Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.4 | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.f.1601.4 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.07665 | + | 1.63937i | 0.784899 | + | 0.619624i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.48223 | + | 3.16517i | 1.65295 | + | 0.954334i | 0.975849 | + | 0.218448i | \(0.0700994\pi\) |
0.677106 | + | 0.735886i | \(0.263234\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.05290i | − | 0.292021i | −0.989283 | − | 0.146011i | \(-0.953357\pi\) | ||
0.989283 | − | 0.146011i | \(-0.0466434\pi\) | |||||||
\(14\) | −2.61811 | − | 0.381412i | −0.699721 | − | 0.101937i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.31842 | − | 4.01562i | 0.562299 | − | 0.973931i | −0.434996 | − | 0.900432i | \(-0.643250\pi\) |
0.997295 | − | 0.0734985i | \(-0.0234164\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.35129 | + | 3.08957i | −1.22767 | + | 0.708795i | −0.966542 | − | 0.256509i | \(-0.917428\pi\) |
−0.261128 | + | 0.965304i | \(0.584094\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.33033 | −1.34963 | ||||||||
\(23\) | 6.10091 | − | 3.52236i | 1.27213 | − | 0.734463i | 0.296739 | − | 0.954959i | \(-0.404101\pi\) |
0.975388 | + | 0.220496i | \(0.0707676\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.526449 | + | 0.911836i | 0.103245 | + | 0.178826i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.45806 | − | 0.978745i | 0.464530 | − | 0.184965i | ||||
\(29\) | 2.98101i | 0.553560i | 0.960933 | + | 0.276780i | \(0.0892674\pi\) | ||||
−0.960933 | + | 0.276780i | \(0.910733\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46948 | + | 3.15781i | 0.982348 | + | 0.567159i | 0.902978 | − | 0.429686i | \(-0.141376\pi\) |
0.0793697 | + | 0.996845i | \(0.474709\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.63684i | 0.795211i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.73991 | + | 3.01361i | 0.286039 | + | 0.495434i | 0.972861 | − | 0.231392i | \(-0.0743279\pi\) |
−0.686821 | + | 0.726826i | \(0.740995\pi\) | |||||||
\(38\) | 3.08957 | − | 5.35129i | 0.501194 | − | 0.868094i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.97007 | 1.08854 | 0.544271 | − | 0.838909i | \(-0.316806\pi\) | ||||
0.544271 | + | 0.838909i | \(0.316806\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.58650 | −0.394437 | −0.197218 | − | 0.980360i | \(-0.563191\pi\) | ||||
−0.197218 | + | 0.980360i | \(0.563191\pi\) | |||||||
\(44\) | 5.48223 | − | 3.16517i | 0.826477 | − | 0.477167i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.52236 | + | 6.10091i | −0.519344 | + | 0.899529i | ||||
\(47\) | −4.07711 | − | 7.06176i | −0.594707 | − | 1.03006i | −0.993588 | − | 0.113060i | \(-0.963935\pi\) |
0.398881 | − | 0.917003i | \(-0.369399\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.62493 | + | 6.80879i | 0.232133 | + | 0.972684i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.911836 | − | 0.526449i | −0.126449 | − | 0.0730053i | ||||
\(53\) | 7.68480 | + | 4.43682i | 1.05559 | + | 0.609445i | 0.924209 | − | 0.381887i | \(-0.124726\pi\) |
0.131380 | + | 0.991332i | \(0.458059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.63937 | + | 2.07665i | −0.219070 | + | 0.277504i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.49051 | − | 2.58163i | −0.195713 | − | 0.338985i | ||||
\(59\) | 0.452296 | − | 0.783400i | 0.0588839 | − | 0.101990i | −0.835081 | − | 0.550127i | \(-0.814579\pi\) |
0.893965 | + | 0.448137i | \(0.147912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.81047 | + | 5.08673i | −1.12807 | + | 0.651289i | −0.943448 | − | 0.331522i | \(-0.892438\pi\) |
−0.184618 | + | 0.982810i | \(0.559105\pi\) | |||||||
\(62\) | −6.31561 | −0.802084 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.91612 | − | 8.51497i | 0.600600 | − | 1.04027i | −0.392131 | − | 0.919909i | \(-0.628262\pi\) |
0.992730 | − | 0.120360i | \(-0.0384047\pi\) | |||||||
\(68\) | −2.31842 | − | 4.01562i | −0.281150 | − | 0.486965i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.4282i | − | 1.71232i | −0.516713 | − | 0.856159i | \(-0.672844\pi\) | ||
0.516713 | − | 0.856159i | \(-0.327156\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.24574 | − | 4.18333i | −0.848050 | − | 0.489622i | 0.0119423 | − | 0.999929i | \(-0.496199\pi\) |
−0.859992 | + | 0.510307i | \(0.829532\pi\) | |||||||
\(74\) | −3.01361 | − | 1.73991i | −0.350325 | − | 0.202260i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.17914i | 0.708795i | ||||||||
\(77\) | 6.19578 | + | 15.5603i | 0.706075 | + | 1.77327i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.73283 | − | 4.73340i | −0.307467 | − | 0.532549i | 0.670340 | − | 0.742054i | \(-0.266148\pi\) |
−0.977808 | + | 0.209505i | \(0.932815\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.03626 | + | 3.48504i | −0.666593 | + | 0.384858i | ||||
\(83\) | −14.6297 | −1.60581 | −0.802907 | − | 0.596105i | \(-0.796714\pi\) | ||||
−0.802907 | + | 0.596105i | \(0.796714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.23997 | − | 1.29325i | 0.241542 | − | 0.139455i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.16517 | + | 5.48223i | −0.337408 | + | 0.584408i | ||||
\(89\) | 1.91982 | + | 3.32522i | 0.203500 | + | 0.352473i | 0.949654 | − | 0.313301i | \(-0.101435\pi\) |
−0.746154 | + | 0.665774i | \(0.768102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.72609 | − | 2.18650i | 0.180943 | − | 0.229207i | ||||
\(92\) | − | 7.04472i | − | 0.734463i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.06176 | + | 4.07711i | 0.728365 | + | 0.420522i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.87891i | − | 0.596913i | −0.954423 | − | 0.298457i | \(-0.903528\pi\) | ||
0.954423 | − | 0.298457i | \(-0.0964718\pi\) | |||||||
\(98\) | −4.81163 | − | 5.08412i | −0.486048 | − | 0.513573i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.35408 | + | 5.80944i | −0.333744 | + | 0.578061i | −0.983243 | − | 0.182301i | \(-0.941645\pi\) |
0.649499 | + | 0.760362i | \(0.274979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.30789 | − | 2.48716i | 0.424469 | − | 0.245067i | −0.272519 | − | 0.962151i | \(-0.587857\pi\) |
0.696988 | + | 0.717083i | \(0.254523\pi\) | |||||||
\(104\) | 1.05290 | 0.103245 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.87365 | −0.861885 | ||||||||
\(107\) | −6.35602 | + | 3.66965i | −0.614460 | + | 0.354759i | −0.774709 | − | 0.632318i | \(-0.782104\pi\) |
0.160249 | + | 0.987077i | \(0.448770\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.381412 | − | 2.61811i | 0.0360400 | − | 0.247389i | ||||
\(113\) | 0.184551i | 0.0173611i | 0.999962 | + | 0.00868054i | \(0.00276314\pi\) | ||||
−0.999962 | + | 0.00868054i | \(0.997237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.58163 | + | 1.49051i | 0.239699 | + | 0.138390i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.904592i | 0.0832745i | ||||||||
\(119\) | 11.3976 | − | 4.53828i | 1.04482 | − | 0.416024i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.5366 | + | 25.1781i | 1.32151 | + | 2.28891i | ||||
\(122\) | 5.08673 | − | 8.81047i | 0.460531 | − | 0.797663i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.46948 | − | 3.15781i | 0.491174 | − | 0.283579i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.70276 | −0.594774 | −0.297387 | − | 0.954757i | \(-0.596115\pi\) | ||||
−0.297387 | + | 0.954757i | \(0.596115\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.24116 | + | 3.88180i | 0.195811 | + | 0.339155i | 0.947166 | − | 0.320743i | \(-0.103933\pi\) |
