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 | 163.19 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.f.163.20 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.76125 | − | 1.36126i | 0.940312 | − | 0.340314i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.2940 | − | 10.2400i | 0.768373 | − | 0.640003i | ||||
\(5\) | −28.6092 | −1.14437 | −0.572185 | − | 0.820125i | \(-0.693904\pi\) | ||||
−0.572185 | + | 0.820125i | \(0.693904\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 25.6487i | 0.523442i | 0.965144 | + | 0.261721i | \(0.0842900\pi\) | ||||
−0.965144 | + | 0.261721i | \(0.915710\pi\) | |||||||
\(8\) | 32.3013 | − | 55.2506i | 0.504708 | − | 0.863290i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −107.606 | + | 38.9445i | −1.07606 | + | 0.389445i | ||||
\(11\) | 108.505i | 0.896732i | 0.893850 | + | 0.448366i | \(0.147994\pi\) | ||||
−0.893850 | + | 0.448366i | \(0.852006\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −88.4493 | −0.523368 | −0.261684 | − | 0.965154i | \(-0.584278\pi\) | ||||
−0.261684 | + | 0.965154i | \(0.584278\pi\) | |||||||
\(14\) | 34.9144 | + | 96.4710i | 0.178135 | + | 0.492199i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 46.2831 | − | 251.781i | 0.180793 | − | 0.983521i | ||||
\(17\) | 504.169 | 1.74453 | 0.872265 | − | 0.489034i | \(-0.162651\pi\) | ||||
0.872265 | + | 0.489034i | \(0.162651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 191.405i | 0.530207i | 0.964220 | + | 0.265104i | \(0.0854062\pi\) | ||||
−0.964220 | + | 0.265104i | \(0.914594\pi\) | |||||||
\(20\) | −351.721 | + | 292.960i | −0.879302 | + | 0.732400i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 147.703 | + | 408.113i | 0.305170 | + | 0.843208i | ||||
\(23\) | 960.592i | 1.81586i | 0.419118 | + | 0.907932i | \(0.362339\pi\) | ||||
−0.419118 | + | 0.907932i | \(0.637661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 193.489 | 0.309582 | ||||||||
\(26\) | −332.680 | + | 120.402i | −0.492129 | + | 0.178110i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 262.643 | + | 315.324i | 0.335004 | + | 0.402199i | ||||
\(29\) | 793.341 | 0.943331 | 0.471665 | − | 0.881778i | \(-0.343653\pi\) | ||||
0.471665 | + | 0.881778i | \(0.343653\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 329.584i | 0.342959i | 0.985188 | + | 0.171480i | \(0.0548547\pi\) | ||||
−0.985188 | + | 0.171480i | \(0.945145\pi\) | |||||||
\(32\) | −168.657 | − | 1010.02i | −0.164704 | − | 0.986343i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1896.30 | − | 686.303i | 1.64040 | − | 0.593688i | ||||
\(35\) | − | 733.789i | − | 0.599011i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 209.943 | 0.153355 | 0.0766775 | − | 0.997056i | \(-0.475569\pi\) | ||||
0.0766775 | + | 0.997056i | \(0.475569\pi\) | |||||||
\(38\) | 260.551 | + | 719.921i | 0.180437 | + | 0.498560i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −924.116 | + | 1580.68i | −0.577573 | + | 0.987923i | ||||
\(41\) | 1056.40 | 0.628435 | 0.314218 | − | 0.949351i | \(-0.398258\pi\) | ||||
0.314218 | + | 0.949351i | \(0.398258\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3334.14i | 1.80322i | 0.432555 | + | 0.901608i | \(0.357612\pi\) | ||||
−0.432555 | + | 0.901608i | \(0.642388\pi\) | |||||||
\(44\) | 1111.09 | + | 1333.95i | 0.573911 | + | 0.689024i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1307.61 | + | 3613.02i | 0.617964 | + | 1.70748i | ||||
\(47\) | − | 1128.36i | − | 0.510799i | −0.966836 | − | 0.255400i | \(-0.917793\pi\) | ||
0.966836 | − | 0.255400i | \(-0.0822071\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1743.15 | 0.726008 | ||||||||
\(50\) | 727.758 | − | 263.387i | 0.291103 | − | 0.105355i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1087.39 | + | 905.724i | −0.402142 | + | 0.334957i | ||||
\(53\) | 1138.62 | 0.405346 | 0.202673 | − | 0.979247i | \(-0.435037\pi\) | ||||
0.202673 | + | 0.979247i | \(0.435037\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3104.23i | − | 1.02619i | ||||||
\(56\) | 1417.10 | + | 828.486i | 0.451882 | + | 0.264185i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2983.95 | − | 1079.94i | 0.887025 | − | 0.321029i | ||||
\(59\) | 4662.09i | 1.33930i | 0.742678 | + | 0.669648i | \(0.233555\pi\) | ||||
−0.742678 | + | 0.669648i | \(0.766445\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5599.68 | −1.50488 | −0.752442 | − | 0.658658i | \(-0.771124\pi\) | ||||
−0.752442 | + | 0.658658i | \(0.771124\pi\) | |||||||
\(62\) | 448.648 | + | 1239.65i | 0.116714 | + | 0.322488i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2009.25 | − | 3569.33i | −0.490540 | − | 0.871419i | ||||
\(65\) | 2530.47 | 0.598927 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7075.70i | − | 1.57623i | −0.615527 | − | 0.788116i | \(-0.711057\pi\) | ||
0.615527 | − | 0.788116i | \(-0.288943\pi\) | |||||||
\(68\) | 6198.24 | − | 5162.71i | 1.34045 | − | 1.11650i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −998.874 | − | 2759.96i | −0.203852 | − | 0.563257i | ||||
\(71\) | 4433.42i | 0.879472i | 0.898127 | + | 0.439736i | \(0.144928\pi\) | ||||
−0.898127 | + | 0.439736i | \(0.855072\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1953.21 | −0.366524 | −0.183262 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183262 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(74\) | 789.648 | − | 285.786i | 0.144202 | − | 0.0521889i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1959.99 | + | 2353.12i | 0.339334 | + | 0.407397i | ||||
\(77\) | −2783.00 | −0.469387 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1759.65i | − | 0.281950i | −0.990013 | − | 0.140975i | \(-0.954976\pi\) | ||
0.990013 | − | 0.140975i | \(-0.0450238\pi\) | |||||||
\(80\) | −1324.12 | + | 7203.27i | −0.206894 | + | 1.12551i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3973.38 | − | 1438.03i | 0.590925 | − | 0.213865i | ||||
\(83\) | 3027.21i | 0.439427i | 0.975564 | + | 0.219714i | \(0.0705123\pi\) | ||||
−0.975564 | + | 0.219714i | \(0.929488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14423.9 | −1.99639 | ||||||||
\(86\) | 4538.62 | + | 12540.5i | 0.613659 | + | 1.69558i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5994.94 | + | 3504.84i | 0.774140 | + | 0.452588i | ||||
\(89\) | −559.336 | −0.0706144 | −0.0353072 | − | 0.999377i | \(-0.511241\pi\) | ||||
−0.0353072 | + | 0.999377i | \(0.511241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2268.61i | − | 0.273953i | ||||||
\(92\) | 9836.50 | + | 11809.5i | 1.16216 | + | 1.39526i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1535.98 | − | 4244.03i | −0.173832 | − | 0.480311i | ||||
\(95\) | − | 5475.95i | − | 0.606753i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2201.78 | −0.234007 | −0.117004 | − | 0.993131i | \(-0.537329\pi\) | ||||
−0.117004 | + | 0.993131i | \(0.537329\pi\) | |||||||
\(98\) | 6556.40 | − | 2372.87i | 0.682674 | − | 0.247071i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2378.74 | − | 1981.33i | 0.237874 | − | 0.198133i | ||||
\(101\) | −731.682 | −0.0717265 | −0.0358632 | − | 0.999357i | \(-0.511418\pi\) | ||||
−0.0358632 | + | 0.999357i | \(0.511418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9853.96i | 0.928831i | 0.885618 | + | 0.464415i | \(0.153735\pi\) | ||||
−0.885618 | + | 0.464415i | \(0.846265\pi\) | |||||||
\(104\) | −2857.03 | + | 4886.87i | −0.264148 | + | 0.451819i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4282.61 | − | 1549.95i | 0.381151 | − | 0.137945i | ||||
\(107\) | 804.642i | 0.0702806i | 0.999382 | + | 0.0351403i | \(0.0111878\pi\) | ||||
−0.999382 | + | 0.0351403i | \(0.988812\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17324.9 | −1.45820 | −0.729102 | − | 0.684405i | \(-0.760062\pi\) | ||||
−0.729102 | + | 0.684405i | \(0.760062\pi\) | |||||||
\(110\) | −4225.66 | − | 11675.8i | −0.349228 | − | 0.964941i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6457.86 | + | 1187.10i | 0.514816 | + | 0.0946348i | ||||
\(113\) | 17147.9 | 1.34293 | 0.671465 | − | 0.741036i | \(-0.265665\pi\) | ||||
