Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [592,8,Mod(1,592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(592, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("592.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 592 = 2^{4} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 592.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: | \(184.931935087\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 10621x^{4} + 102052x^{3} + 31004503x^{2} - 305547358x - 22608804936 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-26.0193\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 592.1 |
$q$-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 | ||||||||
\(3\) | −31.0193 | −0.663296 | −0.331648 | − | 0.943403i | \(-0.607605\pi\) | ||||
−0.331648 | + | 0.943403i | \(0.607605\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −544.510 | −1.94810 | −0.974049 | − | 0.226337i | \(-0.927325\pi\) | ||||
−0.974049 | + | 0.226337i | \(0.927325\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1685.44 | 1.85724 | 0.928622 | − | 0.371026i | \(-0.120994\pi\) | ||||
0.928622 | + | 0.371026i | \(0.120994\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1224.80 | −0.560038 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5629.72 | −1.27530 | −0.637650 | − | 0.770327i | \(-0.720093\pi\) | ||||
−0.637650 | + | 0.770327i | \(0.720093\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5228.81 | 0.660087 | 0.330044 | − | 0.943966i | \(-0.392937\pi\) | ||||
0.330044 | + | 0.943966i | \(0.392937\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16890.3 | 1.29217 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12575.5 | −0.620805 | −0.310402 | − | 0.950605i | \(-0.600464\pi\) | ||||
−0.310402 | + | 0.950605i | \(0.600464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18367.1 | −0.614332 | −0.307166 | − | 0.951656i | \(-0.599381\pi\) | ||||
−0.307166 | + | 0.951656i | \(0.599381\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −52281.0 | −1.23190 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −40252.9 | −0.689843 | −0.344921 | − | 0.938632i | \(-0.612094\pi\) | ||||
−0.344921 | + | 0.938632i | \(0.612094\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 218366. | 2.79509 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 105832. | 1.03477 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18705.8 | 0.142424 | 0.0712118 | − | 0.997461i | \(-0.477313\pi\) | ||||
0.0712118 | + | 0.997461i | \(0.477313\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 169281. | 1.02057 | 0.510284 | − | 0.860006i | \(-0.329540\pi\) | ||||
0.510284 | + | 0.860006i | \(0.329540\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 174630. | 0.845901 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −917737. | −3.61809 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −50653.0 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −162194. | −0.437833 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −26437.9 | −0.0599078 | −0.0299539 | − | 0.999551i | \(-0.509536\pi\) | ||||
−0.0299539 | + | 0.999551i | \(0.509536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −406992. | −0.780632 | −0.390316 | − | 0.920681i | \(-0.627634\pi\) | ||||
−0.390316 | + | 0.920681i | \(0.627634\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 666918. | 1.09101 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −175342. | −0.246345 | −0.123173 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123173 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.01715e6 | 2.44936 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 390084. | 0.411778 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.82314e6 | −1.68211 | −0.841056 | − | 0.540949i | \(-0.818065\pi\) | ||||
−0.841056 | + | 0.540949i | \(0.818065\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.06544e6 | 2.48441 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 569735. | 0.407484 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.24173e6 | 0.787131 | 0.393565 | − | 0.919297i | \(-0.371242\pi\) | ||||
0.393565 | + | 0.919297i | \(0.371242\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.25092e6 | 1.83380 | 0.916899 | − | 0.399120i | \(-0.130684\pi\) | ||||
0.916899 | + | 0.399120i | \(0.130684\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.06433e6 | −1.04013 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.84714e6 | −1.28592 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.66755e6 | 0.677357 | 0.338678 | − | 0.940902i | \(-0.390020\pi\) | ||||
0.338678 | + | 0.940902i | \(0.390020\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.24862e6 | 0.457570 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −262493. | −0.0870388 | −0.0435194 | − | 0.999053i | \(-0.513857\pi\) | ||||
−0.0435194 | + | 0.999053i | \(0.513857\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.68612e6 | 0.808157 | 0.404078 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404078 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.77356e6 | −1.85397 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.48853e6 | −2.36854 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −363284. | −0.0828993 | −0.0414497 | − | 0.999141i | \(-0.513198\pi\) | ||||
−0.0414497 | + | 0.999141i | \(0.513198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −604180. | −0.126319 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.71044e6 | 1.28818 | 0.644091 | − | 0.764948i | \(-0.277236\pi\) | ||||
0.644091 | + | 0.764948i | \(0.277236\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.84750e6 | 1.20939 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −580239. | −0.0944691 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.16083e7 | 1.74543 | 0.872715 | − | 0.488229i | \(-0.162357\pi\) | ||||
0.872715 | + | 0.488229i | \(0.162357\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.81283e6 | 1.22594 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.25097e6 | −0.676939 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00011e7 | 1.19678 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.63488e7 | 1.81880 | 0.909400 | − | 0.415923i | \(-0.136541\pi\) | ||||
0.909400 | + | 0.415923i | \(0.136541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.89530e6 | 0.714216 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.79452e6 | 0.752774 | 0.376387 | − | 0.926462i | \(-0.377166\pi\) | ||||
0.376387 | + | 0.926462i | \(0.377166\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.12543e6 | −0.732683 | −0.366341 | − | 0.930481i | \(-0.619390\pi\) | ||||
