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 | 163.10 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.f.163.9 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16626 | + | 3.82620i | −0.291566 | + | 0.956551i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −13.2797 | − | 8.92473i | −0.829979 | − | 0.557795i | ||||
\(5\) | −39.0789 | −1.56316 | −0.781578 | − | 0.623808i | \(-0.785585\pi\) | ||||
−0.781578 | + | 0.623808i | \(0.785585\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.2052i | 0.249086i | 0.992214 | + | 0.124543i | \(0.0397464\pi\) | ||||
−0.992214 | + | 0.124543i | \(0.960254\pi\) | |||||||
\(8\) | 49.6354 | − | 40.4021i | 0.775553 | − | 0.631282i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 45.5763 | − | 149.524i | 0.455763 | − | 1.49524i | ||||
\(11\) | − | 111.018i | − | 0.917506i | −0.888564 | − | 0.458753i | \(-0.848296\pi\) | ||
0.888564 | − | 0.458753i | \(-0.151704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 208.982 | 1.23658 | 0.618290 | − | 0.785950i | \(-0.287826\pi\) | ||||
0.618290 | + | 0.785950i | \(0.287826\pi\) | |||||||
\(14\) | −46.6996 | − | 14.2345i | −0.238263 | − | 0.0726250i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 96.6986 | + | 237.035i | 0.377729 | + | 0.925916i | ||||
\(17\) | 93.3790 | 0.323111 | 0.161555 | − | 0.986864i | \(-0.448349\pi\) | ||||
0.161555 | + | 0.986864i | \(0.448349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.8894i | 0.0744859i | 0.999306 | + | 0.0372429i | \(0.0118575\pi\) | ||||
−0.999306 | + | 0.0372429i | \(0.988142\pi\) | |||||||
\(20\) | 518.954 | + | 348.768i | 1.29739 | + | 0.871921i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 424.778 | + | 129.477i | 0.877641 | + | 0.267514i | ||||
\(23\) | − | 874.774i | − | 1.65364i | −0.562469 | − | 0.826819i | \(-0.690148\pi\) | ||
0.562469 | − | 0.826819i | \(-0.309852\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 902.160 | 1.44346 | ||||||||
\(26\) | −243.728 | + | 799.608i | −0.360545 | + | 1.18285i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 108.928 | − | 162.081i | 0.138939 | − | 0.206736i | ||||
\(29\) | −1301.62 | −1.54770 | −0.773851 | − | 0.633368i | \(-0.781672\pi\) | ||||
−0.773851 | + | 0.633368i | \(0.781672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 685.305i | 0.713117i | 0.934273 | + | 0.356558i | \(0.116050\pi\) | ||||
−0.934273 | + | 0.356558i | \(0.883950\pi\) | |||||||
\(32\) | −1019.72 | + | 93.5434i | −0.995819 | + | 0.0913509i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −108.905 | + | 357.287i | −0.0942081 | + | 0.309072i | ||||
\(35\) | − | 476.966i | − | 0.389360i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1760.25 | −1.28579 | −0.642897 | − | 0.765953i | \(-0.722268\pi\) | ||||
−0.642897 | + | 0.765953i | \(0.722268\pi\) | |||||||
\(38\) | −102.884 | − | 31.3601i | −0.0712495 | − | 0.0217175i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1939.70 | + | 1578.87i | −1.21231 | + | 0.986793i | ||||
\(41\) | 78.0843 | 0.0464511 | 0.0232255 | − | 0.999730i | \(-0.492606\pi\) | ||||
0.0232255 | + | 0.999730i | \(0.492606\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1622.88i | 0.877709i | 0.898558 | + | 0.438855i | \(0.144616\pi\) | ||||
−0.898558 | + | 0.438855i | \(0.855384\pi\) | |||||||
\(44\) | −990.807 | + | 1474.28i | −0.511780 | + | 0.761510i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3347.06 | + | 1020.22i | 1.58179 | + | 0.482144i | ||||
\(47\) | 2308.86i | 1.04521i | 0.852575 | + | 0.522604i | \(0.175039\pi\) | ||||
−0.852575 | + | 0.522604i | \(0.824961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2252.03 | 0.937956 | ||||||||
\(50\) | −1052.16 | + | 3451.85i | −0.420863 | + | 1.38074i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2775.21 | − | 1865.11i | −1.02634 | − | 0.689759i | ||||
\(53\) | −1313.48 | −0.467598 | −0.233799 | − | 0.972285i | \(-0.575116\pi\) | ||||
−0.233799 | + | 0.972285i | \(0.575116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4338.47i | 1.43420i | ||||||||
\(56\) | 493.116 | + | 605.810i | 0.157243 | + | 0.193179i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1518.03 | − | 4980.25i | 0.451257 | − | 1.48046i | ||||
\(59\) | 5563.78i | 1.59833i | 0.601113 | + | 0.799164i | \(0.294724\pi\) | ||||
−0.601113 | + | 0.799164i | \(0.705276\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2180.26 | 0.585933 | 0.292967 | − | 0.956123i | \(-0.405358\pi\) | ||||
0.292967 | + | 0.956123i | \(0.405358\pi\) | |||||||
\(62\) | −2622.12 | − | 799.247i | −0.682132 | − | 0.207921i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 831.345 | − | 4010.75i | 0.202965 | − | 0.979186i | ||||
\(65\) | −8166.79 | −1.93297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 246.040i | − | 0.0548096i | −0.999624 | − | 0.0274048i | \(-0.991276\pi\) | ||
0.999624 | − | 0.0274048i | \(-0.00872430\pi\) | |||||||
\(68\) | −1240.04 | − | 833.382i | −0.268175 | − | 0.180230i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1824.97 | + | 556.268i | 0.372443 | + | 0.113524i | ||||
\(71\) | 4608.15i | 0.914134i | 0.889432 | + | 0.457067i | \(0.151100\pi\) | ||||
−0.889432 | + | 0.457067i | \(0.848900\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2564.79 | 0.481290 | 0.240645 | − | 0.970613i | \(-0.422641\pi\) | ||||
0.240645 | + | 0.970613i | \(0.422641\pi\) | |||||||
\(74\) | 2052.92 | − | 6735.08i | 0.374894 | − | 1.22993i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 239.980 | − | 357.082i | 0.0415479 | − | 0.0618217i | ||||
\(77\) | 1355.00 | 0.228538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5180.32i | − | 0.830047i | −0.909811 | − | 0.415023i | \(-0.863773\pi\) | ||
0.909811 | − | 0.415023i | \(-0.136227\pi\) | |||||||
\(80\) | −3778.87 | − | 9263.05i | −0.590449 | − | 1.44735i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −91.0669 | + | 298.766i | −0.0135436 | + | 0.0444328i | ||||
\(83\) | 1873.35i | 0.271934i | 0.990713 | + | 0.135967i | \(0.0434141\pi\) | ||||
−0.990713 | + | 0.135967i | \(0.956586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3649.15 | −0.505072 | ||||||||
\(86\) | −6209.48 | − | 1892.71i | −0.839573 | − | 0.255910i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4485.37 | − | 5510.43i | −0.579205 | − | 0.711574i | ||||
\(89\) | −1167.17 | −0.147352 | −0.0736759 | − | 0.997282i | \(-0.523473\pi\) | ||||
−0.0736759 | + | 0.997282i | \(0.523473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2550.67i | 0.308015i | ||||||||
\(92\) | −7807.12 | + | 11616.7i | −0.922391 | + | 1.37248i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8834.19 | − | 2692.75i | −0.999795 | − | 0.304747i | ||||
\(95\) | − | 1050.81i | − | 0.116433i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5739.16 | −0.609965 | −0.304983 | − | 0.952358i | \(-0.598651\pi\) | ||||
−0.304983 | + | 0.952358i | \(0.598651\pi\) | |||||||
\(98\) | −2626.47 | + | 8616.73i | −0.273476 | + | 0.897203i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −11980.4 | − | 8051.53i | −1.19804 | − | 0.805153i | ||||
\(101\) | 15586.7 | 1.52796 | 0.763981 | − | 0.645238i | \(-0.223242\pi\) | ||||
0.763981 | + | 0.645238i | \(0.223242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11127.3i | 1.04885i | 0.851455 | + | 0.524427i | \(0.175720\pi\) | ||||
−0.851455 | + | 0.524427i | \(0.824280\pi\) | |||||||
\(104\) | 10372.9 | − | 8443.31i | 0.959034 | − | 0.780632i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1531.87 | − | 5025.65i | 0.136336 | − | 0.447281i | ||||
\(107\) | 4464.91i | 0.389983i | 0.980805 | + | 0.194991i | \(0.0624679\pi\) | ||||
−0.980805 | + | 0.194991i | \(0.937532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4736.05 | −0.398624 | −0.199312 | − | 0.979936i | \(-0.563871\pi\) | ||||
−0.199312 | + | 0.979936i | \(0.563871\pi\) | |||||||
\(110\) | −16599.9 | − | 5059.80i | −1.37189 | − | 0.418165i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2893.06 | + | 1180.23i | −0.230633 | + | 0.0940869i | ||||
\(113\) | −18346.1 | −1.43677 | −0.718385 | − | 0.695645i | \(-0.755119\pi\) | ||||
