Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,42,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, 42, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.5");
S:= CuspForms(chi, 42);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 42 \) |
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: | \(223.590507958\) |
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 | 21.42.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 | \(0.666667\pi\) | |||||||
\(3\) | 5.23018e9 | − | 3.01964e9i | 0.866025 | − | 0.500000i | ||||
\(4\) | −1.09951e12 | − | 1.90441e12i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.10745e17 | − | 1.24129e16i | 0.998270 | − | 0.0587980i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.82365e19 | − | 3.15865e19i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −1.15013e22 | − | 6.64027e21i | −0.866025 | − | 0.500000i | ||||
\(13\) | − | 6.81363e22i | − | 0.994352i | −0.867650 | − | 0.497176i | \(-0.834370\pi\) | ||
0.867650 | − | 0.497176i | \(-0.165630\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.41785e24 | + | 4.18784e24i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.45919e26 | + | 1.41982e26i | 1.50087 | + | 0.866529i | 0.999999 | + | 0.00100876i | \(0.000321098\pi\) |
0.500873 | + | 0.865521i | \(0.333012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.06475e27 | − | 7.01297e26i | 0.835128 | − | 0.550055i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.27374e28 | + | 3.93823e28i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.20271e29i | − | 1.00000i | ||||||
\(28\) | −2.55356e29 | − | 3.87697e29i | −0.550055 | − | 0.835128i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.95816e30 | − | 3.43994e30i | 1.59293 | − | 0.919680i | 0.600131 | − | 0.799902i | \(-0.295115\pi\) |
0.992801 | − | 0.119778i | \(-0.0382183\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.02050e31 | −1.00000 | ||||||||
\(37\) | 3.23924e31 | − | 5.61053e31i | 0.230307 | − | 0.398904i | −0.727591 | − | 0.686011i | \(-0.759360\pi\) |
0.957899 | + | 0.287107i | \(0.0926935\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.05747e32 | − | 3.56365e32i | −0.497176 | − | 0.861134i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.97879e33 | 0.646095 | 0.323048 | − | 0.946383i | \(-0.395293\pi\) | ||||
0.323048 | + | 0.946383i | \(0.395293\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 2.92042e34i | 1.00000i | ||||||||
\(49\) | 4.42595e34 | − | 5.23191e33i | 0.993086 | − | 0.117392i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.29760e35 | + | 7.49167e34i | −0.861134 | + | 0.497176i | ||||
\(53\) | 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 | ||||||||
\(57\) | 1.71494e36 | 1.73306 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.89124e34 | + | 3.40131e34i | 0.0148233 | + | 0.00855824i | 0.507393 | − | 0.861715i | \(-0.330609\pi\) |
−0.492570 | + | 0.870273i | \(0.663942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.45118e36 | − | 6.88308e36i | 0.448214 | − | 0.893926i | ||||
\(64\) | 1.06338e37 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.54133e37 | + | 4.40171e37i | 0.934389 | + | 1.61841i | 0.775719 | + | 0.631078i | \(0.217387\pi\) |
0.158670 | + | 0.987332i | \(0.449279\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.06634e36 | − | 4.07976e36i | 0.0447792 | − | 0.0258533i | −0.477443 | − | 0.878663i | \(-0.658436\pi\) |
0.522222 | + | 0.852809i | \(0.325103\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.37841e38 | + | 1.37318e38i | 0.866025 | + | 0.500000i | ||||
\(76\) | − | 6.24442e38i | − | 1.73306i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.37702e38 | − | 1.10453e39i | 0.800317 | − | 1.38619i | −0.119090 | − | 0.992883i | \(-0.537998\pi\) |
0.919407 | − | 0.393306i | \(-0.128669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.65140e38 | − | 1.15206e39i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −2.50626e39 | − | 1.25664e39i | −0.893926 | − | 0.448214i | ||||
\(85\) | 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 | ||||||||
\(91\) | −8.45767e38 | − | 1.43594e40i | −0.0584659 | − | 0.992632i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.07748e40 | − | 3.59830e40i | 0.919680 | − | 1.59293i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.81679e40i | 1.08608i | 0.839706 | + | 0.543041i | \(0.182727\pi\) | ||||
