Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(214,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.214");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.h (of order \(3\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 373.12 | ||
Character | \(\chi\) | \(=\) | 441.373 |
Dual form | 441.2.h.h.214.12 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.17631 | 1.53888 | 0.769442 | − | 0.638717i | \(-0.220534\pi\) | ||||
0.769442 | + | 0.638717i | \(0.220534\pi\) | |||||||
\(3\) | 0.507459 | + | 1.65605i | 0.292981 | + | 0.956118i | ||||
\(4\) | 2.73633 | 1.36816 | ||||||||
\(5\) | 0.634145 | + | 1.09837i | 0.283598 | + | 0.491206i | 0.972268 | − | 0.233868i | \(-0.0751385\pi\) |
−0.688670 | + | 0.725075i | \(0.741805\pi\) | |||||||
\(6\) | 1.10439 | + | 3.60407i | 0.450864 | + | 1.47136i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.60248 | 0.566563 | ||||||||
\(9\) | −2.48497 | + | 1.68075i | −0.828324 | + | 0.560250i | ||||
\(10\) | 1.38010 | + | 2.39040i | 0.436425 | + | 0.755910i | ||||
\(11\) | 2.73867 | − | 4.74351i | 0.825739 | − | 1.43022i | −0.0756148 | − | 0.997137i | \(-0.524092\pi\) |
0.901353 | − | 0.433084i | \(-0.142575\pi\) | |||||||
\(12\) | 1.38857 | + | 4.53149i | 0.400847 | + | 1.30813i | ||||
\(13\) | −2.37268 | + | 4.10960i | −0.658062 | + | 1.13980i | 0.323054 | + | 0.946380i | \(0.395290\pi\) |
−0.981117 | + | 0.193417i | \(0.938043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.49715 | + | 1.60755i | −0.386562 | + | 0.415068i | ||||
\(16\) | −1.98516 | −0.496290 | ||||||||
\(17\) | −2.40822 | − | 4.17116i | −0.584079 | − | 1.01165i | −0.994990 | − | 0.0999785i | \(-0.968123\pi\) |
0.410911 | − | 0.911676i | \(-0.365211\pi\) | |||||||
\(18\) | −5.40807 | + | 3.65783i | −1.27469 | + | 0.862159i | ||||
\(19\) | 2.69059 | − | 4.66025i | 0.617265 | − | 1.06913i | −0.372718 | − | 0.927945i | \(-0.621574\pi\) |
0.989983 | − | 0.141189i | \(-0.0450925\pi\) | |||||||
\(20\) | 1.73523 | + | 3.00550i | 0.388009 | + | 0.672051i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.96019 | − | 10.3233i | 1.27072 | − | 2.20095i | ||||
\(23\) | 2.58816 | + | 4.48282i | 0.539668 | + | 0.934732i | 0.998922 | + | 0.0464269i | \(0.0147835\pi\) |
−0.459254 | + | 0.888305i | \(0.651883\pi\) | |||||||
\(24\) | 0.813193 | + | 2.65378i | 0.165992 | + | 0.541701i | ||||
\(25\) | 1.69572 | − | 2.93707i | 0.339144 | − | 0.587415i | ||||
\(26\) | −5.16368 | + | 8.94376i | −1.01268 | + | 1.75402i | ||||
\(27\) | −4.04442 | − | 3.26231i | −0.778348 | − | 0.627833i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.01656 | + | 3.49278i | 0.374466 | + | 0.648594i | 0.990247 | − | 0.139324i | \(-0.0444928\pi\) |
−0.615781 | + | 0.787917i | \(0.711159\pi\) | |||||||
\(30\) | −3.25826 | + | 3.49853i | −0.594875 | + | 0.638741i | ||||
\(31\) | 1.46419 | 0.262976 | 0.131488 | − | 0.991318i | \(-0.458025\pi\) | ||||
0.131488 | + | 0.991318i | \(0.458025\pi\) | |||||||
\(32\) | −7.52529 | −1.33030 | ||||||||
\(33\) | 9.24522 | + | 2.12822i | 1.60939 | + | 0.370476i | ||||
\(34\) | −5.24103 | − | 9.07773i | −0.898830 | − | 1.55682i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.79970 | + | 4.59908i | −1.13328 | + | 0.766514i | ||||
\(37\) | −0.959170 | + | 1.66133i | −0.157687 | + | 0.273121i | −0.934034 | − | 0.357184i | \(-0.883737\pi\) |
0.776347 | + | 0.630305i | \(0.217070\pi\) | |||||||
\(38\) | 5.85557 | − | 10.1421i | 0.949899 | − | 1.64527i | ||||
\(39\) | −8.00971 | − | 1.84381i | −1.28258 | − | 0.295246i | ||||
\(40\) | 1.01621 | + | 1.76012i | 0.160676 | + | 0.278299i | ||||
\(41\) | 1.94808 | − | 3.37418i | 0.304239 | − | 0.526958i | −0.672852 | − | 0.739777i | \(-0.734931\pi\) |
0.977092 | + | 0.212819i | \(0.0682644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.66016 | − | 2.87549i | −0.253173 | − | 0.438508i | 0.711225 | − | 0.702964i | \(-0.248141\pi\) |
−0.964398 | + | 0.264457i | \(0.914807\pi\) | |||||||
\(44\) | 7.49389 | − | 12.9798i | 1.12975 | − | 1.95678i | ||||
\(45\) | −3.42192 | − | 1.66358i | −0.510109 | − | 0.247992i | ||||
\(46\) | 5.63263 | + | 9.75600i | 0.830486 | + | 1.43844i | ||||
\(47\) | −3.15546 | −0.460271 | −0.230135 | − | 0.973159i | \(-0.573917\pi\) | ||||
−0.230135 | + | 0.973159i | \(0.573917\pi\) | |||||||
\(48\) | −1.00739 | − | 3.28752i | −0.145404 | − | 0.474512i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.69042 | − | 6.39199i | 0.521904 | − | 0.903964i | ||||
\(51\) | 5.68555 | − | 6.10481i | 0.796137 | − | 0.854844i | ||||
\(52\) | −6.49243 | + | 11.2452i | −0.900338 | + | 1.55943i | ||||
\(53\) | 3.57149 | + | 6.18601i | 0.490582 | + | 0.849714i | 0.999941 | − | 0.0108405i | \(-0.00345071\pi\) |
−0.509359 | + | 0.860554i | \(0.670117\pi\) | |||||||
\(54\) | −8.80191 | − | 7.09981i | −1.19779 | − | 0.966162i | ||||
\(55\) | 6.94684 | 0.936712 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.08294 | + | 2.09086i | 1.20307 | + | 0.276942i | ||||
\(58\) | 4.38866 | + | 7.60138i | 0.576259 | + | 0.998111i | ||||
\(59\) | −0.308683 | −0.0401871 | −0.0200935 | − | 0.999798i | \(-0.506396\pi\) | ||||
−0.0200935 | + | 0.999798i | \(0.506396\pi\) | |||||||
\(60\) | −4.09669 | + | 4.39879i | −0.528881 | + | 0.567881i | ||||
\(61\) | −10.3429 | −1.32427 | −0.662134 | − | 0.749385i | \(-0.730349\pi\) | ||||
−0.662134 | + | 0.749385i | \(0.730349\pi\) | |||||||
\(62\) | 3.18652 | 0.404689 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.4070 | −1.55088 | ||||||||
\(65\) | −6.01848 | −0.746501 | ||||||||
\(66\) | 20.1205 | + | 4.63167i | 2.47666 | + | 0.570119i | ||||
\(67\) | 4.47310 | 0.546476 | 0.273238 | − | 0.961946i | \(-0.411905\pi\) | ||||
0.273238 | + | 0.961946i | \(0.411905\pi\) | |||||||
\(68\) | −6.58968 | − | 11.4137i | −0.799116 | − | 1.38411i | ||||
\(69\) | −6.11037 | + | 6.56095i | −0.735602 | + | 0.789845i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.96688 | −0.233426 | −0.116713 | − | 0.993166i | \(-0.537236\pi\) | ||||
−0.116713 | + | 0.993166i | \(0.537236\pi\) | |||||||
\(72\) | −3.98212 | + | 2.69337i | −0.469297 | + | 0.317417i | ||||
\(73\) | −5.27515 | − | 9.13683i | −0.617409 | − | 1.06938i | −0.989957 | − | 0.141371i | \(-0.954849\pi\) |
0.372547 | − | 0.928013i | \(-0.378484\pi\) | |||||||
\(74\) | −2.08745 | + | 3.61557i | −0.242662 | + | 0.420302i | ||||
\(75\) | 5.72444 | + | 1.31775i | 0.661001 | + | 0.152160i | ||||
\(76\) | 7.36235 | − | 12.7520i | 0.844520 | − | 1.46275i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −17.4316 | − | 4.01270i | −1.97374 | − | 0.454349i | ||||
\(79\) | −9.01643 | −1.01443 | −0.507214 | − | 0.861820i | \(-0.669325\pi\) | ||||
−0.507214 | + | 0.861820i | \(0.669325\pi\) | |||||||
\(80\) | −1.25888 | − | 2.18044i | −0.140747 | − | 0.243781i | ||||
\(81\) | 3.35017 | − | 8.35323i | 0.372241 | − | 0.928136i | ||||
\(82\) | 4.23963 | − | 7.34326i | 0.468189 | − | 0.810927i | ||||
\(83\) | 5.08023 | + | 8.79921i | 0.557627 | + | 0.965839i | 0.997694 | + | 0.0678739i | \(0.0216216\pi\) |
−0.440066 | + | 0.897965i | \(0.645045\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.05432 | − | 5.29023i | 0.331287 | − | 0.573806i | ||||
\(86\) | −3.61303 | − | 6.25796i | −0.389603 | − | 0.674813i | ||||
\(87\) | −4.76089 | + | 5.11196i | −0.510421 | + | 0.548059i | ||||
\(88\) | 4.38866 | − | 7.60138i | 0.467833 | − | 0.810310i | ||||
\(89\) | 2.59776 | − | 4.49945i | 0.275362 | − | 0.476941i | −0.694864 | − | 0.719141i | \(-0.744536\pi\) |
0.970226 | + | 0.242200i | \(0.0778690\pi\) | |||||||
\(90\) | −7.44716 | − | 3.62047i | −0.784999 | − | 0.381631i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.08205 | + | 12.2665i | 0.738354 | + | 1.27887i | ||||
\(93\) | 0.743014 | + | 2.42476i | 0.0770469 | + | 0.251436i | ||||
\(94\) | −6.86726 | −0.708303 | ||||||||
\(95\) | 6.82490 | 0.700220 | ||||||||
\(96\) | −3.81877 | − | 12.4622i | −0.389752 | − | 1.27192i | ||||
\(97\) | 2.48521 | + | 4.30451i | 0.252335 | + | 0.437057i | 0.964168 | − | 0.265291i | \(-0.0854682\pi\) |
−0.711833 | + | 0.702348i | \(0.752135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.16714 | + | 16.3905i | 0.117302 | + | 1.64731i | ||||
\(100\) | 4.64005 | − | 8.03680i | 0.464005 | − | 0.803680i | ||||
\(101\) | 0.00266904 | − | 0.00462292i | 0.000265580 | − | 0.000459997i | −0.865893 | − | 0.500230i | \(-0.833249\pi\) |
0.866158 | + | 0.499770i | \(0.166582\pi\) | |||||||
\(102\) | 12.3735 | − | 13.2860i | 1.22516 | − | 1.31551i | ||||
\(103\) | 6.51741 | + | 11.2885i | 0.642180 | + | 1.11229i | 0.984945 | + | 0.172867i | \(0.0553030\pi\) |
−0.342765 | + | 0.939421i | \(0.611364\pi\) | |||||||
\(104\) | −3.80217 | + | 6.58555i | −0.372834 | + | 0.645767i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.77268 | + | 13.4627i | 0.754950 | + | 1.30761i | ||||
\(107\) | −4.71081 | + | 8.15936i | −0.455411 | + | 0.788795i | −0.998712 | − | 0.0507430i | \(-0.983841\pi\) |
0.543301 | + | 0.839538i | \(0.317174\pi\) | |||||||
\(108\) | −11.0669 | − | 8.92677i | −1.06491 | − | 0.858979i | ||||
\(109\) | −8.44513 | − | 14.6274i | −0.808896 | − | 1.40105i | −0.913629 | − | 0.406549i | \(-0.866732\pi\) |
0.104732 | − | 0.994500i | \(-0.466601\pi\) | |||||||
\(110\) | 15.1185 | 1.44149 | ||||||||
\(111\) | −3.23798 | − | 0.745372i | −0.307335 | − | 0.0707476i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.07313 | + | 5.32281i | −0.289095 | + | 0.500728i | −0.973594 | − | 0.228286i | \(-0.926688\pi\) |
0.684499 | + | 0.729014i | \(0.260021\pi\) | |||||||
\(114\) | 19.7673 | + | 4.55037i | 1.85138 | + | 0.426181i | ||||
