Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,5,Mod(31,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.g (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: | \(4.03142856027\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(4.05053 - 4.05053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.31 |
Dual form | 39.5.g.a.34.3 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | −0.0127141 | + | 0.999919i | \(0.504047\pi\) |
−0.999919 | + | 0.0127141i | \(0.995953\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | − | 16.8136i | − | 1.05085i | ||||||
\(5\) | 33.5573 | − | 33.5573i | 1.34229 | − | 1.34229i | 0.448521 | − | 0.893772i | \(-0.351951\pi\) |
0.893772 | − | 0.448521i | \(-0.148049\pi\) | |||||||
\(6\) | −21.0472 | + | 21.0472i | −0.584644 | + | 0.584644i | ||||
\(7\) | 23.7132 | + | 23.7132i | 0.483942 | + | 0.483942i | 0.906388 | − | 0.422446i | \(-0.138828\pi\) |
−0.422446 | + | 0.906388i | \(0.638828\pi\) | |||||||
\(8\) | 3.29565 | + | 3.29565i | 0.0514945 | + | 0.0514945i | ||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | 271.850i | 2.71850i | ||||||||
\(11\) | 32.2545 | + | 32.2545i | 0.266566 | + | 0.266566i | 0.827715 | − | 0.561149i | \(-0.189641\pi\) |
−0.561149 | + | 0.827715i | \(0.689641\pi\) | |||||||
\(12\) | − | 87.3662i | − | 0.606710i | ||||||
\(13\) | 72.8001 | + | 152.516i | 0.430770 | + | 0.902462i | ||||
\(14\) | −192.102 | −0.980111 | ||||||||
\(15\) | 174.369 | − | 174.369i | 0.774974 | − | 0.774974i | ||||
\(16\) | 242.320 | 0.946562 | ||||||||
\(17\) | − | 354.222i | − | 1.22568i | −0.790206 | − | 0.612841i | \(-0.790027\pi\) | ||
0.790206 | − | 0.612841i | \(-0.209973\pi\) | |||||||
\(18\) | −109.364 | + | 109.364i | −0.337544 | + | 0.337544i | ||||
\(19\) | −168.478 | + | 168.478i | −0.466699 | + | 0.466699i | −0.900843 | − | 0.434145i | \(-0.857051\pi\) |
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(20\) | −564.221 | − | 564.221i | −1.41055 | − | 1.41055i | ||||
\(21\) | 123.217 | + | 123.217i | 0.279404 | + | 0.279404i | ||||
\(22\) | −261.296 | −0.539867 | ||||||||
\(23\) | 182.161i | 0.344349i | 0.985066 | + | 0.172175i | \(0.0550793\pi\) | ||||
−0.985066 | + | 0.172175i | \(0.944921\pi\) | |||||||
\(24\) | 17.1247 | + | 17.1247i | 0.0297304 | + | 0.0297304i | ||||
\(25\) | − | 1627.19i | − | 2.60350i | ||||||
\(26\) | −912.650 | − | 322.892i | −1.35007 | − | 0.477651i | ||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | 398.704 | − | 398.704i | 0.508551 | − | 0.508551i | ||||
\(29\) | 913.769 | 1.08653 | 0.543264 | − | 0.839562i | \(-0.317188\pi\) | ||||
0.543264 | + | 0.839562i | \(0.317188\pi\) | |||||||
\(30\) | 1412.58i | 1.56953i | ||||||||
\(31\) | −876.095 | + | 876.095i | −0.911650 | + | 0.911650i | −0.996402 | − | 0.0847522i | \(-0.972990\pi\) |
0.0847522 | + | 0.996402i | \(0.472990\pi\) | |||||||
\(32\) | −1034.25 | + | 1034.25i | −1.01001 | + | 1.01001i | ||||
\(33\) | 167.599 | + | 167.599i | 0.153902 | + | 0.153902i | ||||
\(34\) | 1434.79 | + | 1434.79i | 1.24117 | + | 1.24117i | ||||
\(35\) | 1591.50 | 1.29918 | ||||||||
\(36\) | − | 453.968i | − | 0.350284i | ||||||
\(37\) | 112.687 | + | 112.687i | 0.0823135 | + | 0.0823135i | 0.747065 | − | 0.664751i | \(-0.231462\pi\) |
−0.664751 | + | 0.747065i | \(0.731462\pi\) | |||||||
\(38\) | − | 1364.85i | − | 0.945189i | ||||||
\(39\) | 378.280 | + | 792.497i | 0.248705 | + | 0.521037i | ||||
\(40\) | 221.186 | 0.138242 | ||||||||
\(41\) | −1133.48 | + | 1133.48i | −0.674287 | + | 0.674287i | −0.958701 | − | 0.284415i | \(-0.908201\pi\) |
0.284415 | + | 0.958701i | \(0.408201\pi\) | |||||||
\(42\) | −998.190 | −0.565868 | ||||||||
\(43\) | − | 411.247i | − | 0.222416i | −0.993797 | − | 0.111208i | \(-0.964528\pi\) | ||
0.993797 | − | 0.111208i | \(-0.0354720\pi\) | |||||||
\(44\) | 542.315 | − | 542.315i | 0.280121 | − | 0.280121i | ||||
\(45\) | 906.048 | − | 906.048i | 0.447431 | − | 0.447431i | ||||
\(46\) | −737.848 | − | 737.848i | −0.348700 | − | 0.348700i | ||||
\(47\) | −3000.97 | − | 3000.97i | −1.35852 | − | 1.35852i | −0.875746 | − | 0.482772i | \(-0.839630\pi\) |
−0.482772 | − | 0.875746i | \(-0.660370\pi\) | |||||||
\(48\) | 1259.13 | 0.546498 | ||||||||
\(49\) | − | 1276.37i | − | 0.531600i | ||||||
\(50\) | 6590.99 | + | 6590.99i | 2.63639 | + | 2.63639i | ||||
\(51\) | − | 1840.59i | − | 0.707648i | ||||||
\(52\) | 2564.35 | − | 1224.03i | 0.948354 | − | 0.452675i | ||||
\(53\) | −4228.78 | −1.50544 | −0.752720 | − | 0.658341i | \(-0.771259\pi\) | ||||
−0.752720 | + | 0.658341i | \(0.771259\pi\) | |||||||
\(54\) | −568.274 | + | 568.274i | −0.194881 | + | 0.194881i | ||||
\(55\) | 2164.75 | 0.715619 | ||||||||
\(56\) | 156.301i | 0.0498407i | ||||||||
\(57\) | −875.438 | + | 875.438i | −0.269449 | + | 0.269449i | ||||
\(58\) | −3701.25 | + | 3701.25i | −1.10025 | + | 1.10025i | ||||
\(59\) | 1690.19 | + | 1690.19i | 0.485547 | + | 0.485547i | 0.906898 | − | 0.421350i | \(-0.138444\pi\) |
−0.421350 | + | 0.906898i | \(0.638444\pi\) | |||||||
\(60\) | −2931.78 | − | 2931.78i | −0.814383 | − | 0.814383i | ||||
\(61\) | −3760.65 | −1.01066 | −0.505328 | − | 0.862928i | \(-0.668628\pi\) | ||||
−0.505328 | + | 0.862928i | \(0.668628\pi\) | |||||||
\(62\) | − | 7097.31i | − | 1.84633i | ||||||
\(63\) | 640.255 | + | 640.255i | 0.161314 | + | 0.161314i | ||||
\(64\) | − | 4501.45i | − | 1.09899i | ||||||
\(65\) | 7561.01 | + | 2675.06i | 1.78959 | + | 0.633149i | ||||
\(66\) | −1357.73 | −0.311692 | ||||||||
\(67\) | −2631.54 | + | 2631.54i | −0.586219 | + | 0.586219i | −0.936605 | − | 0.350386i | \(-0.886050\pi\) |
0.350386 | + | 0.936605i | \(0.386050\pi\) | |||||||
\(68\) | −5955.76 | −1.28801 | ||||||||
\(69\) | 946.535i | 0.198810i | ||||||||
\(70\) | −6446.43 | + | 6446.43i | −1.31560 | + | 1.31560i | ||||
\(71\) | 297.661 | − | 297.661i | 0.0590479 | − | 0.0590479i | −0.676966 | − | 0.736014i | \(-0.736706\pi\) |
0.736014 | + | 0.676966i | \(0.236706\pi\) | |||||||
\(72\) | 88.9825 | + | 88.9825i | 0.0171648 | + | 0.0171648i | ||||
\(73\) | 2616.29 | + | 2616.29i | 0.490953 | + | 0.490953i | 0.908606 | − | 0.417653i | \(-0.137147\pi\) |
−0.417653 | + | 0.908606i | \(0.637147\pi\) | |||||||
\(74\) | −912.887 | −0.166707 | ||||||||
\(75\) | − | 8455.13i | − | 1.50313i | ||||||
\(76\) | 2832.73 | + | 2832.73i | 0.490431 | + | 0.490431i | ||||
\(77\) | 1529.71i | 0.258005i | ||||||||
\(78\) | −4742.27 | − | 1677.80i | −0.779466 | − | 0.275772i | ||||
\(79\) | 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 | ||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − | 9182.36i | − | 1.36561i | ||||||
\(83\) | −4078.45 | + | 4078.45i | −0.592024 | + | 0.592024i | −0.938178 | − | 0.346154i | \(-0.887488\pi\) |
0.346154 | + | 0.938178i | \(0.387488\pi\) | |||||||
\(84\) | 2071.73 | − | 2071.73i | 0.293612 | − | 0.293612i | ||||
\(85\) | −11886.7 | − | 11886.7i | −1.64522 | − | 1.64522i | ||||
\(86\) | 1665.77 | + | 1665.77i | 0.225226 | + | 0.225226i | ||||
\(87\) | 4748.08 | 0.627307 | ||||||||
\(88\) | 212.599i | 0.0274534i | ||||||||
\(89\) | 1722.86 | + | 1722.86i | 0.217505 | + | 0.217505i | 0.807446 | − | 0.589941i | \(-0.200849\pi\) |
−0.589941 | + | 0.807446i | \(0.700849\pi\) | |||||||
\(90\) | 7339.96i | 0.906167i | ||||||||
\(91\) | −1890.32 | + | 5342.96i | −0.228272 | + | 0.645207i | ||||
\(92\) | 3062.78 | 0.361860 | ||||||||
\(93\) | −4552.33 | + | 4552.33i | −0.526341 | + | 0.526341i | ||||
\(94\) | 24311.0 | 2.75136 | ||||||||
\(95\) | 11307.4i | 1.25289i | ||||||||
\(96\) | −5374.15 | + | 5374.15i | −0.583132 | + | 0.583132i | ||||
\(97\) | 1560.33 | − | 1560.33i | 0.165834 | − | 0.165834i | −0.619311 | − | 0.785146i | \(-0.712588\pi\) |
0.785146 | + | 0.619311i | \(0.212588\pi\) | |||||||
\(98\) | 5169.99 | + | 5169.99i | 0.538316 | + | 0.538316i | ||||
\(99\) | 870.871 | + | 870.871i | 0.0888553 | + | 0.0888553i | ||||
\(100\) | −27359.0 | −2.73590 | ||||||||
\(101\) | 9982.36i | 0.978567i | 0.872125 | + | 0.489283i | \(0.162742\pi\) | ||||
−0.872125 | + | 0.489283i | \(0.837258\pi\) | |||||||
\(102\) | 7455.38 | + | 7455.38i | 0.716587 | + | 0.716587i | ||||
\(103\) | − | 6.56148i | − | 0.000618483i | −1.00000 | 0.000309241i | \(-0.999902\pi\) | |||
1.00000 | 0.000309241i | \(-9.84346e-5\pi\) | ||||||||
\(104\) | −262.716 | + | 742.563i | −0.0242896 | + | 0.0686541i | ||||
\(105\) | 8269.68 | 0.750084 | ||||||||
\(106\) | 17128.8 | − | 17128.8i | 1.52446 | − | 1.52446i | ||||
\(107\) | −6183.10 | −0.540056 | −0.270028 | − | 0.962853i | \(-0.587033\pi\) | ||||
−0.270028 | + | 0.962853i | \(0.587033\pi\) | |||||||
\(108\) | − | 2358.89i | − | 0.202237i | ||||||
\(109\) | 3694.46 | − | 3694.46i | 0.310956 | − | 0.310956i | −0.534324 | − | 0.845280i | \(-0.679434\pi\) |
0.845280 | + | 0.534324i | \(0.179434\pi\) | |||||||
\(110\) | −8768.39 | + | 8768.39i | −0.724660 | + | 0.724660i | ||||
\(111\) | 585.540 | + | 585.540i | 0.0475238 | + | 0.0475238i | ||||
\(112\) | 5746.17 | + | 5746.17i | 0.458081 | + | 0.458081i | ||||
\(113\) | −21267.9 | −1.66559 | −0.832794 | − | 0.553583i | \(-0.813260\pi\) | ||||
