Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,13,Mod(22,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.22");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(21.0218577974\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 3347471347 x^{18} + 50192028136 x^{17} + \cdots + 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | multiple of \( 2^{35}\cdot 3^{11}\cdot 67 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.10 | ||
Root | \(273.019 - 7850.48i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.22 |
Dual form | 23.13.b.c.22.9 |
$q$-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 \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.17467 | 0.143354 | 0.0716771 | − | 0.997428i | \(-0.477165\pi\) | ||||
0.0716771 | + | 0.997428i | \(0.477165\pi\) | |||||||
\(3\) | −251.844 | −0.345465 | −0.172733 | − | 0.984969i | \(-0.555260\pi\) | ||||
−0.172733 | + | 0.984969i | \(0.555260\pi\) | |||||||
\(4\) | −4011.83 | −0.979450 | ||||||||
\(5\) | 7850.48i | 0.502430i | 0.967931 | + | 0.251215i | \(0.0808302\pi\) | ||||
−0.967931 | + | 0.251215i | \(0.919170\pi\) | |||||||
\(6\) | −2310.59 | −0.0495239 | ||||||||
\(7\) | − | 186545.i | − | 1.58561i | −0.609478 | − | 0.792803i | \(-0.708621\pi\) | ||
0.609478 | − | 0.792803i | \(-0.291379\pi\) | |||||||
\(8\) | −74386.7 | −0.283763 | ||||||||
\(9\) | −468016. | −0.880654 | ||||||||
\(10\) | 72025.6i | 0.0720256i | ||||||||
\(11\) | 1.55970e6i | 0.880411i | 0.897897 | + | 0.440205i | \(0.145094\pi\) | ||||
−0.897897 | + | 0.440205i | \(0.854906\pi\) | |||||||
\(12\) | 1.01035e6 | 0.338366 | ||||||||
\(13\) | 2.91464e6 | 0.603844 | 0.301922 | − | 0.953333i | \(-0.402372\pi\) | ||||
0.301922 | + | 0.953333i | \(0.402372\pi\) | |||||||
\(14\) | − | 1.71149e6i | − | 0.227304i | ||||||
\(15\) | − | 1.97710e6i | − | 0.173572i | ||||||
\(16\) | 1.57500e7 | 0.938771 | ||||||||
\(17\) | 3.03835e6i | 0.125877i | 0.998017 | + | 0.0629383i | \(0.0200471\pi\) | ||||
−0.998017 | + | 0.0629383i | \(0.979953\pi\) | |||||||
\(18\) | −4.29389e6 | −0.126246 | ||||||||
\(19\) | 4.66485e7i | 0.991553i | 0.868450 | + | 0.495777i | \(0.165116\pi\) | ||||
−0.868450 | + | 0.495777i | \(0.834884\pi\) | |||||||
\(20\) | − | 3.14947e7i | − | 0.492105i | ||||||
\(21\) | 4.69803e7i | 0.547772i | ||||||||
\(22\) | 1.43098e7i | 0.126211i | ||||||||
\(23\) | 1.33334e8 | − | 6.43178e7i | 0.900684 | − | 0.434475i | ||||
\(24\) | 1.87338e7 | 0.0980301 | ||||||||
\(25\) | 1.82511e8 | 0.747564 | ||||||||
\(26\) | 2.67409e7 | 0.0865636 | ||||||||
\(27\) | 2.51707e8 | 0.649700 | ||||||||
\(28\) | 7.48386e8i | 1.55302i | ||||||||
\(29\) | 3.96458e8 | 0.666514 | 0.333257 | − | 0.942836i | \(-0.391852\pi\) | ||||
0.333257 | + | 0.942836i | \(0.391852\pi\) | |||||||
\(30\) | − | 1.81392e7i | − | 0.0248823i | ||||||
\(31\) | −1.56637e8 | −0.176491 | −0.0882457 | − | 0.996099i | \(-0.528126\pi\) | ||||
−0.0882457 | + | 0.996099i | \(0.528126\pi\) | |||||||
\(32\) | 4.49189e8 | 0.418339 | ||||||||
\(33\) | − | 3.92802e8i | − | 0.304151i | ||||||
\(34\) | 2.78759e7i | 0.0180449i | ||||||||
\(35\) | 1.46447e9 | 0.796657 | ||||||||
\(36\) | 1.87760e9 | 0.862556 | ||||||||
\(37\) | 2.63711e9i | 1.02782i | 0.857844 | + | 0.513910i | \(0.171804\pi\) | ||||
−0.857844 | + | 0.513910i | \(0.828196\pi\) | |||||||
\(38\) | 4.27985e8i | 0.142143i | ||||||||
\(39\) | −7.34035e8 | −0.208607 | ||||||||
\(40\) | − | 5.83971e8i | − | 0.142571i | ||||||
\(41\) | 1.40562e9 | 0.295913 | 0.147956 | − | 0.988994i | \(-0.452731\pi\) | ||||
0.147956 | + | 0.988994i | \(0.452731\pi\) | |||||||
\(42\) | 4.31029e8i | 0.0785254i | ||||||||
\(43\) | 2.75599e9i | 0.435981i | 0.975951 | + | 0.217990i | \(0.0699501\pi\) | ||||
−0.975951 | + | 0.217990i | \(0.930050\pi\) | |||||||
\(44\) | − | 6.25725e9i | − | 0.862318i | ||||||
\(45\) | − | 3.67414e9i | − | 0.442467i | ||||||
\(46\) | 1.22329e9 | − | 5.90095e8i | 0.129117 | − | 0.0622838i | ||||
\(47\) | −8.81837e9 | −0.818091 | −0.409045 | − | 0.912514i | \(-0.634138\pi\) | ||||
−0.409045 | + | 0.912514i | \(0.634138\pi\) | |||||||
\(48\) | −3.96654e9 | −0.324313 | ||||||||
\(49\) | −2.09578e10 | −1.51415 | ||||||||
\(50\) | 1.67448e9 | 0.107166 | ||||||||
\(51\) | − | 7.65191e8i | − | 0.0434860i | ||||||
\(52\) | −1.16930e10 | −0.591435 | ||||||||
\(53\) | − | 1.74988e10i | − | 0.789503i | −0.918788 | − | 0.394751i | \(-0.870831\pi\) | ||
0.918788 | − | 0.394751i | \(-0.129169\pi\) | |||||||
\(54\) | 2.30933e9 | 0.0931373 | ||||||||
\(55\) | −1.22444e10 | −0.442345 | ||||||||
\(56\) | 1.38765e10i | 0.449936i | ||||||||
\(57\) | − | 1.17481e10i | − | 0.342547i | ||||||
\(58\) | 3.63738e9 | 0.0955477 | ||||||||
\(59\) | 2.10425e10 | 0.498867 | 0.249434 | − | 0.968392i | \(-0.419756\pi\) | ||||
0.249434 | + | 0.968392i | \(0.419756\pi\) | |||||||
\(60\) | 7.93176e9i | 0.170005i | ||||||||
\(61\) | − | 8.13588e10i | − | 1.57916i | −0.613649 | − | 0.789579i | \(-0.710299\pi\) | ||
0.613649 | − | 0.789579i | \(-0.289701\pi\) | |||||||
\(62\) | −1.43709e9 | −0.0253008 | ||||||||
\(63\) | 8.73060e10i | 1.39637i | ||||||||
\(64\) | −6.03907e10 | −0.878800 | ||||||||
\(65\) | 2.28813e10i | 0.303390i | ||||||||
\(66\) | − | 3.60383e9i | − | 0.0436014i | ||||||
\(67\) | − | 1.16096e8i | − | 0.00128342i | −1.00000 | 0.000641711i | \(-0.999796\pi\) | |||
1.00000 | 0.000641711i | \(-0.000204263\pi\) | ||||||||
\(68\) | − | 1.21893e10i | − | 0.123290i | ||||||
\(69\) | −3.35793e10 | + | 1.61981e10i | −0.311155 | + | 0.150096i | ||||
\(70\) | 1.34360e10 | 0.114204 | ||||||||
\(71\) | 7.66140e10 | 0.598078 | 0.299039 | − | 0.954241i | \(-0.403334\pi\) | ||||
0.299039 | + | 0.954241i | \(0.403334\pi\) | |||||||
\(72\) | 3.48141e10 | 0.249897 | ||||||||
\(73\) | 1.64447e11 | 1.08665 | 0.543324 | − | 0.839523i | \(-0.317165\pi\) | ||||
0.543324 | + | 0.839523i | \(0.317165\pi\) | |||||||
\(74\) | 2.41946e10i | 0.147343i | ||||||||
\(75\) | −4.59642e10 | −0.258257 | ||||||||
\(76\) | − | 1.87146e11i | − | 0.971176i | ||||||
\(77\) | 2.90955e11 | 1.39599 | ||||||||
\(78\) | −6.73453e9 | −0.0299047 | ||||||||
\(79\) | 3.14639e11i | 1.29435i | 0.762343 | + | 0.647173i | \(0.224049\pi\) | ||||
−0.762343 | + | 0.647173i | \(0.775951\pi\) | |||||||
\(80\) | 1.23645e11i | 0.471667i | ||||||||
\(81\) | 1.85332e11 | 0.656205 | ||||||||
\(82\) | 1.28961e10 | 0.0424203 | ||||||||
\(83\) | 5.71832e11i | 1.74904i | 0.484988 | + | 0.874521i | \(0.338824\pi\) | ||||
−0.484988 | + | 0.874521i | \(0.661176\pi\) | |||||||
\(84\) | − | 1.88477e11i | − | 0.536515i | ||||||
\(85\) | −2.38525e10 | −0.0632442 | ||||||||
\(86\) | 2.52853e10i | 0.0624997i | ||||||||
\(87\) | −9.98457e10 | −0.230257 | ||||||||
\(88\) | − | 1.16021e11i | − | 0.249828i | ||||||
\(89\) | − | 7.59123e11i | − | 1.52747i | −0.645531 | − | 0.763734i | \(-0.723364\pi\) | ||
0.645531 | − | 0.763734i | \(-0.276636\pi\) | |||||||
\(90\) | − | 3.37091e10i | − | 0.0634296i | ||||||
\(91\) | − | 5.43711e11i | − | 0.957459i | ||||||
\(92\) | −5.34911e11 | + | 2.58032e11i | −0.882175 | + | 0.425546i | ||||
\(93\) | 3.94480e10 | 0.0609716 | ||||||||
\(94\) | −8.09057e10 | −0.117277 | ||||||||
\(95\) | −3.66213e11 | −0.498186 | ||||||||
\(96\) | −1.13125e11 | −0.144522 | ||||||||
\(97\) | 6.47739e11i | 0.777624i | 0.921317 | + | 0.388812i | \(0.127114\pi\) | ||||
−0.921317 | + | 0.388812i | \(0.872886\pi\) | |||||||
\(98\) | −1.92281e11 | −0.217060 | ||||||||
\(99\) | − | 7.29965e11i | − | 0.775337i | ||||||
\(100\) | −7.32201e11 | −0.732201 | ||||||||
\(101\) | 1.01010e12 | 0.951563 | 0.475781 | − | 0.879564i | \(-0.342165\pi\) | ||||
0.475781 | + | 0.879564i | \(0.342165\pi\) | |||||||
\(102\) | − | 7.02038e9i | − | 0.00623390i | ||||||
\(103\) | 1.73435e12i | 1.45249i | 0.687437 | + | 0.726244i | \(0.258736\pi\) | ||||
−0.687437 | + | 0.726244i | \(0.741264\pi\) | |||||||
\(104\) | −2.16810e11 | −0.171348 | ||||||||
\(105\) | −3.68817e11 | −0.275217 | ||||||||
\(106\) | − | 1.60546e11i | − | 0.113179i | ||||||
\(107\) | − | 2.71214e12i | − | 1.80721i | −0.428362 | − | 0.903607i | \(-0.640909\pi\) | ||