0.671465 | + | 0.741036i | \(0.265665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 27481.8i | − | 2.07802i | ||||||
\(116\) | 9753.31 | − | 8123.85i | 0.724829 | − | 0.603734i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6346.30 | + | 17535.3i | 0.455782 | + | 1.25936i | ||||
\(119\) | 12931.3i | 0.913160i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2867.76 | 0.195872 | ||||||||
\(122\) | −21061.8 | + | 7622.59i | −1.41506 | + | 0.512133i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3374.95 | + | 4051.89i | 0.219495 | + | 0.263520i | ||||
\(125\) | 12345.2 | 0.790094 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9591.51i | 0.594675i | 0.954772 | + | 0.297337i | \(0.0960986\pi\) | ||||
−0.954772 | + | 0.297337i | \(0.903901\pi\) | |||||||
\(128\) | −12416.1 | − | 10690.0i | −0.757816 | − | 0.652468i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9517.71 | − | 3444.61i | 0.563178 | − | 0.203823i | ||||
\(131\) | − | 4541.75i | − | 0.264655i | −0.991206 | − | 0.132328i | \(-0.957755\pi\) | ||
0.991206 | − | 0.132328i | \(-0.0422451\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4909.28 | −0.277533 | ||||||||
\(134\) | −9631.84 | − | 26613.5i | −0.536414 | − | 1.48215i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16285.3 | − | 27855.6i | 0.880478 | − | 1.50604i | ||||
\(137\) | −4901.64 | −0.261156 | −0.130578 | − | 0.991438i | \(-0.541683\pi\) | ||||
−0.130578 | + | 0.991438i | \(0.541683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8650.79i | − | 0.447740i | −0.974619 | − | 0.223870i | \(-0.928131\pi\) | ||
0.974619 | − | 0.223870i | \(-0.0718691\pi\) | |||||||
\(140\) | −7514.03 | − | 9021.17i | −0.383369 | − | 0.460264i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6035.02 | + | 16675.2i | 0.299297 | + | 0.826978i | ||||
\(143\) | − | 9597.15i | − | 0.469321i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22696.9 | −1.07952 | ||||||||
\(146\) | −7346.49 | + | 2658.81i | −0.344647 | + | 0.124733i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2581.03 | − | 2149.83i | 0.117834 | − | 0.0981476i | ||||
\(149\) | −12692.9 | −0.571727 | −0.285863 | − | 0.958270i | \(-0.592280\pi\) | ||||
−0.285863 | + | 0.958270i | \(0.592280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12765.6i | − | 0.559869i | −0.960019 | − | 0.279934i | \(-0.909687\pi\) | ||
0.960019 | − | 0.279934i | \(-0.0903127\pi\) | |||||||
\(152\) | 10575.2 | + | 6182.63i | 0.457723 | + | 0.267600i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10467.5 | + | 3788.37i | −0.441370 | + | 0.159739i | ||||
\(155\) | − | 9429.14i | − | 0.392472i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −40566.0 | −1.64575 | −0.822873 | − | 0.568225i | \(-0.807630\pi\) | ||||
−0.822873 | + | 0.568225i | \(0.807630\pi\) | |||||||
\(158\) | −2395.34 | − | 6618.49i | −0.0959517 | − | 0.265121i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4825.15 | + | 28895.8i | 0.188482 | + | 1.12874i | ||||
\(161\) | −24637.9 | −0.950499 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6872.98i | − | 0.258684i | −0.991600 | − | 0.129342i | \(-0.958713\pi\) | ||
0.991600 | − | 0.129342i | \(-0.0412865\pi\) | |||||||
\(164\) | 12987.3 | − | 10817.6i | 0.482873 | − | 0.402200i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4120.81 | + | 11386.1i | 0.149543 | + | 0.413199i | ||||
\(167\) | − | 35109.3i | − | 1.25889i | −0.777043 | − | 0.629447i | \(-0.783281\pi\) | ||
0.777043 | − | 0.629447i | \(-0.216719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20737.7 | −0.726086 | ||||||||
\(170\) | −54251.8 | + | 19634.6i | −1.87723 | + | 0.679398i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 34141.8 | + | 40989.9i | 1.15406 | + | 1.38554i | ||||
\(173\) | 2983.45 | 0.0996841 | 0.0498420 | − | 0.998757i | \(-0.484128\pi\) | ||||
0.0498420 | + | 0.998757i | \(0.484128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4962.72i | 0.162048i | ||||||||
\(176\) | 27319.4 | + | 5021.92i | 0.881955 | + | 0.162123i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2103.80 | + | 761.400i | −0.0663995 | + | 0.0240311i | ||||
\(179\) | 45199.3i | 1.41067i | 0.708874 | + | 0.705335i | \(0.249203\pi\) | ||||
−0.708874 | + | 0.705335i | \(0.750797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 27600.9 | 0.842492 | 0.421246 | − | 0.906946i | \(-0.361593\pi\) | ||||
0.421246 | + | 0.906946i | \(0.361593\pi\) | |||||||
\(182\) | −3088.15 | − | 8532.78i | −0.0932301 | − | 0.257601i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 53073.2 | + | 31028.4i | 1.56762 | + | 0.916481i | ||||
\(185\) | −6006.31 | −0.175495 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 54704.7i | 1.56438i | ||||||||
\(188\) | −11554.4 | − | 13872.0i | −0.326913 | − | 0.392484i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7454.16 | − | 20596.4i | −0.206487 | − | 0.570537i | ||||
\(191\) | − | 18822.7i | − | 0.515958i | −0.966151 | − | 0.257979i | \(-0.916943\pi\) | ||
0.966151 | − | 0.257979i | \(-0.0830565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9454.22 | 0.253811 | 0.126906 | − | 0.991915i | \(-0.459495\pi\) | ||||
0.126906 | + | 0.991915i | \(0.459495\pi\) | |||||||
\(194\) | −8281.43 | + | 2997.18i | −0.220040 | + | 0.0796360i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 21430.2 | − | 17849.9i | 0.557845 | − | 0.464647i | ||||
\(197\) | −21650.0 | −0.557860 | −0.278930 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278930 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 25261.4i | − | 0.637898i | −0.947772 | − | 0.318949i | \(-0.896670\pi\) | ||
0.947772 | − | 0.318949i | \(-0.103330\pi\) | |||||||
\(200\) | 6249.93 | − | 10690.4i | 0.156248 | − | 0.267259i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2752.04 | + | 996.006i | −0.0674453 | + | 0.0244095i | ||||
\(203\) | 20348.1i | 0.493779i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30222.8 | −0.719162 | ||||||||
\(206\) | 13413.8 | + | 37063.2i | 0.316094 | + | 0.873390i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4093.70 | + | 22269.9i | −0.0946214 | + | 0.514744i | ||||
\(209\) | −20768.3 | −0.475454 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 21562.9i | − | 0.484331i | −0.970235 | − | 0.242166i | \(-0.922142\pi\) | ||
0.970235 | − | 0.242166i | \(-0.0778577\pi\) | |||||||
\(212\) | 13998.1 | − | 11659.5i | 0.311456 | − | 0.259422i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1095.32 | + | 3026.46i | 0.0239175 | + | 0.0660856i | ||||
\(215\) | − | 95387.3i | − | 2.06354i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8453.38 | −0.179519 | ||||||||
\(218\) | −65163.3 | + | 23583.7i | −1.37117 | + | 0.496247i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −31787.5 | − | 38163.3i | −0.656766 | − | 0.788499i | ||||
\(221\) | −44593.4 | −0.913032 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19294.4i | 0.387992i | 0.981002 | + | 0.193996i | \(0.0621448\pi\) | ||||
−0.981002 | + | 0.193996i | \(0.937855\pi\) | |||||||
\(224\) | 25905.5 | − | 4325.83i | 0.516293 | − | 0.0862130i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 64497.4 | − | 23342.7i | 1.26277 | − | 0.457018i | ||||
\(227\) | − | 64830.0i | − | 1.25813i | −0.777354 | − | 0.629063i | \(-0.783439\pi\) | ||
0.777354 | − | 0.629063i | \(-0.216561\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 39150.9 | 0.746570 | 0.373285 | − | 0.927717i | \(-0.378231\pi\) | ||||
0.373285 | + | 0.927717i | \(0.378231\pi\) | |||||||
\(230\) | −37409.8 | − | 103366.i | −0.707179 | − | 1.95399i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 25626.0 | − | 43832.5i | 0.476107 | − | 0.814368i | ||||
\(233\) | −2307.53 | −0.0425045 | −0.0212522 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212522 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32281.4i | 0.584543i | ||||||||
\(236\) | 47740.0 | + | 57315.6i | 0.857154 | + | 1.02908i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17602.8 | + | 48637.7i | 0.310761 | + | 0.858655i | ||||
\(239\) | 76209.8i | 1.33418i | 0.744976 | + | 0.667091i | \(0.232461\pi\) | ||||
