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 | 19.4 | ||
Character | \(\chi\) | \(=\) | 460.19 |
Dual form | 460.2.o.a.339.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{15}{22}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.587486 | + | 1.28641i | 0.415415 | + | 0.909632i | ||||
\(3\) | 2.19630 | − | 0.644892i | 1.26804 | − | 0.372329i | 0.422556 | − | 0.906337i | \(-0.361133\pi\) |
0.845479 | + | 0.534008i | \(0.179315\pi\) | |||||||
\(4\) | −1.30972 | + | 1.51150i | −0.654861 | + | 0.755750i | ||||
\(5\) | −1.20891 | + | 1.88110i | −0.540641 | + | 0.841254i | ||||
\(6\) | 2.11989 | + | 2.44649i | 0.865443 | + | 0.998775i | ||||
\(7\) | 4.60217 | − | 0.661692i | 1.73946 | − | 0.250096i | 0.801784 | − | 0.597614i | \(-0.203885\pi\) |
0.937673 | + | 0.347518i | \(0.112975\pi\) | |||||||
\(8\) | −2.71386 | − | 0.796860i | −0.959493 | − | 0.281733i | ||||
\(9\) | 1.88410 | − | 1.21083i | 0.628032 | − | 0.403611i | ||||
\(10\) | −3.13009 | − | 0.450039i | −0.989821 | − | 0.142315i | ||||
\(11\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(12\) | −1.90179 | + | 4.16434i | −0.548999 | + | 1.20214i | ||||
\(13\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(14\) | 3.55492 | + | 5.53156i | 0.950092 | + | 1.47837i | ||||
\(15\) | −1.44202 | + | 4.91108i | −0.372329 | + | 1.26804i | ||||
\(16\) | −0.569259 | − | 3.95929i | −0.142315 | − | 0.989821i | ||||
\(17\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(18\) | 2.66451 | + | 1.71238i | 0.628032 | + | 0.403611i | ||||
\(19\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(20\) | −1.25995 | − | 4.29098i | −0.281733 | − | 0.959493i | ||||
\(21\) | 9.68104 | − | 4.42118i | 2.11258 | − | 0.964781i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.02102 | + | 2.61369i | −0.838441 | + | 0.544993i | ||||
\(24\) | −6.47434 | −1.32157 | ||||||||
\(25\) | −2.07708 | − | 4.54816i | −0.415415 | − | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.13979 | + | 1.31539i | −0.219353 | + | 0.253147i | ||||
\(28\) | −5.02741 | + | 7.82281i | −0.950092 | + | 1.47837i | ||||
\(29\) | 0.138754 | + | 0.160130i | 0.0257659 | + | 0.0297354i | 0.768486 | − | 0.639866i | \(-0.221010\pi\) |
−0.742720 | + | 0.669602i | \(0.766465\pi\) | |||||||
\(30\) | −7.16485 | + | 1.03015i | −1.30812 | + | 0.188079i | ||||
\(31\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(32\) | 4.75885 | − | 3.05833i | 0.841254 | − | 0.540641i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.31890 | + | 9.45707i | −0.730027 | + | 1.59854i | ||||
\(36\) | −0.637465 | + | 4.43366i | −0.106244 | + | 0.738944i | ||||
\(37\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.77978 | − | 4.14170i | 0.755750 | − | 0.654861i | ||||
\(41\) | −2.28723 | − | 1.46991i | −0.357206 | − | 0.229562i | 0.349713 | − | 0.936857i | \(-0.386279\pi\) |
−0.706919 | + | 0.707295i | \(0.749915\pi\) | |||||||
\(42\) | 11.3749 | + | 9.85644i | 1.75519 | + | 1.52088i | ||||
\(43\) | −3.29345 | − | 11.2164i | −0.502246 | − | 1.71049i | −0.686072 | − | 0.727533i | \(-0.740667\pi\) |
0.183826 | − | 0.982959i | \(-0.441152\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.00796i | 0.746543i | ||||||||
\(46\) | −5.72458 | − | 3.63719i | −0.844044 | − | 0.536274i | ||||
\(47\) | 13.4570 | 1.96290 | 0.981449 | − | 0.191722i | \(-0.0614072\pi\) | ||||
0.981449 | + | 0.191722i | \(0.0614072\pi\) | |||||||
\(48\) | −3.80358 | − | 8.32868i | −0.548999 | − | 1.20214i | ||||
\(49\) | 14.0257 | − | 4.11831i | 2.00367 | − | 0.588330i | ||||
\(50\) | 4.63056 | − | 5.34396i | 0.654861 | − | 0.755750i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(54\) | −2.36175 | − | 0.693471i | −0.321393 | − | 0.0943695i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.0169 | − | 1.87155i | −1.73946 | − | 0.250096i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.124478 | + | 0.272569i | −0.0163448 | + | 0.0357900i | ||||
\(59\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(60\) | −5.53444 | − | 8.61176i | −0.714494 | − | 1.11177i | ||||
\(61\) | 4.17862 | − | 14.2311i | 0.535018 | − | 1.82210i | −0.0335091 | − | 0.999438i | \(-0.510668\pi\) |
0.568527 | − | 0.822665i | \(-0.307514\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.86973 | − | 6.81916i | 0.991492 | − | 0.859133i | ||||
\(64\) | 6.73003 | + | 4.32513i | 0.841254 | + | 0.540641i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.8872 | + | 6.79877i | −1.81876 | + | 0.830602i | −0.899643 | + | 0.436626i | \(0.856173\pi\) |
−0.919121 | + | 0.393975i | \(0.871100\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.14582 | + | 8.33359i | −0.860256 | + | 1.00325i | ||||
\(70\) | −14.7030 | −1.75734 | ||||||||
\(71\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(72\) | −6.07803 | + | 1.78467i | −0.716302 | + | 0.210325i | ||||
\(73\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.49496 | − | 8.64964i | −0.865443 | − | 0.998775i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(80\) | 8.13600 | + | 3.71558i | 0.909632 | + | 0.415415i | ||||
\(81\) | −4.44617 | + | 9.73575i | −0.494018 | + | 1.08175i | ||||
\(82\) | 0.547203 | − | 3.80588i | 0.0604285 | − | 0.420289i | ||||
\(83\) | −7.29069 | − | 11.3445i | −0.800257 | − | 1.24522i | −0.965868 | − | 0.259034i | \(-0.916596\pi\) |
0.165611 | − | 0.986191i | \(-0.447040\pi\) | |||||||
\(84\) | −5.99685 | + | 20.4234i | −0.654310 | + | 2.22837i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.4941 | − | 10.8262i | 1.34728 | − | 1.16742i | ||||
\(87\) | 0.408012 | + | 0.262213i | 0.0437435 | + | 0.0281122i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.63124 | − | 12.3669i | −0.384911 | − | 1.31089i | −0.893185 | − | 0.449690i | \(-0.851534\pi\) |
0.508274 | − | 0.861195i | \(-0.330284\pi\) | |||||||
\(90\) | −6.44231 | + | 2.94210i | −0.679079 | + | 0.310125i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.31582 | − | 9.50098i | 0.137184 | − | 0.990546i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.90577 | + | 17.3112i | 0.815418 | + | 1.78552i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.47958 | − | 9.78595i | 0.865443 | − | 0.998775i | ||||
