Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (of order \(6\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 116.1 | ||
Character | \(\chi\) | \(=\) | 637.116 |
Dual form | 637.2.r.g.324.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.36789 | + | 1.36710i | −1.67435 | + | 0.966686i | −0.709193 | + | 0.705014i | \(0.750941\pi\) |
−0.965157 | + | 0.261672i | \(0.915726\pi\) | |||||||
\(3\) | −0.577975 | + | 1.00108i | −0.333694 | + | 0.577975i | −0.983233 | − | 0.182353i | \(-0.941629\pi\) |
0.649539 | + | 0.760328i | \(0.274962\pi\) | |||||||
\(4\) | 2.73793 | − | 4.74223i | 1.36896 | − | 2.37112i | ||||
\(5\) | −1.62576 | + | 0.938635i | −0.727063 | + | 0.419770i | −0.817347 | − | 0.576146i | \(-0.804556\pi\) |
0.0902836 | + | 0.995916i | \(0.471223\pi\) | |||||||
\(6\) | − | 3.16060i | − | 1.29031i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 9.50370i | 3.36007i | ||||||||
\(9\) | 0.831889 | + | 1.44087i | 0.277296 | + | 0.480292i | ||||
\(10\) | 2.56642 | − | 4.44516i | 0.811572 | − | 1.40568i | ||||
\(11\) | 1.99163 | + | 1.14987i | 0.600499 | + | 0.346698i | 0.769238 | − | 0.638963i | \(-0.220636\pi\) |
−0.168739 | + | 0.985661i | \(0.553969\pi\) | |||||||
\(12\) | 3.16491 | + | 5.48179i | 0.913631 | + | 1.58246i | ||||
\(13\) | −0.574228 | − | 3.55953i | −0.159262 | − | 0.987236i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.17003i | − | 0.560299i | ||||||
\(16\) | −7.51666 | − | 13.0192i | −1.87917 | − | 3.25481i | ||||
\(17\) | 3.03578 | − | 5.25812i | 0.736285 | − | 1.27528i | −0.217873 | − | 0.975977i | \(-0.569912\pi\) |
0.954157 | − | 0.299305i | \(-0.0967549\pi\) | |||||||
\(18\) | −3.93964 | − | 2.27455i | −0.928583 | − | 0.536117i | ||||
\(19\) | 4.46010 | − | 2.57504i | 1.02322 | − | 0.590754i | 0.108183 | − | 0.994131i | \(-0.465497\pi\) |
0.915034 | + | 0.403377i | \(0.132164\pi\) | |||||||
\(20\) | 10.2797i | 2.29860i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.28794 | −1.34059 | ||||||||
\(23\) | 2.20891 | + | 3.82595i | 0.460590 | + | 0.797765i | 0.998990 | − | 0.0449240i | \(-0.0143046\pi\) |
−0.538401 | + | 0.842689i | \(0.680971\pi\) | |||||||
\(24\) | −9.51399 | − | 5.49290i | −1.94203 | − | 1.12123i | ||||
\(25\) | −0.737930 | + | 1.27813i | −0.147586 | + | 0.255626i | ||||
\(26\) | 6.22595 | + | 7.64354i | 1.22101 | + | 1.49902i | ||||
\(27\) | −5.39110 | −1.03752 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.50488 | 1.39362 | 0.696810 | − | 0.717255i | \(-0.254602\pi\) | ||||
0.696810 | + | 0.717255i | \(0.254602\pi\) | |||||||
\(30\) | 2.96665 | + | 5.13839i | 0.541634 | + | 0.938137i | ||||
\(31\) | 3.75139 | + | 2.16586i | 0.673769 | + | 0.389001i | 0.797503 | − | 0.603315i | \(-0.206154\pi\) |
−0.123734 | + | 0.992315i | \(0.539487\pi\) | |||||||
\(32\) | 19.1363 | + | 11.0484i | 3.38286 | + | 1.95309i | ||||
\(33\) | −2.30222 | + | 1.32919i | −0.400766 | + | 0.231382i | ||||
\(34\) | 16.6009i | 2.84703i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.11062 | 1.51844 | ||||||||
\(37\) | 2.74415 | − | 1.58433i | 0.451135 | − | 0.260463i | −0.257174 | − | 0.966365i | \(-0.582791\pi\) |
0.708309 | + | 0.705902i | \(0.249458\pi\) | |||||||
\(38\) | −7.04068 | + | 12.1948i | −1.14215 | + | 1.97826i | ||||
\(39\) | 3.89527 | + | 1.48247i | 0.623743 | + | 0.237385i | ||||
\(40\) | −8.92050 | − | 15.4508i | −1.41046 | − | 2.44298i | ||||
\(41\) | − | 2.45446i | − | 0.383322i | −0.981461 | − | 0.191661i | \(-0.938613\pi\) | ||
0.981461 | − | 0.191661i | \(-0.0613874\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.17732 | −0.332038 | −0.166019 | − | 0.986123i | \(-0.553091\pi\) | ||||
−0.166019 | + | 0.986123i | \(0.553091\pi\) | |||||||
\(44\) | 10.9059 | − | 6.29651i | 1.64412 | − | 0.949235i | ||||
\(45\) | −2.70491 | − | 1.56168i | −0.403224 | − | 0.232802i | ||||
\(46\) | −10.4609 | − | 6.03961i | −1.54238 | − | 0.890492i | ||||
\(47\) | −7.71162 | + | 4.45231i | −1.12486 | + | 0.649436i | −0.942636 | − | 0.333822i | \(-0.891662\pi\) |
−0.182220 | + | 0.983258i | \(0.558328\pi\) | |||||||
\(48\) | 17.3778 | 2.50827 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.03530i | − | 0.570677i | ||||||
\(51\) | 3.50921 | + | 6.07813i | 0.491388 | + | 0.851108i | ||||
\(52\) | −18.4523 | − | 7.02262i | −2.55888 | − | 0.973863i | ||||
\(53\) | −4.05001 | + | 7.01482i | −0.556312 | + | 0.963560i | 0.441488 | + | 0.897267i | \(0.354451\pi\) |
−0.997800 | + | 0.0662933i | \(0.978883\pi\) | |||||||
\(54\) | 12.7655 | − | 7.37017i | 1.73717 | − | 1.00295i | ||||
\(55\) | −4.31722 | −0.582134 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.95323i | 0.788525i | ||||||||
\(58\) | −17.7707 | + | 10.2599i | −2.33341 | + | 1.34719i | ||||
\(59\) | 6.18303 | + | 3.56978i | 0.804963 | + | 0.464745i | 0.845203 | − | 0.534445i | \(-0.179479\pi\) |
−0.0402409 | + | 0.999190i | \(0.512813\pi\) | |||||||
\(60\) | −10.2908 | − | 5.94139i | −1.32854 | − | 0.767030i | ||||
\(61\) | 4.00490 | + | 6.93668i | 0.512774 | + | 0.888151i | 0.999890 | + | 0.0148140i | \(0.00471562\pi\) |
−0.487116 | + | 0.873337i | \(0.661951\pi\) | |||||||
\(62\) | −11.8438 | −1.50417 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −30.3503 | −3.79379 | ||||||||
\(65\) | 4.27466 | + | 5.24796i | 0.530206 | + | 0.650930i | ||||
\(66\) | 3.63427 | − | 6.29475i | 0.447348 | − | 0.774830i | ||||
\(67\) | 1.00227 | + | 0.578661i | 0.122447 | + | 0.0706947i | 0.559972 | − | 0.828511i | \(-0.310812\pi\) |
−0.437526 | + | 0.899206i | \(0.644145\pi\) | |||||||
\(68\) | −16.6235 | − | 28.7927i | −2.01590 | − | 3.49163i | ||||
\(69\) | −5.10678 | −0.614785 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.11328i | − | 0.606835i | −0.952858 | − | 0.303417i | \(-0.901872\pi\) | ||
0.952858 | − | 0.303417i | \(-0.0981276\pi\) | |||||||
\(72\) | −13.6936 | + | 7.90603i | −1.61381 | + | 0.931735i | ||||
\(73\) | 1.70519 | + | 0.984492i | 0.199578 | + | 0.115226i | 0.596458 | − | 0.802644i | \(-0.296574\pi\) |
−0.396881 | + | 0.917870i | \(0.629907\pi\) | |||||||
\(74\) | −4.33189 | + | 7.50305i | −0.503572 | + | 0.872212i | ||||
\(75\) | −0.853010 | − | 1.47746i | −0.0984971 | − | 0.170602i | ||||
\(76\) | − | 28.2011i | − | 3.23489i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.2503 | + | 1.81491i | −1.27384 | + | 0.205498i | ||||
\(79\) | −1.90604 | − | 3.30136i | −0.214446 | − | 0.371432i | 0.738655 | − | 0.674084i | \(-0.235461\pi\) |
−0.953101 | + | 0.302652i | \(0.902128\pi\) | |||||||
\(80\) | 24.4406 | + | 14.1108i | 2.73254 | + | 1.57764i | ||||
\(81\) | 0.620251 | − | 1.07431i | 0.0689168 | − | 0.119367i | ||||
\(82\) | 3.35549 | + | 5.81188i | 0.370552 | + | 0.641815i | ||||
\(83\) | − | 2.49170i | − | 0.273499i | −0.990606 | − | 0.136750i | \(-0.956334\pi\) | ||
0.990606 | − | 0.136750i | \(-0.0436656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.3980i | 1.23628i | ||||||||
\(86\) | 5.15565 | − | 2.97662i | 0.555948 | − | 0.320977i | ||||
\(87\) | −4.33763 | + | 7.51300i | −0.465043 | + | 0.805478i | ||||
\(88\) | −10.9280 | + | 18.9279i | −1.16493 | + | 2.01772i | ||||
\(89\) | −9.03187 | + | 5.21456i | −0.957377 | + | 0.552742i | −0.895365 | − | 0.445334i | \(-0.853085\pi\) |
−0.0620121 | + | 0.998075i | \(0.519752\pi\) | |||||||
\(90\) | 8.53990 | 0.900185 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 24.1914 | 2.52213 | ||||||||
\(93\) | −4.33642 | + | 2.50363i | −0.449665 | + | 0.259614i | ||||
\(94\) | 12.1735 | − | 21.0851i | 1.25560 | − | 2.17477i | ||||
\(95\) | −4.83404 | + | 8.37280i | −0.495962 | + | 0.859032i | ||||
\(96\) | −22.1206 | + | 12.7714i | −2.25768 | + | 1.30347i | ||||
\(97\) | 2.51219i | 0.255074i | 0.991834 | + | 0.127537i | \(0.0407072\pi\) | ||||
−0.991834 | + | 0.127537i | \(0.959293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.82625i | 0.384553i | ||||||||
\(100\) | 4.04080 | + | 6.99887i | 0.404080 | + | 0.699887i | ||||
\(101\) | −5.34019 | + | 9.24947i | −0.531368 | + | 0.920357i | 0.467961 | + | 0.883749i | \(0.344989\pi\) |
−0.999330 | + | 0.0366080i | \(0.988345\pi\) | |||||||
\(102\) | −16.6188 | − | 9.59489i | −1.64551 | − | 0.950035i | ||||
\(103\) | 5.90150 | + | 10.2217i | 0.581492 | + | 1.00717i | 0.995303 | + | 0.0968106i | \(0.0308641\pi\) |
−0.413811 | + | 0.910363i | \(0.635803\pi\) | |||||||
\(104\) | 33.8287 | − | 5.45729i | 3.31718 | − | 0.535131i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 22.1471i | − | 2.15112i | ||||||
\(107\) | 2.13867 | + | 3.70429i | 0.206753 | + | 0.358107i | 0.950690 | − | 0.310143i | \(-0.100377\pi\) |
−0.743937 | + | 0.668250i | \(0.767044\pi\) | |||||||
\(108\) | −14.7604 | + | 25.5658i | −1.42032 | + | 2.46007i | ||||
\(109\) | 1.74188 | + | 1.00567i | 0.166842 | + | 0.0963260i | 0.581096 | − | 0.813835i | \(-0.302624\pi\) |
−0.414254 | + | 0.910161i | \(0.635958\pi\) | |||||||
\(110\) | 10.2227 | − | 5.90208i | 0.974696 | − | 0.562741i | ||||
\(111\) | 3.66282i | 0.347660i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.16866 | −0.392154 | −0.196077 | − | 0.980588i | \(-0.562820\pi\) | ||||
−0.196077 | + | 0.980588i | \(0.562820\pi\) | |||||||
\(114\) | −8.13867 | − | 14.0966i | −0.762256 | − | 1.32027i | ||||
