Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,12,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(6.14674544448\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 48 x^{8} + 8836 x^{7} - 92554 x^{6} - 2200342 x^{5} - 88894588 x^{4} + 2040335460 x^{3} + 7439251985 x^{2} - 747501940689 x + 34431558027300 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Root | \(7.36621 - 21.0240i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.12.b.a.5.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.7324 | − | 42.0479i | 0.369738 | − | 0.929136i | ||||
\(3\) | 284.352i | 0.675600i | 0.941218 | + | 0.337800i | \(0.109683\pi\) | ||||
−0.941218 | + | 0.337800i | \(0.890317\pi\) | |||||||
\(4\) | −1488.05 | − | 1407.13i | −0.726588 | − | 0.687073i | ||||
\(5\) | − | 10467.0i | − | 1.49792i | −0.662615 | − | 0.748961i | \(-0.730553\pi\) | ||
0.662615 | − | 0.748961i | \(-0.269447\pi\) | |||||||
\(6\) | 11956.4 | + | 4757.90i | 0.627725 | + | 0.249795i | ||||
\(7\) | −70503.2 | −1.58551 | −0.792756 | − | 0.609539i | \(-0.791354\pi\) | ||||
−0.792756 | + | 0.609539i | \(0.791354\pi\) | |||||||
\(8\) | −84065.4 | + | 39024.9i | −0.907032 | + | 0.421063i | ||||
\(9\) | 96290.8 | 0.543564 | ||||||||
\(10\) | −440117. | − | 175139.i | −1.39177 | − | 0.553838i | ||||
\(11\) | − | 177453.i | − | 0.332218i | −0.986107 | − | 0.166109i | \(-0.946880\pi\) | ||
0.986107 | − | 0.166109i | \(-0.0531203\pi\) | |||||||
\(12\) | 400120. | − | 423131.i | 0.464187 | − | 0.490883i | ||||
\(13\) | − | 1.12148e6i | − | 0.837726i | −0.908050 | − | 0.418863i | \(-0.862429\pi\) | ||
0.908050 | − | 0.418863i | \(-0.137571\pi\) | |||||||
\(14\) | −1.17969e6 | + | 2.96451e6i | −0.586223 | + | 1.47316i | ||||
\(15\) | 2.97633e6 | 1.01200 | ||||||||
\(16\) | 234297. | + | 4.18775e6i | 0.0558607 | + | 0.998439i | ||||
\(17\) | 6.79913e6 | 1.16141 | 0.580704 | − | 0.814115i | \(-0.302778\pi\) | ||||
0.580704 | + | 0.814115i | \(0.302778\pi\) | |||||||
\(18\) | 1.61118e6 | − | 4.04882e6i | 0.200976 | − | 0.505045i | ||||
\(19\) | − | 3.43350e6i | − | 0.318121i | −0.987269 | − | 0.159060i | \(-0.949154\pi\) | ||
0.987269 | − | 0.159060i | \(-0.0508465\pi\) | |||||||
\(20\) | −1.47284e7 | + | 1.55755e7i | −1.02918 | + | 1.08837i | ||||
\(21\) | − | 2.00477e7i | − | 1.07117i | ||||||
\(22\) | −7.46151e6 | − | 2.96921e6i | −0.308675 | − | 0.122833i | ||||
\(23\) | 2.44952e7 | 0.793558 | 0.396779 | − | 0.917914i | \(-0.370128\pi\) | ||||
0.396779 | + | 0.917914i | \(0.370128\pi\) | |||||||
\(24\) | −1.10968e7 | − | 2.39042e7i | −0.284470 | − | 0.612791i | ||||
\(25\) | −6.07308e7 | −1.24377 | ||||||||
\(26\) | −4.71557e7 | − | 1.87650e7i | −0.778361 | − | 0.309739i | ||||
\(27\) | 7.77527e7i | 1.04283i | ||||||||
\(28\) | 1.04912e8 | + | 9.92068e7i | 1.15201 | + | 1.08936i | ||||
\(29\) | − | 6.35956e7i | − | 0.575756i | −0.957667 | − | 0.287878i | \(-0.907050\pi\) | ||
0.957667 | − | 0.287878i | \(-0.0929497\pi\) | |||||||
\(30\) | 4.98012e7 | − | 1.25148e8i | 0.374173 | − | 0.940282i | ||||
\(31\) | −8.31656e7 | −0.521740 | −0.260870 | − | 0.965374i | \(-0.584009\pi\) | ||||
−0.260870 | + | 0.965374i | \(0.584009\pi\) | |||||||
\(32\) | 1.80007e8 | + | 6.02196e7i | 0.948339 | + | 0.317258i | ||||
\(33\) | 5.04591e7 | 0.224446 | ||||||||
\(34\) | 1.13766e8 | − | 2.85889e8i | 0.429416 | − | 1.07911i | ||||
\(35\) | 7.37960e8i | 2.37497i | ||||||||
\(36\) | −1.43286e8 | − | 1.35493e8i | −0.394947 | − | 0.373468i | ||||
\(37\) | − | 4.05150e8i | − | 0.960520i | −0.877126 | − | 0.480260i | \(-0.840542\pi\) | ||
0.877126 | − | 0.480260i | \(-0.159458\pi\) | |||||||
\(38\) | −1.44371e8 | − | 5.74507e7i | −0.295578 | − | 0.117621i | ||||
\(39\) | 3.18895e8 | 0.565968 | ||||||||
\(40\) | 4.08475e8 | + | 8.79916e8i | 0.630718 | + | 1.35866i | ||||
\(41\) | −1.21207e9 | −1.63386 | −0.816931 | − | 0.576735i | \(-0.804327\pi\) | ||||
−0.816931 | + | 0.576735i | \(0.804327\pi\) | |||||||
\(42\) | −8.42965e8 | − | 3.35447e8i | −0.995265 | − | 0.396053i | ||||
\(43\) | − | 8.44416e8i | − | 0.875951i | −0.898987 | − | 0.437975i | \(-0.855696\pi\) | ||
0.898987 | − | 0.437975i | \(-0.144304\pi\) | |||||||
\(44\) | −2.49698e8 | + | 2.64059e8i | −0.228258 | + | 0.241385i | ||||
\(45\) | − | 1.00788e9i | − | 0.814216i | ||||||
\(46\) | 4.09865e8 | − | 1.02997e9i | 0.293408 | − | 0.737324i | ||||
\(47\) | 1.31838e9 | 0.838498 | 0.419249 | − | 0.907871i | \(-0.362293\pi\) | ||||
0.419249 | + | 0.907871i | \(0.362293\pi\) | |||||||
\(48\) | −1.19080e9 | + | 6.66229e7i | −0.674545 | + | 0.0377395i | ||||
\(49\) | 2.99337e9 | 1.51385 | ||||||||
\(50\) | −1.01617e9 | + | 2.55360e9i | −0.459868 | + | 1.15563i | ||||
\(51\) | 1.93335e9i | 0.784647i | ||||||||
\(52\) | −1.57806e9 | + | 1.66882e9i | −0.575579 | + | 0.608682i | ||||
\(53\) | − | 1.71718e8i | − | 0.0564025i | −0.999602 | − | 0.0282013i | \(-0.991022\pi\) | ||
0.999602 | − | 0.0282013i | \(-0.00897793\pi\) | |||||||
\(54\) | 3.26934e9 | + | 1.30099e9i | 0.968933 | + | 0.385574i | ||||
\(55\) | −1.85740e9 | −0.497636 | ||||||||
\(56\) | 5.92688e9 | − | 2.75138e9i | 1.43811 | − | 0.667600i | ||||
\(57\) | 9.76323e8 | 0.214923 | ||||||||
\(58\) | −2.67406e9 | − | 1.06411e9i | −0.534955 | − | 0.212879i | ||||
\(59\) | − | 8.98489e9i | − | 1.63616i | −0.575102 | − | 0.818082i | \(-0.695038\pi\) | ||
0.575102 | − | 0.818082i | \(-0.304962\pi\) | |||||||
\(60\) | −4.42893e9 | − | 4.18807e9i | −0.735304 | − | 0.695315i | ||||
\(61\) | 1.06321e10i | 1.61178i | 0.592068 | + | 0.805888i | \(0.298312\pi\) | ||||
−0.592068 | + | 0.805888i | \(0.701688\pi\) | |||||||
\(62\) | −1.39156e9 | + | 3.49694e9i | −0.192907 | + | 0.484768i | ||||
\(63\) | −6.78880e9 | −0.861827 | ||||||||
\(64\) | 5.54405e9 | − | 6.56128e9i | 0.645413 | − | 0.763834i | ||||
\(65\) | −1.17385e10 | −1.25485 | ||||||||
\(66\) | 8.44302e8 | − | 2.12170e9i | 0.0829863 | − | 0.208541i | ||||
\(67\) | 4.61172e9i | 0.417303i | 0.977990 | + | 0.208652i | \(0.0669075\pi\) | ||||
−0.977990 | + | 0.208652i | \(0.933093\pi\) | |||||||
\(68\) | −1.01175e10 | − | 9.56724e9i | −0.843865 | − | 0.797972i | ||||
\(69\) | 6.96528e9i | 0.536128i | ||||||||
\(70\) | 3.10297e10 | + | 1.23478e10i | 2.20667 | + | 0.878116i | ||||
\(71\) | −3.76291e9 | −0.247516 | −0.123758 | − | 0.992312i | \(-0.539495\pi\) | ||||
−0.123758 | + | 0.992312i | \(0.539495\pi\) | |||||||
\(72\) | −8.09472e9 | + | 3.75773e9i | −0.493030 | + | 0.228874i | ||||
\(73\) | 2.35994e10 | 1.33237 | 0.666186 | − | 0.745786i | \(-0.267926\pi\) | ||||
0.666186 | + | 0.745786i | \(0.267926\pi\) | |||||||
\(74\) | −1.70357e10 | − | 6.77914e9i | −0.892454 | − | 0.355140i | ||||
\(75\) | − | 1.72690e10i | − | 0.840290i | ||||||
\(76\) | −4.83137e9 | + | 5.10923e9i | −0.218572 | + | 0.231143i | ||||
\(77\) | 1.25110e10i | 0.526735i | ||||||||
\(78\) | 5.33588e9 | − | 1.34088e10i | 0.209260 | − | 0.525861i | ||||
\(79\) | 1.77494e10 | 0.648986 | 0.324493 | − | 0.945888i | \(-0.394806\pi\) | ||||
0.324493 | + | 0.945888i | \(0.394806\pi\) | |||||||
\(80\) | 4.38334e10 | − | 2.45240e9i | 1.49558 | − | 0.0836750i | ||||
\(81\) | −5.05153e9 | −0.160974 | ||||||||
\(82\) | −2.02808e10 | + | 5.09649e10i | −0.604101 | + | 1.51808i | ||||
\(83\) | − | 4.42674e9i | − | 0.123354i | −0.998096 | − | 0.0616772i | \(-0.980355\pi\) | ||
0.998096 | − | 0.0616772i | \(-0.0196449\pi\) | |||||||
\(84\) | −2.82097e10 | + | 2.98321e10i | −0.735974 | + | 0.778301i | ||||
\(85\) | − | 7.11668e10i | − | 1.73970i | ||||||
\(86\) | −3.55059e10 | − | 1.41291e10i | −0.813878 | − | 0.323872i | ||||
\(87\) | 1.80836e10 | 0.388981 | ||||||||
\(88\) | 6.92507e9 | + | 1.49176e10i | 0.139884 | + | 0.301332i | ||||
\(89\) | −7.93798e9 | −0.150683 | −0.0753416 | − | 0.997158i | \(-0.524005\pi\) | ||||
−0.0753416 | + | 0.997158i | \(0.524005\pi\) | |||||||
\(90\) | −4.23792e10 | − | 1.68643e10i | −0.756518 | − | 0.301046i | ||||
\(91\) | 7.90677e10i | 1.32822i | ||||||||
\(92\) | −3.64502e10 | − | 3.44679e10i | −0.576590 | − | 0.545233i | ||||
\(93\) | − | 2.36483e10i | − | 0.352488i | ||||||
\(94\) | 2.20597e10 | − | 5.54351e10i | 0.310024 | − | 0.779079i | ||||
\(95\) | −3.59386e10 | −0.476520 | ||||||||
\(96\) | −1.71236e10 | + | 5.11853e10i | −0.214340 | + | 0.640698i | ||||
\(97\) | 1.20863e10 | 0.142906 | 0.0714528 | − | 0.997444i | \(-0.477236\pi\) | ||||
0.0714528 | + | 0.997444i | \(0.477236\pi\) | |||||||
\(98\) | 5.00863e10 | − | 1.25865e11i | 0.559726 | − | 1.40657i | ||||
\(99\) | − | 1.70870e10i | − | 0.180582i | ||||||
\(100\) | 9.03707e10 | + | 8.54559e10i | 0.903707 | + | 0.854559i | ||||
\(101\) | − | 3.06086e10i | − | 0.289785i | −0.989447 | − | 0.144892i | \(-0.953716\pi\) | ||
0.989447 | − | 0.144892i | \(-0.0462836\pi\) | |||||||
\(102\) | 8.12933e10 | + | 3.23496e10i | 0.729044 | + | 0.290114i | ||||
\(103\) | 5.88636e10 | 0.500313 | 0.250157 | − | 0.968205i | \(-0.419518\pi\) | ||||
0.250157 | + | 0.968205i | \(0.419518\pi\) | |||||||
\(104\) | 4.37655e10 | + | 9.42774e10i | 0.352735 | + | 0.759844i | ||||
\(105\) | −2.09841e11 | −1.60453 | ||||||||
\(106\) | −7.22038e9 | − | 2.87326e9i | −0.0524056 | − | 0.0208541i | ||||
\(107\) | 2.63056e11i | 1.81316i | 0.422032 | + | 0.906581i | \(0.361317\pi\) | ||||
−0.422032 | + | 0.906581i | \(0.638683\pi\) | |||||||
\(108\) | 1.09408e11 | − | 1.15700e11i | 0.716502 | − | 0.757710i | ||||
\(109\) | 1.30128e11i | 0.810072i | 0.914301 | + | 0.405036i | \(0.132741\pi\) | ||||
−0.914301 | + | 0.405036i | \(0.867259\pi\) | |||||||
\(110\) | −3.10789e10 | + | 7.81000e10i | −0.183995 | + | 0.462371i | ||||
\(111\) | 1.15205e11 | 0.648928 | ||||||||
\(112\) | −1.65187e10 | − | 2.95250e11i | −0.0885679 | − | 1.58304i | ||||
