Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,5,Mod(73,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.73");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.j (of order \(4\), degree \(2\), 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: | \(12.0942856808\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.8 | ||
Root | \(4.05053 + 4.05053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.73 |
Dual form | 117.5.j.b.109.8 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.05053 | + | 4.05053i | 1.01263 | + | 1.01263i | 0.999919 | + | 0.0127141i | \(0.00404712\pi\) |
0.0127141 | + | 0.999919i | \(0.495953\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.8136i | 1.05085i | ||||||||
\(5\) | −33.5573 | − | 33.5573i | −1.34229 | − | 1.34229i | −0.893772 | − | 0.448521i | \(-0.851951\pi\) |
−0.448521 | − | 0.893772i | \(-0.648049\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.7132 | − | 23.7132i | 0.483942 | − | 0.483942i | −0.422446 | − | 0.906388i | \(-0.638828\pi\) |
0.906388 | + | 0.422446i | \(0.138828\pi\) | |||||||
\(8\) | −3.29565 | + | 3.29565i | −0.0514945 | + | 0.0514945i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 271.850i | − | 2.71850i | ||||||
\(11\) | −32.2545 | + | 32.2545i | −0.266566 | + | 0.266566i | −0.827715 | − | 0.561149i | \(-0.810359\pi\) |
0.561149 | + | 0.827715i | \(0.310359\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 72.8001 | − | 152.516i | 0.430770 | − | 0.902462i | ||||
\(14\) | 192.102 | 0.980111 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 242.320 | 0.946562 | ||||||||
\(17\) | − | 354.222i | − | 1.22568i | −0.790206 | − | 0.612841i | \(-0.790027\pi\) | ||
0.790206 | − | 0.612841i | \(-0.209973\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −168.478 | − | 168.478i | −0.466699 | − | 0.466699i | 0.434145 | − | 0.900843i | \(-0.357051\pi\) |
−0.900843 | + | 0.434145i | \(0.857051\pi\) | |||||||
\(20\) | 564.221 | − | 564.221i | 1.41055 | − | 1.41055i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −261.296 | −0.539867 | ||||||||
\(23\) | 182.161i | 0.344349i | 0.985066 | + | 0.172175i | \(0.0550793\pi\) | ||||
−0.985066 | + | 0.172175i | \(0.944921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1627.19i | 2.60350i | ||||||||
\(26\) | 912.650 | − | 322.892i | 1.35007 | − | 0.477651i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 398.704 | + | 398.704i | 0.508551 | + | 0.508551i | ||||
\(29\) | −913.769 | −1.08653 | −0.543264 | − | 0.839562i | \(-0.682812\pi\) | ||||
−0.543264 | + | 0.839562i | \(0.682812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −876.095 | − | 876.095i | −0.911650 | − | 0.911650i | 0.0847522 | − | 0.996402i | \(-0.472990\pi\) |
−0.996402 | + | 0.0847522i | \(0.972990\pi\) | |||||||
\(32\) | 1034.25 | + | 1034.25i | 1.01001 | + | 1.01001i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1434.79 | − | 1434.79i | 1.24117 | − | 1.24117i | ||||
\(35\) | −1591.50 | −1.29918 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 112.687 | − | 112.687i | 0.0823135 | − | 0.0823135i | −0.664751 | − | 0.747065i | \(-0.731462\pi\) |
0.747065 | + | 0.664751i | \(0.231462\pi\) | |||||||
\(38\) | − | 1364.85i | − | 0.945189i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 221.186 | 0.138242 | ||||||||
\(41\) | 1133.48 | + | 1133.48i | 0.674287 | + | 0.674287i | 0.958701 | − | 0.284415i | \(-0.0917993\pi\) |
−0.284415 | + | 0.958701i | \(0.591799\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 411.247i | 0.222416i | 0.993797 | + | 0.111208i | \(0.0354720\pi\) | ||||
−0.993797 | + | 0.111208i | \(0.964528\pi\) | |||||||
\(44\) | −542.315 | − | 542.315i | −0.280121 | − | 0.280121i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −737.848 | + | 737.848i | −0.348700 | + | 0.348700i | ||||
\(47\) | 3000.97 | − | 3000.97i | 1.35852 | − | 1.35852i | 0.482772 | − | 0.875746i | \(-0.339630\pi\) |
0.875746 | − | 0.482772i | \(-0.160370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1276.37i | 0.531600i | ||||||||
\(50\) | −6590.99 | + | 6590.99i | −2.63639 | + | 2.63639i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2564.35 | + | 1224.03i | 0.948354 | + | 0.452675i | ||||
\(53\) | 4228.78 | 1.50544 | 0.752720 | − | 0.658341i | \(-0.228741\pi\) | ||||
0.752720 | + | 0.658341i | \(0.228741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2164.75 | 0.715619 | ||||||||
\(56\) | 156.301i | 0.0498407i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3701.25 | − | 3701.25i | −1.10025 | − | 1.10025i | ||||
\(59\) | −1690.19 | + | 1690.19i | −0.485547 | + | 0.485547i | −0.906898 | − | 0.421350i | \(-0.861556\pi\) |
0.421350 | + | 0.906898i | \(0.361556\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3760.65 | −1.01066 | −0.505328 | − | 0.862928i | \(-0.668628\pi\) | ||||
−0.505328 | + | 0.862928i | \(0.668628\pi\) | |||||||
\(62\) | − | 7097.31i | − | 1.84633i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4501.45i | 1.09899i | ||||||||
\(65\) | −7561.01 | + | 2675.06i | −1.78959 | + | 0.633149i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2631.54 | − | 2631.54i | −0.586219 | − | 0.586219i | 0.350386 | − | 0.936605i | \(-0.386050\pi\) |
−0.936605 | + | 0.350386i | \(0.886050\pi\) | |||||||
\(68\) | 5955.76 | 1.28801 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6446.43 | − | 6446.43i | −1.31560 | − | 1.31560i | ||||
\(71\) | −297.661 | − | 297.661i | −0.0590479 | − | 0.0590479i | 0.676966 | − | 0.736014i | \(-0.263294\pi\) |
−0.736014 | + | 0.676966i | \(0.763294\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2616.29 | − | 2616.29i | 0.490953 | − | 0.490953i | −0.417653 | − | 0.908606i | \(-0.637147\pi\) |
0.908606 | + | 0.417653i | \(0.137147\pi\) | |||||||
\(74\) | 912.887 | 0.166707 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2832.73 | − | 2832.73i | 0.490431 | − | 0.490431i | ||||
\(77\) | 1529.71i | 0.258005i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7885.52 | 1.26350 | 0.631752 | − | 0.775171i | \(-0.282336\pi\) | ||||
0.631752 | + | 0.775171i | \(0.282336\pi\) | |||||||
\(80\) | −8131.61 | − | 8131.61i | −1.27056 | − | 1.27056i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9182.36i | 1.36561i | ||||||||
\(83\) | 4078.45 | + | 4078.45i | 0.592024 | + | 0.592024i | 0.938178 | − | 0.346154i | \(-0.112512\pi\) |
−0.346154 | + | 0.938178i | \(0.612512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11886.7 | + | 11886.7i | −1.64522 | + | 1.64522i | ||||
\(86\) | −1665.77 | + | 1665.77i | −0.225226 | + | 0.225226i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 212.599i | − | 0.0274534i | ||||||
\(89\) | −1722.86 | + | 1722.86i | −0.217505 | + | 0.217505i | −0.807446 | − | 0.589941i | \(-0.799151\pi\) |
0.589941 | + | 0.807446i | \(0.299151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1890.32 | − | 5342.96i | −0.228272 | − | 0.645207i | ||||
\(92\) | −3062.78 | −0.361860 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24311.0 | 2.75136 | ||||||||
\(95\) | 11307.4i | 1.25289i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1560.33 | + | 1560.33i | 0.165834 | + | 0.165834i | 0.785146 | − | 0.619311i | \(-0.212588\pi\) |
−0.619311 | + | 0.785146i | \(0.712588\pi\) | |||||||
\(98\) | −5169.99 | + | 5169.99i | −0.538316 | + | 0.538316i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −27359.0 | −2.73590 | ||||||||
\(101\) | 9982.36i | 0.978567i | 0.872125 | + | 0.489283i | \(0.162742\pi\) | ||||
−0.872125 | + | 0.489283i | \(0.837258\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.56148i | 0.000618483i | 1.00000 | 0.000309241i | \(9.84346e-5\pi\) | |||||
−1.00000 | 0.000309241i | \(0.999902\pi\) | ||||||||
\(104\) | 262.716 | + | 742.563i | 0.0242896 | + | 0.0686541i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17128.8 | + | 17128.8i | 1.52446 | + | 1.52446i | ||||
\(107\) | 6183.10 | 0.540056 | 0.270028 | − | 0.962853i | \(-0.412967\pi\) | ||||
0.270028 | + | 0.962853i | \(0.412967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3694.46 | + | 3694.46i | 0.310956 | + | 0.310956i | 0.845280 | − | 0.534324i | \(-0.179434\pi\) |
