Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(65,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bn (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.4 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.65 |
Dual form | 912.2.bn.m.449.4 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.57313 | − | 0.724745i | 0.908248 | − | 0.418432i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | + | 0.707107i | 0.547723 | + | 0.316228i | 0.748203 | − | 0.663470i | \(-0.230917\pi\) |
−0.200480 | + | 0.979698i | \(0.564250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.267949 | 0.101275 | 0.0506376 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506376 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.94949 | − | 2.28024i | 0.649830 | − | 0.760080i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.27792i | 1.59135i | 0.605723 | + | 0.795676i | \(0.292884\pi\) | ||||
−0.605723 | + | 0.795676i | \(0.707116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.232051 | + | 0.133975i | −0.0643593 | + | 0.0371579i | −0.531834 | − | 0.846848i | \(-0.678497\pi\) |
0.467475 | + | 0.884006i | \(0.345164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.43916 | + | 0.224745i | 0.629788 | + | 0.0580289i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24264 | + | 2.44949i | 1.02899 | + | 0.594089i | 0.916696 | − | 0.399586i | \(-0.130846\pi\) |
0.112296 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.73205 | + | 4.00000i | −0.397360 | + | 0.917663i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.421519 | − | 0.194195i | 0.0919831 | − | 0.0423768i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.57081 | − | 2.63896i | 0.953080 | − | 0.550261i | 0.0590435 | − | 0.998255i | \(-0.481195\pi\) |
0.894036 | + | 0.447995i | \(0.147862\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.03528 | + | 1.79315i | 0.192246 | + | 0.332980i | 0.945994 | − | 0.324184i | \(-0.105090\pi\) |
−0.753748 | + | 0.657163i | \(0.771756\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.46410i | − | 0.442566i | −0.975210 | − | 0.221283i | \(-0.928976\pi\) | ||
0.975210 | − | 0.221283i | \(-0.0710244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.82514 | + | 8.30286i | 0.665872 | + | 1.44534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.328169 | + | 0.189469i | 0.0554708 | + | 0.0320261i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.73205i | − | 1.27114i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) | ||
0.772043 | − | 0.635571i | \(-0.219235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.267949 | + | 0.378937i | −0.0429062 | + | 0.0606785i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.82843 | + | 4.89898i | −0.441726 | + | 0.765092i | −0.997818 | − | 0.0660290i | \(-0.978967\pi\) |
0.556092 | + | 0.831121i | \(0.312300\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.86603 | − | 4.96410i | 0.437065 | − | 0.757018i | −0.560397 | − | 0.828224i | \(-0.689351\pi\) |
0.997462 | + | 0.0712058i | \(0.0226847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.00000 | − | 1.41421i | 0.596285 | − | 0.210819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.656339 | − | 0.378937i | 0.0957369 | − | 0.0552737i | −0.451367 | − | 0.892338i | \(-0.649064\pi\) |
0.547104 | + | 0.837065i | \(0.315730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92820 | −0.989743 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.44949 | + | 0.778539i | 1.18317 | + | 0.109017i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.46739 | − | 9.46979i | −0.751003 | − | 1.30078i | −0.947337 | − | 0.320239i | \(-0.896237\pi\) |
0.196334 | − | 0.980537i | \(-0.437096\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.73205 | + | 6.46410i | −0.503230 | + | 0.871619i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.174235 | + | 7.54782i | 0.0230779 | + | 0.999734i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.60609 | + | 9.71003i | −0.729850 | + | 1.26414i | 0.227096 | + | 0.973872i | \(0.427077\pi\) |
−0.956946 | + | 0.290265i | \(0.906256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.23205 | + | 9.06218i | 0.669895 | + | 1.16029i | 0.977933 | + | 0.208919i | \(0.0669944\pi\) |
−0.308038 | + | 0.951374i | \(0.599672\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.522364 | − | 0.610988i | 0.0658117 | − | 0.0769773i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.378937 | −0.0470014 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.866025 | − | 0.500000i | 0.105802 | − | 0.0610847i | −0.446165 | − | 0.894951i | \(-0.647211\pi\) |
0.551967 | + | 0.833866i | \(0.313877\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.27792 | − | 7.46410i | 0.635387 | − | 0.898572i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.69213 | − | 11.5911i | 0.794210 | − | 1.37561i | −0.129130 | − | 0.991628i | \(-0.541218\pi\) |
0.923340 | − | 0.383984i | \(-0.125448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | − | 2.59808i | 0.175562 | − | 0.304082i | −0.764794 | − | 0.644275i | \(-0.777159\pi\) |
0.940356 | + | 0.340193i | \(0.110493\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.24264 | − | 3.00000i | −0.489898 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41421i | 0.161165i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.06218 | − | 5.23205i | −1.01957 | − | 0.588652i | −0.105594 | − | 0.994409i | \(-0.533674\pi\) |
−0.913981 | + | 0.405758i | \(0.867008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.39898 | − | 8.89060i | −0.155442 | − | 0.987845i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.07055i | − | 0.227273i | −0.993522 | − | 0.113636i | \(-0.963750\pi\) | ||
0.993522 | − | 0.113636i | \(-0.0362499\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | + | 6.00000i | 0.375735 | + | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.92820 | + | 2.07055i | 0.313936 | + | 0.221987i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.67423 | + | 6.36396i | 0.389468 | + | 0.674579i | 0.992378 | − | 0.123231i | \(-0.0393255\pi\) |
−0.602910 | + | 0.797809i | \(0.705992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0621778 | + | 0.0358984i | −0.00651801 | + | 0.00376317i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.78585 | − | 3.87636i | −0.185184 | − | 0.401960i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.94975 | + | 3.67423i | −0.507833 | + | 0.376969i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.464102 | − | 0.267949i | −0.0471224 | − | 0.0272061i | 0.476254 | − | 0.879308i | \(-0.341994\pi\) |
−0.523376 | + | 0.852102i | \(0.675328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.0349 | + | 10.2892i | 1.20955 | + | 1.03411i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.79315 | + | 1.03528i | −0.178425 | + | 0.103014i | −0.586553 | − | 0.809911i | \(-0.699515\pi\) |
0.408127 | + | 0.912925i | \(0.366182\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3.53590i | − | 0.348402i | −0.984710 | − | 0.174201i | \(-0.944266\pi\) | ||
0.984710 | − | 0.174201i | \(-0.0557343\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.653570 | + | 0.0602202i | 0.0637819 | + | 0.00587689i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.89898 | −0.473602 | −0.236801 | − | 0.971558i | \(-0.576099\pi\) | ||||
−0.236801 | + | 0.971558i | \(0.576099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.53590 | − | 3.19615i | −0.530243 | − | 0.306136i | 0.210872 | − | 0.977514i | \(-0.432370\pi\) |
−0.741115 | + | 0.671378i | \(0.765703\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.60376 | − | 12.1635i | −0.531886 | − | 1.15451i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.96524 | 0.373018 | 0.186509 | − | 0.982453i | \(-0.440283\pi\) | ||||
