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 | 59.12 | ||
Character | \(\chi\) | \(=\) | 60.59 |
Dual form | 60.4.h.c.59.10 |
$q$-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 | ||||
\(6\) | −8.56554 | + | 11.9428i | −0.582811 | + | 0.812608i | ||||
\(7\) | 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 | \(-0.674794\pi\) | ||||
−0.521947 | + | 0.852978i | \(0.674794\pi\) | |||||||
\(12\) | −16.7574 | − | 38.0419i | −0.403121 | − | 0.915147i | ||||
\(13\) | 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 | ||||
\(15\) | 41.8173 | + | 40.3276i | 0.719812 | + | 0.694169i | ||||
\(16\) | −34.2101 | + | 54.0895i | −0.534532 | + | 0.845148i | ||||
\(17\) | 10.2873 | 0.146767 | 0.0733834 | − | 0.997304i | \(-0.476620\pi\) | ||||
0.0733834 | + | 0.997304i | \(0.476620\pi\) | |||||||
\(18\) | −49.8183 | + | 57.8804i | −0.652349 | + | 0.757919i | ||||
\(19\) | − | 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 | \(-0.793922\pi\) | ||
0.797646 | − | 0.603125i | \(-0.206078\pi\) | |||||||
\(24\) | 116.747 | + | 13.9308i | 0.992956 | + | 0.118484i | ||||
\(25\) | 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 | \(-0.782591\pi\) | ||
0.775677 | − | 0.631130i | \(-0.217409\pi\) | |||||||
\(30\) | −158.371 | + | 43.8037i | −0.963813 | + | 0.266581i | ||||
\(31\) | − | 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 | ||||
\(36\) | −69.2631 | − | 204.594i | −0.320663 | − | 0.947193i | ||||
\(37\) | − | 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 | \(0.102707\pi\) | ||||
−0.948394 | + | 0.317094i | \(0.897293\pi\) | |||||||
\(42\) | −66.1040 | + | 92.1681i | −0.242859 | + | 0.338615i | ||||
\(43\) | −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 | ||||
\(45\) | 197.919 | + | 227.932i | 0.655644 | + | 0.755070i | ||||
\(46\) | 324.000 | + | 191.446i | 1.03851 | + | 0.613634i | ||||
\(47\) | 69.1174i | 0.214507i | 0.994232 | + | 0.107253i | \(0.0342056\pi\) | ||||
−0.994232 | + | 0.107253i | \(0.965794\pi\) | |||||||
\(48\) | −201.905 | + | 264.247i | −0.607135 | + | 0.794599i | ||||
\(49\) | −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 | \(-0.372514\pi\) | ||||
0.389887 | + | 0.920863i | \(0.372514\pi\) | |||||||
\(54\) | −284.431 | + | 276.700i | −0.716782 | + | 0.697298i | ||||
\(55\) | −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 | \(-0.739156\pi\) | ||||
−0.682612 | + | 0.730781i | \(0.739156\pi\) | |||||||
\(60\) | 121.206 | − | 448.675i | 0.260793 | − | 0.965395i | ||||
\(61\) | −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 | ||||
\(66\) | 326.212 | − | 454.834i | 0.608393 | − | 0.848277i | ||||
\(67\) | −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 | \(-0.257040\pi\) | ||||
0.691296 | + | 0.722572i | \(0.257040\pi\) | |||||||
\(72\) | 597.865 | + | 125.718i | 0.978599 | + | 0.205778i | ||||
\(73\) | 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 | ||||
\(75\) | 80.8255 | + | 644.471i | 0.124439 | + | 0.992227i | ||||
\(76\) | −697.341 | + | 384.063i | −1.05251 | + | 0.579671i | ||||
\(77\) | −293.913 | −0.434993 | ||||||||
\(78\) | −756.095 | − | 542.280i | −1.09758 | − | 0.787194i | ||||
\(79\) | − | 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 | \(0.155498\pi\) | ||||
−0.883032 | + | 0.469312i | \(0.844502\pi\) | |||||||
\(84\) | −129.324 | − | 293.586i | −0.167982 | − | 0.381344i | ||||
\(85\) | 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 | \(-0.675195\pi\) | ||
0.523020 | − | 0.852321i | \(-0.324805\pi\) | |||||||
\(90\) | −839.814 | + | 153.990i | −0.983602 | + | 0.180355i | ||||
\(91\) | 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 | ||||
\(96\) | −352.955 | − | 871.871i | −0.375243 | − | 0.926927i | ||||
\(97\) | 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 | \(0.105285\pi\) | ||||
−0.945795 | + | 0.324763i | \(0.894715\pi\) | |||||||
\(102\) | −88.1163 | + | 122.860i | −0.0855374 | + | 0.119264i | ||||
\(103\) | 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 | ||||
\(105\) | 322.722 | + | 311.225i | 0.299947 | + | 0.289262i | ||||
\(106\) | −432.911 | + | 732.653i | −0.396680 | + | 0.671336i | ||||
\(107\) | 1035.91i | 0.935940i | 0.883744 | + | 0.467970i | \(0.155014\pi\) | ||||
−0.883744 | + | 0.467970i | \(0.844986\pi\) | |||||||
\(108\) | −264.536 | − | 1090.75i | −0.235694 | − | 0.971827i | ||||
\(109\) | 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 | \(-0.429774\pi\) | ||||
0.218835 | + | 0.975762i | \(0.429774\pi\) | |||||||
\(114\) | 1188.48 | + | 852.387i | 0.976412 | + | 0.700293i | ||||
\(115\) | 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 | ||||||||
\(120\) | 918.170 | + | 940.726i | 0.698475 | + | 0.715634i | ||||
