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 | 163.6 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.e.163.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82463 | + | 2.83222i | −0.706157 | + | 0.708055i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.0429591 | − | 15.9999i | −0.00268494 | − | 0.999996i | ||||
\(5\) | −11.7888 | −0.471550 | −0.235775 | − | 0.971808i | \(-0.575763\pi\) | ||||
−0.235775 | + | 0.971808i | \(0.575763\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 58.3756i | 1.19134i | 0.803229 | + | 0.595670i | \(0.203113\pi\) | ||||
−0.803229 | + | 0.595670i | \(0.796887\pi\) | |||||||
\(8\) | 45.4367 | + | 45.0722i | 0.709949 | + | 0.704253i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 33.2988 | − | 33.3884i | 0.332988 | − | 0.333884i | ||||
\(11\) | − | 100.429i | − | 0.829993i | −0.909823 | − | 0.414997i | \(-0.863783\pi\) | ||
0.909823 | − | 0.414997i | \(-0.136217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −170.636 | −1.00968 | −0.504839 | − | 0.863213i | \(-0.668448\pi\) | ||||
−0.504839 | + | 0.863213i | \(0.668448\pi\) | |||||||
\(14\) | −165.333 | − | 164.889i | −0.843535 | − | 0.841273i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −255.996 | + | 1.37469i | −0.999986 | + | 0.00536987i | ||||
\(17\) | 398.571 | 1.37914 | 0.689569 | − | 0.724220i | \(-0.257800\pi\) | ||||
0.689569 | + | 0.724220i | \(0.257800\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 404.608i | 1.12080i | 0.828223 | + | 0.560399i | \(0.189352\pi\) | ||||
−0.828223 | + | 0.560399i | \(0.810648\pi\) | |||||||
\(20\) | 0.506434 | + | 188.619i | 0.00126609 | + | 0.471549i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 284.438 | + | 283.675i | 0.587681 | + | 0.586105i | ||||
\(23\) | 336.123i | 0.635394i | 0.948192 | + | 0.317697i | \(0.102909\pi\) | ||||
−0.948192 | + | 0.317697i | \(0.897091\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −486.025 | −0.777640 | ||||||||
\(26\) | 481.982 | − | 483.278i | 0.712991 | − | 0.714908i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 934.007 | − | 2.50777i | 1.19134 | − | 0.00319868i | ||||
\(29\) | 655.342 | 0.779241 | 0.389621 | − | 0.920975i | \(-0.372606\pi\) | ||||
0.389621 | + | 0.920975i | \(0.372606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 635.277i | 0.661058i | 0.943796 | + | 0.330529i | \(0.107227\pi\) | ||||
−0.943796 | + | 0.330529i | \(0.892773\pi\) | |||||||
\(32\) | 719.201 | − | 728.921i | 0.702345 | − | 0.711837i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1125.81 | + | 1128.84i | −0.973888 | + | 0.976506i | ||||
\(35\) | − | 688.176i | − | 0.561776i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1599.91 | −1.16867 | −0.584336 | − | 0.811512i | \(-0.698645\pi\) | ||||
−0.584336 | + | 0.811512i | \(0.698645\pi\) | |||||||
\(38\) | −1145.94 | − | 1142.87i | −0.793587 | − | 0.791459i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −535.642 | − | 531.345i | −0.334777 | − | 0.332091i | ||||
\(41\) | −2463.27 | −1.46536 | −0.732679 | − | 0.680574i | \(-0.761730\pi\) | ||||
−0.732679 | + | 0.680574i | \(0.761730\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2232.48i | − | 1.20740i | −0.797212 | − | 0.603699i | \(-0.793693\pi\) | ||
0.797212 | − | 0.603699i | \(-0.206307\pi\) | |||||||
\(44\) | −1606.86 | + | 4.31435i | −0.829990 | + | 0.00222849i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −951.976 | − | 949.423i | −0.449894 | − | 0.448688i | ||||
\(47\) | − | 2903.56i | − | 1.31442i | −0.753707 | − | 0.657211i | \(-0.771736\pi\) | ||
0.753707 | − | 0.657211i | \(-0.228264\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1006.72 | −0.419290 | ||||||||
\(50\) | 1372.84 | − | 1376.53i | 0.549136 | − | 0.550613i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.33036 | + | 2730.16i | 0.00271093 | + | 1.00967i | ||||
\(53\) | −1291.73 | −0.459852 | −0.229926 | − | 0.973208i | \(-0.573848\pi\) | ||||
−0.229926 | + | 0.973208i | \(0.573848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1183.94i | 0.391384i | ||||||||
\(56\) | −2631.12 | + | 2652.40i | −0.839005 | + | 0.845790i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1851.10 | + | 1856.07i | −0.550267 | + | 0.551746i | ||||
\(59\) | − | 1157.28i | − | 0.332457i | −0.986087 | − | 0.166229i | \(-0.946841\pi\) | ||
0.986087 | − | 0.166229i | \(-0.0531590\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5921.62 | 1.59141 | 0.795703 | − | 0.605687i | \(-0.207101\pi\) | ||||
0.795703 | + | 0.605687i | \(0.207101\pi\) | |||||||
\(62\) | −1799.24 | − | 1794.42i | −0.468066 | − | 0.466811i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32.9923 | + | 4095.87i | 0.00805476 | + | 0.999968i | ||||
\(65\) | 2011.58 | 0.476114 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3563.26i | − | 0.793775i | −0.917867 | − | 0.396888i | \(-0.870090\pi\) | ||
0.917867 | − | 0.396888i | \(-0.129910\pi\) | |||||||
\(68\) | −17.1222 | − | 6377.11i | −0.00370291 | − | 1.37913i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1949.07 | + | 1943.84i | 0.397769 | + | 0.396702i | ||||
\(71\) | − | 5639.73i | − | 1.11877i | −0.828907 | − | 0.559386i | \(-0.811037\pi\) | ||
0.828907 | − | 0.559386i | \(-0.188963\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5496.39 | −1.03141 | −0.515705 | − | 0.856766i | \(-0.672470\pi\) | ||||
−0.515705 | + | 0.856766i | \(0.672470\pi\) | |||||||
\(74\) | 4519.16 | − | 4531.31i | 0.825266 | − | 0.827485i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6473.71 | − | 17.3816i | 1.12079 | − | 0.00300928i | ||||
\(77\) | 5862.62 | 0.988804 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3220.39i | − | 0.516006i | −0.966144 | − | 0.258003i | \(-0.916936\pi\) | ||
0.966144 | − | 0.258003i | \(-0.0830645\pi\) | |||||||
\(80\) | 3017.88 | − | 16.2058i | 0.471543 | − | 0.00253216i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6957.81 | − | 6976.52i | 1.03477 | − | 1.03755i | ||||
\(83\) | − | 8156.71i | − | 1.18402i | −0.805931 | − | 0.592010i | \(-0.798335\pi\) | ||
0.805931 | − | 0.592010i | \(-0.201665\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4698.65 | −0.650333 | ||||||||
\(86\) | 6322.88 | + | 6305.92i | 0.854905 | + | 0.852612i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4526.57 | − | 4563.17i | 0.584525 | − | 0.589253i | ||||
\(89\) | −910.873 | −0.114995 | −0.0574974 | − | 0.998346i | \(-0.518312\pi\) | ||||
−0.0574974 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9960.97i | − | 1.20287i | ||||||
\(92\) | 5377.95 | − | 14.4396i | 0.635391 | − | 0.00170600i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8223.52 | + | 8201.47i | 0.930683 | + | 0.928188i | ||||
\(95\) | − | 4769.83i | − | 0.528513i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17608.9 | −1.87149 | −0.935747 | − | 0.352673i | \(-0.885273\pi\) | ||||
−0.935747 | + | 0.352673i | \(0.885273\pi\) | |||||||
\(98\) | 2843.60 | − | 2851.24i | 0.296085 | − | 0.296881i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 20.8792 | + | 7776.38i | 0.00208792 | + | 0.777638i | ||||
\(101\) | −6660.82 | −0.652957 | −0.326479 | − | 0.945205i | \(-0.605862\pi\) | ||||
−0.326479 | + | 0.945205i | \(0.605862\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 6753.50i | − | 0.636582i | −0.947993 | − | 0.318291i | \(-0.896891\pi\) | ||
0.947993 | − | 0.318291i | \(-0.103109\pi\) | |||||||
\(104\) | −7753.12 | − | 7690.92i | −0.716820 | − | 0.711069i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3648.64 | − | 3658.45i | 0.324728 | − | 0.325601i | ||||
\(107\) | − | 30.7569i | − | 0.00268643i | −0.999999 | − | 0.00134321i | \(-0.999572\pi\) | ||
0.999999 | − | 0.00134321i | \(-0.000427558\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10691.4 | 0.899872 | 0.449936 | − | 0.893061i | \(-0.351447\pi\) | ||||
0.449936 | + | 0.893061i | \(0.351447\pi\) | |||||||
\(110\) | −3353.17 | − | 3344.18i | −0.277121 | − | 0.276378i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −80.2482 | − | 14943.9i | −0.00639734 | − | 1.19132i | ||||
\(113\) | −10016.2 | −0.784414 | −0.392207 | − | 0.919877i | \(-0.628288\pi\) | ||||
