Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,5,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (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: | \(33.4918680392\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.15 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.f.163.16 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.43802 | − | 3.17113i | 0.609506 | − | 0.792782i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.11208 | − | 15.4626i | −0.257005 | − | 0.966410i | ||||
\(5\) | −22.1491 | −0.885964 | −0.442982 | − | 0.896530i | \(-0.646080\pi\) | ||||
−0.442982 | + | 0.896530i | \(0.646080\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 95.5959i | − | 1.95094i | −0.220138 | − | 0.975469i | \(-0.570651\pi\) | ||
0.220138 | − | 0.975469i | \(-0.429349\pi\) | |||||||
\(8\) | −59.0591 | − | 24.6582i | −0.922798 | − | 0.385284i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −54.0000 | + | 70.2376i | −0.540000 | + | 0.702376i | ||||
\(11\) | 21.8693i | 0.180738i | 0.995908 | + | 0.0903689i | \(0.0288046\pi\) | ||||
−0.995908 | + | 0.0903689i | \(0.971195\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 126.225 | 0.746892 | 0.373446 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373446 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(14\) | −303.147 | − | 233.065i | −1.54667 | − | 1.18911i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −222.182 | + | 127.167i | −0.867897 | + | 0.496745i | ||||
\(17\) | −283.865 | −0.982232 | −0.491116 | − | 0.871094i | \(-0.663411\pi\) | ||||
−0.491116 | + | 0.871094i | \(0.663411\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 323.729i | − | 0.896756i | −0.893844 | − | 0.448378i | \(-0.852002\pi\) | ||
0.893844 | − | 0.448378i | \(-0.147998\pi\) | |||||||
\(20\) | 91.0790 | + | 342.482i | 0.227697 | + | 0.856205i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 69.3502 | + | 53.3178i | 0.143286 | + | 0.110161i | ||||
\(23\) | 229.131i | 0.433139i | 0.976267 | + | 0.216570i | \(0.0694868\pi\) | ||||
−0.976267 | + | 0.216570i | \(0.930513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −134.417 | −0.215067 | ||||||||
\(26\) | 307.739 | − | 400.274i | 0.455235 | − | 0.592122i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1478.16 | + | 393.098i | −1.88541 | + | 0.501401i | ||||
\(29\) | 1209.64 | 1.43834 | 0.719170 | − | 0.694835i | \(-0.244522\pi\) | ||||
0.719170 | + | 0.694835i | \(0.244522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 829.727i | 0.863399i | 0.902017 | + | 0.431700i | \(0.142086\pi\) | ||||
−0.902017 | + | 0.431700i | \(0.857914\pi\) | |||||||
\(32\) | −138.422 | + | 1014.60i | −0.135178 | + | 0.990821i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −692.070 | + | 900.172i | −0.598676 | + | 0.778695i | ||||
\(35\) | 2117.36i | 1.72846i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −318.650 | −0.232761 | −0.116380 | − | 0.993205i | \(-0.537129\pi\) | ||||
−0.116380 | + | 0.993205i | \(0.537129\pi\) | |||||||
\(38\) | −1026.59 | − | 789.259i | −0.710932 | − | 0.546578i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1308.11 | + | 546.156i | 0.817566 | + | 0.341348i | ||||
\(41\) | 328.837 | 0.195620 | 0.0978099 | − | 0.995205i | \(-0.468816\pi\) | ||||
0.0978099 | + | 0.995205i | \(0.468816\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 207.079i | 0.111995i | 0.998431 | + | 0.0559976i | \(0.0178339\pi\) | ||||
−0.998431 | + | 0.0559976i | \(0.982166\pi\) | |||||||
\(44\) | 338.155 | − | 89.9283i | 0.174667 | − | 0.0464506i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 726.602 | + | 558.626i | 0.343385 | + | 0.264001i | ||||
\(47\) | 1226.78i | 0.555356i | 0.960674 | + | 0.277678i | \(0.0895648\pi\) | ||||
−0.960674 | + | 0.277678i | \(0.910435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6737.58 | −2.80616 | ||||||||
\(50\) | −327.712 | + | 426.253i | −0.131085 | + | 0.170501i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −519.046 | − | 1951.76i | −0.191955 | − | 0.721804i | ||||
\(53\) | −2834.27 | −1.00900 | −0.504499 | − | 0.863412i | \(-0.668323\pi\) | ||||
−0.504499 | + | 0.863412i | \(0.668323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 484.385i | − | 0.160127i | ||||||
\(56\) | −2357.22 | + | 5645.81i | −0.751664 | + | 1.80032i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2949.14 | − | 3835.93i | 0.876676 | − | 1.14029i | ||||
\(59\) | 1475.86i | 0.423975i | 0.977272 | + | 0.211988i | \(0.0679937\pi\) | ||||
−0.977272 | + | 0.211988i | \(0.932006\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1872.36 | −0.503187 | −0.251594 | − | 0.967833i | \(-0.580955\pi\) | ||||
−0.251594 | + | 0.967833i | \(0.580955\pi\) | |||||||
\(62\) | 2631.17 | + | 2022.89i | 0.684487 | + | 0.526247i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2879.95 | + | 2912.58i | 0.703113 | + | 0.711078i | ||||
\(65\) | −2795.76 | −0.661719 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 247.871i | 0.0552174i | 0.999619 | + | 0.0276087i | \(0.00878924\pi\) | ||||
−0.999619 | + | 0.0276087i | \(0.991211\pi\) | |||||||
\(68\) | 1167.28 | + | 4389.28i | 0.252439 | + | 0.949239i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6714.43 | + | 5162.18i | 1.37029 | + | 1.05351i | ||||
\(71\) | 4308.28i | 0.854648i | 0.904099 | + | 0.427324i | \(0.140544\pi\) | ||||
−0.904099 | + | 0.427324i | \(0.859456\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3010.75 | 0.564974 | 0.282487 | − | 0.959271i | \(-0.408841\pi\) | ||||
0.282487 | + | 0.959271i | \(0.408841\pi\) | |||||||
\(74\) | −776.875 | + | 1010.48i | −0.141869 | + | 0.184528i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5005.68 | + | 1331.20i | −0.866634 | + | 0.230471i | ||||
\(77\) | 2090.61 | 0.352608 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 7191.93i | − | 1.15237i | −0.817320 | − | 0.576184i | \(-0.804541\pi\) | ||
0.817320 | − | 0.576184i | \(-0.195459\pi\) | |||||||
\(80\) | 4921.12 | − | 2816.63i | 0.768926 | − | 0.440098i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 801.712 | − | 1042.78i | 0.119231 | − | 0.155084i | ||||
\(83\) | − | 3322.48i | − | 0.482287i | −0.970489 | − | 0.241144i | \(-0.922477\pi\) | ||
0.970489 | − | 0.241144i | \(-0.0775225\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6287.36 | 0.870222 | ||||||||
\(86\) | 656.674 | + | 504.863i | 0.0887877 | + | 0.0682617i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 539.256 | − | 1291.58i | 0.0696353 | − | 0.166785i | ||||
\(89\) | −1549.85 | −0.195664 | −0.0978318 | − | 0.995203i | \(-0.531191\pi\) | ||||
−0.0978318 | + | 0.995203i | \(0.531191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 12066.6i | − | 1.45714i | ||||||
\(92\) | 3542.95 | − | 942.204i | 0.418590 | − | 0.111319i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3890.28 | + | 2990.92i | 0.440276 | + | 0.338493i | ||||
\(95\) | 7170.31i | 0.794494i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5837.37 | 0.620403 | 0.310201 | − | 0.950671i | \(-0.399604\pi\) | ||||
0.310201 | + | 0.950671i | \(0.399604\pi\) | |||||||
\(98\) | −16426.4 | + | 21365.7i | −1.71037 | + | 2.22467i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 552.734 | + | 2078.43i | 0.0552734 | + | 0.207843i | ||||
\(101\) | −5499.00 | −0.539065 | −0.269532 | − | 0.962991i | \(-0.586869\pi\) | ||||
−0.269532 | + | 0.962991i | \(0.586869\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17933.3i | − | 1.69038i | −0.534464 | − | 0.845191i | \(-0.679487\pi\) | ||
0.534464 | − | 0.845191i | \(-0.320513\pi\) | |||||||
\(104\) | −7454.72 | − | 3112.47i | −0.689230 | − | 0.287765i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6910.03 | + | 8987.84i | −0.614990 | + | 0.799915i | ||||
\(107\) | − | 8715.17i | − | 0.761217i | −0.924736 | − | 0.380608i | \(-0.875715\pi\) | ||
0.924736 | − | 0.380608i | \(-0.124285\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12162.1 | −1.02366 | −0.511830 | − | 0.859087i | \(-0.671032\pi\) | ||||
−0.511830 | + | 0.859087i | \(0.671032\pi\) | |||||||
\(110\) | −1536.05 | − | 1180.94i | −0.126946 | − | 0.0975985i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12156.6 | + | 21239.7i | 0.969118 | + | 1.69321i | ||||
