Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,15,Mod(5,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.5");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(7.45973808911\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-35})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 23x^{2} - 22x + 51 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(0.500000 + 4.37225i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6.5 |
Dual form | 6.15.b.a.5.4 |
$q$-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 \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 90.5097i | − | 0.707107i | ||||||
\(3\) | 385.790 | + | 2152.70i | 0.176402 | + | 0.984318i | ||||
\(4\) | −8192.00 | −0.500000 | ||||||||
\(5\) | − | 105253.i | − | 1.34723i | −0.739081 | − | 0.673616i | \(-0.764740\pi\) | ||
0.739081 | − | 0.673616i | \(-0.235260\pi\) | |||||||
\(6\) | 194841. | − | 34917.8i | 0.696018 | − | 0.124735i | ||||
\(7\) | −1.21591e6 | −1.47644 | −0.738218 | − | 0.674562i | \(-0.764332\pi\) | ||||
−0.738218 | + | 0.674562i | \(0.764332\pi\) | |||||||
\(8\) | 741455.i | 0.353553i | ||||||||
\(9\) | −4.48530e6 | + | 1.66099e6i | −0.937765 | + | 0.347271i | ||||
\(10\) | −9.52637e6 | −0.952637 | ||||||||
\(11\) | − | 1.71107e7i | − | 0.878047i | −0.898476 | − | 0.439024i | \(-0.855324\pi\) | ||
0.898476 | − | 0.439024i | \(-0.144676\pi\) | |||||||
\(12\) | −3.16040e6 | − | 1.76350e7i | −0.0882008 | − | 0.492159i | ||||
\(13\) | −6.76914e7 | −1.07877 | −0.539387 | − | 0.842058i | \(-0.681344\pi\) | ||||
−0.539387 | + | 0.842058i | \(0.681344\pi\) | |||||||
\(14\) | 1.10051e8i | 1.04400i | ||||||||
\(15\) | 2.26578e8 | − | 4.06054e7i | 1.32611 | − | 0.237654i | ||||
\(16\) | 6.71089e7 | 0.250000 | ||||||||
\(17\) | − | 1.67802e8i | − | 0.408936i | −0.978873 | − | 0.204468i | \(-0.934454\pi\) | ||
0.978873 | − | 0.204468i | \(-0.0655464\pi\) | |||||||
\(18\) | 1.50335e8 | + | 4.05963e8i | 0.245558 | + | 0.663100i | ||||
\(19\) | 8.08356e8 | 0.904331 | 0.452166 | − | 0.891934i | \(-0.350652\pi\) | ||||
0.452166 | + | 0.891934i | \(0.350652\pi\) | |||||||
\(20\) | 8.62229e8i | 0.673616i | ||||||||
\(21\) | −4.69086e8 | − | 2.61749e9i | −0.260446 | − | 1.45328i | ||||
\(22\) | −1.54868e9 | −0.620873 | ||||||||
\(23\) | 1.02641e9i | 0.301457i | 0.988575 | + | 0.150729i | \(0.0481620\pi\) | ||||
−0.988575 | + | 0.150729i | \(0.951838\pi\) | |||||||
\(24\) | −1.59613e9 | + | 2.86046e8i | −0.348009 | + | 0.0623674i | ||||
\(25\) | −4.97458e9 | −0.815036 | ||||||||
\(26\) | 6.12673e9i | 0.762808i | ||||||||
\(27\) | −5.30600e9 | − | 9.01473e9i | −0.507248 | − | 0.861800i | ||||
\(28\) | 9.96072e9 | 0.738218 | ||||||||
\(29\) | 1.38422e10i | 0.802451i | 0.915979 | + | 0.401225i | \(0.131416\pi\) | ||||
−0.915979 | + | 0.401225i | \(0.868584\pi\) | |||||||
\(30\) | −3.67518e9 | − | 2.05075e10i | −0.168047 | − | 0.937698i | ||||
\(31\) | 3.15369e10 | 1.14627 | 0.573136 | − | 0.819460i | \(-0.305727\pi\) | ||||
0.573136 | + | 0.819460i | \(0.305727\pi\) | |||||||
\(32\) | − | 6.07400e9i | − | 0.176777i | ||||||
\(33\) | 3.68342e10 | − | 6.60113e9i | 0.864278 | − | 0.154889i | ||||
\(34\) | −1.51877e10 | −0.289161 | ||||||||
\(35\) | 1.27977e11i | 1.98910i | ||||||||
\(36\) | 3.67436e10 | − | 1.36068e10i | 0.468882 | − | 0.173635i | ||||
\(37\) | −1.41457e11 | −1.49009 | −0.745045 | − | 0.667014i | \(-0.767572\pi\) | ||||
−0.745045 | + | 0.667014i | \(0.767572\pi\) | |||||||
\(38\) | − | 7.31641e10i | − | 0.639459i | ||||||
\(39\) | −2.61147e10 | − | 1.45720e11i | −0.190297 | − | 1.06186i | ||||
\(40\) | 7.80400e10 | 0.476319 | ||||||||
\(41\) | − | 7.34964e10i | − | 0.377380i | −0.982037 | − | 0.188690i | \(-0.939576\pi\) | ||
0.982037 | − | 0.188690i | \(-0.0604241\pi\) | |||||||
\(42\) | −2.36908e11 | + | 4.24568e10i | −1.02763 | + | 0.184163i | ||||
\(43\) | −1.15815e11 | −0.426076 | −0.213038 | − | 0.977044i | \(-0.568336\pi\) | ||||
−0.213038 | + | 0.977044i | \(0.568336\pi\) | |||||||
\(44\) | 1.40170e11i | 0.439024i | ||||||||
\(45\) | 1.74823e11 | + | 4.72089e11i | 0.467854 | + | 1.26339i | ||||
\(46\) | 9.29000e10 | 0.213163 | ||||||||
\(47\) | − | 6.63761e11i | − | 1.31017i | −0.755556 | − | 0.655084i | \(-0.772633\pi\) | ||
0.755556 | − | 0.655084i | \(-0.227367\pi\) | |||||||
\(48\) | 2.58900e10 | + | 1.44466e11i | 0.0441004 | + | 0.246080i | ||||
\(49\) | 8.00210e11 | 1.17986 | ||||||||
\(50\) | 4.50248e11i | 0.576317i | ||||||||
\(51\) | 3.61228e11 | − | 6.47365e10i | 0.402523 | − | 0.0721370i | ||||
\(52\) | 5.54528e11 | 0.539387 | ||||||||
\(53\) | − | 1.04506e12i | − | 0.889635i | −0.895621 | − | 0.444817i | \(-0.853269\pi\) | ||
0.895621 | − | 0.444817i | \(-0.146731\pi\) | |||||||
\(54\) | −8.15920e11 | + | 4.80244e11i | −0.609385 | + | 0.358679i | ||||
\(55\) | −1.80094e12 | −1.18293 | ||||||||
\(56\) | − | 9.01542e11i | − | 0.521999i | ||||||
\(57\) | 3.11856e11 | + | 1.74015e12i | 0.159526 | + | 0.890150i | ||||
\(58\) | 1.25285e12 | 0.567418 | ||||||||
\(59\) | 2.50227e11i | 0.100547i | 0.998735 | + | 0.0502736i | \(0.0160093\pi\) | ||||
−0.998735 | + | 0.0502736i | \(0.983991\pi\) | |||||||
\(60\) | −1.85612e12 | + | 3.32640e11i | −0.663053 | + | 0.118827i | ||||
\(61\) | −5.74063e12 | −1.82663 | −0.913315 | − | 0.407253i | \(-0.866487\pi\) | ||||
−0.913315 | + | 0.407253i | \(0.866487\pi\) | |||||||
\(62\) | − | 2.85440e12i | − | 0.810537i | ||||||
\(63\) | 5.45371e12 | − | 2.01961e12i | 1.38455 | − | 0.512723i | ||||
\(64\) | −5.49756e11 | −0.125000 | ||||||||
\(65\) | 7.12470e12i | 1.45336i | ||||||||
\(66\) | −5.97466e11 | − | 3.33385e12i | −0.109523 | − | 0.611137i | ||||
\(67\) | 4.64817e12 | 0.766935 | 0.383467 | − | 0.923554i | \(-0.374730\pi\) | ||||
0.383467 | + | 0.923554i | \(0.374730\pi\) | |||||||
\(68\) | 1.37464e12i | 0.204468i | ||||||||
\(69\) | −2.20956e12 | + | 3.95979e11i | −0.296730 | + | 0.0531776i | ||||
\(70\) | 1.15832e13 | 1.40651 | ||||||||
\(71\) | − | 4.07288e12i | − | 0.447809i | −0.974611 | − | 0.223904i | \(-0.928120\pi\) | ||
0.974611 | − | 0.223904i | \(-0.0718803\pi\) | |||||||
\(72\) | −1.23155e12 | − | 3.32565e12i | −0.122779 | − | 0.331550i | ||||
\(73\) | 4.29948e12 | 0.389185 | 0.194592 | − | 0.980884i | \(-0.437662\pi\) | ||||
0.194592 | + | 0.980884i | \(0.437662\pi\) | |||||||
\(74\) | 1.28032e13i | 1.05365i | ||||||||
\(75\) | −1.91915e12 | − | 1.07088e13i | −0.143774 | − | 0.802255i | ||||
\(76\) | −6.62205e12 | −0.452166 | ||||||||
\(77\) | 2.08050e13i | 1.29638i | ||||||||
\(78\) | −1.31890e13 | + | 2.36363e12i | −0.750846 | + | 0.134561i | ||||
\(79\) | −1.78802e13 | −0.931071 | −0.465536 | − | 0.885029i | \(-0.654138\pi\) | ||||
−0.465536 | + | 0.885029i | \(0.654138\pi\) | |||||||
\(80\) | − | 7.06338e12i | − | 0.336808i | ||||||
\(81\) | 1.73590e13 | − | 1.49000e13i | 0.758806 | − | 0.651317i | ||||
\(82\) | −6.65213e12 | −0.266848 | ||||||||
\(83\) | − | 5.35709e13i | − | 1.97416i | −0.160229 | − | 0.987080i | \(-0.551223\pi\) | ||
0.160229 | − | 0.987080i | \(-0.448777\pi\) | |||||||
\(84\) | 3.84275e12 | + | 2.14425e13i | 0.130223 | + | 0.726641i | ||||
\(85\) | −1.76616e13 | −0.550932 | ||||||||
\(86\) | 1.04824e13i | 0.301281i | ||||||||
\(87\) | −2.97981e13 | + | 5.34018e12i | −0.789867 | + | 0.141554i | ||||
\(88\) | 1.26868e13 | 0.310437 | ||||||||
\(89\) | 6.15032e13i | 1.39049i | 0.718773 | + | 0.695245i | \(0.244704\pi\) | ||||
−0.718773 | + | 0.695245i | \(0.755296\pi\) | |||||||
\(90\) | 4.27286e13 | − | 1.58232e13i | 0.893350 | − | 0.330823i | ||||
\(91\) | 8.23066e13 | 1.59274 | ||||||||
\(92\) | − | 8.40835e12i | − | 0.150729i | ||||||
\(93\) | 1.21667e13 | + | 6.78897e13i | 0.202204 | + | 1.12830i | ||||
\(94\) | −6.00768e13 | −0.926429 | ||||||||
\(95\) | − | 8.50816e13i | − | 1.21834i | ||||||
\(96\) | 1.30755e13 | − | 2.34329e12i | 0.174005 | − | 0.0311837i | ||||
\(97\) | 1.58213e12 | 0.0195812 | 0.00979061 | − | 0.999952i | \(-0.496884\pi\) | ||||
0.00979061 | + | 0.999952i | \(0.496884\pi\) | |||||||
\(98\) | − | 7.24268e13i | − | 0.834289i | ||||||
\(99\) | 2.84205e13 | + | 7.67464e13i | 0.304920 | + | 0.823402i | ||||
\(100\) | 4.07518e13 | 0.407518 | ||||||||
\(101\) | − | 4.44794e13i | − | 0.414868i | −0.978249 | − | 0.207434i | \(-0.933489\pi\) | ||
0.978249 | − | 0.207434i | \(-0.0665112\pi\) | |||||||
\(102\) | −5.85928e12 | − | 3.26947e13i | −0.0510085 | − | 0.284627i | ||||
\(103\) | −5.24487e13 | −0.426456 | −0.213228 | − | 0.977002i | \(-0.568398\pi\) | ||||
−0.213228 | + | 0.977002i | \(0.568398\pi\) | |||||||
\(104\) | − | 5.01902e13i | − | 0.381404i | ||||||
\(105\) | −2.75498e14 | + | 4.93725e13i | −1.95791 | + | 0.350881i | ||||
\(106\) | −9.45884e13 | −0.629067 | ||||||||
\(107\) | 1.69128e14i | 1.05324i | 0.850100 | + | 0.526621i | \(0.176541\pi\) | ||||
−0.850100 | + | 0.526621i | \(0.823459\pi\) | |||||||
\(108\) | 4.34667e13 | + | 7.38487e13i | 0.253624 | + | 0.430900i | ||||
\(109\) | 1.41557e14 | 0.774363 | 0.387181 | − | 0.922004i | \(-0.373449\pi\) | ||||
0.387181 | + | 0.922004i | \(0.373449\pi\) | |||||||
\(110\) | 1.63002e14i | 0.836460i | ||||||||
\(111\) | −5.45728e13 | − | 3.04515e14i | −0.262854 | − | 1.46672i | ||||
