Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,84,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 84, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 84);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 84 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(43.6272128266\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} + \cdots + 22\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{82}\cdot 3^{30}\cdot 5^{8}\cdot 7^{4}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.25782e10\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.91512e11 | 0.190204 | 0.0951018 | − | 0.995468i | \(-0.469682\pi\) | ||||
0.0951018 | + | 0.995468i | \(0.469682\pi\) | |||||||
\(3\) | 9.95960e19 | 1.57656 | 0.788279 | − | 0.615318i | \(-0.210972\pi\) | ||||
0.788279 | + | 0.615318i | \(0.210972\pi\) | |||||||
\(4\) | −9.32152e24 | −0.963823 | ||||||||
\(5\) | 1.29632e29 | 1.27485 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(6\) | 5.89123e31 | 0.299867 | ||||||||
\(7\) | 1.88228e35 | 1.59630 | 0.798150 | − | 0.602458i | \(-0.205812\pi\) | ||||
0.798150 | + | 0.602458i | \(0.205812\pi\) | |||||||
\(8\) | −1.12345e37 | −0.373526 | ||||||||
\(9\) | 5.92853e39 | 1.48553 | ||||||||
\(10\) | 7.66792e40 | 0.242481 | ||||||||
\(11\) | −1.53986e43 | −0.932579 | −0.466289 | − | 0.884632i | \(-0.654409\pi\) | ||||
−0.466289 | + | 0.884632i | \(0.654409\pi\) | |||||||
\(12\) | −9.28386e44 | −1.51952 | ||||||||
\(13\) | 2.07012e46 | 1.22277 | 0.611387 | − | 0.791332i | \(-0.290612\pi\) | ||||
0.611387 | + | 0.791332i | \(0.290612\pi\) | |||||||
\(14\) | 1.11339e47 | 0.303622 | ||||||||
\(15\) | 1.29109e49 | 2.00987 | ||||||||
\(16\) | 8.35068e49 | 0.892776 | ||||||||
\(17\) | 6.28617e50 | 0.542945 | 0.271473 | − | 0.962446i | \(-0.412489\pi\) | ||||
0.271473 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(18\) | 3.50680e51 | 0.282554 | ||||||||
\(19\) | −1.57680e53 | −1.34741 | −0.673707 | − | 0.738998i | \(-0.735299\pi\) | ||||
−0.673707 | + | 0.738998i | \(0.735299\pi\) | |||||||
\(20\) | −1.20837e54 | −1.22873 | ||||||||
\(21\) | 1.87467e55 | 2.51666 | ||||||||
\(22\) | −9.10848e54 | −0.177380 | ||||||||
\(23\) | −6.31544e55 | −0.194401 | −0.0972006 | − | 0.995265i | \(-0.530989\pi\) | ||||
−0.0972006 | + | 0.995265i | \(0.530989\pi\) | |||||||
\(24\) | −1.11892e57 | −0.588886 | ||||||||
\(25\) | 6.46483e57 | 0.625240 | ||||||||
\(26\) | 1.22450e58 | 0.232576 | ||||||||
\(27\) | 1.92986e59 | 0.765472 | ||||||||
\(28\) | −1.75457e60 | −1.53855 | ||||||||
\(29\) | 1.01915e59 | 0.0208316 | 0.0104158 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104158 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(30\) | 7.63694e60 | 0.382285 | ||||||||
\(31\) | 2.53808e61 | 0.325833 | 0.162917 | − | 0.986640i | \(-0.447910\pi\) | ||||
0.162917 | + | 0.986640i | \(0.447910\pi\) | |||||||
\(32\) | 1.58049e62 | 0.543336 | ||||||||
\(33\) | −1.53364e63 | −1.47026 | ||||||||
\(34\) | 3.71835e62 | 0.103270 | ||||||||
\(35\) | 2.44004e64 | 2.03504 | ||||||||
\(36\) | −5.52629e64 | −1.43179 | ||||||||
\(37\) | −3.48983e64 | −0.290023 | −0.145011 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145011 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(38\) | −9.32694e64 | −0.256283 | ||||||||
\(39\) | 2.06176e66 | 1.92777 | ||||||||
\(40\) | −1.45636e66 | −0.476190 | ||||||||
\(41\) | 2.65816e65 | 0.0311926 | 0.0155963 | − | 0.999878i | \(-0.495035\pi\) | ||||
0.0155963 | + | 0.999878i | \(0.495035\pi\) | |||||||
\(42\) | 1.10889e67 | 0.478678 | ||||||||
\(43\) | 1.23906e67 | 0.201442 | 0.100721 | − | 0.994915i | \(-0.467885\pi\) | ||||
0.100721 | + | 0.994915i | \(0.467885\pi\) | |||||||
\(44\) | 1.43539e68 | 0.898840 | ||||||||
\(45\) | 7.68530e68 | 1.89383 | ||||||||
\(46\) | −3.73566e67 | −0.0369758 | ||||||||
\(47\) | 1.13865e69 | 0.461668 | 0.230834 | − | 0.972993i | \(-0.425855\pi\) | ||||
0.230834 | + | 0.972993i | \(0.425855\pi\) | |||||||
\(48\) | 8.31695e69 | 1.40751 | ||||||||
\(49\) | 2.15257e70 | 1.54818 | ||||||||
\(50\) | 3.82402e69 | 0.118923 | ||||||||
\(51\) | 6.26078e70 | 0.855985 | ||||||||
\(52\) | −1.92967e71 | −1.17854 | ||||||||
\(53\) | 4.75692e71 | 1.31789 | 0.658943 | − | 0.752193i | \(-0.271004\pi\) | ||||
0.658943 | + | 0.752193i | \(0.271004\pi\) | |||||||
\(54\) | 1.14154e71 | 0.145596 | ||||||||
\(55\) | −1.99616e72 | −1.18890 | ||||||||
\(56\) | −2.11465e72 | −0.596260 | ||||||||
\(57\) | −1.57043e73 | −2.12428 | ||||||||
\(58\) | 6.02841e70 | 0.00396224 | ||||||||
\(59\) | 5.56534e73 | 1.79942 | 0.899711 | − | 0.436486i | \(-0.143777\pi\) | ||||
0.899711 | + | 0.436486i | \(0.143777\pi\) | |||||||
\(60\) | −1.20349e74 | −1.93716 | ||||||||
\(61\) | −5.06207e73 | −0.410337 | −0.205168 | − | 0.978727i | \(-0.565774\pi\) | ||||
−0.205168 | + | 0.978727i | \(0.565774\pi\) | |||||||
\(62\) | 1.50131e73 | 0.0619747 | ||||||||
\(63\) | 1.11591e75 | 2.37136 | ||||||||
\(64\) | −7.14141e74 | −0.789432 | ||||||||
\(65\) | 2.68355e75 | 1.55885 | ||||||||
\(66\) | −9.07168e74 | −0.279650 | ||||||||
\(67\) | 4.03675e75 | 0.666695 | 0.333348 | − | 0.942804i | \(-0.391822\pi\) | ||||
0.333348 | + | 0.942804i | \(0.391822\pi\) | |||||||
\(68\) | −5.85967e75 | −0.523303 | ||||||||
\(69\) | −6.28993e75 | −0.306485 | ||||||||
\(70\) | 1.44331e76 | 0.387073 | ||||||||
\(71\) | −9.07289e76 | −1.35059 | −0.675296 | − | 0.737547i | \(-0.735984\pi\) | ||||
−0.675296 | + | 0.737547i | \(0.735984\pi\) | |||||||
\(72\) | −6.66043e76 | −0.554886 | ||||||||
\(73\) | −1.82421e77 | −0.857383 | −0.428692 | − | 0.903451i | \(-0.641025\pi\) | ||||
−0.428692 | + | 0.903451i | \(0.641025\pi\) | |||||||
\(74\) | −2.06427e76 | −0.0551634 | ||||||||
\(75\) | 6.43871e77 | 0.985726 | ||||||||
\(76\) | 1.46981e78 | 1.29867 | ||||||||
\(77\) | −2.89845e78 | −1.48868 | ||||||||
\(78\) | 1.21955e78 | 0.366670 | ||||||||
\(79\) | 6.07683e78 | 1.07684 | 0.538422 | − | 0.842675i | \(-0.319021\pi\) | ||||
0.538422 | + | 0.842675i | \(0.319021\pi\) | |||||||
\(80\) | 1.08252e79 | 1.13816 | ||||||||
\(81\) | −4.43916e78 | −0.278723 | ||||||||
\(82\) | 1.57233e77 | 0.00593294 | ||||||||
\(83\) | −1.68264e79 | −0.383929 | −0.191964 | − | 0.981402i | \(-0.561486\pi\) | ||||
−0.191964 | + | 0.981402i | \(0.561486\pi\) | |||||||
\(84\) | −1.74748e80 | −2.42561 | ||||||||
\(85\) | 8.14892e79 | 0.692173 | ||||||||
\(86\) | 7.32918e78 | 0.0383151 | ||||||||
\(87\) | 1.01503e79 | 0.0328422 | ||||||||
\(88\) | 1.72997e80 | 0.348343 | ||||||||
\(89\) | −1.03901e81 | −1.30898 | −0.654489 | − | 0.756071i | \(-0.727116\pi\) | ||||
−0.654489 | + | 0.756071i | \(0.727116\pi\) | |||||||
\(90\) | 4.54595e80 | 0.360214 | ||||||||
\(91\) | 3.89654e81 | 1.95191 | ||||||||
\(92\) | 5.88695e80 | 0.187368 | ||||||||
\(93\) | 2.52783e81 | 0.513695 | ||||||||
\(94\) | 6.73526e80 | 0.0878109 | ||||||||
\(95\) | −2.04404e82 | −1.71775 | ||||||||
\(96\) | 1.57411e82 | 0.856600 | ||||||||
\(97\) | −1.40939e82 | −0.498891 | −0.249446 | − | 0.968389i | \(-0.580248\pi\) | ||||
−0.249446 | + | 0.968389i | \(0.580248\pi\) | |||||||
\(98\) | 1.27327e82 | 0.294469 | ||||||||
\(99\) | −9.12912e82 | −1.38538 | ||||||||
\(100\) | −6.02620e82 | −0.602620 | ||||||||
\(101\) | 1.22890e83 | 0.813165 | 0.406582 | − | 0.913614i | \(-0.366720\pi\) | ||||
0.406582 | + | 0.913614i | \(0.366720\pi\) | |||||||
\(102\) | 3.70333e82 | 0.162811 | ||||||||
\(103\) | −1.19195e83 | −0.349554 | −0.174777 | − | 0.984608i | \(-0.555920\pi\) | ||||
−0.174777 | + | 0.984608i | \(0.555920\pi\) | |||||||
\(104\) | −2.32568e83 | −0.456738 | ||||||||
\(105\) | 2.43018e84 | 3.20836 | ||||||||
\(106\) | 2.81378e83 | 0.250667 | ||||||||
\(107\) | −1.87371e84 | −1.13051 | −0.565257 | − | 0.824915i | \(-0.691223\pi\) | ||||
