Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,12,Mod(1,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(6.14674544448\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{109}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.72015\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 696.180 | 1.65407 | 0.827036 | − | 0.562149i | \(-0.190025\pi\) | ||||
0.827036 | + | 0.562149i | \(0.190025\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4084.16 | −0.584477 | −0.292238 | − | 0.956346i | \(-0.594400\pi\) | ||||
−0.292238 | + | 0.956346i | \(0.594400\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 73591.5 | 1.65496 | 0.827482 | − | 0.561492i | \(-0.189772\pi\) | ||||
0.827482 | + | 0.561492i | \(0.189772\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 307519. | 1.73595 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −383508. | −0.717985 | −0.358992 | − | 0.933340i | \(-0.616880\pi\) | ||||
−0.358992 | + | 0.933340i | \(0.616880\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.15867e6 | 0.865510 | 0.432755 | − | 0.901512i | \(-0.357541\pi\) | ||||
0.432755 | + | 0.901512i | \(0.357541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.84331e6 | −0.966767 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.51693e6 | −1.11320 | −0.556601 | − | 0.830780i | \(-0.687895\pi\) | ||||
−0.556601 | + | 0.830780i | \(0.687895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.39982e7 | −1.29697 | −0.648483 | − | 0.761229i | \(-0.724596\pi\) | ||||
−0.648483 | + | 0.761229i | \(0.724596\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.12329e7 | 2.73743 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.37394e6 | 0.0445107 | 0.0222554 | − | 0.999752i | \(-0.492915\pi\) | ||||
0.0222554 | + | 0.999752i | \(0.492915\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.21478e7 | −0.658387 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.07624e7 | 1.21732 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.46197e7 | −0.675561 | −0.337781 | − | 0.941225i | \(-0.609676\pi\) | ||||
−0.337781 | + | 0.941225i | \(0.609676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.32297e7 | 0.0829969 | 0.0414985 | − | 0.999139i | \(-0.486787\pi\) | ||||
0.0414985 | + | 0.999139i | \(0.486787\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.66991e8 | −1.18760 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00559e8 | −0.967288 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.67200e7 | −0.0396394 | −0.0198197 | − | 0.999804i | \(-0.506309\pi\) | ||||
−0.0198197 | + | 0.999804i | \(0.506309\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.06644e8 | 1.43162 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03298e9 | 1.39245 | 0.696225 | − | 0.717823i | \(-0.254861\pi\) | ||||
0.696225 | + | 0.717823i | \(0.254861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.93764e8 | 0.201001 | 0.100500 | − | 0.994937i | \(-0.467956\pi\) | ||||
0.100500 | + | 0.994937i | \(0.467956\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.25596e9 | −1.01462 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.16005e9 | −0.737803 | −0.368901 | − | 0.929469i | \(-0.620266\pi\) | ||||
−0.368901 | + | 0.929469i | \(0.620266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.43839e9 | 1.73891 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.53696e9 | −1.84132 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.44363e8 | 0.145956 | 0.0729778 | − | 0.997334i | \(-0.476750\pi\) | ||||
0.0729778 | + | 0.997334i | \(0.476750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.56631e9 | 0.419645 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.74529e9 | −2.14528 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.28304e8 | −0.0233644 | −0.0116822 | − | 0.999932i | \(-0.503719\pi\) | ||||
−0.0116822 | + | 0.999932i | \(0.503719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.96097e9 | 1.20685 | 0.603423 | − | 0.797421i | \(-0.293803\pi\) | ||||
0.603423 | + | 0.797421i | \(0.293803\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.26308e10 | 2.87294 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.73220e9 | −0.505871 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.89243e9 | −0.623678 | −0.311839 | − | 0.950135i | \(-0.600945\pi\) | ||||
−0.311839 | + | 0.950135i | \(0.600945\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.56509e8 | 0.0736240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.12698e10 | −0.741305 | −0.370652 | − | 0.928772i | \(-0.620866\pi\) | ||||
−0.370652 | + | 0.928772i | \(0.620866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.34998e9 | 0.189132 | 0.0945662 | − | 0.995519i | \(-0.469854\pi\) | ||||
0.0945662 | + | 0.995519i | \(0.469854\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.23806e10 | −1.08902 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.82230e10 | −1.18824 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.36237e10 | 1.96068 | 0.980342 | − | 0.197304i | \(-0.0632184\pi\) | ||||
0.980342 | + | 0.197304i | \(0.0632184\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.71083e9 | 0.277583 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.31693e10 | −1.76026 | −0.880130 | − | 0.474733i | \(-0.842545\pi\) | ||||
−0.880130 | + | 0.474733i | \(0.842545\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.66162e10 | 0.650641 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.19487e10 | −1.11743 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.62373e10 | 1.82683 | 0.913416 | − | 0.407028i | \(-0.133435\pi\) | ||||
0.913416 | + | 0.407028i | \(0.133435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.52685e10 | 1.43239 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.21027e9 | 0.137283 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.71710e10 | 0.758047 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.37466e10 | −0.517250 | −0.258625 | − | 0.965978i | \(-0.583269\pi\) | ||||
−0.258625 | + | 0.965978i | \(0.583269\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.17936e11 | −1.24639 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.68061e11 | −1.59111 | −0.795554 | − | 0.605882i | \(-0.792820\pi\) | ||||
−0.795554 | + | 0.605882i | \(0.792820\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.02325e10 | 0.511948 | 0.255974 | − | 0.966684i | \(-0.417604\pi\) | ||||
0.255974 | + | 0.966684i | \(0.417604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.09243e11 | −1.59996 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.39380e11 | 0.960701 | 0.480351 | − | 0.877077i | \(-0.340509\pi\) | ||||
0.480351 | + | 0.877077i | \(0.340509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.19601e11 | 0.744540 | 0.372270 | − | 0.928124i | \(-0.378579\pi\) | ||||
