Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(197.998389976\) |
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: |
\( x^{6} - 2 x^{5} - 27590779188 x^{4} + 26487255863952 x^{3} + \cdots - 30\!\cdots\!08 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{4}\cdot 5^{18} \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-122054.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4096.00 | 0.707107 | ||||||||
\(3\) | 1.08697e6 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298957\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298957\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.45223e9 | 0.835000 | ||||||||
\(7\) | −4.89841e10 | −1.33761 | −0.668805 | − | 0.743438i | \(-0.733194\pi\) | ||||
−0.668805 | + | 0.743438i | \(0.733194\pi\) | |||||||
\(8\) | 6.87195e10 | 0.353553 | ||||||||
\(9\) | 3.34213e11 | 0.394450 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.14584e13 | 1.10082 | 0.550408 | − | 0.834896i | \(-0.314472\pi\) | ||||
0.550408 | + | 0.834896i | \(0.314472\pi\) | |||||||
\(12\) | 1.82363e13 | 0.590434 | ||||||||
\(13\) | 1.28077e14 | 1.52468 | 0.762342 | − | 0.647174i | \(-0.224049\pi\) | ||||
0.762342 | + | 0.647174i | \(0.224049\pi\) | |||||||
\(14\) | −2.00639e14 | −0.945833 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −3.78822e15 | −1.57697 | −0.788486 | − | 0.615053i | \(-0.789134\pi\) | ||||
−0.788486 | + | 0.615053i | \(0.789134\pi\) | |||||||
\(18\) | 1.36894e15 | 0.278918 | ||||||||
\(19\) | −1.02229e16 | −1.05963 | −0.529815 | − | 0.848113i | \(-0.677739\pi\) | ||||
−0.529815 | + | 0.848113i | \(0.677739\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.32442e16 | −1.57954 | ||||||||
\(22\) | 4.69335e16 | 0.778394 | ||||||||
\(23\) | −1.81999e17 | −1.73169 | −0.865845 | − | 0.500312i | \(-0.833218\pi\) | ||||
−0.865845 | + | 0.500312i | \(0.833218\pi\) | |||||||
\(24\) | 7.46959e16 | 0.417500 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.24604e17 | 1.07811 | ||||||||
\(27\) | −5.57697e17 | −0.715075 | ||||||||
\(28\) | −8.21816e17 | −0.668805 | ||||||||
\(29\) | 2.19149e18 | 1.15018 | 0.575088 | − | 0.818092i | \(-0.304968\pi\) | ||||
0.575088 | + | 0.818092i | \(0.304968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.89689e18 | 0.660557 | 0.330278 | − | 0.943884i | \(-0.392857\pi\) | ||||
0.330278 | + | 0.943884i | \(0.392857\pi\) | |||||||
\(32\) | 1.15292e18 | 0.176777 | ||||||||
\(33\) | 1.24549e19 | 1.29992 | ||||||||
\(34\) | −1.55166e19 | −1.11509 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.60717e18 | 0.197225 | ||||||||
\(37\) | −4.56681e19 | −1.14049 | −0.570245 | − | 0.821475i | \(-0.693152\pi\) | ||||
−0.570245 | + | 0.821475i | \(0.693152\pi\) | |||||||
\(38\) | −4.18730e19 | −0.749271 | ||||||||
\(39\) | 1.39216e20 | 1.80045 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.22120e18 | −0.0292172 | −0.0146086 | − | 0.999893i | \(-0.504650\pi\) | ||||
−0.0146086 | + | 0.999893i | \(0.504650\pi\) | |||||||
\(42\) | −2.18088e20 | −1.11690 | ||||||||
\(43\) | 1.22773e19 | 0.0468540 | 0.0234270 | − | 0.999726i | \(-0.492542\pi\) | ||||
0.0234270 | + | 0.999726i | \(0.492542\pi\) | |||||||
\(44\) | 1.92240e20 | 0.550408 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.45466e20 | −1.22449 | ||||||||
\(47\) | −4.60132e20 | −0.577642 | −0.288821 | − | 0.957383i | \(-0.593263\pi\) | ||||
−0.288821 | + | 0.957383i | \(0.593263\pi\) | |||||||
\(48\) | 3.05955e20 | 0.295217 | ||||||||
\(49\) | 1.05837e21 | 0.789199 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.11768e21 | −1.86220 | ||||||||
\(52\) | 2.14878e21 | 0.762342 | ||||||||
\(53\) | −2.54574e21 | −0.711814 | −0.355907 | − | 0.934521i | \(-0.615828\pi\) | ||||
−0.355907 | + | 0.934521i | \(0.615828\pi\) | |||||||
\(54\) | −2.28433e21 | −0.505634 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.36616e21 | −0.472916 | ||||||||
\(57\) | −1.11120e22 | −1.25128 | ||||||||
\(58\) | 8.97634e21 | 0.813297 | ||||||||
\(59\) | −2.20173e21 | −0.161107 | −0.0805536 | − | 0.996750i | \(-0.525669\pi\) | ||||
−0.0805536 | + | 0.996750i | \(0.525669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.41676e21 | 0.357760 | 0.178880 | − | 0.983871i | \(-0.442753\pi\) | ||||
0.178880 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(62\) | 1.18656e22 | 0.467084 | ||||||||
\(63\) | −1.63711e22 | −0.527620 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.10153e22 | 0.919181 | ||||||||
\(67\) | 6.01134e22 | 0.897503 | 0.448752 | − | 0.893656i | \(-0.351869\pi\) | ||||
0.448752 | + | 0.893656i | \(0.351869\pi\) | |||||||
\(68\) | −6.35558e22 | −0.788486 | ||||||||
\(69\) | −1.97827e23 | −2.04490 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.59036e22 | 0.259662 | 0.129831 | − | 0.991536i | \(-0.458557\pi\) | ||||
0.129831 | + | 0.991536i | \(0.458557\pi\) | |||||||
\(72\) | 2.29670e22 | 0.139459 | ||||||||
\(73\) | −1.98356e23 | −1.01370 | −0.506851 | − | 0.862034i | \(-0.669190\pi\) | ||||
−0.506851 | + | 0.862034i | \(0.669190\pi\) | |||||||
\(74\) | −1.87057e23 | −0.806448 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.71512e23 | −0.529815 | ||||||||
\(77\) | −5.61278e23 | −1.47246 | ||||||||
\(78\) | 5.70229e23 | 1.27311 | ||||||||
\(79\) | −7.84538e23 | −1.49374 | −0.746870 | − | 0.664970i | \(-0.768444\pi\) | ||||
−0.746870 | + | 0.664970i | \(0.768444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.89375e23 | −1.23886 | ||||||||
\(82\) | −1.72901e22 | −0.0206597 | ||||||||
\(83\) | −4.60438e23 | −0.472819 | −0.236409 | − | 0.971654i | \(-0.575971\pi\) | ||||
−0.236409 | + | 0.971654i | \(0.575971\pi\) | |||||||
\(84\) | −8.93289e23 | −0.789770 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.02877e22 | 0.0331308 | ||||||||
\(87\) | 2.38208e24 | 1.35821 | ||||||||
\(88\) | 7.87413e23 | 0.389197 | ||||||||
\(89\) | 5.94026e23 | 0.254936 | 0.127468 | − | 0.991843i | \(-0.459315\pi\) | ||||
0.127468 | + | 0.991843i | \(0.459315\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.27374e24 | −2.03943 | ||||||||
\(92\) | −3.05343e24 | −0.865845 | ||||||||