−0.565257 | + | 0.824915i | \(0.691223\pi\) | |||||||
\(108\) | −1.79892e84 | −0.737779 | ||||||||
\(109\) | 1.18472e83 | 0.0331447 | 0.0165724 | − | 0.999863i | \(-0.494725\pi\) | ||||
0.0165724 | + | 0.999863i | \(0.494725\pi\) | |||||||
\(110\) | −1.18075e84 | −0.226133 | ||||||||
\(111\) | −3.47573e84 | −0.457238 | ||||||||
\(112\) | 1.57183e85 | 1.42514 | ||||||||
\(113\) | −2.95724e85 | −1.85409 | −0.927047 | − | 0.374944i | \(-0.877662\pi\) | ||||
−0.927047 | + | 0.374944i | \(0.877662\pi\) | |||||||
\(114\) | −9.28926e84 | −0.404045 | ||||||||
\(115\) | −8.18687e84 | −0.247832 | ||||||||
\(116\) | −9.50004e83 | −0.0200779 | ||||||||
\(117\) | 1.22728e86 | 1.81647 | ||||||||
\(118\) | 3.29196e85 | 0.342257 | ||||||||
\(119\) | 1.18323e86 | 0.866704 | ||||||||
\(120\) | −1.45048e86 | −0.750740 | ||||||||
\(121\) | −3.55244e85 | −0.130297 | ||||||||
\(122\) | −2.99428e85 | −0.0780476 | ||||||||
\(123\) | 2.64742e85 | 0.0491769 | ||||||||
\(124\) | −2.36588e86 | −0.314046 | ||||||||
\(125\) | −5.02317e86 | −0.477763 | ||||||||
\(126\) | 6.60076e86 | 0.451041 | ||||||||
\(127\) | −2.69273e87 | −1.32537 | −0.662686 | − | 0.748898i | \(-0.730584\pi\) | ||||
−0.662686 | + | 0.748898i | \(0.730584\pi\) | |||||||
\(128\) | −1.95098e87 | −0.693489 | ||||||||
\(129\) | 1.23405e87 | 0.317585 | ||||||||
\(130\) | 1.58735e87 | 0.296499 | ||||||||
\(131\) | 1.39054e88 | 1.88984 | 0.944918 | − | 0.327308i | \(-0.106142\pi\) | ||||
0.944918 | + | 0.327308i | \(0.106142\pi\) | |||||||
\(132\) | 1.42959e88 | 1.41707 | ||||||||
\(133\) | −2.96797e88 | −2.15088 | ||||||||
\(134\) | 2.38779e87 | 0.126808 | ||||||||
\(135\) | 2.50173e88 | 0.975862 | ||||||||
\(136\) | −7.06223e87 | −0.202804 | ||||||||
\(137\) | −3.48762e88 | −0.738968 | −0.369484 | − | 0.929237i | \(-0.620466\pi\) | ||||
−0.369484 | + | 0.929237i | \(0.620466\pi\) | |||||||
\(138\) | −3.72057e87 | −0.0582945 | ||||||||
\(139\) | 5.86430e88 | 0.680930 | 0.340465 | − | 0.940257i | \(-0.389416\pi\) | ||||
0.340465 | + | 0.940257i | \(0.389416\pi\) | |||||||
\(140\) | −2.27449e89 | −1.96142 | ||||||||
\(141\) | 1.13405e89 | 0.727846 | ||||||||
\(142\) | −5.36673e88 | −0.256888 | ||||||||
\(143\) | −3.18770e89 | −1.14033 | ||||||||
\(144\) | 4.95072e89 | 1.32625 | ||||||||
\(145\) | 1.32115e88 | 0.0265571 | ||||||||
\(146\) | −1.07904e89 | −0.163077 | ||||||||
\(147\) | 2.14388e90 | 2.44079 | ||||||||
\(148\) | 3.25305e89 | 0.279531 | ||||||||
\(149\) | −1.84246e90 | −1.19720 | −0.598602 | − | 0.801047i | \(-0.704277\pi\) | ||||
−0.598602 | + | 0.801047i | \(0.704277\pi\) | |||||||
\(150\) | 3.80858e89 | 0.187489 | ||||||||
\(151\) | −5.05977e90 | −1.89055 | −0.945274 | − | 0.326277i | \(-0.894206\pi\) | ||||
−0.945274 | + | 0.326277i | \(0.894206\pi\) | |||||||
\(152\) | 1.77146e90 | 0.503295 | ||||||||
\(153\) | 3.72677e90 | 0.806564 | ||||||||
\(154\) | −1.71447e90 | −0.283152 | ||||||||
\(155\) | 3.29018e90 | 0.415388 | ||||||||
\(156\) | −1.92187e91 | −1.85803 | ||||||||
\(157\) | −1.24523e91 | −0.923449 | −0.461724 | − | 0.887023i | \(-0.652769\pi\) | ||||
−0.461724 | + | 0.887023i | \(0.652769\pi\) | |||||||
\(158\) | 3.59452e90 | 0.204820 | ||||||||
\(159\) | 4.73771e91 | 2.07772 | ||||||||
\(160\) | 2.04883e91 | 0.692671 | ||||||||
\(161\) | −1.18874e91 | −0.310323 | ||||||||
\(162\) | −2.62582e90 | −0.0530141 | ||||||||
\(163\) | 7.44217e91 | 1.16390 | 0.581948 | − | 0.813226i | \(-0.302291\pi\) | ||||
0.581948 | + | 0.813226i | \(0.302291\pi\) | |||||||
\(164\) | −2.47781e90 | −0.0300641 | ||||||||
\(165\) | −1.98810e92 | −1.87436 | ||||||||
\(166\) | −9.95303e90 | −0.0730247 | ||||||||
\(167\) | 1.95454e92 | 1.11766 | 0.558832 | − | 0.829281i | \(-0.311249\pi\) | ||||
0.558832 | + | 0.829281i | \(0.311249\pi\) | |||||||
\(168\) | −2.10611e92 | −0.940039 | ||||||||
\(169\) | 1.41925e92 | 0.495176 | ||||||||
\(170\) | 4.82019e91 | 0.131654 | ||||||||
\(171\) | −9.34808e92 | −2.00163 | ||||||||
\(172\) | −1.15499e92 | −0.194155 | ||||||||
\(173\) | 6.54546e92 | 0.865022 | 0.432511 | − | 0.901629i | \(-0.357628\pi\) | ||||
0.432511 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(174\) | 6.00405e90 | 0.00624670 | ||||||||
\(175\) | 1.21686e93 | 0.998071 | ||||||||
\(176\) | −1.28589e93 | −0.832584 | ||||||||
\(177\) | 5.54285e93 | 2.83689 | ||||||||
\(178\) | −6.14584e92 | −0.248973 | ||||||||
\(179\) | −7.33190e92 | −0.235405 | −0.117702 | − | 0.993049i | \(-0.537553\pi\) | ||||
−0.117702 | + | 0.993049i | \(0.537553\pi\) | |||||||
\(180\) | −7.16386e93 | −1.82532 | ||||||||
\(181\) | 1.13855e93 | 0.230511 | 0.115256 | − | 0.993336i | \(-0.463231\pi\) | ||||
0.115256 | + | 0.993336i | \(0.463231\pi\) | |||||||
\(182\) | 2.30485e93 | 0.371261 | ||||||||
\(183\) | −5.04162e93 | −0.646920 | ||||||||
\(184\) | 7.09512e92 | 0.0726139 | ||||||||
\(185\) | −4.52395e93 | −0.369735 | ||||||||
\(186\) | 1.49524e93 | 0.0977067 | ||||||||
\(187\) | −9.67984e93 | −0.506339 | ||||||||
\(188\) | −1.06140e94 | −0.444966 | ||||||||
\(189\) | 3.63253e94 | 1.22192 | ||||||||
\(190\) | −1.20908e94 | −0.326722 | ||||||||
\(191\) | 4.99940e94 | 1.08651 | 0.543254 | − | 0.839568i | \(-0.317192\pi\) | ||||
0.543254 | + | 0.839568i | \(0.317192\pi\) | |||||||
\(192\) | −7.11255e94 | −1.24459 | ||||||||
\(193\) | 9.30186e94 | 1.31202 | 0.656011 | − | 0.754751i | \(-0.272242\pi\) | ||||
0.656011 | + | 0.754751i | \(0.272242\pi\) | |||||||
\(194\) | −8.33674e93 | −0.0948909 | ||||||||
\(195\) | 2.67271e95 | 2.45762 | ||||||||
\(196\) | −2.00652e95 | −1.49217 | ||||||||
\(197\) | −2.51456e95 | −1.51396 | −0.756978 | − | 0.653440i | \(-0.773325\pi\) | ||||
−0.756978 | + | 0.653440i | \(0.773325\pi\) | |||||||
\(198\) | −5.39998e94 | −0.263504 | ||||||||
\(199\) | −1.93622e95 | −0.766572 | −0.383286 | − | 0.923630i | \(-0.625208\pi\) | ||||
−0.383286 | + | 0.923630i | \(0.625208\pi\) | |||||||
\(200\) | −7.26294e94 | −0.233543 | ||||||||
\(201\) | 4.02044e95 | 1.05108 | ||||||||
\(202\) | 7.26908e94 | 0.154667 | ||||||||
\(203\) | 1.91833e94 | 0.0332535 | ||||||||
\(204\) | −5.83600e95 | −0.825017 | ||||||||
\(205\) | 3.44584e94 | 0.0397658 | ||||||||
\(206\) | −7.05054e94 | −0.0664864 | ||||||||
\(207\) | −3.74413e95 | −0.288789 | ||||||||
\(208\) | 1.72869e96 | 1.09166 | ||||||||
\(209\) | 2.42805e96 | 1.25657 | ||||||||
\(210\) | 1.43748e96 | 0.610242 | ||||||||
\(211\) | 3.03696e96 | 1.05856 | 0.529282 | − | 0.848446i | \(-0.322461\pi\) | ||||
0.529282 | + | 0.848446i | \(0.322461\pi\) | |||||||
\(212\) | −4.43418e96 | −1.27021 | ||||||||
\(213\) | −9.03624e96 | −2.12929 | ||||||||
\(214\) | −1.10832e96 | −0.215028 | ||||||||
\(215\) | 1.60622e96 | 0.256809 | ||||||||
\(216\) | −2.16811e96 | −0.285924 | ||||||||
\(217\) | 4.77738e96 | 0.520128 | ||||||||
\(218\) | 7.00774e94 | 0.00630425 | ||||||||
\(219\) | −1.81684e97 | −1.35171 | ||||||||
\(220\) | 1.86073e97 | 1.14589 | ||||||||
\(221\) | 1.30131e97 | 0.663899 | ||||||||
\(222\) | −2.05594e96 | −0.0869683 | ||||||||
\(223\) | −3.38548e97 | −1.18842 | −0.594208 | − | 0.804312i | \(-0.702534\pi\) | ||||
−0.594208 | + | 0.804312i | \(0.702534\pi\) | |||||||
\(224\) | 2.97492e97 | 0.867327 | ||||||||
\(225\) | 3.83269e97 | 0.928815 | ||||||||
\(226\) | −1.74925e97 | −0.352656 | ||||||||
\(227\) | −9.76481e96 | −0.163904 | −0.0819522 | − | 0.996636i | \(-0.526115\pi\) | ||||
−0.0819522 | + | 0.996636i | \(0.526115\pi\) | |||||||
\(228\) | 1.46388e98 | 2.04743 | ||||||||
\(229\) | −4.89770e97 | −0.571241 | −0.285621 | − | 0.958343i | \(-0.592200\pi\) | ||||
−0.285621 | + | 0.958343i | \(0.592200\pi\) | |||||||
\(230\) | −4.84263e96 | −0.0471386 | ||||||||
\(231\) | −2.88674e98 | −2.34698 | ||||||||
\(232\) | −1.14497e96 | −0.00778114 | ||||||||