0.186509 | + | 0.982453i | \(0.440283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.46410 | 0.696031 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.146887 | + | 0.790313i | −0.0135797 | + | 0.0730645i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.13681 | + | 0.656339i | 0.104211 | + | 0.0601665i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.8564 | −1.53240 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.898979 | + | 9.75663i | −0.0810583 | + | 0.879726i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1962 | + | 9.92820i | −1.52591 | + | 0.880986i | −0.526384 | + | 0.850247i | \(0.676453\pi\) |
−0.999527 | + | 0.0307388i | \(0.990214\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.910930 | − | 9.88633i | 0.0802029 | − | 0.870442i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.9348 | + | 6.31319i | 0.955375 | + | 0.551586i | 0.894747 | − | 0.446574i | \(-0.147356\pi\) |
0.0606288 | + | 0.998160i | \(0.480689\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.464102 | + | 1.07180i | −0.0402427 | + | 0.0929366i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.26758 | − | 5.12372i | 0.453362 | − | 0.440980i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.14162 | − | 5.27792i | 0.781021 | − | 0.450923i | −0.0557708 | − | 0.998444i | \(-0.517762\pi\) |
0.836792 | + | 0.547521i | \(0.184428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.40192 | + | 2.42820i | 0.118910 | + | 0.205958i | 0.919336 | − | 0.393474i | \(-0.128727\pi\) |
−0.800426 | + | 0.599431i | \(0.795393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.757875 | − | 1.07180i | 0.0638246 | − | 0.0902616i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.707107 | − | 1.22474i | −0.0591312 | − | 0.102418i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.92820i | 0.243174i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.8990 | + | 5.02118i | −0.898933 | + | 0.414140i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.36156 | + | 1.36345i | 0.193466 | + | 0.111698i | 0.593604 | − | 0.804757i | \(-0.297704\pi\) |
−0.400138 | + | 0.916455i | \(0.631038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000i | 0.162758i | 0.996683 | + | 0.0813788i | \(0.0259324\pi\) | ||||
−0.996683 | + | 0.0813788i | \(0.974068\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.8564 | − | 4.89898i | 1.12022 | − | 0.396059i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.74238 | − | 3.01790i | 0.139952 | − | 0.242403i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.23205 | + | 9.06218i | −0.417563 | + | 0.723241i | −0.995694 | − | 0.0927037i | \(-0.970449\pi\) |
0.578131 | + | 0.815944i | \(0.303782\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.4641 | − | 10.9348i | −1.22638 | − | 0.867184i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.22474 | − | 0.707107i | 0.0965234 | − | 0.0557278i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.19615 | 0.406994 | 0.203497 | − | 0.979076i | \(-0.434769\pi\) | ||||
0.203497 | + | 0.979076i | \(0.434769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.18618 | + | 12.8737i | −0.0923444 | + | 1.00221i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.8840 | − | 18.8516i | −0.842229 | − | 1.45878i | −0.888006 | − | 0.459832i | \(-0.847909\pi\) |
0.0457762 | − | 0.998952i | \(-0.485424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.46410 | + | 11.1962i | −0.497239 | + | 0.861242i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.74434 | + | 11.7474i | 0.439281 | + | 0.898350i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.76268 | + | 15.1774i | −0.666214 | + | 1.15392i | 0.312740 | + | 0.949839i | \(0.398753\pi\) |
−0.978955 | + | 0.204079i | \(0.934580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.401924 | − | 0.696152i | −0.0303826 | − | 0.0526242i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.78182 | + | 19.3381i | −0.133930 | + | 1.45354i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.41421 | −0.105703 | −0.0528516 | − | 0.998602i | \(-0.516831\pi\) | ||||
−0.0528516 | + | 0.998602i | \(0.516831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00000 | + | 1.73205i | −0.222988 | + | 0.128742i | −0.607333 | − | 0.794447i | \(-0.707761\pi\) |
0.384345 | + | 0.923190i | \(0.374427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.7985 | + | 10.4641i | 1.09393 | + | 0.773529i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.46739 | − | 9.46979i | 0.401970 | − | 0.696233i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.9282 | + | 22.3923i | −0.945404 | + | 1.63749i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.378937 | − | 1.33975i | 0.0275636 | − | 0.0974522i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.0053i | 0.941032i | 0.882391 | + | 0.470516i | \(0.155932\pi\) | ||||
−0.882391 | + | 0.470516i | \(0.844068\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.42820 | − | 1.40192i | −0.174786 | − | 0.100913i | 0.410055 | − | 0.912061i | \(-0.365510\pi\) |
−0.584841 | + | 0.811148i | \(0.698843\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.596119 | + | 0.274633i | −0.0426889 | + | 0.0196669i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.656339i | 0.0467622i | 0.999727 | + | 0.0233811i | \(0.00744311\pi\) | ||||
−0.999727 | + | 0.0233811i | \(0.992557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5981 | − | 20.0885i | −0.822166 | − | 1.42403i | −0.904066 | − | 0.427392i | \(-0.859432\pi\) |
0.0819004 | − | 0.996641i | \(-0.473901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | − | 1.41421i | 0.0705346 | − | 0.0997509i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.277401 | + | 0.480473i | 0.0194698 | + | 0.0337226i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.92820 | + | 4.00000i | −0.483887 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.89329 | − | 15.5672i | 0.201098 | − | 1.08199i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1117 | − | 9.14162i | −1.46032 | − | 0.632339i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.52628 | − | 5.50000i | −0.655816 | − | 0.378636i | 0.134865 | − | 0.990864i | \(-0.456940\pi\) |
−0.790681 | + | 0.612228i | \(0.790273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.12701 | − | 23.0844i | 0.145740 | − | 1.58172i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.02030 | − | 4.05317i | 0.478780 | − | 0.276424i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.660254i | − | 0.0448210i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.476756 | − | 5.17423i | 0.0322162 | − | 0.349642i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.31268 | −0.0883003 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.86603 | + | 5.69615i | 0.660678 | + | 0.381443i | 0.792535 | − | 0.609826i | \(-0.208761\pi\) |
−0.131857 | + | 0.991269i | \(0.542094\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.84847 | − | 1.64456i | −0.589898 | − | 0.109638i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.79744 | −0.318418 | −0.159209 | − | 0.987245i | \(-0.550894\pi\) | ||||
−0.159209 | + | 0.987245i | \(0.550894\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3923 | −0.752825 | −0.376412 | − | 0.926452i | \(-0.622842\pi\) | ||||
−0.376412 | + | 0.926452i | \(0.622842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.02494 | + | 2.22474i | 0.0674364 | + | 0.146377i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.5911 | − | 6.69213i | −0.759359 | − | 0.438416i | 0.0697066 | − | 0.997568i | \(-0.477794\pi\) |
−0.829066 | + | 0.559151i | \(0.811127\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.07180 | 0.0699163 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.0479 | − | 1.66294i | −1.17234 | − | 0.108020i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 15.2789i | − | 0.988313i | −0.869373 | − | 0.494156i | \(-0.835477\pi\) | ||
0.869373 | − | 0.494156i | \(-0.164523\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.82051 | − | 5.66987i | 0.632595 | − | 0.365229i | −0.149162 | − | 0.988813i | \(-0.547657\pi\) |