\(113\) | −20473.4 | −1.60337 | −0.801684 | − | 0.597748i | \(-0.796062\pi\) | ||||
−0.801684 | + | 0.597748i | \(0.796062\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5075.04i | − | 0.383746i | ||||||
\(116\) | −4974.15 | − | 18704.2i | −0.369661 | − | 1.39003i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4680.13 | + | 3598.18i | 0.336120 | + | 0.258415i | ||||
\(119\) | 27136.3i | 1.91627i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14162.7 | 0.967334 | ||||||||
\(122\) | −4564.86 | + | 5937.49i | −0.306696 | + | 0.398918i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 12829.7 | − | 3411.90i | 0.834398 | − | 0.221898i | ||||
\(125\) | 16820.4 | 1.07651 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8130.42i | 0.504087i | 0.967716 | + | 0.252044i | \(0.0811026\pi\) | ||||
−0.967716 | + | 0.252044i | \(0.918897\pi\) | |||||||
\(128\) | 16257.5 | − | 2031.76i | 0.992281 | − | 0.124009i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6816.14 | + | 8865.72i | −0.403322 | + | 0.524599i | ||||
\(131\) | − | 16275.6i | − | 0.948406i | −0.880416 | − | 0.474203i | \(-0.842736\pi\) | ||
0.880416 | − | 0.474203i | \(-0.157264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30947.2 | −1.74952 | ||||||||
\(134\) | 786.030 | + | 604.315i | 0.0437754 | + | 0.0336554i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16764.8 | + | 6999.59i | 0.906402 | + | 0.378438i | ||||
\(137\) | 24662.9 | 1.31402 | 0.657011 | − | 0.753881i | \(-0.271821\pi\) | ||||
0.657011 | + | 0.753881i | \(0.271821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 19720.1i | − | 1.02066i | −0.859980 | − | 0.510328i | \(-0.829524\pi\) | ||
0.859980 | − | 0.510328i | \(-0.170476\pi\) | |||||||
\(140\) | 32739.9 | − | 8706.78i | 1.67040 | − | 0.444223i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13662.1 | + | 10503.7i | 0.677549 | + | 0.520913i | ||||
\(143\) | 2760.44i | 0.134992i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26792.5 | −1.27432 | ||||||||
\(146\) | 7340.28 | − | 9547.46i | 0.344355 | − | 0.447901i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1310.31 | + | 4927.14i | 0.0598207 | + | 0.224942i | ||||
\(149\) | 29885.5 | 1.34613 | 0.673066 | − | 0.739583i | \(-0.264977\pi\) | ||||
0.673066 | + | 0.739583i | \(0.264977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5963.00i | − | 0.261524i | −0.991414 | − | 0.130762i | \(-0.958258\pi\) | ||
0.991414 | − | 0.130762i | \(-0.0417423\pi\) | |||||||
\(152\) | −7982.56 | + | 19119.1i | −0.345506 | + | 0.827525i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5096.97 | − | 6629.60i | 0.214917 | − | 0.279541i | ||||
\(155\) | − | 18377.7i | − | 0.764941i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −34987.0 | −1.41941 | −0.709704 | − | 0.704500i | \(-0.751172\pi\) | ||||
−0.709704 | + | 0.704500i | \(0.751172\pi\) | |||||||
\(158\) | −22806.5 | − | 17534.1i | −0.913576 | − | 0.702375i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3065.93 | − | 22472.5i | 0.119763 | − | 0.877832i | ||||
\(161\) | 21903.9 | 0.845027 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14509.8i | − | 0.546118i | −0.961997 | − | 0.273059i | \(-0.911965\pi\) | ||
0.961997 | − | 0.273059i | \(-0.0880354\pi\) | |||||||
\(164\) | −1352.20 | − | 5084.66i | −0.0502753 | − | 0.189049i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10536.0 | − | 8100.28i | −0.382349 | − | 0.293957i | ||||
\(167\) | 44617.8i | 1.59983i | 0.600111 | + | 0.799917i | \(0.295123\pi\) | ||||
−0.600111 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12628.3 | −0.442153 | ||||||||
\(170\) | 15328.7 | − | 19938.0i | 0.530406 | − | 0.689896i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3201.97 | − | 851.526i | 0.108233 | − | 0.0287833i | ||||
\(173\) | −52886.6 | −1.76707 | −0.883534 | − | 0.468367i | \(-0.844842\pi\) | ||||
−0.883534 | + | 0.468367i | \(0.844842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12849.7i | 0.419583i | ||||||||
\(176\) | −2781.04 | − | 4858.95i | −0.0897806 | − | 0.156862i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3778.57 | + | 4914.77i | −0.119258 | + | 0.155119i | ||||
\(179\) | − | 32840.8i | − | 1.02496i | −0.858698 | − | 0.512482i | \(-0.828726\pi\) | ||
0.858698 | − | 0.512482i | \(-0.171274\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22758.6 | −0.694685 | −0.347343 | − | 0.937738i | \(-0.612916\pi\) | ||||
−0.347343 | + | 0.937738i | \(0.612916\pi\) | |||||||
\(182\) | −38264.6 | − | 29418.6i | −1.15519 | − | 0.888135i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5649.94 | − | 13532.2i | 0.166881 | − | 0.399700i | ||||
\(185\) | 7057.80 | 0.206218 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6207.92i | − | 0.177526i | ||||||
\(188\) | 18969.2 | − | 5044.62i | 0.536701 | − | 0.142729i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 22738.0 | + | 17481.4i | 0.629860 | + | 0.484249i | ||||
\(191\) | − | 57503.3i | − | 1.57625i | −0.615513 | − | 0.788127i | \(-0.711051\pi\) | ||
0.615513 | − | 0.788127i | \(-0.288949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −44941.6 | −1.20652 | −0.603259 | − | 0.797545i | \(-0.706131\pi\) | ||||
−0.603259 | + | 0.797545i | \(0.706131\pi\) | |||||||
\(194\) | 14231.6 | − | 18511.0i | 0.378139 | − | 0.491844i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 27705.5 | + | 104180.i | 0.721197 | + | 2.71190i | ||||
\(197\) | −44514.7 | −1.14702 | −0.573510 | − | 0.819198i | \(-0.694419\pi\) | ||||
−0.573510 | + | 0.819198i | \(0.694419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19066.9i | − | 0.481474i | −0.970590 | − | 0.240737i | \(-0.922611\pi\) | ||
0.970590 | − | 0.240737i | \(-0.0773892\pi\) | |||||||
\(200\) | 7938.54 | + | 3314.48i | 0.198464 | + | 0.0828619i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13406.7 | + | 17438.0i | −0.328563 | + | 0.427361i | ||||
\(203\) | − | 115637.i | − | 2.80611i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7283.44 | −0.173312 | ||||||||
\(206\) | −56868.6 | − | 43721.7i | −1.34010 | − | 1.03030i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −28044.8 | + | 16051.6i | −0.648225 | + | 0.371014i | ||||
\(209\) | 7079.72 | 0.162078 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 952.918i | − | 0.0214038i | −0.999943 | − | 0.0107019i | \(-0.996593\pi\) | ||
0.999943 | − | 0.0107019i | \(-0.00340658\pi\) | |||||||
\(212\) | 11654.8 | + | 43825.1i | 0.259318 | + | 0.975106i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −27636.9 | − | 21247.8i | −0.603478 | − | 0.463966i | ||||
\(215\) | − | 4586.61i | − | 0.0992237i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 79318.5 | 1.68444 | ||||||||
\(218\) | −29651.5 | + | 38567.6i | −0.623927 | + | 0.811539i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7489.83 | + | 1991.83i | −0.154749 | + | 0.0411535i | ||||
\(221\) | −35830.8 | −0.733621 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 43342.2i | − | 0.871568i | −0.900051 | − | 0.435784i | \(-0.856471\pi\) | ||
0.900051 | − | 0.435784i | \(-0.143529\pi\) | |||||||
\(224\) | 96991.7 | + | 13232.6i | 1.93303 | + | 0.263724i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −49914.6 | + | 64923.7i | −0.977262 | + | 1.27112i | ||||
\(227\) | − | 6007.51i | − | 0.116585i | −0.998300 | − | 0.0582925i | \(-0.981434\pi\) | ||
0.998300 | − | 0.0582925i | \(-0.0185656\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4076.35 | −0.0777321 | −0.0388660 | − | 0.999244i | \(-0.512375\pi\) | ||||
−0.0388660 | + | 0.999244i | \(0.512375\pi\) | |||||||
\(230\) | −16093.6 | − | 12373.1i | −0.304227 | − | 0.233895i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −71440.4 | − | 29827.6i | −1.32730 | − | 0.554169i | ||||
\(233\) | −37427.6 | −0.689414 | −0.344707 | − | 0.938710i | \(-0.612022\pi\) | ||||
−0.344707 | + | 0.938710i | \(0.612022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 27172.1i | − | 0.492025i | ||||||
\(236\) | 22820.5 | − | 6068.85i | 0.409734 | − | 0.108964i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 86052.8 | + | 66159.0i | 1.51919 | + | 1.16798i | ||||