\(97\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(98\) | 13.5377 | + | 15.6234i | 1.36752 | + | 1.57820i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.59493 | + | 2.81733i | 0.959493 | + | 0.281733i | ||||
\(101\) | −16.6491 | + | 10.6997i | −1.65664 | + | 1.06466i | −0.733889 | + | 0.679270i | \(0.762297\pi\) |
−0.922754 | + | 0.385390i | \(0.874067\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.83998 | + | 2.66703i | 0.575430 | + | 0.262790i | 0.681802 | − | 0.731536i | \(-0.261196\pi\) |
−0.106373 | + | 0.994326i | \(0.533924\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.38681 | + | 23.5558i | −0.330519 | + | 2.29881i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.04876 | + | 17.1945i | −0.488082 | + | 1.66225i | 0.235391 | + | 0.971901i | \(0.424363\pi\) |
−0.723472 | + | 0.690353i | \(0.757455\pi\) | |||||||
\(108\) | −0.495401 | − | 3.44559i | −0.0476699 | − | 0.331552i | ||||
\(109\) | 15.2113 | − | 13.1807i | 1.45698 | − | 1.26248i | 0.554201 | − | 0.832383i | \(-0.313024\pi\) |
0.902782 | − | 0.430099i | \(-0.141521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.23966 | − | 17.8446i | −0.495101 | − | 1.68616i | ||||
\(113\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0555683 | − | 10.7237i | −0.00518177 | − | 0.999987i | ||||
\(116\) | −0.423765 | −0.0393456 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.82689 | − | 12.1789i | 0.714494 | − | 1.11177i | ||||
\(121\) | 7.20347 | + | 8.31325i | 0.654861 | + | 0.755750i | ||||
\(122\) | 20.7619 | − | 2.98512i | 1.87970 | − | 0.270260i | ||||
\(123\) | −5.97139 | − | 1.75336i | −0.538422 | − | 0.158095i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0665 | + | 1.59113i | 0.989821 | + | 0.142315i | ||||
\(126\) | 13.3956 | + | 6.11757i | 1.19338 | + | 0.544996i | ||||
\(127\) | 0.899636 | − | 1.96993i | 0.0798298 | − | 0.174803i | −0.865508 | − | 0.500894i | \(-0.833004\pi\) |
0.945338 | + | 0.326092i | \(0.105732\pi\) | |||||||
\(128\) | −1.61011 | + | 11.1986i | −0.142315 | + | 0.989821i | ||||
\(129\) | −14.4668 | − | 22.5108i | −1.27373 | − | 1.98196i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −17.4921 | − | 15.1570i | −1.51108 | − | 1.30936i | ||||
\(135\) | −1.09647 | − | 3.73425i | −0.0943695 | − | 0.321393i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −14.9185 | − | 4.29663i | −1.26995 | − | 0.365753i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | −8.63780 | − | 18.9141i | −0.730027 | − | 1.59854i | ||||
\(141\) | 29.5555 | − | 8.67829i | 2.48902 | − | 0.730844i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.86658 | − | 6.77039i | −0.488881 | − | 0.564199i | ||||
\(145\) | −0.468962 | + | 0.0674265i | −0.0389452 | + | 0.00559947i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 28.1488 | − | 18.0901i | 2.32167 | − | 1.49205i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.2250 | − | 6.95304i | −1.24728 | − | 0.569615i | −0.321228 | − | 0.947002i | \(-0.604096\pi\) |
−0.926056 | + | 0.377387i | \(0.876823\pi\) | |||||||
\(150\) | 6.72384 | − | 14.7232i | 0.548999 | − | 1.20214i | ||||
\(151\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6491i | 1.00000i | ||||||||
\(161\) | −16.7760 | + | 14.6893i | −1.32213 | + | 1.15768i | ||||
\(162\) | −15.1363 | −1.18922 | ||||||||
\(163\) | 10.4121 | + | 22.7992i | 0.815536 | + | 1.78577i | 0.581500 | + | 0.813546i | \(0.302466\pi\) |
0.234036 | + | 0.972228i | \(0.424807\pi\) | |||||||
\(164\) | 5.21741 | − | 1.53197i | 0.407411 | − | 0.119627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.3106 | − | 16.0436i | 0.800257 | − | 1.24522i | ||||
\(167\) | 15.0052 | + | 17.3169i | 1.16114 | + | 1.34002i | 0.930199 | + | 0.367057i | \(0.119634\pi\) |
0.230939 | + | 0.972968i | \(0.425820\pi\) | |||||||
\(168\) | −29.7960 | + | 4.28402i | −2.29881 | + | 0.330519i | ||||
\(169\) | −12.4734 | − | 3.66252i | −0.959493 | − | 0.281733i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 21.2671 | + | 9.71238i | 1.62160 | + | 0.740562i | ||||
\(173\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(174\) | −0.0976137 | + | 0.678918i | −0.00740008 | + | 0.0514687i | ||||
\(175\) | −12.5685 | − | 19.5570i | −0.950092 | − | 1.47837i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13.7756 | − | 11.9366i | 1.03253 | − | 0.894689i | ||||
\(179\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(180\) | −7.56953 | − | 6.55903i | −0.564199 | − | 0.488881i | ||||
\(181\) | 7.09471 | + | 24.1624i | 0.527346 | + | 1.79597i | 0.601675 | + | 0.798741i | \(0.294500\pi\) |
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 33.9505i | − | 2.50969i | ||||||
\(184\) | 12.9952 | − | 3.88900i | 0.958020 | − | 0.286701i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.6249 | + | 20.3402i | −1.28543 | + | 1.48346i | ||||
\(189\) | −4.37513 | + | 6.80784i | −0.318244 | + | 0.495197i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(192\) | 17.5704 | + | 5.15914i | 1.26804 | + | 0.372329i | ||||
\(193\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −12.1449 | + | 26.5937i | −0.867494 | + | 1.89955i | ||||
\(197\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(200\) | 2.01264 | + | 13.9982i | 0.142315 | + | 0.989821i | ||||
\(201\) | −28.3124 | + | 24.5328i | −1.99700 | + | 1.73041i | ||||
\(202\) | −23.5453 | − | 15.1317i | −1.65664 | − | 1.06466i | ||||
\(203\) | 0.744525 | + | 0.645135i | 0.0522554 | + | 0.0452796i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.53011 | − | 2.52552i | 0.386240 | − | 0.176390i | ||||
\(206\) | 9.07947i | 0.632596i | ||||||||
\(207\) | −4.41124 | + | 9.79324i | −0.306602 | + | 0.680677i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −32.2922 | + | 9.48185i | −2.22837 | + | 0.654310i | ||||
\(211\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25.0853 | + | 3.60672i | −1.71480 | + | 0.246550i | ||||
\(215\) | 25.0807 | + | 7.36437i | 1.71049 | + | 0.502246i | ||||
\(216\) | 4.14141 | − | 2.66152i | 0.281787 | − | 0.181094i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 25.8923 | + | 11.8246i | 1.75365 | + | 0.800864i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.10791 | + | 21.6160i | 0.208121 | + | 1.44751i | 0.779281 | + | 0.626674i | \(0.215584\pi\) |
