Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,16,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(22.8309608160\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 | ||||||||
\(3\) | −2700.00 | −0.712778 | −0.356389 | − | 0.934338i | \(-0.615992\pi\) | ||||
−0.356389 | + | 0.934338i | \(0.615992\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −251890. | −1.44190 | −0.720951 | − | 0.692986i | \(-0.756295\pi\) | ||||
−0.720951 | + | 0.692986i | \(0.756295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.37407e6 | −0.630629 | −0.315315 | − | 0.948987i | \(-0.602110\pi\) | ||||
−0.315315 | + | 0.948987i | \(0.602110\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.05891e6 | −0.491947 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.32867e7 | 0.669745 | 0.334873 | − | 0.942263i | \(-0.391307\pi\) | ||||
0.334873 | + | 0.942263i | \(0.391307\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.23161e8 | −1.42838 | −0.714191 | − | 0.699951i | \(-0.753205\pi\) | ||||
−0.714191 | + | 0.699951i | \(0.753205\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.80103e8 | 1.02776 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.91654e8 | −0.113279 | −0.0566396 | − | 0.998395i | \(-0.518039\pi\) | ||||
−0.0566396 | + | 0.998395i | \(0.518039\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.51546e9 | 1.67222 | 0.836109 | − | 0.548563i | \(-0.184825\pi\) | ||||
0.836109 | + | 0.548563i | \(0.184825\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.70999e9 | 0.449499 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.38808e10 | −1.46248 | −0.731240 | − | 0.682120i | \(-0.761058\pi\) | ||||
−0.731240 | + | 0.682120i | \(0.761058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.29310e10 | 1.07908 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.78011e10 | 1.06343 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.76821e11 | 1.90348 | 0.951739 | − | 0.306909i | \(-0.0992946\pi\) | ||||
0.951739 | + | 0.306909i | \(0.0992946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.52007e11 | 0.992319 | 0.496160 | − | 0.868231i | \(-0.334743\pi\) | ||||
0.496160 | + | 0.868231i | \(0.334743\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.16874e11 | −0.477380 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46115e11 | 0.909306 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.15812e10 | 0.0373735 | 0.0186867 | − | 0.999825i | \(-0.494051\pi\) | ||||
0.0186867 | + | 0.999825i | \(0.494051\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.72536e11 | 1.01812 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.45334e11 | −0.196734 | −0.0983671 | − | 0.995150i | \(-0.531362\pi\) | ||||
−0.0983671 | + | 0.995150i | \(0.531362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.76996e12 | −1.55403 | −0.777017 | − | 0.629480i | \(-0.783268\pi\) | ||||
−0.777017 | + | 0.629480i | \(0.783268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.77807e12 | 0.709340 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.81177e12 | −0.809555 | −0.404777 | − | 0.914415i | \(-0.632651\pi\) | ||||
−0.404777 | + | 0.914415i | \(0.632651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.85949e12 | −0.602307 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.17465e11 | 0.0807429 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.49141e12 | −0.408256 | −0.204128 | − | 0.978944i | \(-0.565436\pi\) | ||||
−0.204128 | + | 0.978944i | \(0.565436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.09035e13 | −0.965707 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.75917e13 | −1.19192 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.58278e13 | 0.828000 | 0.414000 | − | 0.910277i | \(-0.364131\pi\) | ||||
0.414000 | + | 0.910277i | \(0.364131\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.46090e13 | −1.00258 | −0.501292 | − | 0.865278i | \(-0.667142\pi\) | ||||
−0.501292 | + | 0.865278i | \(0.667142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.69945e12 | 0.310236 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.14011e13 | 2.05959 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.07062e13 | 0.417388 | 0.208694 | − | 0.977981i | \(-0.433079\pi\) | ||||
0.208694 | + | 0.977981i | \(0.433079\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.44782e13 | 1.04242 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.19983e11 | 0.00939473 | 0.00469737 | − | 0.999989i | \(-0.498505\pi\) | ||||
0.00469737 | + | 0.999989i | \(0.498505\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.98830e13 | 0.316594 | 0.158297 | − | 0.987392i | \(-0.449400\pi\) | ||||
0.158297 | + | 0.987392i | \(0.449400\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.89137e13 | −0.769147 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.94791e13 | −0.422361 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.48101e14 | 0.867670 | 0.433835 | − | 0.900992i | \(-0.357160\pi\) | ||||
0.433835 | + | 0.900992i | \(0.357160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.47754e13 | −0.266040 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.02807e14 | 1.22484 | 0.612421 | − | 0.790532i | \(-0.290196\pi\) | ||||
0.612421 | + | 0.790532i | \(0.290196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82756e13 | 0.163338 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.77416e14 | −1.35676 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.96151e14 | −1.18902 | −0.594509 | − | 0.804089i | \(-0.702654\pi\) | ||||
−0.594509 | + | 0.804089i | \(0.702654\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.44047e14 | 0.900780 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.10419e14 | −0.707303 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.64118e15 | −2.41118 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.09183e14 | 0.388533 | 0.194266 | − | 0.980949i | \(-0.437767\pi\) | ||||
0.194266 | + | 0.980949i | \(0.437767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.05557e14 | −0.329479 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.48859e15 | 1.38155 | 0.690773 | − | 0.723072i | \(-0.257271\pi\) | ||||
0.690773 | + | 0.723072i | \(0.257271\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.99335e14 | 0.239816 | 0.119908 | − | 0.992785i | \(-0.461740\pi\) | ||||
0.119908 | + | 0.992785i | \(0.461740\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.34510e14 | −0.648133 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.17587e15 | 0.707916 | 0.353958 | − | 0.935261i | \(-0.384836\pi\) | ||||
0.353958 | + | 0.935261i | \(0.384836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.87431e15 | −0.982072 | −0.491036 | − | 0.871139i | \(-0.663382\pi\) | ||||
