Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [81,22,Mod(1,81)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(81, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("81.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(226.376648873\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} - 30906825 x^{18} + 1599806295 x^{17} + 397632537600480 x^{16} + \cdots + 18\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{56}\cdot 3^{135}\cdot 5^{4}\cdot 7^{6} \) |
Twist minimal: | no (minimal twist has level 9) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(1931.83\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 81.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1982.83 | 1.36921 | 0.684607 | − | 0.728912i | \(-0.259974\pi\) | ||||
0.684607 | + | 0.728912i | \(0.259974\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.83448e6 | 0.874748 | ||||||||
\(5\) | 1.02434e7 | 0.469093 | 0.234546 | − | 0.972105i | \(-0.424640\pi\) | ||||
0.234546 | + | 0.972105i | \(0.424640\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.51290e8 | −1.27287 | −0.636434 | − | 0.771331i | \(-0.719591\pi\) | ||||
−0.636434 | + | 0.771331i | \(0.719591\pi\) | |||||||
\(8\) | −5.20838e8 | −0.171497 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.03109e10 | 0.642288 | ||||||||
\(11\) | −8.67734e10 | −1.00870 | −0.504352 | − | 0.863498i | \(-0.668269\pi\) | ||||
−0.504352 | + | 0.863498i | \(0.668269\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.25839e11 | 1.05791 | 0.528954 | − | 0.848651i | \(-0.322585\pi\) | ||||
0.528954 | + | 0.848651i | \(0.322585\pi\) | |||||||
\(14\) | −1.88625e12 | −1.74283 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.87992e12 | −1.10956 | ||||||||
\(17\) | 9.08695e12 | 1.09321 | 0.546606 | − | 0.837390i | \(-0.315920\pi\) | ||||
0.546606 | + | 0.837390i | \(0.315920\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.79971e12 | −0.329273 | −0.164636 | − | 0.986354i | \(-0.552645\pi\) | ||||
−0.164636 | + | 0.986354i | \(0.552645\pi\) | |||||||
\(20\) | 1.87913e13 | 0.410338 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.72057e14 | −1.38113 | ||||||||
\(23\) | −3.86072e13 | −0.194324 | −0.0971620 | − | 0.995269i | \(-0.530976\pi\) | ||||
−0.0971620 | + | 0.995269i | \(0.530976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.71910e14 | −0.779952 | ||||||||
\(26\) | 1.04265e15 | 1.44850 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.74512e15 | −1.11344 | ||||||||
\(29\) | 2.89780e14 | 0.127906 | 0.0639528 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639528 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.04185e15 | 1.32395 | 0.661975 | − | 0.749526i | \(-0.269718\pi\) | ||||
0.661975 | + | 0.749526i | \(0.269718\pi\) | |||||||
\(32\) | −8.58379e15 | −1.34773 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.80179e16 | 1.49684 | ||||||||
\(35\) | −9.74443e15 | −0.597093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.41709e16 | −1.51014 | −0.755071 | − | 0.655642i | \(-0.772398\pi\) | ||||
−0.755071 | + | 0.655642i | \(0.772398\pi\) | |||||||
\(38\) | −1.74484e16 | −0.450845 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.33514e15 | −0.0804482 | ||||||||
\(41\) | −8.86265e16 | −1.03118 | −0.515589 | − | 0.856836i | \(-0.672427\pi\) | ||||
−0.515589 | + | 0.856836i | \(0.672427\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.26915e16 | 0.512938 | 0.256469 | − | 0.966552i | \(-0.417441\pi\) | ||||
0.256469 | + | 0.966552i | \(0.417441\pi\) | |||||||
\(44\) | −1.59184e17 | −0.882361 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.65517e16 | −0.266071 | ||||||||
\(47\) | 7.19545e17 | 1.99540 | 0.997701 | − | 0.0677735i | \(-0.0215895\pi\) | ||||
0.997701 | + | 0.0677735i | \(0.0215895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.46406e17 | 0.620193 | ||||||||
\(50\) | −7.37436e17 | −1.06792 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.64640e17 | 0.925402 | ||||||||
\(53\) | −5.36630e17 | −0.421481 | −0.210740 | − | 0.977542i | \(-0.567587\pi\) | ||||
−0.210740 | + | 0.977542i | \(0.567587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.88854e17 | −0.473175 | ||||||||
\(56\) | 4.95468e17 | 0.218294 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.74586e17 | 0.175130 | ||||||||
\(59\) | 5.37267e18 | 1.36850 | 0.684249 | − | 0.729249i | \(-0.260130\pi\) | ||||
0.684249 | + | 0.729249i | \(0.260130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.17239e18 | 0.389919 | 0.194959 | − | 0.980811i | \(-0.437543\pi\) | ||||
0.194959 | + | 0.980811i | \(0.437543\pi\) | |||||||
\(62\) | 1.19800e19 | 1.81277 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.78630e18 | −0.735772 | ||||||||
\(65\) | 5.38637e18 | 0.496256 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.82952e19 | 1.22618 | 0.613088 | − | 0.790015i | \(-0.289927\pi\) | ||||
0.613088 | + | 0.790015i | \(0.289927\pi\) | |||||||
\(68\) | 1.66698e19 | 0.956284 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.93216e19 | −0.817548 | ||||||||
\(71\) | 1.88011e19 | 0.685442 | 0.342721 | − | 0.939437i | \(-0.388651\pi\) | ||||
0.342721 | + | 0.939437i | \(0.388651\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.15740e19 | 1.94924 | 0.974619 | − | 0.223869i | \(-0.0718689\pi\) | ||||
0.974619 | + | 0.223869i | \(0.0718689\pi\) | |||||||
\(74\) | −8.75835e19 | −2.06771 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.61429e19 | −0.288030 | ||||||||
\(77\) | 8.25467e19 | 1.28395 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.42100e19 | −0.881816 | −0.440908 | − | 0.897552i | \(-0.645344\pi\) | ||||
−0.440908 | + | 0.897552i | \(0.645344\pi\) | |||||||
\(80\) | −4.99869e19 | −0.520488 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.75732e20 | −1.41190 | ||||||||
\(83\) | −4.29574e19 | −0.303891 | −0.151946 | − | 0.988389i | \(-0.548554\pi\) | ||||
−0.151946 | + | 0.988389i | \(0.548554\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.30811e19 | 0.512817 | ||||||||
\(86\) | 1.44135e20 | 0.702322 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.51949e19 | 0.172990 | ||||||||
\(89\) | 1.01476e20 | 0.344958 | 0.172479 | − | 0.985013i | \(-0.444822\pi\) | ||||
0.172479 | + | 0.985013i | \(0.444822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.00225e20 | −1.34658 | ||||||||
\(92\) | −7.08241e19 | −0.169984 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.42674e21 | 2.73213 | ||||||||
\(95\) | −9.01388e19 | −0.154459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.96482e20 | 1.37204 | 0.686019 | − | 0.727584i | \(-0.259357\pi\) | ||||
0.686019 | + | 0.727584i | \(0.259357\pi\) | |||||||
\(98\) | 6.86866e20 | 0.849177 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.82261e20 | −0.682261 | ||||||||
\(101\) | −9.40501e20 | −0.847198 | −0.423599 | − | 0.905850i | \(-0.639233\pi\) | ||||
−0.423599 | + | 0.905850i | \(0.639233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.34162e19 | −0.0318318 | −0.0159159 | − | 0.999873i | \(-0.505066\pi\) | ||||