−0.571160 | + | 0.820839i | \(0.693507\pi\) | |||||||
\(224\) | 19.8774 | − | 17.2238i | 1.32811 | − | 1.15082i | ||||
\(225\) | −9.42048 | − | 6.05417i | −0.628032 | − | 0.403611i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.23753 | + | 17.8374i | 0.347627 | + | 1.18391i | 0.928941 | + | 0.370229i | \(0.120721\pi\) |
−0.581314 | + | 0.813680i | \(0.697461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.58809i | − | 0.104944i | −0.998622 | − | 0.0524721i | \(-0.983290\pi\) | ||
0.998622 | − | 0.0524721i | \(-0.0167101\pi\) | |||||||
\(230\) | 13.7624 | − | 6.37148i | 0.907467 | − | 0.420123i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.248956 | − | 0.545138i | −0.0163448 | − | 0.0357900i | ||||
\(233\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.2682 | + | 25.3139i | −1.06122 | + | 1.65130i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(240\) | 20.2653 | + | 2.91370i | 1.30812 | + | 0.188079i | ||||
\(241\) | −23.4736 | − | 10.7201i | −1.51207 | − | 0.690539i | −0.525041 | − | 0.851077i | \(-0.675950\pi\) |
−0.987030 | + | 0.160538i | \(0.948677\pi\) | |||||||
\(242\) | −6.46234 | + | 14.1506i | −0.415415 | + | 0.909632i | ||||
\(243\) | −2.74351 | + | 19.0816i | −0.175996 | + | 1.22408i | ||||
\(244\) | 16.0374 | + | 24.9547i | 1.02669 | + | 1.59756i | ||||
\(245\) | −9.20883 | + | 31.3624i | −0.588330 | + | 2.00367i | ||||
\(246\) | −1.25256 | − | 8.71175i | −0.0798603 | − | 0.555441i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.3286 | − | 20.2143i | −1.47839 | − | 1.28103i | ||||
\(250\) | 4.45458 | + | 15.1709i | 0.281733 | + | 0.959493i | ||||
\(251\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(252\) | 20.8263i | 1.31193i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.06267 | 0.192169 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.3519 | + | 4.50772i | −0.959493 | + | 0.281733i | ||||
\(257\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(258\) | 20.4591 | − | 31.8351i | 1.27373 | − | 1.98196i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.455316 | + | 0.133693i | 0.0281834 | + | 0.00827539i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.81092 | − | 0.979263i | −0.419979 | − | 0.0603839i | −0.0709143 | − | 0.997482i | \(-0.522592\pi\) |
−0.349065 | + | 0.937098i | \(0.613501\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.9506 | − | 24.8196i | −0.976161 | − | 1.51894i | ||||
\(268\) | 9.22179 | − | 31.4065i | 0.563310 | − | 1.91846i | ||||
\(269\) | 2.38066 | + | 16.5578i | 0.145151 | + | 1.00955i | 0.924015 | + | 0.382356i | \(0.124887\pi\) |
−0.778864 | + | 0.627193i | \(0.784204\pi\) | |||||||
\(270\) | 4.15963 | − | 3.60434i | 0.253147 | − | 0.219353i | ||||
\(271\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.23717 | − | 21.7156i | −0.194855 | − | 1.30712i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.2568 | − | 22.2236i | 1.15082 | − | 1.32811i | ||||
\(281\) | 6.18028 | − | 9.61670i | 0.368684 | − | 0.573684i | −0.606499 | − | 0.795085i | \(-0.707426\pi\) |
0.975183 | + | 0.221401i | \(0.0710628\pi\) | |||||||
\(282\) | 28.5273 | + | 32.9223i | 1.69878 | + | 1.96049i | ||||
\(283\) | −33.2412 | + | 4.77936i | −1.97598 | + | 0.284103i | −0.979339 | + | 0.202225i | \(0.935183\pi\) |
−0.996642 | + | 0.0818787i | \(0.973908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.4989 | − | 5.25135i | −0.678756 | − | 0.309978i | ||||
\(288\) | 5.26300 | − | 11.5244i | 0.310125 | − | 0.679079i | ||||
\(289\) | 2.41935 | − | 16.8270i | 0.142315 | − | 0.989821i | ||||
\(290\) | −0.362247 | − | 0.563667i | −0.0212719 | − | 0.0330997i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(294\) | 39.8084 | + | 25.5833i | 2.32167 | + | 1.49205i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 23.6705i | − | 1.37120i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 22.8902 | 1.32157 | ||||||||
\(301\) | −22.5788 | − | 49.4408i | −1.30142 | − | 2.84972i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.6662 | + | 34.2366i | −1.70428 | + | 1.96684i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.7185 | + | 25.0645i | 1.24360 | + | 1.43519i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.6156 | − | 9.87044i | −1.91855 | − | 0.563336i | −0.965310 | − | 0.261106i | \(-0.915913\pi\) |
−0.953235 | − | 0.302230i | \(-0.902269\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.5463 | + | 2.09144i | 0.827510 | + | 0.118978i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.31373 | + | 23.0475i | 0.186707 | + | 1.29858i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −16.2720 | + | 7.43117i | −0.909632 | + | 0.415415i | ||||
\(321\) | 41.0202i | 2.28952i | ||||||||
\(322\) | −28.7522 | − | 12.9511i | −1.60230 | − | 0.721734i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −8.89233 | − | 19.4715i | −0.494018 | − | 1.08175i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.2123 | + | 26.7884i | −1.28561 | + | 1.48367i | ||||
\(327\) | 24.9086 | − | 38.7585i | 1.37745 | − | 2.14335i | ||||
\(328\) | 5.03590 | + | 5.81174i | 0.278061 | + | 0.320900i | ||||
\(329\) | 61.9312 | − | 8.90436i | 3.41438 | − | 0.490913i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(332\) | 26.6960 | + | 3.83831i | 1.46514 | + | 0.210655i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.4614 | + | 29.4764i | −0.736575 | + | 1.61287i | ||||
\(335\) | 5.20815 | − | 36.2235i | 0.284551 | − | 1.97910i | ||||
\(336\) | −23.0157 | − | 35.8132i | −1.25561 | − | 1.95377i | ||||
\(337\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(338\) | −2.61643 | − | 18.1976i | −0.142315 | − | 0.989821i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 32.2182 | − | 14.7136i | 1.73962 | − | 0.794458i | ||||
\(344\) | 33.0642i | 1.78270i | ||||||||
\(345\) | −7.03765 | − | 23.5166i | −0.378894 | − | 1.26609i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.25180 | + | 13.6895i | 0.335614 | + | 0.734893i | 0.999921 | − | 0.0125674i | \(-0.00400045\pi\) |
−0.664307 | + | 0.747460i | \(0.731273\pi\) | |||||||
