Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 530373x^{4} - 23850203x^{3} + 59940607490x^{2} + 2888057920800x - 684850637484000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{6}\cdot 5^{7}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(89.2274\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −340.910 | −0.235410 | −0.117705 | − | 0.993049i | \(-0.537554\pi\) | ||||
−0.117705 | + | 0.993049i | \(0.537554\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | −1.98093e6 | −0.944582 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.01304e7 | 0.135914 | ||||||||
\(7\) | 6.73159e8 | 0.900717 | 0.450359 | − | 0.892848i | \(-0.351296\pi\) | ||||
0.450359 | + | 0.892848i | \(0.351296\pi\) | |||||||
\(8\) | 1.39026e9 | 0.457773 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.81884e10 | 1.02515 | 0.512576 | − | 0.858642i | \(-0.328691\pi\) | ||||
0.512576 | + | 0.858642i | \(0.328691\pi\) | |||||||
\(12\) | 1.16972e11 | 0.545355 | ||||||||
\(13\) | −4.35956e11 | −0.877077 | −0.438539 | − | 0.898712i | \(-0.644504\pi\) | ||||
−0.438539 | + | 0.898712i | \(0.644504\pi\) | |||||||
\(14\) | −2.29486e11 | −0.212038 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.68036e12 | 0.836818 | ||||||||
\(17\) | 3.38833e12 | 0.407636 | 0.203818 | − | 0.979009i | \(-0.434665\pi\) | ||||
0.203818 | + | 0.979009i | \(0.434665\pi\) | |||||||
\(18\) | −1.18868e12 | −0.0784699 | ||||||||
\(19\) | −4.68698e13 | −1.75380 | −0.876900 | − | 0.480672i | \(-0.840393\pi\) | ||||
−0.876900 | + | 0.480672i | \(0.840393\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.97494e13 | −0.520029 | ||||||||
\(22\) | −3.00643e13 | −0.241331 | ||||||||
\(23\) | 2.77663e13 | 0.139758 | 0.0698788 | − | 0.997555i | \(-0.477739\pi\) | ||||
0.0698788 | + | 0.997555i | \(0.477739\pi\) | |||||||
\(24\) | −8.20934e13 | −0.264296 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.48622e14 | 0.206472 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | −1.33348e15 | −0.850802 | ||||||||
\(29\) | −4.93794e14 | −0.217955 | −0.108977 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108977 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.99343e15 | −0.436821 | −0.218410 | − | 0.975857i | \(-0.570087\pi\) | ||||
−0.218410 | + | 0.975857i | \(0.570087\pi\) | |||||||
\(32\) | −4.17025e15 | −0.654768 | ||||||||
\(33\) | −5.20744e15 | −0.591872 | ||||||||
\(34\) | −1.15512e15 | −0.0959614 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.90709e15 | −0.314861 | ||||||||
\(37\) | −2.48383e16 | −0.849186 | −0.424593 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424593 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(38\) | 1.59784e16 | 0.412862 | ||||||||
\(39\) | 2.57428e16 | 0.506381 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.53977e17 | 1.79153 | 0.895766 | − | 0.444526i | \(-0.146628\pi\) | ||||
0.895766 | + | 0.444526i | \(0.146628\pi\) | |||||||
\(42\) | 1.35509e16 | 0.122420 | ||||||||
\(43\) | −8.38852e16 | −0.591925 | −0.295962 | − | 0.955200i | \(-0.595640\pi\) | ||||
−0.295962 | + | 0.955200i | \(0.595640\pi\) | |||||||
\(44\) | −1.74695e17 | −0.968341 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.46580e15 | −0.0329003 | ||||||||
\(47\) | 1.06134e16 | 0.0294324 | 0.0147162 | − | 0.999892i | \(-0.495316\pi\) | ||||
0.0147162 | + | 0.999892i | \(0.495316\pi\) | |||||||
\(48\) | −2.17322e17 | −0.483137 | ||||||||
\(49\) | −1.05402e17 | −0.188708 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00078e17 | −0.235349 | ||||||||
\(52\) | 8.63600e17 | 0.828472 | ||||||||
\(53\) | 2.83801e17 | 0.222904 | 0.111452 | − | 0.993770i | \(-0.464450\pi\) | ||||
0.111452 | + | 0.993770i | \(0.464450\pi\) | |||||||
\(54\) | 7.01903e16 | 0.0453046 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.35865e17 | 0.412324 | ||||||||
\(57\) | 2.76761e18 | 1.01256 | ||||||||
\(58\) | 1.68339e17 | 0.0513087 | ||||||||
\(59\) | 7.02994e18 | 1.79063 | 0.895314 | − | 0.445436i | \(-0.146951\pi\) | ||||
0.895314 | + | 0.445436i | \(0.146951\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.54670e18 | 1.17506 | 0.587529 | − | 0.809203i | \(-0.300101\pi\) | ||||
0.587529 | + | 0.809203i | \(0.300101\pi\) | |||||||
\(62\) | 6.79580e17 | 0.102832 | ||||||||
\(63\) | 2.34716e18 | 0.300239 | ||||||||
\(64\) | −6.29660e18 | −0.682679 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.77527e18 | 0.139332 | ||||||||
\(67\) | 1.27152e18 | 0.0852192 | 0.0426096 | − | 0.999092i | \(-0.486433\pi\) | ||||
0.0426096 | + | 0.999092i | \(0.486433\pi\) | |||||||
\(68\) | −6.71206e18 | −0.385046 | ||||||||
\(69\) | −1.63957e18 | −0.0806891 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.18512e18 | 0.334867 | 0.167433 | − | 0.985883i | \(-0.446452\pi\) | ||||
0.167433 | + | 0.985883i | \(0.446452\pi\) | |||||||
\(72\) | 4.84753e18 | 0.152591 | ||||||||
\(73\) | −3.67454e19 | −1.00072 | −0.500361 | − | 0.865817i | \(-0.666799\pi\) | ||||
−0.500361 | + | 0.865817i | \(0.666799\pi\) | |||||||
\(74\) | 8.46760e18 | 0.199907 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.28459e19 | 1.65661 | ||||||||
\(77\) | 5.93649e19 | 0.923373 | ||||||||
\(78\) | −8.77597e18 | −0.119207 | ||||||||
\(79\) | −6.42331e19 | −0.763263 | −0.381632 | − | 0.924315i | \(-0.624638\pi\) | ||||
−0.381632 | + | 0.924315i | \(0.624638\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | −5.24921e19 | −0.421744 | ||||||||
\(83\) | 2.62194e20 | 1.85482 | 0.927412 | − | 0.374042i | \(-0.122028\pi\) | ||||
0.927412 | + | 0.374042i | \(0.122028\pi\) | |||||||
\(84\) | 7.87409e19 | 0.491211 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.85973e19 | 0.139345 | ||||||||
\(87\) | 2.91580e19 | 0.125836 | ||||||||
\(88\) | 1.22605e20 | 0.469288 | ||||||||
\(89\) | −2.98217e20 | −1.01377 | −0.506883 | − | 0.862015i | \(-0.669202\pi\) | ||||
−0.506883 | + | 0.862015i | \(0.669202\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.93468e20 | −0.789999 | ||||||||
\(92\) | −5.50032e19 | −0.132013 | ||||||||
\(93\) | 1.17710e20 | 0.252199 | ||||||||
\(94\) | −3.61820e18 | −0.00692867 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.46249e20 | 0.378031 | ||||||||
\(97\) | 6.86712e20 | 0.945522 | 0.472761 | − | 0.881191i | \(-0.343257\pi\) | ||||
0.472761 | + | 0.881191i | \(0.343257\pi\) | |||||||
\(98\) | 3.59327e19 | 0.0444238 | ||||||||
\(99\) | 3.07494e20 | 0.341718 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.72493e21 | −1.55381 | −0.776904 | − | 0.629619i | \(-0.783211\pi\) | ||||
−0.776904 | + | 0.629619i | \(0.783211\pi\) | |||||||
\(102\) | 6.82084e19 | 0.0554034 | ||||||||
\(103\) | 7.93905e20 | 0.582073 | 0.291037 | − | 0.956712i | \(-0.406000\pi\) | ||||
0.291037 | + | 0.956712i | \(0.406000\pi\) | |||||||
\(104\) | −6.06092e20 | −0.401503 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.67505e19 | −0.0524737 | ||||||||
\(107\) | −2.41854e21 | −1.18856 | −0.594282 | − | 0.804257i | \(-0.702564\pi\) | ||||
−0.594282 | + | 0.804257i | \(0.702564\pi\) | |||||||
\(108\) | 4.07856e20 | 0.181785 | ||||||||
\(109\) | −4.56052e20 | −0.184517 | −0.0922584 | − | 0.995735i | \(-0.529409\pi\) | ||||
−0.0922584 | + | 0.995735i | \(0.529409\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.46667e21 | 0.490278 | ||||||||
