Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 549.3 | ||
Character | \(\chi\) | \(=\) | 950.549 |
Dual form | 950.2.u.e.199.3 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.984808 | + | 0.173648i | 0.696364 | + | 0.122788i | ||||
\(3\) | −1.07851 | + | 1.28531i | −0.622676 | + | 0.742076i | −0.981528 | − | 0.191318i | \(-0.938724\pi\) |
0.358852 | + | 0.933394i | \(0.383168\pi\) | |||||||
\(4\) | 0.939693 | + | 0.342020i | 0.469846 | + | 0.171010i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.28531 | + | 1.07851i | −0.524727 | + | 0.440298i | ||||
\(7\) | 2.14383 | − | 1.23774i | 0.810292 | − | 0.467822i | −0.0367651 | − | 0.999324i | \(-0.511705\pi\) |
0.847057 | + | 0.531502i | \(0.178372\pi\) | |||||||
\(8\) | 0.866025 | + | 0.500000i | 0.306186 | + | 0.176777i | ||||
\(9\) | 0.0320889 | + | 0.181985i | 0.0106963 | + | 0.0606617i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.45059 | + | 2.51250i | −0.437371 | + | 0.757548i | −0.997486 | − | 0.0708665i | \(-0.977424\pi\) |
0.560115 | + | 0.828415i | \(0.310757\pi\) | |||||||
\(12\) | −1.45307 | + | 0.838929i | −0.419465 | + | 0.242178i | ||||
\(13\) | 0.833484 | + | 0.993308i | 0.231167 | + | 0.275494i | 0.869142 | − | 0.494563i | \(-0.164672\pi\) |
−0.637975 | + | 0.770057i | \(0.720228\pi\) | |||||||
\(14\) | 2.32619 | − | 0.846665i | 0.621701 | − | 0.226281i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.766044 | + | 0.642788i | 0.191511 | + | 0.160697i | ||||
\(17\) | −1.22411 | − | 0.215843i | −0.296889 | − | 0.0523496i | 0.0232194 | − | 0.999730i | \(-0.492608\pi\) |
−0.320109 | + | 0.947381i | \(0.603719\pi\) | |||||||
\(18\) | 0.184793i | 0.0435560i | ||||||||
\(19\) | 4.22186 | + | 1.08440i | 0.968561 | + | 0.248777i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.721249 | + | 4.09041i | −0.157390 | + | 0.892600i | ||||
\(22\) | −1.86485 | + | 2.22244i | −0.397587 | + | 0.473826i | ||||
\(23\) | 0.750979 | − | 2.06330i | 0.156590 | − | 0.430227i | −0.836445 | − | 0.548052i | \(-0.815370\pi\) |
0.993034 | + | 0.117824i | \(0.0375920\pi\) | |||||||
\(24\) | −1.57667 | + | 0.573861i | −0.321837 | + | 0.117139i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.648336 | + | 1.12295i | 0.127149 | + | 0.220229i | ||||
\(27\) | −4.62772 | − | 2.67181i | −0.890605 | − | 0.514191i | ||||
\(28\) | 2.43788 | − | 0.429863i | 0.460715 | − | 0.0812365i | ||||
\(29\) | 1.12586 | + | 6.38509i | 0.209068 | + | 1.18568i | 0.890909 | + | 0.454181i | \(0.150068\pi\) |
−0.681842 | + | 0.731500i | \(0.738821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.04442 | + | 5.27310i | 0.546795 | + | 0.947076i | 0.998492 | + | 0.0549047i | \(0.0174855\pi\) |
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(32\) | 0.642788 | + | 0.766044i | 0.113630 | + | 0.135419i | ||||
\(33\) | −1.66488 | − | 4.57422i | −0.289818 | − | 0.796270i | ||||
\(34\) | −1.16803 | − | 0.425128i | −0.200315 | − | 0.0729088i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0320889 | + | 0.181985i | −0.00534815 | + | 0.0303309i | ||||
\(37\) | − | 1.44520i | − | 0.237589i | −0.992919 | − | 0.118794i | \(-0.962097\pi\) | ||
0.992919 | − | 0.118794i | \(-0.0379029\pi\) | |||||||
\(38\) | 3.96942 | + | 1.80104i | 0.643924 | + | 0.292167i | ||||
\(39\) | −2.17563 | −0.348380 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.82601 | + | 1.53221i | 0.285175 | + | 0.239290i | 0.774142 | − | 0.633012i | \(-0.218182\pi\) |
−0.488967 | + | 0.872302i | \(0.662626\pi\) | |||||||
\(42\) | −1.42058 | + | 3.90302i | −0.219201 | + | 0.602249i | ||||
\(43\) | 3.14685 | + | 8.64591i | 0.479891 | + | 1.31849i | 0.909586 | + | 0.415515i | \(0.136399\pi\) |
−0.429696 | + | 0.902974i | \(0.641379\pi\) | |||||||
\(44\) | −2.22244 | + | 1.86485i | −0.335045 | + | 0.281136i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.09786 | − | 1.90155i | 0.161870 | − | 0.280368i | ||||
\(47\) | −10.9588 | + | 1.93233i | −1.59851 | + | 0.281860i | −0.900705 | − | 0.434431i | \(-0.856950\pi\) |
−0.697802 | + | 0.716291i | \(0.745838\pi\) | |||||||
\(48\) | −1.65237 | + | 0.291357i | −0.238499 | + | 0.0420538i | ||||
\(49\) | −0.435991 | + | 0.755158i | −0.0622844 | + | 0.107880i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.59763 | − | 1.34057i | 0.223713 | − | 0.187718i | ||||
\(52\) | 0.443488 | + | 1.21847i | 0.0615007 | + | 0.168972i | ||||
\(53\) | 4.11677 | − | 11.3107i | 0.565482 | − | 1.55365i | −0.245999 | − | 0.969270i | \(-0.579116\pi\) |
0.811481 | − | 0.584379i | \(-0.198662\pi\) | |||||||
\(54\) | −4.09346 | − | 3.43482i | −0.557049 | − | 0.467420i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.47548 | 0.330800 | ||||||||
\(57\) | −5.94709 | + | 4.25688i | −0.787711 | + | 0.563838i | ||||
\(58\) | 6.48359i | 0.851337i | ||||||||
\(59\) | 0.351292 | − | 1.99228i | 0.0457343 | − | 0.259372i | −0.953364 | − | 0.301822i | \(-0.902405\pi\) |
0.999099 | + | 0.0424499i | \(0.0135163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.25853 | + | 0.458067i | 0.161138 | + | 0.0586494i | 0.421330 | − | 0.906908i | \(-0.361564\pi\) |
−0.260192 | + | 0.965557i | \(0.583786\pi\) | |||||||
\(62\) | 2.08251 | + | 5.72164i | 0.264479 | + | 0.726650i | ||||
\(63\) | 0.294044 | + | 0.350428i | 0.0370460 | + | 0.0441497i | ||||
\(64\) | 0.500000 | + | 0.866025i | 0.0625000 | + | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.845282 | − | 4.79383i | −0.104047 | − | 0.590080i | ||||
\(67\) | 3.31520 | − | 0.584560i | 0.405016 | − | 0.0714153i | 0.0325710 | − | 0.999469i | \(-0.489630\pi\) |
0.372445 | + | 0.928054i | \(0.378519\pi\) | |||||||
\(68\) | −1.07646 | − | 0.621495i | −0.130540 | − | 0.0753673i | ||||
\(69\) | 1.84205 | + | 3.19052i | 0.221757 | + | 0.384094i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2805 | + | 5.19768i | −1.69478 | + | 0.616851i | −0.995215 | − | 0.0977142i | \(-0.968847\pi\) |
−0.699569 | + | 0.714565i | \(0.746625\pi\) | |||||||
\(72\) | −0.0632028 | + | 0.173648i | −0.00744852 | + | 0.0204646i | ||||
\(73\) | −0.360357 | + | 0.429457i | −0.0421766 | + | 0.0502641i | −0.786720 | − | 0.617310i | \(-0.788223\pi\) |
0.744544 | + | 0.667574i | \(0.232667\pi\) | |||||||
\(74\) | 0.250956 | − | 1.42324i | 0.0291730 | − | 0.165448i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.59636 | + | 2.46296i | 0.412531 | + | 0.282521i | ||||
\(77\) | 7.18185i | 0.818447i | ||||||||
\(78\) | −2.14258 | − | 0.377794i | −0.242599 | − | 0.0427768i | ||||
\(79\) | −4.96611 | − | 4.16706i | −0.558731 | − | 0.468831i | 0.319154 | − | 0.947703i | \(-0.396601\pi\) |
−0.877885 | + | 0.478872i | \(0.841046\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.90420 | − | 2.87689i | 0.878244 | − | 0.319655i | ||||
\(82\) | 1.53221 | + | 1.82601i | 0.169204 | + | 0.201649i | ||||
\(83\) | −7.32198 | + | 4.22735i | −0.803692 | + | 0.464012i | −0.844760 | − | 0.535145i | \(-0.820257\pi\) |
0.0410686 | + | 0.999156i | \(0.486924\pi\) | |||||||
\(84\) | −2.07675 | + | 3.59705i | −0.226593 | + | 0.392470i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.59770 | + | 9.06100i | 0.172284 | + | 0.977073i | ||||
\(87\) | −9.42109 | − | 5.43927i | −1.01005 | − | 0.583151i | ||||
\(88\) | −2.51250 | + | 1.45059i | −0.267834 | + | 0.154634i | ||||
\(89\) | 9.11595 | − | 7.64919i | 0.966289 | − | 0.810812i | −0.0156760 | − | 0.999877i | \(-0.504990\pi\) |
0.981965 | + | 0.189065i | \(0.0605456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.01631 | + | 1.09785i | 0.316195 | + | 0.115086i | ||||
\(92\) | 1.41138 | − | 1.68202i | 0.147146 | − | 0.175362i | ||||
\(93\) | −10.0610 | − | 1.77403i | −1.04328 | − | 0.183958i | ||||
\(94\) | −11.1279 | −1.14775 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.67786 | −0.171246 | ||||||||
\(97\) | 2.66454 | + | 0.469830i | 0.270543 | + | 0.0477040i | 0.307274 | − | 0.951621i | \(-0.400583\pi\) |
−0.0367308 | + | 0.999325i | \(0.511694\pi\) | |||||||
\(98\) | −0.560499 | + | 0.667976i | −0.0566189 | + | 0.0674758i | ||||
\(99\) | −0.503786 | − | 0.183363i | −0.0506324 | − | 0.0184287i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0902852 | − | 0.0757583i | 0.00898372 | − | 0.00753823i | −0.638285 | − | 0.769800i | \(-0.720356\pi\) |
0.647268 | + | 0.762262i | \(0.275911\pi\) | |||||||
\(102\) | 1.80615 | − | 1.04278i | 0.178835 | − | 0.103251i | ||||
\(103\) | −1.50808 | − | 0.870691i | −0.148596 | − | 0.0857918i | 0.423859 | − | 0.905728i | \(-0.360675\pi\) |
−0.572454 | + | 0.819937i | \(0.694009\pi\) | |||||||
\(104\) | 0.225165 | + | 1.27697i | 0.0220792 | + | 0.125217i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.01832 | − | 10.4240i | 0.584551 | − | 1.01247i | ||||
\(107\) | 14.4681 | − | 8.35318i | 1.39869 | − | 0.807533i | 0.404432 | − | 0.914568i | \(-0.367469\pi\) |
0.994255 | + | 0.107035i | \(0.0341358\pi\) | |||||||
\(108\) | −3.43482 | − | 4.09346i | −0.330516 | − | 0.393893i | ||||
\(109\) | 19.0267 | − | 6.92515i | 1.82243 | − | 0.663309i | 0.827649 | − | 0.561246i | \(-0.189678\pi\) |
0.994778 | − | 0.102063i | \(-0.0325442\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.85753 | + | 1.55865i | 0.176309 | + | 0.147941i | ||||
\(112\) | 2.43788 | + | 0.429863i | 0.230358 | + | 0.0406183i | ||||
\(113\) | − | 16.5448i | − | 1.55641i | −0.628012 | − | 0.778204i | \(-0.716131\pi\) | ||
0.628012 | − | 0.778204i | \(-0.283869\pi\) | |||||||
\(114\) | −6.59594 | + | 3.15951i | −0.617766 | + | 0.295915i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.12586 | + | 6.38509i | −0.104534 | + | 0.592840i | ||||
