Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [14,9,Mod(13,14)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(14, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("14.13");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.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: | \(5.70330054086\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.3520512.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 120x^{2} + 3438 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 13.2 | ||
Root | \(8.52807i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 14.13 |
Dual form | 14.9.b.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.3137 | −0.707107 | ||||||||
\(3\) | 126.458i | 1.56121i | 0.625026 | + | 0.780604i | \(0.285088\pi\) | ||||
−0.625026 | + | 0.780604i | \(0.714912\pi\) | |||||||
\(4\) | 128.000 | 0.500000 | ||||||||
\(5\) | − | 143.012i | − | 0.228819i | −0.993434 | − | 0.114409i | \(-0.963502\pi\) | ||
0.993434 | − | 0.114409i | \(-0.0364976\pi\) | |||||||
\(6\) | − | 1430.71i | − | 1.10394i | ||||||
\(7\) | −2350.56 | + | 489.571i | −0.978991 | + | 0.203903i | ||||
\(8\) | −1448.15 | −0.353553 | ||||||||
\(9\) | −9430.58 | −1.43737 | ||||||||
\(10\) | 1617.99i | 0.161799i | ||||||||
\(11\) | −10789.2 | −0.736915 | −0.368457 | − | 0.929645i | \(-0.620114\pi\) | ||||
−0.368457 | + | 0.929645i | \(0.620114\pi\) | |||||||
\(12\) | 16186.6i | 0.780604i | ||||||||
\(13\) | − | 40619.1i | − | 1.42219i | −0.703097 | − | 0.711094i | \(-0.748200\pi\) | ||
0.703097 | − | 0.711094i | \(-0.251800\pi\) | |||||||
\(14\) | 26593.5 | − | 5538.87i | 0.692251 | − | 0.144181i | ||||
\(15\) | 18085.0 | 0.357234 | ||||||||
\(16\) | 16384.0 | 0.250000 | ||||||||
\(17\) | 49662.1i | 0.594607i | 0.954783 | + | 0.297303i | \(0.0960873\pi\) | ||||
−0.954783 | + | 0.297303i | \(0.903913\pi\) | |||||||
\(18\) | 106695. | 1.01637 | ||||||||
\(19\) | 225728.i | 1.73209i | 0.499966 | + | 0.866045i | \(0.333346\pi\) | ||||
−0.499966 | + | 0.866045i | \(0.666654\pi\) | |||||||
\(20\) | − | 18305.5i | − | 0.114409i | ||||||
\(21\) | −61910.1 | − | 297246.i | −0.318335 | − | 1.52841i | ||||
\(22\) | 122065. | 0.521077 | ||||||||
\(23\) | −291129. | −1.04034 | −0.520168 | − | 0.854064i | \(-0.674131\pi\) | ||||
−0.520168 | + | 0.854064i | \(0.674131\pi\) | |||||||
\(24\) | − | 183130.i | − | 0.551970i | ||||||
\(25\) | 370173. | 0.947642 | ||||||||
\(26\) | 459553.i | 1.00564i | ||||||||
\(27\) | − | 362881.i | − | 0.682824i | ||||||
\(28\) | −300871. | + | 62665.1i | −0.489496 | + | 0.101952i | ||||
\(29\) | −686649. | −0.970830 | −0.485415 | − | 0.874284i | \(-0.661331\pi\) | ||||
−0.485415 | + | 0.874284i | \(0.661331\pi\) | |||||||
\(30\) | −204608. | −0.252603 | ||||||||
\(31\) | 1.17948e6i | 1.27716i | 0.769555 | + | 0.638580i | \(0.220478\pi\) | ||||
−0.769555 | + | 0.638580i | \(0.779522\pi\) | |||||||
\(32\) | −185364. | −0.176777 | ||||||||
\(33\) | − | 1.36437e6i | − | 1.15048i | ||||||
\(34\) | − | 561863.i | − | 0.420450i | ||||||
\(35\) | 70014.5 | + | 336158.i | 0.0466569 | + | 0.224012i | ||||
\(36\) | −1.20711e6 | −0.718685 | ||||||||
\(37\) | −116490. | −0.0621558 | −0.0310779 | − | 0.999517i | \(-0.509894\pi\) | ||||
−0.0310779 | + | 0.999517i | \(0.509894\pi\) | |||||||
\(38\) | − | 2.55382e6i | − | 1.22477i | ||||||
\(39\) | 5.13660e6 | 2.22033 | ||||||||
\(40\) | 207103.i | 0.0808997i | ||||||||
\(41\) | 4.08019e6i | 1.44392i | 0.691932 | + | 0.721962i | \(0.256760\pi\) | ||||
−0.691932 | + | 0.721962i | \(0.743240\pi\) | |||||||
\(42\) | 700433. | + | 3.36296e6i | 0.225097 | + | 1.08075i | ||||
\(43\) | 646424. | 0.189079 | 0.0945396 | − | 0.995521i | \(-0.469862\pi\) | ||||
0.0945396 | + | 0.995521i | \(0.469862\pi\) | |||||||
\(44\) | −1.38101e6 | −0.368457 | ||||||||
\(45\) | 1.34868e6i | 0.328897i | ||||||||
\(46\) | 3.29375e6 | 0.735629 | ||||||||
\(47\) | − | 7.85341e6i | − | 1.60941i | −0.593675 | − | 0.804705i | \(-0.702324\pi\) | ||
0.593675 | − | 0.804705i | \(-0.297676\pi\) | |||||||
\(48\) | 2.07188e6i | 0.390302i | ||||||||
\(49\) | 5.28544e6 | − | 2.30153e6i | 0.916847 | − | 0.399239i | ||||
\(50\) | −4.18802e6 | −0.670084 | ||||||||
\(51\) | −6.28017e6 | −0.928305 | ||||||||
\(52\) | − | 5.19925e6i | − | 0.711094i | ||||||
\(53\) | −7.98083e6 | −1.01145 | −0.505725 | − | 0.862695i | \(-0.668775\pi\) | ||||
−0.505725 | + | 0.862695i | \(0.668775\pi\) | |||||||
\(54\) | 4.10553e6i | 0.482830i | ||||||||
\(55\) | 1.54298e6i | 0.168620i | ||||||||
\(56\) | 3.40397e6 | − | 708975.i | 0.346126 | − | 0.0720906i | ||||
\(57\) | −2.85450e7 | −2.70415 | ||||||||
\(58\) | 7.76855e6 | 0.686480 | ||||||||
\(59\) | 5.68993e6i | 0.469568i | 0.972048 | + | 0.234784i | \(0.0754384\pi\) | ||||
−0.972048 | + | 0.234784i | \(0.924562\pi\) | |||||||
\(60\) | 2.31488e6 | 0.178617 | ||||||||
\(61\) | 1.04246e7i | 0.752903i | 0.926436 | + | 0.376451i | \(0.122856\pi\) | ||||
−0.926436 | + | 0.376451i | \(0.877144\pi\) | |||||||
\(62\) | − | 1.33443e7i | − | 0.903089i | ||||||
\(63\) | 2.21671e7 | − | 4.61694e6i | 1.40717 | − | 0.293084i | ||||
\(64\) | 2.09715e6 | 0.125000 | ||||||||
\(65\) | −5.80901e6 | −0.325424 | ||||||||
\(66\) | 1.54361e7i | 0.813510i | ||||||||
\(67\) | 3.25888e7 | 1.61722 | 0.808610 | − | 0.588345i | \(-0.200220\pi\) | ||||
0.808610 | + | 0.588345i | \(0.200220\pi\) | |||||||
\(68\) | 6.35676e6i | 0.297303i | ||||||||
\(69\) | − | 3.68155e7i | − | 1.62418i | ||||||
\(70\) | −792124. | − | 3.80319e6i | −0.0329914 | − | 0.158400i | ||||
\(71\) | −1.34527e7 | −0.529389 | −0.264695 | − | 0.964332i | \(-0.585271\pi\) | ||||
−0.264695 | + | 0.964332i | \(0.585271\pi\) | |||||||
\(72\) | 1.36569e7 | 0.508187 | ||||||||
\(73\) | − | 3.32131e6i | − | 0.116955i | −0.998289 | − | 0.0584773i | \(-0.981375\pi\) | ||
0.998289 | − | 0.0584773i | \(-0.0186245\pi\) | |||||||
\(74\) | 1.31793e6 | 0.0439508 | ||||||||
\(75\) | 4.68112e7i | 1.47947i | ||||||||
\(76\) | 2.88932e7i | 0.866045i | ||||||||
\(77\) | 2.53606e7 | − | 5.28207e6i | 0.721433 | − | 0.150259i | ||||
\(78\) | −5.81140e7 | −1.57001 | ||||||||
\(79\) | 1.56854e7 | 0.402705 | 0.201352 | − | 0.979519i | \(-0.435466\pi\) | ||||
0.201352 | + | 0.979519i | \(0.435466\pi\) | |||||||
\(80\) | − | 2.34311e6i | − | 0.0572047i | ||||||
\(81\) | −1.59849e7 | −0.371339 | ||||||||
\(82\) | − | 4.61620e7i | − | 1.02101i | ||||||
\(83\) | 4.45273e7i | 0.938240i | 0.883134 | + | 0.469120i | \(0.155429\pi\) | ||||
−0.883134 | + | 0.469120i | \(0.844571\pi\) | |||||||
\(84\) | −7.92450e6 | − | 3.80475e7i | −0.159168 | − | 0.764204i | ||||
\(85\) | 7.10228e6 | 0.136057 | ||||||||
\(86\) | −7.31346e6 | −0.133699 | ||||||||
\(87\) | − | 8.68322e7i | − | 1.51567i | ||||||
\(88\) | 1.56244e7 | 0.260539 | ||||||||
\(89\) | − | 3.46802e7i | − | 0.552742i | −0.961051 | − | 0.276371i | \(-0.910868\pi\) | ||
0.961051 | − | 0.276371i | \(-0.0891318\pi\) | |||||||
\(90\) | − | 1.52586e7i | − | 0.232566i | ||||||
\(91\) | 1.98860e7 | + | 9.54776e7i | 0.289989 | + | 1.39231i | ||||
\(92\) | −3.72645e7 | −0.520168 | ||||||||
\(93\) | −1.49155e8 | −1.99391 | ||||||||
\(94\) | 8.88511e7i | 1.13802i | ||||||||
\(95\) | 3.22817e7 | 0.396335 | ||||||||
\(96\) | − | 2.34407e7i | − | 0.275985i | ||||||
\(97\) | 1.47049e7i | 0.166103i | 0.996545 | + | 0.0830513i | \(0.0264665\pi\) | ||||
−0.996545 | + | 0.0830513i | \(0.973533\pi\) | |||||||
\(98\) | −5.97979e7 | + | 2.60389e7i | −0.648309 | + | 0.282304i | ||||
\(99\) | 1.01748e8 | 1.05922 | ||||||||
\(100\) | 4.73821e7 | 0.473821 | ||||||||
\(101\) | 2.31942e7i | 0.222892i | 0.993770 | + | 0.111446i | \(0.0355482\pi\) | ||||
−0.993770 | + | 0.111446i | \(0.964452\pi\) | |||||||
\(102\) | 7.10520e7 | 0.656410 | ||||||||
\(103\) | − | 1.72248e8i | − | 1.53040i | −0.643790 | − | 0.765202i | \(-0.722639\pi\) | ||
0.643790 | − | 0.765202i | \(-0.277361\pi\) | |||||||
\(104\) | 5.88228e7i | 0.502819i | ||||||||
\(105\) | −4.25098e7 | + | 8.85388e6i | −0.349729 | + | 0.0728411i | ||||
\(106\) | 9.02928e7 | 0.715203 | ||||||||
\(107\) | −7.14412e7 | −0.545021 | −0.272511 | − | 0.962153i | \(-0.587854\pi\) | ||||
−0.272511 | + | 0.962153i | \(0.587854\pi\) | |||||||
\(108\) | − | 4.64487e7i | − | 0.341412i | ||||||
\(109\) | 5.22967e7 | 0.370483 | 0.185241 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185241 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(110\) | − | 1.74568e7i | − | 0.119232i | ||||||
\(111\) | − | 1.47311e7i | − | 0.0970381i | ||||||