\(233\) | −7.65637e97 | −0.435263 | −0.217632 | − | 0.976031i | \(-0.569833\pi\) | ||||
−0.217632 | + | 0.976031i | \(0.569833\pi\) | |||||||
\(234\) | 7.25948e97 | 0.345500 | ||||||||
\(235\) | 1.47606e98 | 0.588557 | ||||||||
\(236\) | −5.18774e98 | −1.73432 | ||||||||
\(237\) | 6.05228e98 | 1.69771 | ||||||||
\(238\) | 6.99896e97 | 0.164850 | ||||||||
\(239\) | −5.55817e98 | −1.10007 | −0.550034 | − | 0.835142i | \(-0.685385\pi\) | ||||
−0.550034 | + | 0.835142i | \(0.685385\pi\) | |||||||
\(240\) | 1.07815e99 | 1.79437 | ||||||||
\(241\) | 1.75262e98 | 0.245460 | 0.122730 | − | 0.992440i | \(-0.460835\pi\) | ||||
0.122730 | + | 0.992440i | \(0.460835\pi\) | |||||||
\(242\) | −2.10131e97 | −0.0247829 | ||||||||
\(243\) | −1.21230e99 | −1.20489 | ||||||||
\(244\) | 4.71862e98 | 0.395492 | ||||||||
\(245\) | 2.79043e99 | 1.97369 | ||||||||
\(246\) | 1.56598e97 | 0.00935362 | ||||||||
\(247\) | −3.26416e99 | −1.64758 | ||||||||
\(248\) | −2.85142e98 | −0.121707 | ||||||||
\(249\) | −1.67584e99 | −0.605286 | ||||||||
\(250\) | −2.97127e98 | −0.0908722 | ||||||||
\(251\) | 3.41610e99 | 0.885262 | 0.442631 | − | 0.896704i | \(-0.354045\pi\) | ||||
0.442631 | + | 0.896704i | \(0.354045\pi\) | |||||||
\(252\) | −1.04020e100 | −2.28557 | ||||||||
\(253\) | 9.72492e98 | 0.181294 | ||||||||
\(254\) | −1.59278e99 | −0.252091 | ||||||||
\(255\) | 8.11600e99 | 1.09125 | ||||||||
\(256\) | 5.75271e99 | 0.657528 | ||||||||
\(257\) | 1.76565e100 | 1.71664 | 0.858322 | − | 0.513112i | \(-0.171507\pi\) | ||||
0.858322 | + | 0.513112i | \(0.171507\pi\) | |||||||
\(258\) | 7.29957e98 | 0.0604059 | ||||||||
\(259\) | −6.56882e99 | −0.462964 | ||||||||
\(260\) | −2.50147e100 | −1.50246 | ||||||||
\(261\) | 6.04207e98 | 0.0309460 | ||||||||
\(262\) | 8.22520e99 | 0.359454 | ||||||||
\(263\) | 2.35912e99 | 0.0880210 | 0.0440105 | − | 0.999031i | \(-0.485987\pi\) | ||||
0.0440105 | + | 0.999031i | \(0.485987\pi\) | |||||||
\(264\) | 1.72298e100 | 0.549182 | ||||||||
\(265\) | 6.16652e100 | 1.68010 | ||||||||
\(266\) | −1.75559e100 | −0.409105 | ||||||||
\(267\) | −1.03481e101 | −2.06368 | ||||||||
\(268\) | −3.76286e100 | −0.642576 | ||||||||
\(269\) | −2.86460e100 | −0.419126 | −0.209563 | − | 0.977795i | \(-0.567204\pi\) | ||||
−0.209563 | + | 0.977795i | \(0.567204\pi\) | |||||||
\(270\) | 1.47980e100 | 0.185612 | ||||||||
\(271\) | −1.69133e101 | −1.81971 | −0.909857 | − | 0.414923i | \(-0.863809\pi\) | ||||
−0.909857 | + | 0.414923i | \(0.863809\pi\) | |||||||
\(272\) | 5.24938e100 | 0.484729 | ||||||||
\(273\) | 3.88079e101 | 3.07731 | ||||||||
\(274\) | −2.06297e100 | −0.140554 | ||||||||
\(275\) | −9.95494e100 | −0.583085 | ||||||||
\(276\) | 5.86317e100 | 0.295397 | ||||||||
\(277\) | 1.29126e101 | 0.559891 | 0.279945 | − | 0.960016i | \(-0.409684\pi\) | ||||
0.279945 | + | 0.960016i | \(0.409684\pi\) | |||||||
\(278\) | 3.46881e100 | 0.129515 | ||||||||
\(279\) | 1.50471e101 | 0.484037 | ||||||||
\(280\) | −2.74128e101 | −0.760142 | ||||||||
\(281\) | −3.30498e101 | −0.790417 | −0.395209 | − | 0.918591i | \(-0.629328\pi\) | ||||
−0.395209 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(282\) | 6.70805e100 | 0.138439 | ||||||||
\(283\) | 3.27781e101 | 0.584046 | 0.292023 | − | 0.956411i | \(-0.405672\pi\) | ||||
0.292023 | + | 0.956411i | \(0.405672\pi\) | |||||||
\(284\) | 8.45732e101 | 1.30173 | ||||||||
\(285\) | −2.03578e102 | −2.70813 | ||||||||
\(286\) | −1.88556e101 | −0.216896 | ||||||||
\(287\) | 5.00339e100 | 0.0497927 | ||||||||
\(288\) | 9.36999e101 | 0.807144 | ||||||||
\(289\) | −9.45321e101 | −0.705210 | ||||||||
\(290\) | 7.81478e99 | 0.00505126 | ||||||||
\(291\) | −1.40370e102 | −0.786531 | ||||||||
\(292\) | 1.70044e102 | 0.826365 | ||||||||
\(293\) | −3.08142e101 | −0.129940 | −0.0649702 | − | 0.997887i | \(-0.520695\pi\) | ||||
−0.0649702 | + | 0.997887i | \(0.520695\pi\) | |||||||
\(294\) | 1.26813e102 | 0.464247 | ||||||||
\(295\) | 7.21449e102 | 2.29399 | ||||||||
\(296\) | 3.92066e101 | 0.108331 | ||||||||
\(297\) | −2.97172e102 | −0.713863 | ||||||||
\(298\) | −1.08984e102 | −0.227713 | ||||||||
\(299\) | −1.30737e102 | −0.237709 | ||||||||
\(300\) | −6.00186e102 | −0.950065 | ||||||||
\(301\) | 2.33225e102 | 0.321563 | ||||||||
\(302\) | −2.99292e102 | −0.359589 | ||||||||
\(303\) | 1.22393e103 | 1.28200 | ||||||||
\(304\) | −1.31673e103 | −1.20294 | ||||||||
\(305\) | −6.56209e102 | −0.523117 | ||||||||
\(306\) | 2.20443e102 | 0.153411 | ||||||||
\(307\) | −1.71163e103 | −1.04032 | −0.520160 | − | 0.854069i | \(-0.674128\pi\) | ||||
−0.520160 | + | 0.854069i | \(0.674128\pi\) | |||||||
\(308\) | 2.70179e103 | 1.43482 | ||||||||
\(309\) | −1.18714e103 | −0.551092 | ||||||||
\(310\) | 1.94618e102 | 0.0790084 | ||||||||
\(311\) | −7.45964e101 | −0.0264948 | −0.0132474 | − | 0.999912i | \(-0.504217\pi\) | ||||
−0.0132474 | + | 0.999912i | \(0.504217\pi\) | |||||||
\(312\) | −2.31629e103 | −0.720074 | ||||||||
\(313\) | 2.87040e103 | 0.781362 | 0.390681 | − | 0.920526i | \(-0.372240\pi\) | ||||
0.390681 | + | 0.920526i | \(0.372240\pi\) | |||||||
\(314\) | −7.36567e102 | −0.175643 | ||||||||
\(315\) | 1.44659e104 | 3.02312 | ||||||||
\(316\) | −5.66453e103 | −1.03789 | ||||||||
\(317\) | 2.03249e103 | 0.326640 | 0.163320 | − | 0.986573i | \(-0.447780\pi\) | ||||
0.163320 | + | 0.986573i | \(0.447780\pi\) | |||||||
\(318\) | 2.80241e103 | 0.395190 | ||||||||
\(319\) | −1.56935e102 | −0.0194271 | ||||||||
\(320\) | −9.25758e103 | −1.00641 | ||||||||
\(321\) | −1.86614e104 | −1.78232 | ||||||||
\(322\) | −7.03155e102 | −0.0590245 | ||||||||
\(323\) | −9.91202e103 | −0.731572 | ||||||||
\(324\) | 4.13797e103 | 0.268639 | ||||||||
\(325\) | 1.33830e104 | 0.764527 | ||||||||
\(326\) | 4.40213e103 | 0.221377 | ||||||||
\(327\) | 1.17993e103 | 0.0522546 | ||||||||
\(328\) | −2.98632e102 | −0.0116512 | ||||||||
\(329\) | 2.14326e104 | 0.736961 | ||||||||
\(330\) | −1.17598e104 | −0.356511 | ||||||||
\(331\) | −3.59099e104 | −0.960179 | −0.480089 | − | 0.877220i | \(-0.659396\pi\) | ||||
−0.480089 | + | 0.877220i | \(0.659396\pi\) | |||||||
\(332\) | 1.56848e104 | 0.370039 | ||||||||
\(333\) | −2.06895e104 | −0.430839 | ||||||||
\(334\) | 1.15614e104 | 0.212584 | ||||||||
\(335\) | 5.23294e104 | 0.849936 | ||||||||
\(336\) | 1.56548e105 | 2.24682 | ||||||||
\(337\) | 5.50364e104 | 0.698247 | 0.349124 | − | 0.937077i | \(-0.386479\pi\) | ||||
0.349124 | + | 0.937077i | \(0.386479\pi\) | |||||||
\(338\) | 8.39501e103 | 0.0941842 | ||||||||
\(339\) | −2.94530e105 | −2.92309 | ||||||||
\(340\) | −7.59604e104 | −0.667132 | ||||||||
\(341\) | −3.90830e104 | −0.303865 | ||||||||
\(342\) | −5.52950e104 | −0.380717 | ||||||||
\(343\) | 1.43463e105 | 0.875054 | ||||||||
\(344\) | −1.39203e104 | −0.0752440 | ||||||||
\(345\) | −8.15379e104 | −0.390721 | ||||||||
\(346\) | 3.87172e104 | 0.164530 | ||||||||
\(347\) | −1.48857e105 | −0.561172 | −0.280586 | − | 0.959829i | \(-0.590529\pi\) | ||||
−0.280586 | + | 0.959829i | \(0.590529\pi\) | |||||||
\(348\) | −9.46166e103 | −0.0316540 | ||||||||
\(349\) | 1.75725e105 | 0.521891 | 0.260945 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260945 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(350\) | 7.19787e104 | 0.189837 | ||||||||
\(351\) | 3.99504e105 | 0.935999 | ||||||||
\(352\) | −2.43374e105 | −0.506703 | ||||||||
\(353\) | 2.58199e105 | 0.477863 | 0.238932 | − | 0.971036i | \(-0.423203\pi\) | ||||
0.238932 | + | 0.971036i | \(0.423203\pi\) | |||||||
\(354\) | 3.27867e105 | 0.539587 | ||||||||
\(355\) | −1.17614e106 | −1.72180 | ||||||||
\(356\) | 9.68511e105 | 1.26162 | ||||||||
\(357\) | 1.17845e106 | 1.36641 | ||||||||
\(358\) | −4.33691e104 | −0.0447749 | ||||||||
