Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(101,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(1.20036 + 0.747754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.251 |
Dual form | 325.2.n.d.101.4 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16117 | + | 1.24775i | 1.52818 | + | 0.882295i | 0.999438 | + | 0.0335125i | \(0.0106693\pi\) |
0.528742 | + | 0.848783i | \(0.322664\pi\) | |||||||
\(3\) | −1.41342 | + | 2.44811i | −0.816038 | + | 1.41342i | 0.0925423 | + | 0.995709i | \(0.470501\pi\) |
−0.908580 | + | 0.417710i | \(0.862833\pi\) | |||||||
\(4\) | 2.11378 | + | 3.66117i | 1.05689 | + | 1.83059i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.10929 | + | 3.52720i | −2.49411 | + | 1.43997i | ||||
\(7\) | 1.64996 | − | 0.952606i | 0.623627 | − | 0.360051i | −0.154653 | − | 0.987969i | \(-0.549426\pi\) |
0.778280 | + | 0.627918i | \(0.216093\pi\) | |||||||
\(8\) | 5.55889i | 1.96536i | ||||||||
\(9\) | −2.49551 | − | 4.32235i | −0.831836 | − | 1.44078i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.926118 | + | 0.534695i | 0.279235 | + | 0.161217i | 0.633077 | − | 0.774089i | \(-0.281792\pi\) |
−0.353842 | + | 0.935305i | \(0.615125\pi\) | |||||||
\(12\) | −11.9506 | −3.44985 | ||||||||
\(13\) | −1.40072 | − | 3.32235i | −0.388490 | − | 0.921453i | ||||
\(14\) | 4.75447 | 1.27069 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.70857 | + | 4.69138i | −0.677142 | + | 1.17284i | ||||
\(17\) | −0.318632 | − | 0.551886i | −0.0772795 | − | 0.133852i | 0.824796 | − | 0.565431i | \(-0.191290\pi\) |
−0.902075 | + | 0.431579i | \(0.857957\pi\) | |||||||
\(18\) | − | 12.4551i | − | 2.93570i | ||||||
\(19\) | 4.96410 | − | 2.86603i | 1.13884 | − | 0.657511i | 0.192699 | − | 0.981258i | \(-0.438276\pi\) |
0.946144 | + | 0.323747i | \(0.104943\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.38573i | 1.17526i | ||||||||
\(22\) | 1.33433 | + | 2.31114i | 0.284481 | + | 0.492736i | ||||
\(23\) | −1.90893 | + | 3.30636i | −0.398039 | + | 0.689423i | −0.993484 | − | 0.113973i | \(-0.963642\pi\) |
0.595445 | + | 0.803396i | \(0.296976\pi\) | |||||||
\(24\) | −13.6088 | − | 7.85704i | −2.77788 | − | 1.60381i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.11827 | − | 8.92792i | 0.219311 | − | 1.75091i | ||||
\(27\) | 5.62828 | 1.08316 | ||||||||
\(28\) | 6.97531 | + | 4.02720i | 1.31821 | + | 0.761069i | ||||
\(29\) | −4.72756 | + | 8.18837i | −0.877886 | + | 1.52054i | −0.0242288 | + | 0.999706i | \(0.507713\pi\) |
−0.853657 | + | 0.520836i | \(0.825620\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.46410i | − | 0.262960i | −0.991319 | − | 0.131480i | \(-0.958027\pi\) | ||
0.991319 | − | 0.131480i | \(-0.0419730\pi\) | |||||||
\(32\) | −2.07908 | + | 1.20036i | −0.367534 | + | 0.212196i | ||||
\(33\) | −2.61799 | + | 1.51150i | −0.455733 | + | 0.263118i | ||||
\(34\) | − | 1.59030i | − | 0.272733i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.5499 | − | 18.2730i | 1.75832 | − | 3.04550i | ||||
\(37\) | −0.655970 | − | 0.378725i | −0.107841 | − | 0.0622619i | 0.445110 | − | 0.895476i | \(-0.353165\pi\) |
−0.552950 | + | 0.833214i | \(0.686498\pi\) | |||||||
\(38\) | 14.3044 | 2.32048 | ||||||||
\(39\) | 10.1133 | + | 1.26675i | 1.61942 | + | 0.202842i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.232051 | − | 0.133975i | −0.0362402 | − | 0.0209233i | 0.481770 | − | 0.876297i | \(-0.339994\pi\) |
−0.518011 | + | 0.855374i | \(0.673327\pi\) | |||||||
\(42\) | −6.72006 | + | 11.6395i | −1.03693 | + | 1.79601i | ||||
\(43\) | −0.318632 | − | 0.551886i | −0.0485909 | − | 0.0841618i | 0.840707 | − | 0.541490i | \(-0.182140\pi\) |
−0.889298 | + | 0.457328i | \(0.848806\pi\) | |||||||
\(44\) | 4.52091i | 0.681552i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.25104 | + | 4.76374i | −1.21655 | + | 0.702375i | ||||
\(47\) | − | 9.44613i | − | 1.37786i | −0.724828 | − | 0.688930i | \(-0.758081\pi\) | ||
0.724828 | − | 0.688930i | \(-0.241919\pi\) | |||||||
\(48\) | −7.65668 | − | 13.2618i | −1.10515 | − | 1.91417i | ||||
\(49\) | −1.68508 | + | 2.91865i | −0.240726 | + | 0.416950i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.80144 | 0.252252 | ||||||||
\(52\) | 9.20287 | − | 12.1510i | 1.27621 | − | 1.68504i | ||||
\(53\) | 6.99102 | 0.960290 | 0.480145 | − | 0.877189i | \(-0.340584\pi\) | ||||
0.480145 | + | 0.877189i | \(0.340584\pi\) | |||||||
\(54\) | 12.1637 | + | 7.02271i | 1.65527 | + | 0.955669i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.29543 | + | 9.17196i | 0.707632 | + | 1.22565i | ||||
\(57\) | 16.2036i | 2.14622i | ||||||||
\(58\) | −20.4341 | + | 11.7977i | −2.68313 | + | 1.54911i | ||||
\(59\) | −0.641756 | + | 0.370518i | −0.0835495 | + | 0.0482373i | −0.541193 | − | 0.840899i | \(-0.682027\pi\) |
0.457643 | + | 0.889136i | \(0.348694\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.09928 | − | 3.63606i | −0.268785 | − | 0.465550i | 0.699763 | − | 0.714375i | \(-0.253289\pi\) |
−0.968548 | + | 0.248825i | \(0.919956\pi\) | |||||||
\(62\) | 1.82684 | − | 3.16418i | 0.232009 | − | 0.401851i | ||||
\(63\) | −8.23499 | − | 4.75447i | −1.03751 | − | 0.599007i | ||||
\(64\) | 4.84325 | 0.605406 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.54390 | −0.928589 | ||||||||
\(67\) | 7.01029 | + | 4.04739i | 0.856443 | + | 0.494468i | 0.862820 | − | 0.505512i | \(-0.168696\pi\) |
−0.00637624 | + | 0.999980i | \(0.502030\pi\) | |||||||
\(68\) | 1.34703 | − | 2.33313i | 0.163352 | − | 0.282934i | ||||
\(69\) | −5.39623 | − | 9.34654i | −0.649629 | − | 1.12519i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.45663 | − | 4.88244i | 1.00362 | − | 0.579439i | 0.0943010 | − | 0.995544i | \(-0.469938\pi\) |
0.909317 | + | 0.416105i | \(0.136605\pi\) | |||||||
\(72\) | 24.0274 | − | 13.8723i | 2.83166 | − | 1.63486i | ||||
\(73\) | − | 3.71649i | − | 0.434982i | −0.976062 | − | 0.217491i | \(-0.930213\pi\) | ||
0.976062 | − | 0.217491i | \(-0.0697873\pi\) | |||||||
\(74\) | −0.945110 | − | 1.63698i | −0.109867 | − | 0.190295i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.9860 | + | 12.1163i | 2.40726 | + | 1.38983i | ||||
\(77\) | 2.03741 | 0.232185 | ||||||||
\(78\) | 20.2760 | + | 15.3565i | 2.29580 | + | 1.73879i | ||||
\(79\) | −9.31937 | −1.04851 | −0.524255 | − | 0.851561i | \(-0.675656\pi\) | ||||
−0.524255 | + | 0.851561i | \(0.675656\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.468594 | + | 0.811629i | −0.0520660 | + | 0.0901809i | ||||
\(82\) | −0.334335 | − | 0.579085i | −0.0369211 | − | 0.0639492i | ||||
\(83\) | − | 5.11778i | − | 0.561749i | −0.959744 | − | 0.280875i | \(-0.909376\pi\) | ||
0.959744 | − | 0.280875i | \(-0.0906245\pi\) | |||||||
\(84\) | −19.7181 | + | 11.3842i | −2.15142 | + | 1.24212i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.59030i | − | 0.171486i | ||||||
\(87\) | −13.3640 | − | 23.1472i | −1.43278 | − | 2.48164i | ||||
\(88\) | −2.97231 | + | 5.14819i | −0.316849 | + | 0.548799i | ||||
\(89\) | −10.8932 | − | 6.28917i | −1.15467 | − | 0.666650i | −0.204651 | − | 0.978835i | \(-0.565606\pi\) |
−0.950021 | + | 0.312185i | \(0.898939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.47602 | − | 4.14741i | −0.574043 | − | 0.434767i | ||||
\(92\) | −16.1402 | −1.68273 | ||||||||
\(93\) | 3.58429 | + | 2.06939i | 0.371673 | + | 0.214586i | ||||
\(94\) | 11.7864 | − | 20.4147i | 1.21568 | − | 2.10562i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 6.78645i | − | 0.692639i | ||||||
\(97\) | 3.65597 | − | 2.11078i | 0.371208 | − | 0.214317i | −0.302778 | − | 0.953061i | \(-0.597914\pi\) |
0.673986 | + | 0.738744i | \(0.264581\pi\) | |||||||
\(98\) | −7.28351 | + | 4.20514i | −0.735746 | + | 0.424783i | ||||
\(99\) | − | 5.33734i | − | 0.536423i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.62379 | + | 13.2048i | −0.758595 | + | 1.31393i | 0.184972 | + | 0.982744i | \(0.440781\pi\) |
−0.943567 | + | 0.331181i | \(0.892553\pi\) | |||||||
\(102\) | 3.89322 | + | 2.24775i | 0.385487 | + | 0.222561i | ||||
\(103\) | −13.5269 | −1.33285 | −0.666423 | − | 0.745574i | \(-0.732176\pi\) | ||||
−0.666423 | + | 0.745574i | \(0.732176\pi\) | |||||||
\(104\) | 18.4686 | − | 7.78645i | 1.81099 | − | 0.763524i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.1088 | + | 8.72307i | 1.46750 | + | 0.847259i | ||||
\(107\) | −3.68137 | + | 6.37632i | −0.355891 | + | 0.616422i | −0.987270 | − | 0.159053i | \(-0.949156\pi\) |
0.631379 | + | 0.775475i | \(0.282489\pi\) | |||||||
\(108\) | 11.8969 | + | 20.6061i | 1.14478 | + | 1.98282i | ||||
\(109\) | 10.0760i | 0.965103i | 0.875868 | + | 0.482551i | \(0.160290\pi\) | ||||
−0.875868 | + | 0.482551i | \(0.839710\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.85432 | − | 1.07059i | 0.176004 | − | 0.101616i | ||||
\(112\) | 10.3208i | 0.975223i | ||||||||
\(113\) | −3.34403 | − | 5.79203i | −0.314580 | − | 0.544868i | 0.664768 | − | 0.747050i | \(-0.268530\pi\) |
−0.979348 | + | 0.202181i | \(0.935197\pi\) | |||||||
\(114\) | −20.2181 | + | 35.0187i | −1.89360 | + | 3.27981i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −39.9721 | −3.71131 | ||||||||