\(112\) | −8.15982e13 | −0.369109 | ||||||||
\(113\) | − | 1.21295e14i | − | 0.515577i | −0.966201 | − | 0.257789i | \(-0.917006\pi\) | ||
0.966201 | − | 0.257789i | \(-0.0829938\pi\) | |||||||
\(114\) | 1.57501e14 | − | 2.82260e13i | 0.629431 | − | 0.112802i | ||||
\(115\) | 1.08032e14 | 0.406133 | ||||||||
\(116\) | − | 1.13395e14i | − | 0.401225i | ||||||
\(117\) | 3.03616e14 | − | 1.12435e14i | 1.01164 | − | 0.374627i | ||||
\(118\) | 2.26480e13 | 0.0710976 | ||||||||
\(119\) | 2.04032e14i | 0.603768i | ||||||||
\(120\) | 3.01071e13 | + | 1.67997e14i | 0.0840234 | + | 0.468849i | ||||
\(121\) | 8.69753e13 | 0.229033 | ||||||||
\(122\) | 5.19583e14i | 1.29162i | ||||||||
\(123\) | 1.58216e14 | − | 2.83542e13i | 0.371462 | − | 0.0665705i | ||||
\(124\) | −2.58351e14 | −0.573136 | ||||||||
\(125\) | − | 1.18823e14i | − | 0.249190i | ||||||
\(126\) | −1.82794e14 | − | 4.93614e14i | −0.362550 | − | 0.979025i | ||||
\(127\) | −1.48696e14 | −0.279045 | −0.139522 | − | 0.990219i | \(-0.544557\pi\) | ||||
−0.139522 | + | 0.990219i | \(0.544557\pi\) | |||||||
\(128\) | 4.97582e13i | 0.0883883i | ||||||||
\(129\) | −4.46805e13 | − | 2.49316e14i | −0.0751605 | − | 0.419394i | ||||
\(130\) | 6.44854e14 | 1.02768 | ||||||||
\(131\) | 3.88934e14i | 0.587457i | 0.955889 | + | 0.293729i | \(0.0948962\pi\) | ||||
−0.955889 | + | 0.293729i | \(0.905104\pi\) | |||||||
\(132\) | −3.01746e14 | + | 5.40764e13i | −0.432139 | + | 0.0774445i | ||||
\(133\) | −9.82887e14 | −1.33519 | ||||||||
\(134\) | − | 4.20704e14i | − | 0.542305i | ||||||
\(135\) | −9.48824e14 | + | 5.58470e14i | −1.16105 | + | 0.683381i | ||||
\(136\) | 1.24418e14 | 0.144581 | ||||||||
\(137\) | − | 4.99822e14i | − | 0.551787i | −0.961188 | − | 0.275893i | \(-0.911026\pi\) | ||
0.961188 | − | 0.275893i | \(-0.0889737\pi\) | |||||||
\(138\) | 3.58399e13 | + | 1.99986e14i | 0.0376022 | + | 0.209820i | ||||
\(139\) | 2.14174e13 | 0.0213630 | 0.0106815 | − | 0.999943i | \(-0.496600\pi\) | ||||
0.0106815 | + | 0.999943i | \(0.496600\pi\) | |||||||
\(140\) | − | 1.04839e15i | − | 0.994551i | ||||||
\(141\) | 1.42888e15 | − | 2.56073e14i | 1.28962 | − | 0.231116i | ||||
\(142\) | −3.68635e14 | −0.316649 | ||||||||
\(143\) | 1.15825e15i | 0.947214i | ||||||||
\(144\) | −3.01003e14 | + | 1.11467e14i | −0.234441 | + | 0.0868177i | ||||
\(145\) | 1.45692e15 | 1.08109 | ||||||||
\(146\) | − | 3.89144e14i | − | 0.275195i | ||||||
\(147\) | 3.08713e14 | + | 1.72262e15i | 0.208130 | + | 1.16136i | ||||
\(148\) | 1.15882e15 | 0.745045 | ||||||||
\(149\) | − | 8.78713e14i | − | 0.538943i | −0.963008 | − | 0.269472i | \(-0.913151\pi\) | ||
0.963008 | − | 0.269472i | \(-0.0868491\pi\) | |||||||
\(150\) | −9.69250e14 | + | 1.73701e14i | −0.567280 | + | 0.101663i | ||||
\(151\) | −1.91539e14 | −0.107008 | −0.0535042 | − | 0.998568i | \(-0.517039\pi\) | ||||
−0.0535042 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(152\) | 5.99360e14i | 0.319729i | ||||||||
\(153\) | 2.78717e14 | + | 7.52643e14i | 0.142011 | + | 0.383486i | ||||
\(154\) | 1.88305e15 | 0.916679 | ||||||||
\(155\) | − | 3.31934e15i | − | 1.54430i | ||||||
\(156\) | 2.13932e14 | + | 1.19374e15i | 0.0951487 | + | 0.530928i | ||||
\(157\) | −4.31468e15 | −1.83506 | −0.917531 | − | 0.397663i | \(-0.869821\pi\) | ||||
−0.917531 | + | 0.397663i | \(0.869821\pi\) | |||||||
\(158\) | 1.61833e15i | 0.658367i | ||||||||
\(159\) | 2.24971e15 | − | 4.03176e14i | 0.875684 | − | 0.156933i | ||||
\(160\) | −6.39304e14 | −0.238159 | ||||||||
\(161\) | − | 1.24802e15i | − | 0.445083i | ||||||
\(162\) | −1.34860e15 | − | 1.57116e15i | −0.460550 | − | 0.536557i | ||||
\(163\) | −1.99493e14 | −0.0652550 | −0.0326275 | − | 0.999468i | \(-0.510388\pi\) | ||||
−0.0326275 | + | 0.999468i | \(0.510388\pi\) | |||||||
\(164\) | 6.02082e14i | 0.188690i | ||||||||
\(165\) | −6.94785e14 | − | 3.87689e15i | −0.208671 | − | 1.16438i | ||||
\(166\) | −4.84868e15 | −1.39594 | ||||||||
\(167\) | 3.20465e15i | 0.884638i | 0.896858 | + | 0.442319i | \(0.145844\pi\) | ||||
−0.896858 | + | 0.442319i | \(0.854156\pi\) | |||||||
\(168\) | 1.94075e15 | − | 3.47806e14i | 0.513813 | − | 0.0920815i | ||||
\(169\) | 6.44756e14 | 0.163753 | ||||||||
\(170\) | 1.59855e15i | 0.389568i | ||||||||
\(171\) | −3.62572e15 | + | 1.34267e15i | −0.848050 | + | 0.314048i | ||||
\(172\) | 9.48760e14 | 0.213038 | ||||||||
\(173\) | 3.22827e15i | 0.696061i | 0.937483 | + | 0.348031i | \(0.113149\pi\) | ||||
−0.937483 | + | 0.348031i | \(0.886851\pi\) | |||||||
\(174\) | 4.83338e14 | + | 2.69702e15i | 0.100094 | + | 0.558520i | ||||
\(175\) | 6.04864e15 | 1.20335 | ||||||||
\(176\) | − | 1.14828e15i | − | 0.219512i | ||||||
\(177\) | −5.38664e14 | + | 9.65351e13i | −0.0989704 | + | 0.0177367i | ||||
\(178\) | 5.56663e15 | 0.983224 | ||||||||
\(179\) | − | 1.26665e15i | − | 0.215122i | −0.994198 | − | 0.107561i | \(-0.965696\pi\) | ||
0.994198 | − | 0.107561i | \(-0.0343042\pi\) | |||||||
\(180\) | −1.43215e15 | − | 3.86736e15i | −0.233927 | − | 0.631694i | ||||
\(181\) | 5.69529e15 | 0.894882 | 0.447441 | − | 0.894314i | \(-0.352336\pi\) | ||||
0.447441 | + | 0.894314i | \(0.352336\pi\) | |||||||
\(182\) | − | 7.44954e15i | − | 1.12624i | ||||||
\(183\) | −2.21468e15 | − | 1.23579e16i | −0.322221 | − | 1.79799i | ||||
\(184\) | −7.61037e14 | −0.106581 | ||||||||
\(185\) | 1.48887e16i | 2.00750i | ||||||||
\(186\) | 6.14468e15 | − | 1.10120e15i | 0.797826 | − | 0.142980i | ||||
\(187\) | −2.87121e15 | −0.359065 | ||||||||
\(188\) | 5.43753e15i | 0.655084i | ||||||||
\(189\) | 6.45161e15 | + | 1.09611e16i | 0.748920 | + | 1.27239i | ||||
\(190\) | −7.70070e15 | −0.861500 | ||||||||
\(191\) | − | 1.27381e15i | − | 0.137363i | −0.997639 | − | 0.0686816i | \(-0.978121\pi\) | ||
0.997639 | − | 0.0686816i | \(-0.0218792\pi\) | |||||||
\(192\) | −2.12091e14 | − | 1.18346e15i | −0.0220502 | − | 0.123040i | ||||
\(193\) | −8.57584e15 | −0.859757 | −0.429878 | − | 0.902887i | \(-0.641444\pi\) | ||||
−0.429878 | + | 0.902887i | \(0.641444\pi\) | |||||||
\(194\) | − | 1.43198e14i | − | 0.0138460i | ||||||
\(195\) | −1.53374e16 | + | 2.74864e15i | −1.43057 | + | 0.256375i | ||||
\(196\) | −6.55532e15 | −0.589931 | ||||||||
\(197\) | − | 1.19404e16i | − | 1.03695i | −0.855094 | − | 0.518473i | \(-0.826501\pi\) | ||
0.855094 | − | 0.518473i | \(-0.173499\pi\) | |||||||
\(198\) | 6.94629e15 | − | 2.57233e15i | 0.582233 | − | 0.215611i | ||||
\(199\) | 7.87496e15 | 0.637202 | 0.318601 | − | 0.947889i | \(-0.396787\pi\) | ||||
0.318601 | + | 0.947889i | \(0.396787\pi\) | |||||||
\(200\) | − | 3.68843e15i | − | 0.288159i | ||||||
\(201\) | 1.79322e15 | + | 1.00061e16i | 0.135289 | + | 0.754908i | ||||
\(202\) | −4.02582e15 | −0.293356 | ||||||||
\(203\) | − | 1.68308e16i | − | 1.18477i | ||||||
\(204\) | −2.95918e15 | + | 5.30321e14i | −0.201262 | + | 0.0360685i | ||||
\(205\) | −7.73568e15 | −0.508419 | ||||||||
\(206\) | 4.74712e15i | 0.301550i | ||||||||
\(207\) | −1.70485e15 | − | 4.60376e15i | −0.104687 | − | 0.282696i | ||||
\(208\) | −4.54270e15 | −0.269693 | ||||||||
\(209\) | − | 1.38315e16i | − | 0.794046i | ||||||
\(210\) | 4.46869e15 | + | 2.49352e16i | 0.248110 | + | 1.38445i | ||||
\(211\) | 3.57862e16 | 1.92193 | 0.960967 | − | 0.276664i | \(-0.0892290\pi\) | ||||
0.960967 | + | 0.276664i | \(0.0892290\pi\) | |||||||
\(212\) | 8.56116e15i | 0.444817i | ||||||||
\(213\) | 8.76769e15 | − | 1.57128e15i | 0.440786 | − | 0.0789942i | ||||
\(214\) | 1.53077e16 | 0.744754 | ||||||||
\(215\) | 1.21899e16i | 0.574023i | ||||||||
\(216\) | 6.68402e15 | − | 3.93416e15i | 0.304692 | − | 0.179339i | ||||
\(217\) | −3.83460e16 | −1.69240 | ||||||||
\(218\) | − | 1.28122e16i | − | 0.547557i | ||||||
\(219\) | 1.65870e15 | + | 9.25550e15i | 0.0686528 | + | 0.383082i | ||||
\(220\) | 1.47533e16 | 0.591467 | ||||||||
\(221\) | 1.13588e16i | 0.441149i | ||||||||
\(222\) | −2.75616e16 | + | 4.93936e15i | −1.03713 | + | 0.185866i | ||||
\(223\) | 2.97756e16 | 1.08574 | 0.542870 | − | 0.839816i | \(-0.317337\pi\) | ||||
0.542870 | + | 0.839816i | \(0.317337\pi\) | |||||||
\(224\) | 7.38543e15i | 0.260999i | ||||||||
\(225\) | 2.23125e16 | − | 8.26271e15i | 0.764312 | − | 0.283038i | ||||
\(226\) | −1.09784e16 | −0.364568 | ||||||||
\(227\) | − | 4.31388e16i | − | 1.38895i | −0.719517 | − | 0.694475i | \(-0.755637\pi\) | ||
0.719517 | − | 0.694475i | \(-0.244363\pi\) | |||||||
\(228\) | −2.55473e15 | − | 1.42553e16i | −0.0797628 | − | 0.445075i | ||||
\(229\) | 1.02466e16 | 0.310263 | 0.155131 | − | 0.987894i | \(-0.450420\pi\) | ||||
0.155131 | + | 0.987894i | \(0.450420\pi\) | |||||||
\(230\) | − | 9.77797e15i | − | 0.287180i | ||||||
\(231\) | −4.47870e16 | + | 8.02637e15i | −1.27605 | + | 0.228684i | ||||
\(232\) | −1.02634e16 | −0.283709 | ||||||||
\(233\) | 6.13926e16i | 1.64674i | 0.567506 | + | 0.823369i | \(0.307908\pi\) | ||||
−0.567506 | + | 0.823369i | \(0.692092\pi\) | |||||||
\(234\) | −1.01764e16 | − | 2.74802e16i | −0.264901 | − | 0.715335i | ||||
\(235\) | −6.98626e16 | −1.76510 | ||||||||
\(236\) | − | 2.04986e15i | − | 0.0502736i | ||||||
