Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,10,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, 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("325.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(167.386646753\) |
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: | \(\Z[a_1, a_2, a_3]\) |
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 | \(\chi\) | \(=\) | 325.1 |
$q$-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 | \(0.819457\pi\) | |||||||
\(3\) | −47.8784 | −0.341267 | −0.170633 | − | 0.985335i | \(-0.554581\pi\) | ||||
−0.170633 | + | 0.985335i | \(0.554581\pi\) | |||||||
\(4\) | 944.833 | 1.84538 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1827.45 | 0.575657 | ||||||||
\(7\) | −5947.44 | −0.936244 | −0.468122 | − | 0.883664i | \(-0.655069\pi\) | ||||
−0.468122 | + | 0.883664i | \(0.655069\pi\) | |||||||
\(8\) | −16520.6 | −1.42600 | ||||||||
\(9\) | −17390.7 | −0.883537 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −25205.7 | −0.519076 | −0.259538 | − | 0.965733i | \(-0.583570\pi\) | ||||
−0.259538 | + | 0.965733i | \(0.583570\pi\) | |||||||
\(12\) | −45237.1 | −0.629766 | ||||||||
\(13\) | −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 | \(0.550738\pi\) | |||||||
\(18\) | 663775. | 1.49037 | ||||||||
\(19\) | −904609. | −1.59246 | −0.796232 | − | 0.604992i | \(-0.793176\pi\) | ||||
−0.796232 | + | 0.604992i | \(0.793176\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 284754. | 0.319509 | ||||||||
\(22\) | 962062. | 0.875590 | ||||||||
\(23\) | 435749. | 0.324684 | 0.162342 | − | 0.986735i | \(-0.448095\pi\) | ||||
0.162342 | + | 0.986735i | \(0.448095\pi\) | |||||||
\(24\) | 790979. | 0.486647 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.09013e6 | 0.467841 | ||||||||
\(27\) | 1.77503e6 | 0.642789 | ||||||||
\(28\) | −5.61934e6 | −1.72772 | ||||||||
\(29\) | 6.44791e6 | 1.69289 | 0.846443 | − | 0.532479i | \(-0.178740\pi\) | ||||
0.846443 | + | 0.532479i | \(0.178740\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 1.20681e6 | 0.177143 | ||||||||
\(34\) | 4.17250e6 | 0.535477 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.64313e7 | −1.63046 | ||||||||
\(37\) | −4.14357e6 | −0.363469 | −0.181734 | − | 0.983348i | \(-0.558171\pi\) | ||||
−0.181734 | + | 0.983348i | \(0.558171\pi\) | |||||||
\(38\) | 3.45275e7 | 2.68621 | ||||||||
\(39\) | 1.36745e6 | 0.0946504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.49568e7 | 0.826632 | 0.413316 | − | 0.910588i | \(-0.364370\pi\) | ||||
0.413316 | + | 0.910588i | \(0.364370\pi\) | |||||||
\(42\) | −1.08686e7 | −0.538956 | ||||||||
\(43\) | −4.01789e7 | −1.79221 | −0.896107 | − | 0.443838i | \(-0.853616\pi\) | ||||
−0.896107 | + | 0.443838i | \(0.853616\pi\) | |||||||
\(44\) | −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 | \(0.530024\pi\) | |||||||
\(48\) | −7.02907e6 | −0.191123 | ||||||||
\(49\) | −4.98153e6 | −0.123447 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.23397e6 | 0.108334 | ||||||||
\(52\) | −2.69854e7 | −0.511815 | ||||||||
\(53\) | −1.53111e7 | −0.266542 | −0.133271 | − | 0.991080i | \(-0.542548\pi\) | ||||
−0.133271 | + | 0.991080i | \(0.542548\pi\) | |||||||
\(54\) | −6.77501e7 | −1.08427 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.82552e7 | 1.33509 | ||||||||
\(57\) | 4.33112e7 | 0.543455 | ||||||||
\(58\) | −2.46107e8 | −2.85560 | ||||||||
\(59\) | −1.52760e8 | −1.64126 | −0.820629 | − | 0.571462i | \(-0.806376\pi\) | ||||
−0.820629 | + | 0.571462i | \(0.806376\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 1.03430e8 | 0.827206 | ||||||||
\(64\) | −1.84138e8 | −1.37193 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.60620e7 | −0.298810 | ||||||||
\(67\) | 1.01034e8 | 0.612537 | 0.306268 | − | 0.951945i | \(-0.400920\pi\) | ||||
0.306268 | + | 0.951945i | \(0.400920\pi\) | |||||||
\(68\) | −1.03287e8 | −0.585809 | ||||||||
\(69\) | −2.08630e7 | −0.110804 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.13122e8 | 1.92937 | 0.964685 | − | 0.263406i | \(-0.0848458\pi\) | ||||
0.964685 | + | 0.263406i | \(0.0848458\pi\) | |||||||
\(72\) | 2.87304e8 | 1.25993 | ||||||||
\(73\) | 3.14453e8 | 1.29599 | 0.647997 | − | 0.761643i | \(-0.275607\pi\) | ||||
0.647997 | + | 0.761643i | \(0.275607\pi\) | |||||||
\(74\) | 1.58154e8 | 0.613108 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.54704e8 | −2.93870 | ||||||||
\(77\) | 1.49909e8 | 0.485982 | ||||||||
\(78\) | −5.21937e7 | −0.159659 | ||||||||
\(79\) | −2.00580e8 | −0.579383 | −0.289692 | − | 0.957120i | \(-0.593553\pi\) | ||||
−0.289692 | + | 0.957120i | \(0.593553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.57315e8 | 0.664175 | ||||||||
\(82\) | −5.70879e8 | −1.39438 | ||||||||
\(83\) | −6.34578e7 | −0.146769 | −0.0733843 | − | 0.997304i | \(-0.523380\pi\) | ||||
−0.0733843 | + | 0.997304i | \(0.523380\pi\) | |||||||
\(84\) | 2.69045e8 | 0.589614 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.53357e9 | 3.02315 | ||||||||
\(87\) | −3.08715e8 | −0.577726 | ||||||||
\(88\) | 4.16412e8 | 0.740204 | ||||||||
\(89\) | 3.47074e7 | 0.0586364 | 0.0293182 | − | 0.999570i | \(-0.490666\pi\) | ||||
0.0293182 | + | 0.999570i | \(0.490666\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.69865e8 | 0.259667 | ||||||||
\(92\) | 4.11710e8 | 0.599164 | ||||||||
\(93\) | −3.17102e8 | −0.439568 | ||||||||
\(94\) | 2.40519e8 | 0.317742 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.36692e8 | −0.164257 | ||||||||
\(97\) | 1.25403e9 | 1.43825 | 0.719127 | − | 0.694879i | \(-0.244542\pi\) | ||||
0.719127 | + | 0.694879i | \(0.244542\pi\) | |||||||
\(98\) | 1.90137e8 | 0.208233 | ||||||||
\(99\) | 4.38343e8 | 0.458623 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.06459e8 | −0.866766 | −0.433383 | − | 0.901210i | \(-0.642680\pi\) | ||||
−0.433383 | + | 0.901210i | \(0.642680\pi\) | |||||||
\(102\) | −1.99773e8 | −0.182741 | ||||||||
\(103\) | 4.17013e8 | 0.365075 | 0.182537 | − | 0.983199i | \(-0.441569\pi\) | ||||
0.182537 | + | 0.983199i | \(0.441569\pi\) | |||||||
\(104\) | 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 | \(0.579666\pi\) | |||||||
\(108\) | 1.67710e9 | 1.18619 | ||||||||
