Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,48,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 48, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 48);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 48 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(223.852260248\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 832803191366x^{2} + 3710135215485780x + 13175318942671469337000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{46}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(129356.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 | ||||||||
\(3\) | 2.21918e11 | 1.36095 | 0.680476 | − | 0.732770i | \(-0.261773\pi\) | ||||
0.680476 | + | 0.732770i | \(0.261773\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.08341e16 | −1.15674 | −0.578370 | − | 0.815774i | \(-0.696311\pi\) | ||||
−0.578370 | + | 0.815774i | \(0.696311\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.11073e20 | −1.53393 | −0.766963 | − | 0.641691i | \(-0.778233\pi\) | ||||
−0.766963 | + | 0.641691i | \(0.778233\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.26588e22 | 0.852193 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.19449e24 | 0.402210 | 0.201105 | − | 0.979570i | \(-0.435547\pi\) | ||||
0.201105 | + | 0.979570i | \(0.435547\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.71503e24 | −0.0180345 | −0.00901727 | − | 0.999959i | \(-0.502870\pi\) | ||||
−0.00901727 | + | 0.999959i | \(0.502870\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.84264e27 | −1.57427 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.17417e29 | 1.42620 | 0.713102 | − | 0.701060i | \(-0.247289\pi\) | ||||
0.713102 | + | 0.701060i | \(0.247289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.65620e30 | 1.47368 | 0.736840 | − | 0.676067i | \(-0.236317\pi\) | ||||
0.736840 | + | 0.676067i | \(0.236317\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.46491e31 | −2.08760 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.41759e31 | −0.541006 | −0.270503 | − | 0.962719i | \(-0.587190\pi\) | ||||
−0.270503 | + | 0.962719i | \(0.587190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.40198e32 | 0.338048 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.72142e32 | −0.201159 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.03639e34 | −0.445833 | −0.222916 | − | 0.974838i | \(-0.571558\pi\) | ||||
−0.222916 | + | 0.974838i | \(0.571558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.80854e34 | 0.341789 | 0.170895 | − | 0.985289i | \(-0.445334\pi\) | ||||
0.170895 | + | 0.985289i | \(0.445334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.65078e35 | 0.547389 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.42483e36 | 1.77435 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.41184e36 | 1.18073 | 0.590365 | − | 0.807136i | \(-0.298984\pi\) | ||||
0.590365 | + | 0.807136i | \(0.298984\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.02513e35 | −0.0245442 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.68510e37 | 0.966560 | 0.483280 | − | 0.875466i | \(-0.339445\pi\) | ||||
0.483280 | + | 0.875466i | \(0.339445\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.17109e38 | 0.891597 | 0.445799 | − | 0.895133i | \(-0.352920\pi\) | ||||
0.445799 | + | 0.895133i | \(0.352920\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.98663e38 | −0.985766 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.73873e39 | −1.39075 | −0.695375 | − | 0.718647i | \(-0.744762\pi\) | ||||
−0.695375 | + | 0.718647i | \(0.744762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.09387e39 | 1.35293 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.60570e40 | 1.94100 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.29394e39 | 0.250195 | 0.125097 | − | 0.992144i | \(-0.460076\pi\) | ||||
0.125097 | + | 0.992144i | \(0.460076\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.68309e40 | −0.465253 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.67541e41 | 2.00561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.09596e40 | −0.172182 | −0.0860912 | − | 0.996287i | \(-0.527438\pi\) | ||||
−0.0860912 | + | 0.996287i | \(0.527438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.43092e41 | −0.712889 | −0.356444 | − | 0.934317i | \(-0.616011\pi\) | ||||
−0.356444 | + | 0.934317i | \(0.616011\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.51678e42 | −1.30720 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.37153e40 | 0.0208613 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.19612e43 | −1.46223 | −0.731114 | − | 0.682255i | \(-0.760999\pi\) | ||||
−0.731114 | + | 0.682255i | \(0.760999\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.20226e43 | −0.736283 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.64034e43 | −0.826205 | −0.413103 | − | 0.910684i | \(-0.635555\pi\) | ||||
−0.413103 | + | 0.910684i | \(0.635555\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.87700e43 | 0.631552 | 0.315776 | − | 0.948834i | \(-0.397735\pi\) | ||||
0.315776 | + | 0.948834i | \(0.397735\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.33042e43 | 0.460068 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.32675e44 | −0.616961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.22812e44 | 0.312612 | 0.156306 | − | 0.987709i | \(-0.450041\pi\) | ||||
0.156306 | + | 0.987709i | \(0.450041\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.96015e44 | −1.12596 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.65007e45 | −1.31573 | −0.657867 | − | 0.753134i | \(-0.728541\pi\) | ||||
−0.657867 | + | 0.753134i | \(0.728541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.62045e45 | −1.64975 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.29995e45 | −0.606757 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00200e45 | −0.928177 | −0.464089 | − | 0.885789i | \(-0.653618\pi\) | ||||
−0.464089 | + | 0.885789i | \(0.653618\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.01566e44 | 0.0276637 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.45183e45 | 0.465159 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.10674e46 | −1.70466 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.75152e46 | −0.358328 | −0.179164 | − | 0.983819i | \(-0.557339\pi\) | ||||
−0.179164 | + | 0.983819i | \(0.557339\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.70656e46 | 0.342761 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.93699e46 | −0.232461 | −0.116231 | − | 0.993222i | \(-0.537081\pi\) | ||||
−0.116231 | + | 0.993222i | \(0.537081\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.42094e46 | 0.120868 | 0.0604338 | − | 0.998172i | \(-0.480752\pi\) | ||||
