Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,76,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 76, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 76);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 76 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(320.605553540\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3 x^{5} + \cdots - 67\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{58}\cdot 3^{36}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-4.40594e9\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.26741e11 | 1.68104 | 0.840522 | − | 0.541778i | \(-0.182249\pi\) | ||||
0.840522 | + | 0.541778i | \(0.182249\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.89808e22 | 1.82591 | ||||||||
\(5\) | 4.33451e25 | 0.266419 | 0.133209 | − | 0.991088i | \(-0.457472\pi\) | ||||
0.133209 | + | 0.991088i | \(0.457472\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.24638e31 | 0.864655 | 0.432327 | − | 0.901717i | \(-0.357692\pi\) | ||||
0.432327 | + | 0.901717i | \(0.357692\pi\) | |||||||
\(8\) | 1.01949e34 | 1.38839 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.41626e37 | 0.447861 | ||||||||
\(11\) | −1.56603e38 | −0.138859 | −0.0694296 | − | 0.997587i | \(-0.522118\pi\) | ||||
−0.0694296 | + | 0.997587i | \(0.522118\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.88327e41 | −0.317715 | −0.158857 | − | 0.987302i | \(-0.550781\pi\) | ||||
−0.158857 | + | 0.987302i | \(0.550781\pi\) | |||||||
\(14\) | 1.38747e43 | 1.45352 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.25086e44 | 0.508031 | ||||||||
\(17\) | −9.86838e45 | −0.711888 | −0.355944 | − | 0.934507i | \(-0.615841\pi\) | ||||
−0.355944 | + | 0.934507i | \(0.615841\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.40944e47 | −0.156959 | −0.0784797 | − | 0.996916i | \(-0.525007\pi\) | ||||
−0.0784797 | + | 0.996916i | \(0.525007\pi\) | |||||||
\(20\) | 2.98998e48 | 0.486456 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.11687e49 | −0.233428 | ||||||||
\(23\) | −8.97012e50 | −0.772689 | −0.386344 | − | 0.922355i | \(-0.626262\pi\) | ||||
−0.386344 | + | 0.922355i | \(0.626262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.45910e52 | −0.929021 | ||||||||
\(26\) | −6.15343e52 | −0.534093 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.92919e54 | 1.57878 | ||||||||
\(29\) | −7.48449e54 | −1.08202 | −0.541012 | − | 0.841015i | \(-0.681959\pi\) | ||||
−0.541012 | + | 0.841015i | \(0.681959\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.83848e55 | 1.16645 | 0.583223 | − | 0.812312i | \(-0.301791\pi\) | ||||
0.583223 | + | 0.812312i | \(0.301791\pi\) | |||||||
\(32\) | −1.48239e56 | −0.534365 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.22441e57 | −1.19671 | ||||||||
\(35\) | 1.84060e57 | 0.230360 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.42368e58 | −0.689000 | −0.344500 | − | 0.938786i | \(-0.611952\pi\) | ||||
−0.344500 | + | 0.938786i | \(0.611952\pi\) | |||||||
\(38\) | −4.60523e58 | −0.263856 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.41901e59 | 0.369892 | ||||||||
\(41\) | −3.18294e60 | −1.05544 | −0.527721 | − | 0.849418i | \(-0.676953\pi\) | ||||
−0.527721 | + | 0.849418i | \(0.676953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.58944e61 | −1.43926 | −0.719628 | − | 0.694360i | \(-0.755688\pi\) | ||||
−0.719628 | + | 0.694360i | \(0.755688\pi\) | |||||||
\(44\) | −1.08026e61 | −0.253544 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.93091e62 | −1.29892 | ||||||||
\(47\) | 4.72886e61 | 0.0935593 | 0.0467797 | − | 0.998905i | \(-0.485104\pi\) | ||||
0.0467797 | + | 0.998905i | \(0.485104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.08688e62 | −0.252372 | ||||||||
\(50\) | −8.03489e63 | −1.56173 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.29910e64 | −0.580118 | ||||||||
\(53\) | 7.75824e64 | 1.69597 | 0.847985 | − | 0.530020i | \(-0.177816\pi\) | ||||
0.847985 | + | 0.530020i | \(0.177816\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.78797e63 | −0.0369947 | ||||||||
\(56\) | 4.32917e65 | 1.20048 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.44549e66 | −1.81893 | ||||||||
\(59\) | 8.17255e64 | 0.0320190 | 0.0160095 | − | 0.999872i | \(-0.494904\pi\) | ||||
0.0160095 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.09863e66 | −0.684484 | −0.342242 | − | 0.939612i | \(-0.611186\pi\) | ||||
−0.342242 | + | 0.939612i | \(0.611186\pi\) | |||||||
\(62\) | 3.21464e67 | 1.96085 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.58287e67 | −1.40632 | ||||||||
\(65\) | −8.16306e66 | −0.0846451 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.31126e68 | 1.43483 | 0.717413 | − | 0.696648i | \(-0.245326\pi\) | ||||
0.717413 | + | 0.696648i | \(0.245326\pi\) | |||||||
\(68\) | −6.80729e68 | −1.29984 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.01399e68 | 0.387245 | ||||||||
\(71\) | −2.46110e69 | −0.930981 | −0.465491 | − | 0.885053i | \(-0.654122\pi\) | ||||
−0.465491 | + | 0.885053i | \(0.654122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.09634e69 | −0.546749 | −0.273375 | − | 0.961908i | \(-0.588140\pi\) | ||||
−0.273375 | + | 0.961908i | \(0.588140\pi\) | |||||||
\(74\) | −1.44540e70 | −1.15824 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.72245e69 | −0.286593 | ||||||||
\(77\) | −6.64997e69 | −0.120065 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.26377e69 | 0.0639399 | 0.0319699 | − | 0.999489i | \(-0.489822\pi\) | ||||
0.0319699 | + | 0.999489i | \(0.489822\pi\) | |||||||
\(80\) | 3.14289e70 | 0.135349 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.04000e72 | −1.77424 | ||||||||
\(83\) | 2.78206e69 | 0.00301257 | 0.00150629 | − | 0.999999i | \(-0.499521\pi\) | ||||
0.00150629 | + | 0.999999i | \(0.499521\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.27746e71 | −0.189660 | ||||||||
\(86\) | −8.46075e72 | −2.41945 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.59656e72 | −0.192790 | ||||||||
\(89\) | −1.96684e73 | −1.55469 | −0.777346 | − | 0.629073i | \(-0.783435\pi\) | ||||
−0.777346 | + | 0.629073i | \(0.783435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.99710e72 | −0.274714 | ||||||||
\(92\) | −6.18767e73 | −1.41086 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.54511e73 | 0.157277 | ||||||||
\(95\) | −6.10924e72 | −0.0418169 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.01886e74 | 0.632653 | 0.316326 | − | 0.948650i | \(-0.397551\pi\) | ||||
0.316326 | + | 0.948650i | \(0.397551\pi\) | |||||||
\(98\) | −1.98883e74 | −0.424249 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.69631e75 | −1.69631 | ||||||||
\(101\) | 1.56337e75 | 1.07649 | 0.538247 | − | 0.842787i | \(-0.319087\pi\) | ||||
0.538247 | + | 0.842787i | \(0.319087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.07128e74 | −0.167387 | −0.0836935 | − | 0.996492i | \(-0.526672\pi\) | ||||
−0.0836935 | + | 0.996492i | \(0.526672\pi\) | |||||||
