Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(19,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 11, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.o (of order \(22\), degree \(10\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{22})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 159.1 | ||
Character | \(\chi\) | \(=\) | 460.159 |
Dual form | 460.2.o.a.379.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{13}{22}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.18971 | − | 0.764582i | −0.841254 | − | 0.540641i | ||||
\(3\) | −0.0739958 | − | 0.514652i | −0.0427215 | − | 0.297134i | −0.999969 | − | 0.00786458i | \(-0.997497\pi\) |
0.957248 | − | 0.289270i | \(-0.0934125\pi\) | |||||||
\(4\) | 0.830830 | + | 1.81926i | 0.415415 | + | 0.909632i | ||||
\(5\) | 0.629973 | − | 2.14549i | 0.281733 | − | 0.959493i | ||||
\(6\) | −0.305460 | + | 0.668863i | −0.124703 | + | 0.273062i | ||||
\(7\) | −0.858171 | − | 0.743609i | −0.324358 | − | 0.281058i | 0.477426 | − | 0.878672i | \(-0.341570\pi\) |
−0.801784 | + | 0.597614i | \(0.796115\pi\) | |||||||
\(8\) | 0.402527 | − | 2.79964i | 0.142315 | − | 0.989821i | ||||
\(9\) | 2.61909 | − | 0.769034i | 0.873029 | − | 0.256345i | ||||
\(10\) | −2.38989 | + | 2.07085i | −0.755750 | + | 0.654861i | ||||
\(11\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(12\) | 0.874810 | − | 0.562206i | 0.252536 | − | 0.162295i | ||||
\(13\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(14\) | 0.452426 | + | 1.54082i | 0.120916 | + | 0.411802i | ||||
\(15\) | −1.15080 | − | 0.165460i | −0.297134 | − | 0.0427215i | ||||
\(16\) | −2.61944 | + | 3.02300i | −0.654861 | + | 0.755750i | ||||
\(17\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(18\) | −3.70395 | − | 1.08758i | −0.873029 | − | 0.256345i | ||||
\(19\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(20\) | 4.42662 | − | 0.636451i | 0.989821 | − | 0.142315i | ||||
\(21\) | −0.319199 | + | 0.496683i | −0.0696549 | + | 0.108385i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.96963 | − | 4.37271i | 0.410696 | − | 0.911772i | ||||
\(24\) | −1.47062 | −0.300190 | ||||||||
\(25\) | −4.20627 | − | 2.70320i | −0.841254 | − | 0.540641i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.23756 | − | 2.70989i | −0.238169 | − | 0.521518i | ||||
\(28\) | 0.639827 | − | 2.17905i | 0.120916 | − | 0.411802i | ||||
\(29\) | 1.34473 | − | 2.94454i | 0.249709 | − | 0.546787i | −0.742720 | − | 0.669602i | \(-0.766465\pi\) |
0.992430 | + | 0.122815i | \(0.0391921\pi\) | |||||||
\(30\) | 1.24261 | + | 1.07673i | 0.226868 | + | 0.196583i | ||||
\(31\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(32\) | 5.42771 | − | 1.59372i | 0.959493 | − | 0.281733i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.13603 | + | 1.37274i | −0.361055 | + | 0.232036i | ||||
\(36\) | 3.57509 | + | 4.12588i | 0.595849 | + | 0.687646i | ||||
\(37\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.75302 | − | 2.62732i | −0.909632 | − | 0.415415i | ||||
\(41\) | −10.7829 | − | 3.16615i | −1.68401 | − | 0.494470i | −0.706919 | − | 0.707295i | \(-0.749915\pi\) |
−0.977090 | + | 0.212825i | \(0.931734\pi\) | |||||||
\(42\) | 0.759509 | − | 0.346856i | 0.117195 | − | 0.0535211i | ||||
\(43\) | −10.1596 | + | 1.46073i | −1.54932 | + | 0.222759i | −0.863251 | − | 0.504774i | \(-0.831576\pi\) |
−0.686072 | + | 0.727533i | \(0.740667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 6.10370i | − | 0.909886i | ||||||
\(46\) | −5.68658 | + | 3.69632i | −0.838441 | + | 0.544993i | ||||
\(47\) | 12.1712 | 1.77536 | 0.887679 | − | 0.460462i | \(-0.152316\pi\) | ||||
0.887679 | + | 0.460462i | \(0.152316\pi\) | |||||||
\(48\) | 1.74962 | + | 1.12441i | 0.252536 | + | 0.162295i | ||||
\(49\) | −0.812702 | − | 5.65246i | −0.116100 | − | 0.807495i | ||||
\(50\) | 2.93743 | + | 6.43207i | 0.415415 | + | 0.909632i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(54\) | −0.599585 | + | 4.17020i | −0.0815932 | + | 0.567493i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.42727 | + | 2.10324i | −0.324358 | + | 0.281058i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.85118 | + | 2.47500i | −0.505684 | + | 0.324983i | ||||
\(59\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(60\) | −0.655102 | − | 2.23107i | −0.0845733 | − | 0.288030i | ||||
\(61\) | −1.68634 | − | 0.242459i | −0.215913 | − | 0.0310437i | 0.0335091 | − | 0.999438i | \(-0.489332\pi\) |
−0.249423 | + | 0.968395i | \(0.580241\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.81948 | − | 1.28762i | −0.355222 | − | 0.162224i | ||||
\(64\) | −7.67594 | − | 2.25386i | −0.959493 | − | 0.281733i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.05385 | + | 1.63982i | −0.128748 | + | 0.200336i | −0.899643 | − | 0.436626i | \(-0.856173\pi\) |
0.770895 | + | 0.636963i | \(0.219810\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.39617 | − | 0.690111i | −0.288465 | − | 0.0830796i | ||||
\(70\) | 3.59084 | 0.429187 | ||||||||
\(71\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(72\) | −1.09876 | − | 7.64205i | −0.129490 | − | 0.900625i | ||||
\(73\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.07996 | + | 2.36479i | −0.124703 | + | 0.273062i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(80\) | 4.83564 | + | 7.52440i | 0.540641 | + | 0.841254i | ||||
\(81\) | 5.58593 | − | 3.58986i | 0.620659 | − | 0.398873i | ||||
\(82\) | 10.4078 | + | 12.0112i | 1.14935 | + | 1.32642i | ||||
\(83\) | 3.95775 | + | 13.4789i | 0.434419 | + | 1.47950i | 0.828274 | + | 0.560324i | \(0.189323\pi\) |
−0.393855 | + | 0.919173i | \(0.628859\pi\) | |||||||
\(84\) | −1.16880 | − | 0.168048i | −0.127526 | − | 0.0183355i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 13.2038 | + | 6.02999i | 1.42381 | + | 0.650231i | ||||
\(87\) | −1.61492 | − | 0.474182i | −0.173137 | − | 0.0508377i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.1065 | − | 2.60331i | 1.91928 | − | 0.275951i | 0.924765 | − | 0.380540i | \(-0.124262\pi\) |
0.994516 | + | 0.104589i | \(0.0333526\pi\) | |||||||
