Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [68,2,Mod(9,68)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(68, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("68.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 68 = 2^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 68.h (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.542982733745\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 68.49 |
Dual form | 68.2.h.a.25.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/68\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.707107 | − | 1.70711i | −0.408248 | − | 0.985599i | −0.985599 | − | 0.169102i | \(-0.945913\pi\) |
0.577350 | − | 0.816497i | \(-0.304087\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.70711 | − | 0.707107i | 0.763441 | − | 0.316228i | 0.0332288 | − | 0.999448i | \(-0.489421\pi\) |
0.730213 | + | 0.683220i | \(0.239421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.292893i | −0.267261 | − | 0.110703i | 0.245029 | − | 0.969516i | \(-0.421203\pi\) |
−0.512290 | + | 0.858813i | \(0.671203\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.292893 | + | 0.292893i | −0.0976311 | + | 0.0976311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.29289 | + | 3.12132i | −0.389822 | + | 0.941113i | 0.600155 | + | 0.799884i | \(0.295106\pi\) |
−0.989977 | + | 0.141230i | \(0.954894\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.82843i | 1.89386i | 0.321433 | + | 0.946932i | \(0.395836\pi\) | ||||
−0.321433 | + | 0.946932i | \(0.604164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | − | 2.41421i | −0.623347 | − | 0.623347i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | − | 2.82843i | −0.727607 | − | 0.685994i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.82843 | + | 1.82843i | 0.419470 | + | 0.419470i | 0.885021 | − | 0.465551i | \(-0.154144\pi\) |
−0.465551 | + | 0.885021i | \(0.654144\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421i | 0.308607i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.70711 | − | 6.53553i | 0.564471 | − | 1.36275i | −0.341687 | − | 0.939814i | \(-0.610998\pi\) |
0.906158 | − | 0.422939i | \(-0.139002\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.12132 | + | 1.12132i | −0.224264 | + | 0.224264i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.41421 | − | 1.82843i | −0.849516 | − | 0.351881i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.70711 | − | 1.53553i | 0.688392 | − | 0.285141i | −0.0109378 | − | 0.999940i | \(-0.503482\pi\) |
0.699330 | + | 0.714799i | \(0.253482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.46447 | + | 5.94975i | 0.442631 | + | 1.06861i | 0.975022 | + | 0.222108i | \(0.0712936\pi\) |
−0.532391 | + | 0.846499i | \(0.678706\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.24264 | 1.08670 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | −0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.53553 | − | 6.12132i | −0.416839 | − | 1.00634i | −0.983258 | − | 0.182221i | \(-0.941671\pi\) |
0.566418 | − | 0.824118i | \(-0.308329\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.6569 | − | 4.82843i | 1.86659 | − | 0.773167i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.12132 | − | 0.464466i | −0.175121 | − | 0.0725374i | 0.293400 | − | 0.955990i | \(-0.405213\pi\) |
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | + | 3.00000i | −0.457496 | + | 0.457496i | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.440337 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.292893 | + | 0.707107i | −0.0436619 | + | 0.105409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 3.65685i | − | 0.533407i | −0.963779 | − | 0.266704i | \(-0.914066\pi\) | ||
0.963779 | − | 0.266704i | \(-0.0859344\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.53553 | − | 4.53553i | −0.647933 | − | 0.647933i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.70711 | + | 7.12132i | −0.379071 | + | 0.997184i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.17157 | − | 4.17157i | −0.573010 | − | 0.573010i | 0.359959 | − | 0.932968i | \(-0.382791\pi\) |
−0.932968 | + | 0.359959i | \(0.882791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.24264i | 0.841757i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.82843 | − | 4.41421i | 0.242181 | − | 0.584677i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.82843 | + | 9.82843i | −1.27955 | + | 1.27955i | −0.338634 | + | 0.940918i | \(0.609965\pi\) |
−0.940918 | + | 0.338634i | \(0.890035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70711 | + | 0.707107i | 0.218573 | + | 0.0905357i | 0.489283 | − | 0.872125i | \(-0.337259\pi\) |
−0.270710 | + | 0.962661i | \(0.587259\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.292893 | − | 0.121320i | 0.0369011 | − | 0.0152849i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.82843 | + | 11.6569i | 0.598893 | + | 1.44585i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3137 | 1.38219 | 0.691095 | − | 0.722764i | \(-0.257129\pi\) | ||||
0.691095 | + | 0.722764i | \(0.257129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.0711 | −1.57357 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.464466 | + | 1.12132i | 0.0551220 | + | 0.133076i | 0.949041 | − | 0.315152i | \(-0.102055\pi\) |
−0.893919 | + | 0.448228i | \(0.852055\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.94975 | + | 3.29289i | −0.930448 | + | 0.385404i | −0.795848 | − | 0.605496i | \(-0.792975\pi\) |
−0.134599 | + | 0.990900i | \(0.542975\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.70711 | + | 1.12132i | 0.312590 | + | 0.129479i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.82843 | − | 1.82843i | 0.208369 | − | 0.208369i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.36396 | − | 10.5355i | 0.490984 | − | 1.18534i | −0.463236 | − | 0.886235i | \(-0.653312\pi\) |
0.954220 | − | 0.299105i | \(-0.0966882\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.0711i | 1.11901i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.171573 | + | 0.171573i | 0.0188326 | + | 0.0188326i | 0.716460 | − | 0.697628i | \(-0.245761\pi\) |
−0.697628 | + | 0.716460i | \(0.745761\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.12132 | − | 2.70711i | −0.772416 | − | 0.293627i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.24264 | − | 5.24264i | −0.562070 | − | 0.562070i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 10.8284i | − | 1.14781i | −0.818922 | − | 0.573905i | \(-0.805428\pi\) | ||
0.818922 | − | 0.573905i | \(-0.194572\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | − | 4.82843i | 0.209657 | − | 0.506157i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.41421 | − | 8.41421i | 0.872513 | − | 0.872513i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.41421 | + | 1.82843i | 0.452889 | + | 0.187593i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.878680 | − | 0.363961i | 0.0892164 | − | 0.0369546i | −0.337629 | − | 0.941279i | \(-0.609625\pi\) |
0.426845 | + | 0.904325i | \(0.359625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.535534 | − | 1.29289i | −0.0538232 | − | 0.129941i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.8284 | 1.27648 | 0.638238 | − | 0.769839i | \(-0.279664\pi\) | ||||
0.638238 | + | 0.769839i | \(0.279664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | + | 2.41421i | 0.0975900 | + | 0.235603i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.53553 | − | 1.46447i | 0.341793 | − | 0.141575i | −0.205183 | − | 0.978724i | \(-0.565779\pi\) |
0.546976 | + | 0.837148i | \(0.315779\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.53553 | + | 1.87868i | 0.434425 | + | 0.179945i | 0.589169 | − | 0.808010i | \(-0.299455\pi\) |
−0.154744 | + | 0.987955i | \(0.549455\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.65685 | + | 8.65685i | −0.821672 | + | 0.821672i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.535534 | + | 1.29289i | −0.0503788 | + | 0.121625i | −0.947065 | − | 0.321041i | \(-0.895967\pi\) |
