Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,10,Mod(1,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.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: | \(60.2591928312\) |
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: | \( x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(35.1685\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −38.1685 | −1.68682 | −0.843412 | − | 0.537267i | \(-0.819457\pi\) | ||||
−0.843412 | + | 0.537267i | \(0.819457\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 944.833 | 1.84538 | ||||||||
\(5\) | 109.762 | 0.0785394 | 0.0392697 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392697 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5947.44 | 0.936244 | 0.468122 | − | 0.883664i | \(-0.344931\pi\) | ||||
0.468122 | + | 0.883664i | \(0.344931\pi\) | |||||||
\(8\) | −16520.6 | −1.42600 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4189.45 | −0.132482 | ||||||||
\(11\) | 25205.7 | 0.519076 | 0.259538 | − | 0.965733i | \(-0.416430\pi\) | ||||
0.259538 | + | 0.965733i | \(0.416430\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28561.0 | 0.277350 | ||||||||
\(14\) | −227005. | −1.57928 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 146811. | 0.560039 | ||||||||
\(17\) | −109318. | −0.317447 | −0.158724 | − | 0.987323i | \(-0.550738\pi\) | ||||
−0.158724 | + | 0.987323i | \(0.550738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −904609. | −1.59246 | −0.796232 | − | 0.604992i | \(-0.793176\pi\) | ||||
−0.796232 | + | 0.604992i | \(0.793176\pi\) | |||||||
\(20\) | 103707. | 0.144935 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −962062. | −0.875590 | ||||||||
\(23\) | 435749. | 0.324684 | 0.162342 | − | 0.986735i | \(-0.448095\pi\) | ||||
0.162342 | + | 0.986735i | \(0.448095\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.94108e6 | −0.993832 | ||||||||
\(26\) | −1.09013e6 | −0.467841 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.61934e6 | 1.72772 | ||||||||
\(29\) | −6.44791e6 | −1.69289 | −0.846443 | − | 0.532479i | \(-0.821260\pi\) | ||||
−0.846443 | + | 0.532479i | \(0.821260\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.62308e6 | 1.28805 | 0.644024 | − | 0.765005i | \(-0.277264\pi\) | ||||
0.644024 | + | 0.765005i | \(0.277264\pi\) | |||||||
\(32\) | 2.85499e6 | 0.481315 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.17250e6 | 0.535477 | ||||||||
\(35\) | 652804. | 0.0735320 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.14357e6 | 0.363469 | 0.181734 | − | 0.983348i | \(-0.441829\pi\) | ||||
0.181734 | + | 0.983348i | \(0.441829\pi\) | |||||||
\(38\) | 3.45275e7 | 2.68621 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.81333e6 | −0.111997 | ||||||||
\(41\) | −1.49568e7 | −0.826632 | −0.413316 | − | 0.910588i | \(-0.635630\pi\) | ||||
−0.413316 | + | 0.910588i | \(0.635630\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.01789e7 | 1.79221 | 0.896107 | − | 0.443838i | \(-0.146384\pi\) | ||||
0.896107 | + | 0.443838i | \(0.146384\pi\) | |||||||
\(44\) | 2.38151e7 | 0.957891 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.66319e7 | −0.547685 | ||||||||
\(47\) | −6.30151e6 | −0.188367 | −0.0941834 | − | 0.995555i | \(-0.530024\pi\) | ||||
−0.0941834 | + | 0.995555i | \(0.530024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.98153e6 | −0.123447 | ||||||||
\(50\) | 7.40880e7 | 1.67642 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.69854e7 | 0.511815 | ||||||||
\(53\) | −1.53111e7 | −0.266542 | −0.133271 | − | 0.991080i | \(-0.542548\pi\) | ||||
−0.133271 | + | 0.991080i | \(0.542548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.76663e6 | 0.0407679 | ||||||||
\(56\) | −9.82552e7 | −1.33509 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.46107e8 | 2.85560 | ||||||||
\(59\) | 1.52760e8 | 1.64126 | 0.820629 | − | 0.571462i | \(-0.193624\pi\) | ||||
0.820629 | + | 0.571462i | \(0.193624\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.66321e7 | 0.801114 | 0.400557 | − | 0.916272i | \(-0.368817\pi\) | ||||
0.400557 | + | 0.916272i | \(0.368817\pi\) | |||||||
\(62\) | −2.52793e8 | −2.17271 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.84138e8 | −1.37193 | ||||||||
\(65\) | 3.13492e6 | 0.0217829 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.01034e8 | −0.612537 | −0.306268 | − | 0.951945i | \(-0.599080\pi\) | ||||
−0.306268 | + | 0.951945i | \(0.599080\pi\) | |||||||
\(68\) | −1.03287e8 | −0.585809 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.49165e7 | −0.124036 | ||||||||
\(71\) | −4.13122e8 | −1.92937 | −0.964685 | − | 0.263406i | \(-0.915154\pi\) | ||||
−0.964685 | + | 0.263406i | \(0.915154\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.14453e8 | −1.29599 | −0.647997 | − | 0.761643i | \(-0.724393\pi\) | ||||
−0.647997 | + | 0.761643i | \(0.724393\pi\) | |||||||
\(74\) | −1.58154e8 | −0.613108 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.54704e8 | −2.93870 | ||||||||
\(77\) | 1.49909e8 | 0.485982 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00580e8 | −0.579383 | −0.289692 | − | 0.957120i | \(-0.593553\pi\) | ||||
−0.289692 | + | 0.957120i | \(0.593553\pi\) | |||||||
\(80\) | 1.61143e7 | 0.0439851 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.70879e8 | 1.39438 | ||||||||
\(83\) | −6.34578e7 | −0.146769 | −0.0733843 | − | 0.997304i | \(-0.523380\pi\) | ||||
−0.0733843 | + | 0.997304i | \(0.523380\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.19990e7 | −0.0249321 | ||||||||
\(86\) | −1.53357e9 | −3.02315 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.16412e8 | −0.740204 | ||||||||
\(89\) | −3.47074e7 | −0.0586364 | −0.0293182 | − | 0.999570i | \(-0.509334\pi\) | ||||
−0.0293182 | + | 0.999570i | \(0.509334\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.69865e8 | 0.259667 | ||||||||
\(92\) | 4.11710e8 | 0.599164 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.40519e8 | 0.317742 | ||||||||
\(95\) | −9.92918e7 | −0.125071 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.25403e9 | −1.43825 | −0.719127 | − | 0.694879i | \(-0.755458\pi\) | ||||
−0.719127 | + | 0.694879i | \(0.755458\pi\) | |||||||
\(98\) | 1.90137e8 | 0.208233 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.83399e9 | −1.83399 | ||||||||
\(101\) | 9.06459e8 | 0.866766 | 0.433383 | − | 0.901210i | \(-0.357320\pi\) | ||||
0.433383 | + | 0.901210i | \(0.357320\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.17013e8 | −0.365075 | −0.182537 | − | 0.983199i | \(-0.558431\pi\) | ||||
−0.182537 | + | 0.983199i | \(0.558431\pi\) | |||||||
\(104\) | −4.71844e8 | −0.395502 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.84402e8 | 0.449610 | ||||||||
\(107\) | −6.71636e8 | −0.495344 | −0.247672 | − | 0.968844i | \(-0.579666\pi\) | ||||
−0.247672 | + | 0.968844i | \(0.579666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.66748e9 | 1.13147 | 0.565734 | − | 0.824588i | \(-0.308593\pi\) | ||||