0.0604338 | + | 0.998172i | \(0.480752\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.60032e47 | 2.41481 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.58808e47 | 0.731718 | 0.365859 | − | 0.930670i | \(-0.380775\pi\) | ||||
0.365859 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00272e47 | −0.264301 | −0.132150 | − | 0.991230i | \(-0.542188\pi\) | ||||
−0.132150 | + | 0.991230i | \(0.542188\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.86674e48 | 1.60692 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.99882e47 | −0.282829 | −0.141414 | − | 0.989950i | \(-0.545165\pi\) | ||||
−0.141414 | + | 0.989950i | \(0.545165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.67046e48 | 0.625803 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.15192e46 | −0.0153689 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.30419e49 | −2.18769 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.39295e48 | −0.838227 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.70546e49 | 1.31544 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.45027e49 | 0.765706 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.93451e47 | −0.0324850 | −0.0162425 | − | 0.999868i | \(-0.505170\pi\) | ||||
−0.0162425 | + | 0.999868i | \(0.505170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.81804e49 | 1.21342 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.86188e49 | −1.55471 | −0.777357 | − | 0.629060i | \(-0.783440\pi\) | ||||
−0.777357 | + | 0.629060i | \(0.783440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.83959e50 | −2.26052 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.68917e49 | 0.232688 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.56850e50 | 0.960619 | 0.480310 | − | 0.877099i | \(-0.340524\pi\) | ||||
0.480310 | + | 0.877099i | \(0.340524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.09943e50 | −0.914648 | −0.457324 | − | 0.889300i | \(-0.651192\pi\) | ||||
−0.457324 | + | 0.889300i | \(0.651192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.07773e50 | −1.89275 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.24306e48 | −0.00725368 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.19563e50 | 0.515713 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.57426e51 | 1.84128 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.17929e51 | 1.00402 | 0.502009 | − | 0.864862i | \(-0.332594\pi\) | ||||
0.502009 | + | 0.864862i | \(0.332594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.05626e51 | 0.657377 | 0.328689 | − | 0.944438i | \(-0.393393\pi\) | ||||
0.328689 | + | 0.944438i | \(0.393393\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.66053e51 | 1.21540 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.17433e51 | −0.395361 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.43063e51 | −0.605447 | −0.302724 | − | 0.953078i | \(-0.597896\pi\) | ||||
−0.302724 | + | 0.953078i | \(0.597896\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.84057e51 | 0.340503 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.01748e51 | 0.829863 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.76362e51 | −0.904222 | −0.452111 | − | 0.891962i | \(-0.649329\pi\) | ||||
−0.452111 | + | 0.891962i | \(0.649329\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.17344e51 | −0.633187 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.63045e52 | −1.53530 | −0.767648 | − | 0.640871i | \(-0.778573\pi\) | ||||
−0.767648 | + | 0.640871i | \(0.778573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.26567e52 | −0.999675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.75275e52 | 1.25586 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.14535e52 | −0.800913 | −0.400456 | − | 0.916316i | \(-0.631148\pi\) | ||||
−0.400456 | + | 0.916316i | \(0.631148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.66795e52 | −0.518541 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.57472e52 | −0.234332 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.75744e52 | 0.657935 | 0.328968 | − | 0.944341i | \(-0.393299\pi\) | ||||
0.328968 | + | 0.944341i | \(0.393299\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.66382e53 | 1.46440 | 0.732199 | − | 0.681091i | \(-0.238494\pi\) | ||||
0.732199 | + | 0.681091i | \(0.238494\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.42714e53 | −0.970208 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.59371e53 | −1.36580 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.40253e53 | 0.573634 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.68714e52 | 0.308563 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.33768e53 | 0.332713 | 0.166356 | − | 0.986066i | \(-0.446800\pi\) | ||||
0.166356 | + | 0.986066i | \(0.446800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.53394e53 | 1.27227 | 0.636134 | − | 0.771579i | \(-0.280533\pi\) | ||||
0.636134 | + | 0.771579i | \(0.280533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.85779e52 | 0.0283912 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.89833e53 | 1.19016 | 0.595081 | − | 0.803666i | \(-0.297120\pi\) | ||||
0.595081 | + | 0.803666i | \(0.297120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.17074e54 | −1.11023 | −0.555117 | − | 0.831772i | \(-0.687327\pi\) | ||||
−0.555117 | + | 0.831772i | \(0.687327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.65440e54 | −1.99002 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.15115e54 | 0.683875 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.36963e54 | −1.11806 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.22756e54 | −0.461041 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.97831e54 | 0.592729 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.13707e54 | −0.272364 | −0.136182 | − | 0.990684i | \(-0.543483\pi\) | ||||
−0.136182 | + | 0.990684i | \(0.543483\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.85938e54 | −1.12443 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.69435e54 | −1.03135 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.23026e54 | −0.524280 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.60377e54 | 0.859512 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.18791e53 | −0.0257210 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.34179e55 | −1.52892 | −0.764459 | − | 0.644672i | \(-0.776994\pi\) | ||||
−0.764459 | + | 0.644672i | \(0.776994\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.44259e54 | 0.288082 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.06780e55 | −1.31892 | −0.659462 | − | 0.751738i | \(-0.729216\pi\) | ||||