\(115\) | −3.28253 | + | 5.68551i | −0.306098 | + | 0.530176i | ||||
\(116\) | 5.51797 | + | 9.55741i | 0.512331 | + | 0.887383i | ||||
\(117\) | −1.01117 | − | 14.2001i | −0.0934823 | − | 1.31280i | ||||
\(118\) | −0.671790 | −0.0618432 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.39915 | + | 2.57607i | −0.219012 | + | 0.235162i | ||||
\(121\) | −9.50058 | − | 16.4555i | −0.863689 | − | 1.49595i | ||||
\(122\) | −22.5093 | −2.03790 | ||||||||
\(123\) | 6.57636 | + | 1.51386i | 0.592970 | + | 0.136500i | ||||
\(124\) | 4.00649 | 0.359794 | ||||||||
\(125\) | 10.6428 | 0.951919 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.9305 | −1.23613 | −0.618065 | − | 0.786127i | \(-0.712083\pi\) | ||||
−0.618065 | + | 0.786127i | \(0.712083\pi\) | |||||||
\(128\) | −11.9510 | −1.05633 | ||||||||
\(129\) | 3.91947 | − | 4.20850i | 0.345090 | − | 0.370538i | ||||
\(130\) | −13.0981 | −1.14878 | ||||||||
\(131\) | −0.0895778 | − | 0.155153i | −0.00782645 | − | 0.0135558i | 0.862086 | − | 0.506763i | \(-0.169158\pi\) |
−0.869912 | + | 0.493207i | \(0.835825\pi\) | |||||||
\(132\) | 25.2980 | + | 5.82351i | 2.20191 | + | 0.506872i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.73486 | 0.840964 | ||||||||
\(135\) | 1.01849 | − | 6.51105i | 0.0876574 | − | 0.560382i | ||||
\(136\) | −3.85913 | − | 6.68420i | −0.330917 | − | 0.573166i | ||||
\(137\) | −1.57603 | + | 2.72977i | −0.134649 | + | 0.233220i | −0.925463 | − | 0.378837i | \(-0.876324\pi\) |
0.790814 | + | 0.612056i | \(0.209657\pi\) | |||||||
\(138\) | −13.2981 | + | 14.2787i | −1.13201 | + | 1.21548i | ||||
\(139\) | −9.42857 | + | 16.3308i | −0.799721 | + | 1.38516i | 0.120077 | + | 0.992765i | \(0.461686\pi\) |
−0.919798 | + | 0.392392i | \(0.871648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.60126 | − | 5.22558i | −0.134851 | − | 0.440073i | ||||
\(142\) | −4.28054 | −0.359215 | ||||||||
\(143\) | 12.9959 | + | 22.5096i | 1.08677 | + | 1.88235i | ||||
\(144\) | 4.93307 | − | 3.33656i | 0.411089 | − | 0.278046i | ||||
\(145\) | −2.55758 | + | 4.42986i | −0.212396 | + | 0.367880i | ||||
\(146\) | −11.4804 | − | 19.8846i | −0.950122 | − | 1.64566i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.62461 | + | 4.54595i | −0.215741 | + | 0.373675i | ||||
\(149\) | 10.6370 | + | 18.4238i | 0.871418 | + | 1.50934i | 0.860530 | + | 0.509400i | \(0.170132\pi\) |
0.0108879 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(150\) | 12.4582 | + | 2.86783i | 1.01720 | + | 0.234157i | ||||
\(151\) | −3.18281 | + | 5.51278i | −0.259013 | + | 0.448624i | −0.965978 | − | 0.258625i | \(-0.916731\pi\) |
0.706965 | + | 0.707249i | \(0.250064\pi\) | |||||||
\(152\) | 4.31163 | − | 7.46796i | 0.349719 | − | 0.605731i | ||||
\(153\) | 12.9950 | + | 6.31759i | 1.05059 | + | 0.510747i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.928506 | + | 1.60822i | 0.0745794 | + | 0.129175i | ||||
\(156\) | −21.9172 | − | 5.04527i | −1.75478 | − | 0.403945i | ||||
\(157\) | −1.39595 | −0.111409 | −0.0557045 | − | 0.998447i | \(-0.517740\pi\) | ||||
−0.0557045 | + | 0.998447i | \(0.517740\pi\) | |||||||
\(158\) | −19.6226 | −1.56109 | ||||||||
\(159\) | −8.43193 | + | 9.05370i | −0.668695 | + | 0.718005i | ||||
\(160\) | −4.77212 | − | 8.26556i | −0.377269 | − | 0.653450i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.29101 | − | 18.1792i | 0.572836 | − | 1.42829i | ||||
\(163\) | 9.53086 | − | 16.5079i | 0.746515 | − | 1.29300i | −0.202969 | − | 0.979185i | \(-0.565059\pi\) |
0.949484 | − | 0.313816i | \(-0.101608\pi\) | |||||||
\(164\) | 5.33059 | − | 9.23286i | 0.416249 | − | 0.720965i | ||||
\(165\) | 3.52523 | + | 11.5043i | 0.274439 | + | 0.895607i | ||||
\(166\) | 11.0562 | + | 19.1498i | 0.858124 | + | 1.48631i | ||||
\(167\) | −0.872003 | + | 1.51035i | −0.0674776 | + | 0.116875i | −0.897790 | − | 0.440423i | \(-0.854828\pi\) |
0.830313 | + | 0.557298i | \(0.188162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.75919 | − | 8.24317i | −0.366092 | − | 0.634090i | ||||
\(170\) | 6.64715 | − | 11.5132i | 0.509813 | − | 0.883022i | ||||
\(171\) | 1.14665 | + | 16.1028i | 0.0876867 | + | 1.23141i | ||||
\(172\) | −4.54276 | − | 7.86828i | −0.346382 | − | 0.599951i | ||||
\(173\) | 10.0759 | 0.766056 | 0.383028 | − | 0.923737i | \(-0.374881\pi\) | ||||
0.383028 | + | 0.923737i | \(0.374881\pi\) | |||||||
\(174\) | −10.3612 | + | 11.1252i | −0.785478 | + | 0.843400i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.43669 | + | 9.41662i | −0.409806 | + | 0.709805i | ||||
\(177\) | −0.156644 | − | 0.511193i | −0.0117741 | − | 0.0384236i | ||||
\(178\) | 5.65353 | − | 9.79221i | 0.423750 | − | 0.733957i | ||||
\(179\) | 9.27118 | + | 16.0582i | 0.692961 | + | 1.20024i | 0.970863 | + | 0.239634i | \(0.0770275\pi\) |
−0.277902 | + | 0.960609i | \(0.589639\pi\) | |||||||
\(180\) | −9.36349 | − | 4.55211i | −0.697914 | − | 0.339294i | ||||
\(181\) | 8.80982 | 0.654829 | 0.327414 | − | 0.944881i | \(-0.393823\pi\) | ||||
0.327414 | + | 0.944881i | \(0.393823\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.24858 | − | 17.1283i | −0.387986 | − | 1.26616i | ||||
\(184\) | 4.14747 | + | 7.18363i | 0.305756 | + | 0.529584i | ||||
\(185\) | −2.43301 | −0.178879 | ||||||||
\(186\) | 1.61703 | + | 5.27703i | 0.118566 | + | 0.386930i | ||||
\(187\) | −26.3812 | −1.92919 | ||||||||
\(188\) | −8.63437 | −0.629726 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.8531 | 1.07756 | ||||||||
\(191\) | 4.90939 | 0.355231 | 0.177615 | − | 0.984100i | \(-0.443162\pi\) | ||||
0.177615 | + | 0.984100i | \(0.443162\pi\) | |||||||
\(192\) | −6.29606 | − | 20.5466i | −0.454379 | − | 1.48283i | ||||
\(193\) | −9.76760 | −0.703087 | −0.351544 | − | 0.936171i | \(-0.614343\pi\) | ||||
−0.351544 | + | 0.936171i | \(0.614343\pi\) | |||||||
\(194\) | 5.40859 | + | 9.36796i | 0.388314 | + | 0.672580i | ||||
\(195\) | −3.05413 | − | 9.96688i | −0.218711 | − | 0.713743i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.31445 | 0.236145 | 0.118073 | − | 0.993005i | \(-0.462328\pi\) | ||||
0.118073 | + | 0.993005i | \(0.462328\pi\) | |||||||
\(198\) | 2.54006 | + | 35.6708i | 0.180514 | + | 2.53501i | ||||
\(199\) | 5.54432 | + | 9.60304i | 0.393026 | + | 0.680742i | 0.992847 | − | 0.119393i | \(-0.0380948\pi\) |
−0.599821 | + | 0.800134i | \(0.704761\pi\) | |||||||
\(200\) | 2.71736 | − | 4.70661i | 0.192146 | − | 0.332807i | ||||
\(201\) | 2.26991 | + | 7.40766i | 0.160107 | + | 0.522496i | ||||
\(202\) | 0.00580866 | − | 0.0100609i | 0.000408696 | − | 0.000707883i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 15.5575 | − | 16.7048i | 1.08925 | − | 1.16957i | ||||
\(205\) | 4.94146 | 0.345127 | ||||||||
\(206\) | 14.1839 | + | 24.5673i | 0.988240 | + | 1.71168i | ||||
\(207\) | −13.9660 | − | 6.78963i | −0.970703 | − | 0.471912i | ||||
\(208\) | 4.71014 | − | 8.15821i | 0.326590 | − | 0.565670i | ||||
\(209\) | −14.7373 | − | 25.5257i | −1.01940 | − | 1.76565i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.66118 | + | 6.34135i | −0.252046 | + | 0.436557i | −0.964089 | − | 0.265579i | \(-0.914437\pi\) |
0.712043 | + | 0.702136i | \(0.247770\pi\) | |||||||
\(212\) | 9.77278 | + | 16.9270i | 0.671198 | + | 1.16255i | ||||
\(213\) | −0.998111 | − | 3.25724i | −0.0683894 | − | 0.223183i | ||||
\(214\) | −10.2522 | + | 17.7573i | −0.700825 | + | 1.21386i | ||||
\(215\) | 2.10557 | − | 3.64695i | 0.143599 | − | 0.248720i | ||||
\(216\) | −6.48110 | − | 5.22780i | −0.440983 | − | 0.355707i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.3792 | − | 31.8337i | −1.24480 | − | 2.15605i | ||||
\(219\) | 12.4541 | − | 13.3724i | 0.841569 | − | 0.903626i | ||||
\(220\) | 19.0088 | 1.28158 | ||||||||
\(221\) | 22.8557 | 1.53744 | ||||||||
\(222\) | −7.04685 | − | 1.62216i | −0.472954 | − | 0.108872i | ||||
\(223\) | −2.02765 | − | 3.51199i | −0.135782 | − | 0.235181i | 0.790114 | − | 0.612960i | \(-0.210021\pi\) |
−0.925896 | + | 0.377779i | \(0.876688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.722667 | + | 10.1486i | 0.0481778 | + | 0.676575i | ||||
\(226\) | −6.68808 | + | 11.5841i | −0.444884 | + | 0.770562i | ||||
\(227\) | 0.667087 | − | 1.15543i | 0.0442761 | − | 0.0766884i | −0.843038 | − | 0.537854i | \(-0.819235\pi\) |
0.887314 | + | 0.461165i | \(0.152569\pi\) | |||||||
\(228\) | 24.8539 | + | 5.72129i | 1.64599 | + | 0.378902i | ||||
\(229\) | −7.99832 | − | 13.8535i | −0.528544 | − | 0.915465i | −0.999446 | − | 0.0332795i | \(-0.989405\pi\) |
0.470902 | − | 0.882185i | \(-0.343928\pi\) | |||||||
\(230\) | −7.14381 | + | 12.3734i | −0.471049 | + | 0.815880i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.23150 | + | 5.59712i | 0.212158 | + | 0.367469i | ||||
\(233\) | −4.06542 | + | 7.04151i | −0.266334 | + | 0.461305i | −0.967912 | − | 0.251288i | \(-0.919146\pi\) |
0.701578 | + | 0.712593i | \(0.252479\pi\) | |||||||
\(234\) | −2.20061 | − | 30.9038i | −0.143858 | − | 2.02025i | ||||
\(235\) | −2.00102 | − | 3.46586i | −0.130532 | − | 0.226088i | ||||
\(236\) | −0.844658 | −0.0549825 | ||||||||
\(237\) | −4.57547 | − | 14.9316i | −0.297208 | − | 0.969913i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0509 | − | 19.1407i | 0.714823 | − | 1.23811i | −0.248204 | − | 0.968708i | \(-0.579840\pi\) |
0.963028 | − | 0.269403i | \(-0.0868262\pi\) | |||||||
\(240\) | 2.97208 | − | 3.19124i | 0.191847 | − | 0.205994i | ||||
\(241\) | 13.7973 | − | 23.8977i | 0.888765 | − | 1.53939i | 0.0474292 | − | 0.998875i | \(-0.484897\pi\) |
0.841336 | − | 0.540512i | \(-0.181770\pi\) | |||||||
\(242\) | −20.6762 | − | 35.8122i | −1.32912 | − | 2.30210i | ||||
