Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.100088711424.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 263.4 | ||
Root | \(1.87694 + 1.08365i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.263 |
Dual form | 637.2.g.i.373.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.651388 | − | 1.12824i | 0.460601 | − | 0.797784i | −0.538390 | − | 0.842696i | \(-0.680967\pi\) |
0.998991 | + | 0.0449118i | \(0.0143007\pi\) | |||||||
\(3\) | 2.88145 | 1.66361 | 0.831804 | − | 0.555069i | \(-0.187308\pi\) | ||||
0.831804 | + | 0.555069i | \(0.187308\pi\) | |||||||
\(4\) | 0.151388 | + | 0.262211i | 0.0756939 | + | 0.131106i | ||||
\(5\) | −1.44073 | − | 2.49541i | −0.644313 | − | 1.11598i | −0.984460 | − | 0.175610i | \(-0.943810\pi\) |
0.340147 | − | 0.940372i | \(-0.389523\pi\) | |||||||
\(6\) | 1.87694 | − | 3.25096i | 0.766259 | − | 1.32720i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | 5.30278 | 1.76759 | ||||||||
\(10\) | −3.75389 | −1.18708 | ||||||||
\(11\) | −5.90833 | −1.78143 | −0.890714 | − | 0.454565i | \(-0.849795\pi\) | ||||
−0.890714 | + | 0.454565i | \(0.849795\pi\) | |||||||
\(12\) | 0.436217 | + | 0.755550i | 0.125925 | + | 0.218108i | ||||
\(13\) | 3.31767 | − | 1.41176i | 0.920156 | − | 0.391551i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.15139 | − | 7.19041i | −1.07188 | − | 1.85656i | ||||
\(16\) | 1.65139 | − | 2.86029i | 0.412847 | − | 0.715072i | ||||
\(17\) | 0.436217 | + | 0.755550i | 0.105798 | + | 0.183248i | 0.914064 | − | 0.405570i | \(-0.132927\pi\) |
−0.808266 | + | 0.588818i | \(0.799594\pi\) | |||||||
\(18\) | 3.45416 | − | 5.98279i | 0.814154 | − | 1.41016i | ||||
\(19\) | 2.88145 | 0.661051 | 0.330525 | − | 0.943797i | \(-0.392774\pi\) | ||||
0.330525 | + | 0.943797i | \(0.392774\pi\) | |||||||
\(20\) | 0.436217 | − | 0.755550i | 0.0975411 | − | 0.168946i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.84861 | + | 6.66599i | −0.820527 | + | 1.42119i | ||||
\(23\) | −3.30278 | + | 5.72058i | −0.688676 | + | 1.19282i | 0.283590 | + | 0.958946i | \(0.408475\pi\) |
−0.972266 | + | 0.233877i | \(0.924859\pi\) | |||||||
\(24\) | 8.64436 | 1.76452 | ||||||||
\(25\) | −1.65139 | + | 2.86029i | −0.330278 | + | 0.572058i | ||||
\(26\) | 0.568293 | − | 4.66272i | 0.111451 | − | 0.914435i | ||||
\(27\) | 6.63534 | 1.27697 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.651388 | − | 1.12824i | −0.120960 | − | 0.209508i | 0.799187 | − | 0.601083i | \(-0.205264\pi\) |
−0.920146 | + | 0.391575i | \(0.871931\pi\) | |||||||
\(30\) | −10.8167 | −1.97484 | ||||||||
\(31\) | −0.436217 | + | 0.755550i | −0.0783469 | + | 0.135701i | −0.902537 | − | 0.430613i | \(-0.858298\pi\) |
0.824190 | + | 0.566313i | \(0.191631\pi\) | |||||||
\(32\) | 0.848612 | + | 1.46984i | 0.150015 | + | 0.259833i | ||||
\(33\) | −17.0246 | −2.96360 | ||||||||
\(34\) | 1.13659 | 0.194923 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.802776 | + | 1.39045i | 0.133796 | + | 0.231741i | ||||
\(37\) | −0.697224 | + | 1.20763i | −0.114623 | + | 0.198533i | −0.917629 | − | 0.397438i | \(-0.869899\pi\) |
0.803006 | + | 0.595971i | \(0.203233\pi\) | |||||||
\(38\) | 1.87694 | − | 3.25096i | 0.304481 | − | 0.527376i | ||||
\(39\) | 9.55971 | − | 4.06792i | 1.53078 | − | 0.651388i | ||||
\(40\) | −4.32218 | − | 7.48624i | −0.683397 | − | 1.18368i | ||||
\(41\) | −3.75389 | − | 6.50192i | −0.586259 | − | 1.01543i | −0.994717 | − | 0.102653i | \(-0.967267\pi\) |
0.408458 | − | 0.912777i | \(-0.366066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.75694 | + | 4.77516i | −0.420429 | + | 0.728205i | −0.995981 | − | 0.0895602i | \(-0.971454\pi\) |
0.575552 | + | 0.817765i | \(0.304787\pi\) | |||||||
\(44\) | −0.894449 | − | 1.54923i | −0.134843 | − | 0.233555i | ||||
\(45\) | −7.63985 | − | 13.2326i | −1.13888 | − | 1.97260i | ||||
\(46\) | 4.30278 | + | 7.45263i | 0.634410 | + | 1.09883i | ||||
\(47\) | 6.19912 | + | 10.7372i | 0.904235 | + | 1.56618i | 0.821941 | + | 0.569573i | \(0.192892\pi\) |
0.0822947 | + | 0.996608i | \(0.473775\pi\) | |||||||
\(48\) | 4.75840 | − | 8.24179i | 0.686816 | − | 1.18960i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.15139 | + | 3.72631i | 0.304252 | + | 0.526980i | ||||
\(51\) | 1.25694 | + | 2.17708i | 0.176007 | + | 0.304853i | ||||
\(52\) | 0.872434 | + | 0.656208i | 0.120985 | + | 0.0909997i | ||||
\(53\) | −4.80278 | + | 8.31865i | −0.659712 | + | 1.14265i | 0.320978 | + | 0.947087i | \(0.395988\pi\) |
−0.980690 | + | 0.195568i | \(0.937345\pi\) | |||||||
\(54\) | 4.32218 | − | 7.48624i | 0.588174 | − | 1.01875i | ||||
\(55\) | 8.51229 | + | 14.7437i | 1.14780 | + | 1.98804i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.30278 | 1.09973 | ||||||||
\(58\) | −1.69722 | −0.222856 | ||||||||
\(59\) | −3.31767 | − | 5.74637i | −0.431924 | − | 0.748114i | 0.565115 | − | 0.825012i | \(-0.308832\pi\) |
−0.997039 | + | 0.0768979i | \(0.975498\pi\) | |||||||
\(60\) | 1.25694 | − | 2.17708i | 0.162270 | − | 0.281060i | ||||
\(61\) | 5.76291 | 0.737865 | 0.368932 | − | 0.929456i | \(-0.379723\pi\) | ||||
0.368932 | + | 0.929456i | \(0.379723\pi\) | |||||||
\(62\) | 0.568293 | + | 0.984312i | 0.0721733 | + | 0.125008i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.81665 | 1.10208 | ||||||||
\(65\) | −8.30278 | − | 6.24500i | −1.02983 | − | 0.774597i | ||||
\(66\) | −11.0896 | + | 19.2077i | −1.36504 | + | 2.36431i | ||||
\(67\) | 1.00000 | 0.122169 | 0.0610847 | − | 0.998133i | \(-0.480544\pi\) | ||||
0.0610847 | + | 0.998133i | \(0.480544\pi\) | |||||||
\(68\) | −0.132076 | + | 0.228762i | −0.0160166 | + | 0.0277415i | ||||
\(69\) | −9.51680 | + | 16.4836i | −1.14569 | + | 1.98439i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | + | 3.46410i | −0.237356 | + | 0.411113i | −0.959955 | − | 0.280155i | \(-0.909614\pi\) |
0.722599 | + | 0.691268i | \(0.242948\pi\) | |||||||
\(72\) | 15.9083 | 1.87481 | ||||||||
\(73\) | 2.88145 | − | 4.99082i | 0.337249 | − | 0.584132i | −0.646666 | − | 0.762774i | \(-0.723837\pi\) |
0.983914 | + | 0.178642i | \(0.0571704\pi\) | |||||||
\(74\) | 0.908327 | + | 1.57327i | 0.105591 | + | 0.182889i | ||||
\(75\) | −4.75840 | + | 8.24179i | −0.549452 | + | 0.951680i | ||||
\(76\) | 0.436217 | + | 0.755550i | 0.0500375 | + | 0.0866675i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.63751 | − | 13.4354i | 0.185411 | − | 1.52126i | ||||
\(79\) | −0.302776 | − | 0.524423i | −0.0340649 | − | 0.0590022i | 0.848490 | − | 0.529211i | \(-0.177512\pi\) |
−0.882555 | + | 0.470209i | \(0.844179\pi\) | |||||||
\(80\) | −9.51680 | −1.06401 | ||||||||
\(81\) | 3.21110 | 0.356789 | ||||||||
\(82\) | −9.78095 | −1.08012 | ||||||||
\(83\) | −6.63534 | −0.728323 | −0.364162 | − | 0.931336i | \(-0.618644\pi\) | ||||
−0.364162 | + | 0.931336i | \(0.618644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.25694 | − | 2.17708i | 0.136334 | − | 0.236138i | ||||
\(86\) | 3.59167 | + | 6.22096i | 0.387300 | + | 0.670823i | ||||
\(87\) | −1.87694 | − | 3.25096i | −0.201230 | − | 0.348540i | ||||
\(88\) | −17.7250 | −1.88949 | ||||||||
\(89\) | −4.32218 | + | 7.48624i | −0.458150 | + | 0.793539i | −0.998863 | − | 0.0476677i | \(-0.984821\pi\) |
0.540713 | + | 0.841207i | \(0.318154\pi\) | |||||||
\(90\) | −19.9060 | −2.09828 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | −1.25694 | + | 2.17708i | −0.130339 | + | 0.225753i | ||||
\(94\) | 16.1521 | 1.66597 | ||||||||
\(95\) | −4.15139 | − | 7.19041i | −0.425923 | − | 0.737721i | ||||
\(96\) | 2.44524 | + | 4.23527i | 0.249566 | + | 0.432261i | ||||
\(97\) | 3.88596 | − | 6.73069i | 0.394560 | − | 0.683398i | −0.598485 | − | 0.801134i | \(-0.704230\pi\) |
0.993045 | + | 0.117736i | \(0.0375638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −31.3305 | −3.14884 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −8.64436 | −0.860146 | −0.430073 | − | 0.902794i | \(-0.641512\pi\) | ||||
−0.430073 | + | 0.902794i | \(0.641512\pi\) | |||||||
\(102\) | 3.27502 | 0.324275 | ||||||||
\(103\) | −2.44524 | − | 4.23527i | −0.240936 | − | 0.417314i | 0.720045 | − | 0.693927i | \(-0.244121\pi\) |
−0.960981 | + | 0.276613i | \(0.910788\pi\) | |||||||
\(104\) | 9.95301 | − | 4.23527i | 0.975973 | − | 0.415303i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.25694 | + | 10.8373i | 0.607728 | + | 1.05262i | ||||
\(107\) | −4.65139 | + | 8.05644i | −0.449667 | + | 0.778845i | −0.998364 | − | 0.0571755i | \(-0.981791\pi\) |
0.548698 | + | 0.836021i | \(0.315124\pi\) | |||||||
\(108\) | 1.00451 | + | 1.73986i | 0.0966590 | + | 0.167418i | ||||
\(109\) | 3.10555 | − | 5.37897i | 0.297458 | − | 0.515212i | −0.678096 | − | 0.734974i | \(-0.737195\pi\) |
0.975554 | + | 0.219761i | \(0.0705279\pi\) | |||||||
\(110\) | 22.1792 | 2.11470 | ||||||||
\(111\) | −2.00902 | + | 3.47972i | −0.190688 | + | 0.330281i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.40833 | − | 12.8316i | 0.696917 | − | 1.20710i | −0.272613 | − | 0.962124i | \(-0.587888\pi\) |
0.969530 | − | 0.244972i | \(-0.0787786\pi\) | |||||||
\(114\) | 5.40833 | − | 9.36750i | 0.506536 | − | 0.877346i | ||||
\(115\) | 19.0336 | 1.77489 | ||||||||