−0.534324 | + | 0.845280i | \(0.679434\pi\) | |||||||
\(110\) | 8768.39 | + | 8768.39i | 0.724660 | + | 0.724660i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5746.17 | − | 5746.17i | 0.458081 | − | 0.458081i | ||||
\(113\) | 21267.9 | 1.66559 | 0.832794 | − | 0.553583i | \(-0.186740\pi\) | ||||
0.832794 | + | 0.553583i | \(0.186740\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6112.83 | − | 6112.83i | 0.462218 | − | 0.462218i | ||||
\(116\) | − | 15363.8i | − | 1.14178i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13692.3 | −0.983363 | ||||||||
\(119\) | −8399.72 | − | 8399.72i | −0.593159 | − | 0.593159i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12560.3i | 0.857885i | ||||||||
\(122\) | −15232.6 | − | 15232.6i | −1.02342 | − | 1.02342i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 14730.3 | − | 14730.3i | 0.958009 | − | 0.958009i | ||||
\(125\) | 33630.8 | − | 33630.8i | 2.15237 | − | 2.15237i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 26466.7i | − | 1.64094i | −0.571693 | − | 0.820468i | \(-0.693713\pi\) | ||
0.571693 | − | 0.820468i | \(-0.306287\pi\) | |||||||
\(128\) | −1685.19 | + | 1685.19i | −0.102856 | + | 0.102856i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −41461.5 | − | 19790.7i | −2.45334 | − | 1.17105i | ||||
\(131\) | −21491.7 | −1.25236 | −0.626178 | − | 0.779680i | \(-0.715382\pi\) | ||||
−0.626178 | + | 0.779680i | \(0.715382\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7990.30 | −0.451710 | ||||||||
\(134\) | − | 21318.3i | − | 1.18725i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1167.39 | + | 1167.39i | 0.0631159 | + | 0.0631159i | ||||
\(137\) | 5030.14 | − | 5030.14i | 0.268002 | − | 0.268002i | −0.560292 | − | 0.828295i | \(-0.689311\pi\) |
0.828295 | + | 0.560292i | \(0.189311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12182.9 | 0.630554 | 0.315277 | − | 0.949000i | \(-0.397903\pi\) | ||||
0.315277 | + | 0.949000i | \(0.397903\pi\) | |||||||
\(140\) | − | 26758.9i | − | 1.36525i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 2411.37i | − | 0.119588i | ||||||
\(143\) | 2571.20 | + | 7267.45i | 0.125737 | + | 0.355394i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30663.7 | + | 30663.7i | 1.45844 | + | 1.45844i | ||||
\(146\) | 21194.7 | 0.994311 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1894.68 | + | 1894.68i | 0.0864994 | + | 0.0864994i | ||||
\(149\) | 10032.3 | + | 10032.3i | 0.451887 | + | 0.451887i | 0.895980 | − | 0.444094i | \(-0.146474\pi\) |
−0.444094 | + | 0.895980i | \(0.646474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10057.5 | − | 10057.5i | 0.441098 | − | 0.441098i | −0.451283 | − | 0.892381i | \(-0.649033\pi\) |
0.892381 | + | 0.451283i | \(0.149033\pi\) | |||||||
\(152\) | 1110.49 | 0.0480649 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6196.14 | + | 6196.14i | −0.261264 | + | 0.261264i | ||||
\(155\) | 58798.9i | 2.44740i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8554.44 | 0.347050 | 0.173525 | − | 0.984829i | \(-0.444484\pi\) | ||||
0.173525 | + | 0.984829i | \(0.444484\pi\) | |||||||
\(158\) | 31940.6 | + | 31940.6i | 1.27947 | + | 1.27947i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 69413.7i | − | 2.71147i | ||||||
\(161\) | 4319.61 | + | 4319.61i | 0.166645 | + | 0.166645i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1164.17 | + | 1164.17i | −0.0438170 | + | 0.0438170i | −0.728676 | − | 0.684859i | \(-0.759864\pi\) |
0.684859 | + | 0.728676i | \(0.259864\pi\) | |||||||
\(164\) | −19057.8 | + | 19057.8i | −0.708576 | + | 0.708576i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 33039.8i | 1.19901i | ||||||||
\(167\) | −7534.77 | + | 7534.77i | −0.270170 | + | 0.270170i | −0.829169 | − | 0.558999i | \(-0.811186\pi\) |
0.558999 | + | 0.829169i | \(0.311186\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17961.3 | − | 22206.4i | −0.628875 | − | 0.777506i | ||||
\(170\) | −96295.3 | −3.33202 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6914.56 | −0.233726 | ||||||||
\(173\) | − | 39158.0i | − | 1.30836i | −0.756337 | − | 0.654182i | \(-0.773013\pi\) | ||
0.756337 | − | 0.654182i | \(-0.226987\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 38585.8 | + | 38585.8i | 1.25994 | + | 1.25994i | ||||
\(176\) | −7815.90 | + | 7815.90i | −0.252321 | + | 0.252321i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13957.0 | −0.440505 | ||||||||
\(179\) | − | 37765.1i | − | 1.17865i | −0.807897 | − | 0.589324i | \(-0.799394\pi\) | ||
0.807897 | − | 0.589324i | \(-0.200606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9590.57i | 0.292744i | 0.989230 | + | 0.146372i | \(0.0467596\pi\) | ||||
−0.989230 | + | 0.146372i | \(0.953240\pi\) | |||||||
\(182\) | 13985.0 | − | 29298.6i | 0.422202 | − | 0.884513i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −600.338 | − | 600.338i | −0.0177321 | − | 0.0177321i | ||||
\(185\) | −7562.97 | −0.220978 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11425.2 | + | 11425.2i | 0.326725 | + | 0.326725i | ||||
\(188\) | 50457.2 | + | 50457.2i | 1.42760 | + | 1.42760i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −45800.8 | + | 45800.8i | −1.26872 | + | 1.26872i | ||||
\(191\) | −46392.7 | −1.27170 | −0.635848 | − | 0.771814i | \(-0.719349\pi\) | ||||
−0.635848 | + | 0.771814i | \(0.719349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9357.45 | − | 9357.45i | 0.251213 | − | 0.251213i | −0.570255 | − | 0.821468i | \(-0.693155\pi\) |
0.821468 | + | 0.570255i | \(0.193155\pi\) | |||||||
\(194\) | 12640.4i | 0.335858i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21460.5 | −0.558633 | ||||||||
\(197\) | 4463.00 | + | 4463.00i | 0.114999 | + | 0.114999i | 0.762265 | − | 0.647266i | \(-0.224088\pi\) |
−0.647266 | + | 0.762265i | \(0.724088\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 71326.4i | 1.80113i | 0.434726 | + | 0.900563i | \(0.356845\pi\) | ||||
−0.434726 | + | 0.900563i | \(0.643155\pi\) | |||||||
\(200\) | −5362.65 | − | 5362.65i | −0.134066 | − | 0.134066i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −40433.9 | + | 40433.9i | −0.990929 | + | 0.990929i | ||||
\(203\) | −21668.4 | + | 21668.4i | −0.525816 | + | 0.525816i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 76072.9i | − | 1.81018i | ||||||
\(206\) | −26.5775 | + | 26.5775i | −0.000626296 | + | 0.000626296i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17640.9 | − | 36957.7i | 0.407750 | − | 0.854236i | ||||
\(209\) | 10868.4 | 0.248812 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −45146.1 | −1.01404 | −0.507020 | − | 0.861934i | \(-0.669253\pi\) | ||||
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(212\) | 71101.2i | 1.58199i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25044.8 | + | 25044.8i | 0.546878 | + | 0.546878i | ||||
\(215\) | 13800.4 | − | 13800.4i | 0.298548 | − | 0.298548i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −41550.0 | −0.882371 | ||||||||
\(218\) | 29929.1i | 0.629768i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 36397.3i | 0.752010i | ||||||||
\(221\) | −54024.5 | − | 25787.4i | −1.10613 | − | 0.527986i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22521.9 | + | 22521.9i | 0.452892 | + | 0.452892i | 0.896313 | − | 0.443421i | \(-0.146235\pi\) |
−0.443421 | + | 0.896313i | \(0.646235\pi\) | |||||||
\(224\) | 49050.9 | 0.977577 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 86146.3 | + | 86146.3i | 1.68663 | + | 1.68663i | ||||
\(227\) | −33678.9 | − | 33678.9i | −0.653592 | − | 0.653592i | 0.300264 | − | 0.953856i | \(-0.402925\pi\) |
−0.953856 | + | 0.300264i | \(0.902925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 55067.0 | − | 55067.0i | 1.05008 | − | 1.05008i | 0.0513970 | − | 0.998678i | \(-0.483633\pi\) |
0.998678 | − | 0.0513970i | \(-0.0163674\pi\) | |||||||
\(230\) | 49520.4 | 0.936114 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3011.46 | − | 3011.46i | 0.0559502 | − | 0.0559502i | ||||
\(233\) | 6668.81i | 0.122839i | 0.998112 | + | 0.0614195i | \(0.0195627\pi\) | ||||
