Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(629,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.629");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.f (of order \(2\), degree \(1\), 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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 629.1 | ||
Root | \(0.420861 - 1.68014i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.629 |
Dual form | 1260.2.f.a.629.2 |
$q$-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 \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.95522 | − | 1.08495i | −0.874400 | − | 0.485206i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.37608 | + | 1.16372i | 0.898073 | + | 0.439846i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.74166i | 1.12815i | 0.825723 | + | 0.564076i | \(0.190768\pi\) | ||||
−0.825723 | + | 0.564076i | \(0.809232\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.841723 | 0.233452 | 0.116726 | − | 0.993164i | \(-0.462760\pi\) | ||||
0.116726 | + | 0.993164i | \(0.462760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.36028i | 0.814988i | 0.913208 | + | 0.407494i | \(0.133597\pi\) | ||||
−0.913208 | + | 0.407494i | \(0.866403\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.55066i | − | 1.04399i | −0.852948 | − | 0.521996i | \(-0.825187\pi\) | ||
0.852948 | − | 0.521996i | \(-0.174813\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.64575 | −1.59425 | −0.797125 | − | 0.603815i | \(-0.793647\pi\) | ||||
−0.797125 | + | 0.603815i | \(0.793647\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.64575 | + | 4.24264i | 0.529150 | + | 0.848528i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.979531i | 0.175929i | 0.996124 | + | 0.0879645i | \(0.0280362\pi\) | ||||
−0.996124 | + | 0.0879645i | \(0.971964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.38317 | − | 4.85326i | −0.571860 | − | 0.820352i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.32744i | 0.382629i | 0.981529 | + | 0.191315i | \(0.0612751\pi\) | ||||
−0.981529 | + | 0.191315i | \(0.938725\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3460 | 1.61578 | 0.807890 | − | 0.589333i | \(-0.200610\pi\) | ||||
0.807890 | + | 0.589333i | \(0.200610\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.8127i | 1.64893i | 0.565916 | + | 0.824463i | \(0.308522\pi\) | ||||
−0.565916 | + | 0.824463i | \(0.691478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.91094i | 1.15393i | 0.816769 | + | 0.576965i | \(0.195763\pi\) | ||||
−0.816769 | + | 0.576965i | \(0.804237\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29150 | + | 5.53019i | 0.613072 | + | 0.790027i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.35425 | 0.598102 | 0.299051 | − | 0.954237i | \(-0.403330\pi\) | ||||
0.299051 | + | 0.954237i | \(0.403330\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.05952 | − | 7.31575i | 0.547386 | − | 0.986456i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.38527 | −0.180346 | −0.0901732 | − | 0.995926i | \(-0.528742\pi\) | ||||
−0.0901732 | + | 0.995926i | \(0.528742\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.64575 | − | 0.913230i | −0.204130 | − | 0.113272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1402i | 1.60533i | 0.596432 | + | 0.802664i | \(0.296585\pi\) | ||||
−0.596432 | + | 0.802664i | \(0.703415\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.74166i | 0.444053i | 0.975041 | + | 0.222027i | \(0.0712672\pi\) | ||||
−0.975041 | + | 0.222027i | \(0.928733\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66259 | 1.01388 | 0.506940 | − | 0.861981i | \(-0.330777\pi\) | ||||
0.506940 | + | 0.861981i | \(0.330777\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.35425 | + | 8.89047i | −0.496213 | + | 1.01316i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5830 | 1.64072 | 0.820358 | − | 0.571850i | \(-0.193774\pi\) | ||||
0.820358 | + | 0.571850i | \(0.193774\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.14944i | − | 0.345696i | −0.984949 | − | 0.172848i | \(-0.944703\pi\) | ||
0.984949 | − | 0.172848i | \(-0.0552969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.64575 | − | 6.57008i | 0.395437 | − | 0.712626i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.91044 | 0.414505 | 0.207253 | − | 0.978287i | \(-0.433548\pi\) | ||||
0.207253 | + | 0.978287i | \(0.433548\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | + | 0.979531i | 0.209657 | + | 0.102683i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.93725 | + | 8.89753i | −0.506552 | + | 0.912867i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.8000 | −1.50271 | −0.751357 | − | 0.659896i | \(-0.770600\pi\) | ||||
−0.751357 | + | 0.659896i | \(0.770600\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3460 | −1.02947 | −0.514735 | − | 0.857350i | \(-0.672110\pi\) | ||||
−0.514735 | + | 0.857350i | \(0.672110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.36689 | 0.331750 | 0.165875 | − | 0.986147i | \(-0.446955\pi\) | ||||
0.165875 | + | 0.986147i | \(0.446955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.06275 | −0.102740 | −0.0513698 | − | 0.998680i | \(-0.516359\pi\) | ||||
−0.0513698 | + | 0.998680i | \(0.516359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.8745 | −1.32894 | −0.664468 | − | 0.747316i | \(-0.731342\pi\) | ||||
−0.664468 | + | 0.747316i | \(0.731342\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.9373 | −1.02889 | −0.514445 | − | 0.857523i | \(-0.672002\pi\) | ||||
