Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [125,4,Mod(24,125)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(125, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("125.24");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 125 = 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 125.e (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.37523875072\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 24.4 | ||
Character | \(\chi\) | \(=\) | 125.24 |
Dual form | 125.4.e.a.99.4 |
$q$-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 \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.48841 | + | 0.483614i | 0.526233 | + | 0.170984i | 0.560072 | − | 0.828444i | \(-0.310773\pi\) |
−0.0338391 | + | 0.999427i | \(0.510773\pi\) | |||||||
\(3\) | 4.16357 | − | 5.73067i | 0.801280 | − | 1.10287i | −0.191330 | − | 0.981526i | \(-0.561280\pi\) |
0.992611 | − | 0.121342i | \(-0.0387198\pi\) | |||||||
\(4\) | −4.49065 | − | 3.26265i | −0.561331 | − | 0.407831i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 8.96855 | − | 6.51603i | 0.610232 | − | 0.443360i | ||||
\(7\) | − | 1.18261i | − | 0.0638552i | −0.999490 | − | 0.0319276i | \(-0.989835\pi\) | ||
0.999490 | − | 0.0319276i | \(-0.0101646\pi\) | |||||||
\(8\) | −12.4652 | − | 17.1569i | −0.550889 | − | 0.758233i | ||||
\(9\) | −7.16175 | − | 22.0416i | −0.265250 | − | 0.816356i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.19826 | − | 22.1540i | 0.197305 | − | 0.607243i | −0.802637 | − | 0.596468i | \(-0.796570\pi\) |
0.999942 | − | 0.0107749i | \(-0.00342983\pi\) | |||||||
\(12\) | −37.3943 | + | 12.1501i | −0.899567 | + | 0.292287i | ||||
\(13\) | 34.0413 | − | 11.0607i | 0.726258 | − | 0.235976i | 0.0775239 | − | 0.996990i | \(-0.475299\pi\) |
0.648734 | + | 0.761015i | \(0.275299\pi\) | |||||||
\(14\) | 0.571929 | − | 1.76022i | 0.0109182 | − | 0.0336027i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.46617 | + | 10.6678i | 0.0541589 | + | 0.166684i | ||||
\(17\) | −76.1834 | − | 104.857i | −1.08689 | − | 1.49598i | −0.851699 | − | 0.524032i | \(-0.824427\pi\) |
−0.235194 | − | 0.971948i | \(-0.575573\pi\) | |||||||
\(18\) | − | 36.2705i | − | 0.474947i | ||||||
\(19\) | −85.6642 | + | 62.2387i | −1.03435 | + | 0.751502i | −0.969175 | − | 0.246372i | \(-0.920762\pi\) |
−0.0651781 | + | 0.997874i | \(0.520762\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.77717 | − | 4.92390i | −0.0704238 | − | 0.0511659i | ||||
\(22\) | 21.4280 | − | 29.4931i | 0.207657 | − | 0.285816i | ||||
\(23\) | 71.8250 | + | 23.3374i | 0.651154 | + | 0.211573i | 0.615923 | − | 0.787806i | \(-0.288783\pi\) |
0.0352312 | + | 0.999379i | \(0.488783\pi\) | |||||||
\(24\) | −150.220 | −1.27765 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 56.0166 | 0.422529 | ||||||||
\(27\) | 25.7621 | + | 8.37062i | 0.183627 | + | 0.0596640i | ||||
\(28\) | −3.85845 | + | 5.31070i | −0.0260421 | + | 0.0358439i | ||||
\(29\) | 216.865 | + | 157.562i | 1.38865 | + | 1.00891i | 0.996012 | + | 0.0892210i | \(0.0284377\pi\) |
0.392639 | + | 0.919693i | \(0.371562\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 192.656 | − | 139.973i | 1.11620 | − | 0.810964i | 0.132568 | − | 0.991174i | \(-0.457678\pi\) |
0.983628 | + | 0.180210i | \(0.0576776\pi\) | |||||||
\(32\) | 187.211i | 1.03420i | ||||||||
\(33\) | −96.9866 | − | 133.491i | −0.511612 | − | 0.704174i | ||||
\(34\) | −62.6817 | − | 192.914i | −0.316171 | − | 0.973075i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −39.7531 | + | 122.347i | −0.184042 | + | 0.566423i | ||||
\(37\) | 166.220 | − | 54.0080i | 0.738550 | − | 0.239969i | 0.0845026 | − | 0.996423i | \(-0.473070\pi\) |
0.654047 | + | 0.756454i | \(0.273070\pi\) | |||||||
\(38\) | −157.603 | + | 51.2084i | −0.672806 | + | 0.218608i | ||||
\(39\) | 78.3483 | − | 241.131i | 0.321687 | − | 0.990049i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.36260 | + | 19.5821i | 0.0242359 | + | 0.0745903i | 0.962443 | − | 0.271484i | \(-0.0875144\pi\) |
−0.938207 | + | 0.346074i | \(0.887514\pi\) | |||||||
\(42\) | −7.70595 | − | 10.6063i | −0.0283108 | − | 0.0389665i | ||||
\(43\) | 131.925i | 0.467869i | 0.972252 | + | 0.233934i | \(0.0751601\pi\) | ||||
−0.972252 | + | 0.233934i | \(0.924840\pi\) | |||||||
\(44\) | −104.605 | + | 76.0003i | −0.358406 | + | 0.260397i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 95.6189 | + | 69.4712i | 0.306483 | + | 0.222673i | ||||
\(47\) | 101.704 | − | 139.984i | 0.315640 | − | 0.434441i | −0.621490 | − | 0.783422i | \(-0.713472\pi\) |
0.937130 | + | 0.348981i | \(0.113472\pi\) | |||||||
\(48\) | 75.5651 | + | 24.5526i | 0.227227 | + | 0.0738304i | ||||
\(49\) | 341.601 | 0.995923 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −918.098 | −2.52077 | ||||||||
\(52\) | −188.955 | − | 61.3951i | −0.503909 | − | 0.163730i | ||||
\(53\) | 19.3553 | − | 26.6403i | 0.0501633 | − | 0.0690438i | −0.783198 | − | 0.621772i | \(-0.786413\pi\) |
0.833362 | + | 0.552728i | \(0.186413\pi\) | |||||||
\(54\) | 34.2965 | + | 24.9179i | 0.0864290 | + | 0.0627943i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −20.2899 | + | 14.7415i | −0.0484171 | + | 0.0351771i | ||||
\(57\) | 750.049i | 1.74292i | ||||||||
\(58\) | 246.586 | + | 339.396i | 0.558246 | + | 0.768360i | ||||
\(59\) | 148.786 | + | 457.918i | 0.328311 | + | 1.01044i | 0.969924 | + | 0.243409i | \(0.0782656\pi\) |
−0.641613 | + | 0.767029i | \(0.721734\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −174.560 | + | 537.239i | −0.366395 | + | 1.12765i | 0.582709 | + | 0.812681i | \(0.301993\pi\) |
−0.949103 | + | 0.314965i | \(0.898007\pi\) | |||||||
\(62\) | 354.445 | − | 115.166i | 0.726041 | − | 0.235905i | ||||
\(63\) | −26.0667 | + | 8.46959i | −0.0521285 | + | 0.0169376i | ||||
\(64\) | −62.8084 | + | 193.304i | −0.122673 | + | 0.377548i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −79.7980 | − | 245.593i | −0.148825 | − | 0.458037i | ||||
\(67\) | −198.345 | − | 272.998i | −0.361667 | − | 0.497791i | 0.588946 | − | 0.808173i | \(-0.299543\pi\) |
−0.950612 | + | 0.310381i | \(0.899543\pi\) | |||||||
\(68\) | 719.437i | 1.28301i | ||||||||
\(69\) | 432.787 | − | 314.438i | 0.755094 | − | 0.548608i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −170.875 | − | 124.148i | −0.285622 | − | 0.207517i | 0.435744 | − | 0.900071i | \(-0.356485\pi\) |
−0.721366 | + | 0.692554i | \(0.756485\pi\) | |||||||
\(72\) | −288.892 | + | 397.626i | −0.472865 | + | 0.650842i | ||||
\(73\) | −452.871 | − | 147.147i | −0.726090 | − | 0.235921i | −0.0774284 | − | 0.996998i | \(-0.524671\pi\) |
−0.648662 | + | 0.761077i | \(0.724671\pi\) | |||||||
\(74\) | 273.522 | 0.429680 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 587.751 | 0.887100 | ||||||||
\(77\) | −26.1996 | − | 8.51277i | −0.0387756 | − | 0.0125990i | ||||
\(78\) | 233.229 | − | 321.013i | 0.338564 | − | 0.465994i | ||||
\(79\) | −792.426 | − | 575.731i | −1.12854 | − | 0.819934i | −0.143060 | − | 0.989714i | \(-0.545694\pi\) |
−0.985482 | + | 0.169780i | \(0.945694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 661.474 | − | 480.589i | 0.907372 | − | 0.659244i | ||||
\(82\) | 32.2232i | 0.0433958i | ||||||||
\(83\) | −126.573 | − | 174.213i | −0.167388 | − | 0.230389i | 0.717080 | − | 0.696991i | \(-0.245478\pi\) |
−0.884468 | + | 0.466602i | \(0.845478\pi\) | |||||||
\(84\) | 14.3689 | + | 44.2230i | 0.0186640 | + | 0.0574420i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −63.8008 | + | 196.359i | −0.0799978 | + | 0.246208i | ||||
\(87\) | 1805.87 | − | 586.763i | 2.22540 | − | 0.723075i | ||||
\(88\) | −469.820 | + | 152.654i | −0.569125 | + | 0.184920i | ||||
\(89\) | −120.001 | + | 369.326i | −0.142922 | + | 0.439870i | −0.996738 | − | 0.0807057i | \(-0.974283\pi\) |
0.853816 | + | 0.520576i | \(0.174283\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0805 | − | 40.2577i | −0.0150683 | − | 0.0463753i | ||||
\(92\) | −246.399 | − | 339.139i | −0.279227 | − | 0.384323i | ||||
\(93\) | − | 1686.84i | − | 1.88083i | ||||||
\(94\) | 219.076 | − | 159.168i | 0.240382 | − | 0.174648i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1072.84 | + | 779.466i | 1.14059 | + | 0.828686i | ||||
\(97\) | −325.030 | + | 447.366i | −0.340225 | + | 0.468280i | −0.944507 | − | 0.328491i | \(-0.893460\pi\) |
0.604282 | + | 0.796770i | \(0.293460\pi\) | |||||||
\(98\) | 508.444 | + | 165.203i | 0.524087 | + | 0.170286i | ||||
\(99\) | −539.861 | −0.548062 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −637.953 | −0.628502 | −0.314251 | − | 0.949340i | \(-0.601753\pi\) | ||||
−0.314251 | + | 0.949340i | \(0.601753\pi\) | |||||||
\(102\) | −1366.51 | − | 444.006i | −1.32651 | − | 0.431011i | ||||
\(103\) | −328.881 | + | 452.666i | −0.314618 | + | 0.433034i | −0.936814 | − | 0.349827i | \(-0.886240\pi\) |
0.622197 | + | 0.782861i | \(0.286240\pi\) | |||||||
\(104\) | −614.098 | − | 446.168i | −0.579012 | − | 0.420677i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 41.6922 | − | 30.2912i | 0.0382029 | − | 0.0277560i | ||||
\(107\) | − | 347.014i | − | 0.313524i | −0.987636 | − | 0.156762i | \(-0.949894\pi\) | ||
0.987636 | − | 0.156762i | \(-0.0501056\pi\) | |||||||
\(108\) | −88.3783 | − | 121.642i | −0.0787426 | − | 0.108380i | ||||
\(109\) | 44.4432 | + | 136.782i | 0.0390540 | + | 0.120196i | 0.968683 | − | 0.248301i | \(-0.0798724\pi\) |