−0.744976 | + | 0.667091i | \(0.767539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16314.2 | 0.280888 | 0.140444 | − | 0.990089i | \(-0.455147\pi\) | ||||
0.140444 | + | 0.990089i | \(0.455147\pi\) | |||||||
\(242\) | 10786.3 | − | 3903.75i | 0.184180 | − | 0.0666579i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −68842.2 | + | 57340.9i | −1.15631 | + | 0.963130i | ||||
\(245\) | −49870.1 | −0.830822 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 16929.6i | − | 0.277494i | ||||||
\(248\) | 18209.7 | + | 10646.0i | 0.296073 | + | 0.173094i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 46433.4 | − | 16805.0i | 0.742934 | − | 0.268880i | ||||
\(251\) | − | 33833.6i | − | 0.537033i | −0.963275 | − | 0.268517i | \(-0.913467\pi\) | ||
0.963275 | − | 0.268517i | \(-0.0865334\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −104229. | −1.62834 | ||||||||
\(254\) | 13056.5 | + | 36076.0i | 0.202376 | + | 0.559180i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −61251.8 | − | 23306.4i | −0.934628 | − | 0.355628i | ||||
\(257\) | −57546.1 | −0.871264 | −0.435632 | − | 0.900125i | \(-0.643475\pi\) | ||||
−0.435632 | + | 0.900125i | \(0.643475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5384.76i | 0.0802725i | ||||||||
\(260\) | 31109.5 | − | 25912.1i | 0.460199 | − | 0.383315i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6182.49 | − | 17082.6i | −0.0900659 | − | 0.248859i | ||||
\(263\) | 78541.9i | 1.13551i | 0.823199 | + | 0.567753i | \(0.192187\pi\) | ||||
−0.823199 | + | 0.567753i | \(0.807813\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32574.9 | −0.463865 | ||||||||
\(266\) | −18465.0 | + | 6682.78i | −0.260967 | + | 0.0944483i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −72455.5 | − | 86988.4i | −1.00879 | − | 1.21113i | ||||
\(269\) | −5376.96 | −0.0743074 | −0.0371537 | − | 0.999310i | \(-0.511829\pi\) | ||||
−0.0371537 | + | 0.999310i | \(0.511829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 108113.i | − | 1.47211i | −0.676924 | − | 0.736053i | \(-0.736688\pi\) | ||
0.676924 | − | 0.736053i | \(-0.263312\pi\) | |||||||
\(272\) | 23334.5 | − | 126940.i | 0.315399 | − | 1.71578i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18436.3 | + | 6672.39i | −0.245568 | + | 0.0888752i | ||||
\(275\) | 20994.4i | 0.277612i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −43942.3 | −0.572695 | −0.286347 | − | 0.958126i | \(-0.592441\pi\) | ||||
−0.286347 | + | 0.958126i | \(0.592441\pi\) | |||||||
\(278\) | −11775.9 | − | 32537.8i | −0.152372 | − | 0.421015i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −40542.2 | − | 23702.3i | −0.517120 | − | 0.302326i | ||||
\(281\) | 50871.3 | 0.644259 | 0.322130 | − | 0.946696i | \(-0.395601\pi\) | ||||
0.322130 | + | 0.946696i | \(0.395601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 26395.1i | − | 0.329572i | −0.986329 | − | 0.164786i | \(-0.947307\pi\) | ||
0.986329 | − | 0.164786i | \(-0.0526933\pi\) | |||||||
\(284\) | 45398.4 | + | 54504.3i | 0.562864 | + | 0.675762i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13064.2 | − | 36097.2i | −0.159717 | − | 0.441308i | ||||
\(287\) | 27095.2i | 0.328950i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 170665. | 2.04338 | ||||||||
\(290\) | −85368.6 | + | 30896.3i | −1.01508 | + | 0.367375i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −24012.7 | + | 20000.9i | −0.281627 | + | 0.234576i | ||||
\(293\) | 130791. | 1.52350 | 0.761748 | − | 0.647873i | \(-0.224341\pi\) | ||||
0.761748 | + | 0.647873i | \(0.224341\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 133379.i | − | 1.53265i | ||||||
\(296\) | 6781.44 | − | 11599.5i | 0.0773995 | − | 0.132390i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −47741.2 | + | 17278.3i | −0.537602 | + | 0.194567i | ||||
\(299\) | − | 84963.6i | − | 0.950365i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −85516.3 | −0.943879 | ||||||||
\(302\) | −17377.2 | − | 48014.4i | −0.190531 | − | 0.526451i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 48192.2 | + | 8858.80i | 0.521470 | + | 0.0958579i | ||||
\(305\) | 160202. | 1.72214 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 54227.3i | 0.575362i | 0.957726 | + | 0.287681i | \(0.0928843\pi\) | ||||
−0.957726 | + | 0.287681i | \(0.907116\pi\) | |||||||
\(308\) | −34214.1 | + | 28498.0i | −0.360664 | + | 0.300409i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12835.5 | − | 35465.3i | −0.133564 | − | 0.369046i | ||||
\(311\) | − | 135960.i | − | 1.40569i | −0.711341 | − | 0.702847i | \(-0.751912\pi\) | ||
0.711341 | − | 0.702847i | \(-0.248088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 164388. | 1.67796 | 0.838981 | − | 0.544160i | \(-0.183152\pi\) | ||||
0.838981 | + | 0.544160i | \(0.183152\pi\) | |||||||
\(314\) | −152579. | + | 55220.7i | −1.54751 | + | 0.560070i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18018.9 | − | 21633.1i | −0.180449 | − | 0.216643i | ||||
\(317\) | 120619. | 1.20032 | 0.600160 | − | 0.799880i | \(-0.295104\pi\) | ||||
0.600160 | + | 0.799880i | \(0.295104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 86081.1i | 0.845915i | ||||||||
\(320\) | 57483.1 | + | 102116.i | 0.561359 | + | 0.997225i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −92669.2 | + | 33538.5i | −0.893766 | + | 0.323468i | ||||
\(323\) | 96500.4i | 0.924962i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17113.9 | −0.162025 | ||||||||
\(326\) | −9355.88 | − | 25851.0i | −0.0880338 | − | 0.243244i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 34123.1 | − | 58366.7i | 0.317176 | − | 0.542522i | ||||
\(329\) | 28940.8 | 0.267374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 115682.i | 1.05587i | 0.849284 | + | 0.527936i | \(0.177034\pi\) | ||||
−0.849284 | + | 0.527936i | \(0.822966\pi\) | |||||||
\(332\) | 30998.8 | + | 37216.5i | 0.281235 | + | 0.337644i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −47792.7 | − | 132055.i | −0.428419 | − | 1.18375i | ||||
\(335\) | 202430.i | 1.80379i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 187736. | 1.65306 | 0.826528 | − | 0.562895i | \(-0.190313\pi\) | ||||
0.826528 | + | 0.562895i | \(0.190313\pi\) | |||||||
\(338\) | −77999.7 | + | 28229.4i | −0.682747 | + | 0.247097i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −177327. | + | 147701.i | −1.53397 | + | 1.27769i | ||||
\(341\) | −35761.3 | −0.307542 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 106292.i | 0.903465i | ||||||||
\(344\) | 184213. | + | 107697.i | 1.55670 | + | 0.910097i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11221.5 | − | 4061.23i | 0.0937341 | − | 0.0339239i | ||||
\(347\) | 135244.i | 1.12320i | 0.827408 | + | 0.561601i | \(0.189814\pi\) | ||||
−0.827408 | + | 0.561601i | \(0.810186\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3302.89 | 0.0271171 | 0.0135585 | − | 0.999908i | \(-0.495684\pi\) | ||||
0.0135585 | + | 0.999908i | \(0.495684\pi\) | |||||||
\(350\) | 6755.54 | + | 18666.0i | 0.0551472 | + | 0.152376i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 109591. | − | 18300.1i | 0.884485 | − | 0.147695i | ||||
\(353\) | 42732.8 | 0.342935 | 0.171467 | − | 0.985190i | \(-0.445149\pi\) | ||||
0.171467 | + | 0.985190i | \(0.445149\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 126837.i | − | 1.00644i | ||||||
\(356\) | −6876.46 | + | 5727.63i | −0.0542582 | + | 0.0451934i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 61527.8 | + | 170006.i | 0.480071 | + | 1.32647i | ||||
\(359\) | 175816.i | 1.36418i | 0.731270 | + | 0.682088i | \(0.238928\pi\) | ||||
−0.731270 | + | 0.682088i | \(0.761072\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 93685.2 | 0.718880 | ||||||||
\(362\) | 103814. | − | 37571.9i | 0.792205 | − | 0.286712i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23230.6 | − | 27890.1i | −0.175331 | − | 0.210498i | ||||
\(365\) | 55879.8 | 0.419439 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7929.69i | 0.0588740i | 0.999567 | + | 0.0294370i | \(0.00937145\pi\) | ||||
−0.999567 | + | 0.0294370i | \(0.990629\pi\) | |||||||