\(90\) | −4.66678 | + | 7.26165i | −0.491922 | + | 0.765445i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.59153 | − | 0.0497018i | 0.999987 | − | 0.00518177i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.4803 | − | 9.30591i | −1.49353 | − | 0.959831i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.22184 | − | 2.67545i | −0.124703 | − | 0.273062i | ||||
\(97\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(98\) | −3.35489 | + | 7.34618i | −0.338895 | + | 0.742076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.42315 | − | 9.89821i | 0.142315 | − | 0.989821i | ||||
\(101\) | −6.03671 | + | 1.77254i | −0.600675 | + | 0.176374i | −0.567912 | − | 0.823089i | \(-0.692249\pi\) |
−0.0327629 | + | 0.999463i | \(0.510431\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.26335 | + | 9.74596i | 0.617146 | + | 0.960298i | 0.999344 | + | 0.0362175i | \(0.0115309\pi\) |
−0.382198 | + | 0.924081i | \(0.624833\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.864543 | + | 0.997735i | 0.0843707 | + | 0.0973690i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1368 | + | 2.03256i | 1.36665 | + | 0.196495i | 0.786287 | − | 0.617861i | \(-0.212001\pi\) |
0.580366 | + | 0.814356i | \(0.302910\pi\) | |||||||
\(108\) | 3.90179 | − | 4.50291i | 0.375450 | − | 0.433293i | ||||
\(109\) | 18.1352 | + | 8.28207i | 1.73704 | + | 0.793278i | 0.991997 | + | 0.126258i | \(0.0402968\pi\) |
0.745040 | + | 0.667020i | \(0.232431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.49586 | − | 0.646407i | 0.424819 | − | 0.0610797i | ||||
\(113\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.14079 | − | 6.98051i | −0.759133 | − | 0.650936i | ||||
\(116\) | 6.47413 | 0.601108 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.926454 | + | 3.15521i | −0.0845733 | + | 0.288030i | ||||
\(121\) | −4.56957 | + | 10.0060i | −0.415415 | + | 0.909632i | ||||
\(122\) | 1.82088 | + | 1.57780i | 0.164854 | + | 0.142847i | ||||
\(123\) | −0.831575 | + | 5.78373i | −0.0749806 | + | 0.521502i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.44954 | + | 7.32157i | −0.755750 | + | 0.654861i | ||||
\(126\) | 2.36989 | + | 3.68762i | 0.211126 | + | 0.328519i | ||||
\(127\) | 18.9403 | − | 12.1722i | 1.68068 | − | 1.08011i | 0.815175 | − | 0.579215i | \(-0.196641\pi\) |
0.865508 | − | 0.500894i | \(-0.166996\pi\) | |||||||
\(128\) | 7.40890 | + | 8.55033i | 0.654861 | + | 0.755750i | ||||
\(129\) | 1.50353 | + | 5.12057i | 0.132379 | + | 0.450841i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.50756 | − | 1.14516i | 0.216620 | − | 0.0989270i | ||||
\(135\) | −6.59367 | + | 0.948027i | −0.567493 | + | 0.0815932i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 2.32310 | + | 2.65310i | 0.197756 | + | 0.225847i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | −4.27206 | − | 2.74549i | −0.361055 | − | 0.232036i | ||||
\(141\) | −0.900621 | − | 6.26396i | −0.0758460 | − | 0.527520i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.53576 | + | 9.93194i | −0.377980 | + | 0.827661i | ||||
\(145\) | −5.47034 | − | 4.74008i | −0.454287 | − | 0.393642i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.84891 | + | 0.836517i | −0.234975 | + | 0.0689947i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.97547 | + | 9.29801i | 0.489529 | + | 0.761723i | 0.994866 | − | 0.101200i | \(-0.0322681\pi\) |
−0.505337 | + | 0.862922i | \(0.668632\pi\) | |||||||
\(150\) | 3.09292 | − | 1.98770i | 0.252536 | − | 0.162295i | ||||
\(151\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 12.6491i | − | 1.00000i | ||||||
\(161\) | −4.94186 | + | 2.28789i | −0.389473 | + | 0.180311i | ||||
\(162\) | −9.39039 | −0.737779 | ||||||||
\(163\) | −12.4911 | − | 8.02754i | −0.978378 | − | 0.628765i | −0.0493527 | − | 0.998781i | \(-0.515716\pi\) |
−0.929025 | + | 0.370016i | \(0.879352\pi\) | |||||||
\(164\) | −3.19871 | − | 22.2475i | −0.249777 | − | 1.73724i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.59710 | − | 19.0620i | 0.434419 | − | 1.47950i | ||||
\(167\) | −0.564020 | + | 1.23503i | −0.0436452 | + | 0.0955697i | −0.930199 | − | 0.367057i | \(-0.880366\pi\) |
0.886553 | + | 0.462626i | \(0.153093\pi\) | |||||||
\(168\) | 1.26205 | + | 1.09357i | 0.0973690 | + | 0.0843707i | ||||
\(169\) | −1.85009 | + | 12.8677i | −0.142315 | + | 0.989821i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.0983 | − | 17.2694i | −0.846241 | − | 1.31678i | ||||
\(173\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(174\) | 1.55873 | + | 1.79888i | 0.118167 | + | 0.136372i | ||||
\(175\) | 1.59957 | + | 5.44763i | 0.120916 | + | 0.411802i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −23.5319 | − | 10.7467i | −1.76379 | − | 0.805497i | ||||
\(179\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(180\) | 11.1042 | − | 5.07114i | 0.827661 | − | 0.377980i | ||||
\(181\) | −5.73933 | + | 0.825191i | −0.426601 | + | 0.0613360i | −0.352272 | − | 0.935898i | \(-0.614591\pi\) |
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.885818i | 0.0654815i | ||||||||
\(184\) | −11.4492 | − | 7.27438i | −0.844044 | − | 0.536274i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.1122 | + | 22.1427i | 0.737511 | + | 1.61492i | ||||
\(189\) | −0.953056 | + | 3.24581i | −0.0693246 | + | 0.236098i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(192\) | −0.591966 | + | 4.11722i | −0.0427215 | + | 0.297134i | ||||
\(193\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.60811 | − | 6.17475i | 0.686293 | − | 0.441054i | ||||
\(197\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(200\) | −9.26113 | + | 10.6879i | −0.654861 | + | 0.755750i | ||||
\(201\) | 0.921919 | + | 0.421026i | 0.0650271 | + | 0.0296969i | ||||
\(202\) | 8.53720 | + | 2.50675i | 0.600675 | + | 0.176374i | ||||
\(203\) | −3.34359 | + | 1.52697i | −0.234674 | + | 0.107172i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.5859 | + | 21.1401i | −0.948880 | + | 1.47649i | ||||
\(206\) | − | 16.3837i | − | 1.14151i | ||||||
\(207\) | 1.79587 | − | 12.9672i | 0.124822 | − | 0.901284i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.265707 | − | 1.84803i | −0.0183355 | − | 0.127526i | ||||
\(211\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.2646 | − | 13.2269i | −1.04347 | − | 0.904171i | ||||