0.565734 | + | 0.824588i | \(0.308593\pi\) | |||||||
\(110\) | −1.05598e8 | −0.0687683 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.73149e8 | 0.524333 | ||||||||
\(113\) | 1.84580e9 | 1.06496 | 0.532478 | − | 0.846444i | \(-0.321261\pi\) | ||||
0.532478 | + | 0.846444i | \(0.321261\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.78287e7 | 0.0255005 | ||||||||
\(116\) | −6.09219e9 | −3.12401 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.83063e9 | −2.76851 | ||||||||
\(119\) | −6.50162e8 | −0.297208 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.72262e9 | −0.730560 | ||||||||
\(122\) | −3.30661e9 | −1.35134 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.25770e9 | 2.37694 | ||||||||
\(125\) | −4.27436e8 | −0.156594 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.87922e9 | 0.641006 | 0.320503 | − | 0.947248i | \(-0.396148\pi\) | ||||
0.320503 | + | 0.947248i | \(0.396148\pi\) | |||||||
\(128\) | 5.56650e9 | 1.83290 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.19655e8 | −0.0367439 | ||||||||
\(131\) | −3.46045e9 | −1.02663 | −0.513313 | − | 0.858201i | \(-0.671582\pi\) | ||||
−0.513313 | + | 0.858201i | \(0.671582\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.38011e9 | −1.49093 | ||||||||
\(134\) | 3.85632e9 | 1.03324 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.80600e9 | 0.452680 | ||||||||
\(137\) | −5.04786e9 | −1.22424 | −0.612118 | − | 0.790766i | \(-0.709682\pi\) | ||||
−0.612118 | + | 0.790766i | \(0.709682\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.59716e9 | 0.817322 | 0.408661 | − | 0.912686i | \(-0.365996\pi\) | ||||
0.408661 | + | 0.912686i | \(0.365996\pi\) | |||||||
\(140\) | 6.16791e8 | 0.135694 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.57682e10 | 3.25451 | ||||||||
\(143\) | 7.19899e8 | 0.143966 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.07736e8 | −0.132958 | ||||||||
\(146\) | 1.20022e10 | 2.18611 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.91498e9 | 0.670736 | ||||||||
\(149\) | −1.27561e9 | −0.212022 | −0.106011 | − | 0.994365i | \(-0.533808\pi\) | ||||
−0.106011 | + | 0.994365i | \(0.533808\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.35273e9 | 0.681342 | 0.340671 | − | 0.940183i | \(-0.389346\pi\) | ||||
0.340671 | + | 0.940183i | \(0.389346\pi\) | |||||||
\(152\) | 1.49447e10 | 2.27086 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.72181e9 | −0.819766 | ||||||||
\(155\) | 7.26963e8 | 0.101163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.41002e10 | −1.85215 | −0.926075 | − | 0.377339i | \(-0.876839\pi\) | ||||
−0.926075 | + | 0.377339i | \(0.876839\pi\) | |||||||
\(158\) | 7.65584e9 | 0.977318 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.13370e8 | 0.0378022 | ||||||||
\(161\) | 2.59159e9 | 0.303983 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.24812e8 | 0.0804231 | 0.0402116 | − | 0.999191i | \(-0.487197\pi\) | ||||
0.0402116 | + | 0.999191i | \(0.487197\pi\) | |||||||
\(164\) | −1.41317e10 | −1.52545 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.42209e9 | 0.247573 | ||||||||
\(167\) | 8.33031e8 | 0.0828776 | 0.0414388 | − | 0.999141i | \(-0.486806\pi\) | ||||
0.0414388 | + | 0.999141i | \(0.486806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | 4.57983e8 | 0.0420561 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.79623e10 | 3.30731 | ||||||||
\(173\) | −5.77955e8 | −0.0490553 | −0.0245277 | − | 0.999699i | \(-0.507808\pi\) | ||||
−0.0245277 | + | 0.999699i | \(0.507808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.15444e10 | −0.930469 | ||||||||
\(176\) | 3.70046e9 | 0.290703 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.32473e9 | 0.0989094 | ||||||||
\(179\) | 1.56569e10 | 1.13990 | 0.569952 | − | 0.821678i | \(-0.306962\pi\) | ||||
0.569952 | + | 0.821678i | \(0.306962\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.18552e10 | −1.51356 | −0.756781 | − | 0.653668i | \(-0.773229\pi\) | ||||
−0.756781 | + | 0.653668i | \(0.773229\pi\) | |||||||
\(182\) | −6.48349e9 | −0.438013 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.19882e9 | −0.463000 | ||||||||
\(185\) | 4.54807e8 | 0.0285466 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.75543e9 | −0.164779 | ||||||||
\(188\) | −5.95388e9 | −0.347608 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.78982e9 | 0.210973 | ||||||||
\(191\) | −1.67784e10 | −0.912222 | −0.456111 | − | 0.889923i | \(-0.650758\pi\) | ||||
−0.456111 | + | 0.889923i | \(0.650758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.70036e10 | −1.40092 | −0.700462 | − | 0.713690i | \(-0.747023\pi\) | ||||
−0.700462 | + | 0.713690i | \(0.747023\pi\) | |||||||
\(194\) | 4.78645e10 | 2.42608 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.70671e9 | −0.227806 | ||||||||
\(197\) | −1.58277e10 | −0.748720 | −0.374360 | − | 0.927283i | \(-0.622138\pi\) | ||||
−0.374360 | + | 0.927283i | \(0.622138\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.80397e9 | 0.397960 | 0.198980 | − | 0.980004i | \(-0.436237\pi\) | ||||
0.198980 | + | 0.980004i | \(0.436237\pi\) | |||||||
\(200\) | 3.20677e10 | 1.41721 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.45982e10 | −1.46208 | ||||||||
\(203\) | −3.83485e10 | −1.58495 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.64169e9 | −0.0649232 | ||||||||
\(206\) | 1.59167e10 | 0.615817 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.19306e9 | 0.155327 | ||||||||
\(209\) | −2.28013e10 | −0.826610 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.82054e10 | −0.632308 | −0.316154 | − | 0.948708i | \(-0.602392\pi\) | ||||
−0.316154 | + | 0.948708i | \(0.602392\pi\) | |||||||
\(212\) | −1.44665e10 | −0.491870 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.56353e10 | 0.835558 | ||||||||
\(215\) | 4.41012e9 | 0.140759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.93904e10 | 1.20593 | ||||||||
\(218\) | −6.36453e10 | −1.90859 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.61400e9 | 0.0752322 | ||||||||
\(221\) | −3.12223e9 | −0.0880440 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.53511e10 | 0.415688 | 0.207844 | − | 0.978162i | \(-0.433355\pi\) | ||||
0.207844 | + | 0.978162i | \(0.433355\pi\) | |||||||
\(224\) | 1.69799e10 | 0.450628 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.04514e10 | −1.79639 | ||||||||
\(227\) | −4.20620e10 | −1.05141 | −0.525707 | − | 0.850666i | \(-0.676199\pi\) | ||||
−0.525707 | + | 0.850666i | \(0.676199\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.68760e10 | −1.60698 | −0.803490 | − | 0.595318i | \(-0.797026\pi\) | ||||
−0.803490 | + | 0.595318i | \(0.797026\pi\) | |||||||
\(230\) | −1.82555e9 | −0.0430148 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.06523e11 | 2.41406 | ||||||||
\(233\) | 5.19268e10 | 1.15422 | 0.577112 | − | 0.816665i | \(-0.304180\pi\) | ||||
