Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(59,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.59");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 59.14 | ||
Character | \(\chi\) | \(=\) | 60.59 |
Dual form | 60.4.h.c.59.16 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.43885 | − | 2.43510i | 0.508712 | − | 0.860937i | ||||
\(3\) | 5.17582 | − | 0.459239i | 0.996087 | − | 0.0883806i | ||||
\(4\) | −3.85940 | − | 7.00750i | −0.482425 | − | 0.875937i | ||||
\(5\) | −8.70218 | − | 7.01941i | −0.778346 | − | 0.627835i | ||||
\(6\) | 6.32895 | − | 13.2644i | 0.430631 | − | 0.902528i | ||||
\(7\) | 7.71743 | 0.416702 | 0.208351 | − | 0.978054i | \(-0.433190\pi\) | ||||
0.208351 | + | 0.978054i | \(0.433190\pi\) | |||||||
\(8\) | −22.6171 | − | 0.684751i | −0.999542 | − | 0.0302620i | ||||
\(9\) | 26.5782 | − | 4.75387i | 0.984378 | − | 0.176069i | ||||
\(10\) | −29.6141 | + | 11.0907i | −0.936480 | + | 0.350720i | ||||
\(11\) | 38.0843 | 1.04389 | 0.521947 | − | 0.852978i | \(-0.325206\pi\) | ||||
0.521947 | + | 0.852978i | \(0.325206\pi\) | |||||||
\(12\) | −23.1937 | − | 34.4972i | −0.557953 | − | 0.829873i | ||||
\(13\) | 63.3095i | 1.35068i | 0.737505 | + | 0.675342i | \(0.236004\pi\) | ||||
−0.737505 | + | 0.675342i | \(0.763996\pi\) | |||||||
\(14\) | 11.1043 | − | 18.7927i | 0.211981 | − | 0.358754i | ||||
\(15\) | −48.2645 | − | 32.3348i | −0.830789 | − | 0.556588i | ||||
\(16\) | −34.2101 | + | 54.0895i | −0.534532 | + | 0.845148i | ||||
\(17\) | −10.2873 | −0.146767 | −0.0733834 | − | 0.997304i | \(-0.523380\pi\) | ||||
−0.0733834 | + | 0.997304i | \(0.523380\pi\) | |||||||
\(18\) | 26.6660 | − | 71.5606i | 0.349180 | − | 0.937056i | ||||
\(19\) | − | 99.5136i | − | 1.20158i | −0.799408 | − | 0.600789i | \(-0.794853\pi\) | ||
0.799408 | − | 0.600789i | \(-0.205147\pi\) | |||||||
\(20\) | −15.6033 | + | 88.0712i | −0.174451 | + | 0.984666i | ||||
\(21\) | 39.9440 | − | 3.54414i | 0.415072 | − | 0.0368284i | ||||
\(22\) | 54.7977 | − | 92.7389i | 0.531041 | − | 0.898727i | ||||
\(23\) | 133.054i | 1.20625i | 0.797646 | + | 0.603125i | \(0.206078\pi\) | ||||
−0.797646 | + | 0.603125i | \(0.793922\pi\) | |||||||
\(24\) | −117.376 | + | 6.84249i | −0.998305 | + | 0.0581965i | ||||
\(25\) | 26.4557 | + | 122.168i | 0.211646 | + | 0.977346i | ||||
\(26\) | 154.165 | + | 91.0931i | 1.16285 | + | 0.687109i | ||||
\(27\) | 135.381 | − | 36.8109i | 0.964965 | − | 0.262380i | ||||
\(28\) | −29.7847 | − | 54.0799i | −0.201028 | − | 0.365005i | ||||
\(29\) | 197.127i | 1.26226i | 0.775677 | + | 0.631130i | \(0.217409\pi\) | ||||
−0.775677 | + | 0.631130i | \(0.782591\pi\) | |||||||
\(30\) | −148.184 | + | 71.0036i | −0.901819 | + | 0.432114i | ||||
\(31\) | − | 13.9516i | − | 0.0808315i | −0.999183 | − | 0.0404158i | \(-0.987132\pi\) | ||
0.999183 | − | 0.0404158i | \(-0.0128682\pi\) | |||||||
\(32\) | 82.4899 | + | 161.132i | 0.455696 | + | 0.890135i | ||||
\(33\) | 197.117 | − | 17.4898i | 1.03981 | − | 0.0922600i | ||||
\(34\) | −14.8019 | + | 25.0506i | −0.0746620 | + | 0.126357i | ||||
\(35\) | −67.1584 | − | 54.1718i | −0.324339 | − | 0.261620i | ||||
\(36\) | −135.889 | − | 167.900i | −0.629114 | − | 0.777313i | ||||
\(37\) | − | 272.667i | − | 1.21152i | −0.795649 | − | 0.605758i | \(-0.792870\pi\) | ||
0.795649 | − | 0.605758i | \(-0.207130\pi\) | |||||||
\(38\) | −242.325 | − | 143.186i | −1.03448 | − | 0.611257i | ||||
\(39\) | 29.0742 | + | 327.678i | 0.119374 | + | 1.34540i | ||||
\(40\) | 192.011 | + | 164.717i | 0.758990 | + | 0.651102i | ||||
\(41\) | − | 166.492i | − | 0.634187i | −0.948394 | − | 0.317094i | \(-0.897293\pi\) | ||
0.948394 | − | 0.317094i | \(-0.102707\pi\) | |||||||
\(42\) | 48.8433 | − | 102.367i | 0.179445 | − | 0.376085i | ||||
\(43\) | −273.302 | −0.969260 | −0.484630 | − | 0.874719i | \(-0.661046\pi\) | ||||
−0.484630 | + | 0.874719i | \(0.661046\pi\) | |||||||
\(44\) | −146.982 | − | 266.875i | −0.503601 | − | 0.914386i | ||||
\(45\) | −264.658 | − | 145.194i | −0.876729 | − | 0.480984i | ||||
\(46\) | 324.000 | + | 191.446i | 1.03851 | + | 0.613634i | ||||
\(47\) | − | 69.1174i | − | 0.214507i | −0.994232 | − | 0.107253i | \(-0.965794\pi\) | ||
0.994232 | − | 0.107253i | \(-0.0342056\pi\) | |||||||
\(48\) | −152.225 | + | 295.668i | −0.457746 | + | 0.889083i | ||||
\(49\) | −283.441 | −0.826359 | ||||||||
\(50\) | 335.558 | + | 111.360i | 0.949100 | + | 0.314974i | ||||
\(51\) | −53.2452 | + | 4.72433i | −0.146193 | + | 0.0129713i | ||||
\(52\) | 443.641 | − | 244.337i | 1.18311 | − | 0.651604i | ||||
\(53\) | −300.872 | −0.779773 | −0.389887 | − | 0.920863i | \(-0.627486\pi\) | ||||
−0.389887 | + | 0.920863i | \(0.627486\pi\) | |||||||
\(54\) | 105.155 | − | 382.631i | 0.264996 | − | 0.964250i | ||||
\(55\) | −331.416 | − | 267.329i | −0.812511 | − | 0.655394i | ||||
\(56\) | −174.546 | − | 5.28452i | −0.416511 | − | 0.0126102i | ||||
\(57\) | −45.7005 | − | 515.064i | −0.106196 | − | 1.19688i | ||||
\(58\) | 480.023 | + | 283.637i | 1.08673 | + | 0.642126i | ||||
\(59\) | 618.703 | 1.36522 | 0.682612 | − | 0.730781i | \(-0.260844\pi\) | ||||
0.682612 | + | 0.730781i | \(0.260844\pi\) | |||||||
\(60\) | −40.3144 | + | 463.006i | −0.0867427 | + | 0.996231i | ||||
\(61\) | −439.692 | −0.922899 | −0.461450 | − | 0.887166i | \(-0.652670\pi\) | ||||
−0.461450 | + | 0.887166i | \(0.652670\pi\) | |||||||
\(62\) | −33.9734 | − | 20.0743i | −0.0695908 | − | 0.0411199i | ||||
\(63\) | 205.115 | − | 36.6877i | 0.410192 | − | 0.0733685i | ||||
\(64\) | 511.062 | + | 30.9741i | 0.998168 | + | 0.0604963i | ||||
\(65\) | 444.395 | − | 550.930i | 0.848007 | − | 1.05130i | ||||
\(66\) | 241.034 | − | 505.165i | 0.449533 | − | 0.942144i | ||||
\(67\) | −23.6120 | −0.0430546 | −0.0215273 | − | 0.999768i | \(-0.506853\pi\) | ||||
−0.0215273 | + | 0.999768i | \(0.506853\pi\) | |||||||
\(68\) | 39.7028 | + | 72.0883i | 0.0708040 | + | 0.128559i | ||||
\(69\) | 61.1038 | + | 688.666i | 0.106609 | + | 1.20153i | ||||
\(70\) | −228.545 | + | 85.5920i | −0.390233 | + | 0.146146i | ||||
\(71\) | −827.145 | −1.38259 | −0.691296 | − | 0.722572i | \(-0.742960\pi\) | ||||
−0.691296 | + | 0.722572i | \(0.742960\pi\) | |||||||
\(72\) | −604.376 | + | 89.3192i | −0.989255 | + | 0.146200i | ||||
\(73\) | 152.697i | 0.244820i | 0.992480 | + | 0.122410i | \(0.0390623\pi\) | ||||
−0.992480 | + | 0.122410i | \(0.960938\pi\) | |||||||
\(74\) | −663.970 | − | 392.327i | −1.04304 | − | 0.616312i | ||||
\(75\) | 193.034 | + | 620.172i | 0.297196 | + | 0.954817i | ||||
\(76\) | −697.341 | + | 384.063i | −1.05251 | + | 0.579671i | ||||
\(77\) | 293.913 | 0.434993 | ||||||||
\(78\) | 839.762 | + | 400.683i | 1.21903 | + | 0.581646i | ||||
\(79\) | − | 421.741i | − | 0.600627i | −0.953841 | − | 0.300313i | \(-0.902909\pi\) | ||
0.953841 | − | 0.300313i | \(-0.0970913\pi\) | |||||||
\(80\) | 677.378 | − | 230.562i | 0.946665 | − | 0.322220i | ||||
\(81\) | 683.801 | − | 252.699i | 0.937999 | − | 0.346638i | ||||
\(82\) | −405.424 | − | 239.558i | −0.545995 | − | 0.322619i | ||||
\(83\) | − | 709.755i | − | 0.938624i | −0.883032 | − | 0.469312i | \(-0.844502\pi\) | ||
0.883032 | − | 0.469312i | \(-0.155498\pi\) | |||||||
\(84\) | −178.996 | − | 266.229i | −0.232500 | − | 0.345810i | ||||
\(85\) | 89.5219 | + | 72.2108i | 0.114235 | + | 0.0921454i | ||||
\(86\) | −393.242 | + | 665.517i | −0.493074 | + | 0.834472i | ||||
\(87\) | 90.5283 | + | 1020.29i | 0.111559 | + | 1.25732i | ||||
\(88\) | −861.354 | − | 26.0782i | −1.04342 | − | 0.0315903i | ||||
\(89\) | 1431.26i | 1.70464i | 0.523020 | + | 0.852321i | \(0.324805\pi\) | ||||
−0.523020 | + | 0.852321i | \(0.675195\pi\) | |||||||
\(90\) | −734.366 | + | 435.554i | −0.860099 | + | 0.510126i | ||||
\(91\) | 488.587i | 0.562833i | ||||||||
\(92\) | 932.379 | − | 513.510i | 1.05660 | − | 0.581925i | ||||
\(93\) | −6.40711 | − | 72.2108i | −0.00714393 | − | 0.0805152i | ||||
\(94\) | −168.308 | − | 99.4499i | −0.184677 | − | 0.109122i | ||||
\(95\) | −698.527 | + | 865.985i | −0.754393 | + | 0.935244i | ||||
\(96\) | 500.951 | + | 796.106i | 0.532584 | + | 0.846377i | ||||
\(97\) | 1086.79i | 1.13759i | 0.822478 | + | 0.568797i | \(0.192591\pi\) | ||||
−0.822478 | + | 0.568797i | \(0.807409\pi\) | |||||||
\(98\) | −407.830 | + | 690.207i | −0.420379 | + | 0.711443i | ||||
\(99\) | 1012.21 | − | 181.048i | 1.02759 | − | 0.183798i | ||||
\(100\) | 753.991 | − | 656.885i | 0.753991 | − | 0.656885i | ||||
\(101\) | − | 659.293i | − | 0.649526i | −0.945795 | − | 0.324763i | \(-0.894715\pi\) | ||
0.945795 | − | 0.324763i | \(-0.105285\pi\) | |||||||
\(102\) | −65.1079 | + | 136.455i | −0.0632024 | + | 0.132461i | ||||
\(103\) | 499.463 | 0.477801 | 0.238901 | − | 0.971044i | \(-0.423213\pi\) | ||||
0.238901 | + | 0.971044i | \(0.423213\pi\) | |||||||
\(104\) | 43.3512 | − | 1431.87i | 0.0408744 | − | 1.35007i | ||||
\(105\) | −372.478 | − | 249.542i | −0.346191 | − | 0.231931i | ||||
\(106\) | −432.911 | + | 732.653i | −0.396680 | + | 0.671336i | ||||
\(107\) | − | 1035.91i | − | 0.935940i | −0.883744 | − | 0.467970i | \(-0.844986\pi\) | ||
0.883744 | − | 0.467970i | \(-0.155014\pi\) | |||||||
\(108\) | −780.441 | − | 806.612i | −0.695352 | − | 0.718670i | ||||
\(109\) | 1260.39 | 1.10755 | 0.553776 | − | 0.832666i | \(-0.313186\pi\) | ||||
0.553776 | + | 0.832666i | \(0.313186\pi\) | |||||||
\(110\) | −1127.83 | + | 422.383i | −0.977587 | + | 0.366115i | ||||
\(111\) | −125.219 | − | 1411.27i | −0.107075 | − | 1.20678i | ||||
\(112\) | −264.014 | + | 417.432i | −0.222741 | + | 0.352175i | ||||
\(113\) | −525.733 | −0.437671 | −0.218835 | − | 0.975762i | \(-0.570226\pi\) | ||||
−0.218835 | + | 0.975762i | \(0.570226\pi\) | |||||||
\(114\) | −1319.99 | − | 629.817i | −1.08446 | − | 0.517437i | ||||
\(115\) | 933.964 | − | 1157.86i | 0.757327 | − | 0.938881i | ||||