−0.366341 | + | 0.930481i | \(0.619390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.84675e7 | 2.39987 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.15348e6 | −0.0910264 | −0.0455132 | − | 0.998964i | \(-0.514492\pi\) | ||||
−0.0455132 | + | 0.998964i | \(0.514492\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.60358e6 | −0.636336 | −0.318168 | − | 0.948034i | \(-0.603068\pi\) | ||||
−0.318168 | + | 0.948034i | \(0.603068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.57122e6 | 0.109045 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.76780e6 | −0.506435 | −0.253217 | − | 0.967409i | \(-0.581489\pi\) | ||||
−0.253217 | + | 0.967409i | \(0.581489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.19181e7 | 1.34388 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.40427e6 | −0.369674 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.11953e7 | −1.15299 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.22065e7 | 0.626388 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 820084. | 0.0397366 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.63627e7 | −3.49700 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.49536e6 | −0.194738 | −0.0973691 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973691 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.26246e7 | 0.517791 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.57640e7 | 0.612656 | 0.306328 | − | 0.951926i | \(-0.400900\pi\) | ||||
0.306328 | + | 0.951926i | \(0.400900\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.09566e7 | −1.14097 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.76264e7 | −2.01583 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.27787e6 | −0.308267 | −0.154133 | − | 0.988050i | \(-0.549259\pi\) | ||||
−0.154133 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.30404e7 | −1.67515 | −0.837577 | − | 0.546319i | \(-0.816028\pi\) | ||||
−0.837577 | + | 0.546319i | \(0.816028\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.43899e6 | 0.163400 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.94367e7 | −0.841809 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.01855e7 | −0.277455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.25706e7 | −1.62465 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.61358e7 | 0.647267 | 0.323633 | − | 0.946183i | \(-0.395096\pi\) | ||||
0.323633 | + | 0.946183i | \(0.395096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.32760e7 | 0.786523 | 0.393261 | − | 0.919427i | \(-0.371347\pi\) | ||||
0.393261 | + | 0.919427i | \(0.371347\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.54026e7 | 0.347674 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.21751e7 | −1.98817 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.08133e7 | −0.429232 | −0.214616 | − | 0.976698i | \(-0.568850\pi\) | ||||
−0.214616 | + | 0.976698i | \(0.568850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.65525e7 | 1.11574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.78438e7 | −1.28121 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00702e7 | −0.724711 | −0.362355 | − | 0.932040i | \(-0.618027\pi\) | ||||
−0.362355 | + | 0.932040i | \(0.618027\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.50877e7 | −1.64790 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.26523e7 | −0.708656 | −0.354328 | − | 0.935121i | \(-0.615290\pi\) | ||||
−0.354328 | + | 0.935121i | \(0.615290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.54080e7 | −0.564285 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.24961e7 | 0.344050 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.13528e6 | 0.104773 | 0.0523865 | − | 0.998627i | \(-0.483317\pi\) | ||||
0.0523865 | + | 0.998627i | \(0.483317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.68042e8 | 5.19116 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.85177e7 | −0.522101 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.39174e8 | −1.81373 | −0.906866 | − | 0.421419i | \(-0.861532\pi\) | ||||
−0.906866 | + | 0.421419i | \(0.861532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.11153e7 | −0.766082 | −0.383041 | − | 0.923731i | \(-0.625123\pi\) | ||||
−0.383041 | + | 0.923731i | \(0.625123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00841e8 | −1.21635 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.75811e7 | 0.320265 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.07967e7 | 0.791712 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.78373e8 | 1.92182 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.77318e8 | 1.84135 | 0.920676 | − | 0.390329i | \(-0.127639\pi\) | ||||
0.920676 | + | 0.390329i | \(0.127639\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.75041e7 | −0.675896 | −0.337948 | − | 0.941165i | \(-0.609733\pi\) | ||||
−0.337948 | + | 0.941165i | \(0.609733\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.83163e7 | 0.852943 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.03097e8 | −0.960761 | −0.480380 | − | 0.877060i | \(-0.659501\pi\) | ||||
−0.480380 | + | 0.877060i | \(0.659501\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.78780e8 | −1.60817 | −0.804086 | − | 0.594512i | \(-0.797345\pi\) | ||||
−0.804086 | + | 0.594512i | \(0.797345\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.17263e7 | −0.449288 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.15273e7 | 0.264516 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.43957e7 | 0.116706 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.93019e7 | 0.386338 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.03402e8 | 0.783458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.20832e8 | −1.61836 | −0.809178 | − | 0.587564i | \(-0.800087\pi\) | ||||
−0.809178 | + | 0.587564i | \(0.800087\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.14233e6 | 0.0577325 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.21611e8 | 1.52075 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.85312e8 | 1.89544 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.33216e7 | −0.536047 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.57551e7 | −0.409786 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.27015e8 | −1.37085 | −0.685423 | − | 0.728146i | \(-0.740382\pi\) | ||||
−0.685423 | + | 0.728146i | \(0.740382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.67456e8 | −1.56535 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.27056e8 | 1.28838 | 0.644188 | − | 0.764867i | \(-0.277195\pi\) | ||||
