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 | 163.3 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.e.163.4 |
$q$-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 | \(-0.306096\pi\) | ||||
0.572185 | + | 0.820125i | \(0.306096\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 25.6487i | − | 0.523442i | −0.965144 | − | 0.261721i | \(-0.915710\pi\) | ||
0.965144 | − | 0.261721i | \(-0.0842900\pi\) | |||||||
\(8\) | −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 | \(-0.837349\pi\) | ||||
−0.872265 | + | 0.489034i | \(0.837349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 191.405i | − | 0.530207i | −0.964220 | − | 0.265104i | \(-0.914594\pi\) | ||
0.964220 | − | 0.265104i | \(-0.0854062\pi\) | |||||||
\(20\) | 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 | \(-0.656347\pi\) | ||||
−0.471665 | + | 0.881778i | \(0.656347\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 329.584i | − | 0.342959i | −0.985188 | − | 0.171480i | \(-0.945145\pi\) | ||
0.985188 | − | 0.171480i | \(-0.0548547\pi\) | |||||||
\(32\) | 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 | \(-0.601742\pi\) | ||||
−0.314218 | + | 0.949351i | \(0.601742\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3334.14i | − | 1.80322i | −0.432555 | − | 0.901608i | \(-0.642388\pi\) | ||
0.432555 | − | 0.901608i | \(-0.357612\pi\) | |||||||
\(44\) | −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 | \(-0.564963\pi\) | ||||
−0.202673 | + | 0.979247i | \(0.564963\pi\) | |||||||
\(54\) | 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 | \(0.288943\pi\) | ||||
−0.615527 | + | 0.788116i | \(0.711057\pi\) | |||||||
\(68\) | −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 | \(0.0450238\pi\) | ||||
−0.990013 | + | 0.140975i | \(0.954976\pi\) | |||||||
\(80\) | 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 | \(-0.488759\pi\) | ||||
0.0353072 | + | 0.999377i | \(0.488759\pi\) | |||||||
\(90\) | 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 | \(-0.488582\pi\) | ||||
0.0358632 | + | 0.999357i | \(0.488582\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9853.96i | − | 0.928831i | −0.885618 | − | 0.464415i | \(-0.846265\pi\) | ||
0.885618 | − | 0.464415i | \(-0.153735\pi\) | |||||||
\(104\) | 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 | \(-0.734335\pi\) | ||||
−0.671465 | + | 0.741036i | \(0.734335\pi\) | |||||||
\(114\) | 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 | \(-0.903901\pi\) | ||
0.954772 | − | 0.297337i | \(-0.0960986\pi\) | |||||||
\(128\) | 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 | \(-0.458317\pi\) | ||||
0.130578 | + | 0.991438i | \(0.458317\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8650.79i | 0.447740i | 0.974619 | + | 0.223870i | \(0.0718691\pi\) | ||||
−0.974619 | + | 0.223870i | \(0.928131\pi\) | |||||||
\(140\) | 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 | \(-0.407720\pi\) | ||||
0.285863 | + | 0.958270i | \(0.407720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12765.6i | 0.559869i | 0.960019 | + | 0.279934i | \(0.0903127\pi\) | ||||
−0.960019 | + | 0.279934i | \(0.909687\pi\) | |||||||
\(152\) | −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 | \(0.0412865\pi\) | ||||
−0.991600 | + | 0.129342i | \(0.958713\pi\) | |||||||
\(164\) | −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 | \(-0.515872\pi\) | ||||
−0.0498420 | + | 0.998757i | \(0.515872\pi\) | |||||||
\(174\) | 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 | \(-0.410020\pi\) | ||||