\(348\) | −0.930717 | + | 0.273283i | −0.0498917 | + | 0.0146495i | ||||
\(349\) | 14.9698 | − | 17.2761i | 0.801315 | − | 0.924767i | −0.197138 | − | 0.980376i | \(-0.563165\pi\) |
0.998453 | + | 0.0556092i | \(0.0177101\pi\) | |||||||
\(350\) | 17.7746 | − | 27.6578i | 0.950092 | − | 1.47837i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 23.4484 | + | 10.7085i | 1.24276 | + | 0.567551i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(360\) | 3.99064 | − | 13.5909i | 0.210325 | − | 0.716302i | ||||
\(361\) | 2.70398 | + | 18.8066i | 0.142315 | + | 0.989821i | ||||
\(362\) | −26.9148 | + | 23.3218i | −1.41461 | + | 1.22577i | ||||
\(363\) | 21.1821 | + | 13.6129i | 1.11177 | + | 0.714494i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 43.6744 | − | 19.9454i | 2.28290 | − | 1.04256i | ||||
\(367\) | 7.72343i | 0.403160i | 0.979472 | + | 0.201580i | \(0.0646075\pi\) | ||||
−0.979472 | + | 0.201580i | \(0.935392\pi\) | |||||||
\(368\) | 12.6374 | + | 14.4325i | 0.658768 | + | 0.752346i | ||||
\(369\) | −6.08919 | −0.316990 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.3316 | − | 3.64213i | 1.30812 | − | 0.188079i | ||||
\(376\) | −36.5202 | − | 10.7233i | −1.88339 | − | 0.553012i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −11.3280 | − | 1.62872i | −0.582650 | − | 0.0837725i | ||||
\(379\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.705481 | − | 4.90673i | 0.0361429 | − | 0.251379i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.35200 | + | 21.6329i | −0.324572 | + | 1.10539i | 0.622032 | + | 0.782992i | \(0.286307\pi\) |
−0.946604 | + | 0.322399i | \(0.895511\pi\) | |||||||
\(384\) | 3.68558 | + | 25.6337i | 0.188079 | + | 1.30812i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.7864 | − | 17.1450i | −1.00580 | − | 0.871531i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.02898 | + | 3.66671i | −0.407085 | + | 0.185910i | −0.608424 | − | 0.793612i | \(-0.708198\pi\) |
0.201339 | + | 0.979522i | \(0.435471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −41.3454 | −2.08826 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −16.8251 | + | 10.8128i | −0.841254 | + | 0.540641i | ||||
\(401\) | 28.9589 | + | 4.16366i | 1.44614 | + | 0.207923i | 0.820257 | − | 0.571995i | \(-0.193830\pi\) |
0.625881 | + | 0.779919i | \(0.284740\pi\) | |||||||
\(402\) | −48.1924 | − | 22.0088i | −2.40362 | − | 1.09770i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.63304 | − | 39.1786i | 0.280254 | − | 1.94921i | ||||
\(405\) | −12.9389 | − | 20.1333i | −0.642939 | − | 1.00043i | ||||
\(406\) | −0.392512 | + | 1.33677i | −0.0194801 | + | 0.0663430i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.4752 | + | 9.94528i | 0.765197 | + | 0.491763i | 0.864091 | − | 0.503335i | \(-0.167894\pi\) |
−0.0988936 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(410\) | 6.49772 | + | 5.63031i | 0.320900 | + | 0.278061i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.6800 | + | 5.33406i | −0.575430 | + | 0.262790i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −15.1897 | + | 0.0787106i | −0.746533 | + | 0.00386841i | ||||
\(415\) | 30.1540 | 1.48020 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(420\) | −31.1688 | − | 35.9707i | −1.52088 | − | 1.75519i | ||||
\(421\) | 13.5077 | − | 1.94212i | 0.658326 | − | 0.0946531i | 0.194948 | − | 0.980814i | \(-0.437546\pi\) |
0.463378 | + | 0.886161i | \(0.346637\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.3542 | − | 16.2941i | 1.23276 | − | 0.792248i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.81414 | − | 68.2588i | 0.474939 | − | 3.30328i | ||||
\(428\) | −19.3770 | − | 30.1512i | −0.936622 | − | 1.45741i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.26094 | + | 36.5907i | 0.253705 | + | 1.76456i | ||||
\(431\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(432\) | 5.85684 | + | 3.76396i | 0.281787 | + | 0.181094i | ||||
\(433\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.986499 | + | 0.450519i | −0.0472990 | + | 0.0216007i | ||||
\(436\) | 40.2550i | 1.92786i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.4391 | − | 24.7421i | 1.02091 | − | 1.17819i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8926 | − | 14.8789i | −0.612548 | − | 0.706918i | 0.361726 | − | 0.932284i | \(-0.382188\pi\) |
−0.974274 | + | 0.225367i | \(0.927642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.6532 | + | 8.11970i | 1.31089 | + | 0.384911i | ||||
\(446\) | −25.9812 | + | 16.6971i | −1.23025 | + | 0.790632i | ||||
\(447\) | −37.9227 | − | 5.45247i | −1.79368 | − | 0.257893i | ||||
\(448\) | 33.8346 | + | 15.4518i | 1.59854 | + | 0.730027i | ||||
\(449\) | 14.6620 | − | 32.1054i | 0.691945 | − | 1.51515i | −0.157528 | − | 0.987515i | \(-0.550352\pi\) |
0.849473 | − | 0.527633i | \(-0.176920\pi\) | |||||||
\(450\) | 2.25378 | − | 15.6754i | 0.106244 | − | 0.738944i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.8693 | + | 17.2168i | −0.932512 | + | 0.808026i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(458\) | 2.04295 | − | 0.932982i | 0.0954606 | − | 0.0435954i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.2816 | + | 13.9610i | 0.759133 | + | 0.650936i | ||||
\(461\) | −25.5834 | −1.19154 | −0.595769 | − | 0.803155i | \(-0.703153\pi\) | ||||
−0.595769 | + | 0.803155i | \(0.703153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.3049 | − | 10.9537i | 1.73371 | − | 0.509062i | 0.746075 | − | 0.665862i | \(-0.231936\pi\) |
0.987630 | + | 0.156800i | \(0.0501178\pi\) | |||||||
\(464\) | 0.555015 | − | 0.640521i | 0.0257659 | − | 0.0297354i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.1708 | − | 4.05035i | 1.30359 | − | 0.187428i | 0.544691 | − | 0.838637i | \(-0.316647\pi\) |
0.758899 | + | 0.651209i | \(0.225738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.0149 | + | 41.1398i | −2.95593 | + | 1.89966i | ||||
\(470\) | −42.1215 | − | 6.05615i | −1.94292 | − | 0.279350i | ||||
\(471\) | 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 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(480\) | 8.15732 | + | 27.7813i | 0.372329 | + | 1.26804i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 36.4947i | − | 1.66229i | ||||||