\(117\) | −0.154022 | + | 0.183556i | −0.0142393 | + | 0.0169697i | ||||
\(118\) | 0.691910 | − | 1.90101i | 0.0636955 | − | 0.175002i | ||||
\(119\) | −2.89144 | + | 1.05240i | −0.265057 | + | 0.0964730i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.29155 | + | 2.23703i | 0.117414 | + | 0.203366i | ||||
\(122\) | 1.15987 | + | 0.669649i | 0.105009 | + | 0.0606272i | ||||
\(123\) | −3.93873 | + | 0.694505i | −0.355143 | + | 0.0626214i | ||||
\(124\) | 1.05732 | + | 5.99634i | 0.0949499 | + | 0.538488i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.228725 | + | 0.396164i | 0.0203765 | + | 0.0352931i | ||||
\(127\) | −0.0842392 | − | 0.100392i | −0.00747502 | − | 0.00890838i | 0.762294 | − | 0.647231i | \(-0.224073\pi\) |
−0.769769 | + | 0.638323i | \(0.779629\pi\) | |||||||
\(128\) | 0.342020 | + | 0.939693i | 0.0302306 | + | 0.0830579i | ||||
\(129\) | −14.5066 | − | 5.27997i | −1.27724 | − | 0.464876i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.22302 | − | 12.6074i | 0.194226 | − | 1.10151i | −0.719290 | − | 0.694710i | \(-0.755533\pi\) |
0.913516 | − | 0.406802i | \(-0.133356\pi\) | |||||||
\(132\) | − | 4.86778i | − | 0.423686i | ||||||
\(133\) | 10.3932 | − | 2.90081i | 0.901201 | − | 0.251532i | ||||
\(134\) | 3.36634 | 0.290808 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.952186 | − | 0.798979i | −0.0816492 | − | 0.0685119i | ||||
\(137\) | 5.34535 | − | 14.6862i | 0.456684 | − | 1.25473i | −0.471255 | − | 0.881997i | \(-0.656199\pi\) |
0.927939 | − | 0.372732i | \(-0.121579\pi\) | |||||||
\(138\) | 1.26004 | + | 3.46192i | 0.107261 | + | 0.294698i | ||||
\(139\) | 8.79431 | − | 7.37930i | 0.745924 | − | 0.625904i | −0.188498 | − | 0.982074i | \(-0.560362\pi\) |
0.934421 | + | 0.356169i | \(0.115917\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.33549 | − | 16.1695i | 0.786190 | − | 1.36172i | ||||
\(142\) | −14.9661 | + | 2.63893i | −1.25593 | + | 0.221454i | ||||
\(143\) | −3.70474 | + | 0.653245i | −0.309806 | + | 0.0546271i | ||||
\(144\) | −0.0923963 | + | 0.160035i | −0.00769969 | + | 0.0133363i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.429457 | + | 0.360357i | −0.0355421 | + | 0.0298233i | ||||
\(147\) | −0.500396 | − | 1.37483i | −0.0412720 | − | 0.113394i | ||||
\(148\) | 0.494286 | − | 1.35804i | 0.0406301 | − | 0.111630i | ||||
\(149\) | 11.6068 | + | 9.73926i | 0.950866 | + | 0.797871i | 0.979443 | − | 0.201720i | \(-0.0646532\pi\) |
−0.0285771 | + | 0.999592i | \(0.509098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.78759 | −0.470988 | −0.235494 | − | 0.971876i | \(-0.575671\pi\) | ||||
−0.235494 | + | 0.971876i | \(0.575671\pi\) | |||||||
\(152\) | 3.11404 | + | 3.05004i | 0.252582 | + | 0.247391i | ||||
\(153\) | − | 0.229695i | − | 0.0185698i | ||||||
\(154\) | −1.24711 | + | 7.07274i | −0.100495 | + | 0.569937i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.04442 | − | 0.744109i | −0.163685 | − | 0.0595764i | ||||
\(157\) | −3.76870 | − | 10.3544i | −0.300775 | − | 0.826372i | −0.994366 | − | 0.106003i | \(-0.966195\pi\) |
0.693591 | − | 0.720369i | \(-0.256028\pi\) | |||||||
\(158\) | −4.16706 | − | 4.96611i | −0.331514 | − | 0.395082i | ||||
\(159\) | 10.0979 | + | 17.4900i | 0.800814 | + | 1.38705i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.943857 | − | 5.35288i | −0.0743864 | − | 0.421866i | ||||
\(162\) | 8.28368 | − | 1.46064i | 0.650828 | − | 0.114758i | ||||
\(163\) | 19.2078 | + | 11.0896i | 1.50447 | + | 0.868605i | 0.999987 | + | 0.00518168i | \(0.00164939\pi\) |
0.504481 | + | 0.863423i | \(0.331684\pi\) | |||||||
\(164\) | 1.19184 | + | 2.06434i | 0.0930675 | + | 0.161198i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.94481 | + | 2.89168i | −0.616637 | + | 0.224438i | ||||
\(167\) | 5.94713 | − | 16.3396i | 0.460203 | − | 1.26440i | −0.465130 | − | 0.885242i | \(-0.653993\pi\) |
0.925333 | − | 0.379155i | \(-0.123785\pi\) | |||||||
\(168\) | −2.66982 | + | 3.18177i | −0.205981 | + | 0.245479i | ||||
\(169\) | 1.96546 | − | 11.1467i | 0.151189 | − | 0.857438i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0618692 | + | 0.803112i | −0.00473125 | + | 0.0614155i | ||||
\(172\) | 9.20078i | 0.701553i | ||||||||
\(173\) | 2.11553 | + | 0.373025i | 0.160841 | + | 0.0283606i | 0.253489 | − | 0.967338i | \(-0.418422\pi\) |
−0.0926478 | + | 0.995699i | \(0.529533\pi\) | |||||||
\(174\) | −8.33344 | − | 6.99259i | −0.631757 | − | 0.530107i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.72623 | + | 0.992265i | −0.205497 | + | 0.0747948i | ||||
\(177\) | 2.18183 | + | 2.60020i | 0.163996 | + | 0.195443i | ||||
\(178\) | 10.3057 | − | 5.95001i | 0.772447 | − | 0.445972i | ||||
\(179\) | −5.19089 | + | 8.99089i | −0.387985 | + | 0.672011i | −0.992178 | − | 0.124827i | \(-0.960162\pi\) |
0.604193 | + | 0.796838i | \(0.293496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.89049 | − | 16.3928i | −0.214848 | − | 1.21846i | −0.881170 | − | 0.472800i | \(-0.843243\pi\) |
0.666322 | − | 0.745664i | \(-0.267868\pi\) | |||||||
\(182\) | 2.77984 | + | 1.60494i | 0.206056 | + | 0.118966i | ||||
\(183\) | −1.94609 | + | 1.12358i | −0.143859 | + | 0.0830571i | ||||
\(184\) | 1.68202 | − | 1.41138i | 0.124000 | − | 0.104048i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.60011 | − | 3.49415i | −0.703914 | − | 0.256204i | ||||
\(187\) | 2.31799 | − | 2.76247i | 0.169508 | − | 0.202012i | ||||
\(188\) | −10.9588 | − | 1.93233i | −0.799254 | − | 0.140930i | ||||
\(189\) | −13.2281 | −0.962200 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7916 | −1.57679 | −0.788393 | − | 0.615172i | \(-0.789086\pi\) | ||||
−0.788393 | + | 0.615172i | \(0.789086\pi\) | |||||||
\(192\) | −1.65237 | − | 0.291357i | −0.119249 | − | 0.0210269i | ||||
\(193\) | −14.7264 | + | 17.5503i | −1.06003 | + | 1.26330i | −0.0966060 | + | 0.995323i | \(0.530799\pi\) |
−0.963426 | + | 0.267974i | \(0.913646\pi\) | |||||||
\(194\) | 2.54247 | + | 0.925384i | 0.182539 | + | 0.0664387i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.667976 | + | 0.560499i | −0.0477126 | + | 0.0400356i | ||||
\(197\) | 4.29163 | − | 2.47777i | 0.305766 | − | 0.176534i | −0.339264 | − | 0.940691i | \(-0.610178\pi\) |
0.645030 | + | 0.764157i | \(0.276845\pi\) | |||||||
\(198\) | −0.464292 | − | 0.268059i | −0.0329958 | − | 0.0190501i | ||||
\(199\) | −4.27197 | − | 24.2276i | −0.302832 | − | 1.71745i | −0.633537 | − | 0.773713i | \(-0.718397\pi\) |
0.330704 | − | 0.943734i | \(-0.392714\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.82412 | + | 4.89153i | −0.199198 | + | 0.345022i | ||||
\(202\) | 0.102069 | − | 0.0589295i | 0.00718154 | − | 0.00414626i | ||||
\(203\) | 10.3167 | + | 12.2950i | 0.724094 | + | 0.862941i | ||||
\(204\) | 1.95979 | − | 0.713304i | 0.137212 | − | 0.0499413i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.33398 | − | 1.11934i | −0.0929426 | − | 0.0779881i | ||||
\(207\) | 0.399588 | + | 0.0704581i | 0.0277733 | + | 0.00489717i | ||||
\(208\) | 1.29667i | 0.0899080i | ||||||||
\(209\) | −8.84875 | + | 9.03442i | −0.612081 | + | 0.624924i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.638032 | + | 3.61846i | −0.0439239 | + | 0.249105i | −0.998862 | − | 0.0477014i | \(-0.984810\pi\) |
0.954938 | + | 0.296806i | \(0.0959215\pi\) | |||||||
\(212\) | 7.73700 | − | 9.22060i | 0.531379 | − | 0.633273i | ||||
\(213\) | 8.72096 | − | 23.9607i | 0.597551 | − | 1.64176i | ||||
\(214\) | 15.6988 | − | 5.71391i | 1.07315 | − | 0.390595i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.67181 | − | 4.62772i | −0.181794 | − | 0.314876i | ||||
\(217\) | 13.0535 | + | 7.53642i | 0.886127 | + | 0.511606i | ||||
\(218\) | 19.9402 | − | 3.51599i | 1.35052 | − | 0.238133i | ||||
\(219\) | −0.163339 | − | 0.926343i | −0.0110374 | − | 0.0625965i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.805875 | − | 1.39582i | −0.0542090 | − | 0.0938927i | ||||
\(222\) | 1.55865 | + | 1.85753i | 0.104610 | + | 0.124669i | ||||
\(223\) | −2.54920 | − | 7.00387i | −0.170707 | − | 0.469014i | 0.824607 | − | 0.565706i | \(-0.191396\pi\) |
−0.995314 | + | 0.0966918i | \(0.969174\pi\) | |||||||
\(224\) | 2.32619 | + | 0.846665i | 0.155425 | + | 0.0565702i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.87298 | − | 16.2935i | 0.191108 | − | 1.08383i | ||||
\(227\) | 11.4167i | 0.757750i | 0.925448 | + | 0.378875i | \(0.123689\pi\) | ||||
−0.925448 | + | 0.378875i | \(0.876311\pi\) | |||||||
\(228\) | −7.04438 | + | 1.96614i | −0.466525 | + | 0.130211i | ||||
\(229\) | 3.19332 | 0.211021 | 0.105510 | − | 0.994418i | \(-0.466352\pi\) | ||||
0.105510 | + | 0.994418i | \(0.466352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.23093 | − | 7.74567i | −0.607350 | − | 0.509627i | ||||
\(232\) | −2.21752 | + | 6.09258i | −0.145587 | + | 0.399997i | ||||
\(233\) | 7.96876 | + | 21.8940i | 0.522051 | + | 1.43432i | 0.868234 | + | 0.496156i | \(0.165255\pi\) |
−0.346183 | + | 0.938167i | \(0.612522\pi\) | |||||||
\(234\) | −0.183556 | + | 0.154022i | −0.0119994 | + | 0.0100687i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.01150 | − | 1.75198i | 0.0658433 | − | 0.114044i | ||||
\(237\) | 10.7120 | − | 1.88881i | 0.695817 | − | 0.122691i | ||||
\(238\) | −3.03025 | + | 0.534316i | −0.196422 | + | 0.0346345i | ||||
\(239\) | −4.11104 | + | 7.12053i | −0.265921 | + | 0.460589i | −0.967805 | − | 0.251703i | \(-0.919009\pi\) |
0.701883 | + | 0.712292i | \(0.252343\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9574 | − | 13.3899i | 1.02791 | − | 0.862518i | 0.0373080 | − | 0.999304i | \(-0.488122\pi\) |