\(368\) | 241859. | + | 44459.1i | 1.78594 | + | 0.328296i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22591.2 | + | 8176.13i | −0.165020 | + | 0.0597234i | ||||
\(371\) | 29204.0i | 0.212175i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 246672. | 1.77297 | 0.886486 | − | 0.462755i | \(-0.153139\pi\) | ||||
0.886486 | + | 0.462755i | \(0.153139\pi\) | |||||||
\(374\) | 74467.0 | + | 205758.i | 0.532379 | + | 1.47100i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −62342.3 | − | 36447.4i | −0.440968 | − | 0.257805i | ||||
\(377\) | −70170.4 | −0.493709 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 147423.i | 1.02633i | 0.858291 | + | 0.513163i | \(0.171526\pi\) | ||||
−0.858291 | + | 0.513163i | \(0.828474\pi\) | |||||||
\(380\) | −56073.9 | − | 67321.1i | −0.388324 | − | 0.466212i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −25622.5 | − | 70796.7i | −0.175588 | − | 0.485161i | ||||
\(383\) | − | 122362.i | − | 0.834158i | −0.908870 | − | 0.417079i | \(-0.863054\pi\) | ||
0.908870 | − | 0.417079i | \(-0.136946\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 79619.4 | 0.537153 | ||||||||
\(386\) | 35559.6 | − | 12869.6i | 0.238662 | − | 0.0863755i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27068.6 | + | 22546.3i | −0.179805 | + | 0.149765i | ||||
\(389\) | −183456. | −1.21236 | −0.606182 | − | 0.795326i | \(-0.707300\pi\) | ||||
−0.606182 | + | 0.795326i | \(0.707300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 484301.i | 3.16783i | ||||||||
\(392\) | 56305.9 | − | 96309.8i | 0.366422 | − | 0.626756i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −81431.0 | + | 29471.2i | −0.524562 | + | 0.189848i | ||||
\(395\) | 50342.3i | 0.322656i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 81466.1 | 0.516887 | 0.258444 | − | 0.966026i | \(-0.416790\pi\) | ||||
0.258444 | + | 0.966026i | \(0.416790\pi\) | |||||||
\(398\) | −34387.2 | − | 95014.4i | −0.217086 | − | 0.599823i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8955.24 | − | 48716.8i | 0.0559703 | − | 0.304480i | ||||
\(401\) | 201168. | 1.25104 | 0.625518 | − | 0.780209i | \(-0.284887\pi\) | ||||
0.625518 | + | 0.780209i | \(0.284887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 29151.4i | − | 0.179494i | ||||||
\(404\) | −8995.27 | + | 7492.45i | −0.0551127 | + | 0.0459051i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27699.0 | + | 76534.4i | 0.168040 | + | 0.464306i | ||||
\(407\) | 22779.8i | 0.137518i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −140640. | −0.840742 | −0.420371 | − | 0.907352i | \(-0.638100\pi\) | ||||
−0.420371 | + | 0.907352i | \(0.638100\pi\) | |||||||
\(410\) | −113675. | + | 41141.0i | −0.676237 | + | 0.244741i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 100905. | + | 121144.i | 0.594454 | + | 0.713688i | ||||
\(413\) | −119576. | −0.701044 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 86606.3i | − | 0.502867i | ||||||
\(416\) | 14917.6 | + | 89335.1i | 0.0862009 | + | 0.516221i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −78114.7 | + | 28271.0i | −0.447075 | + | 0.161804i | ||||
\(419\) | − | 153693.i | − | 0.875441i | −0.899111 | − | 0.437720i | \(-0.855786\pi\) | ||
0.899111 | − | 0.437720i | \(-0.144214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 154412. | 0.871197 | 0.435599 | − | 0.900141i | \(-0.356537\pi\) | ||||
0.435599 | + | 0.900141i | \(0.356537\pi\) | |||||||
\(422\) | −29352.6 | − | 81103.5i | −0.164825 | − | 0.455422i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 36778.8 | − | 62909.2i | 0.204581 | − | 0.349931i | ||||
\(425\) | 97550.9 | 0.540074 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 143624.i | − | 0.787720i | ||||||
\(428\) | 8239.57 | + | 9892.24i | 0.0449797 | + | 0.0540017i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −129847. | − | 358775.i | −0.702253 | − | 1.94038i | ||||
\(431\) | − | 191579.i | − | 1.03132i | −0.856793 | − | 0.515660i | \(-0.827547\pi\) | ||
0.856793 | − | 0.515660i | \(-0.172453\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −53963.8 | −0.287824 | −0.143912 | − | 0.989591i | \(-0.545968\pi\) | ||||
−0.143912 | + | 0.989591i | \(0.545968\pi\) | |||||||
\(434\) | −31795.2 | + | 11507.2i | −0.168804 | + | 0.0610929i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −212992. | + | 177408.i | −1.12044 | + | 0.933255i | ||||
\(437\) | −183862. | −0.962784 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16842.9i | − | 0.0873951i | −0.999045 | − | 0.0436976i | \(-0.986086\pi\) | ||
0.999045 | − | 0.0436976i | \(-0.0139138\pi\) | |||||||
\(440\) | −171511. | − | 100271.i | −0.885902 | − | 0.517928i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −167727. | + | 60703.0i | −0.858534 | + | 0.310718i | ||||
\(443\) | − | 161786.i | − | 0.824391i | −0.911095 | − | 0.412195i | \(-0.864762\pi\) | ||
0.911095 | − | 0.412195i | \(-0.135238\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16002.2 | 0.0808089 | ||||||||
\(446\) | 26264.7 | + | 72571.2i | 0.132039 | + | 0.364833i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 91548.6 | − | 51534.6i | 0.456137 | − | 0.256769i | ||||
\(449\) | 127200. | 0.630949 | 0.315475 | − | 0.948934i | \(-0.397836\pi\) | ||||
0.315475 | + | 0.948934i | \(0.397836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 114624.i | 0.563538i | ||||||||
\(452\) | 210815. | − | 175595.i | 1.03187 | − | 0.859479i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −88250.2 | − | 243842.i | −0.428158 | − | 1.18303i | ||||
\(455\) | 64903.1i | 0.313504i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18847.9 | −0.0902463 | −0.0451232 | − | 0.998981i | \(-0.514368\pi\) | ||||
−0.0451232 | + | 0.998981i | \(0.514368\pi\) | |||||||
\(458\) | 147256. | − | 53294.4i | 0.702009 | − | 0.254068i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −281415. | − | 337860.i | −1.32994 | − | 1.59669i | ||||
\(461\) | −58671.8 | −0.276075 | −0.138038 | − | 0.990427i | \(-0.544080\pi\) | ||||
−0.138038 | + | 0.990427i | \(0.544080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 47536.3i | − | 0.221750i | −0.993834 | − | 0.110875i | \(-0.964635\pi\) | ||
0.993834 | − | 0.110875i | \(-0.0353653\pi\) | |||||||
\(464\) | 36718.3 | − | 199749.i | 0.170548 | − | 0.927786i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8679.18 | + | 3141.13i | −0.0399675 | + | 0.0144649i | ||||
\(467\) | − | 150686.i | − | 0.690936i | −0.938431 | − | 0.345468i | \(-0.887720\pi\) | ||
0.938431 | − | 0.345468i | \(-0.112280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 181482. | 0.825066 | ||||||||
\(470\) | 43943.3 | + | 121418.i | 0.198928 | + | 0.549653i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 257583. | + | 150592.i | 1.15620 | + | 0.675954i | ||||
\(473\) | −361770. | −1.61700 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37034.6i | 0.164142i | ||||||||
\(476\) | 132417. | + | 158976.i | 0.584425 | + | 0.701647i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 103741. | + | 286644.i | 0.454041 | + | 1.25455i | ||||
\(479\) | 55229.7i | 0.240714i | 0.992731 | + | 0.120357i | \(0.0384039\pi\) | ||||
−0.992731 | + | 0.120357i | \(0.961596\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18569.3 | −0.0802612 | ||||||||
\(482\) | 61361.9 | − | 22207.8i | 0.264122 | − | 0.0955900i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 35256.1 | − | 29366.0i | 0.150502 | − | 0.125358i | ||||
\(485\) | 62991.1 | 0.267791 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2975.59i | − | 0.0125463i | −0.999980 | − | 0.00627313i | \(-0.998003\pi\) | ||
0.999980 | − | 0.00627313i | \(-0.00199681\pi\) | |||||||
\(488\) | −180877. | + | 309385.i | −0.759528 | + | 1.29915i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −187574. | + | 67886.0i | −0.781232 | + | 0.282740i | ||||
\(491\) | 270712.i | 1.12291i | 0.827508 | + | 0.561454i | \(0.189758\pi\) | ||||
−0.827508 | + | 0.561454i | \(0.810242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 399978. | 1.64567 | ||||||||
\(494\) | −23045.5 | − | 63676.5i | −0.0944350 | − | 0.260931i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 82983.0 | + | 15254.1i | 0.337307 | + | 0.0620047i | ||||