\(113\) | 9.59652e10 | 0.489985 | 0.244992 | − | 0.969525i | \(-0.421215\pi\) | ||||
0.244992 | + | 0.969525i | \(0.421215\pi\) | |||||||
\(114\) | 1.63362e10 | − | 4.10524e10i | 0.0794650 | − | 0.199692i | ||||
\(115\) | − | 2.56393e11i | − | 1.18869i | ||||||
\(116\) | −8.94870e10 | + | 9.46336e10i | −0.395586 | + | 0.418337i | ||||
\(117\) | − | 1.07988e11i | − | 0.455358i | ||||||
\(118\) | −3.77796e11 | − | 1.50339e11i | −1.52022 | − | 0.604951i | ||||
\(119\) | −4.79360e11 | −1.84142 | ||||||||
\(120\) | −2.50206e11 | + | 1.16151e11i | −0.917912 | + | 0.426114i | ||||
\(121\) | 2.53822e11 | 0.889631 | ||||||||
\(122\) | 4.47057e11 | + | 1.77901e11i | 1.49756 | + | 0.595934i | ||||
\(123\) | − | 3.44654e11i | − | 1.10384i | ||||||
\(124\) | 1.23755e11 | + | 1.17025e11i | 0.379090 | + | 0.358474i | ||||
\(125\) | 1.24586e11i | 0.365145i | ||||||||
\(126\) | −1.13593e11 | + | 2.85455e11i | −0.318650 | + | 0.800755i | ||||
\(127\) | 6.41966e10 | 0.172421 | 0.0862107 | − | 0.996277i | \(-0.472524\pi\) | ||||
0.0862107 | + | 0.996277i | \(0.472524\pi\) | |||||||
\(128\) | −1.83123e11 | − | 3.42902e11i | −0.471073 | − | 0.882094i | ||||
\(129\) | 2.40112e11 | 0.591793 | ||||||||
\(130\) | −1.96414e11 | + | 4.93581e11i | −0.463964 | + | 1.16592i | ||||
\(131\) | − | 5.61342e9i | − | 0.0127126i | −0.999980 | − | 0.00635631i | \(-0.997977\pi\) | ||
0.999980 | − | 0.00635631i | \(-0.00202329\pi\) | |||||||
\(132\) | −7.50858e10 | − | 7.10023e10i | −0.163080 | − | 0.154211i | ||||
\(133\) | 2.42073e11i | 0.504384i | ||||||||
\(134\) | 1.93913e11 | + | 7.71652e10i | 0.387731 | + | 0.154293i | ||||
\(135\) | 8.13840e11 | 1.56208 | ||||||||
\(136\) | −5.71572e11 | + | 2.65335e11i | −1.05343 | + | 0.489025i | ||||
\(137\) | −1.10990e10 | −0.0196482 | −0.00982408 | − | 0.999952i | \(-0.503127\pi\) | ||||
−0.00982408 | + | 0.999952i | \(0.503127\pi\) | |||||||
\(138\) | 2.92875e11 | + | 1.16546e11i | 0.498136 | + | 0.198227i | ||||
\(139\) | − | 8.85833e11i | − | 1.44801i | −0.689797 | − | 0.724003i | \(-0.742300\pi\) | ||
0.689797 | − | 0.724003i | \(-0.257700\pi\) | |||||||
\(140\) | 1.03840e12 | − | 1.09812e12i | 1.63178 | − | 1.72563i | ||||
\(141\) | 3.74884e11i | 0.566490i | ||||||||
\(142\) | −6.29626e10 | + | 1.58223e11i | −0.0915159 | + | 0.229976i | ||||
\(143\) | −1.99009e11 | −0.278307 | ||||||||
\(144\) | 2.25606e10 | + | 4.03242e11i | 0.0303639 | + | 0.542715i | ||||
\(145\) | −6.65658e11 | −0.862437 | ||||||||
\(146\) | 3.94875e11 | − | 9.92306e11i | 0.492628 | − | 1.23796i | ||||
\(147\) | 8.51172e11i | 1.02276i | ||||||||
\(148\) | −5.70097e11 | + | 6.02885e11i | −0.659948 | + | 0.697903i | ||||
\(149\) | 6.27189e11i | 0.699639i | 0.936817 | + | 0.349819i | \(0.113757\pi\) | ||||
−0.936817 | + | 0.349819i | \(0.886243\pi\) | |||||||
\(150\) | −7.26123e11 | − | 2.88951e11i | −0.780744 | − | 0.310687i | ||||
\(151\) | −1.68335e12 | −1.74502 | −0.872512 | − | 0.488592i | \(-0.837511\pi\) | ||||
−0.872512 | + | 0.488592i | \(0.837511\pi\) | |||||||
\(152\) | 1.33992e11 | + | 2.88638e11i | 0.133949 | + | 0.288546i | ||||
\(153\) | 6.54694e11 | 0.631299 | ||||||||
\(154\) | 5.26060e11 | + | 2.09339e11i | 0.489409 | + | 0.194754i | ||||
\(155\) | 8.70498e11i | 0.781526i | ||||||||
\(156\) | −4.74532e11 | − | 4.48725e11i | −0.411226 | − | 0.388861i | ||||
\(157\) | − | 2.01565e12i | − | 1.68642i | −0.537581 | − | 0.843212i | \(-0.680662\pi\) | ||
0.537581 | − | 0.843212i | \(-0.319338\pi\) | |||||||
\(158\) | 2.96991e11 | − | 7.46326e11i | 0.239954 | − | 0.602996i | ||||
\(159\) | 4.88284e10 | 0.0381056 | ||||||||
\(160\) | 6.30321e11 | − | 1.88414e12i | 0.475228 | − | 1.42054i | ||||
\(161\) | −1.72699e12 | −1.25820 | ||||||||
\(162\) | −8.45243e10 | + | 2.12406e11i | −0.0595181 | + | 0.149567i | ||||
\(163\) | 1.19891e12i | 0.816121i | 0.912955 | + | 0.408060i | \(0.133795\pi\) | ||||
−0.912955 | + | 0.408060i | \(0.866205\pi\) | |||||||
\(164\) | 1.80362e12 | + | 1.70553e12i | 1.18715 | + | 1.12258i | ||||
\(165\) | − | 5.28157e11i | − | 0.336203i | ||||||
\(166\) | −1.86135e11 | − | 7.40700e10i | −0.114613 | − | 0.0456087i | ||||
\(167\) | 1.37067e12 | 0.816568 | 0.408284 | − | 0.912855i | \(-0.366127\pi\) | ||||
0.408284 | + | 0.912855i | \(0.366127\pi\) | |||||||
\(168\) | 7.82361e11 | + | 1.68532e12i | 0.451031 | + | 0.971587i | ||||
\(169\) | 5.34450e11 | 0.298216 | ||||||||
\(170\) | −2.99242e12 | − | 1.19079e12i | −1.61641 | − | 0.643231i | ||||
\(171\) | − | 3.30614e11i | − | 0.172919i | ||||||
\(172\) | −1.18820e12 | + | 1.25653e12i | −0.601842 | + | 0.636456i | ||||
\(173\) | 2.93882e11i | 0.144185i | 0.997398 | + | 0.0720925i | \(0.0229677\pi\) | ||||
−0.997398 | + | 0.0720925i | \(0.977032\pi\) | |||||||
\(174\) | 3.02582e11 | − | 7.60376e11i | 0.143821 | − | 0.361416i | ||||
\(175\) | 4.28172e12 | 1.97201 | ||||||||
\(176\) | 7.43128e11 | − | 4.15766e10i | 0.331699 | − | 0.0185579i | ||||
\(177\) | 2.55487e12 | 1.10539 | ||||||||
\(178\) | −1.32822e11 | + | 3.33775e11i | −0.0557133 | + | 0.140005i | ||||
\(179\) | 7.29331e11i | 0.296642i | 0.988939 | + | 0.148321i | \(0.0473869\pi\) | ||||
−0.988939 | + | 0.148321i | \(0.952613\pi\) | |||||||
\(180\) | −1.41821e12 | + | 1.49978e12i | −0.559426 | + | 0.591600i | ||||
\(181\) | − | 9.65669e11i | − | 0.369484i | −0.982787 | − | 0.184742i | \(-0.940855\pi\) | ||
0.982787 | − | 0.184742i | \(-0.0591450\pi\) | |||||||
\(182\) | 3.32463e12 | + | 1.32299e12i | 1.23410 | + | 0.491094i | ||||
\(183\) | −3.02326e12 | −1.08892 | ||||||||
\(184\) | −2.05920e12 | + | 9.55924e11i | −0.719782 | + | 0.334138i | ||||
\(185\) | −4.24072e12 | −1.43878 | ||||||||
\(186\) | −9.94363e11 | − | 3.95694e11i | −0.327509 | − | 0.130328i | ||||
\(187\) | − | 1.20652e12i | − | 0.385840i | ||||||
\(188\) | −1.96182e12 | − | 1.85513e12i | −0.609243 | − | 0.576110i | ||||
\(189\) | − | 5.48181e12i | − | 1.65342i | ||||||
\(190\) | −6.01339e11 | + | 1.51114e12i | −0.176187 | + | 0.442752i | ||||
\(191\) | −6.96835e11 | −0.198357 | −0.0991783 | − | 0.995070i | \(-0.531621\pi\) | ||||
−0.0991783 | + | 0.995070i | \(0.531621\pi\) | |||||||
\(192\) | 1.86572e12 | + | 1.57646e12i | 0.516047 | + | 0.436041i | ||||
\(193\) | 3.70530e12 | 0.995997 | 0.497999 | − | 0.867178i | \(-0.334068\pi\) | ||||
0.497999 | + | 0.867178i | \(0.334068\pi\) | |||||||
\(194\) | 2.02233e11 | − | 5.08204e11i | 0.0528376 | − | 0.132779i | ||||
\(195\) | − | 3.33788e12i | − | 0.847775i | ||||||
\(196\) | −4.45429e12 | − | 4.21205e12i | −1.09994 | − | 1.04012i | ||||
\(197\) | 5.75699e12i | 1.38239i | 0.722667 | + | 0.691196i | \(0.242916\pi\) | ||||
−0.722667 | + | 0.691196i | \(0.757084\pi\) | |||||||
\(198\) | −7.18475e11 | − | 2.85908e11i | −0.167785 | − | 0.0667678i | ||||
\(199\) | −2.74148e12 | −0.622720 | −0.311360 | − | 0.950292i | \(-0.600784\pi\) | ||||
−0.311360 | + | 0.950292i | \(0.600784\pi\) | |||||||
\(200\) | 5.10536e12 | − | 2.37001e12i | 1.12814 | − | 0.523704i | ||||
\(201\) | −1.31135e12 | −0.281930 | ||||||||
\(202\) | −1.28703e12 | − | 5.12155e11i | −0.269250 | − | 0.107144i | ||||
\(203\) | 4.48369e12i | 0.912867i | ||||||||
\(204\) | 2.72047e12 | − | 2.87693e12i | 0.539110 | − | 0.570115i | ||||
\(205\) | 1.26868e13i | 2.44740i | ||||||||
\(206\) | 9.84930e11 | − | 2.47509e12i | 0.184985 | − | 0.464859i | ||||
\(207\) | 2.35867e12 | 0.431350 | ||||||||
\(208\) | 4.69647e12 | − | 2.62759e11i | 0.836418 | − | 0.0467960i | ||||
\(209\) | −6.09283e11 | −0.105685 | ||||||||
\(210\) | −3.51114e12 | + | 8.82335e12i | −0.593256 | + | 1.49083i | ||||
\(211\) | − | 9.16702e12i | − | 1.50895i | −0.656329 | − | 0.754475i | \(-0.727892\pi\) | ||
0.656329 | − | 0.754475i | \(-0.272108\pi\) | |||||||
\(212\) | −2.41629e11 | + | 2.55525e11i | −0.0387527 | + | 0.0409814i | ||||
\(213\) | − | 1.06999e12i | − | 0.167222i | ||||||
\(214\) | 1.10609e13 | + | 4.40155e12i | 1.68467 | + | 0.670394i | ||||
\(215\) | −8.83853e12 | −1.31211 | ||||||||
\(216\) | −3.03429e12 | − | 6.53631e12i | −0.439098 | − | 0.945882i | ||||
\(217\) | 5.86344e12 | 0.827226 | ||||||||
\(218\) | 5.47159e12 | + | 2.17735e12i | 0.752667 | + | 0.299514i | ||||
\(219\) | 6.71055e12i | 0.900151i | ||||||||
\(220\) | 2.76392e12 | + | 2.61360e12i | 0.361576 | + | 0.341912i | ||||
\(221\) | − | 7.62507e12i | − | 0.972941i | ||||||
\(222\) | 1.92766e12 | − | 4.84414e12i | 0.239933 | − | 0.602942i | ||||
\(223\) | 4.37572e12 | 0.531340 | 0.265670 | − | 0.964064i | \(-0.414407\pi\) | ||||
0.265670 | + | 0.964064i | \(0.414407\pi\) | |||||||
\(224\) | −1.26910e13 | − | 4.24567e12i | −1.50360 | − | 0.503016i | ||||
\(225\) | −5.84782e12 | −0.676067 | ||||||||
\(226\) | 1.60573e12 | − | 4.03514e12i | 0.181166 | − | 0.455263i | ||||
\(227\) | − | 3.94488e12i | − | 0.434402i | −0.976127 | − | 0.217201i | \(-0.930307\pi\) | ||
0.976127 | − | 0.217201i | \(-0.0696927\pi\) | |||||||
\(228\) | −1.45282e12 | − | 1.37381e12i | −0.156160 | − | 0.147668i | ||||
\(229\) | 6.68785e12i | 0.701764i | 0.936420 | + | 0.350882i | \(0.114118\pi\) | ||||
−0.936420 | + | 0.350882i | \(0.885882\pi\) | |||||||
\(230\) | −1.07808e13 | − | 4.29007e12i | −1.10445 | − | 0.439502i | ||||
\(231\) | −3.55752e12 | −0.355862 | ||||||||
\(232\) | 2.48181e12 | + | 5.34619e12i | 0.242429 | + | 0.522229i | ||||
\(233\) | 6.20865e12 | 0.592298 | 0.296149 | − | 0.955142i | \(-0.404298\pi\) | ||||
0.296149 | + | 0.955142i | \(0.404298\pi\) | |||||||
\(234\) | −4.54066e12 | − | 1.80690e12i | −0.423089 | − | 0.168363i | ||||
\(235\) | − | 1.37995e13i | − | 1.25600i | ||||||
\(236\) | −1.26429e13 | + | 1.33700e13i | −1.12416 | + | 1.18882i | ||||
\(237\) | 5.04709e12i | 0.438455i | ||||||||
\(238\) | −8.02086e12 | + | 2.01561e13i | −0.680844 | + | 1.71093i | ||||