−0.929629 | + | 0.368497i | \(0.879872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 382.566 | − | 1177.42i | 0.327131 | − | 1.00681i | ||||
\(112\) | 12.6159 | − | 4.09914i | 0.0106436 | − | 0.00345832i | ||||
\(113\) | 1243.62 | − | 404.077i | 1.03531 | − | 0.336393i | 0.258423 | − | 0.966032i | \(-0.416797\pi\) |
0.776888 | + | 0.629639i | \(0.216797\pi\) | |||||||
\(114\) | −362.734 | + | 1116.38i | −0.298010 | + | 0.917182i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −459.797 | − | 1415.11i | −0.368027 | − | 1.13267i | ||||
\(117\) | −487.591 | − | 671.111i | −0.385280 | − | 0.530293i | ||||
\(118\) | 753.525i | 0.587861i | ||||||||
\(119\) | −124.006 | + | 90.0955i | −0.0955260 | + | 0.0694037i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 637.818 | + | 463.402i | 0.479202 | + | 0.348161i | ||||
\(122\) | −519.633 | + | 715.214i | −0.385618 | + | 0.530758i | ||||
\(123\) | 138.709 | + | 45.0694i | 0.101683 | + | 0.0330388i | ||||
\(124\) | −1321.83 | −0.957292 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −42.8940 | −0.0303278 | ||||||||
\(127\) | −1927.43 | − | 626.261i | −1.34671 | − | 0.437572i | −0.455125 | − | 0.890427i | \(-0.650406\pi\) |
−0.891584 | + | 0.452855i | \(0.850406\pi\) | |||||||
\(128\) | 693.348 | − | 954.311i | 0.478780 | − | 0.658984i | ||||
\(129\) | 756.018 | + | 549.279i | 0.515997 | + | 0.374894i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 546.263 | − | 396.883i | 0.364330 | − | 0.264701i | −0.390526 | − | 0.920592i | \(-0.627707\pi\) |
0.754856 | + | 0.655891i | \(0.227707\pi\) | |||||||
\(132\) | 915.892i | 0.603926i | ||||||||
\(133\) | 73.6043 | + | 101.308i | 0.0479873 | + | 0.0660488i | ||||
\(134\) | −163.193 | − | 502.256i | −0.105207 | − | 0.323793i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −849.384 | + | 2614.13i | −0.535545 | + | 1.64824i | ||||
\(137\) | 94.5956 | − | 30.7360i | 0.0589916 | − | 0.0191675i | −0.279373 | − | 0.960183i | \(-0.590126\pi\) |
0.338364 | + | 0.941015i | \(0.390126\pi\) | |||||||
\(138\) | 796.233 | − | 258.712i | 0.491158 | − | 0.159587i | ||||
\(139\) | 550.842 | − | 1695.32i | 0.336128 | − | 1.03450i | −0.630035 | − | 0.776566i | \(-0.716960\pi\) |
0.966164 | − | 0.257930i | \(-0.0830403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −378.748 | − | 1165.67i | −0.226215 | − | 0.696218i | ||||
\(142\) | −194.293 | − | 267.421i | −0.114822 | − | 0.158039i | ||||
\(143\) | − | 833.768i | − | 0.487575i | ||||||
\(144\) | 210.311 | − | 152.800i | 0.121708 | − | 0.0884258i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −602.897 | − | 438.030i | −0.341754 | − | 0.248299i | ||||
\(147\) | 1422.28 | − | 1957.60i | 0.798013 | − | 1.09837i | ||||
\(148\) | −922.643 | − | 299.785i | −0.512438 | − | 0.166501i | ||||
\(149\) | 918.569 | 0.505048 | 0.252524 | − | 0.967591i | \(-0.418739\pi\) | ||||
0.252524 | + | 0.967591i | \(0.418739\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 96.9677 | 0.0522591 | 0.0261295 | − | 0.999659i | \(-0.491682\pi\) | ||||
0.0261295 | + | 0.999659i | \(0.491682\pi\) | |||||||
\(152\) | 2135.64 | + | 693.912i | 1.13963 | + | 0.370287i | ||||
\(153\) | −1765.62 | + | 2430.17i | −0.932953 | + | 1.28410i | ||||
\(154\) | −34.8789 | − | 25.3410i | −0.0182508 | − | 0.0132600i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1138.56 | + | 827.213i | −0.584345 | + | 0.424552i | ||||
\(157\) | 3116.13i | 1.58404i | 0.610497 | + | 0.792019i | \(0.290970\pi\) | ||||
−0.610497 | + | 0.792019i | \(0.709030\pi\) | |||||||
\(158\) | −901.024 | − | 1240.15i | −0.453681 | − | 0.624439i | ||||
\(159\) | −72.0793 | − | 221.837i | −0.0359513 | − | 0.110647i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.5991 | − | 84.9412i | 0.0135100 | − | 0.0415796i | ||||
\(162\) | 1216.97 | − | 395.416i | 0.590209 | − | 0.191770i | ||||
\(163\) | −708.216 | + | 230.113i | −0.340317 | + | 0.110576i | −0.474190 | − | 0.880423i | \(-0.657259\pi\) |
0.133872 | + | 0.990999i | \(0.457259\pi\) | |||||||
\(164\) | 35.3172 | − | 108.695i | 0.0168159 | − | 0.0517540i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −104.141 | − | 320.513i | −0.0486922 | − | 0.149859i | ||||
\(167\) | −127.395 | − | 175.344i | −0.0590307 | − | 0.0812488i | 0.778481 | − | 0.627668i | \(-0.215991\pi\) |
−0.837512 | + | 0.546419i | \(0.815991\pi\) | |||||||
\(168\) | 177.652i | 0.0815843i | ||||||||
\(169\) | −740.939 | + | 538.324i | −0.337250 | + | 0.245027i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1985.35 | + | 1442.44i | 0.887855 | + | 0.645064i | ||||
\(172\) | 430.424 | − | 592.428i | 0.190811 | − | 0.262629i | ||||
\(173\) | 16.8682 | + | 5.48081i | 0.00741309 | + | 0.00240866i | 0.312721 | − | 0.949845i | \(-0.398759\pi\) |
−0.305308 | + | 0.952254i | \(0.598759\pi\) | |||||||
\(174\) | 2971.64 | 1.29471 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 261.284 | 0.111903 | ||||||||
\(177\) | 3243.66 | + | 1053.93i | 1.37745 | + | 0.447560i | ||||
\(178\) | −357.222 | + | 491.674i | −0.150421 | + | 0.207037i | ||||
\(179\) | 2206.88 | + | 1603.39i | 0.921509 | + | 0.669515i | 0.943899 | − | 0.330234i | \(-0.107128\pi\) |
−0.0223903 | + | 0.999749i | \(0.507128\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1252.23 | + | 909.799i | −0.514241 | + | 0.373618i | −0.814430 | − | 0.580262i | \(-0.802950\pi\) |
0.300189 | + | 0.953880i | \(0.402950\pi\) | |||||||
\(182\) | − | 66.2460i | − | 0.0269807i | ||||||
\(183\) | 2351.95 | + | 3237.18i | 0.950060 | + | 1.30765i | ||||
\(184\) | −494.916 | − | 1523.20i | −0.198292 | − | 0.610280i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 815.779 | − | 2510.71i | 0.321590 | − | 0.989753i | ||||
\(187\) | −2871.40 | + | 932.973i | −1.12287 | + | 0.364844i | ||||
\(188\) | −913.435 | + | 296.793i | −0.354357 | + | 0.115138i | ||||
\(189\) | 9.89922 | − | 30.4667i | 0.00380985 | − | 0.0117255i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 994.375 | + | 3060.37i | 0.376704 | + | 1.15938i | 0.942322 | + | 0.334708i | \(0.108638\pi\) |
−0.565618 | + | 0.824667i | \(0.691362\pi\) | |||||||
\(192\) | 846.256 | + | 1164.77i | 0.318090 | + | 0.437813i | ||||
\(193\) | 2386.85i | 0.890205i | 0.895480 | + | 0.445102i | \(0.146833\pi\) | ||||
−0.895480 | + | 0.445102i | \(0.853167\pi\) | |||||||
\(194\) | −700.132 | + | 508.676i | −0.259106 | + | 0.188251i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1534.01 | − | 1114.52i | −0.559042 | − | 0.406168i | ||||
\(197\) | −726.915 | + | 1000.51i | −0.262896 | + | 0.361846i | −0.919976 | − | 0.391976i | \(-0.871792\pi\) |
0.657079 | + | 0.753822i | \(0.271792\pi\) | |||||||
\(198\) | −803.536 | − | 261.085i | −0.288408 | − | 0.0937095i | ||||
\(199\) | −2580.97 | −0.919396 | −0.459698 | − | 0.888075i | \(-0.652042\pi\) | ||||
−0.459698 | + | 0.888075i | \(0.652042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2390.28 | −0.838794 | ||||||||
\(202\) | −949.537 | − | 308.523i | −0.330738 | − | 0.107463i | ||||
\(203\) | 186.335 | − | 256.468i | 0.0644243 | − | 0.0886725i | ||||
\(204\) | 4122.86 | + | 2995.43i | 1.41499 | + | 1.02805i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −708.427 | + | 514.702i | −0.239604 | + | 0.174083i | ||||
\(207\) | − | 1750.27i | − | 0.587693i | ||||||
\(208\) | 235.986 | + | 324.807i | 0.0786667 | + | 0.108275i | ||||
\(209\) | 762.201 | + | 2345.81i | 0.252261 | + | 0.776379i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −888.596 | + | 2734.82i | −0.289922 | + | 0.892287i | 0.694958 | + | 0.719050i | \(0.255423\pi\) |
−0.984880 | + | 0.173237i | \(0.944577\pi\) | |||||||
\(212\) | −173.836 | + | 56.4826i | −0.0563164 | + | 0.0182983i | ||||
\(213\) | −1422.90 | + | 462.330i | −0.457727 | + | 0.148724i | ||||
\(214\) | 167.821 | − | 516.500i | 0.0536075 | − | 0.164987i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −177.516 | − | 546.338i | −0.0559187 | − | 0.172100i | ||||
\(217\) | −165.534 | − | 227.838i | −0.0517843 | − | 0.0712749i | ||||
\(218\) | 225.082i | 0.0699287i | ||||||||
\(219\) | −2728.81 | + | 1982.60i | −0.841991 | + | 0.611742i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3753.18 | − | 2726.84i | −1.14238 | − | 0.829988i | ||||
\(222\) | 1138.83 | − | 1567.47i | 0.344294 | − | 0.473880i | ||||
\(223\) | 3938.36 | + | 1279.65i | 1.18266 | + | 0.384268i | 0.833353 | − | 0.552742i | \(-0.186418\pi\) |
0.349303 | + | 0.937010i | \(0.386418\pi\) | |||||||
\(224\) | 221.398 | 0.0660392 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2046.44 | 0.602332 | ||||||||
\(227\) | 2216.13 | + | 720.064i | 0.647972 | + | 0.210539i | 0.614520 | − | 0.788901i | \(-0.289350\pi\) |
0.0334522 | + | 0.999440i | \(0.489350\pi\) | |||||||
\(228\) | 2447.14 | − | 3368.20i | 0.710816 | − | 0.978354i | ||||
\(229\) | −4250.24 | − | 3087.98i | −1.22648 | − | 0.891088i | −0.229857 | − | 0.973224i | \(-0.573826\pi\) |
−0.996621 | + | 0.0821360i | \(0.973826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −157.868 | + | 114.698i | −0.0449651 | + | 0.0326691i | ||||
\(232\) | − | 5684.76i | − | 1.60872i | ||||||
\(233\) | −2231.74 | − | 3071.72i | −0.627493 | − | 0.863671i | 0.370378 | − | 0.928881i | \(-0.379228\pi\) |
−0.997872 | + | 0.0652105i | \(0.979228\pi\) | |||||||
\(234\) | −401.177 | − | 1234.70i | −0.112076 | − | 0.344934i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 825.876 | − | 2541.78i | 0.227796 | − | 0.701085i | ||||
