Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,12,Mod(1,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(147.521890667\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 192.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1190.00 | −0.170299 | −0.0851495 | − | 0.996368i | \(-0.527137\pi\) | ||||
−0.0851495 | + | 0.996368i | \(0.527137\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18480.0 | 0.415588 | 0.207794 | − | 0.978173i | \(-0.433372\pi\) | ||||
0.207794 | + | 0.978173i | \(0.433372\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −135884. | −0.254395 | −0.127197 | − | 0.991877i | \(-0.540598\pi\) | ||||
−0.127197 | + | 0.991877i | \(0.540598\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 848186. | 0.633582 | 0.316791 | − | 0.948495i | \(-0.397395\pi\) | ||||
0.316791 | + | 0.948495i | \(0.397395\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −289170. | −0.0983221 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.12461e6 | −1.21700 | −0.608502 | − | 0.793553i | \(-0.708229\pi\) | ||||
−0.608502 | + | 0.793553i | \(0.708229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.04632e6 | 0.467552 | 0.233776 | − | 0.972291i | \(-0.424892\pi\) | ||||
0.233776 | + | 0.972291i | \(0.424892\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.49064e6 | 0.239940 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.48912e7 | −0.482422 | −0.241211 | − | 0.970473i | \(-0.577545\pi\) | ||||
−0.241211 | + | 0.970473i | \(0.577545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.74120e7 | −0.970998 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.15001e8 | 1.04115 | 0.520576 | − | 0.853815i | \(-0.325717\pi\) | ||||
0.520576 | + | 0.853815i | \(0.325717\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.63991e8 | −1.02880 | −0.514398 | − | 0.857551i | \(-0.671985\pi\) | ||||
−0.514398 | + | 0.857551i | \(0.671985\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.30198e7 | −0.146875 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.19912e7 | −0.0707742 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.23622e8 | 0.530158 | 0.265079 | − | 0.964227i | \(-0.414602\pi\) | ||||
0.265079 | + | 0.964227i | \(0.414602\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.06109e8 | 0.365799 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.05358e8 | 0.142023 | 0.0710113 | − | 0.997476i | \(-0.477377\pi\) | ||||
0.0710113 | + | 0.997476i | \(0.477377\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.41948e9 | −1.47249 | −0.736244 | − | 0.676717i | \(-0.763402\pi\) | ||||
−0.736244 | + | 0.676717i | \(0.763402\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.02683e7 | −0.0567663 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.46928e9 | 1.57048 | 0.785239 | − | 0.619193i | \(-0.212540\pi\) | ||||
0.785239 | + | 0.619193i | \(0.212540\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.63582e9 | −0.827287 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.73128e9 | −0.702637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.83705e8 | 0.158878 | 0.0794389 | − | 0.996840i | \(-0.474687\pi\) | ||||
0.0794389 | + | 0.996840i | \(0.474687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.61702e8 | 0.0433232 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.22625e9 | 0.269941 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.15184e9 | −1.12026 | −0.560130 | − | 0.828404i | \(-0.689249\pi\) | ||||
−0.560130 | + | 0.828404i | \(0.689249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.53273e9 | 1.14193 | 0.570964 | − | 0.820975i | \(-0.306570\pi\) | ||||
0.570964 | + | 0.820975i | \(0.306570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.09123e9 | 0.138529 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00934e9 | −0.107898 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.76495e9 | 0.793118 | 0.396559 | − | 0.918009i | \(-0.370204\pi\) | ||||
0.396559 | + | 0.918009i | \(0.370204\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.61857e9 | −0.278527 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.04016e10 | −0.684196 | −0.342098 | − | 0.939664i | \(-0.611137\pi\) | ||||
−0.342098 | + | 0.939664i | \(0.611137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.17384e10 | −1.79188 | −0.895941 | − | 0.444174i | \(-0.853497\pi\) | ||||
−0.895941 | + | 0.444174i | \(0.853497\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.15211e10 | −0.560606 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.51114e9 | −0.105723 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.98800e10 | −1.45816 | −0.729082 | − | 0.684426i | \(-0.760053\pi\) | ||||
−0.729082 | + | 0.684426i | \(0.760053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.35133e10 | −0.376559 | −0.188279 | − | 0.982116i | \(-0.560291\pi\) | ||||
−0.188279 | + | 0.982116i | \(0.560291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.47828e9 | 0.207254 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.79453e10 | 0.601109 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.15145e10 | 1.54735 | 0.773677 | − | 0.633580i | \(-0.218415\pi\) | ||||
0.773677 | + | 0.633580i | \(0.218415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.56745e10 | 0.263309 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.98497e10 | −0.593976 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00512e9 | −0.0796236 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.07830e10 | 0.363971 | 0.181986 | − | 0.983301i | \(-0.441748\pi\) | ||||
0.181986 | + | 0.983301i | \(0.441748\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.02381e9 | −0.0847983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.61449e11 | −1.52850 | −0.764252 | − | 0.644918i | \(-0.776892\pi\) | ||||
−0.764252 | + | 0.644918i | \(0.776892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.18595e10 | −0.440782 | −0.220391 | − | 0.975412i | \(-0.570733\pi\) | ||||
−0.220391 | + | 0.975412i | \(0.570733\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.34386e9 | −0.0408615 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.20810e11 | 0.832709 | 0.416355 | − | 0.909202i | \(-0.363307\pi\) | ||||
0.416355 | + | 0.909202i | \(0.363307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.25401e10 | −0.264821 | −0.132410 | − | 0.991195i | \(-0.542272\pi\) | ||||
−0.132410 | + | 0.991195i | \(0.542272\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.43402e10 | 0.306087 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.25294e10 | 0.166090 | 0.0830452 | − | 0.996546i | \(-0.473535\pi\) | ||||