0.372270 | + | 0.928124i | \(0.378579\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.16401e10 | −0.0655664 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.69277e10 | 0.137489 | 0.0687445 | − | 0.997634i | \(-0.478101\pi\) | ||||
0.0687445 | + | 0.997634i | \(0.478101\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.61139e9 | −0.0260155 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.56314e11 | 1.50249 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.79591e11 | −1.84231 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.38233e11 | −0.484498 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.19138e11 | 2.30321 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.30718e11 | 0.969289 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.63631e11 | −0.439486 | −0.219743 | − | 0.975558i | \(-0.570522\pi\) | ||||
−0.219743 | + | 0.975558i | \(0.570522\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.34895e11 | 0.332469 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.54332e11 | −0.575981 | −0.287991 | − | 0.957633i | \(-0.592987\pi\) | ||||
−0.287991 | + | 0.957633i | \(0.592987\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.03015e12 | −2.14643 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.70688e11 | −0.711496 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.05270e12 | 1.86355 | 0.931776 | − | 0.363032i | \(-0.118259\pi\) | ||||
0.931776 | + | 0.363032i | \(0.118259\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.02335e11 | −1.47498 | −0.737491 | − | 0.675357i | \(-0.763989\pi\) | ||||
−0.737491 | + | 0.675357i | \(0.763989\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.07607e11 | −1.22038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.44361e11 | −0.621423 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.04759e11 | 0.394850 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.39374e12 | 2.87628 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.08288e12 | 1.20797 | 0.603986 | − | 0.796995i | \(-0.293578\pi\) | ||||
0.603986 | + | 0.796995i | \(0.293578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.99725e11 | 0.932688 | 0.466344 | − | 0.884603i | \(-0.345571\pi\) | ||||
0.466344 | + | 0.884603i | \(0.345571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00408e12 | −1.93247 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.40323e10 | −0.0485098 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.05620e11 | −0.506701 | −0.253351 | − | 0.967375i | \(-0.581533\pi\) | ||||
−0.253351 | + | 0.967375i | \(0.581533\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.09356e11 | 0.241421 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.01110e11 | 0.0736637 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.92020e11 | 0.402999 | 0.201500 | − | 0.979489i | \(-0.435418\pi\) | ||||
0.201500 | + | 0.979489i | \(0.435418\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.09043e12 | 0.694124 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.67821e10 | −0.0338276 | −0.0169138 | − | 0.999857i | \(-0.505384\pi\) | ||||
−0.0169138 | + | 0.999857i | \(0.505384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.49639e11 | −0.250892 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.30473e12 | −2.25147 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.27930e12 | 1.11828 | 0.559138 | − | 0.829075i | \(-0.311132\pi\) | ||||
0.559138 | + | 0.829075i | \(0.311132\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.36581e12 | −1.08961 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.93228e10 | −0.0386464 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.91742e12 | −0.779876 | −0.389938 | − | 0.920841i | \(-0.627503\pi\) | ||||
−0.389938 | + | 0.920841i | \(0.627503\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.61293e12 | −1.38238 | −0.691190 | − | 0.722673i | \(-0.742913\pi\) | ||||
−0.691190 | + | 0.722673i | \(0.742913\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.54226e12 | 1.99621 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.82871e10 | 0.0231683 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.49930e12 | 0.799263 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.67934e12 | 2.01462 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.07217e11 | −0.172846 | −0.0864232 | − | 0.996259i | \(-0.527544\pi\) | ||||
−0.0864232 | + | 0.996259i | \(0.527544\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.64252e12 | 1.24793 | 0.623963 | − | 0.781454i | \(-0.285522\pi\) | ||||
0.623963 | + | 0.781454i | \(0.285522\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.29446e12 | −0.836746 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.86139e12 | −1.16734 | −0.583668 | − | 0.811992i | \(-0.698383\pi\) | ||||
−0.583668 | + | 0.811992i | \(0.698383\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.52349e12 | 1.48180 | 0.740898 | − | 0.671618i | \(-0.234400\pi\) | ||||
0.740898 | + | 0.671618i | \(0.234400\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.79837e12 | −1.03161 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.49138e12 | −1.11803 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.21884e12 | −0.813855 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.22513e11 | 0.0772686 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.36844e12 | 0.931202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.89227e12 | 0.311479 | 0.155740 | − | 0.987798i | \(-0.450224\pi\) | ||||
0.155740 | + | 0.987798i | \(0.450224\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.84583e12 | −1.22617 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.91364e11 | −0.117480 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.73597e11 | 0.137357 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.33219e12 | 0.312839 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.55099e12 | −0.963488 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.33591e12 | 0.769365 | 0.384682 | − | 0.923049i | \(-0.374311\pi\) | ||||
0.384682 | + | 0.923049i | \(0.374311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.88606e12 | −1.14293 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.95535e12 | 0.545673 | 0.272837 | − | 0.962060i | \(-0.412038\pi\) | ||||
0.272837 | + | 0.962060i | \(0.412038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.55285e13 | 1.62943 | 0.814714 | − | 0.579863i | \(-0.196894\pi\) | ||||
0.814714 | + | 0.579863i | \(0.196894\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.96483e13 | −1.96543 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.75664e12 | 0.739973 | 0.369986 | − | 0.929037i | \(-0.379362\pi\) | ||||
