Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(160,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.160");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.h (of order \(2\), degree \(1\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 160.5 | ||
Root | \(-0.599676 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.a.160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −3.33513 | −1.49152 | −0.745758 | − | 0.666217i | \(-0.767913\pi\) | ||||
−0.745758 | + | 0.666217i | \(0.767913\pi\) | |||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −2.60399 | − | 0.468213i | −0.984217 | − | 0.176968i | ||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 3.33513 | 1.05466 | ||||||||
\(11\) | 4.27156i | 1.28792i | 0.765058 | + | 0.643962i | \(0.222710\pi\) | ||||
−0.765058 | + | 0.643962i | \(0.777290\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | − | 3.12311i | − | 0.866194i | −0.901347 | − | 0.433097i | \(-0.857421\pi\) | ||
0.901347 | − | 0.433097i | \(-0.142579\pi\) | |||||||
\(14\) | 2.60399 | + | 0.468213i | 0.695946 | + | 0.125135i | ||||
\(15\) | − | 3.33513i | − | 0.861127i | ||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.33513 | 0.808888 | 0.404444 | − | 0.914563i | \(-0.367465\pi\) | ||||
0.404444 | + | 0.914563i | \(0.367465\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.46228 | −0.335470 | −0.167735 | − | 0.985832i | \(-0.553645\pi\) | ||||
−0.167735 | + | 0.985832i | \(0.553645\pi\) | |||||||
\(20\) | 3.33513 | 0.745758 | ||||||||
\(21\) | 0.468213 | − | 2.60399i | 0.102172 | − | 0.568238i | ||||
\(22\) | − | 4.27156i | − | 0.910699i | ||||||
\(23\) | 1.56155 | − | 4.53448i | 0.325606 | − | 0.945505i | ||||
\(24\) | 3.00000i | 0.612372i | ||||||||
\(25\) | 6.12311 | 1.22462 | ||||||||
\(26\) | 3.12311i | 0.612491i | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.60399 | + | 0.468213i | 0.492108 | + | 0.0884840i | ||||
\(29\) | 8.24621 | 1.53128 | 0.765641 | − | 0.643268i | \(-0.222422\pi\) | ||||
0.765641 | + | 0.643268i | \(0.222422\pi\) | |||||||
\(30\) | 3.33513i | 0.608909i | ||||||||
\(31\) | − | 10.2462i | − | 1.84027i | −0.391597 | − | 0.920137i | \(-0.628077\pi\) | ||
0.391597 | − | 0.920137i | \(-0.371923\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | −4.27156 | −0.743583 | ||||||||
\(34\) | −3.33513 | −0.571970 | ||||||||
\(35\) | 8.68466 | + | 1.56155i | 1.46798 | + | 0.263951i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.87285i | 0.307895i | 0.988079 | + | 0.153948i | \(0.0491987\pi\) | ||||
−0.988079 | + | 0.153948i | \(0.950801\pi\) | |||||||
\(38\) | 1.46228 | 0.237213 | ||||||||
\(39\) | 3.12311 | 0.500097 | ||||||||
\(40\) | −10.0054 | −1.58199 | ||||||||
\(41\) | 11.1231i | 1.73714i | 0.495569 | + | 0.868569i | \(0.334960\pi\) | ||||
−0.495569 | + | 0.868569i | \(0.665040\pi\) | |||||||
\(42\) | −0.468213 | + | 2.60399i | −0.0722469 | + | 0.401805i | ||||
\(43\) | 0.936426i | 0.142804i | 0.997448 | + | 0.0714018i | \(0.0227473\pi\) | ||||
−0.997448 | + | 0.0714018i | \(0.977253\pi\) | |||||||
\(44\) | − | 4.27156i | − | 0.643962i | ||||||
\(45\) | 3.33513 | 0.497172 | ||||||||
\(46\) | −1.56155 | + | 4.53448i | −0.230238 | + | 0.668573i | ||||
\(47\) | 7.12311i | 1.03901i | 0.854467 | + | 0.519506i | \(0.173884\pi\) | ||||
−0.854467 | + | 0.519506i | \(0.826116\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 6.56155 | + | 2.43845i | 0.937365 | + | 0.348350i | ||||
\(50\) | −6.12311 | −0.865938 | ||||||||
\(51\) | 3.33513i | 0.467012i | ||||||||
\(52\) | 3.12311i | 0.433097i | ||||||||
\(53\) | − | 10.0054i | − | 1.37435i | −0.726493 | − | 0.687173i | \(-0.758851\pi\) | ||
0.726493 | − | 0.687173i | \(-0.241149\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | − | 14.2462i | − | 1.92096i | ||||||
\(56\) | −7.81198 | − | 1.40464i | −1.04392 | − | 0.187703i | ||||
\(57\) | − | 1.46228i | − | 0.193684i | ||||||
\(58\) | −8.24621 | −1.08278 | ||||||||
\(59\) | − | 7.12311i | − | 0.927349i | −0.886006 | − | 0.463675i | \(-0.846531\pi\) | ||
0.886006 | − | 0.463675i | \(-0.153469\pi\) | |||||||
\(60\) | 3.33513i | 0.430564i | ||||||||
\(61\) | 1.87285 | 0.239794 | 0.119897 | − | 0.992786i | \(-0.461744\pi\) | ||||
0.119897 | + | 0.992786i | \(0.461744\pi\) | |||||||
\(62\) | 10.2462i | 1.30127i | ||||||||
\(63\) | 2.60399 | + | 0.468213i | 0.328072 | + | 0.0589893i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 10.4160i | 1.29194i | ||||||||
\(66\) | 4.27156 | 0.525792 | ||||||||
\(67\) | − | 4.68213i | − | 0.572013i | −0.958228 | − | 0.286007i | \(-0.907672\pi\) | ||
0.958228 | − | 0.286007i | \(-0.0923280\pi\) | |||||||
\(68\) | −3.33513 | −0.404444 | ||||||||
\(69\) | 4.53448 | + | 1.56155i | 0.545888 | + | 0.187989i | ||||
\(70\) | −8.68466 | − | 1.56155i | −1.03802 | − | 0.186641i | ||||
\(71\) | −11.1231 | −1.32007 | −0.660035 | − | 0.751235i | \(-0.729459\pi\) | ||||
−0.660035 | + | 0.751235i | \(0.729459\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | − | 6.24621i | − | 0.731064i | −0.930799 | − | 0.365532i | \(-0.880887\pi\) | ||
0.930799 | − | 0.365532i | \(-0.119113\pi\) | |||||||
\(74\) | − | 1.87285i | − | 0.217715i | ||||||
\(75\) | 6.12311i | 0.707035i | ||||||||
\(76\) | 1.46228 | 0.167735 | ||||||||
\(77\) | 2.00000 | − | 11.1231i | 0.227921 | − | 1.26760i | ||||
\(78\) | −3.12311 | −0.353622 | ||||||||
\(79\) | − | 16.1498i | − | 1.81700i | −0.417890 | − | 0.908498i | \(-0.637230\pi\) | ||
0.417890 | − | 0.908498i | \(-0.362770\pi\) | |||||||
\(80\) | 3.33513 | 0.372879 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 11.1231i | − | 1.22834i | ||||||
\(83\) | 17.0862 | 1.87546 | 0.937729 | − | 0.347368i | \(-0.112925\pi\) | ||||
0.937729 | + | 0.347368i | \(0.112925\pi\) | |||||||
\(84\) | −0.468213 | + | 2.60399i | −0.0510862 | + | 0.284119i | ||||
\(85\) | −11.1231 | −1.20647 | ||||||||
\(86\) | − | 0.936426i | − | 0.100977i | ||||||
\(87\) | 8.24621i | 0.884087i | ||||||||
\(88\) | 12.8147i | 1.36605i | ||||||||
\(89\) | −10.0054 | −1.06057 | −0.530285 | − | 0.847819i | \(-0.677915\pi\) | ||||
−0.530285 | + | 0.847819i | \(0.677915\pi\) | |||||||
\(90\) | −3.33513 | −0.351554 | ||||||||
\(91\) | −1.46228 | + | 8.13254i | −0.153289 | + | 0.852522i | ||||
\(92\) | −1.56155 | + | 4.53448i | −0.162803 | + | 0.472753i | ||||
\(93\) | 10.2462 | 1.06248 | ||||||||
\(94\) | − | 7.12311i | − | 0.734692i | ||||||
\(95\) | 4.87689 | 0.500359 | ||||||||
\(96\) | − | 5.00000i | − | 0.510310i | ||||||
\(97\) | −1.87285 | −0.190159 | −0.0950797 | − | 0.995470i | \(-0.530311\pi\) | ||||
−0.0950797 | + | 0.995470i | \(0.530311\pi\) | |||||||
\(98\) | −6.56155 | − | 2.43845i | −0.662817 | − | 0.246320i | ||||
\(99\) | − | 4.27156i | − | 0.429308i | ||||||
\(100\) | −6.12311 | −0.612311 | ||||||||
\(101\) | 3.12311i | 0.310761i | 0.987855 | + | 0.155380i | \(0.0496603\pi\) | ||||
−0.987855 | + | 0.155380i | \(0.950340\pi\) | |||||||
\(102\) | − | 3.33513i | − | 0.330227i | ||||||
\(103\) | 5.20798 | 0.513158 | 0.256579 | − | 0.966523i | \(-0.417405\pi\) | ||||
0.256579 | + | 0.966523i | \(0.417405\pi\) | |||||||
\(104\) | − | 9.36932i | − | 0.918737i | ||||||
\(105\) | −1.56155 | + | 8.68466i | −0.152392 | + | 0.847536i | ||||
\(106\) | 10.0054i | 0.971810i | ||||||||
\(107\) | 9.06897i | 0.876730i | 0.898797 | + | 0.438365i | \(0.144442\pi\) | ||||
−0.898797 | + | 0.438365i | \(0.855558\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 12.2888i | 1.17706i | 0.808477 | + | 0.588528i | \(0.200292\pi\) | ||||
−0.808477 | + | 0.588528i | \(0.799708\pi\) | |||||||
\(110\) | 14.2462i | 1.35832i | ||||||||
\(111\) | −1.87285 | −0.177763 | ||||||||
\(112\) | 2.60399 | + | 0.468213i | 0.246054 | + | 0.0442420i | ||||
\(113\) | − | 8.95369i | − | 0.842292i | −0.906993 | − | 0.421146i | \(-0.861628\pi\) | ||
0.906993 | − | 0.421146i | \(-0.138372\pi\) | |||||||
\(114\) | 1.46228i | 0.136955i | ||||||||
\(115\) | −5.20798 | + | 15.1231i | −0.485647 | + | 1.41024i | ||||
