Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.162447943996702457856.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1011.1 | ||
Root | \(1.14839 + 0.825348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1011 |
Dual form | 1078.2.i.b.901.1 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −2.68085 | − | 1.54779i | −1.54779 | − | 0.893615i | −0.998310 | − | 0.0581058i | \(-0.981494\pi\) |
−0.549476 | − | 0.835509i | \(-0.685173\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.559525 | − | 0.323042i | 0.250227 | − | 0.144469i | −0.369641 | − | 0.929175i | \(-0.620519\pi\) |
0.619868 | + | 0.784706i | \(0.287186\pi\) | |||||||
\(6\) | 3.09557 | 1.26376 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 3.29129 | + | 5.70068i | 1.09710 | + | 1.90023i | ||||
\(10\) | −0.323042 | + | 0.559525i | −0.102155 | + | 0.176937i | ||||
\(11\) | −2.94694 | + | 1.52168i | −0.888537 | + | 0.458804i | ||||
\(12\) | −2.68085 | + | 1.54779i | −0.773893 | + | 0.446808i | ||||
\(13\) | 3.09557 | 0.858558 | 0.429279 | − | 0.903172i | \(-0.358768\pi\) | ||||
0.429279 | + | 0.903172i | \(0.358768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.87083 | − | 3.24037i | 0.453743 | − | 0.785905i | −0.544872 | − | 0.838519i | \(-0.683422\pi\) |
0.998615 | + | 0.0526138i | \(0.0167552\pi\) | |||||||
\(18\) | −5.70068 | − | 3.29129i | −1.34366 | − | 0.775764i | ||||
\(19\) | −2.77253 | − | 4.80217i | −0.636062 | − | 1.10169i | −0.986289 | − | 0.165027i | \(-0.947229\pi\) |
0.350227 | − | 0.936665i | \(-0.386105\pi\) | |||||||
\(20\) | − | 0.646084i | − | 0.144469i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.79129 | − | 2.79129i | 0.381904 | − | 0.595105i | ||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 1.54779 | − | 2.68085i | 0.315941 | − | 0.547225i | ||||
\(25\) | −2.29129 | + | 3.96863i | −0.458258 | + | 0.793725i | ||||
\(26\) | −2.68085 | + | 1.54779i | −0.525757 | + | 0.303546i | ||||
\(27\) | − | 11.0901i | − | 2.13430i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.58258i | − | 1.40805i | −0.710176 | − | 0.704024i | \(-0.751385\pi\) | ||
0.710176 | − | 0.704024i | \(-0.248615\pi\) | |||||||
\(30\) | 1.73205 | − | 1.00000i | 0.316228 | − | 0.182574i | ||||
\(31\) | −1.00227 | − | 0.578661i | −0.180013 | − | 0.103931i | 0.407286 | − | 0.913301i | \(-0.366475\pi\) |
−0.587299 | + | 0.809370i | \(0.699809\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 10.2555 | + | 0.481847i | 1.78526 | + | 0.0838788i | ||||
\(34\) | 3.74166i | 0.641689i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.58258 | 1.09710 | ||||||||
\(37\) | 2.79129 | + | 4.83465i | 0.458885 | + | 0.794812i | 0.998902 | − | 0.0468419i | \(-0.0149157\pi\) |
−0.540017 | + | 0.841654i | \(0.681582\pi\) | |||||||
\(38\) | 4.80217 | + | 2.77253i | 0.779014 | + | 0.449764i | ||||
\(39\) | −8.29875 | − | 4.79129i | −1.32886 | − | 0.767220i | ||||
\(40\) | 0.323042 | + | 0.559525i | 0.0510774 | + | 0.0884687i | ||||
\(41\) | −5.03383 | −0.786151 | −0.393076 | − | 0.919506i | \(-0.628589\pi\) | ||||
−0.393076 | + | 0.919506i | \(0.628589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1652i | 1.70267i | 0.524623 | + | 0.851335i | \(0.324206\pi\) | ||||
−0.524623 | + | 0.851335i | \(0.675794\pi\) | |||||||
\(44\) | −0.155657 | + | 3.31297i | −0.0234662 | + | 0.499449i | ||||
\(45\) | 3.68312 | + | 2.12645i | 0.549046 | + | 0.316992i | ||||
\(46\) | 3.46410 | + | 2.00000i | 0.510754 | + | 0.294884i | ||||
\(47\) | −4.35942 | + | 2.51691i | −0.635887 | + | 0.367129i | −0.783028 | − | 0.621986i | \(-0.786326\pi\) |
0.147142 | + | 0.989115i | \(0.452993\pi\) | |||||||
\(48\) | 3.09557i | 0.446808i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 4.58258i | − | 0.648074i | ||||||
\(51\) | −10.0308 | + | 5.79129i | −1.40459 | + | 0.810943i | ||||
\(52\) | 1.54779 | − | 2.68085i | 0.214639 | − | 0.371766i | ||||
\(53\) | 1.20871 | − | 2.09355i | 0.166029 | − | 0.287571i | −0.770991 | − | 0.636846i | \(-0.780239\pi\) |
0.937020 | + | 0.349275i | \(0.113572\pi\) | |||||||
\(54\) | 5.54506 | + | 9.60433i | 0.754588 | + | 1.30698i | ||||
\(55\) | −1.15732 | + | 1.80341i | −0.156053 | + | 0.243171i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.1652i | 2.27358i | ||||||||
\(58\) | 3.79129 | + | 6.56670i | 0.497820 | + | 0.862250i | ||||
\(59\) | 2.68085 | + | 1.54779i | 0.349016 | + | 0.201505i | 0.664252 | − | 0.747509i | \(-0.268750\pi\) |
−0.315236 | + | 0.949013i | \(0.602084\pi\) | |||||||
\(60\) | −1.00000 | + | 1.73205i | −0.129099 | + | 0.223607i | ||||
\(61\) | −4.64336 | − | 8.04254i | −0.594521 | − | 1.02974i | −0.993614 | − | 0.112831i | \(-0.964008\pi\) |
0.399093 | − | 0.916911i | \(-0.369325\pi\) | |||||||
\(62\) | 1.15732 | 0.146980 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.73205 | − | 1.00000i | 0.214834 | − | 0.124035i | ||||
\(66\) | −9.12248 | + | 4.71048i | −1.12290 | + | 0.579820i | ||||
\(67\) | −0.791288 | + | 1.37055i | −0.0966712 | + | 0.167439i | −0.910305 | − | 0.413938i | \(-0.864153\pi\) |
0.813634 | + | 0.581378i | \(0.197486\pi\) | |||||||
\(68\) | −1.87083 | − | 3.24037i | −0.226871 | − | 0.392953i | ||||
\(69\) | 12.3823i | 1.49065i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −5.70068 | + | 3.29129i | −0.671831 | + | 0.387882i | ||||
\(73\) | −3.16300 | + | 5.47847i | −0.370201 | + | 0.641206i | −0.989596 | − | 0.143873i | \(-0.954044\pi\) |
0.619395 | + | 0.785079i | \(0.287378\pi\) | |||||||
\(74\) | −4.83465 | − | 2.79129i | −0.562017 | − | 0.324481i | ||||
\(75\) | 12.2852 | − | 7.09285i | 1.41857 | − | 0.819012i | ||||
\(76\) | −5.54506 | −0.636062 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 9.58258 | 1.08501 | ||||||||
\(79\) | −3.46410 | + | 2.00000i | −0.389742 | + | 0.225018i | −0.682048 | − | 0.731307i | \(-0.738911\pi\) |
0.292306 | + | 0.956325i | \(0.405577\pi\) | |||||||
\(80\) | −0.559525 | − | 0.323042i | −0.0625568 | − | 0.0361172i | ||||
\(81\) | −7.29129 | + | 12.6289i | −0.810143 | + | 1.40321i | ||||
\(82\) | 4.35942 | − | 2.51691i | 0.481417 | − | 0.277946i | ||||
\(83\) | −9.15188 | −1.00455 | −0.502274 | − | 0.864708i | \(-0.667503\pi\) | ||||
−0.502274 | + | 0.864708i | \(0.667503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.41742i | − | 0.262206i | ||||||
\(86\) | −5.58258 | − | 9.66930i | −0.601985 | − | 1.04267i | ||||
\(87\) | −11.7362 | + | 20.3277i | −1.25825 | + | 2.17936i | ||||
\(88\) | −1.52168 | − | 2.94694i | −0.162212 | − | 0.314145i | ||||
\(89\) | −8.48528 | + | 4.89898i | −0.899438 | + | 0.519291i | −0.877018 | − | 0.480458i | \(-0.840471\pi\) |
−0.0224202 | + | 0.999749i | \(0.507137\pi\) | |||||||
\(90\) | −4.25290 | −0.448295 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 1.79129 | + | 3.10260i | 0.185748 | + | 0.321725i | ||||
\(94\) | 2.51691 | − | 4.35942i | 0.259600 | − | 0.449640i | ||||
\(95\) | −3.10260 | − | 1.79129i | −0.318320 | − | 0.183782i | ||||
\(96\) | −1.54779 | − | 2.68085i | −0.157970 | − | 0.273613i | ||||
\(97\) | 15.9891i | 1.62345i | 0.584041 | + | 0.811724i | \(0.301471\pi\) | ||||
−0.584041 | + | 0.811724i | \(0.698529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.3739 | − | 11.7913i | −1.84664 | − | 1.18507i | ||||
\(100\) | 2.29129 | + | 3.96863i | 0.229129 | + | 0.396863i | ||||
\(101\) | −0.255619 | + | 0.442745i | −0.0254351 | + | 0.0440548i | −0.878463 | − | 0.477811i | \(-0.841430\pi\) |
0.853028 | + | 0.521866i | \(0.174764\pi\) | |||||||
\(102\) | 5.79129 | − | 10.0308i | 0.573423 | − | 0.993198i | ||||
\(103\) | −11.7257 | + | 6.76981i | −1.15536 | + | 0.667049i | −0.950188 | − | 0.311676i | \(-0.899110\pi\) |
−0.205174 | + | 0.978725i | \(0.565776\pi\) | |||||||
\(104\) | 3.09557i | 0.303546i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.41742i | 0.234801i | ||||||||
\(107\) | 7.28970 | − | 4.20871i | 0.704722 | − | 0.406872i | −0.104382 | − | 0.994537i | \(-0.533286\pi\) |
0.809104 | + | 0.587666i | \(0.199953\pi\) | |||||||
\(108\) | −9.60433 | − | 5.54506i | −0.924177 | − | 0.533574i | ||||
\(109\) | 1.00905 | + | 0.582576i | 0.0966495 | + | 0.0558006i | 0.547546 | − | 0.836776i | \(-0.315562\pi\) |
−0.450896 | + | 0.892576i | \(0.648896\pi\) | |||||||
\(110\) | 0.100567 | − | 2.14046i | 0.00958872 | − | 0.204085i | ||||
\(111\) | − | 17.2813i | − | 1.64027i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.7477 | −1.57549 | −0.787747 | − | 0.615999i | \(-0.788752\pi\) | ||||
−0.787747 | + | 0.615999i | \(0.788752\pi\) | |||||||
\(114\) | −8.58258 | − | 14.8655i | −0.803832 | − | 1.39228i | ||||
\(115\) | −2.23810 | − | 1.29217i | −0.208704 | − | 0.120495i | ||||
\(116\) | −6.56670 | − | 3.79129i | −0.609703 | − | 0.352012i | ||||
\(117\) | 10.1884 | + | 17.6469i | 0.941920 | + | 1.63145i | ||||
\(118\) | −3.09557 | −0.284971 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 2.00000i | − | 0.182574i | ||||||
\(121\) | 6.36897 | − | 8.96863i | 0.578997 | − | 0.815330i | ||||
\(122\) | 8.04254 | + | 4.64336i | 0.728137 | + | 0.420390i | ||||
\(123\) | 13.4949 | + | 7.79129i | 1.21679 | + | 0.702517i | ||||
\(124\) | −1.00227 | + | 0.578661i | −0.0900065 | + | 0.0519653i | ||||