0.369986 | + | 0.929037i | \(0.379362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.73784e12 | 0.431229 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.73317e13 | 3.24311 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.18729e12 | 0.347332 | 0.173666 | − | 0.984805i | \(-0.444439\pi\) | ||||
0.173666 | + | 0.984805i | \(0.444439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.28156e12 | 0.656173 | 0.328087 | − | 0.944648i | \(-0.393596\pi\) | ||||
0.328087 | + | 0.944648i | \(0.393596\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00140e13 | −0.758180 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.40429e13 | −1.01635 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.62194e13 | −1.12254 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.39772e13 | −2.91160 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.31791e11 | −0.0400284 | −0.0200142 | − | 0.999800i | \(-0.506371\pi\) | ||||
−0.0200142 | + | 0.999800i | \(0.506371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.26918e11 | −0.0319580 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.85296e13 | 1.07621 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.76085e13 | 0.979691 | 0.489845 | − | 0.871809i | \(-0.337053\pi\) | ||||
0.489845 | + | 0.871809i | \(0.337053\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.23045e12 | −0.0656018 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.29470e13 | −1.17274 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.18141e13 | −1.06901 | −0.534505 | − | 0.845165i | \(-0.679502\pi\) | ||||
−0.534505 | + | 0.845165i | \(0.679502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.81485e12 | −0.0853076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.69985e13 | 3.02171 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.09453e13 | −0.473795 | −0.236897 | − | 0.971535i | \(-0.576131\pi\) | ||||
−0.236897 | + | 0.971535i | \(0.576131\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.38029e13 | −1.82042 | −0.910210 | − | 0.414146i | \(-0.864080\pi\) | ||||
−0.910210 | + | 0.414146i | \(0.864080\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.93622e13 | 2.36927 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.23290e13 | 0.472712 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.83236e13 | −1.41198 | −0.705988 | − | 0.708224i | \(-0.749497\pi\) | ||||
−0.705988 | + | 0.708224i | \(0.749497\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.06840e12 | 0.144079 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.88363e13 | −0.641372 | −0.320686 | − | 0.947186i | \(-0.603913\pi\) | ||||
−0.320686 | + | 0.947186i | \(0.603913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.59883e12 | −0.117852 | −0.0589258 | − | 0.998262i | \(-0.518768\pi\) | ||||
−0.0589258 | + | 0.998262i | \(0.518768\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.98013e13 | 1.25386 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.60185e13 | 2.30446 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.19853e12 | 0.239220 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.04555e13 | −0.855568 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.89960e13 | −0.513913 | −0.256957 | − | 0.966423i | \(-0.582720\pi\) | ||||
−0.256957 | + | 0.966423i | \(0.582720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.24015e11 | 0.0136560 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.48081e13 | −0.874018 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.59195e12 | 0.0385245 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.42594e13 | 0.332649 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.17001e14 | −2.63181 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.25138e13 | −0.705373 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.07622e13 | −1.06238 | −0.531189 | − | 0.847253i | \(-0.678255\pi\) | ||||
−0.531189 | + | 0.847253i | \(0.678255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.19326e13 | 0.846799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.89908e13 | 0.954844 | 0.477422 | − | 0.878674i | \(-0.341571\pi\) | ||||
0.477422 | + | 0.878674i | \(0.341571\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.02897e13 | 0.381752 | 0.190876 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190876 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.24277e13 | −1.67917 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.80299e13 | 1.01818 | 0.509091 | − | 0.860712i | \(-0.329982\pi\) | ||||
0.509091 | + | 0.860712i | \(0.329982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.86173e13 | 0.485043 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.70332e13 | 1.58907 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.12256e13 | 1.44379 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.72488e13 | −0.569841 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.32636e13 | 1.23152 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.53702e13 | −1.22104 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.94810e13 | −0.269500 | −0.134750 | − | 0.990880i | \(-0.543023\pi\) | ||||
−0.134750 | + | 0.990880i | \(0.543023\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.14172e12 | −0.0688122 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.81497e13 | 0.364526 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.11994e14 | −1.40356 | −0.701782 | − | 0.712392i | \(-0.747612\pi\) | ||||
−0.701782 | + | 0.712392i | \(0.747612\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.87465e13 | 0.227417 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.07372e12 | −0.0595905 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.07522e14 | 1.22287 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.90653e12 | −0.0430315 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.43917e14 | −1.53568 | −0.767841 | − | 0.640640i | \(-0.778669\pi\) | ||||
−0.767841 | + | 0.640640i | \(0.778669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.17413e14 | 1.21389 | 0.606943 | − | 0.794745i | \(-0.292396\pi\) | ||||
0.606943 | + | 0.794745i | \(0.292396\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.05164e14 | 1.05360 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.14959e12 | −0.0305839 | −0.0152919 | − | 0.999883i | \(-0.504868\pi\) | ||||
−0.0152919 | + | 0.999883i | \(0.504868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.60278e13 | 0.433275 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.33882e14 | −3.04732 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.16645e14 | −1.91748 | −0.958738 | − | 0.284291i | \(-0.908242\pi\) | ||||
−0.958738 | + | 0.284291i | \(0.908242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.94605e13 | 0.682121 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.62349e13 | −0.801394 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.36818e13 | −0.110544 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.32924e14 | −1.04217 | −0.521085 | − | 0.853505i | \(-0.674473\pi\) | ||||