\(109\) | 1.66748e9 | 1.13147 | 0.565734 | − | 0.824588i | \(-0.308593\pi\) | ||||
0.565734 | + | 0.824588i | \(0.308593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.98387e8 | 0.124040 | ||||||||
\(112\) | −8.73149e8 | −0.524333 | ||||||||
\(113\) | 1.84580e9 | 1.06496 | 0.532478 | − | 0.846444i | \(-0.321261\pi\) | ||||
0.532478 | + | 0.846444i | \(0.321261\pi\) | |||||||
\(114\) | −1.65312e9 | −0.916713 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.09219e9 | 3.12401 | ||||||||
\(117\) | 4.96695e8 | 0.245049 | ||||||||
\(118\) | 5.83063e9 | 2.76851 | ||||||||
\(119\) | 6.50162e8 | 0.297208 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.72262e9 | −0.730560 | ||||||||
\(122\) | −3.30661e9 | −1.35134 | ||||||||
\(123\) | −7.16109e8 | −0.282102 | ||||||||
\(124\) | 6.25770e9 | 2.37694 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.94776e9 | −1.39535 | ||||||||
\(127\) | −1.87922e9 | −0.641006 | −0.320503 | − | 0.947248i | \(-0.603852\pi\) | ||||
−0.320503 | + | 0.947248i | \(0.603852\pi\) | |||||||
\(128\) | 5.56650e9 | 1.83290 | ||||||||
\(129\) | 1.92370e9 | 0.611623 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.46045e9 | 1.02663 | 0.513313 | − | 0.858201i | \(-0.328418\pi\) | ||||
0.513313 | + | 0.858201i | \(0.328418\pi\) | |||||||
\(132\) | 1.14023e9 | 0.326896 | ||||||||
\(133\) | 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 | \(0.709682\pi\) | |||||||
\(138\) | 7.96307e8 | 0.186907 | ||||||||
\(139\) | 3.59716e9 | 0.817322 | 0.408661 | − | 0.912686i | \(-0.365996\pi\) | ||||
0.408661 | + | 0.912686i | \(0.365996\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.01706e8 | 0.0642833 | ||||||||
\(142\) | −1.57682e10 | −3.25451 | ||||||||
\(143\) | 7.19899e8 | 0.143966 | ||||||||
\(144\) | −2.55314e9 | −0.494815 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.20022e10 | −2.18611 | ||||||||
\(147\) | 2.38508e8 | 0.0421283 | ||||||||
\(148\) | −3.91498e9 | −0.670736 | ||||||||
\(149\) | 1.27561e9 | 0.212022 | 0.106011 | − | 0.994365i | \(-0.466192\pi\) | ||||
0.106011 | + | 0.994365i | \(0.466192\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 1.90111e9 | 0.280476 | ||||||||
\(154\) | −5.72181e9 | −0.819766 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.29202e9 | 0.174666 | ||||||||
\(157\) | 1.41002e10 | 1.85215 | 0.926075 | − | 0.377339i | \(-0.123161\pi\) | ||||
0.926075 | + | 0.377339i | \(0.123161\pi\) | |||||||
\(158\) | 7.65584e9 | 0.977318 | ||||||||
\(159\) | 7.33072e8 | 0.0909619 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.59159e9 | −0.303983 | ||||||||
\(162\) | −9.82132e9 | −1.12035 | ||||||||
\(163\) | −7.24812e8 | −0.0804231 | −0.0402116 | − | 0.999191i | \(-0.512803\pi\) | ||||
−0.0402116 | + | 0.999191i | \(0.512803\pi\) | |||||||
\(164\) | 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 | \(0.486806\pi\) | |||||||
\(168\) | −4.70430e9 | −0.455621 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.57317e10 | 1.40700 | ||||||||
\(172\) | −3.79623e10 | −3.30731 | ||||||||
\(173\) | −5.77955e8 | −0.0490553 | −0.0245277 | − | 0.999699i | \(-0.507808\pi\) | ||||
−0.0245277 | + | 0.999699i | \(0.507808\pi\) | |||||||
\(174\) | 1.17832e10 | 0.974522 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.70046e9 | −0.290703 | ||||||||
\(177\) | 7.31392e9 | 0.560106 | ||||||||
\(178\) | −1.32473e9 | −0.0989094 | ||||||||
\(179\) | −1.56569e10 | −1.13990 | −0.569952 | − | 0.821678i | \(-0.693038\pi\) | ||||
−0.569952 | + | 0.821678i | \(0.693038\pi\) | |||||||
\(180\) | 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 | ||||||||
\(183\) | −4.14780e9 | −0.273394 | ||||||||
\(184\) | −7.19882e9 | −0.463000 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.21033e10 | 0.741474 | ||||||||
\(187\) | 2.75543e9 | 0.164779 | ||||||||
\(188\) | −5.95388e9 | −0.347608 | ||||||||
\(189\) | −1.05569e10 | −0.601807 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.67784e10 | 0.912222 | 0.456111 | − | 0.889923i | \(-0.349242\pi\) | ||||
0.456111 | + | 0.889923i | \(0.349242\pi\) | |||||||
\(192\) | 8.81622e9 | 0.468195 | ||||||||
\(193\) | 2.70036e10 | 1.40092 | 0.700462 | − | 0.713690i | \(-0.252977\pi\) | ||||
0.700462 | + | 0.713690i | \(0.252977\pi\) | |||||||
\(194\) | −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 | \(0.622138\pi\) | |||||||
\(198\) | −1.67309e10 | −0.773616 | ||||||||
\(199\) | 8.80397e9 | 0.397960 | 0.198980 | − | 0.980004i | \(-0.436237\pi\) | ||||
0.198980 | + | 0.980004i | \(0.436237\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.83736e9 | −0.209038 | ||||||||
\(202\) | 3.45982e10 | 1.46208 | ||||||||
\(203\) | −3.83485e10 | −1.58495 | ||||||||
\(204\) | 4.94523e9 | 0.199917 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.59167e10 | −0.615817 | ||||||||
\(207\) | −7.57796e9 | −0.286870 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | −1.97796e10 | −0.658430 | ||||||||
\(214\) | 2.56353e10 | 0.835558 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.93245e10 | −0.916618 | ||||||||
\(217\) | −3.93904e10 | −1.20593 | ||||||||
\(218\) | −6.36453e10 | −1.90859 | ||||||||
\(219\) | −1.50555e10 | −0.442280 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.12223e9 | 0.0880440 | ||||||||
\(222\) | −7.57215e9 | −0.209233 | ||||||||
\(223\) | −1.53511e10 | −0.415688 | −0.207844 | − | 0.978162i | \(-0.566645\pi\) | ||||
−0.207844 | + | 0.978162i | \(0.566645\pi\) | |||||||
\(224\) | −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 | \(0.676199\pi\) | |||||||
\(228\) | 4.09219e10 | 1.00288 | ||||||||
\(229\) | −6.68760e10 | −1.60698 | −0.803490 | − | 0.595318i | \(-0.797026\pi\) | ||||
−0.803490 | + | 0.595318i | \(0.797026\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.17741e9 | −0.165849 | ||||||||
\(232\) | −1.06523e11 | −2.41406 | ||||||||
\(233\) | 5.19268e10 | 1.15422 | 0.577112 | − | 0.816665i | \(-0.304180\pi\) | ||||
0.577112 | + | 0.816665i | \(0.304180\pi\) | |||||||
\(234\) | −1.89581e10 | −0.413355 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.44333e11 | −3.02874 | ||||||||
\(237\) | 9.60345e9 | 0.197724 | ||||||||
\(238\) | −2.48157e10 | −0.501338 | ||||||||
\(239\) | 7.45881e10 | 1.47870 | 0.739348 | − | 0.673323i | \(-0.235134\pi\) | ||||