\(237\) | −6.89801e15 | − | 3.84908e16i | −0.164242 | − | 0.916470i | ||||
\(238\) | 1.84669e16 | 0.426928 | ||||||||
\(239\) | 5.98554e16i | 1.34375i | 0.740665 | + | 0.671875i | \(0.234511\pi\) | ||||
−0.740665 | + | 0.671875i | \(0.765489\pi\) | |||||||
\(240\) | 1.52054e16 | − | 2.72498e15i | 0.331526 | − | 0.0594135i | ||||
\(241\) | −1.53889e16 | −0.325902 | −0.162951 | − | 0.986634i | \(-0.552101\pi\) | ||||
−0.162951 | + | 0.986634i | \(0.552101\pi\) | |||||||
\(242\) | − | 7.87211e15i | − | 0.161951i | ||||||
\(243\) | 3.87723e16 | + | 3.16206e16i | 0.774958 | + | 0.632013i | ||||
\(244\) | 4.70272e16 | 0.913315 | ||||||||
\(245\) | − | 8.42242e16i | − | 1.58955i | ||||||
\(246\) | −2.56633e15 | − | 1.43201e16i | −0.0470724 | − | 0.262663i | ||||
\(247\) | −5.47188e16 | −0.975569 | ||||||||
\(248\) | 2.33832e16i | 0.405268i | ||||||||
\(249\) | 1.15322e17 | − | 2.06671e16i | 1.94320 | − | 0.348245i | ||||
\(250\) | −1.07546e16 | −0.176204 | ||||||||
\(251\) | 1.01100e17i | 1.61078i | 0.592746 | + | 0.805389i | \(0.298044\pi\) | ||||
−0.592746 | + | 0.805389i | \(0.701956\pi\) | |||||||
\(252\) | −4.46768e16 | + | 1.65446e16i | −0.692275 | + | 0.256362i | ||||
\(253\) | 1.75625e16 | 0.264694 | ||||||||
\(254\) | 1.34584e16i | 0.197314i | ||||||||
\(255\) | −6.81368e15 | − | 3.80202e16i | −0.0971853 | − | 0.542292i | ||||
\(256\) | 4.50360e15 | 0.0625000 | ||||||||
\(257\) | 6.12785e16i | 0.827515i | 0.910387 | + | 0.413758i | \(0.135784\pi\) | ||||
−0.910387 | + | 0.413758i | \(0.864216\pi\) | |||||||
\(258\) | −2.25655e16 | + | 4.04401e15i | −0.296557 | + | 0.0531465i | ||||
\(259\) | 1.71999e17 | 2.20002 | ||||||||
\(260\) | − | 5.83655e16i | − | 0.726680i | ||||||
\(261\) | −2.29917e16 | − | 6.20863e16i | −0.278668 | − | 0.752510i | ||||
\(262\) | 3.52022e16 | 0.415395 | ||||||||
\(263\) | − | 1.18188e17i | − | 1.35795i | −0.734163 | − | 0.678973i | \(-0.762425\pi\) | ||
0.734163 | − | 0.678973i | \(-0.237575\pi\) | |||||||
\(264\) | 4.89444e15 | + | 2.73109e16i | 0.0547615 | + | 0.305568i | ||||
\(265\) | −1.09996e17 | −1.19855 | ||||||||
\(266\) | 8.89608e16i | 0.944120i | ||||||||
\(267\) | −1.32398e17 | + | 2.37273e16i | −1.36868 | + | 0.245285i | ||||
\(268\) | −3.80778e16 | −0.383467 | ||||||||
\(269\) | − | 1.90291e17i | − | 1.86704i | −0.358528 | − | 0.933519i | \(-0.616721\pi\) | ||
0.358528 | − | 0.933519i | \(-0.383279\pi\) | |||||||
\(270\) | 5.05469e16 | + | 8.58777e16i | 0.483224 | + | 0.820983i | ||||
\(271\) | 4.08475e16 | 0.380523 | 0.190261 | − | 0.981733i | \(-0.439066\pi\) | ||||
0.190261 | + | 0.981733i | \(0.439066\pi\) | |||||||
\(272\) | − | 1.12610e16i | − | 0.102234i | ||||||
\(273\) | 3.17531e16 | + | 1.77182e17i | 0.280962 | + | 1.56776i | ||||
\(274\) | −4.52387e16 | −0.390172 | ||||||||
\(275\) | 8.51184e16i | 0.715640i | ||||||||
\(276\) | 1.81007e16 | − | 3.24386e15i | 0.148365 | − | 0.0265888i | ||||
\(277\) | −1.87884e17 | −1.50152 | −0.750760 | − | 0.660575i | \(-0.770313\pi\) | ||||
−0.750760 | + | 0.660575i | \(0.770313\pi\) | |||||||
\(278\) | − | 1.93848e15i | − | 0.0151059i | ||||||
\(279\) | −1.41453e17 | + | 5.23824e16i | −1.07493 | + | 0.398067i | ||||
\(280\) | −9.48896e16 | −0.703254 | ||||||||
\(281\) | − | 1.93819e17i | − | 1.40105i | −0.713629 | − | 0.700523i | \(-0.752950\pi\) | ||
0.713629 | − | 0.700523i | \(-0.247050\pi\) | |||||||
\(282\) | −2.31771e16 | − | 1.29328e17i | −0.163424 | − | 0.911901i | ||||
\(283\) | 1.59111e17 | 1.09445 | 0.547225 | − | 0.836985i | \(-0.315684\pi\) | ||||
0.547225 | + | 0.836985i | \(0.315684\pi\) | |||||||
\(284\) | 3.33650e16i | 0.223904i | ||||||||
\(285\) | 1.83155e17 | − | 3.28237e16i | 1.19924 | − | 0.214918i | ||||
\(286\) | 1.04832e17 | 0.669782 | ||||||||
\(287\) | 8.93649e16i | 0.557177i | ||||||||
\(288\) | 1.00888e16 | + | 2.72437e16i | 0.0613894 | + | 0.165775i | ||||
\(289\) | 1.40220e17 | 0.832771 | ||||||||
\(290\) | − | 1.31866e17i | − | 0.764445i | ||||||
\(291\) | 6.10370e14 | + | 3.40585e15i | 0.00345416 | + | 0.0192741i | ||||
\(292\) | −3.52213e16 | −0.194592 | ||||||||
\(293\) | 1.38296e17i | 0.745997i | 0.927832 | + | 0.372999i | \(0.121670\pi\) | ||||
−0.927832 | + | 0.372999i | \(0.878330\pi\) | |||||||
\(294\) | 1.55913e17 | − | 2.79416e16i | 0.821206 | − | 0.147170i | ||||
\(295\) | 2.63370e16 | 0.135460 | ||||||||
\(296\) | − | 1.04884e17i | − | 0.526827i | ||||||
\(297\) | −1.54248e17 | + | 9.07891e16i | −0.756701 | + | 0.445388i | ||||
\(298\) | −7.95320e16 | −0.381091 | ||||||||
\(299\) | − | 6.94792e16i | − | 0.325204i | ||||||
\(300\) | 1.57217e16 | + | 8.77265e16i | 0.0718868 | + | 0.401127i | ||||
\(301\) | 1.40821e17 | 0.629074 | ||||||||
\(302\) | 1.73361e16i | 0.0756664i | ||||||||
\(303\) | 9.57511e16 | − | 1.71597e16i | 0.408362 | − | 0.0731834i | ||||
\(304\) | 5.42479e16 | 0.226083 | ||||||||
\(305\) | 6.04216e17i | 2.46090i | ||||||||
\(306\) | 6.81215e16 | − | 2.52266e16i | 0.271165 | − | 0.100417i | ||||
\(307\) | −1.59731e17 | −0.621469 | −0.310735 | − | 0.950497i | \(-0.600575\pi\) | ||||
−0.310735 | + | 0.950497i | \(0.600575\pi\) | |||||||
\(308\) | − | 1.70434e17i | − | 0.648190i | ||||||
\(309\) | −2.02342e16 | − | 1.12907e17i | −0.0752276 | − | 0.419768i | ||||
\(310\) | −3.00433e17 | −1.09198 | ||||||||
\(311\) | − | 1.54506e17i | − | 0.549064i | −0.961578 | − | 0.274532i | \(-0.911477\pi\) | ||
0.961578 | − | 0.274532i | \(-0.0885229\pi\) | |||||||
\(312\) | 1.08045e17 | − | 1.93629e16i | 0.375423 | − | 0.0672803i | ||||
\(313\) | −3.11171e17 | −1.05728 | −0.528639 | − | 0.848847i | \(-0.677297\pi\) | ||||
−0.528639 | + | 0.848847i | \(0.677297\pi\) | |||||||
\(314\) | 3.90520e17i | 1.29759i | ||||||||
\(315\) | −2.12569e17 | − | 5.74017e17i | −0.690757 | − | 1.86531i | ||||
\(316\) | 1.46475e17 | 0.465536 | ||||||||
\(317\) | − | 3.75988e17i | − | 1.16885i | −0.811448 | − | 0.584425i | \(-0.801320\pi\) | ||
0.811448 | − | 0.584425i | \(-0.198680\pi\) | |||||||
\(318\) | −3.64913e16 | − | 2.03621e17i | −0.110968 | − | 0.619202i | ||||
\(319\) | 2.36849e17 | 0.704590 | ||||||||
\(320\) | 5.78632e16i | 0.168404i | ||||||||
\(321\) | −3.64081e17 | + | 6.52478e16i | −1.03672 | + | 0.185793i | ||||
\(322\) | −1.12958e17 | −0.314721 | ||||||||
\(323\) | − | 1.35644e17i | − | 0.369814i | ||||||
\(324\) | −1.42205e17 | + | 1.22061e17i | −0.379403 | + | 0.325658i | ||||
\(325\) | 3.36737e17 | 0.879239 | ||||||||
\(326\) | 1.80560e16i | 0.0461423i | ||||||||
\(327\) | 5.46112e16 | + | 3.04729e17i | 0.136599 | + | 0.762220i | ||||
\(328\) | 5.44943e16 | 0.133424 | ||||||||
\(329\) | 8.07073e17i | 1.93438i | ||||||||
\(330\) | −3.50896e17 | + | 6.28848e16i | −0.823343 | + | 0.147553i | ||||
\(331\) | −1.08569e17 | −0.249407 | −0.124703 | − | 0.992194i | \(-0.539798\pi\) | ||||
−0.124703 | + | 0.992194i | \(0.539798\pi\) | |||||||
\(332\) | 4.38853e17i | 0.987080i | ||||||||
\(333\) | 6.34477e17 | − | 2.34958e17i | 1.39735 | − | 0.517465i | ||||
\(334\) | 2.90052e17 | 0.625534 | ||||||||
\(335\) | − | 4.89232e17i | − | 1.03324i | ||||||
\(336\) | −3.14798e16 | − | 1.75657e17i | −0.0651114 | − | 0.363321i | ||||
\(337\) | 1.45112e17 | 0.293963 | 0.146982 | − | 0.989139i | \(-0.453044\pi\) | ||||
0.146982 | + | 0.989139i | \(0.453044\pi\) | |||||||
\(338\) | − | 5.83566e16i | − | 0.115791i | ||||||
\(339\) | 2.61112e17 | − | 4.67945e16i | 0.507492 | − | 0.0909487i | ||||
\(340\) | 1.44684e17 | 0.275466 | ||||||||
\(341\) | − | 5.39618e17i | − | 1.00648i | ||||||
\(342\) | 1.21524e17 | + | 3.28163e17i | 0.222065 | + | 0.599662i | ||||
\(343\) | −1.48325e17 | −0.265556 | ||||||||
\(344\) | − | 8.58719e16i | − | 0.150641i | ||||||
\(345\) | 4.16778e16 | + | 2.32562e17i | 0.0716426 | + | 0.399764i | ||||
\(346\) | 2.92190e17 | 0.492190 | ||||||||
\(347\) | − | 1.27586e17i | − | 0.210619i | −0.994439 | − | 0.105310i | \(-0.966417\pi\) | ||
0.994439 | − | 0.105310i | \(-0.0335834\pi\) | |||||||
\(348\) | 2.44106e17 | − | 4.37468e16i | 0.394934 | − | 0.0707768i | ||||
\(349\) | −7.20869e17 | −1.14309 | −0.571543 | − | 0.820572i | \(-0.693655\pi\) | ||||
−0.571543 | + | 0.820572i | \(0.693655\pi\) | |||||||
\(350\) | − | 5.47460e17i | − | 0.850896i | ||||||
\(351\) | 3.59171e17 | + | 6.10220e17i | 0.547206 | + | 0.929687i | ||||
\(352\) | −1.03930e17 | −0.155218 | ||||||||
\(353\) | 6.22911e17i | 0.912018i | 0.889975 | + | 0.456009i | \(0.150721\pi\) | ||||
−0.889975 | + | 0.456009i | \(0.849279\pi\) | |||||||
\(354\) | 8.73736e15 | + | 4.87543e16i | 0.0125417 | + | 0.0699827i | ||||
\(355\) | −4.28680e17 | −0.603303 | ||||||||
\(356\) | − | 5.03834e17i | − | 0.695245i | ||||||
\(357\) | −4.39221e17 | + | 7.87136e16i | −0.594299 | + | 0.106506i | ||||
\(358\) | −1.14644e17 | −0.152115 | ||||||||
\(359\) | − | 2.75392e17i | − | 0.358336i | −0.983819 | − | 0.179168i | \(-0.942659\pi\) | ||
0.983819 | − | 0.179168i | \(-0.0573405\pi\) | |||||||
\(360\) | −3.50033e17 | + | 1.29623e17i | −0.446675 | + | 0.165412i | ||||
\(361\) | −1.45567e17 | −0.182185 | ||||||||
\(362\) | − | 5.15478e17i | − | 0.632777i | ||||||
\(363\) | 3.35543e16 | + | 1.87232e17i | 0.0404018 | + | 0.225442i | ||||