\(116\) | 0.197224 | − | 0.341603i | 0.0183118 | − | 0.0317170i | ||||
\(117\) | 17.5929 | − | 7.48624i | 1.62646 | − | 0.692103i | ||||
\(118\) | −8.64436 | −0.795778 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.4542 | − | 21.5712i | −1.13690 | − | 1.96918i | ||||
\(121\) | 23.9083 | 2.17348 | ||||||||
\(122\) | 3.75389 | − | 6.50192i | 0.339861 | − | 0.588657i | ||||
\(123\) | −10.8167 | − | 18.7350i | −0.975305 | − | 1.68928i | ||||
\(124\) | −0.264152 | −0.0237215 | ||||||||
\(125\) | −4.89047 | −0.437417 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.45416 | + | 2.51868i | 0.129036 | + | 0.223497i | 0.923303 | − | 0.384071i | \(-0.125478\pi\) |
−0.794267 | + | 0.607569i | \(0.792145\pi\) | |||||||
\(128\) | 4.04584 | − | 7.00759i | 0.357605 | − | 0.619390i | ||||
\(129\) | −7.94399 | + | 13.7594i | −0.699430 | + | 1.21145i | ||||
\(130\) | −12.4542 | + | 5.29958i | −1.09230 | + | 0.464804i | ||||
\(131\) | −8.51229 | − | 14.7437i | −0.743722 | − | 1.28816i | −0.950790 | − | 0.309837i | \(-0.899725\pi\) |
0.207068 | − | 0.978327i | \(-0.433608\pi\) | |||||||
\(132\) | −2.57731 | − | 4.46404i | −0.224326 | − | 0.388544i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.651388 | − | 1.12824i | 0.0562713 | − | 0.0974648i | ||||
\(135\) | −9.55971 | − | 16.5579i | −0.822769 | − | 1.42508i | ||||
\(136\) | 1.30865 | + | 2.26665i | 0.112216 | + | 0.194364i | ||||
\(137\) | −1.34861 | − | 2.33586i | −0.115220 | − | 0.199566i | 0.802648 | − | 0.596453i | \(-0.203424\pi\) |
−0.917868 | + | 0.396887i | \(0.870091\pi\) | |||||||
\(138\) | 12.3982 | + | 21.4744i | 1.05541 | + | 1.82802i | ||||
\(139\) | −8.51229 | + | 14.7437i | −0.722003 | + | 1.25055i | 0.238193 | + | 0.971218i | \(0.423445\pi\) |
−0.960196 | + | 0.279327i | \(0.909889\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.8625 | + | 30.9387i | 1.50429 | + | 2.60551i | ||||
\(142\) | 2.60555 | + | 4.51295i | 0.218653 | + | 0.378718i | ||||
\(143\) | −19.6019 | + | 8.34113i | −1.63919 | + | 0.697520i | ||||
\(144\) | 8.75694 | − | 15.1675i | 0.729745 | − | 1.26396i | ||||
\(145\) | −1.87694 | + | 3.25096i | −0.155872 | + | 0.269978i | ||||
\(146\) | −3.75389 | − | 6.50192i | −0.310674 | − | 0.538103i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.422205 | −0.0347050 | ||||||||
\(149\) | 0.513878 | 0.0420985 | 0.0210493 | − | 0.999778i | \(-0.493299\pi\) | ||||
0.0210493 | + | 0.999778i | \(0.493299\pi\) | |||||||
\(150\) | 6.19912 | + | 10.7372i | 0.506156 | + | 0.876689i | ||||
\(151\) | 3.10555 | − | 5.37897i | 0.252726 | − | 0.437735i | −0.711549 | − | 0.702636i | \(-0.752006\pi\) |
0.964275 | + | 0.264902i | \(0.0853395\pi\) | |||||||
\(152\) | 8.64436 | 0.701150 | ||||||||
\(153\) | 2.31316 | + | 4.00651i | 0.187008 | + | 0.323907i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.51388 | 0.201920 | ||||||||
\(156\) | 2.51388 | + | 1.89083i | 0.201271 | + | 0.151388i | ||||
\(157\) | −4.75840 | + | 8.24179i | −0.379761 | + | 0.657766i | −0.991027 | − | 0.133659i | \(-0.957327\pi\) |
0.611266 | + | 0.791425i | \(0.290661\pi\) | |||||||
\(158\) | −0.788897 | −0.0627613 | ||||||||
\(159\) | −13.8390 | + | 23.9698i | −1.09750 | + | 1.90093i | ||||
\(160\) | 2.44524 | − | 4.23527i | 0.193313 | − | 0.334828i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.09167 | − | 3.62288i | 0.164337 | − | 0.284641i | ||||
\(163\) | −17.2111 | −1.34808 | −0.674039 | − | 0.738696i | \(-0.735442\pi\) | ||||
−0.674039 | + | 0.738696i | \(0.735442\pi\) | |||||||
\(164\) | 1.13659 | − | 1.96862i | 0.0887524 | − | 0.153724i | ||||
\(165\) | 24.5278 | + | 42.4833i | 1.90948 | + | 3.30732i | ||||
\(166\) | −4.32218 | + | 7.48624i | −0.335466 | + | 0.581045i | ||||
\(167\) | −2.44524 | − | 4.23527i | −0.189218 | − | 0.327735i | 0.755772 | − | 0.654835i | \(-0.227262\pi\) |
−0.944990 | + | 0.327100i | \(0.893929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.01388 | − | 9.36750i | 0.693375 | − | 0.720577i | ||||
\(170\) | −1.63751 | − | 2.83625i | −0.125591 | − | 0.217530i | ||||
\(171\) | 15.2797 | 1.16847 | ||||||||
\(172\) | −1.66947 | −0.127296 | ||||||||
\(173\) | 23.9241 | 1.81891 | 0.909456 | − | 0.415799i | \(-0.136498\pi\) | ||||
0.909456 | + | 0.415799i | \(0.136498\pi\) | |||||||
\(174\) | −4.89047 | −0.370746 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.75694 | + | 16.8995i | −0.735457 | + | 1.27385i | ||||
\(177\) | −9.55971 | − | 16.5579i | −0.718552 | − | 1.24457i | ||||
\(178\) | 5.63083 | + | 9.75289i | 0.422049 | + | 0.731010i | ||||
\(179\) | 14.3944 | 1.07589 | 0.537946 | − | 0.842979i | \(-0.319200\pi\) | ||||
0.537946 | + | 0.842979i | \(0.319200\pi\) | |||||||
\(180\) | 2.31316 | − | 4.00651i | 0.172413 | − | 0.298628i | ||||
\(181\) | 9.25264 | 0.687744 | 0.343872 | − | 0.939017i | \(-0.388261\pi\) | ||||
0.343872 | + | 0.939017i | \(0.388261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.6056 | 1.22752 | ||||||||
\(184\) | −9.90833 | + | 17.1617i | −0.730452 | + | 1.26518i | ||||
\(185\) | 4.01804 | 0.295412 | ||||||||
\(186\) | 1.63751 | + | 2.83625i | 0.120068 | + | 0.207964i | ||||
\(187\) | −2.57731 | − | 4.46404i | −0.188472 | − | 0.326443i | ||||
\(188\) | −1.87694 | + | 3.25096i | −0.136890 | + | 0.237101i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.8167 | −0.784723 | ||||||||
\(191\) | 19.3028 | 1.39670 | 0.698350 | − | 0.715757i | \(-0.253918\pi\) | ||||
0.698350 | + | 0.715757i | \(0.253918\pi\) | |||||||
\(192\) | 25.4048 | 1.83343 | ||||||||
\(193\) | −1.81665 | −0.130766 | −0.0653828 | − | 0.997860i | \(-0.520827\pi\) | ||||
−0.0653828 | + | 0.997860i | \(0.520827\pi\) | |||||||
\(194\) | −5.06254 | − | 8.76857i | −0.363469 | − | 0.629547i | ||||
\(195\) | −23.9241 | − | 17.9947i | −1.71324 | − | 1.28863i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.95416 | + | 10.3129i | 0.424217 | + | 0.734765i | 0.996347 | − | 0.0853980i | \(-0.0272162\pi\) |
−0.572130 | + | 0.820163i | \(0.693883\pi\) | |||||||
\(198\) | −20.4083 | + | 35.3483i | −1.45036 | + | 2.51209i | ||||
\(199\) | −0.436217 | − | 0.755550i | −0.0309226 | − | 0.0535595i | 0.850150 | − | 0.526541i | \(-0.176511\pi\) |
−0.881073 | + | 0.472981i | \(0.843178\pi\) | |||||||
\(200\) | −4.95416 | + | 8.58086i | −0.350312 | + | 0.606759i | ||||
\(201\) | 2.88145 | 0.203242 | ||||||||
\(202\) | −5.63083 | + | 9.75289i | −0.396184 | + | 0.686211i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.380571 | + | 0.659168i | −0.0266453 | + | 0.0461510i | ||||
\(205\) | −10.8167 | + | 18.7350i | −0.755468 | + | 1.30851i | ||||
\(206\) | −6.37119 | −0.443902 | ||||||||
\(207\) | −17.5139 | + | 30.3349i | −1.21730 | + | 2.10842i | ||||
\(208\) | 1.44073 | − | 11.8209i | 0.0998964 | − | 0.819629i | ||||
\(209\) | −17.0246 | −1.17761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50000 | − | 12.9904i | −0.516321 | − | 0.894295i | −0.999820 | − | 0.0189499i | \(-0.993968\pi\) |
0.483499 | − | 0.875345i | \(-0.339366\pi\) | |||||||
\(212\) | −2.90833 | −0.199745 | ||||||||
\(213\) | −5.76291 | + | 9.98165i | −0.394868 | + | 0.683931i | ||||
\(214\) | 6.05971 | + | 10.4957i | 0.414234 | + | 0.717474i | ||||
\(215\) | 15.8880 | 1.08355 | ||||||||
\(216\) | 19.9060 | 1.35443 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.04584 | − | 7.00759i | −0.274019 | − | 0.474614i | ||||
\(219\) | 8.30278 | − | 14.3808i | 0.561050 | − | 0.971766i | ||||
\(220\) | −2.57731 | + | 4.46404i | −0.173762 | + | 0.300965i | ||||
\(221\) | 2.51388 | + | 1.89083i | 0.169102 | + | 0.127191i | ||||
\(222\) | 2.61730 | + | 4.53330i | 0.175662 | + | 0.304255i | ||||
\(223\) | 6.76742 | + | 11.7215i | 0.453180 | + | 0.784930i | 0.998582 | − | 0.0532444i | \(-0.0169562\pi\) |
−0.545402 | + | 0.838175i | \(0.683623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.75694 | + | 15.1675i | −0.583796 | + | 1.01116i | ||||
\(226\) | −9.65139 | − | 16.7167i | −0.642001 | − | 1.11198i | ||||
\(227\) | −13.7069 | − | 23.7410i | −0.909759 | − | 1.57575i | −0.814399 | − | 0.580306i | \(-0.802933\pi\) |
−0.0953602 | − | 0.995443i | \(-0.530400\pi\) | |||||||
\(228\) | 1.25694 | + | 2.17708i | 0.0832428 | + | 0.144181i | ||||
\(229\) | −10.3892 | − | 17.9947i | −0.686540 | − | 1.18912i | −0.972950 | − | 0.231015i | \(-0.925796\pi\) |
0.286411 | − | 0.958107i | \(-0.407538\pi\) | |||||||
\(230\) | 12.3982 | − | 21.4744i | 0.817516 | − | 1.41598i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.95416 | − | 3.38471i | −0.128297 | − | 0.222217i | ||||
\(233\) | 11.9542 | + | 20.7052i | 0.783143 | + | 1.35644i | 0.930102 | + | 0.367301i | \(0.119718\pi\) |
−0.146959 | + | 0.989143i | \(0.546948\pi\) | |||||||
\(234\) | 3.01353 | − | 24.7254i | 0.197001 | − | 1.61635i | ||||
\(235\) | 17.8625 | − | 30.9387i | 1.16522 | − | 2.01822i | ||||
\(236\) | 1.00451 | − | 1.73986i | 0.0653880 | − | 0.113255i | ||||
\(237\) | −0.872434 | − | 1.51110i | −0.0566707 | − | 0.0981565i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6056 | 0.750701 | 0.375350 | − | 0.926883i | \(-0.377522\pi\) | ||||
0.375350 | + | 0.926883i | \(0.377522\pi\) | |||||||
\(240\) | −27.4222 | −1.77010 | ||||||||
