Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,10,Mod(1,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("208.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.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: | \(107.127453922\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(35.1685\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −47.8784 | −0.341267 | −0.170633 | − | 0.985335i | \(-0.554581\pi\) | ||||
−0.170633 | + | 0.985335i | \(0.554581\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −109.762 | −0.0785394 | −0.0392697 | − | 0.999229i | \(-0.512503\pi\) | ||||
−0.0392697 | + | 0.999229i | \(0.512503\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5947.44 | −0.936244 | −0.468122 | − | 0.883664i | \(-0.655069\pi\) | ||||
−0.468122 | + | 0.883664i | \(0.655069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −17390.7 | −0.883537 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 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 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5255.24 | 0.0268029 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 109318. | 0.317447 | 0.158724 | − | 0.987323i | \(-0.449262\pi\) | ||||
0.158724 | + | 0.987323i | \(0.449262\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 904609. | 1.59246 | 0.796232 | − | 0.604992i | \(-0.206824\pi\) | ||||
0.796232 | + | 0.604992i | \(0.206824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 284754. | 0.319509 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 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 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.77503e6 | 0.642789 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(-0.722736\pi\) | ||||
−0.644024 | + | 0.765005i | \(0.722736\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.20681e6 | −0.177143 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 652804. | 0.0735320 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.14357e6 | 0.363469 | 0.181734 | − | 0.983348i | \(-0.441829\pi\) | ||||
0.181734 | + | 0.983348i | \(0.441829\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.36745e6 | −0.0946504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.49568e7 | 0.826632 | 0.413316 | − | 0.910588i | \(-0.364370\pi\) | ||||
0.413316 | + | 0.910588i | \(0.364370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.01789e7 | −1.79221 | −0.896107 | − | 0.443838i | \(-0.853616\pi\) | ||||
−0.896107 | + | 0.443838i | \(0.853616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.90884e6 | 0.0693925 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −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 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.23397e6 | −0.108334 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.53111e7 | 0.266542 | 0.133271 | − | 0.991080i | \(-0.457452\pi\) | ||||
0.133271 | + | 0.991080i | \(0.457452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.76663e6 | −0.0407679 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.33112e7 | −0.543455 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 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 | \(0.368817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.03430e8 | 0.827206 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.13492e6 | −0.0217829 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.01034e8 | 0.612537 | 0.306268 | − | 0.951945i | \(-0.400920\pi\) | ||||
0.306268 | + | 0.951945i | \(0.400920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.08630e7 | −0.110804 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −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 | \(0.724393\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.29357e7 | 0.339162 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.49909e8 | −0.485982 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00580e8 | 0.579383 | 0.289692 | − | 0.957120i | \(-0.406447\pi\) | ||||
0.289692 | + | 0.957120i | \(0.406447\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.57315e8 | 0.664175 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −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 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.08715e8 | −0.577726 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.17102e8 | 0.439568 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.92918e7 | −0.125071 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.25403e9 | −1.43825 | −0.719127 | − | 0.694879i | \(-0.755458\pi\) | ||||
−0.719127 | + | 0.694879i | \(0.755458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.38343e8 | −0.458623 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.06459e8 | −0.866766 | −0.433383 | − | 0.901210i | \(-0.642680\pi\) | ||||
−0.433383 | + | 0.901210i | \(0.642680\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.17013e8 | 0.365075 | 0.182537 | − | 0.983199i | \(-0.441569\pi\) | ||||
0.182537 | + | 0.983199i | \(0.441569\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.12552e7 | −0.0250940 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −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 | \(0.308593\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.98387e8 | −0.124040 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.84580e9 | −1.06496 | −0.532478 | − | 0.846444i | \(-0.678739\pi\) | ||||
−0.532478 | + | 0.846444i | \(0.678739\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.78287e7 | −0.0255005 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.96695e8 | −0.245049 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.50162e8 | −0.297208 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.72262e9 | −0.730560 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.16109e8 | −0.282102 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.27436e8 | 0.156594 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.87922e9 | −0.641006 | −0.320503 | − | 0.947248i | \(-0.603852\pi\) | ||||
−0.320503 | + | 0.947248i | \(0.603852\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.92370e9 | 0.611623 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.94831e8 | −0.0504842 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.04786e9 | 1.22424 | 0.612118 | − | 0.790766i | \(-0.290318\pi\) | ||||