\(215\) | −3.26629 | + | 22.7175i | −0.222759 | + | 1.54932i | ||||
\(216\) | −8.08486 | + | 2.37393i | −0.550105 | + | 0.161525i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −15.2434 | − | 23.7191i | −1.03241 | − | 1.60646i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.19543 | − | 7.14991i | 0.414877 | − | 0.478793i | −0.509393 | − | 0.860534i | \(-0.670130\pi\) |
0.924269 | + | 0.381741i | \(0.124675\pi\) | |||||||
\(224\) | −5.84301 | − | 2.66841i | −0.390402 | − | 0.178291i | ||||
\(225\) | −13.0954 | − | 3.84517i | −0.873029 | − | 0.256345i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.2691 | + | 3.48937i | −1.61080 | + | 0.231597i | −0.888127 | − | 0.459598i | \(-0.847994\pi\) |
−0.722668 | + | 0.691195i | \(0.757084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.0042i | 0.991507i | 0.868463 | + | 0.495754i | \(0.165108\pi\) | ||||
−0.868463 | + | 0.495754i | \(0.834892\pi\) | |||||||
\(230\) | 4.34803 | + | 14.5291i | 0.286701 | + | 0.958020i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.70235 | − | 4.95000i | −0.505684 | − | 0.324983i | ||||
\(233\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.66756 | − | 26.1133i | 0.500176 | − | 1.70344i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(240\) | 3.51463 | − | 3.04544i | 0.226868 | − | 0.196583i | ||||
\(241\) | 16.1905 | + | 25.1929i | 1.04292 | + | 1.62282i | 0.743549 | + | 0.668682i | \(0.233141\pi\) |
0.299373 | + | 0.954136i | \(0.403223\pi\) | |||||||
\(242\) | 13.0868 | − | 8.41040i | 0.841254 | − | 0.540641i | ||||
\(243\) | −8.11355 | − | 9.36354i | −0.520485 | − | 0.600671i | ||||
\(244\) | −0.959964 | − | 3.26934i | −0.0614554 | − | 0.209298i | ||||
\(245\) | −12.6393 | − | 1.81726i | −0.807495 | − | 0.116100i | ||||
\(246\) | 5.41147 | − | 6.24517i | 0.345023 | − | 0.398177i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.64406 | − | 3.03424i | 0.421050 | − | 0.192287i | ||||
\(250\) | 15.6505 | − | 2.25020i | 0.989821 | − | 0.142315i | ||||
\(251\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(252\) | − | 6.19918i | − | 0.390511i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −31.8402 | −1.99783 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.27704 | − | 15.8371i | −0.142315 | − | 0.989821i | ||||
\(257\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(258\) | 2.12632 | − | 7.24158i | 0.132379 | − | 0.450841i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.25751 | − | 8.74614i | 0.0778376 | − | 0.541373i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.6294 | − | 17.0090i | 1.21040 | − | 1.04882i | 0.212981 | − | 0.977056i | \(-0.431683\pi\) |
0.997422 | − | 0.0717640i | \(-0.0228629\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.67960 | − | 9.12589i | −0.163989 | − | 0.558495i | ||||
\(268\) | −3.85884 | − | 0.554818i | −0.235716 | − | 0.0338909i | ||||
\(269\) | 16.7308 | − | 19.3084i | 1.02009 | − | 1.17725i | 0.0360466 | − | 0.999350i | \(-0.488524\pi\) |
0.984048 | − | 0.177902i | \(-0.0569310\pi\) | |||||||
\(270\) | 8.56942 | + | 3.91352i | 0.521518 | + | 0.238169i | ||||
\(271\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.735312 | − | 4.93262i | −0.0442606 | − | 0.296909i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.98338 | + | 6.53268i | 0.178291 | + | 0.390402i | ||||
\(281\) | 6.73908 | − | 22.9512i | 0.402020 | − | 1.36915i | −0.471286 | − | 0.881981i | \(-0.656210\pi\) |
0.873305 | − | 0.487173i | \(-0.161972\pi\) | |||||||
\(282\) | −3.71783 | + | 8.14090i | −0.221393 | + | 0.484784i | ||||
\(283\) | −22.1870 | − | 19.2251i | −1.31888 | − | 1.14282i | −0.979339 | − | 0.202225i | \(-0.935183\pi\) |
−0.339541 | − | 0.940591i | \(-0.610272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.89921 | + | 10.7354i | 0.407247 | + | 0.633689i | ||||
\(288\) | 12.9900 | − | 8.34818i | 0.765445 | − | 0.491922i | ||||
\(289\) | 11.1326 | + | 12.8477i | 0.654861 | + | 0.755750i | ||||
\(290\) | 2.88396 | + | 9.82185i | 0.169352 | + | 0.576759i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(294\) | 4.02897 | + | 1.18301i | 0.234975 | + | 0.0689947i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 15.6307i | − | 0.905461i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.19944 | −0.300190 | ||||||||
\(301\) | 9.80488 | + | 6.30121i | 0.565144 | + | 0.363196i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.35893 | + | 2.97565i | 0.0780686 | + | 0.170946i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.58254 | + | 3.46528i | −0.0906160 | + | 0.198421i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.34589 | + | 23.2711i | −0.190960 | + | 1.32815i | 0.638515 | + | 0.769610i | \(0.279549\pi\) |
−0.829474 | + | 0.558545i | \(0.811360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.55232 | − | 3.94460i | 0.258972 | − | 0.224401i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.53877 | + | 5.23802i | −0.255731 | + | 0.295129i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −9.67128 | + | 15.0488i | −0.540641 | + | 0.841254i | ||||
\(321\) | − | 7.42592i | − | 0.414474i | ||||||
\(322\) | 7.62867 | + | 1.05652i | 0.425129 | + | 0.0588776i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 11.1719 | + | 7.17972i | 0.620659 | + | 0.398873i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.72310 | + | 19.1009i | 0.483128 | + | 1.05790i | ||||
\(327\) | 2.92045 | − | 9.94615i | 0.161501 | − | 0.550024i | ||||
\(328\) | −13.2045 | + | 28.9138i | −0.729096 | + | 1.59650i | ||||
\(329\) | −10.4450 | − | 9.05065i | −0.575852 | − | 0.498978i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(332\) | −21.2334 | + | 18.3988i | −1.16533 | + | 1.00977i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.61530 | − | 1.03809i | 0.0883855 | − | 0.0568019i | ||||
\(335\) | 2.85433 | + | 3.29407i | 0.155949 | + | 0.179974i | ||||
\(336\) | −0.665349 | − | 2.26597i | −0.0362978 | − | 0.123619i | ||||
\(337\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(338\) | 12.0395 | − | 13.8943i | 0.654861 | − | 0.755750i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.80315 | + | 12.1419i | −0.421331 | + | 0.655603i | ||||
\(344\) | 29.0312i | 1.56526i | ||||||||
