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 | 99.3 | ||
Character | \(\chi\) | \(=\) | 460.99 |
Dual form | 460.2.o.a.79.3 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{19}{22}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.926113 | − | 1.06879i | 0.654861 | − | 0.755750i | ||||
\(3\) | −1.23141 | + | 0.791378i | −0.710954 | + | 0.456902i | −0.845479 | − | 0.534008i | \(-0.820685\pi\) |
0.134526 | + | 0.990910i | \(0.457049\pi\) | |||||||
\(4\) | −0.284630 | − | 1.97964i | −0.142315 | − | 0.989821i | ||||
\(5\) | 2.03400 | − | 0.928896i | 0.909632 | − | 0.415415i | ||||
\(6\) | −0.294605 | + | 2.04902i | −0.120272 | + | 0.836510i | ||||
\(7\) | −1.19158 | − | 4.05815i | −0.450375 | − | 1.53384i | −0.801784 | − | 0.597614i | \(-0.796115\pi\) |
0.351409 | − | 0.936222i | \(-0.385703\pi\) | |||||||
\(8\) | −2.37942 | − | 1.52916i | −0.841254 | − | 0.540641i | ||||
\(9\) | −0.356159 | + | 0.779879i | −0.118720 | + | 0.259960i | ||||
\(10\) | 0.890917 | − | 3.03418i | 0.281733 | − | 0.959493i | ||||
\(11\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(12\) | 1.91714 | + | 2.21250i | 0.553431 | + | 0.638693i | ||||
\(13\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(14\) | −5.44085 | − | 2.48475i | −1.45413 | − | 0.664079i | ||||
\(15\) | −1.76957 | + | 2.75351i | −0.456902 | + | 0.710954i | ||||
\(16\) | −3.83797 | + | 1.12693i | −0.959493 | + | 0.281733i | ||||
\(17\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(18\) | 0.503685 | + | 1.10292i | 0.118720 | + | 0.259960i | ||||
\(19\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(20\) | −2.41782 | − | 3.76220i | −0.540641 | − | 0.841254i | ||||
\(21\) | 4.67885 | + | 4.05425i | 1.02101 | + | 0.884709i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.12178 | − | 3.64067i | −0.650936 | − | 0.759133i | ||||
\(24\) | 4.14019 | 0.845112 | ||||||||
\(25\) | 3.27430 | − | 3.77875i | 0.654861 | − | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.803554 | − | 5.58884i | −0.154644 | − | 1.07557i | ||||
\(28\) | −7.69453 | + | 3.51397i | −1.45413 | + | 0.664079i | ||||
\(29\) | 1.51259 | − | 10.5203i | 0.280881 | − | 1.95357i | −0.0196728 | − | 0.999806i | \(-0.506262\pi\) |
0.300554 | − | 0.953765i | \(-0.402828\pi\) | |||||||
\(30\) | 1.30410 | + | 4.44137i | 0.238096 | + | 0.810879i | ||||
\(31\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(32\) | −2.34994 | + | 5.14566i | −0.415415 | + | 0.909632i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.19327 | − | 7.14742i | −1.04685 | − | 1.20813i | ||||
\(36\) | 1.64526 | + | 0.483091i | 0.274209 | + | 0.0805151i | ||||
\(37\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.26018 | − | 0.900078i | −0.989821 | − | 0.142315i | ||||
\(41\) | 4.25965 | + | 9.32734i | 0.665246 | + | 1.45669i | 0.877552 | + | 0.479482i | \(0.159176\pi\) |
−0.212306 | + | 0.977203i | \(0.568097\pi\) | |||||||
\(42\) | 8.66629 | − | 1.24602i | 1.33724 | − | 0.192266i | ||||
\(43\) | 7.05450 | + | 10.9770i | 1.07580 | + | 1.67398i | 0.622490 | + | 0.782628i | \(0.286121\pi\) |
0.453312 | + | 0.891352i | \(0.350242\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.91711i | 0.285786i | ||||||||
\(46\) | −6.78224 | − | 0.0351445i | −0.999987 | − | 0.00518177i | ||||
\(47\) | 4.51713 | 0.658891 | 0.329445 | − | 0.944175i | \(-0.393138\pi\) | ||||
0.329445 | + | 0.944175i | \(0.393138\pi\) | |||||||
\(48\) | 3.83428 | − | 4.42500i | 0.553431 | − | 0.638693i | ||||
\(49\) | −9.15994 | + | 5.88674i | −1.30856 | + | 0.840962i | ||||
\(50\) | −1.00632 | − | 6.99909i | −0.142315 | − | 0.989821i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(54\) | −6.71748 | − | 4.31706i | −0.914134 | − | 0.587478i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.37030 | + | 11.4782i | −0.450375 | + | 1.53384i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.84318 | − | 11.3596i | −1.29247 | − | 1.49159i | ||||
\(59\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(60\) | 5.95464 | + | 2.71939i | 0.768741 | + | 0.351072i | ||||
\(61\) | 5.31338 | − | 8.26778i | 0.680308 | − | 1.05858i | −0.313726 | − | 0.949514i | \(-0.601577\pi\) |
0.994034 | − | 0.109067i | \(-0.0347863\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.58926 | + | 0.516057i | 0.452204 | + | 0.0650171i | ||||
\(64\) | 3.32332 | + | 7.27706i | 0.415415 | + | 0.909632i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.31902 | + | 7.20847i | 1.01633 | + | 0.880655i | 0.992886 | − | 0.119070i | \(-0.0379913\pi\) |
0.0234443 | + | 0.999725i | \(0.492537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.72533 | + | 2.01265i | 0.809634 | + | 0.242294i | ||||
\(70\) | −13.3748 | −1.59859 | ||||||||
\(71\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(72\) | 2.04002 | − | 1.31104i | 0.240418 | − | 0.154507i | ||||
\(73\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.04159 | + | 7.24439i | −0.120272 | + | 0.836510i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(80\) | −6.75963 | + | 5.85725i | −0.755750 | + | 0.654861i | ||||
\(81\) | 3.72804 | + | 4.30238i | 0.414226 | + | 0.478043i | ||||
\(82\) | 13.9139 | + | 4.08549i | 1.53653 | + | 0.451167i | ||||
\(83\) | −0.390747 | − | 0.178448i | −0.0428900 | − | 0.0195872i | 0.393855 | − | 0.919173i | \(-0.371141\pi\) |
−0.436745 | + | 0.899586i | \(0.643869\pi\) | |||||||
\(84\) | 6.69422 | − | 10.4164i | 0.730399 | − | 1.13652i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.2654 | + | 2.62617i | 1.96961 | + | 0.283187i | ||||
\(87\) | 6.46292 | + | 14.1518i | 0.692897 | + | 1.51723i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.78487 | + | 13.6695i | 0.931195 | + | 1.44897i | 0.893185 | + | 0.449690i | \(0.148466\pi\) |
0.0380101 | + | 0.999277i | \(0.487898\pi\) | |||||||
\(90\) | 2.04899 | + | 1.77546i | 0.215982 | + | 0.187150i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.31868 | + | 7.21625i | −0.658768 | + | 0.752346i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.18337 | − | 4.82787i | 0.431482 | − | 0.497956i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.17842 | − | 8.19609i | −0.120272 | − | 0.836510i | ||||
