Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(5,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.5");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.g (of order \(6\), 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: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.5 |
Dual form | 21.30.g.a.17.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 7.17445e6 | − | 4.14217e6i | 0.866025 | − | 0.500000i | ||||
\(4\) | −2.68435e8 | − | 4.64944e8i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.24856e12 | − | 1.28880e12i | −0.695807 | − | 0.718229i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.43152e13 | − | 5.94357e13i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −3.85176e15 | − | 2.22381e15i | −0.866025 | − | 0.500000i | ||||
\(13\) | 1.93779e16i | 1.36498i | 0.730893 | + | 0.682492i | \(0.239104\pi\) | ||||
−0.730893 | + | 0.682492i | \(0.760896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.44115e17 | + | 2.49615e17i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.96231e18 | − | 1.13294e18i | −0.563429 | − | 0.325296i | 0.191092 | − | 0.981572i | \(-0.438797\pi\) |
−0.754521 | + | 0.656276i | \(0.772131\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.42962e19 | − | 4.07465e18i | −0.961701 | − | 0.274101i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.31323e19 | + | 1.61310e20i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.68558e20i | − | 1.00000i | ||||||
\(28\) | −2.64060e20 | + | 9.26470e20i | −0.274101 | + | 0.961701i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.74078e21 | + | 2.73709e21i | −1.12488 | + | 0.649448i | −0.942642 | − | 0.333807i | \(-0.891667\pi\) |
−0.182236 | + | 0.983255i | \(0.558333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.68457e22 | −1.00000 | ||||||||
\(37\) | −3.75709e22 | + | 6.50747e22i | −0.685372 | + | 1.18710i | 0.287947 | + | 0.957646i | \(0.407027\pi\) |
−0.973320 | + | 0.229453i | \(0.926306\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.02665e22 | + | 1.39026e23i | 0.682492 | + | 1.18211i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.11042e23 | 1.88038 | 0.940191 | − | 0.340649i | \(-0.110647\pi\) | ||||
0.940191 | + | 0.340649i | \(0.110647\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 2.38780e24i | 1.00000i | ||||||||
\(49\) | −1.02088e23 | + | 3.21829e24i | −0.0317054 | + | 0.999497i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.00963e24 | − | 5.20171e24i | 1.18211 | − | 0.682492i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.87713e25 | −0.650592 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.20660e25 | − | 5.31543e25i | −1.19348 | − | 0.689058i | −0.234389 | − | 0.972143i | \(-0.575309\pi\) |
−0.959095 | + | 0.283085i | \(0.908642\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.19445e26 | + | 2.99838e25i | −0.969908 | + | 0.243472i | ||||
\(64\) | 1.54743e26 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.75561e26 | − | 3.04081e26i | −0.583908 | − | 1.01136i | −0.995011 | − | 0.0997693i | \(-0.968190\pi\) |
0.411103 | − | 0.911589i | \(-0.365144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.71067e27 | − | 9.87658e26i | 1.64054 | − | 0.947164i | 0.659894 | − | 0.751359i | \(-0.270601\pi\) |
0.980643 | − | 0.195805i | \(-0.0627320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.33635e27 | + | 7.71540e26i | 0.866025 | + | 0.500000i | ||||
\(76\) | 1.21648e27i | 0.650592i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.19532e27 | + | 5.53446e27i | −0.974814 | + | 1.68843i | −0.294265 | + | 0.955724i | \(0.595075\pi\) |
−0.680549 | + | 0.732703i | \(0.738259\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.35506e27 | − | 4.07909e27i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 1.94312e27 | + | 7.74070e27i | 0.243472 | + | 0.969908i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.49742e28 | − | 2.41945e28i | 0.980371 | − | 0.949766i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.26750e28 | + | 3.92742e28i | −0.649448 | + | 1.12488i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 7.63732e28i | − | 1.18782i | −0.804531 | − | 0.593911i | \(-0.797583\pi\) | ||