0.612118 | + | 0.790766i | \(0.290318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.59716e9 | −0.817322 | −0.408661 | − | 0.912686i | \(-0.634004\pi\) | ||||
−0.408661 | + | 0.912686i | \(0.634004\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.01706e8 | 0.0642833 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.19899e8 | 0.143966 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.07736e8 | −0.132958 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.38508e8 | 0.0421283 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 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 | \(-0.610654\pi\) | ||||
−0.340671 | + | 0.940183i | \(0.610654\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.90111e9 | −0.280476 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.26963e8 | 0.101163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.41002e10 | −1.85215 | −0.926075 | − | 0.377339i | \(-0.876839\pi\) | ||||
−0.926075 | + | 0.377339i | \(0.876839\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.33072e8 | −0.0909619 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.59159e9 | −0.303983 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.24812e8 | −0.0804231 | −0.0402116 | − | 0.999191i | \(-0.512803\pi\) | ||||
−0.0402116 | + | 0.999191i | \(0.512803\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.32462e8 | 0.0139127 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 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 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.57317e10 | −1.40700 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.77955e8 | 0.0490553 | 0.0245277 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245277 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.15444e10 | 0.930469 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.31392e9 | −0.560106 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(0.773229\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.14780e9 | −0.273394 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.54807e8 | −0.0285466 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.75543e9 | 0.164779 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.05569e10 | −0.601807 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −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 | \(0.747023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.50095e8 | 0.00743378 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.58277e10 | 0.748720 | 0.374360 | − | 0.927283i | \(-0.377862\pi\) | ||||
0.374360 | + | 0.927283i | \(0.377862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.80397e9 | −0.397960 | −0.198980 | − | 0.980004i | \(-0.563763\pi\) | ||||
−0.198980 | + | 0.980004i | \(0.563763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.83736e9 | −0.209038 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.83485e10 | −1.58495 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.64169e9 | −0.0649232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.57796e9 | −0.286870 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.28013e10 | 0.826610 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.82054e10 | 0.632308 | 0.316154 | − | 0.948708i | \(-0.397608\pi\) | ||||
0.316154 | + | 0.948708i | \(0.397608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.97796e10 | 0.658430 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.41012e9 | 0.140759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.93904e10 | 1.20593 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.50555e10 | 0.442280 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.12223e9 | 0.0880440 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.53511e10 | −0.415688 | −0.207844 | − | 0.978162i | \(-0.566645\pi\) | ||||
−0.207844 | + | 0.978162i | \(0.566645\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.37566e10 | 0.878087 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −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 | \(0.797026\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.17741e9 | 0.165849 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.19268e10 | −1.15422 | −0.577112 | − | 0.816665i | \(-0.695820\pi\) | ||||
−0.577112 | + | 0.816665i | \(0.695820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.91668e8 | 0.0147942 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.60345e9 | −0.197724 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(0.315068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.72577e10 | −0.869449 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.46784e8 | 0.00969545 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.58365e10 | 0.441670 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.03826e9 | 0.0500873 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 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 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.74492e8 | 0.00850850 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.64074e10 | −0.949550 | −0.474775 | − | 0.880107i | \(-0.657470\pi\) | ||||
−0.474775 | + | 0.880107i | \(0.657470\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.46436e10 | −0.340295 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.12133e11 | −1.49573 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 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 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.66174e9 | −0.0200107 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 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 | \(-0.446192\pi\) | ||||
0.168239 | + | 0.985746i | \(0.446192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.13286e9 | 0.0886158 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.89261e10 | −0.515874 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.17195e10 | −0.323718 | −0.161859 | − | 0.986814i | \(-0.551749\pi\) | ||||
−0.161859 | + | 0.986814i | \(0.551749\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.15180e11 | 1.13804 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.86953e10 | 0.944318 | 0.472159 | − | 0.881513i | \(-0.343475\pi\) | ||||