−0.392207 | + | 0.919877i | \(0.628288\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3962.47i | − | 0.299620i | ||||||
\(116\) | −28.1529 | − | 10485.4i | −0.00209222 | − | 0.779238i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3277.69 | + | 3268.90i | 0.235398 | + | 0.234767i | ||||
\(119\) | 23266.8i | 1.64302i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4554.98 | 0.311111 | ||||||||
\(122\) | −16726.4 | + | 16771.4i | −1.12378 | + | 1.12680i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10164.4 | − | 27.2909i | 0.661056 | − | 0.00177490i | ||||
\(125\) | 13097.6 | 0.838247 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16087.8i | − | 0.997444i | −0.866762 | − | 0.498722i | \(-0.833803\pi\) | ||
0.866762 | − | 0.498722i | \(-0.166197\pi\) | |||||||
\(128\) | −11693.6 | − | 11475.9i | −0.713720 | − | 0.700431i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5681.97 | + | 5697.25i | −0.336211 | + | 0.337115i | ||||
\(131\) | − | 20906.5i | − | 1.21825i | −0.793073 | − | 0.609127i | \(-0.791520\pi\) | ||
0.793073 | − | 0.609127i | \(-0.208480\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23619.3 | −1.33525 | ||||||||
\(134\) | 10091.9 | + | 10064.9i | 0.562037 | + | 0.560530i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 18109.8 | + | 17964.5i | 0.979117 | + | 0.971262i | ||||
\(137\) | −4676.05 | −0.249137 | −0.124568 | − | 0.992211i | \(-0.539755\pi\) | ||||
−0.124568 | + | 0.992211i | \(0.539755\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9305.07i | − | 0.481604i | −0.970574 | − | 0.240802i | \(-0.922590\pi\) | ||
0.970574 | − | 0.240802i | \(-0.0774104\pi\) | |||||||
\(140\) | −11010.8 | + | 29.5634i | −0.561774 | + | 0.00150834i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15973.0 | + | 15930.1i | 0.792152 | + | 0.790028i | ||||
\(143\) | 17136.8i | 0.838026i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7725.67 | −0.367451 | ||||||||
\(146\) | 15525.3 | − | 15567.0i | 0.728338 | − | 0.730296i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 68.7308 | + | 25598.5i | 0.00313782 | + | 1.16867i | ||||
\(149\) | 24771.6 | 1.11579 | 0.557893 | − | 0.829913i | \(-0.311610\pi\) | ||||
0.557893 | + | 0.829913i | \(0.311610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10209.5i | 0.447767i | 0.974616 | + | 0.223884i | \(0.0718735\pi\) | ||||
−0.974616 | + | 0.223884i | \(0.928126\pi\) | |||||||
\(152\) | −18236.6 | + | 18384.1i | −0.789326 | + | 0.795709i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16559.7 | + | 16604.2i | −0.698251 | + | 0.700128i | ||||
\(155\) | − | 7489.12i | − | 0.311722i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −28973.0 | −1.17542 | −0.587712 | − | 0.809070i | \(-0.699971\pi\) | ||||
−0.587712 | + | 0.809070i | \(0.699971\pi\) | |||||||
\(158\) | 9120.87 | + | 9096.41i | 0.365361 | + | 0.364381i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8478.48 | + | 8593.07i | −0.331191 | + | 0.335667i | ||||
\(161\) | −19621.4 | −0.756970 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17736.4i | − | 0.667560i | −0.942651 | − | 0.333780i | \(-0.891676\pi\) | ||
0.942651 | − | 0.333780i | \(-0.108324\pi\) | |||||||
\(164\) | 105.820 | + | 39412.1i | 0.00393441 | + | 1.46535i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23101.6 | + | 23039.7i | 0.838352 | + | 0.836104i | ||||
\(167\) | 41063.6i | 1.47239i | 0.676767 | + | 0.736197i | \(0.263380\pi\) | ||||
−0.676767 | + | 0.736197i | \(0.736620\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 555.522 | 0.0194504 | ||||||||
\(170\) | 13271.9 | − | 13307.6i | 0.459237 | − | 0.460472i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −35719.5 | + | 95.9053i | −1.20739 | + | 0.00324180i | ||||
\(173\) | −6955.73 | −0.232408 | −0.116204 | − | 0.993225i | \(-0.537073\pi\) | ||||
−0.116204 | + | 0.993225i | \(0.537073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 28372.0i | − | 0.926434i | ||||||
\(176\) | 138.059 | + | 25709.5i | 0.00445696 | + | 0.829981i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2572.88 | − | 2579.80i | 0.0812043 | − | 0.0814227i | ||||
\(179\) | − | 1754.50i | − | 0.0547580i | −0.999625 | − | 0.0273790i | \(-0.991284\pi\) | ||
0.999625 | − | 0.0273790i | \(-0.00871609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −43787.9 | −1.33659 | −0.668293 | − | 0.743898i | \(-0.732975\pi\) | ||||
−0.668293 | + | 0.743898i | \(0.732975\pi\) | |||||||
\(182\) | 28211.7 | + | 28136.0i | 0.851699 | + | 0.849415i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15149.8 | + | 15272.3i | −0.447478 | + | 0.451097i | ||||
\(185\) | 18861.0 | 0.551088 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 40028.1i | − | 1.14468i | ||||||
\(188\) | −46456.8 | + | 124.734i | −1.31442 | + | 0.00352915i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13509.2 | + | 13473.0i | 0.374216 | + | 0.373213i | ||||
\(191\) | 39725.3i | 1.08893i | 0.838783 | + | 0.544466i | \(0.183268\pi\) | ||||
−0.838783 | + | 0.544466i | \(0.816732\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21094.4 | −0.566308 | −0.283154 | − | 0.959074i | \(-0.591381\pi\) | ||||
−0.283154 | + | 0.959074i | \(0.591381\pi\) | |||||||
\(194\) | 49738.5 | − | 49872.3i | 1.32157 | − | 1.32512i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 43.2476 | + | 16107.4i | 0.00112577 | + | 0.419289i | ||||
\(197\) | −28256.1 | −0.728080 | −0.364040 | − | 0.931383i | \(-0.618603\pi\) | ||||
−0.364040 | + | 0.931383i | \(0.618603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24063.5i | 0.607650i | 0.952728 | + | 0.303825i | \(0.0982638\pi\) | ||||
−0.952728 | + | 0.303825i | \(0.901736\pi\) | |||||||
\(200\) | −22083.4 | − | 21906.2i | −0.552085 | − | 0.547656i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18814.3 | − | 18864.9i | 0.461090 | − | 0.462330i | ||||
\(203\) | 38256.0i | 0.928341i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29038.9 | 0.690990 | ||||||||
\(206\) | 19127.4 | + | 19076.1i | 0.450735 | + | 0.449527i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 43682.1 | − | 234.571i | 1.00966 | − | 0.00542184i | ||||
\(209\) | 40634.5 | 0.930255 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 58079.8i | 1.30455i | 0.757983 | + | 0.652274i | \(0.226185\pi\) | ||||
−0.757983 | + | 0.652274i | \(0.773815\pi\) | |||||||
\(212\) | 55.4914 | + | 20667.5i | 0.00123468 | + | 0.459851i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 87.1104 | + | 86.8768i | 0.00190214 | + | 0.00189704i | ||||
\(215\) | 26318.1i | 0.569349i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37084.7 | −0.787545 | ||||||||
\(218\) | −30199.2 | + | 30280.4i | −0.635451 | + | 0.637159i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 18942.9 | − | 50.8608i | 0.391382 | − | 0.00105084i | ||||
\(221\) | −68010.4 | −1.39249 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16661.8i | 0.335053i | 0.985868 | + | 0.167526i | \(0.0535779\pi\) | ||||
−0.985868 | + | 0.167526i | \(0.946422\pi\) | |||||||
\(224\) | 42551.3 | + | 41983.8i | 0.848040 | + | 0.836731i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 28292.0 | − | 28368.0i | 0.553919 | − | 0.555409i | ||||
\(227\) | − | 56258.7i | − | 1.09179i | −0.837855 | − | 0.545894i | \(-0.816190\pi\) | ||
0.837855 | − | 0.545894i | \(-0.183810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2447.82 | 0.0466775 | 0.0233388 | − | 0.999728i | \(-0.492570\pi\) | ||||
0.0233388 | + | 0.999728i | \(0.492570\pi\) | |||||||
\(230\) | 11222.6 | + | 11192.5i | 0.212148 | + | 0.211579i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 29776.6 | + | 29537.7i | 0.553221 | + | 0.548783i | ||||
\(233\) | 76971.2 | 1.41781 | 0.708903 | − | 0.705306i | \(-0.249191\pi\) | ||||
0.708903 | + | 0.705306i | \(0.249191\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34229.3i | 0.619816i | ||||||||
\(236\) | −18516.5 | + | 49.7159i | −0.332456 | + | 0.000892630i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −65896.8 | − | 65720.1i | −1.16335 | − | 1.16023i | ||||
\(239\) | − | 26058.7i | − | 0.456202i | −0.973637 | − | 0.228101i | \(-0.926748\pi\) | ||
