Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(1,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(23.7412619368\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5014x^{3} + 113222x^{2} - 625803x + 567036 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.12286\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.1 |
$q$-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 | ||||||||
\(3\) | 73.9019 | 1.58027 | 0.790134 | − | 0.612934i | \(-0.210011\pi\) | ||||
0.790134 | + | 0.612934i | \(0.210011\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −358.964 | −1.28427 | −0.642134 | − | 0.766592i | \(-0.721951\pi\) | ||||
−0.642134 | + | 0.766592i | \(0.721951\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −109.800 | −0.120993 | −0.0604965 | − | 0.998168i | \(-0.519268\pi\) | ||||
−0.0604965 | + | 0.998168i | \(0.519268\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3274.48 | 1.49725 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7153.73 | −1.62053 | −0.810267 | − | 0.586061i | \(-0.800678\pi\) | ||||
−0.810267 | + | 0.586061i | \(0.800678\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3123.17 | −0.394270 | −0.197135 | − | 0.980376i | \(-0.563164\pi\) | ||||
−0.197135 | + | 0.980376i | \(0.563164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −26528.1 | −2.02949 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23898.6 | −1.17978 | −0.589889 | − | 0.807484i | \(-0.700829\pi\) | ||||
−0.589889 | + | 0.807484i | \(0.700829\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6859.00 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8114.45 | −0.191202 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 50622.1 | 0.867547 | 0.433773 | − | 0.901022i | \(-0.357182\pi\) | ||||
0.433773 | + | 0.901022i | \(0.357182\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50730.0 | 0.649344 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 80367.1 | 0.785788 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −134788. | −1.02626 | −0.513130 | − | 0.858311i | \(-0.671514\pi\) | ||||
−0.513130 | + | 0.858311i | \(0.671514\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 199472. | 1.20259 | 0.601293 | − | 0.799029i | \(-0.294652\pi\) | ||||
0.601293 | + | 0.799029i | \(0.294652\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −528674. | −2.56088 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 39414.3 | 0.155388 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −95421.5 | −0.309699 | −0.154850 | − | 0.987938i | \(-0.549489\pi\) | ||||
−0.154850 | + | 0.987938i | \(0.549489\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −230808. | −0.623052 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −488804. | −1.10762 | −0.553811 | − | 0.832642i | \(-0.686827\pi\) | ||||
−0.553811 | + | 0.832642i | \(0.686827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 162905. | 0.312460 | 0.156230 | − | 0.987721i | \(-0.450066\pi\) | ||||
0.156230 | + | 0.987721i | \(0.450066\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.17542e6 | −1.92287 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −832599. | −1.16975 | −0.584875 | − | 0.811123i | \(-0.698857\pi\) | ||||
−0.584875 | + | 0.811123i | \(0.698857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −811487. | −0.985361 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.76615e6 | −1.86437 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 953158. | 0.879426 | 0.439713 | − | 0.898138i | \(-0.355080\pi\) | ||||
0.439713 | + | 0.898138i | \(0.355080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.56793e6 | 2.08120 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −506893. | −0.362539 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.46032e6 | 1.55958 | 0.779792 | − | 0.626039i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626039i | \(0.215325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.15629e6 | 0.652245 | 0.326122 | − | 0.945328i | \(-0.394258\pi\) | ||||
0.326122 | + | 0.945328i | \(0.394258\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −359539. | −0.181157 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.12110e6 | 0.506348 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.59366e6 | −0.647344 | −0.323672 | − | 0.946169i | \(-0.604917\pi\) | ||||
−0.323672 | + | 0.946169i | \(0.604917\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.74107e6 | 1.37096 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.90057e6 | −1.95654 | −0.978272 | − | 0.207326i | \(-0.933524\pi\) | ||||
−0.978272 | + | 0.207326i | \(0.933524\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.17056e6 | −0.352178 | −0.176089 | − | 0.984374i | \(-0.556345\pi\) | ||||
−0.176089 | + | 0.984374i | \(0.556345\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.74904e6 | 1.02614 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 785482. | 0.196073 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.58482e6 | 1.73082 | 0.865408 | − | 0.501069i | \(-0.167060\pi\) | ||||
0.865408 | + | 0.501069i | \(0.167060\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.22202e6 | −0.255494 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.26944e6 | 1.39549 | 0.697747 | − | 0.716345i | \(-0.254186\pi\) | ||||
0.697747 | + | 0.716345i | \(0.254186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.57871e6 | 1.51515 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.96106e6 | −1.62177 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.80137e6 | −1.17302 | −0.586511 | − | 0.809941i | \(-0.699499\pi\) | ||||
−0.586511 | + | 0.809941i | \(0.699499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 342925. | 0.0477039 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.47414e7 | 1.90041 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.46213e6 | 0.294631 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.56007e6 | −0.729806 | −0.364903 | − | 0.931046i | \(-0.618898\pi\) | ||||
−0.364903 | + | 0.931046i | \(0.618898\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.34248e7 | −2.42634 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −149684. | −0.0144561 | −0.00722805 | − | 0.999974i | \(-0.502301\pi\) | ||||
−0.00722805 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.12098e6 | 0.822453 | 0.411226 | − | 0.911533i | \(-0.365101\pi\) | ||||
0.411226 | + | 0.911533i | \(0.365101\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.91279e6 | 0.245554 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.96589e6 | 0.707538 | 0.353769 | − | 0.935333i | \(-0.384900\pi\) | ||||