\(121\) | 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 | ||||
\(126\) | −384.469 | + | 446.688i | −0.271835 | + | 0.315826i | ||||
\(127\) | −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 | \(-0.754869\pi\) | ||||
−0.717840 | + | 0.696208i | \(0.754869\pi\) | |||||||
\(132\) | 638.195 | + | 1448.80i | 0.420816 | + | 0.955316i | ||||
\(133\) | − | 767.989i | − | 0.500700i | ||||||
\(134\) | 33.9742 | − | 57.4974i | 0.0219024 | − | 0.0370673i | ||||
\(135\) | 919.716 | + | 1270.63i | 0.586345 | + | 0.810062i | ||||
\(136\) | 232.668 | + | 7.04424i | 0.146700 | + | 0.00444146i | ||||
\(137\) | 1787.35 | 1.11462 | 0.557312 | − | 0.830303i | \(-0.311833\pi\) | ||||
0.557312 | + | 0.830303i | \(0.311833\pi\) | |||||||
\(138\) | 1589.05 | + | 1139.68i | 0.980209 | + | 0.703016i | ||||
\(139\) | 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 | ||||||
\(144\) | −1166.38 | + | 1274.97i | −0.674986 | + | 0.737830i | ||||
\(145\) | 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 | \(-0.952750\pi\) | ||
0.989003 | − | 0.147897i | \(-0.0472504\pi\) | |||||||
\(150\) | −1685.64 | − | 730.481i | −0.917549 | − | 0.397623i | ||||
\(151\) | 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 | ||||
\(156\) | 2408.41 | − | 1060.90i | 1.23607 | − | 0.544490i | ||||
\(157\) | − | 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 | ||||||
\(162\) | −1599.24 | + | 1301.53i | −0.775604 | + | 0.631220i | ||||
\(163\) | 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 | ||||
\(165\) | −1592.58 | − | 1535.85i | −0.751408 | − | 0.724639i | ||||
\(166\) | −1728.32 | − | 1021.23i | −0.808096 | − | 0.477489i | ||||
\(167\) | 920.379i | 0.426474i | 0.977001 | + | 0.213237i | \(0.0684006\pi\) | ||||
−0.977001 | + | 0.213237i | \(0.931599\pi\) | |||||||
\(168\) | 900.989 | + | 107.510i | 0.413767 | + | 0.0493724i | ||||
\(169\) | −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 | \(-0.852903\pi\) | ||||
−0.895110 | + | 0.445845i | \(0.852903\pi\) | |||||||
\(174\) | 2354.26 | + | 1688.50i | 1.02572 | + | 0.735659i | ||||
\(175\) | 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 | \(-0.587489\pi\) | ||||
−0.271406 | + | 0.962465i | \(0.587489\pi\) | |||||||
\(180\) | 833.388 | − | 2266.60i | 0.345095 | − | 0.938568i | ||||
\(181\) | −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 | ||||
\(186\) | 166.621 | + | 119.503i | 0.0656843 | + | 0.0471095i | ||||
\(187\) | −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 | \(-0.274519\pi\) | ||||
0.650596 | + | 0.759424i | \(0.274519\pi\) | |||||||
\(192\) | 2630.94 | + | 395.016i | 0.988916 | + | 0.148478i | ||||
\(193\) | − | 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 | ||||
\(195\) | −2553.12 | + | 2647.43i | −0.937603 | + | 0.972238i | ||||
\(196\) | 1093.91 | + | 1986.21i | 0.398656 | + | 0.723839i | ||||
\(197\) | 2448.41 | 0.885491 | 0.442746 | − | 0.896647i | \(-0.354005\pi\) | ||||
0.442746 | + | 0.896647i | \(0.354005\pi\) | |||||||
\(198\) | 1897.29 | − | 2204.33i | 0.680984 | − | 0.791187i | ||||
\(199\) | − | 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 | ||||||
\(204\) | −172.389 | − | 391.349i | −0.0591649 | − | 0.134313i | ||||
\(205\) | −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 | ||||||||
\(210\) | −1222.21 | + | 338.052i | −0.401623 | + | 0.111085i | ||||
\(211\) | 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 | ||||
\(216\) | 3036.71 | + | 925.257i | 0.956582 | + | 0.291462i | ||||
\(217\) | − | 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 | ||||||||
\(222\) | 3256.41 | + | 2335.54i | 0.984488 | + | 0.706085i | ||||
\(223\) | −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 | ||||
\(225\) | 122.372 | + | 3372.78i | 0.0362584 | + | 0.999342i | ||||
\(226\) | −756.453 | + | 1280.21i | −0.222648 | + | 0.376807i | ||||
\(227\) | 6295.62i | 1.84077i | 0.391012 | + | 0.920386i | \(0.372125\pi\) | ||||
−0.391012 | + | 0.920386i | \(0.627875\pi\) | |||||||
\(228\) | −3785.69 | + | 1667.59i | −1.09962 | + | 0.484382i | ||||
\(229\) | 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 | \(-0.534413\pi\) | ||||
−0.107902 | + | 0.994162i | \(0.534413\pi\) | |||||||
\(234\) | −3664.38 | − | 3153.97i | −1.02371 | − | 0.881117i | ||||
\(235\) | −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 | \(-0.343381\pi\) | ||||
0.472417 | + | 0.881375i | \(0.343381\pi\) | |||||||
\(240\) | −3611.87 | + | 882.266i | −0.971438 | + | 0.237292i | ||||
\(241\) | 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 | ||||
\(246\) | −1988.39 | − | 1426.09i | −0.515346 | − | 0.369611i | ||||
\(247\) | 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 | \(-0.562640\pi\) | ||||
