Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,82,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 82, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 82);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 82 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(83.1002571076\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 215736607049989005852988854472x + 10253113298782277175624314846636353390456960 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.38588e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.09951e12 | −0.707107 | ||||||||
\(3\) | 2.69378e19 | 1.27924 | 0.639620 | − | 0.768692i | \(-0.279092\pi\) | ||||
0.639620 | + | 0.768692i | \(0.279092\pi\) | |||||||
\(4\) | 1.20893e24 | 0.500000 | ||||||||
\(5\) | 1.65593e28 | 0.814247 | 0.407124 | − | 0.913373i | \(-0.366532\pi\) | ||||
0.407124 | + | 0.913373i | \(0.366532\pi\) | |||||||
\(6\) | −2.96185e31 | −0.904559 | ||||||||
\(7\) | 2.15367e33 | 0.127852 | 0.0639261 | − | 0.997955i | \(-0.479638\pi\) | ||||
0.0639261 | + | 0.997955i | \(0.479638\pi\) | |||||||
\(8\) | −1.32923e36 | −0.353553 | ||||||||
\(9\) | 2.82220e38 | 0.636453 | ||||||||
\(10\) | −1.82071e40 | −0.575760 | ||||||||
\(11\) | −3.85124e40 | −0.0256564 | −0.0128282 | − | 0.999918i | \(-0.504083\pi\) | ||||
−0.0128282 | + | 0.999918i | \(0.504083\pi\) | |||||||
\(12\) | 3.25658e43 | 0.639620 | ||||||||
\(13\) | −8.46841e43 | −0.0650273 | −0.0325137 | − | 0.999471i | \(-0.510351\pi\) | ||||
−0.0325137 | + | 0.999471i | \(0.510351\pi\) | |||||||
\(14\) | −2.36798e45 | −0.0904052 | ||||||||
\(15\) | 4.46071e47 | 1.04162 | ||||||||
\(16\) | 1.46150e48 | 0.250000 | ||||||||
\(17\) | −7.68035e49 | −1.12772 | −0.563858 | − | 0.825872i | \(-0.690683\pi\) | ||||
−0.563858 | + | 0.825872i | \(0.690683\pi\) | |||||||
\(18\) | −3.10304e50 | −0.450041 | ||||||||
\(19\) | −7.37973e51 | −1.19817 | −0.599087 | − | 0.800684i | \(-0.704469\pi\) | ||||
−0.599087 | + | 0.800684i | \(0.704469\pi\) | |||||||
\(20\) | 2.00189e52 | 0.407124 | ||||||||
\(21\) | 5.80152e52 | 0.163554 | ||||||||
\(22\) | 4.23448e52 | 0.0181418 | ||||||||
\(23\) | −1.05342e55 | −0.745800 | −0.372900 | − | 0.927872i | \(-0.621637\pi\) | ||||
−0.372900 | + | 0.927872i | \(0.621637\pi\) | |||||||
\(24\) | −3.58065e55 | −0.452279 | ||||||||
\(25\) | −1.39380e56 | −0.337001 | ||||||||
\(26\) | 9.31111e55 | 0.0459813 | ||||||||
\(27\) | −4.34255e57 | −0.465063 | ||||||||
\(28\) | 2.60363e57 | 0.0639261 | ||||||||
\(29\) | −1.79362e59 | −1.06319 | −0.531597 | − | 0.846998i | \(-0.678408\pi\) | ||||
−0.531597 | + | 0.846998i | \(0.678408\pi\) | |||||||
\(30\) | −4.90461e59 | −0.736535 | ||||||||
\(31\) | −4.86617e60 | −1.93659 | −0.968297 | − | 0.249800i | \(-0.919635\pi\) | ||||
−0.968297 | + | 0.249800i | \(0.919635\pi\) | |||||||
\(32\) | −1.60694e60 | −0.176777 | ||||||||
\(33\) | −1.03744e60 | −0.0328207 | ||||||||
\(34\) | 8.44463e61 | 0.797416 | ||||||||
\(35\) | 3.56632e61 | 0.104103 | ||||||||
\(36\) | 3.41183e62 | 0.318227 | ||||||||
\(37\) | 2.30511e63 | 0.708796 | 0.354398 | − | 0.935095i | \(-0.384686\pi\) | ||||
0.354398 | + | 0.935095i | \(0.384686\pi\) | |||||||
\(38\) | 8.11410e63 | 0.847236 | ||||||||
\(39\) | −2.28121e63 | −0.0831855 | ||||||||
\(40\) | −2.20111e64 | −0.287880 | ||||||||
\(41\) | −1.35802e65 | −0.653369 | −0.326684 | − | 0.945133i | \(-0.605931\pi\) | ||||
−0.326684 | + | 0.945133i | \(0.605931\pi\) | |||||||
\(42\) | −6.37884e64 | −0.115650 | ||||||||
\(43\) | 2.10516e66 | 1.47168 | 0.735838 | − | 0.677158i | \(-0.236788\pi\) | ||||
0.735838 | + | 0.677158i | \(0.236788\pi\) | |||||||
\(44\) | −4.65586e64 | −0.0128282 | ||||||||
\(45\) | 4.67337e66 | 0.518231 | ||||||||
\(46\) | 1.15824e67 | 0.527360 | ||||||||
\(47\) | 1.03746e68 | 1.97700 | 0.988501 | − | 0.151212i | \(-0.0483177\pi\) | ||||
0.988501 | + | 0.151212i | \(0.0483177\pi\) | |||||||
\(48\) | 3.93697e67 | 0.319810 | ||||||||
\(49\) | −2.79115e68 | −0.983654 | ||||||||
\(50\) | 1.53250e68 | 0.238296 | ||||||||
\(51\) | −2.06892e69 | −1.44262 | ||||||||
\(52\) | −1.02377e68 | −0.0325137 | ||||||||
\(53\) | 2.99301e69 | 0.439476 | 0.219738 | − | 0.975559i | \(-0.429480\pi\) | ||||
0.219738 | + | 0.975559i | \(0.429480\pi\) | |||||||
\(54\) | 4.77468e69 | 0.328849 | ||||||||
\(55\) | −6.37737e68 | −0.0208907 | ||||||||
\(56\) | −2.86272e69 | −0.0452026 | ||||||||
\(57\) | −1.98794e71 | −1.53275 | ||||||||
\(58\) | 1.97211e71 | 0.751791 | ||||||||
\(59\) | −5.68737e71 | −1.08494 | −0.542469 | − | 0.840076i | \(-0.682510\pi\) | ||||
−0.542469 | + | 0.840076i | \(0.682510\pi\) | |||||||
\(60\) | 5.39267e71 | 0.520809 | ||||||||
\(61\) | 5.44662e71 | 0.269320 | 0.134660 | − | 0.990892i | \(-0.457006\pi\) | ||||
0.134660 | + | 0.990892i | \(0.457006\pi\) | |||||||
\(62\) | 5.35041e72 | 1.36938 | ||||||||
\(63\) | 6.07809e71 | 0.0813720 | ||||||||
\(64\) | 1.76685e72 | 0.125000 | ||||||||
\(65\) | −1.40231e72 | −0.0529484 | ||||||||
\(66\) | 1.14068e72 | 0.0232078 | ||||||||
\(67\) | −5.75193e73 | −0.636479 | −0.318240 | − | 0.948010i | \(-0.603092\pi\) | ||||
−0.318240 | + | 0.948010i | \(0.603092\pi\) | |||||||
\(68\) | −9.28497e73 | −0.563858 | ||||||||
\(69\) | −2.83767e74 | −0.954057 | ||||||||
\(70\) | −3.92121e73 | −0.0736122 | ||||||||
\(71\) | 4.64836e74 | 0.491289 | 0.245644 | − | 0.969360i | \(-0.421000\pi\) | ||||
0.245644 | + | 0.969360i | \(0.421000\pi\) | |||||||
\(72\) | −3.75135e74 | −0.225020 | ||||||||
\(73\) | 4.70398e75 | 1.61395 | 0.806974 | − | 0.590587i | \(-0.201104\pi\) | ||||
0.806974 | + | 0.590587i | \(0.201104\pi\) | |||||||
\(74\) | −2.53449e75 | −0.501195 | ||||||||
\(75\) | −3.75460e75 | −0.431105 | ||||||||
\(76\) | −8.92155e75 | −0.599087 | ||||||||
\(77\) | −8.29429e73 | −0.00328023 | ||||||||
\(78\) | 2.50821e75 | 0.0588211 | ||||||||
\(79\) | −4.20695e76 | −0.588939 | −0.294469 | − | 0.955661i | \(-0.595143\pi\) | ||||
−0.294469 | + | 0.955661i | \(0.595143\pi\) | |||||||
\(80\) | 2.42014e76 | 0.203562 | ||||||||
\(81\) | −2.42123e77 | −1.23138 | ||||||||
\(82\) | 1.49315e77 | 0.462002 | ||||||||
\(83\) | −7.46283e77 | −1.41332 | −0.706661 | − | 0.707552i | \(-0.749799\pi\) | ||||
−0.706661 | + | 0.707552i | \(0.749799\pi\) | |||||||
\(84\) | 7.01361e76 | 0.0817768 | ||||||||
\(85\) | −1.27181e78 | −0.918240 | ||||||||
\(86\) | −2.31465e78 | −1.04063 | ||||||||
\(87\) | −4.83163e78 | −1.36008 | ||||||||
\(88\) | 5.11917e76 | 0.00907092 | ||||||||
\(89\) | 5.59868e78 | 0.627755 | 0.313878 | − | 0.949463i | \(-0.398372\pi\) | ||||
0.313878 | + | 0.949463i | \(0.398372\pi\) | |||||||
\(90\) | −5.13842e78 | −0.366444 | ||||||||
\(91\) | −1.82382e77 | −0.00831389 | ||||||||
\(92\) | −1.27350e79 | −0.372900 | ||||||||
\(93\) | −1.31084e80 | −2.47737 | ||||||||
\(94\) | −1.14070e80 | −1.39795 | ||||||||
\(95\) | −1.22203e80 | −0.975610 | ||||||||
\(96\) | −4.32874e79 | −0.226140 | ||||||||
\(97\) | −1.28380e80 | −0.440800 | −0.220400 | − | 0.975410i | \(-0.570736\pi\) | ||||
−0.220400 | + | 0.975410i | \(0.570736\pi\) | |||||||
\(98\) | 3.06890e80 | 0.695548 | ||||||||
\(99\) | −1.08690e79 | −0.0163291 | ||||||||
\(100\) | −1.68501e80 | −0.168501 | ||||||||
\(101\) | −7.72319e79 | −0.0516156 | −0.0258078 | − | 0.999667i | \(-0.508216\pi\) | ||||
−0.0258078 | + | 0.999667i | \(0.508216\pi\) | |||||||
\(102\) | 2.27480e81 | 1.02009 | ||||||||
\(103\) | −3.15136e80 | −0.0951897 | −0.0475948 | − | 0.998867i | \(-0.515156\pi\) | ||||
−0.0475948 | + | 0.998867i | \(0.515156\pi\) | |||||||
\(104\) | 1.12564e80 | 0.0229906 | ||||||||
\(105\) | 9.60690e80 | 0.133173 | ||||||||
\(106\) | −3.29085e81 | −0.310757 | ||||||||
\(107\) | 1.69471e82 | 1.09409 | 0.547045 | − | 0.837103i | \(-0.315753\pi\) | ||||