−0.839706 | + | 0.543041i | \(0.817273\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000e40 | − | 8.66025e40i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.34402e40 | + | 5.39477e40i | 0.509766 | + | 0.294314i | 0.732737 | − | 0.680511i | \(-0.238242\pi\) |
−0.222971 | + | 0.974825i | \(0.571576\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | −4.19486e41 | + | 2.42190e41i | −0.866025 | + | 0.500000i | ||||
\(109\) | 5.64242e41 | + | 9.77296e41i | 0.964322 | + | 1.67025i | 0.711426 | + | 0.702761i | \(0.248050\pi\) |
0.252896 | + | 0.967493i | \(0.418617\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.91254e41i | − | 0.460615i | ||||||
\(112\) | −4.57568e41 | + | 9.12580e41i | −0.448214 | + | 0.893926i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.15219e42 | − | 1.24257e42i | −0.861134 | − | 0.497176i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.48926e42 | + | 4.31152e42i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.31021e43 | − | 7.56452e42i | −1.59293 | − | 0.919680i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.28476e42 | 0.542549 | 0.271274 | − | 0.962502i | \(-0.412555\pi\) | ||||
0.271274 | + | 0.962502i | \(0.412555\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.03494e43 | − | 5.97524e42i | 0.559535 | − | 0.323048i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.35887e43 | + | 2.68694e43i | 1.54923 | + | 0.776782i | ||||
\(134\) | 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 | ||||||||
\(139\) | − | 1.67231e44i | − | 1.95665i | −0.207086 | − | 0.978323i | \(-0.566398\pi\) | ||
0.207086 | − | 0.978323i | \(-0.433602\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.81863e43 | + | 1.52743e44i | 0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.15686e44 | − | 1.61012e44i | 0.801341 | − | 0.598208i | ||||
\(148\) | −1.42463e44 | −0.460615 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.90169e44 | − | 3.29382e44i | −0.407485 | − | 0.705785i | 0.587122 | − | 0.809498i | \(-0.300261\pi\) |
−0.994607 | + | 0.103713i | \(0.966928\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.52444e44 | + | 7.83655e44i | −0.497176 | + | 0.861134i | ||||
\(157\) | −1.21374e45 | + | 7.00754e44i | −1.16999 | + | 0.675495i | −0.953678 | − | 0.300828i | \(-0.902737\pi\) |
−0.216314 | + | 0.976324i | \(0.569404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.07118e45 | + | 1.85534e45i | −0.478649 | + | 0.829045i | −0.999700 | − | 0.0244805i | \(-0.992207\pi\) |
0.521051 | + | 0.853526i | \(0.325540\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.28914e43 | 0.0112644 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.96942e45 | − | 5.17849e45i | 1.50087 | − | 0.866529i | ||||
\(172\) | −2.17570e45 | − | 3.76843e45i | −0.323048 | − | 0.559535i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.28064e45 | + | 8.01739e45i | 0.550055 | + | 0.835128i | ||||
\(176\) | 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 | ||||||||
\(181\) | − | 7.80733e45i | − | 0.407466i | −0.979026 | − | 0.203733i | \(-0.934693\pi\) | ||
0.979026 | − | 0.203733i | \(-0.0653075\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.10830e44 | 0.0171165 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.73419e45 | − | 4.64211e46i | −0.0587980 | − | 0.998270i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | 5.56168e46 | − | 3.21104e46i | 0.866025 | − | 0.500000i | ||||
\(193\) | −6.74472e46 | − | 1.16822e47i | −0.944145 | − | 1.63531i | −0.757454 | − | 0.652889i | \(-0.773557\pi\) |
−0.186692 | − | 0.982419i | \(-0.559777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.86275e46 | − | 7.85357e46i | −0.598208 | − | 0.801341i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.18927e47 | + | 1.26398e47i | −1.63611 | + | 0.944607i | −0.653952 | + | 0.756536i | \(0.726890\pi\) |
−0.982155 | + | 0.188071i | \(0.939776\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.65832e47 | + | 1.53478e47i | 1.61841 | + | 0.934389i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.85344e47 | + | 1.64744e47i | 0.861134 | + | 0.497176i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.34500e47 | −1.87774 | −0.938871 | − | 0.344270i | \(-0.888127\pi\) | ||||