\(237\) | −6598.65 | + | 2144.03i | −1.80856 | + | 0.587636i | ||||
\(238\) | −228.143 | + | 74.1283i | −0.0621359 | + | 0.0201892i | ||||
\(239\) | 2008.57 | − | 6181.73i | 0.543613 | − | 1.67307i | −0.180653 | − | 0.983547i | \(-0.557821\pi\) |
0.724266 | − | 0.689521i | \(-0.242179\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 952.246 | + | 2930.71i | 0.254521 | + | 0.783335i | 0.993924 | + | 0.110071i | \(0.0351080\pi\) |
−0.739403 | + | 0.673263i | \(0.764892\pi\) | |||||||
\(242\) | 725.228 | + | 998.191i | 0.192642 | + | 0.265149i | ||||
\(243\) | − | 5060.28i | − | 1.33587i | ||||||
\(244\) | 2536.71 | − | 1843.03i | 0.665558 | − | 0.483556i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 184.661 | + | 134.164i | 0.0478599 | + | 0.0347722i | ||||
\(247\) | −2227.72 | + | 3066.19i | −0.573872 | + | 0.789867i | ||||
\(248\) | −4802.99 | − | 1560.59i | −1.22980 | − | 0.399586i | ||||
\(249\) | −1525.35 | −0.388213 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7819.56 | 1.96640 | 0.983199 | − | 0.182536i | \(-0.0584305\pi\) | ||||
0.983199 | + | 0.182536i | \(0.0584305\pi\) | |||||||
\(252\) | 144.690 | + | 47.0125i | 0.0361690 | + | 0.0117520i | ||||
\(253\) | 1034.03 | − | 1423.22i | 0.256952 | − | 0.353664i | ||||
\(254\) | −2565.95 | − | 1864.27i | −0.633866 | − | 0.460530i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2808.98 | − | 2040.85i | 0.685787 | − | 0.498253i | ||||
\(257\) | − | 2384.26i | − | 0.578700i | −0.957223 | − | 0.289350i | \(-0.906561\pi\) | ||
0.957223 | − | 0.289350i | \(-0.0934392\pi\) | |||||||
\(258\) | 859.627 | + | 1183.17i | 0.207434 | + | 0.285509i | ||||
\(259\) | −63.8706 | − | 196.574i | −0.0153233 | − | 0.0471602i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1919.78 | − | 5908.48i | 0.455293 | − | 1.40125i | ||||
\(262\) | 1005.00 | − | 326.545i | 0.236982 | − | 0.0770001i | ||||
\(263\) | 2942.84 | − | 956.186i | 0.689974 | − | 0.224186i | 0.0570172 | − | 0.998373i | \(-0.481841\pi\) |
0.632957 | + | 0.774187i | \(0.281841\pi\) | |||||||
\(264\) | −1081.32 | + | 3327.97i | −0.252086 | + | 0.775842i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 60.5597 | + | 186.384i | 0.0139592 | + | 0.0429621i | ||||
\(267\) | 1616.85 | + | 2225.40i | 0.370597 | + | 0.510084i | ||||
\(268\) | 1873.07i | 0.426924i | ||||||||
\(269\) | −1193.33 | + | 867.006i | −0.270478 | + | 0.196514i | −0.714754 | − | 0.699376i | \(-0.753461\pi\) |
0.444275 | + | 0.895890i | \(0.353461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 245.587 | + | 178.429i | 0.0550492 | + | 0.0399956i | 0.614970 | − | 0.788551i | \(-0.289168\pi\) |
−0.559920 | + | 0.828546i | \(0.689168\pi\) | |||||||
\(272\) | 854.530 | − | 1176.16i | 0.190491 | − | 0.262188i | ||||
\(273\) | −285.165 | − | 92.6559i | −0.0632198 | − | 0.0205413i | ||||
\(274\) | 155.662 | 0.0343206 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2969.40 | −0.647597 | ||||||||
\(277\) | −4610.31 | − | 1497.98i | −1.00002 | − | 0.324927i | −0.237148 | − | 0.971473i | \(-0.576213\pi\) |
−0.762875 | + | 0.646546i | \(0.776213\pi\) | |||||||
\(278\) | 1639.76 | − | 2256.94i | 0.353764 | − | 0.486914i | ||||
\(279\) | −4464.99 | − | 3244.00i | −0.958107 | − | 0.696105i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1203.90 | − | 874.687i | 0.255583 | − | 0.185692i | −0.452614 | − | 0.891706i | \(-0.649509\pi\) |
0.708198 | + | 0.706014i | \(0.249509\pi\) | |||||||
\(282\) | − | 1918.16i | − | 0.405052i | ||||||
\(283\) | −1574.63 | − | 2167.29i | −0.330749 | − | 0.455237i | 0.610962 | − | 0.791660i | \(-0.290783\pi\) |
−0.941711 | + | 0.336423i | \(0.890783\pi\) | |||||||
\(284\) | 362.289 | + | 1115.01i | 0.0756969 | + | 0.232971i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 403.222 | − | 1240.99i | 0.0833672 | − | 0.256578i | ||||
\(287\) | 23.1580 | − | 7.52450i | 0.00476298 | − | 0.00154759i | ||||
\(288\) | 4126.42 | − | 1340.76i | 0.844277 | − | 0.274322i | ||||
\(289\) | −3672.97 | + | 11304.2i | −0.747603 | + | 2.30088i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1210.42 | + | 3725.28i | 0.243835 | + | 0.750447i | ||||
\(292\) | 1553.60 | + | 2138.34i | 0.311361 | + | 0.428552i | ||||
\(293\) | 3929.37i | 0.783468i | 0.920078 | + | 0.391734i | \(0.128125\pi\) | ||||
−0.920078 | + | 0.391734i | \(0.871875\pi\) | |||||||
\(294\) | 3063.67 | − | 2225.89i | 0.607744 | − | 0.441552i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2998.57 | − | 2178.59i | −0.588811 | − | 0.427796i | ||||
\(297\) | 370.885 | − | 510.480i | 0.0724611 | − | 0.0997341i | ||||
\(298\) | 1367.21 | + | 444.233i | 0.265773 | + | 0.0863549i | ||||
\(299\) | 2703.14 | 0.522832 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 156.016 | 0.0298758 | ||||||||
\(302\) | 144.328 | + | 46.8950i | 0.0275005 | + | 0.00893544i | ||||
\(303\) | −2656.16 | + | 3655.90i | −0.503606 | + | 0.693154i | ||||
\(304\) | −960.875 | − | 698.116i | −0.181283 | − | 0.131710i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3803.23 | + | 2763.21i | −0.710511 | + | 0.516216i | ||||
\(307\) | − | 8263.41i | − | 1.53621i | −0.640322 | − | 0.768107i | \(-0.721199\pi\) | ||
0.640322 | − | 0.768107i | \(-0.278801\pi\) | |||||||
\(308\) | 89.8790 | + | 123.708i | 0.0166277 | + | 0.0228861i | ||||
\(309\) | 1224.76 | + | 3769.42i | 0.225483 | + | 0.693964i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1483.86 | + | 4566.84i | −0.270552 | + | 0.832675i | 0.719810 | + | 0.694172i | \(0.244229\pi\) |
−0.990362 | + | 0.138503i | \(0.955771\pi\) | |||||||
\(312\) | −5113.68 | + | 1661.54i | −0.927902 | + | 0.301494i | ||||
\(313\) | −9805.98 | + | 3186.15i | −1.77082 | + | 0.575374i | −0.998227 | − | 0.0595277i | \(-0.981041\pi\) |
−0.772593 | + | 0.634902i | \(0.781041\pi\) | |||||||
\(314\) | −1507.00 | + | 4638.08i | −0.270844 | + | 0.833573i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1680.10 | + | 5170.81i | 0.299091 | + | 0.920509i | ||||
\(317\) | 1928.95 | + | 2654.97i | 0.341768 | + | 0.470403i | 0.944957 | − | 0.327195i | \(-0.106104\pi\) |
−0.603189 | + | 0.797598i | \(0.706104\pi\) | |||||||
\(318\) | − | 365.044i | − | 0.0643731i | ||||||
\(319\) | 5051.67 | − | 3670.26i | 0.886644 | − | 0.644185i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1988.62 | − | 1444.82i | −0.345776 | − | 0.251221i | ||||
\(322\) | 82.1576 | − | 113.080i | 0.0142188 | − | 0.0195705i | ||||
\(323\) | 13052.4 | + | 4240.97i | 2.24846 | + | 0.730570i | ||||
\(324\) | −4538.44 | −0.778196 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1165.40 | −0.197993 | ||||||||
\(327\) | 968.896 | + | 314.813i | 0.163853 | + | 0.0532392i | ||||
\(328\) | 256.656 | − | 353.256i | 0.0432056 | − | 0.0594674i | ||||
\(329\) | −165.547 | − | 120.277i | −0.0277413 | − | 0.0201552i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 290.415 | − | 210.999i | 0.0482255 | − | 0.0350379i | −0.563411 | − | 0.826177i | \(-0.690511\pi\) |
0.611637 | + | 0.791139i | \(0.290511\pi\) | |||||||
\(332\) | 1195.29i | 0.197591i | ||||||||
\(333\) | −2380.85 | − | 3276.95i | −0.391801 | − | 0.539267i | ||||
\(334\) | −104.817 | − | 322.595i | −0.0171717 | − | 0.0528491i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 29.0362 | − | 89.3644i | 0.00471445 | − | 0.0145096i | ||||
\(337\) | 1246.37 | − | 404.970i | 0.201466 | − | 0.0654603i | −0.206546 | − | 0.978437i | \(-0.566222\pi\) |
0.408012 | + | 0.912977i | \(0.366222\pi\) | |||||||
\(338\) | −1363.16 | + | 442.919i | −0.219368 | + | 0.0712769i | ||||
\(339\) | 2862.28 | − | 8809.19i | 0.458577 | − | 1.41136i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1714.17 | − | 5275.67i | −0.272221 | − | 0.837810i | ||||
\(342\) | 2257.43 | + | 3107.09i | 0.356923 | + | 0.491263i | ||||
\(343\) | − | 809.619i | − | 0.127450i | ||||||
\(344\) | 2263.42 | − | 1644.47i | 0.354754 | − | 0.257744i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.4562 | + | 16.3154i | 0.00348917 | + | 0.00253503i | ||||
\(347\) | 2278.45 | − | 3136.01i | 0.352488 | − | 0.485158i | −0.595549 | − | 0.803319i | \(-0.703065\pi\) |
0.948037 | + | 0.318161i | \(0.103065\pi\) | |||||||
\(348\) | −10023.9 | − | 3256.97i | −1.54408 | − | 0.501701i | ||||
\(349\) | 7122.39 | 1.09242 | 0.546208 | − | 0.837650i | \(-0.316071\pi\) | ||||
0.546208 | + | 0.837650i | \(0.316071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 969.561 | 0.147440 | ||||||||
\(352\) | 4147.46 | + | 1347.59i | 0.628012 | + | 0.204054i | ||||
\(353\) | −6423.28 | + | 8840.89i | −0.968490 | + | 1.33301i | −0.0256839 | + | 0.999670i | \(0.508176\pi\) |
−0.942806 | + | 0.333342i | \(0.891824\pi\) | |||||||
\(354\) | 4318.20 | + | 3137.36i | 0.648333 | + | 0.471042i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1743.86 | − | 1266.99i | 0.259619 | − | 0.188624i | ||||
\(357\) | 1085.76i | 0.160964i | ||||||||
\(358\) | 2509.33 | + | 3453.79i | 0.370452 | + | 0.509884i | ||||
\(359\) | −603.519 | − | 1857.44i | −0.0887256 | − | 0.273069i | 0.896842 | − | 0.442351i | \(-0.145855\pi\) |
−0.985568 | + | 0.169281i | \(0.945855\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1345.15 | − | 4139.96i | 0.196115 | − | 0.603581i | ||||
\(362\) | −2303.83 | + | 748.559i | −0.334493 | + | 0.108683i | ||||
\(363\) | 5311.21 | − | 1725.72i | 0.767950 | − | 0.249522i | ||||