0.739348 | + | 0.673323i | \(0.235134\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | −4.72577e10 | −0.869449 | ||||||||
\(244\) | 8.18528e10 | 1.47836 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.73328e10 | 0.475857 | ||||||||
\(247\) | 2.58365e10 | 0.441670 | ||||||||
\(248\) | −1.09417e11 | −1.83676 | ||||||||
\(249\) | 3.03826e9 | 0.0500873 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.07873e11 | −1.71546 | −0.857732 | − | 0.514097i | \(-0.828127\pi\) | ||||
−0.857732 | + | 0.514097i | \(0.828127\pi\) | |||||||
\(252\) | 9.77240e10 | 1.52651 | ||||||||
\(253\) | −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 | \(0.342530\pi\) | |||||||
\(258\) | −7.34247e10 | −1.03170 | ||||||||
\(259\) | 2.46436e10 | 0.340295 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.12133e11 | −1.49573 | ||||||||
\(262\) | −1.32080e11 | −1.73174 | ||||||||
\(263\) | 8.15356e10 | 1.05086 | 0.525432 | − | 0.850836i | \(-0.323904\pi\) | ||||
0.525432 | + | 0.850836i | \(0.323904\pi\) | |||||||
\(264\) | −1.99371e10 | −0.252607 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.05351e11 | −2.51494 | ||||||||
\(267\) | −1.66174e9 | −0.0200107 | ||||||||
\(268\) | 9.54605e10 | 1.13036 | ||||||||
\(269\) | 1.00568e11 | 1.17105 | 0.585523 | − | 0.810656i | \(-0.300889\pi\) | ||||
0.585523 | + | 0.810656i | \(0.300889\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | −8.13286e9 | −0.0886158 | ||||||||
\(274\) | 1.92669e11 | 2.06507 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.97120e10 | −0.204475 | ||||||||
\(277\) | 3.17195e10 | 0.323718 | 0.161859 | − | 0.986814i | \(-0.448251\pi\) | ||||
0.161859 | + | 0.986814i | \(0.448251\pi\) | |||||||
\(278\) | −1.37298e11 | −1.37868 | ||||||||
\(279\) | −1.15180e11 | −1.13804 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.86953e10 | 0.944318 | 0.472159 | − | 0.881513i | \(-0.343475\pi\) | ||||
0.472159 | + | 0.881513i | \(0.343475\pi\) | |||||||
\(282\) | −1.15157e10 | −0.108435 | ||||||||
\(283\) | 1.06164e11 | 0.983871 | 0.491935 | − | 0.870632i | \(-0.336290\pi\) | ||||
0.491935 | + | 0.870632i | \(0.336290\pi\) | |||||||
\(284\) | 3.90331e11 | 3.56042 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.74774e10 | −0.242845 | ||||||||
\(287\) | −8.89549e10 | −0.773929 | ||||||||
\(288\) | −4.96501e10 | −0.425260 | ||||||||
\(289\) | −1.06637e11 | −0.899227 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00410e10 | −0.490828 | ||||||||
\(292\) | 2.97106e11 | 2.39160 | ||||||||
\(293\) | −2.26355e11 | −1.79426 | −0.897132 | − | 0.441763i | \(-0.854353\pi\) | ||||
−0.897132 | + | 0.441763i | \(0.854353\pi\) | |||||||
\(294\) | −9.10348e9 | −0.0710631 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.84541e10 | 0.518307 | ||||||||
\(297\) | −4.47407e10 | −0.333656 | ||||||||
\(298\) | −4.86881e10 | −0.357643 | ||||||||
\(299\) | −1.24454e10 | −0.0900511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.38962e11 | 1.67795 | ||||||||
\(302\) | −1.66137e11 | −1.14930 | ||||||||
\(303\) | 4.33998e10 | 0.295798 | ||||||||
\(304\) | −1.32806e11 | −0.891841 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.25625e10 | −0.473114 | ||||||||
\(307\) | 2.23009e10 | 0.143285 | 0.0716424 | − | 0.997430i | \(-0.477176\pi\) | ||||
0.0716424 | + | 0.997430i | \(0.477176\pi\) | |||||||
\(308\) | 1.41639e11 | 0.896820 | ||||||||
\(309\) | −1.99659e10 | −0.124588 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.71805e11 | −1.64754 | −0.823770 | − | 0.566925i | \(-0.808133\pi\) | ||||
−0.823770 | + | 0.566925i | \(0.808133\pi\) | |||||||
\(312\) | −2.25911e10 | −0.134972 | ||||||||
\(313\) | 7.90775e10 | 0.465697 | 0.232849 | − | 0.972513i | \(-0.425195\pi\) | ||||
0.232849 | + | 0.972513i | \(0.425195\pi\) | |||||||
\(314\) | −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 | \(0.690983\pi\) | |||||||
\(318\) | −2.79802e10 | −0.153437 | ||||||||
\(319\) | −1.62524e11 | −0.878736 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.21568e10 | 0.169044 | ||||||||
\(322\) | 9.89171e10 | 0.512767 | ||||||||
\(323\) | 9.88899e10 | 0.505523 | ||||||||
\(324\) | 2.43120e11 | 1.22565 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.76650e10 | 0.135660 | ||||||||
\(327\) | −7.98365e10 | −0.386132 | ||||||||
\(328\) | −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 | ||||||||
\(333\) | 7.20594e10 | 0.321138 | ||||||||
\(334\) | −3.17955e10 | −0.139800 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.18050e10 | 0.178937 | ||||||||
\(337\) | −2.68510e11 | −1.13403 | −0.567017 | − | 0.823706i | \(-0.691903\pi\) | ||||
−0.567017 | + | 0.823706i | \(0.691903\pi\) | |||||||
\(338\) | −3.11352e10 | −0.129756 | ||||||||
\(339\) | −8.83739e10 | −0.363434 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.66939e11 | −0.668595 | ||||||||
\(342\) | −6.00457e11 | −2.37336 | ||||||||
\(343\) | 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 | \(0.669834\pi\) | |||||||
\(348\) | −2.91684e11 | −1.06612 | ||||||||
\(349\) | −3.54006e11 | −1.27731 | −0.638655 | − | 0.769494i | \(-0.720509\pi\) | ||||
−0.638655 | + | 0.769494i | \(0.720509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.06966e10 | −0.178277 | ||||||||
\(352\) | −7.19619e10 | −0.249839 | ||||||||
\(353\) | 2.25650e11 | 0.773481 | 0.386741 | − | 0.922189i | \(-0.373601\pi\) | ||||
0.386741 | + | 0.922189i | \(0.373601\pi\) | |||||||
\(354\) | −2.79161e11 | −0.944801 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.27927e10 | 0.108206 | ||||||||
\(357\) | −3.11287e10 | −0.101427 | ||||||||
\(358\) | 5.97602e11 | 1.92282 | ||||||||
\(359\) | 3.39022e10 | 0.107722 | 0.0538608 | − | 0.998548i | \(-0.482847\pi\) | ||||
0.0538608 | + | 0.998548i | \(0.482847\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.95629e11 | 1.53594 | ||||||||
\(362\) | 8.34178e11 | 2.55312 | ||||||||
\(363\) | 8.24764e10 | 0.249316 | ||||||||
\(364\) | 1.60494e11 | 0.479184 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.58315e11 | 0.461167 | ||||||||
\(367\) | 7.74387e10 | 0.222823 | 0.111412 | − | 0.993774i | \(-0.464463\pi\) | ||||
0.111412 | + | 0.993774i | \(0.464463\pi\) | |||||||
\(368\) | 6.39726e10 | 0.181836 | ||||||||
\(369\) | −2.60109e11 | −0.730360 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.10620e10 | 0.249548 | ||||||||