−0.514445 | + | 0.857523i | \(0.672002\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.9491 | + | 8.29529i | 1.39401 | + | 0.773539i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.91044 | + | 7.98430i | −0.358469 | + | 0.731919i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.569951 | − | 11.1658i | −0.0509780 | − | 0.998700i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.65489i | 0.413054i | 0.978441 | + | 0.206527i | \(0.0662162\pi\) | ||||
−0.978441 | + | 0.206527i | \(0.933784\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.43560 | 0.562281 | 0.281141 | − | 0.959667i | \(-0.409287\pi\) | ||||
0.281141 | + | 0.959667i | \(0.409287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.29570 | − | 10.8127i | 0.459196 | − | 0.937582i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.2288 | 1.21564 | 0.607822 | − | 0.794073i | \(-0.292043\pi\) | ||||
0.607822 | + | 0.794073i | \(0.292043\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 21.1412i | − | 1.79318i | −0.442866 | − | 0.896588i | \(-0.646038\pi\) | ||
0.442866 | − | 0.896588i | \(-0.353962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.14944i | 0.263369i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.53436 | − | 2.76510i | 0.127421 | − | 0.229629i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.41618i | − | 0.197941i | −0.995090 | − | 0.0989706i | \(-0.968445\pi\) | ||
0.995090 | − | 0.0989706i | \(-0.0315550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.29150 | 0.430616 | 0.215308 | − | 0.976546i | \(-0.430924\pi\) | ||||
0.215308 | + | 0.976546i | \(0.430924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.06275 | − | 1.91520i | 0.0853618 | − | 0.153832i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.4651 | −1.47367 | −0.736837 | − | 0.676070i | \(-0.763682\pi\) | ||||
−0.736837 | + | 0.676070i | \(0.763682\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.1669 | − | 8.89753i | −1.43175 | − | 0.701223i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.4821i | 0.888509i | 0.895901 | + | 0.444255i | \(0.146531\pi\) | ||||
−0.895901 | + | 0.444255i | \(0.853469\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2915 | −0.945500 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.3725i | − | 1.54890i | −0.632638 | − | 0.774448i | \(-0.718028\pi\) | ||
0.632638 | − | 0.774448i | \(-0.281972\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.34926 | + | 13.1598i | 0.101994 | + | 0.994785i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.0534i | − | 1.05040i | −0.850979 | − | 0.525200i | \(-0.823990\pi\) | ||
0.850979 | − | 0.525200i | \(-0.176010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.5496i | − | 1.37878i | −0.724389 | − | 0.689392i | \(-0.757878\pi\) | ||
0.724389 | − | 0.689392i | \(-0.242122\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.52517 | − | 4.55066i | 0.185654 | − | 0.334571i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.5730 | −0.919431 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.56812i | − | 0.402895i | −0.979499 | − | 0.201447i | \(-0.935435\pi\) | ||
0.979499 | − | 0.201447i | \(-0.0645645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 6.98233i | − | 0.502599i | −0.967909 | − | 0.251300i | \(-0.919142\pi\) | ||
0.967909 | − | 0.251300i | \(-0.0808579\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.8118 | 1.48278 | 0.741388 | − | 0.671076i | \(-0.234168\pi\) | ||||
0.741388 | + | 0.671076i | \(0.234168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.6714i | 1.89069i | 0.326076 | + | 0.945343i | \(0.394273\pi\) | ||||
−0.326076 | + | 0.945343i | \(0.605727\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.64575 | + | 3.36028i | −0.115509 | + | 0.235846i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.2288 | − | 11.2250i | −1.41284 | − | 0.783986i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.0270 | 1.17778 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.29150 | 0.364282 | 0.182141 | − | 0.983272i | \(-0.441697\pi\) | ||||
0.182141 | + | 0.983272i | \(0.441697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.7313 | − | 21.1412i | 0.800068 | − | 1.44182i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.13990 | + | 2.32744i | −0.0773816 | + | 0.157997i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.82843i | 0.190261i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.7105 | −1.25294 | −0.626472 | − | 0.779444i | \(-0.715502\pi\) | ||||
−0.626472 | + | 0.779444i | \(0.715502\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.9304i | 1.38920i | 0.719397 | + | 0.694599i | \(0.244418\pi\) | ||||
−0.719397 | + | 0.694599i | \(0.755582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6724i | 0.837419i | 0.908120 | + | 0.418709i | \(0.137517\pi\) | ||||
−0.908120 | + | 0.418709i | \(0.862483\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.3542 | 1.07140 | 0.535701 | − | 0.844408i | \(-0.320047\pi\) | ||||
0.535701 | + | 0.844408i | \(0.320047\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.58301 | − | 15.4676i | 0.559894 | − | 1.00900i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.57205i | 0.489795i | 0.969549 | + | 0.244898i | \(0.0787544\pi\) | ||||
−0.969549 | + | 0.244898i | \(0.921246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.6315i | 0.942498i | 0.882000 | + | 0.471249i | \(0.156197\pi\) | ||||