0.472159 | + | 0.881513i | \(0.343475\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.06164e11 | 0.983871 | 0.491935 | − | 0.870632i | \(-0.336290\pi\) | ||||
0.491935 | + | 0.870632i | \(0.336290\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.75393e9 | 0.0426826 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.89549e10 | −0.773929 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.06637e11 | −0.899227 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00410e10 | 0.490828 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.26355e11 | 1.79426 | 0.897132 | − | 0.441763i | \(-0.145647\pi\) | ||||
0.897132 | + | 0.441763i | \(0.145647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.67673e10 | −0.128903 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.47407e10 | 0.333656 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.24454e10 | 0.0900511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.38962e11 | 1.67795 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.33998e10 | 0.295798 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.50892e9 | −0.0629190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.23009e10 | 0.143285 | 0.0716424 | − | 0.997430i | \(-0.477176\pi\) | ||||
0.0716424 | + | 0.997430i | \(0.477176\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.99659e10 | −0.124588 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 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 | \(0.574805\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.13527e10 | −0.0649683 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.03032e11 | 1.12927 | 0.564636 | − | 0.825340i | \(-0.309017\pi\) | ||||
0.564636 | + | 0.825340i | \(0.309017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.62524e11 | 0.878736 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.21568e10 | 0.169044 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.88899e10 | 0.505523 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.54391e10 | −0.275639 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.98365e10 | −0.386132 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.74779e10 | 0.176357 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.24137e11 | −1.48424 | −0.742118 | − | 0.670270i | \(-0.766178\pi\) | ||||
−0.742118 | + | 0.670270i | \(0.766178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.20594e10 | −0.321138 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.10897e10 | −0.0481083 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.68510e11 | 1.13403 | 0.567017 | − | 0.823706i | \(-0.308097\pi\) | ||||
0.567017 | + | 0.823706i | \(0.308097\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.83739e10 | 0.363434 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.66939e11 | −0.668595 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.69628e11 | 1.05182 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.28996e9 | 0.00870247 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −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 | \(0.720509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.06966e10 | 0.178277 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.25650e11 | −0.773481 | −0.386741 | − | 0.922189i | \(-0.626399\pi\) | ||||
−0.386741 | + | 0.922189i | \(0.626399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.53451e10 | 0.151532 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.11287e10 | 0.101427 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.24764e10 | 0.249316 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.45150e10 | 0.101787 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.74387e10 | 0.222823 | 0.111412 | − | 0.993774i | \(-0.464463\pi\) | ||||
0.111412 | + | 0.993774i | \(0.464463\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.60109e11 | −0.730360 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.10620e10 | −0.249548 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.50821e11 | 1.74089 | 0.870446 | − | 0.492264i | \(-0.163831\pi\) | ||||
0.870446 | + | 0.492264i | \(0.163831\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.04649e10 | −0.0534404 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.84159e11 | 0.469522 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.93989e11 | −0.482948 | −0.241474 | − | 0.970407i | \(-0.577631\pi\) | ||||
−0.241474 | + | 0.970407i | \(0.577631\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.99743e10 | 0.218754 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −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 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.98737e11 | 1.58349 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.65681e11 | 0.350353 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.20161e10 | −0.0455044 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.94468e11 | 0.594951 | 0.297476 | − | 0.954729i | \(-0.403855\pi\) | ||||
0.297476 | + | 0.954729i | \(0.403855\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.57591e11 | 0.508806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.43362e11 | 0.856265 | 0.428133 | − | 0.903716i | \(-0.359172\pi\) | ||||
0.428133 | + | 0.903716i | \(0.359172\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.89162e11 | −0.357240 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.82434e10 | −0.0521639 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.04441e11 | 0.188668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.01253e11 | −0.178918 | −0.0894592 | − | 0.995990i | \(-0.528514\pi\) | ||||
−0.0894592 | + | 0.995990i | \(0.528514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.41684e11 | −0.417791 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.08533e11 | −1.53662 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.96526e9 | 0.0115271 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.72226e11 | 0.278925 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −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 | \(0.655990\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.09587e11 | 0.166429 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.12195e11 | −0.315489 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.15239e11 | −0.750038 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.44676e10 | −0.0491307 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 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 | \(0.789740\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.38853e10 | 0.0453742 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.94182e11 | 0.517047 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.78053e11 | −0.228801 | −0.114401 | − | 0.993435i | \(-0.536495\pi\) | ||||
