Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(323,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, 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("756.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.14 | ||
Character | \(\chi\) | \(=\) | 756.323 |
Dual form | 756.2.e.a.323.13 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.310394 | + | 1.37973i | 0.219482 | + | 0.975617i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.80731 | + | 0.856520i | −0.903655 | + | 0.428260i | ||||
\(5\) | − | 1.05392i | − | 0.471328i | −0.971835 | − | 0.235664i | \(-0.924273\pi\) | ||
0.971835 | − | 0.235664i | \(-0.0757266\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −1.74275 | − | 2.22774i | −0.616154 | − | 0.787626i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.45413 | − | 0.327131i | 0.459836 | − | 0.103448i | ||||
\(11\) | 2.97924 | 0.898276 | 0.449138 | − | 0.893462i | \(-0.351731\pi\) | ||||
0.449138 | + | 0.893462i | \(0.351731\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.985148 | 0.273231 | 0.136615 | − | 0.990624i | \(-0.456378\pi\) | ||||
0.136615 | + | 0.990624i | \(0.456378\pi\) | |||||||
\(14\) | 1.37973 | − | 0.310394i | 0.368748 | − | 0.0829563i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.53275 | − | 3.09600i | 0.633186 | − | 0.773999i | ||||
\(17\) | − | 6.35564i | − | 1.54147i | −0.637156 | − | 0.770735i | \(-0.719889\pi\) | ||
0.637156 | − | 0.770735i | \(-0.280111\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26888i | 0.291102i | 0.989351 | + | 0.145551i | \(0.0464955\pi\) | ||||
−0.989351 | + | 0.145551i | \(0.953504\pi\) | |||||||
\(20\) | 0.902706 | + | 1.90477i | 0.201851 | + | 0.425919i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.924740 | + | 4.11055i | 0.197155 | + | 0.876373i | ||||
\(23\) | 2.66217 | 0.555100 | 0.277550 | − | 0.960711i | \(-0.410478\pi\) | ||||
0.277550 | + | 0.960711i | \(0.410478\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.88925 | 0.777849 | ||||||||
\(26\) | 0.305784 | + | 1.35924i | 0.0599692 | + | 0.266569i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.856520 | + | 1.80731i | 0.161867 | + | 0.341550i | ||||
\(29\) | − | 5.12873i | − | 0.952382i | −0.879342 | − | 0.476191i | \(-0.842017\pi\) | ||
0.879342 | − | 0.476191i | \(-0.157983\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.41216i | 1.51087i | 0.655224 | + | 0.755435i | \(0.272574\pi\) | ||||
−0.655224 | + | 0.755435i | \(0.727426\pi\) | |||||||
\(32\) | 5.05779 | + | 2.53353i | 0.894099 | + | 0.447869i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.76907 | − | 1.97275i | 1.50388 | − | 0.338324i | ||||
\(35\) | −1.05392 | −0.178145 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.91591 | 1.46577 | 0.732883 | − | 0.680355i | \(-0.238174\pi\) | ||||
0.732883 | + | 0.680355i | \(0.238174\pi\) | |||||||
\(38\) | −1.75072 | + | 0.393854i | −0.284004 | + | 0.0638916i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.34787 | + | 1.83672i | −0.371231 | + | 0.290411i | ||||
\(41\) | − | 4.54486i | − | 0.709788i | −0.934907 | − | 0.354894i | \(-0.884517\pi\) | ||
0.934907 | − | 0.354894i | \(-0.115483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.646087i | 0.0985273i | 0.998786 | + | 0.0492637i | \(0.0156875\pi\) | ||||
−0.998786 | + | 0.0492637i | \(0.984313\pi\) | |||||||
\(44\) | −5.38442 | + | 2.55178i | −0.811732 | + | 0.384696i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.826321 | + | 3.67307i | 0.121834 | + | 0.541565i | ||||
\(47\) | 4.64851 | 0.678055 | 0.339027 | − | 0.940777i | \(-0.389902\pi\) | ||||
0.339027 | + | 0.940777i | \(0.389902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.20720 | + | 5.36611i | 0.170724 | + | 0.758883i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.78047 | + | 0.843799i | −0.246907 | + | 0.117014i | ||||
\(53\) | − | 2.57717i | − | 0.354002i | −0.984211 | − | 0.177001i | \(-0.943360\pi\) | ||
0.984211 | − | 0.177001i | \(-0.0566396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.13989i | − | 0.423383i | ||||||
\(56\) | −2.22774 | + | 1.74275i | −0.297695 | + | 0.232884i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.07627 | − | 1.59193i | 0.929159 | − | 0.209030i | ||||
\(59\) | −13.7573 | −1.79104 | −0.895521 | − | 0.445019i | \(-0.853197\pi\) | ||||
−0.895521 | + | 0.445019i | \(0.853197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.89018 | 0.626124 | 0.313062 | − | 0.949733i | \(-0.398645\pi\) | ||||
0.313062 | + | 0.949733i | \(0.398645\pi\) | |||||||
\(62\) | −11.6065 | + | 2.61109i | −1.47403 | + | 0.331608i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.92568 | + | 7.76478i | −0.240709 | + | 0.970597i | ||||
\(65\) | − | 1.03827i | − | 0.128782i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.21439i | 1.00355i | 0.864999 | + | 0.501774i | \(0.167319\pi\) | ||||
−0.864999 | + | 0.501774i | \(0.832681\pi\) | |||||||
\(68\) | 5.44374 | + | 11.4866i | 0.660150 | + | 1.39296i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.327131 | − | 1.45413i | −0.0390997 | − | 0.173802i | ||||
\(71\) | 0.583871 | 0.0692927 | 0.0346464 | − | 0.999400i | \(-0.488970\pi\) | ||||
0.0346464 | + | 0.999400i | \(0.488970\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4131 | −1.45284 | −0.726422 | − | 0.687249i | \(-0.758818\pi\) | ||||
−0.726422 | + | 0.687249i | \(0.758818\pi\) | |||||||
\(74\) | 2.76745 | + | 12.3015i | 0.321709 | + | 1.43003i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.08683 | − | 2.29327i | −0.124667 | − | 0.263056i | ||||
\(77\) | − | 2.97924i | − | 0.339516i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.1046i | − | 1.69940i | −0.527269 | − | 0.849699i | \(-0.676784\pi\) | ||
0.527269 | − | 0.849699i | \(-0.323216\pi\) | |||||||
\(80\) | −3.26294 | − | 2.66932i | −0.364808 | − | 0.298439i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.27068 | − | 1.41070i | 0.692481 | − | 0.155786i | ||||
\(83\) | 4.73179 | 0.519382 | 0.259691 | − | 0.965692i | \(-0.416379\pi\) | ||||
0.259691 | + | 0.965692i | \(0.416379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.69835 | −0.726538 | ||||||||
\(86\) | −0.891426 | + | 0.200542i | −0.0961249 | + | 0.0216250i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.19206 | − | 6.63699i | −0.553476 | − | 0.707505i | ||||
\(89\) | 1.74631i | 0.185108i | 0.995708 | + | 0.0925541i | \(0.0295031\pi\) | ||||
−0.995708 | + | 0.0925541i | \(0.970497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.985148i | − | 0.103272i | ||||||
\(92\) | −4.81136 | + | 2.28020i | −0.501619 | + | 0.237727i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.44287 | + | 6.41369i | 0.148821 | + | 0.661521i | ||||
\(95\) | 1.33731 | 0.137205 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00594 | 0.305207 | 0.152604 | − | 0.988287i | \(-0.451234\pi\) | ||||
0.152604 | + | 0.988287i | \(0.451234\pi\) | |||||||
\(98\) | −0.310394 | − | 1.37973i | −0.0313545 | − | 0.139374i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.02908 | + | 3.33122i | −0.702908 | + | 0.333122i | ||||
\(101\) | − | 1.53513i | − | 0.152751i | −0.997079 | − | 0.0763757i | \(-0.975665\pi\) | ||
0.997079 | − | 0.0763757i | \(-0.0243348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.6910i | − | 1.15195i | −0.817468 | − | 0.575974i | \(-0.804623\pi\) | ||
0.817468 | − | 0.575974i | \(-0.195377\pi\) | |||||||
\(104\) | −1.71686 | − | 2.19466i | −0.168352 | − | 0.215204i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.55581 | − | 0.799940i | 0.345370 | − | 0.0776970i | ||||
\(107\) | 15.7149 | 1.51922 | 0.759611 | − | 0.650378i | \(-0.225390\pi\) | ||||
0.759611 | + | 0.650378i | \(0.225390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.34105 | −0.703145 | −0.351573 | − | 0.936161i | \(-0.614353\pi\) | ||||
−0.351573 | + | 0.936161i | \(0.614353\pi\) | |||||||
\(110\) | 4.33220 | − | 0.974604i | 0.413059 | − | 0.0929249i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.09600 | − | 2.53275i | −0.292544 | − | 0.239322i | ||||