0.577112 | + | 0.816665i | \(0.304180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.91668e8 | −0.0147942 | ||||||||
\(236\) | 1.44333e11 | 3.02874 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.48157e10 | 0.501338 | ||||||||
\(239\) | −7.45881e10 | −1.47870 | −0.739348 | − | 0.673323i | \(-0.764866\pi\) | ||||
−0.739348 | + | 0.673323i | \(0.764866\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.74852e10 | 1.09769 | 0.548845 | − | 0.835924i | \(-0.315068\pi\) | ||||
0.548845 | + | 0.835924i | \(0.315068\pi\) | |||||||
\(242\) | 6.57499e10 | 1.23233 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.18528e10 | 1.47836 | ||||||||
\(245\) | −5.46784e8 | −0.00969545 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.58365e10 | −0.441670 | ||||||||
\(248\) | −1.09417e11 | −1.83676 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.63146e10 | 0.264147 | ||||||||
\(251\) | 1.07873e11 | 1.71546 | 0.857732 | − | 0.514097i | \(-0.171873\pi\) | ||||
0.857732 | + | 0.514097i | \(0.171873\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.09833e10 | 0.168536 | ||||||||
\(254\) | −7.17272e10 | −1.08126 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.18186e11 | −1.71984 | ||||||||
\(257\) | 6.64074e10 | 0.949550 | 0.474775 | − | 0.880107i | \(-0.342530\pi\) | ||||
0.474775 | + | 0.880107i | \(0.342530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.46436e10 | 0.340295 | ||||||||
\(260\) | 2.96197e9 | 0.0401977 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.32080e11 | 1.73174 | ||||||||
\(263\) | 8.15356e10 | 1.05086 | 0.525432 | − | 0.850836i | \(-0.323904\pi\) | ||||
0.525432 | + | 0.850836i | \(0.323904\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.68058e9 | −0.0209340 | ||||||||
\(266\) | 2.05351e11 | 2.51494 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.54605e10 | −1.13036 | ||||||||
\(269\) | −1.00568e11 | −1.17105 | −0.585523 | − | 0.810656i | \(-0.699111\pi\) | ||||
−0.585523 | + | 0.810656i | \(0.699111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.98757e10 | −0.336477 | −0.168239 | − | 0.985746i | \(-0.553808\pi\) | ||||
−0.168239 | + | 0.985746i | \(0.553808\pi\) | |||||||
\(272\) | −1.60491e10 | −0.177783 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.92669e11 | 2.06507 | ||||||||
\(275\) | −4.89261e10 | −0.515874 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.17195e10 | −0.323718 | −0.161859 | − | 0.986814i | \(-0.551749\pi\) | ||||
−0.161859 | + | 0.986814i | \(0.551749\pi\) | |||||||
\(278\) | −1.37298e11 | −1.37868 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.07847e10 | −0.104857 | ||||||||
\(281\) | −9.86953e10 | −0.944318 | −0.472159 | − | 0.881513i | \(-0.656525\pi\) | ||||
−0.472159 | + | 0.881513i | \(0.656525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.06164e11 | −0.983871 | −0.491935 | − | 0.870632i | \(-0.663710\pi\) | ||||
−0.491935 | + | 0.870632i | \(0.663710\pi\) | |||||||
\(284\) | −3.90331e11 | −3.56042 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.74774e10 | −0.242845 | ||||||||
\(287\) | −8.89549e10 | −0.773929 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06637e11 | −0.899227 | ||||||||
\(290\) | 2.70132e10 | 0.224277 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.97106e11 | −2.39160 | ||||||||
\(293\) | −2.26355e11 | −1.79426 | −0.897132 | − | 0.441763i | \(-0.854353\pi\) | ||||
−0.897132 | + | 0.441763i | \(0.854353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.67673e10 | 0.128903 | ||||||||
\(296\) | −6.84541e10 | −0.518307 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.86881e10 | 0.357643 | ||||||||
\(299\) | 1.24454e10 | 0.0900511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.38962e11 | 1.67795 | ||||||||
\(302\) | −1.66137e11 | −1.14930 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.32806e11 | −0.891841 | ||||||||
\(305\) | 9.50892e9 | 0.0629190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.23009e10 | −0.143285 | −0.0716424 | − | 0.997430i | \(-0.522824\pi\) | ||||
−0.0716424 | + | 0.997430i | \(0.522824\pi\) | |||||||
\(308\) | 1.41639e11 | 0.896820 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.77471e10 | −0.170643 | ||||||||
\(311\) | 2.71805e11 | 1.64754 | 0.823770 | − | 0.566925i | \(-0.191867\pi\) | ||||
0.823770 | + | 0.566925i | \(0.191867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.90775e10 | −0.465697 | −0.232849 | − | 0.972513i | \(-0.574805\pi\) | ||||
−0.232849 | + | 0.972513i | \(0.574805\pi\) | |||||||
\(314\) | 5.38183e11 | 3.12425 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.89515e11 | −1.06918 | ||||||||
\(317\) | −2.03032e11 | −1.12927 | −0.564636 | − | 0.825340i | \(-0.690983\pi\) | ||||
−0.564636 | + | 0.825340i | \(0.690983\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.62524e11 | −0.878736 | ||||||||
\(320\) | −2.02114e10 | −0.107751 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.89171e10 | −0.512767 | ||||||||
\(323\) | 9.88899e10 | 0.505523 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.54391e10 | −0.275639 | ||||||||
\(326\) | −2.76650e10 | −0.135660 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.47095e11 | 1.17878 | ||||||||
\(329\) | −3.74779e10 | −0.176357 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.24137e11 | 1.48424 | 0.742118 | − | 0.670270i | \(-0.233822\pi\) | ||||
0.742118 | + | 0.670270i | \(0.233822\pi\) | |||||||
\(332\) | −5.99570e10 | −0.270844 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.17955e10 | −0.139800 | ||||||||
\(335\) | −1.10897e10 | −0.0481083 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.68510e11 | 1.13403 | 0.567017 | − | 0.823706i | \(-0.308097\pi\) | ||||
0.567017 | + | 0.823706i | \(0.308097\pi\) | |||||||
\(338\) | −3.11352e10 | −0.129756 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.13370e10 | −0.0460091 | ||||||||
\(341\) | 1.66939e11 | 0.668595 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.69628e11 | −1.05182 | ||||||||
\(344\) | −6.63778e11 | −2.55570 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.20597e10 | 0.0827478 | ||||||||
\(347\) | −2.74715e11 | −1.01719 | −0.508593 | − | 0.861007i | \(-0.669834\pi\) | ||||
−0.508593 | + | 0.861007i | \(0.669834\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.54006e11 | −1.27731 | −0.638655 | − | 0.769494i | \(-0.720509\pi\) | ||||
−0.638655 | + | 0.769494i | \(0.720509\pi\) | |||||||
\(350\) | 4.40634e11 | 1.56954 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.19619e10 | 0.249839 | ||||||||
\(353\) | 2.25650e11 | 0.773481 | 0.386741 | − | 0.922189i | \(-0.373601\pi\) | ||||
0.386741 | + | 0.922189i | \(0.373601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.53451e10 | −0.151532 | ||||||||
\(356\) | −3.27927e10 | −0.108206 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.97602e11 | −1.92282 | ||||||||
\(359\) | −3.39022e10 | −0.107722 | −0.0538608 | − | 0.998548i | \(-0.517153\pi\) | ||||
−0.0538608 | + | 0.998548i | \(0.517153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.95629e11 | 1.53594 | ||||||||
