Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 1596x^{3} + 5754x^{2} + 488987x - 2711704 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(5.77274\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22726 | −0.0542379 | −0.0271189 | − | 0.999632i | \(-0.508633\pi\) | ||||
−0.0271189 | + | 0.999632i | \(0.508633\pi\) | |||||||
\(3\) | −177.437 | −1.26473 | −0.632367 | − | 0.774669i | \(-0.717917\pi\) | ||||
−0.632367 | + | 0.774669i | \(0.717917\pi\) | |||||||
\(4\) | −510.494 | −0.997058 | ||||||||
\(5\) | 1620.18 | 1.15931 | 0.579655 | − | 0.814862i | \(-0.303187\pi\) | ||||
0.579655 | + | 0.814862i | \(0.303187\pi\) | |||||||
\(6\) | 217.762 | 0.0685965 | ||||||||
\(7\) | 1834.42 | 0.288774 | 0.144387 | − | 0.989521i | \(-0.453879\pi\) | ||||
0.144387 | + | 0.989521i | \(0.453879\pi\) | |||||||
\(8\) | 1254.87 | 0.108316 | ||||||||
\(9\) | 11801.0 | 0.599553 | ||||||||
\(10\) | −1988.39 | −0.0628785 | ||||||||
\(11\) | 31779.3 | 0.654452 | 0.327226 | − | 0.944946i | \(-0.393886\pi\) | ||||
0.327226 | + | 0.944946i | \(0.393886\pi\) | |||||||
\(12\) | 90580.6 | 1.26101 | ||||||||
\(13\) | −132363. | −1.28535 | −0.642675 | − | 0.766139i | \(-0.722176\pi\) | ||||
−0.642675 | + | 0.766139i | \(0.722176\pi\) | |||||||
\(14\) | −2251.32 | −0.0156625 | ||||||||
\(15\) | −287481. | −1.46622 | ||||||||
\(16\) | 259833. | 0.991183 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −14482.9 | −0.0325185 | ||||||||
\(19\) | −1603.79 | −0.00282330 | −0.00141165 | − | 0.999999i | \(-0.500449\pi\) | ||||
−0.00141165 | + | 0.999999i | \(0.500449\pi\) | |||||||
\(20\) | −827094. | −1.15590 | ||||||||
\(21\) | −325495. | −0.365223 | ||||||||
\(22\) | −39001.6 | −0.0354961 | ||||||||
\(23\) | −23254.0 | −0.0173270 | −0.00866348 | − | 0.999962i | \(-0.502758\pi\) | ||||
−0.00866348 | + | 0.999962i | \(0.502758\pi\) | |||||||
\(24\) | −222661. | −0.136991 | ||||||||
\(25\) | 671873. | 0.343999 | ||||||||
\(26\) | 162444. | 0.0697147 | ||||||||
\(27\) | 1.39856e6 | 0.506460 | ||||||||
\(28\) | −936463. | −0.287925 | ||||||||
\(29\) | −3.73267e6 | −0.980005 | −0.490002 | − | 0.871721i | \(-0.663004\pi\) | ||||
−0.490002 | + | 0.871721i | \(0.663004\pi\) | |||||||
\(30\) | 352815. | 0.0795246 | ||||||||
\(31\) | −8.91479e6 | −1.73374 | −0.866869 | − | 0.498536i | \(-0.833871\pi\) | ||||
−0.866869 | + | 0.498536i | \(0.833871\pi\) | |||||||
\(32\) | −961376. | −0.162076 | ||||||||
\(33\) | −5.63884e6 | −0.827707 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.97211e6 | 0.334779 | ||||||||
\(36\) | −6.02433e6 | −0.597789 | ||||||||
\(37\) | 1.20475e7 | 1.05679 | 0.528395 | − | 0.848999i | \(-0.322794\pi\) | ||||
0.528395 | + | 0.848999i | \(0.322794\pi\) | |||||||
\(38\) | 1968.28 | 0.000153130 0 | ||||||||
\(39\) | 2.34861e7 | 1.62563 | ||||||||
\(40\) | 2.03312e6 | 0.125572 | ||||||||
\(41\) | 1.26779e7 | 0.700680 | 0.350340 | − | 0.936623i | \(-0.386066\pi\) | ||||
0.350340 | + | 0.936623i | \(0.386066\pi\) | |||||||
\(42\) | 399468. | 0.0198089 | ||||||||
\(43\) | 2.86352e7 | 1.27730 | 0.638650 | − | 0.769498i | \(-0.279493\pi\) | ||||
0.638650 | + | 0.769498i | \(0.279493\pi\) | |||||||
\(44\) | −1.62231e7 | −0.652526 | ||||||||
\(45\) | 1.91198e7 | 0.695067 | ||||||||
\(46\) | 28538.8 | 0.000939777 0 | ||||||||
\(47\) | −7.17761e6 | −0.214555 | −0.107278 | − | 0.994229i | \(-0.534213\pi\) | ||||
−0.107278 | + | 0.994229i | \(0.534213\pi\) | |||||||
\(48\) | −4.61040e7 | −1.25358 | ||||||||
\(49\) | −3.69885e7 | −0.916609 | ||||||||
\(50\) | −824565. | −0.0186578 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.75705e7 | 1.28157 | ||||||||
\(53\) | −5.96065e7 | −1.03765 | −0.518826 | − | 0.854880i | \(-0.673631\pi\) | ||||
−0.518826 | + | 0.854880i | \(0.673631\pi\) | |||||||
\(54\) | −1.71640e6 | −0.0274693 | ||||||||
\(55\) | 5.14884e7 | 0.758712 | ||||||||
\(56\) | 2.30196e6 | 0.0312790 | ||||||||
\(57\) | 284573. | 0.00357072 | ||||||||
\(58\) | 4.58096e6 | 0.0531534 | ||||||||
\(59\) | 1.85990e8 | 1.99828 | 0.999139 | − | 0.0414925i | \(-0.0132113\pi\) | ||||
0.999139 | + | 0.0414925i | \(0.0132113\pi\) | |||||||
\(60\) | 1.46757e8 | 1.46191 | ||||||||
\(61\) | 2.00037e8 | 1.84981 | 0.924905 | − | 0.380198i | \(-0.124144\pi\) | ||||
0.924905 | + | 0.380198i | \(0.124144\pi\) | |||||||
\(62\) | 1.09408e7 | 0.0940343 | ||||||||
\(63\) | 2.16480e7 | 0.173135 | ||||||||
\(64\) | −1.31855e8 | −0.982393 | ||||||||
\(65\) | −2.14453e8 | −1.49012 | ||||||||
\(66\) | 6.92034e6 | 0.0448931 | ||||||||
\(67\) | −1.27030e8 | −0.770137 | −0.385069 | − | 0.922888i | \(-0.625822\pi\) | ||||
−0.385069 | + | 0.922888i | \(0.625822\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.12613e6 | 0.0219140 | ||||||||
\(70\) | −3.64756e6 | −0.0181577 | ||||||||
\(71\) | 3.27860e8 | 1.53118 | 0.765590 | − | 0.643329i | \(-0.222447\pi\) | ||||
0.765590 | + | 0.643329i | \(0.222447\pi\) | |||||||
\(72\) | 1.48087e7 | 0.0649413 | ||||||||
\(73\) | 1.48678e8 | 0.612766 | 0.306383 | − | 0.951908i | \(-0.400881\pi\) | ||||
0.306383 | + | 0.951908i | \(0.400881\pi\) | |||||||
\(74\) | −1.47854e7 | −0.0573181 | ||||||||
\(75\) | −1.19215e8 | −0.435067 | ||||||||
\(76\) | 818726. | 0.00281500 | ||||||||
\(77\) | 5.82968e7 | 0.188989 | ||||||||
\(78\) | −2.88237e7 | −0.0881705 | ||||||||
\(79\) | 2.58778e8 | 0.747491 | 0.373746 | − | 0.927531i | \(-0.378073\pi\) | ||||
0.373746 | + | 0.927531i | \(0.378073\pi\) | |||||||
\(80\) | 4.20977e8 | 1.14909 | ||||||||
\(81\) | −4.80436e8 | −1.24009 | ||||||||
\(82\) | −1.55591e7 | −0.0380034 | ||||||||
\(83\) | 3.45060e8 | 0.798073 | 0.399037 | − | 0.916935i | \(-0.369345\pi\) | ||||
0.399037 | + | 0.916935i | \(0.369345\pi\) | |||||||
\(84\) | 1.66163e8 | 0.364149 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.51430e7 | −0.0692780 | ||||||||
\(87\) | 6.62314e8 | 1.23945 | ||||||||
\(88\) | 3.98789e7 | 0.0708877 | ||||||||
\(89\) | 4.03936e8 | 0.682428 | 0.341214 | − | 0.939986i | \(-0.389162\pi\) | ||||
0.341214 | + | 0.939986i | \(0.389162\pi\) | |||||||
\(90\) | −2.34650e7 | −0.0376990 | ||||||||
\(91\) | −2.42810e8 | −0.371176 | ||||||||
\(92\) | 1.18710e7 | 0.0172760 | ||||||||
\(93\) | 1.58182e9 | 2.19272 | ||||||||
\(94\) | 8.80881e6 | 0.0116370 | ||||||||
\(95\) | −2.59844e6 | −0.00327308 | ||||||||
\(96\) | 1.70584e8 | 0.204983 | ||||||||
\(97\) | 9.89973e8 | 1.13540 | 0.567702 | − | 0.823234i | \(-0.307833\pi\) | ||||
0.567702 | + | 0.823234i | \(0.307833\pi\) | |||||||
\(98\) | 4.53946e7 | 0.0497149 | ||||||||
\(99\) | 3.75028e8 | 0.392378 | ||||||||
\(100\) | −3.42987e8 | −0.342987 | ||||||||
\(101\) | −1.11917e9 | −1.07017 | −0.535084 | − | 0.844799i | \(-0.679720\pi\) | ||||
−0.535084 | + | 0.844799i | \(0.679720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.58796e6 | 0.00576744 | 0.00288372 | − | 0.999996i | \(-0.499082\pi\) | ||||
0.00288372 | + | 0.999996i | \(0.499082\pi\) | |||||||
\(104\) | −1.66098e8 | −0.139224 | ||||||||
\(105\) | −5.27363e8 | −0.423407 | ||||||||
\(106\) | 7.31528e7 | 0.0562801 | ||||||||
\(107\) | −1.55590e9 | −1.14751 | −0.573754 | − | 0.819028i | \(-0.694513\pi\) | ||||
−0.573754 | + | 0.819028i | \(0.694513\pi\) | |||||||
\(108\) | −7.13957e8 | −0.504970 | ||||||||
\(109\) | −6.94766e8 | −0.471432 | −0.235716 | − | 0.971822i | \(-0.575744\pi\) | ||||
−0.235716 | + | 0.971822i | \(0.575744\pi\) | |||||||
\(110\) | −6.31898e7 | −0.0411509 | ||||||||
\(111\) | −2.13767e9 | −1.33656 | ||||||||
\(112\) | 4.76644e8 | 0.286228 | ||||||||
