Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,2,Mod(11,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.e (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.590892974957\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.11 |
Dual form | 74.2.e.a.27.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −1.36603 | + | 2.36603i | −0.788675 | + | 1.36603i | 0.138104 | + | 0.990418i | \(0.455899\pi\) |
−0.926779 | + | 0.375608i | \(0.877434\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.50000 | − | 0.866025i | −0.670820 | − | 0.387298i | 0.125567 | − | 0.992085i | \(-0.459925\pi\) |
−0.796387 | + | 0.604787i | \(0.793258\pi\) | |||||||
\(6\) | − | 2.73205i | − | 1.11536i | ||||||
\(7\) | −2.00000 | + | 3.46410i | −0.755929 | + | 1.30931i | 0.188982 | + | 0.981981i | \(0.439481\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.23205 | − | 3.86603i | −0.744017 | − | 1.28868i | ||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | 1.36603 | + | 2.36603i | 0.394338 | + | 0.683013i | ||||
\(13\) | 5.19615 | + | 3.00000i | 1.44115 | + | 0.832050i | 0.997927 | − | 0.0643593i | \(-0.0205004\pi\) |
0.443227 | + | 0.896410i | \(0.353834\pi\) | |||||||
\(14\) | − | 4.00000i | − | 1.06904i | ||||||
\(15\) | 4.09808 | − | 2.36603i | 1.05812 | − | 0.610905i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.50000 | + | 0.866025i | −0.363803 | + | 0.210042i | −0.670748 | − | 0.741685i | \(-0.734027\pi\) |
0.306944 | + | 0.951727i | \(0.400693\pi\) | |||||||
\(18\) | 3.86603 | + | 2.23205i | 0.911231 | + | 0.526099i | ||||
\(19\) | 4.09808 | + | 2.36603i | 0.940163 | + | 0.542803i | 0.890011 | − | 0.455938i | \(-0.150696\pi\) |
0.0501517 | + | 0.998742i | \(0.484030\pi\) | |||||||
\(20\) | −1.50000 | + | 0.866025i | −0.335410 | + | 0.193649i | ||||
\(21\) | −5.46410 | − | 9.46410i | −1.19236 | − | 2.06524i | ||||
\(22\) | −1.09808 | + | 0.633975i | −0.234111 | + | 0.135164i | ||||
\(23\) | − | 4.73205i | − | 0.986701i | −0.869831 | − | 0.493350i | \(-0.835772\pi\) | ||
0.869831 | − | 0.493350i | \(-0.164228\pi\) | |||||||
\(24\) | −2.36603 | − | 1.36603i | −0.482963 | − | 0.278839i | ||||
\(25\) | −1.00000 | − | 1.73205i | −0.200000 | − | 0.346410i | ||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 2.00000 | + | 3.46410i | 0.377964 | + | 0.654654i | ||||
\(29\) | 7.73205i | 1.43581i | 0.696143 | + | 0.717903i | \(0.254898\pi\) | ||||
−0.696143 | + | 0.717903i | \(0.745102\pi\) | |||||||
\(30\) | −2.36603 | + | 4.09808i | −0.431975 | + | 0.748203i | ||||
\(31\) | 4.73205i | 0.849901i | 0.905216 | + | 0.424951i | \(0.139709\pi\) | ||||
−0.905216 | + | 0.424951i | \(0.860291\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −1.73205 | + | 3.00000i | −0.301511 | + | 0.522233i | ||||
\(34\) | 0.866025 | − | 1.50000i | 0.148522 | − | 0.257248i | ||||
\(35\) | 6.00000 | − | 3.46410i | 1.01419 | − | 0.585540i | ||||
\(36\) | −4.46410 | −0.744017 | ||||||||
\(37\) | −0.500000 | − | 6.06218i | −0.0821995 | − | 0.996616i | ||||
\(38\) | −4.73205 | −0.767640 | ||||||||
\(39\) | −14.1962 | + | 8.19615i | −2.27320 | + | 1.31243i | ||||
\(40\) | 0.866025 | − | 1.50000i | 0.136931 | − | 0.237171i | ||||
\(41\) | 3.23205 | − | 5.59808i | 0.504762 | − | 0.874273i | −0.495223 | − | 0.868766i | \(-0.664914\pi\) |
0.999985 | − | 0.00550690i | \(-0.00175291\pi\) | |||||||
\(42\) | 9.46410 | + | 5.46410i | 1.46034 | + | 0.843129i | ||||
\(43\) | − | 2.53590i | − | 0.386721i | −0.981128 | − | 0.193360i | \(-0.938061\pi\) | ||
0.981128 | − | 0.193360i | \(-0.0619387\pi\) | |||||||
\(44\) | 0.633975 | − | 1.09808i | 0.0955753 | − | 0.165541i | ||||
\(45\) | 7.73205i | 1.15263i | ||||||||
\(46\) | 2.36603 | + | 4.09808i | 0.348851 | + | 0.604228i | ||||
\(47\) | −5.66025 | −0.825633 | −0.412816 | − | 0.910814i | \(-0.635455\pi\) | ||||
−0.412816 | + | 0.910814i | \(0.635455\pi\) | |||||||
\(48\) | 2.73205 | 0.394338 | ||||||||
\(49\) | −4.50000 | − | 7.79423i | −0.642857 | − | 1.11346i | ||||
\(50\) | 1.73205 | + | 1.00000i | 0.244949 | + | 0.141421i | ||||
\(51\) | − | 4.73205i | − | 0.662620i | ||||||
\(52\) | 5.19615 | − | 3.00000i | 0.720577 | − | 0.416025i | ||||
\(53\) | 4.73205 | + | 8.19615i | 0.649997 | + | 1.12583i | 0.983123 | + | 0.182946i | \(0.0585633\pi\) |
−0.333126 | + | 0.942882i | \(0.608103\pi\) | |||||||
\(54\) | −3.46410 | + | 2.00000i | −0.471405 | + | 0.272166i | ||||
\(55\) | −1.90192 | − | 1.09808i | −0.256455 | − | 0.148065i | ||||
\(56\) | −3.46410 | − | 2.00000i | −0.462910 | − | 0.267261i | ||||
\(57\) | −11.1962 | + | 6.46410i | −1.48297 | + | 0.856191i | ||||
\(58\) | −3.86603 | − | 6.69615i | −0.507634 | − | 0.879248i | ||||
\(59\) | 8.19615 | − | 4.73205i | 1.06705 | − | 0.616061i | 0.139675 | − | 0.990197i | \(-0.455394\pi\) |
0.927373 | + | 0.374137i | \(0.122061\pi\) | |||||||
\(60\) | − | 4.73205i | − | 0.610905i | ||||||
\(61\) | 2.30385 | + | 1.33013i | 0.294977 | + | 0.170305i | 0.640184 | − | 0.768221i | \(-0.278858\pi\) |
−0.345207 | + | 0.938527i | \(0.612191\pi\) | |||||||
\(62\) | −2.36603 | − | 4.09808i | −0.300486 | − | 0.520456i | ||||
\(63\) | 17.8564 | 2.24970 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.19615 | − | 9.00000i | −0.644503 | − | 1.11631i | ||||
\(66\) | − | 3.46410i | − | 0.426401i | ||||||
\(67\) | 2.09808 | − | 3.63397i | 0.256321 | − | 0.443961i | −0.708933 | − | 0.705276i | \(-0.750823\pi\) |
0.965253 | + | 0.261316i | \(0.0841563\pi\) | |||||||
\(68\) | 1.73205i | 0.210042i | ||||||||
\(69\) | 11.1962 | + | 6.46410i | 1.34786 | + | 0.778186i | ||||
\(70\) | −3.46410 | + | 6.00000i | −0.414039 | + | 0.717137i | ||||
\(71\) | −4.73205 | + | 8.19615i | −0.561591 | + | 0.972704i | 0.435767 | + | 0.900060i | \(0.356477\pi\) |
−0.997358 | + | 0.0726447i | \(0.976856\pi\) | |||||||
\(72\) | 3.86603 | − | 2.23205i | 0.455615 | − | 0.263050i | ||||
\(73\) | 8.39230 | 0.982245 | 0.491122 | − | 0.871091i | \(-0.336587\pi\) | ||||
0.491122 | + | 0.871091i | \(0.336587\pi\) | |||||||
\(74\) | 3.46410 | + | 5.00000i | 0.402694 | + | 0.581238i | ||||
\(75\) | 5.46410 | 0.630940 | ||||||||
\(76\) | 4.09808 | − | 2.36603i | 0.470082 | − | 0.271402i | ||||
\(77\) | −2.53590 | + | 4.39230i | −0.288992 | + | 0.500550i | ||||
\(78\) | 8.19615 | − | 14.1962i | 0.928032 | − | 1.60740i | ||||
\(79\) | −1.90192 | − | 1.09808i | −0.213983 | − | 0.123543i | 0.389178 | − | 0.921163i | \(-0.372759\pi\) |
−0.603161 | + | 0.797619i | \(0.706092\pi\) | |||||||
\(80\) | 1.73205i | 0.193649i | ||||||||
\(81\) | 1.23205 | − | 2.13397i | 0.136895 | − | 0.237108i | ||||
\(82\) | 6.46410i | 0.713841i | ||||||||
\(83\) | 2.83013 | + | 4.90192i | 0.310647 | + | 0.538056i | 0.978503 | − | 0.206235i | \(-0.0661210\pi\) |
−0.667856 | + | 0.744291i | \(0.732788\pi\) | |||||||
\(84\) | −10.9282 | −1.19236 | ||||||||
\(85\) | 3.00000 | 0.325396 | ||||||||
\(86\) | 1.26795 | + | 2.19615i | 0.136726 | + | 0.236817i | ||||
\(87\) | −18.2942 | − | 10.5622i | −1.96135 | − | 1.13238i | ||||
\(88\) | 1.26795i | 0.135164i | ||||||||
\(89\) | 4.50000 | − | 2.59808i | 0.476999 | − | 0.275396i | −0.242166 | − | 0.970235i | \(-0.577858\pi\) |
0.719165 | + | 0.694839i | \(0.244525\pi\) | |||||||
\(90\) | −3.86603 | − | 6.69615i | −0.407515 | − | 0.705836i | ||||
\(91\) | −20.7846 | + | 12.0000i | −2.17882 | + | 1.25794i | ||||
\(92\) | −4.09808 | − | 2.36603i | −0.427254 | − | 0.246675i | ||||
\(93\) | −11.1962 | − | 6.46410i | −1.16099 | − | 0.670296i | ||||
\(94\) | 4.90192 | − | 2.83013i | 0.505595 | − | 0.291905i | ||||
\(95\) | −4.09808 | − | 7.09808i | −0.420454 | − | 0.728247i | ||||
\(96\) | −2.36603 | + | 1.36603i | −0.241481 | + | 0.139419i | ||||
\(97\) | 5.19615i | 0.527589i | 0.964579 | + | 0.263795i | \(0.0849741\pi\) | ||||
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | 7.79423 | + | 4.50000i | 0.787336 | + | 0.454569i | ||||
\(99\) | −2.83013 | − | 4.90192i | −0.284438 | − | 0.492662i | ||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 6.46410 | 0.643202 | 0.321601 | − | 0.946875i | \(-0.395779\pi\) | ||||
0.321601 | + | 0.946875i | \(0.395779\pi\) | |||||||
\(102\) | 2.36603 | + | 4.09808i | 0.234271 | + | 0.405770i | ||||
\(103\) | 6.92820i | 0.682656i | 0.939944 | + | 0.341328i | \(0.110877\pi\) | ||||
−0.939944 | + | 0.341328i | \(0.889123\pi\) | |||||||
\(104\) | −3.00000 | + | 5.19615i | −0.294174 | + | 0.509525i | ||||
\(105\) | 18.9282i | 1.84720i | ||||||||
\(106\) | −8.19615 | − | 4.73205i | −0.796081 | − | 0.459617i | ||||
\(107\) | −2.19615 | + | 3.80385i | −0.212310 | + | 0.367732i | −0.952437 | − | 0.304735i | \(-0.901432\pi\) |
0.740127 | + | 0.672467i | \(0.234765\pi\) | |||||||
\(108\) | 2.00000 | − | 3.46410i | 0.192450 | − | 0.333333i | ||||
\(109\) | 3.69615 | − | 2.13397i | 0.354027 | − | 0.204398i | −0.312430 | − | 0.949941i | \(-0.601143\pi\) |
0.666458 | + | 0.745543i | \(0.267810\pi\) | |||||||
\(110\) | 2.19615 | 0.209395 | ||||||||
\(111\) | 15.0263 | + | 7.09808i | 1.42623 | + | 0.673720i | ||||
\(112\) | 4.00000 | 0.377964 | ||||||||
\(113\) | 6.80385 | − | 3.92820i | 0.640052 | − | 0.369534i | −0.144582 | − | 0.989493i | \(-0.546184\pi\) |
0.784635 | + | 0.619958i | \(0.212851\pi\) | |||||||
\(114\) | 6.46410 | − | 11.1962i | 0.605419 | − | 1.04862i | ||||
\(115\) | −4.09808 | + | 7.09808i | −0.382148 | + | 0.661899i | ||||
\(116\) | 6.69615 | + | 3.86603i | 0.621722 | + | 0.358951i | ||||
\(117\) | − | 26.7846i | − | 2.47624i | ||||||
\(118\) | −4.73205 | + | 8.19615i | −0.435621 | + | 0.754517i | ||||
\(119\) | − | 6.92820i | − | 0.635107i | ||||||