0.428362 | − | 0.903607i | \(-0.359091\pi\) | |||||||
\(108\) | −1.00981e12 | −0.636349 | ||||||||
\(109\) | 9.62939e11i | 0.574169i | 0.957905 | + | 0.287084i | \(0.0926860\pi\) | ||||
−0.957905 | + | 0.287084i | \(0.907314\pi\) | |||||||
\(110\) | −1.12338e11 | −0.0634121 | ||||||||
\(111\) | − | 6.64140e11i | − | 0.355076i | ||||||
\(112\) | − | 2.93808e12i | − | 1.48852i | ||||||
\(113\) | 1.95847e12i | 0.940691i | 0.882482 | + | 0.470345i | \(0.155871\pi\) | ||||
−0.882482 | + | 0.470345i | \(0.844129\pi\) | |||||||
\(114\) | − | 1.07785e11i | − | 0.0491056i | ||||||
\(115\) | 5.04926e11 | + | 1.04673e12i | 0.218293 | + | 0.452531i | ||||
\(116\) | −1.59052e12 | −0.652817 | ||||||||
\(117\) | −1.36410e12 | −0.531777 | ||||||||
\(118\) | 1.93058e11 | 0.0715147 | ||||||||
\(119\) | 5.66790e11 | 0.199591 | ||||||||
\(120\) | 1.47070e11i | 0.0492533i | ||||||||
\(121\) | 7.05760e11 | 0.224877 | ||||||||
\(122\) | − | 7.46440e11i | − | 0.226379i | ||||||
\(123\) | −3.53996e11 | −0.102227 | ||||||||
\(124\) | 6.28399e11 | 0.172864 | ||||||||
\(125\) | 3.34942e12i | 0.878029i | ||||||||
\(126\) | 8.01004e11i | 0.200176i | ||||||||
\(127\) | 4.83918e12 | 1.15332 | 0.576660 | − | 0.816984i | \(-0.304356\pi\) | ||||
0.576660 | + | 0.816984i | \(0.304356\pi\) | |||||||
\(128\) | −2.39394e12 | −0.544319 | ||||||||
\(129\) | − | 6.94081e11i | − | 0.150616i | ||||||
\(130\) | 2.09928e11i | 0.0434922i | ||||||||
\(131\) | 8.51685e12 | 1.68520 | 0.842600 | − | 0.538540i | \(-0.181024\pi\) | ||||
0.842600 | + | 0.538540i | \(0.181024\pi\) | |||||||
\(132\) | 1.57585e12i | 0.297901i | ||||||||
\(133\) | 8.70204e12 | 1.57221 | ||||||||
\(134\) | − | 1.06515e9i | − | 0.000183984i | ||||||
\(135\) | 1.97602e12i | 0.326429i | ||||||||
\(136\) | − | 2.26013e11i | − | 0.0357191i | ||||||
\(137\) | 1.63849e12i | 0.247811i | 0.992294 | + | 0.123906i | \(0.0395420\pi\) | ||||
−0.992294 | + | 0.123906i | \(0.960458\pi\) | |||||||
\(138\) | −3.08079e11 | + | 1.48612e11i | −0.0446054 | + | 0.0215169i | ||||
\(139\) | −2.48277e11 | −0.0344229 | −0.0172114 | − | 0.999852i | \(-0.505479\pi\) | ||||
−0.0172114 | + | 0.999852i | \(0.505479\pi\) | |||||||
\(140\) | −5.87519e12 | −0.780285 | ||||||||
\(141\) | 2.22086e12 | 0.282622 | ||||||||
\(142\) | 7.02908e11 | 0.0857371 | ||||||||
\(143\) | 4.54597e12i | 0.531631i | ||||||||
\(144\) | −7.37123e12 | −0.826732 | ||||||||
\(145\) | 3.11239e12i | 0.334877i | ||||||||
\(146\) | 1.50875e12 | 0.155776 | ||||||||
\(147\) | 5.27809e12 | 0.523086 | ||||||||
\(148\) | − | 1.05796e13i | − | 1.00670i | ||||||
\(149\) | − | 9.55388e12i | − | 0.873097i | −0.899681 | − | 0.436548i | \(-0.856201\pi\) | ||
0.899681 | − | 0.436548i | \(-0.143799\pi\) | |||||||
\(150\) | −4.21707e11 | −0.0370223 | ||||||||
\(151\) | −1.60623e13 | −1.35502 | −0.677509 | − | 0.735514i | \(-0.736941\pi\) | ||||
−0.677509 | + | 0.735514i | \(0.736941\pi\) | |||||||
\(152\) | − | 3.47003e12i | − | 0.281366i | ||||||
\(153\) | − | 1.42200e12i | − | 0.110854i | ||||||
\(154\) | 2.66941e12 | 0.200120 | ||||||||
\(155\) | − | 1.22967e12i | − | 0.0886747i | ||||||
\(156\) | 2.94482e12 | 0.204320 | ||||||||
\(157\) | 1.83890e13i | 1.22789i | 0.789347 | + | 0.613947i | \(0.210419\pi\) | ||||
−0.789347 | + | 0.613947i | \(0.789581\pi\) | |||||||
\(158\) | 2.88671e12i | 0.185550i | ||||||||
\(159\) | 4.40698e12i | 0.272746i | ||||||||
\(160\) | 3.52634e12i | 0.210186i | ||||||||
\(161\) | −1.19982e13 | − | 2.48727e13i | −0.688906 | − | 1.42813i | ||||
\(162\) | 1.70036e12 | 0.0940698 | ||||||||
\(163\) | −1.60347e13 | −0.854937 | −0.427468 | − | 0.904030i | \(-0.640594\pi\) | ||||
−0.427468 | + | 0.904030i | \(0.640594\pi\) | |||||||
\(164\) | −5.63908e12 | −0.289831 | ||||||||
\(165\) | 3.08368e12 | 0.152815 | ||||||||
\(166\) | 5.24637e12i | 0.250733i | ||||||||
\(167\) | −1.91586e13 | −0.883214 | −0.441607 | − | 0.897209i | \(-0.645591\pi\) | ||||
−0.441607 | + | 0.897209i | \(0.645591\pi\) | |||||||
\(168\) | − | 3.49471e12i | − | 0.155437i | ||||||
\(169\) | −1.48030e13 | −0.635373 | ||||||||
\(170\) | −2.18839e11 | −0.00906633 | ||||||||
\(171\) | − | 2.18322e13i | − | 0.873215i | ||||||
\(172\) | − | 1.10566e13i | − | 0.427021i | ||||||
\(173\) | 3.64376e13 | 1.35917 | 0.679584 | − | 0.733597i | \(-0.262160\pi\) | ||||
0.679584 | + | 0.733597i | \(0.262160\pi\) | |||||||
\(174\) | −9.16051e11 | −0.0330084 | ||||||||
\(175\) | − | 3.40465e13i | − | 1.18534i | ||||||
\(176\) | 2.45652e13i | 0.826504i | ||||||||
\(177\) | −5.29942e12 | −0.172341 | ||||||||
\(178\) | − | 6.96470e12i | − | 0.218969i | ||||||
\(179\) | 6.09040e10 | 0.00185152 | 0.000925758 | − | 1.00000i | \(-0.499705\pi\) | ||||
0.000925758 | 1.00000i | \(0.499705\pi\) | ||||||||
\(180\) | 1.47400e13i | 0.433374i | ||||||||
\(181\) | 4.37064e13i | 1.24301i | 0.783412 | + | 0.621503i | \(0.213478\pi\) | ||||
−0.783412 | + | 0.621503i | \(0.786522\pi\) | |||||||
\(182\) | − | 4.98838e12i | − | 0.137256i | ||||||
\(183\) | 2.04897e13i | 0.545544i | ||||||||
\(184\) | −9.91824e12 | + | 4.78439e12i | −0.255580 | + | 0.123288i | ||||
\(185\) | −2.07025e13 | −0.516408 | ||||||||
\(186\) | 3.61923e11 | 0.00874054 | ||||||||
\(187\) | −4.73892e12 | −0.110823 | ||||||||
\(188\) | 3.53778e13 | 0.801278 | ||||||||
\(189\) | − | 4.69547e13i | − | 1.03017i | ||||||
\(190\) | −3.35988e12 | −0.0714172 | ||||||||
\(191\) | 5.40621e13i | 1.11351i | 0.830678 | + | 0.556753i | \(0.187953\pi\) | ||||
−0.830678 | + | 0.556753i | \(0.812047\pi\) | |||||||
\(192\) | 1.52090e13 | 0.303595 | ||||||||
\(193\) | 8.87390e13 | 1.71700 | 0.858500 | − | 0.512813i | \(-0.171396\pi\) | ||||
0.858500 | + | 0.512813i | \(0.171396\pi\) | |||||||
\(194\) | 5.94279e12i | 0.111476i | ||||||||
\(195\) | − | 5.76252e12i | − | 0.104811i | ||||||
\(196\) | 8.40789e13 | 1.48303 | ||||||||
\(197\) | −1.31393e13 | −0.224788 | −0.112394 | − | 0.993664i | \(-0.535852\pi\) | ||||
−0.112394 | + | 0.993664i | \(0.535852\pi\) | |||||||
\(198\) | − | 6.69719e12i | − | 0.111148i | ||||||
\(199\) | 2.68520e13i | 0.432372i | 0.976352 | + | 0.216186i | \(0.0693617\pi\) | ||||
−0.976352 | + | 0.216186i | \(0.930638\pi\) | |||||||
\(200\) | −1.35764e13 | −0.212131 | ||||||||
\(201\) | 2.92381e10i | 0.000443377i | ||||||||
\(202\) | 9.26736e12 | 0.136411 | ||||||||
\(203\) | − | 7.39573e13i | − | 1.05683i | ||||||
\(204\) | 3.06981e12i | 0.0425923i | ||||||||
\(205\) | 1.10347e13i | 0.148675i | ||||||||
\(206\) | 1.59121e13i | 0.208220i | ||||||||
\(207\) | −6.24022e13 | + | 3.01017e13i | −0.793191 | + | 0.382622i | ||||
\(208\) | 4.59055e13 | 0.566871 | ||||||||
\(209\) | −7.27577e13 | −0.872974 | ||||||||
\(210\) | −3.38378e12 | −0.0394536 | ||||||||
\(211\) | 5.49173e13 | 0.622321 | 0.311161 | − | 0.950357i | \(-0.399282\pi\) | ||||
0.311161 | + | 0.950357i | \(0.399282\pi\) | |||||||
\(212\) | 7.02022e13i | 0.773278i | ||||||||
\(213\) | −1.92948e13 | −0.206615 | ||||||||
\(214\) | − | 2.48830e13i | − | 0.259072i | ||||||
\(215\) | −2.16359e13 | −0.219050 | ||||||||
\(216\) | −1.87237e13 | −0.184361 | ||||||||
\(217\) | 2.92198e13i | 0.279846i | ||||||||
\(218\) | 8.83465e12i | 0.0823096i | ||||||||
\(219\) | −4.14150e13 | −0.375399 | ||||||||
\(220\) | 4.91224e13 | 0.433255 | ||||||||
\(221\) | 8.85570e12i | 0.0760098i | ||||||||
\(222\) | − | 6.09327e12i | − | 0.0509017i | ||||||
\(223\) | 1.44603e14 | 1.17584 | 0.587921 | − | 0.808919i | \(-0.299947\pi\) | ||||
0.587921 | + | 0.808919i | \(0.299947\pi\) | |||||||
\(224\) | − | 8.37939e13i | − | 0.663322i | ||||||
\(225\) | −8.54178e13 | −0.658345 | ||||||||
\(226\) | 1.79684e13i | 0.134852i | ||||||||
\(227\) | − | 1.78521e14i | − | 1.30477i | −0.757887 | − | 0.652386i | \(-0.773768\pi\) | ||
0.757887 | − | 0.652386i | \(-0.226232\pi\) | |||||||
\(228\) | 4.71315e13i | 0.335508i | ||||||||
\(229\) | − | 4.74666e13i | − | 0.329136i | −0.986366 | − | 0.164568i | \(-0.947377\pi\) | ||
0.986366 | − | 0.164568i | \(-0.0526230\pi\) | |||||||
\(230\) | 4.63253e12 | + | 9.60343e12i | 0.0312933 | + | 0.0648723i | ||||