\(364\) | −72.6067 | + | 223.460i | −0.0104550 | + | 0.0321772i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1935.12 | + | 5955.69i | 0.276367 | + | 0.850571i | ||||
\(367\) | 6175.15 | + | 8499.37i | 0.878312 | + | 1.20889i | 0.976886 | + | 0.213763i | \(0.0685719\pi\) |
−0.0985740 | + | 0.995130i | \(0.531428\pi\) | |||||||
\(368\) | 847.104i | 0.119995i | ||||||||
\(369\) | 386.053 | − | 280.484i | 0.0544637 | − | 0.0395702i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.5051 | − | 22.8898i | −0.00440880 | − | 0.00320318i | ||||
\(372\) | −5503.56 | + | 7574.99i | −0.767059 | + | 1.05577i | ||||
\(373\) | 859.018 | + | 279.112i | 0.119245 | + | 0.0387450i | 0.368032 | − | 0.929813i | \(-0.380032\pi\) |
−0.248787 | + | 0.968558i | \(0.580032\pi\) | |||||||
\(374\) | −4725.02 | −0.653275 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3669.44 | −0.503290 | ||||||||
\(377\) | 9125.12 | + | 2964.93i | 1.24660 | + | 0.405044i | ||||
\(378\) | 29.4682 | − | 40.5595i | 0.00400974 | − | 0.00551893i | ||||
\(379\) | 7139.52 | + | 5187.17i | 0.967632 | + | 0.703026i | 0.954911 | − | 0.296893i | \(-0.0959505\pi\) |
0.0127216 | + | 0.999919i | \(0.495950\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11613.9 | + | 8438.00i | −1.56168 | + | 1.13462i | ||||
\(382\) | 5035.99i | 0.674512i | ||||||||
\(383\) | −3587.32 | − | 4937.52i | −0.478599 | − | 0.658734i | 0.499636 | − | 0.866235i | \(-0.333467\pi\) |
−0.978235 | + | 0.207501i | \(0.933467\pi\) | |||||||
\(384\) | −2582.04 | − | 7946.69i | −0.343135 | − | 1.05606i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1154.32 | + | 3552.62i | −0.152210 | + | 0.468455i | ||||
\(387\) | 2907.84 | − | 944.813i | 0.381947 | − | 0.124102i | ||||
\(388\) | 2919.19 | − | 948.504i | 0.381958 | − | 0.124106i | ||||
\(389\) | 2180.80 | − | 6711.81i | 0.284244 | − | 0.874812i | −0.702380 | − | 0.711802i | \(-0.747879\pi\) |
0.986624 | − | 0.163011i | \(-0.0521205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3024.78 | − | 9309.30i | −0.391226 | − | 1.20407i | ||||
\(392\) | −4258.13 | − | 5860.81i | −0.548642 | − | 0.755141i | ||||
\(393\) | − | 4782.90i | − | 0.613907i | ||||||
\(394\) | −1565.81 | + | 1137.63i | −0.200214 | + | 0.145464i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2424.33 | + | 1761.38i | 0.307644 | + | 0.223516i | ||||
\(397\) | 2498.77 | − | 3439.26i | 0.315893 | − | 0.434789i | −0.621315 | − | 0.783561i | \(-0.713401\pi\) |
0.937208 | + | 0.348772i | \(0.113401\pi\) | |||||||
\(398\) | −3841.54 | − | 1248.19i | −0.483817 | − | 0.157202i | ||||
\(399\) | 887.018 | 0.111294 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7335.40 | 0.913497 | 0.456749 | − | 0.889596i | \(-0.349014\pi\) | ||||
0.456749 | + | 0.889596i | \(0.349014\pi\) | |||||||
\(402\) | −3557.73 | − | 1155.98i | −0.441401 | − | 0.143420i | ||||
\(403\) | 5010.07 | − | 6895.77i | 0.619279 | − | 0.852365i | ||||
\(404\) | 2864.82 | + | 2081.41i | 0.352798 | + | 0.256322i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 401.375 | − | 291.616i | 0.0490638 | − | 0.0356469i | ||||
\(407\) | − | 4071.19i | − | 0.495826i | ||||||
\(408\) | 11444.3 | + | 15751.7i | 1.38867 | + | 1.91133i | ||||
\(409\) | 2850.25 | + | 8772.17i | 0.344586 | + | 1.06053i | 0.961805 | + | 0.273736i | \(0.0882594\pi\) |
−0.617219 | + | 0.786792i | \(0.711741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 217.718 | − | 670.067i | 0.0261295 | − | 0.0804185i | ||||
\(412\) | 2953.78 | − | 959.742i | 0.353210 | − | 0.114765i | ||||
\(413\) | 541.540 | − | 175.957i | 0.0645216 | − | 0.0209643i | ||||
\(414\) | 846.458 | − | 2605.13i | 0.100486 | − | 0.309264i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2070.68 | + | 6372.89i | 0.244047 | + | 0.751098i | ||||
\(417\) | −7421.83 | − | 10215.3i | −0.871580 | − | 1.19963i | ||||
\(418\) | 3860.15i | 0.451689i | ||||||||
\(419\) | −13028.6 | + | 9465.86i | −1.51907 | + | 1.10367i | −0.557124 | + | 0.830429i | \(0.688095\pi\) |
−0.961946 | + | 0.273240i | \(0.911905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7316.13 | − | 5315.48i | −0.846950 | − | 0.615346i | 0.0773531 | − | 0.997004i | \(-0.475353\pi\) |
−0.924304 | + | 0.381658i | \(0.875353\pi\) | |||||||
\(422\) | −2645.19 | + | 3640.80i | −0.305133 | + | 0.419979i | ||||
\(423\) | −3813.84 | − | 1239.19i | −0.438382 | − | 0.142439i | ||||
\(424\) | −698.330 | −0.0799857 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2341.46 | −0.266300 | ||||||||
\(427\) | 635.347 | + | 206.437i | 0.0720060 | + | 0.0233962i | ||||
\(428\) | −1132.18 | + | 1558.32i | −0.127865 | + | 0.175991i | ||||
\(429\) | −4778.05 | − | 3471.45i | −0.537730 | − | 0.390684i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4692.76 | + | 3409.49i | −0.524460 | + | 0.381043i | −0.818282 | − | 0.574818i | \(-0.805073\pi\) |
0.293821 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(432\) | 303.838i | 0.0338390i | ||||||||
\(433\) | −2478.33 | − | 3411.13i | −0.275060 | − | 0.378587i | 0.649030 | − | 0.760763i | \(-0.275175\pi\) |
−0.924090 | + | 0.382176i | \(0.875175\pi\) | |||||||
\(434\) | −136.197 | − | 419.172i | −0.0150638 | − | 0.0463615i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 246.693 | − | 759.243i | 0.0270974 | − | 0.0833971i | ||||
\(437\) | −7605.32 | + | 2471.12i | −0.832521 | + | 0.270502i | ||||
\(438\) | −5020.41 | + | 1631.23i | −0.547681 | + | 0.177952i | ||||
\(439\) | 1064.67 | − | 3276.71i | 0.115749 | − | 0.356239i | −0.876354 | − | 0.481668i | \(-0.840031\pi\) |
0.992102 | + | 0.125430i | \(0.0400310\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2446.46 | − | 7529.44i | −0.264168 | − | 0.813027i | ||||
\(442\) | −4267.53 | − | 5873.76i | −0.459244 | − | 0.632095i | ||||
\(443\) | 6083.40i | 0.652441i | 0.945294 | + | 0.326220i | \(0.105775\pi\) | ||||
−0.945294 | + | 0.326220i | \(0.894225\pi\) | |||||||
\(444\) | −5559.46 | + | 4039.18i | −0.594235 | + | 0.431737i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5243.05 | + | 3809.30i | 0.556649 | + | 0.404429i | ||||
\(447\) | 3824.53 | − | 5264.02i | 0.404685 | − | 0.557001i | ||||
\(448\) | 228.605 | + | 74.2781i | 0.0241084 | + | 0.00783328i | ||||
\(449\) | 11313.0 | 1.18907 | 0.594534 | − | 0.804070i | \(-0.297337\pi\) | ||||
0.594534 | + | 0.804070i | \(0.297337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 479.620 | 0.0500763 | ||||||||
\(452\) | −6903.03 | − | 2242.93i | −0.718343 | − | 0.233404i | ||||
\(453\) | 403.732 | − | 555.690i | 0.0418742 | − | 0.0576348i | ||||
\(454\) | 2950.28 | + | 2143.50i | 0.304986 | + | 0.221585i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12868.5 | − | 9349.50i | 1.32154 | − | 0.960154i | ||||
\(457\) | 16237.9i | 1.66209i | 0.556206 | + | 0.831045i | \(0.312257\pi\) | ||||
−0.556206 | + | 0.831045i | \(0.687743\pi\) | |||||||
\(458\) | −4832.71 | − | 6651.66i | −0.493052 | − | 0.678628i | ||||
\(459\) | −1084.92 | − | 3339.05i | −0.110327 | − | 0.339550i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1865.25 | + | 5740.66i | −0.188446 | + | 0.579976i | −0.999991 | − | 0.00431376i | \(-0.998627\pi\) |
0.811545 | + | 0.584290i | \(0.198627\pi\) | |||||||
\(462\) | −290.442 | + | 94.3703i | −0.0292480 | + | 0.00950325i | ||||
\(463\) | −978.735 | + | 318.010i | −0.0982412 | + | 0.0319205i | −0.357725 | − | 0.933827i | \(-0.616448\pi\) |
0.259484 | + | 0.965747i | \(0.416448\pi\) | |||||||
\(464\) | −929.142 | + | 2859.60i | −0.0929619 | + | 0.286107i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1836.22 | − | 5651.29i | −0.182534 | − | 0.561783i | ||||
\(467\) | −4995.54 | − | 6875.76i | −0.495002 | − | 0.681311i | 0.486299 | − | 0.873792i | \(-0.338347\pi\) |
−0.981301 | + | 0.192481i | \(0.938347\pi\) | |||||||
\(468\) | 4604.56i | 0.454799i | ||||||||
\(469\) | −322.851 | + | 234.565i | −0.0317865 | + | 0.0230943i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17857.5 | + | 12974.2i | 1.74698 | + | 1.26926i | ||||
\(472\) | 6001.78 | − | 8260.74i | 0.585284 | − | 0.805575i | ||||
\(473\) | 2922.66 | + | 949.630i | 0.284110 | + | 0.0923130i | ||||
\(474\) | −10858.4 | −1.05220 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 850.817 | 0.0819267 | ||||||||
\(477\) | −725.812 | − | 235.831i | −0.0696701 | − | 0.0226372i | ||||
\(478\) | 5979.15 | − | 8229.60i | 0.572134 | − | 0.787475i | ||||
\(479\) | −2456.46 | − | 1784.72i | −0.234318 | − | 0.170242i | 0.464430 | − | 0.885610i | \(-0.346259\pi\) |
−0.698748 | + | 0.715368i | \(0.746259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5060.97 | − | 3677.01i | 0.479751 | − | 0.348559i | ||||
\(482\) | 4822.62i | 0.455736i | ||||||||
\(483\) | −371.859 | − | 511.820i | −0.0350314 | − | 0.0482166i | ||||
\(484\) | −1352.30 | − | 4161.95i | −0.127000 | − | 0.390867i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2447.23 | − | 7531.79i | 0.228412 | − | 0.702981i | ||||
\(487\) | 12099.9 | − | 3931.48i | 1.12587 | − | 0.365816i | 0.313863 | − | 0.949468i | \(-0.398377\pi\) |
0.812004 | + | 0.583652i | \(0.198377\pi\) | |||||||
\(488\) | 11393.3 | − | 3701.89i | 1.05686 | − | 0.343395i | ||||
\(489\) | −1630.01 | + | 5016.64i | −0.150739 | + | 0.463927i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2121.17 | − | 6528.30i | −0.194964 | − | 0.600037i | −0.999977 | − | 0.00678001i | \(-0.997842\pi\) |