−0.659462 | + | 0.751738i | \(0.729216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.77257e55 | −1.66962 | −0.834811 | − | 0.550536i | \(-0.814423\pi\) | ||||
−0.834811 | + | 0.550536i | \(0.814423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.94430e55 | −0.839655 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.85272e55 | 0.431464 | 0.215732 | − | 0.976453i | \(-0.430786\pi\) | ||||
0.215732 | + | 0.976453i | \(0.430786\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.44462e55 | 1.60874 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.72543e55 | 0.425450 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.05119e55 | 0.775336 | 0.387668 | − | 0.921799i | \(-0.373281\pi\) | ||||
0.387668 | + | 0.921799i | \(0.373281\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.35331e55 | 0.353242 | 0.176621 | − | 0.984279i | \(-0.443483\pi\) | ||||
0.176621 | + | 0.984279i | \(0.443483\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.53461e56 | −1.33122 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.18733e56 | −1.56499 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.49663e54 | −0.0265771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.66181e56 | −1.79065 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.39203e56 | −1.37444 | −0.687222 | − | 0.726448i | \(-0.741170\pi\) | ||||
−0.687222 | + | 0.726448i | \(0.741170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.47124e55 | −0.217598 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.03443e56 | −2.24523 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.45663e56 | −1.73426 | −0.867130 | − | 0.498082i | \(-0.834038\pi\) | ||||
−0.867130 | + | 0.498082i | \(0.834038\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.34329e56 | −1.81115 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.34834e56 | −0.379935 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.28505e57 | 1.73764 | 0.868819 | − | 0.495129i | \(-0.164879\pi\) | ||||
0.868819 | + | 0.495129i | \(0.164879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.55736e56 | −0.289410 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.33195e57 | −1.26321 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.52143e57 | 1.21081 | 0.605403 | − | 0.795919i | \(-0.293012\pi\) | ||||
0.605403 | + | 0.795919i | \(0.293012\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.08539e56 | −0.139447 | −0.0697235 | − | 0.997566i | \(-0.522212\pi\) | ||||
−0.0697235 | + | 0.997566i | \(0.522212\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.69230e55 | 0.0376490 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.86913e56 | 0.135967 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.91573e57 | −1.96478 | −0.982388 | − | 0.186853i | \(-0.940171\pi\) | ||||
−0.982388 | + | 0.186853i | \(0.940171\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.62969e56 | 0.291270 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.99077e57 | 0.853462 | 0.426731 | − | 0.904379i | \(-0.359665\pi\) | ||||
0.426731 | + | 0.904379i | \(0.359665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.40523e57 | 0.580999 | 0.290499 | − | 0.956875i | \(-0.406179\pi\) | ||||
0.290499 | + | 0.956875i | \(0.406179\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.13328e58 | −2.31997 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.53607e57 | −1.48263 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00882e57 | 1.03406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.88695e57 | −0.487667 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.67134e57 | 0.819374 | 0.409687 | − | 0.912226i | \(-0.365638\pi\) | ||||
0.409687 | + | 0.912226i | \(0.365638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.18797e57 | 0.199170 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.04176e57 | −0.0809081 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.47089e56 | 0.00975679 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.41149e58 | −1.36764 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.51772e57 | −0.316369 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.98291e58 | 0.824627 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.66078e58 | −0.592325 | −0.296162 | − | 0.955138i | \(-0.595707\pi\) | ||||
−0.296162 | + | 0.955138i | \(0.595707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.37251e57 | 0.164495 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.17917e58 | 0.573352 | 0.286676 | − | 0.958028i | \(-0.407450\pi\) | ||||
0.286676 | + | 0.958028i | \(0.407450\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.52774e58 | 1.02468 | 0.512342 | − | 0.858782i | \(-0.328778\pi\) | ||||
0.512342 | + | 0.858782i | \(0.328778\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.76026e58 | 1.51209 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.03868e58 | −1.01403 | −0.507014 | − | 0.861938i | \(-0.669251\pi\) | ||||
−0.507014 | + | 0.861938i | \(0.669251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.23796e58 | −0.179319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.96260e58 | 0.995833 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.94466e59 | 2.10177 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.52143e56 | −0.00609655 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.44440e58 | −0.359701 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.04199e59 | 2.13331 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.03088e57 | 0.0123517 | 0.00617585 | − | 0.999981i | \(-0.498034\pi\) | ||||
0.00617585 | + | 0.999981i | \(0.498034\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.90602e59 | 1.00621 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.68811e59 | 1.69142 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.81636e59 | −0.724268 | −0.362134 | − | 0.932126i | \(-0.617952\pi\) | ||||
−0.362134 | + | 0.932126i | \(0.617952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.10933e59 | −0.384917 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.54925e58 | 0.137471 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.05545e59 | −0.541370 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.70706e59 | 0.851689 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.01600e59 | −0.203776 | −0.101888 | − | 0.994796i | \(-0.532488\pi\) | ||||
−0.101888 | + | 0.994796i | \(0.532488\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.81199e59 | −0.843193 | −0.421596 | − | 0.906784i | \(-0.638530\pi\) | ||||
−0.421596 | + | 0.906784i | \(0.638530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.36789e57 | 0.00362781 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.19790e60 | 1.60588 | 0.802941 | − | 0.596059i | \(-0.203268\pi\) | ||||