−0.718385 | + | 0.695645i | \(0.755119\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 34185.2i | 2.58489i | ||||||||
\(116\) | 17285.0 | + | 11616.6i | 1.28456 | + | 0.863301i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21288.2 | − | 6488.84i | −1.52888 | − | 0.466018i | ||||
\(119\) | 1139.71i | 0.0804823i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2315.96 | 0.158183 | ||||||||
\(122\) | −2542.76 | + | 8342.10i | −0.170838 | + | 0.560475i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6116.16 | − | 9100.62i | 0.397773 | − | 0.591872i | ||||
\(125\) | −10831.1 | −0.693190 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8169.42i | − | 0.506505i | −0.967400 | − | 0.253252i | \(-0.918500\pi\) | ||
0.967400 | − | 0.253252i | \(-0.0815003\pi\) | |||||||
\(128\) | 14376.4 | + | 7858.48i | 0.877463 | + | 0.479644i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9524.63 | − | 31247.8i | 0.563588 | − | 1.84898i | ||||
\(131\) | − | 10543.6i | − | 0.614392i | −0.951646 | − | 0.307196i | \(-0.900609\pi\) | ||
0.951646 | − | 0.307196i | \(-0.0993907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −328.191 | −0.0185534 | ||||||||
\(134\) | 941.399 | + | 286.948i | 0.0524281 | + | 0.0159806i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4634.90 | − | 3772.70i | 0.250589 | − | 0.203974i | ||||
\(137\) | 3225.71 | 0.171864 | 0.0859318 | − | 0.996301i | \(-0.472613\pi\) | ||||
0.0859318 | + | 0.996301i | \(0.472613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18794.3i | 0.972742i | 0.873752 | + | 0.486371i | \(0.161680\pi\) | ||||
−0.873752 | + | 0.486371i | \(0.838320\pi\) | |||||||
\(140\) | −4256.79 | + | 6333.94i | −0.217183 | + | 0.323160i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17631.7 | − | 5374.32i | −0.874415 | − | 0.266530i | ||||
\(143\) | − | 23200.8i | − | 1.13457i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 50865.8 | 2.41930 | ||||||||
\(146\) | −2991.22 | + | 9813.41i | −0.140328 | + | 0.460378i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23375.5 | + | 15709.8i | 1.06718 | + | 0.717210i | ||||
\(149\) | −7650.25 | −0.344590 | −0.172295 | − | 0.985045i | \(-0.555118\pi\) | ||||
−0.172295 | + | 0.985045i | \(0.555118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1125.80i | 0.0493751i | 0.999695 | + | 0.0246876i | \(0.00785910\pi\) | ||||
−0.999695 | + | 0.0246876i | \(0.992141\pi\) | |||||||
\(152\) | 1086.39 | + | 1334.67i | 0.0470216 | + | 0.0577677i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1580.29 | + | 5184.51i | −0.0666338 | + | 0.218608i | ||||
\(155\) | − | 26781.0i | − | 1.11471i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3511.62 | −0.142465 | −0.0712326 | − | 0.997460i | \(-0.522693\pi\) | ||||
−0.0712326 | + | 0.997460i | \(0.522693\pi\) | |||||||
\(158\) | 19821.0 | + | 6041.62i | 0.793982 | + | 0.242013i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 39849.5 | − | 3655.57i | 1.55662 | − | 0.142796i | ||||
\(161\) | 10676.8 | 0.411898 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 41947.9i | 1.57883i | 0.613861 | + | 0.789414i | \(0.289615\pi\) | ||||
−0.613861 | + | 0.789414i | \(0.710385\pi\) | |||||||
\(164\) | −1036.93 | − | 696.881i | −0.0385534 | − | 0.0259102i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7167.83 | − | 2184.83i | −0.260119 | − | 0.0792868i | ||||
\(167\) | 6813.40i | 0.244304i | 0.992511 | + | 0.122152i | \(0.0389796\pi\) | ||||
−0.992511 | + | 0.122152i | \(0.961020\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15112.5 | 0.529131 | ||||||||
\(170\) | 4255.87 | − | 13962.4i | 0.147262 | − | 0.483127i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14483.8 | − | 21551.3i | 0.489582 | − | 0.728480i | ||||
\(173\) | 15748.3 | 0.526189 | 0.263095 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263095 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11011.0i | 0.359544i | ||||||||
\(176\) | 26315.2 | − | 10735.3i | 0.849534 | − | 0.346568i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1361.23 | − | 4465.85i | 0.0429628 | − | 0.140950i | ||||
\(179\) | 22497.6i | 0.702151i | 0.936347 | + | 0.351075i | \(0.114184\pi\) | ||||
−0.936347 | + | 0.351075i | \(0.885816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21847.2 | −0.666867 | −0.333434 | − | 0.942774i | \(-0.608207\pi\) | ||||
−0.333434 | + | 0.942774i | \(0.608207\pi\) | |||||||
\(182\) | −9759.38 | − | 2974.75i | −0.294632 | − | 0.0898066i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −35342.7 | − | 43419.8i | −1.04391 | − | 1.28248i | ||||
\(185\) | 68788.7 | 2.00990 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 10366.8i | − | 0.296456i | ||||||
\(188\) | 20606.0 | − | 30660.9i | 0.583012 | − | 0.867500i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4020.60 | + | 1225.52i | 0.111374 | + | 0.0339479i | ||||
\(191\) | − | 18685.5i | − | 0.512199i | −0.966650 | − | 0.256099i | \(-0.917563\pi\) | ||
0.966650 | − | 0.256099i | \(-0.0824375\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 46099.4 | 1.23760 | 0.618800 | − | 0.785548i | \(-0.287619\pi\) | ||||
0.618800 | + | 0.785548i | \(0.287619\pi\) | |||||||
\(194\) | 6693.38 | − | 21959.2i | 0.177845 | − | 0.583462i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −29906.2 | − | 20098.8i | −0.778484 | − | 0.523188i | ||||
\(197\) | 15934.7 | 0.410592 | 0.205296 | − | 0.978700i | \(-0.434184\pi\) | ||||
0.205296 | + | 0.978700i | \(0.434184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 73733.8i | 1.86192i | 0.365124 | + | 0.930959i | \(0.381026\pi\) | ||||
−0.365124 | + | 0.930959i | \(0.618974\pi\) | |||||||
\(200\) | 44779.1 | − | 36449.1i | 1.11948 | − | 0.911228i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18178.3 | + | 59638.1i | −0.445502 | + | 1.46157i | ||||
\(203\) | − | 15886.5i | − | 0.385511i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3051.45 | −0.0726103 | ||||||||
\(206\) | −42575.3 | − | 12977.4i | −1.00328 | − | 0.305810i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20208.3 | + | 49536.0i | 0.467092 | + | 1.14497i | ||||
\(209\) | 2985.21 | 0.0683412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17818.4i | 0.400224i | 0.979773 | + | 0.200112i | \(0.0641307\pi\) | ||||
−0.979773 | + | 0.200112i | \(0.935869\pi\) | |||||||
\(212\) | 17442.6 | + | 11722.5i | 0.388096 | + | 0.260824i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17083.7 | − | 5207.26i | −0.373038 | − | 0.113706i | ||||
\(215\) | − | 63420.5i | − | 1.37200i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8364.29 | −0.177627 | ||||||||
\(218\) | 5523.49 | − | 18121.1i | 0.116225 | − | 0.381304i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 38719.6 | − | 57613.4i | 0.799993 | − | 1.19036i | ||||
\(221\) | 19514.5 | 0.399552 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 67381.1i | 1.35497i | 0.735538 | + | 0.677483i | \(0.236929\pi\) | ||||
−0.735538 | + | 0.677483i | \(0.763071\pi\) | |||||||
\(224\) | −1141.72 | − | 12445.9i | −0.0227542 | − | 0.248044i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21396.4 | − | 70196.0i | 0.418914 | − | 1.37434i | ||||
\(227\) | 62794.3i | 1.21862i | 0.792932 | + | 0.609310i | \(0.208554\pi\) | ||||
−0.792932 | + | 0.609310i | \(0.791446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −40926.3 | −0.780426 | −0.390213 | − | 0.920725i | \(-0.627599\pi\) | ||||
−0.390213 | + | 0.920725i | \(0.627599\pi\) | |||||||
\(230\) | −130800. | − | 39869.0i | −2.47258 | − | 0.753667i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −64606.3 | + | 52588.0i | −1.20033 | + | 0.977037i | ||||
\(233\) | 79254.5 | 1.45986 | 0.729932 | − | 0.683520i | \(-0.239552\pi\) | ||||
0.729932 | + | 0.683520i | \(0.239552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 90227.9i | − | 1.63382i | ||||||
\(236\) | 49655.2 | − | 73885.1i | 0.891540 | − | 1.32658i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4360.76 | − | 1329.20i | −0.0769854 | − | 0.0234659i | ||||
\(239\) | 45131.1i | 0.790096i | 0.918661 | + | 0.395048i | \(0.129272\pi\) | ||||
