Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 501.3 | ||
Root | \(0.354609 + 0.614201i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.501 |
Dual form | 1900.2.i.d.201.3 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.354609 | + | 0.614201i | 0.204734 | + | 0.354609i | 0.950048 | − | 0.312104i | \(-0.101034\pi\) |
−0.745314 | + | 0.666713i | \(0.767701\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.11079 | −1.17577 | −0.587884 | − | 0.808945i | \(-0.700039\pi\) | ||||
−0.587884 | + | 0.808945i | \(0.700039\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.24850 | − | 2.16247i | 0.416168 | − | 0.720825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.52922 | −1.06410 | −0.532051 | − | 0.846713i | \(-0.678578\pi\) | ||||
−0.532051 | + | 0.846713i | \(0.678578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.200785 | − | 0.347770i | 0.0556877 | − | 0.0964540i | −0.836838 | − | 0.547451i | \(-0.815598\pi\) |
0.892525 | + | 0.450997i | \(0.148932\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.74850 | + | 3.02850i | 0.424075 | + | 0.734519i | 0.996334 | − | 0.0855542i | \(-0.0272661\pi\) |
−0.572259 | + | 0.820073i | \(0.693933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35162 | − | 0.251824i | 0.998330 | − | 0.0577725i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.10311 | − | 1.91065i | −0.240719 | − | 0.416938i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.65851 | + | 6.33672i | −0.762852 | + | 1.32130i | 0.178523 | + | 0.983936i | \(0.442868\pi\) |
−0.941375 | + | 0.337362i | \(0.890465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.89858 | 0.750282 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.96540 | − | 6.86827i | 0.736356 | − | 1.27541i | −0.217770 | − | 0.976000i | \(-0.569878\pi\) |
0.954126 | − | 0.299406i | \(-0.0967884\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.73545 | 1.03012 | 0.515059 | − | 0.857155i | \(-0.327770\pi\) | ||||
0.515059 | + | 0.857155i | \(0.327770\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.25150 | − | 2.16765i | −0.217857 | − | 0.377340i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.5292 | 1.73099 | 0.865497 | − | 0.500914i | \(-0.167003\pi\) | ||||
0.865497 | + | 0.500914i | \(0.167003\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.284801 | 0.0456046 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.555394 | + | 0.961971i | 0.0867380 | + | 0.150235i | 0.906130 | − | 0.422998i | \(-0.139022\pi\) |
−0.819392 | + | 0.573233i | \(0.805689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.30390 | − | 7.45457i | −0.656338 | − | 1.13681i | −0.981556 | − | 0.191172i | \(-0.938771\pi\) |
0.325218 | − | 0.945639i | \(-0.394562\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.76162 | − | 6.51532i | 0.548689 | − | 0.950357i | −0.449676 | − | 0.893192i | \(-0.648460\pi\) |
0.998365 | − | 0.0571653i | \(-0.0182062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.67700 | 0.382429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.24007 | + | 2.14787i | −0.173645 | + | 0.300762i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.27773 | − | 9.14130i | 0.724952 | − | 1.25565i | −0.234042 | − | 0.972227i | \(-0.575195\pi\) |
0.958994 | − | 0.283427i | \(-0.0914714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.69779 | + | 2.58347i | 0.224878 | + | 0.342189i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.25618 | + | 7.37192i | 0.554107 | + | 0.959742i | 0.997972 | + | 0.0636484i | \(0.0202736\pi\) |
−0.443865 | + | 0.896094i | \(0.646393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.61079 | − | 7.98612i | 0.590351 | − | 1.02252i | −0.403834 | − | 0.914832i | \(-0.632323\pi\) |
0.994185 | − | 0.107686i | \(-0.0343440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.88383 | + | 6.72700i | −0.489317 | + | 0.847522i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.20623 | − | 7.28540i | 0.513873 | − | 0.890053i | −0.485998 | − | 0.873960i | \(-0.661544\pi\) |
0.999870 | − | 0.0160934i | \(-0.00512290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.18936 | −0.624726 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.31233 | + | 7.46918i | 0.511780 | + | 0.886428i | 0.999907 | + | 0.0136558i | \(0.00434692\pi\) |
−0.488127 | + | 0.872773i | \(0.662320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.870717 | + | 1.50813i | 0.101910 | + | 0.176513i | 0.912471 | − | 0.409140i | \(-0.134171\pi\) |
−0.810562 | + | 0.585653i | \(0.800838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.9787 | 1.25114 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.50544 | + | 7.80366i | 0.506902 | + | 0.877980i | 0.999968 | + | 0.00798806i | \(0.00254271\pi\) |
−0.493066 | + | 0.869992i | \(0.664124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.36304 | − | 4.09291i | −0.262560 | − | 0.454768i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.07857 | −0.447682 | −0.223841 | − | 0.974626i | \(-0.571860\pi\) | ||||
−0.223841 | + | 0.974626i | \(0.571860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.62466 | 0.603027 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.61623 | − | 11.4596i | 0.701319 | − | 1.21472i | −0.266685 | − | 0.963784i | \(-0.585928\pi\) |
0.968004 | − | 0.250936i | \(-0.0807385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.624599 | + | 1.08184i | −0.0654758 | + | 0.113407i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.03384 | + | 3.52272i | 0.210900 | + | 0.365289i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.85162 | − | 6.67120i | −0.391073 | − | 0.677358i | 0.601519 | − | 0.798859i | \(-0.294563\pi\) |
−0.992591 | + | 0.121501i | \(0.961229\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.40625 | + | 7.63186i | −0.442845 | + | 0.767030i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.68773 | + | 15.0476i | −0.864462 | + | 1.49729i | 0.00311897 | + | 0.999995i | \(0.499007\pi\) |
−0.867581 | + | 0.497296i | \(0.834326\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.12614 | 0.702159 | 0.351080 | − | 0.936346i | \(-0.385815\pi\) | ||||
0.351080 | + | 0.936346i | \(0.385815\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.735452 | −0.0710989 | −0.0355494 | − | 0.999368i | \(-0.511318\pi\) | ||||
−0.0355494 | + | 0.999368i | \(0.511318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00468 | + | 13.8645i | 0.766710 | + | 1.32798i | 0.939338 | + | 0.342993i | \(0.111441\pi\) |
−0.172628 | + | 0.984987i | \(0.555226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.73376 | + | 6.46706i | 0.354393 | + | 0.613826i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.34923 | −0.409141 | −0.204571 | − | 0.978852i | \(-0.565580\pi\) | ||||