\(104\) | −1.91999e75 | −0.441111 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.53494e76 | 2.85100 | ||||||||
\(107\) | 8.29288e75 | 0.655864 | 0.327932 | − | 0.944701i | \(-0.393648\pi\) | ||||
0.327932 | + | 0.944701i | \(0.393648\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.14553e76 | 1.63714 | 0.818570 | − | 0.574406i | \(-0.194767\pi\) | ||||
0.818570 | + | 0.574406i | \(0.194767\pi\) | |||||||
\(110\) | −2.21791e75 | −0.0621897 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.07899e76 | 0.439271 | ||||||||
\(113\) | 1.53804e76 | 0.157227 | 0.0786134 | − | 0.996905i | \(-0.474951\pi\) | ||||
0.0786134 | + | 0.996905i | \(0.474951\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.88811e76 | −0.205859 | ||||||||
\(116\) | −5.16286e77 | −1.97568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.67031e76 | 0.0538253 | ||||||||
\(119\) | −4.19049e77 | −0.615537 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24737e78 | −0.980718 | ||||||||
\(122\) | −1.99267e78 | −1.15065 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.78667e78 | 2.12982 | ||||||||
\(125\) | −2.21323e78 | −0.513927 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.95181e78 | 0.249918 | 0.124959 | − | 0.992162i | \(-0.460120\pi\) | ||||
0.124959 | + | 0.992162i | \(0.460120\pi\) | |||||||
\(128\) | −1.91760e79 | −1.82972 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.66721e78 | −0.142292 | ||||||||
\(131\) | 2.48929e78 | 0.0996328 | 0.0498164 | − | 0.998758i | \(-0.484136\pi\) | ||||
0.0498164 | + | 0.998758i | \(0.484136\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.98503e78 | −0.135716 | ||||||||
\(134\) | 1.40867e80 | 2.41201 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00608e80 | −0.988375 | ||||||||
\(137\) | 1.62508e80 | 1.21298 | 0.606491 | − | 0.795090i | \(-0.292577\pi\) | ||||
0.606491 | + | 0.795090i | \(0.292577\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.33640e80 | 1.01273 | 0.506364 | − | 0.862320i | \(-0.330989\pi\) | ||||
0.506364 | + | 0.862320i | \(0.330989\pi\) | |||||||
\(140\) | 1.26966e80 | 0.420616 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.04142e80 | −1.56502 | ||||||||
\(143\) | 2.94926e79 | 0.0441176 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.24416e80 | −0.288272 | ||||||||
\(146\) | −1.33844e81 | −0.919110 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.05149e81 | −1.25805 | ||||||||
\(149\) | −3.44890e81 | −1.10457 | −0.552287 | − | 0.833654i | \(-0.686245\pi\) | ||||
−0.552287 | + | 0.833654i | \(0.686245\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.98374e81 | −0.579597 | −0.289798 | − | 0.957088i | \(-0.593588\pi\) | ||||
−0.289798 | + | 0.957088i | \(0.593588\pi\) | |||||||
\(152\) | −1.43692e81 | −0.217920 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.17282e81 | −0.201835 | ||||||||
\(155\) | 4.26450e81 | 0.310763 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.36792e82 | −1.06692 | −0.533458 | − | 0.845826i | \(-0.679108\pi\) | ||||
−0.533458 | + | 0.845826i | \(0.679108\pi\) | |||||||
\(158\) | 3.02685e81 | 0.107486 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.42542e81 | −0.142365 | ||||||||
\(161\) | −3.80906e82 | −0.668109 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.73833e82 | 0.633506 | 0.316753 | − | 0.948508i | \(-0.397407\pi\) | ||||
0.316753 | + | 0.948508i | \(0.397407\pi\) | |||||||
\(164\) | −2.19562e83 | −1.92714 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.09012e80 | 0.00506426 | ||||||||
\(167\) | 7.47244e82 | 0.332349 | 0.166175 | − | 0.986096i | \(-0.446858\pi\) | ||||
0.166175 | + | 0.986096i | \(0.446858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.15892e83 | −0.899057 | ||||||||
\(170\) | −1.39762e83 | −0.318827 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.78621e84 | −2.62795 | ||||||||
\(173\) | −7.78810e83 | −0.921940 | −0.460970 | − | 0.887416i | \(-0.652498\pi\) | ||||
−0.460970 | + | 0.887416i | \(0.652498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.04423e84 | −0.803283 | ||||||||
\(176\) | −1.13551e83 | −0.0705448 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.42648e84 | −2.61351 | ||||||||
\(179\) | −3.91485e84 | −1.29041 | −0.645203 | − | 0.764011i | \(-0.723227\pi\) | ||||
−0.645203 | + | 0.764011i | \(0.723227\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.40838e84 | −0.957928 | −0.478964 | − | 0.877835i | \(-0.658987\pi\) | ||||
−0.478964 | + | 0.877835i | \(0.658987\pi\) | |||||||
\(182\) | −2.61298e84 | −0.461806 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.14499e84 | −1.07279 | ||||||||
\(185\) | −1.91745e84 | −0.183562 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.54542e84 | 0.0988521 | ||||||||
\(188\) | 3.26201e84 | 0.170831 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.99614e84 | −0.0702960 | ||||||||
\(191\) | 2.54828e85 | 0.737047 | 0.368524 | − | 0.929618i | \(-0.379863\pi\) | ||||
0.368524 | + | 0.929618i | \(0.379863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.92114e85 | −1.35450 | −0.677250 | − | 0.735753i | \(-0.736828\pi\) | ||||
−0.677250 | + | 0.735753i | \(0.736828\pi\) | |||||||
\(194\) | 6.59643e85 | 1.06352 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.19878e85 | −0.460808 | ||||||||
\(197\) | −1.15851e86 | −1.05055 | −0.525276 | − | 0.850932i | \(-0.676038\pi\) | ||||
−0.525276 | + | 0.850932i | \(0.676038\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.78135e86 | 1.72689 | 0.863445 | − | 0.504444i | \(-0.168302\pi\) | ||||
0.863445 | + | 0.504444i | \(0.168302\pi\) | |||||||
\(200\) | −2.50704e86 | −1.28984 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.10818e86 | 1.80963 | ||||||||
\(203\) | −3.17820e86 | −0.935578 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.37965e86 | −0.281189 | ||||||||
\(206\) | −1.65700e86 | −0.281385 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.36553e86 | −0.161409 | ||||||||
\(209\) | 2.20723e85 | 0.0217953 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.21488e86 | 0.429379 | 0.214689 | − | 0.976682i | \(-0.431126\pi\) | ||||
0.214689 | + | 0.976682i | \(0.431126\pi\) | |||||||
\(212\) | 5.35170e87 | 3.09668 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.70963e87 | 1.10254 | ||||||||
\(215\) | −1.12239e87 | −0.383445 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.17780e87 | 1.00857 | ||||||||
\(218\) | 1.35451e88 | 2.75211 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.68240e86 | −0.0675489 | ||||||||
\(221\) | 1.85849e87 | 0.226177 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.14012e88 | 0.989737 | 0.494869 | − | 0.868968i | \(-0.335216\pi\) | ||||
0.494869 | + | 0.868968i | \(0.335216\pi\) | |||||||
\(224\) | −6.29479e87 | −0.462041 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.02541e87 | 0.264305 | ||||||||
\(227\) | −2.58517e88 | −1.15218 | −0.576090 | − | 0.817386i | \(-0.695422\pi\) | ||||
−0.576090 | + | 0.817386i | \(0.695422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.20331e87 | 0.198973 | 0.0994863 | − | 0.995039i | \(-0.468280\pi\) | ||||
