Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,27,Mod(2,21)]
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, 2]))
N = Newforms(chi, 27, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 27);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 27 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.h (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: | \(89.9415133532\) |
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 | 11.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.11 |
Dual form | 21.27.h.a.2.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | 797162. | − | 1.38072e6i | 0.500000 | − | 0.866025i | ||||
\(4\) | −3.35544e7 | + | 5.81180e7i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.21712e10 | − | 9.43182e10i | −0.228831 | − | 0.973466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.27093e12 | − | 2.20132e12i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 5.34966e13 | + | 9.26588e13i | 0.500000 | + | 0.866025i | ||||
\(13\) | 6.05583e14 | 1.99945 | 0.999724 | − | 0.0234733i | \(-0.00747246\pi\) | ||||
0.999724 | + | 0.0234733i | \(0.00747246\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.25180e15 | − | 3.90023e15i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.63184e16 | + | 4.55848e16i | 0.625840 | + | 1.08399i | 0.988378 | + | 0.152017i | \(0.0485769\pi\) |
−0.362538 | + | 0.931969i | \(0.618090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.47901e17 | − | 4.45745e16i | −0.957462 | − | 0.288560i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.45058e17 | + | 1.29048e18i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.05256e18 | −1.00000 | ||||||||
\(28\) | 6.22552e18 | + | 1.87625e18i | 0.957462 | + | 0.288560i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.40525e18 | − | 1.62904e19i | 0.385184 | − | 0.667158i | −0.606611 | − | 0.794999i | \(-0.707471\pi\) |
0.991795 | + | 0.127841i | \(0.0408046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.70582e20 | 1.00000 | ||||||||
\(37\) | −1.31193e20 | − | 2.27232e20i | −0.538625 | − | 0.932926i | −0.998978 | − | 0.0451904i | \(-0.985611\pi\) |
0.460353 | − | 0.887736i | \(-0.347723\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82748e20 | − | 8.36144e20i | 0.999724 | − | 1.73157i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.52622e21 | 1.47022 | 0.735108 | − | 0.677950i | \(-0.237132\pi\) | ||||
0.735108 | + | 0.677950i | \(0.237132\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −7.18019e21 | −1.00000 | ||||||||
\(49\) | −8.40435e21 | + | 4.18230e21i | −0.895273 | + | 0.445519i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.03200e22 | + | 3.51953e22i | −0.999724 | + | 1.73157i | ||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.39201e22 | 1.25168 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.31928e23 | − | 2.28506e23i | −0.814795 | − | 1.41127i | −0.909475 | − | 0.415758i | \(-0.863516\pi\) |
0.0946801 | − | 0.995508i | \(-0.469817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.79446e23 | + | 1.68678e23i | −0.728631 | + | 0.684907i | ||||
\(64\) | 3.02231e23 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.22507e23 | − | 9.05008e23i | 0.953058 | − | 1.65075i | 0.214308 | − | 0.976766i | \(-0.431250\pi\) |
0.738750 | − | 0.673979i | \(-0.235416\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.66365e22 | + | 6.34563e22i | −0.0219138 | + | 0.0379558i | −0.876774 | − | 0.480902i | \(-0.840309\pi\) |
0.854861 | + | 0.518858i | \(0.173643\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.18786e24 | + | 2.05744e24i | 0.500000 | + | 0.866025i | ||||
\(76\) | −3.53240e24 | −1.25168 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.67351e24 | − | 6.36270e24i | −0.786917 | − | 1.36298i | −0.927847 | − | 0.372960i | \(-0.878343\pi\) |
0.140931 | − | 0.990019i | \(-0.454990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.23054e24 | + | 5.59546e24i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 7.55333e24 | − | 7.10006e24i | 0.728631 | − | 0.684907i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.34265e25 | − | 5.71175e25i | −0.457536 | − | 1.94640i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.49950e25 | − | 2.59721e25i | −0.385184 | − | 0.667158i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.79863e25 | 0.267244 | 0.133622 | − | 0.991032i | \(-0.457339\pi\) | ||||