\(116\) | −8.24621 | −0.765641 | ||||||||
\(117\) | 3.12311i | 0.288731i | ||||||||
\(118\) | 7.12311i | 0.655735i | ||||||||
\(119\) | −8.68466 | − | 1.56155i | −0.796121 | − | 0.143147i | ||||
\(120\) | − | 10.0054i | − | 0.913364i | ||||||
\(121\) | −7.24621 | −0.658746 | ||||||||
\(122\) | −1.87285 | −0.169560 | ||||||||
\(123\) | −11.1231 | −1.00294 | ||||||||
\(124\) | 10.2462i | 0.920137i | ||||||||
\(125\) | −3.74571 | −0.335026 | ||||||||
\(126\) | −2.60399 | − | 0.468213i | −0.231982 | − | 0.0417117i | ||||
\(127\) | −6.24621 | −0.554262 | −0.277131 | − | 0.960832i | \(-0.589384\pi\) | ||||
−0.277131 | + | 0.960832i | \(0.589384\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | −0.936426 | −0.0824477 | ||||||||
\(130\) | − | 10.4160i | − | 0.913541i | ||||||
\(131\) | − | 12.0000i | − | 1.04844i | −0.851581 | − | 0.524222i | \(-0.824356\pi\) | ||
0.851581 | − | 0.524222i | \(-0.175644\pi\) | |||||||
\(132\) | 4.27156 | 0.371791 | ||||||||
\(133\) | 3.80776 | + | 0.684658i | 0.330175 | + | 0.0593674i | ||||
\(134\) | 4.68213i | 0.404475i | ||||||||
\(135\) | 3.33513i | 0.287042i | ||||||||
\(136\) | 10.0054 | 0.857956 | ||||||||
\(137\) | − | 14.8028i | − | 1.26469i | −0.774687 | − | 0.632345i | \(-0.782093\pi\) | ||
0.774687 | − | 0.632345i | \(-0.217907\pi\) | |||||||
\(138\) | −4.53448 | − | 1.56155i | −0.386001 | − | 0.132928i | ||||
\(139\) | − | 12.0000i | − | 1.01783i | −0.860818 | − | 0.508913i | \(-0.830047\pi\) | ||
0.860818 | − | 0.508913i | \(-0.169953\pi\) | |||||||
\(140\) | −8.68466 | − | 1.56155i | −0.733988 | − | 0.131975i | ||||
\(141\) | −7.12311 | −0.599874 | ||||||||
\(142\) | 11.1231 | 0.933430 | ||||||||
\(143\) | 13.3405 | 1.11559 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −27.5022 | −2.28393 | ||||||||
\(146\) | 6.24621i | 0.516940i | ||||||||
\(147\) | −2.43845 | + | 6.56155i | −0.201120 | + | 0.541188i | ||||
\(148\) | − | 1.87285i | − | 0.153948i | ||||||
\(149\) | − | 0.410574i | − | 0.0336355i | −0.999859 | − | 0.0168177i | \(-0.994646\pi\) | ||
0.999859 | − | 0.0168177i | \(-0.00535351\pi\) | |||||||
\(150\) | − | 6.12311i | − | 0.499949i | ||||||
\(151\) | −20.4924 | −1.66765 | −0.833825 | − | 0.552029i | \(-0.813854\pi\) | ||||
−0.833825 | + | 0.552029i | \(0.813854\pi\) | |||||||
\(152\) | −4.38684 | −0.355820 | ||||||||
\(153\) | −3.33513 | −0.269629 | ||||||||
\(154\) | −2.00000 | + | 11.1231i | −0.161165 | + | 0.896325i | ||||
\(155\) | 34.1725i | 2.74480i | ||||||||
\(156\) | −3.12311 | −0.250049 | ||||||||
\(157\) | 15.2134 | 1.21416 | 0.607080 | − | 0.794641i | \(-0.292341\pi\) | ||||
0.607080 | + | 0.794641i | \(0.292341\pi\) | |||||||
\(158\) | 16.1498i | 1.28481i | ||||||||
\(159\) | 10.0054 | 0.793480 | ||||||||
\(160\) | 16.6757 | 1.31833 | ||||||||
\(161\) | −6.18938 | + | 11.0766i | −0.487791 | + | 0.872960i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | − | 11.1231i | − | 0.868569i | ||||||
\(165\) | 14.2462 | 1.10907 | ||||||||
\(166\) | −17.0862 | −1.32615 | ||||||||
\(167\) | 5.75379i | 0.445242i | 0.974905 | + | 0.222621i | \(0.0714612\pi\) | ||||
−0.974905 | + | 0.222621i | \(0.928539\pi\) | |||||||
\(168\) | 1.40464 | − | 7.81198i | 0.108370 | − | 0.602707i | ||||
\(169\) | 3.24621 | 0.249709 | ||||||||
\(170\) | 11.1231 | 0.853103 | ||||||||
\(171\) | 1.46228 | 0.111823 | ||||||||
\(172\) | − | 0.936426i | − | 0.0714018i | ||||||
\(173\) | − | 3.12311i | − | 0.237445i | −0.992927 | − | 0.118723i | \(-0.962120\pi\) | ||
0.992927 | − | 0.118723i | \(-0.0378799\pi\) | |||||||
\(174\) | − | 8.24621i | − | 0.625144i | ||||||
\(175\) | −15.9445 | − | 2.86692i | −1.20529 | − | 0.216719i | ||||
\(176\) | − | 4.27156i | − | 0.321981i | ||||||
\(177\) | 7.12311 | 0.535405 | ||||||||
\(178\) | 10.0054 | 0.749936 | ||||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | −3.33513 | −0.248586 | ||||||||
\(181\) | 12.2888 | 0.913421 | 0.456710 | − | 0.889615i | \(-0.349028\pi\) | ||||
0.456710 | + | 0.889615i | \(0.349028\pi\) | |||||||
\(182\) | 1.46228 | − | 8.13254i | 0.108391 | − | 0.602824i | ||||
\(183\) | 1.87285i | 0.138445i | ||||||||
\(184\) | 4.68466 | − | 13.6035i | 0.345358 | − | 1.00286i | ||||
\(185\) | − | 6.24621i | − | 0.459231i | ||||||
\(186\) | −10.2462 | −0.751289 | ||||||||
\(187\) | 14.2462i | 1.04179i | ||||||||
\(188\) | − | 7.12311i | − | 0.519506i | ||||||
\(189\) | −0.468213 | + | 2.60399i | −0.0340575 | + | 0.189413i | ||||
\(190\) | −4.87689 | −0.353807 | ||||||||
\(191\) | 3.45041i | 0.249663i | 0.992178 | + | 0.124832i | \(0.0398390\pi\) | ||||
−0.992178 | + | 0.124832i | \(0.960161\pi\) | |||||||
\(192\) | 7.00000i | 0.505181i | ||||||||
\(193\) | 25.6155 | 1.84385 | 0.921923 | − | 0.387373i | \(-0.126617\pi\) | ||||
0.921923 | + | 0.387373i | \(0.126617\pi\) | |||||||
\(194\) | 1.87285 | 0.134463 | ||||||||
\(195\) | −10.4160 | −0.745903 | ||||||||
\(196\) | −6.56155 | − | 2.43845i | −0.468682 | − | 0.174175i | ||||
\(197\) | 18.4924 | 1.31753 | 0.658765 | − | 0.752349i | \(-0.271079\pi\) | ||||
0.658765 | + | 0.752349i | \(0.271079\pi\) | |||||||
\(198\) | 4.27156i | 0.303566i | ||||||||
\(199\) | 5.20798 | 0.369184 | 0.184592 | − | 0.982815i | \(-0.440904\pi\) | ||||
0.184592 | + | 0.982815i | \(0.440904\pi\) | |||||||
\(200\) | 18.3693 | 1.29891 | ||||||||
\(201\) | 4.68213 | 0.330252 | ||||||||
\(202\) | − | 3.12311i | − | 0.219741i | ||||||
\(203\) | −21.4731 | − | 3.86098i | −1.50711 | − | 0.270988i | ||||
\(204\) | − | 3.33513i | − | 0.233506i | ||||||
\(205\) | − | 37.0970i | − | 2.59097i | ||||||
\(206\) | −5.20798 | −0.362857 | ||||||||
\(207\) | −1.56155 | + | 4.53448i | −0.108535 | + | 0.315168i | ||||
\(208\) | 3.12311i | 0.216548i | ||||||||
\(209\) | − | 6.24621i | − | 0.432059i | ||||||
\(210\) | 1.56155 | − | 8.68466i | 0.107757 | − | 0.599298i | ||||
\(211\) | −10.2462 | −0.705378 | −0.352689 | − | 0.935741i | \(-0.614733\pi\) | ||||
−0.352689 | + | 0.935741i | \(0.614733\pi\) | |||||||
\(212\) | 10.0054i | 0.687173i | ||||||||
\(213\) | − | 11.1231i | − | 0.762143i | ||||||
\(214\) | − | 9.06897i | − | 0.619942i | ||||||
\(215\) | − | 3.12311i | − | 0.212994i | ||||||
\(216\) | − | 3.00000i | − | 0.204124i | ||||||
\(217\) | −4.79741 | + | 26.6811i | −0.325669 | + | 1.81123i | ||||
\(218\) | − | 12.2888i | − | 0.832304i | ||||||
\(219\) | 6.24621 | 0.422080 | ||||||||
\(220\) | 14.2462i | 0.960479i | ||||||||
\(221\) | − | 10.4160i | − | 0.700654i | ||||||
\(222\) | 1.87285 | 0.125698 | ||||||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 13.0200 | + | 2.34107i | 0.869933 | + | 0.156419i | ||||
\(225\) | −6.12311 | −0.408207 | ||||||||
\(226\) | 8.95369i | 0.595591i | ||||||||
\(227\) | 6.67026 | 0.442721 | 0.221360 | − | 0.975192i | \(-0.428950\pi\) | ||||
0.221360 | + | 0.975192i | \(0.428950\pi\) | |||||||
\(228\) | 1.46228i | 0.0968418i | ||||||||
\(229\) | 12.2888 | 0.812068 | 0.406034 | − | 0.913858i | \(-0.366911\pi\) | ||||
0.406034 | + | 0.913858i | \(0.366911\pi\) | |||||||
\(230\) | 5.20798 | − | 15.1231i | 0.343404 | − | 0.997188i | ||||
\(231\) | 11.1231 | + | 2.00000i | 0.731847 | + | 0.131590i | ||||
\(232\) | 24.7386 | 1.62417 | ||||||||
\(233\) | −3.75379 | −0.245919 | −0.122959 | − | 0.992412i | \(-0.539239\pi\) | ||||
−0.122959 | + | 0.992412i | \(0.539239\pi\) | |||||||
\(234\) | − | 3.12311i | − | 0.204164i | ||||||
\(235\) | − | 23.7565i | − | 1.54970i | ||||||
\(236\) | 7.12311i | 0.463675i | ||||||||
\(237\) | 16.1498 | 1.04904 | ||||||||
\(238\) | 8.68466 | + | 1.56155i | 0.562943 | + | 0.101220i | ||||
\(239\) | −1.36932 | −0.0885737 | −0.0442869 | − | 0.999019i | \(-0.514102\pi\) | ||||
−0.0442869 | + | 0.999019i | \(0.514102\pi\) | |||||||
\(240\) | 3.33513i | 0.215282i | ||||||||
\(241\) | 11.4677 | 0.738698 | 0.369349 | − | 0.929291i | \(-0.379581\pi\) | ||||
0.369349 | + | 0.929291i | \(0.379581\pi\) | |||||||
\(242\) | 7.24621 | 0.465804 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −1.87285 | −0.119897 | ||||||||