\(120\) | 2.36603 | + | 4.09808i | 0.215988 | + | 0.374101i | ||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | −2.66025 | −0.240848 | ||||||||
\(123\) | 8.83013 | + | 15.2942i | 0.796186 | + | 1.37903i | ||||
\(124\) | 4.09808 | + | 2.36603i | 0.368018 | + | 0.212475i | ||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | −15.4641 | + | 8.92820i | −1.37765 | + | 0.795388i | ||||
\(127\) | −10.2942 | − | 17.8301i | −0.913465 | − | 1.58217i | −0.809133 | − | 0.587625i | \(-0.800063\pi\) |
−0.104332 | − | 0.994543i | \(-0.533270\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 6.00000 | + | 3.46410i | 0.528271 | + | 0.304997i | ||||
\(130\) | 9.00000 | + | 5.19615i | 0.789352 | + | 0.455733i | ||||
\(131\) | −1.90192 | + | 1.09808i | −0.166172 | + | 0.0959394i | −0.580780 | − | 0.814061i | \(-0.697252\pi\) |
0.414608 | + | 0.910000i | \(0.363919\pi\) | |||||||
\(132\) | 1.73205 | + | 3.00000i | 0.150756 | + | 0.261116i | ||||
\(133\) | −16.3923 | + | 9.46410i | −1.42139 | + | 0.820642i | ||||
\(134\) | 4.19615i | 0.362492i | ||||||||
\(135\) | −6.00000 | − | 3.46410i | −0.516398 | − | 0.298142i | ||||
\(136\) | −0.866025 | − | 1.50000i | −0.0742611 | − | 0.128624i | ||||
\(137\) | 7.39230 | 0.631567 | 0.315784 | − | 0.948831i | \(-0.397733\pi\) | ||||
0.315784 | + | 0.948831i | \(0.397733\pi\) | |||||||
\(138\) | −12.9282 | −1.10052 | ||||||||
\(139\) | −6.09808 | − | 10.5622i | −0.517232 | − | 0.895872i | −0.999800 | − | 0.0200135i | \(-0.993629\pi\) |
0.482568 | − | 0.875859i | \(-0.339704\pi\) | |||||||
\(140\) | − | 6.92820i | − | 0.585540i | ||||||
\(141\) | 7.73205 | − | 13.3923i | 0.651156 | − | 1.12784i | ||||
\(142\) | − | 9.46410i | − | 0.794210i | ||||||
\(143\) | 6.58846 | + | 3.80385i | 0.550954 | + | 0.318094i | ||||
\(144\) | −2.23205 | + | 3.86603i | −0.186004 | + | 0.322169i | ||||
\(145\) | 6.69615 | − | 11.5981i | 0.556085 | − | 0.963168i | ||||
\(146\) | −7.26795 | + | 4.19615i | −0.601500 | + | 0.347276i | ||||
\(147\) | 24.5885 | 2.02802 | ||||||||
\(148\) | −5.50000 | − | 2.59808i | −0.452097 | − | 0.213561i | ||||
\(149\) | −9.92820 | −0.813350 | −0.406675 | − | 0.913573i | \(-0.633312\pi\) | ||||
−0.406675 | + | 0.913573i | \(0.633312\pi\) | |||||||
\(150\) | −4.73205 | + | 2.73205i | −0.386370 | + | 0.223071i | ||||
\(151\) | 6.09808 | − | 10.5622i | 0.496254 | − | 0.859538i | −0.503736 | − | 0.863857i | \(-0.668042\pi\) |
0.999991 | + | 0.00431966i | \(0.00137499\pi\) | |||||||
\(152\) | −2.36603 | + | 4.09808i | −0.191910 | + | 0.332398i | ||||
\(153\) | 6.69615 | + | 3.86603i | 0.541352 | + | 0.312550i | ||||
\(154\) | − | 5.07180i | − | 0.408697i | ||||||
\(155\) | 4.09808 | − | 7.09808i | 0.329165 | − | 0.570131i | ||||
\(156\) | 16.3923i | 1.31243i | ||||||||
\(157\) | −5.69615 | − | 9.86603i | −0.454602 | − | 0.787395i | 0.544063 | − | 0.839045i | \(-0.316885\pi\) |
−0.998665 | + | 0.0516500i | \(0.983552\pi\) | |||||||
\(158\) | 2.19615 | 0.174717 | ||||||||
\(159\) | −25.8564 | −2.05055 | ||||||||
\(160\) | −0.866025 | − | 1.50000i | −0.0684653 | − | 0.118585i | ||||
\(161\) | 16.3923 | + | 9.46410i | 1.29189 | + | 0.745876i | ||||
\(162\) | 2.46410i | 0.193598i | ||||||||
\(163\) | 8.19615 | − | 4.73205i | 0.641972 | − | 0.370643i | −0.143402 | − | 0.989665i | \(-0.545804\pi\) |
0.785374 | + | 0.619022i | \(0.212471\pi\) | |||||||
\(164\) | −3.23205 | − | 5.59808i | −0.252381 | − | 0.437136i | ||||
\(165\) | 5.19615 | − | 3.00000i | 0.404520 | − | 0.233550i | ||||
\(166\) | −4.90192 | − | 2.83013i | −0.380463 | − | 0.219660i | ||||
\(167\) | −6.00000 | − | 3.46410i | −0.464294 | − | 0.268060i | 0.249554 | − | 0.968361i | \(-0.419716\pi\) |
−0.713848 | + | 0.700301i | \(0.753049\pi\) | |||||||
\(168\) | 9.46410 | − | 5.46410i | 0.730171 | − | 0.421565i | ||||
\(169\) | 11.5000 | + | 19.9186i | 0.884615 | + | 1.53220i | ||||
\(170\) | −2.59808 | + | 1.50000i | −0.199263 | + | 0.115045i | ||||
\(171\) | − | 21.1244i | − | 1.61542i | ||||||
\(172\) | −2.19615 | − | 1.26795i | −0.167455 | − | 0.0966802i | ||||
\(173\) | −1.96410 | − | 3.40192i | −0.149328 | − | 0.258643i | 0.781651 | − | 0.623716i | \(-0.214378\pi\) |
−0.930979 | + | 0.365072i | \(0.881044\pi\) | |||||||
\(174\) | 21.1244 | 1.60143 | ||||||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | −0.633975 | − | 1.09808i | −0.0477876 | − | 0.0827706i | ||||
\(177\) | 25.8564i | 1.94349i | ||||||||
\(178\) | −2.59808 | + | 4.50000i | −0.194734 | + | 0.337289i | ||||
\(179\) | − | 23.3205i | − | 1.74306i | −0.490345 | − | 0.871528i | \(-0.663129\pi\) | ||
0.490345 | − | 0.871528i | \(-0.336871\pi\) | |||||||
\(180\) | 6.69615 | + | 3.86603i | 0.499102 | + | 0.288157i | ||||
\(181\) | −2.69615 | + | 4.66987i | −0.200403 | + | 0.347109i | −0.948658 | − | 0.316302i | \(-0.897559\pi\) |
0.748255 | + | 0.663411i | \(0.230892\pi\) | |||||||
\(182\) | 12.0000 | − | 20.7846i | 0.889499 | − | 1.54066i | ||||
\(183\) | −6.29423 | + | 3.63397i | −0.465283 | + | 0.268631i | ||||
\(184\) | 4.73205 | 0.348851 | ||||||||
\(185\) | −4.50000 | + | 9.52628i | −0.330847 | + | 0.700386i | ||||
\(186\) | 12.9282 | 0.947942 | ||||||||
\(187\) | −1.90192 | + | 1.09808i | −0.139082 | + | 0.0802993i | ||||
\(188\) | −2.83013 | + | 4.90192i | −0.206408 | + | 0.357510i | ||||
\(189\) | −8.00000 | + | 13.8564i | −0.581914 | + | 1.00791i | ||||
\(190\) | 7.09808 | + | 4.09808i | 0.514949 | + | 0.297306i | ||||
\(191\) | 6.58846i | 0.476724i | 0.971176 | + | 0.238362i | \(0.0766105\pi\) | ||||
−0.971176 | + | 0.238362i | \(0.923390\pi\) | |||||||
\(192\) | 1.36603 | − | 2.36603i | 0.0985844 | − | 0.170753i | ||||
\(193\) | − | 12.1244i | − | 0.872730i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) | ||
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | −2.59808 | − | 4.50000i | −0.186531 | − | 0.323081i | ||||
\(195\) | 28.3923 | 2.03322 | ||||||||
\(196\) | −9.00000 | −0.642857 | ||||||||
\(197\) | 4.16025 | + | 7.20577i | 0.296406 | + | 0.513390i | 0.975311 | − | 0.220836i | \(-0.0708786\pi\) |
−0.678905 | + | 0.734226i | \(0.737545\pi\) | |||||||
\(198\) | 4.90192 | + | 2.83013i | 0.348365 | + | 0.201128i | ||||
\(199\) | 18.9282i | 1.34178i | 0.741555 | + | 0.670892i | \(0.234089\pi\) | ||||
−0.741555 | + | 0.670892i | \(0.765911\pi\) | |||||||
\(200\) | 1.73205 | − | 1.00000i | 0.122474 | − | 0.0707107i | ||||
\(201\) | 5.73205 | + | 9.92820i | 0.404308 | + | 0.700281i | ||||
\(202\) | −5.59808 | + | 3.23205i | −0.393879 | + | 0.227406i | ||||
\(203\) | −26.7846 | − | 15.4641i | −1.87991 | − | 1.08537i | ||||
\(204\) | −4.09808 | − | 2.36603i | −0.286923 | − | 0.165655i | ||||
\(205\) | −9.69615 | + | 5.59808i | −0.677209 | + | 0.390987i | ||||
\(206\) | −3.46410 | − | 6.00000i | −0.241355 | − | 0.418040i | ||||
\(207\) | −18.2942 | + | 10.5622i | −1.27154 | + | 0.734122i | ||||
\(208\) | − | 6.00000i | − | 0.416025i | ||||||
\(209\) | 5.19615 | + | 3.00000i | 0.359425 | + | 0.207514i | ||||
\(210\) | −9.46410 | − | 16.3923i | −0.653085 | − | 1.13118i | ||||
\(211\) | −8.39230 | −0.577750 | −0.288875 | − | 0.957367i | \(-0.593281\pi\) | ||||
−0.288875 | + | 0.957367i | \(0.593281\pi\) | |||||||
\(212\) | 9.46410 | 0.649997 | ||||||||
\(213\) | −12.9282 | − | 22.3923i | −0.885826 | − | 1.53430i | ||||
\(214\) | − | 4.39230i | − | 0.300252i | ||||||
\(215\) | −2.19615 | + | 3.80385i | −0.149776 | + | 0.259420i | ||||
\(216\) | 4.00000i | 0.272166i | ||||||||
\(217\) | −16.3923 | − | 9.46410i | −1.11278 | − | 0.642465i | ||||
\(218\) | −2.13397 | + | 3.69615i | −0.144531 | + | 0.250335i | ||||
\(219\) | −11.4641 | + | 19.8564i | −0.774672 | + | 1.34177i | ||||
\(220\) | −1.90192 | + | 1.09808i | −0.128228 | + | 0.0740323i | ||||
\(221\) | −10.3923 | −0.699062 | ||||||||
\(222\) | −16.5622 | + | 1.36603i | −1.11158 | + | 0.0916816i | ||||
\(223\) | 8.58846 | 0.575126 | 0.287563 | − | 0.957762i | \(-0.407155\pi\) | ||||
0.287563 | + | 0.957762i | \(0.407155\pi\) | |||||||
\(224\) | −3.46410 | + | 2.00000i | −0.231455 | + | 0.133631i | ||||
\(225\) | −4.46410 | + | 7.73205i | −0.297607 | + | 0.515470i | ||||
\(226\) | −3.92820 | + | 6.80385i | −0.261300 | + | 0.452585i | ||||
\(227\) | 4.09808 | + | 2.36603i | 0.271999 | + | 0.157039i | 0.629796 | − | 0.776761i | \(-0.283139\pi\) |
−0.357797 | + | 0.933799i | \(0.616472\pi\) | |||||||
\(228\) | 12.9282i | 0.856191i | ||||||||
\(229\) | 9.50000 | − | 16.4545i | 0.627778 | − | 1.08734i | −0.360219 | − | 0.932868i | \(-0.617298\pi\) |
0.987997 | − | 0.154475i | \(-0.0493686\pi\) | |||||||
\(230\) | − | 8.19615i | − | 0.540438i | ||||||
\(231\) | −6.92820 | − | 12.0000i | −0.455842 | − | 0.789542i | ||||
\(232\) | −7.73205 | −0.507634 | ||||||||
\(233\) | −25.3923 | −1.66351 | −0.831753 | − | 0.555146i | \(-0.812662\pi\) | ||||
−0.831753 | + | 0.555146i | \(0.812662\pi\) | |||||||
\(234\) | 13.3923 | + | 23.1962i | 0.875482 | + | 1.51638i | ||||
\(235\) | 8.49038 | + | 4.90192i | 0.553851 | + | 0.319766i | ||||
\(236\) | − | 9.46410i | − | 0.616061i | ||||||
\(237\) | 5.19615 | − | 3.00000i | 0.337526 | − | 0.194871i | ||||
\(238\) | 3.46410 | + | 6.00000i | 0.224544 | + | 0.388922i | ||||
\(239\) | 16.3923 | − | 9.46410i | 1.06033 | − | 0.612182i | 0.134807 | − | 0.990872i | \(-0.456959\pi\) |
0.925524 | + | 0.378690i | \(0.123625\pi\) | |||||||
\(240\) | −4.09808 | − | 2.36603i | −0.264530 | − | 0.152726i | ||||
\(241\) | 15.5885 | + | 9.00000i | 1.00414 | + | 0.579741i | 0.909471 | − | 0.415768i | \(-0.136487\pi\) |
0.0946700 | + | 0.995509i | \(0.469820\pi\) | |||||||