0.547045 | + | 0.837103i | \(0.315753\pi\) | |||||||
\(108\) | −5.24982e81 | −0.232532 | ||||||||
\(109\) | 4.82859e82 | 1.47247 | 0.736236 | − | 0.676725i | \(-0.236601\pi\) | ||||
0.736236 | + | 0.676725i | \(0.236601\pi\) | |||||||
\(110\) | 7.01199e80 | 0.0147719 | ||||||||
\(111\) | 6.20946e82 | 0.906720 | ||||||||
\(112\) | 3.14759e81 | 0.0319631 | ||||||||
\(113\) | 7.06228e82 | 0.500343 | 0.250172 | − | 0.968202i | \(-0.419513\pi\) | ||||
0.250172 | + | 0.968202i | \(0.419513\pi\) | |||||||
\(114\) | 2.18576e83 | 1.08382 | ||||||||
\(115\) | −1.74438e83 | −0.607266 | ||||||||
\(116\) | −2.16836e83 | −0.531597 | ||||||||
\(117\) | −2.38996e82 | −0.0413869 | ||||||||
\(118\) | 6.25333e83 | 0.767167 | ||||||||
\(119\) | −1.65409e83 | −0.144181 | ||||||||
\(120\) | −5.92930e83 | −0.368267 | ||||||||
\(121\) | −2.25176e84 | −0.999342 | ||||||||
\(122\) | −5.98862e83 | −0.190438 | ||||||||
\(123\) | −3.65820e84 | −0.835815 | ||||||||
\(124\) | −5.88284e84 | −0.968297 | ||||||||
\(125\) | −9.15680e84 | −1.08865 | ||||||||
\(126\) | −6.68293e83 | −0.0575387 | ||||||||
\(127\) | −1.77729e84 | −0.111098 | −0.0555491 | − | 0.998456i | \(-0.517691\pi\) | ||||
−0.0555491 | + | 0.998456i | \(0.517691\pi\) | |||||||
\(128\) | −1.94267e84 | −0.0883883 | ||||||||
\(129\) | 5.67084e85 | 1.88263 | ||||||||
\(130\) | 1.54185e84 | 0.0374401 | ||||||||
\(131\) | −2.55142e85 | −0.454250 | −0.227125 | − | 0.973866i | \(-0.572933\pi\) | ||||
−0.227125 | + | 0.973866i | \(0.572933\pi\) | |||||||
\(132\) | −1.25419e84 | −0.0164104 | ||||||||
\(133\) | −1.58935e85 | −0.153189 | ||||||||
\(134\) | 6.32432e85 | 0.450059 | ||||||||
\(135\) | −7.19095e85 | −0.378676 | ||||||||
\(136\) | 1.02089e86 | 0.398708 | ||||||||
\(137\) | −6.97596e85 | −0.202498 | −0.101249 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101249 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(138\) | 3.12005e86 | 0.674620 | ||||||||
\(139\) | 4.07982e86 | 0.658478 | 0.329239 | − | 0.944247i | \(-0.393208\pi\) | ||||
0.329239 | + | 0.944247i | \(0.393208\pi\) | |||||||
\(140\) | 4.31142e85 | 0.0520517 | ||||||||
\(141\) | 2.79469e87 | 2.52906 | ||||||||
\(142\) | −5.11093e86 | −0.347394 | ||||||||
\(143\) | 3.26138e84 | 0.00166837 | ||||||||
\(144\) | 4.12465e86 | 0.159113 | ||||||||
\(145\) | −2.97011e87 | −0.865703 | ||||||||
\(146\) | −5.17208e87 | −1.14123 | ||||||||
\(147\) | −7.51876e87 | −1.25833 | ||||||||
\(148\) | 2.78670e87 | 0.354398 | ||||||||
\(149\) | −4.93272e87 | −0.477576 | −0.238788 | − | 0.971072i | \(-0.576750\pi\) | ||||
−0.238788 | + | 0.971072i | \(0.576750\pi\) | |||||||
\(150\) | 4.12823e87 | 0.304837 | ||||||||
\(151\) | −1.01232e88 | −0.571152 | −0.285576 | − | 0.958356i | \(-0.592185\pi\) | ||||
−0.285576 | + | 0.958356i | \(0.592185\pi\) | |||||||
\(152\) | 9.80934e87 | 0.423618 | ||||||||
\(153\) | −2.16755e88 | −0.717739 | ||||||||
\(154\) | 9.11967e85 | 0.00231948 | ||||||||
\(155\) | −8.05803e88 | −1.57687 | ||||||||
\(156\) | −2.75781e87 | −0.0415928 | ||||||||
\(157\) | 1.17061e89 | 1.36294 | 0.681471 | − | 0.731845i | \(-0.261340\pi\) | ||||
0.681471 | + | 0.731845i | \(0.261340\pi\) | |||||||
\(158\) | 4.62559e88 | 0.416442 | ||||||||
\(159\) | 8.06252e88 | 0.562195 | ||||||||
\(160\) | −2.66097e88 | −0.143940 | ||||||||
\(161\) | −2.26871e88 | −0.0953522 | ||||||||
\(162\) | 2.66217e89 | 0.870717 | ||||||||
\(163\) | 1.93542e89 | 0.493375 | 0.246687 | − | 0.969095i | \(-0.420658\pi\) | ||||
0.246687 | + | 0.969095i | \(0.420658\pi\) | |||||||
\(164\) | −1.64174e89 | −0.326684 | ||||||||
\(165\) | −1.71793e88 | −0.0267242 | ||||||||
\(166\) | 8.20547e89 | 0.999369 | ||||||||
\(167\) | 2.65462e89 | 0.253505 | 0.126752 | − | 0.991934i | \(-0.459545\pi\) | ||||
0.126752 | + | 0.991934i | \(0.459545\pi\) | |||||||
\(168\) | −7.71154e88 | −0.0578250 | ||||||||
\(169\) | −1.68877e90 | −0.995771 | ||||||||
\(170\) | 1.39837e90 | 0.649294 | ||||||||
\(171\) | −2.08271e90 | −0.762581 | ||||||||
\(172\) | 2.54498e90 | 0.735838 | ||||||||
\(173\) | −4.22319e90 | −0.965547 | −0.482773 | − | 0.875745i | \(-0.660371\pi\) | ||||
−0.482773 | + | 0.875745i | \(0.660371\pi\) | |||||||
\(174\) | 5.31244e90 | 0.961721 | ||||||||
\(175\) | −3.00179e89 | −0.0430863 | ||||||||
\(176\) | −5.62859e88 | −0.00641411 | ||||||||
\(177\) | −1.53205e91 | −1.38790 | ||||||||
\(178\) | −6.15581e90 | −0.443890 | ||||||||
\(179\) | −2.47654e91 | −1.42330 | −0.711652 | − | 0.702532i | \(-0.752053\pi\) | ||||
−0.711652 | + | 0.702532i | \(0.752053\pi\) | |||||||
\(180\) | 5.64975e90 | 0.259115 | ||||||||
\(181\) | −2.31583e91 | −0.848643 | −0.424321 | − | 0.905512i | \(-0.639487\pi\) | ||||
−0.424321 | + | 0.905512i | \(0.639487\pi\) | |||||||
\(182\) | 2.00531e89 | 0.00587881 | ||||||||
\(183\) | 1.46720e91 | 0.344525 | ||||||||
\(184\) | 1.40023e91 | 0.263680 | ||||||||
\(185\) | 3.81709e91 | 0.577135 | ||||||||
\(186\) | 1.44128e92 | 1.75176 | ||||||||
\(187\) | 2.95788e90 | 0.0289332 | ||||||||
\(188\) | 1.25421e92 | 0.988501 | ||||||||
\(189\) | −9.35241e90 | −0.0594594 | ||||||||
\(190\) | 1.34364e92 | 0.689860 | ||||||||
\(191\) | −1.10964e92 | −0.460607 | −0.230304 | − | 0.973119i | \(-0.573972\pi\) | ||||
−0.230304 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(192\) | 4.75950e91 | 0.159905 | ||||||||
\(193\) | −5.11836e92 | −1.39335 | −0.696675 | − | 0.717387i | \(-0.745338\pi\) | ||||
−0.696675 | + | 0.717387i | \(0.745338\pi\) | |||||||
\(194\) | 1.41155e92 | 0.311692 | ||||||||
\(195\) | −3.77751e91 | −0.0677336 | ||||||||
\(196\) | −3.37430e92 | −0.491827 | ||||||||
\(197\) | 1.19905e93 | 1.42218 | 0.711092 | − | 0.703099i | \(-0.248201\pi\) | ||||
0.711092 | + | 0.703099i | \(0.248201\pi\) | |||||||
\(198\) | 1.19506e91 | 0.0115464 | ||||||||
\(199\) | −8.67630e92 | −0.683573 | −0.341786 | − | 0.939778i | \(-0.611032\pi\) | ||||
−0.341786 | + | 0.939778i | \(0.611032\pi\) | |||||||
\(200\) | 1.85268e92 | 0.119148 | ||||||||
\(201\) | −1.54945e93 | −0.814209 | ||||||||
\(202\) | 8.49173e91 | 0.0364977 | ||||||||
\(203\) | −3.86287e92 | −0.135932 | ||||||||
\(204\) | −2.50117e93 | −0.721309 | ||||||||
\(205\) | −2.24878e93 | −0.532004 | ||||||||
\(206\) | 3.46495e92 | 0.0673093 | ||||||||
\(207\) | −2.97295e93 | −0.474667 | ||||||||
\(208\) | −1.23766e92 | −0.0162568 | ||||||||
\(209\) | 2.84211e92 | 0.0307409 | ||||||||
\(210\) | −1.05629e93 | −0.0941676 | ||||||||
\(211\) | 1.56322e94 | 1.14969 | 0.574845 | − | 0.818262i | \(-0.305062\pi\) | ||||
0.574845 | + | 0.818262i | \(0.305062\pi\) | |||||||
\(212\) | 3.61833e93 | 0.219738 | ||||||||
\(213\) | 1.25217e94 | 0.628476 | ||||||||
\(214\) | −1.86336e94 | −0.773639 | ||||||||
\(215\) | 3.48599e94 | 1.19831 | ||||||||
\(216\) | 5.77223e93 | 0.164425 | ||||||||
\(217\) | −1.04801e94 | −0.247598 | ||||||||
\(218\) | −5.30909e94 | −1.04119 | ||||||||
\(219\) | 1.26715e95 | 2.06463 | ||||||||
\(220\) | −7.70977e92 | −0.0104453 | ||||||||
\(221\) | 6.50403e93 | 0.0733324 | ||||||||
\(222\) | −6.82737e94 | −0.641148 | ||||||||
\(223\) | 1.51413e95 | 1.18527 | 0.592633 | − | 0.805472i | \(-0.298088\pi\) | ||||
0.592633 | + | 0.805472i | \(0.298088\pi\) | |||||||
\(224\) | −3.46081e93 | −0.0226013 | ||||||||
\(225\) | −3.93360e94 | −0.214485 | ||||||||
\(226\) | −7.76506e94 | −0.353796 | ||||||||
\(227\) | −3.54890e95 | −1.35222 | −0.676109 | − | 0.736801i | \(-0.736335\pi\) | ||||
−0.676109 | + | 0.736801i | \(0.736335\pi\) | |||||||
\(228\) | −2.40327e95 | −0.766375 | ||||||||
\(229\) | −7.16704e95 | −1.91427 | −0.957133 | − | 0.289647i | \(-0.906462\pi\) | ||||
−0.957133 | + | 0.289647i | \(0.906462\pi\) | |||||||
\(230\) | 1.91797e95 | 0.429402 | ||||||||
\(231\) | −2.23430e93 | −0.00419620 | ||||||||
\(232\) | 2.38413e95 | 0.375896 | ||||||||