\(239\) | 25648.6i | 0.449022i | 0.974472 | + | 0.224511i | \(0.0720785\pi\) | ||||
−0.974472 | + | 0.224511i | \(0.927922\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 76601.6 | 1.31888 | 0.659438 | − | 0.751759i | \(-0.270794\pi\) | ||||
0.659438 | + | 0.751759i | \(0.270794\pi\) | |||||||
\(242\) | 34529.1 | − | 44911.8i | 0.589596 | − | 0.766884i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7699.30 | + | 28951.5i | 0.129322 | + | 0.486285i | ||||
\(245\) | 149231. | 2.48615 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 40862.6i | − | 0.669780i | ||||||
\(248\) | 20459.5 | − | 49002.9i | 0.332654 | − | 0.796743i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 41008.6 | − | 53339.6i | 0.656137 | − | 0.853434i | ||||
\(251\) | 66642.6i | 1.05780i | 0.848683 | + | 0.528902i | \(0.177396\pi\) | ||||
−0.848683 | + | 0.528902i | \(0.822604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5010.92 | −0.0782846 | ||||||||
\(254\) | 25782.6 | + | 19822.2i | 0.399631 | + | 0.307244i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 33193.3 | − | 56508.2i | 0.506489 | − | 0.862246i | ||||
\(257\) | 59426.4 | 0.899732 | 0.449866 | − | 0.893096i | \(-0.351472\pi\) | ||||
0.449866 | + | 0.893096i | \(0.351472\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30461.6i | 0.454102i | ||||||||
\(260\) | 11496.4 | + | 43229.7i | 0.170065 | + | 0.639492i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −51611.9 | − | 39680.3i | −0.751878 | − | 0.578059i | ||||
\(263\) | 25140.3i | 0.363462i | 0.983348 | + | 0.181731i | \(0.0581700\pi\) | ||||
−0.983348 | + | 0.181731i | \(0.941830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 62776.7 | 0.893936 | ||||||||
\(266\) | −75450.0 | + | 98137.4i | −1.06634 | + | 1.38698i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3832.72 | − | 1019.27i | 0.0533627 | − | 0.0141912i | ||||
\(269\) | 2553.46 | 0.0352877 | 0.0176439 | − | 0.999844i | \(-0.494383\pi\) | ||||
0.0176439 | + | 0.999844i | \(0.494383\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4623.11i | 0.0629499i | 0.999505 | + | 0.0314750i | \(0.0100204\pi\) | ||||
−0.999505 | + | 0.0314750i | \(0.989980\pi\) | |||||||
\(272\) | 63069.6 | − | 36098.2i | 0.852476 | − | 0.487918i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 60128.6 | − | 78209.0i | 0.800904 | − | 1.04173i | ||||
\(275\) | − | 2939.60i | − | 0.0388708i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9854.37 | −0.128431 | −0.0642154 | − | 0.997936i | \(-0.520454\pi\) | ||||
−0.0642154 | + | 0.997936i | \(0.520454\pi\) | |||||||
\(278\) | −62534.9 | − | 48078.0i | −0.809157 | − | 0.622095i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 52210.3 | − | 125050.i | 0.665948 | − | 1.59502i | ||||
\(281\) | −48417.2 | −0.613178 | −0.306589 | − | 0.951842i | \(-0.599188\pi\) | ||||
−0.306589 | + | 0.951842i | \(0.599188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 132230.i | 1.65104i | 0.564373 | + | 0.825520i | \(0.309118\pi\) | ||||
−0.564373 | + | 0.825520i | \(0.690882\pi\) | |||||||
\(284\) | 66617.0 | − | 17716.0i | 0.825940 | − | 0.219649i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8753.71 | + | 6730.03i | 0.107019 | + | 0.0822782i | ||||
\(287\) | − | 31435.5i | − | 0.381642i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2941.65 | −0.0352205 | ||||||||
\(290\) | −65320.8 | + | 84962.5i | −0.776704 | + | 1.01026i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12380.4 | − | 46553.9i | −0.145201 | − | 0.545997i | ||||
\(293\) | −89519.1 | −1.04275 | −0.521375 | − | 0.853327i | \(-0.674581\pi\) | ||||
−0.521375 | + | 0.853327i | \(0.674581\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 32688.9i | − | 0.375627i | ||||||
\(296\) | 18819.1 | + | 7857.31i | 0.214791 | + | 0.0896789i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 72861.5 | − | 94770.6i | 0.820475 | − | 1.06719i | ||||
\(299\) | 28921.9i | 0.323508i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19795.9 | 0.218495 | ||||||||
\(302\) | −18909.4 | − | 14537.9i | −0.207331 | − | 0.159400i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 41167.5 | + | 71926.6i | 0.445459 | + | 0.778292i | ||||
\(305\) | 41471.1 | 0.445806 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 62726.9i | − | 0.665545i | −0.943007 | − | 0.332772i | \(-0.892016\pi\) | ||
0.943007 | − | 0.332772i | \(-0.107984\pi\) | |||||||
\(308\) | −8596.78 | − | 32326.2i | −0.0906221 | − | 0.340764i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −58278.0 | − | 44805.3i | −0.606431 | − | 0.466236i | ||||
\(311\) | 122783.i | 1.26945i | 0.772737 | + | 0.634726i | \(0.218887\pi\) | ||||
−0.772737 | + | 0.634726i | \(0.781113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −48589.1 | −0.495964 | −0.247982 | − | 0.968765i | \(-0.579767\pi\) | ||||
−0.247982 | + | 0.968765i | \(0.579767\pi\) | |||||||
\(314\) | −85299.2 | + | 110948.i | −0.865138 | + | 1.12528i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −111206. | + | 29573.8i | −1.11366 | + | 0.296164i | ||||
\(317\) | −110133. | −1.09598 | −0.547988 | − | 0.836486i | \(-0.684606\pi\) | ||||
−0.547988 | + | 0.836486i | \(0.684606\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 26454.0i | 0.259962i | ||||||||
\(320\) | −63788.3 | − | 64511.0i | −0.622933 | − | 0.629990i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 53402.3 | − | 69460.2i | 0.515049 | − | 0.669922i | ||||
\(323\) | 91895.4i | 0.880823i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16966.7 | −0.160632 | ||||||||
\(326\) | −46012.4 | − | 35375.3i | −0.432952 | − | 0.332862i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19420.8 | − | 8108.51i | −0.180518 | − | 0.0753691i | ||||
\(329\) | 117275. | 1.08346 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 184521.i | 1.68418i | 0.539335 | + | 0.842091i | \(0.318676\pi\) | ||||
−0.539335 | + | 0.842091i | \(0.681324\pi\) | |||||||
\(332\) | −51374.0 | + | 13662.3i | −0.466087 | + | 0.123950i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 141489. | + | 108779.i | 1.26832 | + | 0.975108i | ||||
\(335\) | − | 5490.12i | − | 0.0489207i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 65626.1 | 0.577852 | 0.288926 | − | 0.957351i | \(-0.406702\pi\) | ||||
0.288926 | + | 0.957351i | \(0.406702\pi\) | |||||||
\(338\) | −30788.2 | + | 40046.0i | −0.269495 | + | 0.350531i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −25854.1 | − | 97218.6i | −0.223652 | − | 0.840992i | ||||
\(341\) | −18145.5 | −0.156049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 414560.i | 3.52370i | ||||||||
\(344\) | 5106.19 | − | 12229.9i | 0.0431499 | − | 0.103349i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −128939. | + | 167710.i | −1.07704 | + | 1.40090i | ||||
\(347\) | 104869.i | 0.870941i | 0.900203 | + | 0.435470i | \(0.143418\pi\) | ||||
−0.900203 | + | 0.435470i | \(0.856582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 87343.9 | 0.717104 | 0.358552 | − | 0.933510i | \(-0.383271\pi\) | ||||
0.358552 | + | 0.933510i | \(0.383271\pi\) | |||||||
\(350\) | 40748.1 | + | 31327.9i | 0.332637 | + | 0.255738i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −22188.6 | − | 3027.20i | −0.179079 | − | 0.0244318i | ||||
\(353\) | −48708.6 | −0.390892 | −0.195446 | − | 0.980715i | \(-0.562615\pi\) | ||||
−0.195446 | + | 0.980715i | \(0.562615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 95424.6i | − | 0.757187i | ||||||
\(356\) | 6373.12 | + | 23964.7i | 0.0502866 | + | 0.189091i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −104142. | − | 80066.8i | −0.812572 | − | 0.624721i | ||||
\(359\) | − | 109409.i | − | 0.848911i | −0.905449 | − | 0.424456i | \(-0.860465\pi\) | ||
0.905449 | − | 0.424456i | \(-0.139535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25520.5 | 0.195828 | ||||||||
\(362\) | −55486.0 | + | 72170.4i | −0.423415 | + | 0.550734i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −186580. | + | 49618.7i | −1.40819 | + | 0.374492i | ||||
\(365\) | −66685.4 | −0.500547 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1284.97i | − | 0.00954031i | −0.999989 | − | 0.00477015i | \(-0.998482\pi\) | ||