\(364\) | −6.74256e17 | −0.796370 | ||||||||
\(365\) | − | 4.52531e17i | − | 0.524322i | ||||||
\(366\) | −1.11851e18 | + | 2.00450e17i | −1.27137 | + | 0.227844i | ||||
\(367\) | 4.21095e17 | 0.469588 | 0.234794 | − | 0.972045i | \(-0.424558\pi\) | ||||
0.234794 | + | 0.972045i | \(0.424558\pi\) | |||||||
\(368\) | 6.88812e16i | 0.0753644i | ||||||||
\(369\) | 1.22076e17 | + | 3.29653e17i | 0.131053 | + | 0.353894i | ||||
\(370\) | 1.34757e18 | 1.41952 | ||||||||
\(371\) | 1.27070e18i | 1.31349i | ||||||||
\(372\) | −9.96692e16 | − | 5.56153e17i | −0.101102 | − | 0.564148i | ||||
\(373\) | −7.40270e17 | −0.736933 | −0.368467 | − | 0.929641i | \(-0.620117\pi\) | ||||
−0.368467 | + | 0.929641i | \(0.620117\pi\) | |||||||
\(374\) | 2.59872e17i | 0.253897i | ||||||||
\(375\) | 2.55791e17 | − | 4.58408e16i | 0.245282 | − | 0.0439575i | ||||
\(376\) | 4.92149e17 | 0.463214 | ||||||||
\(377\) | − | 9.36997e17i | − | 0.865663i | ||||||
\(378\) | 9.92085e17 | − | 5.83933e17i | 0.899717 | − | 0.529566i | ||||
\(379\) | −6.56688e17 | −0.584635 | −0.292317 | − | 0.956321i | \(-0.594426\pi\) | ||||
−0.292317 | + | 0.956321i | \(0.594426\pi\) | |||||||
\(380\) | 6.96988e17i | 0.609172i | ||||||||
\(381\) | −5.73656e16 | − | 3.20099e17i | −0.0492240 | − | 0.274669i | ||||
\(382\) | −1.15292e17 | −0.0971304 | ||||||||
\(383\) | 1.86220e17i | 0.154041i | 0.997030 | + | 0.0770203i | \(0.0245406\pi\) | ||||
−0.997030 | + | 0.0770203i | \(0.975459\pi\) | |||||||
\(384\) | −1.07115e17 | + | 1.91962e16i | −0.0870023 | + | 0.0155919i | ||||
\(385\) | 2.18978e18 | 1.74653 | ||||||||
\(386\) | 7.76196e17i | 0.607940i | ||||||||
\(387\) | 5.19467e17 | − | 1.92368e17i | 0.399559 | − | 0.147964i | ||||
\(388\) | −1.29608e16 | −0.00979061 | ||||||||
\(389\) | − | 2.31179e18i | − | 1.71514i | −0.514364 | − | 0.857572i | \(-0.671972\pi\) | ||
0.514364 | − | 0.857572i | \(-0.328028\pi\) | |||||||
\(390\) | 2.48779e17 | + | 1.38818e18i | 0.181284 | + | 1.01156i | ||||
\(391\) | 1.72234e17 | 0.123277 | ||||||||
\(392\) | 5.93320e17i | 0.417145i | ||||||||
\(393\) | −8.37259e17 | + | 1.50047e17i | −0.578245 | + | 0.103628i | ||||
\(394\) | −1.08072e18 | −0.733231 | ||||||||
\(395\) | 1.88194e18i | 1.25437i | ||||||||
\(396\) | −2.32821e17 | − | 6.28707e17i | −0.152460 | − | 0.411701i | ||||
\(397\) | 2.74445e18 | 1.76572 | 0.882860 | − | 0.469636i | \(-0.155615\pi\) | ||||
0.882860 | + | 0.469636i | \(0.155615\pi\) | |||||||
\(398\) | − | 7.12760e17i | − | 0.450570i | ||||||
\(399\) | −3.79188e17 | − | 2.11587e18i | −0.235529 | − | 1.31425i | ||||
\(400\) | −3.33839e17 | −0.203759 | ||||||||
\(401\) | 1.46184e18i | 0.876780i | 0.898785 | + | 0.438390i | \(0.144451\pi\) | ||||
−0.898785 | + | 0.438390i | \(0.855549\pi\) | |||||||
\(402\) | 9.05652e17 | − | 1.62304e17i | 0.533800 | − | 0.0956635i | ||||
\(403\) | −2.13478e18 | −1.23657 | ||||||||
\(404\) | 3.64376e17i | 0.207434i | ||||||||
\(405\) | −1.56827e18 | − | 1.82708e18i | −0.877475 | − | 1.02229i | ||||
\(406\) | −1.52335e18 | −0.837757 | ||||||||
\(407\) | 2.42042e18i | 1.30837i | ||||||||
\(408\) | 4.79992e16 | + | 2.67835e17i | 0.0255043 | + | 0.142313i | ||||
\(409\) | 2.58787e17 | 0.135170 | 0.0675848 | − | 0.997714i | \(-0.478471\pi\) | ||||
0.0675848 | + | 0.997714i | \(0.478471\pi\) | |||||||
\(410\) | 7.00154e17i | 0.359506i | ||||||||
\(411\) | 1.07597e18 | − | 1.92827e17i | 0.543134 | − | 0.0973361i | ||||
\(412\) | 4.29660e17 | 0.213228 | ||||||||
\(413\) | − | 3.04253e17i | − | 0.148451i | ||||||
\(414\) | −4.16685e17 | + | 1.54306e17i | −0.199896 | + | 0.0740251i | ||||
\(415\) | −5.63847e18 | −2.65965 | ||||||||
\(416\) | 4.11158e17i | 0.190702i | ||||||||
\(417\) | 8.26261e15 | + | 4.61052e16i | 0.00376847 | + | 0.0210280i | ||||
\(418\) | −1.25188e18 | −0.561475 | ||||||||
\(419\) | − | 4.32339e18i | − | 1.90689i | −0.301566 | − | 0.953445i | \(-0.597509\pi\) | ||
0.301566 | − | 0.953445i | \(-0.402491\pi\) | |||||||
\(420\) | 2.25688e18 | − | 4.04459e17i | 0.978955 | − | 0.175441i | ||||
\(421\) | 1.31437e18 | 0.560715 | 0.280358 | − | 0.959896i | \(-0.409547\pi\) | ||||
0.280358 | + | 0.959896i | \(0.409547\pi\) | |||||||
\(422\) | − | 3.23900e18i | − | 1.35901i | ||||||
\(423\) | 1.10250e18 | + | 2.97717e18i | 0.454983 | + | 1.22863i | ||||
\(424\) | 7.74868e17 | 0.314533 | ||||||||
\(425\) | 8.34746e17i | 0.333297i | ||||||||
\(426\) | −1.42216e17 | − | 7.93561e17i | −0.0558574 | − | 0.311683i | ||||
\(427\) | 6.98008e18 | 2.69690 | ||||||||
\(428\) | − | 1.38549e18i | − | 0.526621i | ||||||
\(429\) | −2.49336e18 | + | 4.46840e17i | −0.932360 | + | 0.167090i | ||||
\(430\) | 1.10330e18 | 0.405896 | ||||||||
\(431\) | 1.87112e18i | 0.677268i | 0.940918 | + | 0.338634i | \(0.109965\pi\) | ||||
−0.940918 | + | 0.338634i | \(0.890035\pi\) | |||||||
\(432\) | −3.56079e17 | − | 6.04968e17i | −0.126812 | − | 0.215450i | ||||
\(433\) | −2.75784e18 | −0.966392 | −0.483196 | − | 0.875512i | \(-0.660524\pi\) | ||||
−0.483196 | + | 0.875512i | \(0.660524\pi\) | |||||||
\(434\) | 3.47069e18i | 1.19671i | ||||||||
\(435\) | 5.62068e17 | + | 3.13633e18i | 0.190706 | + | 1.06413i | ||||
\(436\) | −1.15963e18 | −0.387181 | ||||||||
\(437\) | 8.29705e17i | 0.272617i | ||||||||
\(438\) | 8.37712e17 | − | 1.50128e17i | 0.270880 | − | 0.0485449i | ||||
\(439\) | 1.83354e18 | 0.583498 | 0.291749 | − | 0.956495i | \(-0.405763\pi\) | ||||
0.291749 | + | 0.956495i | \(0.405763\pi\) | |||||||
\(440\) | − | 1.33532e18i | − | 0.418230i | ||||||
\(441\) | −3.58918e18 | + | 1.32914e18i | −1.10643 | + | 0.409732i | ||||
\(442\) | 1.02808e18 | 0.311940 | ||||||||
\(443\) | 4.33165e17i | 0.129368i | 0.997906 | + | 0.0646841i | \(0.0206040\pi\) | ||||
−0.997906 | + | 0.0646841i | \(0.979396\pi\) | |||||||
\(444\) | 4.47060e17 | + | 2.49459e18i | 0.131427 | + | 0.733362i | ||||
\(445\) | 6.47337e18 | 1.87331 | ||||||||
\(446\) | − | 2.69498e18i | − | 0.767735i | ||||||
\(447\) | 1.89161e18 | − | 3.38999e17i | 0.530492 | − | 0.0950705i | ||||
\(448\) | 6.68453e17 | 0.184554 | ||||||||
\(449\) | − | 4.16940e18i | − | 1.13331i | −0.823955 | − | 0.566656i | \(-0.808237\pi\) | ||
0.823955 | − | 0.566656i | \(-0.191763\pi\) | |||||||
\(450\) | −7.47855e17 | − | 2.01950e18i | −0.200138 | − | 0.540450i | ||||
\(451\) | −1.25757e18 | −0.331357 | ||||||||
\(452\) | 9.93649e17i | 0.257789i | ||||||||
\(453\) | −7.38939e16 | − | 4.12326e17i | −0.0188765 | − | 0.105330i | ||||
\(454\) | −3.90448e18 | −0.982136 | ||||||||
\(455\) | − | 8.66298e18i | − | 2.14579i | ||||||
\(456\) | −1.29024e18 | + | 2.31227e17i | −0.314716 | + | 0.0564008i | ||||
\(457\) | −5.74510e18 | −1.38002 | −0.690008 | − | 0.723802i | \(-0.742393\pi\) | ||||
−0.690008 | + | 0.723802i | \(0.742393\pi\) | |||||||
\(458\) | − | 9.27412e17i | − | 0.219389i | ||||||
\(459\) | −1.51269e18 | + | 8.90358e17i | −0.352421 | + | 0.207432i | ||||
\(460\) | −8.85000e17 | −0.203067 | ||||||||
\(461\) | 8.04024e18i | 1.81703i | 0.417851 | + | 0.908515i | \(0.362783\pi\) | ||||
−0.417851 | + | 0.908515i | \(0.637217\pi\) | |||||||
\(462\) | 7.26464e17 | + | 4.05366e18i | 0.161704 | + | 0.902304i | ||||
\(463\) | −5.73855e18 | −1.25816 | −0.629079 | − | 0.777341i | \(-0.716568\pi\) | ||||
−0.629079 | + | 0.777341i | \(0.716568\pi\) | |||||||
\(464\) | 9.28933e17i | 0.200613i | ||||||||
\(465\) | 7.14557e18 | − | 1.28057e18i | 1.52008 | − | 0.272416i | ||||
\(466\) | 5.55663e18 | 1.16442 | ||||||||
\(467\) | − | 2.96692e18i | − | 0.612474i | −0.951955 | − | 0.306237i | \(-0.900930\pi\) | ||
0.951955 | − | 0.306237i | \(-0.0990700\pi\) | |||||||
\(468\) | −2.48723e18 | + | 9.21063e17i | −0.505818 | + | 0.187313i | ||||
\(469\) | −5.65175e18 | −1.13233 | ||||||||
\(470\) | 6.32324e18i | 1.24812i | ||||||||
\(471\) | −1.66456e18 | − | 9.28823e18i | −0.323708 | − | 1.80629i | ||||
\(472\) | −1.85532e17 | −0.0355488 | ||||||||
\(473\) | 1.98168e18i | 0.374115i | ||||||||
\(474\) | −3.48379e18 | + | 6.24337e17i | −0.648042 | + | 0.116137i | ||||
\(475\) | −4.02124e18 | −0.737062 | ||||||||
\(476\) | − | 1.67143e18i | − | 0.301884i | ||||||
\(477\) | 1.73584e18 | + | 4.68743e18i | 0.308944 | + | 0.834268i | ||||
\(478\) | 5.41750e18 | 0.950174 | ||||||||
\(479\) | 3.00387e18i | 0.519198i | 0.965716 | + | 0.259599i | \(0.0835904\pi\) | ||||
−0.965716 | + | 0.259599i | \(0.916410\pi\) | |||||||
\(480\) | −2.46637e17 | − | 1.37623e18i | −0.0420117 | − | 0.234425i | ||||
\(481\) | 9.57543e18 | 1.60747 | ||||||||
\(482\) | 1.39284e18i | 0.230448i | ||||||||
\(483\) | 2.68662e18 | − | 4.81474e17i | 0.438103 | − | 0.0785133i | ||||
\(484\) | −7.12502e17 | −0.114517 | ||||||||
\(485\) | − | 1.66523e17i | − | 0.0263805i | ||||||
\(486\) | 2.86197e18 | − | 3.50927e18i | 0.446901 | − | 0.547978i | ||||
\(487\) | 8.00668e18 | 1.23240 | 0.616198 | − | 0.787592i | \(-0.288672\pi\) | ||||
0.616198 | + | 0.787592i | \(0.288672\pi\) | |||||||
\(488\) | − | 4.25642e18i | − | 0.645811i | ||||||
\(489\) | −7.69624e16 | − | 4.29449e17i | −0.0115111 | − | 0.0642317i | ||||
\(490\) | −7.62310e18 | −1.12398 | ||||||||
\(491\) | − | 3.66948e18i | − | 0.533377i | −0.963783 | − | 0.266688i | \(-0.914071\pi\) | ||