\(117\) | −10.8648 | + | 14.3453i | −1.00445 | + | 1.32623i | ||||
\(118\) | −1.84926 | −0.170238 | ||||||||
\(119\) | −1.05146 | − | 0.607061i | −0.0963872 | − | 0.0556492i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.92820 | − | 8.53590i | −0.448018 | − | 0.775991i | ||||
\(122\) | − | 10.4775i | − | 0.948592i | ||||||
\(123\) | 0.655970 | − | 0.378725i | 0.0591468 | − | 0.0341484i | ||||
\(124\) | 5.36033 | − | 3.09479i | 0.481372 | − | 0.277920i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.8648 | − | 20.5505i | −1.05700 | − | 1.83078i | ||||
\(127\) | −0.744750 | + | 1.28994i | −0.0660859 | + | 0.114464i | −0.897175 | − | 0.441675i | \(-0.854384\pi\) |
0.831089 | + | 0.556139i | \(0.187718\pi\) | |||||||
\(128\) | 14.6253 | + | 8.44391i | 1.29270 | + | 0.746343i | ||||
\(129\) | 1.80144 | 0.158608 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.12676 | 0.360557 | 0.180278 | − | 0.983616i | \(-0.442300\pi\) | ||||
0.180278 | + | 0.983616i | \(0.442300\pi\) | |||||||
\(132\) | −11.0677 | − | 6.38994i | −0.963319 | − | 0.556172i | ||||
\(133\) | 5.46039 | − | 9.45767i | 0.473476 | − | 0.820084i | ||||
\(134\) | 10.1003 | + | 17.4942i | 0.872533 | + | 1.51127i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.06787 | − | 1.77124i | 0.263068 | − | 0.151882i | ||||
\(137\) | −17.4155 | + | 10.0548i | −1.48790 | + | 0.859041i | −0.999905 | − | 0.0138029i | \(-0.995606\pi\) |
−0.487999 | + | 0.872844i | \(0.662273\pi\) | |||||||
\(138\) | − | 26.9327i | − | 2.29266i | ||||||
\(139\) | −10.4126 | − | 18.0352i | −0.883189 | − | 1.52973i | −0.847776 | − | 0.530355i | \(-0.822059\pi\) |
−0.0354130 | − | 0.999373i | \(-0.511275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.1252 | + | 13.3513i | 1.94749 | + | 1.12439i | ||||
\(142\) | 24.3683 | 2.04494 | ||||||||
\(143\) | 0.479208 | − | 3.82584i | 0.0400734 | − | 0.319933i | ||||
\(144\) | 27.0370 | 2.25308 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.63726 | − | 8.03198i | 0.383783 | − | 0.664731i | ||||
\(147\) | −4.76346 | − | 8.25055i | −0.392883 | − | 0.680494i | ||||
\(148\) | − | 3.20216i | − | 0.263216i | ||||||
\(149\) | 11.5768 | − | 6.68388i | 0.948410 | − | 0.547565i | 0.0558233 | − | 0.998441i | \(-0.482222\pi\) |
0.892587 | + | 0.450876i | \(0.148888\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.2984i | − | 1.48910i | −0.667567 | − | 0.744550i | \(-0.732664\pi\) | ||
0.667567 | − | 0.744550i | \(-0.267336\pi\) | |||||||
\(152\) | 15.9319 | + | 27.5949i | 1.29225 | + | 2.23824i | ||||
\(153\) | −1.59030 | + | 2.75447i | −0.128568 | + | 0.222686i | ||||
\(154\) | 4.40320 | + | 2.54219i | 0.354820 | + | 0.204856i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.7395 | + | 39.7041i | 1.34023 | + | 3.17887i | ||||
\(157\) | −2.42229 | −0.193320 | −0.0966599 | − | 0.995317i | \(-0.530816\pi\) | ||||
−0.0966599 | + | 0.995317i | \(0.530816\pi\) | |||||||
\(158\) | −20.1408 | − | 11.6283i | −1.60231 | − | 0.925096i | ||||
\(159\) | −9.88124 | + | 17.1148i | −0.783633 | + | 1.35729i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.27382i | 0.573258i | ||||||||
\(162\) | −2.02543 | + | 1.16938i | −0.159132 | + | 0.0918752i | ||||
\(163\) | 13.8416 | − | 7.99144i | 1.08416 | − | 0.625938i | 0.152142 | − | 0.988359i | \(-0.451383\pi\) |
0.932015 | + | 0.362421i | \(0.118050\pi\) | |||||||
\(164\) | − | 1.13277i | − | 0.0884545i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.38573 | − | 11.0604i | 0.495629 | − | 0.858454i | ||||
\(167\) | 12.4648 | + | 7.19658i | 0.964558 | + | 0.556888i | 0.897573 | − | 0.440866i | \(-0.145329\pi\) |
0.0669853 | + | 0.997754i | \(0.478662\pi\) | |||||||
\(168\) | −29.9387 | −2.30982 | ||||||||
\(169\) | −9.07597 | + | 9.30735i | −0.698151 | + | 0.715950i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.7759 | − | 14.3044i | −1.89466 | − | 1.09388i | ||||
\(172\) | 1.34703 | − | 2.33313i | 0.102710 | − | 0.177900i | ||||
\(173\) | 12.1745 | + | 21.0868i | 0.925608 | + | 1.60320i | 0.790581 | + | 0.612358i | \(0.209779\pi\) |
0.135027 | + | 0.990842i | \(0.456888\pi\) | |||||||
\(174\) | − | 66.7001i | − | 5.05653i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.01691 | + | 2.89651i | −0.378164 | + | 0.218333i | ||||
\(177\) | − | 2.09479i | − | 0.157454i | ||||||
\(178\) | −15.6947 | − | 27.1840i | −1.17636 | − | 2.03752i | ||||
\(179\) | 1.89414 | − | 3.28075i | 0.141575 | − | 0.245215i | −0.786515 | − | 0.617571i | \(-0.788117\pi\) |
0.928090 | + | 0.372356i | \(0.121450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48794 | 0.630904 | 0.315452 | − | 0.948942i | \(-0.397844\pi\) | ||||
0.315452 | + | 0.948942i | \(0.397844\pi\) | |||||||
\(182\) | −6.65968 | − | 15.7960i | −0.493649 | − | 1.17088i | ||||
\(183\) | 11.8687 | 0.877356 | ||||||||
\(184\) | −18.3797 | − | 10.6115i | −1.35497 | − | 0.782291i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.16418 | + | 8.94462i | 0.378656 | + | 0.655851i | ||||
\(187\) | − | 0.681482i | − | 0.0498349i | ||||||
\(188\) | 34.5839 | − | 19.9670i | 2.52229 | − | 1.45625i | ||||
\(189\) | 9.28645 | − | 5.36153i | 0.675490 | − | 0.389994i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.72155 | + | 4.71386i | 0.196924 | + | 0.341083i | 0.947530 | − | 0.319668i | \(-0.103571\pi\) |
−0.750605 | + | 0.660751i | \(0.770238\pi\) | |||||||
\(192\) | −6.84555 | + | 11.8568i | −0.494035 | + | 0.855693i | ||||
\(193\) | −10.5288 | − | 6.07880i | −0.757879 | − | 0.437562i | 0.0706548 | − | 0.997501i | \(-0.477491\pi\) |
−0.828534 | + | 0.559939i | \(0.810824\pi\) | |||||||
\(194\) | 10.5349 | 0.756363 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.2476 | −1.01768 | ||||||||
\(197\) | −3.79172 | − | 2.18915i | −0.270149 | − | 0.155970i | 0.358807 | − | 0.933412i | \(-0.383184\pi\) |
−0.628955 | + | 0.777442i | \(0.716517\pi\) | |||||||
\(198\) | 6.65968 | − | 11.5349i | 0.473283 | − | 0.819751i | ||||
\(199\) | 10.4186 | + | 18.0456i | 0.738558 | + | 1.27922i | 0.953144 | + | 0.302516i | \(0.0978265\pi\) |
−0.214586 | + | 0.976705i | \(0.568840\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.8170 | + | 11.4413i | −1.39778 | + | 0.807009i | ||||
\(202\) | −32.9526 | + | 19.0252i | −2.31854 | + | 1.33861i | ||||
\(203\) | 18.0140i | 1.26434i | ||||||||
\(204\) | 3.80785 | + | 6.59538i | 0.266603 | + | 0.461769i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −29.2340 | − | 16.8783i | −2.03683 | − | 1.17596i | ||||
\(207\) | 19.0550 | 1.32441 | ||||||||
\(208\) | 19.3803 | + | 2.42749i | 1.34378 | + | 0.168316i | ||||
\(209\) | 6.12979 | 0.424007 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.32684 | − | 9.22635i | 0.366715 | − | 0.635168i | −0.622335 | − | 0.782751i | \(-0.713816\pi\) |
0.989050 | + | 0.147583i | \(0.0471492\pi\) | |||||||
\(212\) | 14.7775 | + | 25.5953i | 1.01492 | + | 1.75789i | ||||
\(213\) | 27.6037i | 1.89138i | ||||||||
\(214\) | −15.9121 | + | 9.18688i | −1.08773 | + | 0.628002i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 31.2870i | 2.12881i | ||||||||
\(217\) | −1.39471 | − | 2.41571i | −0.0946792 | − | 0.163989i | ||||
\(218\) | −12.5723 | + | 21.7759i | −0.851505 | + | 1.47485i | ||||
\(219\) | 9.09839 | + | 5.25296i | 0.614812 | + | 0.354962i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.38724 | + | 1.83164i | −0.0933161 | + | 0.123210i | ||||
\(222\) | 5.34335 | 0.358622 | ||||||||
\(223\) | 18.4804 | + | 10.6697i | 1.23754 | + | 0.714494i | 0.968591 | − | 0.248661i | \(-0.0799905\pi\) |
0.268949 | + | 0.963155i | \(0.413324\pi\) | |||||||
\(224\) | −2.28694 | + | 3.96110i | −0.152803 | + | 0.264662i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 16.6901i | − | 1.11021i | ||||||
\(227\) | −13.5842 | + | 7.84283i | −0.901613 | + | 0.520547i | −0.877723 | − | 0.479168i | \(-0.840938\pi\) |
−0.0238900 | + | 0.999715i | \(0.507605\pi\) | |||||||
\(228\) | −59.3241 | + | 34.2508i | −3.92884 | + | 2.26831i | ||||
\(229\) | 7.62085i | 0.503600i | 0.967779 | + | 0.251800i | \(0.0810225\pi\) | ||||
−0.967779 | + | 0.251800i | \(0.918977\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.87972 | + | 4.98782i | −0.189472 | + | 0.328175i | ||||
\(232\) | −45.5182 | − | 26.2800i | −2.98842 | − | 1.72536i | ||||
\(233\) | −19.0550 | −1.24833 | −0.624166 | − | 0.781292i | \(-0.714561\pi\) | ||||
−0.624166 | + | 0.781292i | \(0.714561\pi\) | |||||||
\(234\) | −41.3802 | + | 17.4461i | −2.70511 | + | 1.14049i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.71306 | − | 1.56639i | −0.176605 | − | 0.101963i | ||||
\(237\) | 13.1722 | − | 22.8149i | 0.855625 | − | 1.48199i | ||||
\(238\) | −1.51493 | − | 2.62393i | −0.0981980 | − | 0.170084i | ||||
\(239\) | 12.7535i | 0.824954i | 0.910968 | + | 0.412477i | \(0.135336\pi\) | ||||
−0.910968 | + | 0.412477i | \(0.864664\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.4550 | + | 12.9644i | −1.44646 | + | 0.835111i | −0.998268 | − | 0.0588285i | \(-0.981263\pi\) |
−0.448187 | + | 0.893940i | \(0.647930\pi\) | |||||||
\(242\) | − | 24.5967i | − | 1.58114i | ||||||