\(116\) | 1381.37 | − | 760.792i | 1.10566 | − | 0.608946i | ||||
\(117\) | 300.965 | + | 1682.65i | 0.237814 | + | 1.32958i | ||||
\(118\) | 890.223 | − | 1506.60i | 0.694506 | − | 1.17537i | ||||
\(119\) | −79.3916 | −0.0611581 | ||||||||
\(120\) | 1069.46 | + | 764.368i | 0.813565 | + | 0.581474i | ||||
\(121\) | 119.411 | 0.0897154 | ||||||||
\(122\) | −632.653 | + | 1070.69i | −0.469490 | + | 0.794558i | ||||
\(123\) | −76.4596 | − | 861.733i | −0.0560498 | − | 0.631706i | ||||
\(124\) | −97.7656 | + | 53.8447i | −0.0708033 | + | 0.0389951i | ||||
\(125\) | 627.328 | − | 1248.83i | 0.448879 | − | 0.893593i | ||||
\(126\) | 205.793 | − | 552.264i | 0.145504 | − | 0.390473i | ||||
\(127\) | −351.089 | −0.245308 | −0.122654 | − | 0.992449i | \(-0.539141\pi\) | ||||
−0.122654 | + | 0.992449i | \(0.539141\pi\) | |||||||
\(128\) | 810.769 | − | 1199.92i | 0.559863 | − | 0.828585i | ||||
\(129\) | −1414.56 | + | 125.511i | −0.965467 | + | 0.0856637i | ||||
\(130\) | −702.149 | − | 1874.85i | −0.473712 | − | 1.26489i | ||||
\(131\) | 2152.61 | 1.43568 | 0.717840 | − | 0.696208i | \(-0.245131\pi\) | ||||
0.717840 | + | 0.696208i | \(0.245131\pi\) | |||||||
\(132\) | −883.314 | − | 1313.80i | −0.582444 | − | 0.866299i | ||||
\(133\) | − | 767.989i | − | 0.500700i | ||||||
\(134\) | −33.9742 | + | 57.4974i | −0.0219024 | + | 0.0370673i | ||||
\(135\) | −1436.50 | − | 629.958i | −0.915808 | − | 0.401616i | ||||
\(136\) | 232.668 | + | 7.04424i | 0.146700 | + | 0.00444146i | ||||
\(137\) | −1787.35 | −1.11462 | −0.557312 | − | 0.830303i | \(-0.688167\pi\) | ||||
−0.557312 | + | 0.830303i | \(0.688167\pi\) | |||||||
\(138\) | 1764.89 | + | 842.095i | 1.08868 | + | 0.519449i | ||||
\(139\) | 1312.49i | 0.800894i | 0.916320 | + | 0.400447i | \(0.131145\pi\) | ||||
−0.916320 | + | 0.400447i | \(0.868855\pi\) | |||||||
\(140\) | −120.418 | + | 679.683i | −0.0726940 | + | 0.410312i | ||||
\(141\) | −31.7414 | − | 357.739i | −0.0189582 | − | 0.213667i | ||||
\(142\) | −1190.14 | + | 2014.18i | −0.703340 | + | 1.19032i | ||||
\(143\) | 2411.10i | 1.40997i | ||||||||
\(144\) | −652.107 | + | 1600.23i | −0.377377 | + | 0.926060i | ||||
\(145\) | 1383.71 | − | 1715.43i | 0.792492 | − | 0.982475i | ||||
\(146\) | 371.833 | + | 219.709i | 0.210775 | + | 0.124543i | ||||
\(147\) | −1467.04 | + | 130.167i | −0.823126 | + | 0.0730341i | ||||
\(148\) | −1910.71 | + | 1052.33i | −1.06121 | + | 0.584466i | ||||
\(149\) | 537.983i | 0.295794i | 0.989003 | + | 0.147897i | \(0.0472504\pi\) | ||||
−0.989003 | + | 0.147897i | \(0.952750\pi\) | |||||||
\(150\) | 1787.93 | + | 422.279i | 0.973224 | + | 0.229859i | ||||
\(151\) | 2913.97i | 1.57043i | 0.619220 | + | 0.785217i | \(0.287449\pi\) | ||||
−0.619220 | + | 0.785217i | \(0.712551\pi\) | |||||||
\(152\) | −68.1420 | + | 2250.70i | −0.0363621 | + | 1.20103i | ||||
\(153\) | −273.418 | + | 48.9045i | −0.144474 | + | 0.0258412i | ||||
\(154\) | 422.897 | − | 715.706i | 0.221286 | − | 0.374502i | ||||
\(155\) | −97.9318 | + | 121.409i | −0.0507489 | + | 0.0629149i | ||||
\(156\) | 2184.00 | − | 1468.38i | 1.12090 | − | 0.753618i | ||||
\(157\) | − | 732.530i | − | 0.372371i | −0.982515 | − | 0.186186i | \(-0.940387\pi\) | ||
0.982515 | − | 0.186186i | \(-0.0596125\pi\) | |||||||
\(158\) | −1026.98 | − | 606.823i | −0.517102 | − | 0.305546i | ||||
\(159\) | −1557.26 | + | 138.172i | −0.776722 | + | 0.0689168i | ||||
\(160\) | 413.209 | − | 1981.23i | 0.204169 | − | 0.978936i | ||||
\(161\) | 1026.84i | 0.502647i | ||||||||
\(162\) | 368.544 | − | 2028.72i | 0.178738 | − | 0.983897i | ||||
\(163\) | 985.415 | 0.473519 | 0.236760 | − | 0.971568i | \(-0.423915\pi\) | ||||
0.236760 | + | 0.971568i | \(0.423915\pi\) | |||||||
\(164\) | −1166.69 | + | 642.559i | −0.555508 | + | 0.305948i | ||||
\(165\) | −1838.12 | − | 1231.45i | −0.867256 | − | 0.581019i | ||||
\(166\) | −1728.32 | − | 1021.23i | −0.808096 | − | 0.477489i | ||||
\(167\) | − | 920.379i | − | 0.426474i | −0.977001 | − | 0.213237i | \(-0.931599\pi\) | ||
0.977001 | − | 0.213237i | \(-0.0684006\pi\) | |||||||
\(168\) | −905.843 | + | 52.8064i | −0.415996 | + | 0.0242506i | ||||
\(169\) | −1811.09 | −0.824347 | ||||||||
\(170\) | 304.649 | − | 114.094i | 0.137444 | − | 0.0514741i | ||||
\(171\) | −473.075 | − | 2644.89i | −0.211561 | − | 1.18281i | ||||
\(172\) | 1054.78 | + | 1915.16i | 0.467595 | + | 0.849011i | ||||
\(173\) | 4073.57 | 1.79022 | 0.895110 | − | 0.445845i | \(-0.147097\pi\) | ||||
0.895110 | + | 0.445845i | \(0.147097\pi\) | |||||||
\(174\) | 2614.77 | + | 1247.61i | 1.13923 | + | 0.543568i | ||||
\(175\) | 204.170 | + | 942.826i | 0.0881932 | + | 0.407262i | ||||
\(176\) | −1302.87 | + | 2059.96i | −0.557995 | + | 0.882245i | ||||
\(177\) | 3202.29 | − | 284.132i | 1.35988 | − | 0.120659i | ||||
\(178\) | 3485.25 | + | 2059.37i | 1.46759 | + | 0.867171i | ||||
\(179\) | 1299.96 | 0.542812 | 0.271406 | − | 0.962465i | \(-0.412511\pi\) | ||||
0.271406 | + | 0.962465i | \(0.412511\pi\) | |||||||
\(180\) | 3.97050 | + | 2414.95i | 0.00164413 | + | 0.999999i | ||||
\(181\) | −1605.85 | −0.659460 | −0.329730 | − | 0.944075i | \(-0.606958\pi\) | ||||
−0.329730 | + | 0.944075i | \(0.606958\pi\) | |||||||
\(182\) | 1189.76 | + | 703.005i | 0.484564 | + | 0.286320i | ||||
\(183\) | −2275.77 | + | 201.924i | −0.919288 | + | 0.0815663i | ||||
\(184\) | 91.1091 | − | 3009.30i | 0.0365035 | − | 1.20570i | ||||
\(185\) | −1913.96 | + | 2372.79i | −0.760633 | + | 0.942979i | ||||
\(186\) | −185.059 | − | 88.2989i | −0.0729527 | − | 0.0348085i | ||||
\(187\) | −391.784 | −0.153209 | ||||||||
\(188\) | −484.340 | + | 266.752i | −0.187894 | + | 0.103483i | ||||
\(189\) | 1044.79 | − | 284.086i | 0.402103 | − | 0.109334i | ||||
\(190\) | 1103.68 | + | 2947.01i | 0.421417 | + | 1.12525i | ||||
\(191\) | −3434.72 | −1.30119 | −0.650596 | − | 0.759424i | \(-0.725481\pi\) | ||||
−0.650596 | + | 0.759424i | \(0.725481\pi\) | |||||||
\(192\) | 2659.39 | − | 74.3834i | 0.999609 | − | 0.0279592i | ||||
\(193\) | − | 1484.34i | − | 0.553603i | −0.960927 | − | 0.276801i | \(-0.910726\pi\) | ||
0.960927 | − | 0.276801i | \(-0.0892744\pi\) | |||||||
\(194\) | 2646.44 | + | 1563.73i | 0.979397 | + | 0.578708i | ||||
\(195\) | 2047.10 | − | 3055.60i | 0.751774 | − | 1.12213i | ||||
\(196\) | 1093.91 | + | 1986.21i | 0.398656 | + | 0.723839i | ||||
\(197\) | −2448.41 | −0.885491 | −0.442746 | − | 0.896647i | \(-0.645995\pi\) | ||||
−0.442746 | + | 0.896647i | \(0.645995\pi\) | |||||||
\(198\) | 1015.55 | − | 2725.33i | 0.364507 | − | 0.978187i | ||||
\(199\) | − | 2111.25i | − | 0.752071i | −0.926605 | − | 0.376036i | \(-0.877287\pi\) | ||
0.926605 | − | 0.376036i | \(-0.122713\pi\) | |||||||
\(200\) | −514.695 | − | 2781.20i | −0.181972 | − | 0.983304i | ||||
\(201\) | −122.211 | + | 10.8435i | −0.0428862 | + | 0.00380519i | ||||
\(202\) | −1605.44 | − | 948.626i | −0.559201 | − | 0.330421i | ||||
\(203\) | 1521.31i | 0.525987i | ||||||||
\(204\) | 238.600 | + | 354.883i | 0.0818890 | + | 0.121798i | ||||
\(205\) | −1168.68 | + | 1448.84i | −0.398165 | + | 0.493617i | ||||
\(206\) | 718.654 | − | 1216.24i | 0.243063 | − | 0.411357i | ||||
\(207\) | 632.524 | + | 3536.35i | 0.212384 | + | 1.18741i | ||||
\(208\) | −3424.38 | − | 2165.82i | −1.14153 | − | 0.721984i | ||||
\(209\) | − | 3789.90i | − | 1.25432i | ||||||
\(210\) | −1143.60 | + | 547.965i | −0.375790 | + | 0.180063i | ||||
\(211\) | 1842.42i | 0.601125i | 0.953762 | + | 0.300563i | \(0.0971744\pi\) | ||||
−0.953762 | + | 0.300563i | \(0.902826\pi\) | |||||||
\(212\) | 1161.19 | + | 2108.36i | 0.376182 | + | 0.683032i | ||||
\(213\) | −4281.15 | + | 379.857i | −1.37718 | + | 0.122194i | ||||
\(214\) | −2522.55 | − | 1490.53i | −0.805785 | − | 0.476123i | ||||
\(215\) | 2378.32 | + | 1918.42i | 0.754420 | + | 0.608536i | ||||
\(216\) | −3087.12 | + | 739.853i | −0.972463 | + | 0.233058i | ||||
\(217\) | − | 107.670i | − | 0.0336827i | ||||||
\(218\) | 1813.51 | − | 3069.16i | 0.563424 | − | 0.953532i | ||||
\(219\) | 70.1245 | + | 790.333i | 0.0216373 | + | 0.243862i | ||||
\(220\) | −594.242 | + | 3354.13i | −0.182108 | + | 1.02789i | ||||
\(221\) | − | 651.284i | − | 0.198236i | ||||||
\(222\) | −3616.76 | − | 1725.69i | −1.09343 | − | 0.521716i | ||||
\(223\) | −1605.50 | −0.482119 | −0.241059 | − | 0.970510i | \(-0.577495\pi\) | ||||
−0.241059 | + | 0.970510i | \(0.577495\pi\) | |||||||
\(224\) | 636.610 | + | 1243.52i | 0.189890 | + | 0.370921i | ||||
\(225\) | 1283.92 | + | 3121.25i | 0.380420 | + | 0.924814i | ||||
\(226\) | −756.453 | + | 1280.21i | −0.222648 | + | 0.376807i | ||||
\(227\) | − | 6295.62i | − | 1.84077i | −0.391012 | − | 0.920386i | \(-0.627875\pi\) | ||
0.391012 | − | 0.920386i | \(-0.372125\pi\) | |||||||
\(228\) | −3432.94 | + | 2308.09i | −0.997157 | + | 0.670424i | ||||
\(229\) | 4350.52 | 1.25542 | 0.627708 | − | 0.778449i | \(-0.283993\pi\) | ||||
0.627708 | + | 0.778449i | \(0.283993\pi\) | |||||||
\(230\) | −1475.67 | − | 3940.29i | −0.423056 | − | 1.12963i | ||||
\(231\) | 1521.24 | − | 134.976i | 0.433291 | − | 0.0384449i | ||||
\(232\) | 134.983 | − | 4458.43i | 0.0381985 | − | 1.26168i | ||||
\(233\) | 767.524 | 0.215803 | 0.107902 | − | 0.994162i | \(-0.465587\pi\) | ||||
0.107902 | + | 0.994162i | \(0.465587\pi\) | |||||||
\(234\) | 4530.47 | + | 1688.21i | 1.26567 | + | 0.471631i | ||||
\(235\) | −485.164 | + | 601.472i | −0.134675 | + | 0.166960i | ||||
\(236\) | −2387.82 | − | 4335.56i | −0.658619 | − | 1.19585i | ||||
\(237\) | −193.680 | − | 2182.85i | −0.0530837 | − | 0.598277i | ||||
\(238\) | −114.233 | + | 193.326i | −0.0311118 | + | 0.0526533i | ||||
\(239\) | −3491.02 | −0.944835 | −0.472417 | − | 0.881375i | \(-0.656619\pi\) | ||||
−0.472417 | + | 0.881375i | \(0.656619\pi\) | |||||||
\(240\) | 3400.10 | − | 1504.42i | 0.914483 | − | 0.404625i | ||||