0.644188 | + | 0.764867i | \(0.277195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.74743e8 | 0.961557 | 0.480778 | − | 0.876842i | \(-0.340354\pi\) | ||||
0.480778 | + | 0.876842i | \(0.340354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.94327e8 | 1.57105 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.66617e8 | 1.38083 | 0.690417 | − | 0.723411i | \(-0.257427\pi\) | ||||
0.690417 | + | 0.723411i | \(0.257427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.54755e7 | 0.479904 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.12688e7 | 0.0549868 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.94730e7 | −0.376554 | −0.188277 | − | 0.982116i | \(-0.560290\pi\) | ||||
−0.188277 | + | 0.982116i | \(0.560290\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.79710e7 | 0.266779 | 0.133389 | − | 0.991064i | \(-0.457414\pi\) | ||||
0.133389 | + | 0.991064i | \(0.457414\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.12713e8 | −0.950980 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.09836e9 | −4.77159 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.60382e7 | −0.405513 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.08153e8 | −0.854447 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.14343e8 | −1.25472 | −0.627358 | − | 0.778731i | \(-0.715864\pi\) | ||||
−0.627358 | + | 0.778731i | \(0.715864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.26613e8 | 0.879756 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.12405e8 | −0.802183 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.09191e8 | 1.13622 | 0.568108 | − | 0.822954i | \(-0.307675\pi\) | ||||
0.568108 | + | 0.822954i | \(0.307675\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.53724e7 | −0.305329 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.29109e7 | −0.0797627 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.09539e8 | 1.04923 | 0.524614 | − | 0.851340i | \(-0.324210\pi\) | ||||
0.524614 | + | 0.851340i | \(0.324210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.92718e8 | 3.27692 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.60080e8 | −1.15774 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.59451e8 | −0.812686 | −0.406343 | − | 0.913721i | \(-0.633196\pi\) | ||||
−0.406343 | + | 0.913721i | \(0.633196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.90601e7 | −0.241304 | −0.120652 | − | 0.992695i | \(-0.538499\pi\) | ||||
−0.120652 | + | 0.992695i | \(0.538499\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.73368e8 | −0.813164 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.22934e9 | −3.56457 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.41348e8 | 0.682283 | 0.341142 | − | 0.940012i | \(-0.389186\pi\) | ||||
0.341142 | + | 0.940012i | \(0.389186\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.07336e8 | −0.571557 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.24454e8 | −0.334609 | −0.167304 | − | 0.985905i | \(-0.553506\pi\) | ||||
−0.167304 | + | 0.985905i | \(0.553506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.05747e8 | −1.06415 | −0.532074 | − | 0.846698i | \(-0.678587\pi\) | ||||
−0.532074 | + | 0.846698i | \(0.678587\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.10226e8 | −0.793819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.45593e7 | −0.111263 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.52195e8 | −0.614601 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.07128e8 | −1.20640 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.99201e8 | 1.15941 | 0.579707 | − | 0.814825i | \(-0.303167\pi\) | ||||
0.579707 | + | 0.814825i | \(0.303167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.76137e8 | −1.53341 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.95803e8 | −1.31964 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.10475e8 | −0.455357 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.85959e8 | −1.44983 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.41781e8 | −0.499312 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.77016e9 | −3.57242 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.21540e8 | 0.634235 | 0.317118 | − | 0.948386i | \(-0.397285\pi\) | ||||
0.317118 | + | 0.948386i | \(0.397285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.52045e8 | 0.485986 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.03297e8 | 0.194726 | 0.0973631 | − | 0.995249i | \(-0.468959\pi\) | ||||
0.0973631 | + | 0.995249i | \(0.468959\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.25918e8 | 0.969422 | 0.484711 | − | 0.874674i | \(-0.338925\pi\) | ||||
0.484711 | + | 0.874674i | \(0.338925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.12405e9 | 2.02627 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.26026e7 | −0.110379 | −0.0551893 | − | 0.998476i | \(-0.517576\pi\) | ||||
−0.0551893 | + | 0.998476i | \(0.517576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.05308e8 | −0.181633 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.57802e7 | 0.0603775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.30976e8 | 0.381381 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.14180e9 | 1.84500 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.66877e8 | 0.422079 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.95528e8 | −0.457523 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.10780e8 | 0.471037 | 0.235518 | − | 0.971870i | \(-0.424321\pi\) | ||||
0.235518 | + | 0.971870i | \(0.424321\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.20400e7 | 0.0920697 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.07998e8 | −1.31956 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.56000e8 | −1.36067 | −0.680335 | − | 0.732901i | \(-0.738166\pi\) | ||||
−0.680335 | + | 0.732901i | \(0.738166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.40952e8 | 0.335916 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.53003e8 | −1.30153 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.01175e9 | 2.69181 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.79885e8 | −0.891392 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.37536e9 | −1.76711 | −0.883555 | − | 0.468327i | \(-0.844857\pi\) | ||||
−0.883555 | + | 0.468327i | \(0.844857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.38134e9 | −1.73945 | −0.869725 | − | 0.493537i | \(-0.835704\pi\) | ||||
−0.869725 | + | 0.493537i | \(0.835704\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.53374e8 | 0.683037 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.48672e8 | −0.784899 | −0.392450 | − | 0.919774i | \(-0.628372\pi\) | ||||