\(97\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(98\) | −2.19145 | + | 15.2418i | −0.221370 | + | 1.53966i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.41254 | − | 5.40641i | −0.841254 | − | 0.540641i | ||||
\(101\) | 4.28165 | − | 9.37551i | 0.426040 | − | 0.932898i | −0.567912 | − | 0.823089i | \(-0.692249\pi\) |
0.993953 | − | 0.109809i | \(-0.0350239\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7138 | − | 11.8831i | 1.35126 | − | 1.17088i | 0.382198 | − | 0.924081i | \(-0.375167\pi\) |
0.969067 | − | 0.246797i | \(-0.0793782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.2828 | + | 3.90017i | 1.29626 | + | 0.380617i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.91069 | + | 10.7532i | −0.668082 | + | 1.03956i | 0.327426 | + | 0.944877i | \(0.393819\pi\) |
−0.995508 | + | 0.0946787i | \(0.969818\pi\) | |||||||
\(108\) | −10.8352 | + | 3.18150i | −1.04262 | + | 0.306140i | ||||
\(109\) | −20.6654 | − | 2.97123i | −1.97938 | − | 0.284592i | −0.991997 | − | 0.126258i | \(-0.959703\pi\) |
−0.987386 | − | 0.158334i | \(-0.949388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.14650 | + | 14.2322i | 0.864263 | + | 1.34482i | ||||
\(113\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.73150 | − | 4.50532i | −0.907467 | − | 0.420123i | ||||
\(116\) | −21.2570 | −1.97366 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.42114 | − | 3.84580i | 0.768741 | − | 0.351072i | ||||
\(121\) | 1.56546 | − | 10.8880i | 0.142315 | − | 0.989821i | ||||
\(122\) | −3.91574 | − | 13.3358i | −0.354514 | − | 1.20737i | ||||
\(123\) | −12.6268 | − | 8.11476i | −1.13852 | − | 0.731683i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.14987 | − | 10.7275i | 0.281733 | − | 0.959493i | ||||
\(126\) | 3.87562 | − | 3.35824i | 0.345267 | − | 0.299176i | ||||
\(127\) | 10.1744 | + | 11.7419i | 0.902832 | + | 1.04192i | 0.998916 | + | 0.0465500i | \(0.0148227\pi\) |
−0.0960844 | + | 0.995373i | \(0.530632\pi\) | |||||||
\(128\) | 10.8554 | + | 3.18744i | 0.959493 | + | 0.281733i | ||||
\(129\) | −17.3739 | − | 7.93441i | −1.52969 | − | 0.698586i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.4087 | − | 2.21544i | 1.33111 | − | 0.191385i | ||||
\(135\) | −6.82588 | − | 10.6213i | −0.587478 | − | 0.914134i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 8.37951 | − | 5.32403i | 0.713312 | − | 0.453212i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | −12.3865 | + | 14.2948i | −1.04685 | + | 1.20813i | ||||
\(141\) | −5.56243 | + | 3.57475i | −0.468441 | + | 0.301049i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.488058 | − | 3.39452i | 0.0406715 | − | 0.282877i | ||||
\(145\) | −6.69566 | − | 22.8033i | −0.556044 | − | 1.89371i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.62099 | − | 14.4979i | 0.546090 | − | 1.19577i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.0949 | + | 13.0798i | −1.23662 | + | 1.07154i | −0.241754 | + | 0.970338i | \(0.577723\pi\) |
−0.994866 | + | 0.101200i | \(0.967732\pi\) | |||||||
\(150\) | 6.77811 | + | 7.82236i | 0.553431 | + | 0.638693i | ||||
\(151\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6491i | 1.00000i | ||||||||
\(161\) | −11.0545 | + | 17.0068i | −0.871220 | + | 1.34032i | ||||
\(162\) | 8.05093 | 0.632541 | ||||||||
\(163\) | 15.5346 | − | 17.9279i | 1.21676 | − | 1.40422i | 0.328743 | − | 0.944419i | \(-0.393375\pi\) |
0.888022 | − | 0.459802i | \(-0.152079\pi\) | |||||||
\(164\) | 17.2524 | − | 11.0874i | 1.34718 | − | 0.865783i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.552599 | + | 0.252364i | −0.0428900 | + | 0.0195872i | ||||
\(167\) | −1.82330 | + | 12.6813i | −0.141091 | + | 0.981312i | 0.789107 | + | 0.614255i | \(0.210544\pi\) |
−0.930199 | + | 0.367057i | \(0.880366\pi\) | |||||||
\(168\) | −4.93336 | − | 16.8015i | −0.380617 | − | 1.29626i | ||||
\(169\) | 10.9363 | + | 7.02833i | 0.841254 | + | 0.540641i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 19.7227 | − | 17.0898i | 1.50384 | − | 1.30308i | ||||
\(173\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(174\) | 21.1107 | + | 6.19867i | 1.60040 | + | 0.469920i | ||||
\(175\) | −19.2363 | − | 8.78493i | −1.45413 | − | 0.664079i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 22.7457 | + | 3.27033i | 1.70486 | + | 0.245122i | ||||
\(179\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(180\) | 3.79519 | − | 0.545666i | 0.282877 | − | 0.0406715i | ||||
\(181\) | −12.7886 | − | 19.8994i | −0.950568 | − | 1.47911i | −0.876238 | − | 0.481878i | \(-0.839955\pi\) |
−0.0743294 | − | 0.997234i | \(-0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.3859i | 1.06344i | ||||||||
\(184\) | 1.86085 | + | 13.4364i | 0.137184 | + | 0.990546i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.28571 | − | 8.94230i | −0.0937699 | − | 0.652184i | ||||
\(189\) | −21.7228 | + | 9.92049i | −1.58010 | + | 0.721610i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(192\) | −9.85126 | − | 6.33102i | −0.710954 | − | 0.456902i | ||||
\(193\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.2608 | + | 16.4579i | 1.01863 | + | 1.17556i | ||||
\(197\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(200\) | −13.5693 | + | 3.98430i | −0.959493 | + | 0.281733i | ||||
\(201\) | −15.9487 | − | 2.29308i | −1.12494 | − | 0.161741i | ||||
\(202\) | −6.05517 | − | 13.2590i | −0.426040 | − | 0.932898i | ||||
\(203\) | −44.4953 | + | 6.39746i | −3.12296 | + | 0.449014i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.3283 | + | 15.0150i | 1.21026 | + | 1.04869i | ||||
\(206\) | − | 25.6623i | − | 1.78798i | ||||||
\(207\) | 3.95113 | − | 1.13795i | 0.274623 | − | 0.0790931i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 16.4698 | − | 10.5845i | 1.13652 | − | 0.730399i | ||||
\(211\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.09289 | + | 17.3448i | 0.348143 | + | 1.18567i | ||||
\(215\) | 24.5454 | + | 15.7743i | 1.67398 | + | 1.07580i | ||||
\(216\) | −6.63425 | + | 14.5270i | −0.451404 | + | 0.988436i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −22.3141 | + | 19.3353i | −1.51130 | + | 1.30955i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.05863 | + | 2.07260i | −0.472681 | + | 0.138792i | −0.509393 | − | 0.860534i | \(-0.670130\pi\) |