\(241\) | 2621.79 | 0.700764 | 0.350382 | − | 0.936607i | \(-0.386052\pi\) | ||||
0.350382 | + | 0.936607i | \(0.386052\pi\) | |||||||
\(242\) | 171.815 | − | 290.778i | 0.0456393 | − | 0.0772393i | ||||
\(243\) | 3423.18 | − | 1621.95i | 0.903692 | − | 0.428182i | ||||
\(244\) | 1696.95 | + | 3081.14i | 0.445230 | + | 0.808402i | ||||
\(245\) | 2466.56 | + | 1989.59i | 0.643194 | + | 0.518818i | ||||
\(246\) | −2208.42 | − | 1053.72i | −0.572372 | − | 0.273101i | ||||
\(247\) | 6300.15 | 1.62295 | ||||||||
\(248\) | −9.55335 | + | 315.543i | −0.00244612 | + | 0.0807945i | ||||
\(249\) | −325.947 | − | 3673.56i | −0.0829561 | − | 0.934951i | ||||
\(250\) | −2138.40 | − | 3324.49i | −0.540977 | − | 0.841038i | ||||
\(251\) | 1555.01 | 0.391041 | 0.195520 | − | 0.980700i | \(-0.437360\pi\) | ||||
0.195520 | + | 0.980700i | \(0.437360\pi\) | |||||||
\(252\) | −1048.71 | − | 1295.75i | −0.262153 | − | 0.323908i | ||||
\(253\) | 5067.28i | 1.25920i | ||||||||
\(254\) | −505.166 | + | 854.936i | −0.124791 | + | 0.211195i | ||||
\(255\) | 496.511 | + | 332.638i | 0.121932 | + | 0.0816887i | ||||
\(256\) | −1755.34 | − | 3700.81i | −0.428550 | − | 0.903518i | ||||
\(257\) | −1090.84 | −0.264765 | −0.132382 | − | 0.991199i | \(-0.542263\pi\) | ||||
−0.132382 | + | 0.991199i | \(0.542263\pi\) | |||||||
\(258\) | −1729.72 | + | 3625.19i | −0.417393 | + | 0.874784i | ||||
\(259\) | − | 2104.29i | − | 0.504841i | ||||||
\(260\) | −5575.74 | − | 987.840i | −1.32997 | − | 0.235628i | ||||
\(261\) | 937.117 | + | 5239.28i | 0.222245 | + | 1.24254i | ||||
\(262\) | 3097.29 | − | 5241.81i | 0.730348 | − | 1.23603i | ||||
\(263\) | − | 3230.93i | − | 0.757521i | −0.925495 | − | 0.378760i | \(-0.876350\pi\) | ||
0.925495 | − | 0.378760i | \(-0.123650\pi\) | |||||||
\(264\) | −4470.19 | + | 260.591i | −1.04213 | + | 0.0607510i | ||||
\(265\) | 2618.24 | + | 2111.95i | 0.606934 | + | 0.489569i | ||||
\(266\) | −1870.13 | − | 1105.02i | −0.431071 | − | 0.254712i | ||||
\(267\) | 657.290 | + | 7407.93i | 0.150657 | + | 1.69797i | ||||
\(268\) | 91.1280 | + | 165.461i | 0.0207706 | + | 0.0377132i | ||||
\(269\) | − | 5506.73i | − | 1.24815i | −0.781366 | − | 0.624073i | \(-0.785477\pi\) | ||
0.781366 | − | 0.624073i | \(-0.214523\pi\) | |||||||
\(270\) | −3600.92 | + | 2591.60i | −0.811648 | + | 0.584146i | ||||
\(271\) | − | 6077.18i | − | 1.36222i | −0.732180 | − | 0.681112i | \(-0.761497\pi\) | ||
0.732180 | − | 0.681112i | \(-0.238503\pi\) | |||||||
\(272\) | 351.929 | − | 556.435i | 0.0784516 | − | 0.124040i | ||||
\(273\) | 224.378 | + | 2528.84i | 0.0497435 | + | 0.560630i | ||||
\(274\) | −2571.73 | + | 4352.37i | −0.567022 | + | 0.959621i | ||||
\(275\) | 1007.55 | + | 4652.69i | 0.220936 | + | 1.02025i | ||||
\(276\) | 4590.00 | − | 3086.02i | 1.00103 | − | 0.673031i | ||||
\(277\) | − | 2208.52i | − | 0.479050i | −0.970890 | − | 0.239525i | \(-0.923008\pi\) | ||
0.970890 | − | 0.239525i | \(-0.0769917\pi\) | |||||||
\(278\) | 3196.05 | + | 1888.49i | 0.689519 | + | 0.407424i | ||||
\(279\) | −66.3240 | − | 370.808i | −0.0142320 | − | 0.0795687i | ||||
\(280\) | 1481.83 | + | 1271.19i | 0.316273 | + | 0.271316i | ||||
\(281\) | 3458.28i | 0.734178i | 0.930186 | + | 0.367089i | \(0.119646\pi\) | ||||
−0.930186 | + | 0.367089i | \(0.880354\pi\) | |||||||
\(282\) | −916.801 | − | 437.441i | −0.193598 | − | 0.0923732i | ||||
\(283\) | 547.429 | 0.114987 | 0.0574934 | − | 0.998346i | \(-0.481689\pi\) | ||||
0.0574934 | + | 0.998346i | \(0.481689\pi\) | |||||||
\(284\) | 3192.28 | + | 5796.21i | 0.666997 | + | 1.21106i | ||||
\(285\) | −3217.76 | + | 4802.97i | −0.668784 | + | 0.998258i | ||||
\(286\) | 5871.25 | + | 3469.21i | 1.21390 | + | 0.717269i | ||||
\(287\) | − | 1284.89i | − | 0.264267i | ||||||
\(288\) | 2958.43 | + | 3890.44i | 0.605303 | + | 0.795995i | ||||
\(289\) | −4807.17 | −0.978459 | ||||||||
\(290\) | −2186.28 | − | 5837.74i | −0.442700 | − | 1.18208i | ||||
\(291\) | 499.096 | + | 5625.02i | 0.100541 | + | 1.13314i | ||||
\(292\) | 1070.03 | − | 589.320i | 0.214447 | − | 0.118107i | ||||
\(293\) | −1475.97 | −0.294290 | −0.147145 | − | 0.989115i | \(-0.547008\pi\) | ||||
−0.147145 | + | 0.989115i | \(0.547008\pi\) | |||||||
\(294\) | −1793.89 | + | 3759.68i | −0.355856 | + | 0.745813i | ||||
\(295\) | −5384.06 | − | 4342.93i | −1.06262 | − | 0.857136i | ||||
\(296\) | −186.709 | + | 6166.91i | −0.0366629 | + | 1.21096i | ||||
\(297\) | 5155.88 | − | 1401.92i | 1.00732 | − | 0.273897i | ||||
\(298\) | 1310.04 | + | 774.079i | 0.254660 | + | 0.150474i | ||||
\(299\) | −8423.61 | −1.62926 | ||||||||
\(300\) | 3600.85 | − | 3746.18i | 0.692985 | − | 0.720952i | ||||
\(301\) | −2109.19 | −0.403893 | ||||||||
\(302\) | 7095.80 | + | 4192.78i | 1.35205 | + | 0.798898i | ||||
\(303\) | −302.773 | − | 3412.38i | −0.0574055 | − | 0.646984i | ||||
\(304\) | 5382.64 | + | 3404.37i | 1.01551 | + | 0.642282i | ||||
\(305\) | 3826.28 | + | 3086.38i | 0.718335 | + | 0.579429i | ||||
\(306\) | −274.321 | + | 736.166i | −0.0512480 | + | 0.137529i | ||||
\(307\) | −8590.08 | −1.59694 | −0.798472 | − | 0.602032i | \(-0.794358\pi\) | ||||
−0.798472 | + | 0.602032i | \(0.794358\pi\) | |||||||
\(308\) | −1134.33 | − | 2059.59i | −0.209851 | − | 0.381027i | ||||
\(309\) | 2585.13 | − | 229.373i | 0.475932 | − | 0.0422284i | ||||
\(310\) | 154.733 | + | 413.163i | 0.0283492 | + | 0.0756971i | ||||
\(311\) | 6221.34 | 1.13434 | 0.567170 | − | 0.823601i | \(-0.308038\pi\) | ||||
0.567170 | + | 0.823601i | \(0.308038\pi\) | |||||||
\(312\) | −433.194 | − | 7431.03i | −0.0786051 | − | 1.34839i | ||||
\(313\) | 209.772i | 0.0378818i | 0.999821 | + | 0.0189409i | \(0.00602944\pi\) | ||||
−0.999821 | + | 0.0189409i | \(0.993971\pi\) | |||||||
\(314\) | −1783.78 | − | 1054.00i | −0.320588 | − | 0.189429i | ||||
\(315\) | −2042.48 | − | 1120.53i | −0.365335 | − | 0.200427i | ||||
\(316\) | −2955.35 | + | 1627.67i | −0.526111 | + | 0.289757i | ||||
\(317\) | 1958.11 | 0.346935 | 0.173467 | − | 0.984840i | \(-0.444503\pi\) | ||||
0.173467 | + | 0.984840i | \(0.444503\pi\) | |||||||
\(318\) | −1904.21 | + | 3990.89i | −0.335794 | + | 0.703767i | ||||
\(319\) | 7507.43i | 1.31767i | ||||||||
\(320\) | −4229.93 | − | 3856.90i | −0.738939 | − | 0.673772i | ||||
\(321\) | −475.732 | − | 5361.70i | −0.0827189 | − | 0.932277i | ||||
\(322\) | 2500.45 | + | 1477.47i | 0.432748 | + | 0.255702i | ||||
\(323\) | 1023.73i | 0.176352i | ||||||||
\(324\) | −4409.85 | − | 3816.47i | −0.756147 | − | 0.654402i | ||||
\(325\) | −7734.41 | + | 1674.90i | −1.32009 | + | 0.285866i | ||||
\(326\) | 1417.87 | − | 2399.58i | 0.240885 | − | 0.407670i | ||||
\(327\) | 6523.53 | − | 578.818i | 1.10322 | − | 0.0978860i | ||||
\(328\) | −114.006 | + | 3765.56i | −0.0191918 | + | 0.633897i | ||||
\(329\) | − | 533.409i | − | 0.0893854i | ||||||
\(330\) | −5643.48 | + | 2704.12i | −0.941404 | + | 0.451081i | ||||
\(331\) | − | 4909.75i | − | 0.815300i | −0.913138 | − | 0.407650i | \(-0.866348\pi\) | ||
0.913138 | − | 0.407650i | \(-0.133652\pi\) | |||||||
\(332\) | −4973.61 | + | 2739.23i | −0.822176 | + | 0.452816i | ||||
\(333\) | −1296.22 | − | 7246.99i | −0.213311 | − | 1.19259i | ||||
\(334\) | −2241.21 | − | 1324.29i | −0.367167 | − | 0.216952i | ||||
\(335\) | 205.475 | + | 165.742i | 0.0335114 | + | 0.0270312i | ||||
\(336\) | −1174.79 | + | 2281.80i | −0.190744 | + | 0.370483i | ||||
\(337\) | − | 3654.04i | − | 0.590648i | −0.955397 | − | 0.295324i | \(-0.904572\pi\) | ||
0.955397 | − | 0.295324i | \(-0.0954276\pi\) | |||||||
\(338\) | −2605.90 | + | 4410.18i | −0.419355 | + | 0.709711i | ||||
\(339\) | −2721.10 | + | 241.437i | −0.435958 | + | 0.0386816i | ||||
\(340\) | 160.516 | − | 906.015i | 0.0256036 | − | 0.144516i | ||||
\(341\) | − | 531.335i | − | 0.0843795i | ||||||
\(342\) | −7121.26 | − | 2653.63i | −1.12595 | − | 0.419567i | ||||
\(343\) | −4834.52 | −0.761048 | ||||||||
\(344\) | 6181.29 | + | 187.144i | 0.968816 | + | 0.0293317i | ||||
\(345\) | 4302.29 | − | 6421.80i | 0.671384 | − | 1.00214i | ||||
\(346\) | 5861.28 | − | 9919.55i | 0.910706 | − | 1.54127i | ||||
\(347\) | 275.386i | 0.0426037i | 0.999773 | + | 0.0213018i | \(0.00678110\pi\) | ||||
−0.999773 | + | 0.0213018i | \(0.993219\pi\) | |||||||
\(348\) | 6800.32 | − | 4572.10i | 1.04752 | − | 0.704282i | ||||
\(349\) | −1012.50 | −0.155295 | −0.0776474 | − | 0.996981i | \(-0.524741\pi\) | ||||
−0.0776474 | + | 0.996981i | \(0.524741\pi\) | |||||||
\(350\) | 2589.64 | + | 859.414i | 0.395492 | + | 0.131250i | ||||
\(351\) | 2330.48 | + | 8570.89i | 0.354393 | + | 1.30336i | ||||
\(352\) | 3141.57 | + | 6136.58i | 0.475699 | + | 0.929207i | ||||
\(353\) | −4042.06 | −0.609454 | −0.304727 | − | 0.952440i | \(-0.598565\pi\) | ||||
−0.304727 | + | 0.952440i | \(0.598565\pi\) | |||||||
\(354\) | 3915.74 | − | 8206.72i | 0.587908 | − | 1.23215i | ||||
\(355\) | 7197.96 | + | 5806.07i | 1.07613 | + | 0.868040i | ||||
\(356\) | 10029.5 | − | 5523.80i | 1.49316 | − | 0.822362i | ||||
\(357\) | −410.916 | + | 36.4597i | −0.0609188 | + | 0.00540519i | ||||
\(358\) | 1870.45 | − | 3165.52i | 0.276135 | − | 0.467327i | ||||
\(359\) | 6296.47 | 0.925668 | 0.462834 | − | 0.886445i | \(-0.346833\pi\) | ||||
0.462834 | + | 0.886445i | \(0.346833\pi\) | |||||||
\(360\) | 5886.35 | + | 3465.09i | 0.861772 | + | 0.507295i | ||||
\(361\) | −3043.96 | −0.443790 | ||||||||
\(362\) | −2310.59 | + | 3910.41i | −0.335475 | + | 0.567753i | ||||
\(363\) | 618.051 | − | 54.8383i | 0.0893643 | − | 0.00792910i | ||||
\(364\) | 3423.77 | − | 1885.65i | 0.493006 | − | 0.271525i | ||||
\(365\) | 1071.84 | − | 1328.80i | 0.153707 | − | 0.190555i | ||||
\(366\) | −2782.79 | + | 5832.26i | −0.397429 | + | 0.832942i | ||||
\(367\) | −410.434 | −0.0583773 | −0.0291887 | − | 0.999574i | \(-0.509292\pi\) | ||||