\(93\) | 3.14882e24 | 0.780031 | ||||||||
\(94\) | −1.88470e24 | −0.408455 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.25319e24 | 0.208750 | ||||||||
\(97\) | 8.71039e24 | 1.27465 | 0.637325 | − | 0.770595i | \(-0.280041\pi\) | ||||
0.637325 | + | 0.770595i | \(0.280041\pi\) | |||||||
\(98\) | 4.33508e24 | 0.558048 | ||||||||
\(99\) | 3.82954e24 | 0.434217 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.81456e24 | 0.690061 | 0.345031 | − | 0.938591i | \(-0.387869\pi\) | ||||
0.345031 | + | 0.938591i | \(0.387869\pi\) | |||||||
\(102\) | −1.68660e25 | −1.31677 | ||||||||
\(103\) | −1.05677e25 | −0.730321 | −0.365161 | − | 0.930945i | \(-0.618986\pi\) | ||||
−0.365161 | + | 0.930945i | \(0.618986\pi\) | |||||||
\(104\) | 8.80140e24 | 0.539057 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.04274e25 | −0.503328 | ||||||||
\(107\) | 4.46639e24 | 0.191716 | 0.0958582 | − | 0.995395i | \(-0.469440\pi\) | ||||
0.0958582 | + | 0.995395i | \(0.469440\pi\) | |||||||
\(108\) | −9.35660e24 | −0.357537 | ||||||||
\(109\) | −4.49825e25 | −1.53184 | −0.765918 | − | 0.642939i | \(-0.777715\pi\) | ||||
−0.765918 | + | 0.642939i | \(0.777715\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.96398e25 | −1.34677 | ||||||||
\(112\) | −1.37878e25 | −0.334402 | ||||||||
\(113\) | −2.79039e25 | −0.605598 | −0.302799 | − | 0.953054i | \(-0.597921\pi\) | ||||
−0.302799 | + | 0.953054i | \(0.597921\pi\) | |||||||
\(114\) | −4.55146e25 | −0.884791 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.67671e25 | 0.575088 | ||||||||
\(117\) | 4.28051e25 | 0.601412 | ||||||||
\(118\) | −9.01830e24 | −0.113920 | ||||||||
\(119\) | 1.85562e26 | 2.10937 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.29472e25 | 0.211794 | ||||||||
\(122\) | 3.03790e25 | 0.252974 | ||||||||
\(123\) | −4.58832e24 | −0.0345016 | ||||||||
\(124\) | 4.86017e25 | 0.330278 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.70561e25 | −0.373084 | ||||||||
\(127\) | −1.91643e26 | −0.965930 | −0.482965 | − | 0.875640i | \(-0.660440\pi\) | ||||
−0.482965 | + | 0.875640i | \(0.660440\pi\) | |||||||
\(128\) | 1.93428e25 | 0.0883883 | ||||||||
\(129\) | 1.33450e25 | 0.0553284 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.22743e26 | −0.761925 | −0.380963 | − | 0.924590i | \(-0.624407\pi\) | ||||
−0.380963 | + | 0.924590i | \(0.624407\pi\) | |||||||
\(132\) | 2.08958e26 | 0.649959 | ||||||||
\(133\) | 5.00759e26 | 1.41737 | ||||||||
\(134\) | 2.46224e26 | 0.634631 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.60325e26 | −0.557543 | ||||||||
\(137\) | −3.59939e26 | −0.703432 | −0.351716 | − | 0.936107i | \(-0.614402\pi\) | ||||
−0.351716 | + | 0.936107i | \(0.614402\pi\) | |||||||
\(138\) | −8.10299e26 | −1.44596 | ||||||||
\(139\) | −5.18148e26 | −0.844829 | −0.422414 | − | 0.906403i | \(-0.638817\pi\) | ||||
−0.422414 | + | 0.906403i | \(0.638817\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.00149e26 | −0.682119 | ||||||||
\(142\) | 1.47061e26 | 0.183609 | ||||||||
\(143\) | 1.46756e27 | 1.67840 | ||||||||
\(144\) | 9.40727e25 | 0.0986126 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.12467e26 | −0.716795 | ||||||||
\(147\) | 1.15042e27 | 0.931940 | ||||||||
\(148\) | −7.66184e26 | −0.570245 | ||||||||
\(149\) | −1.91990e27 | −1.31356 | −0.656780 | − | 0.754082i | \(-0.728082\pi\) | ||||
−0.656780 | + | 0.754082i | \(0.728082\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.20411e27 | −0.697356 | −0.348678 | − | 0.937243i | \(-0.613369\pi\) | ||||
−0.348678 | + | 0.937243i | \(0.613369\pi\) | |||||||
\(152\) | −7.02512e26 | −0.374636 | ||||||||
\(153\) | −1.26607e27 | −0.622037 | ||||||||
\(154\) | −2.29899e27 | −1.04119 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.33566e27 | 0.900226 | ||||||||
\(157\) | −4.32983e27 | −1.54073 | −0.770363 | − | 0.637606i | \(-0.779925\pi\) | ||||
−0.770363 | + | 0.637606i | \(0.779925\pi\) | |||||||
\(158\) | −3.21347e27 | −1.05623 | ||||||||
\(159\) | −2.76715e27 | −0.840559 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.91503e27 | 2.31632 | ||||||||
\(162\) | −3.64288e27 | −0.876006 | ||||||||
\(163\) | 5.02220e27 | 1.11828 | 0.559138 | − | 0.829075i | \(-0.311132\pi\) | ||||
0.559138 | + | 0.829075i | \(0.311132\pi\) | |||||||
\(164\) | −7.08201e25 | −0.0146086 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.88595e27 | −0.334333 | ||||||||
\(167\) | 1.18728e28 | 1.95253 | 0.976265 | − | 0.216580i | \(-0.0694903\pi\) | ||||
0.976265 | + | 0.216580i | \(0.0694903\pi\) | |||||||
\(168\) | −3.65891e27 | −0.558452 | ||||||||
\(169\) | 9.34736e27 | 1.32466 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.41663e27 | −0.417971 | ||||||||
\(172\) | 2.05979e26 | 0.0234270 | ||||||||
\(173\) | −4.16222e27 | −0.440300 | −0.220150 | − | 0.975466i | \(-0.570655\pi\) | ||||
−0.220150 | + | 0.975466i | \(0.570655\pi\) | |||||||
\(174\) | 9.75700e27 | 0.960397 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.22524e27 | 0.275204 | ||||||||
\(177\) | −2.39322e27 | −0.190246 | ||||||||
\(178\) | 2.43313e27 | 0.180267 | ||||||||
\(179\) | 1.09350e28 | 0.755363 | 0.377681 | − | 0.925936i | \(-0.376721\pi\) | ||||
0.377681 | + | 0.925936i | \(0.376721\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.64913e27 | −0.519984 | −0.259992 | − | 0.965611i | \(-0.583720\pi\) | ||||
−0.259992 | + | 0.965611i | \(0.583720\pi\) | |||||||
\(182\) | −2.56972e28 | −1.44210 | ||||||||
\(183\) | 8.06179e27 | 0.422467 | ||||||||
\(184\) | −1.25068e28 | −0.612245 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.28976e28 | 0.551565 | ||||||||
\(187\) | −4.34068e28 | −1.73595 | ||||||||
\(188\) | −7.71973e27 | −0.288821 | ||||||||
\(189\) | 2.73183e28 | 0.956490 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.76410e28 | 0.541511 | 0.270755 | − | 0.962648i | \(-0.412727\pi\) | ||||
0.270755 | + | 0.962648i | \(0.412727\pi\) | |||||||
\(192\) | 5.13307e27 | 0.147609 | ||||||||
\(193\) | −5.06807e27 | −0.136577 | −0.0682883 | − | 0.997666i | \(-0.521754\pi\) | ||||
