Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.32 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.c.323.31 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.40936 | + | 0.117111i | 0.996565 | + | 0.0828097i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.97257 | + | 0.330101i | 0.986285 | + | 0.165051i | ||||
\(5\) | −1.17792 | −0.526780 | −0.263390 | − | 0.964689i | \(-0.584841\pi\) | ||||
−0.263390 | + | 0.964689i | \(0.584841\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.74140 | + | 0.696239i | 0.969230 | + | 0.246158i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.66010 | − | 0.137947i | −0.524971 | − | 0.0436225i | ||||
\(11\) | 2.90595i | 0.876176i | 0.898932 | + | 0.438088i | \(0.144344\pi\) | ||||
−0.898932 | + | 0.438088i | \(0.855656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.05317i | 0.292096i | 0.989278 | + | 0.146048i | \(0.0466554\pi\) | ||||
−0.989278 | + | 0.146048i | \(0.953345\pi\) | |||||||
\(14\) | −0.117111 | + | 1.40936i | −0.0312991 | + | 0.376666i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.78207 | + | 1.30230i | 0.945517 | + | 0.325574i | ||||
\(17\) | 6.48837i | 1.57366i | 0.617169 | + | 0.786830i | \(0.288279\pi\) | ||||
−0.617169 | + | 0.786830i | \(0.711721\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.11597 | −0.714853 | −0.357426 | − | 0.933941i | \(-0.616346\pi\) | ||||
−0.357426 | + | 0.933941i | \(0.616346\pi\) | |||||||
\(20\) | −2.32352 | − | 0.388832i | −0.519556 | − | 0.0869454i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.340317 | + | 4.09552i | −0.0725559 | + | 0.873167i | ||||
\(23\) | 0.812516 | 0.169421 | 0.0847107 | − | 0.996406i | \(-0.473003\pi\) | ||||
0.0847107 | + | 0.996406i | \(0.473003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.61251 | −0.722503 | ||||||||
\(26\) | −0.123337 | + | 1.48429i | −0.0241884 | + | 0.291093i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.330101 | + | 1.97257i | −0.0623832 | + | 0.372781i | ||||
\(29\) | 4.03607 | 0.749480 | 0.374740 | − | 0.927130i | \(-0.377732\pi\) | ||||
0.374740 | + | 0.927130i | \(0.377732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.108779i | 0.0195372i | 0.999952 | + | 0.00976861i | \(0.00310949\pi\) | ||||
−0.999952 | + | 0.00976861i | \(0.996891\pi\) | |||||||
\(32\) | 5.17777 | + | 2.27832i | 0.915308 | + | 0.402754i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.759857 | + | 9.14442i | −0.130314 | + | 1.56826i | ||||
\(35\) | − | 1.17792i | − | 0.199104i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.97034i | − | 1.63911i | −0.572998 | − | 0.819557i | \(-0.694220\pi\) | ||
0.572998 | − | 0.819557i | \(-0.305780\pi\) | |||||||
\(38\) | −4.39151 | − | 0.364913i | −0.712397 | − | 0.0591967i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.22914 | − | 0.820111i | −0.510571 | − | 0.129671i | ||||
\(41\) | 9.44298i | 1.47475i | 0.675486 | + | 0.737373i | \(0.263934\pi\) | ||||
−0.675486 | + | 0.737373i | \(0.736066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.3446 | 1.57754 | 0.788770 | − | 0.614688i | \(-0.210718\pi\) | ||||
0.788770 | + | 0.614688i | \(0.210718\pi\) | |||||||
\(44\) | −0.959257 | + | 5.73219i | −0.144613 | + | 0.864160i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.14512 | + | 0.0951542i | 0.168839 | + | 0.0140297i | ||||
\(47\) | 4.03126 | 0.588019 | 0.294010 | − | 0.955802i | \(-0.405010\pi\) | ||||
0.294010 | + | 0.955802i | \(0.405010\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −5.09132 | − | 0.423064i | −0.720021 | − | 0.0598302i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.347652 | + | 2.07745i | −0.0482106 | + | 0.288090i | ||||
\(53\) | 2.97772 | 0.409022 | 0.204511 | − | 0.978864i | \(-0.434440\pi\) | ||||
0.204511 | + | 0.978864i | \(0.434440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.42296i | − | 0.461552i | ||||||
\(56\) | −0.696239 | + | 2.74140i | −0.0930388 | + | 0.366334i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.68827 | + | 0.472667i | 0.746906 | + | 0.0620642i | ||||
\(59\) | 0.868874i | 0.113118i | 0.998399 | + | 0.0565589i | \(0.0180129\pi\) | ||||
−0.998399 | + | 0.0565589i | \(0.981987\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.33629i | 0.683242i | 0.939838 | + | 0.341621i | \(0.110976\pi\) | ||||
−0.939838 | + | 0.341621i | \(0.889024\pi\) | |||||||
\(62\) | −0.0127391 | + | 0.153308i | −0.00161787 | + | 0.0194701i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.03050 | + | 3.81733i | 0.878813 | + | 0.477167i | ||||
\(65\) | − | 1.24054i | − | 0.153870i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.97987 | −0.486218 | −0.243109 | − | 0.969999i | \(-0.578167\pi\) | ||||
−0.243109 | + | 0.969999i | \(0.578167\pi\) | |||||||
\(68\) | −2.14182 | + | 12.7988i | −0.259734 | + | 1.55208i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.137947 | − | 1.66010i | 0.0164878 | − | 0.198420i | ||||
\(71\) | −0.844302 | −0.100200 | −0.0501001 | − | 0.998744i | \(-0.515954\pi\) | ||||
−0.0501001 | + | 0.998744i | \(0.515954\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.59513 | 0.420778 | 0.210389 | − | 0.977618i | \(-0.432527\pi\) | ||||
0.210389 | + | 0.977618i | \(0.432527\pi\) | |||||||
\(74\) | 1.16763 | − | 14.0518i | 0.135734 | − | 1.63348i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.14647 | − | 1.02859i | −0.705048 | − | 0.117987i | ||||
\(77\) | −2.90595 | −0.331164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.48320i | 1.06694i | 0.845818 | + | 0.533472i | \(0.179113\pi\) | ||||
−0.845818 | + | 0.533472i | \(0.820887\pi\) | |||||||
\(80\) | −4.45496 | − | 1.53400i | −0.498080 | − | 0.171506i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.10587 | + | 13.3085i | −0.122123 | + | 1.46968i | ||||
\(83\) | − | 2.71280i | − | 0.297769i | −0.988855 | − | 0.148884i | \(-0.952432\pi\) | ||
0.988855 | − | 0.148884i | \(-0.0475682\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.64276i | − | 0.828973i | ||||||
\(86\) | 14.5793 | + | 1.21146i | 1.57212 | + | 0.130636i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.02323 | + | 7.96636i | −0.215678 | + | 0.849216i | ||||
\(89\) | − | 2.22575i | − | 0.235930i | −0.993018 | − | 0.117965i | \(-0.962363\pi\) | ||
0.993018 | − | 0.117965i | \(-0.0376370\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.05317 | −0.110402 | ||||||||
\(92\) | 1.60275 | + | 0.268212i | 0.167098 | + | 0.0279631i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.68148 | + | 0.472103i | 0.586000 | + | 0.0486937i | ||||
\(95\) | 3.67035 | 0.376570 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.93019 | −0.399050 | −0.199525 | − | 0.979893i | \(-0.563940\pi\) | ||||
−0.199525 | + | 0.979893i | \(0.563940\pi\) | |||||||
\(98\) | −1.40936 | − | 0.117111i | −0.142366 | − | 0.0118300i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.12593 | − | 1.19249i | −0.712593 | − | 0.119249i | ||||
\(101\) | −18.0700 | −1.79803 | −0.899016 | − | 0.437915i | \(-0.855717\pi\) | ||||
−0.899016 | + | 0.437915i | \(0.855717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.8616i | − | 1.75995i | −0.475017 | − | 0.879977i | \(-0.657558\pi\) | ||
0.475017 | − | 0.879977i | \(-0.342442\pi\) | |||||||
\(104\) | −0.733256 | + | 2.88715i | −0.0719016 | + | 0.283108i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.19667 | + | 0.348723i | 0.407617 | + | 0.0338709i | ||||
\(107\) | − | 7.67720i | − | 0.742183i | −0.928596 | − | 0.371091i | \(-0.878984\pi\) | ||
0.928596 | − | 0.371091i | \(-0.121016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.6991i | − | 1.21635i | −0.793801 | − | 0.608177i | \(-0.791901\pi\) | ||
0.793801 | − | 0.608177i | \(-0.208099\pi\) | |||||||
\(110\) | 0.400865 | − | 4.82418i | 0.0382210 | − | 0.459967i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.30230 | + | 3.78207i | −0.123055 | + | 0.357372i | ||||
\(113\) | 15.4017i | 1.44887i | 0.689342 | + | 0.724437i | \(0.257900\pi\) | ||||
−0.689342 | + | 0.724437i | \(0.742100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.957076 | −0.0892478 | ||||||||