\(242\) | 8.13397 | − | 4.69615i | 0.522872 | − | 0.301880i | ||||
\(243\) | 9.36603 | + | 16.2224i | 0.600831 | + | 1.04067i | ||||
\(244\) | 2.30385 | − | 1.33013i | 0.147489 | − | 0.0851527i | ||||
\(245\) | 15.5885i | 0.995910i | ||||||||
\(246\) | −15.2942 | − | 8.83013i | −0.975124 | − | 0.562988i | ||||
\(247\) | 14.1962 | + | 24.5885i | 0.903280 | + | 1.56453i | ||||
\(248\) | −4.73205 | −0.300486 | ||||||||
\(249\) | −15.4641 | −0.979998 | ||||||||
\(250\) | −6.06218 | − | 10.5000i | −0.383406 | − | 0.664078i | ||||
\(251\) | 18.9282i | 1.19474i | 0.801967 | + | 0.597369i | \(0.203787\pi\) | ||||
−0.801967 | + | 0.597369i | \(0.796213\pi\) | |||||||
\(252\) | 8.92820 | − | 15.4641i | 0.562424 | − | 0.974147i | ||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 17.8301 | + | 10.2942i | 1.11876 | + | 0.645917i | ||||
\(255\) | −4.09808 | + | 7.09808i | −0.256631 | + | 0.444499i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.696152 | + | 0.401924i | −0.0434248 | + | 0.0250713i | −0.521555 | − | 0.853218i | \(-0.674648\pi\) |
0.478130 | + | 0.878289i | \(0.341315\pi\) | |||||||
\(258\) | −6.92820 | −0.431331 | ||||||||
\(259\) | 22.0000 | + | 10.3923i | 1.36701 | + | 0.645746i | ||||
\(260\) | −10.3923 | −0.644503 | ||||||||
\(261\) | 29.8923 | − | 17.2583i | 1.85029 | − | 1.06826i | ||||
\(262\) | 1.09808 | − | 1.90192i | 0.0678394 | − | 0.117501i | ||||
\(263\) | 5.66025 | − | 9.80385i | 0.349026 | − | 0.604531i | −0.637051 | − | 0.770822i | \(-0.719846\pi\) |
0.986077 | + | 0.166291i | \(0.0531791\pi\) | |||||||
\(264\) | −3.00000 | − | 1.73205i | −0.184637 | − | 0.106600i | ||||
\(265\) | − | 16.3923i | − | 1.00697i | ||||||
\(266\) | 9.46410 | − | 16.3923i | 0.580281 | − | 1.00508i | ||||
\(267\) | 14.1962i | 0.868790i | ||||||||
\(268\) | −2.09808 | − | 3.63397i | −0.128160 | − | 0.221980i | ||||
\(269\) | −28.3923 | −1.73111 | −0.865555 | − | 0.500814i | \(-0.833034\pi\) | ||||
−0.865555 | + | 0.500814i | \(0.833034\pi\) | |||||||
\(270\) | 6.92820 | 0.421637 | ||||||||
\(271\) | −8.29423 | − | 14.3660i | −0.503839 | − | 0.872674i | −0.999990 | − | 0.00443801i | \(-0.998587\pi\) |
0.496152 | − | 0.868236i | \(-0.334746\pi\) | |||||||
\(272\) | 1.50000 | + | 0.866025i | 0.0909509 | + | 0.0525105i | ||||
\(273\) | − | 65.5692i | − | 3.96843i | ||||||
\(274\) | −6.40192 | + | 3.69615i | −0.386754 | + | 0.223293i | ||||
\(275\) | −1.26795 | − | 2.19615i | −0.0764602 | − | 0.132433i | ||||
\(276\) | 11.1962 | − | 6.46410i | 0.673929 | − | 0.389093i | ||||
\(277\) | 14.8923 | + | 8.59808i | 0.894792 | + | 0.516608i | 0.875507 | − | 0.483206i | \(-0.160528\pi\) |
0.0192850 | + | 0.999814i | \(0.493861\pi\) | |||||||
\(278\) | 10.5622 | + | 6.09808i | 0.633477 | + | 0.365738i | ||||
\(279\) | 18.2942 | − | 10.5622i | 1.09525 | − | 0.632341i | ||||
\(280\) | 3.46410 | + | 6.00000i | 0.207020 | + | 0.358569i | ||||
\(281\) | 0.696152 | − | 0.401924i | 0.0415290 | − | 0.0239768i | −0.479092 | − | 0.877765i | \(-0.659034\pi\) |
0.520621 | + | 0.853788i | \(0.325701\pi\) | |||||||
\(282\) | 15.4641i | 0.920874i | ||||||||
\(283\) | −8.19615 | − | 4.73205i | −0.487211 | − | 0.281291i | 0.236206 | − | 0.971703i | \(-0.424096\pi\) |
−0.723417 | + | 0.690412i | \(0.757429\pi\) | |||||||
\(284\) | 4.73205 | + | 8.19615i | 0.280796 | + | 0.486352i | ||||
\(285\) | 22.3923 | 1.32641 | ||||||||
\(286\) | −7.60770 | −0.449852 | ||||||||
\(287\) | 12.9282 | + | 22.3923i | 0.763128 | + | 1.32178i | ||||
\(288\) | − | 4.46410i | − | 0.263050i | ||||||
\(289\) | −7.00000 | + | 12.1244i | −0.411765 | + | 0.713197i | ||||
\(290\) | 13.3923i | 0.786423i | ||||||||
\(291\) | −12.2942 | − | 7.09808i | −0.720700 | − | 0.416097i | ||||
\(292\) | 4.19615 | − | 7.26795i | 0.245561 | − | 0.425325i | ||||
\(293\) | −2.30385 | + | 3.99038i | −0.134592 | + | 0.233121i | −0.925442 | − | 0.378890i | \(-0.876306\pi\) |
0.790849 | + | 0.612011i | \(0.209639\pi\) | |||||||
\(294\) | −21.2942 | + | 12.2942i | −1.24190 | + | 0.717014i | ||||
\(295\) | −16.3923 | −0.954397 | ||||||||
\(296\) | 6.06218 | − | 0.500000i | 0.352357 | − | 0.0290619i | ||||
\(297\) | 5.07180 | 0.294295 | ||||||||
\(298\) | 8.59808 | − | 4.96410i | 0.498073 | − | 0.287563i | ||||
\(299\) | 14.1962 | − | 24.5885i | 0.820985 | − | 1.42199i | ||||
\(300\) | 2.73205 | − | 4.73205i | 0.157735 | − | 0.273205i | ||||
\(301\) | 8.78461 | + | 5.07180i | 0.506336 | + | 0.292334i | ||||
\(302\) | 12.1962i | 0.701810i | ||||||||
\(303\) | −8.83013 | + | 15.2942i | −0.507278 | + | 0.878630i | ||||
\(304\) | − | 4.73205i | − | 0.271402i | ||||||
\(305\) | −2.30385 | − | 3.99038i | −0.131918 | − | 0.228489i | ||||
\(306\) | −7.73205 | −0.442012 | ||||||||
\(307\) | −4.00000 | −0.228292 | −0.114146 | − | 0.993464i | \(-0.536413\pi\) | ||||
−0.114146 | + | 0.993464i | \(0.536413\pi\) | |||||||
\(308\) | 2.53590 | + | 4.39230i | 0.144496 | + | 0.250275i | ||||
\(309\) | −16.3923 | − | 9.46410i | −0.932526 | − | 0.538394i | ||||
\(310\) | 8.19615i | 0.465510i | ||||||||
\(311\) | 3.80385 | − | 2.19615i | 0.215696 | − | 0.124532i | −0.388260 | − | 0.921550i | \(-0.626924\pi\) |
0.603956 | + | 0.797018i | \(0.293590\pi\) | |||||||
\(312\) | −8.19615 | − | 14.1962i | −0.464016 | − | 0.803699i | ||||
\(313\) | 8.30385 | − | 4.79423i | 0.469361 | − | 0.270986i | −0.246611 | − | 0.969115i | \(-0.579317\pi\) |
0.715972 | + | 0.698129i | \(0.245984\pi\) | |||||||
\(314\) | 9.86603 | + | 5.69615i | 0.556772 | + | 0.321452i | ||||
\(315\) | −26.7846 | − | 15.4641i | −1.50914 | − | 0.871303i | ||||
\(316\) | −1.90192 | + | 1.09808i | −0.106992 | + | 0.0617716i | ||||
\(317\) | −4.50000 | − | 7.79423i | −0.252745 | − | 0.437767i | 0.711535 | − | 0.702650i | \(-0.248000\pi\) |
−0.964281 | + | 0.264883i | \(0.914667\pi\) | |||||||
\(318\) | 22.3923 | − | 12.9282i | 1.25570 | − | 0.724978i | ||||
\(319\) | 9.80385i | 0.548910i | ||||||||
\(320\) | 1.50000 | + | 0.866025i | 0.0838525 | + | 0.0484123i | ||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | −18.9282 | −1.05483 | ||||||||
\(323\) | −8.19615 | −0.456046 | ||||||||
\(324\) | −1.23205 | − | 2.13397i | −0.0684473 | − | 0.118554i | ||||
\(325\) | − | 12.0000i | − | 0.665640i | ||||||
\(326\) | −4.73205 | + | 8.19615i | −0.262084 | + | 0.453943i | ||||
\(327\) | 11.6603i | 0.644814i | ||||||||
\(328\) | 5.59808 | + | 3.23205i | 0.309102 | + | 0.178460i | ||||
\(329\) | 11.3205 | − | 19.6077i | 0.624120 | − | 1.08101i | ||||
\(330\) | −3.00000 | + | 5.19615i | −0.165145 | + | 0.286039i | ||||
\(331\) | 14.7846 | − | 8.53590i | 0.812636 | − | 0.469175i | −0.0352347 | − | 0.999379i | \(-0.511218\pi\) |
0.847870 | + | 0.530204i | \(0.177885\pi\) | |||||||
\(332\) | 5.66025 | 0.310647 | ||||||||
\(333\) | −22.3205 | + | 15.4641i | −1.22316 | + | 0.847428i | ||||
\(334\) | 6.92820 | 0.379094 | ||||||||
\(335\) | −6.29423 | + | 3.63397i | −0.343890 | + | 0.198545i | ||||
\(336\) | −5.46410 | + | 9.46410i | −0.298091 | + | 0.516309i | ||||
\(337\) | 3.50000 | − | 6.06218i | 0.190657 | − | 0.330228i | −0.754811 | − | 0.655942i | \(-0.772271\pi\) |
0.945468 | + | 0.325714i | \(0.105605\pi\) | |||||||
\(338\) | −19.9186 | − | 11.5000i | −1.08343 | − | 0.625518i | ||||
\(339\) | 21.4641i | 1.16577i | ||||||||
\(340\) | 1.50000 | − | 2.59808i | 0.0813489 | − | 0.140900i | ||||
\(341\) | 6.00000i | 0.324918i | ||||||||
\(342\) | 10.5622 | + | 18.2942i | 0.571137 | + | 0.989239i | ||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 2.53590 | 0.136726 | ||||||||
\(345\) | −11.1962 | − | 19.3923i | −0.602781 | − | 1.04405i | ||||
\(346\) | 3.40192 | + | 1.96410i | 0.182889 | + | 0.105591i | ||||
\(347\) | 28.0526i | 1.50594i | 0.658055 | + | 0.752970i | \(0.271380\pi\) | ||||
−0.658055 | + | 0.752970i | \(0.728620\pi\) | |||||||
\(348\) | −18.2942 | + | 10.5622i | −0.980674 | + | 0.566192i | ||||
\(349\) | 13.6962 | + | 23.7224i | 0.733138 | + | 1.26983i | 0.955535 | + | 0.294877i | \(0.0952785\pi\) |
−0.222397 | + | 0.974956i | \(0.571388\pi\) | |||||||
\(350\) | −6.92820 | + | 4.00000i | −0.370328 | + | 0.213809i | ||||
\(351\) | 20.7846 | + | 12.0000i | 1.10940 | + | 0.640513i | ||||
\(352\) | 1.09808 | + | 0.633975i | 0.0585277 | + | 0.0337910i | ||||
\(353\) | −5.08846 | + | 2.93782i | −0.270831 | + | 0.156364i | −0.629265 | − | 0.777191i | \(-0.716644\pi\) |
0.358434 | + | 0.933555i | \(0.383311\pi\) | |||||||
\(354\) | −12.9282 | − | 22.3923i | −0.687126 | − | 1.19014i | ||||
\(355\) | 14.1962 | − | 8.19615i | 0.753454 | − | 0.435007i | ||||
\(356\) | − | 5.19615i | − | 0.275396i | ||||||
\(357\) | 16.3923 | + | 9.46410i | 0.867573 | + | 0.500893i | ||||
\(358\) | 11.6603 | + | 20.1962i | 0.616264 | + | 1.06740i | ||||
\(359\) | 26.5359 | 1.40051 | 0.700256 | − | 0.713892i | \(-0.253069\pi\) | ||||
0.700256 | + | 0.713892i | \(0.253069\pi\) | |||||||
\(360\) | −7.73205 | −0.407515 | ||||||||
\(361\) | 1.69615 | + | 2.93782i | 0.0892712 | + | 0.154622i | ||||
\(362\) | − | 5.39230i | − | 0.283413i | ||||||
\(363\) | 12.8301 | − | 22.2224i | 0.673407 | − | 1.16638i | ||||
\(364\) | 24.0000i | 1.25794i | ||||||||
\(365\) | −12.5885 | − | 7.26795i | −0.658910 | − | 0.380422i | ||||
\(366\) | 3.63397 | − | 6.29423i | 0.189951 | − | 0.329005i | ||||
\(367\) | 10.1962 | − | 17.6603i | 0.532235 | − | 0.921858i | −0.467057 | − | 0.884227i | \(-0.654686\pi\) |
0.999292 | − | 0.0376305i | \(-0.0119810\pi\) | |||||||
\(368\) | −4.09808 | + | 2.36603i | −0.213627 | + | 0.123338i | ||||
\(369\) | −28.8564 | −1.50220 | ||||||||
\(370\) | −0.866025 | − | 10.5000i | −0.0450225 | − | 0.545869i | ||||