0.804531 | − | 0.593911i | \(-0.202417\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000e28 | − | 8.66025e28i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.87902e29 | + | 1.08485e29i | 1.22403 | + | 0.706693i | 0.965774 | − | 0.259384i | \(-0.0835196\pi\) |
0.258254 | + | 0.966077i | \(0.416853\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −2.64347e29 | + | 1.52621e29i | −0.866025 | + | 0.500000i | ||||
\(109\) | 2.21424e29 | + | 3.83517e29i | 0.634658 | + | 1.09926i | 0.986587 | + | 0.163233i | \(0.0521924\pi\) |
−0.351929 | + | 0.936027i | \(0.614474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.22500e29i | 1.37074i | ||||||||
\(112\) | 5.01640e29 | − | 1.25925e29i | 0.969908 | − | 0.243472i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.15174e30 | + | 6.64956e29i | 1.18211 | + | 0.682492i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.93155e29 | + | 1.37378e30i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.54519e30 | + | 1.46946e30i | 1.12488 | + | 0.649448i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.62357e30 | 1.44485 | 0.722427 | − | 0.691447i | \(-0.243027\pi\) | ||||
0.722427 | + | 0.691447i | \(0.243027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.53623e30 | − | 3.77369e30i | 1.62846 | − | 0.940191i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.89935e29 | + | 3.94356e30i | 0.158401 | + | 0.631014i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.83699e31i | 1.55021i | 0.631831 | + | 0.775107i | \(0.282304\pi\) | ||||
−0.631831 | + | 0.775107i | \(0.717696\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.89068e30 | + | 1.71312e31i | 0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.25983e31 | + | 2.35123e31i | 0.472291 | + | 0.881443i | ||||
\(148\) | 4.03414e31 | 1.37074 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.93538e31 | + | 6.81629e31i | 0.999589 | + | 1.73134i | 0.524625 | + | 0.851334i | \(0.324206\pi\) |
0.474964 | + | 0.880005i | \(0.342461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.30928e31 | − | 7.46389e31i | 0.682492 | − | 1.18211i | ||||
\(157\) | 1.05949e31 | − | 6.11698e30i | 0.152951 | − | 0.0883065i | −0.421571 | − | 0.906795i | \(-0.638521\pi\) |
0.574522 | + | 0.818489i | \(0.305188\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.17537e31 | + | 3.76785e31i | −0.182311 | + | 0.315772i | −0.942667 | − | 0.333734i | \(-0.891691\pi\) |
0.760356 | + | 0.649506i | \(0.225024\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.73964e32 | −0.863182 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.34674e32 | + | 7.77539e31i | −0.563429 | + | 0.325296i | ||||
\(172\) | −2.44556e32 | − | 4.23583e32i | −0.940191 | − | 1.62846i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.16141e31 | − | 3.21434e32i | 0.274101 | − | 0.961701i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.39694e32i | 0.439863i | 0.975515 | + | 0.219931i | \(0.0705833\pi\) | ||||
−0.975515 | + | 0.219931i | \(0.929417\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.80697e32 | −1.37812 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.32755e32 | + | 7.09880e32i | −0.718229 | + | 0.695807i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 1.11019e33 | − | 6.40970e32i | 0.866025 | − | 0.500000i | ||||
\(193\) | −1.19349e33 | − | 2.06719e33i | −0.863453 | − | 1.49554i | −0.868575 | − | 0.495557i | \(-0.834964\pi\) |
0.00512254 | − | 0.999987i | \(-0.498369\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.52373e33 | − | 8.16437e32i | 0.881443 | − | 0.472291i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.54923e33 | + | 8.94450e32i | −0.719030 | + | 0.415132i | −0.814395 | − | 0.580310i | \(-0.802931\pi\) |
0.0953657 | + | 0.995442i | \(0.469598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.51911e33 | − | 1.45441e33i | −1.01136 | − | 0.583908i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.83701e33 | − | 2.79265e33i | −1.18211 | − | 0.682492i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.41087e33 | −1.86868 | −0.934338 | − | 0.356388i | \(-0.884008\pi\) | ||||