−0.204571 | + | 0.978852i | \(0.565580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.501362 | − | 0.868384i | −0.0463509 | − | 0.0802822i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.43923 | − | 9.42102i | −0.498613 | − | 0.863623i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.45543 | 0.132312 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.393896 | + | 0.682247i | −0.0355164 | + | 0.0615162i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.32300 | + | 4.02355i | −0.206133 | + | 0.357032i | −0.950493 | − | 0.310746i | \(-0.899421\pi\) |
0.744360 | + | 0.667778i | \(0.232755\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.05240 | − | 5.28692i | 0.268749 | − | 0.465487i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.24775 | − | 9.08936i | −0.458498 | − | 0.794141i | 0.540384 | − | 0.841418i | \(-0.318279\pi\) |
−0.998882 | + | 0.0472772i | \(0.984946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5370 | + | 0.783372i | −1.17380 | + | 0.0679270i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.696101 | + | 1.20568i | −0.0594719 | + | 0.103008i | −0.894228 | − | 0.447611i | \(-0.852275\pi\) |
0.834757 | + | 0.550619i | \(0.185608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.03766 | − | 5.26138i | 0.257651 | − | 0.446264i | −0.707961 | − | 0.706251i | \(-0.750385\pi\) |
0.965612 | + | 0.259987i | \(0.0837183\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.33562 | 0.449340 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.708615 | + | 1.22736i | −0.0592574 | + | 0.102637i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.949290 | + | 1.64422i | 0.0782961 | + | 0.135613i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0422770 | + | 0.0732259i | 0.00346347 | + | 0.00599890i | 0.867752 | − | 0.496998i | \(-0.165564\pi\) |
−0.864288 | + | 0.502996i | \(0.832231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2216 | −1.23871 | −0.619357 | − | 0.785109i | \(-0.712607\pi\) | ||||
−0.619357 | + | 0.785109i | \(0.712607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.73207 | 0.705946 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.12935 | + | 14.0804i | 0.648793 | + | 1.12374i | 0.983412 | + | 0.181388i | \(0.0580591\pi\) |
−0.334619 | + | 0.942354i | \(0.608608\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.48612 | 0.593688 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3808 | − | 19.7122i | 0.896936 | − | 1.55354i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9461 | −1.17067 | −0.585336 | − | 0.810791i | \(-0.699037\pi\) | ||||
−0.585336 | + | 0.810791i | \(0.699037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.26461 | − | 10.8506i | 0.484770 | − | 0.839647i | −0.515077 | − | 0.857144i | \(-0.672237\pi\) |
0.999847 | + | 0.0174974i | \(0.00556988\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.41937 | + | 11.1187i | 0.493798 | + | 0.855283i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.88845 | − | 9.72466i | 0.373829 | − | 0.743664i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.69242 | + | 15.0557i | 0.660872 | + | 1.14466i | 0.980387 | + | 0.197083i | \(0.0631468\pi\) |
−0.319515 | + | 0.947581i | \(0.603520\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.01856 | + | 5.22830i | −0.226889 | + | 0.392983i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.7830 | 1.55340 | 0.776698 | − | 0.629873i | \(-0.216893\pi\) | ||||
0.776698 | + | 0.629873i | \(0.216893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.814564 | + | 1.41087i | −0.0605460 | + | 0.104869i | −0.894710 | − | 0.446648i | \(-0.852618\pi\) |
0.834164 | + | 0.551517i | \(0.185951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.54011 | 0.483459 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.17087 | − | 10.6883i | −0.451258 | − | 0.781603i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.1277 | −0.882157 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.4016 | −0.969704 | −0.484852 | − | 0.874596i | \(-0.661126\pi\) | ||||
−0.484852 | + | 0.874596i | \(0.661126\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.34693 | − | 9.26116i | −0.384881 | − | 0.666633i | 0.606872 | − | 0.794800i | \(-0.292424\pi\) |
−0.991753 | + | 0.128167i | \(0.959091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.00611 | 0.499165 | 0.249582 | − | 0.968354i | \(-0.419707\pi\) | ||||
0.249582 | + | 0.968354i | \(0.419707\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3909 | − | 17.9976i | 0.736592 | − | 1.27581i | −0.217430 | − | 0.976076i | \(-0.569767\pi\) |
0.954021 | − | 0.299738i | \(-0.0968994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.96627 | 0.420828 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.3355 | + | 21.3657i | −0.865783 | + | 1.49958i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.13533 | + | 15.8229i | 0.634949 | + | 1.09976i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.3578 | + | 0.888745i | −1.06232 | + | 0.0614758i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.61623 | + | 9.72760i | 0.386637 | + | 0.669675i | 0.991995 | − | 0.126278i | \(-0.0403032\pi\) |
−0.605358 | + | 0.795954i | \(0.706970\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.05838 | + | 5.29728i | −0.209557 | + | 0.362963i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.8418 | −1.21118 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.617528 | + | 1.06959i | −0.0417287 | + | 0.0722762i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.40429 | 0.0944630 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.45005 | − | 9.43976i | −0.364962 | − | 0.632133i | 0.623808 | − | 0.781578i | \(-0.285585\pi\) |
−0.988770 | + | 0.149445i | \(0.952251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.96627 | −0.263250 | −0.131625 | − | 0.991300i | \(-0.542020\pi\) | ||||
−0.131625 | + | 0.991300i | \(0.542020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.9139 | −0.721213 | −0.360606 | − | 0.932718i | \(-0.617430\pi\) | ||||
−0.360606 | + | 0.932718i | \(0.617430\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.89314 | + | 6.74311i | 0.256150 | + | 0.443664i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.79547 | − | 13.5021i | −0.510698 | − | 0.884555i | −0.999923 | − | 0.0123973i | \(-0.996054\pi\) |
0.489225 | − | 0.872157i | \(-0.337280\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.19534 | + | 5.53450i | −0.207560 | + | 0.359504i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.09544 | −0.523650 | −0.261825 | − | 0.965115i | \(-0.584324\pi\) | ||||