\(113\) | − | 4.35118i | − | 0.409324i | −0.978833 | − | 0.204662i | \(-0.934390\pi\) | ||
0.978833 | − | 0.204662i | \(-0.0656096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2.80572i | − | 0.261635i | ||||||
\(116\) | 4.39286 | + | 9.26921i | 0.407867 | + | 0.860625i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.27017 | − | 18.9813i | −0.393101 | − | 1.74737i | ||||
\(119\) | −6.35564 | −0.582621 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.12410 | −0.193100 | ||||||||
\(122\) | 1.51788 | + | 6.74713i | 0.137423 | + | 0.610857i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.20519 | − | 15.2034i | −0.647045 | − | 1.36531i | ||||
\(125\) | − | 9.36858i | − | 0.837951i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.4265i | 1.81255i | 0.422684 | + | 0.906277i | \(0.361088\pi\) | ||||
−0.422684 | + | 0.906277i | \(0.638912\pi\) | |||||||
\(128\) | −11.3110 | − | 0.246771i | −0.999762 | − | 0.0218117i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.43253 | − | 0.322273i | 0.125641 | − | 0.0282652i | ||||
\(131\) | −17.1791 | −1.50094 | −0.750471 | − | 0.660903i | \(-0.770173\pi\) | ||||
−0.750471 | + | 0.660903i | \(0.770173\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.26888 | 0.110026 | ||||||||
\(134\) | −11.3336 | + | 2.54970i | −0.979078 | + | 0.220260i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −14.1587 | + | 11.0763i | −1.21410 | + | 0.949782i | ||||
\(137\) | 16.2830i | 1.39115i | 0.718452 | + | 0.695577i | \(0.244851\pi\) | ||||
−0.718452 | + | 0.695577i | \(0.755149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.05732i | − | 0.0896804i | −0.998994 | − | 0.0448402i | \(-0.985722\pi\) | ||
0.998994 | − | 0.0448402i | \(-0.0142779\pi\) | |||||||
\(140\) | 1.90477 | − | 0.902706i | 0.160982 | − | 0.0762926i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.181230 | + | 0.805584i | 0.0152085 | + | 0.0676031i | ||||
\(143\) | 2.93500 | 0.245437 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.40529 | −0.448885 | ||||||||
\(146\) | −3.85295 | − | 17.1267i | −0.318873 | − | 1.41742i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.1138 | + | 7.63666i | −1.32455 | + | 0.627729i | ||||
\(149\) | − | 6.71787i | − | 0.550349i | −0.961394 | − | 0.275175i | \(-0.911264\pi\) | ||
0.961394 | − | 0.275175i | \(-0.0887357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.96946i | 0.404409i | 0.979343 | + | 0.202205i | \(0.0648106\pi\) | ||||
−0.979343 | + | 0.202205i | \(0.935189\pi\) | |||||||
\(152\) | 2.82675 | − | 2.21134i | 0.229280 | − | 0.179364i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.11055 | − | 0.924740i | 0.331238 | − | 0.0745177i | ||||
\(155\) | 8.86577 | 0.712116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.3997 | 1.14922 | 0.574609 | − | 0.818428i | \(-0.305154\pi\) | ||||
0.574609 | + | 0.818428i | \(0.305154\pi\) | |||||||
\(158\) | 20.8402 | − | 4.68837i | 1.65796 | − | 0.372987i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.67014 | − | 5.33052i | 0.211093 | − | 0.421415i | ||||
\(161\) | − | 2.66217i | − | 0.209808i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.22595i | − | 0.174350i | −0.996193 | − | 0.0871749i | \(-0.972216\pi\) | ||
0.996193 | − | 0.0871749i | \(-0.0277839\pi\) | |||||||
\(164\) | 3.89277 | + | 8.21398i | 0.303974 | + | 0.641404i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.46872 | + | 6.52860i | 0.113995 | + | 0.506717i | ||||
\(167\) | −12.4976 | −0.967094 | −0.483547 | − | 0.875318i | \(-0.660652\pi\) | ||||
−0.483547 | + | 0.875318i | \(0.660652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0295 | −0.925345 | ||||||||
\(170\) | −2.07913 | − | 9.24192i | −0.159462 | − | 0.708823i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.553387 | − | 1.16768i | −0.0421953 | − | 0.0890348i | ||||
\(173\) | − | 16.1418i | − | 1.22724i | −0.789603 | − | 0.613619i | \(-0.789713\pi\) | ||
0.789603 | − | 0.613619i | \(-0.210287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.88925i | − | 0.293999i | ||||||
\(176\) | 7.54567 | − | 9.22373i | 0.568776 | − | 0.695265i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.40943 | + | 0.542043i | −0.180595 | + | 0.0406279i | ||||
\(179\) | 14.5759 | 1.08945 | 0.544727 | − | 0.838613i | \(-0.316633\pi\) | ||||
0.544727 | + | 0.838613i | \(0.316633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.95874 | 0.145592 | 0.0727960 | − | 0.997347i | \(-0.476808\pi\) | ||||
0.0727960 | + | 0.997347i | \(0.476808\pi\) | |||||||
\(182\) | 1.35924 | − | 0.305784i | 0.100753 | − | 0.0226662i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.63948 | − | 5.93062i | −0.342027 | − | 0.437211i | ||||
\(185\) | − | 9.39668i | − | 0.690857i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 18.9350i | − | 1.38466i | ||||||
\(188\) | −8.40130 | + | 3.98154i | −0.612728 | + | 0.290384i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.415092 | + | 1.84512i | 0.0301139 | + | 0.133859i | ||||
\(191\) | 26.2224 | 1.89739 | 0.948694 | − | 0.316194i | \(-0.102405\pi\) | ||||
0.948694 | + | 0.316194i | \(0.102405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.4000 | −1.68437 | −0.842186 | − | 0.539187i | \(-0.818732\pi\) | ||||
−0.842186 | + | 0.539187i | \(0.818732\pi\) | |||||||
\(194\) | 0.933027 | + | 4.14739i | 0.0669874 | + | 0.297765i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.80731 | − | 0.856520i | 0.129094 | − | 0.0611800i | ||||
\(197\) | 16.5377i | 1.17826i | 0.808036 | + | 0.589132i | \(0.200530\pi\) | ||||
−0.808036 | + | 0.589132i | \(0.799470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.20608i | − | 0.0854964i | −0.999086 | − | 0.0427482i | \(-0.986389\pi\) | ||
0.999086 | − | 0.0427482i | \(-0.0136113\pi\) | |||||||
\(200\) | −6.77797 | − | 8.66424i | −0.479275 | − | 0.612654i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.11807 | − | 0.476496i | 0.149027 | − | 0.0335261i | ||||
\(203\) | −5.12873 | −0.359966 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.78993 | −0.334543 | ||||||||
\(206\) | 16.1304 | − | 3.62881i | 1.12386 | − | 0.252831i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.49513 | − | 3.05002i | 0.173006 | − | 0.211481i | ||||
\(209\) | 3.78032i | 0.261490i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.33019i | 0.642317i | 0.947025 | + | 0.321159i | \(0.104072\pi\) | ||||
−0.947025 | + | 0.321159i | \(0.895928\pi\) | |||||||
\(212\) | 2.20740 | + | 4.65776i | 0.151605 | + | 0.319896i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.87783 | + | 21.6824i | 0.333441 | + | 1.48218i | ||||
\(215\) | 0.680926 | 0.0464387 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.41216 | 0.571055 | ||||||||
\(218\) | −2.27862 | − | 10.1287i | −0.154328 | − | 0.686000i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.68938 | + | 5.67476i | 0.181318 | + | 0.382592i | ||||
\(221\) | − | 6.26125i | − | 0.421177i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.92491i | − | 0.195866i | −0.995193 | − | 0.0979332i | \(-0.968777\pi\) | ||
0.995193 | − | 0.0979332i | \(-0.0312231\pi\) | |||||||
\(224\) | 2.53353 | − | 5.05779i | 0.169278 | − | 0.337938i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00345 | − | 1.35058i | 0.399344 | − | 0.0898393i | ||||
\(227\) | −23.0959 | −1.53293 | −0.766466 | − | 0.642285i | \(-0.777987\pi\) | ||||
−0.766466 | + | 0.642285i | \(0.777987\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.08386 | 0.600278 | 0.300139 | − | 0.953895i | \(-0.402967\pi\) | ||||
0.300139 | + | 0.953895i | \(0.402967\pi\) | |||||||
\(230\) | 3.87113 | − | 0.870879i | 0.255255 | − | 0.0574240i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.4255 | + | 8.93807i | −0.750120 | + | 0.586813i | ||||
\(233\) | 29.4595i | 1.92996i | 0.262330 | + | 0.964978i | \(0.415509\pi\) | ||||
−0.262330 | + | 0.964978i | \(0.584491\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 4.89917i | − | 0.319586i | ||||||