−0.832794 | + | 0.553583i | \(0.813260\pi\) | |||||||
\(114\) | − | 7091.98i | − | 0.545705i | ||||||
\(115\) | 6112.83 | + | 6112.83i | 0.462218 | + | 0.462218i | ||||
\(116\) | − | 15363.8i | − | 1.14178i | ||||||
\(117\) | 1965.60 | + | 4117.93i | 0.143590 | + | 0.300821i | ||||
\(118\) | −13692.3 | −0.983363 | ||||||||
\(119\) | 8399.72 | − | 8399.72i | 0.593159 | − | 0.593159i | ||||
\(120\) | 1149.32 | 0.0798138 | ||||||||
\(121\) | − | 12560.3i | − | 0.857885i | ||||||
\(122\) | 15232.6 | − | 15232.6i | 1.02342 | − | 1.02342i | ||||
\(123\) | −5889.71 | + | 5889.71i | −0.389300 | + | 0.389300i | ||||
\(124\) | 14730.3 | + | 14730.3i | 0.958009 | + | 0.958009i | ||||
\(125\) | −33630.8 | − | 33630.8i | −2.15237 | − | 2.15237i | ||||
\(126\) | −5186.75 | −0.326704 | ||||||||
\(127\) | 26466.7i | 1.64094i | 0.571693 | + | 0.820468i | \(0.306287\pi\) | ||||
−0.571693 | + | 0.820468i | \(0.693713\pi\) | |||||||
\(128\) | 1685.19 | + | 1685.19i | 0.102856 | + | 0.102856i | ||||
\(129\) | − | 2136.90i | − | 0.128412i | ||||||
\(130\) | −41461.5 | + | 19790.7i | −2.45334 | + | 1.17105i | ||||
\(131\) | 21491.7 | 1.25236 | 0.626178 | − | 0.779680i | \(-0.284618\pi\) | ||||
0.626178 | + | 0.779680i | \(0.284618\pi\) | |||||||
\(132\) | 2817.95 | − | 2817.95i | 0.161728 | − | 0.161728i | ||||
\(133\) | −7990.30 | −0.451710 | ||||||||
\(134\) | − | 21318.3i | − | 1.18725i | ||||||
\(135\) | 4707.96 | − | 4707.96i | 0.258325 | − | 0.258325i | ||||
\(136\) | 1167.39 | − | 1167.39i | 0.0631159 | − | 0.0631159i | ||||
\(137\) | −5030.14 | − | 5030.14i | −0.268002 | − | 0.268002i | 0.560292 | − | 0.828295i | \(-0.310689\pi\) |
−0.828295 | + | 0.560292i | \(0.810689\pi\) | |||||||
\(138\) | −3833.97 | − | 3833.97i | −0.201322 | − | 0.201322i | ||||
\(139\) | 12182.9 | 0.630554 | 0.315277 | − | 0.949000i | \(-0.397903\pi\) | ||||
0.315277 | + | 0.949000i | \(0.397903\pi\) | |||||||
\(140\) | − | 26758.9i | − | 1.36525i | ||||||
\(141\) | −15593.5 | − | 15593.5i | −0.784341 | − | 0.784341i | ||||
\(142\) | 2411.37i | 0.119588i | ||||||||
\(143\) | −2571.20 | + | 7267.45i | −0.125737 | + | 0.355394i | ||||
\(144\) | 6542.64 | 0.315521 | ||||||||
\(145\) | 30663.7 | − | 30663.7i | 1.45844 | − | 1.45844i | ||||
\(146\) | −21194.7 | −0.994311 | ||||||||
\(147\) | − | 6632.23i | − | 0.306920i | ||||||
\(148\) | 1894.68 | − | 1894.68i | 0.0864994 | − | 0.0864994i | ||||
\(149\) | −10032.3 | + | 10032.3i | −0.451887 | + | 0.451887i | −0.895980 | − | 0.444094i | \(-0.853526\pi\) |
0.444094 | + | 0.895980i | \(0.353526\pi\) | |||||||
\(150\) | 34247.8 | + | 34247.8i | 1.52212 | + | 1.52212i | ||||
\(151\) | 10057.5 | + | 10057.5i | 0.441098 | + | 0.441098i | 0.892381 | − | 0.451283i | \(-0.149033\pi\) |
−0.451283 | + | 0.892381i | \(0.649033\pi\) | |||||||
\(152\) | −1110.49 | −0.0480649 | ||||||||
\(153\) | − | 9563.99i | − | 0.408561i | ||||||
\(154\) | −6196.14 | − | 6196.14i | −0.261264 | − | 0.261264i | ||||
\(155\) | 58798.9i | 2.44740i | ||||||||
\(156\) | 13324.7 | − | 6360.27i | 0.547532 | − | 0.261352i | ||||
\(157\) | 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 | ||||
\(159\) | −21973.4 | −0.869166 | ||||||||
\(160\) | 69413.7i | 2.71147i | ||||||||
\(161\) | −4319.61 | + | 4319.61i | −0.166645 | + | 0.166645i | ||||
\(162\) | −2952.84 | + | 2952.84i | −0.112515 | + | 0.112515i | ||||
\(163\) | −1164.17 | − | 1164.17i | −0.0438170 | − | 0.0438170i | 0.684859 | − | 0.728676i | \(-0.259864\pi\) |
−0.728676 | + | 0.684859i | \(0.759864\pi\) | |||||||
\(164\) | 19057.8 | + | 19057.8i | 0.708576 | + | 0.708576i | ||||
\(165\) | 11248.4 | 0.413163 | ||||||||
\(166\) | − | 33039.8i | − | 1.19901i | ||||||
\(167\) | 7534.77 | + | 7534.77i | 0.270170 | + | 0.270170i | 0.829169 | − | 0.558999i | \(-0.188814\pi\) |
−0.558999 | + | 0.829169i | \(0.688814\pi\) | |||||||
\(168\) | 812.161i | 0.0287756i | ||||||||
\(169\) | −17961.3 | + | 22206.4i | −0.628875 | + | 0.777506i | ||||
\(170\) | 96295.3 | 3.33202 | ||||||||
\(171\) | −4548.91 | + | 4548.91i | −0.155566 | + | 0.155566i | ||||
\(172\) | −6914.56 | −0.233726 | ||||||||
\(173\) | − | 39158.0i | − | 1.30836i | −0.756337 | − | 0.654182i | \(-0.773013\pi\) | ||
0.756337 | − | 0.654182i | \(-0.226987\pi\) | |||||||
\(174\) | −19232.3 | + | 19232.3i | −0.635232 | + | 0.635232i | ||||
\(175\) | 38585.8 | − | 38585.8i | 1.25994 | − | 1.25994i | ||||
\(176\) | 7815.90 | + | 7815.90i | 0.252321 | + | 0.252321i | ||||
\(177\) | 8782.49 | + | 8782.49i | 0.280331 | + | 0.280331i | ||||
\(178\) | −13957.0 | −0.440505 | ||||||||
\(179\) | − | 37765.1i | − | 1.17865i | −0.807897 | − | 0.589324i | \(-0.799394\pi\) | ||
0.807897 | − | 0.589324i | \(-0.200606\pi\) | |||||||
\(180\) | −15234.0 | − | 15234.0i | −0.470184 | − | 0.470184i | ||||
\(181\) | − | 9590.57i | − | 0.292744i | −0.989230 | − | 0.146372i | \(-0.953240\pi\) | ||
0.989230 | − | 0.146372i | \(-0.0467596\pi\) | |||||||
\(182\) | −13985.0 | − | 29298.6i | −0.422202 | − | 0.884513i | ||||
\(183\) | −19540.9 | −0.583502 | ||||||||
\(184\) | −600.338 | + | 600.338i | −0.0177321 | + | 0.0177321i | ||||
\(185\) | 7562.97 | 0.220978 | ||||||||
\(186\) | − | 36878.7i | − | 1.06598i | ||||||
\(187\) | 11425.2 | − | 11425.2i | 0.326725 | − | 0.326725i | ||||
\(188\) | −50457.2 | + | 50457.2i | −1.42760 | + | 1.42760i | ||||
\(189\) | 3326.86 | + | 3326.86i | 0.0931347 | + | 0.0931347i | ||||
\(190\) | −45800.8 | − | 45800.8i | −1.26872 | − | 1.26872i | ||||
\(191\) | 46392.7 | 1.27170 | 0.635848 | − | 0.771814i | \(-0.280651\pi\) | ||||
0.635848 | + | 0.771814i | \(0.280651\pi\) | |||||||
\(192\) | − | 23390.2i | − | 0.634500i | ||||||
\(193\) | 9357.45 | + | 9357.45i | 0.251213 | + | 0.251213i | 0.821468 | − | 0.570255i | \(-0.193155\pi\) |
−0.570255 | + | 0.821468i | \(0.693155\pi\) | |||||||
\(194\) | 12640.4i | 0.335858i | ||||||||
\(195\) | 39288.2 | + | 13900.0i | 1.03322 | + | 0.365549i | ||||
\(196\) | −21460.5 | −0.558633 | ||||||||
\(197\) | −4463.00 | + | 4463.00i | −0.114999 | + | 0.114999i | −0.762265 | − | 0.647266i | \(-0.775912\pi\) |
0.647266 | + | 0.762265i | \(0.275912\pi\) | |||||||
\(198\) | −7054.98 | −0.179956 | ||||||||
\(199\) | − | 71326.4i | − | 1.80113i | −0.434726 | − | 0.900563i | \(-0.643155\pi\) | ||
0.434726 | − | 0.900563i | \(-0.356845\pi\) | |||||||
\(200\) | 5362.65 | − | 5362.65i | 0.134066 | − | 0.134066i | ||||
\(201\) | −13673.9 | + | 13673.9i | −0.338454 | + | 0.338454i | ||||
\(202\) | −40433.9 | − | 40433.9i | −0.990929 | − | 0.990929i | ||||
\(203\) | 21668.4 | + | 21668.4i | 0.525816 | + | 0.525816i | ||||
\(204\) | −30947.0 | −0.743633 | ||||||||
\(205\) | 76072.9i | 1.81018i | ||||||||
\(206\) | 26.5775 | + | 26.5775i | 0.000626296 | + | 0.000626296i | ||||
\(207\) | 4918.34i | 0.114783i | ||||||||
\(208\) | 17640.9 | + | 36957.7i | 0.407750 | + | 0.854236i | ||||
\(209\) | −10868.4 | −0.248812 | ||||||||
\(210\) | −33496.6 | + | 33496.6i | −0.759560 | + | 0.759560i | ||||
\(211\) | −45146.1 | −1.01404 | −0.507020 | − | 0.861934i | \(-0.669253\pi\) | ||||
−0.507020 | + | 0.861934i | \(0.669253\pi\) | |||||||
\(212\) | 71101.2i | 1.58199i | ||||||||
\(213\) | 1546.69 | − | 1546.69i | 0.0340913 | − | 0.0340913i | ||||
\(214\) | 25044.8 | − | 25044.8i | 0.546878 | − | 0.546878i | ||||
\(215\) | −13800.4 | − | 13800.4i | −0.298548 | − | 0.298548i | ||||
\(216\) | 462.367 | + | 462.367i | 0.00991013 | + | 0.00991013i | ||||
\(217\) | −41550.0 | −0.882371 | ||||||||
\(218\) | 29929.1i | 0.629768i | ||||||||
\(219\) | 13594.6 | + | 13594.6i | 0.283452 | + | 0.283452i | ||||
\(220\) | − | 36397.3i | − | 0.752010i | ||||||
\(221\) | 54024.5 | − | 25787.4i | 1.10613 | − | 0.527986i | ||||
\(222\) | −4743.50 | −0.0962483 | ||||||||
\(223\) | 22521.9 | − | 22521.9i | 0.452892 | − | 0.452892i | −0.443421 | − | 0.896313i | \(-0.646235\pi\) |
0.896313 | + | 0.443421i | \(0.146235\pi\) | |||||||
\(224\) | −49050.9 | −0.977577 | ||||||||
\(225\) | − | 43934.1i | − | 0.867835i | ||||||
\(226\) | 86146.3 | − | 86146.3i | 1.68663 | − | 1.68663i | ||||
\(227\) | 33678.9 | − | 33678.9i | 0.653592 | − | 0.653592i | −0.300264 | − | 0.953856i | \(-0.597075\pi\) |
0.953856 | + | 0.300264i | \(0.0970749\pi\) | |||||||
\(228\) | 14719.3 | + | 14719.3i | 0.283151 | + | 0.283151i | ||||
\(229\) | 55067.0 | + | 55067.0i | 1.05008 | + | 1.05008i | 0.998678 | + | 0.0513970i | \(0.0163674\pi\) |
0.0513970 | + | 0.998678i | \(0.483633\pi\) | |||||||
\(230\) | −49520.4 | −0.936114 | ||||||||
\(231\) | 7948.61i | 0.148959i | ||||||||
\(232\) | 3011.46 | + | 3011.46i | 0.0559502 | + | 0.0559502i | ||||
\(233\) | 6668.81i | 0.122839i | 0.998112 | + | 0.0614195i | \(0.0195627\pi\) | ||||
−0.998112 | + | 0.0614195i | \(0.980437\pi\) | |||||||
\(234\) | −24641.6 | − | 8718.09i | −0.450025 | − | 0.159217i | ||||
\(235\) | −201409. | −3.64706 | ||||||||
\(236\) | 28418.2 | − | 28418.2i | 0.510239 | − | 0.510239i | ||||
\(237\) | 40974.4 | 0.729484 | ||||||||
\(238\) | 68046.7i | 1.20130i | ||||||||