0.0830452 | + | 0.996546i | \(0.473535\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.77206e10 | 0.0821560 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.00845e10 | 0.211194 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.31663e11 | −0.505772 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66847e11 | −0.935283 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.56021e10 | 0.0819968 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.14526e11 | 0.335659 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.71230e11 | 0.997063 | 0.498532 | − | 0.866872i | \(-0.333873\pi\) | ||||
0.498532 | + | 0.866872i | \(0.333873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.44933e11 | −0.850141 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.37142e11 | 1.21646 | 0.608229 | − | 0.793762i | \(-0.291880\pi\) | ||||
0.608229 | + | 0.793762i | \(0.291880\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.32559e10 | 0.194309 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.70752e10 | −0.0327740 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.62059e11 | −0.640938 | −0.320469 | − | 0.947259i | \(-0.603841\pi\) | ||||
−0.320469 | + | 0.947259i | \(0.603841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.19954e11 | −1.17686 | −0.588428 | − | 0.808550i | \(-0.700253\pi\) | ||||
−0.588428 | + | 0.808550i | \(0.700253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00034e11 | 0.906715 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.15255e11 | −0.161180 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.36852e11 | −0.177307 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.97503e11 | −0.477634 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.19007e12 | −1.32754 | −0.663769 | − | 0.747938i | \(-0.731044\pi\) | ||||
−0.663769 | + | 0.747938i | \(0.731044\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.50709e12 | 1.56231 | 0.781153 | − | 0.624339i | \(-0.214632\pi\) | ||||
0.781153 | + | 0.624339i | \(0.214632\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.20701e11 | −0.405668 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.95149e11 | 0.175203 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.52866e12 | −1.27898 | −0.639490 | − | 0.768800i | \(-0.720854\pi\) | ||||
−0.639490 | + | 0.768800i | \(0.720854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.17540e11 | 0.0917282 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.75190e11 | −0.200489 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.53695e12 | −1.04623 | −0.523116 | − | 0.852261i | \(-0.675231\pi\) | ||||
−0.523116 | + | 0.852261i | \(0.675231\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.92936e10 | 0.0250127 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.64628e11 | −0.574671 | −0.287336 | − | 0.957830i | \(-0.592769\pi\) | ||||
−0.287336 | + | 0.957830i | \(0.592769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.07274e12 | −0.598574 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.97980e11 | 0.155851 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.93014e12 | −0.946966 | −0.473483 | − | 0.880803i | \(-0.657003\pi\) | ||||
−0.473483 | + | 0.880803i | \(0.657003\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.76174e11 | −0.403535 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.49490e12 | −0.646783 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.70894e12 | 0.695080 | 0.347540 | − | 0.937665i | \(-0.387017\pi\) | ||||
0.347540 | + | 0.937665i | \(0.387017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.30945e11 | −0.0501021 | −0.0250511 | − | 0.999686i | \(-0.507975\pi\) | ||||
−0.0250511 | + | 0.999686i | \(0.507975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.83045e12 | 0.659292 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.66110e11 | −0.0902854 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.68120e11 | 0.309600 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.65168e11 | 0.0799799 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.05880e12 | −1.44000 | −0.720002 | − | 0.693972i | \(-0.755859\pi\) | ||||
−0.720002 | + | 0.693972i | \(0.755859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.84580e12 | −1.30257 | −0.651283 | − | 0.758835i | \(-0.725769\pi\) | ||||
−0.651283 | + | 0.758835i | \(0.725769\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.45270e11 | −0.0622951 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.83197e12 | −1.88064 | −0.940322 | − | 0.340286i | \(-0.889476\pi\) | ||||
−0.940322 | + | 0.340286i | \(0.889476\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.02421e12 | −1.14124 | −0.570618 | − | 0.821216i | \(-0.693296\pi\) | ||||
−0.570618 | + | 0.821216i | \(0.693296\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.12988e12 | 0.457907 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.12522e12 | 0.432690 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.25376e11 | −0.0241863 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.79312e11 | −0.160807 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.85714e11 | −0.118943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.40292e12 | 0.889355 | 0.444677 | − | 0.895691i | \(-0.353318\pi\) | ||||
0.444677 | + | 0.895691i | \(0.353318\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.52760e12 | −0.395021 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.68918e12 | 0.250763 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.03055e12 | −0.427555 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.71243e12 | −1.03454 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.04299e12 | −0.771071 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.65520e12 | 0.322419 | 0.161210 | − | 0.986920i | \(-0.448460\pi\) | ||||
0.161210 | + | 0.986920i | \(0.448460\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.79963e12 | −0.323666 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.00927e13 | −1.11138 | −0.555691 | − | 0.831389i | \(-0.687546\pi\) | ||||
−0.555691 | + | 0.831389i | \(0.687546\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.75264e12 | −0.918425 | −0.459213 | − | 0.888326i | \(-0.651868\pi\) | ||||
−0.459213 | + | 0.888326i | \(0.651868\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.10206e11 | −0.0610395 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.29016e12 | −0.313877 | −0.156938 | − | 0.987608i | \(-0.550162\pi\) | ||||
−0.156938 | + | 0.987608i | \(0.550162\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.93844e12 | −0.267451 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.69084e12 | −0.841871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.73649e13 | 1.44040 | 0.720200 | − | 0.693767i | \(-0.244050\pi\) | ||||