0.353769 | + | 0.935333i | \(0.384900\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.55911e7 | 1.15314 | 0.576572 | − | 0.817047i | \(-0.304390\pi\) | ||||
0.576572 | + | 0.817047i | \(0.304390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.05182e6 | −0.489408 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.68951e7 | 1.10150 | 0.550752 | − | 0.834669i | \(-0.314341\pi\) | ||||
0.550752 | + | 0.834669i | \(0.314341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.81715e7 | −1.11416 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.02268e7 | −0.590320 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.62407e6 | 0.142745 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.16887e7 | 1.62613 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.61235e7 | −1.75034 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.83381e6 | 0.450336 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.19961e7 | 0.519668 | 0.259834 | − | 0.965653i | \(-0.416332\pi\) | ||||
0.259834 | + | 0.965653i | \(0.416332\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.20390e7 | 0.493771 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.52350e7 | −0.592096 | −0.296048 | − | 0.955173i | \(-0.595669\pi\) | ||||
−0.296048 | + | 0.955173i | \(0.595669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 753120. | 0.0277577 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.88489e7 | −1.00916 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.60519e7 | −1.53012 | −0.765060 | − | 0.643959i | \(-0.777291\pi\) | ||||
−0.765060 | + | 0.643959i | \(0.777291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.26208e7 | −0.714424 | −0.357212 | − | 0.934023i | \(-0.616273\pi\) | ||||
−0.357212 | + | 0.934023i | \(0.616273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.15306e7 | −1.84852 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.23423e7 | 0.638927 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.83839e7 | 1.31799 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.99704e7 | −1.55713 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.97987e7 | 1.23329 | 0.616646 | − | 0.787240i | \(-0.288491\pi\) | ||||
0.616646 | + | 0.787240i | \(0.288491\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.51439e7 | −0.830675 | −0.415337 | − | 0.909667i | \(-0.636337\pi\) | ||||
−0.415337 | + | 0.909667i | \(0.636337\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.82554e7 | −1.76642 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.16032e7 | −1.54444 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.17788e7 | −1.48029 | −0.740146 | − | 0.672447i | \(-0.765243\pi\) | ||||
−0.740146 | + | 0.672447i | \(0.765243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.04401e7 | 1.38973 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.55833e6 | −0.104967 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.56289e7 | −1.72955 | −0.864773 | − | 0.502162i | \(-0.832538\pi\) | ||||
−0.864773 | + | 0.502162i | \(0.832538\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.89775e8 | 3.28885 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.29897e7 | 1.21270 | 0.606351 | − | 0.795197i | \(-0.292633\pi\) | ||||
0.606351 | + | 0.795197i | \(0.292633\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.29944e7 | −0.844551 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.24597e7 | −0.343493 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.12303e7 | 0.752257 | 0.376128 | − | 0.926568i | \(-0.377255\pi\) | ||||
0.376128 | + | 0.926568i | \(0.377255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.57017e6 | −0.0785661 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.81822e8 | 2.46456 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.58207e7 | 0.597140 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.39469e7 | 0.926925 | 0.463463 | − | 0.886116i | \(-0.346607\pi\) | ||||
0.463463 | + | 0.886116i | \(0.346607\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.54516e7 | 1.03072 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.42529e7 | 0.397737 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.70964e8 | 1.91187 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.82433e6 | −0.0950748 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.01526e8 | −1.05429 | −0.527144 | − | 0.849776i | \(-0.676737\pi\) | ||||
−0.527144 | + | 0.849776i | \(0.676737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.98679e7 | −0.499310 | −0.249655 | − | 0.968335i | \(-0.580317\pi\) | ||||
−0.249655 | + | 0.968335i | \(0.580317\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.28516e7 | 0.800166 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.39368e8 | −1.29876 | −0.649382 | − | 0.760463i | \(-0.724972\pi\) | ||||
−0.649382 | + | 0.760463i | \(0.724972\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.01709e8 | −0.914898 | −0.457449 | − | 0.889236i | \(-0.651237\pi\) | ||||
−0.457449 | + | 0.889236i | \(0.651237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.17775e8 | −1.02298 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.47997e7 | 0.124170 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.75463e8 | 1.42248 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.65761e8 | 1.29893 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.90674e7 | 0.371776 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.48482e7 | 0.695089 | 0.347545 | − | 0.937663i | \(-0.387015\pi\) | ||||
0.347545 | + | 0.937663i | \(0.387015\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.36063e8 | −3.09187 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.84769e7 | −0.401282 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.19021e7 | −0.145505 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.65063e7 | −0.556536 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.46391e7 | 0.465151 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.13197e8 | 0.683548 | 0.341774 | − | 0.939782i | \(-0.388972\pi\) | ||||
0.341774 | + | 0.939782i | \(0.388972\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.66115e8 | 0.972230 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.23618e8 | −1.83629 | −0.918147 | − | 0.396241i | \(-0.870314\pi\) | ||||
−0.918147 | + | 0.396241i | \(0.870314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.63829e7 | 0.145177 | 0.0725887 | − | 0.997362i | \(-0.476874\pi\) | ||||