\(345\) | −2.99015 | + | 4.70620i | −0.160984 | + | 0.253373i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.5771 | − | 17.0801i | −1.42673 | − | 0.916907i | −0.999921 | − | 0.0125674i | \(-0.996000\pi\) |
−0.426814 | − | 0.904339i | \(-0.640364\pi\) | |||||||
\(348\) | −0.479058 | − | 3.33192i | −0.0256802 | − | 0.178610i | ||||
\(349\) | 15.4972 | + | 33.9341i | 0.829544 | + | 1.81645i | 0.465356 | + | 0.885124i | \(0.345926\pi\) |
0.364188 | + | 0.931325i | \(0.381346\pi\) | |||||||
\(350\) | 2.26213 | − | 7.70411i | 0.120916 | − | 0.411802i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 19.7795 | + | 30.7775i | 1.04831 | + | 1.63120i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(360\) | −17.0882 | − | 2.45691i | −0.900625 | − | 0.129490i | ||||
\(361\) | 12.4424 | − | 14.3592i | 0.654861 | − | 0.755750i | ||||
\(362\) | 7.45908 | + | 3.40645i | 0.392040 | + | 0.179039i | ||||
\(363\) | 5.48771 | + | 1.61134i | 0.288030 | + | 0.0845733i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.677280 | − | 1.05387i | 0.0354020 | − | 0.0550866i | ||||
\(367\) | 38.2451i | 1.99638i | 0.0601346 | + | 0.998190i | \(0.480847\pi\) | ||||
−0.0601346 | + | 0.998190i | \(0.519153\pi\) | |||||||
\(368\) | 8.05936 | + | 17.4082i | 0.420123 | + | 0.907467i | ||||
\(369\) | −30.6763 | −1.59694 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.39329 | + | 3.80681i | 0.226868 | + | 0.196583i | ||||
\(376\) | 4.89926 | − | 34.0751i | 0.252660 | − | 1.75729i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 3.61555 | − | 3.13289i | 0.185964 | − | 0.161138i | ||||
\(379\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.66596 | − | 8.84699i | −0.392739 | − | 0.453245i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 38.5483 | + | 5.54241i | 1.96973 | + | 0.283204i | 0.999090 | + | 0.0426504i | \(0.0135802\pi\) |
0.970636 | + | 0.240553i | \(0.0773289\pi\) | |||||||
\(384\) | 3.85222 | − | 4.44569i | 0.196583 | − | 0.226868i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.4855 | + | 11.6388i | −1.29550 | + | 0.591636i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.22297 | − | 11.2392i | 0.366219 | − | 0.569848i | −0.608424 | − | 0.793612i | \(-0.708198\pi\) |
0.974643 | + | 0.223764i | \(0.0718344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −16.1520 | −0.815798 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.1899 | − | 5.63465i | 0.959493 | − | 0.281733i | ||||
\(401\) | −17.3130 | + | 15.0018i | −0.864571 | + | 0.749155i | −0.969439 | − | 0.245331i | \(-0.921103\pi\) |
0.104869 | + | 0.994486i | \(0.466558\pi\) | |||||||
\(402\) | −0.774909 | − | 1.20578i | −0.0386489 | − | 0.0601389i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.24020 | − | 9.50970i | −0.409965 | − | 0.473125i | ||||
\(405\) | −4.18303 | − | 14.2461i | −0.207856 | − | 0.707893i | ||||
\(406\) | 5.14540 | + | 0.739797i | 0.255362 | + | 0.0367155i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.19768 | + | 2.11343i | 0.355902 | + | 0.104502i | 0.454796 | − | 0.890596i | \(-0.349712\pi\) |
−0.0988936 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(410\) | 32.3266 | − | 14.7631i | 1.59650 | − | 0.729096i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.5267 | + | 19.4919i | −0.617146 | + | 0.960298i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.0511 | + | 14.0542i | −0.592277 | + | 0.690724i | ||||
\(415\) | 31.4120 | 1.54196 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(420\) | −1.09686 | + | 2.40178i | −0.0535211 | + | 0.117195i | ||||
\(421\) | −15.3505 | − | 13.3013i | −0.748138 | − | 0.648265i | 0.194948 | − | 0.980814i | \(-0.437546\pi\) |
−0.943086 | + | 0.332548i | \(0.892092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.8776 | − | 9.36010i | 1.54994 | − | 0.455103i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.26687 | + | 1.46205i | 0.0613082 | + | 0.0707534i | ||||
\(428\) | 8.04749 | + | 27.4072i | 0.388990 | + | 1.32478i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.2554 | − | 24.5300i | 1.02502 | − | 1.18294i | ||||
\(431\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(432\) | 11.4337 | + | 3.35724i | 0.550105 | + | 0.161525i | ||||
\(433\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.03471 | + | 3.16607i | −0.0975568 | + | 0.151801i | ||||
\(436\) | 39.8737i | 1.90960i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.47547 | − | 14.1793i | −0.308356 | − | 0.675205i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.6623 | − | 23.3472i | 0.506581 | − | 1.10926i | −0.467693 | − | 0.883891i | \(-0.654915\pi\) |
0.974274 | − | 0.225367i | \(-0.0723580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.82119 | − | 40.4873i | 0.275951 | − | 1.91928i | ||||
\(446\) | −12.8375 | + | 3.76942i | −0.607872 | + | 0.178487i | ||||
\(447\) | 4.34308 | − | 3.76330i | 0.205421 | − | 0.177998i | ||||
\(448\) | 4.91128 | + | 7.64210i | 0.232036 | + | 0.361055i | ||||
\(449\) | 35.6475 | − | 22.9092i | 1.68231 | − | 1.08115i | 0.832835 | − | 0.553521i | \(-0.186716\pi\) |
0.849473 | − | 0.527633i | \(-0.176920\pi\) | |||||||
\(450\) | 12.6399 | + | 14.5872i | 0.595849 | + | 0.687646i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 31.5411 | + | 14.4043i | 1.48030 | + | 0.676029i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(458\) | 11.4720 | − | 17.8507i | 0.536049 | − | 0.834109i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.93577 | − | 20.6099i | 0.276757 | − | 0.960940i | ||||
\(461\) | −40.1683 | −1.87082 | −0.935412 | − | 0.353560i | \(-0.884971\pi\) | ||||
−0.935412 | + | 0.353560i | \(0.884971\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.60772 | + | 39.0025i | 0.260613 | + | 1.81260i | 0.528259 | + | 0.849083i | \(0.322845\pi\) |
−0.267646 | + | 0.963517i | \(0.586246\pi\) | |||||||
\(464\) | 5.37890 | + | 11.7782i | 0.249709 | + | 0.546787i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.5090 | + | 18.6377i | 0.995318 | + | 0.862448i | 0.990496 | − | 0.137540i | \(-0.0439196\pi\) |
0.00482209 | + | 0.999988i | \(0.498465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.12377 | − | 0.623595i | 0.0980666 | − | 0.0287950i | ||||