−0.938871 | + | 0.344270i | \(0.888127\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.21295e48 | − | 7.98910e47i | 1.53610 | − | 1.01175i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.46388e46 | − | 4.26757e46i | 0.0258533 | − | 0.0447792i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.50626e48i | − | 1.81458i | −0.420505 | − | 0.907290i | \(-0.638147\pi\) | ||
0.420505 | − | 0.907290i | \(-0.361853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.65860e48 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | −1.88559e48 | − | 3.26594e48i | −0.866529 | − | 1.50087i | ||||
\(229\) | −4.07972e48 | − | 2.35543e48i | −1.71397 | − | 0.989561i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) |
−0.784929 | − | 0.619585i | \(-0.787301\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | − | 7.70253e48i | − | 1.60063i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11143e49 | − | 6.41682e48i | 1.63882 | − | 0.946173i | 0.657579 | − | 0.753385i | \(-0.271580\pi\) |
0.981240 | − | 0.192788i | \(-0.0617529\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.95760e48 | − | 4.01697e48i | −0.866025 | − | 0.500000i | ||||
\(244\) | − | 1.49591e47i | − | 0.0171165i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.67411e48 | − | 1.67560e49i | 0.861635 | − | 1.49240i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −1.69028e49 | + | 9.95574e47i | −0.998270 | + | 0.0587980i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.16920e49 | − | 2.02512e49i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.13011e48 | − | 1.22260e49i | 0.206454 | − | 0.411755i | ||||
\(260\) | 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 | ||||||||
\(268\) | 5.58845e49 | − | 9.67947e49i | 0.934389 | − | 1.61841i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.60000e49 | − | 4.96521e49i | −1.14453 | − | 0.660796i | −0.196984 | − | 0.980407i | \(-0.563115\pi\) |
−0.947549 | + | 0.319611i | \(0.896448\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.77838e49 | − | 7.25483e49i | −0.546949 | − | 0.830411i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.07368e50 | − | 1.85966e50i | −0.912091 | − | 1.57979i | −0.811105 | − | 0.584901i | \(-0.801133\pi\) |
−0.100987 | − | 0.994888i | \(-0.532200\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.50930e50i | − | 1.83936i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.13079e50 | − | 1.23021e50i | 1.16659 | − | 0.673533i | 0.213718 | − | 0.976895i | \(-0.431443\pi\) |
0.952875 | + | 0.303362i | \(0.0981092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.40403e50 | − | 2.43185e50i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.75646e50 | + | 3.04228e50i | 0.543041 | + | 0.940574i | ||||
\(292\) | −1.55391e49 | − | 8.97148e48i | −0.0447792 | − | 0.0258533i | ||||
\(293\) | 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 | ||||||||
\(300\) | − | 6.03929e50i | − | 1.00000i | ||||||
\(301\) | 4.17021e50 | − | 2.45625e49i | 0.644977 | − | 0.0379891i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.18919e51 | + | 6.86581e50i | −1.50087 | + | 0.866529i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.73958e51i | 1.79518i | 0.440830 | + | 0.897590i | \(0.354684\pi\) | ||||
−0.440830 | + | 0.897590i | \(0.645316\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.51612e50 | 0.588627 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.94246e50 | − | 3.43088e50i | −0.412389 | − | 0.238093i | 0.279427 | − | 0.960167i | \(-0.409856\pi\) |
−0.691816 | + | 0.722074i | \(0.743189\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.80464e51 | −1.60063 | ||||||||
\(317\) | 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 | ||||||||
\(324\) | −1.46266e51 | + | 2.53340e51i | −0.500000 | + | 0.866025i | ||||
\(325\) | 2.68336e51 | − | 1.54924e51i | 0.861134 | − | 0.497176i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.90217e51 | + | 3.40762e51i | 1.67025 | + | 0.964322i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.09456e51 | + | 7.09199e51i | −0.903095 | + | 1.56421i | −0.0796418 | + | 0.996824i | \(0.525378\pi\) |
−0.823454 | + | 0.567384i | \(0.807956\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.18145e51 | − | 2.04633e51i | −0.230307 | − | 0.398904i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.62508e50 | + | 6.15465e51i | 0.0587980 | + | 0.998270i | ||||
\(337\) | 8.26335e51 | 1.26108 | 0.630541 | − | 0.776156i | \(-0.282833\pi\) | ||||
