Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,2,Mod(971,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1620.971");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.e (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: | \(12.9357651274\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 971.37 | ||
Character | \(\chi\) | \(=\) | 1620.971 |
Dual form | 1620.2.e.b.971.38 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.04983 | − | 0.947554i | 0.742341 | − | 0.670022i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.204282 | − | 1.98954i | 0.102141 | − | 0.994770i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.17013i | 1.57616i | 0.615573 | + | 0.788080i | \(0.288925\pi\) | ||||
−0.615573 | + | 0.788080i | \(0.711075\pi\) | |||||||
\(8\) | −1.67074 | − | 2.28224i | −0.590694 | − | 0.806895i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.947554 | + | 1.04983i | 0.299643 | + | 0.331985i | ||||
\(11\) | −6.44191 | −1.94231 | −0.971154 | − | 0.238453i | \(-0.923360\pi\) | ||||
−0.971154 | + | 0.238453i | \(0.923360\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.77467 | 0.492205 | 0.246103 | − | 0.969244i | \(-0.420850\pi\) | ||||
0.246103 | + | 0.969244i | \(0.420850\pi\) | |||||||
\(14\) | 3.95142 | + | 4.37792i | 1.05606 | + | 1.17005i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.91654 | − | 0.812853i | −0.979135 | − | 0.203213i | ||||
\(17\) | − | 0.950682i | − | 0.230574i | −0.993332 | − | 0.115287i | \(-0.963221\pi\) | ||
0.993332 | − | 0.115287i | \(-0.0367788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.19286i | 0.503078i | 0.967847 | + | 0.251539i | \(0.0809366\pi\) | ||||
−0.967847 | + | 0.251539i | \(0.919063\pi\) | |||||||
\(20\) | 1.98954 | + | 0.204282i | 0.444875 | + | 0.0456788i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.76290 | + | 6.10406i | −1.44186 | + | 1.30139i | ||||
\(23\) | −2.02013 | −0.421226 | −0.210613 | − | 0.977569i | \(-0.567546\pi\) | ||||
−0.210613 | + | 0.977569i | \(0.567546\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 1.86310 | − | 1.68160i | 0.365384 | − | 0.329788i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.29663 | + | 0.851880i | 1.56792 | + | 0.160990i | ||||
\(29\) | 6.52706i | 1.21204i | 0.795448 | + | 0.606022i | \(0.207236\pi\) | ||||
−0.795448 | + | 0.606022i | \(0.792764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.84246i | 0.510521i | 0.966872 | + | 0.255260i | \(0.0821612\pi\) | ||||
−0.966872 | + | 0.255260i | \(0.917839\pi\) | |||||||
\(32\) | −4.88192 | + | 2.85778i | −0.863009 | + | 0.505188i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.900823 | − | 0.998053i | −0.154490 | − | 0.171165i | ||||
\(35\) | −4.17013 | −0.704880 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.83599 | −0.959431 | −0.479715 | − | 0.877424i | \(-0.659260\pi\) | ||||
−0.479715 | + | 0.877424i | \(0.659260\pi\) | |||||||
\(38\) | 2.07786 | + | 2.30213i | 0.337073 | + | 0.373455i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.28224 | − | 1.67074i | 0.360855 | − | 0.264167i | ||||
\(41\) | 7.11552i | 1.11126i | 0.831430 | + | 0.555629i | \(0.187522\pi\) | ||||
−0.831430 | + | 0.555629i | \(0.812478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.30982i | 0.809741i | 0.914374 | + | 0.404870i | \(0.132683\pi\) | ||||
−0.914374 | + | 0.404870i | \(0.867317\pi\) | |||||||
\(44\) | −1.31596 | + | 12.8164i | −0.198389 | + | 1.93215i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.12079 | + | 1.91418i | −0.312694 | + | 0.282231i | ||||
\(47\) | 0.403992 | 0.0589283 | 0.0294641 | − | 0.999566i | \(-0.490620\pi\) | ||||
0.0294641 | + | 0.999566i | \(0.490620\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.3900 | −1.48428 | ||||||||
\(50\) | −1.04983 | + | 0.947554i | −0.148468 | + | 0.134004i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.362533 | − | 3.53078i | 0.0502743 | − | 0.489631i | ||||
\(53\) | − | 4.87844i | − | 0.670106i | −0.942199 | − | 0.335053i | \(-0.891246\pi\) | ||
0.942199 | − | 0.335053i | \(-0.108754\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.44191i | − | 0.868627i | ||||||
\(56\) | 9.51725 | − | 6.96718i | 1.27180 | − | 0.931029i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.18474 | + | 6.85230i | 0.812097 | + | 0.899751i | ||||
\(59\) | −2.68783 | −0.349926 | −0.174963 | − | 0.984575i | \(-0.555981\pi\) | ||||
−0.174963 | + | 0.984575i | \(0.555981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.09304 | 0.524060 | 0.262030 | − | 0.965060i | \(-0.415608\pi\) | ||||
0.262030 | + | 0.965060i | \(0.415608\pi\) | |||||||
\(62\) | 2.69338 | + | 2.98409i | 0.342060 | + | 0.378980i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.41728 | + | 7.62606i | −0.302160 | + | 0.953257i | ||||
\(65\) | 1.77467i | 0.220121i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.8959i | 1.33115i | 0.746331 | + | 0.665575i | \(0.231814\pi\) | ||||
−0.746331 | + | 0.665575i | \(0.768186\pi\) | |||||||
\(68\) | −1.89142 | − | 0.194207i | −0.229368 | − | 0.0235510i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.37792 | + | 3.95142i | −0.523262 | + | 0.472285i | ||||
\(71\) | 2.23126 | 0.264802 | 0.132401 | − | 0.991196i | \(-0.457731\pi\) | ||||
0.132401 | + | 0.991196i | \(0.457731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.74662 | −0.204426 | −0.102213 | − | 0.994763i | \(-0.532592\pi\) | ||||
−0.102213 | + | 0.994763i | \(0.532592\pi\) | |||||||
\(74\) | −6.12679 | + | 5.52992i | −0.712225 | + | 0.642840i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.36279 | + | 0.447962i | 0.500447 | + | 0.0513848i | ||||
\(77\) | − | 26.8636i | − | 3.06139i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.247600i | − | 0.0278572i | −0.999903 | − | 0.0139286i | \(-0.995566\pi\) | ||
0.999903 | − | 0.0139286i | \(-0.00443375\pi\) | |||||||
\(80\) | 0.812853 | − | 3.91654i | 0.0908797 | − | 0.437882i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.74234 | + | 7.47008i | 0.744567 | + | 0.824932i | ||||
\(83\) | −11.6728 | −1.28126 | −0.640629 | − | 0.767851i | \(-0.721326\pi\) | ||||
−0.640629 | + | 0.767851i | \(0.721326\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.950682 | 0.103116 | ||||||||
\(86\) | 5.03135 | + | 5.57441i | 0.542544 | + | 0.601104i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.7627 | + | 14.7020i | 1.14731 | + | 1.56724i | ||||
\(89\) | − | 6.13881i | − | 0.650713i | −0.945591 | − | 0.325356i | \(-0.894516\pi\) | ||
0.945591 | − | 0.325356i | \(-0.105484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.40061i | 0.775794i | ||||||||
\(92\) | −0.412675 | + | 4.01913i | −0.0430244 | + | 0.419023i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.424123 | − | 0.382804i | 0.0437449 | − | 0.0394833i | ||||
\(95\) | −2.19286 | −0.224983 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1701 | 1.84489 | 0.922446 | − | 0.386127i | \(-0.126187\pi\) | ||||
0.922446 | + | 0.386127i | \(0.126187\pi\) | |||||||
\(98\) | −10.9077 | + | 9.84505i | −1.10184 | + | 0.994500i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.204282 | + | 1.98954i | −0.0204282 | + | 0.198954i | ||||
\(101\) | − | 10.2399i | − | 1.01891i | −0.860499 | − | 0.509453i | \(-0.829848\pi\) | ||
0.860499 | − | 0.509453i | \(-0.170152\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.65985i | − | 0.951814i | −0.879496 | − | 0.475907i | \(-0.842120\pi\) | ||
0.879496 | − | 0.475907i | \(-0.157880\pi\) | |||||||
\(104\) | −2.96501 | − | 4.05023i | −0.290743 | − | 0.397158i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.62259 | − | 5.12153i | −0.448986 | − | 0.497447i | ||||
\(107\) | −3.23356 | −0.312600 | −0.156300 | − | 0.987710i | \(-0.549957\pi\) | ||||
−0.156300 | + | 0.987710i | \(0.549957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.88351 | 0.276190 | 0.138095 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138095 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(110\) | −6.10406 | − | 6.76290i | −0.581999 | − | 0.644817i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.38970 | − | 16.3325i | 0.320297 | − | 1.54327i | ||||
\(113\) | − | 3.08823i | − | 0.290516i | −0.989394 | − | 0.145258i | \(-0.953599\pi\) | ||
