45i | 1.35593 | − | 0.782847i | 0.366858 | − | 0.930277i | \(-0.380434\pi\) |
0.989072 | + | 0.147430i | \(0.0471002\pi\) | |||||||
\(398\) | −1045.61 | −0.131688 | ||||||||
\(399\) | −72.5383 | + | 8837.27i | −0.00910140 | + | 1.10881i | ||||
\(400\) | 44.0579 | 0.00550724 | ||||||||
\(401\) | 2395.94 | − | 1383.30i | 0.298373 | − | 0.172266i | −0.343339 | − | 0.939212i | \(-0.611558\pi\) |
0.641712 | + | 0.766946i | \(0.278224\pi\) | |||||||
\(402\) | −4531.37 | + | 5895.29i | −0.562199 | + | 0.731418i | ||||
\(403\) | 3184.52 | − | 5515.75i | 0.393628 | − | 0.681784i | ||||
\(404\) | −440.235 | − | 762.510i | −0.0542142 | − | 0.0939017i | ||||
\(405\) | 3150.61 | + | 1832.94i | 0.386556 | + | 0.224887i | ||||
\(406\) | −4664.61 | + | 3524.89i | −0.570199 | + | 0.430880i | ||||
\(407\) | − | 13208.7i | − | 1.60868i | ||||||
\(408\) | 4886.81 | + | 11825.5i | 0.592973 | + | 1.43492i | ||||
\(409\) | −5568.92 | − | 3215.22i | −0.673265 | − | 0.388710i | 0.124048 | − | 0.992276i | \(-0.460412\pi\) |
−0.797313 | + | 0.603567i | \(0.793746\pi\) | |||||||
\(410\) | −1383.30 | − | 798.651i | −0.166626 | − | 0.0962013i | ||||
\(411\) | 3549.08 | + | 8588.32i | 0.425944 | + | 1.03073i | ||||
\(412\) | − | 5284.33i | − | 0.631894i | ||||||
\(413\) | 7836.09 | + | 3313.78i | 0.933628 | + | 0.394819i | ||||
\(414\) | −1404.63 | − | 378.861i | −0.166748 | − | 0.0449759i | ||||
\(415\) | −2166.49 | − | 3752.48i | −0.256263 | − | 0.443860i | ||||
\(416\) | −4075.00 | + | 7058.11i | −0.480272 | + | 0.831856i | ||||
\(417\) | 4155.89 | − | 5406.79i | 0.488045 | − | 0.634944i | ||||
\(418\) | −7861.05 | + | 4538.58i | −0.919848 | + | 0.531075i | ||||
\(419\) | −2189.52 | −0.255287 | −0.127643 | − | 0.991820i | \(-0.540741\pi\) | ||||
−0.127643 | + | 0.991820i | \(0.540741\pi\) | |||||||
\(420\) | 1230.30 | − | 2091.11i | 0.142934 | − | 0.242942i | ||||
\(421\) | −8738.82 | −1.01165 | −0.505825 | − | 0.862636i | \(-0.668812\pi\) | ||||
−0.505825 | + | 0.862636i | \(0.668812\pi\) | |||||||
\(422\) | 4937.85 | − | 2850.87i | 0.569600 | − | 0.328858i | ||||
\(423\) | 4456.36 | − | 4441.64i | 0.512236 | − | 0.510543i | ||||
\(424\) | −5181.22 | + | 8974.13i | −0.593448 | + | 1.02788i | ||||
\(425\) | −1372.30 | − | 2376.89i | −0.156627 | − | 0.271285i | ||||
\(426\) | 553.149 | − | 4174.89i | 0.0629112 | − | 0.474821i | ||||
\(427\) | −3205.21 | − | 4241.57i | −0.363258 | − | 0.480712i | ||||
\(428\) | 7831.99i | 0.884517i | ||||||||
\(429\) | −12327.4 | + | 5094.24i | −1.38735 | + | 0.573315i | ||||
\(430\) | 166.528 | + | 96.1448i | 0.0186760 | + | 0.0107826i | ||||
\(431\) | 3823.61 | + | 2207.56i | 0.427324 | + | 0.246716i | 0.698206 | − | 0.715897i | \(-0.253982\pi\) |
−0.270882 | + | 0.962613i | \(0.587315\pi\) | |||||||
\(432\) | −245.210 | + | 31.6635i | −0.0273094 | + | 0.00352641i | ||||
\(433\) | 10561.3i | 1.17215i | 0.810255 | + | 0.586077i | \(0.199329\pi\) | ||||
−0.810255 | + | 0.586077i | \(0.800671\pi\) | |||||||
\(434\) | 559.590 | + | 4507.33i | 0.0618922 | + | 0.498523i | ||||
\(435\) | −4727.73 | − | 626.398i | −0.521098 | − | 0.0690425i | ||||
\(436\) | −1385.21 | − | 2399.26i | −0.152155 | − | 0.263540i | ||||
\(437\) | 1438.60 | − | 2491.73i | 0.157477 | − | 0.272758i | ||||
\(438\) | −3837.34 | − | 2949.54i | −0.418619 | − | 0.321769i | ||||
\(439\) | 7929.27 | − | 4577.96i | 0.862057 | − | 0.497709i | −0.00264332 | − | 0.999997i | \(-0.500841\pi\) |
0.864701 | + | 0.502287i | \(0.167508\pi\) | |||||||
\(440\) | 6445.68 | 0.698377 | ||||||||
\(441\) | −4498.22 | − | 8095.19i | −0.485717 | − | 0.874116i | ||||
\(442\) | 8432.96 | 0.907500 | ||||||||
\(443\) | −2931.50 | + | 1692.50i | −0.314402 | + | 0.181520i | −0.648894 | − | 0.760878i | \(-0.724768\pi\) |
0.334493 | + | 0.942398i | \(0.391435\pi\) | |||||||
\(444\) | −4774.11 | − | 3669.59i | −0.510291 | − | 0.392232i | ||||
\(445\) | 2598.06 | − | 4499.98i | 0.276764 | − | 0.479369i | ||||
\(446\) | −3949.16 | − | 6840.15i | −0.419278 | − | 0.726212i | ||||
\(447\) | −4435.06 | − | 587.621i | −0.469287 | − | 0.0621779i | ||||
\(448\) | −683.898 | − | 5508.59i | −0.0721231 | − | 0.580930i | ||||
\(449\) | − | 8544.40i | − | 0.898074i | −0.893513 | − | 0.449037i | \(-0.851767\pi\) | ||
0.893513 | − | 0.449037i | \(-0.148233\pi\) | |||||||
\(450\) | −1121.81 | + | 298.600i | −0.117517 | + | 0.0312803i | ||||
\(451\) | 9245.55 | + | 5337.92i | 0.965312 | + | 0.557323i | ||||
\(452\) | −4982.61 | − | 2876.71i | −0.518500 | − | 0.299356i | ||||
\(453\) | −15251.6 | + | 6302.65i | −1.58186 | + | 0.653696i | ||||
\(454\) | 8354.09i | 0.863605i | ||||||||
\(455\) | −2493.53 | − | 3299.78i | −0.256920 | − | 0.339991i | ||||
\(456\) | −1405.84 | + | 10610.6i | −0.144374 | + | 1.08966i | ||||
\(457\) | 7508.15 | + | 13004.5i | 0.768526 | + | 1.33113i | 0.938362 | + | 0.345654i | \(0.112343\pi\) |
−0.169836 | + | 0.985472i | \(0.554324\pi\) | |||||||
\(458\) | 4600.71 | − | 7968.66i | 0.469382 | − | 0.812993i | ||||
\(459\) | 9345.95 | + | 12242.7i | 0.950395 | + | 1.24497i | ||||
\(460\) | −684.055 | + | 394.939i | −0.0693353 | + | 0.0400308i | ||||
\(461\) | −5195.83 | −0.524932 | −0.262466 | − | 0.964941i | \(-0.584536\pi\) | ||||
−0.262466 | + | 0.964941i | \(0.584536\pi\) | |||||||
\(462\) | 4823.49 | − | 8198.38i | 0.485734 | − | 0.825592i | ||||
\(463\) | 5865.44 | 0.588748 | 0.294374 | − | 0.955690i | \(-0.404889\pi\) | ||||
0.294374 | + | 0.955690i | \(0.404889\pi\) | |||||||
\(464\) | 280.152 | − | 161.746i | 0.0280296 | − | 0.0161829i | ||||
\(465\) | −2257.77 | + | 2937.35i | −0.225165 | + | 0.292938i | ||||
\(466\) | 1118.39 | − | 1937.11i | 0.111177 | − | 0.192564i | ||||
\(467\) | 1055.99 | + | 1829.02i | 0.104637 | + | 0.181236i | 0.913590 | − | 0.406637i | \(-0.133299\pi\) |
−0.808953 | + | 0.587873i | \(0.799965\pi\) | |||||||
\(468\) | −1583.50 | + | 5870.83i | −0.156405 | + | 0.579870i | ||||
\(469\) | 14192.9 | + | 6002.01i | 1.39738 | + | 0.590932i | ||||
