Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(49,325)]
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([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.m (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: | \(2.59513806569\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(1.20036 - 0.747754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.199 |
Dual form | 325.2.m.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24775 | + | 2.16117i | −0.882295 | + | 1.52818i | −0.0335125 | + | 0.999438i | \(0.510669\pi\) |
−0.848783 | + | 0.528742i | \(0.822664\pi\) | |||||||
\(3\) | 2.44811 | + | 1.41342i | 1.41342 | + | 0.816038i | 0.995709 | − | 0.0925423i | \(-0.0294993\pi\) |
0.417710 | + | 0.908580i | \(0.362833\pi\) | |||||||
\(4\) | −2.11378 | − | 3.66117i | −1.05689 | − | 1.83059i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.10929 | + | 3.52720i | −2.49411 | + | 1.43997i | ||||
\(7\) | 0.952606 | + | 1.64996i | 0.360051 | + | 0.623627i | 0.987969 | − | 0.154653i | \(-0.0494259\pi\) |
−0.627918 | + | 0.778280i | \(0.716093\pi\) | |||||||
\(8\) | 5.55889 | 1.96536 | ||||||||
\(9\) | 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 | \(0.615125\pi\) | |||||||
\(12\) | − | 11.9506i | − | 3.44985i | ||||||
\(13\) | −3.32235 | + | 1.40072i | −0.921453 | + | 0.388490i | ||||
\(14\) | −4.75447 | −1.27069 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.70857 | + | 4.69138i | −0.677142 | + | 1.17284i | ||||
\(17\) | 0.551886 | − | 0.318632i | 0.133852 | − | 0.0772795i | −0.431579 | − | 0.902075i | \(-0.642043\pi\) |
0.565431 | + | 0.824796i | \(0.308710\pi\) | |||||||
\(18\) | −12.4551 | −2.93570 | ||||||||
\(19\) | −4.96410 | + | 2.86603i | −1.13884 | + | 0.657511i | −0.946144 | − | 0.323747i | \(-0.895057\pi\) |
−0.192699 | + | 0.981258i | \(0.561724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.38573i | 1.17526i | ||||||||
\(22\) | −2.31114 | + | 1.33433i | −0.492736 | + | 0.284481i | ||||
\(23\) | 3.30636 | + | 1.90893i | 0.689423 | + | 0.398039i | 0.803396 | − | 0.595445i | \(-0.203024\pi\) |
−0.113973 | + | 0.993484i | \(0.536358\pi\) | |||||||
\(24\) | 13.6088 | + | 7.85704i | 2.77788 | + | 1.60381i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.11827 | − | 8.92792i | 0.219311 | − | 1.75091i | ||||
\(27\) | 5.62828i | 1.08316i | ||||||||
\(28\) | 4.02720 | − | 6.97531i | 0.761069 | − | 1.31821i | ||||
\(29\) | 4.72756 | − | 8.18837i | 0.877886 | − | 1.52054i | 0.0242288 | − | 0.999706i | \(-0.492287\pi\) |
0.853657 | − | 0.520836i | \(-0.174380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.46410i | − | 0.262960i | −0.991319 | − | 0.131480i | \(-0.958027\pi\) | ||
0.991319 | − | 0.131480i | \(-0.0419730\pi\) | |||||||
\(32\) | −1.20036 | − | 2.07908i | −0.212196 | − | 0.367534i | ||||
\(33\) | 1.51150 | + | 2.61799i | 0.263118 | + | 0.455733i | ||||
\(34\) | 1.59030i | 0.272733i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.5499 | − | 18.2730i | 1.75832 | − | 3.04550i | ||||
\(37\) | 0.378725 | − | 0.655970i | 0.0622619 | − | 0.107841i | −0.833214 | − | 0.552950i | \(-0.813502\pi\) |
0.895476 | + | 0.445110i | \(0.146835\pi\) | |||||||
\(38\) | − | 14.3044i | − | 2.32048i | ||||||
\(39\) | −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 | \(0.673327\pi\) | |||||||
\(42\) | −11.6395 | − | 6.72006i | −1.79601 | − | 1.03693i | ||||
\(43\) | −0.551886 | + | 0.318632i | −0.0841618 | + | 0.0485909i | −0.541490 | − | 0.840707i | \(-0.682140\pi\) |
0.457328 | + | 0.889298i | \(0.348806\pi\) | |||||||
\(44\) | − | 4.52091i | − | 0.681552i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.25104 | + | 4.76374i | −1.21655 | + | 0.702375i | ||||
\(47\) | 9.44613 | 1.37786 | 0.688930 | − | 0.724828i | \(-0.258081\pi\) | ||||
0.688930 | + | 0.724828i | \(0.258081\pi\) | |||||||
\(48\) | −13.2618 | + | 7.65668i | −1.91417 | + | 1.10515i | ||||
\(49\) | 1.68508 | − | 2.91865i | 0.240726 | − | 0.416950i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.80144 | 0.252252 | ||||||||
\(52\) | 12.1510 | + | 9.20287i | 1.68504 | + | 1.27621i | ||||
\(53\) | − | 6.99102i | − | 0.960290i | −0.877189 | − | 0.480145i | \(-0.840584\pi\) | ||
0.877189 | − | 0.480145i | \(-0.159416\pi\) | |||||||
\(54\) | −12.1637 | − | 7.02271i | −1.65527 | − | 0.955669i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.29543 | + | 9.17196i | 0.707632 | + | 1.22565i | ||||
\(57\) | −16.2036 | −2.14622 | ||||||||
\(58\) | 11.7977 | + | 20.4341i | 1.54911 | + | 2.68313i | ||||
\(59\) | 0.641756 | − | 0.370518i | 0.0835495 | − | 0.0482373i | −0.457643 | − | 0.889136i | \(-0.651306\pi\) |
0.541193 | + | 0.840899i | \(0.317973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.09928 | − | 3.63606i | −0.268785 | − | 0.465550i | 0.699763 | − | 0.714375i | \(-0.253289\pi\) |
−0.968548 | + | 0.248825i | \(0.919956\pi\) | |||||||
\(62\) | 3.16418 | + | 1.82684i | 0.401851 | + | 0.232009i | ||||
\(63\) | −4.75447 | + | 8.23499i | −0.599007 | + | 1.03751i | ||||
\(64\) | −4.84325 | −0.605406 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.54390 | −0.928589 | ||||||||
\(67\) | −4.04739 | + | 7.01029i | −0.494468 | + | 0.856443i | −0.999980 | − | 0.00637624i | \(-0.997970\pi\) |
0.505512 | + | 0.862820i | \(0.331304\pi\) | |||||||
\(68\) | −2.33313 | − | 1.34703i | −0.282934 | − | 0.163352i | ||||
\(69\) | 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 | \(0.136605\pi\) | |||||||
\(72\) | 13.8723 | + | 24.0274i | 1.63486 | + | 2.83166i | ||||
\(73\) | −3.71649 | −0.434982 | −0.217491 | − | 0.976062i | \(-0.569787\pi\) | ||||
−0.217491 | + | 0.976062i | \(0.569787\pi\) | |||||||
\(74\) | 0.945110 | + | 1.63698i | 0.109867 | + | 0.190295i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.9860 | + | 12.1163i | 2.40726 | + | 1.38983i | ||||
\(77\) | 2.03741i | 0.232185i | ||||||||
\(78\) | 15.3565 | − | 20.2760i | 1.73879 | − | 2.29580i | ||||
\(79\) | 9.31937 | 1.04851 | 0.524255 | − | 0.851561i | \(-0.324344\pi\) | ||||
0.524255 | + | 0.851561i | \(0.324344\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.468594 | + | 0.811629i | −0.0520660 | + | 0.0901809i | ||||
\(82\) | 0.579085 | − | 0.334335i | 0.0639492 | − | 0.0369211i | ||||
\(83\) | −5.11778 | −0.561749 | −0.280875 | − | 0.959744i | \(-0.590624\pi\) | ||||
−0.280875 | + | 0.959744i | \(0.590624\pi\) | |||||||
\(84\) | 19.7181 | − | 11.3842i | 2.15142 | − | 1.24212i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.59030i | − | 0.171486i | ||||||
\(87\) | 23.1472 | − | 13.3640i | 2.48164 | − | 1.43278i | ||||
\(88\) | 5.14819 | + | 2.97231i | 0.548799 | + | 0.316849i | ||||
\(89\) | 10.8932 | + | 6.28917i | 1.15467 | + | 0.666650i | 0.950021 | − | 0.312185i | \(-0.101061\pi\) |
0.204651 | + | 0.978835i | \(0.434394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.47602 | − | 4.14741i | −0.574043 | − | 0.434767i | ||||
\(92\) | − | 16.1402i | − | 1.68273i | ||||||
\(93\) | 2.06939 | − | 3.58429i | 0.214586 | − | 0.371673i | ||||
\(94\) | −11.7864 | + | 20.4147i | −1.21568 | + | 2.10562i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 6.78645i | − | 0.692639i | ||||||
\(97\) | 2.11078 | + | 3.65597i | 0.214317 | + | 0.371208i | 0.953061 | − | 0.302778i | \(-0.0979142\pi\) |
−0.738744 | + | 0.673986i | \(0.764581\pi\) | |||||||
\(98\) | 4.20514 | + | 7.28351i | 0.424783 | + | 0.735746i | ||||
\(99\) | 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 | \(0.892553\pi\) | |||||||
\(102\) | −2.24775 | + | 3.89322i | −0.222561 | + | 0.385487i | ||||
\(103\) | 13.5269i | 1.33285i | 0.745574 | + | 0.666423i | \(0.232176\pi\) | ||||
−0.745574 | + | 0.666423i | \(0.767824\pi\) | |||||||
\(104\) | −18.4686 | + | 7.78645i | −1.81099 | + | 0.763524i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.1088 | + | 8.72307i | 1.46750 | + | 0.847259i | ||||
\(107\) | −6.37632 | − | 3.68137i | −0.616422 | − | 0.355891i | 0.159053 | − | 0.987270i | \(-0.449156\pi\) |
−0.775475 | + | 0.631379i | \(0.782489\pi\) | |||||||
\(108\) | 20.6061 | − | 11.8969i | 1.98282 | − | 1.14478i | ||||
\(109\) | − | 10.0760i | − | 0.965103i | −0.875868 | − | 0.482551i | \(-0.839710\pi\) | ||
0.875868 | − | 0.482551i | \(-0.160290\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.85432 | − | 1.07059i | 0.176004 | − | 0.101616i | ||||
\(112\) | −10.3208 | −0.975223 | ||||||||
\(113\) | −5.79203 | + | 3.34403i | −0.544868 | + | 0.314580i | −0.747050 | − | 0.664768i | \(-0.768530\pi\) |
0.202181 | + | 0.979348i | \(0.435197\pi\) | |||||||
\(114\) | 20.2181 | − | 35.0187i | 1.89360 | − | 3.27981i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −39.9721 | −3.71131 | ||||||||