\(231\) | −7.32752e13 | −0.482264 | ||||||||
\(232\) | −2.94912e13 | −0.189132 | ||||||||
\(233\) | −8.23059e13 | −0.514394 | −0.257197 | − | 0.966359i | \(-0.582799\pi\) | ||||
−0.257197 | + | 0.966359i | \(0.582799\pi\) | |||||||
\(234\) | −1.25151e13 | −0.0762326 | ||||||||
\(235\) | − | 6.92284e13i | − | 0.411034i | ||||||
\(236\) | −8.44187e13 | −0.488615 | ||||||||
\(237\) | − | 7.92401e13i | − | 0.447152i | ||||||
\(238\) | 5.20011e12 | 0.0286122 | ||||||||
\(239\) | −2.40951e14 | −1.29283 | −0.646415 | − | 0.762986i | \(-0.723733\pi\) | ||||
−0.646415 | + | 0.762986i | \(0.723733\pi\) | |||||||
\(240\) | − | 3.11392e13i | − | 0.162945i | ||||||
\(241\) | 1.81866e14i | 0.928217i | 0.885778 | + | 0.464109i | \(0.153625\pi\) | ||||
−0.885778 | + | 0.464109i | \(0.846375\pi\) | |||||||
\(242\) | 6.47512e12 | 0.0322371 | ||||||||
\(243\) | −1.80442e14 | −0.876396 | ||||||||
\(244\) | 3.26397e14i | 1.54670i | ||||||||
\(245\) | − | 1.64528e14i | − | 0.760754i | ||||||
\(246\) | −3.24780e12 | −0.0146547 | ||||||||
\(247\) | 1.35964e14i | 0.598743i | ||||||||
\(248\) | 1.16517e13 | 0.0500817 | ||||||||
\(249\) | − | 1.44013e14i | − | 0.604233i | ||||||
\(250\) | 3.07298e13i | 0.125869i | ||||||||
\(251\) | − | 3.32738e14i | − | 1.33064i | −0.746560 | − | 0.665318i | \(-0.768296\pi\) | ||
0.746560 | − | 0.665318i | \(-0.231704\pi\) | |||||||
\(252\) | − | 3.50256e14i | − | 1.36767i | ||||||
\(253\) | 1.00317e14 | + | 2.07961e14i | 0.382516 | + | 0.792972i | ||||
\(254\) | 4.43979e13 | 0.165333 | ||||||||
\(255\) | 6.00712e12 | 0.0218487 | ||||||||
\(256\) | 2.25397e14 | 0.800770 | ||||||||
\(257\) | −2.20367e14 | −0.764799 | −0.382400 | − | 0.923997i | \(-0.624902\pi\) | ||||
−0.382400 | + | 0.923997i | \(0.624902\pi\) | |||||||
\(258\) | − | 6.36796e12i | − | 0.0215915i | ||||||
\(259\) | 4.91939e14 | 1.62972 | ||||||||
\(260\) | − | 9.17958e13i | − | 0.297155i | ||||||
\(261\) | −1.85549e14 | −0.586968 | ||||||||
\(262\) | 7.81393e13 | 0.241581 | ||||||||
\(263\) | 5.30387e14i | 1.60272i | 0.598180 | + | 0.801362i | \(0.295891\pi\) | ||||
−0.598180 | + | 0.801362i | \(0.704109\pi\) | |||||||
\(264\) | 2.92192e13i | 0.0863067i | ||||||||
\(265\) | 1.37374e14 | 0.396670 | ||||||||
\(266\) | 7.98384e13 | 0.225384 | ||||||||
\(267\) | 1.91181e14i | 0.527687i | ||||||||
\(268\) | 4.65758e11i | 0.00125705i | ||||||||
\(269\) | 2.90294e14 | 0.766167 | 0.383084 | − | 0.923714i | \(-0.374862\pi\) | ||||
0.383084 | + | 0.923714i | \(0.374862\pi\) | |||||||
\(270\) | 1.81294e13i | 0.0467950i | ||||||||
\(271\) | −1.28018e14 | −0.323189 | −0.161594 | − | 0.986857i | \(-0.551664\pi\) | ||||
−0.161594 | + | 0.986857i | \(0.551664\pi\) | |||||||
\(272\) | 4.78540e13i | 0.118169i | ||||||||
\(273\) | 1.36931e14i | 0.330769i | ||||||||
\(274\) | 1.50326e13i | 0.0355248i | ||||||||
\(275\) | 2.84662e14i | 0.658163i | ||||||||
\(276\) | 1.34714e14 | − | 6.49838e13i | 0.304761 | − | 0.147011i | ||||
\(277\) | 3.87507e14 | 0.857828 | 0.428914 | − | 0.903345i | \(-0.358896\pi\) | ||||
0.428914 | + | 0.903345i | \(0.358896\pi\) | |||||||
\(278\) | −2.27786e12 | −0.00493467 | ||||||||
\(279\) | 7.33084e13 | 0.155428 | ||||||||
\(280\) | −1.08937e14 | −0.226061 | ||||||||
\(281\) | − | 3.13265e14i | − | 0.636317i | −0.948037 | − | 0.318159i | \(-0.896936\pi\) | ||
0.948037 | − | 0.318159i | \(-0.103064\pi\) | |||||||
\(282\) | 2.03756e13 | 0.0405150 | ||||||||
\(283\) | − | 2.66833e14i | − | 0.519422i | −0.965686 | − | 0.259711i | \(-0.916373\pi\) | ||
0.965686 | − | 0.259711i | \(-0.0836273\pi\) | |||||||
\(284\) | −3.07362e14 | −0.585788 | ||||||||
\(285\) | 9.22285e13 | 0.172106 | ||||||||
\(286\) | 4.17078e13i | 0.0762115i | ||||||||
\(287\) | − | 2.62211e14i | − | 0.469201i | ||||||
\(288\) | −2.10227e14 | −0.368412 | ||||||||
\(289\) | 5.73391e14 | 0.984155 | ||||||||
\(290\) | 2.85551e13i | 0.0480061i | ||||||||
\(291\) | − | 1.63129e14i | − | 0.268642i | ||||||
\(292\) | −6.59733e14 | −1.06432 | ||||||||
\(293\) | 5.85575e14i | 0.925500i | 0.886489 | + | 0.462750i | \(0.153137\pi\) | ||||
−0.886489 | + | 0.462750i | \(0.846863\pi\) | |||||||
\(294\) | 4.84248e13 | 0.0749866 | ||||||||
\(295\) | 1.65193e14i | 0.250646i | ||||||||
\(296\) | − | 1.96166e14i | − | 0.291657i | ||||||
\(297\) | 3.92588e14i | 0.572003i | ||||||||
\(298\) | − | 8.76538e13i | − | 0.125162i | ||||||
\(299\) | 3.88619e14 | − | 1.87463e14i | 0.543873 | − | 0.262355i | ||||
\(300\) | 1.84400e14 | 0.252950 | ||||||||
\(301\) | 5.14117e14 | 0.691294 | ||||||||
\(302\) | −1.47366e14 | −0.194248 | ||||||||
\(303\) | −2.54388e14 | −0.328732 | ||||||||
\(304\) | 7.34712e14i | 0.930841i | ||||||||
\(305\) | 6.38705e14 | 0.793417 | ||||||||
\(306\) | − | 1.30464e13i | − | 0.0158913i | ||||||
\(307\) | 2.80726e14 | 0.335315 | 0.167658 | − | 0.985845i | \(-0.446380\pi\) | ||||
0.167658 | + | 0.985845i | \(0.446380\pi\) | |||||||
\(308\) | −1.16726e15 | −1.36730 | ||||||||
\(309\) | − | 4.36785e14i | − | 0.501784i | ||||||
\(310\) | − | 1.12819e13i | − | 0.0127119i | ||||||
\(311\) | −4.43093e14 | −0.489703 | −0.244852 | − | 0.969561i | \(-0.578739\pi\) | ||||
−0.244852 | + | 0.969561i | \(0.578739\pi\) | |||||||
\(312\) | 5.46024e13 | 0.0591949 | ||||||||
\(313\) | − | 1.33364e15i | − | 1.41832i | −0.705050 | − | 0.709158i | \(-0.749075\pi\) | ||
0.705050 | − | 0.709158i | \(-0.250925\pi\) | |||||||
\(314\) | 1.68713e14i | 0.176024i | ||||||||
\(315\) | −6.85393e14 | −0.701579 | ||||||||
\(316\) | − | 1.26228e15i | − | 1.26775i | ||||||
\(317\) | −1.79907e15 | −1.77293 | −0.886465 | − | 0.462796i | \(-0.846846\pi\) | ||||
−0.886465 | + | 0.462796i | \(0.846846\pi\) | |||||||
\(318\) | 4.04326e13i | 0.0390993i | ||||||||
\(319\) | 6.18356e14i | 0.586806i | ||||||||
\(320\) | − | 4.74096e14i | − | 0.441536i | ||||||
\(321\) | 6.83037e14i | 0.624330i | ||||||||
\(322\) | −1.10079e14 | − | 2.28199e14i | −0.0987576 | − | 0.204729i | ||||
\(323\) | −1.41735e14 | −0.124813 | ||||||||
\(324\) | −7.43518e14 | −0.642720 | ||||||||
\(325\) | 5.31953e14 | 0.451412 | ||||||||
\(326\) | −1.47113e14 | −0.122559 | ||||||||
\(327\) | − | 2.42510e14i | − | 0.198355i | ||||||
\(328\) | −1.04559e14 | −0.0839689 | ||||||||
\(329\) | 1.64502e15i | 1.29717i | ||||||||
\(330\) | 2.82918e13 | 0.0219067 | ||||||||
\(331\) | −8.27243e14 | −0.629021 | −0.314510 | − | 0.949254i | \(-0.601840\pi\) | ||||
−0.314510 | + | 0.949254i | \(0.601840\pi\) | |||||||
\(332\) | − | 2.29409e15i | − | 1.71310i | ||||||
\(333\) | − | 1.23421e15i | − | 0.905154i | ||||||
\(334\) | −1.75774e14 | −0.126613 | ||||||||
\(335\) | 9.11411e11 | 0.000644830 | ||||||||
\(336\) | 7.39937e14i | 0.514232i | ||||||||
\(337\) | 1.66354e15i | 1.13567i | 0.823141 | + | 0.567837i | \(0.192220\pi\) | ||||
−0.823141 | + | 0.567837i | \(0.807780\pi\) | |||||||
\(338\) | −1.35812e14 | −0.0910834 | ||||||||
\(339\) | − | 4.93230e14i | − | 0.324976i | ||||||
\(340\) | 9.56922e13 | 0.0619445 | ||||||||
\(341\) | − | 2.44307e14i | − | 0.155385i | ||||||
\(342\) | − | 2.00303e14i | − | 0.125179i | ||||||
\(343\) | 1.32754e15i | 0.815237i | ||||||||
\(344\) | − | 2.05009e14i | − | 0.123715i | ||||||
\(345\) | −1.27163e14 | − | 2.63613e14i | −0.0754127 | − | 0.156334i | ||||
\(346\) | 3.34303e14 | 0.194843 | ||||||||
\(347\) | 1.57272e15 | 0.900896 | 0.450448 | − | 0.892803i | \(-0.351264\pi\) | ||||
0.450448 | + | 0.892803i | \(0.351264\pi\) | |||||||
\(348\) | 4.00563e14 | 0.225526 | ||||||||
\(349\) | 2.92770e15 | 1.62022 | 0.810111 | − | 0.586276i | \(-0.199407\pi\) | ||||
0.810111 | + | 0.586276i | \(0.199407\pi\) | |||||||
\(350\) | − | 3.12365e14i | − | 0.169924i | ||||||
\(351\) | 7.33636e14 | 0.392318 | ||||||||
\(352\) | 7.00600e14i | 0.368311i | ||||||||
\(353\) | 1.99586e15 | 1.03153 | 0.515765 | − | 0.856730i | \(-0.327508\pi\) | ||||
0.515765 | + | 0.856730i | \(0.327508\pi\) | |||||||
\(354\) | −4.86205e13 | −0.0247058 | ||||||||
\(355\) | 6.01456e14i | 0.300493i | ||||||||
\(356\) | 3.04547e15i | 1.49608i | ||||||||
\(357\) | −1.42743e14 | −0.0689516 | ||||||||