0.990601 | + | 0.136786i | \(0.0436773\pi\) | |||||||
\(242\) | 0.883473 | + | 2.42732i | 0.0567918 | + | 0.156034i | ||||
\(243\) | 0.655868 | − | 1.80198i | 0.0420740 | − | 0.115597i | ||||
\(244\) | 1.02596 | + | 0.860884i | 0.0656805 | + | 0.0551124i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.99949 | −0.254998 | ||||||||
\(247\) | 2.44171 | + | 5.09743i | 0.155363 | + | 0.324342i | ||||
\(248\) | 6.08885i | 0.386642i | ||||||||
\(249\) | 2.46333 | − | 13.9703i | 0.156107 | − | 0.885330i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.7939 | − | 3.92864i | −0.681302 | − | 0.247974i | −0.0218955 | − | 0.999760i | \(-0.506970\pi\) |
−0.659406 | + | 0.751787i | \(0.729192\pi\) | |||||||
\(252\) | 0.156457 | + | 0.429863i | 0.00985589 | + | 0.0270788i | ||||
\(253\) | 4.09468 | + | 4.87985i | 0.257430 | + | 0.306793i | ||||
\(254\) | −0.0655264 | − | 0.113495i | −0.00411149 | − | 0.00712132i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.173648 | + | 0.984808i | 0.0108530 | + | 0.0615505i | ||||
\(257\) | 1.82847 | − | 0.322408i | 0.114057 | − | 0.0201112i | −0.116329 | − | 0.993211i | \(-0.537113\pi\) |
0.230385 | + | 0.973100i | \(0.426001\pi\) | |||||||
\(258\) | −13.3694 | − | 7.71881i | −0.832340 | − | 0.480552i | ||||
\(259\) | −1.78878 | − | 3.09826i | −0.111149 | − | 0.192516i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.12586 | + | 0.409781i | −0.0696892 | + | 0.0253648i | ||||
\(262\) | 4.37850 | − | 12.0298i | 0.270505 | − | 0.743205i | ||||
\(263\) | −6.59082 | + | 7.85464i | −0.406407 | + | 0.484338i | −0.929963 | − | 0.367654i | \(-0.880161\pi\) |
0.523555 | + | 0.851992i | \(0.324605\pi\) | |||||||
\(264\) | 0.845282 | − | 4.79383i | 0.0520235 | − | 0.295040i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.7390 | − | 1.05199i | 0.658449 | − | 0.0645014i | ||||
\(267\) | 19.9666i | 1.22193i | ||||||||
\(268\) | 3.31520 | + | 0.584560i | 0.202508 | + | 0.0357077i | ||||
\(269\) | −20.2958 | − | 17.0302i | −1.23746 | − | 1.03835i | −0.997719 | − | 0.0675114i | \(-0.978494\pi\) |
−0.239738 | − | 0.970838i | \(-0.577061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.4094 | + | 8.52031i | −1.42202 | + | 0.517572i | −0.934633 | − | 0.355615i | \(-0.884272\pi\) |
−0.487385 | + | 0.873187i | \(0.662049\pi\) | |||||||
\(272\) | −0.798979 | − | 0.952186i | −0.0484452 | − | 0.0577347i | ||||
\(273\) | −4.66419 | + | 2.69287i | −0.282289 | + | 0.162980i | ||||
\(274\) | 7.81438 | − | 13.5349i | 0.472084 | − | 0.817673i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.639737 | + | 3.62813i | 0.0385076 | + | 0.218388i | ||||
\(277\) | −12.4407 | − | 7.18265i | −0.747490 | − | 0.431564i | 0.0772960 | − | 0.997008i | \(-0.475371\pi\) |
−0.824786 | + | 0.565444i | \(0.808705\pi\) | |||||||
\(278\) | 9.94211 | − | 5.74008i | 0.596288 | − | 0.344267i | ||||
\(279\) | −0.861933 | + | 0.723248i | −0.0516026 | + | 0.0432997i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.2726 | + | 9.19849i | 1.50764 | + | 0.548736i | 0.958025 | − | 0.286683i | \(-0.0925527\pi\) |
0.549614 | + | 0.835419i | \(0.314775\pi\) | |||||||
\(282\) | 12.0015 | − | 14.3028i | 0.714678 | − | 0.851720i | ||||
\(283\) | −19.8587 | − | 3.50163i | −1.18048 | − | 0.208150i | −0.451235 | − | 0.892405i | \(-0.649016\pi\) |
−0.729243 | + | 0.684255i | \(0.760127\pi\) | |||||||
\(284\) | −15.1970 | −0.901776 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.76189 | −0.222445 | ||||||||
\(287\) | 5.81114 | + | 1.02466i | 0.343021 | + | 0.0604838i | ||||
\(288\) | −0.118782 | + | 0.141559i | −0.00699932 | + | 0.00834146i | ||||
\(289\) | −14.5229 | − | 5.28591i | −0.854290 | − | 0.310936i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.47760 | + | 2.91805i | −0.203860 | + | 0.171059i | ||||
\(292\) | −0.485507 | + | 0.280308i | −0.0284122 | + | 0.0164038i | ||||
\(293\) | −17.3197 | − | 9.99952i | −1.01183 | − | 0.584178i | −0.100100 | − | 0.994977i | \(-0.531916\pi\) |
−0.911726 | + | 0.410799i | \(0.865250\pi\) | |||||||
\(294\) | −0.254058 | − | 1.44083i | −0.0148170 | − | 0.0840311i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.722598 | − | 1.25158i | 0.0420002 | − | 0.0727464i | ||||
\(297\) | 13.4259 | − | 7.75144i | 0.779049 | − | 0.449784i | ||||
\(298\) | 9.73926 | + | 11.6068i | 0.564180 | + | 0.672364i | ||||
\(299\) | 2.67542 | − | 0.973773i | 0.154723 | − | 0.0563147i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.4477 | + | 14.6404i | 1.00567 | + | 0.843858i | ||||
\(302\) | −5.69967 | − | 1.00500i | −0.327979 | − | 0.0578315i | ||||
\(303\) | 0.197751i | 0.0113605i | ||||||||
\(304\) | 2.53709 | + | 3.54445i | 0.145512 | + | 0.203288i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.0398862 | − | 0.226206i | 0.00228014 | − | 0.0129313i | ||||
\(307\) | −12.4713 | + | 14.8627i | −0.711772 | + | 0.848257i | −0.993804 | − | 0.111148i | \(-0.964547\pi\) |
0.282032 | + | 0.959405i | \(0.408992\pi\) | |||||||
\(308\) | −2.45634 | + | 6.74873i | −0.139963 | + | 0.384544i | ||||
\(309\) | 2.74559 | − | 0.999312i | 0.156191 | − | 0.0568489i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.69949 | − | 4.67566i | −0.153074 | − | 0.265132i | 0.779282 | − | 0.626673i | \(-0.215584\pi\) |
−0.932356 | + | 0.361541i | \(0.882251\pi\) | |||||||
\(312\) | −1.88415 | − | 1.08782i | −0.106669 | − | 0.0615854i | ||||
\(313\) | 15.9375 | − | 2.81021i | 0.900841 | − | 0.158843i | 0.295999 | − | 0.955188i | \(-0.404347\pi\) |
0.604842 | + | 0.796345i | \(0.293236\pi\) | |||||||
\(314\) | −1.91342 | − | 10.8515i | −0.107980 | − | 0.612388i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.24140 | − | 5.61427i | −0.182343 | − | 0.315827i | ||||
\(317\) | 1.57543 | + | 1.87753i | 0.0884852 | + | 0.105453i | 0.808470 | − | 0.588537i | \(-0.200296\pi\) |
−0.719985 | + | 0.693989i | \(0.755851\pi\) | |||||||
\(318\) | 6.90736 | + | 18.9778i | 0.387345 | + | 1.06422i | ||||
\(319\) | −17.6757 | − | 6.43344i | −0.989651 | − | 0.360203i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.86752 | + | 27.6051i | −0.271678 | + | 1.54076i | ||||
\(322\) | − | 5.43546i | − | 0.302906i | ||||||
\(323\) | −4.93394 | − | 2.23867i | −0.274532 | − | 0.124563i | ||||
\(324\) | 8.41147 | 0.467304 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.9903 | + | 14.2565i | 0.941003 | + | 0.789595i | ||||
\(327\) | −11.6194 | + | 31.9241i | −0.642555 | + | 1.76541i | ||||
\(328\) | 0.815270 | + | 2.23994i | 0.0450158 | + | 0.123680i | ||||
\(329\) | −21.1021 | + | 17.7068i | −1.16340 | + | 0.976206i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.51812 | + | 2.62947i | −0.0834436 | + | 0.144529i | −0.904727 | − | 0.425992i | \(-0.859925\pi\) |
0.821283 | + | 0.570521i | \(0.193259\pi\) | |||||||
\(332\) | −8.32625 | + | 1.46814i | −0.456962 | + | 0.0805748i | ||||
\(333\) | 0.263004 | − | 0.0463747i | 0.0144125 | − | 0.00254132i | ||||
\(334\) | 8.69412 | − | 15.0587i | 0.475721 | − | 0.823973i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.18177 | + | 2.66982i | −0.173580 | + | 0.145651i | ||||
\(337\) | −2.07369 | − | 5.69742i | −0.112961 | − | 0.310358i | 0.870310 | − | 0.492504i | \(-0.163918\pi\) |
−0.983272 | + | 0.182145i | \(0.941696\pi\) | |||||||
\(338\) | 3.87120 | − | 10.6360i | 0.210566 | − | 0.578525i | ||||
\(339\) | 21.2653 | + | 17.8437i | 1.15497 | + | 0.969138i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.6649 | −0.956608 | ||||||||
\(342\) | −0.200388 | + | 0.780168i | −0.0108358 | + | 0.0421866i | ||||
\(343\) | 19.4870i | 1.05220i | ||||||||
\(344\) | −1.59770 | + | 9.06100i | −0.0861422 | + | 0.488537i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.01862 | + | 0.734716i | 0.108522 | + | 0.0394986i | ||||
\(347\) | 0.983940 | + | 2.70335i | 0.0528207 | + | 0.145124i | 0.963297 | − | 0.268437i | \(-0.0865072\pi\) |
−0.910477 | + | 0.413561i | \(0.864285\pi\) | |||||||
\(348\) | −6.99259 | − | 8.33344i | −0.374842 | − | 0.446719i | ||||
\(349\) | 16.3979 | + | 28.4020i | 0.877761 | + | 1.52033i | 0.853793 | + | 0.520613i | \(0.174297\pi\) |
0.0239680 | + | 0.999713i | \(0.492370\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.20320 | − | 6.82367i | −0.0642219 | − | 0.364220i | ||||
\(352\) | −2.85711 | + | 0.503786i | −0.152285 | + | 0.0268519i | ||||
\(353\) | −18.3605 | − | 10.6004i | −0.977231 | − | 0.564204i | −0.0757977 | − | 0.997123i | \(-0.524150\pi\) |
−0.901433 | + | 0.432919i | \(0.857484\pi\) | |||||||
\(354\) | 1.69716 | + | 2.93957i | 0.0902031 | + | 0.156236i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.1824 | − | 4.07005i | 0.592664 | − | 0.215712i | ||||
\(357\) | 1.76577 | − | 4.85142i | 0.0934546 | − | 0.256764i | ||||
\(358\) | −6.67328 | + | 7.95291i | −0.352694 | + | 0.420324i | ||||
\(359\) | −3.22806 | + | 18.3072i | −0.170370 | + | 0.966218i | 0.772983 | + | 0.634427i | \(0.218764\pi\) |
−0.943353 | + | 0.331791i | \(0.892347\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.6482 | + | 9.15633i | 0.876220 | + | 0.481912i | ||||
\(362\) | − | 16.6456i | − | 0.874876i | ||||||
\(363\) | −4.26823 | − | 0.752605i | −0.224024 | − | 0.0395015i | ||||
\(364\) | 2.45892 | + | 2.06328i | 0.128882 | + | 0.108145i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.11163 | + | 0.768571i | −0.110377 | + | 0.0401739i | ||||
\(367\) | 13.9628 | + | 16.6403i | 0.728855 | + | 0.868615i | 0.995459 | − | 0.0951910i | \(-0.0303462\pi\) |
−0.266605 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(368\) | 1.90155 | − | 1.09786i | 0.0991249 | − | 0.0572298i | ||||