\(372\) | −2.99609e11 | −0.811169 | ||||||||
\(373\) | −6.50821e11 | −1.74089 | −0.870446 | − | 0.492264i | \(-0.836169\pi\) | ||||
−0.870446 | + | 0.492264i | \(0.836169\pi\) | |||||||
\(374\) | −1.05171e11 | −0.277954 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.04105e11 | 0.268612 | ||||||||
\(377\) | −1.84159e11 | −0.469522 | ||||||||
\(378\) | 4.02940e11 | 1.01514 | ||||||||
\(379\) | 1.93989e11 | 0.482948 | 0.241474 | − | 0.970407i | \(-0.422369\pi\) | ||||
0.241474 | + | 0.970407i | \(0.422369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.99743e10 | 0.218754 | ||||||||
\(382\) | −6.40406e11 | −1.53876 | ||||||||
\(383\) | −4.44645e11 | −1.05589 | −0.527946 | − | 0.849278i | \(-0.677037\pi\) | ||||
−0.527946 | + | 0.849278i | \(0.677037\pi\) | |||||||
\(384\) | −2.66515e11 | −0.625506 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.03069e12 | −2.36311 | ||||||||
\(387\) | 6.98737e11 | 1.58349 | ||||||||
\(388\) | 1.18485e12 | 2.65412 | ||||||||
\(389\) | −1.69623e11 | −0.375589 | −0.187794 | − | 0.982208i | \(-0.560134\pi\) | ||||
−0.187794 | + | 0.982208i | \(0.560134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.76352e10 | −0.103070 | ||||||||
\(392\) | 8.22978e10 | 0.176036 | ||||||||
\(393\) | −1.65681e11 | −0.350353 | ||||||||
\(394\) | 6.04119e11 | 1.26296 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.14161e11 | 0.846332 | ||||||||
\(397\) | −2.94468e11 | −0.594951 | −0.297476 | − | 0.954729i | \(-0.596145\pi\) | ||||
−0.297476 | + | 0.954729i | \(0.596145\pi\) | |||||||
\(398\) | −3.36034e11 | −0.671289 | ||||||||
\(399\) | −2.57591e11 | −0.508806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.43362e11 | 0.856265 | 0.428133 | − | 0.903716i | \(-0.359172\pi\) | ||||
0.428133 | + | 0.903716i | \(0.359172\pi\) | |||||||
\(402\) | 1.84635e11 | 0.352611 | ||||||||
\(403\) | −1.89162e11 | −0.357240 | ||||||||
\(404\) | −8.56452e11 | −1.59951 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.46371e12 | 2.67354 | ||||||||
\(407\) | 1.04441e11 | 0.188668 | ||||||||
\(408\) | −8.64682e10 | −0.154485 | ||||||||
\(409\) | −1.01253e11 | −0.178918 | −0.0894592 | − | 0.995990i | \(-0.528514\pi\) | ||||
−0.0894592 | + | 0.995990i | \(0.528514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.41684e11 | 0.417791 | ||||||||
\(412\) | 3.94007e11 | 0.673700 | ||||||||
\(413\) | 9.08533e11 | 1.53662 | ||||||||
\(414\) | 2.89239e11 | 0.483900 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.15413e10 | −0.133493 | ||||||||
\(417\) | −1.72226e11 | −0.278925 | ||||||||
\(418\) | −8.70289e11 | −1.39435 | ||||||||
\(419\) | 7.93982e10 | 0.125848 | 0.0629242 | − | 0.998018i | \(-0.479957\pi\) | ||||
0.0629242 | + | 0.998018i | \(0.479957\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 1.09587e11 | 0.166429 | ||||||||
\(424\) | 2.52949e11 | 0.380089 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.54958e11 | 1.11066 | ||||||||
\(427\) | −5.15239e11 | −0.750038 | ||||||||
\(428\) | −6.34583e11 | −0.914096 | ||||||||
\(429\) | −3.44676e10 | −0.0491307 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.72544e11 | −0.380442 | −0.190221 | − | 0.981741i | \(-0.560920\pi\) | ||||
−0.190221 | + | 0.981741i | \(0.560920\pi\) | |||||||
\(432\) | 2.60593e11 | 0.359987 | ||||||||
\(433\) | 1.15522e12 | 1.57931 | 0.789655 | − | 0.613551i | \(-0.210260\pi\) | ||||
0.789655 | + | 0.613551i | \(0.210260\pi\) | |||||||
\(434\) | 1.50347e12 | 2.03419 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.57549e12 | 2.08799 | ||||||||
\(437\) | −3.94182e11 | −0.517047 | ||||||||
\(438\) | 5.74646e11 | 0.746048 | ||||||||
\(439\) | 1.78053e11 | 0.228801 | 0.114401 | − | 0.993435i | \(-0.463505\pi\) | ||||
0.114401 | + | 0.993435i | \(0.463505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.66321e10 | 0.109070 | ||||||||
\(442\) | −1.19171e11 | −0.148515 | ||||||||
\(443\) | 6.55260e10 | 0.0808345 | 0.0404173 | − | 0.999183i | \(-0.487131\pi\) | ||||
0.0404173 | + | 0.999183i | \(0.487131\pi\) | |||||||
\(444\) | 1.87443e11 | 0.228900 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.85928e11 | 0.701192 | ||||||||
\(447\) | −6.10742e10 | −0.0723559 | ||||||||
\(448\) | 1.09515e12 | 1.28446 | ||||||||
\(449\) | −7.98150e11 | −0.926779 | −0.463390 | − | 0.886155i | \(-0.653367\pi\) | ||||
−0.463390 | + | 0.886155i | \(0.653367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.76997e11 | −0.429085 | ||||||||
\(452\) | 1.74397e12 | 1.96525 | ||||||||
\(453\) | −2.08402e11 | −0.232519 | ||||||||
\(454\) | 1.60544e12 | 1.77355 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.15526e11 | −0.774968 | ||||||||
\(457\) | 8.92736e11 | 0.957415 | 0.478708 | − | 0.877974i | \(-0.341105\pi\) | ||||
0.478708 | + | 0.877974i | \(0.341105\pi\) | |||||||
\(458\) | 2.55256e12 | 2.71069 | ||||||||
\(459\) | −1.94042e11 | −0.204051 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.32490e11 | 0.239745 | 0.119872 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119872 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(462\) | 2.73951e11 | 0.279759 | ||||||||
\(463\) | 1.54421e12 | 1.56168 | 0.780841 | − | 0.624730i | \(-0.214791\pi\) | ||||
0.780841 | + | 0.624730i | \(0.214791\pi\) | |||||||
\(464\) | 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 | \(0.792249\pi\) | |||||||
\(468\) | 4.69293e11 | 0.452208 | ||||||||
\(469\) | −6.00895e11 | −0.573484 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.75094e11 | −0.632077 | ||||||||
\(472\) | 2.52369e12 | 2.34044 | ||||||||
\(473\) | 1.01274e12 | 0.930295 | ||||||||
\(474\) | −3.66549e11 | −0.333526 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.14295e11 | 0.548461 | ||||||||
\(477\) | 2.66271e11 | 0.235500 | ||||||||
\(478\) | −2.84692e12 | −2.49430 | ||||||||
\(479\) | 1.54414e12 | 1.34022 | 0.670112 | − | 0.742260i | \(-0.266246\pi\) | ||||
0.670112 | + | 0.742260i | \(0.266246\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.18344e11 | 0.100808 | ||||||||
\(482\) | −2.19412e12 | −1.85161 | ||||||||
\(483\) | 1.24081e11 | 0.103739 | ||||||||
\(484\) | −1.62759e12 | −1.34816 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.80375e12 | 1.46661 | ||||||||