\(112\) | −3.85115e7 | + | 8.02114e6i | −0.244748 | + | 0.0509758i | ||||
\(113\) | 1.70334e8 | 1.04469 | 0.522345 | − | 0.852734i | \(-0.325057\pi\) | ||||
0.522345 | + | 0.852734i | \(0.325057\pi\) | |||||||
\(114\) | 3.22950e8 | 1.91212 | ||||||||
\(115\) | 4.16349e7i | 0.238049i | ||||||||
\(116\) | −8.78911e7 | −0.485415 | ||||||||
\(117\) | 3.83062e8i | 2.04421i | ||||||||
\(118\) | − | 6.43742e7i | − | 0.332035i | ||||||
\(119\) | −2.43132e7 | − | 1.16734e8i | −0.121242 | − | 0.582115i | ||||
\(120\) | −2.61898e7 | −0.126301 | ||||||||
\(121\) | −9.79528e7 | −0.456957 | ||||||||
\(122\) | − | 1.17941e8i | − | 0.532383i | ||||||
\(123\) | −5.15971e8 | −2.25427 | ||||||||
\(124\) | 1.50974e8i | 0.638580i | ||||||||
\(125\) | − | 1.08803e8i | − | 0.445657i | ||||||
\(126\) | −2.50792e8 | + | 5.22347e7i | −0.995021 | + | 0.207242i | ||||
\(127\) | 1.98955e8 | 0.764785 | 0.382393 | − | 0.924000i | \(-0.375100\pi\) | ||||
0.382393 | + | 0.924000i | \(0.375100\pi\) | |||||||
\(128\) | −2.37266e7 | −0.0883883 | ||||||||
\(129\) | 8.17454e7i | 0.295192i | ||||||||
\(130\) | 6.57215e7 | 0.230109 | ||||||||
\(131\) | − | 2.28759e8i | − | 0.776770i | −0.921497 | − | 0.388385i | \(-0.873033\pi\) | ||
0.921497 | − | 0.388385i | \(-0.126967\pi\) | |||||||
\(132\) | − | 1.74640e8i | − | 0.575238i | ||||||
\(133\) | −1.10510e8 | − | 5.30586e8i | −0.353179 | − | 1.69570i | ||||
\(134\) | −3.68700e8 | −1.14355 | ||||||||
\(135\) | −5.18962e7 | −0.156243 | ||||||||
\(136\) | − | 7.19185e7i | − | 0.210225i | ||||||
\(137\) | −1.36959e8 | −0.388783 | −0.194391 | − | 0.980924i | \(-0.562273\pi\) | ||||
−0.194391 | + | 0.980924i | \(0.562273\pi\) | |||||||
\(138\) | 4.16520e8i | 1.14847i | ||||||||
\(139\) | 1.70787e8i | 0.457505i | 0.973485 | + | 0.228752i | \(0.0734646\pi\) | ||||
−0.973485 | + | 0.228752i | \(0.926535\pi\) | |||||||
\(140\) | 8.96186e6 | + | 4.30282e7i | 0.0233284 | + | 0.112006i | ||||
\(141\) | 9.93125e8 | 2.51262 | ||||||||
\(142\) | 1.52200e8 | 0.374335 | ||||||||
\(143\) | 4.38246e8i | 1.04803i | ||||||||
\(144\) | −1.54511e8 | −0.359342 | ||||||||
\(145\) | 9.81990e7i | 0.222144i | ||||||||
\(146\) | 3.75763e7i | 0.0826994i | ||||||||
\(147\) | 2.91047e8 | + | 6.68385e8i | 0.623294 | + | 1.43139i | ||||
\(148\) | −1.49107e7 | −0.0310779 | ||||||||
\(149\) | 6.30533e8 | 1.27927 | 0.639636 | − | 0.768678i | \(-0.279085\pi\) | ||||
0.639636 | + | 0.768678i | \(0.279085\pi\) | |||||||
\(150\) | − | 5.29608e8i | − | 1.04614i | ||||||
\(151\) | −4.37887e8 | −0.842276 | −0.421138 | − | 0.906997i | \(-0.638369\pi\) | ||||
−0.421138 | + | 0.906997i | \(0.638369\pi\) | |||||||
\(152\) | − | 3.26889e8i | − | 0.612386i | ||||||
\(153\) | − | 4.68343e8i | − | 0.854669i | ||||||
\(154\) | −2.86922e8 | + | 5.97598e7i | −0.510130 | + | 0.106249i | ||||
\(155\) | 1.68680e8 | 0.292239 | ||||||||
\(156\) | 6.57485e8 | 1.11017 | ||||||||
\(157\) | 5.31144e8i | 0.874205i | 0.899412 | + | 0.437103i | \(0.143995\pi\) | ||||
−0.899412 | + | 0.437103i | \(0.856005\pi\) | |||||||
\(158\) | −1.77460e8 | −0.284755 | ||||||||
\(159\) | − | 1.00924e9i | − | 1.57908i | ||||||
\(160\) | 2.65092e7i | 0.0404499i | ||||||||
\(161\) | 6.84315e8 | − | 1.42528e8i | 1.01848 | − | 0.212128i | ||||
\(162\) | 1.80849e8 | 0.262576 | ||||||||
\(163\) | −1.39209e9 | −1.97204 | −0.986022 | − | 0.166616i | \(-0.946716\pi\) | ||||
−0.986022 | + | 0.166616i | \(0.946716\pi\) | |||||||
\(164\) | 5.22264e8i | 0.721962i | ||||||||
\(165\) | −1.95122e8 | −0.263251 | ||||||||
\(166\) | − | 5.03769e8i | − | 0.663436i | ||||||
\(167\) | 1.39136e9i | 1.78885i | 0.447214 | + | 0.894427i | \(0.352416\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(168\) | 8.96554e7 | + | 4.30459e8i | 0.112548 | + | 0.540374i | ||||
\(169\) | −8.34181e8 | −1.02262 | ||||||||
\(170\) | −8.03531e7 | −0.0962070 | ||||||||
\(171\) | − | 2.12874e9i | − | 2.48965i | ||||||
\(172\) | 8.27423e7 | 0.0945396 | ||||||||
\(173\) | 5.28638e8i | 0.590165i | 0.955472 | + | 0.295083i | \(0.0953472\pi\) | ||||
−0.955472 | + | 0.295083i | \(0.904653\pi\) | |||||||
\(174\) | 9.82394e8i | 1.07174i | ||||||||
\(175\) | −8.70112e8 | + | 1.81226e8i | −0.927733 | + | 0.193227i | ||||
\(176\) | −1.76770e8 | −0.184229 | ||||||||
\(177\) | −7.19536e8 | −0.733094 | ||||||||
\(178\) | 3.92362e8i | 0.390847i | ||||||||
\(179\) | 1.56548e9 | 1.52488 | 0.762440 | − | 0.647059i | \(-0.224001\pi\) | ||||
0.762440 | + | 0.647059i | \(0.224001\pi\) | |||||||
\(180\) | 1.72632e8i | 0.164449i | ||||||||
\(181\) | − | 5.62709e8i | − | 0.524288i | −0.965029 | − | 0.262144i | \(-0.915570\pi\) | ||
0.965029 | − | 0.262144i | \(-0.0844295\pi\) | |||||||
\(182\) | −2.24984e8 | − | 1.08021e9i | −0.205053 | − | 0.984511i | ||||
\(183\) | −1.31827e9 | −1.17544 | ||||||||
\(184\) | 4.21599e8 | 0.367814 | ||||||||
\(185\) | 1.66594e7i | 0.0142224i | ||||||||
\(186\) | 1.68750e9 | 1.40991 | ||||||||
\(187\) | − | 5.35813e8i | − | 0.438174i | ||||||
\(188\) | − | 1.00524e9i | − | 0.804705i | ||||||
\(189\) | 1.77656e8 | + | 8.52972e8i | 0.139230 | + | 0.668479i | ||||
\(190\) | −3.65226e8 | −0.280251 | ||||||||
\(191\) | 5.16655e8 | 0.388210 | 0.194105 | − | 0.980981i | \(-0.437820\pi\) | ||||
0.194105 | + | 0.980981i | \(0.437820\pi\) | |||||||
\(192\) | 2.65201e8i | 0.195151i | ||||||||
\(193\) | 1.67525e6 | 0.00120740 | 0.000603700 | − | 1.00000i | \(-0.499808\pi\) | ||||
0.000603700 | 1.00000i | \(0.499808\pi\) | ||||||||
\(194\) | − | 1.66367e8i | − | 0.117452i | ||||||
\(195\) | − | 7.34595e8i | − | 0.508054i | ||||||
\(196\) | 6.76536e8 | − | 2.94596e8i | 0.458424 | − | 0.199619i | ||||
\(197\) | −2.80539e8 | −0.186264 | −0.0931320 | − | 0.995654i | \(-0.529688\pi\) | ||||
−0.0931320 | + | 0.995654i | \(0.529688\pi\) | |||||||
\(198\) | −1.15115e9 | −0.748980 | ||||||||
\(199\) | 1.08149e9i | 0.689618i | 0.938673 | + | 0.344809i | \(0.112056\pi\) | ||||
−0.938673 | + | 0.344809i | \(0.887944\pi\) | |||||||
\(200\) | −5.36067e8 | −0.335042 | ||||||||
\(201\) | 4.12111e9i | 2.52482i | ||||||||
\(202\) | − | 2.62413e8i | − | 0.157608i | ||||||
\(203\) | 1.61401e9 | − | 3.36164e8i | 0.950434 | − | 0.197955i | ||||
\(204\) | −8.03861e8 | −0.464152 | ||||||||
\(205\) | 5.83515e8 | 0.330397 | ||||||||
\(206\) | 1.94877e9i | 1.08216i | ||||||||
\(207\) | 2.74551e9 | 1.49535 | ||||||||
\(208\) | − | 6.65503e8i | − | 0.355547i | ||||||
\(209\) | − | 2.43541e9i | − | 1.27640i | ||||||
\(210\) | 4.80943e8 | − | 1.00170e8i | 0.247296 | − | 0.0515064i | ||||
\(211\) | 2.42390e8 | 0.122289 | 0.0611443 | − | 0.998129i | \(-0.480525\pi\) | ||||
0.0611443 | + | 0.998129i | \(0.480525\pi\) | |||||||
\(212\) | −1.02155e9 | −0.505725 | ||||||||
\(213\) | − | 1.70120e9i | − | 0.826487i | ||||||
\(214\) | 8.08265e8 | 0.385388 | ||||||||
\(215\) | − | 9.24464e7i | − | 0.0432649i | ||||||
\(216\) | 5.25507e8i | 0.241415i | ||||||||
\(217\) | −5.77442e8 | − | 2.77245e9i | −0.260417 | − | 1.25033i | ||||
\(218\) | −5.91669e8 | −0.261971 | ||||||||
\(219\) | 4.20005e8 | 0.182590 | ||||||||
\(220\) | 1.97501e8i | 0.0843100i | ||||||||
\(221\) | 2.01723e9 | 0.845643 | ||||||||
\(222\) | 1.66663e8i | 0.0686163i | ||||||||
\(223\) | 1.50987e9i | 0.610547i | 0.952265 | + | 0.305274i | \(0.0987479\pi\) | ||||
−0.952265 | + | 0.305274i | \(0.901252\pi\) | |||||||
\(224\) | 4.35708e8 | − | 9.07488e7i | 0.173063 | − | 0.0360453i | ||||
\(225\) | −3.49094e9 | −1.36211 | ||||||||
\(226\) | −1.92711e9 | −0.738707 | ||||||||
\(227\) | 1.42867e9i | 0.538059i | 0.963132 | + | 0.269029i | \(0.0867028\pi\) | ||||
−0.963132 | + | 0.269029i | \(0.913297\pi\) | |||||||
\(228\) | −3.65376e9 | −1.35208 | ||||||||
\(229\) | − | 8.39434e8i | − | 0.305242i | −0.988285 | − | 0.152621i | \(-0.951229\pi\) | ||
0.988285 | − | 0.152621i | \(-0.0487714\pi\) | |||||||
\(230\) | − | 4.71045e8i | − | 0.168326i | ||||||
\(231\) | 6.67959e8 | + | 3.20704e9i | 0.234586 | + | 1.12631i | ||||
\(232\) | 9.94375e8 | 0.343240 | ||||||||
\(233\) | −3.28463e9 | −1.11446 | −0.557229 | − | 0.830359i | \(-0.688135\pi\) | ||||
−0.557229 | + | 0.830359i | \(0.688135\pi\) | |||||||
\(234\) | − | 4.33385e9i | − | 1.44547i | ||||||
\(235\) | −1.12313e9 | −0.368263 | ||||||||
\(236\) | 7.28311e8i | 0.234784i | ||||||||
\(237\) | 1.98354e9i | 0.628706i | ||||||||
\(238\) | 2.75072e8 | + | 1.32069e9i | 0.0857311 | + | 0.411617i | ||||
\(239\) | −5.17982e9 | −1.58753 | −0.793767 | − | 0.608222i | \(-0.791883\pi\) | ||||