0.133622 | + | 0.991032i | \(0.457339\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.00000e25 | − | 8.66025e25i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.41521e26 | − | 2.45122e26i | −0.963690 | − | 1.66916i | −0.713094 | − | 0.701069i | \(-0.752707\pi\) |
−0.250597 | − | 0.968092i | \(-0.580627\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 1.35981e26 | − | 2.35526e26i | 0.500000 | − | 0.866025i | ||||
\(109\) | 2.82406e26 | − | 4.89141e26i | 0.921148 | − | 1.59547i | 0.123506 | − | 0.992344i | \(-0.460586\pi\) |
0.797642 | − | 0.603131i | \(-0.206080\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.18327e26 | −1.07725 | ||||||||
\(112\) | −3.17938e26 | + | 2.98859e26i | −0.728631 | + | 0.684907i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.69656e26 | − | 1.33308e27i | −0.999724 | − | 1.73157i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.95909e26 | − | 1.03214e27i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.31176e26 | + | 1.09323e27i | 0.385184 | + | 0.667158i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.63575e27 | −1.17884 | −0.589422 | − | 0.807825i | \(-0.700645\pi\) | ||||
−0.589422 | + | 0.807825i | \(0.700645\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.01380e27 | − | 3.48801e27i | 0.735108 | − | 1.27324i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.71597e27 | − | 3.49298e27i | 0.912012 | − | 0.857283i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.50809e26 | −0.0346857 | −0.0173429 | − | 0.999850i | \(-0.505521\pi\) | ||||
−0.0173429 | + | 0.999850i | \(0.505521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.72377e27 | + | 9.91387e27i | −0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.25030e26 | + | 1.49381e28i | −0.0618059 | + | 0.998088i | ||||
\(148\) | 1.76084e28 | 1.07725 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.45342e27 | + | 1.63738e28i | −0.445542 | + | 0.771702i | −0.998090 | − | 0.0617797i | \(-0.980322\pi\) |
0.552548 | + | 0.833481i | \(0.313656\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.23966e28 | + | 5.61126e28i | 0.999724 | + | 1.73157i | ||||
\(157\) | −3.36817e28 | + | 5.83384e28i | −0.956530 | + | 1.65676i | −0.225701 | + | 0.974197i | \(0.572467\pi\) |
−0.730828 | + | 0.682561i | \(0.760866\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.39778e28 | − | 4.15308e28i | −0.418187 | − | 0.724322i | 0.577570 | − | 0.816341i | \(-0.304001\pi\) |
−0.995757 | + | 0.0920196i | \(0.970668\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.74998e29 | 2.99780 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.68979e28 | − | 1.15871e29i | 0.625840 | − | 1.08399i | ||||
\(172\) | −8.47658e28 | + | 1.46819e29i | −0.735108 | + | 1.27324i | ||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.38234e29 | + | 4.16610e28i | 0.957462 | + | 0.288560i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.79314e29 | −1.69503 | −0.847515 | − | 0.530771i | \(-0.821902\pi\) | ||||
−0.847515 | + | 0.530771i | \(0.821902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.20671e29 | −1.62959 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.98501e28 | + | 3.82230e29i | 0.228831 | + | 0.973466i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 2.40927e29 | − | 4.17298e29i | 0.500000 | − | 0.866025i | ||||
\(193\) | −3.49452e29 | + | 6.05268e29i | −0.677864 | + | 1.17409i | 0.297759 | + | 0.954641i | \(0.403761\pi\) |
−0.975623 | + | 0.219453i | \(0.929573\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.89367e28 | − | 6.28779e29i | 0.0618059 | − | 0.998088i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.66194e29 | − | 1.32709e30i | 0.998271 | − | 1.72906i | 0.448233 | − | 0.893917i | \(-0.352053\pi\) |
0.550038 | − | 0.835140i | \(-0.314613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.33045e29 | − | 1.44288e30i | −0.953058 | − | 1.65075i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.36365e30 | − | 2.36192e30i | −0.999724 | − | 1.73157i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.81295e30 | 1.71195 | 0.855974 | − | 0.517019i | \(-0.172958\pi\) | ||||