−0.0159159 | + | 0.999873i | \(0.505066\pi\) | |||||||
\(104\) | −2.73877e20 | −0.181428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.06405e21 | −0.577098 | ||||||||
\(107\) | −1.58939e21 | −0.781088 | −0.390544 | − | 0.920584i | \(-0.627713\pi\) | ||||
−0.390544 | + | 0.920584i | \(0.627713\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.48277e20 | −0.140911 | −0.0704557 | − | 0.997515i | \(-0.522445\pi\) | ||||
−0.0704557 | + | 0.997515i | \(0.522445\pi\) | |||||||
\(110\) | −1.76245e21 | −0.647878 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.64221e21 | 1.41233 | ||||||||
\(113\) | 4.49798e21 | 1.24651 | 0.623253 | − | 0.782020i | \(-0.285811\pi\) | ||||
0.623253 | + | 0.782020i | \(0.285811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.95469e20 | −0.0911559 | ||||||||
\(116\) | 5.31595e20 | 0.111885 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.06531e22 | 1.87377 | ||||||||
\(119\) | −8.64432e21 | −1.39151 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.29378e20 | 0.0174829 | ||||||||
\(122\) | 4.30748e21 | 0.533882 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.10836e22 | 1.15812 | ||||||||
\(125\) | −8.69405e21 | −0.834962 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.85658e22 | 1.50930 | 0.754650 | − | 0.656128i | \(-0.227807\pi\) | ||||
0.754650 | + | 0.656128i | \(0.227807\pi\) | |||||||
\(128\) | 4.54540e21 | 0.340304 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.06803e22 | 0.679481 | ||||||||
\(131\) | −2.91946e22 | −1.71378 | −0.856889 | − | 0.515501i | \(-0.827606\pi\) | ||||
−0.856889 | + | 0.515501i | \(0.827606\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.37108e21 | 0.419121 | ||||||||
\(134\) | 3.62764e22 | 1.67890 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.73283e21 | −0.187483 | ||||||||
\(137\) | 2.54051e22 | 0.931871 | 0.465935 | − | 0.884819i | \(-0.345718\pi\) | ||||
0.465935 | + | 0.884819i | \(0.345718\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.12181e21 | 0.255857 | 0.127929 | − | 0.991783i | \(-0.459167\pi\) | ||||
0.127929 | + | 0.991783i | \(0.459167\pi\) | |||||||
\(140\) | −1.78759e22 | −0.522306 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.72795e22 | 0.938517 | ||||||||
\(143\) | −4.56289e22 | −1.06711 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.96833e21 | 0.0599996 | ||||||||
\(146\) | 1.41919e23 | 2.66892 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.10306e22 | −1.32099 | ||||||||
\(149\) | 8.46647e22 | 1.28602 | 0.643008 | − | 0.765859i | \(-0.277686\pi\) | ||||
0.643008 | + | 0.765859i | \(0.277686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.42695e23 | 1.88430 | 0.942152 | − | 0.335185i | \(-0.108799\pi\) | ||||
0.942152 | + | 0.335185i | \(0.108799\pi\) | |||||||
\(152\) | 4.58322e21 | 0.0564694 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.63676e23 | 1.75800 | ||||||||
\(155\) | 6.18890e22 | 0.621055 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.74777e23 | 1.53298 | 0.766491 | − | 0.642255i | \(-0.222001\pi\) | ||||
0.766491 | + | 0.642255i | \(0.222001\pi\) | |||||||
\(158\) | −1.47146e23 | −1.20740 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.79270e22 | −0.632212 | ||||||||
\(161\) | 3.67267e22 | 0.247349 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.02629e23 | 1.19876 | 0.599378 | − | 0.800466i | \(-0.295414\pi\) | ||||
0.599378 | + | 0.800466i | \(0.295414\pi\) | |||||||
\(164\) | −1.62583e23 | −0.902020 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.51775e22 | −0.416092 | ||||||||
\(167\) | −2.13757e22 | −0.0980385 | −0.0490193 | − | 0.998798i | \(-0.515610\pi\) | ||||
−0.0490193 | + | 0.998798i | \(0.515610\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.94422e22 | 0.119168 | ||||||||
\(170\) | 1.84564e23 | 0.702157 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.33351e23 | 0.448691 | ||||||||
\(173\) | −3.91056e23 | −1.23810 | −0.619048 | − | 0.785353i | \(-0.712481\pi\) | ||||
−0.619048 | + | 0.785353i | \(0.712481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.53794e23 | 0.992776 | ||||||||
\(176\) | 4.23447e23 | 1.11922 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.01209e23 | 0.472321 | ||||||||
\(179\) | −8.21918e23 | −1.81916 | −0.909582 | − | 0.415525i | \(-0.863598\pi\) | ||||
−0.909582 | + | 0.415525i | \(0.863598\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.25876e23 | −1.42968 | −0.714838 | − | 0.699290i | \(-0.753500\pi\) | ||||
−0.714838 | + | 0.699290i | \(0.753500\pi\) | |||||||
\(182\) | −9.91864e23 | −1.84375 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.01081e22 | 0.0333261 | ||||||||
\(185\) | −4.52460e23 | −0.708397 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.88506e23 | −1.10273 | ||||||||
\(188\) | 1.31999e24 | 1.74547 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.78730e23 | −0.211488 | ||||||||
\(191\) | 1.75688e24 | 1.96740 | 0.983699 | − | 0.179823i | \(-0.0575524\pi\) | ||||
0.983699 | + | 0.179823i | \(0.0575524\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.25951e24 | 1.26430 | 0.632151 | − | 0.774845i | \(-0.282172\pi\) | ||||
0.632151 | + | 0.774845i | \(0.282172\pi\) | |||||||
\(194\) | 1.97586e24 | 1.87861 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.35475e23 | 0.542512 | ||||||||
\(197\) | 9.65242e22 | 0.0781162 | 0.0390581 | − | 0.999237i | \(-0.487564\pi\) | ||||
0.0390581 | + | 0.999237i | \(0.487564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00060e24 | −0.728286 | −0.364143 | − | 0.931343i | \(-0.618638\pi\) | ||||
−0.364143 | + | 0.931343i | \(0.618638\pi\) | |||||||
\(200\) | 1.93705e23 | 0.133760 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.86486e24 | −1.16000 | ||||||||
\(203\) | −2.75665e23 | −0.162807 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.07836e23 | −0.483718 | ||||||||
\(206\) | −8.60872e22 | −0.0435846 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.56605e24 | −1.17382 | ||||||||
\(209\) | 7.63581e23 | 0.332138 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.80401e23 | −0.385867 | −0.192934 | − | 0.981212i | \(-0.561800\pi\) | ||||
−0.192934 | + | 0.981212i | \(0.561800\pi\) | |||||||
\(212\) | −9.84435e23 | −0.368689 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.15149e24 | −1.06948 | ||||||||
\(215\) | 7.44607e23 | 0.240615 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.74755e24 | −1.68521 | ||||||||
\(218\) | −6.90575e23 | −0.192938 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.63058e24 | −0.413909 | ||||||||
\(221\) | 4.77827e24 | 1.15652 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.01061e24 | −0.442717 | −0.221359 | − | 0.975193i | \(-0.571049\pi\) | ||||
−0.221359 | + | 0.975193i | \(0.571049\pi\) | |||||||
\(224\) | 8.16567e24 | 1.71549 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.91876e24 | 1.70673 | ||||||||
\(227\) | 1.48594e24 | 0.271474 | 0.135737 | − | 0.990745i | \(-0.456660\pi\) | ||||