−0.521085 | + | 0.853505i | \(0.674473\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.17660e14 | 2.41723 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.27014e13 | 0.241551 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.97449e13 | 0.356738 | 0.178369 | − | 0.983964i | \(-0.442918\pi\) | ||||
0.178369 | + | 0.983964i | \(0.442918\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.30239e14 | 1.60327 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.64598e13 | −0.584705 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.41630e13 | 0.421472 | 0.210736 | − | 0.977543i | \(-0.432414\pi\) | ||||
0.210736 | + | 0.977543i | \(0.432414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.13917e14 | −0.726942 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.53711e14 | 0.953040 | 0.476520 | − | 0.879164i | \(-0.341898\pi\) | ||||
0.476520 | + | 0.879164i | \(0.341898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.15267e14 | 0.694498 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.95862e13 | 0.348928 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.08115e14 | 1.75384 | 0.876921 | − | 0.480635i | \(-0.159594\pi\) | ||||
0.876921 | + | 0.480635i | \(0.159594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.95388e12 | −0.0495495 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.77061e14 | −0.952714 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.19008e14 | −1.14597 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.15252e14 | 1.09547 | 0.547734 | − | 0.836653i | \(-0.315491\pi\) | ||||
0.547734 | + | 0.836653i | \(0.315491\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.17171e14 | −3.55035 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.29414e13 | −0.206815 | −0.103407 | − | 0.994639i | \(-0.532975\pi\) | ||||
−0.103407 | + | 0.994639i | \(0.532975\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.53289e13 | 0.0718347 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.55764e13 | −0.162241 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.41227e12 | 0.0284605 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.78142e14 | −0.769639 | −0.384819 | − | 0.922992i | \(-0.625736\pi\) | ||||
−0.384819 | + | 0.922992i | \(0.625736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.32869e14 | 3.08245 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.44211e12 | −0.0386673 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.57993e14 | 1.02883 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.28187e14 | −2.43972 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.36601e14 | −1.27332 | −0.636662 | − | 0.771143i | \(-0.719685\pi\) | ||||
−0.636662 | + | 0.771143i | \(0.719685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.36951e13 | 0.234722 | 0.117361 | − | 0.993089i | \(-0.462557\pi\) | ||||
0.117361 | + | 0.993089i | \(0.462557\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.56739e14 | −1.28079 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.09505e14 | 0.732918 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.85860e14 | 1.99729 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.09355e14 | −1.02788 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.38853e14 | 0.449707 | 0.224853 | − | 0.974393i | \(-0.427810\pi\) | ||||
0.224853 | + | 0.974393i | \(0.427810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.07253e14 | −0.970093 | −0.485046 | − | 0.874488i | \(-0.661197\pi\) | ||||
−0.485046 | + | 0.874488i | \(0.661197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.12167e14 | 0.653110 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.92328e13 | −0.0577289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.37747e14 | −0.695921 | −0.347961 | − | 0.937509i | \(-0.613126\pi\) | ||||
−0.347961 | + | 0.937509i | \(0.613126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.05737e15 | 3.01866 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.82803e13 | −0.190141 | −0.0950703 | − | 0.995471i | \(-0.530308\pi\) | ||||
−0.0950703 | + | 0.995471i | \(0.530308\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.93048e14 | −1.06774 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.53881e14 | 1.99807 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.19557e14 | 1.86084 | 0.930422 | − | 0.366490i | \(-0.119440\pi\) | ||||
0.930422 | + | 0.366490i | \(0.119440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.96156e14 | −0.999758 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.26370e14 | 1.54273 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.48250e14 | −0.837198 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.95803e14 | −1.39818 | −0.699091 | − | 0.715033i | \(-0.746412\pi\) | ||||
−0.699091 | + | 0.715033i | \(0.746412\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.91492e14 | −1.35513 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.48547e14 | −0.555973 | −0.277987 | − | 0.960585i | \(-0.589667\pi\) | ||||
−0.277987 | + | 0.960585i | \(0.589667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.55882e14 | −1.21419 | −0.607096 | − | 0.794629i | \(-0.707666\pi\) | ||||
−0.607096 | + | 0.794629i | \(0.707666\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.76162e13 | −0.0802386 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.11081e13 | 0.106475 | 0.0532374 | − | 0.998582i | \(-0.483046\pi\) | ||||
0.0532374 | + | 0.998582i | \(0.483046\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.07224e14 | −1.03217 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.21620e14 | −0.838121 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.43103e13 | −0.144315 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.50013e14 | 0.853906 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.36650e14 | 0.253372 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.79608e14 | 1.23144 | 0.615720 | − | 0.787965i | \(-0.288865\pi\) | ||||
0.615720 | + | 0.787965i | \(0.288865\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.93730e13 | −0.0343083 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.03910e13 | 0.121845 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.78668e14 | 0.302320 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.50601e14 | −0.579967 | −0.289984 | − | 0.957032i | \(-0.593650\pi\) | ||||
−0.289984 | + | 0.957032i | \(0.593650\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.12152e14 | 0.666590 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.60616e14 | −0.886579 | −0.443289 | − | 0.896379i | \(-0.646189\pi\) | ||||