−0.491036 | + | 0.871139i | \(0.663382\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.82693e13 | −0.0266390 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.87232e15 | 1.14854 | 0.574269 | − | 0.818667i | \(-0.305286\pi\) | ||||
0.574269 | + | 0.818667i | \(0.305286\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.01534e15 | 2.10875 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.28117e15 | 0.702689 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.63346e14 | 0.0714372 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.30351e15 | −0.551442 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.62403e14 | 0.140228 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.07915e14 | −0.114030 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.05419e16 | −1.75546 | −0.877730 | − | 0.479156i | \(-0.840943\pi\) | ||||
−0.877730 | + | 0.479156i | \(0.840943\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.47890e15 | 1.10768 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.79931e15 | 0.369416 | 0.184708 | − | 0.982793i | \(-0.440866\pi\) | ||||
0.184708 | + | 0.982793i | \(0.440866\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.95271e15 | −1.05455 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.45595e16 | −1.53336 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.99920e15 | 0.660153 | 0.330076 | − | 0.943954i | \(-0.392926\pi\) | ||||
0.330076 | + | 0.943954i | \(0.392926\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.68752e16 | 1.42770 | 0.713850 | − | 0.700299i | \(-0.246950\pi\) | ||||
0.713850 | + | 0.700299i | \(0.246950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.59178e15 | 0.577033 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.39886e16 | −0.956652 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.45393e16 | −2.74463 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.72062e15 | 0.429311 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.09882e16 | −0.552114 | −0.276057 | − | 0.961141i | \(-0.589028\pi\) | ||||
−0.276057 | + | 0.961141i | \(0.589028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.42994e16 | 0.650116 | 0.325058 | − | 0.945694i | \(-0.394616\pi\) | ||||
0.325058 | + | 0.945694i | \(0.394616\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.35287e15 | 0.0557274 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.82891e16 | −1.43083 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.08915e16 | 0.709125 | 0.354563 | − | 0.935032i | \(-0.384630\pi\) | ||||
0.354563 | + | 0.935032i | \(0.384630\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.42682e15 | 0.290996 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.28139e16 | 0.922283 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.65828e16 | 1.19349 | 0.596745 | − | 0.802431i | \(-0.296461\pi\) | ||||
0.596745 | + | 0.802431i | \(0.296461\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.94394e16 | 0.688335 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.23639e16 | 0.691333 | 0.345667 | − | 0.938357i | \(-0.387653\pi\) | ||||
0.345667 | + | 0.938357i | \(0.387653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.32474e16 | 1.04028 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.59920e16 | −0.822643 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.66152e16 | 0.436299 | 0.218149 | − | 0.975915i | \(-0.429998\pi\) | ||||
0.218149 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.52496e16 | −0.680501 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.27351e16 | −0.590180 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.67028e16 | 0.719791 | 0.359896 | − | 0.932993i | \(-0.382812\pi\) | ||||
0.359896 | + | 0.932993i | \(0.382812\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.23330e16 | −1.07837 | −0.539185 | − | 0.842188i | \(-0.681267\pi\) | ||||
−0.539185 | + | 0.842188i | \(0.681267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.64444e16 | 0.714620 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.43610e15 | −0.0538889 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.29606e15 | −0.0758682 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.94229e16 | −0.670629 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.81483e16 | 0.609774 | 0.304887 | − | 0.952388i | \(-0.401381\pi\) | ||||
0.304887 | + | 0.952388i | \(0.401381\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.47351e16 | −0.250662 | −0.125331 | − | 0.992115i | \(-0.539999\pi\) | ||||
−0.125331 | + | 0.992115i | \(0.539999\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.19783e17 | −1.46803 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00451e16 | −0.0621521 | −0.0310761 | − | 0.999517i | \(-0.509893\pi\) | ||||
−0.0310761 | + | 0.999517i | \(0.509893\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.10791e16 | −0.350344 | −0.175172 | − | 0.984538i | \(-0.556048\pi\) | ||||
−0.175172 | + | 0.984538i | \(0.556048\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.59068e16 | −0.297505 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.42964e17 | −1.20039 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.17973e16 | 0.283671 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.68572e17 | 0.719464 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.82033e17 | 1.11996 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.32583e17 | −1.59938 | −0.799689 | − | 0.600415i | \(-0.795002\pi\) | ||||
−0.799689 | + | 0.600415i | \(0.795002\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.94395e15 | −0.00669636 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.97726e17 | 2.24076 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.08869e17 | −0.625786 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.06842e16 | −0.225662 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.19351e16 | 0.161806 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.88493e17 | −0.704447 | −0.352223 | − | 0.935916i | \(-0.614574\pi\) | ||||
−0.352223 | + | 0.935916i | \(0.614574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.32457e17 | −0.530852 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.13606e17 | 1.52498 | 0.762491 | − | 0.646999i | \(-0.223976\pi\) | ||||
0.762491 | + | 0.646999i | \(0.223976\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.90635e17 | 1.18182 | 0.590912 | − | 0.806736i | \(-0.298768\pi\) | ||||
0.590912 | + | 0.806736i | \(0.298768\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.60593e17 | 0.301050 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.97002e17 | −0.346179 | −0.173089 | − | 0.984906i | \(-0.555375\pi\) | ||||