−0.195520 | + | 0.980700i | \(0.562640\pi\) | |||||||
\(252\) | −534.533 | − | 1578.94i | −0.133621 | − | 0.394698i | ||||
\(253\) | 5067.28i | 1.25920i | ||||||||
\(254\) | 505.166 | − | 854.936i | 0.124791 | − | 0.211195i | ||||
\(255\) | 430.187 | + | 414.862i | 0.105645 | + | 0.101881i | ||||
\(256\) | −1755.34 | − | 3700.81i | −0.428550 | − | 0.903518i | ||||
\(257\) | 1090.84 | 0.264765 | 0.132382 | − | 0.991199i | \(-0.457737\pi\) | ||||
0.132382 | + | 0.991199i | \(0.457737\pi\) | |||||||
\(258\) | 2340.98 | − | 3264.00i | 0.564895 | − | 0.787628i | ||||
\(259\) | − | 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 | \(0.123650\pi\) | ||||
−0.925495 | + | 0.378760i | \(0.876350\pi\) | |||||||
\(264\) | −4446.24 | − | 530.543i | −1.03654 | − | 0.123684i | ||||
\(265\) | 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 | \(0.214523\pi\) | ||||
−0.781366 | + | 0.624073i | \(0.785477\pi\) | |||||||
\(270\) | −4417.44 | + | 411.349i | −0.995692 | + | 0.0927183i | ||||
\(271\) | − | 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 | ||||
\(276\) | −5061.65 | + | 2229.65i | −1.10390 | + | 0.486265i | ||||
\(277\) | − | 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 | \(-0.880354\pi\) | ||
0.930186 | − | 0.367089i | \(-0.119646\pi\) | |||||||
\(282\) | −825.459 | − | 592.028i | −0.174310 | − | 0.125017i | ||||
\(283\) | 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 | ||||
\(285\) | 4013.14 | − | 4161.39i | 0.834098 | − | 0.864910i | ||||
\(286\) | 5871.25 | + | 3469.21i | 1.21390 | + | 0.717269i | ||||
\(287\) | 1284.89i | 0.264267i | ||||||||
\(288\) | −1426.43 | − | 4674.74i | −0.291852 | − | 0.956464i | ||||
\(289\) | −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 | \(-0.452992\pi\) | ||||
0.147145 | + | 0.989115i | \(0.452992\pi\) | |||||||
\(294\) | 2427.83 | − | 3385.10i | 0.481611 | − | 0.671506i | ||||
\(295\) | −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 | ||||||||
\(300\) | 4204.19 | − | 3053.65i | 0.809096 | − | 0.587676i | ||||
\(301\) | −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 | ||||
\(306\) | −512.496 | + | 595.433i | −0.0957433 | + | 0.111237i | ||||
\(307\) | −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 | \(-0.691962\pi\) | ||||
−0.567170 | + | 0.823601i | \(0.691962\pi\) | |||||||
\(312\) | −881.950 | + | 7391.21i | −0.160034 | + | 1.34117i | ||||
\(313\) | 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 | ||||
\(315\) | 1527.42 | + | 1759.05i | 0.273208 | + | 0.314639i | ||||
\(316\) | −2955.35 | + | 1627.67i | −0.526111 | + | 0.289757i | ||||
\(317\) | −1958.11 | −0.346935 | −0.173467 | − | 0.984840i | \(-0.555497\pi\) | ||||
−0.173467 | + | 0.984840i | \(0.555497\pi\) | |||||||
\(318\) | −2577.13 | + | 3593.27i | −0.454460 | + | 0.633650i | ||||
\(319\) | 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 | ||||||
\(324\) | −868.276 | − | 5767.00i | −0.148881 | − | 0.988855i | ||||
\(325\) | −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 | ||||||||
\(330\) | 6031.43 | − | 1668.23i | 1.00612 | − | 0.278282i | ||||
\(331\) | − | 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 | ||||
\(336\) | −1558.19 | + | 2039.31i | −0.252995 | + | 0.331111i | ||||
\(337\) | − | 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 | ||||||||
\(342\) | 5759.88 | + | 4957.60i | 0.910698 | + | 0.783848i | ||||
\(343\) | −4834.52 | −0.761048 | ||||||||
\(344\) | −6181.29 | − | 187.144i | −0.968816 | − | 0.0293317i | ||||
\(345\) | 5365.76 | − | 5563.98i | 0.837342 | − | 0.868274i | ||||
\(346\) | 5861.28 | − | 9919.55i | 0.910706 | − | 1.54127i | ||||
\(347\) | − | 275.386i | − | 0.0426037i | −0.999773 | − | 0.0213018i | \(-0.993219\pi\) | ||
0.999773 | − | 0.0213018i | \(-0.00678110\pi\) | |||||||
\(348\) | −7499.09 | + | 3303.34i | −1.15515 | + | 0.508844i | ||||
\(349\) | −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 | \(-0.401435\pi\) | ||||
0.304727 | + | 0.952440i | \(0.401435\pi\) | |||||||
\(354\) | 5299.52 | − | 7389.07i | 0.795668 | − | 1.10939i | ||||
\(355\) | 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 | \(-0.653167\pi\) | ||||
−0.462834 | + | 0.886445i | \(0.653167\pi\) | |||||||
\(360\) | 4320.26 | + | 5290.68i | 0.632494 | + | 0.774565i | ||||
\(361\) | −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 | ||||
\(366\) | 3766.20 | − | 5251.18i | 0.537876 | − | 0.749955i | ||||
\(367\) | −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 | ||||||||
\(372\) | −530.745 | + | 233.793i | −0.0739727 | + | 0.0325849i | ||||
\(373\) | − | 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 | ||||
\(375\) | −3820.45 | + | 6175.64i | −0.526099 | + | 0.850423i | ||||