0.720200 | + | 0.693767i | \(0.244050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.88851e13 | −1.49632 | −0.748162 | − | 0.663516i | \(-0.769063\pi\) | ||||
−0.748162 | + | 0.663516i | \(0.769063\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.94662e12 | 0.140886 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.28021e12 | 0.296232 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.28374e12 | −0.217406 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.73484e12 | 0.236628 | 0.118314 | − | 0.992976i | \(-0.462251\pi\) | ||||
0.118314 | + | 0.992976i | \(0.462251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.02348e12 | 0.122726 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.06022e12 | 0.119658 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.55617e13 | −1.42219 | −0.711096 | − | 0.703095i | \(-0.751801\pi\) | ||||
−0.711096 | + | 0.703095i | \(0.751801\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.13254e12 | 0.220327 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.79071e12 | 0.347051 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.71976e12 | 0.182288 | 0.0911441 | − | 0.995838i | \(-0.470948\pi\) | ||||
0.0911441 | + | 0.995838i | \(0.470948\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.75609e11 | −0.0270567 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.98080e13 | 0.893366 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.32714e13 | 1.00736 | 0.503680 | − | 0.863890i | \(-0.331979\pi\) | ||||
0.503680 | + | 0.863890i | \(0.331979\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.69620e12 | −0.0704931 | −0.0352465 | − | 0.999379i | \(-0.511222\pi\) | ||||
−0.0352465 | + | 0.999379i | \(0.511222\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.80890e12 | 0.152021 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.44254e12 | 0.247017 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.22077e13 | −1.18664 | −0.593322 | − | 0.804965i | \(-0.702184\pi\) | ||||
−0.593322 | + | 0.804965i | \(0.702184\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.68348e12 | −0.342932 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.19732e13 | −0.748185 | −0.374092 | − | 0.927391i | \(-0.622046\pi\) | ||||
−0.374092 | + | 0.927391i | \(0.622046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.26529e12 | −0.205171 | −0.102585 | − | 0.994724i | \(-0.532711\pi\) | ||||
−0.102585 | + | 0.994724i | \(0.532711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.45924e12 | −0.0459707 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.94702e12 | 0.0590229 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.64881e13 | 0.481097 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.48028e12 | 0.210139 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.30466e12 | −0.116457 | −0.0582286 | − | 0.998303i | \(-0.518545\pi\) | ||||
−0.0582286 | + | 0.998303i | \(0.518545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.32069e12 | 0.190779 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.94979e12 | −0.0489583 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.26305e13 | −0.305654 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.62319e13 | −0.611948 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.92320e13 | −0.882482 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.96395e12 | −0.194469 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.49844e13 | −0.313601 | −0.156800 | − | 0.987630i | \(-0.550118\pi\) | ||||
−0.156800 | + | 0.987630i | \(0.550118\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.26019e13 | −0.254486 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.92805e13 | 0.375783 | 0.187891 | − | 0.982190i | \(-0.439835\pi\) | ||||
0.187891 | + | 0.982190i | \(0.439835\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.38955e13 | 1.76665 | 0.883325 | − | 0.468760i | \(-0.155299\pi\) | ||||
0.883325 | + | 0.468760i | \(0.155299\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.29856e12 | −0.0235914 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.75293e13 | 0.307566 | 0.153783 | − | 0.988105i | \(-0.450854\pi\) | ||||
0.153783 | + | 0.988105i | \(0.450854\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.56268e13 | −0.264864 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.93569e13 | 0.480765 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.59530e13 | −0.569012 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.02142e13 | −0.615207 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.03372e13 | −0.152894 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.56322e13 | 0.652671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.01778e13 | 0.279139 | 0.139569 | − | 0.990212i | \(-0.455428\pi\) | ||||
0.139569 | + | 0.990212i | \(0.455428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.32047e13 | 0.176719 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.04303e13 | −0.135067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.21846e13 | 0.278027 | 0.139014 | − | 0.990290i | \(-0.455607\pi\) | ||||
0.139014 | + | 0.990290i | \(0.455607\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.90464e12 | 0.0958923 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.22837e13 | 0.261721 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.67709e13 | −0.759398 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.30610e12 | 0.0474328 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.47701e13 | 0.797840 | 0.398920 | − | 0.916986i | \(-0.369385\pi\) | ||||
0.398920 | + | 0.916986i | \(0.369385\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.57514e14 | 1.62847 | 0.814237 | − | 0.580533i | \(-0.197156\pi\) | ||||
0.814237 | + | 0.580533i | \(0.197156\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.21705e13 | 0.121933 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.54892e13 | −0.247512 | −0.123756 | − | 0.992313i | \(-0.539494\pi\) | ||||
−0.123756 | + | 0.992313i | \(0.539494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.23779e13 | 0.116518 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.19940e13 | −0.292007 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.41138e12 | 0.0832979 | 0.0416489 | − | 0.999132i | \(-0.486739\pi\) | ||||
0.0416489 | + | 0.999132i | \(0.486739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.10250e13 | −0.781395 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.48439e13 | −0.539986 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.77687e13 | 0.305155 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.24601e14 | −0.976922 | −0.488461 | − | 0.872586i | \(-0.662441\pi\) | ||||