0.630541 | + | 0.776156i | \(0.282833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.26253e51 | − | 1.65199e51i | 0.984465 | − | 0.175581i | ||||
\(344\) | 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 | ||||||||
\(349\) | 2.68299e52i | 1.99847i | 0.0390895 | + | 0.999236i | \(0.487554\pi\) | ||||
−0.0390895 | + | 0.999236i | \(0.512446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.50085e52 | −0.994352 | ||||||||
\(352\) | 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 | ||||||||
\(361\) | 2.68940e52 | + | 4.65818e52i | 1.00175 | + | 1.73508i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.00667e52i | 1.00000i | ||||||||
\(364\) | −2.64163e52 | + | 1.73990e52i | −0.830411 | + | 0.546949i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.48734e52 | + | 3.74547e52i | −1.72350 | + | 0.995065i | −0.812139 | + | 0.583464i | \(0.801697\pi\) |
−0.911364 | + | 0.411601i | \(0.864970\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.13686e52 | −1.83936 | ||||||||
\(373\) | 5.23785e52 | − | 9.07222e52i | 0.997980 | − | 1.72855i | 0.443974 | − | 0.896040i | \(-0.353568\pi\) |
0.554006 | − | 0.832512i | \(-0.313098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.33136e53 | 1.82891 | 0.914455 | − | 0.404688i | \(-0.132620\pi\) | ||||
0.914455 | + | 0.404688i | \(0.132620\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.81006e52 | − | 2.19974e52i | 0.469861 | − | 0.271274i | ||||
\(382\) | 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 | ||||||||
\(387\) | 3.60862e52 | − | 6.25032e52i | 0.323048 | − | 0.559535i | ||||
\(388\) | 1.10775e53 | − | 6.39562e52i | 0.940574 | − | 0.543041i | ||||
\(389\) | 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 | ||||||||
\(397\) | −3.26358e53 | − | 1.88423e53i | −1.73176 | − | 0.999834i | −0.874993 | − | 0.484135i | \(-0.839134\pi\) |
−0.856770 | − | 0.515699i | \(-0.827532\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.61415e53 | − | 2.12873e52i | 1.73006 | − | 0.101900i | ||||
\(400\) | −2.19902e53 | −1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.34385e53 | − | 4.05967e53i | −0.914485 | − | 1.58393i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.97412e53 | − | 2.29446e53i | 1.14528 | − | 0.661230i | 0.197550 | − | 0.980293i | \(-0.436701\pi\) |
0.947734 | + | 0.319063i | \(0.103368\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2.37265e53i | − | 0.588627i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.04977e53 | − | 8.74645e53i | −0.978323 | − | 1.69450i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.73208e53 | −1.55033 | −0.775163 | − | 0.631762i | \(-0.782332\pi\) | ||||
−0.775163 | + | 0.631762i | \(0.782332\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.28377e52 | + | 6.43682e51i | 0.0153009 | + | 0.00767185i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 9.22460e53 | + | 5.32582e53i | 0.866025 | + | 0.500000i | ||||
\(433\) | 2.21678e54i | 1.98482i | 0.122989 | + | 0.992408i | \(0.460752\pi\) | ||||
−0.122989 | + | 0.992408i | \(0.539248\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.24078e54 | − | 2.14910e54i | 0.964322 | − | 1.67025i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.01604e53 | − | 2.31866e53i | −0.271191 | − | 0.156572i | 0.358238 | − | 0.933630i | \(-0.383378\pi\) |
−0.629429 | + | 0.777058i | \(0.716711\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.41880e53 | − | 1.49342e54i | 0.394878 | − | 0.918734i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | −7.45108e53 | + | 4.30188e53i | −0.398904 | + | 0.230307i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.24103e54 | − | 1.31996e53i | 0.998270 | − | 0.0587980i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.98923e54 | − | 1.14848e54i | −0.705785 | − | 0.407485i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.40419e54 | − | 4.16417e54i | 0.712338 | − | 1.23380i | −0.251640 | − | 0.967821i | \(-0.580970\pi\) |
0.963977 | − | 0.265984i | \(-0.0856968\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.96507e54 | −1.80626 | −0.903128 | − | 0.429372i | \(-0.858735\pi\) | ||||
−0.903128 | + | 0.429372i | \(0.858735\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | 5.46487e54i | 0.994352i | ||||||||