\(483\) | −27.3720 | + | 43.0809i | −1.24547 | + | 1.96025i | ||||
\(484\) | −22.0000 | −1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −26.1586 | + | 7.68084i | −1.18658 | + | 0.348410i | ||||
\(487\) | −17.9070 | + | 20.6658i | −0.811444 | + | 0.936456i | −0.998950 | − | 0.0458074i | \(-0.985414\pi\) |
0.187507 | + | 0.982263i | \(0.439959\pi\) | |||||||
\(488\) | −22.6804 | + | 35.2913i | −1.02669 | + | 1.59756i | ||||
\(489\) | 37.5711 | + | 43.3594i | 1.69902 | + | 1.96078i | ||||
\(490\) | −45.7551 | + | 6.57859i | −2.06700 | + | 0.297190i | ||||
\(491\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(492\) | 10.4711 | − | 6.72934i | 0.472072 | − | 0.303382i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.2988 | − | 41.8858i | 0.551122 | − | 1.87695i | ||||
\(499\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(500\) | −16.8991 | + | 14.6431i | −0.755750 | + | 0.654861i | ||||
\(501\) | 44.1235 | + | 28.3565i | 1.97129 | + | 1.26687i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.3455 | − | 42.0448i | −0.550457 | − | 1.87468i | −0.480207 | − | 0.877155i | \(-0.659438\pi\) |
−0.0702503 | − | 0.997529i | \(-0.522380\pi\) | |||||||
\(504\) | −26.7912 | + | 12.2351i | −1.19338 | + | 0.544996i | ||||
\(505\) | − | 44.2535i | − | 1.96925i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.7573 | −1.32157 | ||||||||
\(508\) | 1.79927 | + | 3.93986i | 0.0798298 | + | 0.174803i | ||||
\(509\) | −36.1991 | + | 10.6290i | −1.60450 | + | 0.471123i | −0.956793 | − | 0.290770i | \(-0.906089\pi\) |
−0.647703 | + | 0.761893i | \(0.724270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.8178 | − | 17.1007i | −0.654861 | − | 0.755750i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0769 | + | 7.76138i | −0.532174 | + | 0.342007i | ||||
\(516\) | 52.9725 | + | 7.61630i | 2.33198 | + | 0.335289i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.15754 | − | 7.34791i | 0.0945235 | − | 0.321918i | −0.898634 | − | 0.438699i | \(-0.855439\pi\) |
0.993158 | + | 0.116781i | \(0.0372577\pi\) | |||||||
\(522\) | 0.0955073 | + | 0.664268i | 0.00418024 | + | 0.0290742i | ||||
\(523\) | 18.9005 | − | 16.3774i | 0.826462 | − | 0.716134i | −0.135067 | − | 0.990837i | \(-0.543125\pi\) |
0.961529 | + | 0.274703i | \(0.0885794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −40.2165 | − | 34.8478i | −1.75519 | − | 1.52088i | ||||
\(526\) | −2.74158 | − | 9.33697i | −0.119539 | − | 0.407111i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.33721 | − | 21.0194i | 0.405966 | − | 0.913888i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 22.5576 | − | 35.1002i | 0.976161 | − | 1.51894i | ||||
\(535\) | −26.2411 | − | 30.2838i | −1.13450 | − | 1.30928i | ||||
\(536\) | 45.8194 | − | 6.58784i | 1.97910 | − | 0.284551i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.9016 | + | 12.7900i | −0.858020 | + | 0.551416i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 7.08039 | + | 3.23350i | 0.304691 | + | 0.139148i | ||||
\(541\) | 12.0059 | − | 26.2893i | 0.516175 | − | 1.13027i | −0.454692 | − | 0.890649i | \(-0.650251\pi\) |
0.970867 | − | 0.239618i | \(-0.0770221\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.1643 | + | 48.4925i | 1.33739 | + | 2.08101i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.40508 | + | 44.5483i | 0.274364 | + | 1.90824i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.4663 | + | 22.1501i | 1.47367 | + | 0.947072i | 0.997712 | + | 0.0676046i | \(0.0215356\pi\) |
0.475960 | + | 0.879467i | \(0.342101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.35856 | − | 31.8723i | −0.399414 | − | 1.36028i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 26.0334 | − | 16.9219i | 1.10806 | − | 0.720245i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 39.9018 | + | 11.7162i | 1.68616 | + | 0.495101i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.0019 | + | 2.30072i | 0.674998 | + | 0.0970501i | ||||
\(563\) | −4.86723 | − | 2.22279i | −0.205129 | − | 0.0936794i | 0.310201 | − | 0.950671i | \(-0.399604\pi\) |
−0.515330 | + | 0.856992i | \(0.672331\pi\) | |||||||
\(564\) | −25.5923 | + | 56.0393i | −1.07763 | + | 2.35968i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.6769 | − | 39.9541i | −1.07928 | − | 1.67940i | ||||
\(567\) | −14.0199 | + | 47.7476i | −0.588782 | + | 2.00521i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.3655 | − | 26.3118i | 1.27299 | − | 1.10305i | 0.283416 | − | 0.958997i | \(-0.408532\pi\) |
0.989570 | − | 0.144052i | \(-0.0460131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 17.8774i | − | 0.746188i | ||||||
\(575\) | 20.2395 | + | 12.8594i | 0.844044 | + | 0.536274i | ||||
\(576\) | 17.9170 | 0.746543 | ||||||||
\(577\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(578\) | 23.0678 | − | 6.77331i | 0.959493 | − | 0.281733i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.512294 | − | 0.797145i | 0.0212719 | − | 0.0330997i | ||||
\(581\) | −41.0596 | − | 47.3853i | −1.70344 | − | 1.96587i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.1989 | − | 26.7119i | 0.503502 | − | 1.10252i | −0.471813 | − | 0.881699i | \(-0.656400\pi\) |
0.975315 | − | 0.220817i | \(-0.0708725\pi\) | |||||||
\(588\) | −9.52385 | + | 66.2399i | −0.392757 | + | 2.73169i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 30.4501 | − | 13.9061i | 1.24728 | − | 0.569615i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 13.4477 | + | 29.4463i | 0.548999 | + | 1.20214i | ||||
\(601\) | 46.2894 | − | 13.5918i | 1.88818 | − | 0.554421i | 0.893816 | − | 0.448433i | \(-0.148018\pi\) |
0.994367 | − | 0.105988i | \(-0.0338005\pi\) | |||||||
\(602\) | 50.3365 | − | 58.0915i | 2.05156 | − | 2.36763i | ||||
\(603\) | −19.8168 | + | 30.8355i | −0.807001 | + | 1.25572i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.3464 | + | 3.50048i | −0.989821 | + | 0.142315i | ||||
\(606\) | −61.4709 | − | 18.0495i | −2.49708 | − | 0.733210i | ||||
\(607\) | −15.6576 | + | 10.0626i | −0.635524 | + | 0.408427i | −0.818351 | − | 0.574719i | \(-0.805112\pi\) |