0.135737 | + | 0.990745i | \(0.456660\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.85440e24 | −0.475600 | −0.237800 | − | 0.971314i | \(-0.576426\pi\) | ||||
−0.237800 | + | 0.971314i | \(0.576426\pi\) | |||||||
\(230\) | −7.84149e23 | −0.124812 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.50929e23 | −0.0219355 | ||||||||
\(233\) | −5.64192e24 | −0.783772 | −0.391886 | − | 0.920014i | \(-0.628177\pi\) | ||||
−0.391886 | + | 0.920014i | \(0.628177\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.37057e24 | 0.936028 | ||||||||
\(236\) | 9.85605e24 | 1.19709 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.71403e25 | −1.90528 | ||||||||
\(239\) | 5.37400e24 | 0.571637 | 0.285818 | − | 0.958284i | \(-0.407735\pi\) | ||||
0.285818 | + | 0.958284i | \(0.407735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.11925e23 | 0.0401457 | 0.0200729 | − | 0.999799i | \(-0.493610\pi\) | ||||
0.0200729 | + | 0.999799i | \(0.493610\pi\) | |||||||
\(242\) | 2.56535e23 | 0.0239378 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.98520e24 | 0.341080 | ||||||||
\(245\) | 3.54837e24 | 0.290928 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.62723e24 | −0.348340 | ||||||||
\(248\) | −3.14682e24 | −0.227054 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.72389e25 | −1.14324 | ||||||||
\(251\) | 9.06680e24 | 0.576607 | 0.288304 | − | 0.957539i | \(-0.406909\pi\) | ||||
0.288304 | + | 0.957539i | \(0.406909\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.35008e24 | 0.196015 | ||||||||
\(254\) | 3.68130e25 | 2.06655 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.32447e25 | 1.20172 | ||||||||
\(257\) | −9.16702e24 | −0.454915 | −0.227458 | − | 0.973788i | \(-0.573041\pi\) | ||||
−0.227458 | + | 0.973788i | \(0.573041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.20193e25 | 1.92221 | ||||||||
\(260\) | 9.88118e24 | 0.434099 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.78881e25 | −2.34653 | ||||||||
\(263\) | 1.97814e25 | 0.770411 | 0.385206 | − | 0.922831i | \(-0.374131\pi\) | ||||
0.385206 | + | 0.922831i | \(0.374131\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.49690e24 | −0.197714 | ||||||||
\(266\) | 1.65985e25 | 0.573866 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.35622e25 | 1.07259 | ||||||||
\(269\) | 1.02928e25 | 0.316327 | 0.158163 | − | 0.987413i | \(-0.449443\pi\) | ||||
0.158163 | + | 0.987413i | \(0.449443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.42626e25 | 1.25852 | 0.629258 | − | 0.777196i | \(-0.283359\pi\) | ||||
0.629258 | + | 0.777196i | \(0.283359\pi\) | |||||||
\(272\) | −4.43435e25 | −1.21299 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.03742e25 | 1.27593 | ||||||||
\(275\) | 3.22719e25 | 0.786741 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.57773e24 | −0.171199 | −0.0855996 | − | 0.996330i | \(-0.527281\pi\) | ||||
−0.0855996 | + | 0.996330i | \(0.527281\pi\) | |||||||
\(278\) | 1.61042e25 | 0.350323 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.07527e24 | 0.102400 | ||||||||
\(281\) | −2.30632e24 | −0.0448232 | −0.0224116 | − | 0.999749i | \(-0.507134\pi\) | ||||
−0.0224116 | + | 0.999749i | \(0.507134\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.96523e24 | 0.179775 | 0.0898876 | − | 0.995952i | \(-0.471349\pi\) | ||||
0.0898876 | + | 0.995952i | \(0.471349\pi\) | |||||||
\(284\) | 3.44902e25 | 0.599589 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.04744e25 | −1.46111 | ||||||||
\(287\) | 8.43095e25 | 1.31255 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.34807e25 | 0.195112 | ||||||||
\(290\) | 5.88571e24 | 0.0821523 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.31301e26 | 1.70509 | ||||||||
\(293\) | 9.07826e25 | 1.13735 | 0.568673 | − | 0.822563i | \(-0.307457\pi\) | ||||
0.568673 | + | 0.822563i | \(0.307457\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.50343e25 | 0.641952 | ||||||||
\(296\) | 2.30059e25 | 0.258986 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.67876e26 | 1.76083 | ||||||||
\(299\) | −2.03012e25 | −0.205577 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.91507e25 | −0.652903 | ||||||||
\(302\) | 2.82941e26 | 2.58002 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.29418e25 | 0.365349 | ||||||||
\(305\) | 2.22526e25 | 0.182908 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.92837e25 | −0.224736 | −0.112368 | − | 0.993667i | \(-0.535844\pi\) | ||||
−0.112368 | + | 0.993667i | \(0.535844\pi\) | |||||||
\(308\) | 1.51430e26 | 1.12313 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.22716e26 | 0.850358 | ||||||||
\(311\) | 7.77185e25 | 0.520643 | 0.260322 | − | 0.965522i | \(-0.416171\pi\) | ||||
0.260322 | + | 0.965522i | \(0.416171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.19250e26 | 0.746864 | 0.373432 | − | 0.927658i | \(-0.378181\pi\) | ||||
0.373432 | + | 0.927658i | \(0.378181\pi\) | |||||||
\(314\) | 3.46553e26 | 2.09898 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.36137e26 | −0.771366 | ||||||||
\(317\) | 4.56316e25 | 0.250117 | 0.125059 | − | 0.992149i | \(-0.460088\pi\) | ||||
0.125059 | + | 0.992149i | \(0.460088\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.51452e25 | −0.129019 | ||||||||
\(320\) | −6.95147e25 | −0.345145 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.28229e25 | 0.338673 | ||||||||
\(323\) | −7.99625e25 | −0.359965 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.95565e26 | −0.825117 | ||||||||
\(326\) | 4.01779e26 | 1.64136 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.61601e25 | 0.176844 | ||||||||
\(329\) | −6.84496e26 | −2.53988 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.60518e26 | −0.907077 | −0.453538 | − | 0.891237i | \(-0.649838\pi\) | ||||
−0.453538 | + | 0.891237i | \(0.649838\pi\) | |||||||
\(332\) | −7.88045e25 | −0.265828 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.23844e25 | −0.134236 | ||||||||
\(335\) | 1.87405e26 | 0.575190 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.59742e26 | −1.32556 | −0.662781 | − | 0.748813i | \(-0.730624\pi\) | ||||
−0.662781 | + | 0.748813i | \(0.730624\pi\) | |||||||
\(338\) | 5.83789e25 | 0.163166 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.70755e26 | 0.448586 | ||||||||
\(341\) | −5.24272e26 | −1.33547 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.01806e26 | 0.483444 | ||||||||
\(344\) | −3.78605e25 | −0.0879676 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.75398e26 | −1.69522 | ||||||||
\(347\) | 2.10744e26 | 0.446987 | 0.223493 | − | 0.974705i | \(-0.428254\pi\) | ||||
0.223493 | + | 0.974705i | \(0.428254\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.34411e26 | 0.667749 | 0.333875 | − | 0.942617i | \(-0.391644\pi\) | ||||
0.333875 | + | 0.942617i | \(0.391644\pi\) | |||||||
\(350\) | 7.01515e26 | 1.35932 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.44844e26 | 1.35946 | ||||||||
\(353\) | 5.00558e26 | 0.886789 | 0.443394 | − | 0.896327i | \(-0.353774\pi\) | ||||