−0.751355 | + | 0.659898i | \(0.770599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.1777 | − | 2.35680i | −1.40278 | − | 0.204360i | ||||
\(134\) | 9.83224i | 0.849376i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.01562 | + | 2.31842i | 0.344337 | + | 0.198803i | ||||
\(137\) | 15.2098 | + | 8.78137i | 1.29946 | + | 0.750243i | 0.980311 | − | 0.197461i | \(-0.0632697\pi\) |
0.319149 | + | 0.947705i | \(0.396603\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.02268i | 0.510837i | 0.966831 | + | 0.255418i | \(0.0822132\pi\) | ||||
−0.966831 | + | 0.255418i | \(0.917787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.21412 | + | 12.4952i | 0.605396 | + | 1.04858i | ||||
\(143\) | 3.33260 | − | 5.77223i | 0.278686 | − | 0.482698i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.36666 | 0.692430 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.47982 | 0.286039 | ||||||||
\(149\) | 6.06548 | − | 3.50191i | 0.496903 | − | 0.286887i | −0.230530 | − | 0.973065i | \(-0.574046\pi\) |
0.727434 | + | 0.686178i | \(0.240713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.43540 | + | 11.1464i | −0.523706 | + | 0.907085i | 0.475913 | + | 0.879492i | \(0.342118\pi\) |
−0.999619 | + | 0.0275929i | \(0.991216\pi\) | |||||||
\(152\) | −3.08957 | − | 5.35129i | −0.250597 | − | 0.434047i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.1459 | − | 10.3778i | −1.05932 | − | 0.836263i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.56427 | − | 5.52193i | −0.763312 | − | 0.440698i | 0.0671718 | − | 0.997741i | \(-0.478602\pi\) |
−0.830484 | + | 0.557043i | \(0.811936\pi\) | |||||||
\(158\) | 4.73340 | + | 2.73283i | 0.376569 | + | 0.217412i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.4439 | + | 2.68694i | 1.45358 | + | 0.211760i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.62287 | + | 6.27500i | 0.283765 | + | 0.491496i | 0.972309 | − | 0.233699i | \(-0.0750830\pi\) |
−0.688544 | + | 0.725195i | \(0.741750\pi\) | |||||||
\(164\) | 3.48504 | − | 6.03626i | 0.272136 | − | 0.471353i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.6697 | − | 7.31483i | 0.983356 | − | 0.567741i | ||||
\(167\) | 13.8606 | 1.07257 | 0.536283 | − | 0.844038i | \(-0.319828\pi\) | ||||
0.536283 | + | 0.844038i | \(0.319828\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8914 | 0.914724 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.29325 | + | 2.23997i | −0.0986092 | + | 0.170796i | ||||
\(173\) | −0.479402 | − | 0.830348i | −0.0364482 | − | 0.0631302i | 0.847226 | − | 0.531233i | \(-0.178271\pi\) |
−0.883674 | + | 0.468103i | \(0.844938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 6.33033i | − | 0.477167i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.32522 | − | 1.91982i | −0.249236 | − | 0.143896i | ||||
\(179\) | 20.2531 | + | 11.6931i | 1.51379 | + | 0.873984i | 0.999870 | + | 0.0161436i | \(0.00513888\pi\) |
0.513916 | + | 0.857841i | \(0.328194\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.2865i | 1.43355i | 0.697303 | + | 0.716776i | \(0.254383\pi\) | ||||
−0.697303 | + | 0.716776i | \(0.745617\pi\) | |||||||
\(182\) | −0.401588 | + | 2.75661i | −0.0297677 | + | 0.204333i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.52236 | + | 6.10091i | 0.259672 | + | 0.449765i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.4202 | − | 14.6764i | 1.85891 | − | 1.07324i | ||||
\(188\) | −8.15421 | −0.594707 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.44949 | − | 1.41421i | 0.177239 | − | 0.102329i | −0.408756 | − | 0.912644i | \(-0.634037\pi\) |
0.585995 | + | 0.810315i | \(0.300704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.10862 | − | 7.11634i | 0.295745 | − | 0.512246i | −0.679413 | − | 0.733756i | \(-0.737765\pi\) |
0.975158 | + | 0.221511i | \(0.0710987\pi\) | |||||||
\(194\) | 2.93946 | + | 5.09129i | 0.211041 | + | 0.365533i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.70905 | + | 1.99716i | 0.479218 | + | 0.142654i | ||||
\(197\) | − | 3.51321i | − | 0.250306i | −0.992137 | − | 0.125153i | \(-0.960058\pi\) | ||
0.992137 | − | 0.125153i | \(-0.0399422\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.00000 | + | 1.73205i | 0.212664 | + | 0.122782i | 0.602549 | − | 0.798082i | \(-0.294152\pi\) |
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 6.70816i | − | 0.471985i | ||||||
\(203\) | −4.88698 | + | 6.19052i | −0.342999 | + | 0.434489i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.48716 | + | 4.30789i | −0.173289 | + | 0.300145i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.911836 | + | 0.526449i | −0.0632245 | + | 0.0365027i | ||||
\(209\) | −39.1160 | −2.70571 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.96592 | −0.686082 | −0.343041 | − | 0.939320i | \(-0.611457\pi\) | ||||
−0.343041 | + | 0.939320i | \(0.611457\pi\) | |||||||
\(212\) | 7.68480 | − | 4.43682i | 0.527795 | − | 0.304722i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.66965 | − | 6.35602i | 0.250852 | − | 0.434489i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.18138 | + | 15.5242i | 0.419619 | + | 1.05385i | ||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.22804 | − | 2.44106i | −0.284408 | − | 0.164203i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1087i | 0.743894i | 0.928254 | + | 0.371947i | \(0.121310\pi\) | ||||
−0.928254 | + | 0.371947i | \(0.878690\pi\) | |||||||
\(224\) | 0.978745 | + | 2.45806i | 0.0653952 | + | 0.164236i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.0922754 | − | 0.159826i | −0.00613807 | − | 0.0106314i | ||||
\(227\) | −11.7619 | + | 20.3722i | −0.780665 | + | 1.35215i | 0.150889 | + | 0.988551i | \(0.451786\pi\) |
−0.931555 | + | 0.363602i | \(0.881547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.21579 | − | 4.74339i | 0.542915 | − | 0.313452i | −0.203345 | − | 0.979107i | \(-0.565181\pi\) |
0.746259 | + | 0.665655i | \(0.231848\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.98101 | −0.195713 | ||||||||
\(233\) | 8.98361 | − | 5.18669i | 0.588536 | − | 0.339791i | −0.175982 | − | 0.984393i | \(-0.556310\pi\) |
0.764518 | + | 0.644602i | \(0.222977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.452296 | − | 0.783400i | −0.0294420 | − | 0.0509950i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.60149 | + | 9.62908i | −0.492732 | + | 0.624161i | ||||
\(239\) | − | 12.3746i | − | 0.800444i | −0.916418 | − | 0.400222i | \(-0.868933\pi\) | ||
0.916418 | − | 0.400222i | \(-0.131067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8208 | − | 6.24737i | −0.697027 | − | 0.402429i | 0.109212 | − | 0.994018i | \(-0.465167\pi\) |
−0.806239 | + | 0.591590i | \(0.798501\pi\) | |||||||
\(242\) | −25.1781 | − | 14.5366i | −1.61851 | − | 0.934445i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.1735i | 0.651289i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.25300 | + | 5.63436i | 0.206983 | + | 0.358506i | ||||
\(248\) | −3.15781 | + | 5.46948i | −0.200521 | + | 0.347312i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5304 | −0.854034 | −0.427017 | − | 0.904244i | \(-0.640436\pi\) | ||||
−0.427017 | + | 0.904244i | \(0.640436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.5954 | 2.80369 | ||||||||
\(254\) | 5.80476 | − | 3.35138i | 0.364223 | − | 0.210284i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.20899 | + | 3.82609i | 0.137793 | + | 0.238665i | 0.926661 | − | 0.375898i | \(-0.122666\pi\) |
