Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,34,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
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: | yes |
Analytic conductor: | \(34.4914144405\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 1372039866x^{3} - 648067657640x^{2} + 285631173782445856x - 33409741805340964224 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(15553.7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −56118.7 | −0.605498 | −0.302749 | − | 0.953070i | \(-0.597904\pi\) | ||||
−0.302749 | + | 0.953070i | \(0.597904\pi\) | |||||||
\(3\) | 5.48591e7 | 0.735780 | 0.367890 | − | 0.929869i | \(-0.380080\pi\) | ||||
0.367890 | + | 0.929869i | \(0.380080\pi\) | |||||||
\(4\) | −5.44063e9 | −0.633372 | ||||||||
\(5\) | −1.52588e11 | −0.447214 | ||||||||
\(6\) | −3.07862e12 | −0.445513 | ||||||||
\(7\) | 7.38557e13 | 0.839975 | 0.419987 | − | 0.907530i | \(-0.362035\pi\) | ||||
0.419987 | + | 0.907530i | \(0.362035\pi\) | |||||||
\(8\) | 7.87377e14 | 0.989004 | ||||||||
\(9\) | −2.54954e15 | −0.458628 | ||||||||
\(10\) | 8.56303e15 | 0.270787 | ||||||||
\(11\) | 3.54535e16 | 0.232638 | 0.116319 | − | 0.993212i | \(-0.462891\pi\) | ||||
0.116319 | + | 0.993212i | \(0.462891\pi\) | |||||||
\(12\) | −2.98468e17 | −0.466022 | ||||||||
\(13\) | −1.27272e18 | −0.530476 | −0.265238 | − | 0.964183i | \(-0.585451\pi\) | ||||
−0.265238 | + | 0.964183i | \(0.585451\pi\) | |||||||
\(14\) | −4.14468e18 | −0.508603 | ||||||||
\(15\) | −8.37083e18 | −0.329051 | ||||||||
\(16\) | 2.54805e18 | 0.0345325 | ||||||||
\(17\) | 1.95420e20 | 0.974006 | 0.487003 | − | 0.873400i | \(-0.338090\pi\) | ||||
0.487003 | + | 0.873400i | \(0.338090\pi\) | |||||||
\(18\) | 1.43077e20 | 0.277699 | ||||||||
\(19\) | 9.67568e20 | 0.769568 | 0.384784 | − | 0.923007i | \(-0.374276\pi\) | ||||
0.384784 | + | 0.923007i | \(0.374276\pi\) | |||||||
\(20\) | 8.30174e20 | 0.283253 | ||||||||
\(21\) | 4.05165e21 | 0.618036 | ||||||||
\(22\) | −1.98961e21 | −0.140862 | ||||||||
\(23\) | −3.06053e22 | −1.04061 | −0.520305 | − | 0.853981i | \(-0.674182\pi\) | ||||
−0.520305 | + | 0.853981i | \(0.674182\pi\) | |||||||
\(24\) | 4.31948e22 | 0.727689 | ||||||||
\(25\) | 2.32831e22 | 0.200000 | ||||||||
\(26\) | 7.14231e22 | 0.321202 | ||||||||
\(27\) | −4.44830e23 | −1.07323 | ||||||||
\(28\) | −4.01821e23 | −0.532017 | ||||||||
\(29\) | −1.16201e23 | −0.0862271 | −0.0431135 | − | 0.999070i | \(-0.513728\pi\) | ||||
−0.0431135 | + | 0.999070i | \(0.513728\pi\) | |||||||
\(30\) | 4.69760e23 | 0.199239 | ||||||||
\(31\) | −3.89265e23 | −0.0961121 | −0.0480560 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480560 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(32\) | −6.90651e24 | −1.00991 | ||||||||
\(33\) | 1.94495e24 | 0.171170 | ||||||||
\(34\) | −1.09667e25 | −0.589759 | ||||||||
\(35\) | −1.12695e25 | −0.375648 | ||||||||
\(36\) | 1.38711e25 | 0.290482 | ||||||||
\(37\) | −2.73400e25 | −0.364310 | −0.182155 | − | 0.983270i | \(-0.558307\pi\) | ||||
−0.182155 | + | 0.983270i | \(0.558307\pi\) | |||||||
\(38\) | −5.42987e25 | −0.465972 | ||||||||
\(39\) | −6.98200e25 | −0.390314 | ||||||||
\(40\) | −1.20144e26 | −0.442296 | ||||||||
\(41\) | −7.27564e26 | −1.78212 | −0.891061 | − | 0.453883i | \(-0.850038\pi\) | ||||
−0.891061 | + | 0.453883i | \(0.850038\pi\) | |||||||
\(42\) | −2.27373e26 | −0.374220 | ||||||||
\(43\) | −1.74161e27 | −1.94411 | −0.972055 | − | 0.234754i | \(-0.924572\pi\) | ||||
−0.972055 | + | 0.234754i | \(0.924572\pi\) | |||||||
\(44\) | −1.92889e26 | −0.147346 | ||||||||
\(45\) | 3.89029e26 | 0.205105 | ||||||||
\(46\) | 1.71753e27 | 0.630087 | ||||||||
\(47\) | 2.14063e26 | 0.0550714 | 0.0275357 | − | 0.999621i | \(-0.491234\pi\) | ||||
0.0275357 | + | 0.999621i | \(0.491234\pi\) | |||||||
\(48\) | 1.39784e26 | 0.0254083 | ||||||||
\(49\) | −2.27634e27 | −0.294443 | ||||||||
\(50\) | −1.30662e27 | −0.121100 | ||||||||
\(51\) | 1.07206e28 | 0.716654 | ||||||||
\(52\) | 6.92437e27 | 0.335989 | ||||||||
\(53\) | −1.96400e28 | −0.695970 | −0.347985 | − | 0.937500i | \(-0.613134\pi\) | ||||
−0.347985 | + | 0.937500i | \(0.613134\pi\) | |||||||
\(54\) | 2.49633e28 | 0.649838 | ||||||||
\(55\) | −5.40978e27 | −0.104039 | ||||||||
\(56\) | 5.81522e28 | 0.830738 | ||||||||
\(57\) | 5.30799e28 | 0.566233 | ||||||||
\(58\) | 6.52106e27 | 0.0522103 | ||||||||
\(59\) | 2.54315e29 | 1.53573 | 0.767864 | − | 0.640612i | \(-0.221319\pi\) | ||||
0.767864 | + | 0.640612i | \(0.221319\pi\) | |||||||
\(60\) | 4.55425e28 | 0.208412 | ||||||||
\(61\) | −2.81524e29 | −0.980785 | −0.490392 | − | 0.871502i | \(-0.663147\pi\) | ||||
−0.490392 | + | 0.871502i | \(0.663147\pi\) | |||||||
\(62\) | 2.18451e28 | 0.0581957 | ||||||||
\(63\) | −1.88298e29 | −0.385236 | ||||||||
\(64\) | 3.65697e29 | 0.576968 | ||||||||
\(65\) | 1.94201e29 | 0.237236 | ||||||||
\(66\) | −1.09148e29 | −0.103643 | ||||||||
\(67\) | −8.18392e29 | −0.606355 | −0.303178 | − | 0.952934i | \(-0.598048\pi\) | ||||
−0.303178 | + | 0.952934i | \(0.598048\pi\) | |||||||
\(68\) | −1.06321e30 | −0.616908 | ||||||||
\(69\) | −1.67898e30 | −0.765660 | ||||||||
\(70\) | 6.32429e29 | 0.227454 | ||||||||
\(71\) | −3.59524e30 | −1.02321 | −0.511606 | − | 0.859220i | \(-0.670949\pi\) | ||||
−0.511606 | + | 0.859220i | \(0.670949\pi\) | |||||||
\(72\) | −2.00745e30 | −0.453585 | ||||||||
\(73\) | −2.19852e30 | −0.395642 | −0.197821 | − | 0.980238i | \(-0.563387\pi\) | ||||
−0.197821 | + | 0.980238i | \(0.563387\pi\) | |||||||
\(74\) | 1.53429e30 | 0.220589 | ||||||||
\(75\) | 1.27729e30 | 0.147156 | ||||||||
\(76\) | −5.26418e30 | −0.487423 | ||||||||
\(77\) | 2.61844e30 | 0.195410 | ||||||||
\(78\) | 3.91821e30 | 0.236334 | ||||||||
\(79\) | 3.90404e31 | 1.90839 | 0.954194 | − | 0.299188i | \(-0.0967156\pi\) | ||||
0.954194 | + | 0.299188i | \(0.0967156\pi\) | |||||||
\(80\) | −3.88802e29 | −0.0154434 | ||||||||
\(81\) | −1.02299e31 | −0.331032 | ||||||||
\(82\) | 4.08299e31 | 1.07907 | ||||||||
\(83\) | 4.98882e30 | 0.107947 | 0.0539734 | − | 0.998542i | \(-0.482811\pi\) | ||||
0.0539734 | + | 0.998542i | \(0.482811\pi\) | |||||||
\(84\) | −2.20435e31 | −0.391447 | ||||||||
\(85\) | −2.98187e31 | −0.435589 | ||||||||
\(86\) | 9.77368e31 | 1.17715 | ||||||||
\(87\) | −6.37469e30 | −0.0634441 | ||||||||
\(88\) | 2.79153e31 | 0.230080 | ||||||||
\(89\) | −1.23819e32 | −0.846937 | −0.423469 | − | 0.905911i | \(-0.639188\pi\) | ||||
−0.423469 | + | 0.905911i | \(0.639188\pi\) | |||||||
\(90\) | −2.18318e31 | −0.124191 | ||||||||
\(91\) | −9.39972e31 | −0.445587 | ||||||||
\(92\) | 1.66512e32 | 0.659093 | ||||||||
\(93\) | −2.13547e31 | −0.0707173 | ||||||||
\(94\) | −1.20129e31 | −0.0333456 | ||||||||
\(95\) | −1.47639e32 | −0.344161 | ||||||||
\(96\) | −3.78885e32 | −0.743073 | ||||||||
\(97\) | 1.97176e32 | 0.325926 | 0.162963 | − | 0.986632i | \(-0.447895\pi\) | ||||
0.162963 | + | 0.986632i | \(0.447895\pi\) | |||||||
\(98\) | 1.27745e32 | 0.178285 | ||||||||
\(99\) | −9.03903e31 | −0.106694 | ||||||||
\(100\) | −1.26674e32 | −0.126674 | ||||||||
\(101\) | −1.97472e33 | −1.67573 | −0.837865 | − | 0.545878i | \(-0.816196\pi\) | ||||
−0.837865 | + | 0.545878i | \(0.816196\pi\) | |||||||
\(102\) | −6.01624e32 | −0.433932 | ||||||||
\(103\) | 5.57056e32 | 0.342046 | 0.171023 | − | 0.985267i | \(-0.445293\pi\) | ||||
0.171023 | + | 0.985267i | \(0.445293\pi\) | |||||||
\(104\) | −1.00211e33 | −0.524643 | ||||||||
\(105\) | −6.18233e32 | −0.276394 | ||||||||
\(106\) | 1.10217e33 | 0.421409 | ||||||||
\(107\) | 3.76704e33 | 1.23358 | 0.616791 | − | 0.787127i | \(-0.288432\pi\) | ||||
0.616791 | + | 0.787127i | \(0.288432\pi\) | |||||||