0.443394 | + | 0.896327i | \(0.353774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.92587e26 | 0.321536 | ||||||||
\(356\) | 1.86155e26 | 0.301751 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.62973e27 | −2.49083 | ||||||||
\(359\) | −7.99086e26 | −1.18605 | −0.593023 | − | 0.805185i | \(-0.702066\pi\) | ||||
−0.593023 | + | 0.805185i | \(0.702066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.36775e26 | −0.891580 | ||||||||
\(362\) | −1.43929e27 | −1.95753 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.17653e26 | −1.17791 | ||||||||
\(365\) | 7.33160e26 | 0.914373 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.46698e26 | −0.526042 | −0.263021 | − | 0.964790i | \(-0.584719\pi\) | ||||
−0.263021 | + | 0.964790i | \(0.584719\pi\) | |||||||
\(368\) | 1.88400e26 | 0.215615 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.97152e26 | −0.969947 | ||||||||
\(371\) | 5.10490e26 | 0.536490 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.33252e27 | −1.32352 | −0.661761 | − | 0.749714i | \(-0.730191\pi\) | ||||
−0.661761 | + | 0.749714i | \(0.730191\pi\) | |||||||
\(374\) | −1.56348e27 | −1.50987 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.74766e26 | −0.342206 | ||||||||
\(377\) | 1.52378e26 | 0.135312 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.18217e26 | −0.687317 | −0.343658 | − | 0.939095i | \(-0.611666\pi\) | ||||
−0.343658 | + | 0.939095i | \(0.611666\pi\) | |||||||
\(380\) | −1.65358e26 | −0.135113 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.48361e27 | 2.69379 | ||||||||
\(383\) | 1.44791e27 | 1.08931 | 0.544657 | − | 0.838659i | \(-0.316660\pi\) | ||||
0.544657 | + | 0.838659i | \(0.316660\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.45557e26 | 0.602290 | ||||||||
\(386\) | 2.49741e27 | 1.73110 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.82802e27 | 1.20019 | ||||||||
\(389\) | −5.33912e26 | −0.341192 | −0.170596 | − | 0.985341i | \(-0.554569\pi\) | ||||
−0.170596 | + | 0.985341i | \(0.554569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.50822e26 | −0.212437 | ||||||||
\(392\) | −1.80422e26 | −0.106362 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.91392e26 | 0.106958 | ||||||||
\(395\) | −7.60162e26 | −0.413653 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.65812e27 | −1.37175 | −0.685874 | − | 0.727720i | \(-0.740580\pi\) | ||||
−0.685874 | + | 0.727720i | \(0.740580\pi\) | |||||||
\(398\) | −1.98402e27 | −0.997180 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.81489e27 | 0.865407 | ||||||||
\(401\) | 1.28013e27 | 0.594617 | 0.297309 | − | 0.954781i | \(-0.403911\pi\) | ||||
0.297309 | + | 0.954781i | \(0.403911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.17704e27 | 1.40062 | ||||||||
\(404\) | −1.72533e27 | −0.741084 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.46598e26 | −0.222918 | ||||||||
\(407\) | 3.83286e27 | 1.52329 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.59574e27 | 0.602374 | 0.301187 | − | 0.953565i | \(-0.402617\pi\) | ||||
0.301187 | + | 0.953565i | \(0.402617\pi\) | |||||||
\(410\) | −1.80009e27 | −0.662313 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.96461e25 | −0.0278448 | ||||||||
\(413\) | −5.11097e27 | −1.74192 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.40030e26 | −0.142553 | ||||||||
\(416\) | −4.51369e27 | −1.42578 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.51405e27 | 0.454769 | ||||||||
\(419\) | −3.39709e27 | −0.995084 | −0.497542 | − | 0.867440i | \(-0.665764\pi\) | ||||
−0.497542 | + | 0.867440i | \(0.665764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.70761e27 | −0.754438 | −0.377219 | − | 0.926124i | \(-0.623120\pi\) | ||||
−0.377219 | + | 0.926124i | \(0.623120\pi\) | |||||||
\(422\) | −1.94397e27 | −0.528335 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.79497e26 | 0.0722829 | ||||||||
\(425\) | −3.37953e27 | −0.852653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.06657e27 | −0.496315 | ||||||||
\(428\) | −2.91570e27 | −0.683255 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.47643e27 | 0.329454 | ||||||||
\(431\) | −2.25771e26 | −0.0491650 | −0.0245825 | − | 0.999698i | \(-0.507826\pi\) | ||||
−0.0245825 | + | 0.999698i | \(0.507826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.59341e27 | 1.16026 | 0.580128 | − | 0.814525i | \(-0.303003\pi\) | ||||
0.580128 | + | 0.814525i | \(0.303003\pi\) | |||||||
\(434\) | −1.13964e28 | −2.30742 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.38906e26 | −0.123262 | ||||||||
\(437\) | 3.39732e26 | 0.0639855 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.20421e27 | −0.216185 | −0.108093 | − | 0.994141i | \(-0.534474\pi\) | ||||
−0.108093 | + | 0.994141i | \(0.534474\pi\) | |||||||
\(440\) | 4.62949e26 | 0.0811484 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.47452e27 | 1.58352 | ||||||||
\(443\) | 5.09084e27 | 0.830903 | 0.415451 | − | 0.909615i | \(-0.363624\pi\) | ||||
0.415451 | + | 0.909615i | \(0.363624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03945e27 | 0.161817 | ||||||||
\(446\) | −3.98670e27 | −0.606174 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.45574e27 | 0.936540 | ||||||||
\(449\) | 3.77519e27 | 0.534998 | 0.267499 | − | 0.963558i | \(-0.413803\pi\) | ||||
0.267499 | + | 0.963558i | \(0.413803\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.69043e27 | 1.04015 | ||||||||
\(452\) | 8.25146e27 | 1.09038 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.94636e27 | 0.371706 | ||||||||
\(455\) | −5.12400e27 | −0.631669 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.97959e27 | 1.05715 | 0.528575 | − | 0.848887i | \(-0.322727\pi\) | ||||
0.528575 | + | 0.848887i | \(0.322727\pi\) | |||||||
\(458\) | −5.65980e27 | −0.651199 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.25479e26 | −0.0797384 | ||||||||
\(461\) | −1.03690e28 | −1.11398 | −0.556992 | − | 0.830518i | \(-0.688044\pi\) | ||||
−0.556992 | + | 0.830518i | \(0.688044\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.56649e27 | −0.468794 | −0.234397 | − | 0.972141i | \(-0.575312\pi\) | ||||
−0.234397 | + | 0.972141i | \(0.575312\pi\) | |||||||
\(464\) | −1.41410e27 | −0.141920 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.11870e28 | −1.07315 | ||||||||
\(467\) | −9.25506e27 | −0.868064 | −0.434032 | − | 0.900897i | \(-0.642910\pi\) | ||||
−0.434032 | + | 0.900897i | \(0.642910\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.74041e28 | −1.56076 | ||||||||
\(470\) | 1.46146e28 | 1.28162 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.79829e27 | −0.234694 | ||||||||
\(473\) | −6.30769e27 | −0.517403 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.27270e27 | 0.256817 | ||||||||
\(476\) | −1.58578e28 | −1.21722 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.06558e28 | 0.782693 | ||||||||
\(479\) | 7.49323e27 | 0.538451 | 0.269226 | − | 0.963077i | \(-0.413232\pi\) | ||||
0.269226 | + | 0.963077i | \(0.413232\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.32268e28 | −1.59759 | ||||||||