0.963783 | − | 0.266688i | \(-0.0859294\pi\) | |||||||
\(492\) | −1.29611e18 | + | 2.32278e17i | −0.185731 | + | 0.0332852i | ||||
\(493\) | 2.32275e18 | 0.328151 | ||||||||
\(494\) | 4.95258e18i | 0.689831i | ||||||||
\(495\) | 8.07776e18 | − | 2.99133e18i | 1.10931 | − | 0.410798i | ||||
\(496\) | 2.11641e18 | 0.286568 | ||||||||
\(497\) | 4.95224e18i | 0.661161i | ||||||||
\(498\) | −1.87058e18 | − | 1.04378e19i | −0.246246 | − | 1.37405i | ||||
\(499\) | −7.47635e18 | −0.970478 | −0.485239 | − | 0.874382i | \(-0.661267\pi\) | ||||
−0.485239 | + | 0.874382i | \(0.661267\pi\) | |||||||
\(500\) | 9.73398e17i | 0.124595i | ||||||||
\(501\) | −6.89867e18 | + | 1.23632e18i | −0.870766 | + | 0.156052i | ||||
\(502\) | 9.15054e18 | 1.13899 | ||||||||
\(503\) | 1.32965e19i | 1.63215i | 0.577946 | + | 0.816075i | \(0.303855\pi\) | ||||
−0.577946 | + | 0.816075i | \(0.696145\pi\) | |||||||
\(504\) | 1.49745e18 | + | 4.04369e18i | 0.181275 | + | 0.489512i | ||||
\(505\) | −4.68158e18 | −0.558923 | ||||||||
\(506\) | − | 1.58958e18i | − | 0.187167i | ||||||
\(507\) | 2.48741e17 | + | 1.38797e18i | 0.0288862 | + | 0.161185i | ||||
\(508\) | 1.21812e18 | 0.139522 | ||||||||
\(509\) | 1.68157e18i | 0.189973i | 0.995479 | + | 0.0949864i | \(0.0302808\pi\) | ||||
−0.995479 | + | 0.0949864i | \(0.969719\pi\) | |||||||
\(510\) | −3.44120e18 | + | 6.16704e17i | −0.383458 | + | 0.0687204i | ||||
\(511\) | −5.22777e18 | −0.574606 | ||||||||
\(512\) | − | 4.07619e17i | − | 0.0441942i | ||||||
\(513\) | −4.28913e18 | − | 7.28712e18i | −0.458720 | − | 0.779353i | ||||
\(514\) | 5.54629e18 | 0.585142 | ||||||||
\(515\) | 5.52036e18i | 0.574536i | ||||||||
\(516\) | 3.66022e17 | + | 2.04240e18i | 0.0375803 | + | 0.209697i | ||||
\(517\) | −1.13574e19 | −1.15039 | ||||||||
\(518\) | − | 1.55676e19i | − | 1.55565i | ||||||
\(519\) | −6.94951e18 | + | 1.24544e18i | −0.685146 | + | 0.122786i | ||||
\(520\) | −5.28264e18 | −0.513840 | ||||||||
\(521\) | − | 1.66764e19i | − | 1.60043i | −0.599712 | − | 0.800216i | \(-0.704718\pi\) | ||
0.599712 | − | 0.800216i | \(-0.295282\pi\) | |||||||
\(522\) | −5.61941e18 | + | 2.08097e18i | −0.532105 | + | 0.197048i | ||||
\(523\) | 8.62761e18 | 0.806081 | 0.403040 | − | 0.915182i | \(-0.367953\pi\) | ||||
0.403040 | + | 0.915182i | \(0.367953\pi\) | |||||||
\(524\) | − | 3.18614e18i | − | 0.293729i | ||||||
\(525\) | 2.33351e18 | + | 1.30209e19i | 0.212273 | + | 1.18448i | ||||
\(526\) | −1.06971e19 | −0.960213 | ||||||||
\(527\) | − | 5.29197e18i | − | 0.468752i | ||||||
\(528\) | 2.47190e18 | − | 4.42994e17i | 0.216069 | − | 0.0387222i | ||||
\(529\) | 1.05393e19 | 0.909123 | ||||||||
\(530\) | 9.95567e18i | 0.847499i | ||||||||
\(531\) | −4.15623e17 | − | 1.12234e18i | −0.0349171 | − | 0.0942896i | ||||
\(532\) | 8.05181e18 | 0.667594 | ||||||||
\(533\) | 4.97508e18i | 0.407108i | ||||||||
\(534\) | 2.14755e18 | + | 1.19833e19i | 0.173442 | + | 0.967806i | ||||
\(535\) | 1.78011e19 | 1.41896 | ||||||||
\(536\) | 3.44641e18i | 0.271152i | ||||||||
\(537\) | 2.72672e18 | − | 4.88662e17i | 0.211749 | − | 0.0379480i | ||||
\(538\) | −1.72232e19 | −1.32020 | ||||||||
\(539\) | − | 1.36921e19i | − | 1.03598i | ||||||
\(540\) | 7.77276e18 | − | 4.57498e18i | 0.580523 | − | 0.341691i | ||||
\(541\) | −1.62414e19 | −1.19741 | −0.598704 | − | 0.800970i | \(-0.704318\pi\) | ||||
−0.598704 | + | 0.800970i | \(0.704318\pi\) | |||||||
\(542\) | − | 3.69709e18i | − | 0.269070i | ||||||
\(543\) | 2.19719e18 | + | 1.22603e19i | 0.157859 | + | 0.880848i | ||||
\(544\) | −1.01923e18 | −0.0722903 | ||||||||
\(545\) | − | 1.48992e19i | − | 1.04325i | ||||||
\(546\) | 1.60367e19 | − | 2.87396e18i | 1.10858 | − | 0.198670i | ||||
\(547\) | −5.54858e18 | −0.378678 | −0.189339 | − | 0.981912i | \(-0.560635\pi\) | ||||
−0.189339 | + | 0.981912i | \(0.560635\pi\) | |||||||
\(548\) | 4.09454e18i | 0.275893i | ||||||||
\(549\) | 2.57485e19 | − | 9.53510e18i | 1.71295 | − | 0.634335i | ||||
\(550\) | 7.70404e18 | 0.506034 | ||||||||
\(551\) | 1.11894e19i | 0.725681i | ||||||||
\(552\) | −2.93601e17 | − | 1.63829e18i | −0.0188011 | − | 0.104910i | ||||
\(553\) | 2.17407e19 | 1.37467 | ||||||||
\(554\) | 1.70053e19i | 1.06173i | ||||||||
\(555\) | −3.20510e19 | + | 5.74392e18i | −1.97602 | + | 0.354126i | ||||
\(556\) | −1.75451e17 | −0.0106815 | ||||||||
\(557\) | − | 1.31816e19i | − | 0.792471i | −0.918149 | − | 0.396235i | \(-0.870316\pi\) | ||
0.918149 | − | 0.396235i | \(-0.129684\pi\) | |||||||
\(558\) | 4.74111e18 | + | 1.28028e19i | 0.281476 | + | 0.760093i | ||||
\(559\) | 7.83971e18 | 0.459640 | ||||||||
\(560\) | 8.58842e18i | 0.497276i | ||||||||
\(561\) | −1.10768e18 | − | 6.18086e18i | −0.0633397 | − | 0.353434i | ||||
\(562\) | −1.75425e19 | −0.990690 | ||||||||
\(563\) | 1.30154e19i | 0.725939i | 0.931801 | + | 0.362969i | \(0.118237\pi\) | ||||
−0.931801 | + | 0.362969i | \(0.881763\pi\) | |||||||
\(564\) | −1.17054e19 | + | 2.09775e18i | −0.644811 | + | 0.115558i | ||||
\(565\) | −1.27666e19 | −0.694603 | ||||||||
\(566\) | − | 1.44011e19i | − | 0.773894i | ||||||
\(567\) | −2.11070e19 | + | 1.81171e19i | −1.12033 | + | 0.961627i | ||||
\(568\) | 3.01985e18 | 0.158324 | ||||||||
\(569\) | − | 2.97159e19i | − | 1.53888i | −0.638722 | − | 0.769438i | \(-0.720537\pi\) | ||
0.638722 | − | 0.769438i | \(-0.279463\pi\) | |||||||
\(570\) | −2.97086e18 | − | 1.65773e19i | −0.151970 | − | 0.847990i | ||||
\(571\) | 2.21909e19 | 1.12130 | 0.560650 | − | 0.828053i | \(-0.310551\pi\) | ||||
0.560650 | + | 0.828053i | \(0.310551\pi\) | |||||||
\(572\) | − | 9.48834e18i | − | 0.473607i | ||||||
\(573\) | 2.74213e18 | − | 4.91423e17i | 0.135209 | − | 0.0242311i | ||||
\(574\) | 8.08838e18 | 0.393984 | ||||||||
\(575\) | − | 5.10596e18i | − | 0.245699i | ||||||
\(576\) | 2.46582e18 | − | 9.13136e17i | 0.117221 | − | 0.0434088i | ||||
\(577\) | −2.98019e19 | −1.39963 | −0.699814 | − | 0.714325i | \(-0.746734\pi\) | ||||
−0.699814 | + | 0.714325i | \(0.746734\pi\) | |||||||
\(578\) | − | 1.26913e19i | − | 0.588858i | ||||||
\(579\) | −3.30848e18 | − | 1.84612e19i | −0.151662 | − | 0.846274i | ||||
\(580\) | −1.19351e19 | −0.540544 | ||||||||
\(581\) | 6.51373e19i | 2.91472i | ||||||||
\(582\) | 3.08263e17 | − | 5.52444e16i | 0.0136289 | − | 0.00244246i | ||||
\(583\) | −1.78817e19 | −0.781141 | ||||||||
\(584\) | 3.18787e18i | 0.137598i | ||||||||
\(585\) | −1.18340e19 | − | 3.19564e19i | −0.504709 | − | 1.36291i | ||||
\(586\) | 1.25171e19 | 0.527500 | ||||||||
\(587\) | 1.02892e19i | 0.428465i | 0.976783 | + | 0.214233i | \(0.0687251\pi\) | ||||
−0.976783 | + | 0.214233i | \(0.931275\pi\) | |||||||
\(588\) | −2.52898e18 | − | 1.41117e19i | −0.104065 | − | 0.580680i | ||||
\(589\) | 2.54931e19 | 1.03661 | ||||||||
\(590\) | − | 2.38375e18i | − | 0.0957850i | ||||||
\(591\) | 2.57042e19 | − | 4.60650e18i | 1.02068 | − | 0.182919i | ||||
\(592\) | −9.49302e18 | −0.372523 | ||||||||
\(593\) | 3.60491e19i | 1.39802i | 0.715114 | + | 0.699008i | \(0.246375\pi\) | ||||
−0.715114 | + | 0.699008i | \(0.753625\pi\) | |||||||
\(594\) | 8.21729e18 | + | 1.39609e19i | 0.314937 | + | 0.535068i | ||||
\(595\) | 2.14749e19 | 0.813415 | ||||||||
\(596\) | 7.19842e18i | 0.269472i | ||||||||
\(597\) | 3.03809e18 | + | 1.69525e19i | 0.112403 | + | 0.627209i | ||||
\(598\) | −6.28854e18 | −0.229954 | ||||||||
\(599\) | − | 9.79465e18i | − | 0.353998i | −0.984211 | − | 0.176999i | \(-0.943361\pi\) | ||
0.984211 | − | 0.176999i | \(-0.0566390\pi\) | |||||||
\(600\) | 7.94010e18 | − | 1.42296e18i | 0.283640 | − | 0.0508317i | ||||
\(601\) | −7.22930e18 | −0.255255 | −0.127628 | − | 0.991822i | \(-0.540736\pi\) | ||||
−0.127628 | + | 0.991822i | \(0.540736\pi\) | |||||||
\(602\) | − | 1.27457e19i | − | 0.444822i | ||||||
\(603\) | −2.08484e19 | + | 7.72054e18i | −0.719205 | + | 0.266334i | ||||
\(604\) | 1.56909e18 | 0.0535042 | ||||||||
\(605\) | − | 9.15438e18i | − | 0.308561i | ||||||
\(606\) | −1.55312e18 | − | 8.66640e18i | −0.0517485 | − | 0.288756i | ||||
\(607\) | −6.61848e18 | −0.217991 | −0.108995 | − | 0.994042i | \(-0.534763\pi\) | ||||
−0.108995 | + | 0.994042i | \(0.534763\pi\) | |||||||
\(608\) | − | 4.90996e18i | − | 0.159865i | ||||||
\(609\) | 3.62318e19 | − | 6.49317e18i | 1.16619 | − | 0.208995i | ||||
\(610\) | 5.46874e19 | 1.74012 | ||||||||
\(611\) | 4.49310e19i | 1.41337i | ||||||||
\(612\) | −2.28325e18 | − | 6.16565e18i | −0.0710057 | − | 0.191743i | ||||
\(613\) | 6.10503e17 | 0.0187700 | 0.00938501 | − | 0.999956i | \(-0.497013\pi\) | ||||
0.00938501 | + | 0.999956i | \(0.497013\pi\) | |||||||
\(614\) | 1.44572e19i | 0.439445i | ||||||||
\(615\) | −2.98435e18 | − | 1.66526e19i | −0.0896859 | − | 0.500446i | ||||
\(616\) | −1.54260e19 | −0.458340 | ||||||||
\(617\) | − | 6.35333e19i | − | 1.86640i | −0.359353 | − | 0.933202i | \(-0.617002\pi\) | ||
0.359353 | − | 0.933202i | \(-0.382998\pi\) | |||||||
\(618\) | −1.02191e19 | + | 1.83139e18i | −0.296821 | + | 0.0531939i | ||||
\(619\) | 1.54764e19 | 0.444462 | 0.222231 | − | 0.974994i | \(-0.428666\pi\) | ||||
0.222231 | + | 0.974994i | \(0.428666\pi\) | |||||||