\(243\) | 7.11778 | + | 12.3284i | 0.456606 | + | 0.790864i | ||||
\(244\) | 8.87483 | − | 15.3717i | 0.568153 | − | 0.984069i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.89022 | 0.120516 | ||||||||
\(247\) | −16.4752 | − | 12.4780i | −1.04829 | − | 0.793954i | ||||
\(248\) | 8.13878 | 0.516813 | ||||||||
\(249\) | 12.5289 | + | 7.23357i | 0.793987 | + | 0.458409i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.80593 | + | 6.59207i | 0.240228 | + | 0.416088i | 0.960779 | − | 0.277314i | \(-0.0894444\pi\) |
−0.720551 | + | 0.693402i | \(0.756111\pi\) | |||||||
\(252\) | − | 40.1996i | − | 2.53234i | ||||||
\(253\) | −3.53578 | + | 2.04139i | −0.222293 | + | 0.128341i | ||||
\(254\) | −3.21907 | + | 1.85853i | −0.201982 | + | 0.116614i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.2286 | + | 28.1087i | 1.01429 | + | 1.75680i | ||||
\(257\) | −0.167891 | + | 0.290796i | −0.0104728 | + | 0.0181394i | −0.871214 | − | 0.490903i | \(-0.836667\pi\) |
0.860742 | + | 0.509042i | \(0.170000\pi\) | |||||||
\(258\) | 3.89322 | + | 2.24775i | 0.242382 | + | 0.139939i | ||||
\(259\) | −1.44310 | −0.0896700 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 47.1906 | 2.92103 | ||||||||
\(262\) | 8.91865 | + | 5.14918i | 0.550996 | + | 0.318118i | ||||
\(263\) | −2.68795 | + | 4.65566i | −0.165746 | + | 0.287080i | −0.936920 | − | 0.349544i | \(-0.886336\pi\) |
0.771174 | + | 0.636624i | \(0.219670\pi\) | |||||||
\(264\) | −8.40224 | − | 14.5531i | −0.517122 | − | 0.895681i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 23.6017 | − | 13.6264i | 1.44711 | − | 0.835491i | ||||
\(267\) | 30.7932 | − | 17.7785i | 1.88451 | − | 1.08802i | ||||
\(268\) | 34.2212i | 2.09039i | ||||||||
\(269\) | 0.655192 | + | 1.13483i | 0.0399478 | + | 0.0691916i | 0.885308 | − | 0.465005i | \(-0.153948\pi\) |
−0.845360 | + | 0.534197i | \(0.820614\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0851 | − | 5.82266i | −0.612629 | − | 0.353701i | 0.161365 | − | 0.986895i | \(-0.448410\pi\) |
−0.773994 | + | 0.633194i | \(0.781744\pi\) | |||||||
\(272\) | 3.45214 | 0.209317 | ||||||||
\(273\) | 17.8933 | − | 7.54390i | 1.08295 | − | 0.456577i | ||||
\(274\) | −50.1838 | −3.03171 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 22.8129 | − | 39.5130i | 1.37317 | − | 2.37841i | ||||
\(277\) | 10.1581 | + | 17.5943i | 0.610338 | + | 1.05714i | 0.991183 | + | 0.132498i | \(0.0422999\pi\) |
−0.380845 | + | 0.924639i | \(0.624367\pi\) | |||||||
\(278\) | − | 51.9697i | − | 3.11693i | ||||||
\(279\) | −6.32835 | + | 3.65368i | −0.378869 | + | 0.218740i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8744i | 0.708366i | 0.935176 | + | 0.354183i | \(0.115241\pi\) | ||||
−0.935176 | + | 0.354183i | \(0.884759\pi\) | |||||||
\(282\) | 33.3184 | + | 57.7091i | 1.98408 | + | 3.43653i | ||||
\(283\) | 11.3261 | − | 19.6173i | 0.673264 | − | 1.16613i | −0.303709 | − | 0.952765i | \(-0.598225\pi\) |
0.976973 | − | 0.213363i | \(-0.0684418\pi\) | |||||||
\(284\) | 35.7509 | + | 20.6408i | 2.12143 | + | 1.22481i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.80936 | − | 7.67038i | 0.343515 | − | 0.453559i | ||||
\(287\) | −0.510500 | −0.0301339 | ||||||||
\(288\) | 10.3767 | + | 5.99102i | 0.611455 | + | 0.353024i | ||||
\(289\) | 8.29695 | − | 14.3707i | 0.488056 | − | 0.845337i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.9336i | 0.699562i | ||||||||
\(292\) | 13.6067 | − | 7.85584i | 0.796272 | − | 0.459728i | ||||
\(293\) | 16.1191 | − | 9.30636i | 0.941687 | − | 0.543683i | 0.0511983 | − | 0.998689i | \(-0.483696\pi\) |
0.890489 | + | 0.455005i | \(0.150363\pi\) | |||||||
\(294\) | − | 23.7745i | − | 1.38656i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.10529 | − | 3.64647i | 0.122367 | − | 0.211946i | ||||
\(297\) | 5.21245 | + | 3.00941i | 0.302457 | + | 0.174624i | ||||
\(298\) | 33.3593 | 1.93245 | ||||||||
\(299\) | 13.6587 | + | 1.71083i | 0.789905 | + | 0.0989400i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05146 | − | 0.607061i | −0.0606052 | − | 0.0349904i | ||||
\(302\) | 22.8319 | − | 39.5459i | 1.31383 | − | 2.27561i | ||||
\(303\) | −21.5512 | − | 37.3278i | −1.23808 | − | 2.14443i | ||||
\(304\) | 31.0513i | 1.78091i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.87381 | + | 3.96859i | −0.392949 | + | 0.226869i | ||||
\(307\) | 3.14776i | 0.179652i | 0.995957 | + | 0.0898262i | \(0.0286311\pi\) | ||||
−0.995957 | + | 0.0898262i | \(0.971369\pi\) | |||||||
\(308\) | 4.30664 | + | 7.45932i | 0.245394 | + | 0.425034i | ||||
\(309\) | 19.1192 | − | 33.1154i | 1.08765 | − | 1.88387i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.18059 | 0.180355 | 0.0901774 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901774 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(312\) | −7.04170 | + | 56.2186i | −0.398658 | + | 3.18275i | ||||
\(313\) | −35.3533 | −1.99829 | −0.999144 | − | 0.0413596i | \(-0.986831\pi\) | ||||
−0.999144 | + | 0.0413596i | \(0.986831\pi\) | |||||||
\(314\) | −5.23499 | − | 3.02242i | −0.295427 | − | 0.170565i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6991 | − | 34.1198i | −1.10816 | − | 1.91939i | ||||
\(317\) | 13.6357i | 0.765858i | 0.923778 | + | 0.382929i | \(0.125085\pi\) | ||||
−0.923778 | + | 0.382929i | \(0.874915\pi\) | |||||||
\(318\) | −42.7101 | + | 24.6587i | −2.39506 | + | 1.38279i | ||||
\(319\) | −8.75656 | + | 5.05560i | −0.490273 | + | 0.283059i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.4066 | − | 18.0248i | −0.580842 | − | 1.00605i | ||||
\(322\) | −9.07594 | + | 15.7200i | −0.505782 | + | 0.876041i | ||||
\(323\) | −3.16344 | − | 1.82641i | −0.176018 | − | 0.101624i | ||||
\(324\) | −3.96202 | −0.220112 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 39.8854 | 2.20905 | ||||||||
\(327\) | −24.6671 | − | 14.2416i | −1.36409 | − | 0.787560i | ||||
\(328\) | 0.744750 | − | 1.28994i | 0.0411219 | − | 0.0712253i | ||||
\(329\) | −8.99844 | − | 15.5858i | −0.496100 | − | 0.859271i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.9380 | + | 14.3980i | −1.37072 | + | 0.791383i | −0.991018 | − | 0.133727i | \(-0.957305\pi\) |
−0.379698 | + | 0.925110i | \(0.623972\pi\) | |||||||
\(332\) | 18.7371 | − | 10.8179i | 1.02833 | − | 0.593707i | ||||
\(333\) | 3.78044i | 0.207167i | ||||||||
\(334\) | 17.9591 | + | 31.1061i | 0.982679 | + | 1.70205i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −25.2665 | − | 14.5876i | −1.37840 | − | 0.795819i | ||||
\(337\) | 11.7493 | 0.640026 | 0.320013 | − | 0.947413i | \(-0.396313\pi\) | ||||
0.320013 | + | 0.947413i | \(0.396313\pi\) | |||||||
\(338\) | −31.2280 | + | 8.79023i | −1.69858 | + | 0.478125i | ||||
\(339\) | 18.9061 | 1.02684 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.782847 | − | 1.35593i | 0.0423936 | − | 0.0734278i | ||||
\(342\) | −35.6967 | − | 61.8285i | −1.93026 | − | 3.34330i | ||||
\(343\) | 19.7574i | 1.06680i | ||||||||
\(344\) | 3.06787 | − | 1.77124i | 0.165409 | − | 0.0954987i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 60.7630i | 3.26664i | ||||||||
\(347\) | 0.949887 | + | 1.64525i | 0.0509926 | + | 0.0883218i | 0.890395 | − | 0.455189i | \(-0.150428\pi\) |
−0.839402 | + | 0.543510i | \(0.817095\pi\) | |||||||
\(348\) | 56.4973 | − | 97.8562i | 3.02857 | − | 5.24564i | ||||
\(349\) | −8.89329 | − | 5.13454i | −0.476047 | − | 0.274846i | 0.242721 | − | 0.970096i | \(-0.421960\pi\) |
−0.718768 | + | 0.695250i | \(0.755293\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.88364 | − | 18.6991i | −0.420798 | − | 0.998084i | ||||
\(352\) | −2.56730 | −0.136838 | ||||||||
\(353\) | 0.693330 | + | 0.400294i | 0.0369022 | + | 0.0213055i | 0.518338 | − | 0.855176i | \(-0.326551\pi\) |
−0.481435 | + | 0.876482i | \(0.659884\pi\) | |||||||
\(354\) | 2.61378 | − | 4.52720i | 0.138921 | − | 0.240618i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 53.1756i | − | 2.81830i | ||||||
\(357\) | 2.97231 | − | 1.71606i | 0.157311 | − | 0.0908237i | ||||
\(358\) | 8.18714 | − | 4.72685i | 0.432704 | − | 0.249822i | ||||
\(359\) | − | 8.13272i | − | 0.429228i | −0.976699 | − | 0.214614i | \(-0.931151\pi\) | ||
0.976699 | − | 0.214614i | \(-0.0688494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.92820 | − | 12.0000i | 0.364642 | − | 0.631579i | ||||
\(362\) | 18.3439 | + | 10.5909i | 0.964135 | + | 0.556643i | ||||
\(363\) | 27.8625 | 1.46240 | ||||||||
\(364\) | 3.60929 | − | 28.8154i | 0.189178 | − | 1.51034i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.6502 | + | 14.8092i | 1.34076 | + | 0.774087i | ||||
\(367\) | −10.2632 | + | 17.7765i | −0.535737 | + | 0.927924i | 0.463390 | + | 0.886154i | \(0.346633\pi\) |
−0.999127 | + | 0.0417696i | \(0.986700\pi\) | |||||||
\(368\) | −10.3409 | − | 17.9110i | −0.539057 | − | 0.933675i | ||||
\(369\) | 1.33734i | 0.0696191i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5349 | − | 6.65968i | 0.598863 | − | 0.345754i | ||||
\(372\) | 17.4969i | 0.907173i | ||||||||
\(373\) | −8.90292 | − | 15.4203i | −0.460976 | − | 0.798433i | 0.538034 | − | 0.842923i | \(-0.319167\pi\) |