0.855974 | + | 0.517019i | \(0.172958\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.74500e30 | − | 5.25909e29i | −0.737598 | − | 0.222297i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.84104e28 | + | 1.01170e29i | 0.0219138 | + | 0.0379558i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.63067e30 | −1.96605 | −0.983024 | − | 0.183479i | \(-0.941264\pi\) | ||||
−0.983024 | + | 0.183479i | \(0.941264\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.78768e30 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | −2.81589e30 | + | 4.87727e30i | −0.625840 | + | 1.08399i | ||||
\(229\) | 4.65335e30 | + | 8.05983e30i | 0.977021 | + | 1.69225i | 0.673097 | + | 0.739554i | \(0.264964\pi\) |
0.303925 | + | 0.952696i | \(0.401703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.17135e31 | −1.57383 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.50697e30 | − | 1.47345e31i | 0.919503 | − | 1.59263i | 0.119332 | − | 0.992854i | \(-0.461925\pi\) |
0.800171 | − | 0.599772i | \(-0.204742\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.15053e30 | + | 8.92097e30i | 0.500000 | + | 0.866025i | ||||
\(244\) | 1.77070e31 | 1.62959 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.59380e31 | + | 2.76054e31i | 1.25133 | + | 2.16737i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −3.78200e30 | − | 1.60890e31i | −0.228831 | − | 0.973466i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.01412e31 | + | 1.75651e31i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.85234e31 | + | 1.74119e31i | −0.784918 | + | 0.737816i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.50648e31 | + | 6.07341e31i | 0.953058 | + | 1.65075i | ||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.11865e31 | + | 1.93756e31i | 0.263083 | + | 0.455673i | 0.967060 | − | 0.254550i | \(-0.0819273\pi\) |
−0.703977 | + | 0.710223i | \(0.748594\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.95666e31 | − | 2.69936e31i | −1.91440 | − | 0.576960i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.44995e31 | − | 9.43960e31i | 0.964175 | − | 1.67000i | 0.252359 | − | 0.967634i | \(-0.418793\pi\) |
0.711816 | − | 0.702366i | \(-0.247873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.78138e31 | −0.770368 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.01816e31 | − | 8.69171e31i | 0.671925 | − | 1.16381i | −0.305432 | − | 0.952214i | \(-0.598801\pi\) |
0.977357 | − | 0.211595i | \(-0.0678657\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.90503e31 | − | 8.49577e31i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.43380e31 | − | 2.48341e31i | 0.133622 | − | 0.231440i | ||||
\(292\) | −2.45864e30 | − | 4.25848e30i | −0.0219138 | − | 0.0379558i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.59432e32 | −1.00000 | ||||||||
\(301\) | −5.60093e31 | − | 2.38268e32i | −0.336431 | − | 1.43121i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.18528e32 | − | 2.05296e32i | 0.625840 | − | 1.08399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.21072e32 | 0.562658 | 0.281329 | − | 0.959611i | \(-0.409225\pi\) | ||||
0.281329 | + | 0.959611i | \(0.409225\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.51261e32 | −1.92738 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.13363e32 | + | 3.69556e32i | 0.770981 | + | 1.33538i | 0.937026 | + | 0.349260i | \(0.113567\pi\) |
−0.166045 | + | 0.986118i | \(0.553100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.93050e32 | 1.57383 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.16798e32 | − | 3.75505e32i | −0.500000 | − | 0.866025i | ||||
\(325\) | −4.51195e32 | + | 7.81492e32i | −0.999724 | + | 1.73157i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.50246e32 | − | 7.79849e32i | −0.921148 | − | 1.59547i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.32416e32 | + | 7.48967e32i | 0.755333 | + | 1.30827i | 0.945209 | + | 0.326467i | \(0.105858\pi\) |
−0.189876 | + | 0.981808i | \(0.560809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.33474e32 | + | 5.77594e32i | −0.538625 | + | 0.932926i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.59194e32 | + | 6.77223e32i | 0.228831 | + | 0.973466i | ||||