\(359\) | −1.28249e106 | −1.17932 | −0.589662 | − | 0.807650i | \(-0.700739\pi\) | ||||
−0.589662 | + | 0.807650i | \(0.700739\pi\) | |||||||
\(360\) | −8.63408e105 | −0.707396 | ||||||||
\(361\) | 1.11683e106 | 0.815526 | ||||||||
\(362\) | 6.73468e104 | 0.0438441 | ||||||||
\(363\) | −3.53809e105 | −0.205420 | ||||||||
\(364\) | −3.63216e106 | −1.88130 | ||||||||
\(365\) | −2.36476e106 | −1.09303 | ||||||||
\(366\) | −2.98218e105 | −0.123046 | ||||||||
\(367\) | 4.64982e106 | 1.71315 | 0.856573 | − | 0.516026i | \(-0.172589\pi\) | ||||
0.856573 | + | 0.516026i | \(0.172589\pi\) | |||||||
\(368\) | −5.27383e105 | −0.173557 | ||||||||
\(369\) | 1.57590e105 | 0.0463376 | ||||||||
\(370\) | −2.67597e105 | −0.0703250 | ||||||||
\(371\) | 8.95384e106 | 2.10374 | ||||||||
\(372\) | −2.35632e106 | −0.495111 | ||||||||
\(373\) | 3.29206e106 | 0.618801 | 0.309401 | − | 0.950932i | \(-0.399872\pi\) | ||||
0.309401 | + | 0.950932i | \(0.399872\pi\) | |||||||
\(374\) | −5.72575e105 | −0.0963076 | ||||||||
\(375\) | −5.00288e106 | −0.753221 | ||||||||
\(376\) | −1.27922e106 | −0.172445 | ||||||||
\(377\) | 2.10977e105 | 0.0254723 | ||||||||
\(378\) | 2.14869e106 | 0.232414 | ||||||||
\(379\) | −4.41184e106 | −0.427654 | −0.213827 | − | 0.976872i | \(-0.568593\pi\) | ||||
−0.213827 | + | 0.976872i | \(0.568593\pi\) | |||||||
\(380\) | 1.90536e107 | 1.65561 | ||||||||
\(381\) | −2.68185e107 | −2.08952 | ||||||||
\(382\) | 2.95720e106 | 0.206658 | ||||||||
\(383\) | 2.74930e107 | 1.72374 | 0.861872 | − | 0.507126i | \(-0.169292\pi\) | ||||
0.861872 | + | 0.507126i | \(0.169292\pi\) | |||||||
\(384\) | −1.94310e107 | −1.09332 | ||||||||
\(385\) | −3.75733e107 | −1.89784 | ||||||||
\(386\) | 5.50216e106 | 0.249551 | ||||||||
\(387\) | 7.34579e106 | 0.299249 | ||||||||
\(388\) | 1.31377e107 | 0.480842 | ||||||||
\(389\) | −4.29523e107 | −1.41279 | −0.706395 | − | 0.707818i | \(-0.749680\pi\) | ||||
−0.706395 | + | 0.707818i | \(0.749680\pi\) | |||||||
\(390\) | 1.58094e107 | 0.467448 | ||||||||
\(391\) | −3.97000e106 | −0.105549 | ||||||||
\(392\) | −2.41832e107 | −0.578285 | ||||||||
\(393\) | 1.38492e108 | 2.97943 | ||||||||
\(394\) | −1.48739e107 | −0.287960 | ||||||||
\(395\) | 7.87754e107 | 1.37281 | ||||||||
\(396\) | 8.50972e107 | 1.33526 | ||||||||
\(397\) | −1.11042e108 | −1.56921 | −0.784603 | − | 0.619998i | \(-0.787133\pi\) | ||||
−0.784603 | + | 0.619998i | \(0.787133\pi\) | |||||||
\(398\) | −1.14530e107 | −0.145805 | ||||||||
\(399\) | −2.95598e108 | −3.39098 | ||||||||
\(400\) | 5.39857e107 | 0.558199 | ||||||||
\(401\) | 1.54940e108 | 1.44434 | 0.722172 | − | 0.691713i | \(-0.243144\pi\) | ||||
0.722172 | + | 0.691713i | \(0.243144\pi\) | |||||||
\(402\) | 2.37814e107 | 0.199920 | ||||||||
\(403\) | 5.25413e107 | 0.398421 | ||||||||
\(404\) | −1.14552e108 | −0.783747 | ||||||||
\(405\) | −5.75459e107 | −0.355329 | ||||||||
\(406\) | 1.13471e106 | 0.00632493 | ||||||||
\(407\) | 5.37385e107 | 0.270469 | ||||||||
\(408\) | −7.03370e107 | −0.319733 | ||||||||
\(409\) | −2.71809e108 | −1.11621 | −0.558106 | − | 0.829770i | \(-0.688472\pi\) | ||||
−0.558106 | + | 0.829770i | \(0.688472\pi\) | |||||||
\(410\) | 2.03826e106 | 0.00756360 | ||||||||
\(411\) | −3.47353e108 | −1.16503 | ||||||||
\(412\) | 1.11108e108 | 0.336908 | ||||||||
\(413\) | 1.04755e109 | 2.87242 | ||||||||
\(414\) | −2.21470e107 | −0.0549288 | ||||||||
\(415\) | −2.18125e108 | −0.489451 | ||||||||
\(416\) | 3.27181e108 | 0.664377 | ||||||||
\(417\) | 5.84061e108 | 1.07352 | ||||||||
\(418\) | 1.43622e108 | 0.239004 | ||||||||
\(419\) | 7.02063e108 | 1.05802 | 0.529011 | − | 0.848615i | \(-0.322563\pi\) | ||||
0.529011 | + | 0.848615i | \(0.322563\pi\) | |||||||
\(420\) | −2.26530e109 | −3.09229 | ||||||||
\(421\) | −4.20986e108 | −0.520667 | −0.260334 | − | 0.965519i | \(-0.583833\pi\) | ||||
−0.260334 | + | 0.965519i | \(0.583833\pi\) | |||||||
\(422\) | 1.79640e108 | 0.201343 | ||||||||
\(423\) | 6.75052e108 | 0.685823 | ||||||||
\(424\) | −5.34419e108 | −0.492265 | ||||||||
\(425\) | 4.06390e108 | 0.339471 | ||||||||
\(426\) | −5.34505e108 | −0.404998 | ||||||||
\(427\) | −9.52822e108 | −0.655021 | ||||||||
\(428\) | 1.74658e109 | 1.08961 | ||||||||
\(429\) | −3.17482e109 | −1.79780 | ||||||||
\(430\) | 9.50100e107 | 0.0488459 | ||||||||
\(431\) | 1.06853e109 | 0.498862 | 0.249431 | − | 0.968393i | \(-0.419756\pi\) | ||||
0.249431 | + | 0.968393i | \(0.419756\pi\) | |||||||
\(432\) | 1.61156e109 | 0.683396 | ||||||||
\(433\) | 9.15441e107 | 0.0352681 | 0.0176341 | − | 0.999845i | \(-0.494387\pi\) | ||||
0.0176341 | + | 0.999845i | \(0.494387\pi\) | |||||||
\(434\) | 2.82588e108 | 0.0989303 | ||||||||
\(435\) | 1.31581e108 | 0.0418688 | ||||||||
\(436\) | −1.10433e108 | −0.0319456 | ||||||||
\(437\) | 9.95817e108 | 0.261939 | ||||||||
\(438\) | −1.07468e109 | −0.257101 | ||||||||
\(439\) | −2.39899e109 | −0.522096 | −0.261048 | − | 0.965326i | \(-0.584068\pi\) | ||||
−0.261048 | + | 0.965326i | \(0.584068\pi\) | |||||||
\(440\) | 2.24260e109 | 0.444084 | ||||||||
\(441\) | 1.27616e110 | 2.29987 | ||||||||
\(442\) | 7.69742e108 | 0.126276 | ||||||||
\(443\) | −4.73471e108 | −0.0707195 | −0.0353597 | − | 0.999375i | \(-0.511258\pi\) | ||||
−0.0353597 | + | 0.999375i | \(0.511258\pi\) | |||||||
\(444\) | 3.23991e109 | 0.440696 | ||||||||
\(445\) | −1.34689e110 | −1.66875 | ||||||||
\(446\) | −2.00255e109 | −0.226041 | ||||||||
\(447\) | −1.83502e110 | −1.88746 | ||||||||
\(448\) | −1.34421e110 | −1.26017 | ||||||||
\(449\) | 1.44275e110 | 1.23302 | 0.616509 | − | 0.787348i | \(-0.288546\pi\) | ||||
0.616509 | + | 0.787348i | \(0.288546\pi\) | |||||||
\(450\) | 2.26708e109 | 0.176664 | ||||||||
\(451\) | −4.09320e108 | −0.0290895 | ||||||||
\(452\) | 2.75660e110 | 1.78702 | ||||||||
\(453\) | −5.03933e110 | −2.98056 | ||||||||
\(454\) | −5.77601e108 | −0.0311752 | ||||||||
\(455\) | 5.05118e110 | 2.48840 | ||||||||
\(456\) | 1.76430e110 | 0.793473 | ||||||||
\(457\) | −1.50937e110 | −0.619830 | −0.309915 | − | 0.950764i | \(-0.600301\pi\) | ||||
−0.309915 | + | 0.950764i | \(0.600301\pi\) | |||||||
\(458\) | −2.89705e109 | −0.108652 | ||||||||
\(459\) | 1.21314e110 | 0.415610 | ||||||||
\(460\) | 7.63141e109 | 0.238866 | ||||||||
\(461\) | −4.40480e110 | −1.25990 | −0.629952 | − | 0.776634i | \(-0.716926\pi\) | ||||
−0.629952 | + | 0.776634i | \(0.716926\pi\) | |||||||
\(462\) | −1.70754e110 | −0.446405 | ||||||||
\(463\) | 7.22166e110 | 1.72594 | 0.862970 | − | 0.505255i | \(-0.168602\pi\) | ||||
0.862970 | + | 0.505255i | \(0.168602\pi\) | |||||||
\(464\) | 8.51061e108 | 0.0185979 | ||||||||
\(465\) | 3.27689e110 | 0.654884 | ||||||||
\(466\) | −4.52884e109 | −0.0827887 | ||||||||
\(467\) | −2.33305e109 | −0.0390188 | −0.0195094 | − | 0.999810i | \(-0.506210\pi\) | ||||
−0.0195094 | + | 0.999810i | \(0.506210\pi\) | |||||||
\(468\) | −1.14401e111 | −1.75076 | ||||||||
\(469\) | 7.59828e110 | 1.06425 | ||||||||
\(470\) | 8.73109e109 | 0.111946 | ||||||||
\(471\) | −1.24020e111 | −1.45587 | ||||||||
\(472\) | −6.25240e110 | −0.672131 | ||||||||
\(473\) | −1.90798e110 | −0.187861 | ||||||||
\(474\) | 3.58000e110 | 0.322910 | ||||||||
\(475\) | −1.01937e111 | −0.842457 | ||||||||
\(476\) | −1.10295e111 | −0.835349 | ||||||||
\(477\) | 2.82015e111 | 1.95776 | ||||||||
\(478\) | −3.28773e110 | −0.209237 | ||||||||
\(479\) | 2.49098e111 | 1.45361 | 0.726804 | − | 0.686845i | \(-0.241005\pi\) | ||||
0.726804 | + | 0.686845i | \(0.241005\pi\) | |||||||
\(480\) | 2.04055e111 | 1.09204 | ||||||||
\(481\) | −7.22435e110 | −0.354632 | ||||||||
\(482\) | 1.03670e110 | 0.0466874 | ||||||||
\(483\) | −1.18394e111 | −0.489242 | ||||||||
\(484\) | 3.31141e110 | 0.125583 | ||||||||