\(112\) | 2.47747e21 | 0.753736 | ||||||||
\(113\) | 2.66253e21 | 0.737854 | 0.368927 | − | 0.929458i | \(-0.379725\pi\) | ||||
0.368927 | + | 0.929458i | \(0.379725\pi\) | |||||||
\(114\) | −9.43506e20 | −0.238366 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.78172e20 | 0.205876 | ||||||||
\(117\) | −1.52009e21 | −0.292359 | ||||||||
\(118\) | −2.39657e21 | −0.421531 | ||||||||
\(119\) | 2.28089e21 | 0.367165 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.76952e20 | 0.0509378 | ||||||||
\(122\) | −2.23183e21 | −0.276620 | ||||||||
\(123\) | −9.09217e21 | −1.03434 | ||||||||
\(124\) | 3.94885e21 | 0.412613 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.00170e20 | −0.0706792 | ||||||||
\(127\) | 3.90399e21 | 0.317372 | 0.158686 | − | 0.987329i | \(-0.449274\pi\) | ||||
0.158686 | + | 0.987329i | \(0.449274\pi\) | |||||||
\(128\) | 1.08922e22 | 0.815478 | ||||||||
\(129\) | 4.95334e21 | 0.341748 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.19004e22 | −0.698575 | −0.349288 | − | 0.937016i | \(-0.613576\pi\) | ||||
−0.349288 | + | 0.937016i | \(0.613576\pi\) | |||||||
\(132\) | 1.03156e22 | 0.559072 | ||||||||
\(133\) | −3.15508e22 | −1.57968 | ||||||||
\(134\) | −4.33473e20 | −0.0200614 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.71066e21 | 0.186605 | ||||||||
\(137\) | 4.39883e22 | 1.61351 | 0.806754 | − | 0.590887i | \(-0.201222\pi\) | ||||
0.806754 | + | 0.590887i | \(0.201222\pi\) | |||||||
\(138\) | 5.58946e20 | 0.0189950 | ||||||||
\(139\) | 2.38509e22 | 0.751362 | 0.375681 | − | 0.926749i | \(-0.377409\pi\) | ||||
0.375681 | + | 0.926749i | \(0.377409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.26709e20 | −0.0169928 | ||||||||
\(142\) | −3.13130e21 | −0.0788309 | ||||||||
\(143\) | −3.84463e22 | −0.899138 | ||||||||
\(144\) | 1.28326e22 | 0.278939 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.25269e22 | 0.235579 | ||||||||
\(147\) | 6.22390e21 | 0.108951 | ||||||||
\(148\) | 4.92029e22 | 0.802126 | ||||||||
\(149\) | 9.91268e21 | 0.150569 | 0.0752844 | − | 0.997162i | \(-0.476014\pi\) | ||||
0.0752844 | + | 0.997162i | \(0.476014\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.80864e22 | −0.238833 | −0.119416 | − | 0.992844i | \(-0.538102\pi\) | ||||
−0.119416 | + | 0.992844i | \(0.538102\pi\) | |||||||
\(152\) | −6.51611e22 | −0.802843 | ||||||||
\(153\) | 1.18144e22 | 0.135879 | ||||||||
\(154\) | −2.02381e22 | −0.217371 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.09947e22 | −0.478318 | ||||||||
\(157\) | −1.17597e23 | −1.03146 | −0.515729 | − | 0.856752i | \(-0.672479\pi\) | ||||
−0.515729 | + | 0.856752i | \(0.672479\pi\) | |||||||
\(158\) | 2.18977e22 | 0.179679 | ||||||||
\(159\) | −1.67582e22 | −0.128694 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.86911e22 | 0.125882 | ||||||||
\(162\) | −4.14466e21 | −0.0261566 | ||||||||
\(163\) | −3.82771e22 | −0.226448 | −0.113224 | − | 0.993569i | \(-0.536118\pi\) | ||||
−0.113224 | + | 0.993569i | \(0.536118\pi\) | |||||||
\(164\) | −3.05018e23 | −1.69225 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.93844e22 | −0.436643 | ||||||||
\(167\) | 3.13595e23 | 1.43829 | 0.719145 | − | 0.694860i | \(-0.244534\pi\) | ||||
0.719145 | + | 0.694860i | \(0.244534\pi\) | |||||||
\(168\) | −5.52619e22 | −0.238056 | ||||||||
\(169\) | −5.70065e22 | −0.230735 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.63425e23 | −0.584600 | ||||||||
\(172\) | 1.66171e23 | 0.559121 | ||||||||
\(173\) | 4.81111e23 | 1.52322 | 0.761608 | − | 0.648039i | \(-0.224410\pi\) | ||||
0.761608 | + | 0.648039i | \(0.224410\pi\) | |||||||
\(174\) | −9.94025e21 | −0.0296231 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.24566e23 | 0.857866 | ||||||||
\(177\) | −4.15111e23 | −1.03382 | ||||||||
\(178\) | 1.01665e23 | 0.238650 | ||||||||
\(179\) | −3.28060e22 | −0.0726099 | −0.0363050 | − | 0.999341i | \(-0.511559\pi\) | ||||
−0.0363050 | + | 0.999341i | \(0.511559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.50948e23 | −1.08514 | −0.542569 | − | 0.840011i | \(-0.682548\pi\) | ||||
−0.542569 | + | 0.840011i | \(0.682548\pi\) | |||||||
\(182\) | 1.00046e23 | 0.185973 | ||||||||
\(183\) | −3.86576e23 | −0.678420 | ||||||||
\(184\) | 3.86023e22 | 0.0639773 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.01285e22 | −0.0593700 | ||||||||
\(187\) | 2.98812e23 | 0.417889 | ||||||||
\(188\) | −2.10244e22 | −0.0278013 | ||||||||
\(189\) | −1.38598e23 | −0.173343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.18267e24 | 1.32438 | 0.662191 | − | 0.749335i | \(-0.269627\pi\) | ||||
0.662191 | + | 0.749335i | \(0.269627\pi\) | |||||||
\(192\) | 3.71808e23 | 0.394145 | ||||||||
\(193\) | −1.17187e24 | −1.17632 | −0.588161 | − | 0.808744i | \(-0.700148\pi\) | ||||
−0.588161 | + | 0.808744i | \(0.700148\pi\) | |||||||
\(194\) | −2.34107e23 | −0.222585 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.08795e23 | 0.178251 | ||||||||
\(197\) | 6.31695e23 | 0.511225 | 0.255613 | − | 0.966779i | \(-0.417723\pi\) | ||||
0.255613 | + | 0.966779i | \(0.417723\pi\) | |||||||
\(198\) | −1.04828e23 | −0.0804436 | ||||||||
\(199\) | −1.80597e24 | −1.31448 | −0.657239 | − | 0.753682i | \(-0.728276\pi\) | ||||
−0.657239 | + | 0.753682i | \(0.728276\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.50820e22 | −0.0492014 | ||||||||
\(202\) | 5.88046e23 | 0.365781 | ||||||||
\(203\) | −3.32402e23 | −0.196316 | ||||||||
\(204\) | 3.96340e23 | 0.222306 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.70650e23 | −0.137026 | ||||||||
\(207\) | 9.68151e22 | 0.0465859 | ||||||||
\(208\) | −1.60448e24 | −0.733954 | ||||||||
\(209\) | −4.13338e24 | −1.79791 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.94629e23 | 0.115961 | 0.0579803 | − | 0.998318i | \(-0.481534\pi\) | ||||
0.0579803 | + | 0.998318i | \(0.481534\pi\) | |||||||
\(212\) | −5.62191e23 | −0.210551 | ||||||||
\(213\) | −5.42372e23 | −0.193336 | ||||||||
\(214\) | 8.24502e23 | 0.279800 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.86242e23 | −0.0880985 | ||||||||
\(217\) | −1.34190e24 | −0.393452 | ||||||||
\(218\) | 1.55472e23 | 0.0434371 | ||||||||
\(219\) | 2.16978e24 | 0.577767 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.47717e24 | −0.357528 | ||||||||
\(222\) | −5.00003e23 | −0.115416 | ||||||||
\(223\) | −7.94458e24 | −1.74932 | −0.874662 | − | 0.484734i | \(-0.838916\pi\) | ||||
−0.874662 | + | 0.484734i | \(0.838916\pi\) | |||||||
\(224\) | −2.80725e24 | −0.589761 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.07681e23 | −0.173698 | ||||||||
\(227\) | 6.99177e24 | 1.27737 | 0.638684 | − | 0.769469i | \(-0.279479\pi\) | ||||
0.638684 | + | 0.769469i | \(0.279479\pi\) | |||||||
\(228\) | −5.48246e24 | −0.956444 | ||||||||
\(229\) | −1.97790e24 | −0.329558 | −0.164779 | − | 0.986330i | \(-0.552691\pi\) | ||||
−0.164779 | + | 0.986330i | \(0.552691\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.50544e24 | −0.533109 | ||||||||
\(232\) | −6.86501e23 | −0.0997740 | ||||||||
\(233\) | 5.40517e24 | 0.750883 | 0.375441 | − | 0.926846i | \(-0.377491\pi\) | ||||
0.375441 | + | 0.926846i | \(0.377491\pi\) | |||||||