−0.0682883 | + | 0.997666i | \(0.521754\pi\) | |||||||
\(194\) | 3.56778e28 | 0.901314 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.77565e28 | 0.394599 | ||||||||
\(197\) | −5.65172e27 | −0.117856 | −0.0589282 | − | 0.998262i | \(-0.518768\pi\) | ||||
−0.0589282 | + | 0.998262i | \(0.518768\pi\) | |||||||
\(198\) | 1.56858e28 | 0.307038 | ||||||||
\(199\) | 2.19231e28 | 0.402938 | 0.201469 | − | 0.979495i | \(-0.435428\pi\) | ||||
0.201469 | + | 0.979495i | \(0.435428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.53414e28 | 1.05983 | ||||||||
\(202\) | 3.20085e28 | 0.487947 | ||||||||
\(203\) | −1.07348e29 | −1.53849 | ||||||||
\(204\) | −6.90832e28 | −0.931098 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.32852e28 | −0.516415 | ||||||||
\(207\) | −6.08263e28 | −0.683066 | ||||||||
\(208\) | 3.60505e28 | 0.381171 | ||||||||
\(209\) | −1.17138e29 | −1.16646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.10994e28 | 0.805350 | 0.402675 | − | 0.915343i | \(-0.368080\pi\) | ||||
0.402675 | + | 0.915343i | \(0.368080\pi\) | |||||||
\(212\) | −4.27105e28 | −0.355907 | ||||||||
\(213\) | 3.90261e28 | 0.306627 | ||||||||
\(214\) | 1.82943e28 | 0.135564 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.83247e28 | −0.252817 | ||||||||
\(217\) | −1.41901e29 | −0.883567 | ||||||||
\(218\) | −1.84248e29 | −1.08317 | ||||||||
\(219\) | −2.15607e29 | −1.19705 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.85185e29 | −2.40438 | ||||||||
\(222\) | −2.03325e29 | −0.952309 | ||||||||
\(223\) | 1.06006e29 | 0.469374 | 0.234687 | − | 0.972071i | \(-0.424594\pi\) | ||||
0.234687 | + | 0.972071i | \(0.424594\pi\) | |||||||
\(224\) | −5.64748e28 | −0.236458 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.14294e29 | −0.428223 | ||||||||
\(227\) | −5.01045e29 | −1.77645 | −0.888226 | − | 0.459407i | \(-0.848062\pi\) | ||||
−0.888226 | + | 0.459407i | \(0.848062\pi\) | |||||||
\(228\) | −1.86428e29 | −0.625641 | ||||||||
\(229\) | −3.20108e28 | −0.101708 | −0.0508538 | − | 0.998706i | \(-0.516194\pi\) | ||||
−0.0508538 | + | 0.998706i | \(0.516194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.10091e29 | −1.73878 | ||||||||
\(232\) | 1.50598e29 | 0.406648 | ||||||||
\(233\) | −6.19627e29 | −1.58556 | −0.792778 | − | 0.609510i | \(-0.791366\pi\) | ||||
−0.792778 | + | 0.609510i | \(0.791366\pi\) | |||||||
\(234\) | 1.75330e29 | 0.425263 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.69390e28 | −0.0805536 | ||||||||
\(237\) | −8.52768e29 | −1.76391 | ||||||||
\(238\) | 7.60064e29 | 1.49155 | ||||||||
\(239\) | 2.16736e29 | 0.403605 | 0.201803 | − | 0.979426i | \(-0.435320\pi\) | ||||
0.201803 | + | 0.979426i | \(0.435320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.46346e29 | 1.25236 | 0.626178 | − | 0.779681i | \(-0.284619\pi\) | ||||
0.626178 | + | 0.779681i | \(0.284619\pi\) | |||||||
\(242\) | 9.39918e28 | 0.149761 | ||||||||
\(243\) | −4.94192e29 | −0.747855 | ||||||||
\(244\) | 1.24433e29 | 0.178880 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.87938e28 | −0.0243963 | ||||||||
\(247\) | −1.30932e30 | −1.61560 | ||||||||
\(248\) | 1.99072e29 | 0.233542 | ||||||||
\(249\) | −5.00481e29 | −0.558337 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.46681e29 | 0.753726 | 0.376863 | − | 0.926269i | \(-0.377003\pi\) | ||||
0.376863 | + | 0.926269i | \(0.377003\pi\) | |||||||
\(252\) | −2.74662e29 | −0.263810 | ||||||||
\(253\) | −2.08541e30 | −1.90627 | ||||||||
\(254\) | −7.84968e29 | −0.683016 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −2.03309e29 | −0.152754 | −0.0763769 | − | 0.997079i | \(-0.524335\pi\) | ||||
−0.0763769 | + | 0.997079i | \(0.524335\pi\) | |||||||
\(258\) | 5.46612e28 | 0.0391231 | ||||||||
\(259\) | 2.23701e30 | 1.52553 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.32424e29 | 0.453687 | ||||||||
\(262\) | −9.12354e29 | −0.538763 | ||||||||
\(263\) | 3.18718e30 | 1.79457 | 0.897284 | − | 0.441454i | \(-0.145537\pi\) | ||||
0.897284 | + | 0.441454i | \(0.145537\pi\) | |||||||
\(264\) | 8.55894e29 | 0.459590 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.05111e30 | 1.00223 | ||||||||
\(267\) | 6.45688e29 | 0.301046 | ||||||||
\(268\) | 1.00854e30 | 0.448752 | ||||||||
\(269\) | 1.08398e29 | 0.0460382 | 0.0230191 | − | 0.999735i | \(-0.492672\pi\) | ||||
0.0230191 | + | 0.999735i | \(0.492672\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.40525e29 | 0.325413 | 0.162706 | − | 0.986675i | \(-0.447978\pi\) | ||||
0.162706 | + | 0.986675i | \(0.447978\pi\) | |||||||
\(272\) | −1.06629e30 | −0.394243 | ||||||||
\(273\) | −6.81936e30 | −2.40830 | ||||||||
\(274\) | −1.47431e30 | −0.497402 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.31898e30 | −1.02245 | ||||||||
\(277\) | −5.28289e30 | −1.55551 | −0.777757 | − | 0.628564i | \(-0.783643\pi\) | ||||
−0.777757 | + | 0.628564i | \(0.783643\pi\) | |||||||
\(278\) | −2.12233e30 | −0.597384 | ||||||||
\(279\) | 9.68177e29 | 0.260557 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.89709e30 | −1.45147 | −0.725736 | − | 0.687973i | \(-0.758501\pi\) | ||||
−0.725736 | + | 0.687973i | \(0.758501\pi\) | |||||||
\(282\) | −2.04861e30 | −0.482331 | ||||||||
\(283\) | 1.58325e30 | 0.356631 | 0.178315 | − | 0.983973i | \(-0.442935\pi\) | ||||
0.178315 | + | 0.983973i | \(0.442935\pi\) | |||||||
\(284\) | 6.02362e29 | 0.129831 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.01111e30 | 1.18680 | ||||||||
\(287\) | 2.06772e29 | 0.0390812 | ||||||||
\(288\) | 3.85322e29 | 0.0697296 | ||||||||
\(289\) | 8.57999e30 | 1.48684 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.46793e30 | 1.50519 | ||||||||
\(292\) | −3.32787e30 | −0.506851 | ||||||||
\(293\) | 4.96361e30 | 0.724357 | 0.362179 | − | 0.932109i | \(-0.382033\pi\) | ||||
0.362179 | + | 0.932109i | \(0.382033\pi\) | |||||||
\(294\) | 4.71210e30 | 0.658981 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.13829e30 | −0.403224 | ||||||||
\(297\) | −6.39030e30 | −0.787165 | ||||||||
\(298\) | −7.86391e30 | −0.928828 | ||||||||