0.896687 | + | 0.442666i | \(0.145967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.0711i | − | 1.21888i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | − | 2.00000i | −0.184900 | − | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.29289 | + | 2.87868i | 0.118519 | + | 0.263888i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.292893 | − | 0.292893i | −0.0266267 | − | 0.0266267i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.24264i | 0.202212i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.65685 | + | 11.2426i | −0.416522 | + | 1.00557i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.171573 | + | 0.171573i | −0.0152246 | + | 0.0152246i | −0.714678 | − | 0.699453i | \(-0.753427\pi\) |
0.699453 | + | 0.714678i | \(0.253427\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.24264 | + | 3.00000i | 0.637679 | + | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.1213 | + | 4.19239i | −0.884304 | + | 0.366291i | −0.778164 | − | 0.628061i | \(-0.783849\pi\) |
−0.106139 | + | 0.994351i | \(0.533849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.757359 | − | 1.82843i | −0.0656714 | − | 0.158545i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.82843 | −0.759830 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.1421 | 1.03737 | 0.518686 | − | 0.854965i | \(-0.326421\pi\) | ||||
0.518686 | + | 0.854965i | \(0.326421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.70711 | − | 16.1924i | −0.568889 | − | 1.37342i | −0.902492 | − | 0.430707i | \(-0.858264\pi\) |
0.333603 | − | 0.942714i | \(-0.391736\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24264 | + | 2.58579i | −0.525725 | + | 0.217763i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.3137 | − | 8.82843i | −1.78234 | − | 0.738270i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.24264 | − | 5.24264i | 0.435378 | − | 0.435378i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.53553 | + | 10.9497i | −0.374085 | + | 0.903120i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.65685i | 0.791120i | 0.918440 | + | 0.395560i | \(0.129450\pi\) | ||||
−0.918440 | + | 0.395560i | \(0.870550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3137 | + | 10.3137i | 0.839318 | + | 0.839318i | 0.988769 | − | 0.149451i | \(-0.0477507\pi\) |
−0.149451 | + | 0.988769i | \(0.547751\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.70711 | − | 0.0502525i | 0.138011 | − | 0.00406268i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.41421 | + | 8.41421i | 0.675846 | + | 0.675846i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.34315i | 0.187003i | 0.995619 | + | 0.0935017i | \(0.0298061\pi\) | ||||
−0.995619 | + | 0.0935017i | \(0.970194\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.17157 | + | 10.0711i | −0.330827 | + | 0.798688i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.82843 | + | 3.82843i | −0.301722 | + | 0.301722i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.70711 | − | 2.77817i | −0.525341 | − | 0.217603i | 0.104220 | − | 0.994554i | \(-0.466765\pi\) |
−0.629561 | + | 0.776951i | \(0.716765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.6569 | − | 4.41421i | 0.829635 | − | 0.343646i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.70711 | − | 11.3640i | −0.364247 | − | 0.879370i | −0.994669 | − | 0.103117i | \(-0.967118\pi\) |
0.630422 | − | 0.776252i | \(-0.282882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −33.6274 | −2.58672 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.07107 | −0.0819066 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.60660 | + | 23.1924i | 0.730376 | + | 1.76328i | 0.641341 | + | 0.767256i | \(0.278379\pi\) |
0.0890357 | + | 0.996028i | \(0.471621\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.12132 | − | 0.464466i | 0.0847639 | − | 0.0351103i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.7279 | + | 9.82843i | 1.78350 | + | 0.738750i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.0000 | − | 13.0000i | 0.971666 | − | 0.971666i | −0.0279439 | − | 0.999609i | \(-0.508896\pi\) |
0.999609 | + | 0.0279439i | \(0.00889597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.46447 | − | 3.53553i | 0.108853 | − | 0.262794i | −0.860061 | − | 0.510190i | \(-0.829575\pi\) |
0.968914 | + | 0.247396i | \(0.0795749\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.41421i | − | 0.252386i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.65685 | − | 8.65685i | −0.636465 | − | 0.636465i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.7071 | − | 5.70711i | 0.929236 | − | 0.417345i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.58579 | + | 2.58579i | 0.188088 | + | 0.188088i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.343146i | 0.0248292i | 0.999923 | + | 0.0124146i | \(0.00395178\pi\) | ||||
−0.999923 | + | 0.0124146i | \(0.996048\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.94975 | − | 14.3640i | 0.428272 | − | 1.03394i | −0.551563 | − | 0.834133i | \(-0.685968\pi\) |
0.979835 | − | 0.199807i | \(-0.0640316\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 16.4853 | − | 16.4853i | 1.18054 | − | 1.18054i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.6066 | − | 4.80761i | −0.826936 | − | 0.342528i | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) |
−0.755689 | + | 0.654931i | \(0.772698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.53553 | − | 0.636039i | 0.108851 | − | 0.0450876i | −0.327593 | − | 0.944819i | \(-0.606238\pi\) |
0.436444 | + | 0.899731i | \(0.356238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | − | 19.3137i | −0.564276 | − | 1.36228i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.07107 | −0.215547 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.24264 | −0.156633 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.12132 | + | 2.70711i | 0.0779372 | + | 0.188157i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.07107 | + | 3.34315i | −0.558287 | + | 0.231250i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.87868 | − | 0.778175i | −0.129334 | − | 0.0535717i | 0.317078 | − | 0.948399i | \(-0.397298\pi\) |
−0.446412 | + | 0.894828i | \(0.647298\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.58579 | − | 1.58579i | 0.108656 | − | 0.108656i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | + | 7.24264i | −0.204598 | + | 0.493944i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.92893i | − | 0.334598i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.2426 | + | 11.2426i | 0.759707 | + | 0.759707i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.3137 | − | 20.4853i | 1.29918 | − | 1.37799i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1716 | + | 12.1716i | 0.815069 | + | 0.815069i | 0.985389 | − | 0.170320i | \(-0.0544801\pi\) |
−0.170320 | + | 0.985389i | \(0.554480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 0.656854i | − | 0.0437903i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.43503 | + | 17.9497i | −0.493480 | + | 1.19137i | 0.459457 | + | 0.888200i | \(0.348044\pi\) |
−0.952938 | + | 0.303167i | \(0.901956\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.65685 | + | 2.65685i | −0.175570 | + | 0.175570i | −0.789421 | − | 0.613852i | \(-0.789619\pi\) |
0.613852 | + | 0.789421i | \(0.289619\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.41421 | − | 1.82843i | −0.290434 | − | 0.120302i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.29289 | + | 3.43503i | −0.543285 | + | 0.225036i | −0.637411 | − | 0.770524i | \(-0.719995\pi\) |
0.0941253 | + | 0.995560i | \(0.469995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.58579 | − | 6.24264i | −0.168678 | − | 0.407225i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.0711 | −1.36871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.6274 | 1.46365 | 0.731823 | − | 0.681495i | \(-0.238670\pi\) | ||||
0.731823 | + | 0.681495i | \(0.238670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.60660 | + | 18.3640i | 0.489984 | + | 1.18293i | 0.954728 | + | 0.297481i | \(0.0961466\pi\) |