\(485\) | −1.82703e111 | −0.636011 | ||||||||
\(486\) | −7.17089e110 | −0.229175 | ||||||||
\(487\) | −2.28307e111 | −0.669989 | −0.334994 | − | 0.942220i | \(-0.608734\pi\) | ||||
−0.334994 | + | 0.942220i | \(0.608734\pi\) | |||||||
\(488\) | 5.68701e110 | 0.153272 | ||||||||
\(489\) | 7.41210e111 | 1.83495 | ||||||||
\(490\) | 1.65058e111 | 0.375403 | ||||||||
\(491\) | −2.47251e111 | −0.516720 | −0.258360 | − | 0.966049i | \(-0.583182\pi\) | ||||
−0.258360 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(492\) | −2.46780e110 | −0.0473978 | ||||||||
\(493\) | 6.40657e109 | 0.0113104 | ||||||||
\(494\) | −1.93079e111 | −0.313376 | ||||||||
\(495\) | −1.18343e112 | −1.76615 | ||||||||
\(496\) | 2.11947e111 | 0.290896 | ||||||||
\(497\) | −1.70777e112 | −2.15595 | ||||||||
\(498\) | −9.91282e110 | −0.115128 | ||||||||
\(499\) | 9.13024e111 | 0.975685 | 0.487842 | − | 0.872932i | \(-0.337784\pi\) | ||||
0.487842 | + | 0.872932i | \(0.337784\pi\) | |||||||
\(500\) | 4.68236e111 | 0.460479 | ||||||||
\(501\) | 1.94665e112 | 1.76206 | ||||||||
\(502\) | 2.02067e111 | 0.168380 | ||||||||
\(503\) | −3.05195e111 | −0.234157 | −0.117078 | − | 0.993123i | \(-0.537353\pi\) | ||||
−0.117078 | + | 0.993123i | \(0.537353\pi\) | |||||||
\(504\) | −1.25368e112 | −0.885765 | ||||||||
\(505\) | 1.59305e112 | 1.03666 | ||||||||
\(506\) | 5.75241e110 | 0.0344829 | ||||||||
\(507\) | 1.41351e112 | 0.780673 | ||||||||
\(508\) | 2.51003e112 | 1.27742 | ||||||||
\(509\) | −2.28076e112 | −1.06978 | −0.534888 | − | 0.844923i | \(-0.679646\pi\) | ||||
−0.534888 | + | 0.844923i | \(0.679646\pi\) | |||||||
\(510\) | 4.80071e111 | 0.207560 | ||||||||
\(511\) | −3.43366e112 | −1.36864 | ||||||||
\(512\) | 2.22715e112 | 0.818553 | ||||||||
\(513\) | −3.04300e112 | −1.03141 | ||||||||
\(514\) | 1.04440e112 | 0.326512 | ||||||||
\(515\) | −1.54516e112 | −0.445628 | ||||||||
\(516\) | −1.15032e112 | −0.306096 | ||||||||
\(517\) | −1.75337e112 | −0.430542 | ||||||||
\(518\) | −3.88554e111 | −0.0880574 | ||||||||
\(519\) | 6.51902e112 | 1.36376 | ||||||||
\(520\) | −3.01484e112 | −0.582272 | ||||||||
\(521\) | −7.42124e112 | −1.32346 | −0.661730 | − | 0.749742i | \(-0.730177\pi\) | ||||
−0.661730 | + | 0.749742i | \(0.730177\pi\) | |||||||
\(522\) | 3.57396e110 | 0.00588604 | ||||||||
\(523\) | 1.17499e113 | 1.78737 | 0.893684 | − | 0.448698i | \(-0.148112\pi\) | ||||
0.893684 | + | 0.448698i | \(0.148112\pi\) | |||||||
\(524\) | −1.29619e113 | −1.82147 | ||||||||
\(525\) | 1.21194e113 | 1.57352 | ||||||||
\(526\) | 1.39545e111 | 0.0167419 | ||||||||
\(527\) | 1.59548e112 | 0.176910 | ||||||||
\(528\) | −1.28070e113 | −1.31262 | ||||||||
\(529\) | −1.01550e113 | −0.962208 | ||||||||
\(530\) | 3.64757e112 | 0.319562 | ||||||||
\(531\) | 3.29942e113 | 2.67310 | ||||||||
\(532\) | 2.76660e113 | 2.07307 | ||||||||
\(533\) | 5.50271e111 | 0.0381415 | ||||||||
\(534\) | −6.12102e112 | −0.392520 | ||||||||
\(535\) | −2.42894e113 | −1.44123 | ||||||||
\(536\) | −4.53510e112 | −0.249028 | ||||||||
\(537\) | −7.30228e112 | −0.371129 | ||||||||
\(538\) | −1.69445e112 | −0.0797193 | ||||||||
\(539\) | −3.31467e113 | −1.44380 | ||||||||
\(540\) | −2.33199e113 | −0.940557 | ||||||||
\(541\) | 2.95004e113 | 1.10190 | 0.550948 | − | 0.834539i | \(-0.314266\pi\) | ||||
0.550948 | + | 0.834539i | \(0.314266\pi\) | |||||||
\(542\) | −1.00044e113 | −0.346116 | ||||||||
\(543\) | 1.13395e113 | 0.363414 | ||||||||
\(544\) | 9.93525e112 | 0.295002 | ||||||||
\(545\) | 1.53578e112 | 0.0422545 | ||||||||
\(546\) | 2.29554e113 | 0.585315 | ||||||||
\(547\) | −4.88473e113 | −1.15443 | −0.577213 | − | 0.816594i | \(-0.695860\pi\) | ||||
−0.577213 | + | 0.816594i | \(0.695860\pi\) | |||||||
\(548\) | 3.25099e113 | 0.712234 | ||||||||
\(549\) | −3.00106e113 | −0.609569 | ||||||||
\(550\) | −5.88847e112 | −0.110905 | ||||||||
\(551\) | −1.60700e112 | −0.0280688 | ||||||||
\(552\) | 7.06645e112 | 0.114480 | ||||||||
\(553\) | 1.14383e114 | 1.71897 | ||||||||
\(554\) | 7.63796e112 | 0.106493 | ||||||||
\(555\) | −4.50567e113 | −0.582909 | ||||||||
\(556\) | −5.46642e113 | −0.656295 | ||||||||
\(557\) | 9.21576e113 | 1.02693 | 0.513465 | − | 0.858111i | \(-0.328362\pi\) | ||||
0.513465 | + | 0.858111i | \(0.328362\pi\) | |||||||
\(558\) | 8.90054e112 | 0.0920656 | ||||||||
\(559\) | 2.56500e113 | 0.246318 | ||||||||
\(560\) | 2.03760e114 | 1.81684 | ||||||||
\(561\) | −9.64074e113 | −0.798273 | ||||||||
\(562\) | −1.95494e113 | −0.150340 | ||||||||
\(563\) | −9.50601e113 | −0.679047 | −0.339523 | − | 0.940598i | \(-0.610266\pi\) | ||||
−0.339523 | + | 0.940598i | \(0.610266\pi\) | |||||||
\(564\) | −1.05711e114 | −0.701514 | ||||||||
\(565\) | −3.83355e114 | −2.36369 | ||||||||
\(566\) | 1.93886e113 | 0.111088 | ||||||||
\(567\) | −8.35572e113 | −0.444925 | ||||||||
\(568\) | 1.01930e114 | 0.504482 | ||||||||
\(569\) | 1.68386e113 | 0.0774723 | 0.0387362 | − | 0.999249i | \(-0.487667\pi\) | ||||
0.0387362 | + | 0.999249i | \(0.487667\pi\) | |||||||
\(570\) | −1.20419e114 | −0.515097 | ||||||||
\(571\) | 1.04563e114 | 0.415891 | 0.207946 | − | 0.978140i | \(-0.433322\pi\) | ||||
0.207946 | + | 0.978140i | \(0.433322\pi\) | |||||||
\(572\) | 2.97142e114 | 1.09908 | ||||||||
\(573\) | 4.97920e114 | 1.71294 | ||||||||
\(574\) | 2.95957e112 | 0.00947076 | ||||||||
\(575\) | −4.08283e113 | −0.121547 | ||||||||
\(576\) | −4.23380e114 | −1.17273 | ||||||||
\(577\) | −2.49381e114 | −0.642786 | −0.321393 | − | 0.946946i | \(-0.604151\pi\) | ||||
−0.321393 | + | 0.946946i | \(0.604151\pi\) | |||||||
\(578\) | −5.59169e113 | −0.134134 | ||||||||
\(579\) | 9.26428e114 | 2.06848 | ||||||||
\(580\) | −1.23151e113 | −0.0255963 | ||||||||
\(581\) | −3.16720e114 | −0.612866 | ||||||||
\(582\) | −8.30306e113 | −0.149601 | ||||||||
\(583\) | −7.32501e114 | −1.22903 | ||||||||
\(584\) | 2.04941e114 | 0.320255 | ||||||||
\(585\) | 1.59095e115 | 2.31573 | ||||||||
\(586\) | −1.82270e113 | −0.0247152 | ||||||||
\(587\) | 1.19830e115 | 1.51386 | 0.756929 | − | 0.653497i | \(-0.226699\pi\) | ||||
0.756929 | + | 0.653497i | \(0.226699\pi\) | |||||||
\(588\) | −1.99842e115 | −2.35249 | ||||||||
\(589\) | −4.00204e114 | −0.439033 | ||||||||
\(590\) | 4.26746e114 | 0.436326 | ||||||||
\(591\) | −2.50440e115 | −2.38684 | ||||||||
\(592\) | −2.91424e114 | −0.258926 | ||||||||
\(593\) | −3.02933e114 | −0.250944 | −0.125472 | − | 0.992097i | \(-0.540044\pi\) | ||||
−0.125472 | + | 0.992097i | \(0.540044\pi\) | |||||||
\(594\) | −1.75781e114 | −0.135779 | ||||||||
\(595\) | 1.53385e115 | 1.10492 | ||||||||
\(596\) | 1.71745e115 | 1.15389 | ||||||||
\(597\) | −1.92840e115 | −1.20854 | ||||||||
\(598\) | −7.73326e113 | −0.0452130 | ||||||||
\(599\) | 1.70444e115 | 0.929755 | 0.464877 | − | 0.885375i | \(-0.346098\pi\) | ||||
0.464877 | + | 0.885375i | \(0.346098\pi\) | |||||||
\(600\) | −7.23360e114 | −0.368195 | ||||||||
\(601\) | −1.15940e115 | −0.550736 | −0.275368 | − | 0.961339i | \(-0.588800\pi\) | ||||
−0.275368 | + | 0.961339i | \(0.588800\pi\) | |||||||
\(602\) | 1.37955e114 | 0.0611624 | ||||||||
\(603\) | 2.39320e115 | 0.990398 | ||||||||
\(604\) | 4.71648e115 | 1.82215 | ||||||||
\(605\) | −4.60511e114 | −0.166109 | ||||||||
\(606\) | 7.23971e114 | 0.243841 | ||||||||
\(607\) | −9.39775e114 | −0.295592 | −0.147796 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147796 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(608\) | −2.49211e115 | −0.732098 | ||||||||
\(609\) | 1.91058e114 | 0.0524260 | ||||||||
\(610\) | −3.88156e114 | −0.0994988 | ||||||||
\(611\) | 2.35714e115 | 0.564515 | ||||||||
\(612\) | −3.47392e115 | −0.777384 | ||||||||
\(613\) | −5.94029e115 | −1.24222 | −0.621109 | − | 0.783724i | \(-0.713318\pi\) | ||||