0.0994863 | + | 0.995039i | \(0.468280\pi\) | |||||||
\(230\) | −1.27040e88 | −0.346057 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.63040e88 | −1.50227 | ||||||||
\(233\) | −4.08817e88 | −0.684986 | −0.342493 | − | 0.939520i | \(-0.611271\pi\) | ||||
−0.342493 | + | 0.939520i | \(0.611271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.04973e87 | 0.0249259 | ||||||||
\(236\) | 5.63749e87 | 0.0584637 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.36921e89 | −1.03474 | ||||||||
\(239\) | −5.69769e88 | −0.367941 | −0.183970 | − | 0.982932i | \(-0.558895\pi\) | ||||
−0.183970 | + | 0.982932i | \(0.558895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.40344e89 | 0.663064 | 0.331532 | − | 0.943444i | \(-0.392435\pi\) | ||||
0.331532 | + | 0.943444i | \(0.392435\pi\) | |||||||
\(242\) | −4.07567e89 | −1.64863 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.20688e89 | −1.24980 | ||||||||
\(245\) | −2.63836e88 | −0.0672366 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.65436e88 | 0.0498683 | ||||||||
\(248\) | 1.00303e90 | 1.61948 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.23154e89 | −0.863934 | ||||||||
\(251\) | 1.01537e89 | 0.104439 | 0.0522193 | − | 0.998636i | \(-0.483371\pi\) | ||||
0.0522193 | + | 0.998636i | \(0.483371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.40475e89 | 0.107295 | ||||||||
\(254\) | 6.37736e89 | 0.420123 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.40088e90 | −1.66952 | ||||||||
\(257\) | −1.81313e90 | −0.769018 | −0.384509 | − | 0.923121i | \(-0.625629\pi\) | ||||
−0.384509 | + | 0.923121i | \(0.625629\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.87846e90 | −0.595747 | ||||||||
\(260\) | −5.63095e89 | −0.154554 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.13354e89 | 0.167487 | ||||||||
\(263\) | −3.47473e90 | −0.620270 | −0.310135 | − | 0.950693i | \(-0.600374\pi\) | ||||
−0.310135 | + | 0.950693i | \(0.600374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.36281e90 | 0.451838 | ||||||||
\(266\) | −1.95556e90 | −0.228144 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.97395e91 | 2.61986 | ||||||||
\(269\) | 1.34158e91 | 1.02779 | 0.513897 | − | 0.857852i | \(-0.328201\pi\) | ||||
0.513897 | + | 0.857852i | \(0.328201\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.32034e91 | 1.34649 | 0.673246 | − | 0.739418i | \(-0.264899\pi\) | ||||
0.673246 | + | 0.739418i | \(0.264899\pi\) | |||||||
\(272\) | −7.15542e90 | −0.361661 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.30982e91 | 2.03908 | ||||||||
\(275\) | 3.85102e90 | 0.129003 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.73199e91 | −1.46324 | −0.731618 | − | 0.681715i | \(-0.761235\pi\) | ||||
−0.731618 | + | 0.681715i | \(0.761235\pi\) | |||||||
\(278\) | 7.63398e91 | 1.70244 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.87648e91 | 0.319829 | ||||||||
\(281\) | 6.46798e91 | 0.964454 | 0.482227 | − | 0.876046i | \(-0.339828\pi\) | ||||
0.482227 | + | 0.876046i | \(0.339828\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.40884e91 | −0.846757 | −0.423379 | − | 0.905953i | \(-0.639156\pi\) | ||||
−0.423379 | + | 0.905953i | \(0.639156\pi\) | |||||||
\(284\) | −1.69769e92 | −1.69989 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.63646e90 | 0.0741637 | ||||||||
\(287\) | −1.35160e92 | −0.912593 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.47777e91 | −0.493216 | ||||||||
\(290\) | −1.06000e92 | −0.484597 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.82569e92 | −0.998314 | ||||||||
\(293\) | 1.11299e92 | 0.345903 | 0.172951 | − | 0.984930i | \(-0.444670\pi\) | ||||
0.172951 | + | 0.984930i | \(0.444670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.54240e90 | 0.00853045 | ||||||||
\(296\) | −4.50992e92 | −0.956598 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.12690e93 | −1.85684 | ||||||||
\(299\) | 1.68932e92 | 0.245495 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.09957e93 | −1.24446 | ||||||||
\(302\) | −9.74911e92 | −0.974327 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.02197e92 | −0.0797402 | ||||||||
\(305\) | −2.64345e92 | −0.182359 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.54198e92 | 0.299210 | 0.149605 | − | 0.988746i | \(-0.452200\pi\) | ||||
0.149605 | + | 0.988746i | \(0.452200\pi\) | |||||||
\(308\) | −4.58720e92 | −0.219228 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.39339e93 | 0.522406 | ||||||||
\(311\) | 2.52122e93 | 0.837715 | 0.418858 | − | 0.908052i | \(-0.362431\pi\) | ||||
0.418858 | + | 0.908052i | \(0.362431\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.94579e93 | 0.769643 | 0.384822 | − | 0.922991i | \(-0.374263\pi\) | ||||
0.384822 | + | 0.922991i | \(0.374263\pi\) | |||||||
\(314\) | −7.73697e93 | −1.79353 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.39022e92 | 0.116748 | ||||||||
\(317\) | −1.03547e94 | −1.68041 | −0.840203 | − | 0.542272i | \(-0.817564\pi\) | ||||
−0.840203 | + | 0.542272i | \(0.817564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.17209e93 | 0.150249 | ||||||||
\(320\) | −3.28680e93 | −0.374670 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.24458e94 | −1.12312 | ||||||||
\(323\) | 1.39089e93 | 0.111737 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.63115e93 | 0.295164 | ||||||||
\(326\) | 1.87495e94 | 1.06495 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.24499e94 | −1.46536 | ||||||||
\(329\) | 2.00806e93 | 0.0808965 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.31190e94 | 1.38395 | 0.691973 | − | 0.721924i | \(-0.256742\pi\) | ||||
0.691973 | + | 0.721924i | \(0.256742\pi\) | |||||||
\(332\) | 1.91908e92 | 0.00550068 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.44155e94 | 0.558694 | ||||||||
\(335\) | 1.86872e94 | 0.382265 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.32493e94 | 0.707714 | 0.353857 | − | 0.935300i | \(-0.384870\pi\) | ||||
0.353857 | + | 0.935300i | \(0.384870\pi\) | |||||||
\(338\) | −1.03215e95 | −1.51135 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.95063e94 | −0.346302 | ||||||||
\(341\) | −1.54074e94 | −0.161972 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.28264e95 | −1.08287 | ||||||||
\(344\) | −2.63992e95 | −1.99824 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.54469e95 | −1.54982 | ||||||||
\(347\) | −3.28354e95 | −1.79468 | −0.897339 | − | 0.441343i | \(-0.854502\pi\) | ||||
−0.897339 | + | 0.441343i | \(0.854502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.28464e95 | −1.00662 | −0.503309 | − | 0.864106i | \(-0.667884\pi\) | ||||
−0.503309 | + | 0.864106i | \(0.667884\pi\) | |||||||
\(350\) | −3.41192e95 | −1.35035 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.32147e94 | 0.0742014 | ||||||||
\(353\) | 2.28907e95 | 0.657820 | 0.328910 | − | 0.944361i | \(-0.393319\pi\) | ||||
0.328910 | + | 0.944361i | \(0.393319\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.06676e95 | −0.248031 | ||||||||