−0.999010 | + | 0.0444897i | \(0.985834\pi\) | |||||||
\(374\) | 0.850322 | − | 1.47280i | 0.0439691 | − | 0.0761568i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 52.5100 | 2.70800 | ||||||||
\(377\) | 33.8266 | + | 4.23697i | 1.74216 | + | 0.218215i | ||||
\(378\) | 26.7595 | 1.37636 | ||||||||
\(379\) | −1.77150 | − | 1.02277i | −0.0909956 | − | 0.0525363i | 0.453812 | − | 0.891098i | \(-0.350064\pi\) |
−0.544807 | + | 0.838561i | \(0.683397\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.10529 | − | 3.64647i | −0.107857 | − | 0.186814i | ||||
\(382\) | 13.5833i | 0.694982i | ||||||||
\(383\) | 6.84611 | − | 3.95261i | 0.349820 | − | 0.201969i | −0.314786 | − | 0.949163i | \(-0.601933\pi\) |
0.664606 | + | 0.747194i | \(0.268599\pi\) | |||||||
\(384\) | −41.3433 | + | 23.8696i | −2.10979 | + | 1.21809i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.1697 | − | 26.2747i | −0.772117 | − | 1.33735i | ||||
\(387\) | −1.59030 | + | 2.75447i | −0.0808393 | + | 0.140018i | ||||
\(388\) | 15.4558 | + | 8.92343i | 0.784651 | + | 0.453018i | ||||
\(389\) | 9.21171 | 0.467052 | 0.233526 | − | 0.972351i | \(-0.424974\pi\) | ||||
0.233526 | + | 0.972351i | \(0.424974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43298 | 0.123041 | ||||||||
\(392\) | −16.2244 | − | 9.36719i | −0.819458 | − | 0.473114i | ||||
\(393\) | −5.83285 | + | 10.1028i | −0.294228 | + | 0.509618i | ||||
\(394\) | −5.46304 | − | 9.46226i | −0.275224 | − | 0.476702i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 19.5409 | − | 11.2820i | 0.981968 | − | 0.566940i | ||||
\(397\) | −5.50305 | + | 3.17719i | −0.276190 | + | 0.159458i | −0.631697 | − | 0.775215i | \(-0.717641\pi\) |
0.355507 | + | 0.934674i | \(0.384308\pi\) | |||||||
\(398\) | 51.9996i | 2.60651i | ||||||||
\(399\) | 15.4356 | + | 26.7353i | 0.772748 | + | 1.33844i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.61063 | + | 2.08460i | 0.180306 | + | 0.104100i | 0.587437 | − | 0.809270i | \(-0.300137\pi\) |
−0.407130 | + | 0.913370i | \(0.633470\pi\) | |||||||
\(402\) | −57.1038 | −2.84808 | ||||||||
\(403\) | −4.86425 | + | 2.05080i | −0.242306 | + | 0.102157i | ||||
\(404\) | −64.4600 | −3.20701 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.4770 | + | 38.9314i | −1.11552 | + | 1.93213i | ||||
\(407\) | −0.405004 | − | 0.701487i | −0.0200753 | − | 0.0347714i | ||||
\(408\) | 10.0140i | 0.495767i | ||||||||
\(409\) | 8.80580 | − | 5.08403i | 0.435419 | − | 0.251389i | −0.266234 | − | 0.963909i | \(-0.585779\pi\) |
0.701652 | + | 0.712519i | \(0.252446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 56.8467i | − | 2.80404i | ||||||
\(412\) | −28.5929 | − | 49.5244i | −1.40867 | − | 2.43989i | ||||
\(413\) | −0.705915 | + | 1.22268i | −0.0347358 | + | 0.0601642i | ||||
\(414\) | 41.1811 | + | 23.7759i | 2.02394 | + | 1.16852i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.90023 | + | 5.22607i | 0.338311 | + | 0.256229i | ||||
\(417\) | 58.8697 | 2.88286 | ||||||||
\(418\) | 13.2475 | + | 7.64847i | 0.647959 | + | 0.374099i | ||||
\(419\) | −14.2954 | + | 24.7604i | −0.698378 | + | 1.20963i | 0.270651 | + | 0.962677i | \(0.412761\pi\) |
−0.969029 | + | 0.246948i | \(0.920572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.01797i | 0.0983498i | 0.998790 | + | 0.0491749i | \(0.0156592\pi\) | ||||
−0.998790 | + | 0.0491749i | \(0.984341\pi\) | |||||||
\(422\) | 23.0244 | − | 13.2932i | 1.12081 | − | 0.647101i | ||||
\(423\) | −40.8295 | + | 23.5729i | −1.98520 | + | 1.14615i | ||||
\(424\) | 38.8623i | 1.88732i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −34.4427 | + | 59.6564i | −1.66875 | + | 2.89036i | ||||
\(427\) | −6.92747 | − | 3.99957i | −0.335244 | − | 0.193553i | ||||
\(428\) | −31.1264 | −1.50455 | ||||||||
\(429\) | 8.68878 | + | 6.58068i | 0.419498 | + | 0.317718i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.8508 | + | 10.3061i | 0.859842 | + | 0.496430i | 0.863959 | − | 0.503562i | \(-0.167977\pi\) |
−0.00411765 | + | 0.999992i | \(0.501311\pi\) | |||||||
\(432\) | −15.2446 | + | 26.4044i | −0.733455 | + | 1.27038i | ||||
\(433\) | −14.7178 | − | 25.4920i | −0.707292 | − | 1.22507i | −0.965858 | − | 0.259072i | \(-0.916583\pi\) |
0.258566 | − | 0.965994i | \(-0.416750\pi\) | |||||||
\(434\) | − | 6.96103i | − | 0.334140i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.8899 | + | 21.2984i | −1.76670 | + | 1.02001i | ||||
\(437\) | 21.8841i | 1.04686i | ||||||||
\(438\) | 13.1088 | + | 22.7051i | 0.626362 | + | 1.08489i | ||||
\(439\) | 8.47602 | − | 14.6809i | 0.404538 | − | 0.700681i | −0.589729 | − | 0.807601i | \(-0.700765\pi\) |
0.994268 | + | 0.106920i | \(0.0340988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.8205 | 0.800978 | ||||||||
\(442\) | −5.28351 | + | 2.22756i | −0.251311 | + | 0.105954i | ||||
\(443\) | 24.1399 | 1.14692 | 0.573461 | − | 0.819233i | \(-0.305600\pi\) | ||||
0.573461 | + | 0.819233i | \(0.305600\pi\) | |||||||
\(444\) | 7.83925 | + | 4.52599i | 0.372034 | + | 0.214794i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.6262 | + | 46.1180i | 1.26079 | + | 2.18375i | ||||
\(447\) | 37.7885i | 1.78733i | ||||||||
\(448\) | 7.99118 | − | 4.61371i | 0.377548 | − | 0.217977i | ||||
\(449\) | 18.0679 | − | 10.4315i | 0.852676 | − | 0.492293i | −0.00887706 | − | 0.999961i | \(-0.502826\pi\) |
0.861553 | + | 0.507668i | \(0.169492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.143271 | − | 0.248153i | −0.00674637 | − | 0.0116851i | ||||
\(452\) | 14.1371 | − | 24.4861i | 0.664952 | − | 1.15173i | ||||
\(453\) | 44.7965 | + | 25.8633i | 2.10472 | + | 1.21516i | ||||
\(454\) | −39.1437 | −1.83710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −90.0739 | −4.21810 | ||||||||
\(457\) | −26.4708 | − | 15.2830i | −1.23825 | − | 0.714906i | −0.269517 | − | 0.962996i | \(-0.586864\pi\) |
−0.968737 | + | 0.248089i | \(0.920197\pi\) | |||||||
\(458\) | −9.50894 | + | 16.4700i | −0.444324 | + | 0.769591i | ||||
\(459\) | −1.79335 | − | 3.10617i | −0.0837063 | − | 0.144984i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.05146 | − | 2.33911i | 0.188695 | − | 0.108943i | −0.402676 | − | 0.915342i | \(-0.631920\pi\) |
0.591372 | + | 0.806399i | \(0.298587\pi\) | |||||||
\(462\) | −12.4471 | + | 7.18636i | −0.579094 | + | 0.334340i | ||||
\(463\) | − | 14.0011i | − | 0.650688i | −0.945596 | − | 0.325344i | \(-0.894520\pi\) | ||
0.945596 | − | 0.325344i | \(-0.105480\pi\) | |||||||
\(464\) | −25.6098 | − | 44.3575i | −1.18891 | − | 2.05925i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41.1811 | − | 23.7759i | −1.90768 | − | 1.10140i | ||||
\(467\) | −6.98506 | −0.323230 | −0.161615 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161615 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(468\) | −75.4866 | − | 9.45512i | −3.48937 | − | 0.437063i | ||||
\(469\) | 15.4223 | 0.712135 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.42371 | − | 5.93004i | 0.157756 | − | 0.273242i | ||||
\(472\) | −2.05967 | − | 3.56745i | −0.0948039 | − | 0.164205i | ||||
\(473\) | − | 0.681482i | − | 0.0313346i | ||||||
\(474\) | 56.9347 | − | 32.8713i | 2.61510 | − | 1.50983i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 5.13277i | − | 0.235260i | ||||||
\(477\) | −17.4461 | − | 30.2176i | −0.798804 | − | 1.38357i | ||||
\(478\) | −15.9132 | + | 27.5625i | −0.727853 | + | 1.26068i | ||||
\(479\) | −14.1065 | − | 8.14438i | −0.644542 | − | 0.372126i | 0.141820 | − | 0.989892i | \(-0.454704\pi\) |
−0.786362 | + | 0.617766i | \(0.788038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.339423 | + | 2.70985i | −0.0154764 | + | 0.123558i | ||||
\(482\) | −64.7056 | −2.94726 | ||||||||
\(483\) | −17.8071 | − | 10.2810i | −0.810253 | − | 0.467800i | ||||
\(484\) | 20.8343 | − | 36.0860i | 0.947012 | − | 1.64027i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 35.5249i | 1.61144i | ||||||||
\(487\) | −17.3559 | + | 10.0204i | −0.786471 | + | 0.454069i | −0.838719 | − | 0.544565i | \(-0.816695\pi\) |
0.0522474 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(488\) | 20.2125 | − | 11.6697i | 0.914975 | − | 0.528261i | ||||
\(489\) | 45.1810i | 2.04316i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.89916 | + | 13.6818i | −0.356484 | + | 0.617449i | −0.987371 | − | 0.158426i | \(-0.949358\pi\) |
0.630887 | + | 0.775875i | \(0.282691\pi\) | |||||||
\(492\) | 2.77315 | + | 1.60108i | 0.125023 | + | 0.0721823i | ||||
\(493\) | 6.02540 | 0.271370 | ||||||||
\(494\) | −20.0364 | − | 47.5241i | −0.901481 | − | 2.13821i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.86865 | + | 3.96562i | 0.308411 | + | 0.178061i | ||||
\(497\) | 9.30208 | − | 16.1117i | 0.417255 | − | 0.722708i | ||||
\(498\) | 18.0514 | + | 31.2660i | 0.808903 | + | 1.40106i | ||||
\(499\) | 1.24651i | 0.0558016i | 0.999611 | + | 0.0279008i | \(0.00888226\pi\) | ||||
−0.999611 | + | 0.0279008i | \(0.991118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.2361 | + | 20.3436i | −1.57423 | + | 0.908883i | ||||
\(502\) | 18.9955i | 0.847809i | ||||||||
\(503\) | −3.82672 | − | 6.62808i | −0.170625 | − | 0.295532i | 0.768013 | − | 0.640434i | \(-0.221245\pi\) |