0.278930 | + | 0.960311i | \(0.410020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25261.4i | 0.637898i | 0.947772 | + | 0.318949i | \(0.103330\pi\) | ||||
−0.947772 | + | 0.318949i | \(0.896670\pi\) | |||||||
\(200\) | −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 | \(0.0778577\pi\) | ||||
−0.970235 | + | 0.242166i | \(0.922142\pi\) | |||||||
\(212\) | −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 | \(-0.937855\pi\) | ||
0.981002 | − | 0.193996i | \(-0.0621448\pi\) | |||||||
\(224\) | −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 | \(-0.493235\pi\) | ||||
0.0212522 | + | 0.999774i | \(0.493235\pi\) | |||||||
\(234\) | 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 | \(-0.356525\pi\) | ||||
0.435632 | + | 0.900125i | \(0.356525\pi\) | |||||||
\(258\) | 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 | \(-0.488171\pi\) | ||||
0.0371537 | + | 0.999310i | \(0.488171\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 108113.i | 1.47211i | 0.676924 | + | 0.736053i | \(0.263312\pi\) | ||||
−0.676924 | + | 0.736053i | \(0.736688\pi\) | |||||||
\(272\) | −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 | \(-0.604399\pi\) | ||||
−0.322130 | + | 0.946696i | \(0.604399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26395.1i | 0.329572i | 0.986329 | + | 0.164786i | \(0.0526933\pi\) | ||||
−0.986329 | + | 0.164786i | \(0.947307\pi\) | |||||||
\(284\) | −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 | \(-0.775659\pi\) | ||||
−0.761748 | + | 0.647873i | \(0.775659\pi\) | |||||||
\(294\) | 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 | \(-0.907116\pi\) | ||
0.957726 | − | 0.287681i | \(-0.0928843\pi\) | |||||||
\(308\) | 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 | \(-0.704896\pi\) | ||||
−0.600160 | + | 0.799880i | \(0.704896\pi\) | |||||||
\(318\) | 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 | \(-0.822966\pi\) | ||
0.849284 | − | 0.527936i | \(-0.177034\pi\) | |||||||
\(332\) | −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 | \(-0.554851\pi\) | ||||
−0.171467 | + | 0.985190i | \(0.554851\pi\) | |||||||
\(354\) | 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 | \(-0.990629\pi\) | ||
0.999567 | − | 0.0294370i | \(-0.00937145\pi\) | |||||||
\(368\) | −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 | \(-0.828474\pi\) | ||
0.858291 | − | 0.513163i | \(-0.171526\pi\) | |||||||
\(380\) | 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 | \(-0.292700\pi\) | ||||
0.606182 | + | 0.795326i | \(0.292700\pi\) | |||||||
\(390\) | 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 | \(-0.715113\pi\) | ||||
−0.625518 | + | 0.780209i | \(0.715113\pi\) | |||||||
\(402\) | 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 | \(0.0139138\pi\) | ||||
−0.999045 | + | 0.0436976i | \(0.986086\pi\) | |||||||
\(440\) | 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 | \(-0.602164\pi\) | ||||
−0.315475 | + | 0.948934i | \(0.602164\pi\) | |||||||
\(450\) | 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 | \(-0.455920\pi\) | ||||
0.138038 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 47536.3i | 0.221750i | 0.993834 | + | 0.110875i | \(0.0353653\pi\) | ||||
−0.993834 | + | 0.110875i | \(0.964635\pi\) | |||||||
\(464\) | −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 | \(0.00199681\pi\) | ||||
−0.999980 | + | 0.00627313i | \(0.998003\pi\) | |||||||
\(488\) | 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 | \(0.175862\pi\) | ||||
−0.851223 | + | 0.524805i | \(0.824138\pi\) | |||||||
\(500\) | −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 | \(-0.364698\pi\) | ||||