\(245\) | −21.8836 | − | 8.13254i | −1.39809 | − | 0.519569i | ||||
\(246\) | 11.1231 | 0.709183 | ||||||||
\(247\) | 4.56685i | 0.290582i | ||||||||
\(248\) | − | 30.7386i | − | 1.95191i | ||||||
\(249\) | 17.0862i | 1.08280i | ||||||||
\(250\) | 3.74571 | 0.236899 | ||||||||
\(251\) | −0.821147 | −0.0518303 | −0.0259152 | − | 0.999664i | \(-0.508250\pi\) | ||||
−0.0259152 | + | 0.999664i | \(0.508250\pi\) | |||||||
\(252\) | −2.60399 | − | 0.468213i | −0.164036 | − | 0.0294947i | ||||
\(253\) | 19.3693 | + | 6.67026i | 1.21774 | + | 0.419356i | ||||
\(254\) | 6.24621 | 0.391922 | ||||||||
\(255\) | − | 11.1231i | − | 0.696556i | ||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | − | 17.3693i | − | 1.08347i | −0.840550 | − | 0.541734i | \(-0.817768\pi\) | ||
0.840550 | − | 0.541734i | \(-0.182232\pi\) | |||||||
\(258\) | 0.936426 | 0.0582994 | ||||||||
\(259\) | 0.876894 | − | 4.87689i | 0.0544876 | − | 0.303035i | ||||
\(260\) | − | 10.4160i | − | 0.645971i | ||||||
\(261\) | −8.24621 | −0.510428 | ||||||||
\(262\) | 12.0000i | 0.741362i | ||||||||
\(263\) | − | 20.5366i | − | 1.26634i | −0.774011 | − | 0.633172i | \(-0.781753\pi\) | ||
0.774011 | − | 0.633172i | \(-0.218247\pi\) | |||||||
\(264\) | −12.8147 | −0.788689 | ||||||||
\(265\) | 33.3693i | 2.04986i | ||||||||
\(266\) | −3.80776 | − | 0.684658i | −0.233469 | − | 0.0419791i | ||||
\(267\) | − | 10.0054i | − | 0.612320i | ||||||
\(268\) | 4.68213i | 0.286007i | ||||||||
\(269\) | 6.63068i | 0.404280i | 0.979357 | + | 0.202140i | \(0.0647896\pi\) | ||||
−0.979357 | + | 0.202140i | \(0.935210\pi\) | |||||||
\(270\) | − | 3.33513i | − | 0.202970i | ||||||
\(271\) | − | 16.4924i | − | 1.00184i | −0.865493 | − | 0.500922i | \(-0.832994\pi\) | ||
0.865493 | − | 0.500922i | \(-0.167006\pi\) | |||||||
\(272\) | −3.33513 | −0.202222 | ||||||||
\(273\) | −8.13254 | − | 1.46228i | −0.492204 | − | 0.0885012i | ||||
\(274\) | 14.8028i | 0.894270i | ||||||||
\(275\) | 26.1552i | 1.57722i | ||||||||
\(276\) | −4.53448 | − | 1.56155i | −0.272944 | − | 0.0939944i | ||||
\(277\) | 16.2462 | 0.976140 | 0.488070 | − | 0.872804i | \(-0.337701\pi\) | ||||
0.488070 | + | 0.872804i | \(0.337701\pi\) | |||||||
\(278\) | 12.0000i | 0.719712i | ||||||||
\(279\) | 10.2462i | 0.613425i | ||||||||
\(280\) | 26.0540 | + | 4.68466i | 1.55702 | + | 0.279962i | ||||
\(281\) | − | 22.2942i | − | 1.32996i | −0.746860 | − | 0.664981i | \(-0.768440\pi\) | ||
0.746860 | − | 0.664981i | \(-0.231560\pi\) | |||||||
\(282\) | 7.12311 | 0.424175 | ||||||||
\(283\) | −19.3697 | −1.15141 | −0.575703 | − | 0.817659i | \(-0.695272\pi\) | ||||
−0.575703 | + | 0.817659i | \(0.695272\pi\) | |||||||
\(284\) | 11.1231 | 0.660035 | ||||||||
\(285\) | 4.87689i | 0.288882i | ||||||||
\(286\) | −13.3405 | −0.788842 | ||||||||
\(287\) | 5.20798 | − | 28.9645i | 0.307418 | − | 1.70972i | ||||
\(288\) | 5.00000 | 0.294628 | ||||||||
\(289\) | −5.87689 | −0.345700 | ||||||||
\(290\) | 27.5022 | 1.61498 | ||||||||
\(291\) | − | 1.87285i | − | 0.109789i | ||||||
\(292\) | 6.24621i | 0.365532i | ||||||||
\(293\) | −9.18425 | −0.536550 | −0.268275 | − | 0.963342i | \(-0.586454\pi\) | ||||
−0.268275 | + | 0.963342i | \(0.586454\pi\) | |||||||
\(294\) | 2.43845 | − | 6.56155i | 0.142213 | − | 0.382678i | ||||
\(295\) | 23.7565i | 1.38316i | ||||||||
\(296\) | 5.61856i | 0.326572i | ||||||||
\(297\) | 4.27156 | 0.247861 | ||||||||
\(298\) | 0.410574i | 0.0237839i | ||||||||
\(299\) | −14.1617 | − | 4.87689i | −0.818991 | − | 0.282038i | ||||
\(300\) | − | 6.12311i | − | 0.353518i | ||||||
\(301\) | 0.438447 | − | 2.43845i | 0.0252717 | − | 0.140550i | ||||
\(302\) | 20.4924 | 1.17921 | ||||||||
\(303\) | −3.12311 | −0.179418 | ||||||||
\(304\) | 1.46228 | 0.0838675 | ||||||||
\(305\) | −6.24621 | −0.357657 | ||||||||
\(306\) | 3.33513 | 0.190657 | ||||||||
\(307\) | − | 2.24621i | − | 0.128198i | −0.997944 | − | 0.0640990i | \(-0.979583\pi\) | ||
0.997944 | − | 0.0640990i | \(-0.0204174\pi\) | |||||||
\(308\) | −2.00000 | + | 11.1231i | −0.113961 | + | 0.633798i | ||||
\(309\) | 5.20798i | 0.296272i | ||||||||
\(310\) | − | 34.1725i | − | 1.94087i | ||||||
\(311\) | − | 2.63068i | − | 0.149172i | −0.997215 | − | 0.0745862i | \(-0.976236\pi\) | ||
0.997215 | − | 0.0745862i | \(-0.0237636\pi\) | |||||||
\(312\) | 9.36932 | 0.530433 | ||||||||
\(313\) | 14.3922 | 0.813497 | 0.406749 | − | 0.913540i | \(-0.366663\pi\) | ||||
0.406749 | + | 0.913540i | \(0.366663\pi\) | |||||||
\(314\) | −15.2134 | −0.858541 | ||||||||
\(315\) | −8.68466 | − | 1.56155i | −0.489325 | − | 0.0879835i | ||||
\(316\) | 16.1498i | 0.908498i | ||||||||
\(317\) | −14.0000 | −0.786318 | −0.393159 | − | 0.919470i | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(318\) | −10.0054 | −0.561075 | ||||||||
\(319\) | 35.2242i | 1.97218i | ||||||||
\(320\) | −23.3459 | −1.30508 | ||||||||
\(321\) | −9.06897 | −0.506181 | ||||||||
\(322\) | 6.18938 | − | 11.0766i | 0.344921 | − | 0.617276i | ||||
\(323\) | −4.87689 | −0.271358 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | − | 19.1231i | − | 1.06076i | ||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | −12.2888 | −0.679573 | ||||||||
\(328\) | 33.3693i | 1.84251i | ||||||||
\(329\) | 3.33513 | − | 18.5485i | 0.183872 | − | 1.02261i | ||||
\(330\) | −14.2462 | −0.784228 | ||||||||
\(331\) | −16.4924 | −0.906506 | −0.453253 | − | 0.891382i | \(-0.649737\pi\) | ||||
−0.453253 | + | 0.891382i | \(0.649737\pi\) | |||||||
\(332\) | −17.0862 | −0.937729 | ||||||||
\(333\) | − | 1.87285i | − | 0.102632i | ||||||
\(334\) | − | 5.75379i | − | 0.314833i | ||||||
\(335\) | 15.6155i | 0.853167i | ||||||||
\(336\) | −0.468213 | + | 2.60399i | −0.0255431 | + | 0.142059i | ||||
\(337\) | 6.67026i | 0.363352i | 0.983358 | + | 0.181676i | \(0.0581523\pi\) | ||||
−0.983358 | + | 0.181676i | \(0.941848\pi\) | |||||||
\(338\) | −3.24621 | −0.176571 | ||||||||
\(339\) | 8.95369 | 0.486298 | ||||||||
\(340\) | 11.1231 | 0.603235 | ||||||||
\(341\) | 43.7673 | 2.37013 | ||||||||
\(342\) | −1.46228 | −0.0790710 | ||||||||
\(343\) | −15.9445 | − | 9.42190i | −0.860923 | − | 0.508735i | ||||
\(344\) | 2.80928i | 0.151466i | ||||||||
\(345\) | −15.1231 | − | 5.20798i | −0.814201 | − | 0.280388i | ||||
\(346\) | 3.12311i | 0.167899i | ||||||||
\(347\) | −16.4924 | −0.885360 | −0.442680 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442680 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(348\) | − | 8.24621i | − | 0.442043i | ||||||
\(349\) | 9.36932i | 0.501528i | 0.968048 | + | 0.250764i | \(0.0806818\pi\) | ||||
−0.968048 | + | 0.250764i | \(0.919318\pi\) | |||||||
\(350\) | 15.9445 | + | 2.86692i | 0.852270 | + | 0.153243i | ||||
\(351\) | −3.12311 | −0.166699 | ||||||||
\(352\) | − | 21.3578i | − | 1.13837i | ||||||
\(353\) | 17.3693i | 0.924475i | 0.886756 | + | 0.462238i | \(0.152953\pi\) | ||||
−0.886756 | + | 0.462238i | \(0.847047\pi\) | |||||||
\(354\) | −7.12311 | −0.378589 | ||||||||
\(355\) | 37.0970 | 1.96891 | ||||||||
\(356\) | 10.0054 | 0.530285 | ||||||||
\(357\) | 1.56155 | − | 8.68466i | 0.0826461 | − | 0.459641i | ||||
\(358\) | 4.00000 | 0.211407 | ||||||||
\(359\) | 25.3341i | 1.33708i | 0.743676 | + | 0.668540i | \(0.233081\pi\) | ||||
−0.743676 | + | 0.668540i | \(0.766919\pi\) | |||||||
\(360\) | 10.0054 | 0.527331 | ||||||||
\(361\) | −16.8617 | −0.887460 | ||||||||
\(362\) | −12.2888 | −0.645886 | ||||||||
\(363\) | − | 7.24621i | − | 0.380327i | ||||||
\(364\) | 1.46228 | − | 8.13254i | 0.0766443 | − | 0.426261i | ||||
\(365\) | 20.8319i | 1.09039i | ||||||||
\(366\) | − | 1.87285i | − | 0.0978956i | ||||||
\(367\) | 12.6994 | 0.662903 | 0.331452 | − | 0.943472i | \(-0.392462\pi\) | ||||
0.331452 | + | 0.943472i | \(0.392462\pi\) | |||||||
\(368\) | −1.56155 | + | 4.53448i | −0.0814016 | + | 0.236376i | ||||
\(369\) | − | 11.1231i | − | 0.579046i | ||||||