−0.114401 | + | 0.993435i | \(0.536495\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.66321e10 | 0.109070 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 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 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.10742e10 | −0.0723559 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.08402e11 | 0.232519 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.86447e10 | 0.0203941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.92736e11 | −0.957415 | −0.478708 | − | 0.877974i | \(-0.658895\pi\) | ||||
−0.478708 | + | 0.877974i | \(0.658895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.94042e11 | 0.204051 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.32490e11 | 0.239745 | 0.119872 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119872 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.54421e12 | 1.56168 | 0.780841 | − | 0.624730i | \(-0.214791\pi\) | ||||
0.780841 | + | 0.624730i | \(0.214791\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.48058e10 | −0.0345234 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −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 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.75094e11 | 0.632077 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.01274e12 | −0.930295 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.75592e12 | −1.58264 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.66271e11 | −0.235500 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.24081e11 | 0.103739 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.37645e11 | 0.112960 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.55439e11 | −0.205782 | −0.102891 | − | 0.994693i | \(-0.532809\pi\) | ||||
−0.102891 | + | 0.994693i | \(0.532809\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.47028e10 | 0.0274457 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −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 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.81135e10 | 0.0360200 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.45702e12 | 1.80636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.29948e11 | 0.454833 | 0.227417 | − | 0.973798i | \(-0.426972\pi\) | ||||
0.227417 | + | 0.973798i | \(0.426972\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.98842e10 | −0.0282834 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −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 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.90559e10 | −0.0262513 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.60570e12 | 1.02362 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.57722e10 | −0.0286727 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.58834e11 | −0.0977767 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.76715e10 | −0.0167410 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.66627e12 | −0.990779 | −0.495389 | − | 0.868671i | \(-0.664975\pi\) | ||||
−0.495389 | + | 0.868671i | \(0.664975\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.97187e12 | −1.15244 | −0.576222 | − | 0.817293i | \(-0.695474\pi\) | ||||
−0.576222 | + | 0.817293i | \(0.695474\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.52730e11 | −0.317538 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.24021e11 | −0.408887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.61128e12 | −0.894580 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.65660e12 | −1.45011 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.27182e11 | 0.229266 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.37202e10 | 0.0389040 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.49629e11 | −0.389011 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.25563e11 | −0.0640784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.54916e12 | 0.777513 | 0.388756 | − | 0.921341i | \(-0.372905\pi\) | ||||
0.388756 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.04639e12 | 0.516529 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.83027e11 | −0.0888648 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.98052e12 | −0.945879 | −0.472939 | − | 0.881095i | \(-0.656807\pi\) | ||||
−0.472939 | + | 0.881095i | \(0.656807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.50659e12 | −0.707814 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.83283e12 | 2.69586 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.19294e12 | −0.542444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.17754e10 | 0.00974200 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.86577e11 | 0.390273 | 0.195136 | − | 0.980776i | \(-0.437485\pi\) | ||||
0.195136 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.14755e12 | −0.497071 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.31926e11 | −0.0562336 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −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 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.53037e12 | −0.621830 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −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 | \(-0.291450\pi\) | ||||
0.609302 | + | 0.792938i | \(0.291450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.03323e11 | 0.311311 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.45822e11 | −0.322681 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.23415e12 | −1.21470 | −0.607350 | − | 0.794434i | \(-0.707767\pi\) | ||||