\(470\) | 2003.85i | 0.196661i | ||||||||
\(471\) | 2327.79 | + | 5632.95i | 0.227726 | + | 0.551068i | ||||
\(472\) | 8923.64 | + | 5152.07i | 0.870220 | + | 0.502422i | ||||
\(473\) | −1113.02 | − | 642.600i | −0.108196 | − | 0.0624668i | ||||
\(474\) | 1198.11 | + | 2899.27i | 0.116099 | + | 0.280945i | ||||
\(475\) | − | 2295.85i | − | 0.221770i | ||||||
\(476\) | 8179.34 | − | 6180.85i | 0.787604 | − | 0.595166i | ||||
\(477\) | −3248.34 | + | 12043.2i | −0.311806 | + | 1.15602i | ||||
\(478\) | 1505.63 | + | 2607.82i | 0.144071 | + | 0.249538i | ||||
\(479\) | 2712.63 | − | 4698.41i | 0.258754 | − | 0.448175i | −0.707155 | − | 0.707059i | \(-0.750022\pi\) |
0.965908 | + | 0.258884i | \(0.0833549\pi\) | |||||||
\(480\) | 2889.11 | − | 3758.72i | 0.274728 | − | 0.357419i | ||||
\(481\) | −8889.69 | + | 5132.46i | −0.842692 | + | 0.486528i | ||||
\(482\) | 3663.01 | 0.346152 | ||||||||
\(483\) | −24.7474 | + | 3014.95i | −0.00233136 | + | 0.284027i | ||||
\(484\) | −9944.20 | −0.933903 | ||||||||
\(485\) | −1401.01 | + | 808.871i | −0.131168 | + | 0.0757298i | ||||
\(486\) | 6029.00 | − | 2468.12i | 0.562718 | − | 0.230363i | ||||
\(487\) | 5094.94 | − | 8824.69i | 0.474073 | − | 0.821119i | −0.525486 | − | 0.850802i | \(-0.676116\pi\) |
0.999559 | + | 0.0296831i | \(0.00944980\pi\) | |||||||
\(488\) | −3219.40 | − | 5576.17i | −0.298638 | − | 0.517256i | ||||
\(489\) | −581.017 | + | 4385.22i | −0.0537311 | + | 0.405535i | ||||
\(490\) | 2837.40 | + | 805.350i | 0.261593 | + | 0.0742490i | ||||
\(491\) | − | 5998.74i | − | 0.551364i | −0.961249 | − | 0.275682i | \(-0.911096\pi\) | ||
0.961249 | − | 0.275682i | \(-0.0889036\pi\) | |||||||
\(492\) | 4497.87 | − | 1858.72i | 0.412153 | − | 0.170320i | ||||
\(493\) | −17452.2 | − | 10076.0i | −1.59433 | − | 0.920490i | ||||
\(494\) | 6109.07 | + | 3527.07i | 0.556397 | + | 0.321236i | ||||
\(495\) | 7497.82 | − | 1995.74i | 0.680812 | − | 0.181216i | ||||
\(496\) | − | 251.303i | − | 0.0227496i | ||||||
\(497\) | −8661.37 | + | 1075.32i | −0.781722 | + | 0.0970516i | ||||
\(498\) | −7677.16 | − | 1017.18i | −0.690807 | − | 0.0915281i | ||||
\(499\) | −10781.9 | − | 18674.7i | −0.967259 | − | 1.67534i | −0.703418 | − | 0.710776i | \(-0.748344\pi\) |
−0.263841 | − | 0.964566i | \(-0.584989\pi\) | |||||||
\(500\) | −315.141 | + | 545.840i | −0.0281870 | + | 0.0488214i | ||||
\(501\) | −8090.04 | − | 6218.35i | −0.721430 | − | 0.554522i | ||||
\(502\) | −617.785 | + | 356.679i | −0.0549265 | + | 0.0317118i | ||||
\(503\) | 518.980 | 0.0460043 | 0.0230021 | − | 0.999735i | \(-0.492678\pi\) | ||||
0.0230021 | + | 0.999735i | \(0.492678\pi\) | |||||||
\(504\) | −4198.43 | − | 10400.7i | −0.371058 | − | 0.919217i | ||||
\(505\) | 873.093 | 0.0769349 | ||||||||
\(506\) | −2681.90 | + | 1548.40i | −0.235623 | + | 0.136037i | ||||
\(507\) | −832.612 | − | 639.981i | −0.0729341 | − | 0.0560603i | ||||
\(508\) | 3226.99 | − | 5589.31i | 0.281840 | − | 0.488160i | ||||
\(509\) | −7798.66 | − | 13507.7i | −0.679115 | − | 1.17626i | −0.975248 | − | 0.221115i | \(-0.929030\pi\) |
0.296133 | − | 0.955147i | \(-0.404303\pi\) | |||||||
\(510\) | −4862.87 | − | 644.303i | −0.422219 | − | 0.0559416i | ||||
\(511\) | −3906.81 | + | 9238.43i | −0.338214 | + | 0.799773i | ||||
\(512\) | 637.807i | 0.0550534i | ||||||||
\(513\) | 1649.98 | + | 12777.9i | 0.142005 | + | 1.09972i | ||||
\(514\) | −659.567 | − | 380.801i | −0.0565998 | − | 0.0326779i | ||||
\(515\) | 4538.01 | + | 2620.02i | 0.388289 | + | 0.224179i | ||||
\(516\) | −541.472 | + | 223.760i | −0.0461956 | + | 0.0190901i | ||||
\(517\) | − | 13393.1i | − | 1.13932i | ||||||
\(518\) | 2851.16 | − | 6742.13i | 0.241839 | − | 0.571877i | ||||
\(519\) | 132.722 | − | 1001.72i | 0.0112251 | − | 0.0847214i | ||||
\(520\) | −2504.57 | − | 4338.05i | −0.211217 | − | 0.365838i | ||||
\(521\) | 10040.4 | − | 17390.5i | 0.844298 | − | 1.46237i | −0.0419318 | − | 0.999120i | \(-0.513351\pi\) |
0.886230 | − | 0.463246i | \(-0.153315\pi\) | |||||||
\(522\) | −6037.08 | + | 6017.13i | −0.506199 | + | 0.504526i | ||||
\(523\) | −17771.4 | + | 10260.3i | −1.48583 | + | 0.857844i | −0.999870 | − | 0.0161368i | \(-0.994863\pi\) |
−0.485960 | + | 0.873981i | \(0.661530\pi\) | |||||||
\(524\) | 11757.1 | 0.980174 | ||||||||
\(525\) | 1185.78 | + | 2093.33i | 0.0985750 | + | 0.174020i | ||||
\(526\) | 8564.97 | 0.709982 | ||||||||
\(527\) | −13557.6 | + | 7827.49i | −1.12064 | + | 0.647003i | ||||
\(528\) | −320.735 | + | 417.275i | −0.0264360 | + | 0.0343931i | ||||
\(529\) | −5592.70 | + | 9686.85i | −0.459662 | + | 0.796157i | ||||
\(530\) | −1986.32 | − | 3440.41i | −0.162793 | − | 0.281965i | ||||
\(531\) | 11975.5 | + | 3230.07i | 0.978703 | + | 0.263979i | ||||
\(532\) | 8510.47 | − | 1056.59i | 0.693564 | − | 0.0861067i | ||||
\(533\) | − | 8296.53i | − | 0.674226i | ||||||
\(534\) | −3546.85 | − | 8582.94i | −0.287429 | − | 0.695543i | ||||
\(535\) | −6725.86 | − | 3883.18i | −0.543522 | − | 0.313803i | ||||
\(536\) | 16162.8 | + | 9331.57i | 1.30247 | + | 0.751983i | ||||
\(537\) | −9398.28 | − | 22742.7i | −0.755243 | − | 1.82759i | ||||
\(538\) | 2387.07i | 0.191290i | ||||||||
\(539\) | −18964.2 | − | 5382.69i | −1.51549 | − | 0.430147i | ||||
\(540\) | 1361.68 | − | 3264.43i | 0.108513 | − | 0.260146i | ||||
\(541\) | 2325.89 | + | 4028.56i | 0.184839 | + | 0.320150i | 0.943522 | − | 0.331309i | \(-0.107490\pi\) |
−0.758683 | + | 0.651460i | \(0.774157\pi\) | |||||||
\(542\) | 567.149 | − | 982.331i | 0.0449468 | − | 0.0778501i | ||||
\(543\) | 9385.52 | − | 12210.5i | 0.741752 | − | 0.965016i | ||||
\(544\) | 17348.7 | − | 10016.3i | 1.36732 | − | 0.789420i | ||||
\(545\) | 2747.21 | 0.215922 | ||||||||
\(546\) | −7391.89 | − | 60.6743i | −0.579384 | − | 0.00475571i | ||||
\(547\) | 2762.10 | 0.215903 | 0.107951 | − | 0.994156i | \(-0.465571\pi\) | ||||
0.107951 | + | 0.994156i | \(0.465571\pi\) | |||||||