\(470\) | −29.0879 | + | 25.2048i | −1.34173 | + | 1.16261i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(480\) | −6.50989 | + | 0.935981i | −0.297134 | + | 0.0427215i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 42.3513i | − | 1.92905i | ||||||
\(483\) | 1.54315 | + | 2.37404i | 0.0702156 | + | 0.108023i | ||||
\(484\) | −22.0000 | −1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.49360 | + | 17.3434i | 0.113112 | + | 0.786712i | ||||
\(487\) | −3.43790 | − | 7.52795i | −0.155786 | − | 0.341124i | 0.815605 | − | 0.578609i | \(-0.196404\pi\) |
−0.971391 | + | 0.237485i | \(0.923677\pi\) | |||||||
\(488\) | −1.35759 | + | 4.62354i | −0.0614554 | + | 0.209298i | ||||
\(489\) | −3.20710 | + | 7.02257i | −0.145030 | + | 0.317572i | ||||
\(490\) | 13.6477 | + | 11.8258i | 0.616539 | + | 0.534234i | ||||
\(491\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(492\) | −11.2130 | + | 3.29244i | −0.505523 | + | 0.148435i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10.2244 | − | 1.47005i | −0.458168 | − | 0.0658747i | ||||
\(499\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(500\) | −20.3400 | − | 9.28896i | −0.909632 | − | 0.415415i | ||||
\(501\) | 0.677347 | + | 0.198887i | 0.0302616 | + | 0.00888562i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.3604 | + | 4.50894i | −1.39829 | + | 0.201044i | −0.799887 | − | 0.600151i | \(-0.795107\pi\) |
−0.598403 | + | 0.801195i | \(0.704198\pi\) | |||||||
\(504\) | −4.73978 | + | 7.37523i | −0.211126 | + | 0.328519i | ||||
\(505\) | 14.0684i | 0.626034i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.75927 | 0.300190 | ||||||||
\(508\) | 37.8807 | + | 24.3444i | 1.68068 | + | 1.08011i | ||||
\(509\) | −5.43465 | − | 37.7988i | −0.240886 | − | 1.67540i | −0.647703 | − | 0.761893i | \(-0.724270\pi\) |
0.406817 | − | 0.913510i | \(-0.366639\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −9.39977 | + | 20.5826i | −0.415415 | + | 0.909632i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.8556 | − | 7.29827i | 1.09527 | − | 0.321600i | ||||
\(516\) | −8.06648 | + | 6.98965i | −0.355107 | + | 0.307702i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.27690 | − | 0.758704i | −0.231185 | − | 0.0332394i | 0.0257485 | − | 0.999668i | \(-0.491803\pi\) |
−0.256934 | + | 0.966429i | \(0.582712\pi\) | |||||||
\(522\) | −8.18321 | + | 9.44393i | −0.358169 | + | 0.413349i | ||||
\(523\) | −31.2428 | − | 14.2681i | −1.36615 | − | 0.623901i | −0.408746 | − | 0.912648i | \(-0.634034\pi\) |
−0.957405 | + | 0.288747i | \(0.906761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.68527 | − | 1.22632i | 0.117195 | − | 0.0535211i | ||||
\(526\) | −36.3582 | + | 5.22751i | −1.58529 | + | 0.227930i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.2411 | − | 17.2252i | −0.662658 | − | 0.748922i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.78953 | + | 12.9060i | −0.163989 | + | 0.558495i | ||||
\(535\) | 13.2666 | − | 29.0499i | 0.573566 | − | 1.25593i | ||||
\(536\) | 4.16671 | + | 3.61047i | 0.179974 | + | 0.155949i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.6677 | + | 10.1793i | −1.49463 | + | 0.438863i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.20293 | − | 11.2080i | −0.309965 | − | 0.482315i | ||||
\(541\) | 26.8929 | − | 17.2830i | 1.15622 | − | 0.743055i | 0.185349 | − | 0.982673i | \(-0.440658\pi\) |
0.970867 | + | 0.239618i | \(0.0770221\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.849373 | + | 2.89270i | 0.0364501 | + | 0.124138i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.1938 | − | 33.6914i | 1.25052 | − | 1.44318i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.8196 | − | 12.8666i | −1.87359 | − | 0.550136i | −0.997712 | − | 0.0676046i | \(-0.978464\pi\) |
−0.875879 | − | 0.482531i | \(-0.839717\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.60313 | + | 0.661829i | −0.196457 | + | 0.0282462i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.89658 | + | 6.43061i | −0.123287 | + | 0.273705i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.44541 | − | 10.0530i | 0.0610797 | − | 0.424819i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.5656 | + | 22.1527i | −1.07842 | + | 0.934457i | ||||
\(563\) | 17.3716 | + | 27.0308i | 0.732127 | + | 1.13921i | 0.985141 | + | 0.171749i | \(0.0549419\pi\) |
−0.253014 | + | 0.967463i | \(0.581422\pi\) | |||||||
\(564\) | 10.6475 | − | 6.84275i | 0.448342 | − | 0.288132i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11.6969 | + | 39.8361i | 0.491659 | + | 1.67444i | ||||
\(567\) | −7.46313 | − | 1.07304i | −0.313422 | − | 0.0450633i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.3609 | − | 12.9520i | −1.18895 | − | 0.542975i | −0.280048 | − | 0.959986i | \(-0.590351\pi\) |
−0.908902 | + | 0.417011i | \(0.863078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 18.0470i | − | 0.753268i | ||||||
\(575\) | −20.1051 | + | 13.0685i | −0.838441 | + | 0.544993i | ||||
\(576\) | −21.8373 | −0.909886 | ||||||||
\(577\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(578\) | −3.42148 | − | 23.7969i | −0.142315 | − | 0.989821i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.07853 | − | 13.8902i | 0.169352 | − | 0.576759i | ||||
\(581\) | 6.62657 | − | 14.5102i | 0.274917 | − | 0.601983i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.7577 | + | 25.5507i | −1.64097 | + | 1.05459i | −0.701104 | + | 0.713059i | \(0.747309\pi\) |
−0.939870 | + | 0.341532i | \(0.889054\pi\) | |||||||
\(588\) | −3.88881 | − | 4.48792i | −0.160372 | − | 0.185079i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.9509 | + | 18.5960i | −0.489529 | + | 0.761723i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 6.18584 | + | 3.97540i | 0.252536 | + | 0.162295i | ||||
\(601\) | 6.44906 | + | 44.8542i | 0.263063 | + | 1.82964i | 0.509485 | + | 0.860479i | \(0.329836\pi\) |
−0.246422 | + | 0.969163i | \(0.579255\pi\) | |||||||
\(602\) | −6.84719 | − | 14.9933i | −0.279071 | − | 0.611079i | ||||
\(603\) | −1.49905 | + | 5.10529i | −0.0610459 | + | 0.207903i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.5890 | + | 16.1074i | 0.755750 | + | 0.654861i | ||||
\(606\) | 0.658386 | − | 4.57918i | 0.0267451 | − | 0.186016i | ||||