\(369\) | −0.220244 | + | 0.381474i | −0.0114654 | + | 0.0198587i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.17411 | − | 29.3438i | −0.268626 | − | 1.52345i | ||||
\(372\) | −8.84751 | − | 5.10811i | −0.458722 | − | 0.264843i | ||||
\(373\) | 19.4123 | − | 11.2077i | 1.00513 | − | 0.580312i | 0.0953679 | − | 0.995442i | \(-0.469597\pi\) |
0.909762 | + | 0.415130i | \(0.136264\pi\) | |||||||
\(374\) | 2.76247 | − | 2.31799i | 0.142844 | − | 0.119860i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.4568 | − | 3.80596i | −0.539267 | − | 0.196277i | ||||
\(377\) | −5.40397 | + | 6.44020i | −0.278318 | + | 0.331687i | ||||
\(378\) | −13.0271 | − | 2.29703i | −0.670042 | − | 0.118146i | ||||
\(379\) | 8.45251 | 0.434176 | 0.217088 | − | 0.976152i | \(-0.430344\pi\) | ||||
0.217088 | + | 0.976152i | \(0.430344\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.219888 | 0.0112652 | ||||||||
\(382\) | −21.4605 | − | 3.78407i | −1.09802 | − | 0.193610i | ||||
\(383\) | 6.32838 | − | 7.54187i | 0.323365 | − | 0.385372i | −0.579732 | − | 0.814807i | \(-0.696843\pi\) |
0.903098 | + | 0.429435i | \(0.141287\pi\) | |||||||
\(384\) | −1.57667 | − | 0.573861i | −0.0804591 | − | 0.0292847i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.5503 | + | 14.7264i | −0.893286 | + | 0.749556i | ||||
\(387\) | −1.47245 | + | 0.850118i | −0.0748487 | + | 0.0432139i | ||||
\(388\) | 2.34315 | + | 1.35282i | 0.118956 | + | 0.0686791i | ||||
\(389\) | 1.47850 | + | 8.38497i | 0.0749627 | + | 0.425135i | 0.999075 | + | 0.0430125i | \(0.0136955\pi\) |
−0.924112 | + | 0.382122i | \(0.875193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.36463 | + | 2.36360i | −0.0690121 | + | 0.119532i | ||||
\(392\) | −0.755158 | + | 0.435991i | −0.0381412 | + | 0.0220208i | ||||
\(393\) | 13.8069 | + | 16.4544i | 0.696466 | + | 0.830016i | ||||
\(394\) | 4.65669 | − | 1.69490i | 0.234601 | − | 0.0853877i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.410690 | − | 0.344610i | −0.0206380 | − | 0.0173173i | ||||
\(397\) | −24.1425 | − | 4.25698i | −1.21168 | − | 0.213651i | −0.468938 | − | 0.883231i | \(-0.655363\pi\) |
−0.742740 | + | 0.669580i | \(0.766474\pi\) | |||||||
\(398\) | − | 24.6013i | − | 1.23315i | ||||||
\(399\) | −7.48063 | + | 16.4870i | −0.374500 | + | 0.825383i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.863801 | + | 4.89886i | −0.0431362 | + | 0.244637i | −0.998750 | − | 0.0499849i | \(-0.984083\pi\) |
0.955614 | + | 0.294622i | \(0.0951938\pi\) | |||||||
\(402\) | −3.63062 | + | 4.32681i | −0.181079 | + | 0.215802i | ||||
\(403\) | −2.70033 | + | 7.41909i | −0.134513 | + | 0.369571i | ||||
\(404\) | 0.110751 | − | 0.0403101i | 0.00551008 | − | 0.00200550i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.02501 | + | 13.8997i | 0.398274 | + | 0.689831i | ||||
\(407\) | 3.63106 | + | 2.09639i | 0.179985 | + | 0.103914i | ||||
\(408\) | 2.05388 | − | 0.362154i | 0.101682 | − | 0.0179293i | ||||
\(409\) | −3.14232 | − | 17.8210i | −0.155377 | − | 0.881189i | −0.958440 | − | 0.285295i | \(-0.907909\pi\) |
0.803062 | − | 0.595895i | \(-0.203203\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.1114 | + | 22.7096i | 0.646739 | + | 1.12018i | ||||
\(412\) | −1.11934 | − | 1.33398i | −0.0551459 | − | 0.0657203i | ||||
\(413\) | −1.71281 | − | 4.70591i | −0.0842819 | − | 0.231563i | ||||
\(414\) | 0.381282 | + | 0.138775i | 0.0187390 | + | 0.00682043i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.225165 | + | 1.27697i | −0.0110396 | + | 0.0626087i | ||||
\(417\) | 19.2621i | 0.943268i | ||||||||
\(418\) | −10.2831 | + | 7.36059i | −0.502964 | + | 0.360018i | ||||
\(419\) | 10.5816 | 0.516945 | 0.258472 | − | 0.966019i | \(-0.416781\pi\) | ||||
0.258472 | + | 0.966019i | \(0.416781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5815 | − | 15.5917i | −0.905605 | − | 0.759893i | 0.0656729 | − | 0.997841i | \(-0.479081\pi\) |
−0.971278 | + | 0.237949i | \(0.923525\pi\) | |||||||
\(422\) | −1.25668 | + | 3.45269i | −0.0611741 | + | 0.168074i | ||||
\(423\) | −0.703312 | − | 1.93233i | −0.0341962 | − | 0.0939533i | ||||
\(424\) | 9.22060 | − | 7.73700i | 0.447792 | − | 0.375742i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.7492 | − | 22.0823i | 0.617701 | − | 1.06989i | ||||
\(427\) | 3.26504 | − | 0.575715i | 0.158006 | − | 0.0278608i | ||||
\(428\) | 16.4526 | − | 2.90103i | 0.795264 | − | 0.140227i | ||||
\(429\) | 3.15596 | − | 5.46628i | 0.152371 | − | 0.263914i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.3497 | − | 22.9491i | 1.31739 | − | 1.10542i | 0.330536 | − | 0.943794i | \(-0.392771\pi\) |
0.986852 | − | 0.161626i | \(-0.0516738\pi\) | |||||||
\(432\) | −1.82763 | − | 5.02137i | −0.0879318 | − | 0.241591i | ||||
\(433\) | 11.3099 | − | 31.0738i | 0.543521 | − | 1.49331i | −0.298790 | − | 0.954319i | \(-0.596583\pi\) |
0.842311 | − | 0.538992i | \(-0.181195\pi\) | |||||||
\(434\) | 11.5465 | + | 9.68864i | 0.554248 | + | 0.465069i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.2478 | 0.969693 | ||||||||
\(437\) | 5.40796 | − | 7.89659i | 0.258698 | − | 0.377745i | ||||
\(438\) | − | 0.940634i | − | 0.0449452i | ||||||
\(439\) | −1.02662 | + | 5.82227i | −0.0489981 | + | 0.277882i | −0.999456 | − | 0.0329703i | \(-0.989503\pi\) |
0.950458 | + | 0.310852i | \(0.100614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.151418 | − | 0.0551116i | −0.00721038 | − | 0.00262436i | ||||
\(442\) | −0.551251 | − | 1.51455i | −0.0262203 | − | 0.0720398i | ||||
\(443\) | 7.60590 | + | 9.06436i | 0.361367 | + | 0.430661i | 0.915841 | − | 0.401540i | \(-0.131525\pi\) |
−0.554474 | + | 0.832201i | \(0.687081\pi\) | |||||||
\(444\) | 1.21242 | + | 2.09997i | 0.0575388 | + | 0.0996601i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.29426 | − | 7.34013i | −0.0612851 | − | 0.347565i | ||||
\(447\) | −25.0360 | + | 4.41452i | −1.18416 | + | 0.208800i | ||||
\(448\) | 2.14383 | + | 1.23774i | 0.101287 | + | 0.0584778i | ||||
\(449\) | −3.79197 | − | 6.56789i | −0.178954 | − | 0.309958i | 0.762568 | − | 0.646908i | \(-0.223938\pi\) |
−0.941523 | + | 0.336950i | \(0.890605\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.49848 | + | 2.36525i | −0.306001 | + | 0.111375i | ||||
\(452\) | 5.65867 | − | 15.5471i | 0.266161 | − | 0.731273i | ||||
\(453\) | 6.24195 | − | 7.43887i | 0.293273 | − | 0.349509i | ||||
\(454\) | −1.98248 | + | 11.2432i | −0.0930424 | + | 0.527670i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.27877 | + | 0.713026i | −0.340860 | + | 0.0333905i | ||||
\(457\) | − | 13.0616i | − | 0.610995i | −0.952193 | − | 0.305497i | \(-0.901177\pi\) | ||
0.952193 | − | 0.305497i | \(-0.0988227\pi\) | |||||||
\(458\) | 3.14481 | + | 0.554515i | 0.146947 | + | 0.0259108i | ||||
\(459\) | 5.08813 | + | 4.26945i | 0.237493 | + | 0.199281i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.3589 | − | 10.6858i | 1.36738 | − | 0.497685i | 0.449051 | − | 0.893506i | \(-0.351762\pi\) |
0.918328 | + | 0.395821i | \(0.129540\pi\) | |||||||
\(462\) | −7.74567 | − | 9.23093i | −0.360361 | − | 0.429462i | ||||
\(463\) | −12.0928 | + | 6.98180i | −0.562002 | + | 0.324472i | −0.753949 | − | 0.656933i | \(-0.771853\pi\) |
0.191947 | + | 0.981405i | \(0.438520\pi\) | |||||||
\(464\) | −3.24179 | + | 5.61495i | −0.150496 | + | 0.260668i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.04585 | + | 22.9451i | 0.187420 | + | 1.06291i | ||||
\(467\) | −10.2252 | − | 5.90352i | −0.473165 | − | 0.273182i | 0.244399 | − | 0.969675i | \(-0.421409\pi\) |
−0.717564 | + | 0.696493i | \(0.754743\pi\) | |||||||
\(468\) | −0.207513 | + | 0.119808i | −0.00959228 | + | 0.00553811i | ||||
\(469\) | 6.38370 | − | 5.35656i | 0.294772 | − | 0.247343i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.3732 | + | 6.32334i | 0.800517 | + | 0.291364i | ||||
\(472\) | 1.30037 | − | 1.54971i | 0.0598542 | − | 0.0713314i | ||||
\(473\) | −26.2877 | − | 4.63523i | −1.20871 | − | 0.213128i | ||||
\(474\) | 10.8772 | 0.499607 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.07700 | −0.141034 | ||||||||
\(477\) | 2.19049 | + | 0.386242i | 0.100296 | + | 0.0176848i | ||||
\(478\) | −5.28505 | + | 6.29848i | −0.241733 | + | 0.288086i | ||||
\(479\) | −30.1189 | − | 10.9624i | −1.37617 | − | 0.500884i | −0.455153 | − | 0.890413i | \(-0.650415\pi\) |
−0.921014 | + | 0.389529i | \(0.872638\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.43552 | − | 1.20455i | 0.0654543 | − | 0.0549227i | ||||
\(482\) | 18.0401 | − | 10.4155i | 0.821705 | − | 0.474412i | ||||
\(483\) | 7.89809 | + | 4.55996i | 0.359375 | + | 0.207485i | ||||
\(484\) | 0.448551 | + | 2.54386i | 0.0203887 | + | 0.115630i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.958815 | − | 1.66072i | 0.0434927 | − | 0.0753316i | ||||
\(487\) | 15.1334 | − | 8.73726i | 0.685759 | − | 0.395923i | −0.116263 | − | 0.993219i | \(-0.537091\pi\) |
0.802021 | + | 0.597296i | \(0.203758\pi\) | |||||||
\(488\) | 0.860884 | + | 1.02596i | 0.0389704 | + | 0.0464431i | ||||
\(489\) | −34.9693 | + | 12.7278i | −1.58137 | + | 0.575570i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.62811 | − | 1.36614i | −0.0734754 | − | 0.0616531i | 0.605310 | − | 0.795990i | \(-0.293049\pi\) |
−0.678786 | + | 0.734336i | \(0.737493\pi\) | |||||||
\(492\) | −3.93873 | − | 0.694505i | −0.177572 | − | 0.0313107i | ||||
\(493\) | − | 8.05903i | − | 0.362961i | ||||||