\(113\) | −2.09735e9 | −1.21009 | −0.605047 | − | 0.796190i | \(-0.706846\pi\) | ||||
−0.605047 | + | 0.796190i | \(0.706846\pi\) | |||||||
\(114\) | −349246. | −0.000193669 0 | ||||||||
\(115\) | −3.76758e7 | −0.0200873 | ||||||||
\(116\) | 1.90550e9 | 0.977122 | ||||||||
\(117\) | −1.56202e9 | −0.770635 | ||||||||
\(118\) | −2.28259e8 | −0.108382 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.60751e8 | −0.158815 | ||||||||
\(121\) | −1.34802e9 | −0.571693 | ||||||||
\(122\) | −2.45499e8 | −0.100330 | ||||||||
\(123\) | −2.24953e9 | −0.886173 | ||||||||
\(124\) | 4.55095e9 | 1.72864 | ||||||||
\(125\) | −2.07586e9 | −0.760508 | ||||||||
\(126\) | −2.65678e7 | −0.00939050 | ||||||||
\(127\) | −4.92229e9 | −1.67900 | −0.839499 | − | 0.543361i | \(-0.817151\pi\) | ||||
−0.839499 | + | 0.543361i | \(0.817151\pi\) | |||||||
\(128\) | 6.54045e8 | 0.215359 | ||||||||
\(129\) | −5.08096e9 | −1.61544 | ||||||||
\(130\) | 2.63190e8 | 0.0808209 | ||||||||
\(131\) | −4.54604e9 | −1.34869 | −0.674345 | − | 0.738416i | \(-0.735574\pi\) | ||||
−0.674345 | + | 0.738416i | \(0.735574\pi\) | |||||||
\(132\) | 2.87859e9 | 0.825272 | ||||||||
\(133\) | −2.94204e6 | −0.000815297 0 | ||||||||
\(134\) | 1.55899e8 | 0.0417706 | ||||||||
\(135\) | 2.26593e9 | 0.587143 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.25313e9 | 1.27402 | 0.637010 | − | 0.770856i | \(-0.280171\pi\) | ||||
0.637010 | + | 0.770856i | \(0.280171\pi\) | |||||||
\(138\) | −5.06384e6 | −0.00118857 | ||||||||
\(139\) | −1.55602e9 | −0.353549 | −0.176774 | − | 0.984251i | \(-0.556566\pi\) | ||||
−0.176774 | + | 0.984251i | \(0.556566\pi\) | |||||||
\(140\) | −1.51724e9 | −0.333794 | ||||||||
\(141\) | 1.27358e9 | 0.271356 | ||||||||
\(142\) | −4.02371e8 | −0.0830479 | ||||||||
\(143\) | −4.20641e9 | −0.841200 | ||||||||
\(144\) | 3.06629e9 | 0.594267 | ||||||||
\(145\) | −6.04761e9 | −1.13613 | ||||||||
\(146\) | −1.82467e8 | −0.0332351 | ||||||||
\(147\) | 6.56314e9 | 1.15927 | ||||||||
\(148\) | −6.15017e9 | −1.05368 | ||||||||
\(149\) | 2.13936e9 | 0.355587 | 0.177794 | − | 0.984068i | \(-0.443104\pi\) | ||||
0.177794 | + | 0.984068i | \(0.443104\pi\) | |||||||
\(150\) | 1.46309e8 | 0.0235971 | ||||||||
\(151\) | −1.65162e9 | −0.258531 | −0.129266 | − | 0.991610i | \(-0.541262\pi\) | ||||
−0.129266 | + | 0.991610i | \(0.541262\pi\) | |||||||
\(152\) | −2.01255e6 | −0.000305809 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.15455e7 | −0.0102504 | ||||||||
\(155\) | −1.44436e10 | −2.00994 | ||||||||
\(156\) | −1.19895e10 | −1.62084 | ||||||||
\(157\) | −4.44203e9 | −0.583490 | −0.291745 | − | 0.956496i | \(-0.594236\pi\) | ||||
−0.291745 | + | 0.956496i | \(0.594236\pi\) | |||||||
\(158\) | −3.17589e8 | −0.0405423 | ||||||||
\(159\) | 1.05764e10 | 1.31235 | ||||||||
\(160\) | −1.55761e9 | −0.187896 | ||||||||
\(161\) | −4.26577e7 | −0.00500358 | ||||||||
\(162\) | 5.89621e8 | 0.0672598 | ||||||||
\(163\) | −2.66196e9 | −0.295363 | −0.147682 | − | 0.989035i | \(-0.547181\pi\) | ||||
−0.147682 | + | 0.989035i | \(0.547181\pi\) | |||||||
\(164\) | −6.47198e9 | −0.698618 | ||||||||
\(165\) | −9.13596e9 | −0.959569 | ||||||||
\(166\) | −4.23479e8 | −0.0432858 | ||||||||
\(167\) | 1.58326e10 | 1.57518 | 0.787588 | − | 0.616203i | \(-0.211330\pi\) | ||||
0.787588 | + | 0.616203i | \(0.211330\pi\) | |||||||
\(168\) | −4.08454e8 | −0.0395596 | ||||||||
\(169\) | 6.91547e9 | 0.652126 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.89264e7 | −0.00169272 | ||||||||
\(172\) | −1.46181e10 | −1.27354 | ||||||||
\(173\) | 1.27988e10 | 1.08633 | 0.543165 | − | 0.839626i | \(-0.317226\pi\) | ||||
0.543165 | + | 0.839626i | \(0.317226\pi\) | |||||||
\(174\) | −8.12834e8 | −0.0672249 | ||||||||
\(175\) | 1.23250e9 | 0.0993382 | ||||||||
\(176\) | 8.25731e9 | 0.648681 | ||||||||
\(177\) | −3.30016e10 | −2.52729 | ||||||||
\(178\) | −4.95735e8 | −0.0370135 | ||||||||
\(179\) | −8.33273e9 | −0.606665 | −0.303332 | − | 0.952885i | \(-0.598099\pi\) | ||||
−0.303332 | + | 0.952885i | \(0.598099\pi\) | |||||||
\(180\) | −9.76053e9 | −0.693022 | ||||||||
\(181\) | 8.70236e9 | 0.602676 | 0.301338 | − | 0.953517i | \(-0.402567\pi\) | ||||
0.301338 | + | 0.953517i | \(0.402567\pi\) | |||||||
\(182\) | 2.97992e8 | 0.0201318 | ||||||||
\(183\) | −3.54941e10 | −2.33952 | ||||||||
\(184\) | −2.91807e7 | −0.00187679 | ||||||||
\(185\) | 1.95192e10 | 1.22515 | ||||||||
\(186\) | −1.94130e9 | −0.118928 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.66413e9 | 0.213924 | ||||||||
\(189\) | 2.56556e9 | 0.146253 | ||||||||
\(190\) | 3.18897e6 | 0.000177525 0 | ||||||||
\(191\) | 2.29558e10 | 1.24808 | 0.624040 | − | 0.781392i | \(-0.285490\pi\) | ||||
0.624040 | + | 0.781392i | \(0.285490\pi\) | |||||||
\(192\) | 2.33959e10 | 1.24247 | ||||||||
\(193\) | −2.04685e10 | −1.06189 | −0.530943 | − | 0.847407i | \(-0.678162\pi\) | ||||
−0.530943 | + | 0.847407i | \(0.678162\pi\) | |||||||
\(194\) | −1.21496e9 | −0.0615819 | ||||||||
\(195\) | 3.80519e10 | 1.88460 | ||||||||
\(196\) | 1.88824e10 | 0.913913 | ||||||||
\(197\) | −5.81009e9 | −0.274843 | −0.137422 | − | 0.990513i | \(-0.543882\pi\) | ||||
−0.137422 | + | 0.990513i | \(0.543882\pi\) | |||||||
\(198\) | −4.60257e8 | −0.0212818 | ||||||||
\(199\) | −4.49526e9 | −0.203196 | −0.101598 | − | 0.994826i | \(-0.532396\pi\) | ||||
−0.101598 | + | 0.994826i | \(0.532396\pi\) | |||||||
\(200\) | 8.43113e8 | 0.0372607 | ||||||||
\(201\) | 2.25398e10 | 0.974019 | ||||||||
\(202\) | 1.37352e9 | 0.0580436 | ||||||||
\(203\) | −6.84730e9 | −0.283000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.05405e10 | 0.812305 | ||||||||
\(206\) | −8.08516e6 | −0.000312814 0 | ||||||||
\(207\) | −2.74420e8 | −0.0103884 | ||||||||
\(208\) | −3.43922e10 | −1.27402 | ||||||||
\(209\) | −5.09674e7 | −0.00184771 | ||||||||
\(210\) | 6.47213e8 | 0.0229647 | ||||||||
\(211\) | −3.47865e10 | −1.20820 | −0.604101 | − | 0.796908i | \(-0.706467\pi\) | ||||
−0.604101 | + | 0.796908i | \(0.706467\pi\) | |||||||
\(212\) | 3.04287e10 | 1.03460 | ||||||||
\(213\) | −5.81746e10 | −1.93654 | ||||||||
\(214\) | 1.90950e9 | 0.0622384 | ||||||||
\(215\) | 4.63944e10 | 1.48079 | ||||||||
\(216\) | 1.75501e9 | 0.0548578 | ||||||||
\(217\) | −1.63535e10 | −0.500659 | ||||||||
\(218\) | 8.52661e8 | 0.0255695 | ||||||||
\(219\) | −2.63811e10 | −0.774986 | ||||||||
\(220\) | −2.62845e10 | −0.756480 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.62349e9 | 0.0724921 | ||||||||
\(223\) | −2.46348e10 | −0.667078 | −0.333539 | − | 0.942736i | \(-0.608243\pi\) | ||||
−0.333539 | + | 0.942736i | \(0.608243\pi\) | |||||||
\(224\) | −1.76357e9 | −0.0468034 | ||||||||
\(225\) | 7.92877e9 | 0.206246 | ||||||||
\(226\) | 2.57401e9 | 0.0656329 | ||||||||
\(227\) | −4.45657e10 | −1.11400 | −0.556999 | − | 0.830513i | \(-0.688047\pi\) | ||||
−0.556999 | + | 0.830513i | \(0.688047\pi\) | |||||||
\(228\) | −1.45273e8 | −0.00356022 | ||||||||
\(229\) | 6.61817e10 | 1.59030 | 0.795148 | − | 0.606415i | \(-0.207393\pi\) | ||||
0.795148 | + | 0.606415i | \(0.207393\pi\) | |||||||
\(230\) | 4.62381e7 | 0.00108949 | ||||||||
\(231\) | −1.03440e10 | −0.239021 | ||||||||
\(232\) | −4.68401e9 | −0.106150 | ||||||||
\(233\) | 4.35721e10 | 0.968516 | 0.484258 | − | 0.874925i | \(-0.339090\pi\) | ||||
0.484258 | + | 0.874925i | \(0.339090\pi\) | |||||||
\(234\) | 1.91700e9 | 0.0417976 | ||||||||
\(235\) | −1.16291e10 | −0.248736 | ||||||||
\(236\) | −9.49468e10 | −1.99240 | ||||||||