0.973637 | − | 0.228101i | \(-0.0732517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27999.6 | −0.482079 | −0.241039 | − | 0.970515i | \(-0.577488\pi\) | ||||
−0.241039 | + | 0.970515i | \(0.577488\pi\) | |||||||
\(242\) | −12866.1 | + | 12900.7i | −0.219693 | + | 0.220284i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −254.388 | − | 94745.6i | −0.00427284 | − | 1.59140i | ||||
\(245\) | 11867.9 | 0.197716 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 69040.6i | − | 1.13165i | ||||||
\(248\) | −28633.3 | + | 28864.9i | −0.465552 | + | 0.469317i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −36995.9 | + | 37095.3i | −0.591934 | + | 0.593525i | ||||
\(251\) | 19782.5i | 0.314003i | 0.987598 | + | 0.157001i | \(0.0501827\pi\) | ||||
−0.987598 | + | 0.157001i | \(0.949817\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33756.6 | 0.527373 | ||||||||
\(254\) | 45564.1 | + | 45442.0i | 0.706246 | + | 0.704352i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65532.2 | − | 703.829i | 0.999942 | − | 0.0107396i | ||||
\(257\) | −77273.9 | −1.16995 | −0.584974 | − | 0.811052i | \(-0.698895\pi\) | ||||
−0.584974 | + | 0.811052i | \(0.698895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 93395.9i | − | 1.39229i | ||||||
\(260\) | −86.4158 | − | 32185.2i | −0.00127834 | − | 0.476112i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 59211.7 | + | 59053.0i | 0.862592 | + | 0.860279i | ||||
\(263\) | 21212.4i | 0.306675i | 0.988174 | + | 0.153337i | \(0.0490021\pi\) | ||||
−0.988174 | + | 0.153337i | \(0.950998\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15227.8 | 0.216844 | ||||||||
\(266\) | 66715.6 | − | 66895.0i | 0.942897 | − | 0.945432i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −57011.9 | + | 153.074i | −0.793772 | + | 0.00213124i | ||||
\(269\) | −1106.24 | −0.0152878 | −0.00764389 | − | 0.999971i | \(-0.502433\pi\) | ||||
−0.00764389 | + | 0.999971i | \(0.502433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 33038.3i | − | 0.449861i | −0.974375 | − | 0.224931i | \(-0.927784\pi\) | ||
0.974375 | − | 0.224931i | \(-0.0722155\pi\) | |||||||
\(272\) | −102033. | + | 547.910i | −1.37912 | + | 0.00740579i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13208.1 | − | 13243.6i | 0.175930 | − | 0.176403i | ||||
\(275\) | 48811.1i | 0.645436i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28842.5 | 0.375901 | 0.187951 | − | 0.982178i | \(-0.439816\pi\) | ||||
0.187951 | + | 0.982178i | \(0.439816\pi\) | |||||||
\(278\) | 26354.0 | + | 26283.3i | 0.341002 | + | 0.340088i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 31017.6 | − | 31268.5i | 0.395633 | − | 0.398833i | ||||
\(281\) | −32125.8 | −0.406856 | −0.203428 | − | 0.979090i | \(-0.565208\pi\) | ||||
−0.203428 | + | 0.979090i | \(0.565208\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 71340.3i | 0.890763i | 0.895341 | + | 0.445382i | \(0.146932\pi\) | ||||
−0.895341 | + | 0.445382i | \(0.853068\pi\) | |||||||
\(284\) | −90235.3 | + | 242.278i | −1.11877 | + | 0.00300384i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −48535.2 | − | 48405.1i | −0.593369 | − | 0.591778i | ||||
\(287\) | − | 143795.i | − | 1.74574i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 75337.7 | 0.902021 | ||||||||
\(290\) | 21822.1 | − | 21880.8i | 0.259478 | − | 0.260176i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 236.120 | + | 87941.9i | 0.00276928 | + | 1.03141i | ||||
\(293\) | 36641.5 | 0.426813 | 0.213407 | − | 0.976963i | \(-0.431544\pi\) | ||||
0.213407 | + | 0.976963i | \(0.431544\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13642.9i | 0.156770i | ||||||||
\(296\) | −72694.8 | − | 72111.6i | −0.829698 | − | 0.823041i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −69970.4 | + | 70158.5i | −0.787920 | + | 0.790038i | ||||
\(299\) | − | 57354.6i | − | 0.641543i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 130322. | 1.43842 | ||||||||
\(302\) | −28915.7 | − | 28838.1i | −0.317044 | − | 0.316194i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −556.209 | − | 103578.i | −0.00601854 | − | 1.12078i | ||||
\(305\) | −69808.6 | −0.750428 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11668.1i | − | 0.123801i | −0.998082 | − | 0.0619005i | \(-0.980284\pi\) | ||
0.998082 | − | 0.0619005i | \(-0.0197161\pi\) | |||||||
\(308\) | −251.853 | − | 93801.6i | −0.00265488 | − | 0.988800i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21210.8 | + | 21154.0i | 0.220716 | + | 0.220125i | ||||
\(311\) | − | 4336.03i | − | 0.0448303i | −0.999749 | − | 0.0224151i | \(-0.992864\pi\) | ||
0.999749 | − | 0.0224151i | \(-0.00713556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 86498.6 | 0.882918 | 0.441459 | − | 0.897282i | \(-0.354461\pi\) | ||||
0.441459 | + | 0.897282i | \(0.354461\pi\) | |||||||
\(314\) | 81838.0 | − | 82058.1i | 0.830034 | − | 0.832266i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −51526.1 | + | 138.345i | −0.516004 | + | 0.00138545i | ||||
\(317\) | 24632.2 | 0.245124 | 0.122562 | − | 0.992461i | \(-0.460889\pi\) | ||||
0.122562 | + | 0.992461i | \(0.460889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 65815.5i | − | 0.646765i | ||||||
\(320\) | −388.938 | − | 48285.2i | −0.00379822 | − | 0.471535i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 55423.2 | − | 55572.2i | 0.534539 | − | 0.535977i | ||||
\(323\) | 161265.i | 1.54573i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 82933.2 | 0.785167 | ||||||||
\(326\) | 50233.4 | + | 50098.7i | 0.472669 | + | 0.471402i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −111923. | − | 111025.i | −1.04033 | − | 1.03198i | ||||
\(329\) | 169497. | 1.56592 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 187265.i | 1.70923i | 0.519265 | + | 0.854614i | \(0.326206\pi\) | ||||
−0.519265 | + | 0.854614i | \(0.673794\pi\) | |||||||
\(332\) | −130507. | + | 350.405i | −1.18402 | + | 0.00317903i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −116301. | − | 115989.i | −1.04254 | − | 1.03974i | ||||
\(335\) | 42006.4i | 0.374305i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −100959. | −0.888967 | −0.444484 | − | 0.895787i | \(-0.646613\pi\) | ||||
−0.444484 | + | 0.895787i | \(0.646613\pi\) | |||||||
\(338\) | −1569.14 | + | 1573.36i | −0.0137350 | + | 0.0137719i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 201.850 | + | 75178.2i | 0.00174611 | + | 0.650330i | ||||
\(341\) | 63800.3 | 0.548674 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 81392.2i | 0.691823i | ||||||||
\(344\) | 100623. | − | 101437.i | 0.850314 | − | 0.857191i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19647.4 | − | 19700.2i | 0.164116 | − | 0.164558i | ||||
\(347\) | − | 174903.i | − | 1.45257i | −0.687392 | − | 0.726287i | \(-0.741244\pi\) | ||
0.687392 | − | 0.726287i | \(-0.258756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 43896.9 | 0.360399 | 0.180199 | − | 0.983630i | \(-0.442326\pi\) | ||||
0.180199 | + | 0.983630i | \(0.442326\pi\) | |||||||
\(350\) | 80355.9 | + | 80140.4i | 0.655967 | + | 0.654208i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −73205.0 | − | 72228.8i | −0.590820 | − | 0.582941i | ||||
\(353\) | −155579. | −1.24854 | −0.624270 | − | 0.781209i | \(-0.714603\pi\) | ||||
−0.624270 | + | 0.781209i | \(0.714603\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 66485.4i | 0.527557i | ||||||||
\(356\) | 39.1303 | + | 14573.9i | 0.000308755 | + | 0.114994i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4969.13 | + | 4955.81i | 0.0387717 | + | 0.0386677i | ||||
\(359\) | − | 184004.i | − | 1.42771i | −0.700295 | − | 0.713853i | \(-0.746948\pi\) | ||
0.700295 | − | 0.713853i | \(-0.253052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −33386.7 | −0.256188 | ||||||||
\(362\) | 123685. | − | 124017.i | 0.943840 | − | 0.946377i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −159375. | + | 427.914i | −1.20287 | + | 0.00322964i | ||||
\(365\) | 64795.6 | 0.486362 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 165901.i | 1.23173i | 0.787851 | + | 0.615866i | \(0.211194\pi\) | ||||
−0.787851 | + | 0.615866i | \(0.788806\pi\) | |||||||