\(494\) | 1.51946 | + | 5.44399i | 0.0683637 | + | 0.244937i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.05732 | + | 5.99634i | −0.0474749 | + | 0.269244i | ||||
\(497\) | −24.1816 | + | 28.8185i | −1.08469 | + | 1.29269i | ||||
\(498\) | 4.85182 | − | 13.3303i | 0.217415 | − | 0.597344i | ||||
\(499\) | 34.1891 | − | 12.4438i | 1.53051 | − | 0.557062i | 0.566767 | − | 0.823878i | \(-0.308194\pi\) |
0.963747 | + | 0.266817i | \(0.0859719\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5875 | + | 25.2663i | 0.651722 | + | 1.12882i | ||||
\(502\) | −9.94767 | − | 5.74329i | −0.443986 | − | 0.256336i | ||||
\(503\) | −9.07677 | + | 1.60048i | −0.404713 | + | 0.0713619i | −0.372299 | − | 0.928113i | \(-0.621431\pi\) |
−0.0324139 | + | 0.999475i | \(0.510319\pi\) | |||||||
\(504\) | 0.0794355 | + | 0.450501i | 0.00353834 | + | 0.0200669i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.18509 | + | 5.51674i | 0.141595 | + | 0.245249i | ||||
\(507\) | 12.2072 | + | 14.5480i | 0.542142 | + | 0.646100i | ||||
\(508\) | −0.0448227 | − | 0.123149i | −0.00198869 | − | 0.00546387i | ||||
\(509\) | 16.3916 | + | 5.96606i | 0.726546 | + | 0.264441i | 0.678702 | − | 0.734414i | \(-0.262543\pi\) |
0.0478437 | + | 0.998855i | \(0.484765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.240988 | + | 1.36671i | −0.0106607 | + | 0.0604597i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −16.6403 | − | 16.2983i | −0.734686 | − | 0.719588i | ||||
\(514\) | 1.85667 | 0.0818943 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.8259 | − | 9.92310i | −0.520606 | − | 0.436840i | ||||
\(517\) | 11.0418 | − | 30.3371i | 0.485618 | − | 1.33422i | ||||
\(518\) | −1.22360 | − | 3.36181i | −0.0537618 | − | 0.147709i | ||||
\(519\) | −2.76107 | + | 2.31681i | −0.121197 | + | 0.101697i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5137 | + | 18.2102i | −0.460611 | + | 0.797802i | −0.998992 | − | 0.0448997i | \(-0.985703\pi\) |
0.538380 | + | 0.842702i | \(0.319037\pi\) | |||||||
\(522\) | −1.17992 | + | 0.208051i | −0.0516435 | + | 0.00910615i | ||||
\(523\) | 8.44161 | − | 1.48848i | 0.369126 | − | 0.0650868i | 0.0139914 | − | 0.999902i | \(-0.495546\pi\) |
0.355134 | + | 0.934815i | \(0.384435\pi\) | |||||||
\(524\) | 6.40094 | − | 11.0867i | 0.279626 | − | 0.484327i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.85464 | + | 6.59082i | −0.342478 | + | 0.287373i | ||||
\(527\) | −2.58854 | − | 7.11195i | −0.112758 | − | 0.309801i | ||||
\(528\) | 1.66488 | − | 4.57422i | 0.0724546 | − | 0.199067i | ||||
\(529\) | 13.9258 | + | 11.6851i | 0.605469 | + | 0.508049i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.373837 | 0.0162231 | ||||||||
\(532\) | 10.7585 | + | 0.828800i | 0.466440 | + | 0.0359330i | ||||
\(533\) | 3.09086i | 0.133880i | ||||||||
\(534\) | −3.46716 | + | 19.6632i | −0.150038 | + | 0.850911i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.16333 | + | 1.15136i | 0.136635 | + | 0.0497311i | ||||
\(537\) | −5.95770 | − | 16.3687i | −0.257094 | − | 0.706360i | ||||
\(538\) | −17.0302 | − | 20.2958i | −0.734224 | − | 0.875014i | ||||
\(539\) | −1.26489 | − | 2.19086i | −0.0544827 | − | 0.0943668i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.75653 | + | 21.3044i | 0.161506 | + | 0.915946i | 0.952594 | + | 0.304244i | \(0.0984038\pi\) |
−0.791088 | + | 0.611702i | \(0.790485\pi\) | |||||||
\(542\) | −24.5333 | + | 4.32588i | −1.05379 | + | 0.185812i | ||||
\(543\) | 24.1872 | + | 13.9645i | 1.03797 | + | 0.599275i | ||||
\(544\) | −0.621495 | − | 1.07646i | −0.0266464 | − | 0.0461529i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.06094 | + | 1.84203i | −0.216588 | + | 0.0788316i | ||||
\(547\) | −10.7349 | + | 29.4938i | −0.458989 | + | 1.26106i | 0.467249 | + | 0.884126i | \(0.345245\pi\) |
−0.926239 | + | 0.376937i | \(0.876977\pi\) | |||||||
\(548\) | 10.0460 | − | 11.9723i | 0.429143 | − | 0.511432i | ||||
\(549\) | −0.0429766 | + | 0.243732i | −0.00183420 | + | 0.0104022i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.17073 | + | 28.1778i | −0.0924761 | + | 1.20042i | ||||
\(552\) | 3.68410i | 0.156806i | ||||||||
\(553\) | −15.8042 | − | 2.78672i | −0.672065 | − | 0.118503i | ||||
\(554\) | −11.0045 | − | 9.23384i | −0.467535 | − | 0.392308i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.7878 | − | 3.92644i | 0.457505 | − | 0.166518i | ||||
\(557\) | −3.66096 | − | 4.36296i | −0.155120 | − | 0.184864i | 0.682888 | − | 0.730523i | \(-0.260724\pi\) |
−0.838007 | + | 0.545659i | \(0.816279\pi\) | |||||||
\(558\) | −0.974429 | + | 0.562587i | −0.0412509 | + | 0.0238162i | ||||
\(559\) | −5.96520 | + | 10.3320i | −0.252301 | + | 0.436998i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.05068 | + | 5.95868i | 0.0443596 | + | 0.251576i | ||||
\(562\) | 23.2914 | + | 13.4473i | 0.982488 | + | 0.567240i | ||||
\(563\) | 6.97904 | − | 4.02935i | 0.294132 | − | 0.169817i | −0.345672 | − | 0.938355i | \(-0.612349\pi\) |
0.639804 | + | 0.768538i | \(0.279016\pi\) | |||||||
\(564\) | 14.3028 | − | 12.0015i | 0.602257 | − | 0.505353i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18.9490 | − | 6.89686i | −0.796484 | − | 0.289896i | ||||
\(567\) | 13.3844 | − | 15.9509i | 0.562093 | − | 0.669876i | ||||
\(568\) | −14.9661 | − | 2.63893i | −0.627964 | − | 0.110727i | ||||
\(569\) | −22.1220 | −0.927404 | −0.463702 | − | 0.885991i | \(-0.653479\pi\) | ||||
−0.463702 | + | 0.885991i | \(0.653479\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.8413 | 1.91840 | 0.959200 | − | 0.282729i | \(-0.0912396\pi\) | ||||
0.959200 | + | 0.282729i | \(0.0912396\pi\) | |||||||
\(572\) | −3.70474 | − | 0.653245i | −0.154903 | − | 0.0273136i | ||||
\(573\) | 23.5024 | − | 28.0091i | 0.981826 | − | 1.17009i | ||||
\(574\) | 5.54492 | + | 2.01819i | 0.231441 | + | 0.0842375i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.141559 | + | 0.118782i | −0.00589830 | + | 0.00494926i | ||||
\(577\) | −27.4535 | + | 15.8503i | −1.14291 | + | 0.659857i | −0.947148 | − | 0.320796i | \(-0.896050\pi\) |
−0.195757 | + | 0.980652i | \(0.562716\pi\) | |||||||
\(578\) | −13.3844 | − | 7.72749i | −0.556718 | − | 0.321421i | ||||
\(579\) | −6.67507 | − | 37.8562i | −0.277406 | − | 1.57325i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.4647 | + | 18.1254i | −0.434150 | + | 0.751970i | ||||
\(582\) | −3.93148 | + | 2.26984i | −0.162965 | + | 0.0940880i | ||||
\(583\) | 22.4465 | + | 26.7507i | 0.929639 | + | 1.10790i | ||||
\(584\) | −0.526806 | + | 0.191742i | −0.0217994 | + | 0.00793434i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.3201 | − | 12.8551i | −0.632869 | − | 0.531041i | ||||
\(587\) | −12.6088 | − | 2.22328i | −0.520422 | − | 0.0917644i | −0.0927341 | − | 0.995691i | \(-0.529561\pi\) |
−0.427688 | + | 0.903926i | \(0.640672\pi\) | |||||||
\(588\) | − | 1.46306i | − | 0.0603356i | ||||||
\(589\) | 7.13500 | + | 25.5636i | 0.293993 | + | 1.05333i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.44383 | + | 8.18839i | −0.0593914 | + | 0.336825i | ||||
\(592\) | 0.928954 | − | 1.10708i | 0.0381798 | − | 0.0455009i | ||||
\(593\) | −12.6662 | + | 34.8002i | −0.520140 | + | 1.42907i | 0.350225 | + | 0.936665i | \(0.386105\pi\) |
−0.870365 | + | 0.492407i | \(0.836117\pi\) | |||||||
\(594\) | 14.5679 | − | 5.30230i | 0.597730 | − | 0.217556i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.57580 | + | 13.1217i | 0.310317 | + | 0.537485i | ||||
\(597\) | 35.7474 | + | 20.6388i | 1.46304 | + | 0.844688i | ||||
\(598\) | 2.80387 | − | 0.494397i | 0.114659 | − | 0.0202174i | ||||
\(599\) | −1.00225 | − | 5.68403i | −0.0409507 | − | 0.232243i | 0.957462 | − | 0.288558i | \(-0.0931759\pi\) |
−0.998413 | + | 0.0563153i | \(0.982065\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.26350 | − | 14.3128i | −0.337075 | − | 0.583831i | 0.646806 | − | 0.762655i | \(-0.276104\pi\) |
−0.983881 | + | 0.178823i | \(0.942771\pi\) | |||||||
\(602\) | 14.6404 | + | 17.4477i | 0.596697 | + | 0.711116i | ||||
\(603\) | 0.212762 | + | 0.584560i | 0.00866435 | + | 0.0238051i | ||||
\(604\) | −5.43856 | − | 1.97947i | −0.221292 | − | 0.0805436i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.0343390 | + | 0.194746i | −0.00139493 | + | 0.00791103i | ||||
\(607\) | 2.34282i | 0.0950920i | 0.998869 | + | 0.0475460i | \(0.0151401\pi\) | ||||
−0.998869 | + | 0.0475460i | \(0.984860\pi\) | |||||||
\(608\) | 1.88306 | + | 3.93117i | 0.0763683 | + | 0.159430i | ||||
\(609\) | −26.9296 | −1.09124 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0534 | − | 9.27490i | −0.447173 | − | 0.375222i | ||||
\(612\) | 0.0785604 | − | 0.215843i | 0.00317562 | − | 0.00872493i | ||||
\(613\) | 10.2703 | + | 28.2173i | 0.414812 | + | 1.13969i | 0.954601 | + | 0.297886i | \(0.0962816\pi\) |
−0.539789 | + | 0.841800i | \(0.681496\pi\) | |||||||
\(614\) | −14.8627 | + | 12.4713i | −0.599808 | + | 0.503299i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.59092 | + | 6.21966i | −0.144682 | + | 0.250597i | ||||
\(617\) | −15.9792 | + | 2.81756i | −0.643298 | + | 0.113431i | −0.485774 | − | 0.874084i | \(-0.661462\pi\) |
−0.157524 | + | 0.987515i | \(0.550351\pi\) | |||||||
\(618\) | 2.87740 | − | 0.507364i | 0.115746 | − | 0.0204092i | ||||
\(619\) | 23.8503 | − | 41.3099i | 0.958624 | − | 1.66039i | 0.232776 | − | 0.972530i | \(-0.425219\pi\) |
0.725848 | − | 0.687855i | \(-0.241448\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.98807 | + | 7.54188i | −0.360679 | + | 0.302645i | ||||
\(622\) | −1.84656 | − | 5.07338i | −0.0740403 | − | 0.203424i | ||||