0.0367117 | + | 0.999326i | \(0.488312\pi\) | |||||||
\(224\) | 23.6820 | + | 3.40496i | 1.58232 | + | 0.227503i | ||||
\(225\) | 1.78079 | + | 3.89940i | 0.118720 | + | 0.259960i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2604 | − | 17.5215i | −0.747377 | − | 1.16294i | −0.981635 | − | 0.190767i | \(-0.938903\pi\) |
0.234259 | − | 0.972174i | \(-0.424734\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.99126i | 0.461996i | 0.972954 | + | 0.230998i | \(0.0741990\pi\) | ||||
−0.972954 | + | 0.230998i | \(0.925801\pi\) | |||||||
\(230\) | −13.8277 | + | 6.22851i | −0.911772 | + | 0.410696i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.6864 | + | 22.7193i | −1.29247 | + | 1.49159i | ||||
\(233\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.18783 | − | 4.19594i | 0.599348 | − | 0.273713i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(240\) | 3.68856 | − | 12.5621i | 0.238096 | − | 0.810879i | ||||
\(241\) | −3.76699 | + | 3.26411i | −0.242653 | + | 0.210260i | −0.767693 | − | 0.640817i | \(-0.778596\pi\) |
0.525041 | + | 0.851077i | \(0.324050\pi\) | |||||||
\(242\) | −10.1872 | − | 11.7567i | −0.654861 | − | 0.755750i | ||||
\(243\) | 8.25724 | + | 2.42455i | 0.529702 | + | 0.155535i | ||||
\(244\) | −17.8796 | − | 8.16534i | −1.14462 | − | 0.522732i | ||||
\(245\) | −13.1631 | + | 20.4823i | −0.840962 | + | 1.30856i | ||||
\(246\) | −20.3668 | + | 5.98025i | −1.29854 | + | 0.381287i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.622388 | − | 0.0894859i | 0.0394422 | − | 0.00567094i | ||||
\(250\) | −8.54828 | − | 13.3014i | −0.540641 | − | 0.841254i | ||||
\(251\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(252\) | − | 7.25233i | − | 0.456854i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 21.9723 | 1.37866 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.4601 | − | 8.65025i | 0.841254 | − | 0.540641i | ||||
\(257\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(258\) | −24.5705 | + | 11.2210i | −1.52969 | + | 0.698586i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.66584 | + | 4.92654i | 0.474504 | + | 0.304945i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.19700 | + | 10.8880i | −0.197136 | + | 0.671383i | 0.800286 | + | 0.599619i | \(0.204681\pi\) |
−0.997422 | + | 0.0717640i | \(0.977137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.6355 | − | 9.88061i | −1.32407 | − | 0.604684i | ||||
\(268\) | 11.9024 | − | 18.5204i | 0.727052 | − | 1.13132i | ||||
\(269\) | −30.9716 | + | 9.09410i | −1.88837 | + | 0.554477i | −0.894067 | + | 0.447934i | \(0.852160\pi\) |
−0.994308 | + | 0.106543i | \(0.966022\pi\) | |||||||
\(270\) | −17.6735 | − | 2.54106i | −1.07557 | − | 0.154644i | ||||
\(271\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.07009 | − | 13.8866i | 0.124605 | − | 0.835876i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.80686 | + | 26.4773i | 0.227503 | + | 1.58232i | ||||
\(281\) | 6.75192 | − | 3.08350i | 0.402786 | − | 0.183946i | −0.203713 | − | 0.979031i | \(-0.565301\pi\) |
0.606499 | + | 0.795085i | \(0.292574\pi\) | |||||||
\(282\) | −1.33077 | + | 9.25570i | −0.0792461 | + | 0.551169i | ||||
\(283\) | −9.24051 | − | 31.4703i | −0.549291 | − | 1.87071i | −0.488500 | − | 0.872564i | \(-0.662456\pi\) |
−0.0607917 | − | 0.998150i | \(-0.519363\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.7760 | − | 28.4006i | 1.93471 | − | 1.67643i | ||||
\(288\) | −3.17604 | − | 3.66534i | −0.187150 | − | 0.215982i | ||||
\(289\) | 16.3114 | + | 4.78945i | 0.959493 | + | 0.281733i | ||||
\(290\) | −30.5729 | − | 13.9622i | −1.79530 | − | 0.819888i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(294\) | −9.36349 | − | 20.5032i | −0.546090 | − | 1.19577i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 28.2466i | 1.63628i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 14.6378 | 0.845112 | ||||||||
\(301\) | 36.1404 | − | 41.7082i | 2.08310 | − | 2.40402i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.14711 | + | 14.9335i | 0.123348 | + | 0.857906i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.12750 | − | 21.7522i | 0.179080 | − | 1.24553i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6689 | − | 7.49916i | −0.665980 | − | 0.427999i | 0.163494 | − | 0.986544i | \(-0.447724\pi\) |
−0.829474 | + | 0.558545i | \(0.811360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.48330 | + | 25.4858i | −0.425710 | + | 1.44984i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.77991 | − | 2.28439i | 0.438348 | − | 0.128711i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 13.5193 | + | 11.7145i | 0.755750 | + | 0.654861i | ||||
\(321\) | − | 18.7106i | − | 1.04432i | ||||||
\(322\) | 7.93896 | + | 27.5652i | 0.442421 | + | 1.53615i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.45607 | − | 8.60477i | 0.414226 | − | 0.478043i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.77438 | − | 33.2065i | −0.264428 | − | 1.83914i | ||||
\(327\) | 27.7989 | − | 12.6953i | 1.53728 | − | 0.702052i | ||||
\(328\) | 4.12750 | − | 28.7074i | 0.227903 | − | 1.58510i | ||||
\(329\) | −5.38252 | − | 18.3312i | −0.296748 | − | 1.01063i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(332\) | −0.242045 | + | 0.824330i | −0.0132840 | + | 0.0452410i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.8651 | + | 13.6931i | 0.649231 | + | 0.749252i | ||||
\(335\) | 23.6168 | + | 6.93452i | 1.29032 | + | 0.378873i | ||||
\(336\) | −22.5261 | − | 10.2873i | −1.22890 | − | 0.561221i | ||||
\(337\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(338\) | 17.6401 | − | 5.17959i | 0.959493 | − | 0.281733i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4291 | + | 10.7699i | 0.671109 | + | 0.581519i | ||||
\(344\) | − | 36.9065i | − | 1.98986i | ||||||
\(345\) | 15.5489 | − | 2.15341i | 0.837122 | − | 0.115936i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3209 | + | 26.9138i | −1.25193 | + | 1.44481i | −0.403950 | + | 0.914781i | \(0.632363\pi\) |