−0.918661 | + | 0.395048i | \(0.870728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 75653.5 | 1.30255 | 0.651276 | − | 0.758841i | \(-0.274234\pi\) | ||||
0.651276 | + | 0.758841i | \(0.274234\pi\) | |||||||
\(242\) | −2701.02 | + | 8861.32i | −0.0461208 | + | 0.151310i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −28953.1 | − | 19458.2i | −0.486312 | − | 0.326831i | ||||
\(245\) | −88007.0 | −1.46617 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5619.40i | 0.0921078i | ||||||||
\(248\) | 27687.7 | + | 34015.4i | 0.450178 | + | 0.553060i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12631.9 | − | 41442.0i | 0.202111 | − | 0.663072i | ||||
\(251\) | 78270.9i | 1.24238i | 0.783662 | + | 0.621188i | \(0.213350\pi\) | ||||
−0.783662 | + | 0.621188i | \(0.786650\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −97115.9 | −1.51722 | ||||||||
\(254\) | 31257.8 | + | 9527.70i | 0.484498 | + | 0.147680i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −46834.8 | + | 45841.8i | −0.714642 | + | 0.699490i | ||||
\(257\) | −23012.7 | −0.348418 | −0.174209 | − | 0.984709i | \(-0.555737\pi\) | ||||
−0.174209 | + | 0.984709i | \(0.555737\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 21484.2i | − | 0.320273i | ||||||
\(260\) | 108452. | + | 72886.4i | 1.60432 | + | 1.07820i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 40341.9 | + | 12296.6i | 0.587697 | + | 0.179136i | ||||
\(263\) | 86877.1i | 1.25601i | 0.778209 | + | 0.628006i | \(0.216129\pi\) | ||||
−0.778209 | + | 0.628006i | \(0.783871\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 51329.5 | 0.730929 | ||||||||
\(266\) | 382.757 | − | 1255.72i | 0.00540953 | − | 0.0177472i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2195.84 | + | 3267.33i | −0.0305725 | + | 0.0454908i | ||||
\(269\) | −54083.3 | −0.747409 | −0.373705 | − | 0.927548i | \(-0.621913\pi\) | ||||
−0.373705 | + | 0.927548i | \(0.621913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 47957.3i | − | 0.653004i | −0.945197 | − | 0.326502i | \(-0.894130\pi\) | ||
0.945197 | − | 0.326502i | \(-0.105870\pi\) | |||||||
\(272\) | 9029.61 | + | 22134.0i | 0.122048 | + | 0.299173i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3762.03 | + | 12342.2i | −0.0501096 | + | 0.164396i | ||||
\(275\) | − | 100156.i | − | 1.32438i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −73723.5 | −0.960830 | −0.480415 | − | 0.877041i | \(-0.659514\pi\) | ||||
−0.480415 | + | 0.877041i | \(0.659514\pi\) | |||||||
\(278\) | −71911.0 | − | 21919.2i | −0.930477 | − | 0.283618i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19270.4 | − | 23674.4i | −0.245796 | − | 0.301969i | ||||
\(281\) | 56123.9 | 0.710780 | 0.355390 | − | 0.934718i | \(-0.384348\pi\) | ||||
0.355390 | + | 0.934718i | \(0.384348\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 152766.i | − | 1.90746i | −0.300666 | − | 0.953730i | \(-0.597209\pi\) | ||
0.300666 | − | 0.953730i | \(-0.402791\pi\) | |||||||
\(284\) | 41126.5 | − | 61194.6i | 0.509900 | − | 0.758711i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 88771.0 | + | 27058.3i | 1.08527 | + | 0.330802i | ||||
\(287\) | 953.034i | 0.0115703i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −74801.4 | −0.895600 | ||||||||
\(290\) | −59322.9 | + | 194623.i | −0.705385 | + | 2.31418i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −34059.6 | − | 22890.1i | −0.399460 | − | 0.268461i | ||||
\(293\) | −38840.3 | −0.452426 | −0.226213 | − | 0.974078i | \(-0.572634\pi\) | ||||
−0.226213 | + | 0.974078i | \(0.572634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 217426.i | − | 2.49844i | ||||||
\(296\) | −87370.8 | + | 71117.8i | −0.997201 | + | 0.811699i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8922.21 | − | 29271.4i | 0.100471 | − | 0.329618i | ||||
\(299\) | − | 182812.i | − | 2.04486i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19807.6 | −0.218625 | ||||||||
\(302\) | −4307.55 | − | 1312.98i | −0.0472298 | − | 0.0143961i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6373.72 | + | 2600.17i | −0.0689677 | + | 0.0281354i | ||||
\(305\) | −85202.0 | −0.915905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 457.528i | − | 0.00485446i | −0.999997 | − | 0.00242723i | \(-0.999227\pi\) | ||
0.999997 | − | 0.00242723i | \(-0.000772612\pi\) | |||||||
\(308\) | −17993.9 | − | 12093.0i | −0.189681 | − | 0.127477i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 102469. | + | 31233.7i | 1.06628 | + | 0.325012i | ||||
\(311\) | − | 10722.3i | − | 0.110858i | −0.998463 | − | 0.0554292i | \(-0.982347\pi\) | ||
0.998463 | − | 0.0554292i | \(-0.0176527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17952.2 | 0.183244 | 0.0916218 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916218 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(314\) | 4095.48 | − | 13436.2i | 0.0415380 | − | 0.136275i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −46232.9 | + | 68792.9i | −0.462996 | + | 0.688921i | ||||
\(317\) | −61371.8 | −0.610732 | −0.305366 | − | 0.952235i | \(-0.598779\pi\) | ||||
−0.305366 | + | 0.952235i | \(0.598779\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 144503.i | 1.42003i | ||||||||
\(320\) | −32488.0 | + | 156735.i | −0.317266 | + | 1.53062i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12452.0 | + | 40851.6i | −0.120095 | + | 0.394001i | ||||
\(323\) | 2510.90i | 0.0240672i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 188535. | 1.78495 | ||||||||
\(326\) | −160501. | − | 48922.3i | −1.51023 | − | 0.460333i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3875.74 | − | 3154.77i | 0.0360253 | − | 0.0293237i | ||||
\(329\) | −28180.2 | −0.260347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 185899.i | 1.69676i | 0.529389 | + | 0.848379i | \(0.322421\pi\) | ||||
−0.529389 | + | 0.848379i | \(0.677579\pi\) | |||||||
\(332\) | 16719.2 | − | 24877.5i | 0.151684 | − | 0.225700i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26069.4 | − | 7946.22i | −0.233689 | − | 0.0712308i | ||||
\(335\) | 9614.98i | 0.0856759i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −147998. | −1.30315 | −0.651576 | − | 0.758584i | \(-0.725892\pi\) | ||||
−0.651576 | + | 0.758584i | \(0.725892\pi\) | |||||||
\(338\) | −17625.2 | + | 57823.6i | −0.154277 | + | 0.506141i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 48459.4 | + | 32567.6i | 0.419199 | + | 0.281727i | ||||
\(341\) | 76081.3 | 0.654289 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56791.2i | 0.482717i | ||||||||
\(344\) | 65567.9 | + | 80552.5i | 0.554082 | + | 0.680710i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18366.7 | + | 60256.2i | −0.153419 | + | 0.503326i | ||||
\(347\) | 144980.i | 1.20406i | 0.798472 | + | 0.602031i | \(0.205642\pi\) | ||||
−0.798472 | + | 0.602031i | \(0.794358\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −178952. | −1.46921 | −0.734606 | − | 0.678494i | \(-0.762633\pi\) | ||||
−0.734606 | + | 0.678494i | \(0.762633\pi\) | |||||||
\(350\) | −42130.5 | − | 12841.8i | −0.343922 | − | 0.104831i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10385.0 | + | 113207.i | 0.0838150 | + | 0.913670i | ||||
\(353\) | 26395.4 | 0.211826 | 0.105913 | − | 0.994375i | \(-0.466224\pi\) | ||||
0.105913 | + | 0.994375i | \(0.466224\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 180081.i | − | 1.42893i | ||||||
\(356\) | 15499.7 | + | 10416.7i | 0.122299 | + | 0.0821922i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −86080.4 | − | 26238.2i | −0.671643 | − | 0.204723i | ||||
\(359\) | − | 181364.i | − | 1.40722i | −0.710587 | − | 0.703609i | \(-0.751571\pi\) | ||
0.710587 | − | 0.703609i | \(-0.248429\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 129598. | 0.994452 | ||||||||
\(362\) | 25479.6 | − | 83592.0i | 0.194436 | − | 0.637892i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 22764.0 | − | 33872.0i | 0.171809 | − | 0.255646i | ||||
\(365\) | −100229. | −0.752331 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 209000.i | − | 1.55173i | −0.630901 | − | 0.775863i | \(-0.717315\pi\) | ||
0.630901 | − | 0.775863i | \(-0.282685\pi\) | |||||||