−0.934338 | + | 0.356388i | \(0.884008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.44671e33 | + | 2.69247e33i | 1.24915 | + | 0.356029i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.18210e33 | − | 1.41718e34i | 0.947164 | − | 1.64054i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.73361e34i | 1.54359i | 0.635872 | + | 0.771794i | \(0.280641\pi\) | ||||
−0.635872 | + | 0.771794i | \(0.719359\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.27834e34 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 5.03888e33 | + | 8.72760e33i | 0.325296 | + | 0.563429i | ||||
\(229\) | 2.52851e34 | + | 1.45984e34i | 1.53197 | + | 0.884484i | 0.999271 | + | 0.0381794i | \(0.0121558\pi\) |
0.532700 | + | 0.846304i | \(0.321177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.29423e34i | 1.94963i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.24242e34 | − | 1.87201e34i | 0.936747 | − | 0.540831i | 0.0478081 | − | 0.998857i | \(-0.484776\pi\) |
0.888939 | + | 0.458025i | \(0.151443\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.37926e34 | − | 1.95102e34i | −0.866025 | − | 0.500000i | ||||
\(244\) | 5.70740e34i | 1.37812i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.19539e34 | − | 3.80253e34i | 0.444024 | − | 0.769072i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 4.60041e34 | + | 4.74866e34i | 0.695807 | + | 0.718229i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.15384e34 | − | 7.19466e34i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.30778e35 | − | 3.28286e34i | 1.32950 | − | 0.333738i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.42538e34 | + | 1.63252e35i | −0.583908 | + | 1.01136i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.14928e35 | − | 6.63536e34i | −0.605857 | − | 0.349792i | 0.165485 | − | 0.986212i | \(-0.447081\pi\) |
−0.771342 | + | 0.636420i | \(0.780414\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.89581e34 | − | 2.77030e35i | 0.374144 | − | 1.31271i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.76431e34 | − | 8.25203e34i | −0.182828 | − | 0.316668i | 0.760014 | − | 0.649906i | \(-0.225192\pi\) |
−0.942843 | + | 0.333238i | \(0.891859\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.75695e35i | 1.29890i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.02910e35 | + | 3.48090e35i | −1.69570 | + | 0.979013i | −0.745950 | + | 0.666002i | \(0.768004\pi\) |
−0.949750 | + | 0.313010i | \(0.898663\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.40984e35 | − | 4.17397e35i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.16351e35 | − | 5.47936e35i | −0.593911 | − | 1.02868i | ||||
\(292\) | −9.18411e35 | − | 5.30245e35i | −1.64054 | − | 0.947164i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | − | 8.28435e35i | − | 1.00000i | ||||||
\(301\) | −1.13749e36 | − | 1.17415e36i | −1.30838 | − | 1.35054i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.65596e35 | − | 3.26547e35i | 0.563429 | − | 0.325296i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.29328e36i | 1.98130i | 0.136412 | + | 0.990652i | \(0.456443\pi\) | ||||
−0.136412 | + | 0.990652i | \(0.543557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.79746e36 | 1.41339 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.40350e36 | − | 1.38766e36i | −1.56838 | − | 0.905506i | −0.996358 | − | 0.0852700i | \(-0.972825\pi\) |
−0.572025 | − | 0.820236i | \(-0.693842\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.43095e36 | 1.94963 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.26437e36 | + | 2.18995e36i | −0.500000 | + | 0.866025i | ||||
\(325\) | −3.12584e36 | + | 1.80471e36i | −1.18211 | + | 0.682492i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.17719e36 | + | 1.83435e36i | 1.09926 | + | 0.634658i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.46610e36 | + | 4.27141e36i | −0.715327 | + | 1.23898i | 0.247506 | + | 0.968886i | \(0.420389\pi\) |
−0.962833 | + | 0.270097i | \(0.912944\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.57850e36 | + | 4.46610e36i | 0.685372 | + | 1.18710i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.07739e36 | − | 2.98132e36i | 0.718229 | − | 0.695807i | ||||