−0.0291887 | + | 0.999574i | \(0.509292\pi\) | |||||||
\(368\) | −7196.84 | − | 4551.80i | −1.01946 | − | 0.644780i | ||||
\(369\) | −791.482 | − | 4425.06i | −0.111661 | − | 0.624280i | ||||
\(370\) | 3024.07 | + | 8074.78i | 0.424903 | + | 1.13456i | ||||
\(371\) | −2321.96 | −0.324933 | ||||||||
\(372\) | −481.290 | + | 323.588i | −0.0670798 | + | 0.0451002i | ||||
\(373\) | − | 6314.56i | − | 0.876556i | −0.898839 | − | 0.438278i | \(-0.855588\pi\) | ||
0.898839 | − | 0.438278i | \(-0.144412\pi\) | |||||||
\(374\) | −563.720 | + | 954.033i | −0.0779393 | + | 0.131903i | ||||
\(375\) | 2673.42 | − | 6751.83i | 0.368146 | − | 0.929768i | ||||
\(376\) | −47.3282 | + | 1563.23i | −0.00649140 | + | 0.214408i | ||||
\(377\) | −12480.0 | −1.70491 | ||||||||
\(378\) | 811.526 | − | 2952.93i | 0.110424 | − | 0.401805i | ||||
\(379\) | − | 8280.22i | − | 1.12223i | −0.827737 | − | 0.561116i | \(-0.810372\pi\) | ||
0.827737 | − | 0.561116i | \(-0.189628\pi\) | |||||||
\(380\) | 8764.28 | + | 1552.75i | 1.18315 | + | 0.209616i | ||||
\(381\) | −1817.17 | + | 161.234i | −0.244348 | + | 0.0216805i | ||||
\(382\) | −4942.06 | + | 8363.88i | −0.661931 | + | 1.12024i | ||||
\(383\) | 5962.08i | 0.795426i | 0.917510 | + | 0.397713i | \(0.130196\pi\) | ||||
−0.917510 | + | 0.397713i | \(0.869804\pi\) | |||||||
\(384\) | 3645.34 | − | 6582.90i | 0.484442 | − | 0.874824i | ||||
\(385\) | −2557.68 | − | 2063.09i | −0.338575 | − | 0.273104i | ||||
\(386\) | −3614.52 | − | 2135.75i | −0.476617 | − | 0.281624i | ||||
\(387\) | −7263.88 | + | 1299.24i | −0.954118 | + | 0.170657i | ||||
\(388\) | 7615.67 | − | 4194.35i | 0.996461 | − | 0.548804i | ||||
\(389\) | − | 2983.39i | − | 0.388854i | −0.980917 | − | 0.194427i | \(-0.937715\pi\) | ||
0.980917 | − | 0.194427i | \(-0.0622847\pi\) | |||||||
\(390\) | −4495.20 | − | 9381.45i | −0.583650 | − | 1.21807i | ||||
\(391\) | − | 1368.77i | − | 0.177038i | ||||||
\(392\) | 6410.61 | + | 194.087i | 0.825981 | + | 0.0250073i | ||||
\(393\) | 11141.5 | − | 988.561i | 1.43006 | − | 0.126886i | ||||
\(394\) | −3522.90 | + | 5962.11i | −0.450460 | + | 0.762352i | ||||
\(395\) | −2960.37 | + | 3670.06i | −0.377095 | + | 0.467496i | ||||
\(396\) | −5175.22 | − | 6394.33i | −0.656729 | − | 0.811433i | ||||
\(397\) | 10773.3i | 1.36195i | 0.732306 | + | 0.680976i | \(0.238444\pi\) | ||||
−0.732306 | + | 0.680976i | \(0.761556\pi\) | |||||||
\(398\) | −5141.09 | − | 3037.77i | −0.647486 | − | 0.382587i | ||||
\(399\) | −352.691 | − | 3974.97i | −0.0442522 | − | 0.498741i | ||||
\(400\) | −7513.07 | − | 2748.41i | −0.939134 | − | 0.343551i | ||||
\(401\) | 4860.65i | 0.605310i | 0.953100 | + | 0.302655i | \(0.0978731\pi\) | ||||
−0.953100 | + | 0.302655i | \(0.902127\pi\) | |||||||
\(402\) | −149.439 | + | 313.199i | −0.0185407 | + | 0.0388580i | ||||
\(403\) | 883.267 | 0.109178 | ||||||||
\(404\) | −4620.00 | + | 2544.48i | −0.568944 | + | 0.313348i | ||||
\(405\) | −7724.36 | − | 2600.85i | −0.947719 | − | 0.319105i | ||||
\(406\) | 3704.55 | + | 2188.95i | 0.452841 | + | 0.267575i | ||||
\(407\) | − | 10384.3i | − | 1.26470i | ||||||
\(408\) | 1207.48 | − | 70.3907i | 0.146518 | − | 0.00854132i | ||||
\(409\) | 1712.86 | 0.207079 | 0.103540 | − | 0.994625i | \(-0.466983\pi\) | ||||
0.103540 | + | 0.994625i | \(0.466983\pi\) | |||||||
\(410\) | 1846.52 | + | 4930.51i | 0.222422 | + | 0.593904i | ||||
\(411\) | −9250.99 | + | 820.820i | −1.11026 | + | 0.0985111i | ||||
\(412\) | −1927.63 | − | 3499.99i | −0.230503 | − | 0.418524i | ||||
\(413\) | 4774.80 | 0.568892 | ||||||||
\(414\) | 9521.46 | + | 3548.03i | 1.13032 | + | 0.421198i | ||||
\(415\) | −4982.07 | + | 6176.42i | −0.589301 | + | 0.730574i | ||||
\(416\) | −10201.2 | + | 5222.39i | −1.20229 | + | 0.615502i | ||||
\(417\) | 602.748 | + | 6793.23i | 0.0707835 | + | 0.797760i | ||||
\(418\) | −9228.78 | − | 5453.11i | −1.07989 | − | 0.638087i | ||||
\(419\) | 7116.69 | 0.829769 | 0.414884 | − | 0.909874i | \(-0.363822\pi\) | ||||
0.414884 | + | 0.909874i | \(0.363822\pi\) | |||||||
\(420\) | −311.124 | + | 3573.22i | −0.0361459 | + | 0.415131i | ||||
\(421\) | 8339.85 | 0.965462 | 0.482731 | − | 0.875769i | \(-0.339645\pi\) | ||||
0.482731 | + | 0.875769i | \(0.339645\pi\) | |||||||
\(422\) | 4486.47 | + | 2650.97i | 0.517531 | + | 0.305799i | ||||
\(423\) | −328.576 | − | 1837.02i | −0.0377681 | − | 0.211156i | ||||
\(424\) | 6804.84 | + | 206.022i | 0.779416 | + | 0.0235975i | ||||
\(425\) | −272.158 | − | 1256.78i | −0.0310626 | − | 0.143442i | ||||
\(426\) | −5234.96 | + | 10971.6i | −0.595387 | + | 1.24783i | ||||
\(427\) | −3393.30 | −0.384574 | ||||||||
\(428\) | −7259.16 | + | 3998.01i | −0.819825 | + | 0.451521i | ||||
\(429\) | 1107.27 | + | 12479.4i | 0.124614 | + | 1.40445i | ||||
\(430\) | 8093.60 | − | 3031.12i | 0.907693 | − | 0.339939i | ||||
\(431\) | −1347.08 | −0.150549 | −0.0752745 | − | 0.997163i | \(-0.523983\pi\) | ||||
−0.0752745 | + | 0.997163i | \(0.523983\pi\) | |||||||
\(432\) | −2640.30 | + | 8581.98i | −0.294055 | + | 0.955789i | ||||
\(433\) | 3588.36i | 0.398257i | 0.979973 | + | 0.199129i | \(0.0638112\pi\) | ||||
−0.979973 | + | 0.199129i | \(0.936189\pi\) | |||||||
\(434\) | −262.188 | − | 154.922i | −0.0289986 | − | 0.0171348i | ||||
\(435\) | 6374.06 | − | 9514.22i | 0.702559 | − | 1.04867i | ||||
\(436\) | −4864.33 | − | 8832.16i | −0.534311 | − | 0.970146i | ||||
\(437\) | 13240.7 | 1.44940 | ||||||||
\(438\) | 2025.44 | + | 966.414i | 0.220957 | + | 0.105427i | ||||
\(439\) | 3144.53i | 0.341868i | 0.985282 | + | 0.170934i | \(0.0546785\pi\) | ||||
−0.985282 | + | 0.170934i | \(0.945322\pi\) | |||||||
\(440\) | 7312.60 | + | 6273.14i | 0.792306 | + | 0.679682i | ||||
\(441\) | −7533.36 | + | 1347.44i | −0.813450 | + | 0.145497i | ||||
\(442\) | −1585.94 | − | 937.102i | −0.170668 | − | 0.100845i | ||||
\(443\) | 14893.5i | 1.59732i | 0.601781 | + | 0.798661i | \(0.294458\pi\) | ||||
−0.601781 | + | 0.798661i | \(0.705542\pi\) | |||||||
\(444\) | −9406.22 | + | 6324.14i | −1.00540 | + | 0.675969i | ||||
\(445\) | 10046.6 | − | 12455.1i | 1.07023 | − | 1.32680i | ||||
\(446\) | −2310.09 | + | 3909.56i | −0.245259 | + | 0.415074i | ||||
\(447\) | 247.063 | + | 2784.50i | 0.0261424 | + | 0.294636i | ||||
\(448\) | 3944.09 | + | 239.040i | 0.415939 | + | 0.0252089i | ||||
\(449\) | 16537.7i | 1.73823i | 0.494614 | + | 0.869113i | \(0.335309\pi\) | ||||
−0.494614 | + | 0.869113i | \(0.664691\pi\) | |||||||
\(450\) | 9447.91 | + | 1364.55i | 0.989731 | + | 0.142946i | ||||
\(451\) | − | 6340.73i | − | 0.662025i | ||||||
\(452\) | 2029.01 | + | 3684.07i | 0.211143 | + | 0.383372i | ||||
\(453\) | 1338.21 | + | 15082.2i | 0.138796 | + | 1.56429i | ||||
\(454\) | −15330.5 | − | 9058.48i | −1.58479 | − | 0.936422i | ||||
\(455\) | 3429.59 | − | 4251.77i | 0.353366 | − | 0.438079i | ||||
\(456\) | 680.920 | + | 11680.5i | 0.0699277 | + | 1.19954i | ||||
\(457\) | 8780.53i | 0.898765i | 0.893339 | + | 0.449383i | \(0.148356\pi\) | ||||
−0.893339 | + | 0.449383i | \(0.851644\pi\) | |||||||
\(458\) | 6259.76 | − | 10593.9i | 0.638645 | − | 1.08083i | ||||
\(459\) | −1392.70 | + | 378.685i | −0.141625 | + | 0.0385087i | ||||
\(460\) | −11718.3 | − | 2076.09i | −1.18775 | − | 0.210431i | ||||
\(461\) | − | 9038.99i | − | 0.913206i | −0.889671 | − | 0.456603i | \(-0.849066\pi\) | ||
0.889671 | − | 0.456603i | \(-0.150934\pi\) | |||||||
\(462\) | 1860.16 | − | 3898.58i | 0.187321 | − | 0.392593i | ||||
\(463\) | 12668.9 | 1.27165 | 0.635824 | − | 0.771834i | \(-0.280661\pi\) | ||||
0.635824 | + | 0.771834i | \(0.280661\pi\) | |||||||
\(464\) | −10662.5 | − | 6743.72i | −1.06680 | − | 0.674719i | ||||
\(465\) | −451.122 | + | 673.365i | −0.0449898 | + | 0.0671539i | ||||
\(466\) | 1104.35 | − | 1868.99i | 0.109782 | − | 0.185793i | ||||
\(467\) | 1655.54i | 0.164045i | 0.996630 | + | 0.0820226i | \(0.0261380\pi\) | ||||
−0.996630 | + | 0.0820226i | \(0.973862\pi\) | |||||||
\(468\) | 10629.6 | − | 8603.04i | 1.04990 | − | 0.849734i | ||||
\(469\) | −182.224 | −0.0179410 | ||||||||
\(470\) | 766.563 | + | 2046.85i | 0.0752318 | + | 0.200881i | ||||
\(471\) | −336.406 | − | 3791.44i | −0.0329104 | − | 0.370914i | ||||
\(472\) | −13993.2 | − | 423.657i | −1.36460 | − | 0.0413144i | ||||
\(473\) | −10408.5 | −1.01180 | ||||||||
\(474\) | −5594.14 | − | 2669.18i | −0.542083 | − | 0.258648i | ||||
\(475\) | 12157.4 | − | 2632.70i | 1.17436 | − | 0.254309i | ||||
\(476\) | 306.404 | + | 556.336i | 0.0295042 | + | 0.0535706i | ||||
\(477\) | −7996.64 | + | 1430.31i | −0.767591 | + | 0.137294i | ||||
\(478\) | −5023.07 | + | 8500.98i | −0.480648 | + | 0.813443i | ||||
\(479\) | 6638.64 | 0.633251 | 0.316625 | − | 0.948551i | \(-0.397450\pi\) | ||||
0.316625 | + | 0.948551i | \(0.397450\pi\) | |||||||
\(480\) | 1228.84 | − | 10444.2i | 0.116851 | − | 0.993149i | ||||
\(481\) | 17262.4 | 1.63638 | ||||||||
\(482\) | 3772.37 | − | 6384.31i | 0.356487 | − | 0.603314i | ||||
\(483\) | 471.564 | + | 5314.73i | 0.0444242 | + | 0.500680i | ||||
\(484\) | −460.856 | − | 836.774i | −0.0432810 | − | 0.0785851i | ||||
\(485\) | 7628.62 | − | 9457.42i | 0.714222 | − | 0.885442i | ||||
\(486\) | 975.849 | − | 10669.5i | 0.0910811 | − | 0.995843i | ||||
\(487\) | 14551.7 | 1.35401 | 0.677005 | − | 0.735979i | \(-0.263278\pi\) | ||||
0.677005 | + | 0.735979i | \(0.263278\pi\) | |||||||
\(488\) | 9944.55 | + | 301.080i | 0.922476 | + | 0.0279288i | ||||
\(489\) | 5100.33 | − | 452.541i | 0.471666 | − | 0.0418499i | ||||
\(490\) | 8393.86 | − | 3143.57i | 0.773869 | − | 0.289821i | ||||
\(491\) | −19427.2 | −1.78562 | −0.892810 | − | 0.450434i | \(-0.851269\pi\) | ||||
−0.892810 | + | 0.450434i | \(0.851269\pi\) | |||||||
\(492\) | −5743.50 | + | 3861.56i | −0.526295 | + | 0.353847i | ||||
\(493\) | − | 2027.90i | − | 0.185258i | ||||||