\(236\) | 24.8636 | − | 11.7834i | 1.61849 | − | 0.767032i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.97275 | − | 8.76907i | −0.127875 | − | 0.568414i | ||||
\(239\) | −17.3719 | −1.12369 | −0.561846 | − | 0.827242i | \(-0.689909\pi\) | ||||
−0.561846 | + | 0.827242i | \(0.689909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8341 | −0.762299 | −0.381150 | − | 0.924513i | \(-0.624472\pi\) | ||||
−0.381150 | + | 0.924513i | \(0.624472\pi\) | |||||||
\(242\) | −0.659310 | − | 2.93069i | −0.0423820 | − | 0.188392i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.83808 | + | 4.18854i | −0.565800 | + | 0.268144i | ||||
\(245\) | 1.05392i | 0.0673326i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.25004i | 0.0795381i | ||||||||
\(248\) | 18.7401 | − | 14.6603i | 1.19000 | − | 0.930928i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.9261 | − | 2.90795i | 0.817519 | − | 0.183915i | ||||
\(251\) | 22.4110 | 1.41457 | 0.707284 | − | 0.706930i | \(-0.249920\pi\) | ||||
0.707284 | + | 0.706930i | \(0.249920\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.93125 | 0.498633 | ||||||||
\(254\) | −28.1830 | + | 6.34025i | −1.76836 | + | 0.397823i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.17040 | − | 15.6827i | −0.198150 | − | 0.980172i | ||||
\(257\) | 20.2382i | 1.26242i | 0.775611 | + | 0.631211i | \(0.217442\pi\) | ||||
−0.775611 | + | 0.631211i | \(0.782558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.91591i | − | 0.554008i | ||||||
\(260\) | 0.889299 | + | 1.87648i | 0.0551520 | + | 0.116374i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.33228 | − | 23.7025i | −0.329429 | − | 1.46434i | ||||
\(263\) | −25.1291 | −1.54952 | −0.774762 | − | 0.632253i | \(-0.782130\pi\) | ||||
−0.774762 | + | 0.632253i | \(0.782130\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.71614 | −0.166851 | ||||||||
\(266\) | 0.393854 | + | 1.75072i | 0.0241488 | + | 0.107343i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.03579 | − | 14.8460i | −0.429779 | − | 0.906861i | ||||
\(269\) | 4.09135i | 0.249454i | 0.992191 | + | 0.124727i | \(0.0398055\pi\) | ||||
−0.992191 | + | 0.124727i | \(0.960195\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.36584i | − | 0.143715i | −0.997415 | − | 0.0718573i | \(-0.977107\pi\) | ||
0.997415 | − | 0.0718573i | \(-0.0228926\pi\) | |||||||
\(272\) | −19.6770 | − | 16.0972i | −1.19310 | − | 0.976038i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.4662 | + | 5.05416i | −1.35723 | + | 0.305333i | ||||
\(275\) | 11.5870 | 0.698723 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9260 | 1.25732 | 0.628661 | − | 0.777679i | \(-0.283603\pi\) | ||||
0.628661 | + | 0.777679i | \(0.283603\pi\) | |||||||
\(278\) | 1.45881 | − | 0.328185i | 0.0874937 | − | 0.0196832i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.83672 | + | 2.34787i | 0.109765 | + | 0.140312i | ||||
\(281\) | − | 12.7122i | − | 0.758348i | −0.925325 | − | 0.379174i | \(-0.876208\pi\) | ||
0.925325 | − | 0.379174i | \(-0.123792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.4751i | 1.09823i | 0.835747 | + | 0.549115i | \(0.185035\pi\) | ||||
−0.835747 | + | 0.549115i | \(0.814965\pi\) | |||||||
\(284\) | −1.05524 | + | 0.500097i | −0.0626168 | + | 0.0296753i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.911006 | + | 4.04950i | 0.0538689 | + | 0.239452i | ||||
\(287\) | −4.54486 | −0.268275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.3942 | −1.37613 | ||||||||
\(290\) | −1.67777 | − | 7.45784i | −0.0985220 | − | 0.437939i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.4343 | − | 10.6321i | 1.31287 | − | 0.622195i | ||||
\(293\) | 26.8597i | 1.56916i | 0.620028 | + | 0.784579i | \(0.287121\pi\) | ||||
−0.620028 | + | 0.784579i | \(0.712879\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.4991i | 0.844169i | ||||||||
\(296\) | −15.5382 | − | 19.8623i | −0.903137 | − | 1.15448i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.26885 | − | 2.08519i | 0.536930 | − | 0.120792i | ||||
\(299\) | 2.62263 | 0.151671 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.646087 | 0.0372398 | ||||||||
\(302\) | −6.85652 | + | 1.54249i | −0.394548 | + | 0.0887605i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.92846 | + | 3.21376i | 0.225313 | + | 0.184322i | ||||
\(305\) | − | 5.15387i | − | 0.295110i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.6518i | − | 0.950370i | −0.879886 | − | 0.475185i | \(-0.842381\pi\) | ||
0.879886 | − | 0.475185i | \(-0.157619\pi\) | |||||||
\(308\) | 2.55178 | + | 5.38442i | 0.145401 | + | 0.306806i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.75188 | + | 12.2324i | 0.156296 | + | 0.694752i | ||||
\(311\) | −9.01174 | −0.511009 | −0.255505 | − | 0.966808i | \(-0.582242\pi\) | ||||
−0.255505 | + | 0.966808i | \(0.582242\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.50866 | −0.141798 | −0.0708988 | − | 0.997484i | \(-0.522587\pi\) | ||||
−0.0708988 | + | 0.997484i | \(0.522587\pi\) | |||||||
\(314\) | 4.46957 | + | 19.8677i | 0.252233 | + | 1.12120i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.9374 | + | 27.2987i | 0.727784 | + | 1.53567i | ||||
\(317\) | 22.1219i | 1.24249i | 0.783616 | + | 0.621246i | \(0.213373\pi\) | ||||
−0.783616 | + | 0.621246i | \(0.786627\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 15.2797i | − | 0.855501i | ||||||
\(320\) | 8.18347 | + | 2.02951i | 0.457470 | + | 0.113453i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.67307 | − | 0.826321i | 0.204692 | − | 0.0460491i | ||||
\(323\) | 8.06458 | 0.448725 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.83148 | 0.212533 | ||||||||
\(326\) | 3.07121 | − | 0.690922i | 0.170099 | − | 0.0382666i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.1248 | + | 7.92054i | −0.559047 | + | 0.437338i | ||||
\(329\) | − | 4.64851i | − | 0.256281i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.4307i | 1.01304i | 0.862228 | + | 0.506520i | \(0.169068\pi\) | ||||
−0.862228 | + | 0.506520i | \(0.830932\pi\) | |||||||
\(332\) | −8.55182 | + | 4.05288i | −0.469342 | + | 0.222431i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.87918 | − | 17.2433i | −0.212259 | − | 0.943513i | ||||
\(335\) | 8.65733 | 0.473001 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7708 | −1.34935 | −0.674675 | − | 0.738115i | \(-0.735716\pi\) | ||||
−0.674675 | + | 0.738115i | \(0.735716\pi\) | |||||||
\(338\) | −3.73388 | − | 16.5974i | −0.203096 | − | 0.902782i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.1060 | − | 5.73728i | 0.656540 | − | 0.311147i | ||||
\(341\) | 25.0619i | 1.35718i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 1.43932 | − | 1.12597i | 0.0776027 | − | 0.0607080i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.2713 | − | 5.01031i | 1.19731 | − | 0.269356i | ||||
\(347\) | −27.1358 | −1.45673 | −0.728364 | − | 0.685191i | \(-0.759719\pi\) | ||||
−0.728364 | + | 0.685191i | \(0.759719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5396 | 0.671232 | 0.335616 | − | 0.941999i | \(-0.391056\pi\) | ||||
0.335616 | + | 0.941999i | \(0.391056\pi\) | |||||||
\(350\) | 5.36611 | − | 1.20720i | 0.286831 | − | 0.0645275i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0684 | + | 7.54799i | 0.803148 | + | 0.402309i | ||||
\(353\) | 24.6724i | 1.31318i | 0.754247 | + | 0.656590i | \(0.228002\pi\) | ||||
−0.754247 | + | 0.656590i | \(0.771998\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 0.615355i | − | 0.0326596i | ||||||
\(356\) | −1.49575 | − | 3.15612i | −0.0792744 | − | 0.167274i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.52427 | + | 20.1108i | 0.239115 | + | 1.06289i | ||||
\(359\) | 22.8525 | 1.20611 | 0.603054 | − | 0.797700i | \(-0.293950\pi\) | ||||
0.603054 | + | 0.797700i | \(0.293950\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.3899 | 0.915260 | ||||||||