−0.882000 | + | 0.471249i | \(0.843803\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.39082 | − | 15.4688i | −0.152744 | − | 0.988266i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.83039i | − | 0.243722i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.20614 | 0.581086 | 0.290543 | − | 0.956862i | \(-0.406164\pi\) | ||||
0.290543 | + | 0.956862i | \(0.406164\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 28.6078i | − | 1.79856i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.5220i | 1.46726i | 0.679549 | + | 0.733630i | \(0.262176\pi\) | ||||
−0.679549 | + | 0.733630i | \(0.737824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.70850 | + | 5.53019i | −0.168298 | + | 0.343629i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.35425 | −0.268494 | −0.134247 | − | 0.990948i | \(-0.542862\pi\) | ||||
−0.134247 | + | 0.990948i | \(0.542862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.51350 | − | 4.72416i | −0.522980 | − | 0.290203i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.3964 | −0.938734 | −0.469367 | − | 0.883003i | \(-0.655518\pi\) | ||||
−0.469367 | + | 0.883003i | \(0.655518\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.0399i | − | 0.731373i | −0.930738 | − | 0.365686i | \(-0.880834\pi\) | ||
0.930738 | − | 0.365686i | \(-0.119166\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.8745 | + | 9.89949i | −0.957269 | + | 0.596962i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 25.4558i | − | 1.52949i | −0.644331 | − | 0.764747i | \(-0.722864\pi\) | ||
0.644331 | − | 0.764747i | \(-0.277136\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.8661i | − | 1.48339i | −0.670738 | − | 0.741694i | \(-0.734023\pi\) | ||
0.670738 | − | 0.741694i | \(-0.265977\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3436 | 0.912080 | 0.456040 | − | 0.889959i | \(-0.349267\pi\) | ||||
0.456040 | + | 0.889959i | \(0.349267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.5830 | + | 12.0399i | 1.45109 | + | 0.710694i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.70850 | 0.335794 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 29.8209i | − | 1.74215i | −0.491147 | − | 0.871077i | \(-0.663422\pi\) | ||
0.491147 | − | 0.871077i | \(-0.336578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.70850 | + | 1.50295i | 0.157695 | + | 0.0875051i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.43560 | −0.372181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5830 | + | 25.6919i | −0.725272 | + | 1.48086i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.5313 | −1.51422 | −0.757111 | − | 0.653286i | \(-0.773390\pi\) | ||||
−0.757111 | + | 0.653286i | \(0.773390\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.0270 | −0.965513 | −0.482756 | − | 0.875755i | \(-0.660364\pi\) | ||||
−0.482756 | + | 0.875755i | \(0.660364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.59388 | −0.316185 | −0.158092 | − | 0.987424i | \(-0.550534\pi\) | ||||
−0.158092 | + | 0.987424i | \(0.550534\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.8118 | 1.84289 | 0.921446 | − | 0.388506i | \(-0.127009\pi\) | ||||
0.921446 | + | 0.388506i | \(0.127009\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.29150 | −0.296267 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.2915 | 0.850842 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.22699 | + | 3.57113i | 0.123531 | + | 0.198091i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.20614 | + | 18.7970i | −0.507551 | + | 1.03631i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8745 | −1.09240 | −0.546201 | − | 0.837654i | \(-0.683926\pi\) | ||||
−0.546201 | + | 0.837654i | \(0.683926\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.2565 | − | 25.6919i | 0.778914 | − | 1.40370i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.50295i | − | 0.0818709i | −0.999162 | − | 0.0409354i | \(-0.986966\pi\) | ||
0.999162 | − | 0.0409354i | \(-0.0130338\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.66507 | −0.198475 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.76135 | + | 18.1343i | 0.203094 | + | 0.979159i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.0627 | −0.701245 | −0.350622 | − | 0.936517i | \(-0.614030\pi\) | ||||
−0.350622 | + | 0.936517i | \(0.614030\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.0798i | − | 1.28896i | −0.764620 | − | 0.644482i | \(-0.777073\pi\) | ||
0.764620 | − | 0.644482i | \(-0.222927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 20.3725i | − | 1.08432i | −0.840275 | − | 0.542161i | \(-0.817606\pi\) | ||
0.840275 | − | 0.542161i | \(-0.182394\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.05952 | − | 7.31575i | 0.215457 | − | 0.388280i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 21.7142i | − | 1.14603i | −0.819545 | − | 0.573015i | \(-0.805773\pi\) | ||
0.819545 | − | 0.573015i | \(-0.194227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.70850 | −0.0899209 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.9373 | − | 9.39851i | −0.886536 | − | 0.491941i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3436 | 0.800927 | 0.400464 | − | 0.916313i | \(-0.368849\pi\) | ||||
0.400464 | + | 0.916313i | \(0.368849\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3460 | + | 5.06713i | 0.537140 | + | 0.263073i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.9647i | − | 0.723063i | −0.932360 | − | 0.361531i | \(-0.882254\pi\) | ||