0.781756 | + | 0.623584i | \(0.214324\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.64420 | − | 12.9722i | −0.554526 | − | 0.832167i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.48528 | − | 4.89898i | −0.542105 | − | 0.312984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.133975 | − | 1.16025i | −0.00852460 | − | 0.0738252i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.50062 | − | 3.25725i | −0.0950981 | − | 0.206420i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7279 | + | 7.34847i | −0.803379 | + | 0.463831i | −0.844651 | − | 0.535317i | \(-0.820192\pi\) |
0.0412721 | + | 0.999148i | \(0.486859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.9282 | + | 24.1244i | 0.875659 | + | 1.51669i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.79796 | + | 6.92820i | 0.613572 | + | 0.433861i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.05317 | − | 7.02030i | −0.252830 | − | 0.437914i | 0.711474 | − | 0.702713i | \(-0.248028\pi\) |
−0.964304 | + | 0.264798i | \(0.914695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.07180i | − | 0.128735i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.10707 | + | 1.13505i | 0.378018 | + | 0.0702580i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.9754 | − | 14.4195i | −1.54005 | − | 0.889147i | −0.998835 | − | 0.0482609i | \(-0.984632\pi\) |
−0.541213 | − | 0.840886i | \(-0.682035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.4641i | − | 0.949952i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.3923 | + | 7.34847i | 0.635999 | + | 0.449719i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.46739 | + | 9.46979i | −0.333352 | + | 0.577383i | −0.983167 | − | 0.182710i | \(-0.941513\pi\) |
0.649815 | + | 0.760093i | \(0.274847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.46410 | − | 6.00000i | 0.210429 | − | 0.364474i | −0.741420 | − | 0.671042i | \(-0.765847\pi\) |
0.951849 | + | 0.306568i | \(0.0991805\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0717968 | + | 0.101536i | −0.00434534 | + | 0.00614524i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.7124 | − | 7.91688i | 0.826891 | − | 0.477406i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8564 | 1.07289 | 0.536444 | − | 0.843936i | \(-0.319767\pi\) | ||||
0.536444 | + | 0.843936i | \(0.319767\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.61874 | − | 4.80374i | −0.336385 | − | 0.287592i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.70951 | − | 8.15711i | −0.280946 | − | 0.486613i | 0.690672 | − | 0.723168i | \(-0.257315\pi\) |
−0.971618 | + | 0.236556i | \(0.923981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.92820 | − | 5.07180i | 0.174064 | − | 0.301487i | −0.765773 | − | 0.643111i | \(-0.777643\pi\) |
0.939837 | + | 0.341624i | \(0.110977\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.12372 | + | 9.36736i | −0.303503 | + | 0.554875i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.757875 | + | 1.31268i | −0.0447359 | + | 0.0774849i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.50000 | + | 6.06218i | 0.205882 | + | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.924288 | − | 0.0851642i | −0.0541827 | − | 0.00499242i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.9391 | 0.814329 | 0.407164 | − | 0.913355i | \(-0.366518\pi\) | ||||
0.407164 | + | 0.913355i | \(0.366518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7321 | + | 7.92820i | −0.799511 | + | 0.461598i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.3896 | + | 7.46410i | 1.53128 | + | 0.433111i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.707107 | + | 1.22474i | −0.0408930 | + | 0.0708288i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.767949 | − | 1.33013i | 0.0442639 | − | 0.0766672i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.07055 | + | 2.92820i | −0.118950 | + | 0.168221i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.7985i | 0.847358i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | + | 6.92820i | 0.684876 | + | 0.395413i | 0.801690 | − | 0.597740i | \(-0.203935\pi\) |
−0.116814 | + | 0.993154i | \(0.537268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.56262 | − | 5.56244i | −0.145783 | − | 0.316436i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4505i | 0.706004i | 0.935623 | + | 0.353002i | \(0.114839\pi\) | ||||
−0.935623 | + | 0.353002i | \(0.885161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.39230 | − | 14.5359i | −0.474361 | − | 0.821618i | 0.525208 | − | 0.850974i | \(-0.323988\pi\) |
−0.999569 | + | 0.0293564i | \(0.990654\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.07180 | − | 0.378937i | 0.0603889 | − | 0.0213507i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.43211 | + | 7.67664i | 0.248932 | + | 0.431163i | 0.963230 | − | 0.268679i | \(-0.0865871\pi\) |
−0.714298 | + | 0.699842i | \(0.753254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.46410 | + | 5.46410i | −0.529888 | + | 0.305931i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.70674 | + | 3.55051i | −0.430148 | + | 0.198170i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1464 | + | 12.7279i | −0.954053 | + | 0.708201i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.696152 | + | 0.401924i | 0.0386156 | + | 0.0222947i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.0251 | − | 1.01586i | −0.609689 | − | 0.0561770i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.175865 | − | 0.101536i | 0.00969578 | − | 0.00559786i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0718i | 0.993316i | 0.867946 | + | 0.496658i | \(0.165440\pi\) | ||||
−0.867946 | + | 0.496658i | \(0.834560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.6309 | − | 15.0736i | −0.966169 | − | 0.826026i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.41421 | 0.0772667 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.3564 | − | 12.3301i | −1.16336 | − | 0.671665i | −0.211251 | − | 0.977432i | \(-0.567754\pi\) |
−0.952106 | + | 0.305767i | \(0.901087\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.23785 | − | 2.87379i | 0.338793 | − | 0.156083i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.0053 | 0.704278 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.73205 | −0.201512 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.7420 | − | 5.40957i | 0.632169 | − | 0.291241i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.6424 | + | 9.60849i | 0.893410 | + | 0.515811i | 0.875057 | − | 0.484021i | \(-0.160824\pi\) |
0.0183540 | + | 0.999832i | \(0.494157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.39230 | 0.502759 | 0.251379 | − | 0.967889i | \(-0.419116\pi\) | ||||
0.251379 | + | 0.967889i | \(0.419116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.341704 | + | 1.34972i | 0.0182388 | + | 0.0720429i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.17209i | 0.115609i | 0.998328 | + | 0.0578043i | \(0.0184099\pi\) | ||||
−0.998328 | + | 0.0578043i | \(0.981590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.3923 | − | 9.46410i | 0.870013 | − | 0.502302i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.26403 | + | 0.208609i | 0.119825 | + | 0.0110408i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.21166 | + | 3.58630i | 0.327839 | + | 0.189278i | 0.654881 | − | 0.755732i | \(-0.272719\pi\) |
−0.327042 | + | 0.945010i | \(0.606052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | − | 13.8564i | −0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.5174 | + | 12.2166i | −1.39180 | + | 0.641205i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.67423 | − | 2.12132i | 0.192318 | − | 0.111035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.5263 | + | 18.2321i | 0.549467 | + | 0.951705i | 0.998311 | + | 0.0580950i | \(0.0185026\pi\) |