\(241\) | 1.00451 | + | 1.73986i | 0.0647062 | + | 0.112074i | 0.896564 | − | 0.442915i | \(-0.146056\pi\) |
−0.831857 | + | 0.554989i | \(0.812722\pi\) | |||||||
\(242\) | 15.5736 | − | 26.9743i | 1.00111 | − | 1.73397i | ||||
\(243\) | −10.6534 | −0.683415 | ||||||||
\(244\) | 0.872434 | + | 1.51110i | 0.0558519 | + | 0.0967383i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −28.1833 | −1.79690 | ||||||||
\(247\) | 9.55971 | − | 4.06792i | 0.608270 | − | 0.258835i | ||||
\(248\) | −1.30865 | + | 2.26665i | −0.0830994 | + | 0.143932i | ||||
\(249\) | −19.1194 | −1.21164 | ||||||||
\(250\) | −3.18559 | + | 5.51761i | −0.201475 | + | 0.348964i | ||||
\(251\) | 11.2617 | − | 19.5058i | 0.710830 | − | 1.23119i | −0.253716 | − | 0.967279i | \(-0.581653\pi\) |
0.964546 | − | 0.263915i | \(-0.0850138\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.5139 | − | 33.7990i | 1.22683 | − | 2.12493i | ||||
\(254\) | 3.78890 | 0.237737 | ||||||||
\(255\) | 3.62181 | − | 6.27316i | 0.226807 | − | 0.392841i | ||||
\(256\) | 3.54584 | + | 6.14157i | 0.221615 | + | 0.383848i | ||||
\(257\) | 11.3937 | − | 19.7345i | 0.710722 | − | 1.23101i | −0.253865 | − | 0.967240i | \(-0.581702\pi\) |
0.964587 | − | 0.263767i | \(-0.0849649\pi\) | |||||||
\(258\) | 10.3492 | + | 17.9254i | 0.644316 | + | 1.11599i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.380571 | − | 3.12250i | 0.0236020 | − | 0.193649i | ||||
\(261\) | −3.45416 | − | 5.98279i | −0.213807 | − | 0.370325i | ||||
\(262\) | −22.1792 | −1.37024 | ||||||||
\(263\) | −13.4222 | −0.827649 | −0.413824 | − | 0.910357i | \(-0.635807\pi\) | ||||
−0.413824 | + | 0.910357i | \(0.635807\pi\) | |||||||
\(264\) | −51.0737 | −3.14337 | ||||||||
\(265\) | 27.6780 | 1.70024 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.4542 | + | 21.5712i | −0.762182 | + | 1.32014i | ||||
\(268\) | 0.151388 | + | 0.262211i | 0.00924748 | + | 0.0160171i | ||||
\(269\) | −4.75840 | − | 8.24179i | −0.290125 | − | 0.502511i | 0.683714 | − | 0.729750i | \(-0.260363\pi\) |
−0.973839 | + | 0.227239i | \(0.927030\pi\) | |||||||
\(270\) | −24.9083 | −1.51587 | ||||||||
\(271\) | −14.8435 | + | 25.7097i | −0.901678 | + | 1.56175i | −0.0763615 | + | 0.997080i | \(0.524330\pi\) |
−0.825316 | + | 0.564671i | \(0.809003\pi\) | |||||||
\(272\) | 2.88145 | 0.174714 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.51388 | −0.212281 | ||||||||
\(275\) | 9.75694 | − | 16.8995i | 0.588366 | − | 1.01908i | ||||
\(276\) | −5.76291 | −0.346886 | ||||||||
\(277\) | −7.10555 | − | 12.3072i | −0.426931 | − | 0.739467i | 0.569667 | − | 0.821875i | \(-0.307072\pi\) |
−0.996599 | + | 0.0824088i | \(0.973739\pi\) | |||||||
\(278\) | 11.0896 | + | 19.2077i | 0.665110 | + | 1.15200i | ||||
\(279\) | −2.31316 | + | 4.00651i | −0.138485 | + | 0.239864i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.18335 | 0.130248 | 0.0651238 | − | 0.997877i | \(-0.479256\pi\) | ||||
0.0651238 | + | 0.997877i | \(0.479256\pi\) | |||||||
\(282\) | 46.5416 | 2.77151 | ||||||||
\(283\) | 4.01804 | 0.238848 | 0.119424 | − | 0.992843i | \(-0.461895\pi\) | ||||
0.119424 | + | 0.992843i | \(0.461895\pi\) | |||||||
\(284\) | −1.21110 | −0.0718657 | ||||||||
\(285\) | −11.9620 | − | 20.7188i | −0.708570 | − | 1.22728i | ||||
\(286\) | −3.35766 | + | 27.5489i | −0.198543 | + | 1.62900i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.50000 | + | 7.79423i | 0.265165 | + | 0.459279i | ||||
\(289\) | 8.11943 | − | 14.0633i | 0.477613 | − | 0.827251i | ||||
\(290\) | 2.44524 | + | 4.23527i | 0.143589 | + | 0.248704i | ||||
\(291\) | 11.1972 | − | 19.3942i | 0.656393 | − | 1.13691i | ||||
\(292\) | 1.74487 | 0.102111 | ||||||||
\(293\) | −1.74487 | + | 3.02220i | −0.101936 | + | 0.176559i | −0.912482 | − | 0.409116i | \(-0.865837\pi\) |
0.810546 | + | 0.585675i | \(0.199170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.55971 | + | 16.5579i | −0.556588 | + | 0.964039i | ||||
\(296\) | −2.09167 | + | 3.62288i | −0.121576 | + | 0.210576i | ||||
\(297\) | −39.2038 | −2.27483 | ||||||||
\(298\) | 0.334734 | − | 0.579776i | 0.0193906 | − | 0.0335855i | ||||
\(299\) | −2.88145 | + | 23.6417i | −0.166639 | + | 1.36724i | ||||
\(300\) | −2.88145 | −0.166361 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4.04584 | − | 7.00759i | −0.232812 | − | 0.403242i | ||||
\(303\) | −24.9083 | −1.43095 | ||||||||
\(304\) | 4.75840 | − | 8.24179i | 0.272913 | − | 0.472699i | ||||
\(305\) | −8.30278 | − | 14.3808i | −0.475416 | − | 0.823444i | ||||
\(306\) | 6.02706 | 0.344544 | ||||||||
\(307\) | 15.2797 | 0.872059 | 0.436029 | − | 0.899932i | \(-0.356384\pi\) | ||||
0.436029 | + | 0.899932i | \(0.356384\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.04584 | − | 12.2037i | −0.400824 | − | 0.694247i | ||||
\(310\) | 1.63751 | − | 2.83625i | 0.0930043 | − | 0.161088i | ||||
\(311\) | 8.51229 | − | 14.7437i | 0.482687 | − | 0.836039i | −0.517115 | − | 0.855916i | \(-0.672994\pi\) |
0.999802 | + | 0.0198768i | \(0.00632739\pi\) | |||||||
\(312\) | 28.6791 | − | 12.2037i | 1.62364 | − | 0.690901i | ||||
\(313\) | −6.63534 | − | 11.4927i | −0.375052 | − | 0.649609i | 0.615283 | − | 0.788306i | \(-0.289042\pi\) |
−0.990335 | + | 0.138698i | \(0.955708\pi\) | |||||||
\(314\) | 6.19912 | + | 10.7372i | 0.349837 | + | 0.605935i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0916731 | − | 0.158782i | 0.00515701 | − | 0.00893221i | ||||
\(317\) | −4.10555 | − | 7.11102i | −0.230591 | − | 0.399395i | 0.727391 | − | 0.686223i | \(-0.240733\pi\) |
−0.957982 | + | 0.286828i | \(0.907399\pi\) | |||||||
\(318\) | 18.0291 | + | 31.2273i | 1.01102 | + | 1.75114i | ||||
\(319\) | 3.84861 | + | 6.66599i | 0.215481 | + | 0.373224i | ||||
\(320\) | −12.7024 | − | 22.0012i | −0.710085 | − | 1.22990i | ||||
\(321\) | −13.4028 | + | 23.2143i | −0.748069 | + | 1.29569i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.25694 | + | 2.17708i | 0.0699380 | + | 0.121136i | ||||
\(324\) | 0.486122 | + | 0.841988i | 0.0270068 | + | 0.0467771i | ||||
\(325\) | −1.44073 | + | 11.8209i | −0.0799171 | + | 0.655703i | ||||
\(326\) | −11.2111 | + | 19.4182i | −0.620926 | + | 1.07547i | ||||
\(327\) | 8.94850 | − | 15.4993i | 0.494853 | − | 0.857111i | ||||
\(328\) | −11.2617 | − | 19.5058i | −0.621821 | − | 1.07703i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 63.9083 | 3.51804 | ||||||||
\(331\) | 0.697224 | 0.0383229 | 0.0191615 | − | 0.999816i | \(-0.493900\pi\) | ||||
0.0191615 | + | 0.999816i | \(0.493900\pi\) | |||||||
\(332\) | −1.00451 | − | 1.73986i | −0.0551296 | − | 0.0954873i | ||||
\(333\) | −3.69722 | + | 6.40378i | −0.202607 | + | 0.350925i | ||||
\(334\) | −6.37119 | −0.348616 | ||||||||
\(335\) | −1.44073 | − | 2.49541i | −0.0787153 | − | 0.136339i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.11943 | −0.387820 | −0.193910 | − | 0.981019i | \(-0.562117\pi\) | ||||
−0.193910 | + | 0.981019i | \(0.562117\pi\) | |||||||
\(338\) | −4.69722 | − | 16.2717i | −0.255495 | − | 0.885062i | ||||
\(339\) | 21.3468 | − | 36.9737i | 1.15940 | − | 2.00813i | ||||
\(340\) | 0.761141 | 0.0412787 | ||||||||
\(341\) | 2.57731 | − | 4.46404i | 0.139569 | − | 0.241741i | ||||
\(342\) | 9.95301 | − | 17.2391i | 0.538197 | − | 0.932185i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.27082 | + | 14.3255i | −0.445933 | + | 0.772378i | ||||
\(345\) | 54.8444 | 2.95272 | ||||||||
\(346\) | 15.5838 | − | 26.9920i | 0.837793 | − | 1.45110i | ||||
\(347\) | −0.394449 | − | 0.683205i | −0.0211751 | − | 0.0366764i | 0.855244 | − | 0.518226i | \(-0.173407\pi\) |
−0.876419 | + | 0.481550i | \(0.840074\pi\) | |||||||
\(348\) | 0.568293 | − | 0.984312i | 0.0304637 | − | 0.0527647i | ||||
\(349\) | −11.9620 | − | 20.7188i | −0.640313 | − | 1.10905i | −0.985363 | − | 0.170470i | \(-0.945471\pi\) |
0.345050 | − | 0.938584i | \(-0.387862\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.0139 | − | 9.36750i | 1.17501 | − | 0.500000i | ||||
\(352\) | −5.01388 | − | 8.68429i | −0.267241 | − | 0.462874i | ||||
\(353\) | 6.37119 | 0.339104 | 0.169552 | − | 0.985521i | \(-0.445768\pi\) | ||||
0.169552 | + | 0.985521i | \(0.445768\pi\) | |||||||
\(354\) | −24.9083 | −1.32386 | ||||||||
\(355\) | 11.5258 | 0.611727 | ||||||||
\(356\) | −2.61730 | −0.138717 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.37637 | − | 16.2403i | 0.495556 | − | 0.858329i | ||||
\(359\) | 11.4542 | + | 19.8392i | 0.604528 | + | 1.04707i | 0.992126 | + | 0.125244i | \(0.0399714\pi\) |
−0.387598 | + | 0.921828i | \(0.626695\pi\) | |||||||
\(360\) | −22.9196 | − | 39.6978i | −1.20797 | − | 2.09226i | ||||
\(361\) | −10.6972 | −0.563012 | ||||||||
\(362\) | 6.02706 | − | 10.4392i | 0.316775 | − | 0.548671i | ||||
\(363\) | 68.8907 | 3.61583 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.6056 | −0.869174 | ||||||||
\(366\) | 10.8167 | − | 18.7350i | 0.565396 | − | 0.979294i | ||||
\(367\) | −28.2862 | −1.47653 | −0.738265 | − | 0.674511i | \(-0.764354\pi\) | ||||
−0.738265 | + | 0.674511i | \(0.764354\pi\) | |||||||
\(368\) | 10.9083 | + | 18.8938i | 0.568636 | + | 0.984906i | ||||
\(369\) | −19.9060 | − | 34.4782i | −1.03627 | − | 1.79487i | ||||