−0.788868 | + | 0.614563i | \(0.789332\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.32724 | + | 9.11056i | −0.0824709 | + | 0.566103i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.88180 | − | 2.24116i | −0.239819 | − | 0.138459i | ||||
\(263\) | 5.30558 | + | 3.06318i | 0.327156 | + | 0.188884i | 0.654578 | − | 0.755995i | \(-0.272846\pi\) |
−0.327422 | + | 0.944878i | \(0.606180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.1887 | − | 6.04780i | 0.931278 | − | 0.370814i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.91612 | − | 8.51497i | −0.300300 | − | 0.520135i | ||||
\(269\) | 2.09370 | − | 3.62639i | 0.127655 | − | 0.221105i | −0.795113 | − | 0.606462i | \(-0.792588\pi\) |
0.922768 | + | 0.385357i | \(0.125922\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.253692 | − | 0.146469i | 0.0154107 | − | 0.00889737i | −0.492275 | − | 0.870440i | \(-0.663835\pi\) |
0.507686 | + | 0.861542i | \(0.330501\pi\) | |||||||
\(272\) | −4.63684 | −0.281150 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.5627 | −1.06100 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.31099 | + | 12.6630i | −0.439275 | + | 0.760847i | −0.997634 | − | 0.0687531i | \(-0.978098\pi\) |
0.558359 | + | 0.829600i | \(0.311431\pi\) | |||||||
\(278\) | −3.01134 | − | 5.21579i | −0.180608 | − | 0.312822i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.1691i | − | 1.08388i | −0.840419 | − | 0.541938i | \(-0.817691\pi\) | ||
0.840419 | − | 0.541938i | \(-0.182309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3712 | + | 10.6066i | 1.09206 | + | 0.630499i | 0.934123 | − | 0.356951i | \(-0.116184\pi\) |
0.157933 | + | 0.987450i | \(0.449517\pi\) | |||||||
\(284\) | −12.4952 | − | 7.21412i | −0.741455 | − | 0.428079i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.66519i | 0.394121i | ||||||||
\(287\) | 14.4744 | + | 11.4265i | 0.854396 | + | 0.674486i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.25013 | − | 3.89734i | −0.132361 | − | 0.229256i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.24574 | + | 4.18333i | −0.424025 | + | 0.244811i | ||||
\(293\) | 7.64481 | 0.446615 | 0.223307 | − | 0.974748i | \(-0.428315\pi\) | ||||
0.223307 | + | 0.974748i | \(0.428315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.01361 | + | 1.73991i | −0.175163 | + | 0.101130i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.50191 | + | 6.06548i | −0.202860 | + | 0.351364i | ||||
\(299\) | −3.70868 | − | 6.42363i | −0.214479 | − | 0.371488i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.37124 | − | 4.24022i | −0.309593 | − | 0.244402i | ||||
\(302\) | − | 12.8708i | − | 0.740632i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.35129 | + | 3.08957i | 0.306917 | + | 0.177199i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.1561i | − | 0.750859i | −0.926851 | − | 0.375429i | \(-0.877495\pi\) | ||
0.926851 | − | 0.375429i | \(-0.122505\pi\) | |||||||
\(308\) | 16.5735 | + | 2.41446i | 0.944365 | + | 0.137577i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.13043 | − | 5.42207i | 0.177511 | − | 0.307457i | −0.763517 | − | 0.645788i | \(-0.776529\pi\) |
0.941027 | + | 0.338331i | \(0.109862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1392 | − | 8.74065i | 0.855721 | − | 0.494051i | −0.00685609 | − | 0.999976i | \(-0.502182\pi\) |
0.862577 | + | 0.505926i | \(0.168849\pi\) | |||||||
\(314\) | 11.0439 | 0.623241 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.46566 | −0.307467 | ||||||||
\(317\) | 1.32832 | − | 0.766906i | 0.0746058 | − | 0.0430737i | −0.462233 | − | 0.886758i | \(-0.652952\pi\) |
0.536839 | + | 0.843685i | \(0.319618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.43540 | + | 16.3426i | −0.528281 | + | 0.915010i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −17.3163 | + | 6.89498i | −0.965002 | + | 0.384242i | ||||
\(323\) | 28.6516i | 1.59422i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.27500 | − | 3.62287i | −0.347540 | − | 0.200652i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.97007i | 0.384858i | ||||||||
\(329\) | 3.11011 | − | 21.3487i | 0.171466 | − | 1.17699i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.756607 | + | 1.31048i | 0.0415869 | + | 0.0720306i | 0.886070 | − | 0.463552i | \(-0.153425\pi\) |
−0.844483 | + | 0.535583i | \(0.820092\pi\) | |||||||
\(332\) | −7.31483 | + | 12.6697i | −0.401453 | + | 0.695337i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.0036 | + | 6.93030i | −0.656810 | + | 0.379209i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.14064 | −0.171082 | −0.0855408 | − | 0.996335i | \(-0.527262\pi\) | ||||
−0.0855408 | + | 0.996335i | \(0.527262\pi\) | |||||||
\(338\) | −10.2983 | + | 5.94570i | −0.560152 | + | 0.323404i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.9900 | + | 34.6236i | 1.08252 | + | 1.87498i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.78771 | + | 16.8033i | −0.420497 | + | 0.907294i | ||||
\(344\) | − | 2.58650i | − | 0.139455i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.830348 | + | 0.479402i | 0.0446398 | + | 0.0257728i | ||||
\(347\) | −23.7336 | − | 13.7026i | −1.27408 | − | 0.735593i | −0.298330 | − | 0.954463i | \(-0.596430\pi\) |
−0.975754 | + | 0.218870i | \(0.929763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.5594i | 1.04699i | 0.852028 | + | 0.523496i | \(0.175373\pi\) | ||||
−0.852028 | + | 0.523496i | \(0.824627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.16517 | + | 5.48223i | 0.168704 | + | 0.292204i | ||||
\(353\) | −7.40515 | + | 12.8261i | −0.394136 | + | 0.682664i | −0.992991 | − | 0.118194i | \(-0.962290\pi\) |
0.598854 | + | 0.800858i | \(0.295623\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.83964 | 0.203500 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.3862 | −1.23600 | ||||||||
\(359\) | −14.3492 | + | 8.28450i | −0.757321 | + | 0.437239i | −0.828333 | − | 0.560236i | \(-0.810710\pi\) |
0.0710122 | + | 0.997475i | \(0.477377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.59086 | − | 16.6119i | 0.504782 | − | 0.874308i | ||||
\(362\) | −9.64324 | − | 16.7026i | −0.506837 | − | 0.877868i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.03052 | − | 2.58809i | −0.0540138 | − | 0.135653i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.1357 | + | 7.00655i | 0.633479 | + | 0.365739i | 0.782098 | − | 0.623155i | \(-0.214150\pi\) |
−0.148619 | + | 0.988894i | \(0.547483\pi\) | |||||||
\(368\) | −6.10091 | − | 3.52236i | −0.318032 | − | 0.183616i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.68504 | + | 21.8120i | 0.450905 | + | 1.13242i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.31099 | − | 12.6630i | −0.378549 | − | 0.655666i | 0.612303 | − | 0.790624i | \(-0.290243\pi\) |
−0.990851 | + | 0.134958i | \(0.956910\pi\) | |||||||
\(374\) | −14.6764 | + | 25.4202i | −0.758897 | + | 1.31445i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.06176 | − | 4.07711i | 0.364182 | − | 0.210261i | ||||
\(377\) | 3.13870 | 0.161651 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.68145 | 0.240470 | 0.120235 | − | 0.992745i | \(-0.461635\pi\) | ||||
0.120235 | + | 0.992745i | \(0.461635\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.41421 | + | 2.44949i | −0.0723575 | + | 0.125327i | ||||
\(383\) | 5.83621 | + | 10.1086i | 0.298216 | + | 0.516526i | 0.975728 | − | 0.218986i | \(-0.0702749\pi\) |