0.0725887 | + | 0.997362i | \(0.476874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.80486e7 | 0.309849 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.91009e8 | −1.50716 | −0.753581 | − | 0.657355i | \(-0.771675\pi\) | ||||
−0.753581 | + | 0.657355i | \(0.771675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.98873e8 | 1.50227 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.60533e8 | 2.73515 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00022e8 | −1.42155 | −0.710773 | − | 0.703422i | \(-0.751655\pi\) | ||||
−0.710773 | + | 0.703422i | \(0.751655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.30849e8 | 0.602157 | 0.301078 | − | 0.953599i | \(-0.402653\pi\) | ||||
0.301078 | + | 0.953599i | \(0.402653\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.66072e8 | −1.18954 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.91294e8 | 1.26547 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.14218e7 | 0.0904517 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.37225e8 | 2.20525 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.29176e8 | −1.71308 | −0.856539 | − | 0.516083i | \(-0.827390\pi\) | ||||
−0.856539 | + | 0.516083i | \(0.827390\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.62137e8 | −1.40589 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.33983e8 | 2.39435 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.14319e8 | −1.15506 | −0.577530 | − | 0.816370i | \(-0.695983\pi\) | ||||
−0.577530 | + | 0.816370i | \(0.695983\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.04773e7 | 0.0374715 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.41360e8 | −1.53657 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.31366e8 | −1.46218 | −0.731090 | − | 0.682281i | \(-0.760988\pi\) | ||||
−0.731090 | + | 0.682281i | \(0.760988\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.42149e8 | −1.12942 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.76536e8 | −1.85369 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.12548e8 | 0.352537 | 0.176269 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176269 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.25465e8 | 1.29859 | 0.649294 | − | 0.760537i | \(-0.275064\pi\) | ||||
0.649294 | + | 0.760537i | \(0.275064\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.53428e7 | 0.0753850 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.62909e8 | −1.05228 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.22706e8 | −0.912280 | −0.456140 | − | 0.889908i | \(-0.650768\pi\) | ||||
−0.456140 | + | 0.889908i | \(0.650768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.53168e8 | 1.80057 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.95029e8 | 1.06208 | 0.531039 | − | 0.847347i | \(-0.321802\pi\) | ||||
0.531039 | + | 0.847347i | \(0.321802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.22370e7 | 0.0583209 | 0.0291605 | − | 0.999575i | \(-0.490717\pi\) | ||||
0.0291605 | + | 0.999575i | \(0.490717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.81956e8 | 0.465597 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.36709e7 | 0.134015 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.60802e8 | 0.391877 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.84801e8 | −1.15329 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.90759e8 | −0.675299 | −0.337649 | − | 0.941272i | \(-0.609632\pi\) | ||||
−0.337649 | + | 0.941272i | \(0.609632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.83164e8 | −2.00292 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.74925e8 | −1.27340 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.58101e8 | −0.342047 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.78870e7 | −0.0378055 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.10619e7 | −0.0228445 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.15064e8 | −0.837657 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.45260e8 | −0.681023 | −0.340512 | − | 0.940240i | \(-0.610600\pi\) | ||||
−0.340512 | + | 0.940240i | \(0.610600\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.74057e8 | 1.29970 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.53537e8 | −0.289435 | −0.144718 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144718 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.62886e8 | 0.668906 | 0.334453 | − | 0.942412i | \(-0.391449\pi\) | ||||
0.334453 | + | 0.942412i | \(0.391449\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.29062e8 | 0.232654 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.06047e8 | −0.363294 | −0.181647 | − | 0.983364i | \(-0.558143\pi\) | ||||
−0.181647 | + | 0.983364i | \(0.558143\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.64234e8 | 1.66309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.62596e8 | 1.11810 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.63920e8 | 0.270660 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.58438e8 | −0.256017 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.15221e9 | 1.82228 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.14196e7 | 0.141532 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.59579e8 | 0.848131 | 0.424066 | − | 0.905631i | \(-0.360603\pi\) | ||||
0.424066 | + | 0.905631i | \(0.360603\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.12456e8 | −0.463697 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.72068e8 | 0.831363 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.56120e8 | −0.649195 | −0.324597 | − | 0.945852i | \(-0.605229\pi\) | ||||
−0.324597 | + | 0.945852i | \(0.605229\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.24858e9 | 1.74067 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.42697e9 | −1.94883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.79527e8 | 0.240215 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.34291e9 | −1.76068 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.84759e8 | 1.26525 | 0.632626 | − | 0.774458i | \(-0.281977\pi\) | ||||
0.632626 | + | 0.774458i | \(0.281977\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.02914e8 | 0.759218 | 0.379609 | − | 0.925147i | \(-0.376059\pi\) | ||||
0.379609 | + | 0.925147i | \(0.376059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.51000e8 | −0.309812 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.23097e7 | 0.0269949 | 0.0134975 | − | 0.999909i | \(-0.495703\pi\) | ||||
0.0134975 | + | 0.999909i | \(0.495703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.11809e9 | 2.51273 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.93924e8 | 0.225575 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.61552e8 | −1.09684 | −0.548418 | − | 0.836204i | \(-0.684770\pi\) | ||||