\(368\) | −462.064 | − | 86046.3i | −0.00341198 | − | 0.635385i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −53275.2 | + | 53418.5i | −0.389154 | + | 0.390201i | ||||
\(371\) | − | 75405.3i | − | 0.547841i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 130320. | 0.936685 | 0.468343 | − | 0.883547i | \(-0.344851\pi\) | ||||
0.468343 | + | 0.883547i | \(0.344851\pi\) | |||||||
\(374\) | 113369. | + | 113065.i | 0.810493 | + | 0.808320i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 130870. | − | 131928.i | 0.925686 | − | 0.933172i | ||||
\(377\) | −111825. | −0.786783 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 43645.6i | − | 0.303852i | −0.988392 | − | 0.151926i | \(-0.951453\pi\) | ||
0.988392 | − | 0.151926i | \(-0.0485475\pi\) | |||||||
\(380\) | −76316.9 | + | 204.907i | −0.528511 | + | 0.00141903i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −112511. | − | 112209.i | −0.771024 | − | 0.768957i | ||||
\(383\) | − | 273879.i | − | 1.86707i | −0.358485 | − | 0.933535i | \(-0.616707\pi\) | ||
0.358485 | − | 0.933535i | \(-0.383293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −69113.0 | −0.466271 | ||||||||
\(386\) | 59583.9 | − | 59744.1i | 0.399902 | − | 0.400978i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 756.462 | + | 281741.i | 0.00502486 | + | 1.87149i | ||||
\(389\) | 245188. | 1.62032 | 0.810159 | − | 0.586211i | \(-0.199381\pi\) | ||||
0.810159 | + | 0.586211i | \(0.199381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 133969.i | 0.876295i | ||||||||
\(392\) | −45741.9 | − | 45374.9i | −0.297675 | − | 0.295287i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 79812.9 | − | 80027.4i | 0.514139 | − | 0.515521i | ||||
\(395\) | 37964.4i | 0.243323i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4252.39 | −0.0269806 | −0.0134903 | − | 0.999909i | \(-0.504294\pi\) | ||||
−0.0134903 | + | 0.999909i | \(0.504294\pi\) | |||||||
\(398\) | −68153.3 | − | 67970.6i | −0.430250 | − | 0.429096i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 124421. | − | 668.132i | 0.777629 | − | 0.00417583i | ||||
\(401\) | −7331.22 | −0.0455919 | −0.0227959 | − | 0.999740i | \(-0.507257\pi\) | ||||
−0.0227959 | + | 0.999740i | \(0.507257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 108401.i | − | 0.667456i | ||||||
\(404\) | 286.143 | + | 106573.i | 0.00175315 | + | 0.652955i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −108349. | − | 108059.i | −0.657317 | − | 0.655554i | ||||
\(407\) | 160678.i | 0.969990i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28414.0 | −0.169858 | −0.0849289 | − | 0.996387i | \(-0.527066\pi\) | ||||
−0.0849289 | + | 0.996387i | \(0.527066\pi\) | |||||||
\(410\) | −82023.9 | + | 82244.5i | −0.487947 | + | 0.489259i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −108056. | + | 290.124i | −0.636580 | + | 0.00170919i | ||||
\(413\) | 67557.2 | 0.396070 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 96157.5i | 0.558325i | ||||||||
\(416\) | −122721. | + | 124380.i | −0.709142 | + | 0.718727i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −114777. | + | 115086.i | −0.656906 | + | 0.658672i | ||||
\(419\) | 158490.i | 0.902763i | 0.892331 | + | 0.451382i | \(0.149069\pi\) | ||||
−0.892331 | + | 0.451382i | \(0.850931\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −285592. | −1.61132 | −0.805659 | − | 0.592379i | \(-0.798189\pi\) | ||||
−0.805659 | + | 0.592379i | \(0.798189\pi\) | |||||||
\(422\) | −164495. | − | 164054.i | −0.923693 | − | 0.921216i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −58691.8 | − | 58220.9i | −0.326472 | − | 0.323853i | ||||
\(425\) | −193715. | −1.07247 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 345679.i | 1.89591i | ||||||||
\(428\) | −492.109 | + | 1.32129i | −0.00268642 | + | 7.21291e-6i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −74538.8 | − | 74339.0i | −0.403130 | − | 0.402050i | ||||
\(431\) | − | 115124.i | − | 0.619741i | −0.950779 | − | 0.309870i | \(-0.899714\pi\) | ||
0.950779 | − | 0.309870i | \(-0.100286\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 95600.5 | 0.509899 | 0.254950 | − | 0.966954i | \(-0.417941\pi\) | ||||
0.254950 | + | 0.966954i | \(0.417941\pi\) | |||||||
\(434\) | 104750. | − | 105032.i | 0.556130 | − | 0.557625i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −459.292 | − | 171061.i | −0.00241611 | − | 0.899869i | ||||
\(437\) | −135998. | −0.712148 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 371524.i | 1.92778i | 0.266300 | + | 0.963890i | \(0.414199\pi\) | ||||
−0.266300 | + | 0.963890i | \(0.585801\pi\) | |||||||
\(440\) | −53362.6 | + | 53794.1i | −0.275633 | + | 0.277862i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 192104. | − | 192620.i | 0.983313 | − | 0.985957i | ||||
\(443\) | − | 138264.i | − | 0.704536i | −0.935899 | − | 0.352268i | \(-0.885411\pi\) | ||
0.935899 | − | 0.352268i | \(-0.114589\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10738.1 | 0.0542258 | ||||||||
\(446\) | −47190.0 | − | 47063.5i | −0.237236 | − | 0.236600i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −239099. | + | 1925.95i | −1.19130 | + | 0.00959595i | ||||
\(449\) | −128427. | −0.637035 | −0.318518 | − | 0.947917i | \(-0.603185\pi\) | ||||
−0.318518 | + | 0.947917i | \(0.603185\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 247384.i | 1.21624i | ||||||||
\(452\) | 430.286 | + | 160258.i | 0.00210611 | + | 0.784411i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 159337. | + | 158910.i | 0.773046 | + | 0.770973i | ||||
\(455\) | 117427.i | 0.567214i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 293085. | 1.40334 | 0.701668 | − | 0.712504i | \(-0.252439\pi\) | ||||
0.701668 | + | 0.712504i | \(0.252439\pi\) | |||||||
\(458\) | −6914.17 | + | 6932.76i | −0.0329617 | + | 0.0330503i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −63399.4 | + | 170.224i | −0.299619 | + | 0.000804463i | ||||
\(461\) | −296134. | −1.39343 | −0.696717 | − | 0.717346i | \(-0.745357\pi\) | ||||
−0.696717 | + | 0.717346i | \(0.745357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 354683.i | − | 1.65455i | −0.561801 | − | 0.827273i | \(-0.689891\pi\) | ||
0.561801 | − | 0.827273i | \(-0.310109\pi\) | |||||||
\(464\) | −167765. | + | 900.890i | −0.779230 | + | 0.00418442i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −217415. | + | 218000.i | −1.00119 | + | 1.00388i | ||||
\(467\) | 116644.i | 0.534848i | 0.963579 | + | 0.267424i | \(0.0861724\pi\) | ||||
−0.963579 | + | 0.267424i | \(0.913828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 208007. | 0.945656 | ||||||||
\(470\) | −96945.0 | − | 96685.1i | −0.438864 | − | 0.437687i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 52161.4 | − | 52583.2i | 0.234134 | − | 0.236028i | ||||
\(473\) | −224206. | −1.00213 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 196650.i | − | 0.871578i | ||||||
\(476\) | 372268. | − | 999.522i | 1.64302 | − | 0.00441142i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 73804.1 | + | 73606.2i | 0.323017 | + | 0.322151i | ||||
\(479\) | − | 104079.i | − | 0.453618i | −0.973939 | − | 0.226809i | \(-0.927171\pi\) | ||
0.973939 | − | 0.226809i | \(-0.0728293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 273002. | 1.17998 | ||||||||
\(482\) | 79088.5 | − | 79301.1i | 0.340423 | − | 0.341338i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −195.678 | − | 72879.4i | −0.000835316 | − | 0.311110i | ||||
\(485\) | 207587. | 0.882503 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 101284.i | − | 0.427055i | −0.976937 | − | 0.213527i | \(-0.931505\pi\) | ||
0.976937 | − | 0.213527i | \(-0.0684953\pi\) | |||||||
\(488\) | 269059. | + | 266901.i | 1.12982 | + | 1.12075i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −33522.5 | + | 33612.6i | −0.139619 | + | 0.139994i | ||||
\(491\) | 175225.i | 0.726831i | 0.931627 | + | 0.363416i | \(0.118389\pi\) | ||||
−0.931627 | + | 0.363416i | \(0.881611\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 261200. | 1.07468 | ||||||||