−0.261825 | + | 0.965115i | \(0.584324\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.6425 | − | 21.8974i | 0.814373 | − | 1.41054i | −0.0954047 | − | 0.995439i | \(-0.530415\pi\) |
0.909777 | − | 0.415096i | \(-0.136252\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.52378 | − | 13.0316i | 0.482651 | − | 0.835976i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.786163 | − | 1.56392i | 0.0500223 | − | 0.0995101i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.44630 | − | 2.50506i | −0.0916555 | − | 0.158752i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.94461 | + | 6.83226i | −0.248981 | + | 0.431248i | −0.963243 | − | 0.268630i | \(-0.913429\pi\) |
0.714262 | + | 0.699878i | \(0.246762\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.9117 | − | 22.3637i | 0.811751 | − | 1.40599i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.59305 | + | 7.95540i | −0.286507 | + | 0.496244i | −0.972973 | − | 0.230917i | \(-0.925827\pi\) |
0.686467 | + | 0.727161i | \(0.259161\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32.7542 | −2.03525 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.90163 | − | 17.1501i | −0.612896 | − | 1.06157i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.1217 | + | 20.9954i | 0.747454 | + | 1.29463i | 0.949039 | + | 0.315158i | \(0.102058\pi\) |
−0.201585 | + | 0.979471i | \(0.564609\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.38470 | 0.574335 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.712209 | − | 1.23358i | −0.0434241 | − | 0.0752128i | 0.843496 | − | 0.537135i | \(-0.180493\pi\) |
−0.886921 | + | 0.461922i | \(0.847160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.19617 | + | 9.00002i | 0.315645 | + | 0.546712i | 0.979574 | − | 0.201083i | \(-0.0644459\pi\) |
−0.663930 | + | 0.747795i | \(0.731113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.885955 | −0.0536204 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.3078 | −1.22018 | −0.610088 | − | 0.792334i | \(-0.708866\pi\) | ||||
−0.610088 | + | 0.792334i | \(0.708866\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.16074 | − | 12.4028i | 0.428702 | − | 0.742534i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.79547 | + | 13.5021i | −0.465038 | + | 0.805470i | −0.999203 | − | 0.0399101i | \(-0.987293\pi\) |
0.534165 | + | 0.845380i | \(0.320626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.6323 | + | 23.6119i | 0.810358 | + | 1.40358i | 0.912613 | + | 0.408824i | \(0.134061\pi\) |
−0.102255 | + | 0.994758i | \(0.532606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.72771 | − | 2.99249i | −0.101984 | − | 0.176641i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.38546 | − | 4.13174i | 0.140321 | − | 0.243044i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.73164 | − | 4.73134i | 0.160131 | − | 0.277356i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6710 | 0.740249 | 0.370125 | − | 0.928982i | \(-0.379315\pi\) | ||||
0.370125 | + | 0.928982i | \(0.379315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.7590 | −0.798376 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.46915 | + | 2.54464i | 0.0849630 | + | 0.147160i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.3885 | + | 23.1896i | 0.771701 | + | 1.33663i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.3230 | −0.707938 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.28540 | + | 2.22638i | 0.0733619 | + | 0.127066i | 0.900373 | − | 0.435119i | \(-0.143294\pi\) |
−0.827011 | + | 0.562186i | \(0.809961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.52699 | + | 4.37688i | 0.143756 | + | 0.248992i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.7568 | 1.12030 | 0.560152 | − | 0.828390i | \(-0.310743\pi\) | ||||
0.560152 | + | 0.828390i | \(0.310743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.1877 | − | 19.3777i | 0.632368 | − | 1.09529i | −0.354698 | − | 0.934981i | \(-0.615416\pi\) |
0.987066 | − | 0.160313i | \(-0.0512503\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.65313 | − | 11.5236i | 0.373677 | − | 0.647228i | −0.616451 | − | 0.787393i | \(-0.711430\pi\) |
0.990128 | + | 0.140166i | \(0.0447635\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.9948 | + | 24.2397i | −0.783557 | + | 1.35716i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.260798 | − | 0.451716i | −0.0145563 | − | 0.0252123i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.37148 | + | 12.7386i | 0.465801 | + | 0.708792i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.67707 | + | 9.83297i | −0.313943 | + | 0.543764i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.7016 | + | 20.2678i | −0.645131 | + | 1.11740i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6173 | −1.07826 | −0.539132 | − | 0.842221i | \(-0.681248\pi\) | ||||
−0.539132 | + | 0.842221i | \(0.681248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.1458 | − | 22.7692i | 0.720385 | − | 1.24774i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5909 | − | 25.2722i | −0.794819 | − | 1.37667i | −0.922954 | − | 0.384910i | \(-0.874233\pi\) |
0.128136 | − | 0.991757i | \(-0.459101\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.54228 | − | 2.67130i | −0.0837650 | − | 0.145085i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −20.2417 | −1.09615 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4479 | 0.726120 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.03935 | − | 10.4605i | −0.324209 | − | 0.561547i | 0.657143 | − | 0.753766i | \(-0.271765\pi\) |
−0.981352 | + | 0.192219i | \(0.938432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2894 | 1.08607 | 0.543033 | − | 0.839711i | \(-0.317276\pi\) | ||||
0.543033 | + | 0.839711i | \(0.317276\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.782776 | − | 1.35581i | 0.0417815 | − | 0.0723677i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.69387 | −0.356279 | −0.178139 | − | 0.984005i | \(-0.557008\pi\) | ||||
−0.178139 | + | 0.984005i | \(0.557008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.85760 | − | 6.68156i | 0.204166 | − | 0.353626i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.94536 | − | 8.56562i | −0.261006 | − | 0.452076i | 0.705503 | − | 0.708707i | \(-0.250721\pi\) |
−0.966510 | + | 0.256630i | \(0.917388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8732 | − | 2.19169i | 0.993325 | − | 0.115352i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.516108 | + | 0.893925i | 0.0270886 | + | 0.0469189i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.09936 | − | 14.0285i | 0.422783 | − | 0.732282i | −0.573427 | − | 0.819257i | \(-0.694386\pi\) |