\(299\) | −2.33099e31 | −2.64028 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.01391e29 | −0.0626723 | ||||||||
\(302\) | −4.93203e30 | −0.493105 | ||||||||
\(303\) | 8.49419e30 | 0.814871 | ||||||||
\(304\) | −2.87749e30 | −0.264907 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.18584e30 | −0.439846 | ||||||||
\(307\) | 1.29347e31 | 1.05323 | 0.526617 | − | 0.850102i | \(-0.323460\pi\) | ||||
0.526617 | + | 0.850102i | \(0.323460\pi\) | |||||||
\(308\) | −9.41668e30 | −0.736230 | ||||||||
\(309\) | −1.14867e31 | −0.862413 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.68637e30 | −0.116801 | −0.0584007 | − | 0.998293i | \(-0.518600\pi\) | ||||
−0.0584007 | + | 0.998293i | \(0.518600\pi\) | |||||||
\(312\) | 9.56685e30 | 0.636556 | ||||||||
\(313\) | 2.70375e30 | 0.172847 | 0.0864236 | − | 0.996258i | \(-0.472456\pi\) | ||||
0.0864236 | + | 0.996258i | \(0.472456\pi\) | |||||||
\(314\) | −1.77350e31 | −1.08946 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.31624e31 | −0.746870 | ||||||||
\(317\) | 3.29106e31 | 1.79513 | 0.897563 | − | 0.440887i | \(-0.145336\pi\) | ||||
0.897563 | + | 0.440887i | \(0.145336\pi\) | |||||||
\(318\) | −1.13342e31 | −0.594365 | ||||||||
\(319\) | 2.51109e31 | 1.26613 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.85483e30 | 0.226392 | ||||||||
\(322\) | 3.65160e31 | 1.63789 | ||||||||
\(323\) | 3.87266e31 | 1.67100 | ||||||||
\(324\) | −1.49212e31 | −0.619430 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.05709e31 | 0.790740 | ||||||||
\(327\) | −4.88946e31 | −1.80890 | ||||||||
\(328\) | −2.90079e29 | −0.0103298 | ||||||||
\(329\) | 2.25391e31 | 0.772659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.10367e31 | −0.986337 | −0.493168 | − | 0.869934i | \(-0.664161\pi\) | ||||
−0.493168 | + | 0.869934i | \(0.664161\pi\) | |||||||
\(332\) | −7.72486e30 | −0.236409 | ||||||||
\(333\) | −1.52629e31 | −0.449867 | ||||||||
\(334\) | 4.86310e31 | 1.38065 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.49869e31 | −0.394885 | ||||||||
\(337\) | 3.19922e31 | 0.812214 | 0.406107 | − | 0.913825i | \(-0.366886\pi\) | ||||
0.406107 | + | 0.913825i | \(0.366886\pi\) | |||||||
\(338\) | 3.82868e31 | 0.936678 | ||||||||
\(339\) | −3.03307e31 | −0.715132 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.31936e31 | 0.727151 | ||||||||
\(342\) | −1.39945e31 | −0.295550 | ||||||||
\(343\) | 1.38477e31 | 0.281970 | ||||||||
\(344\) | 8.43688e29 | 0.0165654 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.70484e31 | −0.311339 | ||||||||
\(347\) | 4.34215e31 | 0.764867 | 0.382434 | − | 0.923983i | \(-0.375086\pi\) | ||||
0.382434 | + | 0.923983i | \(0.375086\pi\) | |||||||
\(348\) | 3.99647e31 | 0.679103 | ||||||||
\(349\) | 9.72186e31 | 1.59379 | 0.796896 | − | 0.604117i | \(-0.206474\pi\) | ||||
0.796896 | + | 0.604117i | \(0.206474\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.14283e31 | −1.09026 | ||||||||
\(352\) | 1.32106e31 | 0.194598 | ||||||||
\(353\) | −1.03434e32 | −1.47055 | −0.735277 | − | 0.677767i | \(-0.762948\pi\) | ||||
−0.735277 | + | 0.677767i | \(0.762948\pi\) | |||||||
\(354\) | −9.80262e30 | −0.134524 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.96611e30 | 0.127468 | ||||||||
\(357\) | 2.01701e32 | 2.49089 | ||||||||
\(358\) | 4.47897e31 | 0.534122 | ||||||||
\(359\) | 4.33845e31 | 0.499636 | 0.249818 | − | 0.968293i | \(-0.419629\pi\) | ||||
0.249818 | + | 0.968293i | \(0.419629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.14311e31 | 0.122814 | ||||||||
\(362\) | −3.54268e31 | −0.367684 | ||||||||
\(363\) | 2.49429e31 | 0.250100 | ||||||||
\(364\) | −1.05256e32 | −1.01972 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.30211e31 | 0.298729 | ||||||||
\(367\) | −4.71466e31 | −0.412216 | −0.206108 | − | 0.978529i | \(-0.566080\pi\) | ||||
−0.206108 | + | 0.978529i | \(0.566080\pi\) | |||||||
\(368\) | −5.12281e31 | −0.432922 | ||||||||
\(369\) | −1.41078e30 | −0.0115247 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.24701e32 | 0.952129 | ||||||||
\(372\) | 5.28285e31 | 0.390015 | ||||||||
\(373\) | 9.92589e31 | 0.708613 | 0.354306 | − | 0.935129i | \(-0.384717\pi\) | ||||
0.354306 | + | 0.935129i | \(0.384717\pi\) | |||||||
\(374\) | −1.77794e32 | −1.22750 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.16200e31 | −0.204227 | ||||||||
\(377\) | 2.80680e32 | 1.75365 | ||||||||
\(378\) | 1.11896e32 | 0.676341 | ||||||||
\(379\) | −6.28833e31 | −0.367743 | −0.183872 | − | 0.982950i | \(-0.558863\pi\) | ||||
−0.183872 | + | 0.982950i | \(0.558863\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.08310e32 | −1.14064 | ||||||||
\(382\) | 7.22577e31 | 0.382906 | ||||||||
\(383\) | −4.95371e31 | −0.254065 | −0.127033 | − | 0.991899i | \(-0.540545\pi\) | ||||
−0.127033 | + | 0.991899i | \(0.540545\pi\) | |||||||
\(384\) | 2.10250e31 | 0.104375 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.07588e31 | −0.0965742 | ||||||||
\(387\) | 4.10323e30 | 0.0184816 | ||||||||
\(388\) | 1.46136e32 | 0.637325 | ||||||||
\(389\) | −4.10071e32 | −1.73177 | −0.865883 | − | 0.500246i | \(-0.833243\pi\) | ||||
−0.865883 | + | 0.500246i | \(0.833243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.89451e32 | 2.73082 | ||||||||
\(392\) | 7.27306e31 | 0.279024 | ||||||||
\(393\) | −2.42114e32 | −0.899734 | ||||||||
\(394\) | −2.31495e31 | −0.0833370 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.42490e31 | 0.217108 | ||||||||
\(397\) | −1.81115e32 | −0.593026 | −0.296513 | − | 0.955029i | \(-0.595824\pi\) | ||||
−0.296513 | + | 0.955029i | \(0.595824\pi\) | |||||||
\(398\) | 8.97970e31 | 0.284920 | ||||||||
\(399\) | 5.44310e32 | 1.67373 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.30258e32 | 0.376271 | 0.188136 | − | 0.982143i | \(-0.439756\pi\) | ||||
0.188136 | + | 0.982143i | \(0.439756\pi\) | |||||||
\(402\) | 2.67638e32 | 0.749415 | ||||||||
\(403\) | 3.71025e32 | 1.00714 | ||||||||
\(404\) | 1.31107e32 | 0.345031 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.39697e32 | −1.08787 | ||||||||