0.932360 | − | 0.361531i | \(-0.117746\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.19038i | 0.0613075i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.2915 | −0.682739 | −0.341369 | − | 0.939929i | \(-0.610891\pi\) | ||||
−0.341369 | + | 0.939929i | \(0.610891\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4821i | 0.586706i | 0.956004 | + | 0.293353i | \(0.0947712\pi\) | ||||
−0.956004 | + | 0.293353i | \(0.905229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.1593 | − | 12.6587i | 0.925481 | − | 0.645145i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 24.8661i | − | 1.26076i | −0.776286 | − | 0.630381i | \(-0.782899\pi\) | ||
0.776286 | − | 0.630381i | \(-0.217101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.6919i | − | 1.29929i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.5129 | − | 15.8219i | −1.43464 | − | 0.796085i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.2860 | −1.31925 | −0.659627 | − | 0.751593i | \(-0.729286\pi\) | ||||
−0.659627 | + | 0.751593i | \(0.729286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.3494i | 1.61545i | 0.589557 | + | 0.807727i | \(0.299302\pi\) | ||||
−0.589557 | + | 0.807727i | \(0.700698\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.824494i | 0.0410710i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.70850 | −0.431664 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.57113i | − | 0.176581i | −0.996095 | − | 0.0882904i | \(-0.971860\pi\) | ||
0.996095 | − | 0.0882904i | \(-0.0281404\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.29150 | − | 1.61206i | −0.161964 | − | 0.0793245i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.41699 | + | 6.15784i | −0.167734 | + | 0.302276i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.5129 | 1.39295 | 0.696474 | − | 0.717582i | \(-0.254751\pi\) | ||||
0.696474 | + | 0.717582i | \(0.254751\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.87451 | −0.383780 | −0.191890 | − | 0.981416i | \(-0.561462\pi\) | ||||
−0.191890 | + | 0.981416i | \(0.561462\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.2565 | + | 8.89047i | −0.691541 | + | 0.431251i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 14.0534i | − | 0.676928i | −0.940979 | − | 0.338464i | \(-0.890093\pi\) | ||
0.940979 | − | 0.338464i | \(-0.109907\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.50679 | 0.216583 | 0.108291 | − | 0.994119i | \(-0.465462\pi\) | ||||
0.108291 | + | 0.994119i | \(0.465462\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.7932i | 1.66438i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 35.7727i | − | 1.70734i | −0.520815 | − | 0.853670i | \(-0.674372\pi\) | ||
0.520815 | − | 0.853670i | \(-0.325628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.35425 | −0.206877 | −0.103438 | − | 0.994636i | \(-0.532984\pi\) | ||||
−0.103438 | + | 0.994636i | \(0.532984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.64575 | − | 4.24264i | −0.362443 | − | 0.201120i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7299i | 0.647954i | 0.946065 | + | 0.323977i | \(0.105020\pi\) | ||||
−0.946065 | + | 0.323977i | \(0.894980\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.7113i | 1.82285i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.84769 | − | 4.08510i | −0.133502 | − | 0.191513i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.4382i | 1.51739i | 0.651444 | + | 0.758697i | \(0.274164\pi\) | ||||
−0.651444 | + | 0.758697i | \(0.725836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5018 | 0.675418 | 0.337709 | − | 0.941251i | \(-0.390348\pi\) | ||||
0.337709 | + | 0.941251i | \(0.390348\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.9706i | − | 0.788689i | −0.918963 | − | 0.394344i | \(-0.870972\pi\) | ||
0.918963 | − | 0.394344i | \(-0.129028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 14.2098i | − | 0.657552i | −0.944408 | − | 0.328776i | \(-0.893364\pi\) | ||
0.944408 | − | 0.328776i | \(-0.106636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.2915 | + | 31.2221i | −0.706096 | + | 1.44170i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.4575 | −1.86024 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.3068 | − | 12.0399i | 0.885857 | − | 0.552429i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0270 | −0.777984 | −0.388992 | − | 0.921241i | \(-0.627177\pi\) | ||||
−0.388992 | + | 0.921241i | \(0.627177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.95906i | 0.0893256i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.9373 | + | 16.0573i | 1.31397 | + | 0.729126i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.4676i | 0.700904i | 0.936581 | + | 0.350452i | \(0.113972\pi\) | ||||
−0.936581 | + | 0.350452i | \(0.886028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.1916i | 1.18201i | 0.806668 | + | 0.591005i | \(0.201269\pi\) | ||||
−0.806668 | + | 0.591005i | \(0.798731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.75216 | −0.214026 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.35425 | + | 8.89047i | −0.195315 | + | 0.398792i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.2915 | 1.31127 | 0.655634 | − | 0.755079i | \(-0.272401\pi\) | ||||
0.655634 | + | 0.755079i | \(0.272401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.33981i | 0.193503i | 0.995309 | + | 0.0967514i | \(0.0308452\pi\) | ||||
−0.995309 | + | 0.0967514i | \(0.969155\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.2288 | + | 11.2250i | 0.900168 | + | 0.499505i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.57551 | 0.335778 | 0.167889 | − | 0.985806i | \(-0.446305\pi\) | ||||