\(356\) | −1.35674e96 | −2.83872 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.27914e96 | −2.16923 | ||||||||
\(359\) | 3.43961e95 | 0.525372 | 0.262686 | − | 0.964881i | \(-0.415392\pi\) | ||||
0.262686 | + | 0.964881i | \(0.415392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.86478e95 | −0.975364 | ||||||||
\(362\) | −1.44040e96 | −1.61032 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.51647e95 | −0.501602 | ||||||||
\(365\) | −1.77556e95 | −0.145664 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.95272e96 | 1.30516 | 0.652579 | − | 0.757720i | \(-0.273687\pi\) | ||||
0.652579 | + | 0.757720i | \(0.273687\pi\) | |||||||
\(368\) | −6.50411e95 | −0.392550 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.26509e95 | −0.308576 | ||||||||
\(371\) | 3.29445e96 | 1.46643 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.14216e94 | −0.0114326 | −0.00571632 | − | 0.999984i | \(-0.501820\pi\) | ||||
−0.00571632 | + | 0.999984i | \(0.501820\pi\) | |||||||
\(374\) | 5.04952e95 | 0.166175 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.82105e95 | 0.129896 | ||||||||
\(377\) | 1.40953e96 | 0.343775 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.17713e96 | −0.235427 | −0.117713 | − | 0.993048i | \(-0.537556\pi\) | ||||
−0.117713 | + | 0.993048i | \(0.537556\pi\) | |||||||
\(380\) | −4.21420e95 | −0.0763538 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.32627e96 | 1.23901 | ||||||||
\(383\) | −1.08925e97 | −1.46951 | −0.734755 | − | 0.678333i | \(-0.762703\pi\) | ||||
−0.734755 | + | 0.678333i | \(0.762703\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.88243e95 | −0.0319876 | ||||||||
\(386\) | −2.26142e97 | −2.27697 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.39262e97 | 1.15517 | ||||||||
\(389\) | −1.78980e96 | −0.134801 | −0.0674007 | − | 0.997726i | \(-0.521471\pi\) | ||||
−0.0674007 | + | 0.997726i | \(0.521471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.85206e96 | 0.550067 | ||||||||
\(392\) | −6.20554e96 | −0.350390 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.78534e97 | −1.76602 | ||||||||
\(395\) | 4.01539e95 | 0.0170348 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.74242e97 | 0.962698 | 0.481349 | − | 0.876529i | \(-0.340147\pi\) | ||||
0.481349 | + | 0.876529i | \(0.340147\pi\) | |||||||
\(398\) | 9.08780e97 | 2.90298 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.78306e97 | −0.471971 | ||||||||
\(401\) | −5.08366e97 | −1.22536 | −0.612678 | − | 0.790333i | \(-0.709908\pi\) | ||||
−0.612678 | + | 0.790333i | \(0.709908\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.85285e97 | −0.370597 | ||||||||
\(404\) | 1.07843e98 | 1.96558 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.03845e98 | −1.57275 | ||||||||
\(407\) | 6.92762e96 | 0.0956740 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.24764e97 | −0.373201 | −0.186601 | − | 0.982436i | \(-0.559747\pi\) | ||||
−0.186601 | + | 0.982436i | \(0.559747\pi\) | |||||||
\(410\) | −4.50788e97 | −0.472692 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.49821e97 | −0.305633 | ||||||||
\(413\) | 3.47038e96 | 0.0276853 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.20588e95 | 0.000802605 0 | ||||||||
\(416\) | 2.79174e97 | 0.169776 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.21193e96 | 0.0366388 | ||||||||
\(419\) | −3.50672e98 | −1.62883 | −0.814413 | − | 0.580286i | \(-0.802941\pi\) | ||||
−0.814413 | + | 0.580286i | \(0.802941\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68894e98 | 0.656199 | 0.328099 | − | 0.944643i | \(-0.393592\pi\) | ||||
0.328099 | + | 0.944643i | \(0.393592\pi\) | |||||||
\(422\) | 2.03066e98 | 0.721804 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.90948e98 | 2.35466 | ||||||||
\(425\) | 2.42673e98 | 0.661359 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.58971e98 | −0.591842 | ||||||||
\(428\) | 5.72050e98 | 1.19755 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.66732e98 | −0.644587 | ||||||||
\(431\) | 9.95538e98 | 1.60384 | 0.801919 | − | 0.597433i | \(-0.203813\pi\) | ||||
0.801919 | + | 0.597433i | \(0.203813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.16347e98 | 0.834698 | 0.417349 | − | 0.908746i | \(-0.362959\pi\) | ||||
0.417349 | + | 0.908746i | \(0.362959\pi\) | |||||||
\(434\) | 1.36506e99 | 1.69545 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.85962e99 | 2.98927 | ||||||||
\(437\) | 1.26429e98 | 0.121281 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.65566e99 | 1.33829 | 0.669147 | − | 0.743130i | \(-0.266660\pi\) | ||||
0.669147 | + | 0.743130i | \(0.266660\pi\) | |||||||
\(440\) | −6.92030e97 | −0.0513629 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.07244e98 | 0.380214 | ||||||||
\(443\) | 6.77161e97 | 0.0389540 | 0.0194770 | − | 0.999810i | \(-0.493800\pi\) | ||||
0.0194770 | + | 0.999810i | \(0.493800\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.52529e98 | −0.414199 | ||||||||
\(446\) | 3.72526e99 | 1.66379 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.21998e99 | −1.21598 | ||||||||
\(449\) | −2.65101e99 | −0.920819 | −0.460409 | − | 0.887707i | \(-0.652297\pi\) | ||||
−0.460409 | + | 0.887707i | \(0.652297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.98459e98 | 0.146558 | ||||||||
\(452\) | 1.06095e99 | 0.287081 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.44683e99 | −1.93686 | ||||||||
\(455\) | −3.46635e98 | −0.0731888 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.84378e99 | −0.867615 | −0.433807 | − | 0.901006i | \(-0.642830\pi\) | ||||
−0.433807 | + | 0.901006i | \(0.642830\pi\) | |||||||
\(458\) | 2.02688e99 | 0.334482 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.68205e99 | −0.375879 | ||||||||
\(461\) | −1.31364e100 | −1.69704 | −0.848521 | − | 0.529162i | \(-0.822507\pi\) | ||||
−0.848521 | + | 0.529162i | \(0.822507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.77164e99 | 0.853543 | 0.426772 | − | 0.904359i | \(-0.359651\pi\) | ||||
0.426772 | + | 0.904359i | \(0.359651\pi\) | |||||||
\(464\) | −5.42690e99 | −0.549702 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.33577e100 | −1.15149 | ||||||||
\(467\) | −7.55574e99 | −0.601027 | −0.300513 | − | 0.953778i | \(-0.597158\pi\) | ||||
−0.300513 | + | 0.953778i | \(0.597158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.83073e100 | 1.24063 | ||||||||
\(470\) | 6.69731e98 | 0.0419016 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.33187e98 | 0.0444547 | ||||||||
\(473\) | 4.05514e99 | 0.199854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.46596e99 | 0.145819 | ||||||||
\(476\) | −2.89064e100 | −1.12391 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.86167e100 | −0.618524 | ||||||||
\(479\) | −3.90184e100 | −1.19864 | −0.599319 | − | 0.800510i | \(-0.704562\pi\) | ||||
−0.599319 | + | 0.800510i | \(0.704562\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.33100e99 | 0.218905 | ||||||||
\(482\) | 4.58562e100 | 1.11464 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.60447e100 | −1.79070 | ||||||||