0.805013 | − | 0.593257i | \(-0.202158\pi\) | |||||||
\(492\) | −475.850 | − | 654.951i | −0.0436036 | − | 0.0600152i | ||||
\(493\) | − | 34743.5i | − | 3.17398i | ||||||
\(494\) | −4798.62 | + | 3486.40i | −0.437045 | + | 0.317531i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2160.98 | + | 1570.04i | 0.195627 | + | 0.142131i | ||||
\(497\) | −146.819 | + | 202.080i | −0.0132510 | + | 0.0182384i | ||||
\(498\) | −2270.35 | − | 737.681i | −0.204291 | − | 0.0663781i | ||||
\(499\) | −10000.2 | −0.897134 | −0.448567 | − | 0.893749i | \(-0.648065\pi\) | ||||
−0.448567 | + | 0.893749i | \(0.648065\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1535.26 | −0.136907 | ||||||||
\(502\) | 11638.7 | + | 3781.65i | 1.03478 | + | 0.336222i | ||||
\(503\) | −1995.92 | + | 2747.15i | −0.176926 | + | 0.243518i | −0.888265 | − | 0.459331i | \(-0.848089\pi\) |
0.711339 | + | 0.702849i | \(0.248089\pi\) | |||||||
\(504\) | 470.238 | + | 341.648i | 0.0415596 | + | 0.0301948i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2227.35 | − | 1618.27i | 0.195688 | − | 0.142175i | ||||
\(507\) | 6487.43i | 0.568278i | ||||||||
\(508\) | 6612.16 | + | 9100.86i | 0.577494 | + | 0.794853i | ||||
\(509\) | −2003.56 | − | 6166.33i | −0.174472 | − | 0.536970i | 0.825137 | − | 0.564933i | \(-0.191098\pi\) |
−0.999609 | + | 0.0279631i | \(0.991098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −174.018 | + | 535.572i | −0.0150648 | + | 0.0463646i | ||||
\(512\) | −3806.98 | + | 1236.96i | −0.328606 | + | 0.106770i | ||||
\(513\) | −2727.87 | + | 886.338i | −0.234773 | + | 0.0762822i | ||||
\(514\) | 1153.06 | − | 3548.76i | 0.0989482 | − | 0.304531i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1602.91 | − | 4933.24i | −0.136752 | − | 0.420879i | ||||
\(517\) | −2369.10 | − | 3260.79i | −0.201534 | − | 0.277388i | ||||
\(518\) | − | 323.471i | − | 0.0274373i | ||||||
\(519\) | 101.641 | − | 73.8462i | 0.00859639 | − | 0.00624565i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5997.28 | + | 4357.28i | 0.504310 | + | 0.366403i | 0.810661 | − | 0.585516i | \(-0.199108\pi\) |
−0.306351 | + | 0.951919i | \(0.599108\pi\) | |||||||
\(522\) | 5714.85 | − | 7865.82i | 0.479180 | − | 0.659535i | ||||
\(523\) | −8183.77 | − | 2659.07i | −0.684228 | − | 0.222319i | −0.0537826 | − | 0.998553i | \(-0.517128\pi\) |
−0.630446 | + | 0.776233i | \(0.717128\pi\) | |||||||
\(524\) | −3747.96 | −0.312463 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4842.58 | 0.401419 | ||||||||
\(527\) | −29354.4 | − | 9537.83i | −2.42637 | − | 0.788376i | ||||
\(528\) | 1087.87 | − | 1497.33i | 0.0896661 | − | 0.123415i | ||||
\(529\) | −5229.11 | − | 3799.17i | −0.429778 | − | 0.312252i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9027.67 | − | 6558.98i | 0.737792 | − | 0.536037i | ||||
\(532\) | − | 695.082i | − | 0.0566459i | ||||||
\(533\) | 433.182 | + | 596.224i | 0.0352030 | + | 0.0484528i | ||||
\(534\) | 1330.30 | + | 4094.25i | 0.107805 | + | 0.331789i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2211.38 | + | 6805.94i | −0.178204 | + | 0.548455i | ||||
\(537\) | 18377.0 | − | 5971.06i | 1.47677 | − | 0.479833i | ||||
\(538\) | −2195.47 | + | 713.350i | −0.175935 | + | 0.0571649i | ||||
\(539\) | 2458.94 | − | 7567.83i | 0.196501 | − | 0.604767i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1851.10 | − | 5697.10i | −0.147107 | − | 0.452749i | 0.850169 | − | 0.526510i | \(-0.176500\pi\) |
−0.997276 | + | 0.0737611i | \(0.976500\pi\) | |||||||
\(542\) | 279.243 | + | 384.346i | 0.0221301 | + | 0.0304595i | ||||
\(543\) | 10964.1i | 0.866512i | ||||||||
\(544\) | 19630.4 | − | 14262.3i | 1.54715 | − | 1.12407i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −379.634 | − | 275.820i | −0.0297561 | − | 0.0216191i | ||||
\(547\) | −12795.7 | + | 17611.8i | −1.00019 | + | 1.37665i | −0.0749850 | + | 0.997185i | \(0.523891\pi\) |
−0.925207 | + | 0.379462i | \(0.876109\pi\) | |||||||
\(548\) | −525.076 | − | 170.608i | −0.0409309 | − | 0.0132993i | ||||
\(549\) | 13091.8 | 1.01775 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28384.0 | −2.19456 | ||||||||
\(552\) | −10789.5 | − | 3505.74i | −0.831945 | − | 0.270315i | ||||
\(553\) | −680.867 | + | 937.134i | −0.0523570 | + | 0.0720632i | ||||
\(554\) | −6137.59 | − | 4459.22i | −0.470688 | − | 0.341975i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8004.86 | + | 5815.87i | −0.610579 | + | 0.443611i | ||||
\(557\) | 10736.7i | 0.816749i | 0.912814 | + | 0.408375i | \(0.133904\pi\) | ||||
−0.912814 | + | 0.408375i | \(0.866096\pi\) | |||||||
\(558\) | −5076.89 | − | 6987.74i | −0.385165 | − | 0.530134i | ||||
\(559\) | 1459.18 | + | 4490.89i | 0.110406 | + | 0.339794i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6608.71 | + | 20339.5i | −0.497362 | + | 1.53072i | ||||
\(562\) | 2214.92 | − | 719.670i | 0.166247 | − | 0.0540168i | ||||
\(563\) | 5145.09 | − | 1671.74i | 0.385151 | − | 0.125143i | −0.110040 | − | 0.993927i | \(-0.535098\pi\) |
0.495191 | + | 0.868784i | \(0.335098\pi\) | |||||||
\(564\) | −2102.33 | + | 6470.31i | −0.156958 | + | 0.483066i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1295.56 | − | 3987.34i | −0.0962131 | − | 0.296114i | ||||
\(567\) | −568.351 | − | 782.268i | −0.0420961 | − | 0.0579404i | ||||
\(568\) | 4479.21i | 0.330887i | ||||||||
\(569\) | 3521.64 | − | 2558.62i | 0.259464 | − | 0.188511i | −0.450447 | − | 0.892803i | \(-0.648735\pi\) |
0.709911 | + | 0.704292i | \(0.248735\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14846.9 | − | 10786.9i | −1.08813 | − | 0.790575i | −0.109050 | − | 0.994036i | \(-0.534781\pi\) |
−0.979083 | + | 0.203461i | \(0.934781\pi\) | |||||||
\(572\) | −2720.29 | + | 3744.16i | −0.198848 | + | 0.273691i | ||||
\(573\) | 21678.1 | + | 7043.65i | 1.58048 | + | 0.513530i | ||||
\(574\) | 38.1076 | 0.00277105 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4710.56 | 0.340752 | ||||||||
\(577\) | −817.930 | − | 265.761i | −0.0590136 | − | 0.0191747i | 0.279361 | − | 0.960186i | \(-0.409877\pi\) |
−0.338375 | + | 0.941011i | \(0.609877\pi\) | |||||||
\(578\) | −10933.8 | + | 15049.1i | −0.786827 | + | 1.08297i | ||||
\(579\) | 13678.3 | + | 9937.84i | 0.981778 | + | 0.713303i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −206.026 | + | 149.687i | −0.0147116 | + | 0.0106886i | ||||
\(582\) | 6130.13i | 0.436602i | ||||||||
\(583\) | −450.863 | − | 620.560i | −0.0320289 | − | 0.0440840i | ||||
\(584\) | 3120.55 | + | 9604.06i | 0.221112 | + | 0.680512i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1900.30 | + | 5848.52i | −0.133960 | + | 0.412287i | ||||
\(587\) | 19306.5 | − | 6273.05i | 1.35752 | − | 0.441084i | 0.462304 | − | 0.886721i | \(-0.347023\pi\) |
0.895214 | + | 0.445637i | \(0.147023\pi\) | |||||||
\(588\) | −12773.9 | + | 4150.51i | −0.895899 | + | 0.291095i | ||||
\(589\) | −7792.01 | + | 23981.4i | −0.545101 | + | 1.67765i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2707.04 | + | 8331.42i | 0.188414 | + | 0.579880i | ||||
\(592\) | 1152.29 | + | 1585.99i | 0.0799980 | + | 0.110108i | ||||
\(593\) | 20628.0i | 1.42848i | 0.699900 | + | 0.714241i | \(0.253228\pi\) | ||||
−0.699900 | + | 0.714241i | \(0.746772\pi\) | |||||||
\(594\) | 798.905 | − | 580.439i | 0.0551843 | − | 0.0400937i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4124.97 | − | 2996.97i | −0.283499 | − | 0.205974i | ||||
\(597\) | −10746.0 | + | 14790.7i | −0.736694 | + | 1.01397i | ||||
\(598\) | 4023.39 | + | 1307.28i | 0.275132 | + | 0.0893957i | ||||
\(599\) | 2506.63 | 0.170982 | 0.0854909 | − | 0.996339i | \(-0.472754\pi\) | ||||
0.0854909 | + | 0.996339i | \(0.472754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1595.54 | −0.108292 | −0.0541459 | − | 0.998533i | \(-0.517244\pi\) | ||||
−0.0541459 | + | 0.998533i | \(0.517244\pi\) | |||||||
\(602\) | 232.216 | + | 75.4517i | 0.0157217 | + | 0.00510827i | ||||
\(603\) | −4596.82 | + | 6326.98i | −0.310443 | + | 0.427288i | ||||
\(604\) | −435.448 | − | 316.371i | −0.0293346 | − | 0.0213129i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5721.51 | + | 4156.92i | −0.383532 | + | 0.278652i | ||||
\(607\) | − | 26119.6i | − | 1.74656i | −0.487222 | − | 0.873278i | \(-0.661990\pi\) | ||
0.487222 | − | 0.873278i | \(-0.338010\pi\) | |||||||
\(608\) | −11651.7 | − | 16037.3i | −0.777205 | − | 1.06973i | ||||
\(609\) | −693.914 | − | 2135.65i | −0.0461721 | − | 0.142103i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1913.82 | − | 5890.15i | 0.126719 | − | 0.390000i | ||||
\(612\) | 15857.6 | − | 5152.43i | 1.04739 | − | 0.340318i | ||||
\(613\) | 6416.22 | − | 2084.75i | 0.422754 | − | 0.137361i | −0.0899108 | − | 0.995950i | \(-0.528658\pi\) |
0.512665 | + | 0.858589i | \(0.328658\pi\) | |||||||
\(614\) | 3996.30 | − | 12299.4i | 0.262667 | − | 0.808406i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 180.531 | + | 555.616i | 0.0118081 | + | 0.0363416i | ||||
\(617\) | 3731.74 | + | 5136.30i | 0.243491 | + | 0.335137i | 0.913219 | − | 0.407470i | \(-0.133589\pi\) |
−0.669727 | + | 0.742607i | \(0.733589\pi\) | |||||||
\(618\) | 6202.76i | 0.403741i | ||||||||
\(619\) | 4852.37 | − | 3525.45i | 0.315078 | − | 0.228918i | −0.418994 | − | 0.907989i | \(-0.637617\pi\) |