−0.998112 | + | 0.0614195i | \(0.980437\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −201409. | −3.64706 | ||||||||
\(236\) | −28418.2 | − | 28418.2i | −0.510239 | − | 0.510239i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 68046.7i | − | 1.20130i | ||||||
\(239\) | 24924.8 | + | 24924.8i | 0.436350 | + | 0.436350i | 0.890782 | − | 0.454431i | \(-0.150158\pi\) |
−0.454431 | + | 0.890782i | \(0.650158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4314.21 | − | 4314.21i | 0.0742792 | − | 0.0742792i | −0.668991 | − | 0.743270i | \(-0.733274\pi\) |
0.743270 | + | 0.668991i | \(0.233274\pi\) | |||||||
\(242\) | −50875.9 | + | 50875.9i | −0.868723 | + | 0.868723i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 63230.2i | − | 1.06205i | ||||||
\(245\) | 42831.7 | − | 42831.7i | 0.713564 | − | 0.713564i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −37960.9 | + | 13430.4i | −0.622217 | + | 0.220138i | ||||
\(248\) | 5774.61 | 0.0938900 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 272445. | 4.35913 | ||||||||
\(251\) | 100235.i | 1.59100i | 0.605954 | + | 0.795500i | \(0.292791\pi\) | ||||
−0.605954 | + | 0.795500i | \(0.707209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5875.50 | − | 5875.50i | −0.0917918 | − | 0.0917918i | ||||
\(254\) | 107204. | − | 107204.i | 1.66167 | − | 1.66167i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 58371.4 | 0.890676 | ||||||||
\(257\) | − | 14954.5i | − | 0.226415i | −0.993571 | − | 0.113208i | \(-0.963887\pi\) | ||
0.993571 | − | 0.113208i | \(-0.0361125\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5344.34i | − | 0.0796700i | ||||||
\(260\) | −44977.4 | − | 127128.i | −0.665346 | − | 1.88059i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −87052.7 | − | 87052.7i | −1.26818 | − | 1.26818i | ||||
\(263\) | 7574.07 | 0.109501 | 0.0547505 | − | 0.998500i | \(-0.482564\pi\) | ||||
0.0547505 | + | 0.998500i | \(0.482564\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −141907. | − | 141907.i | −2.02074 | − | 2.02074i | ||||
\(266\) | −32365.0 | − | 32365.0i | −0.457417 | − | 0.457417i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 44245.7 | − | 44245.7i | 0.616030 | − | 0.616030i | ||||
\(269\) | −100457. | −1.38827 | −0.694136 | − | 0.719844i | \(-0.744213\pi\) | ||||
−0.694136 | + | 0.719844i | \(0.744213\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 66620.4 | − | 66620.4i | 0.907128 | − | 0.907128i | −0.0889115 | − | 0.996040i | \(-0.528339\pi\) |
0.996040 | + | 0.0889115i | \(0.0283388\pi\) | |||||||
\(272\) | − | 85835.0i | − | 1.16018i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 40749.5 | 0.542776 | ||||||||
\(275\) | −52484.2 | − | 52484.2i | −0.694005 | − | 0.694005i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 70180.3i | 0.914652i | 0.889299 | + | 0.457326i | \(0.151193\pi\) | ||||
−0.889299 | + | 0.457326i | \(0.848807\pi\) | |||||||
\(278\) | 49347.3 | + | 49347.3i | 0.638519 | + | 0.638519i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5245.03 | − | 5245.03i | 0.0669009 | − | 0.0669009i | ||||
\(281\) | 20515.7 | − | 20515.7i | 0.259820 | − | 0.259820i | −0.565161 | − | 0.824981i | \(-0.691186\pi\) |
0.824981 | + | 0.565161i | \(0.191186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 30170.2i | − | 0.376708i | −0.982101 | − | 0.188354i | \(-0.939685\pi\) | ||
0.982101 | − | 0.188354i | \(-0.0603153\pi\) | |||||||
\(284\) | 5004.76 | − | 5004.76i | 0.0620507 | − | 0.0620507i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19022.3 | + | 39851.8i | −0.232558 | + | 0.487209i | ||||
\(287\) | 53756.6 | 0.652631 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −41952.2 | −0.502295 | ||||||||
\(290\) | 248408.i | 2.95373i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 43989.3 | + | 43989.3i | 0.515919 | + | 0.515919i | ||||
\(293\) | 67660.9 | − | 67660.9i | 0.788139 | − | 0.788139i | −0.193050 | − | 0.981189i | \(-0.561838\pi\) |
0.981189 | + | 0.193050i | \(0.0618380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 113437. | 1.30349 | ||||||||
\(296\) | 742.755i | 0.00847739i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 81272.6i | 0.915191i | ||||||||
\(299\) | 27782.4 | + | 13261.3i | 0.310762 | + | 0.148335i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9751.97 | + | 9751.97i | 0.107636 | + | 0.107636i | ||||
\(302\) | 81476.3 | 0.893341 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −40825.6 | − | 40825.6i | −0.441759 | − | 0.441759i | ||||
\(305\) | 126197. | + | 126197.i | 1.35660 | + | 1.35660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −96671.1 | + | 96671.1i | −1.02570 | + | 1.02570i | −0.0260377 | + | 0.999661i | \(0.508289\pi\) |
−0.999661 | + | 0.0260377i | \(0.991711\pi\) | |||||||
\(308\) | −25720.0 | −0.271125 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −238167. | + | 238167.i | −2.47832 | + | 2.47832i | ||||
\(311\) | − | 70642.4i | − | 0.730373i | −0.930934 | − | 0.365186i | \(-0.881005\pi\) | ||
0.930934 | − | 0.365186i | \(-0.118995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 68524.0 | 0.699446 | 0.349723 | − | 0.936853i | \(-0.386276\pi\) | ||||
0.349723 | + | 0.936853i | \(0.386276\pi\) | |||||||
\(314\) | 34650.0 | + | 34650.0i | 0.351435 | + | 0.351435i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 132584.i | 1.32775i | ||||||||
\(317\) | −140417. | − | 140417.i | −1.39734 | − | 1.39734i | −0.807578 | − | 0.589760i | \(-0.799222\pi\) |
−0.589760 | − | 0.807578i | \(-0.700778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29473.2 | − | 29473.2i | 0.289631 | − | 0.289631i | ||||
\(320\) | 151057. | − | 151057.i | 1.47516 | − | 1.47516i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 34993.4i | 0.337501i | ||||||||
\(323\) | −59678.7 | + | 59678.7i | −0.572024 | + | 0.572024i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 248173. | + | 118460.i | 2.34956 | + | 1.12151i | ||||
\(326\) | −9431.05 | −0.0887411 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7471.08 | −0.0694441 | ||||||||
\(329\) | − | 142325.i | − | 1.31489i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −73424.6 | − | 73424.6i | −0.670171 | − | 0.670171i | 0.287585 | − | 0.957755i | \(-0.407148\pi\) |
−0.957755 | + | 0.287585i | \(0.907148\pi\) | |||||||
\(332\) | −68573.6 | + | 68573.6i | −0.622130 | + | 0.622130i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −61039.7 | −0.547166 | ||||||||
\(335\) | 176615.i | 1.57376i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 14312.2i | − | 0.126022i | −0.998013 | − | 0.0630111i | \(-0.979930\pi\) | ||
0.998013 | − | 0.0630111i | \(-0.0200703\pi\) | |||||||
\(338\) | 17194.8 | − | 162700.i | 0.150509 | − | 1.42415i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −199859. | − | 199859.i | −1.72889 | − | 1.72889i | ||||
\(341\) | 56516.0 | 0.486030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 87202.1 | + | 87202.1i | 0.741206 | + | 0.741206i | ||||
\(344\) | −1355.33 | − | 1355.33i | −0.0114532 | − | 0.0114532i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 158611. | − | 158611.i | 1.32489 | − | 1.32489i | ||||
\(347\) | −216160. | −1.79521 | −0.897607 | − | 0.440797i | \(-0.854696\pi\) | ||||
−0.897607 | + | 0.440797i | \(0.854696\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20673.5 | + | 20673.5i | −0.169732 | + | 0.169732i | −0.786862 | − | 0.617130i | \(-0.788295\pi\) |
0.617130 | + | 0.786862i | \(0.288295\pi\) | |||||||
\(350\) | 312586.i | 2.55172i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −66718.7 | −0.538471 | ||||||||
\(353\) | 70477.9 | + | 70477.9i | 0.565592 | + | 0.565592i | 0.930890 | − | 0.365298i | \(-0.119033\pi\) |
−0.365298 | + | 0.930890i | \(0.619033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19977.4i | 0.158519i | ||||||||
\(356\) | −28967.5 | − | 28967.5i | −0.228565 | − | 0.228565i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 152969. | − | 152969.i | 1.19354 | − | 1.19354i | ||||
\(359\) | 90432.4 | − | 90432.4i | 0.701674 | − | 0.701674i | −0.263096 | − | 0.964770i | \(-0.584744\pi\) |