−0.938639 | + | 0.344902i | \(0.887912\pi\) | |||||||
\(504\) | 26.4296 | − | 45.7774i | 1.17727 | − | 2.03909i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.1886 | −0.452938 | ||||||||
\(507\) | −9.95732 | − | 35.3742i | −0.442220 | − | 1.57102i | ||||
\(508\) | −6.29695 | −0.279382 | ||||||||
\(509\) | −22.2777 | − | 12.8621i | −0.987444 | − | 0.570101i | −0.0829345 | − | 0.996555i | \(-0.526429\pi\) |
−0.904509 | + | 0.426454i | \(0.859763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.54035 | − | 6.13207i | −0.156616 | − | 0.271267i | ||||
\(512\) | 47.2215i | 2.08691i | ||||||||
\(513\) | 27.9393 | − | 16.1308i | 1.23355 | − | 0.712192i | ||||
\(514\) | −0.725685 | + | 0.418974i | −0.0320086 | + | 0.0184802i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.80785 | + | 6.59538i | 0.167631 | + | 0.290346i | ||||
\(517\) | 5.05080 | − | 8.74824i | 0.222134 | − | 0.384747i | ||||
\(518\) | −3.11879 | − | 1.80064i | −0.137032 | − | 0.0791154i | ||||
\(519\) | −68.8305 | −3.02132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1519 | −1.32098 | −0.660490 | − | 0.750835i | \(-0.729651\pi\) | ||||
−0.660490 | + | 0.750835i | \(0.729651\pi\) | |||||||
\(522\) | 101.987 | + | 58.8823i | 4.46386 | + | 2.57721i | ||||
\(523\) | 1.96876 | − | 3.41000i | 0.0860880 | − | 0.149109i | −0.819766 | − | 0.572698i | \(-0.805897\pi\) |
0.905854 | + | 0.423589i | \(0.139230\pi\) | |||||||
\(524\) | 8.72307 | + | 15.1088i | 0.381069 | + | 0.660031i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6182 | + | 6.70779i | −0.506579 | + | 0.292473i | ||||
\(527\) | −0.808017 | + | 0.466509i | −0.0351978 | + | 0.0203215i | ||||
\(528\) | − | 16.3759i | − | 0.712672i | ||||||
\(529\) | 4.21200 | + | 7.29539i | 0.183130 | + | 0.317191i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.20301 | + | 1.84926i | 0.138999 | + | 0.0802510i | ||||
\(532\) | 46.1682 | 2.00165 | ||||||||
\(533\) | −0.120072 | + | 0.958614i | −0.00520088 | + | 0.0415222i | ||||
\(534\) | 88.7326 | 3.83983 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −22.4990 | + | 38.9694i | −0.971809 | + | 1.68322i | ||||
\(537\) | 5.35444 | + | 9.27415i | 0.231061 | + | 0.400209i | ||||
\(538\) | 3.27007i | 0.140983i | ||||||||
\(539\) | −3.12117 | + | 1.80201i | −0.134438 | + | 0.0776180i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8881i | 0.683083i | 0.939867 | + | 0.341541i | \(0.110949\pi\) | ||||
−0.939867 | + | 0.341541i | \(0.889051\pi\) | |||||||
\(542\) | −14.5305 | − | 25.1675i | −0.624138 | − | 1.08104i | ||||
\(543\) | −11.9970 | + | 20.7795i | −0.514842 | + | 0.891732i | ||||
\(544\) | 1.32492 | + | 0.764945i | 0.0568057 | + | 0.0327968i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 48.0833 | + | 6.02271i | 2.05778 | + | 0.257748i | ||||
\(547\) | 6.56107 | 0.280531 | 0.140266 | − | 0.990114i | \(-0.455204\pi\) | ||||
0.140266 | + | 0.990114i | \(0.455204\pi\) | |||||||
\(548\) | −73.6249 | − | 42.5074i | −3.14510 | − | 1.81582i | ||||
\(549\) | −10.4775 | + | 18.1476i | −0.447170 | + | 0.774522i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.1972i | 2.30888i | ||||||||
\(552\) | 51.9564 | − | 29.9970i | 2.21141 | − | 1.27676i | ||||
\(553\) | −15.3766 | + | 8.87769i | −0.653880 | + | 0.377518i | ||||
\(554\) | 50.6990i | 2.15399i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 44.0200 | − | 76.2450i | 1.86687 | − | 3.23351i | ||||
\(557\) | −6.79835 | − | 3.92503i | −0.288055 | − | 0.166309i | 0.349009 | − | 0.937119i | \(-0.386518\pi\) |
−0.637065 | + | 0.770810i | \(0.719852\pi\) | |||||||
\(558\) | −18.2356 | −0.771973 | ||||||||
\(559\) | −1.38724 | + | 1.83164i | −0.0586741 | + | 0.0774702i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.66835 | + | 0.963220i | 0.0704377 | + | 0.0406672i | ||||
\(562\) | −14.8163 | + | 25.6626i | −0.624988 | + | 1.08251i | ||||
\(563\) | 7.77976 | + | 13.4749i | 0.327878 | + | 0.567901i | 0.982091 | − | 0.188410i | \(-0.0603333\pi\) |
−0.654213 | + | 0.756310i | \(0.727000\pi\) | |||||||
\(564\) | 112.887i | 4.75341i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 48.9552 | − | 28.2643i | 2.05774 | − | 1.18804i | ||||
\(567\) | 1.78554i | 0.0749857i | ||||||||
\(568\) | 27.1409 | + | 47.0095i | 1.13881 | + | 1.97247i | ||||
\(569\) | 1.73957 | − | 3.01303i | 0.0729267 | − | 0.126313i | −0.827256 | − | 0.561825i | \(-0.810099\pi\) |
0.900183 | + | 0.435512i | \(0.143433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5118 | 0.900240 | 0.450120 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450120 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(572\) | 15.0200 | − | 6.33252i | 0.628018 | − | 0.264776i | ||||
\(573\) | −15.3868 | −0.642791 | ||||||||
\(574\) | −1.10328 | − | 0.636978i | −0.0460500 | − | 0.0265870i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.0864 | − | 20.9342i | −0.503599 | − | 0.872259i | ||||
\(577\) | − | 9.97608i | − | 0.415310i | −0.978202 | − | 0.207655i | \(-0.933417\pi\) | ||
0.978202 | − | 0.207655i | \(-0.0665831\pi\) | |||||||
\(578\) | 35.8623 | − | 20.7051i | 1.49167 | − | 0.861218i | ||||
\(579\) | 29.7632 | − | 17.1838i | 1.23692 | − | 0.714134i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.87523 | − | 8.44414i | −0.202259 | − | 0.350322i | ||||
\(582\) | −14.8902 | + | 25.7907i | −0.617221 | + | 1.06906i | ||||
\(583\) | 6.47451 | + | 3.73806i | 0.268147 | + | 0.154815i | ||||
\(584\) | 20.6595 | 0.854898 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.4482 | 1.91876 | ||||||||
\(587\) | −20.8341 | − | 12.0286i | −0.859915 | − | 0.496472i | 0.00406862 | − | 0.999992i | \(-0.498705\pi\) |
−0.863984 | + | 0.503519i | \(0.832038\pi\) | |||||||
\(588\) | 20.1378 | − | 34.8797i | 0.830469 | − | 1.43841i | ||||
\(589\) | −4.19615 | − | 7.26795i | −0.172899 | − | 0.299471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.7186 | − | 6.18837i | 0.440903 | − | 0.254556i | ||||
\(592\) | 3.55348 | − | 2.05160i | 0.146047 | − | 0.0843203i | ||||
\(593\) | 0.940219i | 0.0386102i | 0.999814 | + | 0.0193051i | \(0.00614538\pi\) | ||||
−0.999814 | + | 0.0193051i | \(0.993855\pi\) | |||||||
\(594\) | 7.51001 | + | 13.0077i | 0.308139 | + | 0.533713i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 48.9417 | + | 28.2565i | 2.00473 | + | 1.15743i | ||||
\(597\) | −58.9037 | −2.41077 | ||||||||
\(598\) | 27.3842 | + | 20.7401i | 1.11982 | + | 0.848128i | ||||
\(599\) | −11.4270 | −0.466896 | −0.233448 | − | 0.972369i | \(-0.575001\pi\) | ||||
−0.233448 | + | 0.972369i | \(0.575001\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0215 | − | 31.2142i | 0.735114 | − | 1.27325i | −0.219560 | − | 0.975599i | \(-0.570462\pi\) |
0.954674 | − | 0.297655i | \(-0.0962045\pi\) | |||||||
\(602\) | −1.51493 | − | 2.62393i | −0.0617437 | − | 0.106943i | ||||
\(603\) | − | 40.4012i | − | 1.64526i | ||||||
\(604\) | 66.9935 | − | 38.6787i | 2.72593 | − | 1.57381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 107.562i | − | 4.36942i | ||||||
\(607\) | 19.9454 | + | 34.5464i | 0.809557 | + | 1.40219i | 0.913171 | + | 0.407576i | \(0.133626\pi\) |
−0.103614 | + | 0.994618i | \(0.533041\pi\) | |||||||
\(608\) | −6.88052 | + | 11.9174i | −0.279042 | + | 0.483315i | ||||
\(609\) | −44.1003 | − | 25.4613i | −1.78704 | − | 1.03175i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.3833 | + | 13.2314i | −1.26963 | + | 0.535285i | ||||
\(612\) | −13.4461 | −0.543528 | ||||||||
\(613\) | −0.299187 | − | 0.172736i | −0.0120841 | − | 0.00697673i | 0.493946 | − | 0.869493i | \(-0.335554\pi\) |
−0.506030 | + | 0.862516i | \(0.668887\pi\) | |||||||
\(614\) | −3.92763 | + | 6.80286i | −0.158506 | + | 0.274541i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3258i | 0.456328i | ||||||||
\(617\) | −33.5022 | + | 19.3425i | −1.34875 | + | 0.778700i | −0.988072 | − | 0.153991i | \(-0.950787\pi\) |
−0.360676 | + | 0.932691i | \(0.617454\pi\) | |||||||
\(618\) | 82.6398 | − | 47.7121i | 3.32426 | − | 1.91926i | ||||
\(619\) | − | 14.8971i | − | 0.598764i | −0.954133 | − | 0.299382i | \(-0.903219\pi\) | ||
0.954133 | − | 0.299382i | \(-0.0967805\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.7440 | + | 18.6091i | −0.431141 | + | 0.746758i | ||||
\(622\) | 6.87381 | + | 3.96859i | 0.275615 | + | 0.159126i | ||||
\(623\) | −23.9644 | −0.960113 | ||||||||
\(624\) | −33.3353 | + | 44.0142i | −1.33448 | + | 1.76198i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −76.4047 | − | 44.1123i | −3.05374 | − | 1.76308i | ||||
\(627\) | −8.66397 | + | 15.0064i | −0.346006 | + | 0.599299i | ||||
\(628\) | −5.12019 | − | 8.86842i | −0.204318 | − | 0.353889i | ||||
\(629\) | 0.482694i | 0.0192463i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.6408 | − | 19.4225i | 1.33922 | − | 0.773198i | 0.352526 | − | 0.935802i | \(-0.385323\pi\) |
0.986691 | + | 0.162604i | \(0.0519893\pi\) | |||||||
\(632\) | − | 51.8053i | − | 2.06071i | ||||||
\(633\) | 15.0581 | + | 26.0814i | 0.598506 | + | 1.03664i | ||||
\(634\) | −17.0140 | + | 29.4691i | −0.675713 | + | 1.17037i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −83.5470 | −3.31285 | ||||||||