−0.793767 | + | 0.608222i | \(0.791883\pi\) | |||||||
\(240\) | 2.96304e8 | 0.0893085 | ||||||||
\(241\) | 1.51987e8i | 0.0450546i | 0.999746 | + | 0.0225273i | \(0.00717127\pi\) | ||||
−0.999746 | + | 0.0225273i | \(0.992829\pi\) | |||||||
\(242\) | 1.10821e9 | 0.323117 | ||||||||
\(243\) | − | 4.40228e9i | − | 1.26256i | ||||||
\(244\) | 1.33435e9i | 0.376451i | ||||||||
\(245\) | −3.29146e8 | − | 7.55881e8i | −0.0913534 | − | 0.209792i | ||||
\(246\) | 5.83755e9 | 1.59401 | ||||||||
\(247\) | 9.16886e9 | 2.46336 | ||||||||
\(248\) | − | 1.70808e9i | − | 0.451544i | ||||||
\(249\) | −5.63082e9 | −1.46479 | ||||||||
\(250\) | 1.23097e9i | 0.315127i | ||||||||
\(251\) | 3.45949e9i | 0.871599i | 0.900044 | + | 0.435800i | \(0.143534\pi\) | ||||
−0.900044 | + | 0.435800i | \(0.856466\pi\) | |||||||
\(252\) | 2.83739e9 | − | 5.90968e8i | 0.703586 | − | 0.146542i | ||||
\(253\) | 3.14104e9 | 0.766639 | ||||||||
\(254\) | −2.25092e9 | −0.540785 | ||||||||
\(255\) | 8.98138e8i | 0.212414i | ||||||||
\(256\) | 2.68435e8 | 0.0625000 | ||||||||
\(257\) | − | 7.64866e9i | − | 1.75329i | −0.481141 | − | 0.876643i | \(-0.659777\pi\) | ||
0.481141 | − | 0.876643i | \(-0.340223\pi\) | |||||||
\(258\) | − | 9.24844e8i | − | 0.208732i | ||||||
\(259\) | 2.73816e8 | − | 5.70301e7i | 0.0608500 | − | 0.0126738i | ||||
\(260\) | −7.43554e8 | −0.162712 | ||||||||
\(261\) | 6.47550e9 | 1.39544 | ||||||||
\(262\) | 2.58811e9i | 0.549260i | ||||||||
\(263\) | −1.63968e9 | −0.342718 | −0.171359 | − | 0.985209i | \(-0.554816\pi\) | ||||
−0.171359 | + | 0.985209i | \(0.554816\pi\) | |||||||
\(264\) | 1.97583e9i | 0.406755i | ||||||||
\(265\) | 1.14135e9i | 0.231439i | ||||||||
\(266\) | 1.25028e9 | + | 6.00290e9i | 0.249735 | + | 1.19904i | ||||
\(267\) | 4.38559e9 | 0.862944 | ||||||||
\(268\) | 4.17137e9 | 0.808610 | ||||||||
\(269\) | 3.97442e9i | 0.759040i | 0.925184 | + | 0.379520i | \(0.123911\pi\) | ||||
−0.925184 | + | 0.379520i | \(0.876089\pi\) | |||||||
\(270\) | 5.87139e8 | 0.110481 | ||||||||
\(271\) | 3.06586e9i | 0.568427i | 0.958761 | + | 0.284213i | \(0.0917324\pi\) | ||||
−0.958761 | + | 0.284213i | \(0.908268\pi\) | |||||||
\(272\) | 8.13665e8i | 0.148652i | ||||||||
\(273\) | −1.20739e10 | + | 2.51473e9i | −2.17368 | + | 0.452732i | ||||
\(274\) | 1.54951e9 | 0.274911 | ||||||||
\(275\) | −3.99385e9 | −0.698331 | ||||||||
\(276\) | − | 4.71238e9i | − | 0.812090i | ||||||
\(277\) | −7.26768e7 | −0.0123446 | −0.00617229 | − | 0.999981i | \(-0.501965\pi\) | ||||
−0.00617229 | + | 0.999981i | \(0.501965\pi\) | |||||||
\(278\) | − | 1.93223e9i | − | 0.323505i | ||||||
\(279\) | − | 1.11232e10i | − | 1.83575i | ||||||
\(280\) | −1.01392e8 | − | 4.86808e8i | −0.0164957 | − | 0.0792001i | ||||
\(281\) | 3.00263e8 | 0.0481589 | 0.0240794 | − | 0.999710i | \(-0.492335\pi\) | ||||
0.0240794 | + | 0.999710i | \(0.492335\pi\) | |||||||
\(282\) | −1.12359e10 | −1.77669 | ||||||||
\(283\) | 8.72850e8i | 0.136080i | 0.997683 | + | 0.0680399i | \(0.0216745\pi\) | ||||
−0.997683 | + | 0.0680399i | \(0.978325\pi\) | |||||||
\(284\) | −1.72194e9 | −0.264695 | ||||||||
\(285\) | 4.08228e9i | 0.618761i | ||||||||
\(286\) | − | 4.95819e9i | − | 0.741070i | ||||||
\(287\) | −1.99754e9 | − | 9.59071e9i | −0.294421 | − | 1.41359i | ||||
\(288\) | 1.74809e9 | 0.254093 | ||||||||
\(289\) | 4.50943e9 | 0.646443 | ||||||||
\(290\) | − | 1.11100e9i | − | 0.157080i | ||||||
\(291\) | −1.85956e9 | −0.259321 | ||||||||
\(292\) | − | 4.25127e8i | − | 0.0584773i | ||||||
\(293\) | 5.29924e9i | 0.719024i | 0.933140 | + | 0.359512i | \(0.117057\pi\) | ||||
−0.933140 | + | 0.359512i | \(0.882943\pi\) | |||||||
\(294\) | −3.29282e9 | − | 7.56192e9i | −0.440736 | − | 1.01214i | ||||
\(295\) | 8.13728e8 | 0.107446 | ||||||||
\(296\) | 1.68695e8 | 0.0219754 | ||||||||
\(297\) | 3.91518e9i | 0.503183i | ||||||||
\(298\) | −7.13367e9 | −0.904582 | ||||||||
\(299\) | 1.18254e10i | 1.47955i | ||||||||
\(300\) | 5.99184e9i | 0.739733i | ||||||||
\(301\) | −1.51946e9 | + | 3.16471e8i | −0.185107 | + | 0.0385539i | ||||
\(302\) | 4.95413e9 | 0.595579 | ||||||||
\(303\) | −2.93309e9 | −0.347981 | ||||||||
\(304\) | 3.69832e9i | 0.433023i | ||||||||
\(305\) | 1.49084e9 | 0.172278 | ||||||||
\(306\) | 5.29869e9i | 0.604343i | ||||||||
\(307\) | 3.75856e9i | 0.423125i | 0.977364 | + | 0.211562i | \(0.0678551\pi\) | ||||
−0.977364 | + | 0.211562i | \(0.932145\pi\) | |||||||
\(308\) | 3.24615e9 | − | 6.76104e8i | 0.360716 | − | 0.0751296i | ||||
\(309\) | 2.17822e10 | 2.38928 | ||||||||
\(310\) | −1.90840e9 | −0.206644 | ||||||||
\(311\) | − | 1.28128e10i | − | 1.36963i | −0.728716 | − | 0.684816i | \(-0.759882\pi\) | ||
0.728716 | − | 0.684816i | \(-0.240118\pi\) | |||||||
\(312\) | −7.43860e9 | −0.785005 | ||||||||
\(313\) | − | 1.48364e9i | − | 0.154579i | −0.997009 | − | 0.0772895i | \(-0.975373\pi\) | ||
0.997009 | − | 0.0772895i | \(-0.0246266\pi\) | |||||||
\(314\) | − | 6.00921e9i | − | 0.618157i | ||||||
\(315\) | −6.60277e8 | − | 3.17016e9i | −0.0670632 | − | 0.321988i | ||||
\(316\) | 2.00773e9 | 0.201352 | ||||||||
\(317\) | 5.48387e9 | 0.543063 | 0.271531 | − | 0.962430i | \(-0.412470\pi\) | ||||
0.271531 | + | 0.962430i | \(0.412470\pi\) | |||||||
\(318\) | 1.14182e10i | 1.11658i | ||||||||
\(319\) | 7.40837e9 | 0.715419 | ||||||||
\(320\) | − | 2.99918e8i | − | 0.0286024i | ||||||
\(321\) | − | 9.03429e9i | − | 0.850891i | ||||||
\(322\) | −7.74214e9 | + | 1.61252e9i | −0.720174 | + | 0.149997i | ||||
\(323\) | −1.12101e10 | −1.02991 | ||||||||
\(324\) | −2.04607e9 | −0.185670 | ||||||||
\(325\) | − | 1.50361e10i | − | 1.34772i | ||||||
\(326\) | 1.57497e10 | 1.39445 | ||||||||
\(327\) | 6.61332e9i | 0.578400i | ||||||||
\(328\) | − | 5.90874e9i | − | 0.510504i | ||||||
\(329\) | 3.84480e9 | + | 1.84599e10i | 0.328164 | + | 1.57560i | ||||
\(330\) | 2.20755e9 | 0.186146 | ||||||||
\(331\) | −2.53902e9 | −0.211521 | −0.105761 | − | 0.994392i | \(-0.533728\pi\) | ||||
−0.105761 | + | 0.994392i | \(0.533728\pi\) | |||||||
\(332\) | 5.69949e9i | 0.469120i | ||||||||
\(333\) | 1.09857e9 | 0.0893408 | ||||||||
\(334\) | − | 1.57415e10i | − | 1.26491i | ||||||
\(335\) | − | 4.66059e9i | − | 0.370051i | ||||||
\(336\) | −1.01434e9 | − | 4.87008e9i | −0.0795838 | − | 0.382102i | ||||
\(337\) | −8.83901e8 | −0.0685305 | −0.0342653 | − | 0.999413i | \(-0.510909\pi\) | ||||
−0.0342653 | + | 0.999413i | \(0.510909\pi\) | |||||||
\(338\) | 9.43768e9 | 0.723100 | ||||||||
\(339\) | 2.15401e10i | 1.63098i | ||||||||
\(340\) | 9.09091e8 | 0.0680287 | ||||||||
\(341\) | − | 1.27257e10i | − | 0.941158i | ||||||
\(342\) | 2.40840e10i | 1.76045i | ||||||||
\(343\) | −1.12970e10 | + | 7.99748e9i | −0.816179 | + | 0.577799i | ||||
\(344\) | −9.36123e8 | −0.0668496 | ||||||||
\(345\) | −5.26505e9 | −0.371643 | ||||||||
\(346\) | − | 5.98085e9i | − | 0.417310i | ||||||
\(347\) | 1.38716e9 | 0.0956770 | 0.0478385 | − | 0.998855i | \(-0.484767\pi\) | ||||
0.0478385 | + | 0.998855i | \(0.484767\pi\) | |||||||
\(348\) | − | 1.11145e10i | − | 0.757833i | ||||||
\(349\) | 1.67059e10i | 1.12608i | 0.826431 | + | 0.563038i | \(0.190367\pi\) | ||||
−0.826431 | + | 0.563038i | \(0.809633\pi\) | |||||||
\(350\) | 9.84419e9 | − | 2.05034e9i | 0.656006 | − | 0.136632i | ||||
\(351\) | −1.47399e10 | −0.971104 | ||||||||
\(352\) | 1.99992e9 | 0.130269 | ||||||||
\(353\) | − | 1.37663e10i | − | 0.886579i | −0.896378 | − | 0.443290i | \(-0.853811\pi\) | ||
0.896378 | − | 0.443290i | \(-0.146189\pi\) | |||||||
\(354\) | 8.14062e9 | 0.518376 | ||||||||
\(355\) | 1.92389e9i | 0.121134i | ||||||||
\(356\) | − | 4.43907e9i | − | 0.276371i | ||||||
\(357\) | 1.47619e10 | − | 3.07459e9i | 0.908802 | − | 0.189284i | ||||
\(358\) | −1.77114e10 | −1.07825 | ||||||||
\(359\) | −2.36428e10 | −1.42338 | −0.711692 | − | 0.702492i | \(-0.752071\pi\) | ||||
−0.711692 | + | 0.702492i | \(0.752071\pi\) | |||||||
\(360\) | − | 1.95310e9i | − | 0.116283i | ||||||
\(361\) | −3.39694e10 | −2.00014 | ||||||||
\(362\) | 6.36633e9i | 0.370727i | ||||||||
\(363\) | − | 1.23869e10i | − | 0.713405i | ||||||
\(364\) | 2.54540e9 | + | 1.22211e10i | 0.144994 | + | 0.696155i | ||||
\(365\) | −4.74986e8 | −0.0267614 | ||||||||
\(366\) | 1.49145e10 | 0.831160 | ||||||||
\(367\) | − | 1.92044e10i | − | 1.05861i | −0.848431 | − | 0.529305i | \(-0.822453\pi\) | ||
0.848431 | − | 0.529305i | \(-0.177547\pi\) | |||||||
\(368\) | −4.76985e9 | −0.260084 | ||||||||