−0.448844 | + | 0.893610i | \(0.648164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.65685 | + | 16.0000i | 0.294484 | + | 0.832927i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.46498 | − | 2.53742i | −0.0760581 | − | 0.131736i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 19.4641i | − | 1.00781i | −0.863758 | − | 0.503906i | \(-0.831896\pi\) | ||
0.863758 | − | 0.503906i | \(-0.168104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.19955 | − | 17.7980i | −0.423423 | − | 0.919083i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.480473 | − | 0.277401i | −0.0247456 | − | 0.0142869i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.7846i | − | 1.22173i | −0.791733 | − | 0.610867i | \(-0.790821\pi\) | ||
0.791733 | − | 0.610867i | \(-0.209179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.8564 | + | 28.0812i | −1.01727 | + | 1.43864i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.26243 | + | 10.8468i | −0.319995 | + | 0.554248i | −0.980487 | − | 0.196586i | \(-0.937015\pi\) |
0.660492 | + | 0.750833i | \(0.270348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | + | 1.73205i | −0.0509647 | + | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.73205 | − | 16.2127i | −0.291377 | − | 0.824137i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.8159 | − | 7.39924i | 0.649790 | − | 0.375156i | −0.138586 | − | 0.990350i | \(-0.544256\pi\) |
0.788376 | + | 0.615194i | \(0.210922\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.8564 | 1.30761 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.7773 | + | 2.00657i | 1.09852 | + | 0.101218i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.39924 | − | 12.8159i | −0.372296 | − | 0.644836i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.1603 | − | 22.7942i | 0.660494 | − | 1.14401i | −0.319992 | − | 0.947420i | \(-0.603680\pi\) |
0.980486 | − | 0.196589i | \(-0.0629865\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0466860 | + | 2.02243i | 0.00233722 | + | 0.101248i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.4016 | + | 19.7482i | −0.569371 | + | 0.986179i | 0.427257 | + | 0.904130i | \(0.359480\pi\) |
−0.996628 | + | 0.0820492i | \(0.973854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.330127 | + | 0.571797i | 0.0164448 | + | 0.0284832i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.57321 | − | 11.8780i | 0.227245 | − | 0.590220i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 40.8091 | 2.02283 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5359 | − | 10.1244i | 0.867094 | − | 0.500617i | 0.000712791 | − | 1.00000i | \(-0.499773\pi\) |
0.866382 | + | 0.499383i | \(0.166440\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5558 | − | 14.9282i | 0.520681 | − | 0.736354i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.50215 | + | 2.60179i | −0.0739158 | + | 0.128026i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.46410 | − | 2.53590i | 0.0718699 | − | 0.124482i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.96524 | + | 2.80385i | 0.194179 | + | 0.137305i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 7.55154i | − | 0.368917i | −0.982840 | − | 0.184458i | \(-0.940947\pi\) | ||
0.982840 | − | 0.184458i | \(-0.0590531\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.7128 | + | 14.2679i | 1.20443 | + | 0.695377i | 0.961537 | − | 0.274676i | \(-0.0885706\pi\) |
0.242892 | + | 0.970053i | \(0.421904\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.415458 | − | 2.23534i | 0.0202003 | − | 0.108686i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 14.6969i | − | 0.712906i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.40192 | + | 2.42820i | 0.0678438 | + | 0.117509i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.00000 | − | 1.41421i | −0.0965609 | − | 0.0682789i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.7279 | + | 22.0454i | 0.613082 | + | 1.06189i | 0.990718 | + | 0.135935i | \(0.0434040\pi\) |
−0.377635 | + | 0.925954i | \(0.623263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.8923 | + | 10.3301i | −0.859849 | + | 0.496434i | −0.863962 | − | 0.503557i | \(-0.832024\pi\) |
0.00411252 | + | 0.999992i | \(0.498691\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.12220 | + | 4.60645i | 0.101752 | + | 0.220862i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.63896 | + | 22.8541i | 0.126239 | + | 1.09326i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.4545 | + | 7.76795i | 0.642147 | + | 0.370744i | 0.785441 | − | 0.618936i | \(-0.212436\pi\) |
−0.143294 | + | 0.989680i | \(0.545769\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.5065 | + | 15.7980i | −0.643165 | + | 0.752284i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.96575 | + | 5.17638i | −0.425976 | + | 0.245937i | −0.697631 | − | 0.716457i | \(-0.745762\pi\) |
0.271655 | + | 0.962395i | \(0.412429\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.3923i | 0.492642i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.70319 | + | 0.433354i | 0.222453 | + | 0.0204969i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.10205 | 0.240781 | 0.120390 | − | 0.992727i | \(-0.461585\pi\) | ||||
0.120390 | + | 0.992727i | \(0.461585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.8564 | − | 14.9282i | −1.21753 | − | 0.702942i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.44949 | + | 3.14626i | 0.0681030 | + | 0.147824i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.101536 | −0.00476008 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.7128 | 1.62380 | 0.811898 | − | 0.583799i | \(-0.198434\pi\) | ||||
0.811898 | + | 0.583799i | \(0.198434\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.2474 | − | 17.7491i | 0.851718 | − | 0.828457i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.9232 | + | 17.8535i | 1.44024 | + | 0.831522i | 0.997865 | − | 0.0653090i | \(-0.0208033\pi\) |
0.442373 | + | 0.896831i | \(0.354137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.58846 | −0.0738219 | −0.0369109 | − | 0.999319i | \(-0.511752\pi\) | ||||
−0.0369109 | + | 0.999319i | \(0.511752\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.553794 | − | 6.01033i | 0.0256816 | − | 0.278722i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6274i | 1.04707i | 0.852004 | + | 0.523536i | \(0.175387\pi\) | ||||
−0.852004 | + | 0.523536i | \(0.824613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.232051 | − | 0.133975i | 0.0107151 | − | 0.00618637i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.66294 | + | 18.0479i | −0.0766243 | + | 0.831604i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 26.2001 | + | 15.1266i | 1.20468 | + | 0.695524i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.9904 | − | 1.50000i | 0.596040 | − | 0.0688247i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.2520 | − | 5.99431i | −1.47672 | − | 0.274461i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.1774 | − | 8.76268i | 0.693474 | − | 0.400377i | −0.111438 | − | 0.993771i | \(-0.535546\pi\) |
0.804912 | + | 0.593394i | \(0.202212\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.03590 | + | 1.79423i | 0.0472329 | + | 0.0818098i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.41421 | − | 2.00000i | 0.0643489 | − | 0.0910032i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.378937 | − | 0.656339i | −0.0172067 | − | 0.0298028i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.0718i | − | 0.501711i | −0.968025 | − | 0.250856i | \(-0.919288\pi\) | ||
0.968025 | − | 0.250856i | \(-0.0807119\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.17423 | − | 3.76588i | 0.369652 | − | 0.170299i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.6317 | + | 14.7985i | 1.15674 | + | 0.667846i | 0.950521 | − | 0.310660i | \(-0.100550\pi\) |
0.206222 | + | 0.978505i | \(0.433883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.1436i | 0.456844i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.46410 | + | 21.1117i | 0.335486 | + | 0.948899i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.79315 | − | 3.10583i | 0.0804338 | − | 0.139315i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.06218 | − | 7.03590i | 0.181848 | − | 0.314970i | −0.760662 | − | 0.649148i | \(-0.775125\pi\) |