\(117\) | −14.3453 | − | 10.8648i | −1.32623 | − | 1.00445i | ||||
\(118\) | 1.84926i | 0.170238i | ||||||||
\(119\) | 1.05146 | + | 0.607061i | 0.0963872 | + | 0.0556492i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.92820 | − | 8.53590i | −0.448018 | − | 0.775991i | ||||
\(122\) | 10.4775 | 0.948592 | ||||||||
\(123\) | −0.378725 | − | 0.655970i | −0.0341484 | − | 0.0591468i | ||||
\(124\) | −5.36033 | + | 3.09479i | −0.481372 | + | 0.277920i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.8648 | − | 20.5505i | −1.05700 | − | 1.83078i | ||||
\(127\) | −1.28994 | − | 0.744750i | −0.114464 | − | 0.0660859i | 0.441675 | − | 0.897175i | \(-0.354384\pi\) |
−0.556139 | + | 0.831089i | \(0.687718\pi\) | |||||||
\(128\) | 8.44391 | − | 14.6253i | 0.746343 | − | 1.29270i | ||||
\(129\) | −1.80144 | −0.158608 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.12676 | 0.360557 | 0.180278 | − | 0.983616i | \(-0.442300\pi\) | ||||
0.180278 | + | 0.983616i | \(0.442300\pi\) | |||||||
\(132\) | 6.38994 | − | 11.0677i | 0.556172 | − | 0.963319i | ||||
\(133\) | −9.45767 | − | 5.46039i | −0.820084 | − | 0.473476i | ||||
\(134\) | −10.1003 | − | 17.4942i | −0.872533 | − | 1.51127i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.06787 | − | 1.77124i | 0.263068 | − | 0.151882i | ||||
\(137\) | −10.0548 | − | 17.4155i | −0.859041 | − | 1.48790i | −0.872844 | − | 0.487999i | \(-0.837727\pi\) |
0.0138029 | − | 0.999905i | \(-0.495606\pi\) | |||||||
\(138\) | −26.9327 | −2.29266 | ||||||||
\(139\) | 10.4126 | + | 18.0352i | 0.883189 | + | 1.52973i | 0.847776 | + | 0.530355i | \(0.177941\pi\) |
0.0354130 | + | 0.999373i | \(0.488725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.1252 | + | 13.3513i | 1.94749 | + | 1.12439i | ||||
\(142\) | 24.3683i | 2.04494i | ||||||||
\(143\) | −3.82584 | − | 0.479208i | −0.319933 | − | 0.0400734i | ||||
\(144\) | −27.0370 | −2.25308 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.63726 | − | 8.03198i | 0.383783 | − | 0.664731i | ||||
\(147\) | 8.25055 | − | 4.76346i | 0.680494 | − | 0.392883i | ||||
\(148\) | −3.20216 | −0.263216 | ||||||||
\(149\) | −11.5768 | + | 6.68388i | −0.948410 | + | 0.547565i | −0.892587 | − | 0.450876i | \(-0.851112\pi\) |
−0.0558233 | + | 0.998441i | \(0.517778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.2984i | − | 1.48910i | −0.667567 | − | 0.744550i | \(-0.732664\pi\) | ||
0.667567 | − | 0.744550i | \(-0.267336\pi\) | |||||||
\(152\) | −27.5949 | + | 15.9319i | −2.23824 | + | 1.29225i | ||||
\(153\) | 2.75447 | + | 1.59030i | 0.222686 | + | 0.128568i | ||||
\(154\) | −4.40320 | − | 2.54219i | −0.354820 | − | 0.204856i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 16.7395 | + | 39.7041i | 1.34023 | + | 3.17887i | ||||
\(157\) | − | 2.42229i | − | 0.193320i | −0.995317 | − | 0.0966599i | \(-0.969184\pi\) | ||
0.995317 | − | 0.0966599i | \(-0.0308159\pi\) | |||||||
\(158\) | −11.6283 | + | 20.1408i | −0.925096 | + | 1.60231i | ||||
\(159\) | 9.88124 | − | 17.1148i | 0.783633 | − | 1.35729i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.27382i | 0.573258i | ||||||||
\(162\) | −1.16938 | − | 2.02543i | −0.0918752 | − | 0.159132i | ||||
\(163\) | −7.99144 | − | 13.8416i | −0.625938 | − | 1.08416i | −0.988359 | − | 0.152142i | \(-0.951383\pi\) |
0.362421 | − | 0.932015i | \(-0.381950\pi\) | |||||||
\(164\) | 1.13277i | 0.0884545i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.38573 | − | 11.0604i | 0.495629 | − | 0.858454i | ||||
\(167\) | −7.19658 | + | 12.4648i | −0.556888 | + | 0.964558i | 0.440866 | + | 0.897573i | \(0.354671\pi\) |
−0.997754 | + | 0.0669853i | \(0.978662\pi\) | |||||||
\(168\) | 29.9387i | 2.30982i | ||||||||
\(169\) | 9.07597 | − | 9.30735i | 0.698151 | − | 0.715950i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.7759 | − | 14.3044i | −1.89466 | − | 1.09388i | ||||
\(172\) | 2.33313 | + | 1.34703i | 0.177900 | + | 0.102710i | ||||
\(173\) | 21.0868 | − | 12.1745i | 1.60320 | − | 0.925608i | 0.612358 | − | 0.790581i | \(-0.290221\pi\) |
0.990842 | − | 0.135027i | \(-0.0431121\pi\) | |||||||
\(174\) | 66.7001i | 5.05653i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.01691 | + | 2.89651i | −0.378164 | + | 0.218333i | ||||
\(177\) | 2.09479 | 0.157454 | ||||||||
\(178\) | −27.1840 | + | 15.6947i | −2.03752 | + | 1.17636i | ||||
\(179\) | −1.89414 | + | 3.28075i | −0.141575 | + | 0.245215i | −0.928090 | − | 0.372356i | \(-0.878550\pi\) |
0.786515 | + | 0.617571i | \(0.211883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48794 | 0.630904 | 0.315452 | − | 0.948942i | \(-0.397844\pi\) | ||||
0.315452 | + | 0.948942i | \(0.397844\pi\) | |||||||
\(182\) | 15.7960 | − | 6.65968i | 1.17088 | − | 0.493649i | ||||
\(183\) | − | 11.8687i | − | 0.877356i | ||||||
\(184\) | 18.3797 | + | 10.6115i | 1.35497 | + | 0.782291i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.16418 | + | 8.94462i | 0.378656 | + | 0.655851i | ||||
\(187\) | 0.681482 | 0.0498349 | ||||||||
\(188\) | −19.9670 | − | 34.5839i | −1.45625 | − | 2.52229i | ||||
\(189\) | −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 | \(0.770238\pi\) | |||||||
\(192\) | −11.8568 | − | 6.84555i | −0.855693 | − | 0.494035i | ||||
\(193\) | −6.07880 | + | 10.5288i | −0.437562 | + | 0.757879i | −0.997501 | − | 0.0706548i | \(-0.977491\pi\) |
0.559939 | + | 0.828534i | \(0.310824\pi\) | |||||||
\(194\) | −10.5349 | −0.756363 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.2476 | −1.01768 | ||||||||
\(197\) | 2.18915 | − | 3.79172i | 0.155970 | − | 0.270149i | −0.777442 | − | 0.628955i | \(-0.783483\pi\) |
0.933412 | + | 0.358807i | \(0.116816\pi\) | |||||||
\(198\) | −11.5349 | − | 6.65968i | −0.819751 | − | 0.473283i | ||||
\(199\) | −10.4186 | − | 18.0456i | −0.738558 | − | 1.27922i | −0.953144 | − | 0.302516i | \(-0.902174\pi\) |
0.214586 | − | 0.976705i | \(-0.431160\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.8170 | + | 11.4413i | −1.39778 | + | 0.807009i | ||||
\(202\) | −19.0252 | − | 32.9526i | −1.33861 | − | 2.31854i | ||||
\(203\) | 18.0140 | 1.26434 | ||||||||
\(204\) | −3.80785 | − | 6.59538i | −0.266603 | − | 0.461769i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −29.2340 | − | 16.8783i | −2.03683 | − | 1.17596i | ||||
\(207\) | 19.0550i | 1.32441i | ||||||||
\(208\) | 2.42749 | − | 19.3803i | 0.168316 | − | 1.34378i | ||||
\(209\) | −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 | \(0.0471492\pi\) | |||||||
\(212\) | −25.5953 | + | 14.7775i | −1.75789 | + | 1.01492i | ||||
\(213\) | 27.6037 | 1.89138 | ||||||||
\(214\) | 15.9121 | − | 9.18688i | 1.08773 | − | 0.628002i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 31.2870i | 2.12881i | ||||||||
\(217\) | 2.41571 | − | 1.39471i | 0.163989 | − | 0.0946792i | ||||
\(218\) | 21.7759 | + | 12.5723i | 1.47485 | + | 0.851505i | ||||
\(219\) | −9.09839 | − | 5.25296i | −0.614812 | − | 0.354962i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.38724 | + | 1.83164i | −0.0933161 | + | 0.123210i | ||||
\(222\) | 5.34335i | 0.358622i | ||||||||
\(223\) | 10.6697 | − | 18.4804i | 0.714494 | − | 1.23754i | −0.248661 | − | 0.968591i | \(-0.579990\pi\) |
0.963155 | − | 0.268949i | \(-0.0866762\pi\) | |||||||
\(224\) | 2.28694 | − | 3.96110i | 0.152803 | − | 0.264662i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 16.6901i | − | 1.11021i | ||||||
\(227\) | −7.84283 | − | 13.5842i | −0.520547 | − | 0.901613i | −0.999715 | − | 0.0238900i | \(-0.992395\pi\) |
0.479168 | − | 0.877723i | \(-0.340938\pi\) | |||||||
\(228\) | 34.2508 | + | 59.3241i | 2.26831 | + | 3.92884i | ||||
\(229\) | − | 7.62085i | − | 0.503600i | −0.967779 | − | 0.251800i | \(-0.918977\pi\) | ||
0.967779 | − | 0.251800i | \(-0.0810225\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.87972 | + | 4.98782i | −0.189472 | + | 0.328175i | ||||
\(232\) | 26.2800 | − | 45.5182i | 1.72536 | − | 2.98842i | ||||
\(233\) | 19.0550i | 1.24833i | 0.781292 | + | 0.624166i | \(0.214561\pi\) | ||||
−0.781292 | + | 0.624166i | \(0.785439\pi\) | |||||||
\(234\) | 41.3802 | − | 17.4461i | 2.70511 | − | 1.14049i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.71306 | − | 1.56639i | −0.176605 | − | 0.101963i | ||||
\(237\) | 22.8149 | + | 13.1722i | 1.48199 | + | 0.855625i | ||||
\(238\) | −2.62393 | + | 1.51493i | −0.170084 | + | 0.0981980i | ||||
\(239\) | − | 12.7535i | − | 0.824954i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) | ||
0.910968 | − | 0.412477i | \(-0.135336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.4550 | + | 12.9644i | −1.44646 | + | 0.835111i | −0.998268 | − | 0.0588285i | \(-0.981263\pi\) |