0.964770 | + | 0.263096i | \(0.0847436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 73551.2i | − | 0.564385i | ||||||
\(362\) | −38846.9 | + | 38846.9i | −0.296442 | + | 0.296442i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 89834.5 | − | 31783.1i | 0.678017 | − | 0.239880i | ||||
\(365\) | −175591. | −1.31801 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −156339. | −1.16074 | −0.580369 | − | 0.814354i | \(-0.697091\pi\) | ||||
−0.580369 | + | 0.814354i | \(0.697091\pi\) | |||||||
\(368\) | 44141.2i | 0.325948i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −30634.1 | − | 30634.1i | −0.223770 | − | 0.223770i | ||||
\(371\) | 100278. | − | 100278.i | 0.728546 | − | 0.728546i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12154.0 | 0.0873580 | 0.0436790 | − | 0.999046i | \(-0.486092\pi\) | ||||
0.0436790 | + | 0.999046i | \(0.486092\pi\) | |||||||
\(374\) | 92556.7i | 0.661705i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19780.3i | 0.139913i | ||||||||
\(377\) | −66522.5 | + | 139364.i | −0.468043 | + | 0.980549i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 56764.9 | + | 56764.9i | 0.395186 | + | 0.395186i | 0.876531 | − | 0.481345i | \(-0.159852\pi\) |
−0.481345 | + | 0.876531i | \(0.659852\pi\) | |||||||
\(380\) | −190118. | −1.31661 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −187915. | − | 187915.i | −1.28776 | − | 1.28776i | ||||
\(383\) | −14158.7 | − | 14158.7i | −0.0965218 | − | 0.0965218i | 0.657197 | − | 0.753719i | \(-0.271742\pi\) |
−0.753719 | + | 0.657197i | \(0.771742\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 51333.0 | − | 51333.0i | 0.346318 | − | 0.346318i | ||||
\(386\) | 75805.3 | 0.508774 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −26234.9 | + | 26234.9i | −0.174267 | + | 0.174267i | ||||
\(389\) | 14487.6i | 0.0957405i | 0.998854 | + | 0.0478703i | \(0.0152434\pi\) | ||||
−0.998854 | + | 0.0478703i | \(0.984757\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64525.4 | 0.422063 | ||||||||
\(392\) | −4206.48 | − | 4206.48i | −0.0273745 | − | 0.0273745i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 36155.0i | 0.232904i | ||||||||
\(395\) | −264617. | − | 264617.i | −1.69599 | − | 1.69599i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 120415. | − | 120415.i | 0.764013 | − | 0.764013i | −0.213032 | − | 0.977045i | \(-0.568334\pi\) |
0.977045 | + | 0.213032i | \(0.0683339\pi\) | |||||||
\(398\) | −288910. | + | 288910.i | −1.82388 | + | 1.82388i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 394300.i | 2.46438i | ||||||||
\(401\) | −31598.4 | + | 31598.4i | −0.196506 | + | 0.196506i | −0.798500 | − | 0.601994i | \(-0.794373\pi\) |
0.601994 | + | 0.798500i | \(0.294373\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −197398. | + | 69838.8i | −1.21544 | + | 0.430018i | ||||
\(404\) | −167840. | −1.02833 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −175537. | −1.06492 | ||||||||
\(407\) | 7269.34i | 0.0438840i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16690.9 | + | 16690.9i | 0.0997776 | + | 0.0997776i | 0.755233 | − | 0.655456i | \(-0.227523\pi\) |
−0.655456 | + | 0.755233i | \(0.727523\pi\) | |||||||
\(410\) | 308136. | − | 308136.i | 1.83305 | − | 1.83305i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −110.322 | −0.000649934 | ||||||||
\(413\) | 80159.5i | 0.469954i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 273724.i | − | 1.58934i | ||||||
\(416\) | 233034. | − | 82446.6i | 1.34658 | − | 0.476416i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 44022.6 | + | 44022.6i | 0.251955 | + | 0.251955i | ||||
\(419\) | 45247.7 | 0.257732 | 0.128866 | − | 0.991662i | \(-0.458866\pi\) | ||||
0.128866 | + | 0.991662i | \(0.458866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 95387.7 | + | 95387.7i | 0.538181 | + | 0.538181i | 0.922994 | − | 0.384814i | \(-0.125734\pi\) |
−0.384814 | + | 0.922994i | \(0.625734\pi\) | |||||||
\(422\) | −182866. | − | 182866.i | −1.02685 | − | 1.02685i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13936.6 | + | 13936.6i | −0.0775219 | + | 0.0775219i | ||||
\(425\) | 576386. | 3.19107 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −89176.8 | + | 89176.8i | −0.489098 | + | 0.489098i | ||||
\(428\) | 103960.i | 0.567519i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 111798. | 0.604639 | ||||||||
\(431\) | 120110. | + | 120110.i | 0.646582 | + | 0.646582i | 0.952165 | − | 0.305583i | \(-0.0988514\pi\) |
−0.305583 | + | 0.952165i | \(0.598851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 104909.i | 0.559549i | 0.960066 | + | 0.279774i | \(0.0902596\pi\) | ||||
−0.960066 | + | 0.279774i | \(0.909740\pi\) | |||||||
\(434\) | −168300. | − | 168300.i | −0.893518 | − | 0.893518i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −62117.4 | + | 62117.4i | −0.326768 | + | 0.326768i | ||||
\(437\) | 30690.1 | − | 30690.1i | 0.160707 | − | 0.160707i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 189251.i | 0.981997i | 0.871160 | + | 0.490998i | \(0.163368\pi\) | ||||
−0.871160 | + | 0.490998i | \(0.836632\pi\) | |||||||
\(440\) | −7134.25 | + | 7134.25i | −0.0368505 | + | 0.0368505i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −114376. | − | 323281.i | −0.585448 | − | 1.65476i | ||||
\(443\) | 154643. | 0.787995 | 0.393998 | − | 0.919111i | \(-0.371092\pi\) | ||||
0.393998 | + | 0.919111i | \(0.371092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 115629. | 0.583910 | ||||||||
\(446\) | 182451.i | 0.917227i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 106744. | + | 106744.i | 0.531846 | + | 0.531846i | ||||
\(449\) | −54131.2 | + | 54131.2i | −0.268507 | + | 0.268507i | −0.828498 | − | 0.559992i | \(-0.810804\pi\) |
0.559992 | + | 0.828498i | \(0.310804\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −73119.3 | −0.359484 | ||||||||
\(452\) | 357591.i | 1.75029i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 272835.i | − | 1.32370i | ||||||
\(455\) | −115861. | + | 242729.i | −0.559649 | + | 1.17246i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −44160.2 | − | 44160.2i | −0.211446 | − | 0.211446i | 0.593436 | − | 0.804881i | \(-0.297771\pi\) |
−0.804881 | + | 0.593436i | \(0.797771\pi\) | |||||||
\(458\) | 446101. | 2.12668 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 102779. | + | 102779.i | 0.485723 | + | 0.485723i | ||||
\(461\) | 145494. | + | 145494.i | 0.684610 | + | 0.684610i | 0.961035 | − | 0.276425i | \(-0.0891499\pi\) |
−0.276425 | + | 0.961035i | \(0.589150\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −168589. | + | 168589.i | −0.786443 | + | 0.786443i | −0.980909 | − | 0.194467i | \(-0.937702\pi\) |
0.194467 | + | 0.980909i | \(0.437702\pi\) | |||||||
\(464\) | −221424. | −1.02847 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27012.2 | + | 27012.2i | −0.124391 | + | 0.124391i | ||||
\(467\) | − | 164176.i | − | 0.752793i | −0.926459 | − | 0.376397i | \(-0.877163\pi\) | ||
0.926459 | − | 0.376397i | \(-0.122837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −124804. | −0.567392 | ||||||||
\(470\) | −815813. | − | 815813.i | −3.69313 | − | 3.69313i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 11140.6i | − | 0.0500061i | ||||||
\(473\) | −13264.6 | − | 13264.6i | −0.0592885 | − | 0.0592885i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 274146. | − | 274146.i | 1.21505 | − | 1.21505i | ||||
\(476\) | 141230. | − | 141230.i | 0.623322 | − | 0.623322i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 201917.i | 0.883726i | ||||||||
\(479\) | −10906.2 | + | 10906.2i | −0.0475337 | + | 0.0475337i | −0.730474 | − | 0.682940i | \(-0.760701\pi\) |
0.682940 | + | 0.730474i | \(0.260701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8982.97 | − | 25390.3i | −0.0388267 | − | 0.109743i | ||||
\(482\) | 34949.7 | 0.150435 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −211184. | −0.901510 | ||||||||
\(485\) | − | 104721.i | − | 0.445196i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 225502. | + | 225502.i | 0.950808 | + | 0.950808i | 0.998846 | − | 0.0480379i | \(-0.0152968\pi\) |