−0.847982 | + | 0.530026i | \(0.822182\pi\) | |||||||
\(348\) | 26.1760 | − | 16.8223i | 1.40318 | − | 0.901770i | ||||
\(349\) | −2.47445 | − | 17.2102i | −0.132454 | − | 0.921239i | −0.942341 | − | 0.334653i | \(-0.891381\pi\) |
0.809887 | − | 0.586586i | \(-0.199528\pi\) | |||||||
\(350\) | −27.2043 | + | 12.4238i | −1.45413 | + | 0.664079i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 24.5604 | − | 21.2817i | 1.30170 | − | 1.12793i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(360\) | 2.93157 | − | 4.56161i | 0.154507 | − | 0.240418i | ||||
\(361\) | 18.2304 | − | 5.35292i | 0.959493 | − | 0.281733i | ||||
\(362\) | −33.1120 | − | 4.76079i | −1.74033 | − | 0.250221i | ||||
\(363\) | 6.68882 | + | 14.6465i | 0.351072 | + | 0.768741i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.3755 | + | 13.3230i | 0.803691 | + | 0.696402i | ||||
\(367\) | 23.3040i | 1.21646i | 0.793762 | + | 0.608229i | \(0.208120\pi\) | ||||
−0.793762 | + | 0.608229i | \(0.791880\pi\) | |||||||
\(368\) | 16.0841 | + | 10.4548i | 0.838441 | + | 0.544993i | ||||
\(369\) | −8.79131 | −0.457657 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.61070 | + | 15.7026i | 0.238096 | + | 0.810879i | ||||
\(376\) | −10.7482 | − | 6.90743i | −0.554294 | − | 0.356223i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −9.51487 | + | 32.4047i | −0.489392 | + | 1.66672i | ||||
\(379\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.8211 | − | 6.40725i | −1.11793 | − | 0.328253i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.6709 | + | 16.6042i | −0.545257 | + | 0.848436i | −0.999090 | − | 0.0426504i | \(-0.986420\pi\) |
0.453833 | + | 0.891087i | \(0.350056\pi\) | |||||||
\(384\) | −15.8899 | + | 4.66570i | −0.810879 | + | 0.238096i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.0733 | + | 1.59210i | −0.562886 | + | 0.0809308i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.78538 | + | 1.54704i | 0.0905223 | + | 0.0784380i | 0.698946 | − | 0.715174i | \(-0.253653\pi\) |
−0.608424 | + | 0.793612i | \(0.708198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 30.7972 | 1.55549 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.30830 | + | 18.1926i | −0.415415 | + | 0.909632i | ||||
\(401\) | −11.2212 | + | 38.2158i | −0.560358 | + | 1.90840i | −0.179558 | + | 0.983747i | \(0.557467\pi\) |
−0.380800 | + | 0.924657i | \(0.624351\pi\) | |||||||
\(402\) | −17.2211 | + | 14.9222i | −0.858913 | + | 0.744252i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −19.7788 | − | 5.80759i | −0.984034 | − | 0.288939i | ||||
\(405\) | 11.5793 | + | 5.28808i | 0.575380 | + | 0.262767i | ||||
\(406\) | −34.3702 | + | 53.4810i | −1.70576 | + | 2.65422i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.8994 | − | 34.8149i | −0.786177 | − | 1.72149i | −0.687283 | − | 0.726389i | \(-0.741197\pi\) |
−0.0988936 | − | 0.995098i | \(-0.531530\pi\) | |||||||
\(410\) | 32.0958 | − | 4.61469i | 1.58510 | − | 0.227903i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −27.4277 | − | 23.7662i | −1.35126 | − | 1.17088i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.44296 | − | 5.27681i | 0.120065 | − | 0.259341i | ||||
\(415\) | −0.960538 | −0.0471509 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(420\) | 3.94027 | − | 27.4052i | 0.192266 | − | 1.33724i | ||||
\(421\) | 11.5152 | + | 39.2171i | 0.561215 | + | 1.91132i | 0.366267 | + | 0.930510i | \(0.380636\pi\) |
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.60882 | + | 3.52281i | −0.0782233 | + | 0.171285i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.8832 | − | 11.7108i | −1.93008 | − | 0.566724i | ||||
\(428\) | 23.2546 | + | 10.6200i | 1.12405 | + | 0.513337i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39.5913 | − | 11.6250i | 1.90926 | − | 0.560609i | ||||
\(431\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(432\) | 9.38225 | + | 20.5443i | 0.451404 | + | 0.988436i | ||||
\(433\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.2911 | + | 22.7814i | 1.26056 | + | 1.09228i | ||||
\(436\) | 41.7557i | 1.99974i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.32855 | − | 9.24026i | −0.0632642 | − | 0.440012i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.505734 | + | 3.51746i | −0.0240281 | + | 0.167119i | −0.998302 | − | 0.0582471i | \(-0.981449\pi\) |
0.974274 | + | 0.225367i | \(0.0723580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.5660 | + | 19.6436i | 1.44897 | + | 0.931195i | ||||
\(446\) | −4.32191 | + | 9.46367i | −0.204648 | + | 0.448118i | ||||
\(447\) | 8.23689 | − | 28.0523i | 0.389592 | − | 1.32683i | ||||
\(448\) | 25.5714 | − | 22.1577i | 1.20813 | − | 1.04685i | ||||
\(449\) | 26.5049 | + | 30.5883i | 1.25084 | + | 1.44355i | 0.849473 | + | 0.527633i | \(0.176920\pi\) |
0.401370 | + | 0.915916i | \(0.368534\pi\) | |||||||
\(450\) | 5.81686 | + | 1.70798i | 0.274209 | + | 0.0805151i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −29.1552 | − | 4.19188i | −1.36832 | − | 0.196735i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(458\) | 7.47220 | + | 6.47470i | 0.349153 | + | 0.302543i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.14904 | + | 20.5472i | −0.286701 | + | 0.958020i | ||||
\(461\) | 34.2638 | 1.59582 | 0.797912 | − | 0.602774i | \(-0.205938\pi\) | ||||
0.797912 | + | 0.602774i | \(0.205938\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.530357 | + | 0.340840i | −0.0246478 | + | 0.0158402i | −0.552907 | − | 0.833243i | \(-0.686481\pi\) |
0.528259 | + | 0.849083i | \(0.322845\pi\) | |||||||
\(464\) | 6.05037 | + | 42.0812i | 0.280881 | + | 1.95357i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.01825 | − | 27.3076i | −0.371040 | − | 1.26365i | −0.907618 | − | 0.419797i | \(-0.862101\pi\) |
0.536578 | − | 0.843851i | \(-0.319717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.3403 | − | 42.3493i | 0.893051 | − | 1.95551i | ||||
\(470\) | 4.02438 | − | 13.7058i | 0.185631 | − | 0.632201i | ||||
\(471\) | 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 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(480\) | −10.0102 | − | 15.5762i | −0.456902 | − | 0.710954i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.04906i | 0.321076i | ||||||||