\(368\) | 207352. | − | 84589.4i | 1.53113 | − | 0.624626i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −80225.8 | + | 263199.i | −0.586017 | + | 1.92257i | ||||
\(371\) | − | 16031.3i | − | 0.116472i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −76595.9 | −0.550539 | −0.275269 | − | 0.961367i | \(-0.588767\pi\) | ||||
−0.275269 | + | 0.961367i | \(0.588767\pi\) | |||||||
\(374\) | 39665.4 | + | 12090.4i | 0.283575 | + | 0.0864365i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 93282.9 | + | 114601.i | 0.659822 | + | 0.810614i | ||||
\(377\) | −272015. | −1.91386 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 232118.i | − | 1.61596i | −0.589211 | − | 0.807979i | \(-0.700561\pi\) | ||
0.589211 | − | 0.807979i | \(-0.299439\pi\) | |||||||
\(380\) | −9378.17 | + | 13954.4i | −0.0649458 | + | 0.0966369i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 71494.6 | + | 21792.3i | 0.489944 | + | 0.149340i | ||||
\(383\) | 85585.3i | 0.583447i | 0.956503 | + | 0.291724i | \(0.0942288\pi\) | ||||
−0.956503 | + | 0.291724i | \(0.905771\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −52951.9 | −0.357240 | ||||||||
\(386\) | −53764.1 | + | 176386.i | −0.360842 | + | 1.18383i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 76214.1 | + | 51220.4i | 0.506258 | + | 0.340236i | ||||
\(389\) | 121738. | 0.804504 | 0.402252 | − | 0.915529i | \(-0.368228\pi\) | ||||
0.402252 | + | 0.915529i | \(0.368228\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 81685.5i | − | 0.534308i | ||||||
\(392\) | 111781. | − | 90986.8i | 0.727435 | − | 0.592115i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18584.0 | + | 60969.2i | −0.119715 | + | 0.392752i | ||||
\(395\) | 202441.i | 1.29749i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −71690.8 | −0.454865 | −0.227432 | − | 0.973794i | \(-0.573033\pi\) | ||||
−0.227432 | + | 0.973794i | \(0.573033\pi\) | |||||||
\(398\) | −282120. | − | 85993.1i | −1.78102 | − | 0.542872i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 87237.5 | + | 213843.i | 0.545235 | + | 1.33652i | ||||
\(401\) | −86280.5 | −0.536567 | −0.268283 | − | 0.963340i | \(-0.586456\pi\) | ||||
−0.268283 | + | 0.963340i | \(0.586456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 143217.i | 0.881826i | ||||||||
\(404\) | −206987. | − | 139107.i | −1.26818 | − | 0.852291i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 60785.0 | + | 18527.9i | 0.368761 | + | 0.112402i | ||||
\(407\) | 195420.i | 1.17972i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 230461. | 1.37769 | 0.688844 | − | 0.724910i | \(-0.258118\pi\) | ||||
0.688844 | + | 0.724910i | \(0.258118\pi\) | |||||||
\(410\) | 3558.79 | − | 11675.5i | 0.0211707 | − | 0.0694554i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 99308.0 | − | 147767.i | 0.585046 | − | 0.870526i | ||||
\(413\) | −67907.1 | −0.398121 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 73208.6i | − | 0.425075i | ||||||
\(416\) | −213103. | + | 19548.9i | −1.23141 | + | 0.112963i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3481.55 | + | 11422.0i | −0.0199260 | + | 0.0653718i | ||||
\(419\) | 55624.6i | 0.316839i | 0.987372 | + | 0.158420i | \(0.0506399\pi\) | ||||
−0.987372 | + | 0.158420i | \(0.949360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 140971. | 0.795366 | 0.397683 | − | 0.917523i | \(-0.369814\pi\) | ||||
0.397683 | + | 0.917523i | \(0.369814\pi\) | |||||||
\(422\) | −68176.8 | − | 20781.0i | −0.382835 | − | 0.116692i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −65195.3 | + | 53067.4i | −0.362647 | + | 0.295186i | ||||
\(425\) | 84242.8 | 0.466396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 26610.5i | 0.145948i | ||||||||
\(428\) | 39848.1 | − | 59292.5i | 0.217530 | − | 0.323677i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 242660. | + | 73965.1i | 1.31238 | + | 0.400027i | ||||
\(431\) | 191015.i | 1.02828i | 0.857705 | + | 0.514142i | \(0.171889\pi\) | ||||
−0.857705 | + | 0.514142i | \(0.828111\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 48243.4 | 0.257313 | 0.128657 | − | 0.991689i | \(-0.458933\pi\) | ||||
0.128657 | + | 0.991689i | \(0.458933\pi\) | |||||||
\(434\) | 9754.97 | − | 32003.5i | 0.0517901 | − | 0.169909i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 62893.1 | + | 42268.0i | 0.330849 | + | 0.222351i | ||||
\(437\) | 23522.1 | 0.123173 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 262210.i | − | 1.36057i | −0.732948 | − | 0.680285i | \(-0.761856\pi\) | ||
0.732948 | − | 0.680285i | \(-0.238144\pi\) | |||||||
\(440\) | 175283. | + | 215342.i | 0.905388 | + | 1.11230i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22759.1 | + | 74666.6i | −0.116496 | + | 0.382192i | ||||
\(443\) | 90983.0i | 0.463610i | 0.972762 | + | 0.231805i | \(0.0744631\pi\) | ||||
−0.972762 | + | 0.231805i | \(0.925537\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45611.9 | 0.230334 | ||||||||
\(446\) | −257814. | − | 78584.2i | −1.29609 | − | 0.395062i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 48952.0 | + | 10146.7i | 0.243901 | + | 0.0505557i | ||||
\(449\) | 283350. | 1.40550 | 0.702748 | − | 0.711438i | \(-0.251956\pi\) | ||||
0.702748 | + | 0.711438i | \(0.251956\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 8668.77i | − | 0.0426191i | ||||||
\(452\) | 243630. | + | 163734.i | 1.19249 | + | 0.801424i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −240264. | − | 73234.7i | −1.16567 | − | 0.355308i | ||||
\(455\) | − | 99677.3i | − | 0.481475i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 198453. | 0.950224 | 0.475112 | − | 0.879925i | \(-0.342407\pi\) | ||||
0.475112 | + | 0.879925i | \(0.342407\pi\) | |||||||
\(458\) | 47730.9 | − | 156592.i | 0.227546 | − | 0.746517i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 305094. | − | 453968.i | 1.44184 | − | 2.14541i | ||||
\(461\) | −208695. | −0.981996 | −0.490998 | − | 0.871161i | \(-0.663368\pi\) | ||||
−0.490998 | + | 0.871161i | \(0.663368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 26197.8i | − | 0.122209i | −0.998131 | − | 0.0611044i | \(-0.980538\pi\) | ||
0.998131 | − | 0.0611044i | \(-0.0194622\pi\) | |||||||
\(464\) | −125865. | − | 308528.i | −0.584612 | − | 1.43304i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −92431.7 | + | 303244.i | −0.425647 | + | 1.39643i | ||||
\(467\) | 96607.8i | 0.442974i | 0.975163 | + | 0.221487i | \(0.0710911\pi\) | ||||
−0.975163 | + | 0.221487i | \(0.928909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3002.97 | 0.0136523 | ||||||||
\(470\) | 345230. | + | 105230.i | 1.56283 | + | 0.476367i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 224788. | + | 276160.i | 1.00900 | + | 1.23959i | ||||
\(473\) | 180170. | 0.805303 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24258.5i | 0.107517i | ||||||||
\(476\) | 10171.6 | − | 15135.0i | 0.0448926 | − | 0.0667986i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −172681. | − | 52634.7i | −0.755767 | − | 0.230365i | ||||
\(479\) | 34253.4i | 0.149291i | 0.997210 | + | 0.0746453i | \(0.0237825\pi\) | ||||
−0.997210 | + | 0.0746453i | \(0.976218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −367861. | −1.58999 | ||||||||
\(482\) | −88232.0 | + | 289466.i | −0.379780 | + | 1.24596i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −30755.1 | − | 20669.3i | −0.131288 | − | 0.0882337i | ||||
\(485\) | 224280. | 0.953470 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 69521.4i | − | 0.293130i | −0.989201 | − | 0.146565i | \(-0.953178\pi\) | ||
0.989201 | − | 0.146565i | \(-0.0468218\pi\) | |||||||
\(488\) | 108218. | − | 88086.9i | 0.454422 | − | 0.369889i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 102639. | − | 336732.i | 0.427486 | − | 1.40247i | ||||
\(491\) | − | 201271.i | − | 0.834867i | −0.908707 | − | 0.417433i | \(-0.862930\pi\) | ||
0.908707 | − | 0.417433i | \(-0.137070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −121544. | −0.500079 | ||||||||