\(362\) | 8.34178e11 | 2.55312 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.60494e11 | 0.479184 | ||||||||
\(365\) | −3.45150e10 | −0.101787 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.74387e10 | −0.222823 | −0.111412 | − | 0.993774i | \(-0.535537\pi\) | ||||
−0.111412 | + | 0.993774i | \(0.535537\pi\) | |||||||
\(368\) | 6.39726e10 | 0.181836 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.73593e10 | −0.0481531 | ||||||||
\(371\) | −9.10620e10 | −0.249548 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.50821e11 | 1.74089 | 0.870446 | − | 0.492264i | \(-0.163831\pi\) | ||||
0.870446 | + | 0.492264i | \(0.163831\pi\) | |||||||
\(374\) | 1.05171e11 | 0.277954 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.04105e11 | 0.268612 | ||||||||
\(377\) | −1.84159e11 | −0.469522 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.93989e11 | 0.482948 | 0.241474 | − | 0.970407i | \(-0.422369\pi\) | ||||
0.241474 | + | 0.970407i | \(0.422369\pi\) | |||||||
\(380\) | −9.38141e10 | −0.230803 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.40406e11 | 1.53876 | ||||||||
\(383\) | −4.44645e11 | −1.05589 | −0.527946 | − | 0.849278i | \(-0.677037\pi\) | ||||
−0.527946 | + | 0.849278i | \(0.677037\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.64544e10 | 0.0381687 | ||||||||
\(386\) | 1.03069e12 | 2.36311 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.18485e12 | −2.65412 | ||||||||
\(389\) | 1.69623e11 | 0.375589 | 0.187794 | − | 0.982208i | \(-0.439866\pi\) | ||||
0.187794 | + | 0.982208i | \(0.439866\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.76352e10 | −0.103070 | ||||||||
\(392\) | 8.22978e10 | 0.176036 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.04119e11 | 1.26296 | ||||||||
\(395\) | −2.20161e10 | −0.0455044 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.94468e11 | 0.594951 | 0.297476 | − | 0.954729i | \(-0.403855\pi\) | ||||
0.297476 | + | 0.954729i | \(0.403855\pi\) | |||||||
\(398\) | −3.36034e11 | −0.671289 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.84971e11 | −0.556584 | ||||||||
\(401\) | −4.43362e11 | −0.856265 | −0.428133 | − | 0.903716i | \(-0.640828\pi\) | ||||
−0.428133 | + | 0.903716i | \(0.640828\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.89162e11 | 0.357240 | ||||||||
\(404\) | 8.56452e11 | 1.59951 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.46371e12 | 2.67354 | ||||||||
\(407\) | 1.04441e11 | 0.188668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.01253e11 | −0.178918 | −0.0894592 | − | 0.995990i | \(-0.528514\pi\) | ||||
−0.0894592 | + | 0.995990i | \(0.528514\pi\) | |||||||
\(410\) | 6.26610e10 | 0.109514 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.94007e11 | −0.673700 | ||||||||
\(413\) | 9.08533e11 | 1.53662 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.96526e9 | −0.0115271 | ||||||||
\(416\) | 8.15413e10 | 0.133493 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.70289e11 | 1.39435 | ||||||||
\(419\) | −7.93982e10 | −0.125848 | −0.0629242 | − | 0.998018i | \(-0.520043\pi\) | ||||
−0.0629242 | + | 0.998018i | \(0.520043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.06765e11 | −0.941350 | −0.470675 | − | 0.882307i | \(-0.655990\pi\) | ||||
−0.470675 | + | 0.882307i | \(0.655990\pi\) | |||||||
\(422\) | 6.94871e11 | 1.06659 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.52949e11 | 0.380089 | ||||||||
\(425\) | 2.12195e11 | 0.315489 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.15239e11 | 0.750038 | ||||||||
\(428\) | −6.34583e11 | −0.914096 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.68328e11 | −0.237436 | ||||||||
\(431\) | 2.72544e11 | 0.380442 | 0.190221 | − | 0.981741i | \(-0.439080\pi\) | ||||
0.190221 | + | 0.981741i | \(0.439080\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.15522e12 | −1.57931 | −0.789655 | − | 0.613551i | \(-0.789740\pi\) | ||||
−0.789655 | + | 0.613551i | \(0.789740\pi\) | |||||||
\(434\) | −1.50347e12 | −2.03419 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.57549e12 | 2.08799 | ||||||||
\(437\) | −3.94182e11 | −0.517047 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.78053e11 | 0.228801 | 0.114401 | − | 0.993435i | \(-0.463505\pi\) | ||||
0.114401 | + | 0.993435i | \(0.463505\pi\) | |||||||
\(440\) | −4.57063e10 | −0.0581351 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.19171e11 | 0.148515 | ||||||||
\(443\) | 6.55260e10 | 0.0808345 | 0.0404173 | − | 0.999183i | \(-0.487131\pi\) | ||||
0.0404173 | + | 0.999183i | \(0.487131\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.80956e9 | −0.00460527 | ||||||||
\(446\) | −5.85928e11 | −0.701192 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.09515e12 | −1.28446 | ||||||||
\(449\) | 7.98150e11 | 0.926779 | 0.463390 | − | 0.886155i | \(-0.346633\pi\) | ||||
0.463390 | + | 0.886155i | \(0.346633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.76997e11 | −0.429085 | ||||||||
\(452\) | 1.74397e12 | 1.96525 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.60544e12 | 1.77355 | ||||||||
\(455\) | 1.86447e10 | 0.0203941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.92736e11 | −0.957415 | −0.478708 | − | 0.877974i | \(-0.658895\pi\) | ||||
−0.478708 | + | 0.877974i | \(0.658895\pi\) | |||||||
\(458\) | 2.55256e12 | 2.71069 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.51901e10 | 0.0470580 | ||||||||
\(461\) | −2.32490e11 | −0.239745 | −0.119872 | − | 0.992789i | \(-0.538249\pi\) | ||||
−0.119872 | + | 0.992789i | \(0.538249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.54421e12 | −1.56168 | −0.780841 | − | 0.624730i | \(-0.785209\pi\) | ||||
−0.780841 | + | 0.624730i | \(0.785209\pi\) | |||||||
\(464\) | −9.46622e11 | −0.948082 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.98197e12 | −1.94697 | ||||||||
\(467\) | −1.63317e12 | −1.58893 | −0.794465 | − | 0.607310i | \(-0.792249\pi\) | ||||
−0.794465 | + | 0.607310i | \(0.792249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00895e11 | −0.573484 | ||||||||
\(470\) | 2.63999e10 | 0.0249553 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.52369e12 | −2.34044 | ||||||||
\(473\) | 1.01274e12 | 0.930295 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.75592e12 | 1.58264 | ||||||||
\(476\) | −6.14295e11 | −0.548461 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.84692e12 | 2.49430 | ||||||||
\(479\) | −1.54414e12 | −1.34022 | −0.670112 | − | 0.742260i | \(-0.733754\pi\) | ||||
−0.670112 | + | 0.742260i | \(0.733754\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.18344e11 | 0.100808 | ||||||||
\(482\) | −2.19412e12 | −1.85161 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.62759e12 | −1.34816 | ||||||||
\(485\) | −1.37645e11 | −0.112960 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.55439e11 | 0.205782 | 0.102891 | − | 0.994693i | \(-0.467191\pi\) | ||||