0.999989 | − | 0.00477015i | \(-0.00151839\pi\) | |||||||
\(368\) | −29137.8 | − | 50908.6i | −0.215160 | − | 0.375920i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17207.1 | − | 22381.2i | 0.125691 | − | 0.163486i | ||||
\(371\) | 270945.i | 1.96849i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −73554.3 | −0.528677 | −0.264339 | − | 0.964430i | \(-0.585154\pi\) | ||||
−0.264339 | + | 0.964430i | \(0.585154\pi\) | |||||||
\(374\) | −19686.1 | − | 15135.1i | −0.140740 | − | 0.108203i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30250.2 | − | 72452.5i | 0.213970 | − | 0.512481i | ||||
\(377\) | 152687. | 1.07428 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 139070.i | − | 0.968176i | −0.875019 | − | 0.484088i | \(-0.839152\pi\) | ||
0.875019 | − | 0.484088i | \(-0.160848\pi\) | |||||||
\(380\) | 110871. | − | 29484.9i | 0.767807 | − | 0.204189i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −182350. | − | 140194.i | −1.24963 | − | 0.960736i | ||||
\(383\) | − | 103923.i | − | 0.708461i | −0.935158 | − | 0.354230i | \(-0.884743\pi\) | ||
0.935158 | − | 0.354230i | \(-0.115257\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −46305.2 | −0.312398 | ||||||||
\(386\) | −109569. | + | 142515.i | −0.735380 | + | 0.956505i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −24003.7 | − | 90260.7i | −0.159447 | − | 0.599563i | ||||
\(389\) | −100082. | −0.661388 | −0.330694 | − | 0.943738i | \(-0.607283\pi\) | ||||
−0.330694 | + | 0.943738i | \(0.607283\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 65042.1i | − | 0.425443i | ||||||
\(392\) | 397915. | + | 166136.i | 2.58952 | + | 1.08117i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −108528. | + | 141162.i | −0.699116 | + | 0.909337i | ||||
\(395\) | 159295.i | 1.02096i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 164388. | 1.04301 | 0.521507 | − | 0.853247i | \(-0.325370\pi\) | ||||
0.521507 | + | 0.853247i | \(0.325370\pi\) | |||||||
\(398\) | −60463.4 | − | 46485.5i | −0.381704 | − | 0.293461i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 29865.0 | − | 17093.4i | 0.186656 | − | 0.106833i | ||||
\(401\) | −156453. | −0.972961 | −0.486481 | − | 0.873691i | \(-0.661720\pi\) | ||||
−0.486481 | + | 0.873691i | \(0.661720\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 104732.i | 0.644866i | ||||||||
\(404\) | 22612.3 | + | 85028.6i | 0.138542 | + | 0.520958i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −366699. | − | 281926.i | −2.22463 | − | 1.71034i | ||||
\(407\) | − | 6968.64i | − | 0.0420687i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 270702. | 1.61825 | 0.809125 | − | 0.587637i | \(-0.199942\pi\) | ||||
0.809125 | + | 0.587637i | \(0.199942\pi\) | |||||||
\(410\) | −17757.2 | + | 23096.7i | −0.105635 | + | 0.137399i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −277294. | + | 73743.1i | −1.63360 | + | 0.434437i | ||||
\(413\) | 141086. | 0.827149 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 73589.9i | 0.427290i | ||||||||
\(416\) | −17472.3 | + | 128068.i | −0.100963 | + | 0.740036i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 17260.5 | − | 22450.7i | 0.0987874 | − | 0.128492i | ||||
\(419\) | − | 57003.2i | − | 0.324692i | −0.986734 | − | 0.162346i | \(-0.948094\pi\) | ||
0.986734 | − | 0.162346i | \(-0.0519060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 233625. | 1.31812 | 0.659059 | − | 0.752091i | \(-0.270955\pi\) | ||||
0.659059 | + | 0.752091i | \(0.270955\pi\) | |||||||
\(422\) | −3021.82 | − | 2323.24i | −0.0169685 | − | 0.0130457i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 167390. | + | 69888.0i | 0.931101 | + | 0.388750i | ||||
\(425\) | 38156.3 | 0.211246 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 178990.i | 0.981687i | ||||||||
\(428\) | −134759. | + | 35837.5i | −0.735647 | + | 0.195637i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14544.7 | − | 11182.3i | −0.0786627 | − | 0.0604774i | ||||
\(431\) | − | 333180.i | − | 1.79360i | −0.442439 | − | 0.896798i | \(-0.645887\pi\) | ||
0.442439 | − | 0.896798i | \(-0.354113\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −215343. | −1.14856 | −0.574282 | − | 0.818657i | \(-0.694719\pi\) | ||||
−0.574282 | + | 0.818657i | \(0.694719\pi\) | |||||||
\(434\) | 193380. | − | 251529.i | 1.02667 | − | 1.33539i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 50011.6 | + | 188057.i | 0.263086 | + | 0.989275i | ||||
\(437\) | 74176.2 | 0.388420 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31238.4i | 0.162091i | 0.996710 | + | 0.0810455i | \(0.0258259\pi\) | ||||
−0.996710 | + | 0.0810455i | \(0.974174\pi\) | |||||||
\(440\) | −11944.0 | + | 28607.3i | −0.0616944 | + | 0.147765i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −87356.3 | + | 113624.i | −0.447146 | + | 0.581601i | ||||
\(443\) | − | 213422.i | − | 1.08751i | −0.839245 | − | 0.543754i | \(-0.817003\pi\) | ||
0.839245 | − | 0.543754i | \(-0.182997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34327.8 | 0.173351 | ||||||||
\(446\) | −137444. | − | 105669.i | −0.690963 | − | 0.531226i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 278430. | − | 275312.i | 1.38727 | − | 1.37173i | ||||
\(449\) | −393053. | −1.94966 | −0.974828 | − | 0.222956i | \(-0.928429\pi\) | ||||
−0.974828 | + | 0.222956i | \(0.928429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7191.43i | 0.0353559i | ||||||||
\(452\) | 84188.3 | + | 316571.i | 0.412074 | + | 1.54951i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19050.6 | − | 14646.5i | −0.0924265 | − | 0.0710593i | ||||
\(455\) | 267264.i | 1.29097i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −72357.5 | −0.346458 | −0.173229 | − | 0.984882i | \(-0.555420\pi\) | ||||
−0.173229 | + | 0.984882i | \(0.555420\pi\) | |||||||
\(458\) | −9938.23 | + | 12926.6i | −0.0473782 | + | 0.0616246i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −78473.1 | + | 20869.0i | −0.370856 | + | 0.0986246i | ||||
\(461\) | 58191.8 | 0.273817 | 0.136908 | − | 0.990584i | \(-0.456283\pi\) | ||||
0.136908 | + | 0.990584i | \(0.456283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 74734.1i | 0.348623i | 0.984691 | + | 0.174312i | \(0.0557700\pi\) | ||||
−0.984691 | + | 0.174312i | \(0.944230\pi\) | |||||||
\(464\) | −268760. | + | 153826.i | −1.24833 | + | 0.714487i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −91249.4 | + | 118688.i | −0.420202 | + | 0.546555i | ||||
\(467\) | 264366.i | 1.21219i | 0.795392 | + | 0.606096i | \(0.207265\pi\) | ||||
−0.795392 | + | 0.606096i | \(0.792735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23695.5 | 0.107726 | ||||||||
\(470\) | −86166.2 | − | 66246.2i | −0.390069 | − | 0.299892i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36391.9 | − | 87162.8i | 0.163351 | − | 0.391244i | ||||
\(473\) | −4528.67 | −0.0202418 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 43514.7i | 0.192863i | ||||||||
\(476\) | 419597. | − | 111587.i | 1.85191 | − | 0.492492i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 81334.9 | + | 62531.9i | 0.355976 | + | 0.273682i | ||||
\(479\) | − | 279681.i | − | 1.21897i | −0.792799 | − | 0.609483i | \(-0.791377\pi\) | ||
0.792799 | − | 0.609483i | \(-0.208623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40221.4 | −0.173847 | ||||||||
\(482\) | 186757. | − | 242913.i | 0.803863 | − | 1.04558i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −58238.3 | − | 218992.i | −0.248610 | − | 0.934841i | ||||
\(485\) | −129293. | −0.549655 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 62506.3i | − | 0.263552i | −0.991280 | − | 0.131776i | \(-0.957932\pi\) | ||
0.991280 | − | 0.131776i | \(-0.0420679\pi\) | |||||||
\(488\) | 110580. | + | 46168.9i | 0.464340 | + | 0.193870i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 363830. | − | 473232.i | 1.51533 | − | 1.97098i | ||||
\(491\) | − | 336874.i | − | 1.39735i | −0.715440 | − | 0.698674i | \(-0.753774\pi\) | ||
0.715440 | − | 0.698674i | \(-0.246226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −343375. | −1.41278 | ||||||||