\(494\) | 195538. | + | 195014.i | 0.801268 | + | 0.799119i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −873.306 | − | 162628.i | −0.00354979 | − | 0.661048i | ||||
\(497\) | 329223. | 1.33284 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 96102.5i | − | 0.385952i | −0.981203 | − | 0.192976i | \(-0.938186\pi\) | ||
0.981203 | − | 0.192976i | \(-0.0618140\pi\) | |||||||
\(500\) | −562.661 | − | 209561.i | −0.00225065 | − | 0.838244i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −56028.4 | − | 55878.2i | −0.222331 | − | 0.221735i | ||||
\(503\) | 164729.i | 0.651080i | 0.945528 | + | 0.325540i | \(0.105546\pi\) | ||||
−0.945528 | + | 0.325540i | \(0.894454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 78522.7 | 0.307902 | ||||||||
\(506\) | −95349.8 | + | 95606.1i | −0.372408 | + | 0.373409i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −257403. | + | 691.117i | −0.997440 | + | 0.00267808i | ||||
\(509\) | 85940.1 | 0.331711 | 0.165856 | − | 0.986150i | \(-0.446961\pi\) | ||||
0.165856 | + | 0.986150i | \(0.446961\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 320855.i | − | 1.22876i | ||||||
\(512\) | −183111. | + | 187590.i | −0.698512 | + | 0.715598i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 218270. | − | 218857.i | 0.826166 | − | 0.828388i | ||||
\(515\) | 79615.3i | 0.300180i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −291602. | −1.09096 | ||||||||
\(518\) | 264518. | + | 263809.i | 0.985815 | + | 0.983172i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 91399.7 | + | 90666.4i | 0.338017 | + | 0.335305i | ||||
\(521\) | 173047. | 0.637514 | 0.318757 | − | 0.947836i | \(-0.396735\pi\) | ||||
0.318757 | + | 0.947836i | \(0.396735\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 252188.i | − | 0.921978i | −0.887406 | − | 0.460989i | \(-0.847495\pi\) | ||
0.887406 | − | 0.460989i | \(-0.152505\pi\) | |||||||
\(524\) | −334502. | + | 898.123i | −1.21825 | + | 0.00327095i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −60078.2 | − | 59917.1i | −0.217143 | − | 0.216560i | ||||
\(527\) | 253203.i | 0.911690i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 166862. | 0.596275 | ||||||||
\(530\) | −43013.0 | + | 43128.6i | −0.153126 | + | 0.153537i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1014.66 | + | 377907.i | 0.00358508 | + | 1.33525i | ||||
\(533\) | 420321. | 1.47954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 362.586i | 0.00126679i | ||||||||
\(536\) | 160604. | − | 161903.i | 0.559019 | − | 0.563540i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3124.71 | − | 3133.11i | 0.0107956 | − | 0.0108246i | ||||
\(539\) | 101104.i | 0.348008i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −472358. | −1.61390 | −0.806950 | − | 0.590620i | \(-0.798883\pi\) | ||||
−0.806950 | + | 0.590620i | \(0.798883\pi\) | |||||||
\(542\) | 93571.7 | + | 93320.8i | 0.318527 | + | 0.317673i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 286652. | − | 290527.i | 0.968630 | − | 0.981721i | ||||
\(545\) | −126038. | −0.424335 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 384377.i | − | 1.28465i | −0.766434 | − | 0.642323i | \(-0.777971\pi\) | ||
0.766434 | − | 0.642323i | \(-0.222029\pi\) | |||||||
\(548\) | 200.879 | + | 74816.5i | 0.000668918 | + | 0.249136i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −138244. | − | 137873.i | −0.457005 | − | 0.455779i | ||||
\(551\) | 265157.i | 0.873372i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 187993. | 0.614739 | ||||||||
\(554\) | −81469.4 | + | 81688.4i | −0.265445 | + | 0.266159i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −148881. | + | 399.737i | −0.481602 | + | 0.00129308i | ||||
\(557\) | 19803.1 | 0.0638297 | 0.0319148 | − | 0.999491i | \(-0.489839\pi\) | ||||
0.0319148 | + | 0.999491i | \(0.489839\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 380940.i | 1.21908i | ||||||||
\(560\) | 946.027 | + | 176171.i | 0.00301667 | + | 0.561768i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 90743.4 | − | 90987.4i | 0.287304 | − | 0.288077i | ||||
\(563\) | 153074.i | 0.482929i | 0.970410 | + | 0.241465i | \(0.0776278\pi\) | ||||
−0.970410 | + | 0.241465i | \(0.922372\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 118078. | 0.369891 | ||||||||
\(566\) | −202052. | − | 201510.i | −0.630710 | − | 0.629019i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 254195. | − | 256251.i | 0.787898 | − | 0.794271i | ||||
\(569\) | 51911.0 | 0.160337 | 0.0801687 | − | 0.996781i | \(-0.474454\pi\) | ||||
0.0801687 | + | 0.996781i | \(0.474454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 107343.i | − | 0.329232i | −0.986358 | − | 0.164616i | \(-0.947361\pi\) | ||
0.986358 | − | 0.164616i | \(-0.0526385\pi\) | |||||||
\(572\) | 274188. | − | 736.182i | 0.838023 | − | 0.00225005i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 407259. | + | 406167.i | 1.23608 | + | 1.23277i | ||||
\(575\) | − | 163364.i | − | 0.494108i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −114098. | −0.342710 | −0.171355 | − | 0.985209i | \(-0.554814\pi\) | ||||
−0.171355 | + | 0.985209i | \(0.554814\pi\) | |||||||
\(578\) | −212801. | + | 213373.i | −0.636968 | + | 0.638681i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 331.888 | + | 123610.i | 0.000986587 | + | 0.367450i | ||||
\(581\) | 476153. | 1.41057 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 129727.i | 0.381674i | ||||||||
\(584\) | −249738. | − | 247734.i | −0.732249 | − | 0.726374i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −103499. | + | 103777.i | −0.301397 | + | 0.302208i | ||||
\(587\) | − | 52235.3i | − | 0.151596i | −0.997123 | − | 0.0757980i | \(-0.975850\pi\) | ||
0.997123 | − | 0.0757980i | \(-0.0241504\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −257038. | −0.740912 | ||||||||
\(590\) | −38639.8 | − | 38536.2i | −0.111002 | − | 0.110704i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 409572. | − | 2199.38i | 1.16866 | − | 0.00627562i | ||||
\(593\) | −277354. | −0.788724 | −0.394362 | − | 0.918955i | \(-0.629034\pi\) | ||||
−0.394362 | + | 0.918955i | \(0.629034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 274287.i | − | 0.774767i | ||||||
\(596\) | −1064.16 | − | 396343.i | −0.00299582 | − | 1.11578i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 162441. | + | 162005.i | 0.454248 | + | 0.453030i | ||||
\(599\) | − | 19107.2i | − | 0.0532528i | −0.999645 | − | 0.0266264i | \(-0.991524\pi\) | ||
0.999645 | − | 0.0266264i | \(-0.00847645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −418892. | −1.15972 | −0.579861 | − | 0.814716i | \(-0.696893\pi\) | ||||
−0.579861 | + | 0.814716i | \(0.696893\pi\) | |||||||
\(602\) | −368112. | + | 369102.i | −1.01575 | + | 1.01848i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 163352. | − | 438.593i | 0.447765 | − | 0.00120223i | ||||
\(605\) | −53697.5 | −0.146704 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 382383.i | 1.03782i | 0.854830 | + | 0.518909i | \(0.173662\pi\) | ||||
−0.854830 | + | 0.518909i | \(0.826338\pi\) | |||||||
\(608\) | 294927. | + | 290994.i | 0.797826 | + | 0.787186i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 197183. | − | 197713.i | 0.529920 | − | 0.531345i | ||||
\(611\) | 495450.i | 1.32714i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −210852. | −0.561121 | −0.280560 | − | 0.959836i | \(-0.590520\pi\) | ||||
−0.280560 | + | 0.959836i | \(0.590520\pi\) | |||||||
\(614\) | 33046.7 | + | 32958.1i | 0.0876579 | + | 0.0874229i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 266378. | + | 264241.i | 0.702000 | + | 0.696368i | ||||
\(617\) | −626580. | −1.64591 | −0.822955 | − | 0.568106i | \(-0.807676\pi\) | ||||
−0.822955 | + | 0.568106i | \(0.807676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 41204.9i | − | 0.107539i | −0.998553 | − | 0.0537697i | \(-0.982876\pi\) | ||
0.998553 | − | 0.0537697i | \(-0.0171237\pi\) | |||||||
\(620\) | −119825. | + | 321.726i | −0.311721 | + | 0.000836956i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12280.6 | + | 12247.7i | 0.0317423 | + | 0.0316572i | ||||