\(337\) | 6.54162e36 | 1.46235 | 0.731176 | − | 0.682189i | \(-0.238972\pi\) | ||||
0.731176 | + | 0.682189i | \(0.238972\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.27518e36 | − | 3.88666e36i | 0.739929 | − | 0.672685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.11165e36i | − | 0.284219i | −0.989851 | − | 0.142109i | \(-0.954612\pi\) | ||
0.989851 | − | 0.142109i | \(-0.0453884\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.10174e37 | 1.36498 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.49782e36 | − | 6.05840e36i | −0.288365 | − | 0.499463i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.31415e37i | 1.00000i | ||||||||
\(364\) | −1.79530e37 | − | 5.11692e36i | −1.31271 | − | 0.374144i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.07606e37 | + | 6.21261e36i | −0.698517 | + | 0.403289i | −0.806795 | − | 0.590832i | \(-0.798800\pi\) |
0.108278 | + | 0.994121i | \(0.465466\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.43471e37 | 1.29890 | ||||||||
\(373\) | −9.84732e36 | + | 1.70561e37i | −0.505289 | + | 0.875187i | 0.494692 | + | 0.869068i | \(0.335281\pi\) |
−0.999981 | + | 0.00611850i | \(0.998052\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.76969e37 | −1.94188 | −0.970939 | − | 0.239329i | \(-0.923073\pi\) | ||||
−0.970939 | + | 0.239329i | \(0.923073\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.31716e37 | − | 1.91516e37i | 1.25128 | − | 0.722427i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.12626e37 | − | 5.41484e37i | 0.940191 | − | 1.62846i | ||||
\(388\) | −3.55093e37 | + | 2.05013e37i | −1.02868 | + | 0.593911i | ||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.91562e37 | − | 4.57009e37i | −1.64446 | − | 0.949428i | −0.979221 | − | 0.202795i | \(-0.934997\pi\) |
−0.665237 | − | 0.746633i | \(-0.731669\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.34371e37 | + | 2.41924e37i | 0.452686 | + | 0.467274i | ||||
\(400\) | −5.36871e37 | −1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.30390e37 | − | 9.18662e37i | −0.886487 | − | 1.53544i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.18314e37 | − | 2.41514e37i | 0.564306 | − | 0.325802i | −0.190566 | − | 0.981674i | \(-0.561032\pi\) |
0.754872 | + | 0.655872i | \(0.227699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.16485e38i | − | 1.41339i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.60912e37 | + | 1.31794e38i | 0.775107 | + | 1.34252i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.21956e38 | −1.96869 | −0.984344 | − | 0.176258i | \(-0.943601\pi\) | ||||
−0.984344 | + | 0.176258i | \(0.943601\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.64450e37 | + | 1.85021e38i | 0.335533 | + | 1.33665i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 1.41920e38 | + | 8.19378e37i | 0.866025 | + | 0.500000i | ||||
\(433\) | 2.59179e38i | 1.52942i | 0.644376 | + | 0.764709i | \(0.277117\pi\) | ||||
−0.644376 | + | 0.764709i | \(0.722883\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.18876e38 | − | 2.05899e38i | 0.634658 | − | 1.09926i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.57263e38 | + | 1.48531e38i | 1.24349 | + | 0.717928i | 0.969803 | − | 0.243891i | \(-0.0784239\pi\) |
0.273686 | + | 0.961819i | \(0.411757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.87778e38 | + | 1.16504e38i | 0.849737 | + | 0.527206i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 2.89428e38 | − | 1.67101e38i | 1.18710 | − | 0.685372i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.93206e38 | − | 1.99432e38i | −0.695807 | − | 0.718229i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.64685e38 | + | 3.26021e38i | 1.73134 | + | 0.999589i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.72451e38 | + | 2.98694e38i | −0.465459 | + | 0.806199i | −0.999222 | − | 0.0394353i | \(-0.987444\pi\) |
0.533763 | + | 0.845634i | \(0.320777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.37446e38 | −1.20063 | −0.600317 | − | 0.799762i | \(-0.704959\pi\) | ||||
−0.600317 | + | 0.799762i | \(0.704959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | − | 7.13991e38i | − | 1.36498i | ||||||