\(108\) | 2.42016e33 | 0.679753 | ||||||||
\(109\) | 7.25238e33 | 1.74962 | 0.874810 | − | 0.484467i | \(-0.160986\pi\) | ||||
0.874810 | + | 0.484467i | \(0.160986\pi\) | |||||||
\(110\) | 3.03590e32 | 0.0629953 | ||||||||
\(111\) | −1.49985e33 | −0.268051 | ||||||||
\(112\) | 1.88188e32 | 0.0290064 | ||||||||
\(113\) | −3.76366e32 | −0.0500976 | −0.0250488 | − | 0.999686i | \(-0.507974\pi\) | ||||
−0.0250488 | + | 0.999686i | \(0.507974\pi\) | |||||||
\(114\) | −2.97878e33 | −0.342853 | ||||||||
\(115\) | 4.67000e33 | 0.465375 | ||||||||
\(116\) | 6.32207e32 | 0.0546138 | ||||||||
\(117\) | 3.24484e33 | 0.243291 | ||||||||
\(118\) | −1.42719e34 | −0.929881 | ||||||||
\(119\) | 1.44329e34 | 0.818140 | ||||||||
\(120\) | −6.59100e33 | −0.325432 | ||||||||
\(121\) | −2.19682e34 | −0.945880 | ||||||||
\(122\) | 1.57988e34 | 0.593863 | ||||||||
\(123\) | −3.99135e34 | −1.31125 | ||||||||
\(124\) | 2.11785e33 | 0.0608747 | ||||||||
\(125\) | −3.55271e33 | −0.0894427 | ||||||||
\(126\) | 1.05671e34 | 0.233260 | ||||||||
\(127\) | −4.97180e34 | −0.963279 | −0.481640 | − | 0.876369i | \(-0.659959\pi\) | ||||
−0.481640 | + | 0.876369i | \(0.659959\pi\) | |||||||
\(128\) | 3.88040e34 | 0.660560 | ||||||||
\(129\) | −9.55430e34 | −1.43044 | ||||||||
\(130\) | −1.08983e34 | −0.143646 | ||||||||
\(131\) | 3.26112e34 | 0.378782 | 0.189391 | − | 0.981902i | \(-0.439349\pi\) | ||||
0.189391 | + | 0.981902i | \(0.439349\pi\) | |||||||
\(132\) | −1.05817e34 | −0.108414 | ||||||||
\(133\) | 7.14604e34 | 0.646418 | ||||||||
\(134\) | 4.59271e34 | 0.367147 | ||||||||
\(135\) | 6.78757e34 | 0.479963 | ||||||||
\(136\) | 1.53869e35 | 0.963296 | ||||||||
\(137\) | −4.83496e34 | −0.268228 | −0.134114 | − | 0.990966i | \(-0.542819\pi\) | ||||
−0.134114 | + | 0.990966i | \(0.542819\pi\) | |||||||
\(138\) | 9.42222e34 | 0.463605 | ||||||||
\(139\) | −1.61945e35 | −0.707334 | −0.353667 | − | 0.935371i | \(-0.615065\pi\) | ||||
−0.353667 | + | 0.935371i | \(0.615065\pi\) | |||||||
\(140\) | 6.13130e34 | 0.237925 | ||||||||
\(141\) | 1.17433e34 | 0.0405204 | ||||||||
\(142\) | 2.01760e35 | 0.619552 | ||||||||
\(143\) | −4.51223e34 | −0.123409 | ||||||||
\(144\) | −6.49637e33 | −0.0158376 | ||||||||
\(145\) | 1.77309e34 | 0.0385619 | ||||||||
\(146\) | 1.23378e35 | 0.239561 | ||||||||
\(147\) | −1.24878e35 | −0.216645 | ||||||||
\(148\) | 1.48747e35 | 0.230744 | ||||||||
\(149\) | −4.97369e35 | −0.690407 | −0.345204 | − | 0.938528i | \(-0.612190\pi\) | ||||
−0.345204 | + | 0.938528i | \(0.612190\pi\) | |||||||
\(150\) | −7.16797e34 | −0.0891026 | ||||||||
\(151\) | 1.20125e35 | 0.133818 | 0.0669090 | − | 0.997759i | \(-0.478686\pi\) | ||||
0.0669090 | + | 0.997759i | \(0.478686\pi\) | |||||||
\(152\) | 7.61841e35 | 0.761106 | ||||||||
\(153\) | −4.98232e35 | −0.446707 | ||||||||
\(154\) | −1.46944e35 | −0.118320 | ||||||||
\(155\) | 5.93972e34 | 0.0429826 | ||||||||
\(156\) | 3.79864e35 | 0.247214 | ||||||||
\(157\) | −1.58453e36 | −0.928018 | −0.464009 | − | 0.885830i | \(-0.653590\pi\) | ||||
−0.464009 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(158\) | −2.19089e36 | −1.15553 | ||||||||
\(159\) | −1.07743e36 | −0.512081 | ||||||||
\(160\) | 1.05385e36 | 0.451647 | ||||||||
\(161\) | −2.26038e36 | −0.874086 | ||||||||
\(162\) | 5.74090e35 | 0.200439 | ||||||||
\(163\) | −3.31440e36 | −1.04546 | −0.522732 | − | 0.852497i | \(-0.675087\pi\) | ||||
−0.522732 | + | 0.852497i | \(0.675087\pi\) | |||||||
\(164\) | 3.95840e36 | 1.12875 | ||||||||
\(165\) | −2.96776e35 | −0.0765496 | ||||||||
\(166\) | −2.79966e35 | −0.0653615 | ||||||||
\(167\) | 7.73877e36 | 1.63625 | 0.818126 | − | 0.575039i | \(-0.195013\pi\) | ||||
0.818126 | + | 0.575039i | \(0.195013\pi\) | |||||||
\(168\) | 3.19018e36 | 0.611240 | ||||||||
\(169\) | −4.13633e36 | −0.718595 | ||||||||
\(170\) | 1.67339e36 | 0.263748 | ||||||||
\(171\) | −2.46686e36 | −0.352946 | ||||||||
\(172\) | 9.47543e36 | 1.23135 | ||||||||
\(173\) | 4.62098e36 | 0.545725 | 0.272862 | − | 0.962053i | \(-0.412030\pi\) | ||||
0.272862 | + | 0.962053i | \(0.412030\pi\) | |||||||
\(174\) | 3.57739e35 | 0.0384153 | ||||||||
\(175\) | 1.71959e36 | 0.167995 | ||||||||
\(176\) | 9.03374e34 | 0.00803357 | ||||||||
\(177\) | 1.39515e37 | 1.12996 | ||||||||
\(178\) | 6.94855e36 | 0.512819 | ||||||||
\(179\) | −1.73851e37 | −1.16977 | −0.584886 | − | 0.811115i | \(-0.698861\pi\) | ||||
−0.584886 | + | 0.811115i | \(0.698861\pi\) | |||||||
\(180\) | −2.11656e36 | −0.129908 | ||||||||
\(181\) | −2.20579e37 | −1.23557 | −0.617785 | − | 0.786347i | \(-0.711970\pi\) | ||||
−0.617785 | + | 0.786347i | \(0.711970\pi\) | |||||||
\(182\) | 5.27500e36 | 0.269802 | ||||||||
\(183\) | −1.54442e37 | −0.721641 | ||||||||
\(184\) | −2.40979e37 | −1.02917 | ||||||||
\(185\) | 4.17176e36 | 0.162924 | ||||||||
\(186\) | 1.19840e36 | 0.0428192 | ||||||||
\(187\) | 6.92833e36 | 0.226591 | ||||||||
\(188\) | −1.16463e36 | −0.0348807 | ||||||||
\(189\) | −3.28532e37 | −0.901485 | ||||||||
\(190\) | 8.28532e36 | 0.208389 | ||||||||
\(191\) | 3.27319e37 | 0.754954 | 0.377477 | − | 0.926019i | \(-0.376792\pi\) | ||||
0.377477 | + | 0.926019i | \(0.376792\pi\) | |||||||
\(192\) | 2.00618e37 | 0.424521 | ||||||||
\(193\) | −8.15189e37 | −1.58330 | −0.791649 | − | 0.610976i | \(-0.790777\pi\) | ||||
−0.791649 | + | 0.610976i | \(0.790777\pi\) | |||||||
\(194\) | −1.10652e37 | −0.197348 | ||||||||
\(195\) | 1.06537e37 | 0.174554 | ||||||||
\(196\) | 1.23847e37 | 0.186492 | ||||||||
\(197\) | 1.16510e38 | 1.61313 | 0.806565 | − | 0.591145i | \(-0.201324\pi\) | ||||
0.806565 | + | 0.591145i | \(0.201324\pi\) | |||||||
\(198\) | 5.07259e36 | 0.0646032 | ||||||||
\(199\) | −1.05328e38 | −1.23443 | −0.617216 | − | 0.786794i | \(-0.711739\pi\) | ||||
−0.617216 | + | 0.786794i | \(0.711739\pi\) | |||||||
\(200\) | 1.83325e37 | 0.197801 | ||||||||
\(201\) | −4.48962e37 | −0.446144 | ||||||||
\(202\) | 1.10819e38 | 1.01465 | ||||||||
\(203\) | −8.58211e36 | −0.0724285 | ||||||||
\(204\) | −5.83265e37 | −0.453909 | ||||||||
\(205\) | 1.11017e38 | 0.796989 | ||||||||
\(206\) | −3.12613e37 | −0.207108 | ||||||||
\(207\) | 7.80296e37 | 0.477253 | ||||||||
\(208\) | −3.24294e36 | −0.0183187 | ||||||||
\(209\) | 3.43037e37 | 0.179031 | ||||||||
\(210\) | 3.46944e37 | 0.167356 | ||||||||
\(211\) | 3.80288e38 | 1.69610 | 0.848051 | − | 0.529915i | \(-0.177776\pi\) | ||||
0.848051 | + | 0.529915i | \(0.177776\pi\) | |||||||
\(212\) | 1.06854e38 | 0.440808 | ||||||||
\(213\) | −1.97232e38 | −0.752858 | ||||||||
\(214\) | −2.11401e38 | −0.746931 | ||||||||
\(215\) | 2.65748e38 | 0.869432 | ||||||||
\(216\) | −3.50249e38 | −1.06143 | ||||||||
\(217\) | −2.87495e37 | −0.0807317 | ||||||||
\(218\) | −4.06994e38 | −1.05939 | ||||||||
\(219\) | −1.20609e38 | −0.291106 | ||||||||
\(220\) | 2.94326e37 | 0.0658953 | ||||||||
\(221\) | −2.48714e38 | −0.516687 | ||||||||
\(222\) | 8.41696e37 | 0.162305 | ||||||||
\(223\) | 4.60089e38 | 0.823780 | 0.411890 | − | 0.911234i | \(-0.364869\pi\) | ||||
0.411890 | + | 0.911234i | \(0.364869\pi\) | |||||||
\(224\) | −5.10085e38 | −0.848301 | ||||||||
\(225\) | −5.93612e37 | −0.0917257 | ||||||||
\(226\) | 2.11212e37 | 0.0303340 | ||||||||
\(227\) | 1.13977e39 | 1.52192 | 0.760958 | − | 0.648801i | \(-0.224729\pi\) | ||||
0.760958 | + | 0.648801i | \(0.224729\pi\) | |||||||
\(228\) | −2.88788e38 | −0.358636 | ||||||||
\(229\) | −1.46028e39 | −1.68713 | −0.843566 | − | 0.537025i | \(-0.819548\pi\) | ||||
−0.843566 | + | 0.537025i | \(0.819548\pi\) | |||||||
\(230\) | −2.62075e38 | −0.281784 | ||||||||
\(231\) | 1.43645e38 | 0.143779 | ||||||||