−0.448187 | + | 0.893940i | \(0.647930\pi\) | |||||||
\(242\) | 24.5967 | 1.58114 | ||||||||
\(243\) | 12.3284 | − | 7.11778i | 0.790864 | − | 0.456606i | ||||
\(244\) | −8.87483 | + | 15.3717i | −0.568153 | + | 0.984069i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.89022 | 0.120516 | ||||||||
\(247\) | 12.4780 | − | 16.4752i | 0.793954 | − | 1.04829i | ||||
\(248\) | − | 8.13878i | − | 0.516813i | ||||||
\(249\) | −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 | \(0.756111\pi\) | |||||||
\(252\) | 40.1996 | 2.53234 | ||||||||
\(253\) | 2.04139 | + | 3.53578i | 0.128341 | + | 0.222293i | ||||
\(254\) | 3.21907 | − | 1.85853i | 0.201982 | − | 0.116614i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.2286 | + | 28.1087i | 1.01429 | + | 1.75680i | ||||
\(257\) | −0.290796 | − | 0.167891i | −0.0181394 | − | 0.0104728i | 0.490903 | − | 0.871214i | \(-0.336667\pi\) |
−0.509042 | + | 0.860742i | \(0.670000\pi\) | |||||||
\(258\) | 2.24775 | − | 3.89322i | 0.139939 | − | 0.242382i | ||||
\(259\) | 1.44310 | 0.0896700 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 47.1906 | 2.92103 | ||||||||
\(262\) | −5.14918 | + | 8.91865i | −0.318118 | + | 0.550996i | ||||
\(263\) | 4.65566 | + | 2.68795i | 0.287080 | + | 0.165746i | 0.636624 | − | 0.771174i | \(-0.280330\pi\) |
−0.349544 | + | 0.936920i | \(0.613664\pi\) | |||||||
\(264\) | 8.40224 | + | 14.5531i | 0.517122 | + | 0.895681i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 23.6017 | − | 13.6264i | 1.44711 | − | 0.835491i | ||||
\(267\) | 17.7785 | + | 30.7932i | 1.08802 | + | 1.88451i | ||||
\(268\) | 34.2212 | 2.09039 | ||||||||
\(269\) | −0.655192 | − | 1.13483i | −0.0399478 | − | 0.0691916i | 0.845360 | − | 0.534197i | \(-0.179386\pi\) |
−0.885308 | + | 0.465005i | \(0.846052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0851 | − | 5.82266i | −0.612629 | − | 0.353701i | 0.161365 | − | 0.986895i | \(-0.448410\pi\) |
−0.773994 | + | 0.633194i | \(0.781744\pi\) | |||||||
\(272\) | 3.45214i | 0.209317i | ||||||||
\(273\) | −7.54390 | − | 17.8933i | −0.456577 | − | 1.08295i | ||||
\(274\) | 50.1838 | 3.03171 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 22.8129 | − | 39.5130i | 1.37317 | − | 2.37841i | ||||
\(277\) | −17.5943 | + | 10.1581i | −1.05714 | + | 0.610338i | −0.924639 | − | 0.380845i | \(-0.875633\pi\) |
−0.132498 | + | 0.991183i | \(0.542300\pi\) | |||||||
\(278\) | −51.9697 | −3.11693 | ||||||||
\(279\) | 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 | \(0.884759\pi\) | |||||||
\(282\) | −57.7091 | + | 33.3184i | −3.43653 | + | 1.98408i | ||||
\(283\) | −19.6173 | − | 11.3261i | −1.16613 | − | 0.673264i | −0.213363 | − | 0.976973i | \(-0.568442\pi\) |
−0.952765 | + | 0.303709i | \(0.901775\pi\) | |||||||
\(284\) | −35.7509 | − | 20.6408i | −2.12143 | − | 1.22481i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.80936 | − | 7.67038i | 0.343515 | − | 0.453559i | ||||
\(287\) | − | 0.510500i | − | 0.0301339i | ||||||
\(288\) | 5.99102 | − | 10.3767i | 0.353024 | − | 0.611455i | ||||
\(289\) | −8.29695 | + | 14.3707i | −0.488056 | + | 0.845337i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.9336i | 0.699562i | ||||||||
\(292\) | 7.85584 | + | 13.6067i | 0.459728 | + | 0.796272i | ||||
\(293\) | −9.30636 | − | 16.1191i | −0.543683 | − | 0.941687i | −0.998689 | − | 0.0511983i | \(-0.983696\pi\) |
0.455005 | − | 0.890489i | \(-0.349637\pi\) | |||||||
\(294\) | 23.7745i | 1.38656i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.10529 | − | 3.64647i | 0.122367 | − | 0.211946i | ||||
\(297\) | −3.00941 | + | 5.21245i | −0.174624 | + | 0.302457i | ||||
\(298\) | − | 33.3593i | − | 1.93245i | ||||||
\(299\) | −13.6587 | − | 1.71083i | −0.789905 | − | 0.0989400i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05146 | − | 0.607061i | −0.0606052 | − | 0.0349904i | ||||
\(302\) | 39.5459 | + | 22.8319i | 2.27561 | + | 1.31383i | ||||
\(303\) | −37.3278 | + | 21.5512i | −2.14443 | + | 1.23808i | ||||
\(304\) | − | 31.0513i | − | 1.78091i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.87381 | + | 3.96859i | −0.392949 | + | 0.226869i | ||||
\(307\) | −3.14776 | −0.179652 | −0.0898262 | − | 0.995957i | \(-0.528631\pi\) | ||||
−0.0898262 | + | 0.995957i | \(0.528631\pi\) | |||||||
\(308\) | 7.45932 | − | 4.30664i | 0.425034 | − | 0.245394i | ||||
\(309\) | −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 | \(0.471257\pi\) | |||||||
\(312\) | −56.2186 | − | 7.04170i | −3.18275 | − | 0.398658i | ||||
\(313\) | 35.3533i | 1.99829i | 0.0413596 | + | 0.999144i | \(0.486831\pi\) | ||||
−0.0413596 | + | 0.999144i | \(0.513169\pi\) | |||||||
\(314\) | 5.23499 | + | 3.02242i | 0.295427 | + | 0.170565i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6991 | − | 34.1198i | −1.10816 | − | 1.91939i | ||||
\(317\) | −13.6357 | −0.765858 | −0.382929 | − | 0.923778i | \(-0.625085\pi\) | ||||
−0.382929 | + | 0.923778i | \(0.625085\pi\) | |||||||
\(318\) | 24.6587 | + | 42.7101i | 1.38279 | + | 2.39506i | ||||
\(319\) | 8.75656 | − | 5.05560i | 0.490273 | − | 0.283059i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.4066 | − | 18.0248i | −0.580842 | − | 1.00605i | ||||
\(322\) | −15.7200 | − | 9.07594i | −0.876041 | − | 0.505782i | ||||
\(323\) | −1.82641 | + | 3.16344i | −0.101624 | + | 0.176018i | ||||
\(324\) | 3.96202 | 0.220112 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 39.8854 | 2.20905 | ||||||||
\(327\) | 14.2416 | − | 24.6671i | 0.787560 | − | 1.36409i | ||||
\(328\) | −1.28994 | − | 0.744750i | −0.0712253 | − | 0.0411219i | ||||
\(329\) | 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 | \(0.623972\pi\) | |||||||
\(332\) | 10.8179 | + | 18.7371i | 0.593707 | + | 1.02833i | ||||
\(333\) | 3.78044 | 0.207167 | ||||||||
\(334\) | −17.9591 | − | 31.1061i | −0.982679 | − | 1.70205i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −25.2665 | − | 14.5876i | −1.37840 | − | 0.795819i | ||||
\(337\) | 11.7493i | 0.640026i | 0.947413 | + | 0.320013i | \(0.103687\pi\) | ||||
−0.947413 | + | 0.320013i | \(0.896313\pi\) | |||||||
\(338\) | 8.79023 | + | 31.2280i | 0.478125 | + | 1.69858i | ||||
\(339\) | −18.9061 | −1.02684 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.782847 | − | 1.35593i | 0.0423936 | − | 0.0734278i | ||||
\(342\) | 61.8285 | − | 35.6967i | 3.34330 | − | 1.93026i | ||||
\(343\) | 19.7574 | 1.06680 | ||||||||
\(344\) | −3.06787 | + | 1.77124i | −0.165409 | + | 0.0954987i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 60.7630i | 3.26664i | ||||||||
\(347\) | −1.64525 | + | 0.949887i | −0.0883218 | + | 0.0509926i | −0.543510 | − | 0.839402i | \(-0.682905\pi\) |
0.455189 | + | 0.890395i | \(0.349572\pi\) | |||||||
\(348\) | −97.8562 | − | 56.4973i | −5.24564 | − | 3.02857i | ||||
\(349\) | 8.89329 | + | 5.13454i | 0.476047 | + | 0.274846i | 0.718768 | − | 0.695250i | \(-0.244707\pi\) |
−0.242721 | + | 0.970096i | \(0.578040\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.88364 | − | 18.6991i | −0.420798 | − | 0.998084i | ||||
\(352\) | − | 2.56730i | − | 0.136838i | ||||||
\(353\) | 0.400294 | − | 0.693330i | 0.0213055 | − | 0.0369022i | −0.855176 | − | 0.518338i | \(-0.826551\pi\) |
0.876482 | + | 0.481435i | \(0.159884\pi\) | |||||||
\(354\) | −2.61378 | + | 4.52720i | −0.138921 | + | 0.240618i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 53.1756i | − | 2.81830i | ||||||
\(357\) | 1.71606 | + | 2.97231i | 0.0908237 | + | 0.157311i | ||||
\(358\) | −4.72685 | − | 8.18714i | −0.249822 | − | 0.432704i | ||||
\(359\) | 8.13272i | 0.429228i | 0.976699 | + | 0.214614i | \(0.0688494\pi\) | ||||
−0.976699 | + | 0.214614i | \(0.931151\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.92820 | − | 12.0000i | 0.364642 | − | 0.631579i | ||||
\(362\) | −10.5909 | + | 18.3439i | −0.556643 | + | 0.964135i | ||||
\(363\) | − | 27.8625i | − | 1.46240i | ||||||
\(364\) | −3.60929 | + | 28.8154i | −0.189178 | + | 1.51034i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.6502 | + | 14.8092i | 1.34076 | + | 0.774087i | ||||
\(367\) | −17.7765 | − | 10.2632i | −0.927924 | − | 0.535737i | −0.0417696 | − | 0.999127i | \(-0.513300\pi\) |
−0.886154 | + | 0.463390i | \(0.846633\pi\) | |||||||
\(368\) | −17.9110 | + | 10.3409i | −0.933675 | + | 0.539057i | ||||
\(369\) | − | 1.33734i | − | 0.0696191i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5349 | − | 6.65968i | 0.598863 | − | 0.345754i | ||||
\(372\) | −17.4969 | −0.907173 | ||||||||