0.942510 | + | 0.334178i | \(0.108459\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.7846 | − | 21.7680i | −1.37535 | − | 0.972523i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.13681 | − | 0.656339i | 0.0506879 | − | 0.0292647i | −0.474442 | − | 0.880287i | \(-0.657350\pi\) |
0.525130 | + | 0.851022i | \(0.324017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.92820 | −0.130303 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.05453 | + | 22.2979i | −0.0912450 | + | 0.990282i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.4906 | − | 37.2228i | −0.952554 | − | 1.64987i | −0.739868 | − | 0.672752i | \(-0.765112\pi\) |
−0.212686 | − | 0.977121i | \(-0.568221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.401924 | − | 0.696152i | 0.0177801 | − | 0.0307960i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.5505 | + | 14.3171i | 0.774874 | + | 0.632116i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.50026 | − | 4.33057i | 0.110175 | − | 0.190828i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00000 | + | 3.46410i | 0.0879599 | + | 0.152351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.78511 | + | 30.2268i | −0.122253 | + | 1.32681i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1769 | 0.445858 | 0.222929 | − | 0.974835i | \(-0.428438\pi\) | ||||
0.222929 | + | 0.974835i | \(0.428438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.40192 | − | 5.42820i | 0.411117 | − | 0.237359i | −0.280152 | − | 0.959956i | \(-0.590385\pi\) |
0.691270 | + | 0.722597i | \(0.257052\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.13681 | − | 0.803848i | −0.0496145 | − | 0.0350828i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.03579 | − | 10.4543i | 0.262923 | − | 0.455396i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.42820 | − | 4.20577i | 0.105574 | − | 0.182860i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2122 | + | 31.7128i | 0.486567 | + | 1.37622i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.51575i | − | 0.0656544i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 3.46410i | −0.259403 | − | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.22474 | + | 1.02494i | −0.0960048 | + | 0.0442296i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 36.5665i | − | 1.57503i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.2321 | + | 21.1865i | 0.525897 | + | 0.910880i | 0.999545 | + | 0.0301660i | \(0.00960358\pi\) |
−0.473648 | + | 0.880714i | \(0.657063\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.46410 | + | 4.89898i | −0.148659 | + | 0.210235i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.52004 | − | 7.82894i | −0.193617 | − | 0.335355i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.8660 | − | 7.42820i | 0.550112 | − | 0.317607i | −0.199055 | − | 0.979988i | \(-0.563787\pi\) |
0.749167 | + | 0.662381i | \(0.230454\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.8638 | + | 5.73630i | 1.31723 | + | 0.244819i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.96575 | + | 1.03528i | −0.381954 | + | 0.0441042i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.42820 | − | 1.40192i | −0.103258 | − | 0.0596159i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.73774 | − | 18.8597i | 0.0737629 | − | 0.800549i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.5259 | + | 13.0053i | −0.954452 | + | 0.551053i | −0.894461 | − | 0.447146i | \(-0.852441\pi\) |
−0.0599911 | + | 0.998199i | \(0.519107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.53590i | 0.0649616i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.10906 | + | 44.5957i | −0.173485 | + | 1.88283i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.0106 | 1.09622 | 0.548109 | − | 0.836407i | \(-0.315348\pi\) | ||||
0.548109 | + | 0.836407i | \(0.315348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.85641 | + | 2.80385i | 0.204311 | + | 0.117959i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.374855 | − | 2.38223i | −0.0157424 | − | 0.100044i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.2528 | 1.05865 | 0.529326 | − | 0.848419i | \(-0.322445\pi\) | ||||
0.529326 | + | 0.848419i | \(0.322445\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8038 | −0.619522 | −0.309761 | − | 0.950814i | \(-0.600249\pi\) | ||||
−0.309761 | + | 0.950814i | \(0.600249\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.42554 | + | 20.4591i | 0.393758 | + | 0.854691i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.7124 | − | 7.91688i | −0.571848 | − | 0.330157i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.0718 | 1.21027 | 0.605137 | − | 0.796121i | \(-0.293118\pi\) | ||||
0.605137 | + | 0.796121i | \(0.293118\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.83592 | − | 0.445584i | −0.200974 | − | 0.0185178i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.554803i | − | 0.0230171i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.9808 | − | 28.8564i | 2.06999 | − | 1.19511i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.738735 | + | 0.864068i | −0.0305429 | + | 0.0357248i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.8898 | − | 16.6796i | −1.19241 | − | 0.688439i | −0.233559 | − | 0.972343i | \(-0.575037\pi\) |
−0.958853 | + | 0.283904i | \(0.908370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.85641 | + | 4.26795i | 0.406126 | + | 0.175858i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.475678 | + | 1.03251i | 0.0195668 | + | 0.0424717i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.1301 | + | 16.8183i | −1.19623 | + | 0.690643i | −0.959712 | − | 0.280984i | \(-0.909339\pi\) |
−0.236517 | + | 0.971627i | \(0.576006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.928203 | + | 1.60770i | 0.0380526 | + | 0.0659091i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −32.8043 | − | 23.1962i | −1.34259 | − | 0.949355i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.36345 | − | 2.36156i | −0.0557089 | − | 0.0964906i | 0.836826 | − | 0.547469i | \(-0.184409\pi\) |
−0.892535 | + | 0.450978i | \(0.851075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 28.3731i | − | 1.15736i | −0.815554 | − | 0.578681i | \(-0.803568\pi\) | ||
0.815554 | − | 0.578681i | \(-0.196432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.548188 | − | 2.94949i | 0.0223239 | − | 0.120113i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.6448 | − | 11.9193i | −0.839330 | − | 0.484588i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 35.2487i | − | 1.43070i | −0.698766 | − | 0.715351i | \(-0.746267\pi\) | ||
0.698766 | − | 0.715351i | \(-0.253733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.784610 | + | 0.554803i | 0.0317940 | + | 0.0224817i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.101536 | + | 0.175865i | −0.00410771 | + | 0.00711475i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.3205 | − | 40.3923i | 0.941906 | − | 1.63143i | 0.180077 | − | 0.983653i | \(-0.442365\pi\) |
0.761830 | − | 0.647777i | \(-0.224301\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | + | 11.3137i | −0.322591 | + | 0.456213i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.9885 | − | 11.5403i | 0.804705 | − | 0.464597i | −0.0404087 | − | 0.999183i | \(-0.512866\pi\) |
0.845114 | + | 0.534587i | \(0.179533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1962 | −0.530398 | −0.265199 | − | 0.964194i | \(-0.585438\pi\) | ||||