0.102891 | + | 0.994693i | \(0.467191\pi\) | |||||||
\(488\) | −1.43121e12 | −1.14239 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.08699e10 | 0.0163545 | ||||||||
\(491\) | −1.58407e12 | −1.23000 | −0.615002 | − | 0.788526i | \(-0.710845\pi\) | ||||
−0.615002 | + | 0.788526i | \(0.710845\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.04872e11 | 0.537402 | ||||||||
\(494\) | 9.86141e11 | 0.745020 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.72340e11 | 0.721357 | ||||||||
\(497\) | −2.45702e12 | −1.80636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.29948e11 | −0.454833 | −0.227417 | − | 0.973798i | \(-0.573028\pi\) | ||||
−0.227417 | + | 0.973798i | \(0.573028\pi\) | |||||||
\(500\) | −4.03856e11 | −0.288976 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.11736e12 | −2.89369 | ||||||||
\(503\) | −5.49263e11 | −0.382582 | −0.191291 | − | 0.981533i | \(-0.561267\pi\) | ||||
−0.191291 | + | 0.981533i | \(0.561267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.94949e10 | 0.0680753 | ||||||||
\(506\) | −4.19217e11 | −0.284290 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.77555e12 | 1.18290 | ||||||||
\(509\) | −1.36923e11 | −0.0904165 | −0.0452083 | − | 0.998978i | \(-0.514395\pi\) | ||||
−0.0452083 | + | 0.998978i | \(0.514395\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.87019e12 | −1.21337 | ||||||||
\(512\) | 1.66095e12 | 1.06817 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.53467e12 | −1.60172 | ||||||||
\(515\) | −4.57722e10 | −0.0286727 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.58834e11 | −0.0977767 | ||||||||
\(518\) | −9.40610e11 | −0.574018 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.17906e10 | −0.0310625 | ||||||||
\(521\) | 1.66627e12 | 0.990779 | 0.495389 | − | 0.868671i | \(-0.335025\pi\) | ||||
0.495389 | + | 0.868671i | \(0.335025\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.97187e12 | 1.15244 | 0.576222 | − | 0.817293i | \(-0.304526\pi\) | ||||
0.576222 | + | 0.817293i | \(0.304526\pi\) | |||||||
\(524\) | −3.26955e12 | −1.89451 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.11209e12 | −1.77262 | ||||||||
\(527\) | −7.24021e11 | −0.408887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.61128e12 | −0.894580 | ||||||||
\(530\) | 6.41452e10 | 0.0353121 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.08330e12 | −2.75134 | ||||||||
\(533\) | −4.27182e11 | −0.229266 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.37202e10 | −0.0389040 | ||||||||
\(536\) | 1.66914e12 | 0.873479 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.83852e12 | 1.97535 | ||||||||
\(539\) | −1.25563e11 | −0.0640784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.54916e12 | 0.777513 | 0.388756 | − | 0.921341i | \(-0.372905\pi\) | ||||
0.388756 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(542\) | 1.14031e12 | 0.567578 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.12101e11 | −0.152792 | ||||||||
\(545\) | 1.83027e11 | 0.0888648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.98052e12 | 0.945879 | 0.472939 | − | 0.881095i | \(-0.343193\pi\) | ||||
0.472939 | + | 0.881095i | \(0.343193\pi\) | |||||||
\(548\) | −4.76939e12 | −2.25918 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.86744e12 | 0.870189 | ||||||||
\(551\) | 5.83283e12 | 2.69586 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.19294e12 | −0.542444 | ||||||||
\(554\) | 1.21068e12 | 0.546056 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.39871e12 | 1.50827 | ||||||||
\(557\) | −8.86577e11 | −0.390273 | −0.195136 | − | 0.980776i | \(-0.562515\pi\) | ||||
−0.195136 | + | 0.980776i | \(0.562515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.14755e12 | 0.497071 | ||||||||
\(560\) | 9.58387e10 | 0.0411808 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.76705e12 | 1.59290 | ||||||||
\(563\) | −3.89786e12 | −1.63508 | −0.817539 | − | 0.575873i | \(-0.804662\pi\) | ||||
−0.817539 | + | 0.575873i | \(0.804662\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.02599e11 | 0.0836410 | ||||||||
\(566\) | 4.05212e12 | 1.65962 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.82501e12 | 2.75129 | ||||||||
\(569\) | 2.26590e12 | 0.906223 | 0.453112 | − | 0.891454i | \(-0.350314\pi\) | ||||
0.453112 | + | 0.891454i | \(0.350314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.09546e12 | −1.21860 | −0.609302 | − | 0.792938i | \(-0.708550\pi\) | ||||
−0.609302 | + | 0.792938i | \(0.708550\pi\) | |||||||
\(572\) | 6.80184e11 | 0.265671 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.39527e12 | 1.30548 | ||||||||
\(575\) | −8.45822e11 | −0.322681 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.23415e12 | −1.21470 | −0.607350 | − | 0.794434i | \(-0.707767\pi\) | ||||
−0.607350 | + | 0.794434i | \(0.707767\pi\) | |||||||
\(578\) | 4.07019e12 | 1.51684 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.68692e11 | −0.245358 | ||||||||
\(581\) | −3.77411e11 | −0.137411 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.85927e11 | −0.138356 | ||||||||
\(584\) | 5.19495e12 | 1.84809 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.63964e12 | 3.02661 | ||||||||
\(587\) | 8.78491e11 | 0.305398 | 0.152699 | − | 0.988273i | \(-0.451204\pi\) | ||||
0.152699 | + | 0.988273i | \(0.451204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.99129e12 | −2.05117 | ||||||||
\(590\) | −6.39983e11 | −0.217437 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.08321e11 | 0.203556 | ||||||||
\(593\) | 1.91730e12 | 0.636712 | 0.318356 | − | 0.947971i | \(-0.396869\pi\) | ||||
0.318356 | + | 0.947971i | \(0.396869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.13632e10 | −0.0233425 | ||||||||
\(596\) | −1.20524e12 | −0.391260 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.75023e11 | −0.151900 | ||||||||
\(599\) | 5.10464e12 | 1.62011 | 0.810054 | − | 0.586355i | \(-0.199438\pi\) | ||||
0.810054 | + | 0.586355i | \(0.199438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.00419e12 | 0.939273 | 0.469636 | − | 0.882860i | \(-0.344385\pi\) | ||||
0.469636 | + | 0.882860i | \(0.344385\pi\) | |||||||
\(602\) | −9.12080e12 | −2.83041 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.11260e12 | 1.25733 | ||||||||
\(605\) | −1.89079e11 | −0.0573778 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.18434e12 | 0.354101 | 0.177051 | − | 0.984202i | \(-0.443344\pi\) | ||||
0.177051 | + | 0.984202i | \(0.443344\pi\) | |||||||
\(608\) | −2.58265e12 | −0.766477 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.62941e11 | −0.106133 | ||||||||
\(611\) | −1.79978e11 | −0.0522436 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.42597e11 | 0.183809 | 0.0919045 | − | 0.995768i | \(-0.470705\pi\) | ||||
0.0919045 | + | 0.995768i | \(0.470705\pi\) | |||||||
\(614\) | 8.51193e11 | 0.241696 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.47659e12 | −0.693011 | ||||||||