\(337\) | 1.32618e33 | 1.83407 | 0.917033 | − | 0.398811i | \(-0.130577\pi\) | ||||
0.917033 | + | 0.398811i | \(0.130577\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.80801e32 | + | 6.99957e32i | 0.638563 | + | 0.769569i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.92956e33 | 1.69327 | 0.846636 | − | 0.532172i | \(-0.178624\pi\) | ||||
0.846636 | + | 0.532172i | \(0.178624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.45416e33 | −1.99945 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.01092e32 | + | 8.67917e32i | −0.283350 | + | 0.490777i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.90014e33 | −1.00000 | ||||||||
\(364\) | 3.77007e33 | + | 1.13622e33i | 1.91440 | + | 0.576960i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.21663e32 | − | 3.83931e32i | 0.101166 | − | 0.175224i | −0.810999 | − | 0.585047i | \(-0.801076\pi\) |
0.912165 | + | 0.409823i | \(0.134409\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.01260e33 | 0.770368 | ||||||||
\(373\) | −2.37405e33 | − | 4.11197e33i | −0.877555 | − | 1.51997i | −0.854016 | − | 0.520246i | \(-0.825840\pi\) |
−0.0235385 | − | 0.999723i | \(-0.507493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.46428e33 | −0.740253 | −0.370127 | − | 0.928981i | \(-0.620686\pi\) | ||||
−0.370127 | + | 0.928981i | \(0.620686\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.10112e33 | + | 3.63925e33i | −0.589422 | + | 1.02091i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.21065e33 | − | 5.56102e33i | −0.735108 | − | 1.27324i | ||||
\(388\) | −6.03519e32 | + | 1.04533e33i | −0.133622 | + | 0.231440i | ||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.61740e33 | − | 9.72961e33i | −0.923121 | − | 1.59889i | −0.794556 | − | 0.607190i | \(-0.792296\pi\) |
−0.128564 | − | 0.991701i | \(-0.541037\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.86061e33 | − | 7.91519e33i | −0.286423 | − | 1.21847i | ||||
\(400\) | 6.71089e33 | 1.00000 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.69566e33 | − | 9.86518e33i | 0.770156 | − | 1.33395i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.69218e33 | + | 2.93095e33i | −0.188818 | + | 0.327043i | −0.944857 | − | 0.327485i | \(-0.893799\pi\) |
0.756038 | + | 0.654527i | \(0.227132\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.89946e34 | 1.92738 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.99935e32 | + | 3.46298e32i | −0.0173429 | + | 0.0300387i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.60701e34 | −1.99745 | −0.998724 | − | 0.0505019i | \(-0.983918\pi\) | ||||
−0.998724 | + | 0.0505019i | \(0.983918\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.86272e34 | + | 1.75094e34i | −1.18737 | + | 1.11612i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 9.12554e33 | + | 1.58059e34i | 0.500000 | + | 0.866025i | ||||
\(433\) | −2.49829e34 | −1.32831 | −0.664155 | − | 0.747595i | \(-0.731209\pi\) | ||||
−0.664155 | + | 0.747595i | \(0.731209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.89519e34 | + | 3.28257e34i | 0.921148 | + | 1.59547i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.21438e34 | + | 3.83542e34i | 0.984495 | + | 1.70520i | 0.644159 | + | 0.764892i | \(0.277208\pi\) |
0.340336 | + | 0.940304i | \(0.389459\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.98879e34 | + | 1.31853e34i | 0.833467 | + | 0.552570i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 1.40367e34 | − | 2.43123e34i | 0.538625 | − | 0.932926i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.70084e33 | − | 2.85059e34i | −0.228831 | − | 0.973466i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.50718e34 | + | 2.61051e34i | 0.445542 | + | 0.771702i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.40107e34 | − | 2.42673e34i | −0.369446 | − | 0.639899i | 0.620033 | − | 0.784576i | \(-0.287119\pi\) |
−0.989479 | + | 0.144677i | \(0.953786\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.48946e34 | 0.999174 | 0.499587 | − | 0.866264i | \(-0.333485\pi\) | ||||
0.499587 | + | 0.866264i | \(0.333485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 1.03301e35 | 1.99945 | ||||||||