\(370\) | 6.24621i | 0.324725i | ||||||||
\(371\) | −4.68466 | + | 26.0540i | −0.243215 | + | 1.35266i | ||||
\(372\) | −10.2462 | −0.531241 | ||||||||
\(373\) | 15.2134i | 0.787719i | 0.919171 | + | 0.393860i | \(0.128860\pi\) | ||||
−0.919171 | + | 0.393860i | \(0.871140\pi\) | |||||||
\(374\) | − | 14.2462i | − | 0.736654i | ||||||
\(375\) | − | 3.74571i | − | 0.193427i | ||||||
\(376\) | 21.3693i | 1.10204i | ||||||||
\(377\) | − | 25.7538i | − | 1.32639i | ||||||
\(378\) | 0.468213 | − | 2.60399i | 0.0240823 | − | 0.133935i | ||||
\(379\) | − | 21.7684i | − | 1.11817i | −0.829112 | − | 0.559083i | \(-0.811153\pi\) | ||
0.829112 | − | 0.559083i | \(-0.188847\pi\) | |||||||
\(380\) | −4.87689 | −0.250179 | ||||||||
\(381\) | − | 6.24621i | − | 0.320003i | ||||||
\(382\) | − | 3.45041i | − | 0.176538i | ||||||
\(383\) | 16.2651 | 0.831107 | 0.415554 | − | 0.909569i | \(-0.363588\pi\) | ||||
0.415554 | + | 0.909569i | \(0.363588\pi\) | |||||||
\(384\) | 3.00000i | 0.153093i | ||||||||
\(385\) | −6.67026 | + | 37.0970i | −0.339948 | + | 1.89064i | ||||
\(386\) | −25.6155 | −1.30380 | ||||||||
\(387\) | − | 0.936426i | − | 0.0476012i | ||||||
\(388\) | 1.87285 | 0.0950797 | ||||||||
\(389\) | − | 14.5722i | − | 0.738842i | −0.929262 | − | 0.369421i | \(-0.879556\pi\) | ||
0.929262 | − | 0.369421i | \(-0.120444\pi\) | |||||||
\(390\) | 10.4160 | 0.527433 | ||||||||
\(391\) | 5.20798 | − | 15.1231i | 0.263379 | − | 0.764808i | ||||
\(392\) | 19.6847 | + | 7.31534i | 0.994225 | + | 0.369481i | ||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | −18.4924 | −0.931635 | ||||||||
\(395\) | 53.8617i | 2.71008i | ||||||||
\(396\) | 4.27156i | 0.214654i | ||||||||
\(397\) | − | 20.4924i | − | 1.02849i | −0.857645 | − | 0.514243i | \(-0.828073\pi\) | ||
0.857645 | − | 0.514243i | \(-0.171927\pi\) | |||||||
\(398\) | −5.20798 | −0.261053 | ||||||||
\(399\) | −0.684658 | + | 3.80776i | −0.0342758 | + | 0.190627i | ||||
\(400\) | −6.12311 | −0.306155 | ||||||||
\(401\) | 11.8782i | 0.593171i | 0.955006 | + | 0.296586i | \(0.0958480\pi\) | ||||
−0.955006 | + | 0.296586i | \(0.904152\pi\) | |||||||
\(402\) | −4.68213 | −0.233524 | ||||||||
\(403\) | −32.0000 | −1.59403 | ||||||||
\(404\) | − | 3.12311i | − | 0.155380i | ||||||
\(405\) | −3.33513 | −0.165724 | ||||||||
\(406\) | 21.4731 | + | 3.86098i | 1.06569 | + | 0.191617i | ||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 10.0054i | 0.495341i | ||||||||
\(409\) | 1.36932i | 0.0677084i | 0.999427 | + | 0.0338542i | \(0.0107782\pi\) | ||||
−0.999427 | + | 0.0338542i | \(0.989222\pi\) | |||||||
\(410\) | 37.0970i | 1.83209i | ||||||||
\(411\) | 14.8028 | 0.730169 | ||||||||
\(412\) | −5.20798 | −0.256579 | ||||||||
\(413\) | −3.33513 | + | 18.5485i | −0.164111 | + | 0.912713i | ||||
\(414\) | 1.56155 | − | 4.53448i | 0.0767461 | − | 0.222858i | ||||
\(415\) | −56.9848 | −2.79728 | ||||||||
\(416\) | 15.6155i | 0.765614i | ||||||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 6.24621i | 0.305512i | ||||||||
\(419\) | −9.59482 | −0.468738 | −0.234369 | − | 0.972148i | \(-0.575302\pi\) | ||||
−0.234369 | + | 0.972148i | \(0.575302\pi\) | |||||||
\(420\) | 1.56155 | − | 8.68466i | 0.0761960 | − | 0.423768i | ||||
\(421\) | − | 25.6294i | − | 1.24910i | −0.780986 | − | 0.624549i | \(-0.785283\pi\) | ||
0.780986 | − | 0.624549i | \(-0.214717\pi\) | |||||||
\(422\) | 10.2462 | 0.498778 | ||||||||
\(423\) | − | 7.12311i | − | 0.346337i | ||||||
\(424\) | − | 30.0162i | − | 1.45771i | ||||||
\(425\) | 20.4214 | 0.990582 | ||||||||
\(426\) | 11.1231i | 0.538916i | ||||||||
\(427\) | −4.87689 | − | 0.876894i | −0.236009 | − | 0.0424359i | ||||
\(428\) | − | 9.06897i | − | 0.438365i | ||||||
\(429\) | 13.3405i | 0.644087i | ||||||||
\(430\) | 3.12311i | 0.150610i | ||||||||
\(431\) | 28.8492i | 1.38962i | 0.719195 | + | 0.694809i | \(0.244511\pi\) | ||||
−0.719195 | + | 0.694809i | \(0.755489\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | −18.1379 | −0.871654 | −0.435827 | − | 0.900031i | \(-0.643544\pi\) | ||||
−0.435827 | + | 0.900031i | \(0.643544\pi\) | |||||||
\(434\) | 4.79741 | − | 26.6811i | 0.230283 | − | 1.28073i | ||||
\(435\) | − | 27.5022i | − | 1.31863i | ||||||
\(436\) | − | 12.2888i | − | 0.588528i | ||||||
\(437\) | −2.28343 | + | 6.63068i | −0.109231 | + | 0.317189i | ||||
\(438\) | −6.24621 | −0.298456 | ||||||||
\(439\) | 21.7538i | 1.03825i | 0.854698 | + | 0.519126i | \(0.173742\pi\) | ||||
−0.854698 | + | 0.519126i | \(0.826258\pi\) | |||||||
\(440\) | − | 42.7386i | − | 2.03748i | ||||||
\(441\) | −6.56155 | − | 2.43845i | −0.312455 | − | 0.116117i | ||||
\(442\) | 10.4160i | 0.495437i | ||||||||
\(443\) | 29.3693 | 1.39538 | 0.697689 | − | 0.716401i | \(-0.254212\pi\) | ||||
0.697689 | + | 0.716401i | \(0.254212\pi\) | |||||||
\(444\) | 1.87285 | 0.0888817 | ||||||||
\(445\) | 33.3693 | 1.58186 | ||||||||
\(446\) | 4.00000i | 0.189405i | ||||||||
\(447\) | 0.410574 | 0.0194195 | ||||||||
\(448\) | −18.2279 | − | 3.27749i | −0.861190 | − | 0.154847i | ||||
\(449\) | 1.50758 | 0.0711470 | 0.0355735 | − | 0.999367i | \(-0.488674\pi\) | ||||
0.0355735 | + | 0.999367i | \(0.488674\pi\) | |||||||
\(450\) | 6.12311 | 0.288646 | ||||||||
\(451\) | −47.5130 | −2.23730 | ||||||||
\(452\) | 8.95369i | 0.421146i | ||||||||
\(453\) | − | 20.4924i | − | 0.962818i | ||||||
\(454\) | −6.67026 | −0.313051 | ||||||||
\(455\) | 4.87689 | − | 27.1231i | 0.228632 | − | 1.27155i | ||||
\(456\) | − | 4.38684i | − | 0.205433i | ||||||
\(457\) | − | 29.6056i | − | 1.38489i | −0.721470 | − | 0.692446i | \(-0.756533\pi\) | ||
0.721470 | − | 0.692446i | \(-0.243467\pi\) | |||||||
\(458\) | −12.2888 | −0.574219 | ||||||||
\(459\) | − | 3.33513i | − | 0.155671i | ||||||
\(460\) | 5.20798 | − | 15.1231i | 0.242824 | − | 0.705118i | ||||
\(461\) | 9.36932i | 0.436373i | 0.975907 | + | 0.218186i | \(0.0700140\pi\) | ||||
−0.975907 | + | 0.218186i | \(0.929986\pi\) | |||||||
\(462\) | −11.1231 | − | 2.00000i | −0.517494 | − | 0.0930484i | ||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −8.24621 | −0.382821 | ||||||||
\(465\) | −34.1725 | −1.58471 | ||||||||
\(466\) | 3.75379 | 0.173891 | ||||||||
\(467\) | 6.67026 | 0.308663 | 0.154332 | − | 0.988019i | \(-0.450678\pi\) | ||||
0.154332 | + | 0.988019i | \(0.450678\pi\) | |||||||
\(468\) | − | 3.12311i | − | 0.144366i | ||||||
\(469\) | −2.19224 | + | 12.1922i | −0.101228 | + | 0.562985i | ||||
\(470\) | 23.7565i | 1.09581i | ||||||||
\(471\) | 15.2134i | 0.700996i | ||||||||
\(472\) | − | 21.3693i | − | 0.983603i | ||||||
\(473\) | −4.00000 | −0.183920 | ||||||||
\(474\) | −16.1498 | −0.741785 | ||||||||
\(475\) | −8.95369 | −0.410823 | ||||||||
\(476\) | 8.68466 | + | 1.56155i | 0.398061 | + | 0.0715737i | ||||
\(477\) | 10.0054i | 0.458116i | ||||||||
\(478\) | 1.36932 | 0.0626311 | ||||||||
\(479\) | −5.84912 | −0.267253 | −0.133626 | − | 0.991032i | \(-0.542662\pi\) | ||||
−0.133626 | + | 0.991032i | \(0.542662\pi\) | |||||||
\(480\) | 16.6757i | 0.761136i | ||||||||
\(481\) | 5.84912 | 0.266697 | ||||||||
\(482\) | −11.4677 | −0.522338 | ||||||||
\(483\) | −11.0766 | − | 6.18938i | −0.504004 | − | 0.281626i | ||||
\(484\) | 7.24621 | 0.329373 | ||||||||
\(485\) | 6.24621 | 0.283626 | ||||||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −14.2462 | −0.645557 | −0.322779 | − | 0.946474i | \(-0.604617\pi\) | ||||
−0.322779 | + | 0.946474i | \(0.604617\pi\) | |||||||
\(488\) | 5.61856 | 0.254340 | ||||||||
\(489\) | 12.0000i | 0.542659i | ||||||||
\(490\) | 21.8836 | + | 8.13254i | 0.988602 | + | 0.367391i | ||||
\(491\) | −32.4924 | −1.46636 | −0.733181 | − | 0.680033i | \(-0.761965\pi\) | ||||
−0.733181 | + | 0.680033i | \(0.761965\pi\) | |||||||
\(492\) | 11.1231 | 0.501468 | ||||||||
\(493\) | 27.5022 | 1.23864 | ||||||||
\(494\) | − | 4.56685i | − | 0.205472i | ||||||
\(495\) | 14.2462i | 0.640320i | ||||||||
\(496\) | 10.2462i | 0.460068i | ||||||||