\(494\) | −21501.0 | − | 6553.71i | −0.0881057 | − | 0.0268555i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −162441. | + | 66268.0i | −0.660286 | + | 0.269365i | ||||
\(497\) | −56243.4 | −0.227698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 54098.6i | 0.217263i | 0.994082 | + | 0.108631i | \(0.0346468\pi\) | ||||
−0.994082 | + | 0.108631i | \(0.965353\pi\) | |||||||
\(500\) | 143833. | + | 96664.6i | 0.575333 | + | 0.386658i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −299480. | − | 91284.6i | −1.18840 | − | 0.362235i | ||||
\(503\) | − | 239548.i | − | 0.946795i | −0.880849 | − | 0.473397i | \(-0.843027\pi\) | ||
0.880849 | − | 0.473397i | \(-0.156973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −609113. | −2.38844 | ||||||||
\(506\) | 113263. | − | 371585.i | 0.442370 | − | 1.45130i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −72909.8 | + | 108487.i | −0.282526 | + | 0.420388i | ||||
\(509\) | 115476. | 0.445714 | 0.222857 | − | 0.974851i | \(-0.428462\pi\) | ||||
0.222857 | + | 0.974851i | \(0.428462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31303.8i | 0.119882i | ||||||||
\(512\) | −120778. | − | 232663.i | −0.460733 | − | 0.887539i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26838.8 | − | 88051.1i | 0.101587 | − | 0.333279i | ||||
\(515\) | − | 434842.i | − | 1.63952i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 256326. | 0.958985 | ||||||||
\(518\) | 82203.0 | + | 25056.3i | 0.306357 | + | 0.0933807i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −405362. | + | 329955.i | −1.49912 | + | 1.22025i | ||||
\(521\) | 217267. | 0.800420 | 0.400210 | − | 0.916424i | \(-0.368937\pi\) | ||||
0.400210 | + | 0.916424i | \(0.368937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39683.4i | 0.145079i | 0.997366 | + | 0.0725397i | \(0.0231104\pi\) | ||||
−0.997366 | + | 0.0725397i | \(0.976890\pi\) | |||||||
\(524\) | −94098.5 | + | 140015.i | −0.342705 | + | 0.509932i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −332409. | − | 101322.i | −1.20144 | − | 0.366210i | ||||
\(527\) | 63993.1i | 0.230416i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −485389. | −1.73452 | ||||||||
\(530\) | −59863.7 | + | 196397.i | −0.213114 | + | 0.699170i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4358.26 | + | 2929.01i | 0.0153989 | + | 0.0103490i | ||||
\(533\) | 16318.2 | 0.0574405 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 174484.i | − | 0.609603i | ||||||
\(536\) | −9940.53 | − | 12212.3i | −0.0346003 | − | 0.0425077i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 63075.4 | − | 206934.i | 0.217919 | − | 0.714935i | ||||
\(539\) | − | 250017.i | − | 0.860580i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −194992. | −0.666228 | −0.333114 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333114 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(542\) | 183494. | + | 55930.8i | 0.624631 | + | 0.190394i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −95220.3 | + | 8734.98i | −0.321760 | + | 0.0295165i | ||||
\(545\) | 185080. | 0.623111 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 94267.3i | − | 0.315055i | −0.987515 | − | 0.157527i | \(-0.949648\pi\) | ||
0.987515 | − | 0.157527i | \(-0.0503523\pi\) | |||||||
\(548\) | −42836.3 | − | 28788.5i | −0.142643 | − | 0.0958647i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 383218. | + | 116809.i | 1.26684 | + | 0.386144i | ||||
\(551\) | − | 34999.7i | − | 0.115282i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 63226.9 | 0.206753 | ||||||||
\(554\) | 85981.1 | − | 282081.i | 0.280145 | − | 0.919083i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 167734. | − | 249582.i | 0.542591 | − | 0.807355i | ||||
\(557\) | −563587. | −1.81656 | −0.908282 | − | 0.418358i | \(-0.862606\pi\) | ||||
−0.908282 | + | 0.418358i | \(0.862606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 339154.i | 1.08536i | ||||||||
\(560\) | 113057. | − | 46121.9i | 0.360515 | − | 0.147072i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −65455.3 | + | 214741.i | −0.207239 | + | 0.679897i | ||||
\(563\) | − | 627590.i | − | 1.97997i | −0.141165 | − | 0.989986i | \(-0.545085\pi\) | ||
0.141165 | − | 0.989986i | \(-0.454915\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 716946. | 2.24590 | ||||||||
\(566\) | 584516. | + | 178166.i | 1.82458 | + | 0.556150i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 186179. | + | 228727.i | 0.577077 | + | 0.708959i | ||||
\(569\) | −77719.7 | −0.240053 | −0.120026 | − | 0.992771i | \(-0.538298\pi\) | ||||
−0.120026 | + | 0.992771i | \(0.538298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 318806.i | − | 0.977811i | −0.872337 | − | 0.488905i | \(-0.837396\pi\) | ||
0.872337 | − | 0.488905i | \(-0.162604\pi\) | |||||||
\(572\) | −207061. | + | 308099.i | −0.632858 | + | 0.941669i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3646.50 | − | 1111.49i | −0.0110676 | − | 0.00337351i | ||||
\(575\) | − | 789186.i | − | 2.38695i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40053.7 | 0.120307 | 0.0601534 | − | 0.998189i | \(-0.480841\pi\) | ||||
0.0601534 | + | 0.998189i | \(0.480841\pi\) | |||||||
\(578\) | 87238.1 | − | 286205.i | 0.261126 | − | 0.856686i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −675480. | − | 453963.i | −2.00797 | − | 1.34947i | ||||
\(581\) | −22864.7 | −0.0677349 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 145821.i | 0.429024i | ||||||||
\(584\) | 127304. | − | 103623.i | 0.373266 | − | 0.303830i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45298.0 | − | 148611.i | 0.131912 | − | 0.432768i | ||||
\(587\) | 13734.6i | 0.0398601i | 0.999801 | + | 0.0199301i | \(0.00634436\pi\) | ||||
−0.999801 | + | 0.0199301i | \(0.993656\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18427.4 | −0.0531171 | ||||||||
\(590\) | 831917. | + | 253577.i | 2.38988 | + | 0.728459i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −170214. | − | 417240.i | −0.485681 | − | 1.19054i | ||||
\(593\) | 537582. | 1.52875 | 0.764373 | − | 0.644775i | \(-0.223049\pi\) | ||||
0.764373 | + | 0.644775i | \(0.223049\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 44538.6i | − | 0.125806i | ||||||
\(596\) | 101593. | + | 68276.4i | 0.286003 | + | 0.192211i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 699476. | + | 213207.i | 1.95601 | + | 0.596210i | ||||
\(599\) | 455415.i | 1.26927i | 0.772812 | + | 0.634635i | \(0.218849\pi\) | ||||
−0.772812 | + | 0.634635i | \(0.781151\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −237993. | −0.658892 | −0.329446 | − | 0.944174i | \(-0.606862\pi\) | ||||
−0.329446 | + | 0.944174i | \(0.606862\pi\) | |||||||
\(602\) | 23100.9 | − | 75788.0i | 0.0637436 | − | 0.209126i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10047.5 | − | 14950.3i | 0.0275412 | − | 0.0409803i | ||||
\(605\) | −90505.0 | −0.247265 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 595989.i | 1.61756i | 0.588109 | + | 0.808781i | \(0.299873\pi\) | ||||
−0.588109 | + | 0.808781i | \(0.700127\pi\) | |||||||
\(608\) | −2515.32 | − | 27419.6i | −0.00680435 | − | 0.0741744i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 99368.1 | − | 326000.i | 0.267047 | − | 0.876109i | ||||
\(611\) | 482511.i | 1.29248i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 547275. | 1.45641 | 0.728206 | − | 0.685358i | \(-0.240354\pi\) | ||||
0.728206 | + | 0.685358i | \(0.240354\pi\) | |||||||
\(614\) | 1750.60 | + | 533.599i | 0.00464354 | + | 0.00141540i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 67256.0 | − | 54744.8i | 0.177243 | − | 0.144272i | ||||
\(617\) | 518155. | 1.36110 | 0.680549 | − | 0.732703i | \(-0.261741\pi\) | ||||
0.680549 | + | 0.732703i | \(0.261741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 204231.i | − | 0.533016i | −0.963833 | − | 0.266508i | \(-0.914130\pi\) | ||
0.963833 | − | 0.266508i | \(-0.0858698\pi\) | |||||||
\(620\) | −239013. | + | 355642.i | −0.621781 | + | 0.925187i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 41025.8 | + | 12505.1i | 0.106042 | + | 0.0323226i | ||||