\(232\) | −9.14941e37 | −0.0852789 | ||||||||
\(233\) | −2.05161e37 | −0.0178124 | −0.00890620 | − | 0.999960i | \(-0.502835\pi\) | ||||
−0.00890620 | + | 0.999960i | \(0.502835\pi\) | |||||||
\(234\) | −1.82096e38 | −0.147313 | ||||||||
\(235\) | −3.26634e37 | −0.0246287 | ||||||||
\(236\) | −1.38364e39 | −0.972688 | ||||||||
\(237\) | 2.14172e39 | 1.40415 | ||||||||
\(238\) | −8.09954e38 | −0.495382 | ||||||||
\(239\) | 9.20750e38 | 0.525505 | 0.262752 | − | 0.964863i | \(-0.415370\pi\) | ||||
0.262752 | + | 0.964863i | \(0.415370\pi\) | |||||||
\(240\) | −2.13293e37 | −0.0113629 | ||||||||
\(241\) | 1.79093e39 | 0.890834 | 0.445417 | − | 0.895323i | \(-0.353056\pi\) | ||||
0.445417 | + | 0.895323i | \(0.353056\pi\) | |||||||
\(242\) | 1.23283e39 | 0.572728 | ||||||||
\(243\) | 1.91164e39 | 0.829663 | ||||||||
\(244\) | 1.53167e39 | 0.621202 | ||||||||
\(245\) | 3.47341e38 | 0.131679 | ||||||||
\(246\) | 2.23989e39 | 0.793959 | ||||||||
\(247\) | −1.23144e39 | −0.408238 | ||||||||
\(248\) | −3.06499e38 | −0.0950552 | ||||||||
\(249\) | 2.73682e38 | 0.0794250 | ||||||||
\(250\) | 1.99374e38 | 0.0541574 | ||||||||
\(251\) | −4.16615e39 | −1.05954 | −0.529772 | − | 0.848140i | \(-0.677723\pi\) | ||||
−0.529772 | + | 0.848140i | \(0.677723\pi\) | |||||||
\(252\) | 1.02446e39 | 0.243998 | ||||||||
\(253\) | −1.08507e39 | −0.242085 | ||||||||
\(254\) | 2.79011e39 | 0.583264 | ||||||||
\(255\) | −1.63583e39 | −0.320497 | ||||||||
\(256\) | −5.31894e39 | −0.976936 | ||||||||
\(257\) | −1.03274e40 | −1.77867 | −0.889336 | − | 0.457254i | \(-0.848833\pi\) | ||||
−0.889336 | + | 0.457254i | \(0.848833\pi\) | |||||||
\(258\) | 5.36175e39 | 0.866126 | ||||||||
\(259\) | −2.01922e39 | −0.306011 | ||||||||
\(260\) | −1.05657e39 | −0.150259 | ||||||||
\(261\) | 2.96260e38 | 0.0395462 | ||||||||
\(262\) | −1.83010e39 | −0.229352 | ||||||||
\(263\) | −7.85107e39 | −0.923972 | −0.461986 | − | 0.886887i | \(-0.652863\pi\) | ||||
−0.461986 | + | 0.886887i | \(0.652863\pi\) | |||||||
\(264\) | 1.53141e39 | 0.169288 | ||||||||
\(265\) | 2.99683e39 | 0.311247 | ||||||||
\(266\) | −4.01027e39 | −0.391405 | ||||||||
\(267\) | −6.79258e39 | −0.623159 | ||||||||
\(268\) | 4.45257e39 | 0.384049 | ||||||||
\(269\) | 1.76099e40 | 1.42838 | 0.714189 | − | 0.699953i | \(-0.246796\pi\) | ||||
0.714189 | + | 0.699953i | \(0.246796\pi\) | |||||||
\(270\) | −3.80910e39 | −0.290616 | ||||||||
\(271\) | 1.63883e40 | 1.17636 | 0.588179 | − | 0.808730i | \(-0.299845\pi\) | ||||
0.588179 | + | 0.808730i | \(0.299845\pi\) | |||||||
\(272\) | 4.97940e38 | 0.0336349 | ||||||||
\(273\) | −5.15660e39 | −0.327853 | ||||||||
\(274\) | 2.71332e39 | 0.162411 | ||||||||
\(275\) | 8.25467e38 | 0.0465276 | ||||||||
\(276\) | 9.13470e39 | 0.484947 | ||||||||
\(277\) | −3.39112e40 | −1.69601 | −0.848003 | − | 0.529991i | \(-0.822195\pi\) | ||||
−0.848003 | + | 0.529991i | \(0.822195\pi\) | |||||||
\(278\) | 9.08817e39 | 0.428289 | ||||||||
\(279\) | 9.92449e38 | 0.0440797 | ||||||||
\(280\) | −8.87333e39 | −0.371517 | ||||||||
\(281\) | 3.38855e40 | 1.33770 | 0.668851 | − | 0.743396i | \(-0.266786\pi\) | ||||
0.668851 | + | 0.743396i | \(0.266786\pi\) | |||||||
\(282\) | −6.59017e38 | −0.0245350 | ||||||||
\(283\) | 2.32437e40 | 0.816263 | 0.408131 | − | 0.912923i | \(-0.366181\pi\) | ||||
0.408131 | + | 0.912923i | \(0.366181\pi\) | |||||||
\(284\) | 1.95604e40 | 0.648074 | ||||||||
\(285\) | −8.09935e39 | −0.253227 | ||||||||
\(286\) | 2.53220e39 | 0.0747238 | ||||||||
\(287\) | −5.37347e40 | −1.49694 | ||||||||
\(288\) | 1.76084e40 | 0.463175 | ||||||||
\(289\) | −2.06553e39 | −0.0513118 | ||||||||
\(290\) | −9.95035e38 | −0.0233492 | ||||||||
\(291\) | 1.08169e40 | 0.239810 | ||||||||
\(292\) | 1.19613e40 | 0.250589 | ||||||||
\(293\) | 3.19376e40 | 0.632393 | 0.316197 | − | 0.948694i | \(-0.397594\pi\) | ||||
0.316197 | + | 0.948694i | \(0.397594\pi\) | |||||||
\(294\) | 7.00797e39 | 0.131178 | ||||||||
\(295\) | −3.88055e40 | −0.686799 | ||||||||
\(296\) | −2.15269e40 | −0.360303 | ||||||||
\(297\) | −1.57708e40 | −0.249674 | ||||||||
\(298\) | 2.79117e40 | 0.418040 | ||||||||
\(299\) | 3.89519e40 | 0.552019 | ||||||||
\(300\) | −6.94924e39 | −0.0932045 | ||||||||
\(301\) | −1.28628e41 | −1.63300 | ||||||||
\(302\) | −6.74127e39 | −0.0810265 | ||||||||
\(303\) | −1.08332e41 | −1.23297 | ||||||||
\(304\) | 2.46541e39 | 0.0265751 | ||||||||
\(305\) | 4.29572e40 | 0.438620 | ||||||||
\(306\) | 2.79601e40 | 0.270480 | ||||||||
\(307\) | −9.23782e40 | −0.846810 | −0.423405 | − | 0.905940i | \(-0.639165\pi\) | ||||
−0.423405 | + | 0.905940i | \(0.639165\pi\) | |||||||
\(308\) | −1.42460e40 | −0.123767 | ||||||||
\(309\) | 3.05596e40 | 0.251670 | ||||||||
\(310\) | −3.33329e39 | −0.0260259 | ||||||||
\(311\) | 2.21387e40 | 0.163910 | 0.0819550 | − | 0.996636i | \(-0.473884\pi\) | ||||
0.0819550 | + | 0.996636i | \(0.473884\pi\) | |||||||
\(312\) | −5.49746e40 | −0.386022 | ||||||||
\(313\) | 2.73315e40 | 0.182046 | 0.0910231 | − | 0.995849i | \(-0.470986\pi\) | ||||
0.0910231 | + | 0.995849i | \(0.470986\pi\) | |||||||
\(314\) | 8.89219e40 | 0.561913 | ||||||||
\(315\) | 2.87320e40 | 0.172283 | ||||||||
\(316\) | −2.12404e41 | −1.20872 | ||||||||
\(317\) | 2.26706e41 | 1.22457 | 0.612286 | − | 0.790636i | \(-0.290250\pi\) | ||||
0.612286 | + | 0.790636i | \(0.290250\pi\) | |||||||
\(318\) | 6.04642e40 | 0.310064 | ||||||||
\(319\) | −4.11974e39 | −0.0200597 | ||||||||
\(320\) | −5.58009e40 | −0.258028 | ||||||||
\(321\) | 2.06656e41 | 0.907644 | ||||||||
\(322\) | 1.26849e41 | 0.529257 | ||||||||
\(323\) | 1.89082e41 | 0.749565 | ||||||||
\(324\) | 5.56572e40 | 0.209666 | ||||||||
\(325\) | −2.96327e40 | −0.106095 | ||||||||
\(326\) | 1.86000e41 | 0.633027 | ||||||||
\(327\) | 3.97859e41 | 1.28733 | ||||||||
\(328\) | −5.72867e41 | −1.76253 | ||||||||
\(329\) | 1.58097e40 | 0.0462586 | ||||||||
\(330\) | 1.66547e40 | 0.0463506 | ||||||||
\(331\) | −2.06805e41 | −0.547520 | −0.273760 | − | 0.961798i | \(-0.588267\pi\) | ||||
−0.273760 | + | 0.961798i | \(0.588267\pi\) | |||||||
\(332\) | −2.71423e40 | −0.0683705 | ||||||||
\(333\) | 6.97046e40 | 0.167083 | ||||||||
\(334\) | −4.34290e41 | −0.990747 | ||||||||
\(335\) | 1.24877e41 | 0.271170 | ||||||||
\(336\) | 1.03238e40 | 0.0213423 | ||||||||
\(337\) | 5.63835e40 | 0.110984 | 0.0554918 | − | 0.998459i | \(-0.482327\pi\) | ||||
0.0554918 | + | 0.998459i | \(0.482327\pi\) | |||||||
\(338\) | 2.32125e41 | 0.435108 | ||||||||
\(339\) | −2.06471e40 | −0.0368608 | ||||||||
\(340\) | 1.62233e41 | 0.275890 | ||||||||
\(341\) | −1.38008e40 | −0.0223593 | ||||||||
\(342\) | 1.38437e41 | 0.213708 | ||||||||
\(343\) | −7.39098e41 | −1.08730 | ||||||||
\(344\) | −1.37130e42 | −1.92273 | ||||||||
\(345\) | 2.56192e41 | 0.342413 | ||||||||
\(346\) | −2.59323e41 | −0.330435 | ||||||||
\(347\) | 2.54567e41 | 0.309289 | 0.154645 | − | 0.987970i | \(-0.450577\pi\) | ||||
0.154645 | + | 0.987970i | \(0.450577\pi\) | |||||||
\(348\) | 3.46823e40 | 0.0401837 | ||||||||
\(349\) | −1.42434e42 | −1.57397 | −0.786983 | − | 0.616974i | \(-0.788358\pi\) | ||||
−0.786983 | + | 0.616974i | \(0.788358\pi\) | |||||||
\(350\) | −9.65009e40 | −0.101721 | ||||||||
\(351\) | 5.66143e41 | 0.569323 | ||||||||
\(352\) | −2.44860e41 | −0.234944 | ||||||||
\(353\) | 4.58433e41 | 0.419752 | 0.209876 | − | 0.977728i | \(-0.432694\pi\) | ||||
0.209876 | + | 0.977728i | \(0.432694\pi\) | |||||||
\(354\) | −7.82941e41 | −0.684187 | ||||||||
\(355\) | 5.48590e41 | 0.457594 | ||||||||
\(356\) | 6.73651e41 | 0.536427 | ||||||||
\(357\) | 7.91774e41 | 0.601971 | ||||||||
\(358\) | 9.75628e41 | 0.708295 | ||||||||