\(497\) | −113711. | −0.460353 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 261354.i | − | 1.04961i | −0.851223 | − | 0.524805i | \(-0.824138\pi\) | ||
0.851223 | − | 0.524805i | \(-0.175862\pi\) | |||||||
\(500\) | 151772. | − | 126416.i | 0.607086 | − | 0.505662i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −46056.2 | − | 127257.i | −0.182760 | − | 0.504979i | ||||
\(503\) | − | 283008.i | − | 1.11857i | −0.828976 | − | 0.559284i | \(-0.811076\pi\) | ||
0.828976 | − | 0.559284i | \(-0.188924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20932.9 | 0.0820816 | ||||||||
\(506\) | −392030. | + | 141882.i | −1.53115 | + | 0.554148i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 98217.4 | + | 117918.i | 0.380593 | + | 0.456932i | ||||
\(509\) | −213678. | −0.824755 | −0.412378 | − | 0.911013i | \(-0.635302\pi\) | ||||
−0.412378 | + | 0.911013i | \(0.635302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 50097.1i | − | 0.191854i | ||||||
\(512\) | −262109. | − | 4281.91i | −0.999867 | − | 0.0163342i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −216445. | + | 78335.0i | −0.819260 | + | 0.296503i | ||||
\(515\) | − | 281914.i | − | 1.06293i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 122432. | 0.458050 | ||||||||
\(518\) | 7330.04 | + | 20253.4i | 0.0273179 | + | 0.0754812i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 81737.4 | − | 139810.i | 0.302283 | − | 0.517048i | ||||
\(521\) | 168525. | 0.620854 | 0.310427 | − | 0.950597i | \(-0.399528\pi\) | ||||
0.310427 | + | 0.950597i | \(0.399528\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 231592.i | − | 0.846681i | −0.905971 | − | 0.423340i | \(-0.860857\pi\) | ||
0.905971 | − | 0.423340i | \(-0.139143\pi\) | |||||||
\(524\) | −46507.7 | − | 55836.1i | −0.169380 | − | 0.203354i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 106916. | + | 295415.i | 0.386429 | + | 1.06773i | ||||
\(527\) | 166166.i | 0.598302i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −642895. | −2.29736 | ||||||||
\(530\) | −122522. | + | 44342.8i | −0.436178 | + | 0.157860i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −60354.5 | + | 50271.2i | −0.213249 | + | 0.177622i | ||||
\(533\) | −93437.8 | −0.328903 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 23020.2i | − | 0.0804269i | ||||||
\(536\) | −390937. | − | 228554.i | −1.36074 | − | 0.795537i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −20224.1 | + | 7319.42i | −0.0698721 | + | 0.0252879i | ||||
\(539\) | 189139.i | 0.651035i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3552.06 | −0.0121363 | −0.00606815 | − | 0.999982i | \(-0.501932\pi\) | ||||
−0.00606815 | + | 0.999982i | \(0.501932\pi\) | |||||||
\(542\) | −147169. | − | 406639.i | −0.500978 | − | 1.38424i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −85031.6 | − | 509218.i | −0.287331 | − | 1.72070i | ||||
\(545\) | 495653. | 1.66872 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 513025.i | 1.71460i | 0.514813 | + | 0.857302i | \(0.327861\pi\) | ||||
−0.514813 | + | 0.857302i | \(0.672139\pi\) | |||||||
\(548\) | −60260.6 | + | 50193.0i | −0.200665 | + | 0.167141i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 28578.7 | + | 78965.1i | 0.0944752 | + | 0.261042i | ||||
\(551\) | 151849.i | 0.500161i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45132.7 | 0.147585 | ||||||||
\(554\) | −165278. | + | 59816.7i | −0.538512 | + | 0.194896i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −88584.4 | − | 106352.i | −0.286555 | − | 0.344031i | ||||
\(557\) | −269383. | −0.868281 | −0.434141 | − | 0.900845i | \(-0.642948\pi\) | ||||
−0.434141 | + | 0.900845i | \(0.642948\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 294903.i | − | 0.943746i | ||||||
\(560\) | −184754. | − | 33962.0i | −0.589140 | − | 0.108297i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 191340. | − | 69248.9i | 0.605805 | − | 0.219250i | ||||
\(563\) | − | 55932.8i | − | 0.176461i | −0.996100 | − | 0.0882307i | \(-0.971879\pi\) | ||
0.996100 | − | 0.0882307i | \(-0.0281213\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −490588. | −1.53681 | ||||||||
\(566\) | −35930.5 | − | 99278.4i | −0.112158 | − | 0.309900i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 244949. | + | 143205.i | 0.759239 | + | 0.443877i | ||||
\(569\) | 424532. | 1.31125 | 0.655625 | − | 0.755086i | \(-0.272405\pi\) | ||||
0.655625 | + | 0.755086i | \(0.272405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29210.9i | − | 0.0895928i | −0.998996 | − | 0.0447964i | \(-0.985736\pi\) | ||
0.998996 | − | 0.0447964i | \(-0.0142639\pi\) | |||||||
\(572\) | −98275.2 | − | 117987.i | −0.300367 | − | 0.360614i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 36883.6 | + | 101912.i | 0.111946 | + | 0.309315i | ||||
\(575\) | 185863.i | 0.562158i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −494524. | −1.48537 | −0.742687 | − | 0.669639i | \(-0.766449\pi\) | ||||
−0.742687 | + | 0.669639i | \(0.766449\pi\) | |||||||
\(578\) | 641915. | − | 232319.i | 1.92142 | − | 0.695392i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −279035. | + | 232417.i | −0.829473 | + | 0.690895i | ||||
\(581\) | −77644.0 | −0.230015 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 123545.i | 0.363486i | ||||||||
\(584\) | −63091.1 | + | 107916.i | −0.184988 | + | 0.316417i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 491936. | − | 178040.i | 1.43256 | − | 0.518467i | ||||
\(587\) | − | 240416.i | − | 0.697729i | −0.937173 | − | 0.348865i | \(-0.886567\pi\) | ||
0.937173 | − | 0.348865i | \(-0.113433\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −63083.9 | −0.181839 | ||||||||
\(590\) | −181563. | − | 501671.i | −0.521583 | − | 1.44117i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9716.81 | − | 52859.8i | 0.0277256 | − | 0.150828i | ||||
\(593\) | −470902. | −1.33912 | −0.669562 | − | 0.742756i | \(-0.733518\pi\) | ||||
−0.669562 | + | 0.742756i | \(0.733518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 369954.i | − | 1.04499i | ||||||
\(596\) | −156046. | + | 129976.i | −0.439299 | + | 0.365907i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −115657. | − | 319569.i | −0.323423 | − | 0.893640i | ||||
\(599\) | − | 10011.2i | − | 0.0279017i | −0.999903 | − | 0.0139509i | \(-0.995559\pi\) | ||
0.999903 | − | 0.0139509i | \(-0.00444084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 392897. | 1.08775 | 0.543876 | − | 0.839165i | \(-0.316956\pi\) | ||||
0.543876 | + | 0.839165i | \(0.316956\pi\) | |||||||
\(602\) | −321648. | + | 116410.i | −0.887540 | + | 0.321215i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −130720. | − | 156939.i | −0.358317 | − | 0.430188i | ||||
\(605\) | −82044.4 | −0.224150 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 433505.i | − | 1.17657i | −0.808655 | − | 0.588283i | \(-0.799804\pi\) | ||
0.808655 | − | 0.588283i | \(-0.200196\pi\) | |||||||
\(608\) | 193322. | − | 32281.8i | 0.522966 | − | 0.0873273i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 602561. | − | 218077.i | 1.61935 | − | 0.586070i | ||||
\(611\) | 99802.2i | 0.267336i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 301951. | 0.803555 | 0.401778 | − | 0.915737i | \(-0.368393\pi\) | ||||
0.401778 | + | 0.915737i | \(0.368393\pi\) | |||||||
\(614\) | 73817.2 | + | 203962.i | 0.195804 | + | 0.541020i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −89894.5 | + | 153762.i | −0.236904 | + | 0.405217i | ||||
\(617\) | 196747. | 0.516817 | 0.258409 | − | 0.966036i | \(-0.416802\pi\) | ||||
0.258409 | + | 0.966036i | \(0.416802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 619149.i | − | 1.61590i | −0.589252 | − | 0.807949i | \(-0.700578\pi\) | ||
0.589252 | − | 0.807949i | \(-0.299422\pi\) | |||||||
\(620\) | −96554.8 | − | 115921.i | −0.251183 | − | 0.301565i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −185077. | − | 511380.i | −0.478378 | − | 1.32179i | ||||
\(623\) | − | 14346.2i | − | 0.0369625i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −474118. | −1.21374 | ||||||||