\(494\) | −129580. | − | 99624.0i | −0.530989 | − | 0.408235i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −105514. | − | 184350.i | −0.428889 | − | 0.749342i | ||||
\(497\) | 411854. | 1.66736 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 319430.i | 1.28285i | 0.767187 | + | 0.641424i | \(0.221656\pi\) | ||||
−0.767187 | + | 0.641424i | \(0.778344\pi\) | |||||||
\(500\) | −69166.9 | − | 260087.i | −0.276668 | − | 1.04035i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 211332. | + | 162476.i | 0.838607 | + | 0.644737i | ||||
\(503\) | 28287.7i | 0.111805i | 0.998436 | + | 0.0559025i | \(0.0178036\pi\) | ||||
−0.998436 | + | 0.0559025i | \(0.982196\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 121798. | 0.477592 | ||||||||
\(506\) | −12216.7 | + | 15890.3i | −0.0477149 | + | 0.0620626i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 125717. | − | 33433.0i | 0.487155 | − | 0.129553i | ||||
\(509\) | 94557.1 | 0.364971 | 0.182486 | − | 0.983209i | \(-0.441586\pi\) | ||||
0.182486 | + | 0.983209i | \(0.441586\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 287815.i | − | 1.10223i | ||||||
\(512\) | −98268.5 | − | 243028.i | −0.374865 | − | 0.927080i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 144883. | − | 188449.i | 0.548392 | − | 0.713291i | ||||
\(515\) | 397206.i | 1.49762i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26828.8 | −0.100374 | ||||||||
\(518\) | 96597.6 | + | 74266.1i | 0.360003 | + | 0.276778i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 165115. | + | 68938.4i | 0.610633 | + | 0.254950i | ||||
\(521\) | 369932. | 1.36285 | 0.681423 | − | 0.731890i | \(-0.261362\pi\) | ||||
0.681423 | + | 0.731890i | \(0.261362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 65267.4i | 0.238612i | 0.992858 | + | 0.119306i | \(0.0380670\pi\) | ||||
−0.992858 | + | 0.119306i | \(0.961933\pi\) | |||||||
\(524\) | −251662. | + | 66926.6i | −0.916549 | + | 0.243745i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 79723.1 | + | 61292.6i | 0.288146 | + | 0.221532i | ||||
\(527\) | − | 235530.i | − | 0.848058i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 227340. | 0.812391 | ||||||||
\(530\) | 153051. | − | 199073.i | 0.544859 | − | 0.708696i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 127257. | + | 478523.i | 0.449634 | + | 1.69075i | ||||
\(533\) | 41507.3 | 0.146107 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 193033.i | 0.674411i | ||||||||
\(536\) | 6112.04 | − | 14639.0i | 0.0212744 | − | 0.0509545i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6225.39 | − | 8097.33i | 0.0215081 | − | 0.0279755i | ||||
\(539\) | − | 147346.i | − | 0.507179i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 176002. | 0.601343 | 0.300671 | − | 0.953728i | \(-0.402789\pi\) | ||||
0.300671 | + | 0.953728i | \(0.402789\pi\) | |||||||
\(542\) | 14660.5 | + | 11271.2i | 0.0499055 | + | 0.0383684i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 39293.3 | − | 288010.i | 0.132776 | − | 0.973216i | ||||
\(545\) | 269380. | 0.906926 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 273097.i | 0.912730i | 0.889793 | + | 0.456365i | \(0.150849\pi\) | ||||
−0.889793 | + | 0.456365i | \(0.849151\pi\) | |||||||
\(548\) | −101416. | − | 381351.i | −0.337710 | − | 1.26988i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9321.85 | − | 7166.82i | −0.0308160 | − | 0.0236920i | ||||
\(551\) | − | 391597.i | − | 1.28984i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −687519. | −2.24820 | ||||||||
\(554\) | −24025.2 | + | 31249.5i | −0.0782794 | + | 0.101818i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −304923. | + | 81090.6i | −0.986372 | + | 0.262314i | ||||
\(557\) | −454335. | −1.46442 | −0.732211 | − | 0.681078i | \(-0.761511\pi\) | ||||
−0.732211 | + | 0.681078i | \(0.761511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26138.5i | 0.0836482i | ||||||||
\(560\) | −269258. | − | 470439.i | −0.858604 | − | 1.50013i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −118042. | + | 153537.i | −0.373736 | + | 0.486117i | ||||
\(563\) | − | 32046.7i | − | 0.101104i | −0.998721 | − | 0.0505518i | \(-0.983902\pi\) | ||
0.998721 | − | 0.0505518i | \(-0.0160980\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 453468. | 1.42053 | ||||||||
\(566\) | 419318. | + | 322380.i | 1.30891 | + | 1.00632i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 106234. | − | 254443.i | 0.329282 | − | 0.788667i | ||||
\(569\) | −277128. | −0.855964 | −0.427982 | − | 0.903787i | \(-0.640775\pi\) | ||||
−0.427982 | + | 0.903787i | \(0.640775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 642532.i | − | 1.97071i | −0.170515 | − | 0.985355i | \(-0.554543\pi\) | ||
0.170515 | − | 0.985355i | \(-0.445457\pi\) | |||||||
\(572\) | 42683.5 | − | 11351.2i | 0.130457 | − | 0.0346935i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −99685.8 | − | 76640.4i | −0.302559 | − | 0.232613i | ||||
\(575\) | − | 30799.0i | − | 0.0931540i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 451002. | 1.35465 | 0.677324 | − | 0.735685i | \(-0.263140\pi\) | ||||
0.677324 | + | 0.735685i | \(0.263140\pi\) | |||||||
\(578\) | −7171.81 | + | 9328.34i | −0.0214671 | + | 0.0279221i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 110173. | + | 414281.i | 0.327506 | + | 1.23151i | ||||
\(581\) | −317615. | −0.940913 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 61983.5i | − | 0.182364i | ||||||
\(584\) | −177812. | − | 74239.5i | −0.521357 | − | 0.217675i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −218250. | + | 283876.i | −0.635563 | + | 0.826674i | ||||
\(587\) | − | 378466.i | − | 1.09838i | −0.835699 | − | 0.549188i | \(-0.814937\pi\) | ||
0.835699 | − | 0.549188i | \(-0.185063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 268607. | 0.774259 | ||||||||
\(590\) | −103661. | − | 79696.4i | −0.297790 | − | 0.228947i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 70798.0 | − | 40521.6i | 0.202012 | − | 0.115623i | ||||
\(593\) | 137966. | 0.392339 | 0.196170 | − | 0.980570i | \(-0.437150\pi\) | ||||
0.196170 | + | 0.980570i | \(0.437150\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 601046.i | − | 1.69775i | ||||||
\(596\) | −122891. | − | 462106.i | −0.345963 | − | 1.30091i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 91715.1 | + | 70512.4i | 0.256471 | + | 0.197180i | ||||
\(599\) | 208851.i | 0.582080i | 0.956711 | + | 0.291040i | \(0.0940013\pi\) | ||||
−0.956711 | + | 0.291040i | \(0.905999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 360007. | 0.996695 | 0.498348 | − | 0.866977i | \(-0.333940\pi\) | ||||
0.498348 | + | 0.866977i | \(0.333940\pi\) | |||||||
\(602\) | 48262.9 | − | 62775.3i | 0.133174 | − | 0.173219i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −92203.3 | + | 24520.4i | −0.252739 | + | 0.0672130i | ||||
\(605\) | −313692. | −0.857023 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 322980.i | − | 0.876593i | −0.898830 | − | 0.438297i | \(-0.855582\pi\) | ||
0.898830 | − | 0.438297i | \(-0.144418\pi\) | |||||||
\(608\) | 328456. | + | 44811.4i | 0.888525 | + | 0.121222i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 101108. | − | 131510.i | 0.271721 | − | 0.353427i | ||||
\(611\) | 154850.i | 0.414791i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −392554. | −1.04467 | −0.522334 | − | 0.852741i | \(-0.674939\pi\) | ||||
−0.522334 | + | 0.852741i | \(0.674939\pi\) | |||||||
\(614\) | −198915. | − | 152930.i | −0.527632 | − | 0.405654i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −123470. | − | 51550.7i | −0.325386 | − | 0.135854i | ||||
\(617\) | 384203. | 1.00923 | 0.504616 | − | 0.863344i | \(-0.331634\pi\) | ||||
0.504616 | + | 0.863344i | \(0.331634\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 695791.i | − | 1.81592i | −0.419052 | − | 0.907962i | \(-0.637638\pi\) | ||
0.419052 | − | 0.907962i | \(-0.362362\pi\) | |||||||
\(620\) | −284166. | + | 75570.6i | −0.739247 | + | 0.196594i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 389360. | + | 299347.i | 1.00640 | + | 0.773739i | ||||