\(376\) | −47.3282 | + | 1563.23i | −0.00649140 | + | 0.214408i | ||||
\(377\) | 12480.0 | 1.70491 | ||||||||
\(378\) | −2195.08 | + | 2135.41i | −0.298684 | + | 0.290565i | ||||
\(379\) | − | 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 | \(-0.869804\pi\) | ||
0.917510 | − | 0.397713i | \(-0.130196\pi\) | |||||||
\(384\) | −4747.44 | + | 5838.23i | −0.630903 | + | 0.775861i | ||||
\(385\) | −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 | \(0.0622847\pi\) | ||||
−0.980917 | + | 0.194427i | \(0.937715\pi\) | |||||||
\(390\) | −2773.19 | − | 10026.4i | −0.360066 | − | 1.30181i | ||||
\(391\) | − | 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 | ||||
\(396\) | 2637.84 | + | 7791.80i | 0.334738 | + | 0.988770i | ||||
\(397\) | 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 | \(-0.902127\pi\) | ||
0.953100 | − | 0.302655i | \(-0.0978731\pi\) | |||||||
\(402\) | 202.249 | − | 281.994i | 0.0250927 | − | 0.0349865i | ||||
\(403\) | 883.267 | 0.109178 | ||||||||
\(404\) | 4620.00 | − | 2544.48i | 0.568944 | − | 0.313348i | ||||
\(405\) | 4176.76 | + | 6998.91i | 0.512457 | + | 0.858713i | ||||
\(406\) | 3704.55 | + | 2188.95i | 0.452841 | + | 0.267575i | ||||
\(407\) | 10384.3i | 1.26470i | ||||||||
\(408\) | 1201.01 | + | 143.310i | 0.145733 | + | 0.0173895i | ||||
\(409\) | 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 | ||||||||
\(414\) | 7701.24 | + | 6628.54i | 0.914240 | + | 0.786896i | ||||
\(415\) | −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 | \(-0.636178\pi\) | ||||
−0.414884 | + | 0.909874i | \(0.636178\pi\) | |||||||
\(420\) | 935.398 | − | 3462.62i | 0.108673 | − | 0.402282i | ||||
\(421\) | 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 | ||||
\(426\) | −7084.94 | + | 9878.46i | −0.805790 | + | 1.12350i | ||||
\(427\) | −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 | \(-0.476017\pi\) | ||||
0.0752745 | + | 0.997163i | \(0.476017\pi\) | |||||||
\(432\) | −6622.47 | + | 6063.37i | −0.737555 | + | 0.675287i | ||||
\(433\) | 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 | ||||
\(435\) | 7949.65 | − | 8243.31i | 0.876222 | − | 0.908590i | ||||
\(436\) | −4864.33 | − | 8832.16i | −0.534311 | − | 0.970146i | ||||
\(437\) | −13240.7 | −1.44940 | ||||||||
\(438\) | −1823.64 | − | 1307.93i | −0.198943 | − | 0.142684i | ||||
\(439\) | 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 | \(-0.705542\pi\) | ||
0.601781 | − | 0.798661i | \(-0.294458\pi\) | |||||||
\(444\) | −10372.8 | + | 4569.19i | −1.10872 | + | 0.488388i | ||||
\(445\) | 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 | \(-0.664691\pi\) | ||
0.494614 | − | 0.869113i | \(-0.335309\pi\) | |||||||
\(450\) | −8389.13 | − | 4554.95i | −0.878816 | − | 0.477161i | ||||
\(451\) | − | 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 | ||||
\(456\) | 1386.30 | − | 11617.9i | 0.142367 | − | 1.19311i | ||||
\(457\) | 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 | \(0.150934\pi\) | ||||
−0.889671 | + | 0.456603i | \(0.849066\pi\) | |||||||
\(462\) | 2517.52 | − | 3510.15i | 0.253519 | − | 0.353479i | ||||
\(463\) | 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 | ||||
\(465\) | 562.633 | − | 583.417i | 0.0561107 | − | 0.0581835i | ||||
\(466\) | 1104.35 | − | 1868.99i | 0.109782 | − | 0.185793i | ||||
\(467\) | − | 1655.54i | − | 0.164045i | −0.996630 | − | 0.0820226i | \(-0.973862\pi\) | ||
0.996630 | − | 0.0820226i | \(-0.0261380\pi\) | |||||||
\(468\) | 12952.7 | − | 4385.01i | 1.27936 | − | 0.433114i | ||||
\(469\) | −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 | ||||||||
\(474\) | 5036.78 | + | 3612.43i | 0.488074 | + | 0.350052i | ||||
\(475\) | 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 | \(-0.602550\pi\) | ||||
−0.316625 | + | 0.948551i | \(0.602550\pi\) | |||||||
\(480\) | 3048.55 | − | 10064.7i | 0.289889 | − | 0.957060i | ||||
\(481\) | 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 | ||||
\(486\) | −8875.07 | + | 6002.03i | −0.828357 | + | 0.560201i | ||||
\(487\) | 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 | \(-0.148731\pi\) | ||||
0.892810 | + | 0.450434i | \(0.148731\pi\) | |||||||
\(492\) | 6333.68 | − | 2789.98i | 0.580375 | − | 0.255654i | ||||
\(493\) | − | 2027.90i | − | 0.185258i | ||||||
\(494\) | −9065.00 | + | 15341.5i | −0.825615 | + | 1.39726i | ||||
\(495\) | −7537.59 | − | 8680.64i | −0.684423 | − | 0.788213i | ||||
\(496\) | 754.633 | + | 477.284i | 0.0683146 | + | 0.0432070i | ||||
\(497\) | 6383.43 | 0.576129 | ||||||||
\(498\) | −8476.50 | − | 6079.44i | −0.762733 | − | 0.547040i | ||||
\(499\) | 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 | \(0.267670\pi\) | ||||