\(494\) | 9065.00 | − | 15341.5i | 0.825615 | − | 1.39726i | ||||
\(495\) | −10079.3 | − | 5529.62i | −0.915213 | − | 0.502097i | ||||
\(496\) | 754.633 | + | 477.284i | 0.0683146 | + | 0.0432070i | ||||
\(497\) | −6383.43 | −0.576129 | ||||||||
\(498\) | −9414.48 | − | 4492.01i | −0.847134 | − | 0.404200i | ||||
\(499\) | 19207.9i | 1.72317i | 0.507613 | + | 0.861585i | \(0.330528\pi\) | ||||
−0.507613 | + | 0.861585i | \(0.669472\pi\) | |||||||
\(500\) | −11172.3 | + | 423.750i | −0.999281 | + | 0.0379014i | ||||
\(501\) | −422.674 | − | 4763.72i | −0.0376920 | − | 0.424805i | ||||
\(502\) | 2237.43 | − | 3786.60i | 0.198927 | − | 0.336662i | ||||
\(503\) | − | 16814.5i | − | 1.49050i | −0.666784 | − | 0.745251i | \(-0.732330\pi\) | ||
0.666784 | − | 0.745251i | \(-0.267670\pi\) | |||||||
\(504\) | −4664.23 | + | 689.315i | −0.412225 | + | 0.0609217i | ||||
\(505\) | −4627.85 | + | 5737.28i | −0.407795 | + | 0.505556i | ||||
\(506\) | 12339.3 | + | 7291.07i | 1.08409 | + | 0.640569i | ||||
\(507\) | −9373.88 | + | 831.723i | −0.821122 | + | 0.0728563i | ||||
\(508\) | 1354.99 | + | 2460.26i | 0.118343 | + | 0.214874i | ||||
\(509\) | 4588.46i | 0.399568i | 0.979840 | + | 0.199784i | \(0.0640240\pi\) | ||||
−0.979840 | + | 0.199784i | \(0.935976\pi\) | |||||||
\(510\) | 1524.41 | − | 730.435i | 0.132357 | − | 0.0634200i | ||||
\(511\) | 1178.43i | 0.102017i | ||||||||
\(512\) | −11537.5 | − | 1050.49i | −0.995881 | − | 0.0906751i | ||||
\(513\) | −3663.19 | − | 13472.2i | −0.315270 | − | 1.15948i | ||||
\(514\) | −1569.55 | + | 2656.29i | −0.134689 | + | 0.227946i | ||||
\(515\) | −4346.41 | − | 3505.94i | −0.371895 | − | 0.299981i | ||||
\(516\) | 6338.88 | + | 9428.14i | 0.540801 | + | 0.804362i | ||||
\(517\) | − | 2632.29i | − | 0.223922i | ||||||
\(518\) | −5124.14 | − | 3027.76i | −0.434637 | − | 0.256819i | ||||
\(519\) | 21084.1 | − | 1870.74i | 1.78321 | − | 0.158221i | ||||
\(520\) | −10428.2 | + | 12156.1i | −0.879433 | + | 1.02516i | ||||
\(521\) | − | 8223.12i | − | 0.691481i | −0.938330 | − | 0.345741i | \(-0.887628\pi\) | ||
0.938330 | − | 0.345741i | \(-0.112372\pi\) | |||||||
\(522\) | 14106.5 | + | 5256.58i | 1.18281 | + | 0.440756i | ||||
\(523\) | −3224.05 | −0.269556 | −0.134778 | − | 0.990876i | \(-0.543032\pi\) | ||||
−0.134778 | + | 0.990876i | \(0.543032\pi\) | |||||||
\(524\) | −8307.77 | − | 15084.4i | −0.692608 | − | 1.25757i | ||||
\(525\) | 1489.73 | + | 4786.13i | 0.123842 | + | 0.397874i | ||||
\(526\) | −7867.64 | − | 4648.84i | −0.652178 | − | 0.385360i | ||||
\(527\) | 143.524i | 0.0118634i | ||||||||
\(528\) | −5797.38 | + | 11260.3i | −0.477838 | + | 0.928109i | ||||
\(529\) | −5536.48 | −0.455040 | ||||||||
\(530\) | 8910.06 | − | 3336.89i | 0.730242 | − | 0.273482i | ||||
\(531\) | 16444.0 | − | 2941.24i | 1.34390 | − | 0.240374i | ||||
\(532\) | −5381.68 | + | 2963.98i | −0.438582 | + | 0.241550i | ||||
\(533\) | 10540.5 | 0.856587 | ||||||||
\(534\) | 18984.8 | + | 9058.37i | 1.53849 | + | 0.734071i | ||||
\(535\) | −7271.51 | + | 9014.70i | −0.587616 | + | 0.728485i | ||||
\(536\) | 534.033 | + | 16.1683i | 0.0430349 | + | 0.00130292i | ||||
\(537\) | 6728.34 | − | 596.991i | 0.540688 | − | 0.0479740i | ||||
\(538\) | −13409.4 | − | 7923.38i | −1.07457 | − | 0.634946i | ||||
\(539\) | −10794.7 | −0.862632 | ||||||||
\(540\) | 1129.59 | + | 12497.5i | 0.0900181 | + | 0.995940i | ||||
\(541\) | −12838.6 | −1.02029 | −0.510143 | − | 0.860090i | \(-0.670408\pi\) | ||||
−0.510143 | + | 0.860090i | \(0.670408\pi\) | |||||||
\(542\) | −14798.5 | − | 8744.17i | −1.17279 | − | 0.692979i | ||||
\(543\) | −8311.61 | + | 737.471i | −0.656879 | + | 0.0582834i | ||||
\(544\) | −848.598 | − | 1657.61i | −0.0668811 | − | 0.130642i | ||||
\(545\) | −10968.1 | − | 8847.17i | −0.862059 | − | 0.695360i | ||||
\(546\) | 6480.81 | + | 3092.24i | 0.507973 | + | 0.242373i | ||||
\(547\) | −12645.7 | −0.988470 | −0.494235 | − | 0.869328i | \(-0.664552\pi\) | ||||
−0.494235 | + | 0.869328i | \(0.664552\pi\) | |||||||
\(548\) | 6898.09 | + | 12524.8i | 0.537722 | + | 0.976340i | ||||
\(549\) | −11686.2 | + | 2090.24i | −0.908481 | + | 0.162494i | ||||
\(550\) | 12779.5 | + | 4241.07i | 0.990760 | + | 0.328800i | ||||
\(551\) | 19616.8 | 1.51670 | ||||||||
\(552\) | −910.423 | − | 15617.4i | −0.0701996 | − | 1.20421i | ||||
\(553\) | − | 3254.75i | − | 0.250283i | ||||||
\(554\) | −5377.95 | − | 3177.73i | −0.412432 | − | 0.243698i | ||||
\(555\) | −8816.63 | + | 13160.1i | −0.674315 | + | 1.00651i | ||||
\(556\) | 9197.30 | − | 5065.44i | 0.701533 | − | 0.386371i | ||||
\(557\) | −1981.68 | −0.150748 | −0.0753739 | − | 0.997155i | \(-0.524015\pi\) | ||||
−0.0753739 | + | 0.997155i | \(0.524015\pi\) | |||||||
\(558\) | −998.383 | − | 372.033i | −0.0757436 | − | 0.0282247i | ||||
\(559\) | − | 17302.6i | − | 1.30916i | ||||||
\(560\) | 5227.62 | − | 1779.34i | 0.394477 | − | 0.134270i | ||||
\(561\) | −2027.80 | + | 179.923i | −0.152610 | + | 0.0135407i | ||||
\(562\) | 8421.26 | + | 4975.97i | 0.632081 | + | 0.373485i | ||||
\(563\) | − | 22599.7i | − | 1.69176i | −0.533371 | − | 0.845881i | \(-0.679075\pi\) | ||
0.533371 | − | 0.845881i | \(-0.320925\pi\) | |||||||
\(564\) | −2384.36 | + | 1603.09i | −0.178013 | + | 0.119685i | ||||
\(565\) | 4575.02 | + | 3690.34i | 0.340660 | + | 0.274785i | ||||
\(566\) | 787.671 | − | 1333.04i | 0.0584952 | − | 0.0989965i | ||||
\(567\) | 5277.19 | − | 1950.19i | 0.390866 | − | 0.144445i | ||||
\(568\) | 18707.6 | + | 566.388i | 1.38196 | + | 0.0418400i | ||||
\(569\) | 17235.1i | 1.26983i | 0.772584 | + | 0.634913i | \(0.218964\pi\) | ||||
−0.772584 | + | 0.634913i | \(0.781036\pi\) | |||||||
\(570\) | 7065.82 | + | 14746.3i | 0.519219 | + | 1.08361i | ||||
\(571\) | 14869.0i | 1.08975i | 0.838516 | + | 0.544877i | \(0.183424\pi\) | ||||
−0.838516 | + | 0.544877i | \(0.816576\pi\) | |||||||
\(572\) | 16895.7 | − | 9305.38i | 1.23505 | − | 0.680205i | ||||
\(573\) | −17777.5 | + | 1577.36i | −1.29610 | + | 0.115000i | ||||
\(574\) | −3128.83 | − | 1848.77i | −0.227517 | − | 0.134436i | ||||
\(575\) | −16255.0 | + | 3520.05i | −1.17892 | + | 0.255298i | ||||
\(576\) | 13730.4 | − | 1606.29i | 0.993226 | − | 0.116196i | ||||
\(577\) | − | 21553.6i | − | 1.55509i | −0.628828 | − | 0.777544i | \(-0.716465\pi\) | ||
0.628828 | − | 0.777544i | \(-0.283535\pi\) | |||||||
\(578\) | −6916.82 | + | 11705.9i | −0.497754 | + | 0.842392i | ||||
\(579\) | −681.668 | − | 7682.69i | −0.0489277 | − | 0.551436i | ||||
\(580\) | −17361.2 | − | 3075.84i | −1.24290 | − | 0.220202i | ||||
\(581\) | − | 5477.49i | − | 0.391127i | ||||||
\(582\) | 14415.6 | + | 6878.24i | 1.02671 | + | 0.489883i | ||||
\(583\) | −11458.5 | −0.814001 | ||||||||
\(584\) | 104.559 | − | 3453.56i | 0.00740874 | − | 0.244708i | ||||
\(585\) | 9192.18 | − | 16755.3i | 0.649658 | − | 1.18418i | ||||
\(586\) | −2123.70 | + | 3594.12i | −0.149709 | + | 0.253365i | ||||
\(587\) | 18603.0i | 1.30805i | 0.756472 | + | 0.654026i | \(0.226921\pi\) | ||||
−0.756472 | + | 0.654026i | \(0.773079\pi\) | |||||||
\(588\) | 6574.04 | + | 9777.92i | 0.461070 | + | 0.685773i | ||||
\(589\) | −1388.37 | −0.0971254 | ||||||||
\(590\) | −18322.3 | + | 6861.87i | −1.27851 | + | 0.478812i | ||||
\(591\) | −12672.5 | + | 1124.40i | −0.882026 | + | 0.0782602i | ||||
\(592\) | 14748.4 | + | 9327.94i | 1.02391 | + | 0.647595i | ||||
\(593\) | 3595.46 | 0.248984 | 0.124492 | − | 0.992221i | \(-0.460270\pi\) | ||||
0.124492 | + | 0.992221i | \(0.460270\pi\) | |||||||
\(594\) | 4004.75 | − | 14572.2i | 0.276628 | − | 1.00657i | ||||
\(595\) | 690.879 | + | 557.282i | 0.0476022 | + | 0.0383972i | ||||
\(596\) | 3769.92 | − | 2076.29i | 0.259097 | − | 0.142698i | ||||
\(597\) | −969.566 | − | 10927.4i | −0.0664685 | − | 0.749128i | ||||
\(598\) | −12120.3 | + | 20512.3i | −0.828825 | + | 1.40269i | ||||
\(599\) | 3960.98 | 0.270185 | 0.135093 | − | 0.990833i | \(-0.456867\pi\) | ||||
0.135093 | + | 0.990833i | \(0.456867\pi\) | |||||||
\(600\) | −3941.21 | − | 14158.6i | −0.268165 | − | 0.963373i | ||||
\(601\) | −10977.3 | −0.745044 | −0.372522 | − | 0.928023i | \(-0.621507\pi\) | ||||
−0.372522 | + | 0.928023i | \(0.621507\pi\) | |||||||
\(602\) | −3034.82 | + | 5136.08i | −0.205465 | + | 0.347726i | ||||
\(603\) | −627.564 | + | 112.248i | −0.0423820 | + | 0.00758060i | ||||
\(604\) | 20419.6 | − | 11246.2i | 1.37560 | − | 0.757617i | ||||
\(605\) | −1039.14 | − | 838.197i | −0.0698297 | − | 0.0563265i | ||||
\(606\) | −8745.13 | − | 4172.64i | −0.586215 | − | 0.279706i | ||||
\(607\) | 23452.6 | 1.56823 | 0.784113 | − | 0.620618i | \(-0.213118\pi\) | ||||
0.784113 | + | 0.620618i | \(0.213118\pi\) | |||||||
\(608\) | 16034.8 | − | 8208.86i | 1.06957 | − | 0.547555i | ||||
\(609\) | 698.646 | + | 7874.04i | 0.0464870 | + | 0.523928i | ||||
\(610\) | 13021.1 | − | 4876.51i | 0.864277 | − | 0.323679i | ||||
\(611\) | 4375.79 | 0.289731 | ||||||||
\(612\) | 1397.93 | + | 1727.23i | 0.0923331 | + | 0.114084i | ||||
\(613\) | − | 8603.86i | − | 0.566895i | −0.958988 | − | 0.283448i | \(-0.908522\pi\) | ||
0.958988 | − | 0.283448i | \(-0.0914782\pi\) | |||||||
\(614\) | −12359.9 | + | 20917.7i | −0.812384 | + | 1.37487i | ||||
\(615\) | −5383.49 | + | 8035.65i | −0.352981 | + | 0.526876i | ||||
\(616\) | −6647.44 | − | 201.257i | −0.434794 | − | 0.0131638i | ||||
\(617\) | 24130.8 | 1.57451 | 0.787254 | − | 0.616629i | \(-0.211502\pi\) | ||||
0.787254 | + | 0.616629i | \(0.211502\pi\) | |||||||
\(618\) | 3161.08 | − | 6625.08i | 0.205756 | − | 0.431229i | ||||
\(619\) | 10237.2i | 0.664728i | 0.943151 | + | 0.332364i | \(0.107846\pi\) | ||||
−0.943151 | + | 0.332364i | \(0.892154\pi\) | |||||||
\(620\) | 1228.73 | + | 217.691i | 0.0795920 | + | 0.0141011i | ||||
\(621\) | 4897.86 | + | 18013.0i | 0.316496 | + | 1.16399i | ||||