\(116\) | 7.96144 | + | 1.33231i | 0.739201 | + | 0.123702i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.101754 | + | 1.22455i | −0.00936725 | + | 0.112729i | ||||
\(119\) | −6.48837 | −0.594788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.55546 | 0.232315 | ||||||||
\(122\) | −0.624936 | + | 7.52074i | −0.0565791 | + | 0.680896i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.0359079 | + | 0.214573i | −0.00322463 | + | 0.0192693i | ||||
\(125\) | 10.1448 | 0.907380 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.1514i | − | 1.52194i | −0.648787 | − | 0.760970i | \(-0.724724\pi\) | ||
0.648787 | − | 0.760970i | \(-0.275276\pi\) | |||||||
\(128\) | 9.46143 | + | 6.20333i | 0.836280 | + | 0.548302i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.145281 | − | 1.74837i | 0.0127420 | − | 0.153342i | ||||
\(131\) | − | 10.5118i | − | 0.918421i | −0.888328 | − | 0.459210i | \(-0.848132\pi\) | ||
0.888328 | − | 0.459210i | \(-0.151868\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 3.11597i | − | 0.270189i | ||||||
\(134\) | −5.60905 | − | 0.466084i | −0.484548 | − | 0.0402636i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.51745 | + | 17.7872i | −0.387369 | + | 1.52524i | ||||
\(137\) | 13.6268i | 1.16422i | 0.813110 | + | 0.582110i | \(0.197773\pi\) | ||||
−0.813110 | + | 0.582110i | \(0.802227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.37620 | −0.456003 | −0.228002 | − | 0.973661i | \(-0.573219\pi\) | ||||
−0.228002 | + | 0.973661i | \(0.573219\pi\) | |||||||
\(140\) | 0.388832 | − | 2.32352i | 0.0328623 | − | 0.196374i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.18992 | − | 0.0988767i | −0.0998560 | − | 0.00829755i | ||||
\(143\) | −3.06045 | −0.255928 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.75416 | −0.394811 | ||||||||
\(146\) | 5.06681 | + | 0.421027i | 0.419332 | + | 0.0348445i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.29122 | − | 19.6672i | 0.270537 | − | 1.61663i | ||||
\(149\) | 17.3187 | 1.41880 | 0.709401 | − | 0.704805i | \(-0.248965\pi\) | ||||
0.709401 | + | 0.704805i | \(0.248965\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.50773i | − | 0.366834i | −0.983035 | − | 0.183417i | \(-0.941284\pi\) | ||
0.983035 | − | 0.183417i | \(-0.0587158\pi\) | |||||||
\(152\) | −8.54211 | − | 2.16946i | −0.692856 | − | 0.175966i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.09552 | − | 0.340317i | −0.330026 | − | 0.0274236i | ||||
\(155\) | − | 0.128132i | − | 0.0102918i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.84696i | − | 0.706064i | −0.935611 | − | 0.353032i | \(-0.885151\pi\) | ||
0.935611 | − | 0.353032i | \(-0.114849\pi\) | |||||||
\(158\) | −1.11058 | + | 13.3652i | −0.0883533 | + | 1.06328i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.09898 | − | 2.68367i | −0.482166 | − | 0.212163i | ||||
\(161\) | 0.812516i | 0.0640352i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.38238 | −0.656558 | −0.328279 | − | 0.944581i | \(-0.606469\pi\) | ||||
−0.328279 | + | 0.944581i | \(0.606469\pi\) | |||||||
\(164\) | −3.11714 | + | 18.6269i | −0.243408 | + | 1.45452i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.317698 | − | 3.82331i | 0.0246582 | − | 0.296746i | ||||
\(167\) | −8.93563 | −0.691460 | −0.345730 | − | 0.938334i | \(-0.612369\pi\) | ||||
−0.345730 | + | 0.938334i | \(0.612369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8908 | 0.914680 | ||||||||
\(170\) | 0.895048 | − | 10.7714i | 0.0686470 | − | 0.826126i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 20.4055 | + | 3.41477i | 1.55590 | + | 0.260374i | ||||
\(173\) | 14.1612 | 1.07666 | 0.538328 | − | 0.842736i | \(-0.319056\pi\) | ||||
0.538328 | + | 0.842736i | \(0.319056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.61251i | − | 0.273080i | ||||||
\(176\) | −3.78440 | + | 10.9905i | −0.285260 | + | 0.828439i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.260659 | − | 3.13688i | 0.0195373 | − | 0.235119i | ||||
\(179\) | − | 20.3695i | − | 1.52249i | −0.648467 | − | 0.761243i | \(-0.724589\pi\) | ||
0.648467 | − | 0.761243i | \(-0.275411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.2659i | − | 1.35770i | −0.734279 | − | 0.678848i | \(-0.762480\pi\) | ||
0.734279 | − | 0.678848i | \(-0.237520\pi\) | |||||||
\(182\) | −1.48429 | − | 0.123337i | −0.110023 | − | 0.00914235i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.22743 | + | 0.565705i | 0.164208 | + | 0.0417044i | ||||
\(185\) | 11.7442i | 0.863453i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.8549 | −1.37880 | ||||||||
\(188\) | 7.95194 | + | 1.33072i | 0.579955 | + | 0.0970529i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.17283 | + | 0.429837i | 0.375277 | + | 0.0311837i | ||||
\(191\) | 7.83849 | 0.567173 | 0.283587 | − | 0.958947i | \(-0.408476\pi\) | ||||
0.283587 | + | 0.958947i | \(0.408476\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0241 | −0.937498 | −0.468749 | − | 0.883331i | \(-0.655295\pi\) | ||||
−0.468749 | + | 0.883331i | \(0.655295\pi\) | |||||||
\(194\) | −5.53903 | − | 0.460266i | −0.397679 | − | 0.0330452i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.97257 | − | 0.330101i | −0.140898 | − | 0.0235786i | ||||
\(197\) | −14.9576 | −1.06568 | −0.532842 | − | 0.846215i | \(-0.678876\pi\) | ||||
−0.532842 | + | 0.846215i | \(0.678876\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 16.9147i | − | 1.19905i | −0.800356 | − | 0.599525i | \(-0.795356\pi\) | ||
0.800356 | − | 0.599525i | \(-0.204644\pi\) | |||||||
\(200\) | −9.90333 | − | 2.51517i | −0.700271 | − | 0.177850i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −25.4671 | − | 2.11619i | −1.79186 | − | 0.148895i | ||||
\(203\) | 4.03607i | 0.283277i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 11.1230i | − | 0.776867i | ||||||
\(206\) | 2.09178 | − | 25.1733i | 0.145741 | − | 1.75391i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.37153 | + | 3.98315i | −0.0950988 | + | 0.276182i | ||||
\(209\) | − | 9.05485i | − | 0.626337i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.68386 | 0.391293 | 0.195647 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195647 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(212\) | 5.87376 | + | 0.982949i | 0.403412 | + | 0.0675092i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.899081 | − | 10.8199i | 0.0614599 | − | 0.739633i | ||||
\(215\) | −12.1851 | −0.831017 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.108779 | −0.00738437 | ||||||||
\(218\) | 1.48720 | − | 17.8976i | 0.100726 | − | 1.21218i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.12992 | − | 6.75204i | 0.0761795 | − | 0.455222i | ||||
\(221\) | −6.83333 | −0.459660 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.43963i | 0.230335i | 0.993346 | + | 0.115167i | \(0.0367404\pi\) | ||||
−0.993346 | + | 0.115167i | \(0.963260\pi\) | |||||||
\(224\) | −2.27832 | + | 5.17777i | −0.152227 | + | 0.345954i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.80371 | + | 21.7065i | −0.119981 | + | 1.44390i | ||||
\(227\) | − | 8.86522i | − | 0.588406i | −0.955743 | − | 0.294203i | \(-0.904946\pi\) | ||
0.955743 | − | 0.294203i | \(-0.0950541\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.3653i | 1.14753i | 0.819019 | + | 0.573767i | \(0.194518\pi\) | ||||
−0.819019 | + | 0.573767i | \(0.805482\pi\) | |||||||
\(230\) | −1.34886 | − | 0.112084i | −0.0889413 | − | 0.00739058i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.0645 | + | 2.81007i | 0.726418 | + | 0.184490i | ||||
\(233\) | 9.99149i | 0.654564i | 0.944927 | + | 0.327282i | \(0.106133\pi\) | ||||
−0.944927 | + | 0.327282i | \(0.893867\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.74848 | −0.309757 | ||||||||
\(236\) | −0.286816 | + | 1.71392i | −0.0186702 | + | 0.111566i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.14442 | − | 0.759857i | −0.592745 | − | 0.0492542i | ||||