\(623\) | − | 53172.8i | − | 0.136998i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 149361. | 0.382365 | ||||||||
\(626\) | −244326. | + | 244983.i | −0.623478 | + | 0.625155i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1244.66 | + | 463567.i | 0.00315595 | + | 1.17542i | ||||
\(629\) | −637678. | −1.61176 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 150814.i | − | 0.378777i | −0.981902 | − | 0.189389i | \(-0.939349\pi\) | ||
0.981902 | − | 0.189389i | \(-0.0606506\pi\) | |||||||
\(632\) | 145150. | − | 146324.i | 0.363399 | − | 0.366338i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −69576.9 | + | 69764.0i | −0.173096 | + | 0.173561i | ||||
\(635\) | 189655.i | 0.470345i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 171782. | 0.423348 | ||||||||
\(638\) | 186404. | + | 185904.i | 0.457946 | + | 0.456718i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 137853. | + | 135286.i | 0.336555 | + | 0.330288i | ||||
\(641\) | −428379. | −1.04259 | −0.521293 | − | 0.853378i | \(-0.674550\pi\) | ||||
−0.521293 | + | 0.853378i | \(0.674550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 85771.0i | 0.207452i | 0.994606 | + | 0.103726i | \(0.0330766\pi\) | ||||
−0.994606 | + | 0.103726i | \(0.966923\pi\) | |||||||
\(644\) | 842.919 | + | 313941.i | 0.00203242 | + | 0.756967i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −456738. | − | 455513.i | −1.09447 | − | 1.09153i | ||||
\(647\) | − | 128368.i | − | 0.306653i | −0.988176 | − | 0.153327i | \(-0.951001\pi\) | ||
0.988176 | − | 0.153327i | \(-0.0489986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −116225. | −0.275937 | ||||||||
\(650\) | −234255. | + | 234885.i | −0.554451 | + | 0.555942i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −283781. | + | 761.940i | −0.667557 | + | 0.00179236i | ||||
\(653\) | 465879. | 1.09256 | 0.546282 | − | 0.837601i | \(-0.316043\pi\) | ||||
0.546282 | + | 0.837601i | \(0.316043\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 246461.i | 0.574468i | ||||||||
\(656\) | 630587. | − | 3386.22i | 1.46534 | − | 0.00786878i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −478766. | + | 480053.i | −1.10579 | + | 1.10876i | ||||
\(659\) | 351017.i | 0.808271i | 0.914699 | + | 0.404135i | \(0.132427\pi\) | ||||
−0.914699 | + | 0.404135i | \(0.867573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −282262. | −0.646026 | −0.323013 | − | 0.946395i | \(-0.604696\pi\) | ||||
−0.323013 | + | 0.946395i | \(0.604696\pi\) | |||||||
\(662\) | −530375. | − | 528953.i | −1.21023 | − | 1.20698i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 367641. | − | 370614.i | 0.833850 | − | 0.840594i | ||||
\(665\) | 278442. | 0.629638 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 220276.i | 0.495125i | ||||||||
\(668\) | 657015. | − | 1764.06i | 1.47239 | − | 0.00395330i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −118971. | − | 118652.i | −0.265029 | − | 0.264318i | ||||
\(671\) | − | 594704.i | − | 1.32086i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −797180. | −1.76006 | −0.880028 | − | 0.474922i | \(-0.842476\pi\) | ||||
−0.880028 | + | 0.474922i | \(0.842476\pi\) | |||||||
\(674\) | 285172. | − | 285939.i | 0.627751 | − | 0.629438i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.8647 | − | 8888.32i | −5.22231e−5 | − | 0.0194503i | ||||
\(677\) | −281346. | −0.613852 | −0.306926 | − | 0.951733i | \(-0.599300\pi\) | ||||
−0.306926 | + | 0.951733i | \(0.599300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.02793e6i | − | 2.22958i | ||||||
\(680\) | −213491. | − | 211779.i | −0.461703 | − | 0.457999i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −180212. | + | 180697.i | −0.387450 | + | 0.388491i | ||||
\(683\) | − | 687094.i | − | 1.47291i | −0.676489 | − | 0.736453i | \(-0.736499\pi\) | ||
0.676489 | − | 0.736453i | \(-0.263501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55124.8 | 0.117480 | ||||||||
\(686\) | −230521. | − | 229903.i | −0.489849 | − | 0.488535i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3068.96 | + | 571506.i | 0.00648357 | + | 1.20738i | ||||
\(689\) | 220414. | 0.464303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 329040.i | 0.689116i | 0.938765 | + | 0.344558i | \(0.111971\pi\) | ||||
−0.938765 | + | 0.344558i | \(0.888029\pi\) | |||||||
\(692\) | 298.812 | + | 111291.i | 0.000624002 | + | 0.232407i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 495364. | + | 494036.i | 1.02850 | + | 1.02574i | ||||
\(695\) | 109695.i | 0.227100i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −981786. | −2.02093 | ||||||||
\(698\) | −123992. | + | 124326.i | −0.254498 | + | 0.255182i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −453951. | + | 1218.84i | −0.926431 | + | 0.00248742i | ||||
\(701\) | 961471. | 1.95659 | 0.978296 | − | 0.207214i | \(-0.0664395\pi\) | ||||
0.978296 | + | 0.207214i | \(0.0664395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 647338.i | − | 1.30985i | ||||||
\(704\) | 411345. | − | 3313.39i | 0.829966 | − | 0.00668539i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 439453. | − | 440635.i | 0.881665 | − | 0.884035i | ||||
\(707\) | − | 388830.i | − | 0.777894i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −598276. | −1.19017 | −0.595085 | − | 0.803663i | \(-0.702882\pi\) | ||||
−0.595085 | + | 0.803663i | \(0.702882\pi\) | |||||||
\(710\) | −188301. | − | 187796.i | −0.373540 | − | 0.372538i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −41387.1 | − | 41055.1i | −0.0816404 | − | 0.0809854i | ||||
\(713\) | −213531. | −0.420032 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 202022.i | − | 0.395171i | ||||||
\(716\) | −28071.9 | + | 75.3717i | −0.0547578 | + | 0.000147022i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 521141. | + | 519744.i | 1.01090 | + | 1.00819i | ||||
\(719\) | 608601.i | 1.17727i | 0.808400 | + | 0.588633i | \(0.200334\pi\) | ||||
−0.808400 | + | 0.588633i | \(0.799666\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 394240. | 0.758385 | ||||||||
\(722\) | 94305.1 | − | 94558.6i | 0.180909 | − | 0.181396i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1881.09 | + | 700604.i | 0.00358866 | + | 1.33658i | ||||
\(725\) | −318513. | −0.605970 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 458391.i | − | 0.867296i | −0.901082 | − | 0.433648i | \(-0.857226\pi\) | ||
0.901082 | − | 0.433648i | \(-0.142774\pi\) | |||||||
\(728\) | 448963. | − | 452594.i | 0.847125 | − | 0.853976i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −183023. | + | 183515.i | −0.343448 | + | 0.344371i | ||||
\(731\) | − | 889801.i | − | 1.66517i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 70695.6 | 0.131578 | 0.0657892 | − | 0.997834i | \(-0.479044\pi\) | ||||
0.0657892 | + | 0.997834i | \(0.479044\pi\) | |||||||
\(734\) | −469868. | − | 468608.i | −0.872135 | − | 0.869796i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 245007. | + | 241740.i | 0.452297 | + | 0.446265i | ||||
\(737\) | −357855. | −0.658828 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 476430.i | − | 0.872390i | −0.899852 | − | 0.436195i | \(-0.856326\pi\) | ||
0.899852 | − | 0.436195i | \(-0.143674\pi\) | |||||||
\(740\) | −810.251 | − | 301775.i | −0.00147964 | − | 0.551086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 213565. | + | 212992.i | 0.387901 | + | 0.386861i | ||||
\(743\) | 126020.i | 0.228277i | 0.993465 | + | 0.114139i | \(0.0364108\pi\) | ||||
−0.993465 | + | 0.114139i | \(0.963589\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −292026. | −0.526149 | ||||||||
\(746\) | −368106. | + | 369095.i | −0.661447 | + | 0.663225i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −640448. | + | 1719.57i | −1.14467 | + | 0.00307339i | ||||
\(749\) | 1795.45 | 0.00320045 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 204276.i | 0.362191i | 0.983465 | + | 0.181096i | \(0.0579644\pi\) | ||||
−0.983465 | + | 0.181096i | \(0.942036\pi\) | |||||||
\(752\) | 3991.48 | + | 743300.i | 0.00705827 | + | 1.31440i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 315863. | − | 316712.i | 0.555592 | − | 0.557086i | ||||