−0.392450 | + | 0.919774i | \(0.628372\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.42930e8 | 0.169560 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.57462e8 | 0.764772 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.64068e8 | −0.415291 | −0.207645 | − | 0.978204i | \(-0.566580\pi\) | ||||
−0.207645 | + | 0.978204i | \(0.566580\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.56521e8 | −0.622596 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.78638e8 | −0.415481 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.46262e9 | −1.57437 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.90647e8 | −0.412528 | −0.206264 | − | 0.978496i | \(-0.566131\pi\) | ||||
−0.206264 | + | 0.978496i | \(0.566131\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.23812e7 | 0.0335506 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.07279e9 | −3.12409 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.58735e7 | −0.0856797 | −0.0428399 | − | 0.999082i | \(-0.513641\pi\) | ||||
−0.0428399 | + | 0.999082i | \(0.513641\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.36872e9 | 2.31955 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.78089e7 | 0.0940121 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.53330e8 | −0.333383 | −0.166691 | − | 0.986009i | \(-0.553308\pi\) | ||||
−0.166691 | + | 0.986009i | \(0.553308\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.39443e8 | 0.129169 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.90315e8 | 0.445943 | 0.222971 | − | 0.974825i | \(-0.428424\pi\) | ||||
0.222971 | + | 0.974825i | \(0.428424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.16660e9 | 4.61415 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.98486e8 | 0.437184 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.97474e7 | 0.0859168 | 0.0429584 | − | 0.999077i | \(-0.486322\pi\) | ||||
0.0429584 | + | 0.999077i | \(0.486322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.06202e8 | 0.428258 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.88988e8 | −0.406372 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.97812e8 | 0.161496 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.09994e8 | −0.168438 | −0.0842189 | − | 0.996447i | \(-0.526839\pi\) | ||||
−0.0842189 | + | 0.996447i | \(0.526839\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.60252e8 | 0.756798 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.55414e8 | 0.430141 | 0.215071 | − | 0.976598i | \(-0.431002\pi\) | ||||
0.215071 | + | 0.976598i | \(0.431002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.85138e8 | 0.673664 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.28982e8 | 0.246082 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.85162e8 | 0.209658 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.80096e9 | 1.30158 | 0.650792 | − | 0.759256i | \(-0.274437\pi\) | ||||
0.650792 | + | 0.759256i | \(0.274437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.87793e8 | 0.204472 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.09286e9 | 1.46189 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.65390e9 | −2.50951 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.64527e9 | 1.11112 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.69929e7 | 0.0112854 | 0.00564272 | − | 0.999984i | \(-0.498204\pi\) | ||||
0.00564272 | + | 0.999984i | \(0.498204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.76374e9 | 1.80514 | 0.902568 | − | 0.430548i | \(-0.141680\pi\) | ||||
0.902568 | + | 0.430548i | \(0.141680\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.14760e8 | 0.137963 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.74607e9 | −1.73520 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.47921e9 | 3.40581 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.13107e8 | 0.558369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.95133e9 | 1.77561 | 0.887804 | − | 0.460222i | \(-0.152230\pi\) | ||||
0.887804 | + | 0.460222i | \(0.152230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.29366e9 | −1.35776 | −0.678878 | − | 0.734251i | \(-0.737533\pi\) | ||||
−0.678878 | + | 0.734251i | \(0.737533\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.15946e8 | 0.184035 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.39331e8 | 0.423793 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.21394e9 | −1.24893 | −0.624467 | − | 0.781052i | \(-0.714684\pi\) | ||||
−0.624467 | + | 0.781052i | \(0.714684\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.47061e9 | −1.37173 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.80148e9 | 1.53100 | 0.765498 | − | 0.643438i | \(-0.222493\pi\) | ||||
0.765498 | + | 0.643438i | \(0.222493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.32082e9 | −3.40027 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.10713e8 | −0.429330 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.24071e9 | −0.646856 | −0.323428 | − | 0.946253i | \(-0.604835\pi\) | ||||
−0.323428 | + | 0.946253i | \(0.604835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.48838e8 | 0.0764003 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.03220e9 | −0.521698 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.79867e9 | −2.38826 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.16764e8 | 0.400304 | 0.200152 | − | 0.979765i | \(-0.435856\pi\) | ||||
0.200152 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.33089e9 | −0.642389 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.07694e9 | 0.511962 | 0.255981 | − | 0.966682i | \(-0.417601\pi\) | ||||
0.255981 | + | 0.966682i | \(0.417601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.16535e9 | −1.48214 | −0.741068 | − | 0.671430i | \(-0.765680\pi\) | ||||
−0.741068 | + | 0.671430i | \(0.765680\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.85921e9 | 1.31874 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.37777e9 | −1.08034 | −0.540171 | − | 0.841555i | \(-0.681640\pi\) | ||||
−0.540171 | + | 0.841555i | \(0.681640\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.81055e9 | 1.25802 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.45614e8 | 0.284708 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.29125e9 | 0.995540 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.01076e9 | −1.71711 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.23299e9 | 0.942047 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.68467e9 | −1.53188 | −0.765939 | − | 0.642914i | \(-0.777725\pi\) | ||||