\(482\) | 8.16779e26 | 0.0549681 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.37341e26 | 0.0152931 | ||||||||
\(485\) | 1.02073e28 | 0.643613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.44040e27 | 0.328531 | 0.164266 | − | 0.986416i | \(-0.447475\pi\) | ||||
0.164266 | + | 0.986416i | \(0.447475\pi\) | |||||||
\(488\) | −1.13146e27 | −0.0668701 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.03584e27 | 0.398343 | ||||||||
\(491\) | −1.09503e28 | −0.606834 | −0.303417 | − | 0.952858i | \(-0.598127\pi\) | ||||
−0.303417 | + | 0.952858i | \(0.598127\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.63322e27 | 0.139828 | ||||||||
\(494\) | −9.17503e27 | −0.476952 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.94837e28 | −1.46901 | ||||||||
\(497\) | −1.78853e28 | −0.872477 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.69149e28 | 0.791067 | 0.395534 | − | 0.918451i | \(-0.370560\pi\) | ||||
0.395534 | + | 0.918451i | \(0.370560\pi\) | |||||||
\(500\) | −1.59490e28 | −0.730381 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.79780e28 | 0.789499 | ||||||||
\(503\) | 1.50401e28 | 0.646827 | 0.323414 | − | 0.946258i | \(-0.395169\pi\) | ||||
0.323414 | + | 0.946258i | \(0.395169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.63391e27 | −0.397414 | ||||||||
\(506\) | 6.64265e27 | 0.268387 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.40586e28 | 1.32026 | ||||||||
\(509\) | 7.64106e27 | 0.290146 | 0.145073 | − | 0.989421i | \(-0.453658\pi\) | ||||
0.145073 | + | 0.989421i | \(0.453658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.80876e28 | −2.48112 | ||||||||
\(512\) | 3.65579e28 | 1.30511 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.81767e28 | −0.622876 | ||||||||
\(515\) | −4.44729e26 | −0.0149321 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.24374e28 | −2.01277 | ||||||||
\(518\) | 8.33173e28 | 2.63192 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.80543e27 | −0.0851067 | ||||||||
\(521\) | 2.10509e28 | 0.625856 | 0.312928 | − | 0.949777i | \(-0.398690\pi\) | ||||
0.312928 | + | 0.949777i | \(0.398690\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.92433e28 | −0.835138 | −0.417569 | − | 0.908645i | \(-0.637118\pi\) | ||||
−0.417569 | + | 0.908645i | \(0.637118\pi\) | |||||||
\(524\) | −5.35570e28 | −1.49912 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.92233e28 | 1.05486 | ||||||||
\(527\) | 5.49019e28 | 1.44736 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.79811e28 | −0.962238 | ||||||||
\(530\) | −1.08994e28 | −0.270712 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.53566e28 | 0.366625 | ||||||||
\(533\) | −4.66033e28 | −1.09089 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.62807e28 | −0.366402 | ||||||||
\(536\) | −9.52885e27 | −0.210286 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.04090e28 | 0.433119 | ||||||||
\(539\) | −3.00589e28 | −0.625591 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.57924e28 | −0.716506 | −0.358253 | − | 0.933625i | \(-0.616627\pi\) | ||||
−0.358253 | + | 0.933625i | \(0.616627\pi\) | |||||||
\(542\) | 8.77653e28 | 1.72318 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.80004e28 | −1.47336 | ||||||||
\(545\) | −3.56753e27 | −0.0661005 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.96222e28 | −0.884726 | −0.442363 | − | 0.896836i | \(-0.645860\pi\) | ||||
−0.442363 | + | 0.896836i | \(0.645860\pi\) | |||||||
\(548\) | 4.66052e28 | 0.815152 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.39899e28 | 1.07722 | ||||||||
\(551\) | −2.54998e27 | −0.0421158 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.05952e28 | 1.12244 | ||||||||
\(554\) | −1.50254e28 | −0.234408 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.48993e28 | 0.223810 | ||||||||
\(557\) | −2.30026e28 | −0.339076 | −0.169538 | − | 0.985524i | \(-0.554228\pi\) | ||||
−0.169538 | + | 0.985524i | \(0.554228\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.82240e28 | 0.542641 | ||||||||
\(560\) | 4.75520e28 | 0.662513 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.57304e27 | −0.0613725 | ||||||||
\(563\) | −5.62134e28 | −0.740461 | −0.370230 | − | 0.928940i | \(-0.620721\pi\) | ||||
−0.370230 | + | 0.928940i | \(0.620721\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.60746e28 | 0.584727 | ||||||||
\(566\) | 1.97594e28 | 0.246151 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.79233e27 | −0.117552 | ||||||||
\(569\) | 8.17427e28 | 0.963319 | 0.481660 | − | 0.876358i | \(-0.340034\pi\) | ||||
0.481660 | + | 0.876358i | \(0.340034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.28184e28 | 0.713523 | 0.356762 | − | 0.934195i | \(-0.383881\pi\) | ||||
0.356762 | + | 0.934195i | \(0.383881\pi\) | |||||||
\(572\) | −8.37052e28 | −0.933456 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.67172e29 | 1.79717 | ||||||||
\(575\) | 1.43584e28 | 0.151563 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.12097e29 | −1.14090 | −0.570449 | − | 0.821333i | \(-0.693231\pi\) | ||||
−0.570449 | + | 0.821333i | \(0.693231\pi\) | |||||||
\(578\) | 2.67299e28 | 0.267150 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.44534e27 | 0.0524845 | ||||||||
\(581\) | 4.08650e28 | 0.386814 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.65652e28 | 0.425149 | ||||||||
\(584\) | −3.72784e28 | −0.334289 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.80007e29 | 1.55727 | ||||||||
\(587\) | 1.68937e29 | 1.43557 | 0.717784 | − | 0.696266i | \(-0.245157\pi\) | ||||
0.717784 | + | 0.696266i | \(0.245157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.31665e28 | −0.435941 | ||||||||
\(590\) | 1.09124e29 | 0.878970 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.15550e29 | 1.67560 | ||||||||
\(593\) | 2.13722e29 | 1.63221 | 0.816104 | − | 0.577906i | \(-0.196130\pi\) | ||||
0.816104 | + | 0.577906i | \(0.196130\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.85471e28 | −0.652749 | ||||||||
\(596\) | 1.55316e29 | 1.12494 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.02539e28 | −0.281479 | ||||||||
\(599\) | 6.63059e28 | 0.455586 | 0.227793 | − | 0.973710i | \(-0.426849\pi\) | ||||
0.227793 | + | 0.973710i | \(0.426849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.56590e29 | −1.70238 | −0.851192 | − | 0.524854i | \(-0.824120\pi\) | ||||
−0.851192 | + | 0.524854i | \(0.824120\pi\) | |||||||
\(602\) | −1.37114e29 | −0.893964 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.61771e29 | 1.64829 | ||||||||
\(605\) | 1.32527e27 | 0.00820109 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.37131e28 | 0.380845 | 0.190422 | − | 0.981702i | \(-0.439014\pi\) | ||||
0.190422 | + | 0.981702i | \(0.439014\pi\) | |||||||
\(608\) | 7.55348e28 | 0.443772 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.41232e28 | 0.250440 | ||||||||
\(611\) | 3.78365e29 | 2.11095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.43258e29 | 1.31139 | 0.655694 | − | 0.755027i | \(-0.272376\pi\) | ||||