−0.173089 | + | 0.984906i | \(0.555375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.08257e17 | 1.16730 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.99872e17 | −0.618456 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.90558e17 | 1.14802 | 0.574010 | − | 0.818848i | \(-0.305387\pi\) | ||||
0.574010 | + | 0.818848i | \(0.305387\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.08912e18 | 1.48576 | 0.742878 | − | 0.669427i | \(-0.233460\pi\) | ||||
0.742878 | + | 0.669427i | \(0.233460\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.81489e17 | −0.873800 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.20276e17 | 0.868467 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.10554e18 | −2.38857 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.17578e17 | −0.873040 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.87746e17 | −0.993327 | −0.496663 | − | 0.867943i | \(-0.665442\pi\) | ||||
−0.496663 | + | 0.867943i | \(0.665442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.03372e18 | −0.979489 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.30344e17 | −0.116423 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.41281e16 | 0.0119011 | 0.00595054 | − | 0.999982i | \(-0.498106\pi\) | ||||
0.00595054 | + | 0.999982i | \(0.498106\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.96542e16 | −0.0235688 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.24816e18 | −0.936411 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.20775e17 | 0.227265 | 0.113632 | − | 0.993523i | \(-0.463751\pi\) | ||||
0.113632 | + | 0.993523i | \(0.463751\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.79452e17 | 0.588665 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.33961e18 | 0.847507 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.83450e17 | 0.408851 | 0.204425 | − | 0.978882i | \(-0.434467\pi\) | ||||
0.204425 | + | 0.978882i | \(0.434467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.18255e17 | −0.349863 | −0.174931 | − | 0.984581i | \(-0.555970\pi\) | ||||
−0.174931 | + | 0.984581i | \(0.555970\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.19893e18 | −0.642056 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.42547e18 | 0.722710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.71739e18 | −1.78500 | −0.892502 | − | 0.451042i | \(-0.851052\pi\) | ||||
−0.892502 | + | 0.451042i | \(0.851052\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.07300e18 | −0.488169 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.22333e18 | 0.527528 | 0.263764 | − | 0.964587i | \(-0.415036\pi\) | ||||
0.263764 | + | 0.964587i | \(0.415036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.64355e18 | 0.672023 | 0.336012 | − | 0.941858i | \(-0.390922\pi\) | ||||
0.336012 | + | 0.941858i | \(0.390922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.43118e18 | 1.71863 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.37107e17 | 0.124066 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.82569e18 | −0.987168 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.34794e17 | −0.276938 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.24549e18 | 0.707625 | 0.353813 | − | 0.935316i | \(-0.384885\pi\) | ||||
0.353813 | + | 0.935316i | \(0.384885\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.98686e18 | −1.19390 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.50202e18 | 0.712225 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.71735e18 | 2.08898 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.80613e18 | 0.980019 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.01920e18 | −0.984735 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.19877e18 | 1.44563 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.88869e18 | 0.641450 | 0.320725 | − | 0.947172i | \(-0.396073\pi\) | ||||
0.320725 | + | 0.947172i | \(0.396073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.08205e17 | −0.170936 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.12389e18 | −0.427986 | −0.213993 | − | 0.976835i | \(-0.568647\pi\) | ||||
−0.213993 | + | 0.976835i | \(0.568647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.59160e18 | −1.65003 | −0.825014 | − | 0.565112i | \(-0.808833\pi\) | ||||
−0.825014 | + | 0.565112i | \(0.808833\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.44319e18 | −0.447331 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.93512e18 | −0.337882 | −0.168941 | − | 0.985626i | \(-0.554035\pi\) | ||||
−0.168941 | + | 0.985626i | \(0.554035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.65398e18 | 1.27484 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.17486e18 | −0.504587 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.24871e18 | −0.189427 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.06420e19 | −1.54134 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.06064e18 | 0.699999 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.86358e18 | 0.510529 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.22509e19 | −1.54688 | −0.773441 | − | 0.633868i | \(-0.781466\pi\) | ||||
−0.773441 | + | 0.633868i | \(0.781466\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.52340e17 | −0.0183858 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.21569e18 | −0.601833 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.59441e18 | −0.175944 | −0.0879721 | − | 0.996123i | \(-0.528039\pi\) | ||||
−0.0879721 | + | 0.996123i | \(0.528039\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.75528e18 | −0.818652 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.57989e18 | 0.664601 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.04526e19 | 1.01046 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.62414e19 | −1.50307 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.24789e18 | −0.110587 | −0.0552937 | − | 0.998470i | \(-0.517609\pi\) | ||||
−0.0552937 | + | 0.998470i | \(0.517609\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.56769e17 | 0.0387709 | 0.0193854 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193854 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.86791e19 | −1.51898 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.38127e19 | 1.85566 | 0.927831 | − | 0.373001i | \(-0.121671\pi\) | ||||
0.927831 | + | 0.373001i | \(0.121671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.81356e17 | −0.0135463 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.11034e17 | −0.0509189 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.02973e19 | 0.707158 | 0.353579 | − | 0.935405i | \(-0.384964\pi\) | ||||