\(469\) | −1.72700e38 | + | 6.05928e38i | −0.320100 | + | 1.12309i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.06752e37 | − | 8.77720e37i | 0.0883065 | − | 0.152951i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.22052e38i | − | 0.650592i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.26101e39 | − | 7.28044e38i | −1.62037 | − | 0.935522i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.51643e38 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.15738e38 | + | 1.58610e39i | 0.983108 | + | 1.70279i | 0.650059 | + | 0.759884i | \(0.274744\pi\) |
0.333049 | + | 0.942909i | \(0.391922\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.60430e38i | 0.364622i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.57782e39i | − | 1.29890i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.53440e38 | − | 2.65765e38i | 0.115739 | − | 0.200466i | −0.802336 | − | 0.596873i | \(-0.796410\pi\) |
0.918075 | + | 0.396407i | \(0.129743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.24810e39 | + | 7.20590e38i | −0.747538 | + | 0.431591i | ||||
\(508\) | −1.24113e39 | − | 2.14970e39i | −0.722427 | − | 1.25128i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.40877e39 | − | 9.71558e38i | −1.82178 | − | 0.519237i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.44140e38 | + | 1.11568e39i | −0.325296 | + | 0.563429i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.50911e39 | − | 2.02599e39i | −1.62846 | − | 0.940191i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.49490e39 | + | 2.59513e39i | 1.71572 | + | 0.990570i | 0.926361 | + | 0.376636i | \(0.122919\pi\) |
0.789357 | + | 0.613934i | \(0.210414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.74154e38 | − | 2.68559e39i | −0.243472 | − | 0.969908i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.54553e39 | − | 2.67694e39i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.56780e39 | − | 1.51885e39i | 0.467274 | − | 0.452686i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.65732e39 | + | 4.60262e39i | −0.620990 | + | 1.07559i | 0.368312 | + | 0.929702i | \(0.379936\pi\) |
−0.989302 | + | 0.145883i | \(0.953398\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.92852e38 | + | 1.71967e39i | 0.219931 | + | 0.380932i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.99595e39 | 1.99071 | 0.995355 | − | 0.0962743i | \(-0.0306926\pi\) | ||||
0.995355 | + | 0.0962743i | \(0.0306926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.31852e39 | + | 3.64800e39i | −1.19348 | + | 0.689058i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.11223e40 | − | 2.79200e39i | 1.89096 | − | 0.474680i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.54096e39 | − | 4.93112e39i | 1.34252 | − | 0.775107i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.76541e40i | 2.56669i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.31667e39 | + | 8.12820e39i | −0.274101 | + | 0.961701i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.34796e39 | + | 1.61911e40i | 0.998834 | + | 1.73003i | 0.541231 | + | 0.840874i | \(0.317959\pi\) |
0.457603 | + | 0.889157i | \(0.348708\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.31002e39 | − | 9.19722e39i | 0.500000 | − | 0.866025i | ||||
\(577\) | −2.01974e39 | + | 1.16610e39i | −0.185458 | + | 0.107074i | −0.589855 | − | 0.807509i | \(-0.700815\pi\) |
0.404396 | + | 0.914584i | \(0.367482\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.71253e40 | − | 9.88730e39i | −1.49554 | − | 0.863453i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 7.55008e39 | − | 1.21690e40i | 0.527206 | − | 0.849737i | ||||
\(589\) | 1.24038e40 | 0.845052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.08291e40 | − | 1.87565e40i | −0.685372 | − | 1.18710i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.40993e39 | + | 1.28344e40i | −0.415132 | + | 0.719030i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.36080e40i | 1.70908i | 0.519385 | + | 0.854540i | \(0.326161\pi\) | ||||
−0.519385 | + | 0.854540i | \(0.673839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.40977e40 | −1.16782 | ||||||||