−0.0480379 | + | 0.998846i | \(0.515297\pi\) | |||||||
\(488\) | 12393.8 | − | 12393.8i | 0.0520432 | − | 0.0520432i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 346982. | 1.44516 | ||||||||
\(491\) | 311585.i | 1.29245i | 0.763147 | + | 0.646225i | \(0.223653\pi\) | ||||
−0.763147 | + | 0.646225i | \(0.776347\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 323677.i | 1.33174i | ||||||||
\(494\) | −208162. | − | 99361.4i | −0.852997 | − | 0.407159i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −212295. | − | 212295.i | −0.862933 | − | 0.862933i | ||||
\(497\) | −14116.9 | −0.0571516 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1928.12 | + | 1928.12i | 0.00774341 | + | 0.00774341i | 0.710968 | − | 0.703224i | \(-0.248257\pi\) |
−0.703224 | + | 0.710968i | \(0.748257\pi\) | |||||||
\(500\) | 565456. | + | 565456.i | 2.26183 | + | 2.26183i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −406003. | + | 406003.i | −1.61110 | + | 1.61110i | ||||
\(503\) | 185299. | 0.732382 | 0.366191 | − | 0.930540i | \(-0.380662\pi\) | ||||
0.366191 | + | 0.930540i | \(0.380662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 334981. | − | 334981.i | 1.31352 | − | 1.31352i | ||||
\(506\) | − | 47597.8i | − | 0.185903i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 445001. | 1.72438 | ||||||||
\(509\) | −103850. | − | 103850.i | −0.400841 | − | 0.400841i | 0.477688 | − | 0.878529i | \(-0.341475\pi\) |
−0.878529 | + | 0.477688i | \(0.841475\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 124081.i | − | 0.475186i | ||||||
\(512\) | 263398. | + | 263398.i | 1.00478 | + | 1.00478i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 60573.7 | − | 60573.7i | 0.229276 | − | 0.229276i | ||||
\(515\) | 220.186 | − | 220.186i | 0.000830185 | − | 0.000830185i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 193589.i | 0.724269i | ||||||||
\(518\) | 21647.4 | − | 21647.4i | 0.0806765 | − | 0.0806765i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16102.4 | − | 33734.5i | 0.0595503 | − | 0.124758i | ||||
\(521\) | −200788. | −0.739712 | −0.369856 | − | 0.929089i | \(-0.620593\pi\) | ||||
−0.369856 | + | 0.929089i | \(0.620593\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9411.84 | −0.0344089 | −0.0172045 | − | 0.999852i | \(-0.505477\pi\) | ||||
−0.0172045 | + | 0.999852i | \(0.505477\pi\) | |||||||
\(524\) | − | 361353.i | − | 1.31604i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30679.0 | + | 30679.0i | 0.110884 | + | 0.110884i | ||||
\(527\) | −310332. | + | 310332.i | −1.11739 | + | 1.11739i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 246658. | 0.881424 | ||||||||
\(530\) | − | 1.14959e6i | − | 4.09254i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 134346.i | − | 0.474681i | ||||||
\(533\) | 255390. | − | 90356.1i | 0.898980 | − | 0.318056i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −207488. | − | 207488.i | −0.724913 | − | 0.724913i | ||||
\(536\) | 17345.3 | 0.0603742 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −406904. | − | 406904.i | −1.40581 | − | 1.40581i | ||||
\(539\) | −41168.7 | − | 41168.7i | −0.141707 | − | 0.141707i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16197.1 | + | 16197.1i | −0.0553406 | + | 0.0553406i | −0.734235 | − | 0.678895i | \(-0.762459\pi\) |
0.678895 | + | 0.734235i | \(0.262459\pi\) | |||||||
\(542\) | 539696. | 1.83718 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 366356. | − | 366356.i | 1.23796 | − | 1.23796i | ||||
\(545\) | − | 247953.i | − | 0.834788i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −211628. | −0.707292 | −0.353646 | − | 0.935379i | \(-0.615058\pi\) | ||||
−0.353646 | + | 0.935379i | \(0.615058\pi\) | |||||||
\(548\) | 84574.9 | + | 84574.9i | 0.281631 | + | 0.281631i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 425178.i | − | 1.40555i | ||||||
\(551\) | 153950. | + | 153950.i | 0.507081 | + | 0.507081i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 186991. | − | 186991.i | 0.611462 | − | 0.611462i | ||||
\(554\) | −284268. | + | 284268.i | −0.926207 | + | 0.926207i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 204839.i | 0.662619i | ||||||||
\(557\) | 143135. | − | 143135.i | 0.461354 | − | 0.461354i | −0.437745 | − | 0.899099i | \(-0.644223\pi\) |
0.899099 | + | 0.437745i | \(0.144223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 62721.8 | + | 29938.8i | 0.200722 | + | 0.0958101i | ||||
\(560\) | −385652. | −1.22976 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 166199. | 0.526206 | ||||||||
\(563\) | 230941.i | 0.728592i | 0.931283 | + | 0.364296i | \(0.118690\pi\) | ||||
−0.931283 | + | 0.364296i | \(0.881310\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −713694. | − | 713694.i | −2.23571 | − | 2.23571i | ||||
\(566\) | 122205. | − | 122205.i | 0.381467 | − | 0.381467i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1961.97 | 0.00608129 | ||||||||
\(569\) | 243018.i | 0.750609i | 0.926902 | + | 0.375305i | \(0.122462\pi\) | ||||
−0.926902 | + | 0.375305i | \(0.877538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 229921.i | − | 0.705189i | −0.935776 | − | 0.352595i | \(-0.885299\pi\) | ||
0.935776 | − | 0.352595i | \(-0.114701\pi\) | |||||||
\(572\) | −122192. | + | 43231.2i | −0.373467 | + | 0.132131i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 217743. | + | 217743.i | 0.660876 | + | 0.660876i | ||||
\(575\) | −296410. | −0.896515 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45748.5 | − | 45748.5i | −0.137412 | − | 0.137412i | 0.635055 | − | 0.772467i | \(-0.280977\pi\) |
−0.772467 | + | 0.635055i | \(0.780977\pi\) | |||||||
\(578\) | −169929. | − | 169929.i | −0.508641 | − | 0.508641i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −515568. | + | 515568.i | −1.53260 | + | 1.53260i | ||||
\(581\) | 193426. | 0.573010 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −136397. | + | 136397.i | −0.401299 | + | 0.401299i | ||||
\(584\) | 17244.7i | 0.0505628i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 548126. | 1.59619 | ||||||||
\(587\) | 183355. | + | 183355.i | 0.532127 | + | 0.532127i | 0.921205 | − | 0.389078i | \(-0.127206\pi\) |
−0.389078 | + | 0.921205i | \(0.627206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 295206.i | 0.850931i | ||||||||
\(590\) | 459479. | + | 459479.i | 1.31996 | + | 1.31996i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 27306.4 | − | 27306.4i | 0.0779149 | − | 0.0779149i | ||||
\(593\) | 83397.8 | − | 83397.8i | 0.237162 | − | 0.237162i | −0.578512 | − | 0.815674i | \(-0.696366\pi\) |
0.815674 | + | 0.578512i | \(0.196366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 563745.i | 1.59239i | ||||||||
\(596\) | −168680. | + | 168680.i | −0.474866 | + | 0.474866i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 58818.3 | + | 166249.i | 0.164479 | + | 0.464897i | ||||
\(599\) | 217649. | 0.606601 | 0.303300 | − | 0.952895i | \(-0.401911\pi\) | ||||
0.303300 | + | 0.952895i | \(0.401911\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −441379. | −1.22197 | −0.610987 | − | 0.791640i | \(-0.709227\pi\) | ||||
−0.610987 | + | 0.791640i | \(0.709227\pi\) | |||||||
\(602\) | 79001.4i | 0.217993i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 169103. | + | 169103.i | 0.463529 | + | 0.463529i | ||||
\(605\) | 421490. | − | 421490.i | 1.15153 | − | 1.15153i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −283335. | −0.768993 | −0.384497 | − | 0.923126i | \(-0.625625\pi\) | ||||
−0.384497 | + | 0.923126i | \(0.625625\pi\) | |||||||
\(608\) | − | 348499.i | − | 0.942745i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.02233e6i | 2.74747i | ||||||||
\(611\) | −239225. | − | 676166.i | −0.640802 | − | 1.81122i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 482403. | + | 482403.i | 1.28377 | + | 1.28377i | 0.938503 | + | 0.345272i | \(0.112213\pi\) |
0.345272 | + | 0.938503i | \(0.387787\pi\) | |||||||
\(614\) | −783139. | −2.07731 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5041.39 | − | 5041.39i | −0.0132858 | − | 0.0132858i | ||||