\(622\) | 8951.60 | − | 15149.6i | 0.577052 | − | 0.976596i | ||||
\(623\) | 11045.6i | 0.710328i | ||||||||
\(624\) | −18718.6 | − | 9637.29i | −1.20087 | − | 0.618270i | ||||
\(625\) | −14225.2 | + | 6464.10i | −0.910412 | + | 0.413702i | ||||
\(626\) | 510.815 | + | 301.831i | 0.0326138 | + | 0.0192709i | ||||
\(627\) | −1740.47 | − | 19615.8i | −0.110858 | − | 1.24941i | ||||
\(628\) | −5133.20 | + | 2827.13i | −0.326174 | + | 0.179641i | ||||
\(629\) | 2805.00i | 0.177810i | ||||||||
\(630\) | −5667.42 | + | 3361.36i | −0.358405 | + | 0.212571i | ||||
\(631\) | 5874.23i | 0.370601i | 0.982682 | + | 0.185301i | \(0.0593259\pi\) | ||||
−0.982682 | + | 0.185301i | \(0.940674\pi\) | |||||||
\(632\) | −288.787 | + | 9538.53i | −0.0181762 | + | 0.600352i | ||||
\(633\) | 846.111 | + | 9536.03i | 0.0531278 | + | 0.598773i | ||||
\(634\) | 2817.43 | − | 4768.18i | 0.176490 | − | 0.298689i | ||||
\(635\) | 3055.24 | + | 2464.44i | 0.190934 | + | 0.154013i | ||||
\(636\) | 6978.33 | + | 10379.2i | 0.435077 | + | 0.647112i | ||||
\(637\) | − | 17944.5i | − | 1.11615i | ||||||
\(638\) | 18281.3 | + | 10802.1i | 1.13443 | + | 0.670312i | ||||
\(639\) | −21984.0 | + | 3932.14i | −1.36099 | + | 0.243432i | ||||
\(640\) | −15478.2 | + | 4750.79i | −0.955982 | + | 0.293424i | ||||
\(641\) | 5137.09i | 0.316541i | 0.987396 | + | 0.158271i | \(0.0505918\pi\) | ||||
−0.987396 | + | 0.158271i | \(0.949408\pi\) | |||||||
\(642\) | −13740.8 | − | 6556.25i | −0.844712 | − | 0.403045i | ||||
\(643\) | 21566.2 | 1.32269 | 0.661343 | − | 0.750084i | \(-0.269987\pi\) | ||||
0.661343 | + | 0.750084i | \(0.269987\pi\) | |||||||
\(644\) | 7195.57 | − | 3962.98i | 0.440287 | − | 0.242490i | ||||
\(645\) | 13190.8 | + | 8837.18i | 0.805250 | + | 0.539478i | ||||
\(646\) | 2492.87 | + | 1472.99i | 0.151828 | + | 0.0897123i | ||||
\(647\) | 10029.7i | 0.609441i | 0.952442 | + | 0.304721i | \(0.0985631\pi\) | ||||
−0.952442 | + | 0.304721i | \(0.901437\pi\) | |||||||
\(648\) | −15638.6 | + | 5247.07i | −0.948059 | + | 0.318093i | ||||
\(649\) | 23562.8 | 1.42515 | ||||||||
\(650\) | −7050.15 | + | 21244.0i | −0.425430 | + | 1.28193i | ||||
\(651\) | −49.4464 | − | 557.282i | −0.00297689 | − | 0.0335509i | ||||
\(652\) | −3803.11 | − | 6905.29i | −0.228437 | − | 0.414773i | ||||
\(653\) | −5024.92 | −0.301134 | −0.150567 | − | 0.988600i | \(-0.548110\pi\) | ||||
−0.150567 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(654\) | 7976.93 | − | 16718.3i | 0.476946 | − | 0.999596i | ||||
\(655\) | −18732.4 | − | 15110.0i | −1.11746 | − | 0.901371i | ||||
\(656\) | 9005.47 | + | 5695.70i | 0.535982 | + | 0.338994i | ||||
\(657\) | 725.903 | + | 4058.42i | 0.0431053 | + | 0.240995i | ||||
\(658\) | −1298.90 | − | 767.498i | −0.0769552 | − | 0.0454714i | ||||
\(659\) | 27944.3 | 1.65183 | 0.825914 | − | 0.563796i | \(-0.190659\pi\) | ||||
0.825914 | + | 0.563796i | \(0.190659\pi\) | |||||||
\(660\) | −1535.34 | + | 17633.3i | −0.0905503 | + | 1.03996i | ||||
\(661\) | 7235.95 | 0.425788 | 0.212894 | − | 0.977075i | \(-0.431711\pi\) | ||||
0.212894 | + | 0.977075i | \(0.431711\pi\) | |||||||
\(662\) | −11955.7 | − | 7064.41i | −0.701922 | − | 0.414753i | ||||
\(663\) | −299.095 | − | 3370.93i | −0.0175202 | − | 0.197460i | ||||
\(664\) | −486.005 | + | 16052.6i | −0.0284046 | + | 0.938194i | ||||
\(665\) | −5390.83 | + | 6683.18i | −0.314357 | + | 0.389718i | ||||
\(666\) | −19512.2 | − | 7270.92i | −1.13526 | − | 0.423037i | ||||
\(667\) | −26228.6 | −1.52260 | ||||||||
\(668\) | −6449.56 | + | 3552.11i | −0.373564 | + | 0.205742i | ||||
\(669\) | −8309.80 | + | 737.310i | −0.480232 | + | 0.0426099i | ||||
\(670\) | 699.247 | − | 261.874i | 0.0403198 | − | 0.0151001i | ||||
\(671\) | −16745.4 | −0.963409 | ||||||||
\(672\) | 3866.05 | + | 6143.89i | 0.221929 | + | 0.352687i | ||||
\(673\) | 22940.3i | 1.31394i | 0.753917 | + | 0.656970i | \(0.228162\pi\) | ||||
−0.753917 | + | 0.656970i | \(0.771838\pi\) | |||||||
\(674\) | −8897.95 | − | 5257.63i | −0.508511 | − | 0.300469i | ||||
\(675\) | 8078.72 | + | 15565.4i | 0.460667 | + | 0.887573i | ||||
\(676\) | 6989.72 | + | 12691.2i | 0.397686 | + | 0.722077i | ||||
\(677\) | −18706.8 | −1.06198 | −0.530991 | − | 0.847377i | \(-0.678180\pi\) | ||||
−0.530991 | + | 0.847377i | \(0.678180\pi\) | |||||||
\(678\) | −3327.34 | + | 6973.54i | −0.188475 | + | 0.395010i | ||||
\(679\) | 8387.22i | 0.474038i | ||||||||
\(680\) | −1975.28 | − | 1694.50i | −0.111395 | − | 0.0955602i | ||||
\(681\) | −2891.19 | − | 32585.0i | −0.162688 | − | 1.83357i | ||||
\(682\) | −1293.85 | − | 764.514i | −0.0726455 | − | 0.0429249i | ||||
\(683\) | 6817.79i | 0.381955i | 0.981594 | + | 0.190978i | \(0.0611658\pi\) | ||||
−0.981594 | + | 0.190978i | \(0.938834\pi\) | |||||||
\(684\) | −16708.3 | + | 13522.8i | −0.934002 | + | 0.755930i | ||||
\(685\) | 15553.8 | + | 12546.1i | 0.867563 | + | 0.699800i | ||||
\(686\) | −6956.16 | + | 11772.5i | −0.387154 | + | 0.655214i | ||||
\(687\) | 22517.5 | − | 1997.93i | 1.25050 | − | 0.110954i | ||||
\(688\) | 9349.68 | − | 14782.8i | 0.518101 | − | 0.819168i | ||||
\(689\) | − | 19048.1i | − | 1.05323i | ||||||
\(690\) | −9447.34 | − | 19716.5i | −0.521238 | − | 1.08782i | ||||
\(691\) | − | 20798.4i | − | 1.14502i | −0.819897 | − | 0.572510i | \(-0.805970\pi\) | ||
0.819897 | − | 0.572510i | \(-0.194030\pi\) | |||||||
\(692\) | −15721.5 | − | 28545.6i | −0.863647 | − | 1.56812i | ||||
\(693\) | 7811.67 | − | 1397.22i | 0.428197 | − | 0.0765890i | ||||
\(694\) | 670.591 | + | 396.240i | 0.0366791 | + | 0.0216730i | ||||
\(695\) | 9212.94 | − | 11421.6i | 0.502830 | − | 0.623373i | ||||
\(696\) | −1348.84 | − | 23138.0i | −0.0734592 | − | 1.26012i | ||||
\(697\) | 1712.75i | 0.0930777i | ||||||||
\(698\) | −1456.84 | + | 2465.54i | −0.0790003 | + | 0.133699i | ||||
\(699\) | 3972.56 | − | 352.477i | 0.214959 | − | 0.0190728i | ||||
\(700\) | 5818.88 | − | 5069.46i | 0.314190 | − | 0.273725i | ||||
\(701\) | 5600.99i | 0.301778i | 0.988551 | + | 0.150889i | \(0.0482136\pi\) | ||||
−0.988551 | + | 0.150889i | \(0.951786\pi\) | |||||||
\(702\) | 24224.2 | + | 6657.30i | 1.30240 | + | 0.357926i | ||||
\(703\) | −27134.0 | −1.45573 | ||||||||
\(704\) | 19463.4 | + | 1179.63i | 1.04198 | + | 0.0631517i | ||||
\(705\) | −2234.90 | + | 3335.92i | −0.119392 | + | 0.178210i | ||||
\(706\) | −5815.94 | + | 9842.82i | −0.310036 | + | 0.524702i | ||||
\(707\) | − | 5088.05i | − | 0.270659i | ||||||
\(708\) | −14350.0 | − | 21343.5i | −0.761731 | − | 1.13296i | ||||
\(709\) | −20409.0 | −1.08106 | −0.540532 | − | 0.841323i | \(-0.681777\pi\) | ||||
−0.540532 | + | 0.841323i | \(0.681777\pi\) | |||||||
\(710\) | 24495.1 | − | 9173.64i | 1.29477 | − | 0.484902i | ||||
\(711\) | −2004.90 | − | 11209.1i | −0.105752 | − | 0.591244i | ||||
\(712\) | 980.055 | − | 32370.8i | 0.0515858 | − | 1.70386i | ||||
\(713\) | 1856.32 | 0.0975030 | ||||||||
\(714\) | −502.466 | + | 1053.08i | −0.0263366 | + | 0.0551969i | ||||
\(715\) | 16924.5 | − | 20981.8i | 0.885230 | − | 1.09745i | ||||
\(716\) | −5017.05 | − | 9109.44i | −0.261866 | − | 0.475469i | ||||
\(717\) | −18068.9 | + | 1603.21i | −0.941138 | + | 0.0835050i | ||||
\(718\) | 9059.70 | − | 15332.5i | 0.470898 | − | 0.796942i | ||||
\(719\) | −12116.1 | −0.628449 | −0.314224 | − | 0.949349i | \(-0.601744\pi\) | ||||
−0.314224 | + | 0.949349i | \(0.601744\pi\) | |||||||
\(720\) | 16907.4 | − | 9348.08i | 0.875143 | − | 0.483864i | ||||
\(721\) | 3854.57 | 0.199101 | ||||||||
\(722\) | −4379.81 | + | 7412.33i | −0.225761 | + | 0.382075i | ||||
\(723\) | 13569.9 | − | 1204.03i | 0.698022 | − | 0.0619339i | ||||
\(724\) | 6197.64 | + | 11253.0i | 0.318140 | + | 0.577646i | ||||
\(725\) | −24082.7 | + | 5215.13i | −1.23367 | + | 0.267152i | ||||
\(726\) | 755.748 | − | 1583.92i | 0.0386342 | − | 0.0809707i | ||||
\(727\) | 23614.9 | 1.20472 | 0.602358 | − | 0.798226i | \(-0.294228\pi\) | ||||
0.602358 | + | 0.798226i | \(0.294228\pi\) | |||||||
\(728\) | 334.560 | − | 11050.4i | 0.0170324 | − | 0.562575i | ||||
\(729\) | 16972.9 | − | 9966.99i | 0.862313 | − | 0.506375i | ||||
\(730\) | −1693.52 | − | 4521.99i | −0.0858632 | − | 0.229269i | ||||
\(731\) | 2811.54 | 0.142255 | ||||||||
\(732\) | 10198.1 | + | 15168.1i | 0.514934 | + | 0.765889i | ||||
\(733\) | 19739.1i | 0.994652i | 0.867564 | + | 0.497326i | \(0.165685\pi\) | ||||
−0.867564 | + | 0.497326i | \(0.834315\pi\) | |||||||
\(734\) | −590.555 | + | 999.447i | −0.0296972 | + | 0.0502592i | ||||
\(735\) | 13680.1 | + | 9165.02i | 0.686530 | + | 0.459942i | ||||
\(736\) | −21439.3 | + | 10975.6i | −1.07373 | + | 0.549684i | ||||
\(737\) | −899.244 | −0.0449445 | ||||||||
\(738\) | −11914.3 | − | 4439.68i | −0.594269 | − | 0.221445i | ||||
\(739\) | − | 37749.9i | − | 1.87909i | −0.342419 | − | 0.939547i | \(-0.611246\pi\) | ||
0.342419 | − | 0.939547i | \(-0.388754\pi\) | |||||||
\(740\) | 24014.1 | + | 4254.51i | 1.19294 | + | 0.211350i | ||||
\(741\) | 32608.5 | − | 2893.28i | 1.61660 | − | 0.143437i | ||||
\(742\) | −3340.96 | + | 5654.20i | −0.165297 | + | 0.279747i | ||||
\(743\) | 1106.26i | 0.0546229i | 0.999627 | + | 0.0273115i | \(0.00869459\pi\) | ||||
−0.999627 | + | 0.0273115i | \(0.991305\pi\) | |||||||
\(744\) | 95.4634 | + | 1637.58i | 0.00470411 | + | 0.0806945i | ||||
\(745\) | 3776.32 | − | 4681.62i | 0.185710 | − | 0.230230i | ||||
\(746\) | −15376.6 | − | 9085.73i | −0.754660 | − | 0.445914i | ||||
\(747\) | −3374.09 | − | 18864.0i | −0.165263 | − | 0.923960i | ||||
\(748\) | 1512.05 | + | 2745.43i | 0.0739119 | + | 0.134202i | ||||
\(749\) | − | 7994.59i | − | 0.390008i | ||||||
\(750\) | −12594.7 | − | 16224.9i | −0.613191 | − | 0.789935i | ||||
\(751\) | 6006.77i | 0.291864i | 0.989295 | + | 0.145932i | \(0.0466181\pi\) | ||||
−0.989295 | + | 0.145932i | \(0.953382\pi\) | |||||||