\(373\) | −15.4203 | + | 8.90292i | −0.798433 | + | 0.460976i | −0.842923 | − | 0.538034i | \(-0.819167\pi\) |
0.0444897 | + | 0.999010i | \(0.485834\pi\) | |||||||
\(374\) | −0.850322 | + | 1.47280i | −0.0439691 | + | 0.0761568i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 52.5100 | 2.70800 | ||||||||
\(377\) | −4.23697 | + | 33.8266i | −0.218215 | + | 1.74216i | ||||
\(378\) | − | 26.7595i | − | 1.37636i | ||||||
\(379\) | 1.77150 | + | 1.02277i | 0.0909956 | + | 0.0525363i | 0.544807 | − | 0.838561i | \(-0.316603\pi\) |
−0.453812 | + | 0.891098i | \(0.649936\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.10529 | − | 3.64647i | −0.107857 | − | 0.186814i | ||||
\(382\) | −13.5833 | −0.694982 | ||||||||
\(383\) | −3.95261 | − | 6.84611i | −0.201969 | − | 0.349820i | 0.747194 | − | 0.664606i | \(-0.231401\pi\) |
−0.949163 | + | 0.314786i | \(0.898067\pi\) | |||||||
\(384\) | 41.3433 | − | 23.8696i | 2.10979 | − | 1.21809i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.1697 | − | 26.2747i | −0.772117 | − | 1.33735i | ||||
\(387\) | −2.75447 | − | 1.59030i | −0.140018 | − | 0.0808393i | ||||
\(388\) | 8.92343 | − | 15.4558i | 0.453018 | − | 0.784651i | ||||
\(389\) | −9.21171 | −0.467052 | −0.233526 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233526 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43298 | 0.123041 | ||||||||
\(392\) | 9.36719 | − | 16.2244i | 0.473114 | − | 0.819458i | ||||
\(393\) | 10.1028 | + | 5.83285i | 0.509618 | + | 0.294228i | ||||
\(394\) | 5.46304 | + | 9.46226i | 0.275224 | + | 0.476702i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 19.5409 | − | 11.2820i | 0.981968 | − | 0.566940i | ||||
\(397\) | −3.17719 | − | 5.50305i | −0.159458 | − | 0.276190i | 0.775215 | − | 0.631697i | \(-0.217641\pi\) |
−0.934674 | + | 0.355507i | \(0.884308\pi\) | |||||||
\(398\) | 51.9996 | 2.60651 | ||||||||
\(399\) | −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 | \(0.633470\pi\) | |||||||
\(402\) | − | 57.1038i | − | 2.84808i | ||||||
\(403\) | 2.05080 | + | 4.86425i | 0.102157 | + | 0.242306i | ||||
\(404\) | 64.4600 | 3.20701 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.4770 | + | 38.9314i | −1.11552 | + | 1.93213i | ||||
\(407\) | 0.701487 | − | 0.405004i | 0.0347714 | − | 0.0200753i | ||||
\(408\) | 10.0140 | 0.495767 | ||||||||
\(409\) | −8.80580 | + | 5.08403i | −0.435419 | + | 0.251389i | −0.701652 | − | 0.712519i | \(-0.747554\pi\) |
0.266234 | + | 0.963909i | \(0.414221\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 56.8467i | − | 2.80404i | ||||||
\(412\) | 49.5244 | − | 28.5929i | 2.43989 | − | 1.40867i | ||||
\(413\) | 1.22268 | + | 0.705915i | 0.0601642 | + | 0.0347358i | ||||
\(414\) | −41.1811 | − | 23.7759i | −2.02394 | − | 1.16852i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.90023 | + | 5.22607i | 0.338311 | + | 0.256229i | ||||
\(417\) | 58.8697i | 2.88286i | ||||||||
\(418\) | 7.64847 | − | 13.2475i | 0.374099 | − | 0.647959i | ||||
\(419\) | 14.2954 | − | 24.7604i | 0.698378 | − | 1.20963i | −0.270651 | − | 0.962677i | \(-0.587239\pi\) |
0.969029 | − | 0.246948i | \(-0.0794277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.01797i | 0.0983498i | 0.998790 | + | 0.0491749i | \(0.0156592\pi\) | ||||
−0.998790 | + | 0.0491749i | \(0.984341\pi\) | |||||||
\(422\) | 13.2932 | + | 23.0244i | 0.647101 | + | 1.12081i | ||||
\(423\) | 23.5729 | + | 40.8295i | 1.14615 | + | 1.98520i | ||||
\(424\) | − | 38.8623i | − | 1.88732i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −34.4427 | + | 59.6564i | −1.66875 | + | 2.89036i | ||||
\(427\) | 3.99957 | − | 6.92747i | 0.193553 | − | 0.335244i | ||||
\(428\) | 31.1264i | 1.50455i | ||||||||
\(429\) | −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 | \(0.501311\pi\) | |||||||
\(432\) | −26.4044 | − | 15.2446i | −1.27038 | − | 0.733455i | ||||
\(433\) | −25.4920 | + | 14.7178i | −1.22507 | + | 0.707292i | −0.965994 | − | 0.258566i | \(-0.916750\pi\) |
−0.259072 | + | 0.965858i | \(0.583417\pi\) | |||||||
\(434\) | 6.96103i | 0.334140i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.8899 | + | 21.2984i | −1.76670 | + | 1.02001i | ||||
\(437\) | −21.8841 | −1.04686 | ||||||||
\(438\) | 22.7051 | − | 13.1088i | 1.08489 | − | 0.626362i | ||||
\(439\) | −8.47602 | + | 14.6809i | −0.404538 | + | 0.700681i | −0.994268 | − | 0.106920i | \(-0.965901\pi\) |
0.589729 | + | 0.807601i | \(0.299235\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.8205 | 0.800978 | ||||||||
\(442\) | −2.22756 | − | 5.28351i | −0.105954 | − | 0.251311i | ||||
\(443\) | − | 24.1399i | − | 1.14692i | −0.819233 | − | 0.573461i | \(-0.805600\pi\) | ||
0.819233 | − | 0.573461i | \(-0.194400\pi\) | |||||||
\(444\) | −7.83925 | − | 4.52599i | −0.372034 | − | 0.214794i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 26.6262 | + | 46.1180i | 1.26079 | + | 2.18375i | ||||
\(447\) | −37.7885 | −1.78733 | ||||||||
\(448\) | −4.61371 | − | 7.99118i | −0.217977 | − | 0.377548i | ||||
\(449\) | −18.0679 | + | 10.4315i | −0.852676 | + | 0.492293i | −0.861553 | − | 0.507668i | \(-0.830508\pi\) |
0.00887706 | + | 0.999961i | \(0.497174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.143271 | − | 0.248153i | −0.00674637 | − | 0.0116851i | ||||
\(452\) | 24.4861 | + | 14.1371i | 1.15173 | + | 0.664952i | ||||
\(453\) | 25.8633 | − | 44.7965i | 1.21516 | − | 2.10472i | ||||
\(454\) | 39.1437 | 1.83710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −90.0739 | −4.21810 | ||||||||
\(457\) | 15.2830 | − | 26.4708i | 0.714906 | − | 1.23825i | −0.248089 | − | 0.968737i | \(-0.579803\pi\) |
0.962996 | − | 0.269517i | \(-0.0868640\pi\) | |||||||
\(458\) | 16.4700 | + | 9.50894i | 0.769591 | + | 0.444324i | ||||
\(459\) | 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 | \(0.298587\pi\) | |||||||
\(462\) | −7.18636 | − | 12.4471i | −0.334340 | − | 0.579094i | ||||
\(463\) | −14.0011 | −0.650688 | −0.325344 | − | 0.945596i | \(-0.605480\pi\) | ||||
−0.325344 | + | 0.945596i | \(0.605480\pi\) | |||||||
\(464\) | 25.6098 | + | 44.3575i | 1.18891 | + | 2.05925i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41.1811 | − | 23.7759i | −1.90768 | − | 1.10140i | ||||
\(467\) | − | 6.98506i | − | 0.323230i | −0.986854 | − | 0.161615i | \(-0.948330\pi\) | ||
0.986854 | − | 0.161615i | \(-0.0516703\pi\) | |||||||
\(468\) | −9.45512 | + | 75.4866i | −0.437063 | + | 3.48937i | ||||
\(469\) | −15.4223 | −0.712135 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.42371 | − | 5.93004i | 0.157756 | − | 0.273242i | ||||
\(472\) | 3.56745 | − | 2.05967i | 0.164205 | − | 0.0948039i | ||||
\(473\) | −0.681482 | −0.0313346 | ||||||||
\(474\) | −56.9347 | + | 32.8713i | −2.61510 | + | 1.50983i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 5.13277i | − | 0.235260i | ||||||
\(477\) | 30.2176 | − | 17.4461i | 1.38357 | − | 0.798804i | ||||
\(478\) | 27.5625 | + | 15.9132i | 1.26068 | + | 0.727853i | ||||
\(479\) | 14.1065 | + | 8.14438i | 0.644542 | + | 0.372126i | 0.786362 | − | 0.617766i | \(-0.211962\pi\) |
−0.141820 | + | 0.989892i | \(0.545296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.339423 | + | 2.70985i | −0.0154764 | + | 0.123558i | ||||
\(482\) | − | 64.7056i | − | 2.94726i | ||||||
\(483\) | −10.2810 | + | 17.8071i | −0.467800 | + | 0.810253i | ||||
\(484\) | −20.8343 | + | 36.0860i | −0.947012 | + | 1.64027i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 35.5249i | 1.61144i | ||||||||
\(487\) | −10.0204 | − | 17.3559i | −0.454069 | − | 0.786471i | 0.544565 | − | 0.838719i | \(-0.316695\pi\) |
−0.998634 | + | 0.0522474i | \(0.983362\pi\) | |||||||
\(488\) | −11.6697 | − | 20.2125i | −0.528261 | − | 0.914975i | ||||
\(489\) | − | 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 | \(0.282691\pi\) | |||||||
\(492\) | −1.60108 | + | 2.77315i | −0.0721823 | + | 0.125023i | ||||
\(493\) | − | 6.02540i | − | 0.271370i | ||||||
\(494\) | 20.0364 | + | 47.5241i | 0.901481 | + | 2.13821i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.86865 | + | 3.96562i | 0.308411 | + | 0.178061i | ||||
\(497\) | 16.1117 | + | 9.30208i | 0.722708 | + | 0.417255i | ||||
\(498\) | 31.2660 | − | 18.0514i | 1.40106 | − | 0.808903i | ||||
\(499\) | − | 1.24651i | − | 0.0558016i | −0.999611 | − | 0.0279008i | \(-0.991118\pi\) | ||
0.999611 | − | 0.0279008i | \(-0.00888226\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.2361 | + | 20.3436i | −1.57423 | + | 0.908883i | ||||
\(502\) | −18.9955 | −0.847809 | ||||||||
\(503\) | −6.62808 | + | 3.82672i | −0.295532 | + | 0.170625i | −0.640434 | − | 0.768013i | \(-0.721245\pi\) |