\(237\) | −4.59169e10 | −0.945378 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.67128e10 | 0.727825 | 0.363912 | − | 0.931433i | \(-0.381441\pi\) | ||||
0.363912 | + | 0.931433i | \(0.381441\pi\) | |||||||
\(240\) | −7.46970e10 | −1.45329 | ||||||||
\(241\) | −3.62693e10 | −0.692568 | −0.346284 | − | 0.938130i | \(-0.612557\pi\) | ||||
−0.346284 | + | 0.938130i | \(0.612557\pi\) | |||||||
\(242\) | 1.65438e9 | 0.0310074 | ||||||||
\(243\) | 5.77194e10 | 1.06192 | ||||||||
\(244\) | −1.02118e11 | −1.84437 | ||||||||
\(245\) | −5.99282e10 | −1.06263 | ||||||||
\(246\) | 2.76076e9 | 0.0480642 | ||||||||
\(247\) | 2.12283e8 | 0.00362893 | ||||||||
\(248\) | −1.11869e10 | −0.187792 | ||||||||
\(249\) | −6.12264e10 | −1.00935 | ||||||||
\(250\) | 2.54763e9 | 0.0412484 | ||||||||
\(251\) | −9.34890e10 | −1.48672 | −0.743359 | − | 0.668892i | \(-0.766769\pi\) | ||||
−0.743359 | + | 0.668892i | \(0.766769\pi\) | |||||||
\(252\) | −1.10512e10 | −0.172626 | ||||||||
\(253\) | −7.38996e8 | −0.0113397 | ||||||||
\(254\) | 6.04094e9 | 0.0910653 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.67068e10 | 0.970712 | ||||||||
\(257\) | 1.91619e10 | 0.273993 | 0.136996 | − | 0.990572i | \(-0.456255\pi\) | ||||
0.136996 | + | 0.990572i | \(0.456255\pi\) | |||||||
\(258\) | 6.23567e9 | 0.0876183 | ||||||||
\(259\) | 2.21002e10 | 0.305174 | ||||||||
\(260\) | 1.09477e11 | 1.48574 | ||||||||
\(261\) | −4.40492e10 | −0.587564 | ||||||||
\(262\) | 5.57918e9 | 0.0731501 | ||||||||
\(263\) | 3.75028e10 | 0.483352 | 0.241676 | − | 0.970357i | \(-0.422303\pi\) | ||||
0.241676 | + | 0.970357i | \(0.422303\pi\) | |||||||
\(264\) | −7.07600e9 | −0.0896541 | ||||||||
\(265\) | −9.65735e10 | −1.20296 | ||||||||
\(266\) | 3.61065e6 | 4.42200e−5 0 | ||||||||
\(267\) | −7.16732e10 | −0.863090 | ||||||||
\(268\) | 6.48478e10 | 0.767872 | ||||||||
\(269\) | 9.36804e10 | 1.09085 | 0.545423 | − | 0.838161i | \(-0.316369\pi\) | ||||
0.545423 | + | 0.838161i | \(0.316369\pi\) | |||||||
\(270\) | −2.78089e9 | −0.0318454 | ||||||||
\(271\) | −9.81985e10 | −1.10597 | −0.552985 | − | 0.833191i | \(-0.686511\pi\) | ||||
−0.552985 | + | 0.833191i | \(0.686511\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.30836e10 | 0.469439 | ||||||||
\(274\) | −6.44698e9 | −0.0691001 | ||||||||
\(275\) | 2.13517e10 | 0.225131 | ||||||||
\(276\) | −2.10636e9 | −0.0218495 | ||||||||
\(277\) | −9.27606e9 | −0.0946683 | −0.0473341 | − | 0.998879i | \(-0.515073\pi\) | ||||
−0.0473341 | + | 0.998879i | \(0.515073\pi\) | |||||||
\(278\) | 1.90965e9 | 0.0191757 | ||||||||
\(279\) | −1.05203e11 | −1.03947 | ||||||||
\(280\) | 3.72960e9 | 0.0362620 | ||||||||
\(281\) | −1.04165e11 | −0.996649 | −0.498325 | − | 0.866991i | \(-0.666051\pi\) | ||||
−0.498325 | + | 0.866991i | \(0.666051\pi\) | |||||||
\(282\) | −1.56301e9 | −0.0147177 | ||||||||
\(283\) | 9.57066e10 | 0.886958 | 0.443479 | − | 0.896285i | \(-0.353744\pi\) | ||||
0.443479 | + | 0.896285i | \(0.353744\pi\) | |||||||
\(284\) | −1.67371e11 | −1.52668 | ||||||||
\(285\) | 4.61060e8 | 0.00413958 | ||||||||
\(286\) | 5.16237e9 | 0.0456249 | ||||||||
\(287\) | 2.32566e10 | 0.202338 | ||||||||
\(288\) | −1.13452e10 | −0.0971730 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 7.42201e9 | 0.0616212 | ||||||||
\(291\) | −1.75658e11 | −1.43598 | ||||||||
\(292\) | −7.58993e10 | −0.610963 | ||||||||
\(293\) | −1.62664e11 | −1.28940 | −0.644698 | − | 0.764437i | \(-0.723017\pi\) | ||||
−0.644698 | + | 0.764437i | \(0.723017\pi\) | |||||||
\(294\) | −8.05470e9 | −0.0628762 | ||||||||
\(295\) | 3.01338e11 | 2.31662 | ||||||||
\(296\) | 1.51180e10 | 0.114468 | ||||||||
\(297\) | 4.44453e10 | 0.331453 | ||||||||
\(298\) | −2.62556e9 | −0.0192863 | ||||||||
\(299\) | 3.07797e9 | 0.0222712 | ||||||||
\(300\) | 6.08587e10 | 0.433788 | ||||||||
\(301\) | 5.25292e10 | 0.368851 | ||||||||
\(302\) | 2.02697e9 | 0.0140222 | ||||||||
\(303\) | 1.98583e11 | 1.35348 | ||||||||
\(304\) | −4.16718e8 | −0.00279841 | ||||||||
\(305\) | 3.24098e11 | 2.14450 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.26286e11 | −1.45390 | −0.726952 | − | 0.686688i | \(-0.759064\pi\) | ||||
−0.726952 | + | 0.686688i | \(0.759064\pi\) | |||||||
\(308\) | −2.97601e10 | −0.188433 | ||||||||
\(309\) | −1.16895e9 | −0.00729428 | ||||||||
\(310\) | 1.77261e10 | 0.109015 | ||||||||
\(311\) | −1.17225e11 | −0.710556 | −0.355278 | − | 0.934761i | \(-0.615614\pi\) | ||||
−0.355278 | + | 0.934761i | \(0.615614\pi\) | |||||||
\(312\) | 2.94720e10 | 0.176082 | ||||||||
\(313\) | −2.85060e11 | −1.67876 | −0.839378 | − | 0.543549i | \(-0.817080\pi\) | ||||
−0.839378 | + | 0.543549i | \(0.817080\pi\) | |||||||
\(314\) | 5.45154e9 | 0.0316472 | ||||||||
\(315\) | 3.50738e10 | 0.200718 | ||||||||
\(316\) | −1.32105e11 | −0.745292 | ||||||||
\(317\) | 9.98016e9 | 0.0555099 | 0.0277550 | − | 0.999615i | \(-0.491164\pi\) | ||||
0.0277550 | + | 0.999615i | \(0.491164\pi\) | |||||||
\(318\) | −1.29800e10 | −0.0711793 | ||||||||
\(319\) | −1.18622e11 | −0.641365 | ||||||||
\(320\) | −2.13629e11 | −1.13890 | ||||||||
\(321\) | 2.76075e11 | 1.45129 | ||||||||
\(322\) | 5.23522e7 | 0.000271384 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.45260e11 | 1.23644 | ||||||||
\(325\) | −8.89312e10 | −0.442159 | ||||||||
\(326\) | 3.26692e9 | 0.0160199 | ||||||||
\(327\) | 1.23277e11 | 0.596236 | ||||||||
\(328\) | 1.59091e10 | 0.0758949 | ||||||||
\(329\) | −1.31668e10 | −0.0619581 | ||||||||
\(330\) | 1.12122e10 | 0.0520450 | ||||||||
\(331\) | −2.14841e11 | −0.983766 | −0.491883 | − | 0.870661i | \(-0.663691\pi\) | ||||
−0.491883 | + | 0.870661i | \(0.663691\pi\) | |||||||
\(332\) | −1.76151e11 | −0.795725 | ||||||||
\(333\) | 1.42172e11 | 0.633601 | ||||||||
\(334\) | −1.94308e10 | −0.0854342 | ||||||||
\(335\) | −2.05811e11 | −0.892828 | ||||||||
\(336\) | −8.45744e10 | −0.362003 | ||||||||
\(337\) | 3.33228e11 | 1.40737 | 0.703683 | − | 0.710514i | \(-0.251537\pi\) | ||||
0.703683 | + | 0.710514i | \(0.251537\pi\) | |||||||
\(338\) | −8.48710e9 | −0.0353699 | ||||||||
\(339\) | 3.72149e11 | 1.53045 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.83306e11 | −1.13465 | ||||||||
\(342\) | 2.32276e7 | 9.18094e−5 0 | ||||||||
\(343\) | −1.41878e11 | −0.553468 | ||||||||
\(344\) | 3.59335e10 | 0.138352 | ||||||||
\(345\) | 6.68509e9 | 0.0254051 | ||||||||
\(346\) | −1.57075e10 | −0.0589203 | ||||||||
\(347\) | 1.63241e10 | 0.0604432 | 0.0302216 | − | 0.999543i | \(-0.490379\pi\) | ||||
0.0302216 | + | 0.999543i | \(0.490379\pi\) | |||||||
\(348\) | −3.38107e11 | −1.23580 | ||||||||
\(349\) | 1.61528e11 | 0.582819 | 0.291410 | − | 0.956598i | \(-0.405876\pi\) | ||||
0.291410 | + | 0.956598i | \(0.405876\pi\) | |||||||
\(350\) | −1.51260e9 | −0.00538789 | ||||||||
\(351\) | −1.85118e11 | −0.650978 | ||||||||
\(352\) | −3.05519e10 | −0.106071 | ||||||||
\(353\) | 2.89170e11 | 0.991212 | 0.495606 | − | 0.868547i | \(-0.334946\pi\) | ||||
0.495606 | + | 0.868547i | \(0.334946\pi\) | |||||||
\(354\) | 4.05016e10 | 0.137075 | ||||||||
\(355\) | 5.31194e11 | 1.77511 | ||||||||
\(356\) | −2.06207e11 | −0.680421 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.02265e10 | 0.0329042 | ||||||||
\(359\) | 2.34120e11 | 0.743898 | 0.371949 | − | 0.928253i | \(-0.378690\pi\) | ||||
0.371949 | + | 0.928253i | \(0.378690\pi\) | |||||||
\(360\) | 2.39928e10 | 0.0752870 | ||||||||
\(361\) | −3.22685e11 | −0.999992 | ||||||||
\(362\) | −1.06801e10 | −0.0326878 | ||||||||