\(370\) | 2.61730 | − | 4.53330i | 0.136067 | − | 0.235675i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.761141 | −0.0394633 | ||||||||
\(373\) | −16.3028 | −0.844126 | −0.422063 | − | 0.906567i | \(-0.638694\pi\) | ||||
−0.422063 | + | 0.906567i | \(0.638694\pi\) | |||||||
\(374\) | −6.71532 | −0.347241 | ||||||||
\(375\) | −14.0917 | −0.727691 | ||||||||
\(376\) | 18.5974 | + | 32.2116i | 0.959086 | + | 1.66119i | ||||
\(377\) | −3.75389 | − | 2.82352i | −0.193335 | − | 0.145418i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.55971 | − | 11.3618i | −0.336950 | − | 0.583614i | 0.646908 | − | 0.762568i | \(-0.276062\pi\) |
−0.983857 | + | 0.178954i | \(0.942729\pi\) | |||||||
\(380\) | 1.25694 | − | 2.17708i | 0.0644796 | − | 0.111682i | ||||
\(381\) | 4.19010 | + | 7.25747i | 0.214666 | + | 0.371812i | ||||
\(382\) | 12.5736 | − | 21.7781i | 0.643321 | − | 1.11426i | ||||
\(383\) | −19.2977 | −0.986069 | −0.493034 | − | 0.870010i | \(-0.664112\pi\) | ||||
−0.493034 | + | 0.870010i | \(0.664112\pi\) | |||||||
\(384\) | 11.6579 | − | 20.1921i | 0.594914 | − | 1.03042i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.18335 | + | 2.04962i | −0.0602307 | + | 0.104323i | ||||
\(387\) | −14.6194 | + | 25.3216i | −0.743147 | + | 1.28717i | ||||
\(388\) | 2.35315 | 0.119463 | ||||||||
\(389\) | 3.51388 | − | 6.08622i | 0.178161 | − | 0.308583i | −0.763090 | − | 0.646292i | \(-0.776319\pi\) |
0.941251 | + | 0.337709i | \(0.109652\pi\) | |||||||
\(390\) | −35.8861 | + | 15.2705i | −1.81716 | + | 0.773252i | ||||
\(391\) | −5.76291 | −0.291443 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.5278 | − | 42.4833i | −1.23726 | − | 2.14300i | ||||
\(394\) | 15.5139 | 0.781578 | ||||||||
\(395\) | −0.872434 | + | 1.51110i | −0.0438969 | + | 0.0760317i | ||||
\(396\) | −4.74306 | − | 8.21522i | −0.238348 | − | 0.412830i | ||||
\(397\) | 5.76291 | 0.289232 | 0.144616 | − | 0.989488i | \(-0.453805\pi\) | ||||
0.144616 | + | 0.989488i | \(0.453805\pi\) | |||||||
\(398\) | −1.13659 | −0.0569719 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.45416 | + | 9.44689i | 0.272708 | + | 0.472344i | ||||
\(401\) | −7.55971 | + | 13.0938i | −0.377514 | + | 0.653874i | −0.990700 | − | 0.136065i | \(-0.956554\pi\) |
0.613186 | + | 0.789939i | \(0.289888\pi\) | |||||||
\(402\) | 1.87694 | − | 3.25096i | 0.0936135 | − | 0.162143i | ||||
\(403\) | −0.380571 | + | 3.12250i | −0.0189576 | + | 0.155543i | ||||
\(404\) | −1.30865 | − | 2.26665i | −0.0651078 | − | 0.112770i | ||||
\(405\) | −4.62632 | − | 8.01302i | −0.229884 | − | 0.398170i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.11943 | − | 7.13506i | 0.204193 | − | 0.353672i | ||||
\(408\) | 3.77082 | + | 6.53125i | 0.186683 | + | 0.323345i | ||||
\(409\) | 8.07607 | + | 13.9882i | 0.399336 | + | 0.691670i | 0.993644 | − | 0.112567i | \(-0.0359074\pi\) |
−0.594308 | + | 0.804237i | \(0.702574\pi\) | |||||||
\(410\) | 14.0917 | + | 24.4075i | 0.695938 | + | 1.20540i | ||||
\(411\) | −3.88596 | − | 6.73069i | −0.191680 | − | 0.332000i | ||||
\(412\) | 0.740358 | − | 1.28234i | 0.0364748 | − | 0.0631763i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 22.8167 | + | 39.5196i | 1.12138 | + | 1.94228i | ||||
\(415\) | 9.55971 | + | 16.5579i | 0.469268 | + | 0.812796i | ||||
\(416\) | 4.89047 | + | 3.67841i | 0.239775 | + | 0.180349i | ||||
\(417\) | −24.5278 | + | 42.4833i | −1.20113 | + | 2.08042i | ||||
\(418\) | −11.0896 | + | 19.2077i | −0.542410 | + | 0.939482i | ||||
\(419\) | −4.19010 | − | 7.25747i | −0.204700 | − | 0.354551i | 0.745337 | − | 0.666688i | \(-0.232289\pi\) |
−0.950037 | + | 0.312137i | \(0.898955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.0278 | −1.51220 | −0.756100 | − | 0.654456i | \(-0.772898\pi\) | ||||
−0.756100 | + | 0.654456i | \(0.772898\pi\) | |||||||
\(422\) | −19.5416 | −0.951272 | ||||||||
\(423\) | 32.8726 | + | 56.9370i | 1.59832 | + | 2.76837i | ||||
\(424\) | −14.4083 | + | 24.9560i | −0.699730 | + | 1.21197i | ||||
\(425\) | −2.88145 | −0.139771 | ||||||||
\(426\) | 7.50778 | + | 13.0038i | 0.363753 | + | 0.630039i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.81665 | −0.136148 | ||||||||
\(429\) | −56.4819 | + | 24.0346i | −2.72697 | + | 1.16040i | ||||
\(430\) | 10.3492 | − | 17.9254i | 0.499085 | − | 0.864440i | ||||
\(431\) | 25.9361 | 1.24930 | 0.624649 | − | 0.780906i | \(-0.285242\pi\) | ||||
0.624649 | + | 0.780906i | \(0.285242\pi\) | |||||||
\(432\) | 10.9575 | − | 18.9790i | 0.527194 | − | 0.913127i | ||||
\(433\) | 4.19010 | − | 7.25747i | 0.201364 | − | 0.348772i | −0.747604 | − | 0.664144i | \(-0.768796\pi\) |
0.948968 | + | 0.315372i | \(0.102129\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.40833 | + | 9.36750i | −0.259309 | + | 0.449137i | ||||
\(436\) | 1.88057 | 0.0900630 | ||||||||
\(437\) | −9.51680 | + | 16.4836i | −0.455250 | + | 0.788516i | ||||
\(438\) | −10.8167 | − | 18.7350i | −0.516840 | − | 0.895193i | ||||
\(439\) | 7.63985 | − | 13.2326i | 0.364630 | − | 0.631558i | −0.624087 | − | 0.781355i | \(-0.714529\pi\) |
0.988717 | + | 0.149797i | \(0.0478621\pi\) | |||||||
\(440\) | 25.5369 | + | 44.2311i | 1.21742 | + | 2.10864i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.77082 | − | 1.60458i | 0.179359 | − | 0.0763223i | ||||
\(443\) | −15.1194 | − | 26.1876i | −0.718346 | − | 1.24421i | −0.961655 | − | 0.274263i | \(-0.911566\pi\) |
0.243309 | − | 0.969949i | \(-0.421767\pi\) | |||||||
\(444\) | −1.21656 | −0.0577356 | ||||||||
\(445\) | 24.9083 | 1.18077 | ||||||||
\(446\) | 17.6329 | 0.834940 | ||||||||
\(447\) | 1.48072 | 0.0700355 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.21110 | + | 7.29384i | −0.198734 | + | 0.344218i | −0.948118 | − | 0.317918i | \(-0.897016\pi\) |
0.749384 | + | 0.662136i | \(0.230350\pi\) | |||||||
\(450\) | 11.4083 | + | 19.7598i | 0.537794 | + | 0.931486i | ||||
\(451\) | 22.1792 | + | 38.4155i | 1.04438 | + | 1.80891i | ||||
\(452\) | 4.48612 | 0.211009 | ||||||||
\(453\) | 8.94850 | − | 15.4993i | 0.420437 | − | 0.728219i | ||||
\(454\) | −35.7140 | −1.67614 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.9083 | 1.16644 | ||||||||
\(457\) | −6.69722 | + | 11.5999i | −0.313283 | + | 0.542622i | −0.979071 | − | 0.203519i | \(-0.934762\pi\) |
0.665788 | + | 0.746141i | \(0.268095\pi\) | |||||||
\(458\) | −27.0697 | −1.26488 | ||||||||
\(459\) | 2.89445 | + | 5.01333i | 0.135101 | + | 0.234002i | ||||
\(460\) | 2.88145 | + | 4.99082i | 0.134348 | + | 0.232698i | ||||
\(461\) | 6.33120 | − | 10.9660i | 0.294873 | − | 0.510736i | −0.680082 | − | 0.733136i | \(-0.738056\pi\) |
0.974955 | + | 0.222400i | \(0.0713892\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.2111 | −1.31108 | −0.655541 | − | 0.755160i | \(-0.727559\pi\) | ||||
−0.655541 | + | 0.755160i | \(0.727559\pi\) | |||||||
\(464\) | −4.30278 | −0.199751 | ||||||||
\(465\) | 7.24362 | 0.335915 | ||||||||
\(466\) | 31.1472 | 1.44287 | ||||||||
\(467\) | 7.07156 | + | 12.2483i | 0.327233 | + | 0.566784i | 0.981962 | − | 0.189080i | \(-0.0605506\pi\) |
−0.654729 | + | 0.755864i | \(0.727217\pi\) | |||||||
\(468\) | 4.62632 | + | 3.47972i | 0.213852 | + | 0.160850i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −23.2708 | − | 40.3062i | −1.07340 | − | 1.85919i | ||||
\(471\) | −13.7111 | + | 23.7483i | −0.631774 | + | 1.09427i | ||||
\(472\) | −9.95301 | − | 17.2391i | −0.458125 | − | 0.793495i | ||||
\(473\) | 16.2889 | − | 28.2132i | 0.748964 | − | 1.29724i | ||||
\(474\) | −2.27317 | −0.104410 | ||||||||
\(475\) | −4.75840 | + | 8.24179i | −0.218330 | + | 0.378159i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.4680 | + | 44.1119i | −1.16610 | + | 2.01975i | ||||
\(478\) | 7.55971 | − | 13.0938i | 0.345773 | − | 0.598897i | ||||
\(479\) | −1.13659 | −0.0519319 | −0.0259660 | − | 0.999663i | \(-0.508266\pi\) | ||||
−0.0259660 | + | 0.999663i | \(0.508266\pi\) | |||||||
\(480\) | 7.04584 | − | 12.2037i | 0.321597 | − | 0.557022i | ||||
\(481\) | −0.608282 | + | 4.99082i | −0.0277353 | + | 0.227562i | ||||
\(482\) | 2.61730 | 0.119215 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.61943 | + | 6.26904i | 0.164520 | + | 0.284956i | ||||
\(485\) | −22.3944 | −1.01688 | ||||||||
\(486\) | −6.93948 | + | 12.0195i | −0.314781 | + | 0.545217i | ||||
\(487\) | 13.8486 | + | 23.9865i | 0.627541 | + | 1.08693i | 0.988044 | + | 0.154174i | \(0.0492717\pi\) |
−0.360503 | + | 0.932758i | \(0.617395\pi\) | |||||||
\(488\) | 17.2887 | 0.782624 | ||||||||
\(489\) | −49.5930 | −2.24267 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.36249 | + | 11.0202i | 0.287135 | + | 0.497333i | 0.973125 | − | 0.230279i | \(-0.0739638\pi\) |
−0.685990 | + | 0.727611i | \(0.740630\pi\) | |||||||
\(492\) | 3.27502 | − | 5.67250i | 0.147649 | − | 0.255736i | ||||
\(493\) | 0.568293 | − | 0.984312i | 0.0255946 | − | 0.0443312i | ||||
\(494\) | 1.63751 | − | 13.4354i | 0.0736750 | − | 0.604488i | ||||
\(495\) | 45.1387 | + | 78.1826i | 2.02884 | + | 3.51405i | ||||
\(496\) | 1.44073 | + | 2.49541i | 0.0646905 | + | 0.112047i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.4542 | + | 21.5712i | −0.558084 | + | 0.966631i | ||||