−0.548418 | + | 0.836204i | \(0.684770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.34185e9 | 2.56972 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.20188e8 | 0.452291 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.58001e8 | 0.694856 | 0.347428 | − | 0.937707i | \(-0.387055\pi\) | ||||
0.347428 | + | 0.937707i | \(0.387055\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.60058e9 | −1.65839 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.04657e8 | −0.106404 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.20948e9 | −1.20675 | −0.603373 | − | 0.797459i | \(-0.706177\pi\) | ||||
−0.603373 | + | 0.797459i | \(0.706177\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.26737e8 | 0.711652 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.20964e8 | 0.404623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.22771e9 | 1.15840 | 0.579198 | − | 0.815187i | \(-0.303366\pi\) | ||||
0.579198 | + | 0.815187i | \(0.303366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.86531e8 | 0.821214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.21666e9 | −1.10655 | −0.553276 | − | 0.832998i | \(-0.686623\pi\) | ||||
−0.553276 | + | 0.832998i | \(0.686623\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.81960e8 | −0.251811 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.33429e8 | 0.467830 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.34163e9 | 1.15561 | 0.577803 | − | 0.816176i | \(-0.303910\pi\) | ||||
0.577803 | + | 0.816176i | \(0.303910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.20980e9 | −1.02351 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.12589e9 | −0.935670 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.72268e9 | −2.22283 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.91153e9 | −1.53325 | −0.766626 | − | 0.642094i | \(-0.778066\pi\) | ||||
−0.766626 | + | 0.642094i | \(0.778066\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.56570e7 | 0.0438647 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.14237e9 | −0.884708 | −0.442354 | − | 0.896841i | \(-0.645856\pi\) | ||||
−0.442354 | + | 0.896841i | \(0.645856\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.22984e8 | −0.474143 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.38661e8 | 0.328123 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.82619e8 | 0.501878 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00435e9 | 1.44858 | 0.724290 | − | 0.689496i | \(-0.242168\pi\) | ||||
0.724290 | + | 0.689496i | \(0.242168\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.40332e9 | −2.41800 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.70143e8 | −0.188699 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.60947e9 | −1.79219 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.67172e9 | −1.12898 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.02610e9 | 0.681461 | 0.340730 | − | 0.940161i | \(-0.389326\pi\) | ||||
0.340730 | + | 0.940161i | \(0.389326\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.29081e9 | 1.49624 | 0.748122 | − | 0.663562i | \(-0.230956\pi\) | ||||
0.748122 | + | 0.663562i | \(0.230956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.72633e9 | −1.75141 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.21237e9 | −0.766082 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.26960e8 | −0.0789171 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.65114e9 | 1.00968 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.13824e8 | −0.248969 | −0.124484 | − | 0.992222i | \(-0.539728\pi\) | ||||
−0.124484 | + | 0.992222i | \(0.539728\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.83448e9 | 1.67790 | 0.838950 | − | 0.544209i | \(-0.183170\pi\) | ||||
0.838950 | + | 0.544209i | \(0.183170\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.57566e9 | 2.08278 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.47217e8 | −0.199029 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.83393e9 | −1.59869 | −0.799344 | − | 0.600874i | \(-0.794819\pi\) | ||||
−0.799344 | + | 0.600874i | \(0.794819\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.65720e9 | −1.47533 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.13580e9 | 1.16720 | 0.583602 | − | 0.812040i | \(-0.301643\pi\) | ||||
0.583602 | + | 0.812040i | \(0.301643\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.80041e9 | 1.50647 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.68022e9 | 1.94893 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.43253e8 | 0.439638 | 0.219819 | − | 0.975541i | \(-0.429453\pi\) | ||||
0.219819 | + | 0.975541i | \(0.429453\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.49677e9 | 1.79494 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.59720e9 | −1.31269 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.23098e8 | −0.0612646 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.59270e9 | 1.27071 | 0.635354 | − | 0.772221i | \(-0.280854\pi\) | ||||
0.635354 | + | 0.772221i | \(0.280854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.92066e9 | −0.927055 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.25804e9 | 0.598053 | 0.299027 | − | 0.954245i | \(-0.403338\pi\) | ||||
0.299027 | + | 0.954245i | \(0.403338\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70904e9 | −1.26847 | −0.634236 | − | 0.773139i | \(-0.718685\pi\) | ||||
−0.634236 | + | 0.773139i | \(0.718685\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.29161e9 | −2.44063 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.94781e9 | −0.884987 | −0.442494 | − | 0.896772i | \(-0.645906\pi\) | ||||
−0.442494 | + | 0.896772i | \(0.645906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.74985e8 | 0.0783241 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.30458e9 | −2.33926 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.16538e9 | −0.506352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.47957e8 | −0.148970 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.12110e9 | 1.31672 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.46097e9 | −0.607390 | −0.303695 | − | 0.952769i | \(-0.598220\pi\) | ||||