\(469\) | 5.90211e54 | + | 8.96095e54i | 1.02793 | + | 1.56067i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.23205e54 | + | 7.33013e54i | −0.675495 | + | 1.16999i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.29132e55i | 1.73306i | ||||||||
\(476\) | 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 | ||||||||
\(481\) | −3.82281e54 | − | 2.20710e54i | −0.396651 | − | 0.229006i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.09479e55 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.33694e54 | + | 9.24385e54i | 0.429486 | + | 0.743891i | 0.996828 | − | 0.0795914i | \(-0.0253616\pi\) |
−0.567342 | + | 0.823482i | \(0.692028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.29384e55i | 0.957299i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.32691e55i | 1.83936i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.50521e54 | + | 9.53530e54i | −0.268976 | + | 0.465879i | −0.968598 | − | 0.248634i | \(-0.920018\pi\) |
0.699622 | + | 0.714513i | \(0.253352\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | 2.76631e53 | − | 1.59713e53i | 0.00975524 | − | 0.00563219i | ||||
\(508\) | −8.00968e54 | − | 1.38732e55i | −0.271274 | − | 0.469861i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.43856e54 | − | 9.47503e53i | 0.0431816 | − | 0.0284415i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.12744e55 | − | 5.41689e55i | 0.866529 | − | 1.50087i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.27586e55 | − | 1.31397e55i | −0.559535 | − | 0.323048i | ||||
\(517\) | 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 | ||||||||
\(523\) | −3.62921e55 | − | 2.09532e55i | −0.676904 | − | 0.390811i | 0.121783 | − | 0.992557i | \(-0.461139\pi\) |
−0.798688 | + | 0.601746i | \(0.794472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.18283e55 | + | 2.59867e55i | 0.893926 | + | 0.448214i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.38697e55 | − | 5.86640e55i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.75111e54 | − | 1.31598e56i | −0.101900 | − | 1.73006i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.72699e55 | + | 1.16515e56i | −0.627014 | + | 1.08602i | 0.361134 | + | 0.932514i | \(0.382390\pi\) |
−0.988148 | + | 0.153506i | \(0.950944\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.35753e55 | − | 4.08337e55i | −0.203733 | − | 0.352876i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.52425e56 | 1.87669 | 0.938345 | − | 0.345700i | \(-0.112359\pi\) | ||||
0.938345 | + | 0.345700i | \(0.112359\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.14871e54 | − | 1.24056e54i | 0.0148233 | − | 0.00855824i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.20682e56 | − | 2.40690e56i | 0.717427 | − | 1.43085i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.18475e56 | + | 1.83872e56i | −1.69450 | + | 0.978323i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.34828e56i | − | 0.642446i | ||||||
\(560\) | 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 | ||||||||
\(567\) | −1.54475e56 | − | 2.34534e56i | −0.550055 | − | 0.835128i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.99927e56 | − | 3.46284e56i | −0.616356 | − | 1.06756i | −0.990145 | − | 0.140047i | \(-0.955275\pi\) |
0.373789 | − | 0.927514i | \(-0.378059\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.93924e56 | − | 3.35886e56i | 0.500000 | − | 0.866025i | ||||
\(577\) | 3.19378e56 | − | 1.84393e56i | 0.794696 | − | 0.458818i | −0.0469175 | − | 0.998899i | \(-0.514940\pi\) |
0.841613 | + | 0.540081i | \(0.181606\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.05521e56 | − | 4.07333e56i | −1.63531 | − | 0.944145i | ||||
\(580\) | 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 | \(0.5\pi\) | |||||||||
\(588\) | −5.43782e56 | − | 2.33721e56i | −0.918734 | − | 0.394878i | ||||
\(589\) | 1.95363e57 | 3.18772 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.56640e56 | + | 2.71308e56i | 0.230307 | + | 0.398904i | ||||
\(593\) | 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 | ||||||||
\(597\) | −7.63352e56 | + | 1.32216e57i | −0.944607 | + | 1.63611i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.83954e57i | 1.98510i | 0.121829 | + | 0.992551i | \(0.461124\pi\) | ||||
−0.121829 | + | 0.992551i | \(0.538876\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85380e57 | 1.86878 | ||||||||