\(239\) | −24924.8 | + | 24924.8i | −0.436350 | + | 0.436350i | −0.890782 | − | 0.454431i | \(-0.849842\pi\) |
0.454431 | + | 0.890782i | \(0.349842\pi\) | |||||||
\(240\) | 42253.1 | − | 42253.1i | 0.733560 | − | 0.733560i | ||||
\(241\) | 4314.21 | + | 4314.21i | 0.0742792 | + | 0.0742792i | 0.743270 | − | 0.668991i | \(-0.233274\pi\) |
−0.668991 | + | 0.743270i | \(0.733274\pi\) | |||||||
\(242\) | 50875.9 | + | 50875.9i | 0.868723 | + | 0.868723i | ||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | 63230.2i | 1.06205i | ||||||||
\(245\) | −42831.7 | − | 42831.7i | −0.713564 | − | 0.713564i | ||||
\(246\) | − | 47713.0i | − | 0.788435i | ||||||
\(247\) | −37960.9 | − | 13430.4i | −0.622217 | − | 0.220138i | ||||
\(248\) | −5774.61 | −0.0938900 | ||||||||
\(249\) | −21192.3 | + | 21192.3i | −0.341805 | + | 0.341805i | ||||
\(250\) | 272445. | 4.35913 | ||||||||
\(251\) | 100235.i | 1.59100i | 0.605954 | + | 0.795500i | \(0.292791\pi\) | ||||
−0.605954 | + | 0.795500i | \(0.707209\pi\) | |||||||
\(252\) | 10765.0 | − | 10765.0i | 0.169517 | − | 0.169517i | ||||
\(253\) | −5875.50 | + | 5875.50i | −0.0917918 | + | 0.0917918i | ||||
\(254\) | −107204. | − | 107204.i | −1.66167 | − | 1.66167i | ||||
\(255\) | −61765.3 | − | 61765.3i | −0.949871 | − | 0.949871i | ||||
\(256\) | 58371.4 | 0.890676 | ||||||||
\(257\) | − | 14954.5i | − | 0.226415i | −0.993571 | − | 0.113208i | \(-0.963887\pi\) | ||
0.993571 | − | 0.113208i | \(-0.0361125\pi\) | |||||||
\(258\) | 8655.60 | + | 8655.60i | 0.130034 | + | 0.130034i | ||||
\(259\) | 5344.34i | 0.0796700i | ||||||||
\(260\) | 44977.4 | − | 127128.i | 0.665346 | − | 1.88059i | ||||
\(261\) | 24671.8 | 0.362176 | ||||||||
\(262\) | −87052.7 | + | 87052.7i | −1.26818 | + | 1.26818i | ||||
\(263\) | −7574.07 | −0.109501 | −0.0547505 | − | 0.998500i | \(-0.517436\pi\) | ||||
−0.0547505 | + | 0.998500i | \(0.517436\pi\) | |||||||
\(264\) | 1104.70i | 0.0158502i | ||||||||
\(265\) | −141907. | + | 141907.i | −2.02074 | + | 2.02074i | ||||
\(266\) | 32365.0 | − | 32365.0i | 0.457417 | − | 0.457417i | ||||
\(267\) | 8952.22 | + | 8952.22i | 0.125576 | + | 0.125576i | ||||
\(268\) | 44245.7 | + | 44245.7i | 0.616030 | + | 0.616030i | ||||
\(269\) | 100457. | 1.38827 | 0.694136 | − | 0.719844i | \(-0.255787\pi\) | ||||
0.694136 | + | 0.719844i | \(0.255787\pi\) | |||||||
\(270\) | 38139.5i | 0.523176i | ||||||||
\(271\) | 66620.4 | + | 66620.4i | 0.907128 | + | 0.907128i | 0.996040 | − | 0.0889115i | \(-0.0283388\pi\) |
−0.0889115 | + | 0.996040i | \(0.528339\pi\) | |||||||
\(272\) | − | 85835.0i | − | 1.16018i | ||||||
\(273\) | −9822.38 | + | 27762.8i | −0.131793 | + | 0.372510i | ||||
\(274\) | 40749.5 | 0.542776 | ||||||||
\(275\) | 52484.2 | − | 52484.2i | 0.694005 | − | 0.694005i | ||||
\(276\) | 15914.7 | 0.208920 | ||||||||
\(277\) | − | 70180.3i | − | 0.914652i | −0.889299 | − | 0.457326i | \(-0.848807\pi\) | ||
0.889299 | − | 0.457326i | \(-0.151193\pi\) | |||||||
\(278\) | −49347.3 | + | 49347.3i | −0.638519 | + | 0.638519i | ||||
\(279\) | −23654.6 | + | 23654.6i | −0.303883 | + | 0.303883i | ||||
\(280\) | 5245.03 | + | 5245.03i | 0.0669009 | + | 0.0669009i | ||||
\(281\) | −20515.7 | − | 20515.7i | −0.259820 | − | 0.259820i | 0.565161 | − | 0.824981i | \(-0.308814\pi\) |
−0.824981 | + | 0.565161i | \(0.808814\pi\) | |||||||
\(282\) | 126324. | 1.58850 | ||||||||
\(283\) | 30170.2i | 0.376708i | 0.982101 | + | 0.188354i | \(0.0603153\pi\) | ||||
−0.982101 | + | 0.188354i | \(0.939685\pi\) | |||||||
\(284\) | −5004.76 | − | 5004.76i | −0.0620507 | − | 0.0620507i | ||||
\(285\) | 58754.8i | 0.723358i | ||||||||
\(286\) | −19022.3 | − | 39851.8i | −0.232558 | − | 0.487209i | ||||
\(287\) | −53756.6 | −0.652631 | ||||||||
\(288\) | −27924.9 | + | 27924.9i | −0.336672 | + | 0.336672i | ||||
\(289\) | −41952.2 | −0.502295 | ||||||||
\(290\) | 248408.i | 2.95373i | ||||||||
\(291\) | 8107.73 | − | 8107.73i | 0.0957444 | − | 0.0957444i | ||||
\(292\) | 43989.3 | − | 43989.3i | 0.515919 | − | 0.515919i | ||||
\(293\) | −67660.9 | − | 67660.9i | −0.788139 | − | 0.788139i | 0.193050 | − | 0.981189i | \(-0.438162\pi\) |
−0.981189 | + | 0.193050i | \(0.938162\pi\) | |||||||
\(294\) | 26864.0 | + | 26864.0i | 0.310797 | + | 0.310797i | ||||
\(295\) | 113437. | 1.30349 | ||||||||
\(296\) | 742.755i | 0.00847739i | ||||||||
\(297\) | 4525.18 | + | 4525.18i | 0.0513006 | + | 0.0513006i | ||||
\(298\) | − | 81272.6i | − | 0.915191i | ||||||
\(299\) | −27782.4 | + | 13261.3i | −0.310762 | + | 0.148335i | ||||
\(300\) | −142161. | −1.57957 | ||||||||
\(301\) | 9751.97 | − | 9751.97i | 0.107636 | − | 0.107636i | ||||
\(302\) | −81476.3 | −0.893341 | ||||||||
\(303\) | 51869.9i | 0.564976i | ||||||||
\(304\) | −40825.6 | + | 40825.6i | −0.441759 | + | 0.441759i | ||||
\(305\) | −126197. | + | 126197.i | −1.35660 | + | 1.35660i | ||||
\(306\) | 38739.3 | + | 38739.3i | 0.413722 | + | 0.413722i | ||||
\(307\) | −96671.1 | − | 96671.1i | −1.02570 | − | 1.02570i | −0.999661 | − | 0.0260377i | \(-0.991711\pi\) |
−0.0260377 | − | 0.999661i | \(-0.508289\pi\) | |||||||
\(308\) | 25720.0 | 0.271125 | ||||||||
\(309\) | − | 34.0945i | − | 0.000357081i | ||||||
\(310\) | −238167. | − | 238167.i | −2.47832 | − | 2.47832i | ||||
\(311\) | − | 70642.4i | − | 0.730373i | −0.930934 | − | 0.365186i | \(-0.881005\pi\) | ||
0.930934 | − | 0.365186i | \(-0.118995\pi\) | |||||||
\(312\) | −1365.11 | + | 3858.47i | −0.0140236 | + | 0.0396375i | ||||
\(313\) | 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 | ||||
\(315\) | 42970.5 | 0.433061 | ||||||||
\(316\) | − | 132584.i | − | 1.32775i | ||||||
\(317\) | 140417. | − | 140417.i | 1.39734 | − | 1.39734i | 0.589760 | − | 0.807578i | \(-0.299222\pi\) |
0.807578 | − | 0.589760i | \(-0.200778\pi\) | |||||||
\(318\) | 89003.9 | − | 89003.9i | 0.880147 | − | 0.880147i | ||||
\(319\) | 29473.2 | + | 29473.2i | 0.289631 | + | 0.289631i | ||||
\(320\) | −151057. | − | 151057.i | −1.47516 | − | 1.47516i | ||||
\(321\) | −32128.3 | −0.311801 | ||||||||
\(322\) | − | 34993.4i | − | 0.337501i | ||||||
\(323\) | 59678.7 | + | 59678.7i | 0.572024 | + | 0.572024i | ||||
\(324\) | − | 12257.1i | − | 0.116761i | ||||||
\(325\) | 248173. | − | 118460.i | 2.34956 | − | 1.12151i | ||||
\(326\) | 9431.05 | 0.0887411 | ||||||||
\(327\) | 19197.0 | − | 19197.0i | 0.179530 | − | 0.179530i | ||||
\(328\) | −7471.08 | −0.0694441 | ||||||||
\(329\) | − | 142325.i | − | 1.31489i | ||||||
\(330\) | −45561.9 | + | 45561.9i | −0.418383 | + | 0.418383i | ||||
\(331\) | −73424.6 | + | 73424.6i | −0.670171 | + | 0.670171i | −0.957755 | − | 0.287585i | \(-0.907148\pi\) |
0.287585 | + | 0.957755i | \(0.407148\pi\) | |||||||
\(332\) | 68573.6 | + | 68573.6i | 0.622130 | + | 0.622130i | ||||
\(333\) | 3042.56 | + | 3042.56i | 0.0274378 | + | 0.0274378i | ||||
\(334\) | −61039.7 | −0.547166 | ||||||||
\(335\) | 176615.i | 1.57376i | ||||||||
\(336\) | 29858.0 | + | 29858.0i | 0.264473 | + | 0.264473i | ||||
\(337\) | 14312.2i | 0.126022i | 0.998013 | + | 0.0630111i | \(0.0200703\pi\) | ||||
−0.998013 | + | 0.0630111i | \(0.979930\pi\) | |||||||
\(338\) | −17194.8 | − | 162700.i | −0.150509 | − | 1.42415i | ||||
\(339\) | −110511. | −0.961628 | ||||||||
\(340\) | −199859. | + | 199859.i | −1.72889 | + | 1.72889i | ||||
\(341\) | −56516.0 | −0.486030 | ||||||||
\(342\) | − | 36851.0i | − | 0.315063i | ||||||
\(343\) | 87202.1 | − | 87202.1i | 0.741206 | − | 0.741206i | ||||
\(344\) | 1355.33 | − | 1355.33i | 0.0114532 | − | 0.0114532i | ||||
\(345\) | 31763.2 | + | 31763.2i | 0.266862 | + | 0.266862i | ||||
\(346\) | 158611. | + | 158611.i | 1.32489 | + | 1.32489i | ||||
\(347\) | 216160. | 1.79521 | 0.897607 | − | 0.440797i | \(-0.145304\pi\) | ||||
0.897607 | + | 0.440797i | \(0.145304\pi\) | |||||||
\(348\) | − | 79832.6i | − | 0.659207i | ||||||
\(349\) | −20673.5 | − | 20673.5i | −0.169732 | − | 0.169732i | 0.617130 | − | 0.786862i | \(-0.288295\pi\) |
−0.786862 | + | 0.617130i | \(0.788295\pi\) | |||||||
\(350\) | 312586.i | 2.55172i | ||||||||
\(351\) | 10213.6 | + | 21397.4i | 0.0829017 | + | 0.173679i | ||||
\(352\) | −66718.7 | −0.538471 | ||||||||
\(353\) | −70477.9 | + | 70477.9i | −0.565592 | + | 0.565592i | −0.930890 | − | 0.365298i | \(-0.880967\pi\) |
0.365298 | + | 0.930890i | \(0.380967\pi\) | |||||||
\(354\) | −71147.5 | −0.567745 | ||||||||
\(355\) | − | 19977.4i | − | 0.158519i | ||||||
\(356\) | 28967.5 | − | 28967.5i | 0.228565 | − | 0.228565i | ||||
\(357\) | 43646.2 | − | 43646.2i | 0.342460 | − | 0.342460i | ||||
\(358\) | 152969. | + | 152969.i | 1.19354 | + | 1.19354i | ||||
\(359\) | −90432.4 | − | 90432.4i | −0.701674 | − | 0.701674i | 0.263096 | − | 0.964770i | \(-0.415256\pi\) |
−0.964770 | + | 0.263096i | \(0.915256\pi\) | |||||||
\(360\) | 5972.03 | 0.0460805 | ||||||||
\(361\) | 73551.2i | 0.564385i | ||||||||
\(362\) | 38846.9 | + | 38846.9i | 0.296442 | + | 0.296442i | ||||
\(363\) | − | 65265.2i | − | 0.495300i | ||||||
\(364\) | 89834.5 | + | 31783.1i | 0.678017 | + | 0.239880i | ||||
\(365\) | 175591. | 1.31801 | ||||||||