−0.303695 | + | 0.952769i | \(0.598220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.98017e8 | 0.122105 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.10771e8 | −0.165876 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.35483e9 | 0.937266 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.26613e9 | 0.496736 | 0.248368 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248368 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.06715e9 | −2.73315 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.83771e9 | −1.46314 | −0.731572 | − | 0.681765i | \(-0.761213\pi\) | ||||
−0.731572 | + | 0.681765i | \(0.761213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.22123e9 | 1.21076 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.40865e9 | 3.11607 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.47884e8 | 0.236728 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.49904e9 | −1.26066 | −0.630328 | − | 0.776329i | \(-0.717080\pi\) | ||||
−0.630328 | + | 0.776329i | \(0.717080\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.39408e9 | 1.91640 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.11713e9 | −0.741754 | −0.370877 | − | 0.928682i | \(-0.620943\pi\) | ||||
−0.370877 | + | 0.928682i | \(0.620943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.37312e7 | 0.0185655 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.91638e9 | −1.33462 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.01744e9 | −0.341977 | −0.170988 | − | 0.985273i | \(-0.554696\pi\) | ||||
−0.170988 | + | 0.985273i | \(0.554696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.28528e8 | 0.0426111 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.51238e8 | −0.180272 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.27410e9 | −1.05625 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.95619e9 | 1.89562 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.78602e9 | 1.18877 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.02605e9 | −0.627650 | −0.313825 | − | 0.949481i | \(-0.601611\pi\) | ||||
−0.313825 | + | 0.949481i | \(0.601611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.04115e8 | −0.0318241 | −0.0159120 | − | 0.999873i | \(-0.505065\pi\) | ||||
−0.0159120 | + | 0.999873i | \(0.505065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.11646e8 | −0.124156 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.76709e9 | −1.41878 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.42227e8 | −0.247363 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.05626e9 | 2.33509 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.52662e9 | 0.436702 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.21843e9 | −0.908669 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.38623e9 | 0.943641 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.80516e9 | 1.59681 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.86709e9 | 0.778487 | 0.389243 | − | 0.921135i | \(-0.372737\pi\) | ||||
0.389243 | + | 0.921135i | \(0.372737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.46481e9 | 1.46479 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.59663e9 | −1.48095 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.20539e9 | 1.09863 | 0.549313 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549313 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.78624e9 | 0.976573 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.24508e8 | 0.235440 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.32816e8 | −0.209417 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.53135e9 | 0.628531 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.90397e9 | 1.69280 | 0.846400 | − | 0.532548i | \(-0.178765\pi\) | ||||
0.846400 | + | 0.532548i | \(0.178765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.08779e8 | −0.123193 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.26345e10 | 3.02127 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.07530e9 | −0.490119 | −0.245060 | − | 0.969508i | \(-0.578808\pi\) | ||||
−0.245060 | + | 0.969508i | \(0.578808\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.06473e9 | −1.41463 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.34178e8 | 0.0309130 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.50410e9 | 0.797414 | 0.398707 | − | 0.917078i | \(-0.369459\pi\) | ||||
0.398707 | + | 0.917078i | \(0.369459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.15559e9 | 1.15892 | 0.579458 | − | 0.815002i | \(-0.303264\pi\) | ||||
0.579458 | + | 0.815002i | \(0.303264\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.50294e9 | −1.66606 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.56806e9 | 0.563336 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.08613e9 | −1.31894 | −0.659471 | − | 0.751730i | \(-0.729220\pi\) | ||||
−0.659471 | + | 0.751730i | \(0.729220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.68533e9 | −0.789045 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.98187e8 | −0.168845 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.81863e9 | −1.42514 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.67104e9 | 0.758129 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.10318e9 | 0.633247 | 0.316623 | − | 0.948551i | \(-0.397451\pi\) | ||||
0.316623 | + | 0.948551i | \(0.397451\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.36818e9 | −0.275892 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.02995e10 | −2.05240 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.15698e9 | 1.60634 | 0.803170 | − | 0.595749i | \(-0.203145\pi\) | ||||
0.803170 | + | 0.595749i | \(0.203145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.41946e8 | −0.183323 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.51647e9 | −1.44578 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.83681e9 | −0.729418 | −0.364709 | − | 0.931122i | \(-0.618831\pi\) | ||||
−0.364709 | + | 0.931122i | \(0.618831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.74255e9 | −1.07906 | −0.539529 | − | 0.841967i | \(-0.681398\pi\) | ||||
−0.539529 | + | 0.841967i | \(0.681398\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.21843e9 | −0.969235 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.13751e10 | −2.08839 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.66716e9 | 0.484048 | 0.242024 | − | 0.970270i | \(-0.422189\pi\) | ||||
0.242024 | + | 0.970270i | \(0.422189\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.09373e9 | 0.196222 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.60034e9 | 0.461197 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.97013e9 | 0.520791 | 0.260396 | − | 0.965502i | \(-0.416147\pi\) | ||||