\(623\) | 148159.i | 0.381727i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −288546. | −0.738679 | ||||||||
\(626\) | −118461. | + | 154082.i | −0.302293 | + | 0.393191i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 143869. | + | 540989.i | 0.364795 | + | 1.37173i | ||||
\(629\) | 90453.5 | 0.228625 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 230753.i | − | 0.579546i | −0.957095 | − | 0.289773i | \(-0.906420\pi\) | ||
0.957095 | − | 0.289773i | \(-0.0935798\pi\) | |||||||
\(632\) | −177340. | + | 424749.i | −0.443989 | + | 1.06340i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −268508. | + | 349247.i | −0.668004 | + | 0.868869i | ||||
\(635\) | − | 180082.i | − | 0.446603i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −850449. | −2.09590 | ||||||||
\(638\) | 83889.0 | + | 64495.5i | 0.206093 | + | 0.158449i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −360090. | + | 45001.6i | −0.879126 | + | 0.109867i | ||||
\(641\) | 518941. | 1.26300 | 0.631498 | − | 0.775377i | \(-0.282440\pi\) | ||||
0.631498 | + | 0.775377i | \(0.282440\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 225212.i | 0.544716i | 0.962196 | + | 0.272358i | \(0.0878035\pi\) | ||||
−0.962196 | + | 0.272358i | \(0.912197\pi\) | |||||||
\(644\) | −90070.8 | − | 338691.i | −0.217176 | − | 0.816643i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 291412. | + | 224043.i | 0.698300 | + | 0.536867i | ||||
\(647\) | 153505.i | 0.366703i | 0.983047 | + | 0.183352i | \(0.0586947\pi\) | ||||
−0.983047 | + | 0.183352i | \(0.941305\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32276.0 | −0.0766284 | ||||||||
\(650\) | −41365.3 | + | 53803.7i | −0.0979061 | + | 0.127346i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −224359. | + | 59665.5i | −0.527774 | + | 0.140355i | ||||
\(653\) | 72240.7 | 0.169416 | 0.0847082 | − | 0.996406i | \(-0.473004\pi\) | ||||
0.0847082 | + | 0.996406i | \(0.473004\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 360490.i | 0.840254i | ||||||||
\(656\) | −73061.5 | + | 41817.1i | −0.169778 | + | 0.0971731i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 285920. | − | 371895.i | 0.660378 | − | 0.858950i | ||||
\(659\) | 234586.i | 0.540171i | 0.962836 | + | 0.270086i | \(0.0870520\pi\) | ||||
−0.962836 | + | 0.270086i | \(0.912948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 597947. | 1.36855 | 0.684274 | − | 0.729225i | \(-0.260119\pi\) | ||||
0.684274 | + | 0.729225i | \(0.260119\pi\) | |||||||
\(662\) | 585138. | + | 449866.i | 1.33519 | + | 1.02652i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −81926.2 | + | 196223.i | −0.185817 | + | 0.445054i | ||||
\(665\) | 685452. | 1.55001 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 277166.i | 0.623001i | ||||||||
\(668\) | 689905. | − | 183472.i | 1.54610 | − | 0.411166i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17409.9 | − | 13385.0i | −0.0387834 | − | 0.0298174i | ||||
\(671\) | − | 40947.2i | − | 0.0909450i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −751705. | −1.65965 | −0.829826 | − | 0.558022i | \(-0.811561\pi\) | ||||
−0.829826 | + | 0.558022i | \(0.811561\pi\) | |||||||
\(674\) | 159998. | − | 208109.i | 0.352204 | − | 0.458111i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 51928.7 | + | 195266.i | 0.113636 | + | 0.427301i | ||||
\(677\) | −84647.6 | −0.184687 | −0.0923437 | − | 0.995727i | \(-0.529436\pi\) | ||||
−0.0923437 | + | 0.995727i | \(0.529436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 558029.i | − | 1.21037i | ||||||
\(680\) | −371326. | − | 155035.i | −0.803040 | − | 0.335283i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −44239.2 | + | 57541.8i | −0.0951128 | + | 0.123713i | ||||
\(683\) | − | 635506.i | − | 1.36232i | −0.732136 | − | 0.681159i | \(-0.761476\pi\) | ||
0.732136 | − | 0.681159i | \(-0.238524\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −546260. | −1.16418 | ||||||||
\(686\) | 1.31462e6 | + | 1.01071e6i | 2.79352 | + | 2.14771i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26333.5 | − | 46009.1i | −0.0556330 | − | 0.0972002i | ||||
\(689\) | −357755. | −0.753612 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 444378.i | − | 0.930672i | −0.885134 | − | 0.465336i | \(-0.845933\pi\) | ||
0.885134 | − | 0.465336i | \(-0.154067\pi\) | |||||||
\(692\) | 217474. | + | 817762.i | 0.454145 | + | 1.70771i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 332553. | + | 255673.i | 0.690466 | + | 0.530844i | ||||
\(695\) | 436782.i | 0.904264i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −93345.3 | −0.192144 | ||||||||
\(698\) | 212947. | − | 276979.i | 0.437079 | − | 0.568506i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 198690. | − | 52839.1i | 0.405489 | − | 0.107835i | ||||
\(701\) | −374624. | −0.762359 | −0.381179 | − | 0.924501i | \(-0.624482\pi\) | ||||
−0.381179 | + | 0.924501i | \(0.624482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 103156.i | 0.208730i | ||||||||
\(704\) | −63695.9 | + | 62982.4i | −0.128519 | + | 0.127079i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −118753. | + | 154461.i | −0.238251 | + | 0.309892i | ||||
\(707\) | 525682.i | 1.05168i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 185631. | 0.369282 | 0.184641 | − | 0.982806i | \(-0.440888\pi\) | ||||
0.184641 | + | 0.982806i | \(0.440888\pi\) | |||||||
\(710\) | −302603. | − | 232647.i | −0.600284 | − | 0.461510i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 91532.8 | + | 38216.5i | 0.180558 | + | 0.0753860i | ||||
\(713\) | −190116. | −0.373972 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 61141.4i | − | 0.119598i | ||||||
\(716\) | −507804. | + | 135044.i | −0.990535 | + | 0.263421i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −346948. | − | 266741.i | −0.673001 | − | 0.517416i | ||||
\(719\) | − | 651163.i | − | 1.25960i | −0.776759 | − | 0.629799i | \(-0.783137\pi\) | ||
0.776759 | − | 0.629799i | \(-0.216863\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.71435e6 | −3.29783 | ||||||||
\(722\) | 62219.6 | − | 80928.7i | 0.119358 | − | 0.155249i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 93585.2 | + | 351906.i | 0.178538 | + | 0.671351i | ||||
\(725\) | −162597. | −0.309340 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 240082.i | − | 0.454246i | −0.973866 | − | 0.227123i | \(-0.927068\pi\) | ||
0.973866 | − | 0.227123i | \(-0.0729320\pi\) | |||||||
\(728\) | −297539. | + | 712640.i | −0.561412 | + | 1.34465i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −162581. | + | 211468.i | −0.305086 | + | 0.396825i | ||||
\(731\) | − | 58782.5i | − | 0.110005i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −55680.1 | −0.103632 | −0.0518158 | − | 0.998657i | \(-0.516501\pi\) | ||||
−0.0518158 | + | 0.998657i | \(0.516501\pi\) | |||||||
\(734\) | −4074.82 | − | 3132.80i | −0.00756338 | − | 0.00581487i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −232476. | − | 31716.8i | −0.429163 | − | 0.0585509i | ||||
\(737\) | −5420.76 | −0.00997988 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 327859.i | 0.600341i | 0.953886 | + | 0.300170i | \(0.0970435\pi\) | ||||
−0.953886 | + | 0.300170i | \(0.902957\pi\) | |||||||
\(740\) | −29022.3 | − | 109132.i | −0.0529990 | − | 0.199291i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 859201. | + | 660571.i | 1.56058 | + | 1.19981i | ||||
\(743\) | − | 12875.8i | − | 0.0233237i | −0.999932 | − | 0.0116618i | \(-0.996288\pi\) | ||
0.999932 | − | 0.0116618i | \(-0.00371217\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −661936. | −1.19262 | ||||||||
\(746\) | −179327. | + | 233250.i | −0.322232 | + | 0.419126i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −95990.4 | + | 25527.5i | −0.171563 | + | 0.0456252i | ||||
\(749\) | −833135. | −1.48509 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 531658.i | 0.942655i | 0.881958 | + | 0.471328i | \(0.156225\pi\) | ||||
−0.881958 | + | 0.471328i | \(0.843775\pi\) | |||||||
\(752\) | −156006. | − | 272568.i | −0.275870 | − | 0.481991i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 372254. | − | 484189.i | 0.654782 | − | 0.851672i | ||||