\(115\) | −7.18233 | − | 4.14672i | −0.669756 | − | 0.386684i | ||||
\(116\) | 20.5478 | − | 35.5899i | 1.90782 | − | 3.30444i | ||||
\(117\) | 4.65114 | − | 3.78853i | 0.429998 | − | 0.350249i | ||||
\(118\) | −19.5210 | −1.79705 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 20.6233 | 1.88264 | ||||||||
\(121\) | −2.85561 | − | 4.94606i | −0.259601 | − | 0.449642i | ||||
\(122\) | −18.9663 | − | 10.9502i | −1.71713 | − | 0.991384i | ||||
\(123\) | 2.45711 | + | 1.41862i | 0.221551 | + | 0.127912i | ||||
\(124\) | 20.5421 | − | 11.8600i | 1.84473 | − | 1.06506i | ||||
\(125\) | − | 12.1569i | − | 1.08735i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.1922 | 1.34809 | 0.674046 | − | 0.738689i | \(-0.264555\pi\) | ||||
0.674046 | + | 0.738689i | \(0.264555\pi\) | |||||||
\(128\) | 33.5934 | − | 19.3952i | 2.96927 | − | 1.71431i | ||||
\(129\) | 1.25844 | − | 2.17968i | 0.110799 | − | 0.191910i | ||||
\(130\) | −17.2964 | − | 6.58270i | −1.51700 | − | 0.577341i | ||||
\(131\) | −0.475488 | − | 0.823570i | −0.0415436 | − | 0.0719556i | 0.844506 | − | 0.535546i | \(-0.179894\pi\) |
−0.886050 | + | 0.463591i | \(0.846561\pi\) | |||||||
\(132\) | 14.5569i | 1.26702i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.16435 | −0.273359 | ||||||||
\(135\) | 8.76464 | − | 5.06027i | 0.754341 | − | 0.435519i | ||||
\(136\) | 49.9716 | + | 28.8511i | 4.28503 | + | 2.47397i | ||||
\(137\) | 10.5983 | + | 6.11895i | 0.905477 | + | 0.522777i | 0.878973 | − | 0.476871i | \(-0.158229\pi\) |
0.0265039 | + | 0.999649i | \(0.491563\pi\) | |||||||
\(138\) | 12.0923 | − | 6.98149i | 1.02936 | − | 0.594304i | ||||
\(139\) | −5.24824 | −0.445150 | −0.222575 | − | 0.974916i | \(-0.571446\pi\) | ||||
−0.222575 | + | 0.974916i | \(0.571446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 10.2933i | − | 0.866852i | ||||||
\(142\) | 6.99037 | + | 12.1077i | 0.586619 | + | 1.01605i | ||||
\(143\) | 2.94934 | − | 7.74955i | 0.246636 | − | 0.648050i | ||||
\(144\) | 12.5061 | − | 21.6611i | 1.04217 | − | 1.80509i | ||||
\(145\) | −12.2012 | + | 7.04434i | −1.01325 | + | 0.585001i | ||||
\(146\) | −5.38360 | −0.445550 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 17.3512i | − | 1.42626i | ||||||
\(149\) | −2.06234 | + | 1.19069i | −0.168953 | + | 0.0975451i | −0.582092 | − | 0.813123i | \(-0.697766\pi\) |
0.413139 | + | 0.910668i | \(0.364432\pi\) | |||||||
\(150\) | 4.03967 | + | 2.33230i | 0.329837 | + | 0.190432i | ||||
\(151\) | 17.5877 | + | 10.1543i | 1.43127 | + | 0.826341i | 0.997217 | − | 0.0745487i | \(-0.0237516\pi\) |
0.434048 | + | 0.900890i | \(0.357085\pi\) | |||||||
\(152\) | 24.4724 | + | 42.3874i | 1.98497 | + | 3.43808i | ||||
\(153\) | 10.1017 | 0.816677 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.13182 | −0.653163 | ||||||||
\(156\) | 17.6952 | − | 14.4134i | 1.41675 | − | 1.15400i | ||||
\(157\) | 5.52023 | − | 9.56132i | 0.440562 | − | 0.763076i | −0.557169 | − | 0.830399i | \(-0.688112\pi\) |
0.997731 | + | 0.0673230i | \(0.0214458\pi\) | |||||||
\(158\) | 9.02658 | + | 5.21150i | 0.718116 | + | 0.414605i | ||||
\(159\) | −4.68161 | − | 8.10879i | −0.371276 | − | 0.643069i | ||||
\(160\) | −41.4815 | −3.27940 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.39178i | 0.266484i | ||||||||
\(163\) | 16.4358 | − | 9.48921i | 1.28735 | − | 0.743253i | 0.309170 | − | 0.951007i | \(-0.399949\pi\) |
0.978181 | + | 0.207754i | \(0.0666154\pi\) | |||||||
\(164\) | −11.6396 | − | 6.72013i | −0.908901 | − | 0.524754i | ||||
\(165\) | 2.49525 | − | 4.32190i | 0.194255 | − | 0.336459i | ||||
\(166\) | 3.40640 | + | 5.90006i | 0.264388 | + | 0.457934i | ||||
\(167\) | 21.7305i | 1.68155i | 0.541382 | + | 0.840776i | \(0.317901\pi\) | ||||
−0.541382 | + | 0.840776i | \(0.682099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3405 | + | 4.08796i | −0.949271 | + | 0.314459i | ||||
\(170\) | −15.5821 | − | 26.9891i | −1.19510 | − | 2.06997i | ||||
\(171\) | 7.42062 | + | 4.28430i | 0.567469 | + | 0.327628i | ||||
\(172\) | −5.96135 | + | 10.3254i | −0.454549 | + | 0.787301i | ||||
\(173\) | −1.45150 | − | 2.51408i | −0.110356 | − | 0.191142i | 0.805558 | − | 0.592517i | \(-0.201866\pi\) |
−0.915914 | + | 0.401375i | \(0.868532\pi\) | |||||||
\(174\) | − | 23.7199i | − | 1.79820i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 34.5727i | − | 2.60601i | ||||||
\(177\) | −7.14728 | + | 4.12648i | −0.537223 | + | 0.310166i | ||||
\(178\) | 14.2576 | − | 24.6950i | 1.06866 | − | 1.85097i | ||||
\(179\) | 9.67514 | − | 16.7578i | 0.723154 | − | 1.25254i | −0.236575 | − | 0.971613i | \(-0.576025\pi\) |
0.959729 | − | 0.280926i | \(-0.0906416\pi\) | |||||||
\(180\) | −14.8117 | + | 8.55154i | −1.10400 | + | 0.637394i | ||||
\(181\) | 9.98016 | 0.741820 | 0.370910 | − | 0.928669i | \(-0.379046\pi\) | ||||
0.370910 | + | 0.928669i | \(0.379046\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.25892 | −0.684439 | ||||||||
\(184\) | −36.3607 | + | 20.9928i | −2.68054 | + | 1.54761i | ||||
\(185\) | −2.97422 | + | 5.15150i | −0.218669 | + | 0.378746i | ||||
\(186\) | 6.84543 | − | 11.8566i | 0.501931 | − | 0.869371i | ||||
\(187\) | 12.0923 | − | 6.98149i | 0.884276 | − | 0.510537i | ||||
\(188\) | 48.7604i | 3.55622i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 26.4345i | − | 1.91776i | ||||||
\(191\) | −2.70243 | − | 4.68074i | −0.195541 | − | 0.338687i | 0.751537 | − | 0.659691i | \(-0.229313\pi\) |
−0.947078 | + | 0.321004i | \(0.895980\pi\) | |||||||
\(192\) | 17.5417 | − | 30.3831i | 1.26596 | − | 2.19271i | ||||
\(193\) | −12.6151 | − | 7.28331i | −0.908052 | − | 0.524264i | −0.0282481 | − | 0.999601i | \(-0.508993\pi\) |
−0.879804 | + | 0.475337i | \(0.842326\pi\) | |||||||
\(194\) | −3.43442 | − | 5.94858i | −0.246577 | − | 0.427083i | ||||
\(195\) | −7.72429 | + | 1.24609i | −0.553148 | + | 0.0892345i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.9055i | 1.13322i | 0.823987 | + | 0.566609i | \(0.191745\pi\) | ||||
−0.823987 | + | 0.566609i | \(0.808255\pi\) | |||||||
\(198\) | −5.23087 | − | 9.06014i | −0.371742 | − | 0.643876i | ||||
\(199\) | 0.186833 | − | 0.323604i | 0.0132442 | − | 0.0229397i | −0.859327 | − | 0.511426i | \(-0.829117\pi\) |
0.872572 | + | 0.488486i | \(0.162451\pi\) | |||||||
\(200\) | −12.1470 | − | 7.01307i | −0.858922 | − | 0.495899i | ||||
\(201\) | −1.15858 | + | 0.668904i | −0.0817196 | + | 0.0471808i | ||||
\(202\) | − | 29.2023i | − | 2.05467i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 38.4319 | 2.69077 | ||||||||
\(205\) | 2.30384 | + | 3.99037i | 0.160907 | + | 0.278699i | ||||
\(206\) | −27.9482 | − | 16.1359i | −1.94724 | − | 1.12424i | ||||
\(207\) | −3.67514 | + | 6.36553i | −0.255440 | + | 0.442435i | ||||
\(208\) | −42.0261 | + | 34.2318i | −2.91399 | + | 2.37355i | ||||
\(209\) | 11.8438 | 0.819254 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.05258 | 0.416677 | 0.208339 | − | 0.978057i | \(-0.433194\pi\) | ||||
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(212\) | 22.1773 | + | 38.4122i | 1.52314 | + | 2.63816i | ||||
\(213\) | 5.11881 | + | 2.95535i | 0.350735 | + | 0.202497i | ||||
\(214\) | −10.1283 | − | 5.84756i | −0.692354 | − | 0.399731i | ||||
\(215\) | 3.53981 | − | 2.04371i | 0.241413 | − | 0.139380i | ||||
\(216\) | − | 51.2354i | − | 3.48613i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.49943 | −0.372468 | ||||||||
\(219\) | −1.97112 | + | 1.13802i | −0.133196 | + | 0.0769006i | ||||
\(220\) | −11.8203 | + | 20.4733i | −0.796921 | + | 1.38031i | ||||
\(221\) | −20.4597 | − | 7.78659i | −1.37627 | − | 0.523783i | ||||
\(222\) | −5.00745 | − | 8.67316i | −0.336078 | − | 0.582104i | ||||
\(223\) | 7.30624i | 0.489262i | 0.969616 | + | 0.244631i | \(0.0786668\pi\) | ||||
−0.969616 | + | 0.244631i | \(0.921333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.45550 | −0.163700 | ||||||||
\(226\) | 9.87091 | − | 5.69898i | 0.656603 | − | 0.379090i | ||||
\(227\) | 13.5891 | + | 7.84570i | 0.901943 | + | 0.520737i | 0.877830 | − | 0.478972i | \(-0.158990\pi\) |
0.0241132 | + | 0.999709i | \(0.492324\pi\) | |||||||
\(228\) | 28.2316 | + | 16.2995i | 1.86969 | + | 1.07946i | ||||
\(229\) | −22.1384 | + | 12.7816i | −1.46295 | + | 0.844632i | −0.999146 | − | 0.0413077i | \(-0.986848\pi\) |
−0.463800 | + | 0.885940i | \(0.653514\pi\) | |||||||
\(230\) | 22.6759 | 1.49521 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 71.3241i | 4.68266i | ||||||||
\(233\) | −8.17026 | − | 14.1513i | −0.535252 | − | 0.927083i | −0.999151 | − | 0.0411952i | \(-0.986883\pi\) |
0.463899 | − | 0.885888i | \(-0.346450\pi\) | |||||||
\(234\) | −5.83409 | + | 15.3294i | −0.381387 | + | 1.00211i | ||||
\(235\) | 8.35818 | − | 14.4768i | 0.545228 | − | 0.944362i | ||||
\(236\) | 33.8574 | − | 19.5476i | 2.20393 | − | 1.27244i | ||||
\(237\) | 4.40658 | 0.286238 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.2505i | 1.11584i | 0.829895 | + | 0.557920i | \(0.188400\pi\) | ||||
−0.829895 | + | 0.557920i | \(0.811600\pi\) | |||||||
\(240\) | −28.2521 | + | 16.3114i | −1.82367 | + | 1.05290i | ||||
\(241\) | 8.75810 | + | 5.05649i | 0.564159 | + | 0.325717i | 0.754813 | − | 0.655940i | \(-0.227728\pi\) |