−0.464743 | + | 0.885445i | \(0.653853\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94975 | − | 1.63604i | 0.253376 | − | 0.104952i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.9497 | − | 4.53553i | −0.699554 | − | 0.289765i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.4853 | + | 12.4853i | −0.794419 | + | 0.794419i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.171573 | − | 0.414214i | 0.0108730 | − | 0.0262497i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 22.9706i | − | 1.44989i | −0.688807 | − | 0.724945i | \(-0.741865\pi\) | ||
0.688807 | − | 0.724945i | \(-0.258135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.8995 | + | 16.8995i | 1.06246 | + | 1.06246i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.414214 | + | 14.0711i | 0.0259391 | + | 0.881164i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.65685 | − | 2.65685i | −0.165730 | − | 0.165730i | 0.619370 | − | 0.785100i | \(-0.287388\pi\) |
−0.785100 | + | 0.619370i | \(0.787388\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.07107i | 0.315101i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.636039 | + | 1.53553i | −0.0393698 | + | 0.0950472i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.34315 | + | 9.34315i | −0.576123 | + | 0.576123i | −0.933833 | − | 0.357710i | \(-0.883558\pi\) |
0.357710 | + | 0.933833i | \(0.383558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.0711 | − | 4.17157i | −0.618661 | − | 0.256258i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.4853 | + | 7.65685i | −1.13128 | + | 0.468592i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.22183 | − | 7.77817i | −0.196438 | − | 0.474244i | 0.794712 | − | 0.606986i | \(-0.207622\pi\) |
−0.991151 | + | 0.132742i | \(0.957622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.3137 | −0.687259 | −0.343629 | − | 0.939105i | \(-0.611656\pi\) | ||||
−0.343629 | + | 0.939105i | \(0.611656\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.65685 | −0.584459 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.05025 | − | 4.94975i | −0.123635 | − | 0.298481i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.9497 | + | 5.77817i | −0.838159 | + | 0.347177i | −0.760127 | − | 0.649774i | \(-0.774864\pi\) |
−0.0780317 | + | 0.996951i | \(0.524864\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.46447 | − | 1.02082i | −0.147544 | − | 0.0611146i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.6569 | − | 10.6569i | 0.635735 | − | 0.635735i | −0.313766 | − | 0.949500i | \(-0.601591\pi\) |
0.949500 | + | 0.313766i | \(0.101591\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.70711 | − | 6.53553i | 0.160921 | − | 0.388497i | −0.822768 | − | 0.568378i | \(-0.807571\pi\) |
0.983688 | + | 0.179881i | \(0.0575712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 8.82843i | − | 0.522951i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.656854 | + | 0.656854i | 0.0387729 | + | 0.0387729i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | + | 16.9706i | 0.0588235 | + | 0.998268i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.24264 | − | 1.24264i | −0.0728449 | − | 0.0728449i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.00000i | − | 0.467365i | −0.972313 | − | 0.233682i | \(-0.924922\pi\) | ||
0.972313 | − | 0.233682i | \(-0.0750776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.82843 | + | 23.7279i | −0.572233 | + | 1.38149i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.4142 | − | 11.4142i | 0.662320 | − | 0.662320i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 44.6274 | + | 18.4853i | 2.58087 | + | 1.06903i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.00000 | − | 1.24264i | 0.172917 | − | 0.0716246i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.07107 | − | 21.8995i | −0.521119 | − | 1.25809i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.41421 | 0.195497 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.34315 | 0.362022 | 0.181011 | − | 0.983481i | \(-0.442063\pi\) | ||||
0.181011 | + | 0.983481i | \(0.442063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.82843 | − | 6.82843i | −0.160904 | − | 0.388456i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7782 | + | 4.87868i | −0.667879 | + | 0.276645i | −0.690750 | − | 0.723094i | \(-0.742719\pi\) |
0.0228708 | + | 0.999738i | \(0.492719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.0208 | + | 8.70711i | 1.18817 | + | 0.492155i | 0.887158 | − | 0.461466i | \(-0.152677\pi\) |
0.301009 | + | 0.953621i | \(0.402677\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.414214 | − | 0.414214i | 0.0233383 | − | 0.0233383i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.150758 | − | 0.363961i | 0.00846739 | − | 0.0204421i | −0.919589 | − | 0.392881i | \(-0.871478\pi\) |
0.928057 | + | 0.372439i | \(0.121478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5563i | 0.759010i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.00000 | − | 5.00000i | −0.279073 | − | 0.279073i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.313708 | − | 10.6569i | −0.0174552 | − | 0.592963i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.65685 | − | 7.65685i | −0.424726 | − | 0.424726i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.07107i | − | 0.501631i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.07107 | + | 2.58579i | −0.0590499 | + | 0.142559i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3137 | − | 20.3137i | 1.11654 | − | 1.11654i | 0.124297 | − | 0.992245i | \(-0.460332\pi\) |
0.992245 | − | 0.124297i | \(-0.0396677\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.53553 | + | 1.05025i | 0.138946 | + | 0.0575535i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.3137 | − | 8.00000i | 1.05522 | − | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.94975 | + | 24.0208i | 0.541997 | + | 1.30850i | 0.923312 | + | 0.384052i | \(0.125472\pi\) |
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.58579 | 0.140441 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.7574 | −1.17823 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.92893 | + | 9.48528i | 0.212142 | + | 0.512157i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.3137 | + | 9.24264i | −1.20133 | + | 0.497607i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.19239 | − | 2.97918i | −0.386108 | − | 0.159931i | 0.181182 | − | 0.983450i | \(-0.442008\pi\) |
−0.567289 | + | 0.823519i | \(0.692008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.8284 | − | 19.8284i | 1.06139 | − | 1.06139i | 0.0634034 | − | 0.997988i | \(-0.479805\pi\) |
0.997988 | − | 0.0634034i | \(-0.0201955\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.4853 | − | 30.1421i | 0.666415 | − | 1.60887i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 15.3137i | − | 0.815066i | −0.913190 | − | 0.407533i | \(-0.866389\pi\) | ||
0.913190 | − | 0.407533i | \(-0.133611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.58579 | + | 1.58579i | 0.0841648 | + | 0.0841648i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00000 | − | 4.24264i | 0.211702 | − | 0.224544i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.4853 | − | 21.4853i | −1.13395 | − | 1.13395i | −0.989514 | − | 0.144436i | \(-0.953863\pi\) |
−0.144436 | − | 0.989514i | \(-0.546137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 12.3137i | − | 0.648090i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.292893 | + | 0.707107i | −0.0153729 | + | 0.0371135i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.2426 | + | 11.2426i | −0.588467 | + | 0.588467i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.53553 | − | 1.46447i | −0.184553 | − | 0.0764445i | 0.288493 | − | 0.957482i | \(-0.406846\pi\) |
−0.473047 | + | 0.881037i | \(0.656846\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.464466 | − | 0.192388i | 0.0241791 | − | 0.0100153i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.72792 | + | 4.17157i | 0.0897092 | + | 0.216577i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.4853 | 0.957132 | 0.478566 | − | 0.878052i | \(-0.341157\pi\) | ||||