\(358\) | 5.58774e11 | 0.000265423 | ||||||||
\(359\) | − | 3.64076e15i | − | 1.70069i | −0.526227 | − | 0.850344i | \(-0.676394\pi\) | ||
0.526227 | − | 0.850344i | \(-0.323606\pi\) | |||||||
\(360\) | 2.73307e14i | 0.125556i | ||||||||
\(361\) | 3.72334e13 | 0.0168225 | ||||||||
\(362\) | 4.00992e14i | 0.178190i | ||||||||
\(363\) | −1.77741e14 | −0.0776871 | ||||||||
\(364\) | 2.18128e15i | 0.937783i | ||||||||
\(365\) | 1.29099e15i | 0.545965i | ||||||||
\(366\) | 1.87987e14i | 0.0782060i | ||||||||
\(367\) | 1.75363e15i | 0.717698i | 0.933396 | + | 0.358849i | \(0.116831\pi\) | ||||
−0.933396 | + | 0.358849i | \(0.883169\pi\) | |||||||
\(368\) | 2.10000e15 | − | 1.01300e15i | 0.845536 | − | 0.407872i | ||||
\(369\) | −6.57850e14 | −0.260597 | ||||||||
\(370\) | −1.89939e14 | −0.0740294 | ||||||||
\(371\) | −3.26432e15 | −1.25184 | ||||||||
\(372\) | −1.58259e14 | −0.0597186 | ||||||||
\(373\) | 5.61125e11i | 0.000208356i | 1.00000 | 0.000104178i | \(3.31609e-5\pi\) | |||||
−1.00000 | 0.000104178i | \(0.999967\pi\) | ||||||||
\(374\) | −4.34781e13 | −0.0158870 | ||||||||
\(375\) | − | 8.43531e14i | − | 0.303328i | ||||||
\(376\) | 6.55969e14 | 0.232144 | ||||||||
\(377\) | 1.15553e15 | 0.402471 | ||||||||
\(378\) | − | 4.30794e14i | − | 0.147679i | ||||||
\(379\) | − | 3.60849e15i | − | 1.21756i | −0.793339 | − | 0.608780i | \(-0.791659\pi\) | ||
0.793339 | − | 0.608780i | \(-0.208341\pi\) | |||||||
\(380\) | 1.46918e15 | 0.487949 | ||||||||
\(381\) | −1.21872e15 | −0.398432 | ||||||||
\(382\) | 4.96002e14i | 0.159626i | ||||||||
\(383\) | − | 2.89206e15i | − | 0.916252i | −0.888887 | − | 0.458126i | \(-0.848521\pi\) | ||
0.888887 | − | 0.458126i | \(-0.151479\pi\) | |||||||
\(384\) | 6.02900e14 | 0.188043 | ||||||||
\(385\) | 2.28413e15i | 0.701385i | ||||||||
\(386\) | 8.14151e14 | 0.246139 | ||||||||
\(387\) | − | 1.28985e15i | − | 0.383948i | ||||||
\(388\) | − | 2.59862e15i | − | 0.761643i | ||||||
\(389\) | 2.80591e15i | 0.809798i | 0.914361 | + | 0.404899i | \(0.132693\pi\) | ||||
−0.914361 | + | 0.404899i | \(0.867307\pi\) | |||||||
\(390\) | − | 5.28693e13i | − | 0.0150250i | ||||||
\(391\) | 1.95420e14 | + | 4.05115e14i | 0.0546902 | + | 0.113375i | ||||
\(392\) | 1.55898e15 | 0.429659 | ||||||||
\(393\) | −2.14492e15 | −0.582178 | ||||||||
\(394\) | −1.20548e14 | −0.0322243 | ||||||||
\(395\) | −2.47007e15 | −0.650319 | ||||||||
\(396\) | 2.92849e15i | 0.759404i | ||||||||
\(397\) | 1.07586e15 | 0.274798 | 0.137399 | − | 0.990516i | \(-0.456126\pi\) | ||||
0.137399 | + | 0.990516i | \(0.456126\pi\) | |||||||
\(398\) | 2.46358e14i | 0.0619824i | ||||||||
\(399\) | −2.19156e15 | −0.543145 | ||||||||
\(400\) | 2.87454e15 | 0.701791 | ||||||||
\(401\) | 3.74352e15i | 0.900355i | 0.892939 | + | 0.450177i | \(0.148639\pi\) | ||||
−0.892939 | + | 0.450177i | \(0.851361\pi\) | |||||||
\(402\) | 2.68250e11i | 6.35600e-5i | ||||||||
\(403\) | −4.56540e14 | −0.106573 | ||||||||
\(404\) | −4.05236e15 | −0.932007 | ||||||||
\(405\) | 1.45494e15i | 0.329697i | ||||||||
\(406\) | − | 6.78534e14i | − | 0.151501i | ||||||
\(407\) | −4.11310e15 | −0.904904 | ||||||||
\(408\) | 5.69200e13i | 0.0123397i | ||||||||
\(409\) | 2.05179e14 | 0.0438322 | 0.0219161 | − | 0.999760i | \(-0.493023\pi\) | ||||
0.0219161 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(410\) | 1.01240e14i | 0.0213133i | ||||||||
\(411\) | − | 4.12644e14i | − | 0.0856101i | ||||||
\(412\) | − | 6.95789e15i | − | 1.42264i | ||||||
\(413\) | − | 3.92537e15i | − | 0.791007i | ||||||
\(414\) | −5.72520e14 | + | 2.76174e14i | −0.113707 | + | 0.0548505i | ||||
\(415\) | −4.48915e15 | −0.878772 | ||||||||
\(416\) | 1.30922e15 | 0.252612 | ||||||||
\(417\) | 6.25270e13 | 0.0118919 | ||||||||
\(418\) | −6.67528e14 | −0.125145 | ||||||||
\(419\) | − | 2.78781e15i | − | 0.515203i | −0.966251 | − | 0.257602i | \(-0.917068\pi\) | ||
0.966251 | − | 0.257602i | \(-0.0829322\pi\) | |||||||
\(420\) | 1.47963e15 | 0.269561 | ||||||||
\(421\) | − | 9.84555e15i | − | 1.76827i | −0.467236 | − | 0.884133i | \(-0.654750\pi\) | ||
0.467236 | − | 0.884133i | \(-0.345250\pi\) | |||||||
\(422\) | 5.03849e14 | 0.0892124 | ||||||||
\(423\) | 4.12714e15 | 0.720455 | ||||||||
\(424\) | 1.30168e15i | 0.224031i | ||||||||
\(425\) | 5.54532e14i | 0.0941007i | ||||||||
\(426\) | −1.77023e14 | −0.0296192 | ||||||||
\(427\) | −1.51771e16 | −2.50392 | ||||||||
\(428\) | 1.08806e16i | 1.77008i | ||||||||
\(429\) | − | 1.14487e15i | − | 0.183660i | ||||||
\(430\) | −1.98502e14 | −0.0314018 | ||||||||
\(431\) | 1.42530e14i | 0.0222353i | 0.999938 | + | 0.0111176i | \(0.00353893\pi\) | ||||
−0.999938 | + | 0.0111176i | \(0.996461\pi\) | |||||||
\(432\) | 3.96438e15 | 0.609920 | ||||||||
\(433\) | − | 1.19687e15i | − | 0.181602i | −0.995869 | − | 0.0908008i | \(-0.971057\pi\) | ||
0.995869 | − | 0.0908008i | \(-0.0289427\pi\) | |||||||
\(434\) | 2.68082e14i | 0.0401171i | ||||||||
\(435\) | − | 7.83836e14i | − | 0.115688i | ||||||
\(436\) | − | 3.86314e15i | − | 0.562369i | ||||||
\(437\) | 3.00033e15 | + | 6.21981e15i | 0.430805 | + | 0.893076i | ||||
\(438\) | −3.79970e14 | −0.0538151 | ||||||||
\(439\) | −1.17513e16 | −1.64173 | −0.820863 | − | 0.571125i | \(-0.806507\pi\) | ||||
−0.820863 | + | 0.571125i | \(0.806507\pi\) | |||||||
\(440\) | 9.10820e14 | 0.125521 | ||||||||
\(441\) | 9.80856e15 | 1.33344 | ||||||||
\(442\) | 8.12482e13i | 0.0108963i | ||||||||
\(443\) | −1.67326e15 | −0.221382 | −0.110691 | − | 0.993855i | \(-0.535306\pi\) | ||||
−0.110691 | + | 0.993855i | \(0.535306\pi\) | |||||||
\(444\) | 2.66441e15i | 0.347779i | ||||||||
\(445\) | 5.95947e15 | 0.767446 | ||||||||
\(446\) | 1.32669e15 | 0.168562 | ||||||||
\(447\) | 2.40609e15i | 0.301625i | ||||||||
\(448\) | 1.12656e16i | 1.39343i | ||||||||
\(449\) | 7.66604e15 | 0.935606 | 0.467803 | − | 0.883833i | \(-0.345046\pi\) | ||||
0.467803 | + | 0.883833i | \(0.345046\pi\) | |||||||
\(450\) | −7.83681e14 | −0.0943765 | ||||||||
\(451\) | 2.19234e15i | 0.260525i | ||||||||
\(452\) | − | 7.85705e15i | − | 0.921359i | ||||||
\(453\) | 4.04519e15 | 0.468112 | ||||||||
\(454\) | − | 1.63787e15i | − | 0.187045i | ||||||
\(455\) | 4.26839e15 | 0.481056 | ||||||||
\(456\) | 8.73905e14i | 0.0972020i | ||||||||
\(457\) | − | 3.53833e15i | − | 0.388419i | −0.980960 | − | 0.194210i | \(-0.937786\pi\) | ||
0.980960 | − | 0.194210i | \(-0.0622142\pi\) | |||||||
\(458\) | − | 4.35491e14i | − | 0.0471831i | ||||||
\(459\) | 7.64776e14i | 0.0817820i | ||||||||
\(460\) | −2.02567e15 | − | 4.19931e15i | −0.213807 | − | 0.443231i | ||||
\(461\) | 1.42057e16 | 1.47998 | 0.739991 | − | 0.672617i | \(-0.234830\pi\) | ||||
0.739991 | + | 0.672617i | \(0.234830\pi\) | |||||||
\(462\) | −6.72276e14 | −0.0691347 | ||||||||
\(463\) | −6.34766e15 | −0.644358 | −0.322179 | − | 0.946679i | \(-0.604415\pi\) | ||||
−0.322179 | + | 0.946679i | \(0.604415\pi\) | |||||||
\(464\) | 6.24420e15 | 0.625704 | ||||||||
\(465\) | 3.09686e14i | 0.0306340i | ||||||||
\(466\) | −7.55130e14 | −0.0737405 | ||||||||
\(467\) | 5.84366e15i | 0.563357i | 0.959509 | + | 0.281678i | \(0.0908911\pi\) | ||||
−0.959509 | + | 0.281678i | \(0.909109\pi\) | |||||||
\(468\) | 5.47252e15 | 0.520849 | ||||||||
\(469\) | −2.16572e13 | −0.00203500 | ||||||||
\(470\) | − | 6.35148e14i | − | 0.0589234i | ||||||
\(471\) | − | 4.63117e15i | − | 0.424195i | ||||||
\(472\) | −1.56528e15 | −0.141560 | ||||||||
\(473\) | −4.29853e15 | −0.383842 | ||||||||
\(474\) | − | 7.27002e14i | − | 0.0641011i | ||||||
\(475\) | 8.51385e15i | 0.741249i | ||||||||
\(476\) | −2.27386e15 | −0.195489 | ||||||||
\(477\) | 8.18972e15i | 0.695279i | ||||||||
\(478\) | −2.21065e15 | −0.185333 | ||||||||
\(479\) | − | 1.06857e16i | − | 0.884690i | −0.896845 | − | 0.442345i | \(-0.854147\pi\) | ||
0.896845 | − | 0.442345i | \(-0.145853\pi\) | |||||||
\(480\) | − | 8.88089e14i | − | 0.0726121i | ||||||
\(481\) | 7.68621e15i | 0.620643i | ||||||||
\(482\) | 1.66856e15i | 0.133064i | ||||||||
\(483\) | 3.02167e15 | + | 6.26405e15i | 0.237993 | + | 0.493369i | ||||