0.996211 | + | 0.0869742i | \(0.0277198\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.77365 | 0.144390 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.4179 | + | 28.4366i | −0.852375 | + | 1.47636i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3003 | −0.533328 | −0.266664 | − | 0.963790i | \(-0.585921\pi\) | ||||
−0.266664 | + | 0.963790i | \(0.585921\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.59238 | − | 2.75809i | −0.0820120 | − | 0.142049i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.2587 | −1.09199 | −0.545993 | − | 0.837790i | \(-0.683847\pi\) | ||||
−0.545993 | + | 0.837790i | \(0.683847\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.29502 | −0.168809 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.79002 | − | 11.7607i | −0.346954 | − | 0.600942i | 0.638753 | − | 0.769412i | \(-0.279451\pi\) |
−0.985707 | + | 0.168470i | \(0.946117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.4938 | −1.09259 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.98771 | + | 15.5672i | −0.455695 | + | 0.789287i | −0.998728 | − | 0.0504248i | \(-0.983942\pi\) |
0.543033 | + | 0.839711i | \(0.317276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.5877 | −1.29402 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.72180 | − | 6.44634i | 0.187740 | − | 0.325175i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.0169 | + | 20.8139i | 0.603112 | + | 1.04462i | 0.992347 | + | 0.123483i | \(0.0394063\pi\) |
−0.389234 | + | 0.921139i | \(0.627260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.28148 | − | 8.03663i | −0.264405 | − | 0.402335i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.91076 | + | 10.2377i | 0.295169 | + | 0.511248i | 0.975024 | − | 0.222098i | \(-0.0712906\pi\) |
−0.679855 | + | 0.733347i | \(0.737957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.15159 | − | 1.99462i | 0.0573649 | − | 0.0993589i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −37.1600 | −1.84195 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6300 | − | 27.0719i | 0.772851 | − | 1.33862i | −0.163143 | − | 0.986602i | \(-0.552163\pi\) |
0.935994 | − | 0.352015i | \(-0.114504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.987375 | −0.0487036 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.2401 | − | 22.9325i | −0.651501 | − | 1.12843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.30872 | 0.210999 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.4217 | −1.09537 | −0.547686 | − | 0.836684i | \(-0.684491\pi\) | ||||
−0.547686 | + | 0.836684i | \(0.684491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6431 | − | 23.6305i | −0.664922 | − | 1.15168i | −0.979306 | − | 0.202384i | \(-0.935131\pi\) |
0.314384 | − | 0.949296i | \(-0.398202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.39281 | − | 16.2688i | −0.456694 | − | 0.791017i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3432 | + | 24.8431i | −0.694115 | + | 1.20224i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00513 | −0.0485279 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.6686 | + | 23.6748i | −0.658395 | + | 1.14037i | 0.322636 | + | 0.946523i | \(0.395431\pi\) |
−0.981031 | + | 0.193850i | \(0.937902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.67761 | + | 6.36980i | −0.176734 | + | 0.306113i | −0.940760 | − | 0.339073i | \(-0.889887\pi\) |
0.764026 | + | 0.645186i | \(0.223220\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.3247 | + | 28.4963i | −0.685243 | + | 1.36316i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.11862 | − | 3.66955i | −0.101116 | − | 0.175138i | 0.811029 | − | 0.585006i | \(-0.198908\pi\) |
−0.912145 | + | 0.409868i | \(0.865575\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.34225 | − | 5.78895i | 0.159155 | − | 0.275664i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.1310 | + | 19.2794i | −0.528849 | + | 0.915993i | 0.470585 | + | 0.882354i | \(0.344043\pi\) |
−0.999434 | + | 0.0336383i | \(0.989291\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0299836 | + | 0.0519332i | −0.00141818 | + | 0.00245635i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.46328 | 0.210635 | 0.105318 | − | 0.994439i | \(-0.466414\pi\) | ||||
0.105318 | + | 0.994439i | \(0.466414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.96011 | − | 3.39501i | −0.0922980 | − | 0.159865i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.39771 | − | 9.34911i | −0.253607 | − | 0.439259i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.7463 | −0.502692 | −0.251346 | − | 0.967897i | \(-0.580873\pi\) | ||||
−0.251346 | + | 0.967897i | \(0.580873\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.81668 | + | 11.8068i | 0.318176 | + | 0.551096i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.9163 | − | 20.6397i | −0.554998 | − | 0.961285i | −0.997904 | − | 0.0647167i | \(-0.979386\pi\) |
0.442906 | − | 0.896568i | \(-0.353948\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.3695 | 1.17902 | 0.589510 | − | 0.807761i | \(-0.299321\pi\) | ||||
0.589510 | + | 0.807761i | \(0.299321\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.62020 | −0.260072 | −0.130036 | − | 0.991509i | \(-0.541509\pi\) | ||||
−0.130036 | + | 0.991509i | \(0.541509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.0847 | + | 22.6633i | −0.604195 | + | 1.04650i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.76548 | + | 9.98611i | −0.265659 | + | 0.460136i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.1894 | + | 26.3089i | 0.698411 | + | 1.20968i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.1785 | − | 22.8259i | −0.603404 | − | 1.04513i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.83611 | + | 11.8405i | −0.312350 | + | 0.541006i | −0.978871 | − | 0.204480i | \(-0.934450\pi\) |
0.666521 | + | 0.745487i | \(0.267783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.11411 | − | 3.66175i | 0.0963951 | − | 0.166961i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.1430 | 0.734532 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.39233 | 0.334979 | 0.167489 | − | 0.985874i | \(-0.446434\pi\) | ||||
0.167489 | + | 0.985874i | \(0.446434\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.30004 | − | 9.17994i | −0.239676 | − | 0.415131i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.979053 | − | 1.69577i | −0.0441840 | − | 0.0765290i | 0.843088 | − | 0.537776i | \(-0.180735\pi\) |