−0.443289 | + | 0.896379i | \(0.646189\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.86292e14 | 0.752037 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.81670e14 | 0.728485 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.29365e14 | −1.22683 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.60119e14 | −0.376374 | −0.188187 | − | 0.982133i | \(-0.560261\pi\) | ||||
−0.188187 | + | 0.982133i | \(0.560261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.95306e13 | −0.0559533 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.34386e15 | 1.86093 | 0.930466 | − | 0.366377i | \(-0.119402\pi\) | ||||
0.930466 | + | 0.366377i | \(0.119402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.86388e14 | 0.929966 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.13029e14 | −0.414994 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.28205e14 | 0.425792 | 0.212896 | − | 0.977075i | \(-0.431710\pi\) | ||||
0.212896 | + | 0.977075i | \(0.431710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.46530e14 | 0.313007 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.27051e15 | −1.57882 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.45999e14 | −0.299222 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.44891e14 | 0.529731 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.58681e15 | 1.84971 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.73999e14 | 0.426838 | 0.213419 | − | 0.976961i | \(-0.431540\pi\) | ||||
0.213419 | + | 0.976961i | \(0.431540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.77988e13 | 0.0869388 | 0.0434694 | − | 0.999055i | \(-0.486159\pi\) | ||||
0.0434694 | + | 0.999055i | \(0.486159\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.64703e15 | −1.80229 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.62173e13 | −0.0923924 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50922e14 | −0.998019 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.94560e13 | −0.0405596 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19688e15 | 1.20518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.69248e14 | −0.561507 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.33487e15 | −1.28997 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.31865e15 | −1.24851 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.17909e15 | −1.09386 | −0.546929 | − | 0.837179i | \(-0.684203\pi\) | ||||
−0.546929 | + | 0.837179i | \(0.684203\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.51525e15 | −2.28656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.88468e14 | −0.435167 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.58961e14 | 0.662658 | 0.331329 | − | 0.943515i | \(-0.392503\pi\) | ||||
0.331329 | + | 0.943515i | \(0.392503\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.44815e15 | 2.09503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.04455e15 | 0.876180 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.94625e15 | 3.24486 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.75401e13 | 0.0383221 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.88953e14 | −0.781578 | −0.390789 | − | 0.920480i | \(-0.627798\pi\) | ||||
−0.390789 | + | 0.920480i | \(0.627798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.24509e14 | 0.173968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.73996e15 | 1.32204 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.70471e15 | −1.27015 | −0.635075 | − | 0.772450i | \(-0.719031\pi\) | ||||
−0.635075 | + | 0.772450i | \(0.719031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.09977e14 | −0.0803591 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.41044e14 | 0.459389 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.26889e14 | 0.370341 | 0.185170 | − | 0.982706i | \(-0.440716\pi\) | ||||
0.185170 | + | 0.982706i | \(0.440716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.85464e14 | −0.472592 | −0.236296 | − | 0.971681i | \(-0.575933\pi\) | ||||
−0.236296 | + | 0.971681i | \(0.575933\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.22732e14 | −0.285900 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.41692e13 | −0.0293053 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.25421e15 | 0.816402 | 0.408201 | − | 0.912892i | \(-0.366156\pi\) | ||||
0.408201 | + | 0.912892i | \(0.366156\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.23203e15 | 2.06416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.64873e15 | −2.91317 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.70417e14 | −0.104794 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.45524e15 | −0.878168 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.56777e15 | 1.52071 | 0.760356 | − | 0.649507i | \(-0.225025\pi\) | ||||
0.760356 | + | 0.649507i | \(0.225025\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.85193e14 | −0.107644 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.38440e15 | −1.93086 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.05019e15 | −0.588123 | −0.294062 | − | 0.955786i | \(-0.595007\pi\) | ||||
−0.294062 | + | 0.955786i | \(0.595007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.95873e15 | 1.07679 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.54152e15 | 2.45100 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.16345e14 | 0.0616455 | 0.0308227 | − | 0.999525i | \(-0.490187\pi\) | ||||
0.0308227 | + | 0.999525i | \(0.490187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.27714e14 | −0.482619 | −0.241310 | − | 0.970448i | \(-0.577577\pi\) | ||||
−0.241310 | + | 0.970448i | \(0.577577\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.11955e15 | −1.08268 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.64565e14 | 0.283178 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.37322e14 | −0.461691 | −0.230845 | − | 0.972990i | \(-0.574149\pi\) | ||||
−0.230845 | + | 0.972990i | \(0.574149\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.82299e15 | −1.84930 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.34412e15 | −0.638576 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.73439e13 | 0.0454230 | 0.0227115 | − | 0.999742i | \(-0.492770\pi\) | ||||
0.0227115 | + | 0.999742i | \(0.492770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.93707e15 | −1.34618 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.70501e15 | −1.21787 | −0.608935 | − | 0.793220i | \(-0.708403\pi\) | ||||
−0.608935 | + | 0.793220i | \(0.708403\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.22797e14 | 0.231225 | 0.115612 | − | 0.993294i | \(-0.463117\pi\) | ||||