0.353579 | + | 0.935405i | \(0.384964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.72700e19 | 1.79631 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.21947e18 | 0.393055 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.52724e18 | −0.456498 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.11070e19 | 1.81077 | 0.905385 | − | 0.424591i | \(-0.139582\pi\) | ||||
0.905385 | + | 0.424591i | \(0.139582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.73179e18 | 0.0967828 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.79745e18 | 0.257458 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.27668e18 | −0.220440 | −0.110220 | − | 0.993907i | \(-0.535156\pi\) | ||||
−0.110220 | + | 0.993907i | \(0.535156\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.64137e18 | 0.0812779 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.71416e19 | −2.71889 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.21403e19 | −1.01249 | −0.506243 | − | 0.862391i | \(-0.668966\pi\) | ||||
−0.506243 | + | 0.862391i | \(0.668966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.84631e19 | 1.25125 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.76036e19 | 0.744064 | 0.372032 | − | 0.928220i | \(-0.378661\pi\) | ||||
0.372032 | + | 0.928220i | \(0.378661\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.49822e19 | 0.609003 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.95529e19 | 0.764503 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.16034e19 | −0.436479 | −0.218239 | − | 0.975895i | \(-0.570031\pi\) | ||||
−0.218239 | + | 0.975895i | \(0.570031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.57684e18 | 0.165669 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.55813e18 | −0.263312 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.73051e19 | −1.25110 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.93839e19 | 0.625911 | 0.312955 | − | 0.949768i | \(-0.398681\pi\) | ||||
0.312955 | + | 0.949768i | \(0.398681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.41723e19 | 0.751660 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.21606e19 | 1.56228 | 0.781142 | − | 0.624353i | \(-0.214637\pi\) | ||||
0.781142 | + | 0.624353i | \(0.214637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.91229e19 | −1.41741 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.37974e19 | 0.383604 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.34181e17 | 0.0250307 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.48323e19 | −1.41616 | −0.708079 | − | 0.706133i | \(-0.750438\pi\) | ||||
−0.708079 | + | 0.706133i | \(0.750438\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.88979e19 | −0.470542 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.17485e19 | −0.522161 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.62740e19 | −1.76610 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.55629e19 | −1.01763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.17874e18 | 0.0469462 | 0.0234731 | − | 0.999724i | \(-0.492528\pi\) | ||||
0.0234731 | + | 0.999724i | \(0.492528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.88732e19 | −0.808229 | −0.404114 | − | 0.914708i | \(-0.632420\pi\) | ||||
−0.404114 | + | 0.914708i | \(0.632420\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.98480e19 | 0.398258 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.31135e18 | −0.122238 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.38146e19 | 0.632259 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.77692e19 | 0.681881 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.41503e19 | −1.11846 | −0.559228 | − | 0.829014i | \(-0.688902\pi\) | ||||
−0.559228 | + | 0.829014i | \(0.688902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.51678e19 | 1.60262 | 0.801310 | − | 0.598249i | \(-0.204137\pi\) | ||||
0.801310 | + | 0.598249i | \(0.204137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.20256e20 | 1.95631 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.55594e20 | −2.44559 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.23040e19 | 0.186879 | 0.0934397 | − | 0.995625i | \(-0.470214\pi\) | ||||
0.0934397 | + | 0.995625i | \(0.470214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.01849e19 | 0.296303 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.08737e20 | 1.54295 | 0.771474 | − | 0.636261i | \(-0.219520\pi\) | ||||
0.771474 | + | 0.636261i | \(0.219520\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.24975e20 | 1.71445 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.96681e19 | 0.393535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.76125e19 | −0.867320 | −0.433660 | − | 0.901077i | \(-0.642778\pi\) | ||||
−0.433660 | + | 0.901077i | \(0.642778\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.06197e19 | −0.131762 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.86084e19 | −0.463389 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.11851e20 | −1.29884 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.01895e20 | 1.14494 | 0.572468 | − | 0.819927i | \(-0.305986\pi\) | ||||
0.572468 | + | 0.819927i | \(0.305986\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.10778e19 | −0.120464 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.50713e20 | 1.58633 | 0.793163 | − | 0.609009i | \(-0.208433\pi\) | ||||
0.793163 | + | 0.609009i | \(0.208433\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.77378e19 | 0.384520 | 0.192260 | − | 0.981344i | \(-0.438418\pi\) | ||||
0.192260 | + | 0.981344i | \(0.438418\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.03381e20 | 1.01986 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.76843e19 | −0.837616 | −0.418808 | − | 0.908075i | \(-0.637552\pi\) | ||||
−0.418808 | + | 0.908075i | \(0.637552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.84519e19 | −0.263217 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.64071e19 | −0.505449 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.19903e20 | −1.04081 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.14560e20 | 1.80446 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.46456e19 | 0.200840 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.54724e19 | −0.359114 | −0.179557 | − | 0.983748i | \(-0.557466\pi\) | ||||
−0.179557 | + | 0.983748i | \(0.557466\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.97422e18 | −0.0533836 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.85976e19 | −0.657383 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.78801e19 | −0.560227 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.24806e19 | −0.296294 | −0.148147 | − | 0.988965i | \(-0.547331\pi\) | ||||