\(617\) | −5.05474e12 | −1.40416 | −0.702078 | − | 0.712100i | \(-0.747744\pi\) | ||||
−0.702078 | + | 0.712100i | \(0.747744\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.09492e11 | −0.0847308 | −0.0423654 | − | 0.999102i | \(-0.513489\pi\) | ||||
−0.0423654 | + | 0.999102i | \(0.513489\pi\) | |||||||
\(620\) | 6.86859e11 | 0.186683 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.03744e13 | −2.77911 | ||||||||
\(623\) | −2.06421e11 | −0.0548980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.74425e12 | 0.981533 | ||||||||
\(626\) | 3.01827e12 | 0.785549 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.33223e13 | −3.41792 | ||||||||
\(629\) | −4.52966e11 | −0.115382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.94237e11 | −0.199443 | −0.0997214 | − | 0.995015i | \(-0.531795\pi\) | ||||
−0.0997214 | + | 0.995015i | \(0.531795\pi\) | |||||||
\(632\) | 3.31370e12 | 0.826202 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.74944e12 | 1.90488 | ||||||||
\(635\) | 2.06268e11 | 0.0503442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.42278e11 | −0.0342380 | ||||||||
\(638\) | 6.20328e12 | 1.48227 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.10991e11 | 0.143954 | ||||||||
\(641\) | −2.30298e12 | −0.538802 | −0.269401 | − | 0.963028i | \(-0.586826\pi\) | ||||
−0.269401 | + | 0.963028i | \(0.586826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.54593e12 | −0.587350 | −0.293675 | − | 0.955905i | \(-0.594878\pi\) | ||||
−0.293675 | + | 0.955905i | \(0.594878\pi\) | |||||||
\(644\) | 2.44862e12 | 0.560964 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.77448e12 | −0.852728 | ||||||||
\(647\) | 2.74568e11 | 0.0616001 | 0.0308000 | − | 0.999526i | \(-0.490194\pi\) | ||||
0.0308000 | + | 0.999526i | \(0.490194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.85043e12 | 0.851937 | ||||||||
\(650\) | 2.11603e12 | 0.464955 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.84826e11 | 0.148411 | ||||||||
\(653\) | 6.05719e12 | 1.30365 | 0.651826 | − | 0.758369i | \(-0.274003\pi\) | ||||
0.651826 | + | 0.758369i | \(0.274003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.79827e11 | −0.0806306 | ||||||||
\(656\) | −2.19582e12 | −0.462946 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.43047e12 | 0.297484 | ||||||||
\(659\) | −4.97718e12 | −1.02801 | −0.514007 | − | 0.857786i | \(-0.671840\pi\) | ||||
−0.514007 | + | 0.857786i | \(0.671840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.79834e12 | 0.366409 | 0.183204 | − | 0.983075i | \(-0.441353\pi\) | ||||
0.183204 | + | 0.983075i | \(0.441353\pi\) | |||||||
\(662\) | −1.23718e13 | −2.50364 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.04836e12 | 0.209292 | ||||||||
\(665\) | −5.90532e11 | −0.117097 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.80967e12 | −0.549653 | ||||||||
\(668\) | 7.87076e11 | 0.152940 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.23278e11 | 0.0811502 | ||||||||
\(671\) | 2.18362e12 | 0.415839 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.37693e12 | 0.258728 | 0.129364 | − | 0.991597i | \(-0.458706\pi\) | ||||
0.129364 | + | 0.991597i | \(0.458706\pi\) | |||||||
\(674\) | −1.02486e13 | −1.91292 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.70729e11 | 0.141952 | ||||||||
\(677\) | −6.49642e11 | −0.118857 | −0.0594285 | − | 0.998233i | \(-0.518928\pi\) | ||||
−0.0594285 | + | 0.998233i | \(0.518928\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.45828e12 | −1.34656 | ||||||||
\(680\) | 1.98230e11 | 0.0355532 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.37181e12 | −1.12780 | ||||||||
\(683\) | 1.10011e12 | 0.193438 | 0.0967190 | − | 0.995312i | \(-0.469165\pi\) | ||||
0.0967190 | + | 0.995312i | \(0.469165\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.54064e11 | −0.0961507 | ||||||||
\(686\) | 1.02913e13 | 1.77424 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.89869e12 | 1.00371 | ||||||||
\(689\) | −4.37301e11 | −0.0739254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.72289e12 | 1.28863 | 0.644315 | − | 0.764760i | \(-0.277142\pi\) | ||||
0.644315 | + | 0.764760i | \(0.277142\pi\) | |||||||
\(692\) | −5.46071e11 | −0.0905256 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.04855e13 | 1.71581 | ||||||||
\(695\) | 3.94832e11 | 0.0641920 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.63505e12 | 0.262412 | ||||||||
\(698\) | 1.35119e13 | 2.15460 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.09076e13 | −1.71707 | ||||||||
\(701\) | −1.40436e12 | −0.219658 | −0.109829 | − | 0.993950i | \(-0.535030\pi\) | ||||
−0.109829 | + | 0.993950i | \(0.535030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.74831e12 | −0.578810 | ||||||||
\(704\) | −4.64131e12 | −0.712137 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.61273e12 | −1.30473 | ||||||||
\(707\) | 5.39111e12 | 0.811505 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.19764e12 | 0.772499 | 0.386250 | − | 0.922394i | \(-0.373770\pi\) | ||||
0.386250 | + | 0.922394i | \(0.373770\pi\) | |||||||
\(710\) | 1.73075e12 | 0.255607 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.73387e11 | 0.0836157 | ||||||||
\(713\) | 2.88600e12 | 0.418209 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.90176e10 | 0.0113070 | ||||||||
\(716\) | 1.47932e13 | 2.10355 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.29400e12 | 0.181707 | ||||||||
\(719\) | 1.27042e13 | 1.77284 | 0.886418 | − | 0.462886i | \(-0.153186\pi\) | ||||
0.886418 | + | 0.462886i | \(0.153186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.48016e12 | −0.341799 | ||||||||
\(722\) | −1.89174e13 | −2.59086 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.06495e13 | −2.79309 | ||||||||
\(725\) | 1.25159e13 | 1.68244 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.91998e11 | 0.131706 | 0.0658531 | − | 0.997829i | \(-0.479023\pi\) | ||||
0.0658531 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(728\) | −2.80627e12 | −0.370286 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.31739e12 | 0.171696 | ||||||||
\(731\) | −4.39227e12 | −0.568933 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.54849e12 | 0.709916 | 0.354958 | − | 0.934882i | \(-0.384495\pi\) | ||||
0.354958 | + | 0.934882i | \(0.384495\pi\) | |||||||
\(734\) | 2.95572e12 | 0.375864 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.24406e12 | 0.156275 | ||||||||
\(737\) | −2.54663e12 | −0.317953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.78597e12 | 1.08365 | 0.541826 | − | 0.840491i | \(-0.317733\pi\) | ||||
0.541826 | + | 0.840491i | \(0.317733\pi\) | |||||||
\(740\) | 4.29717e11 | 0.0526792 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.47570e12 | 0.420944 | ||||||||
\(743\) | −4.04326e12 | −0.486724 | −0.243362 | − | 0.969936i | \(-0.578250\pi\) | ||||
−0.243362 | + | 0.969936i | \(0.578250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.40014e11 | −0.0166521 | ||||||||