−0.887272 | + | 0.461247i | \(0.847402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.7341 | 1.24908 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.4148 | − | 23.2350i | −0.601734 | − | 1.04223i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.72234 | − | 4.71522i | −0.121868 | − | 0.211082i | 0.798636 | − | 0.601814i | \(-0.205555\pi\) |
−0.920505 | + | 0.390732i | \(0.872222\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.88595 | 0.396995 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.29629 | + | 14.3696i | −0.369913 | + | 0.640709i | −0.989552 | − | 0.144179i | \(-0.953946\pi\) |
0.619638 | + | 0.784887i | \(0.287279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.55273 | + | 7.88557i | −0.202194 | + | 0.350210i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.06552 | + | 10.5058i | −0.268849 | + | 0.465661i | −0.968565 | − | 0.248761i | \(-0.919977\pi\) |
0.699716 | + | 0.714422i | \(0.253310\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.70862 | − | 4.69146i | −0.119822 | − | 0.207538i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.9651 | − | 0.981757i | 0.749029 | − | 0.0433456i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2756 | + | 22.9940i | −0.583861 | + | 1.01128i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.16482 | + | 10.6778i | −0.270606 | + | 0.468703i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.1249 | 0.618824 | 0.309412 | − | 0.950928i | \(-0.399868\pi\) | ||||
0.309412 | + | 0.950928i | \(0.399868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.1840 | + | 22.8353i | −0.576495 | + | 0.998519i | 0.419382 | + | 0.907810i | \(0.362247\pi\) |
−0.995877 | + | 0.0907094i | \(0.971087\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0285 | + | 17.3698i | 0.436847 | + | 0.756641i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.2694 | − | 26.4473i | −0.663885 | − | 1.14988i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.2554 | 0.922407 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.446059 | 0.0193210 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.36985 | + | 12.7649i | 0.318032 | + | 0.550848i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.44775 | −0.406943 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6986 | − | 25.4586i | 0.631940 | − | 1.09455i | −0.355214 | − | 0.934785i | \(-0.615592\pi\) |
0.987155 | − | 0.159768i | \(-0.0510745\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.15541 | −0.0495833 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.8762 | − | 18.8381i | 0.465031 | − | 0.805457i | −0.534172 | − | 0.845376i | \(-0.679377\pi\) |
0.999203 | + | 0.0399185i | \(0.0127098\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.5132 | − | 19.9414i | −0.491371 | − | 0.851079i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5263 | − | 30.8867i | 0.661443 | − | 1.31582i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.0155 | − | 24.2755i | −0.595999 | − | 1.03230i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.0716 | + | 20.9086i | −0.511489 | + | 0.885924i | 0.488423 | + | 0.872607i | \(0.337572\pi\) |
−0.999911 | + | 0.0133172i | \(0.995761\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.45663 | −0.146200 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.37649 | − | 7.58030i | 0.184776 | − | 0.320041i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.0693 | 0.635097 | 0.317548 | − | 0.948242i | \(-0.397140\pi\) | ||||
0.317548 | + | 0.948242i | \(0.397140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.35092 | + | 12.7322i | 0.308710 | + | 0.534701i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.302873 | 0.0126971 | 0.00634855 | − | 0.999980i | \(-0.497979\pi\) | ||||
0.00634855 | + | 0.999980i | \(0.497979\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.3107 | 1.26846 | 0.634232 | − | 0.773143i | \(-0.281316\pi\) | ||||
0.634232 | + | 0.773143i | \(0.281316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.75232 | − | 8.23126i | −0.198531 | − | 0.343866i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.6601 | −0.776832 | −0.388416 | − | 0.921484i | \(-0.626978\pi\) | ||||
−0.388416 | + | 0.921484i | \(0.626978\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.79214 | − | 6.56819i | 0.157596 | − | 0.272964i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6876 | 0.526369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.6263 | + | 32.2617i | −0.771422 | + | 1.33614i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.5986 | − | 23.5535i | −0.561275 | − | 0.972156i | −0.997386 | − | 0.0722631i | \(-0.976978\pi\) |
0.436111 | − | 0.899893i | \(-0.356355\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.9585 | − | 1.44433i | 1.02840 | − | 0.0595124i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.48443 | + | 4.30316i | 0.102196 | + | 0.177008i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.7987 | + | 25.6321i | −0.607709 | + | 1.05258i | 0.383908 | + | 0.923371i | \(0.374578\pi\) |
−0.991617 | + | 0.129211i | \(0.958755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.7388 | 0.603221 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.54404 | + | 13.0667i | −0.308241 | + | 0.533889i | −0.977978 | − | 0.208710i | \(-0.933074\pi\) |
0.669737 | + | 0.742599i | \(0.266407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −44.9249 | −1.83253 | −0.916263 | − | 0.400576i | \(-0.868810\pi\) | ||||
−0.916263 | + | 0.400576i | \(0.868810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.5030 | − | 18.1917i | −0.427715 | − | 0.740824i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.9570 | 1.01297 | 0.506487 | − | 0.862247i | \(-0.330944\pi\) | ||||
0.506487 | + | 0.862247i | \(0.330944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.4971 | −0.709020 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.51055 | − | 2.61636i | −0.0611105 | − | 0.105846i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.64316 | − | 16.7024i | −0.389484 | − | 0.674605i | 0.602897 | − | 0.797819i | \(-0.294013\pi\) |
−0.992380 | + | 0.123214i | \(0.960680\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.72294 | − | 16.8406i | 0.391431 | − | 0.677978i | −0.601208 | − | 0.799093i | \(-0.705314\pi\) |
0.992639 | + | 0.121115i | \(0.0386469\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.70324 | −0.0684589 | −0.0342294 | − | 0.999414i | \(-0.510898\pi\) | ||||
−0.0342294 | + | 0.999414i | \(0.510898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.2630 | + | 24.7042i | −0.572354 | + | 0.991346i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.5817 | + | 35.6485i | −0.824588 | + | 1.42823i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.99190 | − | 9.11764i | −0.239293 | − | 0.364124i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.4104 | + | 31.8877i | 0.734071 | + | 1.27145i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.39314 | − | 7.60914i | 0.174888 | − | 0.302915i | −0.765235 | − | 0.643752i | \(-0.777377\pi\) |