\(359\) | 1.13078e42 | 0.784004 | 0.392002 | − | 0.919964i | \(-0.371783\pi\) | ||||
0.392002 | + | 0.919964i | \(0.371783\pi\) | |||||||
\(360\) | 3.06313e41 | 0.202849 | ||||||||
\(361\) | −6.44582e41 | −0.407764 | ||||||||
\(362\) | 1.23786e42 | 0.748135 | ||||||||
\(363\) | −1.20516e42 | −0.695959 | ||||||||
\(364\) | 5.11404e41 | 0.282222 | ||||||||
\(365\) | 3.35467e41 | 0.176937 | ||||||||
\(366\) | 8.66707e41 | 0.436952 | ||||||||
\(367\) | 1.40753e42 | 0.678369 | 0.339185 | − | 0.940720i | \(-0.389849\pi\) | ||||
0.339185 | + | 0.940720i | \(0.389849\pi\) | |||||||
\(368\) | −7.79840e40 | −0.0359349 | ||||||||
\(369\) | 1.85496e42 | 0.817332 | ||||||||
\(370\) | −2.34114e41 | −0.0986503 | ||||||||
\(371\) | −1.45053e42 | −0.584597 | ||||||||
\(372\) | 1.16183e41 | 0.0447904 | ||||||||
\(373\) | −4.43848e42 | −1.63696 | −0.818480 | − | 0.574535i | \(-0.805183\pi\) | ||||
−0.818480 | + | 0.574535i | \(0.805183\pi\) | |||||||
\(374\) | −3.88809e41 | −0.137200 | ||||||||
\(375\) | −1.94899e41 | −0.0658101 | ||||||||
\(376\) | 1.68548e41 | 0.0544658 | ||||||||
\(377\) | 1.47891e41 | 0.0457414 | ||||||||
\(378\) | 1.84368e42 | 0.545847 | ||||||||
\(379\) | −1.41996e42 | −0.402466 | −0.201233 | − | 0.979543i | \(-0.564495\pi\) | ||||
−0.201233 | + | 0.979543i | \(0.564495\pi\) | |||||||
\(380\) | 8.03250e41 | 0.217982 | ||||||||
\(381\) | −2.72748e42 | −0.708761 | ||||||||
\(382\) | −1.83687e42 | −0.457123 | ||||||||
\(383\) | 1.04448e40 | 0.00248955 | 0.00124478 | − | 0.999999i | \(-0.499604\pi\) | ||||
0.00124478 | + | 0.999999i | \(0.499604\pi\) | |||||||
\(384\) | 2.12875e42 | 0.486027 | ||||||||
\(385\) | −3.99543e41 | −0.0873899 | ||||||||
\(386\) | 4.57473e42 | 0.958684 | ||||||||
\(387\) | 4.44030e42 | 0.891624 | ||||||||
\(388\) | −1.07276e42 | −0.206433 | ||||||||
\(389\) | 3.78074e41 | 0.0697282 | 0.0348641 | − | 0.999392i | \(-0.488900\pi\) | ||||
0.0348641 | + | 0.999392i | \(0.488900\pi\) | |||||||
\(390\) | −5.97871e41 | −0.105692 | ||||||||
\(391\) | −5.98090e42 | −1.01356 | ||||||||
\(392\) | −1.79233e42 | −0.291205 | ||||||||
\(393\) | 1.78902e42 | 0.278700 | ||||||||
\(394\) | −6.53838e42 | −0.976747 | ||||||||
\(395\) | −5.95709e42 | −0.853457 | ||||||||
\(396\) | 4.91780e41 | 0.0675772 | ||||||||
\(397\) | −1.40626e43 | −1.85363 | −0.926815 | − | 0.375519i | \(-0.877464\pi\) | ||||
−0.926815 | + | 0.375519i | \(0.877464\pi\) | |||||||
\(398\) | 5.91086e42 | 0.747446 | ||||||||
\(399\) | 3.92025e42 | 0.475621 | ||||||||
\(400\) | 5.93264e40 | 0.00690651 | ||||||||
\(401\) | −3.90184e42 | −0.435900 | −0.217950 | − | 0.975960i | \(-0.569937\pi\) | ||||
−0.217950 | + | 0.975960i | \(0.569937\pi\) | |||||||
\(402\) | 2.51952e42 | 0.270139 | ||||||||
\(403\) | 4.95424e41 | 0.0509852 | ||||||||
\(404\) | 1.07437e43 | 1.06136 | ||||||||
\(405\) | 1.56096e42 | 0.148042 | ||||||||
\(406\) | 4.81617e41 | 0.0438553 | ||||||||
\(407\) | −9.69301e41 | −0.0847522 | ||||||||
\(408\) | 8.44112e42 | 0.708773 | ||||||||
\(409\) | 1.05489e43 | 0.850694 | 0.425347 | − | 0.905030i | \(-0.360152\pi\) | ||||
0.425347 | + | 0.905030i | \(0.360152\pi\) | |||||||
\(410\) | −6.23015e42 | −0.482575 | ||||||||
\(411\) | −2.65242e42 | −0.197357 | ||||||||
\(412\) | −3.03073e42 | −0.216642 | ||||||||
\(413\) | 1.87826e43 | 1.28997 | ||||||||
\(414\) | −4.37892e42 | −0.288976 | ||||||||
\(415\) | −7.61234e41 | −0.0482753 | ||||||||
\(416\) | 8.79002e42 | 0.535735 | ||||||||
\(417\) | −8.88418e42 | −0.520442 | ||||||||
\(418\) | −1.92508e42 | −0.108403 | ||||||||
\(419\) | 2.64714e43 | 1.43300 | 0.716498 | − | 0.697589i | \(-0.245744\pi\) | ||||
0.716498 | + | 0.697589i | \(0.245744\pi\) | |||||||
\(420\) | 3.36358e42 | 0.175060 | ||||||||
\(421\) | 2.92799e43 | 1.46526 | 0.732630 | − | 0.680627i | \(-0.238293\pi\) | ||||
0.732630 | + | 0.680627i | \(0.238293\pi\) | |||||||
\(422\) | −2.13413e43 | −1.02699 | ||||||||
\(423\) | −5.45762e41 | −0.0252573 | ||||||||
\(424\) | −1.54641e43 | −0.688317 | ||||||||
\(425\) | 4.54998e42 | 0.194801 | ||||||||
\(426\) | 1.10684e43 | 0.455854 | ||||||||
\(427\) | −2.07922e43 | −0.823834 | ||||||||
\(428\) | −2.04951e43 | −0.781316 | ||||||||
\(429\) | −2.47537e42 | −0.0908017 | ||||||||
\(430\) | −1.49134e43 | −0.526440 | ||||||||
\(431\) | 7.41005e42 | 0.251736 | 0.125868 | − | 0.992047i | \(-0.459828\pi\) | ||||
0.125868 | + | 0.992047i | \(0.459828\pi\) | |||||||
\(432\) | −1.13345e42 | −0.0370613 | ||||||||
\(433\) | −2.63001e43 | −0.827766 | −0.413883 | − | 0.910330i | \(-0.635828\pi\) | ||||
−0.413883 | + | 0.910330i | \(0.635828\pi\) | |||||||
\(434\) | 1.61338e42 | 0.0488829 | ||||||||
\(435\) | 9.72700e41 | 0.0283731 | ||||||||
\(436\) | −3.94575e43 | −1.10816 | ||||||||
\(437\) | −2.96128e43 | −0.800821 | ||||||||
\(438\) | 6.76840e42 | 0.176264 | ||||||||
\(439\) | 1.79135e43 | 0.449278 | 0.224639 | − | 0.974442i | \(-0.427880\pi\) | ||||
0.224639 | + | 0.974442i | \(0.427880\pi\) | |||||||
\(440\) | −4.25954e42 | −0.102895 | ||||||||
\(441\) | 5.80362e42 | 0.135040 | ||||||||
\(442\) | 1.39575e43 | 0.312853 | ||||||||
\(443\) | −3.40634e43 | −0.735575 | −0.367788 | − | 0.929910i | \(-0.619885\pi\) | ||||
−0.367788 | + | 0.929910i | \(0.619885\pi\) | |||||||
\(444\) | 8.16011e42 | 0.169776 | ||||||||
\(445\) | 1.88932e43 | 0.378762 | ||||||||
\(446\) | −2.58196e43 | −0.498797 | ||||||||
\(447\) | −2.72852e43 | −0.507988 | ||||||||
\(448\) | 2.70088e43 | 0.484638 | ||||||||
\(449\) | 8.25218e43 | 1.42726 | 0.713632 | − | 0.700521i | \(-0.247049\pi\) | ||||
0.713632 | + | 0.700521i | \(0.247049\pi\) | |||||||
\(450\) | 3.33127e42 | 0.0555397 | ||||||||
\(451\) | −2.57947e43 | −0.414589 | ||||||||
\(452\) | 2.04767e42 | 0.0317304 | ||||||||
\(453\) | 6.58996e42 | 0.0984605 | ||||||||
\(454\) | −6.39625e43 | −0.921517 | ||||||||
\(455\) | 1.43428e43 | 0.199272 | ||||||||
\(456\) | 4.17939e43 | 0.560006 | ||||||||
\(457\) | 1.09927e44 | 1.42065 | 0.710323 | − | 0.703876i | \(-0.248549\pi\) | ||||
0.710323 | + | 0.703876i | \(0.248549\pi\) | |||||||
\(458\) | 8.19488e43 | 1.02156 | ||||||||
\(459\) | −8.69288e43 | −1.04533 | ||||||||
\(460\) | −2.54077e43 | −0.294756 | ||||||||
\(461\) | 5.08918e43 | 0.569616 | 0.284808 | − | 0.958585i | \(-0.408070\pi\) | ||||
0.284808 | + | 0.958585i | \(0.408070\pi\) | |||||||
\(462\) | −8.06120e42 | −0.0870576 | ||||||||
\(463\) | 5.67339e43 | 0.591229 | 0.295615 | − | 0.955307i | \(-0.404476\pi\) | ||||
0.295615 | + | 0.955307i | \(0.404476\pi\) | |||||||
\(464\) | −2.96086e41 | −0.00297764 | ||||||||
\(465\) | 3.25847e42 | 0.0316257 | ||||||||
\(466\) | 1.15134e42 | 0.0107854 | ||||||||
\(467\) | 8.56548e43 | 0.774503 | 0.387251 | − | 0.921974i | \(-0.373425\pi\) | ||||
0.387251 | + | 0.921974i | \(0.373425\pi\) | |||||||
\(468\) | −1.76540e43 | −0.154094 | ||||||||
\(469\) | −6.04429e43 | −0.509323 | ||||||||
\(470\) | 1.83303e42 | 0.0149126 | ||||||||
\(471\) | −8.69259e43 | −0.682817 | ||||||||
\(472\) | 2.00242e44 | 1.51884 | ||||||||
\(473\) | −6.17462e43 | −0.452273 | ||||||||
\(474\) | −1.20190e44 | −0.850212 | ||||||||
\(475\) | 2.25280e43 | 0.153914 | ||||||||
\(476\) | −7.85239e43 | −0.518187 | ||||||||
\(477\) | 5.00732e43 | 0.319192 | ||||||||
\(478\) | −5.16713e43 | −0.318192 | ||||||||
\(479\) | −1.29441e44 | −0.770079 | −0.385040 | − | 0.922900i | \(-0.625812\pi\) | ||||
−0.385040 | + | 0.922900i | \(0.625812\pi\) | |||||||
\(480\) | 5.78132e43 | 0.332312 | ||||||||
\(481\) | 3.47961e43 | 0.193258 | ||||||||
\(482\) | −1.00504e44 | −0.539398 | ||||||||
\(483\) | −1.24002e44 | −0.643134 | ||||||||
\(484\) | 1.19521e44 | 0.599094 | ||||||||
\(485\) | −3.00866e43 | −0.145759 | ||||||||