−0.607350 | + | 0.794434i | \(0.707767\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.29289e12 | 0.478089 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.77411e11 | 0.137411 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.85927e11 | 0.138356 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.45183e10 | 0.0192460 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 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 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.57805e11 | −0.255513 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.91730e12 | −0.636712 | −0.318356 | − | 0.947971i | \(-0.603131\pi\) | ||||
−0.318356 | + | 0.947971i | \(0.603131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.13632e10 | 0.0233425 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.21520e11 | 0.135811 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 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 | \(0.344385\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.75705e12 | −0.541199 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.89079e11 | 0.0573778 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.18434e12 | −0.354101 | −0.177051 | − | 0.984202i | \(-0.556656\pi\) | ||||
−0.177051 | + | 0.984202i | \(0.556656\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.83607e12 | 0.540892 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.79978e11 | −0.0522436 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.42597e11 | 0.183809 | 0.0919045 | − | 0.995768i | \(-0.470705\pi\) | ||||
0.0919045 | + | 0.995768i | \(0.470705\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.86017e10 | 0.0221561 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.05474e12 | 1.40416 | 0.702078 | − | 0.712100i | \(-0.252256\pi\) | ||||
0.702078 | + | 0.712100i | \(0.252256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.09492e11 | 0.0847308 | 0.0423654 | − | 0.999102i | \(-0.486511\pi\) | ||||
0.0423654 | + | 0.999102i | \(0.486511\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.73466e11 | 0.208703 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.06421e11 | −0.0548980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.74425e12 | 0.981533 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.09169e12 | −0.282094 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.52966e11 | 0.115382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.94237e11 | 0.199443 | 0.0997214 | − | 0.995015i | \(-0.468205\pi\) | ||||
0.0997214 | + | 0.995015i | \(0.468205\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.71644e11 | −0.215786 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.06268e11 | 0.0503442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.42278e11 | −0.0342380 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.18446e12 | 1.70467 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.30298e12 | 0.538802 | 0.269401 | − | 0.963028i | \(-0.413174\pi\) | ||||
0.269401 | + | 0.963028i | \(0.413174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.54593e12 | 0.587350 | 0.293675 | − | 0.955905i | \(-0.405122\pi\) | ||||
0.293675 | + | 0.955905i | \(0.405122\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.11149e11 | −0.0480365 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 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 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.88595e12 | −0.411543 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.05719e12 | −1.30365 | −0.651826 | − | 0.758369i | \(-0.725997\pi\) | ||||
−0.651826 | + | 0.758369i | \(0.725997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.79827e11 | 0.0806306 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.46855e12 | 1.14506 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(0.441353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.49487e11 | −0.0300465 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.90532e11 | 0.117097 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.80967e12 | 0.549653 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.34986e11 | 0.141860 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.18362e12 | 0.415839 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.37693e12 | 0.258728 | 0.129364 | − | 0.991597i | \(-0.458706\pi\) | ||||
0.129364 | + | 0.991597i | \(0.458706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.44547e12 | −0.638824 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.49642e11 | 0.118857 | 0.0594285 | − | 0.998233i | \(-0.481072\pi\) | ||||
0.0594285 | + | 0.998233i | \(0.481072\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.45828e12 | 1.34656 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.01386e12 | 0.358813 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 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 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.20192e12 | 0.548409 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.37301e11 | 0.0739254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.72289e12 | −1.28863 | −0.644315 | − | 0.764760i | \(-0.722858\pi\) | ||||
−0.644315 | + | 0.764760i | \(0.722858\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.60702e12 | 0.429383 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.94832e11 | 0.0641920 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.63505e12 | 0.262412 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.48617e12 | 0.393898 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.40436e12 | 0.219658 | 0.109829 | − | 0.993950i | \(-0.464970\pi\) | ||||
0.109829 | + | 0.993950i | \(0.464970\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.74831e12 | 0.578810 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.31159e10 | −0.00504877 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.39111e12 | 0.811505 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.19764e12 | 0.772499 | 0.386250 | − | 0.922394i | \(-0.373770\pi\) | ||||
0.386250 | + | 0.922394i | \(0.373770\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.48822e12 | −0.511907 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.88600e12 | −0.418209 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.90176e10 | −0.0113070 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.57116e12 | 0.504630 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.75230e12 | −0.374605 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.25159e13 | −1.68244 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.91998e11 | −0.131706 | −0.0658531 | − | 0.997829i | \(-0.520977\pi\) | ||||