\(362\) | 0.607981 | + | 2.70253i | 0.0319548 | + | 0.142042i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.843799 | + | 1.78047i | 0.0442271 | + | 0.0933219i | ||||
\(365\) | 13.0824i | 0.684767i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.3116i | 1.06026i | 0.847917 | + | 0.530128i | \(0.177856\pi\) | ||||
−0.847917 | + | 0.530128i | \(0.822144\pi\) | |||||||
\(368\) | 6.74259 | − | 8.24206i | 0.351482 | − | 0.429647i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.9649 | − | 2.91667i | 0.674012 | − | 0.151631i | ||||
\(371\) | −2.57717 | −0.133800 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.4192 | 1.52327 | 0.761635 | − | 0.648007i | \(-0.224397\pi\) | ||||
0.761635 | + | 0.648007i | \(0.224397\pi\) | |||||||
\(374\) | 26.1252 | − | 5.87731i | 1.35090 | − | 0.303909i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.10117 | − | 10.3557i | −0.417786 | − | 0.534053i | ||||
\(377\) | − | 5.05256i | − | 0.260220i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.5441i | 0.952546i | 0.879298 | + | 0.476273i | \(0.158013\pi\) | ||||
−0.879298 | + | 0.476273i | \(0.841987\pi\) | |||||||
\(380\) | −2.41693 | + | 1.14543i | −0.123986 | + | 0.0587593i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.13929 | + | 36.1799i | 0.416442 | + | 1.85112i | ||||
\(383\) | −37.8089 | −1.93194 | −0.965972 | − | 0.258648i | \(-0.916723\pi\) | ||||
−0.965972 | + | 0.258648i | \(0.916723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.13989 | −0.160024 | ||||||||
\(386\) | −7.26324 | − | 32.2857i | −0.369689 | − | 1.64330i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.43267 | + | 2.57465i | −0.275802 | + | 0.130708i | ||||
\(389\) | 8.06117i | 0.408718i | 0.978896 | + | 0.204359i | \(0.0655109\pi\) | ||||
−0.978896 | + | 0.204359i | \(0.934489\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 16.9198i | − | 0.855670i | ||||||
\(392\) | 1.74275 | + | 2.22774i | 0.0880219 | + | 0.112518i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.8176 | + | 5.13322i | −1.14953 | + | 0.258608i | ||||
\(395\) | −15.9191 | −0.800974 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.5806 | 1.38423 | 0.692115 | − | 0.721787i | \(-0.256679\pi\) | ||||
0.692115 | + | 0.721787i | \(0.256679\pi\) | |||||||
\(398\) | 1.66406 | − | 0.374359i | 0.0834117 | − | 0.0187649i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.85048 | − | 12.0411i | 0.492524 | − | 0.602055i | ||||
\(401\) | − | 7.24355i | − | 0.361725i | −0.983508 | − | 0.180863i | \(-0.942111\pi\) | ||
0.983508 | − | 0.180863i | \(-0.0578890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.28723i | 0.412816i | ||||||||
\(404\) | 1.31487 | + | 2.77446i | 0.0654173 | + | 0.138035i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.59193 | − | 7.07627i | −0.0790061 | − | 0.351189i | ||||
\(407\) | 26.5627 | 1.31666 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4380 | 1.30728 | 0.653638 | − | 0.756807i | \(-0.273242\pi\) | ||||
0.653638 | + | 0.756807i | \(0.273242\pi\) | |||||||
\(410\) | −1.48677 | − | 6.60881i | −0.0734262 | − | 0.326386i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.0136 | + | 21.1292i | 0.493333 | + | 1.04096i | ||||
\(413\) | 13.7573i | 0.676950i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.98694i | − | 0.244799i | ||||||
\(416\) | 4.98267 | + | 2.49590i | 0.244296 | + | 0.122372i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.21582 | + | 1.17339i | −0.255114 | + | 0.0573923i | ||||
\(419\) | 20.3362 | 0.993487 | 0.496744 | − | 0.867897i | \(-0.334529\pi\) | ||||
0.496744 | + | 0.867897i | \(0.334529\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6537 | 0.665442 | 0.332721 | − | 0.943025i | \(-0.392033\pi\) | ||||
0.332721 | + | 0.943025i | \(0.392033\pi\) | |||||||
\(422\) | −12.8732 | + | 2.89604i | −0.626655 | + | 0.140977i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.74128 | + | 4.49136i | −0.278821 | + | 0.218120i | ||||
\(425\) | − | 24.7187i | − | 1.19903i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.89018i | − | 0.236653i | ||||||
\(428\) | −28.4018 | + | 13.4602i | −1.37285 | + | 0.650622i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.211355 | + | 0.939494i | 0.0101925 | + | 0.0453064i | ||||
\(431\) | −16.9782 | −0.817811 | −0.408906 | − | 0.912577i | \(-0.634089\pi\) | ||||
−0.408906 | + | 0.912577i | \(0.634089\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.624418 | 0.0300076 | 0.0150038 | − | 0.999887i | \(-0.495224\pi\) | ||||
0.0150038 | + | 0.999887i | \(0.495224\pi\) | |||||||
\(434\) | 2.61109 | + | 11.6065i | 0.125336 | + | 0.557131i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.2676 | − | 6.28776i | 0.635401 | − | 0.301129i | ||||
\(437\) | 3.37798i | 0.161591i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.8786i | 1.09194i | 0.837806 | + | 0.545969i | \(0.183838\pi\) | ||||
−0.837806 | + | 0.545969i | \(0.816162\pi\) | |||||||
\(440\) | −6.99487 | + | 5.47203i | −0.333467 | + | 0.260869i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.63883 | − | 1.94345i | 0.410907 | − | 0.0924407i | ||||
\(443\) | −0.212425 | −0.0100926 | −0.00504630 | − | 0.999987i | \(-0.501606\pi\) | ||||
−0.00504630 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.84047 | 0.0872467 | ||||||||
\(446\) | 4.03558 | − | 0.907874i | 0.191090 | − | 0.0429891i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.76478 | + | 1.92568i | 0.366851 | + | 0.0909796i | ||||
\(449\) | 17.6011i | 0.830650i | 0.909673 | + | 0.415325i | \(0.136332\pi\) | ||||
−0.909673 | + | 0.415325i | \(0.863668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.5402i | − | 0.637585i | ||||||
\(452\) | 3.72687 | + | 7.86393i | 0.175297 | + | 0.369888i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.16885 | − | 31.8662i | −0.336451 | − | 1.49555i | ||||
\(455\) | −1.03827 | −0.0486748 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.56351 | 0.400584 | 0.200292 | − | 0.979736i | \(-0.435811\pi\) | ||||
0.200292 | + | 0.979736i | \(0.435811\pi\) | |||||||
\(458\) | 2.81958 | + | 12.5333i | 0.131750 | + | 0.585641i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.40315 | + | 5.07081i | 0.112048 | + | 0.236428i | ||||
\(461\) | 33.2233i | 1.54736i | 0.633575 | + | 0.773681i | \(0.281587\pi\) | ||||
−0.633575 | + | 0.773681i | \(0.718413\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.8819i | − | 0.505723i | −0.967502 | − | 0.252862i | \(-0.918628\pi\) | ||
0.967502 | − | 0.252862i | \(-0.0813717\pi\) | |||||||
\(464\) | −15.8785 | − | 12.9898i | −0.737143 | − | 0.603035i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.6462 | + | 9.14406i | −1.88290 | + | 0.423590i | ||||
\(467\) | −41.7776 | −1.93324 | −0.966618 | − | 0.256224i | \(-0.917522\pi\) | ||||
−0.966618 | + | 0.256224i | \(0.917522\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.21439 | 0.379305 | ||||||||
\(470\) | 6.75953 | − | 1.52067i | 0.311794 | − | 0.0701434i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.9754 | + | 30.6476i | 1.10356 | + | 1.41067i | ||||
\(473\) | 1.92485i | 0.0885047i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.93501i | 0.226434i | ||||||||
\(476\) | 11.4866 | − | 5.44374i | 0.526488 | − | 0.249513i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.39212 | − | 23.9685i | −0.246630 | − | 1.09629i | ||||
\(479\) | −8.46943 | −0.386978 | −0.193489 | − | 0.981102i | \(-0.561980\pi\) | ||||
−0.193489 | + | 0.981102i | \(0.561980\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.78349 | 0.400493 | ||||||||
\(482\) | −3.67323 | − | 16.3278i | −0.167311 | − | 0.743712i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.83892 | − | 1.81934i | 0.174496 | − | 0.0826972i | ||||
\(485\) | − | 3.16803i | − | 0.143853i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1496i | 1.04901i | 0.851408 | + | 0.524504i | \(0.175749\pi\) | ||||
−0.851408 | + | 0.524504i | \(0.824251\pi\) | |||||||
\(488\) | −8.52234 | − | 10.8941i | −0.385788 | − | 0.493151i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.45413 | + | 0.327131i | −0.0656908 | + | 0.0147783i | ||||