\(484\) | −2.83139e15 | −0.220256 | ||||||||
\(485\) | −5.08506e15 | −0.390702 | ||||||||
\(486\) | −1.65550e15 | −0.125635 | ||||||||
\(487\) | 6.89856e15 | 0.517112 | 0.258556 | − | 0.965996i | \(-0.416753\pi\) | ||||
0.258556 | + | 0.965996i | \(0.416753\pi\) | |||||||
\(488\) | 6.05201e15i | 0.448106i | ||||||||
\(489\) | 4.03823e15 | 0.295351 | ||||||||
\(490\) | − | 1.50949e15i | − | 0.109057i | ||||||
\(491\) | 1.37586e16 | 0.981943 | 0.490971 | − | 0.871176i | \(-0.336642\pi\) | ||||
0.490971 | + | 0.871176i | \(0.336642\pi\) | |||||||
\(492\) | 1.42017e15 | 0.100127 | ||||||||
\(493\) | 1.20458e15i | 0.0838985i | ||||||||
\(494\) | 1.24742e15i | 0.0858324i | ||||||||
\(495\) | 5.73057e15 | 0.389553 | ||||||||
\(496\) | −2.46702e15 | −0.165685 | ||||||||
\(497\) | − | 1.42920e16i | − | 0.948317i | ||||||
\(498\) | − | 1.32127e15i | − | 0.0866194i | ||||||
\(499\) | −2.38285e16 | −1.54345 | −0.771727 | − | 0.635954i | \(-0.780607\pi\) | ||||
−0.771727 | + | 0.635954i | \(0.780607\pi\) | |||||||
\(500\) | − | 1.34373e16i | − | 0.859985i | ||||||
\(501\) | 4.82499e15 | 0.305120 | ||||||||
\(502\) | − | 3.05276e15i | − | 0.190752i | ||||||
\(503\) | 3.79419e15i | 0.234267i | 0.993116 | + | 0.117134i | \(0.0373706\pi\) | ||||
−0.993116 | + | 0.117134i | \(0.962629\pi\) | |||||||
\(504\) | − | 6.49440e15i | − | 0.396238i | ||||||
\(505\) | 7.92979e15i | 0.478094i | ||||||||
\(506\) | 9.20372e14 | + | 1.90797e15i | 0.0548353 | + | 0.113676i | ||||
\(507\) | 3.72804e15 | 0.219499 | ||||||||
\(508\) | −1.94139e16 | −1.12962 | ||||||||
\(509\) | −1.66090e16 | −0.955076 | −0.477538 | − | 0.878611i | \(-0.658471\pi\) | ||||
−0.477538 | + | 0.878611i | \(0.658471\pi\) | |||||||
\(510\) | 5.51133e13 | 0.00313210 | ||||||||
\(511\) | − | 3.06768e16i | − | 1.72300i | ||||||
\(512\) | 1.18735e16 | 0.659113 | ||||||||
\(513\) | 1.17418e16i | 0.644212i | ||||||||
\(514\) | −2.02179e15 | −0.109637 | ||||||||
\(515\) | −1.36154e16 | −0.729774 | ||||||||
\(516\) | 2.78453e15i | 0.147521i | ||||||||
\(517\) | − | 1.37540e16i | − | 0.720256i | ||||||
\(518\) | 4.51338e15 | 0.233627 | ||||||||
\(519\) | −9.17660e15 | −0.469545 | ||||||||
\(520\) | − | 1.70206e15i | − | 0.0860906i | ||||||
\(521\) | 3.96036e16i | 1.98020i | 0.140368 | + | 0.990099i | \(0.455171\pi\) | ||||
−0.140368 | + | 0.990099i | \(0.544829\pi\) | |||||||
\(522\) | −1.70235e15 | −0.0841444 | ||||||||
\(523\) | − | 1.42152e16i | − | 0.694612i | −0.937752 | − | 0.347306i | \(-0.887096\pi\) | ||
0.937752 | − | 0.347306i | \(-0.112904\pi\) | |||||||
\(524\) | −3.41681e16 | −1.65057 | ||||||||
\(525\) | 8.57440e15i | 0.409494i | ||||||||
\(526\) | 4.86613e15i | 0.229757i | ||||||||
\(527\) | − | 4.75918e14i | − | 0.0222161i | ||||||
\(528\) | − | 6.18661e15i | − | 0.285528i | ||||||
\(529\) | 1.36411e16 | − | 1.71515e16i | 0.622464 | − | 0.782649i | ||||
\(530\) | 1.26036e15 | 0.0568644 | ||||||||
\(531\) | −9.84821e15 | −0.439329 | ||||||||
\(532\) | −3.49111e16 | −1.53990 | ||||||||
\(533\) | 4.09686e15 | 0.178685 | ||||||||
\(534\) | 1.75402e15i | 0.0756462i | ||||||||
\(535\) | 2.12916e16 | 0.908000 | ||||||||
\(536\) | 8.63601e12i | 0.000364187i | ||||||||
\(537\) | −1.53383e13 | −0.000639635 | ||||||||
\(538\) | 2.66335e15 | 0.109833 | ||||||||
\(539\) | − | 3.26879e16i | − | 1.33307i | ||||||
\(540\) | − | 7.92745e15i | − | 0.319721i | ||||||
\(541\) | 1.68476e16 | 0.671978 | 0.335989 | − | 0.941866i | \(-0.390930\pi\) | ||||
0.335989 | + | 0.941866i | \(0.390930\pi\) | |||||||
\(542\) | −1.17453e15 | −0.0463305 | ||||||||
\(543\) | − | 1.10072e16i | − | 0.429415i | ||||||
\(544\) | 1.36479e15i | 0.0526591i | ||||||||
\(545\) | −7.55953e15 | −0.288480 | ||||||||
\(546\) | 1.25629e15i | 0.0474171i | ||||||||
\(547\) | −1.11358e16 | −0.415717 | −0.207858 | − | 0.978159i | \(-0.566649\pi\) | ||||
−0.207858 | + | 0.978159i | \(0.566649\pi\) | |||||||
\(548\) | − | 6.57334e15i | − | 0.242718i | ||||||
\(549\) | 3.80772e16i | 1.39069i | ||||||||
\(550\) | 2.61168e15i | 0.0943505i | ||||||||
\(551\) | 1.84942e16i | 0.660884i | ||||||||
\(552\) | 2.49785e15 | − | 1.20492e15i | 0.0882941 | − | 0.0425916i | ||||
\(553\) | 5.86944e16 | 2.05233 | ||||||||
\(554\) | 3.55525e15 | 0.122973 | ||||||||
\(555\) | 5.21381e15 | 0.178401 | ||||||||
\(556\) | 9.96043e14 | 0.0337155 | ||||||||
\(557\) | 4.39402e16i | 1.47140i | 0.677307 | + | 0.735701i | \(0.263147\pi\) | ||||
−0.677307 | + | 0.735701i | \(0.736853\pi\) | |||||||
\(558\) | 6.72581e14 | 0.0222812 | ||||||||
\(559\) | 8.03272e15i | 0.263264i | ||||||||
\(560\) | 2.30653e16 | 0.747879 | ||||||||
\(561\) | 1.19347e15 | 0.0382855 | ||||||||
\(562\) | − | 2.87410e15i | − | 0.0912188i | ||||||
\(563\) | − | 7.34378e15i | − | 0.230605i | −0.993330 | − | 0.115303i | \(-0.963216\pi\) | ||
0.993330 | − | 0.115303i | \(-0.0367838\pi\) | |||||||
\(564\) | −8.90969e15 | −0.276814 | ||||||||
\(565\) | −1.53749e16 | −0.472632 | ||||||||
\(566\) | − | 2.44810e15i | − | 0.0744613i | ||||||
\(567\) | − | 3.45727e16i | − | 1.04048i | ||||||
\(568\) | −5.69906e15 | −0.169712 | ||||||||
\(569\) | 2.64256e15i | 0.0778665i | 0.999242 | + | 0.0389332i | \(0.0123960\pi\) | ||||
−0.999242 | + | 0.0389332i | \(0.987604\pi\) | |||||||
\(570\) | 8.46167e14 | 0.0246721 | ||||||||
\(571\) | 6.56969e16i | 1.89552i | 0.318984 | + | 0.947760i | \(0.396658\pi\) | ||||
−0.318984 | + | 0.947760i | \(0.603342\pi\) | |||||||
\(572\) | − | 1.82376e16i | − | 0.520705i | ||||||
\(573\) | − | 1.36152e16i | − | 0.384677i | ||||||
\(574\) | − | 2.40570e15i | − | 0.0672620i | ||||||
\(575\) | 2.43348e16 | − | 1.17387e16i | 0.673319 | − | 0.324797i | ||||
\(576\) | 2.82638e16 | 0.773919 | ||||||||
\(577\) | −2.93905e16 | −0.796439 | −0.398219 | − | 0.917290i | \(-0.630372\pi\) | ||||
−0.398219 | + | 0.917290i | \(0.630372\pi\) | |||||||
\(578\) | 5.26067e15 | 0.141083 | ||||||||
\(579\) | −2.23484e16 | −0.593164 | ||||||||
\(580\) | − | 1.24863e16i | − | 0.327995i | ||||||
\(581\) | 1.06672e17 | 2.77329 | ||||||||
\(582\) | − | 1.49666e15i | − | 0.0385110i | ||||||
\(583\) | 2.72929e16 | 0.695087 | ||||||||
\(584\) | −1.22327e16 | −0.308350 | ||||||||
\(585\) | − | 1.07088e16i | − | 0.267181i | ||||||
\(586\) | 5.37246e15i | 0.132674i | ||||||||
\(587\) | −5.59779e16 | −1.36832 | −0.684160 | − | 0.729332i | \(-0.739831\pi\) | ||||
−0.684160 | + | 0.729332i | \(0.739831\pi\) | |||||||
\(588\) | −2.11748e16 | −0.512336 | ||||||||
\(589\) | − | 7.30687e15i | − | 0.175001i | ||||||
\(590\) | 1.51560e15i | 0.0359312i | ||||||||
\(591\) | 3.30904e15 | 0.0776564 | ||||||||
\(592\) | 4.15343e16i | 0.964888i | ||||||||
\(593\) | −2.18544e16 | −0.502586 | −0.251293 | − | 0.967911i | \(-0.580856\pi\) | ||||
−0.251293 | + | 0.967911i | \(0.580856\pi\) | |||||||
\(594\) | 3.60187e15i | 0.0819991i | ||||||||
\(595\) | 4.44957e15i | 0.100280i | ||||||||
\(596\) | 3.83285e16i | 0.855154i | ||||||||
\(597\) | − | 6.76251e15i | − | 0.149369i | ||||||
\(598\) | 3.56545e15 | − | 1.71991e15i | 0.0779665 | − | 0.0376097i | ||||
\(599\) | 8.34170e16 | 1.80590 | 0.902950 | − | 0.429745i | \(-0.141397\pi\) | ||||
0.902950 | + | 0.429745i | \(0.141397\pi\) | |||||||
\(600\) | 3.41913e15 | 0.0732837 | ||||||||
\(601\) | −2.82324e16 | −0.599103 | −0.299551 | − | 0.954080i | \(-0.596837\pi\) | ||||
−0.299551 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(602\) | 4.71685e15 | 0.0991000 | ||||||||
\(603\) | 5.43348e13i | 0.00113025i | ||||||||
\(604\) | 6.44390e16 | 1.32717 | ||||||||
\(605\) | 5.54055e15i | 0.112985i | ||||||||
\(606\) | −2.33393e15 | −0.0471251 | ||||||||
\(607\) | −6.29603e16 | −1.25874 | −0.629368 | − | 0.777108i | \(-0.716686\pi\) | ||||
−0.629368 | + | 0.777108i | \(0.716686\pi\) | |||||||
\(608\) | 2.09540e16i | 0.414806i | ||||||||
\(609\) | 1.86257e16i | 0.365098i | ||||||||
\(610\) | 5.85991e15 | 0.113740 | ||||||||
\(611\) | −2.57024e16 | −0.493999 | ||||||||
\(612\) | 5.70480e15i | 0.108576i | ||||||||
\(613\) | − | 3.01470e16i | − | 0.568173i | −0.958799 | − | 0.284087i | \(-0.908310\pi\) | ||