−0.190654 | + | 0.981657i | \(0.561061\pi\) | |||||||
\(242\) | 13.5235 | + | 7.80781i | 0.869325 | + | 0.501905i | ||||
\(243\) | −7.36967 | − | 12.7646i | −0.472764 | − | 0.818852i | ||||
\(244\) | 43.8605 | 2.80788 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.75756 | −0.494604 | ||||||||
\(247\) | −11.7270 | − | 14.3972i | −0.746174 | − | 0.916072i | ||||
\(248\) | −20.5837 | + | 35.6521i | −1.30707 | + | 2.26391i | ||||
\(249\) | 2.49439 | + | 1.44014i | 0.158076 | + | 0.0912651i | ||||
\(250\) | 16.6198 | + | 28.7863i | 1.05113 | + | 1.82060i | ||||
\(251\) | 20.8184 | 1.31404 | 0.657022 | − | 0.753871i | \(-0.271816\pi\) | ||||
0.657022 | + | 0.753871i | \(0.271816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1598i | 0.638743i | ||||||||
\(254\) | −35.9735 | + | 20.7693i | −2.25718 | + | 1.30318i | ||||
\(255\) | −11.4103 | − | 6.58773i | −0.714540 | − | 0.412540i | ||||
\(256\) | −22.6800 | + | 39.2829i | −1.41750 | + | 2.45518i | ||||
\(257\) | −14.1148 | − | 24.4475i | −0.880456 | − | 1.52499i | −0.850835 | − | 0.525434i | \(-0.823903\pi\) |
−0.0296216 | − | 0.999561i | \(-0.509430\pi\) | |||||||
\(258\) | 6.88164i | 0.428432i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 36.5908 | − | 5.90287i | 2.26926 | − | 0.366080i | ||||
\(261\) | 6.24323 | + | 10.8136i | 0.386446 | + | 0.669344i | ||||
\(262\) | 2.25181 | + | 1.30008i | 0.139117 | + | 0.0803193i | ||||
\(263\) | −3.05434 | + | 5.29028i | −0.188339 | + | 0.326212i | −0.944697 | − | 0.327946i | \(-0.893644\pi\) |
0.756358 | + | 0.654158i | \(0.226977\pi\) | |||||||
\(264\) | −12.6322 | − | 21.8797i | −0.777460 | − | 1.34660i | ||||
\(265\) | − | 15.2059i | − | 0.934092i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.0555i | − | 0.737787i | ||||||
\(268\) | 5.48829 | − | 3.16867i | 0.335251 | − | 0.193557i | ||||
\(269\) | −2.42062 | + | 4.19264i | −0.147588 | + | 0.255630i | −0.930335 | − | 0.366710i | \(-0.880484\pi\) |
0.782748 | + | 0.622339i | \(0.213818\pi\) | |||||||
\(270\) | −13.8358 | + | 23.9643i | −0.842020 | + | 1.45842i | ||||
\(271\) | −0.258850 | + | 0.149447i | −0.0157240 | + | 0.00907826i | −0.507841 | − | 0.861451i | \(-0.669556\pi\) |
0.492117 | + | 0.870529i | \(0.336223\pi\) | |||||||
\(272\) | −91.2757 | −5.53440 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −33.4609 | −2.02145 | ||||||||
\(275\) | −2.93937 | + | 1.69704i | −0.177250 | + | 0.102336i | ||||
\(276\) | −13.9820 | + | 24.2176i | −0.841618 | + | 1.45773i | ||||
\(277\) | 4.36348 | − | 7.55777i | 0.262176 | − | 0.454102i | −0.704644 | − | 0.709561i | \(-0.748893\pi\) |
0.966820 | + | 0.255459i | \(0.0822265\pi\) | |||||||
\(278\) | 12.4272 | − | 7.17487i | 0.745336 | − | 0.430320i | ||||
\(279\) | 7.20704i | 0.431474i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.7012i | − | 1.47355i | −0.676137 | − | 0.736776i | \(-0.736347\pi\) | ||
0.676137 | − | 0.736776i | \(-0.263653\pi\) | |||||||
\(282\) | 14.0720 | + | 24.3734i | 0.837974 | + | 1.45141i | ||||
\(283\) | 6.12622 | − | 10.6109i | 0.364166 | − | 0.630754i | −0.624476 | − | 0.781044i | \(-0.714687\pi\) |
0.988642 | + | 0.150290i | \(0.0480208\pi\) | |||||||
\(284\) | −24.2484 | − | 13.9998i | −1.43888 | − | 0.830735i | ||||
\(285\) | −5.58791 | − | 9.67855i | −0.330999 | − | 0.573308i | ||||
\(286\) | 3.61071 | + | 22.3821i | 0.213506 | + | 1.32348i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 36.7641i | 2.16634i | ||||||||
\(289\) | −9.93191 | − | 17.2026i | −0.584230 | − | 1.01192i | ||||
\(290\) | 19.2606 | − | 33.3604i | 1.13102 | − | 1.95899i | ||||
\(291\) | −2.51491 | − | 1.45198i | −0.147427 | − | 0.0851167i | ||||
\(292\) | 9.33739 | − | 5.39094i | 0.546429 | − | 0.315481i | ||||
\(293\) | − | 14.6524i | − | 0.856001i | −0.903779 | − | 0.428000i | \(-0.859218\pi\) | ||
0.903779 | − | 0.428000i | \(-0.140782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.4029 | −0.780345 | ||||||||
\(296\) | 15.0570 | + | 26.0796i | 0.875173 | + | 1.51584i | ||||
\(297\) | −10.7371 | − | 6.19905i | −0.623028 | − | 0.359705i | ||||
\(298\) | 3.25559 | − | 5.63884i | 0.188591 | − | 0.326649i | ||||
\(299\) | 12.3502 | − | 10.0597i | 0.714228 | − | 0.581765i | ||||
\(300\) | −9.34193 | −0.539357 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −55.5275 | −3.19525 | ||||||||
\(303\) | −6.17299 | − | 10.6919i | −0.354629 | − | 0.614235i | ||||
\(304\) | −67.0501 | − | 38.7114i | −3.84559 | − | 2.22025i | ||||
\(305\) | −13.0220 | − | 7.51827i | −0.745639 | − | 0.430495i | ||||
\(306\) | −23.9198 | + | 13.8101i | −1.36740 | + | 0.789470i | ||||
\(307\) | 18.8687i | 1.07690i | 0.842659 | + | 0.538448i | \(0.180989\pi\) | ||||
−0.842659 | + | 0.538448i | \(0.819011\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6437 | −0.776162 | ||||||||
\(310\) | 19.2552 | − | 11.1170i | 1.09362 | − | 0.631404i | ||||
\(311\) | −2.85269 | + | 4.94101i | −0.161761 | + | 0.280179i | −0.935500 | − | 0.353325i | \(-0.885051\pi\) |
0.773739 | + | 0.633504i | \(0.218384\pi\) | |||||||
\(312\) | −14.0890 | + | 37.0195i | −0.797631 | + | 2.09582i | ||||
\(313\) | 1.97167 | + | 3.41503i | 0.111445 | + | 0.193029i | 0.916353 | − | 0.400371i | \(-0.131119\pi\) |
−0.804908 | + | 0.593400i | \(0.797785\pi\) | |||||||
\(314\) | 30.1868i | 1.70354i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.8744 | −1.17428 | ||||||||
\(317\) | 3.32654 | − | 1.92058i | 0.186837 | − | 0.107871i | −0.403664 | − | 0.914907i | \(-0.632263\pi\) |
0.590501 | + | 0.807037i | \(0.298930\pi\) | |||||||
\(318\) | 22.1711 | + | 12.8005i | 1.24329 | + | 0.717815i | ||||
\(319\) | 14.9469 | + | 8.62962i | 0.836868 | + | 0.483166i | ||||
\(320\) | 49.3424 | − | 28.4878i | 2.75832 | − | 1.59252i | ||||
\(321\) | −4.94439 | −0.275969 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 31.2690i | − | 1.73985i | ||||||
\(324\) | −3.39641 | − | 5.88275i | −0.188689 | − | 0.326820i | ||||
\(325\) | 4.97329 | + | 1.89275i | 0.275869 | + | 0.104991i | ||||
\(326\) | −25.9454 | + | 44.9388i | −1.43698 | + | 2.48893i | ||||
\(327\) | −2.01352 | + | 1.16251i | −0.111348 | + | 0.0642868i | ||||
\(328\) | 23.3264 | 1.28799 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 13.6450i | 0.751134i | ||||||||
\(331\) | 5.30526 | − | 3.06299i | 0.291603 | − | 0.168357i | −0.347061 | − | 0.937842i | \(-0.612820\pi\) |
0.638665 | + | 0.769485i | \(0.279487\pi\) | |||||||
\(332\) | −11.8162 | − | 6.82209i | −0.648499 | − | 0.374411i | ||||
\(333\) | 4.56565 | + | 2.63598i | 0.250196 | + | 0.144451i | ||||
\(334\) | −29.7077 | − | 51.4553i | −1.62553 | − | 2.81551i | ||||
\(335\) | −2.17261 | −0.118702 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.8026 | 1.13319 | 0.566594 | − | 0.823997i | \(-0.308261\pi\) | ||||
0.566594 | + | 0.823997i | \(0.308261\pi\) | |||||||
\(338\) | 23.6323 | − | 26.5506i | 1.28543 | − | 1.44416i | ||||
\(339\) | 2.40938 | − | 4.17317i | 0.130860 | − | 0.226655i | ||||
\(340\) | 54.0517 | + | 31.2068i | 2.93137 | + | 1.69243i | ||||
\(341\) | 4.98091 | + | 8.62719i | 0.269732 | + | 0.467189i | ||||
\(342\) | −23.4283 | −1.26686 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 20.6926i | − | 1.11567i | ||||||
\(345\) | 8.30242 | − | 4.79340i | 0.446987 | − | 0.258068i | ||||
\(346\) | 6.87400 | + | 3.96871i | 0.369549 | + | 0.213359i | ||||
\(347\) | −8.87542 | + | 15.3727i | −0.476457 | + | 0.825248i | −0.999636 | − | 0.0269746i | \(-0.991413\pi\) |
0.523179 | + | 0.852223i | \(0.324746\pi\) | |||||||
\(348\) | 23.7523 | + | 41.1401i | 1.27326 | + | 2.20534i | ||||
\(349\) | − | 1.00552i | − | 0.0538245i | −0.999638 | − | 0.0269122i | \(-0.991433\pi\) | ||
0.999638 | − | 0.0269122i | \(-0.00856746\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.09572 | + | 19.1898i | 0.165237 | + | 1.02427i | ||||
\(352\) | 25.4083 | + | 44.0085i | 1.35427 | + | 2.34566i | ||||
\(353\) | −10.9309 | − | 6.31096i | −0.581793 | − | 0.335898i | 0.180053 | − | 0.983657i | \(-0.442373\pi\) |
−0.761846 | + | 0.647759i | \(0.775707\pi\) | |||||||
\(354\) | 11.2826 | − | 19.5421i | 0.599666 | − | 1.03865i | ||||
\(355\) | 4.79950 | + | 8.31298i | 0.254731 | + | 0.441207i | ||||
\(356\) | 57.1083i | 3.02674i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 52.9076i | 2.79625i | ||||||||
\(359\) | 9.93763 | − | 5.73750i | 0.524488 | − | 0.302813i | −0.214281 | − | 0.976772i | \(-0.568741\pi\) |
0.738769 | + | 0.673959i | \(0.235407\pi\) | |||||||
\(360\) | 14.8417 | − | 25.7067i | 0.782229 | − | 1.35486i | ||||
\(361\) | 3.76165 | − | 6.51537i | 0.197982 | − | 0.342914i | ||||
\(362\) | −23.6319 | + | 13.6439i | −1.24207 | + | 0.717107i | ||||
\(363\) | 6.60188 | 0.346509 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.69631 | −0.193474 | ||||||||
\(366\) | 21.9241 | − | 12.6579i | 1.14599 | − | 0.661638i | ||||
\(367\) | −14.4557 | + | 25.0380i | −0.754583 | + | 1.30698i | 0.190999 | + | 0.981590i | \(0.438827\pi\) |
−0.945582 | + | 0.325385i | \(0.894506\pi\) | |||||||
\(368\) | 33.2073 | − | 57.5167i | 1.73105 | − | 2.99826i | ||||
\(369\) | 3.53657 | − | 2.04184i | 0.184106 | − | 0.106294i | ||||