\(363\) | 2.39190e11 | 0.723040 | ||||||||
\(364\) | 1.23953e11 | 0.370084 | ||||||||
\(365\) | 2.40886e11 | 0.710385 | ||||||||
\(366\) | 4.35606e10 | 0.126890 | ||||||||
\(367\) | 1.08932e11 | 0.313442 | 0.156721 | − | 0.987643i | \(-0.449908\pi\) | ||||
0.156721 | + | 0.987643i | \(0.449908\pi\) | |||||||
\(368\) | −6.04215e9 | −0.0171742 | ||||||||
\(369\) | 1.49612e11 | 0.420094 | ||||||||
\(370\) | −2.39551e10 | −0.0664494 | ||||||||
\(371\) | −1.09344e11 | −0.299648 | ||||||||
\(372\) | −8.07507e11 | −2.18627 | ||||||||
\(373\) | −6.82746e11 | −1.82629 | −0.913145 | − | 0.407635i | \(-0.866353\pi\) | ||||
−0.913145 | + | 0.407635i | \(0.866353\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.68336e11 | 0.961841 | ||||||||
\(376\) | −9.00696e9 | −0.0232398 | ||||||||
\(377\) | 4.94067e11 | 1.25965 | ||||||||
\(378\) | −3.14861e9 | −0.00793243 | ||||||||
\(379\) | −1.87645e11 | −0.467156 | −0.233578 | − | 0.972338i | \(-0.575043\pi\) | ||||
−0.233578 | + | 0.972338i | \(0.575043\pi\) | |||||||
\(380\) | 1.32649e9 | 0.00326345 | ||||||||
\(381\) | 8.73397e11 | 2.12349 | ||||||||
\(382\) | −2.81728e10 | −0.0676932 | ||||||||
\(383\) | 1.01456e11 | 0.240925 | 0.120462 | − | 0.992718i | \(-0.461562\pi\) | ||||
0.120462 | + | 0.992718i | \(0.461562\pi\) | |||||||
\(384\) | −1.16052e11 | −0.272372 | ||||||||
\(385\) | 9.44515e10 | 0.219097 | ||||||||
\(386\) | 2.51202e10 | 0.0575945 | ||||||||
\(387\) | 3.37924e11 | 0.765808 | ||||||||
\(388\) | −5.05375e11 | −1.13206 | ||||||||
\(389\) | −4.62050e11 | −1.02310 | −0.511548 | − | 0.859255i | \(-0.670928\pi\) | ||||
−0.511548 | + | 0.859255i | \(0.670928\pi\) | |||||||
\(390\) | −4.66997e10 | −0.102217 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.64157e10 | −0.0992836 | ||||||||
\(393\) | 8.06637e11 | 1.70573 | ||||||||
\(394\) | 7.13051e9 | 0.0149069 | ||||||||
\(395\) | 4.19269e11 | 0.866574 | ||||||||
\(396\) | −1.91449e11 | −0.391224 | ||||||||
\(397\) | −8.72806e11 | −1.76344 | −0.881720 | − | 0.471774i | \(-0.843614\pi\) | ||||
−0.881720 | + | 0.471774i | \(0.843614\pi\) | |||||||
\(398\) | 5.51687e9 | 0.0110209 | ||||||||
\(399\) | 5.22027e8 | 0.00103113 | ||||||||
\(400\) | 1.74575e11 | 0.340966 | ||||||||
\(401\) | 1.68101e11 | 0.324654 | 0.162327 | − | 0.986737i | \(-0.448100\pi\) | ||||
0.162327 | + | 0.986737i | \(0.448100\pi\) | |||||||
\(402\) | −2.76622e10 | −0.0528287 | ||||||||
\(403\) | 1.17999e12 | 2.22846 | ||||||||
\(404\) | 5.71332e11 | 1.06702 | ||||||||
\(405\) | −7.78395e11 | −1.43765 | ||||||||
\(406\) | 8.40343e9 | 0.0153493 | ||||||||
\(407\) | 3.82861e11 | 0.691618 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.99127e11 | −1.23538 | −0.617691 | − | 0.786421i | \(-0.711932\pi\) | ||||
−0.617691 | + | 0.786421i | \(0.711932\pi\) | |||||||
\(410\) | −2.52086e10 | −0.0440577 | ||||||||
\(411\) | −9.32102e11 | −1.61130 | ||||||||
\(412\) | −3.36311e9 | −0.00575047 | ||||||||
\(413\) | 3.41185e11 | 0.577052 | ||||||||
\(414\) | 3.36786e8 | 0.000563446 0 | ||||||||
\(415\) | 5.59060e11 | 0.925214 | ||||||||
\(416\) | 1.27251e11 | 0.208324 | ||||||||
\(417\) | 2.76097e11 | 0.447145 | ||||||||
\(418\) | 6.25505e7 | 0.000100216 0 | ||||||||
\(419\) | −9.68451e11 | −1.53502 | −0.767511 | − | 0.641036i | \(-0.778505\pi\) | ||||
−0.767511 | + | 0.641036i | \(0.778505\pi\) | |||||||
\(420\) | 2.69215e11 | 0.422161 | ||||||||
\(421\) | −5.47606e11 | −0.849569 | −0.424784 | − | 0.905295i | \(-0.639650\pi\) | ||||
−0.424784 | + | 0.905295i | \(0.639650\pi\) | |||||||
\(422\) | 4.26921e10 | 0.0655303 | ||||||||
\(423\) | −8.47029e10 | −0.128637 | ||||||||
\(424\) | −7.47983e10 | −0.112395 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.13956e10 | 0.105034 | ||||||||
\(427\) | 3.66954e11 | 0.534178 | ||||||||
\(428\) | 7.94279e11 | 1.14413 | ||||||||
\(429\) | 7.46373e11 | 1.06389 | ||||||||
\(430\) | −5.69381e10 | −0.0803147 | ||||||||
\(431\) | −4.80670e11 | −0.670964 | −0.335482 | − | 0.942047i | \(-0.608899\pi\) | ||||
−0.335482 | + | 0.942047i | \(0.608899\pi\) | |||||||
\(432\) | 3.63392e11 | 0.501994 | ||||||||
\(433\) | −7.09547e11 | −0.970031 | −0.485016 | − | 0.874506i | \(-0.661186\pi\) | ||||
−0.485016 | + | 0.874506i | \(0.661186\pi\) | |||||||
\(434\) | 2.00701e10 | 0.0271547 | ||||||||
\(435\) | 1.07307e12 | 1.43690 | ||||||||
\(436\) | 3.54674e11 | 0.470045 | ||||||||
\(437\) | 3.72946e7 | 4.89192e−5 0 | ||||||||
\(438\) | 3.23765e10 | 0.0420336 | ||||||||
\(439\) | −1.17101e12 | −1.50477 | −0.752387 | − | 0.658721i | \(-0.771098\pi\) | ||||
−0.752387 | + | 0.658721i | \(0.771098\pi\) | |||||||
\(440\) | 6.46111e10 | 0.0821808 | ||||||||
\(441\) | −4.36501e11 | −0.549555 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.75055e11 | −0.586040 | −0.293020 | − | 0.956106i | \(-0.594660\pi\) | ||||
−0.293020 | + | 0.956106i | \(0.594660\pi\) | |||||||
\(444\) | 1.09127e12 | 1.33263 | ||||||||
\(445\) | 6.54450e11 | 0.791146 | ||||||||
\(446\) | 3.02333e10 | 0.0361809 | ||||||||
\(447\) | −3.79603e11 | −0.449723 | ||||||||
\(448\) | −2.41877e11 | −0.283690 | ||||||||
\(449\) | 9.33820e11 | 1.08431 | 0.542156 | − | 0.840278i | \(-0.317608\pi\) | ||||
0.542156 | + | 0.840278i | \(0.317608\pi\) | |||||||
\(450\) | −9.73069e9 | −0.0111863 | ||||||||
\(451\) | 4.02895e11 | 0.458561 | ||||||||
\(452\) | 1.07069e12 | 1.20653 | ||||||||
\(453\) | 2.93058e11 | 0.326973 | ||||||||
\(454\) | 5.46938e10 | 0.0604209 | ||||||||
\(455\) | −3.93397e11 | −0.430308 | ||||||||
\(456\) | 3.57101e8 | 0.000386767 0 | ||||||||
\(457\) | 1.28584e12 | 1.37900 | 0.689498 | − | 0.724288i | \(-0.257831\pi\) | ||||
0.689498 | + | 0.724288i | \(0.257831\pi\) | |||||||
\(458\) | −8.12223e10 | −0.0862543 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.92332e10 | 0.0200282 | ||||||||
\(461\) | 5.18444e11 | 0.534623 | 0.267311 | − | 0.963610i | \(-0.413865\pi\) | ||||
0.267311 | + | 0.963610i | \(0.413865\pi\) | |||||||
\(462\) | 1.26948e10 | 0.0129640 | ||||||||
\(463\) | −7.76808e11 | −0.785596 | −0.392798 | − | 0.919625i | \(-0.628493\pi\) | ||||
−0.392798 | + | 0.919625i | \(0.628493\pi\) | |||||||
\(464\) | −9.69869e11 | −0.971364 | ||||||||
\(465\) | 2.56283e12 | 2.54204 | ||||||||
\(466\) | −5.34744e10 | −0.0525302 | ||||||||
\(467\) | 8.28768e10 | 0.0806319 | 0.0403159 | − | 0.999187i | \(-0.487164\pi\) | ||||
0.0403159 | + | 0.999187i | \(0.487164\pi\) | |||||||
\(468\) | 7.97399e11 | 0.768368 | ||||||||
\(469\) | −2.33026e11 | −0.222396 | ||||||||
\(470\) | 1.42719e10 | 0.0134909 | ||||||||
\(471\) | 7.88182e11 | 0.737959 | ||||||||
\(472\) | 2.33393e11 | 0.216446 | ||||||||
\(473\) | 9.10008e11 | 0.835930 | ||||||||
\(474\) | 5.63522e10 | 0.0512753 | ||||||||
\(475\) | −1.07755e9 | −0.000971213 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.03416e11 | −0.622127 | ||||||||
\(478\) | −4.50562e10 | −0.0394757 | ||||||||
\(479\) | 2.08230e12 | 1.80731 | 0.903657 | − | 0.428257i | \(-0.140872\pi\) | ||||
0.903657 | + | 0.428257i | \(0.140872\pi\) | |||||||
\(480\) | 2.76378e11 | 0.237639 | ||||||||
\(481\) | −1.59464e12 | −1.35835 | ||||||||
\(482\) | 4.45120e10 | 0.0375634 | ||||||||
\(483\) | 7.56907e9 | 0.00632820 | ||||||||
\(484\) | 6.88157e11 | 0.570011 | ||||||||
\(485\) | 1.60394e12 | 1.31629 | ||||||||
\(486\) | −7.08369e10 | −0.0575965 | ||||||||
\(487\) | 2.69427e11 | 0.217051 | 0.108525 | − | 0.994094i | \(-0.465387\pi\) | ||||
0.108525 | + | 0.994094i | \(0.465387\pi\) | |||||||
\(488\) | 2.51021e11 | 0.200364 | ||||||||