\(233\) | −1.74206e94 | −0.0230754 | −0.0115377 | − | 0.999933i | \(-0.503673\pi\) | ||||
−0.0115377 | + | 0.999933i | \(0.503673\pi\) | |||||||
\(234\) | 2.62779e94 | 0.0292649 | ||||||||
\(235\) | 1.71796e96 | 1.60977 | ||||||||
\(236\) | −6.87561e95 | −0.542469 | ||||||||
\(237\) | −1.13326e96 | −0.753393 | ||||||||
\(238\) | 1.81870e95 | 0.101951 | ||||||||
\(239\) | 2.85641e96 | 1.35116 | 0.675579 | − | 0.737288i | \(-0.263894\pi\) | ||||
0.675579 | + | 0.737288i | \(0.263894\pi\) | |||||||
\(240\) | 6.51934e95 | 0.260404 | ||||||||
\(241\) | 1.64482e96 | 0.555174 | 0.277587 | − | 0.960700i | \(-0.410465\pi\) | ||||
0.277587 | + | 0.960700i | \(0.410465\pi\) | |||||||
\(242\) | 2.47583e96 | 0.706641 | ||||||||
\(243\) | −4.59666e96 | −1.11017 | ||||||||
\(244\) | 6.58456e95 | 0.134660 | ||||||||
\(245\) | −4.62195e96 | −0.800938 | ||||||||
\(246\) | 4.02223e96 | 0.591011 | ||||||||
\(247\) | 6.24946e95 | 0.0779140 | ||||||||
\(248\) | 6.46825e96 | 0.684690 | ||||||||
\(249\) | −2.01033e97 | −1.80798 | ||||||||
\(250\) | 1.00680e97 | 0.769792 | ||||||||
\(251\) | 2.49036e97 | 1.61986 | 0.809928 | − | 0.586530i | \(-0.199506\pi\) | ||||
0.809928 | + | 0.586530i | \(0.199506\pi\) | |||||||
\(252\) | 7.34796e95 | 0.0406860 | ||||||||
\(253\) | 4.05695e95 | 0.0191346 | ||||||||
\(254\) | 1.95415e96 | 0.0785583 | ||||||||
\(255\) | −3.42598e97 | −1.17465 | ||||||||
\(256\) | 2.13599e96 | 0.0625000 | ||||||||
\(257\) | −6.39309e97 | −1.59742 | −0.798710 | − | 0.601716i | \(-0.794484\pi\) | ||||
−0.798710 | + | 0.601716i | \(0.794484\pi\) | |||||||
\(258\) | −6.23515e97 | −1.33122 | ||||||||
\(259\) | 4.96444e96 | 0.0906212 | ||||||||
\(260\) | −1.69529e96 | −0.0264742 | ||||||||
\(261\) | −5.06197e97 | −0.676673 | ||||||||
\(262\) | 2.80532e97 | 0.321203 | ||||||||
\(263\) | 1.31373e98 | 1.28914 | 0.644569 | − | 0.764546i | \(-0.277037\pi\) | ||||
0.644569 | + | 0.764546i | \(0.277037\pi\) | |||||||
\(264\) | 1.37899e96 | 0.0116039 | ||||||||
\(265\) | 4.95621e97 | 0.357842 | ||||||||
\(266\) | 1.74751e97 | 0.108321 | ||||||||
\(267\) | 1.50816e98 | 0.803049 | ||||||||
\(268\) | −6.95366e97 | −0.318240 | ||||||||
\(269\) | 1.34185e98 | 0.528126 | 0.264063 | − | 0.964505i | \(-0.414937\pi\) | ||||
0.264063 | + | 0.964505i | \(0.414937\pi\) | |||||||
\(270\) | 7.90653e97 | 0.267765 | ||||||||
\(271\) | 2.31481e98 | 0.674930 | 0.337465 | − | 0.941338i | \(-0.390431\pi\) | ||||
0.337465 | + | 0.941338i | \(0.390431\pi\) | |||||||
\(272\) | −1.12248e98 | −0.281929 | ||||||||
\(273\) | −4.91296e96 | −0.0106355 | ||||||||
\(274\) | 7.67015e97 | 0.143188 | ||||||||
\(275\) | 5.36787e96 | 0.00864624 | ||||||||
\(276\) | −3.43054e98 | −0.477028 | ||||||||
\(277\) | 1.19697e99 | 1.43765 | 0.718827 | − | 0.695189i | \(-0.244680\pi\) | ||||
0.718827 | + | 0.695189i | \(0.244680\pi\) | |||||||
\(278\) | −4.48581e98 | −0.465615 | ||||||||
\(279\) | −1.37333e99 | −1.23255 | ||||||||
\(280\) | −4.74046e97 | −0.0368061 | ||||||||
\(281\) | 2.35229e99 | 1.58083 | 0.790415 | − | 0.612571i | \(-0.209865\pi\) | ||||
0.790415 | + | 0.612571i | \(0.209865\pi\) | |||||||
\(282\) | −3.07279e99 | −1.78832 | ||||||||
\(283\) | −1.76801e99 | −0.891524 | −0.445762 | − | 0.895152i | \(-0.647067\pi\) | ||||
−0.445762 | + | 0.895152i | \(0.647067\pi\) | |||||||
\(284\) | 5.61952e98 | 0.245644 | ||||||||
\(285\) | −3.29189e99 | −1.24804 | ||||||||
\(286\) | −3.58593e96 | −0.00117972 | ||||||||
\(287\) | −2.92472e98 | −0.0835347 | ||||||||
\(288\) | −4.53511e98 | −0.112510 | ||||||||
\(289\) | 1.26044e99 | 0.271743 | ||||||||
\(290\) | 3.26567e99 | 0.612144 | ||||||||
\(291\) | −3.45827e99 | −0.563888 | ||||||||
\(292\) | 5.68676e99 | 0.806974 | ||||||||
\(293\) | 7.41514e99 | 0.916180 | 0.458090 | − | 0.888906i | \(-0.348534\pi\) | ||||
0.458090 | + | 0.888906i | \(0.348534\pi\) | |||||||
\(294\) | 8.26696e99 | 0.889773 | ||||||||
\(295\) | −9.41788e99 | −0.883408 | ||||||||
\(296\) | −3.06401e99 | −0.250597 | ||||||||
\(297\) | 1.67242e98 | 0.0119319 | ||||||||
\(298\) | 5.42358e99 | 0.337697 | ||||||||
\(299\) | 8.92075e98 | 0.0484974 | ||||||||
\(300\) | −4.53904e99 | −0.215552 | ||||||||
\(301\) | 4.53381e99 | 0.188157 | ||||||||
\(302\) | 1.11306e100 | 0.403866 | ||||||||
\(303\) | −2.08046e99 | −0.0660287 | ||||||||
\(304\) | −1.07855e100 | −0.299543 | ||||||||
\(305\) | 9.01921e99 | 0.219293 | ||||||||
\(306\) | 2.38325e100 | 0.507518 | ||||||||
\(307\) | 3.35912e100 | 0.626789 | 0.313395 | − | 0.949623i | \(-0.398534\pi\) | ||||
0.313395 | + | 0.949623i | \(0.398534\pi\) | |||||||
\(308\) | −1.00272e98 | −0.00164012 | ||||||||
\(309\) | −8.48907e99 | −0.121770 | ||||||||
\(310\) | 8.85990e100 | 1.11501 | ||||||||
\(311\) | −1.52457e101 | −1.68404 | −0.842019 | − | 0.539448i | \(-0.818633\pi\) | ||||
−0.842019 | + | 0.539448i | \(0.818633\pi\) | |||||||
\(312\) | 3.03224e99 | 0.0294105 | ||||||||
\(313\) | −1.80423e101 | −1.53726 | −0.768628 | − | 0.639696i | \(-0.779060\pi\) | ||||
−0.768628 | + | 0.639696i | \(0.779060\pi\) | |||||||
\(314\) | −1.28710e101 | −0.963746 | ||||||||
\(315\) | 1.00649e100 | 0.0662570 | ||||||||
\(316\) | −5.08589e100 | −0.294469 | ||||||||
\(317\) | −9.83506e100 | −0.501045 | −0.250523 | − | 0.968111i | \(-0.580602\pi\) | ||||
−0.250523 | + | 0.968111i | \(0.580602\pi\) | |||||||
\(318\) | −8.86483e100 | −0.397532 | ||||||||
\(319\) | 6.90767e99 | 0.0272778 | ||||||||
\(320\) | 2.92577e100 | 0.101781 | ||||||||
\(321\) | 4.56519e101 | 1.39960 | ||||||||
\(322\) | 2.49447e100 | 0.0674242 | ||||||||
\(323\) | 5.66789e101 | 1.35120 | ||||||||
\(324\) | −2.92708e101 | −0.615690 | ||||||||
\(325\) | 1.18033e100 | 0.0219143 | ||||||||
\(326\) | −2.12802e101 | −0.348869 | ||||||||
\(327\) | 1.30072e102 | 1.88364 | ||||||||
\(328\) | 1.80511e101 | 0.231001 | ||||||||
\(329\) | 2.23434e101 | 0.252764 | ||||||||
\(330\) | 1.88888e100 | 0.0188969 | ||||||||
\(331\) | −7.65599e99 | −0.00677591 | −0.00338795 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338795 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(332\) | −9.02201e101 | −0.706661 | ||||||||
\(333\) | 6.50548e101 | 0.451116 | ||||||||
\(334\) | −2.91879e101 | −0.179255 | ||||||||
\(335\) | −9.52479e101 | −0.518252 | ||||||||
\(336\) | 8.47893e100 | 0.0408884 | ||||||||
\(337\) | −4.29366e102 | −1.83576 | −0.917881 | − | 0.396856i | \(-0.870101\pi\) | ||||
−0.917881 | + | 0.396856i | \(0.870101\pi\) | |||||||
\(338\) | 1.85683e102 | 0.704117 | ||||||||
\(339\) | 1.90242e102 | 0.640059 | ||||||||
\(340\) | −1.53753e102 | −0.459120 | ||||||||
\(341\) | 1.87408e101 | 0.0496861 | ||||||||
\(342\) | 2.28996e102 | 0.539226 | ||||||||
\(343\) | −1.21223e102 | −0.253615 | ||||||||
\(344\) | −2.79823e102 | −0.520316 | ||||||||
\(345\) | −4.69898e102 | −0.776838 | ||||||||
\(346\) | 4.64344e102 | 0.682745 | ||||||||
\(347\) | 1.89134e101 | 0.0247415 | 0.0123708 | − | 0.999923i | \(-0.496062\pi\) | ||||
0.0123708 | + | 0.999923i | \(0.496062\pi\) | |||||||
\(348\) | −5.84109e102 | −0.680040 | ||||||||
\(349\) | −1.37592e103 | −1.42614 | −0.713070 | − | 0.701093i | \(-0.752696\pi\) | ||||
−0.713070 | + | 0.701093i | \(0.752696\pi\) | |||||||
\(350\) | 3.30051e101 | 0.0304666 | ||||||||
\(351\) | 3.67745e101 | 0.0302418 | ||||||||
\(352\) | 6.18870e100 | 0.00453546 | ||||||||
\(353\) | 2.78332e103 | 1.81839 | 0.909195 | − | 0.416371i | \(-0.136698\pi\) | ||||
0.909195 | + | 0.416371i | \(0.136698\pi\) | |||||||
\(354\) | 1.68451e103 | 0.981390 | ||||||||
\(355\) | 7.69735e102 | 0.400031 | ||||||||
\(356\) | 6.76839e102 | 0.313878 | ||||||||
\(357\) | −4.45577e102 | −0.184442 | ||||||||
\(358\) | 2.72298e103 | 1.00643 | ||||||||
\(359\) | −5.09879e103 | −1.68322 | −0.841612 | − | 0.540082i | \(-0.818393\pi\) | ||||