\(623\) | − | 14245.6i | − | 0.0367033i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −140583. | −0.359891 | ||||||||
\(626\) | −20937.0 | + | 68688.8i | −0.0534276 | + | 0.175282i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 46633.1 | + | 31340.3i | 0.118243 | + | 0.0794664i | ||||
\(629\) | −164370. | −0.415454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 177036.i | − | 0.444633i | −0.974975 | − | 0.222317i | \(-0.928638\pi\) | ||
0.974975 | − | 0.222317i | \(-0.0713618\pi\) | |||||||
\(632\) | −209296. | − | 257127.i | −0.523994 | − | 0.643745i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 71575.8 | − | 234821.i | 0.178069 | − | 0.584196i | ||||
\(635\) | 319252.i | 0.791746i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 470635. | 1.15986 | ||||||||
\(638\) | −552899. | − | 168529.i | −1.35833 | − | 0.414031i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −561812. | − | 307101.i | −1.37161 | − | 0.749758i | ||||
\(641\) | 218888. | 0.532728 | 0.266364 | − | 0.963873i | \(-0.414178\pi\) | ||||
0.266364 | + | 0.963873i | \(0.414178\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 345184.i | 0.834889i | 0.908702 | + | 0.417445i | \(0.137074\pi\) | ||||
−0.908702 | + | 0.417445i | \(0.862926\pi\) | |||||||
\(644\) | −141784. | − | 95287.5i | −0.341866 | − | 0.229755i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9607.23 | − | 2928.38i | −0.0230215 | − | 0.00701717i | ||||
\(647\) | 398251.i | 0.951366i | 0.879617 | + | 0.475683i | \(0.157799\pi\) | ||||
−0.879617 | + | 0.475683i | \(0.842201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 617681. | 1.46648 | ||||||||
\(650\) | −219882. | + | 721374.i | −0.520431 | + | 1.70739i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 374373. | − | 557053.i | 0.880663 | − | 1.31039i | ||||
\(653\) | −342288. | −0.802722 | −0.401361 | − | 0.915920i | \(-0.631463\pi\) | ||||
−0.401361 | + | 0.915920i | \(0.631463\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 412031.i | 0.960390i | ||||||||
\(656\) | 7550.63 | + | 18508.7i | 0.0175459 | + | 0.0430098i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32865.5 | − | 107823.i | 0.0759082 | − | 0.249035i | ||||
\(659\) | 522927.i | 1.20412i | 0.798450 | + | 0.602061i | \(0.205654\pi\) | ||||
−0.798450 | + | 0.602061i | \(0.794346\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 308588. | 0.706279 | 0.353140 | − | 0.935571i | \(-0.385114\pi\) | ||||
0.353140 | + | 0.935571i | \(0.385114\pi\) | |||||||
\(662\) | −711286. | − | 216807.i | −1.62304 | − | 0.494717i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 75687.4 | + | 92984.7i | 0.171667 | + | 0.210899i | ||||
\(665\) | 12825.3 | 0.0290018 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.13862e6i | 2.55934i | ||||||||
\(668\) | 60807.7 | − | 90479.6i | 0.136272 | − | 0.202767i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −36788.8 | − | 11213.6i | −0.0819533 | − | 0.0249802i | ||||
\(671\) | − | 242048.i | − | 0.537597i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −248520. | −0.548695 | −0.274348 | − | 0.961631i | \(-0.588462\pi\) | ||||
−0.274348 | + | 0.961631i | \(0.588462\pi\) | |||||||
\(674\) | 172604. | − | 566269.i | 0.379955 | − | 1.24653i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −200689. | − | 134875.i | −0.439168 | − | 0.295147i | ||||
\(677\) | 269522. | 0.588054 | 0.294027 | − | 0.955797i | \(-0.405004\pi\) | ||||
0.294027 | + | 0.955797i | \(0.405004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 70047.6i | − | 0.151934i | ||||||
\(680\) | −181127. | + | 147433.i | −0.391710 | + | 0.318843i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −88730.9 | + | 291103.i | −0.190768 | + | 0.625860i | ||||
\(683\) | 124482.i | 0.266848i | 0.991059 | + | 0.133424i | \(0.0425972\pi\) | ||||
−0.991059 | + | 0.133424i | \(0.957403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −126057. | −0.268649 | ||||||||
\(686\) | −217295. | − | 66233.6i | −0.461744 | − | 0.140744i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −384680. | + | 156931.i | −0.812685 | + | 0.331536i | ||||
\(689\) | −274495. | −0.578223 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 890738.i | 1.86549i | 0.360531 | + | 0.932747i | \(0.382596\pi\) | ||||
−0.360531 | + | 0.932747i | \(0.617404\pi\) | |||||||
\(692\) | −209132. | − | 140549.i | −0.436726 | − | 0.293506i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −554723. | − | 169085.i | −1.15175 | − | 0.351064i | ||||
\(695\) | − | 734462.i | − | 1.52055i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7291.43 | 0.0150088 | ||||||||
\(698\) | 208705. | − | 684705.i | 0.428372 | − | 1.40538i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 98270.6 | − | 146223.i | 0.200552 | − | 0.298414i | ||||
\(701\) | −170934. | −0.347851 | −0.173925 | − | 0.984759i | \(-0.555645\pi\) | ||||
−0.173925 | + | 0.984759i | \(0.555645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 47332.1i | − | 0.0957734i | ||||||
\(704\) | −445266. | − | 92294.4i | −0.898409 | − | 0.186222i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30784.0 | + | 100994.i | −0.0617611 | + | 0.202622i | ||||
\(707\) | 190239.i | 0.380594i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −701926. | −1.39637 | −0.698183 | − | 0.715920i | \(-0.746008\pi\) | ||||
−0.698183 | + | 0.715920i | \(0.746008\pi\) | |||||||
\(710\) | 689028. | + | 210022.i | 1.36685 | + | 0.416628i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −57933.2 | + | 47156.3i | −0.114279 | + | 0.0930206i | ||||
\(713\) | 599487. | 1.17924 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 906662.i | 1.77351i | ||||||||
\(716\) | 200785. | − | 298761.i | 0.391657 | − | 0.582770i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 693934. | + | 211518.i | 1.34608 | + | 0.410297i | ||||
\(719\) | 768366.i | 1.48631i | 0.669117 | + | 0.743157i | \(0.266672\pi\) | ||||
−0.669117 | + | 0.743157i | \(0.733328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −135811. | −0.261255 | ||||||||
\(722\) | −151145. | + | 495868.i | −0.289948 | + | 0.951244i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 290124. | + | 194981.i | 0.553486 | + | 0.371975i | ||||
\(725\) | −1.17427e6 | −2.23404 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 255758.i | 0.483905i | 0.970288 | + | 0.241952i | \(0.0777878\pi\) | ||||
−0.970288 | + | 0.241952i | \(0.922212\pi\) | |||||||
\(728\) | 103052. | + | 126604.i | 0.194444 | + | 0.238882i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 116894. | − | 383497.i | 0.219354 | − | 0.719642i | ||||
\(731\) | 151543.i | 0.283597i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 369658. | 0.688006 | 0.344003 | − | 0.938968i | \(-0.388217\pi\) | ||||
0.344003 | + | 0.938968i | \(0.388217\pi\) | |||||||
\(734\) | 799678. | + | 243750.i | 1.48430 | + | 0.452431i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 81829.3 | + | 892023.i | 0.151061 | + | 1.64672i | ||||
\(737\) | −27314.9 | −0.0502881 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.03557e6i | − | 1.89623i | −0.317932 | − | 0.948114i | \(-0.602988\pi\) | ||
0.317932 | − | 0.948114i | \(-0.397012\pi\) | |||||||
\(740\) | −913490. | − | 613920.i | −1.66817 | − | 1.12111i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 61339.1 | + | 18696.8i | 0.111411 | + | 0.0339593i | ||||
\(743\) | 561187.i | 1.01655i | 0.861194 | + | 0.508276i | \(0.169717\pi\) | ||||
−0.861194 | + | 0.508276i | \(0.830283\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 298963. | 0.538648 | ||||||||
\(746\) | 89331.1 | − | 293072.i | 0.160518 | − | 0.526618i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −92520.5 | + | 137667.i | −0.165362 | + | 0.246052i | ||||
\(749\) | −54495.1 | −0.0971391 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 190408.i | − | 0.337603i | −0.985650 | − | 0.168801i | \(-0.946010\pi\) | ||
0.985650 | − | 0.168801i | \(-0.0539896\pi\) | |||||||
\(752\) | −547281. | + | 223264.i | −0.967775 | + | 0.394805i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 317241. | − | 1.04078e6i | 0.558016 | − | 1.83070i | ||||