0.989394 | − | 0.145258i | \(-0.0464012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.02013i | − | 0.188378i | ||||||
\(116\) | 12.9858 | + | 1.33336i | 1.20571 | + | 0.123799i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.82176 | + | 2.54686i | −0.259764 | + | 0.234458i | ||||
\(119\) | 3.96446 | 0.363422 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.4982 | 2.77256 | ||||||||
\(122\) | 4.29699 | − | 3.87838i | 0.389031 | − | 0.351132i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.65518 | + | 0.580662i | 0.507850 | + | 0.0521450i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.16321i | − | 0.191954i | −0.995384 | − | 0.0959771i | \(-0.969402\pi\) | ||
0.995384 | − | 0.0959771i | \(-0.0305976\pi\) | |||||||
\(128\) | 4.68837 | + | 10.2966i | 0.414398 | + | 0.910096i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.68160 | + | 1.86310i | 0.147486 | + | 0.163405i | ||||
\(131\) | −1.91441 | −0.167263 | −0.0836315 | − | 0.996497i | \(-0.526652\pi\) | ||||
−0.0836315 | + | 0.996497i | \(0.526652\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.14452 | −0.792931 | ||||||||
\(134\) | 10.3245 | + | 11.4389i | 0.891901 | + | 0.988168i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.16969 | + | 1.58834i | −0.186049 | + | 0.136199i | ||||
\(137\) | − | 11.6608i | − | 0.996250i | −0.867105 | − | 0.498125i | \(-0.834022\pi\) | ||
0.867105 | − | 0.498125i | \(-0.165978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.66107i | 0.649804i | 0.945748 | + | 0.324902i | \(0.105331\pi\) | ||||
−0.945748 | + | 0.324902i | \(0.894669\pi\) | |||||||
\(140\) | −0.851880 | + | 8.29663i | −0.0719970 | + | 0.701194i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.34244 | − | 2.11424i | 0.196574 | − | 0.177423i | ||||
\(143\) | −11.4323 | −0.956014 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.52706 | −0.542043 | ||||||||
\(146\) | −1.83365 | + | 1.65501i | −0.151754 | + | 0.136970i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.19219 | + | 11.6109i | −0.0979970 | + | 0.954413i | ||||
\(149\) | 3.49438i | 0.286271i | 0.989703 | + | 0.143135i | \(0.0457184\pi\) | ||||
−0.989703 | + | 0.143135i | \(0.954282\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.11211i | 0.578775i | 0.957212 | + | 0.289388i | \(0.0934517\pi\) | ||||
−0.957212 | + | 0.289388i | \(0.906548\pi\) | |||||||
\(152\) | 5.00465 | − | 3.66370i | 0.405931 | − | 0.297165i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −25.4547 | − | 28.2022i | −2.05120 | − | 2.27259i | ||||
\(155\) | −2.84246 | −0.228312 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.15875 | −0.252096 | −0.126048 | − | 0.992024i | \(-0.540229\pi\) | ||||
−0.126048 | + | 0.992024i | \(0.540229\pi\) | |||||||
\(158\) | −0.234614 | − | 0.259938i | −0.0186649 | − | 0.0206795i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.85778 | − | 4.88192i | −0.225927 | − | 0.385949i | ||||
\(161\) | − | 8.42420i | − | 0.663920i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.1062i | 1.10488i | 0.833551 | + | 0.552442i | \(0.186304\pi\) | ||||
−0.833551 | + | 0.552442i | \(0.813696\pi\) | |||||||
\(164\) | 14.1566 | + | 1.45357i | 1.10545 | + | 0.113505i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.2545 | + | 11.0606i | −0.951131 | + | 0.858471i | ||||
\(167\) | 18.3328 | 1.41863 | 0.709317 | − | 0.704890i | \(-0.249003\pi\) | ||||
0.709317 | + | 0.704890i | \(0.249003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.85054 | −0.757734 | ||||||||
\(170\) | 0.998053 | − | 0.900823i | 0.0765472 | − | 0.0690899i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.5641 | + | 1.08470i | 0.805506 | + | 0.0827076i | ||||
\(173\) | − | 7.88176i | − | 0.599239i | −0.954059 | − | 0.299620i | \(-0.903140\pi\) | ||
0.954059 | − | 0.299620i | \(-0.0968598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.17013i | − | 0.315232i | ||||||
\(176\) | 25.2300 | + | 5.23632i | 1.90178 | + | 0.394703i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.81686 | − | 6.44470i | −0.435992 | − | 0.483051i | ||||
\(179\) | 9.84108 | 0.735557 | 0.367778 | − | 0.929914i | \(-0.380119\pi\) | ||||
0.367778 | + | 0.929914i | \(0.380119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3215 | 1.36183 | 0.680913 | − | 0.732364i | \(-0.261583\pi\) | ||||
0.680913 | + | 0.732364i | \(0.261583\pi\) | |||||||
\(182\) | 7.01248 | + | 7.76937i | 0.519799 | + | 0.575904i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.37510 | + | 4.61043i | 0.248816 | + | 0.339885i | ||||
\(185\) | − | 5.83599i | − | 0.429070i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.12420i | 0.447846i | ||||||||
\(188\) | 0.0825282 | − | 0.803758i | 0.00601898 | − | 0.0586201i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.30213 | + | 2.07786i | −0.167014 | + | 0.150744i | ||||
\(191\) | 19.0805 | 1.38061 | 0.690307 | − | 0.723516i | \(-0.257475\pi\) | ||||
0.690307 | + | 0.723516i | \(0.257475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0031 | −0.935983 | −0.467991 | − | 0.883733i | \(-0.655022\pi\) | ||||
−0.467991 | + | 0.883733i | \(0.655022\pi\) | |||||||
\(194\) | 19.0755 | − | 17.2171i | 1.36954 | − | 1.23612i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.12248 | + | 20.6712i | −0.151606 | + | 1.47652i | ||||
\(197\) | 15.8462i | 1.12899i | 0.825436 | + | 0.564496i | \(0.190929\pi\) | ||||
−0.825436 | + | 0.564496i | \(0.809071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.24563i | 0.0883001i | 0.999025 | + | 0.0441500i | \(0.0140580\pi\) | ||||
−0.999025 | + | 0.0441500i | \(0.985942\pi\) | |||||||
\(200\) | 1.67074 | + | 2.28224i | 0.118139 | + | 0.161379i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.70284 | − | 10.7501i | −0.682689 | − | 0.756375i | ||||
\(203\) | −27.2187 | −1.91038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.11552 | −0.496970 | ||||||||
\(206\) | −9.15324 | − | 10.1412i | −0.637736 | − | 0.706571i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.95057 | − | 1.44255i | −0.481935 | − | 0.100023i | ||||
\(209\) | − | 14.1262i | − | 0.977132i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.3244i | − | 1.12382i | −0.827198 | − | 0.561910i | \(-0.810067\pi\) | ||
0.827198 | − | 0.561910i | \(-0.189933\pi\) | |||||||
\(212\) | −9.70586 | − | 0.996577i | −0.666601 | − | 0.0684452i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.39469 | + | 3.06398i | −0.232056 | + | 0.209449i | ||||
\(215\) | −5.30982 | −0.362127 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.8534 | −0.804662 | ||||||||
\(218\) | 3.02719 | − | 2.73228i | 0.205027 | − | 0.185053i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.8164 | − | 1.31596i | −0.864084 | − | 0.0887222i | ||||
\(221\) | − | 1.68715i | − | 0.113490i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.9257i | − | 1.20040i | −0.799851 | − | 0.600198i | \(-0.795088\pi\) | ||
0.799851 | − | 0.600198i | \(-0.204912\pi\) | |||||||
\(224\) | −11.9173 | − | 20.3582i | −0.796257 | − | 1.36024i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.92626 | − | 3.24211i | −0.194652 | − | 0.215662i | ||||
\(227\) | −10.4304 | −0.692293 | −0.346146 | − | 0.938180i | \(-0.612510\pi\) | ||||
−0.346146 | + | 0.938180i | \(0.612510\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.7878 | −1.24153 | −0.620765 | − | 0.783997i | \(-0.713178\pi\) | ||||
−0.620765 | + | 0.783997i | \(0.713178\pi\) | |||||||
\(230\) | −1.91418 | − | 2.12079i | −0.126217 | − | 0.139841i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.8963 | − | 10.9050i | 0.977993 | − | 0.715948i | ||||
\(233\) | 7.28693i | 0.477382i | 0.971096 | + | 0.238691i | \(0.0767184\pi\) | ||||
−0.971096 | + | 0.238691i | \(0.923282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.403992i | 0.0263535i | ||||||||
\(236\) | −0.549074 | + | 5.34754i | −0.0357417 | + | 0.348096i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.16201 | − | 3.75654i | 0.269783 | − | 0.243501i | ||||
\(239\) | −29.6817 | −1.91995 | −0.959973 | − | 0.280091i | \(-0.909635\pi\) | ||||
−0.959973 | + | 0.280091i | \(0.909635\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.7503 | −0.821321 | −0.410661 | − | 0.911788i | \(-0.634702\pi\) | ||||