−0.488461 | + | 0.872586i | \(0.662441\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.22130e12 | 0.0473409 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.93887e12 | 0.0660277 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.05385e14 | 1.47289 | 0.736446 | − | 0.676496i | \(-0.236502\pi\) | ||||
0.736446 | + | 0.676496i | \(0.236502\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.78298e13 | 0.193793 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.75425e13 | 0.659655 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.18102e13 | −0.471705 | −0.235852 | − | 0.971789i | \(-0.575788\pi\) | ||||
−0.235852 | + | 0.971789i | \(0.575788\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.02089e13 | 0.575655 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.94282e14 | 1.82461 | 0.912307 | − | 0.409508i | \(-0.134300\pi\) | ||||
0.912307 | + | 0.409508i | \(0.134300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.98825e12 | 0.0180046 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.38186e13 | −0.490829 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.34095e14 | 0.763291 | 0.381646 | − | 0.924309i | \(-0.375357\pi\) | ||||
0.381646 | + | 0.924309i | \(0.375357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.06094e14 | 0.587109 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.30525e14 | 0.702322 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.74572e13 | 0.248324 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.17524e14 | 0.598109 | 0.299054 | − | 0.954236i | \(-0.403329\pi\) | ||||
0.299054 | + | 0.954236i | \(0.403329\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.26612e13 | 0.112184 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.56980e14 | 1.23767 | 0.618835 | − | 0.785521i | \(-0.287605\pi\) | ||||
0.618835 | + | 0.785521i | \(0.287605\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.39094e14 | −0.651827 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.14927e12 | −0.0189221 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.03867e13 | −0.134870 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.40372e13 | −0.0606460 | −0.0303230 | − | 0.999540i | \(-0.509654\pi\) | ||||
−0.0303230 | + | 0.999540i | \(0.509654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.79804e13 | −0.370046 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.13686e14 | −0.465567 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.60809e13 | 0.0641275 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.74949e14 | −0.679458 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.05803e13 | 0.342655 | 0.171327 | − | 0.985214i | \(-0.445194\pi\) | ||||
0.171327 | + | 0.985214i | \(0.445194\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.25794e13 | 0.156909 | 0.0784546 | − | 0.996918i | \(-0.475001\pi\) | ||||
0.0784546 | + | 0.996918i | \(0.475001\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.45808e14 | 0.523492 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.37792e14 | 1.18171 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.39205e14 | 0.474571 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.80069e13 | −0.0930573 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.45393e14 | −0.794763 | −0.397381 | − | 0.917654i | \(-0.630081\pi\) | ||||
−0.397381 | + | 0.917654i | \(0.630081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.45088e14 | 1.08955 | 0.544775 | − | 0.838583i | \(-0.316615\pi\) | ||||
0.544775 | + | 0.838583i | \(0.316615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.32549e13 | −0.102368 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.51458e13 | −0.225557 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.66129e14 | 0.486283 | 0.243142 | − | 0.969991i | \(-0.421822\pi\) | ||||
0.243142 | + | 0.969991i | \(0.421822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.65933e13 | −0.275762 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.76583e14 | 1.60562 | 0.802808 | − | 0.596238i | \(-0.203338\pi\) | ||||
0.802808 | + | 0.596238i | \(0.203338\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.70023e13 | −0.263513 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.89186e14 | −0.766454 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.12410e13 | 0.0807923 | 0.0403962 | − | 0.999184i | \(-0.487138\pi\) | ||||
0.0403962 | + | 0.999184i | \(0.487138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.43165e13 | −0.0361298 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.66223e14 | 0.901998 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.86526e13 | −0.0448412 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.36591e13 | −0.196324 | −0.0981622 | − | 0.995170i | \(-0.531296\pi\) | ||||
−0.0981622 | + | 0.995170i | \(0.531296\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.02230e14 | −0.234212 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.12974e14 | 0.700090 | 0.350045 | − | 0.936733i | \(-0.386166\pi\) | ||||
0.350045 | + | 0.936733i | \(0.386166\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.73544e13 | 0.0379065 | 0.0189532 | − | 0.999820i | \(-0.493967\pi\) | ||||
0.0189532 | + | 0.999820i | \(0.493967\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.74211e13 | 0.101153 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.41703e14 | 1.33688 | 0.668439 | − | 0.743767i | \(-0.266963\pi\) | ||||
0.668439 | + | 0.743767i | \(0.266963\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.61976e14 | 0.329610 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.71465e14 | −0.738419 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.92884e14 | 0.374593 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.39256e14 | −0.453992 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.85623e13 | 0.0529593 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.54411e14 | −0.642187 | −0.321094 | − | 0.947047i | \(-0.604050\pi\) | ||||
−0.321094 | + | 0.947047i | \(0.604050\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.89673e14 | 0.335898 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.68711e13 | −0.115752 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.66318e13 | −0.0619839 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.20917e14 | −0.200022 | −0.100011 | − | 0.994986i | \(-0.531888\pi\) | ||||
−0.100011 | + | 0.994986i | \(0.531888\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.73479e14 | −0.604043 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.44195e14 | 0.386179 | 0.193090 | − | 0.981181i | \(-0.438149\pi\) | ||||