\(607\) | 32.4017 | − | 9.51399i | 1.31514 | − | 0.386161i | 0.452405 | − | 0.891812i | \(-0.350566\pi\) |
0.862738 | + | 0.505652i | \(0.168748\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.03327 | + | 1.60780i | 0.0418701 | + | 0.0651512i | ||||
\(610\) | 4.53226 | − | 2.91271i | 0.183506 | − | 0.117932i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(614\) | 21.7733 | − | 25.1278i | 0.878700 | − | 1.01407i | ||||
\(615\) | 11.8851 | + | 5.42773i | 0.479253 | + | 0.218867i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(618\) | −8.43192 | + | 1.21233i | −0.339181 | + | 0.0487669i | ||||
\(619\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.2871 | + | 0.0740334i | −0.573321 | + | 0.00297086i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.4743 | − | 11.2300i | −0.700092 | − | 0.449922i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.3854 | + | 22.7408i | 0.415415 | + | 0.909632i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 9.40472 | − | 2.76147i | 0.374693 | − | 0.110020i | ||||
\(631\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.1835 | − | 48.3045i | −0.562854 | − | 1.91691i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23.0121 | − | 10.5093i | 0.909632 | − | 0.415415i | ||||
\(641\) | −43.3740 | + | 6.23624i | −1.71317 | + | 0.246317i | −0.927898 | − | 0.372834i | \(-0.878386\pi\) |
−0.785272 | + | 0.619151i | \(0.787477\pi\) | |||||||
\(642\) | −5.67772 | + | 8.83470i | −0.224082 | + | 0.348678i | ||||
\(643\) | 44.0922i | 1.73883i | 0.494084 | + | 0.869414i | \(0.335503\pi\) | ||||
−0.494084 | + | 0.869414i | \(0.664497\pi\) | |||||||
\(644\) | −8.26813 | − | 7.08970i | −0.325810 | − | 0.279373i | ||||
\(645\) | 11.9333 | 0.469874 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.05423 | − | 49.0633i | −0.277330 | − | 1.92888i | −0.361390 | − | 0.932415i | \(-0.617698\pi\) |
0.0840596 | − | 0.996461i | \(-0.473211\pi\) | |||||||
\(648\) | −7.80182 | − | 17.0836i | −0.306484 | − | 0.671107i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.22624 | − | 29.3941i | 0.165512 | − | 1.15116i | ||||
\(653\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(654\) | −11.0791 | + | 9.60013i | −0.433229 | + | 0.375395i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 37.8165 | − | 24.3032i | 1.47649 | − | 0.948880i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.50659 | + | 18.7537i | 0.214669 | + | 0.731096i | ||||
\(659\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.3297 | + | 19.7880i | 1.68533 | + | 0.769664i | 0.999106 | + | 0.0422726i | \(0.0134598\pi\) |
0.686223 | + | 0.727391i | \(0.259267\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 39.3290 | − | 5.65466i | 1.52626 | − | 0.219443i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.2270 | − | 11.6797i | −0.395991 | − | 0.452241i | ||||
\(668\) | −2.71545 | −0.105064 | ||||||||
\(669\) | −4.13815 | − | 2.65943i | −0.159990 | − | 0.102819i | ||||
\(670\) | −0.877244 | − | 6.10136i | −0.0338909 | − | 0.235716i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.940946 | + | 3.20457i | −0.0362978 | + | 0.123619i | ||||
\(673\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.11985 | + | 14.7439i | −0.0815932 | + | 0.567493i | ||||
\(676\) | −24.9468 | + | 7.32505i | −0.959493 | + | 0.281733i | ||||
\(677\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.59162 | + | 12.2319i | 0.137631 | + | 0.468728i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.8861 | − | 37.9526i | 1.25835 | − | 1.45222i | 0.419595 | − | 0.907711i | \(-0.362172\pi\) |
0.838757 | − | 0.544505i | \(-0.183283\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.5670 | − | 8.47927i | 0.708892 | − | 0.323740i | ||||
\(687\) | 7.72196 | − | 1.11025i | 0.294611 | − | 0.0423587i | ||||
\(688\) | 22.1967 | − | 34.5387i | 0.846241 | − | 1.31678i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 7.15569 | − | 3.31281i | 0.272413 | − | 0.126117i | ||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5600 | + | 40.6408i | 0.704529 | + | 1.54270i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.97759 | + | 4.33031i | −0.0749602 | + | 0.164140i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 7.50819 | − | 52.2206i | 0.284189 | − | 1.97658i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.58171 | + | 7.43609i | −0.324358 | + | 0.281058i | ||||
\(701\) | 28.6276 | + | 44.5455i | 1.08125 | + | 1.68246i | 0.546981 | + | 0.837145i | \(0.315777\pi\) |
0.534270 | + | 0.845314i | \(0.320587\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.0066 | − | 2.01385i | −0.527520 | − | 0.0758460i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.49860 | + | 2.96781i | 0.244405 | + | 0.111616i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.4080 | + | 11.1468i | −0.916661 | + | 0.418625i | −0.817159 | − | 0.576412i | \(-0.804452\pi\) |
−0.0995021 | + | 0.995037i | \(0.531725\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 51.7394i | − | 1.93902i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(720\) | 18.4515 | + | 15.9883i | 0.687646 | + | 0.595849i | ||||
\(721\) | 1.87216 | − | 13.0212i | 0.0697230 | − | 0.484934i | ||||
\(722\) | −25.7816 | + | 7.57017i | −0.959493 | + | 0.281733i | ||||
\(723\) | 11.7676 | − | 10.1966i | 0.437640 | − | 0.379217i | ||||
\(724\) | −6.26965 | − | 9.75577i | −0.233010 | − | 0.362570i | ||||
\(725\) | −13.6160 | + | 8.75045i | −0.505684 | + | 0.324983i | ||||
\(726\) | −5.29680 | − | 6.11283i | −0.196583 | − | 0.226868i | ||||
\(727\) | −14.1953 | − | 48.3448i | −0.526476 | − | 1.79301i | −0.605151 | − | 0.796111i | \(-0.706887\pi\) |
0.0786754 | − | 0.996900i | \(-0.474931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.82624 | − | 10.1860i | 0.326898 | − | 0.377260i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.61154 | + | 0.735964i | −0.0595641 | + | 0.0272020i | ||||
\(733\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(734\) | 29.2415 | − | 45.5007i | 1.07932 | − | 1.67946i | ||||
\(735\) | 6.63931i | 0.244894i | ||||||||
\(736\) | 3.72171 | − | 26.8728i | 0.137184 | − | 0.990546i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 36.4960 | + | 23.4545i | 1.34343 | + | 0.863373i | ||||