\(489\) | 4.72330e11 | 0.373556 | ||||||||
\(490\) | 7.35477e10 | 0.0576350 | ||||||||
\(491\) | −5.87772e10 | −0.0456396 | −0.0228198 | − | 0.999740i | \(-0.507264\pi\) | ||||
−0.0228198 | + | 0.999740i | \(0.507264\pi\) | |||||||
\(492\) | 1.14837e12 | 0.883567 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.60527e8 | −0.000196826 0 | ||||||||
\(495\) | 6.07614e11 | 0.454888 | ||||||||
\(496\) | −2.31635e12 | −1.71845 | ||||||||
\(497\) | 6.01435e11 | 0.442166 | ||||||||
\(498\) | 7.51409e10 | 0.0547450 | ||||||||
\(499\) | 3.13142e11 | 0.226094 | 0.113047 | − | 0.993590i | \(-0.463939\pi\) | ||||
0.113047 | + | 0.993590i | \(0.463939\pi\) | |||||||
\(500\) | 1.05972e12 | 0.758271 | ||||||||
\(501\) | −2.80930e12 | −1.99218 | ||||||||
\(502\) | 1.14736e11 | 0.0806365 | ||||||||
\(503\) | −7.31761e11 | −0.509699 | −0.254849 | − | 0.966981i | \(-0.582026\pi\) | ||||
−0.254849 | + | 0.966981i | \(0.582026\pi\) | |||||||
\(504\) | 2.71654e10 | 0.0187534 | ||||||||
\(505\) | −1.81327e12 | −1.24066 | ||||||||
\(506\) | 9.06943e8 | 0.000615039 0 | ||||||||
\(507\) | −1.22706e12 | −0.824766 | ||||||||
\(508\) | 2.51280e12 | 1.67406 | ||||||||
\(509\) | 2.84601e12 | 1.87935 | 0.939673 | − | 0.342073i | \(-0.111129\pi\) | ||||
0.939673 | + | 0.342073i | \(0.111129\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.72739e11 | 0.176951 | ||||||||
\(512\) | −4.16738e11 | −0.268008 | ||||||||
\(513\) | −2.24300e9 | −0.00142989 | ||||||||
\(514\) | −2.35167e10 | −0.0148608 | ||||||||
\(515\) | 1.06737e10 | 0.00668625 | ||||||||
\(516\) | 2.59380e12 | 1.61069 | ||||||||
\(517\) | −2.28100e11 | −0.140416 | ||||||||
\(518\) | −2.71228e10 | −0.0165520 | ||||||||
\(519\) | −2.27099e12 | −1.37392 | ||||||||
\(520\) | −2.69110e11 | −0.161404 | ||||||||
\(521\) | 1.42270e10 | 0.00845949 | 0.00422974 | − | 0.999991i | \(-0.498654\pi\) | ||||
0.00422974 | + | 0.999991i | \(0.498654\pi\) | |||||||
\(522\) | 5.40599e10 | 0.0318682 | ||||||||
\(523\) | 1.20853e12 | 0.706316 | 0.353158 | − | 0.935564i | \(-0.385108\pi\) | ||||
0.353158 | + | 0.935564i | \(0.385108\pi\) | |||||||
\(524\) | 2.32072e12 | 1.34472 | ||||||||
\(525\) | −2.18692e11 | −0.125636 | ||||||||
\(526\) | −4.60259e10 | −0.0262160 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.46515e12 | −0.820410 | ||||||||
\(529\) | −1.80061e12 | −0.999700 | ||||||||
\(530\) | 1.18521e11 | 0.0652460 | ||||||||
\(531\) | 2.19487e12 | 1.19807 | ||||||||
\(532\) | 1.50189e9 | 0.000812899 0 | ||||||||
\(533\) | −1.67808e12 | −0.900619 | ||||||||
\(534\) | 8.79619e10 | 0.0468122 | ||||||||
\(535\) | −2.52085e12 | −1.33032 | ||||||||
\(536\) | −1.59405e11 | −0.0834184 | ||||||||
\(537\) | 1.47854e12 | 0.767270 | ||||||||
\(538\) | −1.14971e11 | −0.0591652 | ||||||||
\(539\) | −1.17547e12 | −0.599876 | ||||||||
\(540\) | −1.15674e12 | −0.585416 | ||||||||
\(541\) | −2.35337e12 | −1.18115 | −0.590573 | − | 0.806985i | \(-0.701098\pi\) | ||||
−0.590573 | + | 0.806985i | \(0.701098\pi\) | |||||||
\(542\) | 1.20515e11 | 0.0599854 | ||||||||
\(543\) | −1.54412e12 | −0.762224 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.12565e12 | −0.546536 | ||||||||
\(546\) | −5.28749e10 | −0.0254614 | ||||||||
\(547\) | −1.30236e12 | −0.621996 | −0.310998 | − | 0.950411i | \(-0.600663\pi\) | ||||
−0.310998 | + | 0.950411i | \(0.600663\pi\) | |||||||
\(548\) | −2.68169e12 | −1.27027 | ||||||||
\(549\) | 2.36064e12 | 1.10906 | ||||||||
\(550\) | −2.62041e10 | −0.0122106 | ||||||||
\(551\) | 5.98642e9 | 0.00276685 | ||||||||
\(552\) | 5.17775e9 | 0.00237364 | ||||||||
\(553\) | 4.74710e11 | 0.215856 | ||||||||
\(554\) | 1.13842e10 | 0.00513461 | ||||||||
\(555\) | −3.46343e12 | −1.54949 | ||||||||
\(556\) | 7.94340e11 | 0.352509 | ||||||||
\(557\) | 3.33519e12 | 1.46816 | 0.734078 | − | 0.679065i | \(-0.237615\pi\) | ||||
0.734078 | + | 0.679065i | \(0.237615\pi\) | |||||||
\(558\) | 1.29112e11 | 0.0563785 | ||||||||
\(559\) | −3.79025e12 | −1.64178 | ||||||||
\(560\) | 7.72251e11 | 0.331827 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.27838e11 | 0.0540561 | ||||||||
\(563\) | −9.51343e11 | −0.399070 | −0.199535 | − | 0.979891i | \(-0.563943\pi\) | ||||
−0.199535 | + | 0.979891i | \(0.563943\pi\) | |||||||
\(564\) | −6.50152e11 | −0.270557 | ||||||||
\(565\) | −3.39810e12 | −1.40287 | ||||||||
\(566\) | −1.17457e11 | −0.0481067 | ||||||||
\(567\) | −8.81324e11 | −0.358106 | ||||||||
\(568\) | 4.11422e11 | 0.165852 | ||||||||
\(569\) | −8.14899e10 | −0.0325911 | −0.0162955 | − | 0.999867i | \(-0.505187\pi\) | ||||
−0.0162955 | + | 0.999867i | \(0.505187\pi\) | |||||||
\(570\) | −5.65842e8 | −0.000224522 0 | ||||||||
\(571\) | −1.06368e12 | −0.418744 | −0.209372 | − | 0.977836i | \(-0.567142\pi\) | ||||
−0.209372 | + | 0.977836i | \(0.567142\pi\) | |||||||
\(572\) | 2.14734e12 | 0.838725 | ||||||||
\(573\) | −4.07322e12 | −1.57849 | ||||||||
\(574\) | −2.85420e10 | −0.0109744 | ||||||||
\(575\) | −1.56237e10 | −0.00596046 | ||||||||
\(576\) | −1.55601e12 | −0.588996 | ||||||||
\(577\) | −3.44925e12 | −1.29549 | −0.647743 | − | 0.761859i | \(-0.724287\pi\) | ||||
−0.647743 | + | 0.761859i | \(0.724287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.63187e12 | 1.34300 | ||||||||
\(580\) | 3.08727e12 | 1.13279 | ||||||||
\(581\) | 6.32986e11 | 0.230463 | ||||||||
\(582\) | 2.15579e11 | 0.0778848 | ||||||||
\(583\) | −1.89425e12 | −0.679093 | ||||||||
\(584\) | 1.86572e11 | 0.0663725 | ||||||||
\(585\) | −2.53075e12 | −0.893405 | ||||||||
\(586\) | 1.99631e11 | 0.0699341 | ||||||||
\(587\) | −3.31180e12 | −1.15131 | −0.575655 | − | 0.817693i | \(-0.695253\pi\) | ||||
−0.575655 | + | 0.817693i | \(0.695253\pi\) | |||||||
\(588\) | −3.35044e12 | −1.15586 | ||||||||
\(589\) | 1.42975e10 | 0.00489486 | ||||||||
\(590\) | −3.69821e11 | −0.125649 | ||||||||
\(591\) | 1.03093e12 | 0.347604 | ||||||||
\(592\) | 3.13033e12 | 1.04747 | ||||||||
\(593\) | 9.22763e10 | 0.0306439 | 0.0153219 | − | 0.999883i | \(-0.495123\pi\) | ||||
0.0153219 | + | 0.999883i | \(0.495123\pi\) | |||||||
\(594\) | −5.45461e10 | −0.0179773 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.09213e12 | −0.354541 | ||||||||
\(597\) | 7.97627e11 | 0.256989 | ||||||||
\(598\) | −3.77748e9 | −0.00120794 | ||||||||
\(599\) | −4.28034e11 | −0.135849 | −0.0679246 | − | 0.997690i | \(-0.521638\pi\) | ||||
−0.0679246 | + | 0.997690i | \(0.521638\pi\) | |||||||
\(600\) | −1.49600e11 | −0.0471249 | ||||||||
\(601\) | −2.92420e12 | −0.914266 | −0.457133 | − | 0.889398i | \(-0.651124\pi\) | ||||
−0.457133 | + | 0.889398i | \(0.651124\pi\) | |||||||
\(602\) | −6.44671e10 | −0.0200057 | ||||||||
\(603\) | −1.49908e12 | −0.461738 | ||||||||
\(604\) | 8.43140e11 | 0.257771 | ||||||||
\(605\) | −2.18405e12 | −0.662770 | ||||||||
\(606\) | −2.43714e11 | −0.0734097 | ||||||||
\(607\) | 1.45237e12 | 0.434237 | 0.217118 | − | 0.976145i | \(-0.430334\pi\) | ||||
0.217118 | + | 0.976145i | \(0.430334\pi\) | |||||||
\(608\) | 1.54185e9 | 0.000457589 0 | ||||||||
\(609\) | 1.21497e12 | 0.357920 | ||||||||
\(610\) | −3.97753e11 | −0.116313 | ||||||||
\(611\) | 9.50050e11 | 0.275779 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.13743e12 | 1.46951 | 0.734757 | − | 0.678331i | \(-0.237296\pi\) | ||||
0.734757 | + | 0.678331i | \(0.237296\pi\) | |||||||
\(614\) | 2.77713e11 | 0.0788567 | ||||||||
\(615\) | −3.64465e12 | −1.02735 | ||||||||
\(616\) | 7.31548e10 | 0.0204706 | ||||||||
\(617\) | 5.31905e12 | 1.47758 | 0.738790 | − | 0.673936i | \(-0.235397\pi\) | ||||