\(369\) | − | 3.84785e10i | − | 2.07545i | ||||||
\(370\) | − | 1.88480e8i | − | 0.0100568i | ||||||
\(371\) | 1.87594e10 | − | 3.90718e9i | 0.990201 | − | 0.206238i | ||||
\(372\) | −1.90918e10 | −0.996957 | ||||||||
\(373\) | 2.24040e10 | 1.15742 | 0.578709 | − | 0.815534i | \(-0.303557\pi\) | ||||
0.578709 | + | 0.815534i | \(0.303557\pi\) | |||||||
\(374\) | 6.06203e9i | 0.309836i | ||||||||
\(375\) | 1.37590e10 | 0.695764 | ||||||||
\(376\) | 1.13729e10i | 0.569012i | ||||||||
\(377\) | 2.78911e10i | 1.38070i | ||||||||
\(378\) | −2.00995e9 | − | 9.65028e9i | −0.0984504 | − | 0.472686i | ||||
\(379\) | −3.19925e10 | −1.55057 | −0.775284 | − | 0.631613i | \(-0.782393\pi\) | ||||
−0.775284 | + | 0.631613i | \(0.782393\pi\) | |||||||
\(380\) | 4.13206e9 | 0.198168 | ||||||||
\(381\) | 2.51594e10i | 1.19399i | ||||||||
\(382\) | −5.84528e9 | −0.274506 | ||||||||
\(383\) | 2.94595e10i | 1.36908i | 0.728974 | + | 0.684541i | \(0.239997\pi\) | ||||
−0.728974 | + | 0.684541i | \(0.760003\pi\) | |||||||
\(384\) | − | 3.00041e9i | − | 0.137993i | ||||||
\(385\) | −7.55398e8 | − | 3.62686e9i | −0.0343821 | − | 0.165078i | ||||
\(386\) | −1.89533e7 | −0.000853761 | ||||||||
\(387\) | −6.09616e9 | −0.271777 | ||||||||
\(388\) | 1.88223e9i | 0.0830513i | ||||||||
\(389\) | 2.00104e10 | 0.873892 | 0.436946 | − | 0.899488i | \(-0.356060\pi\) | ||||
0.436946 | + | 0.899488i | \(0.356060\pi\) | |||||||
\(390\) | 8.31100e9i | 0.359248i | ||||||||
\(391\) | − | 1.44581e10i | − | 0.618591i | ||||||
\(392\) | −7.65414e9 | + | 3.33297e9i | −0.324154 | + | 0.141152i | ||||
\(393\) | 2.89283e10 | 1.21270 | ||||||||
\(394\) | 3.17394e9 | 0.131709 | ||||||||
\(395\) | − | 2.24320e9i | − | 0.0921465i | ||||||
\(396\) | 1.30238e10 | 0.529609 | ||||||||
\(397\) | 2.67284e10i | 1.07600i | 0.842946 | + | 0.537998i | \(0.180819\pi\) | ||||
−0.842946 | + | 0.537998i | \(0.819181\pi\) | |||||||
\(398\) | − | 1.22356e10i | − | 0.487634i | ||||||
\(399\) | 6.70968e10 | − | 1.39748e10i | 2.64734 | − | 0.551385i | ||||
\(400\) | 6.06491e9 | 0.236910 | ||||||||
\(401\) | −3.64452e10 | −1.40949 | −0.704747 | − | 0.709459i | \(-0.748939\pi\) | ||||
−0.704747 | + | 0.709459i | \(0.748939\pi\) | |||||||
\(402\) | − | 4.66250e10i | − | 1.78531i | ||||||
\(403\) | 4.79096e10 | 1.81636 | ||||||||
\(404\) | 2.96886e9i | 0.111446i | ||||||||
\(405\) | 2.28603e9i | 0.0849694i | ||||||||
\(406\) | −1.82604e10 | + | 3.80326e9i | −0.672058 | + | 0.139975i | ||||
\(407\) | 1.25683e9 | 0.0458035 | ||||||||
\(408\) | 9.09465e9 | 0.328205 | ||||||||
\(409\) | 2.68492e10i | 0.959484i | 0.877410 | + | 0.479742i | \(0.159270\pi\) | ||||
−0.877410 | + | 0.479742i | \(0.840730\pi\) | |||||||
\(410\) | −6.60172e9 | −0.233626 | ||||||||
\(411\) | − | 1.73195e10i | − | 0.606970i | ||||||
\(412\) | − | 2.20478e10i | − | 0.765202i | ||||||
\(413\) | −2.78563e9 | − | 1.33745e10i | −0.0957465 | − | 0.459703i | ||||
\(414\) | −3.10619e10 | −1.05737 | ||||||||
\(415\) | 6.36793e9 | 0.214687 | ||||||||
\(416\) | 7.52931e9i | 0.251410i | ||||||||
\(417\) | −2.15973e10 | −0.714260 | ||||||||
\(418\) | 2.75536e10i | 0.902553i | ||||||||
\(419\) | − | 3.81047e10i | − | 1.23630i | −0.786062 | − | 0.618148i | \(-0.787883\pi\) | ||
0.786062 | − | 0.618148i | \(-0.212117\pi\) | |||||||
\(420\) | −5.44125e9 | + | 1.13330e9i | −0.174864 | + | 0.0364206i | ||||
\(421\) | −1.86146e10 | −0.592551 | −0.296275 | − | 0.955103i | \(-0.595745\pi\) | ||||
−0.296275 | + | 0.955103i | \(0.595745\pi\) | |||||||
\(422\) | −2.74234e9 | −0.0864710 | ||||||||
\(423\) | 7.40622e10i | 2.31332i | ||||||||
\(424\) | 1.15575e10 | 0.357602 | ||||||||
\(425\) | 1.83836e10i | 0.563474i | ||||||||
\(426\) | 1.92468e10i | 0.584414i | ||||||||
\(427\) | −5.10357e9 | − | 2.45036e10i | −0.153519 | − | 0.737085i | ||||
\(428\) | −9.14447e9 | −0.272511 | ||||||||
\(429\) | −5.54197e10 | −1.63619 | ||||||||
\(430\) | 1.04591e9i | 0.0305929i | ||||||||
\(431\) | −2.81734e10 | −0.816452 | −0.408226 | − | 0.912881i | \(-0.633853\pi\) | ||||
−0.408226 | + | 0.912881i | \(0.633853\pi\) | |||||||
\(432\) | − | 5.94544e9i | − | 0.170706i | ||||||
\(433\) | − | 4.31257e10i | − | 1.22683i | −0.789760 | − | 0.613416i | \(-0.789795\pi\) | ||
0.789760 | − | 0.613416i | \(-0.210205\pi\) | |||||||
\(434\) | 6.53301e9 | + | 3.13667e10i | 0.184143 | + | 0.884116i | ||||
\(435\) | −1.24180e10 | −0.346813 | ||||||||
\(436\) | 6.69397e9 | 0.185241 | ||||||||
\(437\) | − | 6.57158e10i | − | 1.80196i | ||||||
\(438\) | −4.75181e9 | −0.129111 | ||||||||
\(439\) | − | 5.77103e9i | − | 0.155380i | −0.996978 | − | 0.0776900i | \(-0.975246\pi\) | ||
0.996978 | − | 0.0776900i | \(-0.0247545\pi\) | |||||||
\(440\) | − | 2.23447e9i | − | 0.0596162i | ||||||
\(441\) | −4.98448e10 | + | 2.17048e10i | −1.31785 | + | 0.573853i | ||||
\(442\) | −2.28224e10 | −0.597960 | ||||||||
\(443\) | 9.16875e9 | 0.238065 | 0.119032 | − | 0.992890i | \(-0.462021\pi\) | ||||
0.119032 | + | 0.992890i | \(0.462021\pi\) | |||||||
\(444\) | − | 1.88558e9i | − | 0.0485190i | ||||||
\(445\) | −4.95969e9 | −0.126478 | ||||||||
\(446\) | − | 1.70822e10i | − | 0.431722i | ||||||
\(447\) | 7.97358e10i | 1.99721i | ||||||||
\(448\) | −4.92948e9 | + | 1.02671e9i | −0.122374 | + | 0.0254879i | ||||
\(449\) | 5.75612e10 | 1.41627 | 0.708133 | − | 0.706079i | \(-0.249538\pi\) | ||||
0.708133 | + | 0.706079i | \(0.249538\pi\) | |||||||
\(450\) | 3.94955e10 | 0.963158 | ||||||||
\(451\) | − | 4.40218e10i | − | 1.06405i | ||||||
\(452\) | 2.18027e10 | 0.522345 | ||||||||
\(453\) | − | 5.53742e10i | − | 1.31497i | ||||||
\(454\) | − | 1.61636e10i | − | 0.380465i | ||||||
\(455\) | 1.36544e10 | − | 2.84393e9i | 0.318587 | − | 0.0663549i | ||||
\(456\) | 4.13376e10 | 0.956062 | ||||||||
\(457\) | 2.88888e10 | 0.662315 | 0.331157 | − | 0.943576i | \(-0.392561\pi\) | ||||
0.331157 | + | 0.943576i | \(0.392561\pi\) | |||||||
\(458\) | 9.49712e9i | 0.215839i | ||||||||
\(459\) | 1.80214e10 | 0.406012 | ||||||||
\(460\) | 5.32926e9i | 0.119024i | ||||||||
\(461\) | 5.22913e10i | 1.15778i | 0.815406 | + | 0.578889i | \(0.196514\pi\) | ||||
−0.815406 | + | 0.578889i | \(0.803486\pi\) | |||||||
\(462\) | −7.55709e9 | − | 3.62835e10i | −0.165877 | − | 0.796419i | ||||
\(463\) | 1.72267e10 | 0.374869 | 0.187434 | − | 0.982277i | \(-0.439983\pi\) | ||||
0.187434 | + | 0.982277i | \(0.439983\pi\) | |||||||
\(464\) | −1.12501e10 | −0.242707 | ||||||||
\(465\) | 2.13309e10i | 0.456245i | ||||||||
\(466\) | 3.71614e10 | 0.788040 | ||||||||
\(467\) | − | 1.99045e10i | − | 0.418488i | −0.977863 | − | 0.209244i | \(-0.932900\pi\) | ||
0.977863 | − | 0.209244i | \(-0.0671003\pi\) | |||||||
\(468\) | 4.90319e10i | 1.02210i | ||||||||
\(469\) | −7.66019e10 | + | 1.59545e10i | −1.58324 | + | 0.329756i | ||||
\(470\) | 1.27068e10 | 0.260402 | ||||||||
\(471\) | −6.71673e10 | −1.36482 | ||||||||
\(472\) | − | 8.23990e9i | − | 0.166018i | ||||||
\(473\) | −6.97438e9 | −0.139335 | ||||||||
\(474\) | − | 2.24412e10i | − | 0.444562i | ||||||
\(475\) | 8.35582e10i | 1.64140i | ||||||||
\(476\) | −3.11209e9 | − | 1.49419e10i | −0.0606211 | − | 0.291057i | ||||
\(477\) | 7.52638e10 | 1.45383 | ||||||||
\(478\) | 5.86030e10 | 1.12256 | ||||||||
\(479\) | 5.05001e8i | 0.00959290i | 0.999988 | + | 0.00479645i | \(0.00152676\pi\) | ||||
−0.999988 | + | 0.00479645i | \(0.998473\pi\) | |||||||
\(480\) | −3.35230e9 | −0.0631506 | ||||||||
\(481\) | 4.73172e9i | 0.0883972i | ||||||||
\(482\) | − | 1.71954e9i | − | 0.0318584i | ||||||
\(483\) | 1.80238e10 | + | 8.65370e10i | 0.331175 | + | 1.59006i | ||||
\(484\) | −1.25380e10 | −0.228479 | ||||||||
\(485\) | 2.10298e9 | 0.0380074 | ||||||||
\(486\) | 4.98061e10i | 0.892766i | ||||||||
\(487\) | 3.73430e10 | 0.663886 | 0.331943 | − | 0.943299i | \(-0.392296\pi\) | ||||
0.331943 | + | 0.943299i | \(0.392296\pi\) | |||||||
\(488\) | − | 1.50964e10i | − | 0.266191i | ||||||
\(489\) | − | 1.76041e11i | − | 3.07877i | ||||||
\(490\) | 3.72386e9 | + | 8.55181e9i | 0.0645966 | + | 0.148345i | ||||
\(491\) | 7.30831e9 | 0.125745 | 0.0628726 | − | 0.998022i | \(-0.479974\pi\) | ||||
0.0628726 | + | 0.998022i | \(0.479974\pi\) | |||||||
\(492\) | −6.60443e10 | −1.12713 | ||||||||
\(493\) | − | 3.41005e10i | − | 0.577262i | ||||||
\(494\) | −1.03734e11 | −1.74186 | ||||||||
\(495\) | − | 1.45512e10i | − | 0.242369i | ||||||
\(496\) | 1.93247e10i | 0.319290i | ||||||||
\(497\) | 3.16213e10 | − | 6.58604e9i | 0.518267 | − | 0.107944i | ||||