\(239\) | 1.79550e13 | 1.48935 | 0.744676 | − | 0.667426i | \(-0.232604\pi\) | ||||
0.744676 | + | 0.667426i | \(0.232604\pi\) | |||||||
\(240\) | 6.97344e11 | + | 1.24641e13i | 0.0565309 | + | 1.01042i | ||||
\(241\) | −9.94501e12 | −0.787973 | −0.393987 | − | 0.919116i | \(-0.628904\pi\) | ||||
−0.393987 | + | 0.919116i | \(0.628904\pi\) | |||||||
\(242\) | 4.24706e12 | − | 1.06727e13i | 0.328930 | − | 0.826589i | ||||
\(243\) | 1.23372e13i | 0.934078i | ||||||||
\(244\) | 1.49607e13 | − | 1.58211e13i | 1.10741 | − | 1.17110i | ||||
\(245\) | − | 3.13317e13i | − | 2.26762i | ||||||
\(246\) | −1.44920e13 | − | 5.76690e12i | −1.02562 | − | 0.408131i | ||||
\(247\) | −3.85059e12 | −0.266498 | ||||||||
\(248\) | 6.99135e12 | − | 3.24553e12i | 0.473235 | − | 0.219685i | ||||
\(249\) | 1.25875e12 | 0.0833382 | ||||||||
\(250\) | 5.23859e12 | + | 2.08463e12i | 0.339269 | + | 0.135008i | ||||
\(251\) | 8.09796e12i | 0.513062i | 0.966536 | + | 0.256531i | \(0.0825796\pi\) | ||||
−0.966536 | + | 0.256531i | \(0.917420\pi\) | |||||||
\(252\) | 1.01021e13 | + | 9.55270e12i | 0.626193 | + | 0.592138i | ||||
\(253\) | − | 4.34675e12i | − | 0.263634i | ||||||
\(254\) | 1.07416e12 | − | 2.69933e12i | 0.0637507 | − | 0.160203i | ||||
\(255\) | 2.02364e13 | 1.17534 | ||||||||
\(256\) | −1.74824e13 | + | 1.96236e12i | −0.993759 | + | 0.111547i | ||||
\(257\) | 1.44416e13 | 0.803494 | 0.401747 | − | 0.915751i | \(-0.368403\pi\) | ||||
0.401747 | + | 0.915751i | \(0.368403\pi\) | |||||||
\(258\) | 4.01765e12 | − | 1.00962e13i | 0.218808 | − | 0.549856i | ||||
\(259\) | 2.85644e13i | 1.52292i | ||||||||
\(260\) | 1.74676e13 | + | 1.65176e13i | 0.911757 | + | 0.862172i | ||||
\(261\) | − | 6.12367e12i | − | 0.312960i | ||||||
\(262\) | −2.36032e11 | − | 9.39260e10i | −0.0118118 | − | 0.00470034i | ||||
\(263\) | −3.40203e13 | −1.66717 | −0.833587 | − | 0.552388i | \(-0.813717\pi\) | ||||
−0.833587 | + | 0.552388i | \(0.813717\pi\) | |||||||
\(264\) | −4.24186e12 | + | 1.96916e12i | −0.203580 | + | 0.0945060i | ||||
\(265\) | −1.79738e12 | −0.0844865 | ||||||||
\(266\) | 1.01786e13 | + | 4.05046e12i | 0.468642 | + | 0.186490i | ||||
\(267\) | − | 2.25718e12i | − | 0.101802i | ||||||
\(268\) | 6.48927e12 | − | 6.86248e12i | 0.286718 | − | 0.303207i | ||||
\(269\) | 1.44957e13i | 0.627484i | 0.949508 | + | 0.313742i | \(0.101583\pi\) | ||||
−0.949508 | + | 0.313742i | \(0.898417\pi\) | |||||||
\(270\) | 1.36175e13 | − | 3.42203e13i | 0.577560 | − | 1.45139i | ||||
\(271\) | −6.60502e12 | −0.274501 | −0.137250 | − | 0.990536i | \(-0.543826\pi\) | ||||
−0.137250 | + | 0.990536i | \(0.543826\pi\) | |||||||
\(272\) | 1.59302e12 | + | 2.84731e13i | 0.0648771 | + | 1.15959i | ||||
\(273\) | −2.24831e13 | −0.897348 | ||||||||
\(274\) | −1.85713e11 | + | 4.66691e11i | −0.00726466 | + | 0.0182558i | ||||
\(275\) | 1.07768e13i | 0.413202i | ||||||||
\(276\) | 9.80103e12 | − | 1.03647e13i | 0.368359 | − | 0.389544i | ||||
\(277\) | 1.55779e13i | 0.573945i | 0.957939 | + | 0.286973i | \(0.0926489\pi\) | ||||
−0.957939 | + | 0.286973i | \(0.907351\pi\) | |||||||
\(278\) | −3.72474e13 | − | 1.48221e13i | −1.34539 | − | 0.535382i | ||||
\(279\) | −8.00808e12 | −0.283599 | ||||||||
\(280\) | −2.87988e13 | − | 6.20369e13i | −1.00001 | − | 2.15417i | ||||
\(281\) | −4.02464e13 | −1.37038 | −0.685192 | − | 0.728363i | \(-0.740282\pi\) | ||||
−0.685192 | + | 0.728363i | \(0.740282\pi\) | |||||||
\(282\) | 1.57631e13 | + | 6.27272e12i | 0.526346 | + | 0.209453i | ||||
\(283\) | − | 2.95788e13i | − | 0.968623i | −0.874896 | − | 0.484312i | \(-0.839070\pi\) | ||
0.874896 | − | 0.484312i | \(-0.160930\pi\) | |||||||
\(284\) | 5.59941e12 | + | 5.29489e12i | 0.179842 | + | 0.170062i | ||||
\(285\) | − | 1.02192e13i | − | 0.321937i | ||||||
\(286\) | −3.32990e12 | + | 8.36791e12i | −0.102901 | + | 0.258585i | ||||
\(287\) | 8.54546e13 | 2.59051 | ||||||||
\(288\) | 1.73330e13 | + | 5.79859e12i | 0.515483 | + | 0.172450i | ||||
\(289\) | 1.19563e13 | 0.348866 | ||||||||
\(290\) | −1.11381e13 | + | 2.79895e13i | −0.318875 | + | 0.801321i | ||||
\(291\) | 3.43677e12i | 0.0965471i | ||||||||
\(292\) | −3.51172e13 | − | 3.32074e13i | −0.968086 | − | 0.915437i | ||||
\(293\) | − | 6.87067e12i | − | 0.185878i | −0.995672 | − | 0.0929388i | \(-0.970374\pi\) | ||
0.995672 | − | 0.0929388i | \(-0.0296261\pi\) | |||||||
\(294\) | 3.57900e13 | + | 1.42422e13i | 0.950279 | + | 0.378151i | ||||
\(295\) | −9.40452e13 | −2.45084 | ||||||||
\(296\) | 1.58109e13 | + | 3.40591e13i | 0.404439 | + | 0.871222i | ||||
\(297\) | 1.37974e13 | 0.346447 | ||||||||
\(298\) | 2.63720e13 | + | 1.04944e13i | 0.650060 | + | 0.258683i | ||||
\(299\) | − | 2.74708e13i | − | 0.664784i | ||||||
\(300\) | −2.42996e13 | + | 2.56971e13i | −0.577341 | + | 0.610545i | ||||
\(301\) | 5.95340e13i | 1.38883i | ||||||||
\(302\) | −2.81665e13 | + | 7.07814e13i | −0.645201 | + | 1.62137i | ||||
\(303\) | 8.70362e12 | 0.195779 | ||||||||
\(304\) | 1.43787e13 | − | 8.04458e11i | 0.317624 | − | 0.0177705i | ||||
\(305\) | 1.11287e14 | 2.41431 | ||||||||
\(306\) | 1.09546e13 | − | 2.75285e13i | 0.233415 | − | 0.586563i | ||||
\(307\) | − | 9.07345e13i | − | 1.89894i | −0.313856 | − | 0.949471i | \(-0.601621\pi\) | ||
0.313856 | − | 0.949471i | \(-0.398379\pi\) | |||||||
\(308\) | 1.76045e13 | − | 1.86170e13i | 0.361905 | − | 0.382719i | ||||
\(309\) | 1.67380e13i | 0.338012i | ||||||||
\(310\) | 3.66026e13 | + | 1.45655e13i | 0.726144 | + | 0.288960i | ||||
\(311\) | 3.13492e13 | 0.611005 | 0.305503 | − | 0.952191i | \(-0.401176\pi\) | ||||
0.305503 | + | 0.952191i | \(0.401176\pi\) | |||||||
\(312\) | −2.68080e13 | + | 1.24448e13i | −0.513351 | + | 0.238308i | ||||
\(313\) | 5.53280e13 | 1.04100 | 0.520501 | − | 0.853861i | \(-0.325745\pi\) | ||||
0.520501 | + | 0.853861i | \(0.325745\pi\) | |||||||
\(314\) | −8.47538e13 | − | 3.37267e13i | −1.56692 | − | 0.623535i | ||||
\(315\) | 7.10587e13i | 1.29095i | ||||||||
\(316\) | −2.64121e13 | − | 2.49757e13i | −0.471545 | − | 0.445901i | ||||
\(317\) | − | 7.13159e13i | − | 1.25130i | −0.780105 | − | 0.625648i | \(-0.784834\pi\) | ||
0.780105 | − | 0.625648i | \(-0.215166\pi\) | |||||||
\(318\) | 8.17017e11 | − | 2.05313e12i | 0.0140891 | − | 0.0354053i | ||||
\(319\) | −1.12852e13 | −0.191276 | ||||||||
\(320\) | −6.86772e13 | − | 5.80298e13i | −1.14416 | − | 0.966777i | ||||
\(321\) | −7.48004e13 | −1.22497 | ||||||||
\(322\) | −2.88968e13 | + | 7.26164e13i | −0.465202 | + | 1.16904i | ||||
\(323\) | − | 2.33448e13i | − | 0.369468i | ||||||
\(324\) | 7.51695e12 | + | 7.10814e12i | 0.116962 | + | 0.110601i | ||||
\(325\) | 6.81082e13i | 1.04194i | ||||||||
\(326\) | 5.04116e13 | + | 2.00606e13i | 0.758287 | + | 0.301751i | ||||
\(327\) | −3.70021e13 | −0.547285 | ||||||||
\(328\) | 1.01893e14 | − | 4.73008e13i | 1.48197 | − | 0.687958i | ||||
\(329\) | −9.29499e13 | −1.32945 | ||||||||
\(330\) | −2.22079e13 | − | 8.83735e12i | −0.312378 | − | 0.124307i | ||||
\(331\) | − | 5.31188e13i | − | 0.734843i | −0.930055 | − | 0.367421i | \(-0.880241\pi\) | ||
0.930055 | − | 0.367421i | \(-0.119759\pi\) | |||||||
\(332\) | −6.22898e12 | + | 6.58722e12i | −0.0847535 | + | 0.0896278i | ||||
\(333\) | − | 3.90122e13i | − | 0.522104i | ||||||
\(334\) | 2.29346e13 | − | 5.76338e13i | 0.301916 | − | 0.758703i | ||||
\(335\) | 4.82711e13 | 0.625087 | ||||||||
\(336\) | 8.39550e13 | − | 4.69712e12i | 1.06950 | − | 0.0598365i | ||||
\(337\) | −7.86684e13 | −0.985907 | −0.492953 | − | 0.870056i | \(-0.664083\pi\) | ||||
−0.492953 | + | 0.870056i | \(0.664083\pi\) | |||||||
\(338\) | 8.94265e12 | − | 2.24725e13i | 0.110262 | − | 0.277083i | ||||
\(339\) | 2.72879e13i | 0.331034i | ||||||||
\(340\) | −1.00141e14 | + | 1.05900e14i | −1.19530 | + | 1.26404i | ||||
\(341\) | 1.47580e13i | 0.173331i | ||||||||
\(342\) | −1.39016e13 | − | 5.53197e12i | −0.160665 | − | 0.0639347i | ||||
\(343\) | −7.16343e13 | −0.814710 | ||||||||
\(344\) | 3.29532e13 | + | 7.09862e13i | 0.368830 | + | 0.794515i | ||||
\(345\) | 7.29059e13 | 0.803078 | ||||||||
\(346\) | 1.23571e13 | + | 4.91736e12i | 0.133967 | + | 0.0533106i | ||||
\(347\) | 1.76592e14i | 1.88434i | 0.335140 | + | 0.942168i | \(0.391216\pi\) | ||||
−0.335140 | + | 0.942168i | \(0.608784\pi\) | |||||||
\(348\) | −2.69093e13 | − | 2.54459e13i | −0.282629 | − | 0.267258i | ||||
\(349\) | 9.38942e13i | 0.970731i | 0.874311 | + | 0.485365i | \(0.161313\pi\) | ||||
−0.874311 | + | 0.485365i | \(0.838687\pi\) | |||||||
\(350\) | 7.16435e13 | − | 1.80037e14i | 0.729126 | − | 1.83226i | ||||
\(351\) | 8.71978e13 | 0.873608 | ||||||||
\(352\) | 1.06861e13 | − | 3.19427e13i | 0.105399 | − | 0.315055i | ||||
\(353\) | −1.67481e13 | −0.162631 | −0.0813157 | − | 0.996688i | \(-0.525912\pi\) | ||||
−0.0813157 | + | 0.996688i | \(0.525912\pi\) | |||||||
\(354\) | 4.27492e13 | − | 1.07427e14i | 0.408705 | − | 1.02706i | ||||
\(355\) | 3.93865e13i | 0.370759i | ||||||||
\(356\) | 1.18121e13 | + | 1.11697e13i | 0.109485 | + | 0.103530i | ||||
\(357\) | − | 1.36307e14i | − | 1.24407i | ||||||
\(358\) | 3.06668e13 | + | 1.22035e13i | 0.275621 | + | 0.109680i | ||||
\(359\) | −9.36639e13 | −0.828996 | −0.414498 | − | 0.910050i | \(-0.636043\pi\) | ||||
−0.414498 | + | 0.910050i | \(0.636043\pi\) | |||||||
\(360\) | 3.93324e13 | + | 8.47278e13i | 0.342836 | + | 0.738520i | ||||
\(361\) | 1.04701e14 | 0.898799 | ||||||||
\(362\) | −4.06043e13 | − | 1.61580e13i | −0.343301 | − | 0.136612i | ||||
\(363\) | 7.21749e13i | 0.601035i | ||||||||
\(364\) | 1.11258e14 | − | 1.17657e14i | 0.912587 | − | 0.965072i | ||||
\(365\) | − | 2.47016e14i | − | 1.99579i | ||||||