\(366\) | 79151.1 | − | 79151.1i | 0.590874 | − | 0.590874i | ||||
\(367\) | −156339. | −1.16074 | −0.580369 | − | 0.814354i | \(-0.697091\pi\) | ||||
−0.580369 | + | 0.814354i | \(0.697091\pi\) | |||||||
\(368\) | 44141.2i | 0.325948i | ||||||||
\(369\) | −30603.8 | + | 30603.8i | −0.224762 | + | 0.224762i | ||||
\(370\) | −30634.1 | + | 30634.1i | −0.223770 | + | 0.223770i | ||||
\(371\) | −100278. | − | 100278.i | −0.728546 | − | 0.728546i | ||||
\(372\) | 76541.1 | + | 76541.1i | 0.553107 | + | 0.553107i | ||||
\(373\) | 12154.0 | 0.0873580 | 0.0436790 | − | 0.999046i | \(-0.486092\pi\) | ||||
0.0436790 | + | 0.999046i | \(0.486092\pi\) | |||||||
\(374\) | 92556.7i | 0.661705i | ||||||||
\(375\) | −174751. | − | 174751.i | −1.24267 | − | 1.24267i | ||||
\(376\) | − | 19780.3i | − | 0.139913i | ||||||
\(377\) | 66522.5 | + | 139364.i | 0.468043 | + | 0.980549i | ||||
\(378\) | −26951.1 | −0.188623 | ||||||||
\(379\) | 56764.9 | − | 56764.9i | 0.395186 | − | 0.395186i | −0.481345 | − | 0.876531i | \(-0.659852\pi\) |
0.876531 | + | 0.481345i | \(0.159852\pi\) | |||||||
\(380\) | 190118. | 1.31661 | ||||||||
\(381\) | 137525.i | 0.947395i | ||||||||
\(382\) | −187915. | + | 187915.i | −1.28776 | + | 1.28776i | ||||
\(383\) | 14158.7 | − | 14158.7i | 0.0965218 | − | 0.0965218i | −0.657197 | − | 0.753719i | \(-0.728258\pi\) |
0.753719 | + | 0.657197i | \(0.228258\pi\) | |||||||
\(384\) | 8756.51 | + | 8756.51i | 0.0593839 | + | 0.0593839i | ||||
\(385\) | 51333.0 | + | 51333.0i | 0.346318 | + | 0.346318i | ||||
\(386\) | −75805.3 | −0.508774 | ||||||||
\(387\) | − | 11103.7i | − | 0.0741387i | ||||||
\(388\) | −26234.9 | − | 26234.9i | −0.174267 | − | 0.174267i | ||||
\(389\) | 14487.6i | 0.0957405i | 0.998854 | + | 0.0478703i | \(0.0152434\pi\) | ||||
−0.998854 | + | 0.0478703i | \(0.984757\pi\) | |||||||
\(390\) | −215440. | + | 102836.i | −1.41644 | + | 0.676105i | ||||
\(391\) | 64525.4 | 0.422063 | ||||||||
\(392\) | 4206.48 | − | 4206.48i | 0.0273745 | − | 0.0273745i | ||||
\(393\) | 111674. | 0.723048 | ||||||||
\(394\) | − | 36155.0i | − | 0.232904i | ||||||
\(395\) | 264617. | − | 264617.i | 1.69599 | − | 1.69599i | ||||
\(396\) | 14642.5 | − | 14642.5i | 0.0933738 | − | 0.0933738i | ||||
\(397\) | 120415. | + | 120415.i | 0.764013 | + | 0.764013i | 0.977045 | − | 0.213032i | \(-0.0683339\pi\) |
−0.213032 | + | 0.977045i | \(0.568334\pi\) | |||||||
\(398\) | 288910. | + | 288910.i | 1.82388 | + | 1.82388i | ||||
\(399\) | −41518.8 | −0.260795 | ||||||||
\(400\) | − | 394300.i | − | 2.46438i | ||||||
\(401\) | 31598.4 | + | 31598.4i | 0.196506 | + | 0.196506i | 0.798500 | − | 0.601994i | \(-0.205627\pi\) |
−0.601994 | + | 0.798500i | \(0.705627\pi\) | |||||||
\(402\) | − | 110773.i | − | 0.685459i | ||||||
\(403\) | −197398. | − | 69838.8i | −1.21544 | − | 0.430018i | ||||
\(404\) | 167840. | 1.02833 | ||||||||
\(405\) | 24463.3 | − | 24463.3i | 0.149144 | − | 0.149144i | ||||
\(406\) | −175537. | −1.06492 | ||||||||
\(407\) | 7269.34i | 0.0438840i | ||||||||
\(408\) | 6065.94 | − | 6065.94i | 0.0364400 | − | 0.0364400i | ||||
\(409\) | 16690.9 | − | 16690.9i | 0.0997776 | − | 0.0997776i | −0.655456 | − | 0.755233i | \(-0.727523\pi\) |
0.755233 | + | 0.655456i | \(0.227523\pi\) | |||||||
\(410\) | −308136. | − | 308136.i | −1.83305 | − | 1.83305i | ||||
\(411\) | −26137.4 | − | 26137.4i | −0.154731 | − | 0.154731i | ||||
\(412\) | −110.322 | −0.000649934 | ||||||||
\(413\) | 80159.5i | 0.469954i | ||||||||
\(414\) | −19921.9 | − | 19921.9i | −0.116233 | − | 0.116233i | ||||
\(415\) | 273724.i | 1.58934i | ||||||||
\(416\) | −233034. | − | 82446.6i | −1.34658 | − | 0.476416i | ||||
\(417\) | 63304.3 | 0.364050 | ||||||||
\(418\) | 44022.6 | − | 44022.6i | 0.251955 | − | 0.251955i | ||||
\(419\) | −45247.7 | −0.257732 | −0.128866 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128866 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(420\) | − | 139043.i | − | 0.788228i | ||||||
\(421\) | 95387.7 | − | 95387.7i | 0.538181 | − | 0.538181i | −0.384814 | − | 0.922994i | \(-0.625734\pi\) |
0.922994 | + | 0.384814i | \(0.125734\pi\) | |||||||
\(422\) | 182866. | − | 182866.i | 1.02685 | − | 1.02685i | ||||
\(423\) | −81026.1 | − | 81026.1i | −0.452839 | − | 0.452839i | ||||
\(424\) | −13936.6 | − | 13936.6i | −0.0775219 | − | 0.0775219i | ||||
\(425\) | −576386. | −3.19107 | ||||||||
\(426\) | 12529.8i | 0.0690441i | ||||||||
\(427\) | −89176.8 | − | 89176.8i | −0.489098 | − | 0.489098i | ||||
\(428\) | 103960.i | 0.567519i | ||||||||
\(429\) | −13360.3 | + | 37762.8i | −0.0725943 | + | 0.205187i | ||||
\(430\) | 111798. | 0.604639 | ||||||||
\(431\) | −120110. | + | 120110.i | −0.646582 | + | 0.646582i | −0.952165 | − | 0.305583i | \(-0.901149\pi\) |
0.305583 | + | 0.952165i | \(0.401149\pi\) | |||||||
\(432\) | 33996.5 | 0.182166 | ||||||||
\(433\) | − | 104909.i | − | 0.559549i | −0.960066 | − | 0.279774i | \(-0.909740\pi\) | ||
0.960066 | − | 0.279774i | \(-0.0902596\pi\) | |||||||
\(434\) | 168300. | − | 168300.i | 0.893518 | − | 0.893518i | ||||
\(435\) | 159333. | − | 159333.i | 0.842030 | − | 0.842030i | ||||
\(436\) | −62117.4 | − | 62117.4i | −0.326768 | − | 0.326768i | ||||
\(437\) | −30690.1 | − | 30690.1i | −0.160707 | − | 0.160707i | ||||
\(438\) | −110131. | −0.574066 | ||||||||
\(439\) | − | 189251.i | − | 0.981997i | −0.871160 | − | 0.490998i | \(-0.836632\pi\) | ||
0.871160 | − | 0.490998i | \(-0.163368\pi\) | |||||||
\(440\) | 7134.25 | + | 7134.25i | 0.0368505 | + | 0.0368505i | ||||
\(441\) | − | 34462.1i | − | 0.177200i | ||||||
\(442\) | −114376. | + | 323281.i | −0.585448 | + | 1.65476i | ||||
\(443\) | −154643. | −0.787995 | −0.393998 | − | 0.919111i | \(-0.628908\pi\) | ||||
−0.393998 | + | 0.919111i | \(0.628908\pi\) | |||||||
\(444\) | 9845.06 | − | 9845.06i | 0.0499404 | − | 0.0499404i | ||||
\(445\) | 115629. | 0.583910 | ||||||||
\(446\) | 182451.i | 0.917227i | ||||||||
\(447\) | −52129.6 | + | 52129.6i | −0.260897 | + | 0.260897i | ||||
\(448\) | 106744. | − | 106744.i | 0.531846 | − | 0.531846i | ||||
\(449\) | 54131.2 | + | 54131.2i | 0.268507 | + | 0.268507i | 0.828498 | − | 0.559992i | \(-0.189196\pi\) |
−0.559992 | + | 0.828498i | \(0.689196\pi\) | |||||||
\(450\) | 177957. | + | 177957.i | 0.878798 | + | 0.878798i | ||||
\(451\) | −73119.3 | −0.359484 | ||||||||
\(452\) | 357591.i | 1.75029i | ||||||||
\(453\) | 52260.2 | + | 52260.2i | 0.254668 | + | 0.254668i | ||||
\(454\) | 272835.i | 1.32370i | ||||||||
\(455\) | 115861. | + | 242729.i | 0.559649 | + | 1.17246i | ||||
\(456\) | −5770.28 | −0.0277503 | ||||||||
\(457\) | −44160.2 | + | 44160.2i | −0.211446 | + | 0.211446i | −0.804881 | − | 0.593436i | \(-0.797771\pi\) |
0.593436 | + | 0.804881i | \(0.297771\pi\) | |||||||
\(458\) | −446101. | −2.12668 | ||||||||
\(459\) | − | 49696.0i | − | 0.235883i | ||||||
\(460\) | 102779. | − | 102779.i | 0.485723 | − | 0.485723i | ||||
\(461\) | −145494. | + | 145494.i | −0.684610 | + | 0.684610i | −0.961035 | − | 0.276425i | \(-0.910850\pi\) |
0.276425 | + | 0.961035i | \(0.410850\pi\) | |||||||
\(462\) | −32196.1 | − | 32196.1i | −0.150841 | − | 0.150841i | ||||
\(463\) | −168589. | − | 168589.i | −0.786443 | − | 0.786443i | 0.194467 | − | 0.980909i | \(-0.437702\pi\) |
−0.980909 | + | 0.194467i | \(0.937702\pi\) | |||||||
\(464\) | 221424. | 1.02847 | ||||||||
\(465\) | 305528.i | 1.41301i | ||||||||
\(466\) | −27012.2 | − | 27012.2i | −0.124391 | − | 0.124391i | ||||
\(467\) | − | 164176.i | − | 0.752793i | −0.926459 | − | 0.376397i | \(-0.877163\pi\) | ||
0.926459 | − | 0.376397i | \(-0.122837\pi\) | |||||||
\(468\) | 69237.4 | − | 33048.9i | 0.316118 | − | 0.150892i | ||||
\(469\) | −124804. | −0.567392 | ||||||||
\(470\) | 815813. | − | 815813.i | 3.69313 | − | 3.69313i | ||||
\(471\) | 44450.2 | 0.200369 | ||||||||
\(472\) | 11140.6i | 0.0500061i | ||||||||
\(473\) | 13264.6 | − | 13264.6i | 0.0592885 | − | 0.0592885i | ||||
\(474\) | −165968. | + | 165968.i | −0.738700 | + | 0.738700i | ||||
\(475\) | 274146. | + | 274146.i | 1.21505 | + | 1.21505i | ||||
\(476\) | −141230. | − | 141230.i | −0.623322 | − | 0.623322i | ||||
\(477\) | −114177. | −0.501813 | ||||||||
\(478\) | − | 201917.i | − | 0.883726i | ||||||
\(479\) | 10906.2 | + | 10906.2i | 0.0475337 | + | 0.0475337i | 0.730474 | − | 0.682940i | \(-0.239299\pi\) |
−0.682940 | + | 0.730474i | \(0.739299\pi\) | |||||||
\(480\) | 360684.i | 1.56547i | ||||||||
\(481\) | −8982.97 | + | 25390.3i | −0.0388267 | + | 0.109743i | ||||
\(482\) | −34949.7 | −0.150435 | ||||||||
\(483\) | −22445.3 | + | 22445.3i | −0.0962126 | + | 0.0962126i | ||||
\(484\) | −211184. | −0.901510 | ||||||||
\(485\) | − | 104721.i | − | 0.445196i | ||||||
\(486\) | −15343.4 | + | 15343.4i | −0.0649605 | + | 0.0649605i | ||||
\(487\) | 225502. | − | 225502.i | 0.950808 | − | 0.950808i | −0.0480379 | − | 0.998846i | \(-0.515297\pi\) |
0.998846 | + | 0.0480379i | \(0.0152968\pi\) | |||||||
\(488\) | −12393.8 | − | 12393.8i | −0.0520432 | − | 0.0520432i | ||||