\(234\) | 5.18212e23 | 0.0688242 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.39258e25 | −1.69140 | ||||||||
\(237\) | 3.79290e24 | 0.440670 | ||||||||
\(238\) | −7.77577e23 | −0.0864341 | ||||||||
\(239\) | −1.53053e25 | −1.62804 | −0.814018 | − | 0.580840i | \(-0.802724\pi\) | ||||
−0.814018 | + | 0.580840i | \(0.802724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34112e25 | −1.30704 | −0.653519 | − | 0.756910i | \(-0.726708\pi\) | ||||
−0.653519 | + | 0.756910i | \(0.726708\pi\) | |||||||
\(242\) | −1.28507e23 | −0.0119912 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | −1.29686e25 | −1.10994 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.09961e24 | 0.243494 | ||||||||
\(247\) | 2.04332e25 | 1.53822 | ||||||||
\(248\) | −2.77138e24 | −0.199965 | ||||||||
\(249\) | −1.54823e25 | −1.07088 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.69729e24 | 0.107940 | 0.0539699 | − | 0.998543i | \(-0.482812\pi\) | ||||
0.0539699 | + | 0.998543i | \(0.482812\pi\) | |||||||
\(252\) | −4.64957e24 | −0.283601 | ||||||||
\(253\) | 2.44867e24 | 0.143273 | ||||||||
\(254\) | −1.33091e24 | −0.0747125 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.49167e24 | 0.490708 | ||||||||
\(257\) | 7.35666e24 | 0.365076 | 0.182538 | − | 0.983199i | \(-0.441569\pi\) | ||||
0.182538 | + | 0.983199i | \(0.441569\pi\) | |||||||
\(258\) | −1.68864e24 | −0.0804507 | ||||||||
\(259\) | −1.67201e25 | −0.764877 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.72175e24 | −0.0726516 | ||||||||
\(262\) | 4.05696e24 | 0.164451 | ||||||||
\(263\) | −4.57145e25 | −1.78040 | −0.890202 | − | 0.455566i | \(-0.849437\pi\) | ||||
−0.890202 | + | 0.455566i | \(0.849437\pi\) | |||||||
\(264\) | −7.23969e24 | −0.270943 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.07560e25 | 0.371872 | ||||||||
\(267\) | 1.76094e25 | 0.585298 | ||||||||
\(268\) | −2.51880e24 | −0.0804966 | ||||||||
\(269\) | −3.25178e25 | −0.999360 | −0.499680 | − | 0.866210i | \(-0.666549\pi\) | ||||
−0.499680 | + | 0.866210i | \(0.666549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.68503e25 | −0.479104 | −0.239552 | − | 0.970884i | \(-0.577001\pi\) | ||||
−0.239552 | + | 0.970884i | \(0.577001\pi\) | |||||||
\(272\) | 1.24703e25 | 0.341117 | ||||||||
\(273\) | 1.73290e25 | 0.456106 | ||||||||
\(274\) | −1.49960e25 | −0.379835 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.24788e24 | 0.0762175 | ||||||||
\(277\) | 6.04936e25 | 1.36670 | 0.683348 | − | 0.730093i | \(-0.260523\pi\) | ||||
0.683348 | + | 0.730093i | \(0.260523\pi\) | |||||||
\(278\) | −8.13100e24 | −0.176878 | ||||||||
\(279\) | −6.95067e24 | −0.145607 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.79283e23 | 0.0190323 | 0.00951616 | − | 0.999955i | \(-0.496971\pi\) | ||||
0.00951616 | + | 0.999955i | \(0.496971\pi\) | |||||||
\(282\) | 2.13651e23 | 0.00400027 | ||||||||
\(283\) | −4.41068e25 | −0.795697 | −0.397849 | − | 0.917451i | \(-0.630243\pi\) | ||||
−0.397849 | + | 0.917451i | \(0.630243\pi\) | |||||||
\(284\) | −1.81951e25 | −0.316309 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.31067e25 | 0.211666 | ||||||||
\(287\) | 1.03651e26 | 1.61366 | ||||||||
\(288\) | −1.45408e25 | −0.218256 | ||||||||
\(289\) | −5.76111e25 | −0.833833 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.05497e25 | −0.545897 | ||||||||
\(292\) | 7.27902e25 | 0.945263 | ||||||||
\(293\) | −8.77281e25 | −1.09908 | −0.549539 | − | 0.835468i | \(-0.685197\pi\) | ||||
−0.549539 | + | 0.835468i | \(0.685197\pi\) | |||||||
\(294\) | −2.12179e24 | −0.0256481 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.45316e25 | −0.388735 | ||||||||
\(297\) | −1.81572e25 | −0.197291 | ||||||||
\(298\) | −3.37933e24 | −0.0354454 | ||||||||
\(299\) | −1.21049e25 | −0.122578 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.64681e25 | −0.533157 | ||||||||
\(302\) | 6.16582e24 | 0.0562235 | ||||||||
\(303\) | 1.01855e26 | 0.897091 | ||||||||
\(304\) | −1.72498e26 | −1.46761 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.02764e24 | −0.0319871 | ||||||||
\(307\) | −1.76055e26 | −1.35113 | −0.675563 | − | 0.737303i | \(-0.736099\pi\) | ||||
−0.675563 | + | 0.737303i | \(0.736099\pi\) | |||||||
\(308\) | −1.17598e26 | −0.872201 | ||||||||
\(309\) | −4.68793e25 | −0.336060 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.72398e26 | −1.82482 | −0.912410 | − | 0.409278i | \(-0.865781\pi\) | ||||
−0.912410 | + | 0.409278i | \(0.865781\pi\) | |||||||
\(312\) | 3.57891e25 | 0.231808 | ||||||||
\(313\) | −9.00000e25 | −0.563672 | −0.281836 | − | 0.959463i | \(-0.590943\pi\) | ||||
−0.281836 | + | 0.959463i | \(0.590943\pi\) | |||||||
\(314\) | 4.00901e25 | 0.242815 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.27241e26 | 0.720965 | ||||||||
\(317\) | −8.30387e25 | −0.455154 | −0.227577 | − | 0.973760i | \(-0.573080\pi\) | ||||
−0.227577 | + | 0.973760i | \(0.573080\pi\) | |||||||
\(318\) | 5.71302e24 | 0.0302957 | ||||||||
\(319\) | −4.35469e25 | −0.223437 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.42812e26 | 0.686218 | ||||||||
\(322\) | −6.37199e24 | −0.0296339 | ||||||||
\(323\) | −1.58811e26 | −0.714912 | ||||||||
\(324\) | −2.40835e25 | −0.104954 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.30490e25 | 0.0533081 | ||||||||
\(327\) | 2.69294e25 | 0.106531 | ||||||||
\(328\) | 2.14067e26 | 0.820116 | ||||||||
\(329\) | 7.14449e24 | 0.0265103 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.84201e25 | −0.342681 | −0.171340 | − | 0.985212i | \(-0.554810\pi\) | ||||
−0.171340 | + | 0.985212i | \(0.554810\pi\) | |||||||
\(332\) | −5.19389e26 | −1.75203 | ||||||||
\(333\) | −8.66056e25 | −0.283062 | ||||||||
\(334\) | −1.06908e26 | −0.338587 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.46292e26 | −0.435170 | ||||||||
\(337\) | 6.17471e26 | 1.78034 | 0.890169 | − | 0.455631i | \(-0.150586\pi\) | ||||
0.890169 | + | 0.455631i | \(0.150586\pi\) | |||||||
\(338\) | 1.94340e25 | 0.0543173 | ||||||||
\(339\) | −1.57220e26 | −0.426000 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.75798e26 | −0.447808 | ||||||||
\(342\) | 5.57131e25 | 0.137621 | ||||||||
\(343\) | −4.46943e26 | −1.07069 | ||||||||
\(344\) | −1.16622e26 | −0.270967 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.64015e26 | −0.358580 | ||||||||
\(347\) | 1.24054e26 | 0.263118 | 0.131559 | − | 0.991308i | \(-0.458002\pi\) | ||||
0.131559 | + | 0.991308i | \(0.458002\pi\) | |||||||
\(348\) | −5.77601e25 | −0.118863 | ||||||||
\(349\) | 8.43585e26 | 1.68446 | 0.842232 | − | 0.539115i | \(-0.181241\pi\) | ||||
0.842232 | + | 0.539115i | \(0.181241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.97596e25 | 0.168794 | ||||||||
\(352\) | −3.67768e26 | −0.671238 | ||||||||
\(353\) | 8.92103e26 | 1.58045 | 0.790224 | − | 0.612818i | \(-0.209964\pi\) | ||||
0.790224 | + | 0.612818i | \(0.209964\pi\) | |||||||
\(354\) | 1.41515e26 | 0.243371 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.90748e26 | 0.957585 | ||||||||
\(357\) | −1.34684e26 | −0.211983 | ||||||||
\(358\) | 1.11839e25 | 0.0170931 | ||||||||
\(359\) | −1.31171e26 | −0.194692 | −0.0973458 | − | 0.995251i | \(-0.531035\pi\) | ||||