0.940123 | + | 0.340837i | \(0.110710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.98313 | + | 6.89899i | −0.158315 | + | 0.274210i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.537502 | − | 0.930981i | 0.0212966 | − | 0.0368868i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.5359 | 0.851946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.9033 | + | 31.0095i | 0.707139 | + | 1.22480i | 0.965914 | + | 0.258863i | \(0.0833478\pi\) |
−0.258775 | + | 0.965938i | \(0.583319\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.30758 | + | 2.26480i | 0.0515661 | + | 0.0893150i | 0.890656 | − | 0.454677i | \(-0.150245\pi\) |
−0.839090 | + | 0.543992i | \(0.816912\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.8849 | −1.21421 | −0.607105 | − | 0.794622i | \(-0.707669\pi\) | ||||
−0.607105 | + | 0.794622i | \(0.707669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.0210 | − | 26.0172i | −0.589626 | − | 1.02126i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.32686 | − | 10.9584i | −0.247969 | − | 0.429495i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.2198 | 0.673864 | 0.336932 | − | 0.941529i | \(-0.390611\pi\) | ||||
0.336932 | + | 0.941529i | \(0.390611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.34838 | 0.169646 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0769444 | − | 0.133272i | 0.00299733 | − | 0.00519153i | −0.864523 | − | 0.502594i | \(-0.832379\pi\) |
0.867520 | + | 0.497402i | \(0.165713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.8595 | − | 24.0054i | 0.539073 | − | 0.933701i | −0.459882 | − | 0.887980i | \(-0.652108\pi\) |
0.998954 | − | 0.0457209i | \(-0.0145585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.497975 | + | 0.862519i | 0.0193398 | + | 0.0334975i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.0149 | + | 50.2552i | 1.12346 | + | 1.94589i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.86527 | − | 6.69485i | 0.149440 | − | 0.258838i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.2725 | + | 28.1848i | −0.628193 | + | 1.08806i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.0820 | 1.85342 | 0.926712 | − | 0.375773i | \(-0.122623\pi\) | ||||
0.926712 | + | 0.375773i | \(0.122623\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.8392 | 1.64644 | 0.823222 | − | 0.567720i | \(-0.192174\pi\) | ||||
0.823222 | + | 0.567720i | \(0.192174\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.9816 | + | 20.7527i | 0.459810 | + | 0.796415i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.40647 | − | 2.43609i | −0.0538962 | − | 0.0933510i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.4022 | −1.58421 | −0.792106 | − | 0.610383i | \(-0.791015\pi\) | ||||
−0.792106 | + | 0.610383i | \(0.791015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.87018 | − | 6.70335i | −0.147657 | − | 0.255749i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.11938 | − | 3.67087i | −0.0807418 | − | 0.139849i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.9248 | 0.643850 | 0.321925 | − | 0.946765i | \(-0.395670\pi\) | ||||
0.321925 | + | 0.946765i | \(0.395670\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.7069 | − | 23.7411i | 0.520683 | − | 0.901849i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.94222 | + | 3.36402i | −0.0735668 | + | 0.127421i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.52869 | − | 9.57597i | 0.209114 | − | 0.362196i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.7780 | + | 32.5244i | 0.709233 | + | 1.22843i | 0.965142 | + | 0.261727i | \(0.0842921\pi\) |
−0.255908 | + | 0.966701i | \(0.582375\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.8192 | − | 2.65152i | 1.72810 | − | 0.100004i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.0257 | − | 46.8099i | 1.01641 | − | 1.76047i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.3872 | − | 26.6514i | 0.577879 | − | 1.00092i | −0.417843 | − | 0.908519i | \(-0.637214\pi\) |
0.995722 | − | 0.0923969i | \(-0.0294529\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.5003 | 0.843826 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.9832 | + | 36.3440i | −0.785827 | + | 1.36109i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.87072 | − | 4.97223i | −0.107209 | − | 0.185691i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.1509 | + | 40.0985i | 0.863383 | + | 1.49542i | 0.868644 | + | 0.495437i | \(0.164992\pi\) |
−0.00526119 | + | 0.999986i | \(0.501675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.1679 | −0.825576 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.9325 | 0.666918 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.93454 | − | 5.08278i | −0.108836 | − | 0.188510i | 0.806463 | − | 0.591285i | \(-0.201379\pi\) |
−0.915299 | + | 0.402775i | \(0.868046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.50625 | −0.129861 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0508 | − | 26.0687i | 0.556673 | − | 0.964186i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.3955 | −0.420901 | −0.210450 | − | 0.977605i | \(-0.567493\pi\) | ||||
−0.210450 | + | 0.977605i | \(0.567493\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.8447 | + | 25.7118i | −0.546812 | + | 0.947107i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.86621 | − | 11.8926i | −0.252578 | − | 0.437477i | 0.711657 | − | 0.702527i | \(-0.247945\pi\) |
−0.964235 | + | 0.265050i | \(0.914612\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.23934 | − | 0.0717198i | 0.0455284 | − | 0.00263469i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.33763 | − | 7.51300i | −0.159132 | − | 0.275625i | 0.775424 | − | 0.631441i | \(-0.217536\pi\) |
−0.934556 | + | 0.355816i | \(0.884203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.09212 | + | 8.81981i | −0.186311 | + | 0.322700i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.28784 | 0.0835957 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.35314 | + | 5.80780i | −0.122358 | + | 0.211930i | −0.920697 | − | 0.390278i | \(-0.872379\pi\) |
0.798339 | + | 0.602208i | \(0.205712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.59517 | −0.203899 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.19480 | + | 12.4618i | 0.261500 | + | 0.452931i | 0.966641 | − | 0.256136i | \(-0.0824497\pi\) |