\(499\) | −15.6653 | − | 27.1330i | −0.701274 | − | 1.21464i | −0.968020 | − | 0.250875i | \(-0.919282\pi\) |
0.266746 | − | 0.963767i | \(-0.414052\pi\) | |||||||
\(500\) | −0.740358 | − | 1.28234i | −0.0331098 | − | 0.0573479i | ||||
\(501\) | −7.04584 | − | 12.2037i | −0.314785 | − | 0.545223i | ||||
\(502\) | −14.6714 | − | 25.4116i | −0.654818 | − | 1.13418i | ||||
\(503\) | 12.9665 | − | 22.4587i | 0.578150 | − | 1.00138i | −0.417542 | − | 0.908658i | \(-0.637108\pi\) |
0.995692 | − | 0.0927268i | \(-0.0295583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.4542 | + | 21.5712i | 0.554203 | + | 0.959908i | ||||
\(506\) | −25.4222 | − | 44.0326i | −1.13015 | − | 1.95749i | ||||
\(507\) | 25.9731 | − | 26.9920i | 1.15350 | − | 1.19876i | ||||
\(508\) | −0.440285 | + | 0.762596i | −0.0195345 | + | 0.0338347i | ||||
\(509\) | 1.30865 | − | 2.26665i | 0.0580049 | − | 0.100467i | −0.835565 | − | 0.549392i | \(-0.814859\pi\) |
0.893570 | + | 0.448924i | \(0.148193\pi\) | |||||||
\(510\) | −4.71841 | − | 8.17252i | −0.208935 | − | 0.361885i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25.4222 | 1.12351 | ||||||||
\(513\) | 19.1194 | 0.844143 | ||||||||
\(514\) | −14.8435 | − | 25.7097i | −0.654718 | − | 1.13400i | ||||
\(515\) | −7.04584 | + | 12.2037i | −0.310477 | + | 0.537761i | ||||
\(516\) | −4.81049 | −0.211770 | ||||||||
\(517\) | −36.6265 | − | 63.4389i | −1.61083 | − | 2.79004i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 68.9361 | 3.02596 | ||||||||
\(520\) | −24.9083 | − | 18.7350i | −1.09230 | − | 0.821584i | ||||
\(521\) | 14.4073 | − | 24.9541i | 0.631194 | − | 1.09326i | −0.356114 | − | 0.934442i | \(-0.615899\pi\) |
0.987308 | − | 0.158817i | \(-0.0507681\pi\) | |||||||
\(522\) | −9.00000 | −0.393919 | ||||||||
\(523\) | 4.62632 | − | 8.01302i | 0.202295 | − | 0.350385i | −0.746973 | − | 0.664855i | \(-0.768493\pi\) |
0.949267 | + | 0.314470i | \(0.101827\pi\) | |||||||
\(524\) | 2.57731 | − | 4.46404i | 0.112590 | − | 0.195012i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.74306 | + | 15.1434i | −0.381216 | + | 0.660285i | ||||
\(527\) | −0.761141 | −0.0331558 | ||||||||
\(528\) | −28.1142 | + | 48.6952i | −1.22351 | + | 2.11919i | ||||
\(529\) | −10.3167 | − | 17.8690i | −0.448550 | − | 0.776912i | ||||
\(530\) | 18.0291 | − | 31.2273i | 0.783133 | − | 1.35643i | ||||
\(531\) | −17.5929 | − | 30.4717i | −0.763465 | − | 1.32236i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.6333 | − | 16.2717i | −0.937043 | − | 0.704804i | ||||
\(534\) | 16.2250 | + | 28.1025i | 0.702124 | + | 1.21611i | ||||
\(535\) | 26.8055 | 1.15890 | ||||||||
\(536\) | 3.00000 | 0.129580 | ||||||||
\(537\) | 41.4769 | 1.78986 | ||||||||
\(538\) | −12.3982 | −0.534526 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.89445 | − | 5.01333i | 0.124557 | − | 0.215739i | ||||
\(541\) | 9.46804 | + | 16.3991i | 0.407063 | + | 0.705054i | 0.994559 | − | 0.104173i | \(-0.0332196\pi\) |
−0.587496 | + | 0.809227i | \(0.699886\pi\) | |||||||
\(542\) | 19.3377 | + | 33.4939i | 0.830627 | + | 1.43869i | ||||
\(543\) | 26.6611 | 1.14414 | ||||||||
\(544\) | −0.740358 | + | 1.28234i | −0.0317426 | + | 0.0549798i | ||||
\(545\) | −17.8970 | −0.766623 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.0000 | 1.23995 | 0.619975 | − | 0.784621i | \(-0.287143\pi\) | ||||
0.619975 | + | 0.784621i | \(0.287143\pi\) | |||||||
\(548\) | 0.408327 | − | 0.707243i | 0.0174429 | − | 0.0302119i | ||||
\(549\) | 30.5594 | 1.30424 | ||||||||
\(550\) | −12.7111 | − | 22.0163i | −0.542003 | − | 0.938777i | ||||
\(551\) | −1.87694 | − | 3.25096i | −0.0799605 | − | 0.138496i | ||||
\(552\) | −28.5504 | + | 49.4507i | −1.21519 | + | 2.10476i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.5139 | −0.786579 | ||||||||
\(555\) | 11.5778 | 0.491450 | ||||||||
\(556\) | −5.15463 | −0.218605 | ||||||||
\(557\) | 16.9083 | 0.716429 | 0.358214 | − | 0.933639i | \(-0.383386\pi\) | ||||
0.358214 | + | 0.933639i | \(0.383386\pi\) | |||||||
\(558\) | 3.01353 | + | 5.21959i | 0.127573 | + | 0.220963i | ||||
\(559\) | −2.40525 | + | 19.7345i | −0.101731 | + | 0.834682i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.42641 | − | 12.8629i | −0.313543 | − | 0.543073i | ||||
\(562\) | 1.42221 | − | 2.46333i | 0.0599921 | − | 0.103909i | ||||
\(563\) | 9.51680 | + | 16.4836i | 0.401085 | + | 0.694700i | 0.993857 | − | 0.110671i | \(-0.0352998\pi\) |
−0.592772 | + | 0.805370i | \(0.701966\pi\) | |||||||
\(564\) | −5.40833 | + | 9.36750i | −0.227732 | + | 0.394443i | ||||
\(565\) | −42.6935 | −1.79613 | ||||||||
\(566\) | 2.61730 | − | 4.53330i | 0.110013 | − | 0.190549i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | + | 10.3923i | −0.251754 | + | 0.436051i | ||||
\(569\) | 13.6972 | − | 23.7243i | 0.574218 | − | 0.994574i | −0.421909 | − | 0.906638i | \(-0.638640\pi\) |
0.996126 | − | 0.0879356i | \(-0.0280270\pi\) | |||||||
\(570\) | −31.1677 | −1.30547 | ||||||||
\(571\) | −10.8625 | + | 18.8144i | −0.454581 | + | 0.787358i | −0.998664 | − | 0.0516739i | \(-0.983544\pi\) |
0.544083 | + | 0.839031i | \(0.316878\pi\) | |||||||
\(572\) | −5.15463 | − | 3.87709i | −0.215526 | − | 0.162109i | ||||
\(573\) | 55.6201 | 2.32356 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.9083 | − | 18.8938i | −0.454909 | − | 0.787925i | ||||
\(576\) | 46.7527 | 1.94803 | ||||||||
\(577\) | −16.8525 | + | 29.1894i | −0.701579 | + | 1.21517i | 0.266333 | + | 0.963881i | \(0.414188\pi\) |
−0.967912 | + | 0.251289i | \(0.919145\pi\) | |||||||
\(578\) | −10.5778 | − | 18.3213i | −0.439978 | − | 0.762065i | ||||
\(579\) | −5.23460 | −0.217543 | ||||||||
\(580\) | −1.13659 | −0.0471942 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −14.5875 | − | 25.2662i | −0.604670 | − | 1.04732i | ||||
\(583\) | 28.3764 | − | 49.1493i | 1.17523 | − | 2.03556i | ||||
\(584\) | 8.64436 | − | 14.9725i | 0.357706 | − | 0.619565i | ||||
\(585\) | −44.0278 | − | 33.1158i | −1.82032 | − | 1.36917i | ||||
\(586\) | 2.27317 | + | 3.93725i | 0.0939038 | + | 0.162646i | ||||
\(587\) | 14.2752 | + | 24.7254i | 0.589200 | + | 1.02052i | 0.994337 | + | 0.106269i | \(0.0338904\pi\) |
−0.405137 | + | 0.914256i | \(0.632776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.25694 | + | 2.17708i | −0.0517913 | + | 0.0897051i | ||||
\(590\) | 12.4542 | + | 21.5712i | 0.512730 | + | 0.888074i | ||||
\(591\) | 17.1566 | + | 29.7162i | 0.705730 | + | 1.22236i | ||||
\(592\) | 2.30278 | + | 3.98852i | 0.0946435 | + | 0.163927i | ||||
\(593\) | 11.3937 | + | 19.7345i | 0.467885 | + | 0.810400i | 0.999327 | − | 0.0366946i | \(-0.0116829\pi\) |
−0.531442 | + | 0.847095i | \(0.678350\pi\) | |||||||
\(594\) | −25.5369 | + | 44.2311i | −1.04779 | + | 1.81483i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0777949 | + | 0.134745i | 0.00318660 | + | 0.00551936i | ||||
\(597\) | −1.25694 | − | 2.17708i | −0.0514431 | − | 0.0891020i | ||||
\(598\) | 24.7965 | + | 18.6509i | 1.01400 | + | 0.762691i | ||||
\(599\) | −3.75694 | + | 6.50721i | −0.153504 | + | 0.265877i | −0.932513 | − | 0.361135i | \(-0.882389\pi\) |
0.779009 | + | 0.627013i | \(0.215723\pi\) | |||||||
\(600\) | −14.2752 | + | 24.7254i | −0.582782 | + | 1.00941i | ||||
\(601\) | 14.7114 | + | 25.4809i | 0.600091 | + | 1.03939i | 0.992807 | + | 0.119728i | \(0.0382023\pi\) |
−0.392716 | + | 0.919660i | \(0.628464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.30278 | 0.215946 | ||||||||
\(604\) | 1.88057 | 0.0765193 | ||||||||
\(605\) | −34.4454 | − | 59.6611i | −1.40040 | − | 2.42557i | ||||
\(606\) | −16.2250 | + | 28.1025i | −0.659095 | + | 1.14159i | ||||
\(607\) | 20.4343 | 0.829404 | 0.414702 | − | 0.909957i | \(-0.363886\pi\) | ||||
0.414702 | + | 0.909957i | \(0.363886\pi\) | |||||||
\(608\) | 2.44524 | + | 4.23527i | 0.0991674 | + | 0.171763i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.6333 | −0.875907 | ||||||||
\(611\) | 35.7250 | + | 26.8708i | 1.44528 | + | 1.08708i | ||||
\(612\) | −0.700369 | + | 1.21307i | −0.0283107 | + | 0.0490356i | ||||
\(613\) | 21.0917 | 0.851885 | 0.425942 | − | 0.904750i | \(-0.359943\pi\) | ||||
0.425942 | + | 0.904750i | \(0.359943\pi\) | |||||||
\(614\) | 9.95301 | − | 17.2391i | 0.401671 | − | 0.695714i | ||||
\(615\) | −31.1677 | + | 53.9840i | −1.25680 | + | 2.17685i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.9222 | − | 36.2383i | 0.842296 | − | 1.45890i | −0.0456524 | − | 0.998957i | \(-0.514537\pi\) |
0.887949 | − | 0.459943i | \(-0.152130\pi\) | |||||||
\(618\) | −18.3583 | −0.738479 | ||||||||
\(619\) | −11.2617 | + | 19.5058i | −0.452644 | + | 0.784003i | −0.998549 | − | 0.0538439i | \(-0.982853\pi\) |
0.545905 | + | 0.837847i | \(0.316186\pi\) | |||||||
\(620\) | 0.380571 | + | 0.659168i | 0.0152841 | + | 0.0264728i | ||||
\(621\) | −21.9150 | + | 37.9580i | −0.879420 | + | 1.52320i | ||||
\(622\) | −11.0896 | − | 19.2077i | −0.444652 | − | 0.770160i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.15139 | − | 34.0612i | 0.166189 | − | 1.36354i | ||||
\(625\) | 15.3028 | + | 26.5052i | 0.612111 | + | 1.06021i | ||||
\(626\) | −17.2887 | −0.690996 | ||||||||
\(627\) | −49.0555 | −1.95909 | ||||||||