\(620\) | 2.71921e19i | 0.772148i | ||||||||
\(621\) | 9.25281e18 | − | 5.44613e18i | 0.259796 | − | 0.152914i | ||||
\(622\) | −1.39843e19 | −0.388247 | ||||||||
\(623\) | − | 7.47823e19i | − | 2.05297i | ||||||
\(624\) | −1.75253e18 | − | 9.77908e18i | −0.0475744 | − | 0.265464i | ||||
\(625\) | −4.28689e19 | −1.15075 | ||||||||
\(626\) | 2.81640e19i | 0.747608i | ||||||||
\(627\) | 2.97751e19 | − | 5.33606e18i | 0.781594 | − | 0.140071i | ||||
\(628\) | 3.53459e19 | 0.917531 | ||||||||
\(629\) | 2.37368e19i | 0.609351i | ||||||||
\(630\) | −5.19541e19 | + | 1.92395e19i | −1.31897 | + | 0.488439i | ||||
\(631\) | −5.77423e19 | −1.44973 | −0.724867 | − | 0.688889i | \(-0.758099\pi\) | ||||
−0.724867 | + | 0.688889i | \(0.758099\pi\) | |||||||
\(632\) | − | 1.32574e19i | − | 0.329183i | ||||||
\(633\) | 1.38060e19 | + | 7.70371e19i | 0.339032 | + | 1.89179i | ||||
\(634\) | −3.40305e19 | −0.826502 | ||||||||
\(635\) | 1.56507e19i | 0.375938i | ||||||||
\(636\) | −1.84297e19 | + | 3.30282e18i | −0.437842 | + | 0.0784665i | ||||
\(637\) | −5.41674e19 | −1.27281 | ||||||||
\(638\) | − | 2.14371e19i | − | 0.498220i | ||||||
\(639\) | 6.76499e18 | + | 1.82681e19i | 0.155511 | + | 0.419939i | ||||
\(640\) | 5.23718e18 | 0.119080 | ||||||||
\(641\) | − | 2.72430e19i | − | 0.612702i | −0.951919 | − | 0.306351i | \(-0.900892\pi\) | ||
0.951919 | − | 0.306351i | \(-0.0991081\pi\) | |||||||
\(642\) | 5.90555e18 | + | 3.29529e19i | 0.131376 | + | 0.733075i | ||||
\(643\) | 5.75196e19 | 1.26572 | 0.632862 | − | 0.774265i | \(-0.281880\pi\) | ||||
0.632862 | + | 0.774265i | \(0.281880\pi\) | |||||||
\(644\) | 1.02238e19i | 0.222541i | ||||||||
\(645\) | −2.62412e19 | + | 4.70273e18i | −0.565022 | + | 0.101259i | ||||
\(646\) | −1.22771e19 | −0.261498 | ||||||||
\(647\) | − | 3.32642e19i | − | 0.700886i | −0.936584 | − | 0.350443i | \(-0.886031\pi\) | ||
0.936584 | − | 0.350443i | \(-0.113969\pi\) | |||||||
\(648\) | 1.10477e19 | + | 1.28710e19i | 0.230275 | + | 0.268278i | ||||
\(649\) | 4.28155e18 | 0.0882852 | ||||||||
\(650\) | − | 3.04779e19i | − | 0.621716i | ||||||
\(651\) | −1.47935e19 | − | 8.25477e19i | −0.298542 | − | 1.66586i | ||||
\(652\) | 1.63424e18 | 0.0326275 | ||||||||
\(653\) | − | 6.10716e18i | − | 0.120628i | −0.998179 | − | 0.0603138i | \(-0.980790\pi\) | ||
0.998179 | − | 0.0603138i | \(-0.0192101\pi\) | |||||||
\(654\) | 2.75810e19 | − | 4.94284e18i | 0.538971 | − | 0.0965900i | ||||
\(655\) | 4.09362e19 | 0.791442 | ||||||||
\(656\) | − | 4.93226e18i | − | 0.0943450i | ||||||
\(657\) | −1.92844e19 | + | 7.14137e18i | −0.364964 | + | 0.135152i | ||||
\(658\) | 7.30479e19 | 1.36781 | ||||||||
\(659\) | − | 6.12820e19i | − | 1.13536i | −0.823248 | − | 0.567682i | \(-0.807840\pi\) | ||
0.823248 | − | 0.567682i | \(-0.192160\pi\) | |||||||
\(660\) | 5.69168e18 | + | 3.17595e19i | 0.104336 | + | 0.582192i | ||||
\(661\) | 3.98614e19 | 0.723006 | 0.361503 | − | 0.932371i | \(-0.382264\pi\) | ||||
0.361503 | + | 0.932371i | \(0.382264\pi\) | |||||||
\(662\) | 9.82650e18i | 0.176357i | ||||||||
\(663\) | −2.44521e19 | + | 4.38211e18i | −0.434231 | + | 0.0778195i | ||||
\(664\) | 3.97204e19 | 0.697971 | ||||||||
\(665\) | 1.03451e20i | 1.79881i | ||||||||
\(666\) | −2.12660e19 | − | 5.74263e19i | −0.365903 | − | 0.988079i | ||||
\(667\) | −1.42078e19 | −0.241905 | ||||||||
\(668\) | − | 2.62525e19i | − | 0.442319i | ||||||
\(669\) | 1.14871e19 | + | 6.40980e19i | 0.191526 | + | 1.06871i | ||||
\(670\) | −4.42802e19 | −0.730611 | ||||||||
\(671\) | 9.82259e19i | 1.60387i | ||||||||
\(672\) | −1.58986e19 | + | 2.84923e18i | −0.256907 | + | 0.0460407i | ||||
\(673\) | 4.02925e19 | 0.644346 | 0.322173 | − | 0.946681i | \(-0.395587\pi\) | ||||
0.322173 | + | 0.946681i | \(0.395587\pi\) | |||||||
\(674\) | − | 1.31340e19i | − | 0.207863i | ||||||
\(675\) | 2.63951e19 | + | 4.48445e19i | 0.413425 | + | 0.702398i | ||||
\(676\) | −5.28184e18 | −0.0818763 | ||||||||
\(677\) | − | 3.44241e19i | − | 0.528132i | −0.964505 | − | 0.264066i | \(-0.914936\pi\) | ||
0.964505 | − | 0.264066i | \(-0.0850636\pi\) | |||||||
\(678\) | −4.23535e18 | − | 2.36332e19i | −0.0643104 | − | 0.358851i | ||||
\(679\) | −1.92372e18 | −0.0289104 | ||||||||
\(680\) | − | 1.30953e19i | − | 0.194784i | ||||||
\(681\) | 9.28650e19 | − | 1.66425e19i | 1.36717 | − | 0.245013i | ||||
\(682\) | −4.88406e19 | −0.711690 | ||||||||
\(683\) | − | 5.94502e19i | − | 0.857450i | −0.903435 | − | 0.428725i | \(-0.858963\pi\) | ||
0.903435 | − | 0.428725i | \(-0.141037\pi\) | |||||||
\(684\) | 2.97019e19 | − | 1.09991e19i | 0.424025 | − | 0.157024i | ||||
\(685\) | −5.26075e19 | −0.743385 | ||||||||
\(686\) | 1.34249e19i | 0.187776i | ||||||||
\(687\) | 3.95302e18 | + | 2.20578e19i | 0.0547308 | + | 0.305397i | ||||
\(688\) | −7.77224e18 | −0.106519 | ||||||||
\(689\) | 7.07419e19i | 0.959715i | ||||||||
\(690\) | 2.10491e19 | − | 3.77225e18i | 0.282676 | − | 0.0506590i | ||||
\(691\) | −5.55637e19 | −0.738661 | −0.369330 | − | 0.929298i | \(-0.620413\pi\) | ||||
−0.369330 | + | 0.929298i | \(0.620413\pi\) | |||||||
\(692\) | − | 2.64460e19i | − | 0.348031i | ||||||
\(693\) | −3.45568e19 | − | 9.33166e19i | −0.450195 | − | 1.21570i | ||||
\(694\) | −1.15478e19 | −0.148930 | ||||||||
\(695\) | − | 2.25423e18i | − | 0.0287809i | ||||||
\(696\) | −3.95950e18 | − | 2.20940e19i | −0.0500468 | − | 0.279260i | ||||
\(697\) | −1.23329e19 | −0.154324 | ||||||||
\(698\) | 6.52456e19i | 0.808283i | ||||||||
\(699\) | −1.32160e20 | + | 2.36847e19i | −1.62091 | + | 0.290487i | ||||
\(700\) | −4.95504e19 | −0.601674 | ||||||||
\(701\) | − | 4.00549e18i | − | 0.0481537i | −0.999710 | − | 0.0240768i | \(-0.992335\pi\) | ||
0.999710 | − | 0.0240768i | \(-0.00766464\pi\) | |||||||
\(702\) | 5.52308e19 | − | 3.25084e19i | 0.657388 | − | 0.386933i | ||||
\(703\) | −1.14348e20 | −1.34754 | ||||||||
\(704\) | 9.40668e18i | 0.109756i | ||||||||
\(705\) | −2.69523e19 | − | 1.50393e20i | −0.311367 | − | 1.73742i | ||||
\(706\) | 5.63795e19 | 0.644894 | ||||||||
\(707\) | 5.40829e19i | 0.612526i | ||||||||
\(708\) | 4.41274e18 | − | 7.90816e17i | 0.0494852 | − | 0.00886835i | ||||
\(709\) | 9.29590e19 | 1.03221 | 0.516105 | − | 0.856525i | \(-0.327381\pi\) | ||||
0.516105 | + | 0.856525i | \(0.327381\pi\) | |||||||
\(710\) | 3.87997e19i | 0.426599i | ||||||||
\(711\) | 8.01981e19 | − | 2.96988e19i | 0.873126 | − | 0.323334i | ||||
\(712\) | −4.56019e19 | −0.491612 | ||||||||
\(713\) | 3.23698e19i | 0.345552i | ||||||||
\(714\) | 7.12435e18 | + | 3.97537e19i | 0.0753108 | + | 0.420233i | ||||
\(715\) | 1.21908e20 | 1.27612 | ||||||||
\(716\) | 1.03764e19i | 0.107561i | ||||||||
\(717\) | −1.28851e20 | + | 2.30917e19i | −1.32268 | + | 0.237040i | ||||
\(718\) | −2.49256e19 | −0.253382 | ||||||||
\(719\) | − | 2.28421e19i | − | 0.229950i | −0.993368 | − | 0.114975i | \(-0.963321\pi\) | ||
0.993368 | − | 0.114975i | \(-0.0366788\pi\) | |||||||
\(720\) | 1.17322e19 | + | 3.16814e19i | 0.116964 | + | 0.315847i | ||||
\(721\) | 6.37728e19 | 0.629635 | ||||||||
\(722\) | 1.31752e19i | 0.128824i | ||||||||
\(723\) | −5.93688e18 | − | 3.31277e19i | −0.0574897 | − | 0.320792i | ||||
\(724\) | −4.66558e19 | −0.447441 | ||||||||
\(725\) | − | 6.88591e19i | − | 0.654026i | ||||||
\(726\) | 1.69463e19 | − | 3.03698e18i | 0.159411 | − | 0.0285684i | ||||
\(727\) | 1.42048e20 | 1.32341 | 0.661704 | − | 0.749765i | \(-0.269834\pi\) | ||||
0.661704 | + | 0.749765i | \(0.269834\pi\) | |||||||
\(728\) | 6.10267e19i | 0.563119i | ||||||||
\(729\) | −5.31118e19 | + | 9.56643e19i | −0.485398 | + | 0.874293i | ||||
\(730\) | −4.09584e19 | −0.370752 | ||||||||
\(731\) | 1.94341e19i | 0.174238i | ||||||||
\(732\) | 1.81427e19 | + | 1.01236e20i | 0.161110 | + | 0.898993i | ||||
\(733\) | 9.48876e19 | 0.834606 | 0.417303 | − | 0.908767i | \(-0.362975\pi\) | ||||
0.417303 | + | 0.908767i | \(0.362975\pi\) | |||||||
\(734\) | − | 3.81131e19i | − | 0.332049i | ||||||
\(735\) | 1.81310e20 | − | 3.24929e19i | 1.56462 | − | 0.280399i | ||||
\(736\) | 6.23442e18 | 0.0532907 | ||||||||
\(737\) | − | 7.95332e19i | − | 0.673405i | ||||||
\(738\) | 2.98368e19 | − | 1.10491e19i | 0.250241 | − | 0.0926685i | ||||
\(739\) | −6.97379e19 | −0.579372 | −0.289686 | − | 0.957122i | \(-0.593551\pi\) | ||||
−0.289686 | + | 0.957122i | \(0.593551\pi\) | |||||||
\(740\) | − | 1.21968e20i | − | 1.00375i | ||||||
\(741\) | −2.11100e19 | − | 1.17793e20i | −0.172092 | − | 0.960270i | ||||
\(742\) | 1.15011e20 | 0.928777 | ||||||||
\(743\) | 1.38432e20i | 1.10743i | 0.832706 | + | 0.553715i | \(0.186790\pi\) | ||||
−0.832706 | + | 0.553715i | \(0.813210\pi\) | |||||||
\(744\) | −5.03372e19 | + | 9.02103e18i | −0.398913 | + | 0.0714900i | ||||
\(745\) | −9.24868e19 | −0.726082 | ||||||||
\(746\) | 6.70016e19i | 0.521091i | ||||||||
\(747\) | 8.89805e19 | + | 2.40282e20i | 0.685568 | + | 1.85130i | ||||
\(748\) | 2.35209e19 | 0.179532 | ||||||||
\(749\) | − | 2.05644e20i | − | 1.55504i | ||||||
\(750\) | −4.14903e18 | − | 2.31515e19i | −0.0310827 | − | 0.173441i | ||||
\(751\) | −1.65143e20 | −1.22569 | −0.612843 | − | 0.790204i | \(-0.709974\pi\) | ||||