0.738790 | + | 0.673936i | \(0.235397\pi\) | |||||||
\(618\) | 1.43461e9 | 0.000395626 0 | ||||||||
\(619\) | 3.23470e12 | 0.885577 | 0.442789 | − | 0.896626i | \(-0.353989\pi\) | ||||
0.442789 | + | 0.896626i | \(0.353989\pi\) | |||||||
\(620\) | 7.37337e12 | 2.00403 | ||||||||
\(621\) | −3.25222e10 | −0.00877540 | ||||||||
\(622\) | 1.43866e11 | 0.0385391 | ||||||||
\(623\) | 7.40989e11 | 0.197068 | ||||||||
\(624\) | 6.10247e12 | 1.61129 | ||||||||
\(625\) | −4.67554e12 | −1.22566 | ||||||||
\(626\) | 3.49844e11 | 0.0910521 | ||||||||
\(627\) | 9.04353e9 | 0.00233687 | ||||||||
\(628\) | 2.26763e12 | 0.581773 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4.30448e10 | −0.0108865 | ||||||||
\(631\) | −7.91021e12 | −1.98635 | −0.993175 | − | 0.116630i | \(-0.962791\pi\) | ||||
−0.993175 | + | 0.116630i | \(0.962791\pi\) | |||||||
\(632\) | 3.24733e11 | 0.0809654 | ||||||||
\(633\) | 6.17242e12 | 1.52805 | ||||||||
\(634\) | −1.22483e10 | −0.00301074 | ||||||||
\(635\) | −7.97501e12 | −1.94648 | ||||||||
\(636\) | −5.39919e12 | −1.30849 | ||||||||
\(637\) | 4.89591e12 | 1.17816 | ||||||||
\(638\) | 1.45580e11 | 0.0347863 | ||||||||
\(639\) | 3.86908e12 | 0.918023 | ||||||||
\(640\) | 1.05967e12 | 0.249668 | ||||||||
\(641\) | 2.28438e12 | 0.534451 | 0.267225 | − | 0.963634i | \(-0.413893\pi\) | ||||
0.267225 | + | 0.963634i | \(0.413893\pi\) | |||||||
\(642\) | −3.38817e11 | −0.0787150 | ||||||||
\(643\) | −7.52203e11 | −0.173534 | −0.0867672 | − | 0.996229i | \(-0.527654\pi\) | ||||
−0.0867672 | + | 0.996229i | \(0.527654\pi\) | |||||||
\(644\) | 2.17765e10 | 0.00498886 | ||||||||
\(645\) | −8.23209e12 | −1.87280 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.59159e12 | −1.03013 | −0.515067 | − | 0.857150i | \(-0.672233\pi\) | ||||
−0.515067 | + | 0.857150i | \(0.672233\pi\) | |||||||
\(648\) | −6.02884e11 | −0.134322 | ||||||||
\(649\) | 5.91064e12 | 1.30778 | ||||||||
\(650\) | 1.09142e11 | 0.0239818 | ||||||||
\(651\) | 2.90172e12 | 0.633201 | ||||||||
\(652\) | 1.35891e12 | 0.294495 | ||||||||
\(653\) | −4.27664e12 | −0.920436 | −0.460218 | − | 0.887806i | \(-0.652229\pi\) | ||||
−0.460218 | + | 0.887806i | \(0.652229\pi\) | |||||||
\(654\) | −1.51294e11 | −0.0323386 | ||||||||
\(655\) | −7.36542e12 | −1.56355 | ||||||||
\(656\) | 3.29413e12 | 0.694502 | ||||||||
\(657\) | 1.75455e12 | 0.367385 | ||||||||
\(658\) | 1.61591e10 | 0.00336048 | ||||||||
\(659\) | −8.26860e12 | −1.70784 | −0.853920 | − | 0.520404i | \(-0.825782\pi\) | ||||
−0.853920 | + | 0.520404i | \(0.825782\pi\) | |||||||
\(660\) | 4.66385e12 | 0.956746 | ||||||||
\(661\) | 4.45784e12 | 0.908276 | 0.454138 | − | 0.890931i | \(-0.349947\pi\) | ||||
0.454138 | + | 0.890931i | \(0.349947\pi\) | |||||||
\(662\) | 2.63667e11 | 0.0533574 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.33005e11 | 0.0864442 | ||||||||
\(665\) | −4.76664e9 | −0.000945182 0 | ||||||||
\(666\) | −1.74483e11 | −0.0343652 | ||||||||
\(667\) | 8.67994e10 | 0.0169805 | ||||||||
\(668\) | −8.08246e12 | −1.57054 | ||||||||
\(669\) | 4.37112e12 | 0.843676 | ||||||||
\(670\) | 2.52585e11 | 0.0484251 | ||||||||
\(671\) | 6.35705e12 | 1.21061 | ||||||||
\(672\) | 3.12923e11 | 0.0591938 | ||||||||
\(673\) | −3.90397e12 | −0.733566 | −0.366783 | − | 0.930307i | \(-0.619541\pi\) | ||||
−0.366783 | + | 0.930307i | \(0.619541\pi\) | |||||||
\(674\) | −4.08959e11 | −0.0763326 | ||||||||
\(675\) | 9.39656e11 | 0.174222 | ||||||||
\(676\) | −3.53030e12 | −0.650207 | ||||||||
\(677\) | −4.84414e12 | −0.886273 | −0.443137 | − | 0.896454i | \(-0.646134\pi\) | ||||
−0.443137 | + | 0.896454i | \(0.646134\pi\) | |||||||
\(678\) | −4.56725e11 | −0.0830082 | ||||||||
\(679\) | 1.81603e12 | 0.327876 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.90761e12 | 1.40891 | ||||||||
\(682\) | 3.47691e11 | 0.0615409 | ||||||||
\(683\) | 3.67160e12 | 0.645598 | 0.322799 | − | 0.946468i | \(-0.395376\pi\) | ||||
0.322799 | + | 0.946468i | \(0.395376\pi\) | |||||||
\(684\) | 9.66179e9 | 0.00168774 | ||||||||
\(685\) | 8.51105e12 | 1.47698 | ||||||||
\(686\) | 1.74122e11 | 0.0300189 | ||||||||
\(687\) | −1.17431e13 | −2.01130 | ||||||||
\(688\) | 7.44037e12 | 1.26604 | ||||||||
\(689\) | 7.88969e12 | 1.33375 | ||||||||
\(690\) | −8.20436e9 | −0.00137792 | ||||||||
\(691\) | −3.94359e12 | −0.658023 | −0.329011 | − | 0.944326i | \(-0.606715\pi\) | ||||
−0.329011 | + | 0.944326i | \(0.606715\pi\) | |||||||
\(692\) | −6.53371e12 | −1.08314 | ||||||||
\(693\) | 6.87960e11 | 0.113309 | ||||||||
\(694\) | −2.00340e10 | −0.00327831 | ||||||||
\(695\) | −2.52104e12 | −0.409873 | ||||||||
\(696\) | 8.31117e11 | 0.134252 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.98238e11 | −0.0316109 | ||||||||
\(699\) | −7.73131e12 | −1.22492 | ||||||||
\(700\) | −6.29184e11 | −0.0990459 | ||||||||
\(701\) | −9.80834e12 | −1.53414 | −0.767069 | − | 0.641564i | \(-0.778286\pi\) | ||||
−0.767069 | + | 0.641564i | \(0.778286\pi\) | |||||||
\(702\) | 2.27188e11 | 0.0353077 | ||||||||
\(703\) | −1.93217e10 | −0.00298364 | ||||||||
\(704\) | −4.19025e12 | −0.642928 | ||||||||
\(705\) | 2.06343e12 | 0.314585 | ||||||||
\(706\) | −3.54887e11 | −0.0537613 | ||||||||
\(707\) | −2.05304e12 | −0.309037 | ||||||||
\(708\) | 1.68471e13 | 2.51986 | ||||||||
\(709\) | −4.04313e12 | −0.600910 | −0.300455 | − | 0.953796i | \(-0.597139\pi\) | ||||
−0.300455 | + | 0.953796i | \(0.597139\pi\) | |||||||
\(710\) | −6.51915e11 | −0.0962783 | ||||||||
\(711\) | 3.05384e12 | 0.448160 | ||||||||
\(712\) | 5.06886e11 | 0.0739180 | ||||||||
\(713\) | 2.07305e11 | 0.0300404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.81515e12 | −0.975211 | ||||||||
\(716\) | 4.25381e12 | 0.604880 | ||||||||
\(717\) | −6.51422e12 | −0.920505 | ||||||||
\(718\) | −2.87327e11 | −0.0403475 | ||||||||
\(719\) | 4.48823e12 | 0.626319 | 0.313159 | − | 0.949701i | \(-0.398613\pi\) | ||||
0.313159 | + | 0.949701i | \(0.398613\pi\) | |||||||
\(720\) | 4.96795e12 | 0.688939 | ||||||||
\(721\) | 1.20851e10 | 0.00166549 | ||||||||
\(722\) | 3.96020e11 | 0.0542374 | ||||||||
\(723\) | 6.43553e12 | 0.875915 | ||||||||
\(724\) | −4.44250e12 | −0.600903 | ||||||||
\(725\) | −2.50788e12 | −0.337121 | ||||||||
\(726\) | −2.93548e11 | −0.0392162 | ||||||||
\(727\) | −1.02503e13 | −1.36092 | −0.680459 | − | 0.732786i | \(-0.738220\pi\) | ||||
−0.680459 | + | 0.732786i | \(0.738220\pi\) | |||||||
\(728\) | −3.04695e11 | −0.0402044 | ||||||||
\(729\) | −7.85147e11 | −0.102962 | ||||||||
\(730\) | −2.95631e11 | −0.0385298 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.81195e13 | 2.33264 | ||||||||
\(733\) | −1.77332e12 | −0.226892 | −0.113446 | − | 0.993544i | \(-0.536189\pi\) | ||||
−0.113446 | + | 0.993544i | \(0.536189\pi\) | |||||||
\(734\) | −1.33688e11 | −0.0170004 | ||||||||
\(735\) | 1.06335e13 | 1.34395 | ||||||||
\(736\) | 2.23558e10 | 0.00280828 | ||||||||
\(737\) | −4.03691e12 | −0.504018 | ||||||||
\(738\) | −1.83613e11 | −0.0227850 | ||||||||
\(739\) | 2.07204e12 | 0.255563 | 0.127781 | − | 0.991802i | \(-0.459214\pi\) | ||||
0.127781 | + | 0.991802i | \(0.459214\pi\) | |||||||
\(740\) | −9.96441e12 | −1.22154 | ||||||||
\(741\) | −3.76669e10 | −0.00458963 | ||||||||
\(742\) | 1.34193e11 | 0.0162523 | ||||||||
\(743\) | −7.60966e12 | −0.916042 | −0.458021 | − | 0.888941i | \(-0.651442\pi\) | ||||
−0.458021 | + | 0.888941i | \(0.651442\pi\) | |||||||
\(744\) | 1.98497e12 | 0.237507 | ||||||||