\(239\) | 24.5708 | 1.58935 | 0.794677 | − | 0.607032i | \(-0.207640\pi\) | ||||
0.794677 | + | 0.607032i | \(0.207640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.1786 | 1.49306 | 0.746532 | − | 0.665349i | \(-0.231717\pi\) | ||||
0.746532 | + | 0.665349i | \(0.231717\pi\) | |||||||
\(242\) | 3.60156 | + | 0.299272i | 0.231517 | + | 0.0192379i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.76152 | + | 10.5262i | −0.112769 | + | 0.673872i | ||||
\(245\) | 1.17792 | 0.0752543 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.28164i | − | 0.208806i | ||||||
\(248\) | −0.0757359 | + | 0.298205i | −0.00480924 | + | 0.0189361i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.2977 | + | 1.18807i | 0.904264 | + | 0.0751399i | ||||
\(251\) | − | 21.3670i | − | 1.34868i | −0.738423 | − | 0.674338i | \(-0.764429\pi\) | ||
0.738423 | − | 0.674338i | \(-0.235571\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.36113i | 0.148443i | ||||||||
\(254\) | 2.00861 | − | 24.1724i | 0.126031 | − | 1.51671i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.6081 | + | 9.85073i | 0.788003 | + | 0.615671i | ||||
\(257\) | 29.5594i | 1.84386i | 0.387352 | + | 0.921932i | \(0.373390\pi\) | ||||
−0.387352 | + | 0.921932i | \(0.626610\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.97034 | 0.619527 | ||||||||
\(260\) | 0.409504 | − | 2.44706i | 0.0253964 | − | 0.151760i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.23104 | − | 14.8149i | 0.0760542 | − | 0.915266i | ||||
\(263\) | −15.8001 | −0.974277 | −0.487139 | − | 0.873325i | \(-0.661959\pi\) | ||||
−0.487139 | + | 0.873325i | \(0.661959\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.50751 | −0.215464 | ||||||||
\(266\) | 0.364913 | − | 4.39151i | 0.0223743 | − | 0.269261i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.85056 | − | 1.31376i | −0.479550 | − | 0.0802505i | ||||
\(269\) | −6.41502 | −0.391131 | −0.195565 | − | 0.980691i | \(-0.562654\pi\) | ||||
−0.195565 | + | 0.980691i | \(0.562654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0927686i | 0.00563529i | 0.999996 | + | 0.00281765i | \(0.000896886\pi\) | ||||
−0.999996 | + | 0.00281765i | \(0.999103\pi\) | |||||||
\(272\) | −8.44977 | + | 24.5394i | −0.512343 | + | 1.48792i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.59585 | + | 19.2051i | −0.0964087 | + | 1.16022i | ||||
\(275\) | − | 10.4978i | − | 0.633040i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.7900i | 1.18907i | 0.804071 | + | 0.594534i | \(0.202663\pi\) | ||||
−0.804071 | + | 0.594534i | \(0.797337\pi\) | |||||||
\(278\) | −7.57698 | − | 0.629610i | −0.454437 | − | 0.0377615i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.820111 | − | 3.22914i | 0.0490110 | − | 0.192978i | ||||
\(281\) | − | 14.4404i | − | 0.861443i | −0.902485 | − | 0.430721i | \(-0.858259\pi\) | ||
0.902485 | − | 0.430721i | \(-0.141741\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3759 | 1.21122 | 0.605612 | − | 0.795760i | \(-0.292929\pi\) | ||||
0.605612 | + | 0.795760i | \(0.292929\pi\) | |||||||
\(284\) | −1.66544 | − | 0.278705i | −0.0988259 | − | 0.0165381i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.31326 | − | 0.358411i | −0.255049 | − | 0.0211933i | ||||
\(287\) | −9.44298 | −0.557402 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −25.0989 | −1.47641 | ||||||||
\(290\) | −6.70030 | − | 0.556762i | −0.393455 | − | 0.0326942i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.09164 | + | 1.18675i | 0.415007 | + | 0.0694496i | ||||
\(293\) | 10.2919 | 0.601262 | 0.300631 | − | 0.953741i | \(-0.402803\pi\) | ||||
0.300631 | + | 0.953741i | \(0.402803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.02346i | − | 0.0595882i | ||||||
\(296\) | 6.94174 | − | 27.3326i | 0.403480 | − | 1.58868i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.4082 | + | 2.02820i | 1.41393 | + | 0.117491i | ||||
\(299\) | 0.855715i | 0.0494873i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3446i | 0.596254i | ||||||||
\(302\) | 0.527903 | − | 6.35300i | 0.0303774 | − | 0.365574i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.7848 | − | 4.05791i | −0.675905 | − | 0.232737i | ||||
\(305\) | − | 6.28571i | − | 0.359919i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.8799 | 1.13461 | 0.567304 | − | 0.823508i | \(-0.307986\pi\) | ||||
0.567304 | + | 0.823508i | \(0.307986\pi\) | |||||||
\(308\) | −5.73219 | − | 0.959257i | −0.326622 | − | 0.0546587i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.0150056 | − | 0.180584i | 0.000852263 | − | 0.0102565i | ||||
\(311\) | −7.94464 | −0.450499 | −0.225250 | − | 0.974301i | \(-0.572320\pi\) | ||||
−0.225250 | + | 0.974301i | \(0.572320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.2451 | −1.59651 | −0.798254 | − | 0.602321i | \(-0.794243\pi\) | ||||
−0.798254 | + | 0.602321i | \(0.794243\pi\) | |||||||
\(314\) | 1.03607 | − | 12.4685i | 0.0584689 | − | 0.703639i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.13042 | + | 18.7063i | −0.176100 | + | 1.05231i | ||||
\(317\) | 13.8609 | 0.778506 | 0.389253 | − | 0.921131i | \(-0.372733\pi\) | ||||
0.389253 | + | 0.921131i | \(0.372733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7286i | 0.656677i | ||||||||
\(320\) | −8.28135 | − | 4.49650i | −0.462941 | − | 0.251362i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0951542 | + | 1.14512i | −0.00530274 | + | 0.0638153i | ||||
\(323\) | − | 20.2176i | − | 1.12494i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.80458i | − | 0.211040i | ||||||
\(326\) | −11.8138 | − | 0.981665i | −0.654303 | − | 0.0543694i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.57457 | + | 25.8869i | −0.363020 | + | 1.42937i | ||||
\(329\) | 4.03126i | 0.222250i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5450 | −0.799468 | −0.399734 | − | 0.916631i | \(-0.630897\pi\) | ||||
−0.399734 | + | 0.916631i | \(0.630897\pi\) | |||||||
\(332\) | 0.895500 | − | 5.35120i | 0.0491469 | − | 0.293685i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.5935 | − | 1.04646i | −0.689085 | − | 0.0572596i | ||||
\(335\) | 4.68795 | 0.256130 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.26170 | 0.286623 | 0.143312 | − | 0.989678i | \(-0.454225\pi\) | ||||
0.143312 | + | 0.989678i | \(0.454225\pi\) | |||||||
\(338\) | 16.7584 | + | 1.39254i | 0.911538 | + | 0.0757444i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.52288 | − | 15.0759i | 0.136823 | − | 0.817604i | ||||
\(341\) | −0.316105 | −0.0171181 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 28.3587 | + | 7.20233i | 1.52900 | + | 0.388324i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.9582 | + | 1.65843i | 1.07296 | + | 0.0891575i | ||||
\(347\) | − | 15.5549i | − | 0.835029i | −0.908670 | − | 0.417514i | \(-0.862901\pi\) | ||
0.908670 | − | 0.417514i | \(-0.137099\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1607i | 0.918594i | 0.888283 | + | 0.459297i | \(0.151899\pi\) | ||||
−0.888283 | + | 0.459297i | \(0.848101\pi\) | |||||||
\(350\) | 0.423064 | − | 5.09132i | 0.0226137 | − | 0.272142i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.62067 | + | 15.0463i | −0.352883 | + | 0.801972i | ||||
\(353\) | − | 15.5438i | − | 0.827314i | −0.910433 | − | 0.413657i | \(-0.864251\pi\) | ||
0.910433 | − | 0.413657i | \(-0.135749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.994517 | 0.0527835 | ||||||||
\(356\) | 0.734724 | − | 4.39046i | 0.0389403 | − | 0.232694i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.38548 | − | 28.7078i | 0.126077 | − | 1.51726i | ||||
\(359\) | 14.9471 | 0.788876 | 0.394438 | − | 0.918923i | \(-0.370939\pi\) | ||||
0.394438 | + | 0.918923i | \(0.370939\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.29073 | −0.488986 | ||||||||
\(362\) | 2.13913 | − | 25.7432i | 0.112430 | − | 1.35303i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.07745 | − | 0.347652i | −0.108888 | − | 0.0182219i | ||||
\(365\) | −4.23476 | −0.221657 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.86184i | − | 0.149387i | −0.997207 | − | 0.0746934i | \(-0.976202\pi\) | ||