\(485\) | 8.75075e99 | 0.168550 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.26161e100 | 0.208251 | 0.104126 | − | 0.994564i | \(-0.466796\pi\) | ||||
0.104126 | + | 0.994564i | \(0.466796\pi\) | |||||||
\(488\) | −6.21752e100 | −0.950328 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.62061e99 | −0.113028 | ||||||||
\(491\) | −6.80665e99 | −0.0826756 | −0.0413378 | − | 0.999145i | \(-0.513162\pi\) | ||||
−0.0413378 | + | 0.999145i | \(0.513162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.38598e100 | 0.770280 | ||||||||
\(494\) | 8.67290e99 | 0.0838308 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.13374e100 | 0.592590 | ||||||||
\(497\) | −1.04508e101 | −0.804977 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.15058e100 | −0.142490 | −0.0712451 | − | 0.997459i | \(-0.522697\pi\) | ||||
−0.0712451 | + | 0.997459i | \(0.522697\pi\) | |||||||
\(500\) | −1.52671e101 | −0.938383 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.31764e100 | 0.175566 | ||||||||
\(503\) | 1.06452e101 | 0.522824 | 0.261412 | − | 0.965227i | \(-0.415812\pi\) | ||||
0.261412 | + | 0.965227i | \(0.415812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.77645e100 | 0.286798 | ||||||||
\(506\) | 4.58989e100 | 0.180367 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.34637e101 | 0.456327 | ||||||||
\(509\) | 4.78996e101 | 1.50805 | 0.754023 | − | 0.656848i | \(-0.228111\pi\) | ||||
0.754023 | + | 0.656848i | \(0.228111\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.73946e101 | −0.472749 | ||||||||
\(512\) | −3.86756e101 | −0.976817 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.92423e101 | −1.29275 | ||||||||
\(515\) | −2.19815e100 | −0.0445950 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.40554e99 | −0.0129916 | ||||||||
\(518\) | −6.13772e101 | −1.00148 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.32219e100 | −0.117520 | ||||||||
\(521\) | −8.84088e101 | −1.16166 | −0.580832 | − | 0.814023i | \(-0.697273\pi\) | ||||
−0.580832 | + | 0.814023i | \(0.697273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.09779e100 | −0.0124942 | −0.00624709 | − | 0.999980i | \(-0.501989\pi\) | ||||
−0.00624709 | + | 0.999980i | \(0.501989\pi\) | |||||||
\(524\) | 1.71713e101 | 0.181920 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.13534e102 | −1.04270 | ||||||||
\(527\) | −9.70899e101 | −0.830378 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.43052e101 | −0.402952 | ||||||||
\(530\) | 1.09877e102 | 0.759559 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.12853e101 | −0.247804 | ||||||||
\(533\) | 5.99435e101 | 0.335330 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.59456e101 | 0.174734 | ||||||||
\(536\) | 4.39531e102 | 1.99209 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.38350e102 | 1.72777 | ||||||||
\(539\) | 9.53224e100 | 0.0350442 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.54819e101 | 0.145526 | 0.0727632 | − | 0.997349i | \(-0.476818\pi\) | ||||
0.0727632 | + | 0.997349i | \(0.476818\pi\) | |||||||
\(542\) | 7.58152e102 | 2.26351 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.46288e102 | 0.380408 | ||||||||
\(545\) | 1.79688e102 | 0.436165 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.65619e102 | 0.773577 | 0.386789 | − | 0.922168i | \(-0.373584\pi\) | ||||
0.386789 | + | 0.922168i | \(0.373584\pi\) | |||||||
\(548\) | 1.12100e103 | 2.21479 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.25829e102 | 0.216860 | ||||||||
\(551\) | 1.05490e102 | 0.169834 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.93375e101 | 0.0552859 | ||||||||
\(554\) | −1.87288e103 | −2.45976 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.61167e103 | 1.84915 | ||||||||
\(557\) | 4.10459e102 | 0.440251 | 0.220126 | − | 0.975472i | \(-0.429353\pi\) | ||||
0.220126 | + | 0.975472i | \(0.429353\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.87661e102 | 0.457273 | ||||||||
\(560\) | 1.33459e102 | 0.117030 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.11335e103 | 1.62129 | ||||||||
\(563\) | 2.03919e102 | 0.146350 | 0.0731751 | − | 0.997319i | \(-0.476687\pi\) | ||||
0.0731751 | + | 0.997319i | \(0.476687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.66665e101 | 0.0418881 | ||||||||
\(566\) | −2.42077e103 | −1.42344 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.50908e103 | −1.29256 | ||||||||
\(569\) | 1.21675e103 | 0.586803 | 0.293401 | − | 0.955989i | \(-0.405213\pi\) | ||||
0.293401 | + | 0.955989i | \(0.405213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.95470e103 | −1.67209 | −0.836044 | − | 0.548663i | \(-0.815137\pi\) | ||||
−0.836044 | + | 0.548663i | \(0.815137\pi\) | |||||||
\(572\) | 2.03443e102 | 0.0805547 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.41623e103 | −1.53411 | ||||||||
\(575\) | 2.20584e103 | 0.717844 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.30970e103 | −0.659877 | −0.329938 | − | 0.944002i | \(-0.607028\pi\) | ||||
−0.329938 | + | 0.944002i | \(0.607028\pi\) | |||||||
\(578\) | −3.09678e103 | −0.829118 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.23785e103 | −0.526357 | ||||||||
\(581\) | 1.18137e101 | 0.00260483 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.21496e103 | −0.235501 | ||||||||
\(584\) | −4.17619e103 | −0.759099 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.63658e103 | 0.581478 | ||||||||
\(587\) | 4.27950e103 | 0.641896 | 0.320948 | − | 0.947097i | \(-0.395999\pi\) | ||||
0.320948 | + | 0.947097i | \(0.395999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.38668e103 | −0.183085 | ||||||||
\(590\) | 1.15745e102 | 0.0143401 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.20755e103 | −0.350033 | ||||||||
\(593\) | −5.73284e103 | −0.587245 | −0.293622 | − | 0.955922i | \(-0.594861\pi\) | ||||
−0.293622 | + | 0.955922i | \(0.594861\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.81637e103 | −0.163990 | ||||||||
\(596\) | −2.37908e104 | −2.01685 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.51970e103 | 0.412687 | ||||||||
\(599\) | 8.09810e103 | 0.568692 | 0.284346 | − | 0.958722i | \(-0.408224\pi\) | ||||
0.284346 | + | 0.958722i | \(0.408224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.48364e103 | 0.0919469 | 0.0459735 | − | 0.998943i | \(-0.485361\pi\) | ||||
0.0459735 | + | 0.998943i | \(0.485361\pi\) | |||||||
\(602\) | −3.59276e104 | −2.09199 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.05821e104 | −1.05829 | ||||||||
\(605\) | −5.40674e103 | −0.261282 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.19159e104 | 1.36280 | 0.681400 | − | 0.731912i | \(-0.261372\pi\) | ||||
0.681400 | + | 0.731912i | \(0.261372\pi\) | |||||||
\(608\) | 2.08934e103 | 0.0838735 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.63725e103 | −0.306554 | ||||||||
\(611\) | −8.90574e102 | −0.0297252 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.90887e104 | 0.563650 | 0.281825 | − | 0.959466i | \(-0.409060\pi\) | ||||