0.115612 | + | 0.993294i | \(0.463117\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.24702e14 | 0.0541839 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.08225e15 | 3.02334 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.19012e14 | 0.0918603 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.73740e15 | 1.54027 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.08963e14 | 0.0441267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.58461e15 | −0.630611 | −0.315305 | − | 0.948990i | \(-0.602107\pi\) | ||||
−0.315305 | + | 0.948990i | \(0.602107\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.31736e15 | 0.515209 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.68295e14 | 0.256869 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.98397e15 | 1.50504 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.46569e15 | −1.28687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.67621e15 | 1.34178 | 0.670890 | − | 0.741557i | \(-0.265912\pi\) | ||||
0.670890 | + | 0.741557i | \(0.265912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.40268e15 | 0.503268 | 0.251634 | − | 0.967822i | \(-0.419032\pi\) | ||||
0.251634 | + | 0.967822i | \(0.419032\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.50931e14 | −0.194321 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.65400e14 | 0.265409 | 0.132704 | − | 0.991156i | \(-0.457634\pi\) | ||||
0.132704 | + | 0.991156i | \(0.457634\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.92058e13 | 0.0167753 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.77798e14 | 0.227198 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.06409e15 | −1.00990 | −0.504951 | − | 0.863148i | \(-0.668490\pi\) | ||||
−0.504951 | + | 0.863148i | \(0.668490\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.03873e15 | 0.336648 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.03018e15 | 0.328325 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.49550e15 | −1.72241 | −0.861207 | − | 0.508254i | \(-0.830291\pi\) | ||||
−0.861207 | + | 0.508254i | \(0.830291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.42413e15 | −1.36370 | −0.681851 | − | 0.731491i | \(-0.738825\pi\) | ||||
−0.681851 | + | 0.731491i | \(0.738825\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.25685e15 | −1.59368 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.20730e15 | 1.25454 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.02523e14 | −0.0300697 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.41093e15 | 1.27258 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.05310e15 | −0.866497 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.72652e15 | −1.04045 | −0.520225 | − | 0.854029i | \(-0.674152\pi\) | ||||
−0.520225 | + | 0.854029i | \(0.674152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.91781e15 | −0.801468 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.80105e15 | 1.02723 | 0.513613 | − | 0.858022i | \(-0.328307\pi\) | ||||
0.513613 | + | 0.858022i | \(0.328307\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.21938e15 | −0.856030 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.44982e15 | 0.902582 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.06733e15 | 1.04712 | 0.523558 | − | 0.851990i | \(-0.324604\pi\) | ||||
0.523558 | + | 0.851990i | \(0.324604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.29939e15 | −1.08920 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.08106e16 | 2.69519 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.14871e14 | 0.126326 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.14416e15 | −1.24218 | −0.621091 | − | 0.783739i | \(-0.713310\pi\) | ||||
−0.621091 | + | 0.783739i | \(0.713310\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.67910e15 | −2.06273 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.68528e15 | 0.862092 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.73185e15 | −1.55008 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.40001e15 | 1.22397 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.86572e15 | −0.639417 | −0.319708 | − | 0.947516i | \(-0.603585\pi\) | ||||
−0.319708 | + | 0.947516i | \(0.603585\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.34051e14 | 0.0514110 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.29839e15 | 0.713283 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.23679e16 | −2.63323 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.54221e15 | 1.16179 | 0.580896 | − | 0.813978i | \(-0.302702\pi\) | ||||
0.580896 | + | 0.813978i | \(0.302702\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.64903e16 | 3.40366 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.81769e13 | 0.00369425 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.81484e15 | 0.363207 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.91511e15 | 0.574512 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.73660e15 | 0.919301 | 0.459651 | − | 0.888100i | \(-0.347975\pi\) | ||||
0.459651 | + | 0.888100i | \(0.347975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.43260e15 | 0.847256 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.76545e15 | 1.08536 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.39886e15 | 0.444781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.01777e16 | −1.85870 | −0.929348 | − | 0.369205i | \(-0.879630\pi\) | ||||
−0.929348 | + | 0.369205i | \(0.879630\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.51462e15 | −1.53167 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.26275e15 | −0.223754 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.29486e15 | 0.924235 | 0.462117 | − | 0.886819i | \(-0.347090\pi\) | ||||
0.462117 | + | 0.886819i | \(0.347090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.77639e15 | −1.68112 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.64330e15 | 0.447792 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.55855e15 | 0.760821 | 0.380411 | − | 0.924818i | \(-0.375783\pi\) | ||||
0.380411 | + | 0.924818i | \(0.375783\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.12916e16 | −1.85676 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.91668e14 | 0.160667 | 0.0803337 | − | 0.996768i | \(-0.474401\pi\) | ||||
0.0803337 | + | 0.996768i | \(0.474401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.42266e15 | −0.706032 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.94258e16 | −3.05573 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.02572e16 | 1.58993 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.23831e15 | 0.800151 | 0.400075 | − | 0.916482i | \(-0.368984\pi\) | ||||
0.400075 | + | 0.916482i | \(0.368984\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.39840e14 | −0.0662098 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.67461e15 | −0.545134 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.31380e15 | −1.06934 | −0.534670 | − | 0.845061i | \(-0.679564\pi\) | ||||