\(626\) | 618305. | − | 223775.i | 1.57781 | − | 0.571034i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −498717. | + | 415397.i | −1.26455 | + | 1.05328i | ||||
\(629\) | 105847. | 0.267532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 308766.i | 0.775479i | 0.921769 | + | 0.387740i | \(0.126744\pi\) | ||||
−0.921769 | + | 0.387740i | \(0.873256\pi\) | |||||||
\(632\) | −97221.8 | − | 56839.1i | −0.243405 | − | 0.142303i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 453678. | − | 164193.i | 1.12867 | − | 0.408486i | ||||
\(635\) | − | 274406.i | − | 0.680528i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −154180. | −0.379970 | ||||||||
\(638\) | 117178. | + | 323772.i | 0.287877 | + | 0.795424i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 355214. | + | 305834.i | 0.867222 | + | 0.746665i | ||||
\(641\) | −342401. | −0.833333 | −0.416666 | − | 0.909059i | \(-0.636802\pi\) | ||||
−0.416666 | + | 0.909059i | \(0.636802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 552948.i | 1.33740i | 0.743531 | + | 0.668702i | \(0.233150\pi\) | ||||
−0.743531 | + | 0.668702i | \(0.766850\pi\) | |||||||
\(644\) | −302897. | + | 252293.i | −0.730338 | + | 0.608322i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 131362. | + | 362962.i | 0.314778 | + | 0.869753i | ||||
\(647\) | − | 576814.i | − | 1.37793i | −0.724794 | − | 0.688965i | \(-0.758065\pi\) | ||
0.724794 | − | 0.688965i | \(-0.241935\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −505858. | −1.20099 | ||||||||
\(650\) | −64369.7 | + | 23296.4i | −0.152354 | + | 0.0551395i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −70379.6 | − | 84496.1i | −0.165558 | − | 0.198766i | ||||
\(653\) | −573591. | −1.34517 | −0.672583 | − | 0.740022i | \(-0.734815\pi\) | ||||
−0.672583 | + | 0.740022i | \(0.734815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 129936.i | 0.302864i | ||||||||
\(656\) | 48893.4 | − | 265982.i | 0.113617 | − | 0.618080i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 108854. | − | 39395.9i | 0.251415 | − | 0.0909911i | ||||
\(659\) | − | 345600.i | − | 0.795797i | −0.917429 | − | 0.397899i | \(-0.869740\pi\) | ||
0.917429 | − | 0.397899i | \(-0.130260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −375167. | −0.858661 | −0.429330 | − | 0.903148i | \(-0.641250\pi\) | ||||
−0.429330 | + | 0.903148i | \(0.641250\pi\) | |||||||
\(662\) | 157473. | + | 435110.i | 0.359328 | + | 0.992849i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 167255. | + | 97783.0i | 0.379353 | + | 0.221782i | ||||
\(665\) | 140451. | 0.317600 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 762077.i | 1.71296i | ||||||||
\(668\) | −359521. | − | 431632.i | −0.805695 | − | 0.967300i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 275560. | + | 761391.i | 0.613855 | + | 1.69613i | ||||
\(671\) | − | 607591.i | − | 1.34948i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −573732. | −1.26672 | −0.633358 | − | 0.773859i | \(-0.718324\pi\) | ||||
−0.633358 | + | 0.773859i | \(0.718324\pi\) | |||||||
\(674\) | 706121. | − | 255557.i | 1.55439 | − | 0.562558i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −254949. | + | 212355.i | −0.557904 | + | 0.464697i | ||||
\(677\) | −27578.5 | −0.0601718 | −0.0300859 | − | 0.999547i | \(-0.509578\pi\) | ||||
−0.0300859 | + | 0.999547i | \(0.509578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 56472.6i | − | 0.122489i | ||||||
\(680\) | −465911. | + | 796928.i | −1.00759 | + | 1.72346i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −134507. | + | 48680.3i | −0.289186 | + | 0.104661i | ||||
\(683\) | 1038.30i | 0.00222578i | 0.999999 | + | 0.00111289i | \(0.000354244\pi\) | ||||
−0.999999 | + | 0.00111289i | \(0.999646\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 140232. | 0.298859 | ||||||||
\(686\) | 144690. | + | 399790.i | 0.307462 | + | 0.849539i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 839476. | + | 154314.i | 1.77350 | + | 0.326009i | ||||
\(689\) | −100710. | −0.212145 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 334105.i | − | 0.699724i | −0.936801 | − | 0.349862i | \(-0.886229\pi\) | ||
0.936801 | − | 0.349862i | \(-0.113771\pi\) | |||||||
\(692\) | 36678.4 | − | 30550.6i | 0.0765945 | − | 0.0637981i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 184101. | + | 508685.i | 0.382241 | + | 1.05616i | ||||
\(695\) | 247492.i | 0.512380i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 532604. | 1.09632 | ||||||||
\(698\) | 12423.0 | − | 4496.08i | 0.0254985 | − | 0.00922832i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 50818.5 | + | 61011.5i | 0.103711 | + | 0.124513i | ||||
\(701\) | 177927. | 0.362082 | 0.181041 | − | 0.983476i | \(-0.442053\pi\) | ||||
0.181041 | + | 0.983476i | \(0.442053\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40184.1i | 0.0813100i | ||||||||
\(704\) | 387289. | − | 218013.i | 0.781429 | − | 0.439883i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 160729. | − | 58170.2i | 0.322466 | − | 0.116706i | ||||
\(707\) | − | 18766.7i | − | 0.0375447i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 724969. | 1.44220 | 0.721102 | − | 0.692829i | \(-0.243636\pi\) | ||||
0.721102 | + | 0.692829i | \(0.243636\pi\) | |||||||
\(710\) | −172657. | − | 477064.i | −0.342506 | − | 0.946368i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18067.3 | + | 30903.7i | −0.0356396 | + | 0.0609607i | ||||
\(713\) | −316595. | −0.622767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 274567.i | 0.537077i | ||||||||
\(716\) | 462842. | + | 555678.i | 0.902832 | + | 1.08392i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 239331. | + | 661289.i | 0.464248 | + | 1.28275i | ||||
\(719\) | 536436.i | 1.03767i | 0.854874 | + | 0.518836i | \(0.173634\pi\) | ||||
−0.854874 | + | 0.518836i | \(0.826366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −252741. | −0.486189 | ||||||||
\(722\) | 352373. | − | 127530.i | 0.675972 | − | 0.244645i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 339324. | − | 282634.i | 0.647348 | − | 0.539197i | ||||
\(725\) | 153502. | 0.292038 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 433953.i | − | 0.821058i | −0.911847 | − | 0.410529i | \(-0.865344\pi\) | ||
0.911847 | − | 0.410529i | \(-0.134656\pi\) | |||||||
\(728\) | −125342. | − | 73278.9i | −0.236501 | − | 0.138266i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 210178. | − | 76066.7i | 0.394403 | − | 0.142741i | ||||
\(731\) | 1.68097e6i | 3.14576i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −780416. | −1.45251 | −0.726254 | − | 0.687427i | \(-0.758740\pi\) | ||||
−0.726254 | + | 0.687427i | \(0.758740\pi\) | |||||||
\(734\) | 10794.3 | + | 29825.5i | 0.0200357 | + | 0.0553600i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 970212. | − | 162010.i | 1.79106 | − | 0.299080i | ||||
\(737\) | 767746. | 1.41346 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 215142.i | − | 0.393947i | −0.980409 | − | 0.196973i | \(-0.936889\pi\) | ||
0.980409 | − | 0.196973i | \(-0.0631112\pi\) | |||||||
\(740\) | −73841.4 | + | 61504.9i | −0.134845 | + | 0.112317i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 39754.1 | + | 109843.i | 0.0722061 | + | 0.199511i | ||||
\(743\) | 289091.i | 0.523670i | 0.965113 | + | 0.261835i | \(0.0843276\pi\) | ||||
−0.965113 | + | 0.261835i | \(0.915672\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 363135. | 0.654267 | ||||||||
\(746\) | 927794. | − | 335784.i | 1.66715 | − | 0.603367i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 560178. | + | 672537.i | 1.00120 | + | 1.20202i | ||||
\(749\) | −20638.0 | −0.0367878 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 684873.i | 1.21431i | 0.794583 | + | 0.607156i | \(0.207690\pi\) | ||||
−0.794583 | + | 0.607156i | \(0.792310\pi\) | |||||||
\(752\) | −284099. | − | 52223.8i | −0.502382 | − | 0.0923491i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −263928. | + | 95519.9i | −0.464241 | + | 0.168016i | ||||