0.997207 | − | 0.0746934i | \(-0.0237978\pi\) | |||||||
\(368\) | 3.07299 | + | 1.05814i | 0.160191 | + | 0.0551591i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.37537 | + | 16.5518i | −0.0715023 | + | 0.860487i | ||||
\(371\) | 2.97772i | 0.154596i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.7327i | 1.07350i | 0.843743 | + | 0.536748i | \(0.180347\pi\) | ||||
−0.843743 | + | 0.536748i | \(0.819653\pi\) | |||||||
\(374\) | −26.5732 | − | 2.20810i | −1.37407 | − | 0.114178i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.0513 | + | 2.80672i | 0.569926 | + | 0.144745i | ||||
\(377\) | 4.25066i | 0.218920i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1561 | 1.44628 | 0.723141 | − | 0.690700i | \(-0.242698\pi\) | ||||
0.723141 | + | 0.690700i | \(0.242698\pi\) | |||||||
\(380\) | 7.24003 | + | 1.21159i | 0.371406 | + | 0.0621531i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.0472 | + | 0.917970i | 0.565225 | + | 0.0469675i | ||||
\(383\) | −29.9733 | −1.53156 | −0.765781 | − | 0.643101i | \(-0.777648\pi\) | ||||
−0.765781 | + | 0.643101i | \(0.777648\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.42296 | 0.174450 | ||||||||
\(386\) | −18.3556 | − | 1.52526i | −0.934278 | − | 0.0776339i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.75257 | − | 1.29736i | −0.393577 | − | 0.0658634i | ||||
\(389\) | −29.4931 | −1.49536 | −0.747679 | − | 0.664060i | \(-0.768832\pi\) | ||||
−0.747679 | + | 0.664060i | \(0.768832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.27190i | 0.266612i | ||||||||
\(392\) | −2.74140 | − | 0.696239i | −0.138461 | − | 0.0351654i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.0806 | − | 1.75169i | −1.06202 | − | 0.0882489i | ||||
\(395\) | − | 11.1704i | − | 0.562045i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.0845i | − | 1.10839i | −0.832386 | − | 0.554196i | \(-0.813026\pi\) | ||
0.832386 | − | 0.554196i | \(-0.186974\pi\) | |||||||
\(398\) | 1.98089 | − | 23.8388i | 0.0992930 | − | 1.19493i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.6628 | − | 4.70456i | −0.683138 | − | 0.235228i | ||||
\(401\) | 7.42054i | 0.370564i | 0.982685 | + | 0.185282i | \(0.0593198\pi\) | ||||
−0.982685 | + | 0.185282i | \(0.940680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.114562 | −0.00570674 | ||||||||
\(404\) | −35.6443 | − | 5.96493i | −1.77337 | − | 0.296766i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.472667 | + | 5.68827i | −0.0234581 | + | 0.282304i | ||||
\(407\) | 28.9733 | 1.43615 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.3983 | 1.84923 | 0.924615 | − | 0.380904i | \(-0.124387\pi\) | ||||
0.924615 | + | 0.380904i | \(0.124387\pi\) | |||||||
\(410\) | 1.30263 | − | 15.6763i | 0.0643321 | − | 0.774199i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.89612 | − | 35.2332i | 0.290481 | − | 1.73582i | ||||
\(413\) | −0.868874 | −0.0427545 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.19546i | 0.156859i | ||||||||
\(416\) | −2.39945 | + | 5.45305i | −0.117643 | + | 0.267358i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.06042 | − | 12.7615i | 0.0518668 | − | 0.624186i | ||||
\(419\) | − | 8.55960i | − | 0.418164i | −0.977898 | − | 0.209082i | \(-0.932952\pi\) | ||
0.977898 | − | 0.209082i | \(-0.0670475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 6.56688i | − | 0.320050i | −0.987113 | − | 0.160025i | \(-0.948842\pi\) | ||
0.987113 | − | 0.160025i | \(-0.0511575\pi\) | |||||||
\(422\) | 8.01059 | + | 0.665640i | 0.389949 | + | 0.0324029i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.16311 | + | 2.07321i | 0.396436 | + | 0.100684i | ||||
\(425\) | − | 23.4393i | − | 1.13697i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.33629 | −0.258241 | ||||||||
\(428\) | 2.53425 | − | 15.1438i | 0.122498 | − | 0.732004i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.1731 | − | 1.42700i | −0.828163 | − | 0.0688163i | ||||
\(431\) | −5.61014 | −0.270231 | −0.135116 | − | 0.990830i | \(-0.543141\pi\) | ||||
−0.135116 | + | 0.990830i | \(0.543141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.96675 | 0.382857 | 0.191429 | − | 0.981507i | \(-0.438688\pi\) | ||||
0.191429 | + | 0.981507i | \(0.438688\pi\) | |||||||
\(434\) | −0.153308 | − | 0.0127391i | −0.00735901 | − | 0.000611498i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.19199 | − | 25.0499i | 0.200760 | − | 1.19967i | ||||
\(437\) | −2.53178 | −0.121111 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.9176i | 1.61880i | 0.587258 | + | 0.809400i | \(0.300208\pi\) | ||||
−0.587258 | + | 0.809400i | \(0.699792\pi\) | |||||||
\(440\) | 2.38320 | − | 9.38370i | 0.113615 | − | 0.447350i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.63060 | − | 0.800256i | −0.458081 | − | 0.0380643i | ||||
\(443\) | − | 6.31862i | − | 0.300207i | −0.988670 | − | 0.150103i | \(-0.952039\pi\) | ||
0.988670 | − | 0.150103i | \(-0.0479606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.62175i | 0.124283i | ||||||||
\(446\) | −0.402817 | + | 4.84767i | −0.0190740 | + | 0.229544i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.81733 | + | 7.03050i | −0.180352 | + | 0.332160i | ||||
\(449\) | 11.9562i | 0.564246i | 0.959378 | + | 0.282123i | \(0.0910387\pi\) | ||||
−0.959378 | + | 0.282123i | \(0.908961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.4408 | −1.29214 | ||||||||
\(452\) | −5.08413 | + | 30.3810i | −0.239137 | + | 1.42900i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.03821 | − | 12.4943i | 0.0487257 | − | 0.586385i | ||||
\(455\) | 1.24054 | 0.0581575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.7774 | 0.504144 | 0.252072 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252072 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(458\) | −2.03366 | + | 24.4739i | −0.0950269 | + | 1.14359i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.88790 | − | 0.315932i | −0.0880238 | − | 0.0147304i | ||||
\(461\) | 2.36887 | 0.110329 | 0.0551647 | − | 0.998477i | \(-0.482432\pi\) | ||||
0.0551647 | + | 0.998477i | \(0.482432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.4537i | 1.78709i | 0.448969 | + | 0.893547i | \(0.351791\pi\) | ||||
−0.448969 | + | 0.893547i | \(0.648209\pi\) | |||||||
\(464\) | 15.2647 | + | 5.25616i | 0.708646 | + | 0.244011i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.17011 | + | 14.0816i | −0.0542043 | + | 0.652316i | ||||
\(467\) | − | 5.09381i | − | 0.235713i | −0.993031 | − | 0.117857i | \(-0.962398\pi\) | ||
0.993031 | − | 0.117857i | \(-0.0376023\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.97987i | − | 0.183773i | ||||||
\(470\) | −6.69231 | − | 0.556098i | −0.308693 | − | 0.0256509i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.604944 | + | 2.38193i | −0.0278448 | + | 0.109637i | ||||
\(473\) | 30.0609i | 1.38220i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.2565 | 0.516483 | ||||||||
\(476\) | −12.7988 | − | 2.14182i | −0.586630 | − | 0.0981701i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.6291 | + | 2.87750i | 1.58390 | + | 0.131614i | ||||
\(479\) | −20.8166 | −0.951137 | −0.475568 | − | 0.879679i | \(-0.657758\pi\) | ||||
−0.475568 | + | 0.879679i | \(0.657758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5004 | 0.478778 | ||||||||
\(482\) | 32.6669 | + | 2.71446i | 1.48794 | + | 0.123640i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.04083 | + | 0.843561i | 0.229129 | + | 0.0383437i | ||||
\(485\) | 4.62943 | 0.210212 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 26.1716i | − | 1.18595i | −0.805222 | − | 0.592973i | \(-0.797954\pi\) | ||
0.805222 | − | 0.592973i | \(-0.202046\pi\) | |||||||
\(488\) | −3.71533 | + | 14.6289i | −0.168185 | + | 0.662219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.66010 | + | 0.137947i | 0.0749959 | + | 0.00623179i | ||||
\(491\) | − | 27.7686i | − | 1.25318i | −0.779349 | − | 0.626590i | \(-0.784450\pi\) | ||