\(548\) | 7809.40 | − | 4508.76i | 0.608761 | − | 0.351468i | ||||
\(549\) | −5471.43 | − | 5489.57i | −0.425346 | − | 0.426756i | ||||
\(550\) | −1235.54 | + | 2140.02i | −0.0957883 | + | 0.165910i | ||||
\(551\) | −8428.57 | − | 14598.7i | −0.651668 | − | 1.12872i | ||||
\(552\) | −479.623 | + | 3619.95i | −0.0369821 | + | 0.279122i | ||||
\(553\) | 5187.01 | − | 3919.65i | 0.398868 | − | 0.301411i | ||||
\(554\) | 9350.36i | 0.717074i | ||||||||
\(555\) | 5518.38 | − | 2280.44i | 0.422058 | − | 0.174413i | ||||
\(556\) | −5730.89 | − | 3308.73i | −0.437130 | − | 0.252377i | ||||
\(557\) | −7775.02 | − | 4488.91i | −0.591451 | − | 0.341474i | 0.174220 | − | 0.984707i | \(-0.444260\pi\) |
−0.765671 | + | 0.643233i | \(0.777593\pi\) | |||||||
\(558\) | 1703.19 | + | 6398.72i | 0.129215 | + | 0.485447i | ||||
\(559\) | 998.770i | 0.0755697i | ||||||||
\(560\) | −150.305 | − | 63.5622i | −0.0113421 | − | 0.00479642i | ||||
\(561\) | 32501.8 | + | 4306.31i | 2.44604 | + | 0.324087i | ||||
\(562\) | −2862.63 | − | 4958.22i | −0.214862 | − | 0.372153i | ||||
\(563\) | −8779.23 | + | 15206.1i | −0.657194 | + | 1.13829i | 0.324145 | + | 0.946007i | \(0.394923\pi\) |
−0.981339 | + | 0.192286i | \(0.938410\pi\) | |||||||
\(564\) | −4840.73 | − | 3720.79i | −0.361404 | − | 0.277790i | ||||
\(565\) | 4940.86 | − | 2852.60i | 0.367900 | − | 0.212407i | ||||
\(566\) | 10987.5 | 0.815970 | ||||||||
\(567\) | −8104.08 | − | 10798.5i | −0.600246 | − | 0.799816i | ||||
\(568\) | −10570.5 | −0.780857 | ||||||||
\(569\) | −9424.90 | + | 5441.47i | −0.694398 | + | 0.400911i | −0.805257 | − | 0.592925i | \(-0.797973\pi\) |
0.110860 | + | 0.993836i | \(0.464640\pi\) | |||||||
\(570\) | −3253.32 | − | 2500.64i | −0.239064 | − | 0.183755i | ||||
\(571\) | −3875.05 | + | 6711.78i | −0.284003 | + | 0.491907i | −0.972367 | − | 0.233458i | \(-0.924996\pi\) |
0.688364 | + | 0.725365i | \(0.258329\pi\) | |||||||
\(572\) | 6471.73 | + | 11209.4i | 0.473071 | + | 0.819384i | ||||
\(573\) | 3290.73 | + | 436.004i | 0.239917 | + | 0.0317876i | ||||
\(574\) | 3566.99 | + | 4720.32i | 0.259378 | + | 0.343244i | ||||
\(575\) | − | 783.260i | − | 0.0568073i | ||||||
\(576\) | −2081.54 | − | 7820.14i | −0.150574 | − | 0.565693i | ||||
\(577\) | −5455.78 | − | 3149.90i | −0.393635 | − | 0.227265i | 0.290099 | − | 0.956997i | \(-0.406312\pi\) |
−0.683734 | + | 0.729731i | \(0.739645\pi\) | |||||||
\(578\) | −10633.6 | − | 6139.32i | −0.765226 | − | 0.441803i | ||||
\(579\) | −7564.06 | + | 3125.81i | −0.542922 | + | 0.224359i | ||||
\(580\) | 4627.80i | 0.331308i | ||||||||
\(581\) | 1977.40 | + | 15927.3i | 0.141198 | + | 1.13731i | ||||
\(582\) | −379.770 | + | 2866.31i | −0.0270480 | + | 0.204145i | ||||
\(583\) | 13275.9 | + | 22994.5i | 0.943108 | + | 1.63351i | ||||
\(584\) | −6074.08 | + | 10520.6i | −0.430389 | + | 0.745456i | ||||
\(585\) | −4256.56 | − | 4270.68i | −0.300833 | − | 0.301830i | ||||
\(586\) | −9696.08 | + | 5598.03i | −0.683518 | + | 0.394629i | ||||
\(587\) | −5755.97 | −0.404727 | −0.202363 | − | 0.979311i | \(-0.564862\pi\) | ||||
−0.202363 | + | 0.979311i | \(0.564862\pi\) | |||||||
\(588\) | −7214.04 | + | 5358.96i | −0.505956 | + | 0.375850i | ||||
\(589\) | −13095.3 | −0.916102 | ||||||||
\(590\) | −3421.05 | + | 1975.14i | −0.238716 | + | 0.137823i | ||||
\(591\) | −1032.14 | + | 1342.81i | −0.0718388 | + | 0.0934619i | ||||
\(592\) | −202.511 | + | 350.760i | −0.0140594 | + | 0.0243516i | ||||
\(593\) | 4828.15 | + | 8362.60i | 0.334348 | + | 0.579108i | 0.983359 | − | 0.181671i | \(-0.0581506\pi\) |
−0.649011 | + | 0.760779i | \(0.724817\pi\) | |||||||
\(594\) | 5338.57 | − | 12798.5i | 0.368762 | − | 0.884056i | ||||
\(595\) | 1252.52 | + | 10088.7i | 0.0862999 | + | 0.695119i | ||||
\(596\) | 4341.32i | 0.298368i | ||||||||
\(597\) | 1206.54 | + | 2919.68i | 0.0827144 | + | 0.200158i | ||||
\(598\) | 2084.19 | + | 1203.31i | 0.142523 | + | 0.0822859i | ||||
\(599\) | −13639.2 | − | 7874.61i | −0.930356 | − | 0.537141i | −0.0434321 | − | 0.999056i | \(-0.513829\pi\) |
−0.886924 | + | 0.461915i | \(0.847163\pi\) | |||||||
\(600\) | 1112.82 | + | 2692.89i | 0.0757180 | + | 0.183228i | ||||
\(601\) | − | 11309.8i | − | 0.767612i | −0.923414 | − | 0.383806i | \(-0.874613\pi\) | ||
0.923414 | − | 0.383806i | \(-0.125387\pi\) | |||||||
\(602\) | −429.408 | − | 568.251i | −0.0290721 | − | 0.0384721i | ||||
\(603\) | 21690.3 | + | 5850.40i | 1.46484 | + | 0.395102i | ||||
\(604\) | 8006.90 | + | 13868.4i | 0.539398 | + | 0.934264i | ||||
\(605\) | 4930.44 | − | 8539.77i | 0.331324 | − | 0.573869i | ||||
\(606\) | 950.972 | − | 1237.21i | 0.0637469 | − | 0.0829344i | ||||
\(607\) | 3.66243 | − | 2.11451i | 0.000244899 | − | 0.000141392i | −0.499878 | − | 0.866096i | \(-0.666622\pi\) |
0.500122 | + | 0.865955i | \(0.333288\pi\) | |||||||
\(608\) | 16757.2 | 1.11775 | ||||||||
\(609\) | 15225.2 | + | 8957.67i | 1.01306 | + | 0.596032i | ||||
\(610\) | 2468.44 | 0.163843 | ||||||||
\(611\) | −9013.74 | + | 5204.09i | −0.596820 | + | 0.344574i | ||||
\(612\) | 10586.0 | − | 10551.0i | 0.699202 | − | 0.696892i | ||||
\(613\) | 10682.8 | − | 18503.2i | 0.703876 | − | 1.21915i | −0.263220 | − | 0.964736i | \(-0.584784\pi\) |
0.967096 | − | 0.254413i | \(-0.0818822\pi\) | |||||||
\(614\) | 2273.10 | + | 3937.12i | 0.149405 | + | 0.258777i | ||||
\(615\) | −633.879 | + | 4784.20i | −0.0415618 | + | 0.313687i | ||||
\(616\) | −21989.7 | − | 9299.17i | −1.43830 | − | 0.608237i | ||||
\(617\) | 28128.0i | 1.83532i | 0.397369 | + | 0.917659i | \(0.369923\pi\) | ||||
−0.397369 | + | 0.917659i | \(0.630077\pi\) | |||||||
\(618\) | 8655.49 | − | 3576.83i | 0.563390 | − | 0.232818i | ||||
\(619\) | 13355.4 | + | 7710.75i | 0.867204 | + | 0.500681i | 0.866418 | − | 0.499319i | \(-0.166416\pi\) |
0.000786155 | 1.00000i | \(0.499750\pi\) | ||||||||
\(620\) | 3113.43 | + | 1797.54i | 0.201674 | + | 0.116437i | ||||
\(621\) | 562.912 | + | 4359.34i | 0.0363750 | + | 0.281698i | ||||