−0.612843 | + | 0.790204i | \(0.709974\pi\) | |||||||
\(752\) | − | 4.45443e19i | − | 0.327542i | ||||||
\(753\) | −2.17639e20 | + | 3.90035e19i | −1.58552 | + | 0.284144i | ||||
\(754\) | −8.48073e19 | −0.612116 | ||||||||
\(755\) | 2.01600e19i | 0.144165i | ||||||||
\(756\) | −5.28515e19 | − | 8.97932e19i | −0.374460 | − | 0.636196i | ||||
\(757\) | 2.40098e20 | 1.68545 | 0.842727 | − | 0.538342i | \(-0.180949\pi\) | ||||
0.842727 | + | 0.538342i | \(0.180949\pi\) | |||||||
\(758\) | 5.94366e19i | 0.413399i | ||||||||
\(759\) | 6.77546e18 | + | 3.78070e19i | 0.0466924 | + | 0.260543i | ||||
\(760\) | 6.30842e19 | 0.430750 | ||||||||
\(761\) | − | 8.81020e19i | − | 0.596064i | −0.954556 | − | 0.298032i | \(-0.903670\pi\) | ||
0.954556 | − | 0.298032i | \(-0.0963303\pi\) | |||||||
\(762\) | −2.89720e19 | + | 5.19214e18i | −0.194220 | + | 0.0348066i | ||||
\(763\) | −1.72120e20 | −1.14330 | ||||||||
\(764\) | 1.04350e19i | 0.0686816i | ||||||||
\(765\) | 7.92176e19 | − | 2.93357e19i | 0.516644 | − | 0.191322i | ||||
\(766\) | 1.68547e19 | 0.108923 | ||||||||
\(767\) | − | 1.69382e19i | − | 0.108468i | ||||||
\(768\) | 1.73745e18 | + | 9.69492e18i | 0.0110251 | + | 0.0615199i | ||||
\(769\) | −1.32173e20 | −0.831107 | −0.415554 | − | 0.909569i | \(-0.636412\pi\) | ||||
−0.415554 | + | 0.909569i | \(0.636412\pi\) | |||||||
\(770\) | − | 1.98196e20i | − | 1.23498i | ||||||
\(771\) | −1.31914e20 | + | 2.36406e19i | −0.814538 | + | 0.145975i | ||||
\(772\) | 7.02533e19 | 0.429878 | ||||||||
\(773\) | − | 7.12550e19i | − | 0.432075i | −0.976385 | − | 0.216037i | \(-0.930687\pi\) | ||
0.976385 | − | 0.216037i | \(-0.0693133\pi\) | |||||||
\(774\) | −1.74111e19 | − | 4.70168e19i | −0.104626 | − | 0.282531i | ||||
\(775\) | −1.56883e20 | −0.934253 | ||||||||
\(776\) | 1.17308e18i | 0.00692301i | ||||||||
\(777\) | 6.63555e19 | + | 3.70263e20i | 0.388088 | + | 2.16552i | ||||
\(778\) | −2.09239e20 | −1.21279 | ||||||||
\(779\) | − | 5.94113e19i | − | 0.341277i | ||||||
\(780\) | 1.25644e20 | − | 2.25169e19i | 0.715284 | − | 0.128187i | ||||
\(781\) | −6.96896e19 | −0.393197 | ||||||||
\(782\) | − | 1.55888e19i | − | 0.0871698i | ||||||
\(783\) | 1.24784e20 | − | 7.34465e19i | 0.691552 | − | 0.407042i | ||||
\(784\) | 5.37012e19 | 0.294966 | ||||||||
\(785\) | 4.54131e20i | 2.47226i | ||||||||
\(786\) | 1.35807e19 | + | 7.57800e19i | 0.0732764 | + | 0.408881i | ||||
\(787\) | −3.27593e19 | −0.175191 | −0.0875956 | − | 0.996156i | \(-0.527918\pi\) | ||||
−0.0875956 | + | 0.996156i | \(0.527918\pi\) | |||||||
\(788\) | 9.78159e19i | 0.518473i | ||||||||
\(789\) | 2.54424e20 | − | 4.55958e19i | 1.33665 | − | 0.239544i | ||||
\(790\) | 1.70334e20 | 0.886973 | ||||||||
\(791\) | 1.47484e20i | 0.761217i | ||||||||
\(792\) | −5.69040e19 | + | 2.10726e19i | −0.291116 | + | 0.107806i | ||||
\(793\) | 3.88592e20 | 1.97052 | ||||||||
\(794\) | − | 2.48399e20i | − | 1.24855i | ||||||
\(795\) | −4.24353e19 | − | 2.36788e20i | −0.211425 | − | 1.17975i | ||||
\(796\) | −6.45117e19 | −0.318601 | ||||||||
\(797\) | − | 2.83169e20i | − | 1.38624i | −0.720823 | − | 0.693120i | \(-0.756236\pi\) | ||
0.720823 | − | 0.693120i | \(-0.243764\pi\) | |||||||
\(798\) | −1.91506e20 | + | 3.43202e19i | −0.929315 | + | 0.166544i | ||||
\(799\) | −1.11381e20 | −0.535775 | ||||||||
\(800\) | 3.02156e19i | 0.144079i | ||||||||
\(801\) | −1.02156e20 | − | 2.75860e20i | −0.482876 | − | 1.30395i | ||||
\(802\) | 1.32311e20 | 0.619977 | ||||||||
\(803\) | − | 7.35669e19i | − | 0.341722i | ||||||
\(804\) | −1.46901e19 | − | 8.19703e19i | −0.0676443 | − | 0.377454i | ||||
\(805\) | −1.31357e20 | −0.599630 | ||||||||
\(806\) | 1.93218e20i | 0.874386i | ||||||||
\(807\) | 4.09641e20 | − | 7.34126e19i | 1.83776 | − | 0.329349i | ||||
\(808\) | 3.29795e19 | 0.146678 | ||||||||
\(809\) | 4.13602e19i | 0.182366i | 0.995834 | + | 0.0911829i | \(0.0290648\pi\) | ||||
−0.995834 | + | 0.0911829i | \(0.970935\pi\) | |||||||
\(810\) | −1.65369e20 | + | 1.41943e20i | −0.722867 | + | 0.620469i | ||||
\(811\) | 4.31837e20 | 1.87143 | 0.935716 | − | 0.352755i | \(-0.114755\pi\) | ||||
0.935716 | + | 0.352755i | \(0.114755\pi\) | |||||||
\(812\) | 1.37878e20i | 0.592384i | ||||||||
\(813\) | 1.57586e19 | + | 8.79326e19i | 0.0671248 | + | 0.374555i | ||||
\(814\) | 2.19072e20 | 0.925157 | ||||||||
\(815\) | 2.09971e19i | 0.0879137i | ||||||||
\(816\) | 2.42416e19 | − | 4.34439e18i | 0.100631 | − | 0.0180342i | ||||
\(817\) | −9.36201e19 | −0.385314 | ||||||||
\(818\) | − | 2.34227e19i | − | 0.0955793i | ||||||
\(819\) | −3.69170e20 | + | 1.36710e20i | −1.49362 | + | 0.553112i | ||||
\(820\) | 6.33707e19 | 0.254209 | ||||||||
\(821\) | 3.79271e20i | 1.50851i | 0.656584 | + | 0.754253i | \(0.272001\pi\) | ||||
−0.656584 | + | 0.754253i | \(0.727999\pi\) | |||||||
\(822\) | −1.74527e19 | − | 9.73856e19i | −0.0688270 | − | 0.384054i | ||||
\(823\) | −3.22818e20 | −1.26229 | −0.631144 | − | 0.775665i | \(-0.717414\pi\) | ||||
−0.631144 | + | 0.775665i | \(0.717414\pi\) | |||||||
\(824\) | − | 3.88884e19i | − | 0.150775i | ||||||
\(825\) | −1.83235e20 | + | 3.28379e19i | −0.704417 | + | 0.126240i | ||||
\(826\) | −2.75378e19 | −0.104971 | ||||||||
\(827\) | − | 2.75227e20i | − | 1.04029i | −0.854079 | − | 0.520143i | \(-0.825879\pi\) | ||
0.854079 | − | 0.520143i | \(-0.174121\pi\) | |||||||
\(828\) | 1.39661e19 | + | 3.77140e19i | 0.0523437 | + | 0.141348i | ||||
\(829\) | −4.31769e20 | −1.60461 | −0.802305 | − | 0.596914i | \(-0.796393\pi\) | ||||
−0.802305 | + | 0.596914i | \(0.796393\pi\) | |||||||
\(830\) | 5.10336e20i | 1.88066i | ||||||||
\(831\) | −7.24838e19 | − | 4.04458e20i | −0.264871 | − | 1.47797i | ||||
\(832\) | 3.72138e19 | 0.134847 | ||||||||
\(833\) | − | 1.34277e20i | − | 0.482488i | ||||||
\(834\) | 4.17297e18 | − | 7.47846e17i | 0.0148690 | − | 0.00266471i | ||||
\(835\) | 3.37298e20 | 1.19181 | ||||||||
\(836\) | 1.13308e20i | 0.397023i | ||||||||
\(837\) | −1.67335e20 | − | 2.84297e20i | −0.581445 | − | 0.987857i | ||||
\(838\) | −3.91308e20 | −1.34838 | ||||||||
\(839\) | 2.03774e20i | 0.696331i | 0.937433 | + | 0.348165i | \(0.113195\pi\) | ||||
−0.937433 | + | 0.348165i | \(0.886805\pi\) | |||||||
\(840\) | −3.66075e19 | − | 2.04269e20i | −0.124055 | − | 0.692226i | ||||
\(841\) | 1.05952e20 | 0.356073 | ||||||||
\(842\) | − | 1.18963e20i | − | 0.396486i | ||||||
\(843\) | 4.17235e20 | − | 7.47736e19i | 1.37908 | − | 0.247147i | ||||
\(844\) | −2.93160e20 | −0.960967 | ||||||||
\(845\) | − | 6.78622e19i | − | 0.220613i | ||||||
\(846\) | 2.69463e20 | − | 9.97867e19i | 0.868772 | − | 0.321722i | ||||
\(847\) | −1.05754e20 | −0.338153 | ||||||||
\(848\) | − | 7.01331e19i | − | 0.222409i | ||||||
\(849\) | 6.13837e19 | + | 3.42520e20i | 0.193063 | + | 1.07729i | ||||
\(850\) | 7.55526e19 | 0.235677 | ||||||||
\(851\) | − | 1.45193e20i | − | 0.449199i | ||||||
\(852\) | −7.18250e19 | + | 1.28719e19i | −0.220393 | + | 0.0394971i | ||||
\(853\) | 2.99936e19 | 0.0912821 | 0.0456411 | − | 0.998958i | \(-0.485467\pi\) | ||||
0.0456411 | + | 0.998958i | \(0.485467\pi\) | |||||||
\(854\) | − | 6.31765e20i | − | 1.90700i | ||||||
\(855\) | 1.41319e20 | + | 3.81616e20i | 0.423096 | + | 1.14252i | ||||
\(856\) | −1.25400e20 | −0.372377 | ||||||||
\(857\) | 2.29562e20i | 0.676137i | 0.941121 | + | 0.338069i | \(0.109774\pi\) | ||||
−0.941121 | + | 0.338069i | \(0.890226\pi\) | |||||||
\(858\) | 4.04433e19 | + | 2.25673e20i | 0.118151 | + | 0.659278i | ||||
\(859\) | 6.64441e18 | 0.0192533 | 0.00962663 | − | 0.999954i | \(-0.496936\pi\) | ||||
0.00962663 | + | 0.999954i | \(0.496936\pi\) | |||||||
\(860\) | − | 9.98594e19i | − | 0.287012i | ||||||
\(861\) | −1.92376e20 | + | 3.44761e19i | −0.548440 | + | 0.0982870i | ||||
\(862\) | 1.69354e20 | 0.478901 | ||||||||
\(863\) | − | 4.95257e20i | − | 1.38917i | −0.719411 | − | 0.694584i | \(-0.755588\pi\) | ||
0.719411 | − | 0.694584i | \(-0.244412\pi\) | |||||||
\(864\) | −5.47555e19 | + | 3.22286e19i | −0.152346 | + | 0.0896697i | ||||
\(865\) | 3.39784e20 | 0.937756 | ||||||||
\(866\) | 2.49611e20i | 0.683342i | ||||||||
\(867\) | 5.40956e19 | + | 3.01853e20i | 0.146902 | + | 0.819712i | ||||
\(868\) | 3.14131e20 | 0.846199 | ||||||||
\(869\) | 3.05942e20i | 0.817524i | ||||||||
\(870\) | 2.83868e20 | − | 5.08725e19i | 0.752457 | − | 0.134849i | ||||
\(871\) | −3.14641e20 | −0.827349 | ||||||||
\(872\) | 1.04958e20i | 0.273779i | ||||||||
\(873\) | −7.09632e18 | + | 2.62789e18i | −0.0183626 | + | 0.00679998i | ||||
\(874\) | 7.50963e19 | 0.192770 | ||||||||
\(875\) | 1.44478e20i | 0.367913i | ||||||||
\(876\) | −1.35880e19 | − | 7.58211e19i | −0.0343264 | − | 0.191541i | ||||
\(877\) | 3.41085e20 | 0.854803 | 0.427401 | − | 0.904062i | \(-0.359429\pi\) | ||||
0.427401 | + | 0.904062i | \(0.359429\pi\) | |||||||
\(878\) | − | 1.65953e20i | − | 0.412595i | ||||||
\(879\) | −2.97711e20 | + | 5.33534e19i | −0.734299 | + | 0.131595i | ||||
\(880\) | −1.20859e20 | −0.295733 | ||||||||
\(881\) | 7.47892e20i | 1.81555i | 0.419461 | + | 0.907773i | \(0.362219\pi\) | ||||
−0.419461 | + | 0.907773i | \(0.637781\pi\) | |||||||