\(489\) | −6049.23 | − | 6049.23i | −0.0252978 | − | 0.0252978i | ||||
\(490\) | 346982. | 1.44516 | ||||||||
\(491\) | 311585.i | 1.29245i | 0.763147 | + | 0.646225i | \(0.223653\pi\) | ||||
−0.763147 | + | 0.646225i | \(0.776347\pi\) | |||||||
\(492\) | 99027.5 | + | 99027.5i | 0.409096 | + | 0.409096i | ||||
\(493\) | − | 323677.i | − | 1.33174i | ||||||
\(494\) | 208162. | − | 99361.4i | 0.852997 | − | 0.407159i | ||||
\(495\) | 58448.2 | 0.238540 | ||||||||
\(496\) | −212295. | + | 212295.i | −0.862933 | + | 0.862933i | ||||
\(497\) | 14116.9 | 0.0571516 | ||||||||
\(498\) | − | 171680.i | − | 0.692247i | ||||||
\(499\) | 1928.12 | − | 1928.12i | 0.00774341 | − | 0.00774341i | −0.703224 | − | 0.710968i | \(-0.748257\pi\) |
0.710968 | + | 0.703224i | \(0.248257\pi\) | |||||||
\(500\) | −565456. | + | 565456.i | −2.26183 | + | 2.26183i | ||||
\(501\) | 39151.8 | + | 39151.8i | 0.155983 | + | 0.155983i | ||||
\(502\) | −406003. | − | 406003.i | −1.61110 | − | 1.61110i | ||||
\(503\) | −185299. | −0.732382 | −0.366191 | − | 0.930540i | \(-0.619338\pi\) | ||||
−0.366191 | + | 0.930540i | \(0.619338\pi\) | |||||||
\(504\) | 4220.11i | 0.0166136i | ||||||||
\(505\) | 334981. | + | 334981.i | 1.31352 | + | 1.31352i | ||||
\(506\) | − | 47597.8i | − | 0.185903i | ||||||
\(507\) | −93329.6 | + | 115388.i | −0.363081 | + | 0.448894i | ||||
\(508\) | 445001. | 1.72438 | ||||||||
\(509\) | 103850. | − | 103850.i | 0.400841 | − | 0.400841i | −0.477688 | − | 0.878529i | \(-0.658525\pi\) |
0.878529 | + | 0.477688i | \(0.158525\pi\) | |||||||
\(510\) | 500365. | 1.92374 | ||||||||
\(511\) | 124081.i | 0.475186i | ||||||||
\(512\) | −263398. | + | 263398.i | −1.00478 | + | 1.00478i | ||||
\(513\) | −23636.8 | + | 23636.8i | −0.0898162 | + | 0.0898162i | ||||
\(514\) | 60573.7 | + | 60573.7i | 0.229276 | + | 0.229276i | ||||
\(515\) | −220.186 | − | 220.186i | −0.000830185 | − | 0.000830185i | ||||
\(516\) | −35929.1 | −0.134942 | ||||||||
\(517\) | − | 193589.i | − | 0.724269i | ||||||
\(518\) | −21647.4 | − | 21647.4i | −0.0806765 | − | 0.0806765i | ||||
\(519\) | − | 203471.i | − | 0.755384i | ||||||
\(520\) | 16102.4 | + | 33734.5i | 0.0595503 | + | 0.124758i | ||||
\(521\) | 200788. | 0.739712 | 0.369856 | − | 0.929089i | \(-0.379407\pi\) | ||||
0.369856 | + | 0.929089i | \(0.379407\pi\) | |||||||
\(522\) | −99933.8 | + | 99933.8i | −0.366751 | + | 0.366751i | ||||
\(523\) | −9411.84 | −0.0344089 | −0.0172045 | − | 0.999852i | \(-0.505477\pi\) | ||||
−0.0172045 | + | 0.999852i | \(0.505477\pi\) | |||||||
\(524\) | − | 361353.i | − | 1.31604i | ||||||
\(525\) | 200498. | − | 200498.i | 0.727429 | − | 0.727429i | ||||
\(526\) | 30679.0 | − | 30679.0i | 0.110884 | − | 0.110884i | ||||
\(527\) | 310332. | + | 310332.i | 1.11739 | + | 1.11739i | ||||
\(528\) | 40612.6 | + | 40612.6i | 0.145678 | + | 0.145678i | ||||
\(529\) | 246658. | 0.881424 | ||||||||
\(530\) | − | 1.14959e6i | − | 4.09254i | ||||||
\(531\) | 45635.1 | + | 45635.1i | 0.161849 | + | 0.161849i | ||||
\(532\) | 134346.i | 0.474681i | ||||||||
\(533\) | −255390. | − | 90356.1i | −0.898980 | − | 0.318056i | ||||
\(534\) | −72522.5 | −0.254326 | ||||||||
\(535\) | −207488. | + | 207488.i | −0.724913 | + | 0.724913i | ||||
\(536\) | −17345.3 | −0.0603742 | ||||||||
\(537\) | − | 196233.i | − | 0.680493i | ||||||
\(538\) | −406904. | + | 406904.i | −1.40581 | + | 1.40581i | ||||
\(539\) | 41168.7 | − | 41168.7i | 0.141707 | − | 0.141707i | ||||
\(540\) | −79158.0 | − | 79158.0i | −0.271461 | − | 0.271461i | ||||
\(541\) | −16197.1 | − | 16197.1i | −0.0553406 | − | 0.0553406i | 0.678895 | − | 0.734235i | \(-0.262459\pi\) |
−0.734235 | + | 0.678895i | \(0.762459\pi\) | |||||||
\(542\) | −539696. | −1.83718 | ||||||||
\(543\) | − | 49834.1i | − | 0.169016i | ||||||
\(544\) | 366356. | + | 366356.i | 1.23796 | + | 1.23796i | ||||
\(545\) | − | 247953.i | − | 0.834788i | ||||||
\(546\) | −72668.3 | − | 152240.i | −0.243759 | − | 0.510674i | ||||
\(547\) | −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 | ||||
\(549\) | −101537. | −0.336885 | ||||||||
\(550\) | 425178.i | 1.40555i | ||||||||
\(551\) | −153950. | + | 153950.i | −0.507081 | + | 0.507081i | ||||
\(552\) | −3119.45 | + | 3119.45i | −0.0102376 | + | 0.0102376i | ||||
\(553\) | 186991. | + | 186991.i | 0.611462 | + | 0.611462i | ||||
\(554\) | 284268. | + | 284268.i | 0.926207 | + | 0.926207i | ||||
\(555\) | 39298.3 | 0.127582 | ||||||||
\(556\) | − | 204839.i | − | 0.662619i | ||||||
\(557\) | −143135. | − | 143135.i | −0.461354 | − | 0.461354i | 0.437745 | − | 0.899099i | \(-0.355777\pi\) |
−0.899099 | + | 0.437745i | \(0.855777\pi\) | |||||||
\(558\) | − | 191627.i | − | 0.615445i | ||||||
\(559\) | 62721.8 | − | 29938.8i | 0.200722 | − | 0.0958101i | ||||
\(560\) | 385652. | 1.22976 | ||||||||
\(561\) | 59367.3 | − | 59367.3i | 0.188635 | − | 0.188635i | ||||
\(562\) | 166199. | 0.526206 | ||||||||
\(563\) | 230941.i | 0.728592i | 0.931283 | + | 0.364296i | \(0.118690\pi\) | ||||
−0.931283 | + | 0.364296i | \(0.881310\pi\) | |||||||
\(564\) | −262183. | + | 262183.i | −0.824226 | + | 0.824226i | ||||
\(565\) | −713694. | + | 713694.i | −2.23571 | + | 2.23571i | ||||
\(566\) | −122205. | − | 122205.i | −0.381467 | − | 0.381467i | ||||
\(567\) | 17286.9 | + | 17286.9i | 0.0537713 | + | 0.0537713i | ||||
\(568\) | 1961.97 | 0.00608129 | ||||||||
\(569\) | 243018.i | 0.750609i | 0.926902 | + | 0.375305i | \(0.122462\pi\) | ||||
−0.926902 | + | 0.375305i | \(0.877538\pi\) | |||||||
\(570\) | −237988. | − | 237988.i | −0.732497 | − | 0.732497i | ||||
\(571\) | 229921.i | 0.705189i | 0.935776 | + | 0.352595i | \(0.114701\pi\) | ||||
−0.935776 | + | 0.352595i | \(0.885299\pi\) | |||||||
\(572\) | 122192. | + | 43231.2i | 0.373467 | + | 0.132131i | ||||
\(573\) | 241064. | 0.734214 | ||||||||
\(574\) | 217743. | − | 217743.i | 0.660876 | − | 0.660876i | ||||
\(575\) | 296410. | 0.896515 | ||||||||
\(576\) | − | 121539.i | − | 0.366329i | ||||||
\(577\) | −45748.5 | + | 45748.5i | −0.137412 | + | 0.137412i | −0.772467 | − | 0.635055i | \(-0.780977\pi\) |
0.635055 | + | 0.772467i | \(0.280977\pi\) | |||||||
\(578\) | 169929. | − | 169929.i | 0.508641 | − | 0.508641i | ||||
\(579\) | 48622.7 | + | 48622.7i | 0.145038 | + | 0.145038i | ||||
\(580\) | −515568. | − | 515568.i | −1.53260 | − | 1.53260i | ||||
\(581\) | −193426. | −0.573010 | ||||||||
\(582\) | 65681.3i | 0.193908i | ||||||||
\(583\) | −136397. | − | 136397.i | −0.401299 | − | 0.401299i | ||||
\(584\) | 17244.7i | 0.0505628i | ||||||||
\(585\) | 204147. | + | 72226.5i | 0.596529 | + | 0.211050i | ||||
\(586\) | 548126. | 1.59619 | ||||||||
\(587\) | −183355. | + | 183355.i | −0.532127 | + | 0.532127i | −0.921205 | − | 0.389078i | \(-0.872794\pi\) |
0.389078 | + | 0.921205i | \(0.372794\pi\) | |||||||
\(588\) | −111512. | −0.322527 | ||||||||
\(589\) | − | 295206.i | − | 0.850931i | ||||||
\(590\) | −459479. | + | 459479.i | −1.31996 | + | 1.31996i | ||||
\(591\) | −23190.4 | + | 23190.4i | −0.0663947 | + | 0.0663947i | ||||
\(592\) | 27306.4 | + | 27306.4i | 0.0779149 | + | 0.0779149i | ||||
\(593\) | −83397.8 | − | 83397.8i | −0.237162 | − | 0.237162i | 0.578512 | − | 0.815674i | \(-0.303634\pi\) |
−0.815674 | + | 0.578512i | \(0.803634\pi\) | |||||||
\(594\) | −36658.8 | −0.103897 | ||||||||
\(595\) | − | 563745.i | − | 1.59239i | ||||||
\(596\) | 168680. | + | 168680.i | 0.474866 | + | 0.474866i | ||||
\(597\) | − | 370623.i | − | 1.03988i | ||||||
\(598\) | 58818.3 | − | 166249.i | 0.164479 | − | 0.464897i | ||||
\(599\) | −217649. | −0.606601 | −0.303300 | − | 0.952895i | \(-0.598089\pi\) | ||||
−0.303300 | + | 0.952895i | \(0.598089\pi\) | |||||||
\(600\) | 27865.1 | − | 27865.1i | 0.0774031 | − | 0.0774031i | ||||
\(601\) | −441379. | −1.22197 | −0.610987 | − | 0.791640i | \(-0.709227\pi\) | ||||
−0.610987 | + | 0.791640i | \(0.709227\pi\) | |||||||
\(602\) | 79001.4i | 0.217993i | ||||||||
\(603\) | −71051.5 | + | 71051.5i | −0.195406 | + | 0.195406i | ||||
\(604\) | 169103. | − | 169103.i | 0.463529 | − | 0.463529i | ||||
\(605\) | −421490. | − | 421490.i | −1.15153 | − | 1.15153i | ||||
\(606\) | −210101. | − | 210101.i | −0.572113 | − | 0.572113i | ||||
\(607\) | −283335. | −0.768993 | −0.384497 | − | 0.923126i | \(-0.625625\pi\) | ||||
−0.384497 | + | 0.923126i | \(0.625625\pi\) | |||||||
\(608\) | − | 348499.i | − | 0.942745i | ||||||
\(609\) | 112592. | + | 112592.i | 0.303580 | + | 0.303580i | ||||
\(610\) | − | 1.02233e6i | − | 2.74747i | ||||||
\(611\) | 239225. | − | 676166.i | 0.640802 | − | 1.81122i | ||||
\(612\) | −160805. | −0.429337 | ||||||||
\(613\) | 482403. | − | 482403.i | 1.28377 | − | 1.28377i | 0.345272 | − | 0.938503i | \(-0.387787\pi\) |
0.938503 | − | 0.345272i | \(-0.112213\pi\) | |||||||
\(614\) | 783139. | 2.07731 | ||||||||
\(615\) | 395286.i | 1.04511i | ||||||||
\(616\) | −5041.39 | + | 5041.39i | −0.0132858 | + | 0.0132858i | ||||
\(617\) | 136398. | − | 136398.i | 0.358293 | − | 0.358293i | −0.504890 | − | 0.863184i | \(-0.668467\pi\) |
0.863184 | + | 0.504890i | \(0.168467\pi\) | |||||||