\(637\) | 12.0571 | + | 1.51022i | 0.477719 | + | 0.0598370i | ||||
\(638\) | −25.2326 | −0.998967 | ||||||||
\(639\) | −42.2072 | − | 24.3683i | −1.66969 | − | 0.963996i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.5908 | + | 32.2003i | 0.734293 | + | 1.27183i | 0.955033 | + | 0.296501i | \(0.0958197\pi\) |
−0.220739 | + | 0.975333i | \(0.570847\pi\) | |||||||
\(642\) | − | 51.9397i | − | 2.04990i | ||||||
\(643\) | −7.88410 | + | 4.55189i | −0.310918 | + | 0.179509i | −0.647337 | − | 0.762204i | \(-0.724118\pi\) |
0.336419 | + | 0.941712i | \(0.390784\pi\) | |||||||
\(644\) | −26.6307 | + | 15.3753i | −1.04940 | + | 0.605870i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.55783 | − | 7.89439i | −0.179325 | − | 0.310601i | ||||
\(647\) | 9.56118 | − | 16.5605i | 0.375889 | − | 0.651059i | −0.614571 | − | 0.788862i | \(-0.710671\pi\) |
0.990460 | + | 0.137803i | \(0.0440041\pi\) | |||||||
\(648\) | −4.51175 | − | 2.60486i | −0.177238 | − | 0.102329i | ||||
\(649\) | −0.792455 | −0.0311066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.88525 | 0.309047 | ||||||||
\(652\) | 58.5161 | + | 33.7843i | 2.29167 | + | 1.32309i | ||||
\(653\) | 17.3162 | − | 29.9926i | 0.677636 | − | 1.17370i | −0.298055 | − | 0.954549i | \(-0.596338\pi\) |
0.975691 | − | 0.219152i | \(-0.0703289\pi\) | |||||||
\(654\) | −35.5399 | − | 61.5570i | −1.38972 | − | 2.40707i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.25705 | − | 0.725758i | 0.0490796 | − | 0.0283361i | ||||
\(657\) | −16.0640 | + | 9.27453i | −0.626714 | + | 0.361834i | ||||
\(658\) | − | 44.9114i | − | 1.75083i | ||||||
\(659\) | 3.34926 | + | 5.80109i | 0.130469 | + | 0.225978i | 0.923857 | − | 0.382737i | \(-0.125018\pi\) |
−0.793389 | + | 0.608715i | \(0.791685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.22004 | + | 3.01379i | 0.203036 | + | 0.117223i | 0.598071 | − | 0.801443i | \(-0.295934\pi\) |
−0.395035 | + | 0.918666i | \(0.629268\pi\) | |||||||
\(662\) | −71.8604 | −2.79294 | ||||||||
\(663\) | −2.52331 | − | 5.98501i | −0.0979974 | − | 0.232438i | ||||
\(664\) | 28.4492 | 1.10404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.71706 | + | 8.17018i | −0.182782 | + | 0.316588i | ||||
\(667\) | −18.0491 | − | 31.2620i | −0.698865 | − | 1.21047i | ||||
\(668\) | 60.8479i | 2.35428i | ||||||||
\(669\) | −52.2411 | + | 30.1614i | −2.01976 | + | 1.16611i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.48990i | − | 0.173330i | ||||||
\(672\) | −6.46481 | − | 11.1974i | −0.249386 | − | 0.431948i | ||||
\(673\) | −11.6784 | + | 20.2276i | −0.450169 | + | 0.779715i | −0.998396 | − | 0.0566140i | \(-0.981970\pi\) |
0.548227 | + | 0.836329i | \(0.315303\pi\) | |||||||
\(674\) | 25.3923 | + | 14.6603i | 0.978075 | + | 0.564692i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −53.2604 | − | 13.5550i | −2.04848 | − | 0.521346i | ||||
\(677\) | 45.4042 | 1.74503 | 0.872513 | − | 0.488590i | \(-0.162489\pi\) | ||||
0.872513 | + | 0.488590i | \(0.162489\pi\) | |||||||
\(678\) | 40.8593 | + | 23.5901i | 1.56919 | + | 0.905973i | ||||
\(679\) | 4.02148 | − | 6.96540i | 0.154330 | − | 0.267308i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 44.3408i | − | 1.69914i | ||||||
\(682\) | 3.38374 | − | 1.95360i | 0.129570 | − | 0.0748073i | ||||
\(683\) | −22.0817 | + | 12.7489i | −0.844934 | + | 0.487823i | −0.858938 | − | 0.512079i | \(-0.828875\pi\) |
0.0140045 | + | 0.999902i | \(0.495542\pi\) | |||||||
\(684\) | − | 120.945i | − | 4.62445i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.6523 | + | 42.6991i | −0.941230 | + | 1.63026i | ||||
\(687\) | −18.6567 | − | 10.7715i | −0.711798 | − | 0.410957i | ||||
\(688\) | 3.45214 | 0.131612 | ||||||||
\(689\) | −9.79246 | − | 23.2266i | −0.373063 | − | 0.884862i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.71257 | + | 3.29815i | 0.217316 | + | 0.125468i | 0.604707 | − | 0.796448i | \(-0.293290\pi\) |
−0.387391 | + | 0.921916i | \(0.626624\pi\) | |||||||
\(692\) | −51.4683 | + | 89.1457i | −1.95653 | + | 3.38881i | ||||
\(693\) | −5.08438 | − | 8.80641i | −0.193140 | − | 0.334528i | ||||
\(694\) | 4.74090i | 0.179962i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 128.673 | − | 74.2892i | 4.87733 | − | 2.81593i | ||||
\(697\) | 0.170754i | 0.00646778i | ||||||||
\(698\) | −12.8133 | − | 22.1933i | −0.484990 | − | 0.840028i | ||||
\(699\) | 26.9327 | − | 46.6487i | 1.01869 | − | 1.76442i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.2474 | −1.10466 | −0.552329 | − | 0.833626i | \(-0.686261\pi\) | ||||
−0.552329 | + | 0.833626i | \(0.686261\pi\) | |||||||
\(702\) | 6.29394 | − | 50.2488i | 0.237550 | − | 1.89652i | ||||
\(703\) | −4.34174 | −0.163752 | ||||||||
\(704\) | 4.48542 | + | 2.58966i | 0.169051 | + | 0.0976015i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.998937 | + | 1.73021i | 0.0375955 | + | 0.0651173i | ||||
\(707\) | 29.0499i | 1.09253i | ||||||||
\(708\) | 7.66938 | − | 4.42792i | 0.288233 | − | 0.166411i | ||||
\(709\) | −9.46865 | + | 5.46673i | −0.355603 | + | 0.205307i | −0.667150 | − | 0.744923i | \(-0.732486\pi\) |
0.311548 | + | 0.950231i | \(0.399153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2566 | + | 40.2815i | 0.872189 | + | 1.51068i | ||||
\(712\) | 34.9608 | − | 60.5538i | 1.31021 | − | 2.26935i | ||||
\(713\) | 4.84084 | + | 2.79486i | 0.181291 | + | 0.104668i | ||||
\(714\) | 8.56490 | 0.320533 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0152 | 0.598516 | ||||||||
\(717\) | −31.2220 | − | 18.0260i | −1.16601 | − | 0.673194i | ||||
\(718\) | 10.1476 | − | 17.5762i | 0.378706 | − | 0.655938i | ||||
\(719\) | 8.02989 | + | 13.9082i | 0.299464 | + | 0.518688i | 0.976014 | − | 0.217710i | \(-0.0698587\pi\) |
−0.676549 | + | 0.736398i | \(0.736525\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3189 | + | 12.8858i | −0.831199 | + | 0.479893i | ||||
\(722\) | 29.9461 | − | 17.2894i | 1.11448 | − | 0.643444i | ||||
\(723\) | − | 73.2966i | − | 2.72593i | ||||||
\(724\) | 17.9416 | + | 31.0758i | 0.666796 | + | 1.15492i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 60.2156 | + | 34.7655i | 2.23481 | + | 1.29027i | ||||
\(727\) | 51.3754 | 1.90541 | 0.952704 | − | 0.303900i | \(-0.0982889\pi\) | ||||
0.952704 | + | 0.303900i | \(0.0982889\pi\) | |||||||
\(728\) | 23.0550 | − | 30.4406i | 0.854475 | − | 1.12820i | ||||
\(729\) | −43.0532 | −1.59456 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.203052 | + | 0.351697i | −0.00751016 | + | 0.0130080i | ||||
\(732\) | 25.0877 | + | 43.4532i | 0.927268 | + | 1.60608i | ||||
\(733\) | 9.82358i | 0.362842i | 0.983406 | + | 0.181421i | \(0.0580697\pi\) | ||||
−0.983406 | + | 0.181421i | \(0.941930\pi\) | |||||||
\(734\) | −44.3613 | + | 25.6120i | −1.63741 | + | 0.945357i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 9.16560i | − | 0.337848i | ||||||
\(737\) | 4.32824 | + | 7.49673i | 0.159433 | + | 0.276146i | ||||
\(738\) | −1.66867 | + | 2.89022i | −0.0614246 | + | 0.106390i | ||||
\(739\) | 42.5082 | + | 24.5421i | 1.56369 | + | 0.902797i | 0.996879 | + | 0.0789487i | \(0.0251563\pi\) |
0.566811 | + | 0.823848i | \(0.308177\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.8339 | − | 22.6967i | 1.97764 | − | 0.833783i | ||||
\(742\) | 33.2386 | 1.22023 | ||||||||
\(743\) | 35.3663 | + | 20.4188i | 1.29746 | + | 0.749091i | 0.979966 | − | 0.199167i | \(-0.0638237\pi\) |
0.317499 | + | 0.948259i | \(0.397157\pi\) | |||||||
\(744\) | −11.5035 | + | 19.9247i | −0.421739 | + | 0.730473i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 44.4346i | − | 1.62687i | ||||||
\(747\) | −22.1208 | + | 12.7715i | −0.809358 | + | 0.467283i | ||||
\(748\) | 2.49503 | − | 1.44050i | 0.0912272 | − | 0.0526700i | ||||
\(749\) | 14.0276i | 0.512557i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.36340 | + | 2.36148i | −0.0497512 | + | 0.0861716i | −0.889829 | − | 0.456295i | \(-0.849176\pi\) |
0.840077 | + | 0.542467i | \(0.182510\pi\) | |||||||
\(752\) | 44.3154 | + | 25.5855i | 1.61601 | + | 0.933006i | ||||
\(753\) | −21.5175 | −0.784142 | ||||||||
\(754\) | 67.8184 | + | 51.3641i | 2.46980 | + | 1.87057i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 39.2590 | + | 22.6662i | 1.42784 | + | 0.824362i | ||||
\(757\) | 7.40301 | − | 12.8224i | 0.269067 | − | 0.466038i | −0.699554 | − | 0.714580i | \(-0.746618\pi\) |
0.968621 | + | 0.248542i | \(0.0799513\pi\) | |||||||
\(758\) | −2.55234 | − | 4.42078i | −0.0927051 | − | 0.160570i | ||||
\(759\) | − | 11.5413i | − | 0.418924i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.84575 | − | 5.68445i | 0.356908 | − | 0.206061i | −0.310815 | − | 0.950470i | \(-0.600602\pi\) |
0.667724 | + | 0.744409i | \(0.267269\pi\) | |||||||
\(762\) | − | 10.5075i | − | 0.380647i | ||||||
\(763\) | 9.59843 | + | 16.6250i | 0.347486 | + | 0.601864i | ||||
\(764\) | −11.5055 | + | 19.9281i | −0.416255 | + | 0.720975i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.7275 | 0.712784 | ||||||||
\(767\) | 2.12991 | + | 1.61314i | 0.0769065 | + | 0.0582472i | ||||