−0.705141 | + | 0.709067i | \(0.749116\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.3144 | 0.664771 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.9650 | −1.84748 | −0.923740 | − | 0.383020i | \(-0.874884\pi\) | ||||
−0.923740 | + | 0.383020i | \(0.874884\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.9009 | − | 43.1296i | −0.901472 | − | 1.56140i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.41831 | 0.123428 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9988 | + | 20.7825i | −0.432687 | + | 0.749435i | −0.997104 | − | 0.0760546i | \(-0.975768\pi\) |
0.564417 | + | 0.825490i | \(0.309101\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.51495 | −0.234630 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.9925 | + | 38.0920i | −0.791014 | + | 1.37008i | 0.134326 | + | 0.990937i | \(0.457113\pi\) |
−0.925340 | + | 0.379139i | \(0.876220\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.6149 | − | 20.1177i | −0.416683 | − | 0.721717i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.65911 | + | 4.04627i | 0.0952725 | + | 0.144973i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.2192 | − | 26.3604i | −0.544585 | − | 0.943250i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.4594 | − | 26.7765i | 0.552474 | − | 0.956914i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4815 | −0.587501 | −0.293751 | − | 0.955882i | \(-0.594904\pi\) | ||||
−0.293751 | + | 0.955882i | \(0.594904\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.59691 | + | 14.8903i | −0.306058 | + | 0.530108i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.5295 | 0.481055 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.85155 | − | 3.20699i | −0.0657506 | − | 0.113883i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.9346 | 1.69793 | 0.848966 | − | 0.528448i | \(-0.177226\pi\) | ||||
0.848966 | + | 0.528448i | \(0.177226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.3089 | 0.930740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.5208 | − | 28.6149i | −0.583733 | − | 1.01106i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.07295 | − | 5.32251i | −0.108442 | − | 0.187827i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.505111 | − | 0.874879i | 0.0177808 | − | 0.0307972i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.7879 | 0.414441 | 0.207221 | − | 0.978294i | \(-0.433558\pi\) | ||||
0.207221 | + | 0.978294i | \(0.433558\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.9432 | + | 27.6144i | −0.559840 | + | 0.969671i | 0.437669 | + | 0.899136i | \(0.355804\pi\) |
−0.997509 | + | 0.0705351i | \(0.977529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.68522 | + | 6.38298i | −0.129246 | + | 0.223861i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.6062 | − | 31.3556i | −0.720919 | − | 1.09699i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.55963 | + | 2.70136i | 0.0544979 | + | 0.0943932i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.2579 | + | 28.1596i | −0.567406 | + | 0.982776i | 0.429415 | + | 0.903107i | \(0.358720\pi\) |
−0.996821 | + | 0.0796688i | \(0.974614\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.6985 | − | 42.7790i | 0.860934 | − | 1.49118i | −0.0100940 | − | 0.999949i | \(-0.503213\pi\) |
0.871028 | − | 0.491233i | \(-0.163454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0147 | − | 20.8101i | 0.417794 | − | 0.723640i | −0.577924 | − | 0.816091i | \(-0.696137\pi\) |
0.995717 | + | 0.0924511i | \(0.0294702\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.42673 | 0.292672 | 0.146336 | − | 0.989235i | \(-0.453252\pi\) | ||||
0.146336 | + | 0.989235i | \(0.453252\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.20132 | − | 12.4731i | −0.249811 | − | 0.432686i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.68075 | + | 8.10730i | 0.162178 | + | 0.280901i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3601 | 0.772879 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.0809 | − | 19.1926i | −0.382554 | − | 0.662603i | 0.608872 | − | 0.793268i | \(-0.291622\pi\) |
−0.991427 | + | 0.130665i | \(0.958289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.9488 | − | 29.3561i | −0.584440 | − | 1.01228i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.0574 | −0.380836 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.52752 | −0.155568 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.66830 | + | 16.7460i | −0.331815 | + | 0.574721i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.5213 | + | 66.7208i | −1.32049 | + | 2.28716i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4153 | − | 33.6283i | −0.664767 | − | 1.15141i | −0.979348 | − | 0.202180i | \(-0.935198\pi\) |
0.314582 | − | 0.949230i | \(-0.398136\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.9215 | − | 31.0409i | −0.612186 | − | 1.06034i | −0.990871 | − | 0.134812i | \(-0.956957\pi\) |
0.378685 | − | 0.925526i | \(-0.376376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.06313 | − | 15.6978i | 0.309230 | − | 0.535602i | −0.668964 | − | 0.743295i | \(-0.733262\pi\) |
0.978194 | + | 0.207692i | \(0.0665953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.22533 | − | 2.12233i | 0.0417590 | − | 0.0723287i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.5099 | −1.65130 | −0.825648 | − | 0.564186i | \(-0.809190\pi\) | ||||
−0.825648 | + | 0.564186i | \(0.809190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.38363 | 0.114914 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.9007 | − | 27.5409i | −0.539395 | − | 0.934259i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.68909 | − | 2.92560i | −0.0572328 | − | 0.0991301i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.2351 | −0.651008 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4708 | + | 23.3322i | 0.454878 | + | 0.787872i | 0.998681 | − | 0.0513410i | \(-0.0163495\pi\) |
−0.543803 | + | 0.839213i | \(0.683016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.49326 | + | 7.78255i | 0.151554 | + | 0.262499i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.0603 | 0.911685 | 0.455843 | − | 0.890060i | \(-0.349338\pi\) | ||||
0.455843 | + | 0.890060i | \(0.349338\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3088 | − | 31.7118i | 0.616140 | − | 1.06719i | −0.374043 | − | 0.927411i | \(-0.622029\pi\) |
0.990183 | − | 0.139775i | \(-0.0446379\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.2342 | − | 36.7786i | 0.712973 | − | 1.23491i | −0.250763 | − | 0.968049i | \(-0.580681\pi\) |