\(604\) | −4.18186e56 | + | 7.24319e56i | −0.407485 | + | 0.705785i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.82664e57 | − | 1.05461e57i | −1.60800 | − | 0.928376i | −0.989818 | − | 0.142337i | \(-0.954538\pi\) |
−0.618177 | − | 0.786039i | \(-0.712128\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.23063e57 | + | 2.13152e57i | 0.885499 | + | 1.53373i | 0.845140 | + | 0.534545i | \(0.179517\pi\) |
0.0403591 | + | 0.999185i | \(0.487150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.28222e57 | + | 1.31764e57i | −1.34493 | + | 0.776493i | −0.987526 | − | 0.157458i | \(-0.949670\pi\) |
−0.357400 | + | 0.933951i | \(0.616337\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.98987e57 | 0.994352 | ||||||||
\(625\) | −1.03398e57 | + | 1.79090e57i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.66904e57 | + | 1.54097e57i | 1.16999 | + | 0.675495i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.15205e57 | −0.458002 | −0.229001 | − | 0.973426i | \(-0.573546\pi\) | ||||
−0.229001 | + | 0.973426i | \(0.573546\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.36458e57 | + | 2.51989e57i | −1.62617 | + | 0.938871i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.56483e56 | − | 3.01568e57i | −0.116729 | − | 0.987477i | ||||
\(638\) | 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 | ||||||||
\(643\) | 6.08414e57i | 1.64390i | 0.569562 | + | 0.821948i | \(0.307113\pi\) | ||||
−0.569562 | + | 0.821948i | \(0.692887\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 3.93154e57 | − | 7.84113e57i | 0.824427 | − | 1.64425i | ||||
\(652\) | 4.71111e57 | 0.957299 | ||||||||
\(653\) | 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 | ||||||||
\(657\) | − | 2.97602e56i | − | 0.0517065i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.98743e56 | − | 4.03419e56i | 0.107198 | − | 0.0618909i | −0.445442 | − | 0.895311i | \(-0.646954\pi\) |
0.552641 | + | 0.833420i | \(0.313620\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.56801e57 | − | 1.31082e58i | −0.907290 | − | 1.57147i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.70949e58 | 1.81367 | 0.906835 | − | 0.421487i | \(-0.138492\pi\) | ||||
0.906835 | + | 0.421487i | \(0.138492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.67477e57 | − | 5.00838e57i | 0.866025 | − | 0.500000i | ||||
\(676\) | −5.81547e55 | − | 1.00727e56i | −0.00563219 | − | 0.00975524i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.22030e56 | + | 1.22586e58i | 0.0638594 | + | 1.08420i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | −1.97240e58 | − | 1.13876e58i | −1.50087 | − | 0.866529i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.84502e58 | −1.97912 | ||||||||
\(688\) | −4.78442e57 | + | 8.28686e57i | −0.323048 | + | 0.559535i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.35341e58 | − | 7.81393e57i | −0.835854 | − | 0.482580i | 0.0199989 | − | 0.999800i | \(-0.493634\pi\) |
−0.855853 | + | 0.517220i | \(0.826967\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.46228e57 | − | 1.88717e58i | 0.448214 | − | 0.893926i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.59318e58 | − | 9.19825e57i | 0.691324 | − | 0.399136i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.69787e58 | − | 4.67284e58i | 0.983496 | − | 1.70347i | 0.335060 | − | 0.942197i | \(-0.391244\pi\) |
0.648437 | − | 0.761269i | \(-0.275423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.32589e58 | − | 4.02856e58i | −0.800317 | − | 1.38619i | ||||
\(712\) | 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 | ||||||||
\(721\) | 2.03617e58 | + | 1.02094e58i | 0.526189 | + | 0.263831i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.87530e58 | − | 6.71222e58i | 0.946173 | − | 1.63882i | ||||
\(724\) | −1.48684e58 | + | 8.58425e57i | −0.352876 | + | 0.203733i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.51197e58i | 1.85599i | 0.372598 | + | 0.927993i | \(0.378467\pi\) | ||||
−0.372598 | + | 0.927993i | \(0.621533\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.85193e58 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.51712e56 | − | 7.82388e56i | −0.00855824 | − | 0.0148233i | ||||
\(733\) | 5.32997e58 | + | 3.07726e58i | 0.981959 | + | 0.566935i | 0.902861 | − | 0.429932i | \(-0.141463\pi\) |
0.0790983 | + | 0.996867i | \(0.474796\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.28190e58 | + | 1.08806e59i | 0.979220 | + | 1.69606i | 0.665241 | + | 0.746629i | \(0.268329\pi\) |