\(622\) | − | 4804.64i | − | 0.309724i | ||||||
\(623\) | −15355.5 | + | 11603.6i | −0.987489 | + | 0.746212i | ||||
\(624\) | 405.459 | + | 53.7211i | 0.0260118 | + | 0.00344642i | ||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −5605.77 | + | 9709.49i | −0.357910 | + | 0.619919i | ||||
\(627\) | 21744.1 | + | 16713.5i | 1.38497 | + | 1.06455i | ||||
\(628\) | 5122.07 | − | 2957.23i | 0.325466 | − | 0.187908i | ||||
\(629\) | 25231.0 | 1.59941 | ||||||||
\(630\) | 4257.90 | + | 599.750i | 0.269268 | + | 0.0379279i | ||||
\(631\) | −15008.7 | −0.946886 | −0.473443 | − | 0.880824i | \(-0.656989\pi\) | ||||
−0.473443 | + | 0.880824i | \(0.656989\pi\) | |||||||
\(632\) | 6819.09 | − | 3937.00i | 0.429191 | − | 0.247794i | ||||
\(633\) | −13658.4 | − | 10498.4i | −0.857618 | − | 0.659202i | ||||
\(634\) | −2639.15 | + | 4571.15i | −0.165322 | + | 0.286346i | ||||
\(635\) | 3199.95 | + | 5542.47i | 0.199978 | + | 0.346372i | ||||
\(636\) | 11999.3 | + | 1589.84i | 0.748118 | + | 0.0991215i | ||||
\(637\) | 3746.21 | + | 14854.8i | 0.233015 | + | 0.923967i | ||||
\(638\) | 18143.7i | 1.12589i | ||||||||
\(639\) | −12295.9 | + | 3272.88i | −0.761218 | + | 0.202618i | ||||
\(640\) | −4089.02 | − | 2360.80i | −0.252551 | − | 0.145810i | ||||
\(641\) | −5560.90 | − | 3210.59i | −0.342656 | − | 0.197832i | 0.318790 | − | 0.947825i | \(-0.396723\pi\) |
−0.661446 | + | 0.749993i | \(0.730057\pi\) | |||||||
\(642\) | −12828.4 | + | 5301.28i | −0.788627 | + | 0.325896i | ||||
\(643\) | 1853.26i | 0.113663i | 0.998384 | + | 0.0568316i | \(0.0180998\pi\) | ||||
−0.998384 | + | 0.0568316i | \(0.981900\pi\) | |||||||
\(644\) | 2903.46 | − | 360.468i | 0.177659 | − | 0.0220566i | ||||
\(645\) | 76.3090 | − | 575.941i | 0.00465839 | − | 0.0351592i | ||||
\(646\) | −8669.49 | − | 15016.0i | −0.528013 | − | 0.914546i | ||||
\(647\) | −807.258 | + | 1398.21i | −0.0490519 | + | 0.0849604i | −0.889509 | − | 0.456918i | \(-0.848953\pi\) |
0.840457 | + | 0.541878i | \(0.182287\pi\) | |||||||
\(648\) | −8128.89 | − | 14187.9i | −0.492798 | − | 0.860113i | ||||
\(649\) | 22865.2 | − | 13201.2i | 1.38295 | − | 0.798449i | ||||
\(650\) | 1920.35 | 0.115881 | ||||||||
\(651\) | 11940.2 | − | 6763.62i | 0.718853 | − | 0.407200i | ||||
\(652\) | 4292.53 | 0.257835 | ||||||||
\(653\) | 23827.4 | − | 13756.8i | 1.42793 | − | 0.824416i | 0.430973 | − | 0.902365i | \(-0.358171\pi\) |
0.996957 | + | 0.0779494i | \(0.0248373\pi\) | |||||||
\(654\) | 2992.26 | − | 3892.91i | 0.178909 | − | 0.232760i | ||||
\(655\) | −5829.29 | + | 10096.6i | −0.347739 | + | 0.602302i | ||||
\(656\) | −163.678 | − | 283.498i | −0.00974169 | − | 0.0168731i | ||||
\(657\) | −3808.12 | + | 14118.6i | −0.226132 | + | 0.838385i | ||||
\(658\) | 2890.95 | − | 6836.21i | 0.171278 | − | 0.405020i | ||||
\(659\) | 26973.3i | 1.59443i | 0.603694 | + | 0.797216i | \(0.293695\pi\) | ||||
−0.603694 | + | 0.797216i | \(0.706305\pi\) | |||||||
\(660\) | −2875.50 | − | 6958.35i | −0.169589 | − | 0.410384i | ||||
\(661\) | 2260.12 | + | 1304.88i | 0.132993 | + | 0.0767837i | 0.565021 | − | 0.825077i | \(-0.308868\pi\) |
−0.432027 | + | 0.901861i | \(0.642202\pi\) | |||||||
\(662\) | 9151.18 | + | 5283.44i | 0.537267 | + | 0.310191i | ||||
\(663\) | −9730.89 | − | 23547.5i | −0.570010 | − | 1.37935i | ||||
\(664\) | 19437.9i | 1.13605i | ||||||||
\(665\) | −3312.22 | + | 7832.39i | −0.193146 | + | 0.456733i | ||||
\(666\) | 2779.13 | − | 10303.6i | 0.161696 | − | 0.599486i | ||||
\(667\) | −2875.52 | − | 4980.54i | −0.166927 | − | 0.289126i | ||||
\(668\) | −4950.77 | + | 8574.98i | −0.286753 | + | 0.496671i | ||||
\(669\) | −14542.9 | + | 18920.2i | −0.840450 | + | 1.09342i | ||||
\(670\) | −6196.31 | + | 3577.44i | −0.357290 | + | 0.206281i | ||||
\(671\) | −16498.2 | −0.949191 | ||||||||
\(672\) | −15279.0 | + | 8654.92i | −0.877085 | + | 0.496831i | ||||
\(673\) | −1477.40 | −0.0846206 | −0.0423103 | − | 0.999105i | \(-0.513472\pi\) | ||||
−0.0423103 | + | 0.999105i | \(0.513472\pi\) | |||||||
\(674\) | 6694.61 | − | 3865.13i | 0.382592 | − | 0.220889i | ||||
\(675\) | 2128.26 | + | 2787.90i | 0.121358 | + | 0.158972i | ||||
\(676\) | −509.524 | + | 882.522i | −0.0289898 | + | 0.0502117i | ||||
\(677\) | −8237.90 | − | 14268.5i | −0.467664 | − | 0.810017i | 0.531654 | − | 0.846962i | \(-0.321571\pi\) |
−0.999317 | + | 0.0369447i | \(0.988237\pi\) | |||||||
\(678\) | 1339.31 | − | 10108.5i | 0.0758644 | − | 0.572586i | ||||
\(679\) | 5946.55 | − | 738.270i | 0.336093 | − | 0.0417264i | ||||
\(680\) | 12312.4i | 0.694351i | ||||||||
\(681\) | 23327.3 | − | 9639.87i | 1.31263 | − | 0.542439i | ||||
\(682\) | 12206.5 | + | 7047.41i | 0.685352 | + | 0.395688i | ||||
\(683\) | −372.803 | − | 215.238i | −0.0208857 | − | 0.0120583i | 0.489521 | − | 0.871992i | \(-0.337172\pi\) |
−0.510406 | + | 0.859933i | \(0.670505\pi\) | |||||||
\(684\) | 12081.7 | − | 3215.86i | 0.675373 | − | 0.179768i | ||||
\(685\) | 8941.95i | 0.498766i | ||||||||
\(686\) | −8518.02 | − | 6840.99i | −0.474081 | − | 0.380744i | ||||
\(687\) | −27559.9 | − | 3651.53i | −1.53053 | − | 0.202787i | ||||
\(688\) | 19.7042 | + | 34.1287i | 0.00109188 | + | 0.00189120i | ||||
\(689\) | 10317.1 | − | 17869.8i | 0.570466 | − | 0.988077i | ||||
\(690\) | −1109.91 | − | 853.127i | −0.0612372 | − | 0.0470695i | ||||
\(691\) | 7713.33 | − | 4453.29i | 0.424644 | − | 0.245168i | −0.272418 | − | 0.962179i | \(-0.587823\pi\) |
0.697062 | + | 0.717011i | \(0.254490\pi\) | |||||||
\(692\) | −980.541 | −0.0538650 | ||||||||
\(693\) | −28458.4 | − | 4008.53i | −1.55995 | − | 0.219728i | ||||
\(694\) | 5959.68 | 0.325974 | ||||||||
\(695\) | 5682.87 | − | 3281.01i | 0.310163 | − | 0.179073i | ||||
\(696\) | 16962.3 | + | 13038.0i | 0.923787 | + | 0.710062i | ||||
\(697\) | −10196.4 | + | 17660.6i | −0.554110 | + | 0.959747i | ||||
\(698\) | 4127.71 | + | 7149.40i | 0.223834 | + | 0.387692i | ||||