0.655694 | + | 0.755027i | \(0.272376\pi\) | |||||||
\(614\) | −5.80647e28 | −0.307712 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.29934e28 | −0.220194 | ||||||||
\(617\) | −2.30434e28 | −0.116025 | −0.0580127 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580127 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.66125e29 | −1.78188 | −0.890938 | − | 0.454125i | \(-0.849952\pi\) | ||||
−0.890938 | + | 0.454125i | \(0.849952\pi\) | |||||||
\(620\) | 1.13534e29 | 0.543267 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.54103e29 | 0.712872 | ||||||||
\(623\) | −9.65326e28 | −0.439086 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.82841e28 | 0.388278 | ||||||||
\(626\) | 2.36452e29 | 1.02262 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.20624e29 | 1.34097 | ||||||||
\(629\) | −4.01379e29 | −1.65091 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.86516e28 | −0.352678 | −0.176339 | − | 0.984330i | \(-0.556425\pi\) | ||||
−0.176339 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(632\) | 3.86514e28 | 0.151229 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.04800e28 | 0.342464 | ||||||||
\(635\) | 1.90177e29 | 0.708001 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.82154e29 | 0.656107 | ||||||||
\(638\) | −4.98588e28 | −0.176654 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.65603e28 | 0.159634 | ||||||||
\(641\) | −2.13941e29 | −0.721581 | −0.360790 | − | 0.932647i | \(-0.617493\pi\) | ||||
−0.360790 | + | 0.932647i | \(0.617493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.22607e29 | −0.726647 | −0.363323 | − | 0.931663i | \(-0.618358\pi\) | ||||
−0.363323 | + | 0.931663i | \(0.618358\pi\) | |||||||
\(644\) | 6.73743e28 | 0.216368 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.58552e29 | −0.492869 | ||||||||
\(647\) | −1.83534e29 | −0.561333 | −0.280666 | − | 0.959805i | \(-0.590555\pi\) | ||||
−0.280666 | + | 0.959805i | \(0.590555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.66205e29 | −1.38041 | ||||||||
\(650\) | −3.87773e29 | −1.12976 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.71718e29 | 1.04861 | ||||||||
\(653\) | −4.04588e29 | −1.12312 | −0.561558 | − | 0.827437i | \(-0.689798\pi\) | ||||
−0.561558 | + | 0.827437i | \(0.689798\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.99052e29 | −0.803921 | ||||||||
\(656\) | 4.32490e29 | 1.14416 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.35724e30 | −3.47764 | ||||||||
\(659\) | 1.05672e29 | 0.266479 | 0.133240 | − | 0.991084i | \(-0.457462\pi\) | ||||
0.133240 | + | 0.991084i | \(0.457462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.72335e29 | 0.909532 | 0.454766 | − | 0.890611i | \(-0.349723\pi\) | ||||
0.454766 | + | 0.890611i | \(0.349723\pi\) | |||||||
\(662\) | −5.16564e29 | −1.24198 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.23739e28 | 0.0521166 | ||||||||
\(665\) | 8.57482e28 | 0.196606 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.11876e28 | −0.0248551 | ||||||||
\(668\) | −3.92132e28 | −0.0857589 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.71593e29 | 0.787558 | ||||||||
\(671\) | −1.88505e29 | −0.393312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.57345e29 | 1.12711 | 0.563554 | − | 0.826079i | \(-0.309434\pi\) | ||||
0.563554 | + | 0.826079i | \(0.309434\pi\) | |||||||
\(674\) | −9.11591e29 | −1.81498 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.40110e28 | 0.104242 | ||||||||
\(677\) | −9.43636e29 | −1.79318 | −0.896589 | − | 0.442863i | \(-0.853963\pi\) | ||||
−0.896589 | + | 0.442863i | \(0.853963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.47943e29 | −1.74642 | ||||||||
\(680\) | −4.84802e28 | −0.0879469 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.03954e30 | −1.82855 | ||||||||
\(683\) | 2.26004e29 | 0.391469 | 0.195735 | − | 0.980657i | \(-0.437291\pi\) | ||||
0.195735 | + | 0.980657i | \(0.437291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.60235e29 | 0.437134 | ||||||||
\(686\) | 4.00148e29 | 0.661938 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.54729e29 | −0.569138 | ||||||||
\(689\) | −2.82181e29 | −0.445888 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.59020e29 | 0.243743 | 0.121872 | − | 0.992546i | \(-0.461110\pi\) | ||||
0.121872 | + | 0.992546i | \(0.461110\pi\) | |||||||
\(692\) | −7.17383e29 | −1.08302 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.17869e29 | 0.612021 | ||||||||
\(695\) | 8.31948e28 | 0.120021 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.05345e29 | −1.12730 | ||||||||
\(698\) | 6.63081e29 | 0.914292 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.49028e29 | 0.868429 | ||||||||
\(701\) | −8.48451e28 | −0.111838 | −0.0559188 | − | 0.998435i | \(-0.517809\pi\) | ||||
−0.0559188 | + | 0.998435i | \(0.517809\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.88691e29 | 0.497249 | ||||||||
\(704\) | 5.88870e29 | 0.742176 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.92524e29 | 1.21420 | ||||||||
\(707\) | 8.94689e29 | 1.07837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.48138e30 | −1.73333 | −0.866663 | − | 0.498894i | \(-0.833740\pi\) | ||||
−0.866663 | + | 0.498894i | \(0.833740\pi\) | |||||||
\(710\) | 3.81868e29 | 0.440251 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.28523e28 | −0.0591594 | ||||||||
\(713\) | −2.33259e29 | −0.257275 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.67394e29 | −0.500576 | ||||||||
\(716\) | −1.50779e30 | −1.59131 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.58445e30 | −1.62395 | ||||||||
\(719\) | 3.93222e29 | 0.397178 | 0.198589 | − | 0.980083i | \(-0.436364\pi\) | ||||
0.198589 | + | 0.980083i | \(0.436364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.13014e28 | 0.0405177 | ||||||||
\(722\) | −1.26262e30 | −1.22076 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.33160e30 | −1.25061 | ||||||||
\(725\) | −1.07772e29 | −0.0997603 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.86883e30 | 1.68058 | 0.840289 | − | 0.542139i | \(-0.182385\pi\) | ||||
0.840289 | + | 0.542139i | \(0.182385\pi\) | |||||||
\(728\) | 2.60536e29 | 0.230934 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.45373e30 | 1.25197 | ||||||||
\(731\) | 6.60544e29 | 0.560750 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.56464e30 | −1.29069 | −0.645347 | − | 0.763890i | \(-0.723287\pi\) | ||||
−0.645347 | + | 0.763890i | \(0.723287\pi\) | |||||||
\(734\) | −8.85729e29 | −0.720265 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.31396e29 | 0.261897 | ||||||||
\(737\) | −1.58754e30 | −1.23685 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.06934e29 | −0.686766 | −0.343383 | − | 0.939195i | \(-0.611573\pi\) | ||||
−0.343383 | + | 0.939195i | \(0.611573\pi\) | |||||||
\(740\) | −8.30027e29 | −0.619668 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.01222e30 | 0.734569 | ||||||||
\(743\) | 5.31590e29 | 0.380359 | 0.190180 | − | 0.981749i | \(-0.439093\pi\) | ||||