0.478566 | + | 0.878052i | \(0.341157\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 22.4853 | 1.16113 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4853 | + | 25.3137i | 0.540019 | + | 1.30372i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1213 | + | 4.19239i | −0.519897 | + | 0.215349i | −0.627172 | − | 0.778881i | \(-0.715788\pi\) |
0.107275 | + | 0.994229i | \(0.465788\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.414214 | + | 0.171573i | 0.0212208 | + | 0.00878994i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.3137 | + | 18.3137i | −0.935787 | + | 0.935787i | −0.998059 | − | 0.0622724i | \(-0.980165\pi\) |
0.0622724 | + | 0.998059i | \(0.480165\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.82843 | − | 4.41421i | 0.0931853 | − | 0.224969i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 1.75736i | − | 0.0893316i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.48528 | − | 1.48528i | −0.0753068 | − | 0.0753068i | 0.668450 | − | 0.743757i | \(-0.266958\pi\) |
−0.743757 | + | 0.668450i | \(0.766958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.6066 | + | 11.9497i | −1.34555 | + | 0.604325i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.3137 | + | 14.3137i | 0.722031 | + | 0.722031i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 21.0711i | − | 1.06020i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.22183 | + | 17.4350i | −0.362453 | + | 0.875039i | 0.632487 | + | 0.774571i | \(0.282034\pi\) |
−0.994940 | + | 0.100468i | \(0.967966\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.58579 | + | 2.58579i | −0.129451 | + | 0.129451i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.53553 | + | 3.53553i | 0.426244 | + | 0.176556i | 0.585484 | − | 0.810684i | \(-0.300904\pi\) |
−0.159240 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.6274 | + | 16.8284i | −2.02380 | + | 0.838284i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.12132 | + | 17.1924i | 0.353861 | + | 0.854297i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.3848 | 1.10957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.6569 | −0.576394 | −0.288197 | − | 0.957571i | \(-0.593056\pi\) | ||||
−0.288197 | + | 0.957571i | \(0.593056\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.58579 | − | 20.7279i | −0.423506 | − | 1.02243i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.82843 | − | 4.07107i | 0.483625 | − | 0.200324i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.414214 | + | 0.171573i | 0.0203329 | + | 0.00842218i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.8995 | + | 22.8995i | −1.12139 | + | 1.12139i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.6360 | + | 32.9203i | −0.666164 | + | 1.60826i | 0.121810 | + | 0.992553i | \(0.461130\pi\) |
−0.787974 | + | 0.615709i | \(0.788870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.17157i | 0.0570990i | 0.999592 | + | 0.0285495i | \(0.00908882\pi\) | ||||
−0.999592 | + | 0.0285495i | \(0.990911\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.07107 | + | 1.07107i | 0.0520771 | + | 0.0520771i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.53553 | − | 0.192388i | 0.317020 | − | 0.00933220i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.00000 | − | 1.00000i | −0.0483934 | − | 0.0483934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 42.6274i | 2.05807i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.87868 | − | 19.0208i | 0.379503 | − | 0.916200i | −0.612556 | − | 0.790427i | \(-0.709859\pi\) |
0.992059 | − | 0.125774i | \(-0.0401413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.82843 | − | 5.82843i | 0.280096 | − | 0.280096i | −0.553051 | − | 0.833147i | \(-0.686537\pi\) |
0.833147 | + | 0.553051i | \(0.186537\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6569 | − | 5.24264i | −0.606850 | − | 0.251365i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.8995 | − | 7.00000i | 0.808412 | − | 0.334855i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.67767 | − | 13.7071i | −0.270980 | − | 0.654205i | 0.728545 | − | 0.684998i | \(-0.240197\pi\) |
−0.999526 | + | 0.0307930i | \(0.990197\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.65685 | 0.126517 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.6569 | −1.02895 | −0.514474 | − | 0.857506i | \(-0.672013\pi\) | ||||
−0.514474 | + | 0.857506i | \(0.672013\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.65685 | − | 18.4853i | −0.362970 | − | 0.876286i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.4853 | − | 6.82843i | 0.779727 | − | 0.322974i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.6066 | − | 8.12132i | −0.925293 | − | 0.383269i | −0.131402 | − | 0.991329i | \(-0.541948\pi\) |
−0.793891 | + | 0.608060i | \(0.791948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.89949 | − | 2.89949i | 0.136532 | − | 0.136532i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.3137 | − | 24.8995i | 0.484580 | − | 1.16988i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9.65685i | − | 0.452720i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00000 | + | 3.00000i | 0.140334 | + | 0.140334i | 0.773784 | − | 0.633450i | \(-0.218362\pi\) |
−0.633450 | + | 0.773784i | \(0.718362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.07107 | + | 17.9706i | 0.376725 | + | 0.838794i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.48528 | + | 5.48528i | 0.255475 | + | 0.255475i | 0.823211 | − | 0.567736i | \(-0.192180\pi\) |
−0.567736 | + | 0.823211i | \(0.692180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.65685i | 0.355844i | 0.984045 | + | 0.177922i | \(0.0569375\pi\) | ||||
−0.984045 | + | 0.177922i | \(0.943062\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.41421 | − | 20.3137i | 0.390200 | − | 0.942026i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.9706 | + | 19.9706i | −0.924127 | + | 0.924127i | −0.997318 | − | 0.0731905i | \(-0.976682\pi\) |
0.0731905 | + | 0.997318i | \(0.476682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | − | 3.31371i | −0.369406 | − | 0.153013i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.00000 | − | 1.65685i | 0.184310 | − | 0.0763438i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.48528 | − | 13.2426i | −0.252214 | − | 0.608897i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.10051 | −0.188144 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.44365 | 0.111887 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.15076 | + | 7.60660i | 0.143962 | + | 0.347555i | 0.979370 | − | 0.202076i | \(-0.0647687\pi\) |
−0.835408 | + | 0.549630i | \(0.814769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 41.7990 | − | 17.3137i | 1.90587 | − | 0.789437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.24264 | + | 3.82843i | 0.420555 | + | 0.174199i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.24264 | − | 1.24264i | 0.0564254 | − | 0.0564254i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.39340 | − | 3.36396i | 0.0631409 | − | 0.152436i | −0.889160 | − | 0.457597i | \(-0.848710\pi\) |
0.952301 | + | 0.305161i | \(0.0987103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4142i | 0.606612i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.7990 | − | 16.7990i | −0.758128 | − | 0.758128i | 0.217854 | − | 0.975981i | \(-0.430094\pi\) |
−0.975981 | + | 0.217854i | \(0.930094\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.4645 | − | 5.87868i | −0.696485 | − | 0.264762i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.82843 | − | 1.82843i | −0.0821817 | − | 0.0821817i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.928932i | − | 0.0416683i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.3640 | − | 34.6777i | 0.643019 | − | 1.55239i | −0.179567 | − | 0.983746i | \(-0.557470\pi\) |