0.193090 | + | 0.981181i | \(0.438149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.19339e14 | −1.26708 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.54834e12 | 0.0144411 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.92222e14 | −0.284343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.60223e14 | −1.24468 | −0.622340 | − | 0.782747i | \(-0.713818\pi\) | ||||
−0.622340 | + | 0.782747i | \(0.713818\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.34405e14 | −0.331787 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.21648e15 | 1.68453 | 0.842266 | − | 0.539062i | \(-0.181221\pi\) | ||||
0.842266 | + | 0.539062i | \(0.181221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.92124e14 | 0.260303 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.60676e14 | −0.345587 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.57278e14 | −1.24191 | −0.620955 | − | 0.783846i | \(-0.713255\pi\) | ||||
−0.620955 | + | 0.783846i | \(0.713255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.86525e14 | −0.744684 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.24091e13 | 0.0899804 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.17129e13 | 0.0750647 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.35535e14 | −0.399521 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.69023e14 | −0.546731 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.39668e15 | −1.59400 | −0.797000 | − | 0.603979i | \(-0.793581\pi\) | ||||
−0.797000 | + | 0.603979i | \(0.793581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.14451e15 | −1.27897 | −0.639483 | − | 0.768805i | \(-0.720852\pi\) | ||||
−0.639483 | + | 0.768805i | \(0.720852\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.12910e14 | −0.232981 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.16837e15 | 1.25205 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.31061e14 | −0.767269 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.63260e14 | −0.373420 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.93634e13 | 0.0899830 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.43764e14 | −0.141809 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.15272e14 | 0.401305 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.22281e14 | 0.210458 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.32189e14 | 0.864807 | 0.432403 | − | 0.901680i | \(-0.357666\pi\) | ||||
0.432403 | + | 0.901680i | \(0.357666\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.18196e13 | −0.0289265 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.06227e13 | 0.0450987 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.90223e13 | 0.0602642 | 0.0301321 | − | 0.999546i | \(-0.490407\pi\) | ||||
0.0301321 | + | 0.999546i | \(0.490407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.44800e14 | 0.380642 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.80333e14 | 0.486792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.36983e14 | −0.605995 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.46648e13 | −0.0521263 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.24654e14 | 0.177546 | 0.0887728 | − | 0.996052i | \(-0.471706\pi\) | ||||
0.0887728 | + | 0.996052i | \(0.471706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.20398e15 | −0.932941 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.35253e14 | 0.178747 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.12470e15 | −1.58307 | −0.791537 | − | 0.611122i | \(-0.790719\pi\) | ||||
−0.791537 | + | 0.611122i | \(0.790719\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.87100e13 | −0.0282850 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.44358e13 | 0.0461764 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.52164e15 | −1.77241 | −0.886206 | − | 0.463291i | \(-0.846669\pi\) | ||||
−0.886206 | + | 0.463291i | \(0.846669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.83532e15 | 1.95481 | 0.977403 | − | 0.211386i | \(-0.0677978\pi\) | ||||
0.977403 | + | 0.211386i | \(0.0677978\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.22929e15 | −0.831387 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.06023e14 | 0.468431 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.62921e15 | −1.06050 | −0.530250 | − | 0.847842i | \(-0.677902\pi\) | ||||
−0.530250 | + | 0.847842i | \(0.677902\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.17753e15 | −0.752037 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.49726e14 | −0.156493 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.57278e13 | −0.0404177 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.96006e13 | −0.0359661 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.99007e15 | 1.77081 | 0.885404 | − | 0.464822i | \(-0.153882\pi\) | ||||
0.885404 | + | 0.464822i | \(0.153882\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.27548e14 | −0.481016 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.90317e15 | −1.08579 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.26562e14 | 0.126878 | 0.0634389 | − | 0.997986i | \(-0.479793\pi\) | ||||
0.0634389 | + | 0.997986i | \(0.479793\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.56679e14 | 0.0861324 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.22088e15 | −0.658893 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.50028e15 | 1.85462 | 0.927311 | − | 0.374293i | \(-0.122114\pi\) | ||||
0.927311 | + | 0.374293i | \(0.122114\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.20578e15 | −0.627275 | −0.313638 | − | 0.949543i | \(-0.601548\pi\) | ||||
−0.313638 | + | 0.949543i | \(0.601548\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.17561e14 | 0.264373 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.17548e14 | 0.159278 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.22942e15 | −1.09813 | −0.549067 | − | 0.835779i | \(-0.685017\pi\) | ||||
−0.549067 | + | 0.835779i | \(0.685017\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.16430e14 | 0.249814 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.09441e15 | 0.995026 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.15369e15 | −1.47159 | −0.735795 | − | 0.677204i | \(-0.763191\pi\) | ||||
−0.735795 | + | 0.677204i | \(0.763191\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.04665e13 | −0.0139640 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.64703e15 | 0.741539 | 0.370770 | − | 0.928725i | \(-0.379094\pi\) | ||||