\(628\) | −2.88145 | −0.114983 | ||||||||
\(629\) | −1.21656 | −0.0485076 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.04584 | + | 10.4717i | −0.240681 | + | 0.416872i | −0.960908 | − | 0.276866i | \(-0.910704\pi\) |
0.720227 | + | 0.693738i | \(0.244037\pi\) | |||||||
\(632\) | −0.908327 | − | 1.57327i | −0.0361313 | − | 0.0625813i | ||||
\(633\) | −21.6109 | − | 37.4312i | −0.858956 | − | 1.48776i | ||||
\(634\) | −10.6972 | −0.424841 | ||||||||
\(635\) | 4.19010 | − | 7.25747i | 0.166279 | − | 0.288004i | ||||
\(636\) | −8.38021 | −0.332297 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.0278 | 0.397003 | ||||||||
\(639\) | −10.6056 | + | 18.3694i | −0.419549 | + | 0.726680i | ||||
\(640\) | −23.3158 | −0.921637 | ||||||||
\(641\) | −1.75694 | − | 3.04311i | −0.0693949 | − | 0.120196i | 0.829240 | − | 0.558892i | \(-0.188774\pi\) |
−0.898635 | + | 0.438697i | \(0.855440\pi\) | |||||||
\(642\) | 17.4608 | + | 30.2430i | 0.689122 | + | 1.19359i | ||||
\(643\) | 4.19010 | − | 7.25747i | 0.165242 | − | 0.286207i | −0.771499 | − | 0.636230i | \(-0.780493\pi\) |
0.936741 | + | 0.350023i | \(0.113826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 45.7805 | 1.80261 | ||||||||
\(646\) | 3.27502 | 0.128854 | ||||||||
\(647\) | −2.27317 | −0.0893676 | −0.0446838 | − | 0.999001i | \(-0.514228\pi\) | ||||
−0.0446838 | + | 0.999001i | \(0.514228\pi\) | |||||||
\(648\) | 9.63331 | 0.378432 | ||||||||
\(649\) | 19.6019 | + | 33.9515i | 0.769441 | + | 1.33271i | ||||
\(650\) | 12.3982 | + | 9.32544i | 0.486299 | + | 0.365774i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.60555 | − | 4.51295i | −0.102041 | − | 0.176741i | ||||
\(653\) | −10.8764 | + | 18.8384i | −0.425625 | + | 0.737204i | −0.996479 | − | 0.0838475i | \(-0.973279\pi\) |
0.570853 | + | 0.821052i | \(0.306612\pi\) | |||||||
\(654\) | −11.6579 | − | 20.1921i | −0.455860 | − | 0.789572i | ||||
\(655\) | −24.5278 | + | 42.4833i | −0.958379 | + | 1.65996i | ||||
\(656\) | −24.7965 | −0.968141 | ||||||||
\(657\) | 15.2797 | − | 26.4652i | 0.596118 | − | 1.03251i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.8167 | + | 20.4670i | −0.460311 | + | 0.797283i | −0.998976 | − | 0.0452373i | \(-0.985596\pi\) |
0.538665 | + | 0.842520i | \(0.318929\pi\) | |||||||
\(660\) | −7.42641 | + | 12.8629i | −0.289073 | + | 0.500688i | ||||
\(661\) | −9.78095 | −0.380435 | −0.190217 | − | 0.981742i | \(-0.560919\pi\) | ||||
−0.190217 | + | 0.981742i | \(0.560919\pi\) | |||||||
\(662\) | 0.454163 | − | 0.786634i | 0.0176516 | − | 0.0305734i | ||||
\(663\) | 7.24362 | + | 5.44835i | 0.281319 | + | 0.211596i | ||||
\(664\) | −19.9060 | −0.772504 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.81665 | + | 8.34269i | 0.186642 | + | 0.323273i | ||||
\(667\) | 8.60555 | 0.333208 | ||||||||
\(668\) | 0.740358 | − | 1.28234i | 0.0286453 | − | 0.0496151i | ||||
\(669\) | 19.5000 | + | 33.7750i | 0.753914 | + | 1.30582i | ||||
\(670\) | −3.75389 | −0.145025 | ||||||||
\(671\) | −34.0491 | −1.31445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.10555 | − | 10.5751i | −0.235352 | − | 0.407641i | 0.724023 | − | 0.689776i | \(-0.242291\pi\) |
−0.959375 | + | 0.282135i | \(0.908958\pi\) | |||||||
\(674\) | −4.63751 | + | 8.03240i | −0.178630 | + | 0.309397i | ||||
\(675\) | −10.9575 | + | 18.9790i | −0.421755 | + | 0.730501i | ||||
\(676\) | 3.82086 | + | 0.945417i | 0.146956 | + | 0.0363622i | ||||
\(677\) | −3.18559 | − | 5.51761i | −0.122432 | − | 0.212059i | 0.798294 | − | 0.602268i | \(-0.205736\pi\) |
−0.920726 | + | 0.390209i | \(0.872403\pi\) | |||||||
\(678\) | −27.8100 | − | 48.1684i | −1.06804 | − | 1.84990i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.77082 | − | 6.53125i | 0.144604 | − | 0.250462i | ||||
\(681\) | −39.4958 | − | 68.4087i | −1.51348 | − | 2.62143i | ||||
\(682\) | −3.35766 | − | 5.81564i | −0.128571 | − | 0.222692i | ||||
\(683\) | −1.80278 | − | 3.12250i | −0.0689813 | − | 0.119479i | 0.829472 | − | 0.558549i | \(-0.188642\pi\) |
−0.898453 | + | 0.439069i | \(0.855308\pi\) | |||||||
\(684\) | 2.31316 | + | 4.00651i | 0.0884459 | + | 0.153193i | ||||
\(685\) | −3.88596 | + | 6.73069i | −0.148475 | + | 0.257166i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.9361 | − | 51.8508i | −1.14213 | − | 1.97823i | ||||
\(688\) | 9.10555 | + | 15.7713i | 0.347146 | + | 0.601274i | ||||
\(689\) | −4.19010 | + | 34.3789i | −0.159630 | + | 1.30973i | ||||
\(690\) | 35.7250 | − | 61.8775i | 1.36003 | − | 2.35564i | ||||
\(691\) | −16.4563 | + | 28.5031i | −0.626026 | + | 1.08431i | 0.362315 | + | 0.932056i | \(0.381986\pi\) |
−0.988341 | + | 0.152254i | \(0.951347\pi\) | |||||||
\(692\) | 3.62181 | + | 6.27316i | 0.137681 | + | 0.238470i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.02776 | −0.0390131 | ||||||||
\(695\) | 49.0555 | 1.86078 | ||||||||
\(696\) | −5.63083 | − | 9.75289i | −0.213436 | − | 0.369682i | ||||
\(697\) | 3.27502 | − | 5.67250i | 0.124050 | − | 0.214861i | ||||
\(698\) | −31.1677 | −1.17971 | ||||||||
\(699\) | 34.4454 | + | 59.6611i | 1.30284 | + | 2.25659i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0278 | −1.02082 | −0.510412 | − | 0.859930i | \(-0.670507\pi\) | ||||
−0.510412 | + | 0.859930i | \(0.670507\pi\) | |||||||
\(702\) | 3.77082 | − | 30.9387i | 0.142320 | − | 1.16771i | ||||
\(703\) | −2.00902 | + | 3.47972i | −0.0757716 | + | 0.131240i | ||||
\(704\) | −52.0917 | −1.96328 | ||||||||
\(705\) | 51.4699 | − | 89.1486i | 1.93847 | − | 3.35753i | ||||
\(706\) | 4.15012 | − | 7.18821i | 0.156192 | − | 0.270532i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.89445 | − | 5.01333i | 0.108780 | − | 0.188413i | ||||
\(709\) | 0.275019 | 0.0103286 | 0.00516428 | − | 0.999987i | \(-0.498356\pi\) | ||||
0.00516428 | + | 0.999987i | \(0.498356\pi\) | |||||||
\(710\) | 7.50778 | − | 13.0038i | 0.281762 | − | 0.488026i | ||||
\(711\) | −1.60555 | − | 2.78090i | −0.0602129 | − | 0.104292i | ||||
\(712\) | −12.9665 | + | 22.4587i | −0.485942 | + | 0.841676i | ||||
\(713\) | −2.88145 | − | 4.99082i | −0.107911 | − | 0.186908i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 49.0555 | + | 36.8975i | 1.83457 | + | 1.37989i | ||||
\(716\) | 2.17914 | + | 3.77439i | 0.0814384 | + | 0.141056i | ||||
\(717\) | 33.4409 | 1.24887 | ||||||||
\(718\) | 29.8444 | 1.11378 | ||||||||
\(719\) | 21.6509 | 0.807442 | 0.403721 | − | 0.914882i | \(-0.367717\pi\) | ||||
0.403721 | + | 0.914882i | \(0.367717\pi\) | |||||||
\(720\) | −50.4654 | −1.88074 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.96804 | + | 12.0690i | −0.259324 | + | 0.449162i | ||||
\(723\) | 2.89445 | + | 5.01333i | 0.107646 | + | 0.186448i | ||||
\(724\) | 1.40074 | + | 2.42615i | 0.0520580 | + | 0.0901671i | ||||
\(725\) | 4.30278 | 0.159801 | ||||||||
\(726\) | 44.8746 | − | 77.7251i | 1.66545 | − | 2.88465i | ||||
\(727\) | −23.3958 | −0.867701 | −0.433850 | − | 0.900985i | \(-0.642845\pi\) | ||||
−0.433850 | + | 0.900985i | \(0.642845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.3305 | −1.49372 | ||||||||
\(730\) | −10.8167 | + | 18.7350i | −0.400342 | + | 0.693413i | ||||
\(731\) | −4.81049 | −0.177923 | ||||||||
\(732\) | 2.51388 | + | 4.35416i | 0.0929156 | + | 0.160935i | ||||
\(733\) | 20.0381 | + | 34.7070i | 0.740124 | + | 1.28193i | 0.952438 | + | 0.304731i | \(0.0985666\pi\) |
−0.212314 | + | 0.977201i | \(0.568100\pi\) | |||||||
\(734\) | −18.4253 | + | 31.9136i | −0.680091 | + | 1.17795i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.2111 | −0.413247 | ||||||||
\(737\) | −5.90833 | −0.217636 | ||||||||
\(738\) | −51.8662 | −1.90922 | ||||||||
\(739\) | −18.7889 | −0.691161 | −0.345580 | − | 0.938389i | \(-0.612318\pi\) | ||||
−0.345580 | + | 0.938389i | \(0.612318\pi\) | |||||||
\(740\) | 0.608282 | + | 1.05358i | 0.0223609 | + | 0.0387302i | ||||
\(741\) | 27.5459 | − | 11.7215i | 1.01192 | − | 0.430600i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.8486 | + | 32.6468i | 0.691489 | + | 1.19769i | 0.971350 | + | 0.237653i | \(0.0763781\pi\) |
−0.279862 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(744\) | −3.77082 | + | 6.53125i | −0.138245 | + | 0.239447i | ||||
\(745\) | −0.740358 | − | 1.28234i | −0.0271246 | − | 0.0469812i | ||||
\(746\) | −10.6194 | + | 18.3934i | −0.388805 | + | 0.673430i | ||||
\(747\) | −35.1857 | −1.28738 | ||||||||
\(748\) | 0.780347 | − | 1.35160i | 0.0285323 | − | 0.0494194i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9.17914 | + | 15.8987i | −0.335175 | + | 0.580540i | ||||
\(751\) | 2.19722 | − | 3.80570i | 0.0801779 | − | 0.138872i | −0.823148 | − | 0.567826i | \(-0.807785\pi\) |
0.903326 | + | 0.428954i | \(0.141118\pi\) | |||||||
\(752\) | 40.9486 | 1.49324 | ||||||||
\(753\) | 32.4500 | − | 56.2050i | 1.18254 | − | 2.04822i | ||||
\(754\) | −5.63083 | + | 2.39607i | −0.205063 | + | 0.0872597i | ||||
\(755\) | −17.8970 | −0.651339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1194 | + | 38.3120i | 0.803944 | + | 1.39247i | 0.917001 | + | 0.398884i | \(0.130602\pi\) |
−0.113057 | + | 0.993588i | \(0.536064\pi\) | |||||||
\(758\) | −17.0917 | −0.620798 | ||||||||