\(469\) | −9.69433e34 | − | 2.92167e34i | −1.82503 | − | 0.550028i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.36995e34 | + | 9.30103e34i | 0.956530 | + | 1.65676i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.84350e34 | −1.25168 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.94480e34 | − | 1.37608e35i | −1.07695 | − | 1.86534i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.99815e34 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.65560e34 | + | 1.49919e35i | −0.998667 | + | 1.72974i | −0.454632 | + | 0.890679i | \(0.650229\pi\) |
−0.544035 | + | 0.839063i | \(0.683104\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.64568e34 | −0.836375 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.47149e34 | −0.770368 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.73884e34 | − | 1.34041e35i | −0.650682 | − | 1.12701i | −0.982958 | − | 0.183832i | \(-0.941150\pi\) |
0.332276 | − | 0.943182i | \(-0.392183\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.19218e35 | − | 3.79696e35i | 1.49890 | − | 2.59617i | ||||
\(508\) | 8.84412e34 | − | 1.53185e35i | 0.589422 | − | 1.02091i | ||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.79736e33 | + | 2.04859e33i | 0.0419632 | + | 0.0126469i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.06657e35 | − | 1.84735e35i | −0.625840 | − | 1.08399i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.35144e35 | + | 2.34076e35i | 0.735108 | + | 1.27324i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.72383e35 | − | 2.98576e35i | −0.786995 | − | 1.36312i | −0.927800 | − | 0.373078i | \(-0.878302\pi\) |
0.140805 | − | 0.990037i | \(-0.455031\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.67718e35 | − | 1.57653e35i | 0.728631 | − | 0.684907i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.27026e35 | + | 2.20016e35i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.83176e34 | + | 3.33169e35i | 0.286423 | + | 1.21847i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.47223e34 | + | 1.29423e35i | 0.219728 | + | 0.380581i | 0.954725 | − | 0.297490i | \(-0.0961496\pi\) |
−0.734997 | + | 0.678071i | \(0.762816\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.02375e35 | + | 5.23728e35i | −0.847515 | + | 1.46794i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.53378e34 | −0.0645557 | −0.0322778 | − | 0.999479i | \(-0.510276\pi\) | ||||
−0.0322778 | + | 0.999479i | \(0.510276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.35343e35 | + | 5.80831e35i | −0.814795 | + | 1.41127i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.18672e35 | + | 4.87547e35i | −1.14674 | + | 1.07793i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.41575e33 | − | 1.45765e34i | 0.0173429 | − | 0.0300387i | ||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.52984e36 | 2.93962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.99379e35 | + | 1.80641e35i | 0.957462 | + | 0.288560i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.02488e35 | − | 1.04354e36i | 0.878373 | − | 1.52139i | 0.0252467 | − | 0.999681i | \(-0.491963\pi\) |
0.853126 | − | 0.521705i | \(-0.174704\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.84116e35 | − | 6.65308e35i | −0.500000 | − | 0.866025i | ||||
\(577\) | −5.63846e35 | + | 9.76610e35i | −0.717587 | + | 1.24290i | 0.244366 | + | 0.969683i | \(0.421420\pi\) |
−0.961953 | + | 0.273215i | \(0.911913\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.57139e35 | + | 9.64993e35i | 0.677864 | + | 1.17409i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | −8.37131e35 | − | 5.54999e35i | −0.833467 | − | 0.552570i | ||||
\(589\) | 9.90125e35 | 0.964254 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.90839e35 | + | 1.02336e36i | −0.538625 | + | 0.932926i | ||||
\(593\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.22156e36 | − | 2.11580e36i | −0.998271 | − | 1.72906i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.61995e36 | 1.21376 | 0.606882 | − | 0.794792i | \(-0.292420\pi\) | ||||
0.606882 | + | 0.794792i | \(0.292420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.65628e36 | −1.90612 | ||||||||