\(604\) | 2.11279e40 | − | 3.65947e40i | 0.999589 | − | 1.73134i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.05609e39 | + | 1.76443e39i | 0.134564 | + | 0.0776907i | 0.565771 | − | 0.824562i | \(-0.308579\pi\) |
−0.431207 | + | 0.902253i | \(0.641912\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.86435e39 | − | 1.70856e40i | −0.376610 | − | 0.652308i | 0.613957 | − | 0.789340i | \(-0.289577\pi\) |
−0.990567 | + | 0.137032i | \(0.956244\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.88869e40 | − | 2.82248e40i | 1.62061 | − | 0.935658i | 0.633849 | − | 0.773457i | \(-0.281474\pi\) |
0.986758 | − | 0.162201i | \(-0.0518593\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.62705e40 | −1.36498 | ||||||||
\(625\) | −1.73472e40 | + | 3.00463e40i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.68811e39 | − | 3.28403e39i | −0.152951 | − | 0.0883065i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.60894e40 | −0.905636 | −0.452818 | − | 0.891603i | \(-0.649581\pi\) | ||||
−0.452818 | + | 0.891603i | \(0.649581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.75178e40 | + | 3.89814e40i | −1.61832 | + | 0.934338i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.23636e40 | − | 1.97826e39i | −1.36430 | − | 0.0432774i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.72150e40i | − | 1.28353i | −0.766900 | − | 0.641767i | \(-0.778202\pi\) | ||
0.766900 | − | 0.641767i | \(-0.221798\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.89277e40 | − | 1.98129e40i | 1.25981 | − | 0.316245i | ||||
\(652\) | 2.33579e40 | 0.364622 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.35567e41i | − | 1.89433i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.40088e40 | − | 3.69555e40i | 0.819065 | − | 0.472888i | −0.0310288 | − | 0.999518i | \(-0.509878\pi\) |
0.850094 | + | 0.526631i | \(0.176545\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.18092e40 | + | 1.24377e41i | 0.771794 | + | 1.33679i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.74264e41 | −1.71786 | −0.858932 | − | 0.512089i | \(-0.828872\pi\) | ||||
−0.858932 | + | 0.512089i | \(0.828872\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.17139e40 | − | 5.29511e40i | 0.866025 | − | 0.500000i | ||||
\(676\) | 4.66982e40 | + | 8.08836e40i | 0.431591 | + | 0.747538i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.84296e40 | + | 9.53568e40i | −0.853128 | + | 0.826494i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 7.23024e40 | + | 4.17438e40i | 0.563429 | + | 0.325296i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.41876e41 | 1.76897 | ||||||||
\(688\) | −1.31295e41 | + | 2.27410e41i | −0.940191 | + | 1.62846i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.50166e41 | + | 1.44433e41i | 1.68188 | + | 0.971036i | 0.960409 | + | 0.278595i | \(0.0898688\pi\) |
0.721475 | + | 0.692441i | \(0.243464\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.74041e41 | + | 4.36889e40i | −0.969908 | + | 0.243472i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.47451e41 | − | 8.51309e40i | 0.772317 | − | 0.445898i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.63119e40 | − | 8.02145e40i | 0.214448 | − | 0.371435i | −0.738654 | − | 0.674085i | \(-0.764538\pi\) |
0.953102 | + | 0.302650i | \(0.0978715\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.19296e41 | + | 3.79832e41i | 0.974814 | + | 1.68843i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.47919e40 | − | 3.77618e41i | −0.344120 | − | 1.37085i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.55084e41 | − | 2.68613e41i | 0.540831 | − | 0.936747i | ||||
\(724\) | 1.11444e41 | − | 6.43423e40i | 0.380932 | − | 0.219931i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.63965e40i | 0.149361i | 0.997208 | + | 0.0746804i | \(0.0237937\pi\) | ||||
−0.997208 | + | 0.0746804i | \(0.976206\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.23258e41 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.36410e41 | + | 4.09475e41i | 0.689058 | + | 1.19348i | ||||
\(733\) | −4.94052e41 | − | 2.85241e41i | −1.41177 | − | 0.815087i | −0.416217 | − | 0.909265i | \(-0.636644\pi\) |