−0.677511 | + | 0.735512i | \(0.736942\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.21725i | 0.418247i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.09129 | − | 2.93946i | −0.258471 | − | 0.149228i | ||||
\(389\) | 11.3452 | + | 6.55018i | 0.575226 | + | 0.332107i | 0.759234 | − | 0.650818i | \(-0.225574\pi\) |
−0.184008 | + | 0.982925i | \(0.558907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 32.6652i | − | 1.65195i | ||||||
\(392\) | −6.80879 | + | 1.62493i | −0.343896 | + | 0.0820715i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.75661 | + | 3.04253i | 0.0884966 | + | 0.153281i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.5700 | − | 15.3402i | 1.33351 | − | 0.769903i | 0.347675 | − | 0.937615i | \(-0.386971\pi\) |
0.985836 | + | 0.167712i | \(0.0536378\pi\) | |||||||
\(398\) | −3.46410 | −0.173640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.88085 | + | 3.97266i | −0.343613 | + | 0.198385i | −0.661869 | − | 0.749620i | \(-0.730236\pi\) |
0.318255 | + | 0.948005i | \(0.396903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.32485 | − | 5.75880i | 0.165622 | − | 0.286866i | ||||
\(404\) | 3.35408 | + | 5.80944i | 0.166872 | + | 0.289030i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.13699 | − | 7.80464i | 0.0564281 | − | 0.387338i | ||||
\(407\) | 22.0284i | 1.09191i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.4957 | − | 19.9161i | −1.70570 | − | 0.984789i | −0.939729 | − | 0.341919i | \(-0.888923\pi\) |
−0.765975 | − | 0.642870i | \(-0.777744\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 4.97432i | − | 0.245067i | ||||||
\(413\) | 2.22354 | − | 0.885365i | 0.109413 | − | 0.0435660i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.526449 | − | 0.911836i | 0.0258113 | − | 0.0447064i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.8754 | − | 19.5580i | 1.65690 | − | 0.956613i | ||||
\(419\) | 11.0357 | 0.539131 | 0.269566 | − | 0.962982i | \(-0.413120\pi\) | ||||
0.269566 | + | 0.962982i | \(0.413120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.78421 | −0.379379 | −0.189690 | − | 0.981844i | \(-0.560748\pi\) | ||||
−0.189690 | + | 0.981844i | \(0.560748\pi\) | |||||||
\(422\) | 8.63074 | − | 4.98296i | 0.420138 | − | 0.242567i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.43682 | + | 7.68480i | −0.215471 | + | 0.373207i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.6353 | − | 3.88028i | −1.28897 | − | 0.187780i | ||||
\(428\) | 7.33930i | 0.354759i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.86273 | + | 5.11690i | 0.426903 | + | 0.246472i | 0.698026 | − | 0.716072i | \(-0.254062\pi\) |
−0.271124 | + | 0.962545i | \(0.587395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 40.3902i | − | 1.94103i | −0.241047 | − | 0.970513i | \(-0.577491\pi\) | ||
0.241047 | − | 0.970513i | \(-0.422509\pi\) | |||||||
\(434\) | −13.1153 | − | 10.3536i | −0.629555 | − | 0.496990i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | −21.7651 | + | 37.6983i | −1.04117 | + | 1.80336i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.2331 | − | 6.48543i | 0.536126 | − | 0.309533i | −0.207381 | − | 0.978260i | \(-0.566494\pi\) |
0.743508 | + | 0.668728i | \(0.233161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.88212 | 0.232219 | ||||||||
\(443\) | −7.49547 | + | 4.32751i | −0.356120 | + | 0.205606i | −0.667378 | − | 0.744720i | \(-0.732583\pi\) |
0.311257 | + | 0.950326i | \(0.399250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.55435 | − | 9.62042i | −0.263006 | − | 0.455540i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.07665 | − | 1.63937i | −0.0981124 | − | 0.0774529i | ||||
\(449\) | 25.4407i | 1.20062i | 0.799768 | + | 0.600310i | \(0.204956\pi\) | ||||
−0.799768 | + | 0.600310i | \(0.795044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.2115 | + | 22.0614i | 1.79931 | + | 1.03883i | ||||
\(452\) | 0.159826 | + | 0.0922754i | 0.00751757 | + | 0.00434027i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 23.5238i | − | 1.10403i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2697 | + | 26.4480i | 0.714289 | + | 1.23718i | 0.963233 | + | 0.268666i | \(0.0865829\pi\) |
−0.248945 | + | 0.968518i | \(0.580084\pi\) | |||||||
\(458\) | −4.74339 | + | 8.21579i | −0.221644 | + | 0.383899i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.6680 | −0.729734 | −0.364867 | − | 0.931060i | \(-0.618886\pi\) | ||||
−0.364867 | + | 0.931060i | \(0.618886\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.0462 | −1.48931 | −0.744656 | − | 0.667448i | \(-0.767387\pi\) | ||||
−0.744656 | + | 0.667448i | \(0.767387\pi\) | |||||||
\(464\) | 2.58163 | − | 1.49051i | 0.119849 | − | 0.0691950i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.18669 | + | 8.98361i | −0.240269 | + | 0.416158i | ||||
\(467\) | −0.349579 | − | 0.605489i | −0.0161766 | − | 0.0280187i | 0.857824 | − | 0.513944i | \(-0.171816\pi\) |
−0.874000 | + | 0.485925i | \(0.838483\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.1682 | − | 9.62326i | 1.11599 | − | 0.444361i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.783400 | + | 0.452296i | 0.0360589 | + | 0.0208186i | ||||
\(473\) | −14.1798 | − | 8.18669i | −0.651986 | − | 0.376424i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.76855 | − | 12.1398i | 0.0810611 | − | 0.556426i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.18728 | + | 10.7167i | 0.283000 | + | 0.490170i | ||||
\(479\) | 4.27280 | − | 7.40071i | 0.195229 | − | 0.338147i | −0.751746 | − | 0.659452i | \(-0.770788\pi\) |
0.946976 | + | 0.321305i | \(0.104122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.17302 | − | 1.83195i | 0.144677 | − | 0.0835295i | ||||
\(482\) | 12.4947 | 0.569120 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 29.0731 | 1.32151 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9089 | + | 20.6268i | −0.539643 | + | 0.934689i | 0.459280 | + | 0.888292i | \(0.348108\pi\) |
−0.998923 | + | 0.0463978i | \(0.985226\pi\) | |||||||
\(488\) | −5.08673 | − | 8.81047i | −0.230265 | − | 0.398831i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.9104i | − | 0.582638i | −0.956626 | − | 0.291319i | \(-0.905906\pi\) | ||
0.956626 | − | 0.291319i | \(-0.0940941\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.9706 | + | 6.91124i | 0.539129 | + | 0.311267i | ||||
\(494\) | −5.63436 | − | 3.25300i | −0.253502 | − | 0.146359i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.31561i | − | 0.283579i | ||||||
\(497\) | 23.6532 | − | 29.9624i | 1.06099 | − | 1.34400i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.16823 | − | 14.1478i | −0.365660 | − | 0.633342i | 0.623222 | − | 0.782045i | \(-0.285823\pi\) |
−0.988882 | + | 0.148703i | \(0.952490\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.7177 | − | 6.76522i | 0.522987 | − | 0.301947i | ||||
\(503\) | −28.3413 | −1.26368 | −0.631838 | − | 0.775100i | \(-0.717699\pi\) | ||||
−0.631838 | + | 0.775100i | \(0.717699\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −38.6208 | + | 22.2977i | −1.71690 | + | 0.991254i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.35138 | + | 5.80476i | −0.148693 | + | 0.257545i | ||||
\(509\) | 1.18911 | + | 2.05959i | 0.0527062 | + | 0.0912898i | 0.891175 | − | 0.453660i | \(-0.149882\pi\) |
−0.838469 | + | 0.544950i | \(0.816549\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.18883 | − | 20.5658i | −0.362253 | − | 0.909776i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.82609 | − | 2.20899i | −0.168762 | − | 0.0974346i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 51.6189i | − | 2.27020i | ||||||