\(699\) | −6699.57 | − | 887.655i | −0.362519 | − | 0.0480318i | ||||
\(700\) | 1862.60 | − | 1407.50i | 0.100571 | − | 0.0759980i | ||||
\(701\) | 17716.9i | 0.954579i | 0.878746 | + | 0.477289i | \(0.158381\pi\) | ||||
−0.878746 | + | 0.477289i | \(0.841619\pi\) | |||||||
\(702\) | −10688.0 | + | 1380.12i | −0.574632 | + | 0.0742011i | ||||
\(703\) | 18278.0 | + | 10552.8i | 0.980611 | + | 0.566156i | ||||
\(704\) | −14918.0 | − | 8612.93i | −0.798643 | − | 0.461097i | ||||
\(705\) | 5595.39 | − | 2312.26i | 0.298914 | − | 0.123525i | ||||
\(706\) | 13659.3i | 0.728153i | ||||||||
\(707\) | −2978.59 | − | 1259.61i | −0.158446 | − | 0.0670049i | ||||
\(708\) | 1580.90 | − | 11931.8i | 0.0839177 | − | 0.633368i | ||||
\(709\) | −17844.9 | − | 30908.2i | −0.945245 | − | 1.63721i | −0.755261 | − | 0.655425i | \(-0.772490\pi\) |
−0.189984 | − | 0.981787i | \(-0.560844\pi\) | |||||||
\(710\) | 2026.20 | − | 3509.48i | 0.107101 | − | 0.185505i | ||||
\(711\) | 6713.19 | − | 6691.00i | 0.354099 | − | 0.352929i | ||||
\(712\) | −20187.1 | + | 11655.0i | −1.06256 | + | 0.613469i | ||||
\(713\) | −4467.65 | −0.234663 | ||||||||
\(714\) | 15660.4 | + | 9213.72i | 0.820832 | + | 0.482934i | ||||
\(715\) | −12835.0 | −0.671332 | ||||||||
\(716\) | −20680.0 | + | 11939.6i | −1.07940 | + | 0.623190i | ||||
\(717\) | 5544.52 | − | 7213.39i | 0.288792 | − | 0.375717i | ||||
\(718\) | 9539.13 | − | 16522.2i | 0.495818 | − | 0.858781i | ||||
\(719\) | 182.576 | + | 316.231i | 0.00947001 | + | 0.0164025i | 0.870722 | − | 0.491776i | \(-0.163652\pi\) |
−0.861252 | + | 0.508179i | \(0.830319\pi\) | |||||||
\(720\) | −229.704 | − | 61.9565i | −0.0118897 | − | 0.00320692i | ||||
\(721\) | −11701.7 | − | 15485.3i | −0.604432 | − | 0.799865i | ||||
\(722\) | − | 2707.83i | − | 0.139577i | ||||||
\(723\) | −4226.79 | − | 10228.3i | −0.217422 | − | 0.526133i | ||||
\(724\) | −12942.5 | − | 7472.33i | −0.664368 | − | 0.383573i | ||||
\(725\) | −3974.21 | − | 2294.51i | −0.203584 | − | 0.117539i | ||||
\(726\) | −6730.99 | − | 16288.2i | −0.344091 | − | 0.832658i | ||||
\(727\) | − | 20316.5i | − | 1.03645i | −0.855245 | − | 0.518225i | \(-0.826593\pi\) | ||
0.855245 | − | 0.518225i | \(-0.173407\pi\) | |||||||
\(728\) | 2285.97 | + | 18412.8i | 0.116379 | + | 0.937394i | ||||
\(729\) | −13848.7 | − | 13986.9i | −0.703587 | − | 0.710609i | ||||
\(730\) | −2328.62 | − | 4033.28i | −0.118063 | − | 0.204491i | ||||
\(731\) | 1227.48 | − | 2126.06i | 0.0621067 | − | 0.107572i | ||||
\(732\) | −4583.46 | + | 5963.06i | −0.231434 | + | 0.301094i | ||||
\(733\) | −8355.35 | + | 4823.97i | −0.421026 | + | 0.243079i | −0.695516 | − | 0.718510i | \(-0.744824\pi\) |
0.274490 | + | 0.961590i | \(0.411491\pi\) | |||||||
\(734\) | −7330.54 | −0.368631 | ||||||||
\(735\) | −1025.31 | − | 8852.22i | −0.0514545 | − | 0.444244i | ||||
\(736\) | 5716.94 | 0.286317 | ||||||||
\(737\) | 41414.1 | − | 23910.4i | 2.06989 | − | 1.19505i | ||||
\(738\) | 6089.00 | + | 6109.18i | 0.303711 | + | 0.304718i | ||||
\(739\) | 13850.5 | − | 23989.8i | 0.689446 | − | 1.19416i | −0.282572 | − | 0.959246i | \(-0.591187\pi\) |
0.972017 | − | 0.234909i | \(-0.0754792\pi\) | |||||||
\(740\) | −2897.08 | − | 5017.88i | −0.143917 | − | 0.249272i | ||||
\(741\) | 2799.40 | − | 21128.4i | 0.138783 | − | 1.04747i | ||||
\(742\) | 1812.95 | + | 14602.7i | 0.0896973 | + | 0.722485i | ||||
\(743\) | − | 28617.3i | − | 1.41301i | −0.707709 | − | 0.706504i | \(-0.750271\pi\) | ||
0.707709 | − | 0.706504i | \(-0.249729\pi\) | |||||||
\(744\) | 15360.0 | − | 6347.45i | 0.756890 | − | 0.312781i | ||||
\(745\) | −3728.19 | − | 2152.47i | −0.183343 | − | 0.105853i | ||||
\(746\) | −3116.67 | − | 1799.41i | −0.152962 | − | 0.0883124i | ||||
\(747\) | 6018.47 | + | 22610.8i | 0.294785 | + | 1.10748i | ||||
\(748\) | − | 31814.8i | − | 1.55517i | ||||||
\(749\) | 17343.3 | + | 22951.0i | 0.846076 | + | 1.11964i | ||||
\(750\) | −1107.37 | − | 146.721i | −0.0539140 | − | 0.00714331i | ||||
\(751\) | 13096.8 | + | 22684.3i | 0.636362 | + | 1.10221i | 0.986225 | + | 0.165411i | \(0.0528950\pi\) |
−0.349862 | + | 0.936801i | \(0.613772\pi\) | |||||||
\(752\) | −205.337 | + | 355.655i | −0.00995729 | + | 0.0172465i | ||||
\(753\) | 1708.83 | + | 1313.48i | 0.0827002 | + | 0.0635669i | ||||
\(754\) | 12211.0 | − | 7050.03i | 0.589786 | − | 0.340513i | ||||
\(755\) | −15879.6 | −0.765455 | ||||||||
\(756\) | −9355.00 | + | 9172.26i | −0.450050 | + | 0.441259i | ||||
\(757\) | 31415.1 | 1.50832 | 0.754162 | − | 0.656689i | \(-0.228044\pi\) | ||||
0.754162 | + | 0.656689i | \(0.228044\pi\) | |||||||
\(758\) | −10902.7 | + | 6294.66i | −0.522431 | + | 0.301626i | ||||
\(759\) | 7418.30 | + | 5702.02i | 0.354766 | + | 0.272688i | ||||
\(760\) | −5149.64 | + | 8919.44i | −0.245786 | + | 0.425713i | ||||
\(761\) | −5159.76 | − | 8936.96i | −0.245783 | − | 0.425709i | 0.716568 | − | 0.697517i | \(-0.245712\pi\) |
−0.962352 | + | 0.271808i | \(0.912378\pi\) | |||||||
\(762\) | 11339.3 | + | 1502.40i | 0.539081 | + | 0.0714252i | ||||
\(763\) | −9372.21 | − | 3963.39i | −0.444688 | − | 0.188053i | ||||
\(764\) | − | 3221.18i | − | 0.152537i | ||||||
\(765\) | 3812.22 | + | 14322.2i | 0.180171 | + | 0.676888i | ||||
\(766\) | −4749.65 | − | 2742.21i | −0.224036 | − | 0.129347i | ||||
\(767\) | −17769.3 | − | 10259.1i | −0.836520 | − | 0.482965i | ||||
\(768\) | −19313.8 | + | 7981.31i | −0.907455 | + | 0.375001i | ||||
\(769\) | − | 13235.4i | − | 0.620652i | −0.950630 | − | 0.310326i | \(-0.899562\pi\) | ||
0.950630 | − | 0.310326i | \(-0.100438\pi\) | |||||||
\(770\) | 7302.49 | − | 5518.25i | 0.341771 | − | 0.258265i | ||||
\(771\) | −302.238 | + | 2281.13i | −0.0141178 | + | 0.106554i | ||||
\(772\) | 3971.03 | + | 6878.03i | 0.185130 | + | 0.320655i | ||||
\(773\) | 15411.2 | − | 26693.0i | 0.717080 | − | 1.24202i | −0.245072 | − | 0.969505i | \(-0.578812\pi\) |
0.962152 | − | 0.272514i | \(-0.0878550\pi\) | |||||||