\(371\) | −37.8564 | −1.96541 | ||||||||
\(372\) | −11.1962 | + | 6.46410i | −0.580493 | + | 0.335148i | ||||
\(373\) | −10.8923 | + | 18.8660i | −0.563982 | + | 0.976846i | 0.433161 | + | 0.901316i | \(0.357398\pi\) |
−0.997144 | + | 0.0755294i | \(0.975935\pi\) | |||||||
\(374\) | 1.09808 | − | 1.90192i | 0.0567802 | − | 0.0983461i | ||||
\(375\) | −28.6865 | − | 16.5622i | −1.48137 | − | 0.855267i | ||||
\(376\) | − | 5.66025i | − | 0.291905i | ||||||
\(377\) | −23.1962 | + | 40.1769i | −1.19466 | + | 2.06922i | ||||
\(378\) | − | 16.0000i | − | 0.822951i | ||||||
\(379\) | 8.39230 | + | 14.5359i | 0.431084 | + | 0.746659i | 0.996967 | − | 0.0778265i | \(-0.0247980\pi\) |
−0.565883 | + | 0.824485i | \(0.691465\pi\) | |||||||
\(380\) | −8.19615 | −0.420454 | ||||||||
\(381\) | 56.2487 | 2.88171 | ||||||||
\(382\) | −3.29423 | − | 5.70577i | −0.168547 | − | 0.291933i | ||||
\(383\) | 1.60770 | + | 0.928203i | 0.0821494 | + | 0.0474290i | 0.540512 | − | 0.841336i | \(-0.318231\pi\) |
−0.458363 | + | 0.888765i | \(0.651564\pi\) | |||||||
\(384\) | 2.73205i | 0.139419i | ||||||||
\(385\) | 7.60770 | − | 4.39230i | 0.387724 | − | 0.223853i | ||||
\(386\) | 6.06218 | + | 10.5000i | 0.308557 | + | 0.534436i | ||||
\(387\) | −9.80385 | + | 5.66025i | −0.498358 | + | 0.287727i | ||||
\(388\) | 4.50000 | + | 2.59808i | 0.228453 | + | 0.131897i | ||||
\(389\) | −9.69615 | − | 5.59808i | −0.491614 | − | 0.283834i | 0.233630 | − | 0.972326i | \(-0.424940\pi\) |
−0.725244 | + | 0.688492i | \(0.758273\pi\) | |||||||
\(390\) | −24.5885 | + | 14.1962i | −1.24508 | + | 0.718850i | ||||
\(391\) | 4.09808 | + | 7.09808i | 0.207249 | + | 0.358965i | ||||
\(392\) | 7.79423 | − | 4.50000i | 0.393668 | − | 0.227284i | ||||
\(393\) | − | 6.00000i | − | 0.302660i | ||||||
\(394\) | −7.20577 | − | 4.16025i | −0.363022 | − | 0.209591i | ||||
\(395\) | 1.90192 | + | 3.29423i | 0.0956962 | + | 0.165751i | ||||
\(396\) | −5.66025 | −0.284438 | ||||||||
\(397\) | −5.00000 | −0.250943 | −0.125471 | − | 0.992097i | \(-0.540044\pi\) | ||||
−0.125471 | + | 0.992097i | \(0.540044\pi\) | |||||||
\(398\) | −9.46410 | − | 16.3923i | −0.474393 | − | 0.821672i | ||||
\(399\) | − | 51.7128i | − | 2.58888i | ||||||
\(400\) | −1.00000 | + | 1.73205i | −0.0500000 | + | 0.0866025i | ||||
\(401\) | − | 26.7846i | − | 1.33756i | −0.743461 | − | 0.668780i | \(-0.766817\pi\) | ||
0.743461 | − | 0.668780i | \(-0.233183\pi\) | |||||||
\(402\) | −9.92820 | − | 5.73205i | −0.495174 | − | 0.285889i | ||||
\(403\) | −14.1962 | + | 24.5885i | −0.707161 | + | 1.22484i | ||||
\(404\) | 3.23205 | − | 5.59808i | 0.160801 | − | 0.278515i | ||||
\(405\) | −3.69615 | + | 2.13397i | −0.183663 | + | 0.106038i | ||||
\(406\) | 30.9282 | 1.53494 | ||||||||
\(407\) | −0.633975 | − | 7.68653i | −0.0314250 | − | 0.381007i | ||||
\(408\) | 4.73205 | 0.234271 | ||||||||
\(409\) | 2.08846 | − | 1.20577i | 0.103268 | − | 0.0596216i | −0.447477 | − | 0.894296i | \(-0.647677\pi\) |
0.550744 | + | 0.834674i | \(0.314344\pi\) | |||||||
\(410\) | 5.59808 | − | 9.69615i | 0.276469 | − | 0.478859i | ||||
\(411\) | −10.0981 | + | 17.4904i | −0.498101 | + | 0.862737i | ||||
\(412\) | 6.00000 | + | 3.46410i | 0.295599 | + | 0.170664i | ||||
\(413\) | 37.8564i | 1.86279i | ||||||||
\(414\) | 10.5622 | − | 18.2942i | 0.519103 | − | 0.899112i | ||||
\(415\) | − | 9.80385i | − | 0.481252i | ||||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | 33.3205 | 1.63171 | ||||||||
\(418\) | −6.00000 | −0.293470 | ||||||||
\(419\) | −18.9282 | − | 32.7846i | −0.924703 | − | 1.60163i | −0.792038 | − | 0.610472i | \(-0.790980\pi\) |
−0.132665 | − | 0.991161i | \(-0.542354\pi\) | |||||||
\(420\) | 16.3923 | + | 9.46410i | 0.799863 | + | 0.461801i | ||||
\(421\) | − | 20.6603i | − | 1.00692i | −0.864019 | − | 0.503460i | \(-0.832060\pi\) | ||
0.864019 | − | 0.503460i | \(-0.167940\pi\) | |||||||
\(422\) | 7.26795 | − | 4.19615i | 0.353798 | − | 0.204266i | ||||
\(423\) | 12.6340 | + | 21.8827i | 0.614285 | + | 1.06397i | ||||
\(424\) | −8.19615 | + | 4.73205i | −0.398040 | + | 0.229809i | ||||
\(425\) | 3.00000 | + | 1.73205i | 0.145521 | + | 0.0840168i | ||||
\(426\) | 22.3923 | + | 12.9282i | 1.08491 | + | 0.626373i | ||||
\(427\) | −9.21539 | + | 5.32051i | −0.445964 | + | 0.257477i | ||||
\(428\) | 2.19615 | + | 3.80385i | 0.106155 | + | 0.183866i | ||||
\(429\) | −18.0000 | + | 10.3923i | −0.869048 | + | 0.501745i | ||||
\(430\) | − | 4.39230i | − | 0.211816i | ||||||
\(431\) | 13.9019 | + | 8.02628i | 0.669632 | + | 0.386612i | 0.795937 | − | 0.605379i | \(-0.206979\pi\) |
−0.126305 | + | 0.991991i | \(0.540312\pi\) | |||||||
\(432\) | −2.00000 | − | 3.46410i | −0.0962250 | − | 0.166667i | ||||
\(433\) | −33.3923 | −1.60473 | −0.802366 | − | 0.596832i | \(-0.796426\pi\) | ||||
−0.802366 | + | 0.596832i | \(0.796426\pi\) | |||||||
\(434\) | 18.9282 | 0.908583 | ||||||||
\(435\) | 18.2942 | + | 31.6865i | 0.877141 | + | 1.51925i | ||||
\(436\) | − | 4.26795i | − | 0.204398i | ||||||
\(437\) | 11.1962 | − | 19.3923i | 0.535585 | − | 0.927660i | ||||
\(438\) | − | 22.9282i | − | 1.09555i | ||||||
\(439\) | −8.19615 | − | 4.73205i | −0.391181 | − | 0.225848i | 0.291491 | − | 0.956574i | \(-0.405849\pi\) |
−0.682672 | + | 0.730725i | \(0.739182\pi\) | |||||||
\(440\) | 1.09808 | − | 1.90192i | 0.0523487 | − | 0.0906707i | ||||
\(441\) | −20.0885 | + | 34.7942i | −0.956593 | + | 1.65687i | ||||
\(442\) | 9.00000 | − | 5.19615i | 0.428086 | − | 0.247156i | ||||
\(443\) | −2.53590 | −0.120484 | −0.0602421 | − | 0.998184i | \(-0.519187\pi\) | ||||
−0.0602421 | + | 0.998184i | \(0.519187\pi\) | |||||||
\(444\) | 13.6603 | − | 9.46410i | 0.648287 | − | 0.449146i | ||||
\(445\) | −9.00000 | −0.426641 | ||||||||
\(446\) | −7.43782 | + | 4.29423i | −0.352191 | + | 0.203338i | ||||
\(447\) | 13.5622 | − | 23.4904i | 0.641469 | − | 1.11106i | ||||
\(448\) | 2.00000 | − | 3.46410i | 0.0944911 | − | 0.163663i | ||||
\(449\) | −21.5885 | − | 12.4641i | −1.01882 | − | 0.588217i | −0.105060 | − | 0.994466i | \(-0.533503\pi\) |
−0.913763 | + | 0.406249i | \(0.866837\pi\) | |||||||
\(450\) | − | 8.92820i | − | 0.420880i | ||||||
\(451\) | 4.09808 | − | 7.09808i | 0.192971 | − | 0.334235i | ||||
\(452\) | − | 7.85641i | − | 0.369534i | ||||||
\(453\) | 16.6603 | + | 28.8564i | 0.782767 | + | 1.35579i | ||||
\(454\) | −4.73205 | −0.222086 | ||||||||
\(455\) | 41.5692 | 1.94880 | ||||||||
\(456\) | −6.46410 | − | 11.1962i | −0.302709 | − | 0.524308i | ||||
\(457\) | 17.3038 | + | 9.99038i | 0.809440 | + | 0.467330i | 0.846761 | − | 0.531973i | \(-0.178549\pi\) |
−0.0373215 | + | 0.999303i | \(0.511883\pi\) | |||||||
\(458\) | 19.0000i | 0.887812i | ||||||||
\(459\) | −6.00000 | + | 3.46410i | −0.280056 | + | 0.161690i | ||||
\(460\) | 4.09808 | + | 7.09808i | 0.191074 | + | 0.330950i | ||||
\(461\) | −29.1962 | + | 16.8564i | −1.35980 | + | 0.785081i | −0.989597 | − | 0.143869i | \(-0.954045\pi\) |
−0.370204 | + | 0.928951i | \(0.620712\pi\) | |||||||
\(462\) | 12.0000 | + | 6.92820i | 0.558291 | + | 0.322329i | ||||
\(463\) | −12.5885 | − | 7.26795i | −0.585035 | − | 0.337770i | 0.178097 | − | 0.984013i | \(-0.443006\pi\) |
−0.763132 | + | 0.646243i | \(0.776339\pi\) | |||||||
\(464\) | 6.69615 | − | 3.86603i | 0.310861 | − | 0.179476i | ||||
\(465\) | 11.1962 | + | 19.3923i | 0.519209 | + | 0.899297i | ||||
\(466\) | 21.9904 | − | 12.6962i | 1.01868 | − | 0.588138i | ||||
\(467\) | − | 30.2487i | − | 1.39974i | −0.714269 | − | 0.699872i | \(-0.753240\pi\) | ||
0.714269 | − | 0.699872i | \(-0.246760\pi\) | |||||||
\(468\) | −23.1962 | − | 13.3923i | −1.07224 | − | 0.619060i | ||||
\(469\) | 8.39230 | + | 14.5359i | 0.387521 | + | 0.671205i | ||||
\(470\) | −9.80385 | −0.452218 | ||||||||
\(471\) | 31.1244 | 1.43413 | ||||||||
\(472\) | 4.73205 | + | 8.19615i | 0.217810 | + | 0.377258i | ||||
\(473\) | − | 3.21539i | − | 0.147844i | ||||||
\(474\) | −3.00000 | + | 5.19615i | −0.137795 | + | 0.238667i | ||||
\(475\) | − | 9.46410i | − | 0.434243i | ||||||
\(476\) | −6.00000 | − | 3.46410i | −0.275010 | − | 0.158777i | ||||
\(477\) | 21.1244 | − | 36.5885i | 0.967218 | − | 1.67527i | ||||
\(478\) | −9.46410 | + | 16.3923i | −0.432878 | + | 0.749767i | ||||
\(479\) | −8.19615 | + | 4.73205i | −0.374492 | + | 0.216213i | −0.675419 | − | 0.737434i | \(-0.736037\pi\) |
0.300927 | + | 0.953647i | \(0.402704\pi\) | |||||||
\(480\) | 4.73205 | 0.215988 | ||||||||
\(481\) | 15.5885 | − | 33.0000i | 0.710772 | − | 1.50467i | ||||
\(482\) | −18.0000 | −0.819878 | ||||||||
\(483\) | −44.7846 | + | 25.8564i | −2.03777 | + | 1.17651i | ||||
\(484\) | −4.69615 | + | 8.13397i | −0.213461 | + | 0.369726i | ||||
\(485\) | 4.50000 | − | 7.79423i | 0.204334 | − | 0.353918i | ||||
\(486\) | −16.2224 | − | 9.36603i | −0.735864 | − | 0.424852i | ||||
\(487\) | − | 28.0526i | − | 1.27118i | −0.772026 | − | 0.635591i | \(-0.780756\pi\) | ||
0.772026 | − | 0.635591i | \(-0.219244\pi\) | |||||||
\(488\) | −1.33013 | + | 2.30385i | −0.0602120 | + | 0.104290i | ||||
\(489\) | 25.8564i | 1.16927i | ||||||||
\(490\) | −7.79423 | − | 13.5000i | −0.352107 | − | 0.609868i | ||||
\(491\) | 28.9808 | 1.30788 | 0.653942 | − | 0.756545i | \(-0.273114\pi\) | ||||
0.653942 | + | 0.756545i | \(0.273114\pi\) | |||||||
\(492\) | 17.6603 | 0.796186 | ||||||||
\(493\) | −6.69615 | − | 11.5981i | −0.301580 | − | 0.522351i | ||||
\(494\) | −24.5885 | − | 14.1962i | −1.10629 | − | 0.638715i | ||||
\(495\) | 9.80385i | 0.440650i | ||||||||