\(407\) | −5.23282e32 | −1.25547 | ||||||||
\(408\) | −2.82965e32 | −0.658385 | ||||||||
\(409\) | 8.59252e32 | 1.93901 | 0.969503 | − | 0.245081i | \(-0.0788144\pi\) | ||||
0.969503 | + | 0.245081i | \(0.0788144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.91243e32 | −0.830661 | ||||||||
\(412\) | −1.77296e32 | −0.365161 | ||||||||
\(413\) | 1.07850e32 | 0.215498 | ||||||||
\(414\) | −2.49145e32 | −0.483000 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.47663e32 | 0.269529 | ||||||||
\(417\) | −5.63211e32 | −0.997631 | ||||||||
\(418\) | −4.79796e32 | −0.824809 | ||||||||
\(419\) | −4.67029e32 | −0.779235 | −0.389618 | − | 0.920977i | \(-0.627393\pi\) | ||||
−0.389618 | + | 0.920977i | \(0.627393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.42072e32 | −1.16659 | −0.583297 | − | 0.812259i | \(-0.698238\pi\) | ||||
−0.583297 | + | 0.812259i | \(0.698238\pi\) | |||||||
\(422\) | 3.73143e32 | 0.569468 | ||||||||
\(423\) | −1.53782e32 | −0.227851 | ||||||||
\(424\) | −1.74942e32 | −0.251664 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.59851e32 | 0.216818 | ||||||||
\(427\) | −3.63303e32 | −0.478543 | ||||||||
\(428\) | 7.49336e31 | 0.0958582 | ||||||||
\(429\) | 1.59519e33 | 1.98196 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.06420e33 | 1.24755 | 0.623774 | − | 0.781605i | \(-0.285599\pi\) | ||||
0.623774 | + | 0.781605i | \(0.285599\pi\) | |||||||
\(432\) | −1.56978e32 | −0.178769 | ||||||||
\(433\) | 9.20340e32 | 1.01824 | 0.509119 | − | 0.860696i | \(-0.329971\pi\) | ||||
0.509119 | + | 0.860696i | \(0.329971\pi\) | |||||||
\(434\) | −5.81227e32 | −0.624776 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.54681e32 | −0.765918 | ||||||||
\(437\) | 1.86055e33 | 1.83495 | ||||||||
\(438\) | −8.83127e32 | −0.846441 | ||||||||
\(439\) | −3.84917e32 | −0.358559 | −0.179279 | − | 0.983798i | \(-0.557377\pi\) | ||||
−0.179279 | + | 0.983798i | \(0.557377\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.53721e32 | 0.311300 | ||||||||
\(442\) | −1.98732e33 | −1.70016 | ||||||||
\(443\) | −8.53492e32 | −0.709827 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(444\) | −8.32818e32 | −0.673384 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.34200e32 | 0.331897 | ||||||||
\(447\) | −2.08687e33 | −1.55114 | ||||||||
\(448\) | −2.31321e32 | −0.167201 | ||||||||
\(449\) | 3.42652e32 | 0.240865 | 0.120432 | − | 0.992722i | \(-0.461572\pi\) | ||||
0.120432 | + | 0.992722i | \(0.461572\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.83681e31 | −0.0321627 | ||||||||
\(452\) | −4.68150e32 | −0.302799 | ||||||||
\(453\) | −1.30883e33 | −0.823485 | ||||||||
\(454\) | −2.05228e33 | −1.25614 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.63609e32 | −0.442395 | ||||||||
\(457\) | 4.52087e32 | 0.254841 | 0.127421 | − | 0.991849i | \(-0.459330\pi\) | ||||
0.127421 | + | 0.991849i | \(0.459330\pi\) | |||||||
\(458\) | −1.31116e32 | −0.0719181 | ||||||||
\(459\) | 2.11268e33 | 1.12765 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.47159e33 | 1.24944 | 0.624718 | − | 0.780850i | \(-0.285214\pi\) | ||||
0.624718 | + | 0.780850i | \(0.285214\pi\) | |||||||
\(462\) | −2.49893e33 | −1.22950 | ||||||||
\(463\) | −1.72628e33 | −0.826703 | −0.413351 | − | 0.910572i | \(-0.635642\pi\) | ||||
−0.413351 | + | 0.910572i | \(0.635642\pi\) | |||||||
\(464\) | 6.16849e32 | 0.287544 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.53799e33 | −1.12116 | ||||||||
\(467\) | −1.88292e33 | −0.809787 | −0.404893 | − | 0.914364i | \(-0.632691\pi\) | ||||
−0.404893 | + | 0.914364i | \(0.632691\pi\) | |||||||
\(468\) | 7.18150e32 | 0.300706 | ||||||||
\(469\) | −2.94460e33 | −1.20051 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.70639e33 | −1.81939 | ||||||||
\(472\) | −1.51302e32 | −0.0569600 | ||||||||
\(473\) | 1.40678e32 | 0.0515775 | ||||||||
\(474\) | −3.49294e33 | −1.24727 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.11322e33 | 1.05469 | ||||||||
\(477\) | −8.50822e32 | −0.280775 | ||||||||
\(478\) | 8.87749e32 | 0.285392 | ||||||||
\(479\) | 1.07303e33 | 0.336061 | 0.168030 | − | 0.985782i | \(-0.446259\pi\) | ||||
0.168030 | + | 0.985782i | \(0.446259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.84904e33 | −1.73889 | ||||||||
\(482\) | 3.05704e33 | 0.885549 | ||||||||
\(483\) | 9.69036e33 | 2.73527 | ||||||||
\(484\) | 3.84991e32 | 0.105897 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.02421e33 | −0.528814 | ||||||||
\(487\) | −6.26292e33 | −1.59465 | −0.797324 | − | 0.603552i | \(-0.793752\pi\) | ||||
−0.797324 | + | 0.603552i | \(0.793752\pi\) | |||||||
\(488\) | 5.09676e32 | 0.126487 | ||||||||
\(489\) | 5.45897e33 | 1.32054 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.10431e33 | 0.713586 | 0.356793 | − | 0.934183i | \(-0.383870\pi\) | ||||
0.356793 | + | 0.934183i | \(0.383870\pi\) | |||||||
\(492\) | −7.69792e31 | −0.0172508 | ||||||||
\(493\) | −8.30184e33 | −1.81379 | ||||||||
\(494\) | −5.36298e33 | −1.14240 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.15401e32 | 0.165139 | ||||||||
\(497\) | −1.75870e33 | −0.347326 | ||||||||
\(498\) | −2.04997e33 | −0.394804 | ||||||||
\(499\) | 7.12443e33 | 1.33811 | 0.669057 | − | 0.743211i | \(-0.266698\pi\) | ||||
0.669057 | + | 0.743211i | \(0.266698\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.29054e34 | 2.30568 | ||||||||
\(502\) | 3.05840e33 | 0.532965 | ||||||||
\(503\) | −1.03191e34 | −1.75406 | −0.877028 | − | 0.480439i | \(-0.840477\pi\) | ||||
−0.877028 | + | 0.480439i | \(0.840477\pi\) | |||||||
\(504\) | −1.12501e33 | −0.186542 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.54183e33 | −1.34794 | ||||||||
\(507\) | 1.01603e34 | 1.56425 | ||||||||
\(508\) | −3.21523e33 | −0.482965 | ||||||||
\(509\) | −4.04421e32 | −0.0592736 | −0.0296368 | − | 0.999561i | \(-0.509435\pi\) | ||||
−0.0296368 | + | 0.999561i | \(0.509435\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.71629e33 | 1.35594 | ||||||||
\(512\) | 3.24519e32 | 0.0441942 | ||||||||
\(513\) | 5.70128e33 | 0.757714 | ||||||||