\(483\) | 0.153852 | − | 29.6906i | 0.00700051 | − | 1.35097i | ||||
\(484\) | −22.0000 | −1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.2385 | − | 6.57987i | 0.464427 | − | 0.298469i | ||||
\(487\) | 6.10153 | + | 42.4371i | 0.276487 | + | 1.92301i | 0.373311 | + | 0.927706i | \(0.378222\pi\) |
−0.0968243 | + | 0.995301i | \(0.530868\pi\) | |||||||
\(488\) | −25.2856 | + | 11.5475i | −1.14462 | + | 0.522732i | ||||
\(489\) | −4.94170 | + | 34.3703i | −0.223471 | + | 1.55428i | ||||
\(490\) | 9.70069 | + | 33.0375i | 0.438233 | + | 1.49248i | ||||
\(491\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(492\) | −12.4704 | + | 27.3063i | −0.562207 | + | 1.23106i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.480760 | − | 0.748077i | 0.0215434 | − | 0.0335221i | ||||
\(499\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(500\) | −22.1331 | − | 3.18226i | −0.989821 | − | 0.142315i | ||||
\(501\) | −7.79051 | − | 17.0588i | −0.348054 | − | 0.762132i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.2716 | − | 33.0992i | −0.948452 | − | 1.47582i | −0.878202 | − | 0.478291i | \(-0.841257\pi\) |
−0.0702503 | − | 0.997529i | \(-0.522380\pi\) | |||||||
\(504\) | −7.75123 | − | 6.71648i | −0.345267 | − | 0.299176i | ||||
\(505\) | − | 23.0470i | − | 1.02558i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.0291 | −0.845112 | ||||||||
\(508\) | 20.3488 | − | 23.4838i | 0.902832 | − | 1.04192i | ||||
\(509\) | 37.9574 | − | 24.3937i | 1.68243 | − | 1.08123i | 0.836117 | − | 0.548551i | \(-0.184820\pi\) |
0.846315 | − | 0.532682i | \(-0.178816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.22022 | − | 22.3971i | 0.142315 | − | 0.989821i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.8558 | − | 36.9090i | 0.742754 | − | 1.62640i | ||||
\(516\) | −10.7622 | + | 36.6526i | −0.473778 | + | 1.61354i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.6725 | + | 38.3912i | −1.08092 | + | 1.68195i | −0.518801 | + | 0.854895i | \(0.673621\pi\) |
−0.562123 | + | 0.827054i | \(0.690015\pi\) | |||||||
\(522\) | 12.3649 | − | 3.63066i | 0.541196 | − | 0.158909i | ||||
\(523\) | 44.8580 | + | 6.44960i | 1.96150 | + | 0.282021i | 0.999973 | + | 0.00731877i | \(0.00232966\pi\) |
0.961529 | + | 0.274703i | \(0.0885794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30.6400 | − | 4.40536i | 1.33724 | − | 0.192266i | ||||
\(526\) | 8.67621 | + | 13.5004i | 0.378301 | + | 0.588647i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.50900 | + | 22.7307i | −0.152565 | + | 0.988293i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −30.5972 | + | 13.9733i | −1.32407 | + | 0.604684i | ||||
\(535\) | −4.06769 | + | 28.2914i | −0.175862 | + | 1.22314i | ||||
\(536\) | −8.77155 | − | 29.8732i | −0.378873 | − | 1.29032i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.9636 | + | 41.5244i | −0.817577 | + | 1.79024i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.0835 | + | 16.5359i | −0.821222 | + | 0.711593i | ||||
\(541\) | 30.4344 | + | 35.1231i | 1.30848 | + | 1.51006i | 0.687199 | + | 0.726470i | \(0.258840\pi\) |
0.621277 | + | 0.783591i | \(0.286614\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.4959 | + | 14.3837i | 1.35162 | + | 0.617264i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.7933 | + | 13.1525i | −1.91873 | + | 0.563391i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.85872 | − | 15.0185i | −0.293257 | − | 0.642144i | 0.704455 | − | 0.709749i | \(-0.251192\pi\) |
−0.997712 | + | 0.0676046i | \(0.978464\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.55546 | + | 7.08843i | 0.194422 | + | 0.302527i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −12.9247 | − | 15.0731i | −0.550114 | − | 0.641552i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 31.8242 | + | 20.4522i | 1.34482 | + | 0.864263i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.95743 | − | 10.0721i | 0.124751 | − | 0.424864i | ||||
\(563\) | −34.0951 | + | 29.5436i | −1.43694 | + | 1.24511i | −0.515330 | + | 0.856992i | \(0.672331\pi\) |
−0.921608 | + | 0.388123i | \(0.873124\pi\) | |||||||
\(564\) | 8.65997 | + | 9.99414i | 0.364650 | + | 0.420829i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −42.1929 | − | 19.2689i | −1.77350 | − | 0.809931i | ||||
\(567\) | 13.0175 | − | 20.2556i | 0.546682 | − | 0.850654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.80238 | − | 0.978035i | −0.285171 | − | 0.0410014i | −0.00175481 | − | 0.999998i | \(-0.500559\pi\) |
−0.283416 | + | 0.958997i | \(0.591468\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 61.3329i | − | 2.55998i | ||||||
\(575\) | −23.9788 | − | 0.124255i | −0.999987 | − | 0.00518177i | ||||
\(576\) | −6.85885 | −0.285786 | ||||||||
\(577\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(578\) | 20.2251 | − | 12.9979i | 0.841254 | − | 0.540641i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −43.2367 | + | 19.7455i | −1.79530 | + | 0.819888i | ||||
\(581\) | −0.258563 | + | 1.79834i | −0.0107270 | + | 0.0746079i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.8240 | + | 34.4187i | 1.23097 | + | 1.42061i | 0.873597 | + | 0.486651i | \(0.161782\pi\) |
0.357372 | + | 0.933962i | \(0.383673\pi\) | |||||||
\(588\) | −30.5853 | − | 8.98065i | −1.26132 | − | 0.370356i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.1897 | + | 26.1596i | 1.23662 | + | 1.07154i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 13.5562 | − | 15.6447i | 0.553431 | − | 0.638693i | ||||
\(601\) | 41.0148 | − | 26.3586i | 1.67303 | − | 1.07519i | 0.779214 | − | 0.626758i | \(-0.215619\pi\) |
0.893816 | − | 0.448433i | \(-0.148018\pi\) | |||||||
\(602\) | −11.1073 | − | 77.2531i | −0.452700 | − | 3.14860i | ||||
\(603\) | −8.58463 | + | 3.92047i | −0.349593 | + | 0.159654i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.92970 | − | 23.6004i | −0.281733 | − | 0.959493i | ||||
\(606\) | 17.9492 | + | 11.5353i | 0.729138 | + | 0.468588i | ||||
\(607\) | −3.74237 | + | 8.19465i | −0.151898 | + | 0.332611i | −0.970249 | − | 0.242108i | \(-0.922161\pi\) |