0.412378 | + | 0.911013i | \(0.364698\pi\) | |||||||
\(510\) | 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 | \(-0.600472\pi\) | ||||
−0.310427 | + | 0.950597i | \(0.600472\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 231592.i | 0.846681i | 0.905971 | + | 0.423340i | \(0.139143\pi\) | ||||
−0.905971 | + | 0.423340i | \(0.860857\pi\) | |||||||
\(524\) | 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 | \(-0.672139\pi\) | ||
0.514813 | − | 0.857302i | \(-0.327861\pi\) | |||||||
\(548\) | 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 | \(-0.357052\pi\) | ||||
0.434141 | + | 0.900845i | \(0.357052\pi\) | |||||||
\(558\) | 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 | \(-0.727595\pi\) | ||||
−0.655625 | + | 0.755086i | \(0.727595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29210.9i | 0.0895928i | 0.998996 | + | 0.0447964i | \(0.0142639\pi\) | ||||
−0.998996 | + | 0.0447964i | \(0.985736\pi\) | |||||||
\(572\) | 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 | \(-0.266482\pi\) | ||||
0.669562 | + | 0.742756i | \(0.266482\pi\) | |||||||
\(594\) | 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 | \(0.200196\pi\) | ||||
−0.808655 | + | 0.588283i | \(0.799804\pi\) | |||||||
\(608\) | −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 | \(-0.583198\pi\) | ||||
−0.258409 | + | 0.966036i | \(0.583198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 619149.i | 1.61590i | 0.589252 | + | 0.807949i | \(0.299422\pi\) | ||||
−0.589252 | + | 0.807949i | \(0.700578\pi\) | |||||||
\(620\) | 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 | \(-0.873256\pi\) | ||
0.921769 | − | 0.387740i | \(-0.126744\pi\) | |||||||
\(632\) | 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 | \(-0.363198\pi\) | ||||
0.416666 | + | 0.909059i | \(0.363198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 552948.i | − | 1.33740i | −0.743531 | − | 0.668702i | \(-0.766850\pi\) | ||
0.743531 | − | 0.668702i | \(-0.233150\pi\) | |||||||
\(644\) | 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 | \(-0.265185\pi\) | ||||
0.672583 | + | 0.740022i | \(0.265185\pi\) | |||||||
\(654\) | 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 | \(-0.490422\pi\) | ||||
0.0300859 | + | 0.999547i | \(0.490422\pi\) | |||||||
\(678\) | 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 | \(0.113771\pi\) | ||||
−0.936801 | + | 0.349862i | \(0.886229\pi\) | |||||||
\(692\) | −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 | \(-0.557947\pi\) | ||||
−0.181041 | + | 0.983476i | \(0.557947\pi\) | |||||||
\(702\) | 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 | \(0.134656\pi\) | ||||
−0.911847 | + | 0.410529i | \(0.865344\pi\) | |||||||
\(728\) | 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 | \(0.0631112\pi\) | ||||
−0.980409 | + | 0.196973i | \(0.936889\pi\) | |||||||
\(740\) | 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 | \(-0.792310\pi\) | ||
0.794583 | − | 0.607156i | \(-0.207690\pi\) | |||||||
\(752\) | 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 | \(-0.730316\pi\) | ||||
−0.662057 | + | 0.749454i | \(0.730316\pi\) | |||||||
\(762\) | 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 | \(-0.234255\pi\) | ||||
0.741205 | + | 0.671279i | \(0.234255\pi\) | |||||||
\(774\) | 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 | \(0.322641\pi\) | ||||
−0.528803 | + | 0.848744i | \(0.677359\pi\) | |||||||
\(788\) | 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 | \(-0.476221\pi\) | ||||
0.0746356 | + | 0.997211i | \(0.476221\pi\) | |||||||