−0.0973458 | + | 0.995251i | \(0.531035\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.48257e27 | 2.07582 | ||||||||
\(362\) | 1.87823e26 | 0.255452 | ||||||||
\(363\) | −2.22587e25 | −0.0294090 | ||||||||
\(364\) | 5.81341e26 | 0.746219 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.31788e26 | 0.159707 | ||||||||
\(367\) | 6.63211e25 | 0.0781012 | 0.0390506 | − | 0.999237i | \(-0.487567\pi\) | ||||
0.0390506 | + | 0.999237i | \(0.487567\pi\) | |||||||
\(368\) | 1.02190e26 | 0.116952 | ||||||||
\(369\) | 5.36884e26 | 0.597177 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.91043e26 | 0.200773 | ||||||||
\(372\) | −2.33176e26 | −0.238222 | ||||||||
\(373\) | 1.49862e27 | 1.48850 | 0.744252 | − | 0.667899i | \(-0.232806\pi\) | ||||
0.744252 | + | 0.667899i | \(0.232806\pi\) | |||||||
\(374\) | −1.01868e26 | −0.0983751 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.47553e25 | 0.0134734 | ||||||||
\(377\) | 2.15273e26 | 0.191163 | ||||||||
\(378\) | 4.72492e25 | 0.0408066 | ||||||||
\(379\) | 2.60984e26 | 0.219231 | 0.109615 | − | 0.993974i | \(-0.465038\pi\) | ||||
0.109615 | + | 0.993974i | \(0.465038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.30527e26 | −0.183235 | ||||||||
\(382\) | −4.03184e26 | −0.311772 | ||||||||
\(383\) | 6.73245e26 | 0.506508 | 0.253254 | − | 0.967400i | \(-0.418499\pi\) | ||||
0.253254 | + | 0.967400i | \(0.418499\pi\) | |||||||
\(384\) | −6.43175e26 | −0.470816 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.99501e26 | 0.276918 | ||||||||
\(387\) | −2.92489e26 | −0.197308 | ||||||||
\(388\) | −1.36033e27 | −0.893123 | ||||||||
\(389\) | 9.85802e26 | 0.629969 | 0.314984 | − | 0.949097i | \(-0.398001\pi\) | ||||
0.314984 | + | 0.949097i | \(0.398001\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.40815e25 | 0.0569703 | ||||||||
\(392\) | −1.46536e26 | −0.0863857 | ||||||||
\(393\) | 7.02707e26 | 0.403323 | ||||||||
\(394\) | −2.15351e26 | −0.120347 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.09125e26 | −0.322780 | ||||||||
\(397\) | −2.43807e27 | −1.25819 | −0.629093 | − | 0.777330i | \(-0.716574\pi\) | ||||
−0.629093 | + | 0.777330i | \(0.716574\pi\) | |||||||
\(398\) | 6.15673e26 | 0.309441 | ||||||||
\(399\) | 1.86305e27 | 0.912028 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.26497e26 | 0.151657 | 0.0758286 | − | 0.997121i | \(-0.475840\pi\) | ||||
0.0758286 | + | 0.997121i | \(0.475840\pi\) | |||||||
\(402\) | 2.55962e25 | 0.0115825 | ||||||||
\(403\) | 8.69049e26 | 0.383126 | ||||||||
\(404\) | 3.41697e27 | 1.46770 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.13319e26 | 0.0462146 | ||||||||
\(407\) | −2.19045e27 | −0.870546 | ||||||||
\(408\) | −2.78160e26 | −0.107736 | ||||||||
\(409\) | 4.25757e27 | 1.60719 | 0.803596 | − | 0.595176i | \(-0.202918\pi\) | ||||
0.803596 | + | 0.595176i | \(0.202918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.59746e27 | −0.931559 | ||||||||
\(412\) | −1.57267e27 | −0.549816 | ||||||||
\(413\) | 4.73227e27 | 1.61285 | ||||||||
\(414\) | −3.30052e25 | −0.0109668 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.81805e27 | 0.574283 | ||||||||
\(417\) | −1.40837e27 | −0.433799 | ||||||||
\(418\) | 1.40911e27 | 0.423246 | ||||||||
\(419\) | −5.00076e26 | −0.146483 | −0.0732417 | − | 0.997314i | \(-0.523334\pi\) | ||||
−0.0732417 | + | 0.997314i | \(0.523334\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.63434e27 | −1.29130 | −0.645648 | − | 0.763635i | \(-0.723413\pi\) | ||||
−0.645648 | + | 0.763635i | \(0.723413\pi\) | |||||||
\(422\) | −1.00442e26 | −0.0272982 | ||||||||
\(423\) | 3.70065e25 | 0.00981080 | ||||||||
\(424\) | 3.94557e26 | 0.102039 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.84900e26 | 0.0455130 | ||||||||
\(427\) | 4.40697e27 | 1.05840 | ||||||||
\(428\) | 4.79096e27 | 1.12270 | ||||||||
\(429\) | 2.27022e27 | 0.519118 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.30727e27 | 0.720209 | 0.360105 | − | 0.932912i | \(-0.382741\pi\) | ||||
0.360105 | + | 0.932912i | \(0.382741\pi\) | |||||||
\(432\) | −7.57754e26 | −0.161046 | ||||||||
\(433\) | −2.58162e27 | −0.535512 | −0.267756 | − | 0.963487i | \(-0.586282\pi\) | ||||
−0.267756 | + | 0.963487i | \(0.586282\pi\) | |||||||
\(434\) | 4.57466e26 | 0.0926224 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.03408e26 | 0.174291 | ||||||||
\(437\) | −1.30140e27 | −0.245107 | ||||||||
\(438\) | −7.39699e26 | −0.136012 | ||||||||
\(439\) | 6.51723e27 | 1.17000 | 0.585000 | − | 0.811034i | \(-0.301095\pi\) | ||||
0.585000 | + | 0.811034i | \(0.301095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.67515e26 | −0.0629028 | ||||||||
\(442\) | 5.03580e26 | 0.0841656 | ||||||||
\(443\) | −1.02894e28 | −1.67939 | −0.839694 | − | 0.543060i | \(-0.817266\pi\) | ||||
−0.839694 | + | 0.543060i | \(0.817266\pi\) | |||||||
\(444\) | −2.90538e27 | −0.463108 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.70838e27 | 0.411808 | ||||||||
\(447\) | −5.85334e26 | −0.0869310 | ||||||||
\(448\) | −4.23862e27 | −0.614901 | ||||||||
\(449\) | 2.52487e27 | 0.357810 | 0.178905 | − | 0.983866i | \(-0.442745\pi\) | ||||
0.178905 | + | 0.983866i | \(0.442745\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.35790e28 | 1.83659 | ||||||||
\(452\) | −5.27429e27 | −0.696964 | ||||||||
\(453\) | 1.06798e27 | 0.137890 | ||||||||
\(454\) | −2.38356e27 | −0.300705 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.84770e27 | 0.463522 | ||||||||
\(457\) | −4.85166e27 | −0.571176 | −0.285588 | − | 0.958352i | \(-0.592189\pi\) | ||||
−0.285588 | + | 0.958352i | \(0.592189\pi\) | |||||||
\(458\) | 6.74286e26 | 0.0775812 | ||||||||
\(459\) | −6.97628e26 | −0.0784496 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.01408e28 | −1.08946 | −0.544731 | − | 0.838611i | \(-0.683368\pi\) | ||||
−0.544731 | + | 0.838611i | \(0.683368\pi\) | |||||||
\(462\) | 1.19504e27 | 0.125499 | ||||||||
\(463\) | 9.15460e27 | 0.939808 | 0.469904 | − | 0.882718i | \(-0.344289\pi\) | ||||
0.469904 | + | 0.882718i | \(0.344289\pi\) | |||||||
\(464\) | −1.81734e27 | −0.182389 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.84267e27 | −0.176765 | ||||||||
\(467\) | −3.58291e27 | −0.336054 | −0.168027 | − | 0.985782i | \(-0.553740\pi\) | ||||
−0.168027 | + | 0.985782i | \(0.553740\pi\) | |||||||
\(468\) | 3.01119e27 | 0.276157 | ||||||||
\(469\) | 8.55935e26 | 0.0767584 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.94401e27 | 0.595512 | ||||||||
\(472\) | 9.77343e27 | 0.819702 | ||||||||
\(473\) | −7.39770e27 | −0.606813 | ||||||||
\(474\) | −1.29304e27 | −0.103738 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.51829e27 | −0.346817 | ||||||||
\(477\) | 9.89554e26 | 0.0743013 | ||||||||
\(478\) | 5.21772e27 | 0.383255 | ||||||||
\(479\) | −9.63095e27 | −0.692064 | −0.346032 | − | 0.938223i | \(-0.612471\pi\) | ||||
−0.346032 | + | 0.938223i | \(0.612471\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.08284e28 | 0.744802 | ||||||||
\(482\) | 4.57200e27 | 0.307690 | ||||||||
\(483\) | −1.10369e27 | −0.0726781 | ||||||||
\(484\) | −7.46717e26 | −0.0481149 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.44738e26 | 0.0151015 | ||||||||