0.818351 | + | 0.574719i | \(0.194888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 49.7291 | − | 43.0905i | 2.01512 | − | 1.74612i | ||||
\(610\) | −20.3522 | − | 23.4877i | −0.824035 | − | 0.950988i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(614\) | −18.8218 | + | 5.52657i | −0.759585 | + | 0.223034i | ||||
\(615\) | −33.2207 | − | 4.77642i | −1.33959 | − | 0.192604i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(618\) | 20.3086 | + | 31.6008i | 0.816932 | + | 1.27117i | ||||
\(619\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.8386 | + | 20.3726i | −0.715839 | + | 0.817524i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.0051 | − | 51.9387i | 1.80309 | − | 2.08088i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.55787 | − | 24.7455i | −0.142315 | − | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 4.76354 | − | 10.4307i | 0.189784 | − | 0.415569i | ||||
\(631\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.6017 | + | 14.4320i | 1.25408 | + | 0.572717i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.0407 | − | 3.60031i | 0.989821 | − | 0.142315i | ||||
\(641\) | −16.9498 | − | 26.3744i | −0.669477 | − | 1.04173i | −0.995351 | − | 0.0963128i | \(-0.969295\pi\) |
0.325875 | − | 0.945413i | \(-0.394341\pi\) | |||||||
\(642\) | −19.9977 | − | 17.3281i | −0.789247 | − | 0.683887i | ||||
\(643\) | − | 23.5457i | − | 0.928551i | −0.885691 | − | 0.464276i | \(-0.846315\pi\) | ||
0.885691 | − | 0.464276i | \(-0.153685\pi\) | |||||||
\(644\) | 36.8138 | + | 17.0434i | 1.45067 | + | 0.671605i | ||||
\(645\) | −42.7088 | −1.68166 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.5849 | + | 22.2263i | −1.35967 | + | 0.873808i | −0.998281 | − | 0.0586071i | \(-0.981334\pi\) |
−0.361390 | + | 0.932415i | \(0.617698\pi\) | |||||||
\(648\) | −2.29153 | − | 15.9380i | −0.0900200 | − | 0.626103i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −39.9124 | − | 25.6502i | −1.56309 | − | 1.00454i | ||||
\(653\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(654\) | 12.1762 | − | 41.4685i | 0.476129 | − | 1.62155i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −26.8597 | − | 30.9977i | −1.04869 | − | 1.21026i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.5770 | − | 11.2240i | −0.958112 | − | 0.437555i | ||||
\(659\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.2620 | + | 1.76301i | 0.476936 | + | 0.0685731i | 0.376591 | − | 0.926380i | \(-0.377096\pi\) |
0.100345 | + | 0.994953i | \(0.468005\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.656876 | + | 1.02212i | 0.0254917 | + | 0.0396659i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.0230 | + | 27.3352i | −1.66586 | + | 1.05842i | ||||
\(668\) | 25.6235 | 0.991403 | ||||||||
\(669\) | 7.05184 | − | 8.13826i | 0.272640 | − | 0.314643i | ||||
\(670\) | 29.2834 | − | 18.8193i | 1.13132 | − | 0.727052i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −31.8568 | + | 14.5485i | −1.22890 | + | 0.561221i | ||||
\(673\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.7499 | − | 15.2631i | −0.914134 | − | 0.587478i | ||||
\(676\) | 10.8008 | − | 23.6504i | 0.415415 | − | 0.909632i | ||||
\(677\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.7322 | + | 12.6649i | 1.06270 | + | 0.485319i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.6674 | − | 9.59201i | 1.24998 | − | 0.367028i | 0.411226 | − | 0.911534i | \(-0.365101\pi\) |
0.838757 | + | 0.544505i | \(0.183283\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.0215 | − | 3.30999i | 0.878966 | − | 0.126376i | ||||
\(687\) | −5.53273 | − | 8.60910i | −0.211087 | − | 0.328457i | ||||
\(688\) | −39.4453 | − | 34.1796i | −1.50384 | − | 1.30308i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.0984 | − | 18.6128i | 0.460580 | − | 0.708576i | ||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.16740 | + | 49.8504i | 0.272071 | + | 1.89229i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.26241 | − | 43.5560i | 0.237376 | − | 1.65099i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −20.6857 | − | 13.2939i | −0.782965 | − | 0.503181i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.9158 | + | 40.5815i | −0.450375 | + | 1.53384i | ||||
\(701\) | −33.5018 | + | 29.0294i | −1.26534 | + | 1.09643i | −0.274475 | + | 0.961594i | \(0.588504\pi\) |
−0.990868 | + | 0.134832i | \(0.956950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.99339 | + | 12.4380i | −0.301049 | + | 0.468441i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.1492 | − | 6.20391i | −1.62279 | − | 0.233322i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.5597 | + | 3.81871i | −0.997470 | + | 0.143415i | −0.621664 | − | 0.783284i | \(-0.713543\pi\) |
−0.375806 | + | 0.926698i | \(0.622634\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 45.9591i | − | 1.72239i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(720\) | −2.16045 | − | 7.35781i | −0.0805151 | − | 0.274209i | ||||
\(721\) | −64.5646 | − | 41.4931i | −2.40451 | − | 1.54529i | ||||
\(722\) | 11.1622 | − | 24.4419i | 0.415415 | − | 0.909632i | ||||
\(723\) | 2.05555 | − | 7.00056i | 0.0764467 | − | 0.260354i | ||||
\(724\) | −35.7537 | + | 30.9808i | −1.32878 | + | 1.15139i | ||||
\(725\) | −34.8009 | − | 40.1624i | −1.29247 | − | 1.49159i | ||||
\(726\) | 21.8486 | + | 6.41534i | 0.810879 | + | 0.238096i | ||||
\(727\) | 23.8246 | + | 10.8803i | 0.883604 | + | 0.403528i | 0.804928 | − | 0.593372i | \(-0.202204\pi\) |
0.0786754 | + | 0.996900i | \(0.474931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.4736 | + | 8.36059i | −1.05458 | + | 0.309652i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 28.4789 | − | 4.09465i | 1.05261 | − | 0.151343i | ||||
\(733\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(734\) | 24.9071 | + | 21.5821i | 0.919337 | + | 0.796610i | ||||
\(735\) | − | 35.6390i | − | 1.31457i | ||||||
\(736\) | 26.0696 | − | 7.50823i | 0.960940 | − | 0.276757i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −8.14175 | + | 9.39608i | −0.299702 | + | 0.345874i | ||||