0.344902 | + | 0.938639i | \(0.387912\pi\) | |||||||
\(504\) | −26.4296 | + | 45.7774i | −1.17727 | + | 2.03909i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.1886 | −0.452938 | ||||||||
\(507\) | 35.3742 | − | 9.95732i | 1.57102 | − | 0.442220i | ||||
\(508\) | 6.29695i | 0.279382i | ||||||||
\(509\) | 22.2777 | + | 12.8621i | 0.987444 | + | 0.570101i | 0.904509 | − | 0.426454i | \(-0.140237\pi\) |
0.0829345 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.54035 | − | 6.13207i | −0.156616 | − | 0.271267i | ||||
\(512\) | −47.2215 | −2.08691 | ||||||||
\(513\) | −16.1308 | − | 27.9393i | −0.712192 | − | 1.23355i | ||||
\(514\) | 0.725685 | − | 0.418974i | 0.0320086 | − | 0.0184802i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.80785 | + | 6.59538i | 0.167631 | + | 0.290346i | ||||
\(517\) | 8.74824 | + | 5.05080i | 0.384747 | + | 0.222134i | ||||
\(518\) | −1.80064 | + | 3.11879i | −0.0791154 | + | 0.137032i | ||||
\(519\) | 68.8305 | 3.02132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.1519 | −1.32098 | −0.660490 | − | 0.750835i | \(-0.729651\pi\) | ||||
−0.660490 | + | 0.750835i | \(0.729651\pi\) | |||||||
\(522\) | −58.8823 | + | 101.987i | −2.57721 | + | 4.46386i | ||||
\(523\) | −3.41000 | − | 1.96876i | −0.149109 | − | 0.0860880i | 0.423589 | − | 0.905854i | \(-0.360770\pi\) |
−0.572698 | + | 0.819766i | \(0.694103\pi\) | |||||||
\(524\) | −8.72307 | − | 15.1088i | −0.381069 | − | 0.660031i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6182 | + | 6.70779i | −0.506579 | + | 0.292473i | ||||
\(527\) | −0.466509 | − | 0.808017i | −0.0203215 | − | 0.0351978i | ||||
\(528\) | −16.3759 | −0.712672 | ||||||||
\(529\) | −4.21200 | − | 7.29539i | −0.183130 | − | 0.317191i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.20301 | + | 1.84926i | 0.138999 | + | 0.0802510i | ||||
\(532\) | 46.1682i | 2.00165i | ||||||||
\(533\) | 0.958614 | + | 0.120072i | 0.0415222 | + | 0.00520088i | ||||
\(534\) | −88.7326 | −3.83983 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −22.4990 | + | 38.9694i | −0.971809 | + | 1.68322i | ||||
\(537\) | −9.27415 | + | 5.35444i | −0.400209 | + | 0.231061i | ||||
\(538\) | 3.27007 | 0.140983 | ||||||||
\(539\) | 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 | \(0.889051\pi\) | |||||||
\(542\) | 25.1675 | − | 14.5305i | 1.08104 | − | 0.624138i | ||||
\(543\) | 20.7795 | + | 11.9970i | 0.891732 | + | 0.514842i | ||||
\(544\) | −1.32492 | − | 0.764945i | −0.0568057 | − | 0.0327968i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 48.0833 | + | 6.02271i | 2.05778 | + | 0.257748i | ||||
\(547\) | 6.56107i | 0.280531i | 0.990114 | + | 0.140266i | \(0.0447956\pi\) | ||||
−0.990114 | + | 0.140266i | \(0.955204\pi\) | |||||||
\(548\) | −42.5074 | + | 73.6249i | −1.81582 | + | 3.14510i | ||||
\(549\) | 10.4775 | − | 18.1476i | 0.447170 | − | 0.774522i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.1972i | 2.30888i | ||||||||
\(552\) | 29.9970 | + | 51.9564i | 1.27676 | + | 2.21141i | ||||
\(553\) | 8.87769 | + | 15.3766i | 0.377518 | + | 0.653880i | ||||
\(554\) | − | 50.6990i | − | 2.15399i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 44.0200 | − | 76.2450i | 1.86687 | − | 3.23351i | ||||
\(557\) | 3.92503 | − | 6.79835i | 0.166309 | − | 0.288055i | −0.770810 | − | 0.637065i | \(-0.780148\pi\) |
0.937119 | + | 0.349009i | \(0.113482\pi\) | |||||||
\(558\) | 18.2356i | 0.771973i | ||||||||
\(559\) | 1.38724 | − | 1.83164i | 0.0586741 | − | 0.0774702i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.66835 | + | 0.963220i | 0.0704377 | + | 0.0406672i | ||||
\(562\) | −25.6626 | − | 14.8163i | −1.08251 | − | 0.624988i | ||||
\(563\) | 13.4749 | − | 7.77976i | 0.567901 | − | 0.327878i | −0.188410 | − | 0.982091i | \(-0.560333\pi\) |
0.756310 | + | 0.654213i | \(0.227000\pi\) | |||||||
\(564\) | − | 112.887i | − | 4.75341i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 48.9552 | − | 28.2643i | 2.05774 | − | 1.18804i | ||||
\(567\) | −1.78554 | −0.0749857 | ||||||||
\(568\) | 47.0095 | − | 27.1409i | 1.97247 | − | 1.13881i | ||||
\(569\) | −1.73957 | + | 3.01303i | −0.0729267 | + | 0.126313i | −0.900183 | − | 0.435512i | \(-0.856567\pi\) |
0.827256 | + | 0.561825i | \(0.189901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5118 | 0.900240 | 0.450120 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450120 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(572\) | 6.33252 | + | 15.0200i | 0.264776 | + | 0.628018i | ||||
\(573\) | 15.3868i | 0.642791i | ||||||||
\(574\) | 1.10328 | + | 0.636978i | 0.0460500 | + | 0.0265870i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −12.0864 | − | 20.9342i | −0.503599 | − | 0.872259i | ||||
\(577\) | 9.97608 | 0.415310 | 0.207655 | − | 0.978202i | \(-0.433417\pi\) | ||||
0.207655 | + | 0.978202i | \(0.433417\pi\) | |||||||
\(578\) | −20.7051 | − | 35.8623i | −0.861218 | − | 1.49167i | ||||
\(579\) | −29.7632 | + | 17.1838i | −1.23692 | + | 0.714134i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.87523 | − | 8.44414i | −0.202259 | − | 0.350322i | ||||
\(582\) | −25.7907 | − | 14.8902i | −1.06906 | − | 0.617221i | ||||
\(583\) | 3.73806 | − | 6.47451i | 0.154815 | − | 0.268147i | ||||
\(584\) | −20.6595 | −0.854898 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.4482 | 1.91876 | ||||||||
\(587\) | 12.0286 | − | 20.8341i | 0.496472 | − | 0.859915i | −0.503519 | − | 0.863984i | \(-0.667962\pi\) |
0.999992 | + | 0.00406862i | \(0.00129509\pi\) | |||||||
\(588\) | −34.8797 | − | 20.1378i | −1.43841 | − | 0.830469i | ||||
\(589\) | 4.19615 | + | 7.26795i | 0.172899 | + | 0.299471i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.7186 | − | 6.18837i | 0.440903 | − | 0.254556i | ||||
\(592\) | 2.05160 | + | 3.55348i | 0.0843203 | + | 0.146047i | ||||
\(593\) | 0.940219 | 0.0386102 | 0.0193051 | − | 0.999814i | \(-0.493855\pi\) | ||||
0.0193051 | + | 0.999814i | \(0.493855\pi\) | |||||||
\(594\) | −7.51001 | − | 13.0077i | −0.308139 | − | 0.533713i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 48.9417 | + | 28.2565i | 2.00473 | + | 1.15743i | ||||
\(597\) | − | 58.9037i | − | 2.41077i | ||||||
\(598\) | 20.7401 | − | 27.3842i | 0.848128 | − | 1.11982i | ||||
\(599\) | 11.4270 | 0.466896 | 0.233448 | − | 0.972369i | \(-0.424999\pi\) | ||||
0.233448 | + | 0.972369i | \(0.424999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0215 | − | 31.2142i | 0.735114 | − | 1.27325i | −0.219560 | − | 0.975599i | \(-0.570462\pi\) |
0.954674 | − | 0.297655i | \(-0.0962045\pi\) | |||||||
\(602\) | 2.62393 | − | 1.51493i | 0.106943 | − | 0.0617437i | ||||
\(603\) | −40.4012 | −1.64526 | ||||||||
\(604\) | −66.9935 | + | 38.6787i | −2.72593 | + | 1.57381i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 107.562i | − | 4.36942i | ||||||
\(607\) | −34.5464 | + | 19.9454i | −1.40219 | + | 0.809557i | −0.994618 | − | 0.103614i | \(-0.966959\pi\) |
−0.407576 | + | 0.913171i | \(0.633626\pi\) | |||||||
\(608\) | 11.9174 | + | 6.88052i | 0.483315 | + | 0.279042i | ||||
\(609\) | 44.1003 | + | 25.4613i | 1.78704 | + | 1.03175i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.3833 | + | 13.2314i | −1.26963 | + | 0.535285i | ||||
\(612\) | − | 13.4461i | − | 0.543528i | ||||||
\(613\) | −0.172736 | + | 0.299187i | −0.00697673 | + | 0.0120841i | −0.869493 | − | 0.493946i | \(-0.835554\pi\) |
0.862516 | + | 0.506030i | \(0.168887\pi\) | |||||||
\(614\) | 3.92763 | − | 6.80286i | 0.158506 | − | 0.274541i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3258i | 0.456328i | ||||||||
\(617\) | −19.3425 | − | 33.5022i | −0.778700 | − | 1.34875i | −0.932691 | − | 0.360676i | \(-0.882546\pi\) |
0.153991 | − | 0.988072i | \(-0.450787\pi\) | |||||||
\(618\) | −47.7121 | − | 82.6398i | −1.91926 | − | 3.32426i | ||||
\(619\) | 14.8971i | 0.598764i | 0.954133 | + | 0.299382i | \(0.0967805\pi\) | ||||
−0.954133 | + | 0.299382i | \(0.903219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.7440 | + | 18.6091i | −0.431141 | + | 0.746758i | ||||
\(622\) | −3.96859 | + | 6.87381i | −0.159126 | + | 0.275615i | ||||
\(623\) | 23.9644i | 0.960113i | ||||||||
\(624\) | 33.3353 | − | 44.0142i | 1.33448 | − | 1.76198i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −76.4047 | − | 44.1123i | −3.05374 | − | 1.76308i | ||||
\(627\) | −15.0064 | − | 8.66397i | −0.599299 | − | 0.346006i | ||||
\(628\) | −8.86842 | + | 5.12019i | −0.353889 | + | 0.204318i | ||||
\(629\) | − | 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 | \(0.0519893\pi\) | |||||||
\(632\) | 51.8053 | 2.06071 | ||||||||