\(243\) | 15.5334 | + | 1.30911i | 0.996467 | + | 0.0839796i | ||||
\(244\) | −28.3015 | −1.81182 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 14.3122 | + | 3.29462i | 0.912513 | + | 0.210057i | ||||
\(247\) | 12.7678 | + | 22.1145i | 0.812397 | + | 1.40711i | ||||
\(248\) | 2.34633 | 0.148992 | ||||||||
\(249\) | −11.9939 | + | 12.8783i | −0.760082 | + | 0.816131i | ||||
\(250\) | 23.1620 | 1.46489 | ||||||||
\(251\) | 16.5610 | 1.04532 | 0.522661 | − | 0.852541i | \(-0.324939\pi\) | ||||
0.522661 | + | 0.852541i | \(0.324939\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.3524 | 1.78250 | ||||||||
\(254\) | −30.3171 | −1.90226 | ||||||||
\(255\) | 10.3108 | + | 2.37351i | 0.645688 | + | 0.148635i | ||||
\(256\) | −1.19503 | −0.0746896 | ||||||||
\(257\) | 1.03287 | + | 1.78898i | 0.0644285 | + | 0.111593i | 0.896440 | − | 0.443164i | \(-0.146144\pi\) |
−0.832012 | + | 0.554758i | \(0.812811\pi\) | |||||||
\(258\) | 8.53000 | − | 9.15900i | 0.531054 | − | 0.570214i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.4686 | −1.02134 | ||||||||
\(261\) | −10.8816 | − | 5.29014i | −0.673553 | − | 0.327451i | ||||
\(262\) | −0.194949 | − | 0.337662i | −0.0120440 | − | 0.0208608i | ||||
\(263\) | −5.06482 | + | 8.77252i | −0.312310 | + | 0.540937i | −0.978862 | − | 0.204522i | \(-0.934436\pi\) |
0.666552 | + | 0.745458i | \(0.267769\pi\) | |||||||
\(264\) | 14.8153 | + | 3.41043i | 0.911819 | + | 0.209898i | ||||
\(265\) | −4.52969 | + | 7.84565i | −0.278257 | + | 0.481954i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.76955 | + | 2.01872i | 0.536688 | + | 0.123544i | ||||
\(268\) | 12.2399 | 0.747670 | ||||||||
\(269\) | −7.54972 | − | 13.0765i | −0.460315 | − | 0.797289i | 0.538662 | − | 0.842522i | \(-0.318930\pi\) |
−0.998976 | + | 0.0452336i | \(0.985597\pi\) | |||||||
\(270\) | 2.21654 | − | 14.1701i | 0.134895 | − | 0.862363i | ||||
\(271\) | −14.4026 | + | 24.9459i | −0.874893 | + | 1.51536i | −0.0180156 | + | 0.999838i | \(0.505735\pi\) |
−0.856877 | + | 0.515521i | \(0.827598\pi\) | |||||||
\(272\) | 4.78070 | + | 8.28041i | 0.289872 | + | 0.502074i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.42993 | + | 5.94082i | −0.207210 | + | 0.358898i | ||||
\(275\) | −9.28802 | − | 16.0873i | −0.560089 | − | 0.970102i | ||||
\(276\) | −16.7200 | + | 17.9529i | −1.00642 | + | 1.08064i | ||||
\(277\) | 1.34982 | − | 2.33795i | 0.0811026 | − | 0.140474i | −0.822621 | − | 0.568590i | \(-0.807489\pi\) |
0.903724 | + | 0.428116i | \(0.140823\pi\) | |||||||
\(278\) | −20.5195 | + | 35.5408i | −1.23068 | + | 2.13160i | ||||
\(279\) | −3.63846 | + | 2.46093i | −0.217829 | + | 0.147332i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.46312 | − | 4.26626i | −0.146938 | − | 0.254503i | 0.783157 | − | 0.621825i | \(-0.213608\pi\) |
−0.930094 | + | 0.367321i | \(0.880275\pi\) | |||||||
\(282\) | −3.48485 | − | 11.3725i | −0.207520 | − | 0.677222i | ||||
\(283\) | −3.58157 | −0.212903 | −0.106451 | − | 0.994318i | \(-0.533949\pi\) | ||||
−0.106451 | + | 0.994318i | \(0.533949\pi\) | |||||||
\(284\) | −5.38203 | −0.319365 | ||||||||
\(285\) | 3.46336 | + | 11.3024i | 0.205152 | + | 0.669493i | ||||
\(286\) | 28.2832 | + | 48.9879i | 1.67242 | + | 2.89672i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 18.7001 | − | 12.6481i | 1.10192 | − | 0.745298i | ||||
\(289\) | −3.09903 | + | 5.36768i | −0.182296 | + | 0.315746i | ||||
\(290\) | −5.56609 | + | 9.64075i | −0.326852 | + | 0.566125i | ||||
\(291\) | −5.86732 | + | 6.29998i | −0.343949 | + | 0.369312i | ||||
\(292\) | −14.4345 | − | 25.0014i | −0.844718 | − | 1.46309i | ||||
\(293\) | −12.1955 | + | 21.1232i | −0.712469 | + | 1.23403i | 0.251459 | + | 0.967868i | \(0.419090\pi\) |
−0.963928 | + | 0.266164i | \(0.914244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.195750 | − | 0.339048i | −0.0113970 | − | 0.0197401i | ||||
\(296\) | −1.53705 | + | 2.66225i | −0.0893394 | + | 0.154740i | ||||
\(297\) | −26.5511 | + | 10.2503i | −1.54065 | + | 0.594784i | ||||
\(298\) | 23.1494 | + | 40.0960i | 1.34101 | + | 2.32270i | ||||
\(299\) | −24.5634 | −1.42054 | ||||||||
\(300\) | 15.6639 | + | 3.60579i | 0.904358 | + | 0.208180i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.92678 | + | 11.9975i | −0.398591 | + | 0.690380i | ||||
\(303\) | 0.00901018 | + | 0.00207412i | 0.000517622 | + | 0.000119155i | ||||
\(304\) | −5.34126 | + | 9.25134i | −0.306342 | + | 0.530600i | ||||
\(305\) | −6.55887 | − | 11.3603i | −0.375560 | − | 0.650489i | ||||
\(306\) | 28.2812 | + | 13.7491i | 1.61673 | + | 0.785981i | ||||
\(307\) | 23.9025 | 1.36419 | 0.682094 | − | 0.731265i | \(-0.261070\pi\) | ||||
0.682094 | + | 0.731265i | \(0.261070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.3869 | + | 16.5216i | −0.875332 | + | 0.939879i | ||||
\(310\) | 2.02072 | + | 3.49998i | 0.114769 | + | 0.198786i | ||||
\(311\) | 12.9416 | 0.733853 | 0.366926 | − | 0.930250i | \(-0.380410\pi\) | ||||
0.366926 | + | 0.930250i | \(0.380410\pi\) | |||||||
\(312\) | −12.8354 | − | 2.95467i | −0.726663 | − | 0.167275i | ||||
\(313\) | 26.8681 | 1.51867 | 0.759336 | − | 0.650698i | \(-0.225524\pi\) | ||||
0.759336 | + | 0.650698i | \(0.225524\pi\) | |||||||
\(314\) | −3.03802 | −0.171446 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.6719 | −1.38790 | ||||||||
\(317\) | 8.31169 | 0.466831 | 0.233415 | − | 0.972377i | \(-0.425010\pi\) | ||||
0.233415 | + | 0.972377i | \(0.425010\pi\) | |||||||
\(318\) | −18.3505 | + | 19.7037i | −1.02904 | + | 1.10493i | ||||
\(319\) | 22.0907 | 1.23684 | ||||||||
\(320\) | −7.86786 | − | 13.6275i | −0.439827 | − | 0.761803i | ||||
\(321\) | −15.9028 | − | 3.66078i | −0.887608 | − | 0.204325i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.9182 | −1.44212 | ||||||||
\(324\) | 9.16716 | − | 22.8572i | 0.509287 | − | 1.26984i | ||||
\(325\) | 8.04680 | + | 13.9375i | 0.446356 | + | 0.773111i | ||||
\(326\) | 20.7421 | − | 35.9264i | 1.14880 | − | 1.98978i | ||||
\(327\) | 19.9381 | − | 21.4083i | 1.10258 | − | 1.18388i | ||||
\(328\) | 3.12177 | − | 5.40706i | 0.172371 | − | 0.298555i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.67201 | + | 25.0369i | 0.422330 | + | 1.37824i | ||||
\(331\) | 12.3978 | 0.681443 | 0.340722 | − | 0.940164i | \(-0.389329\pi\) | ||||
0.340722 | + | 0.940164i | \(0.389329\pi\) | |||||||
\(332\) | 13.9012 | + | 24.0775i | 0.762926 | + | 1.32143i | ||||
\(333\) | −0.408770 | − | 5.74049i | −0.0224005 | − | 0.314577i | ||||
\(334\) | −1.89775 | + | 3.28700i | −0.103840 | + | 0.179857i | ||||
\(335\) | 2.83659 | + | 4.91312i | 0.154980 | + | 0.268433i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.9588 | + | 22.4454i | −0.705913 | + | 1.22268i | 0.260448 | + | 0.965488i | \(0.416130\pi\) |
−0.966361 | + | 0.257189i | \(0.917204\pi\) | |||||||
\(338\) | −10.3575 | − | 17.9397i | −0.563373 | − | 0.975791i | ||||
\(339\) | −10.3743 | − | 2.38813i | −0.563455 | − | 0.129705i | ||||
\(340\) | 8.35762 | − | 14.4758i | 0.453256 | − | 0.785062i | ||||
\(341\) | 4.00992 | − | 6.94538i | 0.217149 | − | 0.376113i | ||||
\(342\) | 2.49547 | + | 35.0447i | 0.134940 | + | 1.89500i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.66038 | − | 4.60792i | −0.143438 | − | 0.248442i | ||||
\(345\) | −11.0812 | − | 2.55086i | −0.596592 | − | 0.137334i | ||||
\(346\) | 21.9283 | 1.17887 | ||||||||
\(347\) | −16.8483 | −0.904464 | −0.452232 | − | 0.891900i | \(-0.649372\pi\) | ||||
−0.452232 | + | 0.891900i | \(0.649372\pi\) | |||||||
\(348\) | −13.0274 | + | 13.9880i | −0.698340 | + | 0.749835i | ||||
\(349\) | −15.5503 | − | 26.9340i | −0.832390 | − | 1.44174i | −0.896138 | − | 0.443776i | \(-0.853639\pi\) |
0.0637477 | − | 0.997966i | \(-0.479695\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.0029 | − | 8.88050i | 1.22780 | − | 0.474006i | ||||
\(352\) | −20.6092 | + | 35.6963i | −1.09848 | + | 1.90262i | ||||
\(353\) | 1.32969 | − | 2.30309i | 0.0707722 | − | 0.122581i | −0.828468 | − | 0.560037i | \(-0.810787\pi\) |
0.899240 | + | 0.437456i | \(0.144120\pi\) | |||||||
\(354\) | −0.340905 | − | 1.11251i | −0.0181189 | − | 0.0591294i | ||||
\(355\) | −1.24729 | − | 2.16036i | −0.0661991 | − | 0.114660i | ||||
\(356\) | 7.10833 | − | 12.3120i | 0.376741 | − | 0.652534i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.1770 | + | 34.9476i | 1.06639 | + | 1.84704i | ||||
\(359\) | 16.2715 | − | 28.1830i | 0.858775 | − | 1.48744i | −0.0143230 | − | 0.999897i | \(-0.504559\pi\) |
0.873098 | − | 0.487545i | \(-0.162107\pi\) | |||||||
\(360\) | −5.48356 | − | 2.66586i | −0.289009 | − | 0.140503i | ||||
\(361\) | −4.97859 | − | 8.62318i | −0.262031 | − | 0.453852i | ||||
\(362\) | 19.1729 | 1.00771 | ||||||||
\(363\) | 22.4299 | − | 24.0839i | 1.17726 | − | 1.26407i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.69042 | − | 11.5881i | 0.350192 | − | 0.606551i | ||||
\(366\) | −11.4225 | − | 37.2764i | −0.597065 | − | 1.94847i | ||||
\(367\) | 7.07678 | − | 12.2573i | 0.369405 | − | 0.639828i | −0.620068 | − | 0.784548i | \(-0.712895\pi\) |
0.989473 | + | 0.144720i | \(0.0462283\pi\) | |||||||
\(368\) | −5.13790 | − | 8.89911i | −0.267832 | − | 0.463898i | ||||
\(369\) | 0.830215 | + | 11.6590i | 0.0432193 | + | 0.606942i | ||||
\(370\) | −5.29499 | −0.275273 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.03313 | + | 6.63494i | 0.105413 | + | 0.344005i | ||||
\(373\) | −1.33814 | − | 2.31773i | −0.0692863 | − | 0.120007i | 0.829301 | − | 0.558802i | \(-0.188739\pi\) |
−0.898587 | + | 0.438795i | \(0.855406\pi\) | |||||||