\(125\) | 6.19115i | 0.553753i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.58258i | 0.495373i | 0.968840 | + | 0.247687i | \(0.0796704\pi\) | ||||
−0.968840 | + | 0.247687i | \(0.920330\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 17.2813 | − | 29.9320i | 1.52153 | − | 2.63537i | ||||
\(130\) | −1.00000 | + | 1.73205i | −0.0877058 | + | 0.151911i | ||||
\(131\) | 4.71078 | + | 8.15932i | 0.411583 | + | 0.712883i | 0.995063 | − | 0.0992448i | \(-0.0316427\pi\) |
−0.583480 | + | 0.812127i | \(0.698309\pi\) | |||||||
\(132\) | 5.54506 | − | 8.64064i | 0.482636 | − | 0.752071i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 1.58258i | − | 0.136714i | ||||||
\(135\) | −3.58258 | − | 6.20520i | −0.308339 | − | 0.534059i | ||||
\(136\) | 3.24037 | + | 1.87083i | 0.277859 | + | 0.160422i | ||||
\(137\) | −7.58258 | + | 13.1334i | −0.647823 | + | 1.12206i | 0.335819 | + | 0.941927i | \(0.390987\pi\) |
−0.983642 | + | 0.180136i | \(0.942346\pi\) | |||||||
\(138\) | −6.19115 | − | 10.7234i | −0.527025 | − | 0.912835i | ||||
\(139\) | −3.23042 | −0.274001 | −0.137000 | − | 0.990571i | \(-0.543746\pi\) | ||||
−0.137000 | + | 0.990571i | \(0.543746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.5826 | 1.31229 | ||||||||
\(142\) | −1.73205 | + | 1.00000i | −0.145350 | + | 0.0839181i | ||||
\(143\) | −9.12248 | + | 4.71048i | −0.762860 | + | 0.393910i | ||||
\(144\) | 3.29129 | − | 5.70068i | 0.274274 | − | 0.475056i | ||||
\(145\) | −2.44949 | − | 4.24264i | −0.203419 | − | 0.352332i | ||||
\(146\) | − | 6.32599i | − | 0.523543i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.58258 | 0.458885 | ||||||||
\(149\) | −12.1244 | + | 7.00000i | −0.993266 | + | 0.573462i | −0.906249 | − | 0.422744i | \(-0.861067\pi\) |
−0.0870170 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(150\) | −7.09285 | + | 12.2852i | −0.579129 | + | 1.00308i | ||||
\(151\) | 3.10260 | + | 1.79129i | 0.252486 | + | 0.145773i | 0.620902 | − | 0.783888i | \(-0.286766\pi\) |
−0.368416 | + | 0.929661i | \(0.620100\pi\) | |||||||
\(152\) | 4.80217 | − | 2.77253i | 0.389507 | − | 0.224882i | ||||
\(153\) | 24.6297 | 1.99120 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.747727 | −0.0600589 | ||||||||
\(156\) | −8.29875 | + | 4.79129i | −0.664432 | + | 0.383610i | ||||
\(157\) | 17.7636 | + | 10.2558i | 1.41769 | + | 0.818506i | 0.996096 | − | 0.0882774i | \(-0.0281362\pi\) |
0.421597 | + | 0.906783i | \(0.361470\pi\) | |||||||
\(158\) | 2.00000 | − | 3.46410i | 0.159111 | − | 0.275589i | ||||
\(159\) | −6.48074 | + | 3.74166i | −0.513956 | + | 0.296733i | ||||
\(160\) | 0.646084 | 0.0510774 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 14.5826i | − | 1.14572i | ||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | −2.51691 | + | 4.35942i | −0.196538 | + | 0.340414i | ||||
\(165\) | 5.89389 | − | 3.04336i | 0.458839 | − | 0.236926i | ||||
\(166\) | 7.92576 | − | 4.57594i | 0.615158 | − | 0.355162i | ||||
\(167\) | 6.19115 | 0.479085 | 0.239543 | − | 0.970886i | \(-0.423002\pi\) | ||||
0.239543 | + | 0.970886i | \(0.423002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.41742 | −0.262879 | ||||||||
\(170\) | 1.20871 | + | 2.09355i | 0.0927040 | + | 0.160568i | ||||
\(171\) | 18.2504 | − | 31.6106i | 1.39564 | − | 2.41732i | ||||
\(172\) | 9.66930 | + | 5.58258i | 0.737278 | + | 0.425667i | ||||
\(173\) | −11.4806 | − | 19.8850i | −0.872853 | − | 1.51183i | −0.859032 | − | 0.511922i | \(-0.828934\pi\) |
−0.0138210 | − | 0.999904i | \(-0.504400\pi\) | |||||||
\(174\) | − | 23.4724i | − | 1.77944i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.79129 | + | 1.79129i | 0.210401 | + | 0.135023i | ||||
\(177\) | −4.79129 | − | 8.29875i | −0.360135 | − | 0.623773i | ||||
\(178\) | 4.89898 | − | 8.48528i | 0.367194 | − | 0.635999i | ||||
\(179\) | 3.58258 | − | 6.20520i | 0.267774 | − | 0.463799i | −0.700512 | − | 0.713640i | \(-0.747045\pi\) |
0.968287 | + | 0.249842i | \(0.0803785\pi\) | |||||||
\(180\) | 3.68312 | − | 2.12645i | 0.274523 | − | 0.158496i | ||||
\(181\) | − | 16.6352i | − | 1.23648i | −0.785988 | − | 0.618242i | \(-0.787845\pi\) | ||
0.785988 | − | 0.618242i | \(-0.212155\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.7477i | 2.12509i | ||||||||
\(184\) | 3.46410 | − | 2.00000i | 0.255377 | − | 0.147442i | ||||
\(185\) | 3.12359 | + | 1.80341i | 0.229651 | + | 0.132589i | ||||
\(186\) | −3.10260 | − | 1.79129i | −0.227494 | − | 0.131344i | ||||
\(187\) | −0.582415 | + | 12.3960i | −0.0425904 | + | 0.906485i | ||||
\(188\) | 5.03383i | 0.367129i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.58258 | 0.259907 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 2.68085 | + | 1.54779i | 0.193473 | + | 0.111702i | ||||
\(193\) | 17.6066 | + | 10.1652i | 1.26735 | + | 0.731704i | 0.974485 | − | 0.224451i | \(-0.0720589\pi\) |
0.292862 | + | 0.956155i | \(0.405392\pi\) | |||||||
\(194\) | −7.99455 | − | 13.8470i | −0.573975 | − | 0.994155i | ||||
\(195\) | −6.19115 | −0.443357 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.7477i | − | 1.33572i | −0.744287 | − | 0.667860i | \(-0.767210\pi\) | ||
0.744287 | − | 0.667860i | \(-0.232790\pi\) | |||||||
\(198\) | 21.8079 | + | 1.02462i | 1.54982 | + | 0.0728168i | ||||
\(199\) | −21.3300 | − | 12.3149i | −1.51204 | − | 0.872978i | −0.999901 | − | 0.0140770i | \(-0.995519\pi\) |
−0.512141 | − | 0.858901i | \(-0.671148\pi\) | |||||||
\(200\) | −3.96863 | − | 2.29129i | −0.280624 | − | 0.162019i | ||||
\(201\) | 4.24264 | − | 2.44949i | 0.299253 | − | 0.172774i | ||||
\(202\) | − | 0.511238i | − | 0.0359706i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 11.5826i | 0.810943i | ||||||||
\(205\) | −2.81655 | + | 1.62614i | −0.196716 | + | 0.113574i | ||||
\(206\) | 6.76981 | − | 11.7257i | 0.471675 | − | 0.816965i | ||||
\(207\) | 13.1652 | − | 22.8027i | 0.915041 | − | 1.58490i | ||||
\(208\) | −1.54779 | − | 2.68085i | −0.107320 | − | 0.185883i | ||||
\(209\) | 15.4779 | + | 9.93280i | 1.07063 | + | 0.687066i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.7477i | − | 0.739904i | −0.929051 | − | 0.369952i | \(-0.879374\pi\) | ||
0.929051 | − | 0.369952i | \(-0.120626\pi\) | |||||||
\(212\) | −1.20871 | − | 2.09355i | −0.0830147 | − | 0.143786i | ||||
\(213\) | −5.36169 | − | 3.09557i | −0.367377 | − | 0.212105i | ||||
\(214\) | −4.20871 | + | 7.28970i | −0.287702 | + | 0.498314i | ||||
\(215\) | 3.60681 | + | 6.24718i | 0.245983 | + | 0.426054i | ||||
\(216\) | 11.0901 | 0.754588 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.16515 | −0.0789140 | ||||||||
\(219\) | 16.9590 | − | 9.79129i | 1.14598 | − | 0.661634i | ||||
\(220\) | 0.983134 | + | 1.90397i | 0.0662829 | + | 0.128366i | ||||
\(221\) | 5.79129 | − | 10.0308i | 0.389564 | − | 0.674745i | ||||
\(222\) | 8.64064 | + | 14.9660i | 0.579922 | + | 1.00445i | ||||
\(223\) | 6.32599i | 0.423620i | 0.977311 | + | 0.211810i | \(0.0679358\pi\) | ||||
−0.977311 | + | 0.211810i | \(0.932064\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −30.1652 | −2.01101 | ||||||||
\(226\) | 14.5040 | − | 8.37386i | 0.964789 | − | 0.557021i | ||||
\(227\) | −5.86811 | + | 10.1639i | −0.389480 | + | 0.674599i | −0.992380 | − | 0.123218i | \(-0.960679\pi\) |
0.602900 | + | 0.797817i | \(0.294012\pi\) | |||||||
\(228\) | 14.8655 | + | 8.58258i | 0.984489 | + | 0.568395i | ||||
\(229\) | −11.2829 | + | 6.51419i | −0.745595 | + | 0.430470i | −0.824100 | − | 0.566444i | \(-0.808319\pi\) |
0.0785048 | + | 0.996914i | \(0.474985\pi\) | |||||||
\(230\) | 2.58434 | 0.170406 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.58258 | 0.497820 | ||||||||
\(233\) | −7.65120 | + | 4.41742i | −0.501247 | + | 0.289395i | −0.729228 | − | 0.684270i | \(-0.760121\pi\) |
0.227981 | + | 0.973665i | \(0.426787\pi\) | |||||||
\(234\) | −17.6469 | − | 10.1884i | −1.15361 | − | 0.666038i | ||||
\(235\) | −1.62614 | + | 2.81655i | −0.106077 | + | 0.183732i | ||||
\(236\) | 2.68085 | − | 1.54779i | 0.174508 | − | 0.100752i | ||||
\(237\) | 12.3823 | 0.804316 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 17.5826i | − | 1.13732i | −0.822572 | − | 0.568661i | \(-0.807462\pi\) | ||
0.822572 | − | 0.568661i | \(-0.192538\pi\) | |||||||
\(240\) | 1.00000 | + | 1.73205i | 0.0645497 | + | 0.111803i | ||||
\(241\) | −12.9610 | + | 22.4490i | −0.834889 | + | 1.44607i | 0.0592326 | + | 0.998244i | \(0.481135\pi\) |
−0.894121 | + | 0.447825i | \(0.852199\pi\) | |||||||
\(242\) | −1.03137 | + | 10.9515i | −0.0662992 | + | 0.703992i | ||||
\(243\) | 10.2806 | − | 5.93553i | 0.659503 | − | 0.380764i | ||||
\(244\) | −9.28672 | −0.594521 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.5826 | −0.993509 | ||||||||
\(247\) | −8.58258 | − | 14.8655i | −0.546096 | − | 0.945866i | ||||
\(248\) | 0.578661 | − | 1.00227i | 0.0367450 | − | 0.0636442i | ||||
\(249\) | 24.5348 | + | 14.1652i | 1.55483 | + | 0.897680i | ||||
\(250\) | −3.09557 | − | 5.36169i | −0.195781 | − | 0.339103i | ||||
\(251\) | 2.07310i | 0.130853i | 0.997857 | + | 0.0654264i | \(0.0208407\pi\) | ||||