\(491\) | 6.91483 | 0.312062 | 0.156031 | − | 0.987752i | \(-0.450130\pi\) | ||||
0.156031 | + | 0.987752i | \(0.450130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.5964 | −1.46807 | ||||||||
\(494\) | −1.72472 | + | 0.388005i | −0.0775987 | + | 0.0174572i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.0440 | + | 21.3059i | 1.16941 | + | 0.956662i | ||||
\(497\) | − | 0.583871i | − | 0.0261902i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.58869i | 0.339717i | 0.985468 | + | 0.169858i | \(0.0543310\pi\) | ||||
−0.985468 | + | 0.169858i | \(0.945669\pi\) | |||||||
\(500\) | 8.02438 | + | 16.9319i | 0.358861 | + | 0.757219i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.95623 | + | 30.9211i | 0.310472 | + | 1.38008i | ||||
\(503\) | 19.2293 | 0.857390 | 0.428695 | − | 0.903449i | \(-0.358973\pi\) | ||||
0.428695 | + | 0.903449i | \(0.358973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.61791 | −0.0719961 | ||||||||
\(506\) | 2.46181 | + | 10.9430i | 0.109441 | + | 0.486475i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.4957 | − | 36.9170i | −0.776245 | − | 1.63792i | ||||
\(509\) | − | 23.2826i | − | 1.03198i | −0.856593 | − | 0.515992i | \(-0.827423\pi\) | ||
0.856593 | − | 0.515992i | \(-0.172577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4131i | 0.549123i | ||||||||
\(512\) | 20.6539 | − | 9.24212i | 0.912782 | − | 0.408448i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.9232 | + | 6.28181i | −1.23164 | + | 0.277079i | ||||
\(515\) | −12.3214 | −0.542945 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.8490 | 0.609080 | ||||||||
\(518\) | 12.3015 | − | 2.76745i | 0.540499 | − | 0.121595i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.31300 | + | 1.80944i | −0.101432 | + | 0.0793492i | ||||
\(521\) | − | 29.5778i | − | 1.29583i | −0.761714 | − | 0.647914i | \(-0.775642\pi\) | ||
0.761714 | − | 0.647914i | \(-0.224358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 35.2794i | − | 1.54266i | −0.636434 | − | 0.771331i | \(-0.719591\pi\) | ||
0.636434 | − | 0.771331i | \(-0.280409\pi\) | |||||||
\(524\) | 31.0479 | − | 14.7142i | 1.35633 | − | 0.642794i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.79991 | − | 34.6713i | −0.340092 | − | 1.51174i | ||||
\(527\) | 53.4647 | 2.32896 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.9129 | −0.691864 | ||||||||
\(530\) | −0.843075 | − | 3.74754i | −0.0366208 | − | 0.162783i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.29327 | + | 1.08683i | −0.0994258 | + | 0.0471199i | ||||
\(533\) | − | 4.47736i | − | 0.193936i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.5623i | − | 0.716052i | ||||||
\(536\) | 18.2996 | − | 14.3156i | 0.790420 | − | 0.618340i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.64496 | + | 1.26993i | −0.243371 | + | 0.0547506i | ||||
\(539\) | −2.97924 | −0.128325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4892 | −0.536955 | −0.268477 | − | 0.963286i | \(-0.586520\pi\) | ||||
−0.268477 | + | 0.963286i | \(0.586520\pi\) | |||||||
\(542\) | 3.26422 | − | 0.734343i | 0.140210 | − | 0.0315427i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.1022 | − | 32.1455i | 0.690376 | − | 1.37823i | ||||
\(545\) | 7.73690i | 0.331412i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2389i | 1.20741i | 0.797209 | + | 0.603703i | \(0.206309\pi\) | ||||
−0.797209 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(548\) | −13.9468 | − | 29.4285i | −0.595776 | − | 1.25712i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.59654 | + | 15.9870i | 0.153357 | + | 0.681686i | ||||
\(551\) | 6.50777 | 0.277240 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.1046 | −0.642312 | ||||||||
\(554\) | 6.49531 | + | 28.8723i | 0.275959 | + | 1.22666i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.905613 | + | 1.91090i | 0.0384065 | + | 0.0810402i | ||||
\(557\) | − | 44.4589i | − | 1.88378i | −0.335918 | − | 0.941891i | \(-0.609047\pi\) | ||
0.335918 | − | 0.941891i | \(-0.390953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.636491i | 0.0269207i | ||||||||
\(560\) | −2.66932 | + | 3.26294i | −0.112799 | + | 0.137884i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.5395 | − | 3.94580i | 0.739857 | − | 0.166444i | ||||
\(563\) | 9.21017 | 0.388162 | 0.194081 | − | 0.980985i | \(-0.437827\pi\) | ||||
0.194081 | + | 0.980985i | \(0.437827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.58581 | −0.192926 | ||||||||
\(566\) | −25.4906 | + | 5.73456i | −1.07145 | + | 0.241041i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.01754 | − | 1.30071i | −0.0426950 | − | 0.0545768i | ||||
\(569\) | − | 26.5427i | − | 1.11273i | −0.830939 | − | 0.556363i | \(-0.812196\pi\) | ||
0.830939 | − | 0.556363i | \(-0.187804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 16.7288i | − | 0.700077i | −0.936735 | − | 0.350039i | \(-0.886168\pi\) | ||
0.936735 | − | 0.350039i | \(-0.113832\pi\) | |||||||
\(572\) | −5.30445 | + | 2.51388i | −0.221790 | + | 0.105111i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.41070 | − | 6.27068i | −0.0588814 | − | 0.261733i | ||||
\(575\) | 10.3538 | 0.431785 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.4646 | −1.22663 | −0.613314 | − | 0.789839i | \(-0.710164\pi\) | ||||
−0.613314 | + | 0.789839i | \(0.710164\pi\) | |||||||
\(578\) | −7.26141 | − | 32.2777i | −0.302035 | − | 1.34257i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.76903 | − | 4.62974i | 0.405637 | − | 0.192239i | ||||
\(581\) | − | 4.73179i | − | 0.196308i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7.67803i | − | 0.317992i | ||||||
\(584\) | 21.6329 | + | 27.6532i | 0.895175 | + | 1.14430i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.0591 | + | 8.33708i | −1.53090 | + | 0.344402i | ||||
\(587\) | 19.5265 | 0.805943 | 0.402972 | − | 0.915212i | \(-0.367977\pi\) | ||||
0.402972 | + | 0.915212i | \(0.367977\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.6741 | −0.439817 | ||||||||
\(590\) | −20.0048 | + | 4.50043i | −0.823585 | + | 0.185280i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 22.5817 | − | 27.6036i | 0.928103 | − | 1.13450i | ||||
\(593\) | − | 1.64809i | − | 0.0676788i | −0.999427 | − | 0.0338394i | \(-0.989227\pi\) | ||
0.999427 | − | 0.0338394i | \(-0.0107735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.69835i | 0.274606i | ||||||||
\(596\) | 5.75399 | + | 12.1413i | 0.235693 | + | 0.497326i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.814049 | + | 3.61852i | 0.0332889 | + | 0.147972i | ||||
\(599\) | −5.92633 | −0.242143 | −0.121072 | − | 0.992644i | \(-0.538633\pi\) | ||||
−0.121072 | + | 0.992644i | \(0.538633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.0438 | −1.34788 | −0.673941 | − | 0.738785i | \(-0.735400\pi\) | ||||
−0.673941 | + | 0.738785i | \(0.735400\pi\) | |||||||
\(602\) | 0.200542 | + | 0.891426i | 0.00817346 | + | 0.0363318i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.25645 | − | 8.98137i | −0.173192 | − | 0.365447i | ||||
\(605\) | 2.23864i | 0.0910137i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.4880i | 0.709815i | 0.934901 | + | 0.354907i | \(0.115488\pi\) | ||||
−0.934901 | + | 0.354907i | \(0.884512\pi\) | |||||||
\(608\) | −3.21475 | + | 6.41775i | −0.130375 | + | 0.260274i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.11096 | − | 1.59973i | 0.287914 | − | 0.0647713i | ||||
\(611\) | 4.57947 | 0.185265 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6723 | 0.875336 | 0.437668 | − | 0.899137i | \(-0.355805\pi\) | ||||
0.437668 | + | 0.899137i | \(0.355805\pi\) | |||||||
\(614\) | 22.9750 | − | 5.16863i | 0.927197 | − | 0.208589i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.63699 | + | 5.19206i | −0.267412 | + | 0.209194i | ||||
\(617\) | 6.28958i | 0.253209i | 0.991953 | + | 0.126604i | \(0.0404079\pi\) | ||||