\(604\) | −6.34408e35 | − | 1.09883e36i | −0.445542 | − | 0.771702i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.40186e36 | + | 2.42809e36i | 0.923106 | + | 1.59887i | 0.794580 | + | 0.607160i | \(0.207691\pi\) |
0.128526 | + | 0.991706i | \(0.458975\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.37994e35 | − | 1.62465e36i | 0.543518 | − | 0.941401i | −0.455181 | − | 0.890399i | \(-0.650425\pi\) |
0.998699 | − | 0.0510016i | \(-0.0162414\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.20032e35 | − | 5.54312e35i | 0.163386 | − | 0.282993i | −0.772695 | − | 0.634778i | \(-0.781092\pi\) |
0.936081 | + | 0.351784i | \(0.114425\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.34820e36 | −1.99945 | ||||||||
\(625\) | −1.11022e36 | − | 1.92296e36i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.26034e36 | − | 3.91502e36i | −0.956530 | − | 1.65676i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.33927e36 | 1.72598 | 0.862988 | − | 0.505224i | \(-0.168590\pi\) | ||||
0.862988 | + | 0.505224i | \(0.168590\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.24238e36 | − | 3.88391e36i | 0.855974 | − | 1.48259i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.08954e36 | + | 2.53273e36i | −1.79005 | + | 0.890792i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.75982e36 | 1.79335 | 0.896677 | − | 0.442685i | \(-0.145974\pi\) | ||||
0.896677 | + | 0.442685i | \(0.145974\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.11718e36 | + | 1.99013e36i | −0.561314 | + | 0.527630i | ||||
\(652\) | 3.21825e36 | 0.836375 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.86250e35 | 0.0438275 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.06329e35 | − | 1.22340e36i | 0.153599 | − | 0.266041i | −0.778949 | − | 0.627087i | \(-0.784247\pi\) |
0.932548 | + | 0.361046i | \(0.117580\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.28571e36 | + | 9.15512e36i | −0.983024 | + | 1.70265i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.56032e36 | 0.440656 | 0.220328 | − | 0.975426i | \(-0.429287\pi\) | ||||
0.220328 | + | 0.975426i | \(0.429287\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.01939e36 | − | 5.22973e36i | 0.500000 | − | 0.866025i | ||||
\(676\) | −9.22740e36 | + | 1.59823e37i | −1.49890 | + | 2.59617i | ||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.98777e35 | − | 1.69643e36i | −0.0611538 | − | 0.260153i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | 4.48944e36 | + | 7.77594e36i | 0.625840 | + | 1.08399i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.48379e37 | 1.95404 | ||||||||
\(688\) | −5.68854e36 | − | 9.85284e36i | −0.735108 | − | 1.27324i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.99662e36 | + | 1.38506e37i | 0.976545 | + | 1.69142i | 0.674741 | + | 0.738055i | \(0.264256\pi\) |
0.301804 | + | 0.953370i | \(0.402411\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.05963e36 | + | 6.63599e36i | −0.728631 | + | 0.684907i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.90556e36 | − | 1.19608e37i | 0.674186 | − | 1.16772i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.80625e35 | + | 1.52529e36i | 0.0769821 | + | 0.133337i | 0.901946 | − | 0.431848i | \(-0.142138\pi\) |
−0.824964 | + | 0.565185i | \(0.808805\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.33756e36 | + | 1.61731e37i | −0.786917 | + | 1.36298i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.99817e37 | + | 1.87827e37i | −1.40435 | + | 1.32008i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.35629e37 | − | 2.34916e37i | −0.919503 | − | 1.59263i | ||||
\(724\) | 1.27277e37 | − | 2.20450e37i | 0.847515 | − | 1.46794i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.41492e36 | 0.404803 | 0.202402 | − | 0.979303i | \(-0.435125\pi\) | ||||
0.202402 | + | 0.979303i | \(0.435125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.64232e37 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.41154e37 | − | 2.44485e37i | 0.814795 | − | 1.41127i | ||||
\(733\) | −1.71737e37 | − | 2.97457e37i | −0.973893 | − | 1.68683i | −0.683540 | − | 0.729913i | \(-0.739560\pi\) |