−0.621109 | + | 0.783724i | \(0.713318\pi\) | |||||||
\(614\) | −1.01245e115 | −0.197873 | ||||||||
\(615\) | 3.43192e114 | 0.0626931 | ||||||||
\(616\) | 3.25627e115 | 0.556060 | ||||||||
\(617\) | 5.16421e115 | 0.824460 | 0.412230 | − | 0.911080i | \(-0.364750\pi\) | ||||
0.412230 | + | 0.911080i | \(0.364750\pi\) | |||||||
\(618\) | −7.02206e114 | −0.104820 | ||||||||
\(619\) | −4.23803e115 | −0.591564 | −0.295782 | − | 0.955255i | \(-0.595580\pi\) | ||||
−0.295782 | + | 0.955255i | \(0.595580\pi\) | |||||||
\(620\) | −3.06695e115 | −0.400361 | ||||||||
\(621\) | −1.21879e115 | −0.148809 | ||||||||
\(622\) | −4.41247e113 | −0.00503942 | ||||||||
\(623\) | −1.95570e116 | −2.08952 | ||||||||
\(624\) | 1.72171e116 | 1.72107 | ||||||||
\(625\) | −1.31961e116 | −1.23432 | ||||||||
\(626\) | 1.69788e115 | 0.148618 | ||||||||
\(627\) | 2.41824e116 | 1.98106 | ||||||||
\(628\) | 1.16074e116 | 0.890041 | ||||||||
\(629\) | −2.19377e115 | −0.157467 | ||||||||
\(630\) | 8.55673e115 | 0.575009 | ||||||||
\(631\) | 7.05248e115 | 0.443735 | 0.221867 | − | 0.975077i | \(-0.428785\pi\) | ||||
0.221867 | + | 0.975077i | \(0.428785\pi\) | |||||||
\(632\) | −6.82704e115 | −0.402229 | ||||||||
\(633\) | 3.02469e116 | 1.66889 | ||||||||
\(634\) | 1.20224e115 | 0.0621281 | ||||||||
\(635\) | −3.49065e116 | −1.68965 | ||||||||
\(636\) | −4.41626e116 | −2.00256 | ||||||||
\(637\) | 4.45608e116 | 1.89307 | ||||||||
\(638\) | −9.28292e113 | −0.00369510 | ||||||||
\(639\) | −5.37889e116 | −2.00635 | ||||||||
\(640\) | −2.52911e116 | −0.884093 | ||||||||
\(641\) | 1.01008e116 | 0.330939 | 0.165470 | − | 0.986215i | \(-0.447086\pi\) | ||||
0.165470 | + | 0.986215i | \(0.447086\pi\) | |||||||
\(642\) | −1.10384e116 | −0.339004 | ||||||||
\(643\) | 6.25253e116 | 1.80012 | 0.900058 | − | 0.435771i | \(-0.143524\pi\) | ||||
0.900058 | + | 0.435771i | \(0.143524\pi\) | |||||||
\(644\) | 1.10809e116 | 0.299096 | ||||||||
\(645\) | 1.59973e116 | 0.404873 | ||||||||
\(646\) | −5.86308e115 | −0.139148 | ||||||||
\(647\) | −3.41819e116 | −0.760796 | −0.380398 | − | 0.924823i | \(-0.624213\pi\) | ||||
−0.380398 | + | 0.924823i | \(0.624213\pi\) | |||||||
\(648\) | 4.98719e115 | 0.104110 | ||||||||
\(649\) | −8.56985e116 | −1.67810 | ||||||||
\(650\) | 7.91618e115 | 0.145416 | ||||||||
\(651\) | 4.75808e116 | 0.820012 | ||||||||
\(652\) | −6.93723e116 | −1.12179 | ||||||||
\(653\) | 5.33406e116 | 0.809395 | 0.404698 | − | 0.914451i | \(-0.367377\pi\) | ||||
0.404698 | + | 0.914451i | \(0.367377\pi\) | |||||||
\(654\) | 6.97943e114 | 0.00993901 | ||||||||
\(655\) | 1.80259e117 | 2.40925 | ||||||||
\(656\) | 2.21975e115 | 0.0278480 | ||||||||
\(657\) | −1.08148e117 | −1.27367 | ||||||||
\(658\) | 1.26776e116 | 0.140173 | ||||||||
\(659\) | −3.76058e116 | −0.390401 | −0.195200 | − | 0.980763i | \(-0.562536\pi\) | ||||
−0.195200 | + | 0.980763i | \(0.562536\pi\) | |||||||
\(660\) | 1.85321e117 | 1.80655 | ||||||||
\(661\) | 3.94843e116 | 0.361463 | 0.180731 | − | 0.983532i | \(-0.442154\pi\) | ||||
0.180731 | + | 0.983532i | \(0.442154\pi\) | |||||||
\(662\) | −2.12411e116 | −0.182629 | ||||||||
\(663\) | 1.29606e117 | 1.04668 | ||||||||
\(664\) | 1.89037e116 | 0.143408 | ||||||||
\(665\) | −3.84745e117 | −2.74205 | ||||||||
\(666\) | −1.22381e116 | −0.0819471 | ||||||||
\(667\) | −6.43640e114 | −0.00404968 | ||||||||
\(668\) | −1.82193e117 | −1.07723 | ||||||||
\(669\) | −3.37180e117 | −1.87361 | ||||||||
\(670\) | 3.09535e116 | 0.161661 | ||||||||
\(671\) | 7.79490e116 | 0.382671 | ||||||||
\(672\) | 2.96290e117 | 1.36739 | ||||||||
\(673\) | 6.70569e116 | 0.290950 | 0.145475 | − | 0.989362i | \(-0.453529\pi\) | ||||
0.145475 | + | 0.989362i | \(0.453529\pi\) | |||||||
\(674\) | 3.25547e116 | 0.132809 | ||||||||
\(675\) | 1.24762e117 | 0.478604 | ||||||||
\(676\) | −1.32295e117 | −0.477261 | ||||||||
\(677\) | 3.62398e117 | 1.22958 | 0.614789 | − | 0.788692i | \(-0.289241\pi\) | ||||
0.614789 | + | 0.788692i | \(0.289241\pi\) | |||||||
\(678\) | −1.74218e117 | −0.555982 | ||||||||
\(679\) | −2.65287e117 | −0.796380 | ||||||||
\(680\) | −9.15495e116 | −0.258545 | ||||||||
\(681\) | −9.72536e116 | −0.258405 | ||||||||
\(682\) | −2.31181e116 | −0.0577963 | ||||||||
\(683\) | 5.22001e117 | 1.22804 | 0.614019 | − | 0.789291i | \(-0.289552\pi\) | ||||
0.614019 | + | 0.789291i | \(0.289552\pi\) | |||||||
\(684\) | 8.71383e117 | 1.92922 | ||||||||
\(685\) | −4.52109e117 | −0.942073 | ||||||||
\(686\) | 8.48603e116 | 0.166439 | ||||||||
\(687\) | −4.87791e117 | −0.900595 | ||||||||
\(688\) | 1.03470e117 | 0.179843 | ||||||||
\(689\) | 9.84739e117 | 1.61148 | ||||||||
\(690\) | −4.82307e116 | −0.0743167 | ||||||||
\(691\) | −3.99891e116 | −0.0580234 | −0.0290117 | − | 0.999579i | \(-0.509236\pi\) | ||||
−0.0290117 | + | 0.999579i | \(0.509236\pi\) | |||||||
\(692\) | −6.10137e117 | −0.833728 | ||||||||
\(693\) | −1.71835e118 | −2.21148 | ||||||||
\(694\) | −8.80507e116 | −0.106737 | ||||||||
\(695\) | 7.60204e117 | 0.868082 | ||||||||
\(696\) | −1.14035e116 | −0.0122674 | ||||||||
\(697\) | 1.67097e116 | 0.0169359 | ||||||||
\(698\) | 1.03944e117 | 0.0992655 | ||||||||
\(699\) | −7.62544e117 | −0.686218 | ||||||||
\(700\) | −1.13430e118 | −0.961963 | ||||||||
\(701\) | −3.54961e117 | −0.283715 | −0.141858 | − | 0.989887i | \(-0.545307\pi\) | ||||
−0.141858 | + | 0.989887i | \(0.545307\pi\) | |||||||
\(702\) | 2.36311e117 | 0.178031 | ||||||||
\(703\) | 5.50275e117 | 0.390781 | ||||||||
\(704\) | 1.09968e118 | 0.736208 | ||||||||
\(705\) | 1.47010e118 | 0.927894 | ||||||||
\(706\) | 1.52728e117 | 0.0908914 | ||||||||
\(707\) | 2.31312e118 | 1.29806 | ||||||||
\(708\) | −5.16678e118 | −2.73426 | ||||||||
\(709\) | 2.71692e118 | 1.35599 | 0.677997 | − | 0.735065i | \(-0.262848\pi\) | ||||
0.677997 | + | 0.735065i | \(0.262848\pi\) | |||||||
\(710\) | −6.95702e117 | −0.327493 | ||||||||
\(711\) | 3.60266e118 | 1.59969 | ||||||||
\(712\) | 1.16728e118 | 0.488938 | ||||||||
\(713\) | −1.60291e117 | −0.0633424 | ||||||||
\(714\) | 6.97068e117 | 0.259896 | ||||||||
\(715\) | −4.13229e118 | −1.45375 | ||||||||
\(716\) | 6.83444e117 | 0.226889 | ||||||||
\(717\) | −5.53572e118 | −1.73432 | ||||||||
\(718\) | −7.58607e117 | −0.224312 | ||||||||
\(719\) | 1.50770e118 | 0.420792 | 0.210396 | − | 0.977616i | \(-0.432525\pi\) | ||||
0.210396 | + | 0.977616i | \(0.432525\pi\) | |||||||
\(720\) | 6.41775e118 | 1.69077 | ||||||||
\(721\) | −2.24358e118 | −0.557993 | ||||||||
\(722\) | 6.60618e117 | 0.155116 | ||||||||
\(723\) | 1.74554e118 | 0.386982 | ||||||||
\(724\) | −1.06130e118 | −0.222172 | ||||||||
\(725\) | 6.58864e116 | 0.0130247 | ||||||||
\(726\) | −2.09282e117 | −0.0390717 | ||||||||
\(727\) | −7.57719e118 | −1.33607 | −0.668037 | − | 0.744128i | \(-0.732865\pi\) | ||||
−0.668037 | + | 0.744128i | \(0.732865\pi\) | |||||||
\(728\) | −4.37758e118 | −0.729091 | ||||||||
\(729\) | −1.03024e119 | −1.62086 | ||||||||
\(730\) | −1.39879e118 | −0.207899 | ||||||||
\(731\) | 7.78893e117 | 0.109372 | ||||||||
\(732\) | 4.69956e118 | 0.623516 | ||||||||
\(733\) | 5.66552e118 | 0.710272 | 0.355136 | − | 0.934815i | \(-0.384435\pi\) | ||||
0.355136 | + | 0.934815i | \(0.384435\pi\) | |||||||
\(734\) | 2.75042e118 | 0.325847 | ||||||||
\(735\) | 2.77916e119 | 3.11164 | ||||||||
\(736\) | −9.98151e117 | −0.105625 | ||||||||
\(737\) | −6.21604e118 | −0.621746 | ||||||||
\(738\) | 9.32163e116 | 0.00881359 | ||||||||
\(739\) | 1.67362e119 | 1.49593 | 0.747967 | − | 0.663736i | \(-0.231030\pi\) | ||||
0.747967 | + | 0.663736i | \(0.231030\pi\) | |||||||
\(740\) | 4.21701e118 | 0.356359 | ||||||||
\(741\) | −3.25097e119 | −2.59751 | ||||||||
\(742\) | 5.29631e118 | 0.400139 | ||||||||