−0.0658531 | + | 0.997829i | \(0.520977\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.80211e12 | −0.367461 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.39227e12 | −0.568933 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.54849e12 | 0.709916 | 0.354958 | − | 0.934882i | \(-0.384495\pi\) | ||||
0.354958 | + | 0.934882i | \(0.384495\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.61791e10 | −0.00330873 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.54663e12 | 0.317953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.78597e12 | −1.08365 | −0.541826 | − | 0.840491i | \(-0.682267\pi\) | ||||
−0.541826 | + | 0.840491i | \(0.682267\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23701e12 | −0.150727 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −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 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.10357e12 | 0.129676 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.99451e12 | 0.463763 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.52936e11 | 0.0290156 | 0.0145078 | − | 0.999895i | \(-0.495382\pi\) | ||||
0.0145078 | + | 0.999895i | \(0.495382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.16479e12 | −0.585431 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.77765e11 | 0.0535122 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.99638e12 | 1.10640 | 0.553199 | − | 0.833049i | \(-0.313407\pi\) | ||||
0.553199 | + | 0.833049i | \(0.313407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.25864e11 | −0.0575156 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.98848e12 | −0.323013 | −0.161507 | − | 0.986872i | \(-0.551635\pi\) | ||||
−0.161507 | + | 0.986872i | \(0.551635\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.91726e12 | −1.05933 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.08670e11 | 0.0220284 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.36299e12 | 0.455203 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.54887e13 | 1.59715 | 0.798576 | − | 0.601894i | \(-0.205587\pi\) | ||||
0.798576 | + | 0.601894i | \(0.205587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.17948e12 | 0.324050 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.07589e13 | 1.08383 | 0.541915 | − | 0.840434i | \(-0.317700\pi\) | ||||
0.541915 | + | 0.840434i | \(0.317700\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.28559e13 | 1.28010 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.17990e12 | 0.116131 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.35301e13 | 1.31638 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04130e13 | −1.00149 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.14452e13 | 1.08817 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.54767e12 | 0.145467 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.29304e13 | −1.20151 | −0.600755 | − | 0.799433i | \(-0.705133\pi\) | ||||
−0.600755 | + | 0.799433i | \(0.705133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.90379e12 | −0.358625 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.09778e13 | 0.997059 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.47430e12 | 0.222189 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.04635e10 | 0.00714409 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.24713e13 | 1.09484 | 0.547418 | − | 0.836859i | \(-0.315611\pi\) | ||||
0.547418 | + | 0.836859i | \(0.315611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.88868e11 | −0.0597965 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.03585e11 | −0.0518075 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.92600e12 | −0.672719 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.84459e11 | 0.0238747 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.81502e12 | −0.399639 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −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 | \(-0.654112\pi\) | ||||
−0.465464 | + | 0.885067i | \(0.654112\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.43040e12 | −0.114829 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.95569e10 | 0.00631638 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.63462e13 | −2.85403 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.95406e12 | 0.229426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.50113e13 | −1.92129 | −0.960643 | − | 0.277786i | \(-0.910399\pi\) | ||||
−0.960643 | + | 0.277786i | \(0.910399\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.29351e13 | −0.982808 | −0.491404 | − | 0.870932i | \(-0.663516\pi\) | ||||
−0.491404 | + | 0.870932i | \(0.663516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.34250e12 | 0.176051 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −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 | \(0.395453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.51868e12 | 0.110474 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.44571e11 | −0.0391879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.14353e10 | −0.00650916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.17561e13 | −0.827943 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.72537e12 | −0.322264 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.95364e10 | −0.00604149 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.02452e13 | 0.683983 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.08296e12 | −0.335762 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.80556e12 | 0.118012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.84928e12 | −0.119600 | −0.0598002 | − | 0.998210i | \(-0.519046\pi\) | ||||
−0.0598002 | + | 0.998210i | \(0.519046\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.72675e12 | 0.110505 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.34715e13 | −1.48637 | −0.743185 | − | 0.669086i | \(-0.766686\pi\) | ||||
−0.743185 | + | 0.669086i | \(0.766686\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.25121e12 | −0.0784079 | −0.0392039 | − | 0.999231i | \(-0.512482\pi\) | ||||