−0.841612 | + | 0.540082i | \(0.818393\pi\) | |||||||
\(360\) | −6.21197e102 | −0.183222 | ||||||||
\(361\) | 1.65253e103 | 0.435619 | ||||||||
\(362\) | 2.54629e103 | 0.600081 | ||||||||
\(363\) | −6.06575e103 | −1.27840 | ||||||||
\(364\) | −2.20486e101 | −0.00415695 | ||||||||
\(365\) | 7.78946e103 | 1.31415 | ||||||||
\(366\) | −1.61320e103 | −0.243616 | ||||||||
\(367\) | 7.65169e103 | 1.03462 | 0.517311 | − | 0.855798i | \(-0.326933\pi\) | ||||
0.517311 | + | 0.855798i | \(0.326933\pi\) | |||||||
\(368\) | −1.53957e103 | −0.186450 | ||||||||
\(369\) | −3.83260e103 | −0.415839 | ||||||||
\(370\) | −4.19694e103 | −0.408096 | ||||||||
\(371\) | 6.44595e102 | 0.0561880 | ||||||||
\(372\) | −1.58471e104 | −1.23868 | ||||||||
\(373\) | 1.10313e104 | 0.773430 | 0.386715 | − | 0.922199i | \(-0.373610\pi\) | ||||
0.386715 | + | 0.922199i | \(0.373610\pi\) | |||||||
\(374\) | −3.25223e102 | −0.0204588 | ||||||||
\(375\) | −2.46664e104 | −1.39264 | ||||||||
\(376\) | −1.37902e104 | −0.698976 | ||||||||
\(377\) | 1.51891e103 | 0.0691367 | ||||||||
\(378\) | 1.02831e103 | 0.0420441 | ||||||||
\(379\) | −2.28475e104 | −0.839365 | −0.419682 | − | 0.907671i | \(-0.637859\pi\) | ||||
−0.419682 | + | 0.907671i | \(0.637859\pi\) | |||||||
\(380\) | −1.47734e104 | −0.487805 | ||||||||
\(381\) | −4.78763e103 | −0.142121 | ||||||||
\(382\) | 1.22006e104 | 0.325699 | ||||||||
\(383\) | 7.62871e104 | 1.83189 | 0.915947 | − | 0.401298i | \(-0.131441\pi\) | ||||
0.915947 | + | 0.401298i | \(0.131441\pi\) | |||||||
\(384\) | −5.23313e103 | −0.113070 | ||||||||
\(385\) | −1.37347e102 | −0.00267092 | ||||||||
\(386\) | 5.62770e104 | 0.985247 | ||||||||
\(387\) | 5.94118e104 | 0.936653 | ||||||||
\(388\) | −1.55202e104 | −0.220400 | ||||||||
\(389\) | 6.74768e104 | 0.863368 | 0.431684 | − | 0.902025i | \(-0.357920\pi\) | ||||
0.431684 | + | 0.902025i | \(0.357920\pi\) | |||||||
\(390\) | 4.15342e103 | 0.0478949 | ||||||||
\(391\) | 8.09060e104 | 0.841051 | ||||||||
\(392\) | 3.71008e104 | 0.347774 | ||||||||
\(393\) | −6.87298e104 | −0.581094 | ||||||||
\(394\) | −1.31837e105 | −1.00564 | ||||||||
\(395\) | −6.96641e104 | −0.479542 | ||||||||
\(396\) | −1.31398e103 | −0.00816456 | ||||||||
\(397\) | −2.50030e105 | −1.40274 | −0.701368 | − | 0.712799i | \(-0.747427\pi\) | ||||
−0.701368 | + | 0.712799i | \(0.747427\pi\) | |||||||
\(398\) | 9.53969e104 | 0.483359 | ||||||||
\(399\) | −4.28136e104 | −0.195966 | ||||||||
\(400\) | −2.03705e104 | −0.0842503 | ||||||||
\(401\) | 7.15970e103 | 0.0267638 | 0.0133819 | − | 0.999910i | \(-0.495740\pi\) | ||||
0.0133819 | + | 0.999910i | \(0.495740\pi\) | |||||||
\(402\) | 1.70363e105 | 0.575733 | ||||||||
\(403\) | 4.12087e104 | 0.125932 | ||||||||
\(404\) | −9.33676e103 | −0.0258078 | ||||||||
\(405\) | −4.00938e105 | −1.00265 | ||||||||
\(406\) | 4.24727e104 | 0.0961182 | ||||||||
\(407\) | −8.87751e103 | −0.0181852 | ||||||||
\(408\) | 2.75007e105 | 0.510043 | ||||||||
\(409\) | −5.18525e105 | −0.870914 | −0.435457 | − | 0.900209i | \(-0.643413\pi\) | ||||
−0.435457 | + | 0.900209i | \(0.643413\pi\) | |||||||
\(410\) | 2.47256e105 | 0.376184 | ||||||||
\(411\) | −1.87917e105 | −0.259044 | ||||||||
\(412\) | −3.80976e104 | −0.0475948 | ||||||||
\(413\) | −1.22487e105 | −0.138712 | ||||||||
\(414\) | 3.26880e105 | 0.335640 | ||||||||
\(415\) | −1.23579e106 | −1.15079 | ||||||||
\(416\) | 1.36082e104 | 0.0114953 | ||||||||
\(417\) | 1.09901e106 | 0.842351 | ||||||||
\(418\) | −3.12493e104 | −0.0217371 | ||||||||
\(419\) | 1.13062e106 | 0.713919 | 0.356960 | − | 0.934120i | \(-0.383813\pi\) | ||||
0.356960 | + | 0.934120i | \(0.383813\pi\) | |||||||
\(420\) | 1.16140e105 | 0.0665866 | ||||||||
\(421\) | 2.52430e106 | 1.31437 | 0.657183 | − | 0.753731i | \(-0.271748\pi\) | ||||
0.657183 | + | 0.753731i | \(0.271748\pi\) | |||||||
\(422\) | −1.71878e106 | −0.812953 | ||||||||
\(423\) | 2.92792e106 | 1.25827 | ||||||||
\(424\) | −3.97839e105 | −0.155378 | ||||||||
\(425\) | 1.07049e106 | 0.380041 | ||||||||
\(426\) | −1.37677e106 | −0.444400 | ||||||||
\(427\) | 1.17302e105 | 0.0344332 | ||||||||
\(428\) | 2.04878e106 | 0.547045 | ||||||||
\(429\) | 8.78546e103 | 0.00213424 | ||||||||
\(430\) | −3.83289e106 | −0.847332 | ||||||||
\(431\) | 2.23744e105 | 0.0450217 | 0.0225108 | − | 0.999747i | \(-0.492834\pi\) | ||||
0.0225108 | + | 0.999747i | \(0.492834\pi\) | |||||||
\(432\) | −6.34664e105 | −0.116266 | ||||||||
\(433\) | −4.63717e106 | −0.773559 | −0.386780 | − | 0.922172i | \(-0.626413\pi\) | ||||
−0.386780 | + | 0.922172i | \(0.626413\pi\) | |||||||
\(434\) | 1.15230e106 | 0.175078 | ||||||||
\(435\) | −8.00084e106 | −1.10744 | ||||||||
\(436\) | 5.83740e106 | 0.736236 | ||||||||
\(437\) | 7.77392e106 | 0.893598 | ||||||||
\(438\) | −1.39325e107 | −1.45991 | ||||||||
\(439\) | −8.66735e106 | −0.828082 | −0.414041 | − | 0.910258i | \(-0.635883\pi\) | ||||
−0.414041 | + | 0.910258i | \(0.635883\pi\) | |||||||
\(440\) | 8.47698e104 | 0.00738597 | ||||||||
\(441\) | −7.87720e106 | −0.626050 | ||||||||
\(442\) | −7.15126e105 | −0.0518538 | ||||||||
\(443\) | 9.95720e106 | 0.658850 | 0.329425 | − | 0.944182i | \(-0.393145\pi\) | ||||
0.329425 | + | 0.944182i | \(0.393145\pi\) | |||||||
\(444\) | 7.50678e106 | 0.453360 | ||||||||
\(445\) | 9.27101e106 | 0.511148 | ||||||||
\(446\) | −1.66480e107 | −0.838110 | ||||||||
\(447\) | −1.32877e107 | −0.610934 | ||||||||
\(448\) | 3.80520e105 | 0.0159815 | ||||||||
\(449\) | 3.96267e107 | 1.52059 | 0.760294 | − | 0.649579i | \(-0.225055\pi\) | ||||
0.760294 | + | 0.649579i | \(0.225055\pi\) | |||||||
\(450\) | 4.32504e106 | 0.151664 | ||||||||
\(451\) | 5.23004e105 | 0.0167631 | ||||||||
\(452\) | 8.53777e106 | 0.250172 | ||||||||
\(453\) | −2.72697e107 | −0.730641 | ||||||||
\(454\) | 3.90206e107 | 0.956163 | ||||||||
\(455\) | −3.02011e105 | −0.00676957 | ||||||||
\(456\) | 2.64242e107 | 0.541909 | ||||||||
\(457\) | 4.31708e107 | 0.810184 | 0.405092 | − | 0.914276i | \(-0.367240\pi\) | ||||
0.405092 | + | 0.914276i | \(0.367240\pi\) | |||||||
\(458\) | 7.88024e107 | 1.35359 | ||||||||
\(459\) | 3.33523e107 | 0.524459 | ||||||||
\(460\) | −2.10883e107 | −0.303633 | ||||||||
\(461\) | −8.16084e107 | −1.07609 | −0.538043 | − | 0.842917i | \(-0.680836\pi\) | ||||
−0.538043 | + | 0.842917i | \(0.680836\pi\) | |||||||
\(462\) | 2.45664e105 | 0.00296716 | ||||||||
\(463\) | −6.62658e107 | −0.733262 | −0.366631 | − | 0.930366i | \(-0.619489\pi\) | ||||
−0.366631 | + | 0.930366i | \(0.619489\pi\) | |||||||
\(464\) | −2.62138e107 | −0.265798 | ||||||||
\(465\) | −2.17066e108 | −2.01719 | ||||||||
\(466\) | 1.91542e106 | 0.0163167 | ||||||||
\(467\) | −8.07914e107 | −0.631003 | −0.315502 | − | 0.948925i | \(-0.602173\pi\) | ||||
−0.315502 | + | 0.948925i | \(0.602173\pi\) | |||||||
\(468\) | −2.88928e106 | −0.0206934 | ||||||||
\(469\) | −1.23878e107 | −0.0813753 | ||||||||
\(470\) | −1.88891e108 | −1.13828 | ||||||||
\(471\) | 3.15338e108 | 1.74353 | ||||||||
\(472\) | 7.55981e107 | 0.383584 | ||||||||
\(473\) | −8.10746e106 | −0.0377580 | ||||||||
\(474\) | 1.24603e108 | 0.532730 | ||||||||
\(475\) | 1.02859e108 | 0.403786 | ||||||||
\(476\) | −1.99968e107 | −0.0720905 | ||||||||
\(477\) | 8.44688e107 | 0.279706 | ||||||||
\(478\) | −3.14066e108 | −0.955413 | ||||||||
\(479\) | 4.07310e107 | 0.113851 | 0.0569254 | − | 0.998378i | \(-0.481870\pi\) | ||||
0.0569254 | + | 0.998378i | \(0.481870\pi\) | |||||||
\(480\) | −7.16809e107 | −0.184134 | ||||||||
\(481\) | −1.95206e107 | −0.0460911 | ||||||||
\(482\) | −1.80850e108 | −0.392568 | ||||||||
\(483\) | −6.11141e107 | −0.121978 | ||||||||
\(484\) | −2.72221e108 | −0.499671 | ||||||||