\(743\) | 1.58886e119 | 1.13514 | 0.567571 | − | 0.823325i | \(-0.307883\pi\) | ||||
0.567571 | + | 0.823325i | \(0.307883\pi\) | |||||||
\(744\) | −2.83990e118 | −0.191879 | ||||||||
\(745\) | −2.38843e119 | −1.52625 | ||||||||
\(746\) | 1.94729e118 | 0.117698 | ||||||||
\(747\) | −9.97558e118 | −0.570339 | ||||||||
\(748\) | 9.02309e118 | 0.488021 | ||||||||
\(749\) | −3.52684e119 | −1.80464 | ||||||||
\(750\) | −2.95926e118 | −0.143265 | ||||||||
\(751\) | 3.41276e119 | 1.56332 | 0.781662 | − | 0.623703i | \(-0.214372\pi\) | ||||
0.781662 | + | 0.623703i | \(0.214372\pi\) | |||||||
\(752\) | 9.50852e118 | 0.412166 | ||||||||
\(753\) | 3.40230e119 | 1.39567 | ||||||||
\(754\) | 1.24795e117 | 0.00484492 | ||||||||
\(755\) | −6.55911e119 | −2.41016 | ||||||||
\(756\) | −3.38607e119 | −1.17772 | ||||||||
\(757\) | 1.90008e119 | 0.625596 | 0.312798 | − | 0.949820i | \(-0.398734\pi\) | ||||
0.312798 | + | 0.949820i | \(0.398734\pi\) | |||||||
\(758\) | −2.60966e118 | −0.0813414 | ||||||||
\(759\) | 9.68563e118 | 0.285821 | ||||||||
\(760\) | 2.29639e119 | 0.641625 | ||||||||
\(761\) | 8.92334e118 | 0.236083 | 0.118041 | − | 0.993009i | \(-0.462338\pi\) | ||||
0.118041 | + | 0.993009i | \(0.462338\pi\) | |||||||
\(762\) | −1.58635e119 | −0.397435 | ||||||||
\(763\) | 2.22996e118 | 0.0529090 | ||||||||
\(764\) | −4.66020e119 | −1.04720 | ||||||||
\(765\) | 4.83111e119 | 1.02825 | ||||||||
\(766\) | 1.62624e119 | 0.327862 | ||||||||
\(767\) | 1.15209e120 | 2.20029 | ||||||||
\(768\) | 5.72947e119 | 1.03663 | ||||||||
\(769\) | −1.09409e120 | −1.87547 | −0.937734 | − | 0.347354i | \(-0.887080\pi\) | ||||
−0.937734 | + | 0.347354i | \(0.887080\pi\) | |||||||
\(770\) | −2.22251e119 | −0.360976 | ||||||||
\(771\) | 1.75852e120 | 2.70639 | ||||||||
\(772\) | −8.67074e119 | −1.26456 | ||||||||
\(773\) | −1.21377e120 | −1.67760 | −0.838800 | − | 0.544440i | \(-0.816742\pi\) | ||||
−0.838800 | + | 0.544440i | \(0.816742\pi\) | |||||||
\(774\) | 4.34512e118 | 0.0569183 | ||||||||
\(775\) | 1.64083e119 | 0.203724 | ||||||||
\(776\) | 1.58339e119 | 0.186349 | ||||||||
\(777\) | −6.54228e119 | −0.729889 | ||||||||
\(778\) | −2.54068e119 | −0.268718 | ||||||||
\(779\) | −4.19138e118 | −0.0420293 | ||||||||
\(780\) | −2.49137e120 | −2.36871 | ||||||||
\(781\) | 1.39710e120 | 1.25953 | ||||||||
\(782\) | −2.34830e118 | −0.0200758 | ||||||||
\(783\) | 1.96682e118 | 0.0159460 | ||||||||
\(784\) | 1.79754e120 | 1.38218 | ||||||||
\(785\) | −1.61422e120 | −1.17726 | ||||||||
\(786\) | 8.19197e119 | 0.566699 | ||||||||
\(787\) | −5.27952e119 | −0.346452 | −0.173226 | − | 0.984882i | \(-0.555419\pi\) | ||||
−0.173226 | + | 0.984882i | \(0.555419\pi\) | |||||||
\(788\) | 2.34395e120 | 1.45919 | ||||||||
\(789\) | 2.34959e119 | 0.138770 | ||||||||
\(790\) | 4.65966e119 | 0.261114 | ||||||||
\(791\) | −5.56635e120 | −2.95969 | ||||||||
\(792\) | 1.02561e120 | 0.517475 | ||||||||
\(793\) | −1.04791e120 | −0.501749 | ||||||||
\(794\) | −6.56825e119 | −0.298469 | ||||||||
\(795\) | 6.14161e120 | 2.64878 | ||||||||
\(796\) | 1.80486e120 | 0.738839 | ||||||||
\(797\) | 3.56779e120 | 1.38637 | 0.693185 | − | 0.720759i | \(-0.256207\pi\) | ||||
0.693185 | + | 0.720759i | \(0.256207\pi\) | |||||||
\(798\) | −1.74850e120 | −0.644978 | ||||||||
\(799\) | 7.15776e119 | 0.250660 | ||||||||
\(800\) | 1.02176e120 | 0.339715 | ||||||||
\(801\) | −6.15977e120 | −1.94453 | ||||||||
\(802\) | 9.16486e119 | 0.274720 | ||||||||
\(803\) | 2.80903e120 | 0.799577 | ||||||||
\(804\) | −3.74766e120 | −1.01306 | ||||||||
\(805\) | −1.54099e120 | −0.395614 | ||||||||
\(806\) | 3.10789e119 | 0.0757811 | ||||||||
\(807\) | −2.85303e120 | −0.660777 | ||||||||
\(808\) | −1.38061e120 | −0.303738 | ||||||||
\(809\) | 7.60349e120 | 1.58909 | 0.794546 | − | 0.607204i | \(-0.207709\pi\) | ||||
0.794546 | + | 0.607204i | \(0.207709\pi\) | |||||||
\(810\) | −3.40391e119 | −0.0675850 | ||||||||
\(811\) | −7.88182e120 | −1.48683 | −0.743415 | − | 0.668831i | \(-0.766795\pi\) | ||||
−0.743415 | + | 0.668831i | \(0.766795\pi\) | |||||||
\(812\) | −1.78817e119 | −0.0320504 | ||||||||
\(813\) | −1.68450e121 | −2.86888 | ||||||||
\(814\) | 3.17870e119 | 0.0514442 | ||||||||
\(815\) | 9.64747e120 | 1.48379 | ||||||||
\(816\) | 5.22818e120 | 0.764203 | ||||||||
\(817\) | −1.95374e120 | −0.271426 | ||||||||
\(818\) | −1.60778e120 | −0.212307 | ||||||||
\(819\) | 2.31007e121 | 2.89964 | ||||||||
\(820\) | −3.21205e119 | −0.0383272 | ||||||||
\(821\) | 3.97486e118 | 0.00450900 | 0.00225450 | − | 0.999997i | \(-0.499282\pi\) | ||||
0.00225450 | + | 0.999997i | \(0.499282\pi\) | |||||||
\(822\) | −2.05464e120 | −0.221592 | ||||||||
\(823\) | 3.80677e120 | 0.390358 | 0.195179 | − | 0.980768i | \(-0.437471\pi\) | ||||
0.195179 | + | 0.980768i | \(0.437471\pi\) | |||||||
\(824\) | 1.33910e120 | 0.130568 | ||||||||
\(825\) | −9.91473e120 | −0.919267 | ||||||||
\(826\) | 6.19639e120 | 0.546345 | ||||||||
\(827\) | −2.39747e120 | −0.201036 | −0.100518 | − | 0.994935i | \(-0.532050\pi\) | ||||
−0.100518 | + | 0.994935i | \(0.532050\pi\) | |||||||
\(828\) | 3.49010e120 | 0.278342 | ||||||||
\(829\) | −1.98319e121 | −1.50436 | −0.752178 | − | 0.658960i | \(-0.770997\pi\) | ||||
−0.752178 | + | 0.658960i | \(0.770997\pi\) | |||||||
\(830\) | −1.29024e120 | −0.0930954 | ||||||||
\(831\) | 1.28604e121 | 0.882700 | ||||||||
\(832\) | −1.47836e121 | −0.965297 | ||||||||
\(833\) | 1.35314e121 | 0.840575 | ||||||||
\(834\) | 3.45479e120 | 0.204188 | ||||||||
\(835\) | 2.53372e121 | 1.42485 | ||||||||
\(836\) | −2.26331e121 | −1.21111 | ||||||||
\(837\) | 4.89815e120 | 0.249417 | ||||||||
\(838\) | 4.15279e120 | 0.201240 | ||||||||
\(839\) | 6.17252e120 | 0.284669 | 0.142335 | − | 0.989819i | \(-0.454539\pi\) | ||||
0.142335 | + | 0.989819i | \(0.454539\pi\) | |||||||
\(840\) | −2.73020e121 | −1.19841 | ||||||||
\(841\) | −2.39246e121 | −0.999566 | ||||||||
\(842\) | −2.49018e120 | −0.0990328 | ||||||||
\(843\) | −3.29163e121 | −1.24614 | ||||||||
\(844\) | −2.83091e121 | −1.02027 | ||||||||
\(845\) | 1.83980e121 | 0.631274 | ||||||||
\(846\) | 3.99302e120 | 0.130446 | ||||||||
\(847\) | −6.68667e120 | −0.207993 | ||||||||
\(848\) | 3.97236e121 | 1.17658 | ||||||||
\(849\) | 3.26457e121 | 0.920781 | ||||||||
\(850\) | 2.40385e120 | 0.0645686 | ||||||||
\(851\) | 2.20398e120 | 0.0563808 | ||||||||
\(852\) | 8.42315e121 | 2.05226 | ||||||||
\(853\) | 6.46044e121 | 1.49926 | 0.749630 | − | 0.661857i | \(-0.230231\pi\) | ||||
0.749630 | + | 0.661857i | \(0.230231\pi\) | |||||||
\(854\) | −5.63606e120 | −0.124587 | ||||||||
\(855\) | −1.21181e122 | −2.55178 | ||||||||
\(856\) | 2.10503e121 | 0.422276 | ||||||||
\(857\) | 1.10370e121 | 0.210934 | 0.105467 | − | 0.994423i | \(-0.466366\pi\) | ||||
0.105467 | + | 0.994423i | \(0.466366\pi\) | |||||||
\(858\) | −1.87794e121 | −0.341948 | ||||||||
\(859\) | −2.24938e121 | −0.390253 | −0.195127 | − | 0.980778i | \(-0.562512\pi\) | ||||
−0.195127 | + | 0.980778i | \(0.562512\pi\) | |||||||
\(860\) | −1.49724e121 | −0.247518 | ||||||||
\(861\) | 4.98318e120 | 0.0785011 | ||||||||
\(862\) | 6.32049e120 | 0.0948853 | ||||||||
\(863\) | −3.01758e121 | −0.431729 | −0.215864 | − | 0.976423i | \(-0.569257\pi\) | ||||
−0.215864 | + | 0.976423i | \(0.569257\pi\) | |||||||
\(864\) | 3.05013e121 | 0.415908 | ||||||||
\(865\) | 8.48505e121 | 1.10277 | ||||||||
\(866\) | 5.41494e119 | 0.00670813 | ||||||||
\(867\) | −9.41502e121 | −1.11180 | ||||||||
\(868\) | −4.45324e121 | −0.501311 | ||||||||
\(869\) | −9.35748e121 | −1.00424 | ||||||||
\(870\) | 7.78320e119 | 0.00796360 | ||||||||
\(871\) | 8.35655e121 | 0.815217 | ||||||||
\(872\) | −1.33097e120 | −0.0123804 | ||||||||
\(873\) | −8.35563e121 | −0.741120 | ||||||||