−0.410661 | + | 0.911788i | \(0.634702\pi\) | |||||||
\(242\) | 32.0179 | − | 28.8987i | 2.05819 | − | 1.85768i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.836133 | − | 8.14327i | 0.0535279 | − | 0.521319i | ||||
\(245\) | − | 10.3900i | − | 0.663790i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.89161i | 0.247618i | ||||||||
\(248\) | 6.48718 | − | 4.74900i | 0.411937 | − | 0.301562i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.947554 | − | 1.04983i | −0.0599286 | − | 0.0663970i | ||||
\(251\) | 2.89830 | 0.182939 | 0.0914694 | − | 0.995808i | \(-0.470844\pi\) | ||||
0.0914694 | + | 0.995808i | \(0.470844\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.0135 | 0.818151 | ||||||||
\(254\) | −2.04976 | − | 2.27101i | −0.128614 | − | 0.142496i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.6785 | + | 6.36714i | 0.917409 | + | 0.397946i | ||||
\(257\) | 9.96613i | 0.621670i | 0.950464 | + | 0.310835i | \(0.100609\pi\) | ||||
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 24.3368i | − | 1.51222i | ||||||
\(260\) | 3.53078 | + | 0.362533i | 0.218970 | + | 0.0224833i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.00981 | + | 1.81401i | −0.124166 | + | 0.112070i | ||||
\(263\) | −1.22162 | −0.0753281 | −0.0376640 | − | 0.999290i | \(-0.511992\pi\) | ||||
−0.0376640 | + | 0.999290i | \(0.511992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.87844 | 0.299680 | ||||||||
\(266\) | −9.60019 | + | 8.66493i | −0.588625 | + | 0.531281i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.6779 | + | 2.22584i | 1.32419 | + | 0.135965i | ||||
\(269\) | − | 19.0910i | − | 1.16400i | −0.813190 | − | 0.581998i | \(-0.802271\pi\) | ||
0.813190 | − | 0.581998i | \(-0.197729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.0019i | − | 0.729061i | −0.931191 | − | 0.364531i | \(-0.881229\pi\) | ||
0.931191 | − | 0.364531i | \(-0.118771\pi\) | |||||||
\(272\) | −0.772764 | + | 3.72338i | −0.0468557 | + | 0.225763i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.0492 | − | 12.2418i | −0.667509 | − | 0.739557i | ||||
\(275\) | 6.44191 | 0.388462 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.0283 | −1.44372 | −0.721860 | − | 0.692039i | \(-0.756712\pi\) | ||||
−0.721860 | + | 0.692039i | \(0.756712\pi\) | |||||||
\(278\) | 7.25928 | + | 8.04282i | 0.435383 | + | 0.482376i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.96718 | + | 9.51725i | 0.416369 | + | 0.568764i | ||||
\(281\) | 1.54857i | 0.0923797i | 0.998933 | + | 0.0461898i | \(0.0147079\pi\) | ||||
−0.998933 | + | 0.0461898i | \(0.985292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5575i | 1.45979i | 0.683559 | + | 0.729895i | \(0.260431\pi\) | ||||
−0.683559 | + | 0.729895i | \(0.739569\pi\) | |||||||
\(284\) | 0.455806 | − | 4.43919i | 0.0270471 | − | 0.263417i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0019 | + | 10.8327i | −0.709689 | + | 0.640551i | ||||
\(287\) | −29.6726 | −1.75152 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0962 | 0.946836 | ||||||||
\(290\) | −6.85230 | + | 6.18474i | −0.402381 | + | 0.363181i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.356802 | + | 3.47496i | −0.0208802 | + | 0.203357i | ||||
\(293\) | 27.1687i | 1.58721i | 0.608431 | + | 0.793607i | \(0.291799\pi\) | ||||
−0.608431 | + | 0.793607i | \(0.708201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.68783i | − | 0.156492i | ||||||
\(296\) | 9.75040 | + | 13.3192i | 0.566730 | + | 0.774160i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.31111 | + | 3.66850i | 0.191808 | + | 0.212511i | ||||
\(299\) | −3.58507 | −0.207330 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.1426 | −1.27628 | ||||||||
\(302\) | 6.73911 | + | 7.46650i | 0.387792 | + | 0.429649i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.78248 | − | 8.58844i | 0.102232 | − | 0.492581i | ||||
\(305\) | 4.09304i | 0.234367i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.96646i | − | 0.226378i | −0.993573 | − | 0.113189i | \(-0.963893\pi\) | ||
0.993573 | − | 0.113189i | \(-0.0361065\pi\) | |||||||
\(308\) | −53.4461 | − | 5.48773i | −3.04538 | − | 0.312693i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.98409 | + | 2.69338i | −0.169485 | + | 0.152974i | ||||
\(311\) | 19.3841 | 1.09917 | 0.549586 | − | 0.835437i | \(-0.314785\pi\) | ||||
0.549586 | + | 0.835437i | \(0.314785\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.9702 | 1.24183 | 0.620915 | − | 0.783878i | \(-0.286761\pi\) | ||||
0.620915 | + | 0.783878i | \(0.286761\pi\) | |||||||
\(314\) | −3.31615 | + | 2.99309i | −0.187141 | + | 0.168910i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.492610 | − | 0.0505801i | −0.0277115 | − | 0.00284535i | ||||
\(317\) | 26.6227i | 1.49528i | 0.664104 | + | 0.747640i | \(0.268813\pi\) | ||||
−0.664104 | + | 0.747640i | \(0.731187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 42.0467i | − | 2.35416i | ||||||
\(320\) | −7.62606 | − | 2.41728i | −0.426310 | − | 0.135130i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.98238 | − | 8.84397i | −0.444841 | − | 0.492855i | ||||
\(323\) | 2.08472 | 0.115997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.77467 | −0.0984411 | ||||||||
\(326\) | 13.3664 | + | 14.8091i | 0.740297 | + | 0.820201i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.2394 | − | 11.8882i | 0.896669 | − | 0.656414i | ||||
\(329\) | 1.68470i | 0.0928804i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 33.2166i | − | 1.82575i | −0.408238 | − | 0.912876i | \(-0.633857\pi\) | ||
0.408238 | − | 0.912876i | \(-0.366143\pi\) | |||||||
\(332\) | −2.38454 | + | 23.2235i | −0.130869 | + | 1.27456i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.2463 | − | 17.3713i | 1.05311 | − | 0.950516i | ||||
\(335\) | −10.8959 | −0.595309 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.61717 | 0.0880927 | 0.0440463 | − | 0.999029i | \(-0.485975\pi\) | ||||
0.0440463 | + | 0.999029i | \(0.485975\pi\) | |||||||
\(338\) | −10.3414 | + | 9.33392i | −0.562497 | + | 0.507698i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.194207 | − | 1.89142i | 0.0105323 | − | 0.102577i | ||||
\(341\) | − | 18.3109i | − | 0.991588i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.1366i | − | 0.763302i | ||||||
\(344\) | 12.1183 | − | 8.87132i | 0.653376 | − | 0.478309i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.46840 | − | 8.27450i | −0.401503 | − | 0.444840i | ||||
\(347\) | −5.18596 | −0.278397 | −0.139198 | − | 0.990265i | \(-0.544453\pi\) | ||||
−0.139198 | + | 0.990265i | \(0.544453\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.3343 | −0.981414 | −0.490707 | − | 0.871325i | \(-0.663261\pi\) | ||||
−0.490707 | + | 0.871325i | \(0.663261\pi\) | |||||||
\(350\) | −3.95142 | − | 4.37792i | −0.211212 | − | 0.234010i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 31.4489 | − | 18.4095i | 1.67623 | − | 0.981231i | ||||
\(353\) | 10.6975i | 0.569368i | 0.958621 | + | 0.284684i | \(0.0918886\pi\) | ||||
−0.958621 | + | 0.284684i | \(0.908111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.23126i | 0.118423i | ||||||||
\(356\) | −12.2134 | − | 1.25405i | −0.647309 | − | 0.0664643i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.3314 | − | 9.32495i | 0.546034 | − | 0.492839i | ||||
\(359\) | −15.1958 | −0.802005 | −0.401002 | − | 0.916077i | \(-0.631338\pi\) | ||||
−0.401002 | + | 0.916077i | \(0.631338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1913 | 0.746913 | ||||||||
\(362\) | 19.2344 | − | 17.3606i | 1.01094 | − | 0.912454i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.7238 | + | 1.51181i | 0.771737 | + | 0.0792403i | ||||
\(365\) | − | 1.74662i | − | 0.0914221i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5582i | 1.28193i | 0.767571 | + | 0.640964i | \(0.221465\pi\) | ||||
−0.767571 | + | 0.640964i | \(0.778535\pi\) | |||||||
\(368\) | 7.91192 | + | 1.64207i | 0.412437 | + | 0.0855987i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.52992 | − | 6.12679i | −0.287487 | − | 0.318517i | ||||
\(371\) | 20.3437 | 1.05619 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.6090 | 0.963538 | 0.481769 | − | 0.876298i | \(-0.339994\pi\) | ||||