−0.765939 | + | 0.642914i | \(0.777725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.64855e8 | −0.108518 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.10447e9 | 0.849820 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.90209e9 | −3.54320 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.99019e9 | 0.780807 | 0.390404 | − | 0.920644i | \(-0.372335\pi\) | ||||
0.390404 | + | 0.920644i | \(0.372335\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.24295e9 | 0.480698 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.03457e9 | 0.394433 | 0.197217 | − | 0.980360i | \(-0.436810\pi\) | ||||
0.197217 | + | 0.980360i | \(0.436810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.35235e8 | −0.0884173 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.75456e9 | −1.39136 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.42414e8 | −0.161652 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.69821e9 | 0.611843 | 0.305922 | − | 0.952057i | \(-0.401035\pi\) | ||||
0.305922 | + | 0.952057i | \(0.401035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32305e9 | 0.470049 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.98691e8 | −0.349899 | −0.174950 | − | 0.984577i | \(-0.555976\pi\) | ||||
−0.174950 | + | 0.984577i | \(0.555976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.24420e9 | −1.46648 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.09833e9 | 0.374288 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.86581e9 | 1.63547 | 0.817735 | − | 0.575594i | \(-0.195229\pi\) | ||||
0.817735 | + | 0.575594i | \(0.195229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.52729e9 | 1.50094 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.94382e9 | −0.635691 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.42438e9 | 1.42734 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.87127e8 | 0.314164 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.21331e8 | −0.0694956 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.29363e9 | −0.710544 | −0.355272 | − | 0.934763i | \(-0.615612\pi\) | ||||
−0.355272 | + | 0.934763i | \(0.615612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.41986e8 | 0.0434000 | 0.0217000 | − | 0.999765i | \(-0.493092\pi\) | ||||
0.0217000 | + | 0.999765i | \(0.493092\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.14164e10 | −3.44328 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.12880e9 | −0.633574 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.78453e9 | −0.524117 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.52088e9 | −0.440823 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.38239e8 | −0.0395444 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.28082e8 | 0.177328 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.31709e9 | 1.20304 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.13560e10 | −3.12366 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.73035e9 | 1.82746 | 0.913729 | − | 0.406324i | \(-0.133190\pi\) | ||||
0.913729 | + | 0.406324i | \(0.133190\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.89575e9 | 0.508139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.68474e9 | 1.23964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.10936e9 | 0.551056 | 0.275528 | − | 0.961293i | \(-0.411147\pi\) | ||||
0.275528 | + | 0.961293i | \(0.411147\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.98173e9 | −1.02700 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.43571e8 | −0.0874955 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.12291e8 | −0.153964 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.55545e8 | −0.212431 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.46338e9 | −1.33958 | −0.669790 | − | 0.742551i | \(-0.733616\pi\) | ||||
−0.669790 | + | 0.742551i | \(0.733616\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.12809e9 | −0.515286 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.19606e9 | −0.525140 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.38438e9 | 0.563113 | 0.281557 | − | 0.959545i | \(-0.409149\pi\) | ||||
0.281557 | + | 0.959545i | \(0.409149\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.22964e9 | 0.986584 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.01831e9 | −0.234605 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.69886e9 | 1.06930 | 0.534650 | − | 0.845073i | \(-0.320443\pi\) | ||||
0.534650 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.04617e9 | −0.459954 | −0.229977 | − | 0.973196i | \(-0.573865\pi\) | ||||
−0.229977 | + | 0.973196i | \(0.573865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.50029e9 | −1.22136 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.78988e9 | −1.92817 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.13969e9 | −1.33055 | −0.665274 | − | 0.746599i | \(-0.731685\pi\) | ||||
−0.665274 | + | 0.746599i | \(0.731685\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.09393e9 | 0.448319 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.13100e10 | 2.39247 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.02638e10 | 2.14520 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.48719e9 | 0.720161 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.29772e9 | 0.264819 | 0.132410 | − | 0.991195i | \(-0.457729\pi\) | ||||
0.132410 | + | 0.991195i | \(0.457729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.10920e9 | −0.626968 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.19800e9 | 0.637269 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.01765e9 | −0.200404 | −0.100202 | − | 0.994967i | \(-0.531949\pi\) | ||||
−0.100202 | + | 0.994967i | \(0.531949\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.15410e10 | 2.24613 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.54562e9 | 1.06670 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.36024e9 | −0.258595 | −0.129298 | − | 0.991606i | \(-0.541272\pi\) | ||||
−0.129298 | + | 0.991606i | \(0.541272\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.83436e9 | 1.09631 | 0.548154 | − | 0.836378i | \(-0.315331\pi\) | ||||
0.548154 | + | 0.836378i | \(0.315331\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.04242e9 | −0.379346 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.64658e9 | −1.22027 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.09613e9 | −0.743384 | −0.371692 | − | 0.928356i | \(-0.621222\pi\) | ||||
−0.371692 | + | 0.928356i | \(0.621222\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.77956e8 | −0.175452 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.16831e8 | −0.162609 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.20044e8 | −0.0911861 | −0.0455930 | − | 0.998960i | \(-0.514518\pi\) | ||||