\(752\) | 3738.53 | + | 2364.51i | 0.181290 | + | 0.114661i | ||||
\(753\) | 8048.44 | − | 714.121i | 0.389511 | − | 0.0345604i | ||||
\(754\) | −17956.9 | + | 30390.0i | −0.867310 | + | 1.46782i | ||||
\(755\) | 20454.4 | − | 25357.9i | 0.985974 | − | 1.22234i | ||||
\(756\) | −6023.00 | − | 6224.98i | −0.289755 | − | 0.299471i | ||||
\(757\) | 36209.4i | 1.73851i | 0.494363 | + | 0.869255i | \(0.335401\pi\) | ||||
−0.494363 | + | 0.869255i | \(0.664599\pi\) | |||||||
\(758\) | −20163.1 | − | 11914.0i | −0.966172 | − | 0.570893i | ||||
\(759\) | 2327.09 | + | 26227.3i | 0.111289 | + | 1.25427i | ||||
\(760\) | 16391.6 | − | 19107.7i | 0.782350 | − | 0.911986i | ||||
\(761\) | 15892.1i | 0.757014i | 0.925598 | + | 0.378507i | \(0.123562\pi\) | ||||
−0.925598 | + | 0.378507i | \(0.876438\pi\) | |||||||
\(762\) | −2222.03 | + | 4656.98i | −0.105637 | + | 0.221397i | ||||
\(763\) | 9726.95 | 0.461519 | ||||||||
\(764\) | 13256.0 | + | 24068.8i | 0.627727 | + | 1.13976i | ||||
\(765\) | 2722.61 | + | 1493.66i | 0.128675 | + | 0.0705926i | ||||
\(766\) | 14518.3 | + | 8578.57i | 0.684812 | + | 0.404643i | ||||
\(767\) | 39169.8i | 1.84399i | ||||||||
\(768\) | −10784.9 | − | 18348.6i | −0.506727 | − | 0.862107i | ||||
\(769\) | 5305.55 | 0.248795 | 0.124397 | − | 0.992232i | \(-0.460300\pi\) | ||||
0.124397 | + | 0.992232i | \(0.460300\pi\) | |||||||
\(770\) | −8703.96 | + | 3259.71i | −0.407362 | + | 0.152561i | ||||
\(771\) | −5645.97 | + | 500.955i | −0.263729 | + | 0.0234001i | ||||
\(772\) | −10401.5 | + | 5728.67i | −0.484921 | + | 0.267072i | ||||
\(773\) | 5334.58 | 0.248217 | 0.124108 | − | 0.992269i | \(-0.460393\pi\) | ||||
0.124108 | + | 0.992269i | \(0.460393\pi\) | |||||||
\(774\) | −7287.87 | + | 19557.7i | −0.338446 | + | 0.908251i | ||||
\(775\) | 1704.44 | − | 369.099i | 0.0790004 | − | 0.0171076i | ||||
\(776\) | 744.179 | − | 24580.0i | 0.0344259 | − | 1.13707i | ||||
\(777\) | −966.370 | − | 10891.4i | −0.0446182 | − | 0.502866i | ||||
\(778\) | −7264.86 | − | 4292.67i | −0.334779 | − | 0.197814i | ||||
\(779\) | −16568.2 | −0.762026 | ||||||||
\(780\) | −29312.7 | − | 2552.28i | −1.34559 | − | 0.117162i | ||||
\(781\) | −31501.2 | −1.44328 | ||||||||
\(782\) | −3333.09 | − | 1969.46i | −0.152418 | − | 0.0900611i | ||||
\(783\) | 7256.43 | + | 26687.2i | 0.331192 | + | 1.21804i | ||||
\(784\) | 9696.54 | − | 15331.2i | 0.441716 | − | 0.698396i | ||||
\(785\) | −5141.93 | + | 6374.60i | −0.233788 | + | 0.289834i | ||||
\(786\) | 13623.8 | − | 28553.0i | 0.618248 | − | 1.29574i | ||||
\(787\) | −20007.5 | −0.906212 | −0.453106 | − | 0.891457i | \(-0.649684\pi\) | ||||
−0.453106 | + | 0.891457i | \(0.649684\pi\) | |||||||
\(788\) | 9449.38 | + | 17157.2i | 0.427183 | + | 0.775635i | ||||
\(789\) | −1483.77 | − | 16722.7i | −0.0669501 | − | 0.754556i | ||||
\(790\) | 4677.41 | + | 12489.5i | 0.210652 | + | 0.562475i | ||||
\(791\) | −4057.31 | −0.182378 | ||||||||
\(792\) | −23017.2 | + | 3401.66i | −1.03268 | + | 0.152617i | ||||
\(793\) | − | 27836.7i | − | 1.24655i | ||||||
\(794\) | 26233.9 | + | 15501.2i | 1.17255 | + | 0.692840i | ||||
\(795\) | 14521.4 | + | 9728.65i | 0.647827 | + | 0.434012i | ||||
\(796\) | −14794.5 | + | 8148.14i | −0.658767 | + | 0.362818i | ||||
\(797\) | 39622.6 | 1.76098 | 0.880492 | − | 0.474061i | \(-0.157212\pi\) | ||||
0.880492 | + | 0.474061i | \(0.157212\pi\) | |||||||
\(798\) | −10186.9 | − | 4860.57i | −0.451896 | − | 0.215617i | ||||
\(799\) | 711.032i | 0.0314825i | ||||||||
\(800\) | −17502.9 | + | 14340.5i | −0.773524 | + | 0.633767i | ||||
\(801\) | 6804.02 | + | 38040.3i | 0.300135 | + | 1.67801i | ||||
\(802\) | 11836.2 | + | 6993.77i | 0.521134 | + | 0.307928i | ||||
\(803\) | 5815.36i | 0.255566i | ||||||||
\(804\) | 547.648 | + | 814.546i | 0.0240225 | + | 0.0357299i | ||||
\(805\) | 7207.80 | − | 8935.73i | 0.315580 | − | 0.391234i | ||||
\(806\) | 1270.89 | − | 2150.84i | 0.0555400 | − | 0.0939952i | ||||
\(807\) | −2528.90 | − | 28501.8i | −0.110312 | − | 1.24326i | ||||
\(808\) | −451.451 | + | 14911.3i | −0.0196559 | + | 0.649228i | ||||
\(809\) | − | 23692.9i | − | 1.02966i | −0.857291 | − | 0.514832i | \(-0.827854\pi\) | ||
0.857291 | − | 0.514832i | \(-0.172146\pi\) | |||||||
\(810\) | −17447.6 | + | 15067.3i | −0.756845 | + | 0.653594i | ||||
\(811\) | 28377.6i | 1.22870i | 0.789035 | + | 0.614348i | \(0.210581\pi\) | ||||
−0.789035 | + | 0.614348i | \(0.789419\pi\) | |||||||
\(812\) | 10660.6 | − | 5871.36i | 0.460731 | − | 0.253749i | ||||
\(813\) | −2790.88 | − | 31454.4i | −0.120394 | − | 1.35689i | ||||
\(814\) | −25286.8 | − | 14941.5i | −1.08882 | − | 0.643365i | ||||
\(815\) | −8575.25 | − | 6917.03i | −0.368562 | − | 0.297292i | ||||
\(816\) | 1565.99 | − | 3041.63i | 0.0671819 | − | 0.130488i | ||||
\(817\) | 27197.3i | 1.16464i | ||||||||
\(818\) | 2464.55 | − | 4170.98i | 0.105344 | − | 0.178282i | ||||
\(819\) | 2322.68 | + | 12985.8i | 0.0990977 | + | 0.554040i | ||||
\(820\) | 14663.2 | + | 2597.83i | 0.624463 | + | 0.110634i | ||||
\(821\) | 12131.0i | 0.515682i | 0.966187 | + | 0.257841i | \(0.0830111\pi\) | ||||
−0.966187 | + | 0.257841i | \(0.916989\pi\) | |||||||
\(822\) | −11312.0 | + | 23708.1i | −0.479991 | + | 1.00598i | ||||
\(823\) | −28687.2 | −1.21503 | −0.607516 | − | 0.794307i | \(-0.707834\pi\) | ||||
−0.607516 | + | 0.794307i | \(0.707834\pi\) | |||||||
\(824\) | −11296.4 | − | 342.008i | −0.477583 | − | 0.0144592i | ||||
\(825\) | 7351.57 | + | 23618.8i | 0.310241 | + | 0.996728i | ||||
\(826\) | 6870.24 | − | 11627.1i | 0.289402 | − | 0.489780i | ||||
\(827\) | − | 10990.2i | − | 0.462113i | −0.972940 | − | 0.231056i | \(-0.925782\pi\) | ||
0.972940 | − | 0.231056i | \(-0.0742182\pi\) | |||||||
\(828\) | 22339.8 | − | 18080.6i | 0.937634 | − | 0.758869i | ||||
\(829\) | 492.369 | 0.0206281 | 0.0103140 | − | 0.999947i | \(-0.496717\pi\) | ||||
0.0103140 | + | 0.999947i | \(0.496717\pi\) | |||||||
\(830\) | 7871.71 | + | 21018.8i | 0.329194 | + | 0.879003i | ||||
\(831\) | −1014.24 | − | 11430.9i | −0.0423387 | − | 0.477176i | ||||
\(832\) | −1960.95 | + | 32355.1i | −0.0817113 | + | 1.34821i | ||||
\(833\) | 2915.85 | 0.121282 | ||||||||
\(834\) | 17409.4 | + | 8306.71i | 0.722830 | + | 0.344890i | ||||
\(835\) | −6460.52 | + | 8009.30i | −0.267755 | + | 0.331944i | ||||
\(836\) | −26557.7 | + | 14626.7i | −1.09871 | + | 0.605116i | ||||
\(837\) | −513.570 | − | 1888.77i | −0.0212086 | − | 0.0779995i | ||||
\(838\) | 10239.9 | − | 17329.8i | 0.422113 | − | 0.714379i | ||||
\(839\) | −41413.1 | −1.70410 | −0.852049 | − | 0.523462i | \(-0.824640\pi\) | ||||
−0.852049 | + | 0.523462i | \(0.824640\pi\) | |||||||
\(840\) | 8253.48 | + | 5898.96i | 0.339014 | + | 0.242302i | ||||
\(841\) | −14470.0 | −0.593301 | ||||||||
\(842\) | 11999.8 | − | 20308.4i | 0.491142 | − | 0.831202i | ||||
\(843\) | 1588.18 | + | 17899.5i | 0.0648870 | + | 0.731305i | ||||
\(844\) | 12910.8 | − | 7110.64i | 0.526548 | − | 0.289998i | ||||
\(845\) | 15760.4 | + | 12712.8i | 0.641628 | + | 0.517554i | ||||
\(846\) | −4946.09 | − | 1843.09i | −0.201005 | − | 0.0749014i | ||||
\(847\) | 921.548 | 0.0373846 | ||||||||
\(848\) | 10292.9 | − | 16274.0i | 0.416814 | − | 0.659024i | ||||
\(849\) | 2833.39 | − | 251.401i | 0.114537 | − | 0.0101626i | ||||
\(850\) | −3451.98 | − | 1145.60i | −0.139297 | − | 0.0462278i | ||||
\(851\) | 36279.5 | 1.46139 | ||||||||
\(852\) | 19184.5 | + | 28534.1i | 0.771421 | + | 1.14737i | ||||
\(853\) | − | 271.689i | − | 0.0109056i | −0.999985 | − | 0.00545279i | \(-0.998264\pi\) | ||
0.999985 | − | 0.00545279i | \(-0.00173569\pi\) | |||||||
\(854\) | −4882.46 | + | 8263.01i | −0.195637 | + | 0.331094i | ||||
\(855\) | −14448.8 | + | 26337.0i | −0.577940 | + | 1.05346i | ||||
\(856\) | −709.343 | + | 23429.3i | −0.0283234 | + | 0.935511i | ||||
\(857\) | −19071.8 | −0.760185 | −0.380093 | − | 0.924948i | \(-0.624108\pi\) | ||||
−0.380093 | + | 0.924948i | \(0.624108\pi\) | |||||||
\(858\) | 31981.7 | + | 15259.7i | 1.27254 | + | 0.607177i | ||||
\(859\) | − | 12820.4i | − | 0.509228i | −0.967043 | − | 0.254614i | \(-0.918052\pi\) | ||
0.967043 | − | 0.254614i | \(-0.0819485\pi\) | |||||||
\(860\) | 4264.43 | − | 24070.0i | 0.169088 | − | 0.954397i | ||||
\(861\) | −590.072 | − | 6650.36i | −0.0233561 | − | 0.263233i | ||||
\(862\) | −1938.25 | + | 3280.27i | −0.0765860 | + | 0.129613i | ||||
\(863\) | − | 15268.4i | − | 0.602251i | −0.953585 | − | 0.301125i | \(-0.902638\pi\) | ||
0.953585 | − | 0.301125i | \(-0.0973623\pi\) | |||||||
\(864\) | 17099.0 | + | 18777.6i | 0.673285 | + | 0.739383i | ||||
\(865\) | −35448.9 | − | 28594.1i | −1.39341 | − | 1.12396i | ||||
\(866\) | 8738.00 | + | 5163.12i | 0.342875 | + | 0.202598i | ||||
\(867\) | −24881.0 | + | 2207.64i | −0.974631 | + | 0.0864768i | ||||
\(868\) | −754.500 | + | 415.543i | −0.0295039 | + | 0.0162494i | ||||
\(869\) | − | 16061.7i | − | 0.626991i | ||||||
\(870\) | −13996.7 | − | 29211.0i | −0.545440 | − | 1.13833i | ||||
\(871\) | − | 1494.86i | − | 0.0581532i | ||||||
\(872\) | −28506.2 | − | 863.050i | −1.10704 | − | 0.0335167i | ||||
\(873\) | 5166.46 | + | 28884.9i | 0.200296 | + | 1.11982i | ||||
\(874\) | 19051.5 | − | 32242.5i | 0.737329 | − | 1.24785i | ||||
\(875\) | 4841.36 | − | 9637.79i | 0.187049 | − | 0.372362i | ||||
\(876\) | 5267.62 | − | 3541.61i | 0.203169 | − | 0.136598i | ||||
\(877\) | − | 15862.9i | − | 0.610778i | −0.952228 | − | 0.305389i | \(-0.901214\pi\) | ||
0.952228 | − | 0.305389i | \(-0.0987864\pi\) | |||||||
\(878\) | 7657.23 | + | 4524.51i | 0.294327 | + | 0.173912i | ||||
\(879\) | −7639.33 | + | 677.821i | −0.293138 | + | 0.0260095i | ||||
\(880\) | 25797.5 | − | 8780.77i | 0.988218 | − | 0.336363i | ||||
\(881\) | − | 16628.9i | − | 0.635916i | −0.948105 | − | 0.317958i | \(-0.897003\pi\) | ||