0.481769 | + | 0.876298i | \(0.339994\pi\) | |||||||
\(374\) | 5.80302 | + | 6.42937i | 0.300067 | + | 0.332455i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.674964 | − | 0.922009i | −0.0348086 | − | 0.0475490i | ||||
\(377\) | 11.5834i | 0.596575i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.9052i | 1.43339i | 0.697386 | + | 0.716696i | \(0.254347\pi\) | ||||
−0.697386 | + | 0.716696i | \(0.745653\pi\) | |||||||
\(380\) | −0.447962 | + | 4.36279i | −0.0229800 | + | 0.223806i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.0312 | − | 18.0798i | 1.02489 | − | 0.925042i | ||||
\(383\) | −7.40233 | −0.378241 | −0.189121 | − | 0.981954i | \(-0.560564\pi\) | ||||
−0.189121 | + | 0.981954i | \(0.560564\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 26.8636 | 1.36909 | ||||||||
\(386\) | −13.6510 | + | 12.3211i | −0.694818 | + | 0.627129i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.71181 | − | 36.1501i | 0.188439 | − | 1.83524i | ||||
\(389\) | − | 17.9397i | − | 0.909579i | −0.890599 | − | 0.454789i | \(-0.849715\pi\) | ||
0.890599 | − | 0.454789i | \(-0.150285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.92050i | 0.0971239i | ||||||||
\(392\) | 17.3589 | + | 23.7124i | 0.876756 | + | 1.19766i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15.0151 | + | 16.6358i | 0.756450 | + | 0.838097i | ||||
\(395\) | 0.247600 | 0.0124581 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.9101 | −1.40077 | −0.700383 | − | 0.713768i | \(-0.746987\pi\) | ||||
−0.700383 | + | 0.713768i | \(0.746987\pi\) | |||||||
\(398\) | 1.18030 | + | 1.30769i | 0.0591630 | + | 0.0655488i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.91654 | + | 0.812853i | 0.195827 | + | 0.0406426i | ||||
\(401\) | − | 3.99705i | − | 0.199603i | −0.995007 | − | 0.0998015i | \(-0.968179\pi\) | ||
0.995007 | − | 0.0998015i | \(-0.0318208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.04443i | 0.251281i | ||||||||
\(404\) | −20.3726 | − | 2.09182i | −1.01358 | − | 0.104072i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28.5749 | + | 25.7912i | −1.41815 | + | 1.27999i | ||||
\(407\) | 37.5949 | 1.86351 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.1291 | 1.09421 | 0.547107 | − | 0.837063i | \(-0.315729\pi\) | ||||
0.547107 | + | 0.837063i | \(0.315729\pi\) | |||||||
\(410\) | −7.47008 | + | 6.74234i | −0.368921 | + | 0.332981i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −19.2187 | − | 1.97333i | −0.946836 | − | 0.0972190i | ||||
\(413\) | − | 11.2086i | − | 0.551539i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.6728i | − | 0.572996i | ||||||
\(416\) | −8.66380 | + | 5.07161i | −0.424778 | + | 0.248656i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.3854 | − | 14.8301i | −0.654700 | − | 0.725365i | ||||
\(419\) | 31.6137 | 1.54443 | 0.772215 | − | 0.635362i | \(-0.219149\pi\) | ||||
0.772215 | + | 0.635362i | \(0.219149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0566 | 1.46487 | 0.732435 | − | 0.680837i | \(-0.238384\pi\) | ||||
0.732435 | + | 0.680837i | \(0.238384\pi\) | |||||||
\(422\) | −15.4683 | − | 17.1379i | −0.752984 | − | 0.834258i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.1338 | + | 8.15059i | −0.540705 | + | 0.395828i | ||||
\(425\) | 0.950682i | 0.0461148i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0685i | 0.826002i | ||||||||
\(428\) | −0.660558 | + | 6.43331i | −0.0319293 | + | 0.310966i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.57441 | + | 5.03135i | −0.268822 | + | 0.242633i | ||||
\(431\) | 25.0832 | 1.20822 | 0.604108 | − | 0.796902i | \(-0.293529\pi\) | ||||
0.604108 | + | 0.796902i | \(0.293529\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.4297 | 1.41430 | 0.707151 | − | 0.707062i | \(-0.249980\pi\) | ||||
0.707151 | + | 0.707062i | \(0.249980\pi\) | |||||||
\(434\) | −12.4441 | + | 11.2318i | −0.597334 | + | 0.539141i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.589048 | − | 5.73685i | 0.0282103 | − | 0.274745i | ||||
\(437\) | − | 4.42987i | − | 0.211909i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.6552i | 1.36764i | 0.729651 | + | 0.683819i | \(0.239682\pi\) | ||||
−0.729651 | + | 0.683819i | \(0.760318\pi\) | |||||||
\(440\) | −14.7020 | + | 10.7627i | −0.700891 | + | 0.513093i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.59866 | − | 1.77122i | −0.0760407 | − | 0.0842482i | ||||
\(443\) | −29.8579 | −1.41859 | −0.709297 | − | 0.704910i | \(-0.750987\pi\) | ||||
−0.709297 | + | 0.704910i | \(0.750987\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.13881 | 0.291008 | ||||||||
\(446\) | −16.9856 | − | 18.8190i | −0.804292 | − | 0.891104i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −31.8016 | − | 10.0804i | −1.50249 | − | 0.476252i | ||||
\(449\) | 14.7017i | 0.693815i | 0.937899 | + | 0.346908i | \(0.112768\pi\) | ||||
−0.937899 | + | 0.346908i | \(0.887232\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 45.8375i | − | 2.15841i | ||||||
\(452\) | −6.14415 | − | 0.630868i | −0.288997 | − | 0.0296735i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.9502 | + | 9.88341i | −0.513918 | + | 0.463852i | ||||
\(455\) | −7.40061 | −0.346946 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.83336 | −0.413207 | −0.206604 | − | 0.978425i | \(-0.566241\pi\) | ||||
−0.206604 | + | 0.978425i | \(0.566241\pi\) | |||||||
\(458\) | −19.7239 | + | 17.8024i | −0.921639 | + | 0.831853i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.01913 | − | 0.412675i | −0.187393 | − | 0.0192411i | ||||
\(461\) | 0.913372i | 0.0425400i | 0.999774 | + | 0.0212700i | \(0.00677096\pi\) | ||||
−0.999774 | + | 0.0212700i | \(0.993229\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.87134i | − | 0.365812i | −0.983130 | − | 0.182906i | \(-0.941450\pi\) | ||
0.983130 | − | 0.182906i | \(-0.0585505\pi\) | |||||||
\(464\) | 5.30554 | − | 25.5635i | 0.246303 | − | 1.18675i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.90476 | + | 7.65003i | 0.319857 | + | 0.354381i | ||||
\(467\) | 28.6765 | 1.32699 | 0.663495 | − | 0.748181i | \(-0.269072\pi\) | ||||
0.663495 | + | 0.748181i | \(0.269072\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.4375 | −2.09811 | ||||||||
\(470\) | 0.382804 | + | 0.424123i | 0.0176575 | + | 0.0195633i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.49066 | + | 6.13429i | 0.206699 | + | 0.282353i | ||||
\(473\) | − | 34.2054i | − | 1.57277i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.19286i | − | 0.100616i | ||||||
\(476\) | 0.809867 | − | 7.88746i | 0.0371202 | − | 0.361521i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −31.1607 | + | 28.1250i | −1.42526 | + | 1.28641i | ||||
\(479\) | −26.3817 | −1.20541 | −0.602706 | − | 0.797963i | \(-0.705911\pi\) | ||||
−0.602706 | + | 0.797963i | \(0.705911\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3570 | −0.472237 | ||||||||
\(482\) | −13.3857 | + | 12.0816i | −0.609701 | + | 0.550304i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.23022 | − | 60.6773i | 0.283192 | − | 2.75806i | ||||
\(485\) | 18.1701i | 0.825060i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.87222i | − | 0.356724i | −0.983965 | − | 0.178362i | \(-0.942920\pi\) | ||
0.983965 | − | 0.178362i | \(-0.0570799\pi\) | |||||||
\(488\) | −6.83839 | − | 9.34132i | −0.309559 | − | 0.422862i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.84505 | − | 10.9077i | −0.444754 | − | 0.492759i | ||||
\(491\) | 19.4940 | 0.879751 | 0.439876 | − | 0.898059i | \(-0.355023\pi\) | ||||
0.439876 | + | 0.898059i | \(0.355023\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.20516 | 0.279466 | ||||||||
\(494\) | 3.68752 | + | 4.08553i | 0.165909 | + | 0.183817i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.31050 | − | 11.1326i | 0.103745 | − | 0.499868i | ||||
\(497\) | 9.30465i | 0.417371i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.846463i | − | 0.0378929i | −0.999821 | − | 0.0189464i | \(-0.993969\pi\) | ||
0.999821 | − | 0.0189464i | \(-0.00603120\pi\) | |||||||
\(500\) | −1.98954 | − | 0.204282i | −0.0889749 | − | 0.00913575i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.04272 | − | 2.74629i | 0.135803 | − | 0.122573i | ||||