−0.0455930 | + | 0.998960i | \(0.514518\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.46544e8 | −0.0774108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.87499e9 | 0.664160 | 0.332080 | − | 0.943251i | \(-0.392250\pi\) | ||||
0.332080 | + | 0.943251i | \(0.392250\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.93110e9 | 1.17459 | 0.587293 | − | 0.809375i | \(-0.300194\pi\) | ||||
0.587293 | + | 0.809375i | \(0.300194\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.26004e9 | −0.713827 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.95650e10 | 3.24169 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.45204e10 | 4.01742 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.20745e9 | −0.519665 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.36988e8 | 0.102060 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.27564e9 | −0.202128 | −0.101064 | − | 0.994880i | \(-0.532225\pi\) | ||||
−0.101064 | + | 0.994880i | \(0.532225\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.85006e9 | 1.07345 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.44777e9 | 0.379369 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.05473e10 | 1.61679 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.21502e8 | 0.0487450 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.45969e9 | 1.26868 | 0.634339 | − | 0.773055i | \(-0.281272\pi\) | ||||
0.634339 | + | 0.773055i | \(0.281272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.53383e9 | 0.375871 | 0.187935 | − | 0.982181i | \(-0.439820\pi\) | ||||
0.187935 | + | 0.982181i | \(0.439820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.87423e9 | −1.00871 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.30854e8 | 0.135119 | 0.0675595 | − | 0.997715i | \(-0.478479\pi\) | ||||
0.0675595 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.99061e9 | −1.00383 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.85018e9 | −1.25724 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.54702e9 | 0.639044 | 0.319522 | − | 0.947579i | \(-0.396478\pi\) | ||||
0.319522 | + | 0.947579i | \(0.396478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.58365e9 | −1.19351 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.28997e9 | −0.452599 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.26043e9 | −0.716015 | −0.358007 | − | 0.933719i | \(-0.616544\pi\) | ||||
−0.358007 | + | 0.933719i | \(0.616544\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.97829e8 | −0.134385 | −0.0671925 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671925 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.03968e9 | 0.271809 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.68562e10 | 2.22271 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.52962e8 | −0.0982500 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.04186e9 | 0.909276 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.83017e10 | −2.33864 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.48723e9 | −0.314530 | −0.157265 | − | 0.987556i | \(-0.550268\pi\) | ||||
−0.157265 | + | 0.987556i | \(0.550268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.31101e10 | 2.89226 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.47115e9 | −0.801532 | −0.400766 | − | 0.916180i | \(-0.631256\pi\) | ||||
−0.400766 | + | 0.916180i | \(0.631256\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.75549e10 | 3.37796 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.04312e9 | −0.854575 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.86398e9 | 0.584143 | 0.292071 | − | 0.956397i | \(-0.405655\pi\) | ||||
0.292071 | + | 0.956397i | \(0.405655\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.05189e9 | 0.600533 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.42040e9 | −0.637797 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.53287e9 | −1.11034 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.51546e9 | −0.866527 | −0.433264 | − | 0.901267i | \(-0.642638\pi\) | ||||
−0.433264 | + | 0.901267i | \(0.642638\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.16216e10 | 1.32647 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.88810e10 | 3.26336 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.32470e8 | 0.0371910 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.27026e9 | −0.915902 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.02509e10 | −1.12396 | −0.561978 | − | 0.827152i | \(-0.689960\pi\) | ||||
−0.561978 | + | 0.827152i | \(0.689960\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.30350e8 | 0.100996 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.96158e9 | −0.318319 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.31372e10 | 1.39809 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.01078e9 | 0.528012 | 0.264006 | − | 0.964521i | \(-0.414956\pi\) | ||||
0.264006 | + | 0.964521i | \(0.414956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.44951e8 | 0.0464268 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.81405e9 | −0.704032 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.60286e10 | 1.63993 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.46520e9 | 0.249767 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.55089e10 | −1.55607 | −0.778035 | − | 0.628221i | \(-0.783783\pi\) | ||||
−0.778035 | + | 0.628221i | \(0.783783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.36949e10 | −1.36077 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.79822e9 | −0.176953 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.08470e9 | 0.398086 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.09964e8 | 0.0878322 | 0.0439161 | − | 0.999035i | \(-0.486017\pi\) | ||||
0.0439161 | + | 0.999035i | \(0.486017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.91954e9 | 0.757101 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.11814e9 | 0.484620 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.80412e9 | −0.638128 | −0.319064 | − | 0.947733i | \(-0.603369\pi\) | ||||
−0.319064 | + | 0.947733i | \(0.603369\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.40703e10 | 3.16498 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.38784e9 | −0.863832 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.88530e9 | −0.901020 | −0.450510 | − | 0.892771i | \(-0.648758\pi\) | ||||