0.281825 | + | 0.959466i | \(0.409060\pi\) | |||||||
\(614\) | 1.81079e104 | 0.502985 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.77961e103 | −0.166697 | ||||||||
\(617\) | 4.16335e104 | 0.963273 | 0.481636 | − | 0.876371i | \(-0.340043\pi\) | ||||
0.481636 | + | 0.876371i | \(0.340043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.63359e104 | 1.15448 | 0.577239 | − | 0.816575i | \(-0.304130\pi\) | ||||
0.577239 | + | 0.816575i | \(0.304130\pi\) | |||||||
\(620\) | 2.94168e104 | 0.567424 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.23787e104 | 1.40824 | ||||||||
\(623\) | −8.35197e104 | −1.34427 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.54985e104 | 0.792101 | ||||||||
\(626\) | 9.62511e104 | 1.29380 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.63341e105 | −1.94809 | ||||||||
\(629\) | 4.36546e104 | 0.490490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.77847e104 | −0.476637 | −0.238319 | − | 0.971187i | \(-0.576596\pi\) | ||||
−0.238319 | + | 0.971187i | \(0.576596\pi\) | |||||||
\(632\) | 9.44436e103 | 0.0887733 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.38330e105 | −2.82484 | ||||||||
\(635\) | 8.46013e103 | 0.0665828 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.14632e104 | 0.0801824 | ||||||||
\(638\) | 3.82971e104 | 0.252575 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.31187e104 | −0.487472 | ||||||||
\(641\) | 1.19877e104 | 0.0663069 | 0.0331534 | − | 0.999450i | \(-0.489445\pi\) | ||||
0.0331534 | + | 0.999450i | \(0.489445\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.25954e105 | 1.11201 | 0.556006 | − | 0.831178i | \(-0.312333\pi\) | ||||
0.556006 | + | 0.831178i | \(0.312333\pi\) | |||||||
\(644\) | −2.62752e105 | −1.21991 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.54462e104 | 0.187836 | ||||||||
\(647\) | −3.62715e103 | −0.0141467 | −0.00707334 | − | 0.999975i | \(-0.502252\pi\) | ||||
−0.00707334 | + | 0.999975i | \(0.502252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.27985e103 | −0.00444613 | ||||||||
\(650\) | 1.51319e105 | 0.496183 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.95835e105 | 1.15672 | ||||||||
\(653\) | −3.74683e105 | −1.03376 | −0.516880 | − | 0.856058i | \(-0.672907\pi\) | ||||
−0.516880 | + | 0.856058i | \(0.672907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.07899e104 | 0.0265440 | ||||||||
\(656\) | −2.30791e105 | −0.536197 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.56115e104 | 0.135991 | ||||||||
\(659\) | 8.83130e105 | 1.72911 | 0.864553 | − | 0.502542i | \(-0.167602\pi\) | ||||
0.864553 | + | 0.502542i | \(0.167602\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.25607e105 | 0.569036 | 0.284518 | − | 0.958671i | \(-0.408166\pi\) | ||||
0.284518 | + | 0.958671i | \(0.408166\pi\) | |||||||
\(662\) | 1.40888e106 | 2.32647 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.83629e103 | 0.00418261 | ||||||||
\(665\) | −2.59422e104 | −0.0361572 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.71368e105 | 0.836068 | ||||||||
\(668\) | 5.15455e105 | 0.606839 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.10588e105 | 0.642603 | ||||||||
\(671\) | 9.55064e104 | 0.0950469 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.25330e106 | 1.11555 | 0.557777 | − | 0.829991i | \(-0.311654\pi\) | ||||
0.557777 | + | 0.829991i | \(0.311654\pi\) | |||||||
\(674\) | 1.41313e106 | 1.18970 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.17905e106 | −1.64160 | ||||||||
\(677\) | 1.53726e106 | 1.09565 | 0.547824 | − | 0.836594i | \(-0.315456\pi\) | ||||
0.547824 | + | 0.836594i | \(0.315456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.57284e105 | 0.547026 | ||||||||
\(680\) | −4.36084e105 | −0.263322 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.03422e105 | −0.272281 | ||||||||
\(683\) | −1.70977e106 | −0.875311 | −0.437655 | − | 0.899143i | \(-0.644191\pi\) | ||||
−0.437655 | + | 0.899143i | \(0.644191\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.04394e105 | 0.323161 | ||||||||
\(686\) | −4.19092e106 | −1.82035 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.87756e106 | −0.731186 | ||||||||
\(689\) | −1.46109e106 | −0.538835 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.55165e106 | 1.50571 | 0.752856 | − | 0.658185i | \(-0.228676\pi\) | ||||
0.752856 | + | 0.658185i | \(0.228676\pi\) | |||||||
\(692\) | −5.37230e106 | −1.68338 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.07287e107 | −3.01693 | ||||||||
\(695\) | 1.01271e106 | 0.269809 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.14105e106 | 0.751356 | ||||||||
\(698\) | −7.46487e106 | −1.69217 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.20317e106 | −1.46672 | ||||||||
\(701\) | 6.86314e106 | 1.32464 | 0.662319 | − | 0.749222i | \(-0.269573\pi\) | ||||
0.662319 | + | 0.749222i | \(0.269573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.23492e105 | 0.108145 | ||||||||
\(704\) | 1.18750e106 | 0.195281 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.47932e106 | 1.10582 | ||||||||
\(707\) | 6.63868e106 | 0.930795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.47111e105 | −0.0563873 | −0.0281936 | − | 0.999602i | \(-0.508976\pi\) | ||||
−0.0281936 | + | 0.999602i | \(0.508976\pi\) | |||||||
\(710\) | −3.48556e106 | −0.416950 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.00519e107 | −2.15851 | ||||||||
\(713\) | −8.82524e106 | −0.901299 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.27836e105 | 0.0117538 | ||||||||
\(716\) | −2.70049e107 | −2.35616 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.12386e107 | 0.883174 | ||||||||
\(719\) | 4.46581e106 | 0.333094 | 0.166547 | − | 0.986034i | \(-0.446738\pi\) | ||||
0.166547 | + | 0.986034i | \(0.446738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.15346e106 | −0.144732 | ||||||||
\(722\) | −2.56975e107 | −1.63963 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.04094e107 | −1.74909 | ||||||||
\(725\) | 1.84051e107 | 1.00522 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.07466e106 | 0.348470 | 0.174235 | − | 0.984704i | \(-0.444255\pi\) | ||||
0.174235 | + | 0.984704i | \(0.444255\pi\) | |||||||
\(728\) | −8.15300e106 | −0.381409 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.80148e106 | −0.244868 | ||||||||
\(731\) | 2.55535e107 | 1.02459 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.53195e107 | 1.64016 | 0.820080 | − | 0.572249i | \(-0.193929\pi\) | ||||
0.820080 | + | 0.572249i | \(0.193929\pi\) | |||||||
\(734\) | 6.38035e107 | 2.19403 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.32972e107 | 0.412897 | ||||||||
\(737\) | −6.75157e106 | −0.199239 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.01848e107 | −0.804679 | −0.402339 | − | 0.915491i | \(-0.631803\pi\) | ||||
−0.402339 | + | 0.915491i | \(0.631803\pi\) | |||||||
\(740\) | −1.32267e107 | −0.335168 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.07643e108 | 2.46513 | ||||||||