0.167889 | + | 0.985806i | \(0.446305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.5830 | + | 10.0808i | 0.910539 | + | 0.445951i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.58301 | − | 3.65292i | −0.290082 | − | 0.160967i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.6000 | −1.30181 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.0381 | 1.35980 | 0.679902 | − | 0.733303i | \(-0.262022\pi\) | ||||
0.679902 | + | 0.733303i | \(0.262022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.36689 | 0.147224 | 0.0736119 | − | 0.997287i | \(-0.476547\pi\) | ||||
0.0736119 | + | 0.997287i | \(0.476547\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.29150 | −0.143380 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.4575 | 1.54163 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.70850 | 0.377207 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.07790 | + | 1.15303i | 0.0898354 | + | 0.0498498i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.6921 | + | 16.0573i | −0.891271 | + | 0.691638i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8745 | 0.510525 | 0.255262 | − | 0.966872i | \(-0.417838\pi\) | ||||
0.255262 | + | 0.966872i | \(0.417838\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.1277 | + | 15.0532i | 1.16202 | + | 0.644808i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4558i | 1.08841i | 0.838951 | + | 0.544207i | \(0.183169\pi\) | ||||
−0.838951 | + | 0.544207i | \(0.816831\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.43560 | 0.274166 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.6504 | + | 16.9706i | 1.47348 | + | 0.721662i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.5203 | 0.742357 | 0.371179 | − | 0.928561i | \(-0.378954\pi\) | ||||
0.371179 | + | 0.928561i | \(0.378954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.10132i | 0.384945i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.6632i | 1.88233i | 0.337947 | + | 0.941165i | \(0.390267\pi\) | ||||
−0.337947 | + | 0.941165i | \(0.609733\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.3847 | + | 11.8664i | 0.899662 | + | 0.499224i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 37.1818i | − | 1.55874i | −0.626563 | − | 0.779371i | \(-0.715539\pi\) | ||
0.626563 | − | 0.779371i | \(-0.284461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.41699 | 0.0592994 | 0.0296497 | − | 0.999560i | \(-0.490561\pi\) | ||||
0.0296497 | + | 0.999560i | \(0.490561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.2288 | − | 32.4382i | −0.843597 | − | 1.35277i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.1485 | 0.838794 | 0.419397 | − | 0.907803i | \(-0.362241\pi\) | ||||
0.419397 | + | 0.907803i | \(0.362241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.66507 | − | 7.48331i | 0.152053 | − | 0.310460i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.2921i | 0.674750i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 10.6387i | − | 0.439106i | −0.975601 | − | 0.219553i | \(-0.929540\pi\) | ||
0.975601 | − | 0.219553i | \(-0.0704599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.45751 | 0.183669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 15.1894i | − | 0.623752i | −0.950123 | − | 0.311876i | \(-0.899043\pi\) | ||
0.950123 | − | 0.311876i | \(-0.100957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.3083 | − | 11.3684i | 0.668577 | − | 0.466059i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.1916i | 1.07016i | 0.844801 | + | 0.535080i | \(0.179719\pi\) | ||||
−0.844801 | + | 0.535080i | \(0.820281\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 38.3643i | − | 1.56491i | −0.622705 | − | 0.782457i | \(-0.713966\pi\) | ||
0.622705 | − | 0.782457i | \(-0.286034\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.86565 | + | 3.25486i | 0.238473 | + | 0.132329i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.6601 | −0.554447 | −0.277223 | − | 0.960805i | \(-0.589414\pi\) | ||||
−0.277223 | + | 0.960805i | \(0.589414\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.65882i | 0.269387i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3157i | 0.497425i | 0.968577 | + | 0.248713i | \(0.0800075\pi\) | ||||
−0.968577 | + | 0.248713i | \(0.919992\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.5203 | −1.18844 | −0.594220 | − | 0.804302i | \(-0.702539\pi\) | ||||
−0.594220 | + | 0.804302i | \(0.702539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.1003i | 0.928479i | 0.885710 | + | 0.464240i | \(0.153672\pi\) | ||||
−0.885710 | + | 0.464240i | \(0.846328\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.29150 | + | 4.55066i | 0.372256 | + | 0.182318i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | + | 22.4499i | −0.440000 | + | 0.897998i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.82087 | −0.311839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.1660 | 0.842606 | 0.421303 | − | 0.906920i | \(-0.361573\pi\) | ||||
0.421303 | + | 0.906920i | \(0.361573\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.05034 | − | 9.10132i | 0.200417 | − | 0.361175i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.61226 | + | 4.65489i | 0.143123 | + | 0.184433i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.6946i | 1.09387i | 0.837175 | + | 0.546935i | \(0.184205\pi\) | ||||
−0.837175 | + | 0.546935i | \(0.815795\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.83925 | −0.230277 | −0.115139 | − | 0.993349i | \(-0.536731\pi\) | ||||