−0.450510 | + | 0.892771i | \(0.648758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.97904e9 | 0.268975 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.40609e10 | 1.25763 | 0.628814 | − | 0.777556i | \(-0.283541\pi\) | ||||
0.628814 | + | 0.777556i | \(0.283541\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.42312e10 | −1.26094 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.21897e9 | −0.721432 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.94412e9 | −0.169058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.89107e10 | −1.62918 | −0.814590 | − | 0.580038i | \(-0.803038\pi\) | ||||
−0.814590 | + | 0.580038i | \(0.803038\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.75069e9 | 0.832248 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.81191e10 | −1.53222 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.68703e9 | −0.141348 | −0.0706738 | − | 0.997499i | \(-0.522515\pi\) | ||||
−0.0706738 | + | 0.997499i | \(0.522515\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.02936e9 | −0.583539 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.35093e10 | 1.11118 | 0.555591 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555591 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.45008e10 | −1.18183 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.38685e9 | −0.677304 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.49280e9 | 0.519575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.04375e10 | −1.62064 | −0.810318 | − | 0.585990i | \(-0.800706\pi\) | ||||
−0.810318 | + | 0.585990i | \(0.800706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.59089e9 | −0.753648 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.22437e9 | −0.251083 | −0.125541 | − | 0.992088i | \(-0.540067\pi\) | ||||
−0.125541 | + | 0.992088i | \(0.540067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.69652e10 | 2.85258 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.64819e9 | 0.202524 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.85588e8 | 0.0368033 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.47776e9 | 0.111000 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.97966e9 | 0.147375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.13331e10 | 0.836187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.34167e10 | 0.981147 | 0.490574 | − | 0.871400i | \(-0.336787\pi\) | ||||
0.490574 | + | 0.871400i | \(0.336787\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.60167e9 | −0.695949 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.30921e10 | −0.940573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.69984e10 | 1.21047 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.07934e10 | −2.17357 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.04838e10 | 0.733528 | 0.366764 | − | 0.930314i | \(-0.380466\pi\) | ||||
0.366764 | + | 0.930314i | \(0.380466\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.20502e9 | 0.152932 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.42179e10 | −0.977508 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.51221e10 | −1.03064 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.69416e10 | 2.49592 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.04800e9 | 0.539052 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.66031e9 | 0.575060 | 0.287530 | − | 0.957772i | \(-0.407166\pi\) | ||||
0.287530 | + | 0.957772i | \(0.407166\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.78352e9 | −0.512393 | −0.256196 | − | 0.966625i | \(-0.582469\pi\) | ||||
−0.256196 | + | 0.966625i | \(0.582469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.45239e9 | 0.160056 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.18186e10 | 1.41181 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.47528e9 | 0.479568 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.07940e10 | −0.686575 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.91243e9 | 0.499009 | 0.249505 | − | 0.968374i | \(-0.419732\pi\) | ||||
0.249505 | + | 0.968374i | \(0.419732\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.48091e9 | 0.280199 | 0.140100 | − | 0.990137i | \(-0.455258\pi\) | ||||
0.140100 | + | 0.990137i | \(0.455258\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.81332e10 | 2.36437 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.15443e8 | 0.0439851 | 0.0219926 | − | 0.999758i | \(-0.492999\pi\) | ||||
0.0219926 | + | 0.999758i | \(0.492999\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.36866e10 | −1.44398 | −0.721990 | − | 0.691903i | \(-0.756773\pi\) | ||||
−0.721990 | + | 0.691903i | \(0.756773\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.48645e9 | −0.452556 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.53668e10 | −1.52057 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.32246e10 | 1.38053 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.79153e10 | 1.05605 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.37629e10 | −1.38909 | −0.694547 | − | 0.719447i | \(-0.744395\pi\) | ||||
−0.694547 | + | 0.719447i | \(0.744395\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.69000e10 | −0.979715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.86048e9 | 0.221945 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.92800e10 | 1.09928 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.05733e10 | 1.16336 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.25860e10 | 0.705846 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.03893e9 | 0.113409 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.28503e10 | −1.81225 | −0.906126 | − | 0.423009i | \(-0.860974\pi\) | ||||
−0.906126 | + | 0.423009i | \(0.860974\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.22494e10 | −0.670242 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.67832e9 | −0.308168 | −0.154084 | − | 0.988058i | \(-0.549243\pi\) | ||||
−0.154084 | + | 0.988058i | \(0.549243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.22964e10 | 0.661914 | 0.330957 | − | 0.943646i | \(-0.392628\pi\) | ||||
0.330957 | + | 0.943646i | \(0.392628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.38220e9 | 0.0738006 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.75550e10 | −0.929743 | −0.464871 | − | 0.885378i | \(-0.653899\pi\) | ||||
−0.464871 | + | 0.885378i | \(0.653899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.88523e9 | −0.204108 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.82290e9 | 0.407663 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.04518e9 | 0.105721 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.71931e9 | 0.447115 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.00241e10 | −1.01860 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.28704e11 | −6.49479 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.75144e7 | −0.00488169 | −0.00244084 | − | 0.999997i | \(-0.500777\pi\) | ||||