\(739\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.33457 | + | 4.54512i | 0.0489605 | + | 0.166744i | 0.980344 | − | 0.197295i | \(-0.0632156\pi\) |
−0.931384 | + | 0.364039i | \(0.881397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.5532 | + | 40.6258i | −0.679736 | + | 1.48842i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.278336 | − | 0.241179i | 0.0101838 | − | 0.00882429i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 51.8729 | + | 15.2313i | 1.89540 | + | 0.556538i | ||||
\(750\) | 21.0528 | + | 9.61451i | 0.768741 | + | 0.351072i | ||||
\(751\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(752\) | −17.3366 | + | 5.09049i | −0.632201 | + | 0.185631i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 25.8220 | + | 40.1798i | 0.939137 | + | 1.46133i | ||||
\(757\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.9908 | − | 38.0734i | 1.19591 | − | 1.38016i | 0.289820 | − | 0.957081i | \(-0.406404\pi\) |
0.906094 | − | 0.423077i | \(-0.139050\pi\) | |||||||
\(762\) | −27.0568 | + | 17.3884i | −0.980165 | + | 0.629914i | ||||
\(763\) | 12.5667 | + | 87.4036i | 0.454947 | + | 3.16422i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.86400 | + | 26.7823i | 0.284138 | + | 0.967685i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −9.72920 | + | 21.3040i | −0.351072 | + | 0.768741i | ||||
\(769\) | 1.75240 | − | 5.96813i | 0.0631932 | − | 0.215216i | −0.921843 | − | 0.387563i | \(-0.873317\pi\) |
0.985036 | + | 0.172347i | \(0.0551351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(774\) | −8.55348 | + | 13.3095i | −0.307449 | + | 0.478399i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.30692 | − | 0.475464i | 0.118559 | − | 0.0170462i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −60.0117 | −2.14464 | ||||||||
\(784\) | 28.5217 | − | 32.9157i | 1.01863 | − | 1.17556i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.7378 | − | 23.1712i | 1.80861 | − | 0.825964i | 0.859410 | − | 0.511286i | \(-0.170831\pi\) |
0.949199 | − | 0.314678i | \(-0.101896\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.67970 | − | 15.9376i | −0.166602 | − | 0.567394i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 11.7497 | + | 25.7283i | 0.415415 | + | 0.909632i | ||||
\(801\) | −13.7894 | + | 1.98262i | −0.487224 | + | 0.0700523i | ||||
\(802\) | 30.4526 | + | 47.3852i | 1.07532 | + | 1.67323i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 32.2255i | 1.13650i | ||||||||
\(805\) | −6.68738 | + | 44.8603i | −0.235699 | + | 1.58112i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.9419 | − | 35.7088i | 1.08921 | − | 1.25701i | ||||
\(808\) | −24.5245 | + | 15.7610i | −0.862771 | + | 0.554469i | ||||
\(809\) | 3.10861 | + | 21.6209i | 0.109293 | + | 0.760150i | 0.968588 | + | 0.248670i | \(0.0799935\pi\) |
−0.859295 | + | 0.511480i | \(0.829097\pi\) | |||||||
\(810\) | 16.3756 | − | 7.47848i | 0.575380 | − | 0.262767i | ||||
\(811\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(812\) | 25.3294 | + | 86.2640i | 0.888887 | + | 3.02727i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.9442 | − | 50.8954i | 0.523473 | − | 1.78279i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −51.9346 | − | 15.2494i | −1.81585 | − | 0.533182i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 24.7922 | − | 38.5775i | 0.865783 | − | 1.34718i | ||||
\(821\) | −8.19029 | + | 2.40489i | −0.285843 | + | 0.0839311i | −0.421511 | − | 0.906823i | \(-0.638500\pi\) |
0.135668 | + | 0.990754i | \(0.456682\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.8343 | − | 52.1899i | −0.830813 | − | 1.81923i | −0.421238 | − | 0.906950i | \(-0.638404\pi\) |
−0.409575 | − | 0.912277i | \(-0.634323\pi\) | |||||||
\(824\) | −50.8023 | + | 7.30426i | −1.76978 | + | 0.254456i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 47.4342i | − | 1.64945i | −0.565536 | − | 0.824724i | \(-0.691331\pi\) | ||
0.565536 | − | 0.824724i | \(-0.308669\pi\) | |||||||
\(828\) | −3.37735 | − | 7.49794i | −0.117371 | − | 0.260571i | ||||
\(829\) | −57.5114 | −1.99746 | −0.998728 | − | 0.0504313i | \(-0.983940\pi\) | ||||
−0.998728 | + | 0.0504313i | \(0.983940\pi\) | |||||||
\(830\) | −0.889567 | + | 1.02661i | −0.0308773 | + | 0.0356343i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.07106 | + | 27.4875i | 0.279311 | + | 0.951244i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(840\) | −25.6413 | − | 29.5916i | −0.884709 | − | 1.02101i | ||||
\(841\) | −80.5636 | − | 23.6556i | −2.77805 | − | 0.815710i | ||||
\(842\) | 52.5792 | + | 24.0121i | 1.81200 | + | 0.827512i | ||||
\(843\) | −5.87416 | + | 9.14037i | −0.202317 | + | 0.314811i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.7730 | + | 4.13693i | 0.989821 | + | 0.142315i | ||||
\(846\) | 2.27521 | + | 4.98201i | 0.0782233 | + | 0.171285i | ||||
\(847\) | −46.0507 | + | 6.62108i | −1.58232 | + | 0.227503i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.2837 | + | 31.4400i | 1.24525 | + | 1.07902i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(854\) | −49.4527 | + | 31.7813i | −1.69224 | + | 1.08753i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32.8869 | − | 15.0190i | 1.12405 | − | 0.513337i | ||||
\(857\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(860\) | 24.2412 | − | 53.0809i | 0.826619 | − | 1.81004i | ||||
\(861\) | −17.8851 | + | 60.9109i | −0.609521 | + | 2.07584i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.6823 | + | 40.0255i | 1.18060 | + | 1.36248i | 0.917511 | + | 0.397711i | \(0.130195\pi\) |
0.263088 | + | 0.964772i | \(0.415259\pi\) | |||||||
\(864\) | 30.6465 | + | 8.99864i | 1.04262 | + | 0.306140i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.8762 | + | 7.01069i | −0.810879 | + | 0.238096i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 48.6971 | − | 7.00159i | 1.65099 | − | 0.237376i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 44.6282 | + | 38.6705i | 1.51130 | + | 1.30955i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −47.2869 | −1.59859 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.6069 | + | 53.1524i | 0.525811 | + | 1.79075i | 0.607771 | + | 0.794113i | \(0.292064\pi\) |
−0.0819595 | + | 0.996636i | \(0.526118\pi\) | |||||||