\(487\) | −2.55439e11 | −0.205782 | −0.102891 | − | 0.994693i | \(-0.532809\pi\) | ||||
−0.102891 | + | 0.994693i | \(0.532809\pi\) | |||||||
\(488\) | −1.43121e12 | −1.14239 | ||||||||
\(489\) | 3.47028e10 | 0.0274457 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.58407e12 | 1.23000 | 0.615002 | − | 0.788526i | \(-0.289155\pi\) | ||||
0.615002 | + | 0.788526i | \(0.289155\pi\) | |||||||
\(492\) | −6.76603e11 | −0.520584 | ||||||||
\(493\) | −7.04872e11 | −0.537402 | ||||||||
\(494\) | −9.86141e11 | −0.745020 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.72340e11 | 0.721357 | ||||||||
\(497\) | −2.45702e12 | −1.80636 | ||||||||
\(498\) | −1.15966e11 | −0.0844884 | ||||||||
\(499\) | −6.29948e11 | −0.454833 | −0.227417 | − | 0.973798i | \(-0.573028\pi\) | ||||
−0.227417 | + | 0.973798i | \(0.573028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.98842e10 | −0.0282834 | ||||||||
\(502\) | 4.11736e12 | 2.89369 | ||||||||
\(503\) | −5.49263e11 | −0.382582 | −0.191291 | − | 0.981533i | \(-0.561267\pi\) | ||||
−0.191291 | + | 0.981533i | \(0.561267\pi\) | |||||||
\(504\) | −1.70872e12 | −1.17960 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.19217e11 | 0.284290 | ||||||||
\(507\) | −3.90559e10 | −0.0262513 | ||||||||
\(508\) | −1.77555e12 | −1.18290 | ||||||||
\(509\) | 1.36923e11 | 0.0904165 | 0.0452083 | − | 0.998978i | \(-0.485605\pi\) | ||||
0.0452083 | + | 0.998978i | \(0.485605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.87019e12 | −1.21337 | ||||||||
\(512\) | 1.66095e12 | 1.06817 | ||||||||
\(513\) | −1.60570e12 | −1.02362 | ||||||||
\(514\) | −2.53467e12 | −1.60172 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.81758e12 | 1.12867 | ||||||||
\(517\) | 1.58834e11 | 0.0977767 | ||||||||
\(518\) | −9.40610e11 | −0.574018 | ||||||||
\(519\) | 2.76715e10 | 0.0167410 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.66627e12 | −0.990779 | −0.495389 | − | 0.868671i | \(-0.664975\pi\) | ||||
−0.495389 | + | 0.868671i | \(0.664975\pi\) | |||||||
\(522\) | 4.27996e12 | 2.52303 | ||||||||
\(523\) | −1.97187e12 | −1.15244 | −0.576222 | − | 0.817293i | \(-0.695474\pi\) | ||||
−0.576222 | + | 0.817293i | \(0.695474\pi\) | |||||||
\(524\) | 3.26955e12 | 1.89451 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.11209e12 | −1.77262 | ||||||||
\(527\) | −7.24021e11 | −0.408887 | ||||||||
\(528\) | 1.77172e11 | 0.0992072 | ||||||||
\(529\) | −1.61128e12 | −0.894580 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.65660e12 | 1.45011 | ||||||||
\(532\) | 5.08330e12 | 2.75134 | ||||||||
\(533\) | −4.27182e11 | −0.229266 | ||||||||
\(534\) | 6.34260e10 | 0.0337545 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.66914e12 | −0.873479 | ||||||||
\(537\) | 7.49629e11 | 0.389011 | ||||||||
\(538\) | −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 | ||||||||
\(543\) | 1.04639e12 | 0.516529 | ||||||||
\(544\) | −3.12101e11 | −0.152792 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.10419e11 | 0.149479 | ||||||||
\(547\) | −1.98052e12 | −0.945879 | −0.472939 | − | 0.881095i | \(-0.656807\pi\) | ||||
−0.472939 | + | 0.881095i | \(0.656807\pi\) | |||||||
\(548\) | −4.76939e12 | −2.25918 | ||||||||
\(549\) | −1.50659e12 | −0.707814 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.83283e12 | −2.69586 | ||||||||
\(552\) | 3.44668e11 | 0.158007 | ||||||||
\(553\) | 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 | \(0.562515\pi\) | |||||||
\(558\) | 4.39623e12 | 1.91967 | ||||||||
\(559\) | 1.14755e12 | 0.497071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.31926e11 | −0.0562336 | ||||||||
\(562\) | −3.76705e12 | −1.59290 | ||||||||
\(563\) | −3.89786e12 | −1.63508 | −0.817539 | − | 0.575873i | \(-0.804662\pi\) | ||||
−0.817539 | + | 0.575873i | \(0.804662\pi\) | |||||||
\(564\) | 2.85062e11 | 0.118627 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.05212e12 | −1.65962 | ||||||||
\(567\) | −1.53037e12 | −0.621830 | ||||||||
\(568\) | −6.82501e12 | −2.75129 | ||||||||
\(569\) | −2.26590e12 | −0.906223 | −0.453112 | − | 0.891454i | \(-0.649686\pi\) | ||||
−0.453112 | + | 0.891454i | \(0.649686\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −8.03323e11 | −0.311311 | ||||||||
\(574\) | 3.39527e12 | 1.30548 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.20228e12 | 1.21215 | ||||||||
\(577\) | 3.23415e12 | 1.21470 | 0.607350 | − | 0.794434i | \(-0.292233\pi\) | ||||
0.607350 | + | 0.794434i | \(0.292233\pi\) | |||||||
\(578\) | 4.07019e12 | 1.51684 | ||||||||
\(579\) | −1.29289e12 | −0.478089 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.77411e11 | 0.137411 | ||||||||
\(582\) | 2.29167e12 | 0.827941 | ||||||||
\(583\) | 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 | \(0.451204\pi\) | |||||||
\(588\) | 2.25350e11 | 0.0777427 | ||||||||
\(589\) | −5.99129e12 | −2.05117 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.57805e11 | 0.255513 | ||||||||
\(592\) | −6.08321e11 | −0.203556 | ||||||||
\(593\) | 1.91730e12 | 0.636712 | 0.318356 | − | 0.947971i | \(-0.396869\pi\) | ||||
0.318356 | + | 0.947971i | \(0.396869\pi\) | |||||||
\(594\) | 1.70769e12 | 0.562819 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.20524e12 | 0.391260 | ||||||||
\(597\) | −4.21520e11 | −0.135811 | ||||||||
\(598\) | 4.75023e11 | 0.151900 | ||||||||
\(599\) | −5.10464e12 | −1.62011 | −0.810054 | − | 0.586355i | \(-0.800562\pi\) | ||||
−0.810054 | + | 0.586355i | \(0.800562\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | −1.75705e12 | −0.541199 | ||||||||
\(604\) | 4.11260e12 | 1.25733 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.65650e12 | −0.498960 | ||||||||
\(607\) | −1.18434e12 | −0.354101 | −0.177051 | − | 0.984202i | \(-0.556656\pi\) | ||||
−0.177051 | + | 0.984202i | \(0.556656\pi\) | |||||||
\(608\) | −2.58265e12 | −0.766477 | ||||||||
\(609\) | 1.83607e12 | 0.540892 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.79978e11 | 0.0522436 | ||||||||
\(612\) | 1.79623e12 | 0.517584 | ||||||||
\(613\) | −6.42597e11 | −0.183809 | −0.0919045 | − | 0.995768i | \(-0.529295\pi\) | ||||
−0.0919045 | + | 0.995768i | \(0.529295\pi\) | |||||||
\(614\) | −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 | \(0.747744\pi\) | |||||||