\(743\) | 6.62438e107 | 1.44233 | 0.721165 | − | 0.692764i | \(-0.243607\pi\) | ||||
0.721165 | + | 0.692764i | \(0.243607\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.49493e107 | −0.294279 | ||||||||
\(746\) | −1.02667e106 | −0.0192188 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.06604e107 | 0.180495 | ||||||||
\(749\) | 3.52148e107 | 0.567096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.02618e108 | 1.49529 | 0.747645 | − | 0.664099i | \(-0.231185\pi\) | ||||
0.747645 | + | 0.664099i | \(0.231185\pi\) | |||||||
\(752\) | 3.42883e106 | 0.0475310 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.60553e107 | 0.577901 | ||||||||
\(755\) | −1.29331e107 | −0.154415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.55357e107 | −0.924808 | −0.462404 | − | 0.886669i | \(-0.653013\pi\) | ||||
−0.462404 | + | 0.886669i | \(0.653013\pi\) | |||||||
\(758\) | −3.84618e107 | −0.395762 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.22833e106 | −0.0580580 | ||||||||
\(761\) | −1.22517e108 | −1.08711 | −0.543553 | − | 0.839375i | \(-0.682921\pi\) | ||||
−0.543553 | + | 0.839375i | \(0.682921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.76035e108 | 1.41556 | ||||||||
\(764\) | 1.75782e108 | 1.34578 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.55902e108 | −2.47031 | ||||||||
\(767\) | −1.53911e106 | −0.0101729 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.12833e108 | 0.676393 | 0.338197 | − | 0.941075i | \(-0.390183\pi\) | ||||
0.338197 | + | 0.941075i | \(0.390183\pi\) | |||||||
\(770\) | −9.41810e106 | −0.0537726 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.77426e108 | −2.47319 | ||||||||
\(773\) | −2.94129e107 | −0.145147 | −0.0725734 | − | 0.997363i | \(-0.523121\pi\) | ||||
−0.0725734 | + | 0.997363i | \(0.523121\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.41938e108 | −1.08365 | ||||||||
\(776\) | 2.05821e108 | 0.878367 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.84801e107 | −0.226607 | ||||||||
\(779\) | 4.48618e107 | 0.165662 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.85416e107 | 0.129275 | ||||||||
\(782\) | 2.89233e108 | 0.924687 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.41351e107 | −0.128213 | ||||||||
\(785\) | −1.02638e108 | −0.284246 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.86662e108 | 1.98032 | 0.990161 | − | 0.139936i | \(-0.0446896\pi\) | ||||
0.990161 | + | 0.139936i | \(0.0446896\pi\) | |||||||
\(788\) | −7.99152e108 | −1.91821 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.31199e107 | 0.0286362 | ||||||||
\(791\) | 6.53111e107 | 0.135947 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14854e108 | 0.217471 | ||||||||
\(794\) | 8.96061e108 | 1.61834 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.91860e109 | 3.15314 | ||||||||
\(797\) | −9.68204e107 | −0.151803 | −0.0759014 | − | 0.997115i | \(-0.524183\pi\) | ||||
−0.0759014 | + | 0.997115i | \(0.524183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.66662e107 | −0.0666037 | ||||||||
\(800\) | 3.64534e108 | 0.496436 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.66104e109 | −2.05988 | ||||||||
\(803\) | 6.41499e107 | 0.0759212 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.65104e108 | −0.177997 | ||||||||
\(806\) | −6.05404e108 | −0.622990 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.59385e109 | 1.49459 | ||||||||
\(809\) | −1.25823e109 | −1.12640 | −0.563199 | − | 0.826321i | \(-0.690430\pi\) | ||||
−0.563199 | + | 0.826321i | \(0.690430\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.83325e109 | −1.49603 | −0.748014 | − | 0.663683i | \(-0.768992\pi\) | ||||
−0.748014 | + | 0.663683i | \(0.768992\pi\) | |||||||
\(812\) | −2.19235e109 | −1.70828 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.26354e108 | 0.160832 | ||||||||
\(815\) | 2.48728e108 | 0.168778 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.64966e108 | 0.225905 | ||||||||
\(818\) | −1.06114e109 | −0.627368 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.51694e108 | −0.513426 | ||||||||
\(821\) | −5.30578e108 | −0.273452 | −0.136726 | − | 0.990609i | \(-0.543658\pi\) | ||||
−0.136726 | + | 0.990609i | \(0.543658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.35738e107 | −0.0204989 | −0.0102495 | − | 0.999947i | \(-0.503263\pi\) | ||||
−0.0102495 | + | 0.999947i | \(0.503263\pi\) | |||||||
\(824\) | −5.17014e108 | −0.232398 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.13392e108 | 0.0465403 | ||||||||
\(827\) | −9.43799e107 | −0.0370188 | −0.0185094 | − | 0.999829i | \(-0.505892\pi\) | ||||
−0.0185094 | + | 0.999829i | \(0.505892\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.56308e109 | −1.63480 | −0.817398 | − | 0.576073i | \(-0.804584\pi\) | ||||
−0.817398 | + | 0.576073i | \(0.804584\pi\) | |||||||
\(830\) | 3.94012e106 | 0.00134921 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.42806e109 | 0.446809 | ||||||||
\(833\) | 6.00676e108 | 0.179661 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.23893e108 | 0.0885440 | ||||||||
\(836\) | 1.52257e108 | 0.0397961 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.14579e110 | −2.73813 | ||||||||
\(839\) | −7.28934e108 | −0.166577 | −0.0832884 | − | 0.996525i | \(-0.526542\pi\) | ||||
−0.0832884 | + | 0.996525i | \(0.526542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.17112e108 | 0.170778 | ||||||||
\(842\) | 5.51846e109 | 1.10310 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.28707e109 | 0.784006 | ||||||||
\(845\) | −1.36924e109 | −0.239526 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.29682e109 | −0.847983 | ||||||||
\(848\) | 5.62539e109 | 0.861605 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.92913e109 | 1.11177 | ||||||||
\(851\) | 3.96810e109 | 0.532382 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.01292e110 | −1.24448 | −0.622240 | − | 0.782827i | \(-0.713777\pi\) | ||||
−0.622240 | + | 0.782827i | \(0.713777\pi\) | |||||||
\(854\) | −8.46165e109 | −0.994913 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.45455e109 | 0.910593 | ||||||||
\(857\) | −1.65427e110 | −1.70540 | −0.852698 | − | 0.522405i | \(-0.825035\pi\) | ||||
−0.852698 | + | 0.522405i | \(0.825035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.68954e109 | 0.537444 | 0.268722 | − | 0.963218i | \(-0.413399\pi\) | ||||
0.268722 | + | 0.963218i | \(0.413399\pi\) | |||||||
\(860\) | −7.74236e109 | −0.700134 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.25283e110 | 2.69612 | ||||||||
\(863\) | 9.44371e108 | 0.0749442 | 0.0374721 | − | 0.999298i | \(-0.488069\pi\) | ||||
0.0374721 | + | 0.999298i | \(0.488069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.37576e109 | −0.245622 | ||||||||
\(866\) | 2.01386e110 | 1.40316 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.88188e110 | 1.84156 | ||||||||
\(869\) | −1.45073e108 | −0.00887864 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.11929e109 | −0.455866 | ||||||||