0.370770 | + | 0.928725i | \(0.379094\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.94862e14 | 0.0861845 | 0.0430922 | − | 0.999071i | \(-0.486279\pi\) | ||||
0.0430922 | + | 0.999071i | \(0.486279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.13673e14 | −0.0928422 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.50639e15 | 0.643062 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.17875e15 | 0.913836 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.66628e14 | −0.0686717 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.59322e15 | −0.645204 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.38596e15 | −0.551555 | −0.275777 | − | 0.961222i | \(-0.588935\pi\) | ||||
−0.275777 | + | 0.961222i | \(0.588935\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.31291e15 | 0.513469 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.41764e14 | −0.169799 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.38748e15 | −0.524154 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.14206e14 | −0.228065 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.58508e15 | −0.943529 | −0.471764 | − | 0.881725i | \(-0.656383\pi\) | ||||
−0.471764 | + | 0.881725i | \(0.656383\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.96300e15 | −1.78067 | −0.890337 | − | 0.455303i | \(-0.849531\pi\) | ||||
−0.890337 | + | 0.455303i | \(0.849531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.10470e14 | 0.144778 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.12484e15 | 1.08356 | 0.541782 | − | 0.840519i | \(-0.317750\pi\) | ||||
0.541782 | + | 0.840519i | \(0.317750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.35937e14 | 0.284989 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.36423e14 | −0.246849 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.29342e15 | −1.41508 | −0.707540 | − | 0.706674i | \(-0.750195\pi\) | ||||
−0.707540 | + | 0.706674i | \(0.750195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.39199e14 | −0.207161 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.87412e15 | −0.597294 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.93625e15 | 1.54713 | 0.773566 | − | 0.633716i | \(-0.218471\pi\) | ||||
0.773566 | + | 0.633716i | \(0.218471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.32360e14 | 0.287393 | 0.143696 | − | 0.989622i | \(-0.454101\pi\) | ||||
0.143696 | + | 0.989622i | \(0.454101\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.46845e15 | −0.445178 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.10975e14 | −0.0330906 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.71251e15 | −0.502275 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.45214e14 | 0.186149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.02358e15 | −0.290501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.51685e15 | 0.423507 | 0.211753 | − | 0.977323i | \(-0.432083\pi\) | ||||
0.211753 | + | 0.977323i | \(0.432083\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.80311e14 | −0.186869 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.42102e15 | 1.73527 | 0.867634 | − | 0.497203i | \(-0.165640\pi\) | ||||
0.867634 | + | 0.497203i | \(0.165640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.68870e14 | 0.151262 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.45252e15 | −0.641657 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.67035e15 | 0.944916 | 0.472458 | − | 0.881353i | \(-0.343367\pi\) | ||||
0.472458 | + | 0.881353i | \(0.343367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.30850e14 | 0.109151 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.12689e15 | −0.530253 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.10272e14 | 0.100662 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.15581e15 | −0.520573 | −0.260286 | − | 0.965531i | \(-0.583817\pi\) | ||||
−0.260286 | + | 0.965531i | \(0.583817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.48280e14 | −0.0352411 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.56745e14 | 0.200417 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.50636e14 | −0.172842 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.99508e14 | −0.181217 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.84907e15 | 1.52821 | 0.764104 | − | 0.645094i | \(-0.223182\pi\) | ||||
0.764104 | + | 0.645094i | \(0.223182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12847e15 | 0.247876 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.14041e14 | −0.154413 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.98357e15 | −0.635227 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.12308e14 | 0.191244 | 0.0956218 | − | 0.995418i | \(-0.469516\pi\) | ||||
0.0956218 | + | 0.995418i | \(0.469516\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.35488e15 | −0.486055 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.44202e15 | 0.496314 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.37153e14 | 0.0274488 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.21966e15 | 0.831615 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.99411e15 | −0.775195 | −0.387597 | − | 0.921829i | \(-0.626695\pi\) | ||||
−0.387597 | + | 0.921829i | \(0.626695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.58364e14 | −0.183184 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.58908e15 | −0.863903 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.45245e15 | −1.01096 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.31749e15 | 0.605858 | 0.302929 | − | 0.953013i | \(-0.402036\pi\) | ||||
0.302929 | + | 0.953013i | \(0.402036\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.01132e16 | 1.79202 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.60662e15 | 0.454994 | 0.227497 | − | 0.973779i | \(-0.426946\pi\) | ||||
0.227497 | + | 0.973779i | \(0.426946\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.73029e14 | 0.0813406 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.19102e15 | −0.201765 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.46259e15 | −1.24550 | −0.622752 | − | 0.782419i | \(-0.713985\pi\) | ||||
−0.622752 | + | 0.782419i | \(0.713985\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.04009e15 | 0.171030 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.12334e16 | 1.82001 | 0.910003 | − | 0.414602i | \(-0.136079\pi\) | ||||
0.910003 | + | 0.414602i | \(0.136079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.41618e15 | 0.226078 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.97948e14 | −0.125520 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.23258e15 | 0.346064 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.15071e15 | −0.634020 | −0.317010 | − | 0.948422i | \(-0.602679\pi\) | ||||