0.822587 | − | 0.568640i | \(-0.192530\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.0711 | + | 16.0711i | −0.718002 | + | 0.718002i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.29289 | + | 3.02082i | 0.325174 | + | 0.134691i | 0.539298 | − | 0.842115i | \(-0.318690\pi\) |
−0.214124 | + | 0.976806i | \(0.568690\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.8995 | − | 9.07107i | 0.974515 | − | 0.403657i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.7782 | + | 57.4056i | 1.05603 | + | 2.54947i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.68629 | 0.296365 | 0.148182 | − | 0.988960i | \(-0.452658\pi\) | ||||
0.148182 | + | 0.988960i | \(0.452658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.58579 | 0.291338 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.72792 | − | 11.4142i | −0.208743 | − | 0.503950i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.82843 | − | 2.82843i | 0.300896 | − | 0.124635i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4142 | + | 4.72792i | 0.501997 | + | 0.207934i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.7990 | − | 32.7990i | 1.43972 | − | 1.43972i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5355 | + | 25.4350i | −0.461570 | + | 1.11433i | 0.506183 | + | 0.862426i | \(0.331056\pi\) |
−0.967753 | + | 0.251902i | \(0.918944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.0000i | 1.48672i | 0.668894 | + | 0.743358i | \(0.266768\pi\) | ||||
−0.668894 | + | 0.743358i | \(0.733232\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.58579 | − | 1.58579i | −0.0692094 | − | 0.0692094i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.43503 | − | 24.8198i | 0.410996 | − | 1.08117i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.1213 | − | 19.1213i | −0.831362 | − | 0.831362i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.75736i | − | 0.249848i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.17157 | − | 7.65685i | 0.137376 | − | 0.331655i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.00000 | − | 5.00000i | 0.216169 | − | 0.216169i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.3848 | − | 13.0000i | −1.35435 | − | 0.560991i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.0208 | − | 8.29289i | 0.862358 | − | 0.357200i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.02082 | − | 7.29289i | −0.129875 | − | 0.313546i | 0.845543 | − | 0.533907i | \(-0.179277\pi\) |
−0.975418 | + | 0.220361i | \(0.929277\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.07107 | −0.303449 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.07107 | 0.388562 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.39340 | − | 22.6777i | −0.401633 | − | 0.969627i | −0.987270 | − | 0.159054i | \(-0.949156\pi\) |
0.585637 | − | 0.810573i | \(-0.300844\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.707107 | + | 0.292893i | −0.0301786 | + | 0.0125004i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.58579 | + | 3.97056i | 0.408368 | + | 0.169152i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.17157 | + | 6.17157i | −0.262442 | + | 0.262442i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.65685 | + | 20.8995i | −0.367463 | + | 0.887134i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.8284i | 0.967272i | 0.875269 | + | 0.483636i | \(0.160684\pi\) | ||||
−0.875269 | + | 0.483636i | \(0.839316\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.4853 | − | 20.4853i | −0.866435 | − | 0.866435i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.7279 | − | 17.6569i | −0.790693 | − | 0.745473i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.2843 | + | 27.2843i | 1.14989 | + | 1.14989i | 0.986573 | + | 0.163322i | \(0.0522210\pi\) |
0.163322 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.58579i | 0.108785i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.94975 | − | 7.12132i | 0.123878 | − | 0.299067i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.4853 | + | 19.4853i | −0.816865 | + | 0.816865i | −0.985653 | − | 0.168787i | \(-0.946015\pi\) |
0.168787 | + | 0.985653i | \(0.446015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.5355 | − | 9.74874i | −0.984931 | − | 0.407972i | −0.168681 | − | 0.985671i | \(-0.553951\pi\) |
−0.816250 | + | 0.577699i | \(0.803951\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.585786 | − | 0.242641i | 0.0244716 | − | 0.0101365i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.29289 | + | 10.3640i | 0.179026 | + | 0.432207i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.79899 | 0.0748929 | 0.0374465 | − | 0.999299i | \(-0.488078\pi\) | ||||
0.0374465 | + | 0.999299i | \(0.488078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.7279 | −1.19389 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0710678 | − | 0.171573i | −0.00294839 | − | 0.00711804i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.4142 | − | 7.62742i | 0.762639 | − | 0.315895i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.82843 | − | 2.00000i | −0.199631 | − | 0.0826898i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.6569 | + | 20.6569i | −0.852600 | + | 0.852600i | −0.990453 | − | 0.137853i | \(-0.955980\pi\) |
0.137853 | + | 0.990453i | \(0.455980\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.37258 | + | 15.3848i | −0.262578 | + | 0.633919i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.2132i | 0.954864i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.4853 | − | 23.4853i | −0.964425 | − | 0.964425i | 0.0349637 | − | 0.999389i | \(-0.488868\pi\) |
−0.999389 | + | 0.0349637i | \(0.988868\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.24264 | + | 4.00000i | 0.173931 | + | 0.163984i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.17157 | − | 2.17157i | −0.0888766 | − | 0.0888766i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.3137i | 1.52460i | 0.647226 | + | 0.762298i | \(0.275929\pi\) | ||||
−0.647226 | + | 0.762298i | \(0.724071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.94975 | − | 4.70711i | 0.0795319 | − | 0.192007i | −0.879112 | − | 0.476615i | \(-0.841864\pi\) |
0.958644 | + | 0.284608i | \(0.0918635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.31371 | + | 3.31371i | −0.134945 | + | 0.134945i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.707107 | − | 0.292893i | −0.0287480 | − | 0.0119078i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7071 | − | 6.09188i | 0.596943 | − | 0.247262i | −0.0636914 | − | 0.997970i | \(-0.520287\pi\) |
0.660634 | + | 0.750708i | \(0.270287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.17157 | + | 5.24264i | 0.0879966 | + | 0.212443i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.9706 | 1.01020 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.343146 | 0.0138595 | 0.00692976 | − | 0.999976i | \(-0.497794\pi\) | ||||
0.00692976 | + | 0.999976i | \(0.497794\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.58579 | + | 3.82843i | 0.0639451 | + | 0.154377i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.5061 | − | 13.0503i | 1.26839 | − | 0.525383i | 0.355914 | − | 0.934519i | \(-0.384170\pi\) |
0.912474 | + | 0.409135i | \(0.134170\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.3640 | − | 5.12132i | −0.496950 | − | 0.205843i | 0.120109 | − | 0.992761i | \(-0.461676\pi\) |
−0.617058 | + | 0.786918i | \(0.711676\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.8995 | + | 23.8995i | −0.959054 | + | 0.959054i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.17157 | + | 7.65685i | −0.127066 | + | 0.306765i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5563i | 0.582254i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.4142 | + | 11.4142i | 0.455840 | + | 0.455840i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.70711 | + | 25.5355i | −0.387048 | + | 1.01817i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.3137 | + | 10.3137i | 0.410582 | + | 0.410582i | 0.881941 | − | 0.471359i | \(-0.156236\pi\) |