\(498\) | 6.37055e10 | 1.03576 | ||||||||
\(499\) | 9.61811e10 | 1.55127 | 0.775635 | − | 0.631181i | \(-0.217430\pi\) | ||||
0.775635 | + | 0.631181i | \(0.217430\pi\) | |||||||
\(500\) | − | 1.39268e10i | − | 0.222829i | ||||||
\(501\) | −1.75949e11 | −2.79277 | ||||||||
\(502\) | − | 3.91396e10i | − | 0.616314i | ||||||
\(503\) | − | 5.20858e10i | − | 0.813669i | −0.913502 | − | 0.406834i | \(-0.866633\pi\) | ||
0.913502 | − | 0.406834i | \(-0.133367\pi\) | |||||||
\(504\) | −3.21014e10 | + | 6.68605e9i | −0.497510 | + | 0.103621i | ||||
\(505\) | 3.31705e9 | 0.0510019 | ||||||||
\(506\) | −3.55368e10 | −0.542096 | ||||||||
\(507\) | − | 1.05489e11i | − | 1.59652i | ||||||
\(508\) | 2.54662e10 | 0.382393 | ||||||||
\(509\) | 1.19801e11i | 1.78480i | 0.451241 | + | 0.892402i | \(0.350982\pi\) | ||||
−0.451241 | + | 0.892402i | \(0.649018\pi\) | |||||||
\(510\) | − | 1.01613e10i | − | 0.150199i | ||||||
\(511\) | 1.62602e9 | + | 7.80692e9i | 0.0238474 | + | 0.114498i | ||||
\(512\) | −3.03700e9 | −0.0441942 | ||||||||
\(513\) | 8.19122e10 | 1.18271 | ||||||||
\(514\) | 8.65347e10i | 1.23976i | ||||||||
\(515\) | −2.46336e10 | −0.350186 | ||||||||
\(516\) | 1.04634e10i | 0.147596i | ||||||||
\(517\) | 8.47317e10i | 1.18600i | ||||||||
\(518\) | −3.09788e9 | + | 6.45222e8i | −0.0430274 | + | 0.00896170i | ||||
\(519\) | −6.68504e10 | −0.921371 | ||||||||
\(520\) | 8.41235e9 | 0.115055 | ||||||||
\(521\) | 1.22726e11i | 1.66565i | 0.553535 | + | 0.832826i | \(0.313278\pi\) | ||||
−0.553535 | + | 0.832826i | \(0.686722\pi\) | |||||||
\(522\) | −7.32619e10 | −0.986726 | ||||||||
\(523\) | − | 1.22825e9i | − | 0.0164165i | −0.999966 | − | 0.00820827i | \(-0.997387\pi\) | ||
0.999966 | − | 0.00820827i | \(-0.00261280\pi\) | |||||||
\(524\) | − | 2.92811e10i | − | 0.388385i | ||||||
\(525\) | −2.29174e10 | − | 1.10032e11i | −0.301668 | − | 1.44838i | ||||
\(526\) | 1.85509e10 | 0.242338 | ||||||||
\(527\) | −5.85757e10 | −0.759408 | ||||||||
\(528\) | − | 2.23539e10i | − | 0.287619i | ||||||
\(529\) | 6.44495e9 | 0.0822994 | ||||||||
\(530\) | − | 1.29129e10i | − | 0.163652i | ||||||
\(531\) | − | 5.36593e10i | − | 0.674943i | ||||||
\(532\) | −1.41453e10 | − | 6.79150e10i | −0.176589 | − | 0.847850i | ||||
\(533\) | 1.65734e11 | 2.05353 | ||||||||
\(534\) | −4.96173e10 | −0.610194 | ||||||||
\(535\) | 1.02169e10i | 0.124711i | ||||||||
\(536\) | −4.71936e10 | −0.571774 | ||||||||
\(537\) | 1.97967e11i | 2.38065i | ||||||||
\(538\) | − | 4.49654e10i | − | 0.536722i | ||||||
\(539\) | −5.70255e10 | + | 2.48316e10i | −0.675638 | + | 0.294205i | ||||
\(540\) | −6.64272e9 | −0.0781216 | ||||||||
\(541\) | 9.53630e10 | 1.11324 | 0.556622 | − | 0.830766i | \(-0.312097\pi\) | ||||
0.556622 | + | 0.830766i | \(0.312097\pi\) | |||||||
\(542\) | − | 3.46862e10i | − | 0.401938i | ||||||
\(543\) | 7.11590e10 | 0.818522 | ||||||||
\(544\) | − | 9.20556e9i | − | 0.105113i | ||||||
\(545\) | − | 7.47904e9i | − | 0.0847735i | ||||||
\(546\) | 1.36600e11 | − | 2.84510e10i | 1.53703 | − | 0.320130i | ||||
\(547\) | −1.37958e11 | −1.54098 | −0.770492 | − | 0.637450i | \(-0.779989\pi\) | ||||
−0.770492 | + | 0.637450i | \(0.779989\pi\) | |||||||
\(548\) | −1.75307e10 | −0.194391 | ||||||||
\(549\) | − | 9.83097e10i | − | 1.08220i | ||||||
\(550\) | 4.51853e10 | 0.493795 | ||||||||
\(551\) | − | 1.54996e11i | − | 1.68156i | ||||||
\(552\) | 5.33145e10i | 0.574235i | ||||||||
\(553\) | −3.68694e10 | + | 7.67912e9i | −0.394245 | + | 0.0821128i | ||||
\(554\) | 8.22244e8 | 0.00872894 | ||||||||
\(555\) | −2.10672e9 | −0.0222042 | ||||||||
\(556\) | 2.18607e10i | 0.228752i | ||||||||
\(557\) | −3.15909e10 | −0.328202 | −0.164101 | − | 0.986444i | \(-0.552472\pi\) | ||||
−0.164101 | + | 0.986444i | \(0.552472\pi\) | |||||||
\(558\) | 1.25845e11i | 1.29807i | ||||||||
\(559\) | − | 2.62572e10i | − | 0.268906i | ||||||
\(560\) | 1.14712e9 | + | 5.50761e9i | 0.0116642 | + | 0.0560029i | ||||
\(561\) | 6.77578e10 | 0.684081 | ||||||||
\(562\) | −3.39708e9 | −0.0340535 | ||||||||
\(563\) | 8.09863e10i | 0.806080i | 0.915182 | + | 0.403040i | \(0.132046\pi\) | ||||
−0.915182 | + | 0.403040i | \(0.867954\pi\) | |||||||
\(564\) | 1.27120e11 | 1.25631 | ||||||||
\(565\) | − | 2.43598e10i | − | 0.239045i | ||||||
\(566\) | − | 9.87517e9i | − | 0.0962230i | ||||||
\(567\) | 3.75735e10 | − | 7.82576e9i | 0.363538 | − | 0.0757172i | ||||
\(568\) | 1.94816e10 | 0.187167 | ||||||||
\(569\) | 1.21889e11 | 1.16283 | 0.581415 | − | 0.813607i | \(-0.302499\pi\) | ||||
0.581415 | + | 0.813607i | \(0.302499\pi\) | |||||||
\(570\) | − | 4.61857e10i | − | 0.437530i | ||||||
\(571\) | 3.93072e10 | 0.369767 | 0.184883 | − | 0.982760i | \(-0.440809\pi\) | ||||
0.184883 | + | 0.982760i | \(0.440809\pi\) | |||||||
\(572\) | 5.60955e10i | 0.524015i | ||||||||
\(573\) | 6.53351e10i | 0.606077i | ||||||||
\(574\) | 2.25996e10 | + | 1.08507e11i | 0.208187 | + | 0.999559i | ||||
\(575\) | −1.07768e11 | −0.985866 | ||||||||
\(576\) | −1.97774e10 | −0.179671 | ||||||||
\(577\) | 6.82213e10i | 0.615484i | 0.951470 | + | 0.307742i | \(0.0995734\pi\) | ||||
−0.951470 | + | 0.307742i | \(0.900427\pi\) | |||||||
\(578\) | −5.10184e10 | −0.457104 | ||||||||
\(579\) | 2.11849e8i | 0.00188500i | ||||||||
\(580\) | 1.25695e10i | 0.111072i | ||||||||
\(581\) | −2.17993e10 | − | 1.04664e11i | −0.191310 | − | 0.918529i | ||||
\(582\) | 2.10385e10 | 0.183367 | ||||||||
\(583\) | 8.61065e10 | 0.745352 | ||||||||
\(584\) | 4.80976e9i | 0.0413497i | ||||||||
\(585\) | 5.47824e10 | 0.467754 | ||||||||
\(586\) | − | 5.99541e10i | − | 0.508427i | ||||||
\(587\) | 1.89401e11i | 1.59525i | 0.603152 | + | 0.797626i | \(0.293911\pi\) | ||||
−0.603152 | + | 0.797626i | \(0.706089\pi\) | |||||||
\(588\) | 3.72540e10 | + | 8.55533e10i | 0.311647 | + | 0.715694i | ||||
\(589\) | −2.66242e11 | −2.21216 | ||||||||
\(590\) | −9.20628e9 | −0.0759759 | ||||||||
\(591\) | − | 3.54764e10i | − | 0.290797i | ||||||
\(592\) | −1.90857e9 | −0.0155389 | ||||||||
\(593\) | − | 2.23276e11i | − | 1.80561i | −0.430055 | − | 0.902803i | \(-0.641506\pi\) | ||
0.430055 | − | 0.902803i | \(-0.358494\pi\) | |||||||
\(594\) | − | 4.42952e10i | − | 0.355804i | ||||||
\(595\) | −1.66943e10 | + | 3.47707e9i | −0.133199 | + | 0.0277425i | ||||
\(596\) | 8.07082e10 | 0.639636 | ||||||||
\(597\) | −1.36762e11 | −1.07664 | ||||||||
\(598\) | − | 1.33789e11i | − | 1.04620i | ||||||
\(599\) | 6.72450e10 | 0.522339 | 0.261170 | − | 0.965293i | \(-0.415892\pi\) | ||||
0.261170 | + | 0.965293i | \(0.415892\pi\) | |||||||
\(600\) | − | 6.77899e10i | − | 0.523070i | ||||||
\(601\) | − | 1.74729e11i | − | 1.33927i | −0.742692 | − | 0.669633i | \(-0.766452\pi\) | ||
0.742692 | − | 0.669633i | \(-0.233548\pi\) | |||||||
\(602\) | 1.71907e10 | − | 3.58046e9i | 0.130890 | − | 0.0272617i | ||||
\(603\) | −3.07331e11 | −2.32454 | ||||||||
\(604\) | −5.60495e10 | −0.421138 | ||||||||
\(605\) | 1.40084e10i | 0.104560i | ||||||||
\(606\) | 3.31841e10 | 0.246059 | ||||||||
\(607\) | − | 1.40790e11i | − | 1.03709i | −0.855050 | − | 0.518545i | \(-0.826474\pi\) | ||
0.855050 | − | 0.518545i | \(-0.173526\pi\) | |||||||
\(608\) | − | 4.18418e10i | − | 0.306193i | ||||||
\(609\) | 4.25105e10 | + | 2.04104e11i | 0.309049 | + | 1.48382i | ||||
\(610\) | −1.68669e10 | −0.121819 | ||||||||
\(611\) | −3.18998e11 | −2.28888 | ||||||||
\(612\) | − | 5.99479e10i | − | 0.427335i | ||||||
\(613\) | 7.54986e9 | 0.0534684 | 0.0267342 | − | 0.999643i | \(-0.491489\pi\) | ||||
0.0267342 | + | 0.999643i | \(0.491489\pi\) | |||||||
\(614\) | − | 4.25233e10i | − | 0.299194i | ||||||
\(615\) | 7.37900e10i | 0.515819i | ||||||||
\(616\) | −3.67260e10 | + | 7.64925e9i | −0.255065 | + | 0.0531246i | ||||
\(617\) | 2.51744e11 | 1.73708 | 0.868538 | − | 0.495623i | \(-0.165060\pi\) | ||||
0.868538 | + | 0.495623i | \(0.165060\pi\) | |||||||
\(618\) | −2.46437e11 | −1.68948 | ||||||||
\(619\) | 1.71138e11i | 1.16569i | 0.812582 | + | 0.582847i | \(0.198061\pi\) | ||||
−0.812582 | + | 0.582847i | \(0.801939\pi\) | |||||||
\(620\) | 2.15911e10 | 0.146119 | ||||||||
\(621\) | 1.05645e11i | 0.710367i | ||||||||
\(622\) | 1.44961e11i | 0.968476i | ||||||||
\(623\) | 1.69785e10 | + | 8.15179e10i | 0.112706 | + | 0.541129i | ||||
\(624\) | 8.41581e10 | 0.555083 | ||||||||
\(625\) | 1.29039e11 | 0.845667 | ||||||||
\(626\) | 1.67854e10i | 0.109304i | ||||||||
\(627\) | 3.07977e11 | 1.99273 | ||||||||