0.802941 | + | 0.596059i | \(0.203268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.14123e59 | 0.955705 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.89423e60 | −2.97735 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.62063e58 | 0.0777713 | 0.0388857 | − | 0.999244i | \(-0.487619\pi\) | ||||
0.0388857 | + | 0.999244i | \(0.487619\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.47995e60 | 1.17173 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.64063e60 | −1.14079 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.19544e60 | −0.730542 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.19138e60 | 1.17778 | 0.588892 | − | 0.808212i | \(-0.299565\pi\) | ||||
0.588892 | + | 0.808212i | \(0.299565\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.74135e60 | 0.823696 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.21233e59 | −0.383780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.32206e60 | 0.485393 | 0.242696 | − | 0.970102i | \(-0.421968\pi\) | ||||
0.242696 | + | 0.970102i | \(0.421968\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.21840e60 | 1.04209 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.81384e58 | 0.00804039 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.08671e60 | −1.53589 | −0.767947 | − | 0.640513i | \(-0.778722\pi\) | ||||
−0.767947 | + | 0.640513i | \(0.778722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.98273e59 | −0.0442106 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.42858e60 | −0.675995 | −0.337997 | − | 0.941147i | \(-0.609750\pi\) | ||||
−0.337997 | + | 0.941147i | \(0.609750\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.09092e60 | 0.713664 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.91942e60 | 0.759813 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.62159e60 | −0.769208 | −0.384604 | − | 0.923082i | \(-0.625662\pi\) | ||||
−0.384604 | + | 0.923082i | \(0.625662\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.36118e60 | −0.771585 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.96661e61 | −2.11589 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.78680e60 | −0.361611 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.94362e61 | −1.64829 | −0.824146 | − | 0.566377i | \(-0.808345\pi\) | ||||
−0.824146 | + | 0.566377i | \(0.808345\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.08238e61 | −3.07646 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.48633e61 | −1.66597 | −0.832984 | − | 0.553296i | \(-0.813370\pi\) | ||||
−0.832984 | + | 0.553296i | \(0.813370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.03403e59 | −0.00616401 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.45444e61 | 1.30244 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.00478e61 | 0.474902 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.77202e61 | 0.746397 | 0.373199 | − | 0.927751i | \(-0.378261\pi\) | ||||
0.373199 | + | 0.927751i | \(0.378261\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.48079e61 | 1.30736 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.88170e60 | 0.264115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.08785e61 | 1.52196 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.65902e61 | −1.24479 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.32251e61 | −1.50959 | −0.754797 | − | 0.655958i | \(-0.772265\pi\) | ||||
−0.754797 | + | 0.655958i | \(0.772265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.68512e61 | 1.85416 | 0.927078 | − | 0.374868i | \(-0.122312\pi\) | ||||
0.927078 | + | 0.374868i | \(0.122312\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.20563e61 | −1.18519 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.82033e61 | 0.482126 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.14301e61 | 1.09352 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.19694e59 | −0.00987192 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.27735e61 | −0.771898 | −0.385949 | − | 0.922520i | \(-0.626126\pi\) | ||||
−0.385949 | + | 0.922520i | \(0.626126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.16297e61 | −0.679711 | −0.339855 | − | 0.940478i | \(-0.610378\pi\) | ||||
−0.339855 | + | 0.940478i | \(0.610378\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.09167e61 | 0.701861 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.97261e61 | −0.797269 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.66474e62 | 1.32871 | 0.664353 | − | 0.747419i | \(-0.268707\pi\) | ||||
0.664353 | + | 0.747419i | \(0.268707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.60739e62 | 1.15296 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.29305e62 | −0.833929 | −0.416965 | − | 0.908923i | \(-0.636906\pi\) | ||||
−0.416965 | + | 0.908923i | \(0.636906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.85066e62 | 1.07366 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.61705e62 | 1.36642 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.47587e62 | −0.693839 | −0.346920 | − | 0.937895i | \(-0.612772\pi\) | ||||
−0.346920 | + | 0.937895i | \(0.612772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.17975e61 | 0.388760 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.34404e62 | 0.894659 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.29851e60 | −0.0319997 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.90700e62 | −0.591998 | −0.295999 | − | 0.955188i | \(-0.595653\pi\) | ||||
−0.295999 | + | 0.955188i | \(0.595653\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.02404e62 | −0.286893 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.19785e61 | 0.0555939 | 0.0277970 | − | 0.999614i | \(-0.491151\pi\) | ||||
0.0277970 | + | 0.999614i | \(0.491151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.68005e62 | 0.383857 | 0.191929 | − | 0.981409i | \(-0.438526\pi\) | ||||
0.191929 | + | 0.981409i | \(0.438526\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.60604e62 | −0.538068 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.37225e62 | −0.256145 | −0.128073 | − | 0.991765i | \(-0.540879\pi\) | ||||
−0.128073 | + | 0.991765i | \(0.540879\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.32856e63 | 2.24295 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.39400e62 | −0.823985 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.59334e62 | 0.358610 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.97815e62 | 0.498175 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.87931e62 | 0.213214 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.62356e63 | 1.66949 | 0.834745 | − | 0.550637i | \(-0.185615\pi\) | ||||