\(497\) | 28.9645 | + | 5.20798i | 1.29923 | + | 0.233610i | ||||
\(498\) | − | 17.0862i | − | 0.765652i | ||||||
\(499\) | 5.75379 | 0.257575 | 0.128787 | − | 0.991672i | \(-0.458891\pi\) | ||||
0.128787 | + | 0.991672i | \(0.458891\pi\) | |||||||
\(500\) | 3.74571 | 0.167513 | ||||||||
\(501\) | −5.75379 | −0.257060 | ||||||||
\(502\) | 0.821147 | 0.0366496 | ||||||||
\(503\) | −34.1725 | −1.52368 | −0.761838 | − | 0.647768i | \(-0.775703\pi\) | ||||
−0.761838 | + | 0.647768i | \(0.775703\pi\) | |||||||
\(504\) | 7.81198 | + | 1.40464i | 0.347973 | + | 0.0625676i | ||||
\(505\) | − | 10.4160i | − | 0.463505i | ||||||
\(506\) | −19.3693 | − | 6.67026i | −0.861071 | − | 0.296529i | ||||
\(507\) | 3.24621i | 0.144169i | ||||||||
\(508\) | 6.24621 | 0.277131 | ||||||||
\(509\) | − | 15.6155i | − | 0.692146i | −0.938208 | − | 0.346073i | \(-0.887515\pi\) | ||
0.938208 | − | 0.346073i | \(-0.112485\pi\) | |||||||
\(510\) | 11.1231i | 0.492539i | ||||||||
\(511\) | −2.92456 | + | 16.2651i | −0.129375 | + | 0.719525i | ||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 1.46228i | 0.0645612i | ||||||||
\(514\) | 17.3693i | 0.766128i | ||||||||
\(515\) | −17.3693 | −0.765384 | ||||||||
\(516\) | 0.936426 | 0.0412239 | ||||||||
\(517\) | −30.4268 | −1.33817 | ||||||||
\(518\) | −0.876894 | + | 4.87689i | −0.0385285 | + | 0.214278i | ||||
\(519\) | 3.12311 | 0.137089 | ||||||||
\(520\) | 31.2479i | 1.37031i | ||||||||
\(521\) | 3.33513 | 0.146115 | 0.0730574 | − | 0.997328i | \(-0.476724\pi\) | ||||
0.0730574 | + | 0.997328i | \(0.476724\pi\) | |||||||
\(522\) | 8.24621 | 0.360927 | ||||||||
\(523\) | 11.8782 | 0.519400 | 0.259700 | − | 0.965689i | \(-0.416376\pi\) | ||||
0.259700 | + | 0.965689i | \(0.416376\pi\) | |||||||
\(524\) | 12.0000i | 0.524222i | ||||||||
\(525\) | 2.86692 | − | 15.9445i | 0.125123 | − | 0.695876i | ||||
\(526\) | 20.5366i | 0.895440i | ||||||||
\(527\) | − | 34.1725i | − | 1.48858i | ||||||
\(528\) | 4.27156 | 0.185896 | ||||||||
\(529\) | −18.1231 | − | 14.1617i | −0.787961 | − | 0.615725i | ||||
\(530\) | − | 33.3693i | − | 1.44947i | ||||||
\(531\) | 7.12311i | 0.309116i | ||||||||
\(532\) | −3.80776 | − | 0.684658i | −0.165088 | − | 0.0296837i | ||||
\(533\) | 34.7386 | 1.50470 | ||||||||
\(534\) | 10.0054i | 0.432976i | ||||||||
\(535\) | − | 30.2462i | − | 1.30766i | ||||||
\(536\) | − | 14.0464i | − | 0.606712i | ||||||
\(537\) | − | 4.00000i | − | 0.172613i | ||||||
\(538\) | − | 6.63068i | − | 0.285869i | ||||||
\(539\) | −10.4160 | + | 28.0281i | −0.448648 | + | 1.20725i | ||||
\(540\) | − | 3.33513i | − | 0.143521i | ||||||
\(541\) | 22.8769 | 0.983555 | 0.491777 | − | 0.870721i | \(-0.336347\pi\) | ||||
0.491777 | + | 0.870721i | \(0.336347\pi\) | |||||||
\(542\) | 16.4924i | 0.708410i | ||||||||
\(543\) | 12.2888i | 0.527364i | ||||||||
\(544\) | −16.6757 | −0.714963 | ||||||||
\(545\) | − | 40.9848i | − | 1.75560i | ||||||
\(546\) | 8.13254 | + | 1.46228i | 0.348041 | + | 0.0625798i | ||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | 14.8028i | 0.632345i | ||||||||
\(549\) | −1.87285 | −0.0799314 | ||||||||
\(550\) | − | 26.1552i | − | 1.11526i | ||||||
\(551\) | −12.0583 | −0.513699 | ||||||||
\(552\) | 13.6035 | + | 4.68466i | 0.579001 | + | 0.199392i | ||||
\(553\) | −7.56155 | + | 42.0540i | −0.321550 | + | 1.78832i | ||||
\(554\) | −16.2462 | −0.690235 | ||||||||
\(555\) | 6.24621 | 0.265137 | ||||||||
\(556\) | 12.0000i | 0.508913i | ||||||||
\(557\) | − | 15.8545i | − | 0.671777i | −0.941902 | − | 0.335889i | \(-0.890963\pi\) | ||
0.941902 | − | 0.335889i | \(-0.109037\pi\) | |||||||
\(558\) | − | 10.2462i | − | 0.433757i | ||||||
\(559\) | 2.92456 | 0.123696 | ||||||||
\(560\) | −8.68466 | − | 1.56155i | −0.366994 | − | 0.0659877i | ||||
\(561\) | −14.2462 | −0.601476 | ||||||||
\(562\) | 22.2942i | 0.940425i | ||||||||
\(563\) | 0.821147 | 0.0346072 | 0.0173036 | − | 0.999850i | \(-0.494492\pi\) | ||||
0.0173036 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(564\) | 7.12311 | 0.299937 | ||||||||
\(565\) | 29.8617i | 1.25629i | ||||||||
\(566\) | 19.3697 | 0.814168 | ||||||||
\(567\) | −2.60399 | − | 0.468213i | −0.109357 | − | 0.0196631i | ||||
\(568\) | −33.3693 | −1.40015 | ||||||||
\(569\) | − | 0.641132i | − | 0.0268777i | −0.999910 | − | 0.0134388i | \(-0.995722\pi\) | ||
0.999910 | − | 0.0134388i | \(-0.00427784\pi\) | |||||||
\(570\) | − | 4.87689i | − | 0.204271i | ||||||
\(571\) | 24.6929i | 1.03337i | 0.856177 | + | 0.516683i | \(0.172834\pi\) | ||||
−0.856177 | + | 0.516683i | \(0.827166\pi\) | |||||||
\(572\) | −13.3405 | −0.557796 | ||||||||
\(573\) | −3.45041 | −0.144143 | ||||||||
\(574\) | −5.20798 | + | 28.9645i | −0.217377 | + | 1.20895i | ||||
\(575\) | 9.56155 | − | 27.7651i | 0.398744 | − | 1.15789i | ||||
\(576\) | −7.00000 | −0.291667 | ||||||||
\(577\) | − | 27.1231i | − | 1.12915i | −0.825382 | − | 0.564575i | \(-0.809040\pi\) | ||
0.825382 | − | 0.564575i | \(-0.190960\pi\) | |||||||
\(578\) | 5.87689 | 0.244447 | ||||||||
\(579\) | 25.6155i | 1.06455i | ||||||||
\(580\) | 27.5022 | 1.14197 | ||||||||
\(581\) | −44.4924 | − | 8.00000i | −1.84586 | − | 0.331896i | ||||
\(582\) | 1.87285i | 0.0776322i | ||||||||
\(583\) | 42.7386 | 1.77005 | ||||||||
\(584\) | − | 18.7386i | − | 0.775410i | ||||||
\(585\) | − | 10.4160i | − | 0.430647i | ||||||
\(586\) | 9.18425 | 0.379398 | ||||||||
\(587\) | 32.4924i | 1.34111i | 0.741862 | + | 0.670553i | \(0.233943\pi\) | ||||
−0.741862 | + | 0.670553i | \(0.766057\pi\) | |||||||
\(588\) | 2.43845 | − | 6.56155i | 0.100560 | − | 0.270594i | ||||
\(589\) | 14.9828i | 0.617356i | ||||||||
\(590\) | − | 23.7565i | − | 0.978040i | ||||||
\(591\) | 18.4924i | 0.760677i | ||||||||
\(592\) | − | 1.87285i | − | 0.0769738i | ||||||
\(593\) | 17.3693i | 0.713272i | 0.934243 | + | 0.356636i | \(0.116076\pi\) | ||||
−0.934243 | + | 0.356636i | \(0.883924\pi\) | |||||||
\(594\) | −4.27156 | −0.175264 | ||||||||
\(595\) | 28.9645 | + | 5.20798i | 1.18743 | + | 0.213507i | ||||
\(596\) | 0.410574i | 0.0168177i | ||||||||
\(597\) | 5.20798i | 0.213149i | ||||||||
\(598\) | 14.1617 | + | 4.87689i | 0.579114 | + | 0.199431i | ||||
\(599\) | −14.6307 | −0.597794 | −0.298897 | − | 0.954285i | \(-0.596619\pi\) | ||||
−0.298897 | + | 0.954285i | \(0.596619\pi\) | |||||||
\(600\) | 18.3693i | 0.749924i | ||||||||
\(601\) | − | 33.3693i | − | 1.36116i | −0.732672 | − | 0.680581i | \(-0.761727\pi\) | ||
0.732672 | − | 0.680581i | \(-0.238273\pi\) | |||||||
\(602\) | −0.438447 | + | 2.43845i | −0.0178698 | + | 0.0993837i | ||||
\(603\) | 4.68213i | 0.190671i | ||||||||
\(604\) | 20.4924 | 0.833825 | ||||||||
\(605\) | 24.1671 | 0.982531 | ||||||||
\(606\) | 3.12311 | 0.126867 | ||||||||
\(607\) | − | 22.7386i | − | 0.922933i | −0.887158 | − | 0.461466i | \(-0.847324\pi\) | ||
0.887158 | − | 0.461466i | \(-0.152676\pi\) | |||||||
\(608\) | 7.31140 | 0.296516 | ||||||||
\(609\) | 3.86098 | − | 21.4731i | 0.156455 | − | 0.870133i | ||||
\(610\) | 6.24621 | 0.252902 | ||||||||
\(611\) | 22.2462 | 0.899985 | ||||||||
\(612\) | 3.33513 | 0.134815 | ||||||||
\(613\) | − | 41.8944i | − | 1.69210i | −0.533103 | − | 0.846050i | \(-0.678974\pi\) | ||
0.533103 | − | 0.846050i | \(-0.321026\pi\) | |||||||
\(614\) | 2.24621i | 0.0906497i | ||||||||
\(615\) | 37.0970 | 1.49590 | ||||||||
\(616\) | 6.00000 | − | 33.3693i | 0.241747 | − | 1.34449i | ||||
\(617\) | 11.0571i | 0.445142i | 0.974916 | + | 0.222571i | \(0.0714449\pi\) | ||||
−0.974916 | + | 0.222571i | \(0.928555\pi\) | |||||||
\(618\) | − | 5.20798i | − | 0.209496i | ||||||
\(619\) | −29.7856 | −1.19719 | −0.598593 | − | 0.801053i | \(-0.704273\pi\) | ||||
−0.598593 | + | 0.801053i | \(0.704273\pi\) | |||||||
\(620\) | − | 34.1725i | − | 1.37240i | ||||||
\(621\) | −4.53448 | − | 1.56155i | −0.181963 | − | 0.0626630i | ||||
\(622\) | 2.63068i | 0.105481i | ||||||||
\(623\) | 26.0540 | + | 4.68466i | 1.04383 | + | 0.187687i | ||||