−0.471359 | + | 0.881941i | \(0.656236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.75736i | 0.149342i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.171573 | + | 0.414214i | −0.00680866 | + | 0.0164376i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.9706 | − | 30.9706i | 1.22710 | − | 1.22710i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.464466 | − | 0.192388i | −0.0183740 | − | 0.00761076i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.9203 | + | 17.7782i | −1.69525 | + | 0.702196i | −0.999865 | − | 0.0164412i | \(-0.994766\pi\) |
−0.695385 | + | 0.718637i | \(0.744766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.12132 | + | 5.12132i | 0.0836567 | + | 0.201965i | 0.960172 | − | 0.279408i | \(-0.0901382\pi\) |
−0.876516 | + | 0.481373i | \(0.840138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.4853 | 0.570357 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.9706 | 1.29621 | 0.648103 | − | 0.761552i | \(-0.275563\pi\) | ||||
0.648103 | + | 0.761552i | \(0.275563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.9706 | − | 43.3848i | −0.705406 | − | 1.70300i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.41421 | + | 3.48528i | −0.329779 | + | 0.136599i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.7487 | − | 17.2929i | −1.63375 | − | 0.676723i | −0.638109 | − | 0.769946i | \(-0.720283\pi\) |
−0.995645 | + | 0.0932228i | \(0.970283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.3137 | + | 14.3137i | −0.559283 | + | 0.559283i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.36396 | − | 3.29289i | 0.0532132 | − | 0.128468i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.68629i | 0.104643i | 0.998630 | + | 0.0523215i | \(0.0166621\pi\) | ||||
−0.998630 | + | 0.0523215i | \(0.983338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.00000 | + | 9.00000i | 0.350059 | + | 0.350059i | 0.860132 | − | 0.510072i | \(-0.170381\pi\) |
−0.510072 | + | 0.860132i | \(0.670381\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48.6274 | − | 18.4853i | −1.88853 | − | 0.717909i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.58579 | − | 2.58579i | −0.100272 | − | 0.100272i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 28.3848i | − | 1.09906i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.1716 | − | 29.3848i | 0.470580 | − | 1.13608i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.41421 | + | 4.41421i | −0.170409 | + | 0.170409i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6777 | + | 11.8787i | 1.10544 | + | 0.457889i | 0.859366 | − | 0.511361i | \(-0.170858\pi\) |
0.246077 | + | 0.969250i | \(0.420858\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.00000 | − | 2.89949i | 0.269430 | − | 0.111602i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.636039 | + | 1.53553i | 0.0244450 | + | 0.0590154i | 0.935631 | − | 0.352981i | \(-0.114832\pi\) |
−0.911186 | + | 0.411996i | \(0.864832\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.727922 | −0.0279351 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35.8995 | 1.37567 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.63604 | + | 3.94975i | 0.0626013 | + | 0.151133i | 0.952085 | − | 0.305835i | \(-0.0989355\pi\) |
−0.889483 | + | 0.456968i | \(0.848936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7279 | − | 8.58579i | 0.791973 | − | 0.328046i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.41421 | + | 2.65685i | 0.244718 | + | 0.101365i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.4853 | − | 28.4853i | 1.08520 | − | 1.08520i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.70711 | − | 6.53553i | 0.102983 | − | 0.248623i | −0.863986 | − | 0.503515i | \(-0.832040\pi\) |
0.966970 | + | 0.254892i | \(0.0820398\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.07107i | 0.0406865i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8995 | − | 22.8995i | −0.868627 | − | 0.868627i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.05025 | + | 4.56497i | 0.0776589 | + | 0.172911i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.7279 | + | 11.7279i | 0.443591 | + | 0.443591i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.5147i | − | 0.737061i | −0.929616 | − | 0.368530i | \(-0.879861\pi\) | ||
0.929616 | − | 0.368530i | \(-0.120139\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.55635 | − | 15.8284i | 0.247277 | − | 0.596980i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.82843 | + | 8.82843i | −0.332498 | + | 0.332498i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.07107 | − | 3.75736i | −0.341153 | − | 0.141310i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.12132 | + | 1.29289i | −0.117224 | + | 0.0485556i | −0.440524 | − | 0.897741i | \(-0.645207\pi\) |
0.323301 | + | 0.946296i | \(0.395207\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.80761 | + | 4.36396i | 0.0677907 | + | 0.163661i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.5563 | 1.70610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.6274 | −1.59418 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.0000 | − | 38.6274i | −0.597531 | − | 1.44257i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.8787 | − | 5.74874i | 0.517587 | − | 0.214392i | −0.108569 | − | 0.994089i | \(-0.534627\pi\) |
0.626157 | + | 0.779697i | \(0.284627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.82843 | − | 1.17157i | −0.105336 | − | 0.0436317i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.9706 | − | 25.9706i | 0.965856 | − | 0.965856i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.43503 | + | 5.87868i | −0.0904347 | + | 0.218329i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.6569i | − | 0.729032i | −0.931197 | − | 0.364516i | \(-0.881234\pi\) | ||
0.931197 | − | 0.364516i | \(-0.118766\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7782 | + | 15.7782i | 0.584377 | + | 0.584377i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.4853 | − | 0.514719i | 0.646716 | − | 0.0190376i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.34315 | + | 3.34315i | 0.123482 | + | 0.123482i | 0.766147 | − | 0.642665i | \(-0.222171\pi\) |
−0.642665 | + | 0.766147i | \(0.722171\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.8995i | 0.807775i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.6274 | + | 35.3137i | −0.538808 | + | 1.30080i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.9706 | + | 11.9706i | −0.440344 | + | 0.440344i | −0.892128 | − | 0.451783i | \(-0.850788\pi\) |
0.451783 | + | 0.892128i | \(0.350788\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.1421 | + | 12.4853i | 1.10730 | + | 0.458658i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.0208 | − | 10.7782i | 0.954611 | − | 0.395413i | 0.149649 | − | 0.988739i | \(-0.452186\pi\) |
0.804962 | + | 0.593326i | \(0.202186\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.82843 | + | 16.4853i | 0.250174 | + | 0.603974i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.100505 | −0.00367729 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.92893 | −0.107021 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.6360 | + | 42.5772i | 0.643548 | + | 1.55366i | 0.821860 | + | 0.569689i | \(0.192936\pi\) |
−0.178312 | + | 0.983974i | \(0.557064\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −39.2132 | + | 16.2426i | −1.42901 | + | 0.591915i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.8995 | + | 10.3137i | 0.906185 | + | 0.375354i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.0000 | + | 33.0000i | −1.19941 | + | 1.19941i | −0.225061 | + | 0.974345i | \(0.572258\pi\) |
−0.974345 | + | 0.225061i | \(0.927742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.8995 | − | 40.7990i | 0.613413 | − | 1.48091i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.8579i | 0.647347i | 0.946169 | + | 0.323674i | \(0.104918\pi\) | ||||
−0.946169 | + | 0.323674i | \(0.895082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.65685 | − | 2.65685i | −0.0961846 | − | 0.0961846i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.87868 | − | 1.29289i | 0.104079 | − | 0.0467447i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −67.1127 | − | 67.1127i | −2.42330 | − | 2.42330i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.79899i | 0.136995i | 0.997651 | + | 0.0684975i | \(0.0218205\pi\) | ||||