−0.148147 | + | 0.988965i | \(0.547331\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.25774e20 | −0.850693 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.83155e19 | −0.579330 | −0.289665 | − | 0.957128i | \(-0.593544\pi\) | ||||
−0.289665 | + | 0.957128i | \(0.593544\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.38883e19 | −0.215624 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.69667e19 | 0.475077 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.89308e17 | −0.00592459 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.33859e20 | 1.35894 | 0.679469 | − | 0.733704i | \(-0.262210\pi\) | ||||
0.679469 | + | 0.733704i | \(0.262210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.73826e19 | −0.492767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.83316e19 | −0.428723 | −0.214362 | − | 0.976754i | \(-0.568767\pi\) | ||||
−0.214362 | + | 0.976754i | \(0.568767\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.74961e20 | −1.99205 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.43768e20 | −0.741486 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.00108e20 | 0.501288 | 0.250644 | − | 0.968079i | \(-0.419358\pi\) | ||||
0.250644 | + | 0.968079i | \(0.419358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.10614e19 | −0.199654 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.76601e20 | 1.77828 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.53995e19 | −0.345791 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.21712e20 | −0.542195 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.18610e19 | −0.310984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.49686e20 | −0.629361 | −0.314680 | − | 0.949198i | \(-0.601897\pi\) | ||||
−0.314680 | + | 0.949198i | \(0.601897\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.64487e20 | 0.671998 | 0.335999 | − | 0.941862i | \(-0.390926\pi\) | ||||
0.335999 | + | 0.941862i | \(0.390926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.22174e20 | 0.485046 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.91327e19 | −0.112409 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.03657e20 | 1.13885 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.11727e20 | −0.407333 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.92827e19 | 0.281012 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.96191e20 | −1.02075 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.53097e20 | −0.513051 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.23778e20 | −0.403392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.38037e19 | 0.297331 | 0.148666 | − | 0.988888i | \(-0.452502\pi\) | ||||
0.148666 | + | 0.988888i | \(0.452502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.49299e20 | 0.768638 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.72121e20 | 1.41605 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.13080e20 | −0.329974 | −0.164987 | − | 0.986296i | \(-0.552758\pi\) | ||||
−0.164987 | + | 0.986296i | \(0.552758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.73713e20 | 0.493219 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.15207e21 | 3.18303 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.03501e20 | −0.547178 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.46775e19 | 0.0384108 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.47728e19 | 0.0631046 | 0.0315523 | − | 0.999502i | \(-0.489955\pi\) | ||||
0.0315523 | + | 0.999502i | \(0.489955\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.95145e20 | 2.21975 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.23994e19 | 0.0540772 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.09568e20 | −0.962750 | −0.481375 | − | 0.876515i | \(-0.659862\pi\) | ||||
−0.481375 | + | 0.876515i | \(0.659862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.23510e20 | −1.65608 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.52653e19 | 0.167773 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.29562e20 | 0.715476 | 0.357738 | − | 0.933822i | \(-0.383548\pi\) | ||||
0.357738 | + | 0.933822i | \(0.383548\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.37338e20 | −1.13626 | −0.568128 | − | 0.822940i | \(-0.692332\pi\) | ||||
−0.568128 | + | 0.822940i | \(0.692332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.11000e20 | −0.434634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.86419e20 | −1.57814 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.04184e19 | −0.118127 | −0.0590637 | − | 0.998254i | \(-0.518812\pi\) | ||||
−0.0590637 | + | 0.998254i | \(0.518812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.37848e19 | 0.178667 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.16078e20 | −0.772421 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.51132e20 | −0.273427 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.74603e20 | −1.01321 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.89721e20 | −0.497960 | −0.248980 | − | 0.968509i | \(-0.580095\pi\) | ||||
−0.248980 | + | 0.968509i | \(0.580095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.90396e20 | 1.65937 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.71217e19 | 0.0443007 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.21501e20 | −0.671256 | −0.335628 | − | 0.941995i | \(-0.608948\pi\) | ||||
−0.335628 | + | 0.941995i | \(0.608948\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.63342e19 | −0.103005 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.64914e20 | 0.249717 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.12785e20 | −0.166553 | −0.0832764 | − | 0.996526i | \(-0.526538\pi\) | ||||
−0.0832764 | + | 0.996526i | \(0.526538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.06529e19 | 0.0585508 | 0.0292754 | − | 0.999571i | \(-0.490680\pi\) | ||||
0.0292754 | + | 0.999571i | \(0.490680\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.46163e20 | −0.205333 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.80231e20 | 0.795125 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.03515e21 | −1.38385 | −0.691923 | − | 0.721972i | \(-0.743236\pi\) | ||||
−0.691923 | + | 0.721972i | \(0.743236\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.56003e20 | 0.855611 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.08656e20 | 1.15635 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.85246e20 | 0.354214 | 0.177107 | − | 0.984192i | \(-0.443326\pi\) | ||||
0.177107 | + | 0.984192i | \(0.443326\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.66853e20 | −0.202195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.11031e21 | −1.31312 | −0.656559 | − | 0.754275i | \(-0.727989\pi\) | ||||