\(487\) | 1.93192e27 | 0.116664 | 0.0583318 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583318 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(488\) | 9.10161e27 | 0.537910 | ||||||||
\(489\) | 2.26022e27 | 0.130740 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.62908e27 | −0.478199 | −0.239100 | − | 0.970995i | \(-0.576852\pi\) | ||||
−0.239100 | + | 0.970995i | \(0.576852\pi\) | |||||||
\(492\) | 1.80110e28 | 0.977021 | ||||||||
\(493\) | −1.67314e27 | −0.0888463 | ||||||||
\(494\) | −6.96587e27 | −0.362112 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.33655e27 | −0.365540 | ||||||||
\(497\) | 6.18305e27 | 0.301620 | ||||||||
\(498\) | 5.27806e27 | 0.252096 | ||||||||
\(499\) | −3.45711e28 | −1.61681 | −0.808403 | − | 0.588629i | \(-0.799668\pi\) | ||||
−0.808403 | + | 0.588629i | \(0.799668\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.85175e28 | −0.830397 | ||||||||
\(502\) | −5.78622e26 | −0.0254101 | ||||||||
\(503\) | −2.28934e28 | −0.984569 | −0.492285 | − | 0.870434i | \(-0.663838\pi\) | ||||
−0.492285 | + | 0.870434i | \(0.663838\pi\) | |||||||
\(504\) | 3.26316e27 | 0.137441 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.34774e26 | −0.0337278 | ||||||||
\(507\) | 3.36617e27 | 0.133215 | ||||||||
\(508\) | −7.73353e27 | −0.299784 | ||||||||
\(509\) | −3.01380e28 | −1.14440 | −0.572199 | − | 0.820115i | \(-0.693910\pi\) | ||||
−0.572199 | + | 0.820115i | \(0.693910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.47355e28 | −0.901367 | ||||||||
\(512\) | −2.60785e28 | −0.930995 | ||||||||
\(513\) | 9.65008e27 | 0.337519 | ||||||||
\(514\) | −2.50796e27 | −0.0859423 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.81222e27 | −0.322809 | ||||||||
\(517\) | 9.35977e26 | 0.0301727 | ||||||||
\(518\) | 5.70004e27 | 0.180059 | ||||||||
\(519\) | −2.84091e28 | −0.879429 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.99529e27 | −0.237705 | −0.118853 | − | 0.992912i | \(-0.537922\pi\) | ||||
−0.118853 | + | 0.992912i | \(0.537922\pi\) | |||||||
\(522\) | 5.86962e26 | 0.0171029 | ||||||||
\(523\) | −2.08661e28 | −0.595901 | −0.297950 | − | 0.954581i | \(-0.596303\pi\) | ||||
−0.297950 | + | 0.954581i | \(0.596303\pi\) | |||||||
\(524\) | 2.35739e28 | 0.659862 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.55845e28 | 0.419124 | ||||||||
\(527\) | −6.75441e27 | −0.178064 | ||||||||
\(528\) | −1.91653e28 | −0.495289 | ||||||||
\(529\) | −3.87006e28 | −0.980468 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.45119e28 | 0.596876 | ||||||||
\(532\) | 6.25001e28 | 1.49214 | ||||||||
\(533\) | −6.71272e28 | −1.57131 | ||||||||
\(534\) | −6.00322e27 | −0.137785 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.76774e27 | 0.0390111 | ||||||||
\(537\) | 1.93716e27 | 0.0419214 | ||||||||
\(538\) | 1.10856e28 | 0.235259 | ||||||||
\(539\) | −9.29526e27 | −0.193455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.81219e28 | −1.36369 | −0.681844 | − | 0.731497i | \(-0.738822\pi\) | ||||
−0.681844 | + | 0.731497i | \(0.738822\pi\) | |||||||
\(542\) | 5.74442e27 | 0.112786 | ||||||||
\(543\) | 3.25329e28 | 0.626505 | ||||||||
\(544\) | −1.41302e28 | −0.266907 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.90762e27 | −0.107372 | ||||||||
\(547\) | 5.16259e27 | 0.0920450 | 0.0460225 | − | 0.998940i | \(-0.485345\pi\) | ||||
0.0460225 | + | 0.998940i | \(0.485345\pi\) | |||||||
\(548\) | −8.71379e28 | −1.52409 | ||||||||
\(549\) | 2.28269e28 | 0.391686 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.31440e28 | 0.382250 | ||||||||
\(552\) | −2.27943e27 | −0.0369373 | ||||||||
\(553\) | −4.32391e28 | −0.687484 | ||||||||
\(554\) | −2.06228e28 | −0.321733 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.72470e28 | −0.709724 | ||||||||
\(557\) | 8.97767e28 | 1.32338 | 0.661689 | − | 0.749778i | \(-0.269840\pi\) | ||||
0.661689 | + | 0.749778i | \(0.269840\pi\) | |||||||
\(558\) | 2.36955e27 | 0.0342773 | ||||||||
\(559\) | 3.65703e28 | 0.519164 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.76445e28 | −0.241268 | ||||||||
\(562\) | −3.33847e26 | −0.00448039 | ||||||||
\(563\) | −7.85492e26 | −0.0103467 | −0.00517337 | − | 0.999987i | \(-0.501647\pi\) | ||||
−0.00517337 | + | 0.999987i | \(0.501647\pi\) | |||||||
\(564\) | 1.24147e27 | 0.0160511 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.50364e28 | 0.187315 | ||||||||
\(567\) | 8.18405e27 | 0.100080 | ||||||||
\(568\) | 1.27697e28 | 0.153293 | ||||||||
\(569\) | −9.58086e28 | −1.12908 | −0.564541 | − | 0.825405i | \(-0.690947\pi\) | ||||
−0.564541 | + | 0.825405i | \(0.690947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.50183e26 | −0.00738511 | −0.00369255 | − | 0.999993i | \(-0.501175\pi\) | ||||
−0.00369255 | + | 0.999993i | \(0.501175\pi\) | |||||||
\(572\) | 7.61596e28 | 0.849310 | ||||||||
\(573\) | −6.98355e28 | −0.764632 | ||||||||
\(574\) | −3.53356e28 | −0.379872 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.19549e28 | −0.227560 | ||||||||
\(577\) | 1.67471e29 | 1.70448 | 0.852242 | − | 0.523148i | \(-0.175242\pi\) | ||||
0.852242 | + | 0.523148i | \(0.175242\pi\) | |||||||
\(578\) | 1.96402e28 | 0.196292 | ||||||||
\(579\) | 6.91975e28 | 0.679150 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.76498e29 | 1.67067 | ||||||||
\(582\) | 1.38238e28 | 0.128510 | ||||||||
\(583\) | 2.50280e28 | 0.228510 | ||||||||
\(584\) | −5.10856e28 | −0.458104 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.99074e28 | 0.258734 | ||||||||
\(587\) | −2.23014e29 | −1.89510 | −0.947551 | − | 0.319603i | \(-0.896450\pi\) | ||||
−0.947551 | + | 0.319603i | \(0.896450\pi\) | |||||||
\(588\) | −1.23291e28 | −0.102913 | ||||||||
\(589\) | 9.34317e28 | 0.766097 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.73010e28 | −0.295156 | ||||||||
\(592\) | −9.14138e28 | −0.710614 | ||||||||
\(593\) | 1.71015e29 | 1.30605 | 0.653024 | − | 0.757337i | \(-0.273500\pi\) | ||||
0.653024 | + | 0.757337i | \(0.273500\pi\) | |||||||
\(594\) | 6.18997e27 | 0.0464441 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.96363e28 | −0.142225 | ||||||||
\(597\) | 1.06641e29 | 0.758914 | ||||||||
\(598\) | 4.12668e27 | 0.0288561 | ||||||||
\(599\) | −1.56747e29 | −1.07701 | −0.538504 | − | 0.842623i | \(-0.681010\pi\) | ||||
−0.538504 | + | 0.842623i | \(0.681010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.53561e29 | −1.01883 | −0.509413 | − | 0.860522i | \(-0.670137\pi\) | ||||
−0.509413 | + | 0.860522i | \(0.670137\pi\) | |||||||
\(602\) | 1.92505e28 | 0.125510 | ||||||||
\(603\) | 4.43352e27 | 0.0284064 | ||||||||
\(604\) | 3.58279e28 | 0.225597 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.47235e28 | −0.211184 | ||||||||
\(607\) | −2.86065e29 | −1.70995 | −0.854976 | − | 0.518667i | \(-0.826428\pi\) | ||||
−0.854976 | + | 0.518667i | \(0.826428\pi\) | |||||||
\(608\) | 1.95459e29 | 1.14833 | ||||||||
\(609\) | 1.96280e28 | 0.113343 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.62697e27 | −0.0258145 | ||||||||
\(612\) | −2.34035e28 | −0.128349 | ||||||||
\(613\) | −4.90169e28 | −0.264247 | −0.132124 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132124 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(614\) | 6.00189e28 | 0.318068 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.25325e28 | 0.422695 | ||||||||