−0.534670 | + | 0.845061i | \(0.679564\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.66829e14 | −0.0528609 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.81344e15 | −1.10975 | −0.554877 | − | 0.831932i | \(-0.687235\pi\) | ||||
−0.554877 | + | 0.831932i | \(0.687235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.80161e15 | 1.23219 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.18498e15 | 1.12948 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.48663e14 | −0.0202222 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.19554e15 | 0.294405 | 0.147203 | − | 0.989106i | \(-0.452973\pi\) | ||||
0.147203 | + | 0.989106i | \(0.452973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.22586e16 | 1.62048 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.32704e16 | 1.72940 | 0.864702 | − | 0.502286i | \(-0.167507\pi\) | ||||
0.864702 | + | 0.502286i | \(0.167507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.25307e14 | −0.0546441 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.56615e14 | −0.108510 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.44599e16 | −1.80596 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.32208e15 | 0.532246 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.77266e15 | −0.822375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.47345e15 | 0.296155 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.40226e15 | 0.165565 | 0.0827826 | − | 0.996568i | \(-0.473619\pi\) | ||||
0.0827826 | + | 0.996568i | \(0.473619\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.51866e16 | −1.76822 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.98165e15 | 0.227539 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.22415e15 | 1.04454 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.26346e15 | −0.141105 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.09627e15 | 0.341049 | 0.170525 | − | 0.985353i | \(-0.445454\pi\) | ||||
0.170525 | + | 0.985353i | \(0.445454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.56000e15 | 0.821324 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.95948e16 | 3.17130 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.28474e15 | −0.135794 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.12951e14 | −0.0430547 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.61990e15 | −0.783691 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.62765e16 | −1.65137 | −0.825683 | − | 0.564135i | \(-0.809210\pi\) | ||||
−0.825683 | + | 0.564135i | \(0.809210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.55106e16 | 1.55244 | 0.776219 | − | 0.630463i | \(-0.217135\pi\) | ||||
0.776219 | + | 0.630463i | \(0.217135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.04947e16 | −3.01111 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.41790e15 | −0.235544 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.71236e15 | −0.260691 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.62217e16 | 2.48656 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.57057e15 | −0.521209 | −0.260605 | − | 0.965446i | \(-0.583922\pi\) | ||||
−0.260605 | + | 0.965446i | \(0.583922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.05461e15 | 0.374326 | 0.187163 | − | 0.982329i | \(-0.440071\pi\) | ||||
0.187163 | + | 0.982329i | \(0.440071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.58317e15 | 0.781899 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.59579e14 | 0.0862582 | 0.0431291 | − | 0.999070i | \(-0.486267\pi\) | ||||
0.0431291 | + | 0.999070i | \(0.486267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.05269e16 | −0.933791 | −0.466895 | − | 0.884313i | \(-0.654627\pi\) | ||||
−0.466895 | + | 0.884313i | \(0.654627\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.66801e16 | −2.33551 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.24078e16 | −1.93576 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.31907e14 | 0.0197714 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.20076e15 | 0.101034 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.15316e15 | 0.510984 | 0.255492 | − | 0.966811i | \(-0.417762\pi\) | ||||
0.255492 | + | 0.966811i | \(0.417762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.63240e15 | −0.543617 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.31134e16 | −1.06087 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.83640e15 | 0.146641 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.01728e16 | −0.801827 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.50543e15 | −0.194935 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.29723e13 | −0.00176438 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.77560e16 | 1.34625 | 0.673126 | − | 0.739528i | \(-0.264951\pi\) | ||||
0.673126 | + | 0.739528i | \(0.264951\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.75812e16 | 1.31593 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.26793e16 | 1.67585 | 0.837925 | − | 0.545785i | \(-0.183769\pi\) | ||||
0.837925 | + | 0.545785i | \(0.183769\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.65429e15 | −0.120684 | −0.0603421 | − | 0.998178i | \(-0.519219\pi\) | ||||
−0.0603421 | + | 0.998178i | \(0.519219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.29225e16 | 3.81174 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.31182e15 | −0.164397 | −0.0821986 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821986 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.30903e15 | −0.653606 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.70765e15 | 0.395688 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.05651e16 | −1.40774 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.98606e15 | −0.539800 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.34529e16 | −0.897921 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.43381e16 | 1.60414 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.39330e16 | 0.906874 | 0.453437 | − | 0.891288i | \(-0.350198\pi\) | ||||
0.453437 | + | 0.891288i | \(0.350198\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.32246e16 | −0.850050 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.04171e15 | 0.256565 | 0.128283 | − | 0.991738i | \(-0.459054\pi\) | ||||
0.128283 | + | 0.991738i | \(0.459054\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.26327e16 | −0.791975 | −0.395988 | − | 0.918256i | \(-0.629598\pi\) | ||||
−0.395988 | + | 0.918256i | \(0.629598\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.64808e14 | 0.0225880 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.96489e16 | −1.20160 | −0.600798 | − | 0.799401i | \(-0.705151\pi\) | ||||