\(623\) | 10.0753 | − | 27.6818i | 0.403660 | − | 1.10905i | ||||
\(624\) | −1.66663 | − | 1.39847i | −0.0667186 | − | 0.0559835i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 16.1834 | 0.646818 | ||||||||
\(627\) | −2.06862 | − | 21.1171i | −0.0826128 | − | 0.843336i | ||||
\(628\) | − | 11.0189i | − | 0.439704i | ||||||
\(629\) | −0.311935 | + | 1.76907i | −0.0124377 | + | 0.0705376i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.5071 | + | 4.18824i | 0.458090 | + | 0.166731i | 0.560750 | − | 0.827985i | \(-0.310513\pi\) |
−0.102660 | + | 0.994717i | \(0.532735\pi\) | |||||||
\(632\) | −2.21725 | − | 6.09184i | −0.0881973 | − | 0.242320i | ||||
\(633\) | −3.96273 | − | 4.72260i | −0.157504 | − | 0.187706i | ||||
\(634\) | 1.22547 | + | 2.12258i | 0.0486696 | + | 0.0842983i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.50696 | + | 19.8889i | 0.139060 | + | 0.788648i | ||||
\(637\) | −1.11350 | + | 0.196339i | −0.0441183 | + | 0.00777925i | ||||
\(638\) | −16.2900 | − | 9.40506i | −0.644929 | − | 0.372350i | ||||
\(639\) | −1.40415 | − | 2.43205i | −0.0555471 | − | 0.0962104i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.9385 | − | 10.1688i | 1.10350 | − | 0.401643i | 0.274897 | − | 0.961474i | \(-0.411356\pi\) |
0.828607 | + | 0.559831i | \(0.189134\pi\) | |||||||
\(642\) | −9.58714 | + | 26.3404i | −0.378374 | + | 1.03957i | ||||
\(643\) | −13.5109 | + | 16.1016i | −0.532817 | + | 0.634987i | −0.963561 | − | 0.267487i | \(-0.913807\pi\) |
0.430744 | + | 0.902474i | \(0.358251\pi\) | |||||||
\(644\) | 0.943857 | − | 5.35288i | 0.0371932 | − | 0.210933i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.47024 | − | 3.06143i | −0.175879 | − | 0.120451i | ||||
\(647\) | 10.8225i | 0.425476i | 0.977109 | + | 0.212738i | \(0.0682381\pi\) | ||||
−0.977109 | + | 0.212738i | \(0.931762\pi\) | |||||||
\(648\) | 8.28368 | + | 1.46064i | 0.325414 | + | 0.0573792i | ||||
\(649\) | 4.49602 | + | 3.77261i | 0.176484 | + | 0.148088i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.7649 | + | 8.64972i | −0.931420 | + | 0.339009i | ||||
\(652\) | 14.2565 | + | 16.9903i | 0.558328 | + | 0.665390i | ||||
\(653\) | −37.1937 | + | 21.4738i | −1.45550 | + | 0.840334i | −0.998785 | − | 0.0492789i | \(-0.984308\pi\) |
−0.456716 | + | 0.889613i | \(0.650974\pi\) | |||||||
\(654\) | −16.9865 | + | 29.4214i | −0.664223 | + | 1.15047i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.413923 | + | 2.34748i | 0.0161610 | + | 0.0916536i | ||||
\(657\) | −0.0897182 | − | 0.0517988i | −0.00350024 | − | 0.00202086i | ||||
\(658\) | −23.8563 | + | 13.7734i | −0.930015 | + | 0.536944i | ||||
\(659\) | 4.59278 | − | 3.85380i | 0.178909 | − | 0.150123i | −0.548935 | − | 0.835865i | \(-0.684967\pi\) |
0.727845 | + | 0.685742i | \(0.240522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.9338 | − | 6.16342i | −0.658650 | − | 0.239729i | −0.00899680 | − | 0.999960i | \(-0.502864\pi\) |
−0.649654 | + | 0.760230i | \(0.725086\pi\) | |||||||
\(662\) | −1.95166 | + | 2.32590i | −0.0758535 | + | 0.0903986i | ||||
\(663\) | 2.66320 | + | 0.469594i | 0.103430 | + | 0.0182375i | ||||
\(664\) | −8.45470 | −0.328106 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.267061 | 0.0103484 | ||||||||
\(667\) | 14.0198 | + | 2.47207i | 0.542850 | + | 0.0957191i | ||||
\(668\) | 11.1770 | − | 13.3202i | 0.432449 | − | 0.515373i | ||||
\(669\) | 11.7515 | + | 4.27719i | 0.454339 | + | 0.165366i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.97651 | + | 2.49759i | −0.114907 | + | 0.0964183i | ||||
\(672\) | −3.59705 | + | 2.07675i | −0.138759 | + | 0.0801126i | ||||
\(673\) | 23.6912 | + | 13.6781i | 0.913231 | + | 0.527254i | 0.881469 | − | 0.472242i | \(-0.156555\pi\) |
0.0317614 | + | 0.999495i | \(0.489888\pi\) | |||||||
\(674\) | −1.05284 | − | 5.97096i | −0.0405539 | − | 0.229993i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.65932 | − | 9.80223i | 0.217666 | − | 0.377009i | ||||
\(677\) | −26.1566 | + | 15.1015i | −1.00528 | + | 0.580398i | −0.909806 | − | 0.415034i | \(-0.863770\pi\) |
−0.0954734 | + | 0.995432i | \(0.530436\pi\) | |||||||
\(678\) | 17.8437 | + | 21.2653i | 0.685284 | + | 0.816689i | ||||
\(679\) | 6.29385 | − | 2.29077i | 0.241536 | − | 0.0879118i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6740 | − | 12.3129i | −0.562308 | − | 0.471833i | ||||
\(682\) | −17.3965 | − | 3.06748i | −0.666148 | − | 0.117460i | ||||
\(683\) | 42.2829i | 1.61791i | 0.587871 | + | 0.808955i | \(0.299966\pi\) | ||||
−0.587871 | + | 0.808955i | \(0.700034\pi\) | |||||||
\(684\) | −0.332819 | + | 0.733518i | −0.0127256 | + | 0.0280468i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.38388 | + | 19.1909i | −0.129197 | + | 0.732712i | ||||
\(687\) | −3.44402 | + | 4.10442i | −0.131398 | + | 0.156594i | ||||
\(688\) | −3.14685 | + | 8.64591i | −0.119973 | + | 0.329622i | ||||
\(689\) | 14.6663 | − | 5.33810i | 0.558742 | − | 0.203365i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.96853 | − | 13.8019i | −0.303137 | − | 0.525049i | 0.673708 | − | 0.738998i | \(-0.264701\pi\) |
−0.976845 | + | 0.213949i | \(0.931367\pi\) | |||||||
\(692\) | 1.86037 | + | 1.07408i | 0.0707205 | + | 0.0408305i | ||||
\(693\) | −1.30699 | + | 0.230457i | −0.0496484 | + | 0.00875435i | ||||
\(694\) | 0.499559 | + | 2.83314i | 0.0189630 | + | 0.107545i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.43927 | − | 9.42109i | −0.206175 | − | 0.357106i | ||||
\(697\) | −1.90452 | − | 2.26972i | −0.0721387 | − | 0.0859716i | ||||
\(698\) | 11.2168 | + | 30.8180i | 0.424564 | + | 1.16648i | ||||
\(699\) | −36.7350 | − | 13.3704i | −1.38945 | − | 0.505717i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.03691 | + | 5.88059i | −0.0391634 | + | 0.222107i | −0.998108 | − | 0.0614872i | \(-0.980416\pi\) |
0.958944 | + | 0.283594i | \(0.0915268\pi\) | |||||||
\(702\) | − | 6.92893i | − | 0.261516i | ||||||
\(703\) | 1.56716 | − | 6.10141i | 0.0591067 | − | 0.230119i | ||||
\(704\) | −2.90119 | −0.109343 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.2408 | − | 13.6277i | −0.611231 | − | 0.512884i | ||||
\(707\) | 0.0997871 | − | 0.274163i | 0.00375288 | − | 0.0103110i | ||||
\(708\) | 1.16093 | + | 3.18962i | 0.0436303 | + | 0.119873i | ||||
\(709\) | −35.7131 | + | 29.9669i | −1.34123 | + | 1.12543i | −0.359928 | + | 0.932980i | \(0.617199\pi\) |
−0.981307 | + | 0.192450i | \(0.938357\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.598986 | − | 1.03747i | 0.0224637 | − | 0.0389083i | ||||
\(712\) | 11.7192 | − | 2.06642i | 0.439197 | − | 0.0774423i | ||||
\(713\) | 13.1663 | − | 2.32157i | 0.493080 | − | 0.0869434i | ||||
\(714\) | 2.58139 | − | 4.47109i | 0.0966059 | − | 0.167326i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.95291 | + | 6.67328i | −0.297214 | + | 0.249392i | ||||
\(717\) | −4.71833 | − | 12.9635i | −0.176209 | − | 0.484131i | ||||
\(718\) | −6.35803 | + | 17.4685i | −0.237280 | + | 0.651920i | ||||
\(719\) | 31.8698 | + | 26.7420i | 1.18854 | + | 0.997307i | 0.999883 | + | 0.0152650i | \(0.00485920\pi\) |
0.188661 | + | 0.982042i | \(0.439585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.31076 | −0.160541 | ||||||||
\(722\) | 14.8053 | + | 11.9081i | 0.550995 | + | 0.443175i | ||||
\(723\) | 34.9514i | 1.29986i | ||||||||
\(724\) | 2.89049 | − | 16.3928i | 0.107424 | − | 0.609232i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.07270 | − | 1.48234i | −0.151152 | − | 0.0550149i | ||||
\(727\) | 7.10304 | + | 19.5154i | 0.263437 | + | 0.723787i | 0.998930 | + | 0.0462546i | \(0.0147286\pi\) |
−0.735493 | + | 0.677533i | \(0.763049\pi\) | |||||||
\(728\) | 2.06328 | + | 2.45892i | 0.0764701 | + | 0.0911335i | ||||
\(729\) | 14.2260 | + | 24.6401i | 0.526888 | + | 0.912596i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.98592 | − | 11.2627i | −0.0734521 | − | 0.416567i | ||||
\(732\) | −2.21301 | + | 0.390214i | −0.0817953 | + | 0.0144227i | ||||
\(733\) | 25.5184 | + | 14.7331i | 0.942545 | + | 0.544179i | 0.890757 | − | 0.454480i | \(-0.150175\pi\) |
0.0517877 | + | 0.998658i | \(0.483508\pi\) | |||||||
\(734\) | 10.8612 | + | 18.8121i | 0.400893 | + | 0.694367i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.06330 | − | 0.750979i | 0.0760542 | − | 0.0276814i | ||||
\(737\) | −3.34031 | + | 9.17742i | −0.123042 | + | 0.338054i | ||||
\(738\) | −0.283140 | + | 0.337433i | −0.0104225 | + | 0.0124211i | ||||
\(739\) | −4.63253 | + | 26.2724i | −0.170410 | + | 0.966446i | 0.772898 | + | 0.634530i | \(0.218806\pi\) |
−0.943309 | + | 0.331916i | \(0.892305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.18520 | − | 2.35924i | −0.337427 | − | 0.0866690i | ||||
\(742\) | − | 29.7965i | − | 1.09386i | ||||||
\(743\) | −44.5252 | − | 7.85099i | −1.63347 | − | 0.288025i | −0.719708 | − | 0.694276i | \(-0.755725\pi\) |
−0.913761 | + | 0.406252i | \(0.866836\pi\) | |||||||
\(744\) | −7.82608 | − | 6.56686i | −0.286918 | − | 0.240753i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21.0636 | − | 7.66651i | 0.771192 | − | 0.280691i | ||||
\(747\) | −1.00427 | − | 1.19684i | −0.0367443 | − | 0.0437901i | ||||
\(748\) | 3.12302 | − | 1.80307i | 0.114189 | − | 0.0659269i | ||||
\(749\) | 20.6782 | − | 35.8156i | 0.755564 | − | 1.30867i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.599478 | − | 3.39981i | −0.0218753 | − | 0.124061i | 0.971915 | − | 0.235334i | \(-0.0756183\pi\) |
−0.993790 | + | 0.111273i | \(0.964507\pi\) | |||||||
\(752\) | −9.63702 | − | 5.56394i | −0.351426 | − | 0.202896i | ||||