\(617\) | −2.77126e29 | −1.39535 | −0.697676 | − | 0.716413i | \(-0.745783\pi\) | ||||
−0.697676 | + | 0.716413i | \(0.745783\pi\) | |||||||
\(618\) | 1.59816e28 | 0.0791118 | ||||||||
\(619\) | −8.92512e28 | −0.434373 | −0.217186 | − | 0.976130i | \(-0.569688\pi\) | ||||
−0.217186 | + | 0.976130i | \(0.569688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.71683e27 | −0.0268964 | ||||||||
\(622\) | 9.28631e28 | 0.429580 | ||||||||
\(623\) | −2.00748e29 | −0.913116 | ||||||||
\(624\) | 9.47429e28 | 0.423749 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.06818e28 | 0.132694 | ||||||||
\(627\) | 2.44072e29 | 1.03803 | ||||||||
\(628\) | 2.32952e29 | 0.974296 | ||||||||
\(629\) | −8.41603e28 | −0.346159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.08364e28 | 0.281805 | 0.140902 | − | 0.990024i | \(-0.455000\pi\) | ||||
0.140902 | + | 0.990024i | \(0.455000\pi\) | |||||||
\(632\) | −8.93006e28 | −0.349402 | ||||||||
\(633\) | −1.73976e28 | −0.0669499 | ||||||||
\(634\) | 2.83087e28 | 0.107148 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.31968e28 | 0.121562 | ||||||||
\(637\) | 4.59508e28 | 0.165512 | ||||||||
\(638\) | 1.48456e28 | 0.0525992 | ||||||||
\(639\) | 3.20265e28 | 0.111622 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.59855e28 | 0.0876440 | 0.0438220 | − | 0.999039i | \(-0.486047\pi\) | ||||
0.0438220 | + | 0.999039i | \(0.486047\pi\) | |||||||
\(642\) | −4.86860e28 | −0.161542 | ||||||||
\(643\) | 1.38976e29 | 0.453652 | 0.226826 | − | 0.973935i | \(-0.427165\pi\) | ||||
0.226826 | + | 0.973935i | \(0.427165\pi\) | |||||||
\(644\) | −3.70259e28 | −0.118906 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.41400e28 | 0.168297 | ||||||||
\(647\) | −4.60493e29 | −1.40841 | −0.704203 | − | 0.709999i | \(-0.748695\pi\) | ||||
−0.704203 | + | 0.709999i | \(0.748695\pi\) | |||||||
\(648\) | 1.69023e28 | 0.0508637 | ||||||||
\(649\) | 6.19959e29 | 1.83567 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.92377e28 | 0.227160 | ||||||||
\(652\) | 7.58243e28 | 0.213899 | ||||||||
\(653\) | 6.22853e29 | 1.72901 | 0.864504 | − | 0.502625i | \(-0.167632\pi\) | ||||
0.864504 | + | 0.502625i | \(0.167632\pi\) | |||||||
\(654\) | −9.18049e27 | −0.0250784 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.66691e29 | 1.49919 | ||||||||
\(657\) | −1.28123e29 | −0.333574 | ||||||||
\(658\) | −2.43562e27 | −0.00624077 | ||||||||
\(659\) | 6.30181e29 | 1.58916 | 0.794582 | − | 0.607157i | \(-0.207690\pi\) | ||||
0.794582 | + | 0.607157i | \(0.207690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.89533e29 | −0.951545 | −0.475773 | − | 0.879568i | \(-0.657832\pi\) | ||||
−0.475773 | + | 0.879568i | \(0.657832\pi\) | |||||||
\(662\) | 3.35524e28 | 0.0806704 | ||||||||
\(663\) | 8.72252e28 | 0.206419 | ||||||||
\(664\) | 3.64517e29 | 0.849089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.95247e28 | 0.0666356 | ||||||||
\(667\) | −1.37108e28 | −0.0304609 | ||||||||
\(668\) | −6.21211e29 | −1.35858 | ||||||||
\(669\) | 4.69120e29 | 1.00997 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.77344e29 | 1.20461 | ||||||||
\(672\) | 1.65765e29 | 0.340499 | ||||||||
\(673\) | 2.70633e29 | 0.547297 | 0.273648 | − | 0.961830i | \(-0.411770\pi\) | ||||
0.273648 | + | 0.961830i | \(0.411770\pi\) | |||||||
\(674\) | −2.10502e29 | −0.419109 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.12926e29 | 0.217948 | ||||||||
\(677\) | −4.23921e29 | −0.805572 | −0.402786 | − | 0.915294i | \(-0.631958\pi\) | ||||
−0.402786 | + | 0.915294i | \(0.631958\pi\) | |||||||
\(678\) | 5.35977e28 | 0.100285 | ||||||||
\(679\) | 4.62267e29 | 0.851648 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.12857e29 | −0.737488 | ||||||||
\(682\) | 5.99311e28 | 0.105418 | ||||||||
\(683\) | −9.87881e29 | −1.71115 | −0.855573 | − | 0.517682i | \(-0.826795\pi\) | ||||
−0.855573 | + | 0.517682i | \(0.826795\pi\) | |||||||
\(684\) | 3.23734e29 | 0.552203 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.52367e29 | 0.252051 | ||||||||
\(687\) | 1.16793e29 | 0.190271 | ||||||||
\(688\) | −3.08728e29 | −0.495333 | ||||||||
\(689\) | −1.23725e29 | −0.195504 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.20248e29 | −0.184314 | −0.0921569 | − | 0.995744i | \(-0.529376\pi\) | ||||
−0.0921569 | + | 0.995744i | \(0.529376\pi\) | |||||||
\(692\) | −9.53049e29 | −1.43880 | ||||||||
\(693\) | 2.06993e29 | 0.307791 | ||||||||
\(694\) | −4.22911e28 | −0.0619405 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.05372e28 | 0.0576045 | ||||||||
\(697\) | 5.21725e29 | 0.730293 | ||||||||
\(698\) | −2.87586e29 | −0.396539 | ||||||||
\(699\) | −3.19170e29 | −0.433522 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.01199e29 | 0.397022 | 0.198511 | − | 0.980099i | \(-0.436389\pi\) | ||||
0.198511 | + | 0.980099i | \(0.436389\pi\) | |||||||
\(702\) | −3.05999e28 | −0.0397356 | ||||||||
\(703\) | 1.16416e30 | 1.48930 | ||||||||
\(704\) | −5.55288e29 | −0.699850 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.04126e29 | −0.372053 | ||||||||
\(707\) | −1.16115e30 | −1.39954 | ||||||||
\(708\) | 8.22306e29 | 0.976527 | ||||||||
\(709\) | −4.42994e29 | −0.518337 | −0.259168 | − | 0.965832i | \(-0.583448\pi\) | ||||
−0.259168 | + | 0.965832i | \(0.583448\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.23967e29 | −0.254421 | ||||||||
\(712\) | −4.14599e29 | −0.464075 | ||||||||
\(713\) | −5.53502e28 | −0.0610491 | ||||||||
\(714\) | 4.59151e28 | 0.0499028 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.49864e28 | 0.0685861 | ||||||||
\(717\) | 9.03763e29 | 0.939947 | ||||||||
\(718\) | 4.47176e28 | 0.0458323 | ||||||||
\(719\) | 1.48484e30 | 1.49978 | 0.749888 | − | 0.661565i | \(-0.230108\pi\) | ||||
0.749888 | + | 0.661565i | \(0.230108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.34425e29 | 0.524283 | ||||||||
\(722\) | −5.05422e29 | −0.488668 | ||||||||
\(723\) | 7.91918e29 | 0.754619 | ||||||||
\(724\) | 1.09139e30 | 1.02500 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.58819e27 | 0.00692315 | ||||||||
\(727\) | 1.41765e30 | 1.27484 | 0.637421 | − | 0.770516i | \(-0.280001\pi\) | ||||
0.637421 | + | 0.770516i | \(0.280001\pi\) | |||||||
\(728\) | −4.07997e29 | −0.361640 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.84231e29 | −0.241290 | ||||||||
\(732\) | 7.65782e29 | 0.640824 | ||||||||
\(733\) | 1.26744e30 | 1.04553 | 0.522764 | − | 0.852477i | \(-0.324901\pi\) | ||||
0.522764 | + | 0.852477i | \(0.324901\pi\) | |||||||
\(734\) | −2.26095e28 | −0.0183858 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.15793e29 | −0.0915089 | ||||||||
\(737\) | 1.12133e29 | 0.0873627 | ||||||||
\(738\) | −1.83029e29 | −0.140581 | ||||||||
\(739\) | −1.86110e30 | −1.40930 | −0.704650 | − | 0.709555i | \(-0.748896\pi\) | ||||
−0.704650 | + | 0.709555i | \(0.748896\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.20656e30 | −0.888091 | ||||||||
\(742\) | −6.51285e28 | −0.0472640 | ||||||||
\(743\) | 5.15013e29 | 0.368499 | 0.184249 | − | 0.982880i | \(-0.441015\pi\) | ||||
0.184249 | + | 0.982880i | \(0.441015\pi\) | |||||||