0.779349 | − | 0.626590i | \(-0.215550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.1875i | 1.17943i | ||||||||
\(494\) | 0.384314 | − | 4.62499i | 0.0172911 | − | 0.208088i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.141662 | + | 0.411408i | −0.00636081 | + | 0.0184728i | ||||
\(497\) | − | 0.844302i | − | 0.0378721i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.7781 | −0.616791 | −0.308395 | − | 0.951258i | \(-0.599792\pi\) | ||||
−0.308395 | + | 0.951258i | \(0.599792\pi\) | |||||||
\(500\) | 20.0114 | + | 3.34882i | 0.894936 | + | 0.149764i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.50231 | − | 30.1138i | 0.111683 | − | 1.34404i | ||||
\(503\) | 32.5875 | 1.45300 | 0.726502 | − | 0.687165i | \(-0.241145\pi\) | ||||
0.726502 | + | 0.687165i | \(0.241145\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.2850 | 0.947168 | ||||||||
\(506\) | −0.276513 | + | 3.32767i | −0.0122925 | + | 0.147933i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.66169 | − | 33.8323i | 0.251197 | − | 1.50107i | ||||
\(509\) | −17.1161 | −0.758657 | −0.379328 | − | 0.925262i | \(-0.623845\pi\) | ||||
−0.379328 | + | 0.925262i | \(0.623845\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.59513i | 0.159039i | ||||||||
\(512\) | 16.6156 | + | 15.3597i | 0.734313 | + | 0.678811i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.46172 | + | 41.6597i | −0.152690 | + | 1.83753i | ||||
\(515\) | 21.0394i | 0.927109i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.7146i | 0.515209i | ||||||||
\(518\) | 14.0518 | + | 1.16763i | 0.617399 | + | 0.0513028i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.863714 | − | 3.40082i | 0.0378764 | − | 0.149136i | ||||
\(521\) | 22.6308i | 0.991471i | 0.868473 | + | 0.495736i | \(0.165102\pi\) | ||||
−0.868473 | + | 0.495736i | \(0.834898\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0252 | −0.831914 | −0.415957 | − | 0.909384i | \(-0.636553\pi\) | ||||
−0.415957 | + | 0.909384i | \(0.636553\pi\) | |||||||
\(524\) | 3.46996 | − | 20.7353i | 0.151586 | − | 0.905825i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.2680 | − | 1.85036i | −0.970931 | − | 0.0806796i | ||||
\(527\) | −0.705796 | −0.0307450 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3398 | −0.971296 | ||||||||
\(530\) | −4.94333 | − | 0.410766i | −0.214724 | − | 0.0178425i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.02859 | − | 6.14647i | 0.0445948 | − | 0.266483i | ||||
\(533\) | −9.94503 | −0.430767 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.04310i | 0.390967i | ||||||||
\(536\) | −10.9104 | − | 2.77094i | −0.471257 | − | 0.119686i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.04105 | − | 0.751267i | −0.389787 | − | 0.0323894i | ||||
\(539\) | − | 2.90595i | − | 0.125168i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3996i | 0.748066i | 0.927415 | + | 0.374033i | \(0.122025\pi\) | ||||
−0.927415 | + | 0.374033i | \(0.877975\pi\) | |||||||
\(542\) | −0.0108642 | + | 0.130744i | −0.000466657 | + | 0.00561594i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.7826 | + | 33.5953i | −0.633797 | + | 1.44038i | ||||
\(545\) | 14.9585i | 0.640751i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.96571 | 0.212318 | 0.106159 | − | 0.994349i | \(-0.466145\pi\) | ||||
0.106159 | + | 0.994349i | \(0.466145\pi\) | |||||||
\(548\) | −4.49824 | + | 26.8799i | −0.192155 | + | 1.14825i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.22940 | − | 14.7951i | 0.0524218 | − | 0.630865i | ||||
\(551\) | −12.5763 | −0.535768 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.48320 | −0.403267 | ||||||||
\(554\) | −2.31762 | + | 27.8912i | −0.0984663 | + | 1.18498i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.6049 | − | 1.77469i | −0.449749 | − | 0.0752635i | ||||
\(557\) | −5.67400 | −0.240415 | −0.120208 | − | 0.992749i | \(-0.538356\pi\) | ||||
−0.120208 | + | 0.992749i | \(0.538356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.8946i | 0.460793i | ||||||||
\(560\) | 1.53400 | − | 4.45496i | 0.0648231 | − | 0.188256i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.69113 | − | 20.3517i | 0.0713358 | − | 0.858484i | ||||
\(563\) | − | 25.4752i | − | 1.07365i | −0.843693 | − | 0.536826i | \(-0.819623\pi\) | ||
0.843693 | − | 0.536826i | \(-0.180377\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 18.1420i | − | 0.763238i | ||||||
\(566\) | 28.7169 | + | 2.38624i | 1.20706 | + | 0.100301i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.31457 | − | 0.587836i | −0.0971170 | − | 0.0246650i | ||||
\(569\) | − | 19.5120i | − | 0.817986i | −0.912537 | − | 0.408993i | \(-0.865880\pi\) | ||
0.912537 | − | 0.408993i | \(-0.134120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.0268 | −1.59137 | −0.795686 | − | 0.605709i | \(-0.792889\pi\) | ||||
−0.795686 | + | 0.605709i | \(0.792889\pi\) | |||||||
\(572\) | −6.03695 | − | 1.01026i | −0.252418 | − | 0.0422410i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.3085 | − | 1.10587i | −0.555487 | − | 0.0461582i | ||||
\(575\) | −2.93522 | −0.122407 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.32632 | 0.221738 | 0.110869 | − | 0.993835i | \(-0.464637\pi\) | ||||
0.110869 | + | 0.993835i | \(0.464637\pi\) | |||||||
\(578\) | −35.3733 | − | 2.93935i | −1.47134 | − | 0.122261i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.37791 | − | 1.56935i | −0.389397 | − | 0.0651638i | ||||
\(581\) | 2.71280 | 0.112546 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.65311i | 0.358375i | ||||||||
\(584\) | 9.85566 | + | 2.50307i | 0.407830 | + | 0.103578i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5050 | + | 1.20530i | 0.599197 | + | 0.0497903i | ||||
\(587\) | 25.6946i | 1.06053i | 0.847832 | + | 0.530265i | \(0.177908\pi\) | ||||
−0.847832 | + | 0.530265i | \(0.822092\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.338951i | − | 0.0139662i | ||||||
\(590\) | 0.119858 | − | 1.44242i | 0.00493448 | − | 0.0593836i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.9843 | − | 37.7085i | 0.533652 | − | 1.54981i | ||||
\(593\) | 35.9249i | 1.47526i | 0.675205 | + | 0.737630i | \(0.264055\pi\) | ||||
−0.675205 | + | 0.737630i | \(0.735945\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.64276 | 0.313322 | ||||||||
\(596\) | 34.1623 | + | 5.71692i | 1.39934 | + | 0.234174i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.100213 | + | 1.20601i | −0.00409803 | + | 0.0493173i | ||||
\(599\) | 8.08090 | 0.330177 | 0.165088 | − | 0.986279i | \(-0.447209\pi\) | ||||
0.165088 | + | 0.986279i | \(0.447209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.0492 | 1.59285 | 0.796425 | − | 0.604738i | \(-0.206722\pi\) | ||||
0.796425 | + | 0.604738i | \(0.206722\pi\) | |||||||
\(602\) | −1.21146 | + | 14.5793i | −0.0493756 | + | 0.594206i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.48801 | − | 8.89181i | 0.0605461 | − | 0.361803i | ||||
\(605\) | −3.01012 | −0.122379 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.0636i | 1.58554i | 0.609519 | + | 0.792772i | \(0.291363\pi\) | ||||
−0.609519 | + | 0.792772i | \(0.708637\pi\) | |||||||
\(608\) | −16.1338 | − | 7.09917i | −0.654311 | − | 0.287909i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.736123 | − | 8.85880i | 0.0298047 | − | 0.358682i | ||||
\(611\) | 4.24559i | 0.171758i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.0877i | 1.09406i | 0.837112 | + | 0.547031i | \(0.184242\pi\) | ||||
−0.837112 | + | 0.547031i | \(0.815758\pi\) | |||||||
\(614\) | 28.0179 | + | 2.32815i | 1.13071 | + | 0.0939566i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.96636 | − | 2.02323i | −0.320974 | − | 0.0815184i | ||||
\(617\) | − | 10.2143i | − | 0.411213i | −0.978635 | − | 0.205607i | \(-0.934083\pi\) | ||
0.978635 | − | 0.205607i | \(-0.0659167\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.5400 | 1.14712 | 0.573560 | − | 0.819164i | \(-0.305562\pi\) | ||||
0.573560 | + | 0.819164i | \(0.305562\pi\) | |||||||