−0.666784 | + | 0.745251i | \(0.732330\pi\) | |||||||
\(504\) | 4613.99 | + | 970.221i | 0.407784 | + | 0.0857481i | ||||
\(505\) | −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 | \(-0.935976\pi\) | ||
0.979840 | − | 0.199784i | \(-0.0640240\pi\) | |||||||
\(510\) | −1629.21 | + | 450.622i | −0.141456 | + | 0.0391252i | ||||
\(511\) | 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 | ||||
\(516\) | 4579.84 | + | 10396.9i | 0.390729 | + | 0.887015i | ||||
\(517\) | − | 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 | \(0.112372\pi\) | ||||
−0.938330 | + | 0.345741i | \(0.887628\pi\) | |||||||
\(522\) | 11409.8 | + | 9820.52i | 0.956691 | + | 0.823434i | ||||
\(523\) | −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 | ||||
\(525\) | 623.765 | + | 4973.66i | 0.0518540 | + | 0.413463i | ||||
\(526\) | −7867.64 | − | 4648.84i | −0.652178 | − | 0.385360i | ||||
\(527\) | − | 143.524i | − | 0.0118634i | ||||||
\(528\) | 7689.41 | − | 10063.6i | 0.633785 | − | 0.829477i | ||||
\(529\) | −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 | ||||||||
\(534\) | 17093.3 | + | 12259.5i | 1.38520 | + | 0.993484i | ||||
\(535\) | −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 | ||||||||
\(540\) | 5354.38 | − | 11348.8i | 0.426696 | − | 0.904395i | ||||
\(541\) | −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 | ||||
\(546\) | −5835.12 | − | 4185.01i | −0.457362 | − | 0.328025i | ||||
\(547\) | −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 | ||||||||
\(552\) | 1853.55 | − | 15533.7i | 0.142921 | − | 1.19775i | ||||
\(553\) | − | 3254.75i | − | 0.250283i | ||||||
\(554\) | 5377.95 | + | 3177.73i | 0.412432 | + | 0.243698i | ||||
\(555\) | 10996.0 | − | 11402.2i | 0.840997 | − | 0.872064i | ||||
\(556\) | 9197.30 | − | 5065.44i | 0.701533 | − | 0.386371i | ||||
\(557\) | 1981.68 | 0.150748 | 0.0753739 | − | 0.997155i | \(-0.475985\pi\) | ||||
0.0753739 | + | 0.997155i | \(0.475985\pi\) | |||||||
\(558\) | 807.522 | + | 695.044i | 0.0612637 | + | 0.0527304i | ||||
\(559\) | − | 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 | \(0.320925\pi\) | ||||
−0.533371 | + | 0.845881i | \(0.679075\pi\) | |||||||
\(564\) | 2629.36 | − | 1158.23i | 0.196305 | − | 0.0864722i | ||||
\(565\) | 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 | \(-0.781036\pi\) | ||
0.772584 | − | 0.634913i | \(-0.218964\pi\) | |||||||
\(570\) | 4359.06 | + | 15760.0i | 0.320318 | + | 1.15810i | ||||
\(571\) | 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 | ||||
\(576\) | 13435.9 | + | 3252.76i | 0.971923 | + | 0.235298i | ||||
\(577\) | − | 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 | ||||||||
\(582\) | −12979.3 | − | 9308.93i | −0.924418 | − | 0.663003i | ||||
\(583\) | −11458.5 | −0.814001 | ||||||||
\(584\) | −104.559 | + | 3453.56i | −0.00740874 | + | 0.244708i | ||||
\(585\) | −14430.3 | + | 12530.1i | −1.01986 | + | 0.885568i | ||||
\(586\) | −2123.70 | + | 3594.12i | −0.149709 | + | 0.253365i | ||||
\(587\) | − | 18603.0i | − | 1.30805i | −0.756472 | − | 0.654026i | \(-0.773079\pi\) | ||
0.756472 | − | 0.654026i | \(-0.226921\pi\) | |||||||
\(588\) | 4749.75 | + | 10782.7i | 0.333123 | + | 0.756240i | ||||
\(589\) | −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 | \(-0.539730\pi\) | ||||
−0.124492 | + | 0.992221i | \(0.539730\pi\) | |||||||
\(594\) | 10832.4 | − | 10537.9i | 0.748244 | − | 0.727905i | ||||
\(595\) | 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 | \(-0.543133\pi\) | ||||
−0.135093 | + | 0.990833i | \(0.543133\pi\) | |||||||
\(600\) | 1386.73 | + | 14631.4i | 0.0943552 | + | 0.995539i | ||||
\(601\) | −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 | ||||
\(606\) | −7873.84 | − | 5647.20i | −0.527810 | − | 0.378551i | ||||
\(607\) | 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 | ||||||||
\(612\) | −712.531 | − | 2104.72i | −0.0470627 | − | 0.139017i | ||||
\(613\) | − | 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 | ||||
\(615\) | −6714.22 | + | 6962.25i | −0.440233 | + | 0.456496i | ||||
\(616\) | −6647.44 | − | 201.257i | −0.434794 | − | 0.0131638i | ||||
\(617\) | −24130.8 | −1.57451 | −0.787254 | − | 0.616629i | \(-0.788498\pi\) | ||||
−0.787254 | + | 0.616629i | \(0.788498\pi\) | |||||||
\(618\) | −4278.17 | + | 5965.01i | −0.278468 | + | 0.388265i | ||||
\(619\) | 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 | ||||||
\(624\) | −16729.3 | − | 12782.5i | −1.07325 | − | 0.820048i | ||||
\(625\) | −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 | ||||||
\(630\) | −6481.21 | + | 1188.41i | −0.409869 | + | 0.0751544i | ||||
\(631\) | 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 | ||||