\(628\) | 6.79864e10i | 0.437103i | ||||||||
\(629\) | − | 5.78514e9i | − | 0.0369582i | ||||||
\(630\) | 7.47019e9 | + | 3.58663e10i | 0.0474208 | + | 0.227680i | ||||
\(631\) | −1.69838e11 | −1.07131 | −0.535657 | − | 0.844436i | \(-0.679936\pi\) | ||||
−0.535657 | + | 0.844436i | \(0.679936\pi\) | |||||||
\(632\) | −2.27149e10 | −0.142378 | ||||||||
\(633\) | 3.06522e10i | 0.190918i | ||||||||
\(634\) | −6.20429e10 | −0.384003 | ||||||||
\(635\) | − | 2.84529e10i | − | 0.174997i | ||||||
\(636\) | − | 1.29182e11i | − | 0.789542i | ||||||
\(637\) | −9.34861e10 | − | 2.14690e11i | −0.567792 | − | 1.30393i | ||||
\(638\) | −8.38162e10 | −0.505877 | ||||||||
\(639\) | 1.26867e11 | 0.760928 | ||||||||
\(640\) | 3.39318e9i | 0.0202249i | ||||||||
\(641\) | 2.76886e11 | 1.64010 | 0.820048 | − | 0.572295i | \(-0.193947\pi\) | ||||
0.820048 | + | 0.572295i | \(0.193947\pi\) | |||||||
\(642\) | 1.02211e11i | 0.601671i | ||||||||
\(643\) | 6.05874e10i | 0.354436i | 0.984172 | + | 0.177218i | \(0.0567098\pi\) | ||||
−0.984172 | + | 0.177218i | \(0.943290\pi\) | |||||||
\(644\) | 8.75923e10 | − | 1.82436e10i | 0.509240 | − | 0.106064i | ||||
\(645\) | 1.16906e10 | 0.0675455 | ||||||||
\(646\) | 1.26828e11 | 0.728258 | ||||||||
\(647\) | − | 2.20967e11i | − | 1.26099i | −0.776194 | − | 0.630494i | \(-0.782852\pi\) | ||
0.776194 | − | 0.630494i | \(-0.217148\pi\) | |||||||
\(648\) | 2.31486e10 | 0.131288 | ||||||||
\(649\) | − | 6.13896e10i | − | 0.346032i | ||||||
\(650\) | 1.70114e11i | 0.952985i | ||||||||
\(651\) | 3.50598e11 | − | 7.30220e10i | 1.95202 | − | 0.406565i | ||||
\(652\) | −1.78187e11 | −0.986022 | ||||||||
\(653\) | 3.84633e10 | 0.211541 | 0.105770 | − | 0.994391i | \(-0.466269\pi\) | ||||
0.105770 | + | 0.994391i | \(0.466269\pi\) | |||||||
\(654\) | − | 7.48212e10i | − | 0.408991i | ||||||
\(655\) | −3.27152e10 | −0.177740 | ||||||||
\(656\) | 6.68498e10i | 0.360981i | ||||||||
\(657\) | 3.13218e10i | 0.168107i | ||||||||
\(658\) | −4.34990e10 | − | 2.08850e11i | −0.232047 | − | 1.11412i | ||||
\(659\) | 2.57573e11 | 1.36571 | 0.682856 | − | 0.730553i | \(-0.260738\pi\) | ||||
0.682856 | + | 0.730553i | \(0.260738\pi\) | |||||||
\(660\) | −2.49756e10 | −0.131625 | ||||||||
\(661\) | 2.65141e10i | 0.138890i | 0.997586 | + | 0.0694449i | \(0.0221228\pi\) | ||||
−0.997586 | + | 0.0694449i | \(0.977877\pi\) | |||||||
\(662\) | 2.87257e10 | 0.149568 | ||||||||
\(663\) | 2.55095e11i | 1.32022i | ||||||||
\(664\) | − | 6.44824e10i | − | 0.331718i | ||||||
\(665\) | −7.58801e10 | + | 1.58042e10i | −0.388009 | + | 0.0808140i | ||||
\(666\) | −1.24289e10 | −0.0631735 | ||||||||
\(667\) | 1.99903e11 | 1.00999 | ||||||||
\(668\) | 1.78095e11i | 0.894427i | ||||||||
\(669\) | −1.90934e11 | −0.953191 | ||||||||
\(670\) | 5.27285e10i | 0.261665i | ||||||||
\(671\) | − | 1.12472e11i | − | 0.554825i | ||||||
\(672\) | 1.14759e10 | + | 5.50987e10i | 0.0562742 | + | 0.270187i | ||||
\(673\) | −3.00891e11 | −1.46673 | −0.733363 | − | 0.679837i | \(-0.762050\pi\) | ||||
−0.733363 | + | 0.679837i | \(0.762050\pi\) | |||||||
\(674\) | 1.00002e10 | 0.0484584 | ||||||||
\(675\) | − | 1.34329e11i | − | 0.647073i | ||||||
\(676\) | −1.06775e11 | −0.511309 | ||||||||
\(677\) | 2.60587e11i | 1.24050i | 0.784403 | + | 0.620252i | \(0.212970\pi\) | ||||
−0.784403 | + | 0.620252i | \(0.787030\pi\) | |||||||
\(678\) | − | 2.43698e11i | − | 1.15328i | ||||||
\(679\) | −7.19912e9 | − | 3.45648e10i | −0.0338688 | − | 0.162613i | ||||
\(680\) | −1.02852e10 | −0.0481035 | ||||||||
\(681\) | −1.80667e11 | −0.840021 | ||||||||
\(682\) | 1.43974e11i | 0.665499i | ||||||||
\(683\) | −2.85098e11 | −1.31012 | −0.655061 | − | 0.755576i | \(-0.727357\pi\) | ||||
−0.655061 | + | 0.755576i | \(0.727357\pi\) | |||||||
\(684\) | − | 2.72479e11i | − | 1.24483i | ||||||
\(685\) | 1.95867e10i | 0.0889608i | ||||||||
\(686\) | 1.27811e11 | − | 9.04812e10i | 0.577126 | − | 0.408566i | ||||
\(687\) | 1.06153e11 | 0.476547 | ||||||||
\(688\) | 1.05910e10 | 0.0472698 | ||||||||
\(689\) | 3.24174e11i | 1.43847i | ||||||||
\(690\) | 5.95673e10 | 0.262792 | ||||||||
\(691\) | 2.05251e11i | 0.900269i | 0.892961 | + | 0.450135i | \(0.148624\pi\) | ||||
−0.892961 | + | 0.450135i | \(0.851376\pi\) | |||||||
\(692\) | 6.76656e10i | 0.295083i | ||||||||
\(693\) | −2.39165e11 | + | 4.98129e10i | −1.03697 | + | 0.215978i | ||||
\(694\) | −1.56939e10 | −0.0676539 | ||||||||
\(695\) | 2.44246e10 | 0.104686 | ||||||||
\(696\) | 1.25746e11i | 0.535869i | ||||||||
\(697\) | −2.02631e11 | −0.858567 | ||||||||
\(698\) | − | 1.89005e11i | − | 0.796256i | ||||||
\(699\) | − | 4.15368e11i | − | 1.73990i | ||||||
\(700\) | −1.11374e11 | + | 2.31969e10i | −0.463866 | + | 0.0966136i | ||||
\(701\) | 4.37725e10 | 0.181271 | 0.0906356 | − | 0.995884i | \(-0.471110\pi\) | ||||
0.0906356 | + | 0.995884i | \(0.471110\pi\) | |||||||
\(702\) | 1.66763e11 | 0.686674 | ||||||||
\(703\) | − | 2.62950e10i | − | 0.107659i | ||||||
\(704\) | −2.26265e10 | −0.0921143 | ||||||||
\(705\) | − | 1.42029e11i | − | 0.574936i | ||||||
\(706\) | 1.55748e11i | 0.626906i | ||||||||
\(707\) | −1.13552e10 | − | 5.45194e10i | −0.0454484 | − | 0.218209i | ||||
\(708\) | −9.21006e10 | −0.366547 | ||||||||
\(709\) | −6.28400e10 | −0.248686 | −0.124343 | − | 0.992239i | \(-0.539682\pi\) | ||||
−0.124343 | + | 0.992239i | \(0.539682\pi\) | |||||||
\(710\) | − | 2.17664e10i | − | 0.0856549i | ||||||
\(711\) | −1.47922e11 | −0.578836 | ||||||||
\(712\) | 5.02224e10i | 0.195424i | ||||||||
\(713\) | − | 3.43382e11i | − | 1.32868i | ||||||
\(714\) | −1.67012e11 | + | 3.47850e10i | −0.642620 | + | 0.133844i | ||||
\(715\) | 6.26744e10 | 0.239809 | ||||||||
\(716\) | 2.00382e11 | 0.762440 | ||||||||
\(717\) | − | 6.55029e11i | − | 2.47847i | ||||||
\(718\) | 2.67488e11 | 1.00648 | ||||||||
\(719\) | 3.21811e11i | 1.20416i | 0.798434 | + | 0.602082i | \(0.205662\pi\) | ||||
−0.798434 | + | 0.602082i | \(0.794338\pi\) | |||||||
\(720\) | 2.20969e10i | 0.0822243i | ||||||||
\(721\) | 8.43279e10 | + | 4.04880e11i | 0.312054 | + | 1.49825i | ||||
\(722\) | 3.84320e11 | 1.41431 | ||||||||
\(723\) | −1.92200e10 | −0.0703396 | ||||||||
\(724\) | − | 7.20268e10i | − | 0.262144i | ||||||
\(725\) | −2.54179e11 | −0.919999 | ||||||||
\(726\) | 1.40142e11i | 0.504453i | ||||||||
\(727\) | 1.50767e10i | 0.0539720i | 0.999636 | + | 0.0269860i | \(0.00859096\pi\) | ||||
−0.999636 | + | 0.0269860i | \(0.991409\pi\) | |||||||
\(728\) | −2.87979e10 | − | 1.38266e11i | −0.102526 | − | 0.492256i | ||||
\(729\) | 4.51826e11 | 1.59978 | ||||||||
\(730\) | 5.37385e9 | 0.0189232 | ||||||||
\(731\) | 3.21028e10i | 0.112428i | ||||||||
\(732\) | −1.68738e11 | −0.587719 | ||||||||
\(733\) | − | 3.80728e11i | − | 1.31886i | −0.751766 | − | 0.659430i | \(-0.770798\pi\) | ||
0.751766 | − | 0.659430i | \(-0.229202\pi\) | |||||||
\(734\) | 2.17273e11i | 0.748551i | ||||||||
\(735\) | 9.55870e10 | − | 4.16231e10i | 0.327529 | − | 0.142622i | ||||
\(736\) | 5.39647e10 | 0.183907 | ||||||||
\(737\) | −3.51606e11 | −1.19175 | ||||||||
\(738\) | 4.35335e11i | 1.46757i | ||||||||
\(739\) | 1.87656e11 | 0.629194 | 0.314597 | − | 0.949225i | \(-0.398131\pi\) | ||||
0.314597 | + | 0.949225i | \(0.398131\pi\) | |||||||
\(740\) | 2.13241e9i | 0.00711121i | ||||||||
\(741\) | 1.15947e12i | 3.84581i | ||||||||
\(742\) | −2.12238e11 | + | 4.42048e10i | −0.700178 | + | 0.145832i | ||||
\(743\) | −3.02086e11 | −0.991233 | −0.495616 | − | 0.868542i | \(-0.665058\pi\) | ||||
−0.495616 | + | 0.868542i | \(0.665058\pi\) | |||||||
\(744\) | 2.16000e11 | 0.704955 | ||||||||
\(745\) | − | 9.01737e10i | − | 0.292722i | ||||||
\(746\) | −2.53472e11 | −0.818418 | ||||||||
\(747\) | − | 4.19918e11i | − | 1.34860i | ||||||
\(748\) | − | 6.85841e10i | − | 0.219087i | ||||||
\(749\) | 1.67927e11 | − | 3.49755e10i | 0.533571 | − | 0.111132i | ||||
\(750\) | −1.55665e11 | −0.491979 | ||||||||
\(751\) | 4.59708e11 | 1.44518 | 0.722591 | − | 0.691275i | \(-0.242951\pi\) | ||||
0.722591 | + | 0.691275i | \(0.242951\pi\) | |||||||
\(752\) | − | 1.28670e11i | − | 0.402352i | ||||||
\(753\) | −4.37479e11 | −1.36075 | ||||||||
\(754\) | − | 3.15552e11i | − | 0.976304i | ||||||
\(755\) | 6.26230e10i | 0.192729i | ||||||||
\(756\) | 2.27400e10 | + | 1.09180e11i | 0.0696150 | + | 0.334239i | ||||
\(757\) | 4.87501e11 | 1.48454 | 0.742270 | − | 0.670101i | \(-0.233749\pi\) | ||||
0.742270 | + | 0.670101i | \(0.233749\pi\) | |||||||