−0.991953 | + | 0.126604i | \(0.959592\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 35.8504i | − | 1.44095i | −0.693481 | − | 0.720475i | \(-0.743924\pi\) | ||
0.693481 | − | 0.720475i | \(-0.256076\pi\) | |||||||
\(620\) | −16.0232 | + | 7.59371i | −0.643507 | + | 0.304971i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.79719 | − | 12.4338i | −0.112157 | − | 0.498549i | ||||
\(623\) | 1.74631 | 0.0699643 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.57248 | 0.382899 | ||||||||
\(626\) | −0.778673 | − | 3.46127i | −0.0311220 | − | 0.138340i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.0247 | + | 12.3336i | −1.03850 | + | 0.492165i | ||||
\(629\) | − | 56.6663i | − | 2.25943i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.9763i | − | 1.23315i | −0.787298 | − | 0.616573i | \(-0.788520\pi\) | ||
0.787298 | − | 0.616573i | \(-0.211480\pi\) | |||||||
\(632\) | −33.6491 | + | 26.3234i | −1.33849 | + | 1.04709i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30.5223 | + | 6.86652i | −1.21220 | + | 0.272704i | ||||
\(635\) | 21.5279 | 0.854309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.985148 | −0.0390330 | ||||||||
\(638\) | 21.0819 | − | 4.74274i | 0.834641 | − | 0.187767i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.260078 | + | 11.9209i | −0.0102805 | + | 0.471216i | ||||
\(641\) | 4.95455i | 0.195693i | 0.995202 | + | 0.0978466i | \(0.0311954\pi\) | ||||
−0.995202 | + | 0.0978466i | \(0.968805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4.37251i | − | 0.172435i | −0.996276 | − | 0.0862175i | \(-0.972522\pi\) | ||
0.996276 | − | 0.0862175i | \(-0.0274780\pi\) | |||||||
\(644\) | 2.28020 | + | 4.81136i | 0.0898525 | + | 0.189594i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.50320 | + | 11.1269i | 0.0984870 | + | 0.437784i | ||||
\(647\) | −31.7458 | −1.24805 | −0.624027 | − | 0.781402i | \(-0.714505\pi\) | ||||
−0.624027 | + | 0.781402i | \(0.714505\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.9862 | −1.60885 | ||||||||
\(650\) | 1.18927 | + | 5.28641i | 0.0466470 | + | 0.207350i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.90657 | + | 4.02298i | 0.0746671 | + | 0.157552i | ||||
\(653\) | − | 0.116763i | − | 0.00456930i | −0.999997 | − | 0.00228465i | \(-0.999273\pi\) | ||
0.999997 | − | 0.00228465i | \(-0.000727227\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1054i | 0.707437i | ||||||||
\(656\) | −14.0709 | − | 11.5110i | −0.549375 | − | 0.449428i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.41369 | − | 1.44287i | 0.250032 | − | 0.0562489i | ||||
\(659\) | 3.95369 | 0.154014 | 0.0770069 | − | 0.997031i | \(-0.475464\pi\) | ||||
0.0770069 | + | 0.997031i | \(0.475464\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.7062 | 1.50550 | 0.752749 | − | 0.658307i | \(-0.228727\pi\) | ||||
0.752749 | + | 0.658307i | \(0.228727\pi\) | |||||||
\(662\) | −25.4293 | + | 5.72077i | −0.988339 | + | 0.222344i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.24631 | − | 10.5412i | −0.320019 | − | 0.409079i | ||||
\(665\) | − | 1.33731i | − | 0.0518585i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 13.6535i | − | 0.528667i | ||||||
\(668\) | 22.5871 | − | 10.7045i | 0.873920 | − | 0.414168i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.68719 | + | 11.9448i | 0.103815 | + | 0.461467i | ||||
\(671\) | 14.5690 | 0.562432 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.45012 | −0.248634 | −0.124317 | − | 0.992243i | \(-0.539674\pi\) | ||||
−0.124317 | + | 0.992243i | \(0.539674\pi\) | |||||||
\(674\) | −7.68870 | − | 34.1770i | −0.296158 | − | 1.31645i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.7410 | − | 10.3035i | 0.836193 | − | 0.396288i | ||||
\(677\) | − | 30.4104i | − | 1.16877i | −0.811478 | − | 0.584384i | \(-0.801336\pi\) | ||
0.811478 | − | 0.584384i | \(-0.198664\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.00594i | − | 0.115358i | ||||||
\(680\) | 11.6735 | + | 14.9222i | 0.447659 | + | 0.572241i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −34.5786 | + | 7.77906i | −1.32408 | + | 0.297876i | ||||
\(683\) | −16.9861 | −0.649953 | −0.324977 | − | 0.945722i | \(-0.605356\pi\) | ||||
−0.324977 | + | 0.945722i | \(0.605356\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.1611 | 0.655690 | ||||||||
\(686\) | −1.37973 | + | 0.310394i | −0.0526783 | + | 0.0118509i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00028 | + | 1.63637i | 0.0762601 | + | 0.0623862i | ||||
\(689\) | − | 2.53890i | − | 0.0967243i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.74292i | − | 0.104346i | −0.998638 | − | 0.0521729i | \(-0.983385\pi\) | ||
0.998638 | − | 0.0521729i | \(-0.0166147\pi\) | |||||||
\(692\) | 13.8258 | + | 29.1732i | 0.525577 | + | 1.10900i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.42280 | − | 37.4401i | −0.319725 | − | 1.42121i | ||||
\(695\) | −1.11433 | −0.0422689 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.8855 | −1.09412 | ||||||||
\(698\) | 3.89223 | + | 17.3013i | 0.147323 | + | 0.654865i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.33122 | + | 7.02908i | 0.125908 | + | 0.265674i | ||||
\(701\) | 8.97421i | 0.338951i | 0.985534 | + | 0.169476i | \(0.0542074\pi\) | ||||
−0.985534 | + | 0.169476i | \(0.945793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3133i | 0.426688i | ||||||||
\(704\) | −5.73706 | + | 23.1332i | −0.216223 | + | 0.871864i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.0413 | + | 7.65818i | −1.28116 | + | 0.288219i | ||||
\(707\) | −1.53513 | −0.0577346 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.13240 | 0.117640 | 0.0588200 | − | 0.998269i | \(-0.481266\pi\) | ||||
0.0588200 | + | 0.998269i | \(0.481266\pi\) | |||||||
\(710\) | 0.849023 | − | 0.191002i | 0.0318633 | − | 0.00716820i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.89032 | − | 3.04337i | 0.145796 | − | 0.114055i | ||||
\(713\) | 22.3946i | 0.838684i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.09326i | − | 0.115681i | ||||||
\(716\) | −26.3432 | + | 12.4846i | −0.984491 | + | 0.466570i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.09328 | + | 31.5303i | 0.264719 | + | 1.17670i | ||||
\(719\) | −29.4070 | −1.09670 | −0.548348 | − | 0.836250i | \(-0.684743\pi\) | ||||
−0.548348 | + | 0.836250i | \(0.684743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6910 | −0.435395 | ||||||||
\(722\) | 5.39773 | + | 23.9934i | 0.200883 | + | 0.892942i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.54005 | + | 1.67770i | −0.131565 | + | 0.0623512i | ||||
\(725\) | − | 19.9469i | − | 0.740809i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 11.0639i | − | 0.410338i | −0.978727 | − | 0.205169i | \(-0.934226\pi\) | ||
0.978727 | − | 0.205169i | \(-0.0657743\pi\) | |||||||
\(728\) | −2.19466 | + | 1.71686i | −0.0813394 | + | 0.0636312i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.0502 | + | 4.06071i | −0.668070 | + | 0.150294i | ||||
\(731\) | 4.10630 | 0.151877 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.1305 | −0.817410 | −0.408705 | − | 0.912667i | \(-0.634019\pi\) | ||||
−0.408705 | + | 0.912667i | \(0.634019\pi\) | |||||||
\(734\) | −28.0245 | + | 6.30460i | −1.03440 | + | 0.232707i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.4647 | + | 6.74467i | 0.496315 | + | 0.248612i | ||||
\(737\) | 24.4727i | 0.901463i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.76011i | − | 0.211889i | −0.994372 | − | 0.105944i | \(-0.966213\pi\) | ||
0.994372 | − | 0.105944i | \(-0.0337866\pi\) | |||||||
\(740\) | 8.04844 | + | 16.9827i | 0.295867 | + | 0.624297i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.799940 | − | 3.55581i | −0.0293667 | − | 0.130538i | ||||
\(743\) | 51.9086 | 1.90434 | 0.952170 | − | 0.305567i | \(-0.0988461\pi\) | ||||
0.952170 | + | 0.305567i | \(0.0988461\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.08011 | −0.259395 | ||||||||