\(636\) | −5041.85 | − | 11445.8i | −0.314343 | − | 0.713607i | ||||
\(637\) | − | 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 | \(-0.949408\pi\) | ||
0.987396 | − | 0.158271i | \(-0.0505918\pi\) | |||||||
\(642\) | −12371.8 | − | 8873.16i | −0.760552 | − | 0.545476i | ||||
\(643\) | 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 | ||||
\(645\) | −11428.8 | − | 11021.6i | −0.697685 | − | 0.672830i | ||||
\(646\) | 2492.87 | + | 1472.99i | 0.151828 | + | 0.0897123i | ||||
\(647\) | − | 10029.7i | − | 0.609441i | −0.952442 | − | 0.304721i | \(-0.901437\pi\) | ||
0.952442 | − | 0.304721i | \(-0.0985631\pi\) | |||||||
\(648\) | 15292.5 | + | 6183.54i | 0.927080 | + | 0.374865i | ||||
\(649\) | 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 | \(-0.451890\pi\) | ||||
0.150567 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(654\) | −10795.9 | + | 15052.6i | −0.645493 | + | 0.900005i | ||||
\(655\) | −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 | \(-0.809341\pi\) | ||||
−0.825914 | + | 0.563796i | \(0.809341\pi\) | |||||||
\(660\) | −4616.03 | + | 17087.5i | −0.272241 | + | 1.00777i | ||||
\(661\) | 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 | ||||
\(666\) | 15782.0 | + | 13583.8i | 0.918231 | + | 0.790332i | ||||
\(667\) | −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 | ||||||||
\(672\) | −2723.90 | − | 6728.60i | −0.156364 | − | 0.386252i | ||||
\(673\) | 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 | ||||
\(675\) | −915.536 | + | 17513.1i | −0.0522059 | + | 0.998636i | ||||
\(676\) | 6989.72 | + | 12691.2i | 0.397686 | + | 0.722077i | ||||
\(677\) | 18706.8 | 1.06198 | 0.530991 | − | 0.847377i | \(-0.321820\pi\) | ||||
0.530991 | + | 0.847377i | \(0.321820\pi\) | |||||||
\(678\) | −4503.19 | + | 6278.75i | −0.255079 | + | 0.355655i | ||||
\(679\) | 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 | \(-0.938834\pi\) | ||
0.981594 | − | 0.190978i | \(-0.0611658\pi\) | |||||||
\(684\) | −20359.9 | + | 6892.62i | −1.13813 | + | 0.385301i | ||||
\(685\) | 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 | ||||||||
\(690\) | 5828.27 | + | 21071.9i | 0.321563 | + | 1.16260i | ||||
\(691\) | − | 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 | ||||
\(696\) | 2746.13 | − | 23014.0i | 0.149557 | − | 1.25337i | ||||
\(697\) | 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 | \(-0.951786\pi\) | ||
0.988551 | − | 0.150889i | \(-0.0482136\pi\) | |||||||
\(702\) | −17517.7 | − | 18007.2i | −0.941829 | − | 0.968145i | ||||
\(703\) | −27134.0 | −1.45573 | ||||||||
\(704\) | −19463.4 | − | 1179.63i | −1.04198 | − | 0.0631517i | ||||
\(705\) | −2787.34 | + | 2890.30i | −0.148904 | + | 0.154404i | ||||
\(706\) | −5815.94 | + | 9842.82i | −0.310036 | + | 0.524702i | ||||
\(707\) | 5088.05i | 0.270659i | ||||||||
\(708\) | 10367.9 | + | 23536.7i | 0.550351 | + | 1.24938i | ||||
\(709\) | −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 | ||||||||
\(714\) | −680.031 | + | 948.161i | −0.0356436 | + | 0.0496975i | ||||
\(715\) | 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 | \(-0.398256\pi\) | ||||
0.314224 | + | 0.949349i | \(0.398256\pi\) | |||||||
\(720\) | −19099.6 | + | 2907.74i | −0.988609 | + | 0.150507i | ||||
\(721\) | 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 | ||||
\(726\) | −1022.82 | + | 1426.11i | −0.0522871 | + | 0.0729034i | ||||
\(727\) | 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 | ||||||||
\(732\) | 7368.12 | + | 16726.7i | 0.372040 | + | 0.844588i | ||||
\(733\) | 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 | ||||
\(735\) | −11852.7 | − | 11430.5i | −0.594823 | − | 0.573633i | ||||
\(736\) | −21439.3 | + | 10975.6i | −1.07373 | + | 0.549684i | ||||
\(737\) | 899.244 | 0.0449445 | ||||||||
\(738\) | −9636.62 | − | 8294.35i | −0.480663 | − | 0.413712i | ||||
\(739\) | − | 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 | \(-0.991305\pi\) | ||
0.999627 | − | 0.0273115i | \(-0.00869459\pi\) | |||||||
\(744\) | 194.356 | − | 1628.81i | 0.00957721 | − | 0.0802621i | ||||
\(745\) | 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 | ||||||||
\(750\) | −9541.23 | − | 18189.0i | −0.464528 | − | 0.885558i | ||||
\(751\) | 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 | ||||
\(756\) | −2041.54 | − | 8417.78i | −0.0982143 | − | 0.404963i | ||||
\(757\) | 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 | \(-0.876438\pi\) | ||
0.925598 | − | 0.378507i | \(-0.123562\pi\) | |||||||
\(762\) | 3007.27 | − | 4193.00i | 0.142968 | − | 0.199339i | ||||
\(763\) | 9726.95 | 0.461519 | ||||||||
\(764\) | −13256.0 | − | 24068.8i | −0.627727 | − | 1.13976i | ||||
\(765\) | 2036.05 | + | 2344.81i | 0.0962268 | + | 0.110819i | ||||