\(755\) | − | 43995.1i | − | 0.0771810i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 523077. | 0.912797 | 0.456398 | − | 0.889776i | \(-0.349139\pi\) | ||||
0.456398 | + | 0.889776i | \(0.349139\pi\) | |||||||
\(758\) | 888130. | + | 270711.i | 1.54575 | + | 0.471159i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −42454.8 | − | 52157.3i | −0.0735021 | − | 0.0903000i | ||||
\(761\) | −160897. | −0.277830 | −0.138915 | − | 0.990304i | \(-0.544362\pi\) | ||||
−0.138915 | + | 0.990304i | \(0.544362\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 57804.5i | − | 0.0992916i | ||||||
\(764\) | −166763. | + | 248137.i | −0.285702 | + | 0.425114i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −327467. | − | 99815.1i | −0.558097 | − | 0.170113i | ||||
\(767\) | 1.16273e6i | 1.97646i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −595609. | −1.00718 | −0.503591 | − | 0.863942i | \(-0.667988\pi\) | ||||
−0.503591 | + | 0.863942i | \(0.667988\pi\) | |||||||
\(770\) | 61755.9 | − | 202605.i | 0.104159 | − | 0.341718i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −612184. | − | 411424.i | −1.02718 | − | 0.690328i | ||||
\(773\) | −583394. | −0.976345 | −0.488172 | − | 0.872747i | \(-0.662336\pi\) | ||||
−0.488172 | + | 0.872747i | \(0.662336\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 618255.i | 1.02935i | ||||||||
\(776\) | −284866. | + | 231874.i | −0.473060 | + | 0.385060i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −141979. | + | 465796.i | −0.234566 | + | 0.769549i | ||||
\(779\) | 2099.64i | 0.00345995i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 511588. | 0.838723 | ||||||||
\(782\) | 312545. | + | 95266.9i | 0.511092 | + | 0.155786i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 217768. | + | 533810.i | 0.354293 | + | 0.868469i | ||||
\(785\) | 137230. | 0.222695 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 174412.i | 0.281597i | 0.990038 | + | 0.140798i | \(0.0449669\pi\) | ||||
−0.990038 | + | 0.140798i | \(0.955033\pi\) | |||||||
\(788\) | −211607. | − | 142212.i | −0.340782 | − | 0.229026i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −774581. | − | 236100.i | −1.24112 | − | 0.378305i | ||||
\(791\) | − | 223918.i | − | 0.357879i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 455635. | 0.724553 | ||||||||
\(794\) | 83610.4 | − | 274303.i | 0.132623 | − | 0.435101i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 658054. | − | 979159.i | 1.03857 | − | 1.54535i | ||||
\(797\) | 847152. | 1.33366 | 0.666829 | − | 0.745211i | \(-0.267651\pi\) | ||||
0.666829 | + | 0.745211i | \(0.267651\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 215599.i | 0.337718i | ||||||||
\(800\) | −919949. | + | 84391.1i | −1.43742 | + | 0.131861i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 100626. | − | 330127.i | 0.156445 | − | 0.513254i | ||||
\(803\) | − | 284739.i | − | 0.441586i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −417237. | −0.643860 | ||||||||
\(806\) | −547975. | − | 167028.i | −0.843512 | − | 0.257111i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 773654. | − | 629737.i | 1.18502 | − | 0.964576i | ||||
\(809\) | 43118.8 | 0.0658824 | 0.0329412 | − | 0.999457i | \(-0.489513\pi\) | ||||
0.0329412 | + | 0.999457i | \(0.489513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 372984.i | 0.567085i | 0.958960 | + | 0.283543i | \(0.0915097\pi\) | ||||
−0.958960 | + | 0.283543i | \(0.908490\pi\) | |||||||
\(812\) | −141783. | + | 210967.i | −0.215036 | + | 0.319966i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −747716. | − | 227911.i | −1.12847 | − | 0.343967i | ||||
\(815\) | − | 1.63928e6i | − | 2.46795i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43638.4 | −0.0653769 | ||||||||
\(818\) | −268778. | + | 881791.i | −0.401687 | + | 1.31783i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 40522.2 | + | 27233.3i | 0.0602650 | + | 0.0405017i | ||||
\(821\) | −1.33004e6 | −1.97324 | −0.986620 | − | 0.163037i | \(-0.947871\pi\) | ||||
−0.986620 | + | 0.163037i | \(0.947871\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 734655.i | 1.08464i | 0.840173 | + | 0.542318i | \(0.182453\pi\) | ||||
−0.840173 | + | 0.542318i | \(0.817547\pi\) | |||||||
\(824\) | 449566. | + | 552308.i | 0.662123 | + | 0.813442i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 79197.6 | − | 259826.i | 0.116079 | − | 0.380823i | ||||
\(827\) | − | 1.27112e6i | − | 1.85856i | −0.369375 | − | 0.929281i | \(-0.620428\pi\) | ||
0.369375 | − | 0.929281i | \(-0.379572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −427267. | −0.621714 | −0.310857 | − | 0.950457i | \(-0.600616\pi\) | ||||
−0.310857 | + | 0.950457i | \(0.600616\pi\) | |||||||
\(830\) | 280111. | + | 85380.6i | 0.406606 | + | 0.123938i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 173736. | − | 838174.i | 0.250983 | − | 1.21084i | ||||
\(833\) | 210293. | 0.303064 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 266260.i | − | 0.381885i | ||||||
\(836\) | −39642.6 | − | 26642.2i | −0.0567217 | − | 0.0381204i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −212831. | − | 64873.0i | −0.303073 | − | 0.0923796i | ||||
\(839\) | − | 694916.i | − | 0.987207i | −0.869687 | − | 0.493604i | \(-0.835679\pi\) | ||
0.869687 | − | 0.493604i | \(-0.164321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 986927. | 1.39538 | ||||||||
\(842\) | −164410. | + | 539385.i | −0.231902 | + | 0.760808i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 159024. | − | 236622.i | 0.223243 | − | 0.332178i | ||||
\(845\) | −590581. | −0.827115 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28266.7i | 0.0394011i | ||||||||
\(848\) | −127012. | − | 311341.i | −0.176625 | − | 0.432957i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −98249.3 | + | 322330.i | −0.135985 | + | 0.446131i | ||||
\(851\) | 1.53982e6i | 2.12624i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 144629. | 0.198773 | 0.0993867 | − | 0.995049i | \(-0.468312\pi\) | ||||
0.0993867 | + | 0.995049i | \(0.468312\pi\) | |||||||
\(854\) | −101817. | − | 31034.8i | −0.139606 | − | 0.0425534i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 180392. | + | 221618.i | 0.246189 | + | 0.302452i | ||||
\(857\) | −636010. | −0.865968 | −0.432984 | − | 0.901402i | \(-0.642539\pi\) | ||||
−0.432984 | + | 0.901402i | \(0.642539\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.34994e6i | − | 1.82948i | −0.404041 | − | 0.914741i | \(-0.632395\pi\) | ||
0.404041 | − | 0.914741i | \(-0.367605\pi\) | |||||||
\(860\) | −566011. | + | 842203.i | −0.765293 | + | 1.13873i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −730862. | − | 222774.i | −0.983605 | − | 0.299812i | ||||
\(863\) | 916363.i | 1.23040i | 0.788372 | + | 0.615199i | \(0.210924\pi\) | ||||
−0.788372 | + | 0.615199i | \(0.789076\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −615427. | −0.822515 | ||||||||
\(866\) | −56264.6 | + | 184589.i | −0.0750238 | + | 0.246133i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 111075. | + | 74649.0i | 0.147427 | + | 0.0990797i | ||||
\(869\) | −575110. | −0.761573 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 51418.0i | − | 0.0677764i | ||||||
\(872\) | −235076. | + | 191346.i | −0.309154 | + | 0.251644i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27433.0 | + | 90000.5i | −0.0359129 | + | 0.117821i | ||||
\(875\) | − | 132196.i | − | 0.172664i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −546256. | −0.710226 | −0.355113 | − | 0.934823i | \(-0.615558\pi\) | ||||
−0.355113 | + | 0.934823i | \(0.615558\pi\) | |||||||
\(878\) | 1.00327e6 | + | 305807.i | 1.30145 | + | 0.396696i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.02837e6 | + | 419524.i | −1.32795 | + | 0.541740i | ||||
\(881\) | 446863. | 0.575735 | 0.287867 | − | 0.957670i | \(-0.407054\pi\) | ||||
0.287867 | + | 0.957670i | \(0.407054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 140436.i | − | 0.180119i | −0.995936 | − | 0.0900593i | \(-0.971294\pi\) | ||
0.995936 | − | 0.0900593i | \(-0.0287056\pi\) | |||||||