\(872\) | 4.22634e110 | 2.27298 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.13095e109 | 0.203878 | ||||||||
\(875\) | −9.39823e109 | −0.444370 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.65254e110 | −0.717246 | −0.358623 | − | 0.933482i | \(-0.616754\pi\) | ||||
−0.358623 | + | 0.933482i | \(0.616754\pi\) | |||||||
\(878\) | 5.40972e110 | 2.24973 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.92186e108 | −0.0187944 | ||||||||
\(881\) | 3.05928e110 | 1.11950 | 0.559748 | − | 0.828663i | \(-0.310898\pi\) | ||||
0.559748 | + | 0.828663i | \(0.310898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.03341e110 | −0.347334 | −0.173667 | − | 0.984804i | \(-0.555562\pi\) | ||||
−0.173667 | + | 0.984804i | \(0.555562\pi\) | |||||||
\(884\) | 1.28200e110 | 0.412979 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.21256e109 | 0.0654834 | ||||||||
\(887\) | 4.02103e110 | 1.14078 | 0.570390 | − | 0.821374i | \(-0.306792\pi\) | ||||
0.570390 | + | 0.821374i | \(0.306792\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.28813e109 | 0.216093 | ||||||||
\(890\) | −2.78556e110 | −0.696286 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.86467e110 | 1.80717 | ||||||||
\(893\) | −6.66506e108 | −0.0146850 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.69689e110 | −0.343788 | ||||||||
\(896\) | −8.14288e110 | −1.58208 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.66195e110 | −1.54794 | ||||||||
\(899\) | −7.36360e110 | −1.26212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.65613e110 | −1.20734 | ||||||||
\(902\) | 1.62867e110 | 0.246370 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.56802e110 | 0.218291 | ||||||||
\(905\) | −1.91082e110 | −0.255210 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.12894e111 | −1.38803 | −0.694013 | − | 0.719963i | \(-0.744159\pi\) | ||||
−0.694013 | + | 0.719963i | \(0.744159\pi\) | |||||||
\(908\) | −1.78328e111 | −2.10377 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.13260e110 | −0.123034 | ||||||||
\(911\) | 1.25185e110 | 0.130501 | 0.0652506 | − | 0.997869i | \(-0.479215\pi\) | ||||
0.0652506 | + | 0.997869i | \(0.479215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.35678e107 | −0.000418323 0 | ||||||||
\(914\) | −1.58266e111 | −1.45850 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.27910e110 | 0.363306 | ||||||||
\(917\) | 1.05705e110 | 0.0861480 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.73300e111 | 1.30157 | 0.650785 | − | 0.759262i | \(-0.274440\pi\) | ||||
0.650785 | + | 0.759262i | \(0.274440\pi\) | |||||||
\(920\) | −3.96390e110 | −0.285811 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.29221e111 | −2.85280 | ||||||||
\(923\) | 4.63492e110 | 0.295787 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.08783e111 | 0.640095 | ||||||||
\(926\) | 2.53932e111 | 1.43484 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.10949e111 | 0.578196 | ||||||||
\(929\) | −6.51740e110 | −0.326201 | −0.163100 | − | 0.986609i | \(-0.552149\pi\) | ||||
−0.163100 | + | 0.986609i | \(0.552149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.57910e109 | 0.0396122 | ||||||||
\(932\) | −2.82005e111 | −1.25072 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.46877e111 | −1.01035 | ||||||||
\(935\) | 6.69863e109 | 0.0263360 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.15863e111 | 1.87197 | 0.935987 | − | 0.352035i | \(-0.114510\pi\) | ||||
0.935987 | + | 0.352035i | \(0.114510\pi\) | |||||||
\(938\) | 5.98174e111 | 2.08555 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.41392e110 | 0.0455125 | ||||||||
\(941\) | −5.35193e110 | −0.165539 | −0.0827694 | − | 0.996569i | \(-0.526376\pi\) | ||||
−0.0827694 | + | 0.996569i | \(0.526376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.85514e111 | 0.815528 | ||||||||
\(944\) | 5.92580e109 | 0.0162666 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.32498e111 | 0.335963 | ||||||||
\(947\) | −6.35901e111 | −1.54976 | −0.774881 | − | 0.632107i | \(-0.782190\pi\) | ||||
−0.774881 | + | 0.632107i | \(0.782190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.71452e110 | 0.173710 | ||||||||
\(950\) | 1.13247e111 | 0.245127 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.27219e111 | −0.854603 | ||||||||
\(953\) | 2.74523e111 | 0.527952 | 0.263976 | − | 0.964529i | \(-0.414966\pi\) | ||||
0.263976 | + | 0.964529i | \(0.414966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.10455e111 | 0.196363 | ||||||||
\(956\) | −3.93032e111 | −0.671825 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.27489e112 | −2.01496 | ||||||||
\(959\) | 6.90073e111 | 1.04881 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.56535e111 | 0.360595 | ||||||||
\(962\) | 2.72208e111 | 0.367990 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.68106e111 | 1.21069 | ||||||||
\(965\) | −2.99997e111 | −0.360864 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.60617e111 | −0.735287 | −0.367643 | − | 0.929967i | \(-0.619835\pi\) | ||||
−0.367643 | + | 0.929967i | \(0.619835\pi\) | |||||||
\(968\) | −1.27169e112 | −1.36162 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.85923e111 | 0.283341 | ||||||||
\(971\) | −1.03596e112 | −0.987695 | −0.493847 | − | 0.869549i | \(-0.664410\pi\) | ||||
−0.493847 | + | 0.869549i | \(0.664410\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.92126e111 | 0.875659 | ||||||||
\(974\) | 4.12219e111 | 0.350080 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.42203e111 | −0.347739 | ||||||||
\(977\) | 2.05932e112 | 1.55839 | 0.779197 | − | 0.626779i | \(-0.215627\pi\) | ||||
0.779197 | + | 0.626779i | \(0.215627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.08014e111 | 0.215883 | ||||||||
\(980\) | −1.81996e111 | −0.122768 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.22401e111 | −0.138981 | ||||||||
\(983\) | 9.74562e111 | 0.586209 | 0.293105 | − | 0.956080i | \(-0.405312\pi\) | ||||
0.293105 | + | 0.956080i | \(0.405312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.02158e111 | −0.279886 | ||||||||
\(986\) | 2.41330e112 | 1.29487 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.83100e111 | 0.0910550 | ||||||||
\(989\) | 2.32276e112 | 1.11210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.65057e112 | 1.17646 | 0.588230 | − | 0.808694i | \(-0.299825\pi\) | ||||
0.588230 | + | 0.808694i | \(0.299825\pi\) | |||||||
\(992\) | −1.45844e112 | −0.623307 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.41470e112 | −1.35320 | ||||||||
\(995\) | 1.20558e112 | 0.460075 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.01612e112 | −0.713587 | −0.356793 | − | 0.934183i | \(-0.616130\pi\) | ||||
−0.356793 | + | 0.934183i | \(0.616130\pi\) | |||||||
\(998\) | −7.02683e111 | −0.239532 | ||||||||
\(999\) | 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 | 9.76.a.c.1.6 | 6 | ||
3.2 | odd | 2 | 1.76.a.a.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.76.a.a.1.1 | ✓ | 6 | 3.2 | odd | 2 | ||
9.76.a.c.1.6 | 6 | 1.1 | even | 1 | trivial |