\(766\) | 14518.3 | + | 8578.57i | 0.684812 | + | 0.404643i | ||||
\(767\) | − | 39169.8i | − | 1.84399i | ||||||
\(768\) | −7385.78 | − | 19960.8i | −0.347020 | − | 0.937858i | ||||
\(769\) | 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 | \(-0.539607\pi\) | ||||
−0.124108 | + | 0.992269i | \(0.539607\pi\) | |||||||
\(774\) | 13615.4 | − | 15818.8i | 0.632296 | − | 0.734620i | ||||
\(775\) | 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 | ||||||||
\(780\) | 28405.4 | + | 7673.48i | 1.30394 | + | 0.352249i | ||||
\(781\) | −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 | ||||
\(786\) | 18438.2 | − | 25708.3i | 0.836731 | − | 1.16665i | ||||
\(787\) | −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 | ||||||||
\(792\) | −22769.3 | − | 4787.88i | −1.02155 | − | 0.214811i | ||||
\(793\) | − | 27836.7i | − | 1.24655i | ||||||
\(794\) | −26233.9 | − | 15501.2i | −1.17255 | − | 0.692840i | ||||
\(795\) | 12581.7 | + | 12133.5i | 0.561290 | + | 0.541295i | ||||
\(796\) | −14794.5 | + | 8148.14i | −0.658767 | + | 0.362818i | ||||
\(797\) | −39622.6 | −1.76098 | −0.880492 | − | 0.474061i | \(-0.842788\pi\) | ||||
−0.880492 | + | 0.474061i | \(0.842788\pi\) | |||||||
\(798\) | 9171.98 | + | 6578.24i | 0.406873 | + | 0.291814i | ||||
\(799\) | 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 | ||||||
\(804\) | 395.676 | + | 898.245i | 0.0173562 | + | 0.0394013i | ||||
\(805\) | 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 | \(0.172146\pi\) | ||||
−0.857291 | + | 0.514832i | \(0.827854\pi\) | |||||||
\(810\) | −23052.8 | + | 100.409i | −0.999991 | + | 0.00435559i | ||||
\(811\) | 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 | ||||
\(816\) | −2077.06 | + | 2718.39i | −0.0891074 | + | 0.116621i | ||||
\(817\) | 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 | \(-0.916989\pi\) | ||
0.966187 | − | 0.257841i | \(-0.0830111\pi\) | |||||||
\(822\) | −15309.6 | + | 21346.0i | −0.649615 | + | 0.905752i | ||||
\(823\) | −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 | ||||
\(825\) | −3078.18 | − | 24544.2i | −0.129901 | − | 1.03578i | ||||
\(826\) | 6870.24 | − | 11627.1i | 0.289402 | − | 0.489780i | ||||
\(827\) | 10990.2i | 0.462113i | 0.972940 | + | 0.231056i | \(0.0742182\pi\) | ||||
−0.972940 | + | 0.231056i | \(0.925782\pi\) | |||||||
\(828\) | −27222.1 | + | 9215.77i | −1.14255 | + | 0.386799i | ||||
\(829\) | 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 | ||||||||
\(834\) | −15674.9 | − | 11242.2i | −0.650813 | − | 0.466770i | ||||
\(835\) | −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 | \(-0.175360\pi\) | ||||
0.852049 | + | 0.523462i | \(0.175360\pi\) | |||||||
\(840\) | 7085.91 | + | 7259.99i | 0.291056 | + | 0.298206i | ||||
\(841\) | −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 | ||||
\(846\) | −4000.54 | − | 3443.31i | −0.162579 | − | 0.139933i | ||||
\(847\) | 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 | ||||||||
\(852\) | −13860.8 | − | 31466.2i | −0.557352 | − | 1.26527i | ||||
\(853\) | − | 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 | ||||
\(855\) | 22682.4 | − | 19695.6i | 0.907276 | − | 0.787808i | ||||
\(856\) | −709.343 | + | 23429.3i | −0.0283234 | + | 0.935511i | ||||
\(857\) | 19071.8 | 0.760185 | 0.380093 | − | 0.924948i | \(-0.375892\pi\) | ||||
0.380093 | + | 0.924948i | \(0.375892\pi\) | |||||||
\(858\) | 28795.3 | + | 20652.3i | 1.14575 | + | 0.821747i | ||||
\(859\) | − | 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 | \(0.0973623\pi\) | ||||
−0.953585 | + | 0.301125i | \(0.902638\pi\) | |||||||
\(864\) | −5236.13 | − | 24850.7i | −0.206177 | − | 0.978515i | ||||
\(865\) | −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 | ||||||||
\(870\) | 8634.89 | + | 31219.1i | 0.336494 | + | 1.21658i | ||||
\(871\) | − | 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 | ||||
\(876\) | 5808.90 | − | 2558.81i | 0.224046 | − | 0.0986921i | ||||
\(877\) | − | 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 | \(0.102997\pi\) | ||||
−0.948105 | + | 0.317958i | \(0.897003\pi\) | |||||||
\(882\) | 14120.6 | − | 16405.7i | 0.539075 | − | 0.626313i | ||||
\(883\) | 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 | ||||
\(885\) | −25872.5 | − | 24950.8i | −0.982705 | − | 0.947697i | ||||
\(886\) | 36267.2 | + | 21429.6i | 1.37519 | + | 0.812576i | ||||
\(887\) | − | 22448.4i | − | 0.849766i | −0.905248 | − | 0.424883i | \(-0.860315\pi\) | ||
0.905248 | − | 0.424883i | \(-0.139685\pi\) | |||||||
\(888\) | 3798.46 | − | 31833.1i | 0.143545 | − | 1.20298i | ||||
\(889\) | −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 | ||||||||