0.182827 | + | 0.983145i | \(0.441475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.05124 | + | 0.936772i | 0.0831206 | + | 0.0379599i | ||||
\(610\) | −19.4840 | + | 42.6640i | −0.788884 | + | 1.72742i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(614\) | −7.05123 | − | 49.0424i | −0.284564 | − | 1.97919i | ||||
\(615\) | 10.5171 | − | 9.11313i | 0.424091 | − | 0.367477i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(618\) | 5.85528 | + | 19.9412i | 0.235534 | + | 0.802155i | ||||
\(619\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.14510 | − | 8.26827i | 0.0459513 | − | 0.331794i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.8946 | − | 54.5117i | −0.997383 | − | 2.18396i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3715 | + | 18.8937i | −0.654861 | + | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −27.7018 | + | 17.8029i | −1.10367 | + | 0.709284i | ||||
\(631\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.61805 | + | 4.07377i | 0.103894 | + | 0.161663i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.1191 | − | 16.5668i | −0.755750 | − | 0.654861i | ||||
\(641\) | −9.83148 | − | 33.4830i | −0.388320 | − | 1.32250i | −0.889413 | − | 0.457104i | \(-0.848887\pi\) |
0.501093 | − | 0.865393i | \(-0.332931\pi\) | |||||||
\(642\) | −52.7690 | + | 24.0988i | −2.08262 | + | 0.951103i | ||||
\(643\) | 4.47645i | 0.176534i | 0.996097 | + | 0.0882670i | \(0.0281329\pi\) | ||||
−0.996097 | + | 0.0882670i | \(0.971867\pi\) | |||||||
\(644\) | −0.231088 | − | 44.5958i | −0.00910616 | − | 1.75732i | ||||
\(645\) | 59.8341 | 2.35597 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.10309 | − | 1.20478i | 0.161309 | − | 0.0473647i | −0.200081 | − | 0.979779i | \(-0.564120\pi\) |
0.361390 | + | 0.932415i | \(0.382302\pi\) | |||||||
\(648\) | 19.8243 | − | 22.8784i | 0.778771 | − | 0.898750i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −48.0979 | − | 14.1228i | −1.88366 | − | 0.553093i | ||||
\(653\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(654\) | 64.4929 | + | 9.27267i | 2.52187 | + | 0.362590i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.51778 | + | 9.89257i | −0.176390 | + | 0.386240i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 47.8384 | + | 74.4380i | 1.86493 | + | 2.90189i | ||||
\(659\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.6644 | + | 33.5029i | −1.50387 | + | 1.30311i | −0.686223 | + | 0.727391i | \(0.740733\pi\) |
−0.817647 | + | 0.575720i | \(0.804722\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.7459 | + | 36.5971i | 0.417021 | + | 1.42024i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.976463 | − | 0.281228i | −0.0378088 | − | 0.0108892i | ||||
\(668\) | −45.8272 | −1.77311 | ||||||||
\(669\) | 20.7659 | + | 45.4709i | 0.802856 | + | 1.75801i | ||||
\(670\) | 49.6581 | − | 14.5809i | 1.91846 | − | 0.563310i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 32.5492 | − | 50.6475i | 1.25561 | − | 1.95377i | ||||
\(673\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.35003 | + | 2.45179i | 0.321393 | + | 0.0943695i | ||||
\(676\) | 21.8726 | − | 14.0567i | 0.841254 | − | 0.540641i | ||||
\(677\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.0064 | + | 35.7986i | 0.881607 | + | 1.37181i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.12120 | + | 21.7084i | 0.119429 | + | 0.830649i | 0.958187 | + | 0.286144i | \(0.0923735\pi\) |
−0.838757 | + | 0.544505i | \(0.816717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 37.8555 | + | 32.8020i | 1.44533 | + | 1.25239i | ||||
\(687\) | −1.02415 | − | 3.48793i | −0.0390737 | − | 0.133073i | ||||
\(688\) | −42.5343 | + | 19.4248i | −1.62160 | + | 0.740562i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 26.1175 | − | 22.8690i | 0.994277 | − | 0.870607i | ||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.9376 | + | 16.0848i | −0.529063 | + | 0.610571i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.898338 | − | 1.03674i | −0.0340514 | − | 0.0392974i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 31.0187 | + | 9.10791i | 1.17408 | + | 0.344740i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 46.0217 | + | 6.61692i | 1.73946 | + | 0.250096i | ||||
\(701\) | 19.6779 | + | 8.98661i | 0.743225 | + | 0.339420i | 0.750780 | − | 0.660552i | \(-0.229678\pi\) |
−0.00755520 | + | 0.999971i | \(0.502405\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.4052 | + | 66.0882i | −0.730844 | + | 2.48902i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −69.5419 | + | 60.2584i | −2.61539 | + | 2.26625i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.2789 | − | 17.5718i | −0.761590 | − | 0.659921i | 0.184863 | − | 0.982764i | \(-0.440816\pi\) |
−0.946452 | + | 0.322843i | \(0.895361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 36.4555i | 1.36623i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(720\) | 19.8279 | − | 2.85083i | 0.738944 | − | 0.106244i | ||||
\(721\) | 28.6413 | + | 8.40985i | 1.06666 | + | 0.313199i | ||||
\(722\) | −22.6045 | + | 14.5270i | −0.841254 | + | 0.540641i | ||||
\(723\) | −58.4685 | − | 8.40650i | −2.17447 | − | 0.312641i | ||||
\(724\) | −45.8135 | − | 20.9223i | −1.70265 | − | 0.777572i | ||||
\(725\) | 0.440096 | − | 0.963677i | 0.0163448 | − | 0.0357900i | ||||
\(726\) | −5.06767 | + | 35.2464i | −0.188079 | + | 1.30812i | ||||
\(727\) | 23.2102 | + | 36.1158i | 0.860820 | + | 1.33946i | 0.939495 | + | 0.342562i | \(0.111295\pi\) |
−0.0786754 | + | 0.996900i | \(0.525069\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.71040 | + | 11.8961i | 0.0633482 | + | 0.440596i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 51.3162 | + | 44.4657i | 1.89670 | + | 1.64350i | ||||
\(733\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(734\) | −9.93552 | + | 4.53740i | −0.366727 | + | 0.167479i | ||||
\(735\) | 74.8200i | 2.75978i | ||||||||
\(736\) | −11.1419 | + | 24.7358i | −0.410696 | + | 0.911772i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.57731 | − | 7.83321i | −0.131683 | − | 0.288345i | ||||