\(617\) | −136398. | − | 136398.i | −0.358293 | − | 0.358293i | 0.504890 | − | 0.863184i | \(-0.331533\pi\) |
−0.863184 | + | 0.504890i | \(0.831533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 130340. | − | 130340.i | 0.340170 | − | 0.340170i | −0.516261 | − | 0.856431i | \(-0.672677\pi\) |
0.856431 | + | 0.516261i | \(0.172677\pi\) | |||||||
\(620\) | −988623. | −2.57186 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 286139. | − | 286139.i | 0.739600 | − | 0.739600i | ||||
\(623\) | 81708.7i | 0.210519i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.24013e6 | −3.17473 | ||||||||
\(626\) | 277559. | + | 277559.i | 0.708282 | + | 0.708282i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 143831.i | 0.364698i | ||||||||
\(629\) | −39916.3 | − | 39916.3i | −0.100890 | − | 0.100890i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −145847. | + | 145847.i | −0.366302 | + | 0.366302i | −0.866127 | − | 0.499825i | \(-0.833398\pi\) |
0.499825 | + | 0.866127i | \(0.333398\pi\) | |||||||
\(632\) | −25987.9 | + | 25987.9i | −0.0650635 | + | 0.0650635i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 1.13753e6i | − | 2.82998i | ||||||
\(635\) | −888150. | + | 888150.i | −2.20262 | + | 2.20262i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 194667. | + | 92920.0i | 0.479749 | + | 0.228997i | ||||
\(638\) | 238764. | 0.586580 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 113101. | 0.276126 | ||||||||
\(641\) | 207974.i | 0.506165i | 0.967445 | + | 0.253083i | \(0.0814445\pi\) | ||||
−0.967445 | + | 0.253083i | \(0.918556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30795.0 | − | 30795.0i | −0.0744831 | − | 0.0744831i | 0.668884 | − | 0.743367i | \(-0.266772\pi\) |
−0.743367 | + | 0.668884i | \(0.766772\pi\) | |||||||
\(644\) | −72628.3 | + | 72628.3i | −0.175119 | + | 0.175119i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −483461. | −1.15850 | ||||||||
\(647\) | 216754.i | 0.517795i | 0.965905 | + | 0.258898i | \(0.0833592\pi\) | ||||
−0.965905 | + | 0.258898i | \(0.916641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 109032.i | − | 0.258861i | ||||||
\(650\) | 525407. | + | 1.48506e6i | 1.24357 | + | 3.51492i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19574.0 | − | 19574.0i | −0.0460452 | − | 0.0460452i | ||||
\(653\) | −622399. | −1.45963 | −0.729815 | − | 0.683645i | \(-0.760394\pi\) | ||||
−0.729815 | + | 0.683645i | \(0.760394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 721203. | + | 721203.i | 1.68103 | + | 1.68103i | ||||
\(656\) | 274664. | + | 274664.i | 0.638254 | + | 0.638254i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 576491. | − | 576491.i | 1.33150 | − | 1.33150i | ||||
\(659\) | −127164. | −0.292814 | −0.146407 | − | 0.989224i | \(-0.546771\pi\) | ||||
−0.146407 | + | 0.989224i | \(0.546771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 512043. | − | 512043.i | 1.17194 | − | 1.17194i | 0.190187 | − | 0.981748i | \(-0.439091\pi\) |
0.981748 | − | 0.190187i | \(-0.0609095\pi\) | |||||||
\(662\) | − | 594817.i | − | 1.35727i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −26882.3 | −0.0609720 | ||||||||
\(665\) | 268133. | + | 268133.i | 0.606328 | + | 0.606328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 166453.i | − | 0.374145i | ||||||
\(668\) | −126687. | − | 126687.i | −0.283909 | − | 0.283909i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −715384. | + | 715384.i | −1.59364 | + | 1.59364i | ||||
\(671\) | 121298. | − | 121298.i | 0.269406 | − | 0.269406i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 70363.7i | 0.155353i | 0.996979 | + | 0.0776763i | \(0.0247501\pi\) | ||||
−0.996979 | + | 0.0776763i | \(0.975250\pi\) | |||||||
\(674\) | 57972.1 | − | 57972.1i | 0.127614 | − | 0.127614i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 373370. | − | 301995.i | 0.817044 | − | 0.660855i | ||||
\(677\) | −289817. | −0.632334 | −0.316167 | − | 0.948704i | \(-0.602396\pi\) | ||||
−0.316167 | + | 0.948704i | \(0.602396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 74000.9 | 0.160508 | ||||||||
\(680\) | − | 78349.1i | − | 0.169440i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 228920. | + | 228920.i | 0.492170 | + | 0.492170i | ||||
\(683\) | −126812. | + | 126812.i | −0.271844 | + | 0.271844i | −0.829842 | − | 0.557998i | \(-0.811570\pi\) |
0.557998 | + | 0.829842i | \(0.311570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −337596. | −0.719476 | ||||||||
\(686\) | 706430.i | 1.50114i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 99653.4i | 0.210531i | ||||||||
\(689\) | 307856. | − | 644957.i | 0.648498 | − | 1.35860i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 512067. | + | 512067.i | 1.07243 | + | 1.07243i | 0.997163 | + | 0.0752718i | \(0.0239824\pi\) |
0.0752718 | + | 0.997163i | \(0.476018\pi\) | |||||||
\(692\) | 658388. | 1.37490 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −875563. | − | 875563.i | −1.81789 | − | 1.81789i | ||||
\(695\) | −408827. | − | 408827.i | −0.846388 | − | 0.846388i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 401502. | − | 401502.i | 0.826461 | − | 0.826461i | ||||
\(698\) | −167478. | −0.343753 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −648768. | + | 648768.i | −1.32402 | + | 1.32402i | ||||
\(701\) | 718609.i | 1.46237i | 0.682181 | + | 0.731184i | \(0.261032\pi\) | ||||
−0.682181 | + | 0.731184i | \(0.738968\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37970.7 | −0.0768312 | ||||||||
\(704\) | −145192. | − | 145192.i | −0.292952 | − | 0.292952i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 570946.i | 1.14547i | ||||||||
\(707\) | 236713. | + | 236713.i | 0.473570 | + | 0.473570i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −360756. | + | 360756.i | −0.717664 | + | 0.717664i | −0.968126 | − | 0.250462i | \(-0.919417\pi\) |
0.250462 | + | 0.968126i | \(0.419417\pi\) | |||||||
\(710\) | −80919.1 | + | 80919.1i | −0.160522 | + | 0.160522i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 11355.9i | − | 0.0224006i | ||||||
\(713\) | 159590. | − | 159590.i | 0.313926 | − | 0.313926i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 157594. | − | 330159.i | 0.308267 | − | 0.645819i | ||||
\(716\) | 634968. | 1.23858 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 732599. | 1.42108 | ||||||||
\(719\) | − | 756213.i | − | 1.46280i | −0.681946 | − | 0.731402i | \(-0.738866\pi\) | ||
0.681946 | − | 0.731402i | \(-0.261134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 155.593 | + | 155.593i | 0.000299310 | + | 0.000299310i | ||||
\(722\) | 297921. | − | 297921.i | 0.571515 | − | 0.571515i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −161252. | −0.307630 | ||||||||
\(725\) | − | 1.48688e6i | − | 2.82878i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2488.50i | − | 0.00470835i | −0.999997 | − | 0.00235417i | \(-0.999251\pi\) | ||
0.999997 | − | 0.00235417i | \(-0.000749357\pi\) | |||||||
\(728\) | 23838.3 | + | 11378.7i | 0.0449794 | + | 0.0214699i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −711239. | − | 711239.i | −1.33466 | − | 1.33466i | ||||
\(731\) | 145673. | 0.272611 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 269312. | + | 269312.i | 0.501243 | + | 0.501243i | 0.911824 | − | 0.410581i | \(-0.134674\pi\) |
−0.410581 | + | 0.911824i | \(0.634674\pi\) | |||||||
\(734\) | −633254. | − | 633254.i | −1.17540 | − | 1.17540i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −188401. | + | 188401.i | −0.347798 | + | 0.347798i | ||||
\(737\) | 169758. | 0.312532 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −710849. | + | 710849.i | −1.30163 | + | 1.30163i | −0.374342 | + | 0.927291i | \(0.622131\pi\) |
−0.927291 | + | 0.374342i | \(0.877869\pi\) | |||||||
\(740\) | − | 127161.i | − | 0.232215i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 812357. | 1.47550 | ||||||||
\(743\) | 516575. | + | 516575.i | 0.935741 | + | 0.935741i | 0.998057 | − | 0.0623154i | \(-0.0198485\pi\) |
−0.0623154 | + | 0.998057i | \(0.519848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 673317.i | − | 1.21313i | ||||||