\(374\) | −57.4137 | −2.96879 | ||||||||
\(375\) | 5.40077 | + | 17.6249i | 0.278894 | + | 0.910147i | ||||
\(376\) | −5.05656 | −0.260772 | ||||||||
\(377\) | −19.1386 | −0.985687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.312929 | −0.0160741 | −0.00803705 | − | 0.999968i | \(-0.502558\pi\) | ||||
−0.00803705 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(380\) | 18.6752 | 0.958017 | ||||||||
\(381\) | −7.06914 | − | 23.0695i | −0.362163 | − | 1.18189i | ||||
\(382\) | 10.6844 | 0.546659 | ||||||||
\(383\) | −4.49440 | − | 7.78453i | −0.229653 | − | 0.397771i | 0.728052 | − | 0.685522i | \(-0.240426\pi\) |
−0.957705 | + | 0.287751i | \(0.907093\pi\) | |||||||
\(384\) | −6.06465 | − | 19.7914i | −0.309485 | − | 1.00998i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.2573 | −1.08197 | ||||||||
\(387\) | 8.95843 | + | 4.35519i | 0.455383 | + | 0.221387i | ||||
\(388\) | 6.80036 | + | 11.7786i | 0.345236 | + | 0.597966i | ||||
\(389\) | 13.4934 | − | 23.3713i | 0.684144 | − | 1.18497i | −0.289560 | − | 0.957160i | \(-0.593509\pi\) |
0.973705 | − | 0.227813i | \(-0.0731575\pi\) | |||||||
\(390\) | −6.64674 | − | 21.6910i | −0.336571 | − | 1.09837i | ||||
\(391\) | 12.4657 | − | 21.5912i | 0.630417 | − | 1.09191i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.211484 | − | 0.227079i | 0.0106680 | − | 0.0114546i | ||||
\(394\) | 7.21328 | 0.363400 | ||||||||
\(395\) | −5.71772 | − | 9.90339i | −0.287690 | − | 0.498293i | ||||
\(396\) | 3.19368 | + | 44.8498i | 0.160488 | + | 2.25379i | ||||
\(397\) | 14.7503 | − | 25.5482i | 0.740295 | − | 1.28223i | −0.212066 | − | 0.977255i | \(-0.568019\pi\) |
0.952361 | − | 0.304973i | \(-0.0986475\pi\) | |||||||
\(398\) | 12.0662 | + | 20.8992i | 0.604822 | + | 1.04758i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.36628 | + | 5.83056i | −0.168314 | + | 0.291528i | ||||
\(401\) | 17.1392 | + | 29.6860i | 0.855891 | + | 1.48245i | 0.875816 | + | 0.482645i | \(0.160324\pi\) |
−0.0199251 | + | 0.999801i | \(0.506343\pi\) | |||||||
\(402\) | 4.94004 | + | 16.1214i | 0.246387 | + | 0.804061i | ||||
\(403\) | −3.47404 | + | 6.01721i | −0.173054 | + | 0.299739i | ||||
\(404\) | 0.00730338 | − | 0.0126498i | 0.000363357 | − | 0.000629352i | ||||
\(405\) | 11.2994 | − | 1.61743i | 0.561473 | − | 0.0803706i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.25369 | + | 9.09966i | 0.260416 | + | 0.451054i | ||||
\(408\) | 9.11099 | − | 9.78284i | 0.451061 | − | 0.484323i | ||||
\(409\) | −10.9845 | −0.543149 | −0.271574 | − | 0.962417i | \(-0.587544\pi\) | ||||
−0.271574 | + | 0.962417i | \(0.587544\pi\) | |||||||
\(410\) | 10.7542 | 0.531110 | ||||||||
\(411\) | −5.32038 | − | 1.22474i | −0.262435 | − | 0.0604117i | ||||
\(412\) | 17.8338 | + | 30.8890i | 0.878608 | + | 1.52179i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −30.3943 | − | 14.7764i | −1.49380 | − | 0.726218i | ||||
\(415\) | −6.44320 | + | 11.1599i | −0.316284 | + | 0.547820i | ||||
\(416\) | 17.8551 | − | 30.9259i | 0.875417 | − | 1.51627i | ||||
\(417\) | −31.8291 | − | 7.32695i | −1.55868 | − | 0.358802i | ||||
\(418\) | −32.0729 | − | 55.5519i | −1.56874 | − | 2.71713i | ||||
\(419\) | 3.33207 | − | 5.77132i | 0.162782 | − | 0.281947i | −0.773083 | − | 0.634305i | \(-0.781286\pi\) |
0.935866 | + | 0.352357i | \(0.114620\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.0430 | − | 29.5193i | −0.830625 | − | 1.43868i | −0.897543 | − | 0.440926i | \(-0.854650\pi\) |
0.0669186 | − | 0.997758i | \(-0.478683\pi\) | |||||||
\(422\) | −7.96787 | + | 13.8008i | −0.387870 | + | 0.671810i | ||||
\(423\) | 7.84122 | − | 5.30353i | 0.381253 | − | 0.257867i | ||||
\(424\) | 5.72325 | + | 9.91297i | 0.277946 | + | 0.481416i | ||||
\(425\) | −16.3347 | −0.792348 | ||||||||
\(426\) | −2.17220 | − | 7.08877i | −0.105243 | − | 0.343452i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.8903 | + | 22.3267i | −0.623077 | + | 1.07920i | ||||
\(429\) | −30.6821 | + | 32.9446i | −1.48134 | + | 1.59058i | ||||
\(430\) | 4.58237 | − | 7.93690i | 0.220982 | − | 0.382751i | ||||
\(431\) | −1.12969 | − | 1.95669i | −0.0544155 | − | 0.0942504i | 0.837535 | − | 0.546384i | \(-0.183996\pi\) |
−0.891950 | + | 0.452134i | \(0.850663\pi\) | |||||||
\(432\) | 8.02881 | + | 6.47622i | 0.386287 | + | 0.311587i | ||||
\(433\) | −34.3904 | −1.65270 | −0.826348 | − | 0.563160i | \(-0.809585\pi\) | ||||
−0.826348 | + | 0.563160i | \(0.809585\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.63392 | − | 1.98750i | −0.413965 | − | 0.0952933i | ||||
\(436\) | −23.1086 | − | 40.0254i | −1.10670 | − | 1.91687i | ||||
\(437\) | 27.8547 | 1.33247 | ||||||||
\(438\) | 27.1039 | − | 29.1026i | 1.29508 | − | 1.39058i | ||||
\(439\) | −5.99139 | −0.285953 | −0.142977 | − | 0.989726i | \(-0.545667\pi\) | ||||
−0.142977 | + | 0.989726i | \(0.545667\pi\) | |||||||
\(440\) | 11.1322 | 0.530706 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 49.7411 | 2.36594 | ||||||||
\(443\) | −39.4380 | −1.87376 | −0.936879 | − | 0.349654i | \(-0.886299\pi\) | ||||
−0.936879 | + | 0.349654i | \(0.886299\pi\) | |||||||
\(444\) | −8.86018 | − | 2.03958i | −0.420486 | − | 0.0967944i | ||||
\(445\) | 6.58942 | 0.312369 | ||||||||
\(446\) | −4.41280 | − | 7.64319i | −0.208952 | − | 0.361916i | ||||
\(447\) | −25.1129 | + | 26.9647i | −1.18780 | + | 1.27539i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.45092 | 0.115666 | 0.0578330 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578330 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(450\) | 1.57275 | + | 22.0866i | 0.0741400 | + | 1.04117i | ||||
\(451\) | −10.6703 | − | 18.4815i | −0.502444 | − | 0.870259i | ||||
\(452\) | −8.40909 | + | 14.5650i | −0.395530 | + | 0.685078i | ||||
\(453\) | −10.7446 | − | 2.47336i | −0.504824 | − | 0.116209i | ||||
\(454\) | 1.45179 | − | 2.51457i | 0.0681358 | − | 0.118015i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.5552 | + | 3.35057i | 0.681612 | + | 0.156905i | ||||
\(457\) | 11.0212 | 0.515548 | 0.257774 | − | 0.966205i | \(-0.417011\pi\) | ||||
0.257774 | + | 0.966205i | \(0.417011\pi\) | |||||||
\(458\) | −17.4068 | − | 30.1495i | −0.813368 | − | 1.40879i | ||||
\(459\) | −3.86779 | + | 24.7263i | −0.180533 | + | 1.15412i | ||||
\(460\) | −8.98208 | + | 15.5574i | −0.418792 | + | 0.725369i | ||||
\(461\) | −14.6540 | − | 25.3814i | −0.682503 | − | 1.18213i | −0.974215 | − | 0.225624i | \(-0.927558\pi\) |
0.291711 | − | 0.956506i | \(-0.405775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.593566 | − | 1.02809i | 0.0275853 | − | 0.0477792i | −0.851903 | − | 0.523699i | \(-0.824552\pi\) |
0.879489 | + | 0.475920i | \(0.157885\pi\) | |||||||
\(464\) | −4.00319 | − | 6.93374i | −0.185844 | − | 0.321891i | ||||
\(465\) | −2.19211 | + | 2.35375i | −0.101656 | + | 0.109153i | ||||
\(466\) | −8.84761 | + | 15.3245i | −0.409858 | + | 0.709894i | ||||
\(467\) | 11.0573 | − | 19.1519i | 0.511673 | − | 0.886243i | −0.488236 | − | 0.872712i | \(-0.662359\pi\) |
0.999908 | − | 0.0135313i | \(-0.00430729\pi\) | |||||||
\(468\) | −2.76688 | − | 38.8562i | −0.127899 | − | 1.79613i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.35483 | − | 7.54280i | −0.200874 | − | 0.347923i | ||||
\(471\) | −0.708387 | − | 2.31176i | −0.0326408 | − | 0.106520i | ||||
\(472\) | −0.494658 | −0.0227685 | ||||||||
\(473\) | −18.1865 | −0.836218 | ||||||||
\(474\) | −9.95764 | − | 32.4958i | −0.457369 | − | 1.49258i | ||||
\(475\) | −9.12499 | − | 15.8050i | −0.418683 | − | 0.725181i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.2722 | − | 9.36927i | −0.882413 | − | 0.428990i | ||||
\(478\) | 24.0502 | − | 41.6562i | 1.10003 | − | 1.90531i | ||||
\(479\) | −12.5714 | + | 21.7743i | −0.574402 | + | 0.994894i | 0.421704 | + | 0.906734i | \(0.361432\pi\) |
−0.996106 | + | 0.0881606i | \(0.971901\pi\) | |||||||
\(480\) | 11.2665 | − | 12.0973i | 0.514242 | − | 0.552163i | ||||
\(481\) | −4.55160 | − | 7.88361i | −0.207535 | − | 0.359462i | ||||
\(482\) | 30.0273 | − | 52.0088i | 1.36771 | − | 2.36894i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.9967 | − | 45.0276i | −1.18167 | − | 2.04671i | ||||
\(485\) | −3.15197 | + | 5.45937i | −0.143123 | + | 0.247897i | ||||
\(486\) | 33.8055 | + | 2.84904i | 1.53345 | + | 0.129235i | ||||
\(487\) | −6.78904 | − | 11.7590i | −0.307641 | − | 0.532849i | 0.670205 | − | 0.742176i | \(-0.266206\pi\) |
−0.977846 | + | 0.209327i | \(0.932873\pi\) | |||||||
\(488\) | −16.5743 | −0.750281 | ||||||||
\(489\) | 32.1744 | + | 7.40644i | 1.45498 | + | 0.334931i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.25177 | − | 12.5604i | 0.327268 | − | 0.566844i | −0.654701 | − | 0.755888i | \(-0.727205\pi\) |
0.981969 | + | 0.189044i | \(0.0605387\pi\) | |||||||
\(492\) | 17.9951 | + | 4.14241i | 0.811281 | + | 0.186754i | ||||
\(493\) | 9.71263 | − | 16.8228i | 0.437435 | − | 0.757659i | ||||
\(494\) | 27.7868 | + | 48.1281i | 1.25019 | + | 2.16538i | ||||
\(495\) | −17.2627 | + | 11.6759i | −0.775901 | + | 0.524792i | ||||
\(496\) | −2.90664 | −0.130512 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −26.1024 | + | 28.0272i | −1.16968 | + | 1.25593i | ||||
\(499\) | −6.99574 | − | 12.1170i | −0.313172 | − | 0.542431i | 0.665875 | − | 0.746063i | \(-0.268058\pi\) |
−0.979047 | + | 0.203633i | \(0.934725\pi\) | |||||||
\(500\) | 29.1221 | 1.30238 | ||||||||
\(501\) | −2.94372 | − | 0.677635i | −0.131516 | − | 0.0302745i | ||||
\(502\) | 36.0419 | 1.60863 | ||||||||
\(503\) | −28.4011 | −1.26634 | −0.633171 | − | 0.774012i | \(-0.718247\pi\) | ||||