0.260396 | + | 0.965502i | \(0.416147\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.29670e10 | 2.24791 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.26837e9 | −1.07438 | −0.537189 | − | 0.843462i | \(-0.680514\pi\) | ||||
−0.537189 | + | 0.843462i | \(0.680514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.46559e9 | −1.09570 | −0.547849 | − | 0.836577i | \(-0.684553\pi\) | ||||
−0.547849 | + | 0.836577i | \(0.684553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.06835e9 | 0.681707 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.56594e8 | 0.141928 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.49326e9 | −1.22770 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.62617e9 | 0.587506 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.28043e9 | 0.365376 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.86287e9 | −1.56279 | −0.781395 | − | 0.624037i | \(-0.785491\pi\) | ||||
−0.781395 | + | 0.624037i | \(0.785491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.00946e9 | 1.09843 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.30615e9 | −0.667392 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.53441e9 | 0.388498 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.93213e10 | −2.92943 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.04849e10 | 1.57240 | 0.786198 | − | 0.617974i | \(-0.212046\pi\) | ||||
0.786198 | + | 0.617974i | \(0.212046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.27539e8 | −0.137592 | −0.0687961 | − | 0.997631i | \(-0.521916\pi\) | ||||
−0.0687961 | + | 0.997631i | \(0.521916\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.32155e9 | −0.634134 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.07688e10 | 1.56316 | 0.781578 | − | 0.623808i | \(-0.214415\pi\) | ||||
0.781578 | + | 0.623808i | \(0.214415\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.76004e10 | −2.52736 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.61861e9 | −0.229936 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.05077e9 | 0.990925 | 0.495462 | − | 0.868629i | \(-0.334999\pi\) | ||||
0.495462 | + | 0.868629i | \(0.334999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.46880e9 | 0.760409 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.83297e9 | −0.527299 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.71506e8 | 0.132235 | 0.0661175 | − | 0.997812i | \(-0.478939\pi\) | ||||
0.0661175 | + | 0.997812i | \(0.478939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.03635e9 | −0.947637 | −0.473819 | − | 0.880622i | \(-0.657125\pi\) | ||||
−0.473819 | + | 0.880622i | \(0.657125\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.51597e9 | 0.735063 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.70343e8 | −0.0356483 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.82324e9 | −0.890328 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.36548e9 | 1.08019 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.27175e9 | −1.05698 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.35466e9 | 1.18297 | 0.591487 | − | 0.806314i | \(-0.298541\pi\) | ||||
0.591487 | + | 0.806314i | \(0.298541\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.07702e9 | 0.510246 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.64449e9 | 0.699140 | 0.349570 | − | 0.936910i | \(-0.386328\pi\) | ||||
0.349570 | + | 0.936910i | \(0.386328\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.20298e8 | 0.0883015 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.39160e10 | −2.90184 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.50975e10 | −1.81314 | −0.906571 | − | 0.422054i | \(-0.861309\pi\) | ||||
−0.906571 | + | 0.422054i | \(0.861309\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.65310e10 | 1.96508 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.94975e9 | 0.229419 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.97687e9 | −0.346731 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.25008e9 | −0.144133 | −0.0720666 | − | 0.997400i | \(-0.522959\pi\) | ||||
−0.0720666 | + | 0.997400i | \(0.522959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.57205e9 | 0.293571 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.12004e9 | 0.917511 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.16817e10 | 1.30675 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.15061e10 | −2.38172 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.65921e9 | 0.510857 | 0.255428 | − | 0.966828i | \(-0.417784\pi\) | ||||
0.255428 | + | 0.966828i | \(0.417784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.54496e8 | 0.0710499 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.20873e10 | 2.37399 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.64354e7 | 0.00174909 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.70761e9 | −0.601441 | −0.300720 | − | 0.953712i | \(-0.597227\pi\) | ||||
−0.300720 | + | 0.953712i | \(0.597227\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.48364e10 | 2.59146 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00977e10 | 1.04330 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.02007e9 | −0.820554 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.21722e10 | −2.24642 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.08664e10 | 1.09027 | 0.545136 | − | 0.838347i | \(-0.316478\pi\) | ||||
0.545136 | + | 0.838347i | \(0.316478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.00149e9 | −0.0995111 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.66996e9 | 0.951569 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.83778e9 | −0.666395 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.49074e9 | −0.336936 | −0.168468 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168468 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.69907e10 | −1.62429 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.89319e9 | −0.368633 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.94782e9 | −0.182677 | −0.0913386 | − | 0.995820i | \(-0.529115\pi\) | ||||
−0.0913386 | + | 0.995820i | \(0.529115\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.15272e10 | 1.99978 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.14006e10 | 1.04904 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.89076e9 | −0.536928 | −0.268464 | − | 0.963290i | \(-0.586516\pi\) | ||||
−0.268464 | + | 0.963290i | \(0.586516\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.58311e9 | 0.142938 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.25115e10 | 1.11905 | 0.559525 | − | 0.828813i | \(-0.310984\pi\) | ||||