\(518\) | −3.40585 | − | 8.55360i | −0.149645 | − | 0.375824i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.14185 | − | 7.17389i | 0.181458 | − | 0.314294i | −0.760919 | − | 0.648846i | \(-0.775252\pi\) |
0.942377 | + | 0.334552i | \(0.108585\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.2532 | + | 20.9308i | −1.58524 | + | 0.915239i | −0.591166 | + | 0.806550i | \(0.701332\pi\) |
−0.994076 | + | 0.108689i | \(0.965335\pi\) | |||||||
\(524\) | 4.48232 | 0.195811 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.12635 | −0.267122 | ||||||||
\(527\) | 25.3611 | − | 14.6422i | 1.10475 | − | 0.637826i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.3140 | − | 23.0606i | 0.578871 | − | 1.00263i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −10.1299 | + | 12.8319i | −0.439186 | + | 0.556333i | ||||
\(533\) | − | 7.33877i | − | 0.317877i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.51497 | + | 4.91612i | 0.367791 | + | 0.212344i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.18740i | 0.180531i | ||||||||
\(539\) | −12.6427 | + | 42.4705i | −0.544559 | + | 1.82933i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9652 | − | 39.7769i | −0.987352 | − | 1.71014i | −0.630978 | − | 0.775801i | \(-0.717346\pi\) |
−0.356374 | − | 0.934343i | \(-0.615987\pi\) | |||||||
\(542\) | −0.146469 | + | 0.253692i | −0.00629139 | + | 0.0108970i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.01562 | − | 2.31842i | 0.172168 | − | 0.0994014i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.88688 | −0.208948 | −0.104474 | − | 0.994528i | \(-0.533316\pi\) | ||||
−0.104474 | + | 0.994528i | \(0.533316\pi\) | |||||||
\(548\) | 15.2098 | − | 8.78137i | 0.649730 | − | 0.375122i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.21004 | − | 15.9523i | −0.392361 | − | 0.679589i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.08467 | − | 14.3097i | 0.0886490 | − | 0.608511i | ||||
\(554\) | − | 14.6220i | − | 0.621229i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.21579 | + | 3.01134i | 0.221199 | + | 0.127709i | ||||
\(557\) | 25.4332 | + | 14.6839i | 1.07764 | + | 0.622175i | 0.930258 | − | 0.366905i | \(-0.119583\pi\) |
0.147380 | + | 0.989080i | \(0.452916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.72332i | 0.115184i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.08453 | + | 15.7349i | 0.383208 | + | 0.663735i | ||||
\(563\) | 1.36961 | − | 2.37223i | 0.0577220 | − | 0.0999775i | −0.835720 | − | 0.549155i | \(-0.814950\pi\) |
0.893442 | + | 0.449178i | \(0.148283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.2133 | −0.891660 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.4282 | 0.605396 | ||||||||
\(569\) | −0.798865 | + | 0.461225i | −0.0334902 | + | 0.0193356i | −0.516652 | − | 0.856196i | \(-0.672822\pi\) |
0.483161 | + | 0.875531i | \(0.339488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2761 | − | 21.2629i | 0.513740 | − | 0.889824i | −0.486133 | − | 0.873885i | \(-0.661593\pi\) |
0.999873 | − | 0.0159389i | \(-0.00507372\pi\) | |||||||
\(572\) | −3.33260 | − | 5.77223i | −0.139343 | − | 0.241349i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.2484 | − | 2.65847i | −0.761675 | − | 0.110962i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4982 | − | 13.5667i | −0.978241 | − | 0.564788i | −0.0765024 | − | 0.997069i | \(-0.524375\pi\) |
−0.901739 | + | 0.432282i | \(0.857709\pi\) | |||||||
\(578\) | 3.89734 | + | 2.25013i | 0.162108 | + | 0.0935932i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.3806 | − | 23.9834i | −1.26040 | − | 0.995000i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.0866 | + | 48.6474i | 1.16323 | + | 2.01477i | ||||
\(584\) | 4.18333 | − | 7.24574i | 0.173108 | − | 0.299831i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.62060 | + | 3.82240i | −0.273494 | + | 0.157902i | ||||
\(587\) | −8.71353 | −0.359646 | −0.179823 | − | 0.983699i | \(-0.557552\pi\) | ||||
−0.179823 | + | 0.983699i | \(0.557552\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.0250 | −1.60800 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.73991 | − | 3.01361i | 0.0715098 | − | 0.123859i | ||||
\(593\) | 9.13432 | + | 15.8211i | 0.375102 | + | 0.649695i | 0.990342 | − | 0.138644i | \(-0.0442744\pi\) |
−0.615241 | + | 0.788339i | \(0.710941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.00381i | − | 0.286887i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.42363 | + | 3.70868i | 0.262682 | + | 0.151659i | ||||
\(599\) | −9.94576 | − | 5.74219i | −0.406373 | − | 0.234619i | 0.282857 | − | 0.959162i | \(-0.408718\pi\) |
−0.689230 | + | 0.724543i | \(0.742051\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.4022i | 1.40329i | 0.712525 | + | 0.701647i | \(0.247552\pi\) | ||||
−0.712525 | + | 0.701647i | \(0.752448\pi\) | |||||||
\(602\) | 6.77174 | + | 0.986520i | 0.275996 | + | 0.0402076i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.43540 | + | 11.1464i | 0.261853 | + | 0.453543i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.4152 | − | 22.7564i | 1.59981 | − | 0.923653i | 0.608293 | − | 0.793713i | \(-0.291855\pi\) |
0.991522 | − | 0.129941i | \(-0.0414787\pi\) | |||||||
\(608\) | −6.17914 | −0.250597 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.43531 | + | 4.29278i | −0.300800 | + | 0.173667i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.85205 | + | 10.1361i | −0.236362 | + | 0.409391i | −0.959668 | − | 0.281137i | \(-0.909289\pi\) |
0.723306 | + | 0.690528i | \(0.242622\pi\) | |||||||
\(614\) | 6.57805 | + | 11.3935i | 0.265469 | + | 0.459805i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.5603 | + | 6.19578i | −0.626944 | + | 0.249635i | ||||
\(617\) | 24.0582i | 0.968547i | 0.874917 | + | 0.484273i | \(0.160916\pi\) | ||||
−0.874917 | + | 0.484273i | \(0.839084\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.32794 | − | 1.92139i | −0.133761 | − | 0.0772271i | 0.431626 | − | 0.902053i | \(-0.357940\pi\) |
−0.565387 | + | 0.824825i | \(0.691273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.26087i | 0.251038i | ||||||||
\(623\) | −1.46448 | + | 10.0526i | −0.0586733 | + | 0.402749i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.74065 | + | 15.1392i | −0.349347 | + | 0.605086i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.56427 | + | 5.52193i | −0.381656 | + | 0.220349i | ||||
\(629\) | 16.1353 | 0.643358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.4387 | −1.01270 | −0.506349 | − | 0.862328i | \(-0.669005\pi\) | ||||
−0.506349 | + | 0.862328i | \(0.669005\pi\) | |||||||
\(632\) | 4.73340 | − | 2.73283i | 0.188284 | − | 0.108706i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.766906 | + | 1.32832i | −0.0304577 | + | 0.0527543i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.16896 | − | 1.71089i | 0.284044 | − | 0.0677879i | ||||
\(638\) | − | 18.8708i | − | 0.747102i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.2380 | − | 19.7673i | −1.35232 | − | 0.780762i | −0.363745 | − | 0.931499i | \(-0.618502\pi\) |
−0.988574 | + | 0.150737i | \(0.951835\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.2816i | − | 0.484341i | −0.970234 | − | 0.242170i | \(-0.922141\pi\) | ||
0.970234 | − | 0.242170i | \(-0.0778593\pi\) | |||||||
\(644\) | 11.5489 | − | 14.6294i | 0.455090 | − | 0.576479i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.3258 | − | 24.8131i | −0.563642 | − | 0.976257i | ||||