\(370\) | − | 16.2642i | − | 0.845538i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 27.4191i | 1.42161i | ||||||||
\(373\) | −11.7444 | − | 20.3419i | −0.608103 | − | 1.05326i | −0.991553 | − | 0.129703i | \(-0.958598\pi\) |
0.383450 | − | 0.923562i | \(-0.374736\pi\) | |||||||
\(374\) | −19.0888 | + | 33.0628i | −0.987058 | + | 1.70964i | ||||
\(375\) | 12.1701 | + | 7.02641i | 0.628461 | + | 0.362842i | ||||
\(376\) | −42.3134 | − | 73.2890i | −2.18215 | − | 3.77959i | ||||
\(377\) | −4.30951 | − | 26.7138i | −0.221951 | − | 1.37583i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 37.6063i | − | 1.93171i | −0.259088 | − | 0.965854i | \(-0.583422\pi\) | ||
0.259088 | − | 0.965854i | \(-0.416578\pi\) | |||||||
\(380\) | 26.4705 | + | 45.8483i | 1.35791 | + | 2.35197i | ||||
\(381\) | −8.78073 | + | 15.2087i | −0.449850 | + | 0.779164i | ||||
\(382\) | 12.7981 | + | 7.38898i | 0.654808 | + | 0.378053i | ||||
\(383\) | 21.9263 | − | 12.6592i | 1.12038 | − | 0.646853i | 0.178883 | − | 0.983870i | \(-0.442752\pi\) |
0.941498 | + | 0.337018i | \(0.109418\pi\) | |||||||
\(384\) | 44.8397i | 2.28822i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 39.8281 | 2.02720 | ||||||||
\(387\) | −1.81129 | − | 3.13725i | −0.0920730 | − | 0.159475i | ||||
\(388\) | 11.9134 | + | 6.87820i | 0.604811 | + | 0.349188i | ||||
\(389\) | −0.659447 | + | 1.14220i | −0.0334353 | + | 0.0579117i | −0.882259 | − | 0.470765i | \(-0.843978\pi\) |
0.848824 | + | 0.528676i | \(0.177311\pi\) | |||||||
\(390\) | 16.5867 | − | 13.5105i | 0.839901 | − | 0.684130i | ||||
\(391\) | 26.8231 | 1.35650 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.09928 | 0.0554514 | ||||||||
\(394\) | −21.7444 | − | 37.6624i | −1.09547 | − | 1.89740i | ||||
\(395\) | 6.19754 | + | 3.57815i | 0.311832 | + | 0.180036i | ||||
\(396\) | 18.1450 | + | 10.4760i | 0.911819 | + | 0.526439i | ||||
\(397\) | 32.3466 | − | 18.6753i | 1.62343 | − | 0.937287i | 0.637435 | − | 0.770504i | \(-0.279995\pi\) |
0.985994 | − | 0.166783i | \(-0.0533379\pi\) | |||||||
\(398\) | 1.02168i | 0.0512121i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.1871 | 1.10935 | ||||||||
\(401\) | −23.6584 | + | 13.6592i | −1.18144 | + | 0.682106i | −0.956348 | − | 0.292231i | \(-0.905602\pi\) |
−0.225095 | + | 0.974337i | \(0.572269\pi\) | |||||||
\(402\) | 1.82892 | − | 3.16778i | 0.0912181 | − | 0.157994i | ||||
\(403\) | 5.55531 | − | 14.5969i | 0.276730 | − | 0.727122i | ||||
\(404\) | 29.2421 | + | 50.6488i | 1.45485 | + | 2.51987i | ||||
\(405\) | 2.32876i | 0.115717i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.28710 | 0.361208 | ||||||||
\(408\) | −57.7647 | + | 33.3505i | −2.85978 | + | 1.65110i | ||||
\(409\) | −20.7042 | − | 11.9536i | −1.02375 | − | 0.591065i | −0.108565 | − | 0.994089i | \(-0.534626\pi\) |
−0.915189 | + | 0.403024i | \(0.867959\pi\) | |||||||
\(410\) | −10.9105 | − | 6.29916i | −0.538830 | − | 0.311093i | ||||
\(411\) | −12.2511 | + | 7.07320i | −0.604305 | + | 0.348895i | ||||
\(412\) | 64.6315 | 3.18417 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 20.0972i | − | 0.987721i | ||||||
\(415\) | 2.33879 | + | 4.05091i | 0.114807 | + | 0.198851i | ||||
\(416\) | 28.3384 | − | 74.4606i | 1.38940 | − | 3.65073i | ||||
\(417\) | 3.03335 | − | 5.25392i | 0.148544 | − | 0.257285i | ||||
\(418\) | −28.0448 | + | 16.1917i | −1.37172 | + | 0.791962i | ||||
\(419\) | 16.4726 | 0.804739 | 0.402369 | − | 0.915477i | \(-0.368187\pi\) | ||||
0.402369 | + | 0.915477i | \(0.368187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.9857i | 1.16899i | 0.811397 | + | 0.584495i | \(0.198708\pi\) | ||||
−0.811397 | + | 0.584495i | \(0.801292\pi\) | |||||||
\(422\) | −14.3318 | + | 8.27449i | −0.697663 | + | 0.402796i | ||||
\(423\) | −12.8304 | − | 7.40766i | −0.623837 | − | 0.360173i | ||||
\(424\) | −66.6668 | − | 38.4901i | −3.23763 | − | 1.86924i | ||||
\(425\) | 4.48038 | + | 7.76025i | 0.217331 | + | 0.376428i | ||||
\(426\) | −16.1610 | −0.783005 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 23.4221 | 1.13215 | ||||||||
\(429\) | 6.05329 | + | 7.43158i | 0.292256 | + | 0.358800i | ||||
\(430\) | −5.58791 | + | 9.67855i | −0.269473 | + | 0.466741i | ||||
\(431\) | −19.6500 | − | 11.3449i | −0.946508 | − | 0.546467i | −0.0545135 | − | 0.998513i | \(-0.517361\pi\) |
−0.891994 | + | 0.452046i | \(0.850694\pi\) | |||||||
\(432\) | 40.5230 | + | 70.1880i | 1.94967 | + | 3.37692i | ||||
\(433\) | −17.0937 | −0.821470 | −0.410735 | − | 0.911755i | \(-0.634728\pi\) | ||||
−0.410735 | + | 0.911755i | \(0.634728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 16.2858i | − | 0.780845i | ||||||
\(436\) | 9.53827 | − | 5.50692i | 0.456800 | − | 0.263734i | ||||
\(437\) | 19.7039 | + | 11.3761i | 0.942566 | + | 0.544191i | ||||
\(438\) | 3.11159 | − | 5.38943i | 0.148677 | − | 0.257517i | ||||
\(439\) | 17.7006 | + | 30.6584i | 0.844805 | + | 1.46325i | 0.885790 | + | 0.464086i | \(0.153617\pi\) |
−0.0409849 | + | 0.999160i | \(0.513050\pi\) | |||||||
\(440\) | − | 41.0296i | − | 1.95601i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 59.0913 | − | 9.53268i | 2.81069 | − | 0.453423i | ||||
\(443\) | 8.13161 | + | 14.0844i | 0.386345 | + | 0.669168i | 0.991955 | − | 0.126593i | \(-0.0404042\pi\) |
−0.605610 | + | 0.795761i | \(0.707071\pi\) | |||||||
\(444\) | 17.3700 | + | 10.0286i | 0.824342 | + | 0.475934i | ||||
\(445\) | 9.78912 | − | 16.9553i | 0.464049 | − | 0.803756i | ||||
\(446\) | −9.98836 | − | 17.3003i | −0.472963 | − | 0.819195i | ||||
\(447\) | − | 2.75276i | − | 0.130201i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.1472i | 0.714839i | 0.933944 | + | 0.357419i | \(0.116343\pi\) | ||||
−0.933944 | + | 0.357419i | \(0.883657\pi\) | |||||||
\(450\) | 5.81436 | − | 3.35692i | 0.274092 | − | 0.158247i | ||||
\(451\) | 2.82230 | − | 4.88837i | 0.132897 | − | 0.230184i | ||||
\(452\) | −11.4135 | + | 19.7687i | −0.536845 | + | 0.929844i | ||||
\(453\) | −20.3305 | + | 11.7378i | −0.955209 | + | 0.551490i | ||||
\(454\) | −42.9034 | −2.01356 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −56.5778 | −2.64950 | ||||||||
\(457\) | −34.2065 | + | 19.7491i | −1.60011 | + | 0.923826i | −0.608650 | + | 0.793439i | \(0.708289\pi\) |
−0.991463 | + | 0.130387i | \(0.958378\pi\) | |||||||
\(458\) | 34.9475 | − | 60.5308i | 1.63299 | − | 2.82842i | ||||
\(459\) | −16.3662 | + | 28.3471i | −0.763908 | + | 1.32313i | ||||
\(460\) | −39.3294 | + | 22.7069i | −1.83375 | + | 1.05871i | ||||
\(461\) | − | 19.0149i | − | 0.885614i | −0.896617 | − | 0.442807i | \(-0.853983\pi\) | ||
0.896617 | − | 0.442807i | \(-0.146017\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.48740i | − | 0.115599i | −0.998328 | − | 0.0577996i | \(-0.981592\pi\) | ||
0.998328 | − | 0.0577996i | \(-0.0184084\pi\) | |||||||
\(464\) | −56.4116 | − | 97.7078i | −2.61884 | − | 4.53597i | ||||
\(465\) | 4.69999 | − | 8.14062i | 0.217957 | − | 0.377512i | ||||
\(466\) | 38.6925 | + | 22.3391i | 1.79240 | + | 1.03484i | ||||
\(467\) | −7.43931 | − | 12.8853i | −0.344250 | − | 0.596259i | 0.640967 | − | 0.767568i | \(-0.278534\pi\) |
−0.985217 | + | 0.171309i | \(0.945200\pi\) | |||||||
\(468\) | −5.23157 | − | 32.4295i | −0.241830 | − | 1.49906i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 45.7059i | 2.10826i | ||||||||
\(471\) | 6.38111 | + | 11.0524i | 0.294026 | + | 0.509268i | ||||
\(472\) | −33.9261 | + | 58.7617i | −1.56158 | + | 2.70473i | ||||
\(473\) | −4.33642 | − | 2.50363i | −0.199389 | − | 0.115117i | ||||
\(474\) | −10.4343 | + | 6.02423i | −0.479262 | + | 0.276702i | ||||
\(475\) | 7.60079i | 0.348748i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.4766 | −0.617053 | ||||||||
\(478\) | −23.5831 | − | 40.8472i | −1.07867 | − | 1.86831i | ||||
\(479\) | −14.6183 | − | 8.43988i | −0.667927 | − | 0.385628i | 0.127364 | − | 0.991856i | \(-0.459348\pi\) |
−0.795291 | + | 0.606228i | \(0.792682\pi\) | |||||||
\(480\) | 23.9753 | − | 41.5264i | 1.09432 | − | 1.89541i | ||||
\(481\) | −7.21525 | − | 8.85811i | −0.328987 | − | 0.403895i | ||||
\(482\) | −27.6509 | −1.25947 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −31.2738 | −1.42154 | ||||||||
\(485\) | −2.35803 | − | 4.08422i | −0.107073 | − | 0.185455i | ||||
\(486\) | 34.9011 | + | 20.1502i | 1.58315 | + | 0.914029i | ||||
\(487\) | −3.84982 | − | 2.22270i | −0.174452 | − | 0.100720i | 0.410231 | − | 0.911981i | \(-0.365448\pi\) |
−0.584683 | + | 0.811262i | \(0.698781\pi\) | |||||||
\(488\) | −65.9242 | + | 38.0613i | −2.98425 | + | 1.72296i | ||||
\(489\) | 21.9381i | 0.992076i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9816 | −0.766368 | −0.383184 | − | 0.923672i | \(-0.625172\pi\) | ||||
−0.383184 | + | 0.923672i | \(0.625172\pi\) | |||||||
\(492\) | 13.4548 | − | 7.76814i | 0.606590 | − | 0.350215i | ||||
\(493\) | 22.7832 | − | 39.4616i | 1.02610 | − | 1.77726i | ||||
\(494\) | 47.4508 | + | 18.0589i | 2.13491 | + | 0.812509i | ||||
\(495\) | −3.59145 | − | 6.22058i | −0.161424 | − | 0.279594i | ||||
\(496\) | − | 65.1202i | − | 2.92399i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.87526 | −0.352899 | ||||||||
\(499\) | 35.5080 | − | 20.5006i | 1.58956 | − | 0.917731i | 0.596177 | − | 0.802853i | \(-0.296686\pi\) |