\(746\) | 49230.3 | + | 49230.3i | 0.0884616 | + | 0.0884616i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −192100. | + | 192100.i | −0.343340 | + | 0.343340i | ||||
\(749\) | 146621. | − | 146621.i | 0.261356 | − | 0.261356i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 628582.i | − | 1.11450i | −0.830343 | − | 0.557252i | \(-0.811856\pi\) | ||
0.830343 | − | 0.557252i | \(-0.188144\pi\) | |||||||
\(752\) | 727194. | − | 727194.i | 1.28592 | − | 1.28592i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −833952. | + | 295049.i | −1.46689 | + | 0.518981i | ||||
\(755\) | −675004. | −1.18417 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 874918. | 1.52678 | 0.763389 | − | 0.645940i | \(-0.223534\pi\) | ||||
0.763389 | + | 0.645940i | \(0.223534\pi\) | |||||||
\(758\) | 459856.i | 0.800357i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −37265.1 | − | 37265.1i | −0.0645171 | − | 0.0645171i | ||||
\(761\) | −176909. | + | 176909.i | −0.305479 | + | 0.305479i | −0.843153 | − | 0.537674i | \(-0.819303\pi\) |
0.537674 | + | 0.843153i | \(0.319303\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 175215. | 0.300969 | ||||||||
\(764\) | − | 780031.i | − | 1.33636i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 114700.i | − | 0.195482i | ||||||
\(767\) | 134735. | + | 380827.i | 0.229029 | + | 0.647347i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 64761.1 | + | 64761.1i | 0.109512 | + | 0.109512i | 0.759740 | − | 0.650228i | \(-0.225326\pi\) |
−0.650228 | + | 0.759740i | \(0.725326\pi\) | |||||||
\(770\) | 415852. | 0.701387 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 157333. | + | 157333.i | 0.263988 | + | 0.263988i | ||||
\(773\) | −65728.0 | − | 65728.0i | −0.110000 | − | 0.110000i | 0.649965 | − | 0.759964i | \(-0.274784\pi\) |
−0.759964 | + | 0.649965i | \(0.774784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.42557e6 | − | 1.42557e6i | 2.37348 | − | 2.37348i | ||||
\(776\) | −10284.6 | −0.0170791 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −58682.3 | + | 58682.3i | −0.0969501 | + | 0.0969501i | ||||
\(779\) | − | 381932.i | − | 0.629377i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19201.8 | 0.0314803 | ||||||||
\(782\) | 261362. | + | 261362.i | 0.427395 | + | 0.427395i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 309290.i | 0.503193i | ||||||||
\(785\) | −287064. | − | 287064.i | −0.465843 | − | 0.465843i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 853121. | − | 853121.i | 1.37740 | − | 1.37740i | 0.528420 | − | 0.848983i | \(-0.322785\pi\) |
0.848983 | − | 0.528420i | \(-0.177215\pi\) | |||||||
\(788\) | −75039.2 | + | 75039.2i | −0.120847 | + | 0.120847i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 2.14368e6i | − | 3.43484i | ||||||
\(791\) | 504329. | − | 504329.i | 0.806048 | − | 0.806048i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −273775. | + | 573559.i | −0.435360 | + | 0.912078i | ||||
\(794\) | 975493. | 1.54733 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.19926e6 | −1.89272 | ||||||||
\(797\) | 264563.i | 0.416498i | 0.978076 | + | 0.208249i | \(0.0667765\pi\) | ||||
−0.978076 | + | 0.208249i | \(0.933224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.06301e6 | − | 1.06301e6i | −1.66511 | − | 1.66511i | ||||
\(800\) | −1.68293e6 | + | 1.68293e6i | −2.62958 | + | 2.62958i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −255980. | −0.397977 | ||||||||
\(803\) | 168774.i | 0.261743i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 289909.i | − | 0.447373i | ||||||
\(806\) | −1.08245e6 | − | 516685.i | −1.66625 | − | 0.795345i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −32898.4 | − | 32898.4i | −0.0503908 | − | 0.0503908i | ||||
\(809\) | 903066. | 1.37982 | 0.689910 | − | 0.723895i | \(-0.257650\pi\) | ||||
0.689910 | + | 0.723895i | \(0.257650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 158801. | + | 158801.i | 0.241442 | + | 0.241442i | 0.817446 | − | 0.576005i | \(-0.195389\pi\) |
−0.576005 | + | 0.817446i | \(0.695389\pi\) | |||||||
\(812\) | −364324. | − | 364324.i | −0.552555 | − | 0.552555i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29444.7 | + | 29444.7i | −0.0444384 | + | 0.0444384i | ||||
\(815\) | 78133.2 | 0.117631 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 69286.2 | − | 69286.2i | 0.103801 | − | 0.103801i | ||||
\(818\) | 135214.i | 0.202076i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.27906e6 | 1.90223 | ||||||||
\(821\) | −566290. | − | 566290.i | −0.840142 | − | 0.840142i | 0.148735 | − | 0.988877i | \(-0.452480\pi\) |
−0.988877 | + | 0.148735i | \(0.952480\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 664034.i | 0.980371i | 0.871618 | + | 0.490186i | \(0.163071\pi\) | ||||
−0.871618 | + | 0.490186i | \(0.836929\pi\) | |||||||
\(824\) | −21.6244 | − | 21.6244i | −3.18485e−5 | − | 3.18485e-5i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −324689. | + | 324689.i | −0.475891 | + | 0.475891i | ||||
\(827\) | 694781. | − | 694781.i | 1.01587 | − | 1.01587i | 0.0159954 | − | 0.999872i | \(-0.494908\pi\) |
0.999872 | − | 0.0159954i | \(-0.00509171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.07123e6i | 1.55874i | 0.626564 | + | 0.779370i | \(0.284461\pi\) | ||||
−0.626564 | + | 0.779370i | \(0.715539\pi\) | |||||||
\(830\) | 1.10873e6 | − | 1.10873e6i | 1.60942 | − | 1.60942i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 686543. | + | 327706.i | 0.991794 | + | 0.473410i | ||||
\(833\) | 452119. | 0.651573 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 505694. | 0.725295 | ||||||||
\(836\) | 182737.i | 0.261465i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 183277. | + | 183277.i | 0.260988 | + | 0.260988i | ||||
\(839\) | −710646. | + | 710646.i | −1.00955 | + | 1.00955i | −0.00959972 | + | 0.999954i | \(0.503056\pi\) |
−0.999954 | + | 0.00959972i | \(0.996944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 127693. | 0.180541 | ||||||||
\(842\) | 772742.i | 1.08996i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 759070.i | − | 1.06561i | ||||||
\(845\) | −142453. | + | 1.34792e6i | −0.199507 | + | 1.88778i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 297844. | + | 297844.i | 0.415167 | + | 0.415167i | ||||
\(848\) | 1.02472e6 | 1.42499 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.33467e6 | + | 2.33467e6i | 3.23138 | + | 3.23138i | ||||
\(851\) | 20527.2 | + | 20527.2i | 0.0283446 | + | 0.0283446i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −719087. | + | 719087.i | −0.988288 | + | 0.988288i | −0.999932 | − | 0.0116445i | \(-0.996293\pi\) |
0.0116445 | + | 0.999932i | \(0.496293\pi\) | |||||||
\(854\) | −722427. | −0.990555 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20377.3 | + | 20377.3i | −0.0278099 | + | 0.0278099i | ||||
\(857\) | 625779.i | 0.852038i | 0.904714 | + | 0.426019i | \(0.140084\pi\) | ||||
−0.904714 | + | 0.426019i | \(0.859916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.38660e6 | −1.87917 | −0.939585 | − | 0.342315i | \(-0.888789\pi\) | ||||
−0.939585 | + | 0.342315i | \(0.888789\pi\) | |||||||
\(860\) | 232034. | + | 232034.i | 0.313729 | + | 0.313729i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 973017.i | 1.30950i | ||||||||
\(863\) | 251871. | + | 251871.i | 0.338187 | + | 0.338187i | 0.855685 | − | 0.517497i | \(-0.173136\pi\) |
−0.517497 | + | 0.855685i | \(0.673136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.31404e6 | + | 1.31404e6i | −1.75621 | + | 1.75621i | ||||
\(866\) | −424938. | + | 424938.i | −0.566618 | + | 0.566618i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 698606.i | − | 0.927242i | ||||||
\(869\) | −254343. | + | 254343.i | −0.336807 | + | 0.336807i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −592928. | + | 209776.i | −0.781566 | + | 0.276515i | ||||
\(872\) | −24351.3 | −0.0320250 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 248623. | 0.325475 | ||||||||
\(875\) | − | 1.59499e6i | − | 2.08325i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 248488. | + | 248488.i | 0.323077 | + | 0.323077i | 0.849946 | − | 0.526869i | \(-0.176634\pi\) |