−0.997651 | + | 0.0684975i | \(0.978179\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.65685 | + | 6.41421i | −0.0956843 | + | 0.231002i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.7990 | − | 14.7990i | 0.532283 | − | 0.532283i | −0.388968 | − | 0.921251i | \(-0.627168\pi\) |
0.921251 | + | 0.388968i | \(0.127168\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.43503 | − | 3.90812i | −0.338916 | − | 0.140384i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.65685 | − | 3.58579i | 0.310563 | − | 0.128639i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.20101 | − | 2.89949i | −0.0430307 | − | 0.103885i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.10051 | −0.146728 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.1716 | −0.685136 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.65685 | + | 4.00000i | 0.0591357 | + | 0.142766i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.6066 | + | 13.5061i | −1.16230 | + | 0.481440i | −0.878640 | − | 0.477485i | \(-0.841549\pi\) |
−0.283660 | + | 0.958925i | \(0.591549\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.5563 | + | 9.34315i | 0.803027 | + | 0.332625i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.757359 | − | 0.757359i | 0.0269286 | − | 0.0269286i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.82843 | + | 11.6569i | −0.171462 | + | 0.413947i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.1421i | 0.714368i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.3137 | − | 34.3137i | −1.21545 | − | 1.21545i | −0.969207 | − | 0.246247i | \(-0.920803\pi\) |
−0.246247 | − | 0.969207i | \(-0.579197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3431 | + | 10.9706i | −0.365914 | + | 0.388111i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.17157 | + | 3.17157i | 0.112062 | + | 0.112062i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 29.0711i | − | 1.02590i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.82843 | + | 9.24264i | −0.134934 | + | 0.325760i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.0000 | + | 11.0000i | −0.387218 | + | 0.387218i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.5061 | + | 11.3934i | 0.967063 | + | 0.400571i | 0.809618 | − | 0.586957i | \(-0.199674\pi\) |
0.157445 | + | 0.987528i | \(0.449674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.0208 | − | 9.12132i | 0.773255 | − | 0.320293i | 0.0390652 | − | 0.999237i | \(-0.487562\pi\) |
0.734190 | + | 0.678944i | \(0.237562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | + | 19.3137i | 0.280572 | + | 0.677361i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.4142 | −0.469879 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.9706 | −0.383811 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.828427 | + | 2.00000i | 0.0289476 | + | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.46447 | + | 2.26346i | −0.190711 | + | 0.0789952i | −0.475995 | − | 0.879448i | \(-0.657912\pi\) |
0.285284 | + | 0.958443i | \(0.407912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.9203 | + | 11.5650i | 0.973241 | + | 0.403130i | 0.811918 | − | 0.583772i | \(-0.198424\pi\) |
0.161323 | + | 0.986902i | \(0.448424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.00000 | + | 7.00000i | −0.243709 | + | 0.243709i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.39340 | − | 3.36396i | 0.0484532 | − | 0.116976i | −0.897800 | − | 0.440404i | \(-0.854835\pi\) |
0.946253 | + | 0.323428i | \(0.104835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 29.6569i | − | 1.03003i | −0.857183 | − | 0.515013i | \(-0.827787\pi\) | ||
0.857183 | − | 0.515013i | \(-0.172213\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.7279 | + | 19.7279i | 0.684354 | + | 0.684354i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.778175 | + | 26.4350i | 0.0269622 | + | 0.915919i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0711 | − | 16.0711i | −0.556162 | − | 0.556162i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 30.7696i | − | 1.06355i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.32233 | + | 5.60660i | −0.0801758 | + | 0.193561i | −0.958884 | − | 0.283797i | \(-0.908406\pi\) |
0.878709 | + | 0.477359i | \(0.158406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.12132 | + | 9.12132i | −0.314528 | + | 0.314528i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.7279 | − | 10.6569i | −0.886117 | − | 0.367042i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −57.4056 | + | 23.7782i | −1.97481 | + | 0.817994i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.121320 | + | 0.292893i | 0.00416862 | + | 0.0100639i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0711 | −0.448598 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −46.8701 | −1.60668 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.29289 | + | 20.0208i | 0.283943 | + | 0.685500i | 0.999920 | − | 0.0126242i | \(-0.00401850\pi\) |
−0.715977 | + | 0.698124i | \(0.754018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.82843 | + | 0.757359i | −0.0625309 | + | 0.0259011i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.9497 | − | 4.94975i | −0.408196 | − | 0.169080i | 0.169131 | − | 0.985594i | \(-0.445904\pi\) |
−0.577326 | + | 0.816513i | \(0.695904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.8284 | − | 11.8284i | 0.403581 | − | 0.403581i | −0.475912 | − | 0.879493i | \(-0.657882\pi\) |
0.879493 | + | 0.475912i | \(0.157882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.656854 | − | 1.58579i | 0.0223855 | − | 0.0540435i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 14.0000i | − | 0.476566i | −0.971196 | − | 0.238283i | \(-0.923415\pi\) | ||
0.971196 | − | 0.238283i | \(-0.0765845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.7990 | + | 32.7990i | 1.11520 | + | 1.11520i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.2635 | − | 13.7071i | 0.959877 | − | 0.465518i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.2426 | + | 27.2426i | 0.924143 | + | 0.924143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 77.2548i | 2.61768i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.150758 | + | 0.363961i | −0.00510237 | + | 0.0123182i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.58579 | − | 6.58579i | 0.222640 | − | 0.222640i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.94975 | − | 3.29289i | −0.268444 | − | 0.111193i | 0.244401 | − | 0.969674i | \(-0.421409\pi\) |
−0.512845 | + | 0.858481i | \(0.671409\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.6569 | + | 5.65685i | −0.460634 | + | 0.190801i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.70711 | − | 8.94975i | −0.124896 | − | 0.301525i | 0.849048 | − | 0.528316i | \(-0.177176\pi\) |
−0.973943 | + | 0.226791i | \(0.927176\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3431 | 0.482685 | 0.241343 | − | 0.970440i | \(-0.422412\pi\) | ||||
0.241343 | + | 0.970440i | \(0.422412\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 47.4558 | 1.59521 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.5772 | + | 32.7782i | 0.455877 | + | 1.10058i | 0.970052 | + | 0.242898i | \(0.0780981\pi\) |
−0.514175 | + | 0.857685i | \(0.671902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.171573 | − | 0.0710678i | 0.00575437 | − | 0.00238354i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.4350 | − | 13.0208i | −1.05311 | − | 0.436214i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.68629 | − | 6.68629i | 0.223748 | − | 0.223748i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.0000 | − | 31.3848i | 0.434542 | − | 1.04908i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 89.2548i | − | 2.98013i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.2721 | + | 18.2721i | 0.609408 | + | 0.609408i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.715729 | + | 24.3137i | 0.0238444 | + | 0.810007i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.24264 | − | 4.24264i | −0.141186 | − | 0.141186i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.07107i | − | 0.235050i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.90812 | − | 7.02082i | 0.0965624 | − | 0.233122i | −0.868216 | − | 0.496187i | \(-0.834733\pi\) |