−0.656559 | + | 0.754275i | \(0.727989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.08628e20 | −0.702541 | −0.351271 | − | 0.936274i | \(-0.614250\pi\) | ||||
−0.351271 | + | 0.936274i | \(0.614250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38034e21 | −1.55524 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.81747e20 | 0.749830 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.51846e20 | −0.914663 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.61488e20 | −0.798283 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.13612e18 | −0.00423364 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.09902e21 | 1.09846 | 0.549230 | − | 0.835671i | \(-0.314921\pi\) | ||||
0.549230 | + | 0.835671i | \(0.314921\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.16797e21 | 1.14000 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.65540e21 | 2.53120 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.24076e20 | 0.860324 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.08229e18 | −0.00462171 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.12045e20 | 0.543686 | 0.271843 | − | 0.962342i | \(-0.412367\pi\) | ||||
0.271843 | + | 0.962342i | \(0.412367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.77921e20 | −0.241179 | −0.120589 | − | 0.992702i | \(-0.538478\pi\) | ||||
−0.120589 | + | 0.992702i | \(0.538478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.88386e21 | −1.59717 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.83600e20 | −0.234922 | −0.117461 | − | 0.993078i | \(-0.537475\pi\) | ||||
−0.117461 | + | 0.993078i | \(0.537475\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.85134e20 | 0.554549 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.63946e20 | 0.446046 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.90607e21 | 1.47330 | 0.736648 | − | 0.676276i | \(-0.236407\pi\) | ||||
0.736648 | + | 0.676276i | \(0.236407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.05118e20 | −0.532662 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.10942e20 | −0.155748 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.01338e21 | 1.45306 | 0.726532 | − | 0.687133i | \(-0.241131\pi\) | ||||
0.726532 | + | 0.687133i | \(0.241131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.25330e20 | −0.0884185 | −0.0442092 | − | 0.999022i | \(-0.514077\pi\) | ||||
−0.0442092 | + | 0.999022i | \(0.514077\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.67225e20 | −0.115332 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.25510e21 | 1.52056 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.22262e21 | −2.78380 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.78930e20 | 0.502114 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.06524e21 | −0.671476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.25299e20 | −0.447100 | −0.223550 | − | 0.974693i | \(-0.571765\pi\) | ||||
−0.223550 | + | 0.974693i | \(0.571765\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.90345e21 | 1.14753 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.62800e19 | 0.0154957 | 0.00774785 | − | 0.999970i | \(-0.497534\pi\) | ||||
0.00774785 | + | 0.999970i | \(0.497534\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.24840e20 | −0.245020 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.92674e21 | −1.08697 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.75876e21 | 0.970623 | 0.485311 | − | 0.874341i | \(-0.338706\pi\) | ||||
0.485311 | + | 0.874341i | \(0.338706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.76303e21 | −0.951876 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.59471e21 | −0.842379 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.12829e21 | 0.583145 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.12559e21 | 1.07496 | 0.537482 | − | 0.843275i | \(-0.319376\pi\) | ||||
0.537482 | + | 0.843275i | \(0.319376\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.19857e20 | 0.207779 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.25068e21 | −2.05860 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.70193e19 | 0.0222859 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.31904e20 | 0.246748 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.49002e21 | −1.58468 | −0.792342 | − | 0.610078i | \(-0.791138\pi\) | ||||
−0.792342 | + | 0.610078i | \(0.791138\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.40612e20 | 0.0624966 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.91229e21 | −0.832025 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.04543e21 | −0.871243 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.51367e20 | 0.313332 | 0.156666 | − | 0.987652i | \(-0.449925\pi\) | ||||
0.156666 | + | 0.987652i | \(0.449925\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04543e21 | −0.426848 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.63005e21 | −1.45125 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.52359e21 | 1.37940 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.13451e21 | −0.818284 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.39878e21 | 1.65145 | 0.825726 | − | 0.564071i | \(-0.190766\pi\) | ||||
0.825726 | + | 0.564071i | \(0.190766\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.11308e20 | −0.151235 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.94062e21 | −1.05901 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.82288e21 | 2.05401 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.31541e21 | 0.454520 | 0.227260 | − | 0.973834i | \(-0.427023\pi\) | ||||
0.227260 | + | 0.973834i | \(0.427023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.62599e21 | 0.888866 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.30873e20 | 0.176040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.19995e20 | −0.201423 | −0.100711 | − | 0.994916i | \(-0.532112\pi\) | ||||
−0.100711 | + | 0.994916i | \(0.532112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.94475e21 | −0.619025 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.96305e20 | 0.279544 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.77691e21 | −0.848649 | −0.424324 | − | 0.905510i | \(-0.639488\pi\) | ||||
−0.424324 | + | 0.905510i | \(0.639488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.68497e21 | 1.70252 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.92644e21 | 0.565378 | 0.282689 | − | 0.959212i | \(-0.408774\pi\) | ||||
0.282689 | + | 0.959212i | \(0.408774\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.76782e21 | 0.796095 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.13748e21 | −0.602558 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.61573e21 | −0.446433 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.65899e21 | 1.26180 | 0.630902 | − | 0.775862i | \(-0.282685\pi\) | ||||