−0.115139 | + | 0.993349i | \(0.536731\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.29888i | 0.247634i | 0.992305 | + | 0.123817i | \(0.0395136\pi\) | ||||
−0.992305 | + | 0.123817i | \(0.960486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.18319i | − | 0.203458i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −36.1033 | −1.41283 | −0.706415 | − | 0.707798i | \(-0.749689\pi\) | ||||
−0.706415 | + | 0.707798i | \(0.749689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.5830 | − | 6.98233i | −0.491659 | − | 0.272822i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.5073i | 1.50003i | 0.661421 | + | 0.750015i | \(0.269954\pi\) | ||||
−0.661421 | + | 0.750015i | \(0.730046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 11.0604i | − | 0.430199i | −0.976592 | − | 0.215099i | \(-0.930992\pi\) | ||
0.976592 | − | 0.215099i | \(-0.0690076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.0856 | + | 15.3956i | −0.856441 | + | 0.597017i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.8127i | − | 0.418670i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.5783i | 1.75692i | 0.477820 | + | 0.878458i | \(0.341427\pi\) | ||||
−0.477820 | + | 0.878458i | \(0.658573\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.27841i | 0.279732i | 0.990170 | + | 0.139866i | \(0.0446672\pi\) | ||||
−0.990170 | + | 0.139866i | \(0.955333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.1660 | − | 17.2231i | −1.34955 | − | 0.660962i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5203 | 0.670394 | 0.335197 | − | 0.942148i | \(-0.391197\pi\) | ||||
0.335197 | + | 0.942148i | \(0.391197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.8203 | − | 15.4375i | −1.06296 | − | 0.589838i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.66507 | 0.139628 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 10.0808i | − | 0.383494i | −0.981444 | − | 0.191747i | \(-0.938585\pi\) | ||
0.981444 | − | 0.191747i | \(-0.0614152\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.9373 | + | 41.3357i | −0.870060 | + | 1.56795i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.7656i | 1.31684i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 28.6965i | − | 1.08385i | −0.840426 | − | 0.541926i | \(-0.817695\pi\) | ||
0.840426 | − | 0.541926i | \(-0.182305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.5914 | 0.399462 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.5830 | − | 12.0399i | −0.924539 | − | 0.452807i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.83399 | 0.256656 | 0.128328 | − | 0.991732i | \(-0.459039\pi\) | ||||
0.128328 | + | 0.991732i | \(0.459039\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.48925i | − | 0.280475i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.41699 | − | 6.15784i | 0.127788 | − | 0.230290i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.3105 | 1.80168 | 0.900839 | − | 0.434154i | \(-0.142953\pi\) | ||||
0.900839 | + | 0.434154i | \(0.142953\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | + | 3.91813i | 0.297936 | + | 0.145919i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | + | 3.74166i | −0.222834 | + | 0.138962i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.6504 | 1.28511 | 0.642556 | − | 0.766239i | \(-0.277874\pi\) | ||||
0.642556 | + | 0.766239i | \(0.277874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.3338 | −1.34385 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.1252 | 1.18657 | 0.593286 | − | 0.804992i | \(-0.297830\pi\) | ||||
0.593286 | + | 0.804992i | \(0.297830\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −49.1660 | −1.81105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1660 | 1.22003 | 0.610016 | − | 0.792389i | \(-0.291163\pi\) | ||||
0.610016 | + | 0.792389i | \(0.291163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.0627 | −0.479226 | −0.239613 | − | 0.970869i | \(-0.577021\pi\) | ||||
−0.239613 | + | 0.970869i | \(0.577021\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.62144 | + | 4.72416i | −0.0960423 | + | 0.173080i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.52517 | − | 1.23674i | −0.0922677 | − | 0.0451895i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.7085 | −0.682683 | −0.341341 | − | 0.939939i | \(-0.610881\pi\) | ||||
−0.341341 | + | 0.939939i | \(0.610881\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.3460 | − | 5.74103i | −0.376531 | − | 0.208938i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.15784i | − | 0.223810i | −0.993719 | − | 0.111905i | \(-0.964305\pi\) | ||
0.993719 | − | 0.111905i | \(-0.0356953\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.45150 | −0.342617 | −0.171308 | − | 0.985217i | \(-0.554799\pi\) | ||||
−0.171308 | + | 0.985217i | \(0.554799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.9669 | − | 16.1461i | −1.19348 | − | 0.584527i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.16601 | −0.0421022 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 38.3643i | − | 1.38345i | −0.722159 | − | 0.691727i | \(-0.756850\pi\) | ||
0.722159 | − | 0.691727i | \(-0.243150\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 44.4524i | − | 1.59884i | −0.600772 | − | 0.799420i | \(-0.705140\pi\) | ||