\(758\) | 3.61953e11 | 1.09642 | ||||||||
\(759\) | 3.97209e11i | 1.19688i | ||||||||
\(760\) | −4.67490e10 | −0.140126 | ||||||||
\(761\) | − | 3.71594e11i | − | 1.10798i | −0.832525 | − | 0.553988i | \(-0.813105\pi\) | ||
0.832525 | − | 0.553988i | \(-0.186895\pi\) | |||||||
\(762\) | − | 2.84646e11i | − | 0.844277i | ||||||
\(763\) | −1.22926e11 | + | 2.56029e10i | −0.362699 | + | 0.0755426i | ||||
\(764\) | 6.61318e10 | 0.194105 | ||||||||
\(765\) | −6.69786e10 | −0.195565 | ||||||||
\(766\) | − | 3.33296e11i | − | 0.968088i | ||||||
\(767\) | 2.31120e11 | 0.667815 | ||||||||
\(768\) | 3.39458e10i | 0.0975755i | ||||||||
\(769\) | − | 2.03480e11i | − | 0.581856i | −0.956745 | − | 0.290928i | \(-0.906036\pi\) | ||
0.956745 | − | 0.290928i | \(-0.0939641\pi\) | |||||||
\(770\) | 8.54635e9 | + | 4.10332e10i | 0.0243118 | + | 0.116727i | ||||
\(771\) | 9.67233e11 | 2.73724 | ||||||||
\(772\) | 2.14432e8 | 0.000603700 | ||||||||
\(773\) | − | 4.31921e11i | − | 1.20972i | −0.796331 | − | 0.604861i | \(-0.793228\pi\) | ||
0.796331 | − | 0.604861i | \(-0.206772\pi\) | |||||||
\(774\) | 6.89701e10 | 0.192175 | ||||||||
\(775\) | 4.36613e11i | 1.21029i | ||||||||
\(776\) | − | 2.12950e10i | − | 0.0587261i | ||||||
\(777\) | 7.21191e9 | + | 3.46262e10i | 0.0197864 | + | 0.0949994i | ||||
\(778\) | −2.26392e11 | −0.617935 | ||||||||
\(779\) | −9.21011e11 | −2.50101 | ||||||||
\(780\) | − | 9.40282e10i | − | 0.254027i | ||||||
\(781\) | 1.45143e11 | 0.390115 | ||||||||
\(782\) | 1.63574e11i | 0.437410i | ||||||||
\(783\) | 2.49172e11i | 0.662906i | ||||||||
\(784\) | 8.65967e10 | − | 3.77083e10i | 0.229212 | − | 0.0998097i | ||||
\(785\) | 7.59599e10 | 0.200035 | ||||||||
\(786\) | −3.27287e11 | −0.857508 | ||||||||
\(787\) | 4.11125e11i | 1.07170i | 0.844312 | + | 0.535852i | \(0.180009\pi\) | ||||
−0.844312 | + | 0.535852i | \(0.819991\pi\) | |||||||
\(788\) | −3.59091e10 | −0.0931320 | ||||||||
\(789\) | − | 2.07351e11i | − | 0.535054i | ||||||
\(790\) | 2.53789e10i | 0.0651574i | ||||||||
\(791\) | −4.00380e11 | + | 8.33906e10i | −1.02274 | + | 0.213015i | ||||
\(792\) | −1.47347e11 | −0.374490 | ||||||||
\(793\) | 4.23437e11 | 1.07077 | ||||||||
\(794\) | − | 3.02397e11i | − | 0.760845i | ||||||
\(795\) | −1.44333e11 | −0.361324 | ||||||||
\(796\) | 1.38430e11i | 0.344809i | ||||||||
\(797\) | − | 4.63797e10i | − | 0.114946i | −0.998347 | − | 0.0574731i | \(-0.981696\pi\) | ||
0.998347 | − | 0.0574731i | \(-0.0183044\pi\) | |||||||
\(798\) | −7.59113e11 | + | 1.58107e11i | −1.87195 | + | 0.389888i | ||||
\(799\) | 3.90017e11 | 0.956966 | ||||||||
\(800\) | −6.86166e10 | −0.167521 | ||||||||
\(801\) | 3.27055e11i | 0.794494i | ||||||||
\(802\) | 4.12331e11 | 0.996663 | ||||||||
\(803\) | 3.58341e10i | 0.0861856i | ||||||||
\(804\) | 5.27502e11i | 1.26241i | ||||||||
\(805\) | −2.03832e10 | − | 9.78651e10i | −0.0485389 | − | 0.233048i | ||||
\(806\) | −5.42035e11 | −1.28436 | ||||||||
\(807\) | −5.02596e11 | −1.18502 | ||||||||
\(808\) | − | 3.35888e10i | − | 0.0788042i | ||||||
\(809\) | 6.26109e10 | 0.146169 | 0.0730846 | − | 0.997326i | \(-0.476716\pi\) | ||||
0.0730846 | + | 0.997326i | \(0.476716\pi\) | |||||||
\(810\) | − | 2.58635e10i | − | 0.0600824i | ||||||
\(811\) | − | 7.64797e11i | − | 1.76792i | −0.467562 | − | 0.883960i | \(-0.654868\pi\) | ||
0.467562 | − | 0.883960i | \(-0.345132\pi\) | |||||||
\(812\) | 2.06593e11 | − | 4.30290e10i | 0.475217 | − | 0.0989776i | ||||
\(813\) | −3.87701e11 | −0.887432 | ||||||||
\(814\) | −1.42194e10 | −0.0323880 | ||||||||
\(815\) | 1.99085e11i | 0.451241i | ||||||||
\(816\) | −1.02894e11 | −0.232076 | ||||||||
\(817\) | 1.45916e11i | 0.327502i | ||||||||
\(818\) | − | 3.03764e11i | − | 0.678458i | ||||||
\(819\) | −1.87536e11 | − | 9.00409e11i | −0.416821 | − | 2.00126i | ||||
\(820\) | 7.46899e10 | 0.165199 | ||||||||
\(821\) | 1.18664e11 | 0.261184 | 0.130592 | − | 0.991436i | \(-0.458312\pi\) | ||||
0.130592 | + | 0.991436i | \(0.458312\pi\) | |||||||
\(822\) | 1.95948e11i | 0.429193i | ||||||||
\(823\) | −4.97104e10 | −0.108355 | −0.0541774 | − | 0.998531i | \(-0.517254\pi\) | ||||
−0.0541774 | + | 0.998531i | \(0.517254\pi\) | |||||||
\(824\) | 2.49442e11i | 0.541080i | ||||||||
\(825\) | − | 5.05054e11i | − | 1.09024i | ||||||
\(826\) | 3.15158e10 | + | 1.51315e11i | 0.0677030 | + | 0.325059i | ||||
\(827\) | −4.23663e11 | −0.905730 | −0.452865 | − | 0.891579i | \(-0.649598\pi\) | ||||
−0.452865 | + | 0.891579i | \(0.649598\pi\) | |||||||
\(828\) | 3.51426e11 | 0.747674 | ||||||||
\(829\) | 3.27268e11i | 0.692925i | 0.938064 | + | 0.346462i | \(0.112617\pi\) | ||||
−0.938064 | + | 0.346462i | \(0.887383\pi\) | |||||||
\(830\) | −7.20449e10 | −0.151807 | ||||||||
\(831\) | − | 9.19054e9i | − | 0.0192725i | ||||||
\(832\) | − | 8.51844e10i | − | 0.177773i | ||||||
\(833\) | 1.14299e11 | + | 2.62486e11i | 0.237390 | + | 0.545163i | ||||
\(834\) | 2.44346e11 | 0.505058 | ||||||||
\(835\) | 1.98982e11 | 0.409324 | ||||||||
\(836\) | − | 3.11733e11i | − | 0.638201i | ||||||
\(837\) | 4.28012e11 | 0.872076 | ||||||||
\(838\) | 4.31105e11i | 0.874193i | ||||||||
\(839\) | − | 2.88363e11i | − | 0.581958i | −0.956730 | − | 0.290979i | \(-0.906019\pi\) | ||
0.956730 | − | 0.290979i | \(-0.0939809\pi\) | |||||||
\(840\) | 6.15607e10 | − | 1.28218e10i | 0.123648 | − | 0.0257532i | ||||
\(841\) | −2.87590e10 | −0.0574896 | ||||||||
\(842\) | 2.10600e11 | 0.418997 | ||||||||
\(843\) | 3.79706e10i | 0.0751860i | ||||||||
\(844\) | 3.10260e10 | 0.0611443 | ||||||||
\(845\) | 1.19298e11i | 0.233995i | ||||||||
\(846\) | − | 8.37918e11i | − | 1.63576i | ||||||
\(847\) | 2.30244e11 | − | 4.79549e10i | 0.447357 | − | 0.0931749i | ||||
\(848\) | −1.30758e11 | −0.252863 | ||||||||
\(849\) | −1.10379e11 | −0.212449 | ||||||||
\(850\) | − | 2.07986e11i | − | 0.398436i | ||||||
\(851\) | 3.39136e10 | 0.0646629 | ||||||||
\(852\) | − | 2.17753e11i | − | 0.413243i | ||||||
\(853\) | 8.59016e11i | 1.62258i | 0.584647 | + | 0.811288i | \(0.301233\pi\) | ||||
−0.584647 | + | 0.811288i | \(0.698767\pi\) | |||||||
\(854\) | 5.77403e10 | + | 2.77226e11i | 0.108554 | + | 0.521198i | ||||
\(855\) | −3.04436e11 | −0.569680 | ||||||||
\(856\) | 1.03458e11 | 0.192694 | ||||||||
\(857\) | 7.24754e11i | 1.34359i | 0.740736 | + | 0.671796i | \(0.234477\pi\) | ||||
−0.740736 | + | 0.671796i | \(0.765523\pi\) | |||||||
\(858\) | 6.27002e11 | 1.15696 | ||||||||
\(859\) | 8.52093e11i | 1.56500i | 0.622651 | + | 0.782500i | \(0.286056\pi\) | ||||
−0.622651 | + | 0.782500i | \(0.713944\pi\) | |||||||
\(860\) | − | 1.18331e10i | − | 0.0216325i | ||||||
\(861\) | 1.21282e12 | − | 2.52605e11i | 2.20691 | − | 0.459652i | ||||
\(862\) | 3.18746e11 | 0.577319 | ||||||||
\(863\) | 9.96876e10 | 0.179721 | 0.0898603 | − | 0.995954i | \(-0.471358\pi\) | ||||
0.0898603 | + | 0.995954i | \(0.471358\pi\) | |||||||
\(864\) | 6.72649e10i | 0.120707i | ||||||||
\(865\) | 7.56015e10 | 0.135041 | ||||||||
\(866\) | 4.87912e11i | 0.867501i | ||||||||
\(867\) | 5.70252e11i | 1.00923i | ||||||||
\(868\) | −7.39126e10 | − | 3.54873e11i | −0.130209 | − | 0.625164i | ||||
\(869\) | −1.69232e11 | −0.296759 | ||||||||
\(870\) | 1.40494e11 | 0.245234 | ||||||||
\(871\) | − | 1.32373e12i | − | 2.29999i | ||||||
\(872\) | −7.57336e10 | −0.130985 | ||||||||
\(873\) | − | 1.38676e11i | − | 0.238751i | ||||||
\(874\) | 7.43490e11i | 1.27418i | ||||||||
\(875\) | 5.32669e10 | + | 2.55748e11i | 0.0908709 | + | 0.436295i | ||||
\(876\) | 5.37606e10 | 0.0912952 | ||||||||
\(877\) | −6.19031e11 | −1.04644 | −0.523219 | − | 0.852198i | \(-0.675269\pi\) | ||||
−0.523219 | + | 0.852198i | \(0.675269\pi\) | |||||||
\(878\) | 6.52918e10i | 0.109870i | ||||||||
\(879\) | −6.70131e11 | −1.12255 | ||||||||
\(880\) | 2.52802e10i | 0.0421550i | ||||||||
\(881\) | − | 5.89739e10i | − | 0.0978940i | −0.998801 | − | 0.0489470i | \(-0.984413\pi\) | ||
0.998801 | − | 0.0489470i | \(-0.0155865\pi\) | |||||||
\(882\) | 5.63929e11 | − | 2.45561e11i | 0.931859 | − | 0.405776i | ||||
\(883\) | −5.12329e11 | −0.842764 | −0.421382 | − | 0.906883i | \(-0.638455\pi\) | ||||
−0.421382 | + | 0.906883i | \(0.638455\pi\) | |||||||
\(884\) | 2.58206e11 | 0.422821 | ||||||||
\(885\) | 1.02902e11i | 0.167746i | ||||||||
\(886\) | −1.03733e11 | −0.168337 | ||||||||
\(887\) | − | 9.83599e11i | − | 1.58900i | −0.607265 | − | 0.794499i | \(-0.707733\pi\) | ||
0.607265 | − | 0.794499i | \(-0.292267\pi\) | |||||||