0.734072 | + | 0.679071i | \(0.237617\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1655.02 | + | 1202.44i | 0.106946 | + | 0.0777009i | ||||
\(622\) | −4417.18 | + | 6079.73i | −0.284747 | + | 0.391921i | ||||
\(623\) | 436.770 | + | 141.915i | 0.0280880 | + | 0.00912633i | ||||
\(624\) | 2843.90 | 0.182448 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16136.2 | −1.03024 | ||||||||
\(627\) | 16616.6 | + | 5399.05i | 1.05838 | + | 0.343887i | ||||
\(628\) | 10166.8 | − | 13993.4i | 0.646019 | − | 0.889169i | ||||
\(629\) | −18326.3 | − | 13314.8i | −1.16171 | − | 0.844034i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14269.4 | − | 10367.4i | 0.900250 | − | 0.654070i | −0.0382803 | − | 0.999267i | \(-0.512188\pi\) |
0.938530 | + | 0.345197i | \(0.112188\pi\) | |||||||
\(632\) | 20772.1i | 1.30739i | ||||||||
\(633\) | 11972.6 | + | 16478.9i | 0.751766 | + | 1.03472i | ||||
\(634\) | 1587.09 | + | 4884.55i | 0.0994184 | + | 0.305978i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −400.094 | + | 1231.36i | −0.0249446 | + | 0.0767716i | ||||
\(637\) | 11628.6 | − | 3778.35i | 0.723297 | − | 0.235013i | ||||
\(638\) | 9293.96 | − | 3019.79i | 0.576726 | − | 0.187390i | ||||
\(639\) | −1512.66 | + | 4655.48i | −0.0936461 | + | 0.288213i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8585.30 | + | 26422.8i | 0.529015 | + | 1.62814i | 0.756236 | + | 0.654299i | \(0.227036\pi\) |
−0.227221 | + | 0.973843i | \(0.572964\pi\) | |||||||
\(642\) | −2261.15 | − | 3112.21i | −0.139004 | − | 0.191323i | ||||
\(643\) | − | 7215.33i | − | 0.442527i | −0.975214 | − | 0.221263i | \(-0.928982\pi\) | ||
0.975214 | − | 0.221263i | \(-0.0710181\pi\) | |||||||
\(644\) | −401.071 | + | 291.395i | −0.0245410 | + | 0.0178301i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17376.3 | + | 12624.6i | 1.05830 | + | 0.768900i | ||||
\(647\) | 10027.9 | − | 13802.3i | 0.609334 | − | 0.838676i | −0.387189 | − | 0.922001i | \(-0.626554\pi\) |
0.996522 | + | 0.0833244i | \(0.0265538\pi\) | |||||||
\(648\) | −16490.8 | − | 5358.18i | −0.999721 | − | 0.324829i | ||||
\(649\) | 11215.7 | 0.678359 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1994.88 | −0.120100 | ||||||||
\(652\) | 3931.13 | + | 1277.30i | 0.236127 | + | 0.0767223i | ||||
\(653\) | −5562.33 | + | 7655.89i | −0.333340 | + | 0.458803i | −0.942481 | − | 0.334259i | \(-0.891514\pi\) |
0.609142 | + | 0.793061i | \(0.291514\pi\) | |||||||
\(654\) | 1289.87 | + | 937.144i | 0.0771221 | + | 0.0560325i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −186.843 | + | 135.749i | −0.0111204 | + | 0.00807946i | ||||
\(657\) | 11035.8i | 0.655326i | ||||||||
\(658\) | −188.234 | − | 259.082i | −0.0111522 | − | 0.0153497i | ||||
\(659\) | 4965.73 | + | 15282.9i | 0.293531 | + | 0.903397i | 0.983711 | + | 0.179759i | \(0.0575317\pi\) |
−0.690179 | + | 0.723638i | \(0.742468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4844.24 | − | 14909.0i | 0.285051 | − | 0.877298i | −0.701332 | − | 0.712835i | \(-0.747411\pi\) |
0.986383 | − | 0.164463i | \(-0.0525891\pi\) | |||||||
\(662\) | 534.299 | − | 173.604i | 0.0313688 | − | 0.0101923i | ||||
\(663\) | −31253.3 | + | 10154.8i | −1.83073 | + | 0.594841i | ||||
\(664\) | −1411.19 | + | 4343.19i | −0.0824769 | + | 0.253838i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1958.90 | − | 6028.87i | −0.113973 | − | 0.350772i | ||||
\(667\) | 11899.3 | + | 16377.9i | 0.690767 | + | 0.950759i | ||||
\(668\) | 1203.06i | 0.0696821i | ||||||||
\(669\) | 23730.9 | − | 17241.5i | 1.37144 | − | 0.996406i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10645.5 | + | 7734.38i | 0.612464 | + | 0.444981i | ||||
\(672\) | 921.807 | − | 1268.76i | 0.0529159 | − | 0.0728325i | ||||
\(673\) | −8548.51 | − | 2777.58i | −0.489630 | − | 0.159090i | 0.0537886 | − | 0.998552i | \(-0.482870\pi\) |
−0.543418 | + | 0.839462i | \(0.682870\pi\) | |||||||
\(674\) | 2050.96 | 0.117211 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5083.66 | 0.289239 | ||||||||
\(677\) | 5438.99 | + | 1767.23i | 0.308770 | + | 0.100325i | 0.459303 | − | 0.888279i | \(-0.348099\pi\) |
−0.150533 | + | 0.988605i | \(0.548099\pi\) | |||||||
\(678\) | 8520.50 | − | 11727.5i | 0.482637 | − | 0.664293i | ||||
\(679\) | 529.061 | + | 384.386i | 0.0299021 | + | 0.0217251i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13353.5 | − | 9701.86i | 0.751404 | − | 0.545927i | ||||
\(682\) | − | 8681.36i | − | 0.487429i | ||||||
\(683\) | −4557.14 | − | 6272.37i | −0.255306 | − | 0.351399i | 0.662054 | − | 0.749456i | \(-0.269685\pi\) |
−0.917361 | + | 0.398057i | \(0.869685\pi\) | |||||||
\(684\) | −4209.32 | − | 12955.0i | −0.235303 | − | 0.724189i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 391.544 | − | 1205.05i | 0.0217918 | − | 0.0670684i | ||||
\(687\) | −35392.3 | + | 11499.7i | −1.96551 | + | 0.638631i | ||||
\(688\) | −1407.34 | + | 457.274i | −0.0779862 | + | 0.0253392i | ||||
\(689\) | 364.219 | − | 1120.95i | 0.0201388 | − | 0.0619809i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3235.80 | − | 9958.77i | −0.178141 | − | 0.548262i | 0.821622 | − | 0.570033i | \(-0.193070\pi\) |
−0.999763 | + | 0.0217707i | \(0.993070\pi\) | |||||||
\(692\) | −57.8672 | − | 79.6473i | −0.00317887 | − | 0.00437534i | ||||
\(693\) | 638.448i | 0.0349966i | ||||||||
\(694\) | 4907.89 | − | 3565.79i | 0.268445 | − | 0.195037i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −32577.5 | − | 23668.9i | −1.77421 | − | 1.28904i | ||||
\(697\) | 1568.60 | − | 2158.99i | 0.0852439 | − | 0.117328i | ||||
\(698\) | 10601.1 | + | 3444.49i | 0.574865 | + | 0.186785i | ||||
\(699\) | −26895.0 | −1.45531 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8823.63 | 0.475412 | 0.237706 | − | 0.971337i | \(-0.423605\pi\) | ||||
0.237706 | + | 0.971337i | \(0.423605\pi\) | |||||||
\(702\) | 1443.11 | + | 468.894i | 0.0775877 | + | 0.0252098i | ||||
\(703\) | −10877.7 | + | 14971.8i | −0.583584 | + | 0.803234i | ||||
\(704\) | 3830.35 | + | 2782.91i | 0.205059 | + | 0.148984i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13836.1 | + | 10052.5i | −0.737575 | + | 0.535879i | ||||
\(707\) | 754.452i | 0.0401331i | ||||||||
\(708\) | −11127.5 | − | 15315.7i | −0.590675 | − | 0.812995i | ||||
\(709\) | −7039.37 | − | 21665.0i | −0.372876 | − | 1.14759i | −0.944900 | − | 0.327358i | \(-0.893842\pi\) |
0.572024 | − | 0.820237i | \(-0.306158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7014.88 | + | 21589.6i | −0.370012 | + | 1.13878i | ||||
\(712\) | 7832.30 | − | 2544.87i | 0.412258 | − | 0.133951i | ||||
\(713\) | 17104.1 | − | 5557.47i | 0.898394 | − | 0.291906i | ||||
\(714\) | −525.087 | + | 1616.05i | −0.0275223 | + | 0.0847048i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4679.02 | − | 14400.6i | −0.244222 | − | 0.751639i | ||||
\(717\) | −27062.7 | − | 37248.5i | −1.40959 | − | 1.94013i | ||||
\(718\) | − | 3056.51i | − | 0.158869i | ||||||
\(719\) | −20157.2 | + | 14645.1i | −1.04553 | + | 0.759624i | −0.971358 | − | 0.237621i | \(-0.923632\pi\) |
−0.0741754 | + | 0.997245i | \(0.523632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 535.330 | + | 388.940i | 0.0276515 | + | 0.0200900i | ||||
\(722\) | 4004.29 | − | 5511.43i | 0.206405 | − | 0.284092i | ||||
\(723\) | 20759.7 | + | 6745.23i | 1.06786 | + | 0.346968i | ||||
\(724\) | 8591.68 | 0.441032 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8739.84 | 0.446785 | ||||||||
\(727\) | −33574.1 | − | 10908.9i | −1.71278 | − | 0.556518i | −0.721992 | − | 0.691902i | \(-0.756773\pi\) |
−0.990793 | + | 0.135384i | \(0.956773\pi\) | |||||||
\(728\) | −527.645 | + | 726.241i | −0.0268624 | + | 0.0369729i | ||||
\(729\) | −11139.0 | − | 8092.96i | −0.565920 | − | 0.411165i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13833.3 | − | 10050.5i | 0.699922 | − | 0.508523i | ||||
\(732\) | − | 22210.6i | − | 1.12149i | ||||||
\(733\) | 8613.37 | + | 11855.3i | 0.434027 | + | 0.597388i | 0.968872 | − | 0.247563i | \(-0.0796297\pi\) |
−0.534844 | + | 0.844951i | \(0.679630\pi\) | |||||||
\(734\) | 5080.76 | + | 15637.0i | 0.255496 | + | 0.786336i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4369.00 | + | 13446.4i | −0.218809 | + | 0.673425i | ||||
\(737\) | −7475.73 | + | 2429.01i | −0.373639 | + | 0.121403i | ||||
\(738\) | 710.251 | − | 230.775i | 0.0354264 | − | 0.0115108i | ||||
\(739\) | −2051.60 | + | 6314.18i | −0.102124 | + | 0.314304i | −0.989045 | − | 0.147617i | \(-0.952840\pi\) |
0.886921 | + | 0.461921i | \(0.152840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8296.05 | + | 25532.6i | 0.411286 | + | 1.26581i | ||||
\(742\) | −35.8228 | − | 49.3058i | −0.00177237 | − | 0.00243945i | ||||
\(743\) | − | 15188.5i | − | 0.749950i | −0.927035 | − | 0.374975i | \(-0.877651\pi\) | ||
0.927035 | − | 0.374975i | \(-0.122349\pi\) | |||||||
\(744\) | −28940.8 | + | 21026.7i | −1.42611 | + | 1.03613i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1143.59 | + | 830.867i | 0.0561258 | + | 0.0407778i | ||||
\(747\) | −2933.44 | + | 4037.54i | −0.143680 | + | 0.197759i | ||||
\(748\) | 15938.4 | + | 5178.70i | 0.779098 | + | 0.253144i | ||||
\(749\) | −410.384 | −0.0200201 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9087.13 | −0.441537 | −0.220768 | − | 0.975326i | \(-0.570856\pi\) | ||||
−0.220768 | + | 0.975326i | \(0.570856\pi\) | |||||||
\(752\) | 1845.84 | + | 599.749i | 0.0895090 | + | 0.0290832i | ||||