0.958799 | − | 0.284087i | \(-0.0916904\pi\) | |||||||
\(614\) | 2.57557e15 | 0.0480688 | ||||||||
\(615\) | − | 2.77904e15i | − | 0.0513622i | ||||||
\(616\) | −2.16431e16 | −0.396128 | ||||||||
\(617\) | − | 7.67733e16i | − | 1.39155i | −0.718259 | − | 0.695776i | \(-0.755061\pi\) | ||
0.718259 | − | 0.695776i | \(-0.244939\pi\) | |||||||
\(618\) | − | 4.00736e15i | − | 0.0719329i | ||||||
\(619\) | − | 2.94639e16i | − | 0.523776i | −0.965098 | − | 0.261888i | \(-0.915655\pi\) | ||
0.965098 | − | 0.261888i | \(-0.0843451\pi\) | |||||||
\(620\) | 4.93323e15i | 0.0868523i | ||||||||
\(621\) | 3.35610e16 | − | 1.61893e16i | 0.585175 | − | 0.282278i | ||||
\(622\) | −4.06524e15 | −0.0702011 | ||||||||
\(623\) | −1.41611e17 | −2.42196 | ||||||||
\(624\) | −1.15610e16 | −0.195834 | ||||||||
\(625\) | 1.82638e16 | 0.306415 | ||||||||
\(626\) | − | 1.22357e16i | − | 0.203322i | ||||||
\(627\) | 1.83236e16 | 0.301582 | ||||||||
\(628\) | − | 7.37736e16i | − | 1.20266i | ||||||
\(629\) | −8.01246e15 | −0.129379 | ||||||||
\(630\) | −6.28826e15 | −0.100574 | ||||||||
\(631\) | 8.23161e16i | 1.30409i | 0.758179 | + | 0.652046i | \(0.226089\pi\) | ||||
−0.758179 | + | 0.652046i | \(0.773911\pi\) | |||||||
\(632\) | − | 2.34050e16i | − | 0.367287i | ||||||
\(633\) | −1.38306e16 | −0.214990 | ||||||||
\(634\) | −1.65058e16 | −0.254157 | ||||||||
\(635\) | 3.79899e16i | 0.579463i | ||||||||
\(636\) | − | 1.76800e16i | − | 0.267141i | ||||||
\(637\) | −6.10843e16 | −0.914309 | ||||||||
\(638\) | 5.67322e15i | 0.0841212i | ||||||||
\(639\) | −3.58565e16 | −0.526700 | ||||||||
\(640\) | − | 1.87936e16i | − | 0.273483i | ||||||
\(641\) | − | 1.15769e17i | − | 1.66895i | −0.551048 | − | 0.834473i | \(-0.685772\pi\) | ||
0.551048 | − | 0.834473i | \(-0.314228\pi\) | |||||||
\(642\) | 6.26664e15i | 0.0895003i | ||||||||
\(643\) | − | 2.91827e16i | − | 0.412914i | −0.978456 | − | 0.206457i | \(-0.933807\pi\) | ||
0.978456 | − | 0.206457i | \(-0.0661933\pi\) | |||||||
\(644\) | 4.81346e16 | + | 9.97850e16i | 0.674748 | + | 1.39878i | ||||
\(645\) | 5.44886e15 | 0.0756742 | ||||||||
\(646\) | −1.30037e15 | −0.0178925 | ||||||||
\(647\) | −1.31350e17 | −1.79063 | −0.895313 | − | 0.445437i | \(-0.853048\pi\) | ||||
−0.895313 | + | 0.445437i | \(0.853048\pi\) | |||||||
\(648\) | −1.37862e16 | −0.186206 | ||||||||
\(649\) | 3.28200e16i | 0.439208i | ||||||||
\(650\) | 4.88049e15 | 0.0647118 | ||||||||
\(651\) | − | 7.35884e15i | − | 0.0966770i | ||||||
\(652\) | 6.43282e16 | 0.837367 | ||||||||
\(653\) | −2.11441e16 | −0.272716 | −0.136358 | − | 0.990660i | \(-0.543540\pi\) | ||||
−0.136358 | + | 0.990660i | \(0.543540\pi\) | |||||||
\(654\) | − | 2.22495e15i | − | 0.0284351i | ||||||
\(655\) | 6.68613e16i | 0.846695i | ||||||||
\(656\) | 2.21384e16 | 0.277794 | ||||||||
\(657\) | −7.69638e16 | −0.956961 | ||||||||
\(658\) | 1.50926e16i | 0.185955i | ||||||||
\(659\) | − | 4.73654e16i | − | 0.578294i | −0.957285 | − | 0.289147i | \(-0.906628\pi\) | ||
0.957285 | − | 0.289147i | \(-0.0933717\pi\) | |||||||
\(660\) | −1.23712e16 | −0.149674 | ||||||||
\(661\) | − | 9.89472e15i | − | 0.118630i | −0.998239 | − | 0.0593150i | \(-0.981108\pi\) | ||
0.998239 | − | 0.0593150i | \(-0.0188916\pi\) | |||||||
\(662\) | −7.58969e15 | −0.0901729 | ||||||||
\(663\) | − | 2.23026e15i | − | 0.0262587i | ||||||
\(664\) | − | 4.25367e16i | − | 0.496312i | ||||||
\(665\) | 6.83152e16i | 0.789928i | ||||||||
\(666\) | − | 1.13234e16i | − | 0.129758i | ||||||
\(667\) | 5.28612e16 | − | 2.54993e16i | 0.600319 | − | 0.289583i | ||||
\(668\) | 7.68611e16 | 0.865064 | ||||||||
\(669\) | −3.64175e16 | −0.406212 | ||||||||
\(670\) | 8.36190e12 | 9.24391e−5 | ||||||||
\(671\) | 1.26895e17 | 1.39031 | ||||||||
\(672\) | 2.11030e16i | 0.229155i | ||||||||
\(673\) | 1.14542e17 | 1.23274 | 0.616372 | − | 0.787455i | \(-0.288602\pi\) | ||||
0.616372 | + | 0.787455i | \(0.288602\pi\) | |||||||
\(674\) | 1.52624e16i | 0.162804i | ||||||||
\(675\) | 4.59393e16 | 0.485692 | ||||||||
\(676\) | 5.93869e16 | 0.622315 | ||||||||
\(677\) | − | 1.11716e17i | − | 1.16033i | −0.814499 | − | 0.580165i | \(-0.802988\pi\) | ||
0.814499 | − | 0.580165i | \(-0.197012\pi\) | |||||||
\(678\) | − | 4.52522e15i | − | 0.0465867i | ||||||
\(679\) | 1.20832e17 | 1.23301 | ||||||||
\(680\) | 1.77431e15 | 0.0179463 | ||||||||
\(681\) | 4.49595e16i | 0.450753i | ||||||||
\(682\) | − | 2.24143e15i | − | 0.0222751i | ||||||
\(683\) | −1.59995e17 | −1.57610 | −0.788048 | − | 0.615613i | \(-0.788908\pi\) | ||||
−0.788048 | + | 0.615613i | \(0.788908\pi\) | |||||||
\(684\) | 8.75870e16i | 0.855270i | ||||||||
\(685\) | −1.28629e16 | −0.124508 | ||||||||
\(686\) | 1.21798e16i | 0.116868i | ||||||||
\(687\) | 1.19542e16i | 0.113705i | ||||||||
\(688\) | 4.34068e16i | 0.409286i | ||||||||
\(689\) | − | 5.10028e16i | − | 0.476736i | ||||||
\(690\) | −1.16667e15 | − | 2.41857e15i | −0.0108107 | − | 0.0224111i | ||||
\(691\) | 1.99962e17 | 1.83687 | 0.918435 | − | 0.395572i | \(-0.129454\pi\) | ||||
0.918435 | + | 0.395572i | \(0.129454\pi\) | |||||||
\(692\) | −1.46181e17 | −1.33124 | ||||||||
\(693\) | −1.36171e17 | −1.22938 | ||||||||
\(694\) | 1.44292e16 | 0.129147 | ||||||||
\(695\) | − | 1.94909e15i | − | 0.0172951i | ||||||
\(696\) | 7.42719e15 | 0.0653384 | ||||||||
\(697\) | 4.27076e15i | 0.0372484i | ||||||||
\(698\) | 2.68607e16 | 0.232266 | ||||||||
\(699\) | 2.07283e16 | 0.177705 | ||||||||
\(700\) | 1.36588e17i | 1.16098i | ||||||||
\(701\) | 2.17146e17i | 1.82997i | 0.403486 | + | 0.914986i | \(0.367798\pi\) | ||||
−0.403486 | + | 0.914986i | \(0.632202\pi\) | |||||||
\(702\) | 6.73087e15 | 0.0562404 | ||||||||
\(703\) | −1.23017e17 | −1.01914 | ||||||||
\(704\) | − | 9.41914e16i | − | 0.773705i | ||||||
\(705\) | 1.74348e16i | 0.141998i | ||||||||
\(706\) | 1.83114e16 | 0.147874 | ||||||||
\(707\) | − | 1.88430e17i | − | 1.50880i | ||||||
\(708\) | 2.12604e16 | 0.168799 | ||||||||
\(709\) | 1.05419e17i | 0.829931i | 0.909837 | + | 0.414965i | \(0.136206\pi\) | ||||
−0.909837 | + | 0.414965i | \(0.863794\pi\) | |||||||
\(710\) | 5.51817e15i | 0.0430769i | ||||||||
\(711\) | − | 1.47256e17i | − | 1.13987i | ||||||
\(712\) | 5.64686e16i | 0.433438i | ||||||||
\(713\) | −2.08849e16 | + | 1.00745e16i | −0.158963 | + | 0.0766810i | ||||
\(714\) | −1.30962e15 | −0.00988451 | ||||||||
\(715\) | −3.56880e16 | −0.267107 | ||||||||
\(716\) | −2.44336e14 | −0.00181347 | ||||||||
\(717\) | 6.06821e16 | 0.446628 | ||||||||
\(718\) | − | 3.34027e16i | − | 0.243801i | ||||||
\(719\) | 7.44887e16 | 0.539159 | 0.269579 | − | 0.962978i | \(-0.413115\pi\) | ||||
0.269579 | + | 0.962978i | \(0.413115\pi\) | |||||||
\(720\) | − | 5.78676e16i | − | 0.415375i | ||||||
\(721\) | 3.23534e17 | 2.30307 | ||||||||
\(722\) | 3.41604e14 | 0.00241157 | ||||||||
\(723\) | − | 4.58019e16i | − | 0.320667i | ||||||
\(724\) | − | 1.75342e17i | − | 1.21746i | ||||||
\(725\) | 7.23578e16 | 0.498262 | ||||||||
\(726\) | −1.63072e15 | −0.0111368 | ||||||||
\(727\) | 1.35202e17i | 0.915751i | 0.889016 | + | 0.457876i | \(0.151390\pi\) | ||||
−0.889016 | + | 0.457876i | \(0.848610\pi\) | |||||||
\(728\) | 4.04449e16i | 0.271691i | ||||||||
\(729\) | −5.30495e16 | −0.353441 | ||||||||
\(730\) | 1.18444e16i | 0.0782665i | ||||||||
\(731\) | −8.37368e15 | −0.0548798 | ||||||||
\(732\) | − | 8.22012e16i | − | 0.534333i | ||||||
\(733\) | 1.66675e17i | 1.07460i | 0.843392 | + | 0.537299i | \(0.180555\pi\) | ||||
−0.843392 | + | 0.537299i | \(0.819445\pi\) | |||||||
\(734\) | 1.60890e16i | 0.102885i | ||||||||
\(735\) | 4.14355e16i | 0.262814i | ||||||||
\(736\) | 5.98919e16 | − | 2.88908e16i | 0.376792 | − | 0.181758i | ||||
\(737\) | 1.81075e14 | 0.00112994 | ||||||||
\(738\) | −6.03556e15 | −0.0373576 | ||||||||
\(739\) | −1.60012e17 | −0.982393 | −0.491197 | − | 0.871049i | \(-0.663440\pi\) | ||||
−0.491197 | + | 0.871049i | \(0.663440\pi\) | |||||||
\(740\) | 8.30550e16 | 0.505796 | ||||||||
\(741\) | − | 3.42416e16i | − | 0.206845i | ||||||
\(742\) | −2.99491e16 | −0.179457 | ||||||||