0.964778 | + | 0.263064i | \(0.0847332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.75736 | + | 3.75736i | −0.124624 | + | 0.124624i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.80761 | + | 1.16295i | 0.0930203 | + | 0.0385303i | 0.428708 | − | 0.903443i | \(-0.358969\pi\) |
−0.335688 | + | 0.941973i | \(0.608969\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.757359 | + | 0.313708i | −0.0250649 | + | 0.0103822i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.41421 | − | 5.82843i | −0.0798114 | − | 0.192682i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.38478 | 0.276890 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3431 | −0.473137 | −0.236568 | − | 0.971615i | \(-0.576023\pi\) | ||||
−0.236568 | + | 0.971615i | \(0.576023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.48528 | − | 10.8284i | −0.147795 | − | 0.356809i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.65685 | + | 3.17157i | −0.252028 | + | 0.104394i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.70711 | + | 4.02082i | 0.319168 | + | 0.132204i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.17157 | + | 1.17157i | −0.0384795 | + | 0.0384795i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.9203 | − | 45.6777i | 0.620755 | − | 1.49864i | −0.230063 | − | 0.973176i | \(-0.573893\pi\) |
0.850818 | − | 0.525460i | \(-0.176107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 16.5858i | − | 0.543577i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.6569 | + | 16.6569i | 0.545321 | + | 0.545321i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.6569 | − | 18.7279i | 0.577441 | − | 0.612469i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5147 | + | 16.5147i | 0.539512 | + | 0.539512i | 0.923386 | − | 0.383873i | \(-0.125410\pi\) |
−0.383873 | + | 0.923386i | \(0.625410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 42.0416i | − | 1.37198i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.636039 | − | 1.53553i | 0.0207343 | − | 0.0500570i | −0.913173 | − | 0.407571i | \(-0.866376\pi\) |
0.933908 | + | 0.357514i | \(0.116376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.07107 | + | 6.07107i | −0.197701 | + | 0.197701i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.24264 | + | 2.58579i | 0.203073 | + | 0.0841156i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.36396 | − | 3.46447i | 0.271792 | − | 0.112580i | −0.242625 | − | 0.970120i | \(-0.578008\pi\) |
0.514417 | + | 0.857540i | \(0.328008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4853 | − | 54.2843i | −0.729903 | − | 1.76214i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.727922 | −0.0236045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.1421 | 0.393322 | 0.196661 | − | 0.980472i | \(-0.436990\pi\) | ||||
0.196661 | + | 0.980472i | \(0.436990\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.242641 | + | 0.585786i | 0.00785167 | + | 0.0189556i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.1421 | − | 9.58579i | 0.748079 | − | 0.309864i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.58579 | − | 3.55635i | −0.277250 | − | 0.114841i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.40559 | + | 7.40559i | −0.238890 | + | 0.238890i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.606602 | + | 1.46447i | −0.0195475 | + | 0.0471918i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 28.7279i | − | 0.924785i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.3431 | − | 23.3431i | −0.750665 | − | 0.750665i | 0.223938 | − | 0.974603i | \(-0.428109\pi\) |
−0.974603 | + | 0.223938i | \(0.928109\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.9706 | + | 8.07107i | −0.577298 | + | 0.259280i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.3137 | + | 26.3137i | 0.844447 | + | 0.844447i | 0.989434 | − | 0.144987i | \(-0.0463139\pi\) |
−0.144987 | + | 0.989434i | \(0.546314\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.4142i | 0.430040i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.65685 | + | 18.4853i | −0.245216 | + | 0.592003i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.1421 | − | 27.1421i | 0.868354 | − | 0.868354i | −0.123936 | − | 0.992290i | \(-0.539552\pi\) |
0.992290 | + | 0.123936i | \(0.0395519\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.7990 | + | 14.0000i | 1.08022 | + | 0.447442i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.87868 | + | 0.778175i | −0.0599816 | + | 0.0248452i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.0503 | − | 36.3345i | −0.480029 | − | 1.15889i | −0.959595 | − | 0.281386i | \(-0.909206\pi\) |
0.479566 | − | 0.877506i | \(-0.340794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.2132 | −0.739634 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.17157 | 0.164613 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4853 | + | 27.7279i | 0.365211 | + | 0.881697i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.9203 | + | 17.3640i | −1.33164 | + | 0.551584i | −0.931123 | − | 0.364704i | \(-0.881170\pi\) |
−0.400519 | + | 0.916288i | \(0.631170\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −49.0416 | − | 20.3137i | −1.55629 | − | 0.644636i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.17157 | − | 2.17157i | 0.0688435 | − | 0.0688435i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.8492 | + | 28.6066i | −0.375269 | + | 0.905980i | 0.617569 | + | 0.786516i | \(0.288118\pi\) |
−0.992839 | + | 0.119464i | \(0.961882\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.6569i | 1.00158i |
(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 | 68.2.h.a.49.1 | yes | 4 | |
3.2 | odd | 2 | 612.2.w.a.253.1 | 4 | |||
4.3 | odd | 2 | 272.2.v.c.49.1 | 4 | |||
17.2 | even | 8 | 1156.2.h.a.757.1 | 4 | |||
17.3 | odd | 16 | 1156.2.b.d.577.1 | 4 | |||
17.4 | even | 4 | 1156.2.h.a.733.1 | 4 | |||
17.5 | odd | 16 | 1156.2.a.g.1.4 | 4 | |||
17.6 | odd | 16 | 1156.2.e.f.829.1 | 8 | |||
17.7 | odd | 16 | 1156.2.e.f.905.1 | 8 | |||
17.8 | even | 8 | inner | 68.2.h.a.25.1 | ✓ | 4 | |
17.9 | even | 8 | 1156.2.h.b.977.1 | 4 | |||
17.10 | odd | 16 | 1156.2.e.f.905.4 | 8 | |||
17.11 | odd | 16 | 1156.2.e.f.829.4 | 8 | |||
17.12 | odd | 16 | 1156.2.a.g.1.1 | 4 | |||
17.13 | even | 4 | 1156.2.h.c.733.1 | 4 | |||
17.14 | odd | 16 | 1156.2.b.d.577.4 | 4 | |||
17.15 | even | 8 | 1156.2.h.c.757.1 | 4 | |||
17.16 | even | 2 | 1156.2.h.b.1001.1 | 4 | |||
51.8 | odd | 8 | 612.2.w.a.433.1 | 4 | |||
68.39 | even | 16 | 4624.2.a.bl.1.1 | 4 | |||
68.59 | odd | 8 | 272.2.v.c.161.1 | 4 | |||
68.63 | even | 16 | 4624.2.a.bl.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
68.2.h.a.25.1 | ✓ | 4 | 17.8 | even | 8 | inner | |
68.2.h.a.49.1 | yes | 4 | 1.1 | even | 1 | trivial | |
272.2.v.c.49.1 | 4 | 4.3 | odd | 2 | |||
272.2.v.c.161.1 | 4 | 68.59 | odd | 8 | |||
612.2.w.a.253.1 | 4 | 3.2 | odd | 2 | |||
612.2.w.a.433.1 | 4 | 51.8 | odd | 8 | |||
1156.2.a.g.1.1 | 4 | 17.12 | odd | 16 | |||
1156.2.a.g.1.4 | 4 | 17.5 | odd | 16 | |||
1156.2.b.d.577.1 | 4 | 17.3 | odd | 16 | |||
1156.2.b.d.577.4 | 4 | 17.14 | odd | 16 | |||
1156.2.e.f.829.1 | 8 | 17.6 | odd | 16 | |||
1156.2.e.f.829.4 | 8 | 17.11 | odd | 16 | |||
1156.2.e.f.905.1 | 8 | 17.7 | odd | 16 | |||
1156.2.e.f.905.4 | 8 | 17.10 | odd | 16 | |||
1156.2.h.a.733.1 | 4 | 17.4 | even | 4 | |||
1156.2.h.a.757.1 | 4 | 17.2 | even | 8 | |||
1156.2.h.b.977.1 | 4 | 17.9 | even | 8 | |||
1156.2.h.b.1001.1 | 4 | 17.16 | even | 2 | |||
1156.2.h.c.733.1 | 4 | 17.13 | even | 4 | |||
1156.2.h.c.757.1 | 4 | 17.15 | even | 8 | |||
4624.2.a.bl.1.1 | 4 | 68.39 | even | 16 | |||
4624.2.a.bl.1.4 | 4 | 68.63 | even | 16 |