0.993380 | − | 0.114878i | \(-0.0366476\pi\) | |||||||
\(500\) | −57.6510 | − | 33.2848i | −2.57823 | − | 1.48854i | ||||
\(501\) | −21.7540 | − | 12.5597i | −0.971896 | − | 0.561124i | ||||
\(502\) | −49.2956 | + | 28.4608i | −2.20017 | + | 1.27027i | ||||
\(503\) | −37.2910 | −1.66272 | −0.831361 | − | 0.555732i | \(-0.812438\pi\) | ||||
−0.831361 | + | 0.555732i | \(0.812438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 20.0499i | − | 0.892210i | ||||||
\(506\) | −13.8895 | − | 24.0573i | −0.617464 | − | 1.06948i | ||||
\(507\) | 3.04013 | − | 14.7166i | 0.135017 | − | 0.653588i | ||||
\(508\) | 41.5952 | − | 72.0451i | 1.84549 | − | 3.19648i | ||||
\(509\) | 7.11501 | − | 4.10785i | 0.315367 | − | 0.182077i | −0.333958 | − | 0.942588i | \(-0.608385\pi\) |
0.649326 | + | 0.760510i | \(0.275051\pi\) | |||||||
\(510\) | 36.0244 | 1.59519 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 46.4428i | − | 2.05250i | ||||||
\(513\) | −24.0448 | + | 13.8823i | −1.06160 | + | 0.612918i | ||||
\(514\) | 66.8445 | + | 38.5927i | 2.94838 | + | 1.70225i | ||||
\(515\) | −19.1889 | − | 11.0787i | −0.845563 | − | 0.488186i | ||||
\(516\) | −6.89103 | − | 11.9356i | −0.303360 | − | 0.525436i | ||||
\(517\) | −20.4783 | −0.900633 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.35573 | 0.147300 | ||||||||
\(520\) | −49.8751 | + | 40.6251i | −2.18717 | + | 1.78153i | ||||
\(521\) | −16.9997 | + | 29.4443i | −0.744768 | + | 1.28998i | 0.205534 | + | 0.978650i | \(0.434107\pi\) |
−0.950303 | + | 0.311327i | \(0.899227\pi\) | |||||||
\(522\) | −29.5665 | − | 17.0702i | −1.29409 | − | 0.747145i | ||||
\(523\) | 11.4391 | + | 19.8131i | 0.500197 | + | 0.866366i | 1.00000 | 0.000227041i | \(7.22694e-5\pi\) | |
−0.499803 | + | 0.866139i | \(0.666594\pi\) | |||||||
\(524\) | −5.20742 | −0.227487 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 16.7024i | − | 0.728258i | ||||||
\(527\) | 22.7768 | − | 13.1502i | 0.992171 | − | 0.572830i | ||||
\(528\) | 34.6101 | + | 19.9821i | 1.50621 | + | 0.869611i | ||||
\(529\) | 1.74142 | − | 3.01623i | 0.0757139 | − | 0.131140i | ||||
\(530\) | 20.7880 | + | 36.0059i | 0.902974 | + | 1.56400i | ||||
\(531\) | 11.8786i | 0.515489i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.73672 | + | 1.40942i | −0.378429 | + | 0.0610487i | ||||
\(534\) | 16.4811 | + | 28.5462i | 0.713208 | + | 1.23531i | ||||
\(535\) | −6.95394 | − | 4.01486i | −0.300645 | − | 0.173578i | ||||
\(536\) | −5.49943 | + | 9.52528i | −0.237539 | + | 0.411430i | ||||
\(537\) | 11.1840 | + | 19.3712i | 0.482624 | + | 0.835930i | ||||
\(538\) | − | 13.2369i | − | 0.570685i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 55.4187i | − | 2.38484i | ||||||
\(541\) | −34.2065 | + | 19.7491i | −1.47065 | + | 0.849082i | −0.999457 | − | 0.0329468i | \(-0.989511\pi\) |
−0.471196 | + | 0.882029i | \(0.656177\pi\) | |||||||
\(542\) | 0.408618 | − | 0.707747i | 0.0175517 | − | 0.0304004i | ||||
\(543\) | −5.76829 | + | 9.99096i | −0.247541 | + | 0.428753i | ||||
\(544\) | 116.187 | − | 67.0808i | 4.98149 | − | 2.87607i | ||||
\(545\) | −3.77584 | −0.161739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.0129 | 1.58256 | 0.791279 | − | 0.611455i | \(-0.209416\pi\) | ||||
0.791279 | + | 0.611455i | \(0.209416\pi\) | |||||||
\(548\) | 58.0350 | − | 33.5065i | 2.47913 | − | 1.43133i | ||||
\(549\) | −6.66326 | + | 11.5411i | −0.284381 | + | 0.492563i | ||||
\(550\) | 4.64006 | − | 8.03682i | 0.197853 | − | 0.342691i | ||||
\(551\) | 33.4725 | − | 19.3254i | 1.42598 | − | 0.823288i | ||||
\(552\) | − | 48.5334i | − | 2.06572i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 23.8613i | 1.01377i | ||||||||
\(555\) | −3.43805 | − | 5.95488i | −0.145937 | − | 0.252771i | ||||
\(556\) | −14.3693 | + | 24.8884i | −0.609394 | + | 1.05550i | ||||
\(557\) | 20.8597 | + | 12.0433i | 0.883853 | + | 0.510293i | 0.871927 | − | 0.489636i | \(-0.162870\pi\) |
0.0119264 | + | 0.999929i | \(0.496204\pi\) | |||||||
\(558\) | −9.85275 | − | 17.0655i | −0.417100 | − | 0.722438i | ||||
\(559\) | 1.25028 | + | 7.75024i | 0.0528811 | + | 0.327800i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.1405i | 0.681453i | ||||||||
\(562\) | 33.7691 | + | 58.4897i | 1.42446 | + | 2.46724i | ||||
\(563\) | 3.24699 | − | 5.62395i | 0.136844 | − | 0.237021i | −0.789456 | − | 0.613807i | \(-0.789637\pi\) |
0.926300 | + | 0.376786i | \(0.122971\pi\) | |||||||
\(564\) | −48.8132 | − | 28.1823i | −2.05541 | − | 1.18669i | ||||
\(565\) | 6.77725 | − | 3.91285i | 0.285121 | − | 0.164615i | ||||
\(566\) | 33.5006i | 1.40814i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 48.5951 | 2.03900 | ||||||||
\(569\) | 14.3819 | + | 24.9102i | 0.602921 | + | 1.04429i | 0.992376 | + | 0.123244i | \(0.0393298\pi\) |
−0.389456 | + | 0.921045i | \(0.627337\pi\) | |||||||
\(570\) | 26.4631 | + | 15.2785i | 1.10842 | + | 0.639945i | ||||
\(571\) | −1.24308 | + | 2.15307i | −0.0520211 | + | 0.0901032i | −0.890863 | − | 0.454271i | \(-0.849900\pi\) |
0.838842 | + | 0.544375i | \(0.183233\pi\) | |||||||
\(572\) | −28.6751 | − | 35.2042i | −1.19897 | − | 1.47196i | ||||
\(573\) | 6.24775 | 0.261003 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.52009 | −0.271906 | ||||||||
\(576\) | −25.2481 | − | 43.7310i | −1.05200 | − | 1.82212i | ||||
\(577\) | 12.6221 | + | 7.28737i | 0.525465 | + | 0.303377i | 0.739168 | − | 0.673521i | \(-0.235219\pi\) |
−0.213703 | + | 0.976899i | \(0.568552\pi\) | |||||||
\(578\) | 47.0353 | + | 27.1559i | 1.95641 | + | 1.12953i | ||||
\(579\) | 14.5824 | − | 8.41914i | 0.606023 | − | 0.349888i | ||||
\(580\) | 77.1476i | 3.20338i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.94003 | 0.329125 | ||||||||
\(583\) | −16.1322 | + | 9.31395i | −0.668129 | + | 0.385745i | ||||
\(584\) | −9.35632 | + | 16.2056i | −0.387167 | + | 0.670594i | ||||
\(585\) | −4.00562 | + | 10.5250i | −0.165612 | + | 0.435154i | ||||
\(586\) | 20.0313 | + | 34.6952i | 0.827484 | + | 1.43324i | ||||
\(587\) | − | 8.69744i | − | 0.358982i | −0.983760 | − | 0.179491i | \(-0.942555\pi\) | ||
0.983760 | − | 0.179491i | \(-0.0574450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.3087 | 0.919215 | ||||||||
\(590\) | 31.7365 | − | 18.3231i | 1.30657 | − | 0.754349i | ||||
\(591\) | −15.9227 | − | 9.19297i | −0.654972 | − | 0.378148i | ||||
\(592\) | −41.2536 | − | 23.8178i | −1.69551 | − | 0.978906i | ||||
\(593\) | −15.6144 | + | 9.01495i | −0.641205 | + | 0.370200i | −0.785078 | − | 0.619396i | \(-0.787377\pi\) |
0.143874 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(594\) | 33.8989 | 1.39089 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.0401i | 0.534143i | ||||||||
\(597\) | 0.215970 | + | 0.374070i | 0.00883905 | + | 0.0153097i | ||||
\(598\) | −15.4912 | + | 40.7041i | −0.633484 | + | 1.66451i | ||||
\(599\) | −0.00705812 | + | 0.0122250i | −0.000288387 | + | 0.000499501i | −0.866170 | − | 0.499750i | \(-0.833425\pi\) |
0.865881 | + | 0.500250i | \(0.166758\pi\) | |||||||
\(600\) | 14.0413 | − | 8.10676i | 0.573234 | − | 0.330957i | ||||
\(601\) | −13.7533 | −0.561007 | −0.280504 | − | 0.959853i | \(-0.590501\pi\) | ||||
−0.280504 | + | 0.959853i | \(0.590501\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.92553i | 0.0784136i | ||||||||
\(604\) | 96.3077 | − | 55.6033i | 3.91870 | − | 2.26246i | ||||
\(605\) | 9.28508 | + | 5.36075i | 0.377492 | + | 0.217945i | ||||
\(606\) | 29.2339 | + | 16.8782i | 1.18755 | + | 0.685630i | ||||
\(607\) | 11.8742 | + | 20.5667i | 0.481959 | + | 0.834778i | 0.999786 | − | 0.0207079i | \(-0.00659200\pi\) |
−0.517826 | + | 0.855486i | \(0.673259\pi\) | |||||||
\(608\) | 113.800 | 4.61519 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 41.1129 | 1.66461 | ||||||||
\(611\) | 20.2764 | + | 24.8931i | 0.820294 | + | 1.00707i | ||||
\(612\) | 27.6578 | − | 47.9048i | 1.11800 | − | 1.93644i | ||||
\(613\) | −1.89149 | − | 1.09205i | −0.0763964 | − | 0.0441075i | 0.461315 | − | 0.887236i | \(-0.347378\pi\) |
−0.537712 | + | 0.843129i | \(0.680711\pi\) | |||||||
\(614\) | −25.7955 | − | 44.6791i | −1.04102 | − | 1.80310i | ||||
\(615\) | −5.32625 | −0.214775 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.6673i | − | 0.590485i | −0.955422 | − | 0.295243i | \(-0.904600\pi\) | ||
0.955422 | − | 0.295243i | \(-0.0954005\pi\) | |||||||
\(618\) | 32.3067 | − | 18.6523i | 1.29957 | − | 0.750305i | ||||
\(619\) | −18.4159 | − | 10.6324i | −0.740198 | − | 0.427354i | 0.0819430 | − | 0.996637i | \(-0.473887\pi\) |
−0.822141 | + | 0.569283i | \(0.807221\pi\) | |||||||
\(620\) | −22.2643 | + | 38.5630i | −0.894158 | + | 1.54873i | ||||
\(621\) | −11.9085 | − | 20.6261i | −0.477870 | − | 0.827695i | ||||
\(622\) | − | 15.5997i | − | 0.625490i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.97880 | − | 61.8567i | −0.399472 | − | 2.47625i | ||||
\(625\) | 7.72127 | + | 13.3736i | 0.308851 | + | 0.534945i | ||||
\(626\) | −9.33739 | − | 5.39094i | −0.373197 | − | 0.215465i | ||||
\(627\) | −6.84543 | + | 11.8566i | −0.273380 | + | 0.473508i | ||||
\(628\) | −30.2280 | − | 52.3564i | −1.20623 | − | 2.08925i | ||||