\(618\) | 138.101 | + | 138.101i | 0.000361592 | + | 0.000361592i | ||||
\(619\) | 130340. | + | 130340.i | 0.340170 | + | 0.340170i | 0.856431 | − | 0.516261i | \(-0.172677\pi\) |
−0.516261 | + | 0.856431i | \(0.672677\pi\) | |||||||
\(620\) | 988623. | 2.57186 | ||||||||
\(621\) | 25556.5i | 0.0662701i | ||||||||
\(622\) | 286139. | + | 286139.i | 0.739600 | + | 0.739600i | ||||
\(623\) | 81708.7i | 0.210519i | ||||||||
\(624\) | 91664.8 | + | 192038.i | 0.235415 | + | 0.493193i | ||||
\(625\) | −1.24013e6 | −3.17473 | ||||||||
\(626\) | −277559. | + | 277559.i | −0.708282 | + | 0.708282i | ||||
\(627\) | −56473.6 | −0.143652 | ||||||||
\(628\) | − | 143831.i | − | 0.364698i | ||||||
\(629\) | 39916.3 | − | 39916.3i | 0.100890 | − | 0.100890i | ||||
\(630\) | −174054. | + | 174054.i | −0.438532 | + | 0.438532i | ||||
\(631\) | −145847. | − | 145847.i | −0.366302 | − | 0.366302i | 0.499825 | − | 0.866127i | \(-0.333398\pi\) |
−0.866127 | + | 0.499825i | \(0.833398\pi\) | |||||||
\(632\) | 25987.9 | + | 25987.9i | 0.0650635 | + | 0.0650635i | ||||
\(633\) | −234586. | −0.585456 | ||||||||
\(634\) | 1.13753e6i | 2.82998i | ||||||||
\(635\) | 888150. | + | 888150.i | 2.20262 | + | 2.20262i | ||||
\(636\) | 369453.i | 0.913365i | ||||||||
\(637\) | 194667. | − | 92920.0i | 0.479749 | − | 0.228997i | ||||
\(638\) | −238764. | −0.586580 | ||||||||
\(639\) | 8036.84 | − | 8036.84i | 0.0196826 | − | 0.0196826i | ||||
\(640\) | 113101. | 0.276126 | ||||||||
\(641\) | 207974.i | 0.506165i | 0.967445 | + | 0.253083i | \(0.0814445\pi\) | ||||
−0.967445 | + | 0.253083i | \(0.918556\pi\) | |||||||
\(642\) | 130137. | − | 130137.i | 0.315740 | − | 0.315740i | ||||
\(643\) | −30795.0 | + | 30795.0i | −0.0744831 | + | 0.0744831i | −0.743367 | − | 0.668884i | \(-0.766772\pi\) |
0.668884 | + | 0.743367i | \(0.266772\pi\) | |||||||
\(644\) | 72628.3 | + | 72628.3i | 0.175119 | + | 0.175119i | ||||
\(645\) | −71708.8 | − | 71708.8i | −0.172367 | − | 0.172367i | ||||
\(646\) | −483461. | −1.15850 | ||||||||
\(647\) | 216754.i | 0.517795i | 0.965905 | + | 0.258898i | \(0.0833592\pi\) | ||||
−0.965905 | + | 0.258898i | \(0.916641\pi\) | |||||||
\(648\) | 2402.53 | + | 2402.53i | 0.00572161 | + | 0.00572161i | ||||
\(649\) | 109032.i | 0.258861i | ||||||||
\(650\) | −525407. | + | 1.48506e6i | −1.24357 | + | 3.51492i | ||||
\(651\) | −215900. | −0.509437 | ||||||||
\(652\) | −19574.0 | + | 19574.0i | −0.0460452 | + | 0.0460452i | ||||
\(653\) | 622399. | 1.45963 | 0.729815 | − | 0.683645i | \(-0.239606\pi\) | ||||
0.729815 | + | 0.683645i | \(0.239606\pi\) | |||||||
\(654\) | 155516.i | 0.363597i | ||||||||
\(655\) | 721203. | − | 721203.i | 1.68103 | − | 1.68103i | ||||
\(656\) | −274664. | + | 274664.i | −0.638254 | + | 0.638254i | ||||
\(657\) | 70639.8 | + | 70639.8i | 0.163651 | + | 0.163651i | ||||
\(658\) | 576491. | + | 576491.i | 1.33150 | + | 1.33150i | ||||
\(659\) | 127164. | 0.292814 | 0.146407 | − | 0.989224i | \(-0.453229\pi\) | ||||
0.146407 | + | 0.989224i | \(0.453229\pi\) | |||||||
\(660\) | − | 189126.i | − | 0.434173i | ||||||
\(661\) | 512043. | + | 512043.i | 1.17194 | + | 1.17194i | 0.981748 | + | 0.190187i | \(0.0609095\pi\) |
0.190187 | + | 0.981748i | \(0.439091\pi\) | |||||||
\(662\) | − | 594817.i | − | 1.35727i | ||||||
\(663\) | 280720. | − | 133995.i | 0.638625 | − | 0.304833i | ||||
\(664\) | −26882.3 | −0.0609720 | ||||||||
\(665\) | −268133. | + | 268133.i | −0.606328 | + | 0.606328i | ||||
\(666\) | −24647.9 | −0.0555690 | ||||||||
\(667\) | 166453.i | 0.374145i | ||||||||
\(668\) | 126687. | − | 126687.i | 0.283909 | − | 0.283909i | ||||
\(669\) | 117027. | − | 117027.i | 0.261477 | − | 0.261477i | ||||
\(670\) | −715384. | − | 715384.i | −1.59364 | − | 1.59364i | ||||
\(671\) | −121298. | − | 121298.i | −0.269406 | − | 0.269406i | ||||
\(672\) | −254876. | −0.564404 | ||||||||
\(673\) | − | 70363.7i | − | 0.155353i | −0.996979 | − | 0.0776763i | \(-0.975250\pi\) | ||
0.996979 | − | 0.0776763i | \(-0.0247501\pi\) | |||||||
\(674\) | −57972.1 | − | 57972.1i | −0.127614 | − | 0.127614i | ||||
\(675\) | − | 228288.i | − | 0.501045i | ||||||
\(676\) | 373370. | + | 301995.i | 0.817044 | + | 0.660855i | ||||
\(677\) | 289817. | 0.632334 | 0.316167 | − | 0.948704i | \(-0.397604\pi\) | ||||
0.316167 | + | 0.948704i | \(0.397604\pi\) | |||||||
\(678\) | 447629. | − | 447629.i | 0.973776 | − | 0.973776i | ||||
\(679\) | 74000.9 | 0.160508 | ||||||||
\(680\) | − | 78349.1i | − | 0.169440i | ||||||
\(681\) | 175001. | − | 175001.i | 0.377351 | − | 0.377351i | ||||
\(682\) | 228920. | − | 228920.i | 0.492170 | − | 0.492170i | ||||
\(683\) | 126812. | + | 126812.i | 0.271844 | + | 0.271844i | 0.829842 | − | 0.557998i | \(-0.188430\pi\) |
−0.557998 | + | 0.829842i | \(0.688430\pi\) | |||||||
\(684\) | 76483.7 | + | 76483.7i | 0.163477 | + | 0.163477i | ||||
\(685\) | −337596. | −0.719476 | ||||||||
\(686\) | 706430.i | 1.50114i | ||||||||
\(687\) | 286137. | + | 286137.i | 0.606261 | + | 0.606261i | ||||
\(688\) | − | 99653.4i | − | 0.210531i | ||||||
\(689\) | −307856. | − | 644957.i | −0.648498 | − | 1.35860i | ||||
\(690\) | −257316. | −0.540466 | ||||||||
\(691\) | 512067. | − | 512067.i | 1.07243 | − | 1.07243i | 0.0752718 | − | 0.997163i | \(-0.476018\pi\) |
0.997163 | − | 0.0752718i | \(-0.0239824\pi\) | |||||||
\(692\) | −658388. | −1.37490 | ||||||||
\(693\) | 41302.2i | 0.0860016i | ||||||||
\(694\) | −875563. | + | 875563.i | −1.81789 | + | 1.81789i | ||||
\(695\) | 408827. | − | 408827.i | 0.846388 | − | 0.846388i | ||||
\(696\) | 15648.0 | + | 15648.0i | 0.0323029 | + | 0.0323029i | ||||
\(697\) | 401502. | + | 401502.i | 0.826461 | + | 0.826461i | ||||
\(698\) | 167478. | 0.343753 | ||||||||
\(699\) | 34652.1i | 0.0709211i | ||||||||
\(700\) | −648768. | − | 648768.i | −1.32402 | − | 1.32402i | ||||
\(701\) | 718609.i | 1.46237i | 0.682181 | + | 0.731184i | \(0.261032\pi\) | ||||
−0.682181 | + | 0.731184i | \(0.738968\pi\) | |||||||
\(702\) | −128041. | − | 45300.5i | −0.259822 | − | 0.0919240i | ||||
\(703\) | −37970.7 | −0.0768312 | ||||||||
\(704\) | 145192. | − | 145192.i | 0.292952 | − | 0.292952i | ||||
\(705\) | −1.04655e6 | −2.10563 | ||||||||
\(706\) | − | 570946.i | − | 1.14547i | ||||||
\(707\) | −236713. | + | 236713.i | −0.473570 | + | 0.473570i | ||||
\(708\) | 147666. | − | 147666.i | 0.294586 | − | 0.294586i | ||||
\(709\) | −360756. | − | 360756.i | −0.717664 | − | 0.717664i | 0.250462 | − | 0.968126i | \(-0.419417\pi\) |
−0.968126 | + | 0.250462i | \(0.919417\pi\) | |||||||
\(710\) | 80919.1 | + | 80919.1i | 0.160522 | + | 0.160522i | ||||
\(711\) | 212909. | 0.421168 | ||||||||
\(712\) | 11355.9i | 0.0224006i | ||||||||
\(713\) | −159590. | − | 159590.i | −0.313926 | − | 0.313926i | ||||
\(714\) | 353581.i | 0.693573i | ||||||||
\(715\) | 157594. | + | 330159.i | 0.308267 | + | 0.645819i | ||||
\(716\) | −634968. | −1.23858 | ||||||||
\(717\) | −129513. | + | 129513.i | −0.251927 | + | 0.251927i | ||||
\(718\) | 732599. | 1.42108 | ||||||||
\(719\) | − | 756213.i | − | 1.46280i | −0.681946 | − | 0.731402i | \(-0.738866\pi\) | ||
0.681946 | − | 0.731402i | \(-0.261134\pi\) | |||||||
\(720\) | 219553. | − | 219553.i | 0.423521 | − | 0.423521i | ||||
\(721\) | 155.593 | − | 155.593i | 0.000299310 | − | 0.000299310i | ||||
\(722\) | −297921. | − | 297921.i | −0.571515 | − | 0.571515i | ||||
\(723\) | 22417.3 | + | 22417.3i | 0.0428851 | + | 0.0428851i | ||||
\(724\) | −161252. | −0.307630 | ||||||||
\(725\) | − | 1.48688e6i | − | 2.82878i | ||||||
\(726\) | 264359. | + | 264359.i | 0.501557 | + | 0.501557i | ||||
\(727\) | 2488.50i | 0.00470835i | 0.999997 | + | 0.00235417i | \(0.000749357\pi\) | ||||
−0.999997 | + | 0.00235417i | \(0.999251\pi\) | |||||||
\(728\) | −23838.3 | + | 11378.7i | −0.0449794 | + | 0.0214699i | ||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | −711239. | + | 711239.i | −1.33466 | + | 1.33466i | ||||
\(731\) | −145673. | −0.272611 | ||||||||
\(732\) | 328554.i | 0.613174i | ||||||||
\(733\) | 269312. | − | 269312.i | 0.501243 | − | 0.501243i | −0.410581 | − | 0.911824i | \(-0.634674\pi\) |
0.911824 | + | 0.410581i | \(0.134674\pi\) | |||||||
\(734\) | 633254. | − | 633254.i | 1.17540 | − | 1.17540i | ||||
\(735\) | −222560. | − | 222560.i | −0.411976 | − | 0.411976i | ||||
\(736\) | −188401. | − | 188401.i | −0.347798 | − | 0.347798i | ||||
\(737\) | −169758. | −0.312532 | ||||||||
\(738\) | − | 247924.i | − | 0.455203i | ||||||
\(739\) | −710849. | − | 710849.i | −1.30163 | − | 1.30163i | −0.927291 | − | 0.374342i | \(-0.877869\pi\) |
−0.374342 | − | 0.927291i | \(-0.622131\pi\) | |||||||
\(740\) | − | 127161.i | − | 0.232215i | ||||||
\(741\) | −197250. | − | 69786.4i | −0.359237 | − | 0.127097i | ||||
\(742\) | 812357. | 1.47550 | ||||||||
\(743\) | −516575. | + | 516575.i | −0.935741 | + | 0.935741i | −0.998057 | − | 0.0623154i | \(-0.980152\pi\) |
0.0623154 | + | 0.998057i | \(0.480152\pi\) | |||||||
\(744\) | −30005.7 | −0.0542074 | ||||||||
\(745\) | 673317.i | 1.21313i | ||||||||