−0.526869 | + | 0.849946i | \(0.676634\pi\) | |||||||
\(878\) | −766569. | + | 766569.i | −0.994403 | + | 0.994403i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 524562. | 0.677378 | ||||||||
\(881\) | 1.01415e6i | 1.30662i | 0.757089 | + | 0.653312i | \(0.226621\pi\) | ||||
−0.757089 | + | 0.653312i | \(0.773379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.21924e6i | − | 1.56375i | −0.623433 | − | 0.781877i | \(-0.714263\pi\) | ||
0.623433 | − | 0.781877i | \(-0.285737\pi\) | |||||||
\(884\) | 433580. | − | 908349.i | 0.554836 | − | 1.16238i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 626388. | + | 626388.i | 0.797950 | + | 0.797950i | ||||
\(887\) | −904300. | −1.14938 | −0.574692 | − | 0.818370i | \(-0.694878\pi\) | ||||
−0.574692 | + | 0.818370i | \(0.694878\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −627608. | − | 627608.i | −0.794118 | − | 0.794118i | ||||
\(890\) | 468359. | + | 468359.i | 0.591287 | + | 0.591287i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −378674. | + | 378674.i | −0.475923 | + | 0.475923i | ||||
\(893\) | −1.01120e6 | −1.26804 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.26729e6 | + | 1.26729e6i | −1.58209 | + | 1.58209i | ||||
\(896\) | 79922.4i | 0.0995526i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −438520. | −0.543797 | ||||||||
\(899\) | 800549. | + | 800549.i | 0.990532 | + | 0.990532i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.49793e6i | − | 1.84519i | ||||||
\(902\) | −296172. | − | 296172.i | −0.364025 | − | 0.364025i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −70091.5 | + | 70091.5i | −0.0857687 | + | 0.0857687i | ||||
\(905\) | 321834. | − | 321834.i | 0.392948 | − | 0.392948i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.40623e6i | − | 1.70940i | −0.519124 | − | 0.854699i | \(-0.673742\pi\) | ||
0.519124 | − | 0.854699i | \(-0.326258\pi\) | |||||||
\(908\) | 566265. | − | 566265.i | 0.686828 | − | 0.686828i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.45248e6 | + | 513883.i | −1.75400 | + | 0.620557i | ||||
\(911\) | 320928. | 0.386697 | 0.193348 | − | 0.981130i | \(-0.438065\pi\) | ||||
0.193348 | + | 0.981130i | \(0.438065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −263097. | −0.315627 | ||||||||
\(914\) | − | 357745.i | − | 0.428234i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 925876. | + | 925876.i | 1.10347 | + | 1.10347i | ||||
\(917\) | −509635. | + | 509635.i | −0.606067 | + | 0.606067i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −824931. | −0.976757 | −0.488378 | − | 0.872632i | \(-0.662411\pi\) | ||||
−0.488378 | + | 0.872632i | \(0.662411\pi\) | |||||||
\(920\) | 40291.5i | 0.0476034i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.17866e6i | 1.38652i | ||||||||
\(923\) | −67067.8 | + | 23728.3i | −0.0787246 | + | 0.0278525i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 183364. | + | 183364.i | 0.214304 | + | 0.214304i | ||||
\(926\) | −1.36575e6 | −1.59276 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −945070. | − | 945070.i | −1.09741 | − | 1.09741i | ||||
\(929\) | −678405. | − | 678405.i | −0.786064 | − | 0.786064i | 0.194783 | − | 0.980846i | \(-0.437600\pi\) |
−0.980846 | + | 0.194783i | \(0.937600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 215041. | − | 215041.i | 0.248097 | − | 0.248097i | ||||
\(932\) | −112127. | −0.129086 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 665000. | − | 665000.i | 0.762303 | − | 0.762303i | ||||
\(935\) | − | 766802.i | − | 0.877122i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.11931e6 | 1.27488 | 0.637441 | − | 0.770499i | \(-0.279993\pi\) | ||||
0.637441 | + | 0.770499i | \(0.279993\pi\) | |||||||
\(938\) | −505523. | − | 505523.i | −0.574560 | − | 0.574560i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 3.38642e6i | − | 3.83252i | ||||||
\(941\) | −498975. | − | 498975.i | −0.563507 | − | 0.563507i | 0.366795 | − | 0.930302i | \(-0.380455\pi\) |
−0.930302 | + | 0.366795i | \(0.880455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −206475. | + | 206475.i | −0.232190 | + | 0.232190i | ||||
\(944\) | −409567. | + | 409567.i | −0.459601 | + | 0.459601i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 107457.i | − | 0.120075i | ||||||
\(947\) | 672812. | − | 672812.i | 0.750228 | − | 0.750228i | −0.224293 | − | 0.974522i | \(-0.572007\pi\) |
0.974522 | + | 0.224293i | \(0.0720073\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −208560. | − | 589492.i | −0.231579 | − | 0.654554i | ||||
\(950\) | 2.22087e6 | 2.46080 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 55365.1 | 0.0610889 | ||||||||
\(953\) | 226250.i | 0.249117i | 0.992212 | + | 0.124558i | \(0.0397514\pi\) | ||||
−0.992212 | + | 0.124558i | \(0.960249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.55682e6 | + | 1.55682e6i | 1.70699 | + | 1.70699i | ||||
\(956\) | −419076. | + | 419076.i | −0.458540 | + | 0.458540i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −88351.7 | −0.0962684 | ||||||||
\(959\) | − | 238561.i | − | 0.259395i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 611566.i | 0.662211i | ||||||||
\(962\) | 66458.2 | − | 139230.i | 0.0718123 | − | 0.150447i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 72537.6 | + | 72537.6i | 0.0780565 | + | 0.0780565i | ||||
\(965\) | −628022. | −0.674404 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −652291. | − | 652291.i | −0.697571 | − | 0.697571i | 0.266315 | − | 0.963886i | \(-0.414194\pi\) |
−0.963886 | + | 0.266315i | \(0.914194\pi\) | |||||||
\(968\) | −41394.3 | − | 41394.3i | −0.0441764 | − | 0.0441764i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 424177. | − | 424177.i | 0.450821 | − | 0.450821i | ||||
\(971\) | −330964. | −0.351028 | −0.175514 | − | 0.984477i | \(-0.556159\pi\) | ||||
−0.175514 | + | 0.984477i | \(0.556159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 288896. | − | 288896.i | 0.305151 | − | 0.305151i | ||||
\(974\) | 1.82681e6i | 1.92564i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −911280. | −0.956648 | ||||||||
\(977\) | 812569. | + | 812569.i | 0.851278 | + | 0.851278i | 0.990291 | − | 0.139013i | \(-0.0443930\pi\) |
−0.139013 | + | 0.990291i | \(0.544393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 111140.i | − | 0.115959i | ||||||
\(980\) | 720156. | + | 720156.i | 0.749850 | + | 0.749850i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.26209e6 | + | 1.26209e6i | −1.30878 | + | 1.30878i | ||||
\(983\) | −1.32394e6 | + | 1.32394e6i | −1.37013 | + | 1.37013i | −0.509898 | + | 0.860235i | \(0.670317\pi\) |
−0.860235 | + | 0.509898i | \(0.829683\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 299533.i | − | 0.308725i | ||||||
\(986\) | −1.31107e6 | + | 1.31107e6i | −1.34856 | + | 1.34856i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −225814. | − | 638260.i | −0.231333 | − | 0.653858i | ||||
\(989\) | −74913.1 | −0.0765888 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −424185. | −0.431925 | −0.215962 | − | 0.976402i | \(-0.569289\pi\) | ||||
−0.215962 | + | 0.976402i | \(0.569289\pi\) | |||||||
\(992\) | − | 1.81221e6i | − | 1.84156i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −57181.2 | − | 57181.2i | −0.0578736 | − | 0.0578736i | ||||
\(995\) | 2.39352e6 | − | 2.39352e6i | 2.41764 | − | 2.41764i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.53487e6 | 1.54412 | 0.772060 | − | 0.635549i | \(-0.219226\pi\) | ||||
0.772060 | + | 0.635549i | \(0.219226\pi\) | |||||||
\(998\) | 15619.8i | 0.0156825i | ||||||||
\(999\) | 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 | 117.5.j.b.73.8 | 20 | ||
3.2 | odd | 2 | 39.5.g.a.34.3 | yes | 20 | ||
13.5 | odd | 4 | inner | 117.5.j.b.109.8 | 20 | ||
39.5 | even | 4 | 39.5.g.a.31.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.3 | ✓ | 20 | 39.5 | even | 4 | ||
39.5.g.a.34.3 | yes | 20 | 3.2 | odd | 2 | ||
117.5.j.b.73.8 | 20 | 1.1 | even | 1 | trivial | ||
117.5.j.b.109.8 | 20 | 13.5 | odd | 4 | inner |