\(798\) | 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 | \(-0.448937\pi\) | ||||
0.159734 | + | 0.987160i | \(0.448937\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 577209.i | 0.877589i | 0.898587 | + | 0.438794i | \(0.144594\pi\) | ||||
−0.898587 | + | 0.438794i | \(0.855406\pi\) | |||||||
\(812\) | −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 | \(-0.316208\pi\) | ||||
0.545847 | + | 0.837885i | \(0.316208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 171095.i | 0.252602i | 0.991992 | + | 0.126301i | \(0.0403106\pi\) | ||||
−0.991992 | + | 0.126301i | \(0.959689\pi\) | |||||||
\(824\) | −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 | \(-0.780476\pi\) | ||||
−0.771465 | + | 0.636271i | \(0.780476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 401245.i | − | 0.543780i | −0.962328 | − | 0.271890i | \(-0.912351\pi\) | ||
0.962328 | − | 0.271890i | \(-0.0876487\pi\) | |||||||
\(860\) | 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 | \(-0.606654\pi\) | ||||
−0.328830 | + | 0.944389i | \(0.606654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 233561.i | 0.299557i | 0.988720 | + | 0.149778i | \(0.0478560\pi\) | ||||
−0.988720 | + | 0.149778i | \(0.952144\pi\) | |||||||
\(884\) | 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 | \(-0.914242\pi\) | ||
0.963926 | − | 0.266169i | \(-0.0857579\pi\) | |||||||
\(908\) | 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 | \(0.303979\pi\) | ||||
−0.577626 | + | 0.816301i | \(0.696021\pi\) | |||||||
\(920\) | 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 | \(-0.451540\pi\) | ||||
0.151656 | + | 0.988433i | \(0.451540\pi\) | |||||||
\(930\) | 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 | \(-0.423354\pi\) | ||||
0.238470 | + | 0.971150i | \(0.423354\pi\) | |||||||
\(942\) | 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 | \(-0.816204\pi\) | ||||
−0.837878 | + | 0.545857i | \(0.816204\pi\) | |||||||
\(954\) | 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 | \(0.302003\pi\) | ||||
−0.582682 | + | 0.812700i | \(0.697997\pi\) | |||||||
\(968\) | −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 | \(-0.347410\pi\) | ||||
0.461226 | + | 0.887283i | \(0.347410\pi\) | |||||||
\(978\) | 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 | \(-0.806504\pi\) | ||
0.820858 | − | 0.571133i | \(-0.193496\pi\) | |||||||
\(992\) | −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.e.163.3 | 22 | ||
3.2 | odd | 2 | 324.5.d.f.163.20 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.e.163.4 | 22 | ||
9.2 | odd | 6 | 36.5.f.a.31.10 | yes | 44 | ||
9.4 | even | 3 | 108.5.f.a.19.18 | 44 | |||
9.5 | odd | 6 | 36.5.f.a.7.5 | ✓ | 44 | ||
9.7 | even | 3 | 108.5.f.a.91.13 | 44 | |||
12.11 | even | 2 | 324.5.d.f.163.19 | 22 | |||
36.7 | odd | 6 | 108.5.f.a.91.18 | 44 | |||
36.11 | even | 6 | 36.5.f.a.31.5 | yes | 44 | ||
36.23 | even | 6 | 36.5.f.a.7.10 | yes | 44 | ||
36.31 | odd | 6 | 108.5.f.a.19.13 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.5 | ✓ | 44 | 9.5 | odd | 6 | ||
36.5.f.a.7.10 | yes | 44 | 36.23 | even | 6 | ||
36.5.f.a.31.5 | yes | 44 | 36.11 | even | 6 | ||
36.5.f.a.31.10 | yes | 44 | 9.2 | odd | 6 | ||
108.5.f.a.19.13 | 44 | 36.31 | odd | 6 | |||
108.5.f.a.19.18 | 44 | 9.4 | even | 3 | |||
108.5.f.a.91.13 | 44 | 9.7 | even | 3 | |||
108.5.f.a.91.18 | 44 | 36.7 | odd | 6 | |||
324.5.d.e.163.3 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.e.163.4 | 22 | 4.3 | odd | 2 | inner | ||
324.5.d.f.163.19 | 22 | 12.11 | even | 2 | |||
324.5.d.f.163.20 | 22 | 3.2 | odd | 2 |