−0.633171 | + | 0.774012i | \(0.718247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.00677023 | 0.000301271 | ||||||||
\(506\) | 61.7036 | 2.74306 | ||||||||
\(507\) | 11.2360 | − | 12.0645i | 0.499007 | − | 0.535803i | ||||
\(508\) | −38.1184 | −1.69123 | ||||||||
\(509\) | −1.72997 | − | 2.99639i | −0.0766794 | − | 0.132813i | 0.825136 | − | 0.564934i | \(-0.191098\pi\) |
−0.901815 | + | 0.432122i | \(0.857765\pi\) | |||||||
\(510\) | 22.4395 | + | 5.16550i | 0.993639 | + | 0.228732i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.3013 | 0.941392 | ||||||||
\(513\) | −26.0851 | + | 10.0704i | −1.15168 | + | 0.444619i | ||||
\(514\) | 2.24784 | + | 3.89337i | 0.0991480 | + | 0.171729i | ||||
\(515\) | −8.26597 | + | 14.3171i | −0.364242 | + | 0.630886i | ||||
\(516\) | 10.7250 | − | 11.5158i | 0.472141 | − | 0.506956i | ||||
\(517\) | −8.64174 | + | 14.9679i | −0.380063 | + | 0.658289i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.11310 | + | 16.6861i | 0.224440 | + | 0.732440i | ||||
\(520\) | −9.64451 | −0.422940 | ||||||||
\(521\) | 3.56797 | + | 6.17991i | 0.156316 | + | 0.270747i | 0.933537 | − | 0.358480i | \(-0.116705\pi\) |
−0.777222 | + | 0.629227i | \(0.783372\pi\) | |||||||
\(522\) | −23.6817 | − | 11.5130i | −1.03652 | − | 0.503910i | ||||
\(523\) | −6.53235 | + | 11.3144i | −0.285640 | + | 0.494743i | −0.972764 | − | 0.231797i | \(-0.925539\pi\) |
0.687124 | + | 0.726540i | \(0.258873\pi\) | |||||||
\(524\) | −0.245114 | − | 0.424551i | −0.0107079 | − | 0.0185466i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.0226 | + | 19.0917i | −0.480609 | + | 0.832439i | ||||
\(527\) | −3.52608 | − | 6.10735i | −0.153598 | − | 0.266040i | ||||
\(528\) | −18.3532 | − | 4.22486i | −0.798723 | − | 0.183863i | ||||
\(529\) | −1.89710 | + | 3.28587i | −0.0824825 | + | 0.142864i | ||||
\(530\) | −9.85801 | + | 17.0746i | −0.428205 | + | 0.741672i | ||||
\(531\) | 0.767068 | − | 0.518818i | 0.0332879 | − | 0.0225148i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.24434 | + | 16.0117i | 0.400417 | + | 0.693542i | ||||
\(534\) | 19.0853 | + | 4.39337i | 0.825900 | + | 0.190120i | ||||
\(535\) | −11.9493 | −0.516615 | ||||||||
\(536\) | 7.16806 | 0.309613 | ||||||||
\(537\) | −21.8883 | + | 23.5024i | −0.944550 | + | 1.01420i | ||||
\(538\) | −16.4305 | − | 28.4585i | −0.708371 | − | 1.22693i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.78691 | − | 17.8164i | 0.119930 | − | 0.766695i | ||||
\(541\) | −2.46788 | + | 4.27450i | −0.106103 | + | 0.183775i | −0.914188 | − | 0.405290i | \(-0.867171\pi\) |
0.808086 | + | 0.589065i | \(0.200504\pi\) | |||||||
\(542\) | −31.3444 | + | 54.2901i | −1.34636 | + | 2.33196i | ||||
\(543\) | 4.47062 | + | 14.5895i | 0.191853 | + | 0.626094i | ||||
\(544\) | 18.1225 | + | 31.3892i | 0.776997 | + | 1.34580i | ||||
\(545\) | 10.7109 | − | 18.5518i | 0.458803 | − | 0.794670i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.559964 | + | 0.969887i | 0.0239423 | + | 0.0414694i | 0.877748 | − | 0.479122i | \(-0.159045\pi\) |
−0.853806 | + | 0.520591i | \(0.825712\pi\) | |||||||
\(548\) | −4.31254 | + | 7.46954i | −0.184223 | + | 0.319083i | ||||
\(549\) | 25.7017 | − | 17.3838i | 1.09692 | − | 0.741921i | ||||
\(550\) | −20.2136 | − | 35.0110i | −0.861912 | − | 1.49288i | ||||
\(551\) | 21.7030 | 0.924578 | ||||||||
\(552\) | −9.79175 | + | 10.5138i | −0.416764 | + | 0.447497i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.93762 | − | 5.08811i | 0.124808 | − | 0.216173i | ||||
\(555\) | −1.23465 | − | 4.02918i | −0.0524081 | − | 0.171029i | ||||
\(556\) | −25.7997 | + | 44.6863i | −1.09415 | + | 1.89512i | ||||
\(557\) | 5.47832 | + | 9.48873i | 0.232124 | + | 0.402050i | 0.958433 | − | 0.285318i | \(-0.0920992\pi\) |
−0.726309 | + | 0.687368i | \(0.758766\pi\) | |||||||
\(558\) | −7.91842 | + | 5.35575i | −0.335213 | + | 0.226727i | ||||
\(559\) | 15.7561 | 0.666413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.3874 | − | 43.6885i | −0.565215 | − | 1.84453i | ||||
\(562\) | −5.36052 | − | 9.28470i | −0.226120 | − | 0.391651i | ||||
\(563\) | 4.76096 | 0.200650 | 0.100325 | − | 0.994955i | \(-0.468012\pi\) | ||||
0.100325 | + | 0.994955i | \(0.468012\pi\) | |||||||
\(564\) | −4.38159 | − | 14.2989i | −0.184498 | − | 0.602093i | ||||
\(565\) | −7.79523 | −0.327948 | ||||||||
\(566\) | −7.79462 | −0.327632 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.15189 | −0.132250 | ||||||||
\(569\) | 3.49976 | 0.146718 | 0.0733588 | − | 0.997306i | \(-0.476628\pi\) | ||||
0.0733588 | + | 0.997306i | \(0.476628\pi\) | |||||||
\(570\) | 7.53734 | + | 24.5974i | 0.315704 | + | 1.03027i | ||||
\(571\) | 7.06101 | 0.295494 | 0.147747 | − | 0.989025i | \(-0.452798\pi\) | ||||
0.147747 | + | 0.989025i | \(0.452798\pi\) | |||||||
\(572\) | 35.5612 | + | 61.5937i | 1.48689 | + | 2.57536i | ||||
\(573\) | 2.49131 | + | 8.13017i | 0.104076 | + | 0.339643i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.5552 | 0.732101 | ||||||||
\(576\) | 30.8312 | − | 20.8531i | 1.28463 | − | 0.868881i | ||||
\(577\) | 6.44149 | + | 11.1570i | 0.268163 | + | 0.464472i | 0.968387 | − | 0.249451i | \(-0.0802502\pi\) |
−0.700225 | + | 0.713923i | \(0.746917\pi\) | |||||||
\(578\) | −6.74445 | + | 11.6817i | −0.280532 | + | 0.485896i | ||||
\(579\) | −4.95665 | − | 16.1756i | −0.205991 | − | 0.672235i | ||||
\(580\) | −6.99838 | + | 12.1216i | −0.290592 | + | 0.503320i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.7691 | + | 13.7107i | −0.529297 | + | 0.568328i | ||||
\(583\) | 39.1245 | 1.62037 | ||||||||
\(584\) | −8.45333 | − | 14.6416i | −0.349801 | − | 0.605874i | ||||
\(585\) | 14.9558 | − | 10.1156i | 0.618345 | − | 0.418227i | ||||
\(586\) | −26.5412 | + | 45.9707i | −1.09641 | + | 1.89903i | ||||
\(587\) | 19.5044 | + | 33.7826i | 0.805034 | + | 1.39436i | 0.916268 | + | 0.400565i | \(0.131186\pi\) |
−0.111235 | + | 0.993794i | \(0.535481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.93953 | − | 6.82347i | 0.162326 | − | 0.281156i | ||||
\(590\) | −0.426012 | − | 0.737874i | −0.0175386 | − | 0.0303778i | ||||
\(591\) | 1.68195 | + | 5.48889i | 0.0691861 | + | 0.225783i | ||||
\(592\) | 1.90411 | − | 3.29801i | 0.0782583 | − | 0.135547i | ||||
\(593\) | 20.1513 | − | 34.9031i | 0.827515 | − | 1.43330i | −0.0724676 | − | 0.997371i | \(-0.523087\pi\) |
0.899982 | − | 0.435927i | \(-0.143579\pi\) | |||||||
\(594\) | −57.7835 | + | 22.3079i | −2.37089 | + | 0.915304i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.1064 | + | 50.4137i | 1.19224 | + | 2.06503i | ||||
\(597\) | −13.0896 | + | 14.0548i | −0.535720 | + | 0.575224i | ||||
\(598\) | −53.4577 | −2.18605 | ||||||||
\(599\) | −12.7821 | −0.522261 | −0.261130 | − | 0.965304i | \(-0.584095\pi\) | ||||
−0.261130 | + | 0.965304i | \(0.584095\pi\) | |||||||
\(600\) | 9.17330 | + | 2.11166i | 0.374499 | + | 0.0862084i | ||||
\(601\) | 4.86311 | + | 8.42316i | 0.198371 | + | 0.343588i | 0.948000 | − | 0.318270i | \(-0.103102\pi\) |
−0.749630 | + | 0.661858i | \(0.769768\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.1155 | + | 7.51816i | −0.452659 | + | 0.306163i | ||||
\(604\) | −8.70921 | + | 15.0848i | −0.354373 | + | 0.613792i | ||||
\(605\) | 12.0495 | − | 20.8703i | 0.489881 | − | 0.848499i | ||||
\(606\) | 0.0196090 | + | 0.00451392i | 0.000796560 | + | 0.000183365i | ||||
\(607\) | 20.7437 | + | 35.9291i | 0.841959 | + | 1.45832i | 0.888236 | + | 0.459388i | \(0.151931\pi\) |
−0.0462763 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(608\) | −20.2475 | + | 35.0697i | −0.821145 | + | 1.42226i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.2742 | − | 24.7236i | −0.577943 | − | 1.00103i | ||||
\(611\) | 7.48688 | − | 12.9677i | 0.302887 | − | 0.524615i | ||||
\(612\) | 35.5587 | + | 17.2870i | 1.43737 | + | 0.698786i | ||||
\(613\) | −7.64783 | − | 13.2464i | −0.308893 | − | 0.535018i | 0.669228 | − | 0.743057i | \(-0.266625\pi\) |
−0.978120 | + | 0.208039i | \(0.933292\pi\) | |||||||
\(614\) | 52.0193 | 2.09933 | ||||||||
\(615\) | 2.50759 | + | 8.18329i | 0.101116 | + | 0.329982i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.66563 | + | 4.61700i | −0.107314 | + | 0.185873i | −0.914681 | − | 0.404176i | \(-0.867558\pi\) |
0.807367 | + | 0.590049i | \(0.200892\pi\) | |||||||
\(618\) | −33.4867 | + | 35.9561i | −1.34703 | + | 1.44637i | ||||
\(619\) | −6.34205 | + | 10.9847i | −0.254908 | + | 0.441514i | −0.964871 | − | 0.262726i | \(-0.915379\pi\) |
0.709962 | + | 0.704240i | \(0.248712\pi\) | |||||||
\(620\) | 2.54070 | + | 4.40062i | 0.102037 | + | 0.176733i | ||||
\(621\) | 4.15678 | − | 26.5738i | 0.166806 | − | 1.06637i | ||||
\(622\) | 28.1650 | 1.12931 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 15.9006 | + | 3.66026i | 0.636532 | + | 0.146528i | ||||
\(625\) | −1.72954 | − | 2.99566i | −0.0691817 | − | 0.119826i | ||||
\(626\) | 58.4733 | 2.33706 | ||||||||
\(627\) | 34.7932 | − | 37.3588i | 1.38951 | − | 1.49197i | ||||
\(628\) | −3.81978 | −0.152426 | ||||||||
\(629\) | 9.23957 | 0.368406 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.123764 | 0.00492698 | 0.00246349 | − | 0.999997i | \(-0.499216\pi\) | ||||
0.00246349 | + | 0.999997i | \(0.499216\pi\) | |||||||
\(632\) | −14.4487 | −0.574737 | ||||||||
\(633\) | −12.3595 | − | 2.84511i | −0.491245 | − | 0.113083i | ||||
\(634\) | 18.0888 | 0.718399 | ||||||||
\(635\) | −8.83394 | − | 15.3008i | −0.350564 | − | 0.607195i | ||||
\(636\) | −23.0725 | + | 24.7739i | −0.914885 | + | 0.982349i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 48.0763 | 1.90336 | ||||||||