0.559525 | + | 0.828813i | \(0.310984\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.78759e10 | −1.58388 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.38037e10 | 2.08940 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.84457e8 | −0.0856072 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.24647e10 | 1.07385 | 0.536925 | − | 0.843630i | \(-0.319586\pi\) | ||||
0.536925 | + | 0.843630i | \(0.319586\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.17169e10 | −2.70712 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.26154e10 | 1.06681 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.27300e10 | 1.06658 | 0.533290 | − | 0.845933i | \(-0.320956\pi\) | ||||
0.533290 | + | 0.845933i | \(0.320956\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.67626e10 | −2.22168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.03284e10 | −1.67208 | −0.836041 | − | 0.548666i | \(-0.815136\pi\) | ||||
−0.836041 | + | 0.548666i | \(0.815136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.71191e9 | −0.139522 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.80909e10 | 2.26856 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.68397e9 | −0.614897 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.40790e9 | −0.746020 | −0.373010 | − | 0.927827i | \(-0.621674\pi\) | ||||
−0.373010 | + | 0.927827i | \(0.621674\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.32287e10 | −1.82530 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.86805e9 | 0.301206 | 0.150603 | − | 0.988594i | \(-0.451878\pi\) | ||||
0.150603 | + | 0.988594i | \(0.451878\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.01192e10 | 0.780892 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.74293e8 | 0.0592150 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.35271e9 | 0.254106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.22111e10 | 3.17065 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.08325e10 | −0.806422 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.57660e10 | 1.90109 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.08450e10 | 1.52437 | 0.762185 | − | 0.647359i | \(-0.224127\pi\) | ||||
0.762185 | + | 0.647359i | \(0.224127\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.18787e10 | −2.31064 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.85509e9 | −0.133274 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.61127e9 | −0.257160 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.52854e10 | −1.78478 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.08677e9 | 0.146006 | 0.0730028 | − | 0.997332i | \(-0.476742\pi\) | ||||
0.0730028 | + | 0.997332i | \(0.476742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.98979e10 | 1.38005 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.55455e10 | −1.75631 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.37385e9 | 0.570717 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.99524e9 | 0.134806 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.31751e9 | 0.557104 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.85609e10 | −1.23248 | −0.616238 | − | 0.787560i | \(-0.711344\pi\) | ||||
−0.616238 | + | 0.787560i | \(0.711344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.76811e10 | 1.16396 | 0.581979 | − | 0.813204i | \(-0.302279\pi\) | ||||
0.581979 | + | 0.813204i | \(0.302279\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.14427e10 | 2.05212 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.43273e10 | 2.22120 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.11736e9 | −0.0716832 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.12290e9 | 0.0714246 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.32701e10 | 1.46757 | 0.733784 | − | 0.679383i | \(-0.237753\pi\) | ||||
0.733784 | + | 0.679383i | \(0.237753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.10963e10 | −0.693874 | −0.346937 | − | 0.937888i | \(-0.612778\pi\) | ||||
−0.346937 | + | 0.937888i | \(0.612778\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.68196e10 | −1.66289 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.85391e9 | 0.421375 | 0.210688 | − | 0.977553i | \(-0.432430\pi\) | ||||
0.210688 | + | 0.977553i | \(0.432430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.93058e9 | −0.117692 | −0.0588459 | − | 0.998267i | \(-0.518742\pi\) | ||||
−0.0588459 | + | 0.998267i | \(0.518742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.38486e10 | −1.44165 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.93934e10 | 1.16251 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.62007e10 | −1.55743 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.60310e10 | 0.944977 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.22571e10 | −0.716508 | −0.358254 | − | 0.933624i | \(-0.616628\pi\) | ||||
−0.358254 | + | 0.933624i | \(0.616628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.17827e8 | 0.0532077 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.91934e10 | 1.67837 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.90231e10 | 1.08463 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.47943e9 | −0.196751 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.64336e9 | 0.0921627 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.83044e9 | −0.268679 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.04007e10 | −1.12545 | −0.562723 | − | 0.826646i | \(-0.690246\pi\) | ||||
−0.562723 | + | 0.826646i | \(0.690246\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.06221e9 | 0.441136 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.22548e10 | 0.665080 | 0.332540 | − | 0.943089i | \(-0.392094\pi\) | ||||
0.332540 | + | 0.943089i | \(0.392094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.32872e9 | −0.502164 | −0.251082 | − | 0.967966i | \(-0.580786\pi\) | ||||
−0.251082 | + | 0.967966i | \(0.580786\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.96638e9 | 0.211779 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.79054e9 | 0.306677 | 0.153339 | − | 0.988174i | \(-0.450998\pi\) | ||||
0.153339 | + | 0.988174i | \(0.450998\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.83898e10 | −0.966099 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.18836e10 | 0.619270 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.42598e10 | −2.80484 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.97728e9 | 0.255228 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.14808e10 | −1.09270 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.07976e9 | −0.0544876 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.87189e10 | −0.937090 | −0.468545 | − | 0.883440i | \(-0.655222\pi\) | ||||