0.600772 | − | 0.799420i | \(-0.294860\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.15580 | + | 2.59160i | −0.149281 | + | 0.0930929i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 47.0813i | − | 1.68686i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0000 | −0.500959 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.1033 | + | 20.0338i | 1.28858 | + | 0.715036i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.6000 | 1.05513 | 0.527564 | − | 0.849516i | \(-0.323106\pi\) | ||||
0.527564 | + | 0.849516i | \(0.323106\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.9878 | − | 12.7279i | −0.924019 | − | 0.452553i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0327i | 0.567908i | 0.958838 | + | 0.283954i | \(0.0916464\pi\) | ||||
−0.958838 | + | 0.283954i | \(0.908354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.5830 | −0.940439 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.4125i | 1.14381i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.8669 | + | 37.1069i | 0.911687 | + | 1.30784i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.6887i | 0.868007i | 0.900911 | + | 0.434003i | \(0.142899\pi\) | ||||
−0.900911 | + | 0.434003i | \(0.857101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.0399i | − | 0.422778i | −0.977402 | − | 0.211389i | \(-0.932201\pi\) | ||
0.977402 | − | 0.211389i | \(-0.0677988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.2050 | 1.72147 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.89949i | 0.345495i | 0.984966 | + | 0.172747i | \(0.0552644\pi\) | ||||
−0.984966 | + | 0.172747i | \(0.944736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3157i | 0.429297i | 0.976691 | + | 0.214649i | \(0.0688607\pi\) | ||||
−0.976691 | + | 0.214649i | \(0.931139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.0627 | 1.28880 | 0.644399 | − | 0.764689i | \(-0.277108\pi\) | ||||
0.644399 | + | 0.764689i | \(0.277108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27.6510i | − | 0.960357i | −0.877171 | − | 0.480179i | \(-0.840572\pi\) | ||
0.877171 | − | 0.480179i | \(-0.159428\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.5830 | + | 14.4207i | −0.643863 | + | 0.499646i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4575 | − | 22.4499i | 0.431110 | − | 0.776912i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.82087 | 0.270006 | 0.135003 | − | 0.990845i | \(-0.456896\pi\) | ||||
0.135003 | + | 0.990845i | \(0.456896\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 24.0326 | + | 13.3357i | 0.826745 | + | 0.458762i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.12824 | − | 3.49117i | −0.244929 | − | 0.119958i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 17.7951i | − | 0.610007i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.4148 | −0.459312 | −0.229656 | − | 0.973272i | \(-0.573760\pi\) | ||||
−0.229656 | + | 0.973272i | \(0.573760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 24.2907i | − | 0.829753i | −0.909878 | − | 0.414877i | \(-0.863825\pi\) | ||
0.909878 | − | 0.414877i | \(-0.136175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8546i | 1.08687i | 0.839453 | + | 0.543433i | \(0.182876\pi\) | ||||
−0.839453 | + | 0.543433i | \(0.817124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.6863 | 1.04457 | 0.522286 | − | 0.852770i | \(-0.325079\pi\) | ||||
0.522286 | + | 0.852770i | \(0.325079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.1033 | + | 39.8328i | −0.751534 | + | 1.35435i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.5646i | 1.85098i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.0604i | 0.374767i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.6396 | − | 27.1941i | 0.393492 | − | 0.919328i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 16.9706i | − | 0.573055i | −0.958072 | − | 0.286528i | \(-0.907499\pi\) | ||
0.958072 | − | 0.286528i | \(-0.0925010\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.3730 | −0.922221 | −0.461111 | − | 0.887343i | \(-0.652549\pi\) | ||||
−0.461111 | + | 0.887343i | \(0.652549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.9529i | 0.806079i | 0.915183 | + | 0.403040i | \(0.132046\pi\) | ||||
−0.915183 | + | 0.403040i | \(0.867954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 32.4125i | − | 1.08830i | −0.838987 | − | 0.544152i | \(-0.816852\pi\) | ||
0.838987 | − | 0.544152i | \(-0.183148\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.41699 | + | 11.0604i | −0.181680 | + | 0.370953i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36.0000 | 1.20469 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.2473 | + | 27.4775i | −0.509661 | + | 0.918470i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.38527 | −0.0462012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.6315i | 0.487446i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.1255 | + | 36.2686i | −0.668994 | + | 1.20561i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 37.9176i | − | 1.25903i | −0.776988 | − | 0.629516i | \(-0.783253\pi\) | ||
0.776988 | − | 0.629516i | \(-0.216747\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.6729i | − | 1.08250i | −0.840861 | − | 0.541252i | \(-0.817951\pi\) | ||
0.840861 | − | 0.541252i | \(-0.182049\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7841 | 0.389997 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.2915 | + | 7.48925i | 0.504970 | + | 0.247317i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.1255 | 0.531931 | 0.265965 | − | 0.963983i | \(-0.414309\pi\) | ||||