\(633\) | 26.0814 | − | 15.0581i | 1.03664 | − | 0.598506i | ||||
\(634\) | 17.0140 | − | 29.4691i | 0.675713 | − | 1.17037i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −83.5470 | −3.31285 | ||||||||
\(637\) | −1.51022 | + | 12.0571i | −0.0598370 | + | 0.477719i | ||||
\(638\) | 25.2326i | 0.998967i | ||||||||
\(639\) | 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 | \(0.570847\pi\) | |||||||
\(642\) | 51.9397 | 2.04990 | ||||||||
\(643\) | 4.55189 | + | 7.88410i | 0.179509 | + | 0.310918i | 0.941712 | − | 0.336419i | \(-0.109216\pi\) |
−0.762204 | + | 0.647337i | \(0.775882\pi\) | |||||||
\(644\) | 26.6307 | − | 15.3753i | 1.04940 | − | 0.605870i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.55783 | − | 7.89439i | −0.179325 | − | 0.310601i | ||||
\(647\) | 16.5605 | + | 9.56118i | 0.651059 | + | 0.375889i | 0.788862 | − | 0.614571i | \(-0.210671\pi\) |
−0.137803 | + | 0.990460i | \(0.544004\pi\) | |||||||
\(648\) | −2.60486 | + | 4.51175i | −0.102329 | + | 0.177238i | ||||
\(649\) | 0.792455 | 0.0311066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.88525 | 0.309047 | ||||||||
\(652\) | −33.7843 | + | 58.5161i | −1.32309 | + | 2.29167i | ||||
\(653\) | −29.9926 | − | 17.3162i | −1.17370 | − | 0.677636i | −0.219152 | − | 0.975691i | \(-0.570329\pi\) |
−0.954549 | + | 0.298055i | \(0.903662\pi\) | |||||||
\(654\) | 35.5399 | + | 61.5570i | 1.38972 | + | 2.40707i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.25705 | − | 0.725758i | 0.0490796 | − | 0.0283361i | ||||
\(657\) | −9.27453 | − | 16.0640i | −0.361834 | − | 0.626714i | ||||
\(658\) | −44.9114 | −1.75083 | ||||||||
\(659\) | −3.34926 | − | 5.80109i | −0.130469 | − | 0.225978i | 0.793389 | − | 0.608715i | \(-0.208315\pi\) |
−0.923857 | + | 0.382737i | \(0.874982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.22004 | + | 3.01379i | 0.203036 | + | 0.117223i | 0.598071 | − | 0.801443i | \(-0.295934\pi\) |
−0.395035 | + | 0.918666i | \(0.629268\pi\) | |||||||
\(662\) | − | 71.8604i | − | 2.79294i | ||||||
\(663\) | −5.98501 | + | 2.52331i | −0.232438 | + | 0.0979974i | ||||
\(664\) | −28.4492 | −1.10404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.71706 | + | 8.17018i | −0.182782 | + | 0.316588i | ||||
\(667\) | 31.2620 | − | 18.0491i | 1.21047 | − | 0.698865i | ||||
\(668\) | 60.8479 | 2.35428 | ||||||||
\(669\) | 52.2411 | − | 30.1614i | 2.01976 | − | 1.16611i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.48990i | − | 0.173330i | ||||||
\(672\) | 11.1974 | − | 6.46481i | 0.431948 | − | 0.249386i | ||||
\(673\) | 20.2276 | + | 11.6784i | 0.779715 | + | 0.450169i | 0.836329 | − | 0.548227i | \(-0.184697\pi\) |
−0.0566140 | + | 0.998396i | \(0.518030\pi\) | |||||||
\(674\) | −25.3923 | − | 14.6603i | −0.978075 | − | 0.564692i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −53.2604 | − | 13.5550i | −2.04848 | − | 0.521346i | ||||
\(677\) | 45.4042i | 1.74503i | 0.488590 | + | 0.872513i | \(0.337511\pi\) | ||||
−0.488590 | + | 0.872513i | \(0.662489\pi\) | |||||||
\(678\) | 23.5901 | − | 40.8593i | 0.905973 | − | 1.56919i | ||||
\(679\) | −4.02148 | + | 6.96540i | −0.154330 | + | 0.267308i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 44.3408i | − | 1.69914i | ||||||
\(682\) | 1.95360 | + | 3.38374i | 0.0748073 | + | 0.129570i | ||||
\(683\) | 12.7489 | + | 22.0817i | 0.487823 | + | 0.844934i | 0.999902 | − | 0.0140045i | \(-0.00445791\pi\) |
−0.512079 | + | 0.858938i | \(0.671125\pi\) | |||||||
\(684\) | 120.945i | 4.62445i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.6523 | + | 42.6991i | −0.941230 | + | 1.63026i | ||||
\(687\) | 10.7715 | − | 18.6567i | 0.410957 | − | 0.711798i | ||||
\(688\) | − | 3.45214i | − | 0.131612i | ||||||
\(689\) | 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 | \(0.626624\pi\) | |||||||
\(692\) | −89.1457 | − | 51.4683i | −3.38881 | − | 1.95653i | ||||
\(693\) | −8.80641 | + | 5.08438i | −0.334528 | + | 0.193140i | ||||
\(694\) | − | 4.74090i | − | 0.179962i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 128.673 | − | 74.2892i | 4.87733 | − | 2.81593i | ||||
\(697\) | −0.170754 | −0.00646778 | ||||||||
\(698\) | −22.1933 | + | 12.8133i | −0.840028 | + | 0.484990i | ||||
\(699\) | −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 | \(0.686261\pi\) | |||||||
\(702\) | 50.2488 | + | 6.29394i | 1.89652 | + | 0.237550i | ||||
\(703\) | 4.34174i | 0.163752i | ||||||||
\(704\) | −4.48542 | − | 2.58966i | −0.169051 | − | 0.0976015i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.998937 | + | 1.73021i | 0.0375955 | + | 0.0651173i | ||||
\(707\) | −29.0499 | −1.09253 | ||||||||
\(708\) | −4.42792 | − | 7.66938i | −0.166411 | − | 0.288233i | ||||
\(709\) | 9.46865 | − | 5.46673i | 0.355603 | − | 0.205307i | −0.311548 | − | 0.950231i | \(-0.600847\pi\) |
0.667150 | + | 0.744923i | \(0.267514\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2566 | + | 40.2815i | 0.872189 | + | 1.51068i | ||||
\(712\) | 60.5538 | + | 34.9608i | 2.26935 | + | 1.31021i | ||||
\(713\) | 2.79486 | − | 4.84084i | 0.104668 | − | 0.181291i | ||||
\(714\) | −8.56490 | −0.320533 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0152 | 0.598516 | ||||||||
\(717\) | 18.0260 | − | 31.2220i | 0.673194 | − | 1.16601i | ||||
\(718\) | −17.5762 | − | 10.1476i | −0.655938 | − | 0.378706i | ||||
\(719\) | −8.02989 | − | 13.9082i | −0.299464 | − | 0.518688i | 0.676549 | − | 0.736398i | \(-0.263475\pi\) |
−0.976014 | + | 0.217710i | \(0.930141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3189 | + | 12.8858i | −0.831199 | + | 0.479893i | ||||
\(722\) | 17.2894 | + | 29.9461i | 0.643444 | + | 1.11448i | ||||
\(723\) | −73.2966 | −2.72593 | ||||||||
\(724\) | −17.9416 | − | 31.0758i | −0.666796 | − | 1.15492i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 60.2156 | + | 34.7655i | 2.23481 | + | 1.29027i | ||||
\(727\) | 51.3754i | 1.90541i | 0.303900 | + | 0.952704i | \(0.401711\pi\) | ||||
−0.303900 | + | 0.952704i | \(0.598289\pi\) | |||||||
\(728\) | −30.4406 | − | 23.0550i | −1.12820 | − | 0.854475i | ||||
\(729\) | 43.0532 | 1.59456 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.203052 | + | 0.351697i | −0.00751016 | + | 0.0130080i | ||||
\(732\) | −43.4532 | + | 25.0877i | −1.60608 | + | 0.927268i | ||||
\(733\) | 9.82358 | 0.362842 | 0.181421 | − | 0.983406i | \(-0.441930\pi\) | ||||
0.181421 | + | 0.983406i | \(0.441930\pi\) | |||||||
\(734\) | 44.3613 | − | 25.6120i | 1.63741 | − | 0.945357i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 9.16560i | − | 0.337848i | ||||||
\(737\) | −7.49673 | + | 4.32824i | −0.276146 | + | 0.159433i | ||||
\(738\) | 2.89022 | + | 1.66867i | 0.106390 | + | 0.0614246i | ||||
\(739\) | −42.5082 | − | 24.5421i | −1.56369 | − | 0.902797i | −0.996879 | − | 0.0789487i | \(-0.974844\pi\) |
−0.566811 | − | 0.823848i | \(-0.691823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.8339 | − | 22.6967i | 1.97764 | − | 0.833783i | ||||
\(742\) | 33.2386i | 1.22023i | ||||||||
\(743\) | 20.4188 | − | 35.3663i | 0.749091 | − | 1.29746i | −0.199167 | − | 0.979966i | \(-0.563824\pi\) |
0.948259 | − | 0.317499i | \(-0.102843\pi\) | |||||||
\(744\) | 11.5035 | − | 19.9247i | 0.421739 | − | 0.730473i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 44.4346i | − | 1.62687i | ||||||
\(747\) | −12.7715 | − | 22.1208i | −0.467283 | − | 0.809358i | ||||
\(748\) | −1.44050 | − | 2.49503i | −0.0526700 | − | 0.0912272i | ||||
\(749\) | − | 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 | \(0.182510\pi\) | |||||||
\(752\) | −25.5855 | + | 44.3154i | −0.933006 | + | 1.61601i | ||||
\(753\) | 21.5175i | 0.784142i | ||||||||
\(754\) | −67.8184 | − | 51.3641i | −2.46980 | − | 1.87057i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 39.2590 | + | 22.6662i | 1.42784 | + | 0.824362i | ||||
\(757\) | 12.8224 | + | 7.40301i | 0.466038 | + | 0.269067i | 0.714580 | − | 0.699554i | \(-0.246618\pi\) |
−0.248542 | + | 0.968621i | \(0.579951\pi\) | |||||||
\(758\) | −4.42078 | + | 2.55234i | −0.160570 | + | 0.0927051i | ||||
\(759\) | 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 | \(0.267269\pi\) | |||||||
\(762\) | 10.5075 | 0.380647 | ||||||||
\(763\) | 16.6250 | − | 9.59843i | 0.601864 | − | 0.347486i | ||||
\(764\) | 11.5055 | − | 19.9281i | 0.416255 | − | 0.720975i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.7275 | 0.712784 | ||||||||
\(767\) | −1.61314 | + | 2.12991i | −0.0582472 | + | 0.0769065i | ||||
\(768\) | 91.7512i | 3.31078i | ||||||||
\(769\) | −18.2352 | − | 10.5281i | −0.657579 | − | 0.379654i | 0.133775 | − | 0.991012i | \(-0.457290\pi\) |