\(366\) | −5.05865e13 | + | 1.27122e14i | −0.402613 | + | 1.01175i | ||||
\(367\) | 1.95745e14 | 1.53471 | 0.767356 | − | 0.641221i | \(-0.221572\pi\) | ||||
0.767356 | + | 0.641221i | \(0.221572\pi\) | |||||||
\(368\) | 5.73916e12 | + | 1.02580e14i | 0.0443287 | + | 0.792319i | ||||
\(369\) | −1.16711e14 | −0.888109 | ||||||||
\(370\) | −7.09575e13 | + | 1.78314e14i | −0.531972 | + | 1.33683i | ||||
\(371\) | 1.21067e13i | 0.0894269i | ||||||||
\(372\) | −3.32762e13 | + | 3.51900e13i | −0.242185 | + | 0.256114i | ||||
\(373\) | 8.96613e13i | 0.642993i | 0.946911 | + | 0.321497i | \(0.104186\pi\) | ||||
−0.946911 | + | 0.321497i | \(0.895814\pi\) | |||||||
\(374\) | −5.07318e13 | − | 2.01881e13i | −0.358498 | − | 0.142660i | ||||
\(375\) | −3.54264e13 | −0.246692 | ||||||||
\(376\) | −1.10830e14 | + | 5.14496e13i | −0.760544 | + | 0.353060i | ||||
\(377\) | −7.13210e13 | −0.482325 | ||||||||
\(378\) | −2.30499e14 | − | 9.17239e13i | −1.53626 | − | 0.611333i | ||||
\(379\) | − | 1.15327e14i | − | 0.757560i | −0.925487 | − | 0.378780i | \(-0.876344\pi\) | ||
0.925487 | − | 0.378780i | \(-0.123656\pi\) | |||||||
\(380\) | 5.34785e13 | + | 5.05701e13i | 0.346234 | + | 0.327404i | ||||
\(381\) | 1.82544e13i | 0.116488i | ||||||||
\(382\) | −1.16597e13 | + | 2.93005e13i | −0.0733399 | + | 0.184300i | ||||
\(383\) | −1.11809e14 | −0.693241 | −0.346620 | − | 0.938006i | \(-0.612671\pi\) | ||||
−0.346620 | + | 0.938006i | \(0.612671\pi\) | |||||||
\(384\) | 9.75050e13 | − | 5.20714e13i | 0.595943 | − | 0.318257i | ||||
\(385\) | 1.30953e14 | 0.789007 | ||||||||
\(386\) | 6.19986e13 | − | 1.55800e14i | 0.368258 | − | 0.925417i | ||||
\(387\) | − | 8.13094e13i | − | 0.476136i | ||||||
\(388\) | −1.79851e13 | − | 1.70070e13i | −0.103834 | − | 0.0981867i | ||||
\(389\) | − | 1.78296e12i | − | 0.0101489i | −0.999987 | − | 0.00507445i | \(-0.998385\pi\) | ||
0.999987 | − | 0.00507445i | \(-0.00161525\pi\) | |||||||
\(390\) | −1.40351e14 | − | 5.58508e13i | −0.787699 | − | 0.313454i | ||||
\(391\) | 1.66546e14 | 0.921644 | ||||||||
\(392\) | −2.51639e14 | + | 1.16816e14i | −1.37311 | + | 0.637424i | ||||
\(393\) | 1.59619e12 | 0.00858865 | ||||||||
\(394\) | 2.42069e14 | + | 9.63284e13i | 1.28443 | + | 0.511122i | ||||
\(395\) | − | 1.85784e14i | − | 0.972129i | ||||||
\(396\) | −2.40436e13 | + | 2.54264e13i | −0.124073 | + | 0.131208i | ||||
\(397\) | − | 1.20974e14i | − | 0.615666i | −0.951440 | − | 0.307833i | \(-0.900396\pi\) | ||
0.951440 | − | 0.307833i | \(-0.0996037\pi\) | |||||||
\(398\) | −4.58715e13 | + | 1.15273e14i | −0.230243 | + | 0.578591i | ||||
\(399\) | −6.88339e13 | −0.340762 | ||||||||
\(400\) | −1.42291e13 | − | 2.54326e14i | −0.0694778 | − | 1.24183i | ||||
\(401\) | 1.71934e14 | 0.828072 | 0.414036 | − | 0.910260i | \(-0.364119\pi\) | ||||
0.414036 | + | 0.910260i | \(0.364119\pi\) | |||||||
\(402\) | −2.19421e13 | + | 5.51397e13i | −0.104240 | + | 0.261951i | ||||
\(403\) | 9.32683e13i | 0.437075i | ||||||||
\(404\) | −4.30701e13 | + | 4.55472e13i | −0.199103 | + | 0.210554i | ||||
\(405\) | 5.28746e13i | 0.241126i | ||||||||
\(406\) | 1.88530e14 | + | 7.50230e13i | 0.848178 | + | 0.337521i | ||||
\(407\) | −7.18950e13 | −0.319102 | ||||||||
\(408\) | −7.54487e13 | − | 1.62528e14i | −0.330386 | − | 0.711700i | ||||
\(409\) | −1.44862e14 | −0.625861 | −0.312930 | − | 0.949776i | \(-0.601311\pi\) | ||||
−0.312930 | + | 0.949776i | \(0.601311\pi\) | |||||||
\(410\) | 5.33452e14 | + | 2.12280e14i | 2.27397 | + | 0.904895i | ||||
\(411\) | − | 3.15603e12i | − | 0.0132743i | ||||||
\(412\) | −8.75921e13 | − | 8.28285e13i | −0.363522 | − | 0.343752i | ||||
\(413\) | 6.33463e14i | 2.59416i | ||||||||
\(414\) | 3.94662e13 | − | 9.91770e13i | 0.159486 | − | 0.400783i | ||||
\(415\) | −4.63349e13 | −0.184775 | ||||||||
\(416\) | 6.75348e13 | − | 2.01873e14i | 0.265775 | − | 0.794448i | ||||
\(417\) | 2.51889e14 | 0.978273 | ||||||||
\(418\) | −1.01948e13 | + | 2.56191e13i | −0.0390759 | + | 0.0981961i | ||||
\(419\) | 3.35193e14i | 1.26799i | 0.773336 | + | 0.633997i | \(0.218587\pi\) | ||||
−0.773336 | + | 0.633997i | \(0.781413\pi\) | |||||||
\(420\) | 3.12254e14 | + | 2.95272e14i | 1.16583 | + | 1.10243i | ||||
\(421\) | 1.42923e14i | 0.526686i | 0.964702 | + | 0.263343i | \(0.0848250\pi\) | ||||
−0.964702 | + | 0.263343i | \(0.915175\pi\) | |||||||
\(422\) | −3.85454e14 | − | 1.53386e14i | −1.40202 | − | 0.557915i | ||||
\(423\) | 1.26948e14 | 0.455777 | ||||||||
\(424\) | 6.70128e12 | + | 1.44355e13i | 0.0237490 | + | 0.0511589i | ||||
\(425\) | −4.12917e14 | −1.44452 | ||||||||
\(426\) | −4.49909e13 | − | 1.79036e13i | −0.155372 | − | 0.0618282i | ||||
\(427\) | − | 7.49596e14i | − | 2.55549i | ||||||
\(428\) | 3.70152e14 | − | 3.91440e14i | 1.24578 | − | 1.31742i | ||||
\(429\) | − | 5.65887e13i | − | 0.188025i | ||||||
\(430\) | −1.47890e14 | + | 3.71642e14i | −0.485135 | + | 1.21912i | ||||
\(431\) | −2.65512e14 | −0.859924 | −0.429962 | − | 0.902847i | \(-0.641473\pi\) | ||||
−0.429962 | + | 0.902847i | \(0.641473\pi\) | |||||||
\(432\) | −3.25609e14 | + | 1.82172e13i | −1.04120 | + | 0.0582534i | ||||
\(433\) | −1.09976e14 | −0.347227 | −0.173614 | − | 0.984814i | \(-0.555544\pi\) | ||||
−0.173614 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(434\) | 9.81095e13 | − | 2.46545e14i | 0.305856 | − | 0.768605i | ||||
\(435\) | − | 1.89281e14i | − | 0.582662i | ||||||
\(436\) | 1.83106e14 | − | 1.93637e14i | 0.556579 | − | 0.588589i | ||||
\(437\) | − | 8.41044e13i | − | 0.252447i | ||||||
\(438\) | 2.82165e14 | + | 1.12284e14i | 0.836363 | + | 0.332820i | ||||
\(439\) | −4.19854e14 | −1.22897 | −0.614487 | − | 0.788927i | \(-0.710637\pi\) | ||||
−0.614487 | + | 0.788927i | \(0.710637\pi\) | |||||||
\(440\) | 1.56143e14 | − | 7.24850e13i | 0.451371 | − | 0.209536i | ||||
\(441\) | 2.88234e14 | 0.822873 | ||||||||
\(442\) | −3.20618e14 | − | 1.27586e14i | −0.903994 | − | 0.359733i | ||||
\(443\) | 4.39100e14i | 1.22277i | 0.791335 | + | 0.611383i | \(0.209386\pi\) | ||||
−0.791335 | + | 0.611383i | \(0.790614\pi\) | |||||||
\(444\) | −1.71432e14 | − | 1.62108e14i | −0.471503 | − | 0.445861i | ||||
\(445\) | 8.30872e13i | 0.225712i | ||||||||
\(446\) | 7.32163e13 | − | 1.83990e14i | 0.196456 | − | 0.493687i | ||||
\(447\) | −1.78343e14 | −0.472676 | ||||||||
\(448\) | −3.90873e14 | + | 4.62591e14i | −1.02331 | + | 1.21107i | ||||
\(449\) | −2.29397e14 | −0.593242 | −0.296621 | − | 0.954995i | \(-0.595860\pi\) | ||||
−0.296621 | + | 0.954995i | \(0.595860\pi\) | |||||||
\(450\) | −9.78481e13 | + | 2.45889e14i | −0.249968 | + | 0.628159i | ||||
\(451\) | 2.15085e14i | 0.542798i | ||||||||
\(452\) | −1.42801e14 | − | 1.35035e14i | −0.356017 | − | 0.336655i | ||||
\(453\) | − | 4.78665e14i | − | 1.17894i | ||||||
\(454\) | −1.65874e14 | − | 6.60074e13i | −0.403619 | − | 0.160615i | ||||
\(455\) | 8.27605e14 | 1.98957 | ||||||||
\(456\) | −8.20750e13 | + | 3.81009e13i | −0.194942 | + | 0.0904958i | ||||
\(457\) | 7.94851e14 | 1.86529 | 0.932646 | − | 0.360794i | \(-0.117494\pi\) | ||||
0.932646 | + | 0.360794i | \(0.117494\pi\) | |||||||
\(458\) | 2.81210e14 | + | 1.11904e14i | 0.652035 | + | 0.259469i | ||||
\(459\) | 5.28651e14i | 1.21115i | ||||||||
\(460\) | −3.60777e14 | + | 3.81526e14i | −0.816715 | + | 0.863686i | ||||
\(461\) | − | 1.44773e14i | − | 0.323841i | −0.986804 | − | 0.161920i | \(-0.948231\pi\) | ||
0.986804 | − | 0.161920i | \(-0.0517688\pi\) | |||||||
\(462\) | −5.95260e13 | + | 1.49586e14i | −0.131576 | + | 0.330645i | ||||
\(463\) | −5.29259e13 | −0.115604 | −0.0578020 | − | 0.998328i | \(-0.518409\pi\) | ||||
−0.0578020 | + | 0.998328i | \(0.518409\pi\) | |||||||
\(464\) | 2.66323e14 | − | 1.49003e13i | 0.574857 | − | 0.0321621i | ||||
\(465\) | −2.47528e14 | −0.527999 | ||||||||
\(466\) | 1.03886e14 | − | 2.61061e14i | 0.218995 | − | 0.550325i | ||||
\(467\) | − | 6.96522e14i | − | 1.45108i | −0.688179 | − | 0.725541i | \(-0.741590\pi\) | ||
0.688179 | − | 0.725541i | \(-0.258410\pi\) | |||||||
\(468\) | −1.51952e14 | + | 1.60692e14i | −0.312864 | + | 0.330857i | ||||
\(469\) | − | 3.25141e14i | − | 0.661639i | ||||||
\(470\) | −5.80241e14 | − | 2.30899e14i | −1.16700 | − | 0.464392i | ||||
\(471\) | 5.73155e14 | 1.13935 | ||||||||
\(472\) | 3.50634e14 | + | 7.55319e14i | 0.688927 | + | 1.48405i | ||||
\(473\) | −1.49844e14 | −0.291006 | ||||||||
\(474\) | 2.12219e14 | + | 8.44500e13i | 0.407384 | + | 0.162113i | ||||
\(475\) | 2.08519e14i | 0.395668i | ||||||||
\(476\) | 7.13314e14 | + | 6.74521e14i | 1.33796 | + | 1.26519i | ||||
\(477\) | − | 1.65349e13i | − | 0.0306584i | ||||||
\(478\) | 3.00431e14 | − | 7.54971e14i | 0.550670 | − | 1.38381i | ||||
\(479\) | −7.63619e12 | −0.0138367 | −0.00691833 | − | 0.999976i | \(-0.502202\pi\) | ||||
−0.00691833 | + | 0.999976i | \(0.502202\pi\) | |||||||
\(480\) | 5.35759e14 | + | 1.79233e14i | 0.959716 | + | 0.321064i | ||||
\(481\) | −4.54366e14 | −0.804652 | ||||||||
\(482\) | −1.66404e14 | + | 4.18167e14i | −0.291343 | + | 0.732134i | ||||
\(483\) | − | 4.91074e14i | − | 0.850037i | ||||||
\(484\) | −3.77701e14 | − | 3.57160e14i | −0.646396 | − | 0.611242i | ||||
\(485\) | − | 1.26508e14i | − | 0.214061i | ||||||
\(486\) | 5.18755e14 | + | 2.06432e14i | 0.867886 | + | 0.345364i | ||||
\(487\) | 6.21942e14 | 1.02882 | 0.514411 | − | 0.857544i | \(-0.328010\pi\) | ||||
0.514411 | + | 0.857544i | \(0.328010\pi\) | |||||||
\(488\) | −4.14916e14 | − | 8.93791e14i | −0.678659 | − | 1.46193i | ||||
\(489\) | −3.40913e14 | −0.551372 | ||||||||
\(490\) | −1.31743e15 | − | 5.24255e14i | −2.10693 | − | 0.838426i | ||||
\(491\) | 7.67233e14i | 1.21333i | 0.794957 | + | 0.606665i | \(0.207493\pi\) | ||||