−0.997857 | + | 0.0654264i | \(0.979159\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1652 | + | 7.16515i | 0.701947 | + | 0.450469i | ||||
\(254\) | −2.79129 | − | 4.83465i | −0.175141 | − | 0.303353i | ||||
\(255\) | −3.74166 | + | 6.48074i | −0.234312 | + | 0.405840i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.24264 | − | 2.44949i | 0.264649 | − | 0.152795i | −0.361805 | − | 0.932254i | \(-0.617839\pi\) |
0.626453 | + | 0.779459i | \(0.284506\pi\) | |||||||
\(258\) | 34.5625i | 2.15177i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 2.00000i | − | 0.124035i | ||||||
\(261\) | 43.2258 | − | 24.9564i | 2.67561 | − | 1.54476i | ||||
\(262\) | −8.15932 | − | 4.71078i | −0.504084 | − | 0.291033i | ||||
\(263\) | −24.5348 | − | 14.1652i | −1.51288 | − | 0.873461i | −0.999886 | − | 0.0150671i | \(-0.995204\pi\) |
−0.512992 | − | 0.858394i | \(-0.671463\pi\) | |||||||
\(264\) | −0.481847 | + | 10.2555i | −0.0296556 | + | 0.631185i | ||||
\(265\) | − | 1.56186i | − | 0.0959442i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.3303 | 1.85618 | ||||||||
\(268\) | 0.791288 | + | 1.37055i | 0.0483356 | + | 0.0837197i | ||||
\(269\) | −17.5301 | − | 10.1210i | −1.06883 | − | 0.617088i | −0.140967 | − | 0.990014i | \(-0.545021\pi\) |
−0.927861 | + | 0.372926i | \(0.878355\pi\) | |||||||
\(270\) | 6.20520 | + | 3.58258i | 0.377637 | + | 0.218029i | ||||
\(271\) | −2.44949 | − | 4.24264i | −0.148796 | − | 0.257722i | 0.781987 | − | 0.623295i | \(-0.214206\pi\) |
−0.930783 | + | 0.365573i | \(0.880873\pi\) | |||||||
\(272\) | −3.74166 | −0.226871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 15.1652i | − | 0.916160i | ||||||
\(275\) | 0.713309 | − | 15.1819i | 0.0430142 | − | 0.915505i | ||||
\(276\) | 10.7234 | + | 6.19115i | 0.645472 | + | 0.372663i | ||||
\(277\) | −1.73205 | − | 1.00000i | −0.104069 | − | 0.0600842i | 0.447062 | − | 0.894503i | \(-0.352470\pi\) |
−0.551131 | + | 0.834419i | \(0.685804\pi\) | |||||||
\(278\) | 2.79763 | − | 1.61521i | 0.167790 | − | 0.0968738i | ||||
\(279\) | − | 7.61816i | − | 0.456087i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.16515i | − | 0.427437i | −0.976895 | − | 0.213719i | \(-0.931442\pi\) | ||
0.976895 | − | 0.213719i | \(-0.0685575\pi\) | |||||||
\(282\) | −13.4949 | + | 7.79129i | −0.803610 | + | 0.463964i | ||||
\(283\) | 7.80636 | − | 13.5210i | 0.464040 | − | 0.803740i | −0.535118 | − | 0.844777i | \(-0.679733\pi\) |
0.999158 | + | 0.0410370i | \(0.0130661\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 5.54506 | + | 9.60433i | 0.328461 | + | 0.568911i | ||||
\(286\) | 5.54506 | − | 8.64064i | 0.327886 | − | 0.510932i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.58258i | 0.387882i | ||||||||
\(289\) | 1.50000 | + | 2.59808i | 0.0882353 | + | 0.152828i | ||||
\(290\) | 4.24264 | + | 2.44949i | 0.249136 | + | 0.143839i | ||||
\(291\) | 24.7477 | − | 42.8643i | 1.45074 | − | 2.51275i | ||||
\(292\) | 3.16300 | + | 5.47847i | 0.185100 | + | 0.320603i | ||||
\(293\) | −21.3993 | −1.25016 | −0.625081 | − | 0.780560i | \(-0.714934\pi\) | ||||
−0.625081 | + | 0.780560i | \(0.714934\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | 0.116445 | ||||||||
\(296\) | −4.83465 | + | 2.79129i | −0.281008 | + | 0.162240i | ||||
\(297\) | 16.8756 | + | 32.6820i | 0.979224 | + | 1.89640i | ||||
\(298\) | 7.00000 | − | 12.1244i | 0.405499 | − | 0.702345i | ||||
\(299\) | −6.19115 | − | 10.7234i | −0.358043 | − | 0.620149i | ||||
\(300\) | − | 14.1857i | − | 0.819012i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.58258 | −0.206154 | ||||||||
\(303\) | 1.37055 | − | 0.791288i | 0.0787361 | − | 0.0454583i | ||||
\(304\) | −2.77253 | + | 4.80217i | −0.159016 | + | 0.275423i | ||||
\(305\) | −5.19615 | − | 3.00000i | −0.297531 | − | 0.171780i | ||||
\(306\) | −21.3300 | + | 12.3149i | −1.21935 | + | 0.703994i | ||||
\(307\) | −8.12940 | −0.463969 | −0.231985 | − | 0.972719i | \(-0.574522\pi\) | ||||
−0.231985 | + | 0.972719i | \(0.574522\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 41.9129 | 2.38434 | ||||||||
\(310\) | 0.647551 | − | 0.373864i | 0.0367784 | − | 0.0212340i | ||||
\(311\) | −8.60206 | − | 4.96640i | −0.487778 | − | 0.281619i | 0.235874 | − | 0.971784i | \(-0.424205\pi\) |
−0.723652 | + | 0.690165i | \(0.757538\pi\) | |||||||
\(312\) | 4.79129 | − | 8.29875i | 0.271253 | − | 0.469824i | ||||
\(313\) | 0.885491 | − | 0.511238i | 0.0500509 | − | 0.0288969i | −0.474766 | − | 0.880112i | \(-0.657467\pi\) |
0.524817 | + | 0.851215i | \(0.324134\pi\) | |||||||
\(314\) | −20.5117 | −1.15754 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000i | 0.225018i | ||||||||
\(317\) | 4.58258 | + | 7.93725i | 0.257383 | + | 0.445801i | 0.965540 | − | 0.260254i | \(-0.0838064\pi\) |
−0.708157 | + | 0.706055i | \(0.750473\pi\) | |||||||
\(318\) | 3.74166 | − | 6.48074i | 0.209822 | − | 0.363422i | ||||
\(319\) | 11.5383 | + | 22.3454i | 0.646019 | + | 1.25110i | ||||
\(320\) | −0.559525 | + | 0.323042i | −0.0312784 | + | 0.0180586i | ||||
\(321\) | −26.0568 | −1.45435 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.7477 | −1.15443 | ||||||||
\(324\) | 7.29129 | + | 12.6289i | 0.405072 | + | 0.701605i | ||||
\(325\) | −7.09285 | + | 12.2852i | −0.393441 | + | 0.681459i | ||||
\(326\) | 3.46410 | + | 2.00000i | 0.191859 | + | 0.110770i | ||||
\(327\) | −1.80341 | − | 3.12359i | −0.0997286 | − | 0.172735i | ||||
\(328\) | − | 5.03383i | − | 0.277946i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.58258 | + | 5.58258i | −0.197214 | + | 0.307311i | ||||
\(331\) | 7.20871 | + | 12.4859i | 0.396227 | + | 0.686285i | 0.993257 | − | 0.115934i | \(-0.0369861\pi\) |
−0.597030 | + | 0.802219i | \(0.703653\pi\) | |||||||
\(332\) | −4.57594 | + | 7.92576i | −0.251137 | + | 0.434982i | ||||
\(333\) | −18.3739 | + | 31.8245i | −1.00688 | + | 1.74397i | ||||
\(334\) | −5.36169 | + | 3.09557i | −0.293379 | + | 0.169382i | ||||
\(335\) | 1.02248i | 0.0558639i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.1652i | 1.58873i | 0.607443 | + | 0.794364i | \(0.292195\pi\) | ||||
−0.607443 | + | 0.794364i | \(0.707805\pi\) | |||||||
\(338\) | 2.95958 | − | 1.70871i | 0.160980 | − | 0.0929417i | ||||
\(339\) | 44.8981 | + | 25.9219i | 2.43853 | + | 1.40788i | ||||
\(340\) | −2.09355 | − | 1.20871i | −0.113539 | − | 0.0655516i | ||||
\(341\) | 3.83417 | + | 0.180145i | 0.207632 | + | 0.00975541i | ||||
\(342\) | 36.5008i | 1.97374i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.1652 | −0.601985 | ||||||||
\(345\) | 4.00000 | + | 6.92820i | 0.215353 | + | 0.373002i | ||||
\(346\) | 19.8850 | + | 11.4806i | 1.06902 | + | 0.617200i | ||||
\(347\) | 0.723000 | + | 0.417424i | 0.0388127 | + | 0.0224085i | 0.519281 | − | 0.854604i | \(-0.326200\pi\) |
−0.480468 | + | 0.877012i | \(0.659533\pi\) | |||||||
\(348\) | 11.7362 | + | 20.3277i | 0.629127 | + | 1.08968i | ||||
\(349\) | 2.07310 | 0.110970 | 0.0554852 | − | 0.998460i | \(-0.482329\pi\) | ||||
0.0554852 | + | 0.998460i | \(0.482329\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 34.3303i | − | 1.83242i | ||||||
\(352\) | −3.31297 | − | 0.155657i | −0.176582 | − | 0.00829654i | ||||
\(353\) | −6.48074 | − | 3.74166i | −0.344935 | − | 0.199148i | 0.317517 | − | 0.948253i | \(-0.397151\pi\) |
−0.662452 | + | 0.749104i | \(0.730484\pi\) | |||||||
\(354\) | 8.29875 | + | 4.79129i | 0.441074 | + | 0.254654i | ||||
\(355\) | 1.11905 | − | 0.646084i | 0.0593930 | − | 0.0342906i | ||||
\(356\) | 9.79796i | 0.519291i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.16515i | 0.378690i | ||||||||
\(359\) | −0.361500 | + | 0.208712i | −0.0190792 | + | 0.0110154i | −0.509509 | − | 0.860465i | \(-0.670173\pi\) |
0.490430 | + | 0.871481i | \(0.336840\pi\) | |||||||
\(360\) | −2.12645 | + | 3.68312i | −0.112074 | + | 0.194117i | ||||
\(361\) | −5.87386 | + | 10.1738i | −0.309151 | + | 0.535465i | ||||
\(362\) | 8.31759 | + | 14.4065i | 0.437163 | + | 0.757189i | ||||
\(363\) | −30.9557 | + | 14.1857i | −1.62475 | + | 0.744556i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.08712i | 0.213930i | ||||||||
\(366\) | −14.3739 | − | 24.8963i | −0.751334 | − | 1.30135i | ||||
\(367\) | −1.23583 | − | 0.713507i | −0.0645098 | − | 0.0372447i | 0.467398 | − | 0.884047i | \(-0.345191\pi\) |
−0.531908 | + | 0.846802i | \(0.678525\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | −16.5678 | − | 28.6962i | −0.862484 | − | 1.49387i | ||||
\(370\) | −3.60681 | −0.187509 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.58258 | 0.185748 | ||||||||
\(373\) | 0.361500 | − | 0.208712i | 0.0187178 | − | 0.0108067i | −0.490612 | − | 0.871378i | \(-0.663227\pi\) |
0.509330 | + | 0.860571i | \(0.329893\pi\) | |||||||
\(374\) | −5.69361 | − | 11.0265i | −0.294410 | − | 0.570165i | ||||
\(375\) | 9.58258 | − | 16.5975i | 0.494842 | − | 0.857092i | ||||
\(376\) | −2.51691 | − | 4.35942i | −0.129800 | − | 0.224820i | ||||
\(377\) | − | 23.4724i | − | 1.20889i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3303 | 0.736098 | 0.368049 | − | 0.929806i | \(-0.380026\pi\) | ||||
0.368049 | + | 0.929806i | \(0.380026\pi\) | |||||||