\(746\) | −2.48408e13 | −2.93658 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.60342e12 | −0.304080 | ||||||||
\(749\) | −3.99451e12 | −0.463763 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.52936e11 | −0.0290156 | −0.0145078 | − | 0.999895i | \(-0.504618\pi\) | ||||
−0.0145078 | + | 0.999895i | \(0.504618\pi\) | |||||||
\(752\) | −9.25130e11 | −0.105493 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.02906e12 | 0.792001 | ||||||||
\(755\) | 4.77765e11 | 0.0535122 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.99638e12 | 1.10640 | 0.553199 | − | 0.833049i | \(-0.313407\pi\) | ||||
0.553199 | + | 0.833049i | \(0.313407\pi\) | |||||||
\(758\) | −7.40426e12 | −0.814649 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.64036e12 | 0.178352 | ||||||||
\(761\) | 2.98848e12 | 0.323013 | 0.161507 | − | 0.986872i | \(-0.448365\pi\) | ||||
0.161507 | + | 0.986872i | \(0.448365\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.91726e12 | 1.05933 | ||||||||
\(764\) | −1.58528e13 | −1.68339 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.69714e13 | 1.78110 | ||||||||
\(767\) | 4.36299e12 | 0.455203 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.54887e13 | 1.59715 | 0.798576 | − | 0.601894i | \(-0.205587\pi\) | ||||
0.798576 | + | 0.601894i | \(0.205587\pi\) | |||||||
\(770\) | −6.28038e11 | −0.0643839 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.55139e13 | −2.58523 | ||||||||
\(773\) | −1.07589e13 | −1.08383 | −0.541915 | − | 0.840434i | \(-0.682300\pi\) | ||||
−0.541915 | + | 0.840434i | \(0.682300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.28559e13 | −1.28010 | ||||||||
\(776\) | 2.07173e13 | 2.05095 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.47427e12 | −0.633552 | ||||||||
\(779\) | 1.35301e13 | 1.31638 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04130e13 | −1.00149 | ||||||||
\(782\) | 1.81816e12 | 0.173861 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.31343e11 | −0.0691351 | ||||||||
\(785\) | −1.54767e12 | −0.145467 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.29304e13 | 1.20151 | 0.600755 | − | 0.799433i | \(-0.294867\pi\) | ||||
0.600755 | + | 0.799433i | \(0.294867\pi\) | |||||||
\(788\) | −1.49545e13 | −1.38167 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.40321e11 | 0.0767579 | ||||||||
\(791\) | 1.09778e13 | 0.997059 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.47430e12 | 0.222189 | ||||||||
\(794\) | −1.12394e13 | −1.00358 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.31828e12 | 0.734387 | ||||||||
\(797\) | −1.24713e13 | −1.09484 | −0.547418 | − | 0.836859i | \(-0.684389\pi\) | ||||
−0.547418 | + | 0.836859i | \(0.684389\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.88868e11 | 0.0597965 | ||||||||
\(800\) | −5.54175e12 | −0.478346 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.69224e13 | 1.44437 | ||||||||
\(803\) | −7.92600e12 | −0.672719 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.84459e11 | 0.0238747 | ||||||||
\(806\) | −7.22002e12 | −0.602602 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.49752e13 | −1.23601 | ||||||||
\(809\) | 2.40763e13 | 1.97616 | 0.988079 | − | 0.153948i | \(-0.0491989\pi\) | ||||
0.988079 | + | 0.153948i | \(0.0491989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.14686e13 | 0.930928 | 0.465464 | − | 0.885067i | \(-0.345888\pi\) | ||||
0.465464 | + | 0.885067i | \(0.345888\pi\) | |||||||
\(812\) | −3.62330e13 | −2.92484 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.98637e12 | −0.318249 | ||||||||
\(815\) | 7.95569e10 | 0.00631638 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.63462e13 | −2.85403 | ||||||||
\(818\) | 3.86469e12 | 0.301804 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.55113e12 | −0.119808 | ||||||||
\(821\) | 2.50113e13 | 1.92129 | 0.960643 | − | 0.277786i | \(-0.0896005\pi\) | ||||
0.960643 | + | 0.277786i | \(0.0896005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.29351e13 | 0.982808 | 0.491404 | − | 0.870932i | \(-0.336484\pi\) | ||||
0.491404 | + | 0.870932i | \(0.336484\pi\) | |||||||
\(824\) | 6.88929e12 | 0.520597 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.46773e13 | −2.59200 | ||||||||
\(827\) | −1.00464e13 | −0.746851 | −0.373425 | − | 0.927660i | \(-0.621817\pi\) | ||||
−0.373425 | + | 0.927660i | \(0.621817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.77304e12 | 0.645141 | 0.322570 | − | 0.946545i | \(-0.395453\pi\) | ||||
0.322570 | + | 0.946545i | \(0.395453\pi\) | |||||||
\(830\) | 2.65853e11 | 0.0194442 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.25916e12 | −0.380506 | ||||||||
\(833\) | 5.44571e11 | 0.0391879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.14353e10 | 0.00650916 | ||||||||
\(836\) | −2.15434e13 | −1.52541 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.03051e12 | 0.212284 | ||||||||
\(839\) | 1.54259e13 | 1.07478 | 0.537392 | − | 0.843332i | \(-0.319410\pi\) | ||||
0.537392 | + | 0.843332i | \(0.319410\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.70683e13 | 1.86586 | ||||||||
\(842\) | 2.31593e13 | 1.58789 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.72010e13 | −1.16685 | ||||||||
\(845\) | 8.95364e10 | 0.00604149 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.02452e13 | −0.683983 | ||||||||
\(848\) | −2.24784e12 | −0.149274 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.09914e12 | −0.532174 | ||||||||
\(851\) | 1.80556e12 | 0.118012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.84928e12 | −0.119600 | −0.0598002 | − | 0.998210i | \(-0.519046\pi\) | ||||
−0.0598002 | + | 0.998210i | \(0.519046\pi\) | |||||||
\(854\) | −1.96659e13 | −1.26518 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.10958e13 | 0.706361 | ||||||||
\(857\) | 2.34715e13 | 1.48637 | 0.743185 | − | 0.669086i | \(-0.233314\pi\) | ||||
0.743185 | + | 0.669086i | \(0.233314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.25121e12 | 0.0784079 | 0.0392039 | − | 0.999231i | \(-0.487518\pi\) | ||||
0.0392039 | + | 0.999231i | \(0.487518\pi\) | |||||||
\(860\) | 4.16683e12 | 0.259754 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.04026e13 | −0.641739 | ||||||||
\(863\) | −2.38217e13 | −1.46192 | −0.730961 | − | 0.682419i | \(-0.760928\pi\) | ||||
−0.730961 | + | 0.682419i | \(0.760928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.34375e10 | −0.00385278 | ||||||||
\(866\) | 4.40928e13 | 2.66402 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.72173e13 | 2.22539 | ||||||||
\(869\) | −5.05575e12 | −0.300744 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.88564e12 | −0.169887 | ||||||||
\(872\) | −2.75478e13 | −1.61348 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.50453e13 | 0.872168 | ||||||||
\(875\) | −2.54215e12 | −0.146611 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.35717e13 | −0.774707 | −0.387353 | − | 0.921931i | \(-0.626611\pi\) | ||||