\(753\) | 16.6908 | − | 9.63642i | 0.608246 | − | 0.351171i | ||||
\(754\) | −6.44020 | + | 5.40397i | −0.234538 | + | 0.196801i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.4303 | − | 4.52427i | −0.452086 | − | 0.164546i | ||||
\(757\) | 25.9373 | − | 30.9109i | 0.942708 | − | 1.12348i | −0.0494862 | − | 0.998775i | \(-0.515758\pi\) |
0.992194 | − | 0.124701i | \(-0.0397972\pi\) | |||||||
\(758\) | 8.32410 | + | 1.46776i | 0.302345 | + | 0.0533116i | ||||
\(759\) | −10.6883 | −0.387960 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.4450 | −0.451132 | −0.225566 | − | 0.974228i | \(-0.572423\pi\) | ||||
−0.225566 | + | 0.974228i | \(0.572423\pi\) | |||||||
\(762\) | 0.216547 | + | 0.0381832i | 0.00784469 | + | 0.00138323i | ||||
\(763\) | 32.2185 | − | 38.3965i | 1.16639 | − | 1.39005i | ||||
\(764\) | −20.4774 | − | 7.45317i | −0.740847 | − | 0.269646i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.54187 | − | 6.32838i | 0.272499 | − | 0.228654i | ||||
\(767\) | 2.27174 | − | 1.31159i | 0.0820277 | − | 0.0473587i | ||||
\(768\) | −1.45307 | − | 0.838929i | −0.0524331 | − | 0.0302722i | ||||
\(769\) | −5.55178 | − | 31.4857i | −0.200202 | − | 1.13540i | −0.904813 | − | 0.425810i | \(-0.859989\pi\) |
0.704610 | − | 0.709594i | \(-0.251122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.55762 | + | 2.69787i | −0.0560962 | + | 0.0971615i | ||||
\(772\) | −19.8409 | + | 11.4551i | −0.714089 | + | 0.412279i | ||||
\(773\) | −22.6745 | − | 27.0224i | −0.815545 | − | 0.971929i | 0.184395 | − | 0.982852i | \(-0.440967\pi\) |
−0.999940 | + | 0.0109230i | \(0.996523\pi\) | |||||||
\(774\) | −1.59770 | + | 0.581515i | −0.0574281 | + | 0.0209021i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.07264 | + | 1.73915i | 0.0744035 | + | 0.0624320i | ||||
\(777\) | 5.91144 | + | 1.04235i | 0.212072 | + | 0.0373940i | ||||
\(778\) | 8.51432i | 0.305253i | ||||||||
\(779\) | 6.04765 | + | 8.44888i | 0.216679 | + | 0.302712i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.65603 | − | 43.4195i | 0.273954 | − | 1.55367i | ||||
\(782\) | −1.75433 | + | 2.09073i | −0.0627347 | + | 0.0747643i | ||||
\(783\) | 11.8496 | − | 32.5565i | 0.423470 | − | 1.16347i | ||||
\(784\) | −0.819394 | + | 0.298235i | −0.0292641 | + | 0.0106513i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.7399 | + | 18.6020i | 0.383078 | + | 0.663511i | ||||
\(787\) | −34.2030 | − | 19.7471i | −1.21921 | − | 0.703909i | −0.254458 | − | 0.967084i | \(-0.581897\pi\) |
−0.964748 | + | 0.263175i | \(0.915230\pi\) | |||||||
\(788\) | 4.88026 | − | 0.860522i | 0.173852 | − | 0.0306548i | ||||
\(789\) | −2.98743 | − | 16.9425i | −0.106355 | − | 0.603171i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.4782 | − | 35.4694i | −0.728123 | − | 1.26115i | ||||
\(792\) | −0.344610 | − | 0.410690i | −0.0122452 | − | 0.0145932i | ||||
\(793\) | 0.593962 | + | 1.63190i | 0.0210922 | + | 0.0579504i | ||||
\(794\) | −23.0365 | − | 8.38460i | −0.817535 | − | 0.297558i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.27197 | − | 24.2276i | 0.151416 | − | 0.858724i | ||||
\(797\) | 18.0151i | 0.638128i | 0.947733 | + | 0.319064i | \(0.103369\pi\) | ||||
−0.947733 | + | 0.319064i | \(0.896631\pi\) | |||||||
\(798\) | −10.2299 | + | 14.9375i | −0.362135 | + | 0.528783i | ||||
\(799\) | 13.8318 | 0.489335 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.68456 | + | 1.41351i | 0.0595210 | + | 0.0499440i | ||||
\(802\) | −1.70136 | + | 4.67444i | −0.0600770 | + | 0.165060i | ||||
\(803\) | −0.556279 | − | 1.52837i | −0.0196307 | − | 0.0539348i | ||||
\(804\) | −4.32681 | + | 3.63062i | −0.152595 | + | 0.128042i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.94762 | + | 6.83747i | −0.139049 | + | 0.240840i | ||||
\(807\) | 43.7783 | − | 7.71929i | 1.54107 | − | 0.271732i | ||||
\(808\) | 0.116068 | − | 0.0204660i | 0.00408327 | − | 0.000719991i | ||||
\(809\) | 14.5518 | − | 25.2045i | 0.511615 | − | 0.886144i | −0.488294 | − | 0.872679i | \(-0.662381\pi\) |
0.999909 | − | 0.0134647i | \(-0.00428607\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.3496 | − | 10.3626i | 0.433654 | − | 0.363879i | −0.399675 | − | 0.916657i | \(-0.630877\pi\) |
0.833328 | + | 0.552779i | \(0.186432\pi\) | |||||||
\(812\) | 5.48943 | + | 15.0821i | 0.192641 | + | 0.529277i | ||||
\(813\) | 14.2959 | − | 39.2776i | 0.501378 | − | 1.37753i | ||||
\(814\) | 3.21186 | + | 2.69507i | 0.112576 | + | 0.0944622i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.08556 | 0.0730092 | ||||||||
\(817\) | 3.90998 | + | 39.9142i | 0.136793 | + | 1.39642i | ||||
\(818\) | − | 18.0959i | − | 0.632707i | ||||||
\(819\) | −0.103002 | + | 0.584152i | −0.00359917 | + | 0.0204119i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.8660 | − | 10.1424i | −0.972530 | − | 0.353972i | −0.193598 | − | 0.981081i | \(-0.562016\pi\) |
−0.778932 | + | 0.627109i | \(0.784238\pi\) | |||||||
\(822\) | 8.96874 | + | 24.6414i | 0.312821 | + | 0.859468i | ||||
\(823\) | −15.2315 | − | 18.1522i | −0.530937 | − | 0.632746i | 0.432194 | − | 0.901781i | \(-0.357740\pi\) |
−0.963130 | + | 0.269035i | \(0.913295\pi\) | |||||||
\(824\) | −0.870691 | − | 1.50808i | −0.0303320 | − | 0.0525365i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.869617 | − | 4.93184i | −0.0302579 | − | 0.171601i | ||||
\(827\) | 37.4692 | − | 6.60682i | 1.30293 | − | 0.229742i | 0.521241 | − | 0.853410i | \(-0.325469\pi\) |
0.781689 | + | 0.623668i | \(0.214358\pi\) | |||||||
\(828\) | 0.351391 | + | 0.202876i | 0.0122117 | + | 0.00705042i | ||||
\(829\) | 11.9638 | + | 20.7219i | 0.415520 | + | 0.719701i | 0.995483 | − | 0.0949413i | \(-0.0302664\pi\) |
−0.579963 | + | 0.814643i | \(0.696933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.6494 | − | 8.24369i | 0.785698 | − | 0.285971i | ||||
\(832\) | −0.443488 | + | 1.21847i | −0.0153752 | + | 0.0422429i | ||||
\(833\) | 0.696694 | − | 0.830288i | 0.0241390 | − | 0.0287678i | ||||
\(834\) | −3.34482 | + | 18.9694i | −0.115822 | + | 0.656858i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.4051 | + | 5.46312i | −0.394452 | + | 0.188946i | ||||
\(837\) | − | 32.5365i | − | 1.12463i | ||||||
\(838\) | 10.4208 | + | 1.83747i | 0.359982 | + | 0.0634745i | ||||
\(839\) | −13.6980 | − | 11.4940i | −0.472908 | − | 0.396817i | 0.374946 | − | 0.927047i | \(-0.377661\pi\) |
−0.847854 | + | 0.530230i | \(0.822106\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.2507 | + | 4.45888i | −0.422437 | + | 0.153755i | ||||
\(842\) | −15.5917 | − | 18.5815i | −0.537325 | − | 0.640359i | ||||
\(843\) | −39.0796 | + | 22.5626i | −1.34597 | + | 0.777099i | ||||
\(844\) | −1.83714 | + | 3.18202i | −0.0632369 | + | 0.109530i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.357081 | − | 2.02511i | −0.0122767 | − | 0.0696246i | ||||
\(847\) | 5.53773 | + | 3.19721i | 0.190279 | + | 0.109858i | ||||
\(848\) | 10.4240 | − | 6.01832i | 0.357963 | − | 0.206670i | ||||
\(849\) | 25.9184 | − | 21.7481i | 0.889518 | − | 0.746394i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.98187 | − | 1.08531i | −0.102217 | − | 0.0372040i | ||||
\(852\) | 16.3901 | − | 19.5329i | 0.561514 | − | 0.669186i | ||||
\(853\) | 35.3934 | + | 6.24081i | 1.21185 | + | 0.213681i | 0.742813 | − | 0.669499i | \(-0.233491\pi\) |
0.469033 | + | 0.883181i | \(0.344602\pi\) | |||||||
\(854\) | 3.31541 | 0.113451 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.7064 | 0.571012 | ||||||||
\(857\) | −5.25121 | − | 0.925930i | −0.179378 | − | 0.0316292i | 0.0832376 | − | 0.996530i | \(-0.473474\pi\) |
−0.262615 | + | 0.964901i | \(0.584585\pi\) | |||||||
\(858\) | 4.05722 | − | 4.83521i | 0.138511 | − | 0.165071i | ||||
\(859\) | −8.81020 | − | 3.20665i | −0.300600 | − | 0.109410i | 0.187317 | − | 0.982300i | \(-0.440021\pi\) |
−0.487917 | + | 0.872890i | \(0.662243\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.58436 | + | 6.36403i | −0.258474 | + | 0.216886i | ||||
\(862\) | 30.9192 | − | 17.8512i | 1.05311 | − | 0.608015i | ||||
\(863\) | 4.57608 | + | 2.64200i | 0.155772 | + | 0.0899348i | 0.575860 | − | 0.817549i | \(-0.304667\pi\) |
−0.420088 | + | 0.907483i | \(0.638001\pi\) | |||||||
\(864\) | −0.927912 | − | 5.26245i | −0.0315682 | − | 0.179032i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.5340 | − | 28.6378i | 0.561849 | − | 0.973151i | ||||
\(867\) | 22.4571 | − | 12.9656i | 0.762684 | − | 0.440336i | ||||
\(868\) | 9.68864 | + | 11.5465i | 0.328854 | + | 0.391913i | ||||
\(869\) | 17.6736 | − | 6.43265i | 0.599535 | − | 0.218213i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.34382 | + | 2.80580i | 0.113301 | + | 0.0950707i | ||||
\(872\) | 19.9402 | + | 3.51599i | 0.675260 | + | 0.119066i | ||||
\(873\) | 0.499982i | 0.0169218i | ||||||||
\(874\) | 6.69703 | − | 6.83754i | 0.226530 | − | 0.231283i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.163339 | − | 0.926343i | 0.00551872 | − | 0.0312982i | ||||
\(877\) | 32.4457 | − | 38.6673i | 1.09561 | − | 1.30570i | 0.147045 | − | 0.989130i | \(-0.453024\pi\) |
0.948569 | − | 0.316572i | \(-0.102532\pi\) | |||||||
\(878\) | −2.02205 | + | 5.55555i | −0.0682410 | + | 0.187491i | ||||
\(879\) | 31.5319 | − | 11.4767i | 1.06354 | − | 0.387098i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.2170 | − | 17.6964i | −0.344221 | − | 0.596208i | 0.640991 | − | 0.767549i | \(-0.278524\pi\) |
−0.985212 | + | 0.171340i | \(0.945190\pi\) | |||||||
\(882\) | −0.139548 | − | 0.0805678i | −0.00469881 | − | 0.00271286i | ||||