\(647\) | −6.69470 | + | 11.5956i | −0.263196 | + | 0.455869i | −0.967089 | − | 0.254437i | \(-0.918110\pi\) |
0.703893 | + | 0.710306i | \(0.251443\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.95918 | − | 2.86319i | 0.194665 | − | 0.112390i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.24574 | 0.283765 | ||||||||
\(653\) | 42.9355 | − | 24.7888i | 1.68020 | − | 0.970062i | 0.718670 | − | 0.695352i | \(-0.244751\pi\) |
0.961527 | − | 0.274710i | \(-0.0885819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.48504 | − | 6.03626i | −0.136068 | − | 0.235676i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.98090 | + | 20.0435i | 0.311128 | + | 0.781379i | ||||
\(659\) | − | 40.7622i | − | 1.58787i | −0.608002 | − | 0.793936i | \(-0.708029\pi\) | ||
0.608002 | − | 0.793936i | \(-0.291971\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.9652 | − | 17.8778i | −1.20441 | − | 0.695365i | −0.242875 | − | 0.970057i | \(-0.578091\pi\) |
−0.961532 | + | 0.274692i | \(0.911424\pi\) | |||||||
\(662\) | −1.31048 | − | 0.756607i | −0.0509333 | − | 0.0294064i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.6297i | − | 0.567741i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.5002 | + | 18.1869i | 0.406569 | + | 0.704199i | ||||
\(668\) | 6.93030 | − | 12.0036i | 0.268141 | − | 0.464435i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −64.4014 | −2.48619 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.1987 | −1.35681 | −0.678406 | − | 0.734687i | \(-0.737329\pi\) | ||||
−0.678406 | + | 0.734687i | \(0.737329\pi\) | |||||||
\(674\) | 2.71987 | − | 1.57032i | 0.104766 | − | 0.0604865i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.94570 | − | 10.2983i | 0.228681 | − | 0.396087i | ||||
\(677\) | −19.2211 | − | 33.2919i | −0.738727 | − | 1.27951i | −0.953069 | − | 0.302754i | \(-0.902094\pi\) |
0.214341 | − | 0.976759i | \(-0.431239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.63771 | − | 12.2084i | 0.369862 | − | 0.468517i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −34.6236 | − | 19.9900i | −1.32581 | − | 0.765455i | ||||
\(683\) | −33.2574 | − | 19.2012i | −1.27256 | − | 0.734712i | −0.297089 | − | 0.954850i | \(-0.596016\pi\) |
−0.975469 | + | 0.220138i | \(0.929349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.65731 | − | 18.4460i | −0.0632764 | − | 0.704270i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.29325 | + | 2.23997i | 0.0493046 | + | 0.0853981i | ||||
\(689\) | 4.67152 | − | 8.09131i | 0.177971 | − | 0.308254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6209 | − | 10.1735i | 0.670332 | − | 0.387016i | −0.125870 | − | 0.992047i | \(-0.540172\pi\) |
0.796203 | + | 0.605030i | \(0.206839\pi\) | |||||||
\(692\) | −0.958803 | −0.0364482 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.4052 | 1.04029 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.1595 | − | 27.9892i | 0.612086 | − | 1.06016i | ||||
\(698\) | −9.77972 | − | 16.9390i | −0.370168 | − | 0.641149i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.98574i | − | 0.263848i | −0.991260 | − | 0.131924i | \(-0.957885\pi\) | ||
0.991260 | − | 0.131924i | \(-0.0421154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.6215 | − | 10.7511i | −0.702323 | − | 0.405487i | ||||
\(704\) | −5.48223 | − | 3.16517i | −0.206619 | − | 0.119292i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 14.8103i | − | 0.557393i | ||||||
\(707\) | −16.4891 | + | 6.56558i | −0.620135 | + | 0.246924i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.01348 | + | 10.4157i | 0.225841 | + | 0.391168i | 0.956571 | − | 0.291498i | \(-0.0941537\pi\) |
−0.730730 | + | 0.682666i | \(0.760820\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.32522 | + | 1.91982i | −0.124618 | + | 0.0719482i | ||||
\(713\) | 44.4917 | 1.66623 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.2531 | − | 11.6931i | 0.756893 | − | 0.436992i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.28450 | − | 14.3492i | 0.309175 | − | 0.535507i | ||||
\(719\) | −0.835694 | − | 1.44746i | −0.0311661 | − | 0.0539813i | 0.850022 | − | 0.526748i | \(-0.176589\pi\) |
−0.881188 | + | 0.472766i | \(0.843255\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.0233 | + | 1.89727i | 0.485015 | + | 0.0706579i | ||||
\(722\) | 19.1817i | 0.713869i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.7026 | + | 9.64324i | 0.620746 | + | 0.358388i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.5043i | 1.57640i | 0.615422 | + | 0.788198i | \(0.288986\pi\) | ||||
−0.615422 | + | 0.788198i | \(0.711014\pi\) | |||||||
\(728\) | 2.18650 | + | 1.72609i | 0.0810370 | + | 0.0639731i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.99658 | + | 10.3864i | −0.221792 | + | 0.384154i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.6053 | − | 15.9379i | 1.01963 | − | 0.588681i | 0.105630 | − | 0.994405i | \(-0.466314\pi\) |
0.913996 | + | 0.405724i | \(0.132981\pi\) | |||||||
\(734\) | −14.0131 | −0.517233 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.04472 | 0.259672 | ||||||||
\(737\) | 53.9026 | − | 31.1207i | 1.98553 | − | 1.14634i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.20932 | − | 14.2190i | 0.301985 | − | 0.523053i | −0.674601 | − | 0.738183i | \(-0.735684\pi\) |
0.976585 | + | 0.215130i | \(0.0690176\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.4274 | − | 14.5472i | −0.676493 | − | 0.534044i | ||||
\(743\) | − | 4.52385i | − | 0.165964i | −0.996551 | − | 0.0829821i | \(-0.973556\pi\) | ||
0.996551 | − | 0.0829821i | \(-0.0264444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12.6630 | + | 7.31099i | 0.463626 | + | 0.267674i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 29.3527i | − | 1.07324i | ||||||
\(749\) | −19.2151 | − | 2.79930i | −0.702106 | − | 0.102284i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.69875 | + | 15.0667i | 0.317422 | + | 0.549791i | 0.979949 | − | 0.199247i | \(-0.0638495\pi\) |
−0.662527 | + | 0.749038i | \(0.730516\pi\) | |||||||
\(752\) | −4.07711 | + | 7.06176i | −0.148677 | + | 0.257516i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.71820 | + | 1.56935i | −0.0989908 | + | 0.0571524i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.25454 | −0.190980 | −0.0954898 | − | 0.995430i | \(-0.530442\pi\) | ||||
−0.0954898 | + | 0.995430i | \(0.530442\pi\) | |||||||
\(758\) | −4.05425 | + | 2.34072i | −0.147257 | + | 0.0850189i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.31402 | + | 12.6683i | 0.265133 | + | 0.459224i | 0.967598 | − | 0.252494i | \(-0.0812508\pi\) |
−0.702465 | + | 0.711718i | \(0.747917\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.91612 | − | 1.95749i | 0.177975 | − | 0.0708659i | ||||
\(764\) | − | 2.82843i | − | 0.102329i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.1086 | − | 5.83621i | −0.365239 | − | 0.210871i | ||||
\(767\) | −0.824840 | − | 0.476222i | −0.0297832 | − | 0.0171954i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 12.4548i | − | 0.449131i | −0.974459 | − | 0.224566i | \(-0.927904\pi\) | ||
0.974459 | − | 0.224566i | \(-0.0720963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.10862 | − | 7.11634i | −0.147873 | − | 0.256123i | ||||
\(773\) | 4.15288 | − | 7.19300i | 0.149369 | − | 0.258714i | −0.781626 | − | 0.623748i | \(-0.785609\pi\) |
0.930994 | + | 0.365034i | \(0.118943\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.87891 | 0.211041 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.1004 | −0.469670 | ||||||||