\(755\) | − | 120358.i | − | 0.211145i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 588244. | 1.02652 | 0.513258 | − | 0.858235i | \(-0.328438\pi\) | ||||
0.513258 | + | 0.858235i | \(0.328438\pi\) | |||||||
\(758\) | 123614. | + | 123282.i | 0.215144 | + | 0.214567i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 214987. | − | 216725.i | 0.372207 | − | 0.375217i | ||||
\(761\) | 50737.5 | 0.0876113 | 0.0438056 | − | 0.999040i | \(-0.486052\pi\) | ||||
0.0438056 | + | 0.999040i | \(0.486052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 624116.i | 1.07205i | ||||||||
\(764\) | 635603. | − | 1706.56i | 1.08893 | − | 0.00292372i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 775685. | + | 773605.i | 1.32199 | + | 1.31844i | ||||
\(767\) | 197474.i | 0.335675i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 882679. | 1.49262 | 0.746312 | − | 0.665597i | \(-0.231823\pi\) | ||||
0.746312 | + | 0.665597i | \(0.231823\pi\) | |||||||
\(770\) | 195218. | − | 195743.i | 0.329260 | − | 0.330146i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 906.197 | + | 337509.i | 0.00152051 | + | 0.566306i | ||||
\(773\) | 100820. | 0.168728 | 0.0843642 | − | 0.996435i | \(-0.473114\pi\) | ||||
0.0843642 | + | 0.996435i | \(0.473114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 308760.i | − | 0.514065i | ||||||
\(776\) | −800090. | − | 793671.i | −1.32866 | − | 1.31801i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −692565. | + | 694427.i | −1.14420 | + | 1.14727i | ||||
\(779\) | − | 996658.i | − | 1.64237i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −566393. | −0.928573 | ||||||||
\(782\) | −379430. | − | 378412.i | −0.620466 | − | 0.618802i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 257716. | − | 1383.92i | 0.419284 | − | 0.00225153i | ||||
\(785\) | 341556. | 0.554272 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 113818.i | − | 0.183765i | −0.995770 | − | 0.0918826i | \(-0.970712\pi\) | ||
0.995770 | − | 0.0918826i | \(-0.0292884\pi\) | |||||||
\(788\) | 1213.86 | + | 452095.i | 0.00195485 | + | 0.728078i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −107524. | − | 107235.i | −0.172286 | − | 0.171824i | ||||
\(791\) | − | 584701.i | − | 0.934504i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.01044e6 | −1.60681 | ||||||||
\(794\) | 12011.4 | − | 12043.7i | 0.0190526 | − | 0.0191038i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 385015. | − | 1033.75i | 0.607648 | − | 0.00163151i | ||||
\(797\) | 701182. | 1.10386 | 0.551930 | − | 0.833890i | \(-0.313892\pi\) | ||||
0.551930 | + | 0.833890i | \(0.313892\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.15727e6i | − | 1.81277i | ||||||
\(800\) | −349550. | + | 354274.i | −0.546171 | + | 0.553553i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20708.0 | − | 20763.6i | 0.0321950 | − | 0.0322816i | ||||
\(803\) | 551998.i | 0.856064i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 231312. | 0.356949 | ||||||||
\(806\) | 307015. | + | 306192.i | 0.472596 | + | 0.471329i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −302646. | − | 300218.i | −0.463566 | − | 0.459847i | ||||
\(809\) | −514560. | −0.786211 | −0.393105 | − | 0.919493i | \(-0.628599\pi\) | ||||
−0.393105 | + | 0.919493i | \(0.628599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36669.2i | 0.0557519i | 0.999611 | + | 0.0278759i | \(0.00887434\pi\) | ||||
−0.999611 | + | 0.0278759i | \(0.991126\pi\) | |||||||
\(812\) | 612094. | − | 1643.44i | 0.928338 | − | 0.00249254i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −455075. | − | 453855.i | −0.686807 | − | 0.684965i | ||||
\(815\) | 209090.i | 0.314788i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 903279. | 1.35325 | ||||||||
\(818\) | 80258.9 | − | 80474.7i | 0.119946 | − | 0.120269i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1247.48 | − | 464620.i | −0.00185527 | − | 0.690987i | ||||
\(821\) | 478983. | 0.710614 | 0.355307 | − | 0.934750i | \(-0.384376\pi\) | ||||
0.355307 | + | 0.934750i | \(0.384376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 784187.i | 1.15776i | 0.815411 | + | 0.578882i | \(0.196511\pi\) | ||||
−0.815411 | + | 0.578882i | \(0.803489\pi\) | |||||||
\(824\) | 304395. | − | 306857.i | 0.448315 | − | 0.451941i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −190824. | + | 191337.i | −0.279687 | + | 0.280439i | ||||
\(827\) | − | 1.21724e6i | − | 1.77978i | −0.456175 | − | 0.889890i | \(-0.650781\pi\) | ||
0.456175 | − | 0.889890i | \(-0.349219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −335235. | −0.487799 | −0.243900 | − | 0.969801i | \(-0.578427\pi\) | ||||
−0.243900 | + | 0.969801i | \(0.578427\pi\) | |||||||
\(830\) | −272339. | − | 271609.i | −0.395325 | − | 0.394265i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5629.66 | − | 698901.i | −0.00813271 | − | 1.00965i | ||||
\(833\) | −401248. | −0.578259 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 484089.i | − | 0.694308i | ||||||
\(836\) | −1745.62 | − | 650149.i | −0.00249768 | − | 0.930252i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −448879. | − | 447675.i | −0.639206 | − | 0.637492i | ||||
\(839\) | − | 933549.i | − | 1.32621i | −0.748525 | − | 0.663107i | \(-0.769238\pi\) | ||
0.748525 | − | 0.663107i | \(-0.230762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −277808. | −0.392783 | ||||||||
\(842\) | 806690. | − | 808859.i | 1.13784 | − | 1.14090i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 929274. | − | 2495.06i | 1.30454 | − | 0.00350264i | ||||
\(845\) | −6548.91 | −0.00917182 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 265900.i | 0.370639i | ||||||||
\(848\) | 330677. | − | 1775.72i | 0.459846 | − | 0.00246935i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 547174. | − | 548645.i | 0.757334 | − | 0.759370i | ||||
\(851\) | − | 537768.i | − | 0.742567i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 249820. | 0.343343 | 0.171672 | − | 0.985154i | \(-0.445083\pi\) | ||||
0.171672 | + | 0.985154i | \(0.445083\pi\) | |||||||
\(854\) | −979039. | − | 976413.i | −1.34241 | − | 1.33881i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1386.28 | − | 1397.49i | 0.00189193 | − | 0.00190723i | ||||
\(857\) | −660987. | −0.899976 | −0.449988 | − | 0.893035i | \(-0.648572\pi\) | ||||
−0.449988 | + | 0.893035i | \(0.648572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 827557.i | − | 1.12153i | −0.827974 | − | 0.560766i | \(-0.810507\pi\) | ||
0.827974 | − | 0.560766i | \(-0.189493\pi\) | |||||||
\(860\) | 421089. | − | 1130.60i | 0.569347 | − | 0.00152867i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 326056. | + | 325181.i | 0.438811 | + | 0.437634i | ||||
\(863\) | 1.22724e6i | 1.64781i | 0.566728 | + | 0.823905i | \(0.308209\pi\) | ||||
−0.566728 | + | 0.823905i | \(0.691791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 81999.4 | 0.109592 | ||||||||
\(866\) | −270036. | + | 270762.i | −0.360069 | + | 0.361037i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1593.13 | + | 593353.i | 0.00211451 | + | 0.787542i | ||||
\(869\) | −323422. | −0.428282 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 608019.i | 0.801458i | ||||||||
\(872\) | 485781. | + | 481884.i | 0.638863 | + | 0.633738i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 384144. | − | 385177.i | 0.502888 | − | 0.504240i | ||||
\(875\) | 764581.i | 0.998637i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −626211. | −0.814182 | −0.407091 | − | 0.913388i | \(-0.633457\pi\) | ||||
−0.407091 | + | 0.913388i | \(0.633457\pi\) | |||||||
\(878\) | −1.05224e6 | − | 1.04942e6i | −1.36498 | − | 1.36132i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1627.54 | − | 303083.i | −0.00210168 | − | 0.391378i | ||||
\(881\) | −447853. | −0.577011 | −0.288505 | − | 0.957478i | \(-0.593158\pi\) | ||||
−0.288505 | + | 0.957478i | \(0.593158\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.38655e6i | 1.77833i | 0.457582 | + | 0.889167i | \(0.348715\pi\) | ||||
−0.457582 | + | 0.889167i | \(0.651285\pi\) | |||||||