\(753\) | 32557.3 | − | 44811.3i | 1.57564 | − | 2.16868i | ||||
\(754\) | 12148.1 | + | 8826.08i | 0.586745 | + | 0.426295i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −143.856 | + | 104.517i | −0.00692062 | + | 0.00502812i | ||||
\(757\) | 13103.6i | 0.629140i | 0.949234 | + | 0.314570i | \(0.101860\pi\) | ||||
−0.949234 | + | 0.314570i | \(0.898140\pi\) | |||||||
\(758\) | 8117.96 | + | 11173.4i | 0.388994 | + | 0.535405i | ||||
\(759\) | −3850.74 | − | 11851.4i | −0.184154 | − | 0.566769i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9148.33 | − | 28155.7i | 0.435777 | − | 1.34119i | −0.456510 | − | 0.889718i | \(-0.650901\pi\) |
0.892288 | − | 0.451467i | \(-0.149099\pi\) | |||||||
\(762\) | −21367.0 | + | 6942.57i | −1.01581 | + | 0.330056i | ||||
\(763\) | 161.760 | − | 52.5592i | 0.00767513 | − | 0.00249380i | ||||
\(764\) | 5519.52 | − | 16987.3i | 0.261373 | − | 0.804425i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2951.55 | − | 9083.94i | −0.139222 | − | 0.428480i | ||||
\(767\) | 10129.8 | + | 13942.4i | 0.476877 | + | 0.656365i | ||||
\(768\) | − | 24594.6i | − | 1.15557i | ||||||
\(769\) | −29802.3 | + | 21652.6i | −1.39753 | + | 1.01536i | −0.402534 | + | 0.915405i | \(0.631870\pi\) |
−0.994992 | + | 0.0999568i | \(0.968130\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13663.4 | − | 9927.04i | −0.638230 | − | 0.463701i | ||||
\(772\) | 7787.46 | − | 10718.5i | 0.363053 | − | 0.499699i | ||||
\(773\) | −28237.4 | − | 9174.90i | −1.31388 | − | 0.426906i | −0.433492 | − | 0.901158i | \(-0.642719\pi\) |
−0.880389 | + | 0.474252i | \(0.842719\pi\) | |||||||
\(774\) | 4784.98 | 0.222213 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11727.0 | 0.542491 | ||||||||
\(777\) | −1392.43 | − | 452.427i | −0.0642897 | − | 0.0208890i | ||||
\(778\) | 6491.85 | − | 8935.27i | 0.299157 | − | 0.411754i | ||||
\(779\) | −1763.81 | − | 1281.48i | −0.0811232 | − | 0.0589395i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3980.38 | + | 2891.92i | −0.182368 | + | 0.132498i | ||||
\(782\) | − | 15318.9i | − | 0.700515i | ||||||
\(783\) | 4268.02 | + | 5874.42i | 0.194798 | + | 0.268116i | ||||
\(784\) | 1184.05 | + | 3644.13i | 0.0539381 | + | 0.166004i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2313.08 | − | 7118.93i | 0.104968 | − | 0.323058i | ||||
\(787\) | −28425.6 | + | 9236.05i | −1.28750 | + | 0.418335i | −0.871216 | − | 0.490899i | \(-0.836668\pi\) |
−0.416286 | + | 0.909234i | \(0.636668\pi\) | |||||||
\(788\) | 6528.64 | − | 2121.28i | 0.295144 | − | 0.0958980i | ||||
\(789\) | 6773.14 | − | 20845.6i | 0.305615 | − | 0.940586i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −477.867 | − | 1470.72i | −0.0214804 | − | 0.0661099i | ||||
\(792\) | 6729.47 | + | 9262.32i | 0.301921 | + | 0.415558i | ||||
\(793\) | 20219.1i | 0.905423i | ||||||||
\(794\) | 5382.47 | − | 3910.59i | 0.240575 | − | 0.174788i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11590.2 | + | 8420.78i | 0.516086 | + | 0.374958i | ||||
\(797\) | 6471.90 | − | 8907.81i | 0.287637 | − | 0.395898i | −0.640608 | − | 0.767868i | \(-0.721318\pi\) |
0.928245 | + | 0.371970i | \(0.121318\pi\) | |||||||
\(798\) | 1320.25 | + | 428.975i | 0.0585668 | + | 0.0190295i | ||||
\(799\) | −22426.5 | −0.992982 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8999.95 | 0.397001 | ||||||||
\(802\) | 10918.1 | + | 3547.50i | 0.480712 | + | 0.156193i | ||||
\(803\) | −6519.77 | + | 8973.70i | −0.286523 | + | 0.394365i | ||||
\(804\) | 10733.9 | + | 7798.65i | 0.470841 | + | 0.342086i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10792.0 | − | 7840.81i | 0.471626 | − | 0.342656i | ||||
\(807\) | 10448.4i | 0.455765i | ||||||||
\(808\) | 7952.20 | + | 10945.3i | 0.346234 | + | 0.476551i | ||||
\(809\) | −2620.85 | − | 8066.15i | −0.113899 | − | 0.350545i | 0.877817 | − | 0.478996i | \(-0.158999\pi\) |
−0.991716 | + | 0.128452i | \(0.958999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10024.8 | − | 30853.2i | 0.434055 | − | 1.33588i | −0.459997 | − | 0.887921i | \(-0.652149\pi\) |
0.894052 | − | 0.447964i | \(-0.147851\pi\) | |||||||
\(812\) | −1673.53 | + | 543.762i | −0.0723268 | + | 0.0235004i | ||||
\(813\) | 2045.04 | − | 664.473i | 0.0882197 | − | 0.0286643i | ||||
\(814\) | 1968.89 | − | 6059.61i | 0.0847781 | − | 0.260920i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3182.28 | − | 9794.06i | −0.136522 | − | 0.420172i | ||||
\(817\) | −8210.83 | − | 11301.2i | −0.351604 | − | 0.483942i | ||||
\(818\) | 14435.0i | 0.617003i | ||||||||
\(819\) | −793.665 | + | 576.632i | −0.0338619 | + | 0.0246021i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20550.8 | + | 14931.0i | 0.873601 | + | 0.634709i | 0.931551 | − | 0.363611i | \(-0.118456\pi\) |
−0.0579495 | + | 0.998320i | \(0.518456\pi\) | |||||||
\(822\) | 648.108 | − | 892.045i | 0.0275005 | − | 0.0378511i | ||||
\(823\) | −40857.0 | − | 13275.2i | −1.73048 | − | 0.562267i | −0.736962 | − | 0.675934i | \(-0.763740\pi\) |
−0.993519 | + | 0.113667i | \(0.963740\pi\) | |||||||
\(824\) | 11865.9 | 0.501660 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 891.130 | 0.0375380 | ||||||||
\(827\) | 29110.9 | + | 9458.71i | 1.22405 | + | 0.397717i | 0.848554 | − | 0.529109i | \(-0.177474\pi\) |
0.375492 | + | 0.926826i | \(0.377474\pi\) | |||||||
\(828\) | −5710.53 | + | 7859.87i | −0.239679 | + | 0.329890i | ||||
\(829\) | 17898.0 | + | 13003.6i | 0.749846 | + | 0.544795i | 0.895779 | − | 0.444499i | \(-0.146618\pi\) |
−0.145933 | + | 0.989294i | \(0.546618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27779.8 | + | 20183.2i | −1.15965 | + | 0.842536i | ||||
\(832\) | 7275.04i | 0.303145i | ||||||||
\(833\) | −26024.4 | − | 35819.4i | −1.08246 | − | 1.48988i | ||||
\(834\) | −6106.49 | − | 18793.8i | −0.253538 | − | 0.780309i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4230.78 | − | 13021.0i | 0.175030 | − | 0.538686i | ||||
\(837\) | 6134.90 | − | 1993.35i | 0.253349 | − | 0.0823181i | ||||
\(838\) | −23969.8 | + | 7788.26i | −0.988094 | + | 0.321051i | ||||
\(839\) | 10771.3 | − | 33150.6i | 0.443226 | − | 1.36411i | −0.441192 | − | 0.897413i | \(-0.645444\pi\) |
0.884418 | − | 0.466696i | \(-0.154556\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14668.2 | + | 45144.1i | 0.601427 | + | 1.85100i | ||||
\(842\) | −8318.77 | − | 11449.8i | −0.340479 | − | 0.468630i | ||||
\(843\) | − | 10541.0i | − | 0.430666i | ||||||
\(844\) | 12913.1 | − | 9381.93i | 0.526644 | − | 0.382629i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5077.28 | − | 3688.86i | −0.206336 | − | 0.149912i | ||||
\(847\) | 548.026 | − | 754.293i | 0.0222319 | − | 0.0305995i | ||||
\(848\) | 351.281 | + | 114.138i | 0.0142253 | + | 0.00462207i | ||||
\(849\) | −18976.1 | −0.767089 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13199.1 | 0.531681 | ||||||||
\(852\) | 7898.18 | + | 2566.27i | 0.317591 | + | 0.103191i | ||||
\(853\) | −14739.6 | + | 20287.3i | −0.591646 | + | 0.814331i | −0.994912 | − | 0.100752i | \(-0.967875\pi\) |
0.403265 | + | 0.915083i | \(0.367875\pi\) | |||||||
\(854\) | 845.822 | + | 614.526i | 0.0338916 | + | 0.0246237i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5953.67 | + | 4325.59i | −0.237725 | + | 0.172717i | ||||
\(857\) | − | 45770.6i | − | 1.82438i | −0.409767 | − | 0.912190i | \(-0.634390\pi\) | ||
0.409767 | − | 0.912190i | \(-0.365610\pi\) | |||||||
\(858\) | −5432.86 | − | 7477.69i | −0.216171 | − | 0.297534i | ||||
\(859\) | 2248.85 | + | 6921.23i | 0.0893243 | + | 0.274912i | 0.985733 | − | 0.168316i | \(-0.0538330\pi\) |
−0.896409 | + | 0.443228i | \(0.853833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 53.2997 | − | 164.040i | 0.00210970 | − | 0.00649298i | ||||
\(862\) | −8633.64 | + | 2805.24i | −0.341140 | + | 0.110843i | ||||
\(863\) | 44371.3 | − | 14417.1i | 1.75019 | − | 0.568672i | 0.754081 | − | 0.656782i | \(-0.228083\pi\) |
0.996111 | + | 0.0881101i | \(0.0280827\pi\) | |||||||
\(864\) | −1567.07 | + | 4822.94i | −0.0617046 | + | 0.189907i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2039.10 | − | 6275.72i | −0.0800133 | − | 0.246256i | ||||
\(867\) | 49488.2 | + | 68114.7i | 1.93853 | + | 2.66816i | ||||
\(868\) | 1563.22i | 0.0611280i | ||||||||
\(869\) | −18458.8 | + | 13411.1i | −0.720567 | + | 0.523522i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9771.46 | − | 7099.38i | −0.380130 | − | 0.276181i | ||||
\(872\) | 1792.76 | − | 2467.52i | 0.0696221 | − | 0.0958266i | ||||
\(873\) | 12188.5 | + | 3960.27i | 0.472528 | + | 0.153534i | ||||
\(874\) | −12514.9 | −0.484352 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18722.7 | 0.722123 | ||||||||
\(877\) | 33210.6 | + | 10790.8i | 1.27873 | + | 0.415484i | 0.868132 | − | 0.496334i | \(-0.165321\pi\) |
0.410595 | + | 0.911818i | \(0.365321\pi\) | |||||||
\(878\) | 3169.33 | − | 4362.20i | 0.121822 | − | 0.167673i | ||||
\(879\) | 22517.9 | + | 16360.2i | 0.864062 | + | 0.627778i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27671.6 | + | 20104.6i | −1.05821 | + | 0.768833i | −0.973756 | − | 0.227594i | \(-0.926914\pi\) |
−0.0844522 | + | 0.996428i | \(0.526914\pi\) | |||||||
\(882\) | − | 12390.1i | − | 0.473010i | ||||||
\(883\) | 27589.2 | + | 37973.3i | 1.05147 | + | 1.44723i | 0.887525 | + | 0.460760i | \(0.152423\pi\) |