\(883\) | −0.124596 | + | 0.0219697i | −0.00419300 | + | 0.000739339i | −0.175744 | − | 0.984436i | \(-0.556233\pi\) |
0.171551 | + | 0.985175i | \(0.445122\pi\) | |||||||
\(884\) | −0.279877 | − | 1.58726i | −0.00941329 | − | 0.0533854i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.91634 | + | 10.2474i | 0.198763 | + | 0.344268i | ||||
\(887\) | 16.6336 | + | 19.8231i | 0.558500 | + | 0.665594i | 0.969228 | − | 0.246163i | \(-0.0791700\pi\) |
−0.410728 | + | 0.911758i | \(0.634726\pi\) | |||||||
\(888\) | 0.829342 | + | 2.27860i | 0.0278309 | + | 0.0764648i | ||||
\(889\) | −0.304854 | − | 0.110958i | −0.0102245 | − | 0.00372141i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.23758 | + | 24.0325i | −0.141964 | + | 0.805120i | ||||
\(892\) | − | 7.45336i | − | 0.249557i | ||||||
\(893\) | −48.3620 | − | 3.72565i | −1.61837 | − | 0.124674i | ||||
\(894\) | −25.4222 | −0.850247 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.89633 | + | 1.59121i | 0.0633520 | + | 0.0531586i | ||||
\(897\) | −1.63385 | + | 4.48897i | −0.0545527 | + | 0.149882i | ||||
\(898\) | −2.59386 | − | 7.12658i | −0.0865583 | − | 0.237817i | ||||
\(899\) | −30.2416 | + | 25.3757i | −1.00861 | + | 0.846327i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.48071 | + | 12.9570i | −0.249218 | + | 0.431659i | ||||
\(902\) | −6.81047 | + | 1.20087i | −0.226764 | + | 0.0399846i | ||||
\(903\) | −37.6350 | + | 6.63606i | −1.25241 | + | 0.220834i | ||||
\(904\) | 8.27242 | − | 14.3283i | 0.275137 | − | 0.476551i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.43887 | − | 6.24195i | 0.247140 | − | 0.207375i | ||||
\(907\) | −18.4176 | − | 50.6020i | −0.611547 | − | 1.68021i | −0.726777 | − | 0.686874i | \(-0.758982\pi\) |
0.115229 | − | 0.993339i | \(-0.463240\pi\) | |||||||
\(908\) | −3.90473 | + | 10.7281i | −0.129583 | + | 0.356026i | ||||
\(909\) | 0.0166840 | + | 0.0139996i | 0.000553374 | + | 0.000464336i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.63989 | 0.0874634 | 0.0437317 | − | 0.999043i | \(-0.486075\pi\) | ||||
0.0437317 | + | 0.999043i | \(0.486075\pi\) | |||||||
\(912\) | −7.29201 | − | 0.561752i | −0.241463 | − | 0.0186015i | ||||
\(913\) | − | 24.5287i | − | 0.811781i | ||||||
\(914\) | 2.26812 | − | 12.8631i | 0.0750227 | − | 0.425475i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.00074 | + | 1.09218i | 0.0991474 | + | 0.0360867i | ||||
\(917\) | −10.8389 | − | 29.7796i | −0.357932 | − | 0.983410i | ||||
\(918\) | 4.26945 | + | 5.08813i | 0.140913 | + | 0.167933i | ||||
\(919\) | −15.6083 | − | 27.0343i | −0.514869 | − | 0.891779i | −0.999851 | − | 0.0172553i | \(-0.994507\pi\) |
0.484982 | − | 0.874524i | \(-0.338826\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.65286 | − | 32.0589i | −0.186268 | − | 1.05638i | ||||
\(922\) | 30.7684 | − | 5.42530i | 1.01330 | − | 0.178673i | ||||
\(923\) | −17.0655 | − | 9.85275i | −0.561717 | − | 0.324307i | ||||
\(924\) | −6.02506 | − | 10.4357i | −0.198210 | − | 0.343310i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.1215 | + | 4.77583i | −0.431199 | + | 0.156944i | ||||
\(927\) | 0.110060 | − | 0.302388i | 0.00361485 | − | 0.00993172i | ||||
\(928\) | −4.16757 | + | 4.96672i | −0.136807 | + | 0.163040i | ||||
\(929\) | −0.849031 | + | 4.81509i | −0.0278558 | + | 0.157978i | −0.995563 | − | 0.0940997i | \(-0.970003\pi\) |
0.967707 | + | 0.252078i | \(0.0811139\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.65958 | + | 2.71538i | −0.0871642 | + | 0.0889931i | ||||
\(932\) | 23.2991i | 0.763187i | ||||||||
\(933\) | 8.92110 | + | 1.57303i | 0.292064 | + | 0.0514987i | ||||
\(934\) | −9.04471 | − | 7.58941i | −0.295952 | − | 0.248333i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.225165 | + | 0.0819532i | −0.00735974 | + | 0.00267872i | ||||
\(937\) | −5.11059 | − | 6.09056i | −0.166956 | − | 0.198970i | 0.676079 | − | 0.736829i | \(-0.263678\pi\) |
−0.843035 | + | 0.537859i | \(0.819233\pi\) | |||||||
\(938\) | 7.21688 | − | 4.16667i | 0.235639 | − | 0.136046i | ||||
\(939\) | −13.5767 | + | 23.5155i | −0.443059 | + | 0.767401i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.40739 | − | 24.9956i | −0.143677 | − | 0.814832i | −0.968420 | − | 0.249325i | \(-0.919791\pi\) |
0.824743 | − | 0.565508i | \(-0.191320\pi\) | |||||||
\(942\) | 16.0113 | + | 9.24411i | 0.521675 | + | 0.301189i | ||||
\(943\) | 4.53269 | − | 2.61695i | 0.147605 | − | 0.0852197i | ||||
\(944\) | 1.54971 | − | 1.30037i | 0.0504389 | − | 0.0423233i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.0834 | − | 9.12962i | −0.815532 | − | 0.296829i | ||||
\(947\) | −19.0425 | + | 22.6940i | −0.618799 | + | 0.737456i | −0.980863 | − | 0.194697i | \(-0.937628\pi\) |
0.362064 | + | 0.932153i | \(0.382072\pi\) | |||||||
\(948\) | 10.7120 | + | 1.88881i | 0.347908 | + | 0.0613456i | ||||
\(949\) | −0.726934 | −0.0235973 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.11233 | −0.133351 | ||||||||
\(952\) | −3.03025 | − | 0.534316i | −0.0982111 | − | 0.0173173i | ||||
\(953\) | −9.63837 | + | 11.4866i | −0.312217 | + | 0.372086i | −0.899218 | − | 0.437500i | \(-0.855864\pi\) |
0.587001 | + | 0.809586i | \(0.300308\pi\) | |||||||
\(954\) | 2.09014 | + | 0.760748i | 0.0676708 | + | 0.0246301i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.29848 | + | 5.28505i | −0.203707 | + | 0.170931i | ||||
\(957\) | 27.3324 | − | 15.7803i | 0.883530 | − | 0.510106i | ||||
\(958\) | −27.7577 | − | 16.0259i | −0.896811 | − | 0.517774i | ||||
\(959\) | −6.71823 | − | 38.1010i | −0.216943 | − | 1.23034i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.03703 | + | 5.26029i | −0.0979688 | + | 0.169687i | ||||
\(962\) | 1.62288 | − | 0.936972i | 0.0523239 | − | 0.0302092i | ||||
\(963\) | 1.98442 | + | 2.36494i | 0.0639471 | + | 0.0762092i | ||||
\(964\) | 19.5747 | − | 7.12460i | 0.630458 | − | 0.229468i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.98627 | + | 5.86218i | 0.224779 | + | 0.188612i | ||||
\(967\) | −13.6825 | − | 2.41259i | −0.439998 | − | 0.0775835i | −0.0507392 | − | 0.998712i | \(-0.516158\pi\) |
−0.389259 | + | 0.921128i | \(0.627269\pi\) | |||||||
\(968\) | 2.58310i | 0.0830240i | ||||||||
\(969\) | 8.19869 | − | 3.92724i | 0.263380 | − | 0.126161i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.47187 | + | 14.0186i | −0.0793260 | + | 0.449880i | 0.919111 | + | 0.393998i | \(0.128908\pi\) |
−0.998437 | + | 0.0558821i | \(0.982203\pi\) | |||||||
\(972\) | 1.23263 | − | 1.46899i | 0.0395366 | − | 0.0471179i | ||||
\(973\) | 9.71985 | − | 26.7051i | 0.311604 | − | 0.856125i | ||||
\(974\) | 16.4207 | − | 5.97664i | 0.526152 | − | 0.191504i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.669649 | + | 1.15987i | 0.0214349 | + | 0.0371264i | ||||
\(977\) | 7.14552 | + | 4.12547i | 0.228606 | + | 0.131985i | 0.609929 | − | 0.792456i | \(-0.291198\pi\) |
−0.381323 | + | 0.924442i | \(0.624531\pi\) | |||||||
\(978\) | −36.6482 | + | 6.46207i | −1.17188 | + | 0.206634i | ||||
\(979\) | 5.99507 | + | 33.9997i | 0.191603 | + | 1.08664i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.87082 | + | 3.24035i | 0.0597307 | + | 0.103457i | ||||
\(982\) | −1.36614 | − | 1.62811i | −0.0435954 | − | 0.0519549i | ||||
\(983\) | −4.49274 | − | 12.3437i | −0.143296 | − | 0.393703i | 0.847194 | − | 0.531283i | \(-0.178290\pi\) |
−0.990491 | + | 0.137580i | \(0.956068\pi\) | |||||||
\(984\) | −3.75829 | − | 1.36791i | −0.119810 | − | 0.0436073i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.39944 | − | 7.93660i | 0.0445671 | − | 0.252753i | ||||
\(987\) | − | 46.2197i | − | 1.47119i | ||||||
\(988\) | 0.551036 | + | 5.62513i | 0.0175308 | + | 0.178959i | ||||
\(989\) | 20.2023 | 0.642396 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4973 | − | 16.3602i | −0.619352 | − | 0.519698i | 0.278248 | − | 0.960509i | \(-0.410246\pi\) |
−0.897600 | + | 0.440811i | \(0.854691\pi\) | |||||||
\(992\) | −2.08251 | + | 5.72164i | −0.0661197 | + | 0.181662i | ||||
\(993\) | −1.74238 | − | 4.78716i | −0.0552929 | − | 0.151916i | ||||
\(994\) | −28.8185 | + | 24.1816i | −0.914068 | + | 0.766994i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.09289 | − | 12.2852i | 0.224747 | − | 0.389273i | ||||
\(997\) | 22.1625 | − | 3.90784i | 0.701892 | − | 0.123763i | 0.188698 | − | 0.982035i | \(-0.439573\pi\) |
0.513194 | + | 0.858273i | \(0.328462\pi\) | |||||||
\(998\) | 35.8305 | − | 6.31789i | 1.13420 | − | 0.199989i | ||||
\(999\) | −3.86130 | + | 6.68796i | −0.122166 | + | 0.211598i |
(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 | 950.2.u.e.549.3 | 24 | ||
5.2 | odd | 4 | 190.2.k.b.131.2 | ✓ | 12 | ||
5.3 | odd | 4 | 950.2.l.h.701.1 | 12 | |||
5.4 | even | 2 | inner | 950.2.u.e.549.2 | 24 | ||
19.9 | even | 9 | inner | 950.2.u.e.199.2 | 24 | ||
95.9 | even | 18 | inner | 950.2.u.e.199.3 | 24 | ||
95.22 | even | 36 | 3610.2.a.be.1.2 | 6 | |||
95.28 | odd | 36 | 950.2.l.h.351.1 | 12 | |||
95.47 | odd | 36 | 190.2.k.b.161.2 | yes | 12 | ||
95.92 | odd | 36 | 3610.2.a.bc.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.k.b.131.2 | ✓ | 12 | 5.2 | odd | 4 | ||
190.2.k.b.161.2 | yes | 12 | 95.47 | odd | 36 | ||
950.2.l.h.351.1 | 12 | 95.28 | odd | 36 | |||
950.2.l.h.701.1 | 12 | 5.3 | odd | 4 | |||
950.2.u.e.199.2 | 24 | 19.9 | even | 9 | inner | ||
950.2.u.e.199.3 | 24 | 95.9 | even | 18 | inner | ||
950.2.u.e.549.2 | 24 | 5.4 | even | 2 | inner | ||
950.2.u.e.549.3 | 24 | 1.1 | even | 1 | trivial | ||
3610.2.a.bc.1.5 | 6 | 95.92 | odd | 36 | |||
3610.2.a.be.1.2 | 6 | 95.22 | even | 36 |