\(746\) | 9.13155 | + | 40.5906i | 0.334330 | + | 1.48613i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.2182 | + | 34.2214i | 0.592997 | + | 1.25126i | ||||
\(749\) | − | 15.7149i | − | 0.574212i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36.7888i | − | 1.34244i | −0.741257 | − | 0.671221i | \(-0.765770\pi\) | ||
0.741257 | − | 0.671221i | \(-0.234230\pi\) | |||||||
\(752\) | 11.7735 | − | 14.3918i | 0.429335 | − | 0.524814i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.97117 | − | 1.56828i | 0.253875 | − | 0.0571136i | ||||
\(755\) | 5.23743 | 0.190610 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.2356 | 1.17162 | 0.585812 | − | 0.810447i | \(-0.300776\pi\) | ||||
0.585812 | + | 0.810447i | \(0.300776\pi\) | |||||||
\(758\) | −25.5858 | + | 5.75597i | −0.929319 | + | 0.209066i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.33058 | − | 2.97917i | −0.0845392 | − | 0.108066i | ||||
\(761\) | − | 13.8150i | − | 0.500793i | −0.968143 | − | 0.250396i | \(-0.919439\pi\) | ||
0.968143 | − | 0.250396i | \(-0.0805609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.34105i | 0.265764i | ||||||||
\(764\) | −47.3921 | + | 22.4600i | −1.71459 | + | 0.812576i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.7357 | − | 52.1660i | −0.424026 | − | 1.88484i | ||||
\(767\) | −13.5529 | −0.489368 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.3420 | −1.70720 | −0.853599 | − | 0.520931i | \(-0.825585\pi\) | ||||
−0.853599 | + | 0.520931i | \(0.825585\pi\) | |||||||
\(770\) | −0.974604 | − | 4.33220i | −0.0351223 | − | 0.156122i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 42.2912 | − | 20.0426i | 1.52209 | − | 0.721349i | ||||
\(773\) | 12.7984i | 0.460325i | 0.973152 | + | 0.230163i | \(0.0739259\pi\) | ||||
−0.973152 | + | 0.230163i | \(0.926074\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.7170i | 1.17523i | ||||||||
\(776\) | −5.23859 | − | 6.69647i | −0.188055 | − | 0.240389i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.1222 | + | 2.50214i | −0.398752 | + | 0.0897061i | ||||
\(779\) | 5.76690 | 0.206621 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73949 | 0.0622440 | ||||||||
\(782\) | 23.3447 | − | 5.25180i | 0.834806 | − | 0.187804i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.53275 | + | 3.09600i | −0.0904552 | + | 0.110571i | ||||
\(785\) | − | 15.1761i | − | 0.541660i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5078i | 1.26572i | 0.774267 | + | 0.632858i | \(0.218119\pi\) | ||||
−0.774267 | + | 0.632858i | \(0.781881\pi\) | |||||||
\(788\) | −14.1649 | − | 29.8888i | −0.504604 | − | 1.06475i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.94118 | − | 21.9640i | −0.175799 | − | 0.781444i | ||||
\(791\) | −4.35118 | −0.154710 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.81755 | 0.171076 | ||||||||
\(794\) | 8.56086 | + | 38.0538i | 0.303813 | + | 1.35048i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.03303 | + | 2.17975i | 0.0366147 | + | 0.0772593i | ||||
\(797\) | 30.3922i | 1.07655i | 0.842770 | + | 0.538273i | \(0.180923\pi\) | ||||
−0.842770 | + | 0.538273i | \(0.819077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29.5442i | − | 1.04520i | ||||||
\(800\) | 19.6710 | + | 9.85351i | 0.695475 | + | 0.348374i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.99414 | − | 2.24835i | 0.352905 | − | 0.0793922i | ||||
\(803\) | −36.9817 | −1.30505 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.80572 | −0.0988886 | ||||||||
\(806\) | −11.4341 | + | 2.57231i | −0.402750 | + | 0.0906056i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.41988 | + | 2.67535i | −0.120311 | + | 0.0941183i | ||||
\(809\) | − | 41.0141i | − | 1.44198i | −0.692946 | − | 0.720989i | \(-0.743688\pi\) | ||
0.692946 | − | 0.720989i | \(-0.256312\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 46.2839i | 1.62525i | 0.582788 | + | 0.812624i | \(0.301962\pi\) | ||||
−0.582788 | + | 0.812624i | \(0.698038\pi\) | |||||||
\(812\) | 9.26921 | − | 4.39286i | 0.325286 | − | 0.154159i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.24489 | + | 36.6493i | 0.288983 | + | 1.28456i | ||||
\(815\) | −2.34598 | −0.0821760 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.819810 | −0.0286815 | ||||||||
\(818\) | 8.20621 | + | 36.4773i | 0.286923 | + | 1.27540i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.65690 | − | 4.10267i | 0.302312 | − | 0.143272i | ||||
\(821\) | − | 4.65424i | − | 0.162434i | −0.996696 | − | 0.0812170i | \(-0.974119\pi\) | ||
0.996696 | − | 0.0812170i | \(-0.0258807\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24.1740i | − | 0.842654i | −0.906909 | − | 0.421327i | \(-0.861564\pi\) | ||
0.906909 | − | 0.421327i | \(-0.138436\pi\) | |||||||
\(824\) | −26.0445 | + | 20.3744i | −0.907303 | + | 0.709776i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.9813 | + | 4.27017i | −0.660444 | + | 0.148578i | ||||
\(827\) | −36.6008 | −1.27273 | −0.636367 | − | 0.771386i | \(-0.719564\pi\) | ||||
−0.636367 | + | 0.771386i | \(0.719564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.1578 | −1.29054 | −0.645272 | − | 0.763953i | \(-0.723256\pi\) | ||||
−0.645272 | + | 0.763953i | \(0.723256\pi\) | |||||||
\(830\) | 6.88064 | − | 1.54792i | 0.238830 | − | 0.0537290i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.89708 | + | 7.64946i | −0.0657693 | + | 0.265197i | ||||
\(833\) | 6.35564i | 0.220210i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.1715i | 0.455819i | ||||||||
\(836\) | −3.23792 | − | 6.83221i | −0.111986 | − | 0.236297i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.31223 | + | 28.0584i | 0.218052 | + | 0.969263i | ||||
\(839\) | −3.38158 | −0.116745 | −0.0583726 | − | 0.998295i | \(-0.518591\pi\) | ||||
−0.0583726 | + | 0.998295i | \(0.518591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.69611 | 0.0929694 | ||||||||
\(842\) | 4.23803 | + | 18.8384i | 0.146052 | + | 0.649216i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.99150 | − | 16.8626i | −0.275079 | − | 0.580433i | ||||
\(845\) | 12.6781i | 0.436141i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12410i | 0.0729851i | ||||||||
\(848\) | −7.97893 | − | 6.52733i | −0.273997 | − | 0.224149i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34.1051 | − | 7.67253i | 1.16979 | − | 0.263166i | ||||
\(851\) | 23.7356 | 0.813647 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2168 | 0.966124 | 0.483062 | − | 0.875586i | \(-0.339525\pi\) | ||||
0.483062 | + | 0.875586i | \(0.339525\pi\) | |||||||
\(854\) | 6.74713 | − | 1.51788i | 0.230882 | − | 0.0519409i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.3872 | − | 35.0089i | −0.936074 | − | 1.19658i | ||||
\(857\) | − | 17.3707i | − | 0.593373i | −0.954975 | − | 0.296686i | \(-0.904118\pi\) | ||
0.954975 | − | 0.296686i | \(-0.0958816\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.9940i | 1.56930i | 0.619941 | + | 0.784648i | \(0.287156\pi\) | ||||
−0.619941 | + | 0.784648i | \(0.712844\pi\) | |||||||
\(860\) | −1.23064 | + | 0.583227i | −0.0419646 | + | 0.0198879i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.26993 | − | 23.4253i | −0.179495 | − | 0.797870i | ||||
\(863\) | −1.05635 | −0.0359586 | −0.0179793 | − | 0.999838i | \(-0.505723\pi\) | ||||
−0.0179793 | + | 0.999838i | \(0.505723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.0122 | −0.578432 | ||||||||
\(866\) | 0.193816 | + | 0.861528i | 0.00658613 | + | 0.0292759i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −15.2034 | + | 7.20519i | −0.516037 | + | 0.244560i | ||||
\(869\) | − | 45.0002i | − | 1.52653i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.09239i | 0.274200i | ||||||||
\(872\) | 12.7936 | + | 16.3540i | 0.433246 | + | 0.553816i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.66071 | + | 1.04851i | −0.157651 | + | 0.0354663i | ||||
\(875\) | −9.36858 | −0.316716 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.34738 | 0.146801 | 0.0734003 | − | 0.997303i | \(-0.476615\pi\) | ||||