\(514\) | −8.32753e32 | −0.108013 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.23892e32 | 0.0276642 | ||||||||
\(517\) | −5.27236e33 | −0.635877 | ||||||||
\(518\) | 9.16279e33 | 1.07871 | ||||||||
\(519\) | −4.52420e33 | −0.519936 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.14369e33 | 1.00150 | 0.500749 | − | 0.865593i | \(-0.333058\pi\) | ||||
0.500749 | + | 0.865593i | \(0.333058\pi\) | |||||||
\(522\) | 3.00001e33 | 0.320805 | ||||||||
\(523\) | 1.50595e33 | 0.157231 | 0.0786156 | − | 0.996905i | \(-0.474950\pi\) | ||||
0.0786156 | + | 0.996905i | \(0.474950\pi\) | |||||||
\(524\) | −3.73700e33 | −0.380963 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.30547e34 | 1.26895 | ||||||||
\(527\) | −1.09740e34 | −1.04168 | ||||||||
\(528\) | 3.50574e33 | 0.324979 | ||||||||
\(529\) | 2.20777e34 | 1.99875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.35849e32 | −0.0635487 | ||||||||
\(532\) | 8.40134e33 | 0.708685 | ||||||||
\(533\) | −5.40640e32 | −0.0445470 | ||||||||
\(534\) | 2.64474e33 | 0.212871 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.13096e33 | 0.317315 | ||||||||
\(537\) | 1.18860e34 | 0.891984 | ||||||||
\(538\) | 4.43999e32 | 0.0325539 | ||||||||
\(539\) | 1.21272e34 | 0.868762 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.92779e32 | 0.0542234 | 0.0271117 | − | 0.999632i | \(-0.491369\pi\) | ||||
0.0271117 | + | 0.999632i | \(0.491369\pi\) | |||||||
\(542\) | 3.44279e33 | 0.230102 | ||||||||
\(543\) | −9.40134e33 | −0.614033 | ||||||||
\(544\) | −4.36752e33 | −0.278772 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.79321e34 | −1.70293 | ||||||||
\(547\) | 2.56023e34 | 1.52559 | 0.762794 | − | 0.646641i | \(-0.223827\pi\) | ||||
0.762794 | + | 0.646641i | \(0.223827\pi\) | |||||||
\(548\) | −6.03878e33 | −0.351716 | ||||||||
\(549\) | 2.47878e33 | 0.141118 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.24034e34 | −1.21876 | ||||||||
\(552\) | −1.35946e34 | −0.722981 | ||||||||
\(553\) | 3.84298e34 | 1.99804 | ||||||||
\(554\) | −2.16387e34 | −1.09992 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.69308e33 | −0.422414 | ||||||||
\(557\) | 2.77017e34 | 1.31618 | 0.658091 | − | 0.752938i | \(-0.271364\pi\) | ||||
0.658091 | + | 0.752938i | \(0.271364\pi\) | |||||||
\(558\) | 3.96565e33 | 0.184241 | ||||||||
\(559\) | 1.57244e33 | 0.0714375 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.71819e34 | −2.04993 | ||||||||
\(562\) | −2.41545e34 | −1.02635 | ||||||||
\(563\) | −1.80222e33 | −0.0748951 | −0.0374476 | − | 0.999299i | \(-0.511923\pi\) | ||||
−0.0374476 | + | 0.999299i | \(0.511923\pi\) | |||||||
\(564\) | −8.39110e33 | −0.341060 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.48499e33 | 0.252176 | ||||||||
\(567\) | 4.35652e34 | 1.65711 | ||||||||
\(568\) | 2.46728e33 | 0.0918044 | ||||||||
\(569\) | −2.00804e34 | −0.730920 | −0.365460 | − | 0.930827i | \(-0.619088\pi\) | ||||
−0.365460 | + | 0.930827i | \(0.619088\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.27237e34 | 1.14002 | 0.570008 | − | 0.821639i | \(-0.306940\pi\) | ||||
0.570008 | + | 0.821639i | \(0.306940\pi\) | |||||||
\(572\) | 2.46215e34 | 0.839198 | ||||||||
\(573\) | 1.91753e34 | 0.639453 | ||||||||
\(574\) | 8.46937e32 | 0.0276346 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.57828e33 | 0.0493063 | ||||||||
\(577\) | −1.86866e34 | −0.571257 | −0.285629 | − | 0.958340i | \(-0.592202\pi\) | ||||
−0.285629 | + | 0.958340i | \(0.592202\pi\) | |||||||
\(578\) | 3.51436e34 | 1.05135 | ||||||||
\(579\) | −5.50883e33 | −0.161279 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.25541e34 | 0.632447 | ||||||||
\(582\) | 3.87806e34 | 1.06433 | ||||||||
\(583\) | −2.91701e34 | −0.783575 | ||||||||
\(584\) | −1.36309e34 | −0.358398 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.03310e34 | 0.512198 | ||||||||
\(587\) | 2.44688e33 | 0.0603443 | 0.0301721 | − | 0.999545i | \(-0.490394\pi\) | ||||
0.0301721 | + | 0.999545i | \(0.490394\pi\) | |||||||
\(588\) | 1.93008e34 | 0.465970 | ||||||||
\(589\) | −2.96146e34 | −0.699945 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.14325e33 | −0.139173 | ||||||||
\(592\) | −1.28544e34 | −0.285122 | ||||||||
\(593\) | −3.48844e34 | −0.757613 | −0.378806 | − | 0.925476i | \(-0.623665\pi\) | ||||
−0.378806 | + | 0.925476i | \(0.623665\pi\) | |||||||
\(594\) | −2.61747e34 | −0.556610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.22106e34 | −0.656780 | ||||||||
\(597\) | 2.38297e34 | 0.475817 | ||||||||
\(598\) | −9.54772e34 | −1.86696 | ||||||||
\(599\) | 6.48903e34 | 1.24264 | 0.621319 | − | 0.783558i | \(-0.286597\pi\) | ||||
0.621319 | + | 0.783558i | \(0.286597\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.18034e34 | −0.400492 | −0.200246 | − | 0.979746i | \(-0.564174\pi\) | ||||
−0.200246 | + | 0.979746i | \(0.564174\pi\) | |||||||
\(602\) | −2.46330e33 | −0.0443160 | ||||||||
\(603\) | 2.00907e34 | 0.354020 | ||||||||
\(604\) | −2.02016e34 | −0.348678 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.47922e34 | 0.576201 | ||||||||
\(607\) | −7.37348e34 | −1.19623 | −0.598114 | − | 0.801411i | \(-0.704083\pi\) | ||||
−0.598114 | + | 0.801411i | \(0.704083\pi\) | |||||||
\(608\) | −1.17862e34 | −0.187318 | ||||||||
\(609\) | −1.16684e35 | −1.81675 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.89324e34 | −0.880722 | ||||||||
\(612\) | −2.12412e34 | −0.311018 | ||||||||
\(613\) | 1.05162e35 | 1.50870 | 0.754349 | − | 0.656473i | \(-0.227953\pi\) | ||||
0.754349 | + | 0.656473i | \(0.227953\pi\) | |||||||
\(614\) | 5.29804e34 | 0.744750 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.85707e34 | −0.520593 | ||||||||
\(617\) | 8.12769e34 | 1.07499 | 0.537493 | − | 0.843268i | \(-0.319372\pi\) | ||||
0.537493 | + | 0.843268i | \(0.319372\pi\) | |||||||
\(618\) | −4.70496e34 | −0.609818 | ||||||||
\(619\) | 4.81305e34 | 0.611346 | 0.305673 | − | 0.952137i | \(-0.401119\pi\) | ||||
0.305673 | + | 0.952137i | \(0.401119\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.01500e35 | 1.23829 | ||||||||