\(503\) | −18.5253 | −0.826002 | −0.413001 | − | 0.910731i | \(-0.635519\pi\) | ||||
−0.413001 | + | 0.910731i | \(0.635519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2399 | 0.455668 | ||||||||
\(506\) | 13.6619 | − | 12.3310i | 0.607347 | − | 0.548179i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.30380 | − | 0.441905i | −0.190950 | − | 0.0196064i | ||||
\(509\) | 27.3040i | 1.21023i | 0.796138 | + | 0.605115i | \(0.206873\pi\) | ||||
−0.796138 | + | 0.605115i | \(0.793127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.28361i | − | 0.322208i | ||||||
\(512\) | 21.4432 | − | 7.22431i | 0.947663 | − | 0.319272i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.44345 | + | 10.4627i | 0.416533 | + | 0.461491i | ||||
\(515\) | 9.65985 | 0.425664 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.60248 | −0.114457 | ||||||||
\(518\) | −23.0605 | − | 25.5495i | −1.01322 | − | 1.12258i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.05023 | − | 2.96501i | 0.177615 | − | 0.130024i | ||||
\(521\) | 25.9868i | 1.13850i | 0.822163 | + | 0.569252i | \(0.192767\pi\) | ||||
−0.822163 | + | 0.569252i | \(0.807233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.1683i | 1.31917i | 0.751631 | + | 0.659584i | \(0.229268\pi\) | ||||
−0.751631 | + | 0.659584i | \(0.770732\pi\) | |||||||
\(524\) | −0.391079 | + | 3.80880i | −0.0170844 | + | 0.166388i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.28249 | + | 1.15755i | −0.0559191 | + | 0.0504715i | ||||
\(527\) | 2.70227 | 0.117713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.9191 | −0.822568 | ||||||||
\(530\) | 5.12153 | − | 4.62259i | 0.222465 | − | 0.200793i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.86806 | + | 18.1934i | −0.0809906 | + | 0.788784i | ||||
\(533\) | 12.6277i | 0.546967i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 3.23356i | − | 0.139799i | ||||||
\(536\) | 24.8672 | − | 18.2042i | 1.07410 | − | 0.786304i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.0897 | − | 20.0423i | −0.779904 | − | 0.864083i | ||||
\(539\) | 66.9311 | 2.88293 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.2068 | −1.47067 | −0.735333 | − | 0.677706i | \(-0.762974\pi\) | ||||
−0.735333 | + | 0.677706i | \(0.762974\pi\) | |||||||
\(542\) | −11.3724 | − | 12.5999i | −0.488487 | − | 0.541212i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.71684 | + | 4.64115i | 0.116483 | + | 0.198988i | ||||
\(545\) | 2.88351i | 0.123516i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.0152i | − | 0.684761i | −0.939561 | − | 0.342380i | \(-0.888767\pi\) | ||
0.939561 | − | 0.342380i | \(-0.111233\pi\) | |||||||
\(548\) | −23.1996 | − | 2.38209i | −0.991039 | − | 0.101758i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.76290 | − | 6.10406i | 0.288371 | − | 0.260278i | ||||
\(551\) | −14.3130 | −0.609753 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03252 | 0.0439073 | ||||||||
\(554\) | −25.2256 | + | 22.7681i | −1.07173 | + | 0.967324i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.2420 | + | 1.56502i | 0.646405 | + | 0.0663715i | ||||
\(557\) | 16.0344i | 0.679401i | 0.940534 | + | 0.339701i | \(0.110326\pi\) | ||||
−0.940534 | + | 0.339701i | \(0.889674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.42320i | 0.398559i | ||||||||
\(560\) | 16.3325 | + | 3.38970i | 0.690172 | + | 0.143241i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.46735 | + | 1.62573i | 0.0618964 | + | 0.0685772i | ||||
\(563\) | −4.47364 | −0.188541 | −0.0942707 | − | 0.995547i | \(-0.530052\pi\) | ||||
−0.0942707 | + | 0.995547i | \(0.530052\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.08823 | 0.129923 | ||||||||
\(566\) | 23.2695 | + | 25.7812i | 0.978092 | + | 1.08366i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.72785 | − | 5.09229i | −0.156417 | − | 0.213668i | ||||
\(569\) | 41.0451i | 1.72070i | 0.509705 | + | 0.860349i | \(0.329755\pi\) | ||||
−0.509705 | + | 0.860349i | \(0.670245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 45.2501i | − | 1.89366i | −0.321741 | − | 0.946828i | \(-0.604268\pi\) | ||
0.321741 | − | 0.946828i | \(-0.395732\pi\) | |||||||
\(572\) | −2.33540 | + | 22.7450i | −0.0976481 | + | 0.951014i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −31.1512 | + | 28.1164i | −1.30023 | + | 1.17356i | ||||
\(575\) | 2.02013 | 0.0842452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.1400 | −1.12985 | −0.564927 | − | 0.825141i | \(-0.691096\pi\) | ||||
−0.564927 | + | 0.825141i | \(0.691096\pi\) | |||||||
\(578\) | 16.8983 | − | 15.2520i | 0.702875 | − | 0.634401i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.33336 | + | 12.9858i | −0.0553647 | + | 0.539208i | ||||
\(581\) | − | 48.6771i | − | 2.01947i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.4265i | 1.30155i | ||||||||
\(584\) | 2.91814 | + | 3.98621i | 0.120753 | + | 0.164950i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.7438 | + | 28.5225i | 1.06347 | + | 1.17825i | ||||
\(587\) | −17.5383 | −0.723883 | −0.361941 | − | 0.932201i | \(-0.617886\pi\) | ||||
−0.361941 | + | 0.932201i | \(0.617886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.23313 | −0.256831 | ||||||||
\(590\) | −2.54686 | − | 2.82176i | −0.104853 | − | 0.116170i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.8569 | + | 4.74380i | 0.939412 | + | 0.194969i | ||||
\(593\) | − | 15.6793i | − | 0.643872i | −0.946761 | − | 0.321936i | \(-0.895666\pi\) | ||
0.946761 | − | 0.321936i | \(-0.104334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.96446i | 0.162527i | ||||||||
\(596\) | 6.95221 | + | 0.713837i | 0.284773 | + | 0.0292399i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.76371 | + | 3.39705i | −0.153909 | + | 0.138916i | ||||
\(599\) | 7.21949 | 0.294980 | 0.147490 | − | 0.989064i | \(-0.452881\pi\) | ||||
0.147490 | + | 0.989064i | \(0.452881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.9916 | 1.87604 | 0.938019 | − | 0.346583i | \(-0.112658\pi\) | ||||
0.938019 | + | 0.346583i | \(0.112658\pi\) | |||||||
\(602\) | −23.2460 | + | 20.9814i | −0.947436 | + | 0.855136i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.1498 | + | 1.45287i | 0.575748 | + | 0.0591166i | ||||
\(605\) | 30.4982i | 1.23993i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.14863i | − | 0.0872103i | −0.999049 | − | 0.0436052i | \(-0.986116\pi\) | ||
0.999049 | − | 0.0436052i | \(-0.0138844\pi\) | |||||||
\(608\) | −6.26672 | − | 10.7054i | −0.254149 | − | 0.434161i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.87838 | + | 4.29699i | 0.157031 | + | 0.173980i | ||||
\(611\) | 0.716953 | 0.0290048 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.8432 | −1.81120 | −0.905601 | − | 0.424131i | \(-0.860579\pi\) | ||||
−0.905601 | + | 0.424131i | \(0.860579\pi\) | |||||||
\(614\) | −3.75844 | − | 4.16411i | −0.151678 | − | 0.168050i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −61.3092 | + | 44.8819i | −2.47022 | + | 1.80835i | ||||
\(617\) | 34.4459i | 1.38674i | 0.720581 | + | 0.693371i | \(0.243875\pi\) | ||||
−0.720581 | + | 0.693371i | \(0.756125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.7731i | 0.513396i | 0.966492 | + | 0.256698i | \(0.0826345\pi\) | ||||
−0.966492 | + | 0.256698i | \(0.917365\pi\) | |||||||
\(620\) | −0.580662 | + | 5.65518i | −0.0233199 | + | 0.227118i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.3500 | − | 18.3675i | 0.815961 | − | 0.736469i | ||||
\(623\) | 25.5996 | 1.02563 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.0650 | − | 20.8180i | 0.921862 | − | 0.832054i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.645275 | + | 6.28446i | −0.0257493 | + | 0.250777i | ||||
\(629\) | 5.54817i | 0.221220i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.9765i | − | 0.516586i | −0.966067 | − | 0.258293i | \(-0.916840\pi\) | ||
0.966067 | − | 0.258293i | \(-0.0831600\pi\) | |||||||
\(632\) | −0.565083 | + | 0.413674i | −0.0224778 | + | 0.0164551i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.2265 | + | 27.9493i | 1.00187 | + | 1.11001i | ||||
\(635\) | 2.16321 | 0.0858445 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.4388 | −0.730570 | ||||||||