\(745\) | 3.46616e12 | 0.412236 | ||||||||
\(746\) | 8.37909e11 | 0.0990541 | ||||||||
\(747\) | 4.07205e12 | 0.478487 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.85419e12 | −0.331371 | ||||||||
\(750\) | −4.52045e11 | −0.0521682 | ||||||||
\(751\) | 7.56877e12 | 0.868252 | 0.434126 | − | 0.900852i | \(-0.357057\pi\) | ||||
0.434126 | + | 0.900852i | \(0.357057\pi\) | |||||||
\(752\) | −1.86498e12 | −0.212664 | ||||||||
\(753\) | 1.65884e13 | 1.88030 | ||||||||
\(754\) | −6.06350e11 | −0.0683207 | ||||||||
\(755\) | −2.67592e12 | −0.299718 | ||||||||
\(756\) | −1.30970e12 | −0.145822 | ||||||||
\(757\) | −6.86633e12 | −0.759965 | −0.379982 | − | 0.924994i | \(-0.624070\pi\) | ||||
−0.379982 | + | 0.924994i | \(0.624070\pi\) | |||||||
\(758\) | 2.30290e11 | 0.0253375 | ||||||||
\(759\) | 1.31125e11 | 0.0143416 | ||||||||
\(760\) | −3.26070e9 | −0.000354528 0 | ||||||||
\(761\) | 9.51816e12 | 1.02878 | 0.514389 | − | 0.857557i | \(-0.328019\pi\) | ||||
0.514389 | + | 0.857557i | \(0.328019\pi\) | |||||||
\(762\) | −1.07189e12 | −0.115173 | ||||||||
\(763\) | −1.27450e12 | −0.136138 | ||||||||
\(764\) | −1.17188e13 | −1.24441 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.24513e11 | −0.0130672 | ||||||||
\(767\) | −2.46182e13 | −2.56849 | ||||||||
\(768\) | −1.18363e13 | −1.22769 | ||||||||
\(769\) | −6.30061e12 | −0.649702 | −0.324851 | − | 0.945765i | \(-0.605314\pi\) | ||||
−0.324851 | + | 0.945765i | \(0.605314\pi\) | |||||||
\(770\) | −1.15917e11 | −0.0118833 | ||||||||
\(771\) | −3.40003e12 | −0.346528 | ||||||||
\(772\) | 1.04490e13 | 1.05876 | ||||||||
\(773\) | −1.40318e13 | −1.41354 | −0.706768 | − | 0.707446i | \(-0.749847\pi\) | ||||
−0.706768 | + | 0.707446i | \(0.749847\pi\) | |||||||
\(774\) | −4.14722e11 | −0.0415358 | ||||||||
\(775\) | −5.98961e12 | −0.596404 | ||||||||
\(776\) | 1.24229e12 | 0.122983 | ||||||||
\(777\) | −3.92140e12 | −0.385964 | ||||||||
\(778\) | 5.67057e11 | 0.0554905 | ||||||||
\(779\) | −2.03327e10 | −0.00197823 | ||||||||
\(780\) | −1.94252e13 | −1.87906 | ||||||||
\(781\) | 1.04192e13 | 1.00208 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.22036e12 | −0.496333 | ||||||||
\(784\) | −9.61082e12 | −0.908528 | ||||||||
\(785\) | −7.19691e12 | −0.676445 | ||||||||
\(786\) | −9.89955e11 | −0.0925154 | ||||||||
\(787\) | −1.03038e13 | −0.957440 | −0.478720 | − | 0.877968i | \(-0.658899\pi\) | ||||
−0.478720 | + | 0.877968i | \(0.658899\pi\) | |||||||
\(788\) | 2.96602e12 | 0.274035 | ||||||||
\(789\) | −6.65440e12 | −0.611312 | ||||||||
\(790\) | −5.14553e11 | −0.0470011 | ||||||||
\(791\) | −3.84744e12 | −0.349444 | ||||||||
\(792\) | 4.70610e11 | 0.0425009 | ||||||||
\(793\) | −2.64776e13 | −2.37765 | ||||||||
\(794\) | 1.07116e12 | 0.0956452 | ||||||||
\(795\) | 1.71357e13 | 1.52143 | ||||||||
\(796\) | 2.29480e12 | 0.202599 | ||||||||
\(797\) | 1.57641e13 | 1.38390 | 0.691952 | − | 0.721944i | \(-0.256751\pi\) | ||||
0.691952 | + | 0.721944i | \(0.256751\pi\) | |||||||
\(798\) | −6.40665e8 | −5.59265e−5 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −6.45923e11 | −0.0557540 | ||||||||
\(801\) | 4.76684e12 | 0.409152 | ||||||||
\(802\) | −2.06304e11 | −0.0176086 | ||||||||
\(803\) | 4.72489e12 | 0.401026 | ||||||||
\(804\) | −1.15064e13 | −0.971154 | ||||||||
\(805\) | −6.91134e10 | −0.00580070 | ||||||||
\(806\) | −1.44816e12 | −0.120867 | ||||||||
\(807\) | −1.66224e13 | −1.37963 | ||||||||
\(808\) | −1.40442e12 | −0.115916 | ||||||||
\(809\) | −1.37214e13 | −1.12623 | −0.563117 | − | 0.826377i | \(-0.690398\pi\) | ||||
−0.563117 | + | 0.826377i | \(0.690398\pi\) | |||||||
\(810\) | 9.55295e11 | 0.0779750 | ||||||||
\(811\) | −1.55198e13 | −1.25977 | −0.629887 | − | 0.776687i | \(-0.716899\pi\) | ||||
−0.629887 | + | 0.776687i | \(0.716899\pi\) | |||||||
\(812\) | 3.49550e12 | 0.282168 | ||||||||
\(813\) | 1.74241e13 | 1.39876 | ||||||||
\(814\) | −4.69871e11 | −0.0375119 | ||||||||
\(815\) | −4.31286e12 | −0.342418 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.59250e10 | −0.00360620 | ||||||||
\(818\) | 8.58013e11 | 0.0670045 | ||||||||
\(819\) | −2.86540e12 | −0.222540 | ||||||||
\(820\) | −1.04858e13 | −0.809915 | ||||||||
\(821\) | −3.40134e12 | −0.261280 | −0.130640 | − | 0.991430i | \(-0.541703\pi\) | ||||
−0.130640 | + | 0.991430i | \(0.541703\pi\) | |||||||
\(822\) | 1.14393e12 | 0.0873933 | ||||||||
\(823\) | −4.01848e12 | −0.305325 | −0.152663 | − | 0.988278i | \(-0.548785\pi\) | ||||
−0.152663 | + | 0.988278i | \(0.548785\pi\) | |||||||
\(824\) | 8.26702e9 | 0.000624707 0 | ||||||||
\(825\) | −3.78858e12 | −0.284731 | ||||||||
\(826\) | −4.18724e11 | −0.0312981 | ||||||||
\(827\) | 4.31147e12 | 0.320517 | 0.160258 | − | 0.987075i | \(-0.448767\pi\) | ||||
0.160258 | + | 0.987075i | \(0.448767\pi\) | |||||||
\(828\) | 1.40090e11 | 0.0103579 | ||||||||
\(829\) | 4.42248e12 | 0.325215 | 0.162608 | − | 0.986691i | \(-0.448010\pi\) | ||||
0.162608 | + | 0.986691i | \(0.448010\pi\) | |||||||
\(830\) | −6.86114e11 | −0.0501816 | ||||||||
\(831\) | 1.64592e12 | 0.119730 | ||||||||
\(832\) | 1.74527e13 | 1.26272 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −3.38843e11 | −0.0242522 | ||||||||
\(835\) | 2.56518e13 | 1.82612 | ||||||||
\(836\) | 2.60186e10 | 0.00184228 | ||||||||
\(837\) | −1.24679e13 | −0.878068 | ||||||||
\(838\) | 1.18854e12 | 0.0832563 | ||||||||
\(839\) | −1.12787e13 | −0.785835 | −0.392917 | − | 0.919574i | \(-0.628534\pi\) | ||||
−0.392917 | + | 0.919574i | \(0.628534\pi\) | |||||||
\(840\) | −6.61771e11 | −0.0458618 | ||||||||
\(841\) | −5.74353e11 | −0.0395910 | ||||||||
\(842\) | 6.72056e11 | 0.0460788 | ||||||||
\(843\) | 1.84827e13 | 1.26050 | ||||||||
\(844\) | 1.77583e13 | 1.20465 | ||||||||
\(845\) | 1.12043e13 | 0.756016 | ||||||||
\(846\) | 1.03953e11 | 0.00697701 | ||||||||
\(847\) | −2.47285e12 | −0.165090 | ||||||||
\(848\) | −1.54877e13 | −1.02850 | ||||||||
\(849\) | −1.69819e13 | −1.12177 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.80152e11 | −0.0183110 | ||||||||
\(852\) | 2.96978e13 | 1.93084 | ||||||||
\(853\) | 3.07683e12 | 0.198991 | 0.0994954 | − | 0.995038i | \(-0.468277\pi\) | ||||
0.0994954 | + | 0.995038i | \(0.468277\pi\) | |||||||
\(854\) | −4.50349e11 | −0.0289727 | ||||||||
\(855\) | −3.06642e10 | −0.00196238 | ||||||||
\(856\) | −1.95246e12 | −0.124294 | ||||||||
\(857\) | 3.10840e13 | 1.96845 | 0.984223 | − | 0.176930i | \(-0.0566166\pi\) | ||||
0.984223 | + | 0.176930i | \(0.0566166\pi\) | |||||||
\(858\) | −9.15996e11 | −0.0577033 | ||||||||
\(859\) | −7.61893e12 | −0.477446 | −0.238723 | − | 0.971088i | \(-0.576729\pi\) | ||||
−0.238723 | + | 0.971088i | \(0.576729\pi\) | |||||||
\(860\) | −2.36840e13 | −1.47643 | ||||||||
\(861\) | −4.12659e12 | −0.255904 | ||||||||
\(862\) | 5.89908e11 | 0.0363917 | ||||||||
\(863\) | −2.61427e13 | −1.60436 | −0.802179 | − | 0.597083i | \(-0.796326\pi\) | ||||
−0.802179 | + | 0.597083i | \(0.796326\pi\) | |||||||
\(864\) | −1.34454e12 | −0.0820849 | ||||||||
\(865\) | 2.07364e13 | 1.25939 | ||||||||
\(866\) | 8.70801e11 | 0.0526124 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.34837e12 | 0.499186 | ||||||||
\(869\) | 8.22380e12 | 0.489197 | ||||||||
\(870\) | −1.31694e12 | −0.0779345 | ||||||||
\(871\) | 1.68140e13 | 0.989896 | ||||||||
\(872\) | −8.71840e11 | −0.0510638 | ||||||||
\(873\) | 1.16827e13 | 0.680735 | ||||||||
\(874\) | −4.57703e7 | −2.65327e−6 0 | ||||||||
\(875\) | −3.80802e12 | −0.219615 | ||||||||
\(876\) | 1.34674e13 | 0.772706 | ||||||||