\(486\) | −1.07279e44 | −0.502359 | ||||||||
\(487\) | 2.61068e44 | 1.18175 | 0.590876 | − | 0.806762i | \(-0.298782\pi\) | ||||
0.590876 | + | 0.806762i | \(0.298782\pi\) | |||||||
\(488\) | −2.21666e44 | −0.970000 | ||||||||
\(489\) | −1.81825e44 | −0.769231 | ||||||||
\(490\) | −1.94923e43 | −0.0797313 | ||||||||
\(491\) | −1.66397e44 | −0.658114 | −0.329057 | − | 0.944310i | \(-0.606731\pi\) | ||||
−0.329057 | + | 0.944310i | \(0.606731\pi\) | |||||||
\(492\) | 2.17154e44 | 0.830509 | ||||||||
\(493\) | −2.27080e43 | −0.0839857 | ||||||||
\(494\) | 6.91068e43 | 0.247187 | ||||||||
\(495\) | 1.37925e43 | 0.0477152 | ||||||||
\(496\) | −9.91868e41 | −0.00331899 | ||||||||
\(497\) | −2.65529e44 | −0.859472 | ||||||||
\(498\) | −1.53587e43 | −0.0480917 | ||||||||
\(499\) | 6.52589e43 | 0.197688 | 0.0988441 | − | 0.995103i | \(-0.468485\pi\) | ||||
0.0988441 | + | 0.995103i | \(0.468485\pi\) | |||||||
\(500\) | 1.93290e43 | 0.0566505 | ||||||||
\(501\) | 4.24542e44 | 1.20392 | ||||||||
\(502\) | 2.33799e44 | 0.641552 | ||||||||
\(503\) | −1.10537e43 | −0.0293519 | −0.0146759 | − | 0.999892i | \(-0.504672\pi\) | ||||
−0.0146759 | + | 0.999892i | \(0.504672\pi\) | |||||||
\(504\) | −1.48262e44 | −0.381000 | ||||||||
\(505\) | 3.01319e44 | 0.749409 | ||||||||
\(506\) | 6.08926e43 | 0.146582 | ||||||||
\(507\) | −2.26915e44 | −0.528727 | ||||||||
\(508\) | 2.70497e44 | 0.610114 | ||||||||
\(509\) | −4.80472e44 | −1.04912 | −0.524559 | − | 0.851374i | \(-0.675770\pi\) | ||||
−0.524559 | + | 0.851374i | \(0.675770\pi\) | |||||||
\(510\) | 9.18005e43 | 0.194061 | ||||||||
\(511\) | −1.62373e44 | −0.332329 | ||||||||
\(512\) | −3.48319e43 | −0.0690276 | ||||||||
\(513\) | −4.30404e44 | −0.825923 | ||||||||
\(514\) | 5.79562e44 | 1.07698 | ||||||||
\(515\) | −8.50000e43 | −0.152968 | ||||||||
\(516\) | 5.19814e44 | 0.905999 | ||||||||
\(517\) | 7.58928e42 | 0.0128117 | ||||||||
\(518\) | 1.13316e44 | 0.185289 | ||||||||
\(519\) | 2.53503e44 | 0.401533 | ||||||||
\(520\) | 1.52909e44 | 0.234627 | ||||||||
\(521\) | −2.39684e44 | −0.356301 | −0.178150 | − | 0.984003i | \(-0.557011\pi\) | ||||
−0.178150 | + | 0.984003i | \(0.557011\pi\) | |||||||
\(522\) | −1.66257e43 | −0.0239451 | ||||||||
\(523\) | 7.19573e44 | 1.00415 | 0.502073 | − | 0.864825i | \(-0.332571\pi\) | ||||
0.502073 | + | 0.864825i | \(0.332571\pi\) | |||||||
\(524\) | −1.77425e44 | −0.239910 | ||||||||
\(525\) | 9.43349e43 | 0.123607 | ||||||||
\(526\) | 4.40592e44 | 0.559463 | ||||||||
\(527\) | −7.60702e43 | −0.0936138 | ||||||||
\(528\) | 4.95583e42 | 0.00591094 | ||||||||
\(529\) | 7.16821e43 | 0.0828690 | ||||||||
\(530\) | −1.68178e44 | −0.188460 | ||||||||
\(531\) | −6.48388e44 | −0.704329 | ||||||||
\(532\) | −3.88789e44 | −0.409423 | ||||||||
\(533\) | 9.25982e44 | 0.945374 | ||||||||
\(534\) | 3.81191e44 | 0.377322 | ||||||||
\(535\) | −5.74805e44 | −0.551674 | ||||||||
\(536\) | −6.44383e44 | −0.599688 | ||||||||
\(537\) | −9.53729e44 | −0.860695 | ||||||||
\(538\) | −9.88243e44 | −0.864880 | ||||||||
\(539\) | −8.07041e43 | −0.0684985 | ||||||||
\(540\) | −3.69286e44 | −0.303995 | ||||||||
\(541\) | 8.82482e44 | 0.704613 | 0.352307 | − | 0.935885i | \(-0.385397\pi\) | ||||
0.352307 | + | 0.935885i | \(0.385397\pi\) | |||||||
\(542\) | −9.19689e44 | −0.712283 | ||||||||
\(543\) | −1.21007e45 | −0.909107 | ||||||||
\(544\) | −1.34967e45 | −0.983662 | ||||||||
\(545\) | −1.10663e45 | −0.782454 | ||||||||
\(546\) | 2.89382e44 | 0.198515 | ||||||||
\(547\) | −5.81429e44 | −0.386996 | −0.193498 | − | 0.981101i | \(-0.561983\pi\) | ||||
−0.193498 | + | 0.981101i | \(0.561983\pi\) | |||||||
\(548\) | 2.63052e44 | 0.169888 | ||||||||
\(549\) | 7.17759e44 | 0.449816 | ||||||||
\(550\) | −4.63241e43 | −0.0281723 | ||||||||
\(551\) | −1.12433e44 | −0.0663576 | ||||||||
\(552\) | −1.32199e45 | −0.757240 | ||||||||
\(553\) | 2.88335e45 | 1.60300 | ||||||||
\(554\) | 1.90306e45 | 1.02693 | ||||||||
\(555\) | 2.28859e44 | 0.119876 | ||||||||
\(556\) | 8.81085e44 | 0.448006 | ||||||||
\(557\) | 2.61541e45 | 1.29101 | 0.645504 | − | 0.763757i | \(-0.276647\pi\) | ||||
0.645504 | + | 0.763757i | \(0.276647\pi\) | |||||||
\(558\) | −5.56950e43 | −0.0266902 | ||||||||
\(559\) | 2.21657e45 | 1.03130 | ||||||||
\(560\) | −2.87152e43 | −0.0129721 | ||||||||
\(561\) | 3.80082e44 | 0.166721 | ||||||||
\(562\) | −1.90161e45 | −0.809976 | ||||||||
\(563\) | 1.43034e45 | 0.591632 | 0.295816 | − | 0.955245i | \(-0.404408\pi\) | ||||
0.295816 | + | 0.955245i | \(0.404408\pi\) | |||||||
\(564\) | −6.38908e43 | −0.0256645 | ||||||||
\(565\) | 5.74290e43 | 0.0224043 | ||||||||
\(566\) | −1.30441e45 | −0.494245 | ||||||||
\(567\) | −7.55537e44 | −0.278058 | ||||||||
\(568\) | −2.83081e45 | −1.01196 | ||||||||
\(569\) | 5.30235e45 | 1.84127 | 0.920633 | − | 0.390430i | \(-0.127674\pi\) | ||||
0.920633 | + | 0.390430i | \(0.127674\pi\) | |||||||
\(570\) | 4.54525e44 | 0.153328 | ||||||||
\(571\) | −3.41063e45 | −1.11774 | −0.558868 | − | 0.829257i | \(-0.688764\pi\) | ||||
−0.558868 | + | 0.829257i | \(0.688764\pi\) | |||||||
\(572\) | 2.45493e44 | 0.0781637 | ||||||||
\(573\) | 1.79564e45 | 0.555480 | ||||||||
\(574\) | 3.01552e45 | 0.906393 | ||||||||
\(575\) | −7.12586e44 | −0.208122 | ||||||||
\(576\) | −9.32360e44 | −0.264614 | ||||||||
\(577\) | 2.80984e45 | 0.774962 | 0.387481 | − | 0.921878i | \(-0.373345\pi\) | ||||
0.387481 | + | 0.921878i | \(0.373345\pi\) | |||||||
\(578\) | 1.15915e44 | 0.0310692 | ||||||||
\(579\) | −4.47205e45 | −1.16496 | ||||||||
\(580\) | −9.64672e43 | −0.0244240 | ||||||||
\(581\) | 3.68453e44 | 0.0906725 | ||||||||
\(582\) | −6.07028e44 | −0.145204 | ||||||||
\(583\) | −6.96309e44 | −0.161909 | ||||||||
\(584\) | −1.73106e45 | −0.391292 | ||||||||
\(585\) | −4.95124e44 | −0.108803 | ||||||||
\(586\) | −1.79230e45 | −0.382913 | ||||||||
\(587\) | −5.96514e45 | −1.23906 | −0.619529 | − | 0.784973i | \(-0.712677\pi\) | ||||
−0.619529 | + | 0.784973i | \(0.712677\pi\) | |||||||
\(588\) | 6.79412e44 | 0.137217 | ||||||||
\(589\) | −3.76641e44 | −0.0739648 | ||||||||
\(590\) | 2.17771e45 | 0.415855 | ||||||||
\(591\) | 6.39162e45 | 1.18691 | ||||||||
\(592\) | −6.96638e43 | −0.0125805 | ||||||||
\(593\) | −1.29305e45 | −0.227099 | −0.113549 | − | 0.993532i | \(-0.536222\pi\) | ||||
−0.113549 | + | 0.993532i | \(0.536222\pi\) | |||||||
\(594\) | 8.85038e44 | 0.151177 | ||||||||
\(595\) | −2.20228e45 | −0.365884 | ||||||||
\(596\) | 2.70600e45 | 0.437285 | ||||||||
\(597\) | −5.77818e45 | −0.908270 | ||||||||
\(598\) | −2.18593e45 | −0.334246 | ||||||||
\(599\) | −1.23551e46 | −1.83782 | −0.918910 | − | 0.394467i | \(-0.870929\pi\) | ||||
−0.918910 | + | 0.394467i | \(0.870929\pi\) | |||||||
\(600\) | 1.00571e45 | 0.145538 | ||||||||
\(601\) | −4.92073e45 | −0.692788 | −0.346394 | − | 0.938089i | \(-0.612594\pi\) | ||||
−0.346394 | + | 0.938089i | \(0.612594\pi\) | |||||||
\(602\) | 7.21841e45 | 0.988780 | ||||||||
\(603\) | 2.08653e45 | 0.278092 | ||||||||
\(604\) | −6.53556e44 | −0.0847566 | ||||||||
\(605\) | 3.35208e45 | 0.423010 | ||||||||
\(606\) | 6.07943e45 | 0.746559 | ||||||||
\(607\) | 2.23242e45 | 0.266786 | 0.133393 | − | 0.991063i | \(-0.457413\pi\) | ||||
0.133393 | + | 0.991063i | \(0.457413\pi\) | |||||||
\(608\) | −6.68252e45 | −0.777197 | ||||||||
\(609\) | −4.70807e44 | −0.0532914 | ||||||||
\(610\) | −2.41070e45 | −0.265584 | ||||||||
\(611\) | −2.72441e44 | −0.0292141 | ||||||||
\(612\) | 2.71069e45 | 0.282932 | ||||||||
\(613\) | 1.28306e45 | 0.130362 | 0.0651808 | − | 0.997873i | \(-0.479238\pi\) | ||||
0.0651808 | + | 0.997873i | \(0.479238\pi\) | |||||||
\(614\) | 5.18414e45 | 0.512742 | ||||||||