−0.794957 | + | 0.606665i | \(0.792507\pi\) | |||||||
\(492\) | −4.84972e14 | + | 5.12864e14i | −0.758418 | + | 0.802036i | ||||
\(493\) | − | 4.32395e14i | − | 0.668687i | ||||||
\(494\) | −6.44297e13 | + | 1.61909e14i | −0.0985343 | + | 0.247613i | ||||
\(495\) | −1.78851e14 | −0.270497 | ||||||||
\(496\) | −1.94855e13 | − | 3.48277e14i | −0.0291448 | − | 0.520926i | ||||
\(497\) | 2.65297e14 | 0.392439 | ||||||||
\(498\) | 2.10620e13 | − | 5.29280e13i | 0.0308133 | − | 0.0774326i | ||||
\(499\) | 1.22133e15i | 1.76717i | 0.468268 | + | 0.883586i | \(0.344878\pi\) | ||||
−0.468268 | + | 0.883586i | \(0.655122\pi\) | |||||||
\(500\) | 1.75309e14 | − | 1.85391e14i | 0.250881 | − | 0.265310i | ||||
\(501\) | 3.89753e14i | 0.551674i | ||||||||
\(502\) | 3.40502e14 | + | 1.35498e14i | 0.476705 | + | 0.189698i | ||||
\(503\) | −6.20160e14 | −0.858776 | −0.429388 | − | 0.903120i | \(-0.641271\pi\) | ||||
−0.429388 | + | 0.903120i | \(0.641271\pi\) | |||||||
\(504\) | 5.70704e14 | − | 2.64932e14i | 0.781704 | − | 0.362883i | ||||
\(505\) | −3.20381e14 | −0.434075 | ||||||||
\(506\) | −1.82772e14 | − | 7.27316e13i | −0.244952 | − | 0.0974754i | ||||
\(507\) | 1.51972e14i | 0.201475i | ||||||||
\(508\) | −9.55278e13 | − | 9.03326e13i | −0.125279 | − | 0.118466i | ||||
\(509\) | − | 1.04994e14i | − | 0.136213i | −0.997678 | − | 0.0681065i | \(-0.978304\pi\) | ||
0.997678 | − | 0.0681065i | \(-0.0216958\pi\) | |||||||
\(510\) | 3.38605e14 | − | 8.50900e14i | 0.434567 | − | 1.09205i | ||||
\(511\) | −1.66383e15 | −2.11249 | ||||||||
\(512\) | −2.10010e14 | + | 7.67933e14i | −0.263788 | + | 0.964581i | ||||
\(513\) | 2.66964e14 | 0.331747 | ||||||||
\(514\) | 2.41643e14 | − | 6.07238e14i | 0.297082 | − | 0.746555i | ||||
\(515\) | − | 6.16128e14i | − | 0.749430i | ||||||
\(516\) | −3.57299e14 | − | 3.37867e14i | −0.429990 | − | 0.406605i | ||||
\(517\) | − | 2.33950e14i | − | 0.278564i | ||||||
\(518\) | 1.20107e15 | + | 4.77951e14i | 1.41500 | + | 0.563079i | ||||
\(519\) | −8.35661e13 | −0.0974114 | ||||||||
\(520\) | 9.86806e14 | − | 4.58095e14i | 1.13819 | − | 0.528369i | ||||
\(521\) | 5.40389e14 | 0.616736 | 0.308368 | − | 0.951267i | \(-0.400217\pi\) | ||||
0.308368 | + | 0.951267i | \(0.400217\pi\) | |||||||
\(522\) | −2.57487e14 | − | 1.02464e14i | −0.290783 | − | 0.115713i | ||||
\(523\) | − | 6.71719e14i | − | 0.750634i | −0.926897 | − | 0.375317i | \(-0.877534\pi\) | ||
0.926897 | − | 0.375317i | \(-0.122466\pi\) | |||||||
\(524\) | −7.89879e12 | + | 8.35306e12i | −0.00873450 | + | 0.00923684i | ||||
\(525\) | 1.21752e15i | 1.33229i | ||||||||
\(526\) | −5.69241e14 | + | 1.43048e15i | −0.616417 | + | 1.54903i | ||||
\(527\) | −5.65454e14 | −0.605953 | ||||||||
\(528\) | 1.18224e13 | + | 2.11310e14i | 0.0125377 | + | 0.224096i | ||||
\(529\) | −3.52793e14 | −0.370266 | ||||||||
\(530\) | −3.00745e13 | + | 7.55761e13i | −0.0312379 | + | 0.0784995i | ||||
\(531\) | − | 8.65162e14i | − | 0.889360i | ||||||
\(532\) | 3.40627e14 | − | 3.60217e14i | 0.346549 | − | 0.366480i | ||||
\(533\) | 1.35931e15i | 1.36873i | ||||||||
\(534\) | −9.49098e13 | − | 3.77681e13i | −0.0945876 | − | 0.0376399i | ||||
\(535\) | 2.75341e15 | 2.71597 | ||||||||
\(536\) | −1.79972e14 | − | 3.87686e14i | −0.175711 | − | 0.378507i | ||||
\(537\) | −2.07387e14 | −0.200412 | ||||||||
\(538\) | 6.09515e14 | + | 2.42549e14i | 0.583018 | + | 0.232005i | ||||
\(539\) | − | 5.31181e14i | − | 0.502927i | ||||||
\(540\) | −1.21104e15 | − | 1.14518e15i | −1.13499 | − | 1.07326i | ||||
\(541\) | − | 8.46704e14i | − | 0.785501i | −0.919645 | − | 0.392750i | \(-0.871524\pi\) | ||
0.919645 | − | 0.392750i | \(-0.128476\pi\) | |||||||
\(542\) | −1.10518e14 | + | 2.77727e14i | −0.101493 | + | 0.255048i | ||||
\(543\) | 2.74590e14 | 0.249624 | ||||||||
\(544\) | 1.22389e15 | + | 4.09441e14i | 1.10141 | + | 0.368466i | ||||
\(545\) | 1.36205e15 | 1.21342 | ||||||||
\(546\) | −3.76196e14 | + | 9.45366e14i | −0.331783 | + | 0.833759i | ||||
\(547\) | 1.21824e15i | 1.06366i | 0.846850 | + | 0.531832i | \(0.178496\pi\) | ||||
−0.846850 | + | 0.531832i | \(0.821504\pi\) | |||||||
\(548\) | 1.65159e13 | + | 1.56177e13i | 0.0142761 | + | 0.0134997i | ||||
\(549\) | 1.02377e15i | 0.876104i | ||||||||
\(550\) | 4.53144e14 | + | 1.80323e14i | 0.383921 | + | 0.152776i | ||||
\(551\) | −2.18355e14 | −0.183160 | ||||||||
\(552\) | −2.71819e14 | − | 5.85539e14i | −0.225743 | − | 0.486285i | ||||
\(553\) | −1.25139e15 | −1.02897 | ||||||||
\(554\) | 6.55019e14 | + | 2.60656e14i | 0.533273 | + | 0.212209i | ||||
\(555\) | − | 1.20586e15i | − | 0.972043i | ||||||
\(556\) | −1.24648e15 | + | 1.31817e15i | −0.994886 | + | 1.05210i | ||||
\(557\) | − | 2.98945e14i | − | 0.236259i | −0.992998 | − | 0.118129i | \(-0.962310\pi\) | ||
0.992998 | − | 0.118129i | \(-0.0376898\pi\) | |||||||
\(558\) | −1.33995e14 | + | 3.36723e14i | −0.104857 | + | 0.263502i | ||||
\(559\) | −9.46993e14 | −0.733807 | ||||||||
\(560\) | −3.09039e15 | + | 1.72902e14i | −2.37126 | + | 0.132668i | ||||
\(561\) | 3.43078e14 | 0.260674 | ||||||||
\(562\) | −6.73419e14 | + | 1.69228e15i | −0.506682 | + | 1.27327i | ||||
\(563\) | − | 1.79792e15i | − | 1.33960i | −0.742542 | − | 0.669799i | \(-0.766380\pi\) | ||
0.742542 | − | 0.669799i | \(-0.233620\pi\) | |||||||
\(564\) | 5.27509e14 | − | 5.57847e14i | 0.389220 | − | 0.411605i | ||||
\(565\) | − | 1.00447e15i | − | 0.733958i | ||||||
\(566\) | −1.24373e15 | − | 4.94925e14i | −0.899983 | − | 0.358137i | ||||
\(567\) | 3.56149e14 | 0.255226 | ||||||||
\(568\) | 3.16331e14 | − | 1.46847e14i | 0.224505 | − | 0.104220i | ||||
\(569\) | 1.49115e15 | 1.04810 | 0.524051 | − | 0.851687i | \(-0.324420\pi\) | ||||
0.524051 | + | 0.851687i | \(0.324420\pi\) | |||||||
\(570\) | −4.29697e14 | − | 1.70992e14i | −0.299123 | − | 0.119032i | ||||
\(571\) | − | 1.07492e15i | − | 0.741098i | −0.928813 | − | 0.370549i | \(-0.879169\pi\) | ||
0.928813 | − | 0.370549i | \(-0.120831\pi\) | |||||||
\(572\) | 2.96136e14 | + | 2.80031e14i | 0.202215 | + | 0.191217i | ||||
\(573\) | − | 1.98147e14i | − | 0.134010i | ||||||
\(574\) | 1.42986e15 | − | 3.59319e15i | 0.957808 | − | 2.40693i | ||||
\(575\) | −1.48762e15 | −0.987002 | ||||||||
\(576\) | 5.33841e14 | − | 6.31791e14i | 0.350823 | − | 0.415193i | ||||
\(577\) | 1.22495e15 | 0.797352 | 0.398676 | − | 0.917092i | \(-0.369470\pi\) | ||||
0.398676 | + | 0.917092i | \(0.369470\pi\) | |||||||
\(578\) | 2.00058e14 | − | 5.02738e14i | 0.128989 | − | 0.324144i | ||||
\(579\) | 1.05361e15i | 0.672896i | ||||||||
\(580\) | 9.90534e14 | + | 9.36665e14i | 0.626636 | + | 0.592557i | ||||
\(581\) | 3.12099e14i | 0.195580i | ||||||||
\(582\) | 1.44509e14 | + | 5.75055e13i | 0.0897054 | + | 0.0356971i | ||||
\(583\) | −3.04718e13 | −0.0187379 | ||||||||
\(584\) | −1.98389e15 | + | 9.20964e14i | −1.20850 | + | 0.561012i | ||||
\(585\) | −1.13031e15 | −0.682090 | ||||||||
\(586\) | −2.88897e14 | − | 1.14963e14i | −0.172706 | − | 0.0687259i | ||||
\(587\) | 3.42431e14i | 0.202798i | 0.994846 | + | 0.101399i | \(0.0323319\pi\) | ||||
−0.994846 | + | 0.101399i | \(0.967668\pi\) | |||||||
\(588\) | 1.19771e15 | − | 1.26659e15i | 0.702708 | − | 0.743122i | ||||
\(589\) | 2.85549e14i | 0.165977i | ||||||||
\(590\) | −1.57360e15 | + | 3.95441e15i | −0.906169 | + | 2.27717i | ||||
\(591\) | −1.63701e15 | −0.933945 | ||||||||
\(592\) | 1.69667e15 | − | 9.49254e13i | 0.959020 | − | 0.0536554i | ||||
\(593\) | −2.01818e15 | −1.13021 | −0.565105 | − | 0.825019i | \(-0.691164\pi\) | ||||
−0.565105 | + | 0.825019i | \(0.691164\pi\) | |||||||
\(594\) | 2.30864e14 | − | 5.80152e14i | 0.128095 | − | 0.321897i | ||||
\(595\) | 5.01749e15i | 2.75831i | ||||||||
\(596\) | 8.82534e14 | − | 9.33290e14i | 0.480703 | − | 0.508349i | ||||
\(597\) | − | 7.79545e14i | − | 0.420710i | ||||||
\(598\) | −1.15509e15 | − | 4.59654e14i | −0.617675 | − | 0.245796i | ||||
\(599\) | 3.55347e15 | 1.88280 | 0.941402 | − | 0.337287i | \(-0.109509\pi\) | ||||
0.941402 | + | 0.337287i | \(0.109509\pi\) | |||||||
\(600\) | 6.73919e14 | + | 1.45172e15i | 0.353815 | + | 0.762169i | ||||
\(601\) | −3.15707e14 | −0.164238 | −0.0821192 | − | 0.996623i | \(-0.526169\pi\) | ||||
−0.0821192 | + | 0.996623i | \(0.526169\pi\) | |||||||
\(602\) | 2.50328e15 | + | 9.96147e14i | 1.29041 | + | 0.513503i | ||||
\(603\) | 4.44066e14i | 0.226831i | ||||||||
\(604\) | 2.50492e15 | + | 2.36869e15i | 1.26791 | + | 1.19896i | ||||
\(605\) | − | 2.65677e15i | − | 1.33260i | ||||||
\(606\) | 1.45633e14 | − | 3.65969e14i | 0.0723868 | − | 0.181905i | ||||
\(607\) | 3.02066e15 | 1.48787 | 0.743934 | − | 0.668253i | \(-0.232957\pi\) | ||||
0.743934 | + | 0.668253i | \(0.232957\pi\) | |||||||
\(608\) | 2.06764e14 | − | 6.18053e14i | 0.100926 | − | 0.301686i | ||||
\(609\) | −1.27495e15 | −0.616733 | ||||||||
\(610\) | 1.86209e15 | − | 4.67937e15i | 0.892663 | − | 2.24323i | ||||
\(611\) | − | 1.47853e15i | − | 0.702431i | ||||||
\(612\) | −9.74219e14 | − | 9.21236e14i | −0.458695 | − | 0.433749i | ||||
\(613\) | 2.56623e15i | 1.19746i | 0.800949 | + | 0.598732i | \(0.204329\pi\) | ||||
−0.800949 | + | 0.598732i | \(0.795671\pi\) | |||||||
\(614\) | −3.81520e15 | − | 1.51821e15i | −1.76437 | − | 0.702110i | ||||
\(615\) | −3.60751e15 | −1.65346 | ||||||||
\(616\) | −4.88239e14 | − | 1.05174e15i | −0.221788 | − | 0.477765i | ||||
\(617\) | 9.15832e14 | 0.412332 | 0.206166 | − | 0.978517i | \(-0.433901\pi\) | ||||
0.206166 | + | 0.978517i | \(0.433901\pi\) | |||||||
\(618\) | 7.03798e14 | + | 2.80067e14i | 0.314059 | + | 0.124976i | ||||
\(619\) | 2.56124e15i | 1.13280i | 0.824131 | + | 0.566399i | \(0.191664\pi\) | ||||
−0.824131 | + | 0.566399i | \(0.808336\pi\) | |||||||