\(755\) | 132075.i | 0.231701i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 614542. | 1.07241 | 0.536204 | − | 0.844089i | \(-0.319858\pi\) | ||||
0.536204 | + | 0.844089i | \(0.319858\pi\) | |||||||
\(758\) | −441008. | − | 339055.i | −0.767552 | − | 0.590109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 176807. | − | 423472.i | 0.306106 | − | 0.733158i | ||||
\(761\) | −820697. | −1.41714 | −0.708571 | − | 0.705639i | \(-0.750660\pi\) | ||||
−0.708571 | + | 0.705639i | \(0.750660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16265e6i | 1.99710i | ||||||||
\(764\) | −889149. | + | 236458.i | −1.52331 | + | 0.405105i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −329554. | − | 253368.i | −0.561654 | − | 0.431811i | ||||
\(767\) | 186290.i | 0.316664i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −131443. | −0.222273 | −0.111136 | − | 0.993805i | \(-0.535449\pi\) | ||||
−0.111136 | + | 0.993805i | \(0.535449\pi\) | |||||||
\(770\) | −112893. | + | 146840.i | −0.190409 | + | 0.247664i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 184803. | + | 694912.i | 0.310081 | + | 1.16599i | ||||
\(773\) | −629.598 | −0.00105367 | −0.000526834 | − | 1.00000i | \(-0.500168\pi\) | ||||
−0.000526834 | 1.00000i | \(0.500168\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 111529.i | − | 0.185689i | ||||||
\(776\) | −344750. | − | 143939.i | −0.572507 | − | 0.239031i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −244002. | + | 317372.i | −0.403120 | + | 0.524336i | ||||
\(779\) | − | 106454.i | − | 0.175423i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −94219.0 | −0.154467 | ||||||||
\(782\) | −206257. | − | 158574.i | −0.337283 | − | 0.259310i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.49697e6 | − | 856796.i | 2.43545 | − | 1.39394i | ||||
\(785\) | 774931. | 1.25755 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 479245.i | − | 0.773763i | −0.922130 | − | 0.386881i | \(-0.873552\pi\) | ||
0.922130 | − | 0.386881i | \(-0.126448\pi\) | |||||||
\(788\) | 183048. | + | 688311.i | 0.294790 | + | 1.10849i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 505144. | + | 388365.i | 0.809396 | + | 0.622279i | ||||
\(791\) | 1.95717e6i | 3.12807i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −236338. | −0.375826 | ||||||||
\(794\) | 400783. | − | 521296.i | 0.635723 | − | 0.826882i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −294823. | + | 78404.5i | −0.465302 | + | 0.123741i | ||||
\(797\) | −688016. | −1.08313 | −0.541567 | − | 0.840658i | \(-0.682169\pi\) | ||||
−0.541567 | + | 0.840658i | \(0.682169\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 348240.i | − | 0.545488i | ||||||
\(800\) | 18606.3 | − | 136380.i | 0.0290724 | − | 0.213093i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −381436. | + | 496133.i | −0.593026 | + | 0.771346i | ||||
\(803\) | 65842.9i | 0.102112i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −485153. | −0.748664 | ||||||||
\(806\) | 332118. | + | 255339.i | 0.511238 | + | 0.393050i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 324766. | + | 135595.i | 0.497448 | + | 0.207693i | ||||
\(809\) | −423910. | −0.647703 | −0.323852 | − | 0.946108i | \(-0.604978\pi\) | ||||
−0.323852 | + | 0.946108i | \(0.604978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 257508.i | − | 0.391515i | −0.980652 | − | 0.195757i | \(-0.937283\pi\) | ||
0.980652 | − | 0.195757i | \(-0.0627165\pi\) | |||||||
\(812\) | −1.78804e6 | + | 475509.i | −2.71185 | + | 0.721185i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22098.4 | − | 16989.7i | −0.0333513 | − | 0.0256411i | ||||
\(815\) | 321379.i | 0.483841i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 67037.5 | 0.100432 | ||||||||
\(818\) | 659979. | − | 858432.i | 0.986333 | − | 1.28292i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29950.1 | + | 112621.i | 0.0445421 | + | 0.167491i | ||||
\(821\) | −878068. | −1.30269 | −0.651347 | − | 0.758780i | \(-0.725796\pi\) | ||||
−0.651347 | + | 0.758780i | \(0.725796\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 659598.i | − | 0.973822i | −0.873452 | − | 0.486911i | \(-0.838124\pi\) | ||
0.873452 | − | 0.486911i | \(-0.161876\pi\) | |||||||
\(824\) | −442201. | + | 1.05912e6i | −0.651277 | + | 1.55988i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 343971. | − | 447402.i | 0.504152 | − | 0.655749i | ||||
\(827\) | − | 853638.i | − | 1.24814i | −0.781369 | − | 0.624069i | \(-0.785478\pi\) | ||
0.781369 | − | 0.624069i | \(-0.214522\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 542017. | 0.788685 | 0.394343 | − | 0.918963i | \(-0.370972\pi\) | ||||
0.394343 | + | 0.918963i | \(0.370972\pi\) | |||||||
\(830\) | 233363. | + | 179414.i | 0.338747 | + | 0.260435i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 363521. | + | 367639.i | 0.525149 | + | 0.531098i | ||||
\(833\) | 1.91256e6 | 2.75630 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 988244.i | − | 1.41740i | ||||||
\(836\) | −29112.4 | − | 109471.i | −0.0416548 | − | 0.156634i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −180764. | − | 138975.i | −0.257410 | − | 0.197901i | ||||
\(839\) | 1.17490e6i | 1.66908i | 0.550947 | + | 0.834540i | \(0.314267\pi\) | ||||
−0.550947 | + | 0.834540i | \(0.685733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 755956. | 1.06882 | ||||||||
\(842\) | 569582. | − | 740853.i | 0.803401 | − | 1.04498i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14734.6 | + | 3918.48i | −0.0206848 | + | 0.00550088i | ||||
\(845\) | 279706. | 0.391732 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.35390e6i | − | 1.88721i | ||||||
\(848\) | 629724. | − | 360425.i | 0.875706 | − | 0.501214i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 93025.9 | − | 120998.i | 0.128756 | − | 0.167472i | ||||
\(851\) | − | 73012.3i | − | 0.100818i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.17515e6 | 1.61508 | 0.807541 | − | 0.589812i | \(-0.200798\pi\) | ||||
0.807541 | + | 0.589812i | \(0.200798\pi\) | |||||||
\(854\) | 567600. | + | 436382.i | 0.778263 | + | 0.598344i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −214900. | + | 514710.i | −0.293284 | + | 0.702449i | ||||
\(857\) | 895397. | 1.21914 | 0.609570 | − | 0.792732i | \(-0.291342\pi\) | ||||
0.609570 | + | 0.792732i | \(0.291342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.06038e6i | − | 1.43707i | −0.695493 | − | 0.718533i | \(-0.744814\pi\) | ||
0.695493 | − | 0.718533i | \(-0.255186\pi\) | |||||||
\(860\) | −70920.8 | + | 18860.5i | −0.0958908 | + | 0.0255010i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.05656e6 | − | 812301.i | −1.42193 | − | 1.09321i | ||||
\(863\) | 150213.i | 0.201691i | 0.994902 | + | 0.100845i | \(0.0321547\pi\) | ||||
−0.994902 | + | 0.100845i | \(0.967845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.17139e6 | 1.56556 | ||||||||
\(866\) | −525012. | + | 682881.i | −0.700057 | + | 0.910561i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −326164. | − | 1.22647e6i | −0.432909 | − | 1.62786i | ||||
\(869\) | 157282. | 0.208277 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31287.5i | 0.0412414i | ||||||||
\(872\) | 718283. | + | 299895.i | 0.944631 | + | 0.394399i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 180843. | − | 235222.i | 0.236744 | − | 0.307932i | ||||
\(875\) | − | 1.60796e6i | − | 2.10020i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.17774e6 | −1.53126 | −0.765632 | − | 0.643279i | \(-0.777574\pi\) | ||||
−0.765632 | + | 0.643279i | \(0.777574\pi\) | |||||||
\(878\) | 99060.8 | + | 76159.8i | 0.128503 | + | 0.0987955i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 61597.6 | + | 107621.i | 0.0795424 | + | 0.138974i | ||||
\(881\) | 1.15136e6 | 1.48341 | 0.741703 | − | 0.670728i | \(-0.234018\pi\) | ||||
0.741703 | + | 0.670728i | \(0.234018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 109897.i | 0.140950i | 0.997514 | + | 0.0704752i | \(0.0224516\pi\) | ||||
−0.997514 | + | 0.0704752i | \(0.977548\pi\) | |||||||