\(629\) | − | 19.2388i | − | 0.767099i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.4910i | 1.37307i | 0.727099 | + | 0.686533i | \(0.240868\pi\) | ||||
−0.727099 | + | 0.686533i | \(0.759132\pi\) | |||||||
\(632\) | 31.3751 | − | 18.1144i | 1.24804 | − | 0.720554i | ||||
\(633\) | −3.49824 | + | 6.05913i | −0.139043 | + | 0.240829i | ||||
\(634\) | −5.25126 | + | 9.09544i | −0.208554 | + | 0.361226i | ||||
\(635\) | −24.6990 | + | 14.2599i | −0.980148 | + | 0.565889i | ||||
\(636\) | −51.2717 | −2.03305 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −47.1902 | −1.86828 | ||||||||
\(639\) | 7.36760 | − | 4.25368i | 0.291458 | − | 0.168273i | ||||
\(640\) | −36.4100 | + | 63.0639i | −1.43923 | + | 2.49282i | ||||
\(641\) | 10.8972 | − | 18.8745i | 0.430414 | − | 0.745500i | −0.566494 | − | 0.824066i | \(-0.691701\pi\) |
0.996909 | + | 0.0785658i | \(0.0250341\pi\) | |||||||
\(642\) | 11.7078 | − | 6.75949i | 0.462069 | − | 0.266776i | ||||
\(643\) | 5.81898i | 0.229478i | 0.993396 | + | 0.114739i | \(0.0366032\pi\) | ||||
−0.993396 | + | 0.114739i | \(0.963397\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.72485i | 0.186041i | ||||||||
\(646\) | 42.7479 | + | 74.0415i | 1.68189 | + | 2.91312i | ||||
\(647\) | 16.5354 | − | 28.6402i | 0.650074 | − | 1.12596i | −0.333031 | − | 0.942916i | \(-0.608071\pi\) |
0.983105 | − | 0.183045i | \(-0.0585954\pi\) | |||||||
\(648\) | 10.2099 | + | 5.89468i | 0.401082 | + | 0.231565i | ||||
\(649\) | 8.20954 | + | 14.2193i | 0.322253 | + | 0.558158i | ||||
\(650\) | −14.3638 | + | 2.31718i | −0.563394 | + | 0.0908873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 103.923i | − | 4.06995i | ||||||
\(653\) | 0.869964 | + | 1.50682i | 0.0340443 | + | 0.0589665i | 0.882546 | − | 0.470227i | \(-0.155828\pi\) |
−0.848501 | + | 0.529193i | \(0.822495\pi\) | |||||||
\(654\) | 3.17853 | − | 5.50538i | 0.124290 | − | 0.215277i | ||||
\(655\) | 1.54606 | + | 0.892620i | 0.0604097 | + | 0.0348775i | ||||
\(656\) | −31.9552 | + | 18.4493i | −1.24764 | + | 0.720325i | ||||
\(657\) | 3.27596i | 0.127807i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.9823 | 1.09003 | 0.545017 | − | 0.838425i | \(-0.316523\pi\) | ||||
0.545017 | + | 0.838425i | \(0.316523\pi\) | |||||||
\(660\) | −13.6636 | − | 23.6661i | −0.531856 | − | 0.921201i | ||||
\(661\) | −18.0422 | − | 10.4167i | −0.701762 | − | 0.405163i | 0.106241 | − | 0.994340i | \(-0.466118\pi\) |
−0.808003 | + | 0.589178i | \(0.799452\pi\) | |||||||
\(662\) | −8.37484 | + | 14.5057i | −0.325497 | + | 0.563778i | ||||
\(663\) | 19.6202 | − | 15.9814i | 0.761986 | − | 0.620665i | ||||
\(664\) | 23.6804 | 0.918976 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.4146 | −0.558555 | ||||||||
\(667\) | 16.5776 | + | 28.7133i | 0.641888 | + | 1.11178i | ||||
\(668\) | 103.051 | + | 59.4965i | 3.98716 | + | 2.30199i | ||||
\(669\) | −7.31414 | − | 4.22282i | −0.282781 | − | 0.163264i | ||||
\(670\) | 5.14449 | − | 2.97017i | 0.198749 | − | 0.114748i | ||||
\(671\) | 18.4204i | 0.711112i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.06203 | −0.272221 | −0.136111 | − | 0.990694i | \(-0.543460\pi\) | ||||
−0.136111 | + | 0.990694i | \(0.543460\pi\) | |||||||
\(674\) | −49.2582 | + | 28.4392i | −1.89735 | + | 1.09544i | ||||
\(675\) | 3.97825 | − | 6.89053i | 0.153123 | − | 0.265217i | ||||
\(676\) | −14.4014 | + | 69.7142i | −0.553900 | + | 2.68132i | ||||
\(677\) | 2.61495 | + | 4.52922i | 0.100501 | + | 0.174072i | 0.911891 | − | 0.410432i | \(-0.134622\pi\) |
−0.811390 | + | 0.584505i | \(0.801289\pi\) | |||||||
\(678\) | 13.1755i | 0.506001i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −108.323 | −4.15399 | ||||||||
\(681\) | −15.7084 | + | 9.06924i | −0.601946 | + | 0.347534i | ||||
\(682\) | −23.5885 | − | 13.6188i | −0.903250 | − | 0.521492i | ||||
\(683\) | −24.1982 | − | 13.9708i | −0.925917 | − | 0.534579i | −0.0403993 | − | 0.999184i | \(-0.512863\pi\) |
−0.885518 | + | 0.464605i | \(0.846196\pi\) | |||||||
\(684\) | 40.6343 | − | 23.4602i | 1.55369 | − | 0.897023i | ||||
\(685\) | −22.9738 | −0.877785 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 29.5498i | − | 1.12740i | ||||||
\(688\) | 16.3662 | + | 28.3471i | 0.623955 | + | 1.08072i | ||||
\(689\) | 27.2951 | + | 10.3880i | 1.03986 | + | 0.395752i | ||||
\(690\) | −13.1061 | + | 22.7005i | −0.498942 | + | 0.864193i | ||||
\(691\) | −22.0416 | + | 12.7257i | −0.838503 | + | 0.484110i | −0.856755 | − | 0.515723i | \(-0.827523\pi\) |
0.0182518 | + | 0.999833i | \(0.494190\pi\) | |||||||
\(692\) | −15.8965 | −0.604293 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 48.5344i | − | 1.84234i | ||||||
\(695\) | 8.53239 | − | 4.92618i | 0.323652 | − | 0.186861i | ||||
\(696\) | −71.4013 | − | 41.2236i | −2.70646 | − | 1.56258i | ||||
\(697\) | −12.9058 | − | 7.45119i | −0.488844 | − | 0.282234i | ||||
\(698\) | 1.37465 | + | 2.38097i | 0.0520314 | + | 0.0901210i | ||||
\(699\) | 18.8888 | 0.714441 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.9541 | −0.678117 | −0.339058 | − | 0.940765i | \(-0.610108\pi\) | ||||
−0.339058 | + | 0.940765i | \(0.610108\pi\) | |||||||
\(702\) | −33.5647 | − | 41.2071i | −1.26682 | − | 1.55526i | ||||
\(703\) | 8.15944 | − | 14.1326i | 0.307739 | − | 0.533020i | ||||
\(704\) | −60.4465 | − | 34.8988i | −2.27816 | − | 1.31530i | ||||
\(705\) | 9.66164 | + | 16.7345i | 0.363878 | + | 0.630256i | ||||
\(706\) | 34.5109 | 1.29883 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 45.1921i | 1.69842i | ||||||||
\(709\) | −25.3044 | + | 14.6095i | −0.950328 | + | 0.548672i | −0.893183 | − | 0.449694i | \(-0.851533\pi\) |
−0.0571454 | + | 0.998366i | \(0.518200\pi\) | |||||||
\(710\) | −22.7294 | − | 13.1228i | −0.853018 | − | 0.492490i | ||||
\(711\) | 3.17123 | − | 5.49273i | 0.118930 | − | 0.205994i | ||||
\(712\) | −49.5576 | − | 85.8363i | −1.85725 | − | 3.21685i | ||||
\(713\) | 19.1368i | 0.716679i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47907 | + | 15.3673i | 0.0927120 | + | 0.574704i | ||||
\(716\) | −52.9797 | − | 91.7636i | −1.97994 | − | 3.42937i | ||||
\(717\) | −17.2691 | − | 9.97034i | −0.644927 | − | 0.372349i | ||||
\(718\) | −15.6875 | + | 27.1715i | −0.585451 | + | 1.01403i | ||||
\(719\) | −19.3600 | − | 33.5325i | −0.722005 | − | 1.25055i | −0.960195 | − | 0.279331i | \(-0.909887\pi\) |
0.238189 | − | 0.971219i | \(-0.423446\pi\) | |||||||
\(720\) | 46.9545i | 1.74989i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.5702i | 0.765544i | ||||||||
\(723\) | −10.1239 | + | 5.84505i | −0.376513 | + | 0.217380i | ||||
\(724\) | 27.3250 | − | 47.3283i | 1.01553 | − | 1.75894i | ||||
\(725\) | −5.53807 | + | 9.59223i | −0.205679 | + | 0.356246i | ||||
\(726\) | −15.6325 | + | 9.02544i | −0.580177 | + | 0.334966i | ||||
\(727\) | −27.9441 | −1.03639 | −0.518194 | − | 0.855263i | \(-0.673396\pi\) | ||||
−0.518194 | + | 0.855263i | \(0.673396\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7594 | 0.768868 | ||||||||
\(730\) | 8.75246 | − | 5.05324i | 0.323943 | − | 0.187029i | ||||
\(731\) | −6.60986 | + | 11.4486i | −0.244475 | + | 0.423443i | ||||
\(732\) | −25.3503 | + | 43.9080i | −0.936973 | + | 1.62289i | ||||
\(733\) | 37.8831 | − | 21.8718i | 1.39924 | − | 0.807854i | 0.404931 | − | 0.914347i | \(-0.367296\pi\) |
0.994313 | + | 0.106493i | \(0.0339622\pi\) | |||||||
\(734\) | − | 79.0497i | − | 2.91778i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 97.6195i | 3.59830i | ||||||||
\(737\) | 1.33077 | + | 2.30496i | 0.0490195 | + | 0.0849042i | ||||
\(738\) | −5.58280 | + | 9.66969i | −0.205506 | + | 0.355946i | ||||
\(739\) | −6.27411 | − | 3.62236i | −0.230797 | − | 0.133251i | 0.380143 | − | 0.924928i | \(-0.375875\pi\) |
−0.610940 | + | 0.791677i | \(0.709208\pi\) | |||||||
\(740\) | 16.2864 | + | 28.2089i | 0.598701 | + | 1.03698i | ||||
\(741\) | 21.1907 | − | 3.41851i | 0.778461 | − | 0.125582i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 33.9142i | − | 1.24419i | −0.782941 | − | 0.622096i | \(-0.786281\pi\) | ||
0.782941 | − | 0.622096i | \(-0.213719\pi\) | |||||||
\(744\) | −23.7938 | − | 41.2120i | −0.872322 | − | 1.51091i | ||||
\(745\) | 2.23525 | − | 3.87156i | 0.0818931 | − | 0.141843i | ||||
\(746\) | 55.6189 | + | 32.1116i | 2.03635 | + | 1.17569i | ||||
\(747\) | 3.59022 | − | 2.07282i | 0.131359 | − | 0.0758404i | ||||
\(748\) | − | 76.4593i | − | 2.79563i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −38.4232 | −1.40302 | ||||||||
\(751\) | 19.2487 | + | 33.3396i | 0.702393 | + | 1.21658i | 0.967624 | + | 0.252396i | \(0.0812186\pi\) |
−0.265231 | + | 0.964185i | \(0.585448\pi\) | |||||||
\(752\) | 115.931 | + | 66.9330i | 4.22758 | + | 2.44079i | ||||
\(753\) | −12.0325 | + | 20.8409i | −0.438489 | + | 0.759485i | ||||
\(754\) | 46.7250 | + | 57.3639i | 1.70162 | + | 2.08907i | ||||
\(755\) | −38.1245 | −1.38749 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.18792 | 0.297595 | 0.148797 | − | 0.988868i | \(-0.452460\pi\) | ||||
0.148797 | + | 0.988868i | \(0.452460\pi\) | |||||||
\(758\) | 51.4117 | + | 89.0476i | 1.86736 | + | 3.23435i | ||||
\(759\) | −10.1708 | − | 5.87213i | −0.369177 | − | 0.213145i | ||||