\(779\) | −37.2989 | + | 21.5345i | −1.33637 | + | 0.771554i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.6678 | − | 79.0990i | 1.63412 | − | 2.83038i | ||||
\(782\) | 16.3326 | + | 28.2889i | 0.584053 | + | 1.01161i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.08412 | − | 4.81163i | 0.181576 | − | 0.171844i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.8271 | − | 25.3036i | −1.56227 | − | 0.901975i | −0.997027 | − | 0.0770479i | \(-0.975451\pi\) |
−0.565239 | − | 0.824927i | \(-0.691216\pi\) | |||||||
\(788\) | −3.04253 | − | 1.75661i | −0.108386 | − | 0.0625765i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.302547 | + | 0.383247i | −0.0107573 | + | 0.0136267i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.35580 | + | 9.27652i | 0.190190 | + | 0.329419i | ||||
\(794\) | −15.3402 | + | 26.5700i | −0.544404 | + | 0.942935i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.00000 | − | 1.73205i | 0.106332 | − | 0.0613909i | ||||
\(797\) | −36.6354 | −1.29769 | −0.648846 | − | 0.760920i | \(-0.724748\pi\) | ||||
−0.648846 | + | 0.760920i | \(0.724748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.8098 | −1.33761 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.97266 | − | 6.88085i | 0.140280 | − | 0.242971i | ||||
\(803\) | −26.4819 | − | 45.8680i | −0.934525 | − | 1.61865i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.64969i | 0.234225i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.80944 | − | 3.35408i | −0.204375 | − | 0.117996i | ||||
\(809\) | 37.7055 | + | 21.7693i | 1.32566 | + | 0.765368i | 0.984624 | − | 0.174685i | \(-0.0558906\pi\) |
0.341031 | + | 0.940052i | \(0.389224\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 13.8915i | − | 0.487795i | −0.969801 | − | 0.243897i | \(-0.921574\pi\) | ||
0.969801 | − | 0.243897i | \(-0.0784260\pi\) | |||||||
\(812\) | 2.91765 | + | 7.32751i | 0.102390 | + | 0.257145i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.0142 | − | 19.0772i | −0.386048 | − | 0.668654i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8411 | − | 7.99115i | 0.484238 | − | 0.279575i | ||||
\(818\) | 39.8323 | 1.39270 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.26634 | − | 4.77257i | 0.288497 | − | 0.166564i | −0.348767 | − | 0.937210i | \(-0.613399\pi\) |
0.637264 | + | 0.770646i | \(0.280066\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.39798 | + | 9.34957i | −0.188162 | + | 0.325905i | −0.944637 | − | 0.328116i | \(-0.893586\pi\) |
0.756476 | + | 0.654022i | \(0.226920\pi\) | |||||||
\(824\) | 2.48716 | + | 4.30789i | 0.0866444 | + | 0.150072i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.48296 | + | 1.87852i | −0.0515988 | + | 0.0653621i | ||||
\(827\) | − | 10.5599i | − | 0.367204i | −0.983001 | − | 0.183602i | \(-0.941224\pi\) | ||
0.983001 | − | 0.183602i | \(-0.0587757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.7288 | + | 17.7413i | 1.06726 | + | 0.616181i | 0.927431 | − | 0.373995i | \(-0.122012\pi\) |
0.139826 | + | 0.990176i | \(0.455346\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.05290i | 0.0365027i | ||||||||
\(833\) | 31.1088 | + | 9.26051i | 1.07786 | + | 0.320858i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −19.5580 | + | 33.8754i | −0.676427 | + | 1.17161i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.55723 | + | 5.51787i | −0.330149 | + | 0.190612i | ||||
\(839\) | −32.5932 | −1.12524 | −0.562621 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562621 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.1136 | 0.693571 | ||||||||
\(842\) | 6.74132 | − | 3.89211i | 0.232321 | − | 0.134131i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.98296 | + | 8.63074i | −0.171521 | + | 0.297082i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.0888 | + | 76.1168i | −0.381017 | + | 2.61540i | ||||
\(848\) | − | 8.87365i | − | 0.304722i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.2300 | + | 12.2572i | 0.727756 | + | 0.420170i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2310i | 0.692695i | 0.938106 | + | 0.346347i | \(0.112578\pi\) | ||||
−0.938106 | + | 0.346347i | \(0.887422\pi\) | |||||||
\(854\) | 25.0070 | − | 9.95722i | 0.855721 | − | 0.340729i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.66965 | − | 6.35602i | −0.125426 | − | 0.217244i | ||||
\(857\) | 22.4855 | − | 38.9461i | 0.768091 | − | 1.33037i | −0.170506 | − | 0.985357i | \(-0.554540\pi\) |
0.938597 | − | 0.345016i | \(-0.112126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.8490 | − | 21.8521i | 1.29139 | − | 0.745585i | 0.312490 | − | 0.949921i | \(-0.398837\pi\) |
0.978901 | + | 0.204336i | \(0.0655036\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.2338 | −0.348565 | ||||||||
\(863\) | −30.8636 | + | 17.8191i | −1.05061 | + | 0.606569i | −0.922819 | − | 0.385233i | \(-0.874121\pi\) |
−0.127788 | + | 0.991801i | \(0.540788\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20.1951 | + | 34.9789i | 0.686257 | + | 1.18863i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16.5350 | + | 2.40885i | 0.561235 | + | 0.0817617i | ||||
\(869\) | − | 34.5994i | − | 1.17371i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.96539 | − | 5.17617i | −0.303781 | − | 0.175388i | ||||
\(872\) | 1.73205 | + | 1.00000i | 0.0586546 | + | 0.0338643i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 43.5303i | − | 1.47243i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.2453 | + | 31.6018i | 0.616100 | + | 1.06712i | 0.990190 | + | 0.139724i | \(0.0446216\pi\) |
−0.374091 | + | 0.927392i | \(0.622045\pi\) | |||||||
\(878\) | −6.48543 | + | 11.2331i | −0.218873 | + | 0.379099i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.487935 | −0.0164390 | −0.00821948 | − | 0.999966i | \(-0.502616\pi\) | ||||
−0.00821948 | + | 0.999966i | \(0.502616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.26720 | −0.210908 | −0.105454 | − | 0.994424i | \(-0.533630\pi\) | ||||
−0.105454 | + | 0.994424i | \(0.533630\pi\) | |||||||
\(884\) | −4.22804 | + | 2.44106i | −0.142204 | + | 0.0821017i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.32751 | − | 7.49547i | 0.145386 | − | 0.251815i | ||||
\(887\) | −28.4598 | − | 49.2939i | −0.955588 | − | 1.65513i | −0.733017 | − | 0.680210i | \(-0.761888\pi\) |
−0.222571 | − | 0.974917i | \(-0.571445\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.9193 | − | 10.9883i | −0.466838 | − | 0.368536i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.62042 | + | 5.55435i | 0.322115 | + | 0.185973i | ||||
\(893\) | 43.6356 | + | 25.1930i | 1.46021 | + | 0.843052i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.61811 | + | 0.381412i | 0.0874651 | + | 0.0127421i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.7203 | − | 22.0323i | −0.424483 | − | 0.735226i | ||||
\(899\) | −9.41346 | + | 16.3046i | −0.313957 | + | 0.543789i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.6332 | − | 20.5728i | 1.18711 | − | 0.685380i | ||||
\(902\) | −44.1229 | −1.46913 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.184551 | −0.00613807 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.33031 | − | 14.4285i | 0.276603 | − | 0.479091i | −0.693935 | − | 0.720038i | \(-0.744124\pi\) |
0.970538 | + | 0.240946i | \(0.0774578\pi\) | |||||||
\(908\) | 11.7619 | + | 20.3722i | 0.390333 | + | 0.676076i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.02653i | 0.265931i | 0.991121 | + | 0.132965i | \(0.0424499\pi\) | ||||