−0.290354 | − | 0.956919i | \(-0.593773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.77714e37 | + | 3.07809e37i | −0.906448 | + | 1.57001i | −0.0874864 | + | 0.996166i | \(0.527883\pi\) |
−0.818962 | + | 0.573848i | \(0.805450\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.08206e37 | 2.50267 | ||||||||
\(742\) | 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 | ||||||||
\(751\) | −2.41685e37 | − | 4.18611e37i | −0.999841 | − | 1.73178i | −0.515368 | − | 0.856969i | \(-0.672345\pi\) |
−0.484473 | − | 0.874806i | \(-0.660989\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.52293e37 | − | 7.60359e36i | −0.957462 | − | 0.288560i | ||||
\(757\) | −5.22180e37 | −1.94793 | −0.973966 | − | 0.226692i | \(-0.927209\pi\) | ||||
−0.973966 | + | 0.226692i | \(0.927209\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.23962e37 | − | 1.57912e37i | −1.76393 | − | 0.531612i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.61684e37 | + | 2.80044e37i | 0.500000 | + | 0.866025i | ||||
\(769\) | 6.53834e37 | 1.98804 | 0.994021 | − | 0.109192i | \(-0.0348264\pi\) | ||||
0.994021 | + | 0.109192i | \(0.0348264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.34513e37 | − | 4.06189e37i | −0.677864 | − | 1.17409i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.40149e37 | + | 2.42745e37i | 0.385184 | + | 0.667158i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.27481e36 | + | 3.94558e37i | 0.246508 | + | 1.04867i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.52369e37 | + | 2.33612e37i | 0.833467 | + | 0.552570i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.57646e36 | − | 2.73052e36i | 0.0354824 | − | 0.0614573i | −0.847739 | − | 0.530414i | \(-0.822037\pi\) |
0.883221 | + | 0.468957i | \(0.155370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.98932e37 | − | 1.38379e38i | −1.62914 | − | 2.82175i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.14184e37 | + | 8.90592e37i | 0.998271 | + | 1.72906i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.11809e38 | 1.90612 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.65605e36 | 0.116609 | 0.0583047 | − | 0.998299i | \(-0.481431\pi\) | ||||
0.0583047 | + | 0.998299i | \(0.481431\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.56697e37 | 0.526166 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.64861e37 | + | 1.15157e38i | 0.920119 | + | 1.59369i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.08670e38 | + | 1.02149e38i | −1.45686 | + | 1.36944i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.72019e37 | + | 4.71150e37i | −0.342295 | + | 0.592873i | −0.984859 | − | 0.173360i | \(-0.944538\pi\) |
0.642563 | + | 0.766233i | \(0.277871\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.73078e37 | + | 1.51221e38i | −0.999641 | + | 1.73143i | −0.476610 | + | 0.879115i | \(0.658135\pi\) |
−0.523031 | + | 0.852314i | \(0.675199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.68899e37 | − | 1.50498e38i | −0.964175 | − | 1.67000i | ||||
\(832\) | 1.83026e38 | 1.99945 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.81153e37 | + | 6.60176e37i | −0.385184 | + | 0.667158i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.05281e38 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.43870e37 | + | 1.63483e38i | −0.855974 | + | 1.48259i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.41379e37 | + | 7.90889e37i | −0.728631 | + | 0.684907i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.00057e37 | − | 1.38574e38i | −0.671925 | − | 1.16381i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.37475e38 | 1.08614 | 0.543072 | − | 0.839686i | \(-0.317261\pi\) | ||||
0.543072 | + | 0.839686i | \(0.317261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.61698e36 | − | 1.31930e37i | −0.0549379 | − | 0.0951552i | 0.837249 | − | 0.546822i | \(-0.184163\pi\) |
−0.892186 | + | 0.451667i | \(0.850829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.56404e38 | −1.00000 | ||||||||
\(868\) | 8.91173e37 | − | 8.37695e37i | 0.561314 | − | 0.527630i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.16421e38 | − | 5.48058e38i | 1.90559 | − | 3.30058i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.28593e37 | − | 3.95935e37i | −0.133622 | − | 0.231440i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.83972e36 | −0.0438275 | ||||||||