\(739\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.8772 | − | 7.74637i | 1.97656 | − | 0.284187i | 0.980344 | − | 0.197295i | \(-0.0632156\pi\) |
0.996218 | − | 0.0868918i | \(-0.0276935\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.4851 | − | 20.2342i | 1.15352 | − | 0.741325i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27.4727 | − | 12.5464i | −1.00517 | − | 0.459048i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.8578 | + | 82.4727i | −0.433274 | + | 3.01349i | ||||
\(750\) | 19.5672 | + | 30.4472i | 0.714494 | + | 1.11177i | ||||
\(751\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(752\) | −7.66050 | − | 53.2799i | −0.279350 | − | 1.94292i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.55984 | − | 15.5294i | −0.165840 | − | 0.564798i | ||||
\(757\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.1941 | − | 37.6498i | −0.623285 | − | 1.36480i | −0.913106 | − | 0.407723i | \(-0.866323\pi\) |
0.289820 | − | 0.957081i | \(-0.406404\pi\) | |||||||
\(762\) | 6.72654 | − | 1.97509i | 0.243677 | − | 0.0715500i | ||||
\(763\) | 61.2836 | − | 70.7251i | 2.21862 | − | 2.56042i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.5606 | + | 4.53773i | −1.14033 | + | 0.163955i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30.8104 | + | 19.8006i | −1.11177 | + | 0.714494i | ||||
\(769\) | −24.3130 | − | 3.49568i | −0.876749 | − | 0.126058i | −0.310778 | − | 0.950482i | \(-0.600590\pi\) |
−0.565971 | + | 0.824425i | \(0.691499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(774\) | 10.4314 | − | 35.5260i | 0.374948 | − | 1.27696i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.43382 | − | 8.17445i | −0.338219 | − | 0.293068i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.368784 | −0.0131793 | ||||||||
\(784\) | −24.2898 | − | 53.1873i | −0.867494 | − | 1.89955i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0110 | + | 43.5860i | −0.998484 | + | 1.55367i | −0.176390 | + | 0.984320i | \(0.556442\pi\) |
−0.822095 | + | 0.569351i | \(0.807195\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.5904 | + | 2.24155i | −0.555031 | + | 0.0798015i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −23.7942 | − | 15.2916i | −0.841254 | − | 0.540641i | ||||
\(801\) | −21.8158 | − | 18.9035i | −0.770824 | − | 0.667923i | ||||
\(802\) | 11.6567 | + | 39.6992i | 0.411614 | + | 1.40183i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 74.9253i | − | 2.64241i | ||||||
\(805\) | −7.35150 | − | 49.3153i | −0.259106 | − | 1.73814i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.9067 | + | 34.8307i | 0.559941 | + | 1.22610i | ||||
\(808\) | 53.7093 | − | 15.7705i | 1.88949 | − | 0.554803i | ||||
\(809\) | −4.03422 | + | 4.65573i | −0.141835 | + | 0.163687i | −0.822223 | − | 0.569166i | \(-0.807266\pi\) |
0.680387 | + | 0.732853i | \(0.261812\pi\) | |||||||
\(810\) | 18.2984 | − | 28.4728i | 0.642939 | − | 1.00043i | ||||
\(811\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(812\) | −1.95024 | + | 0.280402i | −0.0684400 | + | 0.00984019i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.4749 | − | 7.97609i | −1.94320 | − | 0.279390i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.70232 | + | 25.7502i | −0.129448 | + | 0.900334i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.42559 | + | 11.6665i | −0.119627 | + | 0.407411i | ||||
\(821\) | 8.15534 | + | 56.7216i | 0.284623 | + | 1.97960i | 0.148955 | + | 0.988844i | \(0.452409\pi\) |
0.135668 | + | 0.990754i | \(0.456682\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.7692 | + | 12.7049i | 0.689112 | + | 0.442865i | 0.837770 | − | 0.546023i | \(-0.183859\pi\) |
−0.148658 | + | 0.988889i | \(0.547495\pi\) | |||||||
\(824\) | −13.7236 | − | 11.8916i | −0.478084 | − | 0.414263i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 47.4342i | − | 1.64945i | −0.565536 | − | 0.824724i | \(-0.691331\pi\) | ||
0.565536 | − | 0.824724i | \(-0.308669\pi\) | |||||||
\(828\) | −9.02498 | − | 19.4940i | −0.313640 | − | 0.677463i | ||||
\(829\) | −21.2495 | −0.738025 | −0.369012 | − | 0.929424i | \(-0.620304\pi\) | ||||
−0.369012 | + | 0.929424i | \(0.620304\pi\) | |||||||
\(830\) | 17.7150 | + | 38.7905i | 0.614898 | + | 1.34644i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50.7148 | + | 7.29169i | −1.75506 | + | 0.252339i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(840\) | 27.9620 | − | 61.2282i | 0.964781 | − | 2.11258i | ||||
\(841\) | 4.12074 | − | 28.6604i | 0.142095 | − | 0.988289i | ||||
\(842\) | 10.4340 | + | 16.2356i | 0.359578 | + | 0.559515i | ||||
\(843\) | 7.37202 | − | 25.1068i | 0.253906 | − | 0.864723i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.9688 | − | 19.0361i | 0.755750 | − | 0.654861i | ||||
\(846\) | 35.8562 | + | 23.0434i | 1.23276 | + | 0.792248i | ||||
\(847\) | 38.6524 | + | 33.4925i | 1.32811 | + | 1.15082i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −69.9254 | + | 31.9339i | −2.39983 | + | 1.09597i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(854\) | 93.5748 | − | 27.4760i | 3.20206 | − | 0.940210i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.4032 | − | 42.6402i | 0.936622 | − | 1.45741i | ||||
\(857\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(860\) | −43.9800 | + | 28.2642i | −1.49971 | + | 0.963803i | ||||
\(861\) | −28.6415 | − | 4.11803i | −0.976101 | − | 0.140342i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.472935 | + | 1.03558i | −0.0160989 | + | 0.0352517i | −0.917511 | − | 0.397711i | \(-0.869805\pi\) |
0.901412 | + | 0.432963i | \(0.142532\pi\) | |||||||
\(864\) | −1.40120 | + | 9.74559i | −0.0476699 | + | 0.331552i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.53795 | − | 38.5173i | −0.188079 | − | 1.30812i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.15911 | − | 1.00437i | −0.0392974 | − | 0.0340514i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −51.7846 | + | 23.6492i | −1.75365 | + | 0.800864i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.9829 | 1.75734 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.8686 | + | 7.45758i | −1.74750 | + | 0.251252i | −0.940619 | − | 0.339464i | \(-0.889754\pi\) |
−0.806879 | + | 0.590717i | \(0.798845\pi\) | |||||||