\(380\) | −3.10260 | + | 1.79129i | −0.159160 | + | 0.0918911i | ||||
\(381\) | 8.64064 | − | 14.9660i | 0.442673 | − | 0.766733i | ||||
\(382\) | −15.5885 | − | 9.00000i | −0.797575 | − | 0.460480i | ||||
\(383\) | −4.12586 | + | 2.38207i | −0.210822 | + | 0.121718i | −0.601693 | − | 0.798727i | \(-0.705507\pi\) |
0.390872 | + | 0.920445i | \(0.372174\pi\) | |||||||
\(384\) | −3.09557 | −0.157970 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.3303 | −1.03479 | ||||||||
\(387\) | −63.6489 | + | 36.7477i | −3.23546 | + | 1.86799i | ||||
\(388\) | 13.8470 | + | 7.99455i | 0.702973 | + | 0.405862i | ||||
\(389\) | −5.00000 | + | 8.66025i | −0.253510 | + | 0.439092i | −0.964490 | − | 0.264120i | \(-0.914918\pi\) |
0.710980 | + | 0.703213i | \(0.248252\pi\) | |||||||
\(390\) | 5.36169 | − | 3.09557i | 0.271500 | − | 0.156750i | ||||
\(391\) | −14.9666 | −0.756895 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 29.1652i | − | 1.47119i | ||||||
\(394\) | 9.37386 | + | 16.2360i | 0.472248 | + | 0.817958i | ||||
\(395\) | −1.29217 | + | 2.23810i | −0.0650160 | + | 0.112611i | ||||
\(396\) | −19.3985 | + | 10.0166i | −0.974811 | + | 0.503353i | ||||
\(397\) | 20.6537 | − | 11.9244i | 1.03658 | − | 0.598469i | 0.117716 | − | 0.993047i | \(-0.462443\pi\) |
0.918862 | + | 0.394578i | \(0.129109\pi\) | |||||||
\(398\) | 24.6297 | 1.23458 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.58258 | 0.229129 | ||||||||
\(401\) | 0.791288 | + | 1.37055i | 0.0395150 | + | 0.0684420i | 0.885107 | − | 0.465388i | \(-0.154085\pi\) |
−0.845592 | + | 0.533831i | \(0.820752\pi\) | |||||||
\(402\) | −2.44949 | + | 4.24264i | −0.122169 | + | 0.211604i | ||||
\(403\) | −3.10260 | − | 1.79129i | −0.154552 | − | 0.0892304i | ||||
\(404\) | 0.255619 | + | 0.442745i | 0.0127175 | + | 0.0220274i | ||||
\(405\) | 9.42157i | 0.468161i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.5826 | − | 10.0000i | −0.772400 | − | 0.495682i | ||||
\(408\) | −5.79129 | − | 10.0308i | −0.286711 | − | 0.496599i | ||||
\(409\) | 4.96640 | − | 8.60206i | 0.245573 | − | 0.425345i | −0.716720 | − | 0.697361i | \(-0.754357\pi\) |
0.962293 | + | 0.272017i | \(0.0876906\pi\) | |||||||
\(410\) | 1.62614 | − | 2.81655i | 0.0803092 | − | 0.139100i | ||||
\(411\) | 40.6554 | − | 23.4724i | 2.00538 | − | 1.15781i | ||||
\(412\) | 13.5396i | 0.667049i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 26.3303i | 1.29406i | ||||||||
\(415\) | −5.12070 | + | 2.95644i | −0.251365 | + | 0.145126i | ||||
\(416\) | 2.68085 | + | 1.54779i | 0.131439 | + | 0.0758865i | ||||
\(417\) | 8.66025 | + | 5.00000i | 0.424094 | + | 0.244851i | ||||
\(418\) | −18.3706 | − | 0.863127i | −0.898537 | − | 0.0422169i | ||||
\(419\) | 5.67991i | 0.277482i | 0.990329 | + | 0.138741i | \(0.0443055\pi\) | ||||
−0.990329 | + | 0.138741i | \(0.955694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.58258 | −0.0771300 | −0.0385650 | − | 0.999256i | \(-0.512279\pi\) | ||||
−0.0385650 | + | 0.999256i | \(0.512279\pi\) | |||||||
\(422\) | 5.37386 | + | 9.30780i | 0.261596 | + | 0.453097i | ||||
\(423\) | −28.6962 | − | 16.5678i | −1.39526 | − | 0.805552i | ||||
\(424\) | 2.09355 | + | 1.20871i | 0.101672 | + | 0.0587003i | ||||
\(425\) | 8.57321 | + | 14.8492i | 0.415862 | + | 0.720294i | ||||
\(426\) | 6.19115 | 0.299962 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 8.41742i | − | 0.406872i | ||||||
\(429\) | 31.7468 | + | 1.49159i | 1.53275 | + | 0.0720148i | ||||
\(430\) | −6.24718 | − | 3.60681i | −0.301266 | − | 0.173936i | ||||
\(431\) | −15.5130 | − | 8.95644i | −0.747235 | − | 0.431416i | 0.0774588 | − | 0.996996i | \(-0.475319\pi\) |
−0.824694 | + | 0.565579i | \(0.808653\pi\) | |||||||
\(432\) | −9.60433 | + | 5.54506i | −0.462089 | + | 0.266787i | ||||
\(433\) | − | 28.1017i | − | 1.35048i | −0.737597 | − | 0.675241i | \(-0.764040\pi\) | ||
0.737597 | − | 0.675241i | \(-0.235960\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.1652i | 0.727113i | ||||||||
\(436\) | 1.00905 | − | 0.582576i | 0.0483248 | − | 0.0279003i | ||||
\(437\) | −11.0901 | + | 19.2087i | −0.530513 | + | 0.918875i | ||||
\(438\) | −9.79129 | + | 16.9590i | −0.467846 | + | 0.810333i | ||||
\(439\) | 1.15732 | + | 2.00454i | 0.0552360 | + | 0.0956715i | 0.892321 | − | 0.451401i | \(-0.149076\pi\) |
−0.837085 | + | 0.547072i | \(0.815742\pi\) | |||||||
\(440\) | −1.80341 | − | 1.15732i | −0.0859740 | − | 0.0551732i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.5826i | 0.550927i | ||||||||
\(443\) | 1.58258 | + | 2.74110i | 0.0751904 | + | 0.130234i | 0.901169 | − | 0.433468i | \(-0.142710\pi\) |
−0.825979 | + | 0.563701i | \(0.809377\pi\) | |||||||
\(444\) | −14.9660 | − | 8.64064i | −0.710256 | − | 0.410066i | ||||
\(445\) | −3.16515 | + | 5.48220i | −0.150043 | + | 0.259881i | ||||
\(446\) | −3.16300 | − | 5.47847i | −0.149772 | − | 0.259413i | ||||
\(447\) | 43.3380 | 2.04982 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.8348 | 0.605714 | 0.302857 | − | 0.953036i | \(-0.402060\pi\) | ||||
0.302857 | + | 0.953036i | \(0.402060\pi\) | |||||||
\(450\) | 26.1238 | − | 15.0826i | 1.23149 | − | 0.710999i | ||||
\(451\) | 14.8344 | − | 7.65988i | 0.698525 | − | 0.360690i | ||||
\(452\) | −8.37386 | + | 14.5040i | −0.393873 | + | 0.682209i | ||||
\(453\) | −5.54506 | − | 9.60433i | −0.260530 | − | 0.451251i | ||||
\(454\) | − | 11.7362i | − | 0.550808i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −17.1652 | −0.803832 | ||||||||
\(457\) | 12.8474 | − | 7.41742i | 0.600974 | − | 0.346972i | −0.168451 | − | 0.985710i | \(-0.553876\pi\) |
0.769425 | + | 0.638738i | \(0.220543\pi\) | |||||||
\(458\) | 6.51419 | − | 11.2829i | 0.304388 | − | 0.527216i | ||||
\(459\) | −35.9361 | − | 20.7477i | −1.67735 | − | 0.968421i | ||||
\(460\) | −2.23810 | + | 1.29217i | −0.104352 | + | 0.0602476i | ||||
\(461\) | −26.2983 | −1.22483 | −0.612417 | − | 0.790535i | \(-0.709803\pi\) | ||||
−0.612417 | + | 0.790535i | \(0.709803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1652 | −0.611836 | −0.305918 | − | 0.952058i | \(-0.598963\pi\) | ||||
−0.305918 | + | 0.952058i | \(0.598963\pi\) | |||||||
\(464\) | −6.56670 | + | 3.79129i | −0.304852 | + | 0.176006i | ||||
\(465\) | 2.00454 | + | 1.15732i | 0.0929583 | + | 0.0536695i | ||||
\(466\) | 4.41742 | − | 7.65120i | 0.204633 | − | 0.354435i | ||||
\(467\) | 0.442745 | − | 0.255619i | 0.0204878 | − | 0.0118286i | −0.489721 | − | 0.871879i | \(-0.662901\pi\) |
0.510209 | + | 0.860050i | \(0.329568\pi\) | |||||||
\(468\) | 20.3768 | 0.941920 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 3.25227i | − | 0.150016i | ||||||
\(471\) | −31.7477 | − | 54.9887i | −1.46286 | − | 2.53374i | ||||
\(472\) | −1.54779 | + | 2.68085i | −0.0712427 | + | 0.123396i | ||||
\(473\) | −16.9898 | − | 32.9031i | −0.781192 | − | 1.51289i | ||||
\(474\) | −10.7234 | + | 6.19115i | −0.492541 | + | 0.284369i | ||||
\(475\) | 25.4107 | 1.16592 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.9129 | 0.728601 | ||||||||
\(478\) | 8.79129 | + | 15.2270i | 0.402104 | + | 0.696465i | ||||
\(479\) | −3.23042 | + | 5.59525i | −0.147602 | + | 0.255653i | −0.930341 | − | 0.366697i | \(-0.880489\pi\) |
0.782739 | + | 0.622350i | \(0.213822\pi\) | |||||||
\(480\) | −1.73205 | − | 1.00000i | −0.0790569 | − | 0.0456435i | ||||
\(481\) | 8.64064 | + | 14.9660i | 0.393979 | + | 0.682392i | ||||
\(482\) | − | 25.9219i | − | 1.18071i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.58258 | − | 10.0000i | −0.208299 | − | 0.454545i | ||||
\(485\) | 5.16515 | + | 8.94630i | 0.234537 | + | 0.406231i | ||||
\(486\) | −5.93553 | + | 10.2806i | −0.269241 | + | 0.466339i | ||||
\(487\) | 16.7477 | − | 29.0079i | 0.758912 | − | 1.31447i | −0.184494 | − | 0.982834i | \(-0.559065\pi\) |
0.943406 | − | 0.331640i | \(-0.107602\pi\) | |||||||
\(488\) | 8.04254 | − | 4.64336i | 0.364069 | − | 0.210195i | ||||
\(489\) | 12.3823i | 0.559947i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.4955i | − | 0.970076i | −0.874493 | − | 0.485038i | \(-0.838806\pi\) | ||
0.874493 | − | 0.485038i | \(-0.161194\pi\) | |||||||
\(492\) | 13.4949 | − | 7.79129i | 0.608397 | − | 0.351258i | ||||
\(493\) | −24.5704 | − | 14.1857i | −1.10659 | − | 0.638892i | ||||
\(494\) | 14.8655 | + | 8.58258i | 0.668829 | + | 0.386148i | ||||
\(495\) | −14.0897 | − | 0.661992i | −0.633286 | − | 0.0297543i | ||||
\(496\) | 1.15732i | 0.0519653i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −28.3303 | −1.26951 | ||||||||
\(499\) | −13.9564 | − | 24.1733i | −0.624776 | − | 1.08214i | −0.988584 | − | 0.150670i | \(-0.951857\pi\) |
0.363808 | − | 0.931474i | \(-0.381476\pi\) | |||||||
\(500\) | 5.36169 | + | 3.09557i | 0.239782 | + | 0.138438i | ||||
\(501\) | −16.5975 | − | 9.58258i | −0.741522 | − | 0.428118i | ||||
\(502\) | −1.03655 | − | 1.79535i | −0.0462634 | − | 0.0801306i | ||||
\(503\) | 31.9782 | 1.42584 | 0.712919 | − | 0.701246i | \(-0.247373\pi\) | ||||
0.712919 | + | 0.701246i | \(0.247373\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.330303i | 0.0146983i | ||||||||