−0.995555 | + | 0.0941784i | \(0.969978\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.82697e41 | − | 6.62851e41i | −0.971652 | − | 1.68295i | −0.690568 | − | 0.723268i | \(-0.742639\pi\) |
−0.281085 | − | 0.959683i | \(-0.590694\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.63748e41i | − | 0.888048i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.90692e41 | + | 5.03494e41i | −0.584325 | + | 1.01208i | 0.410634 | + | 0.911800i | \(0.365307\pi\) |
−0.994959 | + | 0.100281i | \(0.968026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.26752e41 | + | 1.50133e41i | 0.961701 | + | 0.274101i | ||||
\(757\) | −1.10661e42 | −1.98201 | −0.991004 | − | 0.133833i | \(-0.957271\pi\) | ||||
−0.991004 | + | 0.133833i | \(0.957271\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.17814e41 | − | 7.64215e41i | 0.347921 | − | 1.22070i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −5.96030e41 | − | 3.44118e41i | −0.866025 | − | 0.500000i | ||||
\(769\) | 1.40269e42i | 2.00000i | 0.00120402 | + | 0.999999i | \(0.499617\pi\) | ||||
−0.00120402 | + | 0.999999i | \(0.500383\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.40751e41 | + | 1.10981e42i | −0.863453 | + | 1.49554i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.83039e41 | − | 5.09823e41i | −1.12488 | − | 0.649448i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.02277e41 | − | 7.77231e41i | 0.984508 | − | 0.953773i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.88620e41 | − | 4.89287e41i | −0.849737 | − | 0.527206i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.65774e42 | − | 9.57099e41i | 1.68999 | − | 0.975716i | 0.735475 | − | 0.677552i | \(-0.236959\pi\) |
0.954515 | − | 0.298164i | \(-0.0963741\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.03002e42 | − | 1.78404e42i | 0.940554 | − | 1.62909i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.31738e41 | + | 4.80204e41i | 0.719030 | + | 0.415132i | ||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.56166e42i | 1.16782i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.48784e42i | 1.64066i | 0.571889 | + | 0.820331i | \(0.306211\pi\) | ||||
−0.571889 | + | 0.820331i | \(0.693789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.09939e42 | −0.699584 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.78774e42 | − | 1.03215e42i | −1.05946 | − | 0.611680i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.81023e41 | − | 2.31459e42i | −0.332336 | − | 1.32391i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.86909e42 | + | 3.23735e42i | 0.996166 | + | 1.72541i | 0.573844 | + | 0.818965i | \(0.305452\pi\) |
0.422322 | + | 0.906446i | \(0.361215\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.33636e42 | − | 1.92625e42i | 1.60041 | − | 0.923998i | 0.609008 | − | 0.793164i | \(-0.291568\pi\) |
0.991404 | − | 0.130834i | \(-0.0417656\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.83626e41 | − | 3.94692e41i | −0.316668 | − | 0.182828i | ||||
\(832\) | 2.99858e42i | 1.36498i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.55619e42 | + | 2.69541e42i | 0.649448 | + | 1.12488i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.56769e42 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.52621e42 | + | 4.37552e42i | 0.934338 | + | 1.61832i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.76083e42 | − | 6.93040e41i | 0.969908 | − | 0.243472i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.88370e42 | + | 4.99471e42i | −0.979013 | + | 1.69570i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.15806e42i | − | 1.95291i | −0.215717 | − | 0.976456i | \(-0.569209\pi\) | ||
0.215717 | − | 0.976456i | \(-0.430791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.01322e42 | + | 2.31703e42i | 1.14972 | + | 0.663790i | 0.948819 | − | 0.315821i | \(-0.102280\pi\) |
0.200900 | + | 0.979612i | \(0.435613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.99279e42i | − | 1.00000i | ||||||
\(868\) | −1.28398e42 | − | 5.11495e42i | −0.316245 | − | 1.25981i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.89245e42 | − | 3.40201e42i | 1.38049 | − | 0.797025i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.53929e42 | − | 2.62076e42i | −1.02868 | − | 0.593911i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.78547e42 | −1.89433 | ||||||||