\(774\) | −733.018 | − | 735.448i | −0.0340411 | − | 0.0341539i | ||||
\(775\) | −3087.34 | + | 1782.47i | −0.143097 | + | 0.0826173i | ||||
\(776\) | 7257.25 | 0.335722 | ||||||||
\(777\) | −22116.2 | − | 181.535i | −1.02112 | − | 0.00838161i | ||||
\(778\) | 11562.8 | 0.532837 | ||||||||
\(779\) | −14773.1 | + | 8529.23i | −0.679461 | + | 0.392287i | ||||
\(780\) | −3565.76 | + | 4639.03i | −0.163685 | + | 0.212954i | ||||
\(781\) | −13542.4 | + | 23456.2i | −0.620469 | + | 1.07468i | ||||
\(782\) | −2957.71 | − | 5122.91i | −0.135253 | − | 0.234264i | ||||
\(783\) | 23768.0 | + | 9914.23i | 1.08480 | + | 0.452498i | ||||
\(784\) | 421.072 | + | 433.690i | 0.0191815 | + | 0.0197563i | ||||
\(785\) | 5864.90i | 0.266659i | ||||||||
\(786\) | 7958.10 | + | 19257.6i | 0.361140 | + | 0.873913i | ||||
\(787\) | −17768.5 | − | 10258.6i | −0.804800 | − | 0.464651i | 0.0403468 | − | 0.999186i | \(-0.487154\pi\) |
−0.845147 | + | 0.534534i | \(0.820487\pi\) | |||||||
\(788\) | 1423.31 | + | 821.746i | 0.0643441 | + | 0.0371491i | ||||
\(789\) | −9883.22 | − | 23916.2i | −0.445947 | − | 1.07914i | ||||
\(790\) | 3018.65i | 0.135948i | ||||||||
\(791\) | −20971.4 | + | 2603.62i | −0.942676 | + | 0.117034i | ||||
\(792\) | −33605.7 | − | 9064.26i | −1.50774 | − | 0.406672i | ||||
\(793\) | 6410.65 | + | 11103.6i | 0.287073 | + | 0.497225i | ||||
\(794\) | 10649.8 | − | 18446.1i | 0.476006 | − | 0.824466i | ||||
\(795\) | −7314.68 | + | 9516.36i | −0.326321 | + | 0.424542i | ||||
\(796\) | 2654.88 | − | 1532.79i | 0.118216 | − | 0.0682518i | ||||
\(797\) | −12338.0 | −0.548349 | −0.274175 | − | 0.961680i | \(-0.588405\pi\) | ||||
−0.274175 | + | 0.961680i | \(0.588405\pi\) | |||||||
\(798\) | 7491.17 | + | 13224.6i | 0.332312 | + | 0.586649i | ||||
\(799\) | 25583.1 | 1.13275 | ||||||||
\(800\) | 3950.64 | − | 2280.91i | 0.174595 | − | 0.100803i | ||||
\(801\) | −19873.6 | + | 19807.9i | −0.876652 | + | 0.873755i | ||||
\(802\) | 2379.01 | − | 4120.57i | 0.104745 | − | 0.181424i | ||||
\(803\) | 15563.7 | + | 26957.1i | 0.683974 | + | 1.18468i | ||||
\(804\) | 2863.37 | − | 21611.2i | 0.125601 | − | 0.947971i | ||||
\(805\) | −1130.01 | + | 2672.13i | −0.0494752 | + | 0.116994i | ||||
\(806\) | − | 10953.5i | − | 0.478687i | ||||||
\(807\) | 6665.46 | − | 2754.47i | 0.290750 | − | 0.120151i | ||||
\(808\) | −3391.99 | − | 1958.36i | −0.147685 | − | 0.0852661i | ||||
\(809\) | −9637.68 | − | 5564.32i | −0.418841 | − | 0.241818i | 0.275740 | − | 0.961232i | \(-0.411077\pi\) |
−0.694581 | + | 0.719414i | \(0.744410\pi\) | |||||||
\(810\) | 6268.68 | + | 20.7485i | 0.271924 | + | 0.000900036i | ||||
\(811\) | − | 10747.8i | − | 0.465357i | −0.972554 | − | 0.232679i | \(-0.925251\pi\) | ||
0.972554 | − | 0.232679i | \(-0.0747490\pi\) | |||||||
\(812\) | 6676.52 | − | 15787.9i | 0.288546 | − | 0.682325i | ||||
\(813\) | −3397.42 | − | 450.139i | −0.146559 | − | 0.0194183i | ||||
\(814\) | −11358.3 | − | 19673.1i | −0.489075 | − | 0.847102i | ||||
\(815\) | −2128.28 | + | 3686.29i | −0.0914729 | + | 0.158436i | ||||
\(816\) | −797.068 | − | 612.660i | −0.0341948 | − | 0.0262836i | ||||
\(817\) | 1778.44 | − | 1026.78i | 0.0761564 | − | 0.0439689i | ||||
\(818\) | −11059.1 | −0.472706 | ||||||||
\(819\) | 8360.16 | + | 20710.5i | 0.356688 | + | 0.883620i | ||||
\(820\) | 4683.07 | 0.199439 | ||||||||
\(821\) | 20479.9 | − | 11824.1i | 0.870587 | − | 0.502634i | 0.00304382 | − | 0.999995i | \(-0.499031\pi\) |
0.867543 | + | 0.497362i | \(0.165698\pi\) | |||||||
\(822\) | 12671.1 | + | 9739.57i | 0.537660 | + | 0.413268i | ||||
\(823\) | −11311.0 | + | 19591.2i | −0.479073 | + | 0.829779i | −0.999712 | − | 0.0239982i | \(-0.992360\pi\) |
0.520639 | + | 0.853777i | \(0.325694\pi\) | |||||||
\(824\) | −11753.5 | − | 20357.7i | −0.496910 | − | 0.860673i | ||||
\(825\) | 7401.31 | + | 980.632i | 0.312340 | + | 0.0413833i | ||||
\(826\) | 14520.6 | − | 1802.75i | 0.611666 | − | 0.0759391i | ||||
\(827\) | 39892.0i | 1.67736i | 0.544621 | + | 0.838682i | \(0.316673\pi\) | ||||
−0.544621 | + | 0.838682i | \(0.683327\pi\) | |||||||
\(828\) | 4121.83 | − | 1097.13i | 0.172999 | − | 0.0460483i | ||||
\(829\) | 17056.9 | + | 9847.79i | 0.714608 | + | 0.412579i | 0.812765 | − | 0.582592i | \(-0.197961\pi\) |
−0.0981571 | + | 0.995171i | \(0.531295\pi\) | |||||||
\(830\) | −6453.55 | − | 3725.96i | −0.269887 | − | 0.155819i | ||||
\(831\) | 26109.2 | − | 10789.5i | 1.08991 | − | 0.450401i | ||||
\(832\) | 13386.8i | 0.557815i | ||||||||
\(833\) | 10281.9 | − | 36225.0i | 0.427667 | − | 1.50675i | ||||
\(834\) | 1540.45 | − | 11626.5i | 0.0639586 | − | 0.482727i | ||||
\(835\) | −4909.28 | − | 8503.13i | −0.203464 | − | 0.352411i | ||||
\(836\) | 13306.5 | − | 23047.5i | 0.550496 | − | 0.953488i | ||||
\(837\) | 15902.0 | − | 12139.4i | 0.656693 | − | 0.501313i | ||||
\(838\) | −3261.07 | + | 1882.78i | −0.134429 | + | 0.0776128i | ||||
\(839\) | 14471.2 | 0.595473 | 0.297736 | − | 0.954648i | \(-0.403768\pi\) | ||||
0.297736 | + | 0.954648i | \(0.403768\pi\) | |||||||
\(840\) | 88.5864 | − | 10792.4i | 0.00363871 | − | 0.443301i | ||||
\(841\) | −9305.58 | −0.381548 | ||||||||
\(842\) | −13015.6 | + | 7514.56i | −0.532716 | + | 0.307564i | ||||
\(843\) | −10541.7 | + | 13714.7i | −0.430695 | + | 0.560332i | ||||
\(844\) | −8358.37 | + | 14477.1i | −0.340885 | + | 0.590430i | ||||
\(845\) | −505.255 | − | 875.127i | −0.0205696 | − | 0.0356275i | ||||
\(846\) | 2817.92 | − | 10447.4i | 0.114518 | − | 0.424574i | ||||
\(847\) | −29140.7 | + | 22020.6i | −1.18216 | + | 0.893316i | ||||
\(848\) | − | 814.164i | − | 0.0329700i | ||||||
\(849\) | −12678.6 | − | 30680.6i | −0.512519 | − | 1.24023i | ||||
\(850\) | −4087.81 | − | 2360.10i | −0.164954 | − | 0.0952361i | ||||
\(851\) | 6235.80 | + | 3600.24i | 0.251187 | + | 0.145023i | ||||
\(852\) | 4715.62 | + | 11411.2i | 0.189618 | + | 0.458851i | ||||
\(853\) | 19866.7i | 0.797446i | 0.917071 | + | 0.398723i | \(0.130547\pi\) | ||||