\(615\) | 6.09031e45 | 0.586408 | ||||||||
\(616\) | 2.06170e45 | 0.193261 | ||||||||
\(617\) | 1.81527e46 | 1.65667 | 0.828333 | − | 0.560235i | \(-0.189289\pi\) | ||||
0.828333 | + | 0.560235i | \(0.189289\pi\) | |||||||
\(618\) | −1.71496e45 | −0.152386 | ||||||||
\(619\) | −1.88787e46 | −1.63334 | −0.816670 | − | 0.577104i | \(-0.804183\pi\) | ||||
−0.816670 | + | 0.577104i | \(0.804183\pi\) | |||||||
\(620\) | −3.23158e44 | −0.0272240 | ||||||||
\(621\) | 1.36142e46 | 1.11681 | ||||||||
\(622\) | −1.24239e45 | −0.0992472 | ||||||||
\(623\) | −9.14471e45 | −0.711406 | ||||||||
\(624\) | −1.77905e44 | −0.0134785 | ||||||||
\(625\) | 5.42101e44 | 0.0400000 | ||||||||
\(626\) | −1.53381e45 | −0.110229 | ||||||||
\(627\) | 1.88187e45 | 0.131727 | ||||||||
\(628\) | 8.62084e45 | 0.587781 | ||||||||
\(629\) | −5.34279e45 | −0.354840 | ||||||||
\(630\) | −1.61240e45 | −0.104317 | ||||||||
\(631\) | −1.84920e46 | −1.16547 | −0.582733 | − | 0.812664i | \(-0.698017\pi\) | ||||
−0.582733 | + | 0.812664i | \(0.698017\pi\) | |||||||
\(632\) | 3.07395e46 | 1.88740 | ||||||||
\(633\) | 2.08622e46 | 1.24796 | ||||||||
\(634\) | −1.27224e46 | −0.741476 | ||||||||
\(635\) | 7.58636e45 | 0.430792 | ||||||||
\(636\) | 5.86192e45 | 0.324338 | ||||||||
\(637\) | 2.89713e45 | 0.156195 | ||||||||
\(638\) | 2.31195e44 | 0.0121461 | ||||||||
\(639\) | 9.16623e45 | 0.469274 | ||||||||
\(640\) | −5.92103e45 | −0.295411 | ||||||||
\(641\) | −2.03686e46 | −0.990382 | −0.495191 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495191 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(642\) | −1.15973e46 | −0.549577 | ||||||||
\(643\) | −3.33285e46 | −1.53934 | −0.769671 | − | 0.638440i | \(-0.779580\pi\) | ||||
−0.769671 | + | 0.638440i | \(0.779580\pi\) | |||||||
\(644\) | 1.22979e46 | 0.553622 | ||||||||
\(645\) | 1.45787e46 | 0.639711 | ||||||||
\(646\) | −1.06110e46 | −0.453860 | ||||||||
\(647\) | −2.86276e46 | −1.19361 | −0.596807 | − | 0.802385i | \(-0.703564\pi\) | ||||
−0.596807 | + | 0.802385i | \(0.703564\pi\) | |||||||
\(648\) | −8.05480e45 | −0.327391 | ||||||||
\(649\) | 9.01638e45 | 0.357269 | ||||||||
\(650\) | 1.66295e45 | 0.0642405 | ||||||||
\(651\) | −1.57717e45 | −0.0594007 | ||||||||
\(652\) | 1.80324e46 | 0.662168 | ||||||||
\(653\) | −4.94384e43 | −0.00177010 | −0.000885048 | − | 1.00000i | \(-0.500282\pi\) | ||||
−0.000885048 | 1.00000i | \(0.500282\pi\) | ||||||||
\(654\) | −2.23273e46 | −0.779478 | ||||||||
\(655\) | −4.97607e45 | −0.169397 | ||||||||
\(656\) | −1.85387e45 | −0.0615412 | ||||||||
\(657\) | 5.60522e45 | 0.181453 | ||||||||
\(658\) | −8.87222e44 | −0.0280095 | ||||||||
\(659\) | 3.69093e45 | 0.113639 | 0.0568194 | − | 0.998384i | \(-0.481904\pi\) | ||||
0.0568194 | + | 0.998384i | \(0.481904\pi\) | |||||||
\(660\) | 1.61464e45 | 0.0484844 | ||||||||
\(661\) | −1.92860e46 | −0.564830 | −0.282415 | − | 0.959292i | \(-0.591136\pi\) | ||||
−0.282415 | + | 0.959292i | \(0.591136\pi\) | |||||||
\(662\) | 1.16056e46 | 0.331522 | ||||||||
\(663\) | −1.36442e46 | −0.380168 | ||||||||
\(664\) | 3.92808e45 | 0.106760 | ||||||||
\(665\) | −1.09040e46 | −0.289087 | ||||||||
\(666\) | −3.91173e45 | −0.101168 | ||||||||
\(667\) | 3.55638e45 | 0.0897287 | ||||||||
\(668\) | −4.21037e46 | −1.03636 | ||||||||
\(669\) | 2.52400e46 | 0.606120 | ||||||||
\(670\) | −7.00792e45 | −0.164193 | ||||||||
\(671\) | −9.98104e45 | −0.228168 | ||||||||
\(672\) | −2.79828e46 | −0.624163 | ||||||||
\(673\) | 6.71207e46 | 1.46086 | 0.730428 | − | 0.682989i | \(-0.239320\pi\) | ||||
0.730428 | + | 0.682989i | \(0.239320\pi\) | |||||||
\(674\) | −3.16417e45 | −0.0672003 | ||||||||
\(675\) | −1.03570e46 | −0.214646 | ||||||||
\(676\) | 2.25042e46 | 0.455138 | ||||||||
\(677\) | 6.40029e46 | 1.26324 | 0.631621 | − | 0.775278i | \(-0.282390\pi\) | ||||
0.631621 | + | 0.775278i | \(0.282390\pi\) | |||||||
\(678\) | 1.15869e45 | 0.0223191 | ||||||||
\(679\) | 1.45625e46 | 0.273770 | ||||||||
\(680\) | −2.34786e46 | −0.430799 | ||||||||
\(681\) | 6.25268e46 | 1.11980 | ||||||||
\(682\) | 7.74485e44 | 0.0135385 | ||||||||
\(683\) | 8.73990e46 | 1.49130 | 0.745650 | − | 0.666338i | \(-0.232139\pi\) | ||||
0.745650 | + | 0.666338i | \(0.232139\pi\) | |||||||
\(684\) | 1.34212e46 | 0.223546 | ||||||||
\(685\) | 7.37757e45 | 0.119955 | ||||||||
\(686\) | 4.14772e46 | 0.658357 | ||||||||
\(687\) | −8.01093e46 | −1.24136 | ||||||||
\(688\) | −4.43770e45 | −0.0671350 | ||||||||
\(689\) | 2.49962e46 | 0.369196 | ||||||||
\(690\) | −1.43772e46 | −0.207331 | ||||||||
\(691\) | 4.89363e46 | 0.689039 | 0.344519 | − | 0.938779i | \(-0.388042\pi\) | ||||
0.344519 | + | 0.938779i | \(0.388042\pi\) | |||||||
\(692\) | −2.51410e46 | −0.345647 | ||||||||
\(693\) | −6.67584e45 | −0.0896205 | ||||||||
\(694\) | −1.42859e46 | −0.187274 | ||||||||
\(695\) | 2.47109e46 | 0.316329 | ||||||||
\(696\) | −5.01928e45 | −0.0627464 | ||||||||
\(697\) | −1.42181e47 | −1.73580 | ||||||||
\(698\) | 7.99324e46 | 0.953034 | ||||||||
\(699\) | −1.12550e45 | −0.0131060 | ||||||||
\(700\) | −9.35562e45 | −0.106403 | ||||||||
\(701\) | −3.51093e46 | −0.390009 | −0.195004 | − | 0.980802i | \(-0.562472\pi\) | ||||
−0.195004 | + | 0.980802i | \(0.562472\pi\) | |||||||
\(702\) | −3.17712e46 | −0.344724 | ||||||||
\(703\) | −2.64533e46 | −0.280361 | ||||||||
\(704\) | 1.29652e46 | 0.134225 | ||||||||
\(705\) | −1.79188e45 | −0.0181213 | ||||||||
\(706\) | −2.57267e46 | −0.254159 | ||||||||
\(707\) | −1.45845e47 | −1.40757 | ||||||||
\(708\) | −7.59049e46 | −0.715684 | ||||||||
\(709\) | 9.47916e46 | 0.873187 | 0.436593 | − | 0.899659i | \(-0.356185\pi\) | ||||
0.436593 | + | 0.899659i | \(0.356185\pi\) | |||||||
\(710\) | −3.07862e46 | −0.277072 | ||||||||
\(711\) | −9.95351e46 | −0.875241 | ||||||||
\(712\) | −9.74920e46 | −0.837624 | ||||||||
\(713\) | 1.19136e46 | 0.100015 | ||||||||
\(714\) | −4.44333e46 | −0.364492 | ||||||||
\(715\) | 6.88511e45 | 0.0551901 | ||||||||
\(716\) | 9.45857e46 | 0.740901 | ||||||||
\(717\) | 5.05115e46 | 0.386656 | ||||||||
\(718\) | −6.34577e46 | −0.474713 | ||||||||
\(719\) | −1.57057e46 | −0.114823 | −0.0574116 | − | 0.998351i | \(-0.518285\pi\) | ||||
−0.0574116 | + | 0.998351i | \(0.518285\pi\) | |||||||
\(720\) | 9.91267e44 | 0.00708279 | ||||||||
\(721\) | 4.11417e46 | 0.287310 | ||||||||
\(722\) | 3.61731e46 | 0.246900 | ||||||||
\(723\) | 9.82486e46 | 0.655457 | ||||||||
\(724\) | 1.20009e47 | 0.782576 | ||||||||
\(725\) | −2.70552e45 | −0.0172454 | ||||||||
\(726\) | 6.76317e46 | 0.421402 | ||||||||
\(727\) | 5.94494e46 | 0.362101 | 0.181051 | − | 0.983474i | \(-0.442050\pi\) | ||||
0.181051 | + | 0.983474i | \(0.442050\pi\) | |||||||
\(728\) | −7.40112e46 | −0.440687 | ||||||||
\(729\) | 1.61739e47 | 0.941480 | ||||||||
\(730\) | −1.88260e46 | −0.107135 | ||||||||
\(731\) | −3.40345e47 | −1.89358 | ||||||||
\(732\) | 8.40259e46 | 0.457068 | ||||||||
\(733\) | 2.58199e47 | 1.37322 | 0.686608 | − | 0.727028i | \(-0.259099\pi\) | ||||
0.686608 | + | 0.727028i | \(0.259099\pi\) | |||||||
\(734\) | −7.89885e46 | −0.410751 | ||||||||
\(735\) | 1.90548e46 | 0.0968866 | ||||||||
\(736\) | 2.11376e47 | 1.05093 | ||||||||
\(737\) | −2.90149e46 | −0.141061 | ||||||||
\(738\) | −1.04098e47 | −0.494893 | ||||||||
\(739\) | −1.03631e47 | −0.481790 | −0.240895 | − | 0.970551i | \(-0.577441\pi\) | ||||
−0.240895 | + | 0.970551i | \(0.577441\pi\) | |||||||
\(740\) | −2.26970e46 | −0.103192 | ||||||||
\(741\) | −6.75556e46 | −0.300373 | ||||||||
\(742\) | 8.14018e46 | 0.353973 | ||||||||
\(743\) | −2.33354e47 | −0.992428 | −0.496214 | − | 0.868200i | \(-0.665277\pi\) | ||||