\(620\) | 1.22490e15 | − | 1.29535e15i | 0.536966 | − | 0.567848i | ||||
\(621\) | 1.90457e15i | 0.827548i | ||||||||
\(622\) | 5.24549e14 | − | 1.31817e15i | 0.225912 | − | 0.567707i | ||||
\(623\) | 5.59653e14 | 0.238910 | ||||||||
\(624\) | 7.47160e13 | + | 1.33545e15i | 0.0316154 | + | 0.565084i | ||||
\(625\) | −1.66132e15 | −0.696810 | ||||||||
\(626\) | 9.25771e14 | − | 2.32643e15i | 0.384897 | − | 0.967232i | ||||
\(627\) | − | 1.73251e14i | − | 0.0714011i | ||||||
\(628\) | −2.83627e15 | + | 2.99939e15i | −1.15870 | + | 1.22534i | ||||
\(629\) | − | 2.75467e15i | − | 1.11555i | ||||||
\(630\) | 2.98787e15 | + | 1.18898e15i | 1.19947 | + | 0.477312i | ||||
\(631\) | −1.75943e15 | −0.700179 | −0.350090 | − | 0.936716i | \(-0.613849\pi\) | ||||
−0.350090 | + | 0.936716i | \(0.613849\pi\) | |||||||
\(632\) | −1.49211e15 | + | 6.92669e14i | −0.588650 | + | 0.273264i | ||||
\(633\) | 2.60666e15 | 1.01945 | ||||||||
\(634\) | −2.99868e15 | − | 1.19329e15i | −1.16263 | − | 0.462651i | ||||
\(635\) | − | 6.71948e14i | − | 0.258274i | ||||||
\(636\) | −7.26593e13 | − | 6.87077e13i | −0.0276871 | − | 0.0261813i | ||||
\(637\) | − | 3.35699e15i | − | 1.26819i | ||||||
\(638\) | −1.88829e14 | + | 4.74519e14i | −0.0707220 | + | 0.177722i | ||||
\(639\) | −3.62334e14 | −0.134541 | ||||||||
\(640\) | −3.58917e15 | + | 1.91675e15i | −1.32131 | + | 0.705630i | ||||
\(641\) | −2.71995e15 | −0.992755 | −0.496377 | − | 0.868107i | \(-0.665337\pi\) | ||||
−0.496377 | + | 0.868107i | \(0.665337\pi\) | |||||||
\(642\) | −1.25159e15 | + | 3.14520e15i | −0.452919 | + | 1.13817i | ||||
\(643\) | − | 1.66231e15i | − | 0.596419i | −0.954500 | − | 0.298210i | \(-0.903611\pi\) | ||
0.954500 | − | 0.298210i | \(-0.0963895\pi\) | |||||||
\(644\) | 2.56986e15 | + | 2.43010e15i | 0.914190 | + | 0.864472i | ||||
\(645\) | − | 2.51326e15i | − | 0.886459i | ||||||
\(646\) | −9.81601e14 | − | 3.90615e14i | −0.343286 | − | 0.136606i | ||||
\(647\) | 2.35217e15 | 0.815635 | 0.407817 | − | 0.913063i | \(-0.366290\pi\) | ||||
0.407817 | + | 0.913063i | \(0.366290\pi\) | |||||||
\(648\) | 4.24659e14 | − | 1.97135e14i | 0.146008 | − | 0.0677801i | ||||
\(649\) | −1.59439e15 | −0.543563 | ||||||||
\(650\) | 2.86381e15 | + | 1.13962e15i | 0.968101 | + | 0.385243i | ||||
\(651\) | 1.66728e15i | 0.558874i | ||||||||
\(652\) | 1.68702e15 | − | 1.78404e15i | 0.560735 | − | 0.592984i | ||||
\(653\) | 4.70527e15i | 1.55082i | 0.631457 | + | 0.775411i | \(0.282457\pi\) | ||||
−0.631457 | + | 0.775411i | \(0.717543\pi\) | |||||||
\(654\) | −6.19134e14 | + | 1.55586e15i | −0.202352 | + | 0.508502i | ||||
\(655\) | −5.87559e13 | −0.0190425 | ||||||||
\(656\) | −2.83984e14 | − | 5.07584e15i | −0.0912688 | − | 1.63131i | ||||
\(657\) | 2.27241e15 | 0.724230 | ||||||||
\(658\) | −1.55528e15 | + | 3.90835e15i | −0.491547 | + | 1.23524i | ||||
\(659\) | − | 1.75566e15i | − | 0.550262i | −0.961407 | − | 0.275131i | \(-0.911279\pi\) | ||
0.961407 | − | 0.275131i | \(-0.0887212\pi\) | |||||||
\(660\) | −7.43184e14 | + | 7.85926e14i | −0.230996 | + | 0.244281i | ||||
\(661\) | − | 2.25236e15i | − | 0.694271i | −0.937815 | − | 0.347135i | \(-0.887154\pi\) | ||
0.937815 | − | 0.347135i | \(-0.112846\pi\) | |||||||
\(662\) | −2.23354e15 | − | 8.88806e14i | −0.682769 | − | 0.271699i | ||||
\(663\) | 2.16821e15 | 0.657319 | ||||||||
\(664\) | 1.72753e14 | + | 3.72136e14i | 0.0519399 | + | 0.111886i | ||||
\(665\) | 2.53378e15 | 0.755528 | ||||||||
\(666\) | −1.64038e15 | − | 6.52768e14i | −0.485106 | − | 0.193042i | ||||
\(667\) | − | 1.55779e15i | − | 0.456896i | ||||||
\(668\) | −2.03963e15 | − | 1.92871e15i | −0.593309 | − | 0.561042i | ||||
\(669\) | 1.24425e15i | 0.358974i | ||||||||
\(670\) | 8.07692e14 | − | 2.02970e15i | 0.231118 | − | 0.580791i | ||||
\(671\) | 1.88669e15 | 0.535461 | ||||||||
\(672\) | 1.20727e15 | − | 3.60873e15i | 0.339838 | − | 1.01583i | ||||
\(673\) | 5.61222e15 | 1.56694 | 0.783470 | − | 0.621430i | \(-0.213448\pi\) | ||||
0.783470 | + | 0.621430i | \(0.213448\pi\) | |||||||
\(674\) | −1.31631e15 | + | 3.30784e15i | −0.364527 | + | 0.916042i | ||||
\(675\) | − | 4.72198e15i | − | 1.29704i | ||||||
\(676\) | −7.95290e14 | − | 7.52039e14i | −0.216680 | − | 0.204896i | ||||
\(677\) | 5.99957e15i | 1.62137i | 0.585482 | + | 0.810685i | \(0.300905\pi\) | ||||
−0.585482 | + | 0.810685i | \(0.699095\pi\) | |||||||
\(678\) | 1.14740e15 | + | 4.56593e14i | 0.307576 | + | 0.122396i | ||||
\(679\) | −8.52124e14 | −0.226579 | ||||||||
\(680\) | 2.77728e15 | + | 5.98267e15i | 0.732521 | + | 1.57796i | ||||
\(681\) | 1.12174e15 | 0.293482 | ||||||||
\(682\) | 6.20541e14 | + | 2.46936e14i | 0.161048 | + | 0.0640871i | ||||
\(683\) | 1.11579e15i | 0.287255i | 0.989632 | + | 0.143627i | \(0.0458767\pi\) | ||||
−0.989632 | + | 0.143627i | \(0.954123\pi\) | |||||||
\(684\) | −4.65216e14 | + | 4.91971e14i | −0.118808 | + | 0.125641i | ||||
\(685\) | 1.16174e14i | 0.0294314i | ||||||||
\(686\) | −1.19861e15 | + | 3.01207e15i | −0.301229 | + | 0.756977i | ||||
\(687\) | −1.90171e15 | −0.474112 | ||||||||
\(688\) | 3.53621e15 | − | 1.97844e14i | 0.874583 | − | 0.0489313i | ||||
\(689\) | −1.92578e14 | −0.0472499 | ||||||||
\(690\) | 1.21989e15 | − | 3.06554e15i | 0.296928 | − | 0.746169i | ||||
\(691\) | − | 2.73412e15i | − | 0.660221i | −0.943942 | − | 0.330110i | \(-0.892914\pi\) | ||
0.943942 | − | 0.330110i | \(-0.107086\pi\) | |||||||
\(692\) | 4.13530e14 | − | 4.37312e14i | 0.0990656 | − | 0.104763i | ||||
\(693\) | 1.20469e15i | 0.286314i | ||||||||
\(694\) | 7.42532e15 | + | 2.95481e15i | 1.75081 | + | 0.696710i | ||||
\(695\) | −9.27205e15 | −2.16900 | ||||||||
\(696\) | −1.52020e15 | + | 7.05709e14i | −0.352818 | + | 0.163785i | ||||
\(697\) | −8.24101e15 | −1.89758 | ||||||||
\(698\) | 3.94805e15 | + | 1.57108e15i | 0.901941 | + | 0.358916i | ||||
\(699\) | 1.76545e15i | 0.400156i | ||||||||
\(700\) | −6.37142e15 | − | 6.02491e15i | −1.43284 | − | 1.35491i | ||||
\(701\) | 3.90980e15i | 0.872380i | 0.899855 | + | 0.436190i | \(0.143672\pi\) | ||||
−0.899855 | + | 0.436190i | \(0.856328\pi\) | |||||||
\(702\) | 1.45903e15 | − | 3.66648e15i | 0.323006 | − | 0.811700i | ||||
\(703\) | −1.39108e15 | −0.305561 | ||||||||
\(704\) | −1.16432e15 | − | 9.83807e14i | −0.253759 | − | 0.214417i | ||||
\(705\) | 3.92393e15 | 0.848557 | ||||||||
\(706\) | −2.80236e14 | + | 7.04222e14i | −0.0601310 | + | 0.151107i | ||||
\(707\) | 2.15800e15i | 0.459457i | ||||||||
\(708\) | −3.80179e15 | − | 3.59503e15i | −0.803165 | − | 0.759486i | ||||
\(709\) | − | 7.61120e15i | − | 1.59551i | −0.602983 | − | 0.797754i | \(-0.706021\pi\) | ||
0.602983 | − | 0.797754i | \(-0.293979\pi\) | |||||||
\(710\) | 1.65612e15 | + | 6.59032e14i | 0.344486 | + | 0.137084i | ||||
\(711\) | 1.70910e15 | 0.352765 | ||||||||
\(712\) | 6.67310e14 | − | 3.09779e14i | 0.136674 | − | 0.0634471i | ||||
\(713\) | −2.03716e15 | −0.414031 | ||||||||
\(714\) | −5.73143e15 | − | 2.28075e15i | −1.15591 | − | 0.459978i | ||||
\(715\) | 2.08304e15i | 0.416882i | ||||||||
\(716\) | 1.02626e15 | − | 1.08528e15i | 0.203815 | − | 0.215537i | ||||
\(717\) | 5.10555e15i | 1.00621i | ||||||||
\(718\) | −1.56722e15 | + | 3.93837e15i | −0.306511 | + | 0.770251i | ||||
\(719\) | 6.49581e15 | 1.26074 | 0.630368 | − | 0.776296i | \(-0.282904\pi\) | ||||
0.630368 | + | 0.776296i | \(0.282904\pi\) | |||||||
\(720\) | 4.22075e15 | − | 2.36143e14i | 0.812945 | − | 0.0454827i | ||||
\(721\) | −4.15007e15 | −0.793252 | ||||||||
\(722\) | 1.75191e15 | − | 4.40247e15i | 0.332320 | − | 0.835107i | ||||
\(723\) | − | 2.82789e15i | − | 0.532355i | ||||||
\(724\) | −1.35882e15 | + | 1.43697e15i | −0.253863 | + | 0.268463i | ||||
\(725\) | 3.86222e15i | 0.716106i | ||||||||
\(726\) | 3.03481e15 | + | 1.20766e15i | 0.558444 | + | 0.222225i | ||||
\(727\) | −6.35413e15 | −1.16043 | −0.580213 | − | 0.814465i | \(-0.697031\pi\) | ||||
−0.580213 | + | 0.814465i | \(0.697031\pi\) | |||||||
\(728\) | −3.08561e15 | − | 6.64686e15i | −0.559265 | − | 1.20474i | ||||
\(729\) | −4.40299e15 | −0.792038 | ||||||||
\(730\) | −1.03865e16 | − | 4.13318e15i | −1.85436 | − | 0.737918i | ||||
\(731\) | − | 5.74129e15i | − | 1.01734i | ||||||
\(732\) | 4.49877e15 | + | 4.25411e15i | 0.791194 | + | 0.748165i | ||||
\(733\) | 3.12820e15i | 0.546038i | 0.962009 | + | 0.273019i | \(0.0880222\pi\) | ||||
−0.962009 | + | 0.273019i | \(0.911978\pi\) | |||||||
\(734\) | 3.27528e15 | − | 8.23066e15i | 0.567441 | − | 1.42596i | ||||
\(735\) | 8.90925e15 | 1.53201 | ||||||||
\(736\) | 4.40931e15 | + | 1.47509e15i | 0.752562 | + | 0.251763i | ||||
\(737\) | 8.18362e14 | 0.138635 | ||||||||
\(738\) | −1.95285e15 | + | 4.90745e15i | −0.328367 | + | 0.825174i | ||||
\(739\) | 5.30842e15i | 0.885973i | 0.896528 | + | 0.442987i | \(0.146081\pi\) | ||||
−0.896528 | + | 0.442987i | \(0.853919\pi\) | |||||||
\(740\) | 6.31042e15 | + | 5.96723e15i | 1.04540 | + | 0.988549i | ||||
\(741\) | − | 1.09492e15i | − | 0.180046i | ||||||
\(742\) | 5.09060e14 | + | 2.02574e14i | 0.0830897 | + | 0.0330645i | ||||
\(743\) | −7.29953e15 | −1.18265 | −0.591326 | − | 0.806433i | \(-0.701395\pi\) | ||||
−0.591326 | + | 0.806433i | \(0.701395\pi\) | |||||||
\(744\) | 9.22874e14 | + | 1.98801e15i | 0.148420 | + | 0.319718i | ||||
\(745\) | 6.56481e15 | 1.04800 | ||||||||
\(746\) | 3.77007e15 | + | 1.50025e15i | 0.597428 | + | 0.237739i | ||||
\(747\) | − | 4.26254e14i | − | 0.0670510i | ||||||
\(748\) | −1.69773e15 | + | 1.79537e15i | −0.265100 | + | 0.280347i | ||||
\(749\) | − | 1.85462e16i | − | 2.87479i | ||||||
\(750\) | −5.92769e14 | + | 1.48961e15i | −0.0912113 | + | 0.229210i | ||||