\(877\) | −4.23941e42 | + | 7.34287e42i | −0.899106 | + | 1.55730i | −0.0704672 | + | 0.997514i | \(0.522449\pi\) |
−0.828639 | + | 0.559783i | \(0.810884\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00856e43 | −1.93762 | −0.968812 | − | 0.247797i | \(-0.920293\pi\) | ||||
−0.968812 | + | 0.247797i | \(0.920293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.77282e42 | − | 5.95885e42i | −1.00534 | − | 1.03774i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.06033e42 | − | 4.65363e42i | 1.33679 | − | 0.771794i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −3.43152e42 | − | 5.94357e42i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.30244e43 | − | 3.71218e42i | −1.80836 | − | 0.515414i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.05605e42 | + | 1.22214e43i | 0.918874 | + | 1.59154i | 0.801129 | + | 0.598492i | \(0.204233\pi\) |
0.117745 | + | 0.993044i | \(0.462434\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 2.70523e42 | − | 4.68559e42i | 0.325296 | − | 0.563429i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 1.56749e43i | − | 1.76897i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.27677e42 | + | 7.40758e42i | −0.460300 | + | 0.797262i | −0.998976 | − | 0.0452508i | \(-0.985591\pi\) |
0.538676 | + | 0.842513i | \(0.318925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.49917e42 | + | 1.64531e43i | 0.990652 | + | 1.71586i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.39962e43 | −1.37074 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.28958e43 | − | 7.44538e42i | 1.22403 | − | 0.706693i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.84645e42 | − | 6.19960e42i | 0.342996 | − | 0.552832i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.90131e42i | 0.723152i | 0.932343 | + | 0.361576i | \(0.117761\pi\) | ||||
−0.932343 | + | 0.361576i | \(0.882239\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.29918e43 | −1.81101 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 2.46152e43 | − | 1.42116e43i | 1.68843 | − | 0.974814i | ||||
\(949\) | 1.91387e43 | + | 3.31492e43i | 1.29286 | + | 2.23931i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.10238e42 | − | 1.05696e43i | 0.343566 | − | 0.595073i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.74076e43 | − | 1.00503e43i | −0.936747 | − | 0.540831i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.22345e43 | −1.65820 | −0.829099 | − | 0.559101i | \(-0.811146\pi\) | ||||
−0.829099 | + | 0.559101i | \(0.811146\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 2.09489e43i | 1.00000i | ||||||||
\(973\) | 2.36750e43 | − | 2.29359e43i | 1.11341 | − | 1.07865i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.49508e43 | + | 2.58956e43i | −0.682492 | + | 1.18211i | ||||
\(976\) | 2.65362e43 | − | 1.53207e43i | 1.19348 | − | 0.689058i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.03928e43 | 1.26932 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.35729e43 | −0.888048 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.76601e43 | + | 4.79086e43i | 0.997207 | + | 1.72721i | 0.563287 | + | 0.826261i | \(0.309537\pi\) |
0.433920 | + | 0.900951i | \(0.357130\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.08601e43i | 1.43065i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.25437e43 | − | 2.45626e43i | 1.40526 | − | 0.811326i | 0.410331 | − | 0.911936i | \(-0.365413\pi\) |
0.994926 | + | 0.100611i | \(0.0320797\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.69987e43 | + | 2.13612e43i | 1.18710 | + | 0.685372i |
(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 | 21.30.g.a.5.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.30.g.a.5.1 | ✓ | 2 | |
7.3 | odd | 6 | inner | 21.30.g.a.17.1 | yes | 2 | |
21.17 | even | 6 | inner | 21.30.g.a.17.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.g.a.5.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.30.g.a.5.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.30.g.a.17.1 | yes | 2 | 7.3 | odd | 6 | inner | |
21.30.g.a.17.1 | yes | 2 | 21.17 | even | 6 | inner |