\(506\) | −13.2519 | − | 0.622627i | −0.589118 | − | 0.0276792i | ||||
\(507\) | 9.16159 | + | 5.28944i | 0.406880 | + | 0.234912i | ||||
\(508\) | 4.83465 | + | 2.79129i | 0.214503 | + | 0.123843i | ||||
\(509\) | 15.5255 | − | 8.96368i | 0.688158 | − | 0.397308i | −0.114764 | − | 0.993393i | \(-0.536611\pi\) |
0.802922 | + | 0.596085i | \(0.203278\pi\) | |||||||
\(510\) | − | 7.48331i | − | 0.331367i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −53.2566 | + | 30.7477i | −2.35134 | + | 1.35755i | ||||
\(514\) | −2.44949 | + | 4.24264i | −0.108042 | + | 0.187135i | ||||
\(515\) | −4.37386 | + | 7.57575i | −0.192735 | + | 0.333828i | ||||
\(516\) | −17.2813 | − | 29.9320i | −0.760766 | − | 1.31768i | ||||
\(517\) | 9.01703 | − | 14.0509i | 0.396569 | − | 0.617956i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 71.0780i | 3.11998i | ||||||||
\(520\) | 1.00000 | + | 1.73205i | 0.0438529 | + | 0.0759555i | ||||
\(521\) | −30.8175 | − | 17.7925i | −1.35014 | − | 0.779504i | −0.361872 | − | 0.932228i | \(-0.617862\pi\) |
−0.988269 | + | 0.152724i | \(0.951196\pi\) | |||||||
\(522\) | −24.9564 | + | 43.2258i | −1.09231 | + | 1.89194i | ||||
\(523\) | 13.3514 | + | 23.1253i | 0.583817 | + | 1.01120i | 0.995022 | + | 0.0996575i | \(0.0317747\pi\) |
−0.411205 | + | 0.911543i | \(0.634892\pi\) | |||||||
\(524\) | 9.42157 | 0.411583 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.3303 | 1.23526 | ||||||||
\(527\) | −3.75015 | + | 2.16515i | −0.163359 | + | 0.0943155i | ||||
\(528\) | −4.71048 | − | 9.12248i | −0.204997 | − | 0.397005i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0.780929 | + | 1.35261i | 0.0339214 | + | 0.0587536i | ||||
\(531\) | 20.3768i | 0.884280i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.5826 | −0.674956 | ||||||||
\(534\) | −26.2668 | + | 15.1652i | −1.13668 | + | 0.656260i | ||||
\(535\) | 2.71918 | − | 4.70976i | 0.117560 | − | 0.203621i | ||||
\(536\) | −1.37055 | − | 0.791288i | −0.0591988 | − | 0.0341784i | ||||
\(537\) | −19.2087 | + | 11.0901i | −0.828915 | + | 0.478574i | ||||
\(538\) | 20.2420 | 0.872695 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.16515 | −0.308339 | ||||||||
\(541\) | −8.01270 | + | 4.62614i | −0.344493 | + | 0.198893i | −0.662257 | − | 0.749277i | \(-0.730401\pi\) |
0.317764 | + | 0.948170i | \(0.397068\pi\) | |||||||
\(542\) | 4.24264 | + | 2.44949i | 0.182237 | + | 0.105215i | ||||
\(543\) | −25.7477 | + | 44.5964i | −1.10494 | + | 1.91381i | ||||
\(544\) | 3.24037 | − | 1.87083i | 0.138930 | − | 0.0802111i | ||||
\(545\) | 0.752785 | 0.0322458 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.74773i | 0.117484i | 0.998273 | + | 0.0587422i | \(0.0187090\pi\) | ||||
−0.998273 | + | 0.0587422i | \(0.981291\pi\) | |||||||
\(548\) | 7.58258 | + | 13.1334i | 0.323912 | + | 0.561031i | ||||
\(549\) | 30.5653 | − | 52.9406i | 1.30449 | − | 2.25945i | ||||
\(550\) | 6.97322 | + | 13.5046i | 0.297339 | + | 0.575838i | ||||
\(551\) | −36.4128 | + | 21.0229i | −1.55124 | + | 0.895607i | ||||
\(552\) | −12.3823 | −0.527025 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | −5.58258 | − | 9.66930i | −0.236967 | − | 0.410439i | ||||
\(556\) | −1.61521 | + | 2.79763i | −0.0685001 | + | 0.118646i | ||||
\(557\) | −8.58480 | − | 4.95644i | −0.363750 | − | 0.210011i | 0.306975 | − | 0.951718i | \(-0.400683\pi\) |
−0.670724 | + | 0.741707i | \(0.734017\pi\) | |||||||
\(558\) | 3.80908 | + | 6.59752i | 0.161251 | + | 0.279295i | ||||
\(559\) | 34.5625i | 1.46184i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.7477 | − | 32.3303i | 0.875970 | − | 1.36499i | ||||
\(562\) | 3.58258 | + | 6.20520i | 0.151122 | + | 0.261751i | ||||
\(563\) | 21.2111 | − | 36.7388i | 0.893942 | − | 1.54835i | 0.0588344 | − | 0.998268i | \(-0.481262\pi\) |
0.835108 | − | 0.550086i | \(-0.185405\pi\) | |||||||
\(564\) | 7.79129 | − | 13.4949i | 0.328072 | − | 0.568238i | ||||
\(565\) | −9.37077 | + | 5.41022i | −0.394231 | + | 0.227610i | ||||
\(566\) | 15.6127i | 0.656251i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.00000i | 0.0839181i | ||||||||
\(569\) | −13.4195 | + | 7.74773i | −0.562573 | + | 0.324802i | −0.754178 | − | 0.656671i | \(-0.771964\pi\) |
0.191605 | + | 0.981472i | \(0.438631\pi\) | |||||||
\(570\) | −9.60433 | − | 5.54506i | −0.402281 | − | 0.232257i | ||||
\(571\) | −3.10260 | − | 1.79129i | −0.129840 | − | 0.0749631i | 0.433673 | − | 0.901070i | \(-0.357217\pi\) |
−0.563513 | + | 0.826107i | \(0.690551\pi\) | |||||||
\(572\) | −0.481847 | + | 10.2555i | −0.0201470 | + | 0.428806i | ||||
\(573\) | − | 55.7203i | − | 2.32775i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.3303 | 0.764426 | ||||||||
\(576\) | −3.29129 | − | 5.70068i | −0.137137 | − | 0.237528i | ||||
\(577\) | −0.233559 | − | 0.134846i | −0.00972320 | − | 0.00561369i | 0.495131 | − | 0.868819i | \(-0.335120\pi\) |
−0.504854 | + | 0.863205i | \(0.668454\pi\) | |||||||
\(578\) | −2.59808 | − | 1.50000i | −0.108066 | − | 0.0623918i | ||||
\(579\) | −31.4670 | − | 54.5024i | −1.30772 | − | 2.26504i | ||||
\(580\) | −4.89898 | −0.203419 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 49.4955i | 2.05165i | ||||||||
\(583\) | −0.376289 | + | 8.00885i | −0.0155843 | + | 0.331693i | ||||
\(584\) | −5.47847 | − | 3.16300i | −0.226701 | − | 0.130886i | ||||
\(585\) | 11.4014 | + | 6.58258i | 0.471388 | + | 0.272156i | ||||
\(586\) | 18.5324 | − | 10.6997i | 0.765565 | − | 0.441999i | ||||
\(587\) | − | 17.0397i | − | 0.703305i | −0.936131 | − | 0.351652i | \(-0.885620\pi\) | ||
0.936131 | − | 0.351652i | \(-0.114380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.41742i | 0.264425i | ||||||||
\(590\) | −1.73205 | + | 1.00000i | −0.0713074 | + | 0.0411693i | ||||
\(591\) | −29.0175 | + | 50.2598i | −1.19362 | + | 2.06741i | ||||
\(592\) | 2.79129 | − | 4.83465i | 0.114721 | − | 0.198703i | ||||
\(593\) | 0.0674228 | + | 0.116780i | 0.00276872 | + | 0.00479557i | 0.867406 | − | 0.497600i | \(-0.165785\pi\) |
−0.864638 | + | 0.502396i | \(0.832452\pi\) | |||||||
\(594\) | −30.9557 | − | 19.8656i | −1.27013 | − | 0.815096i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.0000i | 0.573462i | ||||||||
\(597\) | 38.1216 | + | 66.0285i | 1.56021 | + | 2.70237i | ||||
\(598\) | 10.7234 | + | 6.19115i | 0.438512 | + | 0.253175i | ||||
\(599\) | 1.41742 | − | 2.45505i | 0.0579144 | − | 0.100311i | −0.835615 | − | 0.549316i | \(-0.814888\pi\) |
0.893529 | + | 0.449005i | \(0.148222\pi\) | |||||||
\(600\) | 7.09285 | + | 12.2852i | 0.289564 | + | 0.501540i | ||||
\(601\) | 1.42701 | 0.0582091 | 0.0291045 | − | 0.999576i | \(-0.490734\pi\) | ||||
0.0291045 | + | 0.999576i | \(0.490734\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.4174 | −0.424230 | ||||||||
\(604\) | 3.10260 | − | 1.79129i | 0.126243 | − | 0.0728865i | ||||
\(605\) | 0.666353 | − | 7.07561i | 0.0270911 | − | 0.287665i | ||||
\(606\) | −0.791288 | + | 1.37055i | −0.0321439 | + | 0.0556748i | ||||
\(607\) | 23.4724 | + | 40.6554i | 0.952716 | + | 1.65015i | 0.739510 | + | 0.673146i | \(0.235057\pi\) |
0.213206 | + | 0.977007i | \(0.431609\pi\) | |||||||
\(608\) | − | 5.54506i | − | 0.224882i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −13.4949 | + | 7.79129i | −0.545945 | + | 0.315202i | ||||
\(612\) | 12.3149 | − | 21.3300i | 0.497799 | − | 0.862213i | ||||
\(613\) | 12.0489 | + | 6.95644i | 0.486651 | + | 0.280968i | 0.723184 | − | 0.690655i | \(-0.242678\pi\) |
−0.236533 | + | 0.971623i | \(0.576011\pi\) | |||||||
\(614\) | 7.04027 | − | 4.06470i | 0.284122 | − | 0.164038i | ||||
\(615\) | 10.0677 | 0.405967 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.9129 | 1.04321 | 0.521607 | − | 0.853186i | \(-0.325333\pi\) | ||||
0.521607 | + | 0.853186i | \(0.325333\pi\) | |||||||
\(618\) | −36.2976 | + | 20.9564i | −1.46010 | + | 0.842992i | ||||
\(619\) | 0.676305 | + | 0.390465i | 0.0271830 | + | 0.0156941i | 0.513530 | − | 0.858072i | \(-0.328338\pi\) |
−0.486347 | + | 0.873766i | \(0.661671\pi\) | |||||||
\(620\) | −0.373864 | + | 0.647551i | −0.0150147 | + | 0.0260063i | ||||
\(621\) | −38.4173 | + | 22.1803i | −1.54163 | + | 0.890063i | ||||
\(622\) | 9.93280 | 0.398269 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.58258i | 0.383610i | ||||||||
\(625\) | −9.45644 | − | 16.3790i | −0.378258 | − | 0.655161i | ||||
\(626\) | −0.511238 | + | 0.885491i | −0.0204332 | + | 0.0353913i | ||||
\(627\) | −26.1199 | − | 50.5848i | −1.04313 | − | 2.02016i | ||||
\(628\) | 17.7636 | − | 10.2558i | 0.708847 | − | 0.409253i | ||||
\(629\) | 20.8881 | 0.832863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.16515 | −0.205621 | −0.102811 | − | 0.994701i | \(-0.532784\pi\) | ||||
−0.102811 | + | 0.994701i | \(0.532784\pi\) | |||||||
\(632\) | −2.00000 | − | 3.46410i | −0.0795557 | − | 0.137795i | ||||
\(633\) | −16.6352 | + | 28.8130i | −0.661189 | + | 1.14521i | ||||
\(634\) | −7.93725 | − | 4.58258i | −0.315229 | − | 0.181997i | ||||
\(635\) | 1.80341 | + | 3.12359i | 0.0715660 | + | 0.123956i | ||||
\(636\) | 7.48331i | 0.296733i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21.1652 | − | 13.5826i | −0.837936 | − | 0.537739i | ||||