\(620\) | 0.0422966 | − | 0.252750i | 0.00169867 | − | 0.0101507i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.1968 | − | 0.930401i | −0.448952 | − | 0.0373057i | ||||
\(623\) | 2.22575 | 0.0891730 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.11281 | 0.244512 | ||||||||
\(626\) | −39.8074 | − | 3.30780i | −1.59102 | − | 0.132206i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.92039 | − | 17.4512i | 0.116536 | − | 0.696380i | ||||
\(629\) | 64.6912 | 2.57941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.9037i | − | 0.712734i | −0.934346 | − | 0.356367i | \(-0.884015\pi\) | ||
0.934346 | − | 0.356367i | \(-0.115985\pi\) | |||||||
\(632\) | −6.60258 | + | 25.9972i | −0.262636 | + | 1.03411i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.5350 | + | 1.62326i | 0.775832 | + | 0.0644679i | ||||
\(635\) | 20.2029i | 0.801728i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.05317i | − | 0.0417280i | ||||||
\(638\) | −1.37355 | + | 16.5298i | −0.0543792 | + | 0.654421i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.1448 | − | 7.30700i | −0.440536 | − | 0.288835i | ||||
\(641\) | − | 36.5576i | − | 1.44394i | −0.691925 | − | 0.721969i | \(-0.743237\pi\) | ||
0.691925 | − | 0.721969i | \(-0.256763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.5306 | 1.12514 | 0.562568 | − | 0.826751i | \(-0.309813\pi\) | ||||
0.562568 | + | 0.826751i | \(0.309813\pi\) | |||||||
\(644\) | −0.268212 | + | 1.60275i | −0.0105691 | + | 0.0631570i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.36769 | − | 28.4938i | 0.0931556 | − | 1.12107i | ||||
\(647\) | 25.0326 | 0.984134 | 0.492067 | − | 0.870557i | \(-0.336242\pi\) | ||||
0.492067 | + | 0.870557i | \(0.336242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.52490 | −0.0991112 | ||||||||
\(650\) | 0.445556 | − | 5.36201i | 0.0174762 | − | 0.210315i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.5348 | − | 2.76703i | −0.647554 | − | 0.108365i | ||||
\(653\) | 43.1196 | 1.68740 | 0.843699 | − | 0.536816i | \(-0.180373\pi\) | ||||
0.843699 | + | 0.536816i | \(0.180373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.3820i | 0.483806i | ||||||||
\(656\) | −12.2975 | + | 35.7140i | −0.480139 | + | 1.39440i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.472103 | + | 5.68148i | −0.0184045 | + | 0.221487i | ||||
\(659\) | 8.36352i | 0.325796i | 0.986643 | + | 0.162898i | \(0.0520842\pi\) | ||||
−0.986643 | + | 0.162898i | \(0.947916\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 8.48754i | − | 0.330127i | −0.986283 | − | 0.165064i | \(-0.947217\pi\) | ||
0.986283 | − | 0.165064i | \(-0.0527829\pi\) | |||||||
\(662\) | −20.4991 | − | 1.70338i | −0.796722 | − | 0.0662037i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.88876 | − | 7.43687i | 0.0732981 | − | 0.288607i | ||||
\(665\) | 3.67035i | 0.142330i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.27937 | 0.126978 | ||||||||
\(668\) | −17.6262 | − | 2.94966i | −0.681977 | − | 0.114126i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.60699 | + | 0.549009i | 0.255250 | + | 0.0212100i | ||||
\(671\) | −15.5070 | −0.598641 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.4287 | −0.980206 | −0.490103 | − | 0.871664i | \(-0.663041\pi\) | ||||
−0.490103 | + | 0.871664i | \(0.663041\pi\) | |||||||
\(674\) | 7.41562 | + | 0.616201i | 0.285639 | + | 0.0237352i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.4555 | + | 3.92518i | 0.902135 | + | 0.150968i | ||||
\(677\) | 17.0820 | 0.656515 | 0.328258 | − | 0.944588i | \(-0.393539\pi\) | ||||
0.328258 | + | 0.944588i | \(0.393539\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.93019i | − | 0.150827i | ||||||
\(680\) | 5.32118 | − | 20.9518i | 0.204058 | − | 0.803466i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.445505 | − | 0.0370193i | −0.0170593 | − | 0.00141754i | ||||
\(683\) | 44.0552i | 1.68573i | 0.538128 | + | 0.842863i | \(0.319132\pi\) | ||||
−0.538128 | + | 0.842863i | \(0.680868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 16.0513i | − | 0.613288i | ||||||
\(686\) | 0.117111 | − | 1.40936i | 0.00447130 | − | 0.0538095i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 39.1240 | + | 13.4718i | 1.49159 | + | 0.513606i | ||||
\(689\) | 3.13604i | 0.119474i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3483 | −0.698002 | −0.349001 | − | 0.937122i | \(-0.613479\pi\) | ||||
−0.349001 | + | 0.937122i | \(0.613479\pi\) | |||||||
\(692\) | 27.9339 | + | 4.67462i | 1.06189 | + | 0.177703i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.82164 | − | 21.9223i | 0.0691485 | − | 0.832161i | ||||
\(695\) | 6.33271 | 0.240213 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −61.2695 | −2.32075 | ||||||||
\(698\) | −2.00971 | + | 24.1856i | −0.0760685 | + | 0.915439i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.19249 | − | 7.12593i | 0.0450721 | − | 0.269335i | ||||
\(701\) | −33.6724 | −1.27179 | −0.635894 | − | 0.771777i | \(-0.719368\pi\) | ||||
−0.635894 | + | 0.771777i | \(0.719368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.0673i | 1.17172i | ||||||||
\(704\) | −11.0930 | + | 20.4303i | −0.418082 | + | 0.769995i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.82035 | − | 21.9068i | 0.0685096 | − | 0.824472i | ||||
\(707\) | − | 18.0700i | − | 0.679592i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.9147i | 0.597689i | 0.954302 | + | 0.298845i | \(0.0966013\pi\) | ||||
−0.954302 | + | 0.298845i | \(0.903399\pi\) | |||||||
\(710\) | 1.40163 | + | 0.116468i | 0.0526022 | + | 0.00437098i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.54966 | − | 6.10168i | 0.0580759 | − | 0.228670i | ||||
\(713\) | 0.0883844i | 0.00331002i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.60495 | 0.134818 | ||||||||
\(716\) | 6.72399 | − | 40.1802i | 0.251287 | − | 1.50161i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.0657 | + | 1.75046i | 0.786167 | + | 0.0653266i | ||||
\(719\) | −34.6441 | −1.29201 | −0.646004 | − | 0.763334i | \(-0.723561\pi\) | ||||
−0.646004 | + | 0.763334i | \(0.723561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.8616 | 0.665200 | ||||||||
\(722\) | −13.0939 | − | 1.08804i | −0.487306 | − | 0.0404928i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.02960 | − | 36.0308i | 0.224088 | − | 1.33907i | ||||
\(725\) | −14.5804 | −0.541501 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 38.6477i | − | 1.43336i | −0.697400 | − | 0.716682i | \(-0.745660\pi\) | ||
0.697400 | − | 0.716682i | \(-0.254340\pi\) | |||||||
\(728\) | −2.88715 | − | 0.733256i | −0.107005 | − | 0.0271763i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.96828 | − | 0.495935i | −0.220896 | − | 0.0183554i | ||||
\(731\) | 67.1197i | 2.48251i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 4.45768i | − | 0.164648i | −0.996606 | − | 0.0823240i | \(-0.973766\pi\) | ||
0.996606 | − | 0.0823240i | \(-0.0262342\pi\) | |||||||
\(734\) | 0.335152 | − | 4.03335i | 0.0123707 | − | 0.148874i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.20702 | + | 1.85117i | 0.155073 | + | 0.0682350i | ||||
\(737\) | − | 11.5653i | − | 0.426013i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.0619 | −1.17942 | −0.589709 | − | 0.807616i | \(-0.700757\pi\) | ||||
−0.589709 | + | 0.807616i | \(0.700757\pi\) | |||||||
\(740\) | −3.87678 | + | 23.1663i | −0.142513 | + | 0.851611i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.348723 | + | 4.19667i | −0.0128020 | + | 0.154065i | ||||
\(743\) | 44.9201 | 1.64796 | 0.823979 | − | 0.566620i | \(-0.191749\pi\) | ||||
0.823979 | + | 0.566620i | \(0.191749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.4000 | −0.747397 | ||||||||
\(746\) | −2.42801 | + | 29.2197i | −0.0888959 | + | 1.06981i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −37.1925 | − | 6.22401i | −1.35989 | − | 0.227572i | ||||
\(749\) | 7.67720 | 0.280519 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 20.4697i | − | 0.746951i | −0.927640 | − | 0.373475i | \(-0.878166\pi\) | ||