\(618\) | 7.62068e11 | 0.210158 | ||||||||
\(619\) | −3.09492e11 | −0.0847308 | −0.0423654 | − | 0.999102i | \(-0.513489\pi\) | ||||
−0.0423654 | + | 0.999102i | \(0.513489\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.73466e11 | 0.208703 | ||||||||
\(622\) | 1.03744e13 | 2.77911 | ||||||||
\(623\) | −2.06421e11 | −0.0548980 | ||||||||
\(624\) | 2.00757e11 | 0.0530079 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.01827e12 | −0.785549 | ||||||||
\(627\) | −1.09169e12 | −0.282094 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 8.71644e11 | 0.215786 | ||||||||
\(634\) | 7.74944e12 | 1.90488 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.92631e11 | 0.167859 | ||||||||
\(637\) | 1.42278e11 | 0.0342380 | ||||||||
\(638\) | 6.20328e12 | 1.48227 | ||||||||
\(639\) | −7.18446e12 | −1.70467 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.30298e12 | 0.538802 | 0.269401 | − | 0.963028i | \(-0.413174\pi\) | ||||
0.269401 | + | 0.963028i | \(0.413174\pi\) | |||||||
\(642\) | −1.22738e12 | −0.285148 | ||||||||
\(643\) | 2.54593e12 | 0.587350 | 0.293675 | − | 0.955905i | \(-0.405122\pi\) | ||||
0.293675 | + | 0.955905i | \(0.405122\pi\) | |||||||
\(644\) | −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 | \(0.490194\pi\) | |||||||
\(648\) | −4.25099e12 | −0.947115 | ||||||||
\(649\) | 3.85043e12 | 0.851937 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88595e12 | 0.411543 | ||||||||
\(652\) | −6.84826e11 | −0.148411 | ||||||||
\(653\) | 6.05719e12 | 1.30365 | 0.651826 | − | 0.758369i | \(-0.274003\pi\) | ||||
0.651826 | + | 0.758369i | \(0.274003\pi\) | |||||||
\(654\) | 3.04724e12 | 0.651338 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.19582e12 | 0.462946 | ||||||||
\(657\) | −5.46855e12 | −1.14506 | ||||||||
\(658\) | −1.43047e12 | −0.297484 | ||||||||
\(659\) | 4.97718e12 | 1.02801 | 0.514007 | − | 0.857786i | \(-0.328160\pi\) | ||||
0.514007 | + | 0.857786i | \(0.328160\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | −1.49487e11 | −0.0300465 | ||||||||
\(664\) | 1.04836e12 | 0.209292 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.75040e12 | −0.541703 | ||||||||
\(667\) | 2.80967e12 | 0.549653 | ||||||||
\(668\) | 7.87076e11 | 0.152940 | ||||||||
\(669\) | 7.34986e11 | 0.141860 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.18362e12 | −0.415839 | ||||||||
\(672\) | 8.12969e11 | 0.153784 | ||||||||
\(673\) | −1.37693e12 | −0.258728 | −0.129364 | − | 0.991597i | \(-0.541294\pi\) | ||||
−0.129364 | + | 0.991597i | \(0.541294\pi\) | |||||||
\(674\) | 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 | \(0.518928\pi\) | |||||||
\(678\) | 3.37310e12 | 0.613049 | ||||||||
\(679\) | −7.45828e12 | −1.34656 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.01386e12 | 0.358813 | ||||||||
\(682\) | 6.37181e12 | 1.12780 | ||||||||
\(683\) | 1.10011e12 | 0.193438 | 0.0967190 | − | 0.995312i | \(-0.469165\pi\) | ||||
0.0967190 | + | 0.995312i | \(0.469165\pi\) | |||||||
\(684\) | 1.48639e13 | 2.59645 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.02913e13 | −1.77424 | ||||||||
\(687\) | 3.20192e12 | 0.548409 | ||||||||
\(688\) | −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 | ||||||||
\(693\) | −2.60702e12 | −0.429383 | ||||||||
\(694\) | 1.04855e13 | 1.71581 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.10016e12 | 0.823838 | ||||||||
\(697\) | −1.63505e12 | −0.262412 | ||||||||
\(698\) | 1.35119e13 | 2.15460 | ||||||||
\(699\) | −2.48617e12 | −0.393898 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.40436e12 | 0.219658 | 0.109829 | − | 0.993950i | \(-0.464970\pi\) | ||||
0.109829 | + | 0.993950i | \(0.464970\pi\) | |||||||
\(702\) | 1.93501e12 | 0.300723 | ||||||||
\(703\) | 3.74831e12 | 0.578810 | ||||||||
\(704\) | 4.64131e12 | 0.712137 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.61273e12 | −1.30473 | ||||||||
\(707\) | 5.39111e12 | 0.811505 | ||||||||
\(708\) | 6.91043e12 | 1.03361 | ||||||||
\(709\) | 5.19764e12 | 0.772499 | 0.386250 | − | 0.922394i | \(-0.373770\pi\) | ||||
0.386250 | + | 0.922394i | \(0.373770\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.48822e12 | 0.511907 | ||||||||
\(712\) | −5.73387e11 | −0.0836157 | ||||||||
\(713\) | 2.88600e12 | 0.418209 | ||||||||
\(714\) | 1.18814e12 | 0.171090 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.47932e13 | −2.10355 | ||||||||
\(717\) | −3.57116e12 | −0.504630 | ||||||||
\(718\) | −1.29400e12 | −0.181707 | ||||||||
\(719\) | −1.27042e13 | −1.77284 | −0.886418 | − | 0.462886i | \(-0.846814\pi\) | ||||
−0.886418 | + | 0.462886i | \(0.846814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.48016e12 | −0.341799 | ||||||||
\(722\) | −1.89174e13 | −2.59086 | ||||||||
\(723\) | −2.75230e12 | −0.374605 | ||||||||
\(724\) | −2.06495e13 | −2.79309 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.14800e12 | −0.420552 | ||||||||
\(727\) | −9.91998e11 | −0.131706 | −0.0658531 | − | 0.997829i | \(-0.520977\pi\) | ||||
−0.0658531 | + | 0.997829i | \(0.520977\pi\) | |||||||
\(728\) | −2.80627e12 | −0.370286 | ||||||||
\(729\) | −2.80211e12 | −0.367461 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.39227e12 | 0.568933 | ||||||||
\(732\) | −3.91898e12 | −0.504514 | ||||||||
\(733\) | −5.54849e12 | −0.709916 | −0.354958 | − | 0.934882i | \(-0.615505\pi\) | ||||
−0.354958 | + | 0.934882i | \(0.615505\pi\) | |||||||
\(734\) | −2.95572e12 | −0.375864 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.24406e12 | 0.156275 | ||||||||
\(737\) | −2.54663e12 | −0.317953 | ||||||||
\(738\) | 9.92797e12 | 1.23199 | ||||||||
\(739\) | 8.78597e12 | 1.08365 | 0.541826 | − | 0.840491i | \(-0.317733\pi\) | ||||
0.541826 | + | 0.840491i | \(0.317733\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23701e12 | −0.150727 | ||||||||
\(742\) | −3.47570e12 | −0.420944 | ||||||||
\(743\) | −4.04326e12 | −0.486724 | −0.243362 | − | 0.969936i | \(-0.578250\pi\) | ||||
−0.243362 | + | 0.969936i | \(0.578250\pi\) | |||||||
\(744\) | 5.23871e12 | 0.626825 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.48408e13 | 2.93658 | ||||||||
\(747\) | 1.10357e12 | 0.129676 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 5.16479e12 | 0.585431 | ||||||||