\(639\) | 4.88764 | − | 3.30583i | 0.193352 | − | 0.130777i | ||||
\(640\) | −7.57868 | − | 13.1267i | −0.299573 | − | 0.518876i | ||||
\(641\) | −2.96588 | + | 5.13706i | −0.117145 | + | 0.202902i | −0.918635 | − | 0.395107i | \(-0.870708\pi\) |
0.801490 | + | 0.598008i | \(0.204041\pi\) | |||||||
\(642\) | −34.6095 | − | 7.96699i | −1.36593 | − | 0.314432i | ||||
\(643\) | 23.4140 | − | 40.5542i | 0.923358 | − | 1.59930i | 0.129178 | − | 0.991621i | \(-0.458766\pi\) |
0.794180 | − | 0.607682i | \(-0.207900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.10801 | + | 1.63624i | 0.279877 | + | 0.0644269i | ||||
\(646\) | −56.4060 | −2.21926 | ||||||||
\(647\) | −19.5701 | − | 33.8964i | −0.769379 | − | 1.33260i | −0.937900 | − | 0.346905i | \(-0.887233\pi\) |
0.168521 | − | 0.985698i | \(-0.446101\pi\) | |||||||
\(648\) | 5.36858 | − | 13.3859i | 0.210898 | − | 0.525847i | ||||
\(649\) | −0.845379 | + | 1.46424i | −0.0331840 | + | 0.0574764i | ||||
\(650\) | 17.5123 | + | 30.3322i | 0.686890 | + | 1.18973i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 26.0796 | − | 45.1711i | 1.02135 | − | 1.76904i | ||||
\(653\) | −21.6640 | − | 37.5232i | −0.847779 | − | 1.46840i | −0.883186 | − | 0.469023i | \(-0.844606\pi\) |
0.0354068 | − | 0.999373i | \(-0.488727\pi\) | |||||||
\(654\) | 43.3914 | − | 46.5911i | 1.69674 | − | 1.82186i | ||||
\(655\) | 0.113611 | − | 0.196779i | 0.00443913 | − | 0.00768881i | ||||
\(656\) | −3.86726 | + | 6.69828i | −0.150991 | + | 0.261524i | ||||
\(657\) | 28.4653 | + | 13.8386i | 1.11054 | + | 0.539893i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.43895 | + | 5.95643i | 0.133962 | + | 0.232030i | 0.925201 | − | 0.379478i | \(-0.123897\pi\) |
−0.791238 | + | 0.611508i | \(0.790563\pi\) | |||||||
\(660\) | 9.64620 | + | 31.4795i | 0.375478 | + | 1.22534i | ||||
\(661\) | −38.7671 | −1.50786 | −0.753932 | − | 0.656952i | \(-0.771845\pi\) | ||||
−0.753932 | + | 0.656952i | \(0.771845\pi\) | |||||||
\(662\) | 26.9814 | 1.04866 | ||||||||
\(663\) | 11.5983 | + | 37.8501i | 0.450441 | + | 1.46997i | ||||
\(664\) | 8.14097 | + | 14.1006i | 0.315931 | + | 0.547209i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.889611 | − | 12.4931i | −0.0344717 | − | 0.484097i | ||||
\(667\) | −10.4383 | + | 18.0797i | −0.404174 | + | 0.700050i | ||||
\(668\) | −2.38609 | + | 4.13282i | −0.0923205 | + | 0.159904i | ||||
\(669\) | 4.78707 | − | 5.14007i | 0.185079 | − | 0.198727i | ||||
\(670\) | 6.17331 | + | 10.6925i | 0.238496 | + | 0.413087i | ||||
\(671\) | −28.3257 | + | 49.0615i | −1.09350 | + | 1.89400i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.9897 | + | 31.1591i | 0.693452 | + | 1.20109i | 0.970700 | + | 0.240295i | \(0.0772443\pi\) |
−0.277248 | + | 0.960798i | \(0.589422\pi\) | |||||||
\(674\) | −28.2025 | + | 48.8481i | −1.08632 | + | 1.88156i | ||||
\(675\) | −16.4399 | + | 6.34678i | −0.632771 | + | 0.244288i | ||||
\(676\) | −13.0227 | − | 22.5560i | −0.500874 | − | 0.867539i | ||||
\(677\) | −4.46658 | −0.171664 | −0.0858322 | − | 0.996310i | \(-0.527355\pi\) | ||||
−0.0858322 | + | 0.996310i | \(0.527355\pi\) | |||||||
\(678\) | −22.5777 | − | 5.19731i | −0.867092 | − | 0.199602i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.89449 | − | 8.47750i | 0.187695 | − | 0.325097i | ||||
\(681\) | 2.25196 | + | 0.518394i | 0.0862953 | + | 0.0198649i | ||||
\(682\) | 8.72682 | − | 15.1153i | 0.334167 | − | 0.578795i | ||||
\(683\) | 13.3356 | + | 23.0980i | 0.510274 | + | 0.883821i | 0.999929 | + | 0.0119046i | \(0.00378945\pi\) |
−0.489655 | + | 0.871916i | \(0.662877\pi\) | |||||||
\(684\) | 3.13762 | + | 44.0625i | 0.119970 | + | 1.68477i | ||||
\(685\) | −3.99773 | −0.152745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.8832 | − | 20.2757i | 0.720439 | − | 0.773565i | ||||
\(688\) | 3.29569 | + | 5.70831i | 0.125647 | + | 0.217627i | ||||
\(689\) | −33.8960 | −1.29134 | ||||||||
\(690\) | −24.1162 | − | 5.55146i | −0.918086 | − | 0.211340i | ||||
\(691\) | 41.0440 | 1.56139 | 0.780694 | − | 0.624913i | \(-0.214866\pi\) | ||||
0.780694 | + | 0.624913i | \(0.214866\pi\) | |||||||
\(692\) | 27.5709 | 1.04809 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.6671 | −1.39187 | ||||||||
\(695\) | −23.9163 | −0.907197 | ||||||||
\(696\) | −7.62923 | + | 8.19182i | −0.289185 | + | 0.310510i | ||||
\(697\) | −18.7656 | −0.710799 | ||||||||
\(698\) | −33.8424 | − | 58.6167i | −1.28095 | − | 2.21867i | ||||
\(699\) | −13.7241 | − | 3.15924i | −0.519093 | − | 0.119493i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.63355 | 0.363854 | 0.181927 | − | 0.983312i | \(-0.441767\pi\) | ||||
0.181927 | + | 0.983312i | \(0.441767\pi\) | |||||||
\(702\) | 50.0615 | − | 19.3267i | 1.88945 | − | 0.729441i | ||||
\(703\) | 5.16148 | + | 8.93994i | 0.194669 | + | 0.337176i | ||||
\(704\) | −33.9788 | + | 58.8529i | −1.28062 | + | 2.21810i | ||||
\(705\) | 4.72419 | − | 5.07256i | 0.177923 | − | 0.191044i | ||||
\(706\) | 2.89382 | − | 5.01224i | 0.108910 | − | 0.188638i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.428629 | − | 1.39879i | −0.0161089 | − | 0.0525698i | ||||
\(709\) | −10.1426 | −0.380914 | −0.190457 | − | 0.981696i | \(-0.560997\pi\) | ||||
−0.190457 | + | 0.981696i | \(0.560997\pi\) | |||||||
\(710\) | −2.71448 | − | 4.70162i | −0.101873 | − | 0.176449i | ||||
\(711\) | 22.4056 | − | 15.1544i | 0.840275 | − | 0.568333i | ||||
\(712\) | 4.16286 | − | 7.21029i | 0.156010 | − | 0.270217i | ||||
\(713\) | 3.78954 | + | 6.56368i | 0.141919 | + | 0.245812i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.4826 | + | 28.5487i | −0.616415 | + | 1.06766i | ||||
\(716\) | 25.3690 | + | 43.9404i | 0.948085 | + | 1.64213i | ||||
\(717\) | 37.3058 | + | 8.58767i | 1.39321 | + | 0.320712i | ||||
\(718\) | 35.4118 | − | 61.3350i | 1.32156 | − | 2.28900i | ||||
\(719\) | −20.6844 | + | 35.8264i | −0.771397 | + | 1.33610i | 0.165400 | + | 0.986227i | \(0.447109\pi\) |
−0.936797 | + | 0.349873i | \(0.886225\pi\) | |||||||
\(720\) | 6.79305 | + | 3.30248i | 0.253162 | + | 0.123076i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.8350 | − | 18.7667i | −0.403236 | − | 0.698425i | ||||
\(723\) | 46.5773 | + | 10.7219i | 1.73223 | + | 0.398753i | ||||
\(724\) | 24.1066 | 0.895914 | ||||||||
\(725\) | 13.6781 | 0.507991 | ||||||||
\(726\) | 48.8144 | − | 52.4140i | 1.81167 | − | 1.94526i | ||||
\(727\) | 4.86372 | + | 8.42422i | 0.180386 | + | 0.312437i | 0.942012 | − | 0.335580i | \(-0.108932\pi\) |
−0.761626 | + | 0.648016i | \(0.775599\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.71460 | + | 26.3883i | 0.211652 | + | 0.977345i | ||||
\(730\) | 14.5604 | − | 25.2194i | 0.538906 | − | 0.933412i | ||||
\(731\) | −7.99607 | + | 13.8496i | −0.295745 | + | 0.512246i | ||||
\(732\) | −14.3618 | − | 46.8685i | −0.530829 | − | 1.73231i | ||||
\(733\) | 14.4554 | + | 25.0375i | 0.533922 | + | 0.924780i | 0.999215 | + | 0.0396234i | \(0.0126158\pi\) |
−0.465292 | + | 0.885157i | \(0.654051\pi\) | |||||||
\(734\) | 15.4013 | − | 26.6758i | 0.568471 | − | 0.984621i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.4766 | − | 33.7345i | −0.717918 | − | 1.24347i | ||||
\(737\) | 12.2503 | − | 21.2182i | 0.451247 | − | 0.781582i | ||||
\(738\) | 1.80681 | + | 25.3735i | 0.0665095 | + | 0.934013i | ||||
\(739\) | 6.67467 | + | 11.5609i | 0.245532 | + | 0.425273i | 0.962281 | − | 0.272058i | \(-0.0877041\pi\) |
−0.716749 | + | 0.697331i | \(0.754371\pi\) | |||||||
\(740\) | −6.65752 | −0.244735 | ||||||||
\(741\) | −30.1435 | + | 32.3663i | −1.10735 | + | 1.18901i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.9100 | − | 34.4851i | 0.730425 | − | 1.26513i | −0.226276 | − | 0.974063i | \(-0.572655\pi\) |
0.956702 | − | 0.291071i | \(-0.0940115\pi\) | |||||||
\(744\) | 1.19067 | + | 3.88563i | 0.0436519 | + | 0.142454i | ||||
\(745\) | −13.4908 | + | 23.3668i | −0.494265 | + | 0.856092i | ||||
\(746\) | −2.91221 | − | 5.04410i | −0.106624 | − | 0.184678i | ||||
\(747\) | −27.4135 | − | 13.3272i | −1.00301 | − | 0.487617i | ||||
\(748\) | −72.1877 | −2.63944 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.7538 | + | 38.3573i | 0.429186 | + | 1.40061i | ||||
\(751\) | 19.2173 | + | 33.2853i | 0.701248 | + | 1.21460i | 0.968029 | + | 0.250840i | \(0.0807069\pi\) |
−0.266780 | + | 0.963757i | \(0.585960\pi\) | |||||||
\(752\) | 6.26409 | 0.228428 | ||||||||
\(753\) | 8.40402 | + | 27.4258i | 0.306260 | + | 0.999451i | ||||
\(754\) | −41.6515 | −1.51686 | ||||||||
\(755\) | −8.07344 | −0.293823 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.66698 | −0.205970 | −0.102985 | − | 0.994683i | \(-0.532839\pi\) | ||||
−0.102985 | + | 0.994683i | \(0.532839\pi\) | |||||||
\(758\) | −0.681032 | −0.0247362 | ||||||||
\(759\) | 14.3877 | + | 46.9528i | 0.522239 | + | 1.70428i | ||||
\(760\) | 10.9368 | 0.396719 | ||||||||
\(761\) | 26.1661 | + | 45.3210i | 0.948519 | + | 1.64288i | 0.748546 | + | 0.663082i | \(0.230752\pi\) |
0.199973 | + | 0.979801i | \(0.435915\pi\) | |||||||
\(762\) | −15.3846 | − | 50.2064i | −0.557327 | − | 1.81879i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.4337 | 0.486014 | ||||||||
\(765\) | 1.30166 | + | 18.2796i | 0.0470616 | + | 0.660901i | ||||
\(766\) | −9.78121 | − | 16.9416i | −0.353410 | − | 0.612123i | ||||
\(767\) | 0.732404 | − | 1.26856i | 0.0264456 | − | 0.0458051i | ||||
\(768\) | −0.606430 | − | 1.97903i | −0.0218826 | − | 0.0714120i | ||||
\(769\) | −1.17360 | + | 2.03274i | −0.0423212 | + | 0.0733025i | −0.886410 | − | 0.462901i | \(-0.846809\pi\) |