\(496\) | 4.09808 | − | 2.36603i | 0.184009 | − | 0.106238i | ||||
\(497\) | −18.9282 | − | 32.7846i | −0.849046 | − | 1.47059i | ||||
\(498\) | 13.3923 | − | 7.73205i | 0.600124 | − | 0.346481i | ||||
\(499\) | 1.90192 | + | 1.09808i | 0.0851418 | + | 0.0491566i | 0.541966 | − | 0.840400i | \(-0.317680\pi\) |
−0.456825 | + | 0.889557i | \(0.651013\pi\) | |||||||
\(500\) | 10.5000 | + | 6.06218i | 0.469574 | + | 0.271109i | ||||
\(501\) | 16.3923 | − | 9.46410i | 0.732354 | − | 0.422825i | ||||
\(502\) | −9.46410 | − | 16.3923i | −0.422404 | − | 0.731624i | ||||
\(503\) | 16.0981 | − | 9.29423i | 0.717778 | − | 0.414409i | −0.0961565 | − | 0.995366i | \(-0.530655\pi\) |
0.813934 | + | 0.580957i | \(0.197322\pi\) | |||||||
\(504\) | 17.8564i | 0.795388i | ||||||||
\(505\) | −9.69615 | − | 5.59808i | −0.431473 | − | 0.249111i | ||||
\(506\) | 3.00000 | + | 5.19615i | 0.133366 | + | 0.230997i | ||||
\(507\) | −62.8372 | −2.79070 | ||||||||
\(508\) | −20.5885 | −0.913465 | ||||||||
\(509\) | 18.8205 | + | 32.5981i | 0.834204 | + | 1.44488i | 0.894677 | + | 0.446714i | \(0.147406\pi\) |
−0.0604722 | + | 0.998170i | \(0.519261\pi\) | |||||||
\(510\) | − | 8.19615i | − | 0.362932i | ||||||
\(511\) | −16.7846 | + | 29.0718i | −0.742507 | + | 1.28606i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 16.3923 | + | 9.46410i | 0.723738 | + | 0.417850i | ||||
\(514\) | 0.401924 | − | 0.696152i | 0.0177281 | − | 0.0307060i | ||||
\(515\) | 6.00000 | − | 10.3923i | 0.264392 | − | 0.457940i | ||||
\(516\) | 6.00000 | − | 3.46410i | 0.264135 | − | 0.152499i | ||||
\(517\) | −7.17691 | −0.315640 | ||||||||
\(518\) | −24.2487 | + | 2.00000i | −1.06543 | + | 0.0878750i | ||||
\(519\) | 10.7321 | 0.471085 | ||||||||
\(520\) | 9.00000 | − | 5.19615i | 0.394676 | − | 0.227866i | ||||
\(521\) | −16.7321 | + | 28.9808i | −0.733044 | + | 1.26967i | 0.222532 | + | 0.974925i | \(0.428568\pi\) |
−0.955576 | + | 0.294745i | \(0.904765\pi\) | |||||||
\(522\) | −17.2583 | + | 29.8923i | −0.755377 | + | 1.30835i | ||||
\(523\) | 16.0981 | + | 9.29423i | 0.703920 | + | 0.406408i | 0.808806 | − | 0.588076i | \(-0.200114\pi\) |
−0.104886 | + | 0.994484i | \(0.533448\pi\) | |||||||
\(524\) | 2.19615i | 0.0959394i | ||||||||
\(525\) | −10.9282 | + | 18.9282i | −0.476946 | + | 0.826095i | ||||
\(526\) | 11.3205i | 0.493598i | ||||||||
\(527\) | −4.09808 | − | 7.09808i | −0.178515 | − | 0.309197i | ||||
\(528\) | 3.46410 | 0.150756 | ||||||||
\(529\) | 0.607695 | 0.0264215 | ||||||||
\(530\) | 8.19615 | + | 14.1962i | 0.356018 | + | 0.616641i | ||||
\(531\) | −36.5885 | − | 21.1244i | −1.58780 | − | 0.916719i | ||||
\(532\) | 18.9282i | 0.820642i | ||||||||
\(533\) | 33.5885 | − | 19.3923i | 1.45488 | − | 0.839974i | ||||
\(534\) | −7.09808 | − | 12.2942i | −0.307164 | − | 0.532023i | ||||
\(535\) | 6.58846 | − | 3.80385i | 0.284844 | − | 0.164455i | ||||
\(536\) | 3.63397 | + | 2.09808i | 0.156964 | + | 0.0906231i | ||||
\(537\) | 55.1769 | + | 31.8564i | 2.38106 | + | 1.37471i | ||||
\(538\) | 24.5885 | − | 14.1962i | 1.06008 | − | 0.612040i | ||||
\(539\) | −5.70577 | − | 9.88269i | −0.245765 | − | 0.425677i | ||||
\(540\) | −6.00000 | + | 3.46410i | −0.258199 | + | 0.149071i | ||||
\(541\) | 27.5885i | 1.18612i | 0.805158 | + | 0.593060i | \(0.202080\pi\) | ||||
−0.805158 | + | 0.593060i | \(0.797920\pi\) | |||||||
\(542\) | 14.3660 | + | 8.29423i | 0.617074 | + | 0.356268i | ||||
\(543\) | −7.36603 | − | 12.7583i | −0.316106 | − | 0.547512i | ||||
\(544\) | −1.73205 | −0.0742611 | ||||||||
\(545\) | −7.39230 | −0.316652 | ||||||||
\(546\) | 32.7846 | + | 56.7846i | 1.40305 | + | 2.43016i | ||||
\(547\) | − | 18.5885i | − | 0.794785i | −0.917649 | − | 0.397393i | \(-0.869915\pi\) | ||
0.917649 | − | 0.397393i | \(-0.130085\pi\) | |||||||
\(548\) | 3.69615 | − | 6.40192i | 0.157892 | − | 0.273477i | ||||
\(549\) | − | 11.8756i | − | 0.506840i | ||||||
\(550\) | 2.19615 | + | 1.26795i | 0.0936443 | + | 0.0540655i | ||||
\(551\) | −18.2942 | + | 31.6865i | −0.779360 | + | 1.34989i | ||||
\(552\) | −6.46410 | + | 11.1962i | −0.275130 | + | 0.476540i | ||||
\(553\) | 7.60770 | − | 4.39230i | 0.323512 | − | 0.186780i | ||||
\(554\) | −17.1962 | −0.730595 | ||||||||
\(555\) | −16.3923 | − | 23.6603i | −0.695815 | − | 1.00432i | ||||
\(556\) | −12.1962 | −0.517232 | ||||||||
\(557\) | 29.8923 | − | 17.2583i | 1.26658 | − | 0.731259i | 0.292239 | − | 0.956345i | \(-0.405600\pi\) |
0.974339 | + | 0.225086i | \(0.0722665\pi\) | |||||||
\(558\) | −10.5622 | + | 18.2942i | −0.447133 | + | 0.774456i | ||||
\(559\) | 7.60770 | − | 13.1769i | 0.321771 | − | 0.557324i | ||||
\(560\) | −6.00000 | − | 3.46410i | −0.253546 | − | 0.146385i | ||||
\(561\) | − | 6.00000i | − | 0.253320i | ||||||
\(562\) | −0.401924 | + | 0.696152i | −0.0169541 | + | 0.0293654i | ||||
\(563\) | − | 42.5885i | − | 1.79489i | −0.441127 | − | 0.897445i | \(-0.645421\pi\) | ||
0.441127 | − | 0.897445i | \(-0.354579\pi\) | |||||||
\(564\) | −7.73205 | − | 13.3923i | −0.325578 | − | 0.563918i | ||||
\(565\) | −13.6077 | −0.572480 | ||||||||
\(566\) | 9.46410 | 0.397806 | ||||||||
\(567\) | 4.92820 | + | 8.53590i | 0.206965 | + | 0.358474i | ||||
\(568\) | −8.19615 | − | 4.73205i | −0.343903 | − | 0.198552i | ||||
\(569\) | − | 16.5167i | − | 0.692414i | −0.938158 | − | 0.346207i | \(-0.887469\pi\) | ||
0.938158 | − | 0.346207i | \(-0.112531\pi\) | |||||||
\(570\) | −19.3923 | + | 11.1962i | −0.812254 | + | 0.468955i | ||||
\(571\) | 18.4904 | + | 32.0263i | 0.773798 | + | 1.34026i | 0.935467 | + | 0.353413i | \(0.114979\pi\) |
−0.161669 | + | 0.986845i | \(0.551688\pi\) | |||||||
\(572\) | 6.58846 | − | 3.80385i | 0.275477 | − | 0.159047i | ||||
\(573\) | −15.5885 | − | 9.00000i | −0.651217 | − | 0.375980i | ||||
\(574\) | −22.3923 | − | 12.9282i | −0.934637 | − | 0.539613i | ||||
\(575\) | −8.19615 | + | 4.73205i | −0.341803 | + | 0.197340i | ||||
\(576\) | 2.23205 | + | 3.86603i | 0.0930021 | + | 0.161084i | ||||
\(577\) | −27.5885 | + | 15.9282i | −1.14852 | + | 0.663100i | −0.948527 | − | 0.316697i | \(-0.897426\pi\) |
−0.199996 | + | 0.979797i | \(0.564093\pi\) | |||||||
\(578\) | − | 14.0000i | − | 0.582323i | ||||||
\(579\) | 28.6865 | + | 16.5622i | 1.19217 | + | 0.688301i | ||||
\(580\) | −6.69615 | − | 11.5981i | −0.278043 | − | 0.481584i | ||||
\(581\) | −22.6410 | −0.939308 | ||||||||
\(582\) | 14.1962 | 0.588449 | ||||||||
\(583\) | 6.00000 | + | 10.3923i | 0.248495 | + | 0.430405i | ||||
\(584\) | 8.39230i | 0.347276i | ||||||||
\(585\) | −23.1962 | + | 40.1769i | −0.959043 | + | 1.66111i | ||||
\(586\) | − | 4.60770i | − | 0.190342i | ||||||
\(587\) | 13.9019 | + | 8.02628i | 0.573794 | + | 0.331280i | 0.758663 | − | 0.651483i | \(-0.225853\pi\) |
−0.184869 | + | 0.982763i | \(0.559186\pi\) | |||||||
\(588\) | 12.2942 | − | 21.2942i | 0.507005 | − | 0.878159i | ||||
\(589\) | −11.1962 | + | 19.3923i | −0.461329 | + | 0.799046i | ||||
\(590\) | 14.1962 | − | 8.19615i | 0.584446 | − | 0.337430i | ||||
\(591\) | −22.7321 | −0.935072 | ||||||||
\(592\) | −5.00000 | + | 3.46410i | −0.205499 | + | 0.142374i | ||||
\(593\) | 30.4641 | 1.25101 | 0.625505 | − | 0.780220i | \(-0.284893\pi\) | ||||
0.625505 | + | 0.780220i | \(0.284893\pi\) | |||||||
\(594\) | −4.39230 | + | 2.53590i | −0.180218 | + | 0.104049i | ||||
\(595\) | −6.00000 | + | 10.3923i | −0.245976 | + | 0.426043i | ||||
\(596\) | −4.96410 | + | 8.59808i | −0.203338 | + | 0.352191i | ||||
\(597\) | −44.7846 | − | 25.8564i | −1.83291 | − | 1.05823i | ||||
\(598\) | 28.3923i | 1.16105i | ||||||||
\(599\) | −0.633975 | + | 1.09808i | −0.0259035 | + | 0.0448662i | −0.878687 | − | 0.477399i | \(-0.841580\pi\) |
0.852783 | + | 0.522265i | \(0.174913\pi\) | |||||||
\(600\) | 5.46410i | 0.223071i | ||||||||
\(601\) | −7.89230 | − | 13.6699i | −0.321934 | − | 0.557606i | 0.658953 | − | 0.752184i | \(-0.271000\pi\) |
−0.980887 | + | 0.194578i | \(0.937666\pi\) | |||||||
\(602\) | −10.1436 | −0.413422 | ||||||||
\(603\) | −18.7321 | −0.762828 | ||||||||
\(604\) | −6.09808 | − | 10.5622i | −0.248127 | − | 0.429769i | ||||
\(605\) | 14.0885 | + | 8.13397i | 0.572777 | + | 0.330693i | ||||
\(606\) | − | 17.6603i | − | 0.717399i | ||||||
\(607\) | −34.6865 | + | 20.0263i | −1.40788 | + | 0.812842i | −0.995184 | − | 0.0980258i | \(-0.968747\pi\) |
−0.412699 | + | 0.910867i | \(0.635414\pi\) | |||||||
\(608\) | 2.36603 | + | 4.09808i | 0.0959550 | + | 0.166199i | ||||
\(609\) | 73.1769 | − | 42.2487i | 2.96528 | − | 1.71200i | ||||
\(610\) | 3.99038 | + | 2.30385i | 0.161566 | + | 0.0932801i | ||||
\(611\) | −29.4115 | − | 16.9808i | −1.18986 | − | 0.686968i | ||||
\(612\) | 6.69615 | − | 3.86603i | 0.270676 | − | 0.156275i | ||||
\(613\) | −16.6962 | − | 28.9186i | −0.674351 | − | 1.16801i | −0.976658 | − | 0.214800i | \(-0.931090\pi\) |
0.302307 | − | 0.953211i | \(-0.402243\pi\) | |||||||
\(614\) | 3.46410 | − | 2.00000i | 0.139800 | − | 0.0807134i | ||||
\(615\) | − | 30.5885i | − | 1.23345i | ||||||
\(616\) | −4.39230 | − | 2.53590i | −0.176971 | − | 0.102174i | ||||
\(617\) | 5.66025 | + | 9.80385i | 0.227873 | + | 0.394688i | 0.957178 | − | 0.289501i | \(-0.0934895\pi\) |
−0.729304 | + | 0.684189i | \(0.760156\pi\) | |||||||
\(618\) | 18.9282 | 0.761404 | ||||||||
\(619\) | −41.1769 | −1.65504 | −0.827520 | − | 0.561436i | \(-0.810249\pi\) | ||||
−0.827520 | + | 0.561436i | \(0.810249\pi\) | |||||||
\(620\) | −4.09808 | − | 7.09808i | −0.164583 | − | 0.285066i | ||||
\(621\) | − | 18.9282i | − | 0.759563i | ||||||
\(622\) | −2.19615 | + | 3.80385i | −0.0880577 | + | 0.152520i | ||||