\(760\) | −79.5726 | − | 45.9413i | −2.88640 | − | 1.66647i | ||||
\(761\) | −8.71186 | + | 5.02979i | −0.315805 | + | 0.182330i | −0.649521 | − | 0.760344i | \(-0.725031\pi\) |
0.333716 | + | 0.942674i | \(0.391697\pi\) | |||||||
\(762\) | − | 48.0166i | − | 1.73946i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −29.5962 | −1.07075 | ||||||||
\(765\) | −16.4230 | + | 9.48184i | −0.593776 | + | 0.342816i | ||||
\(766\) | −34.6127 | + | 59.9509i | −1.25061 | + | 2.16612i | ||||
\(767\) | 9.15626 | − | 24.0586i | 0.330613 | − | 0.868705i | ||||
\(768\) | −26.2170 | − | 45.4091i | −0.946024 | − | 1.63856i | ||||
\(769\) | − | 2.53594i | − | 0.0914482i | −0.998954 | − | 0.0457241i | \(-0.985440\pi\) | ||
0.998954 | − | 0.0457241i | \(-0.0145595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.6320 | 1.17521 | ||||||||
\(772\) | −69.0783 | + | 39.8824i | −2.48618 | + | 1.43540i | ||||
\(773\) | 25.3049 | + | 14.6098i | 0.910152 | + | 0.525477i | 0.880480 | − | 0.474083i | \(-0.157220\pi\) |
0.0296721 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(774\) | 8.57786 | + | 4.95243i | 0.308325 | + | 0.178012i | ||||
\(775\) | −5.53652 | + | 3.19651i | −0.198878 | + | 0.114822i | ||||
\(776\) | −23.8751 | −0.857066 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 3.60612i | − | 0.129286i | ||||||
\(779\) | −6.32032 | − | 10.9471i | −0.226449 | − | 0.392221i | ||||
\(780\) | −15.2393 | + | 40.0421i | −0.545655 | + | 1.43374i | ||||
\(781\) | 5.87959 | − | 10.1838i | 0.210388 | − | 0.364403i | ||||
\(782\) | −63.5140 | + | 36.6698i | −2.27126 | + | 1.31131i | ||||
\(783\) | −40.4595 | −1.44591 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.7259i | 0.739739i | ||||||||
\(786\) | −2.60298 | + | 1.50283i | −0.0928451 | + | 0.0536041i | ||||
\(787\) | 0.129425 | + | 0.0747235i | 0.00461350 | + | 0.00266360i | 0.502305 | − | 0.864691i | \(-0.332485\pi\) |
−0.497691 | + | 0.867354i | \(0.665819\pi\) | |||||||
\(788\) | 75.4275 | + | 43.5481i | 2.68699 | + | 1.55134i | ||||
\(789\) | −3.53067 | − | 6.11530i | −0.125695 | − | 0.217710i | ||||
\(790\) | −19.5668 | −0.696155 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36.3636 | −1.29212 | ||||||||
\(793\) | 22.3916 | − | 18.2388i | 0.795150 | − | 0.647678i | ||||
\(794\) | −51.0621 | + | 88.4421i | −1.81213 | + | 3.13869i | ||||
\(795\) | 15.2224 | + | 8.78865i | 0.539882 | + | 0.311701i | ||||
\(796\) | −1.02307 | − | 1.77201i | −0.0362618 | − | 0.0628073i | ||||
\(797\) | 29.7429 | 1.05355 | 0.526773 | − | 0.850006i | \(-0.323402\pi\) | ||||
0.526773 | + | 0.850006i | \(0.323402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.0649i | 1.91268i | ||||||||
\(800\) | −28.2425 | + | 16.3058i | −0.998525 | + | 0.576499i | ||||
\(801\) | −15.0270 | − | 8.67587i | −0.530954 | − | 0.306547i | ||||
\(802\) | 37.3469 | − | 64.6868i | 1.31877 | − | 2.28417i | ||||
\(803\) | 2.26407 | + | 3.92149i | 0.0798974 | + | 0.138386i | ||||
\(804\) | 7.32565i | 0.258356i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.80105 | + | 42.1584i | 0.239557 | + | 1.48497i | ||||
\(807\) | −2.79812 | − | 4.84648i | −0.0984984 | − | 0.170604i | ||||
\(808\) | −87.9042 | − | 50.7515i | −3.09246 | − | 1.78543i | ||||
\(809\) | −17.4451 | + | 30.2158i | −0.613336 | + | 1.06233i | 0.377337 | + | 0.926076i | \(0.376840\pi\) |
−0.990674 | + | 0.136254i | \(0.956494\pi\) | |||||||
\(810\) | −3.18365 | − | 5.51424i | −0.111862 | − | 0.193751i | ||||
\(811\) | − | 31.6196i | − | 1.11031i | −0.831745 | − | 0.555157i | \(-0.812658\pi\) | ||
0.831745 | − | 0.555157i | \(-0.187342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 0.345507i | − | 0.0121174i | ||||||
\(814\) | −17.2550 | + | 9.96220i | −0.604789 | + | 0.349175i | ||||
\(815\) | −17.8138 | + | 30.8544i | −0.623991 | + | 1.08078i | ||||
\(816\) | 52.7551 | − | 91.3745i | 1.84680 | − | 3.19875i | ||||
\(817\) | −9.71106 | + | 5.60668i | −0.339747 | + | 0.196153i | ||||
\(818\) | 65.3668 | 2.28550 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.2310 | 0.881105 | ||||||||
\(821\) | 4.94391 | − | 2.85437i | 0.172544 | − | 0.0996181i | −0.411241 | − | 0.911527i | \(-0.634905\pi\) |
0.583785 | + | 0.811909i | \(0.301571\pi\) | |||||||
\(822\) | 19.3396 | − | 33.4971i | 0.674545 | − | 1.16835i | ||||
\(823\) | 0.00433157 | − | 0.00750250i | 0.000150989 | − | 0.000261521i | −0.865950 | − | 0.500131i | \(-0.833285\pi\) |
0.866101 | + | 0.499869i | \(0.166619\pi\) | |||||||
\(824\) | −97.1439 | + | 56.0861i | −3.38417 | + | 1.95385i | ||||
\(825\) | − | 3.92340i | − | 0.136595i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 52.4236i | − | 1.82295i | −0.411359 | − | 0.911473i | \(-0.634946\pi\) | ||
0.411359 | − | 0.911473i | \(-0.365054\pi\) | |||||||
\(828\) | 20.1246 | + | 34.8568i | 0.699377 | + | 1.21136i | ||||
\(829\) | 8.73616 | − | 15.1315i | 0.303419 | − | 0.525538i | −0.673489 | − | 0.739197i | \(-0.735205\pi\) |
0.976908 | + | 0.213660i | \(0.0685384\pi\) | |||||||
\(830\) | −11.0760 | − | 6.39473i | −0.384454 | − | 0.221964i | ||||
\(831\) | 5.04397 | + | 8.73641i | 0.174973 | + | 0.303063i | ||||
\(832\) | 17.4280 | + | 108.033i | 0.604206 | + | 3.74536i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.5876i | 0.574381i | ||||||||
\(835\) | −20.3970 | − | 35.3286i | −0.705866 | − | 1.22260i | ||||
\(836\) | 32.4275 | − | 56.1661i | 1.12153 | − | 1.94255i | ||||
\(837\) | −20.2241 | − | 11.6764i | −0.699047 | − | 0.403595i | ||||
\(838\) | −39.0053 | + | 22.5197i | −1.34741 | + | 0.777930i | ||||
\(839\) | − | 19.7237i | − | 0.680939i | −0.940256 | − | 0.340470i | \(-0.889414\pi\) | ||
0.940256 | − | 0.340470i | \(-0.110586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3232 | 0.942179 | ||||||||
\(842\) | −32.7909 | − | 56.7954i | −1.13005 | − | 1.95730i | ||||
\(843\) | 24.7280 | + | 14.2767i | 0.851676 | + | 0.491716i | ||||
\(844\) | 16.5716 | − | 28.7028i | 0.570416 | − | 0.987990i | ||||
\(845\) | 16.2257 | − | 18.2293i | 0.558180 | − | 0.627107i | ||||
\(846\) | 40.5081 | 1.39270 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 121.770 | 4.18161 | ||||||||
\(849\) | 7.08160 | + | 12.2657i | 0.243040 | + | 0.420958i | ||||
\(850\) | −21.2181 | − | 12.2503i | −0.727775 | − | 0.420181i | ||||
\(851\) | 12.1232 | + | 6.99931i | 0.415576 | + | 0.239933i | ||||
\(852\) | 28.0299 | − | 16.1831i | 0.960289 | − | 0.554423i | ||||
\(853\) | 1.74842i | 0.0598648i | 0.999552 | + | 0.0299324i | \(0.00952921\pi\) | ||||
−0.999552 | + | 0.0299324i | \(0.990471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.0856 | −0.550114 | ||||||||
\(856\) | −35.2044 | + | 20.3253i | −1.20326 | + | 0.694704i | ||||
\(857\) | −1.67801 | + | 2.90639i | −0.0573196 | + | 0.0992805i | −0.893261 | − | 0.449538i | \(-0.851589\pi\) |
0.835942 | + | 0.548818i | \(0.184922\pi\) | |||||||
\(858\) | −24.4932 | − | 9.32169i | −0.836186 | − | 0.318237i | ||||
\(859\) | −14.9108 | − | 25.8263i | −0.508750 | − | 0.881181i | −0.999949 | − | 0.0101332i | \(-0.996774\pi\) |
0.491199 | − | 0.871048i | \(-0.336559\pi\) | |||||||
\(860\) | − | 22.3821i | − | 0.763224i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 62.0387 | 2.11305 | ||||||||
\(863\) | 0.340244 | − | 0.196440i | 0.0115820 | − | 0.00668690i | −0.494198 | − | 0.869349i | \(-0.664538\pi\) |
0.505780 | + | 0.862663i | \(0.331205\pi\) | |||||||
\(864\) | −103.166 | − | 59.5628i | −3.50977 | − | 2.02637i | ||||
\(865\) | 4.71960 | + | 2.72487i | 0.160471 | + | 0.0926482i | ||||
\(866\) | 40.4759 | − | 23.3688i | 1.37543 | − | 0.794104i | ||||
\(867\) | 22.9616 | 0.779817 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 8.76678i | − | 0.297393i | ||||||
\(870\) | 22.2643 | + | 38.5630i | 0.754832 | + | 1.30741i | ||||
\(871\) | 1.48423 | − | 3.89990i | 0.0502913 | − | 0.132143i | ||||
\(872\) | −9.55762 | + | 16.5543i | −0.323662 | + | 0.560599i | ||||
\(873\) | −3.61975 | + | 2.08986i | −0.122510 | + | 0.0707312i | ||||
\(874\) | −62.2089 | −2.10425 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.4633i | 0.421097i | ||||||||
\(877\) | 44.9539 | − | 25.9541i | 1.51798 | − | 0.876409i | 0.518208 | − | 0.855255i | \(-0.326599\pi\) |
0.999776 | − | 0.0211538i | \(-0.00673397\pi\) | |||||||
\(878\) | −83.8263 | − | 48.3971i | −2.82900 | − | 1.63332i | ||||
\(879\) | 14.6682 | + | 8.46871i | 0.494747 | + | 0.285642i | ||||
\(880\) | 32.4511 | + | 56.2070i | 1.09393 | + | 1.89474i | ||||
\(881\) | −10.0487 | −0.338548 | −0.169274 | − | 0.985569i | \(-0.554142\pi\) | ||||
−0.169274 | + | 0.985569i | \(0.554142\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.1835 | −1.92438 | −0.962189 | − | 0.272383i | \(-0.912188\pi\) | ||||
−0.962189 | + | 0.272383i | \(0.912188\pi\) | |||||||
\(884\) | −92.9430 | + | 75.7055i | −3.12601 | + | 2.54625i | ||||
\(885\) | 7.74652 | − | 13.4174i | 0.260397 | − | 0.451020i | ||||
\(886\) | −38.5095 | − | 22.2335i | −1.29375 | − | 0.746948i | ||||
\(887\) | −0.353960 | − | 0.613076i | −0.0118848 | − | 0.0205851i | 0.860022 | − | 0.510257i | \(-0.170450\pi\) |
−0.871907 | + | 0.489672i | \(0.837116\pi\) | |||||||