\(639\) | 6.58258 | + | 11.4014i | 0.260403 | + | 0.451031i | ||||
\(640\) | 0.323042 | − | 0.559525i | 0.0127694 | − | 0.0221172i | ||||
\(641\) | −14.9564 | + | 25.9053i | −0.590744 | + | 1.02320i | 0.403389 | + | 0.915029i | \(0.367832\pi\) |
−0.994132 | + | 0.108170i | \(0.965501\pi\) | |||||||
\(642\) | 22.5658 | − | 13.0284i | 0.890602 | − | 0.514189i | ||||
\(643\) | − | 16.7700i | − | 0.661346i | −0.943745 | − | 0.330673i | \(-0.892724\pi\) | ||
0.943745 | − | 0.330673i | \(-0.107276\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 22.3303i | − | 0.879255i | ||||||
\(646\) | 17.9681 | − | 10.3739i | 0.706944 | − | 0.408154i | ||||
\(647\) | 38.7677 | + | 22.3825i | 1.52411 | + | 0.879948i | 0.999592 | + | 0.0285507i | \(0.00908921\pi\) |
0.524522 | + | 0.851397i | \(0.324244\pi\) | |||||||
\(648\) | −12.6289 | − | 7.29129i | −0.496109 | − | 0.286429i | ||||
\(649\) | −10.2555 | − | 0.481847i | −0.402565 | − | 0.0189142i | ||||
\(650\) | − | 14.1857i | − | 0.556409i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 3.00000 | + | 5.19615i | 0.117399 | + | 0.203341i | 0.918736 | − | 0.394872i | \(-0.129211\pi\) |
−0.801337 | + | 0.598213i | \(0.795878\pi\) | |||||||
\(654\) | 3.12359 | + | 1.80341i | 0.122142 | + | 0.0705188i | ||||
\(655\) | 5.27160 | + | 3.04356i | 0.205979 | + | 0.118922i | ||||
\(656\) | 2.51691 | + | 4.35942i | 0.0982689 | + | 0.170207i | ||||
\(657\) | −41.6413 | −1.62458 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.3303i | 1.18150i | 0.806854 | + | 0.590750i | \(0.201168\pi\) | ||||
−0.806854 | + | 0.590750i | \(0.798832\pi\) | |||||||
\(660\) | 0.311314 | − | 6.62594i | 0.0121179 | − | 0.257914i | ||||
\(661\) | −22.0063 | − | 12.7053i | −0.855945 | − | 0.494180i | 0.00670702 | − | 0.999978i | \(-0.497865\pi\) |
−0.862652 | + | 0.505797i | \(0.831198\pi\) | |||||||
\(662\) | −12.4859 | − | 7.20871i | −0.485277 | − | 0.280175i | ||||
\(663\) | −31.0511 | + | 17.9274i | −1.20592 | + | 0.696241i | ||||
\(664\) | − | 9.15188i | − | 0.355162i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 36.7477i | − | 1.42395i | ||||||
\(667\) | −26.2668 | + | 15.1652i | −1.01706 | + | 0.587197i | ||||
\(668\) | 3.09557 | − | 5.36169i | 0.119771 | − | 0.207450i | ||||
\(669\) | 9.79129 | − | 16.9590i | 0.378553 | − | 0.655673i | ||||
\(670\) | −0.511238 | − | 0.885491i | −0.0197509 | − | 0.0342095i | ||||
\(671\) | 25.9219 | + | 16.6352i | 1.00070 | + | 0.642194i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.3303i | 0.706581i | 0.935514 | + | 0.353291i | \(0.114937\pi\) | ||||
−0.935514 | + | 0.353291i | \(0.885063\pi\) | |||||||
\(674\) | −14.5826 | − | 25.2578i | −0.561700 | − | 0.972893i | ||||
\(675\) | 44.0126 | + | 25.4107i | 1.69404 | + | 0.978057i | ||||
\(676\) | −1.70871 | + | 2.95958i | −0.0657197 | + | 0.113830i | ||||
\(677\) | 15.7335 | + | 27.2512i | 0.604687 | + | 1.04735i | 0.992101 | + | 0.125443i | \(0.0400351\pi\) |
−0.387414 | + | 0.921906i | \(0.626632\pi\) | |||||||
\(678\) | −51.8438 | −1.99105 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.41742 | 0.0927040 | ||||||||
\(681\) | 31.4630 | − | 18.1652i | 1.20566 | − | 0.696090i | ||||
\(682\) | −3.41056 | + | 1.76108i | −0.130597 | + | 0.0674351i | ||||
\(683\) | −22.7477 | + | 39.4002i | −0.870418 | + | 1.50761i | −0.00885223 | + | 0.999961i | \(0.502818\pi\) |
−0.861565 | + | 0.507647i | \(0.830516\pi\) | |||||||
\(684\) | −18.2504 | − | 31.6106i | −0.697821 | − | 1.20866i | ||||
\(685\) | 9.79796i | 0.374361i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.3303 | 1.53870 | ||||||||
\(688\) | 9.66930 | − | 5.58258i | 0.368639 | − | 0.212834i | ||||
\(689\) | 3.74166 | − | 6.48074i | 0.142546 | − | 0.246897i | ||||
\(690\) | −6.92820 | − | 4.00000i | −0.263752 | − | 0.152277i | ||||
\(691\) | 32.6129 | − | 18.8291i | 1.24065 | − | 0.716291i | 0.271426 | − | 0.962459i | \(-0.412505\pi\) |
0.969227 | + | 0.246168i | \(0.0791716\pi\) | |||||||
\(692\) | −22.9612 | −0.872853 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.834849 | −0.0316904 | ||||||||
\(695\) | −1.80750 | + | 1.04356i | −0.0685624 | + | 0.0395845i | ||||
\(696\) | −20.3277 | − | 11.7362i | −0.770520 | − | 0.444860i | ||||
\(697\) | −9.41742 | + | 16.3115i | −0.356710 | + | 0.617841i | ||||
\(698\) | −1.79535 | + | 1.03655i | −0.0679552 | + | 0.0392339i | ||||
\(699\) | 27.3489 | 1.03443 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.3303i | − | 0.918943i | −0.888193 | − | 0.459471i | \(-0.848039\pi\) | ||
0.888193 | − | 0.459471i | \(-0.151961\pi\) | |||||||
\(702\) | 17.1652 | + | 29.7309i | 0.647857 | + | 1.12212i | ||||
\(703\) | 15.4779 | − | 26.8085i | 0.583759 | − | 1.01110i | ||||
\(704\) | 2.94694 | − | 1.52168i | 0.111067 | − | 0.0573506i | ||||
\(705\) | 8.71884 | − | 5.03383i | 0.328371 | − | 0.189585i | ||||
\(706\) | 7.48331 | 0.281638 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.58258 | −0.360135 | ||||||||
\(709\) | −7.83485 | − | 13.5704i | −0.294244 | − | 0.509645i | 0.680565 | − | 0.732688i | \(-0.261734\pi\) |
−0.974809 | + | 0.223042i | \(0.928401\pi\) | |||||||
\(710\) | −0.646084 | + | 1.11905i | −0.0242471 | + | 0.0419972i | ||||
\(711\) | −22.8027 | − | 13.1652i | −0.855168 | − | 0.493732i | ||||
\(712\) | −4.89898 | − | 8.48528i | −0.183597 | − | 0.317999i | ||||
\(713\) | 4.62929i | 0.173368i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.58258 | + | 5.58258i | −0.133981 | + | 0.208776i | ||||
\(716\) | −3.58258 | − | 6.20520i | −0.133887 | − | 0.231899i | ||||
\(717\) | −27.2141 | + | 47.1362i | −1.01633 | + | 1.76033i | ||||
\(718\) | 0.208712 | − | 0.361500i | 0.00778907 | − | 0.0134911i | ||||
\(719\) | 13.7302 | − | 7.92713i | 0.512050 | − | 0.295632i | −0.221626 | − | 0.975132i | \(-0.571136\pi\) |
0.733676 | + | 0.679500i | \(0.237803\pi\) | |||||||
\(720\) | − | 4.25290i | − | 0.158496i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 11.7477i | − | 0.437205i | ||||||
\(723\) | 69.4926 | − | 40.1216i | 2.58446 | − | 1.49214i | ||||
\(724\) | −14.4065 | − | 8.31759i | −0.535413 | − | 0.309121i | ||||
\(725\) | 30.0924 | + | 17.3739i | 1.11760 | + | 0.645249i | ||||
\(726\) | 19.7156 | − | 27.7630i | 0.731715 | − | 1.03038i | ||||
\(727\) | 52.2484i | 1.93778i | 0.247483 | + | 0.968892i | \(0.420396\pi\) | ||||
−0.247483 | + | 0.968892i | \(0.579604\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | −2.04356 | − | 3.53955i | −0.0756356 | − | 0.131005i | ||||
\(731\) | 36.1792 | + | 20.8881i | 1.33814 | + | 0.772574i | ||||
\(732\) | 24.8963 | + | 14.3739i | 0.920192 | + | 0.531273i | ||||
\(733\) | −11.4806 | − | 19.8850i | −0.424045 | − | 0.734468i | 0.572285 | − | 0.820055i | \(-0.306057\pi\) |
−0.996331 | + | 0.0855865i | \(0.972724\pi\) | |||||||
\(734\) | 1.42701 | 0.0526720 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 4.00000i | − | 0.147442i | ||||||
\(737\) | 0.246339 | − | 5.24303i | 0.00907400 | − | 0.193129i | ||||
\(738\) | 28.6962 | + | 16.5678i | 1.05632 | + | 0.609868i | ||||
\(739\) | 6.56670 | + | 3.79129i | 0.241560 | + | 0.139465i | 0.615894 | − | 0.787829i | \(-0.288795\pi\) |
−0.374333 | + | 0.927294i | \(0.622128\pi\) | |||||||
\(740\) | 3.12359 | − | 1.80341i | 0.114825 | − | 0.0662945i | ||||
\(741\) | 53.1360i | 1.95200i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 43.9129i | − | 1.61101i | −0.592591 | − | 0.805504i | \(-0.701895\pi\) | ||
0.592591 | − | 0.805504i | \(-0.298105\pi\) | |||||||
\(744\) | −3.10260 | + | 1.79129i | −0.113747 | + | 0.0656718i | ||||
\(745\) | −4.52259 | + | 7.83335i | −0.165695 | + | 0.286992i | ||||
\(746\) | −0.208712 | + | 0.361500i | −0.00764149 | + | 0.0132355i | ||||
\(747\) | −30.1215 | − | 52.1719i | −1.10209 | − | 1.90887i | ||||
\(748\) | 10.4440 | + | 6.70239i | 0.381872 | + | 0.245063i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19.1652i | 0.699812i | ||||||||
\(751\) | −6.74773 | − | 11.6874i | −0.246228 | − | 0.426480i | 0.716248 | − | 0.697846i | \(-0.245858\pi\) |
−0.962476 | + | 0.271366i | \(0.912525\pi\) | |||||||
\(752\) | 4.35942 | + | 2.51691i | 0.158972 | + | 0.0917824i | ||||
\(753\) | 3.20871 | − | 5.55765i | 0.116932 | − | 0.202532i | ||||
\(754\) | 11.7362 | + | 20.3277i | 0.427408 | + | 0.740292i | ||||
\(755\) | 2.31464 | 0.0842385 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.1652 | −1.78694 | −0.893469 | − | 0.449125i | \(-0.851736\pi\) | ||||
−0.893469 | + | 0.449125i | \(0.851736\pi\) | |||||||
\(758\) | −12.4104 | + | 7.16515i | −0.450766 | + | 0.260250i | ||||
\(759\) | −18.8419 | − | 36.4899i | −0.683918 | − | 1.32450i | ||||
\(760\) | 1.79129 | − | 3.10260i | 0.0649768 | − | 0.112543i | ||||
\(761\) | 10.3766 | + | 17.9728i | 0.376152 | + | 0.651515i | 0.990499 | − | 0.137522i | \(-0.0439137\pi\) |
−0.614347 | + | 0.789036i | \(0.710580\pi\) | |||||||
\(762\) | 17.2813i | 0.626034i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 13.7810 | − | 7.95644i | 0.498252 | − | 0.287666i | ||||
\(766\) | 2.38207 | − | 4.12586i | 0.0860676 | − | 0.149073i | ||||
\(767\) | 8.29875 | + | 4.79129i | 0.299651 | + | 0.173003i | ||||