\(624\) | −3.12311 | −0.125024 | ||||||||
\(625\) | −18.1231 | −0.724924 | ||||||||
\(626\) | −14.3922 | −0.575229 | ||||||||
\(627\) | 6.24621 | 0.249450 | ||||||||
\(628\) | −15.2134 | −0.607080 | ||||||||
\(629\) | 6.24621i | 0.249053i | ||||||||
\(630\) | 8.68466 | + | 1.56155i | 0.346005 | + | 0.0622138i | ||||
\(631\) | − | 9.47954i | − | 0.377375i | −0.982037 | − | 0.188687i | \(-0.939577\pi\) | ||
0.982037 | − | 0.188687i | \(-0.0604233\pi\) | |||||||
\(632\) | − | 48.4494i | − | 1.92721i | ||||||
\(633\) | − | 10.2462i | − | 0.407250i | ||||||
\(634\) | 14.0000 | 0.556011 | ||||||||
\(635\) | 20.8319 | 0.826690 | ||||||||
\(636\) | −10.0054 | −0.396740 | ||||||||
\(637\) | 7.61553 | − | 20.4924i | 0.301738 | − | 0.811939i | ||||
\(638\) | − | 35.2242i | − | 1.39454i | ||||||
\(639\) | 11.1231 | 0.440023 | ||||||||
\(640\) | −10.0054 | −0.395498 | ||||||||
\(641\) | 46.0507i | 1.81889i | 0.415820 | + | 0.909447i | \(0.363495\pi\) | ||||
−0.415820 | + | 0.909447i | \(0.636505\pi\) | |||||||
\(642\) | 9.06897 | 0.357924 | ||||||||
\(643\) | 35.6347 | 1.40530 | 0.702649 | − | 0.711537i | \(-0.252001\pi\) | ||||
0.702649 | + | 0.711537i | \(0.252001\pi\) | |||||||
\(644\) | 6.18938 | − | 11.0766i | 0.243896 | − | 0.436480i | ||||
\(645\) | 3.12311 | 0.122972 | ||||||||
\(646\) | 4.87689 | 0.191879 | ||||||||
\(647\) | 35.6155i | 1.40019i | 0.714049 | + | 0.700095i | \(0.246859\pi\) | ||||
−0.714049 | + | 0.700095i | \(0.753141\pi\) | |||||||
\(648\) | 3.00000 | 0.117851 | ||||||||
\(649\) | 30.4268 | 1.19435 | ||||||||
\(650\) | 19.1231i | 0.750070i | ||||||||
\(651\) | −26.6811 | − | 4.79741i | −1.04571 | − | 0.188025i | ||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | 14.0000 | 0.547862 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(654\) | 12.2888 | 0.480531 | ||||||||
\(655\) | 40.0216i | 1.56377i | ||||||||
\(656\) | − | 11.1231i | − | 0.434284i | ||||||
\(657\) | 6.24621i | 0.243688i | ||||||||
\(658\) | −3.33513 | + | 18.5485i | −0.130017 | + | 0.723096i | ||||
\(659\) | − | 24.2824i | − | 0.945906i | −0.881088 | − | 0.472953i | \(-0.843188\pi\) | ||
0.881088 | − | 0.472953i | \(-0.156812\pi\) | |||||||
\(660\) | −14.2462 | −0.554533 | ||||||||
\(661\) | −38.1487 | −1.48381 | −0.741907 | − | 0.670503i | \(-0.766078\pi\) | ||||
−0.741907 | + | 0.670503i | \(0.766078\pi\) | |||||||
\(662\) | 16.4924 | 0.640996 | ||||||||
\(663\) | 10.4160 | 0.404523 | ||||||||
\(664\) | 51.2587 | 1.98922 | ||||||||
\(665\) | −12.6994 | − | 2.28343i | −0.492461 | − | 0.0885475i | ||||
\(666\) | 1.87285i | 0.0725716i | ||||||||
\(667\) | 12.8769 | − | 37.3923i | 0.498595 | − | 1.44784i | ||||
\(668\) | − | 5.75379i | − | 0.222621i | ||||||
\(669\) | 4.00000 | 0.154649 | ||||||||
\(670\) | − | 15.6155i | − | 0.603280i | ||||||
\(671\) | 8.00000i | 0.308837i | ||||||||
\(672\) | −2.34107 | + | 13.0200i | −0.0903086 | + | 0.502256i | ||||
\(673\) | −13.1231 | −0.505859 | −0.252929 | − | 0.967485i | \(-0.581394\pi\) | ||||
−0.252929 | + | 0.967485i | \(0.581394\pi\) | |||||||
\(674\) | − | 6.67026i | − | 0.256929i | ||||||
\(675\) | − | 6.12311i | − | 0.235678i | ||||||
\(676\) | −3.24621 | −0.124854 | ||||||||
\(677\) | −9.18425 | −0.352979 | −0.176490 | − | 0.984302i | \(-0.556474\pi\) | ||||
−0.176490 | + | 0.984302i | \(0.556474\pi\) | |||||||
\(678\) | −8.95369 | −0.343864 | ||||||||
\(679\) | 4.87689 | + | 0.876894i | 0.187158 | + | 0.0336521i | ||||
\(680\) | −33.3693 | −1.27965 | ||||||||
\(681\) | 6.67026i | 0.255605i | ||||||||
\(682\) | −43.7673 | −1.67594 | ||||||||
\(683\) | 7.12311 | 0.272558 | 0.136279 | − | 0.990670i | \(-0.456486\pi\) | ||||
0.136279 | + | 0.990670i | \(0.456486\pi\) | |||||||
\(684\) | −1.46228 | −0.0559116 | ||||||||
\(685\) | 49.3693i | 1.88630i | ||||||||
\(686\) | 15.9445 | + | 9.42190i | 0.608765 | + | 0.359730i | ||||
\(687\) | 12.2888i | 0.468848i | ||||||||
\(688\) | − | 0.936426i | − | 0.0357009i | ||||||
\(689\) | −31.2479 | −1.19045 | ||||||||
\(690\) | 15.1231 | + | 5.20798i | 0.575727 | + | 0.198265i | ||||
\(691\) | − | 2.24621i | − | 0.0854499i | −0.999087 | − | 0.0427250i | \(-0.986396\pi\) | ||
0.999087 | − | 0.0427250i | \(-0.0136039\pi\) | |||||||
\(692\) | 3.12311i | 0.118723i | ||||||||
\(693\) | −2.00000 | + | 11.1231i | −0.0759737 | + | 0.422532i | ||||
\(694\) | 16.4924 | 0.626044 | ||||||||
\(695\) | 40.0216i | 1.51811i | ||||||||
\(696\) | 24.7386i | 0.937715i | ||||||||
\(697\) | 37.0970i | 1.40515i | ||||||||
\(698\) | − | 9.36932i | − | 0.354634i | ||||||
\(699\) | − | 3.75379i | − | 0.141981i | ||||||
\(700\) | 15.9445 | + | 2.86692i | 0.602646 | + | 0.108359i | ||||
\(701\) | 13.7511i | 0.519372i | 0.965693 | + | 0.259686i | \(0.0836191\pi\) | ||||
−0.965693 | + | 0.259686i | \(0.916381\pi\) | |||||||
\(702\) | 3.12311 | 0.117874 | ||||||||
\(703\) | − | 2.73863i | − | 0.103290i | ||||||
\(704\) | 29.9009i | 1.12693i | ||||||||
\(705\) | 23.7565 | 0.894721 | ||||||||
\(706\) | − | 17.3693i | − | 0.653703i | ||||||
\(707\) | 1.46228 | − | 8.13254i | 0.0549947 | − | 0.305856i | ||||
\(708\) | −7.12311 | −0.267703 | ||||||||
\(709\) | − | 27.7328i | − | 1.04153i | −0.853701 | − | 0.520763i | \(-0.825648\pi\) | ||
0.853701 | − | 0.520763i | \(-0.174352\pi\) | |||||||
\(710\) | −37.0970 | −1.39223 | ||||||||
\(711\) | 16.1498i | 0.605665i | ||||||||
\(712\) | −30.0162 | −1.12490 | ||||||||
\(713\) | −46.4613 | − | 16.0000i | −1.73999 | − | 0.599205i | ||||
\(714\) | −1.56155 | + | 8.68466i | −0.0584396 | + | 0.325015i | ||||
\(715\) | −44.4924 | −1.66392 | ||||||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | − | 1.36932i | − | 0.0511381i | ||||||
\(718\) | − | 25.3341i | − | 0.945459i | ||||||
\(719\) | − | 2.63068i | − | 0.0981079i | −0.998796 | − | 0.0490540i | \(-0.984379\pi\) | ||
0.998796 | − | 0.0490540i | \(-0.0156206\pi\) | |||||||
\(720\) | −3.33513 | −0.124293 | ||||||||
\(721\) | −13.5616 | − | 2.43845i | −0.505059 | − | 0.0908125i | ||||
\(722\) | 16.8617 | 0.627529 | ||||||||
\(723\) | 11.4677i | 0.426487i | ||||||||
\(724\) | −12.2888 | −0.456710 | ||||||||
\(725\) | 50.4924 | 1.87524 | ||||||||
\(726\) | 7.24621i | 0.268932i | ||||||||
\(727\) | −52.7210 | −1.95531 | −0.977656 | − | 0.210209i | \(-0.932586\pi\) | ||||
−0.977656 | + | 0.210209i | \(0.932586\pi\) | |||||||
\(728\) | −4.38684 | + | 24.3976i | −0.162587 | + | 0.904236i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | − | 20.8319i | − | 0.771025i | ||||||
\(731\) | 3.12311i | 0.115512i | ||||||||
\(732\) | − | 1.87285i | − | 0.0692226i | ||||||
\(733\) | −8.54312 | −0.315547 | −0.157774 | − | 0.987475i | \(-0.550432\pi\) | ||||
−0.157774 | + | 0.987475i | \(0.550432\pi\) | |||||||
\(734\) | −12.6994 | −0.468743 | ||||||||
\(735\) | 8.13254 | − | 21.8836i | 0.299973 | − | 0.807190i | ||||
\(736\) | −7.80776 | + | 22.6724i | −0.287798 | + | 0.835717i | ||||
\(737\) | 20.0000 | 0.736709 | ||||||||
\(738\) | 11.1231i | 0.409447i | ||||||||
\(739\) | 14.7386 | 0.542169 | 0.271085 | − | 0.962555i | \(-0.412618\pi\) | ||||
0.271085 | + | 0.962555i | \(0.412618\pi\) | |||||||
\(740\) | 6.24621i | 0.229615i | ||||||||
\(741\) | −4.56685 | −0.167768 | ||||||||
\(742\) | 4.68466 | − | 26.0540i | 0.171979 | − | 0.956472i | ||||
\(743\) | − | 7.19612i | − | 0.264000i | −0.991250 | − | 0.132000i | \(-0.957860\pi\) | ||
0.991250 | − | 0.132000i | \(-0.0421399\pi\) | |||||||
\(744\) | 30.7386 | 1.12693 | ||||||||
\(745\) | 1.36932i | 0.0501679i | ||||||||
\(746\) | − | 15.2134i | − | 0.557001i | ||||||
\(747\) | −17.0862 | −0.625153 | ||||||||
\(748\) | − | 14.2462i | − | 0.520893i | ||||||
\(749\) | 4.24621 | − | 23.6155i | 0.155153 | − | 0.862893i | ||||
\(750\) | 3.74571i | 0.136774i | ||||||||
\(751\) | 3.03984i | 0.110925i | 0.998461 | + | 0.0554626i | \(0.0176634\pi\) | ||||
−0.998461 | + | 0.0554626i | \(0.982337\pi\) | |||||||
\(752\) | − | 7.12311i | − | 0.259753i | ||||||
\(753\) | − | 0.821147i | − | 0.0299243i | ||||||