\(884\) | 2921.67 | + | 1.08816e6i | 0.00373875 | + | 1.39248i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 391595. | + | 390545.i | 0.498850 | + | 0.497513i | ||||
\(887\) | 1.53191e6i | 1.94709i | 0.228490 | + | 0.973546i | \(0.426621\pi\) | ||||
−0.228490 | + | 0.973546i | \(0.573379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 939134. | 1.18829 | ||||||||
\(890\) | −30331.0 | + | 30412.6i | −0.0382919 | + | 0.0383949i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 266588. | − | 715.777i | 0.335051 | − | 0.000899598i | ||||
\(893\) | 1.17480e6 | 1.47320 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20683.4i | 0.0258211i | ||||||||
\(896\) | 669911. | − | 682621.i | 0.834451 | − | 0.850283i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 362758. | − | 363734.i | 0.449847 | − | 0.451056i | ||||
\(899\) | 416323.i | 0.515124i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −514844. | −0.634200 | ||||||||
\(902\) | −700646. | − | 698767.i | −0.861164 | − | 0.858854i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −455103. | − | 451451.i | −0.556894 | − | 0.552426i | ||||
\(905\) | 516205. | 0.630268 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 326429.i | 0.396802i | 0.980121 | + | 0.198401i | \(0.0635749\pi\) | ||||
−0.980121 | + | 0.198401i | \(0.936425\pi\) | |||||||
\(908\) | −900136. | + | 2416.82i | −1.09178 | + | 0.00293139i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −332580. | − | 331689.i | −0.401619 | − | 0.400542i | ||||
\(911\) | − | 1.29034e6i | − | 1.55477i | −0.629026 | − | 0.777384i | \(-0.716546\pi\) | ||
0.629026 | − | 0.777384i | \(-0.283454\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −819172. | −0.982729 | ||||||||
\(914\) | −827856. | + | 830082.i | −0.990975 | + | 0.993639i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −105.156 | − | 39164.9i | −0.000125327 | − | 0.0466774i | ||||
\(917\) | 1.22043e6 | 1.45135 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 844321.i | − | 0.999715i | −0.866108 | − | 0.499858i | \(-0.833386\pi\) | ||
0.866108 | − | 0.499858i | \(-0.166614\pi\) | |||||||
\(920\) | 178597. | − | 180042.i | 0.211008 | − | 0.212715i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 836468. | − | 838717.i | 0.983983 | − | 0.986628i | ||||
\(923\) | 962338.i | 1.12960i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 777598. | 0.908807 | ||||||||
\(926\) | 1.00454e6 | + | 1.00185e6i | 1.17151 | + | 1.16837i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 471322. | − | 477693.i | 0.547296 | − | 0.554693i | ||||
\(929\) | −603267. | −0.699002 | −0.349501 | − | 0.936936i | \(-0.613649\pi\) | ||||
−0.349501 | + | 0.936936i | \(0.613649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 407325.i | − | 0.469940i | ||||||
\(932\) | −3306.62 | − | 1.23154e6i | −0.00380673 | − | 1.41780i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −330363. | − | 329477.i | −0.378702 | − | 0.377687i | ||||
\(935\) | 471882.i | 0.539772i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −109044. | −0.124200 | −0.0621002 | − | 0.998070i | \(-0.519780\pi\) | ||||
−0.0621002 | + | 0.998070i | \(0.519780\pi\) | |||||||
\(938\) | −587544. | + | 589123.i | −0.667782 | + | 0.669577i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 547667. | − | 1470.46i | 0.619814 | − | 0.00166417i | ||||
\(941\) | −690952. | −0.780312 | −0.390156 | − | 0.920749i | \(-0.627579\pi\) | ||||
−0.390156 | + | 0.920749i | \(0.627579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 827961.i | − | 0.931079i | ||||||
\(944\) | 1590.90 | + | 296261.i | 0.00178525 | + | 0.332453i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 633299. | − | 635001.i | 0.707663 | − | 0.709565i | ||||
\(947\) | − | 1.20349e6i | − | 1.34197i | −0.741472 | − | 0.670984i | \(-0.765872\pi\) | ||
0.741472 | − | 0.670984i | \(-0.234128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 937880. | 1.04139 | ||||||||
\(950\) | 556956. | + | 555462.i | 0.617125 | + | 0.615471i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.04869e6 | + | 1.05717e6i | −1.15710 | + | 1.16646i | ||||
\(953\) | −1.58732e6 | −1.74775 | −0.873873 | − | 0.486154i | \(-0.838400\pi\) | ||||
−0.873873 | + | 0.486154i | \(0.838400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 468312.i | − | 0.513486i | ||||||
\(956\) | −416938. | + | 1119.46i | −0.456201 | + | 0.00122488i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 294773. | + | 293983.i | 0.321187 | + | 0.320325i | ||||
\(959\) | − | 272967.i | − | 0.296806i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 519945. | 0.563002 | ||||||||
\(962\) | −771129. | + | 773202.i | −0.833253 | + | 0.835493i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1202.84 | + | 447992.i | 0.00129435 | + | 0.482077i | ||||
\(965\) | 248677. | 0.267043 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 986601.i | 1.05509i | 0.849528 | + | 0.527544i | \(0.176887\pi\) | ||||
−0.849528 | + | 0.527544i | \(0.823113\pi\) | |||||||
\(968\) | 206963. | + | 205303.i | 0.220873 | + | 0.219101i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −586355. | + | 587932.i | −0.623186 | + | 0.624861i | ||||
\(971\) | − | 1.42706e6i | − | 1.51358i | −0.653658 | − | 0.756790i | \(-0.726767\pi\) | ||
0.653658 | − | 0.756790i | \(-0.273233\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 543189. | 0.573754 | ||||||||
\(974\) | 286859. | + | 286090.i | 0.302378 | + | 0.301568i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.51591e6 | + | 8140.38i | −1.59138 | + | 0.00854565i | ||||
\(977\) | −1.60332e6 | −1.67969 | −0.839847 | − | 0.542823i | \(-0.817355\pi\) | ||||
−0.839847 | + | 0.542823i | \(0.817355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 91478.3i | 0.0954449i | ||||||||
\(980\) | −509.836 | − | 189886.i | −0.000530858 | − | 0.197716i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −496277. | − | 494946.i | −0.514637 | − | 0.513257i | ||||
\(983\) | 1.46864e6i | 1.51987i | 0.649997 | + | 0.759936i | \(0.274770\pi\) | ||||
−0.649997 | + | 0.759936i | \(0.725230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 333104. | 0.343326 | ||||||||
\(986\) | −737793. | + | 739777.i | −0.758893 | + | 0.760934i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.10465e6 | + | 2965.92i | −1.13164 | + | 0.00303841i | ||||
\(989\) | 750388. | 0.767173 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.48147e6i | 1.50850i | 0.656585 | + | 0.754252i | \(0.272000\pi\) | ||||
−0.656585 | + | 0.754252i | \(0.728000\pi\) | |||||||
\(992\) | 463067. | + | 456891.i | 0.470566 | + | 0.464290i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −929931. | + | 932432.i | −0.941192 | + | 0.943722i | ||||
\(995\) | − | 283679.i | − | 0.286537i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46935.8 | −0.0472187 | −0.0236093 | − | 0.999721i | \(-0.507516\pi\) | ||||
−0.0236093 | + | 0.999721i | \(0.507516\pi\) | |||||||
\(998\) | 272184. | + | 271454.i | 0.273276 | + | 0.272543i | ||||
\(999\) | 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.163.6 | 22 | ||
3.2 | odd | 2 | 324.5.d.f.163.17 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.e.163.5 | 22 | ||
9.2 | odd | 6 | 36.5.f.a.31.3 | yes | 44 | ||
9.4 | even | 3 | 108.5.f.a.19.10 | 44 | |||
9.5 | odd | 6 | 36.5.f.a.7.13 | yes | 44 | ||
9.7 | even | 3 | 108.5.f.a.91.20 | 44 | |||
12.11 | even | 2 | 324.5.d.f.163.18 | 22 | |||
36.7 | odd | 6 | 108.5.f.a.91.10 | 44 | |||
36.11 | even | 6 | 36.5.f.a.31.13 | yes | 44 | ||
36.23 | even | 6 | 36.5.f.a.7.3 | ✓ | 44 | ||
36.31 | odd | 6 | 108.5.f.a.19.20 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.3 | ✓ | 44 | 36.23 | even | 6 | ||
36.5.f.a.7.13 | yes | 44 | 9.5 | odd | 6 | ||
36.5.f.a.31.3 | yes | 44 | 9.2 | odd | 6 | ||
36.5.f.a.31.13 | yes | 44 | 36.11 | even | 6 | ||
108.5.f.a.19.10 | 44 | 9.4 | even | 3 | |||
108.5.f.a.19.20 | 44 | 36.31 | odd | 6 | |||
108.5.f.a.91.10 | 44 | 36.7 | odd | 6 | |||
108.5.f.a.91.20 | 44 | 9.7 | even | 3 | |||
324.5.d.e.163.5 | 22 | 4.3 | odd | 2 | inner | ||
324.5.d.e.163.6 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.f.163.17 | 22 | 3.2 | odd | 2 | |||
324.5.d.f.163.18 | 22 | 12.11 | even | 2 |