\(739\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.1174 | − | 34.7619i | −1.47176 | − | 1.27529i | −0.885049 | − | 0.465498i | \(-0.845875\pi\) |
−0.586715 | − | 0.809793i | \(-0.699579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.7132 | − | 6.96282i | 0.868784 | − | 0.255098i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7314 | + | 32.2587i | 0.758521 | + | 1.18028i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.6203 | − | 12.2565i | −0.388058 | − | 0.447843i | ||||
\(750\) | −2.31613 | − | 7.88803i | −0.0845733 | − | 0.288030i | ||||
\(751\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(752\) | −31.8819 | + | 36.7937i | −1.16261 | + | 1.34173i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.69681 | + | 0.962856i | −0.243561 | + | 0.0350187i | ||||
\(757\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.391715 | − | 0.251740i | −0.0141996 | − | 0.00912556i | 0.533522 | − | 0.845786i | \(-0.320868\pi\) |
−0.547721 | + | 0.836661i | \(0.684505\pi\) | |||||||
\(762\) | 2.35604 | + | 16.3866i | 0.0853503 | + | 0.593625i | ||||
\(763\) | −9.40447 | − | 20.5929i | −0.340465 | − | 0.745514i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.6238 | − | 36.0672i | −1.50393 | − | 1.30316i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −7.98213 | + | 2.34376i | −0.288030 | + | 0.0845733i | ||||
\(769\) | −26.4727 | + | 22.9387i | −0.954629 | + | 0.827191i | −0.985036 | − | 0.172347i | \(-0.944865\pi\) |
0.0304075 | + | 0.999538i | \(0.490319\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(774\) | 39.2193 | + | 5.63888i | 1.40971 | + | 0.202685i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17.1865 | + | 7.84882i | −0.616167 | + | 0.281394i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.64355 | −0.344632 | ||||||||
\(784\) | 19.2162 | + | 12.3495i | 0.686293 | + | 0.441054i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5593 | + | 52.9902i | −0.554630 | + | 1.88890i | −0.108071 | + | 0.994143i | \(0.534467\pi\) |
−0.446560 | + | 0.894754i | \(0.647351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.2062 | − | 8.84373i | −0.363351 | − | 0.314845i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −27.1386 | − | 7.96860i | −0.959493 | − | 0.281733i | ||||
\(801\) | 45.4204 | − | 20.7428i | 1.60485 | − | 0.732910i | ||||
\(802\) | 32.0676 | − | 4.61063i | 1.13235 | − | 0.162807i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.02701i | 0.0714873i | ||||||||
\(805\) | 1.79542 | + | 12.0440i | 0.0632802 | + | 0.424496i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.1751 | − | 7.18180i | −0.393382 | − | 0.252811i | ||||
\(808\) | 2.53253 | + | 17.6141i | 0.0890939 | + | 0.619662i | ||||
\(809\) | 14.8538 | + | 32.5252i | 0.522230 | + | 1.14352i | 0.968588 | + | 0.248670i | \(0.0799935\pi\) |
−0.446358 | + | 0.894854i | \(0.647279\pi\) | |||||||
\(810\) | −5.91569 | + | 20.1470i | −0.207856 | + | 0.707893i | ||||
\(811\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(812\) | −5.55591 | − | 4.81422i | −0.194974 | − | 0.168946i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.0921 | + | 21.7424i | −0.878937 | + | 0.761603i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.94728 | − | 8.01759i | −0.242906 | − | 0.280328i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −49.7469 | − | 7.15253i | −1.73724 | − | 0.249777i | ||||
\(821\) | −35.9357 | + | 41.4720i | −1.25416 | + | 1.44738i | −0.409300 | + | 0.912400i | \(0.634227\pi\) |
−0.844863 | + | 0.534982i | \(0.820318\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.1899 | + | 6.80918i | 0.808351 | + | 0.237353i | 0.659693 | − | 0.751536i | \(-0.270686\pi\) |
0.148658 | + | 0.988889i | \(0.452505\pi\) | |||||||
\(824\) | 29.8063 | − | 13.6121i | 1.03835 | − | 0.474200i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.4342i | 1.64945i | 0.565536 | + | 0.824724i | \(0.308669\pi\) | ||||
−0.565536 | + | 0.824724i | \(0.691331\pi\) | |||||||
\(828\) | 25.0828 | − | 7.50638i | 0.871689 | − | 0.260865i | ||||
\(829\) | −26.5328 | −0.921521 | −0.460760 | − | 0.887525i | \(-0.652423\pi\) | ||||
−0.460760 | + | 0.887525i | \(0.652423\pi\) | |||||||
\(830\) | −37.3713 | − | 24.0171i | −1.29718 | − | 0.833645i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.29443 | + | 1.98814i | 0.0794022 | + | 0.0688024i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(840\) | 3.14130 | − | 2.01879i | 0.108385 | − | 0.0696549i | ||||
\(841\) | 12.1289 | + | 13.9975i | 0.418239 | + | 0.482674i | ||||
\(842\) | 8.09277 | + | 27.5614i | 0.278895 | + | 0.949830i | ||||
\(843\) | −12.3105 | − | 1.76999i | −0.423998 | − | 0.0609616i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.4420 | + | 12.0757i | 0.909632 | + | 0.415415i | ||||
\(846\) | −45.0817 | − | 13.2372i | −1.54994 | − | 0.455103i | ||||
\(847\) | 11.3620 | − | 5.18884i | 0.390402 | − | 0.178291i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.25251 | + | 12.8412i | −0.283225 | + | 0.440707i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(854\) | −0.389358 | − | 2.70804i | −0.0133235 | − | 0.0926673i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.3809 | − | 38.7597i | 0.388990 | − | 1.32478i | ||||
\(857\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(860\) | −44.0429 | + | 12.9322i | −1.50185 | + | 0.440983i | ||||
\(861\) | 5.01447 | − | 4.34506i | 0.170893 | − | 0.148079i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.9744 | + | 24.4047i | −1.29266 | + | 0.830745i | −0.992393 | − | 0.123108i | \(-0.960714\pi\) |
−0.300272 | + | 0.953854i | \(0.597077\pi\) | |||||||
\(864\) | −11.0359 | − | 12.7362i | −0.375450 | − | 0.433293i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.78835 | − | 6.68011i | 0.196583 | − | 0.226868i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 4.84143 | − | 2.21101i | 0.164140 | − | 0.0749602i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 30.4867 | − | 47.4382i | 1.03241 | − | 1.60646i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.6955 | 0.429187 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.2297 | + | 13.1966i | 0.513100 | + | 0.444604i | 0.872524 | − | 0.488570i | \(-0.162481\pi\) |