−0.496214 | + | 0.868200i | \(0.665277\pi\) | |||||||
\(744\) | −1.68142e46 | −0.0699397 | ||||||||
\(745\) | 7.58925e46 | 0.308760 | ||||||||
\(746\) | 2.49081e47 | 0.991176 | ||||||||
\(747\) | −1.27192e46 | −0.0495075 | ||||||||
\(748\) | −3.76945e46 | −0.143516 | ||||||||
\(749\) | 2.78217e47 | 1.03618 | ||||||||
\(750\) | 1.09375e46 | 0.0398479 | ||||||||
\(751\) | −1.20809e47 | −0.430568 | −0.215284 | − | 0.976552i | \(-0.569068\pi\) | ||||
−0.215284 | + | 0.976552i | \(0.569068\pi\) | |||||||
\(752\) | 5.45442e44 | 0.00190175 | ||||||||
\(753\) | −2.28551e47 | −0.779591 | ||||||||
\(754\) | −8.29945e45 | −0.0276963 | ||||||||
\(755\) | −1.83297e46 | −0.0598452 | ||||||||
\(756\) | 1.78742e47 | 0.570976 | ||||||||
\(757\) | 5.96569e47 | 1.86457 | 0.932285 | − | 0.361724i | \(-0.117812\pi\) | ||||
0.932285 | + | 0.361724i | \(0.117812\pi\) | |||||||
\(758\) | 7.96864e46 | 0.243693 | ||||||||
\(759\) | −5.95258e46 | −0.178121 | ||||||||
\(760\) | −1.16248e47 | −0.340377 | ||||||||
\(761\) | −3.41953e47 | −0.979760 | −0.489880 | − | 0.871790i | \(-0.662959\pi\) | ||||
−0.489880 | + | 0.871790i | \(0.662959\pi\) | |||||||
\(762\) | 1.53063e47 | 0.429153 | ||||||||
\(763\) | 5.35630e47 | 1.46964 | ||||||||
\(764\) | −1.78082e47 | −0.478167 | ||||||||
\(765\) | 7.60241e46 | 0.199773 | ||||||||
\(766\) | −5.86149e44 | −0.00150742 | ||||||||
\(767\) | −3.23671e47 | −0.814668 | ||||||||
\(768\) | −2.91792e47 | −0.718809 | ||||||||
\(769\) | −7.47483e47 | −1.80226 | −0.901129 | − | 0.433551i | \(-0.857260\pi\) | ||||
−0.901129 | + | 0.433551i | \(0.857260\pi\) | |||||||
\(770\) | 2.24218e46 | 0.0529144 | ||||||||
\(771\) | −5.66554e47 | −1.30871 | ||||||||
\(772\) | 4.43514e47 | 1.00282 | ||||||||
\(773\) | 1.39866e47 | 0.309565 | 0.154782 | − | 0.987949i | \(-0.450532\pi\) | ||||
0.154782 | + | 0.987949i | \(0.450532\pi\) | |||||||
\(774\) | −2.49184e47 | −0.539877 | ||||||||
\(775\) | −9.06329e45 | −0.0192224 | ||||||||
\(776\) | 1.55251e47 | 0.322342 | ||||||||
\(777\) | −1.10772e47 | −0.225156 | ||||||||
\(778\) | −2.12170e46 | −0.0422203 | ||||||||
\(779\) | −7.03968e47 | −1.37147 | ||||||||
\(780\) | −5.79627e46 | −0.110557 | ||||||||
\(781\) | −1.27464e47 | −0.238038 | ||||||||
\(782\) | 3.35640e47 | 0.613709 | ||||||||
\(783\) | 5.16898e46 | 0.0925414 | ||||||||
\(784\) | −5.80022e45 | −0.0101679 | ||||||||
\(785\) | 2.41780e47 | 0.415022 | ||||||||
\(786\) | −1.00397e47 | −0.168753 | ||||||||
\(787\) | 6.12282e47 | 1.00779 | 0.503893 | − | 0.863766i | \(-0.331901\pi\) | ||||
0.503893 | + | 0.863766i | \(0.331901\pi\) | |||||||
\(788\) | −6.33886e47 | −1.02171 | ||||||||
\(789\) | −4.30702e47 | −0.679840 | ||||||||
\(790\) | 3.34304e47 | 0.516767 | ||||||||
\(791\) | −2.77968e46 | −0.0420807 | ||||||||
\(792\) | −7.11713e46 | −0.105521 | ||||||||
\(793\) | 3.58300e47 | 0.520283 | ||||||||
\(794\) | 7.89176e47 | 1.12237 | ||||||||
\(795\) | 1.64404e47 | 0.229009 | ||||||||
\(796\) | 5.73049e47 | 0.781855 | ||||||||
\(797\) | −7.29365e47 | −0.974726 | −0.487363 | − | 0.873199i | \(-0.662041\pi\) | ||||
−0.487363 | + | 0.873199i | \(0.662041\pi\) | |||||||
\(798\) | −2.19999e47 | −0.287988 | ||||||||
\(799\) | 4.18321e46 | 0.0536399 | ||||||||
\(800\) | −1.60805e47 | −0.201983 | ||||||||
\(801\) | 3.15681e47 | 0.388430 | ||||||||
\(802\) | 2.18966e47 | 0.263937 | ||||||||
\(803\) | −7.79452e46 | −0.0920414 | ||||||||
\(804\) | 2.44264e47 | 0.282575 | ||||||||
\(805\) | 3.44906e47 | 0.390903 | ||||||||
\(806\) | −2.78026e46 | −0.0308714 | ||||||||
\(807\) | 9.66061e47 | 1.05097 | ||||||||
\(808\) | −1.55485e48 | −1.65730 | ||||||||
\(809\) | 4.30397e47 | 0.449489 | 0.224744 | − | 0.974418i | \(-0.427845\pi\) | ||||
0.224744 | + | 0.974418i | \(0.427845\pi\) | |||||||
\(810\) | −8.75991e46 | −0.0896390 | ||||||||
\(811\) | 1.20340e48 | 1.20660 | 0.603302 | − | 0.797513i | \(-0.293851\pi\) | ||||
0.603302 | + | 0.797513i | \(0.293851\pi\) | |||||||
\(812\) | 4.66921e46 | 0.0458742 | ||||||||
\(813\) | 8.99045e47 | 0.865541 | ||||||||
\(814\) | 5.43959e46 | 0.0513173 | ||||||||
\(815\) | 5.05737e47 | 0.467546 | ||||||||
\(816\) | 2.73165e46 | 0.0247479 | ||||||||
\(817\) | −1.68512e48 | −1.49613 | ||||||||
\(818\) | −5.91992e47 | −0.515094 | ||||||||
\(819\) | 2.39650e47 | 0.204359 | ||||||||
\(820\) | −6.04004e47 | −0.504791 | ||||||||
\(821\) | 1.31428e48 | 1.07653 | 0.538264 | − | 0.842776i | \(-0.319080\pi\) | ||||
0.538264 | + | 0.842776i | \(0.319080\pi\) | |||||||
\(822\) | 1.48850e47 | 0.119499 | ||||||||
\(823\) | 1.85531e48 | 1.45989 | 0.729945 | − | 0.683506i | \(-0.239546\pi\) | ||||
0.729945 | + | 0.683506i | \(0.239546\pi\) | |||||||
\(824\) | 4.38613e47 | 0.338285 | ||||||||
\(825\) | 4.52844e46 | 0.0342340 | ||||||||
\(826\) | −1.05406e48 | −0.781076 | ||||||||
\(827\) | 3.05619e47 | 0.221993 | 0.110997 | − | 0.993821i | \(-0.464596\pi\) | ||||
0.110997 | + | 0.993821i | \(0.464596\pi\) | |||||||
\(828\) | −4.24530e47 | −0.302279 | ||||||||
\(829\) | −1.49161e48 | −1.04113 | −0.520567 | − | 0.853821i | \(-0.674279\pi\) | ||||
−0.520567 | + | 0.853821i | \(0.674279\pi\) | |||||||
\(830\) | 4.27195e46 | 0.0292306 | ||||||||
\(831\) | −1.86034e48 | −1.24789 | ||||||||
\(832\) | −4.65428e47 | −0.306068 | ||||||||
\(833\) | −4.44841e47 | −0.286789 | ||||||||
\(834\) | 4.98569e47 | 0.315127 | ||||||||
\(835\) | −1.18084e48 | −0.731754 | ||||||||
\(836\) | −1.86634e47 | −0.113393 | ||||||||
\(837\) | 1.73157e47 | 0.103150 | ||||||||
\(838\) | −1.48554e48 | −0.867676 | ||||||||
\(839\) | 1.58547e48 | 0.907999 | 0.454000 | − | 0.891002i | \(-0.349997\pi\) | ||||
0.454000 | + | 0.891002i | \(0.349997\pi\) | |||||||
\(840\) | −4.86782e47 | −0.273355 | ||||||||
\(841\) | −1.80257e48 | −0.992565 | ||||||||
\(842\) | −1.64315e48 | −0.887212 | ||||||||
\(843\) | 1.85893e48 | 0.984254 | ||||||||
\(844\) | −2.06900e48 | −1.07426 | ||||||||
\(845\) | 6.31153e47 | 0.321365 | ||||||||
\(846\) | 3.06274e46 | 0.0152933 | ||||||||
\(847\) | −1.62248e48 | −0.794515 | ||||||||
\(848\) | −5.00438e46 | −0.0240336 | ||||||||
\(849\) | 1.27513e48 | 0.600589 | ||||||||
\(850\) | −2.55339e47 | −0.117952 | ||||||||
\(851\) | 8.36751e47 | 0.379104 | ||||||||
\(852\) | 1.07306e48 | 0.476839 | ||||||||
\(853\) | 1.56569e48 | 0.682414 | 0.341207 | − | 0.939988i | \(-0.389164\pi\) | ||||
0.341207 | + | 0.939988i | \(0.389164\pi\) | |||||||
\(854\) | 1.16683e48 | 0.498830 | ||||||||
\(855\) | 3.76413e47 | 0.157842 | ||||||||
\(856\) | 2.96608e48 | 1.22002 | ||||||||
\(857\) | −3.16984e48 | −1.27895 | −0.639476 | − | 0.768811i | \(-0.720849\pi\) | ||||
−0.639476 | + | 0.768811i | \(0.720849\pi\) | |||||||
\(858\) | 1.38914e47 | 0.0549802 | ||||||||
\(859\) | −8.88897e47 | −0.345115 | −0.172558 | − | 0.984999i | \(-0.555203\pi\) | ||||
−0.172558 | + | 0.984999i | \(0.555203\pi\) | |||||||
\(860\) | −1.44584e48 | −0.550674 | ||||||||
\(861\) | −2.94784e48 | −1.10142 | ||||||||
\(862\) | −4.15842e47 | −0.152426 | ||||||||
\(863\) | 4.50727e48 | 1.62082 | 0.810411 | − | 0.585862i | \(-0.199244\pi\) | ||||
0.810411 | + | 0.585862i | \(0.199244\pi\) | |||||||
\(864\) | 3.07223e48 | 1.08387 | ||||||||
\(865\) | −7.05106e47 | −0.244055 | ||||||||
\(866\) | 1.47593e48 | 0.501211 | ||||||||
\(867\) | −1.13313e47 | −0.0377542 | ||||||||
\(868\) | 1.56415e47 | 0.0511332 | ||||||||
\(869\) | 1.38412e48 | 0.443963 | ||||||||
\(870\) | −5.45867e46 | −0.0171798 | ||||||||
\(871\) | 1.04158e48 | 0.321657 | ||||||||
\(872\) | 5.71036e48 | 1.73038 | ||||||||
\(873\) | −5.02708e47 | −0.149479 | ||||||||
\(874\) | 1.66183e48 | 0.484895 | ||||||||
\(875\) | −2.62388e47 | −0.0751296 | ||||||||
\(876\) | 6.56186e47 | 0.184378 | ||||||||