0.927640 | − | 0.373475i | \(-0.121834\pi\) | |||||||
\(752\) | 15.2465 | + | 5.24989i | 0.555982 | + | 0.191444i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.497797 | + | 5.99069i | −0.0181287 | + | 0.218168i | ||||
\(755\) | 5.30973i | 0.193241i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 11.4003i | − | 0.414352i | −0.978304 | − | 0.207176i | \(-0.933573\pi\) | ||
0.978304 | − | 0.207176i | \(-0.0664273\pi\) | |||||||
\(758\) | 39.6820 | + | 3.29738i | 1.44131 | + | 0.119766i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.0619 | + | 2.55544i | 0.364983 | + | 0.0926956i | ||||
\(761\) | − | 32.5142i | − | 1.17864i | −0.807901 | − | 0.589319i | \(-0.799396\pi\) | ||
0.807901 | − | 0.589319i | \(-0.200604\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6991 | 0.459739 | ||||||||
\(764\) | 15.4620 | + | 2.58749i | 0.559395 | + | 0.0936123i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.2430 | − | 3.51019i | −1.52630 | − | 0.126828i | ||||
\(767\) | −0.915070 | −0.0330413 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.1134 | 0.905614 | 0.452807 | − | 0.891609i | \(-0.350423\pi\) | ||||
0.452807 | + | 0.891609i | \(0.350423\pi\) | |||||||
\(770\) | 4.82418 | + | 0.400865i | 0.173851 | + | 0.0144462i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.6910 | − | 4.29928i | −0.924640 | − | 0.154735i | ||||
\(773\) | −42.4890 | −1.52822 | −0.764112 | − | 0.645083i | \(-0.776823\pi\) | ||||
−0.764112 | + | 0.645083i | \(0.776823\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.392964i | − | 0.0141157i | ||||||
\(776\) | −10.7742 | − | 2.73635i | −0.386771 | − | 0.0982292i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.5663 | − | 3.45395i | −1.49022 | − | 0.123830i | ||||
\(779\) | − | 29.4240i | − | 1.05423i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 2.45350i | − | 0.0877930i | ||||||
\(782\) | −0.617396 | + | 7.42999i | −0.0220780 | + | 0.265696i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.78207 | − | 1.30230i | −0.135074 | − | 0.0465105i | ||||
\(785\) | 10.4210i | 0.371941i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.1415 | 0.682322 | 0.341161 | − | 0.940005i | \(-0.389180\pi\) | ||||
0.341161 | + | 0.940005i | \(0.389180\pi\) | |||||||
\(788\) | −29.5049 | − | 4.93751i | −1.05107 | − | 0.175892i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.30817 | − | 15.7431i | 0.0465428 | − | 0.560115i | ||||
\(791\) | −15.4017 | −0.547623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.62001 | −0.199572 | ||||||||
\(794\) | 2.58633 | − | 31.1250i | 0.0917856 | − | 1.10458i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.58356 | − | 33.3654i | 0.197904 | − | 1.18261i | ||||
\(797\) | −14.9802 | −0.530625 | −0.265312 | − | 0.964162i | \(-0.585475\pi\) | ||||
−0.265312 | + | 0.964162i | \(0.585475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.1563i | 0.925343i | ||||||||
\(800\) | −18.7047 | − | 8.23045i | −0.661313 | − | 0.290990i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.869023 | + | 10.4582i | −0.0306863 | + | 0.369291i | ||||
\(803\) | 10.4473i | 0.368675i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 0.957076i | − | 0.0337325i | ||||||
\(806\) | −0.161459 | − | 0.0134164i | −0.00568714 | − | 0.000472574i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −49.5370 | − | 12.5810i | −1.74271 | − | 0.442599i | ||||
\(809\) | 20.4899i | 0.720388i | 0.932877 | + | 0.360194i | \(0.117289\pi\) | ||||
−0.932877 | + | 0.360194i | \(0.882711\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.0258 | 0.668087 | 0.334043 | − | 0.942558i | \(-0.391587\pi\) | ||||
0.334043 | + | 0.942558i | \(0.391587\pi\) | |||||||
\(812\) | −1.33231 | + | 7.96144i | −0.0467550 | + | 0.279392i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 40.8337 | + | 3.39308i | 1.43122 | + | 0.118927i | ||||
\(815\) | 9.87374 | 0.345862 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.2335 | −1.12771 | ||||||||
\(818\) | 52.7076 | + | 4.37974i | 1.84288 | + | 0.153134i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.67173 | − | 21.9410i | 0.128222 | − | 0.766212i | ||||
\(821\) | 39.0750 | 1.36373 | 0.681863 | − | 0.731480i | \(-0.261170\pi\) | ||||
0.681863 | + | 0.731480i | \(0.261170\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.1369i | 1.32937i | 0.747124 | + | 0.664684i | \(0.231434\pi\) | ||||
−0.747124 | + | 0.664684i | \(0.768566\pi\) | |||||||
\(824\) | 12.4359 | − | 48.9656i | 0.433226 | − | 1.70580i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.22455 | − | 0.101754i | −0.0426077 | − | 0.00354049i | ||||
\(827\) | 13.8842i | 0.482802i | 0.970425 | + | 0.241401i | \(0.0776070\pi\) | ||||
−0.970425 | + | 0.241401i | \(0.922393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.705296i | 0.0244960i | 0.999925 | + | 0.0122480i | \(0.00389875\pi\) | ||||
−0.999925 | + | 0.0122480i | \(0.996101\pi\) | |||||||
\(830\) | −0.374222 | + | 4.50354i | −0.0129894 | + | 0.156320i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.02029 | + | 7.40429i | −0.139378 | + | 0.256698i | ||||
\(833\) | − | 6.48837i | − | 0.224809i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5254 | 0.364248 | ||||||||
\(836\) | 2.98902 | − | 17.8613i | 0.103377 | − | 0.617747i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.00242 | − | 12.0635i | 0.0346280 | − | 0.416728i | ||||
\(839\) | −50.4627 | −1.74217 | −0.871083 | − | 0.491136i | \(-0.836582\pi\) | ||||
−0.871083 | + | 0.491136i | \(0.836582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.7101 | −0.438280 | ||||||||
\(842\) | 0.769051 | − | 9.25507i | 0.0265033 | − | 0.318951i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.2118 | + | 1.87625i | 0.385927 | + | 0.0645832i | ||||
\(845\) | −14.0064 | −0.481835 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.55546i | 0.0878068i | ||||||||
\(848\) | 11.2619 | + | 3.87787i | 0.386737 | + | 0.133167i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.74499 | − | 33.0343i | 0.0941524 | − | 1.13307i | ||||
\(851\) | − | 8.10106i | − | 0.277701i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.7370i | 0.367628i | 0.982961 | + | 0.183814i | \(0.0588444\pi\) | ||||
−0.982961 | + | 0.183814i | \(0.941156\pi\) | |||||||
\(854\) | −7.52074 | − | 0.624936i | −0.257354 | − | 0.0213849i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.34516 | − | 21.0462i | 0.182694 | − | 0.719345i | ||||
\(857\) | 9.75153i | 0.333106i | 0.986033 | + | 0.166553i | \(0.0532637\pi\) | ||||
−0.986033 | + | 0.166553i | \(0.946736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.9169 | 0.986630 | 0.493315 | − | 0.869851i | \(-0.335785\pi\) | ||||
0.493315 | + | 0.869851i | \(0.335785\pi\) | |||||||
\(860\) | −24.0360 | − | 4.02232i | −0.819620 | − | 0.137160i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.90669 | − | 0.657007i | −0.269303 | − | 0.0223777i | ||||
\(863\) | −16.0259 | −0.545528 | −0.272764 | − | 0.962081i | \(-0.587938\pi\) | ||||
−0.272764 | + | 0.962081i | \(0.587938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.6807 | −0.567161 | ||||||||
\(866\) | 11.2280 | + | 0.932990i | 0.381542 | + | 0.0317043i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.214573 | − | 0.0359079i | −0.00728310 | − | 0.00121880i | ||||
\(869\) | −27.5577 | −0.934831 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.19146i | − | 0.142022i | ||||||
\(872\) | 8.84161 | − | 34.8133i | 0.299415 | − | 1.17893i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.56817 | − | 0.296498i | −0.120695 | − | 0.0100292i | ||||
\(875\) | 10.1448i | 0.342958i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.24225i | 0.0757154i | 0.999283 | + | 0.0378577i | \(0.0120534\pi\) | ||||
−0.999283 | + | 0.0378577i | \(0.987947\pi\) | |||||||
\(878\) | −3.97211 | + | 47.8020i | −0.134052 | + | 1.61324i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.45771 | − | 12.9459i | 0.150269 | − | 0.436406i | ||||
\(881\) | − | 9.97799i | − | 0.336167i | −0.985773 | − | 0.168083i | \(-0.946242\pi\) | ||