\(623\) | 20.7846i | 0.832718i | ||||||||
\(624\) | 14.1962 | + | 8.19615i | 0.568301 | + | 0.328109i | ||||
\(625\) | 5.50000 | − | 9.52628i | 0.220000 | − | 0.381051i | ||||
\(626\) | −4.79423 | + | 8.30385i | −0.191616 | + | 0.331888i | ||||
\(627\) | −14.1962 | + | 8.19615i | −0.566940 | + | 0.327323i | ||||
\(628\) | −11.3923 | −0.454602 | ||||||||
\(629\) | 6.00000 | + | 8.66025i | 0.239236 | + | 0.345307i | ||||
\(630\) | 30.9282 | 1.23221 | ||||||||
\(631\) | 10.6865 | − | 6.16987i | 0.425424 | − | 0.245619i | −0.271971 | − | 0.962305i | \(-0.587676\pi\) |
0.697395 | + | 0.716687i | \(0.254342\pi\) | |||||||
\(632\) | 1.09808 | − | 1.90192i | 0.0436791 | − | 0.0756545i | ||||
\(633\) | 11.4641 | − | 19.8564i | 0.455657 | − | 0.789221i | ||||
\(634\) | 7.79423 | + | 4.50000i | 0.309548 | + | 0.178718i | ||||
\(635\) | 35.6603i | 1.41513i | ||||||||
\(636\) | −12.9282 | + | 22.3923i | −0.512637 | + | 0.887913i | ||||
\(637\) | − | 54.0000i | − | 2.13956i | ||||||
\(638\) | −4.90192 | − | 8.49038i | −0.194069 | − | 0.336137i | ||||
\(639\) | 42.2487 | 1.67133 | ||||||||
\(640\) | −1.73205 | −0.0684653 | ||||||||
\(641\) | 23.4282 | + | 40.5788i | 0.925358 | + | 1.60277i | 0.790984 | + | 0.611837i | \(0.209569\pi\) |
0.134375 | + | 0.990931i | \(0.457097\pi\) | |||||||
\(642\) | 10.3923 | + | 6.00000i | 0.410152 | + | 0.236801i | ||||
\(643\) | 9.12436i | 0.359829i | 0.983682 | + | 0.179915i | \(0.0575822\pi\) | ||||
−0.983682 | + | 0.179915i | \(0.942418\pi\) | |||||||
\(644\) | 16.3923 | − | 9.46410i | 0.645947 | − | 0.372938i | ||||
\(645\) | −6.00000 | − | 10.3923i | −0.236250 | − | 0.409197i | ||||
\(646\) | 7.09808 | − | 4.09808i | 0.279270 | − | 0.161237i | ||||
\(647\) | −8.19615 | − | 4.73205i | −0.322224 | − | 0.186036i | 0.330159 | − | 0.943925i | \(-0.392897\pi\) |
−0.652383 | + | 0.757889i | \(0.726231\pi\) | |||||||
\(648\) | 2.13397 | + | 1.23205i | 0.0838304 | + | 0.0483995i | ||||
\(649\) | 10.3923 | − | 6.00000i | 0.407934 | − | 0.235521i | ||||
\(650\) | 6.00000 | + | 10.3923i | 0.235339 | + | 0.407620i | ||||
\(651\) | 44.7846 | − | 25.8564i | 1.75525 | − | 1.01339i | ||||
\(652\) | − | 9.46410i | − | 0.370643i | ||||||
\(653\) | 5.89230 | + | 3.40192i | 0.230584 | + | 0.133128i | 0.610841 | − | 0.791753i | \(-0.290831\pi\) |
−0.380258 | + | 0.924881i | \(0.624165\pi\) | |||||||
\(654\) | −5.83013 | − | 10.0981i | −0.227976 | − | 0.394866i | ||||
\(655\) | 3.80385 | 0.148629 | ||||||||
\(656\) | −6.46410 | −0.252381 | ||||||||
\(657\) | −18.7321 | − | 32.4449i | −0.730807 | − | 1.26579i | ||||
\(658\) | 22.6410i | 0.882639i | ||||||||
\(659\) | −7.26795 | + | 12.5885i | −0.283119 | + | 0.490377i | −0.972151 | − | 0.234354i | \(-0.924703\pi\) |
0.689032 | + | 0.724731i | \(0.258036\pi\) | |||||||
\(660\) | − | 6.00000i | − | 0.233550i | ||||||
\(661\) | 25.2846 | + | 14.5981i | 0.983457 | + | 0.567799i | 0.903312 | − | 0.428984i | \(-0.141128\pi\) |
0.0801452 | + | 0.996783i | \(0.474462\pi\) | |||||||
\(662\) | −8.53590 | + | 14.7846i | −0.331757 | + | 0.574620i | ||||
\(663\) | 14.1962 | − | 24.5885i | 0.551333 | − | 0.954937i | ||||
\(664\) | −4.90192 | + | 2.83013i | −0.190232 | + | 0.109830i | ||||
\(665\) | 32.7846 | 1.27133 | ||||||||
\(666\) | 11.5981 | − | 24.5526i | 0.449416 | − | 0.951392i | ||||
\(667\) | 36.5885 | 1.41671 | ||||||||
\(668\) | −6.00000 | + | 3.46410i | −0.232147 | + | 0.134030i | ||||
\(669\) | −11.7321 | + | 20.3205i | −0.453587 | + | 0.785636i | ||||
\(670\) | 3.63397 | − | 6.29423i | 0.140393 | − | 0.243167i | ||||
\(671\) | 2.92116 | + | 1.68653i | 0.112770 | + | 0.0651079i | ||||
\(672\) | − | 10.9282i | − | 0.421565i | ||||||
\(673\) | 6.19615 | − | 10.7321i | 0.238844 | − | 0.413690i | −0.721539 | − | 0.692374i | \(-0.756565\pi\) |
0.960383 | + | 0.278684i | \(0.0898982\pi\) | |||||||
\(674\) | 7.00000i | 0.269630i | ||||||||
\(675\) | −4.00000 | − | 6.92820i | −0.153960 | − | 0.266667i | ||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 7.14359 | 0.274551 | 0.137275 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137275 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(678\) | −10.7321 | − | 18.5885i | −0.412162 | − | 0.713885i | ||||
\(679\) | −18.0000 | − | 10.3923i | −0.690777 | − | 0.398820i | ||||
\(680\) | 3.00000i | 0.115045i | ||||||||
\(681\) | −11.1962 | + | 6.46410i | −0.429037 | + | 0.247705i | ||||
\(682\) | −3.00000 | − | 5.19615i | −0.114876 | − | 0.198971i | ||||
\(683\) | 26.7846 | − | 15.4641i | 1.02488 | − | 0.591717i | 0.109370 | − | 0.994001i | \(-0.465117\pi\) |
0.915515 | + | 0.402284i | \(0.131783\pi\) | |||||||
\(684\) | −18.2942 | − | 10.5622i | −0.699497 | − | 0.403855i | ||||
\(685\) | −11.0885 | − | 6.40192i | −0.423668 | − | 0.244605i | ||||
\(686\) | −6.92820 | + | 4.00000i | −0.264520 | + | 0.152721i | ||||
\(687\) | 25.9545 | + | 44.9545i | 0.990225 | + | 1.71512i | ||||
\(688\) | −2.19615 | + | 1.26795i | −0.0837275 | + | 0.0483401i | ||||
\(689\) | 56.7846i | 2.16332i | ||||||||
\(690\) | 19.3923 | + | 11.1962i | 0.738252 | + | 0.426230i | ||||
\(691\) | 5.90192 | + | 10.2224i | 0.224520 | + | 0.388880i | 0.956175 | − | 0.292795i | \(-0.0945853\pi\) |
−0.731655 | + | 0.681675i | \(0.761252\pi\) | |||||||
\(692\) | −3.92820 | −0.149328 | ||||||||
\(693\) | 22.6410 | 0.860061 | ||||||||
\(694\) | −14.0263 | − | 24.2942i | −0.532430 | − | 0.922196i | ||||
\(695\) | 21.1244i | 0.801292i | ||||||||
\(696\) | 10.5622 | − | 18.2942i | 0.400358 | − | 0.693441i | ||||
\(697\) | 11.1962i | 0.424085i | ||||||||
\(698\) | −23.7224 | − | 13.6962i | −0.897907 | − | 0.518407i | ||||
\(699\) | 34.6865 | − | 60.0788i | 1.31197 | − | 2.27239i | ||||
\(700\) | 4.00000 | − | 6.92820i | 0.151186 | − | 0.261861i | ||||
\(701\) | 22.3923 | − | 12.9282i | 0.845746 | − | 0.488291i | −0.0134675 | − | 0.999909i | \(-0.504287\pi\) |
0.859213 | + | 0.511618i | \(0.170954\pi\) | |||||||
\(702\) | −24.0000 | −0.905822 | ||||||||
\(703\) | 12.2942 | − | 26.0263i | 0.463686 | − | 0.981600i | ||||
\(704\) | −1.26795 | −0.0477876 | ||||||||
\(705\) | −23.1962 | + | 13.3923i | −0.873618 | + | 0.504383i | ||||
\(706\) | 2.93782 | − | 5.08846i | 0.110566 | − | 0.191507i | ||||
\(707\) | −12.9282 | + | 22.3923i | −0.486215 | + | 0.842149i | ||||
\(708\) | 22.3923 | + | 12.9282i | 0.841554 | + | 0.485872i | ||||
\(709\) | 30.0000i | 1.12667i | 0.826227 | + | 0.563337i | \(0.190483\pi\) | ||||
−0.826227 | + | 0.563337i | \(0.809517\pi\) | |||||||
\(710\) | −8.19615 | + | 14.1962i | −0.307596 | + | 0.532772i | ||||
\(711\) | 9.80385i | 0.367673i | ||||||||
\(712\) | 2.59808 | + | 4.50000i | 0.0973670 | + | 0.168645i | ||||
\(713\) | 22.3923 | 0.838598 | ||||||||
\(714\) | −18.9282 | −0.708370 | ||||||||
\(715\) | −6.58846 | − | 11.4115i | −0.246394 | − | 0.426768i | ||||
\(716\) | −20.1962 | − | 11.6603i | −0.754766 | − | 0.435764i | ||||
\(717\) | 51.7128i | 1.93125i | ||||||||
\(718\) | −22.9808 | + | 13.2679i | −0.857634 | + | 0.495155i | ||||
\(719\) | −13.2224 | − | 22.9019i | −0.493114 | − | 0.854098i | 0.506855 | − | 0.862031i | \(-0.330808\pi\) |
−0.999969 | + | 0.00793367i | \(0.997475\pi\) | |||||||
\(720\) | 6.69615 | − | 3.86603i | 0.249551 | − | 0.144078i | ||||
\(721\) | −24.0000 | − | 13.8564i | −0.893807 | − | 0.516040i | ||||
\(722\) | −2.93782 | − | 1.69615i | −0.109334 | − | 0.0631243i | ||||
\(723\) | −42.5885 | + | 24.5885i | −1.58388 | + | 0.914455i | ||||
\(724\) | 2.69615 | + | 4.66987i | 0.100202 | + | 0.173554i | ||||
\(725\) | 13.3923 | − | 7.73205i | 0.497378 | − | 0.287161i | ||||
\(726\) | 25.6603i | 0.952341i | ||||||||
\(727\) | −22.3923 | − | 12.9282i | −0.830485 | − | 0.479481i | 0.0235340 | − | 0.999723i | \(-0.492508\pi\) |
−0.854019 | + | 0.520243i | \(0.825842\pi\) | |||||||
\(728\) | −12.0000 | − | 20.7846i | −0.444750 | − | 0.770329i | ||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 14.5359 | 0.537998 | ||||||||
\(731\) | 2.19615 | + | 3.80385i | 0.0812276 | + | 0.140690i | ||||
\(732\) | 7.26795i | 0.268631i | ||||||||
\(733\) | −18.1962 | + | 31.5167i | −0.672090 | + | 1.16409i | 0.305220 | + | 0.952282i | \(0.401270\pi\) |
−0.977310 | + | 0.211813i | \(0.932063\pi\) | |||||||
\(734\) | 20.3923i | 0.752694i | ||||||||
\(735\) | −36.8827 | − | 21.2942i | −1.36044 | − | 0.785449i | ||||
\(736\) | 2.36603 | − | 4.09808i | 0.0872129 | − | 0.151057i | ||||
\(737\) | 2.66025 | − | 4.60770i | 0.0979917 | − | 0.169727i | ||||
\(738\) | 24.9904 | − | 14.4282i | 0.919909 | − | 0.531110i | ||||
\(739\) | −44.9808 | −1.65464 | −0.827322 | − | 0.561728i | \(-0.810137\pi\) | ||||
−0.827322 | + | 0.561728i | \(0.810137\pi\) | |||||||
\(740\) | 6.00000 | + | 8.66025i | 0.220564 | + | 0.318357i | ||||
\(741\) | −77.5692 | −2.84958 | ||||||||
\(742\) | 32.7846 | − | 18.9282i | 1.20356 | − | 0.694876i | ||||
\(743\) | −11.9545 | + | 20.7058i | −0.438567 | + | 0.759621i | −0.997579 | − | 0.0695386i | \(-0.977847\pi\) |
0.559012 | + | 0.829160i | \(0.311181\pi\) | |||||||
\(744\) | 6.46410 | − | 11.1962i | 0.236985 | − | 0.410471i | ||||
\(745\) | 14.8923 | + | 8.59808i | 0.545612 | + | 0.315009i | ||||
\(746\) | − | 21.7846i | − | 0.797591i | ||||||
\(747\) | 12.6340 | − | 21.8827i | 0.462253 | − | 0.800646i | ||||
\(748\) | 2.19615i | 0.0802993i | ||||||||
\(749\) | −8.78461 | − | 15.2154i | −0.320983 | − | 0.555958i | ||||
\(750\) | 33.1244 | 1.20953 | ||||||||
\(751\) | −15.6077 | −0.569533 | −0.284766 | − | 0.958597i | \(-0.591916\pi\) | ||||
−0.284766 | + | 0.958597i | \(0.591916\pi\) | |||||||