\(877\) | −3.88746e48 | −1.07195 | −0.535973 | − | 0.844235i | \(-0.680055\pi\) | ||||
−0.535973 | + | 0.844235i | \(0.680055\pi\) | |||||||
\(878\) | −1.00528e48 | −0.272037 | ||||||||
\(879\) | 1.75207e48 | 0.465302 | ||||||||
\(880\) | −1.37844e46 | −0.00359272 | ||||||||
\(881\) | −4.23545e48 | −1.08342 | −0.541711 | − | 0.840565i | \(-0.682223\pi\) | ||||
−0.541711 | + | 0.840565i | \(0.682223\pi\) | |||||||
\(882\) | −3.25691e47 | −0.0817663 | ||||||||
\(883\) | 2.06647e48 | 0.509188 | 0.254594 | − | 0.967048i | \(-0.418058\pi\) | ||||
0.254594 | + | 0.967048i | \(0.418058\pi\) | |||||||
\(884\) | 1.35316e48 | 0.327255 | ||||||||
\(885\) | −2.12883e48 | −0.505333 | ||||||||
\(886\) | 1.91160e48 | 0.445389 | ||||||||
\(887\) | −1.92447e48 | −0.440121 | −0.220060 | − | 0.975486i | \(-0.570625\pi\) | ||||
−0.220060 | + | 0.975486i | \(0.570625\pi\) | |||||||
\(888\) | −1.18095e48 | −0.265104 | ||||||||
\(889\) | −3.67195e48 | −0.809130 | ||||||||
\(890\) | −1.06026e48 | −0.229340 | ||||||||
\(891\) | −3.62687e47 | −0.0770105 | ||||||||
\(892\) | −2.50317e48 | −0.521759 | ||||||||
\(893\) | 2.07120e47 | 0.0423812 | ||||||||
\(894\) | 1.53121e48 | 0.307585 | ||||||||
\(895\) | 2.65275e48 | 0.523138 | ||||||||
\(896\) | 2.86590e48 | 0.554854 | ||||||||
\(897\) | 2.13686e48 | 0.406164 | ||||||||
\(898\) | −4.63102e48 | −0.864205 | ||||||||
\(899\) | 4.52331e46 | 0.00828746 | ||||||||
\(900\) | 3.22962e47 | 0.0580965 | ||||||||
\(901\) | −3.83806e48 | −0.677879 | ||||||||
\(902\) | 1.44757e48 | 0.251033 | ||||||||
\(903\) | −7.05639e48 | −1.20153 | ||||||||
\(904\) | −2.96342e47 | −0.0495467 | ||||||||
\(905\) | 3.36577e48 | 0.552564 | ||||||||
\(906\) | −3.69820e47 | −0.0596177 | ||||||||
\(907\) | −2.02864e48 | −0.321133 | −0.160567 | − | 0.987025i | \(-0.551332\pi\) | ||||
−0.160567 | + | 0.987025i | \(0.551332\pi\) | |||||||
\(908\) | −6.20107e48 | −0.963940 | ||||||||
\(909\) | 5.03465e48 | 0.768537 | ||||||||
\(910\) | −8.04902e47 | −0.120659 | ||||||||
\(911\) | 3.08415e48 | 0.454028 | 0.227014 | − | 0.973891i | \(-0.427104\pi\) | ||||
0.227014 | + | 0.973891i | \(0.427104\pi\) | |||||||
\(912\) | 1.35250e47 | 0.0195534 | ||||||||
\(913\) | 1.76871e47 | 0.0251125 | ||||||||
\(914\) | −6.16894e48 | −0.860198 | ||||||||
\(915\) | 2.35659e48 | 0.322728 | ||||||||
\(916\) | 7.94481e48 | 1.06858 | ||||||||
\(917\) | 2.40852e48 | 0.318168 | ||||||||
\(918\) | 4.87833e48 | 0.632946 | ||||||||
\(919\) | −7.76805e48 | −0.989933 | −0.494967 | − | 0.868912i | \(-0.664820\pi\) | ||||
−0.494967 | + | 0.868912i | \(0.664820\pi\) | |||||||
\(920\) | 3.67705e48 | 0.460257 | ||||||||
\(921\) | −5.06778e48 | −0.623066 | ||||||||
\(922\) | −2.85598e48 | −0.344902 | ||||||||
\(923\) | 4.57572e48 | 0.542789 | ||||||||
\(924\) | −7.81521e47 | −0.0910653 | ||||||||
\(925\) | −6.36560e47 | −0.0728619 | ||||||||
\(926\) | −3.18383e48 | −0.357988 | ||||||||
\(927\) | −1.42024e48 | −0.156872 | ||||||||
\(928\) | 8.02544e47 | 0.0870818 | ||||||||
\(929\) | −1.29507e49 | −1.38049 | −0.690244 | − | 0.723576i | \(-0.742497\pi\) | ||||
−0.690244 | + | 0.723576i | \(0.742497\pi\) | |||||||
\(930\) | −1.82861e47 | −0.0191493 | ||||||||
\(931\) | −2.20251e48 | −0.226594 | ||||||||
\(932\) | 1.11621e47 | 0.0112819 | ||||||||
\(933\) | 1.21451e48 | 0.120602 | ||||||||
\(934\) | −4.80683e48 | −0.468960 | ||||||||
\(935\) | −1.05718e48 | −0.101334 | ||||||||
\(936\) | 2.55491e48 | 0.240616 | ||||||||
\(937\) | 1.36587e49 | 1.26388 | 0.631940 | − | 0.775017i | \(-0.282259\pi\) | ||||
0.631940 | + | 0.775017i | \(0.282259\pi\) | |||||||
\(938\) | 3.39198e48 | 0.308394 | ||||||||
\(939\) | 1.49938e48 | 0.133946 | ||||||||
\(940\) | 1.77709e47 | 0.0155991 | ||||||||
\(941\) | −1.17124e45 | −0.000101022 0 | −5.05109e−5 | − | 1.00000i | \(-0.500016\pi\) | ||||
−5.05109e−5 | 1.00000i | \(0.500016\pi\) | ||||||||
\(942\) | 4.87817e48 | 0.413444 | ||||||||
\(943\) | 2.22673e49 | 1.85449 | ||||||||
\(944\) | 6.48009e47 | 0.0530326 | ||||||||
\(945\) | 5.01301e48 | 0.403156 | ||||||||
\(946\) | 3.46511e48 | 0.273851 | ||||||||
\(947\) | 1.87235e49 | 1.45416 | 0.727081 | − | 0.686551i | \(-0.240876\pi\) | ||||
0.727081 | + | 0.686551i | \(0.240876\pi\) | |||||||
\(948\) | −1.16523e49 | −0.889352 | ||||||||
\(949\) | 2.79809e48 | 0.209879 | ||||||||
\(950\) | −1.26424e48 | −0.0931944 | ||||||||
\(951\) | 1.24369e49 | 0.901015 | ||||||||
\(952\) | 1.13641e49 | 0.809144 | ||||||||
\(953\) | −2.01399e49 | −1.40937 | −0.704685 | − | 0.709521i | \(-0.748912\pi\) | ||||
−0.704685 | + | 0.709521i | \(0.748912\pi\) | |||||||
\(954\) | −2.81004e48 | −0.193270 | ||||||||
\(955\) | −4.99449e48 | −0.337626 | ||||||||
\(956\) | −5.00946e48 | −0.332840 | ||||||||
\(957\) | −2.26005e47 | −0.0147595 | ||||||||
\(958\) | 7.26405e48 | 0.466282 | ||||||||
\(959\) | −3.57089e48 | −0.225305 | ||||||||
\(960\) | −3.06119e48 | −0.189852 | ||||||||
\(961\) | −1.62519e49 | −0.990762 | ||||||||
\(962\) | −1.95271e48 | −0.117017 | ||||||||
\(963\) | −9.60423e48 | −0.565756 | ||||||||
\(964\) | −9.74376e48 | −0.564229 | ||||||||
\(965\) | 1.24388e49 | 0.708072 | ||||||||
\(966\) | 6.95884e48 | 0.389417 | ||||||||
\(967\) | 1.68504e49 | 0.926985 | 0.463493 | − | 0.886101i | \(-0.346596\pi\) | ||||
0.463493 | + | 0.886101i | \(0.346596\pi\) | |||||||
\(968\) | −1.72973e49 | −0.935478 | ||||||||
\(969\) | 1.03729e49 | 0.551514 | ||||||||
\(970\) | 1.68842e48 | 0.0882566 | ||||||||
\(971\) | −1.57857e49 | −0.811234 | −0.405617 | − | 0.914043i | \(-0.632943\pi\) | ||||
−0.405617 | + | 0.914043i | \(0.632943\pi\) | |||||||
\(972\) | −1.04005e49 | −0.525485 | ||||||||
\(973\) | −1.19606e49 | −0.594143 | ||||||||
\(974\) | −1.46508e49 | −0.715549 | ||||||||
\(975\) | −1.62562e48 | −0.0780627 | ||||||||
\(976\) | −7.17338e47 | −0.0338690 | ||||||||
\(977\) | −1.78305e49 | −0.827759 | −0.413880 | − | 0.910332i | \(-0.635827\pi\) | ||||
−0.413880 | + | 0.910332i | \(0.635827\pi\) | |||||||
\(978\) | 1.02038e49 | 0.465768 | ||||||||
\(979\) | −4.38981e48 | −0.197030 | ||||||||
\(980\) | −1.88975e48 | −0.0834017 | ||||||||
\(981\) | −1.84903e49 | −0.802425 | ||||||||
\(982\) | 9.33798e48 | 0.398486 | ||||||||
\(983\) | 1.52674e48 | 0.0640667 | 0.0320333 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320333 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(984\) | −3.14269e49 | −1.29683 | ||||||||
\(985\) | −1.77780e49 | −0.721414 | ||||||||
\(986\) | 1.27435e48 | 0.0508532 | ||||||||
\(987\) | 8.67307e47 | 0.0340361 | ||||||||
\(988\) | 6.69980e48 | 0.258566 | ||||||||
\(989\) | 5.33025e49 | 2.02306 | ||||||||
\(990\) | −7.74016e47 | −0.0288914 | ||||||||
\(991\) | 1.40402e49 | 0.515416 | 0.257708 | − | 0.966223i | \(-0.417033\pi\) | ||||
0.257708 | + | 0.966223i | \(0.417033\pi\) | |||||||
\(992\) | 2.68847e48 | 0.0970648 | ||||||||
\(993\) | −1.13451e49 | −0.402854 | ||||||||
\(994\) | 1.49011e49 | 0.520408 | ||||||||
\(995\) | 1.60717e49 | 0.552055 | ||||||||
\(996\) | −1.48900e48 | −0.0503056 | ||||||||
\(997\) | −7.92661e48 | −0.263401 | −0.131701 | − | 0.991290i | \(-0.542044\pi\) | ||||
−0.131701 | + | 0.991290i | \(0.542044\pi\) | |||||||
\(998\) | −3.66225e48 | −0.119700 | ||||||||
\(999\) | 1.21617e49 | 0.390988 |
(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 | 5.34.a.a.1.2 | ✓ | 5 | |
5.2 | odd | 4 | 25.34.b.b.24.4 | 10 | |||
5.3 | odd | 4 | 25.34.b.b.24.7 | 10 | |||
5.4 | even | 2 | 25.34.a.b.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.a.a.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
25.34.a.b.1.4 | 5 | 5.4 | even | 2 | |||
25.34.b.b.24.4 | 10 | 5.2 | odd | 4 | |||
25.34.b.b.24.7 | 10 | 5.3 | odd | 4 |