−0.991121 | + | 0.132965i | \(0.957550\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −80.2031 | − | 46.3053i | −2.65434 | − | 1.53248i | ||||
\(914\) | −26.4480 | − | 15.2697i | −0.874821 | − | 0.505078i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 9.48678i | − | 0.313452i | ||||||
\(917\) | −1.70961 | + | 11.7352i | −0.0564563 | + | 0.387532i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.85733 | + | 11.8772i | 0.226202 | + | 0.391794i | 0.956680 | − | 0.291143i | \(-0.0940356\pi\) |
−0.730477 | + | 0.682937i | \(0.760702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.5689 | − | 7.83402i | 0.446869 | − | 0.258000i | ||||
\(923\) | −15.1915 | −0.500033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 27.7528 | − | 16.0231i | 0.912014 | − | 0.526551i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.49051 | + | 2.58163i | −0.0489283 | + | 0.0847463i | ||||
\(929\) | −22.9480 | − | 39.7470i | −0.752898 | − | 1.30406i | −0.946413 | − | 0.322960i | \(-0.895322\pi\) |
0.193515 | − | 0.981097i | \(-0.438011\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.7317 | − | 31.4154i | −0.974417 | − | 1.02960i | ||||
\(932\) | − | 10.3734i | − | 0.339791i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.605489 | + | 0.349579i | 0.0198122 | + | 0.0114386i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.17552i | 0.201746i | 0.994899 | + | 0.100873i | \(0.0321635\pi\) | ||||
−0.994899 | + | 0.100873i | \(0.967836\pi\) | |||||||
\(938\) | −16.1187 | + | 20.4181i | −0.526293 | + | 0.666675i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.7048 | + | 28.9335i | −0.544560 | + | 0.943206i | 0.454074 | + | 0.890964i | \(0.349970\pi\) |
−0.998634 | + | 0.0522424i | \(0.983363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.5237 | − | 24.5511i | 1.38476 | − | 0.799494i | ||||
\(944\) | −0.904592 | −0.0294420 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.3734 | 0.532345 | ||||||||
\(947\) | 5.67563 | − | 3.27683i | 0.184433 | − | 0.106483i | −0.404941 | − | 0.914343i | \(-0.632708\pi\) |
0.589374 | + | 0.807860i | \(0.299375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.40462 | + | 7.62903i | −0.142980 | + | 0.247649i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.53828 | + | 11.3976i | 0.147087 | + | 0.369399i | ||||
\(953\) | − | 46.5253i | − | 1.50710i | −0.657389 | − | 0.753551i | \(-0.728339\pi\) | ||
0.657389 | − | 0.753551i | \(-0.271661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.7167 | − | 6.18728i | −0.346602 | − | 0.200111i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.54561i | 0.276096i | ||||||||
\(959\) | 17.1894 | + | 43.1703i | 0.555076 | + | 1.39404i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.44349 | + | 7.69635i | 0.143338 | + | 0.248269i | ||||
\(962\) | −1.83195 | + | 3.17302i | −0.0590643 | + | 0.102302i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.8208 | + | 6.24737i | −0.348514 | + | 0.201214i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.93169 | −0.190750 | −0.0953752 | − | 0.995441i | \(-0.530405\pi\) | ||||
−0.0953752 | + | 0.995441i | \(0.530405\pi\) | |||||||
\(968\) | −25.1781 | + | 14.5366i | −0.809253 | + | 0.467223i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.170069 | − | 0.294568i | −0.00545777 | − | 0.00945314i | 0.863284 | − | 0.504719i | \(-0.168404\pi\) |
−0.868741 | + | 0.495266i | \(0.835071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.87339 | + | 12.5070i | −0.316526 | + | 0.400955i | ||||
\(974\) | − | 23.8178i | − | 0.763171i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.81047 | + | 5.08673i | 0.282016 | + | 0.162822i | ||||
\(977\) | −17.9168 | − | 10.3443i | −0.573210 | − | 0.330943i | 0.185220 | − | 0.982697i | \(-0.440700\pi\) |
−0.758430 | + | 0.651754i | \(0.774033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.3062i | 0.776829i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.45520 | + | 11.1807i | 0.205994 | + | 0.356791i | ||||
\(983\) | −10.6129 | + | 18.3821i | −0.338499 | + | 0.586297i | −0.984151 | − | 0.177335i | \(-0.943252\pi\) |
0.645652 | + | 0.763632i | \(0.276586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −13.8225 | −0.440197 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.50600 | 0.206983 | ||||||||
\(989\) | −15.7800 | + | 9.11057i | −0.501774 | + | 0.289699i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.1034 | + | 50.4085i | −0.924499 | + | 1.60128i | −0.132134 | + | 0.991232i | \(0.542183\pi\) |
−0.792365 | + | 0.610048i | \(0.791150\pi\) | |||||||
\(992\) | 3.15781 | + | 5.46948i | 0.100260 | + | 0.173656i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.50310 | + | 37.7748i | −0.174548 | + | 1.19814i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.1542 | − | 19.1416i | −1.05000 | − | 0.606220i | −0.127354 | − | 0.991857i | \(-0.540648\pi\) |
−0.922651 | + | 0.385637i | \(0.873982\pi\) | |||||||
\(998\) | 14.1478 | + | 8.16823i | 0.447841 | + | 0.258561i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.bf.f.1151.4 | 32 | ||
3.2 | odd | 2 | inner | 3150.2.bf.f.1151.14 | 32 | ||
5.2 | odd | 4 | 630.2.bo.a.269.6 | yes | 16 | ||
5.3 | odd | 4 | 630.2.bo.b.269.1 | yes | 16 | ||
5.4 | even | 2 | inner | 3150.2.bf.f.1151.13 | 32 | ||
7.5 | odd | 6 | inner | 3150.2.bf.f.1601.16 | 32 | ||
15.2 | even | 4 | 630.2.bo.b.269.3 | yes | 16 | ||
15.8 | even | 4 | 630.2.bo.a.269.8 | yes | 16 | ||
15.14 | odd | 2 | inner | 3150.2.bf.f.1151.3 | 32 | ||
21.5 | even | 6 | inner | 3150.2.bf.f.1601.4 | 32 | ||
35.3 | even | 12 | 4410.2.d.a.4409.6 | 16 | |||
35.12 | even | 12 | 630.2.bo.a.89.8 | yes | 16 | ||
35.17 | even | 12 | 4410.2.d.b.4409.5 | 16 | |||
35.18 | odd | 12 | 4410.2.d.a.4409.11 | 16 | |||
35.19 | odd | 6 | inner | 3150.2.bf.f.1601.3 | 32 | ||
35.32 | odd | 12 | 4410.2.d.b.4409.12 | 16 | |||
35.33 | even | 12 | 630.2.bo.b.89.3 | yes | 16 | ||
105.17 | odd | 12 | 4410.2.d.a.4409.12 | 16 | |||
105.32 | even | 12 | 4410.2.d.a.4409.5 | 16 | |||
105.38 | odd | 12 | 4410.2.d.b.4409.11 | 16 | |||
105.47 | odd | 12 | 630.2.bo.b.89.1 | yes | 16 | ||
105.53 | even | 12 | 4410.2.d.b.4409.6 | 16 | |||
105.68 | odd | 12 | 630.2.bo.a.89.6 | ✓ | 16 | ||
105.89 | even | 6 | inner | 3150.2.bf.f.1601.15 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.bo.a.89.6 | ✓ | 16 | 105.68 | odd | 12 | ||
630.2.bo.a.89.8 | yes | 16 | 35.12 | even | 12 | ||
630.2.bo.a.269.6 | yes | 16 | 5.2 | odd | 4 | ||
630.2.bo.a.269.8 | yes | 16 | 15.8 | even | 4 | ||
630.2.bo.b.89.1 | yes | 16 | 105.47 | odd | 12 | ||
630.2.bo.b.89.3 | yes | 16 | 35.33 | even | 12 | ||
630.2.bo.b.269.1 | yes | 16 | 5.3 | odd | 4 | ||
630.2.bo.b.269.3 | yes | 16 | 15.2 | even | 4 | ||
3150.2.bf.f.1151.3 | 32 | 15.14 | odd | 2 | inner | ||
3150.2.bf.f.1151.4 | 32 | 1.1 | even | 1 | trivial | ||
3150.2.bf.f.1151.13 | 32 | 5.4 | even | 2 | inner | ||
3150.2.bf.f.1151.14 | 32 | 3.2 | odd | 2 | inner | ||
3150.2.bf.f.1601.3 | 32 | 35.19 | odd | 6 | inner | ||
3150.2.bf.f.1601.4 | 32 | 21.5 | even | 6 | inner | ||
3150.2.bf.f.1601.15 | 32 | 105.89 | even | 6 | inner | ||
3150.2.bf.f.1601.16 | 32 | 7.5 | odd | 6 | inner | ||
4410.2.d.a.4409.5 | 16 | 105.32 | even | 12 | |||
4410.2.d.a.4409.6 | 16 | 35.3 | even | 12 | |||
4410.2.d.a.4409.11 | 16 | 35.18 | odd | 12 | |||
4410.2.d.a.4409.12 | 16 | 105.17 | odd | 12 | |||
4410.2.d.b.4409.5 | 16 | 35.17 | even | 12 | |||
4410.2.d.b.4409.6 | 16 | 105.53 | even | 12 | |||
4410.2.d.b.4409.11 | 16 | 105.38 | odd | 12 | |||
4410.2.d.b.4409.12 | 16 | 35.32 | odd | 12 |