\(752\) | 2.83013 | + | 4.90192i | 0.103204 | + | 0.178755i | ||||
\(753\) | −44.7846 | − | 25.8564i | −1.63204 | − | 0.942260i | ||||
\(754\) | − | 46.3923i | − | 1.68951i | ||||||
\(755\) | −18.2942 | + | 10.5622i | −0.665795 | + | 0.384397i | ||||
\(756\) | 8.00000 | + | 13.8564i | 0.290957 | + | 0.503953i | ||||
\(757\) | −6.69615 | + | 3.86603i | −0.243376 | + | 0.140513i | −0.616727 | − | 0.787177i | \(-0.711542\pi\) |
0.373352 | + | 0.927690i | \(0.378209\pi\) | |||||||
\(758\) | −14.5359 | − | 8.39230i | −0.527968 | − | 0.304822i | ||||
\(759\) | 14.1962 | + | 8.19615i | 0.515288 | + | 0.297501i | ||||
\(760\) | 7.09808 | − | 4.09808i | 0.257474 | − | 0.148653i | ||||
\(761\) | 1.16025 | + | 2.00962i | 0.0420592 | + | 0.0728486i | 0.886289 | − | 0.463133i | \(-0.153275\pi\) |
−0.844229 | + | 0.535982i | \(0.819942\pi\) | |||||||
\(762\) | −48.7128 | + | 28.1244i | −1.76468 | + | 1.01884i | ||||
\(763\) | 17.0718i | 0.618041i | ||||||||
\(764\) | 5.70577 | + | 3.29423i | 0.206428 | + | 0.119181i | ||||
\(765\) | −6.69615 | − | 11.5981i | −0.242100 | − | 0.419329i | ||||
\(766\) | −1.85641 | −0.0670747 | ||||||||
\(767\) | 56.7846 | 2.05037 | ||||||||
\(768\) | −1.36603 | − | 2.36603i | −0.0492922 | − | 0.0853766i | ||||
\(769\) | 33.7128i | 1.21572i | 0.794046 | + | 0.607858i | \(0.207971\pi\) | ||||
−0.794046 | + | 0.607858i | \(0.792029\pi\) | |||||||
\(770\) | −4.39230 | + | 7.60770i | −0.158288 | + | 0.274162i | ||||
\(771\) | − | 2.19615i | − | 0.0790925i | ||||||
\(772\) | −10.5000 | − | 6.06218i | −0.377903 | − | 0.218183i | ||||
\(773\) | 4.03590 | − | 6.99038i | 0.145161 | − | 0.251427i | −0.784272 | − | 0.620417i | \(-0.786963\pi\) |
0.929433 | + | 0.368991i | \(0.120297\pi\) | |||||||
\(774\) | 5.66025 | − | 9.80385i | 0.203454 | − | 0.352392i | ||||
\(775\) | 8.19615 | − | 4.73205i | 0.294414 | − | 0.169980i | ||||
\(776\) | −5.19615 | −0.186531 | ||||||||
\(777\) | −54.6410 | + | 37.8564i | −1.96024 | + | 1.35809i | ||||
\(778\) | 11.1962 | 0.401402 | ||||||||
\(779\) | 26.4904 | − | 15.2942i | 0.949116 | − | 0.547973i | ||||
\(780\) | 14.1962 | − | 24.5885i | 0.508304 | − | 0.880408i | ||||
\(781\) | −6.00000 | + | 10.3923i | −0.214697 | + | 0.371866i | ||||
\(782\) | −7.09808 | − | 4.09808i | −0.253827 | − | 0.146547i | ||||
\(783\) | 30.9282i | 1.10528i | ||||||||
\(784\) | −4.50000 | + | 7.79423i | −0.160714 | + | 0.278365i | ||||
\(785\) | 19.7321i | 0.704267i | ||||||||
\(786\) | 3.00000 | + | 5.19615i | 0.107006 | + | 0.185341i | ||||
\(787\) | −29.1769 | −1.04004 | −0.520022 | − | 0.854153i | \(-0.674076\pi\) | ||||
−0.520022 | + | 0.854153i | \(0.674076\pi\) | |||||||
\(788\) | 8.32051 | 0.296406 | ||||||||
\(789\) | 15.4641 | + | 26.7846i | 0.550537 | + | 0.953557i | ||||
\(790\) | −3.29423 | − | 1.90192i | −0.117203 | − | 0.0676674i | ||||
\(791\) | 31.4256i | 1.11737i | ||||||||
\(792\) | 4.90192 | − | 2.83013i | 0.174182 | − | 0.100564i | ||||
\(793\) | 7.98076 | + | 13.8231i | 0.283405 | + | 0.490872i | ||||
\(794\) | 4.33013 | − | 2.50000i | 0.153670 | − | 0.0887217i | ||||
\(795\) | 38.7846 | + | 22.3923i | 1.37555 | + | 0.794173i | ||||
\(796\) | 16.3923 | + | 9.46410i | 0.581010 | + | 0.335446i | ||||
\(797\) | 18.0000 | − | 10.3923i | 0.637593 | − | 0.368114i | −0.146094 | − | 0.989271i | \(-0.546670\pi\) |
0.783687 | + | 0.621156i | \(0.213337\pi\) | |||||||
\(798\) | 25.8564 | + | 44.7846i | 0.915307 | + | 1.58536i | ||||
\(799\) | 8.49038 | − | 4.90192i | 0.300368 | − | 0.173418i | ||||
\(800\) | − | 2.00000i | − | 0.0707107i | ||||||
\(801\) | −20.0885 | − | 11.5981i | −0.709791 | − | 0.409798i | ||||
\(802\) | 13.3923 | + | 23.1962i | 0.472899 | + | 0.819085i | ||||
\(803\) | 10.6410 | 0.375513 | ||||||||
\(804\) | 11.4641 | 0.404308 | ||||||||
\(805\) | −16.3923 | − | 28.3923i | −0.577753 | − | 1.00070i | ||||
\(806\) | − | 28.3923i | − | 1.00008i | ||||||
\(807\) | 38.7846 | − | 67.1769i | 1.36528 | − | 2.36474i | ||||
\(808\) | 6.46410i | 0.227406i | ||||||||
\(809\) | −37.1769 | − | 21.4641i | −1.30707 | − | 0.754638i | −0.325464 | − | 0.945554i | \(-0.605521\pi\) |
−0.981606 | + | 0.190917i | \(0.938854\pi\) | |||||||
\(810\) | 2.13397 | − | 3.69615i | 0.0749802 | − | 0.129870i | ||||
\(811\) | 7.80385 | − | 13.5167i | 0.274030 | − | 0.474634i | −0.695860 | − | 0.718178i | \(-0.744977\pi\) |
0.969890 | + | 0.243543i | \(0.0783099\pi\) | |||||||
\(812\) | −26.7846 | + | 15.4641i | −0.939956 | + | 0.542684i | ||||
\(813\) | 45.3205 | 1.58946 | ||||||||
\(814\) | 4.39230 | + | 6.33975i | 0.153950 | + | 0.222208i | ||||
\(815\) | −16.3923 | −0.574197 | ||||||||
\(816\) | −4.09808 | + | 2.36603i | −0.143461 | + | 0.0828275i | ||||
\(817\) | 6.00000 | − | 10.3923i | 0.209913 | − | 0.363581i | ||||
\(818\) | −1.20577 | + | 2.08846i | −0.0421588 | + | 0.0730212i | ||||
\(819\) | 92.7846 | + | 53.5692i | 3.24216 | + | 1.87186i | ||||
\(820\) | 11.1962i | 0.390987i | ||||||||
\(821\) | 22.7321 | − | 39.3731i | 0.793354 | − | 1.37413i | −0.130525 | − | 0.991445i | \(-0.541666\pi\) |
0.923879 | − | 0.382684i | \(-0.125000\pi\) | |||||||
\(822\) | − | 20.1962i | − | 0.704422i | ||||||
\(823\) | −3.70577 | − | 6.41858i | −0.129175 | − | 0.223738i | 0.794182 | − | 0.607680i | \(-0.207900\pi\) |
−0.923357 | + | 0.383942i | \(0.874566\pi\) | |||||||
\(824\) | −6.92820 | −0.241355 | ||||||||
\(825\) | 6.92820 | 0.241209 | ||||||||
\(826\) | −18.9282 | − | 32.7846i | −0.658596 | − | 1.14072i | ||||
\(827\) | 19.6077 | + | 11.3205i | 0.681826 | + | 0.393653i | 0.800543 | − | 0.599276i | \(-0.204545\pi\) |
−0.118716 | + | 0.992928i | \(0.537878\pi\) | |||||||
\(828\) | 21.1244i | 0.734122i | ||||||||
\(829\) | −31.9808 | + | 18.4641i | −1.11074 | + | 0.641285i | −0.939020 | − | 0.343861i | \(-0.888265\pi\) |
−0.171717 | + | 0.985146i | \(0.554932\pi\) | |||||||
\(830\) | 4.90192 | + | 8.49038i | 0.170148 | + | 0.294705i | ||||
\(831\) | −40.6865 | + | 23.4904i | −1.41140 | + | 0.814872i | ||||
\(832\) | −5.19615 | − | 3.00000i | −0.180144 | − | 0.104006i | ||||
\(833\) | 13.5000 | + | 7.79423i | 0.467747 | + | 0.270054i | ||||
\(834\) | −28.8564 | + | 16.6603i | −0.999216 | + | 0.576897i | ||||
\(835\) | 6.00000 | + | 10.3923i | 0.207639 | + | 0.359641i | ||||
\(836\) | 5.19615 | − | 3.00000i | 0.179713 | − | 0.103757i | ||||
\(837\) | 18.9282i | 0.654254i | ||||||||
\(838\) | 32.7846 | + | 18.9282i | 1.13253 | + | 0.653864i | ||||
\(839\) | −10.0981 | − | 17.4904i | −0.348624 | − | 0.603835i | 0.637381 | − | 0.770549i | \(-0.280018\pi\) |
−0.986005 | + | 0.166714i | \(0.946684\pi\) | |||||||
\(840\) | −18.9282 | −0.653085 | ||||||||
\(841\) | −30.7846 | −1.06154 | ||||||||
\(842\) | 10.3301 | + | 17.8923i | 0.356000 | + | 0.616610i | ||||
\(843\) | 2.19615i | 0.0756395i | ||||||||
\(844\) | −4.19615 | + | 7.26795i | −0.144438 | + | 0.250173i | ||||
\(845\) | − | 39.8372i | − | 1.37044i | ||||||
\(846\) | −21.8827 | − | 12.6340i | −0.752342 | − | 0.434365i | ||||
\(847\) | 18.7846 | − | 32.5359i | 0.645447 | − | 1.11795i | ||||
\(848\) | 4.73205 | − | 8.19615i | 0.162499 | − | 0.281457i | ||||
\(849\) | 22.3923 | − | 12.9282i | 0.768502 | − | 0.443695i | ||||
\(850\) | −3.46410 | −0.118818 | ||||||||
\(851\) | −28.6865 | + | 2.36603i | −0.983362 | + | 0.0811063i | ||||
\(852\) | −25.8564 | −0.885826 | ||||||||
\(853\) | 19.2846 | − | 11.1340i | 0.660292 | − | 0.381220i | −0.132096 | − | 0.991237i | \(-0.542171\pi\) |
0.792388 | + | 0.610017i | \(0.208837\pi\) | |||||||
\(854\) | 5.32051 | − | 9.21539i | 0.182064 | − | 0.315344i | ||||
\(855\) | −18.2942 | + | 31.6865i | −0.625649 | + | 1.08366i | ||||
\(856\) | −3.80385 | − | 2.19615i | −0.130013 | − | 0.0750629i | ||||
\(857\) | − | 37.0526i | − | 1.26569i | −0.774278 | − | 0.632846i | \(-0.781887\pi\) | ||
0.774278 | − | 0.632846i | \(-0.218113\pi\) | |||||||
\(858\) | 10.3923 | − | 18.0000i | 0.354787 | − | 0.614510i | ||||
\(859\) | − | 21.4641i | − | 0.732346i | −0.930547 | − | 0.366173i | \(-0.880668\pi\) | ||
0.930547 | − | 0.366173i | \(-0.119332\pi\) | |||||||
\(860\) | 2.19615 | + | 3.80385i | 0.0748882 | + | 0.129710i | ||||
\(861\) | −70.6410 | −2.40744 | ||||||||
\(862\) | −16.0526 | −0.546752 | ||||||||
\(863\) | 8.19615 | + | 14.1962i | 0.279000 | + | 0.483243i | 0.971137 | − | 0.238524i | \(-0.0766636\pi\) |
−0.692136 | + | 0.721767i | \(0.743330\pi\) | |||||||
\(864\) | 3.46410 | + | 2.00000i | 0.117851 | + | 0.0680414i | ||||
\(865\) | 6.80385i | 0.231338i | ||||||||
\(866\) | 28.9186 | − | 16.6962i | 0.982693 | − | 0.567358i | ||||
\(867\) | −19.1244 | − | 33.1244i | −0.649497 | − | 1.12496i | ||||
\(868\) | −16.3923 | + | 9.46410i | −0.556391 | + | 0.321233i | ||||
\(869\) | −2.41154 | − | 1.39230i | −0.0818060 | − | 0.0472307i | ||||
\(870\) | −31.6865 | − | 18.2942i | −1.07427 | − | 0.620232i | ||||
\(871\) | 21.8038 | − | 12.5885i | 0.738795 | − | 0.426544i | ||||
\(872\) | 2.13397 | + | 3.69615i | 0.0722655 | + | 0.125168i | ||||
\(873\) | 20.0885 | − | 11.5981i | 0.679891 | − | 0.392535i | ||||
\(874\) | 22.3923i | 0.757431i | ||||||||
\(875\) | −42.0000 | − | 24.2487i | −1.41986 | − | 0.819756i | ||||
\(876\) | 11.4641 | + | 19.8564i | 0.387336 | + | 0.670886i | ||||
\(877\) | 44.1769 | 1.49175 | 0.745874 | − | 0.666087i | \(-0.232032\pi\) | ||||
0.745874 | + | 0.666087i | \(0.232032\pi\) | |||||||
\(878\) | 9.46410 | 0.319398 | ||||||||
\(879\) | −6.29423 | − | 10.9019i | −0.212299 | − | 0.367713i | ||||
\(880\) | 2.19615i | 0.0740323i | ||||||||
\(881\) | 24.4808 | − | 42.4019i | 0.824778 | − | 1.42856i | −0.0773111 | − | 0.997007i | \(-0.524633\pi\) |