−0.791354 | + | 0.611358i | \(0.790623\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.474602 | − | 0.822034i | −0.0170924 | − | 0.0296048i | ||||
\(772\) | 51.3970 | 1.84982 | ||||||||
\(773\) | 7.04144 | + | 12.1961i | 0.253263 | + | 0.438664i | 0.964422 | − | 0.264367i | \(-0.0851629\pi\) |
−0.711159 | + | 0.703031i | \(0.751830\pi\) | |||||||
\(774\) | 6.87381 | − | 3.96859i | 0.247074 | − | 0.142648i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.7336 | + | 20.3231i | 0.421210 | + | 0.729558i | ||||
\(777\) | 3.53288 | + | 2.03971i | 0.126741 | + | 0.0731741i | ||||
\(778\) | 11.4940 | − | 19.9081i | 0.412078 | − | 0.713740i | ||||
\(779\) | 1.53590 | 0.0550293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4425 | 0.373660 | ||||||||
\(782\) | −3.03576 | + | 5.25809i | −0.108558 | + | 0.188029i | ||||
\(783\) | 46.0864 | + | 26.6080i | 1.64699 | + | 0.950893i | ||||
\(784\) | 9.12832 | + | 15.8107i | 0.326011 | + | 0.564668i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.2116 | + | 14.5559i | −0.899267 | + | 0.519192i | ||||
\(787\) | 16.5121 | + | 28.5998i | 0.588593 | + | 1.01947i | 0.994417 | + | 0.105522i | \(0.0336514\pi\) |
−0.405823 | + | 0.913951i | \(0.633015\pi\) | |||||||
\(788\) | −18.5095 | −0.659374 | ||||||||
\(789\) | 7.59839 | + | 13.1608i | 0.270510 | + | 0.468537i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0350 | − | 6.37109i | −0.392361 | − | 0.226530i | ||||
\(792\) | 29.6697i | 1.05427i | ||||||||
\(793\) | 12.0676 | + | 9.13974i | 0.428534 | + | 0.324562i | ||||
\(794\) | 15.8574 | 0.562758 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.0454 | + | 76.2890i | −1.56115 | + | 2.70399i | ||||
\(797\) | −14.6718 | + | 8.47079i | −0.519703 | + | 0.300051i | −0.736813 | − | 0.676096i | \(-0.763670\pi\) |
0.217110 | + | 0.976147i | \(0.430337\pi\) | |||||||
\(798\) | 77.0395 | 2.72717 | ||||||||
\(799\) | 5.21319 | − | 3.00984i | 0.184429 | − | 0.106480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 62.7787i | 2.21817i | ||||||||
\(802\) | −9.01036 | + | 5.20213i | −0.318167 | + | 0.183694i | ||||
\(803\) | −3.44191 | − | 1.98719i | −0.121462 | − | 0.0701263i | ||||
\(804\) | 83.7774 | + | 48.3689i | 2.95460 | + | 1.70584i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.0714 | − | 1.63726i | −0.460420 | − | 0.0576701i | ||||
\(807\) | − | 3.70425i | − | 0.130396i | ||||||
\(808\) | −42.3798 | + | 73.4039i | −1.49092 | + | 2.58234i | ||||
\(809\) | −25.8818 | + | 44.8285i | −0.909954 | + | 1.57609i | −0.0958292 | + | 0.995398i | \(0.530550\pi\) |
−0.814125 | + | 0.580689i | \(0.802783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6699i | 0.796047i | 0.917375 | + | 0.398023i | \(0.130304\pi\) | ||||
−0.917375 | + | 0.398023i | \(0.869696\pi\) | |||||||
\(812\) | −38.0776 | − | 65.9524i | −1.33626 | − | 2.31448i | ||||
\(813\) | −16.4597 | − | 28.5091i | −0.577267 | − | 0.999856i | ||||
\(814\) | 2.02138i | 0.0708494i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.87932 | + | 8.45123i | −0.170810 | + | 0.295852i | ||||
\(817\) | 1.82641 | − | 3.16344i | 0.0638981 | − | 0.110675i | ||||
\(818\) | − | 25.3745i | − | 0.887198i | ||||||
\(819\) | 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 | \(0.833397\pi\) | |||||||
\(822\) | 122.856 | + | 70.9307i | 4.28508 | + | 2.47399i | ||||
\(823\) | 22.3718 | − | 12.9164i | 0.779831 | − | 0.450236i | −0.0565391 | − | 0.998400i | \(-0.518007\pi\) |
0.836371 | + | 0.548165i | \(0.184673\pi\) | |||||||
\(824\) | 75.1946i | 2.61953i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.05121 | + | 1.76162i | −0.106165 | + | 0.0612945i | ||||
\(827\) | 16.0820 | 0.559227 | 0.279613 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279613 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(828\) | 69.7635 | − | 40.2780i | 2.42445 | − | 1.39976i | ||||
\(829\) | 11.2909 | − | 19.5564i | 0.392149 | − | 0.679222i | −0.600584 | − | 0.799562i | \(-0.705065\pi\) |
0.992733 | + | 0.120340i | \(0.0383984\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.4304 | −1.99224 | ||||||||
\(832\) | 16.0910 | − | 6.78404i | 0.557854 | − | 0.235194i | ||||
\(833\) | − | 2.14768i | − | 0.0744128i | ||||||
\(834\) | −127.228 | − | 73.4549i | −4.40553 | − | 2.54354i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.9570 | + | 22.4422i | 0.448128 | + | 0.776181i | ||||
\(837\) | 8.24037 | 0.284829 | ||||||||
\(838\) | 35.6744 | + | 61.7898i | 1.23235 | + | 2.13449i | ||||
\(839\) | −15.4533 | + | 8.92198i | −0.533508 | + | 0.308021i | −0.742444 | − | 0.669908i | \(-0.766333\pi\) |
0.208936 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.1996 | − | 52.3073i | −1.04137 | − | 1.80370i | ||||
\(842\) | −4.36118 | − | 2.51793i | −0.150296 | − | 0.0867736i | ||||
\(843\) | −16.7835 | + | 29.0698i | −0.578053 | + | 1.00122i | ||||
\(844\) | −45.0390 | −1.55031 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −117.653 | −4.04498 | ||||||||
\(847\) | 9.38927 | − | 16.2627i | 0.322619 | − | 0.558793i | ||||
\(848\) | 32.7975 | + | 18.9356i | 1.12627 | + | 0.650252i | ||||
\(849\) | −32.0169 | − | 55.4550i | −1.09882 | − | 1.90321i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.50440 | − | 1.44591i | 0.0858497 | − | 0.0495653i | ||||
\(852\) | −58.3482 | − | 101.062i | −1.99898 | − | 3.46233i | ||||
\(853\) | 19.7936 | 0.677720 | 0.338860 | − | 0.940837i | \(-0.389959\pi\) | ||||
0.338860 | + | 0.940837i | \(0.389959\pi\) | |||||||
\(854\) | 9.98097 | + | 17.2875i | 0.341542 | + | 0.591568i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35.4452 | − | 20.4643i | −1.21149 | − | 0.699456i | ||||
\(857\) | − | 11.7302i | − | 0.400696i | −0.979725 | − | 0.200348i | \(-0.935793\pi\) | ||
0.979725 | − | 0.200348i | \(-0.0642073\pi\) | |||||||
\(858\) | 25.0634 | − | 10.5669i | 0.855652 | − | 0.360748i | ||||
\(859\) | −5.37452 | −0.183376 | −0.0916882 | − | 0.995788i | \(-0.529226\pi\) | ||||
−0.0916882 | + | 0.995788i | \(0.529226\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.721551 | − | 1.24976i | 0.0245904 | − | 0.0425918i | ||||
\(862\) | −44.5467 | + | 25.7191i | −1.51727 | + | 0.875995i | ||||
\(863\) | 25.3234 | 0.862017 | 0.431008 | − | 0.902348i | \(-0.358158\pi\) | ||||
0.431008 | + | 0.902348i | \(0.358158\pi\) | |||||||
\(864\) | 11.7017 | − | 6.75596i | 0.398099 | − | 0.229842i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 73.4567i | − | 2.49616i | ||||||
\(867\) | −40.6237 | + | 23.4541i | −1.37965 | + | 0.796544i | ||||
\(868\) | −10.2126 | − | 5.89623i | −0.346637 | − | 0.200131i | ||||
\(869\) | 8.63084 | + | 4.98302i | 0.292781 | + | 0.169037i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.62739 | − | 28.9599i | 0.122909 | − | 0.981268i | ||||
\(872\) | − | 56.0112i | − | 1.89678i | ||||||
\(873\) | −10.5349 | + | 18.2470i | −0.356553 | + | 0.617567i | ||||
\(874\) | 27.3060 | − | 47.2954i | 0.923640 | − | 1.59979i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 44.4144i | 1.50062i | ||||||||
\(877\) | −10.3458 | − | 17.9194i | −0.349352 | − | 0.605095i | 0.636783 | − | 0.771043i | \(-0.280265\pi\) |
−0.986134 | + | 0.165949i | \(0.946931\pi\) | |||||||
\(878\) | −21.1520 | − | 36.6363i | −0.713845 | − | 1.23642i | ||||
\(879\) | − | 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 | \(-0.136765\pi\) | |||||||
\(882\) | −20.9879 | + | 36.3521i | −0.706699 | + | 1.22404i | ||||
\(883\) | − | 45.8550i | − | 1.54314i | −0.636142 | − | 0.771572i | \(-0.719471\pi\) | ||
0.636142 | − | 0.771572i | \(-0.280529\pi\) | |||||||
\(884\) | 9.63829 | + | 1.20725i | 0.324171 | + | 0.0406042i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.1705 | + | 30.1207i | 1.75270 | + | 1.01192i | ||||
\(887\) | −0.937332 | − | 0.541169i | −0.0314725 | − | 0.0181707i | 0.484181 | − | 0.874968i | \(-0.339118\pi\) |
−0.515654 | + | 0.856797i | \(0.672451\pi\) | |||||||
\(888\) | 10.3080 | − | 5.95131i | 0.345913 | − | 0.199713i | ||||
\(889\) | − | 2.83781i | − | 0.0951772i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.867947 | + | 0.501109i | −0.0290773 | + | 0.0167878i | ||||
\(892\) | −90.2133 | −3.02056 | ||||||||
\(893\) | −46.8916 | + | 27.0729i | −1.56917 | + | 0.905959i | ||||
\(894\) | 47.1507 | − | 81.6675i | 1.57696 | − | 2.73137i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 32.1749 | 1.07489 | ||||||||
\(897\) | −31.0200 | − | 23.4938i | −1.03573 | − | 0.784436i | ||||
\(898\) | − | 52.0637i | − | 1.73739i | ||||||
\(899\) | −11.9886 | − | 6.92163i | −0.399842 | − | 0.230849i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.22756 | − | 3.85824i | −0.0742107 | − | 0.128537i | ||||