−0.265199 | + | 0.964194i | \(0.585438\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.73069 | − | 26.5861i | −0.270093 | − | 1.06686i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.984508 | + | 1.70522i | 0.0394435 | + | 0.0683181i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −39.8368 | + | 0.919596i | −1.59093 | + | 0.0367251i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.9396 | − | 32.8043i | 0.755170 | − | 1.30799i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.47372 | + | 9.48076i | 0.217905 | + | 0.377423i | 0.954167 | − | 0.299273i | \(-0.0967442\pi\) |
−0.736262 | + | 0.676697i | \(0.763411\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.9722 | − | 1.74810i | −0.754077 | − | 0.0694809i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.0812 | −1.11437 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.60770 | − | 0.928203i | 0.0636992 | − | 0.0367768i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.3843 | − | 37.8564i | −0.529473 | − | 1.49758i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.2127 | + | 28.0812i | −0.640363 | + | 1.10914i | 0.344989 | + | 0.938607i | \(0.387883\pi\) |
−0.985352 | + | 0.170534i | \(0.945451\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.20577 | + | 10.7487i | −0.244732 | + | 0.423888i | −0.962056 | − | 0.272852i | \(-0.912033\pi\) |
0.717324 | + | 0.696739i | \(0.245367\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.10634 | − | 11.4641i | 0.319187 | − | 0.451399i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.3548i | 1.19337i | 0.802475 | + | 0.596686i | \(0.203516\pi\) | ||||
−0.802475 | + | 0.596686i | \(0.796484\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.2487 | − | 29.5885i | −2.01169 | − | 1.16145i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.478516 | − | 1.03867i | −0.0187545 | − | 0.0407086i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.86748i | − | 0.0730802i | −0.999332 | − | 0.0365401i | \(-0.988366\pi\) | ||
0.999332 | − | 0.0365401i | \(-0.0116337\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.92820 | + | 15.4641i | 0.348854 | + | 0.604232i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00000 | − | 8.48528i | −0.117041 | − | 0.331042i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.84392 | + | 3.19376i | 0.0718289 | + | 0.124411i | 0.899703 | − | 0.436503i | \(-0.143783\pi\) |
−0.827874 | + | 0.560914i | \(0.810450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.3205 | + | 16.9282i | −1.14044 | + | 0.658431i | −0.946538 | − | 0.322591i | \(-0.895446\pi\) |
−0.193897 | + | 0.981022i | \(0.562113\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.06502 | + | 0.951356i | −0.0801986 | + | 0.0369476i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.32628 | + | 0.984508i | −0.0514310 | + | 0.0381776i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.46410 | + | 5.46410i | 0.366451 | + | 0.211571i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.6488 | + | 1.81045i | 0.759667 | + | 0.0699960i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.8294 | + | 27.6143i | −1.84643 | + | 1.06604i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.9808i | 1.15567i | 0.816152 | + | 0.577837i | \(0.196103\pi\) | ||||
−0.816152 | + | 0.577837i | \(0.803897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.1117 | + | 3.82577i | −0.581650 | + | 0.147254i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.1518 | 1.15883 | 0.579413 | − | 0.815034i | \(-0.303282\pi\) | ||||
0.579413 | + | 0.815034i | \(0.303282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.124356 | − | 0.0717968i | −0.00477233 | − | 0.00275531i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.54701 | + | 3.47692i | −0.289202 | + | 0.133236i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.1122 | 0.999155 | 0.499577 | − | 0.866269i | \(-0.333489\pi\) | ||||
0.499577 | + | 0.866269i | \(0.333489\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.9282 | 0.570377 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.9216 | + | 8.25651i | −0.683752 | + | 0.315006i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.53742 | + | 1.46498i | 0.0966681 | + | 0.0558114i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.8564 | 0.679290 | 0.339645 | − | 0.940554i | \(-0.389693\pi\) | ||||
0.339645 | + | 0.940554i | \(0.389693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.22474 | + | 2.75699i | 0.122498 | + | 0.104730i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.96524i | 0.150410i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | + | 13.8564i | −0.909065 | + | 0.524849i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.0844 | − | 2.12701i | −0.873134 | − | 0.0804508i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.2049 | − | 19.7482i | −1.29190 | − | 0.745880i | −0.312911 | − | 0.949782i | \(-0.601304\pi\) |
−0.978991 | + | 0.203902i | \(0.934637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.9282 | + | 13.3923i | 1.16648 | + | 0.505100i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.68608 | − | 0.776779i | 0.0635014 | − | 0.0292552i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.480473 | + | 0.277401i | −0.0180701 | + | 0.0104328i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.83975 | − | 6.65064i | −0.144205 | − | 0.249770i | 0.784871 | − | 0.619659i | \(-0.212729\pi\) |
−0.929076 | + | 0.369889i | \(0.879396\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.5969 | + | 10.4641i | −1.10997 | + | 0.392434i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.50266 | − | 11.2629i | −0.243527 | − | 0.421800i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.00000i | − | 0.0747958i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.0733 | − | 24.0358i | −0.413541 | − | 0.897634i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.46979 | − | 5.46739i | −0.353164 | − | 0.203899i | 0.312914 | − | 0.949781i | \(-0.398695\pi\) |
−0.666078 | + | 0.745882i | \(0.732028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 0.947441i | − | 0.0352846i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.3397 | − | 16.0368i | 0.421730 | − | 0.596416i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.10583 | − | 5.37945i | 0.115348 | − | 0.199788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.79423 | − | 15.2321i | 0.326160 | − | 0.564925i | −0.655587 | − | 0.755120i | \(-0.727579\pi\) |
0.981746 | + | 0.190195i | \(0.0609119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.3190 | − | 14.0406i | 0.899472 | − | 0.519310i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.7128 | 0.728109 | 0.364055 | − | 0.931378i | \(-0.381392\pi\) | ||||
0.364055 | + | 0.931378i | \(0.381392\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.8990 | − | 1.55708i | −0.623328 | − | 0.0574337i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.63896 | + | 4.57081i | 0.0972073 | + | 0.168368i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.5981 | + | 39.1410i | −0.831284 | + | 1.43983i | 0.0657370 | + | 0.997837i | \(0.479060\pi\) |
−0.897021 | + | 0.441989i | \(0.854273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.05165 | − | 1.72814i | −0.0386333 | − | 0.0634846i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.53553 | + | 6.12372i | −0.129706 | + | 0.224658i | −0.923563 | − | 0.383447i | \(-0.874737\pi\) |
0.793857 | + | 0.608105i | \(0.208070\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.92820 | + | 3.33975i | 0.0706439 | + | 0.122359i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.72135 | − | 4.03652i | −0.172745 | − | 0.147689i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.31268 | −0.0479642 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.4545 | + | 14.6962i | −0.928847 | + | 0.536270i | −0.886447 | − | 0.462830i | \(-0.846834\pi\) |
−0.0424005 | + | 0.999101i | \(0.513501\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.6969 | + | 20.7846i | −0.535586 | + | 0.757433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.41421 | + | 2.44949i | −0.0514685 | + | 0.0891461i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6962 | + | 21.9904i | −0.461450 | + | 0.799254i | −0.999033 | − | 0.0439562i | \(-0.986004\pi\) |