\(768\) | −91.7512 | −3.31078 | ||||||||
\(769\) | 18.2352 | + | 10.5281i | 0.657579 | + | 0.379654i | 0.791354 | − | 0.611358i | \(-0.209377\pi\) |
−0.133775 | + | 0.991012i | \(0.542710\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.474602 | − | 0.822034i | −0.0170924 | − | 0.0296048i | ||||
\(772\) | − | 51.3970i | − | 1.84982i | ||||||
\(773\) | −12.1961 | + | 7.04144i | −0.438664 | + | 0.253263i | −0.703031 | − | 0.711159i | \(-0.748170\pi\) |
0.264367 | + | 0.964422i | \(0.414837\pi\) | |||||||
\(774\) | −6.87381 | + | 3.96859i | −0.247074 | + | 0.142648i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.7336 | + | 20.3231i | 0.421210 | + | 0.729558i | ||||
\(777\) | 2.03971 | − | 3.53288i | 0.0731741 | − | 0.126741i | ||||
\(778\) | 19.9081 | + | 11.4940i | 0.713740 | + | 0.412078i | ||||
\(779\) | −1.53590 | −0.0550293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4425 | 0.373660 | ||||||||
\(782\) | 5.25809 | + | 3.03576i | 0.188029 | + | 0.108558i | ||||
\(783\) | −26.6080 | + | 46.0864i | −0.950893 | + | 1.64699i | ||||
\(784\) | −9.12832 | − | 15.8107i | −0.326011 | − | 0.564668i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.2116 | + | 14.5559i | −0.899267 | + | 0.519192i | ||||
\(787\) | 28.5998 | − | 16.5121i | 1.01947 | − | 0.588593i | 0.105522 | − | 0.994417i | \(-0.466349\pi\) |
0.913951 | + | 0.405823i | \(0.133015\pi\) | |||||||
\(788\) | − | 18.5095i | − | 0.659374i | ||||||
\(789\) | −7.59839 | − | 13.1608i | −0.270510 | − | 0.468537i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0350 | − | 6.37109i | −0.392361 | − | 0.226530i | ||||
\(792\) | 29.6697 | 1.05427 | ||||||||
\(793\) | −9.13974 | + | 12.0676i | −0.324562 | + | 0.428534i | ||||
\(794\) | −15.8574 | −0.562758 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.0454 | + | 76.2890i | −1.56115 | + | 2.70399i | ||||
\(797\) | 8.47079 | + | 14.6718i | 0.300051 | + | 0.519703i | 0.976147 | − | 0.217110i | \(-0.0696630\pi\) |
−0.676096 | + | 0.736813i | \(0.736330\pi\) | |||||||
\(798\) | 77.0395i | 2.72717i | ||||||||
\(799\) | −5.21319 | + | 3.00984i | −0.184429 | + | 0.106480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 62.7787i | 2.21817i | ||||||||
\(802\) | 5.20213 | + | 9.01036i | 0.183694 | + | 0.318167i | ||||
\(803\) | 1.98719 | − | 3.44191i | 0.0701263 | − | 0.121462i | ||||
\(804\) | −83.7774 | − | 48.3689i | −2.95460 | − | 1.70584i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.0714 | − | 1.63726i | −0.460420 | − | 0.0576701i | ||||
\(807\) | −3.70425 | −0.130396 | ||||||||
\(808\) | −73.4039 | − | 42.3798i | −2.58234 | − | 1.49092i | ||||
\(809\) | 25.8818 | − | 44.8285i | 0.909954 | − | 1.57609i | 0.0958292 | − | 0.995398i | \(-0.469450\pi\) |
0.814125 | − | 0.580689i | \(-0.197217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6699i | 0.796047i | 0.917375 | + | 0.398023i | \(0.130304\pi\) | ||||
−0.917375 | + | 0.398023i | \(0.869696\pi\) | |||||||
\(812\) | −65.9524 | + | 38.0776i | −2.31448 | + | 1.33626i | ||||
\(813\) | 28.5091 | − | 16.4597i | 0.999856 | − | 0.577267i | ||||
\(814\) | − | 2.02138i | − | 0.0708494i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.87932 | + | 8.45123i | −0.170810 | + | 0.295852i | ||||
\(817\) | −3.16344 | − | 1.82641i | −0.110675 | − | 0.0638981i | ||||
\(818\) | 25.3745 | 0.887198 | ||||||||
\(819\) | −4.26109 | + | 34.0192i | −0.148895 | + | 1.18873i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.8230 | − | 14.3315i | −0.866328 | − | 0.500174i | −0.000201482 | − | 1.00000i | \(-0.500064\pi\) |
−0.866126 | + | 0.499826i | \(0.833397\pi\) | |||||||
\(822\) | 70.9307 | − | 122.856i | 2.47399 | − | 4.28508i | ||||
\(823\) | 12.9164 | + | 22.3718i | 0.450236 | + | 0.779831i | 0.998400 | − | 0.0565391i | \(-0.0180066\pi\) |
−0.548165 | + | 0.836371i | \(0.684673\pi\) | |||||||
\(824\) | − | 75.1946i | − | 2.61953i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.05121 | + | 1.76162i | −0.106165 | + | 0.0612945i | ||||
\(827\) | − | 16.0820i | − | 0.559227i | −0.960113 | − | 0.279613i | \(-0.909794\pi\) | ||
0.960113 | − | 0.279613i | \(-0.0902063\pi\) | |||||||
\(828\) | 40.2780 | + | 69.7635i | 1.39976 | + | 2.42445i | ||||
\(829\) | −11.2909 | + | 19.5564i | −0.392149 | + | 0.679222i | −0.992733 | − | 0.120340i | \(-0.961602\pi\) |
0.600584 | + | 0.799562i | \(0.294935\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.4304 | −1.99224 | ||||||||
\(832\) | −6.78404 | − | 16.0910i | −0.235194 | − | 0.557854i | ||||
\(833\) | 2.14768 | 0.0744128 | ||||||||
\(834\) | 127.228 | + | 73.4549i | 4.40553 | + | 2.54354i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.9570 | + | 22.4422i | 0.448128 | + | 0.776181i | ||||
\(837\) | − | 8.24037i | − | 0.284829i | ||||||
\(838\) | −61.7898 | + | 35.6744i | −2.13449 | + | 1.23235i | ||||
\(839\) | 15.4533 | − | 8.92198i | 0.533508 | − | 0.308021i | −0.208936 | − | 0.977929i | \(-0.567000\pi\) |
0.742444 | + | 0.669908i | \(0.233667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.1996 | − | 52.3073i | −1.04137 | − | 1.80370i | ||||
\(842\) | −2.51793 | + | 4.36118i | −0.0867736 | + | 0.150296i | ||||
\(843\) | −29.0698 | − | 16.7835i | −1.00122 | − | 0.578053i | ||||
\(844\) | 45.0390 | 1.55031 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −117.653 | −4.04498 | ||||||||
\(847\) | −16.2627 | − | 9.38927i | −0.558793 | − | 0.322619i | ||||
\(848\) | −18.9356 | + | 32.7975i | −0.650252 | + | 1.12627i | ||||
\(849\) | 32.0169 | + | 55.4550i | 1.09882 | + | 1.90321i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.50440 | − | 1.44591i | 0.0858497 | − | 0.0495653i | ||||
\(852\) | −101.062 | + | 58.3482i | −3.46233 | + | 1.99898i | ||||
\(853\) | 19.7936i | 0.677720i | 0.940837 | + | 0.338860i | \(0.110041\pi\) | ||||
−0.940837 | + | 0.338860i | \(0.889959\pi\) | |||||||
\(854\) | −9.98097 | − | 17.2875i | −0.341542 | − | 0.591568i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35.4452 | − | 20.4643i | −1.21149 | − | 0.699456i | ||||
\(857\) | −11.7302 | −0.400696 | −0.200348 | − | 0.979725i | \(-0.564207\pi\) | ||||
−0.200348 | + | 0.979725i | \(0.564207\pi\) | |||||||
\(858\) | 10.5669 | + | 25.0634i | 0.360748 | + | 0.855652i | ||||
\(859\) | 5.37452 | 0.183376 | 0.0916882 | − | 0.995788i | \(-0.470774\pi\) | ||||
0.0916882 | + | 0.995788i | \(0.470774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.721551 | − | 1.24976i | 0.0245904 | − | 0.0425918i | ||||
\(862\) | 25.7191 | + | 44.5467i | 0.875995 | + | 1.51727i | ||||
\(863\) | 25.3234i | 0.862017i | 0.902348 | + | 0.431008i | \(0.141842\pi\) | ||||
−0.902348 | + | 0.431008i | \(0.858158\pi\) | |||||||
\(864\) | −11.7017 | + | 6.75596i | −0.398099 | + | 0.229842i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 73.4567i | − | 2.49616i | ||||||
\(867\) | 23.4541 | + | 40.6237i | 0.796544 | + | 1.37965i | ||||
\(868\) | 5.89623 | − | 10.2126i | 0.200131 | − | 0.346637i | ||||
\(869\) | −8.63084 | − | 4.98302i | −0.292781 | − | 0.169037i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.62739 | − | 28.9599i | 0.122909 | − | 0.981268i | ||||
\(872\) | −56.0112 | −1.89678 | ||||||||
\(873\) | −18.2470 | − | 10.5349i | −0.617567 | − | 0.356553i | ||||
\(874\) | −27.3060 | + | 47.2954i | −0.923640 | + | 1.59979i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.4144i | 1.50062i | ||||||||
\(877\) | −17.9194 | + | 10.3458i | −0.605095 | + | 0.349352i | −0.771043 | − | 0.636783i | \(-0.780265\pi\) |
0.165949 | + | 0.986134i | \(0.446931\pi\) | |||||||
\(878\) | 36.6363 | − | 21.1520i | 1.23642 | − | 0.713845i | ||||
\(879\) | 52.6151i | 1.77466i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.1997 | − | 41.9150i | 0.815307 | − | 1.41215i | −0.0937999 | − | 0.995591i | \(-0.529901\pi\) |
0.909107 | − | 0.416562i | \(-0.136765\pi\) | |||||||
\(882\) | 36.3521 | + | 20.9879i | 1.22404 | + | 0.706699i | ||||
\(883\) | 45.8550 | 1.54314 | 0.771572 | − | 0.636142i | \(-0.219471\pi\) | ||||
0.771572 | + | 0.636142i | \(0.219471\pi\) | |||||||
\(884\) | −9.63829 | − | 1.20725i | −0.324171 | − | 0.0406042i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.1705 | + | 30.1207i | 1.75270 | + | 1.01192i | ||||
\(887\) | −0.541169 | + | 0.937332i | −0.0181707 | + | 0.0314725i | −0.874968 | − | 0.484181i | \(-0.839118\pi\) |
0.856797 | + | 0.515654i | \(0.172451\pi\) | |||||||
\(888\) | 5.95131 | + | 10.3080i | 0.199713 | + | 0.345913i | ||||
\(889\) | 2.83781i | 0.0951772i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.867947 | + | 0.501109i | −0.0290773 | + | 0.0167878i | ||||
\(892\) | 90.2133i | 3.02056i | ||||||||
\(893\) | −27.0729 | − | 46.8916i | −0.905959 | − | 1.56917i | ||||
\(894\) | −47.1507 | + | 81.6675i | −1.57696 | + | 2.73137i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 32.1749 | 1.07489 | ||||||||
\(897\) | −23.4938 | + | 31.0200i | −0.784436 | + | 1.03573i | ||||
\(898\) | 52.0637 | 1.73739 | ||||||||
\(899\) | 11.9886 | + | 6.92163i | 0.399842 | + | 0.230849i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.22756 | − | 3.85824i | −0.0742107 | − | 0.128537i | ||||