0.0734003 | + | 0.997303i | \(0.476615\pi\) | |||||||
\(878\) | −31.5663 | + | 7.10139i | −1.06531 | + | 0.239660i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.72110 | − | 7.95255i | −0.327698 | − | 0.268080i | ||||
\(881\) | − | 58.0353i | − | 1.95526i | −0.210331 | − | 0.977630i | \(-0.567454\pi\) | ||
0.210331 | − | 0.977630i | \(-0.432546\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 37.8799i | − | 1.27476i | −0.770550 | − | 0.637379i | \(-0.780018\pi\) | ||
0.770550 | − | 0.637379i | \(-0.219982\pi\) | |||||||
\(884\) | 5.36289 | + | 11.3160i | 0.180373 | + | 0.380599i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0659353 | − | 0.293089i | −0.00221514 | − | 0.00984650i | ||||
\(887\) | −4.92085 | −0.165226 | −0.0826130 | − | 0.996582i | \(-0.526327\pi\) | ||||
−0.0826130 | + | 0.996582i | \(0.526327\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.4265 | 0.685081 | ||||||||
\(890\) | 0.571272 | + | 2.53935i | 0.0191491 | + | 0.0851194i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.50524 | + | 5.28622i | 0.0838818 | + | 0.176996i | ||||
\(893\) | 5.89842i | 0.197383i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 15.3619i | − | 0.513491i | ||||||
\(896\) | −0.246771 | + | 11.3110i | −0.00824404 | + | 0.377875i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.2848 | + | 5.46329i | −0.810396 | + | 0.182312i | ||||
\(899\) | 43.1437 | 1.43892 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.3796 | −0.545684 | ||||||||
\(902\) | 18.6819 | − | 4.20281i | 0.622039 | − | 0.139938i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.69331 | + | 7.58300i | −0.322395 | + | 0.252207i | ||||
\(905\) | − | 2.06436i | − | 0.0686216i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.3942i | − | 1.34127i | −0.741789 | − | 0.670633i | \(-0.766022\pi\) | ||
0.741789 | − | 0.670633i | \(-0.233978\pi\) | |||||||
\(908\) | 41.7416 | − | 19.7821i | 1.38524 | − | 0.656494i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.322273 | − | 1.43253i | −0.0106832 | − | 0.0474880i | ||||
\(911\) | −24.4159 | −0.808934 | −0.404467 | − | 0.914553i | \(-0.632543\pi\) | ||||
−0.404467 | + | 0.914553i | \(0.632543\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.0972 | 0.466548 | ||||||||
\(914\) | 2.65806 | + | 11.8153i | 0.0879209 | + | 0.390817i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.4174 | + | 7.78051i | −0.542445 | + | 0.257075i | ||||
\(917\) | 17.1791i | 0.567303i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.922920i | 0.0304443i | 0.999884 | + | 0.0152222i | \(0.00484555\pi\) | ||||
−0.999884 | + | 0.0152222i | \(0.995154\pi\) | |||||||
\(920\) | −6.25042 | + | 4.88965i | −0.206070 | + | 0.161207i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −45.8392 | + | 10.3123i | −1.50963 | + | 0.339618i | ||||
\(923\) | 0.575199 | 0.0189329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.6762 | 1.14015 | ||||||||
\(926\) | 15.0140 | − | 3.37767i | 0.493392 | − | 0.110997i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.9938 | − | 25.9400i | 0.426542 | − | 0.851524i | ||||
\(929\) | − | 18.1210i | − | 0.594530i | −0.954795 | − | 0.297265i | \(-0.903926\pi\) | ||
0.954795 | − | 0.297265i | \(-0.0960744\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.26888i | − | 0.0415860i | ||||||
\(932\) | −25.2327 | − | 53.2425i | −0.826523 | − | 1.74402i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.9675 | − | 57.6418i | −0.424310 | − | 1.88610i | ||||
\(935\) | −19.9560 | −0.652632 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.1414 | 1.89940 | 0.949699 | − | 0.313165i | \(-0.101389\pi\) | ||||
0.949699 | + | 0.313165i | \(0.101389\pi\) | |||||||
\(938\) | 2.54970 | + | 11.3336i | 0.0832506 | + | 0.370057i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.19624 | + | 8.85432i | 0.136866 | + | 0.288796i | ||||
\(941\) | − | 11.4151i | − | 0.372121i | −0.982538 | − | 0.186061i | \(-0.940428\pi\) | ||
0.982538 | − | 0.186061i | \(-0.0595721\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 12.0992i | − | 0.394004i | ||||||
\(944\) | −34.8436 | + | 42.5924i | −1.13406 | + | 1.38627i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.65577 | + | 0.597462i | −0.0863467 | + | 0.0194252i | ||||
\(947\) | 53.1805 | 1.72813 | 0.864067 | − | 0.503377i | \(-0.167909\pi\) | ||||
0.864067 | + | 0.503377i | \(0.167909\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.2287 | −0.396962 | ||||||||
\(950\) | −6.80898 | + | 1.53180i | −0.220912 | + | 0.0496981i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.0763 | + | 14.1587i | 0.358984 | + | 0.458887i | ||||
\(953\) | 32.5256i | 1.05361i | 0.849987 | + | 0.526803i | \(0.176609\pi\) | ||||
−0.849987 | + | 0.526803i | \(0.823391\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 27.6364i | − | 0.894293i | ||||||
\(956\) | 31.3963 | − | 14.8793i | 1.01543 | − | 0.481232i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.62886 | − | 11.6855i | −0.0849347 | − | 0.377542i | ||||
\(959\) | 16.2830 | 0.525807 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.7645 | −1.28273 | ||||||||
\(962\) | 2.72634 | + | 12.1188i | 0.0879008 | + | 0.390727i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.3878 | − | 10.1361i | 0.688856 | − | 0.326462i | ||||
\(965\) | 24.6618i | 0.793892i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 34.1888i | − | 1.09944i | −0.835350 | − | 0.549719i | \(-0.814735\pi\) | ||
0.835350 | − | 0.549719i | \(-0.185265\pi\) | |||||||
\(968\) | 3.70177 | + | 4.73196i | 0.118980 | + | 0.152091i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.37103 | − | 0.983338i | 0.140345 | − | 0.0315731i | ||||
\(971\) | 14.1172 | 0.453041 | 0.226521 | − | 0.974006i | \(-0.427265\pi\) | ||||
0.226521 | + | 0.974006i | \(0.427265\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.05732 | −0.0338960 | ||||||||
\(974\) | −31.9402 | + | 7.18549i | −1.02343 | + | 0.230238i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.3856 | − | 15.1400i | 0.396453 | − | 0.484619i | ||||
\(977\) | 23.3492i | 0.747007i | 0.927629 | + | 0.373504i | \(0.121844\pi\) | ||||
−0.927629 | + | 0.373504i | \(0.878156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.20267i | 0.166278i | ||||||||
\(980\) | −0.902706 | − | 1.90477i | −0.0288359 | − | 0.0608455i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.14632 | + | 9.54060i | 0.0684919 | + | 0.304453i | ||||
\(983\) | −27.3413 | −0.872052 | −0.436026 | − | 0.899934i | \(-0.643614\pi\) | ||||
−0.436026 | + | 0.899934i | \(0.643614\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.4295 | 0.555350 | ||||||||
\(986\) | −10.1177 | − | 44.9742i | −0.322214 | − | 1.43227i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.07068 | − | 2.25921i | −0.0340630 | − | 0.0718750i | ||||
\(989\) | 1.71999i | 0.0546926i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2385i | 0.865259i | 0.901572 | + | 0.432629i | \(0.142414\pi\) | ||||
−0.901572 | + | 0.432629i | \(0.857586\pi\) | |||||||
\(992\) | −21.3124 | + | 42.5470i | −0.676671 | + | 1.35087i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.805584 | − | 0.181230i | 0.0255516 | − | 0.00574827i | ||||
\(995\) | −1.27111 | −0.0402969 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.6550 | 1.79428 | 0.897141 | − | 0.441744i | \(-0.145640\pi\) | ||||
0.897141 | + | 0.441744i | \(0.145640\pi\) | |||||||
\(998\) | −10.4704 | + | 2.35549i | −0.331433 | + | 0.0745616i | ||||
\(999\) | 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 | 756.2.e.a.323.14 | yes | 24 | |
3.2 | odd | 2 | inner | 756.2.e.a.323.11 | ✓ | 24 | |
4.3 | odd | 2 | inner | 756.2.e.a.323.12 | yes | 24 | |
12.11 | even | 2 | inner | 756.2.e.a.323.13 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.e.a.323.11 | ✓ | 24 | 3.2 | odd | 2 | inner | |
756.2.e.a.323.12 | yes | 24 | 4.3 | odd | 2 | inner | |
756.2.e.a.323.13 | yes | 24 | 12.11 | even | 2 | inner | |
756.2.e.a.323.14 | yes | 24 | 1.1 | even | 1 | trivial |