0.844089 | + | 0.536203i | \(0.180142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.43849 | + | 2.61831i | −0.0878201 | + | 0.0942960i | ||||
\(772\) | −26.7274 | −0.961939 | ||||||||
\(773\) | 18.1814 | + | 31.4912i | 0.653941 | + | 1.13266i | 0.982158 | + | 0.188057i | \(0.0602189\pi\) |
−0.328217 | + | 0.944602i | \(0.606448\pi\) | |||||||
\(774\) | 19.4963 | + | 9.47824i | 0.700781 | + | 0.340688i | ||||
\(775\) | 2.48285 | − | 4.30042i | 0.0891866 | − | 0.154476i | ||||
\(776\) | 3.98251 | + | 6.89790i | 0.142964 | + | 0.247620i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 29.3659 | − | 50.8633i | 1.05282 | − | 1.82354i | ||||
\(779\) | −10.4830 | − | 18.1571i | −0.375592 | − | 0.650545i | ||||
\(780\) | −8.35711 | − | 27.2727i | −0.299232 | − | 0.976518i | ||||
\(781\) | −5.38663 | + | 9.32991i | −0.192749 | + | 0.333851i | ||||
\(782\) | 27.1292 | − | 46.9892i | 0.970139 | − | 1.68033i | ||||
\(783\) | 3.23875 | − | 20.7049i | 0.115744 | − | 0.739934i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.885235 | − | 1.53327i | −0.0315954 | − | 0.0547248i | ||||
\(786\) | 0.460255 | − | 0.494194i | 0.0164167 | − | 0.0176273i | ||||
\(787\) | 31.7692 | 1.13245 | 0.566224 | − | 0.824251i | \(-0.308404\pi\) | ||||
0.566224 | + | 0.824251i | \(0.308404\pi\) | |||||||
\(788\) | 9.06944 | 0.323085 | ||||||||
\(789\) | −17.0979 | − | 3.93587i | −0.608700 | − | 0.140121i | ||||
\(790\) | −12.4435 | − | 21.5528i | −0.442721 | − | 0.766816i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.87032 | + | 26.2655i | 0.0664589 | + | 0.933302i | ||||
\(793\) | 24.5403 | − | 42.5050i | 0.871451 | − | 1.50940i | ||||
\(794\) | 32.1012 | − | 55.6009i | 1.13923 | − | 1.97320i | ||||
\(795\) | −15.2914 | − | 3.52003i | −0.542329 | − | 0.124842i | ||||
\(796\) | 15.1711 | + | 26.2771i | 0.537725 | + | 0.931367i | ||||
\(797\) | 7.45306 | − | 12.9091i | 0.264001 | − | 0.457263i | −0.703301 | − | 0.710893i | \(-0.748291\pi\) |
0.967301 | + | 0.253630i | \(0.0816245\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.59903 | + | 13.1619i | 0.268834 | + | 0.465635i | ||||
\(800\) | −12.7608 | + | 22.1023i | −0.451162 | + | 0.781436i | ||||
\(801\) | 1.10709 | + | 15.5472i | 0.0391171 | + | 0.549333i | ||||
\(802\) | 37.3002 | + | 64.6059i | 1.31712 | + | 2.28131i | ||||
\(803\) | −57.7875 | −2.03928 | ||||||||
\(804\) | 6.21123 | + | 20.2698i | 0.219053 | + | 0.714860i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.56059 | + | 13.0953i | −0.266311 | + | 0.461263i | ||||
\(807\) | 17.8241 | − | 19.1385i | 0.627438 | − | 0.673706i | ||||
\(808\) | 0.00427709 | − | 0.00740814i | 0.000150467 | − | 0.000260617i | ||||
\(809\) | −23.9018 | − | 41.3992i | −0.840344 | − | 1.45552i | −0.889604 | − | 0.456733i | \(-0.849020\pi\) |
0.0492597 | − | 0.998786i | \(-0.484314\pi\) | |||||||
\(810\) | 24.5911 | − | 3.52003i | 0.864042 | − | 0.123681i | ||||
\(811\) | 32.1131 | 1.12764 | 0.563821 | − | 0.825897i | \(-0.309331\pi\) | ||||
0.563821 | + | 0.825897i | \(0.309331\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −48.6203 | − | 11.1922i | −1.70519 | − | 0.392529i | ||||
\(814\) | 11.4337 | + | 19.8037i | 0.400750 | + | 0.694119i | ||||
\(815\) | 24.1758 | 0.846841 | ||||||||
\(816\) | −11.2867 | + | 12.1190i | −0.395115 | + | 0.424251i | ||||
\(817\) | −17.8673 | −0.625098 | ||||||||
\(818\) | −23.9057 | −0.835843 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.5215 | 0.472190 | ||||||||
\(821\) | 47.1070 | 1.64405 | 0.822023 | − | 0.569455i | \(-0.192846\pi\) | ||||
0.822023 | + | 0.569455i | \(0.192846\pi\) | |||||||
\(822\) | −11.5788 | − | 2.66540i | −0.403857 | − | 0.0929667i | ||||
\(823\) | 33.7910 | 1.17788 | 0.588941 | − | 0.808176i | \(-0.299545\pi\) | ||||
0.588941 | + | 0.808176i | \(0.299545\pi\) | |||||||
\(824\) | 10.4440 | + | 18.0896i | 0.363835 | + | 0.630181i | ||||
\(825\) | 21.9281 | − | 23.5450i | 0.763437 | − | 0.819733i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.98023 | 0.103633 | 0.0518164 | − | 0.998657i | \(-0.483499\pi\) | ||||
0.0518164 | + | 0.998657i | \(0.483499\pi\) | |||||||
\(828\) | −38.2155 | − | 18.5787i | −1.32808 | − | 0.645653i | ||||
\(829\) | 3.03978 | + | 5.26506i | 0.105576 | + | 0.182863i | 0.913973 | − | 0.405774i | \(-0.132998\pi\) |
−0.808397 | + | 0.588637i | \(0.799665\pi\) | |||||||
\(830\) | −14.0224 | + | 24.2875i | −0.486725 | + | 0.843032i | ||||
\(831\) | 4.55673 | + | 1.04894i | 0.158071 | + | 0.0363875i | ||||
\(832\) | 29.4379 | − | 50.9880i | 1.02058 | − | 1.76769i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −69.2700 | − | 15.9457i | −2.39862 | − | 0.552155i | ||||
\(835\) | −2.21190 | −0.0765461 | ||||||||
\(836\) | −40.3260 | − | 69.8467i | −1.39471 | − | 2.41570i | ||||
\(837\) | −5.92178 | − | 4.77664i | −0.204687 | − | 0.165105i | ||||
\(838\) | 7.25163 | − | 12.5602i | 0.250503 | − | 0.433885i | ||||
\(839\) | −1.85858 | − | 3.21915i | −0.0641653 | − | 0.111138i | 0.832158 | − | 0.554538i | \(-0.187105\pi\) |
−0.896323 | + | 0.443401i | \(0.853772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.36697 | − | 11.0279i | 0.219551 | − | 0.380273i | ||||
\(842\) | −37.0909 | − | 64.2433i | −1.27824 | − | 2.21397i | ||||
\(843\) | 5.81518 | − | 6.24399i | 0.200285 | − | 0.215055i | ||||
\(844\) | −10.0182 | + | 17.3520i | −0.344841 | + | 0.597281i | ||||
\(845\) | 6.03604 | − | 10.4547i | 0.207646 | − | 0.359653i | ||||
\(846\) | 17.0649 | − | 11.5421i | 0.586705 | − | 0.396827i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.08999 | − | 12.2802i | −0.243471 | − | 0.421705i | ||||
\(849\) | −1.81750 | − | 5.93125i | −0.0623765 | − | 0.203560i | ||||
\(850\) | −35.5493 | −1.21933 | ||||||||
\(851\) | −9.92993 | −0.340394 | ||||||||
\(852\) | −2.73116 | − | 8.91289i | −0.0935680 | − | 0.305351i | ||||
\(853\) | 0.553861 | + | 0.959315i | 0.0189638 | + | 0.0328463i | 0.875352 | − | 0.483487i | \(-0.160630\pi\) |
−0.856388 | + | 0.516333i | \(0.827297\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.9597 | + | 11.4709i | −0.580009 | + | 0.392298i | ||||
\(856\) | −7.54899 | + | 13.0752i | −0.258019 | + | 0.446902i | ||||
\(857\) | −19.2597 | + | 33.3589i | −0.657900 | + | 1.13952i | 0.323258 | + | 0.946311i | \(0.395222\pi\) |
−0.981158 | + | 0.193206i | \(0.938111\pi\) | |||||||
\(858\) | −66.7737 | + | 71.6976i | −2.27962 | + | 2.44772i | ||||
\(859\) | −17.4437 | − | 30.2134i | −0.595171 | − | 1.03087i | −0.993523 | − | 0.113634i | \(-0.963751\pi\) |
0.398352 | − | 0.917233i | \(-0.369582\pi\) | |||||||
\(860\) | 5.76153 | − | 9.97926i | 0.196467 | − | 0.340290i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.45857 | − | 4.25836i | −0.0837391 | − | 0.145040i | ||||
\(863\) | −1.07924 | + | 1.86931i | −0.0367379 | + | 0.0636319i | −0.883810 | − | 0.467847i | \(-0.845030\pi\) |
0.847072 | + | 0.531478i | \(0.178363\pi\) | |||||||
\(864\) | 30.4354 | + | 24.5499i | 1.03543 | + | 0.835203i | ||||
\(865\) | 6.38957 | + | 11.0671i | 0.217252 | + | 0.376291i | ||||
\(866\) | −74.8441 | −2.54331 | ||||||||
\(867\) | −10.4617 | − | 2.40826i | −0.355299 | − | 0.0817888i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.6930 | + | 42.7695i | −0.837652 | + | 1.45086i | ||||
\(870\) | −18.7901 | − | 4.32542i | −0.637044 | − | 0.146645i | ||||
\(871\) | −10.6132 | + | 18.3826i | −0.359615 | + | 0.622872i | ||||
\(872\) | −13.5332 | − | 23.4401i | −0.458291 | − | 0.793783i | ||||
\(873\) | −13.4105 | − | 6.51957i | −0.453876 | − | 0.220654i | ||||
\(874\) | 60.6205 | 2.05052 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 34.0785 | − | 36.5914i | 1.15140 | − | 1.23631i | ||||
\(877\) | −9.43950 | − | 16.3497i | −0.318749 | − | 0.552090i | 0.661478 | − | 0.749965i | \(-0.269929\pi\) |
−0.980227 | + | 0.197875i | \(0.936596\pi\) | |||||||
\(878\) | −13.0391 | −0.440049 | ||||||||
\(879\) | −41.1697 | − | 9.47714i | −1.38862 | − | 0.319656i | ||||
\(880\) | −13.7906 | −0.464881 | ||||||||
\(881\) | 18.7203 | 0.630704 | 0.315352 | − | 0.948975i | \(-0.397877\pi\) | ||||
0.315352 | + | 0.948975i | \(0.397877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.3717 | −0.449993 | −0.224996 | − | 0.974360i | \(-0.572237\pi\) | ||||
−0.224996 | + | 0.974360i | \(0.572237\pi\) | |||||||
\(884\) | 62.5407 | 2.10347 | ||||||||
\(885\) | 0.462144 | − | 0.496223i | 0.0155348 | − | 0.0166804i | ||||
\(886\) | −85.8294 | −2.88350 | ||||||||
\(887\) | 20.6284 | + | 35.7294i | 0.692633 | + | 1.19968i | 0.970972 | + | 0.239193i | \(0.0768829\pi\) |
−0.278339 | + | 0.960483i | \(0.589784\pi\) | |||||||
\(888\) | −5.18880 | − | 1.19445i | −0.174125 | − | 0.0400830i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14.3406 | 0.480699 | ||||||||
\(891\) | −30.4486 | − | 38.7682i | −1.02007 | − | 1.29878i | ||||
\(892\) | −5.54832 | − | 9.60997i | −0.185772 | − | 0.321766i | ||||
\(893\) | −8.49006 | + | 14.7052i | −0.284109 | + | 0.492091i | ||||
\(894\) | −54.6534 | + | 58.6836i | −1.82788 | + | 1.96267i | ||||
\(895\) | −11.7585 | + | 20.3664i | −0.393045 | + | 0.680774i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.4649 | − | 40.6782i | −0.416192 | − | 1.35820i | ||||
\(898\) | 5.33396 | 0.177996 | ||||||||
\(899\) | 2.95262 | + | 5.11408i | 0.0984753 | + | 0.170564i | ||||
\(900\) | 1.97745 | + | 27.7700i | 0.0659151 | + | 0.925666i | ||||
\(901\) | 17.2019 | − | 29.7945i | 0.573078 | − | 0.992599i | ||||
\(902\) | −23.2219 | − | 40.2215i | −0.773204 | − | 1.33923i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.92463 | + | 8.52971i | −0.163791 | + | 0.283694i | ||||
\(905\) | 5.58670 | + | 9.67645i | 0.185708 | + | 0.321656i | ||||