\(638\) | −39.8415 | − | 44.1419i | −1.57734 | − | 1.74759i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.2966 | + | 4.68837i | −0.407007 | + | 0.185324i | ||||
\(641\) | 30.5564i | 1.20691i | 0.797398 | + | 0.603453i | \(0.206209\pi\) | ||||
−0.797398 | + | 0.603453i | \(0.793791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.17425i | 0.243489i | 0.992561 | + | 0.121744i | \(0.0388488\pi\) | ||||
−0.992561 | + | 0.121744i | \(0.961151\pi\) | |||||||
\(644\) | −16.7603 | − | 1.72091i | −0.660447 | − | 0.0678133i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.18860 | − | 1.97538i | 0.0861091 | − | 0.0777204i | ||||
\(647\) | 9.68580 | 0.380788 | 0.190394 | − | 0.981708i | \(-0.439023\pi\) | ||||
0.190394 | + | 0.981708i | \(0.439023\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.3148 | 0.679663 | ||||||||
\(650\) | −1.86310 | + | 1.68160i | −0.0730769 | + | 0.0659577i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28.0649 | + | 2.88164i | 1.09911 | + | 0.112854i | ||||
\(653\) | 16.3465i | 0.639688i | 0.947470 | + | 0.319844i | \(0.103631\pi\) | ||||
−0.947470 | + | 0.319844i | \(0.896369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.91441i | − | 0.0748023i | ||||||
\(656\) | 5.78387 | − | 27.8682i | 0.225822 | − | 1.08807i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.59634 | + | 1.76864i | 0.0622319 | + | 0.0689490i | ||||
\(659\) | 23.0858 | 0.899295 | 0.449648 | − | 0.893206i | \(-0.351550\pi\) | ||||
0.449648 | + | 0.893206i | \(0.351550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4701 | 0.718403 | 0.359202 | − | 0.933260i | \(-0.383049\pi\) | ||||
0.359202 | + | 0.933260i | \(0.383049\pi\) | |||||||
\(662\) | −31.4746 | − | 34.8718i | −1.22329 | − | 1.35533i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.5022 | + | 26.6402i | 0.756832 | + | 1.03384i | ||||
\(665\) | − | 9.14452i | − | 0.354609i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 13.1855i | − | 0.510545i | ||||||
\(668\) | 3.74505 | − | 36.4738i | 0.144900 | − | 1.41121i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.4389 | + | 10.3245i | −0.441922 | + | 0.398870i | ||||
\(671\) | −26.3670 | −1.01789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.3154 | −1.16857 | −0.584286 | − | 0.811548i | \(-0.698625\pi\) | ||||
−0.584286 | + | 0.811548i | \(0.698625\pi\) | |||||||
\(674\) | 1.69775 | − | 1.53235i | 0.0653948 | − | 0.0590240i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.01228 | + | 19.5980i | −0.0773956 | + | 0.753771i | ||||
\(677\) | − | 42.3891i | − | 1.62915i | −0.580061 | − | 0.814573i | \(-0.696971\pi\) | ||
0.580061 | − | 0.814573i | \(-0.303029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 75.7715i | 2.90784i | ||||||||
\(680\) | −1.58834 | − | 2.16969i | −0.0609100 | − | 0.0832037i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.3505 | − | 19.2233i | −0.664386 | − | 0.736097i | ||||
\(683\) | −20.7847 | −0.795303 | −0.397652 | − | 0.917536i | \(-0.630175\pi\) | ||||
−0.397652 | + | 0.917536i | \(0.630175\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.6608 | 0.445536 | ||||||||
\(686\) | −13.3952 | − | 14.8410i | −0.511429 | − | 0.566631i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.31611 | − | 20.7961i | 0.164550 | − | 0.792845i | ||||
\(689\) | − | 8.65764i | − | 0.329830i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 42.6767i | − | 1.62350i | −0.584007 | − | 0.811748i | \(-0.698516\pi\) | ||
0.584007 | − | 0.811748i | \(-0.301484\pi\) | |||||||
\(692\) | −15.6811 | − | 1.61010i | −0.596105 | − | 0.0612068i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.44437 | + | 4.91398i | −0.206665 | + | 0.186532i | ||||
\(695\) | −7.66107 | −0.290601 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.76460 | 0.256227 | ||||||||
\(698\) | −19.2479 | + | 17.3728i | −0.728544 | + | 0.657569i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.29663 | − | 0.851880i | −0.313583 | − | 0.0321981i | ||||
\(701\) | 26.5424i | 1.00249i | 0.865305 | + | 0.501247i | \(0.167125\pi\) | ||||
−0.865305 | + | 0.501247i | \(0.832875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 12.7975i | − | 0.482668i | ||||||
\(704\) | 15.5719 | − | 49.1264i | 0.586888 | − | 1.85152i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.1364 | + | 11.2305i | 0.381489 | + | 0.422665i | ||||
\(707\) | 42.7016 | 1.60596 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.2540 | 1.73711 | 0.868553 | − | 0.495596i | \(-0.165050\pi\) | ||||
0.868553 | + | 0.495596i | \(0.165050\pi\) | |||||||
\(710\) | 2.11424 | + | 2.34244i | 0.0793461 | + | 0.0879104i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.0103 | + | 10.2563i | −0.525057 | + | 0.384372i | ||||
\(713\) | − | 5.74213i | − | 0.215045i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 11.4323i | − | 0.427543i | ||||||
\(716\) | 2.01035 | − | 19.5792i | 0.0751304 | − | 0.731710i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.9530 | + | 14.3989i | −0.595361 | + | 0.537361i | ||||
\(719\) | −44.9992 | −1.67819 | −0.839094 | − | 0.543986i | \(-0.816914\pi\) | ||||
−0.839094 | + | 0.543986i | \(0.816914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.2828 | 1.50021 | ||||||||
\(722\) | 14.8985 | − | 13.4471i | 0.554464 | − | 0.500448i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.74275 | − | 36.4514i | 0.139098 | − | 1.35470i | ||||
\(725\) | − | 6.52706i | − | 0.242409i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6578i | 1.32247i | 0.750177 | + | 0.661237i | \(0.229968\pi\) | ||||
−0.750177 | + | 0.661237i | \(0.770032\pi\) | |||||||
\(728\) | 16.8900 | − | 12.3645i | 0.625985 | − | 0.458257i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.65501 | − | 1.83365i | −0.0612548 | − | 0.0678664i | ||||
\(731\) | 5.04795 | 0.186705 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.1392 | −1.74113 | −0.870563 | − | 0.492057i | \(-0.836245\pi\) | ||||
−0.870563 | + | 0.492057i | \(0.836245\pi\) | |||||||
\(734\) | 23.2702 | + | 25.7819i | 0.858920 | + | 0.951628i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.86211 | − | 5.77308i | 0.363522 | − | 0.212798i | ||||
\(737\) | − | 70.1906i | − | 2.58551i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 40.9282i | − | 1.50557i | −0.658268 | − | 0.752784i | \(-0.728711\pi\) | ||
0.658268 | − | 0.752784i | \(-0.271289\pi\) | |||||||
\(740\) | −11.6109 | − | 1.19219i | −0.426826 | − | 0.0438256i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.3574 | − | 19.2768i | 0.784056 | − | 0.707673i | ||||
\(743\) | 33.8553 | 1.24203 | 0.621014 | − | 0.783799i | \(-0.286721\pi\) | ||||
0.621014 | + | 0.783799i | \(0.286721\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.49438 | −0.128024 | ||||||||
\(746\) | 19.5363 | − | 17.6331i | 0.715274 | − | 0.645592i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.1843 | + | 1.25106i | 0.445504 | + | 0.0457434i | ||||
\(749\) | − | 13.4844i | − | 0.492708i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.85461i | 0.250128i | 0.992149 | + | 0.125064i | \(0.0399137\pi\) | ||||
−0.992149 | + | 0.125064i | \(0.960086\pi\) | |||||||
\(752\) | −1.58225 | − | 0.328386i | −0.0576987 | − | 0.0119750i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.9759 | + | 12.1606i | 0.399718 | + | 0.442862i | ||||
\(755\) | −7.11211 | −0.258836 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.8568 | 1.48497 | 0.742483 | − | 0.669865i | \(-0.233648\pi\) | ||||
0.742483 | + | 0.669865i | \(0.233648\pi\) | |||||||
\(758\) | 26.4417 | + | 29.2957i | 0.960404 | + | 1.06407i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.66370 | + | 5.00465i | 0.132896 | + | 0.181538i | ||||
\(761\) | 27.9013i | 1.01142i | 0.862703 | + | 0.505710i | \(0.168769\pi\) | ||||
−0.862703 | + | 0.505710i | \(0.831231\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0246i | 0.435319i | ||||||||
\(764\) | 3.89779 | − | 37.9614i | 0.141017 | − | 1.37339i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.77118 | + | 7.01411i | −0.280784 | + | 0.253430i | ||||
\(767\) | −4.77002 | −0.172235 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.12340 | 0.220816 | 0.110408 | − | 0.993886i | \(-0.464784\pi\) | ||||