−0.00244084 | + | 0.999997i | \(0.500777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.54848e10 | −0.769035 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.68618e10 | −0.830786 | −0.415393 | − | 0.909642i | \(-0.636356\pi\) | ||||
−0.415393 | + | 0.909642i | \(0.636356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.81287e10 | −1.37495 | −0.687476 | − | 0.726207i | \(-0.741281\pi\) | ||||
−0.687476 | + | 0.726207i | \(0.741281\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.09733e10 | 1.01710 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.49073e10 | −0.717241 | −0.358621 | − | 0.933483i | \(-0.616753\pi\) | ||||
−0.358621 | + | 0.933483i | \(0.616753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.57664e9 | −0.361676 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.40136e9 | 0.161095 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.22053e9 | 0.151338 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.57817e10 | 3.53333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.52879e9 | 0.302036 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.16653e9 | 0.145353 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.29270e10 | 1.04426 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.12780e10 | 0.961664 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.32779e10 | 1.49240 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00171e10 | −0.890790 | −0.445395 | − | 0.895334i | \(-0.646937\pi\) | ||||
−0.445395 | + | 0.895334i | \(0.646937\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.54676e9 | −0.421582 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.55429e10 | 0.681113 | 0.340556 | − | 0.940224i | \(-0.389385\pi\) | ||||
0.340556 | + | 0.940224i | \(0.389385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.77779e10 | −1.64282 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.49090e10 | 2.36957 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.65692e10 | 1.13785 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.07850e9 | 0.300841 | 0.150420 | − | 0.988622i | \(-0.451937\pi\) | ||||
0.150420 | + | 0.988622i | \(0.451937\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.97394e9 | −0.420686 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.37252e9 | −0.0574532 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.10609e10 | −0.459509 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.95205e9 | 0.410330 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.26783e9 | −0.379248 | −0.189624 | − | 0.981857i | \(-0.560727\pi\) | ||||
−0.189624 | + | 0.981857i | \(0.560727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.70493e10 | −1.50472 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.20419e9 | −0.129161 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.85495e10 | −1.54233 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.95508e10 | −1.17349 | −0.586746 | − | 0.809771i | \(-0.699591\pi\) | ||||
−0.586746 | + | 0.809771i | \(0.699591\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.63136e10 | −0.643014 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.39298e10 | 0.544979 | 0.272489 | − | 0.962159i | \(-0.412153\pi\) | ||||
0.272489 | + | 0.962159i | \(0.412153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.06420e9 | 0.0413269 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.71257e10 | −3.74389 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.48316e10 | 0.950122 | 0.475061 | − | 0.879953i | \(-0.342426\pi\) | ||||
0.475061 | + | 0.879953i | \(0.342426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.40452e10 | 0.533454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.94189e9 | 0.0732137 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.01791e10 | −1.12949 | −0.564744 | − | 0.825266i | \(-0.691025\pi\) | ||||
−0.564744 | + | 0.825266i | \(0.691025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.65515e10 | −3.58713 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.26658e9 | 0.120476 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.56373e10 | −0.572526 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.14339e9 | 0.0415589 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.41279e9 | 0.0509783 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.67567e10 | 1.31671 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.93661e10 | 1.04437 | 0.522184 | − | 0.852833i | \(-0.325118\pi\) | ||||
0.522184 | + | 0.852833i | \(0.325118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.16472e9 | −0.252968 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.39542e10 | 0.839683 | 0.419841 | − | 0.907598i | \(-0.362086\pi\) | ||||
0.419841 | + | 0.907598i | \(0.362086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.93961e10 | −3.11117 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.54177e10 | −1.22378 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.91663e10 | 1.00058 | 0.500289 | − | 0.865859i | \(-0.333227\pi\) | ||||
0.500289 | + | 0.865859i | \(0.333227\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.53513e10 | −2.22595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.05377e10 | 0.356372 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.44637e9 | −0.149303 | −0.0746514 | − | 0.997210i | \(-0.523784\pi\) | ||||
−0.0746514 | + | 0.997210i | \(0.523784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.61375e10 | 1.87166 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.16707e9 | 0.303473 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.63826e10 | 0.538514 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.36917e10 | −1.09968 | −0.549838 | − | 0.835271i | \(-0.685311\pi\) | ||||
−0.549838 | + | 0.835271i | \(0.685311\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.64017e9 | −0.312437 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.73474e10 | 3.13288 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.98360e9 | −0.255132 | −0.127566 | − | 0.991830i | \(-0.540717\pi\) | ||||
−0.127566 | + | 0.991830i | \(0.540717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.36069e9 | −0.170115 |
(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 | 592.8.a.c.1.3 | 6 | ||
4.3 | odd | 2 | 74.8.a.c.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.8.a.c.1.4 | ✓ | 6 | 4.3 | odd | 2 | ||
592.8.a.c.1.3 | 6 | 1.1 | even | 1 | trivial |