\(906\) | −23.3835 | − | 5.38281i | −0.776865 | − | 0.178832i | ||||
\(907\) | −1.84519 | + | 3.19595i | −0.0612684 | + | 0.106120i | −0.895033 | − | 0.446001i | \(-0.852848\pi\) |
0.833764 | + | 0.552121i | \(0.186181\pi\) | |||||||
\(908\) | 1.82537 | − | 3.16163i | 0.0605770 | − | 0.104922i | ||||
\(909\) | 0.00113747 | + | 0.0159738i | 3.77274e−5 | + | 0.000529818i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.43831 | − | 5.95533i | −0.113916 | − | 0.197309i | 0.803430 | − | 0.595400i | \(-0.203006\pi\) |
−0.917346 | + | 0.398091i | \(0.869673\pi\) | |||||||
\(912\) | −18.0311 | − | 4.15070i | −0.597069 | − | 0.137443i | ||||
\(913\) | 55.6522 | 1.84182 | ||||||||
\(914\) | 23.9855 | 0.793369 | ||||||||
\(915\) | 15.4848 | − | 16.6267i | 0.511912 | − | 0.549661i | ||||
\(916\) | −21.8860 | − | 37.9077i | −0.723135 | − | 1.25251i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.41751 | + | 53.8120i | −0.277819 | + | 1.77606i | ||||
\(919\) | −18.6473 | + | 32.2981i | −0.615119 | + | 1.06542i | 0.375245 | + | 0.926926i | \(0.377559\pi\) |
−0.990364 | + | 0.138491i | \(0.955775\pi\) | |||||||
\(920\) | −5.26019 | + | 9.11092i | −0.173423 | + | 0.300378i | ||||
\(921\) | 12.1295 | + | 39.5836i | 0.399681 | + | 1.30432i | ||||
\(922\) | −31.8916 | − | 55.2378i | −1.05029 | − | 1.81916i | ||||
\(923\) | 4.66677 | − | 8.08309i | 0.153609 | − | 0.266058i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.25297 | + | 5.63431i | 0.106957 | + | 0.185255i | ||||
\(926\) | 1.29178 | − | 2.23743i | 0.0424506 | − | 0.0735267i | ||||
\(927\) | −35.1687 | − | 17.0974i | −1.15509 | − | 0.561554i | ||||
\(928\) | −15.1752 | − | 26.2842i | −0.498150 | − | 0.862821i | ||||
\(929\) | 17.9787 | 0.589861 | 0.294930 | − | 0.955519i | \(-0.404704\pi\) | ||||
0.294930 | + | 0.955519i | \(0.404704\pi\) | |||||||
\(930\) | −4.77070 | + | 5.12250i | −0.156438 | + | 0.167973i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11.1243 | + | 19.2679i | −0.364389 | + | 0.631141i | ||||
\(933\) | 6.56734 | + | 21.4319i | 0.215005 | + | 0.701650i | ||||
\(934\) | 24.0642 | − | 41.6804i | 0.787405 | − | 1.36383i | ||||
\(935\) | −16.7295 | − | 28.9764i | −0.547113 | − | 0.947628i | ||||
\(936\) | −1.62037 | − | 22.7554i | −0.0529636 | − | 0.743784i | ||||
\(937\) | −34.7312 | −1.13462 | −0.567310 | − | 0.823504i | \(-0.692016\pi\) | ||||
−0.567310 | + | 0.823504i | \(0.692016\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.6344 | + | 44.4947i | 0.444943 | + | 1.45203i | ||||
\(940\) | −5.47544 | − | 9.48374i | −0.178589 | − | 0.309326i | ||||
\(941\) | −43.3025 | −1.41162 | −0.705810 | − | 0.708401i | \(-0.749417\pi\) | ||||
−0.705810 | + | 0.708401i | \(0.749417\pi\) | |||||||
\(942\) | −1.54167 | − | 5.03110i | −0.0502304 | − | 0.163922i | ||||
\(943\) | 20.1678 | 0.656752 | ||||||||
\(944\) | 0.612785 | 0.0199444 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.5796 | −1.28684 | ||||||||
\(947\) | 38.2591 | 1.24325 | 0.621626 | − | 0.783314i | \(-0.286472\pi\) | ||||
0.621626 | + | 0.783314i | \(0.286472\pi\) | |||||||
\(948\) | −12.5200 | − | 40.8578i | −0.406630 | − | 1.32700i | ||||
\(949\) | 50.0649 | 1.62518 | ||||||||
\(950\) | −19.8588 | − | 34.3965i | −0.644305 | − | 1.11597i | ||||
\(951\) | 4.21784 | + | 13.7645i | 0.136773 | + | 0.446345i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8757 | −1.55085 | −0.775423 | − | 0.631442i | \(-0.782463\pi\) | ||||
−0.775423 | + | 0.631442i | \(0.782463\pi\) | |||||||
\(954\) | −41.9423 | − | 20.3905i | −1.35793 | − | 0.660165i | ||||
\(955\) | 3.11326 | + | 5.39233i | 0.100743 | + | 0.174492i | ||||
\(956\) | 30.2389 | − | 52.3753i | 0.977996 | − | 1.69394i | ||||
\(957\) | 11.2101 | + | 36.5832i | 0.362372 | + | 1.18257i | ||||
\(958\) | −27.3593 | + | 47.3877i | −0.883939 | + | 1.53103i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 18.5752 | − | 19.9450i | 0.599512 | − | 0.643721i | ||||
\(961\) | −28.8562 | −0.930844 | ||||||||
\(962\) | −9.90570 | − | 17.1572i | −0.319373 | − | 0.553170i | ||||
\(963\) | −2.00761 | − | 28.1935i | −0.0646943 | − | 0.908522i | ||||
\(964\) | 37.7541 | − | 65.3920i | 1.21598 | − | 2.10613i | ||||
\(965\) | −6.19407 | − | 10.7284i | −0.199394 | − | 0.345361i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.5575 | − | 26.9463i | 0.500294 | − | 0.866535i | −0.499706 | − | 0.866195i | \(-0.666559\pi\) |
1.00000 | 0.000339469i | \(-0.000108056\pi\) | ||||||||
\(968\) | −15.2245 | − | 26.3696i | −0.489334 | − | 0.847551i | ||||
\(969\) | −13.1524 | − | 42.9216i | −0.422516 | − | 1.37884i | ||||
\(970\) | −6.85966 | + | 11.8813i | −0.220250 | + | 0.381485i | ||||
\(971\) | 15.1312 | − | 26.2080i | 0.485583 | − | 0.841055i | −0.514279 | − | 0.857623i | \(-0.671941\pi\) |
0.999863 | + | 0.0165676i | \(0.00527387\pi\) | |||||||
\(972\) | 42.5045 | + | 3.58216i | 1.36333 | + | 0.114898i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.7751 | − | 25.5911i | −0.473423 | − | 0.819993i | ||||
\(975\) | −18.9976 | + | 20.3985i | −0.608412 | + | 0.653276i | ||||
\(976\) | 20.5323 | 0.657221 | ||||||||
\(977\) | 38.2201 | 1.22277 | 0.611385 | − | 0.791333i | \(-0.290613\pi\) | ||||
0.611385 | + | 0.791333i | \(0.290613\pi\) | |||||||
\(978\) | 70.0215 | + | 16.1187i | 2.23904 | + | 0.515420i | ||||
\(979\) | −14.2288 | − | 24.6450i | −0.454754 | − | 0.787657i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.5709 | + | 22.1545i | 1.45497 | + | 0.707339i | ||||
\(982\) | 15.7821 | − | 27.3354i | 0.503627 | − | 0.872308i | ||||
\(983\) | 18.6964 | − | 32.3832i | 0.596324 | − | 1.03286i | −0.397035 | − | 0.917803i | \(-0.629961\pi\) |
0.993359 | − | 0.115059i | \(-0.0367058\pi\) | |||||||
\(984\) | 10.5385 | + | 2.42593i | 0.335955 | + | 0.0773357i | ||||
\(985\) | 2.10184 | + | 3.64050i | 0.0669703 | + | 0.115996i | ||||
\(986\) | 21.1377 | − | 36.6116i | 0.673162 | − | 1.16595i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 34.9370 | + | 60.5126i | 1.11149 | + | 1.92516i | ||||
\(989\) | 8.59353 | − | 14.8844i | 0.273258 | − | 0.473297i | ||||
\(990\) | −37.5690 | + | 25.4104i | −1.19402 | + | 0.807595i | ||||
\(991\) | 11.9299 | + | 20.6631i | 0.378965 | + | 0.656386i | 0.990912 | − | 0.134512i | \(-0.0429468\pi\) |
−0.611947 | + | 0.790899i | \(0.709613\pi\) | |||||||
\(992\) | −11.0184 | −0.349835 | ||||||||
\(993\) | 6.29136 | + | 20.5313i | 0.199650 | + | 0.651540i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.03180 | + | 12.1794i | −0.222923 | + | 0.386114i | ||||
\(996\) | −32.8192 | + | 35.2393i | −1.03992 | + | 1.11660i | ||||
\(997\) | −25.8413 | + | 44.7585i | −0.818403 | + | 1.41751i | 0.0884560 | + | 0.996080i | \(0.471807\pi\) |
−0.906859 | + | 0.421435i | \(0.861527\pi\) | |||||||
\(998\) | −15.2249 | − | 26.3703i | −0.481936 | − | 0.834738i | ||||
\(999\) | 9.29907 | − | 3.59000i | 0.294210 | − | 0.113583i |
(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 | 441.2.h.h.373.12 | 24 | ||
3.2 | odd | 2 | 1323.2.h.h.226.1 | 24 | |||
7.2 | even | 3 | 441.2.f.h.148.1 | ✓ | 24 | ||
7.3 | odd | 6 | 441.2.g.h.67.1 | 24 | |||
7.4 | even | 3 | 441.2.g.h.67.2 | 24 | |||
7.5 | odd | 6 | 441.2.f.h.148.2 | yes | 24 | ||
7.6 | odd | 2 | inner | 441.2.h.h.373.11 | 24 | ||
9.2 | odd | 6 | 1323.2.g.h.667.12 | 24 | |||
9.7 | even | 3 | 441.2.g.h.79.2 | 24 | |||
21.2 | odd | 6 | 1323.2.f.h.442.11 | 24 | |||
21.5 | even | 6 | 1323.2.f.h.442.12 | 24 | |||
21.11 | odd | 6 | 1323.2.g.h.361.12 | 24 | |||
21.17 | even | 6 | 1323.2.g.h.361.11 | 24 | |||
21.20 | even | 2 | 1323.2.h.h.226.2 | 24 | |||
63.2 | odd | 6 | 1323.2.f.h.883.11 | 24 | |||
63.5 | even | 6 | 3969.2.a.bi.1.1 | 12 | |||
63.11 | odd | 6 | 1323.2.h.h.802.1 | 24 | |||
63.16 | even | 3 | 441.2.f.h.295.1 | yes | 24 | ||
63.20 | even | 6 | 1323.2.g.h.667.11 | 24 | |||
63.23 | odd | 6 | 3969.2.a.bi.1.2 | 12 | |||
63.25 | even | 3 | inner | 441.2.h.h.214.12 | 24 | ||
63.34 | odd | 6 | 441.2.g.h.79.1 | 24 | |||
63.38 | even | 6 | 1323.2.h.h.802.2 | 24 | |||
63.40 | odd | 6 | 3969.2.a.bh.1.12 | 12 | |||
63.47 | even | 6 | 1323.2.f.h.883.12 | 24 | |||
63.52 | odd | 6 | inner | 441.2.h.h.214.11 | 24 | ||
63.58 | even | 3 | 3969.2.a.bh.1.11 | 12 | |||
63.61 | odd | 6 | 441.2.f.h.295.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.1 | ✓ | 24 | 7.2 | even | 3 | ||
441.2.f.h.148.2 | yes | 24 | 7.5 | odd | 6 | ||
441.2.f.h.295.1 | yes | 24 | 63.16 | even | 3 | ||
441.2.f.h.295.2 | yes | 24 | 63.61 | odd | 6 | ||
441.2.g.h.67.1 | 24 | 7.3 | odd | 6 | |||
441.2.g.h.67.2 | 24 | 7.4 | even | 3 | |||
441.2.g.h.79.1 | 24 | 63.34 | odd | 6 | |||
441.2.g.h.79.2 | 24 | 9.7 | even | 3 | |||
441.2.h.h.214.11 | 24 | 63.52 | odd | 6 | inner | ||
441.2.h.h.214.12 | 24 | 63.25 | even | 3 | inner | ||
441.2.h.h.373.11 | 24 | 7.6 | odd | 2 | inner | ||
441.2.h.h.373.12 | 24 | 1.1 | even | 1 | trivial | ||
1323.2.f.h.442.11 | 24 | 21.2 | odd | 6 | |||
1323.2.f.h.442.12 | 24 | 21.5 | even | 6 | |||
1323.2.f.h.883.11 | 24 | 63.2 | odd | 6 | |||
1323.2.f.h.883.12 | 24 | 63.47 | even | 6 | |||
1323.2.g.h.361.11 | 24 | 21.17 | even | 6 | |||
1323.2.g.h.361.12 | 24 | 21.11 | odd | 6 | |||
1323.2.g.h.667.11 | 24 | 63.20 | even | 6 | |||
1323.2.g.h.667.12 | 24 | 9.2 | odd | 6 | |||
1323.2.h.h.226.1 | 24 | 3.2 | odd | 2 | |||
1323.2.h.h.226.2 | 24 | 21.20 | even | 2 | |||
1323.2.h.h.802.1 | 24 | 63.11 | odd | 6 | |||
1323.2.h.h.802.2 | 24 | 63.38 | even | 6 | |||
3969.2.a.bh.1.11 | 12 | 63.58 | even | 3 | |||
3969.2.a.bh.1.12 | 12 | 63.40 | odd | 6 | |||
3969.2.a.bi.1.1 | 12 | 63.5 | even | 6 | |||
3969.2.a.bi.1.2 | 12 | 63.23 | odd | 6 |