0.834745 | + | 0.550637i | \(0.185615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.28384e61 | −0.0212939 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.33539e63 | 1.12940 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.40066e62 | 0.414492 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.09889e62 | −0.0765640 | −0.0382820 | − | 0.999267i | \(-0.512189\pi\) | ||||
−0.0382820 | + | 0.999267i | \(0.512189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.94481e63 | −1.23060 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.66145e63 | −1.53004 | −0.765020 | − | 0.644007i | \(-0.777271\pi\) | ||||
−0.765020 | + | 0.644007i | \(0.777271\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.21690e63 | −0.635849 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.34544e62 | −0.396485 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.93270e63 | 1.26734 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.22266e63 | 0.873997 | 0.436999 | − | 0.899462i | \(-0.356041\pi\) | ||||
0.436999 | + | 0.899462i | \(0.356041\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.83743e63 | −2.08947 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.07975e63 | −1.00385 | −0.501924 | − | 0.864912i | \(-0.667374\pi\) | ||||
−0.501924 | + | 0.864912i | \(0.667374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.05595e62 | 0.268897 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.02793e63 | −1.36051 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.72771e63 | −1.41291 | −0.706453 | − | 0.707760i | \(-0.749706\pi\) | ||||
−0.706453 | + | 0.707760i | \(0.749706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.30631e63 | −0.968754 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.44444e63 | −0.296443 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.46476e62 | −0.139812 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.27137e63 | −0.559374 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.98009e63 | −1.09000 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.17638e64 | 1.67826 | 0.839132 | − | 0.543928i | \(-0.183064\pi\) | ||||
0.839132 | + | 0.543928i | \(0.183064\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.38331e63 | 0.832254 | 0.416127 | − | 0.909306i | \(-0.363387\pi\) | ||||
0.416127 | + | 0.909306i | \(0.363387\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.92066e63 | −0.705710 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.47188e63 | 0.487461 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.09283e63 | −0.707313 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.60786e63 | −0.146733 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.08652e62 | −0.0174315 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.10635e64 | −0.846408 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.27768e64 | 0.895419 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.47354e63 | 0.544163 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.64596e62 | −0.0450087 | −0.0225043 | − | 0.999747i | \(-0.507164\pi\) | ||||
−0.0225043 | + | 0.999747i | \(0.507164\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.69231e64 | 1.99298 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.17521e63 | 0.305727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.77108e64 | 0.804519 | 0.402259 | − | 0.915526i | \(-0.368225\pi\) | ||||
0.402259 | + | 0.915526i | \(0.368225\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.45717e64 | −0.607519 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.71648e64 | −0.657015 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.36411e64 | −0.479523 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.75592e64 | −1.85879 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.48786e64 | 0.441535 | 0.220767 | − | 0.975327i | \(-0.429144\pi\) | ||||
0.220767 | + | 0.975327i | \(0.429144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.89456e62 | −0.0160795 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.11247e64 | 0.780689 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.11252e64 | −0.948770 | −0.474385 | − | 0.880317i | \(-0.657330\pi\) | ||||
−0.474385 | + | 0.880317i | \(0.657330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.54134e64 | 0.327160 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.84157e64 | 1.72714 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.04135e64 | −0.906586 | −0.453293 | − | 0.891362i | \(-0.649751\pi\) | ||||
−0.453293 | + | 0.891362i | \(0.649751\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.68666e64 | −0.279305 | −0.139652 | − | 0.990201i | \(-0.544598\pi\) | ||||
−0.139652 | + | 0.990201i | \(0.544598\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.96856e64 | 0.452806 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.30129e64 | −0.182886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.79059e63 | −0.126817 | −0.0634084 | − | 0.997988i | \(-0.520197\pi\) | ||||
−0.0634084 | + | 0.997988i | \(0.520197\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.45000e65 | 1.73150 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.83279e65 | 2.01824 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.90700e63 | 0.100631 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.89689e63 | 0.0177778 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.78831e64 | −0.241183 | −0.120591 | − | 0.992702i | \(-0.538479\pi\) | ||||
−0.120591 | + | 0.992702i | \(0.538479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.30770e64 | 0.503688 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.19662e65 | 1.61975 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.49430e65 | 1.01778 | 0.508889 | − | 0.860832i | \(-0.330056\pi\) | ||||
0.508889 | + | 0.860832i | \(0.330056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.02134e65 | 2.53059 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.59809e65 | −1.51098 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.99285e65 | −1.60899 | −0.804496 | − | 0.593957i | \(-0.797565\pi\) | ||||
−0.804496 | + | 0.593957i | \(0.797565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.56472e65 | −0.777831 | −0.388916 | − | 0.921273i | \(-0.627150\pi\) | ||||
−0.388916 | + | 0.921273i | \(0.627150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.71025e65 | −1.24610 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.27955e65 | 0.969611 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.61159e64 | −0.338961 | −0.169480 | − | 0.985534i | \(-0.554209\pi\) | ||||
−0.169480 | + | 0.985534i | \(0.554209\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.55462e65 | 0.930721 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.43572e63 | 0.0250816 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.58806e65 | −0.496072 | −0.248036 | − | 0.968751i | \(-0.579785\pi\) | ||||