0.537584 | + | 0.843210i | \(0.319337\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 39.3949 | + | 27.8564i | 1.42994 | + | 1.01112i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.1208i | 1.16438i | 0.813054 | + | 0.582188i | \(0.197803\pi\) | ||||
−0.813054 | + | 0.582188i | \(0.802197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.48334 | − | 0.856406i | −0.0537005 | − | 0.0310040i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.4347 | + | 3.79796i | 0.738817 | + | 0.137315i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.00429i | − | 0.108479i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4282 | − | 23.2583i | −0.484233 | − | 0.838717i | 0.515603 | − | 0.856828i | \(-0.327568\pi\) |
−0.999836 | + | 0.0181110i | \(0.994235\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.4641 | − | 8.10634i | −0.412870 | − | 0.291943i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.3538 | + | 35.2538i | 0.732075 | + | 1.26799i | 0.955995 | + | 0.293384i | \(0.0947813\pi\) |
−0.223920 | + | 0.974608i | \(0.571885\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.40192 | + | 3.69615i | −0.229964 | + | 0.132770i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.50152 | − | 3.25921i | −0.0538669 | − | 0.116924i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.6969 | − | 19.7990i | −0.526572 | − | 0.709372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.1769 | + | 35.3205i | 2.18908 | + | 1.26387i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.4299 | − | 2.64048i | 0.372733 | − | 0.0943631i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.8159 | + | 7.39924i | −0.457417 | + | 0.264090i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 37.9282i | − | 1.35199i | −0.736904 | − | 0.675997i | \(-0.763713\pi\) | ||
0.736904 | − | 0.675997i | \(-0.236287\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −49.7400 | − | 4.58307i | −1.77079 | − | 0.163161i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.06248 | 0.0377775 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.42820 | − | 1.40192i | −0.0862280 | − | 0.0497838i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.2075 | − | 24.3271i | −0.397490 | − | 0.862792i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −54.0918 | −1.91603 | −0.958016 | − | 0.286716i | \(-0.907437\pi\) | ||||
−0.958016 | + | 0.286716i | \(0.907437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.71281 | 0.131350 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.6742 | + | 4.02834i | 0.765821 | + | 0.142335i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.7124 | + | 7.91688i | 0.483901 | + | 0.279380i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.73774 | + | 18.8597i | −0.0611713 | + | 0.663893i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.0197i | 1.30155i | 0.759273 | + | 0.650773i | \(0.225555\pi\) | ||||
−0.759273 | + | 0.650773i | \(0.774445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.1962 | + | 16.8564i | −1.02522 | + | 0.591908i | −0.915610 | − | 0.402067i | \(-0.868292\pi\) |
−0.109605 | + | 0.993975i | \(0.534959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.10102 | − | 11.9494i | 0.0386145 | − | 0.419083i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.36396 | + | 3.67423i | 0.222920 | + | 0.128703i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.8923 | + | 20.0622i | 0.521016 | + | 0.701887i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0393581 | + | 0.211764i | −0.00137528 | + | 0.00739963i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.41851 | + | 2.55103i | −0.154207 | + | 0.0890314i | −0.575118 | − | 0.818071i | \(-0.695044\pi\) |
0.420911 | + | 0.907102i | \(0.361710\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | − | 6.92820i | −0.139431 | − | 0.241502i | 0.787850 | − | 0.615867i | \(-0.211194\pi\) |
−0.927281 | + | 0.374365i | \(0.877861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.8338 | − | 22.3923i | 0.551260 | − | 0.779600i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.2474 | − | 21.2132i | −0.425886 | − | 0.737655i | 0.570617 | − | 0.821216i | \(-0.306704\pi\) |
−0.996503 | + | 0.0835608i | \(0.973371\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 21.3397i | − | 0.741160i | −0.928801 | − | 0.370580i | \(-0.879159\pi\) | ||
0.928801 | − | 0.370580i | \(-0.120841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.0905 | − | 12.9413i | 0.974448 | − | 0.448930i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.3939 | − | 16.9706i | −1.01844 | − | 0.587995i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.7846i | − | 1.06535i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.3205 | − | 3.48477i | −0.425859 | − | 0.120451i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.6772 | + | 21.9575i | −0.437664 | + | 0.758056i | −0.997509 | − | 0.0705412i | \(-0.977527\pi\) |
0.559845 | + | 0.828597i | \(0.310861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3564 | − | 21.4019i | 0.426083 | − | 0.737997i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.3205 | − | 9.41902i | −0.458783 | − | 0.324408i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.8338 | + | 9.14162i | −0.544698 | + | 0.314481i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.51666 | −0.155194 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.930692 | − | 10.1008i | 0.0319413 | − | 0.346659i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4046 | − | 35.3417i | −0.699459 | − | 1.21150i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.1603 | + | 47.0429i | −0.929949 | + | 1.61072i | −0.146548 | + | 0.989204i | \(0.546816\pi\) |
−0.783401 | + | 0.621516i | \(0.786517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.27135 | + | 18.4495i | −0.0434792 | + | 0.630959i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.1117 | − | 36.5665i | 0.721161 | − | 1.24909i | −0.239374 | − | 0.970927i | \(-0.576942\pi\) |
0.960535 | − | 0.278160i | \(-0.0897245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.33013 | + | 10.9641i | 0.215981 | + | 0.374090i | 0.953576 | − | 0.301154i | \(-0.0973717\pi\) |
−0.737594 | + | 0.675244i | \(0.764038\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.240881 | + | 2.61428i | −0.00820920 | + | 0.0890945i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.31268 | 0.0446841 | 0.0223420 | − | 0.999750i | \(-0.492888\pi\) | ||||
0.0223420 | + | 0.999750i | \(0.492888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.4641 | + | 12.3923i | −0.729801 | + | 0.421351i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.89949 | + | 7.00000i | 0.336204 | + | 0.237732i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.6143 | − | 47.8294i | 0.936752 | − | 1.62250i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.133975 | + | 0.232051i | −0.00453956 | + | 0.00786274i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.51575 | + | 0.535898i | −0.0513003 | + | 0.0181374i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3.03150i | − | 0.102483i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.232051 | + | 0.133975i | 0.00783580 | + | 0.00452400i | 0.503913 | − | 0.863755i | \(-0.331893\pi\) |
−0.496077 | + | 0.868279i | \(0.665227\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.9280 | − | 10.1023i | 0.739613 | − | 0.340741i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 48.3335i | − | 1.62840i | −0.580588 | − | 0.814198i | \(-0.697177\pi\) | ||
0.580588 | − | 0.814198i | \(-0.302823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.8660 | − | 22.2846i | −0.432976 | − | 0.749937i | 0.564152 | − | 0.825671i | \(-0.309203\pi\) |
−0.997128 | + | 0.0757343i | \(0.975870\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.8564 | + | 22.4243i | −0.533007 | + | 0.753786i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.08604 | + | 1.88108i | 0.0364658 | + | 0.0631606i | 0.883682 | − | 0.468087i | \(-0.155057\pi\) |