−0.917071 | + | 0.398723i | \(0.869453\pi\) | |||||||
\(854\) | −8421.19 | − | 3561.21i | −0.337432 | − | 0.142696i | ||||
\(855\) | −3228.55 | + | 11969.8i | −0.129139 | + | 0.478783i | ||||
\(856\) | 17420.1 | + | 30172.5i | 0.695569 | + | 1.20476i | ||||
\(857\) | −3508.78 | + | 6077.39i | −0.139857 | + | 0.242240i | −0.927442 | − | 0.373966i | \(-0.877998\pi\) |
0.787585 | + | 0.616206i | \(0.211331\pi\) | |||||||
\(858\) | −13979.9 | + | 18187.8i | −0.556253 | + | 0.723683i | ||||
\(859\) | 25313.0 | − | 14614.5i | 1.00543 | − | 0.580487i | 0.0955821 | − | 0.995422i | \(-0.469529\pi\) |
0.909851 | + | 0.414934i | \(0.136195\pi\) | |||||||
\(860\) | −563.767 | −0.0223538 | ||||||||
\(861\) | 9064.66 | − | 15407.0i | 0.358795 | − | 0.609836i | ||||
\(862\) | 7593.17 | 0.300028 | ||||||||
\(863\) | −37613.6 | + | 21716.2i | −1.48364 | + | 0.856580i | −0.999827 | − | 0.0185910i | \(-0.994082\pi\) |
−0.483813 | + | 0.875171i | \(0.660749\pi\) | |||||||
\(864\) | −20348.6 | + | 15533.9i | −0.801243 | + | 0.611661i | ||||
\(865\) | 486.162 | − | 842.058i | 0.0191098 | − | 0.0330992i | ||||
\(866\) | 9081.70 | + | 15730.0i | 0.356361 | + | 0.617236i | ||||
\(867\) | −4872.71 | + | 36776.7i | −0.190872 | + | 1.44060i | ||||
\(868\) | −8028.28 | − | 10624.1i | −0.313937 | − | 0.415444i | ||||
\(869\) | − | 20175.7i | − | 0.787587i | ||||||
\(870\) | −7580.13 | + | 3132.45i | −0.295391 | + | 0.122069i | ||||
\(871\) | −32184.2 | − | 18581.6i | −1.25203 | − | 0.722861i | ||||
\(872\) | −10673.0 | − | 6162.04i | −0.414486 | − | 0.239304i | ||||
\(873\) | 8441.87 | − | 2247.02i | 0.327278 | − | 0.0871137i | ||||
\(874\) | − | 4948.23i | − | 0.191506i | ||||||
\(875\) | 285.224 | + | 2297.39i | 0.0110198 | + | 0.0887613i | ||||
\(876\) | 14067.1 | + | 1863.81i | 0.542561 | + | 0.0718863i | ||||
\(877\) | 1134.15 | + | 1964.40i | 0.0436687 | + | 0.0756364i | 0.887034 | − | 0.461705i | \(-0.152762\pi\) |
−0.843365 | + | 0.537341i | \(0.819429\pi\) | |||||||
\(878\) | 7873.23 | − | 13636.8i | 0.302629 | − | 0.524170i | ||||
\(879\) | 26819.9 | + | 20614.9i | 1.02914 | + | 0.791040i | ||||
\(880\) | −438.581 | + | 253.215i | −0.0168007 | + | 0.00969986i | ||||
\(881\) | −23261.7 | −0.889566 | −0.444783 | − | 0.895638i | \(-0.646719\pi\) | ||||
−0.444783 | + | 0.895638i | \(0.646719\pi\) | |||||||
\(882\) | −13660.7 | − | 8188.93i | −0.521521 | − | 0.312625i | ||||
\(883\) | 1480.02 | 0.0564062 | 0.0282031 | − | 0.999602i | \(-0.491021\pi\) | ||||
0.0282031 | + | 0.999602i | \(0.491021\pi\) | |||||||
\(884\) | −21411.9 | + | 12362.2i | −0.814660 | + | 0.470344i | ||||
\(885\) | 9462.83 | + | 7273.53i | 0.359423 | + | 0.276268i | ||||
\(886\) | −2910.79 | + | 5041.63i | −0.110372 | + | 0.191170i | ||||
\(887\) | 6182.71 | + | 10708.8i | 0.234042 | + | 0.405372i | 0.958994 | − | 0.283427i | \(-0.0914714\pi\) |
−0.724952 | + | 0.688799i | \(0.758138\pi\) | |||||||
\(888\) | −26554.1 | − | 3518.27i | −1.00349 | − | 0.132957i | ||||
\(889\) | −2920.65 | − | 23524.9i | −0.110186 | − | 0.887516i | ||||
\(890\) | − | 8936.35i | − | 0.336570i | ||||||
\(891\) | −41897.8 | − | 138.676i | −1.57534 | − | 0.00521418i | ||||
\(892\) | 20054.4 | + | 11578.4i | 0.752770 | + | 0.434612i | ||||
\(893\) | 18533.1 | + | 10700.1i | 0.694499 | + | 0.400969i | ||||
\(894\) | −7110.88 | + | 2938.53i | −0.266022 | + | 0.109932i | ||||
\(895\) | − | 23679.1i | − | 0.884364i | ||||||
\(896\) | 10544.0 | + | 13953.2i | 0.393135 | + | 0.520249i | ||||
\(897\) | 955.052 | − | 7208.24i | 0.0355499 | − | 0.268312i | ||||
\(898\) | −7347.37 | − | 12726.0i | −0.273034 | − | 0.472910i | ||||
\(899\) | −13087.7 | + | 22668.6i | −0.485539 | + | 0.840978i | ||||
\(900\) | 2410.63 | − | 2402.67i | 0.0892826 | − | 0.0889876i | ||||
\(901\) | −43923.6 | + | 25359.3i | −1.62409 | + | 0.937671i | ||||
\(902\) | 18360.4 | 0.677755 | ||||||||
\(903\) | −1091.24 | + | 1854.76i | −0.0402151 | + | 0.0683527i | ||||
\(904\) | −25593.8 | −0.941634 | ||||||||
\(905\) | 12834.0 | − | 7409.72i | 0.471400 | − | 0.272163i | ||||
\(906\) | −17296.1 | + | 22502.1i | −0.634242 | + | 0.825146i | ||||
\(907\) | 10238.6 | − | 17733.8i | 0.374827 | − | 0.649220i | −0.615474 | − | 0.788157i | \(-0.711035\pi\) |
0.990301 | + | 0.138937i | \(0.0443686\pi\) | |||||||
\(908\) | −12246.5 | − | 21211.6i | −0.447594 | − | 0.775255i | ||||
\(909\) | −4552.03 | − | 1227.79i | −0.166096 | − | 0.0448000i | ||||
\(910\) | −6551.37 | − | 2770.49i | −0.238655 | − | 0.100924i | ||||
\(911\) | − | 5201.00i | − | 0.189151i | −0.995518 | − | 0.0945756i | \(-0.969851\pi\) | ||
0.995518 | − | 0.0945756i | \(-0.0301494\pi\) | |||||||
\(912\) | −321.174 | − | 777.201i | −0.0116613 | − | 0.0282190i | ||||
\(913\) | 43133.4 | + | 24903.1i | 1.56353 | + | 0.902707i | ||||
\(914\) | 22365.3 | + | 12912.6i | 0.809384 | + | 0.467298i | ||||
\(915\) | −2848.36 | − | 6892.67i | −0.102911 | − | 0.249033i | ||||
\(916\) | 26977.3i | 0.973095i | ||||||||
\(917\) | 34453.3 | − | 26035.2i | 1.24073 | − | 0.937576i | ||||
\(918\) | 24447.4 | + | 10197.6i | 0.878959 | + | 0.366636i | ||||
\(919\) | 7336.39 | + | 12707.0i | 0.263336 | + | 0.456110i | 0.967126 | − | 0.254297i | \(-0.0818440\pi\) |
−0.703791 | + | 0.710407i | \(0.748511\pi\) | |||||||
\(920\) | −1756.87 | + | 3042.98i | −0.0629589 | + | 0.109048i | ||||
\(921\) | 8370.76 | − | 10890.3i | 0.299485 | − | 0.389629i | ||||
\(922\) | −7738.67 | + | 4467.92i | −0.276420 | + | 0.159591i | ||||
\(923\) | 21048.5 | 0.750618 | ||||||||
\(924\) | −228.904 | + | 27887.2i | −0.00814978 | + | 0.992880i | ||||
\(925\) | 5745.60 | 0.204232 | ||||||||
\(926\) | 8735.99 | − | 5043.72i | 0.310024 | − | 0.178992i | ||||
\(927\) | −19975.3 | − | 20041.6i | −0.707741 | − | 0.710088i | ||||
\(928\) | 16747.4 | − | 29007.3i | 0.592414 | − | 1.02609i | ||||
\(929\) | 19941.3 | + | 34539.4i | 0.704256 | + | 1.21981i | 0.966959 | + | 0.254930i | \(0.0820525\pi\) |