0.948105 | − | 0.317958i | \(-0.102997\pi\) | |||||||
\(882\) | −7558.24 | + | 20283.2i | −0.288548 | + | 0.774345i | ||||
\(883\) | 23628.7 | 0.900531 | 0.450266 | − | 0.892895i | \(-0.351329\pi\) | ||||
0.450266 | + | 0.892895i | \(0.351329\pi\) | |||||||
\(884\) | −4563.87 | + | 2513.56i | −0.173642 | + | 0.0956339i | ||||
\(885\) | −29861.4 | − | 20005.7i | −1.13421 | − | 0.759868i | ||||
\(886\) | 36267.2 | + | 21429.6i | 1.37519 | + | 0.812576i | ||||
\(887\) | 22448.4i | 0.849766i | 0.905248 | + | 0.424883i | \(0.139685\pi\) | ||||
−0.905248 | + | 0.424883i | \(0.860315\pi\) | |||||||
\(888\) | 1865.72 | + | 32004.6i | 0.0705060 | + | 1.20946i | ||||
\(889\) | −2709.50 | −0.102220 | ||||||||
\(890\) | −15873.7 | − | 42385.4i | −0.597852 | − | 1.59636i | ||||
\(891\) | 26042.1 | − | 9623.85i | 0.979172 | − | 0.361853i | ||||
\(892\) | 6196.28 | + | 11250.6i | 0.232586 | + | 0.422306i | ||||
\(893\) | −6878.13 | −0.257747 | ||||||||
\(894\) | 7136.02 | + | 3404.87i | 0.266962 | + | 0.127378i | ||||
\(895\) | −11312.4 | − | 9124.93i | −0.422495 | − | 0.340796i | ||||
\(896\) | 6257.05 | − | 9260.29i | 0.233296 | − | 0.345273i | ||||
\(897\) | −43599.1 | + | 3868.45i | −1.62289 | + | 0.143995i | ||||
\(898\) | 40271.0 | + | 23795.4i | 1.49650 | + | 0.884256i | ||||
\(899\) | 2750.23 | 0.102030 | ||||||||
\(900\) | 16917.0 | − | 21043.2i | 0.626555 | − | 0.779377i | ||||
\(901\) | 3095.16 | 0.114445 | ||||||||
\(902\) | −15440.3 | − | 9123.38i | −0.569962 | − | 0.336780i | ||||
\(903\) | −10916.8 | + | 968.622i | −0.402312 | + | 0.0356963i | ||||
\(904\) | 11890.5 | + | 359.996i | 0.437471 | + | 0.0132448i | ||||
\(905\) | 13974.4 | + | 11272.2i | 0.513288 | + | 0.414032i | ||||
\(906\) | 38652.1 | + | 18442.4i | 1.41736 | + | 0.676277i | ||||
\(907\) | −41932.0 | −1.53509 | −0.767546 | − | 0.640994i | \(-0.778523\pi\) | ||||
−0.767546 | + | 0.640994i | \(0.778523\pi\) | |||||||
\(908\) | −44116.6 | + | 24297.3i | −1.61240 | + | 0.888034i | ||||
\(909\) | −3134.20 | − | 17522.8i | −0.114362 | − | 0.639379i | ||||
\(910\) | −5418.79 | − | 14469.1i | −0.197397 | − | 0.527082i | ||||
\(911\) | −8399.36 | −0.305470 | −0.152735 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152735 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(912\) | 29423.0 | + | 15148.5i | 1.06830 | + | 0.550017i | ||||
\(913\) | − | 27030.5i | − | 0.979824i | ||||||
\(914\) | 21381.4 | + | 12633.9i | 0.773780 | + | 0.457212i | ||||
\(915\) | 21221.5 | + | 14217.4i | 0.766734 | + | 0.513674i | ||||
\(916\) | −16790.4 | − | 30486.2i | −0.605644 | − | 1.09967i | ||||
\(917\) | 16612.6 | 0.598251 | ||||||||
\(918\) | −1081.76 | + | 3936.24i | −0.0388926 | + | 0.141520i | ||||
\(919\) | − | 31517.0i | − | 1.13128i | −0.824651 | − | 0.565642i | \(-0.808629\pi\) | ||
0.824651 | − | 0.565642i | \(-0.191371\pi\) | |||||||
\(920\) | −21916.4 | + | 25547.9i | −0.785392 | + | 0.915532i | ||||
\(921\) | −44460.7 | + | 3944.90i | −1.59069 | + | 0.141139i | ||||
\(922\) | −22010.8 | − | 13005.8i | −0.786213 | − | 0.464558i | ||||
\(923\) | − | 52366.1i | − | 1.86744i | ||||||
\(924\) | −6816.91 | − | 10139.2i | −0.242706 | − | 0.360989i | ||||
\(925\) | 33311.2 | − | 7213.58i | 1.18407 | − | 0.256412i | ||||
\(926\) | 18228.7 | − | 30849.9i | 0.646902 | − | 1.09481i | ||||
\(927\) | 13274.8 | − | 2374.38i | 0.470337 | − | 0.0841262i | ||||
\(928\) | −31763.4 | + | 16261.0i | −1.12358 | + | 0.575207i | ||||
\(929\) | − | 10778.3i | − | 0.380650i | −0.981721 | − | 0.190325i | \(-0.939046\pi\) | ||
0.981721 | − | 0.190325i | \(-0.0609542\pi\) | |||||||
\(930\) | 990.612 | + | 2067.40i | 0.0349284 | + | 0.0728954i | ||||
\(931\) | 28206.3i | 0.992935i | ||||||||
\(932\) | −2962.18 | − | 5378.42i | −0.104109 | − | 0.189030i | ||||
\(933\) | 32200.5 | − | 2857.08i | 1.12990 | − | 0.100254i | ||||
\(934\) | 4031.39 | + | 2382.07i | 0.141233 | + | 0.0834517i | ||||
\(935\) | 3409.38 | + | 2750.10i | 0.119250 | + | 0.0961901i | ||||
\(936\) | −5654.75 | − | 38262.7i | −0.197469 | − | 1.33617i | ||||
\(937\) | − | 6351.95i | − | 0.221461i | −0.993850 | − | 0.110731i | \(-0.964681\pi\) | ||
0.993850 | − | 0.110731i | \(-0.0353191\pi\) | |||||||
\(938\) | −262.193 | + | 443.733i | −0.00912677 | + | 0.0154460i | ||||
\(939\) | 96.3354 | + | 1085.74i | 0.00334801 | + | 0.0377336i | ||||
\(940\) | 6087.26 | + | 1078.46i | 0.211217 | + | 0.0374209i | ||||
\(941\) | − | 13679.4i | − | 0.473895i | −0.971522 | − | 0.236948i | \(-0.923853\pi\) | ||
0.971522 | − | 0.236948i | \(-0.0761469\pi\) | |||||||
\(942\) | −9716.57 | − | 4636.15i | −0.336075 | − | 0.160354i | ||||
\(943\) | 22152.5 | 0.764989 | ||||||||
\(944\) | −21165.9 | + | 33465.3i | −0.729757 | + | 1.15382i | ||||
\(945\) | −11086.1 | − | 4861.66i | −0.381619 | − | 0.167354i | ||||
\(946\) | −14976.3 | + | 25345.7i | −0.514717 | + | 0.871100i | ||||
\(947\) | − | 15932.0i | − | 0.546696i | −0.961915 | − | 0.273348i | \(-0.911869\pi\) | ||
0.961915 | − | 0.273348i | \(-0.0881311\pi\) | |||||||
\(948\) | −14548.9 | + | 9781.71i | −0.498444 | + | 0.335122i | ||||
\(949\) | −9667.18 | −0.330674 | ||||||||
\(950\) | 11081.8 | − | 33392.5i | 0.378466 | − | 1.14042i | ||||
\(951\) | 10134.8 | − | 899.239i | 0.345577 | − | 0.0306623i | ||||
\(952\) | 1795.60 | + | 54.3634i | 0.0611301 | + | 0.00185076i | ||||
\(953\) | −47059.7 | −1.59959 | −0.799797 | − | 0.600270i | \(-0.795060\pi\) | ||||
−0.799797 | + | 0.600270i | \(0.795060\pi\) | |||||||
\(954\) | −8023.06 | + | 21530.6i | −0.272281 | + | 0.730691i | ||||
\(955\) | 29889.5 | + | 24109.7i | 1.01278 | + | 0.816934i | ||||
\(956\) | 13473.3 | + | 24463.3i | 0.455812 | + | 0.827616i | ||||
\(957\) | 3447.71 | + | 38857.1i | 0.116456 | + | 1.31251i | ||||
\(958\) | 9552.03 | − | 16165.7i | 0.322142 | − | 0.545189i | ||||
\(959\) | −13793.7 | −0.464466 | ||||||||
\(960\) | −23664.6 | − | 18020.1i | −0.795596 | − | 0.605828i | ||||
\(961\) | 29596.4 | 0.993466 | ||||||||
\(962\) | 24838.0 | − | 42035.6i | 0.832443 | − | 1.40882i | ||||
\(963\) | −4924.60 | − | 27532.7i | −0.164790 | − | 0.921318i | ||||
\(964\) | −10118.5 | − | 18372.2i | −0.338066 | − | 0.613825i | ||||
\(965\) | −10419.2 | + | 12917.0i | −0.347571 | + | 0.430895i | ||||
\(966\) | 13620.4 | + | 6498.81i | 0.453653 | + | 0.216455i | ||||
\(967\) | 16341.1 | 0.543429 | 0.271715 | − | 0.962378i | \(-0.412409\pi\) | ||||
0.271715 | + | 0.962378i | \(0.412409\pi\) | |||||||
\(968\) | −2700.73 | − | 81.7669i | −0.0896743 | − | 0.00271497i | ||||
\(969\) | 470.135 | + | 5298.62i | 0.0155861 | + | 0.175662i | ||||
\(970\) | −12053.3 | − | 32184.3i | −0.398977 | − | 1.06533i | ||||
\(971\) | 6032.45 | 0.199372 | 0.0996862 | − | 0.995019i | \(-0.468216\pi\) | ||||
0.0996862 | + | 0.995019i | \(0.468216\pi\) | |||||||
\(972\) | −24577.3 | − | 17728.2i | −0.811024 | − | 0.585012i | ||||
\(973\) | 10129.1i | 0.333734i | ||||||||
\(974\) | 20937.8 | − | 35434.9i | 0.688800 | − | 1.16572i | ||||
\(975\) | −39262.7 | + | 12220.9i | −1.28966 | + | 0.401418i | ||||
\(976\) | 15041.9 | − | 23782.7i | 0.493319 | − | 0.779986i | ||||
\(977\) | 39186.7 | 1.28321 | 0.641604 | − | 0.767036i | \(-0.278269\pi\) | ||||
0.641604 | + | 0.767036i | \(0.278269\pi\) | |||||||
\(978\) | 6236.64 | − | 13070.9i | 0.203912 | − | 0.427364i | ||||
\(979\) | 54508.4i | 1.77947i | ||||||||
\(980\) | 4422.63 | − | 24963.0i | 0.144159 | − | 0.813688i | ||||
\(981\) | 33498.8 | − | 5991.72i | 1.09025 | − | 0.195006i | ||||
\(982\) | −27953.0 | + | 47307.2i | −0.908365 | + | 1.53731i | ||||
\(983\) | 21033.5i | 0.682467i | 0.939979 | + | 0.341234i | \(0.110845\pi\) | ||||
−0.939979 | + | 0.341234i | \(0.889155\pi\) | |||||||
\(984\) | 1139.22 | + | 19542.2i | 0.0369075 | + | 0.633113i | ||||
\(985\) | 21306.5 | + | 17186.4i | 0.689219 | + | 0.555943i | ||||
\(986\) | −4938.14 | − | 2917.86i | −0.159495 | − | 0.0942429i | ||||
\(987\) | −244.962 | − | 2760.83i | −0.00789993 | − | 0.0890356i | ||||
\(988\) | −24314.8 | − | 44148.3i | −0.782953 | − | 1.42160i | ||||
\(989\) | − | 36364.0i | − | 1.16917i | ||||||
\(990\) | −27967.8 | + | 16587.7i | −0.897853 | + | 0.532518i | ||||
\(991\) | 17073.9i | 0.547296i | 0.961830 | + | 0.273648i | \(0.0882303\pi\) | ||||
−0.961830 | + | 0.273648i | \(0.911770\pi\) | |||||||
\(992\) | 2248.04 | − | 1150.86i | 0.0719510 | − | 0.0368346i | ||||
\(993\) | −2254.75 | − | 25412.0i | −0.0720567 | − | 0.812110i | ||||
\(994\) | −9184.82 | + | 15544.3i | −0.293083 | + | 0.496011i | ||||
\(995\) | −14819.7 | + | 18372.4i | −0.472177 | + | 0.585372i | ||||
\(996\) | −24484.5 | + | 16461.8i | −0.778938 | + | 0.523708i | ||||
\(997\) | − | 14259.5i | − | 0.452962i | −0.974016 | − | 0.226481i | \(-0.927278\pi\) | ||
0.974016 | − | 0.226481i | \(-0.0727221\pi\) | |||||||
\(998\) | 46773.0 | + | 27637.3i | 1.48354 | + | 0.876597i | ||||
\(999\) | −10037.1 | − | 36913.8i | −0.317878 | − | 1.16907i |
(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 | 60.4.h.c.59.14 | yes | 24 | |
3.2 | odd | 2 | inner | 60.4.h.c.59.12 | yes | 24 | |
4.3 | odd | 2 | inner | 60.4.h.c.59.15 | yes | 24 | |
5.4 | even | 2 | inner | 60.4.h.c.59.11 | yes | 24 | |
12.11 | even | 2 | inner | 60.4.h.c.59.9 | ✓ | 24 | |
15.14 | odd | 2 | inner | 60.4.h.c.59.13 | yes | 24 | |
20.19 | odd | 2 | inner | 60.4.h.c.59.10 | yes | 24 | |
60.59 | even | 2 | inner | 60.4.h.c.59.16 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.h.c.59.9 | ✓ | 24 | 12.11 | even | 2 | inner | |
60.4.h.c.59.10 | yes | 24 | 20.19 | odd | 2 | inner | |
60.4.h.c.59.11 | yes | 24 | 5.4 | even | 2 | inner | |
60.4.h.c.59.12 | yes | 24 | 3.2 | odd | 2 | inner | |
60.4.h.c.59.13 | yes | 24 | 15.14 | odd | 2 | inner | |
60.4.h.c.59.14 | yes | 24 | 1.1 | even | 1 | trivial | |
60.4.h.c.59.15 | yes | 24 | 4.3 | odd | 2 | inner | |
60.4.h.c.59.16 | yes | 24 | 60.59 | even | 2 | inner |