0.985773 | − | 0.168083i | \(-0.0537578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8382 | 0.667609 | 0.333805 | − | 0.942642i | \(-0.391667\pi\) | ||||
0.333805 | + | 0.942642i | \(0.391667\pi\) | |||||||
\(884\) | −13.4792 | − | 2.25569i | −0.453356 | − | 0.0758671i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.739977 | − | 8.90518i | 0.0248600 | − | 0.299176i | ||||
\(887\) | −34.8500 | −1.17015 | −0.585074 | − | 0.810980i | \(-0.698935\pi\) | ||||
−0.585074 | + | 0.810980i | \(0.698935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.1514 | 0.575239 | ||||||||
\(890\) | −0.307035 | + | 3.69498i | −0.0102918 | + | 0.123856i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.13543 | + | 6.78492i | −0.0380169 | + | 0.227176i | ||||
\(893\) | −12.5613 | −0.420347 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.9935i | 0.802016i | ||||||||
\(896\) | −6.20333 | + | 9.46143i | −0.207239 | + | 0.316084i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.40019 | + | 16.8505i | −0.0467251 | + | 0.562308i | ||||
\(899\) | 0.439039i | 0.0146428i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.3206i | 0.643661i | ||||||||
\(902\) | −38.6739 | − | 3.21361i | −1.28770 | − | 0.107002i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.7233 | + | 42.2222i | −0.356651 | + | 1.40429i | ||||
\(905\) | 21.5157i | 0.715207i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.69626 | −0.122732 | −0.0613662 | − | 0.998115i | \(-0.519546\pi\) | ||||
−0.0613662 | + | 0.998115i | \(0.519546\pi\) | |||||||
\(908\) | 2.92642 | − | 17.4873i | 0.0971167 | − | 0.580336i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.74837 | + | 0.145281i | 0.0579578 | + | 0.00481601i | ||||
\(911\) | 51.1975 | 1.69625 | 0.848125 | − | 0.529796i | \(-0.177732\pi\) | ||||
0.848125 | + | 0.529796i | \(0.177732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.88327 | 0.260898 | ||||||||
\(914\) | 15.1892 | + | 1.26214i | 0.502413 | + | 0.0417480i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.73232 | + | 34.2543i | −0.189401 | + | 1.13180i | ||||
\(917\) | 10.5118 | 0.347130 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 50.4632i | − | 1.66463i | −0.554306 | − | 0.832313i | \(-0.687016\pi\) | ||
0.554306 | − | 0.832313i | \(-0.312984\pi\) | |||||||
\(920\) | −2.62372 | − | 0.666354i | −0.0865016 | − | 0.0219690i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.33858 | + | 0.277420i | 0.109950 | + | 0.00913634i | ||||
\(923\) | − | 0.889190i | − | 0.0292681i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.0180i | 1.18426i | ||||||||
\(926\) | −4.50334 | + | 54.1950i | −0.147989 | + | 1.78096i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.8978 | + | 9.19546i | 0.686005 | + | 0.301856i | ||||
\(929\) | 8.22557i | 0.269872i | 0.990854 | + | 0.134936i | \(0.0430829\pi\) | ||||
−0.990854 | + | 0.134936i | \(0.956917\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.11597 | 0.102122 | ||||||||
\(932\) | −3.29820 | + | 19.7089i | −0.108036 | + | 0.645587i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.596539 | − | 7.17899i | 0.0195194 | − | 0.234904i | ||||
\(935\) | 22.2095 | 0.726327 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.968784 | 0.0316488 | 0.0158244 | − | 0.999875i | \(-0.494963\pi\) | ||||
0.0158244 | + | 0.999875i | \(0.494963\pi\) | |||||||
\(938\) | 0.466084 | − | 5.60905i | 0.0152182 | − | 0.183142i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.36672 | − | 1.56748i | −0.305509 | − | 0.0511256i | ||||
\(941\) | 11.2805 | 0.367734 | 0.183867 | − | 0.982951i | \(-0.441138\pi\) | ||||
0.183867 | + | 0.982951i | \(0.441138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.67257i | 0.249853i | ||||||||
\(944\) | −1.13153 | + | 3.28614i | −0.0368282 | + | 0.106955i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.52045 | + | 42.3666i | −0.114460 | + | 1.37746i | ||||
\(947\) | 57.8442i | 1.87968i | 0.341609 | + | 0.939842i | \(0.389028\pi\) | ||||
−0.341609 | + | 0.939842i | \(0.610972\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.78627i | 0.122907i | ||||||||
\(950\) | 15.8644 | + | 1.31825i | 0.514709 | + | 0.0427698i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.7872 | − | 4.51745i | −0.576486 | − | 0.146412i | ||||
\(953\) | 23.4368i | 0.759193i | 0.925152 | + | 0.379596i | \(0.123937\pi\) | ||||
−0.925152 | + | 0.379596i | \(0.876063\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.23309 | −0.298776 | ||||||||
\(956\) | 48.4677 | + | 8.11086i | 1.56756 | + | 0.262324i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.3381 | − | 2.43785i | −0.947870 | − | 0.0787633i | ||||
\(959\) | −13.6268 | −0.440034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9882 | 0.999618 | ||||||||
\(962\) | 14.7988 | + | 1.22971i | 0.477134 | + | 0.0396475i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 45.7214 | + | 7.65128i | 1.47259 | + | 0.246431i | ||||
\(965\) | 15.3413 | 0.493855 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 44.8294i | − | 1.44162i | −0.693135 | − | 0.720808i | \(-0.743771\pi\) | ||
0.693135 | − | 0.720808i | \(-0.256229\pi\) | |||||||
\(968\) | 7.00554 | + | 1.77921i | 0.225166 | + | 0.0571861i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.52452 | + | 0.542155i | 0.209490 | + | 0.0174076i | ||||
\(971\) | 13.3436i | 0.428216i | 0.976810 | + | 0.214108i | \(0.0686844\pi\) | ||||
−0.976810 | + | 0.214108i | \(0.931316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 5.37620i | − | 0.172353i | ||||||
\(974\) | 3.06497 | − | 36.8850i | 0.0982079 | − | 1.18187i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.94943 | + | 20.1822i | −0.222446 | + | 0.646017i | ||||
\(977\) | 11.0654i | 0.354015i | 0.984210 | + | 0.177007i | \(0.0566416\pi\) | ||||
−0.984210 | + | 0.177007i | \(0.943358\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.46793 | 0.206716 | ||||||||
\(980\) | 2.32352 | + | 0.388832i | 0.0742222 | + | 0.0124208i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.25200 | − | 39.1359i | 0.103775 | − | 1.24888i | ||||
\(983\) | 48.7128 | 1.55370 | 0.776849 | − | 0.629687i | \(-0.216817\pi\) | ||||
0.776849 | + | 0.629687i | \(0.216817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.6188 | 0.561381 | ||||||||
\(986\) | −3.06684 | + | 36.9076i | −0.0976680 | + | 1.17538i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.08327 | − | 6.47326i | 0.0344635 | − | 0.205942i | ||||
\(989\) | 8.40517 | 0.267269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.6581i | 1.41861i | 0.704901 | + | 0.709306i | \(0.250991\pi\) | ||||
−0.704901 | + | 0.709306i | \(0.749009\pi\) | |||||||
\(992\) | −0.247832 | + | 0.563230i | −0.00786868 | + | 0.0178826i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.0988767 | − | 1.18992i | 0.00313618 | − | 0.0377420i | ||||
\(995\) | 19.9241i | 0.631636i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 20.5408i | − | 0.650534i | −0.945622 | − | 0.325267i | \(-0.894546\pi\) | ||
0.945622 | − | 0.325267i | \(-0.105454\pi\) | |||||||
\(998\) | −19.4182 | − | 1.61356i | −0.614672 | − | 0.0510762i | ||||
\(999\) | 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 | 1512.2.j.c.323.32 | yes | 32 | |
3.2 | odd | 2 | inner | 1512.2.j.c.323.1 | ✓ | 32 | |
4.3 | odd | 2 | 6048.2.j.c.5615.9 | 32 | |||
8.3 | odd | 2 | inner | 1512.2.j.c.323.2 | yes | 32 | |
8.5 | even | 2 | 6048.2.j.c.5615.23 | 32 | |||
12.11 | even | 2 | 6048.2.j.c.5615.24 | 32 | |||
24.5 | odd | 2 | 6048.2.j.c.5615.10 | 32 | |||
24.11 | even | 2 | inner | 1512.2.j.c.323.31 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.1 | ✓ | 32 | 3.2 | odd | 2 | inner | |
1512.2.j.c.323.2 | yes | 32 | 8.3 | odd | 2 | inner | |
1512.2.j.c.323.31 | yes | 32 | 24.11 | even | 2 | inner | |
1512.2.j.c.323.32 | yes | 32 | 1.1 | even | 1 | trivial | |
6048.2.j.c.5615.9 | 32 | 4.3 | odd | 2 | |||
6048.2.j.c.5615.10 | 32 | 24.5 | odd | 2 | |||
6048.2.j.c.5615.23 | 32 | 8.5 | even | 2 | |||
6048.2.j.c.5615.24 | 32 | 12.11 | even | 2 |