\(744\) | 1.63647e29 | 0.115450 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.10895e29 | −0.350408 | ||||||||
\(747\) | 9.14214e29 | 0.618275 | ||||||||
\(748\) | −5.91926e29 | −0.394731 | ||||||||
\(749\) | −1.62806e30 | −1.07056 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.60839e30 | −1.02842 | −0.514211 | − | 0.857663i | \(-0.671915\pi\) | ||||
−0.514211 | + | 0.857663i | \(0.671915\pi\) | |||||||
\(752\) | 3.90611e28 | 0.0246296 | ||||||||
\(753\) | −1.00223e29 | −0.0623191 | ||||||||
\(754\) | −7.33885e28 | −0.0450017 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.74552e29 | 0.163737 | ||||||||
\(757\) | −2.14104e29 | −0.125927 | −0.0629634 | − | 0.998016i | \(-0.520055\pi\) | ||||
−0.0629634 | + | 0.998016i | \(0.520055\pi\) | |||||||
\(758\) | −8.89718e28 | −0.0516090 | ||||||||
\(759\) | −1.44591e29 | −0.0827187 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.25293e30 | 0.697250 | 0.348625 | − | 0.937262i | \(-0.386649\pi\) | ||||
0.348625 | + | 0.937262i | \(0.386649\pi\) | |||||||
\(762\) | 7.85887e28 | 0.0431353 | ||||||||
\(763\) | −3.06996e29 | −0.166198 | ||||||||
\(764\) | −2.34279e30 | −1.25099 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.29516e29 | −0.119237 | ||||||||
\(767\) | −3.06475e30 | −1.57052 | ||||||||
\(768\) | −5.60474e29 | −0.283310 | ||||||||
\(769\) | 2.53517e30 | 1.26410 | 0.632048 | − | 0.774929i | \(-0.282215\pi\) | ||||
0.632048 | + | 0.774929i | \(0.282215\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.34403e29 | −0.210777 | ||||||||
\(772\) | 2.32139e30 | 1.11113 | ||||||||
\(773\) | −1.70099e30 | −0.803187 | −0.401594 | − | 0.915818i | \(-0.631544\pi\) | ||||
−0.401594 | + | 0.915818i | \(0.631544\pi\) | |||||||
\(774\) | 9.97125e28 | 0.0464483 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.54707e29 | 0.432835 | ||||||||
\(777\) | 9.87306e29 | 0.441602 | ||||||||
\(778\) | −3.36069e29 | −0.148301 | ||||||||
\(779\) | −7.21686e30 | −3.14199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.10022e29 | 0.343290 | ||||||||
\(782\) | −3.20733e28 | −0.0134113 | ||||||||
\(783\) | 1.01668e29 | 0.0419454 | ||||||||
\(784\) | −3.87919e29 | −0.157915 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.39560e29 | −0.0949460 | ||||||||
\(787\) | 4.98615e30 | 1.94998 | 0.974991 | − | 0.222246i | \(-0.0713388\pi\) | ||||
0.974991 | + | 0.222246i | \(0.0713388\pi\) | |||||||
\(788\) | −1.25135e30 | −0.482894 | ||||||||
\(789\) | 2.69940e30 | 1.02792 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.79231e30 | 0.664598 | ||||||||
\(792\) | 4.27496e29 | 0.156429 | ||||||||
\(793\) | −2.85408e30 | −1.03062 | ||||||||
\(794\) | 8.31160e29 | 0.296189 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.57751e30 | 1.24163 | ||||||||
\(797\) | −4.48685e30 | −1.53684 | −0.768420 | − | 0.639946i | \(-0.778957\pi\) | ||||
−0.768420 | + | 0.639946i | \(0.778957\pi\) | |||||||
\(798\) | −6.35130e29 | −0.214700 | ||||||||
\(799\) | 3.59616e28 | 0.0119977 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.03982e30 | −0.337922 | ||||||||
\(802\) | −1.11306e29 | −0.0357016 | ||||||||
\(803\) | −3.24052e30 | −1.02589 | ||||||||
\(804\) | 1.48732e29 | 0.0464747 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.96267e29 | −0.0901915 | ||||||||
\(807\) | 1.92014e30 | 0.576981 | ||||||||
\(808\) | −2.39810e30 | −0.711292 | ||||||||
\(809\) | −5.22233e30 | −1.52899 | −0.764496 | − | 0.644629i | \(-0.777012\pi\) | ||||
−0.764496 | + | 0.644629i | \(0.777012\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.36541e30 | −1.81597 | −0.907983 | − | 0.419007i | \(-0.862378\pi\) | ||||
−0.907983 | + | 0.419007i | \(0.862378\pi\) | |||||||
\(812\) | 6.58466e29 | 0.185436 | ||||||||
\(813\) | 9.94992e29 | 0.276611 | ||||||||
\(814\) | 7.46744e29 | 0.204935 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.36359e29 | −0.196944 | ||||||||
\(817\) | 3.93168e30 | 1.03812 | ||||||||
\(818\) | −1.45145e30 | −0.378348 | ||||||||
\(819\) | −1.02326e30 | −0.263333 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.95104e29 | −0.199444 | −0.0997220 | − | 0.995015i | \(-0.531795\pi\) | ||||
−0.0997220 | + | 0.995015i | \(0.531795\pi\) | |||||||
\(822\) | 8.85501e29 | 0.219298 | ||||||||
\(823\) | 1.00191e30 | 0.244980 | 0.122490 | − | 0.992470i | \(-0.460912\pi\) | ||||
0.122490 | + | 0.992470i | \(0.460912\pi\) | |||||||
\(824\) | 1.10373e30 | 0.266458 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.61328e30 | −0.379680 | ||||||||
\(827\) | −4.61386e30 | −1.07215 | −0.536076 | − | 0.844170i | \(-0.680094\pi\) | ||||
−0.536076 | + | 0.844170i | \(0.680094\pi\) | |||||||
\(828\) | −1.91784e29 | −0.0440042 | ||||||||
\(829\) | −2.84827e30 | −0.645294 | −0.322647 | − | 0.946519i | \(-0.604573\pi\) | ||||
−0.322647 | + | 0.946519i | \(0.604573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.57209e30 | −0.789062 | ||||||||
\(832\) | 2.74505e30 | 0.598763 | ||||||||
\(833\) | −3.57138e29 | −0.0769243 | ||||||||
\(834\) | 4.80127e29 | 0.102121 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.18794e30 | 1.69828 | ||||||||
\(837\) | 4.10430e29 | 0.0840662 | ||||||||
\(838\) | 1.70481e29 | 0.0344836 | ||||||||
\(839\) | −6.35489e30 | −1.26943 | −0.634713 | − | 0.772748i | \(-0.718882\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.88901e30 | −0.952496 | ||||||||
\(842\) | 1.57989e30 | 0.303984 | ||||||||
\(843\) | −5.78257e28 | −0.0109883 | ||||||||
\(844\) | −5.83641e29 | −0.109534 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.26159e28 | −0.00230956 | ||||||||
\(847\) | 2.53749e29 | 0.0458806 | ||||||||
\(848\) | 1.04449e30 | 0.186530 | ||||||||
\(849\) | 2.60446e30 | 0.459396 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.89666e29 | −0.118680 | ||||||||
\(852\) | 1.07440e30 | 0.182621 | ||||||||
\(853\) | −7.05513e30 | −1.18451 | −0.592257 | − | 0.805749i | \(-0.701763\pi\) | ||||
−0.592257 | + | 0.805749i | \(0.701763\pi\) | |||||||
\(854\) | −1.50238e30 | −0.249156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.36239e30 | −0.544093 | ||||||||
\(857\) | −3.70327e30 | −0.591953 | −0.295976 | − | 0.955195i | \(-0.595645\pi\) | ||||
−0.295976 | + | 0.955195i | \(0.595645\pi\) | |||||||
\(858\) | −7.73939e29 | −0.122205 | ||||||||
\(859\) | −5.45289e29 | −0.0850548 | −0.0425274 | − | 0.999095i | \(-0.513541\pi\) | ||||
−0.0425274 | + | 0.999095i | \(0.513541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.12048e30 | −0.931649 | ||||||||
\(862\) | −1.12748e30 | −0.169544 | ||||||||
\(863\) | 7.07308e30 | 1.05074 | 0.525370 | − | 0.850874i | \(-0.323927\pi\) | ||||
0.525370 | + | 0.850874i | \(0.323927\pi\) | |||||||
\(864\) | 8.58618e29 | 0.126010 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.80098e29 | 0.126065 | ||||||||
\(867\) | 3.40188e30 | 0.481414 | ||||||||
\(868\) | 2.65821e30 | 0.371648 | ||||||||
\(869\) | −5.66462e30 | −0.782461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.54327e29 | −0.0747439 | ||||||||
\(872\) | −6.34030e29 | −0.0844669 | ||||||||
\(873\) | 2.39442e30 | 0.315174 | ||||||||
\(874\) | 4.43660e29 | 0.0577006 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.29819e30 | −0.545748 | ||||||||