\(485\) | −2.12588e108 | −0.358920 | ||||||||
\(486\) | 5.05408e108 | 0.785007 | ||||||||
\(487\) | 8.18293e108 | 1.16946 | 0.584731 | − | 0.811227i | \(-0.301200\pi\) | ||||
0.584731 | + | 0.811227i | \(0.301200\pi\) | |||||||
\(488\) | −7.23980e107 | −0.0952190 | ||||||||
\(489\) | 5.21360e108 | 0.631145 | ||||||||
\(490\) | 5.08189e108 | 0.566348 | ||||||||
\(491\) | −4.58698e107 | −0.0470681 | −0.0235341 | − | 0.999723i | \(-0.507492\pi\) | ||||
−0.0235341 | + | 0.999723i | \(0.507492\pi\) | |||||||
\(492\) | −4.42249e108 | −0.417908 | ||||||||
\(493\) | 1.37757e109 | 1.19898 | ||||||||
\(494\) | −6.87135e107 | −0.0550935 | ||||||||
\(495\) | −1.79982e107 | −0.0132959 | ||||||||
\(496\) | −7.11192e108 | −0.484149 | ||||||||
\(497\) | 1.00110e108 | 0.0628124 | ||||||||
\(498\) | 2.21038e109 | 1.27843 | ||||||||
\(499\) | −1.29605e109 | −0.691116 | −0.345558 | − | 0.938397i | \(-0.612310\pi\) | ||||
−0.345558 | + | 0.938397i | \(0.612310\pi\) | |||||||
\(500\) | −1.10699e109 | −0.544325 | ||||||||
\(501\) | 7.15098e108 | 0.324293 | ||||||||
\(502\) | −2.73818e109 | −1.14541 | ||||||||
\(503\) | −3.21057e109 | −1.23902 | −0.619511 | − | 0.784988i | \(-0.712669\pi\) | ||||
−0.619511 | + | 0.784988i | \(0.712669\pi\) | |||||||
\(504\) | −8.07917e107 | −0.0287694 | ||||||||
\(505\) | −1.27890e108 | −0.0420279 | ||||||||
\(506\) | −4.46067e107 | −0.0135302 | ||||||||
\(507\) | −4.54919e109 | −1.27383 | ||||||||
\(508\) | −2.14861e108 | −0.0555491 | ||||||||
\(509\) | −4.21642e109 | −1.00664 | −0.503319 | − | 0.864100i | \(-0.667888\pi\) | ||||
−0.503319 | + | 0.864100i | \(0.667888\pi\) | |||||||
\(510\) | 3.76691e109 | 0.830602 | ||||||||
\(511\) | 1.01308e109 | 0.206347 | ||||||||
\(512\) | −2.34854e108 | −0.0441942 | ||||||||
\(513\) | 3.20468e109 | 0.557226 | ||||||||
\(514\) | 7.02927e109 | 1.12955 | ||||||||
\(515\) | −5.21842e108 | −0.0775079 | ||||||||
\(516\) | 6.85562e109 | 0.941313 | ||||||||
\(517\) | −3.99549e108 | −0.0507228 | ||||||||
\(518\) | −5.45846e108 | −0.0640789 | ||||||||
\(519\) | −1.13764e110 | −1.23517 | ||||||||
\(520\) | 1.86399e108 | 0.0187201 | ||||||||
\(521\) | 6.70105e109 | 0.622609 | 0.311304 | − | 0.950310i | \(-0.399234\pi\) | ||||
0.311304 | + | 0.950310i | \(0.399234\pi\) | |||||||
\(522\) | 5.56569e109 | 0.478480 | ||||||||
\(523\) | 1.39503e110 | 1.10986 | 0.554928 | − | 0.831898i | \(-0.312746\pi\) | ||||
0.554928 | + | 0.831898i | \(0.312746\pi\) | |||||||
\(524\) | −3.08448e109 | −0.227125 | ||||||||
\(525\) | −8.08618e108 | −0.0551178 | ||||||||
\(526\) | −1.44447e110 | −0.911559 | ||||||||
\(527\) | 3.73739e110 | 2.18393 | ||||||||
\(528\) | −1.51622e108 | −0.00820518 | ||||||||
\(529\) | −8.85370e109 | −0.443782 | ||||||||
\(530\) | −5.44941e109 | −0.253033 | ||||||||
\(531\) | −1.60509e110 | −0.690513 | ||||||||
\(532\) | −1.92141e109 | −0.0765946 | ||||||||
\(533\) | 1.15002e109 | 0.0424869 | ||||||||
\(534\) | −1.65824e110 | −0.567842 | ||||||||
\(535\) | 2.80632e110 | 0.890860 | ||||||||
\(536\) | 7.64563e109 | 0.225029 | ||||||||
\(537\) | −6.67126e110 | −1.82075 | ||||||||
\(538\) | −1.47538e110 | −0.373441 | ||||||||
\(539\) | 1.07494e109 | 0.0252370 | ||||||||
\(540\) | −8.69332e109 | −0.189338 | ||||||||
\(541\) | 7.78185e109 | 0.157251 | 0.0786256 | − | 0.996904i | \(-0.474947\pi\) | ||||
0.0786256 | + | 0.996904i | \(0.474947\pi\) | |||||||
\(542\) | −2.54516e110 | −0.477247 | ||||||||
\(543\) | −6.23835e110 | −1.08562 | ||||||||
\(544\) | 1.23418e110 | 0.199354 | ||||||||
\(545\) | 7.99580e110 | 1.19896 | ||||||||
\(546\) | 5.40186e108 | 0.00752041 | ||||||||
\(547\) | −2.81651e110 | −0.364103 | −0.182051 | − | 0.983289i | \(-0.558274\pi\) | ||||
−0.182051 | + | 0.983289i | \(0.558274\pi\) | |||||||
\(548\) | −8.43342e109 | −0.101249 | ||||||||
\(549\) | 1.53715e110 | 0.171410 | ||||||||
\(550\) | −5.90203e108 | −0.00611382 | ||||||||
\(551\) | 1.32365e111 | 1.27389 | ||||||||
\(552\) | 3.77191e110 | 0.337310 | ||||||||
\(553\) | −9.06038e109 | −0.0752971 | ||||||||
\(554\) | −1.31609e111 | −1.01657 | ||||||||
\(555\) | 1.02824e111 | 0.738294 | ||||||||
\(556\) | 4.93220e110 | 0.329239 | ||||||||
\(557\) | −3.50511e110 | −0.217554 | −0.108777 | − | 0.994066i | \(-0.534693\pi\) | ||||
−0.108777 | + | 0.994066i | \(0.534693\pi\) | |||||||
\(558\) | 1.50999e111 | 0.871546 | ||||||||
\(559\) | −1.78273e110 | −0.0956992 | ||||||||
\(560\) | 5.21219e109 | 0.0260258 | ||||||||
\(561\) | 7.96790e109 | 0.0370124 | ||||||||
\(562\) | −2.58637e111 | −1.11782 | ||||||||
\(563\) | −2.55312e111 | −1.02679 | −0.513395 | − | 0.858152i | \(-0.671612\pi\) | ||||
−0.513395 | + | 0.858152i | \(0.671612\pi\) | |||||||
\(564\) | 3.37857e111 | 1.26453 | ||||||||
\(565\) | 1.16946e111 | 0.407403 | ||||||||
\(566\) | 1.94394e111 | 0.630403 | ||||||||
\(567\) | −5.21452e110 | −0.157435 | ||||||||
\(568\) | −6.17873e110 | −0.173697 | ||||||||
\(569\) | 2.41238e111 | 0.631538 | 0.315769 | − | 0.948836i | \(-0.397738\pi\) | ||||
0.315769 | + | 0.948836i | \(0.397738\pi\) | |||||||
\(570\) | 3.61947e111 | 0.882496 | ||||||||
\(571\) | −4.06873e111 | −0.924052 | −0.462026 | − | 0.886866i | \(-0.652877\pi\) | ||||
−0.462026 | + | 0.886866i | \(0.652877\pi\) | |||||||
\(572\) | 3.94277e108 | 0.000834185 0 | ||||||||
\(573\) | −2.98913e111 | −0.589227 | ||||||||
\(574\) | 3.21576e110 | 0.0590680 | ||||||||
\(575\) | 1.46825e111 | 0.251335 | ||||||||
\(576\) | 4.98640e110 | 0.0795567 | ||||||||
\(577\) | −6.19248e111 | −0.920967 | −0.460484 | − | 0.887668i | \(-0.652324\pi\) | ||||
−0.460484 | + | 0.887668i | \(0.652324\pi\) | |||||||
\(578\) | −1.38586e111 | −0.192151 | ||||||||
\(579\) | −1.37878e112 | −1.78243 | ||||||||
\(580\) | −3.59065e111 | −0.432851 | ||||||||
\(581\) | −1.60725e111 | −0.180696 | ||||||||
\(582\) | 3.80241e111 | 0.398729 | ||||||||
\(583\) | −1.15268e110 | −0.0112754 | ||||||||
\(584\) | −6.25266e111 | −0.570617 | ||||||||
\(585\) | −3.95760e110 | −0.0336992 | ||||||||
\(586\) | −8.15303e111 | −0.647837 | ||||||||
\(587\) | −9.44491e110 | −0.0700414 | −0.0350207 | − | 0.999387i | \(-0.511150\pi\) | ||||
−0.0350207 | + | 0.999387i | \(0.511150\pi\) | |||||||
\(588\) | −9.08962e111 | −0.629164 | ||||||||
\(589\) | 3.59110e112 | 2.32038 | ||||||||
\(590\) | 1.03551e112 | 0.624664 | ||||||||
\(591\) | 3.22999e112 | 1.81931 | ||||||||
\(592\) | 3.36892e111 | 0.177199 | ||||||||
\(593\) | 3.51703e112 | 1.72767 | 0.863836 | − | 0.503773i | \(-0.168055\pi\) | ||||
0.863836 | + | 0.503773i | \(0.168055\pi\) | |||||||
\(594\) | −1.83884e110 | −0.00843710 | ||||||||
\(595\) | −2.73906e111 | −0.117399 | ||||||||
\(596\) | −5.96329e111 | −0.238788 | ||||||||
\(597\) | −2.33721e112 | −0.874453 | ||||||||
\(598\) | −9.80847e110 | −0.0342928 | ||||||||
\(599\) | −8.52279e111 | −0.278481 | −0.139240 | − | 0.990259i | \(-0.544466\pi\) | ||||
−0.139240 | + | 0.990259i | \(0.544466\pi\) | |||||||
\(600\) | 4.99073e111 | 0.152419 | ||||||||
\(601\) | −1.13950e112 | −0.325312 | −0.162656 | − | 0.986683i | \(-0.552006\pi\) | ||||
−0.162656 | + | 0.986683i | \(0.552006\pi\) | |||||||
\(602\) | −4.98498e111 | −0.133047 | ||||||||
\(603\) | −1.62331e112 | −0.405089 | ||||||||
\(604\) | −1.22382e112 | −0.285576 | ||||||||
\(605\) | −3.72875e112 | −0.813712 | ||||||||
\(606\) | 2.28749e111 | 0.0466893 | ||||||||
\(607\) | 5.48765e112 | 1.04772 | 0.523859 | − | 0.851805i | \(-0.324492\pi\) | ||||
0.523859 | + | 0.851805i | \(0.324492\pi\) | |||||||
\(608\) | 1.18588e112 | 0.211809 | ||||||||
\(609\) | −1.04057e112 | −0.173889 | ||||||||
\(610\) | −9.91673e111 | −0.155064 | ||||||||
\(611\) | −8.78562e111 | −0.128559 | ||||||||
\(612\) | −2.62041e112 | −0.358869 | ||||||||
\(613\) | 3.54802e112 | 0.454817 | 0.227408 | − | 0.973799i | \(-0.426975\pi\) | ||||