−0.248036 | + | 0.968751i | \(0.579785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.25864e65 | −1.52163 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.01082e65 | −1.61151 | −0.805753 | − | 0.592251i | \(-0.798239\pi\) | ||||
−0.805753 | + | 0.592251i | \(0.798239\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.62211e65 | −0.899978 | −0.449989 | − | 0.893034i | \(-0.648572\pi\) | ||||
−0.449989 | + | 0.893034i | \(0.648572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.72491e64 | 0.108828 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.66660e65 | 1.42376 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.17847e65 | −1.22377 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.39022e65 | 0.806677 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.87695e65 | 1.68396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.92614e65 | −1.57069 | −0.785345 | − | 0.619059i | \(-0.787514\pi\) | ||||
−0.785345 | + | 0.619059i | \(0.787514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.52336e65 | −0.370675 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.75487e64 | 0.0375768 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.92601e64 | −0.0243995 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.98268e65 | −0.704086 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.70256e66 | −1.86183 | −0.930915 | − | 0.365236i | \(-0.880988\pi\) | ||||
−0.930915 | + | 0.365236i | \(0.880988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.06741e65 | −0.819929 | −0.409964 | − | 0.912102i | \(-0.634459\pi\) | ||||
−0.409964 | + | 0.912102i | \(0.634459\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.48560e66 | −1.40361 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.90914e65 | 0.255573 | 0.127786 | − | 0.991802i | \(-0.459213\pi\) | ||||
0.127786 | + | 0.991802i | \(0.459213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.47603e64 | −0.0692536 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.38770e65 | −0.713520 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.73213e65 | 0.263935 | 0.131967 | − | 0.991254i | \(-0.457871\pi\) | ||||
0.131967 | + | 0.991254i | \(0.457871\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.73248e66 | 1.79840 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.78482e65 | 0.538204 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.84754e65 | −0.447637 | −0.223819 | − | 0.974631i | \(-0.571852\pi\) | ||||
−0.223819 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.69856e65 | 0.302713 | 0.151356 | − | 0.988479i | \(-0.451636\pi\) | ||||
0.151356 | + | 0.988479i | \(0.451636\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.07454e64 | −0.0350050 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.67221e66 | 2.61483 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.61476e65 | 0.241198 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.19686e66 | −2.08079 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.68164e65 | −0.286731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.43578e66 | 1.54389 | 0.771945 | − | 0.635689i | \(-0.219284\pi\) | ||||
0.771945 | + | 0.635689i | \(0.219284\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.09487e65 | −0.0680013 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.52339e66 | 1.06691 | 0.533454 | − | 0.845829i | \(-0.320894\pi\) | ||||
0.533454 | + | 0.845829i | \(0.320894\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.94547e66 | 0.549648 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.80801e66 | −1.79499 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.36076e66 | 0.827087 | 0.413543 | − | 0.910484i | \(-0.364291\pi\) | ||||
0.413543 | + | 0.910484i | \(0.364291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.83633e66 | −1.11119 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.05912e67 | −2.27228 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.25183e64 | −0.00451214 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.04623e66 | −0.383020 | −0.191510 | − | 0.981491i | \(-0.561338\pi\) | ||||
−0.191510 | + | 0.981491i | \(0.561338\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.00626e66 | −0.525770 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.47341e66 | 1.05801 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.02362e66 | 1.37851 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.11151e66 | 0.587203 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.21798e67 | −1.62655 | −0.813275 | − | 0.581879i | \(-0.802318\pi\) | ||||
−0.813275 | + | 0.581879i | \(0.802318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.39317e67 | 1.74002 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.87401e67 | 2.18942 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.26221e66 | 0.356578 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.52742e67 | 1.56233 | 0.781166 | − | 0.624323i | \(-0.214625\pi\) | ||||
0.781166 | + | 0.624323i | \(0.214625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.78278e66 | 0.266405 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.06331e66 | −0.184910 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.99969e64 | 0.00839063 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.34287e67 | 1.05520 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.76158e66 | −0.424045 | −0.212023 | − | 0.977265i | \(-0.568005\pi\) | ||||
−0.212023 | + | 0.977265i | \(0.568005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.68901e66 | −0.185402 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.44159e66 | 0.480746 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.48940e66 | −0.150713 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.68143e65 | 0.0435896 | 0.0217948 | − | 0.999762i | \(-0.493062\pi\) | ||||
0.0217948 | + | 0.999762i | \(0.493062\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.28906e67 | −0.685768 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.54923e67 | 1.27160 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.73856e67 | 1.74889 | 0.874443 | − | 0.485129i | \(-0.161227\pi\) | ||||
0.874443 | + | 0.485129i | \(0.161227\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.85408e67 | −2.12988 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.42874e67 | −0.588124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.50450e67 | 0.581095 | 0.290548 | − | 0.956861i | \(-0.406163\pi\) | ||||
0.290548 | + | 0.956861i | \(0.406163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.97882e65 | −0.0361702 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.97073e66 | −0.203138 | −0.101569 | − | 0.994829i | \(-0.532386\pi\) | ||||