0.265965 | + | 0.963983i | \(0.414309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.14944i | 0.103665i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.87451 | + | 6.15784i | −0.324672 | + | 0.202468i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.0651 | −1.57697 | −0.788483 | − | 0.615057i | \(-0.789133\pi\) | ||||
−0.788483 | + | 0.615057i | \(0.789133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.1660 | − | 19.5292i | 0.824783 | − | 0.640043i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.5830 | + | 13.6412i | 0.803950 | + | 0.446113i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9694 | 0.913721 | 0.456860 | − | 0.889538i | \(-0.348974\pi\) | ||||
0.456860 | + | 0.889538i | \(0.348974\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7313 | 0.382430 | 0.191215 | − | 0.981548i | \(-0.438757\pi\) | ||||
0.191215 | + | 0.981548i | \(0.438757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −79.1032 | −2.57596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.0627 | 0.424482 | 0.212241 | − | 0.977217i | \(-0.431924\pi\) | ||||
0.212241 | + | 0.977217i | \(0.431924\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.29150 | 0.236692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.8118 | −1.45160 | −0.725798 | − | 0.687908i | \(-0.758529\pi\) | ||||
−0.725798 | + | 0.687908i | \(0.758529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.04115 | + | 10.8869i | −0.195487 | + | 0.352291i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.8086 | + | 16.5583i | 1.09174 | + | 0.534696i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0405 | 0.969049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.57551 | + | 13.6520i | −0.243864 | + | 0.439473i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.4205i | − | 1.26768i | −0.773465 | − | 0.633839i | \(-0.781478\pi\) | ||
0.773465 | − | 0.633839i | \(-0.218522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.0540 | 1.09285 | 0.546423 | − | 0.837510i | \(-0.315989\pi\) | ||||
0.546423 | + | 0.837510i | \(0.315989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.6025 | − | 50.2332i | 0.788720 | − | 1.61040i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.6863 | −0.597827 | −0.298913 | − | 0.954280i | \(-0.596624\pi\) | ||||
−0.298913 | + | 0.954280i | \(0.596624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.6315i | 0.467625i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.0921i | 1.31063i | 0.755354 | + | 0.655317i | \(0.227465\pi\) | ||||
−0.755354 | + | 0.655317i | \(0.772535\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.6915 | − | 22.5798i | −1.29654 | − | 0.719452i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 82.6714i | − | 2.62880i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.4575 | −1.22164 | −0.610822 | − | 0.791768i | \(-0.709161\pi\) | ||||
−0.610822 | + | 0.791768i | \(0.709161\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.9373 | − | 52.1484i | 0.917373 | − | 1.65322i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0565 | −0.920228 | −0.460114 | − | 0.887860i | \(-0.652192\pi\) | ||||
−0.460114 | + | 0.887860i | \(0.652192\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1260.2.f.a.629.1 | ✓ | 8 | |
3.2 | odd | 2 | 1260.2.f.b.629.8 | yes | 8 | ||
4.3 | odd | 2 | 5040.2.k.f.1889.1 | 8 | |||
5.2 | odd | 4 | 6300.2.d.f.3401.8 | 16 | |||
5.3 | odd | 4 | 6300.2.d.f.3401.10 | 16 | |||
5.4 | even | 2 | 1260.2.f.b.629.2 | yes | 8 | ||
7.6 | odd | 2 | inner | 1260.2.f.a.629.8 | yes | 8 | |
12.11 | even | 2 | 5040.2.k.e.1889.8 | 8 | |||
15.2 | even | 4 | 6300.2.d.f.3401.7 | 16 | |||
15.8 | even | 4 | 6300.2.d.f.3401.9 | 16 | |||
15.14 | odd | 2 | inner | 1260.2.f.a.629.7 | yes | 8 | |
20.19 | odd | 2 | 5040.2.k.e.1889.2 | 8 | |||
21.20 | even | 2 | 1260.2.f.b.629.1 | yes | 8 | ||
28.27 | even | 2 | 5040.2.k.f.1889.8 | 8 | |||
35.13 | even | 4 | 6300.2.d.f.3401.12 | 16 | |||
35.27 | even | 4 | 6300.2.d.f.3401.6 | 16 | |||
35.34 | odd | 2 | 1260.2.f.b.629.7 | yes | 8 | ||
60.59 | even | 2 | 5040.2.k.f.1889.7 | 8 | |||
84.83 | odd | 2 | 5040.2.k.e.1889.1 | 8 | |||
105.62 | odd | 4 | 6300.2.d.f.3401.5 | 16 | |||
105.83 | odd | 4 | 6300.2.d.f.3401.11 | 16 | |||
105.104 | even | 2 | inner | 1260.2.f.a.629.2 | yes | 8 | |
140.139 | even | 2 | 5040.2.k.e.1889.7 | 8 | |||
420.419 | odd | 2 | 5040.2.k.f.1889.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.f.a.629.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1260.2.f.a.629.2 | yes | 8 | 105.104 | even | 2 | inner | |
1260.2.f.a.629.7 | yes | 8 | 15.14 | odd | 2 | inner | |
1260.2.f.a.629.8 | yes | 8 | 7.6 | odd | 2 | inner | |
1260.2.f.b.629.1 | yes | 8 | 21.20 | even | 2 | ||
1260.2.f.b.629.2 | yes | 8 | 5.4 | even | 2 | ||
1260.2.f.b.629.7 | yes | 8 | 35.34 | odd | 2 | ||
1260.2.f.b.629.8 | yes | 8 | 3.2 | odd | 2 | ||
5040.2.k.e.1889.1 | 8 | 84.83 | odd | 2 | |||
5040.2.k.e.1889.2 | 8 | 20.19 | odd | 2 | |||
5040.2.k.e.1889.7 | 8 | 140.139 | even | 2 | |||
5040.2.k.e.1889.8 | 8 | 12.11 | even | 2 | |||
5040.2.k.f.1889.1 | 8 | 4.3 | odd | 2 | |||
5040.2.k.f.1889.2 | 8 | 420.419 | odd | 2 | |||
5040.2.k.f.1889.7 | 8 | 60.59 | even | 2 | |||
5040.2.k.f.1889.8 | 8 | 28.27 | even | 2 | |||
6300.2.d.f.3401.5 | 16 | 105.62 | odd | 4 | |||
6300.2.d.f.3401.6 | 16 | 35.27 | even | 4 | |||
6300.2.d.f.3401.7 | 16 | 15.2 | even | 4 | |||
6300.2.d.f.3401.8 | 16 | 5.2 | odd | 4 | |||
6300.2.d.f.3401.9 | 16 | 15.8 | even | 4 | |||
6300.2.d.f.3401.10 | 16 | 5.3 | odd | 4 | |||
6300.2.d.f.3401.11 | 16 | 105.83 | odd | 4 | |||
6300.2.d.f.3401.12 | 16 | 35.13 | even | 4 |