\(754\) | 25.7538i | 0.937898i | ||||||||
\(755\) | 68.3449 | 2.48733 | ||||||||
\(756\) | 0.468213 | − | 2.60399i | 0.0170287 | − | 0.0947063i | ||||
\(757\) | − | 12.2888i | − | 0.446645i | −0.974745 | − | 0.223322i | \(-0.928310\pi\) | ||
0.974745 | − | 0.223322i | \(-0.0716903\pi\) | |||||||
\(758\) | 21.7684i | 0.790663i | ||||||||
\(759\) | −6.67026 | + | 19.3693i | −0.242115 | + | 0.703062i | ||||
\(760\) | 14.6307 | 0.530711 | ||||||||
\(761\) | 20.8769i | 0.756787i | 0.925645 | + | 0.378393i | \(0.123523\pi\) | ||||
−0.925645 | + | 0.378393i | \(0.876477\pi\) | |||||||
\(762\) | 6.24621i | 0.226276i | ||||||||
\(763\) | 5.75379 | − | 32.0000i | 0.208301 | − | 1.15848i | ||||
\(764\) | − | 3.45041i | − | 0.124832i | ||||||
\(765\) | 11.1231 | 0.402157 | ||||||||
\(766\) | −16.2651 | −0.587681 | ||||||||
\(767\) | −22.2462 | −0.803264 | ||||||||
\(768\) | − | 17.0000i | − | 0.613435i | ||||||
\(769\) | −37.3276 | −1.34607 | −0.673034 | − | 0.739612i | \(-0.735009\pi\) | ||||
−0.673034 | + | 0.739612i | \(0.735009\pi\) | |||||||
\(770\) | 6.67026 | − | 37.0970i | 0.240380 | − | 1.33688i | ||||
\(771\) | 17.3693 | 0.625541 | ||||||||
\(772\) | −25.6155 | −0.921923 | ||||||||
\(773\) | 14.5722 | 0.524127 | 0.262064 | − | 0.965051i | \(-0.415597\pi\) | ||||
0.262064 | + | 0.965051i | \(0.415597\pi\) | |||||||
\(774\) | 0.936426i | 0.0336592i | ||||||||
\(775\) | − | 62.7386i | − | 2.25364i | ||||||
\(776\) | −5.61856 | −0.201694 | ||||||||
\(777\) | 4.87689 | + | 0.876894i | 0.174958 | + | 0.0314584i | ||||
\(778\) | 14.5722i | 0.522440i | ||||||||
\(779\) | − | 16.2651i | − | 0.582757i | ||||||
\(780\) | 10.4160 | 0.372952 | ||||||||
\(781\) | − | 47.5130i | − | 1.70015i | ||||||
\(782\) | −5.20798 | + | 15.1231i | −0.186237 | + | 0.540801i | ||||
\(783\) | − | 8.24621i | − | 0.294696i | ||||||
\(784\) | −6.56155 | − | 2.43845i | −0.234341 | − | 0.0870874i | ||||
\(785\) | −50.7386 | −1.81094 | ||||||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | 29.7856 | 1.06174 | 0.530872 | − | 0.847452i | \(-0.321865\pi\) | ||||
0.530872 | + | 0.847452i | \(0.321865\pi\) | |||||||
\(788\) | −18.4924 | −0.658765 | ||||||||
\(789\) | 20.5366 | 0.731124 | ||||||||
\(790\) | − | 53.8617i | − | 1.91631i | ||||||
\(791\) | −4.19224 | + | 23.3153i | −0.149059 | + | 0.828998i | ||||
\(792\) | − | 12.8147i | − | 0.455350i | ||||||
\(793\) | − | 5.84912i | − | 0.207708i | ||||||
\(794\) | 20.4924i | 0.727249i | ||||||||
\(795\) | −33.3693 | −1.18349 | ||||||||
\(796\) | −5.20798 | −0.184592 | ||||||||
\(797\) | 17.4968 | 0.619769 | 0.309884 | − | 0.950774i | \(-0.399710\pi\) | ||||
0.309884 | + | 0.950774i | \(0.399710\pi\) | |||||||
\(798\) | 0.684658 | − | 3.80776i | 0.0242366 | − | 0.134793i | ||||
\(799\) | 23.7565i | 0.840444i | ||||||||
\(800\) | −30.6155 | −1.08242 | ||||||||
\(801\) | 10.0054 | 0.353523 | ||||||||
\(802\) | − | 11.8782i | − | 0.419436i | ||||||
\(803\) | 26.6811 | 0.941554 | ||||||||
\(804\) | −4.68213 | −0.165126 | ||||||||
\(805\) | 20.6424 | − | 36.9420i | 0.727549 | − | 1.30203i | ||||
\(806\) | 32.0000 | 1.12715 | ||||||||
\(807\) | −6.63068 | −0.233411 | ||||||||
\(808\) | 9.36932i | 0.329611i | ||||||||
\(809\) | 16.2462 | 0.571186 | 0.285593 | − | 0.958351i | \(-0.407809\pi\) | ||||
0.285593 | + | 0.958351i | \(0.407809\pi\) | |||||||
\(810\) | 3.33513 | 0.117185 | ||||||||
\(811\) | 13.7538i | 0.482961i | 0.970406 | + | 0.241480i | \(0.0776330\pi\) | ||||
−0.970406 | + | 0.241480i | \(0.922367\pi\) | |||||||
\(812\) | 21.4731 | + | 3.86098i | 0.753557 | + | 0.135494i | ||||
\(813\) | 16.4924 | 0.578415 | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | −40.0216 | −1.40189 | ||||||||
\(816\) | − | 3.33513i | − | 0.116753i | ||||||
\(817\) | − | 1.36932i | − | 0.0479063i | ||||||
\(818\) | − | 1.36932i | − | 0.0478770i | ||||||
\(819\) | 1.46228 | − | 8.13254i | 0.0510962 | − | 0.284174i | ||||
\(820\) | 37.0970i | 1.29548i | ||||||||
\(821\) | 28.7386 | 1.00299 | 0.501493 | − | 0.865162i | \(-0.332784\pi\) | ||||
0.501493 | + | 0.865162i | \(0.332784\pi\) | |||||||
\(822\) | −14.8028 | −0.516307 | ||||||||
\(823\) | 9.75379 | 0.339996 | 0.169998 | − | 0.985444i | \(-0.445624\pi\) | ||||
0.169998 | + | 0.985444i | \(0.445624\pi\) | |||||||
\(824\) | 15.6240 | 0.544286 | ||||||||
\(825\) | −26.1552 | −0.910607 | ||||||||
\(826\) | 3.33513 | − | 18.5485i | 0.116044 | − | 0.645385i | ||||
\(827\) | 6.14441i | 0.213662i | 0.994277 | + | 0.106831i | \(0.0340704\pi\) | ||||
−0.994277 | + | 0.106831i | \(0.965930\pi\) | |||||||
\(828\) | 1.56155 | − | 4.53448i | 0.0542677 | − | 0.157584i | ||||
\(829\) | − | 12.8769i | − | 0.447233i | −0.974677 | − | 0.223617i | \(-0.928214\pi\) | ||
0.974677 | − | 0.223617i | \(-0.0717863\pi\) | |||||||
\(830\) | 56.9848 | 1.97797 | ||||||||
\(831\) | 16.2462i | 0.563575i | ||||||||
\(832\) | − | 21.8617i | − | 0.757919i | ||||||
\(833\) | 21.8836 | + | 8.13254i | 0.758223 | + | 0.281776i | ||||
\(834\) | −12.0000 | −0.415526 | ||||||||
\(835\) | − | 19.1896i | − | 0.664085i | ||||||
\(836\) | 6.24621i | 0.216030i | ||||||||
\(837\) | −10.2462 | −0.354161 | ||||||||
\(838\) | 9.59482 | 0.331448 | ||||||||
\(839\) | 44.5884 | 1.53936 | 0.769682 | − | 0.638428i | \(-0.220415\pi\) | ||||
0.769682 | + | 0.638428i | \(0.220415\pi\) | |||||||
\(840\) | −4.68466 | + | 26.0540i | −0.161636 | + | 0.898948i | ||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 25.6294i | 0.883246i | ||||||||
\(843\) | 22.2942 | 0.767854 | ||||||||
\(844\) | 10.2462 | 0.352689 | ||||||||
\(845\) | −10.8265 | −0.372444 | ||||||||
\(846\) | 7.12311i | 0.244897i | ||||||||
\(847\) | 18.8691 | + | 3.39277i | 0.648349 | + | 0.116577i | ||||
\(848\) | 10.0054i | 0.343587i | ||||||||
\(849\) | − | 19.3697i | − | 0.664765i | ||||||
\(850\) | −20.4214 | −0.700447 | ||||||||
\(851\) | 8.49242 | + | 2.92456i | 0.291116 | + | 0.100253i | ||||
\(852\) | 11.1231i | 0.381071i | ||||||||
\(853\) | 8.00000i | 0.273915i | 0.990577 | + | 0.136957i | \(0.0437323\pi\) | ||||
−0.990577 | + | 0.136957i | \(0.956268\pi\) | |||||||
\(854\) | 4.87689 | + | 0.876894i | 0.166884 | + | 0.0300067i | ||||
\(855\) | −4.87689 | −0.166786 | ||||||||
\(856\) | 27.2069i | 0.929913i | ||||||||
\(857\) | − | 33.3693i | − | 1.13987i | −0.821688 | − | 0.569937i | \(-0.806968\pi\) | ||
0.821688 | − | 0.569937i | \(-0.193032\pi\) | |||||||
\(858\) | − | 13.3405i | − | 0.455438i | ||||||
\(859\) | − | 12.0000i | − | 0.409435i | −0.978821 | − | 0.204717i | \(-0.934372\pi\) | ||
0.978821 | − | 0.204717i | \(-0.0656275\pi\) | |||||||
\(860\) | 3.12311i | 0.106497i | ||||||||
\(861\) | 28.9645 | + | 5.20798i | 0.987107 | + | 0.177488i | ||||
\(862\) | − | 28.8492i | − | 0.982608i | ||||||
\(863\) | −56.0000 | −1.90626 | −0.953131 | − | 0.302558i | \(-0.902160\pi\) | ||||
−0.953131 | + | 0.302558i | \(0.902160\pi\) | |||||||
\(864\) | 5.00000i | 0.170103i | ||||||||
\(865\) | 10.4160i | 0.354154i | ||||||||
\(866\) | 18.1379 | 0.616352 | ||||||||
\(867\) | − | 5.87689i | − | 0.199590i | ||||||
\(868\) | 4.79741 | − | 26.6811i | 0.162835 | − | 0.905614i | ||||
\(869\) | 68.9848 | 2.34015 | ||||||||
\(870\) | 27.5022i | 0.932412i | ||||||||
\(871\) | −14.6228 | −0.495474 | ||||||||
\(872\) | 36.8665i | 1.24846i | ||||||||
\(873\) | 1.87285 | 0.0633865 | ||||||||
\(874\) | 2.28343 | − | 6.63068i | 0.0772380 | − | 0.224286i | ||||
\(875\) | 9.75379 | + | 1.75379i | 0.329738 | + | 0.0592889i | ||||
\(876\) | −6.24621 | −0.211040 | ||||||||
\(877\) | −7.75379 | −0.261827 | −0.130913 | − | 0.991394i | \(-0.541791\pi\) | ||||
−0.130913 | + | 0.991394i | \(0.541791\pi\) | |||||||
\(878\) | − | 21.7538i | − | 0.734155i | ||||||
\(879\) | − | 9.18425i | − | 0.309777i | ||||||
\(880\) | 14.2462i | 0.480240i | ||||||||
\(881\) | −2.51398 | −0.0846983 | −0.0423492 | − | 0.999103i | \(-0.513484\pi\) | ||||
−0.0423492 | + | 0.999103i | \(0.513484\pi\) | |||||||
\(882\) | 6.56155 | + | 2.43845i | 0.220939 | + | 0.0821068i | ||||