−0.101569 | + | 0.994829i | \(0.532386\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.63622e67 | −1.16139 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.73887e67 | −1.12126 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.98539e67 | −1.12240 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.14848e67 | 0.303797 | 0.151898 | − | 0.988396i | \(-0.451461\pi\) | ||||
0.151898 | + | 0.988396i | \(0.451461\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.52752e67 | −1.87055 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.25690e67 | −0.760415 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.51013e66 | 0.0770141 | 0.0385070 | − | 0.999258i | \(-0.487740\pi\) | ||||
0.0385070 | + | 0.999258i | \(0.487740\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.43608e67 | −0.296141 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.99687e67 | 0.580937 | 0.290468 | − | 0.956885i | \(-0.406189\pi\) | ||||
0.290468 | + | 0.956885i | \(0.406189\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.22448e67 | 0.405418 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.20350e67 | −1.40590 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.92657e65 | 0.00310523 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.28547e68 | 1.94892 | 0.974461 | − | 0.224557i | \(-0.0720935\pi\) | ||||
0.974461 | + | 0.224557i | \(0.0720935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.65476e68 | −2.36025 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.24752e67 | 0.838474 | 0.419237 | − | 0.907877i | \(-0.362298\pi\) | ||||
0.419237 | + | 0.907877i | \(0.362298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.14802e66 | 0.115541 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.07344e68 | −2.46489 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.27281e68 | 1.42440 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.15385e67 | −0.332308 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.03883e66 | 0.0896831 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.49461e67 | 0.700345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.00261e67 | 0.264297 | 0.132149 | − | 0.991230i | \(-0.457812\pi\) | ||||
0.132149 | + | 0.991230i | \(0.457812\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.85175e68 | 2.36484 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.55233e67 | 0.433839 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.74601e66 | 0.0128566 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.67524e67 | −0.393874 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.46726e67 | −0.161415 | −0.0807077 | − | 0.996738i | \(-0.525718\pi\) | ||||
−0.0807077 | + | 0.996738i | \(0.525718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.21574e68 | −1.98349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.35998e68 | −0.790986 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.63103e67 | 0.254017 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.85543e68 | −0.959936 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.37634e68 | 1.64785 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.87119e68 | −1.32212 | −0.661061 | − | 0.750332i | \(-0.729894\pi\) | ||||
−0.661061 | + | 0.750332i | \(0.729894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.03047e67 | −0.175132 | −0.0875661 | − | 0.996159i | \(-0.527909\pi\) | ||||
−0.0875661 | + | 0.996159i | \(0.527909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.62786e67 | −0.189781 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.70218e68 | 1.04595 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.59575e68 | 1.31393 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.83312e66 | 0.0235748 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.55050e68 | 0.830923 | 0.415462 | − | 0.909611i | \(-0.363620\pi\) | ||||
0.415462 | + | 0.909611i | \(0.363620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.96708e68 | −0.912922 | −0.456461 | − | 0.889743i | \(-0.650883\pi\) | ||||
−0.456461 | + | 0.889743i | \(0.650883\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.36712e67 | 0.185044 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.78282e68 | 1.58767 | 0.793835 | − | 0.608133i | \(-0.208081\pi\) | ||||
0.793835 | + | 0.608133i | \(0.208081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.50860e68 | −0.391330 | −0.195665 | − | 0.980671i | \(-0.562687\pi\) | ||||
−0.195665 | + | 0.980671i | \(0.562687\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.09089e69 | −2.67397 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.32942e68 | 1.92956 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.11074e68 | 1.77594 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.32159e67 | −0.0687539 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.78467e67 | −0.113207 | −0.0566034 | − | 0.998397i | \(-0.518027\pi\) | ||||
−0.0566034 | + | 0.998397i | \(0.518027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.32977e68 | −0.801233 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.63705e68 | 1.16152 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.98598e68 | 1.15636 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.21157e68 | 1.28578 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.33764e68 | 0.790712 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.55719e68 | −0.638782 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.70885e68 | −0.889910 | −0.444955 | − | 0.895553i | \(-0.646780\pi\) | ||||
−0.444955 | + | 0.895553i | \(0.646780\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.15713e69 | −1.45270 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.18679e69 | 1.41034 | 0.705168 | − | 0.709040i | \(-0.250871\pi\) | ||||
0.705168 | + | 0.709040i | \(0.250871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.90685e67 | 0.0214525 | 0.0107262 | − | 0.999942i | \(-0.496586\pi\) | ||||
0.0107262 | + | 0.999942i | \(0.496586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.89431e69 | −2.01779 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.52667e68 | 0.860054 | 0.430027 | − | 0.902816i | \(-0.358504\pi\) | ||||
0.430027 | + | 0.902816i | \(0.358504\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.69839e68 | 0.926448 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.55538e69 | 1.40731 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.46698e68 | 0.125736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.24749e67 | 0.0263706 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.96874e68 | −0.305364 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.61085e69 | −1.17454 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.64441e67 | 0.0528267 | 0.0264134 | − | 0.999651i | \(-0.491591\pi\) | ||||