\(768\) | 2.68085 | − | 1.54779i | 0.0967367 | − | 0.0558509i | ||||
\(769\) | −29.7984 | −1.07456 | −0.537279 | − | 0.843404i | \(-0.680548\pi\) | ||||
−0.537279 | + | 0.843404i | \(0.680548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.1652 | −0.546160 | ||||||||
\(772\) | 17.6066 | − | 10.1652i | 0.633674 | − | 0.365852i | ||||
\(773\) | 44.3385 | + | 25.5989i | 1.59475 | + | 0.920727i | 0.992477 | + | 0.122435i | \(0.0390702\pi\) |
0.602270 | + | 0.798293i | \(0.294263\pi\) | |||||||
\(774\) | 36.7477 | − | 63.6489i | 1.32087 | − | 2.28781i | ||||
\(775\) | 4.59298 | − | 2.65176i | 0.164985 | − | 0.0952540i | ||||
\(776\) | −15.9891 | −0.573975 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 10.0000i | − | 0.358517i | ||||||
\(779\) | 13.9564 | + | 24.1733i | 0.500041 | + | 0.866097i | ||||
\(780\) | −3.09557 | + | 5.36169i | −0.110839 | + | 0.191979i | ||||
\(781\) | −5.89389 | + | 3.04336i | −0.210900 | + | 0.108900i | ||||
\(782\) | 12.9615 | − | 7.48331i | 0.463502 | − | 0.267603i | ||||
\(783\) | −84.0917 | −3.00519 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.2523 | 0.472994 | ||||||||
\(786\) | 14.5826 | + | 25.2578i | 0.520143 | + | 0.900915i | ||||
\(787\) | −20.1887 | + | 34.9678i | −0.719648 | + | 1.24647i | 0.241492 | + | 0.970403i | \(0.422363\pi\) |
−0.961139 | + | 0.276063i | \(0.910970\pi\) | |||||||
\(788\) | −16.2360 | − | 9.37386i | −0.578384 | − | 0.333930i | ||||
\(789\) | 43.8493 | + | 75.9492i | 1.56108 | + | 2.70386i | ||||
\(790\) | − | 2.58434i | − | 0.0919465i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 11.7913 | − | 18.3739i | 0.418985 | − | 0.652887i | ||||
\(793\) | −14.3739 | − | 24.8963i | −0.510431 | − | 0.884092i | ||||
\(794\) | −11.9244 | + | 20.6537i | −0.423181 | + | 0.732972i | ||||
\(795\) | −2.41742 | + | 4.18710i | −0.0857372 | + | 0.148501i | ||||
\(796\) | −21.3300 | + | 12.3149i | −0.756021 | + | 0.436489i | ||||
\(797\) | − | 36.2311i | − | 1.28337i | −0.766968 | − | 0.641686i | \(-0.778235\pi\) | ||
0.766968 | − | 0.641686i | \(-0.221765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.8348i | 0.666329i | ||||||||
\(800\) | −3.96863 | + | 2.29129i | −0.140312 | + | 0.0810093i | ||||
\(801\) | −55.8550 | − | 32.2479i | −1.97354 | − | 1.13942i | ||||
\(802\) | −1.37055 | − | 0.791288i | −0.0483958 | − | 0.0279413i | ||||
\(803\) | 0.984684 | − | 20.9578i | 0.0347487 | − | 0.739586i | ||||
\(804\) | − | 4.89898i | − | 0.172774i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.58258 | 0.126191 | ||||||||
\(807\) | 31.3303 | + | 54.2657i | 1.10288 | + | 1.91024i | ||||
\(808\) | −0.442745 | − | 0.255619i | −0.0155757 | − | 0.00899265i | ||||
\(809\) | −28.7219 | − | 16.5826i | −1.00981 | − | 0.583012i | −0.0986718 | − | 0.995120i | \(-0.531459\pi\) |
−0.911135 | + | 0.412108i | \(0.864793\pi\) | |||||||
\(810\) | −4.71078 | − | 8.15932i | −0.165520 | − | 0.286689i | ||||
\(811\) | 30.3097 | 1.06432 | 0.532158 | − | 0.846645i | \(-0.321381\pi\) | ||||
0.532158 | + | 0.846645i | \(0.321381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.1652i | 0.531865i | ||||||||
\(814\) | 18.4949 | + | 0.868966i | 0.648246 | + | 0.0304572i | ||||
\(815\) | −2.23810 | − | 1.29217i | −0.0783972 | − | 0.0452627i | ||||
\(816\) | 10.0308 | + | 5.79129i | 0.351148 | + | 0.202736i | ||||
\(817\) | 53.6169 | − | 30.9557i | 1.87582 | − | 1.08300i | ||||
\(818\) | 9.93280i | 0.347292i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.25227i | 0.113574i | ||||||||
\(821\) | 9.95536 | − | 5.74773i | 0.347444 | − | 0.200597i | −0.316115 | − | 0.948721i | \(-0.602378\pi\) |
0.663559 | + | 0.748124i | \(0.269045\pi\) | |||||||
\(822\) | −23.4724 | + | 40.6554i | −0.818695 | + | 1.41802i | ||||
\(823\) | 20.1652 | − | 34.9271i | 0.702913 | − | 1.21748i | −0.264526 | − | 0.964378i | \(-0.585216\pi\) |
0.967439 | − | 0.253103i | \(-0.0814510\pi\) | |||||||
\(824\) | −6.76981 | − | 11.7257i | −0.235837 | − | 0.408482i | ||||
\(825\) | −25.4107 | + | 39.5964i | −0.884686 | + | 1.37857i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.1652i | − | 0.527344i | −0.964612 | − | 0.263672i | \(-0.915066\pi\) | ||
0.964612 | − | 0.263672i | \(-0.0849337\pi\) | |||||||
\(828\) | −13.1652 | − | 22.8027i | −0.457521 | − | 0.792449i | ||||
\(829\) | 3.68312 | + | 2.12645i | 0.127920 | + | 0.0738546i | 0.562594 | − | 0.826733i | \(-0.309803\pi\) |
−0.434675 | + | 0.900588i | \(0.643137\pi\) | |||||||
\(830\) | 2.95644 | − | 5.12070i | 0.102620 | − | 0.177742i | ||||
\(831\) | 3.09557 | + | 5.36169i | 0.107384 | + | 0.185995i | ||||
\(832\) | −3.09557 | −0.107320 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.0000 | −0.346272 | ||||||||
\(835\) | 3.46410 | − | 2.00000i | 0.119880 | − | 0.0692129i | ||||
\(836\) | 16.3410 | − | 8.43782i | 0.565165 | − | 0.291828i | ||||
\(837\) | −6.41742 | + | 11.1153i | −0.221819 | + | 0.384201i | ||||
\(838\) | −2.83995 | − | 4.91895i | −0.0981046 | − | 0.169922i | ||||
\(839\) | 24.6297i | 0.850313i | 0.905120 | + | 0.425157i | \(0.139781\pi\) | ||||
−0.905120 | + | 0.425157i | \(0.860219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4955 | −0.982602 | ||||||||
\(842\) | 1.37055 | − | 0.791288i | 0.0472323 | − | 0.0272696i | ||||
\(843\) | −11.0901 | + | 19.2087i | −0.381964 | + | 0.661581i | ||||
\(844\) | −9.30780 | − | 5.37386i | −0.320388 | − | 0.184976i | ||||
\(845\) | −1.91213 | + | 1.10397i | −0.0657794 | + | 0.0379778i | ||||
\(846\) | 33.1355 | 1.13922 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.41742 | −0.0830147 | ||||||||
\(849\) | −41.8553 | + | 24.1652i | −1.43647 | + | 0.829346i | ||||
\(850\) | −14.8492 | − | 8.57321i | −0.509325 | − | 0.294059i | ||||
\(851\) | 11.1652 | − | 19.3386i | 0.382736 | − | 0.662919i | ||||
\(852\) | −5.36169 | + | 3.09557i | −0.183688 | + | 0.106053i | ||||
\(853\) | −30.1748 | −1.03317 | −0.516583 | − | 0.856237i | \(-0.672796\pi\) | ||||
−0.516583 | + | 0.856237i | \(0.672796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 23.5826i | − | 0.806507i | ||||||
\(856\) | 4.20871 | + | 7.28970i | 0.143851 | + | 0.249157i | ||||
\(857\) | 10.6463 | − | 18.4400i | 0.363671 | − | 0.629897i | −0.624891 | − | 0.780712i | \(-0.714857\pi\) |
0.988562 | + | 0.150815i | \(0.0481899\pi\) | |||||||
\(858\) | −28.2393 | + | 14.5816i | −0.964075 | + | 0.497809i | ||||
\(859\) | −27.4848 | + | 15.8683i | −0.937768 | + | 0.541421i | −0.889260 | − | 0.457402i | \(-0.848780\pi\) |
−0.0485080 | + | 0.998823i | \(0.515447\pi\) | |||||||
\(860\) | 7.21362 | 0.245983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.9129 | 0.610115 | ||||||||
\(863\) | 16.5826 | + | 28.7219i | 0.564477 | + | 0.977704i | 0.997098 | + | 0.0761276i | \(0.0242556\pi\) |
−0.432621 | + | 0.901576i | \(0.642411\pi\) | |||||||
\(864\) | 5.54506 | − | 9.60433i | 0.188647 | − | 0.326746i | ||||
\(865\) | −12.8474 | − | 7.41742i | −0.436823 | − | 0.252200i | ||||
\(866\) | 14.0509 | + | 24.3368i | 0.477467 | + | 0.826998i | ||||
\(867\) | − | 9.28672i | − | 0.315394i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.16515 | − | 11.1652i | 0.243061 | − | 0.378752i | ||||
\(870\) | −7.58258 | − | 13.1334i | −0.257073 | − | 0.445264i | ||||
\(871\) | −2.44949 | + | 4.24264i | −0.0829978 | + | 0.143756i | ||||
\(872\) | −0.582576 | + | 1.00905i | −0.0197285 | + | 0.0341708i | ||||
\(873\) | −91.1487 | + | 52.6248i | −3.08492 | + | 1.78108i | ||||
\(874\) | − | 22.1803i | − | 0.750258i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 19.5826i | − | 0.661634i | ||||||
\(877\) | −21.7937 | + | 12.5826i | −0.735920 | + | 0.424883i | −0.820584 | − | 0.571526i | \(-0.806352\pi\) |
0.0846642 | + | 0.996410i | \(0.473018\pi\) | |||||||
\(878\) | −2.00454 | − | 1.15732i | −0.0676500 | − | 0.0390577i | ||||
\(879\) | 57.3683 | + | 33.1216i | 1.93498 | + | 1.11716i | ||||
\(880\) | 2.14046 | + | 0.100567i | 0.0721548 | + | 0.00339013i | ||||
\(881\) | − | 22.1803i | − | 0.747272i | −0.927575 | − | 0.373636i | \(-0.878111\pi\) | ||
0.927575 | − | 0.373636i | \(-0.121889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1652 | 1.04879 | 0.524395 | − | 0.851475i | \(-0.324291\pi\) | ||||
0.524395 | + | 0.851475i | \(0.324291\pi\) | |||||||
\(884\) | −5.79129 | − | 10.0308i | −0.194782 | − | 0.337372i | ||||
\(885\) | −5.36169 | − | 3.09557i | −0.180231 | − | 0.104057i | ||||
\(886\) | −2.74110 | − | 1.58258i | −0.0920891 | − | 0.0531677i | ||||
\(887\) | 14.4554 | + | 25.0375i | 0.485365 | + | 0.840676i | 0.999859 | − | 0.0168179i | \(-0.00535356\pi\) |
−0.514494 | + | 0.857494i | \(0.672020\pi\) | |||||||
\(888\) | 17.2813 | 0.579922 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 6.33030i | − | 0.212192i | ||||||
\(891\) | 2.26988 | − | 48.3116i | 0.0760438 | − | 1.61850i | ||||
\(892\) | 5.47847 | + | 3.16300i | 0.183433 | + | 0.105905i | ||||
\(893\) | 24.1733 | + | 13.9564i | 0.808927 | + | 0.467034i | ||||
\(894\) | −37.5318 | + | 21.6690i | −1.25525 | + | 0.724720i | ||||
\(895\) | − | 4.62929i | − | 0.154740i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.3303i | 1.27981i | ||||||||
\(898\) | −11.1153 | + | 6.41742i | −0.370923 | + | 0.214152i | ||||