0.163948 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(884\) | 7957.47 | + | 24490.6i | 0.302759 | + | 0.931796i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2942.02 | + | 9054.61i | −0.111557 | + | 0.343336i | ||||
\(887\) | −23565.0 | + | 7656.74i | −0.892036 | + | 0.289840i | −0.718946 | − | 0.695066i | \(-0.755375\pi\) |
−0.173090 | + | 0.984906i | \(0.555375\pi\) | |||||||
\(888\) | −24969.5 | + | 8113.08i | −0.943606 | + | 0.306596i | ||||
\(889\) | −740.625 | + | 2279.41i | −0.0279413 | + | 0.0859943i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5885.49 | − | 18113.7i | −0.221292 | − | 0.681068i | ||||
\(892\) | −13510.7 | − | 18595.9i | −0.507145 | − | 0.698025i | ||||
\(893\) | 18321.5i | 0.686569i | ||||||||
\(894\) | 8238.23 | − | 5985.43i | 0.308197 | − | 0.223918i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1128.58 | − | 819.963i | −0.0420795 | − | 0.0305726i | ||||
\(897\) | 11254.7 | − | 15490.8i | 0.418935 | − | 0.576615i | ||||
\(898\) | 16838.3 | + | 5471.11i | 0.625727 | + | 0.203311i | ||||
\(899\) | 63834.9 | 2.36820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4267.98 | −0.157810 | ||||||||
\(902\) | 713.872 | + | 231.951i | 0.0263518 | + | 0.00856223i | ||||
\(903\) | 649.585 | − | 894.077i | 0.0239389 | − | 0.0329491i | ||||
\(904\) | −22434.7 | − | 16299.7i | −0.825405 | − | 0.599692i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 869.659 | − | 631.845i | 0.0318902 | − | 0.0231696i | ||||
\(907\) | − | 5545.03i | − | 0.202999i | −0.994836 | − | 0.101499i | \(-0.967636\pi\) | ||
0.994836 | − | 0.101499i | \(-0.0323640\pi\) | |||||||
\(908\) | −7602.54 | − | 10464.0i | −0.277863 | − | 0.382445i | ||||
\(909\) | 4568.86 | + | 14061.5i | 0.166710 | + | 0.513081i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11280.5 | + | 34717.8i | −0.410252 | + | 1.26263i | 0.506177 | + | 0.862429i | \(0.331058\pi\) |
−0.916429 | + | 0.400196i | \(0.868942\pi\) | |||||||
\(912\) | −8001.35 | + | 2599.79i | −0.290516 | + | 0.0943945i | ||||
\(913\) | −4770.61 | + | 1550.06i | −0.172929 | + | 0.0561880i | ||||
\(914\) | −7852.86 | + | 24168.6i | −0.284190 | + | 0.874646i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9011.33 | + | 27734.0i | 0.325047 | + | 1.00039i | ||||
\(917\) | −469.359 | − | 646.018i | −0.0169025 | − | 0.0232643i | ||||
\(918\) | − | 5494.57i | − | 0.197547i | ||||||
\(919\) | 11538.5 | − | 8383.20i | 0.414167 | − | 0.300910i | −0.361120 | − | 0.932519i | \(-0.617605\pi\) |
0.775287 | + | 0.631610i | \(0.217605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −47354.8 | − | 34405.3i | −1.69424 | − | 1.23094i | ||||
\(922\) | −5552.53 | + | 7642.40i | −0.198333 | + | 0.272982i | ||||
\(923\) | −7189.98 | − | 2336.17i | −0.256404 | − | 0.0833108i | ||||
\(924\) | 1083.15 | 0.0385638 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1610.56 | −0.0571557 | ||||||||
\(927\) | 12332.9 | + | 4007.19i | 0.436963 | + | 0.141978i | ||||
\(928\) | −29497.3 | + | 40599.5i | −1.04342 | + | 1.43615i | ||||
\(929\) | −2382.32 | − | 1730.86i | −0.0841350 | − | 0.0611276i | 0.544923 | − | 0.838486i | \(-0.316559\pi\) |
−0.629058 | + | 0.777359i | \(0.716559\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29263.0 | + | 21260.8i | −1.03014 | + | 0.748438i | ||||
\(932\) | 21075.4i | 0.740716i | ||||||||
\(933\) | 19992.9 | + | 27517.9i | 0.701542 | + | 0.965589i | ||||
\(934\) | −4110.20 | − | 12649.9i | −0.143993 | − | 0.443166i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5436.25 | + | 16731.0i | −0.189839 | + | 0.584264i | ||||
\(937\) | −27716.1 | + | 9005.50i | −0.966323 | + | 0.313978i | −0.749331 | − | 0.662196i | \(-0.769625\pi\) |
−0.216993 | + | 0.976173i | \(0.569625\pi\) | |||||||
\(938\) | −593.975 | + | 192.994i | −0.0206759 | + | 0.00671800i | ||||
\(939\) | −22569.1 | + | 69460.6i | −0.784361 | + | 2.41402i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10416.1 | − | 32057.5i | −0.360845 | − | 1.11057i | −0.952542 | − | 0.304406i | \(-0.901542\pi\) |
0.591697 | − | 0.806160i | \(-0.298458\pi\) | |||||||
\(942\) | 20304.8 | + | 27947.1i | 0.702299 | + | 0.966631i | ||||
\(943\) | 1554.97i | 0.0536975i | ||||||||
\(944\) | −4369.24 | + | 3174.44i | −0.150643 | + | 0.109448i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3890.87 | + | 2826.88i | 0.133724 | + | 0.0971563i | ||||
\(947\) | −14117.7 | + | 19431.3i | −0.484438 | + | 0.666772i | −0.979350 | − | 0.202171i | \(-0.935200\pi\) |
0.494912 | + | 0.868943i | \(0.335200\pi\) | |||||||
\(948\) | 36627.4 | + | 11901.0i | 1.25486 | + | 0.407727i | ||||
\(949\) | −17043.9 | −0.583000 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23246.0 | 0.792644 | ||||||||
\(952\) | 3091.51 | + | 1004.49i | 0.105248 | + | 0.0341973i | ||||
\(953\) | −21529.5 | + | 29632.9i | −0.731805 | + | 1.00724i | 0.267244 | + | 0.963629i | \(0.413887\pi\) |
−0.999048 | + | 0.0436139i | \(0.986113\pi\) | |||||||
\(954\) | −966.256 | − | 702.026i | −0.0327921 | − | 0.0238249i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29188.6 | + | 21206.7i | −0.987475 | + | 0.717443i | ||||
\(957\) | − | 44230.9i | − | 1.49402i | ||||||
\(958\) | −2793.11 | − | 3844.38i | −0.0941975 | − | 0.129652i | ||||
\(959\) | −36.3488 | − | 111.870i | −0.00122395 | − | 0.00376692i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8318.09 | − | 25600.4i | 0.279215 | − | 0.859335i | ||||
\(962\) | 9311.06 | − | 3025.35i | 0.312059 | − | 0.101394i | ||||
\(963\) | −7648.74 | + | 2485.23i | −0.255947 | + | 0.0831623i | ||||
\(964\) | 5285.67 | − | 16267.6i | 0.176598 | − | 0.543512i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −305.956 | − | 941.636i | −0.0101905 | − | 0.0313630i | ||||
\(967\) | −4694.17 | − | 6460.97i | −0.156106 | − | 0.214861i | 0.723799 | − | 0.690010i | \(-0.242394\pi\) |
−0.879905 | + | 0.475149i | \(0.842394\pi\) | |||||||
\(968\) | − | 16719.3i | − | 0.555145i | ||||||
\(969\) | 78648.2 | − | 57141.2i | 2.60737 | − | 1.89437i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3656.19 | − | 2656.38i | −0.120837 | − | 0.0877932i | 0.525725 | − | 0.850654i | \(-0.323794\pi\) |
−0.646562 | + | 0.762861i | \(0.723794\pi\) | |||||||
\(972\) | −16509.9 | + | 22723.9i | −0.544810 | + | 0.749867i | ||||
\(973\) | −2004.91 | − | 651.434i | −0.0660579 | − | 0.0214635i | ||||
\(974\) | 19910.9 | 0.655017 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6336.20 | −0.207804 | ||||||||
\(977\) | −1677.36 | − | 545.007i | −0.0549267 | − | 0.0178468i | 0.281425 | − | 0.959583i | \(-0.409193\pi\) |
−0.336352 | + | 0.941737i | \(0.609193\pi\) | |||||||
\(978\) | −4852.24 | + | 6678.54i | −0.158648 | + | 0.218360i | ||||
\(979\) | 7318.23 | + | 5317.00i | 0.238909 | + | 0.173577i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2696.61 | − | 1959.20i | 0.0877635 | − | 0.0637639i | ||||
\(982\) | − | 10742.6i | − | 0.349095i | ||||||
\(983\) | −18302.6 | − | 25191.3i | −0.593857 | − | 0.817374i | 0.401271 | − | 0.915959i | \(-0.368568\pi\) |
−0.995129 | + | 0.0985849i | \(0.968568\pi\) | |||||||
\(984\) | −955.789 | − | 2941.62i | −0.0309649 | − | 0.0953001i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16802.5 | − | 51712.7i | 0.542697 | − | 1.67025i | ||||
\(987\) | −1378.53 | + | 447.912i | −0.0444571 | + | 0.0144450i | ||||
\(988\) | 20007.8 | − | 6500.93i | 0.644264 | − | 0.209334i | ||||
\(989\) | −3078.78 | + | 9475.50i | −0.0989883 | + | 0.304655i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4516.20 | + | 13899.4i | 0.144765 | + | 0.445540i | 0.996981 | − | 0.0776501i | \(-0.0247417\pi\) |
−0.852216 | + | 0.523190i | \(0.824742\pi\) | |||||||
\(992\) | 26204.4 | + | 36067.3i | 0.838701 | + | 1.15437i | ||||
\(993\) | − | 2542.78i | − | 0.0812616i | ||||||
\(994\) | −316.256 | + | 229.774i | −0.0100916 | + | 0.00733197i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6849.81 | + | 4976.68i | 0.217916 | + | 0.158325i | ||||
\(997\) | −7437.62 | + | 10237.0i | −0.236261 | + | 0.325185i | −0.910640 | − | 0.413200i | \(-0.864411\pi\) |
0.674380 | + | 0.738385i | \(0.264411\pi\) | |||||||
\(998\) | −14884.4 | − | 4836.23i | −0.472102 | − | 0.153395i | ||||
\(999\) | 4734.25 | 0.149935 |
(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 | 125.4.e.a.24.4 | 24 | ||
5.2 | odd | 4 | 125.4.d.b.101.5 | 48 | |||
5.3 | odd | 4 | 125.4.d.b.101.8 | 48 | |||
5.4 | even | 2 | 25.4.e.a.4.3 | ✓ | 24 | ||
15.14 | odd | 2 | 225.4.m.a.154.4 | 24 | |||
25.6 | even | 5 | 25.4.e.a.19.3 | yes | 24 | ||
25.8 | odd | 20 | 125.4.d.b.26.8 | 48 | |||
25.12 | odd | 20 | 625.4.a.g.1.9 | 24 | |||
25.13 | odd | 20 | 625.4.a.g.1.16 | 24 | |||
25.17 | odd | 20 | 125.4.d.b.26.5 | 48 | |||
25.19 | even | 10 | inner | 125.4.e.a.99.4 | 24 | ||
75.56 | odd | 10 | 225.4.m.a.19.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.4.e.a.4.3 | ✓ | 24 | 5.4 | even | 2 | ||
25.4.e.a.19.3 | yes | 24 | 25.6 | even | 5 | ||
125.4.d.b.26.5 | 48 | 25.17 | odd | 20 | |||
125.4.d.b.26.8 | 48 | 25.8 | odd | 20 | |||
125.4.d.b.101.5 | 48 | 5.2 | odd | 4 | |||
125.4.d.b.101.8 | 48 | 5.3 | odd | 4 | |||
125.4.e.a.24.4 | 24 | 1.1 | even | 1 | trivial | ||
125.4.e.a.99.4 | 24 | 25.19 | even | 10 | inner | ||
225.4.m.a.19.4 | 24 | 75.56 | odd | 10 | |||
225.4.m.a.154.4 | 24 | 15.14 | odd | 2 | |||
625.4.a.g.1.9 | 24 | 25.12 | odd | 20 | |||
625.4.a.g.1.16 | 24 | 25.13 | odd | 20 |