\(888\) | 2.13329e10i | 0.0343081i | ||||||||
\(889\) | −4.67655e11 | + | 9.74026e10i | −0.748718 | + | 0.155942i | ||||
\(890\) | 5.61125e10 | 0.0894333 | ||||||||
\(891\) | 1.72464e11 | 0.273645 | ||||||||
\(892\) | 1.93263e11i | 0.305274i | ||||||||
\(893\) | 1.77273e12 | 2.78764 | ||||||||
\(894\) | − | 9.02108e11i | − | 1.41224i | ||||||
\(895\) | − | 2.23882e11i | − | 0.348922i | ||||||
\(896\) | 5.57707e10 | − | 1.16158e10i | 0.0865314 | − | 0.0180227i | ||||
\(897\) | −1.49541e12 | −2.30989 | ||||||||
\(898\) | −6.51231e11 | −1.00145 | ||||||||
\(899\) | − | 8.09893e11i | − | 1.23991i | ||||||
\(900\) | −4.46841e11 | −0.681056 | ||||||||
\(901\) | − | 3.96345e11i | − | 0.601415i | ||||||
\(902\) | 4.98050e11i | 0.752396i | ||||||||
\(903\) | −4.00202e10 | − | 1.92147e11i | −0.0601906 | − | 0.288990i | ||||
\(904\) | −2.46670e11 | −0.369354 | ||||||||
\(905\) | −8.04741e10 | −0.119967 | ||||||||
\(906\) | 6.26488e11i | 0.929822i | ||||||||
\(907\) | −6.57609e11 | −0.971715 | −0.485857 | − | 0.874038i | \(-0.661493\pi\) | ||||
−0.485857 | + | 0.874038i | \(0.661493\pi\) | |||||||
\(908\) | 1.82870e11i | 0.269029i | ||||||||
\(909\) | − | 2.18735e11i | − | 0.320378i | ||||||
\(910\) | −1.54482e11 | + | 3.21754e10i | −0.225275 | + | 0.0469200i | ||||
\(911\) | 1.06492e11 | 0.154612 | 0.0773058 | − | 0.997007i | \(-0.475368\pi\) | ||||
0.0773058 | + | 0.997007i | \(0.475368\pi\) | |||||||
\(912\) | −4.67682e11 | −0.676038 | ||||||||
\(913\) | − | 4.80412e11i | − | 0.691403i | ||||||
\(914\) | −3.26839e11 | −0.468327 | ||||||||
\(915\) | 1.88528e11i | 0.268962i | ||||||||
\(916\) | − | 1.07448e11i | − | 0.152621i | ||||||
\(917\) | 1.11994e11 | + | 5.37711e11i | 0.158386 | + | 0.760451i | ||||
\(918\) | −2.03889e11 | −0.287094 | ||||||||
\(919\) | −5.32765e11 | −0.746919 | −0.373459 | − | 0.927647i | \(-0.621828\pi\) | ||||
−0.373459 | + | 0.927647i | \(0.621828\pi\) | |||||||
\(920\) | − | 6.02937e10i | − | 0.0841629i | ||||||
\(921\) | −4.75300e11 | −0.660586 | ||||||||
\(922\) | − | 5.91608e11i | − | 0.818673i | ||||||
\(923\) | 5.46436e11i | 0.752891i | ||||||||
\(924\) | 8.54987e10 | + | 4.10501e11i | 0.117293 | + | 0.563153i | ||||
\(925\) | −4.31214e10 | −0.0589014 | ||||||||
\(926\) | −1.94898e11 | −0.265072 | ||||||||
\(927\) | 1.62440e12i | 2.19976i | ||||||||
\(928\) | 1.27280e11 | 0.171620 | ||||||||
\(929\) | 5.11415e11i | 0.686611i | 0.939224 | + | 0.343305i | \(0.111547\pi\) | ||||
−0.939224 | + | 0.343305i | \(0.888453\pi\) | |||||||
\(930\) | − | 2.41332e11i | − | 0.322614i | ||||||
\(931\) | 5.19519e11 | + | 1.19307e12i | 0.691517 | + | 1.58806i | ||||
\(932\) | −4.20433e11 | −0.557229 | ||||||||
\(933\) | 1.62028e12 | 2.13828 | ||||||||
\(934\) | 2.25193e11i | 0.295916i | ||||||||
\(935\) | −7.66276e10 | −0.100263 | ||||||||
\(936\) | − | 5.54733e11i | − | 0.722737i | ||||||
\(937\) | − | 7.02976e11i | − | 0.911974i | −0.889986 | − | 0.455987i | \(-0.849286\pi\) | ||
0.889986 | − | 0.455987i | \(-0.150714\pi\) | |||||||
\(938\) | 8.66651e11 | − | 1.80505e11i | 1.11952 | − | 0.233173i | ||||
\(939\) | 1.87618e11 | 0.241330 | ||||||||
\(940\) | −1.43761e11 | −0.184132 | ||||||||
\(941\) | − | 8.73030e11i | − | 1.11345i | −0.830697 | − | 0.556725i | \(-0.812058\pi\) | ||
0.830697 | − | 0.556725i | \(-0.187942\pi\) | |||||||
\(942\) | 7.59911e11 | 0.965071 | ||||||||
\(943\) | − | 1.18786e12i | − | 1.50217i | ||||||
\(944\) | 9.32238e10i | 0.117392i | ||||||||
\(945\) | 1.21985e11 | − | 2.54069e10i | 0.152961 | − | 0.0318585i | ||||
\(946\) | 7.89061e10 | 0.0985249 | ||||||||
\(947\) | 8.59495e11 | 1.06867 | 0.534335 | − | 0.845273i | \(-0.320562\pi\) | ||||
0.534335 | + | 0.845273i | \(0.320562\pi\) | |||||||
\(948\) | 2.53893e11i | 0.314353i | ||||||||
\(949\) | −1.34908e11 | −0.166331 | ||||||||
\(950\) | − | 9.45353e11i | − | 1.16065i | ||||||
\(951\) | 6.93478e11i | 0.847834i | ||||||||
\(952\) | 3.52092e10 | + | 1.69049e11i | 0.0428656 | + | 0.205809i | ||||
\(953\) | −3.61718e11 | −0.438529 | −0.219264 | − | 0.975665i | \(-0.570366\pi\) | ||||
−0.219264 | + | 0.975665i | \(0.570366\pi\) | |||||||
\(954\) | −8.51513e11 | −1.02801 | ||||||||
\(955\) | − | 7.38878e10i | − | 0.0888299i | ||||||
\(956\) | −6.63017e11 | −0.793767 | ||||||||
\(957\) | 9.36847e11i | 1.11692i | ||||||||
\(958\) | − | 5.71343e9i | − | 0.00678320i | ||||||
\(959\) | 3.21929e11 | − | 6.70510e10i | 0.380615 | − | 0.0792740i | ||||
\(960\) | 3.79269e10 | 0.0446542 | ||||||||
\(961\) | −5.38293e11 | −0.631139 | ||||||||
\(962\) | − | 5.35333e10i | − | 0.0625063i | ||||||
\(963\) | 6.73732e11 | 0.783397 | ||||||||
\(964\) | 1.94544e10i | 0.0225273i | ||||||||
\(965\) | − | 2.39581e8i | − | 0.000276276i | ||||||
\(966\) | −2.03916e11 | − | 9.79054e11i | −0.234176 | − | 1.12434i | ||||
\(967\) | 7.03562e11 | 0.804631 | 0.402315 | − | 0.915501i | \(-0.368206\pi\) | ||||
0.402315 | + | 0.915501i | \(0.368206\pi\) | |||||||
\(968\) | 1.41851e11 | 0.161559 | ||||||||
\(969\) | − | 1.41761e12i | − | 1.60791i | ||||||
\(970\) | −2.37925e10 | −0.0268753 | ||||||||
\(971\) | 8.72568e11i | 0.981572i | 0.871280 | + | 0.490786i | \(0.163290\pi\) | ||||
−0.871280 | + | 0.490786i | \(0.836710\pi\) | |||||||
\(972\) | − | 5.63492e11i | − | 0.631281i | ||||||
\(973\) | −8.36124e10 | − | 4.01445e11i | −0.0932866 | − | 0.447893i | ||||
\(974\) | −4.22488e11 | −0.469439 | ||||||||
\(975\) | 1.90143e12 | 2.10408 | ||||||||
\(976\) | 1.70796e11i | 0.188226i | ||||||||
\(977\) | 1.52543e12 | 1.67422 | 0.837111 | − | 0.547033i | \(-0.184243\pi\) | ||||
0.837111 | + | 0.547033i | \(0.184243\pi\) | |||||||
\(978\) | 1.99167e12i | 2.17702i | ||||||||
\(979\) | 3.74171e11i | 0.407323i | ||||||||
\(980\) | −4.21307e10 | − | 9.67527e10i | −0.0456767 | − | 0.104896i | ||||
\(981\) | −4.93188e11 | −0.532520 | ||||||||
\(982\) | −8.26841e10 | −0.0889152 | ||||||||
\(983\) | − | 1.55846e10i | − | 0.0166910i | −0.999965 | − | 0.00834548i | \(-0.997344\pi\) | ||
0.999965 | − | 0.00834548i | \(-0.00265648\pi\) | |||||||
\(984\) | 7.47206e11 | 0.797003 | ||||||||
\(985\) | 4.01205e10i | 0.0426208i | ||||||||
\(986\) | 3.85803e11i | 0.408186i | ||||||||
\(987\) | −2.33440e12 | + | 4.86205e11i | −2.45984 | + | 0.512332i | ||||
\(988\) | 1.17361e12 | 1.23168 | ||||||||
\(989\) | −1.88193e11 | −0.196706 | ||||||||
\(990\) | 1.64628e11i | 0.171381i | ||||||||
\(991\) | −1.08092e12 | −1.12073 | −0.560364 | − | 0.828246i | \(-0.689339\pi\) | ||||
−0.560364 | + | 0.828246i | \(0.689339\pi\) | |||||||
\(992\) | − | 2.18634e11i | − | 0.225772i | ||||||
\(993\) | − | 3.21079e11i | − | 0.330229i | ||||||
\(994\) | −3.57754e11 | + | 7.45126e10i | −0.366470 | + | 0.0763280i | ||||
\(995\) | 1.54665e11 | 0.157798 | ||||||||
\(996\) | −7.20746e11 | −0.732394 | ||||||||
\(997\) | 1.06050e12i | 1.07332i | 0.843799 | + | 0.536659i | \(0.180314\pi\) | ||||
−0.843799 | + | 0.536659i | \(0.819686\pi\) | |||||||
\(998\) | −1.08816e12 | −1.09691 | ||||||||
\(999\) | 4.22720e10i | 0.0424415i |
(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 | 14.9.b.a.13.2 | yes | 4 | |
3.2 | odd | 2 | 126.9.c.a.55.4 | 4 | |||
4.3 | odd | 2 | 112.9.c.c.97.1 | 4 | |||
5.2 | odd | 4 | 350.9.d.a.349.4 | 8 | |||
5.3 | odd | 4 | 350.9.d.a.349.5 | 8 | |||
5.4 | even | 2 | 350.9.b.a.251.3 | 4 | |||
7.2 | even | 3 | 98.9.d.a.31.3 | 8 | |||
7.3 | odd | 6 | 98.9.d.a.19.3 | 8 | |||
7.4 | even | 3 | 98.9.d.a.19.4 | 8 | |||
7.5 | odd | 6 | 98.9.d.a.31.4 | 8 | |||
7.6 | odd | 2 | inner | 14.9.b.a.13.1 | ✓ | 4 | |
21.20 | even | 2 | 126.9.c.a.55.3 | 4 | |||
28.27 | even | 2 | 112.9.c.c.97.4 | 4 | |||
35.13 | even | 4 | 350.9.d.a.349.8 | 8 | |||
35.27 | even | 4 | 350.9.d.a.349.1 | 8 | |||
35.34 | odd | 2 | 350.9.b.a.251.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.9.b.a.13.1 | ✓ | 4 | 7.6 | odd | 2 | inner | |
14.9.b.a.13.2 | yes | 4 | 1.1 | even | 1 | trivial | |
98.9.d.a.19.3 | 8 | 7.3 | odd | 6 | |||
98.9.d.a.19.4 | 8 | 7.4 | even | 3 | |||
98.9.d.a.31.3 | 8 | 7.2 | even | 3 | |||
98.9.d.a.31.4 | 8 | 7.5 | odd | 6 | |||
112.9.c.c.97.1 | 4 | 4.3 | odd | 2 | |||
112.9.c.c.97.4 | 4 | 28.27 | even | 2 | |||
126.9.c.a.55.3 | 4 | 21.20 | even | 2 | |||
126.9.c.a.55.4 | 4 | 3.2 | odd | 2 | |||
350.9.b.a.251.3 | 4 | 5.4 | even | 2 | |||
350.9.b.a.251.4 | 4 | 35.34 | odd | 2 | |||
350.9.d.a.349.1 | 8 | 35.27 | even | 4 | |||
350.9.d.a.349.4 | 8 | 5.2 | odd | 4 | |||
350.9.d.a.349.5 | 8 | 5.3 | odd | 4 | |||
350.9.d.a.349.8 | 8 | 35.13 | even | 4 |