0.963736 | − | 0.266857i | \(-0.0859852\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.22635 | − | 12.5164i | 0.242364 | − | 0.419787i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.33971 | + | 14.4448i | 0.279391 | + | 0.483919i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.7284 | − | 29.2995i | 0.492868 | − | 0.980469i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.04195 | + | 1.80470i | −0.0347896 | + | 0.0602573i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.7433 | − | 39.3926i | 0.758533 | − | 1.31382i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.9125 | 1.22973 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.49538 | + | 16.4465i | −0.315986 | + | 0.547305i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.8140 | + | 46.4433i | 0.890345 | + | 1.54212i | 0.839462 | + | 0.543418i | \(0.182870\pi\) |
0.0508831 | + | 0.998705i | \(0.483796\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.6934 | + | 37.5740i | 0.719523 | + | 1.24625i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1631 | −0.336719 | −0.168360 | − | 0.985726i | \(-0.553847\pi\) | ||||
−0.168360 | + | 0.985726i | \(0.553847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3942 | 0.476379 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.3246 | + | 28.2751i | 0.539087 | + | 0.933725i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.6831 | −0.550325 | −0.275163 | − | 0.961398i | \(-0.588732\pi\) | ||||
−0.275163 | + | 0.961398i | \(0.588732\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.911632 | + | 1.57899i | −0.0300393 | + | 0.0520296i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.46341 | 0.113999 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.89702 | − | 15.4101i | 0.292216 | − | 0.506134i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.49844 | − | 7.79152i | −0.147589 | − | 0.255631i | 0.782747 | − | 0.622340i | \(-0.213818\pi\) |
−0.930336 | + | 0.366709i | \(0.880485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.6493 | − | 0.674135i | 0.381790 | − | 0.0220939i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.00594 | + | 12.1346i | 0.229364 | + | 0.397270i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.9187 | − | 34.5001i | 0.650714 | − | 1.12707i | −0.332236 | − | 0.943196i | \(-0.607803\pi\) |
0.982950 | − | 0.183874i | \(-0.0588637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.8691 | 0.517868 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.92236 | + | 10.2578i | −0.193063 | + | 0.334396i | −0.946264 | − | 0.323395i | \(-0.895176\pi\) |
0.753201 | + | 0.657791i | \(0.228509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.12765 | −0.264673 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.69404 | − | 11.5944i | −0.217527 | − | 0.376768i | 0.736524 | − | 0.676411i | \(-0.236466\pi\) |
−0.954051 | + | 0.299643i | \(0.903132\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.699307 | 0.0227005 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.43704 | 0.306017 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.0994 | + | 40.0094i | 0.748264 | + | 1.29603i | 0.948654 | + | 0.316315i | \(0.102446\pi\) |
−0.200390 | + | 0.979716i | \(0.564221\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.8507 | −0.641682 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.16542 | − | 3.75062i | 0.0699252 | − | 0.121114i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.89541 | 0.0611424 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.918216 | + | 1.59040i | −0.0295891 | + | 0.0512498i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.8556 | + | 20.5345i | 0.381251 | + | 0.660346i | 0.991241 | − | 0.132063i | \(-0.0421602\pi\) |
−0.609991 | + | 0.792409i | \(0.708827\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.85543 | + | 9.65898i | −0.155979 | + | 0.310291i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.2724 | + | 29.9166i | 0.554296 | + | 0.960069i | 0.997958 | + | 0.0638748i | \(0.0203458\pi\) |
−0.443662 | + | 0.896194i | \(0.646321\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.44951 | + | 16.3670i | −0.302937 | + | 0.524703i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.4467 | 1.67792 | 0.838959 | − | 0.544195i | \(-0.183165\pi\) | ||||
0.838959 | + | 0.544195i | \(0.183165\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.3502 | + | 40.4437i | −0.746275 | + | 1.29259i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.9755 | 1.27632 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.01464 | + | 12.1497i | 0.223732 | + | 0.387515i | 0.955938 | − | 0.293568i | \(-0.0948426\pi\) |
−0.732206 | + | 0.681083i | \(0.761509\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.5980 | −0.528320 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62.9834 | 2.00276 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.94168 | − | 8.55924i | −0.156978 | − | 0.271893i | 0.776800 | − | 0.629748i | \(-0.216842\pi\) |
−0.933777 | + | 0.357854i | \(0.883508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.95647 | − | 12.0490i | −0.220757 | − | 0.382362i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.2210 | + | 36.7559i | −0.672077 | + | 1.16407i | 0.305237 | + | 0.952276i | \(0.401264\pi\) |
−0.977314 | + | 0.211795i | \(0.932069\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 41.0490 | 1.29873 |
(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 | 1900.2.i.d.501.3 | 8 | ||
5.2 | odd | 4 | 1900.2.s.d.349.6 | 16 | |||
5.3 | odd | 4 | 1900.2.s.d.349.3 | 16 | |||
5.4 | even | 2 | 380.2.i.c.121.2 | ✓ | 8 | ||
15.14 | odd | 2 | 3420.2.t.w.1261.4 | 8 | |||
19.11 | even | 3 | inner | 1900.2.i.d.201.3 | 8 | ||
20.19 | odd | 2 | 1520.2.q.m.881.3 | 8 | |||
95.49 | even | 6 | 380.2.i.c.201.2 | yes | 8 | ||
95.64 | even | 6 | 7220.2.a.r.1.3 | 4 | |||
95.68 | odd | 12 | 1900.2.s.d.49.6 | 16 | |||
95.69 | odd | 6 | 7220.2.a.p.1.2 | 4 | |||
95.87 | odd | 12 | 1900.2.s.d.49.3 | 16 | |||
285.239 | odd | 6 | 3420.2.t.w.3241.4 | 8 | |||
380.239 | odd | 6 | 1520.2.q.m.961.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.c.121.2 | ✓ | 8 | 5.4 | even | 2 | ||
380.2.i.c.201.2 | yes | 8 | 95.49 | even | 6 | ||
1520.2.q.m.881.3 | 8 | 20.19 | odd | 2 | |||
1520.2.q.m.961.3 | 8 | 380.239 | odd | 6 | |||
1900.2.i.d.201.3 | 8 | 19.11 | even | 3 | inner | ||
1900.2.i.d.501.3 | 8 | 1.1 | even | 1 | trivial | ||
1900.2.s.d.49.3 | 16 | 95.87 | odd | 12 | |||
1900.2.s.d.49.6 | 16 | 95.68 | odd | 12 | |||
1900.2.s.d.349.3 | 16 | 5.3 | odd | 4 | |||
1900.2.s.d.349.6 | 16 | 5.2 | odd | 4 | |||
3420.2.t.w.1261.4 | 8 | 15.14 | odd | 2 | |||
3420.2.t.w.3241.4 | 8 | 285.239 | odd | 6 | |||
7220.2.a.p.1.2 | 4 | 95.69 | odd | 6 | |||
7220.2.a.r.1.3 | 4 | 95.64 | even | 6 |