\(759\) | 56.2283 | − | 97.3903i | 2.04096 | − | 3.53505i | ||||
\(760\) | −12.4542 | − | 21.5712i | −0.451760 | − | 0.782471i | ||||
\(761\) | −4.28219 | −0.155229 | −0.0776147 | − | 0.996983i | \(-0.524730\pi\) | ||||
−0.0776147 | + | 0.996983i | \(0.524730\pi\) | |||||||
\(762\) | 10.9175 | 0.395500 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.92221 | + | 5.06141i | 0.105722 | + | 0.183115i | ||||
\(765\) | 6.66527 | − | 11.5446i | 0.240983 | − | 0.417395i | ||||
\(766\) | −12.5703 | + | 21.7724i | −0.454184 | + | 0.786670i | ||||
\(767\) | −19.1194 | − | 14.3808i | −0.690363 | − | 0.519262i | ||||
\(768\) | 10.2172 | + | 17.6966i | 0.368680 | + | 0.638573i | ||||
\(769\) | 15.4518 | + | 26.7632i | 0.557205 | + | 0.965107i | 0.997728 | + | 0.0673662i | \(0.0214596\pi\) |
−0.440523 | + | 0.897741i | \(0.645207\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.8305 | − | 56.8641i | 1.18236 | − | 2.04791i | ||||
\(772\) | −0.275019 | − | 0.476347i | −0.00989816 | − | 0.0171441i | ||||
\(773\) | 17.4608 | + | 30.2430i | 0.628021 | + | 1.08776i | 0.987948 | + | 0.154784i | \(0.0494681\pi\) |
−0.359927 | + | 0.932980i | \(0.617199\pi\) | |||||||
\(774\) | 19.0458 | + | 32.9884i | 0.684588 | + | 1.18574i | ||||
\(775\) | −1.44073 | − | 2.49541i | −0.0517524 | − | 0.0896379i | ||||
\(776\) | 11.6579 | − | 20.1921i | 0.418494 | − | 0.724853i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.57779 | − | 7.92897i | −0.164122 | − | 0.284267i | ||||
\(779\) | −10.8167 | − | 18.7350i | −0.387547 | − | 0.671251i | ||||
\(780\) | 1.09660 | − | 8.99734i | 0.0392644 | − | 0.322156i | ||||
\(781\) | 11.8167 | − | 20.4670i | 0.422833 | − | 0.732368i | ||||
\(782\) | −3.75389 | + | 6.50192i | −0.134239 | + | 0.232508i | ||||
\(783\) | −4.32218 | − | 7.48624i | −0.154462 | − | 0.267536i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 27.4222 | 0.978740 | ||||||||
\(786\) | −63.9083 | −2.27953 | ||||||||
\(787\) | −20.7785 | − | 35.9893i | −0.740672 | − | 1.28288i | −0.952190 | − | 0.305507i | \(-0.901174\pi\) |
0.211518 | − | 0.977374i | \(-0.432159\pi\) | |||||||
\(788\) | −1.80278 | + | 3.12250i | −0.0642212 | + | 0.111234i | ||||
\(789\) | −38.6755 | −1.37688 | ||||||||
\(790\) | 1.13659 | + | 1.96862i | 0.0404379 | + | 0.0700405i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −93.9916 | −3.33985 | ||||||||
\(793\) | 19.1194 | − | 8.13583i | 0.678951 | − | 0.288912i | ||||
\(794\) | 3.75389 | − | 6.50192i | 0.133220 | − | 0.230745i | ||||
\(795\) | 79.7527 | 2.82854 | ||||||||
\(796\) | 0.132076 | − | 0.228762i | 0.00468131 | − | 0.00810826i | ||||
\(797\) | −17.2887 | + | 29.9449i | −0.612398 | + | 1.06070i | 0.378437 | + | 0.925627i | \(0.376462\pi\) |
−0.990835 | + | 0.135077i | \(0.956872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.40833 | + | 9.36750i | −0.191333 | + | 0.331398i | ||||
\(800\) | −5.60555 | −0.198186 | ||||||||
\(801\) | −22.9196 | + | 39.6978i | −0.809823 | + | 1.40265i | ||||
\(802\) | 9.84861 | + | 17.0583i | 0.347767 | + | 0.602349i | ||||
\(803\) | −17.0246 | + | 29.4874i | −0.600784 | + | 1.04059i | ||||
\(804\) | 0.436217 | + | 0.755550i | 0.0153842 | + | 0.0266462i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.27502 | + | 2.46333i | 0.115358 | + | 0.0867672i | ||||
\(807\) | −13.7111 | − | 23.7483i | −0.482654 | − | 0.835981i | ||||
\(808\) | −25.9331 | −0.912323 | ||||||||
\(809\) | −16.0278 | −0.563506 | −0.281753 | − | 0.959487i | \(-0.590916\pi\) | ||||
−0.281753 | + | 0.959487i | \(0.590916\pi\) | |||||||
\(810\) | −12.0541 | −0.423539 | ||||||||
\(811\) | 21.9150 | 0.769541 | 0.384771 | − | 0.923012i | \(-0.374281\pi\) | ||||
0.384771 | + | 0.923012i | \(0.374281\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −42.7708 | + | 74.0812i | −1.50004 | + | 2.59814i | ||||
\(814\) | −5.36669 | − | 9.29538i | −0.188102 | − | 0.325803i | ||||
\(815\) | 24.7965 | + | 42.9488i | 0.868583 | + | 1.50443i | ||||
\(816\) | 8.30278 | 0.290655 | ||||||||
\(817\) | −7.94399 | + | 13.7594i | −0.277925 | + | 0.481380i | ||||
\(818\) | 21.0426 | 0.735738 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.55004 | −0.228737 | ||||||||
\(821\) | −0.922205 | + | 1.59731i | −0.0321852 | + | 0.0557464i | −0.881669 | − | 0.471868i | \(-0.843580\pi\) |
0.849484 | + | 0.527614i | \(0.176913\pi\) | |||||||
\(822\) | −10.1251 | −0.353153 | ||||||||
\(823\) | 22.1333 | + | 38.3360i | 0.771519 | + | 1.33631i | 0.936731 | + | 0.350051i | \(0.113836\pi\) |
−0.165212 | + | 0.986258i | \(0.552831\pi\) | |||||||
\(824\) | −7.33571 | − | 12.7058i | −0.255552 | − | 0.442628i | ||||
\(825\) | 28.1142 | − | 48.6952i | 0.978810 | − | 1.69535i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.7527 | 1.79962 | 0.899809 | − | 0.436283i | \(-0.143705\pi\) | ||||
0.899809 | + | 0.436283i | \(0.143705\pi\) | |||||||
\(828\) | −10.6056 | −0.368568 | ||||||||
\(829\) | −15.6238 | −0.542638 | −0.271319 | − | 0.962489i | \(-0.587460\pi\) | ||||
−0.271319 | + | 0.962489i | \(0.587460\pi\) | |||||||
\(830\) | 24.9083 | 0.864581 | ||||||||
\(831\) | −20.4743 | − | 35.4626i | −0.710246 | − | 1.23018i | ||||
\(832\) | 29.2508 | − | 12.4470i | 1.01409 | − | 0.431521i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 31.9542 | + | 55.3462i | 1.10648 | + | 1.91648i | ||||
\(835\) | −7.04584 | + | 12.2037i | −0.243831 | + | 0.422328i | ||||
\(836\) | −2.57731 | − | 4.46404i | −0.0891382 | − | 0.154392i | ||||
\(837\) | −2.89445 | + | 5.01333i | −0.100047 | + | 0.173286i | ||||
\(838\) | −10.9175 | −0.377140 | ||||||||
\(839\) | 11.8300 | − | 20.4901i | 0.408415 | − | 0.707396i | −0.586297 | − | 0.810096i | \(-0.699415\pi\) |
0.994712 | + | 0.102700i | \(0.0327481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.6514 | − | 23.6449i | 0.470738 | − | 0.815341i | ||||
\(842\) | −20.2111 | + | 35.0067i | −0.696521 | + | 1.20641i | ||||
\(843\) | 6.29121 | 0.216681 | ||||||||
\(844\) | 2.27082 | − | 3.93317i | 0.0781648 | − | 0.135385i | ||||
\(845\) | −36.3623 | − | 8.99734i | −1.25090 | − | 0.309518i | ||||
\(846\) | 85.6512 | 2.94475 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.8625 | + | 27.4746i | 0.544720 | + | 0.943483i | ||||
\(849\) | 11.5778 | 0.397349 | ||||||||
\(850\) | −1.87694 | + | 3.25096i | −0.0643786 | + | 0.111507i | ||||
\(851\) | −4.60555 | − | 7.97705i | −0.157876 | − | 0.273450i | ||||
\(852\) | −3.48974 | −0.119556 | ||||||||
\(853\) | −14.1431 | −0.484251 | −0.242126 | − | 0.970245i | \(-0.577845\pi\) | ||||
−0.242126 | + | 0.970245i | \(0.577845\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −22.0139 | − | 38.1292i | −0.752859 | − | 1.30399i | ||||
\(856\) | −13.9542 | + | 24.1693i | −0.476943 | + | 0.826090i | ||||
\(857\) | 23.7920 | − | 41.2089i | 0.812719 | − | 1.40767i | −0.0982356 | − | 0.995163i | \(-0.531320\pi\) |
0.910954 | − | 0.412507i | \(-0.135347\pi\) | |||||||
\(858\) | −9.67494 | + | 79.3808i | −0.330297 | + | 2.71002i | ||||
\(859\) | −12.3982 | − | 21.4744i | −0.423023 | − | 0.732697i | 0.573211 | − | 0.819408i | \(-0.305698\pi\) |
−0.996234 | + | 0.0867110i | \(0.972364\pi\) | |||||||
\(860\) | 2.40525 | + | 4.16601i | 0.0820183 | + | 0.142060i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.8944 | − | 29.2620i | 0.575427 | − | 0.996669i | ||||
\(863\) | 5.90833 | + | 10.2335i | 0.201122 | + | 0.348353i | 0.948890 | − | 0.315607i | \(-0.102208\pi\) |
−0.747768 | + | 0.663960i | \(0.768875\pi\) | |||||||
\(864\) | 5.63083 | + | 9.75289i | 0.191565 | + | 0.331800i | ||||
\(865\) | −34.4680 | − | 59.7004i | −1.17195 | − | 2.02987i | ||||
\(866\) | −5.45877 | − | 9.45486i | −0.185496 | − | 0.321289i | ||||
\(867\) | 23.3958 | − | 40.5226i | 0.794562 | − | 1.37622i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.78890 | + | 3.09846i | 0.0606842 | + | 0.105108i | ||||
\(870\) | 7.04584 | + | 12.2037i | 0.238876 | + | 0.413746i | ||||
\(871\) | 3.31767 | − | 1.41176i | 0.112415 | − | 0.0478356i | ||||
\(872\) | 9.31665 | − | 16.1369i | 0.315502 | − | 0.546465i | ||||
\(873\) | 20.6064 | − | 35.6913i | 0.697421 | − | 1.20797i | ||||
\(874\) | 12.3982 | + | 21.4744i | 0.419377 | + | 0.726382i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.02776 | 0.169872 | ||||||||
\(877\) | −38.3944 | −1.29649 | −0.648244 | − | 0.761432i | \(-0.724496\pi\) | ||||
−0.648244 | + | 0.761432i | \(0.724496\pi\) | |||||||
\(878\) | −9.95301 | − | 17.2391i | −0.335898 | − | 0.581792i | ||||
\(879\) | −5.02776 | + | 8.70833i | −0.169582 | + | 0.293725i | ||||
\(880\) | 56.2283 | 1.89546 | ||||||||
\(881\) | −17.7249 | − | 30.7005i | −0.597168 | − | 1.03433i | −0.993237 | − | 0.116105i | \(-0.962959\pi\) |
0.396069 | − | 0.918221i | \(-0.370374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.6056 | −1.06361 | −0.531806 | − | 0.846866i | \(-0.678486\pi\) | ||||
−0.531806 | + | 0.846866i | \(0.678486\pi\) | |||||||
\(884\) | −0.115227 | + | 0.945417i | −0.00387552 | + | 0.0317978i | ||||
\(885\) | −27.5459 | + | 47.7109i | −0.925944 | + | 1.60378i | ||||
\(886\) | −39.3944 | −1.32348 | ||||||||
\(887\) | −23.0516 | + | 39.9266i | −0.773998 | + | 1.34060i | 0.161358 | + | 0.986896i | \(0.448413\pi\) |