\(755\) | 365213.i | 0.640697i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −646906. | −1.12888 | −0.564442 | − | 0.825472i | \(-0.690909\pi\) | ||||
−0.564442 | + | 0.825472i | \(0.690909\pi\) | |||||||
\(758\) | 200680. | + | 554493.i | 0.349273 | + | 0.965067i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −302549. | − | 176880.i | −0.523804 | − | 0.306233i | ||||
\(761\) | 766822. | 1.32411 | 0.662057 | − | 0.749454i | \(-0.269684\pi\) | ||||
0.662057 | + | 0.749454i | \(0.269684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 444361.i | − | 0.763286i | ||||||
\(764\) | −192745. | − | 231405.i | −0.330214 | − | 0.396448i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −166566. | − | 460233.i | −0.283876 | − | 0.784369i | ||||
\(767\) | − | 412359.i | − | 0.700946i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −579735. | −0.980340 | −0.490170 | − | 0.871627i | \(-0.663065\pi\) | ||||
−0.490170 | + | 0.871627i | \(0.663065\pi\) | |||||||
\(770\) | 299468. | − | 108382.i | 0.505091 | − | 0.182801i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 116230. | − | 96811.6i | 0.195022 | − | 0.162440i | ||||
\(773\) | −885783. | −1.48241 | −0.741205 | − | 0.671279i | \(-0.765745\pi\) | ||||
−0.741205 | + | 0.671279i | \(0.765745\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 63770.7i | 0.106174i | ||||||||
\(776\) | −71120.3 | + | 121649.i | −0.118105 | + | 0.202016i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −690024. | + | 249731.i | −1.14000 | + | 0.412584i | ||||
\(779\) | 202200.i | 0.333201i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −481046. | −0.788651 | ||||||||
\(782\) | 659257. | + | 1.82157e6i | 1.07806 | + | 2.97875i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 80678.1 | − | 438892.i | 0.131257 | − | 0.714045i | ||||
\(785\) | 1.16056e6 | 1.88334 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.05137e6i | − | 1.69749i | −0.528803 | − | 0.848744i | \(-0.677359\pi\) | ||
0.528803 | − | 0.848744i | \(-0.322641\pi\) | |||||||
\(788\) | −266164. | + | 221697.i | −0.428644 | + | 0.357032i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 68528.8 | + | 189350.i | 0.109804 | + | 0.303397i | ||||
\(791\) | 439820.i | 0.702946i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 495287. | 0.787609 | ||||||||
\(794\) | 306414. | − | 110896.i | 0.486035 | − | 0.175904i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −258678. | − | 310563.i | −0.408256 | − | 0.490143i | ||||
\(797\) | −94818.4 | −0.149271 | −0.0746356 | − | 0.997211i | \(-0.523779\pi\) | ||||
−0.0746356 | + | 0.997211i | \(0.523779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 568882.i | − | 0.891105i | ||||||
\(800\) | −32633.2 | − | 195426.i | −0.0509894 | − | 0.305354i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 756643. | − | 273841.i | 1.17636 | − | 0.425745i | ||||
\(803\) | − | 211932.i | − | 0.328674i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 704871. | 1.08772 | ||||||||
\(806\) | −39682.6 | − | 109646.i | −0.0610843 | − | 0.168780i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23634.3 | + | 40425.8i | −0.0362009 | + | 0.0619208i | ||||
\(809\) | −209085. | −0.319467 | −0.159734 | − | 0.987160i | \(-0.551063\pi\) | ||||
−0.159734 | + | 0.987160i | \(0.551063\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 577209.i | − | 0.877589i | −0.898587 | − | 0.438794i | \(-0.855406\pi\) | ||
0.898587 | − | 0.438794i | \(-0.144594\pi\) | |||||||
\(812\) | 208366. | + | 250159.i | 0.316020 | + | 0.379406i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 31009.1 | + | 85680.4i | 0.0467994 | + | 0.129310i | ||||
\(815\) | 196631.i | 0.296030i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −638171. | −0.956078 | ||||||||
\(818\) | −528983. | + | 191447.i | −0.790560 | + | 0.286116i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −371558. | + | 309483.i | −0.552585 | + | 0.460266i | ||||
\(821\) | −735846. | −1.09169 | −0.545847 | − | 0.837885i | \(-0.683792\pi\) | ||||
−0.545847 | + | 0.837885i | \(0.683792\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 171095.i | − | 0.252602i | −0.991992 | − | 0.126301i | \(-0.959689\pi\) | ||
0.991992 | − | 0.126301i | \(-0.0403106\pi\) | |||||||
\(824\) | 544437. | + | 318296.i | 0.801850 | + | 0.468788i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −449757. | + | 162774.i | −0.659200 | + | 0.238575i | ||||
\(827\) | − | 1.03882e6i | − | 1.51890i | −0.650563 | − | 0.759452i | \(-0.725467\pi\) | ||
0.650563 | − | 0.759452i | \(-0.274533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −802150. | −1.16720 | −0.583601 | − | 0.812040i | \(-0.698357\pi\) | ||||
−0.583601 | + | 0.812040i | \(0.698357\pi\) | |||||||
\(830\) | −117893. | − | 325748.i | −0.171133 | − | 0.472852i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 177717. | + | 315705.i | 0.256733 | + | 0.456073i | ||||
\(833\) | 878840. | 1.26654 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.00445e6i | 1.44064i | ||||||||
\(836\) | −255325. | + | 212668.i | −0.365326 | + | 0.304292i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −209216. | − | 578078.i | −0.297925 | − | 0.823187i | ||||
\(839\) | − | 562970.i | − | 0.799763i | −0.916567 | − | 0.399881i | \(-0.869051\pi\) | ||
0.916567 | − | 0.399881i | \(-0.130949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −77891.1 | −0.110127 | ||||||||
\(842\) | 580781. | − | 210194.i | 0.819197 | − | 0.296481i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −220805. | − | 265094.i | −0.309973 | − | 0.372147i | ||||
\(845\) | 593291. | 0.830910 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 73554.1i | 0.102527i | ||||||||
\(848\) | 52698.6 | − | 286682.i | 0.0732837 | − | 0.398666i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 366913. | − | 132792.i | 0.507838 | − | 0.183795i | ||||
\(851\) | 201670.i | 0.278472i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −662811. | −0.910944 | −0.455472 | − | 0.890250i | \(-0.650530\pi\) | ||||
−0.455472 | + | 0.890250i | \(0.650530\pi\) | |||||||
\(854\) | −195509. | − | 540206.i | −0.268072 | − | 0.740703i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44456.9 | + | 25991.0i | 0.0606725 | + | 0.0354712i | ||||
\(857\) | 1.13320e6 | 1.54293 | 0.771465 | − | 0.636271i | \(-0.219524\pi\) | ||||
0.771465 | + | 0.636271i | \(0.219524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 401245.i | 0.543780i | 0.962328 | + | 0.271890i | \(0.0876487\pi\) | ||||
−0.962328 | + | 0.271890i | \(0.912351\pi\) | |||||||
\(860\) | −976770. | − | 1.17269e6i | −1.32067 | − | 1.58557i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −260788. | − | 720576.i | −0.350973 | − | 0.969762i | ||||
\(863\) | 1.22445e6i | 1.64407i | 0.569437 | + | 0.822035i | \(0.307161\pi\) | ||||
−0.569437 | + | 0.822035i | \(0.692839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −85354.1 | −0.114075 | ||||||||
\(866\) | −202971. | + | 73458.6i | −0.270644 | + | 0.0979505i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −103926. | + | 86563.0i | −0.137938 | + | 0.114893i | ||||
\(869\) | 190930. | 0.252834 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 625841.i | 0.824950i | ||||||||
\(872\) | −559618. | + | 957212.i | −0.735967 | + | 1.25885i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −691550. | + | 250283.i | −0.905317 | + | 0.327649i | ||||
\(875\) | 316638.i | 0.413568i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 131862. | 0.171443 | 0.0857216 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857216 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(878\) | −22927.5 | − | 63350.2i | −0.0297418 | − | 0.0821787i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −781588. | − | 143673.i | −1.00928 | − | 0.185529i | ||||
\(881\) | 510450. | 0.657660 | 0.328830 | − | 0.944389i | \(-0.393346\pi\) | ||||
0.328830 | + | 0.944389i | \(0.393346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 233561.i | − | 0.299557i | −0.988720 | − | 0.149778i | \(-0.952144\pi\) | ||
0.988720 | − | 0.149778i | \(-0.0478560\pi\) | |||||||