0.227408 | + | 0.973799i | \(0.426975\pi\) | |||||||
\(614\) | −3.69339e112 | −0.443207 | ||||||||
\(615\) | −6.05772e112 | −0.680561 | ||||||||
\(616\) | 1.10250e110 | 0.00115974 | ||||||||
\(617\) | −9.42261e112 | −0.928159 | −0.464079 | − | 0.885794i | \(-0.653615\pi\) | ||||
−0.464079 | + | 0.885794i | \(0.653615\pi\) | |||||||
\(618\) | 9.33383e111 | 0.0861047 | ||||||||
\(619\) | 3.52629e111 | 0.0304682 | 0.0152341 | − | 0.999884i | \(-0.495151\pi\) | ||||
0.0152341 | + | 0.999884i | \(0.495151\pi\) | |||||||
\(620\) | −9.74156e112 | −0.788434 | ||||||||
\(621\) | 4.57451e112 | 0.346844 | ||||||||
\(622\) | 1.67628e113 | 1.19079 | ||||||||
\(623\) | 1.20577e112 | 0.0802599 | ||||||||
\(624\) | −3.33399e111 | −0.0207964 | ||||||||
\(625\) | −9.39837e112 | −0.549429 | ||||||||
\(626\) | 1.98377e113 | 1.08700 | ||||||||
\(627\) | 7.65602e111 | 0.0393249 | ||||||||
\(628\) | 1.41519e113 | 0.681471 | ||||||||
\(629\) | −1.77040e113 | −0.799321 | ||||||||
\(630\) | −1.10665e112 | −0.0468507 | ||||||||
\(631\) | −1.55289e113 | −0.616527 | −0.308263 | − | 0.951301i | \(-0.599748\pi\) | ||||
−0.308263 | + | 0.951301i | \(0.599748\pi\) | |||||||
\(632\) | 5.59199e112 | 0.208221 | ||||||||
\(633\) | 4.21098e113 | 1.47073 | ||||||||
\(634\) | 1.08138e113 | 0.354293 | ||||||||
\(635\) | −2.94306e112 | −0.0904615 | ||||||||
\(636\) | 9.74699e112 | 0.281098 | ||||||||
\(637\) | 2.36366e112 | 0.0639644 | ||||||||
\(638\) | −7.59506e111 | −0.0192883 | ||||||||
\(639\) | 1.31186e113 | 0.312682 | ||||||||
\(640\) | −3.21692e112 | −0.0719700 | ||||||||
\(641\) | 4.55438e113 | 0.956487 | 0.478244 | − | 0.878227i | \(-0.341274\pi\) | ||||
0.478244 | + | 0.878227i | \(0.341274\pi\) | |||||||
\(642\) | −5.01948e113 | −0.989669 | ||||||||
\(643\) | −8.10226e113 | −1.49990 | −0.749949 | − | 0.661496i | \(-0.769922\pi\) | ||||
−0.749949 | + | 0.661496i | \(0.769922\pi\) | |||||||
\(644\) | −2.74270e112 | −0.0476761 | ||||||||
\(645\) | 9.39050e113 | 1.53292 | ||||||||
\(646\) | −6.23191e113 | −0.955442 | ||||||||
\(647\) | −7.61202e113 | −1.09617 | −0.548083 | − | 0.836424i | \(-0.684642\pi\) | ||||
−0.548083 | + | 0.836424i | \(0.684642\pi\) | |||||||
\(648\) | 3.21836e113 | 0.435359 | ||||||||
\(649\) | 2.19034e112 | 0.0278356 | ||||||||
\(650\) | −1.29779e112 | −0.0154957 | ||||||||
\(651\) | −2.82312e113 | −0.316737 | ||||||||
\(652\) | 2.33978e113 | 0.246687 | ||||||||
\(653\) | 9.46822e113 | 0.938176 | 0.469088 | − | 0.883151i | \(-0.344583\pi\) | ||||
0.469088 | + | 0.883151i | \(0.344583\pi\) | |||||||
\(654\) | −1.43015e114 | −1.33194 | ||||||||
\(655\) | −4.22497e113 | −0.369872 | ||||||||
\(656\) | −1.98474e113 | −0.163342 | ||||||||
\(657\) | 1.32756e114 | 1.02720 | ||||||||
\(658\) | −2.45668e113 | −0.178731 | ||||||||
\(659\) | −1.13280e114 | −0.774986 | −0.387493 | − | 0.921873i | \(-0.626659\pi\) | ||||
−0.387493 | + | 0.921873i | \(0.626659\pi\) | |||||||
\(660\) | −2.07684e112 | −0.0133621 | ||||||||
\(661\) | −2.33352e114 | −1.41206 | −0.706029 | − | 0.708183i | \(-0.749515\pi\) | ||||
−0.706029 | + | 0.708183i | \(0.749515\pi\) | |||||||
\(662\) | 8.41785e111 | 0.00479129 | ||||||||
\(663\) | 1.75205e113 | 0.0938097 | ||||||||
\(664\) | 9.91981e113 | 0.499685 | ||||||||
\(665\) | −2.63185e113 | −0.124734 | ||||||||
\(666\) | −7.15285e113 | −0.318987 | ||||||||
\(667\) | 1.88943e114 | 0.792930 | ||||||||
\(668\) | 3.20924e113 | 0.126752 | ||||||||
\(669\) | 4.07874e114 | 1.51624 | ||||||||
\(670\) | 1.04726e114 | 0.366459 | ||||||||
\(671\) | −2.09762e112 | −0.00690979 | ||||||||
\(672\) | −9.32268e112 | −0.0289125 | ||||||||
\(673\) | 3.04730e114 | 0.889827 | 0.444914 | − | 0.895573i | \(-0.353234\pi\) | ||||
0.444914 | + | 0.895573i | \(0.353234\pi\) | |||||||
\(674\) | 4.72092e114 | 1.29808 | ||||||||
\(675\) | 6.05266e113 | 0.156727 | ||||||||
\(676\) | −2.04160e114 | −0.497886 | ||||||||
\(677\) | 1.93415e114 | 0.444272 | 0.222136 | − | 0.975016i | \(-0.428697\pi\) | ||||
0.222136 | + | 0.975016i | \(0.428697\pi\) | |||||||
\(678\) | −2.09174e114 | −0.452590 | ||||||||
\(679\) | −2.76488e113 | −0.0563572 | ||||||||
\(680\) | 1.69053e114 | 0.324647 | ||||||||
\(681\) | −9.55998e114 | −1.72981 | ||||||||
\(682\) | −2.06057e113 | −0.0351334 | ||||||||
\(683\) | 3.94780e114 | 0.634331 | 0.317166 | − | 0.948370i | \(-0.397269\pi\) | ||||
0.317166 | + | 0.948370i | \(0.397269\pi\) | |||||||
\(684\) | −2.51784e114 | −0.381291 | ||||||||
\(685\) | −1.15517e114 | −0.164884 | ||||||||
\(686\) | 1.33286e114 | 0.179333 | ||||||||
\(687\) | −1.93064e115 | −2.44881 | ||||||||
\(688\) | 3.07669e114 | 0.367919 | ||||||||
\(689\) | −2.53460e113 | −0.0285780 | ||||||||
\(690\) | 5.16659e114 | 0.549308 | ||||||||
\(691\) | −1.75270e115 | −1.75730 | −0.878649 | − | 0.477468i | \(-0.841555\pi\) | ||||
−0.878649 | + | 0.477468i | \(0.841555\pi\) | |||||||
\(692\) | −5.10552e114 | −0.482773 | ||||||||
\(693\) | −2.34082e112 | −0.00208772 | ||||||||
\(694\) | −2.07955e113 | −0.0174949 | ||||||||
\(695\) | 6.75589e114 | 0.536164 | ||||||||
\(696\) | 6.42234e114 | 0.480861 | ||||||||
\(697\) | 1.04300e115 | 0.736815 | ||||||||
\(698\) | 1.51284e115 | 1.00843 | ||||||||
\(699\) | −4.69273e113 | −0.0295189 | ||||||||
\(700\) | −3.62894e113 | −0.0215432 | ||||||||
\(701\) | 6.82707e114 | 0.382521 | 0.191260 | − | 0.981539i | \(-0.438743\pi\) | ||||
0.191260 | + | 0.981539i | \(0.438743\pi\) | |||||||
\(702\) | −4.04339e113 | −0.0213842 | ||||||||
\(703\) | −1.70111e115 | −0.849261 | ||||||||
\(704\) | −6.80454e112 | −0.00320705 | ||||||||
\(705\) | 4.62780e115 | 2.05928 | ||||||||
\(706\) | −3.06029e115 | −1.28580 | ||||||||
\(707\) | −1.66332e113 | −0.00659917 | ||||||||
\(708\) | −1.85214e115 | −0.693948 | ||||||||
\(709\) | 2.03694e114 | 0.0720783 | 0.0360392 | − | 0.999350i | \(-0.488526\pi\) | ||||
0.0360392 | + | 0.999350i | \(0.488526\pi\) | |||||||
\(710\) | −8.46333e114 | −0.282864 | ||||||||
\(711\) | −1.18729e115 | −0.374832 | ||||||||
\(712\) | −7.44192e114 | −0.221945 | ||||||||
\(713\) | 5.12610e115 | 1.44431 | ||||||||
\(714\) | 4.89917e114 | 0.130420 | ||||||||
\(715\) | 5.40062e112 | 0.00135847 | ||||||||
\(716\) | −2.99395e115 | −0.711652 | ||||||||
\(717\) | 7.69456e115 | 1.72845 | ||||||||
\(718\) | 5.60618e115 | 1.19022 | ||||||||
\(719\) | −5.76168e115 | −1.15619 | −0.578095 | − | 0.815969i | \(-0.696204\pi\) | ||||
−0.578095 | + | 0.815969i | \(0.696204\pi\) | |||||||
\(720\) | 6.83013e114 | 0.129558 | ||||||||
\(721\) | −6.78698e113 | −0.0121702 | ||||||||
\(722\) | −1.81697e115 | −0.308029 | ||||||||
\(723\) | 4.43080e115 | 0.710201 | ||||||||
\(724\) | −2.79967e115 | −0.424321 | ||||||||
\(725\) | 2.49996e115 | 0.358297 | ||||||||
\(726\) | 6.66936e115 | 0.903963 | ||||||||
\(727\) | −1.53192e116 | −1.96378 | −0.981889 | − | 0.189456i | \(-0.939328\pi\) | ||||
−0.981889 | + | 0.189456i | \(0.939328\pi\) | |||||||
\(728\) | 2.42427e113 | 0.00293941 | ||||||||
\(729\) | −1.64605e115 | −0.188789 | ||||||||
\(730\) | −8.56460e115 | −0.929247 | ||||||||
\(731\) | −1.61683e116 | −1.65963 | ||||||||
\(732\) | 1.77374e115 | 0.172262 | ||||||||
\(733\) | 1.27965e116 | 1.17592 | 0.587961 | − | 0.808889i | \(-0.299931\pi\) | ||||
0.587961 | + | 0.808889i | \(0.299931\pi\) | |||||||
\(734\) | −8.41312e115 | −0.731588 | ||||||||
\(735\) | −1.24505e116 | −1.02459 | ||||||||
\(736\) | 1.69277e115 | 0.131840 | ||||||||
\(737\) | 2.21520e114 | 0.0163298 | ||||||||
\(738\) | 4.21398e115 | 0.294042 | ||||||||
\(739\) | 3.22829e115 | 0.213242 | 0.106621 | − | 0.994300i | \(-0.465997\pi\) | ||||
0.106621 | + | 0.994300i | \(0.465997\pi\) | |||||||
\(740\) | 4.61458e115 | 0.288568 | ||||||||
\(741\) | 1.68347e115 | 0.0996707 | ||||||||