\(751\) | 1.15655e16 | 1.76663 | 0.883313 | − | 0.468784i | \(-0.155308\pi\) | ||||
0.883313 | + | 0.468784i | \(0.155308\pi\) | |||||||
\(752\) | 3.08892e14 | + | 5.52105e15i | 0.0468391 | + | 0.837189i | ||||
\(753\) | −2.30267e15 | −0.346625 | ||||||||
\(754\) | −1.19337e15 | + | 2.99890e15i | −0.178334 | + | 0.448146i | ||||
\(755\) | 1.76197e16i | 2.61391i | ||||||||
\(756\) | −7.71360e15 | + | 8.15722e15i | −1.13602 | + | 1.20136i | ||||
\(757\) | 5.46519e15i | 0.799057i | 0.916721 | + | 0.399529i | \(0.130826\pi\) | ||||
−0.916721 | + | 0.399529i | \(0.869174\pi\) | |||||||
\(758\) | −4.84928e15 | − | 1.92971e15i | −0.703876 | − | 0.280098i | ||||
\(759\) | 1.23601e15 | 0.178111 | ||||||||
\(760\) | 3.02119e15 | − | 1.40250e15i | 0.432219 | − | 0.200645i | ||||
\(761\) | 1.25601e16 | 1.78393 | 0.891965 | − | 0.452105i | \(-0.149327\pi\) | ||||
0.891965 | + | 0.452105i | \(0.149327\pi\) | |||||||
\(762\) | 7.67561e14 | + | 3.05441e14i | 0.108233 | + | 0.0430700i | ||||
\(763\) | − | 9.17441e15i | − | 1.28438i | ||||||
\(764\) | 1.03693e15 | + | 9.80535e14i | 0.144124 | + | 0.136286i | ||||
\(765\) | − | 6.85271e15i | − | 0.945636i | ||||||
\(766\) | −1.87084e15 | + | 4.70134e15i | −0.256317 | + | 0.644115i | ||||
\(767\) | −1.00763e16 | −1.37066 | ||||||||
\(768\) | −5.58001e14 | − | 4.97116e15i | −0.0753612 | − | 0.671384i | ||||
\(769\) | 6.63595e15 | 0.889832 | 0.444916 | − | 0.895572i | \(-0.353234\pi\) | ||||
0.444916 | + | 0.895572i | \(0.353234\pi\) | |||||||
\(770\) | 2.19116e15 | − | 5.50629e15i | 0.291726 | − | 0.733095i | ||||
\(771\) | 4.10650e15i | 0.542841i | ||||||||
\(772\) | −5.51368e15 | − | 5.21382e15i | −0.723680 | − | 0.684323i | ||||
\(773\) | − | 1.04365e16i | − | 1.36009i | −0.733170 | − | 0.680045i | \(-0.761960\pi\) | ||
0.733170 | − | 0.680045i | \(-0.238040\pi\) | |||||||
\(774\) | −3.41889e15 | − | 1.36050e15i | −0.442395 | − | 0.176045i | ||||
\(775\) | 5.05072e15 | 0.648924 | ||||||||
\(776\) | −1.01604e15 | + | 4.71667e14i | −0.129620 | + | 0.0601722i | ||||
\(777\) | −8.12234e15 | −1.02888 | ||||||||
\(778\) | −7.49697e13 | − | 2.98332e13i | −0.00942970 | − | 0.00375243i | ||||
\(779\) | 4.16163e15i | 0.519766i | ||||||||
\(780\) | −4.69682e15 | + | 4.96694e15i | −0.582484 | + | 0.615983i | ||||
\(781\) | 6.67739e14i | 0.0822291i | ||||||||
\(782\) | 2.78672e15 | − | 7.00293e15i | 0.340766 | − | 0.856333i | ||||
\(783\) | 4.94473e15 | 0.600417 | ||||||||
\(784\) | 7.01337e14 | + | 1.25355e16i | 0.0845646 | + | 1.51148i | ||||
\(785\) | −2.10979e16 | −2.52613 | ||||||||
\(786\) | 2.67081e13 | − | 6.71164e13i | 0.00317555 | − | 0.00798003i | ||||
\(787\) | − | 8.64759e15i | − | 1.02102i | −0.859872 | − | 0.510510i | \(-0.829457\pi\) | ||
0.859872 | − | 0.510510i | \(-0.170543\pi\) | |||||||
\(788\) | 8.10081e15 | − | 8.56671e15i | 0.949805 | − | 1.00443i | ||||
\(789\) | − | 9.67374e15i | − | 1.12634i | ||||||
\(790\) | −7.81182e15 | − | 3.10861e15i | −0.903240 | − | 0.359433i | ||||
\(791\) | −6.76585e15 | −0.776876 | ||||||||
\(792\) | 6.66820e14 | + | 1.43643e15i | 0.0760362 | + | 0.163793i | ||||
\(793\) | 1.19236e16 | 1.35023 | ||||||||
\(794\) | −5.08671e15 | − | 2.02419e15i | −0.572037 | − | 0.227635i | ||||
\(795\) | − | 5.11089e14i | − | 0.0570791i | ||||||
\(796\) | 4.07946e15 | + | 3.85760e15i | 0.452461 | + | 0.427854i | ||||
\(797\) | 1.23890e16i | 1.36463i | 0.731056 | + | 0.682317i | \(0.239028\pi\) | ||||
−0.731056 | + | 0.682317i | \(0.760972\pi\) | |||||||
\(798\) | −1.15176e15 | + | 2.89432e15i | −0.125993 | + | 0.316614i | ||||
\(799\) | 8.96383e15 | 0.973838 | ||||||||
\(800\) | −1.09320e16 | − | 3.65718e15i | −1.17951 | − | 0.394595i | ||||
\(801\) | −7.64354e14 | −0.0819060 | ||||||||
\(802\) | 2.87687e15 | − | 7.22947e15i | 0.306169 | − | 0.769392i | ||||
\(803\) | − | 4.18778e15i | − | 0.442638i | ||||||
\(804\) | 1.95136e15 | + | 1.84524e15i | 0.204847 | + | 0.193707i | ||||
\(805\) | 1.80765e16i | 1.88468i | ||||||||
\(806\) | 3.92174e15 | + | 1.56060e15i | 0.406103 | + | 0.161603i | ||||
\(807\) | −4.12190e15 | −0.423929 | ||||||||
\(808\) | 1.19450e15 | + | 2.57312e15i | 0.122018 | + | 0.262844i | ||||
\(809\) | −1.18494e16 | −1.20221 | −0.601104 | − | 0.799171i | \(-0.705272\pi\) | ||||
−0.601104 | + | 0.799171i | \(0.705272\pi\) | |||||||
\(810\) | 2.22327e15 | + | 8.84720e14i | 0.224039 | + | 0.0891535i | ||||
\(811\) | 2.92755e15i | 0.293014i | 0.989210 | + | 0.146507i | \(0.0468032\pi\) | ||||
−0.989210 | + | 0.146507i | \(0.953197\pi\) | |||||||
\(812\) | 6.30912e15 | − | 6.67197e15i | 0.627207 | − | 0.663279i | ||||
\(813\) | − | 1.87815e15i | − | 0.185453i | ||||||
\(814\) | −1.20298e15 | + | 3.02303e15i | −0.117984 | + | 0.296489i | ||||
\(815\) | 1.25490e16 | 1.22248 | ||||||||
\(816\) | −8.09639e15 | + | 4.52978e14i | −0.783422 | + | 0.0438310i | ||||
\(817\) | −2.89930e15 | −0.278658 | ||||||||
\(818\) | −2.42390e15 | + | 6.09116e15i | −0.231404 | + | 0.581510i | ||||
\(819\) | 7.61348e15i | 0.721975i | ||||||||
\(820\) | 1.78519e16 | − | 1.88786e16i | 1.68154 | − | 1.77825i | ||||
\(821\) | 1.19987e16i | 1.12265i | 0.827594 | + | 0.561326i | \(0.189709\pi\) | ||||
−0.827594 | + | 0.561326i | \(0.810291\pi\) | |||||||
\(822\) | −1.32705e14 | − | 5.28081e13i | −0.0123336 | − | 0.00490801i | ||||
\(823\) | −2.06230e16 | −1.90393 | −0.951967 | − | 0.306202i | \(-0.900942\pi\) | ||||
−0.951967 | + | 0.306202i | \(0.900942\pi\) | |||||||
\(824\) | −4.94839e15 | + | 2.29714e15i | −0.453800 | + | 0.210663i | ||||
\(825\) | −3.06442e15 | −0.279159 | ||||||||
\(826\) | 2.66358e16 | + | 1.05994e16i | 2.41032 | + | 0.959157i | ||||
\(827\) | 9.90088e15i | 0.890007i | 0.895529 | + | 0.445004i | \(0.146798\pi\) | ||||
−0.895529 | + | 0.445004i | \(0.853202\pi\) | |||||||
\(828\) | −3.50982e15 | − | 3.31894e15i | −0.313414 | − | 0.296369i | ||||
\(829\) | − | 7.04297e15i | − | 0.624749i | −0.949959 | − | 0.312375i | \(-0.898876\pi\) | ||
0.949959 | − | 0.312375i | \(-0.101124\pi\) | |||||||
\(830\) | −7.75294e14 | + | 1.94828e15i | −0.0683183 | + | 0.171681i | ||||
\(831\) | −4.42962e15 | −0.387758 | ||||||||
\(832\) | −7.35833e15 | − | 6.21753e15i | −0.639883 | − | 0.540679i | ||||
\(833\) | 2.03523e16 | 1.75819 | ||||||||
\(834\) | 4.21470e15 | − | 1.05914e16i | 0.361704 | − | 0.908949i | ||||
\(835\) | − | 1.43469e16i | − | 1.22315i | ||||||
\(836\) | 9.06646e14 | + | 8.57339e14i | 0.0767897 | + | 0.0726136i | ||||
\(837\) | − | 6.46635e15i | − | 0.544088i | ||||||
\(838\) | 1.40941e16 | + | 5.60858e15i | 1.17814 | + | 0.468825i | ||||
\(839\) | 3.44381e15 | 0.285988 | 0.142994 | − | 0.989724i | \(-0.454327\pi\) | ||||
0.142994 | + | 0.989724i | \(0.454327\pi\) | |||||||
\(840\) | 1.76403e16 | − | 8.18900e15i | 1.45536 | − | 0.675608i | ||||
\(841\) | 8.15611e15 | 0.668505 | ||||||||
\(842\) | 6.00963e15 | + | 2.39145e15i | 0.489363 | + | 0.194736i | ||||
\(843\) | − | 1.14442e16i | − | 0.925832i | ||||||
\(844\) | −1.28992e16 | + | 1.36410e16i | −1.03676 | + | 1.09638i | ||||
\(845\) | − | 5.59411e15i | − | 0.446704i | ||||||
\(846\) | 2.12414e15 | − | 5.33788e15i | 0.168518 | − | 0.423479i | ||||
\(847\) | −1.78953e16 | −1.41052 | ||||||||
\(848\) | 7.19113e14 | − | 4.02330e13i | 0.0563145 | − | 0.00315069i | ||||
\(849\) | 8.41080e15 | 0.654402 | ||||||||
\(850\) | −6.90910e15 | + | 1.73623e16i | −0.534094 | + | 1.34216i | ||||
\(851\) | − | 9.92425e15i | − | 0.762228i | ||||||
\(852\) | −1.50561e15 | + | 1.59221e15i | −0.114894 | + | 0.121501i | ||||
\(853\) | 2.35072e16i | 1.78231i | 0.453704 | + | 0.891153i | \(0.350102\pi\) | ||||
−0.453704 | + | 0.891153i | \(0.649898\pi\) | |||||||
\(854\) | −3.15190e16 | − | 1.25426e16i | −2.37440 | − | 0.944861i | ||||
\(855\) | −3.46055e15 | −0.259019 | ||||||||
\(856\) | −1.02657e16 | − | 2.21139e16i | −0.763455 | − | 1.64460i | ||||
\(857\) | −7.74414e15 | −0.572240 | −0.286120 | − | 0.958194i | \(-0.592366\pi\) | ||||
−0.286120 | + | 0.958194i | \(0.592366\pi\) | |||||||
\(858\) | −2.37944e15 | − | 9.46865e14i | −0.174700 | − | 0.0695197i | ||||
\(859\) | 6.93775e15i | 0.506123i | 0.967450 | + | 0.253061i | \(0.0814375\pi\) | ||||
−0.967450 | + | 0.253061i | \(0.918563\pi\) | |||||||
\(860\) | 1.31522e16 | + | 1.24369e16i | 0.953360 | + | 0.901513i | ||||
\(861\) | 2.42992e16i | 1.75015i | ||||||||
\(862\) | −4.44266e15 | + | 1.11642e16i | −0.317946 | + | 0.798986i | ||||
\(863\) | 1.06340e16 | 0.756201 | 0.378101 | − | 0.925765i | \(-0.376577\pi\) | ||||
0.378101 | + | 0.925765i | \(0.376577\pi\) | |||||||
\(864\) | −4.68223e15 | + | 1.39960e16i | −0.330847 | + | 0.988959i | ||||
\(865\) | 3.07608e15 | 0.215978 | ||||||||
\(866\) | −1.84016e15 | + | 4.62425e15i | −0.128383 | + | 0.322621i | ||||
\(867\) | 3.39981e15i | 0.235694i | ||||||||
\(868\) | −8.72511e15 | − | 8.25060e15i | −0.601052 | − | 0.568365i | ||||
\(869\) | − | 3.14968e15i | − | 0.215604i | ||||||
\(870\) | −7.95889e15 | − | 3.16714e15i | −0.541373 | − | 0.215432i | ||||
\(871\) | 5.17194e15 | 0.349586 | ||||||||
\(872\) | −5.07821e15 | − | 1.09392e16i | −0.341091 | − | 0.734761i | ||||
\(873\) | 1.16380e15 | 0.0776784 | ||||||||
\(874\) | −3.53641e15 | − | 1.40727e15i | −0.234558 | − | 0.0933393i | ||||
\(875\) | − | 8.78372e15i | − | 0.578941i | ||||||
\(876\) | 9.44259e15 | − | 9.98565e15i | 0.618470 | − | 0.654039i | ||||
\(877\) | − | 1.60338e16i | − | 1.04361i | −0.853064 | − | 0.521807i | \(-0.825258\pi\) | ||
0.853064 | − | 0.521807i | \(-0.174742\pi\) | |||||||
\(878\) | −7.02516e15 | + | 1.76540e16i | −0.454398 | + | 1.14189i | ||||
\(879\) | 1.95369e15 | 0.125579 | ||||||||
\(880\) | −4.35184e14 | − | 7.77835e15i | −0.0277983 | − | 0.496859i | ||||
\(881\) | −1.14261e16 | −0.725319 | −0.362659 | − | 0.931922i | \(-0.618131\pi\) | ||||