−0.262704 | + | 0.964877i | \(0.584614\pi\) | |||||||
\(930\) | −836.882 | + | 6316.36i | −0.0295080 | + | 0.222711i | ||||
\(931\) | 22599.5 | − | 21942.0i | 0.795564 | − | 0.772417i | ||||
\(932\) | 6557.95i | 0.230486i | ||||||||
\(933\) | −13416.1 | + | 5544.12i | −0.470764 | + | 0.194541i | ||||
\(934\) | 3145.58 | + | 1816.10i | 0.110200 | + | 0.0636237i | ||||
\(935\) | 27321.6 | + | 15774.1i | 0.955627 | + | 0.551731i | ||||
\(936\) | 6957.65 | + | 26139.2i | 0.242968 | + | 0.912808i | ||||
\(937\) | 7011.20i | 0.244446i | 0.992503 | + | 0.122223i | \(0.0390023\pi\) | ||||
−0.992503 | + | 0.122223i | \(0.960998\pi\) | |||||||
\(938\) | 26300.1 | − | 3265.19i | 0.915490 | − | 0.113659i | ||||
\(939\) | 33580.6 | + | 4449.24i | 1.16705 | + | 0.154628i | ||||
\(940\) | −2937.51 | − | 5087.91i | −0.101926 | − | 0.176542i | ||||
\(941\) | 28387.5 | − | 49168.6i | 0.983428 | − | 1.70335i | 0.334704 | − | 0.942323i | \(-0.391364\pi\) |
0.648724 | − | 0.761024i | \(-0.275303\pi\) | |||||||
\(942\) | 8310.81 | + | 6388.04i | 0.287453 | + | 0.220949i | ||||
\(943\) | −5040.03 | + | 2909.86i | −0.174046 | + | 0.100486i | ||||
\(944\) | −809.584 | −0.0279128 | ||||||||
\(945\) | −3238.54 | − | 12581.5i | −0.111481 | − | 0.433096i | ||||
\(946\) | −2210.30 | −0.0759652 | ||||||||
\(947\) | 507.141 | − | 292.798i | 0.0174022 | − | 0.0100472i | −0.491274 | − | 0.871005i | \(-0.663469\pi\) |
0.508676 | + | 0.860958i | \(0.330135\pi\) | |||||||
\(948\) | −7292.22 | − | 5605.11i | −0.249831 | − | 0.192031i | ||||
\(949\) | 12095.1 | − | 20949.2i | 0.413722 | − | 0.716587i | ||||
\(950\) | −1974.21 | − | 3419.44i | −0.0674231 | − | 0.116780i | ||||
\(951\) | 15809.5 | + | 2094.66i | 0.539071 | + | 0.0714239i | ||||
\(952\) | 17763.1 | − | 42004.2i | 0.604731 | − | 1.43001i | ||||
\(953\) | 19659.9i | 0.668256i | 0.942528 | + | 0.334128i | \(0.108442\pi\) | ||||
−0.942528 | + | 0.334128i | \(0.891558\pi\) | |||||||
\(954\) | 5517.95 | + | 20730.4i | 0.187264 | + | 0.703535i | ||||
\(955\) | 2766.24 | + | 1597.09i | 0.0937315 | + | 0.0541159i | ||||
\(956\) | −7645.79 | − | 4414.30i | −0.258664 | − | 0.149339i | ||||
\(957\) | 50663.1 | − | 20936.2i | 1.71129 | − | 0.707181i | ||||
\(958\) | − | 9330.40i | − | 0.314668i | ||||||
\(959\) | 12900.5 | − | 30505.9i | 0.434390 | − | 1.02720i | ||||
\(960\) | 1022.79 | − | 7719.48i | 0.0343858 | − | 0.259526i | ||||
\(961\) | −4728.41 | − | 8189.85i | −0.158719 | − | 0.274910i | ||||
\(962\) | −8826.87 | + | 15288.6i | −0.295831 | + | 0.512395i | ||||
\(963\) | 29605.8 | + | 29703.9i | 0.990688 | + | 0.993972i | ||||
\(964\) | −9300.63 | + | 5369.72i | −0.310740 | + | 0.179406i | ||||
\(965\) | −7875.52 | −0.262717 | ||||||||
\(966\) | 2555.71 | + | 4511.75i | 0.0851229 | + | 0.150272i | ||||
\(967\) | 3382.88 | 0.112498 | 0.0562492 | − | 0.998417i | \(-0.482086\pi\) | ||||
0.0562492 | + | 0.998417i | \(0.482086\pi\) | |||||||
\(968\) | −38309.7 | + | 22118.1i | −1.27203 | + | 0.734405i | ||||
\(969\) | −31925.7 | + | 41535.1i | −1.05841 | + | 1.37699i | ||||
\(970\) | −1391.10 | + | 2409.46i | −0.0460471 | + | 0.0797559i | ||||
\(971\) | 23213.3 | + | 40206.6i | 0.767199 | + | 1.32883i | 0.939076 | + | 0.343709i | \(0.111683\pi\) |
−0.171877 | + | 0.985118i | \(0.554983\pi\) | |||||||
\(972\) | −11690.0 | + | 15104.8i | −0.385757 | + | 0.498444i | ||||
\(973\) | −24120.9 | + | 2994.63i | −0.794737 | + | 0.0986675i | ||||
\(974\) | − | 17524.7i | − | 0.576516i | ||||||
\(975\) | −2215.92 | − | 5362.24i | −0.0727858 | − | 0.176132i | ||||
\(976\) | 438.113 | + | 252.945i | 0.0143685 | + | 0.00829566i | ||||
\(977\) | 6254.69 | + | 3611.14i | 0.204816 | + | 0.118251i | 0.598900 | − | 0.800824i | \(-0.295605\pi\) |
−0.394084 | + | 0.919074i | \(0.628938\pi\) | |||||||
\(978\) | 2905.51 | + | 7030.97i | 0.0949979 | + | 0.229883i | ||||
\(979\) | 59727.6i | 1.94985i | ||||||||
\(980\) | −8384.93 | + | 2114.59i | −0.273313 | + | 0.0689267i | ||||
\(981\) | −14323.1 | − | 3863.27i | −0.466157 | − | 0.125734i | ||||
\(982\) | −5158.35 | − | 8934.53i | −0.167627 | − | 0.290338i | ||||
\(983\) | 2487.41 | − | 4308.32i | 0.0807080 | − | 0.139790i | −0.822846 | − | 0.568264i | \(-0.807615\pi\) |
0.903554 | + | 0.428474i | \(0.140949\pi\) | |||||||
\(984\) | 13193.7 | − | 17164.9i | 0.427439 | − | 0.556095i | ||||
\(985\) | −1411.38 | + | 814.860i | −0.0456551 | + | 0.0263590i | ||||
\(986\) | −34657.7 | −1.11940 | ||||||||
\(987\) | −22424.8 | − | 184.068i | −0.723191 | − | 0.00593611i | ||||
\(988\) | −20681.8 | −0.665968 | ||||||||
\(989\) | 606.739 | − | 350.301i | 0.0195078 | − | 0.0112628i | ||||
\(990\) | 9451.11 | − | 9419.88i | 0.303410 | − | 0.302407i | ||||
\(991\) | 14642.5 | − | 25361.6i | 0.469359 | − | 0.812954i | −0.530027 | − | 0.847981i | \(-0.677818\pi\) |
0.999386 | + | 0.0350269i | \(0.0111517\pi\) | |||||||
\(992\) | −13010.1 | − | 22534.2i | −0.416402 | − | 0.721230i | ||||
\(993\) | 4193.40 | − | 31649.7i | 0.134012 | − | 1.01145i | ||||
\(994\) | −11975.6 | + | 9049.54i | −0.382135 | + | 0.288767i | ||||
\(995\) | 3039.90i | 0.0968556i | ||||||||
\(996\) | 20984.0 | − | 8671.51i | 0.667573 | − | 0.275871i | ||||
\(997\) | −655.300 | − | 378.338i | −0.0208160 | − | 0.0120181i | 0.489556 | − | 0.871972i | \(-0.337159\pi\) |
−0.510372 | + | 0.859954i | \(0.670492\pi\) | |||||||
\(998\) | −32117.0 | − | 18542.8i | −1.01868 | − | 0.588137i | ||||
\(999\) | −31977.9 | + | 4129.24i | −1.01275 | + | 0.130774i |
(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 | 105.4.s.a.101.11 | yes | 32 | |
3.2 | odd | 2 | 105.4.s.b.101.6 | yes | 32 | ||
7.5 | odd | 6 | 105.4.s.b.26.6 | yes | 32 | ||
21.5 | even | 6 | inner | 105.4.s.a.26.11 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.s.a.26.11 | ✓ | 32 | 21.5 | even | 6 | inner | |
105.4.s.a.101.11 | yes | 32 | 1.1 | even | 1 | trivial | |
105.4.s.b.26.6 | yes | 32 | 7.5 | odd | 6 | ||
105.4.s.b.101.6 | yes | 32 | 3.2 | odd | 2 |