\(742\) | −7.08740e114 | −0.0397309 | ||||||||
\(743\) | 2.55795e116 | 1.35783 | 0.678913 | − | 0.734219i | \(-0.262451\pi\) | ||||
0.678913 | + | 0.734219i | \(0.262451\pi\) | |||||||
\(744\) | 1.74241e116 | 0.875882 | ||||||||
\(745\) | −8.16823e115 | −0.388865 | ||||||||
\(746\) | −1.21291e116 | −0.546897 | ||||||||
\(747\) | −2.10616e116 | −0.899513 | ||||||||
\(748\) | 3.57586e114 | 0.0144666 | ||||||||
\(749\) | 3.64985e115 | 0.139882 | ||||||||
\(750\) | 2.71210e116 | 0.984748 | ||||||||
\(751\) | −3.19459e116 | −1.09900 | −0.549499 | − | 0.835494i | \(-0.685182\pi\) | ||||
−0.549499 | + | 0.835494i | \(0.685182\pi\) | |||||||
\(752\) | 1.51625e116 | 0.494251 | ||||||||
\(753\) | 6.70849e116 | 2.07218 | ||||||||
\(754\) | −1.67006e115 | −0.0488870 | ||||||||
\(755\) | −1.67633e116 | −0.465059 | ||||||||
\(756\) | −1.13064e115 | −0.0297297 | ||||||||
\(757\) | −2.48299e116 | −0.618860 | −0.309430 | − | 0.950922i | \(-0.600138\pi\) | ||||
−0.309430 | + | 0.950922i | \(0.600138\pi\) | |||||||
\(758\) | 2.51211e116 | 0.593520 | ||||||||
\(759\) | 1.09285e115 | 0.0244777 | ||||||||
\(760\) | 1.62436e116 | 0.344930 | ||||||||
\(761\) | 6.23857e116 | 1.25605 | 0.628025 | − | 0.778194i | \(-0.283864\pi\) | ||||
0.628025 | + | 0.778194i | \(0.283864\pi\) | |||||||
\(762\) | 5.26405e115 | 0.100495 | ||||||||
\(763\) | 1.03992e116 | 0.188259 | ||||||||
\(764\) | −1.34147e116 | −0.230304 | ||||||||
\(765\) | −3.58931e116 | −0.584417 | ||||||||
\(766\) | −8.38785e116 | −1.29535 | ||||||||
\(767\) | 4.81630e115 | 0.0705507 | ||||||||
\(768\) | 5.75389e115 | 0.0799525 | ||||||||
\(769\) | −8.17099e116 | −1.07710 | −0.538552 | − | 0.842592i | \(-0.681029\pi\) | ||||
−0.538552 | + | 0.842592i | \(0.681029\pi\) | |||||||
\(770\) | 1.51015e114 | 0.00188863 | ||||||||
\(771\) | −1.72216e117 | −2.04348 | ||||||||
\(772\) | −6.18772e116 | −0.696675 | ||||||||
\(773\) | 1.05233e117 | 1.12431 | 0.562153 | − | 0.827033i | \(-0.309973\pi\) | ||||
0.562153 | + | 0.827033i | \(0.309973\pi\) | |||||||
\(774\) | −6.53240e116 | −0.662314 | ||||||||
\(775\) | 6.78249e116 | 0.652634 | ||||||||
\(776\) | 1.70646e116 | 0.155846 | ||||||||
\(777\) | 1.33731e116 | 0.115926 | ||||||||
\(778\) | −7.41915e116 | −0.610493 | ||||||||
\(779\) | 1.00218e117 | 0.782849 | ||||||||
\(780\) | −4.56673e115 | −0.0338668 | ||||||||
\(781\) | −1.79019e115 | −0.0126047 | ||||||||
\(782\) | −8.89571e116 | −0.594713 | ||||||||
\(783\) | 7.78889e116 | 0.494452 | ||||||||
\(784\) | −4.07927e116 | −0.245913 | ||||||||
\(785\) | 1.93845e117 | 1.10977 | ||||||||
\(786\) | 7.55692e116 | 0.410896 | ||||||||
\(787\) | −2.70781e117 | −1.39843 | −0.699216 | − | 0.714910i | \(-0.746468\pi\) | ||||
−0.699216 | + | 0.714910i | \(0.746468\pi\) | |||||||
\(788\) | 1.44957e117 | 0.711092 | ||||||||
\(789\) | 3.53892e117 | 1.64912 | ||||||||
\(790\) | 7.65964e116 | 0.339087 | ||||||||
\(791\) | 1.52098e116 | 0.0639700 | ||||||||
\(792\) | 1.44473e115 | 0.00577322 | ||||||||
\(793\) | −4.61242e115 | −0.0175132 | ||||||||
\(794\) | 2.74911e117 | 0.991885 | ||||||||
\(795\) | 1.33510e117 | 0.457766 | ||||||||
\(796\) | −1.04890e117 | −0.341786 | ||||||||
\(797\) | −2.00940e117 | −0.622306 | −0.311153 | − | 0.950360i | \(-0.600715\pi\) | ||||
−0.311153 | + | 0.950360i | \(0.600715\pi\) | |||||||
\(798\) | 4.70741e116 | 0.138569 | ||||||||
\(799\) | −7.96804e117 | −2.22950 | ||||||||
\(800\) | 2.23976e116 | 0.0595739 | ||||||||
\(801\) | 1.58006e117 | 0.399537 | ||||||||
\(802\) | −7.87217e115 | −0.0189249 | ||||||||
\(803\) | −1.81161e116 | −0.0414082 | ||||||||
\(804\) | −1.87317e117 | −0.407105 | ||||||||
\(805\) | −3.75682e116 | −0.0776403 | ||||||||
\(806\) | −4.53095e116 | −0.0890471 | ||||||||
\(807\) | 3.61466e117 | 0.675599 | ||||||||
\(808\) | 1.02659e116 | 0.0182489 | ||||||||
\(809\) | 6.39070e117 | 1.08052 | 0.540261 | − | 0.841498i | \(-0.318326\pi\) | ||||
0.540261 | + | 0.841498i | \(0.318326\pi\) | |||||||
\(810\) | 4.40836e117 | 0.708980 | ||||||||
\(811\) | −1.12578e118 | −1.72230 | −0.861151 | − | 0.508350i | \(-0.830256\pi\) | ||||
−0.861151 | + | 0.508350i | \(0.830256\pi\) | |||||||
\(812\) | −4.66993e116 | −0.0679659 | ||||||||
\(813\) | 6.23559e117 | 0.863397 | ||||||||
\(814\) | 9.76093e115 | 0.0128589 | ||||||||
\(815\) | 3.20492e117 | 0.401729 | ||||||||
\(816\) | −3.02373e117 | −0.360655 | ||||||||
\(817\) | −1.55355e118 | −1.76332 | ||||||||
\(818\) | 5.70124e117 | 0.615829 | ||||||||
\(819\) | −5.14718e115 | −0.00529141 | ||||||||
\(820\) | −2.71860e117 | −0.266002 | ||||||||
\(821\) | −1.95190e118 | −1.81785 | −0.908927 | − | 0.416955i | \(-0.863097\pi\) | ||||
−0.908927 | + | 0.416955i | \(0.863097\pi\) | |||||||
\(822\) | 2.06617e117 | 0.183171 | ||||||||
\(823\) | −7.18378e117 | −0.606261 | −0.303131 | − | 0.952949i | \(-0.598032\pi\) | ||||
−0.303131 | + | 0.952949i | \(0.598032\pi\) | |||||||
\(824\) | 4.18887e116 | 0.0336546 | ||||||||
\(825\) | 1.44599e116 | 0.0110606 | ||||||||
\(826\) | 1.34676e117 | 0.0980841 | ||||||||
\(827\) | 1.72528e118 | 1.19643 | 0.598214 | − | 0.801336i | \(-0.295877\pi\) | ||||
0.598214 | + | 0.801336i | \(0.295877\pi\) | |||||||
\(828\) | −3.59408e117 | −0.237333 | ||||||||
\(829\) | −2.41901e118 | −1.52118 | −0.760589 | − | 0.649234i | \(-0.775090\pi\) | ||||
−0.760589 | + | 0.649234i | \(0.775090\pi\) | |||||||
\(830\) | 1.35877e118 | 0.813734 | ||||||||
\(831\) | 3.22439e118 | 1.83910 | ||||||||
\(832\) | −1.49624e116 | −0.00812842 | ||||||||
\(833\) | 2.14370e118 | 1.10928 | ||||||||
\(834\) | −1.20838e118 | −0.595632 | ||||||||
\(835\) | 4.39587e117 | 0.206416 | ||||||||
\(836\) | 3.43590e116 | 0.0153704 | ||||||||
\(837\) | 2.11316e118 | 0.900639 | ||||||||
\(838\) | −1.24313e118 | −0.504817 | ||||||||
\(839\) | 3.03813e118 | 1.17556 | 0.587782 | − | 0.809019i | \(-0.300001\pi\) | ||||
0.587782 | + | 0.809019i | \(0.300001\pi\) | |||||||
\(840\) | −1.27698e117 | −0.0470838 | ||||||||
\(841\) | 3.71065e117 | 0.130380 | ||||||||
\(842\) | −2.77550e118 | −0.929397 | ||||||||
\(843\) | 6.33657e118 | 2.02226 | ||||||||
\(844\) | 1.88982e118 | 0.574845 | ||||||||
\(845\) | −2.79649e118 | −0.810804 | ||||||||
\(846\) | −3.21928e118 | −0.889731 | ||||||||
\(847\) | −4.84954e117 | −0.127768 | ||||||||
\(848\) | 4.37429e117 | 0.109869 | ||||||||
\(849\) | −4.76262e118 | −1.14047 | ||||||||
\(850\) | −1.17702e118 | −0.268730 | ||||||||
\(851\) | −2.42824e118 | −0.528620 | ||||||||
\(852\) | 1.51378e118 | 0.314238 | ||||||||
\(853\) | −6.30022e118 | −1.24715 | −0.623577 | − | 0.781762i | \(-0.714321\pi\) | ||||
−0.623577 | + | 0.781762i | \(0.714321\pi\) | |||||||
\(854\) | −1.28975e117 | −0.0243479 | ||||||||
\(855\) | −3.44882e118 | −0.620930 | ||||||||
\(856\) | −2.25266e118 | −0.386819 | ||||||||
\(857\) | 3.80553e118 | 0.623292 | 0.311646 | − | 0.950198i | \(-0.399120\pi\) | ||||
0.311646 | + | 0.950198i | \(0.399120\pi\) | |||||||
\(858\) | −9.65972e115 | −0.00150914 | ||||||||
\(859\) | 2.11862e118 | 0.315740 | 0.157870 | − | 0.987460i | \(-0.449537\pi\) | ||||
0.157870 | + | 0.987460i | \(0.449537\pi\) | |||||||
\(860\) | 4.21430e118 | 0.599154 | ||||||||
\(861\) | −7.87855e117 | −0.106861 | ||||||||
\(862\) | −2.46009e117 | −0.0318351 | ||||||||
\(863\) | −5.31849e118 | −0.656676 | −0.328338 | − | 0.944560i | \(-0.606489\pi\) | ||||
−0.328338 | + | 0.944560i | \(0.606489\pi\) | |||||||
\(864\) | 6.97820e117 | 0.0822123 | ||||||||
\(865\) | −6.99330e118 | −0.786194 | ||||||||
\(866\) | 5.09863e118 | 0.546989 | ||||||||
\(867\) | 3.39534e118 | 0.347624 | ||||||||
\(868\) | −1.26697e118 | −0.123799 | ||||||||
\(869\) | 1.62019e117 | 0.0151101 | ||||||||
\(870\) | 8.79701e118 | 0.783079 | ||||||||
\(871\) | 4.87097e117 | 0.0413886 | ||||||||