\(874\) | 5.89038e120 | 0.0498217 | ||||||||
\(875\) | −9.45499e121 | −0.762653 | ||||||||
\(876\) | 1.69357e122 | 1.30281 | ||||||||
\(877\) | −2.36614e121 | −0.173603 | −0.0868014 | − | 0.996226i | \(-0.527665\pi\) | ||||
−0.0868014 | + | 0.996226i | \(0.527665\pi\) | |||||||
\(878\) | −1.41903e121 | −0.0993045 | ||||||||
\(879\) | −3.06897e121 | −0.204859 | ||||||||
\(880\) | −1.66693e122 | −1.06142 | ||||||||
\(881\) | 3.87807e121 | 0.235568 | 0.117784 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117784 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(882\) | 7.54863e121 | 0.437443 | ||||||||
\(883\) | 3.20084e122 | 1.76968 | 0.884840 | − | 0.465895i | \(-0.154267\pi\) | ||||
0.884840 | + | 0.465895i | \(0.154267\pi\) | |||||||
\(884\) | −1.21302e122 | −0.639881 | ||||||||
\(885\) | 7.18534e122 | 3.61661 | ||||||||
\(886\) | −2.80064e120 | −0.0134511 | ||||||||
\(887\) | −1.80096e122 | −0.825418 | −0.412709 | − | 0.910863i | \(-0.635417\pi\) | ||||
−0.412709 | + | 0.910863i | \(0.635417\pi\) | |||||||
\(888\) | 3.90482e121 | 0.170790 | ||||||||
\(889\) | −5.06845e122 | −2.11569 | ||||||||
\(890\) | −7.96701e121 | −0.317402 | ||||||||
\(891\) | 6.83570e121 | 0.259931 | ||||||||
\(892\) | 3.15578e122 | 1.14542 | ||||||||
\(893\) | −1.79542e122 | −0.622058 | ||||||||
\(894\) | −1.08544e122 | −0.359002 | ||||||||
\(895\) | −9.50452e121 | −0.300106 | ||||||||
\(896\) | −3.67229e122 | −1.10702 | ||||||||
\(897\) | −1.30209e122 | −0.374761 | ||||||||
\(898\) | 8.53407e121 | 0.234525 | ||||||||
\(899\) | 2.58669e120 | 0.00678762 | ||||||||
\(900\) | −3.57265e122 | −0.895213 | ||||||||
\(901\) | 2.99028e122 | 0.715540 | ||||||||
\(902\) | −2.42118e120 | −0.00553294 | ||||||||
\(903\) | 2.32283e122 | 0.506962 | ||||||||
\(904\) | 3.32233e122 | 0.692553 | ||||||||
\(905\) | 1.47593e122 | 0.293867 | ||||||||
\(906\) | −2.98083e122 | −0.566913 | ||||||||
\(907\) | −8.61403e122 | −1.56496 | −0.782481 | − | 0.622674i | \(-0.786046\pi\) | ||||
−0.782481 | + | 0.622674i | \(0.786046\pi\) | |||||||
\(908\) | 9.10229e121 | 0.157975 | ||||||||
\(909\) | 7.28555e122 | 1.20798 | ||||||||
\(910\) | 2.98783e122 | 0.473302 | ||||||||
\(911\) | 4.80408e122 | 0.727106 | 0.363553 | − | 0.931573i | \(-0.381564\pi\) | ||||
0.363553 | + | 0.931573i | \(0.381564\pi\) | |||||||
\(912\) | −1.31141e123 | −1.89650 | ||||||||
\(913\) | 2.59104e122 | 0.358044 | ||||||||
\(914\) | −8.92809e121 | −0.117894 | ||||||||
\(915\) | −6.53558e122 | −0.824725 | ||||||||
\(916\) | 4.56540e122 | 0.550575 | ||||||||
\(917\) | 2.61738e123 | 3.01675 | ||||||||
\(918\) | 7.17589e121 | 0.0790505 | ||||||||
\(919\) | 5.26540e122 | 0.554418 | 0.277209 | − | 0.960810i | \(-0.410590\pi\) | ||||
0.277209 | + | 0.960810i | \(0.410590\pi\) | |||||||
\(920\) | 9.19758e121 | 0.0925718 | ||||||||
\(921\) | −1.70471e123 | −1.64012 | ||||||||
\(922\) | −2.60549e122 | −0.239639 | ||||||||
\(923\) | −1.87820e123 | −1.65147 | ||||||||
\(924\) | 2.69088e123 | 2.26208 | ||||||||
\(925\) | −2.25611e122 | −0.181334 | ||||||||
\(926\) | 4.27170e122 | 0.328280 | ||||||||
\(927\) | −7.06652e122 | −0.519274 | ||||||||
\(928\) | 1.61076e121 | 0.0113185 | ||||||||
\(929\) | −1.51288e123 | −1.01661 | −0.508303 | − | 0.861178i | \(-0.669727\pi\) | ||||
−0.508303 | + | 0.861178i | \(0.669727\pi\) | |||||||
\(930\) | 1.93832e122 | 0.124561 | ||||||||
\(931\) | −3.39417e123 | −2.08604 | ||||||||
\(932\) | 7.13690e122 | 0.419517 | ||||||||
\(933\) | −7.42950e121 | −0.0417707 | ||||||||
\(934\) | −1.38003e121 | −0.00742152 | ||||||||
\(935\) | −1.25482e123 | −0.645506 | ||||||||
\(936\) | −1.37879e123 | −0.678500 | ||||||||
\(937\) | 1.88293e123 | 0.886425 | 0.443212 | − | 0.896417i | \(-0.353839\pi\) | ||||
0.443212 | + | 0.896417i | \(0.353839\pi\) | |||||||
\(938\) | 4.49447e122 | 0.202424 | ||||||||
\(939\) | 2.85880e123 | 1.23186 | ||||||||
\(940\) | −1.37591e123 | −0.567264 | ||||||||
\(941\) | 3.80840e123 | 1.50236 | 0.751179 | − | 0.660098i | \(-0.229485\pi\) | ||||
0.751179 | + | 0.660098i | \(0.229485\pi\) | |||||||
\(942\) | −7.33591e122 | −0.276912 | ||||||||
\(943\) | −1.67875e121 | −0.00606387 | ||||||||
\(944\) | 4.64744e123 | 1.60648 | ||||||||
\(945\) | 4.70894e123 | 1.55777 | ||||||||
\(946\) | −1.12859e122 | −0.0357318 | ||||||||
\(947\) | −5.36351e123 | −1.62527 | −0.812635 | − | 0.582774i | \(-0.801967\pi\) | ||||
−0.812635 | + | 0.582774i | \(0.801967\pi\) | |||||||
\(948\) | −5.64164e123 | −1.63629 | ||||||||
\(949\) | −3.77632e123 | −1.04839 | ||||||||
\(950\) | −6.02971e122 | −0.160238 | ||||||||
\(951\) | 2.02428e123 | 0.514966 | ||||||||
\(952\) | −1.32931e123 | −0.323737 | ||||||||
\(953\) | 4.22287e123 | 0.984582 | 0.492291 | − | 0.870431i | \(-0.336159\pi\) | ||||
0.492291 | + | 0.870431i | \(0.336159\pi\) | |||||||
\(954\) | 1.66816e123 | 0.372374 | ||||||||
\(955\) | 6.48084e123 | 1.38513 | ||||||||
\(956\) | 5.18106e123 | 1.06027 | ||||||||
\(957\) | −1.56301e122 | −0.0306279 | ||||||||
\(958\) | 1.47345e123 | 0.276482 | ||||||||
\(959\) | −6.56467e123 | −1.17962 | ||||||||
\(960\) | −9.22018e123 | −1.58666 | ||||||||
\(961\) | −5.42346e123 | −0.893833 | ||||||||
\(962\) | −4.27329e122 | −0.0674524 | ||||||||
\(963\) | −1.11083e124 | −1.67942 | ||||||||
\(964\) | −1.63371e123 | −0.236580 | ||||||||
\(965\) | 1.20582e124 | 1.67263 | ||||||||
\(966\) | −7.00314e122 | −0.0930555 | ||||||||
\(967\) | −3.96913e123 | −0.505239 | −0.252619 | − | 0.967566i | \(-0.581292\pi\) | ||||
−0.252619 | + | 0.967566i | \(0.581292\pi\) | |||||||
\(968\) | 3.99100e122 | 0.0486693 | ||||||||
\(969\) | −9.87197e123 | −1.15337 | ||||||||
\(970\) | −1.08071e123 | −0.120972 | ||||||||
\(971\) | 1.03876e124 | 1.11408 | 0.557041 | − | 0.830485i | \(-0.311937\pi\) | ||||
0.557041 | + | 0.830485i | \(0.311937\pi\) | |||||||
\(972\) | 1.13005e124 | 1.16130 | ||||||||
\(973\) | 1.10382e124 | 1.08697 | ||||||||
\(974\) | −1.35046e123 | −0.127434 | ||||||||
\(975\) | 1.33289e124 | 1.20532 | ||||||||
\(976\) | −4.22718e123 | −0.366339 | ||||||||
\(977\) | −3.73334e123 | −0.310079 | −0.155040 | − | 0.987908i | \(-0.549551\pi\) | ||||
−0.155040 | + | 0.987908i | \(0.549551\pi\) | |||||||
\(978\) | 4.38435e123 | 0.349014 | ||||||||
\(979\) | 1.59993e124 | 1.22073 | ||||||||
\(980\) | −2.60111e124 | −1.90229 | ||||||||
\(981\) | 7.02362e122 | 0.0492376 | ||||||||
\(982\) | −1.46252e123 | −0.0982821 | ||||||||
\(983\) | 3.54597e123 | 0.228436 | 0.114218 | − | 0.993456i | \(-0.463564\pi\) | ||||
0.114218 | + | 0.993456i | \(0.463564\pi\) | |||||||
\(984\) | −2.97426e122 | −0.0183689 | ||||||||
\(985\) | −3.25969e124 | −1.93007 | ||||||||
\(986\) | 3.78956e121 | 0.00215128 | ||||||||
\(987\) | 2.13460e124 | 1.16186 | ||||||||
\(988\) | 3.04269e124 | 1.58798 | ||||||||
\(989\) | −7.82520e122 | −0.0391606 | ||||||||
\(990\) | −7.00013e123 | −0.335928 | ||||||||
\(991\) | −4.20643e123 | −0.193579 | −0.0967893 | − | 0.995305i | \(-0.530857\pi\) | ||||
−0.0967893 | + | 0.995305i | \(0.530857\pi\) | |||||||
\(992\) | 4.01142e123 | 0.177037 | ||||||||
\(993\) | −3.57648e124 | −1.51378 | ||||||||
\(994\) | −1.01017e124 | −0.410070 | ||||||||
\(995\) | −2.50998e124 | −0.977263 | ||||||||
\(996\) | 1.56214e124 | 0.583388 | ||||||||
\(997\) | 1.41892e124 | 0.508286 | 0.254143 | − | 0.967167i | \(-0.418207\pi\) | ||||
0.254143 | + | 0.967167i | \(0.418207\pi\) | |||||||
\(998\) | 5.40065e123 | 0.185579 | ||||||||
\(999\) | −6.73487e123 | −0.222004 |
(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 | 1.84.a.a.1.4 | ✓ | 7 | |
3.2 | odd | 2 | 9.84.a.c.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.84.a.a.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.84.a.c.1.4 | 7 | 3.2 | odd | 2 |