0.190180 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.67253e29 | 0.603260 | ||||||||
\(746\) | −2.64217e30 | −1.81219 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.44650e30 | −0.964607 | ||||||||
\(749\) | 1.51197e30 | 0.994222 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.95212e29 | 0.508468 | 0.254234 | − | 0.967143i | \(-0.418177\pi\) | ||||
0.254234 | + | 0.967143i | \(0.418177\pi\) | |||||||
\(752\) | −3.51132e30 | −2.21403 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.02140e29 | 0.185272 | ||||||||
\(755\) | 1.46168e30 | 0.883913 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.04161e30 | 0.612630 | 0.306315 | − | 0.951930i | \(-0.400904\pi\) | ||||
0.306315 | + | 0.951930i | \(0.400904\pi\) | |||||||
\(758\) | −1.62239e30 | −0.941084 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.69477e28 | 0.0264894 | ||||||||
\(761\) | −1.41338e30 | −0.786539 | −0.393269 | − | 0.919423i | \(-0.628656\pi\) | ||||
−0.393269 | + | 0.919423i | \(0.628656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.31312e29 | 0.179362 | ||||||||
\(764\) | 3.22296e30 | 1.72098 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.87096e30 | 1.49150 | ||||||||
\(767\) | 2.82516e30 | 1.44774 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.24769e30 | 1.61938 | 0.809688 | − | 0.586861i | \(-0.199637\pi\) | ||||
0.809688 | + | 0.586861i | \(0.199637\pi\) | |||||||
\(770\) | 1.67660e30 | 0.824664 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.31055e30 | 1.10595 | ||||||||
\(773\) | −3.03297e30 | −1.43213 | −0.716067 | − | 0.698031i | \(-0.754060\pi\) | ||||
−0.716067 | + | 0.698031i | \(0.754060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.24702e30 | −1.03262 | ||||||||
\(776\) | −5.19005e29 | −0.235301 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.05866e30 | −0.467165 | ||||||||
\(779\) | 7.79888e29 | 0.339538 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.63144e30 | −0.691408 | ||||||||
\(782\) | −6.95621e29 | −0.290872 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.69043e30 | −0.688144 | ||||||||
\(785\) | 1.79031e30 | 0.719111 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.69463e30 | 1.44489 | 0.722447 | − | 0.691427i | \(-0.243017\pi\) | ||||
0.722447 | + | 0.691427i | \(0.243017\pi\) | |||||||
\(788\) | 1.77072e29 | 0.0683319 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.50727e30 | −0.566380 | ||||||||
\(791\) | −4.27889e30 | −1.58664 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14233e30 | 0.412498 | ||||||||
\(794\) | −5.27061e30 | −1.87822 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.83557e30 | −0.637067 | ||||||||
\(797\) | 5.77690e28 | 0.0197871 | 0.00989356 | − | 0.999951i | \(-0.496851\pi\) | ||||
0.00989356 | + | 0.999951i | \(0.496851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.53846e30 | 2.18140 | ||||||||
\(800\) | 3.19240e30 | 1.05117 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.53828e30 | 0.814158 | ||||||||
\(803\) | −6.21072e30 | −1.96620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.76205e29 | 0.116029 | ||||||||
\(806\) | 6.29954e30 | 1.91774 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.89849e29 | 0.145292 | ||||||||
\(809\) | 1.52694e30 | 0.447056 | 0.223528 | − | 0.974697i | \(-0.428243\pi\) | ||||
0.223528 | + | 0.974697i | \(0.428243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.21814e30 | 0.918092 | 0.459046 | − | 0.888412i | \(-0.348191\pi\) | ||||
0.459046 | + | 0.888412i | \(0.348191\pi\) | |||||||
\(812\) | −5.05701e29 | −0.142415 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.59992e30 | 2.08571 | ||||||||
\(815\) | 2.07560e30 | 0.562328 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.39664e29 | −0.168896 | ||||||||
\(818\) | 3.16408e30 | 0.824779 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.66541e30 | −0.423131 | ||||||||
\(821\) | 6.21750e30 | 1.55960 | 0.779799 | − | 0.626030i | \(-0.215321\pi\) | ||||
0.779799 | + | 0.626030i | \(0.215321\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.59262e30 | 0.633929 | 0.316965 | − | 0.948437i | \(-0.397336\pi\) | ||||
0.316965 | + | 0.948437i | \(0.397336\pi\) | |||||||
\(824\) | 2.26128e28 | 0.00545907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.01342e31 | −2.38506 | ||||||||
\(827\) | 7.60849e30 | 1.76804 | 0.884018 | − | 0.467454i | \(-0.154829\pi\) | ||||
0.884018 | + | 0.467454i | \(0.154829\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.02047e28 | −0.00457752 | −0.00228876 | − | 0.999997i | \(-0.500729\pi\) | ||||
−0.00228876 | + | 0.999997i | \(0.500729\pi\) | |||||||
\(830\) | −8.72506e29 | −0.195186 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.56850e30 | −0.778378 | ||||||||
\(833\) | 3.14778e30 | 0.678003 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.18959e29 | −0.0459891 | ||||||||
\(836\) | 1.40077e30 | 0.290537 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.73587e30 | −1.36248 | ||||||||
\(839\) | −2.31080e30 | −0.461595 | −0.230798 | − | 0.973002i | \(-0.574134\pi\) | ||||
−0.230798 | + | 0.973002i | \(0.574134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.04887e30 | −0.983640 | ||||||||
\(842\) | −5.36873e30 | −1.03299 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.79852e30 | −0.337536 | ||||||||
\(845\) | 3.01587e29 | 0.0559008 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.23076e29 | −0.0222534 | ||||||||
\(848\) | 2.61871e30 | 0.467660 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.70104e30 | −1.16746 | ||||||||
\(851\) | 1.70532e30 | 0.293457 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.67813e30 | 0.281747 | 0.140874 | − | 0.990028i | \(-0.455009\pi\) | ||||
0.140874 | + | 0.990028i | \(0.455009\pi\) | |||||||
\(854\) | −4.09766e30 | −0.679561 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.27813e29 | 0.133955 | ||||||||
\(857\) | 5.99035e30 | 0.957533 | 0.478766 | − | 0.877942i | \(-0.341084\pi\) | ||||
0.478766 | + | 0.877942i | \(0.341084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.30587e30 | 0.359671 | 0.179836 | − | 0.983697i | \(-0.442443\pi\) | ||||
0.179836 | + | 0.983697i | \(0.442443\pi\) | |||||||
\(860\) | 1.36597e30 | 0.210478 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.47666e29 | −0.0673175 | ||||||||
\(863\) | −5.11930e30 | −0.760496 | −0.380248 | − | 0.924884i | \(-0.624161\pi\) | ||||
−0.380248 | + | 0.924884i | \(0.624161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.00573e30 | −0.580782 | ||||||||
\(866\) | 1.10908e31 | 1.58864 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.05437e31 | −1.47414 | ||||||||
\(869\) | 6.43946e30 | 0.889491 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.62035e30 | 1.29718 | ||||||||
\(872\) | 1.81396e29 | 0.0241659 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.73633e29 | 0.0876099 | ||||||||
\(875\) | 8.27056e30 | 1.06280 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.87157e30 | −0.862105 | −0.431052 | − | 0.902327i | \(-0.641858\pi\) | ||||