\(884\) | −548229. | + | 456638.i | −0.701549 | + | 0.584343i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −220232. | − | 608517.i | −0.280552 | − | 0.775184i | ||||
\(887\) | 640030.i | 0.813491i | 0.913541 | + | 0.406746i | \(0.133336\pi\) | ||||
−0.913541 | + | 0.406746i | \(0.866664\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −246009. | −0.311278 | ||||||||
\(890\) | 60188.2 | − | 21783.1i | 0.0759856 | − | 0.0275004i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 197576. | + | 237205.i | 0.248316 | + | 0.298122i | ||||
\(893\) | 215973. | 0.270830 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.29312e6i | − | 1.61433i | ||||||
\(896\) | 274185. | − | 318455.i | 0.341529 | − | 0.396673i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 478431. | − | 173152.i | 0.593289 | − | 0.214721i | ||||
\(899\) | 261472.i | 0.323524i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 574055. | 0.707137 | ||||||||
\(902\) | 156033. | + | 431130.i | 0.191780 | + | 0.529902i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 553899. | − | 947430.i | 0.677788 | − | 1.15934i | ||||
\(905\) | −789640. | −0.964122 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 437927.i | 0.532338i | 0.963926 | + | 0.266169i | \(0.0857579\pi\) | ||||
−0.963926 | + | 0.266169i | \(0.914242\pi\) | |||||||
\(908\) | −663862. | − | 797017.i | −0.805204 | − | 0.966710i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 88349.7 | + | 244116.i | 0.106690 | + | 0.294791i | ||||
\(911\) | − | 769134.i | − | 0.926756i | −0.886161 | − | 0.463378i | \(-0.846637\pi\) | ||
0.886161 | − | 0.463378i | \(-0.153363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −328467. | −0.394048 | ||||||||
\(914\) | −70891.5 | + | 25656.8i | −0.0848597 | + | 0.0307121i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 481320. | − | 400907.i | 0.573644 | − | 0.477807i | ||||
\(917\) | 116490. | 0.138532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.37883e6i | − | 1.63260i | −0.577626 | − | 0.816301i | \(-0.696021\pi\) | ||
0.577626 | − | 0.816301i | \(-0.303979\pi\) | |||||||
\(920\) | −1.51838e6 | − | 887698.i | −1.79393 | − | 1.04879i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −220679. | + | 79867.4i | −0.259597 | + | 0.0939524i | ||||
\(923\) | − | 392132.i | − | 0.460288i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40621.6 | 0.0474759 | ||||||||
\(926\) | −64709.1 | − | 178796.i | −0.0754646 | − | 0.208514i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −133802. | − | 801287.i | −0.155370 | − | 0.930448i | ||||
\(929\) | −261770. | −0.303311 | −0.151656 | − | 0.988433i | \(-0.548460\pi\) | ||||
−0.151656 | + | 0.988433i | \(0.548460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 333647.i | 0.384935i | ||||||||
\(932\) | −28368.6 | + | 23629.2i | −0.0326593 | + | 0.0272030i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −205122. | − | 566766.i | −0.235135 | − | 0.649695i | ||||
\(935\) | − | 1.56506e6i | − | 1.79022i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.29656e6 | 1.47677 | 0.738384 | − | 0.674380i | \(-0.235589\pi\) | ||||
0.738384 | + | 0.674380i | \(0.235589\pi\) | |||||||
\(938\) | 682600. | − | 247044.i | 0.775819 | − | 0.280781i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 330563. | + | 396866.i | 0.374109 | + | 0.449147i | ||||
\(941\) | −422321. | −0.476939 | −0.238470 | − | 0.971150i | \(-0.576646\pi\) | ||||
−0.238470 | + | 0.971150i | \(0.576646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.01477e6i | 1.14115i | ||||||||
\(944\) | 1.17383e6 | + | 215776.i | 1.31723 | + | 0.242136i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.36071e6 | + | 492462.i | −1.52048 | + | 0.550288i | ||||
\(947\) | 975543.i | 1.08779i | 0.839152 | + | 0.543897i | \(0.183052\pi\) | ||||
−0.839152 | + | 0.543897i | \(0.816948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 172760. | 0.191827 | ||||||||
\(950\) | 50413.6 | + | 139296.i | 0.0558600 | + | 0.154345i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 714460. | + | 417697.i | 0.788322 | + | 0.460879i | ||||
\(953\) | 1.52194e6 | 1.67576 | 0.837878 | − | 0.545857i | \(-0.183796\pi\) | ||||
0.837878 | + | 0.545857i | \(0.183796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 538502.i | 0.590447i | ||||||||
\(956\) | 780392. | + | 936921.i | 0.853880 | + | 1.02515i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 75181.7 | + | 207732.i | 0.0819184 | + | 0.226346i | ||||
\(959\) | − | 125721.i | − | 0.136700i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 814896. | 0.882379 | ||||||||
\(962\) | −69843.8 | + | 25277.6i | −0.0754705 | + | 0.0273140i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 200567. | − | 167058.i | 0.215826 | − | 0.179769i | ||||
\(965\) | −270478. | −0.290454 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1.51989e6i | − | 1.62540i | −0.582682 | − | 0.812700i | \(-0.697997\pi\) | ||
0.582682 | − | 0.812700i | \(-0.302003\pi\) | |||||||
\(968\) | 92632.3 | − | 158445.i | 0.0988580 | − | 0.169094i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 236925. | − | 85747.1i | 0.251807 | − | 0.0911331i | ||||
\(971\) | − | 606895.i | − | 0.643687i | −0.946793 | − | 0.321844i | \(-0.895697\pi\) | ||
0.946793 | − | 0.321844i | \(-0.104303\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 221881. | 0.234366 | ||||||||
\(974\) | −4050.53 | − | 11191.9i | −0.00426967 | − | 0.0117974i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −259170. | + | 1.40989e6i | −0.272073 | + | 1.48009i | ||||
\(977\) | −880507. | −0.922452 | −0.461226 | − | 0.887283i | \(-0.652590\pi\) | ||||
−0.461226 | + | 0.887283i | \(0.652590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 60690.6i | − | 0.0633222i | ||||||
\(980\) | −613101. | + | 510672.i | −0.638381 | + | 0.531728i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 368508. | + | 1.01821e6i | 0.382141 | + | 1.05588i | ||||
\(983\) | − | 1.79064e6i | − | 1.85311i | −0.376164 | − | 0.926553i | \(-0.622757\pi\) | ||
0.376164 | − | 0.926553i | \(-0.377243\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 619390. | 0.638398 | ||||||||
\(986\) | 1.50442e6 | − | 544473.i | 1.54744 | − | 0.560044i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −173360. | − | 208132.i | −0.177597 | − | 0.213219i | ||||
\(989\) | −3.20275e6 | −3.27439 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.12180e6i | 1.14227i | 0.820858 | + | 0.571133i | \(0.193496\pi\) | ||||
−0.820858 | + | 0.571133i | \(0.806504\pi\) | |||||||
\(992\) | 332884. | − | 55586.6i | 0.338275 | − | 0.0564867i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −427696. | + | 154790.i | −0.432875 | + | 0.156664i | ||||
\(995\) | 722709.i | 0.729991i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 841168. | 0.846238 | 0.423119 | − | 0.906074i | \(-0.360935\pi\) | ||||
0.423119 | + | 0.906074i | \(0.360935\pi\) | |||||||
\(998\) | −355769. | − | 983016.i | −0.357197 | − | 0.986960i | ||||
\(999\) | 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.163.19 | 22 | ||
3.2 | odd | 2 | 324.5.d.e.163.4 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.f.163.20 | 22 | ||
9.2 | odd | 6 | 108.5.f.a.91.18 | 44 | |||
9.4 | even | 3 | 36.5.f.a.7.10 | yes | 44 | ||
9.5 | odd | 6 | 108.5.f.a.19.13 | 44 | |||
9.7 | even | 3 | 36.5.f.a.31.5 | yes | 44 | ||
12.11 | even | 2 | 324.5.d.e.163.3 | 22 | |||
36.7 | odd | 6 | 36.5.f.a.31.10 | yes | 44 | ||
36.11 | even | 6 | 108.5.f.a.91.13 | 44 | |||
36.23 | even | 6 | 108.5.f.a.19.18 | 44 | |||
36.31 | odd | 6 | 36.5.f.a.7.5 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.5 | ✓ | 44 | 36.31 | odd | 6 | ||
36.5.f.a.7.10 | yes | 44 | 9.4 | even | 3 | ||
36.5.f.a.31.5 | yes | 44 | 9.7 | even | 3 | ||
36.5.f.a.31.10 | yes | 44 | 36.7 | odd | 6 | ||
108.5.f.a.19.13 | 44 | 9.5 | odd | 6 | |||
108.5.f.a.19.18 | 44 | 36.23 | even | 6 | |||
108.5.f.a.91.13 | 44 | 36.11 | even | 6 | |||
108.5.f.a.91.18 | 44 | 9.2 | odd | 6 | |||
324.5.d.e.163.3 | 22 | 12.11 | even | 2 | |||
324.5.d.e.163.4 | 22 | 3.2 | odd | 2 | |||
324.5.d.f.163.19 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.f.163.20 | 22 | 4.3 | odd | 2 | inner |