−0.359424 | + | 0.933174i | \(0.617027\pi\) | |||||||
\(882\) | −3.13729 | + | 21.8203i | −0.105638 | + | 0.734728i | ||||
\(883\) | 56.0021 | − | 16.4437i | 1.88462 | − | 0.553375i | 0.889232 | − | 0.457456i | \(-0.151239\pi\) |
0.995389 | − | 0.0959188i | \(-0.0305789\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.5359 | + | 19.6242i | −1.02587 | + | 0.659288i | ||||
\(887\) | −38.9028 | − | 44.8963i | −1.30623 | − | 1.50747i | −0.708269 | − | 0.705943i | \(-0.750523\pi\) |
−0.597960 | − | 0.801526i | \(-0.704022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.3054 | − | 3.63837i | −0.848716 | − | 0.122027i | ||||
\(890\) | −37.8814 | + | 43.7174i | −1.26979 | + | 1.46541i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.1549 | + | 5.33077i | 0.607872 | + | 0.178487i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −8.04436 | + | 1.15660i | −0.269044 | + | 0.0386827i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 12.8470i | − | 0.429187i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −59.9262 | −1.99976 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −3.88471 | − | 27.0187i | −0.129490 | − | 0.900625i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.51741 | − | 5.51236i | 0.0837742 | − | 0.183440i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.84518 | + | 12.8335i | −0.0613360 | + | 0.426601i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.4661 | − | 31.5980i | 1.21084 | − | 1.04920i | 0.213449 | − | 0.976954i | \(-0.431530\pi\) |
0.997387 | − | 0.0722410i | \(-0.0230151\pi\) | |||||||
\(908\) | −26.5116 | − | 41.2528i | −0.879817 | − | 1.36902i | ||||
\(909\) | −14.4475 | + | 9.28487i | −0.479195 | + | 0.307960i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.90051 | + | 0.558041i | 0.0628291 | + | 0.0184483i | ||||
\(916\) | −27.2967 | + | 12.4660i | −0.901907 | + | 0.411887i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | −22.8198 | + | 19.9814i | −0.752346 | + | 0.658768i | ||||
\(921\) | 12.2241 | 0.402799 | ||||||||
\(922\) | 47.7887 | + | 30.7119i | 1.57384 | + | 1.01144i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.1490 | − | 50.6893i | 0.760725 | − | 1.66575i | ||||
\(927\) | 23.8992 | + | 20.7088i | 0.784954 | + | 0.680166i | ||||
\(928\) | 2.60601 | − | 18.1252i | 0.0855466 | − | 0.594990i | ||||
\(929\) | −46.4406 | + | 13.6362i | −1.52367 | + | 0.447389i | −0.933105 | − | 0.359605i | \(-0.882912\pi\) |
−0.590561 | + | 0.806993i | \(0.701093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.3395 | − | 38.6188i | −0.371040 | − | 1.26365i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(938\) | −3.00347 | − | 0.881897i | −0.0980666 | − | 0.0287950i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 53.8774 | − | 7.74641i | 1.75729 | − | 0.252660i | ||||
\(941\) | 10.6110 | − | 16.5110i | 0.345907 | − | 0.538242i | −0.624092 | − | 0.781351i | \(-0.714531\pi\) |
0.969999 | + | 0.243109i | \(0.0781673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.0830 | + | 40.9144i | −1.14246 | + | 1.33236i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.36346 | + | 4.08955i | 0.207003 | + | 0.133033i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.3823 | + | 51.2001i | 0.759823 | + | 1.66378i | 0.747865 | + | 0.663851i | \(0.231079\pi\) |
0.0119574 | + | 0.999929i | \(0.496194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.46053 | + | 3.86379i | 0.273062 | + | 0.124703i | ||||
\(961\) | −29.7443 | − | 8.73371i | −0.959493 | − | 0.281733i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.5885 | − | 5.54819i | 1.24350 | − | 0.178788i | ||||
\(964\) | −32.3810 | + | 50.3858i | −1.04292 | + | 1.62282i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.0207496 | − | 4.00429i | −0.000667607 | − | 0.128836i | ||||
\(967\) | 61.4860 | 1.97726 | 0.988629 | − | 0.150377i | \(-0.0480486\pi\) | ||||
0.988629 | + | 0.150377i | \(0.0480486\pi\) | |||||||
\(968\) | 26.1737 | + | 16.8208i | 0.841254 | + | 0.540641i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(972\) | 10.2938 | − | 22.5402i | 0.330173 | − | 0.722978i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.66562 | + | 11.5846i | −0.0533699 | + | 0.371196i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.15022 | − | 4.46269i | 0.164854 | − | 0.142847i | ||||
\(977\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(978\) | 9.18485 | − | 5.90275i | 0.293699 | − | 0.188749i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −7.19504 | − | 24.5040i | −0.229837 | − | 0.782753i | ||||
\(981\) | 53.8669 | + | 7.74489i | 1.71984 | + | 0.247275i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1290 | + | 7.36585i | 0.514434 | + | 0.234934i | 0.655678 | − | 0.755041i | \(-0.272383\pi\) |
−0.141244 | + | 0.989975i | \(0.545110\pi\) | |||||||
\(984\) | 15.8576 | + | 4.65622i | 0.505523 | + | 0.148435i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.88505 | + | 6.04525i | −0.123662 | + | 0.192422i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6233 | + | 47.3020i | −0.433195 | + | 1.50412i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 11.0402 | + | 9.56636i | 0.349821 | + | 0.303122i | ||||
\(997\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 460.2.o.a.159.1 | ✓ | 40 | |
4.3 | odd | 2 | inner | 460.2.o.a.159.4 | yes | 40 | |
5.4 | even | 2 | inner | 460.2.o.a.159.4 | yes | 40 | |
20.19 | odd | 2 | CM | 460.2.o.a.159.1 | ✓ | 40 | |
23.11 | odd | 22 | inner | 460.2.o.a.379.1 | yes | 40 | |
92.11 | even | 22 | inner | 460.2.o.a.379.4 | yes | 40 | |
115.34 | odd | 22 | inner | 460.2.o.a.379.4 | yes | 40 | |
460.379 | even | 22 | inner | 460.2.o.a.379.1 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.o.a.159.1 | ✓ | 40 | 1.1 | even | 1 | trivial | |
460.2.o.a.159.1 | ✓ | 40 | 20.19 | odd | 2 | CM | |
460.2.o.a.159.4 | yes | 40 | 4.3 | odd | 2 | inner | |
460.2.o.a.159.4 | yes | 40 | 5.4 | even | 2 | inner | |
460.2.o.a.379.1 | yes | 40 | 23.11 | odd | 22 | inner | |
460.2.o.a.379.1 | yes | 40 | 460.379 | even | 22 | inner | |
460.2.o.a.379.4 | yes | 40 | 92.11 | even | 22 | inner | |
460.2.o.a.379.4 | yes | 40 | 115.34 | odd | 22 | inner |