−0.431052 | + | 0.902327i | \(0.641858\pi\) | |||||||
\(878\) | −2.38776e30 | −0.296004 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.33753e30 | 0.525018 | ||||||||
\(881\) | 5.75159e30 | 0.687924 | 0.343962 | − | 0.938984i | \(-0.388231\pi\) | ||||
0.343962 | + | 0.938984i | \(0.388231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.44146e30 | 0.518726 | 0.259363 | − | 0.965780i | \(-0.416487\pi\) | ||||
0.259363 | + | 0.965780i | \(0.416487\pi\) | |||||||
\(884\) | 8.76564e30 | 1.01166 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.00943e31 | 1.13768 | ||||||||
\(887\) | −4.85663e30 | −0.540925 | −0.270463 | − | 0.962730i | \(-0.587177\pi\) | ||||
−0.270463 | + | 0.962730i | \(0.587177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.76615e31 | −1.92114 | ||||||||
\(890\) | 2.06106e30 | 0.221562 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.68842e30 | −0.387266 | ||||||||
\(893\) | −6.33179e30 | −0.657031 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.41923e30 | −0.853356 | ||||||||
\(896\) | −4.32399e30 | −0.433163 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.48558e30 | 0.732527 | ||||||||
\(899\) | 1.75081e30 | 0.169341 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.87632e30 | −0.460768 | ||||||||
\(902\) | 1.52488e31 | 1.42419 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.34272e30 | −0.213773 | ||||||||
\(905\) | −7.43543e30 | −0.670650 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.25564e31 | −1.10660 | −0.553298 | − | 0.832984i | \(-0.686631\pi\) | ||||
−0.553298 | + | 0.832984i | \(0.686631\pi\) | |||||||
\(908\) | 2.72592e30 | 0.237471 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.01600e31 | −0.864890 | ||||||||
\(911\) | 5.33864e30 | 0.449249 | 0.224625 | − | 0.974445i | \(-0.427884\pi\) | ||||
0.224625 | + | 0.974445i | \(0.427884\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.72756e30 | 0.306536 | ||||||||
\(914\) | 1.78050e31 | 1.44746 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.23633e30 | −0.416030 | ||||||||
\(917\) | 2.77726e31 | 2.18141 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.80818e31 | 1.38813 | 0.694063 | − | 0.719914i | \(-0.255819\pi\) | ||||
0.694063 | + | 0.719914i | \(0.255819\pi\) | |||||||
\(920\) | 2.05975e29 | 0.0156330 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.05601e31 | −1.52528 | ||||||||
\(923\) | 9.88636e30 | 0.725134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.64276e31 | 1.17784 | ||||||||
\(926\) | −9.05459e30 | −0.641880 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.48741e30 | −0.172383 | ||||||||
\(929\) | −2.43205e31 | −1.66651 | −0.833254 | − | 0.552890i | \(-0.813525\pi\) | ||||
−0.833254 | + | 0.552890i | \(0.813525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.04828e30 | −0.204213 | ||||||||
\(932\) | −1.03500e31 | −0.685602 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.83512e31 | −1.18857 | ||||||||
\(935\) | −8.07697e30 | −0.517281 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.65121e31 | 1.03404 | 0.517018 | − | 0.855974i | \(-0.327042\pi\) | ||||
0.517018 | + | 0.855974i | \(0.327042\pi\) | |||||||
\(938\) | −3.45094e31 | −2.13701 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.35212e31 | 0.818788 | ||||||||
\(941\) | 1.09085e31 | 0.653241 | 0.326620 | − | 0.945156i | \(-0.394090\pi\) | ||||
0.326620 | + | 0.945156i | \(0.394090\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.42162e30 | 0.200382 | ||||||||
\(944\) | −2.62182e31 | −1.51844 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.25071e31 | −0.708435 | ||||||||
\(947\) | −2.89763e31 | −1.62318 | −0.811592 | − | 0.584225i | \(-0.801399\pi\) | ||||
−0.811592 | + | 0.584225i | \(0.801399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.76364e31 | 2.06211 | ||||||||
\(950\) | 6.48923e30 | 0.351637 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.50229e30 | 0.238641 | ||||||||
\(953\) | 1.18340e31 | 0.620376 | 0.310188 | − | 0.950675i | \(-0.399608\pi\) | ||||
0.310188 | + | 0.950675i | \(0.399608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.79964e31 | 0.922892 | ||||||||
\(956\) | 9.85849e30 | 0.500038 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.48578e31 | 0.737255 | ||||||||
\(959\) | −2.41677e31 | −1.18615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.56784e31 | 0.752845 | ||||||||
\(962\) | −4.60548e31 | −2.18744 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.55668e29 | 0.0351174 | ||||||||
\(965\) | 1.29017e31 | 0.593075 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.41768e31 | 1.08748 | 0.543739 | − | 0.839254i | \(-0.317008\pi\) | ||||
0.543739 | + | 0.839254i | \(0.317008\pi\) | |||||||
\(968\) | −6.73848e28 | −0.00299827 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.02395e31 | 0.881244 | ||||||||
\(971\) | 2.60921e31 | 1.12384 | 0.561922 | − | 0.827190i | \(-0.310062\pi\) | ||||
0.561922 | + | 0.827190i | \(0.310062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.72619e30 | −0.325672 | ||||||||
\(974\) | 1.07874e31 | 0.449830 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.06011e31 | −0.432640 | ||||||||
\(977\) | 1.30979e31 | 0.528822 | 0.264411 | − | 0.964410i | \(-0.414823\pi\) | ||||
0.264411 | + | 0.964410i | \(0.414823\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.80538e30 | −0.347960 | ||||||||
\(980\) | 6.50942e30 | 0.254489 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.17126e31 | −0.830885 | ||||||||
\(983\) | 2.83479e31 | 1.07327 | 0.536636 | − | 0.843814i | \(-0.319695\pi\) | ||||
0.536636 | + | 0.843814i | \(0.319695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.88735e29 | 0.0366437 | ||||||||
\(986\) | 5.22123e30 | 0.191454 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.48856e30 | −0.304709 | ||||||||
\(989\) | −2.80642e30 | −0.0996762 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.80586e31 | −0.975646 | −0.487823 | − | 0.872942i | \(-0.662209\pi\) | ||||
−0.487823 | + | 0.872942i | \(0.662209\pi\) | |||||||
\(992\) | −5.18619e31 | −1.78433 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.54636e31 | −1.19461 | ||||||||
\(995\) | −1.02495e31 | −0.341634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.09168e30 | 0.166174 | 0.0830868 | − | 0.996542i | \(-0.473522\pi\) | ||||
0.0830868 | + | 0.996542i | \(0.473522\pi\) | |||||||
\(998\) | 3.35394e31 | 1.08314 | ||||||||
\(999\) | 0 | 0 |
(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 | 81.22.a.d.1.17 | 20 | ||
3.2 | odd | 2 | 81.22.a.c.1.4 | 20 | |||
9.2 | odd | 6 | 9.22.c.a.4.17 | ✓ | 40 | ||
9.4 | even | 3 | 27.22.c.a.19.4 | 40 | |||
9.5 | odd | 6 | 9.22.c.a.7.17 | yes | 40 | ||
9.7 | even | 3 | 27.22.c.a.10.4 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.22.c.a.4.17 | ✓ | 40 | 9.2 | odd | 6 | ||
9.22.c.a.7.17 | yes | 40 | 9.5 | odd | 6 | ||
27.22.c.a.10.4 | 40 | 9.7 | even | 3 | |||
27.22.c.a.19.4 | 40 | 9.4 | even | 3 | |||
81.22.a.c.1.4 | 20 | 3.2 | odd | 2 | |||
81.22.a.d.1.17 | 20 | 1.1 | even | 1 | trivial |