\(877\) | 3.00641e13 | 1.71613 | 0.858065 | − | 0.513541i | \(-0.171667\pi\) | ||||
0.858065 | + | 0.513541i | \(0.171667\pi\) | |||||||
\(878\) | 1.43714e12 | 0.0816158 | ||||||||
\(879\) | 2.88626e13 | 1.63074 | ||||||||
\(880\) | 1.33784e13 | 0.752023 | ||||||||
\(881\) | 2.06409e13 | 1.15435 | 0.577175 | − | 0.816620i | \(-0.304155\pi\) | ||||
0.577175 | + | 0.816620i | \(0.304155\pi\) | |||||||
\(882\) | 5.35702e11 | 0.0298067 | ||||||||
\(883\) | 1.85711e13 | 1.02805 | 0.514026 | − | 0.857774i | \(-0.328153\pi\) | ||||
0.514026 | + | 0.857774i | \(0.328153\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.34687e13 | −2.92991 | ||||||||
\(886\) | 5.83017e11 | 0.0317855 | ||||||||
\(887\) | −1.35590e11 | −0.00735482 | −0.00367741 | − | 0.999993i | \(-0.501171\pi\) | ||||
−0.00367741 | + | 0.999993i | \(0.501171\pi\) | |||||||
\(888\) | −2.68250e12 | −0.144771 | ||||||||
\(889\) | −9.02957e12 | −0.484852 | ||||||||
\(890\) | −8.03182e11 | −0.0429101 | ||||||||
\(891\) | −1.52679e13 | −0.811578 | ||||||||
\(892\) | 1.25759e13 | 0.665115 | ||||||||
\(893\) | 1.15114e10 | 0.000605754 0 | ||||||||
\(894\) | 4.65872e11 | 0.0243920 | ||||||||
\(895\) | −1.35006e13 | −0.703313 | ||||||||
\(896\) | 1.19980e12 | 0.0621901 | ||||||||
\(897\) | −5.46146e11 | −0.0281672 | ||||||||
\(898\) | −1.14604e12 | −0.0588108 | ||||||||
\(899\) | 3.32759e13 | 1.69907 | ||||||||
\(900\) | −4.04759e12 | −0.205639 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4.94458e11 | −0.0248714 | ||||||||
\(903\) | −9.32064e12 | −0.466499 | ||||||||
\(904\) | −2.63190e12 | −0.131073 | ||||||||
\(905\) | 1.40994e13 | 0.698688 | ||||||||
\(906\) | −3.59660e11 | −0.0177343 | ||||||||
\(907\) | 1.36972e13 | 0.672045 | 0.336022 | − | 0.941854i | \(-0.390918\pi\) | ||||
0.336022 | + | 0.941854i | \(0.390918\pi\) | |||||||
\(908\) | 2.27505e13 | 1.11072 | ||||||||
\(909\) | −1.32074e13 | −0.641622 | ||||||||
\(910\) | 4.82802e11 | 0.0233390 | ||||||||
\(911\) | 2.24844e13 | 1.08156 | 0.540778 | − | 0.841165i | \(-0.318130\pi\) | ||||
0.540778 | + | 0.841165i | \(0.318130\pi\) | |||||||
\(912\) | 7.39413e10 | 0.00353924 | ||||||||
\(913\) | 1.09658e13 | 0.522300 | ||||||||
\(914\) | −1.57806e12 | −0.0747938 | ||||||||
\(915\) | −5.75070e13 | −2.71223 | ||||||||
\(916\) | −3.37853e13 | −1.58562 | ||||||||
\(917\) | −8.33936e12 | −0.389467 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.66637e12 | 0.447037 | 0.223519 | − | 0.974700i | \(-0.428246\pi\) | ||||
0.223519 | + | 0.974700i | \(0.428246\pi\) | |||||||
\(920\) | −4.72781e10 | −0.00217578 | ||||||||
\(921\) | 4.01516e13 | 1.83880 | ||||||||
\(922\) | −6.36267e11 | −0.0289968 | ||||||||
\(923\) | −4.33966e13 | −1.96810 | ||||||||
\(924\) | 5.28056e12 | 0.238318 | ||||||||
\(925\) | 8.09439e12 | 0.363535 | ||||||||
\(926\) | 9.53348e11 | 0.0426091 | ||||||||
\(927\) | 7.77444e10 | 0.00345788 | ||||||||
\(928\) | 3.58850e12 | 0.158835 | ||||||||
\(929\) | −8.19216e12 | −0.360851 | −0.180425 | − | 0.983589i | \(-0.557747\pi\) | ||||
−0.180425 | + | 0.983589i | \(0.557747\pi\) | |||||||
\(930\) | −3.14527e12 | −0.137875 | ||||||||
\(931\) | 5.93219e10 | 0.00258786 | ||||||||
\(932\) | −2.22433e13 | −0.965667 | ||||||||
\(933\) | 2.08001e13 | 0.898665 | ||||||||
\(934\) | −1.01712e11 | −0.00437330 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.96012e12 | −0.0834723 | ||||||||
\(937\) | 3.49872e12 | 0.148279 | 0.0741396 | − | 0.997248i | \(-0.476379\pi\) | ||||
0.0741396 | + | 0.997248i | \(0.476379\pi\) | |||||||
\(938\) | 2.85984e11 | 0.0120623 | ||||||||
\(939\) | 5.05803e13 | 2.12318 | ||||||||
\(940\) | 5.93656e12 | 0.248004 | ||||||||
\(941\) | 1.51926e12 | 0.0631655 | 0.0315827 | − | 0.999501i | \(-0.489945\pi\) | ||||
0.0315827 | + | 0.999501i | \(0.489945\pi\) | |||||||
\(942\) | −9.67307e11 | −0.0400254 | ||||||||
\(943\) | −2.94811e11 | −0.0121406 | ||||||||
\(944\) | 4.83263e13 | 1.98066 | ||||||||
\(945\) | 4.15668e12 | 0.169552 | ||||||||
\(946\) | −1.11682e12 | −0.0453391 | ||||||||
\(947\) | 2.12785e13 | 0.859738 | 0.429869 | − | 0.902891i | \(-0.358560\pi\) | ||||
0.429869 | + | 0.902891i | \(0.358560\pi\) | |||||||
\(948\) | 2.34403e13 | 0.942597 | ||||||||
\(949\) | −1.96795e13 | −0.787619 | ||||||||
\(950\) | 1.32243e9 | 5.26765e−5 0 | ||||||||
\(951\) | −1.77085e12 | −0.0702053 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.61359e12 | 0.377544 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(954\) | 8.63276e11 | 0.0337429 | ||||||||
\(955\) | 3.71927e13 | 1.44691 | ||||||||
\(956\) | −1.87417e13 | −0.725684 | ||||||||
\(957\) | 2.10479e13 | 0.811157 | ||||||||
\(958\) | −2.55553e12 | −0.0980249 | ||||||||
\(959\) | 9.63648e12 | 0.367904 | ||||||||
\(960\) | 3.79057e13 | 1.44040 | ||||||||
\(961\) | 5.30339e13 | 2.00585 | ||||||||
\(962\) | 1.95705e12 | 0.0736738 | ||||||||
\(963\) | −1.83612e13 | −0.687992 | ||||||||
\(964\) | 1.85153e13 | 0.690531 | ||||||||
\(965\) | −3.31627e13 | −1.23106 | ||||||||
\(966\) | −9.28924e9 | −0.000343228 0 | ||||||||
\(967\) | −1.08700e13 | −0.399772 | −0.199886 | − | 0.979819i | \(-0.564057\pi\) | ||||
−0.199886 | + | 0.979819i | \(0.564057\pi\) | |||||||
\(968\) | −1.69159e12 | −0.0619236 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.96846e12 | −0.0713925 | ||||||||
\(971\) | 2.79438e13 | 1.00879 | 0.504393 | − | 0.863474i | \(-0.331716\pi\) | ||||
0.504393 | + | 0.863474i | \(0.331716\pi\) | |||||||
\(972\) | −2.94654e13 | −1.05880 | ||||||||
\(973\) | −2.85441e12 | −0.102096 | ||||||||
\(974\) | −3.30658e11 | −0.0117724 | ||||||||
\(975\) | 1.57797e13 | 0.559214 | ||||||||
\(976\) | 5.19763e13 | 1.83350 | ||||||||
\(977\) | −1.49620e13 | −0.525369 | −0.262685 | − | 0.964882i | \(-0.584608\pi\) | ||||
−0.262685 | + | 0.964882i | \(0.584608\pi\) | |||||||
\(978\) | −5.79674e11 | −0.0202609 | ||||||||
\(979\) | 1.28368e13 | 0.446616 | ||||||||
\(980\) | 3.05930e13 | 1.05951 | ||||||||
\(981\) | −8.19893e12 | −0.282648 | ||||||||
\(982\) | 7.21350e10 | 0.00247540 | ||||||||
\(983\) | −2.54966e13 | −0.870946 | −0.435473 | − | 0.900202i | \(-0.643419\pi\) | ||||
−0.435473 | + | 0.900202i | \(0.643419\pi\) | |||||||
\(984\) | −2.82286e12 | −0.0959869 | ||||||||
\(985\) | −9.41343e12 | −0.318629 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.33628e12 | 0.0783605 | ||||||||
\(988\) | −1.08369e11 | −0.00361826 | ||||||||
\(989\) | −6.65884e11 | −0.0221317 | ||||||||
\(990\) | −7.45702e11 | −0.0246721 | ||||||||
\(991\) | 9.59893e12 | 0.316149 | 0.158074 | − | 0.987427i | \(-0.449471\pi\) | ||||
0.158074 | + | 0.987427i | \(0.449471\pi\) | |||||||
\(992\) | 8.57047e12 | 0.280997 | ||||||||
\(993\) | 3.81209e13 | 1.24420 | ||||||||
\(994\) | −7.38119e11 | −0.0239821 | ||||||||
\(995\) | −7.28315e12 | −0.235568 | ||||||||
\(996\) | 3.12557e13 | 1.00638 | ||||||||
\(997\) | 3.17533e13 | 1.01780 | 0.508898 | − | 0.860827i | \(-0.330053\pi\) | ||||
0.508898 | + | 0.860827i | \(0.330053\pi\) | |||||||
\(998\) | −3.84308e11 | −0.0122629 | ||||||||
\(999\) | 1.68492e13 | 0.535222 |
(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 | 289.10.a.a.1.3 | 5 | ||
17.16 | even | 2 | 17.10.a.a.1.3 | ✓ | 5 | ||
51.50 | odd | 2 | 153.10.a.c.1.3 | 5 | |||
68.67 | odd | 2 | 272.10.a.f.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.a.1.3 | ✓ | 5 | 17.16 | even | 2 | ||
153.10.a.c.1.3 | 5 | 51.50 | odd | 2 | |||
272.10.a.f.1.1 | 5 | 68.67 | odd | 2 | |||
289.10.a.a.1.3 | 5 | 1.1 | even | 1 | trivial |