−0.0392039 | + | 0.999231i | \(0.512482\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.25902e12 | 0.264116 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −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 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.10563e12 | 0.306876 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.05575e12 | 0.300744 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.88564e12 | 0.169887 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.18084e13 | 1.27075 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.54215e12 | −0.146611 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.35717e13 | −0.774707 | −0.387353 | − | 0.921931i | \(-0.626611\pi\) | ||||
−0.387353 | + | 0.921931i | \(0.626611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.08375e13 | −0.612323 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.38436e12 | 0.133346 | 0.0666730 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666730 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.99779e11 | 0.0332023 | 0.0166011 | − | 0.999862i | \(-0.494715\pi\) | ||||
0.0166011 | + | 0.999862i | \(0.494715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.02792e11 | 0.0439904 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −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 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.48579e12 | 0.344757 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.70040e12 | −0.299967 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.71854e12 | −0.0895274 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.95867e11 | −0.0307315 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.27050e13 | −2.18052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.67378e12 | 0.0846130 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.14411e13 | −0.572628 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.39887e12 | 0.118874 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.43855e13 | 1.19646 | 0.598231 | − | 0.801323i | \(-0.295870\pi\) | ||||
0.598231 | + | 0.801323i | \(0.295870\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.57639e13 | 0.765820 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.55272e11 | 0.0214722 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.05809e13 | 0.961173 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.41793e13 | 0.655746 | 0.327873 | − | 0.944722i | \(-0.393668\pi\) | ||||
0.327873 | + | 0.944722i | \(0.393668\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.06773e12 | −0.0488984 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.17992e13 | −0.535111 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.04299e12 | −0.361226 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.25212e12 | −0.322557 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.30136e13 | −0.562250 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.02442e11 | −0.0129417 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.35575e12 | 0.396506 | 0.198253 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.78610e12 | 0.158927 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.23413e13 | 0.513106 | 0.256553 | − | 0.966530i | \(-0.417413\pi\) | ||||
0.256553 | + | 0.966530i | \(0.417413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.51742e12 | 0.268394 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.15875e12 | 0.0472656 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −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 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.72086e12 | −0.385383 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.90544e12 | −0.153374 | −0.0766870 | − | 0.997055i | \(-0.524434\pi\) | ||||
−0.0766870 | + | 0.997055i | \(0.524434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.84163e12 | 0.0716454 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.78137e12 | −0.299883 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.00219e13 | −1.14618 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.74255e13 | 0.659069 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.16802e13 | 0.437655 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.96398e12 | 0.110028 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.06697e13 | 0.392405 | 0.196203 | − | 0.980563i | \(-0.437139\pi\) | ||||
0.196203 | + | 0.980563i | \(0.437139\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.73469e12 | −0.172518 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 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 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.65434e12 | 0.0940665 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.66167e13 | −1.63688 | −0.818438 | − | 0.574594i | \(-0.805160\pi\) | ||||
−0.818438 | + | 0.574594i | \(0.805160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.74824e11 | 0.0304368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.89986e13 | −0.999694 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 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 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.79438e12 | −0.0601849 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.75079e13 | −0.581903 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.25008e13 | 0.741081 | 0.370540 | − | 0.928816i | \(-0.379172\pi\) | ||||
0.370540 | + | 0.928816i | \(0.379172\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.55192e13 | 0.506520 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.66342e11 | 0.0312556 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.13756e13 | −1.00569 | −0.502844 | − | 0.864377i | \(-0.667713\pi\) | ||||
−0.502844 | + | 0.864377i | \(0.667713\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 208.10.a.h.1.3 | 5 | ||
4.3 | odd | 2 | 13.10.a.b.1.5 | ✓ | 5 | ||
12.11 | even | 2 | 117.10.a.e.1.1 | 5 | |||
20.19 | odd | 2 | 325.10.a.b.1.1 | 5 | |||
52.51 | 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 | 4.3 | odd | 2 | ||
117.10.a.e.1.1 | 5 | 12.11 | even | 2 | |||
169.10.a.b.1.1 | 5 | 52.51 | odd | 2 | |||
208.10.a.h.1.3 | 5 | 1.1 | even | 1 | trivial | ||
325.10.a.b.1.1 | 5 | 20.19 | odd | 2 |