−0.317010 | + | 0.948422i | \(0.602679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.07565e14 | 0.136617 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.79344e15 | −0.266059 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.93212e15 | 1.45216 | 0.726080 | − | 0.687610i | \(-0.241340\pi\) | ||||
0.726080 | + | 0.687610i | \(0.241340\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.91705e14 | 0.0708558 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.37276e16 | 1.94974 | 0.974872 | − | 0.222765i | \(-0.0715082\pi\) | ||||
0.974872 | + | 0.222765i | \(0.0715082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.86140e14 | −0.110056 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.00634e14 | 0.0690848 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.21791e15 | −0.709777 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.85267e15 | 0.382522 | 0.191261 | − | 0.981539i | \(-0.438742\pi\) | ||||
0.191261 | + | 0.981539i | \(0.438742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.21150e15 | −0.821103 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.44730e15 | −0.709895 | −0.354948 | − | 0.934886i | \(-0.615501\pi\) | ||||
−0.354948 | + | 0.934886i | \(0.615501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.77512e15 | 0.998960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.00421e15 | 0.127206 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.31671e14 | 0.0664029 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.41341e15 | 0.174056 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.65014e15 | 0.200370 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.81911e15 | 0.217809 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.33904e15 | −0.394240 | −0.197120 | − | 0.980379i | \(-0.563159\pi\) | ||||
−0.197120 | + | 0.980379i | \(0.563159\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.03902e14 | 0.105244 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.01143e14 | 0.0690251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.38916e15 | 0.723504 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.39873e14 | −0.0156212 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.31632e15 | −0.365289 | −0.182644 | − | 0.983179i | \(-0.558466\pi\) | ||||
−0.182644 | + | 0.983179i | \(0.558466\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.75926e16 | −1.91128 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.81335e15 | 0.515785 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.31274e15 | 0.455846 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.27476e14 | 0.0341430 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.65495e15 | 0.581599 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.29315e15 | 0.841400 | 0.420700 | − | 0.907200i | \(-0.361785\pi\) | ||||
0.420700 | + | 0.907200i | \(0.361785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.67813e16 | 1.67962 | 0.839811 | − | 0.542879i | \(-0.182666\pi\) | ||||
0.839811 | + | 0.542879i | \(0.182666\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.12177e14 | −0.0406992 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.82897e15 | 0.178172 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.16312e15 | −0.688464 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.25562e14 | 0.0877696 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.03242e15 | 0.190163 | 0.0950813 | − | 0.995470i | \(-0.469689\pi\) | ||||
0.0950813 | + | 0.995470i | \(0.469689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.59910e15 | −0.516915 | −0.258457 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258457 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.56554e15 | 0.142615 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.09682e16 | 1.88486 | 0.942432 | − | 0.334399i | \(-0.108533\pi\) | ||||
0.942432 | + | 0.334399i | \(0.108533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.75589e16 | 1.55757 | 0.778783 | − | 0.627293i | \(-0.215837\pi\) | ||||
0.778783 | + | 0.627293i | \(0.215837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.82646e15 | −0.685109 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.16545e16 | 1.00681 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.14791e15 | 0.0978659 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.35309e15 | −0.197992 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.17140e14 | 0.0512499 | 0.0256249 | − | 0.999672i | \(-0.491842\pi\) | ||||
0.0256249 | + | 0.999672i | \(0.491842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.02480e15 | 0.0839965 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.33949e15 | −0.431965 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.27656e15 | 0.101937 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.93134e15 | −0.388692 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.52246e15 | −0.118455 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.33001e15 | −0.255760 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.46292e15 | −0.565834 | −0.282917 | − | 0.959144i | \(-0.591302\pi\) | ||||
−0.282917 | + | 0.959144i | \(0.591302\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.54596e14 | −0.0265412 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.16990e16 | −1.60341 | −0.801707 | − | 0.597717i | \(-0.796075\pi\) | ||||
−0.801707 | + | 0.597717i | \(0.796075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.63489e15 | 0.411077 | 0.205538 | − | 0.978649i | \(-0.434105\pi\) | ||||
0.205538 | + | 0.978649i | \(0.434105\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.73126e14 | 0.0340769 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.74062e15 | 0.621560 | 0.310780 | − | 0.950482i | \(-0.399410\pi\) | ||||
0.310780 | + | 0.950482i | \(0.399410\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.29686e15 | 0.161267 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.00661e15 | 0.277762 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.41906e15 | 0.370950 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.43431e15 | 0.502505 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.81771e15 | 0.121324 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.11644e15 | 0.139496 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.97195e15 | −0.388704 | −0.194352 | − | 0.980932i | \(-0.562260\pi\) | ||||
−0.194352 | + | 0.980932i | \(0.562260\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.04603e15 | −0.0672366 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.75775e15 | 0.238540 | 0.119270 | − | 0.992862i | \(-0.461945\pi\) | ||||