−0.468545 | + | 0.883440i | \(0.655222\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.14876e10 | −1.06715 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.71691e10 | 0.845927 | 0.422964 | − | 0.906147i | \(-0.360990\pi\) | ||||
0.422964 | + | 0.906147i | \(0.360990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.07048e9 | −0.247848 | −0.123924 | − | 0.992292i | \(-0.539548\pi\) | ||||
−0.123924 | + | 0.992292i | \(0.539548\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.52675e10 | −3.16516 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.31390e10 | 1.11330 | 0.556650 | − | 0.830747i | \(-0.312086\pi\) | ||||
0.556650 | + | 0.830747i | \(0.312086\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.31717e9 | −0.0628762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.74199e9 | 0.414036 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.71079e9 | 0.268359 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.64480e10 | −0.766887 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.16840e10 | −0.540527 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.68864e10 | −1.23416 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.27791e10 | −1.03753 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.32188e9 | −0.0597428 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.65443e10 | −1.19042 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.75358e10 | 0.780369 | 0.390184 | − | 0.920737i | \(-0.372411\pi\) | ||||
0.390184 | + | 0.920737i | \(0.372411\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.90138e8 | −0.0216444 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.89796e10 | 1.26992 | 0.634962 | − | 0.772543i | \(-0.281016\pi\) | ||||
0.634962 | + | 0.772543i | \(0.281016\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.20036e10 | −2.26144 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.06740e10 | −1.32372 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.67280e9 | 0.0716395 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.54457e10 | 1.08146 | 0.540729 | − | 0.841197i | \(-0.318148\pi\) | ||||
0.540729 | + | 0.841197i | \(0.318148\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.55154e10 | −1.07620 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.84285e10 | 0.771406 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.84073e9 | −0.201101 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.98665e10 | 1.23142 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.45187e10 | 1.41254 | 0.706268 | − | 0.707945i | \(-0.250378\pi\) | ||||
0.706268 | + | 0.707945i | \(0.250378\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.56599e9 | 0.226057 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.13467e10 | −0.457385 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.13698e10 | −2.45535 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.01764e10 | 0.404116 | 0.202058 | − | 0.979374i | \(-0.435237\pi\) | ||||
0.202058 | + | 0.979374i | \(0.435237\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.68179e10 | 1.05705 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.96144e9 | 0.233232 | 0.116616 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116616 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.47443e10 | −0.960914 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.16762e9 | 0.122102 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.69268e10 | −1.79554 | −0.897772 | − | 0.440461i | \(-0.854815\pi\) | ||||
−0.897772 | + | 0.440461i | \(0.854815\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.65584e9 | 0.138853 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.52273e10 | −0.574103 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.55628e9 | −0.207950 | −0.103975 | − | 0.994580i | \(-0.533156\pi\) | ||||
−0.103975 | + | 0.994580i | \(0.533156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.64440e10 | 1.35399 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.12587e10 | 2.62813 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.05652e9 | 0.185134 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.22765e10 | 0.446213 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.93587e10 | 1.05936 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.79008e10 | 0.641248 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.14955e10 | 0.764461 | 0.382231 | − | 0.924067i | \(-0.375156\pi\) | ||||
0.382231 | + | 0.924067i | \(0.375156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.21140e10 | 0.427715 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.64141e10 | −0.575375 | −0.287688 | − | 0.957724i | \(-0.592886\pi\) | ||||
−0.287688 | + | 0.957724i | \(0.592886\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.48377e9 | 0.0864403 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.17089e10 | −0.404575 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.51550e10 | 1.20602 | 0.603012 | − | 0.797732i | \(-0.293967\pi\) | ||||
0.603012 | + | 0.797732i | \(0.293967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.58089e10 | 1.90092 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.10527e10 | 1.72654 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.34333e10 | −0.451073 | −0.225536 | − | 0.974235i | \(-0.572413\pi\) | ||||
−0.225536 | + | 0.974235i | \(0.572413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00279e10 | 1.66796 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.75608e9 | 0.223658 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.24659e9 | 0.271074 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.25370e10 | −1.38838 | −0.694191 | − | 0.719791i | \(-0.744238\pi\) | ||||
−0.694191 | + | 0.719791i | \(0.744238\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.13539e10 | 1.34028 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.65098e10 | 1.17497 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.44581e10 | 0.781609 | 0.390805 | − | 0.920474i | \(-0.372197\pi\) | ||||
0.390805 | + | 0.920474i | \(0.372197\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.66875e9 | −0.243358 |
(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 | 76.8.a.a.1.5 | ✓ | 5 | |
4.3 | odd | 2 | 304.8.a.g.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.a.a.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
304.8.a.g.1.1 | 5 | 4.3 | odd | 2 |