\(877\) | −1.58002e31 | −1.98229 | −0.991146 | − | 0.132779i | \(-0.957610\pi\) | ||||
−0.991146 | + | 0.132779i | \(0.957610\pi\) | |||||||
\(878\) | −2.22179e30 | −0.275429 | ||||||||
\(879\) | 5.18026e30 | 0.634553 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.64321e30 | 1.15339 | 0.576693 | − | 0.816961i | \(-0.304343\pi\) | ||||
0.576693 | + | 0.816961i | \(0.304343\pi\) | |||||||
\(882\) | 1.25289e29 | 0.0148079 | ||||||||
\(883\) | 7.91697e30 | 0.924638 | 0.462319 | − | 0.886714i | \(-0.347018\pi\) | ||||
0.462319 | + | 0.886714i | \(0.347018\pi\) | |||||||
\(884\) | 2.92617e30 | 0.337715 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.50776e30 | 0.395344 | ||||||||
\(887\) | −7.76439e30 | −0.864787 | −0.432394 | − | 0.901685i | \(-0.642331\pi\) | ||||
−0.432394 | + | 0.901685i | \(0.642331\pi\) | |||||||
\(888\) | 2.03906e30 | 0.224436 | ||||||||
\(889\) | 2.62801e30 | 0.285863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.07217e30 | 0.113906 | ||||||||
\(892\) | 1.57377e31 | 1.65238 | ||||||||
\(893\) | −4.97447e29 | −0.0516186 | ||||||||
\(894\) | 1.99546e29 | 0.0204644 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.33221e30 | 0.734515 | ||||||||
\(897\) | 7.14782e29 | 0.0707706 | ||||||||
\(898\) | −8.60752e29 | −0.0842318 | ||||||||
\(899\) | 9.84344e29 | 0.0952073 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.61613e29 | 0.0908636 | ||||||||
\(902\) | −4.62920e30 | −0.432352 | ||||||||
\(903\) | 3.33438e30 | 0.307818 | ||||||||
\(904\) | 3.70160e30 | 0.337770 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.64086e29 | −0.0324607 | ||||||||
\(907\) | 1.25327e31 | 1.10451 | 0.552253 | − | 0.833677i | \(-0.313768\pi\) | ||||
0.552253 | + | 0.833677i | \(0.313768\pi\) | |||||||
\(908\) | −1.38502e31 | −1.20658 | ||||||||
\(909\) | −6.01446e30 | −0.517936 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.93009e30 | 0.835623 | 0.417811 | − | 0.908534i | \(-0.362797\pi\) | ||||
0.417811 | + | 0.908534i | \(0.362797\pi\) | |||||||
\(912\) | 1.01858e31 | 0.847326 | ||||||||
\(913\) | 2.31225e31 | 1.90148 | ||||||||
\(914\) | 1.65398e30 | 0.134460 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.91809e30 | 0.311295 | ||||||||
\(917\) | −8.01087e30 | −0.629219 | ||||||||
\(918\) | 2.37828e29 | 0.0184678 | ||||||||
\(919\) | 2.22319e31 | 1.70673 | 0.853364 | − | 0.521316i | \(-0.174559\pi\) | ||||
0.853364 | + | 0.521316i | \(0.174559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.03959e31 | 0.780072 | ||||||||
\(922\) | 3.45709e30 | 0.256470 | ||||||||
\(923\) | −4.00431e30 | −0.293704 | ||||||||
\(924\) | 6.94403e30 | 0.503566 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.12089e30 | −0.221240 | ||||||||
\(927\) | 2.76818e30 | 0.194024 | ||||||||
\(928\) | 2.05925e30 | 0.142710 | ||||||||
\(929\) | −1.62508e31 | −1.11355 | −0.556773 | − | 0.830664i | \(-0.687961\pi\) | ||||
−0.556773 | + | 0.830664i | \(0.687961\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.94018e30 | 0.330957 | ||||||||
\(932\) | −1.07073e31 | −0.709271 | ||||||||
\(933\) | 1.60848e31 | 1.05356 | ||||||||
\(934\) | 1.22145e30 | 0.0791103 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.11331e30 | −0.133834 | ||||||||
\(937\) | 1.81129e30 | 0.113428 | 0.0567142 | − | 0.998390i | \(-0.481938\pi\) | ||||
0.0567142 | + | 0.998390i | \(0.481938\pi\) | |||||||
\(938\) | −2.91797e29 | −0.0180697 | ||||||||
\(939\) | 5.31441e30 | 0.325436 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.25431e31 | −1.94880 | −0.974402 | − | 0.224812i | \(-0.927823\pi\) | ||||
−0.974402 | + | 0.224812i | \(0.927823\pi\) | |||||||
\(942\) | −2.36728e30 | −0.140189 | ||||||||
\(943\) | 4.27536e30 | 0.250380 | ||||||||
\(944\) | 2.58727e31 | 1.49843 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.52195e30 | 0.142850 | ||||||||
\(947\) | −1.36434e31 | −0.764270 | −0.382135 | − | 0.924107i | \(-0.624811\pi\) | ||||
−0.382135 | + | 0.924107i | \(0.624811\pi\) | |||||||
\(948\) | −7.51348e30 | −0.416249 | ||||||||
\(949\) | 1.60194e31 | 0.877710 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.90335e30 | 0.262783 | ||||||||
\(952\) | 3.17102e30 | 0.168078 | ||||||||
\(953\) | −1.03136e31 | −0.540673 | −0.270337 | − | 0.962766i | \(-0.587135\pi\) | ||||
−0.270337 | + | 0.962766i | \(0.587135\pi\) | |||||||
\(954\) | −3.37348e29 | −0.0174912 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.03188e31 | 1.53781 | ||||||||
\(957\) | 2.57140e30 | 0.129001 | ||||||||
\(958\) | 3.28328e30 | 0.162918 | ||||||||
\(959\) | 2.96111e31 | 1.45331 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.68517e31 | −0.809187 | ||||||||
\(962\) | −3.69151e30 | −0.175334 | ||||||||
\(963\) | −8.43291e30 | −0.396188 | ||||||||
\(964\) | 2.65667e31 | 1.23461 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.76260e29 | 0.0171091 | ||||||||
\(967\) | −3.33709e31 | −1.50103 | −0.750517 | − | 0.660851i | \(-0.770196\pi\) | ||||
−0.750517 | + | 0.660851i | \(0.770196\pi\) | |||||||
\(968\) | 5.24061e29 | 0.0233180 | ||||||||
\(969\) | 9.37760e30 | 0.412755 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.13037e30 | 0.0917598 | 0.0458799 | − | 0.998947i | \(-0.485391\pi\) | ||||
0.0458799 | + | 0.998947i | \(0.485391\pi\) | |||||||
\(972\) | 1.42211e30 | 0.0605950 | ||||||||
\(973\) | 1.60555e31 | 0.676765 | ||||||||
\(974\) | −6.58611e29 | −0.0274637 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.40943e31 | 0.983310 | ||||||||
\(977\) | −4.34834e31 | −1.75562 | −0.877811 | − | 0.479008i | \(-0.840997\pi\) | ||||
−0.877811 | + | 0.479008i | \(0.840997\pi\) | |||||||
\(978\) | −7.70532e29 | −0.0307774 | ||||||||
\(979\) | −2.62993e31 | −1.03926 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.59015e30 | −0.0615056 | ||||||||
\(982\) | 2.94174e30 | 0.112573 | ||||||||
\(983\) | 4.41457e31 | 1.67138 | 0.835692 | − | 0.549198i | \(-0.185067\pi\) | ||||
0.835692 | + | 0.549198i | \(0.185067\pi\) | |||||||
\(984\) | −1.26405e31 | −0.473494 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.70389e29 | 0.0209153 | ||||||||
\(987\) | −4.21875e29 | −0.0153057 | ||||||||
\(988\) | −4.04768e31 | −1.45297 | ||||||||
\(989\) | −2.32918e30 | −0.0827260 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.77164e31 | −1.31147 | −0.655734 | − | 0.754992i | \(-0.727641\pi\) | ||||
−0.655734 | + | 0.754992i | \(0.727641\pi\) | |||||||
\(992\) | 8.31311e30 | 0.286017 | ||||||||
\(993\) | 5.81161e30 | 0.197847 | ||||||||
\(994\) | −2.10786e30 | −0.0710044 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.06694e31 | 1.01154 | ||||||||
\(997\) | −2.89594e31 | −0.945126 | −0.472563 | − | 0.881297i | \(-0.656671\pi\) | ||||
−0.472563 | + | 0.881297i | \(0.656671\pi\) | |||||||
\(998\) | 1.17856e31 | 0.380612 | ||||||||
\(999\) | 5.11398e30 | 0.163426 |
(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 | 75.22.a.j.1.3 | yes | 6 | |
5.2 | odd | 4 | 75.22.b.i.49.6 | 12 | |||
5.3 | odd | 4 | 75.22.b.i.49.7 | 12 | |||
5.4 | even | 2 | 75.22.a.i.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.22.a.i.1.4 | ✓ | 6 | 5.4 | even | 2 | ||
75.22.a.j.1.3 | yes | 6 | 1.1 | even | 1 | trivial | |
75.22.b.i.49.6 | 12 | 5.2 | odd | 4 | |||
75.22.b.i.49.7 | 12 | 5.3 | odd | 4 |