\(746\) | −49230.3 | + | 49230.3i | −0.0884616 | + | 0.0884616i | ||||
\(747\) | −110118. | + | 110118.i | −0.197341 | + | 0.197341i | ||||
\(748\) | −192100. | − | 192100.i | −0.343340 | − | 0.343340i | ||||
\(749\) | −146621. | − | 146621.i | −0.261356 | − | 0.261356i | ||||
\(750\) | 1.41567e6 | 2.51674 | ||||||||
\(751\) | 628582.i | 1.11450i | 0.830343 | + | 0.557252i | \(0.188144\pi\) | ||||
−0.830343 | + | 0.557252i | \(0.811856\pi\) | |||||||
\(752\) | −727194. | − | 727194.i | −1.28592 | − | 1.28592i | ||||
\(753\) | 520834.i | 0.918564i | ||||||||
\(754\) | −833952. | − | 295049.i | −1.46689 | − | 0.518981i | ||||
\(755\) | 675004. | 1.18417 | ||||||||
\(756\) | 55936.7 | − | 55936.7i | 0.0978708 | − | 0.0978708i | ||||
\(757\) | 874918. | 1.52678 | 0.763389 | − | 0.645940i | \(-0.223534\pi\) | ||||
0.763389 | + | 0.645940i | \(0.223534\pi\) | |||||||
\(758\) | 459856.i | 0.800357i | ||||||||
\(759\) | −30530.0 | + | 30530.0i | −0.0529960 | + | 0.0529960i | ||||
\(760\) | −37265.1 | + | 37265.1i | −0.0645171 | + | 0.0645171i | ||||
\(761\) | 176909. | + | 176909.i | 0.305479 | + | 0.305479i | 0.843153 | − | 0.537674i | \(-0.180697\pi\) |
−0.537674 | + | 0.843153i | \(0.680697\pi\) | |||||||
\(762\) | −557049. | − | 557049.i | −0.959363 | − | 0.959363i | ||||
\(763\) | 175215. | 0.300969 | ||||||||
\(764\) | − | 780031.i | − | 1.33636i | ||||||
\(765\) | −320942. | − | 320942.i | −0.548408 | − | 0.548408i | ||||
\(766\) | 114700.i | 0.195482i | ||||||||
\(767\) | −134735. | + | 380827.i | −0.229029 | + | 0.647347i | ||||
\(768\) | 303306. | 0.514232 | ||||||||
\(769\) | 64761.1 | − | 64761.1i | 0.109512 | − | 0.109512i | −0.650228 | − | 0.759740i | \(-0.725326\pi\) |
0.759740 | + | 0.650228i | \(0.225326\pi\) | |||||||
\(770\) | −415852. | −0.701387 | ||||||||
\(771\) | − | 77705.8i | − | 0.130721i | ||||||
\(772\) | 157333. | − | 157333.i | 0.263988 | − | 0.263988i | ||||
\(773\) | 65728.0 | − | 65728.0i | 0.110000 | − | 0.110000i | −0.649965 | − | 0.759964i | \(-0.725216\pi\) |
0.759964 | + | 0.649965i | \(0.225216\pi\) | |||||||
\(774\) | 44975.8 | + | 44975.8i | 0.0750753 | + | 0.0750753i | ||||
\(775\) | 1.42557e6 | + | 1.42557e6i | 2.37348 | + | 2.37348i | ||||
\(776\) | 10284.6 | 0.0170791 | ||||||||
\(777\) | 27770.0i | 0.0459975i | ||||||||
\(778\) | −58682.3 | − | 58682.3i | −0.0969501 | − | 0.0969501i | ||||
\(779\) | − | 381932.i | − | 0.629377i | ||||||
\(780\) | 233709. | − | 660577.i | 0.384138 | − | 1.08576i | ||||
\(781\) | 19201.8 | 0.0314803 | ||||||||
\(782\) | −261362. | + | 261362.i | −0.427395 | + | 0.427395i | ||||
\(783\) | 128198. | 0.209102 | ||||||||
\(784\) | − | 309290.i | − | 0.503193i | ||||||
\(785\) | 287064. | − | 287064.i | 0.465843 | − | 0.465843i | ||||
\(786\) | −452339. | + | 452339.i | −0.732182 | + | 0.732182i | ||||
\(787\) | 853121. | + | 853121.i | 1.37740 | + | 1.37740i | 0.848983 | + | 0.528420i | \(0.177215\pi\) |
0.528420 | + | 0.848983i | \(0.322785\pi\) | |||||||
\(788\) | 75039.2 | + | 75039.2i | 0.120847 | + | 0.120847i | ||||
\(789\) | −39356.0 | −0.0632204 | ||||||||
\(790\) | 2.14368e6i | 3.43484i | ||||||||
\(791\) | −504329. | − | 504329.i | −0.806048 | − | 0.806048i | ||||
\(792\) | 5740.17i | 0.00915112i | ||||||||
\(793\) | −273775. | − | 573559.i | −0.435360 | − | 0.912078i | ||||
\(794\) | −975493. | −1.54733 | ||||||||
\(795\) | −737369. | + | 737369.i | −1.16668 | + | 1.16668i | ||||
\(796\) | −1.19926e6 | −1.89272 | ||||||||
\(797\) | 264563.i | 0.416498i | 0.978076 | + | 0.208249i | \(0.0667765\pi\) | ||||
−0.978076 | + | 0.208249i | \(0.933224\pi\) | |||||||
\(798\) | 168173. | − | 168173.i | 0.264090 | − | 0.264090i | ||||
\(799\) | −1.06301e6 | + | 1.06301e6i | −1.66511 | + | 1.66511i | ||||
\(800\) | 1.68293e6 | + | 1.68293e6i | 2.62958 | + | 2.62958i | ||||
\(801\) | 46517.1 | + | 46517.1i | 0.0725016 | + | 0.0725016i | ||||
\(802\) | −255980. | −0.397977 | ||||||||
\(803\) | 168774.i | 0.261743i | ||||||||
\(804\) | 229908. | + | 229908.i | 0.355665 | + | 0.355665i | ||||
\(805\) | 289909.i | 0.447373i | ||||||||
\(806\) | 1.08245e6 | − | 516685.i | 1.66625 | − | 0.795345i | ||||
\(807\) | 521989. | 0.801520 | ||||||||
\(808\) | −32898.4 | + | 32898.4i | −0.0503908 | + | 0.0503908i | ||||
\(809\) | −903066. | −1.37982 | −0.689910 | − | 0.723895i | \(-0.742350\pi\) | ||||
−0.689910 | + | 0.723895i | \(0.742350\pi\) | |||||||
\(810\) | 198179.i | 0.302056i | ||||||||
\(811\) | 158801. | − | 158801.i | 0.241442 | − | 0.241442i | −0.576005 | − | 0.817446i | \(-0.695389\pi\) |
0.817446 | + | 0.576005i | \(0.195389\pi\) | |||||||
\(812\) | 364324. | − | 364324.i | 0.552555 | − | 0.552555i | ||||
\(813\) | 346170. | + | 346170.i | 0.523731 | + | 0.523731i | ||||
\(814\) | −29444.7 | − | 29444.7i | −0.0444384 | − | 0.0444384i | ||||
\(815\) | −78133.2 | −0.117631 | ||||||||
\(816\) | − | 446012.i | − | 0.669832i | ||||||
\(817\) | 69286.2 | + | 69286.2i | 0.103801 | + | 0.103801i | ||||
\(818\) | 135214.i | 0.202076i | ||||||||
\(819\) | −51038.6 | + | 144260.i | −0.0760905 | + | 0.215069i | ||||
\(820\) | 1.27906e6 | 1.90223 | ||||||||
\(821\) | 566290. | − | 566290.i | 0.840142 | − | 0.840142i | −0.148735 | − | 0.988877i | \(-0.547520\pi\) |
0.988877 | + | 0.148735i | \(0.0475203\pi\) | |||||||
\(822\) | 211740. | 0.313372 | ||||||||
\(823\) | − | 664034.i | − | 0.980371i | −0.871618 | − | 0.490186i | \(-0.836929\pi\) | ||
0.871618 | − | 0.490186i | \(-0.163071\pi\) | |||||||
\(824\) | 21.6244 | − | 21.6244i | 3.18485e−5 | − | 3.18485e-5i | ||||
\(825\) | 272716. | − | 272716.i | 0.400684 | − | 0.400684i | ||||
\(826\) | −324689. | − | 324689.i | −0.475891 | − | 0.475891i | ||||
\(827\) | −694781. | − | 694781.i | −1.01587 | − | 1.01587i | −0.999872 | − | 0.0159954i | \(-0.994908\pi\) |
−0.0159954 | − | 0.999872i | \(-0.505092\pi\) | |||||||
\(828\) | 82695.2 | 0.120620 | ||||||||
\(829\) | − | 1.07123e6i | − | 1.55874i | −0.626564 | − | 0.779370i | \(-0.715539\pi\) | ||
0.626564 | − | 0.779370i | \(-0.284461\pi\) | |||||||
\(830\) | −1.10873e6 | − | 1.10873e6i | −1.60942 | − | 1.60942i | ||||
\(831\) | − | 364668.i | − | 0.528074i | ||||||
\(832\) | 686543. | − | 327706.i | 0.991794 | − | 0.473410i | ||||
\(833\) | −452119. | −0.651573 | ||||||||
\(834\) | −256416. | + | 256416.i | −0.368649 | + | 0.368649i | ||||
\(835\) | 505694. | 0.725295 | ||||||||
\(836\) | 182737.i | 0.261465i | ||||||||
\(837\) | −122913. | + | 122913.i | −0.175447 | + | 0.175447i | ||||
\(838\) | 183277. | − | 183277.i | 0.260988 | − | 0.260988i | ||||
\(839\) | 710646. | + | 710646.i | 1.00955 | + | 1.00955i | 0.999954 | + | 0.00959972i | \(0.00305573\pi\) |
0.00959972 | + | 0.999954i | \(0.496944\pi\) | |||||||
\(840\) | 27254.0 | + | 27254.0i | 0.0386252 | + | 0.0386252i | ||||
\(841\) | 127693. | 0.180541 | ||||||||
\(842\) | 772742.i | 1.08996i | ||||||||
\(843\) | −106603. | − | 106603.i | −0.150007 | − | 0.150007i | ||||
\(844\) | 759070.i | 1.06561i | ||||||||
\(845\) | 142453. | + | 1.34792e6i | 0.199507 | + | 1.88778i | ||||
\(846\) | 656398. | 0.917120 | ||||||||
\(847\) | 297844. | − | 297844.i | 0.415167 | − | 0.415167i | ||||
\(848\) | −1.02472e6 | −1.42499 | ||||||||
\(849\) | 156769.i | 0.217493i | ||||||||
\(850\) | 2.33467e6 | − | 2.33467e6i | 3.23138 | − | 3.23138i | ||||
\(851\) | −20527.2 | + | 20527.2i | −0.0283446 | + | 0.0283446i | ||||
\(852\) | −26005.5 | − | 26005.5i | −0.0358250 | − | 0.0358250i | ||||
\(853\) | −719087. | − | 719087.i | −0.988288 | − | 0.988288i | 0.0116445 | − | 0.999932i | \(-0.496293\pi\) |
−0.999932 | + | 0.0116445i | \(0.996293\pi\) | |||||||
\(854\) | 722427. | 0.990555 | ||||||||
\(855\) | 305299.i | 0.417631i | ||||||||
\(856\) | −20377.3 | − | 20377.3i | −0.0278099 | − | 0.0278099i | ||||
\(857\) | 625779.i | 0.852038i | 0.904714 | + | 0.426019i | \(0.140084\pi\) | ||||
−0.904714 | + | 0.426019i | \(0.859916\pi\) | |||||||
\(858\) | −98843.0 | − | 207076.i | −0.134268 | − | 0.281290i | ||||
\(859\) | −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 | ||||
\(861\) | −279327. | −0.376797 | ||||||||
\(862\) | − | 973017.i | − | 1.30950i | ||||||
\(863\) | −251871. | + | 251871.i | −0.338187 | + | 0.338187i | −0.855685 | − | 0.517497i | \(-0.826864\pi\) |
0.517497 | + | 0.855685i | \(0.326864\pi\) | |||||||
\(864\) | −145102. | + | 145102.i | −0.194377 | + | 0.194377i | ||||
\(865\) | −1.31404e6 | − | 1.31404e6i | −1.75621 | − | 1.75621i | ||||
\(866\) | 424938. | + | 424938.i | 0.566618 | + | 0.566618i | ||||
\(867\) | −217990. | −0.290000 | ||||||||
\(868\) | 698606.i | 0.927242i | ||||||||
\(869\) | 254343. | + | 254343.i | 0.336807 | + | 0.336807i | ||||
\(870\) | 1.29077e6i | 1.70533i | ||||||||
\(871\) | −592928. | − | 209776.i | −0.781566 | − | 0.276515i | ||||
\(872\) | 24351.3 | 0.0320250 | ||||||||
\(873\) | 42129.0 | − | 42129.0i | 0.0552781 | − | 0.0552781i | ||||
\(874\) | 248623. | 0.325475 | ||||||||
\(875\) | − | 1.59499e6i | − | 2.08325i | ||||||
\(876\) | 228575. | − | 228575.i | 0.297866 | − | 0.297866i | ||||