−0.387353 | + | 0.921931i | \(0.626611\pi\) | |||||||
\(878\) | −6.79601e12 | −0.385948 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.06171e11 | 0.0228316 | ||||||||
\(881\) | −2.38436e12 | −0.133346 | −0.0666730 | − | 0.997775i | \(-0.521238\pi\) | ||||
−0.0666730 | + | 0.997775i | \(0.521238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.99779e11 | −0.0332023 | −0.0166011 | − | 0.999862i | \(-0.505285\pi\) | ||||
−0.0166011 | + | 0.999862i | \(0.505285\pi\) | |||||||
\(884\) | −2.94999e12 | −0.162474 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.50103e12 | −0.136354 | ||||||||
\(887\) | −1.02483e13 | −0.555897 | −0.277949 | − | 0.960596i | \(-0.589654\pi\) | ||||
−0.277949 | + | 0.960596i | \(0.589654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.11766e13 | 0.600138 | ||||||||
\(890\) | 1.45405e11 | 0.00776828 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.45042e13 | 0.767101 | ||||||||
\(893\) | 5.70040e12 | 0.299967 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.71854e12 | 0.0895274 | ||||||||
\(896\) | 3.31065e13 | 1.71604 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.04642e13 | −1.56331 | ||||||||
\(899\) | −4.27050e13 | −2.18052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.67378e12 | 0.0846130 | ||||||||
\(902\) | 1.43894e13 | 0.723791 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.04937e13 | −1.51863 | ||||||||
\(905\) | −2.39887e12 | −0.118874 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.43855e13 | −1.19646 | −0.598231 | − | 0.801323i | \(-0.704130\pi\) | ||||
−0.598231 | + | 0.801323i | \(0.704130\pi\) | |||||||
\(908\) | −3.97416e13 | −1.94026 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.11641e11 | −0.0344013 | ||||||||
\(911\) | −2.90386e13 | −1.39683 | −0.698415 | − | 0.715693i | \(-0.746111\pi\) | ||||
−0.698415 | + | 0.715693i | \(0.746111\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.59949e12 | −0.0761841 | ||||||||
\(914\) | 3.40744e13 | 1.61499 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.31867e13 | −2.96549 | ||||||||
\(917\) | −2.05809e13 | −0.961173 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.41793e13 | −0.655746 | −0.327873 | − | 0.944722i | \(-0.606332\pi\) | ||||
−0.327873 | + | 0.944722i | \(0.606332\pi\) | |||||||
\(920\) | −7.90158e11 | −0.0363638 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.87378e12 | 0.404408 | ||||||||
\(923\) | −1.17992e13 | −0.535111 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.04299e12 | −0.361226 | ||||||||
\(926\) | 5.89402e13 | 2.63428 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.84087e13 | −0.814812 | ||||||||
\(929\) | 3.56246e13 | 1.56920 | 0.784601 | − | 0.620001i | \(-0.212868\pi\) | ||||
0.784601 | + | 0.620001i | \(0.212868\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.50634e12 | 0.196585 | ||||||||
\(932\) | 4.90621e13 | 2.12998 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.23355e13 | 2.68025 | ||||||||
\(935\) | −3.02442e11 | −0.0129417 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.35575e12 | 0.396506 | 0.198253 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(938\) | 2.29353e13 | 0.967366 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.53510e11 | −0.0273009 | ||||||||
\(941\) | −1.23413e13 | −0.513106 | −0.256553 | − | 0.966530i | \(-0.582587\pi\) | ||||
−0.256553 | + | 0.966530i | \(0.582587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.51742e12 | −0.268394 | ||||||||
\(944\) | 2.24269e13 | 0.919168 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.86546e13 | −1.56924 | ||||||||
\(947\) | −2.93722e12 | −0.118676 | −0.0593379 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593379 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.98110e12 | −0.359444 | ||||||||
\(950\) | −6.70206e13 | −2.66964 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.07411e13 | 0.423819 | ||||||||
\(953\) | 3.90544e12 | 0.153374 | 0.0766870 | − | 0.997055i | \(-0.475566\pi\) | ||||
0.0766870 | + | 0.997055i | \(0.475566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.84163e12 | −0.0716454 | ||||||||
\(956\) | −7.04733e13 | −2.72875 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.89375e13 | 2.26072 | ||||||||
\(959\) | −3.00219e13 | −1.14618 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.74255e13 | 0.659069 | ||||||||
\(962\) | −4.51703e12 | −0.170045 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.43139e13 | 2.02565 | ||||||||
\(965\) | −2.96398e12 | −0.110028 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.06697e13 | −0.392405 | −0.196203 | − | 0.980563i | \(-0.562861\pi\) | ||||
−0.196203 | + | 0.980563i | \(0.562861\pi\) | |||||||
\(968\) | 2.84587e13 | 1.04178 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.25371e12 | 0.190543 | ||||||||
\(971\) | 3.10264e12 | 0.112007 | 0.0560034 | − | 0.998431i | \(-0.482164\pi\) | ||||
0.0560034 | + | 0.998431i | \(0.482164\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.13939e13 | 0.765213 | ||||||||
\(974\) | −9.74972e12 | −0.347118 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.27185e13 | 0.448655 | ||||||||
\(977\) | 4.66167e13 | 1.63688 | 0.818438 | − | 0.574594i | \(-0.194840\pi\) | ||||
0.818438 | + | 0.574594i | \(0.194840\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.74824e11 | −0.0304368 | ||||||||
\(980\) | −5.16619e11 | −0.0178918 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.04614e13 | 2.07480 | ||||||||
\(983\) | 3.22316e13 | 1.10101 | 0.550505 | − | 0.834832i | \(-0.314435\pi\) | ||||
0.550505 | + | 0.834832i | \(0.314435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.73728e12 | −0.0588040 | ||||||||
\(986\) | −2.69039e13 | −0.906502 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.44112e13 | −0.815047 | ||||||||
\(989\) | 1.75079e13 | 0.581903 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.25008e13 | −0.741081 | −0.370540 | − | 0.928816i | \(-0.620828\pi\) | ||||
−0.370540 | + | 0.928816i | \(0.620828\pi\) | |||||||
\(992\) | 1.89088e13 | 0.619957 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.37807e13 | 3.04701 | ||||||||
\(995\) | 9.66342e11 | 0.0312556 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.13756e13 | −1.00569 | −0.502844 | − | 0.864377i | \(-0.667713\pi\) | ||||
−0.502844 | + | 0.864377i | \(0.667713\pi\) | |||||||
\(998\) | 2.40442e13 | 0.767224 | ||||||||
\(999\) | 0 | 0 |
(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 | 117.10.a.e.1.1 | 5 | ||
3.2 | odd | 2 | 13.10.a.b.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 208.10.a.h.1.3 | 5 | |||
15.14 | odd | 2 | 325.10.a.b.1.1 | 5 | |||
39.38 | odd | 2 | 169.10.a.b.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.10.a.b.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
117.10.a.e.1.1 | 5 | 1.1 | even | 1 | trivial | ||
169.10.a.b.1.1 | 5 | 39.38 | odd | 2 | |||
208.10.a.h.1.3 | 5 | 12.11 | even | 2 | |||
325.10.a.b.1.1 | 5 | 15.14 | odd | 2 |