−0.935356 | + | 0.353708i | \(0.884921\pi\) | |||||||
\(888\) | −6.02706 | + | 10.4392i | −0.202255 | + | 0.350316i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.2250 | − | 28.1025i | 0.543863 | − | 0.941998i | ||||
\(891\) | −18.9722 | −0.635594 | ||||||||
\(892\) | −2.04901 | + | 3.54899i | −0.0686059 | + | 0.118829i | ||||
\(893\) | 17.8625 | + | 30.9387i | 0.597745 | + | 1.03533i | ||||
\(894\) | 0.964521 | − | 1.67060i | 0.0322584 | − | 0.0558732i | ||||
\(895\) | −20.7385 | − | 35.9201i | −0.693211 | − | 1.20068i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.30278 | + | 68.1225i | −0.277222 | + | 2.27454i | ||||
\(898\) | 5.48612 | + | 9.50224i | 0.183074 | + | 0.317094i | ||||
\(899\) | 1.13659 | 0.0379073 | ||||||||
\(900\) | −5.30278 | −0.176759 | ||||||||
\(901\) | −8.38021 | −0.279185 | ||||||||
\(902\) | 57.7890 | 1.92416 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.2250 | − | 38.4948i | 0.739192 | − | 1.28032i | ||||
\(905\) | −13.3305 | − | 23.0892i | −0.443122 | − | 0.767510i | ||||
\(906\) | −11.6579 | − | 20.1921i | −0.387307 | − | 0.670836i | ||||
\(907\) | 18.8444 | 0.625718 | 0.312859 | − | 0.949800i | \(-0.398713\pi\) | ||||
0.312859 | + | 0.949800i | \(0.398713\pi\) | |||||||
\(908\) | 4.15012 | − | 7.18821i | 0.137726 | − | 0.238549i | ||||
\(909\) | −45.8391 | −1.52039 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.9361 | −0.362329 | −0.181164 | − | 0.983453i | \(-0.557987\pi\) | ||||
−0.181164 | + | 0.983453i | \(0.557987\pi\) | |||||||
\(912\) | 13.7111 | − | 23.7483i | 0.454020 | − | 0.786386i | ||||
\(913\) | 39.2038 | 1.29746 | ||||||||
\(914\) | 8.72498 | + | 15.1121i | 0.288597 | + | 0.499864i | ||||
\(915\) | −23.9241 | − | 41.4377i | −0.790905 | − | 1.36989i | ||||
\(916\) | 3.14561 | − | 5.44835i | 0.103934 | − | 0.180019i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.54163 | 0.248911 | ||||||||
\(919\) | −11.4500 | −0.377699 | −0.188850 | − | 0.982006i | \(-0.560476\pi\) | ||||
−0.188850 | + | 0.982006i | \(0.560476\pi\) | |||||||
\(920\) | 57.1008 | 1.88256 | ||||||||
\(921\) | 44.0278 | 1.45076 | ||||||||
\(922\) | −8.24813 | − | 14.2862i | −0.271638 | − | 0.470490i | ||||
\(923\) | −1.74487 | + | 14.3163i | −0.0574330 | + | 0.471226i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.30278 | − | 3.98852i | −0.0757148 | − | 0.131142i | ||||
\(926\) | −18.3764 | + | 31.8288i | −0.603885 | + | 1.04596i | ||||
\(927\) | −12.9665 | − | 22.4587i | −0.425877 | − | 0.737641i | ||||
\(928\) | 1.10555 | − | 1.91487i | 0.0362915 | − | 0.0628587i | ||||
\(929\) | 8.38021 | 0.274946 | 0.137473 | − | 0.990506i | \(-0.456102\pi\) | ||||
0.137473 | + | 0.990506i | \(0.456102\pi\) | |||||||
\(930\) | 4.71841 | − | 8.17252i | 0.154723 | − | 0.267988i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.61943 | + | 6.26904i | −0.118558 | + | 0.205349i | ||||
\(933\) | 24.5278 | − | 42.4833i | 0.803003 | − | 1.39084i | ||||
\(934\) | 18.4253 | 0.602895 | ||||||||
\(935\) | −7.42641 | + | 12.8629i | −0.242869 | + | 0.420662i | ||||
\(936\) | 52.7786 | − | 22.4587i | 1.72512 | − | 0.734086i | ||||
\(937\) | 46.4474 | 1.51737 | 0.758685 | − | 0.651458i | \(-0.225842\pi\) | ||||
0.758685 | + | 0.651458i | \(0.225842\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.1194 | − | 33.1158i | −0.623939 | − | 1.08069i | ||||
\(940\) | 10.8167 | 0.352800 | ||||||||
\(941\) | −22.3513 | + | 38.7135i | −0.728630 | + | 1.26202i | 0.228832 | + | 0.973466i | \(0.426509\pi\) |
−0.957462 | + | 0.288559i | \(0.906824\pi\) | |||||||
\(942\) | 17.8625 | + | 30.9387i | 0.581991 | + | 1.00804i | ||||
\(943\) | 49.5930 | 1.61497 | ||||||||
\(944\) | −21.9150 | −0.713274 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.2208 | − | 36.7555i | −0.689947 | − | 1.19502i | ||||
\(947\) | −26.5597 | + | 46.0028i | −0.863075 | + | 1.49489i | 0.00587143 | + | 0.999983i | \(0.498131\pi\) |
−0.868946 | + | 0.494907i | \(0.835202\pi\) | |||||||
\(948\) | 0.264152 | − | 0.457524i | 0.00857925 | − | 0.0148597i | ||||
\(949\) | 2.51388 | − | 20.6258i | 0.0816039 | − | 0.669543i | ||||
\(950\) | 6.19912 | + | 10.7372i | 0.201126 | + | 0.348361i | ||||
\(951\) | −11.8300 | − | 20.4901i | −0.383613 | − | 0.664437i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.8028 | + | 36.0315i | −0.673868 | + | 1.16717i | 0.302930 | + | 0.953013i | \(0.402035\pi\) |
−0.976798 | + | 0.214161i | \(0.931298\pi\) | |||||||
\(954\) | 33.1791 | + | 57.4680i | 1.07421 | + | 1.86059i | ||||
\(955\) | −27.8100 | − | 48.1684i | −0.899911 | − | 1.55869i | ||||
\(956\) | 1.75694 | + | 3.04311i | 0.0568235 | + | 0.0984211i | ||||
\(957\) | 11.0896 | + | 19.2077i | 0.358476 | + | 0.620898i | ||||
\(958\) | −0.740358 | + | 1.28234i | −0.0239199 | + | 0.0414305i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −36.6013 | − | 63.3954i | −1.18130 | − | 2.04608i | ||||
\(961\) | 15.1194 | + | 26.1876i | 0.487724 | + | 0.844762i | ||||
\(962\) | 5.23460 | + | 3.93725i | 0.168770 | + | 0.126942i | ||||
\(963\) | −24.6653 | + | 42.7215i | −0.794827 | + | 1.37668i | ||||
\(964\) | −0.304141 | + | 0.526788i | −0.00979573 | + | 0.0169667i | ||||
\(965\) | 2.61730 | + | 4.53330i | 0.0842539 | + | 0.145932i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.4500 | 0.721942 | 0.360971 | − | 0.932577i | \(-0.382445\pi\) | ||||
0.360971 | + | 0.932577i | \(0.382445\pi\) | |||||||
\(968\) | 71.7250 | 2.30533 | ||||||||
\(969\) | 3.62181 | + | 6.27316i | 0.116349 | + | 0.201523i | ||||
\(970\) | −14.5875 | + | 25.2662i | −0.468375 | + | 0.811250i | ||||
\(971\) | 10.1251 | 0.324929 | 0.162465 | − | 0.986714i | \(-0.448056\pi\) | ||||
0.162465 | + | 0.986714i | \(0.448056\pi\) | |||||||
\(972\) | −1.61279 | − | 2.79344i | −0.0517303 | − | 0.0895996i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 36.0833 | 1.15618 | ||||||||
\(975\) | −4.15139 | + | 34.0612i | −0.132951 | + | 1.09083i | ||||
\(976\) | 9.51680 | − | 16.4836i | 0.304625 | − | 0.527626i | ||||
\(977\) | −40.0278 | −1.28060 | −0.640301 | − | 0.768124i | \(-0.721190\pi\) | ||||
−0.640301 | + | 0.768124i | \(0.721190\pi\) | |||||||
\(978\) | −32.3043 | + | 55.9526i | −1.03298 | + | 1.78917i | ||||
\(979\) | 25.5369 | − | 44.2311i | 0.816161 | − | 1.41363i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.4680 | − | 28.5235i | 0.525784 | − | 0.910685i | ||||
\(982\) | 16.5778 | 0.529019 | ||||||||
\(983\) | 6.50327 | − | 11.2640i | 0.207422 | − | 0.359265i | −0.743480 | − | 0.668758i | \(-0.766826\pi\) |
0.950902 | + | 0.309493i | \(0.100159\pi\) | |||||||
\(984\) | −32.4500 | − | 56.2050i | −1.03447 | − | 1.79175i | ||||
\(985\) | 17.1566 | − | 29.7162i | 0.546656 | − | 0.946836i | ||||
\(986\) | −0.740358 | − | 1.28234i | −0.0235778 | − | 0.0408380i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.51388 | + | 1.89083i | 0.0799771 | + | 0.0601554i | ||||
\(989\) | −18.2111 | − | 31.5426i | −0.579079 | − | 1.00299i | ||||
\(990\) | 117.611 | 3.73793 | ||||||||
\(991\) | −46.3305 | −1.47174 | −0.735869 | − | 0.677124i | \(-0.763226\pi\) | ||||
−0.735869 | + | 0.677124i | \(0.763226\pi\) | |||||||
\(992\) | −1.48072 | −0.0470128 | ||||||||
\(993\) | 2.00902 | 0.0637543 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.25694 | + | 2.17708i | −0.0398476 | + | 0.0690182i | ||||
\(996\) | −2.89445 | − | 5.01333i | −0.0917141 | − | 0.158854i | ||||
\(997\) | 22.0871 | + | 38.2560i | 0.699506 | + | 1.21158i | 0.968638 | + | 0.248476i | \(0.0799298\pi\) |
−0.269132 | + | 0.963103i | \(0.586737\pi\) | |||||||
\(998\) | −40.8167 | −1.29203 | ||||||||
\(999\) | −4.62632 | + | 8.01302i | −0.146370 | + | 0.253521i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.g.i.263.4 | 8 | ||
7.2 | even | 3 | 637.2.h.j.471.1 | 8 | |||
7.3 | odd | 6 | 637.2.f.h.393.4 | yes | 8 | ||
7.4 | even | 3 | 637.2.f.h.393.3 | yes | 8 | ||
7.5 | odd | 6 | 637.2.h.j.471.2 | 8 | |||
7.6 | odd | 2 | inner | 637.2.g.i.263.3 | 8 | ||
13.9 | even | 3 | 637.2.h.j.165.1 | 8 | |||
91.3 | odd | 6 | 8281.2.a.bu.1.1 | 4 | |||
91.9 | even | 3 | inner | 637.2.g.i.373.4 | 8 | ||
91.10 | odd | 6 | 8281.2.a.bo.1.3 | 4 | |||
91.48 | odd | 6 | 637.2.h.j.165.2 | 8 | |||
91.61 | odd | 6 | inner | 637.2.g.i.373.3 | 8 | ||
91.74 | even | 3 | 637.2.f.h.295.3 | ✓ | 8 | ||
91.81 | even | 3 | 8281.2.a.bu.1.2 | 4 | |||
91.87 | odd | 6 | 637.2.f.h.295.4 | yes | 8 | ||
91.88 | even | 6 | 8281.2.a.bo.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.h.295.3 | ✓ | 8 | 91.74 | even | 3 | ||
637.2.f.h.295.4 | yes | 8 | 91.87 | odd | 6 | ||
637.2.f.h.393.3 | yes | 8 | 7.4 | even | 3 | ||
637.2.f.h.393.4 | yes | 8 | 7.3 | odd | 6 | ||
637.2.g.i.263.3 | 8 | 7.6 | odd | 2 | inner | ||
637.2.g.i.263.4 | 8 | 1.1 | even | 1 | trivial | ||
637.2.g.i.373.3 | 8 | 91.61 | odd | 6 | inner | ||
637.2.g.i.373.4 | 8 | 91.9 | even | 3 | inner | ||
637.2.h.j.165.1 | 8 | 13.9 | even | 3 | |||
637.2.h.j.165.2 | 8 | 91.48 | odd | 6 | |||
637.2.h.j.471.1 | 8 | 7.2 | even | 3 | |||
637.2.h.j.471.2 | 8 | 7.5 | odd | 6 | |||
8281.2.a.bo.1.3 | 4 | 91.10 | odd | 6 | |||
8281.2.a.bo.1.4 | 4 | 91.88 | even | 6 | |||
8281.2.a.bu.1.1 | 4 | 91.3 | odd | 6 | |||
8281.2.a.bu.1.2 | 4 | 91.81 | even | 3 |