\(877\) | 248488. | − | 248488.i | 0.323077 | − | 0.323077i | −0.526869 | − | 0.849946i | \(-0.676634\pi\) |
0.849946 | + | 0.526869i | \(0.176634\pi\) | |||||||
\(878\) | 766569. | + | 766569.i | 0.994403 | + | 0.994403i | ||||
\(879\) | −351577. | − | 351577.i | −0.455032 | − | 0.455032i | ||||
\(880\) | 524562. | 0.677378 | ||||||||
\(881\) | 1.01415e6i | 1.30662i | 0.757089 | + | 0.653312i | \(0.226621\pi\) | ||||
−0.757089 | + | 0.653312i | \(0.773379\pi\) | |||||||
\(882\) | 139590. | + | 139590.i | 0.179439 | + | 0.179439i | ||||
\(883\) | 1.21924e6i | 1.56375i | 0.623433 | + | 0.781877i | \(0.285737\pi\) | ||||
−0.623433 | + | 0.781877i | \(0.714263\pi\) | |||||||
\(884\) | −433580. | − | 908349.i | −0.554836 | − | 1.16238i | ||||
\(885\) | 589434. | 0.752573 | ||||||||
\(886\) | 626388. | − | 626388.i | 0.797950 | − | 0.797950i | ||||
\(887\) | 904300. | 1.14938 | 0.574692 | − | 0.818370i | \(-0.305122\pi\) | ||||
0.574692 | + | 0.818370i | \(0.305122\pi\) | |||||||
\(888\) | 3859.47i | 0.00489443i | ||||||||
\(889\) | −627608. | + | 627608.i | −0.794118 | + | 0.794118i | ||||
\(890\) | −468359. | + | 468359.i | −0.591287 | + | 0.591287i | ||||
\(891\) | 23513.5 | + | 23513.5i | 0.0296184 | + | 0.0296184i | ||||
\(892\) | −378674. | − | 378674.i | −0.475923 | − | 0.475923i | ||||
\(893\) | 1.01120e6 | 1.26804 | ||||||||
\(894\) | − | 422305.i | − | 0.528386i | ||||||
\(895\) | −1.26729e6 | − | 1.26729e6i | −1.58209 | − | 1.58209i | ||||
\(896\) | 79922.4i | 0.0995526i | ||||||||
\(897\) | −144362. | + | 68907.8i | −0.179419 | + | 0.0856414i | ||||
\(898\) | −438520. | −0.543797 | ||||||||
\(899\) | −800549. | + | 800549.i | −0.990532 | + | 0.990532i | ||||
\(900\) | −738692. | −0.911966 | ||||||||
\(901\) | 1.49793e6i | 1.84519i | ||||||||
\(902\) | 296172. | − | 296172.i | 0.364025 | − | 0.364025i | ||||
\(903\) | 50672.7 | − | 50672.7i | 0.0621439 | − | 0.0621439i | ||||
\(904\) | −70091.5 | − | 70091.5i | −0.0857687 | − | 0.0857687i | ||||
\(905\) | −321834. | − | 321834.i | −0.392948 | − | 0.392948i | ||||
\(906\) | −423363. | −0.515771 | ||||||||
\(907\) | 1.40623e6i | 1.70940i | 0.519124 | + | 0.854699i | \(0.326258\pi\) | ||||
−0.519124 | + | 0.854699i | \(0.673742\pi\) | |||||||
\(908\) | −566265. | − | 566265.i | −0.686828 | − | 0.686828i | ||||
\(909\) | 269524.i | 0.326189i | ||||||||
\(910\) | −1.45248e6 | − | 513883.i | −1.75400 | − | 0.620557i | ||||
\(911\) | −320928. | −0.386697 | −0.193348 | − | 0.981130i | \(-0.561935\pi\) | ||||
−0.193348 | + | 0.981130i | \(0.561935\pi\) | |||||||
\(912\) | −212136. | + | 212136.i | −0.255050 | + | 0.255050i | ||||
\(913\) | −263097. | −0.315627 | ||||||||
\(914\) | − | 357745.i | − | 0.428234i | ||||||
\(915\) | −655741. | + | 655741.i | −0.783231 | + | 0.783231i | ||||
\(916\) | 925876. | − | 925876.i | 1.10347 | − | 1.10347i | ||||
\(917\) | 509635. | + | 509635.i | 0.606067 | + | 0.606067i | ||||
\(918\) | 201295. | + | 201295.i | 0.238862 | + | 0.238862i | ||||
\(919\) | −824931. | −0.976757 | −0.488378 | − | 0.872632i | \(-0.662411\pi\) | ||||
−0.488378 | + | 0.872632i | \(0.662411\pi\) | |||||||
\(920\) | 40291.5i | 0.0476034i | ||||||||
\(921\) | −502318. | − | 502318.i | −0.592187 | − | 0.592187i | ||||
\(922\) | − | 1.17866e6i | − | 1.38652i | ||||||
\(923\) | 67067.8 | + | 23728.3i | 0.0787246 | + | 0.0278525i | ||||
\(924\) | 133645. | 0.156534 | ||||||||
\(925\) | 183364. | − | 183364.i | 0.214304 | − | 0.214304i | ||||
\(926\) | 1.36575e6 | 1.59276 | ||||||||
\(927\) | − | 177.160i | − | 0.000206161i | ||||||
\(928\) | −945070. | + | 945070.i | −1.09741 | + | 1.09741i | ||||
\(929\) | 678405. | − | 678405.i | 0.786064 | − | 0.786064i | −0.194783 | − | 0.980846i | \(-0.562400\pi\) |
0.980846 | + | 0.194783i | \(0.0624001\pi\) | |||||||
\(930\) | −1.23755e6 | − | 1.23755e6i | −1.43086 | − | 1.43086i | ||||
\(931\) | 215041. | + | 215041.i | 0.248097 | + | 0.248097i | ||||
\(932\) | 112127. | 0.129086 | ||||||||
\(933\) | − | 367069.i | − | 0.421681i | ||||||
\(934\) | 665000. | + | 665000.i | 0.762303 | + | 0.762303i | ||||
\(935\) | − | 766802.i | − | 0.877122i | ||||||
\(936\) | −7093.33 | + | 20049.2i | −0.00809652 | + | 0.0228847i | ||||
\(937\) | 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 | ||||
\(939\) | 356061. | 0.403825 | ||||||||
\(940\) | 3.38642e6i | 3.83252i | ||||||||
\(941\) | 498975. | − | 498975.i | 0.563507 | − | 0.563507i | −0.366795 | − | 0.930302i | \(-0.619545\pi\) |
0.930302 | + | 0.366795i | \(0.119545\pi\) | |||||||
\(942\) | −180047. | + | 180047.i | −0.202901 | + | 0.202901i | ||||
\(943\) | −206475. | − | 206475.i | −0.232190 | − | 0.232190i | ||||
\(944\) | 409567. | + | 409567.i | 0.459601 | + | 0.459601i | ||||
\(945\) | 223281. | 0.250028 | ||||||||
\(946\) | 107457.i | 0.120075i | ||||||||
\(947\) | −672812. | − | 672812.i | −0.750228 | − | 0.750228i | 0.224293 | − | 0.974522i | \(-0.427993\pi\) |
−0.974522 | + | 0.224293i | \(0.927993\pi\) | |||||||
\(948\) | − | 688928.i | − | 0.766580i | ||||||
\(949\) | −208560. | + | 589492.i | −0.231579 | + | 0.654554i | ||||
\(950\) | −2.22087e6 | −2.46080 | ||||||||
\(951\) | 729629. | − | 729629.i | 0.806754 | − | 0.806754i | ||||
\(952\) | 55365.1 | 0.0610889 | ||||||||
\(953\) | 226250.i | 0.249117i | 0.992212 | + | 0.124558i | \(0.0397514\pi\) | ||||
−0.992212 | + | 0.124558i | \(0.960249\pi\) | |||||||
\(954\) | 462478. | − | 462478.i | 0.508153 | − | 0.508153i | ||||
\(955\) | 1.55682e6 | − | 1.55682e6i | 1.70699 | − | 1.70699i | ||||
\(956\) | 419076. | + | 419076.i | 0.458540 | + | 0.458540i | ||||
\(957\) | 153147. | + | 153147.i | 0.167219 | + | 0.167219i | ||||
\(958\) | −88351.7 | −0.0962684 | ||||||||
\(959\) | − | 238561.i | − | 0.259395i | ||||||
\(960\) | −784913. | − | 784913.i | −0.851686 | − | 0.851686i | ||||
\(961\) | − | 611566.i | − | 0.662211i | ||||||
\(962\) | −66458.2 | − | 139230.i | −0.0718123 | − | 0.150447i | ||||
\(963\) | −166944. | −0.180019 | ||||||||
\(964\) | 72537.6 | − | 72537.6i | 0.0780565 | − | 0.0780565i | ||||
\(965\) | 628022. | 0.674404 | ||||||||
\(966\) | − | 181831.i | − | 0.194856i | ||||||
\(967\) | −652291. | + | 652291.i | −0.697571 | + | 0.697571i | −0.963886 | − | 0.266315i | \(-0.914194\pi\) |
0.266315 | + | 0.963886i | \(0.414194\pi\) | |||||||
\(968\) | 41394.3 | − | 41394.3i | 0.0441764 | − | 0.0441764i | ||||
\(969\) | 310100. | + | 310100.i | 0.330258 | + | 0.330258i | ||||
\(970\) | 424177. | + | 424177.i | 0.450821 | + | 0.450821i | ||||
\(971\) | 330964. | 0.351028 | 0.175514 | − | 0.984477i | \(-0.443841\pi\) | ||||
0.175514 | + | 0.984477i | \(0.443841\pi\) | |||||||
\(972\) | − | 63690.0i | − | 0.0674122i | ||||||
\(973\) | 288896. | + | 288896.i | 0.305151 | + | 0.305151i | ||||
\(974\) | 1.82681e6i | 1.92564i | ||||||||
\(975\) | 1.28954e6 | − | 615534.i | 1.35652 | − | 0.647504i | ||||
\(976\) | −911280. | −0.956648 | ||||||||
\(977\) | −812569. | + | 812569.i | −0.851278 | + | 0.851278i | −0.990291 | − | 0.139013i | \(-0.955607\pi\) |
0.139013 | + | 0.990291i | \(0.455607\pi\) | |||||||
\(978\) | 49005.2 | 0.0512347 | ||||||||
\(979\) | 111140.i | 0.115959i | ||||||||
\(980\) | −720156. | + | 720156.i | −0.749850 | + | 0.749850i | ||||
\(981\) | 99750.5 | − | 99750.5i | 0.103652 | − | 0.103652i | ||||
\(982\) | −1.26209e6 | − | 1.26209e6i | −1.30878 | − | 1.30878i | ||||
\(983\) | 1.32394e6 | + | 1.32394e6i | 1.37013 | + | 1.37013i | 0.860235 | + | 0.509898i | \(0.170317\pi\) |
0.509898 | + | 0.860235i | \(0.329683\pi\) | |||||||
\(984\) | −38820.9 | −0.0400936 | ||||||||
\(985\) | 299533.i | 0.308725i | ||||||||
\(986\) | 1.31107e6 | + | 1.31107e6i | 1.34856 | + | 1.34856i | ||||
\(987\) | − | 739541.i | − | 0.759151i | ||||||
\(988\) | −225814. | + | 638260.i | −0.231333 | + | 0.653858i | ||||
\(989\) | 74913.1 | 0.0765888 | ||||||||
\(990\) | −236746. | + | 236746.i | −0.241553 | + | 0.241553i | ||||
\(991\) | −424185. | −0.431925 | −0.215962 | − | 0.976402i | \(-0.569289\pi\) | ||||
−0.215962 | + | 0.976402i | \(0.569289\pi\) | |||||||
\(992\) | − | 1.81221e6i | − | 1.84156i | ||||||
\(993\) | −381525. | + | 381525.i | −0.386923 | + | 0.386923i | ||||
\(994\) | −57181.2 | + | 57181.2i | −0.0578736 | + | 0.0578736i | ||||
\(995\) | −2.39352e6 | − | 2.39352e6i | −2.41764 | − | 2.41764i | ||||
\(996\) | 356319. | + | 356319.i | 0.359187 | + | 0.359187i | ||||
\(997\) | 1.53487e6 | 1.54412 | 0.772060 | − | 0.635549i | \(-0.219226\pi\) | ||||
0.772060 | + | 0.635549i | \(0.219226\pi\) | |||||||
\(998\) | 15619.8i | 0.0156825i | ||||||||
\(999\) | 15809.6 | + | 15809.6i | 0.0158413 | + | 0.0158413i |
(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 | 39.5.g.a.31.3 | ✓ | 20 | |
3.2 | odd | 2 | 117.5.j.b.109.8 | 20 | |||
13.8 | odd | 4 | inner | 39.5.g.a.34.3 | yes | 20 | |
39.8 | even | 4 | 117.5.j.b.73.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.3 | ✓ | 20 | 1.1 | even | 1 | trivial | |
39.5.g.a.34.3 | yes | 20 | 13.8 | odd | 4 | inner | |
117.5.j.b.73.8 | 20 | 39.8 | even | 4 | |||
117.5.j.b.109.8 | 20 | 3.2 | odd | 2 |