\(884\) | 147339. | + | 554036.i | 0.188544 | + | 0.708979i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −676789. | − | 520329.i | −0.862156 | − | 0.662842i | ||||
\(887\) | 988937.i | 1.25696i | 0.777826 | + | 0.628480i | \(0.216323\pi\) | ||||
−0.777826 | + | 0.628480i | \(0.783677\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 777235. | 0.983442 | ||||||||
\(890\) | 83692.1 | − | 108858.i | 0.105658 | − | 0.137429i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −670181. | + | 178227.i | −0.842292 | + | 0.223997i | ||||
\(893\) | 397145. | 0.498019 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 727395.i | 0.908081i | ||||||||
\(896\) | −194228. | − | 1.55415e6i | −0.241933 | − | 1.93588i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −958272. | + | 1.24642e6i | −1.18833 | + | 1.54565i | ||||
\(899\) | 1.00367e6i | 1.24186i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 804551. | 0.991070 | ||||||||
\(902\) | 22804.9 | + | 17532.9i | 0.0280295 | + | 0.0215496i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.20914e6 | + | 504836.i | 1.47958 | + | 0.617751i | ||||
\(905\) | 504082. | 0.615467 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 514619.i | − | 0.625563i | −0.949825 | − | 0.312781i | \(-0.898739\pi\) | ||
0.949825 | − | 0.312781i | \(-0.101261\pi\) | |||||||
\(908\) | −92891.5 | + | 24703.4i | −0.112669 | + | 0.0299630i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 847527. | + | 651595.i | 1.02346 | + | 0.786856i | ||||
\(911\) | 1.14551e6i | 1.38026i | 0.723684 | + | 0.690131i | \(0.242447\pi\) | ||||
−0.723684 | + | 0.690131i | \(0.757553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 72660.2 | 0.0871676 | ||||||||
\(914\) | −176409. | + | 229455.i | −0.211168 | + | 0.274666i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16762.3 | + | 63030.8i | 0.0199775 | + | 0.0751211i | ||||
\(917\) | −1.55588e6 | −1.85028 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 329486.i | 0.390127i | 0.980791 | + | 0.195063i | \(0.0624913\pi\) | ||||
−0.980791 | + | 0.195063i | \(0.937509\pi\) | |||||||
\(920\) | −125141. | + | 299727.i | −0.147851 | + | 0.354120i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 141873. | − | 184533.i | 0.166893 | − | 0.217077i | ||||
\(923\) | 543811.i | 0.638329i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42831.9 | 0.0500592 | ||||||||
\(926\) | 236991. | + | 182203.i | 0.276382 | + | 0.212488i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −167442. | + | 1.22731e6i | −0.194432 | + | 1.42514i | ||||
\(929\) | −907069. | −1.05101 | −0.525507 | − | 0.850789i | \(-0.676124\pi\) | ||||
−0.525507 | + | 0.850789i | \(0.676124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.18115e6i | 2.51644i | ||||||||
\(932\) | 153905. | + | 578727.i | 0.177183 | + | 0.666257i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 838337. | + | 644530.i | 0.961003 | + | 0.738838i | ||||
\(935\) | 137500.i | 0.157282i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.29741e6 | 1.47774 | 0.738872 | − | 0.673846i | \(-0.235359\pi\) | ||||
0.738872 | + | 0.673846i | \(0.235359\pi\) | |||||||
\(938\) | 57770.1 | − | 75141.3i | 0.0656595 | − | 0.0854030i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −420150. | + | 111734.i | −0.475498 | + | 0.126453i | ||||
\(941\) | 109957. | 0.124178 | 0.0620888 | − | 0.998071i | \(-0.480224\pi\) | ||||
0.0620888 | + | 0.998071i | \(0.480224\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 75346.6i | 0.0847306i | ||||||||
\(944\) | −187680. | − | 327908.i | −0.210608 | − | 0.367967i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11041.0 | + | 14361.0i | −0.0123375 | + | 0.0160473i | ||||
\(947\) | − | 550631.i | − | 0.613989i | −0.951711 | − | 0.306995i | \(-0.900677\pi\) | ||
0.951711 | − | 0.306995i | \(-0.0993234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 380031. | 0.421975 | ||||||||
\(950\) | 137991. | + | 106090.i | 0.152898 | + | 0.117551i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 669132. | − | 1.60265e6i | 0.738309 | − | 1.76833i | ||||
\(953\) | −802951. | −0.884104 | −0.442052 | − | 0.896989i | \(-0.645749\pi\) | ||||
−0.442052 | + | 0.896989i | \(0.645749\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.27365e6i | 1.39650i | ||||||||
\(956\) | 396593. | − | 105469.i | 0.433939 | − | 0.115401i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −886904. | − | 681869.i | −0.966374 | − | 0.742967i | ||||
\(959\) | − | 2.35767e6i | − | 2.56357i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 235074. | 0.254541 | ||||||||
\(962\) | −98060.8 | + | 127547.i | −0.105961 | + | 0.137823i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −314992. | − | 1.18446e6i | −0.338958 | − | 1.27458i | ||||
\(965\) | 995416. | 1.06893 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 954387.i | 1.02064i | 0.859985 | + | 0.510319i | \(0.170473\pi\) | ||||
−0.859985 | + | 0.510319i | \(0.829527\pi\) | |||||||
\(968\) | −836438. | − | 349227.i | −0.892654 | − | 0.372698i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −315218. | + | 410003.i | −0.335018 | + | 0.435756i | ||||
\(971\) | − | 708749.i | − | 0.751716i | −0.926677 | − | 0.375858i | \(-0.877348\pi\) | ||
0.926677 | − | 0.375858i | \(-0.122652\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.88516e6 | −1.99123 | ||||||||
\(974\) | −198215. | − | 152392.i | −0.208939 | − | 0.160636i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 416004. | − | 238102.i | 0.436715 | − | 0.249956i | ||||
\(977\) | −623105. | −0.652788 | −0.326394 | − | 0.945234i | \(-0.605834\pi\) | ||||
−0.326394 | + | 0.945234i | \(0.605834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 33894.1i | − | 0.0353638i | ||||||
\(980\) | −613652. | − | 2.30750e6i | −0.638954 | − | 2.40264i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.06827e6 | − | 821307.i | −1.10779 | − | 0.851692i | ||||
\(983\) | − | 1.73566e6i | − | 1.79621i | −0.439781 | − | 0.898105i | \(-0.644944\pi\) | ||
0.439781 | − | 0.898105i | \(-0.355056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 985961. | 1.01622 | ||||||||
\(986\) | −837157. | + | 1.08889e6i | −0.861099 | + | 1.12003i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −631841. | + | 168030.i | −0.647282 | + | 0.172137i | ||||
\(989\) | −47448.1 | −0.0485095 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 106256.i | − | 0.108195i | −0.998536 | − | 0.0540974i | \(-0.982772\pi\) | ||
0.998536 | − | 0.0540974i | \(-0.0172282\pi\) | |||||||
\(992\) | −841842. | − | 114853.i | −0.855475 | − | 0.116713i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.00411e6 | − | 1.30604e6i | 1.01627 | − | 1.32186i | ||||
\(995\) | 422314.i | 0.426569i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.53009e6 | −1.53931 | −0.769656 | − | 0.638459i | \(-0.779572\pi\) | ||||
−0.769656 | + | 0.638459i | \(0.779572\pi\) | |||||||
\(998\) | 1.01295e6 | + | 778779.i | 1.01702 | + | 0.781903i | ||||
\(999\) | 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 | 324.5.d.f.163.15 | 22 | ||
3.2 | odd | 2 | 324.5.d.e.163.8 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.f.163.16 | 22 | ||
9.2 | odd | 6 | 108.5.f.a.91.22 | 44 | |||
9.4 | even | 3 | 36.5.f.a.7.15 | yes | 44 | ||
9.5 | odd | 6 | 108.5.f.a.19.8 | 44 | |||
9.7 | even | 3 | 36.5.f.a.31.1 | yes | 44 | ||
12.11 | even | 2 | 324.5.d.e.163.7 | 22 | |||
36.7 | odd | 6 | 36.5.f.a.31.15 | yes | 44 | ||
36.11 | even | 6 | 108.5.f.a.91.8 | 44 | |||
36.23 | even | 6 | 108.5.f.a.19.22 | 44 | |||
36.31 | odd | 6 | 36.5.f.a.7.1 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.1 | ✓ | 44 | 36.31 | odd | 6 | ||
36.5.f.a.7.15 | yes | 44 | 9.4 | even | 3 | ||
36.5.f.a.31.1 | yes | 44 | 9.7 | even | 3 | ||
36.5.f.a.31.15 | yes | 44 | 36.7 | odd | 6 | ||
108.5.f.a.19.8 | 44 | 9.5 | odd | 6 | |||
108.5.f.a.19.22 | 44 | 36.23 | even | 6 | |||
108.5.f.a.91.8 | 44 | 36.11 | even | 6 | |||
108.5.f.a.91.22 | 44 | 9.2 | odd | 6 | |||
324.5.d.e.163.7 | 22 | 12.11 | even | 2 | |||
324.5.d.e.163.8 | 22 | 3.2 | odd | 2 | |||
324.5.d.f.163.15 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.f.163.16 | 22 | 4.3 | odd | 2 | inner |