\(902\) | − | 0.715068i | − | 0.0238092i | ||||||
\(903\) | 2.97231 | − | 1.71606i | 0.0989122 | − | 0.0571070i | ||||
\(904\) | 32.1973 | − | 18.5891i | 1.07086 | − | 0.618264i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 64.5420 | + | 111.790i | 2.14426 | + | 3.71397i | ||||
\(907\) | 22.7653 | − | 39.4307i | 0.755910 | − | 1.30928i | −0.189010 | − | 0.981975i | \(-0.560528\pi\) |
0.944920 | − | 0.327300i | \(-0.106139\pi\) | |||||||
\(908\) | −57.4279 | − | 33.1560i | −1.90581 | − | 1.10032i | ||||
\(909\) | 76.1009 | 2.52411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7417 | 1.31670 | 0.658350 | − | 0.752712i | \(-0.271255\pi\) | ||||
0.658350 | + | 0.752712i | \(0.271255\pi\) | |||||||
\(912\) | −76.0171 | − | 43.8885i | −2.51718 | − | 1.45329i | ||||
\(913\) | 2.73645 | − | 4.73967i | 0.0905632 | − | 0.156860i | ||||
\(914\) | −38.1387 | − | 66.0582i | −1.26152 | − | 2.18501i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.9012 | + | 16.1088i | −0.921883 | + | 0.532250i | ||||
\(917\) | 6.80900 | − | 3.93118i | 0.224853 | − | 0.129819i | ||||
\(918\) | − | 8.95062i | − | 0.295415i | ||||||
\(919\) | −23.4969 | − | 40.6978i | −0.775091 | − | 1.34250i | −0.934743 | − | 0.355323i | \(-0.884371\pi\) |
0.159653 | − | 0.987173i | \(-0.448963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.70608 | − | 4.44911i | −0.253924 | − | 0.146603i | ||||
\(922\) | 11.6745 | 0.384481 | ||||||||
\(923\) | −28.0665 | − | 21.2569i | −0.923821 | − | 0.699680i | ||||
\(924\) | −24.3484 | −0.801002 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.4700 | − | 30.2589i | 0.574099 | − | 0.994369i | ||||
\(927\) | 33.7565 | + | 58.4680i | 1.10871 | + | 1.92034i | ||||
\(928\) | − | 22.6991i | − | 0.745134i | ||||||
\(929\) | −13.1821 | + | 7.61066i | −0.432489 | + | 0.249698i | −0.700406 | − | 0.713744i | \(-0.746998\pi\) |
0.267917 | + | 0.963442i | \(0.413665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.3180i | 0.633121i | ||||||||
\(932\) | −40.2780 | − | 69.7635i | −1.31935 | − | 2.28518i | ||||
\(933\) | −4.49551 | + | 7.78645i | −0.147176 | + | 0.254917i | ||||
\(934\) | −15.0959 | − | 8.71564i | −0.493954 | − | 0.285184i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −79.7441 | − | 60.3963i | −2.60652 | − | 1.97412i | ||||
\(937\) | −6.07285 | −0.198392 | −0.0991958 | − | 0.995068i | \(-0.531627\pi\) | ||||
−0.0991958 | + | 0.995068i | \(0.531627\pi\) | |||||||
\(938\) | 33.3302 | + | 19.2432i | 1.08827 | + | 0.628313i | ||||
\(939\) | 49.9691 | − | 86.5490i | 1.63068 | − | 2.82442i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 0.0496576i | − | 0.00161879i | −1.00000 | 0.000809396i | \(-0.999742\pi\) | |||
1.00000 | 0.000809396i | \(-0.000257639\pi\) | ||||||||
\(942\) | 14.7985 | − | 8.54390i | 0.482160 | − | 0.278375i | ||||
\(943\) | 0.885936 | − | 0.511495i | 0.0288500 | − | 0.0166566i | ||||
\(944\) | − | 4.01429i | − | 0.130654i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.850322 | − | 1.47280i | 0.0276464 | − | 0.0478849i | ||||
\(947\) | 16.1584 | + | 9.32907i | 0.525078 | + | 0.303154i | 0.739010 | − | 0.673695i | \(-0.235294\pi\) |
−0.213932 | + | 0.976849i | \(0.568627\pi\) | |||||||
\(948\) | 111.372 | 3.61720 | ||||||||
\(949\) | −12.3475 | + | 5.20576i | −0.400816 | + | 0.168986i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.3818 | − | 19.2730i | −1.08248 | − | 0.624969i | ||||
\(952\) | 3.37458 | − | 5.84495i | 0.109371 | − | 0.189436i | ||||
\(953\) | 0.764764 | + | 1.32461i | 0.0247731 | + | 0.0429083i | 0.878146 | − | 0.478392i | \(-0.158780\pi\) |
−0.853373 | + | 0.521301i | \(0.825447\pi\) | |||||||
\(954\) | − | 87.0739i | − | 2.81912i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −46.6927 | + | 26.9581i | −1.51015 | + | 0.871886i | ||||
\(957\) | − | 28.5827i | − | 0.923948i | ||||||
\(958\) | −20.3244 | − | 35.2028i | −0.656650 | − | 1.13735i | ||||
\(959\) | −19.1566 | + | 33.1802i | −0.618598 | + | 1.07144i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | −4.11477 | + | 5.43293i | −0.132666 | + | 0.175165i | ||||
\(963\) | 36.7475 | 1.18417 | ||||||||
\(964\) | −94.9299 | − | 54.8078i | −3.05749 | − | 1.76524i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −25.6562 | − | 44.4379i | −0.825475 | − | 1.42976i | ||||
\(967\) | − | 32.1716i | − | 1.03457i | −0.855813 | − | 0.517285i | \(-0.826943\pi\) | ||
0.855813 | − | 0.517285i | \(-0.173057\pi\) | |||||||
\(968\) | 47.4501 | − | 27.3953i | 1.52510 | − | 0.880519i | ||||
\(969\) | 8.94253 | − | 5.16297i | 0.287276 | − | 0.165859i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.62705 | + | 14.9425i | 0.276855 | + | 0.479527i | 0.970601 | − | 0.240692i | \(-0.0773745\pi\) |
−0.693746 | + | 0.720219i | \(0.744041\pi\) | |||||||
\(972\) | −30.0908 | + | 52.1188i | −0.965164 | + | 1.67171i | ||||
\(973\) | −34.3609 | − | 19.8383i | −1.10156 | − | 0.635986i | ||||
\(974\) | −50.0122 | −1.60249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7442 | 0.728023 | ||||||||
\(977\) | 13.6164 | + | 7.86142i | 0.435626 | + | 0.251509i | 0.701741 | − | 0.712432i | \(-0.252407\pi\) |
−0.266114 | + | 0.963942i | \(0.585740\pi\) | |||||||
\(978\) | −56.3748 | + | 97.6440i | −1.80267 | + | 3.12231i | ||||
\(979\) | −6.72557 | − | 11.6490i | −0.214950 | − | 0.372304i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.5518 | − | 25.1447i | 1.39050 | − | 0.802807i | ||||
\(982\) | −34.1429 | + | 19.7124i | −1.08954 | + | 0.629049i | ||||
\(983\) | 38.5356i | 1.22910i | 0.788880 | + | 0.614548i | \(0.210662\pi\) | ||||
−0.788880 | + | 0.614548i | \(0.789338\pi\) | |||||||
\(984\) | 2.10529 | + | 3.64647i | 0.0671141 | + | 0.116245i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.0219 | + | 7.51821i | 0.414703 | + | 0.239429i | ||||
\(987\) | 50.8743 | 1.61935 | ||||||||
\(988\) | 10.8590 | − | 86.6944i | 0.345469 | − | 2.75812i | ||||
\(989\) | 2.43298 | 0.0773642 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.29571 | + | 7.44040i | −0.136458 | + | 0.236352i | −0.926153 | − | 0.377147i | \(-0.876905\pi\) |
0.789696 | + | 0.613499i | \(0.210238\pi\) | |||||||
\(992\) | 1.75745 | + | 3.04399i | 0.0557991 | + | 0.0966468i | ||||
\(993\) | − | 81.4014i | − | 2.58320i | ||||||
\(994\) | 40.2068 | − | 23.2134i | 1.27528 | − | 0.736285i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 61.1606i | 1.93795i | ||||||||
\(997\) | −10.2687 | − | 17.7859i | −0.325213 | − | 0.563285i | 0.656343 | − | 0.754463i | \(-0.272103\pi\) |
−0.981555 | + | 0.191178i | \(0.938769\pi\) | |||||||
\(998\) | −1.55534 | + | 2.69393i | −0.0492335 | + | 0.0852750i | ||||
\(999\) | −3.69198 | − | 2.13157i | −0.116809 | − | 0.0674398i |
(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 | 325.2.n.d.251.4 | 8 | ||
5.2 | odd | 4 | 325.2.m.b.199.1 | 8 | |||
5.3 | odd | 4 | 325.2.m.c.199.4 | 8 | |||
5.4 | even | 2 | 65.2.m.a.56.1 | yes | 8 | ||
13.6 | odd | 12 | 4225.2.a.bi.1.1 | 4 | |||
13.7 | odd | 12 | 4225.2.a.bl.1.4 | 4 | |||
13.10 | even | 6 | inner | 325.2.n.d.101.4 | 8 | ||
15.14 | odd | 2 | 585.2.bu.c.316.4 | 8 | |||
20.19 | odd | 2 | 1040.2.da.b.641.1 | 8 | |||
65.4 | even | 6 | 845.2.c.g.506.1 | 8 | |||
65.9 | even | 6 | 845.2.c.g.506.8 | 8 | |||
65.19 | odd | 12 | 845.2.a.m.1.4 | 4 | |||
65.23 | odd | 12 | 325.2.m.b.49.1 | 8 | |||
65.24 | odd | 12 | 845.2.e.n.146.4 | 8 | |||
65.29 | even | 6 | 845.2.m.g.361.4 | 8 | |||
65.34 | odd | 4 | 845.2.e.n.191.4 | 8 | |||
65.44 | odd | 4 | 845.2.e.m.191.1 | 8 | |||
65.49 | even | 6 | 65.2.m.a.36.1 | ✓ | 8 | ||
65.54 | odd | 12 | 845.2.e.m.146.1 | 8 | |||
65.59 | odd | 12 | 845.2.a.l.1.1 | 4 | |||
65.62 | odd | 12 | 325.2.m.c.49.4 | 8 | |||
65.64 | even | 2 | 845.2.m.g.316.4 | 8 | |||
195.59 | even | 12 | 7605.2.a.cj.1.4 | 4 | |||
195.149 | even | 12 | 7605.2.a.cf.1.1 | 4 | |||
195.179 | odd | 6 | 585.2.bu.c.361.4 | 8 | |||
260.179 | odd | 6 | 1040.2.da.b.881.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.1 | ✓ | 8 | 65.49 | even | 6 | ||
65.2.m.a.56.1 | yes | 8 | 5.4 | even | 2 | ||
325.2.m.b.49.1 | 8 | 65.23 | odd | 12 | |||
325.2.m.b.199.1 | 8 | 5.2 | odd | 4 | |||
325.2.m.c.49.4 | 8 | 65.62 | odd | 12 | |||
325.2.m.c.199.4 | 8 | 5.3 | odd | 4 | |||
325.2.n.d.101.4 | 8 | 13.10 | even | 6 | inner | ||
325.2.n.d.251.4 | 8 | 1.1 | even | 1 | trivial | ||
585.2.bu.c.316.4 | 8 | 15.14 | odd | 2 | |||
585.2.bu.c.361.4 | 8 | 195.179 | odd | 6 | |||
845.2.a.l.1.1 | 4 | 65.59 | odd | 12 | |||
845.2.a.m.1.4 | 4 | 65.19 | odd | 12 | |||
845.2.c.g.506.1 | 8 | 65.4 | even | 6 | |||
845.2.c.g.506.8 | 8 | 65.9 | even | 6 | |||
845.2.e.m.146.1 | 8 | 65.54 | odd | 12 | |||
845.2.e.m.191.1 | 8 | 65.44 | odd | 4 | |||
845.2.e.n.146.4 | 8 | 65.24 | odd | 12 | |||
845.2.e.n.191.4 | 8 | 65.34 | odd | 4 | |||
845.2.m.g.316.4 | 8 | 65.64 | even | 2 | |||
845.2.m.g.361.4 | 8 | 65.29 | even | 6 | |||
1040.2.da.b.641.1 | 8 | 20.19 | odd | 2 | |||
1040.2.da.b.881.1 | 8 | 260.179 | odd | 6 | |||
4225.2.a.bi.1.1 | 4 | 13.6 | odd | 12 | |||
4225.2.a.bl.1.4 | 4 | 13.7 | odd | 12 | |||
7605.2.a.cf.1.1 | 4 | 195.149 | even | 12 | |||
7605.2.a.cj.1.4 | 4 | 195.59 | even | 12 |