\(888\) | −34.8104 | −1.16816 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 53.5309i | 1.79436i | ||||||||
\(891\) | 2.47062 | − | 1.42641i | 0.0827689 | − | 0.0477867i | ||||
\(892\) | 34.6479 | + | 20.0040i | 1.16010 | + | 0.669782i | ||||
\(893\) | −22.9297 | + | 39.7155i | −0.767314 | + | 1.32903i | ||||
\(894\) | 3.76330 | + | 6.51822i | 0.125863 | + | 0.218002i | ||||
\(895\) | 36.3257i | 1.21423i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.93246 | + | 18.1778i | 0.0979119 | + | 0.606938i | ||||
\(898\) | −20.7077 | − | 35.8668i | −0.691025 | − | 1.19689i | ||||
\(899\) | 28.1537 | + | 16.2545i | 0.938978 | + | 0.542119i | ||||
\(900\) | −6.72300 | + | 11.6446i | −0.224100 | + | 0.388153i | ||||
\(901\) | 24.5899 | + | 42.5909i | 0.819208 | + | 1.41891i | ||||
\(902\) | 15.4335i | 0.513879i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 39.6177i | − | 1.31766i | ||||||
\(905\) | −16.2254 | + | 9.36773i | −0.539350 | + | 0.311394i | ||||
\(906\) | 32.0935 | − | 55.5876i | 1.06624 | − | 1.84678i | ||||
\(907\) | 22.1896 | − | 38.4336i | 0.736795 | − | 1.27617i | −0.217136 | − | 0.976141i | \(-0.569672\pi\) |
0.953931 | − | 0.300025i | \(-0.0969952\pi\) | |||||||
\(908\) | 74.4123 | − | 42.9619i | 2.46946 | − | 1.42574i | ||||
\(909\) | −17.7698 | −0.589386 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9184 | 0.958109 | 0.479055 | − | 0.877785i | \(-0.340980\pi\) | ||||
0.479055 | + | 0.877785i | \(0.340980\pi\) | |||||||
\(912\) | 77.5066 | − | 44.7484i | 2.56650 | − | 1.48177i | ||||
\(913\) | 2.86512 | − | 4.96254i | 0.0948217 | − | 0.164236i | ||||
\(914\) | 53.9981 | − | 93.5275i | 1.78610 | − | 3.09362i | ||||
\(915\) | 15.0528 | − | 8.69075i | 0.497631 | − | 0.287307i | ||||
\(916\) | 139.981i | 4.62509i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 89.4969i | − | 2.95384i | ||||||
\(919\) | −12.8806 | − | 22.3098i | −0.424891 | − | 0.735932i | 0.571520 | − | 0.820588i | \(-0.306354\pi\) |
−0.996410 | + | 0.0846563i | \(0.973021\pi\) | |||||||
\(920\) | 39.4092 | − | 68.2588i | 1.29928 | − | 2.25042i | ||||
\(921\) | −18.8892 | − | 10.9057i | −0.622419 | − | 0.359354i | ||||
\(922\) | 25.9953 | + | 45.0252i | 0.856111 | + | 1.48283i | ||||
\(923\) | −18.2009 | + | 2.93619i | −0.599089 | + | 0.0966458i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.67651i | 0.153763i | ||||||||
\(926\) | 3.40052 | + | 5.88988i | 0.111748 | + | 0.193554i | ||||
\(927\) | −9.81879 | + | 17.0066i | −0.322491 | + | 0.558571i | ||||
\(928\) | 143.616 | + | 82.9166i | 4.71442 | + | 2.72187i | ||||
\(929\) | −47.5549 | + | 27.4558i | −1.56023 | + | 0.900797i | −0.562993 | + | 0.826462i | \(0.690350\pi\) |
−0.997233 | + | 0.0743356i | \(0.976316\pi\) | |||||||
\(930\) | 25.7014i | 0.842783i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −89.4784 | −2.93096 | ||||||||
\(933\) | −3.29757 | − | 5.71156i | −0.107958 | − | 0.186988i | ||||
\(934\) | 35.2309 | + | 20.3406i | 1.15279 | + | 0.665564i | ||||
\(935\) | −13.1061 | + | 22.7005i | −0.428616 | + | 0.742385i | ||||
\(936\) | 36.0050 | + | 44.2031i | 1.17686 | + | 1.44482i | ||||
\(937\) | 23.1364 | 0.755835 | 0.377917 | − | 0.925839i | \(-0.376640\pi\) | ||||
0.377917 | + | 0.925839i | \(0.376640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.55830 | −0.148755 | ||||||||
\(940\) | −45.7682 | − | 79.2729i | −1.49280 | − | 2.58560i | ||||
\(941\) | −0.302692 | − | 0.174759i | −0.00986748 | − | 0.00569699i | 0.495058 | − | 0.868860i | \(-0.335147\pi\) |
−0.504926 | + | 0.863163i | \(0.668480\pi\) | |||||||
\(942\) | −30.2195 | − | 17.4472i | −0.984605 | − | 0.568462i | ||||
\(943\) | 9.39062 | − | 5.42168i | 0.305801 | − | 0.176554i | ||||
\(944\) | − | 107.331i | − | 3.49333i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.6909 | 0.445128 | ||||||||
\(947\) | 15.1884 | − | 8.76900i | 0.493555 | − | 0.284954i | −0.232493 | − | 0.972598i | \(-0.574688\pi\) |
0.726048 | + | 0.687644i | \(0.241355\pi\) | |||||||
\(948\) | 12.0649 | − | 20.8970i | 0.391850 | − | 0.678703i | ||||
\(949\) | 2.52516 | − | 6.63500i | 0.0819703 | − | 0.215381i | ||||
\(950\) | −10.3911 | − | 17.9978i | −0.337130 | − | 0.583927i | ||||
\(951\) | 4.44019i | 0.143983i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8790 | −1.55095 | −0.775477 | − | 0.631376i | \(-0.782491\pi\) | ||||
−0.775477 | + | 0.631376i | \(0.782491\pi\) | |||||||
\(954\) | 31.9112 | − | 18.4239i | 1.03316 | − | 0.596497i | ||||
\(955\) | 8.78702 | + | 5.07319i | 0.284341 | + | 0.164164i | ||||
\(956\) | 81.8057 | + | 47.2305i | 2.64579 | + | 1.52754i | ||||
\(957\) | −17.2779 | + | 9.97541i | −0.558516 | + | 0.322459i | ||||
\(958\) | 46.1527 | 1.49112 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 65.8610i | 2.12566i | ||||||||
\(961\) | −6.11807 | − | 10.5968i | −0.197357 | − | 0.341833i | ||||
\(962\) | 29.1948 | + | 11.1110i | 0.941279 | + | 0.358234i | ||||
\(963\) | −3.55828 | + | 6.16311i | −0.114664 | + | 0.198604i | ||||
\(964\) | 47.9581 | − | 27.6886i | 1.54463 | − | 0.891791i | ||||
\(965\) | 27.3455 | 0.880282 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.4683i | 0.400955i | 0.979698 | + | 0.200477i | \(0.0642493\pi\) | ||||
−0.979698 | + | 0.200477i | \(0.935751\pi\) | |||||||
\(968\) | 47.0059 | − | 27.1389i | 1.51083 | − | 0.872276i | ||||
\(969\) | 31.3028 | + | 18.0727i | 1.00559 | + | 0.580579i | ||||
\(970\) | 11.1671 | + | 6.44732i | 0.358554 | + | 0.207011i | ||||
\(971\) | 19.6189 | + | 33.9810i | 0.629602 | + | 1.09050i | 0.987632 | + | 0.156792i | \(0.0501153\pi\) |
−0.358030 | + | 0.933710i | \(0.616551\pi\) | |||||||
\(972\) | −80.7105 | −2.58879 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.1546 | 0.389458 | ||||||||
\(975\) | −4.76923 | + | 3.88471i | −0.152738 | + | 0.124410i | ||||
\(976\) | 60.2069 | − | 104.281i | 1.92718 | − | 3.33797i | ||||
\(977\) | 21.1382 | + | 12.2041i | 0.676269 | + | 0.390444i | 0.798448 | − | 0.602064i | \(-0.205655\pi\) |
−0.122179 | + | 0.992508i | \(0.538988\pi\) | |||||||
\(978\) | −29.9916 | − | 51.9470i | −0.959026 | − | 1.66108i | ||||
\(979\) | −23.9842 | −0.766538 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.34643i | 0.106843i | ||||||||
\(982\) | 40.2105 | − | 23.2155i | 1.28317 | − | 0.740837i | ||||
\(983\) | −47.4783 | − | 27.4116i | −1.51432 | − | 0.874295i | −0.999859 | − | 0.0167828i | \(-0.994658\pi\) |
−0.514464 | − | 0.857512i | \(-0.672009\pi\) | |||||||
\(984\) | −13.4821 | + | 23.3517i | −0.429794 | + | 0.744424i | ||||
\(985\) | −14.9294 | − | 25.8585i | −0.475691 | − | 0.823921i | ||||
\(986\) | 124.587i | 3.96767i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −100.383 | + | 16.1939i | −3.19360 | + | 0.515195i | ||||
\(989\) | −4.80951 | − | 8.33031i | −0.152933 | − | 0.264889i | ||||
\(990\) | 17.0083 | + | 9.81976i | 0.540560 | + | 0.312092i | ||||
\(991\) | 19.0686 | − | 33.0278i | 0.605734 | − | 1.04916i | −0.386201 | − | 0.922415i | \(-0.626213\pi\) |
0.991935 | − | 0.126748i | \(-0.0404539\pi\) | |||||||
\(992\) | 47.8585 | + | 82.8934i | 1.51951 | + | 2.63187i | ||||
\(993\) | 7.08134i | 0.224719i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.701472i | 0.0222382i | ||||||||
\(996\) | 13.6590 | − | 7.88600i | 0.432801 | − | 0.249878i | ||||
\(997\) | −26.5130 | + | 45.9219i | −0.839676 | + | 1.45436i | 0.0504904 | + | 0.998725i | \(0.483922\pi\) |
−0.890166 | + | 0.455636i | \(0.849412\pi\) | |||||||
\(998\) | −56.0527 | + | 97.0860i | −1.77432 | + | 3.07321i | ||||
\(999\) | −14.7940 | + | 8.54130i | −0.468060 | + | 0.270235i |
(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 | 637.2.r.g.116.1 | 32 | ||
7.2 | even | 3 | inner | 637.2.r.g.324.15 | 32 | ||
7.3 | odd | 6 | 637.2.c.g.246.1 | ✓ | 16 | ||
7.4 | even | 3 | 637.2.c.g.246.2 | yes | 16 | ||
7.5 | odd | 6 | inner | 637.2.r.g.324.16 | 32 | ||
7.6 | odd | 2 | inner | 637.2.r.g.116.2 | 32 | ||
13.12 | even | 2 | inner | 637.2.r.g.116.15 | 32 | ||
91.12 | odd | 6 | inner | 637.2.r.g.324.2 | 32 | ||
91.18 | odd | 12 | 8281.2.a.cs.1.2 | 16 | |||
91.25 | even | 6 | 637.2.c.g.246.16 | yes | 16 | ||
91.31 | even | 12 | 8281.2.a.cs.1.1 | 16 | |||
91.38 | odd | 6 | 637.2.c.g.246.15 | yes | 16 | ||
91.51 | even | 6 | inner | 637.2.r.g.324.1 | 32 | ||
91.60 | odd | 12 | 8281.2.a.cs.1.16 | 16 | |||
91.73 | even | 12 | 8281.2.a.cs.1.15 | 16 | |||
91.90 | odd | 2 | inner | 637.2.r.g.116.16 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.1 | ✓ | 16 | 7.3 | odd | 6 | ||
637.2.c.g.246.2 | yes | 16 | 7.4 | even | 3 | ||
637.2.c.g.246.15 | yes | 16 | 91.38 | odd | 6 | ||
637.2.c.g.246.16 | yes | 16 | 91.25 | even | 6 | ||
637.2.r.g.116.1 | 32 | 1.1 | even | 1 | trivial | ||
637.2.r.g.116.2 | 32 | 7.6 | odd | 2 | inner | ||
637.2.r.g.116.15 | 32 | 13.12 | even | 2 | inner | ||
637.2.r.g.116.16 | 32 | 91.90 | odd | 2 | inner | ||
637.2.r.g.324.1 | 32 | 91.51 | even | 6 | inner | ||
637.2.r.g.324.2 | 32 | 91.12 | odd | 6 | inner | ||
637.2.r.g.324.15 | 32 | 7.2 | even | 3 | inner | ||
637.2.r.g.324.16 | 32 | 7.5 | odd | 6 | inner | ||
8281.2.a.cs.1.1 | 16 | 91.31 | even | 12 | |||
8281.2.a.cs.1.2 | 16 | 91.18 | odd | 12 | |||
8281.2.a.cs.1.15 | 16 | 91.73 | even | 12 | |||
8281.2.a.cs.1.16 | 16 | 91.60 | odd | 12 |