\(894\) | 6425.05 | + | 4608.11i | 0.240364 | + | 0.172392i | ||||
\(895\) | −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 | ||||||||
\(900\) | 23162.5 | − | 13874.4i | 0.857869 | − | 0.513868i | ||||
\(901\) | 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 | ||||
\(906\) | −34801.1 | − | 24959.7i | −1.27615 | − | 0.915266i | ||||
\(907\) | −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 | \(-0.451192\pi\) | ||||
0.152735 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(912\) | 26296.1 | + | 20092.3i | 0.954772 | + | 0.729520i | ||||
\(913\) | − | 27030.5i | − | 0.979824i | ||||||
\(914\) | −21381.4 | − | 12633.9i | −0.773780 | − | 0.457212i | ||||
\(915\) | −18386.7 | − | 17731.7i | −0.664314 | − | 0.640648i | ||||
\(916\) | −16790.4 | − | 30486.2i | −0.605644 | − | 1.09967i | ||||
\(917\) | −16612.6 | −0.598251 | ||||||||
\(918\) | −2926.03 | + | 2846.49i | −0.105200 | + | 0.102340i | ||||
\(919\) | − | 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 | ||||||||
\(924\) | 4925.22 | + | 11181.0i | 0.175355 | + | 0.398082i | ||||
\(925\) | 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 | \(0.0609542\pi\) | ||||
−0.981721 | + | 0.190325i | \(0.939046\pi\) | |||||||
\(930\) | 611.130 | + | 2209.52i | 0.0215481 | + | 0.0779064i | ||||
\(931\) | 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 | ||||
\(936\) | −7959.15 | + | 37850.5i | −0.277941 | + | 1.32178i | ||||
\(937\) | − | 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 | \(0.0761469\pi\) | ||||
−0.971522 | + | 0.236948i | \(0.923853\pi\) | |||||||
\(942\) | 8748.49 | + | 6274.51i | 0.302592 | + | 0.217022i | ||||
\(943\) | 22152.5 | 0.764989 | ||||||||
\(944\) | 21165.9 | − | 33465.3i | 0.729757 | − | 1.15382i | ||||
\(945\) | 7097.85 | + | 9805.99i | 0.244331 | + | 0.337554i | ||||
\(946\) | −14976.3 | + | 25345.7i | −0.514717 | + | 0.871100i | ||||
\(947\) | 15932.0i | 0.546696i | 0.961915 | + | 0.273348i | \(0.0881311\pi\) | ||||
−0.961915 | + | 0.273348i | \(0.911869\pi\) | |||||||
\(948\) | −16043.8 | + | 7067.29i | −0.549662 | + | 0.242125i | ||||
\(949\) | −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 | \(-0.204940\pi\) | ||||
0.799797 | + | 0.600270i | \(0.204940\pi\) | |||||||
\(954\) | −14988.9 | + | 17414.6i | −0.508684 | + | 0.591005i | ||||
\(955\) | 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 | ||||||||
\(960\) | 20122.1 | + | 21905.2i | 0.676499 | + | 0.736444i | ||||
\(961\) | 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 | ||||
\(966\) | 12263.4 | + | 8795.42i | 0.408455 | + | 0.292948i | ||||
\(967\) | 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 | \(-0.531784\pi\) | ||||
−0.0996862 | + | 0.995019i | \(0.531784\pi\) | |||||||
\(972\) | −1845.61 | − | 30247.7i | −0.0609032 | − | 0.998144i | ||||
\(973\) | 10129.1i | 0.333734i | ||||||||
\(974\) | −20937.8 | + | 35434.9i | −0.688800 | + | 1.16572i | ||||
\(975\) | −40801.1 | + | 5117.02i | −1.34019 | + | 0.168078i | ||||
\(976\) | 15041.9 | − | 23782.7i | 0.493319 | − | 0.779986i | ||||
\(977\) | −39186.7 | −1.28321 | −0.641604 | − | 0.767036i | \(-0.721731\pi\) | ||||
−0.641604 | + | 0.767036i | \(0.721731\pi\) | |||||||
\(978\) | −8440.61 | + | 11768.7i | −0.275972 | + | 0.384785i | ||||
\(979\) | 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 | \(-0.889155\pi\) | ||
0.939979 | − | 0.341234i | \(-0.110845\pi\) | |||||||
\(984\) | −2319.36 | + | 19437.5i | −0.0751408 | + | 0.629720i | ||||
\(985\) | 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 | ||||||||
\(990\) | 31983.7 | − | 5864.60i | 1.02678 | − | 0.188272i | ||||
\(991\) | 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 | ||||
\(996\) | 27000.5 | − | 11893.7i | 0.858978 | − | 0.378379i | ||||
\(997\) | − | 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.59.12 | yes | 24 | |
3.2 | odd | 2 | inner | 60.4.h.c.59.14 | yes | 24 | |
4.3 | odd | 2 | inner | 60.4.h.c.59.9 | ✓ | 24 | |
5.4 | even | 2 | inner | 60.4.h.c.59.13 | yes | 24 | |
12.11 | even | 2 | inner | 60.4.h.c.59.15 | yes | 24 | |
15.14 | odd | 2 | inner | 60.4.h.c.59.11 | yes | 24 | |
20.19 | odd | 2 | inner | 60.4.h.c.59.16 | yes | 24 | |
60.59 | even | 2 | inner | 60.4.h.c.59.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.h.c.59.9 | ✓ | 24 | 4.3 | odd | 2 | inner | |
60.4.h.c.59.10 | yes | 24 | 60.59 | even | 2 | inner | |
60.4.h.c.59.11 | yes | 24 | 15.14 | odd | 2 | inner | |
60.4.h.c.59.12 | yes | 24 | 1.1 | even | 1 | trivial | |
60.4.h.c.59.13 | yes | 24 | 5.4 | even | 2 | inner | |
60.4.h.c.59.14 | yes | 24 | 3.2 | odd | 2 | inner | |
60.4.h.c.59.15 | yes | 24 | 12.11 | even | 2 | inner | |
60.4.h.c.59.16 | yes | 24 | 20.19 | odd | 2 | inner |