0.902089 | − | 0.431550i | \(-0.142033\pi\) | |||||||
\(882\) | − | 40.1769i | − | 1.35283i | ||||||
\(883\) | 30.8827 | + | 17.8301i | 1.03929 | + | 0.600032i | 0.919631 | − | 0.392784i | \(-0.128488\pi\) |
0.119654 | + | 0.992816i | \(0.461821\pi\) | |||||||
\(884\) | −5.19615 | + | 9.00000i | −0.174766 | + | 0.302703i | ||||
\(885\) | 22.3923 | − | 38.7846i | 0.752709 | − | 1.30373i | ||||
\(886\) | 2.19615 | − | 1.26795i | 0.0737812 | − | 0.0425976i | ||||
\(887\) | 27.1244 | 0.910747 | 0.455373 | − | 0.890301i | \(-0.349506\pi\) | ||||
0.455373 | + | 0.890301i | \(0.349506\pi\) | |||||||
\(888\) | −7.09808 | + | 15.0263i | −0.238196 | + | 0.504249i | ||||
\(889\) | 82.3538 | 2.76206 | ||||||||
\(890\) | 7.79423 | − | 4.50000i | 0.261263 | − | 0.150840i | ||||
\(891\) | 1.56218 | − | 2.70577i | 0.0523349 | − | 0.0906468i | ||||
\(892\) | 4.29423 | − | 7.43782i | 0.143781 | − | 0.249037i | ||||
\(893\) | −23.1962 | − | 13.3923i | −0.776230 | − | 0.448156i | ||||
\(894\) | 27.1244i | 0.907174i | ||||||||
\(895\) | −20.1962 | + | 34.9808i | −0.675083 | + | 1.16928i | ||||
\(896\) | 4.00000i | 0.133631i | ||||||||
\(897\) | 38.7846 | + | 67.1769i | 1.29498 | + | 2.24297i | ||||
\(898\) | 24.9282 | 0.831865 | ||||||||
\(899\) | −36.5885 | −1.22029 | ||||||||
\(900\) | 4.46410 | + | 7.73205i | 0.148803 | + | 0.257735i | ||||
\(901\) | −14.1962 | − | 8.19615i | −0.472942 | − | 0.273053i | ||||
\(902\) | 8.19615i | 0.272902i | ||||||||
\(903\) | −24.0000 | + | 13.8564i | −0.798670 | + | 0.461112i | ||||
\(904\) | 3.92820 | + | 6.80385i | 0.130650 | + | 0.226293i | ||||
\(905\) | 8.08846 | − | 4.66987i | 0.268869 | − | 0.155232i | ||||
\(906\) | −28.8564 | − | 16.6603i | −0.958690 | − | 0.553500i | ||||
\(907\) | 40.0981 | + | 23.1506i | 1.33143 | + | 0.768704i | 0.985520 | − | 0.169562i | \(-0.0542352\pi\) |
0.345915 | + | 0.938266i | \(0.387568\pi\) | |||||||
\(908\) | 4.09808 | − | 2.36603i | 0.135999 | − | 0.0785193i | ||||
\(909\) | −14.4282 | − | 24.9904i | −0.478553 | − | 0.828879i | ||||
\(910\) | −36.0000 | + | 20.7846i | −1.19339 | + | 0.689003i | ||||
\(911\) | − | 2.87564i | − | 0.0952743i | −0.998865 | − | 0.0476372i | \(-0.984831\pi\) | ||
0.998865 | − | 0.0476372i | \(-0.0151691\pi\) | |||||||
\(912\) | 11.1962 | + | 6.46410i | 0.370742 | + | 0.214048i | ||||
\(913\) | 3.58846 | + | 6.21539i | 0.118761 | + | 0.205699i | ||||
\(914\) | −19.9808 | −0.660905 | ||||||||
\(915\) | 12.5885 | 0.416162 | ||||||||
\(916\) | −9.50000 | − | 16.4545i | −0.313889 | − | 0.543671i | ||||
\(917\) | − | 8.78461i | − | 0.290093i | ||||||
\(918\) | 3.46410 | − | 6.00000i | 0.114332 | − | 0.198030i | ||||
\(919\) | 28.0526i | 0.925369i | 0.886523 | + | 0.462684i | \(0.153114\pi\) | ||||
−0.886523 | + | 0.462684i | \(0.846886\pi\) | |||||||
\(920\) | −7.09808 | − | 4.09808i | −0.234017 | − | 0.135110i | ||||
\(921\) | 5.46410 | − | 9.46410i | 0.180048 | − | 0.311853i | ||||
\(922\) | 16.8564 | − | 29.1962i | 0.555136 | − | 0.961524i | ||||
\(923\) | −49.1769 | + | 28.3923i | −1.61868 | + | 0.934544i | ||||
\(924\) | −13.8564 | −0.455842 | ||||||||
\(925\) | −10.0000 | + | 6.92820i | −0.328798 | + | 0.227798i | ||||
\(926\) | 14.5359 | 0.477679 | ||||||||
\(927\) | 26.7846 | − | 15.4641i | 0.879722 | − | 0.507908i | ||||
\(928\) | −3.86603 | + | 6.69615i | −0.126909 | + | 0.219812i | ||||
\(929\) | 18.6962 | − | 32.3827i | 0.613401 | − | 1.06244i | −0.377262 | − | 0.926107i | \(-0.623134\pi\) |
0.990663 | − | 0.136335i | \(-0.0435323\pi\) | |||||||
\(930\) | −19.3923 | − | 11.1962i | −0.635899 | − | 0.367136i | ||||
\(931\) | − | 42.5885i | − | 1.39578i | ||||||
\(932\) | −12.6962 | + | 21.9904i | −0.415876 | + | 0.720319i | ||||
\(933\) | 12.0000i | 0.392862i | ||||||||
\(934\) | 15.1244 | + | 26.1962i | 0.494884 | + | 0.857164i | ||||
\(935\) | 3.80385 | 0.124399 | ||||||||
\(936\) | 26.7846 | 0.875482 | ||||||||
\(937\) | −18.0885 | − | 31.3301i | −0.590924 | − | 1.02351i | −0.994108 | − | 0.108392i | \(-0.965430\pi\) |
0.403184 | − | 0.915119i | \(-0.367903\pi\) | |||||||
\(938\) | −14.5359 | − | 8.39230i | −0.474614 | − | 0.274018i | ||||
\(939\) | 26.1962i | 0.854879i | ||||||||
\(940\) | 8.49038 | − | 4.90192i | 0.276926 | − | 0.159883i | ||||
\(941\) | −29.8923 | − | 51.7750i | −0.974461 | − | 1.68782i | −0.681701 | − | 0.731630i | \(-0.738760\pi\) |
−0.292760 | − | 0.956186i | \(-0.594574\pi\) | |||||||
\(942\) | −26.9545 | + | 15.5622i | −0.878225 | + | 0.507043i | ||||
\(943\) | −26.4904 | − | 15.2942i | −0.862645 | − | 0.498049i | ||||
\(944\) | −8.19615 | − | 4.73205i | −0.266762 | − | 0.154015i | ||||
\(945\) | 24.0000 | − | 13.8564i | 0.780720 | − | 0.450749i | ||||
\(946\) | 1.60770 | + | 2.78461i | 0.0522707 | + | 0.0905355i | ||||
\(947\) | −45.3731 | + | 26.1962i | −1.47443 | + | 0.851261i | −0.999585 | − | 0.0288107i | \(-0.990828\pi\) |
−0.474842 | + | 0.880071i | \(0.657495\pi\) | |||||||
\(948\) | − | 6.00000i | − | 0.194871i | ||||||
\(949\) | 43.6077 | + | 25.1769i | 1.41557 | + | 0.817277i | ||||
\(950\) | 4.73205 | + | 8.19615i | 0.153528 | + | 0.265918i | ||||
\(951\) | 24.5885 | 0.797335 | ||||||||
\(952\) | 6.92820 | 0.224544 | ||||||||
\(953\) | −3.92820 | − | 6.80385i | −0.127247 | − | 0.220398i | 0.795362 | − | 0.606135i | \(-0.207281\pi\) |
−0.922609 | + | 0.385736i | \(0.873947\pi\) | |||||||
\(954\) | 42.2487i | 1.36785i | ||||||||
\(955\) | 5.70577 | − | 9.88269i | 0.184634 | − | 0.319796i | ||||
\(956\) | − | 18.9282i | − | 0.612182i | ||||||
\(957\) | −23.1962 | − | 13.3923i | −0.749825 | − | 0.432912i | ||||
\(958\) | 4.73205 | − | 8.19615i | 0.152886 | − | 0.264806i | ||||
\(959\) | −14.7846 | + | 25.6077i | −0.477420 | + | 0.826916i | ||||
\(960\) | −4.09808 | + | 2.36603i | −0.132265 | + | 0.0763631i | ||||
\(961\) | 8.60770 | 0.277668 | ||||||||
\(962\) | 3.00000 | + | 36.3731i | 0.0967239 | + | 1.17271i | ||||
\(963\) | 19.6077 | 0.631849 | ||||||||
\(964\) | 15.5885 | − | 9.00000i | 0.502070 | − | 0.289870i | ||||
\(965\) | −10.5000 | + | 18.1865i | −0.338007 | + | 0.585445i | ||||
\(966\) | 25.8564 | − | 44.7846i | 0.831916 | − | 1.44092i | ||||
\(967\) | −9.21539 | − | 5.32051i | −0.296347 | − | 0.171096i | 0.344454 | − | 0.938803i | \(-0.388064\pi\) |
−0.640801 | + | 0.767707i | \(0.721397\pi\) | |||||||
\(968\) | − | 9.39230i | − | 0.301880i | ||||||
\(969\) | 11.1962 | − | 19.3923i | 0.359672 | − | 0.622971i | ||||
\(970\) | 9.00000i | 0.288973i | ||||||||
\(971\) | 6.29423 | + | 10.9019i | 0.201991 | + | 0.349859i | 0.949170 | − | 0.314764i | \(-0.101925\pi\) |
−0.747179 | + | 0.664623i | \(0.768592\pi\) | |||||||
\(972\) | 18.7321 | 0.600831 | ||||||||
\(973\) | 48.7846 | 1.56396 | ||||||||
\(974\) | 14.0263 | + | 24.2942i | 0.449431 | + | 0.778437i | ||||
\(975\) | 28.3923 | + | 16.3923i | 0.909281 | + | 0.524974i | ||||
\(976\) | − | 2.66025i | − | 0.0851527i | ||||||
\(977\) | −49.9808 | + | 28.8564i | −1.59903 | + | 0.923198i | −0.607351 | + | 0.794434i | \(0.707768\pi\) |
−0.991675 | + | 0.128765i | \(0.958899\pi\) | |||||||
\(978\) | −12.9282 | − | 22.3923i | −0.413398 | − | 0.716027i | ||||
\(979\) | 5.70577 | − | 3.29423i | 0.182357 | − | 0.105284i | ||||
\(980\) | 13.5000 | + | 7.79423i | 0.431242 | + | 0.248978i | ||||
\(981\) | −16.5000 | − | 9.52628i | −0.526804 | − | 0.304151i | ||||
\(982\) | −25.0981 | + | 14.4904i | −0.800912 | + | 0.462407i | ||||
\(983\) | −9.75833 | − | 16.9019i | −0.311242 | − | 0.539088i | 0.667389 | − | 0.744709i | \(-0.267412\pi\) |
−0.978632 | + | 0.205621i | \(0.934078\pi\) | |||||||
\(984\) | −15.2942 | + | 8.83013i | −0.487562 | + | 0.281494i | ||||
\(985\) | − | 14.4115i | − | 0.459190i | ||||||
\(986\) | 11.5981 | + | 6.69615i | 0.369358 | + | 0.213249i | ||||
\(987\) | 30.9282 | + | 53.5692i | 0.984456 | + | 1.70513i | ||||
\(988\) | 28.3923 | 0.903280 | ||||||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | −4.90192 | − | 8.49038i | −0.155793 | − | 0.269842i | ||||
\(991\) | − | 44.1051i | − | 1.40105i | −0.713630 | − | 0.700523i | \(-0.752950\pi\) | ||
0.713630 | − | 0.700523i | \(-0.247050\pi\) | |||||||
\(992\) | −2.36603 | + | 4.09808i | −0.0751214 | + | 0.130114i | ||||
\(993\) | 46.6410i | 1.48011i | ||||||||
\(994\) | 32.7846 | + | 18.9282i | 1.03986 | + | 0.600366i | ||||
\(995\) | 16.3923 | − | 28.3923i | 0.519671 | − | 0.900097i | ||||
\(996\) | −7.73205 | + | 13.3923i | −0.244999 | + | 0.424351i | ||||
\(997\) | −20.4115 | + | 11.7846i | −0.646440 | + | 0.373222i | −0.787091 | − | 0.616837i | \(-0.788414\pi\) |
0.140651 | + | 0.990059i | \(0.455080\pi\) | |||||||
\(998\) | −2.19615 | −0.0695180 | ||||||||
\(999\) | −2.00000 | − | 24.2487i | −0.0632772 | − | 0.767195i |
(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 | 74.2.e.a.11.1 | ✓ | 4 | |
3.2 | odd | 2 | 666.2.s.e.307.2 | 4 | |||
4.3 | odd | 2 | 592.2.w.d.529.2 | 4 | |||
37.8 | odd | 12 | 2738.2.a.f.1.1 | 2 | |||
37.27 | even | 6 | inner | 74.2.e.a.27.1 | yes | 4 | |
37.29 | odd | 12 | 2738.2.a.j.1.1 | 2 | |||
111.101 | odd | 6 | 666.2.s.e.397.2 | 4 | |||
148.27 | odd | 6 | 592.2.w.d.545.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.e.a.11.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
74.2.e.a.27.1 | yes | 4 | 37.27 | even | 6 | inner | |
592.2.w.d.529.2 | 4 | 4.3 | odd | 2 | |||
592.2.w.d.545.2 | 4 | 148.27 | odd | 6 | |||
666.2.s.e.307.2 | 4 | 3.2 | odd | 2 | |||
666.2.s.e.397.2 | 4 | 111.101 | odd | 6 | |||
2738.2.a.f.1.1 | 2 | 37.8 | odd | 12 | |||
2738.2.a.j.1.1 | 2 | 37.29 | odd | 12 |