0.630902 | + | 0.775862i | \(0.282685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.66691e21 | 0.708022 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.60188e21 | −0.937404 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.09746e21 | −0.790290 | −0.395145 | − | 0.918619i | \(-0.629306\pi\) | ||||
−0.395145 | + | 0.918619i | \(0.629306\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.79105e21 | 0.698158 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.86875e20 | −0.192984 | −0.0964918 | − | 0.995334i | \(-0.530762\pi\) | ||||
−0.0964918 | + | 0.995334i | \(0.530762\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.57544e21 | 0.619323 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.40773e20 | −0.0803535 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.11494e21 | −1.18270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.55474e21 | −1.03280 | −0.516400 | − | 0.856348i | \(-0.672728\pi\) | ||||
−0.516400 | + | 0.856348i | \(0.672728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.81460e19 | −0.00848283 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.72043e21 | 1.02952 | 0.514761 | − | 0.857334i | \(-0.327881\pi\) | ||||
0.514761 | + | 0.857334i | \(0.327881\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.00575e21 | 1.07079 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.00663e19 | 0.0167993 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.59847e21 | −0.328982 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.11657e19 | 0.00629207 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.02204e22 | 2.02421 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.26237e21 | −1.02249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.96603e21 | 0.374782 | 0.187391 | − | 0.982285i | \(-0.439997\pi\) | ||||
0.187391 | + | 0.982285i | \(0.439997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.66092e20 | −0.161989 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.94678e21 | −0.724302 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.95270e21 | 1.43207 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.37452e21 | −0.419587 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.02993e22 | −1.78595 | −0.892975 | − | 0.450106i | \(-0.851386\pi\) | ||||
−0.892975 | + | 0.450106i | \(0.851386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.38886e20 | 0.0917057 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.50228e21 | 0.584935 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.29354e21 | 0.212038 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.26550e21 | −1.32984 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.84532e21 | −0.291420 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.32458e21 | 1.29047 | 0.645236 | − | 0.763984i | \(-0.276759\pi\) | ||||
0.645236 | + | 0.763984i | \(0.276759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.59463e21 | −1.30789 | −0.653944 | − | 0.756543i | \(-0.726887\pi\) | ||||
−0.653944 | + | 0.756543i | \(0.726887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.66929e21 | 0.249374 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.17337e22 | −1.72089 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.80476e22 | −2.59868 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.13449e21 | −0.443136 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.11082e20 | −0.0709442 | −0.0354721 | − | 0.999371i | \(-0.511293\pi\) | ||||
−0.0354721 | + | 0.999371i | \(0.511293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.28710e21 | −0.856943 | −0.428471 | − | 0.903555i | \(-0.640948\pi\) | ||||
−0.428471 | + | 0.903555i | \(0.640948\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.84878e21 | −0.515132 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.98458e20 | −0.0392276 | −0.0196138 | − | 0.999808i | \(-0.506244\pi\) | ||||
−0.0196138 | + | 0.999808i | \(0.506244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.25860e22 | 1.62453 | 0.812264 | − | 0.583290i | \(-0.198235\pi\) | ||||
0.812264 | + | 0.583290i | \(0.198235\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.00369e22 | 1.27231 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.48031e20 | 0.0682288 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.15215e21 | −0.996835 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.78618e21 | 1.05526 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.01678e21 | 1.06374 | 0.531872 | − | 0.846825i | \(-0.321489\pi\) | ||||
0.531872 | + | 0.846825i | \(0.321489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.26363e22 | 2.62323 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.30299e21 | −0.376011 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.34125e22 | −1.49998 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.16519e21 | 0.347755 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.43758e21 | −0.479004 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.15377e20 | −0.0546580 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.62091e21 | 0.585719 | 0.292859 | − | 0.956156i | \(-0.405393\pi\) | ||||
0.292859 | + | 0.956156i | \(0.405393\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.15849e22 | 1.18617 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.75411e22 | −1.76482 | −0.882412 | − | 0.470478i | \(-0.844082\pi\) | ||||
−0.882412 | + | 0.470478i | \(0.844082\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.44480e22 | 1.42843 | 0.714213 | − | 0.699928i | \(-0.246785\pi\) | ||||
0.714213 | + | 0.699928i | \(0.246785\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.10190e20 | −0.0884318 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.02914e21 | 0.289226 | 0.144613 | − | 0.989488i | \(-0.453806\pi\) | ||||
0.144613 | + | 0.989488i | \(0.453806\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.70410e21 | −0.629100 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.62937e21 | 0.703632 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.41080e21 | 0.581118 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.69146e21 | −0.596190 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.18249e21 | −0.191138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.35319e20 | 0.0719105 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.82261e21 | 0.661995 | 0.330998 | − | 0.943632i | \(-0.392615\pi\) | ||||
0.330998 | + | 0.943632i | \(0.392615\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.06281e21 | −0.504380 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.07941e22 | 0.882809 | 0.441404 | − | 0.897308i | \(-0.354480\pi\) | ||||