\(877\) | −1.78298e38 | − | 3.08821e38i | −0.982091 | − | 1.70103i | −0.654212 | − | 0.756311i | \(-0.727000\pi\) |
−0.327878 | − | 0.944720i | \(-0.606334\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.11158e37 | −0.308080 | −0.154040 | − | 0.988065i | \(-0.549229\pi\) | ||||
−0.154040 | + | 0.988065i | \(0.549229\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.84379e37 | + | 2.48600e38i | 0.269756 | + | 1.14757i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.22488e38 | − | 3.85361e38i | 0.983024 | − | 1.70265i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.27093e38 | + | 2.20132e38i | −0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.73631e38 | − | 1.12605e38i | −1.40768 | − | 0.424245i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.48658e38 | + | 2.57483e38i | −0.528802 | + | 0.915911i | 0.470634 | + | 0.882328i | \(0.344025\pi\) |
−0.999436 | + | 0.0335829i | \(0.989308\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −1.88971e38 | − | 3.27308e38i | −0.625840 | − | 1.08399i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.24561e38 | −1.95404 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.03304e38 | + | 5.25338e38i | 0.909445 | + | 1.57520i | 0.814837 | + | 0.579690i | \(0.196826\pi\) |
0.0946072 | + | 0.995515i | \(0.469840\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.65139e37 | − | 1.67167e38i | 0.281329 | − | 0.487276i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.90984e38 | 1.07725 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.59728e38 | + | 6.23067e38i | −0.963690 | + | 1.66916i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.11839e38 | − | 2.73040e38i | −1.04323 | − | 0.691640i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.52639e38 | 1.98678 | 0.993392 | − | 0.114771i | \(-0.0366135\pi\) | ||||
0.993392 | + | 0.114771i | \(0.0366135\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.80341e38 | 1.54196 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 3.93040e38 | − | 6.80766e38i | 0.786917 | − | 1.36298i | ||||
\(949\) | −2.21865e37 | + | 3.84281e37i | −0.0438155 | + | 0.0758906i | ||||
\(950\) | 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 | ||||||||
\(961\) | 1.21191e38 | + | 2.09909e38i | 0.203267 | + | 0.352068i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.70893e38 | + | 9.88816e38i | 0.919503 | + | 1.59263i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.90224e38 | 0.758316 | 0.379158 | − | 0.925332i | \(-0.376214\pi\) | ||||
0.379158 | + | 0.925332i | \(0.376214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | −6.91292e38 | −1.00000 | ||||||||
\(973\) | 5.56074e36 | + | 2.36558e37i | 0.00793717 | + | 0.0337654i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.19350e38 | + | 1.24595e39i | 0.999724 | + | 1.73157i | ||||
\(976\) | −5.94150e38 | + | 1.02910e39i | −0.814795 | + | 1.41127i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.43568e39 | −1.84230 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.13916e39 | −2.50267 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.03092e38 | − | 1.04459e39i | 0.678306 | − | 1.17486i | −0.297184 | − | 0.954820i | \(-0.596048\pi\) |
0.975491 | − | 0.220041i | \(-0.0706190\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.37882e39 | 1.51067 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.34984e38 | + | 7.53414e38i | −0.452310 | + | 0.783423i | −0.998529 | − | 0.0542188i | \(-0.982733\pi\) |
0.546219 | + | 0.837642i | \(0.316066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.31665e38 | + | 9.20871e38i | 0.538625 | + | 0.932926i |
(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 | 21.27.h.a.11.1 | yes | 2 | |
3.2 | odd | 2 | CM | 21.27.h.a.11.1 | yes | 2 | |
7.2 | even | 3 | inner | 21.27.h.a.2.1 | ✓ | 2 | |
21.2 | odd | 6 | inner | 21.27.h.a.2.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.27.h.a.2.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
21.27.h.a.2.1 | ✓ | 2 | 21.2 | odd | 6 | inner | |
21.27.h.a.11.1 | yes | 2 | 1.1 | even | 1 | trivial | |
21.27.h.a.11.1 | yes | 2 | 3.2 | odd | 2 | CM |