\(743\) | 2.39870e17i | 1.42575i | 0.701293 | + | 0.712873i | \(0.252607\pi\) | ||||
−0.701293 | + | 0.712873i | \(0.747393\pi\) | |||||||
\(744\) | −2.93441e15 | −0.0173015 | ||||||||
\(745\) | 7.50025e16 | 0.438670 | ||||||||
\(746\) | 5.14814e12i | 2.98688e-5i | ||||||||
\(747\) | − | 2.67626e17i | − | 1.54030i | ||||||
\(748\) | 1.90117e16 | 0.108546 | ||||||||
\(749\) | −5.05937e17 | −2.86553 | ||||||||
\(750\) | − | 7.73912e15i | − | 0.0434834i | ||||||
\(751\) | 2.21865e17i | 1.23666i | 0.785920 | + | 0.618329i | \(0.212190\pi\) | ||||
−0.785920 | + | 0.618329i | \(0.787810\pi\) | |||||||
\(752\) | −1.38889e17 | −0.768000 | ||||||||
\(753\) | 8.37980e16i | 0.459689i | ||||||||
\(754\) | 1.06016e16 | 0.0576959 | ||||||||
\(755\) | − | 1.26096e17i | − | 0.680803i | ||||||
\(756\) | 1.88374e17i | 1.00900i | ||||||||
\(757\) | − | 2.13854e17i | − | 1.13643i | −0.822881 | − | 0.568214i | \(-0.807634\pi\) | ||
0.822881 | − | 0.568214i | \(-0.192366\pi\) | |||||||
\(758\) | − | 3.31067e16i | − | 0.174542i | ||||||
\(759\) | −2.52641e16 | − | 5.23736e16i | −0.132146 | − | 0.273944i | ||||
\(760\) | 2.72413e16 | 0.141367 | ||||||||
\(761\) | −1.83421e17 | −0.944367 | −0.472184 | − | 0.881500i | \(-0.656534\pi\) | ||||
−0.472184 | + | 0.881500i | \(0.656534\pi\) | |||||||
\(762\) | −1.11814e16 | −0.0571169 | ||||||||
\(763\) | 1.79631e17 | 0.910406 | ||||||||
\(764\) | − | 2.16888e17i | − | 1.09062i | ||||||
\(765\) | 1.11634e16 | 0.0556963 | ||||||||
\(766\) | − | 2.65337e16i | − | 0.131349i | ||||||
\(767\) | 6.13312e16 | 0.301238 | ||||||||
\(768\) | −5.67648e16 | −0.276638 | ||||||||
\(769\) | − | 1.53717e17i | − | 0.743300i | −0.928373 | − | 0.371650i | \(-0.878792\pi\) | ||
0.928373 | − | 0.371650i | \(-0.121208\pi\) | |||||||
\(770\) | 2.09562e16i | 0.100547i | ||||||||
\(771\) | 5.54981e16 | 0.264212 | ||||||||
\(772\) | −3.56005e17 | −1.68172 | ||||||||
\(773\) | − | 2.93224e17i | − | 1.37443i | −0.726454 | − | 0.687215i | \(-0.758833\pi\) | ||
0.726454 | − | 0.687215i | \(-0.241167\pi\) | |||||||
\(774\) | − | 1.18339e16i | − | 0.0550406i | ||||||
\(775\) | −2.85879e16 | −0.131939 | ||||||||
\(776\) | − | 4.81831e16i | − | 0.220661i | ||||||
\(777\) | −1.23892e17 | −0.563011 | ||||||||
\(778\) | 2.57434e16i | 0.116088i | ||||||||
\(779\) | 6.55698e16i | 0.293413i | ||||||||
\(780\) | 2.31182e16i | 0.102657i | ||||||||
\(781\) | 1.19495e17i | 0.526555i | ||||||||
\(782\) | 1.79292e15 | + | 3.71679e15i | 0.00784007 | + | 0.0162528i | ||||
\(783\) | 9.97914e16 | 0.433035 | ||||||||
\(784\) | −3.30084e17 | −1.42144 | ||||||||
\(785\) | −1.44363e17 | −0.616932 | ||||||||
\(786\) | −1.96789e16 | −0.0834577 | ||||||||
\(787\) | 1.57526e17i | 0.662986i | 0.943458 | + | 0.331493i | \(0.107552\pi\) | ||||
−0.943458 | + | 0.331493i | \(0.892448\pi\) | |||||||
\(788\) | 5.27124e16 | 0.220169 | ||||||||
\(789\) | − | 1.33575e17i | − | 0.553685i | ||||||
\(790\) | −2.26621e16 | −0.0932261 | ||||||||
\(791\) | 3.65343e17 | 1.49157 | ||||||||
\(792\) | 5.42996e16i | 0.220012i | ||||||||
\(793\) | − | 2.37131e17i | − | 0.953564i | ||||||
\(794\) | 9.87067e15 | 0.0393934 | ||||||||
\(795\) | −3.45969e16 | −0.137036 | ||||||||
\(796\) | − | 1.07725e17i | − | 0.423486i | ||||||
\(797\) | 1.26188e17i | 0.492342i | 0.969226 | + | 0.246171i | \(0.0791726\pi\) | ||||
−0.969226 | + | 0.246171i | \(0.920827\pi\) | |||||||
\(798\) | −2.01068e16 | −0.0778621 | ||||||||
\(799\) | − | 2.67933e16i | − | 0.102978i | ||||||
\(800\) | 8.19817e16 | 0.312735 | ||||||||
\(801\) | 3.55281e17i | 1.34517i | ||||||||
\(802\) | 3.43456e16i | 0.129070i | ||||||||
\(803\) | 2.56488e17i | 0.956697i | ||||||||
\(804\) | − | 1.17298e14i | − | 0.000434266i | ||||||
\(805\) | 1.95263e17 | − | 9.41914e16i | 0.717536 | − | 0.346127i | ||||
\(806\) | −4.18860e15 | −0.0152777 | ||||||||
\(807\) | −7.31087e16 | −0.264684 | ||||||||
\(808\) | −7.51382e16 | −0.270018 | ||||||||
\(809\) | 2.18223e17 | 0.778411 | 0.389205 | − | 0.921151i | \(-0.372750\pi\) | ||||
0.389205 | + | 0.921151i | \(0.372750\pi\) | |||||||
\(810\) | 1.33486e16i | 0.0472635i | ||||||||
\(811\) | 5.43014e17 | 1.90847 | 0.954236 | − | 0.299055i | \(-0.0966714\pi\) | ||||
0.954236 | + | 0.299055i | \(0.0966714\pi\) | |||||||
\(812\) | 2.96704e17i | 1.03511i | ||||||||
\(813\) | 3.22407e16 | 0.111651 | ||||||||
\(814\) | −3.77363e16 | −0.129722 | ||||||||
\(815\) | − | 1.25880e17i | − | 0.429546i | ||||||
\(816\) | − | 1.20517e16i | − | 0.0408234i | ||||||
\(817\) | −1.28563e17 | −0.432298 | ||||||||
\(818\) | 1.88245e15 | 0.00628353 | ||||||||
\(819\) | 2.54465e17i | 0.843190i | ||||||||
\(820\) | − | 4.42695e16i | − | 0.145620i | ||||||
\(821\) | 1.57873e17 | 0.515525 | 0.257762 | − | 0.966208i | \(-0.417015\pi\) | ||||
0.257762 | + | 0.966208i | \(0.417015\pi\) | |||||||
\(822\) | − | 3.78588e15i | − | 0.0122726i | ||||||
\(823\) | 3.83737e17 | 1.23491 | 0.617454 | − | 0.786607i | \(-0.288164\pi\) | ||||
0.617454 | + | 0.786607i | \(0.288164\pi\) | |||||||
\(824\) | − | 1.29012e17i | − | 0.412162i | ||||||
\(825\) | − | 7.16905e16i | − | 0.227372i | ||||||
\(826\) | − | 3.60140e16i | − | 0.113394i | ||||||
\(827\) | − | 1.90457e16i | − | 0.0595340i | −0.999557 | − | 0.0297670i | \(-0.990523\pi\) | ||
0.999557 | − | 0.0297670i | \(-0.00947652\pi\) | |||||||
\(828\) | 2.50347e17 | − | 1.20763e17i | 0.776890 | − | 0.374759i | ||||
\(829\) | −1.91078e17 | −0.588687 | −0.294343 | − | 0.955700i | \(-0.595101\pi\) | ||||
−0.294343 | + | 0.955700i | \(0.595101\pi\) | |||||||
\(830\) | −4.11865e16 | −0.125976 | ||||||||
\(831\) | −9.75912e16 | −0.296350 | ||||||||
\(832\) | −1.76017e17 | −0.530658 | ||||||||
\(833\) | − | 6.36771e16i | − | 0.190596i | ||||||
\(834\) | 5.73665e14 | 0.00170476 | ||||||||
\(835\) | − | 1.50404e17i | − | 0.443754i | ||||||
\(836\) | 2.91891e17 | 0.855034 | ||||||||
\(837\) | −3.94266e16 | −0.114667 | ||||||||
\(838\) | − | 2.55772e16i | − | 0.0738566i | ||||||
\(839\) | 6.54049e17i | 1.87516i | 0.347769 | + | 0.937580i | \(0.386939\pi\) | ||||
−0.347769 | + | 0.937580i | \(0.613061\pi\) | |||||||
\(840\) | 2.74351e16 | 0.0780964 | ||||||||
\(841\) | −1.96636e17 | −0.555759 | ||||||||
\(842\) | − | 9.03297e16i | − | 0.253488i | ||||||
\(843\) | 7.88939e16i | 0.219825i | ||||||||
\(844\) | −2.20319e17 | −0.609532 | ||||||||
\(845\) | − | 1.16210e17i | − | 0.319231i | ||||||
\(846\) | 3.78651e16 | 0.103280 | ||||||||
\(847\) | − | 1.31656e17i | − | 0.356566i | ||||||
\(848\) | − | 2.75606e17i | − | 0.741162i | ||||||
\(849\) | 6.72002e16i | 0.179442i | ||||||||
\(850\) | 5.08765e15i | 0.0134897i | ||||||||
\(851\) | 1.69613e17 | + | 3.51615e17i | 0.446562 | + | 0.925742i | ||||
\(852\) | 7.74073e16 | 0.202369 | ||||||||
\(853\) | −3.97491e16 | −0.103189 | −0.0515945 | − | 0.998668i | \(-0.516430\pi\) | ||||
−0.0515945 | + | 0.998668i | \(0.516430\pi\) | |||||||
\(854\) | −1.39245e17 | −0.358948 | ||||||||
\(855\) | 1.71393e17 | 0.438730 | ||||||||
\(856\) | 2.01747e17i | 0.512820i | ||||||||
\(857\) | 3.41589e17 | 0.862222 | 0.431111 | − | 0.902299i | \(-0.358122\pi\) | ||||
0.431111 | + | 0.902299i | \(0.358122\pi\) | |||||||
\(858\) | − | 1.05039e16i | − | 0.0263284i | ||||||
\(859\) | 3.27050e16 | 0.0814056 | 0.0407028 | − | 0.999171i | \(-0.487040\pi\) | ||||
0.0407028 | + | 0.999171i | \(0.487040\pi\) | |||||||
\(860\) | 8.67993e16 | 0.214548 | ||||||||
\(861\) | 6.60362e16i | 0.162093i | ||||||||
\(862\) | 1.30767e15i | 0.00318752i | ||||||||
\(863\) | 2.31877e17 | 0.561298 | 0.280649 | − | 0.959810i | \(-0.409450\pi\) | ||||
0.280649 | + | 0.959810i | \(0.409450\pi\) | |||||||
\(864\) | 1.13064e17 | 0.271795 | ||||||||
\(865\) | 2.86053e17i | 0.682888i | ||||||||
\(866\) | − | 1.09809e16i | − | 0.0260334i | ||||||
\(867\) | −1.44405e17 | −0.339991 | ||||||||
\(868\) | − | 1.17225e17i | − | 0.274095i | ||||||
\(869\) | −4.90744e17 | −1.13956 | ||||||||
\(870\) | − | 7.19144e15i | − | 0.0165844i | ||||||
\(871\) | − | 3.38379e14i | − | 0.000774986i | ||||||
\(872\) | − | 7.16298e16i | − | 0.162928i | ||||||