\(622\) | −6.90737e33 | −0.0825910 | ||||||||
\(623\) | −2.90978e34 | −0.341004 | ||||||||
\(624\) | 3.91858e34 | 0.450113 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.10746e34 | 0.122221 | ||||||||
\(627\) | −1.27325e35 | −1.37743 | ||||||||
\(628\) | −7.26425e34 | −0.770363 | ||||||||
\(629\) | 1.73001e35 | 1.79852 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.11675e34 | 0.611158 | 0.305579 | − | 0.952167i | \(-0.401150\pi\) | ||||
0.305579 | + | 0.952167i | \(0.401150\pi\) | |||||||
\(632\) | −5.39130e34 | −0.528117 | ||||||||
\(633\) | 9.90222e34 | 0.951012 | ||||||||
\(634\) | 1.34802e35 | 1.26935 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.64250e34 | −0.420279 | ||||||||
\(637\) | 1.35553e35 | 1.20328 | ||||||||
\(638\) | 1.02854e35 | 0.895289 | ||||||||
\(639\) | 1.19995e34 | 0.102424 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.15866e34 | 0.751807 | 0.375904 | − | 0.926659i | \(-0.377332\pi\) | ||||
0.375904 | + | 0.926659i | \(0.377332\pi\) | |||||||
\(642\) | 1.98854e34 | 0.160083 | ||||||||
\(643\) | −5.09730e34 | −0.402442 | −0.201221 | − | 0.979546i | \(-0.564491\pi\) | ||||
−0.201221 | + | 0.979546i | \(0.564491\pi\) | |||||||
\(644\) | 1.49569e35 | 1.15816 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.58624e35 | 1.18158 | ||||||||
\(647\) | −2.28658e35 | −1.67064 | −0.835320 | − | 0.549765i | \(-0.814717\pi\) | ||||
−0.835320 | + | 0.549765i | \(0.814717\pi\) | |||||||
\(648\) | −6.11174e34 | −0.438003 | ||||||||
\(649\) | −2.52283e34 | −0.177349 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.54242e35 | −1.04338 | ||||||||
\(652\) | 8.42585e34 | 0.559138 | ||||||||
\(653\) | 1.93736e35 | 1.26124 | 0.630618 | − | 0.776093i | \(-0.282801\pi\) | ||||
0.630618 | + | 0.776093i | \(0.282801\pi\) | |||||||
\(654\) | −2.00272e35 | −1.27908 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.18816e33 | −0.00730429 | ||||||||
\(657\) | −6.62933e34 | −0.399855 | ||||||||
\(658\) | 9.23202e34 | 0.546353 | ||||||||
\(659\) | −2.14078e35 | −1.24310 | −0.621548 | − | 0.783376i | \(-0.713496\pi\) | ||||
−0.621548 | + | 0.783376i | \(0.713496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.52863e35 | 0.854641 | 0.427320 | − | 0.904100i | \(-0.359458\pi\) | ||||
0.427320 | + | 0.904100i | \(0.359458\pi\) | |||||||
\(662\) | −1.27126e35 | −0.697445 | ||||||||
\(663\) | −5.27381e35 | −2.83926 | ||||||||
\(664\) | −3.16410e34 | −0.167167 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.25168e34 | −0.318104 | ||||||||
\(667\) | −3.98848e35 | −1.99175 | ||||||||
\(668\) | 1.99193e35 | 0.976265 | ||||||||
\(669\) | 1.15225e35 | 0.554268 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.49840e34 | 0.393827 | ||||||||
\(672\) | −6.13863e34 | −0.279226 | ||||||||
\(673\) | −2.04386e35 | −0.912564 | −0.456282 | − | 0.889835i | \(-0.650819\pi\) | ||||
−0.456282 | + | 0.889835i | \(0.650819\pi\) | |||||||
\(674\) | 1.31040e35 | 0.574322 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.56823e35 | 0.662331 | ||||||||
\(677\) | 4.21908e34 | 0.174928 | 0.0874640 | − | 0.996168i | \(-0.472124\pi\) | ||||
0.0874640 | + | 0.996168i | \(0.472124\pi\) | |||||||
\(678\) | −1.24235e35 | −0.505675 | ||||||||
\(679\) | −4.26671e35 | −1.70498 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.44620e35 | −2.09776 | ||||||||
\(682\) | 1.35961e35 | 0.514173 | ||||||||
\(683\) | −2.99380e35 | −1.11164 | −0.555820 | − | 0.831303i | \(-0.687595\pi\) | ||||
−0.555820 | + | 0.831303i | \(0.687595\pi\) | |||||||
\(684\) | −5.73215e34 | −0.208986 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.67203e34 | 0.199383 | ||||||||
\(687\) | −3.47948e34 | −0.120103 | ||||||||
\(688\) | 3.45575e33 | 0.0117135 | ||||||||
\(689\) | −3.26052e35 | −1.08529 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.03613e34 | 0.257971 | 0.128986 | − | 0.991646i | \(-0.458828\pi\) | ||||
0.128986 | + | 0.991646i | \(0.458828\pi\) | |||||||
\(692\) | −6.98304e34 | −0.220150 | ||||||||
\(693\) | −1.87586e35 | −0.580812 | ||||||||
\(694\) | 1.77854e35 | 0.540843 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.63695e35 | 0.480198 | ||||||||
\(697\) | 1.59909e34 | 0.0460746 | ||||||||
\(698\) | 3.98207e35 | 1.12698 | ||||||||
\(699\) | −6.73516e35 | −1.87233 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.53710e35 | −1.21704 | −0.608518 | − | 0.793540i | \(-0.708235\pi\) | ||||
−0.608518 | + | 0.793540i | \(0.708235\pi\) | |||||||
\(702\) | −2.92570e35 | −0.770932 | ||||||||
\(703\) | 4.66860e35 | 1.20850 | ||||||||
\(704\) | 5.41106e34 | 0.137602 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.23667e35 | −1.03984 | ||||||||
\(707\) | −3.82789e35 | −0.923032 | ||||||||
\(708\) | −4.01515e34 | −0.0951232 | ||||||||
\(709\) | −1.72814e35 | −0.402255 | −0.201128 | − | 0.979565i | \(-0.564461\pi\) | ||||
−0.201128 | + | 0.979565i | \(0.564461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.62203e35 | −0.589206 | ||||||||
\(712\) | 4.08212e34 | 0.0901334 | ||||||||
\(713\) | −5.27229e35 | −1.14388 | ||||||||
\(714\) | 8.26166e35 | 1.76133 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.83459e35 | 0.377681 | ||||||||
\(717\) | 2.35585e35 | 0.476604 | ||||||||
\(718\) | 1.77703e35 | 0.353296 | ||||||||
\(719\) | 9.50282e35 | 1.85670 | 0.928349 | − | 0.371709i | \(-0.121228\pi\) | ||||
0.928349 | + | 0.371709i | \(0.121228\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.17647e35 | 0.976884 | ||||||||
\(722\) | 4.68219e34 | 0.0868429 | ||||||||
\(723\) | 8.11256e35 | 1.47887 | ||||||||
\(724\) | −1.45108e35 | −0.259992 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.02166e35 | 0.176848 | ||||||||
\(727\) | 1.71833e35 | 0.292367 | 0.146183 | − | 0.989258i | \(-0.453301\pi\) | ||||
0.146183 | + | 0.989258i | \(0.453301\pi\) | |||||||
\(728\) | −4.31128e35 | −0.721048 | ||||||||
\(729\) | 2.16385e35 | 0.355741 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.65090e34 | −0.0738873 | ||||||||
\(732\) | 1.35254e35 | 0.211233 | ||||||||