\(882\) | −11.1063 | − | 7.13758i | −0.373968 | − | 0.240335i | ||||
\(883\) | 21.9537 | − | 48.0719i | 0.738801 | − | 1.61775i | −0.0467162 | − | 0.998908i | \(-0.514876\pi\) |
0.785517 | − | 0.618840i | \(-0.212397\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.29106 | + | 3.79809i | 0.110565 | + | 0.127599i | ||||
\(887\) | 53.5159 | + | 15.7137i | 1.79689 | + | 0.527614i | 0.997333 | − | 0.0729794i | \(-0.0232507\pi\) |
0.799555 | + | 0.600593i | \(0.205069\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.5267 | − | 55.2806i | 1.19153 | − | 1.85405i | ||||
\(890\) | 49.3024 | − | 14.4765i | 1.65262 | − | 0.485254i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.11211 | + | 13.3836i | 0.204648 | + | 0.448118i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −22.3537 | − | 34.7831i | −0.747621 | − | 1.16332i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 47.8510i | − | 1.59859i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 57.2390 | 1.91009 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 7.21254 | − | 4.63522i | 0.240418 | − | 0.154507i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.4966 | + | 79.9605i | −0.382582 | + | 2.66092i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.4964 | − | 28.5961i | −1.47911 | − | 0.950568i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.1818 | − | 34.6759i | 0.338080 | − | 1.15139i | −0.598554 | − | 0.801083i | \(-0.704258\pi\) |
0.936633 | − | 0.350311i | \(-0.113924\pi\) | |||||||
\(908\) | −31.4812 | + | 27.2786i | −1.04474 | + | 0.905273i | ||||
\(909\) | 5.78682 | + | 6.67834i | 0.191937 | + | 0.221507i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.3630 | + | 29.2609i | 0.441767 | + | 0.967335i | ||||
\(916\) | 13.8402 | − | 1.98992i | 0.457293 | − | 0.0657488i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 16.2660 | + | 25.6011i | 0.536274 | + | 0.844044i | ||||
\(921\) | 20.3039 | 0.669035 | ||||||||
\(922\) | 31.7321 | − | 36.6208i | 1.04504 | − | 1.20604i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.126884 | + | 0.882497i | −0.00416966 | + | 0.0290006i | ||||
\(927\) | 4.38308 | + | 14.9274i | 0.143959 | + | 0.490281i | ||||
\(928\) | 50.5794 | + | 32.5054i | 1.66035 | + | 1.06704i | ||||
\(929\) | 12.3765 | − | 27.1007i | 0.406059 | − | 0.889145i | −0.590561 | − | 0.806993i | \(-0.701093\pi\) |
0.996620 | − | 0.0821520i | \(-0.0261793\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.6120 | − | 16.7201i | −1.19798 | − | 0.547099i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(938\) | −27.3513 | − | 59.8910i | −0.893051 | − | 1.95551i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.9216 | − | 16.9943i | −0.356223 | − | 0.554294i | ||||
\(941\) | −36.2284 | − | 31.3921i | −1.18101 | − | 1.02335i | −0.999199 | − | 0.0400189i | \(-0.987258\pi\) |
−0.181812 | − | 0.983333i | \(-0.558196\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.6601 | − | 44.6259i | 0.672785 | − | 1.45322i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −34.9691 | + | 40.3565i | −1.13755 | + | 1.31280i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.68773 | + | 46.5142i | 0.217322 | + | 1.51151i | 0.747865 | + | 0.663851i | \(0.231079\pi\) |
−0.530543 | + | 0.847658i | \(0.678012\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −25.9183 | − | 3.72649i | −0.836510 | − | 0.120272i | ||||
\(961\) | 12.8779 | + | 28.1986i | 0.415415 | + | 0.909632i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.92493 | − | 9.21937i | −0.190928 | − | 0.297090i | ||||
\(964\) | 7.53397 | + | 6.52822i | 0.242653 | + | 0.210260i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −31.5906 | − | 27.6613i | −1.01641 | − | 0.889988i | ||||
\(967\) | −61.6303 | −1.98190 | −0.990948 | − | 0.134244i | \(-0.957140\pi\) | ||||
−0.990948 | + | 0.134244i | \(0.957140\pi\) | |||||||
\(968\) | −20.3745 | + | 23.5134i | −0.654861 | + | 0.755750i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(972\) | 2.44948 | − | 17.0365i | 0.0785670 | − | 0.546446i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 51.0071 | + | 32.7803i | 1.63437 | + | 1.05035i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.0754 | + | 37.7193i | −0.354514 | + | 1.20737i | ||||
\(977\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(978\) | 32.1581 | + | 37.1124i | 1.02830 | + | 1.18672i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 44.2942 | + | 20.2285i | 1.41493 | + | 0.646175i | ||||
\(981\) | 9.67735 | − | 15.0583i | 0.308974 | − | 0.480773i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.0671341 | − | 0.00965242i | −0.00214124 | − | 0.000307864i | 0.141244 | − | 0.989975i | \(-0.454890\pi\) |
−0.143385 | + | 0.989667i | \(0.545799\pi\) | |||||||
\(984\) | 17.6358 | + | 38.6169i | 0.562207 | + | 1.23106i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.1350 | + | 18.3136i | 0.672733 | + | 0.582927i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.9411 | − | 59.9510i | 0.570495 | − | 1.90633i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.354300 | − | 1.20664i | −0.0112264 | − | 0.0382337i | ||||
\(997\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(998\) | 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.99.3 | yes | 40 | |
4.3 | odd | 2 | inner | 460.2.o.a.99.2 | yes | 40 | |
5.4 | even | 2 | inner | 460.2.o.a.99.2 | yes | 40 | |
20.19 | odd | 2 | CM | 460.2.o.a.99.3 | yes | 40 | |
23.10 | odd | 22 | inner | 460.2.o.a.79.3 | yes | 40 | |
92.79 | even | 22 | inner | 460.2.o.a.79.2 | ✓ | 40 | |
115.79 | odd | 22 | inner | 460.2.o.a.79.2 | ✓ | 40 | |
460.79 | even | 22 | inner | 460.2.o.a.79.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.o.a.79.2 | ✓ | 40 | 92.79 | even | 22 | inner | |
460.2.o.a.79.2 | ✓ | 40 | 115.79 | odd | 22 | inner | |
460.2.o.a.79.3 | yes | 40 | 23.10 | odd | 22 | inner | |
460.2.o.a.79.3 | yes | 40 | 460.79 | even | 22 | inner | |
460.2.o.a.99.2 | yes | 40 | 4.3 | odd | 2 | inner | |
460.2.o.a.99.2 | yes | 40 | 5.4 | even | 2 | inner | |
460.2.o.a.99.3 | yes | 40 | 1.1 | even | 1 | trivial | |
460.2.o.a.99.3 | yes | 40 | 20.19 | odd | 2 | CM |