0.313979 | + | 0.949430i | \(0.398338\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.16849e59i | − | 1.72327i | ||||||
\(742\) | 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 | ||||||||
\(751\) | −8.26198e57 | + | 1.43102e58i | −0.0925690 | + | 0.160334i | −0.908591 | − | 0.417686i | \(-0.862841\pi\) |
0.816022 | + | 0.578020i | \(0.196175\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.53984e58 | + | 5.62475e58i | −0.835128 | + | 0.550055i | ||||
\(757\) | −2.03933e59 | −1.94098 | −0.970490 | − | 0.241141i | \(-0.922478\pi\) | ||||
−0.970490 | + | 0.241141i | \(0.922478\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 1.31042e59 | + | 1.98957e59i | 1.06086 | + | 1.61066i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.22303e59 | − | 7.06114e58i | −0.866025 | − | 0.500000i | ||||
\(769\) | 2.63478e59i | 1.81658i | 0.418344 | + | 0.908289i | \(0.362611\pi\) | ||||
−0.418344 | + | 0.908289i | \(0.637389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.48318e59 | + | 2.56894e59i | −0.944145 | + | 1.63531i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.70946e59 | + | 1.56431e59i | 1.59293 | + | 0.919680i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.85658e57 | − | 8.24549e58i | −0.0270832 | − | 0.459818i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.51025e58 | + | 1.98002e59i | −0.394878 | + | 0.918734i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.30796e59 | − | 1.33250e59i | 0.990251 | − | 0.571722i | 0.0849019 | − | 0.996389i | \(-0.472942\pi\) |
0.905349 | + | 0.424667i | \(0.139609\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.31753e57 | − | 4.01407e57i | 0.00850990 | − | 0.0147396i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.81426e59 | + | 2.77952e59i | 1.63611 | + | 0.944607i | ||||
\(797\) | 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 | ||||||||
\(804\) | − | 6.75005e59i | − | 1.86878i | ||||||
\(805\) | 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 | ||||||||
\(811\) | − | 8.16079e59i | − | 1.89149i | −0.324906 | − | 0.945746i | \(-0.605333\pi\) | ||
0.324906 | − | 0.945746i | \(-0.394667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.99727e59 | −1.32159 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.86623e59 | + | 2.80952e59i | 0.969707 | + | 0.559860i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.68988e59 | − | 2.35150e59i | −0.888877 | − | 0.445683i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.34637e59 | + | 5.79609e59i | 0.573955 | + | 0.994119i | 0.996154 | + | 0.0876158i | \(0.0279248\pi\) |
−0.422200 | + | 0.906503i | \(0.638742\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.28312e59 | + | 1.89551e59i | −0.485198 | + | 0.280129i | −0.722580 | − | 0.691287i | \(-0.757044\pi\) |
0.237382 | + | 0.971416i | \(0.423711\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.12310e60 | − | 6.48424e59i | −1.57979 | − | 0.912091i | ||||
\(832\) | − | 7.24550e59i | − | 0.994352i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.57720e59 | − | 1.31241e60i | −0.919680 | − | 1.59293i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.08485e59 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.17542e59 | + | 1.58923e60i | 0.938871 | + | 1.62617i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.71081e59 | + | 9.39532e59i | −0.448214 | + | 0.893926i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.42962e59 | − | 1.28685e60i | 0.673533 | − | 1.16659i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 8.59336e59i | − | 0.707470i | −0.935346 | − | 0.353735i | \(-0.884912\pi\) | ||
0.935346 | − | 0.353735i | \(-0.115088\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −6.43015e59 | − | 3.71245e59i | −0.458523 | − | 0.264728i | 0.252900 | − | 0.967492i | \(-0.418616\pi\) |
−0.711423 | + | 0.702764i | \(0.751949\pi\) | |||||||
\(860\) | 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 | ||||||||
\(867\) | − | 1.69587e60i | − | 1.00000i | ||||||
\(868\) | −2.85511e60 | − | 1.43155e60i | −1.64425 | − | 0.824427i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.99917e60 | − | 1.73157e60i | 1.60927 | − | 0.929112i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.83732e60 | + | 1.06078e60i | 0.940574 | + | 0.543041i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.08363e59 | −0.0517065 | ||||||||