0.110408 | + | 0.993886i | \(0.464784\pi\) | |||||||
\(770\) | 28.2022 | − | 25.4547i | 1.01634 | − | 0.917323i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.65629 | + | 25.8702i | −0.0956020 | + | 0.931087i | ||||
\(773\) | 14.8193i | 0.533012i | 0.963833 | + | 0.266506i | \(0.0858692\pi\) | ||||
−0.963833 | + | 0.266506i | \(0.914131\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.84246i | − | 0.102104i | ||||||
\(776\) | −30.3574 | − | 41.4685i | −1.08977 | − | 1.48863i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.9988 | − | 18.8336i | −0.609438 | − | 0.675218i | ||||
\(779\) | −15.6034 | −0.559049 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.3736 | −0.514328 | ||||||||
\(782\) | 1.81978 | + | 2.01620i | 0.0650751 | + | 0.0720991i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 40.6927 | + | 8.44551i | 1.45331 | + | 0.301625i | ||||
\(785\) | − | 3.15875i | − | 0.112741i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.7271i | 0.560609i | 0.959911 | + | 0.280305i | \(0.0904355\pi\) | ||||
−0.959911 | + | 0.280305i | \(0.909564\pi\) | |||||||
\(788\) | 31.5266 | + | 3.23708i | 1.12309 | + | 0.115316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.259938 | − | 0.234614i | 0.00924816 | − | 0.00834720i | ||||
\(791\) | 12.8783 | 0.457900 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.26380 | 0.257945 | ||||||||
\(794\) | −29.3008 | + | 26.4463i | −1.03985 | + | 0.938544i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.47822 | + | 0.254459i | 0.0878383 | + | 0.00901904i | ||||
\(797\) | 43.3678i | 1.53617i | 0.640350 | + | 0.768083i | \(0.278789\pi\) | ||||
−0.640350 | + | 0.768083i | \(0.721211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.384068i | − | 0.0135873i | ||||||
\(800\) | 4.88192 | − | 2.85778i | 0.172602 | − | 0.101038i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.78742 | − | 4.19622i | −0.133738 | − | 0.148174i | ||||
\(803\) | 11.2515 | 0.397058 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.42420 | 0.296914 | ||||||||
\(806\) | 4.77987 | + | 5.29579i | 0.168364 | + | 0.186536i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.3699 | + | 17.1081i | −0.822150 | + | 0.601862i | ||||
\(809\) | 0.395982i | 0.0139220i | 0.999976 | + | 0.00696100i | \(0.00221577\pi\) | ||||
−0.999976 | + | 0.00696100i | \(0.997784\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.9241i | 1.61261i | 0.591498 | + | 0.806307i | \(0.298537\pi\) | ||||
−0.591498 | + | 0.806307i | \(0.701463\pi\) | |||||||
\(812\) | −5.56027 | + | 54.1526i | −0.195127 | + | 1.90038i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 39.4682 | − | 35.6232i | 1.38336 | − | 1.24859i | ||||
\(815\) | −14.1062 | −0.494119 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.6437 | −0.407362 | ||||||||
\(818\) | 23.2318 | − | 20.9685i | 0.812279 | − | 0.733147i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.45357 | + | 14.1566i | −0.0507609 | + | 0.494370i | ||||
\(821\) | 34.0437i | 1.18813i | 0.804415 | + | 0.594067i | \(0.202479\pi\) | ||||
−0.804415 | + | 0.594067i | \(0.797521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.5134i | − | 0.366475i | −0.983069 | − | 0.183238i | \(-0.941342\pi\) | ||
0.983069 | − | 0.183238i | \(-0.0586578\pi\) | |||||||
\(824\) | −22.0462 | + | 16.1391i | −0.768014 | + | 0.562231i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.6207 | − | 11.7671i | −0.369543 | − | 0.409430i | ||||
\(827\) | 40.8826 | 1.42163 | 0.710813 | − | 0.703381i | \(-0.248327\pi\) | ||||
0.710813 | + | 0.703381i | \(0.248327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.0184 | 0.834194 | 0.417097 | − | 0.908862i | \(-0.363048\pi\) | ||||
0.417097 | + | 0.908862i | \(0.363048\pi\) | |||||||
\(830\) | −11.0606 | − | 12.2545i | −0.383920 | − | 0.425359i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.28988 | + | 13.5337i | −0.148725 | + | 0.469198i | ||||
\(833\) | 9.87754i | 0.342237i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.3328i | 0.634432i | ||||||||
\(836\) | −28.1047 | − | 2.88573i | −0.972021 | − | 0.0998050i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 33.1890 | − | 29.9557i | 1.14649 | − | 1.03480i | ||||
\(839\) | 34.1904 | 1.18038 | 0.590192 | − | 0.807263i | \(-0.299052\pi\) | ||||
0.590192 | + | 0.807263i | \(0.299052\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.6025 | −0.469052 | ||||||||
\(842\) | 31.5543 | − | 28.4803i | 1.08743 | − | 0.981495i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −32.4781 | − | 3.33478i | −1.11794 | − | 0.114788i | ||||
\(845\) | − | 9.85054i | − | 0.338869i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 127.181i | 4.37000i | ||||||||
\(848\) | −3.96546 | + | 19.1066i | −0.136174 | + | 0.656124i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.900823 | + | 0.998053i | 0.0308980 | + | 0.0342329i | ||||
\(851\) | 11.7895 | 0.404137 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.7483 | −0.847366 | −0.423683 | − | 0.905811i | \(-0.639263\pi\) | ||||
−0.423683 | + | 0.905811i | \(0.639263\pi\) | |||||||
\(854\) | 16.1733 | + | 17.9190i | 0.553440 | + | 0.613176i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.40243 | + | 7.37979i | 0.184651 | + | 0.252236i | ||||
\(857\) | − | 10.6711i | − | 0.364518i | −0.983251 | − | 0.182259i | \(-0.941659\pi\) | ||
0.983251 | − | 0.182259i | \(-0.0583410\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.8104i | 0.812401i | 0.913784 | + | 0.406200i | \(0.133146\pi\) | ||||
−0.913784 | + | 0.406200i | \(0.866854\pi\) | |||||||
\(860\) | −1.08470 | + | 10.5641i | −0.0369880 | + | 0.360233i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.3331 | − | 23.7677i | 0.896909 | − | 0.809532i | ||||
\(863\) | 53.1072 | 1.80779 | 0.903896 | − | 0.427753i | \(-0.140695\pi\) | ||||
0.903896 | + | 0.427753i | \(0.140695\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.88176 | 0.267988 | ||||||||
\(866\) | 30.8962 | − | 27.8863i | 1.04989 | − | 0.947614i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.42143 | + | 23.5828i | −0.0821888 | + | 0.800454i | ||||
\(869\) | 1.59502i | 0.0541072i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.3367i | 0.655200i | ||||||||
\(872\) | −4.81758 | − | 6.58087i | −0.163144 | − | 0.222856i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.19754 | − | 4.65061i | −0.141984 | − | 0.157309i | ||||
\(875\) | 4.17013 | 0.140976 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.4276 | −1.39891 | −0.699456 | − | 0.714676i | \(-0.746574\pi\) | ||||
−0.699456 | + | 0.714676i | \(0.746574\pi\) | |||||||
\(878\) | 27.1524 | + | 30.0831i | 0.916348 | + | 1.01525i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.23632 | + | 25.2300i | −0.176516 | + | 0.850502i | ||||
\(881\) | 18.8579i | 0.635340i | 0.948201 | + | 0.317670i | \(0.102900\pi\) | ||||
−0.948201 | + | 0.317670i | \(0.897100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 36.0305i | − | 1.21252i | −0.795266 | − | 0.606261i | \(-0.792669\pi\) | ||
0.795266 | − | 0.606261i | \(-0.207331\pi\) | |||||||
\(884\) | −3.35665 | − | 0.344653i | −0.112896 | − | 0.0115919i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.3457 | + | 28.2920i | −1.05308 | + | 0.950489i | ||||
\(887\) | 19.3362 | 0.649245 | 0.324623 | − | 0.945844i | \(-0.394763\pi\) | ||||
0.324623 | + | 0.945844i | \(0.394763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.02088 | 0.302551 | ||||||||
\(890\) | 6.44470 | − | 5.81686i | 0.216027 | − | 0.194981i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −35.6640 | − | 3.66190i | −1.19412 | − | 0.122609i | ||||
\(893\) | 0.885900i | 0.0296455i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.84108i | 0.328951i | ||||||||
\(896\) | −42.9380 | + | 19.5511i | −1.43446 | + | 0.653157i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.9306 | + | 15.4343i | 0.464872 | + | 0.515048i | ||||
\(899\) | −18.5529 | −0.618774 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.63785 | −0.154509 | ||||||||
\(902\) | −43.4336 | − | 48.1216i | −1.44618 | − | 1.60227i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.04809 | + | 5.15961i | −0.234416 | + | 0.171606i | ||||