\(754\) | 7.02906e12 | 0.792001 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.97448e12 | −1.11056 | ||||||||
\(757\) | −9.99638e12 | −1.10640 | −0.553199 | − | 0.833049i | \(-0.686593\pi\) | ||||
−0.553199 | + | 0.833049i | \(0.686593\pi\) | |||||||
\(758\) | −7.40426e12 | −0.814649 | ||||||||
\(759\) | 5.25864e11 | 0.0575156 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.98848e12 | −0.323013 | −0.161507 | − | 0.986872i | \(-0.551635\pi\) | ||||
−0.161507 | + | 0.986872i | \(0.551635\pi\) | |||||||
\(762\) | −3.43418e12 | −0.369000 | ||||||||
\(763\) | −9.91726e12 | −1.05933 | ||||||||
\(764\) | 1.58528e13 | 1.68339 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.69714e13 | 1.78110 | ||||||||
\(767\) | 4.36299e12 | 0.455203 | ||||||||
\(768\) | 5.65858e12 | 0.586924 | ||||||||
\(769\) | 1.54887e13 | 1.59715 | 0.798576 | − | 0.601894i | \(-0.205587\pi\) | ||||
0.798576 | + | 0.601894i | \(0.205587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.17948e12 | −0.324050 | ||||||||
\(772\) | 2.55139e13 | 2.58523 | ||||||||
\(773\) | −1.07589e13 | −1.08383 | −0.541915 | − | 0.840434i | \(-0.682300\pi\) | ||||
−0.541915 | + | 0.840434i | \(0.682300\pi\) | |||||||
\(774\) | −2.66697e13 | −2.67106 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.07173e13 | −2.05095 | ||||||||
\(777\) | −1.17990e12 | −0.116131 | ||||||||
\(778\) | 6.47427e12 | 0.633552 | ||||||||
\(779\) | −1.35301e13 | −1.31638 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04130e13 | −1.00149 | ||||||||
\(782\) | 1.81816e12 | 0.173861 | ||||||||
\(783\) | 1.14452e13 | 1.08817 | ||||||||
\(784\) | −7.31343e11 | −0.0691351 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.32379e12 | 0.590985 | ||||||||
\(787\) | −1.29304e13 | −1.20151 | −0.600755 | − | 0.799433i | \(-0.705133\pi\) | ||||
−0.600755 | + | 0.799433i | \(0.705133\pi\) | |||||||
\(788\) | −1.49545e13 | −1.38167 | ||||||||
\(789\) | −3.90379e12 | −0.358625 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.09778e13 | −0.997059 | ||||||||
\(792\) | −7.24168e12 | −0.653997 | ||||||||
\(793\) | −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 | \(0.684389\pi\) | |||||||
\(798\) | 9.83185e12 | 0.858267 | ||||||||
\(799\) | 6.88868e11 | 0.0597965 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.03585e11 | −0.0518075 | ||||||||
\(802\) | −1.69224e13 | −1.44437 | ||||||||
\(803\) | −7.92600e12 | −0.672719 | ||||||||
\(804\) | −4.57049e12 | −0.385755 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.22002e12 | 0.602602 | ||||||||
\(807\) | −4.81502e12 | −0.399639 | ||||||||
\(808\) | 1.49752e13 | 1.23601 | ||||||||
\(809\) | −2.40763e13 | −1.97616 | −0.988079 | − | 0.153948i | \(-0.950801\pi\) | ||||
−0.988079 | + | 0.153948i | \(0.950801\pi\) | |||||||
\(810\) | 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 | ||||||||
\(813\) | 1.43040e12 | 0.114829 | ||||||||
\(814\) | −3.98637e12 | −0.318249 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.68403e11 | 0.0606713 | ||||||||
\(817\) | 3.63462e13 | 2.85403 | ||||||||
\(818\) | 3.86469e12 | 0.301804 | ||||||||
\(819\) | −2.95406e12 | −0.229426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.50113e13 | −1.92129 | −0.960643 | − | 0.277786i | \(-0.910399\pi\) | ||||
−0.960643 | + | 0.277786i | \(0.910399\pi\) | |||||||
\(822\) | −9.22470e12 | −0.704740 | ||||||||
\(823\) | −1.29351e13 | −0.982808 | −0.491404 | − | 0.870932i | \(-0.663516\pi\) | ||||
−0.491404 | + | 0.870932i | \(0.663516\pi\) | |||||||
\(824\) | −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 | \(0.621817\pi\) | |||||||
\(828\) | −7.15990e12 | −0.529384 | ||||||||
\(829\) | 8.77304e12 | 0.645141 | 0.322570 | − | 0.946545i | \(-0.395453\pi\) | ||||
0.322570 | + | 0.946545i | \(0.395453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.51868e12 | −0.110474 | ||||||||
\(832\) | 5.25916e12 | 0.380506 | ||||||||
\(833\) | 5.44571e11 | 0.0391879 | ||||||||
\(834\) | 6.57361e12 | 0.470497 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.15434e13 | 1.52541 | ||||||||
\(837\) | 1.17561e13 | 0.827943 | ||||||||
\(838\) | −3.03051e12 | −0.212284 | ||||||||
\(839\) | −1.54259e13 | −1.07478 | −0.537392 | − | 0.843332i | \(-0.680590\pi\) | ||||
−0.537392 | + | 0.843332i | \(0.680590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.70683e13 | 1.86586 | ||||||||
\(842\) | 2.31593e13 | 1.58789 | ||||||||
\(843\) | −4.72537e12 | −0.322264 | ||||||||
\(844\) | −1.72010e13 | −1.16685 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.18279e12 | −0.280737 | ||||||||
\(847\) | 1.02452e13 | 0.683983 | ||||||||
\(848\) | −2.24784e12 | −0.149274 | ||||||||
\(849\) | −5.08296e12 | −0.335762 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.80556e12 | −0.118012 | ||||||||
\(852\) | −1.86884e13 | −1.21505 | ||||||||
\(853\) | 1.84928e12 | 0.119600 | 0.0598002 | − | 0.998210i | \(-0.480954\pi\) | ||||
0.0598002 | + | 0.998210i | \(0.480954\pi\) | |||||||
\(854\) | 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 | \(0.233314\pi\) | |||||||
\(858\) | 1.31558e12 | 0.0828749 | ||||||||
\(859\) | 1.25121e12 | 0.0784079 | 0.0392039 | − | 0.999231i | \(-0.487518\pi\) | ||||
0.0392039 | + | 0.999231i | \(0.487518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.25902e12 | 0.264116 | ||||||||
\(862\) | 1.04026e13 | 0.641739 | ||||||||
\(863\) | −2.38217e13 | −1.46192 | −0.730961 | − | 0.682419i | \(-0.760928\pi\) | ||||
−0.730961 | + | 0.682419i | \(0.760928\pi\) | |||||||
\(864\) | 5.06768e12 | 0.309384 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.40928e13 | −2.66402 | ||||||||
\(867\) | 5.10563e12 | 0.306876 | ||||||||
\(868\) | −3.72173e13 | −2.22539 | ||||||||
\(869\) | 5.05575e12 | 0.300744 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.88564e12 | −0.169887 | ||||||||
\(872\) | −2.75478e13 | −1.61348 | ||||||||
\(873\) | −2.18084e13 | −1.27075 | ||||||||
\(874\) | 1.50453e13 | 0.872168 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.42249e13 | −0.816173 | ||||||||
\(877\) | 1.35717e13 | 0.774707 | 0.387353 | − | 0.921931i | \(-0.373389\pi\) | ||||
0.387353 | + | 0.921931i | \(0.373389\pi\) | |||||||
\(878\) | −6.79601e12 | −0.385948 | ||||||||