−0.362659 | + | 0.931922i | \(0.618131\pi\) | |||||||
\(882\) | 4.82285e15 | − | 1.21196e16i | 0.304247 | − | 0.764561i | ||||
\(883\) | − | 2.92988e16i | − | 1.83682i | −0.395631 | − | 0.918409i | \(-0.629474\pi\) | ||
0.395631 | − | 0.918409i | \(-0.370526\pi\) | |||||||
\(884\) | −1.07294e16 | + | 1.13465e16i | −0.668481 | + | 0.706927i | ||||
\(885\) | − | 2.67420e16i | − | 1.65579i | ||||||
\(886\) | 1.84633e16 | + | 7.34721e15i | 1.13612 | + | 0.452103i | ||||
\(887\) | 1.75093e16 | 1.07075 | 0.535375 | − | 0.844614i | \(-0.320170\pi\) | ||||
0.535375 | + | 0.844614i | \(0.320170\pi\) | |||||||
\(888\) | −9.68479e15 | + | 4.49588e15i | −0.588598 | + | 0.273239i | ||||
\(889\) | −4.52606e15 | −0.273376 | ||||||||
\(890\) | 3.49364e15 | + | 1.39025e15i | 0.209717 | + | 0.0834541i | ||||
\(891\) | 8.96408e14i | 0.0534784i | ||||||||
\(892\) | −6.51130e15 | − | 6.15719e15i | −0.386065 | − | 0.365070i | ||||
\(893\) | − | 4.52665e15i | − | 0.266744i | ||||||
\(894\) | −2.98410e15 | + | 7.49893e15i | −0.174766 | + | 0.439181i | ||||
\(895\) | 7.63394e15 | 0.444347 | ||||||||
\(896\) | 1.29107e16 | + | 2.41757e16i | 0.746891 | + | 1.39857i | ||||
\(897\) | 7.81140e15 | 0.449128 | ||||||||
\(898\) | −3.83836e15 | + | 9.64565e15i | −0.219344 | + | 0.551203i | ||||
\(899\) | 5.28897e15i | 0.300395i | ||||||||
\(900\) | 8.70186e15 | + | 8.22862e15i | 0.491223 | + | 0.464508i | ||||
\(901\) | − | 1.16753e15i | − | 0.0655063i | ||||||
\(902\) | 9.04386e15 | + | 3.59888e15i | 0.504333 | + | 0.200693i | ||||
\(903\) | −1.69286e16 | −0.938294 | ||||||||
\(904\) | −8.06736e15 | + | 3.74503e15i | −0.444432 | + | 0.206314i | ||||
\(905\) | −1.01077e16 | −0.553458 | ||||||||
\(906\) | −2.01269e16 | − | 8.00922e15i | −1.09540 | − | 0.435898i | ||||
\(907\) | 2.44390e16i | 1.32204i | 0.750370 | + | 0.661018i | \(0.229875\pi\) | ||||
−0.750370 | + | 0.661018i | \(0.770125\pi\) | |||||||
\(908\) | −5.55095e15 | + | 5.87019e15i | −0.298466 | + | 0.315631i | ||||
\(909\) | − | 2.94732e15i | − | 0.157517i | ||||||
\(910\) | 1.38478e16 | − | 3.47990e16i | 0.735620 | − | 1.84859i | ||||
\(911\) | 1.21506e15 | 0.0641576 | 0.0320788 | − | 0.999485i | \(-0.489787\pi\) | ||||
0.0320788 | + | 0.999485i | \(0.489787\pi\) | |||||||
\(912\) | 2.28750e14 | + | 4.08860e15i | 0.0120057 | + | 0.214587i | ||||
\(913\) | −7.85537e14 | −0.0409805 | ||||||||
\(914\) | 1.32998e16 | − | 3.34218e16i | 0.689668 | − | 1.73311i | ||||
\(915\) | 3.16446e16i | 1.63111i | ||||||||
\(916\) | 9.41064e15 | − | 9.95187e15i | 0.482163 | − | 0.509894i | ||||
\(917\) | 3.95764e14i | 0.0201560i | ||||||||
\(918\) | 2.22287e16 | + | 8.84560e15i | 1.12533 | + | 0.447809i | ||||
\(919\) | 1.48461e16 | 0.747095 | 0.373548 | − | 0.927611i | \(-0.378141\pi\) | ||||
0.373548 | + | 0.927611i | \(0.378141\pi\) | |||||||
\(920\) | 1.00057e16 | + | 2.15538e16i | 0.500512 | + | 1.07818i | ||||
\(921\) | 2.58006e16 | 1.28293 | ||||||||
\(922\) | −6.08739e15 | − | 2.42240e15i | −0.300892 | − | 0.119736i | ||||
\(923\) | 4.22002e15i | 0.207350i | ||||||||
\(924\) | 5.29378e15 | + | 5.00589e15i | 0.258565 | + | 0.244503i | ||||
\(925\) | 2.46051e16i | 1.19466i | ||||||||
\(926\) | −8.85578e14 | + | 2.22542e15i | −0.0427432 | + | 0.107412i | ||||
\(927\) | 5.66802e15 | 0.271952 | ||||||||
\(928\) | 3.82970e15 | − | 1.14476e16i | 0.182663 | − | 0.546012i | ||||
\(929\) | 2.85016e16 | 1.35140 | 0.675698 | − | 0.737179i | \(-0.263843\pi\) | ||||
0.675698 | + | 0.737179i | \(0.263843\pi\) | |||||||
\(930\) | −4.14174e15 | + | 1.04080e16i | −0.195221 | + | 0.490583i | ||||
\(931\) | − | 1.02777e16i | − | 0.481586i | ||||||
\(932\) | −9.23880e15 | − | 8.73636e15i | −0.430356 | − | 0.406952i | ||||
\(933\) | 8.91423e15i | 0.412795i | ||||||||
\(934\) | −2.92873e16 | − | 1.16545e16i | −1.34825 | − | 0.536520i | ||||
\(935\) | −1.26287e16 | −0.577958 | ||||||||
\(936\) | 4.21421e15 | + | 9.07804e15i | 0.191734 | + | 0.413024i | ||||
\(937\) | −3.85184e16 | −1.74221 | −0.871106 | − | 0.491096i | \(-0.836597\pi\) | ||||
−0.871106 | + | 0.491096i | \(0.836597\pi\) | |||||||
\(938\) | −1.36715e16 | − | 5.44039e15i | −0.614753 | − | 0.244633i | ||||
\(939\) | 1.57327e16i | 0.703301i | ||||||||
\(940\) | −1.94177e16 | + | 2.05344e16i | −0.862967 | + | 0.912598i | ||||
\(941\) | − | 2.94192e16i | − | 1.29983i | −0.760005 | − | 0.649917i | \(-0.774804\pi\) | ||
0.760005 | − | 0.649917i | \(-0.225196\pi\) | |||||||
\(942\) | 9.59026e15 | − | 2.40999e16i | 0.421260 | − | 1.05861i | ||||
\(943\) | −2.96899e16 | −1.29657 | ||||||||
\(944\) | 3.76265e16 | − | 2.10513e15i | 1.63361 | − | 0.0913973i | ||||
\(945\) | −5.73783e16 | −2.47670 | ||||||||
\(946\) | −2.50725e15 | + | 6.30062e15i | −0.107596 | + | 0.270385i | ||||
\(947\) | 1.23589e16i | 0.527297i | 0.964619 | + | 0.263649i | \(0.0849259\pi\) | ||||
−0.964619 | + | 0.263649i | \(0.915074\pi\) | |||||||
\(948\) | 7.10189e15 | − | 7.51033e15i | 0.301251 | − | 0.318576i | ||||
\(949\) | − | 2.64662e16i | − | 1.11616i | ||||||
\(950\) | 8.76780e15 | + | 3.48903e15i | 0.367630 | + | 0.146293i | ||||
\(951\) | 2.02788e16 | 0.845377 | ||||||||
\(952\) | 4.02976e16 | − | 1.87070e16i | 1.67023 | − | 0.775355i | ||||
\(953\) | 3.43202e15 | 0.141429 | 0.0707145 | − | 0.997497i | \(-0.477472\pi\) | ||||
0.0707145 | + | 0.997497i | \(0.477472\pi\) | |||||||
\(954\) | −6.95256e14 | − | 2.76668e14i | −0.0284858 | − | 0.0113356i | ||||
\(955\) | 7.29380e15i | 0.297123i | ||||||||
\(956\) | −2.67180e16 | − | 2.52650e16i | −1.08215 | − | 1.02329i | ||||
\(957\) | − | 3.20898e15i | − | 0.129226i | ||||||
\(958\) | −1.27772e14 | + | 3.21086e14i | −0.00511594 | + | 0.0128562i | ||||
\(959\) | 7.82516e14 | 0.0311524 | ||||||||
\(960\) | 1.65009e16 | − | 1.95285e16i | 0.653155 | − | 0.772997i | ||||
\(961\) | −1.84920e16 | −0.727787 | ||||||||
\(962\) | −7.60265e15 | + | 1.91052e16i | −0.297510 | + | 0.747632i | ||||
\(963\) | 2.53298e16i | 0.985570i | ||||||||
\(964\) | 1.47987e16 | + | 1.39939e16i | 0.572532 | + | 0.541395i | ||||
\(965\) | − | 3.87835e16i | − | 1.49193i | ||||||
\(966\) | −2.06486e16 | − | 8.21686e15i | −0.789801 | − | 0.314291i | ||||
\(967\) | −1.06675e16 | −0.405712 | −0.202856 | − | 0.979209i | \(-0.565022\pi\) | ||||
−0.202856 | + | 0.979209i | \(0.565022\pi\) | |||||||
\(968\) | −2.13377e16 | + | 9.90538e15i | −0.806924 | + | 0.374590i | ||||
\(969\) | 6.63815e15 | 0.249613 | ||||||||
\(970\) | −5.31940e15 | − | 2.11678e15i | −0.198892 | − | 0.0791466i | ||||
\(971\) | − | 4.21885e16i | − | 1.56851i | −0.620437 | − | 0.784256i | \(-0.713045\pi\) | ||
0.620437 | − | 0.784256i | \(-0.286955\pi\) | |||||||
\(972\) | 1.73600e16 | − | 1.83585e16i | 0.641780 | − | 0.678690i | ||||
\(973\) | 6.24540e16i | 2.29583i | ||||||||
\(974\) | 1.04066e16 | − | 2.61514e16i | 0.380395 | − | 0.955917i | ||||
\(975\) | −1.93667e16 | −0.703932 | ||||||||
\(976\) | −4.45246e16 | + | 2.49107e15i | −1.60926 | + | 0.0900350i | ||||
\(977\) | 1.40324e16 | 0.504326 | 0.252163 | − | 0.967685i | \(-0.418858\pi\) | ||||
0.252163 | + | 0.967685i | \(0.418858\pi\) | |||||||
\(978\) | −5.70429e15 | + | 1.43347e16i | −0.203863 | + | 0.512299i | ||||
\(979\) | 1.40862e15i | 0.0500596i | ||||||||
\(980\) | −4.40877e16 | + | 4.66233e16i | −1.55802 | + | 1.64763i | ||||
\(981\) | 1.25301e16i | 0.440326i | ||||||||
\(982\) | 3.22605e16 | + | 1.28377e16i | 1.12735 | + | 0.448614i | ||||
\(983\) | 4.61601e16 | 1.60407 | 0.802033 | − | 0.597280i | \(-0.203752\pi\) | ||||
0.802033 | + | 0.597280i | \(0.203752\pi\) | |||||||
\(984\) | 1.34501e16 | + | 2.89735e16i | 0.464785 | + | 1.00122i | ||||
\(985\) | 6.02587e16 | 2.07071 | ||||||||
\(986\) | −1.81813e16 | − | 7.23501e15i | −0.621301 | − | 0.247239i | ||||
\(987\) | − | 2.64305e16i | − | 0.898176i | ||||||
\(988\) | 5.72988e15 | + | 5.41826e15i | 0.193634 | + | 0.183104i | ||||
\(989\) | − | 2.06842e16i | − | 0.695118i | ||||||
\(990\) | −2.99261e15 | + | 7.52030e15i | −0.100013 | + | 0.251329i | ||||
\(991\) | −4.19157e16 | −1.39307 | −0.696534 | − | 0.717524i | \(-0.745275\pi\) | ||||
−0.696534 | + | 0.717524i | \(0.745275\pi\) | |||||||
\(992\) | −1.49704e16 | − | 5.00820e15i | −0.494787 | − | 0.165526i | ||||
\(993\) | 1.51045e16 | 0.496460 | ||||||||
\(994\) | 4.43906e15 | − | 1.11552e16i | 0.145100 | − | 0.364630i | ||||
\(995\) | 2.86952e16i | 0.932785i | ||||||||
\(996\) | −1.87309e15 | − | 1.77123e15i | −0.0605526 | − | 0.0572595i | ||||
\(997\) | 2.51325e16i | 0.808002i | 0.914759 | + | 0.404001i | \(0.132381\pi\) | ||||
−0.914759 | + | 0.404001i | \(0.867619\pi\) | |||||||
\(998\) | 5.13542e16 | + | 2.04358e16i | 1.64194 | + | 0.653390i | ||||
\(999\) | 3.15015e16 | 1.00166 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8.12.b.a.5.5 | ✓ | 10 | |
3.2 | odd | 2 | 72.12.d.b.37.6 | 10 | |||
4.3 | odd | 2 | 32.12.b.a.17.4 | 10 | |||
8.3 | odd | 2 | 32.12.b.a.17.7 | 10 | |||
8.5 | even | 2 | inner | 8.12.b.a.5.6 | yes | 10 | |
16.3 | odd | 4 | 256.12.a.o.1.7 | 10 | |||
16.5 | even | 4 | 256.12.a.p.1.7 | 10 | |||
16.11 | odd | 4 | 256.12.a.o.1.4 | 10 | |||
16.13 | even | 4 | 256.12.a.p.1.4 | 10 | |||
24.5 | odd | 2 | 72.12.d.b.37.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.12.b.a.5.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8.12.b.a.5.6 | yes | 10 | 8.5 | even | 2 | inner | |
32.12.b.a.17.4 | 10 | 4.3 | odd | 2 | |||
32.12.b.a.17.7 | 10 | 8.3 | odd | 2 | |||
72.12.d.b.37.5 | 10 | 24.5 | odd | 2 | |||
72.12.d.b.37.6 | 10 | 3.2 | odd | 2 | |||
256.12.a.o.1.4 | 10 | 16.11 | odd | 4 | |||
256.12.a.o.1.7 | 10 | 16.3 | odd | 4 | |||
256.12.a.p.1.4 | 10 | 16.13 | even | 4 | |||
256.12.a.p.1.7 | 10 | 16.5 | even | 4 |