\(882\) | 1.20300e20 | + | 3.24856e20i | 0.289724 | + | 0.782367i | ||||
\(883\) | 1.47899e20 | 0.353379 | 0.176690 | − | 0.984267i | \(-0.443461\pi\) | ||||
0.176690 | + | 0.984267i | \(0.443461\pi\) | |||||||
\(884\) | − | 9.30511e19i | − | 0.220575i | ||||||
\(885\) | 1.01606e19 | + | 5.66958e19i | 0.0238954 | + | 0.133336i | ||||
\(886\) | 3.92057e19 | 0.0914772 | ||||||||
\(887\) | − | 6.65945e20i | − | 1.54160i | −0.637074 | − | 0.770802i | \(-0.719856\pi\) | ||
0.637074 | − | 0.770802i | \(-0.280144\pi\) | |||||||
\(888\) | 2.25784e20 | − | 4.04633e19i | 0.518565 | − | 0.0929331i | ||||
\(889\) | 1.80801e20 | 0.411992 | ||||||||
\(890\) | − | 5.85902e20i | − | 1.32463i | ||||||
\(891\) | −2.54949e20 | − | 2.97025e20i | −0.571887 | − | 0.666267i | ||||
\(892\) | −2.43922e20 | −0.542870 | ||||||||
\(893\) | − | 5.36556e20i | − | 1.18483i | ||||||
\(894\) | −3.06827e19 | − | 1.71209e20i | −0.0672250 | − | 0.375114i | ||||
\(895\) | −1.33318e20 | −0.289820 | ||||||||
\(896\) | − | 6.05014e19i | − | 0.130500i | ||||||
\(897\) | 1.49568e20 | − | 2.68044e19i | 0.320105 | − | 0.0573666i | ||||
\(898\) | −3.77371e20 | −0.801372 | ||||||||
\(899\) | 4.36540e20i | 0.919827i | ||||||||
\(900\) | −1.82784e20 | + | 6.76881e19i | −0.382156 | + | 0.141519i | ||||
\(901\) | −1.75364e20 | −0.363804 | ||||||||
\(902\) | 1.13822e20i | 0.234305i | ||||||||
\(903\) | 5.43274e19 | + | 3.03146e20i | 0.110970 | + | 0.619209i | ||||
\(904\) | 8.99348e19 | 0.182284 | ||||||||
\(905\) | − | 5.99443e20i | − | 1.20561i | ||||||
\(906\) | −3.73195e19 | + | 6.68811e18i | −0.0744798 | + | 0.0133477i | ||||
\(907\) | 4.65845e20 | 0.922551 | 0.461276 | − | 0.887257i | \(-0.347392\pi\) | ||||
0.461276 | + | 0.887257i | \(0.347392\pi\) | |||||||
\(908\) | 3.53393e20i | 0.694475i | ||||||||
\(909\) | 7.38797e19 | + | 1.99504e20i | 0.144071 | + | 0.389048i | ||||
\(910\) | −7.84083e20 | −1.51730 | ||||||||
\(911\) | − | 8.03939e19i | − | 0.154381i | −0.997016 | − | 0.0771906i | \(-0.975405\pi\) | ||
0.997016 | − | 0.0771906i | \(-0.0245950\pi\) | |||||||
\(912\) | 2.09283e19 | + | 1.16780e20i | 0.0398814 | + | 0.222537i | ||||
\(913\) | −9.16633e20 | −1.73341 | ||||||||
\(914\) | 5.19987e20i | 0.975818i | ||||||||
\(915\) | −1.30070e21 | + | 2.33101e20i | −2.42231 | + | 0.434106i | ||||
\(916\) | −8.39398e19 | −0.155131 | ||||||||
\(917\) | − | 4.72908e20i | − | 0.867343i | ||||||
\(918\) | 8.05860e19 | + | 1.36913e20i | 0.146677 | + | 0.249199i | ||||
\(919\) | 4.27284e20 | 0.771807 | 0.385903 | − | 0.922539i | \(-0.373890\pi\) | ||||
0.385903 | + | 0.922539i | \(0.373890\pi\) | |||||||
\(920\) | 8.01011e19i | 0.143590i | ||||||||
\(921\) | −6.16225e19 | − | 3.43853e20i | −0.109628 | − | 0.611723i | ||||
\(922\) | 7.27719e20 | 1.28483 | ||||||||
\(923\) | 2.75699e20i | 0.483084i | ||||||||
\(924\) | 3.66895e20 | − | 6.57520e19i | 0.638025 | − | 0.114342i | ||||
\(925\) | 7.03690e20 | 1.21448 | ||||||||
\(926\) | 5.19394e20i | 0.889652i | ||||||||
\(927\) | 2.35248e20 | − | 8.71165e19i | 0.399916 | − | 0.148096i | ||||
\(928\) | 8.40774e19 | 0.141855 | ||||||||
\(929\) | − | 2.96529e20i | − | 0.496543i | −0.968691 | − | 0.248271i | \(-0.920138\pi\) | ||
0.968691 | − | 0.248271i | \(-0.0798624\pi\) | |||||||
\(930\) | −1.15904e20 | − | 6.46743e20i | −0.192627 | − | 1.07486i | ||||
\(931\) | 6.46855e20 | 1.06699 | ||||||||
\(932\) | − | 5.02928e20i | − | 0.823369i | ||||||
\(933\) | 3.32606e20 | − | 5.96070e19i | 0.540454 | − | 0.0968558i | ||||
\(934\) | −2.68535e20 | −0.433085 | ||||||||
\(935\) | 3.02202e20i | 0.483744i | ||||||||
\(936\) | 8.33651e19 | + | 2.25118e20i | 0.132450 | + | 0.357667i | ||||
\(937\) | −9.58472e20 | −1.51148 | −0.755740 | − | 0.654872i | \(-0.772723\pi\) | ||||
−0.755740 | + | 0.654872i | \(0.772723\pi\) | |||||||
\(938\) | 5.11538e20i | 0.800678i | ||||||||
\(939\) | −1.20047e20 | − | 6.69859e20i | −0.186505 | − | 1.04070i | ||||
\(940\) | 5.72314e20 | 0.882551 | ||||||||
\(941\) | 3.90634e20i | 0.597920i | 0.954266 | + | 0.298960i | \(0.0966397\pi\) | ||||
−0.954266 | + | 0.298960i | \(0.903360\pi\) | |||||||
\(942\) | −8.40674e20 | + | 1.50659e20i | −1.27724 | + | 0.228896i | ||||
\(943\) | 7.54374e19 | 0.113764 | ||||||||
\(944\) | 1.67924e19i | 0.0251368i | ||||||||
\(945\) | 1.15368e21 | − | 6.79048e20i | 1.71421 | − | 1.00897i | ||||
\(946\) | 1.79361e20 | 0.264539 | ||||||||
\(947\) | 1.28178e21i | 1.87656i | 0.345873 | + | 0.938281i | \(0.387583\pi\) | ||||
−0.345873 | + | 0.938281i | \(0.612417\pi\) | |||||||
\(948\) | 5.65085e19 | + | 3.15317e20i | 0.0821212 | + | 0.458235i | ||||
\(949\) | −2.91038e20 | −0.419842 | ||||||||
\(950\) | 3.63961e20i | 0.521182i | ||||||||
\(951\) | 8.09390e20 | − | 1.45052e20i | 1.15052 | − | 0.206187i | ||||
\(952\) | −1.51281e20 | −0.213464 | ||||||||
\(953\) | − | 9.39108e20i | − | 1.31542i | −0.753270 | − | 0.657711i | \(-0.771525\pi\) | ||
0.753270 | − | 0.657711i | \(-0.228475\pi\) | |||||||
\(954\) | 4.24257e20 | − | 1.57110e20i | 0.589917 | − | 0.218457i | ||||
\(955\) | −1.34071e20 | −0.185060 | ||||||||
\(956\) | − | 4.90336e20i | − | 0.671875i | ||||||
\(957\) | 9.13740e19 | + | 5.09865e20i | 0.124291 | + | 0.693540i | ||||
\(958\) | 2.71880e20 | 0.367129 | ||||||||
\(959\) | 6.07738e20i | 0.814678i | ||||||||
\(960\) | −1.24562e20 | + | 2.23231e19i | −0.165763 | + | 0.0297068i | ||||
\(961\) | 2.37635e20 | 0.313940 | ||||||||
\(962\) | − | 8.66669e20i | − | 1.13665i | ||||||
\(963\) | −2.80918e20 | − | 7.58588e20i | −0.365760 | − | 0.987693i | ||||
\(964\) | 1.26066e20 | 0.162951 | ||||||||
\(965\) | 9.02629e20i | 1.15829i | ||||||||
\(966\) | −4.35781e19 | − | 2.43165e20i | −0.0555173 | − | 0.309786i | ||||
\(967\) | −1.52276e21 | −1.92596 | −0.962978 | − | 0.269580i | \(-0.913115\pi\) | ||||
−0.962978 | + | 0.269580i | \(0.913115\pi\) | |||||||
\(968\) | 6.44883e19i | 0.0809755i | ||||||||
\(969\) | 2.92001e20 | − | 5.23301e19i | 0.364014 | − | 0.0652357i | ||||
\(970\) | −1.50719e19 | −0.0186538 | ||||||||
\(971\) | − | 1.35292e20i | − | 0.166240i | −0.996540 | − | 0.0831201i | \(-0.973511\pi\) | ||
0.996540 | − | 0.0831201i | \(-0.0264885\pi\) | |||||||
\(972\) | −3.17623e20 | − | 2.59036e20i | −0.387479 | − | 0.316007i | ||||
\(973\) | −2.60416e19 | −0.0315411 | ||||||||
\(974\) | − | 7.24682e20i | − | 0.871435i | ||||||
\(975\) | 1.29910e20 | + | 7.24895e20i | 0.155099 | + | 0.865451i | ||||
\(976\) | −3.85247e20 | −0.456658 | ||||||||
\(977\) | − | 4.13780e20i | − | 0.486976i | −0.969904 | − | 0.243488i | \(-0.921708\pi\) | ||
0.969904 | − | 0.243488i | \(-0.0782917\pi\) | |||||||
\(978\) | −3.88693e19 | + | 6.96584e18i | −0.0454187 | + | 0.00813957i | ||||
\(979\) | 1.05236e21 | 1.22092 | ||||||||
\(980\) | 6.89964e20i | 0.794775i | ||||||||
\(981\) | −6.34924e20 | + | 2.35123e20i | −0.726170 | + | 0.268914i | ||||
\(982\) | −3.32123e20 | −0.377154 | ||||||||
\(983\) | 1.09669e21i | 1.23655i | 0.785963 | + | 0.618273i | \(0.212168\pi\) | ||||
−0.785963 | + | 0.618273i | \(0.787832\pi\) | |||||||
\(984\) | 2.10234e19 | + | 1.17310e20i | 0.0235362 | + | 0.131332i | ||||
\(985\) | −1.25676e21 | −1.39701 | ||||||||
\(986\) | − | 2.10231e20i | − | 0.232038i | ||||||
\(987\) | −1.73739e21 | + | 3.11361e20i | −1.90404 | + | 0.341228i | ||||
\(988\) | 4.48256e20 | 0.487784 | ||||||||
\(989\) | − | 1.18874e20i | − | 0.128444i | ||||||
\(990\) | −2.70745e20 | − | 7.31115e20i | −0.290478 | − | 0.784403i | ||||
\(991\) | 9.67265e20 | 1.03046 | 0.515229 | − | 0.857053i | \(-0.327707\pi\) | ||||
0.515229 | + | 0.857053i | \(0.327707\pi\) | |||||||
\(992\) | − | 1.91555e20i | − | 0.202634i | ||||||
\(993\) | −4.18847e19 | − | 2.33716e20i | −0.0439957 | − | 0.245496i | ||||
\(994\) | 4.48226e20 | 0.467511 | ||||||||
\(995\) | − | 8.28860e20i | − | 0.858459i | ||||||
\(996\) | −9.44720e20 | + | 1.69305e20i | −0.971601 | + | 0.174123i | ||||
\(997\) | −8.31286e20 | −0.848954 | −0.424477 | − | 0.905439i | \(-0.639542\pi\) | ||||
−0.424477 | + | 0.905439i | \(0.639542\pi\) | |||||||
\(998\) | 6.76682e20i | 0.686232i | ||||||||
\(999\) | 7.50571e20 | + | 1.27520e21i | 0.755846 | + | 1.28416i |
(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 | 6.15.b.a.5.2 | ✓ | 4 | |
3.2 | odd | 2 | inner | 6.15.b.a.5.4 | yes | 4 | |
4.3 | odd | 2 | 48.15.e.d.17.1 | 4 | |||
5.2 | odd | 4 | 150.15.b.a.149.7 | 8 | |||
5.3 | odd | 4 | 150.15.b.a.149.2 | 8 | |||
5.4 | even | 2 | 150.15.d.a.101.3 | 4 | |||
12.11 | even | 2 | 48.15.e.d.17.2 | 4 | |||
15.2 | even | 4 | 150.15.b.a.149.1 | 8 | |||
15.8 | even | 4 | 150.15.b.a.149.8 | 8 | |||
15.14 | odd | 2 | 150.15.d.a.101.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.15.b.a.5.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
6.15.b.a.5.4 | yes | 4 | 3.2 | odd | 2 | inner | |
48.15.e.d.17.1 | 4 | 4.3 | odd | 2 | |||
48.15.e.d.17.2 | 4 | 12.11 | even | 2 | |||
150.15.b.a.149.1 | 8 | 15.2 | even | 4 | |||
150.15.b.a.149.2 | 8 | 5.3 | odd | 4 | |||
150.15.b.a.149.7 | 8 | 5.2 | odd | 4 | |||
150.15.b.a.149.8 | 8 | 15.8 | even | 4 | |||
150.15.d.a.101.1 | 4 | 15.14 | odd | 2 | |||
150.15.d.a.101.3 | 4 | 5.4 | even | 2 |