\(882\) | 44.4237 | + | 13.0440i | 1.49582 | + | 0.439214i | ||||
\(883\) | 36.2139 | − | 23.2732i | 1.21869 | − | 0.783207i | 0.236601 | − | 0.971607i | \(-0.423967\pi\) |
0.982092 | + | 0.188400i | \(0.0603302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.5662 | − | 25.3264i | 0.388574 | − | 0.850857i | ||||
\(887\) | 6.77782 | − | 47.1408i | 0.227577 | − | 1.58283i | −0.480692 | − | 0.876890i | \(-0.659614\pi\) |
0.708269 | − | 0.705943i | \(-0.249477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.83679 | − | 9.66123i | 0.0951430 | − | 0.324027i | ||||
\(890\) | 5.80054 | + | 40.3436i | 0.194434 | + | 1.35232i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −36.7430 | − | 23.6133i | −1.23025 | − | 0.790632i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −15.2649 | − | 51.9876i | −0.510536 | − | 1.73873i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 52.6030i | 1.75734i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 49.9146 | 1.66567 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 21.4891 | − | 6.30976i | 0.716302 | − | 0.210325i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −81.4739 | − | 94.0259i | −2.71128 | − | 3.12899i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −54.0287 | − | 15.8643i | −1.79597 | − | 0.527346i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8855 | + | 3.00288i | 0.693491 | + | 0.0997090i | 0.480042 | − | 0.877245i | \(-0.340621\pi\) |
0.213449 | + | 0.976954i | \(0.431530\pi\) | |||||||
\(908\) | −33.8209 | − | 15.4455i | −1.12239 | − | 0.512576i | ||||
\(909\) | −18.4128 | + | 40.3185i | −0.610715 | + | 1.33728i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 63.8643 | + | 41.0431i | 2.11129 | + | 1.35684i | ||||
\(916\) | 2.40040 | + | 2.07996i | 0.0793115 | + | 0.0687238i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | −8.39445 | + | 29.1468i | −0.276757 | + | 0.960940i | ||||
\(921\) | −80.1954 | −2.64253 | ||||||||
\(922\) | −15.0299 | − | 32.9109i | −0.494983 | − | 1.08386i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 36.0071 | + | 41.5544i | 1.18327 | + | 1.36556i | ||||
\(927\) | 14.2324 | − | 2.04631i | 0.467453 | − | 0.0672096i | ||||
\(928\) | 1.15004 | + | 0.337682i | 0.0377519 | + | 0.0110849i | ||||
\(929\) | −47.8515 | + | 30.7523i | −1.56996 | + | 1.00895i | −0.590561 | + | 0.806993i | \(0.701093\pi\) |
−0.979395 | + | 0.201956i | \(0.935270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.7604 | + | 33.8598i | 0.712021 | + | 1.10793i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(938\) | −90.5307 | − | 58.1805i | −2.95593 | − | 1.89966i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.9550 | − | 57.7436i | −0.553012 | − | 1.88339i | ||||
\(941\) | 55.5128 | − | 25.3518i | 1.80967 | − | 0.826446i | 0.862215 | − | 0.506542i | \(-0.169076\pi\) |
0.947450 | − | 0.319905i | \(-0.103651\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.0389 | − | 0.0675656i | 0.424605 | − | 0.00220024i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.51708 | − | 16.4601i | −0.244531 | − | 0.535448i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.1942 | − | 25.6134i | 0.721213 | − | 0.832324i | −0.270239 | − | 0.962793i | \(-0.587103\pi\) |
0.991452 | + | 0.130469i | \(0.0416483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −30.9459 | + | 26.8148i | −0.998775 | + | 0.865443i | ||||
\(961\) | 26.0789 | + | 16.7599i | 0.841254 | + | 0.540641i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.3073 | + | 38.5093i | 0.364374 | + | 1.24094i | ||||
\(964\) | 46.9473 | − | 21.4401i | 1.51207 | − | 0.690539i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −71.5006 | − | 9.90235i | −2.30049 | − | 0.318603i | ||||
\(967\) | −56.7816 | −1.82597 | −0.912987 | − | 0.407988i | \(-0.866230\pi\) | ||||
−0.912987 | + | 0.407988i | \(0.866230\pi\) | |||||||
\(968\) | −12.9247 | − | 28.3011i | −0.415415 | − | 0.909632i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(972\) | −25.2485 | − | 29.1383i | −0.809847 | − | 0.934613i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −37.1049 | − | 10.8950i | −1.18892 | − | 0.349097i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −58.7236 | − | 8.44318i | −1.87970 | − | 0.270260i | ||||
\(977\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(978\) | −33.7056 | + | 73.8050i | −1.07779 | + | 2.36002i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −35.3432 | − | 54.9951i | −1.12900 | − | 1.75675i | ||||
\(981\) | 12.7000 | − | 43.2521i | 0.405479 | − | 1.38093i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.3021 | − | 11.5263i | 0.424270 | − | 0.367632i | −0.416399 | − | 0.909182i | \(-0.636708\pi\) |
0.840668 | + | 0.541550i | \(0.182162\pi\) | |||||||
\(984\) | 14.8083 | + | 9.51672i | 0.472072 | + | 0.303382i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 130.277 | − | 59.4956i | 4.14677 | − | 1.89377i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.5594 | + | 36.4935i | 1.35331 | + | 1.16043i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 61.1079 | − | 8.78598i | 1.93628 | − | 0.278395i | ||||
\(997\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(998\) | 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.19.4 | yes | 40 | |
4.3 | odd | 2 | inner | 460.2.o.a.19.1 | ✓ | 40 | |
5.4 | even | 2 | inner | 460.2.o.a.19.1 | ✓ | 40 | |
20.19 | odd | 2 | CM | 460.2.o.a.19.4 | yes | 40 | |
23.17 | odd | 22 | inner | 460.2.o.a.339.4 | yes | 40 | |
92.63 | even | 22 | inner | 460.2.o.a.339.1 | yes | 40 | |
115.109 | odd | 22 | inner | 460.2.o.a.339.1 | yes | 40 | |
460.339 | even | 22 | inner | 460.2.o.a.339.4 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.o.a.19.1 | ✓ | 40 | 4.3 | odd | 2 | inner | |
460.2.o.a.19.1 | ✓ | 40 | 5.4 | even | 2 | inner | |
460.2.o.a.19.4 | yes | 40 | 1.1 | even | 1 | trivial | |
460.2.o.a.19.4 | yes | 40 | 20.19 | odd | 2 | CM | |
460.2.o.a.339.1 | yes | 40 | 92.63 | even | 22 | inner | |
460.2.o.a.339.1 | yes | 40 | 115.109 | odd | 22 | inner | |
460.2.o.a.339.4 | yes | 40 | 23.17 | odd | 22 | inner | |
460.2.o.a.339.4 | yes | 40 | 460.339 | even | 22 | inner |