0.119270 | + | 0.992862i | \(0.461945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.34954e16 | −0.846061 | −0.423030 | − | 0.906115i | \(-0.639034\pi\) | ||||
−0.423030 | + | 0.906115i | \(0.639034\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.77893e15 | 0.110146 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.17242e16 | 1.94004 | 0.970020 | − | 0.243025i | \(-0.0781398\pi\) | ||||
0.970020 | + | 0.243025i | \(0.0781398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.86033e15 | 0.414367 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.73798e14 | −0.0282661 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.24608e16 | 0.734279 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.03364e15 | −0.118371 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.06922e15 | −0.176469 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.88591e16 | −1.07113 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.44621e15 | −0.193355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.37436e15 | −0.353308 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.55824e14 | 0.00853234 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.10011e16 | −0.595110 | −0.297555 | − | 0.954705i | \(-0.596171\pi\) | ||||
−0.297555 | + | 0.954705i | \(0.596171\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.53337e15 | −0.509501 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.68524e16 | −1.41786 | −0.708928 | − | 0.705281i | \(-0.750821\pi\) | ||||
−0.708928 | + | 0.705281i | \(0.750821\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.83624e15 | 0.0957946 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.17824e15 | −0.112277 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.92638e15 | 0.505545 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.69307e16 | 1.85846 | 0.929228 | − | 0.369506i | \(-0.120473\pi\) | ||||
0.929228 | + | 0.369506i | \(0.120473\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.64120e15 | −0.181058 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.82252e15 | −0.433494 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.06024e16 | −0.514783 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.06225e15 | −0.146927 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.35447e16 | −0.642221 | −0.321110 | − | 0.947042i | \(-0.604056\pi\) | ||||
−0.321110 | + | 0.947042i | \(0.604056\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.25485e15 | −0.386799 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.68517e15 | 0.216958 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.15206e15 | −0.0527245 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.01961e15 | −0.272270 | −0.136135 | − | 0.990690i | \(-0.543468\pi\) | ||||
−0.136135 | + | 0.990690i | \(0.543468\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.28166e16 | 1.01998 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.63146e15 | −0.381365 | −0.190683 | − | 0.981652i | \(-0.561070\pi\) | ||||
−0.190683 | + | 0.981652i | \(0.561070\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.56891e15 | −0.0685149 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.15550e14 | −0.0136205 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.74754e16 | −1.59890 | −0.799450 | − | 0.600733i | \(-0.794876\pi\) | ||||
−0.799450 | + | 0.600733i | \(0.794876\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.69201e16 | −1.13530 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.25961e15 | 0.177573 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.58712e16 | −1.47821 | −0.739104 | − | 0.673592i | \(-0.764751\pi\) | ||||
−0.739104 | + | 0.673592i | \(0.764751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.01997e15 | 0.245231 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.79732e15 | −0.152919 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.69085e15 | −0.266366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.48442e15 | 0.0584224 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.13373e15 | 0.277570 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.76650e15 | 0.221826 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.66314e16 | −0.632534 | −0.316267 | − | 0.948670i | \(-0.602429\pi\) | ||||
−0.316267 | + | 0.948670i | \(0.602429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.73658e15 | −0.328519 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.14015e15 | 0.116747 | 0.0583734 | − | 0.998295i | \(-0.481409\pi\) | ||||
0.0583734 | + | 0.998295i | \(0.481409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.33047e16 | −0.489087 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.77205e15 | −0.355190 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.43733e16 | −0.875980 | −0.437990 | − | 0.898980i | \(-0.644310\pi\) | ||||
−0.437990 | + | 0.898980i | \(0.644310\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.10765e16 | −0.393639 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.51195e15 | −0.0882736 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.37201e16 | −0.476775 | −0.238387 | − | 0.971170i | \(-0.576619\pi\) | ||||
−0.238387 | + | 0.971170i | \(0.576619\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.32004e15 | 0.320272 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.10886e16 | 0.376820 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.11377e16 | 0.710360 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.95853e16 | −0.983267 | −0.491633 | − | 0.870802i | \(-0.663600\pi\) | ||||
−0.491633 | + | 0.870802i | \(0.663600\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.90321e15 | 0.161161 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.97880e15 | 0.194351 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.90504e16 | 0.612465 | 0.306233 | − | 0.951957i | \(-0.400931\pi\) | ||||
0.306233 | + | 0.951957i | \(0.400931\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.20873e15 | 0.102029 |
(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 | 192.12.a.p.1.1 | 1 | ||
4.3 | odd | 2 | 192.12.a.f.1.1 | 1 | |||
8.3 | odd | 2 | 48.12.a.g.1.1 | 1 | |||
8.5 | even | 2 | 24.12.a.b.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 72.12.a.b.1.1 | 1 | |||
24.11 | even | 2 | 144.12.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.12.a.b.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
48.12.a.g.1.1 | 1 | 8.3 | odd | 2 | |||
72.12.a.b.1.1 | 1 | 24.5 | odd | 2 | |||
144.12.a.h.1.1 | 1 | 24.11 | even | 2 | |||
192.12.a.f.1.1 | 1 | 4.3 | odd | 2 | |||
192.12.a.p.1.1 | 1 | 1.1 | even | 1 | trivial |