\(879\) | 1.08375e13 | 0.612323 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.38436e12 | 0.133346 | 0.0666730 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666730 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(882\) | −3.30662e12 | −0.183982 | ||||||||
\(883\) | 5.99779e11 | 0.0332023 | 0.0166011 | − | 0.999862i | \(-0.494715\pi\) | ||||
0.0166011 | + | 0.999862i | \(0.494715\pi\) | |||||||
\(884\) | 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 | \(0.589654\pi\) | |||||||
\(888\) | −3.27747e12 | −0.176881 | ||||||||
\(889\) | 1.11766e13 | 0.600138 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.48579e12 | −0.344757 | ||||||||
\(892\) | −1.45042e13 | −0.767101 | ||||||||
\(893\) | 5.70040e12 | 0.299967 | ||||||||
\(894\) | 2.33111e12 | 0.122052 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.31065e13 | −1.71604 | ||||||||
\(897\) | 5.95867e11 | 0.0307315 | ||||||||
\(898\) | 3.04642e13 | 1.56331 | ||||||||
\(899\) | 4.27050e13 | 2.18052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.67378e12 | 0.0846130 | ||||||||
\(902\) | 1.43894e13 | 0.723791 | ||||||||
\(903\) | −1.14411e13 | −0.572628 | ||||||||
\(904\) | −3.04937e13 | −1.51863 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.95437e12 | 0.392219 | ||||||||
\(907\) | 2.43855e13 | 1.19646 | 0.598231 | − | 0.801323i | \(-0.295870\pi\) | ||||
0.598231 | + | 0.801323i | \(0.295870\pi\) | |||||||
\(908\) | −3.97416e13 | −1.94026 | ||||||||
\(909\) | 1.57639e13 | 0.765820 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.90386e13 | 1.39683 | 0.698415 | − | 0.715693i | \(-0.253889\pi\) | ||||
0.698415 | + | 0.715693i | \(0.253889\pi\) | |||||||
\(912\) | 6.35855e12 | 0.304356 | ||||||||
\(913\) | 1.59949e12 | 0.0761841 | ||||||||
\(914\) | −3.40744e13 | −1.61499 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.31867e13 | −2.96549 | ||||||||
\(917\) | −2.05809e13 | −0.961173 | ||||||||
\(918\) | 7.40630e12 | 0.344199 | ||||||||
\(919\) | −1.41793e13 | −0.655746 | −0.327873 | − | 0.944722i | \(-0.606332\pi\) | ||||
−0.327873 | + | 0.944722i | \(0.606332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.06773e12 | −0.0488984 | ||||||||
\(922\) | −8.87378e12 | −0.404408 | ||||||||
\(923\) | −1.17992e13 | −0.535111 | ||||||||
\(924\) | −6.78146e12 | −0.306055 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.89402e13 | −2.63428 | ||||||||
\(927\) | −7.25212e12 | −0.322557 | ||||||||
\(928\) | 1.84087e13 | 0.814812 | ||||||||
\(929\) | −3.56246e13 | −1.56920 | −0.784601 | − | 0.620001i | \(-0.787132\pi\) | ||||
−0.784601 | + | 0.620001i | \(0.787132\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.50634e12 | 0.196585 | ||||||||
\(932\) | 4.90621e13 | 2.12998 | ||||||||
\(933\) | 1.30136e13 | 0.562250 | ||||||||
\(934\) | 6.23355e13 | 2.68025 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.20568e12 | −0.349441 | ||||||||
\(937\) | −9.35575e12 | −0.396506 | −0.198253 | − | 0.980151i | \(-0.563527\pi\) | ||||
−0.198253 | + | 0.980151i | \(0.563527\pi\) | |||||||
\(938\) | 2.29353e13 | 0.967366 | ||||||||
\(939\) | −3.78610e12 | −0.158927 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.23413e13 | 0.513106 | 0.256553 | − | 0.966530i | \(-0.417413\pi\) | ||||
0.256553 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(942\) | 2.57673e13 | 1.06620 | ||||||||
\(943\) | 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 | \(0.518899\pi\) | |||||||
\(948\) | 9.07366e12 | 0.364876 | ||||||||
\(949\) | −8.98110e12 | −0.359444 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.72086e12 | 0.385383 | ||||||||
\(952\) | −1.07411e13 | −0.423819 | ||||||||
\(953\) | 3.90544e12 | 0.153374 | 0.0766870 | − | 0.997055i | \(-0.475566\pi\) | ||||
0.0766870 | + | 0.997055i | \(0.475566\pi\) | |||||||
\(954\) | −1.01631e13 | −0.397247 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.04733e13 | 2.72875 | ||||||||
\(957\) | 7.78137e12 | 0.299883 | ||||||||
\(958\) | −5.89375e13 | −2.26072 | ||||||||
\(959\) | 3.00219e13 | 1.14618 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.74255e13 | 0.659069 | ||||||||
\(962\) | −4.51703e12 | −0.170045 | ||||||||
\(963\) | 1.16802e13 | 0.437655 | ||||||||
\(964\) | 5.43139e13 | 2.02565 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.73599e12 | −0.174990 | ||||||||
\(967\) | 1.06697e13 | 0.392405 | 0.196203 | − | 0.980563i | \(-0.437139\pi\) | ||||
0.196203 | + | 0.980563i | \(0.437139\pi\) | |||||||
\(968\) | 2.84587e13 | 1.04178 | ||||||||
\(969\) | −4.73469e12 | −0.172518 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.10264e12 | −0.112007 | −0.0560034 | − | 0.998431i | \(-0.517836\pi\) | ||||
−0.0560034 | + | 0.998431i | \(0.517836\pi\) | |||||||
\(972\) | −4.46506e13 | −1.60446 | ||||||||
\(973\) | −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 | \(0.194840\pi\) | |||||||
\(978\) | −1.32455e12 | −0.0462961 | ||||||||
\(979\) | −8.74824e11 | −0.0304368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.89986e13 | −0.999694 | ||||||||
\(982\) | −6.04614e13 | −2.07480 | ||||||||
\(983\) | 3.22316e13 | 1.10101 | 0.550505 | − | 0.834832i | \(-0.314435\pi\) | ||||
0.550505 | + | 0.834832i | \(0.314435\pi\) | |||||||
\(984\) | 1.18305e13 | 0.402278 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.69039e13 | 0.906502 | ||||||||
\(987\) | −1.79438e12 | −0.0601849 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −1.55192e13 | −0.506520 | ||||||||
\(994\) | 9.37807e13 | 3.04701 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.87064e12 | 0.0924299 | ||||||||
\(997\) | 3.13756e13 | 1.00569 | 0.502844 | − | 0.864377i | \(-0.332287\pi\) | ||||
0.502844 | + | 0.864377i | \(0.332287\pi\) | |||||||
\(998\) | 2.40442e13 | 0.767224 | ||||||||
\(999\) | −7.35495e12 | −0.233633 |
(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 | 325.10.a.b.1.1 | 5 | ||
5.4 | even | 2 | 13.10.a.b.1.5 | ✓ | 5 | ||
15.14 | odd | 2 | 117.10.a.e.1.1 | 5 | |||
20.19 | odd | 2 | 208.10.a.h.1.3 | 5 | |||
65.64 | even | 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 | 5.4 | even | 2 | ||
117.10.a.e.1.1 | 5 | 15.14 | odd | 2 | |||
169.10.a.b.1.1 | 5 | 65.64 | even | 2 | |||
208.10.a.h.1.3 | 5 | 20.19 | odd | 2 | |||
325.10.a.b.1.1 | 5 | 1.1 | even | 1 | trivial |