0.0264134 | + | 0.999651i | \(0.491591\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.70241e69 | 1.11513 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.82470e68 | −0.610078 | −0.305039 | − | 0.952340i | \(-0.598670\pi\) | ||||
−0.305039 | + | 0.952340i | \(0.598670\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.96558e68 | 0.115722 | 0.0578609 | − | 0.998325i | \(-0.481572\pi\) | ||||
0.0578609 | + | 0.998325i | \(0.481572\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.85551e68 | 0.271062 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.52341e69 | −1.86534 | −0.932670 | − | 0.360731i | \(-0.882527\pi\) | ||||
−0.932670 | + | 0.360731i | \(0.882527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.92383e67 | 0.0498297 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.50829e68 | −0.452873 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.53588e69 | −2.04952 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.77525e69 | −0.761061 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.26417e67 | 0.0132785 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.94715e68 | −0.152381 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.73850e68 | 0.356829 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.35154e69 | −1.86130 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.13022e69 | −1.69393 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.85786e69 | −0.582428 | −0.291214 | − | 0.956658i | \(-0.594059\pi\) | ||||
−0.291214 | + | 0.956658i | \(0.594059\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.65487e68 | −0.198102 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.88130e69 | −0.531835 | −0.265918 | − | 0.963996i | \(-0.585675\pi\) | ||||
−0.265918 | + | 0.963996i | \(0.585675\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.97099e69 | −0.529202 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.40044e69 | 1.12228 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.84316e69 | 2.38482 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.45864e69 | 0.796143 | 0.398071 | − | 0.917354i | \(-0.369680\pi\) | ||||
0.398071 | + | 0.917354i | \(0.369680\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.68557e69 | −0.806126 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.16858e67 | 0.0149002 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.02051e69 | 0.399144 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.48557e68 | 0.103002 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.44629e69 | −0.615153 | −0.307576 | − | 0.951523i | \(-0.599518\pi\) | ||||
−0.307576 | + | 0.951523i | \(0.599518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.17489e70 | 1.99379 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.83597e69 | 0.780306 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.32458e69 | −0.663546 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.88144e69 | 0.420464 | 0.210232 | − | 0.977652i | \(-0.432578\pi\) | ||||
0.210232 | + | 0.977652i | \(0.432578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.00479e70 | 1.39455 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.65396e69 | 0.482400 | 0.241200 | − | 0.970475i | \(-0.422459\pi\) | ||||
0.241200 | + | 0.970475i | \(0.422459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.16347e69 | −0.522914 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.98694e69 | −0.356927 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.53356e69 | 0.288075 | 0.144038 | − | 0.989572i | \(-0.453991\pi\) | ||||
0.144038 | + | 0.989572i | \(0.453991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.05262e68 | −0.0113898 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.34009e70 | −1.38004 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.10317e69 | −0.402195 | −0.201097 | − | 0.979571i | \(-0.564451\pi\) | ||||
−0.201097 | + | 0.979571i | \(0.564451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.12463e69 | −0.384862 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.74725e69 | −0.244044 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.74218e70 | −1.47352 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.09660e70 | −0.883180 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.13016e69 | 0.623565 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.01468e70 | −1.47168 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.82974e69 | 0.196890 | 0.0984451 | − | 0.995142i | \(-0.468613\pi\) | ||||
0.0984451 | + | 0.995142i | \(0.468613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.31556e70 | 2.86041 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.13025e70 | 1.34517 | 0.672587 | − | 0.740018i | \(-0.265183\pi\) | ||||
0.672587 | + | 0.740018i | \(0.265183\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.33190e70 | 1.40300 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.44722e68 | −0.00829711 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.95878e70 | 1.61655 | 0.808277 | − | 0.588802i | \(-0.200400\pi\) | ||||
0.808277 | + | 0.588802i | \(0.200400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.16931e69 | −0.373322 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.53793e69 | −0.225235 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.99760e69 | 0.283772 | 0.141886 | − | 0.989883i | \(-0.454683\pi\) | ||||
0.141886 | + | 0.989883i | \(0.454683\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.05206e70 | −1.37671 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.75072e70 | 2.90333 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.17621e70 | −0.482359 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.56295e70 | −1.39341 | −0.696706 | − | 0.717357i | \(-0.745352\pi\) | ||||
−0.696706 | + | 0.717357i | \(0.745352\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.50689e68 | 0.0168101 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.60988e70 | 1.28425 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.80387e69 | −0.298770 | −0.149385 | − | 0.988779i | \(-0.547729\pi\) | ||||
−0.149385 | + | 0.988779i | \(0.547729\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.33632e69 | −0.237514 |
(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 | 16.48.a.d.1.4 | 4 | ||
4.3 | odd | 2 | 1.48.a.a.1.3 | ✓ | 4 | ||
12.11 | even | 2 | 9.48.a.c.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.48.a.a.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
9.48.a.c.1.2 | 4 | 12.11 | even | 2 | |||
16.48.a.d.1.4 | 4 | 1.1 | even | 1 | trivial |