\(902\) | 0.715068 | 0.0238092 | ||||||||
\(903\) | −1.71606 | − | 2.97231i | −0.0571070 | − | 0.0989122i | ||||
\(904\) | −32.1973 | + | 18.5891i | −1.07086 | + | 0.618264i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 64.5420 | + | 111.790i | 2.14426 | + | 3.71397i | ||||
\(907\) | 39.4307 | + | 22.7653i | 1.30928 | + | 0.755910i | 0.981975 | − | 0.189010i | \(-0.0605278\pi\) |
0.327300 | + | 0.944920i | \(0.393861\pi\) | |||||||
\(908\) | −33.1560 | + | 57.4279i | −1.10032 | + | 1.90581i | ||||
\(909\) | −76.1009 | −2.52411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.7417 | 1.31670 | 0.658350 | − | 0.752712i | \(-0.271255\pi\) | ||||
0.658350 | + | 0.752712i | \(0.271255\pi\) | |||||||
\(912\) | 43.8885 | − | 76.0171i | 1.45329 | − | 2.51718i | ||||
\(913\) | −4.73967 | − | 2.73645i | −0.156860 | − | 0.0905632i | ||||
\(914\) | 38.1387 | + | 66.0582i | 1.26152 | + | 2.18501i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.9012 | + | 16.1088i | −0.921883 | + | 0.532250i | ||||
\(917\) | 3.93118 | + | 6.80900i | 0.129819 | + | 0.224853i | ||||
\(918\) | −8.95062 | −0.295415 | ||||||||
\(919\) | 23.4969 | + | 40.6978i | 0.775091 | + | 1.34250i | 0.934743 | + | 0.355323i | \(0.115629\pi\) |
−0.159653 | + | 0.987173i | \(0.551037\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.70608 | − | 4.44911i | −0.253924 | − | 0.146603i | ||||
\(922\) | 11.6745i | 0.384481i | ||||||||
\(923\) | −21.2569 | + | 28.0665i | −0.699680 | + | 0.923821i | ||||
\(924\) | 24.3484 | 0.801002 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.4700 | − | 30.2589i | 0.574099 | − | 0.994369i | ||||
\(927\) | −58.4680 | + | 33.7565i | −1.92034 | + | 1.10871i | ||||
\(928\) | −22.6991 | −0.745134 | ||||||||
\(929\) | 13.1821 | − | 7.61066i | 0.432489 | − | 0.249698i | −0.267917 | − | 0.963442i | \(-0.586335\pi\) |
0.700406 | + | 0.713744i | \(0.253002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.3180i | 0.633121i | ||||||||
\(932\) | 69.7635 | − | 40.2780i | 2.28518 | − | 1.31935i | ||||
\(933\) | 7.78645 | + | 4.49551i | 0.254917 | + | 0.147176i | ||||
\(934\) | 15.0959 | + | 8.71564i | 0.493954 | + | 0.285184i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −79.7441 | − | 60.3963i | −2.60652 | − | 1.97412i | ||||
\(937\) | − | 6.07285i | − | 0.198392i | −0.995068 | − | 0.0991958i | \(-0.968373\pi\) | ||
0.995068 | − | 0.0991958i | \(-0.0316270\pi\) | |||||||
\(938\) | 19.2432 | − | 33.3302i | 0.628313 | − | 1.08827i | ||||
\(939\) | −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 | \(-0.000257639\pi\) | ||||||||
\(942\) | 8.54390 | + | 14.7985i | 0.278375 | + | 0.482160i | ||||
\(943\) | −0.511495 | − | 0.885936i | −0.0166566 | − | 0.0288500i | ||||
\(944\) | 4.01429i | 0.130654i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.850322 | − | 1.47280i | 0.0276464 | − | 0.0478849i | ||||
\(947\) | −9.32907 | + | 16.1584i | −0.303154 | + | 0.525078i | −0.976849 | − | 0.213932i | \(-0.931373\pi\) |
0.673695 | + | 0.739010i | \(0.264706\pi\) | |||||||
\(948\) | − | 111.372i | − | 3.61720i | ||||||
\(949\) | 12.3475 | − | 5.20576i | 0.400816 | − | 0.168986i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.3818 | − | 19.2730i | −1.08248 | − | 0.624969i | ||||
\(952\) | 5.84495 | + | 3.37458i | 0.189436 | + | 0.109371i | ||||
\(953\) | 1.32461 | − | 0.764764i | 0.0429083 | − | 0.0247731i | −0.478392 | − | 0.878146i | \(-0.658780\pi\) |
0.521301 | + | 0.853373i | \(0.325447\pi\) | |||||||
\(954\) | 87.0739i | 2.81912i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −46.6927 | + | 26.9581i | −1.51015 | + | 0.871886i | ||||
\(957\) | 28.5827 | 0.923948 | ||||||||
\(958\) | −35.2028 | + | 20.3244i | −1.13735 | + | 0.656650i | ||||
\(959\) | 19.1566 | − | 33.1802i | 0.618598 | − | 1.07144i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | −5.43293 | − | 4.11477i | −0.175165 | − | 0.132666i | ||||
\(963\) | − | 36.7475i | − | 1.18417i | ||||||
\(964\) | 94.9299 | + | 54.8078i | 3.05749 | + | 1.76524i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −25.6562 | − | 44.4379i | −0.825475 | − | 1.42976i | ||||
\(967\) | 32.1716 | 1.03457 | 0.517285 | − | 0.855813i | \(-0.326943\pi\) | ||||
0.517285 | + | 0.855813i | \(0.326943\pi\) | |||||||
\(968\) | −27.3953 | − | 47.4501i | −0.880519 | − | 1.52510i | ||||
\(969\) | −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 | \(0.744041\pi\) | |||||||
\(972\) | −52.1188 | − | 30.0908i | −1.67171 | − | 0.965164i | ||||
\(973\) | −19.8383 | + | 34.3609i | −0.635986 | + | 1.10156i | ||||
\(974\) | 50.0122 | 1.60249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7442 | 0.728023 | ||||||||
\(977\) | −7.86142 | + | 13.6164i | −0.251509 | + | 0.435626i | −0.963942 | − | 0.266114i | \(-0.914260\pi\) |
0.712432 | + | 0.701741i | \(0.247593\pi\) | |||||||
\(978\) | 97.6440 | + | 56.3748i | 3.12231 | + | 1.80267i | ||||
\(979\) | 6.72557 | + | 11.6490i | 0.214950 | + | 0.372304i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.5518 | − | 25.1447i | 1.39050 | − | 0.802807i | ||||
\(982\) | −19.7124 | − | 34.1429i | −0.629049 | − | 1.08954i | ||||
\(983\) | 38.5356 | 1.22910 | 0.614548 | − | 0.788880i | \(-0.289338\pi\) | ||||
0.614548 | + | 0.788880i | \(0.289338\pi\) | |||||||
\(984\) | −2.10529 | − | 3.64647i | −0.0671141 | − | 0.116245i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.0219 | + | 7.51821i | 0.414703 | + | 0.239429i | ||||
\(987\) | 50.8743i | 1.61935i | ||||||||
\(988\) | −86.6944 | − | 10.8590i | −2.75812 | − | 0.345469i | ||||
\(989\) | −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 | \(0.210238\pi\) | |||||||
\(992\) | −3.04399 | + | 1.75745i | −0.0966468 | + | 0.0557991i | ||||
\(993\) | −81.4014 | −2.58320 | ||||||||
\(994\) | −40.2068 | + | 23.2134i | −1.27528 | + | 0.736285i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 61.1606i | 1.93795i | ||||||||
\(997\) | 17.7859 | − | 10.2687i | 0.563285 | − | 0.325213i | −0.191178 | − | 0.981555i | \(-0.561231\pi\) |
0.754463 | + | 0.656343i | \(0.227897\pi\) | |||||||
\(998\) | 2.69393 | + | 1.55534i | 0.0852750 | + | 0.0492335i | ||||
\(999\) | 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.m.b.199.1 | 8 | ||
5.2 | odd | 4 | 65.2.m.a.56.1 | yes | 8 | ||
5.3 | odd | 4 | 325.2.n.d.251.4 | 8 | |||
5.4 | even | 2 | 325.2.m.c.199.4 | 8 | |||
13.10 | even | 6 | 325.2.m.c.49.4 | 8 | |||
15.2 | even | 4 | 585.2.bu.c.316.4 | 8 | |||
20.7 | even | 4 | 1040.2.da.b.641.1 | 8 | |||
65.2 | even | 12 | 845.2.e.m.146.1 | 8 | |||
65.7 | even | 12 | 845.2.a.l.1.1 | 4 | |||
65.12 | odd | 4 | 845.2.m.g.316.4 | 8 | |||
65.17 | odd | 12 | 845.2.c.g.506.1 | 8 | |||
65.22 | odd | 12 | 845.2.c.g.506.8 | 8 | |||
65.23 | odd | 12 | 325.2.n.d.101.4 | 8 | |||
65.32 | even | 12 | 845.2.a.m.1.4 | 4 | |||
65.33 | even | 12 | 4225.2.a.bl.1.4 | 4 | |||
65.37 | even | 12 | 845.2.e.n.146.4 | 8 | |||
65.42 | odd | 12 | 845.2.m.g.361.4 | 8 | |||
65.47 | even | 4 | 845.2.e.n.191.4 | 8 | |||
65.49 | even | 6 | inner | 325.2.m.b.49.1 | 8 | ||
65.57 | even | 4 | 845.2.e.m.191.1 | 8 | |||
65.58 | even | 12 | 4225.2.a.bi.1.1 | 4 | |||
65.62 | odd | 12 | 65.2.m.a.36.1 | ✓ | 8 | ||
195.32 | odd | 12 | 7605.2.a.cf.1.1 | 4 | |||
195.62 | even | 12 | 585.2.bu.c.361.4 | 8 | |||
195.137 | odd | 12 | 7605.2.a.cj.1.4 | 4 | |||
260.127 | even | 12 | 1040.2.da.b.881.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.1 | ✓ | 8 | 65.62 | odd | 12 | ||
65.2.m.a.56.1 | yes | 8 | 5.2 | odd | 4 | ||
325.2.m.b.49.1 | 8 | 65.49 | even | 6 | inner | ||
325.2.m.b.199.1 | 8 | 1.1 | even | 1 | trivial | ||
325.2.m.c.49.4 | 8 | 13.10 | even | 6 | |||
325.2.m.c.199.4 | 8 | 5.4 | even | 2 | |||
325.2.n.d.101.4 | 8 | 65.23 | odd | 12 | |||
325.2.n.d.251.4 | 8 | 5.3 | odd | 4 | |||
585.2.bu.c.316.4 | 8 | 15.2 | even | 4 | |||
585.2.bu.c.361.4 | 8 | 195.62 | even | 12 | |||
845.2.a.l.1.1 | 4 | 65.7 | even | 12 | |||
845.2.a.m.1.4 | 4 | 65.32 | even | 12 | |||
845.2.c.g.506.1 | 8 | 65.17 | odd | 12 | |||
845.2.c.g.506.8 | 8 | 65.22 | odd | 12 | |||
845.2.e.m.146.1 | 8 | 65.2 | even | 12 | |||
845.2.e.m.191.1 | 8 | 65.57 | even | 4 | |||
845.2.e.n.146.4 | 8 | 65.37 | even | 12 | |||
845.2.e.n.191.4 | 8 | 65.47 | even | 4 | |||
845.2.m.g.316.4 | 8 | 65.12 | odd | 4 | |||
845.2.m.g.361.4 | 8 | 65.42 | odd | 12 | |||
1040.2.da.b.641.1 | 8 | 20.7 | even | 4 | |||
1040.2.da.b.881.1 | 8 | 260.127 | even | 12 | |||
4225.2.a.bi.1.1 | 4 | 65.58 | even | 12 | |||
4225.2.a.bl.1.4 | 4 | 65.33 | even | 12 | |||
7605.2.a.cf.1.1 | 4 | 195.32 | odd | 12 | |||
7605.2.a.cj.1.4 | 4 | 195.137 | odd | 12 |