−0.600798 | + | 0.799401i | \(0.705151\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.20419e16 | −0.727334 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.34068e15 | −0.199300 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.62387e16 | 0.956905 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.83104e15 | 0.455819 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.10828e15 | 0.0637223 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.87200e14 | −0.0560695 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.89588e15 | −0.162478 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.92712e15 | 0.550225 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.47558e16 | 0.807969 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.75609e15 | 0.0949961 | 0.0474981 | − | 0.998871i | \(-0.484875\pi\) | ||||
0.0474981 | + | 0.998871i | \(0.484875\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.16820e16 | −2.76209 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.30636e16 | 1.21780 | 0.608899 | − | 0.793247i | \(-0.291611\pi\) | ||||
0.608899 | + | 0.793247i | \(0.291611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.42260e16 | 1.26384 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.26355e16 | −1.16674 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.87167e16 | −0.953229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.41404e14 | 0.0473741 | 0.0236870 | − | 0.999719i | \(-0.492459\pi\) | ||||
0.0236870 | + | 0.999719i | \(0.492459\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.53396e16 | −1.75725 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.30581e16 | −0.641607 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.37512e14 | 0.0260981 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.85226e16 | 0.888718 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.77556e16 | 0.841876 | 0.420938 | − | 0.907089i | \(-0.361701\pi\) | ||||
0.420938 | + | 0.907089i | \(0.361701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.81314e16 | −2.25530 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.41064e16 | 1.57938 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.02075e16 | −0.467150 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.10107e16 | 0.498020 | 0.249010 | − | 0.968501i | \(-0.419895\pi\) | ||||
0.249010 | + | 0.968501i | \(0.419895\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.41253e16 | 0.631446 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.50908e16 | −1.10859 | −0.554295 | − | 0.832320i | \(-0.687012\pi\) | ||||
−0.554295 | + | 0.832320i | \(0.687012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.41925e15 | 0.0619790 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.72795e16 | −1.17750 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.97365e16 | 0.842064 | 0.421032 | − | 0.907046i | \(-0.361668\pi\) | ||||
0.421032 | + | 0.907046i | \(0.361668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.88152e15 | 0.163696 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.03992e16 | 1.68415 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.28343e16 | 0.528884 | 0.264442 | − | 0.964402i | \(-0.414812\pi\) | ||||
0.264442 | + | 0.964402i | \(0.414812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.47997e15 | 0.101025 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.99228e16 | 0.802296 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.74699e16 | 3.08411 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.52335e16 | −0.993112 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.28619e16 | 1.66773 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.89608e16 | −0.729383 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.73110e16 | −1.79935 | −0.899676 | − | 0.436558i | \(-0.856197\pi\) | ||||
−0.899676 | + | 0.436558i | \(0.856197\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.35094e16 | 2.38813 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.69052e16 | 1.00030 | 0.500149 | − | 0.865939i | \(-0.333278\pi\) | ||||
0.500149 | + | 0.865939i | \(0.333278\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.64042e16 | −2.44104 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.59318e16 | −0.942557 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.19615e16 | −0.429899 | −0.214950 | − | 0.976625i | \(-0.568959\pi\) | ||||
−0.214950 | + | 0.976625i | \(0.568959\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.69078e16 | −1.31164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.67795e16 | 1.29249 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.93179e16 | −1.71380 | −0.856900 | − | 0.515483i | \(-0.827613\pi\) | ||||
−0.856900 | + | 0.515483i | \(0.827613\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.98547e16 | 0.682281 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.94330e16 | −2.01968 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.66221e14 | 0.00894669 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.42856e16 | 1.47183 | 0.735915 | − | 0.677074i | \(-0.236753\pi\) | ||||
0.735915 | + | 0.677074i | \(0.236753\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.35623e16 | −0.445772 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.66430e16 | −0.866075 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.10581e16 | 0.677011 | 0.338506 | − | 0.940964i | \(-0.390079\pi\) | ||||
0.338506 | + | 0.940964i | \(0.390079\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.51755e15 | −0.0482539 |
(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 | 8.12.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 72.12.a.e.1.2 | 2 | |||
4.3 | odd | 2 | 16.12.a.d.1.1 | 2 | |||
5.2 | odd | 4 | 200.12.c.c.49.1 | 4 | |||
5.3 | odd | 4 | 200.12.c.c.49.4 | 4 | |||
5.4 | even | 2 | 200.12.a.d.1.1 | 2 | |||
8.3 | odd | 2 | 64.12.a.k.1.2 | 2 | |||
8.5 | even | 2 | 64.12.a.h.1.1 | 2 | |||
12.11 | even | 2 | 144.12.a.p.1.2 | 2 | |||
16.3 | odd | 4 | 256.12.b.k.129.1 | 4 | |||
16.5 | even | 4 | 256.12.b.h.129.1 | 4 | |||
16.11 | odd | 4 | 256.12.b.k.129.4 | 4 | |||
16.13 | even | 4 | 256.12.b.h.129.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.12.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.12.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
64.12.a.h.1.1 | 2 | 8.5 | even | 2 | |||
64.12.a.k.1.2 | 2 | 8.3 | odd | 2 | |||
72.12.a.e.1.2 | 2 | 3.2 | odd | 2 | |||
144.12.a.p.1.2 | 2 | 12.11 | even | 2 | |||
200.12.a.d.1.1 | 2 | 5.4 | even | 2 | |||
200.12.c.c.49.1 | 4 | 5.2 | odd | 4 | |||
200.12.c.c.49.4 | 4 | 5.3 | odd | 4 | |||
256.12.b.h.129.1 | 4 | 16.5 | even | 4 | |||
256.12.b.h.129.4 | 4 | 16.13 | even | 4 | |||
256.12.b.k.129.1 | 4 | 16.3 | odd | 4 | |||
256.12.b.k.129.4 | 4 | 16.11 | odd | 4 |