\(905\) | 18.3215i | 0.609027i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.1102i | − | 0.568134i | −0.958804 | − | 0.284067i | \(-0.908316\pi\) | ||
0.958804 | − | 0.284067i | \(-0.0916838\pi\) | |||||||
\(908\) | −2.13075 | + | 20.7518i | −0.0707114 | + | 0.688672i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.76937 | + | 7.01248i | −0.257552 | + | 0.232461i | ||||
\(911\) | 11.3283 | 0.375324 | 0.187662 | − | 0.982234i | \(-0.439909\pi\) | ||||
0.187662 | + | 0.982234i | \(0.439909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 75.1952 | 2.48860 | ||||||||
\(914\) | −9.27352 | + | 8.37009i | −0.306741 | + | 0.276858i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.83799 | + | 37.3790i | −0.126811 | + | 1.23504i | ||||
\(917\) | − | 7.98334i | − | 0.263633i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.3567i | 1.10034i | 0.835054 | + | 0.550169i | \(0.185437\pi\) | ||||
−0.835054 | + | 0.550169i | \(0.814563\pi\) | |||||||
\(920\) | −4.61043 | + | 3.37510i | −0.152001 | + | 0.111274i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.865470 | + | 0.958885i | 0.0285027 | + | 0.0315792i | ||||
\(923\) | 3.95976 | 0.130337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.83599 | 0.191886 | ||||||||
\(926\) | −7.45853 | − | 8.26357i | −0.245102 | − | 0.271558i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −18.6529 | − | 31.8646i | −0.612311 | − | 1.04601i | ||||
\(929\) | − | 10.4925i | − | 0.344248i | −0.985075 | − | 0.172124i | \(-0.944937\pi\) | ||
0.985075 | − | 0.172124i | \(-0.0550630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 22.7838i | − | 0.746708i | ||||||
\(932\) | 14.4976 | + | 1.48859i | 0.474886 | + | 0.0487602i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.1054 | − | 27.1725i | 0.985079 | − | 0.889113i | ||||
\(935\) | −6.12420 | −0.200283 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.4458 | 0.961952 | 0.480976 | − | 0.876734i | \(-0.340282\pi\) | ||||
0.480976 | + | 0.876734i | \(0.340282\pi\) | |||||||
\(938\) | −47.7016 | + | 43.0545i | −1.55751 | + | 1.40578i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.803758 | + | 0.0825282i | 0.0262157 | + | 0.00269177i | ||||
\(941\) | 36.0415i | 1.17492i | 0.809254 | + | 0.587459i | \(0.199872\pi\) | ||||
−0.809254 | + | 0.587459i | \(0.800128\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.3743i | − | 0.468091i | ||||||
\(944\) | 10.5270 | + | 2.18481i | 0.342624 | + | 0.0711095i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.4115 | − | 35.9098i | −1.05379 | − | 1.16753i | ||||
\(947\) | 12.1726 | 0.395557 | 0.197778 | − | 0.980247i | \(-0.436627\pi\) | ||||
0.197778 | + | 0.980247i | \(0.436627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.09967 | −0.100620 | ||||||||
\(950\) | −2.07786 | − | 2.30213i | −0.0674146 | − | 0.0746911i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.62357 | − | 9.04787i | −0.214671 | − | 0.293243i | ||||
\(953\) | 25.0300i | 0.810801i | 0.914139 | + | 0.405400i | \(0.132868\pi\) | ||||
−0.914139 | + | 0.405400i | \(0.867132\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.0805i | 0.617430i | ||||||||
\(956\) | −6.06342 | + | 59.0528i | −0.196105 | + | 1.90991i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.6963 | + | 24.9981i | −0.894827 | + | 0.807653i | ||||
\(959\) | 48.6270 | 1.57025 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.9204 | 0.739369 | ||||||||
\(962\) | −10.8730 | + | 9.81379i | −0.350561 | + | 0.316409i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.60466 | + | 25.3673i | −0.0838905 | + | 0.817026i | ||||
\(965\) | − | 13.0031i | − | 0.418584i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.75536i | − | 0.0886063i | −0.999018 | − | 0.0443032i | \(-0.985893\pi\) | ||
0.999018 | − | 0.0443032i | \(-0.0141068\pi\) | |||||||
\(968\) | −50.9544 | − | 69.6043i | −1.63774 | − | 2.23717i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.2171 | + | 19.0755i | 0.552809 | + | 0.612476i | ||||
\(971\) | −33.6700 | −1.08052 | −0.540261 | − | 0.841497i | \(-0.681675\pi\) | ||||
−0.540261 | + | 0.841497i | \(0.681675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.9476 | −1.02419 | ||||||||
\(974\) | −7.45936 | − | 8.26448i | −0.239013 | − | 0.264811i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.0305 | − | 3.32704i | −0.513125 | − | 0.106496i | ||||
\(977\) | − | 56.0751i | − | 1.79400i | −0.442030 | − | 0.897000i | \(-0.645742\pi\) | ||
0.442030 | − | 0.897000i | \(-0.354258\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39.5457i | 1.26388i | ||||||||
\(980\) | −20.6712 | − | 2.12248i | −0.660318 | − | 0.0678001i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.4654 | − | 18.4716i | 0.653076 | − | 0.589453i | ||||
\(983\) | 15.0532 | 0.480124 | 0.240062 | − | 0.970758i | \(-0.422832\pi\) | ||||
0.240062 | + | 0.970758i | \(0.422832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.8462 | −0.504901 | ||||||||
\(986\) | 6.51435 | − | 5.87972i | 0.207459 | − | 0.187249i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.74252 | + | 0.794985i | 0.246322 | + | 0.0252919i | ||||
\(989\) | − | 10.7265i | − | 0.341084i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 32.4096i | − | 1.02953i | −0.857333 | − | 0.514763i | \(-0.827880\pi\) | ||
0.857333 | − | 0.514763i | \(-0.172120\pi\) | |||||||
\(992\) | −8.12311 | − | 13.8766i | −0.257909 | − | 0.440584i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.81666 | + | 9.76829i | 0.279648 | + | 0.309831i | ||||
\(995\) | −1.24563 | −0.0394890 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.1499 | −1.39824 | −0.699120 | − | 0.715004i | \(-0.746425\pi\) | ||||
−0.699120 | + | 0.715004i | \(0.746425\pi\) | |||||||
\(998\) | −0.802069 | − | 0.888641i | −0.0253891 | − | 0.0281294i | ||||
\(999\) | 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 | 1620.2.e.b.971.37 | 48 | ||
3.2 | odd | 2 | inner | 1620.2.e.b.971.12 | 48 | ||
4.3 | odd | 2 | inner | 1620.2.e.b.971.11 | 48 | ||
9.2 | odd | 6 | 540.2.q.a.71.22 | 48 | |||
9.4 | even | 3 | 540.2.q.a.251.15 | 48 | |||
9.5 | odd | 6 | 180.2.q.a.11.10 | yes | 48 | ||
9.7 | even | 3 | 180.2.q.a.131.3 | yes | 48 | ||
12.11 | even | 2 | inner | 1620.2.e.b.971.38 | 48 | ||
36.7 | odd | 6 | 180.2.q.a.131.10 | yes | 48 | ||
36.11 | even | 6 | 540.2.q.a.71.15 | 48 | |||
36.23 | even | 6 | 180.2.q.a.11.3 | ✓ | 48 | ||
36.31 | odd | 6 | 540.2.q.a.251.22 | 48 | |||
45.7 | odd | 12 | 900.2.o.b.599.15 | 48 | |||
45.14 | odd | 6 | 900.2.r.f.551.15 | 48 | |||
45.23 | even | 12 | 900.2.o.b.299.2 | 48 | |||
45.32 | even | 12 | 900.2.o.c.299.23 | 48 | |||
45.34 | even | 6 | 900.2.r.f.851.22 | 48 | |||
45.43 | odd | 12 | 900.2.o.c.599.10 | 48 | |||
180.7 | even | 12 | 900.2.o.b.599.2 | 48 | |||
180.23 | odd | 12 | 900.2.o.b.299.15 | 48 | |||
180.43 | even | 12 | 900.2.o.c.599.23 | 48 | |||
180.59 | even | 6 | 900.2.r.f.551.22 | 48 | |||
180.79 | odd | 6 | 900.2.r.f.851.15 | 48 | |||
180.167 | odd | 12 | 900.2.o.c.299.10 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.2.q.a.11.3 | ✓ | 48 | 36.23 | even | 6 | ||
180.2.q.a.11.10 | yes | 48 | 9.5 | odd | 6 | ||
180.2.q.a.131.3 | yes | 48 | 9.7 | even | 3 | ||
180.2.q.a.131.10 | yes | 48 | 36.7 | odd | 6 | ||
540.2.q.a.71.15 | 48 | 36.11 | even | 6 | |||
540.2.q.a.71.22 | 48 | 9.2 | odd | 6 | |||
540.2.q.a.251.15 | 48 | 9.4 | even | 3 | |||
540.2.q.a.251.22 | 48 | 36.31 | odd | 6 | |||
900.2.o.b.299.2 | 48 | 45.23 | even | 12 | |||
900.2.o.b.299.15 | 48 | 180.23 | odd | 12 | |||
900.2.o.b.599.2 | 48 | 180.7 | even | 12 | |||
900.2.o.b.599.15 | 48 | 45.7 | odd | 12 | |||
900.2.o.c.299.10 | 48 | 180.167 | odd | 12 | |||
900.2.o.c.299.23 | 48 | 45.32 | even | 12 | |||
900.2.o.c.599.10 | 48 | 45.43 | odd | 12 | |||
900.2.o.c.599.23 | 48 | 180.43 | even | 12 | |||
900.2.r.f.551.15 | 48 | 45.14 | odd | 6 | |||
900.2.r.f.551.22 | 48 | 180.59 | even | 6 | |||
900.2.r.f.851.15 | 48 | 180.79 | odd | 6 | |||
900.2.r.f.851.22 | 48 | 45.34 | even | 6 | |||
1620.2.e.b.971.11 | 48 | 4.3 | odd | 2 | inner | ||
1620.2.e.b.971.12 | 48 | 3.2 | odd | 2 | inner | ||
1620.2.e.b.971.37 | 48 | 1.1 | even | 1 | trivial | ||
1620.2.e.b.971.38 | 48 | 12.11 | even | 2 | inner |