\(883\) | 24.4924 | 0.824236 | 0.412118 | − | 0.911131i | \(-0.364789\pi\) | ||||
0.412118 | + | 0.911131i | \(0.364789\pi\) | |||||||
\(884\) | 10.4160i | 0.350327i | ||||||||
\(885\) | −23.7565 | −0.798566 | ||||||||
\(886\) | −29.3693 | −0.986681 | ||||||||
\(887\) | − | 49.8617i | − | 1.67419i | −0.547055 | − | 0.837097i | \(-0.684251\pi\) | ||
0.547055 | − | 0.837097i | \(-0.315749\pi\) | |||||||
\(888\) | −5.61856 | −0.188546 | ||||||||
\(889\) | 16.2651 | + | 2.92456i | 0.545513 | + | 0.0980865i | ||||
\(890\) | −33.3693 | −1.11854 | ||||||||
\(891\) | 4.27156i | 0.143103i | ||||||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | − | 10.4160i | − | 0.348557i | ||||||
\(894\) | −0.410574 | −0.0137316 | ||||||||
\(895\) | 13.3405 | 0.445925 | ||||||||
\(896\) | −7.81198 | − | 1.40464i | −0.260980 | − | 0.0469257i | ||||
\(897\) | 4.87689 | − | 14.1617i | 0.162835 | − | 0.472845i | ||||
\(898\) | −1.50758 | −0.0503085 | ||||||||
\(899\) | − | 84.4924i | − | 2.81798i | ||||||
\(900\) | 6.12311 | 0.204104 | ||||||||
\(901\) | − | 33.3693i | − | 1.11169i | ||||||
\(902\) | 47.5130 | 1.58201 | ||||||||
\(903\) | 2.43845 | + | 0.438447i | 0.0811464 | + | 0.0145906i | ||||
\(904\) | − | 26.8611i | − | 0.893386i | ||||||
\(905\) | −40.9848 | −1.36238 | ||||||||
\(906\) | 20.4924i | 0.680815i | ||||||||
\(907\) | 38.0335i | 1.26288i | 0.775425 | + | 0.631440i | \(0.217536\pi\) | ||||
−0.775425 | + | 0.631440i | \(0.782464\pi\) | |||||||
\(908\) | −6.67026 | −0.221360 | ||||||||
\(909\) | − | 3.12311i | − | 0.103587i | ||||||
\(910\) | −4.87689 | + | 27.1231i | −0.161667 | + | 0.899122i | ||||
\(911\) | − | 15.5087i | − | 0.513825i | −0.966435 | − | 0.256913i | \(-0.917295\pi\) | ||
0.966435 | − | 0.256913i | \(-0.0827053\pi\) | |||||||
\(912\) | 1.46228i | 0.0484209i | ||||||||
\(913\) | 72.9848i | 2.41545i | ||||||||
\(914\) | 29.6056i | 0.979267i | ||||||||
\(915\) | − | 6.24621i | − | 0.206493i | ||||||
\(916\) | −12.2888 | −0.406034 | ||||||||
\(917\) | −5.61856 | + | 31.2479i | −0.185541 | + | 1.03190i | ||||
\(918\) | 3.33513i | 0.110076i | ||||||||
\(919\) | 0.936426i | 0.0308899i | 0.999881 | + | 0.0154449i | \(0.00491647\pi\) | ||||
−0.999881 | + | 0.0154449i | \(0.995084\pi\) | |||||||
\(920\) | −15.6240 | + | 45.3693i | −0.515107 | + | 1.49578i | ||||
\(921\) | 2.24621 | 0.0740152 | ||||||||
\(922\) | − | 9.36932i | − | 0.308562i | ||||||
\(923\) | 34.7386i | 1.14344i | ||||||||
\(924\) | −11.1231 | − | 2.00000i | −0.365923 | − | 0.0657952i | ||||
\(925\) | 11.4677i | 0.377055i | ||||||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | −5.20798 | −0.171053 | ||||||||
\(928\) | −41.2311 | −1.35348 | ||||||||
\(929\) | 27.1231i | 0.889880i | 0.895560 | + | 0.444940i | \(0.146775\pi\) | ||||
−0.895560 | + | 0.444940i | \(0.853225\pi\) | |||||||
\(930\) | 34.1725 | 1.12056 | ||||||||
\(931\) | −9.59482 | − | 3.56569i | −0.314458 | − | 0.116861i | ||||
\(932\) | 3.75379 | 0.122959 | ||||||||
\(933\) | 2.63068 | 0.0861247 | ||||||||
\(934\) | −6.67026 | −0.218258 | ||||||||
\(935\) | − | 47.5130i | − | 1.55384i | ||||||
\(936\) | 9.36932i | 0.306246i | ||||||||
\(937\) | 35.2242 | 1.15072 | 0.575362 | − | 0.817899i | \(-0.304861\pi\) | ||||
0.575362 | + | 0.817899i | \(0.304861\pi\) | |||||||
\(938\) | 2.19224 | − | 12.1922i | 0.0715790 | − | 0.398091i | ||||
\(939\) | 14.3922i | 0.469673i | ||||||||
\(940\) | 23.7565i | 0.774852i | ||||||||
\(941\) | −40.4322 | −1.31805 | −0.659025 | − | 0.752121i | \(-0.729031\pi\) | ||||
−0.659025 | + | 0.752121i | \(0.729031\pi\) | |||||||
\(942\) | − | 15.2134i | − | 0.495679i | ||||||
\(943\) | 50.4376 | + | 17.3693i | 1.64247 | + | 0.565623i | ||||
\(944\) | 7.12311i | 0.231837i | ||||||||
\(945\) | 1.56155 | − | 8.68466i | 0.0507973 | − | 0.282512i | ||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 32.4924 | 1.05586 | 0.527931 | − | 0.849287i | \(-0.322968\pi\) | ||||
0.527931 | + | 0.849287i | \(0.322968\pi\) | |||||||
\(948\) | −16.1498 | −0.524521 | ||||||||
\(949\) | −19.5076 | −0.633243 | ||||||||
\(950\) | 8.95369 | 0.290496 | ||||||||
\(951\) | − | 14.0000i | − | 0.453981i | ||||||
\(952\) | −26.0540 | − | 4.68466i | −0.844414 | − | 0.151831i | ||||
\(953\) | − | 10.2360i | − | 0.331575i | −0.986161 | − | 0.165788i | \(-0.946983\pi\) | ||
0.986161 | − | 0.165788i | \(-0.0530166\pi\) | |||||||
\(954\) | − | 10.0054i | − | 0.323937i | ||||||
\(955\) | − | 11.5076i | − | 0.372376i | ||||||
\(956\) | 1.36932 | 0.0442869 | ||||||||
\(957\) | −35.2242 | −1.13864 | ||||||||
\(958\) | 5.84912 | 0.188976 | ||||||||
\(959\) | −6.93087 | + | 38.5464i | −0.223809 | + | 1.24473i | ||||
\(960\) | − | 23.3459i | − | 0.753486i | ||||||
\(961\) | −73.9848 | −2.38661 | ||||||||
\(962\) | −5.84912 | −0.188583 | ||||||||
\(963\) | − | 9.06897i | − | 0.292243i | ||||||
\(964\) | −11.4677 | −0.369349 | ||||||||
\(965\) | −85.4312 | −2.75013 | ||||||||
\(966\) | 11.0766 | + | 6.18938i | 0.356385 | + | 0.199140i | ||||
\(967\) | 24.0000 | 0.771788 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(968\) | −21.7386 | −0.698706 | ||||||||
\(969\) | − | 4.87689i | − | 0.156668i | ||||||
\(970\) | −6.24621 | −0.200554 | ||||||||
\(971\) | −6.67026 | −0.214059 | −0.107029 | − | 0.994256i | \(-0.534134\pi\) | ||||
−0.107029 | + | 0.994256i | \(0.534134\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −5.61856 | + | 31.2479i | −0.180123 | + | 1.00176i | ||||
\(974\) | 14.2462 | 0.456478 | ||||||||
\(975\) | 19.1231 | 0.612430 | ||||||||
\(976\) | −1.87285 | −0.0599486 | ||||||||
\(977\) | 27.3222i | 0.874114i | 0.899434 | + | 0.437057i | \(0.143979\pi\) | ||||
−0.899434 | + | 0.437057i | \(0.856021\pi\) | |||||||
\(978\) | − | 12.0000i | − | 0.383718i | ||||||
\(979\) | − | 42.7386i | − | 1.36593i | ||||||
\(980\) | 21.8836 | + | 8.13254i | 0.699047 | + | 0.259785i | ||||
\(981\) | − | 12.2888i | − | 0.392352i | ||||||
\(982\) | 32.4924 | 1.03687 | ||||||||
\(983\) | −49.1553 | −1.56781 | −0.783905 | − | 0.620881i | \(-0.786775\pi\) | ||||
−0.783905 | + | 0.620881i | \(0.786775\pi\) | |||||||
\(984\) | −33.3693 | −1.06377 | ||||||||
\(985\) | −61.6747 | −1.96512 | ||||||||
\(986\) | −27.5022 | −0.875849 | ||||||||
\(987\) | 18.5485 | + | 3.33513i | 0.590406 | + | 0.106158i | ||||
\(988\) | − | 4.56685i | − | 0.145291i | ||||||
\(989\) | 4.24621 | + | 1.46228i | 0.135022 | + | 0.0464978i | ||||
\(990\) | − | 14.2462i | − | 0.452774i | ||||||
\(991\) | −36.4924 | −1.15922 | −0.579610 | − | 0.814894i | \(-0.696795\pi\) | ||||
−0.579610 | + | 0.814894i | \(0.696795\pi\) | |||||||
\(992\) | 51.2311i | 1.62659i | ||||||||
\(993\) | − | 16.4924i | − | 0.523371i | ||||||
\(994\) | −28.9645 | − | 5.20798i | −0.918698 | − | 0.165187i | ||||
\(995\) | −17.3693 | −0.550644 | ||||||||
\(996\) | − | 17.0862i | − | 0.541398i | ||||||
\(997\) | 44.8769i | 1.42127i | 0.703563 | + | 0.710633i | \(0.251591\pi\) | ||||
−0.703563 | + | 0.710633i | \(0.748409\pi\) | |||||||
\(998\) | −5.75379 | −0.182133 | ||||||||
\(999\) | 1.87285 | 0.0592544 |
(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 | 483.2.h.a.160.5 | yes | 8 | |
3.2 | odd | 2 | 1449.2.h.d.1126.7 | 8 | |||
7.6 | odd | 2 | inner | 483.2.h.a.160.4 | yes | 8 | |
21.20 | even | 2 | 1449.2.h.d.1126.1 | 8 | |||
23.22 | odd | 2 | inner | 483.2.h.a.160.8 | yes | 8 | |
69.68 | even | 2 | 1449.2.h.d.1126.2 | 8 | |||
161.160 | even | 2 | inner | 483.2.h.a.160.1 | ✓ | 8 | |
483.482 | odd | 2 | 1449.2.h.d.1126.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.a.160.1 | ✓ | 8 | 161.160 | even | 2 | inner | |
483.2.h.a.160.4 | yes | 8 | 7.6 | odd | 2 | inner | |
483.2.h.a.160.5 | yes | 8 | 1.1 | even | 1 | trivial | |
483.2.h.a.160.8 | yes | 8 | 23.22 | odd | 2 | inner | |
1449.2.h.d.1126.1 | 8 | 21.20 | even | 2 | |||
1449.2.h.d.1126.2 | 8 | 69.68 | even | 2 | |||
1449.2.h.d.1126.7 | 8 | 3.2 | odd | 2 | |||
1449.2.h.d.1126.8 | 8 | 483.482 | odd | 2 |