0.441404 | + | 0.897308i | \(0.354480\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.10919e22 | 1.69594 | 0.847971 | − | 0.530043i | \(-0.177824\pi\) | ||||
0.847971 | + | 0.530043i | \(0.177824\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.07645e22 | 0.850983 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.24547e22 | −0.968069 | −0.484034 | − | 0.875049i | \(-0.660829\pi\) | ||||
−0.484034 | + | 0.875049i | \(0.660829\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.44853e22 | 1.10704 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.37105e21 | −0.178179 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.83200e22 | −1.35375 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.42829e22 | −1.03787 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.08369e22 | −1.48898 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.68780e22 | 1.88886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.69142e20 | 0.0462469 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.02765e22 | −0.698536 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.32578e22 | 1.55490 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.58767e21 | −0.367431 | −0.183716 | − | 0.982979i | \(-0.558813\pi\) | ||||
−0.183716 | + | 0.982979i | \(0.558813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.05078e22 | −0.679648 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.11450e22 | −1.98153 | −0.990765 | − | 0.135588i | \(-0.956708\pi\) | ||||
−0.990765 | + | 0.135588i | \(0.956708\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.31075e22 | 0.820331 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.67367e22 | −1.03041 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.84645e21 | −0.232965 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.73672e21 | 0.580158 | 0.290079 | − | 0.957003i | \(-0.406318\pi\) | ||||
0.290079 | + | 0.957003i | \(0.406318\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.79946e21 | −0.457212 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.32671e20 | −0.0134193 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.10691e20 | 0.0403291 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.11298e21 | −0.117977 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.80710e22 | −0.992806 | −0.496403 | − | 0.868092i | \(-0.665346\pi\) | ||||
−0.496403 | + | 0.868092i | \(0.665346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.86309e22 | −1.00719 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.73452e21 | 0.305059 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.08969e21 | 0.109395 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.05347e22 | −0.542719 | −0.271360 | − | 0.962478i | \(-0.587473\pi\) | ||||
−0.271360 | + | 0.962478i | \(0.587473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.31973e22 | 1.17610 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.01869e21 | −0.200522 | −0.100261 | − | 0.994961i | \(-0.531968\pi\) | ||||
−0.100261 | + | 0.994961i | \(0.531968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.85878e21 | 0.287720 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00058e22 | 0.966981 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.63291e22 | 1.25260 | 0.626298 | − | 0.779583i | \(-0.284569\pi\) | ||||
0.626298 | + | 0.779583i | \(0.284569\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.65705e21 | −0.452218 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.22484e21 | 0.240835 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.44141e22 | −1.56149 | −0.780747 | − | 0.624847i | \(-0.785161\pi\) | ||||
−0.780747 | + | 0.624847i | \(0.785161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.96848e22 | −0.879235 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.06658e22 | −0.908682 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.61741e21 | −0.416312 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.59075e20 | −0.0153024 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.30037e21 | −0.348258 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.74943e21 | 0.361431 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.26402e21 | −0.0514110 | −0.0257055 | − | 0.999670i | \(-0.508183\pi\) | ||||
−0.0257055 | + | 0.999670i | \(0.508183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.37152e21 | 0.135020 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.49909e22 | 0.591130 | 0.295565 | − | 0.955323i | \(-0.404492\pi\) | ||||
0.295565 | + | 0.955323i | \(0.404492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.31877e22 | −0.900349 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.87335e22 | 1.09864 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.01531e22 | 1.13533 | 0.567665 | − | 0.823259i | \(-0.307847\pi\) | ||||
0.567665 | + | 0.823259i | \(0.307847\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.14767e22 | −0.796340 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.32306e22 | 0.483128 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.62494e21 | −0.346136 | −0.173068 | − | 0.984910i | \(-0.555368\pi\) | ||||
−0.173068 | + | 0.984910i | \(0.555368\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.53025e21 | 0.0896173 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.04317e22 | −0.363894 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.61489e22 | 2.27274 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.39779e22 | 0.811444 | 0.405722 | − | 0.913997i | \(-0.367020\pi\) | ||||
0.405722 | + | 0.913997i | \(0.367020\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.30774e22 | 1.10258 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.53852e22 | 0.505162 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.91661e21 | 0.0619899 | 0.0309949 | − | 0.999520i | \(-0.490132\pi\) | ||||
0.0309949 | + | 0.999520i | \(0.490132\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.24742e21 | 0.0397440 |
(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 | 16.16.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 144.16.a.m.1.1 | 1 | |||
4.3 | odd | 2 | 8.16.a.b.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 64.16.a.d.1.1 | 1 | |||
8.5 | even | 2 | 64.16.a.h.1.1 | 1 | |||
12.11 | even | 2 | 72.16.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.16.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
16.16.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
64.16.a.d.1.1 | 1 | 8.3 | odd | 2 | |||
64.16.a.h.1.1 | 1 | 8.5 | even | 2 | |||
72.16.a.c.1.1 | 1 | 12.11 | even | 2 | |||
144.16.a.m.1.1 | 1 | 3.2 | odd | 2 |