\(873\) | − | 3.03152e17i | − | 0.684817i | ||||||
\(874\) | 2.75270e16 | + | 5.70647e16i | 0.0617577 | + | 0.128026i | ||||
\(875\) | 6.24817e17 | 1.39221 | ||||||||
\(876\) | 1.66150e17 | 0.367685 | ||||||||
\(877\) | −1.89485e17 | −0.416463 | −0.208232 | − | 0.978080i | \(-0.566771\pi\) | ||||
−0.208232 | + | 0.978080i | \(0.566771\pi\) | |||||||
\(878\) | −1.07815e17 | −0.235348 | ||||||||
\(879\) | − | 1.47474e17i | − | 0.319728i | ||||||
\(880\) | −1.92849e17 | −0.415261 | ||||||||
\(881\) | − | 3.28345e16i | − | 0.0702223i | −0.999383 | − | 0.0351111i | \(-0.988821\pi\) | ||
0.999383 | − | 0.0351111i | \(-0.0111785\pi\) | |||||||
\(882\) | 8.99903e16 | 0.191154 | ||||||||
\(883\) | −6.29031e17 | −1.32711 | −0.663556 | − | 0.748126i | \(-0.730954\pi\) | ||||
−0.663556 | + | 0.748126i | \(0.730954\pi\) | |||||||
\(884\) | − | 3.55275e16i | − | 0.0744477i | ||||||
\(885\) | − | 4.16030e16i | − | 0.0865895i | ||||||
\(886\) | −1.53516e16 | −0.0317360 | ||||||||
\(887\) | −3.82030e17 | −0.784432 | −0.392216 | − | 0.919873i | \(-0.628291\pi\) | ||||
−0.392216 | + | 0.919873i | \(0.628291\pi\) | |||||||
\(888\) | 4.94031e16i | 0.100757i | ||||||||
\(889\) | − | 9.02725e17i | − | 1.82871i | ||||||
\(890\) | 5.46762e16 | 0.110017 | ||||||||
\(891\) | 2.89062e17i | 0.577730i | ||||||||
\(892\) | −5.80123e17 | −1.15168 | ||||||||
\(893\) | − | 4.11364e17i | − | 0.811180i | ||||||
\(894\) | 2.20751e16i | 0.0432392i | ||||||||
\(895\) | 4.78125e14i | 0.000930259i | ||||||||
\(896\) | 4.46578e17i | 0.863076i | ||||||||
\(897\) | −9.78715e16 | + | 4.72115e16i | −0.187889 | + | 0.0906344i | ||||
\(898\) | 7.03334e16 | 0.134123 | ||||||||
\(899\) | −6.20999e16 | −0.117634 | ||||||||
\(900\) | 3.42681e17 | 0.644816 | ||||||||
\(901\) | 5.31676e16 | 0.0993799 | ||||||||
\(902\) | 2.01140e16i | 0.0373473i | ||||||||
\(903\) | −1.29477e17 | −0.238818 | ||||||||
\(904\) | − | 1.45684e17i | − | 0.266933i | ||||||
\(905\) | −3.43116e17 | −0.624524 | ||||||||
\(906\) | 3.71133e16 | 0.0671058 | ||||||||
\(907\) | 8.24798e17i | 1.48151i | 0.671777 | + | 0.740754i | \(0.265531\pi\) | ||||
−0.671777 | + | 0.740754i | \(0.734469\pi\) | |||||||
\(908\) | 7.16196e17i | 1.27796i | ||||||||
\(909\) | −4.72744e17 | −0.837997 | ||||||||
\(910\) | 3.91611e16 | 0.0689615 | ||||||||
\(911\) | − | 1.71355e17i | − | 0.299768i | −0.988704 | − | 0.149884i | \(-0.952110\pi\) | ||
0.988704 | − | 0.149884i | \(-0.0478901\pi\) | |||||||
\(912\) | − | 1.85033e17i | − | 0.321573i | ||||||
\(913\) | −8.91887e17 | −1.53987 | ||||||||
\(914\) | − | 3.24630e16i | − | 0.0556816i | ||||||
\(915\) | −1.60854e17 | −0.274098 | ||||||||
\(916\) | 1.90428e17i | 0.322372i | ||||||||
\(917\) | − | 1.58878e18i | − | 2.67206i | ||||||
\(918\) | 7.01657e15i | 0.0117238i | ||||||||
\(919\) | − | 6.13338e17i | − | 1.01814i | −0.860726 | − | 0.509069i | \(-0.829990\pi\) | ||
0.860726 | − | 0.509069i | \(-0.170010\pi\) | |||||||
\(920\) | −3.75597e16 | − | 7.78629e16i | −0.0619435 | − | 0.128411i | ||||
\(921\) | −7.06993e16 | −0.115840 | ||||||||
\(922\) | 1.30332e17 | 0.212162 | ||||||||
\(923\) | 2.23302e17 | 0.361146 | ||||||||
\(924\) | 2.93967e17 | 0.472354 | ||||||||
\(925\) | 4.81300e17i | 0.768361i | ||||||||
\(926\) | −5.82377e16 | −0.0923715 | ||||||||
\(927\) | − | 8.11701e17i | − | 1.27914i | ||||||
\(928\) | 1.78084e17 | 0.278829 | ||||||||
\(929\) | −6.79449e17 | −1.05697 | −0.528485 | − | 0.848943i | \(-0.677240\pi\) | ||||
−0.528485 | + | 0.848943i | \(0.677240\pi\) | |||||||
\(930\) | 2.84127e15i | 0.00439152i | ||||||||
\(931\) | − | 9.77648e17i | − | 1.50136i | ||||||
\(932\) | 3.30197e17 | 0.503823 | ||||||||
\(933\) | 1.11590e17 | 0.169175 | ||||||||
\(934\) | 5.36137e16i | 0.0807596i | ||||||||
\(935\) | − | 3.72028e16i | − | 0.0556809i | ||||||
\(936\) | 1.01471e17 | 0.150899 | ||||||||
\(937\) | 9.84332e17i | 1.45447i | 0.686390 | + | 0.727234i | \(0.259195\pi\) | ||||
−0.686390 | + | 0.727234i | \(0.740805\pi\) | |||||||
\(938\) | −1.98698e14 | −0.000291726 | ||||||||
\(939\) | 3.35870e17i | 0.489979i | ||||||||
\(940\) | 2.77732e17i | 0.402587i | ||||||||
\(941\) | 9.37248e17i | 1.34995i | 0.737842 | + | 0.674974i | \(0.235845\pi\) | ||||
−0.737842 | + | 0.674974i | \(0.764155\pi\) | |||||||
\(942\) | − | 4.24895e16i | − | 0.0608101i | ||||||
\(943\) | 1.87416e17 | − | 9.04061e16i | 0.266524 | − | 0.128566i | ||||
\(944\) | 3.31418e17 | 0.468322 | ||||||||
\(945\) | 3.68617e17 | 0.517588 | ||||||||
\(946\) | −3.94376e16 | −0.0550254 | ||||||||
\(947\) | −5.36903e17 | −0.744383 | −0.372191 | − | 0.928156i | \(-0.621393\pi\) | ||||
−0.372191 | + | 0.928156i | \(0.621393\pi\) | |||||||
\(948\) | 3.17897e17i | 0.437963i | ||||||||
\(949\) | 4.79304e17 | 0.656166 | ||||||||
\(950\) | 7.81118e16i | 0.106261i | ||||||||
\(951\) | 4.53084e17 | 0.612485 | ||||||||
\(952\) | −4.21616e16 | −0.0566364 | ||||||||
\(953\) | 1.32415e17i | 0.176759i | 0.996087 | + | 0.0883794i | \(0.0281688\pi\) | ||||
−0.996087 | + | 0.0883794i | \(0.971831\pi\) | |||||||
\(954\) | 7.51380e16i | 0.0996712i | ||||||||
\(955\) | −4.24413e17 | −0.559459 | ||||||||
\(956\) | 9.66654e17 | 1.26626 | ||||||||
\(957\) | − | 1.55729e17i | − | 0.202721i | ||||||
\(958\) | − | 9.80381e16i | − | 0.126824i | ||||||
\(959\) | 3.05652e17 | 0.392931 | ||||||||
\(960\) | 1.19398e17i | 0.152535i | ||||||||
\(961\) | −7.63128e17 | −0.968851 | ||||||||
\(962\) | 7.05185e16i | 0.0889719i | ||||||||
\(963\) | 1.26932e18i | 1.59153i | ||||||||
\(964\) | − | 7.29615e17i | − | 0.909142i | ||||||
\(965\) | 6.96643e17i | 0.862674i | ||||||||
\(966\) | 2.77228e16 | + | 5.74706e16i | 0.0341173 | + | 0.0707266i | ||||
\(967\) | 3.05768e17 | 0.373967 | 0.186984 | − | 0.982363i | \(-0.440129\pi\) | ||||
0.186984 | + | 0.982363i | \(0.440129\pi\) | |||||||
\(968\) | −5.24991e16 | −0.0638116 | ||||||||
\(969\) | 3.56950e16 | 0.0431186 | ||||||||
\(970\) | −4.66538e16 | −0.0560088 | ||||||||
\(971\) | − | 2.11293e17i | − | 0.252098i | −0.992024 | − | 0.126049i | \(-0.959770\pi\) | ||
0.992024 | − | 0.126049i | \(-0.0402296\pi\) | |||||||
\(972\) | 7.23903e17 | 0.858386 | ||||||||
\(973\) | 4.63148e16i | 0.0545811i | ||||||||
\(974\) | 6.32920e16 | 0.0741302 | ||||||||
\(975\) | −1.33969e17 | −0.155947 | ||||||||
\(976\) | − | 1.28140e18i | − | 1.48247i | ||||||
\(977\) | 8.07021e16i | 0.0927934i | 0.998923 | + | 0.0463967i | \(0.0147738\pi\) | ||||
−0.998923 | + | 0.0463967i | \(0.985226\pi\) | |||||||
\(978\) | 3.70495e16 | 0.0423398 | ||||||||
\(979\) | 1.18400e18 | 1.34480 | ||||||||
\(980\) | 6.60059e17i | 0.745120i | ||||||||
\(981\) | − | 4.50670e17i | − | 0.505644i | ||||||
\(982\) | 1.26231e17 | 0.140766 | ||||||||
\(983\) | − | 6.49313e17i | − | 0.719669i | −0.933016 | − | 0.359834i | \(-0.882833\pi\) | ||
0.933016 | − | 0.359834i | \(-0.117167\pi\) | |||||||
\(984\) | 2.63326e16 | 0.0290083 | ||||||||
\(985\) | − | 1.03149e17i | − | 0.112940i | ||||||
\(986\) | 1.10516e16i | 0.0120272i | ||||||||
\(987\) | − | 4.14290e17i | − | 0.448127i | ||||||
\(988\) | − | 5.45462e17i | − | 0.586439i | ||||||
\(989\) | 1.77259e17 | + | 3.67466e17i | 0.189423 | + | 0.392681i | ||||
\(990\) | 5.25761e16 | 0.0558441 | ||||||||
\(991\) | 1.27432e17 | 0.134535 | 0.0672677 | − | 0.997735i | \(-0.478572\pi\) | ||||
0.0672677 | + | 0.997735i | \(0.478572\pi\) | |||||||
\(992\) | −7.03594e16 | −0.0738333 | ||||||||
\(993\) | 2.08336e17 | 0.217305 | ||||||||
\(994\) | − | 1.31124e17i | − | 0.135945i | ||||||
\(995\) | −2.10801e17 | −0.217237 | ||||||||
\(996\) | 5.77753e17i | 0.591816i | ||||||||
\(997\) | −1.28143e18 | −1.30474 | −0.652369 | − | 0.757902i | \(-0.726225\pi\) | ||||
−0.652369 | + | 0.757902i | \(0.726225\pi\) | |||||||
\(998\) | −2.18619e17 | −0.221261 | ||||||||
\(999\) | 6.63779e17i | 0.667775i |
(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 | 23.13.b.c.22.10 | yes | 20 | |
23.22 | odd | 2 | inner | 23.13.b.c.22.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.13.b.c.22.9 | ✓ | 20 | 23.22 | odd | 2 | inner | |
23.13.b.c.22.10 | yes | 20 | 1.1 | even | 1 | trivial |