−0.847217 | + | 0.531248i | \(0.821723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.60770 | + | 2.66025i | −0.154537 | + | 0.0892221i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.9239 | − | 7.38370i | 1.57201 | − | 0.247363i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.378937 | + | 3.28169i | 0.0126807 | + | 0.109818i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.73205 | − | 1.00000i | −0.0578961 | − | 0.0334263i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.224745 | + | 2.43916i | −0.00750401 | + | 0.0814411i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.41851 | − | 2.55103i | 0.147365 | − | 0.0850815i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 53.5692i | − | 1.78465i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.244083 | − | 2.64903i | 0.00812257 | − | 0.0881543i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.89898 | −0.162848 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.4449 | + | 13.5359i | 0.778474 | + | 0.449452i | 0.835889 | − | 0.548898i | \(-0.184953\pi\) |
−0.0574152 | + | 0.998350i | \(0.518286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.13505 | + | 6.10707i | −0.0376473 | + | 0.202559i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.3147 | 0.706189 | 0.353094 | − | 0.935588i | \(-0.385129\pi\) | ||||
0.353094 | + | 0.935588i | \(0.385129\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9282 | 0.361671 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.7251 | + | 23.2800i | 0.354561 | + | 0.769612i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.92996 | + | 1.69161i | 0.0967559 | + | 0.0558620i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.9808 | −0.659105 | −0.329552 | − | 0.944137i | \(-0.606898\pi\) | ||||
−0.329552 | + | 0.944137i | \(0.606898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.8988 | + | 2.20204i | 0.787491 | + | 0.0725597i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.58630i | 0.118045i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0885 | + | 11.5981i | −0.660504 | + | 0.381342i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.06269 | − | 6.89320i | −0.264814 | − | 0.226402i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.22955 | − | 5.32868i | −0.302812 | − | 0.174828i | 0.340894 | − | 0.940102i | \(-0.389270\pi\) |
−0.643705 | + | 0.765273i | \(0.722604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | − | 27.7128i | 0.393284 | − | 0.908251i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.02345 | + | 19.5863i | 0.295415 | + | 0.641227i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.6675 | + | 18.2832i | −1.03564 | + | 0.597926i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.8923 | + | 30.9904i | 0.584516 | + | 1.01241i | 0.994936 | + | 0.100515i | \(0.0320490\pi\) |
−0.410419 | + | 0.911897i | \(0.634618\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.7370 | − | 16.7846i | −0.774628 | − | 0.547745i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.6264 | + | 21.8695i | 0.411608 | + | 0.712927i | 0.995066 | − | 0.0992170i | \(-0.0316338\pi\) |
−0.583457 | + | 0.812144i | \(0.698300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.8564i | 0.972258i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.41145 | − | 1.37290i | 0.0459143 | − | 0.0446604i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.06678 | − | 2.34795i | −0.132152 | − | 0.0762982i | 0.432466 | − | 0.901650i | \(-0.357643\pi\) |
−0.564619 | + | 0.825352i | \(0.690977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.803848i | 0.0260940i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.5359 | + | 8.86422i | 0.406504 | + | 0.287442i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.15471 | − | 7.19617i | 0.134584 | − | 0.233107i | −0.790854 | − | 0.612004i | \(-0.790363\pi\) |
0.925439 | + | 0.378898i | \(0.123697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.19615 | + | 15.9282i | −0.297581 | + | 0.515425i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.9282 | + | 15.4548i | −0.353259 | + | 0.499583i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.44949 | − | 1.41421i | 0.0790981 | − | 0.0456673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.9282 | 0.804136 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.55051 | + | 11.1708i | −0.307761 | + | 0.359975i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.98262 | − | 3.43400i | −0.0638228 | − | 0.110544i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.59808 | + | 16.6244i | −0.308653 | + | 0.534603i | −0.978068 | − | 0.208286i | \(-0.933212\pi\) |
0.669415 | + | 0.742889i | \(0.266545\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.7491 | + | 32.4495i | −0.570183 | + | 1.04243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.7685 | − | 46.3644i | 0.859043 | − | 1.48791i | −0.0138004 | − | 0.999905i | \(-0.504393\pi\) |
0.872843 | − | 0.488001i | \(-0.162274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.375644 | + | 0.650635i | 0.0120426 | + | 0.0208584i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.38643 | + | 0.127746i | 0.0444014 | + | 0.00409116i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.04008 | −0.289218 | −0.144609 | − | 0.989489i | \(-0.546192\pi\) | ||||
−0.144609 | + | 0.989489i | \(0.546192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.5885 | + | 19.3923i | −1.07349 | + | 0.619781i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.0802 | + | 6.39230i | −0.577255 | + | 0.204091i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.2635 | + | 28.1691i | −0.518724 | + | 0.898456i | 0.481040 | + | 0.876699i | \(0.340259\pi\) |
−0.999763 | + | 0.0217569i | \(0.993074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.464102 | + | 0.803848i | −0.0147875 | + | 0.0256127i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.203072 | − | 0.287187i | 0.00646385 | − | 0.00914127i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 30.2533i | − | 0.961999i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.3827 | + | 29.0885i | 1.60046 | + | 0.924025i | 0.991395 | + | 0.130904i | \(0.0417880\pi\) |
0.609064 | + | 0.793121i | \(0.291545\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.0974 | + | 28.4293i | 0.415635 | + | 0.902177i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 32.8043i | − | 1.03997i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.08846 | + | 10.5455i | 0.192823 | + | 0.333980i | 0.946185 | − | 0.323627i | \(-0.104902\pi\) |
−0.753361 | + | 0.657607i | \(0.771569\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −38.6603 | − | 10.9348i | −1.22316 | − | 0.345961i |
(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 | 912.2.bn.m.65.4 | 8 | ||
3.2 | odd | 2 | inner | 912.2.bn.m.65.3 | 8 | ||
4.3 | odd | 2 | 57.2.f.a.8.2 | ✓ | 8 | ||
12.11 | even | 2 | 57.2.f.a.8.3 | yes | 8 | ||
19.12 | odd | 6 | inner | 912.2.bn.m.449.3 | 8 | ||
57.50 | even | 6 | inner | 912.2.bn.m.449.4 | 8 | ||
76.11 | odd | 6 | 1083.2.d.b.1082.6 | 8 | |||
76.27 | even | 6 | 1083.2.d.b.1082.3 | 8 | |||
76.31 | even | 6 | 57.2.f.a.50.3 | yes | 8 | ||
228.11 | even | 6 | 1083.2.d.b.1082.4 | 8 | |||
228.107 | odd | 6 | 57.2.f.a.50.2 | yes | 8 | ||
228.179 | odd | 6 | 1083.2.d.b.1082.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.f.a.8.2 | ✓ | 8 | 4.3 | odd | 2 | ||
57.2.f.a.8.3 | yes | 8 | 12.11 | even | 2 | ||
57.2.f.a.50.2 | yes | 8 | 228.107 | odd | 6 | ||
57.2.f.a.50.3 | yes | 8 | 76.31 | even | 6 | ||
912.2.bn.m.65.3 | 8 | 3.2 | odd | 2 | inner | ||
912.2.bn.m.65.4 | 8 | 1.1 | even | 1 | trivial | ||
912.2.bn.m.449.3 | 8 | 19.12 | odd | 6 | inner | ||
912.2.bn.m.449.4 | 8 | 57.50 | even | 6 | inner | ||
1083.2.d.b.1082.3 | 8 | 76.27 | even | 6 | |||
1083.2.d.b.1082.4 | 8 | 228.11 | even | 6 | |||
1083.2.d.b.1082.5 | 8 | 228.179 | odd | 6 | |||
1083.2.d.b.1082.6 | 8 | 76.11 | odd | 6 |