\(899\) | −4.38774 | + | 7.59979i | −0.146339 | + | 0.253467i | ||||
\(900\) | −15.0826 | + | 26.1238i | −0.502753 | + | 0.870793i | ||||
\(901\) | −4.52259 | − | 7.83335i | −0.150669 | − | 0.260967i | ||||
\(902\) | −9.01703 | + | 14.0509i | −0.300234 | + | 0.467842i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.7477i | − | 0.557021i | ||||||
\(905\) | −5.37386 | − | 9.30780i | −0.178633 | − | 0.309402i | ||||
\(906\) | 9.60433 | + | 5.54506i | 0.319083 | + | 0.184222i | ||||
\(907\) | 19.9564 | − | 34.5656i | 0.662643 | − | 1.14773i | −0.317276 | − | 0.948333i | \(-0.602768\pi\) |
0.979919 | − | 0.199398i | \(-0.0638985\pi\) | |||||||
\(908\) | 5.86811 | + | 10.1639i | 0.194740 | + | 0.337299i | ||||
\(909\) | −3.36526 | −0.111619 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.1652 | −0.502444 | −0.251222 | − | 0.967930i | \(-0.580832\pi\) | ||||
−0.251222 | + | 0.967930i | \(0.580832\pi\) | |||||||
\(912\) | 14.8655 | − | 8.58258i | 0.492244 | − | 0.284197i | ||||
\(913\) | 26.9701 | − | 13.9262i | 0.892579 | − | 0.460891i | ||||
\(914\) | −7.41742 | + | 12.8474i | −0.245347 | + | 0.424953i | ||||
\(915\) | 9.28672 | + | 16.0851i | 0.307010 | + | 0.531756i | ||||
\(916\) | 13.0284i | 0.430470i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 41.4955 | 1.36955 | ||||||||
\(919\) | −30.7400 | + | 17.7477i | −1.01402 | + | 0.585443i | −0.912366 | − | 0.409376i | \(-0.865746\pi\) |
−0.101652 | + | 0.994820i | \(0.532413\pi\) | |||||||
\(920\) | 1.29217 | − | 2.23810i | 0.0426015 | − | 0.0737880i | ||||
\(921\) | 21.7937 | + | 12.5826i | 0.718126 | + | 0.414610i | ||||
\(922\) | 22.7750 | − | 13.1492i | 0.750055 | − | 0.433044i | ||||
\(923\) | 6.19115 | 0.203784 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.5826 | −0.841150 | ||||||||
\(926\) | 11.4014 | − | 6.58258i | 0.374672 | − | 0.216317i | ||||
\(927\) | −77.1850 | − | 44.5628i | −2.53509 | − | 1.46363i | ||||
\(928\) | 3.79129 | − | 6.56670i | 0.124455 | − | 0.215563i | ||||
\(929\) | 33.5228 | − | 19.3544i | 1.09985 | − | 0.634996i | 0.163665 | − | 0.986516i | \(-0.447668\pi\) |
0.936181 | + | 0.351520i | \(0.114335\pi\) | |||||||
\(930\) | −2.31464 | −0.0759002 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.83485i | 0.289395i | ||||||||
\(933\) | 15.3739 | + | 26.6283i | 0.503318 | + | 0.871772i | ||||
\(934\) | −0.255619 | + | 0.442745i | −0.00836411 | + | 0.0144871i | ||||
\(935\) | 3.67855 | + | 7.12402i | 0.120302 | + | 0.232980i | ||||
\(936\) | −17.6469 | + | 10.1884i | −0.576806 | + | 0.333019i | ||||
\(937\) | 44.7650 | 1.46241 | 0.731205 | − | 0.682158i | \(-0.238958\pi\) | ||||
0.731205 | + | 0.682158i | \(0.238958\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.16515 | −0.103291 | ||||||||
\(940\) | 1.62614 | + | 2.81655i | 0.0530387 | + | 0.0918658i | ||||
\(941\) | −15.7335 | + | 27.2512i | −0.512897 | + | 0.888364i | 0.486991 | + | 0.873407i | \(0.338094\pi\) |
−0.999888 | + | 0.0149568i | \(0.995239\pi\) | |||||||
\(942\) | 54.9887 | + | 31.7477i | 1.79163 | + | 1.03440i | ||||
\(943\) | 10.0677 | + | 17.4377i | 0.327848 | + | 0.567849i | ||||
\(944\) | − | 3.09557i | − | 0.100752i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.1652 | + | 20.0000i | 1.01327 | + | 0.650256i | ||||
\(947\) | 2.79129 | + | 4.83465i | 0.0907047 | + | 0.157105i | 0.907808 | − | 0.419386i | \(-0.137755\pi\) |
−0.817103 | + | 0.576491i | \(0.804421\pi\) | |||||||
\(948\) | 6.19115 | − | 10.7234i | 0.201079 | − | 0.348279i | ||||
\(949\) | −9.79129 | + | 16.9590i | −0.317839 | + | 0.550513i | ||||
\(950\) | −22.0063 | + | 12.7053i | −0.713978 | + | 0.412216i | ||||
\(951\) | − | 28.3714i | − | 0.920006i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.3303i | 0.593777i | 0.954912 | + | 0.296888i | \(0.0959489\pi\) | ||||
−0.954912 | + | 0.296888i | \(0.904051\pi\) | |||||||
\(954\) | −13.7810 | + | 7.95644i | −0.446175 | + | 0.257599i | ||||
\(955\) | 10.0715 | + | 5.81475i | 0.325904 | + | 0.188161i | ||||
\(956\) | −15.2270 | − | 8.79129i | −0.492475 | − | 0.284331i | ||||
\(957\) | 3.65364 | − | 77.7634i | 0.118106 | − | 2.51373i | ||||
\(958\) | − | 6.46084i | − | 0.208740i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | −14.8303 | − | 25.6868i | −0.478397 | − | 0.828608i | ||||
\(962\) | −14.9660 | − | 8.64064i | −0.482524 | − | 0.278585i | ||||
\(963\) | 47.9850 | + | 27.7042i | 1.54630 | + | 0.892754i | ||||
\(964\) | 12.9610 | + | 22.4490i | 0.417444 | + | 0.723035i | ||||
\(965\) | 13.1351 | 0.422833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.5826i | − | 1.01563i | −0.861467 | − | 0.507814i | \(-0.830454\pi\) | ||
0.861467 | − | 0.507814i | \(-0.169546\pi\) | |||||||
\(968\) | 8.96863 | + | 6.36897i | 0.288263 | + | 0.204706i | ||||
\(969\) | 55.6214 | + | 32.1131i | 1.78682 | + | 1.03162i | ||||
\(970\) | −8.94630 | − | 5.16515i | −0.287249 | − | 0.165843i | ||||
\(971\) | −15.4088 | + | 8.89626i | −0.494491 | + | 0.285494i | −0.726436 | − | 0.687235i | \(-0.758824\pi\) |
0.231945 | + | 0.972729i | \(0.425491\pi\) | |||||||
\(972\) | − | 11.8711i | − | 0.380764i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 33.4955i | 1.07326i | ||||||||
\(975\) | 38.0297 | − | 21.9564i | 1.21792 | − | 0.703169i | ||||
\(976\) | −4.64336 | + | 8.04254i | −0.148630 | + | 0.257435i | ||||
\(977\) | 4.58258 | − | 7.93725i | 0.146610 | − | 0.253935i | −0.783363 | − | 0.621565i | \(-0.786497\pi\) |
0.929972 | + | 0.367630i | \(0.119831\pi\) | |||||||
\(978\) | −6.19115 | − | 10.7234i | −0.197971 | − | 0.342896i | ||||
\(979\) | 17.5510 | − | 27.3489i | 0.560931 | − | 0.874075i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.66970i | 0.244875i | ||||||||
\(982\) | 10.7477 | + | 18.6156i | 0.342974 | + | 0.594048i | ||||
\(983\) | −1.46939 | − | 0.848352i | −0.0468662 | − | 0.0270582i | 0.476384 | − | 0.879237i | \(-0.341947\pi\) |
−0.523250 | + | 0.852179i | \(0.675281\pi\) | |||||||
\(984\) | −7.79129 | + | 13.4949i | −0.248377 | + | 0.430202i | ||||
\(985\) | −6.05630 | − | 10.4898i | −0.192970 | − | 0.334234i | ||||
\(986\) | 28.3714 | 0.903529 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.1652 | −0.546096 | ||||||||
\(989\) | 38.6772 | − | 22.3303i | 1.22986 | − | 0.710062i | ||||
\(990\) | 12.5330 | − | 6.47156i | 0.398326 | − | 0.205680i | ||||
\(991\) | 13.3303 | − | 23.0888i | 0.423451 | − | 0.733439i | −0.572823 | − | 0.819679i | \(-0.694152\pi\) |
0.996274 | + | 0.0862402i | \(0.0274852\pi\) | |||||||
\(992\) | −0.578661 | − | 1.00227i | −0.0183725 | − | 0.0318221i | ||||
\(993\) | − | 44.6302i | − | 1.41630i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.9129 | −0.504472 | ||||||||
\(996\) | 24.5348 | − | 14.1652i | 0.777414 | − | 0.448840i | ||||
\(997\) | 16.8908 | − | 29.2557i | 0.534937 | − | 0.926539i | −0.464229 | − | 0.885715i | \(-0.653669\pi\) |
0.999166 | − | 0.0408234i | \(-0.0129981\pi\) | |||||||
\(998\) | 24.1733 | + | 13.9564i | 0.765191 | + | 0.441783i | ||||
\(999\) | 53.6169 | − | 30.9557i | 1.69636 | − | 0.979396i |
(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 | 1078.2.i.b.1011.1 | 16 | ||
7.2 | even | 3 | inner | 1078.2.i.b.901.8 | 16 | ||
7.3 | odd | 6 | 154.2.c.a.153.1 | ✓ | 8 | ||
7.4 | even | 3 | 154.2.c.a.153.4 | yes | 8 | ||
7.5 | odd | 6 | inner | 1078.2.i.b.901.5 | 16 | ||
7.6 | odd | 2 | inner | 1078.2.i.b.1011.4 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.b.1011.5 | 16 | ||
21.11 | odd | 6 | 1386.2.e.b.307.6 | 8 | |||
21.17 | even | 6 | 1386.2.e.b.307.7 | 8 | |||
28.3 | even | 6 | 1232.2.e.e.769.7 | 8 | |||
28.11 | odd | 6 | 1232.2.e.e.769.2 | 8 | |||
77.10 | even | 6 | 154.2.c.a.153.5 | yes | 8 | ||
77.32 | odd | 6 | 154.2.c.a.153.8 | yes | 8 | ||
77.54 | even | 6 | inner | 1078.2.i.b.901.1 | 16 | ||
77.65 | odd | 6 | inner | 1078.2.i.b.901.4 | 16 | ||
77.76 | even | 2 | inner | 1078.2.i.b.1011.8 | 16 | ||
231.32 | even | 6 | 1386.2.e.b.307.2 | 8 | |||
231.164 | odd | 6 | 1386.2.e.b.307.3 | 8 | |||
308.87 | odd | 6 | 1232.2.e.e.769.8 | 8 | |||
308.263 | even | 6 | 1232.2.e.e.769.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.c.a.153.1 | ✓ | 8 | 7.3 | odd | 6 | ||
154.2.c.a.153.4 | yes | 8 | 7.4 | even | 3 | ||
154.2.c.a.153.5 | yes | 8 | 77.10 | even | 6 | ||
154.2.c.a.153.8 | yes | 8 | 77.32 | odd | 6 | ||
1078.2.i.b.901.1 | 16 | 77.54 | even | 6 | inner | ||
1078.2.i.b.901.4 | 16 | 77.65 | odd | 6 | inner | ||
1078.2.i.b.901.5 | 16 | 7.5 | odd | 6 | inner | ||
1078.2.i.b.901.8 | 16 | 7.2 | even | 3 | inner | ||
1078.2.i.b.1011.1 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.i.b.1011.4 | 16 | 7.6 | odd | 2 | inner | ||
1078.2.i.b.1011.5 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.b.1011.8 | 16 | 77.76 | even | 2 | inner | ||
1232.2.e.e.769.1 | 8 | 308.263 | even | 6 | |||
1232.2.e.e.769.2 | 8 | 28.11 | odd | 6 | |||
1232.2.e.e.769.7 | 8 | 28.3 | even | 6 | |||
1232.2.e.e.769.8 | 8 | 308.87 | odd | 6 | |||
1386.2.e.b.307.2 | 8 | 231.32 | even | 6 | |||
1386.2.e.b.307.3 | 8 | 231.164 | odd | 6 | |||
1386.2.e.b.307.6 | 8 | 21.11 | odd | 6 | |||
1386.2.e.b.307.7 | 8 | 21.17 | even | 6 |