\(872\) | −6.41829e118 | −0.520597 | ||||||||
\(873\) | −3.62314e118 | −0.280548 | ||||||||
\(874\) | −8.54752e118 | −0.631869 | ||||||||
\(875\) | −1.97207e118 | −0.139186 | ||||||||
\(876\) | 1.53189e119 | 1.03231 | ||||||||
\(877\) | −5.34719e118 | −0.344066 | −0.172033 | − | 0.985091i | \(-0.555034\pi\) | ||||
−0.172033 | + | 0.985091i | \(0.555034\pi\) | |||||||
\(878\) | 9.52985e118 | 0.585542 | ||||||||
\(879\) | 1.99748e119 | 1.17201 | ||||||||
\(880\) | −9.32054e116 | −0.00522267 | ||||||||
\(881\) | 3.52621e119 | 1.88705 | 0.943527 | − | 0.331296i | \(-0.107486\pi\) | ||||
0.943527 | + | 0.331296i | \(0.107486\pi\) | |||||||
\(882\) | 8.66107e118 | 0.442684 | ||||||||
\(883\) | 3.55834e118 | 0.173716 | 0.0868578 | − | 0.996221i | \(-0.472317\pi\) | ||||
0.0868578 | + | 0.996221i | \(0.472317\pi\) | |||||||
\(884\) | 7.86289e117 | 0.0366662 | ||||||||
\(885\) | −2.53697e119 | −1.13009 | ||||||||
\(886\) | −1.09481e119 | −0.465877 | ||||||||
\(887\) | 1.29338e119 | 0.525801 | 0.262900 | − | 0.964823i | \(-0.415321\pi\) | ||||
0.262900 | + | 0.964823i | \(0.415321\pi\) | |||||||
\(888\) | −8.25379e118 | −0.320574 | ||||||||
\(889\) | −3.82769e117 | −0.0142042 | ||||||||
\(890\) | −1.01936e119 | −0.361436 | ||||||||
\(891\) | 9.32472e117 | 0.0315928 | ||||||||
\(892\) | 1.83047e119 | 0.592633 | ||||||||
\(893\) | −7.65616e119 | −2.36879 | ||||||||
\(894\) | 1.46100e119 | 0.431996 | ||||||||
\(895\) | −4.10097e119 | −1.15892 | ||||||||
\(896\) | −4.18387e117 | −0.0113007 | ||||||||
\(897\) | 2.40306e118 | 0.0620398 | ||||||||
\(898\) | −4.35701e119 | −1.07522 | ||||||||
\(899\) | 8.72808e119 | 2.05898 | ||||||||
\(900\) | −4.75543e118 | −0.107243 | ||||||||
\(901\) | −2.29874e119 | −0.495604 | ||||||||
\(902\) | −5.75049e117 | −0.0118533 | ||||||||
\(903\) | 1.22131e119 | 0.240698 | ||||||||
\(904\) | −9.38738e118 | −0.176898 | ||||||||
\(905\) | −3.83485e119 | −0.691005 | ||||||||
\(906\) | 2.99834e119 | 0.516641 | ||||||||
\(907\) | 4.19243e119 | 0.690830 | 0.345415 | − | 0.938450i | \(-0.387738\pi\) | ||||
0.345415 | + | 0.938450i | \(0.387738\pi\) | |||||||
\(908\) | −4.29036e119 | −0.676109 | ||||||||
\(909\) | −2.17964e118 | −0.0328509 | ||||||||
\(910\) | 3.32064e117 | 0.00478681 | ||||||||
\(911\) | 9.31240e119 | 1.28401 | 0.642003 | − | 0.766702i | \(-0.278104\pi\) | ||||
0.642003 | + | 0.766702i | \(0.278104\pi\) | |||||||
\(912\) | −2.90538e119 | −0.383188 | ||||||||
\(913\) | 2.87411e118 | 0.0362608 | ||||||||
\(914\) | −4.74667e119 | −0.572886 | ||||||||
\(915\) | 2.42958e119 | 0.280528 | ||||||||
\(916\) | −8.66441e119 | −0.957133 | ||||||||
\(917\) | −5.49492e118 | −0.0580769 | ||||||||
\(918\) | −3.66712e119 | −0.370849 | ||||||||
\(919\) | −6.05994e119 | −0.586395 | −0.293197 | − | 0.956052i | \(-0.594719\pi\) | ||||
−0.293197 | + | 0.956052i | \(0.594719\pi\) | |||||||
\(920\) | 2.31868e119 | 0.214701 | ||||||||
\(921\) | 9.04874e119 | 0.801813 | ||||||||
\(922\) | 8.97293e119 | 0.760908 | ||||||||
\(923\) | −3.93642e118 | −0.0319472 | ||||||||
\(924\) | −2.70110e117 | −0.00209810 | ||||||||
\(925\) | −3.21287e119 | −0.238865 | ||||||||
\(926\) | 7.28600e119 | 0.518494 | ||||||||
\(927\) | −8.89376e118 | −0.0605838 | ||||||||
\(928\) | 2.88224e119 | 0.187948 | ||||||||
\(929\) | 1.78670e120 | 1.11536 | 0.557681 | − | 0.830055i | \(-0.311691\pi\) | ||||
0.557681 | + | 0.830055i | \(0.311691\pi\) | |||||||
\(930\) | 2.38666e120 | 1.42637 | ||||||||
\(931\) | 2.05979e120 | 1.17859 | ||||||||
\(932\) | −2.10602e118 | −0.0115377 | ||||||||
\(933\) | −4.10686e120 | −2.15429 | ||||||||
\(934\) | 8.88311e119 | 0.446187 | ||||||||
\(935\) | 4.89804e118 | 0.0235588 | ||||||||
\(936\) | 3.17680e118 | 0.0146325 | ||||||||
\(937\) | 9.18961e119 | 0.405363 | 0.202681 | − | 0.979245i | \(-0.435034\pi\) | ||||
0.202681 | + | 0.979245i | \(0.435034\pi\) | |||||||
\(938\) | 1.36205e119 | 0.0575410 | ||||||||
\(939\) | −4.86020e120 | −1.96652 | ||||||||
\(940\) | 2.07688e120 | 0.804885 | ||||||||
\(941\) | 8.77906e118 | 0.0325888 | 0.0162944 | − | 0.999867i | \(-0.494813\pi\) | ||||
0.0162944 | + | 0.999867i | \(0.494813\pi\) | |||||||
\(942\) | −3.46718e120 | −1.23286 | ||||||||
\(943\) | 1.43055e120 | 0.487283 | ||||||||
\(944\) | −8.31210e119 | −0.271235 | ||||||||
\(945\) | −1.54869e119 | −0.0484147 | ||||||||
\(946\) | 8.91424e118 | 0.0266989 | ||||||||
\(947\) | −5.56825e120 | −1.59788 | −0.798941 | − | 0.601409i | \(-0.794606\pi\) | ||||
−0.798941 | + | 0.601409i | \(0.794606\pi\) | |||||||
\(948\) | −1.37003e120 | −0.376697 | ||||||||
\(949\) | −3.98352e119 | −0.104951 | ||||||||
\(950\) | −1.13095e120 | −0.285520 | ||||||||
\(951\) | −2.64935e120 | −0.640957 | ||||||||
\(952\) | 2.19867e119 | 0.0509757 | ||||||||
\(953\) | 4.55605e119 | 0.101234 | 0.0506169 | − | 0.998718i | \(-0.483881\pi\) | ||||
0.0506169 | + | 0.998718i | \(0.483881\pi\) | |||||||
\(954\) | −9.28744e119 | −0.197782 | ||||||||
\(955\) | −1.83749e120 | −0.375048 | ||||||||
\(956\) | 3.45319e120 | 0.675579 | ||||||||
\(957\) | 1.86078e119 | 0.0348948 | ||||||||
\(958\) | −4.47842e119 | −0.0805047 | ||||||||
\(959\) | −1.50239e119 | −0.0258898 | ||||||||
\(960\) | 7.88140e119 | 0.130202 | ||||||||
\(961\) | 1.73657e121 | 2.75040 | ||||||||
\(962\) | 2.14631e119 | 0.0325914 | ||||||||
\(963\) | 4.78282e120 | 0.696338 | ||||||||
\(964\) | 1.98847e120 | 0.277587 | ||||||||
\(965\) | −8.47564e120 | −1.13453 | ||||||||
\(966\) | 6.71957e119 | 0.0862517 | ||||||||
\(967\) | 5.91369e120 | 0.727924 | 0.363962 | − | 0.931414i | \(-0.381424\pi\) | ||||
0.363962 | + | 0.931414i | \(0.381424\pi\) | |||||||
\(968\) | 2.99310e120 | 0.353321 | ||||||||
\(969\) | 1.52681e121 | 1.72851 | ||||||||
\(970\) | 2.33743e120 | 0.253795 | ||||||||
\(971\) | −1.75570e121 | −1.82840 | −0.914202 | − | 0.405258i | \(-0.867182\pi\) | ||||
−0.914202 | + | 0.405258i | \(0.867182\pi\) | |||||||
\(972\) | −5.55702e120 | −0.555084 | ||||||||
\(973\) | 8.78658e119 | 0.0841880 | ||||||||
\(974\) | −8.99723e120 | −0.826934 | ||||||||
\(975\) | 3.17955e119 | 0.0280336 | ||||||||
\(976\) | 7.96024e119 | 0.0673300 | ||||||||
\(977\) | 3.67319e120 | 0.298067 | 0.149034 | − | 0.988832i | \(-0.452384\pi\) | ||||
0.149034 | + | 0.988832i | \(0.452384\pi\) | |||||||
\(978\) | −5.73241e120 | −0.446287 | ||||||||
\(979\) | −2.15618e119 | −0.0161060 | ||||||||
\(980\) | −5.58759e120 | −0.400469 | ||||||||
\(981\) | 1.36273e121 | 0.937160 | ||||||||
\(982\) | 5.04344e119 | 0.0332822 | ||||||||
\(983\) | −6.03863e120 | −0.382403 | −0.191201 | − | 0.981551i | \(-0.561238\pi\) | ||||
−0.191201 | + | 0.981551i | \(0.561238\pi\) | |||||||
\(984\) | 4.86258e120 | 0.295505 | ||||||||
\(985\) | 1.98554e121 | 1.15801 | ||||||||
\(986\) | −1.51465e121 | −0.847807 | ||||||||
\(987\) | 6.01883e120 | 0.323346 | ||||||||
\(988\) | 7.55513e119 | 0.0389570 | ||||||||
\(989\) | −2.21761e121 | −1.09758 | ||||||||
\(990\) | 1.97893e119 | 0.00940166 | ||||||||
\(991\) | −1.08669e121 | −0.495591 | −0.247796 | − | 0.968812i | \(-0.579706\pi\) | ||||
−0.247796 | + | 0.968812i | \(0.579706\pi\) | |||||||
\(992\) | 7.81964e120 | 0.342345 | ||||||||
\(993\) | −2.06236e119 | −0.00866801 | ||||||||
\(994\) | −1.10072e120 | −0.0444151 | ||||||||
\(995\) | −1.43673e121 | −0.556597 | ||||||||
\(996\) | −2.43033e121 | −0.903988 | ||||||||
\(997\) | −3.79923e121 | −1.35688 | −0.678441 | − | 0.734655i | \(-0.737344\pi\) | ||||
−0.678441 | + | 0.734655i | \(0.737344\pi\) | |||||||
\(998\) | 1.42503e121 | 0.488693 | ||||||||
\(999\) | −1.00100e121 | −0.329635 |
(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 | 2.82.a.a.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.82.a.a.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial |