Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(91,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.e (of order \(2\), degree \(1\), 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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.3 | ||
Character | \(\chi\) | \(=\) | 276.91 |
Dual form | 276.2.e.a.91.2 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36293 | + | 0.377393i | −0.963736 | + | 0.266857i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.71515 | − | 1.02872i | 0.857574 | − | 0.514360i | ||||
\(5\) | − | 2.63738i | − | 1.17947i | −0.807596 | − | 0.589736i | \(-0.799232\pi\) | ||
0.807596 | − | 0.589736i | \(-0.200768\pi\) | |||||||
\(6\) | 0.377393 | + | 1.36293i | 0.154070 | + | 0.556413i | ||||
\(7\) | 3.76288 | 1.42224 | 0.711118 | − | 0.703072i | \(-0.248189\pi\) | ||||
0.711118 | + | 0.703072i | \(0.248189\pi\) | |||||||
\(8\) | −1.94939 | + | 2.04936i | −0.689215 | + | 0.724557i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.995329 | + | 3.59456i | 0.314751 | + | 1.13670i | ||||
\(11\) | −0.443928 | −0.133849 | −0.0669247 | − | 0.997758i | \(-0.521319\pi\) | ||||
−0.0669247 | + | 0.997758i | \(0.521319\pi\) | |||||||
\(12\) | −1.02872 | − | 1.71515i | −0.296966 | − | 0.495121i | ||||
\(13\) | −3.89773 | −1.08103 | −0.540517 | − | 0.841333i | \(-0.681771\pi\) | ||||
−0.540517 | + | 0.841333i | \(0.681771\pi\) | |||||||
\(14\) | −5.12854 | + | 1.42009i | −1.37066 | + | 0.379534i | ||||
\(15\) | −2.63738 | −0.680969 | ||||||||
\(16\) | 1.88347 | − | 3.52882i | 0.470868 | − | 0.882204i | ||||
\(17\) | − | 5.41690i | − | 1.31379i | −0.753982 | − | 0.656895i | \(-0.771869\pi\) | ||
0.753982 | − | 0.656895i | \(-0.228131\pi\) | |||||||
\(18\) | 1.36293 | − | 0.377393i | 0.321245 | − | 0.0889524i | ||||
\(19\) | 0.874510 | 0.200626 | 0.100313 | − | 0.994956i | \(-0.468016\pi\) | ||||
0.100313 | + | 0.994956i | \(0.468016\pi\) | |||||||
\(20\) | −2.71313 | − | 4.52350i | −0.606673 | − | 1.01149i | ||||
\(21\) | − | 3.76288i | − | 0.821129i | ||||||
\(22\) | 0.605043 | − | 0.167536i | 0.128995 | − | 0.0357187i | ||||
\(23\) | 4.40961 | + | 1.88557i | 0.919466 | + | 0.393169i | ||||
\(24\) | 2.04936 | + | 1.94939i | 0.418323 | + | 0.397918i | ||||
\(25\) | −1.95578 | −0.391155 | ||||||||
\(26\) | 5.31232 | − | 1.47098i | 1.04183 | − | 0.288482i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 6.45391 | − | 3.87095i | 1.21967 | − | 0.731542i | ||||
\(29\) | −5.34393 | −0.992343 | −0.496171 | − | 0.868225i | \(-0.665261\pi\) | ||||
−0.496171 | + | 0.868225i | \(0.665261\pi\) | |||||||
\(30\) | 3.59456 | − | 0.995329i | 0.656274 | − | 0.181721i | ||||
\(31\) | − | 0.598213i | − | 0.107442i | −0.998556 | − | 0.0537211i | \(-0.982892\pi\) | ||
0.998556 | − | 0.0537211i | \(-0.0171082\pi\) | |||||||
\(32\) | −1.23528 | + | 5.52033i | −0.218370 | + | 0.975866i | ||||
\(33\) | 0.443928i | 0.0772780i | ||||||||
\(34\) | 2.04430 | + | 7.38284i | 0.350595 | + | 1.26615i | ||||
\(35\) | − | 9.92416i | − | 1.67749i | ||||||
\(36\) | −1.71515 | + | 1.02872i | −0.285858 | + | 0.171453i | ||||
\(37\) | − | 8.26643i | − | 1.35899i | −0.733679 | − | 0.679496i | \(-0.762198\pi\) | ||
0.733679 | − | 0.679496i | \(-0.237802\pi\) | |||||||
\(38\) | −1.19189 | + | 0.330034i | −0.193351 | + | 0.0535386i | ||||
\(39\) | 3.89773i | 0.624136i | ||||||||
\(40\) | 5.40493 | + | 5.14129i | 0.854595 | + | 0.812910i | ||||
\(41\) | 3.00019 | 0.468551 | 0.234276 | − | 0.972170i | \(-0.424728\pi\) | ||||
0.234276 | + | 0.972170i | \(0.424728\pi\) | |||||||
\(42\) | 1.42009 | + | 5.12854i | 0.219124 | + | 0.791351i | ||||
\(43\) | 0.586065 | 0.0893740 | 0.0446870 | − | 0.999001i | \(-0.485771\pi\) | ||||
0.0446870 | + | 0.999001i | \(0.485771\pi\) | |||||||
\(44\) | −0.761403 | + | 0.456678i | −0.114786 | + | 0.0688468i | ||||
\(45\) | 2.63738i | 0.393157i | ||||||||
\(46\) | −6.72158 | − | 0.905744i | −0.991043 | − | 0.133545i | ||||
\(47\) | − | 3.89063i | − | 0.567507i | −0.958897 | − | 0.283753i | \(-0.908420\pi\) | ||
0.958897 | − | 0.283753i | \(-0.0915797\pi\) | |||||||
\(48\) | −3.52882 | − | 1.88347i | −0.509341 | − | 0.271856i | ||||
\(49\) | 7.15930 | 1.02276 | ||||||||
\(50\) | 2.66558 | − | 0.738096i | 0.376970 | − | 0.104383i | ||||
\(51\) | −5.41690 | −0.758517 | ||||||||
\(52\) | −6.68518 | + | 4.00967i | −0.927068 | + | 0.556041i | ||||
\(53\) | 3.21010i | 0.440941i | 0.975394 | + | 0.220470i | \(0.0707593\pi\) | ||||
−0.975394 | + | 0.220470i | \(0.929241\pi\) | |||||||
\(54\) | −0.377393 | − | 1.36293i | −0.0513567 | − | 0.185471i | ||||
\(55\) | 1.17081i | 0.157872i | ||||||||
\(56\) | −7.33534 | + | 7.71149i | −0.980226 | + | 1.03049i | ||||
\(57\) | − | 0.874510i | − | 0.115832i | ||||||
\(58\) | 7.28339 | − | 2.01676i | 0.956356 | − | 0.264814i | ||||
\(59\) | 12.1857i | 1.58645i | 0.608931 | + | 0.793223i | \(0.291599\pi\) | ||||
−0.608931 | + | 0.793223i | \(0.708401\pi\) | |||||||
\(60\) | −4.52350 | + | 2.71313i | −0.583981 | + | 0.350263i | ||||
\(61\) | 12.2477i | 1.56816i | 0.620658 | + | 0.784081i | \(0.286866\pi\) | ||||
−0.620658 | + | 0.784081i | \(0.713134\pi\) | |||||||
\(62\) | 0.225762 | + | 0.815322i | 0.0286718 | + | 0.103546i | ||||
\(63\) | −3.76288 | −0.474079 | ||||||||
\(64\) | −0.399731 | − | 7.99001i | −0.0499664 | − | 0.998751i | ||||
\(65\) | 10.2798i | 1.27505i | ||||||||
\(66\) | −0.167536 | − | 0.605043i | −0.0206222 | − | 0.0744756i | ||||
\(67\) | −15.2528 | −1.86342 | −0.931710 | − | 0.363202i | \(-0.881683\pi\) | ||||
−0.931710 | + | 0.363202i | \(0.881683\pi\) | |||||||
\(68\) | −5.57247 | − | 9.29078i | −0.675761 | − | 1.12667i | ||||
\(69\) | 1.88557 | − | 4.40961i | 0.226996 | − | 0.530854i | ||||
\(70\) | 3.74531 | + | 13.5259i | 0.447650 | + | 1.61666i | ||||
\(71\) | 1.61736i | 0.191945i | 0.995384 | + | 0.0959726i | \(0.0305961\pi\) | ||||
−0.995384 | + | 0.0959726i | \(0.969404\pi\) | |||||||
\(72\) | 1.94939 | − | 2.04936i | 0.229738 | − | 0.241519i | ||||
\(73\) | 14.9948 | 1.75501 | 0.877505 | − | 0.479568i | \(-0.159206\pi\) | ||||
0.877505 | + | 0.479568i | \(0.159206\pi\) | |||||||
\(74\) | 3.11969 | + | 11.2665i | 0.362657 | + | 1.30971i | ||||
\(75\) | 1.95578i | 0.225833i | ||||||||
\(76\) | 1.49991 | − | 0.899626i | 0.172052 | − | 0.103194i | ||||
\(77\) | −1.67045 | −0.190366 | ||||||||
\(78\) | −1.47098 | − | 5.31232i | −0.166555 | − | 0.601502i | ||||
\(79\) | 10.9038 | 1.22677 | 0.613387 | − | 0.789782i | \(-0.289807\pi\) | ||||
0.613387 | + | 0.789782i | \(0.289807\pi\) | |||||||
\(80\) | −9.30683 | − | 4.96743i | −1.04054 | − | 0.555375i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.08905 | + | 1.13225i | −0.451560 | + | 0.125036i | ||||
\(83\) | 11.6833 | 1.28241 | 0.641205 | − | 0.767370i | \(-0.278435\pi\) | ||||
0.641205 | + | 0.767370i | \(0.278435\pi\) | |||||||
\(84\) | −3.87095 | − | 6.45391i | −0.422356 | − | 0.704179i | ||||
\(85\) | −14.2864 | −1.54958 | ||||||||
\(86\) | −0.798764 | + | 0.221177i | −0.0861330 | + | 0.0238501i | ||||
\(87\) | 5.34393i | 0.572929i | ||||||||
\(88\) | 0.865391 | − | 0.909768i | 0.0922510 | − | 0.0969816i | ||||
\(89\) | 13.2311i | 1.40249i | 0.712918 | + | 0.701247i | \(0.247373\pi\) | ||||
−0.712918 | + | 0.701247i | \(0.752627\pi\) | |||||||
\(90\) | −0.995329 | − | 3.59456i | −0.104917 | − | 0.378900i | ||||
\(91\) | −14.6667 | −1.53749 | ||||||||
\(92\) | 9.50285 | − | 1.30221i | 0.990741 | − | 0.135765i | ||||
\(93\) | −0.598213 | −0.0620318 | ||||||||
\(94\) | 1.46830 | + | 5.30265i | 0.151443 | + | 0.546927i | ||||
\(95\) | − | 2.30642i | − | 0.236633i | ||||||
\(96\) | 5.52033 | + | 1.23528i | 0.563417 | + | 0.126076i | ||||
\(97\) | 1.29344i | 0.131329i | 0.997842 | + | 0.0656646i | \(0.0209167\pi\) | ||||
−0.997842 | + | 0.0656646i | \(0.979083\pi\) | |||||||
\(98\) | −9.75761 | + | 2.70187i | −0.985667 | + | 0.272930i | ||||
\(99\) | 0.443928 | 0.0446165 | ||||||||
\(100\) | −3.35445 | + | 2.01195i | −0.335445 | + | 0.201195i | ||||
\(101\) | 13.3947 | 1.33282 | 0.666410 | − | 0.745586i | \(-0.267830\pi\) | ||||
0.666410 | + | 0.745586i | \(0.267830\pi\) | |||||||
\(102\) | 7.38284 | − | 2.04430i | 0.731011 | − | 0.202416i | ||||
\(103\) | −4.33560 | −0.427200 | −0.213600 | − | 0.976921i | \(-0.568519\pi\) | ||||
−0.213600 | + | 0.976921i | \(0.568519\pi\) | |||||||
\(104\) | 7.59820 | − | 7.98783i | 0.745065 | − | 0.783271i | ||||
\(105\) | −9.92416 | −0.968498 | ||||||||
\(106\) | −1.21147 | − | 4.37514i | −0.117668 | − | 0.424951i | ||||
\(107\) | 18.8035 | 1.81780 | 0.908901 | − | 0.417012i | \(-0.136923\pi\) | ||||
0.908901 | + | 0.417012i | \(0.136923\pi\) | |||||||
\(108\) | 1.02872 | + | 1.71515i | 0.0989886 | + | 0.165040i | ||||
\(109\) | − | 1.41395i | − | 0.135432i | −0.997705 | − | 0.0677159i | \(-0.978429\pi\) | ||
0.997705 | − | 0.0677159i | \(-0.0215711\pi\) | |||||||
\(110\) | −0.441855 | − | 1.59573i | −0.0421292 | − | 0.152147i | ||||
\(111\) | −8.26643 | −0.784614 | ||||||||
\(112\) | 7.08728 | − | 13.2785i | 0.669685 | − | 1.25470i | ||||
\(113\) | 7.50077i | 0.705613i | 0.935696 | + | 0.352807i | \(0.114773\pi\) | ||||
−0.935696 | + | 0.352807i | \(0.885227\pi\) | |||||||
\(114\) | 0.330034 | + | 1.19189i | 0.0309105 | + | 0.111631i | ||||
\(115\) | 4.97297 | − | 11.6298i | 0.463732 | − | 1.08449i | ||||
\(116\) | −9.16563 | + | 5.49741i | −0.851008 | + | 0.510421i | ||||
\(117\) | 3.89773 | 0.360345 | ||||||||
\(118\) | −4.59881 | − | 16.6083i | −0.423355 | − | 1.52892i | ||||
\(119\) | − | 20.3832i | − | 1.86852i | ||||||
\(120\) | 5.14129 | − | 5.40493i | 0.469334 | − | 0.493401i | ||||
\(121\) | −10.8029 | −0.982084 | ||||||||
\(122\) | −4.62222 | − | 16.6928i | −0.418476 | − | 1.51130i | ||||
\(123\) | − | 3.00019i | − | 0.270518i | ||||||
\(124\) | −0.615394 | − | 1.02602i | −0.0552640 | − | 0.0921397i | ||||
\(125\) | − | 8.02878i | − | 0.718116i | ||||||
\(126\) | 5.12854 | − | 1.42009i | 0.456887 | − | 0.126511i | ||||
\(127\) | − | 14.2562i | − | 1.26503i | −0.774547 | − | 0.632516i | \(-0.782022\pi\) | ||
0.774547 | − | 0.632516i | \(-0.217978\pi\) | |||||||
\(128\) | 3.56018 | + | 10.7390i | 0.314678 | + | 0.949198i | ||||
\(129\) | − | 0.586065i | − | 0.0516001i | ||||||
\(130\) | −3.87952 | − | 14.0106i | −0.340257 | − | 1.22881i | ||||
\(131\) | 9.62271i | 0.840740i | 0.907353 | + | 0.420370i | \(0.138100\pi\) | ||||
−0.907353 | + | 0.420370i | \(0.861900\pi\) | |||||||
\(132\) | 0.456678 | + | 0.761403i | 0.0397487 | + | 0.0662716i | ||||
\(133\) | 3.29068 | 0.285338 | ||||||||
\(134\) | 20.7884 | − | 5.75629i | 1.79585 | − | 0.497267i | ||||
\(135\) | 2.63738 | 0.226990 | ||||||||
\(136\) | 11.1012 | + | 10.5597i | 0.951916 | + | 0.905484i | ||||
\(137\) | 0.547723i | 0.0467951i | 0.999726 | + | 0.0233976i | \(0.00744836\pi\) | ||||
−0.999726 | + | 0.0233976i | \(0.992552\pi\) | |||||||
\(138\) | −0.905744 | + | 6.72158i | −0.0771021 | + | 0.572179i | ||||
\(139\) | 14.0406i | 1.19091i | 0.803389 | + | 0.595455i | \(0.203028\pi\) | ||||
−0.803389 | + | 0.595455i | \(0.796972\pi\) | |||||||
\(140\) | −10.2092 | − | 17.0214i | −0.862833 | − | 1.43857i | ||||
\(141\) | −3.89063 | −0.327650 | ||||||||
\(142\) | −0.610380 | − | 2.20434i | −0.0512220 | − | 0.184984i | ||||
\(143\) | 1.73031 | 0.144696 | ||||||||
\(144\) | −1.88347 | + | 3.52882i | −0.156956 | + | 0.294068i | ||||
\(145\) | 14.0940i | 1.17044i | ||||||||
\(146\) | −20.4369 | + | 5.65894i | −1.69137 | + | 0.468337i | ||||
\(147\) | − | 7.15930i | − | 0.590489i | ||||||
\(148\) | −8.50384 | − | 14.1781i | −0.699011 | − | 1.16544i | ||||
\(149\) | − | 17.8061i | − | 1.45873i | −0.684125 | − | 0.729365i | \(-0.739816\pi\) | ||
0.684125 | − | 0.729365i | \(-0.260184\pi\) | |||||||
\(150\) | −0.738096 | − | 2.66558i | −0.0602653 | − | 0.217644i | ||||
\(151\) | 23.1344i | 1.88265i | 0.337502 | + | 0.941325i | \(0.390418\pi\) | ||||
−0.337502 | + | 0.941325i | \(0.609582\pi\) | |||||||
\(152\) | −1.70476 | + | 1.79218i | −0.138275 | + | 0.145365i | ||||
\(153\) | 5.41690i | 0.437930i | ||||||||
\(154\) | 2.27670 | − | 0.630417i | 0.183462 | − | 0.0508004i | ||||
\(155\) | −1.57772 | −0.126725 | ||||||||
\(156\) | 4.00967 | + | 6.68518i | 0.321030 | + | 0.535243i | ||||
\(157\) | − | 16.2745i | − | 1.29884i | −0.760428 | − | 0.649422i | \(-0.775011\pi\) | ||
0.760428 | − | 0.649422i | \(-0.224989\pi\) | |||||||
\(158\) | −14.8611 | + | 4.11502i | −1.18229 | + | 0.327374i | ||||
\(159\) | 3.21010 | 0.254577 | ||||||||
\(160\) | 14.5592 | + | 3.25792i | 1.15101 | + | 0.257561i | ||||
\(161\) | 16.5928 | + | 7.09519i | 1.30770 | + | 0.559179i | ||||
\(162\) | −1.36293 | + | 0.377393i | −0.107082 | + | 0.0296508i | ||||
\(163\) | 24.0378i | 1.88279i | 0.337308 | + | 0.941394i | \(0.390484\pi\) | ||||
−0.337308 | + | 0.941394i | \(0.609516\pi\) | |||||||
\(164\) | 5.14577 | − | 3.08636i | 0.401817 | − | 0.241004i | ||||
\(165\) | 1.17081 | 0.0911473 | ||||||||
\(166\) | −15.9235 | + | 4.40920i | −1.23590 | + | 0.342220i | ||||
\(167\) | − | 12.2209i | − | 0.945684i | −0.881147 | − | 0.472842i | \(-0.843228\pi\) | ||
0.881147 | − | 0.472842i | \(-0.156772\pi\) | |||||||
\(168\) | 7.71149 | + | 7.33534i | 0.594955 | + | 0.565934i | ||||
\(169\) | 2.19227 | 0.168636 | ||||||||
\(170\) | 19.4714 | − | 5.39160i | 1.49339 | − | 0.413517i | ||||
\(171\) | −0.874510 | −0.0668754 | ||||||||
\(172\) | 1.00519 | − | 0.602896i | 0.0766449 | − | 0.0459704i | ||||
\(173\) | 12.3773 | 0.941026 | 0.470513 | − | 0.882393i | \(-0.344069\pi\) | ||||
0.470513 | + | 0.882393i | \(0.344069\pi\) | |||||||
\(174\) | −2.01676 | − | 7.28339i | −0.152890 | − | 0.552153i | ||||
\(175\) | −7.35936 | −0.556315 | ||||||||
\(176\) | −0.836126 | + | 1.56654i | −0.0630253 | + | 0.118082i | ||||
\(177\) | 12.1857 | 0.915935 | ||||||||
\(178\) | −4.99333 | − | 18.0331i | −0.374266 | − | 1.35163i | ||||
\(179\) | 5.33092i | 0.398451i | 0.979954 | + | 0.199226i | \(0.0638427\pi\) | ||||
−0.979954 | + | 0.199226i | \(0.936157\pi\) | |||||||
\(180\) | 2.71313 | + | 4.52350i | 0.202224 | + | 0.337162i | ||||
\(181\) | − | 10.2332i | − | 0.760625i | −0.924858 | − | 0.380312i | \(-0.875816\pi\) | ||
0.924858 | − | 0.380312i | \(-0.124184\pi\) | |||||||
\(182\) | 19.9897 | − | 5.53511i | 1.48173 | − | 0.410290i | ||||
\(183\) | 12.2477 | 0.905379 | ||||||||
\(184\) | −12.4603 | + | 5.36114i | −0.918583 | + | 0.395228i | ||||
\(185\) | −21.8017 | −1.60289 | ||||||||
\(186\) | 0.815322 | − | 0.225762i | 0.0597823 | − | 0.0165536i | ||||
\(187\) | 2.40471i | 0.175850i | ||||||||
\(188\) | −4.00237 | − | 6.67301i | −0.291903 | − | 0.486679i | ||||
\(189\) | 3.76288i | 0.273710i | ||||||||
\(190\) | 0.870425 | + | 3.14348i | 0.0631473 | + | 0.228052i | ||||
\(191\) | −18.0753 | −1.30788 | −0.653941 | − | 0.756546i | \(-0.726886\pi\) | ||||
−0.653941 | + | 0.756546i | \(0.726886\pi\) | |||||||
\(192\) | −7.99001 | + | 0.399731i | −0.576629 | + | 0.0288481i | ||||
\(193\) | −0.0704641 | −0.00507212 | −0.00253606 | − | 0.999997i | \(-0.500807\pi\) | ||||
−0.00253606 | + | 0.999997i | \(0.500807\pi\) | |||||||
\(194\) | −0.488137 | − | 1.76287i | −0.0350462 | − | 0.126567i | ||||
\(195\) | 10.2798 | 0.736151 | ||||||||
\(196\) | 12.2793 | − | 7.36491i | 0.877090 | − | 0.526065i | ||||
\(197\) | −16.3762 | −1.16676 | −0.583379 | − | 0.812200i | \(-0.698270\pi\) | ||||
−0.583379 | + | 0.812200i | \(0.698270\pi\) | |||||||
\(198\) | −0.605043 | + | 0.167536i | −0.0429985 | + | 0.0119062i | ||||
\(199\) | −0.218434 | −0.0154844 | −0.00774218 | − | 0.999970i | \(-0.502464\pi\) | ||||
−0.00774218 | + | 0.999970i | \(0.502464\pi\) | |||||||
\(200\) | 3.81258 | − | 4.00808i | 0.269590 | − | 0.283414i | ||||
\(201\) | 15.2528i | 1.07585i | ||||||||
\(202\) | −18.2560 | + | 5.05506i | −1.28449 | + | 0.355673i | ||||
\(203\) | −20.1086 | −1.41135 | ||||||||
\(204\) | −9.29078 | + | 5.57247i | −0.650485 | + | 0.390151i | ||||
\(205\) | − | 7.91265i | − | 0.552643i | ||||||
\(206\) | 5.90912 | − | 1.63623i | 0.411708 | − | 0.114001i | ||||
\(207\) | −4.40961 | − | 1.88557i | −0.306489 | − | 0.131056i | ||||
\(208\) | −7.34125 | + | 13.7544i | −0.509024 | + | 0.953693i | ||||
\(209\) | −0.388220 | −0.0268537 | ||||||||
\(210\) | 13.5259 | − | 3.74531i | 0.933377 | − | 0.258451i | ||||
\(211\) | − | 10.1413i | − | 0.698157i | −0.937094 | − | 0.349078i | \(-0.886495\pi\) | ||
0.937094 | − | 0.349078i | \(-0.113505\pi\) | |||||||
\(212\) | 3.30229 | + | 5.50580i | 0.226802 | + | 0.378140i | ||||
\(213\) | 1.61736 | 0.110820 | ||||||||
\(214\) | −25.6278 | + | 7.09631i | −1.75188 | + | 0.485094i | ||||
\(215\) | − | 1.54568i | − | 0.105414i | ||||||
\(216\) | −2.04936 | − | 1.94939i | −0.139441 | − | 0.132639i | ||||
\(217\) | − | 2.25101i | − | 0.152808i | ||||||
\(218\) | 0.533615 | + | 1.92711i | 0.0361409 | + | 0.130520i | ||||
\(219\) | − | 14.9948i | − | 1.01326i | ||||||
\(220\) | 1.20443 | + | 2.00811i | 0.0812029 | + | 0.135387i | ||||
\(221\) | 21.1136i | 1.42025i | ||||||||
\(222\) | 11.2665 | − | 3.11969i | 0.756161 | − | 0.209380i | ||||
\(223\) | − | 16.1279i | − | 1.08001i | −0.841663 | − | 0.540003i | \(-0.818423\pi\) | ||
0.841663 | − | 0.540003i | \(-0.181577\pi\) | |||||||
\(224\) | −4.64823 | + | 20.7724i | −0.310573 | + | 1.38791i | ||||
\(225\) | 1.95578 | 0.130385 | ||||||||
\(226\) | −2.83074 | − | 10.2230i | −0.188298 | − | 0.680025i | ||||
\(227\) | 7.08184 | 0.470038 | 0.235019 | − | 0.971991i | \(-0.424485\pi\) | ||||
0.235019 | + | 0.971991i | \(0.424485\pi\) | |||||||
\(228\) | −0.899626 | − | 1.49991i | −0.0595792 | − | 0.0993343i | ||||
\(229\) | − | 3.37854i | − | 0.223260i | −0.993750 | − | 0.111630i | \(-0.964393\pi\) | ||
0.993750 | − | 0.111630i | \(-0.0356072\pi\) | |||||||
\(230\) | −2.38879 | + | 17.7274i | −0.157512 | + | 1.16891i | ||||
\(231\) | 1.67045i | 0.109908i | ||||||||
\(232\) | 10.4174 | − | 10.9516i | 0.683937 | − | 0.719009i | ||||
\(233\) | −13.6186 | −0.892181 | −0.446091 | − | 0.894988i | \(-0.647184\pi\) | ||||
−0.446091 | + | 0.894988i | \(0.647184\pi\) | |||||||
\(234\) | −5.31232 | + | 1.47098i | −0.347277 | + | 0.0961607i | ||||
\(235\) | −10.2611 | −0.669359 | ||||||||
\(236\) | 12.5357 | + | 20.9003i | 0.816005 | + | 1.36050i | ||||
\(237\) | − | 10.9038i | − | 0.708278i | ||||||
\(238\) | 7.69246 | + | 27.7808i | 0.498628 | + | 1.80076i | ||||
\(239\) | 24.4272i | 1.58006i | 0.613066 | + | 0.790032i | \(0.289936\pi\) | ||||
−0.613066 | + | 0.790032i | \(0.710064\pi\) | |||||||
\(240\) | −4.96743 | + | 9.30683i | −0.320646 | + | 0.600753i | ||||
\(241\) | 18.5960i | 1.19787i | 0.800797 | + | 0.598936i | \(0.204410\pi\) | ||||
−0.800797 | + | 0.598936i | \(0.795590\pi\) | |||||||
\(242\) | 14.7236 | − | 4.07695i | 0.946470 | − | 0.262076i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 12.5995 | + | 21.0067i | 0.806600 | + | 1.34482i | ||||
\(245\) | − | 18.8818i | − | 1.20631i | ||||||
\(246\) | 1.13225 | + | 4.08905i | 0.0721897 | + | 0.260708i | ||||
\(247\) | −3.40860 | −0.216884 | ||||||||
\(248\) | 1.22595 | + | 1.16615i | 0.0778481 | + | 0.0740508i | ||||
\(249\) | − | 11.6833i | − | 0.740400i | ||||||
\(250\) | 3.03001 | + | 10.9427i | 0.191634 | + | 0.692074i | ||||
\(251\) | 11.0122 | 0.695081 | 0.347541 | − | 0.937665i | \(-0.387017\pi\) | ||||
0.347541 | + | 0.937665i | \(0.387017\pi\) | |||||||
\(252\) | −6.45391 | + | 3.87095i | −0.406558 | + | 0.243847i | ||||
\(253\) | −1.95755 | − | 0.837058i | −0.123070 | − | 0.0526254i | ||||
\(254\) | 5.38019 | + | 19.4302i | 0.337583 | + | 1.21916i | ||||
\(255\) | 14.2864i | 0.894650i | ||||||||
\(256\) | −8.90508 | − | 13.2928i | −0.556567 | − | 0.830802i | ||||
\(257\) | −1.80376 | −0.112516 | −0.0562579 | − | 0.998416i | \(-0.517917\pi\) | ||||
−0.0562579 | + | 0.998416i | \(0.517917\pi\) | |||||||
\(258\) | 0.221177 | + | 0.798764i | 0.0137699 | + | 0.0497289i | ||||
\(259\) | − | 31.1056i | − | 1.93281i | ||||||
\(260\) | 10.5750 | + | 17.6314i | 0.655835 | + | 1.09345i | ||||
\(261\) | 5.34393 | 0.330781 | ||||||||
\(262\) | −3.63155 | − | 13.1151i | −0.224358 | − | 0.810252i | ||||
\(263\) | −12.9884 | −0.800899 | −0.400450 | − | 0.916319i | \(-0.631146\pi\) | ||||
−0.400450 | + | 0.916319i | \(0.631146\pi\) | |||||||
\(264\) | −0.909768 | − | 0.865391i | −0.0559923 | − | 0.0532611i | ||||
\(265\) | 8.46625 | 0.520078 | ||||||||
\(266\) | −4.48496 | + | 1.24188i | −0.274991 | + | 0.0761445i | ||||
\(267\) | 13.2311 | 0.809731 | ||||||||
\(268\) | −26.1607 | + | 15.6908i | −1.59802 | + | 0.958469i | ||||
\(269\) | −3.59883 | −0.219425 | −0.109712 | − | 0.993963i | \(-0.534993\pi\) | ||||
−0.109712 | + | 0.993963i | \(0.534993\pi\) | |||||||
\(270\) | −3.59456 | + | 0.995329i | −0.218758 | + | 0.0605738i | ||||
\(271\) | 17.7331i | 1.07721i | 0.842560 | + | 0.538603i | \(0.181048\pi\) | ||||
−0.842560 | + | 0.538603i | \(0.818952\pi\) | |||||||
\(272\) | −19.1152 | − | 10.2026i | −1.15903 | − | 0.618621i | ||||
\(273\) | 14.6667i | 0.887668i | ||||||||
\(274\) | −0.206707 | − | 0.746507i | −0.0124876 | − | 0.0450982i | ||||
\(275\) | 0.868224 | 0.0523559 | ||||||||
\(276\) | −1.30221 | − | 9.50285i | −0.0783841 | − | 0.572005i | ||||
\(277\) | −4.19147 | −0.251841 | −0.125920 | − | 0.992040i | \(-0.540188\pi\) | ||||
−0.125920 | + | 0.992040i | \(0.540188\pi\) | |||||||
\(278\) | −5.29883 | − | 19.1364i | −0.317803 | − | 1.14772i | ||||
\(279\) | 0.598213i | 0.0358141i | ||||||||
\(280\) | 20.3381 | + | 19.3461i | 1.21544 | + | 1.15615i | ||||
\(281\) | − | 15.5993i | − | 0.930574i | −0.885160 | − | 0.465287i | \(-0.845951\pi\) | ||
0.885160 | − | 0.465287i | \(-0.154049\pi\) | |||||||
\(282\) | 5.30265 | − | 1.46830i | 0.315768 | − | 0.0874359i | ||||
\(283\) | 13.8442 | 0.822952 | 0.411476 | − | 0.911421i | \(-0.365013\pi\) | ||||
0.411476 | + | 0.911421i | \(0.365013\pi\) | |||||||
\(284\) | 1.66381 | + | 2.77401i | 0.0987289 | + | 0.164607i | ||||
\(285\) | −2.30642 | −0.136620 | ||||||||
\(286\) | −2.35829 | + | 0.653007i | −0.139449 | + | 0.0386131i | ||||
\(287\) | 11.2894 | 0.666391 | ||||||||
\(288\) | 1.23528 | − | 5.52033i | 0.0727898 | − | 0.325289i | ||||
\(289\) | −12.3428 | −0.726046 | ||||||||
\(290\) | −5.31897 | − | 19.2091i | −0.312341 | − | 1.12800i | ||||
\(291\) | 1.29344 | 0.0758230 | ||||||||
\(292\) | 25.7183 | − | 15.4255i | 1.50505 | − | 0.902707i | ||||
\(293\) | − | 7.35396i | − | 0.429623i | −0.976656 | − | 0.214811i | \(-0.931086\pi\) | ||
0.976656 | − | 0.214811i | \(-0.0689137\pi\) | |||||||
\(294\) | 2.70187 | + | 9.75761i | 0.157576 | + | 0.569075i | ||||
\(295\) | 32.1384 | 1.87117 | ||||||||
\(296\) | 16.9409 | + | 16.1145i | 0.984667 | + | 0.936637i | ||||
\(297\) | − | 0.443928i | − | 0.0257593i | ||||||
\(298\) | 6.71989 | + | 24.2684i | 0.389272 | + | 1.40583i | ||||
\(299\) | −17.1874 | − | 7.34944i | −0.993975 | − | 0.425029i | ||||
\(300\) | 2.01195 | + | 3.35445i | 0.116160 | + | 0.193669i | ||||
\(301\) | 2.20529 | 0.127111 | ||||||||
\(302\) | −8.73076 | − | 31.5305i | −0.502399 | − | 1.81438i | ||||
\(303\) | − | 13.3947i | − | 0.769504i | ||||||
\(304\) | 1.64711 | − | 3.08598i | 0.0944684 | − | 0.176993i | ||||
\(305\) | 32.3020 | 1.84960 | ||||||||
\(306\) | −2.04430 | − | 7.38284i | −0.116865 | − | 0.422049i | ||||
\(307\) | 6.72809i | 0.383993i | 0.981396 | + | 0.191996i | \(0.0614961\pi\) | ||||
−0.981396 | + | 0.191996i | \(0.938504\pi\) | |||||||
\(308\) | −2.86507 | + | 1.71843i | −0.163253 | + | 0.0979164i | ||||
\(309\) | 4.33560i | 0.246644i | ||||||||
\(310\) | 2.15031 | − | 0.595419i | 0.122130 | − | 0.0338175i | ||||
\(311\) | − | 2.75954i | − | 0.156479i | −0.996935 | − | 0.0782396i | \(-0.975070\pi\) | ||
0.996935 | − | 0.0782396i | \(-0.0249299\pi\) | |||||||
\(312\) | −7.98783 | − | 7.59820i | −0.452222 | − | 0.430163i | ||||
\(313\) | 1.14544i | 0.0647439i | 0.999476 | + | 0.0323719i | \(0.0103061\pi\) | ||||
−0.999476 | + | 0.0323719i | \(0.989694\pi\) | |||||||
\(314\) | 6.14187 | + | 22.1809i | 0.346606 | + | 1.25174i | ||||
\(315\) | 9.92416i | 0.559163i | ||||||||
\(316\) | 18.7016 | − | 11.2170i | 1.05205 | − | 0.631003i | ||||
\(317\) | −25.3550 | −1.42408 | −0.712038 | − | 0.702141i | \(-0.752228\pi\) | ||||
−0.712038 | + | 0.702141i | \(0.752228\pi\) | |||||||
\(318\) | −4.37514 | + | 1.21147i | −0.245345 | + | 0.0679358i | ||||
\(319\) | 2.37232 | 0.132824 | ||||||||
\(320\) | −21.0727 | + | 1.05424i | −1.17800 | + | 0.0589340i | ||||
\(321\) | − | 18.8035i | − | 1.04951i | ||||||
\(322\) | −25.2925 | − | 3.40821i | −1.40950 | − | 0.189932i | ||||
\(323\) | − | 4.73713i | − | 0.263581i | ||||||
\(324\) | 1.71515 | − | 1.02872i | 0.0952860 | − | 0.0571511i | ||||
\(325\) | 7.62308 | 0.422852 | ||||||||
\(326\) | −9.07172 | − | 32.7619i | −0.502436 | − | 1.81451i | ||||
\(327\) | −1.41395 | −0.0781915 | ||||||||
\(328\) | −5.84855 | + | 6.14846i | −0.322932 | + | 0.339492i | ||||
\(329\) | − | 14.6400i | − | 0.807129i | ||||||
\(330\) | −1.59573 | + | 0.441855i | −0.0878419 | + | 0.0243233i | ||||
\(331\) | − | 22.6100i | − | 1.24276i | −0.783509 | − | 0.621380i | \(-0.786572\pi\) | ||
0.783509 | − | 0.621380i | \(-0.213428\pi\) | |||||||
\(332\) | 20.0386 | − | 12.0189i | 1.09976 | − | 0.659620i | ||||
\(333\) | 8.26643i | 0.452997i | ||||||||
\(334\) | 4.61209 | + | 16.6563i | 0.252363 | + | 0.911389i | ||||
\(335\) | 40.2273i | 2.19785i | ||||||||
\(336\) | −13.2785 | − | 7.08728i | −0.724403 | − | 0.386643i | ||||
\(337\) | − | 20.9510i | − | 1.14128i | −0.821202 | − | 0.570638i | \(-0.806696\pi\) | ||
0.821202 | − | 0.570638i | \(-0.193304\pi\) | |||||||
\(338\) | −2.98790 | + | 0.827346i | −0.162520 | + | 0.0450017i | ||||
\(339\) | 7.50077 | 0.407386 | ||||||||
\(340\) | −24.5033 | + | 14.6967i | −1.32888 | + | 0.797042i | ||||
\(341\) | 0.265564i | 0.0143811i | ||||||||
\(342\) | 1.19189 | − | 0.330034i | 0.0644503 | − | 0.0178462i | ||||
\(343\) | 0.599411 | 0.0323652 | ||||||||
\(344\) | −1.14247 | + | 1.20106i | −0.0615979 | + | 0.0647566i | ||||
\(345\) | −11.6298 | − | 4.97297i | −0.626128 | − | 0.267736i | ||||
\(346\) | −16.8693 | + | 4.67109i | −0.906900 | + | 0.251120i | ||||
\(347\) | − | 5.06673i | − | 0.271996i | −0.990709 | − | 0.135998i | \(-0.956576\pi\) | ||
0.990709 | − | 0.135998i | \(-0.0434241\pi\) | |||||||
\(348\) | 5.49741 | + | 9.16563i | 0.294692 | + | 0.491329i | ||||
\(349\) | 24.6005 | 1.31683 | 0.658416 | − | 0.752654i | \(-0.271227\pi\) | ||||
0.658416 | + | 0.752654i | \(0.271227\pi\) | |||||||
\(350\) | 10.0303 | − | 2.77737i | 0.536141 | − | 0.148457i | ||||
\(351\) | − | 3.89773i | − | 0.208045i | ||||||
\(352\) | 0.548378 | − | 2.45063i | 0.0292286 | − | 0.130619i | ||||
\(353\) | −1.34090 | −0.0713690 | −0.0356845 | − | 0.999363i | \(-0.511361\pi\) | ||||
−0.0356845 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(354\) | −16.6083 | + | 4.59881i | −0.882720 | + | 0.244424i | ||||
\(355\) | 4.26559 | 0.226394 | ||||||||
\(356\) | 13.6111 | + | 22.6933i | 0.721387 | + | 1.20274i | ||||
\(357\) | −20.3832 | −1.07879 | ||||||||
\(358\) | −2.01185 | − | 7.26566i | −0.106330 | − | 0.384002i | ||||
\(359\) | −12.1085 | −0.639064 | −0.319532 | − | 0.947576i | \(-0.603526\pi\) | ||||
−0.319532 | + | 0.947576i | \(0.603526\pi\) | |||||||
\(360\) | −5.40493 | − | 5.14129i | −0.284865 | − | 0.270970i | ||||
\(361\) | −18.2352 | −0.959749 | ||||||||
\(362\) | 3.86192 | + | 13.9471i | 0.202978 | + | 0.733042i | ||||
\(363\) | 10.8029i | 0.567007i | ||||||||
\(364\) | −25.1556 | + | 15.0879i | −1.31851 | + | 0.790822i | ||||
\(365\) | − | 39.5470i | − | 2.06999i | ||||||
\(366\) | −16.6928 | + | 4.62222i | −0.872547 | + | 0.241607i | ||||
\(367\) | 21.2655 | 1.11005 | 0.555024 | − | 0.831834i | \(-0.312709\pi\) | ||||
0.555024 | + | 0.831834i | \(0.312709\pi\) | |||||||
\(368\) | 14.9592 | − | 12.0093i | 0.779802 | − | 0.626026i | ||||
\(369\) | −3.00019 | −0.156184 | ||||||||
\(370\) | 29.7142 | − | 8.22782i | 1.54477 | − | 0.427744i | ||||
\(371\) | 12.0792i | 0.627122i | ||||||||
\(372\) | −1.02602 | + | 0.615394i | −0.0531969 | + | 0.0319067i | ||||
\(373\) | 10.5684i | 0.547213i | 0.961842 | + | 0.273606i | \(0.0882165\pi\) | ||||
−0.961842 | + | 0.273606i | \(0.911783\pi\) | |||||||
\(374\) | −0.907523 | − | 3.27745i | −0.0469269 | − | 0.169473i | ||||
\(375\) | −8.02878 | −0.414604 | ||||||||
\(376\) | 7.97330 | + | 7.58437i | 0.411191 | + | 0.391134i | ||||
\(377\) | 20.8292 | 1.07276 | ||||||||
\(378\) | −1.42009 | − | 5.12854i | −0.0730414 | − | 0.263784i | ||||
\(379\) | −17.7038 | −0.909383 | −0.454691 | − | 0.890649i | \(-0.650250\pi\) | ||||
−0.454691 | + | 0.890649i | \(0.650250\pi\) | |||||||
\(380\) | −2.37266 | − | 3.95585i | −0.121715 | − | 0.202931i | ||||
\(381\) | −14.2562 | −0.730367 | ||||||||
\(382\) | 24.6353 | − | 6.82149i | 1.26045 | − | 0.349018i | ||||
\(383\) | −37.1701 | −1.89930 | −0.949652 | − | 0.313307i | \(-0.898563\pi\) | ||||
−0.949652 | + | 0.313307i | \(0.898563\pi\) | |||||||
\(384\) | 10.7390 | − | 3.56018i | 0.548020 | − | 0.181680i | ||||
\(385\) | 4.40561i | 0.224531i | ||||||||
\(386\) | 0.0960376 | − | 0.0265927i | 0.00488818 | − | 0.00135353i | ||||
\(387\) | −0.586065 | −0.0297913 | ||||||||
\(388\) | 1.33059 | + | 2.21845i | 0.0675505 | + | 0.112625i | ||||
\(389\) | − | 12.8197i | − | 0.649987i | −0.945716 | − | 0.324993i | \(-0.894638\pi\) | ||
0.945716 | − | 0.324993i | \(-0.105362\pi\) | |||||||
\(390\) | −14.0106 | + | 3.87952i | −0.709455 | + | 0.196447i | ||||
\(391\) | 10.2139 | − | 23.8864i | 0.516541 | − | 1.20799i | ||||
\(392\) | −13.9563 | + | 14.6720i | −0.704899 | + | 0.741046i | ||||
\(393\) | 9.62271 | 0.485402 | ||||||||
\(394\) | 22.3196 | − | 6.18027i | 1.12445 | − | 0.311358i | ||||
\(395\) | − | 28.7575i | − | 1.44695i | ||||||
\(396\) | 0.761403 | − | 0.456678i | 0.0382619 | − | 0.0229489i | ||||
\(397\) | −9.42657 | −0.473106 | −0.236553 | − | 0.971619i | \(-0.576018\pi\) | ||||
−0.236553 | + | 0.971619i | \(0.576018\pi\) | |||||||
\(398\) | 0.297710 | − | 0.0824354i | 0.0149228 | − | 0.00413211i | ||||
\(399\) | − | 3.29068i | − | 0.164740i | ||||||
\(400\) | −3.68364 | + | 6.90157i | −0.184182 | + | 0.345079i | ||||
\(401\) | 15.9154i | 0.794778i | 0.917650 | + | 0.397389i | \(0.130084\pi\) | ||||
−0.917650 | + | 0.397389i | \(0.869916\pi\) | |||||||
\(402\) | −5.75629 | − | 20.7884i | −0.287097 | − | 1.03683i | ||||
\(403\) | 2.33167i | 0.116149i | ||||||||
\(404\) | 22.9738 | − | 13.7794i | 1.14299 | − | 0.685549i | ||||
\(405\) | − | 2.63738i | − | 0.131052i | ||||||
\(406\) | 27.4066 | − | 7.58884i | 1.36016 | − | 0.376628i | ||||
\(407\) | 3.66970i | 0.181900i | ||||||||
\(408\) | 10.5597 | − | 11.1012i | 0.522781 | − | 0.549589i | ||||
\(409\) | −7.65459 | −0.378495 | −0.189247 | − | 0.981929i | \(-0.560605\pi\) | ||||
−0.189247 | + | 0.981929i | \(0.560605\pi\) | |||||||
\(410\) | 2.98618 | + | 10.7844i | 0.147477 | + | 0.532602i | ||||
\(411\) | 0.547723 | 0.0270172 | ||||||||
\(412\) | −7.43620 | + | 4.46012i | −0.366355 | + | 0.219734i | ||||
\(413\) | 45.8535i | 2.25630i | ||||||||
\(414\) | 6.72158 | + | 0.905744i | 0.330348 | + | 0.0445149i | ||||
\(415\) | − | 30.8133i | − | 1.51257i | ||||||
\(416\) | 4.81480 | − | 21.5167i | 0.236065 | − | 1.05495i | ||||
\(417\) | 14.0406 | 0.687572 | ||||||||
\(418\) | 0.529116 | − | 0.146511i | 0.0258799 | − | 0.00716611i | ||||
\(419\) | −14.8784 | −0.726856 | −0.363428 | − | 0.931622i | \(-0.618394\pi\) | ||||
−0.363428 | + | 0.931622i | \(0.618394\pi\) | |||||||
\(420\) | −17.0214 | + | 10.2092i | −0.830559 | + | 0.498157i | ||||
\(421\) | − | 27.5405i | − | 1.34224i | −0.741347 | − | 0.671122i | \(-0.765813\pi\) | ||
0.741347 | − | 0.671122i | \(-0.234187\pi\) | |||||||
\(422\) | 3.82726 | + | 13.8219i | 0.186308 | + | 0.672839i | ||||
\(423\) | 3.89063i | 0.189169i | ||||||||
\(424\) | −6.57864 | − | 6.25774i | −0.319487 | − | 0.303903i | ||||
\(425\) | 10.5942i | 0.513896i | ||||||||
\(426\) | −2.20434 | + | 0.610380i | −0.106801 | + | 0.0295730i | ||||
\(427\) | 46.0868i | 2.23030i | ||||||||
\(428\) | 32.2508 | − | 19.3435i | 1.55890 | − | 0.935005i | ||||
\(429\) | − | 1.73031i | − | 0.0835402i | ||||||
\(430\) | 0.583327 | + | 2.10665i | 0.0281305 | + | 0.101591i | ||||
\(431\) | −3.16378 | −0.152394 | −0.0761969 | − | 0.997093i | \(-0.524278\pi\) | ||||
−0.0761969 | + | 0.997093i | \(0.524278\pi\) | |||||||
\(432\) | 3.52882 | + | 1.88347i | 0.169780 | + | 0.0906185i | ||||
\(433\) | 25.1258i | 1.20747i | 0.797186 | + | 0.603734i | \(0.206321\pi\) | ||||
−0.797186 | + | 0.603734i | \(0.793679\pi\) | |||||||
\(434\) | 0.849515 | + | 3.06796i | 0.0407780 | + | 0.147267i | ||||
\(435\) | 14.0940 | 0.675754 | ||||||||
\(436\) | −1.45456 | − | 2.42513i | −0.0696607 | − | 0.116143i | ||||
\(437\) | 3.85624 | + | 1.64895i | 0.184469 | + | 0.0788800i | ||||
\(438\) | 5.65894 | + | 20.4369i | 0.270395 | + | 0.976511i | ||||
\(439\) | − | 5.17548i | − | 0.247012i | −0.992344 | − | 0.123506i | \(-0.960586\pi\) | ||
0.992344 | − | 0.123506i | \(-0.0394139\pi\) | |||||||
\(440\) | −2.39940 | − | 2.28236i | −0.114387 | − | 0.108807i | ||||
\(441\) | −7.15930 | −0.340919 | ||||||||
\(442\) | −7.96812 | − | 28.7763i | −0.379005 | − | 1.36875i | ||||
\(443\) | − | 8.90381i | − | 0.423033i | −0.977374 | − | 0.211516i | \(-0.932160\pi\) | ||
0.977374 | − | 0.211516i | \(-0.0678402\pi\) | |||||||
\(444\) | −14.1781 | + | 8.50384i | −0.672865 | + | 0.403574i | ||||
\(445\) | 34.8955 | 1.65420 | ||||||||
\(446\) | 6.08657 | + | 21.9812i | 0.288208 | + | 1.04084i | ||||
\(447\) | −17.8061 | −0.842198 | ||||||||
\(448\) | −1.50414 | − | 30.0655i | −0.0710640 | − | 1.42046i | ||||
\(449\) | −6.09398 | −0.287593 | −0.143796 | − | 0.989607i | \(-0.545931\pi\) | ||||
−0.143796 | + | 0.989607i | \(0.545931\pi\) | |||||||
\(450\) | −2.66558 | + | 0.738096i | −0.125657 | + | 0.0347942i | ||||
\(451\) | −1.33187 | −0.0627153 | ||||||||
\(452\) | 7.71619 | + | 12.8649i | 0.362939 | + | 0.605116i | ||||
\(453\) | 23.1344 | 1.08695 | ||||||||
\(454\) | −9.65204 | + | 2.67264i | −0.452993 | + | 0.125433i | ||||
\(455\) | 38.6816i | 1.81342i | ||||||||
\(456\) | 1.79218 | + | 1.70476i | 0.0839267 | + | 0.0798329i | ||||
\(457\) | 6.46875i | 0.302595i | 0.988488 | + | 0.151298i | \(0.0483452\pi\) | ||||
−0.988488 | + | 0.151298i | \(0.951655\pi\) | |||||||
\(458\) | 1.27504 | + | 4.60471i | 0.0595787 | + | 0.215164i | ||||
\(459\) | 5.41690 | 0.252839 | ||||||||
\(460\) | −3.43443 | − | 25.0626i | −0.160131 | − | 1.16855i | ||||
\(461\) | −16.0481 | −0.747434 | −0.373717 | − | 0.927543i | \(-0.621917\pi\) | ||||
−0.373717 | + | 0.927543i | \(0.621917\pi\) | |||||||
\(462\) | −0.630417 | − | 2.27670i | −0.0293296 | − | 0.105922i | ||||
\(463\) | − | 1.86102i | − | 0.0864888i | −0.999065 | − | 0.0432444i | \(-0.986231\pi\) | ||
0.999065 | − | 0.0432444i | \(-0.0137694\pi\) | |||||||
\(464\) | −10.0651 | + | 18.8577i | −0.467262 | + | 0.875448i | ||||
\(465\) | 1.57772i | 0.0731648i | ||||||||
\(466\) | 18.5611 | − | 5.13955i | 0.859827 | − | 0.238085i | ||||
\(467\) | 25.3051 | 1.17098 | 0.585491 | − | 0.810679i | \(-0.300902\pi\) | ||||
0.585491 | + | 0.810679i | \(0.300902\pi\) | |||||||
\(468\) | 6.68518 | − | 4.00967i | 0.309023 | − | 0.185347i | ||||
\(469\) | −57.3943 | −2.65022 | ||||||||
\(470\) | 13.9851 | − | 3.87246i | 0.645085 | − | 0.178623i | ||||
\(471\) | −16.2745 | −0.749888 | ||||||||
\(472\) | −24.9729 | − | 23.7548i | −1.14947 | − | 1.09340i | ||||
\(473\) | −0.260171 | −0.0119627 | ||||||||
\(474\) | 4.11502 | + | 14.8611i | 0.189009 | + | 0.682593i | ||||
\(475\) | −1.71034 | −0.0784760 | ||||||||
\(476\) | −20.9686 | − | 34.9601i | −0.961092 | − | 1.60240i | ||||
\(477\) | − | 3.21010i | − | 0.146980i | ||||||
\(478\) | −9.21866 | − | 33.2925i | −0.421651 | − | 1.52276i | ||||
\(479\) | −3.31118 | −0.151291 | −0.0756457 | − | 0.997135i | \(-0.524102\pi\) | ||||
−0.0756457 | + | 0.997135i | \(0.524102\pi\) | |||||||
\(480\) | 3.25792 | − | 14.5592i | 0.148703 | − | 0.664534i | ||||
\(481\) | 32.2203i | 1.46912i | ||||||||
\(482\) | −7.01800 | − | 25.3450i | −0.319661 | − | 1.15443i | ||||
\(483\) | 7.09519 | − | 16.5928i | 0.322842 | − | 0.755000i | ||||
\(484\) | −18.5286 | + | 11.1132i | −0.842210 | + | 0.505145i | ||||
\(485\) | 3.41130 | 0.154899 | ||||||||
\(486\) | 0.377393 | + | 1.36293i | 0.0171189 | + | 0.0618237i | ||||
\(487\) | 22.6258i | 1.02527i | 0.858605 | + | 0.512637i | \(0.171331\pi\) | ||||
−0.858605 | + | 0.512637i | \(0.828669\pi\) | |||||||
\(488\) | −25.1000 | − | 23.8757i | −1.13622 | − | 1.08080i | ||||
\(489\) | 24.0378 | 1.08703 | ||||||||
\(490\) | 7.12586 | + | 25.7345i | 0.321913 | + | 1.16257i | ||||
\(491\) | − | 25.1776i | − | 1.13625i | −0.822942 | − | 0.568125i | \(-0.807669\pi\) | ||
0.822942 | − | 0.568125i | \(-0.192331\pi\) | |||||||
\(492\) | −3.08636 | − | 5.14577i | −0.139144 | − | 0.231989i | ||||
\(493\) | 28.9475i | 1.30373i | ||||||||
\(494\) | 4.64568 | − | 1.28638i | 0.209019 | − | 0.0578771i | ||||
\(495\) | − | 1.17081i | − | 0.0526239i | ||||||
\(496\) | −2.11098 | − | 1.12672i | −0.0947860 | − | 0.0505911i | ||||
\(497\) | 6.08593i | 0.272991i | ||||||||
\(498\) | 4.40920 | + | 15.9235i | 0.197581 | + | 0.713550i | ||||
\(499\) | 33.4253i | 1.49632i | 0.663516 | + | 0.748162i | \(0.269063\pi\) | ||||
−0.663516 | + | 0.748162i | \(0.730937\pi\) | |||||||
\(500\) | −8.25936 | − | 13.7705i | −0.369370 | − | 0.615838i | ||||
\(501\) | −12.2209 | −0.545991 | ||||||||
\(502\) | −15.0088 | + | 4.15591i | −0.669875 | + | 0.185488i | ||||
\(503\) | −1.88385 | −0.0839966 | −0.0419983 | − | 0.999118i | \(-0.513372\pi\) | ||||
−0.0419983 | + | 0.999118i | \(0.513372\pi\) | |||||||
\(504\) | 7.33534 | − | 7.71149i | 0.326742 | − | 0.343497i | ||||
\(505\) | − | 35.3268i | − | 1.57202i | ||||||
\(506\) | 2.98390 | + | 0.402085i | 0.132650 | + | 0.0178749i | ||||
\(507\) | − | 2.19227i | − | 0.0973620i | ||||||
\(508\) | −14.6656 | − | 24.4515i | −0.650682 | − | 1.08486i | ||||
\(509\) | −10.9621 | −0.485886 | −0.242943 | − | 0.970041i | \(-0.578113\pi\) | ||||
−0.242943 | + | 0.970041i | \(0.578113\pi\) | |||||||
\(510\) | −5.39160 | − | 19.4714i | −0.238744 | − | 0.862207i | ||||
\(511\) | 56.4237 | 2.49604 | ||||||||
\(512\) | 17.1536 | + | 14.7565i | 0.758090 | + | 0.652150i | ||||
\(513\) | 0.874510i | 0.0386106i | ||||||||
\(514\) | 2.45840 | − | 0.680729i | 0.108435 | − | 0.0300256i | ||||
\(515\) | 11.4346i | 0.503870i | ||||||||
\(516\) | −0.602896 | − | 1.00519i | −0.0265410 | − | 0.0442509i | ||||
\(517\) | 1.72716i | 0.0759605i | ||||||||
\(518\) | 11.7390 | + | 42.3947i | 0.515784 | + | 1.86272i | ||||
\(519\) | − | 12.3773i | − | 0.543301i | ||||||
\(520\) | −21.0670 | − | 20.0393i | −0.923847 | − | 0.878783i | ||||
\(521\) | − | 16.8720i | − | 0.739174i | −0.929196 | − | 0.369587i | \(-0.879499\pi\) | ||
0.929196 | − | 0.369587i | \(-0.120501\pi\) | |||||||
\(522\) | −7.28339 | + | 2.01676i | −0.318785 | + | 0.0882713i | ||||
\(523\) | 11.4507 | 0.500705 | 0.250353 | − | 0.968155i | \(-0.419453\pi\) | ||||
0.250353 | + | 0.968155i | \(0.419453\pi\) | |||||||
\(524\) | 9.89908 | + | 16.5044i | 0.432443 | + | 0.720997i | ||||
\(525\) | 7.35936i | 0.321189i | ||||||||
\(526\) | 17.7023 | − | 4.90173i | 0.771855 | − | 0.213726i | ||||
\(527\) | −3.24046 | −0.141157 | ||||||||
\(528\) | 1.56654 | + | 0.836126i | 0.0681749 | + | 0.0363877i | ||||
\(529\) | 15.8892 | + | 16.6293i | 0.690837 | + | 0.723011i | ||||
\(530\) | −11.5389 | + | 3.19511i | −0.501218 | + | 0.138787i | ||||
\(531\) | − | 12.1857i | − | 0.528815i | ||||||
\(532\) | 5.64400 | − | 3.38519i | 0.244699 | − | 0.146766i | ||||
\(533\) | −11.6939 | −0.506520 | ||||||||
\(534\) | −18.0331 | + | 4.99333i | −0.780367 | + | 0.216083i | ||||
\(535\) | − | 49.5920i | − | 2.14405i | ||||||
\(536\) | 29.7336 | − | 31.2583i | 1.28430 | − | 1.35015i | ||||
\(537\) | 5.33092 | 0.230046 | ||||||||
\(538\) | 4.90495 | − | 1.35818i | 0.211468 | − | 0.0585551i | ||||
\(539\) | −3.17821 | −0.136895 | ||||||||
\(540\) | 4.52350 | − | 2.71313i | 0.194660 | − | 0.116754i | ||||
\(541\) | 29.3626 | 1.26240 | 0.631198 | − | 0.775622i | \(-0.282563\pi\) | ||||
0.631198 | + | 0.775622i | \(0.282563\pi\) | |||||||
\(542\) | −6.69233 | − | 24.1689i | −0.287460 | − | 1.03814i | ||||
\(543\) | −10.2332 | −0.439147 | ||||||||
\(544\) | 29.9031 | + | 6.69141i | 1.28208 | + | 0.286892i | ||||
\(545\) | −3.72912 | −0.159738 | ||||||||
\(546\) | −5.53511 | − | 19.9897i | −0.236881 | − | 0.855478i | ||||
\(547\) | 16.9183i | 0.723375i | 0.932299 | + | 0.361687i | \(0.117799\pi\) | ||||
−0.932299 | + | 0.361687i | \(0.882201\pi\) | |||||||
\(548\) | 0.563454 | + | 0.939426i | 0.0240695 | + | 0.0401303i | ||||
\(549\) | − | 12.2477i | − | 0.522721i | ||||||
\(550\) | −1.18333 | + | 0.327662i | −0.0504572 | + | 0.0139715i | ||||
\(551\) | −4.67332 | −0.199090 | ||||||||
\(552\) | 5.36114 | + | 12.4603i | 0.228185 | + | 0.530344i | ||||
\(553\) | 41.0298 | 1.74476 | ||||||||
\(554\) | 5.71267 | − | 1.58183i | 0.242708 | − | 0.0672056i | ||||
\(555\) | 21.8017i | 0.925431i | ||||||||
\(556\) | 14.4439 | + | 24.0817i | 0.612556 | + | 1.02129i | ||||
\(557\) | 25.7916i | 1.09282i | 0.837516 | + | 0.546412i | \(0.184007\pi\) | ||||
−0.837516 | + | 0.546412i | \(0.815993\pi\) | |||||||
\(558\) | −0.225762 | − | 0.815322i | −0.00955725 | − | 0.0345153i | ||||
\(559\) | −2.28432 | −0.0966164 | ||||||||
\(560\) | −35.0205 | − | 18.6919i | −1.47989 | − | 0.789875i | ||||
\(561\) | 2.40471 | 0.101527 | ||||||||
\(562\) | 5.88705 | + | 21.2607i | 0.248330 | + | 0.896827i | ||||
\(563\) | −10.3819 | −0.437544 | −0.218772 | − | 0.975776i | \(-0.570205\pi\) | ||||
−0.218772 | + | 0.975776i | \(0.570205\pi\) | |||||||
\(564\) | −6.67301 | + | 4.00237i | −0.280985 | + | 0.168530i | ||||
\(565\) | 19.7824 | 0.832251 | ||||||||
\(566\) | −18.8687 | + | 5.22471i | −0.793109 | + | 0.219611i | ||||
\(567\) | 3.76288 | 0.158026 | ||||||||
\(568\) | −3.31455 | − | 3.15287i | −0.139075 | − | 0.132291i | ||||
\(569\) | − | 10.9488i | − | 0.458999i | −0.973309 | − | 0.229499i | \(-0.926291\pi\) | ||
0.973309 | − | 0.229499i | \(-0.0737088\pi\) | |||||||
\(570\) | 3.14348 | − | 0.870425i | 0.131666 | − | 0.0364581i | ||||
\(571\) | −2.07053 | −0.0866489 | −0.0433245 | − | 0.999061i | \(-0.513795\pi\) | ||||
−0.0433245 | + | 0.999061i | \(0.513795\pi\) | |||||||
\(572\) | 2.96774 | − | 1.78001i | 0.124087 | − | 0.0744258i | ||||
\(573\) | 18.0753i | 0.755106i | ||||||||
\(574\) | −15.3866 | + | 4.26053i | −0.642225 | + | 0.177831i | ||||
\(575\) | −8.62420 | − | 3.68775i | −0.359654 | − | 0.153790i | ||||
\(576\) | 0.399731 | + | 7.99001i | 0.0166555 | + | 0.332917i | ||||
\(577\) | 0.754391 | 0.0314057 | 0.0157029 | − | 0.999877i | \(-0.495001\pi\) | ||||
0.0157029 | + | 0.999877i | \(0.495001\pi\) | |||||||
\(578\) | 16.8223 | − | 4.65808i | 0.699716 | − | 0.193751i | ||||
\(579\) | 0.0704641i | 0.00292839i | ||||||||
\(580\) | 14.4988 | + | 24.1733i | 0.602028 | + | 1.00374i | ||||
\(581\) | 43.9629 | 1.82389 | ||||||||
\(582\) | −1.76287 | + | 0.488137i | −0.0730733 | + | 0.0202339i | ||||
\(583\) | − | 1.42505i | − | 0.0590197i | ||||||
\(584\) | −29.2308 | + | 30.7297i | −1.20958 | + | 1.27161i | ||||
\(585\) | − | 10.2798i | − | 0.425017i | ||||||
\(586\) | 2.77533 | + | 10.0229i | 0.114648 | + | 0.414043i | ||||
\(587\) | − | 8.98386i | − | 0.370803i | −0.982663 | − | 0.185402i | \(-0.940641\pi\) | ||
0.982663 | − | 0.185402i | \(-0.0593586\pi\) | |||||||
\(588\) | −7.36491 | − | 12.2793i | −0.303724 | − | 0.506388i | ||||
\(589\) | − | 0.523143i | − | 0.0215557i | ||||||
\(590\) | −43.8023 | + | 12.1288i | −1.80331 | + | 0.499335i | ||||
\(591\) | 16.3762i | 0.673628i | ||||||||
\(592\) | −29.1707 | − | 15.5696i | −1.19891 | − | 0.639905i | ||||
\(593\) | 10.0225 | 0.411575 | 0.205787 | − | 0.978597i | \(-0.434024\pi\) | ||||
0.205787 | + | 0.978597i | \(0.434024\pi\) | |||||||
\(594\) | 0.167536 | + | 0.605043i | 0.00687407 | + | 0.0248252i | ||||
\(595\) | −53.7581 | −2.20387 | ||||||||
\(596\) | −18.3174 | − | 30.5400i | −0.750312 | − | 1.25097i | ||||
\(597\) | 0.218434i | 0.00893990i | ||||||||
\(598\) | 26.1989 | + | 3.53034i | 1.07135 | + | 0.144366i | ||||
\(599\) | − | 42.5653i | − | 1.73917i | −0.493781 | − | 0.869586i | \(-0.664386\pi\) | ||
0.493781 | − | 0.869586i | \(-0.335614\pi\) | |||||||
\(600\) | −4.00808 | − | 3.81258i | −0.163629 | − | 0.155648i | ||||
\(601\) | 26.9032 | 1.09741 | 0.548703 | − | 0.836017i | \(-0.315122\pi\) | ||||
0.548703 | + | 0.836017i | \(0.315122\pi\) | |||||||
\(602\) | −3.00566 | + | 0.832263i | −0.122501 | + | 0.0339205i | ||||
\(603\) | 15.2528 | 0.621140 | ||||||||
\(604\) | 23.7988 | + | 39.6789i | 0.968360 | + | 1.61451i | ||||
\(605\) | 28.4914i | 1.15834i | ||||||||
\(606\) | 5.05506 | + | 18.2560i | 0.205348 | + | 0.741598i | ||||
\(607\) | 4.29457i | 0.174311i | 0.996195 | + | 0.0871557i | \(0.0277778\pi\) | ||||
−0.996195 | + | 0.0871557i | \(0.972222\pi\) | |||||||
\(608\) | −1.08027 | + | 4.82759i | −0.0438107 | + | 0.195784i | ||||
\(609\) | 20.1086i | 0.814841i | ||||||||
\(610\) | −44.0253 | + | 12.1905i | −1.78253 | + | 0.493581i | ||||
\(611\) | 15.1646i | 0.613495i | ||||||||
\(612\) | 5.57247 | + | 9.29078i | 0.225254 | + | 0.375558i | ||||
\(613\) | 43.1668i | 1.74349i | 0.489958 | + | 0.871746i | \(0.337012\pi\) | ||||
−0.489958 | + | 0.871746i | \(0.662988\pi\) | |||||||
\(614\) | −2.53914 | − | 9.16991i | −0.102471 | − | 0.370067i | ||||
\(615\) | −7.91265 | −0.319069 | ||||||||
\(616\) | 3.25637 | − | 3.42335i | 0.131203 | − | 0.137931i | ||||
\(617\) | 12.4584i | 0.501555i | 0.968045 | + | 0.250777i | \(0.0806862\pi\) | ||||
−0.968045 | + | 0.250777i | \(0.919314\pi\) | |||||||
\(618\) | −1.63623 | − | 5.90912i | −0.0658187 | − | 0.237700i | ||||
\(619\) | 22.8503 | 0.918430 | 0.459215 | − | 0.888325i | \(-0.348131\pi\) | ||||
0.459215 | + | 0.888325i | \(0.348131\pi\) | |||||||
\(620\) | −2.70602 | + | 1.62303i | −0.108676 | + | 0.0651824i | ||||
\(621\) | −1.88557 | + | 4.40961i | −0.0756654 | + | 0.176951i | ||||
\(622\) | 1.04143 | + | 3.76106i | 0.0417576 | + | 0.150805i | ||||
\(623\) | 49.7871i | 1.99468i | ||||||||
\(624\) | 13.7544 | + | 7.34125i | 0.550615 | + | 0.293885i | ||||
\(625\) | −30.9538 | −1.23815 | ||||||||
\(626\) | −0.432280 | − | 1.56115i | −0.0172774 | − | 0.0623960i | ||||
\(627\) | 0.388220i | 0.0155040i | ||||||||
\(628\) | −16.7419 | − | 27.9131i | −0.668073 | − | 1.11385i | ||||
\(629\) | −44.7784 | −1.78543 | ||||||||
\(630\) | −3.74531 | − | 13.5259i | −0.149217 | − | 0.538885i | ||||
\(631\) | −21.4492 | −0.853877 | −0.426939 | − | 0.904281i | \(-0.640408\pi\) | ||||
−0.426939 | + | 0.904281i | \(0.640408\pi\) | |||||||
\(632\) | −21.2558 | + | 22.3458i | −0.845511 | + | 0.888868i | ||||
\(633\) | −10.1413 | −0.403081 | ||||||||
\(634\) | 34.5570 | − | 9.56879i | 1.37243 | − | 0.380025i | ||||
\(635\) | −37.5990 | −1.49207 | ||||||||
\(636\) | 5.50580 | − | 3.30229i | 0.218319 | − | 0.130944i | ||||
\(637\) | −27.9050 | −1.10564 | ||||||||
\(638\) | −3.23330 | + | 0.895298i | −0.128008 | + | 0.0354452i | ||||
\(639\) | − | 1.61736i | − | 0.0639817i | ||||||
\(640\) | 28.3227 | − | 9.38955i | 1.11955 | − | 0.371154i | ||||
\(641\) | − | 8.45936i | − | 0.334125i | −0.985946 | − | 0.167062i | \(-0.946572\pi\) | ||
0.985946 | − | 0.167062i | \(-0.0534281\pi\) | |||||||
\(642\) | 7.09631 | + | 25.6278i | 0.280069 | + | 1.01145i | ||||
\(643\) | −33.3589 | −1.31555 | −0.657773 | − | 0.753216i | \(-0.728502\pi\) | ||||
−0.657773 | + | 0.753216i | \(0.728502\pi\) | |||||||
\(644\) | 35.7581 | − | 4.90008i | 1.40907 | − | 0.193090i | ||||
\(645\) | −1.54568 | −0.0608609 | ||||||||
\(646\) | 1.78776 | + | 6.45637i | 0.0703385 | + | 0.254022i | ||||
\(647\) | − | 10.1383i | − | 0.398580i | −0.979941 | − | 0.199290i | \(-0.936136\pi\) | ||
0.979941 | − | 0.199290i | \(-0.0638635\pi\) | |||||||
\(648\) | −1.94939 | + | 2.04936i | −0.0765794 | + | 0.0805064i | ||||
\(649\) | − | 5.40959i | − | 0.212345i | ||||||
\(650\) | −10.3897 | + | 2.87690i | −0.407518 | + | 0.112841i | ||||
\(651\) | −2.25101 | −0.0882239 | ||||||||
\(652\) | 24.7282 | + | 41.2285i | 0.968431 | + | 1.61463i | ||||
\(653\) | 28.2360 | 1.10496 | 0.552480 | − | 0.833526i | \(-0.313681\pi\) | ||||
0.552480 | + | 0.833526i | \(0.313681\pi\) | |||||||
\(654\) | 1.92711 | − | 0.533615i | 0.0753560 | − | 0.0208660i | ||||
\(655\) | 25.3788 | 0.991630 | ||||||||
\(656\) | 5.65077 | − | 10.5871i | 0.220626 | − | 0.413358i | ||||
\(657\) | −14.9948 | −0.585003 | ||||||||
\(658\) | 5.52504 | + | 19.9533i | 0.215388 | + | 0.777859i | ||||
\(659\) | 2.19610 | 0.0855478 | 0.0427739 | − | 0.999085i | \(-0.486380\pi\) | ||||
0.0427739 | + | 0.999085i | \(0.486380\pi\) | |||||||
\(660\) | 2.00811 | − | 1.20443i | 0.0781655 | − | 0.0468825i | ||||
\(661\) | 30.6073i | 1.19049i | 0.803546 | + | 0.595243i | \(0.202944\pi\) | ||||
−0.803546 | + | 0.595243i | \(0.797056\pi\) | |||||||
\(662\) | 8.53288 | + | 30.8159i | 0.331640 | + | 1.19769i | ||||
\(663\) | 21.1136 | 0.819984 | ||||||||
\(664\) | −22.7754 | + | 23.9433i | −0.883856 | + | 0.929179i | ||||
\(665\) | − | 8.67877i | − | 0.336548i | ||||||
\(666\) | −3.11969 | − | 11.2665i | −0.120886 | − | 0.436570i | ||||
\(667\) | −23.5646 | − | 10.0764i | −0.912426 | − | 0.390158i | ||||
\(668\) | −12.5719 | − | 20.9607i | −0.486422 | − | 0.810994i | ||||
\(669\) | −16.1279 | −0.623542 | ||||||||
\(670\) | −15.1815 | − | 54.8270i | −0.586513 | − | 2.11815i | ||||
\(671\) | − | 5.43712i | − | 0.209898i | ||||||
\(672\) | 20.7724 | + | 4.64823i | 0.801312 | + | 0.179309i | ||||
\(673\) | −28.2666 | −1.08960 | −0.544799 | − | 0.838567i | \(-0.683394\pi\) | ||||
−0.544799 | + | 0.838567i | \(0.683394\pi\) | |||||||
\(674\) | 7.90678 | + | 28.5548i | 0.304558 | + | 1.09989i | ||||
\(675\) | − | 1.95578i | − | 0.0752778i | ||||||
\(676\) | 3.76006 | − | 2.25523i | 0.144618 | − | 0.0867395i | ||||
\(677\) | 9.48783i | 0.364647i | 0.983239 | + | 0.182323i | \(0.0583618\pi\) | ||||
−0.983239 | + | 0.182323i | \(0.941638\pi\) | |||||||
\(678\) | −10.2230 | + | 2.83074i | −0.392613 | + | 0.108714i | ||||
\(679\) | 4.86708i | 0.186781i | ||||||||
\(680\) | 27.8498 | − | 29.2780i | 1.06799 | − | 1.12276i | ||||
\(681\) | − | 7.08184i | − | 0.271377i | ||||||
\(682\) | −0.100222 | − | 0.361944i | −0.00383770 | − | 0.0138596i | ||||
\(683\) | 15.6468i | 0.598709i | 0.954142 | + | 0.299354i | \(0.0967713\pi\) | ||||
−0.954142 | + | 0.299354i | \(0.903229\pi\) | |||||||
\(684\) | −1.49991 | + | 0.899626i | −0.0573507 | + | 0.0343981i | ||||
\(685\) | 1.44455 | 0.0551936 | ||||||||
\(686\) | −0.816955 | + | 0.226214i | −0.0311915 | + | 0.00863688i | ||||
\(687\) | −3.37854 | −0.128899 | ||||||||
\(688\) | 1.10384 | − | 2.06811i | 0.0420833 | − | 0.0788461i | ||||
\(689\) | − | 12.5121i | − | 0.476672i | ||||||
\(690\) | 17.7274 | + | 2.38879i | 0.674869 | + | 0.0909397i | ||||
\(691\) | − | 6.15202i | − | 0.234034i | −0.993130 | − | 0.117017i | \(-0.962667\pi\) | ||
0.993130 | − | 0.117017i | \(-0.0373332\pi\) | |||||||
\(692\) | 21.2288 | − | 12.7327i | 0.807000 | − | 0.484026i | ||||
\(693\) | 1.67045 | 0.0634552 | ||||||||
\(694\) | 1.91215 | + | 6.90558i | 0.0725841 | + | 0.262132i | ||||
\(695\) | 37.0305 | 1.40465 | ||||||||
\(696\) | −10.9516 | − | 10.4174i | −0.415120 | − | 0.394871i | ||||
\(697\) | − | 16.2517i | − | 0.615578i | ||||||
\(698\) | −33.5287 | + | 9.28405i | −1.26908 | + | 0.351406i | ||||
\(699\) | 13.6186i | 0.515101i | ||||||||
\(700\) | −12.6224 | + | 7.57072i | −0.477081 | + | 0.286146i | ||||
\(701\) | − | 22.5282i | − | 0.850880i | −0.904987 | − | 0.425440i | \(-0.860119\pi\) | ||
0.904987 | − | 0.425440i | \(-0.139881\pi\) | |||||||
\(702\) | 1.47098 | + | 5.31232i | 0.0555184 | + | 0.200501i | ||||
\(703\) | − | 7.22907i | − | 0.272650i | ||||||
\(704\) | 0.177452 | + | 3.54699i | 0.00668797 | + | 0.133682i | ||||
\(705\) | 10.2611i | 0.386454i | ||||||||
\(706\) | 1.82755 | − | 0.506047i | 0.0687808 | − | 0.0190453i | ||||
\(707\) | 50.4026 | 1.89558 | ||||||||
\(708\) | 20.9003 | − | 12.5357i | 0.785483 | − | 0.471120i | ||||
\(709\) | − | 27.8820i | − | 1.04713i | −0.851985 | − | 0.523565i | \(-0.824602\pi\) | ||
0.851985 | − | 0.523565i | \(-0.175398\pi\) | |||||||
\(710\) | −5.81370 | + | 1.60980i | −0.218184 | + | 0.0604149i | ||||
\(711\) | −10.9038 | −0.408925 | ||||||||
\(712\) | −27.1153 | − | 25.7926i | −1.01619 | − | 0.966620i | ||||
\(713\) | 1.12797 | − | 2.63788i | 0.0422430 | − | 0.0987896i | ||||
\(714\) | 27.7808 | − | 7.69246i | 1.03967 | − | 0.287883i | ||||
\(715\) | − | 4.56349i | − | 0.170665i | ||||||
\(716\) | 5.48402 | + | 9.14331i | 0.204947 | + | 0.341702i | ||||
\(717\) | 24.4272 | 0.912250 | ||||||||
\(718\) | 16.5031 | − | 4.56968i | 0.615889 | − | 0.170539i | ||||
\(719\) | − | 3.48406i | − | 0.129934i | −0.997887 | − | 0.0649668i | \(-0.979306\pi\) | ||
0.997887 | − | 0.0649668i | \(-0.0206942\pi\) | |||||||
\(720\) | 9.30683 | + | 4.96743i | 0.346845 | + | 0.185125i | ||||
\(721\) | −16.3144 | −0.607579 | ||||||||
\(722\) | 24.8533 | − | 6.88185i | 0.924945 | − | 0.256116i | ||||
\(723\) | 18.5960 | 0.691592 | ||||||||
\(724\) | −10.5271 | − | 17.5514i | −0.391235 | − | 0.652292i | ||||
\(725\) | 10.4515 | 0.388160 | ||||||||
\(726\) | −4.07695 | − | 14.7236i | −0.151310 | − | 0.546445i | ||||
\(727\) | −37.4694 | −1.38966 | −0.694832 | − | 0.719172i | \(-0.744521\pi\) | ||||
−0.694832 | + | 0.719172i | \(0.744521\pi\) | |||||||
\(728\) | 28.5911 | − | 30.0573i | 1.05966 | − | 1.11400i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 14.9248 | + | 53.8998i | 0.552391 | + | 1.99492i | ||||
\(731\) | − | 3.17465i | − | 0.117419i | ||||||
\(732\) | 21.0067 | − | 12.5995i | 0.776430 | − | 0.465691i | ||||
\(733\) | 21.7887i | 0.804784i | 0.915467 | + | 0.402392i | \(0.131821\pi\) | ||||
−0.915467 | + | 0.402392i | \(0.868179\pi\) | |||||||
\(734\) | −28.9833 | + | 8.02544i | −1.06979 | + | 0.296224i | ||||
\(735\) | −18.8818 | −0.696465 | ||||||||
\(736\) | −15.8561 | + | 22.0133i | −0.584464 | + | 0.811420i | ||||
\(737\) | 6.77113 | 0.249418 | ||||||||
\(738\) | 4.08905 | − | 1.13225i | 0.150520 | − | 0.0416788i | ||||
\(739\) | 38.4986i | 1.41619i | 0.706116 | + | 0.708096i | \(0.250446\pi\) | ||||
−0.706116 | + | 0.708096i | \(0.749554\pi\) | |||||||
\(740\) | −37.3932 | + | 22.4279i | −1.37460 | + | 0.824464i | ||||
\(741\) | 3.40860i | 0.125218i | ||||||||
\(742\) | −4.55862 | − | 16.4631i | −0.167352 | − | 0.604380i | ||||
\(743\) | −16.0420 | −0.588524 | −0.294262 | − | 0.955725i | \(-0.595074\pi\) | ||||
−0.294262 | + | 0.955725i | \(0.595074\pi\) | |||||||
\(744\) | 1.16615 | − | 1.22595i | 0.0427532 | − | 0.0449456i | ||||
\(745\) | −46.9613 | −1.72053 | ||||||||
\(746\) | −3.98845 | − | 14.4040i | −0.146028 | − | 0.527369i | ||||
\(747\) | −11.6833 | −0.427470 | ||||||||
\(748\) | 2.47378 | + | 4.12444i | 0.0904502 | + | 0.150805i | ||||
\(749\) | 70.7554 | 2.58534 | ||||||||
\(750\) | 10.9427 | − | 3.03001i | 0.399569 | − | 0.110640i | ||||
\(751\) | 14.1886 | 0.517751 | 0.258876 | − | 0.965911i | \(-0.416648\pi\) | ||||
0.258876 | + | 0.965911i | \(0.416648\pi\) | |||||||
\(752\) | −13.7293 | − | 7.32789i | −0.500657 | − | 0.267221i | ||||
\(753\) | − | 11.0122i | − | 0.401305i | ||||||
\(754\) | −28.3887 | + | 7.86079i | −1.03385 | + | 0.286273i | ||||
\(755\) | 61.0142 | 2.22053 | ||||||||
\(756\) | 3.87095 | + | 6.45391i | 0.140785 | + | 0.234726i | ||||
\(757\) | − | 44.8913i | − | 1.63160i | −0.578333 | − | 0.815801i | \(-0.696297\pi\) | ||
0.578333 | − | 0.815801i | \(-0.303703\pi\) | |||||||
\(758\) | 24.1290 | − | 6.68129i | 0.876405 | − | 0.242675i | ||||
\(759\) | −0.837058 | + | 1.95755i | −0.0303833 | + | 0.0710545i | ||||
\(760\) | 4.72667 | + | 4.49611i | 0.171454 | + | 0.163091i | ||||
\(761\) | −29.9876 | −1.08705 | −0.543525 | − | 0.839393i | \(-0.682911\pi\) | ||||
−0.543525 | + | 0.839393i | \(0.682911\pi\) | |||||||
\(762\) | 19.4302 | − | 5.38019i | 0.703881 | − | 0.194904i | ||||
\(763\) | − | 5.32052i | − | 0.192616i | ||||||
\(764\) | −31.0018 | + | 18.5944i | −1.12161 | + | 0.672722i | ||||
\(765\) | 14.2864 | 0.516527 | ||||||||
\(766\) | 50.6602 | − | 14.0277i | 1.83043 | − | 0.506843i | ||||
\(767\) | − | 47.4966i | − | 1.71500i | ||||||
\(768\) | −13.2928 | + | 8.90508i | −0.479664 | + | 0.321334i | ||||
\(769\) | − | 48.7531i | − | 1.75808i | −0.476746 | − | 0.879041i | \(-0.658184\pi\) | ||
0.476746 | − | 0.879041i | \(-0.341816\pi\) | |||||||
\(770\) | −1.66265 | − | 6.00454i | −0.0599177 | − | 0.216388i | ||||
\(771\) | 1.80376i | 0.0649610i | ||||||||
\(772\) | −0.120856 | + | 0.0724878i | −0.00434972 | + | 0.00260889i | ||||
\(773\) | − | 20.1101i | − | 0.723310i | −0.932312 | − | 0.361655i | \(-0.882212\pi\) | ||
0.932312 | − | 0.361655i | \(-0.117788\pi\) | |||||||
\(774\) | 0.798764 | − | 0.221177i | 0.0287110 | − | 0.00795004i | ||||
\(775\) | 1.16997i | 0.0420266i | ||||||||
\(776\) | −2.65073 | − | 2.52143i | −0.0951556 | − | 0.0905140i | ||||
\(777\) | −31.1056 | −1.11591 | ||||||||
\(778\) | 4.83808 | + | 17.4724i | 0.173454 | + | 0.626416i | ||||
\(779\) | 2.62370 | 0.0940037 | ||||||||
\(780\) | 17.6314 | − | 10.5750i | 0.631304 | − | 0.378646i | ||||
\(781\) | − | 0.717991i | − | 0.0256917i | ||||||
\(782\) | −4.90632 | + | 36.4101i | −0.175450 | + | 1.30202i | ||||
\(783\) | − | 5.34393i | − | 0.190976i | ||||||
\(784\) | 13.4843 | − | 25.2638i | 0.481583 | − | 0.902280i | ||||
\(785\) | −42.9220 | −1.53195 | ||||||||
\(786\) | −13.1151 | + | 3.63155i | −0.467799 | + | 0.129533i | ||||
\(787\) | −37.2635 | −1.32830 | −0.664151 | − | 0.747599i | \(-0.731207\pi\) | ||||
−0.664151 | + | 0.747599i | \(0.731207\pi\) | |||||||
\(788\) | −28.0877 | + | 16.8465i | −1.00058 | + | 0.600133i | ||||
\(789\) | 12.9884i | 0.462399i | ||||||||
\(790\) | 10.8529 | + | 39.1944i | 0.386128 | + | 1.39447i | ||||
\(791\) | 28.2245i | 1.00355i | ||||||||
\(792\) | −0.865391 | + | 0.909768i | −0.0307503 | + | 0.0323272i | ||||
\(793\) | − | 47.7383i | − | 1.69524i | ||||||
\(794\) | 12.8477 | − | 3.55752i | 0.455949 | − | 0.126252i | ||||
\(795\) | − | 8.46625i | − | 0.300267i | ||||||
\(796\) | −0.374646 | + | 0.224707i | −0.0132790 | + | 0.00796454i | ||||
\(797\) | 10.1031i | 0.357872i | 0.983861 | + | 0.178936i | \(0.0572655\pi\) | ||||
−0.983861 | + | 0.178936i | \(0.942735\pi\) | |||||||
\(798\) | 1.24188 | + | 4.48496i | 0.0439621 | + | 0.158766i | ||||
\(799\) | −21.0752 | −0.745585 | ||||||||
\(800\) | 2.41594 | − | 10.7965i | 0.0854164 | − | 0.381715i | ||||
\(801\) | − | 13.2311i | − | 0.467498i | ||||||
\(802\) | −6.00637 | − | 21.6916i | −0.212092 | − | 0.765956i | ||||
\(803\) | −6.65662 | −0.234907 | ||||||||
\(804\) | 15.6908 | + | 26.1607i | 0.553372 | + | 0.922618i | ||||
\(805\) | 18.7127 | − | 43.7616i | 0.659536 | − | 1.54239i | ||||
\(806\) | −0.879957 | − | 3.17790i | −0.0309952 | − | 0.111937i | ||||
\(807\) | 3.59883i | 0.126685i | ||||||||
\(808\) | −26.1115 | + | 27.4505i | −0.918599 | + | 0.965704i | ||||
\(809\) | −11.5458 | −0.405930 | −0.202965 | − | 0.979186i | \(-0.565058\pi\) | ||||
−0.202965 | + | 0.979186i | \(0.565058\pi\) | |||||||
\(810\) | 0.995329 | + | 3.59456i | 0.0349723 | + | 0.126300i | ||||
\(811\) | − | 19.6062i | − | 0.688466i | −0.938884 | − | 0.344233i | \(-0.888139\pi\) | ||
0.938884 | − | 0.344233i | \(-0.111861\pi\) | |||||||
\(812\) | −34.4892 | + | 20.6861i | −1.21033 | + | 0.725940i | ||||
\(813\) | 17.7331 | 0.621925 | ||||||||
\(814\) | −1.38492 | − | 5.00154i | −0.0485414 | − | 0.175304i | ||||
\(815\) | 63.3969 | 2.22070 | ||||||||
\(816\) | −10.2026 | + | 19.1152i | −0.357161 | + | 0.669167i | ||||
\(817\) | 0.512519 | 0.0179308 | ||||||||
\(818\) | 10.4327 | − | 2.88879i | 0.364769 | − | 0.101004i | ||||
\(819\) | 14.6667 | 0.512496 | ||||||||
\(820\) | −8.13990 | − | 13.5714i | −0.284258 | − | 0.473933i | ||||
\(821\) | −29.5246 | −1.03041 | −0.515207 | − | 0.857066i | \(-0.672285\pi\) | ||||
−0.515207 | + | 0.857066i | \(0.672285\pi\) | |||||||
\(822\) | −0.746507 | + | 0.206707i | −0.0260374 | + | 0.00720973i | ||||
\(823\) | − | 0.192280i | − | 0.00670247i | −0.999994 | − | 0.00335124i | \(-0.998933\pi\) | ||
0.999994 | − | 0.00335124i | \(-0.00106673\pi\) | |||||||
\(824\) | 8.45179 | − | 8.88520i | 0.294432 | − | 0.309531i | ||||
\(825\) | − | 0.868224i | − | 0.0302277i | ||||||
\(826\) | −17.3048 | − | 62.4950i | −0.602111 | − | 2.17448i | ||||
\(827\) | 19.9788 | 0.694730 | 0.347365 | − | 0.937730i | \(-0.387077\pi\) | ||||
0.347365 | + | 0.937730i | \(0.387077\pi\) | |||||||
\(828\) | −9.50285 | + | 1.30221i | −0.330247 | + | 0.0452551i | ||||
\(829\) | 48.6264 | 1.68887 | 0.844433 | − | 0.535661i | \(-0.179938\pi\) | ||||
0.844433 | + | 0.535661i | \(0.179938\pi\) | |||||||
\(830\) | 11.6287 | + | 41.9964i | 0.403640 | + | 1.45772i | ||||
\(831\) | 4.19147i | 0.145400i | ||||||||
\(832\) | 1.55804 | + | 31.1429i | 0.0540154 | + | 1.07968i | ||||
\(833\) | − | 38.7812i | − | 1.34369i | ||||||
\(834\) | −19.1364 | + | 5.29883i | −0.662638 | + | 0.183484i | ||||
\(835\) | −32.2312 | −1.11541 | ||||||||
\(836\) | −0.665854 | + | 0.399369i | −0.0230291 | + | 0.0138125i | ||||
\(837\) | 0.598213 | 0.0206773 | ||||||||
\(838\) | 20.2782 | − | 5.61499i | 0.700497 | − | 0.193967i | ||||
\(839\) | 41.6351 | 1.43740 | 0.718701 | − | 0.695319i | \(-0.244737\pi\) | ||||
0.718701 | + | 0.695319i | \(0.244737\pi\) | |||||||
\(840\) | 19.3461 | − | 20.3381i | 0.667503 | − | 0.701733i | ||||
\(841\) | −0.442430 | −0.0152562 | ||||||||
\(842\) | 10.3936 | + | 37.5358i | 0.358188 | + | 1.29357i | ||||
\(843\) | −15.5993 | −0.537267 | ||||||||
\(844\) | −10.4326 | − | 17.3939i | −0.359104 | − | 0.598721i | ||||
\(845\) | − | 5.78184i | − | 0.198901i | ||||||
\(846\) | −1.46830 | − | 5.30265i | −0.0504811 | − | 0.182309i | ||||
\(847\) | −40.6502 | −1.39676 | ||||||||
\(848\) | 11.3278 | + | 6.04613i | 0.389000 | + | 0.207625i | ||||
\(849\) | − | 13.8442i | − | 0.475132i | ||||||
\(850\) | −3.99819 | − | 14.4392i | −0.137137 | − | 0.495260i | ||||
\(851\) | 15.5869 | − | 36.4517i | 0.534313 | − | 1.24955i | ||||
\(852\) | 2.77401 | − | 1.66381i | 0.0950361 | − | 0.0570012i | ||||
\(853\) | −51.2775 | −1.75571 | −0.877854 | − | 0.478928i | \(-0.841025\pi\) | ||||
−0.877854 | + | 0.478928i | \(0.841025\pi\) | |||||||
\(854\) | −17.3929 | − | 62.8131i | −0.595171 | − | 2.14942i | ||||
\(855\) | 2.30642i | 0.0788777i | ||||||||
\(856\) | −36.6554 | + | 38.5351i | −1.25286 | + | 1.31710i | ||||
\(857\) | 23.4840 | 0.802199 | 0.401099 | − | 0.916035i | \(-0.368628\pi\) | ||||
0.401099 | + | 0.916035i | \(0.368628\pi\) | |||||||
\(858\) | 0.653007 | + | 2.35829i | 0.0222933 | + | 0.0805107i | ||||
\(859\) | 3.41554i | 0.116537i | 0.998301 | + | 0.0582684i | \(0.0185579\pi\) | ||||
−0.998301 | + | 0.0582684i | \(0.981442\pi\) | |||||||
\(860\) | −1.59007 | − | 2.65106i | −0.0542208 | − | 0.0904005i | ||||
\(861\) | − | 11.2894i | − | 0.384741i | ||||||
\(862\) | 4.31200 | − | 1.19399i | 0.146867 | − | 0.0406674i | ||||
\(863\) | 11.9996i | 0.408471i | 0.978922 | + | 0.204236i | \(0.0654709\pi\) | ||||
−0.978922 | + | 0.204236i | \(0.934529\pi\) | |||||||
\(864\) | −5.52033 | − | 1.23528i | −0.187806 | − | 0.0420252i | ||||
\(865\) | − | 32.6435i | − | 1.10991i | ||||||
\(866\) | −9.48229 | − | 34.2446i | −0.322221 | − | 1.16368i | ||||
\(867\) | 12.3428i | 0.419183i | ||||||||
\(868\) | −2.31566 | − | 3.86081i | −0.0785985 | − | 0.131045i | ||||
\(869\) | −4.84051 | −0.164203 | ||||||||
\(870\) | −19.2091 | + | 5.31897i | −0.651249 | + | 0.180330i | ||||
\(871\) | 59.4511 | 2.01442 | ||||||||
\(872\) | 2.89769 | + | 2.75634i | 0.0981280 | + | 0.0933415i | ||||
\(873\) | − | 1.29344i | − | 0.0437764i | ||||||
\(874\) | −5.87809 | − | 0.792082i | −0.198829 | − | 0.0267926i | ||||
\(875\) | − | 30.2114i | − | 1.02133i | ||||||
\(876\) | −15.4255 | − | 25.7183i | −0.521178 | − | 0.868942i | ||||
\(877\) | 6.90835 | 0.233279 | 0.116639 | − | 0.993174i | \(-0.462788\pi\) | ||||
0.116639 | + | 0.993174i | \(0.462788\pi\) | |||||||
\(878\) | 1.95319 | + | 7.05381i | 0.0659170 | + | 0.238055i | ||||
\(879\) | −7.35396 | −0.248043 | ||||||||
\(880\) | 4.13156 | + | 2.20518i | 0.139275 | + | 0.0743367i | ||||
\(881\) | 45.9651i | 1.54860i | 0.632816 | + | 0.774302i | \(0.281899\pi\) | ||||
−0.632816 | + | 0.774302i | \(0.718101\pi\) | |||||||
\(882\) | 9.75761 | − | 2.70187i | 0.328556 | − | 0.0909767i | ||||
\(883\) | − | 3.13486i | − | 0.105497i | −0.998608 | − | 0.0527483i | \(-0.983202\pi\) | ||
0.998608 | − | 0.0527483i | \(-0.0167981\pi\) | |||||||
\(884\) | 21.7200 | + | 36.2129i | 0.730521 | + | 1.21797i | ||||
\(885\) | − | 32.1384i | − | 1.08032i | ||||||
\(886\) | 3.36024 | + | 12.1353i | 0.112889 | + | 0.407692i | ||||
\(887\) | − | 36.0841i | − | 1.21159i | −0.795622 | − | 0.605793i | \(-0.792856\pi\) | ||
0.795622 | − | 0.605793i | \(-0.207144\pi\) | |||||||
\(888\) | 16.1145 | − | 16.9409i | 0.540768 | − | 0.568498i | ||||
\(889\) | − | 53.6444i | − | 1.79918i | ||||||
\(890\) | −47.5600 | + | 13.1693i | −1.59422 | + | 0.441436i | ||||
\(891\) | −0.443928 | −0.0148722 | ||||||||
\(892\) | −16.5911 | − | 27.6618i | −0.555512 | − | 0.926186i | ||||
\(893\) | − | 3.40240i | − | 0.113857i | ||||||
\(894\) | 24.2684 | − | 6.71989i | 0.811656 | − | 0.224747i | ||||
\(895\) | 14.0597 | 0.469962 | ||||||||
\(896\) | 13.3965 | + | 40.4094i | 0.447547 | + | 1.34998i | ||||
\(897\) | −7.34944 | + | 17.1874i | −0.245391 | + | 0.573872i | ||||
\(898\) | 8.30566 | − | 2.29983i | 0.277163 | − | 0.0767462i | ||||
\(899\) | 3.19681i | 0.106620i | ||||||||
\(900\) | 3.35445 | − | 2.01195i | 0.111815 | − | 0.0670648i | ||||
\(901\) | 17.3888 | 0.579304 | ||||||||
\(902\) | 1.81524 | − | 0.502639i | 0.0604410 | − | 0.0167360i | ||||
\(903\) | − | 2.20529i | − | 0.0733876i | ||||||
\(904\) | −15.3718 | − | 14.6220i | −0.511257 | − | 0.486319i | ||||
\(905\) | −26.9887 | −0.897136 | ||||||||
\(906\) | −31.5305 | + | 8.73076i | −1.04753 | + | 0.290060i | ||||
\(907\) | −15.9472 | −0.529518 | −0.264759 | − | 0.964315i | \(-0.585292\pi\) | ||||
−0.264759 | + | 0.964315i | \(0.585292\pi\) | |||||||
\(908\) | 12.1464 | − | 7.28523i | 0.403093 | − | 0.241769i | ||||
\(909\) | −13.3947 | −0.444273 | ||||||||
\(910\) | −14.5982 | − | 52.7203i | −0.483925 | − | 1.74766i | ||||
\(911\) | 38.4869 | 1.27513 | 0.637563 | − | 0.770398i | \(-0.279942\pi\) | ||||
0.637563 | + | 0.770398i | \(0.279942\pi\) | |||||||
\(912\) | −3.08598 | − | 1.64711i | −0.102187 | − | 0.0545414i | ||||
\(913\) | −5.18655 | −0.171650 | ||||||||
\(914\) | −2.44126 | − | 8.81644i | −0.0807498 | − | 0.291622i | ||||
\(915\) | − | 32.3020i | − | 1.06787i | ||||||
\(916\) | −3.47557 | − | 5.79470i | −0.114836 | − | 0.191462i | ||||
\(917\) | 36.2092i | 1.19573i | ||||||||
\(918\) | −7.38284 | + | 2.04430i | −0.243670 | + | 0.0674720i | ||||
\(919\) | 15.0013 | 0.494846 | 0.247423 | − | 0.968908i | \(-0.420416\pi\) | ||||
0.247423 | + | 0.968908i | \(0.420416\pi\) | |||||||
\(920\) | 14.1394 | + | 32.8625i | 0.466161 | + | 1.08344i | ||||
\(921\) | 6.72809 | 0.221698 | ||||||||
\(922\) | 21.8724 | − | 6.05644i | 0.720329 | − | 0.199458i | ||||
\(923\) | − | 6.30402i | − | 0.207499i | ||||||
\(924\) | 1.71843 | + | 2.86507i | 0.0565321 | + | 0.0942539i | ||||
\(925\) | 16.1673i | 0.531577i | ||||||||
\(926\) | 0.702335 | + | 2.53643i | 0.0230802 | + | 0.0833523i | ||||
\(927\) | 4.33560 | 0.142400 | ||||||||
\(928\) | 6.60127 | − | 29.5003i | 0.216697 | − | 0.968394i | ||||
\(929\) | −15.7205 | −0.515772 | −0.257886 | − | 0.966175i | \(-0.583026\pi\) | ||||
−0.257886 | + | 0.966175i | \(0.583026\pi\) | |||||||
\(930\) | −0.595419 | − | 2.15031i | −0.0195246 | − | 0.0705116i | ||||
\(931\) | 6.26087 | 0.205192 | ||||||||
\(932\) | −23.3578 | + | 14.0097i | −0.765112 | + | 0.458902i | ||||
\(933\) | −2.75954 | −0.0903433 | ||||||||
\(934\) | −34.4891 | + | 9.54999i | −1.12852 | + | 0.312485i | ||||
\(935\) | 6.34214 | 0.207410 | ||||||||
\(936\) | −7.59820 | + | 7.98783i | −0.248355 | + | 0.261090i | ||||
\(937\) | − | 1.61758i | − | 0.0528441i | −0.999651 | − | 0.0264220i | \(-0.991589\pi\) | ||
0.999651 | − | 0.0264220i | \(-0.00841137\pi\) | |||||||
\(938\) | 78.2244 | − | 21.6602i | 2.55412 | − | 0.707232i | ||||
\(939\) | 1.14544 | 0.0373799 | ||||||||
\(940\) | −17.5993 | + | 10.5558i | −0.574025 | + | 0.344291i | ||||
\(941\) | 46.9526i | 1.53061i | 0.643667 | + | 0.765305i | \(0.277412\pi\) | ||||
−0.643667 | + | 0.765305i | \(0.722588\pi\) | |||||||
\(942\) | 22.1809 | − | 6.14187i | 0.722694 | − | 0.200113i | ||||
\(943\) | 13.2297 | + | 5.65707i | 0.430817 | + | 0.184220i | ||||
\(944\) | 43.0012 | + | 22.9515i | 1.39957 | + | 0.747006i | ||||
\(945\) | 9.92416 | 0.322833 | ||||||||
\(946\) | 0.354594 | − | 0.0981866i | 0.0115288 | − | 0.00319232i | ||||
\(947\) | 7.94250i | 0.258097i | 0.991638 | + | 0.129048i | \(0.0411922\pi\) | ||||
−0.991638 | + | 0.129048i | \(0.958808\pi\) | |||||||
\(948\) | −11.2170 | − | 18.7016i | −0.364310 | − | 0.607401i | ||||
\(949\) | −58.4457 | −1.89723 | ||||||||
\(950\) | 2.33108 | − | 0.645473i | 0.0756302 | − | 0.0209419i | ||||
\(951\) | 25.3550i | 0.822191i | ||||||||
\(952\) | 41.7724 | + | 39.7348i | 1.35385 | + | 1.28781i | ||||
\(953\) | − | 50.7392i | − | 1.64361i | −0.569772 | − | 0.821803i | \(-0.692969\pi\) | ||
0.569772 | − | 0.821803i | \(-0.307031\pi\) | |||||||
\(954\) | 1.21147 | + | 4.37514i | 0.0392228 | + | 0.141650i | ||||
\(955\) | 47.6714i | 1.54261i | ||||||||
\(956\) | 25.1287 | + | 41.8963i | 0.812721 | + | 1.35502i | ||||
\(957\) | − | 2.37232i | − | 0.0766862i | ||||||
\(958\) | 4.51290 | − | 1.24962i | 0.145805 | − | 0.0403732i | ||||
\(959\) | 2.06102i | 0.0665537i | ||||||||
\(960\) | 1.05424 | + | 21.0727i | 0.0340256 | + | 0.680118i | ||||
\(961\) | 30.6421 | 0.988456 | ||||||||
\(962\) | −12.1597 | − | 43.9139i | −0.392045 | − | 1.41584i | ||||
\(963\) | −18.8035 | −0.605934 | ||||||||
\(964\) | 19.1301 | + | 31.8949i | 0.616138 | + | 1.02726i | ||||
\(965\) | 0.185841i | 0.00598242i | ||||||||
\(966\) | −3.40821 | + | 25.2925i | −0.109657 | + | 0.813774i | ||||
\(967\) | 4.98236i | 0.160222i | 0.996786 | + | 0.0801110i | \(0.0255275\pi\) | ||||
−0.996786 | + | 0.0801110i | \(0.974473\pi\) | |||||||
\(968\) | 21.0592 | − | 22.1391i | 0.676867 | − | 0.711576i | ||||
\(969\) | −4.73713 | −0.152179 | ||||||||
\(970\) | −4.64936 | + | 1.28740i | −0.149282 | + | 0.0413360i | ||||
\(971\) | −25.0545 | −0.804038 | −0.402019 | − | 0.915631i | \(-0.631691\pi\) | ||||
−0.402019 | + | 0.915631i | \(0.631691\pi\) | |||||||
\(972\) | −1.02872 | − | 1.71515i | −0.0329962 | − | 0.0550134i | ||||
\(973\) | 52.8332i | 1.69376i | ||||||||
\(974\) | −8.53884 | − | 30.8374i | −0.273602 | − | 0.988094i | ||||
\(975\) | − | 7.62308i | − | 0.244134i | ||||||
\(976\) | 43.2200 | + | 23.0683i | 1.38344 | + | 0.738397i | ||||
\(977\) | 31.9225i | 1.02129i | 0.859791 | + | 0.510645i | \(0.170594\pi\) | ||||
−0.859791 | + | 0.510645i | \(0.829406\pi\) | |||||||
\(978\) | −32.7619 | + | 9.07172i | −1.04761 | + | 0.290081i | ||||
\(979\) | − | 5.87366i | − | 0.187723i | ||||||
\(980\) | −19.4241 | − | 32.3851i | −0.620479 | − | 1.03450i | ||||
\(981\) | 1.41395i | 0.0451439i | ||||||||
\(982\) | 9.50186 | + | 34.3153i | 0.303216 | + | 1.09504i | ||||
\(983\) | −26.8959 | −0.857847 | −0.428924 | − | 0.903341i | \(-0.641107\pi\) | ||||
−0.428924 | + | 0.903341i | \(0.641107\pi\) | |||||||
\(984\) | 6.14846 | + | 5.84855i | 0.196006 | + | 0.186445i | ||||
\(985\) | 43.1903i | 1.37616i | ||||||||
\(986\) | −10.9246 | − | 39.4534i | −0.347910 | − | 1.25645i | ||||
\(987\) | −14.6400 | −0.465996 | ||||||||
\(988\) | −5.84626 | + | 3.50649i | −0.185994 | + | 0.111556i | ||||
\(989\) | 2.58431 | + | 1.10507i | 0.0821764 | + | 0.0351391i | ||||
\(990\) | 0.441855 | + | 1.59573i | 0.0140431 | + | 0.0507155i | ||||
\(991\) | 57.1447i | 1.81526i | 0.419769 | + | 0.907631i | \(0.362111\pi\) | ||||
−0.419769 | + | 0.907631i | \(0.637889\pi\) | |||||||
\(992\) | 3.30234 | + | 0.738964i | 0.104849 | + | 0.0234621i | ||||
\(993\) | −22.6100 | −0.717508 | ||||||||
\(994\) | −2.29679 | − | 8.29469i | −0.0728498 | − | 0.263092i | ||||
\(995\) | 0.576093i | 0.0182634i | ||||||||
\(996\) | −12.0189 | − | 20.0386i | −0.380832 | − | 0.634948i | ||||
\(997\) | 12.7009 | 0.402242 | 0.201121 | − | 0.979566i | \(-0.435542\pi\) | ||||
0.201121 | + | 0.979566i | \(0.435542\pi\) | |||||||
\(998\) | −12.6145 | − | 45.5564i | −0.399305 | − | 1.44206i | ||||
\(999\) | 8.26643 | 0.261538 |
(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 | 276.2.e.a.91.3 | yes | 24 | |
3.2 | odd | 2 | 828.2.e.f.91.22 | 24 | |||
4.3 | odd | 2 | inner | 276.2.e.a.91.1 | ✓ | 24 | |
8.3 | odd | 2 | 4416.2.i.d.1471.6 | 24 | |||
8.5 | even | 2 | 4416.2.i.d.1471.7 | 24 | |||
12.11 | even | 2 | 828.2.e.f.91.24 | 24 | |||
23.22 | odd | 2 | inner | 276.2.e.a.91.4 | yes | 24 | |
69.68 | even | 2 | 828.2.e.f.91.21 | 24 | |||
92.91 | even | 2 | inner | 276.2.e.a.91.2 | yes | 24 | |
184.45 | odd | 2 | 4416.2.i.d.1471.8 | 24 | |||
184.91 | even | 2 | 4416.2.i.d.1471.5 | 24 | |||
276.275 | odd | 2 | 828.2.e.f.91.23 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.e.a.91.1 | ✓ | 24 | 4.3 | odd | 2 | inner | |
276.2.e.a.91.2 | yes | 24 | 92.91 | even | 2 | inner | |
276.2.e.a.91.3 | yes | 24 | 1.1 | even | 1 | trivial | |
276.2.e.a.91.4 | yes | 24 | 23.22 | odd | 2 | inner | |
828.2.e.f.91.21 | 24 | 69.68 | even | 2 | |||
828.2.e.f.91.22 | 24 | 3.2 | odd | 2 | |||
828.2.e.f.91.23 | 24 | 276.275 | odd | 2 | |||
828.2.e.f.91.24 | 24 | 12.11 | even | 2 | |||
4416.2.i.d.1471.5 | 24 | 184.91 | even | 2 | |||
4416.2.i.d.1471.6 | 24 | 8.3 | odd | 2 | |||
4416.2.i.d.1471.7 | 24 | 8.5 | even | 2 | |||
4416.2.i.d.1471.8 | 24 | 184.45 | odd | 2 |