\(884\) | −259146. | − | 174162.i | −0.331620 | − | 0.222868i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −348119. | − | 106110.i | −0.443466 | − | 0.135173i | ||||
\(887\) | − | 354688.i | − | 0.450816i | −0.974264 | − | 0.225408i | \(-0.927628\pi\) | ||
0.974264 | − | 0.225408i | \(-0.0723715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 99709.4 | 0.126163 | ||||||||
\(890\) | −53195.5 | + | 174520.i | −0.0671575 | + | 0.220326i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 601358. | − | 894798.i | 0.755794 | − | 1.12459i | ||||
\(893\) | −62084.0 | −0.0778532 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 879182.i | − | 1.09757i | ||||||
\(896\) | −95914.4 | + | 175466.i | −0.119472 | + | 0.218564i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −330460. | + | 1.08415e6i | −0.409795 | + | 1.34443i | ||||
\(899\) | − | 892005.i | − | 1.10369i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −122652. | −0.151086 | ||||||||
\(902\) | 33168.5 | + | 10110.1i | 0.0407674 | + | 0.0124263i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −910617. | + | 741222.i | −1.11429 | + | 0.907008i | ||||
\(905\) | 853766. | 1.04242 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.47749e6i | − | 1.79602i | −0.439978 | − | 0.898008i | \(-0.645014\pi\) | ||
0.439978 | − | 0.898008i | \(-0.354986\pi\) | |||||||
\(908\) | 560422. | − | 833887.i | 0.679741 | − | 1.01143i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 381386. | + | 116250.i | 0.460555 | + | 0.140382i | ||||
\(911\) | − | 48152.2i | − | 0.0580202i | −0.999579 | − | 0.0290101i | \(-0.990765\pi\) | ||
0.999579 | − | 0.0290101i | \(-0.00923549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 207976. | 0.249501 | ||||||||
\(914\) | −231449. | + | 759323.i | −0.277053 | + | 0.908938i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 543487. | + | 365256.i | 0.647737 | + | 0.435318i | ||||
\(917\) | 128687. | 0.153036 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 346372.i | 0.410120i | 0.978749 | + | 0.205060i | \(0.0657390\pi\) | ||||
−0.978749 | + | 0.205060i | \(0.934261\pi\) | |||||||
\(920\) | 1.38115e6 | + | 1.69680e6i | 1.63180 | + | 2.00472i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 243393. | − | 798508.i | 0.286317 | − | 0.939329i | ||||
\(923\) | 963021.i | 1.13040i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.58803e6 | −1.85599 | ||||||||
\(926\) | 100238. | + | 30553.5i | 0.116899 | + | 0.0356319i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.32728e6 | − | 121758.i | 1.54123 | − | 0.141384i | ||||
\(929\) | 870783. | 1.00897 | 0.504485 | − | 0.863420i | \(-0.331682\pi\) | ||||
0.504485 | + | 0.863420i | \(0.331682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 60555.8i | 0.0698645i | ||||||||
\(932\) | −1.05247e6 | − | 707325.i | −1.21166 | − | 0.814305i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −369641. | − | 112670.i | −0.423727 | − | 0.129156i | ||||
\(935\) | 405122.i | 0.463407i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00280e6 | −1.14219 | −0.571094 | − | 0.820885i | \(-0.693481\pi\) | ||||
−0.571094 | + | 0.820885i | \(0.693481\pi\) | |||||||
\(938\) | −3502.26 | + | 11490.0i | −0.00398054 | + | 0.0130591i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −805259. | + | 1.19820e6i | −0.911339 | + | 1.35604i | ||||
\(941\) | −1.26190e6 | −1.42510 | −0.712550 | − | 0.701622i | \(-0.752460\pi\) | ||||
−0.712550 | + | 0.701622i | \(0.752460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 68306.1i | − | 0.0768132i | ||||||
\(944\) | −1.31881e6 | + | 538010.i | −1.47992 | + | 0.603735i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −210125. | + | 689366.i | −0.234799 | + | 0.770314i | ||||
\(947\) | 187145.i | 0.208678i | 0.994542 | + | 0.104339i | \(0.0332728\pi\) | ||||
−0.994542 | + | 0.104339i | \(0.966727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 535996. | 0.595153 | ||||||||
\(950\) | −92818.1 | − | 28291.8i | −0.102845 | − | 0.0313483i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 46046.6 | + | 56569.9i | 0.0508070 | + | 0.0624183i | ||||
\(953\) | 194925. | 0.214626 | 0.107313 | − | 0.994225i | \(-0.465775\pi\) | ||||
0.107313 | + | 0.994225i | \(0.465775\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 730210.i | 0.800647i | ||||||||
\(956\) | 402782. | − | 599325.i | 0.440712 | − | 0.655763i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −131060. | − | 39948.5i | −0.142804 | − | 0.0435281i | ||||
\(959\) | 39370.4i | 0.0428088i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 453878. | 0.491465 | ||||||||
\(962\) | 429023. | − | 1.40751e6i | 0.463586 | − | 1.52090i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.00465e6 | − | 675187.i | −1.08109 | − | 0.726557i | ||||
\(965\) | −1.80151e6 | −1.93456 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 432253.i | 0.462259i | 0.972923 | + | 0.231129i | \(0.0742421\pi\) | ||||
−0.972923 | + | 0.231129i | \(0.925758\pi\) | |||||||
\(968\) | 114953. | − | 93569.5i | 0.122679 | − | 0.0998581i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −261570. | + | 858141.i | −0.278000 | + | 0.912043i | ||||
\(971\) | 756598.i | 0.802467i | 0.915976 | + | 0.401233i | \(0.131418\pi\) | ||||
−0.915976 | + | 0.401233i | \(0.868582\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −229389. | −0.242296 | ||||||||
\(974\) | 266003. | + | 81080.4i | 0.280394 | + | 0.0854669i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 210828. | + | 516796.i | 0.221324 | + | 0.542525i | ||||
\(977\) | 1.80719e6 | 1.89328 | 0.946638 | − | 0.322299i | \(-0.104456\pi\) | ||||
0.946638 | + | 0.322299i | \(0.104456\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 129578.i | 0.135196i | ||||||||
\(980\) | 1.16870e6 | + | 785438.i | 1.21689 | + | 0.817824i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 770102. | + | 234735.i | 0.798593 | + | 0.243419i | ||||
\(983\) | − | 209985.i | − | 0.217311i | −0.994079 | − | 0.108655i | \(-0.965346\pi\) | ||
0.994079 | − | 0.108655i | \(-0.0346545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −622709. | −0.641819 | ||||||||
\(986\) | 141752. | − | 465051.i | 0.145806 | − | 0.478351i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 50151.6 | − | 74623.7i | 0.0513773 | − | 0.0764475i | ||||
\(989\) | 1.41966e6 | 1.45141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.66713e6i | − | 1.69755i | −0.528754 | − | 0.848775i | \(-0.677341\pi\) | ||
0.528754 | − | 0.848775i | \(-0.322659\pi\) | |||||||
\(992\) | −64105.7 | − | 698818.i | −0.0651439 | − | 0.710135i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 65594.7 | − | 215199.i | 0.0663889 | − | 0.217804i | ||||
\(995\) | − | 2.88144e6i | − | 2.91047i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.34283e6 | 1.35093 | 0.675464 | − | 0.737393i | \(-0.263943\pi\) | ||||
0.675464 | + | 0.737393i | \(0.263943\pi\) | |||||||
\(998\) | −206992. | − | 63093.3i | −0.207823 | − | 0.0633464i | ||||
\(999\) | 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.163.10 | 22 | ||
3.2 | odd | 2 | 324.5.d.e.163.13 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.f.163.9 | 22 | ||
9.2 | odd | 6 | 108.5.f.a.91.2 | 44 | |||
9.4 | even | 3 | 36.5.f.a.7.6 | ✓ | 44 | ||
9.5 | odd | 6 | 108.5.f.a.19.17 | 44 | |||
9.7 | even | 3 | 36.5.f.a.31.21 | yes | 44 | ||
12.11 | even | 2 | 324.5.d.e.163.14 | 22 | |||
36.7 | odd | 6 | 36.5.f.a.31.6 | yes | 44 | ||
36.11 | even | 6 | 108.5.f.a.91.17 | 44 | |||
36.23 | even | 6 | 108.5.f.a.19.2 | 44 | |||
36.31 | odd | 6 | 36.5.f.a.7.21 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.6 | ✓ | 44 | 9.4 | even | 3 | ||
36.5.f.a.7.21 | yes | 44 | 36.31 | odd | 6 | ||
36.5.f.a.31.6 | yes | 44 | 36.7 | odd | 6 | ||
36.5.f.a.31.21 | yes | 44 | 9.7 | even | 3 | ||
108.5.f.a.19.2 | 44 | 36.23 | even | 6 | |||
108.5.f.a.19.17 | 44 | 9.5 | odd | 6 | |||
108.5.f.a.91.2 | 44 | 9.2 | odd | 6 | |||
108.5.f.a.91.17 | 44 | 36.11 | even | 6 | |||
324.5.d.e.163.13 | 22 | 3.2 | odd | 2 | |||
324.5.d.e.163.14 | 22 | 12.11 | even | 2 | |||
324.5.d.f.163.9 | 22 | 4.3 | odd | 2 | inner | ||
324.5.d.f.163.10 | 22 | 1.1 | even | 1 | trivial |