\(877\) | −1.36347e59 | + | 2.36160e59i | −0.0635556 | + | 0.110082i | −0.896052 | − | 0.443948i | \(-0.853577\pi\) |
0.832497 | + | 0.554030i | \(0.186911\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.45751e60 | 0.590766 | 0.295383 | − | 0.955379i | \(-0.404553\pi\) | ||||
0.295383 | + | 0.955379i | \(0.404553\pi\) | |||||||
\(884\) | 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 | ||||||||
\(889\) | 1.53523e60 | − | 9.04248e58i | 0.541610 | − | 0.0319008i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.77294e60 | + | 2.75566e60i | −1.57147 | + | 0.907290i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.82365e60 | − | 3.15865e60i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.10692e60 | − | 1.38772e60i | 0.539572 | − | 0.355388i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.88158e60 | − | 3.25900e60i | −0.440123 | − | 0.762316i | 0.557575 | − | 0.830127i | \(-0.311732\pi\) |
−0.997698 | + | 0.0678108i | \(0.978399\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −4.14646e60 | + | 7.18188e60i | −0.866529 | + | 1.50087i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.03593e61i | 1.97912i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.50317e60 | + | 6.06767e60i | −0.625883 | + | 1.08406i | 0.362486 | + | 0.931989i | \(0.381928\pi\) |
−0.988369 | + | 0.152072i | \(0.951405\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.25292e60 | + | 9.09832e60i | 0.897590 | + | 1.55467i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.94607e60 | 0.460615 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.40805e60 | − | 1.96764e60i | 0.509766 | − | 0.294314i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.16271e61 | + | 4.99741e60i | 1.59222 | + | 0.684347i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.63882e61i | 1.96729i | 0.180118 | + | 0.983645i | \(0.442352\pi\) | ||||
−0.180118 | + | 0.983645i | \(0.557648\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.14401e60 | −0.476186 | ||||||||
\(940\) | 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 | \(0.666667\pi\) | |||||||
\(948\) | −1.46688e61 | + | 8.46902e60i | −1.38619 | + | 0.800317i | ||||
\(949\) | −2.77980e59 | − | 4.81475e59i | −0.0257073 | − | 0.0445263i | ||||
\(950\) | 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 | ||||||||
\(961\) | 1.66712e61 | − | 2.88754e61i | 1.19162 | − | 2.06395i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.44405e61 | − | 1.41107e61i | −1.63882 | − | 0.946173i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.01411e60 | 0.378380 | 0.189190 | − | 0.981940i | \(-0.439414\pi\) | ||||
0.189190 | + | 0.981940i | \(0.439414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | 1.76668e61i | 1.00000i | ||||||||
\(973\) | −2.07581e60 | − | 3.52430e61i | −0.115047 | − | 1.95326i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.35631e60 | − | 1.62056e61i | 0.497176 | − | 0.861134i | ||||
\(976\) | −2.84883e59 | + | 1.64477e59i | −0.0148233 | + | 0.00855824i | ||||
\(977\) | 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 | ||||||||
\(981\) | 4.11592e61 | 1.92864 | ||||||||
\(982\) | 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 | ||||||||
\(988\) | −4.25472e61 | −1.72327 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.56736e61 | − | 4.44679e61i | −0.977184 | − | 1.69253i | −0.672532 | − | 0.740068i | \(-0.734793\pi\) |
−0.304652 | − | 0.952464i | \(-0.598540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.94565e61i | 1.80619i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.45749e61 | − | 8.41480e60i | 0.490178 | − | 0.283004i | −0.234470 | − | 0.972123i | \(-0.575336\pi\) |
0.724648 | + | 0.689119i | \(0.242002\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.23584e61 | − | 7.13510e60i | −0.398904 | − | 0.230307i |
(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 | 21.42.g.a.5.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.42.g.a.5.1 | ✓ | 2 | |
7.3 | odd | 6 | inner | 21.42.g.a.17.1 | yes | 2 | |
21.17 | even | 6 | inner | 21.42.g.a.17.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.42.g.a.5.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.42.g.a.5.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.42.g.a.17.1 | yes | 2 | 7.3 | odd | 6 | inner | |
21.42.g.a.17.1 | yes | 2 | 21.17 | even | 6 | inner |