\(733\) | −5.57098e35 | −0.855327 | −0.427664 | − | 0.903938i | \(-0.640663\pi\) | ||||
−0.427664 | + | 0.903938i | \(0.640663\pi\) | |||||||
\(734\) | −1.93113e35 | −0.291481 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.09830e35 | −0.306122 | ||||||||
\(737\) | 6.88801e35 | 0.987985 | ||||||||
\(738\) | −5.77856e33 | −0.00814921 | ||||||||
\(739\) | 6.81418e35 | 0.944839 | 0.472420 | − | 0.881374i | \(-0.343381\pi\) | ||||
0.472420 | + | 0.881374i | \(0.343381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.42319e36 | −1.90781 | ||||||||
\(742\) | 5.10775e35 | 0.673257 | ||||||||
\(743\) | 7.94423e35 | 1.02965 | 0.514827 | − | 0.857294i | \(-0.327856\pi\) | ||||
0.514827 | + | 0.857294i | \(0.327856\pi\) | |||||||
\(744\) | 2.16386e35 | 0.275782 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.06564e35 | 0.501065 | ||||||||
\(747\) | −1.53884e35 | −0.186503 | ||||||||
\(748\) | −7.28246e35 | −0.867977 | ||||||||
\(749\) | −2.18782e35 | −0.256442 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.09984e35 | 1.03166 | 0.515828 | − | 0.856692i | \(-0.327484\pi\) | ||||
0.515828 | + | 0.856692i | \(0.327484\pi\) | |||||||
\(752\) | −1.29516e35 | −0.144411 | ||||||||
\(753\) | 8.11619e35 | 0.890051 | ||||||||
\(754\) | 1.14966e36 | 1.24002 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.58325e35 | 0.478245 | ||||||||
\(757\) | 9.30502e35 | 0.955034 | 0.477517 | − | 0.878623i | \(-0.341537\pi\) | ||||
0.477517 | + | 0.878623i | \(0.341537\pi\) | |||||||
\(758\) | −2.57570e35 | −0.260034 | ||||||||
\(759\) | −2.26677e36 | −2.25105 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.13441e36 | 1.09009 | 0.545045 | − | 0.838407i | \(-0.316513\pi\) | ||||
0.545045 | + | 0.838407i | \(0.316513\pi\) | |||||||
\(762\) | −8.53236e35 | −0.806552 | ||||||||
\(763\) | 2.20342e36 | 2.04900 | ||||||||
\(764\) | 2.95967e35 | 0.270755 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.02904e35 | −0.179651 | ||||||||
\(767\) | −2.81992e35 | −0.245637 | ||||||||
\(768\) | 8.61186e34 | 0.0738043 | ||||||||
\(769\) | −2.29001e36 | −1.93090 | −0.965448 | − | 0.260597i | \(-0.916081\pi\) | ||||
−0.965448 | + | 0.260597i | \(0.916081\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.20990e35 | −0.180382 | ||||||||
\(772\) | −8.50281e34 | −0.0682883 | ||||||||
\(773\) | −3.21550e35 | −0.254100 | −0.127050 | − | 0.991896i | \(-0.540551\pi\) | ||||
−0.127050 | + | 0.991896i | \(0.540551\pi\) | |||||||
\(774\) | 1.68068e34 | 0.0130684 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.98574e35 | 0.450657 | ||||||||
\(777\) | 2.43156e36 | 1.80145 | ||||||||
\(778\) | −1.67965e36 | −1.22454 | ||||||||
\(779\) | 4.31529e34 | 0.0309594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.11397e35 | 0.285840 | ||||||||
\(782\) | 2.82399e36 | 1.93098 | ||||||||
\(783\) | −1.22219e36 | −0.822461 | ||||||||
\(784\) | 2.97905e35 | 0.197300 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.91701e35 | −0.636208 | ||||||||
\(787\) | −3.25977e35 | −0.205827 | −0.102914 | − | 0.994690i | \(-0.532817\pi\) | ||||
−0.102914 | + | 0.994690i | \(0.532817\pi\) | |||||||
\(788\) | −9.48202e34 | −0.0589282 | ||||||||
\(789\) | 3.46437e36 | 2.11915 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.36685e36 | 0.810054 | ||||||||
\(792\) | 2.63164e35 | 0.153519 | ||||||||
\(793\) | 9.49918e35 | 0.545470 | ||||||||
\(794\) | −7.41849e35 | −0.419333 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.67809e35 | 0.201469 | ||||||||
\(797\) | 8.54851e35 | 0.460958 | 0.230479 | − | 0.973077i | \(-0.425971\pi\) | ||||
0.230479 | + | 0.973077i | \(0.425971\pi\) | |||||||
\(798\) | 2.22949e36 | 1.18350 | ||||||||
\(799\) | 1.74308e36 | 0.910925 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.98532e35 | 0.100559 | ||||||||
\(802\) | 5.33538e35 | 0.266064 | ||||||||
\(803\) | −2.27284e36 | −1.11590 | ||||||||
\(804\) | 1.09625e36 | 0.529917 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.51972e36 | 0.712156 | ||||||||
\(807\) | 1.17825e35 | 0.0543651 | ||||||||
\(808\) | 5.37013e35 | 0.243973 | ||||||||
\(809\) | −3.81958e36 | −1.70867 | −0.854336 | − | 0.519721i | \(-0.826036\pi\) | ||||
−0.854336 | + | 0.519721i | \(0.826036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.53614e36 | −1.10005 | −0.550025 | − | 0.835148i | \(-0.685382\pi\) | ||||
−0.550025 | + | 0.835148i | \(0.685382\pi\) | |||||||
\(812\) | −1.80100e36 | −0.769243 | ||||||||
\(813\) | 9.13625e35 | 0.384270 | ||||||||
\(814\) | −2.14336e36 | −0.887750 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.15902e36 | −0.465549 | ||||||||
\(817\) | −1.25509e35 | −0.0496478 | ||||||||
\(818\) | 3.51949e36 | 1.37108 | ||||||||
\(819\) | −2.09677e36 | −0.804455 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.03536e35 | −0.224602 | −0.112301 | − | 0.993674i | \(-0.535822\pi\) | ||||
−0.112301 | + | 0.993674i | \(0.535822\pi\) | |||||||
\(822\) | −1.60253e36 | −0.587366 | ||||||||
\(823\) | 3.78844e36 | 1.36761 | 0.683804 | − | 0.729665i | \(-0.260324\pi\) | ||||
0.683804 | + | 0.729665i | \(0.260324\pi\) | |||||||
\(824\) | −7.26205e35 | −0.258208 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.41753e35 | 0.152380 | ||||||||
\(827\) | 3.11766e36 | 1.05928 | 0.529639 | − | 0.848223i | \(-0.322328\pi\) | ||||
0.529639 | + | 0.848223i | \(0.322328\pi\) | |||||||
\(828\) | −1.02050e36 | −0.341533 | ||||||||
\(829\) | 5.42365e36 | 1.78797 | 0.893984 | − | 0.448099i | \(-0.147899\pi\) | ||||
0.893984 | + | 0.448099i | \(0.147899\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.74233e36 | −1.83686 | ||||||||
\(832\) | 6.04827e35 | 0.190586 | ||||||||
\(833\) | −4.00934e36 | −1.24454 | ||||||||
\(834\) | −2.30691e36 | −0.705432 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.96525e36 | −0.583228 | ||||||||
\(837\) | −1.61558e36 | −0.472347 | ||||||||
\(838\) | −1.91295e36 | −0.551003 | ||||||||
\(839\) | −3.97800e35 | −0.112886 | −0.0564431 | − | 0.998406i | \(-0.517976\pi\) | ||||
−0.0564431 | + | 0.998406i | \(0.517976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.17226e36 | 0.322904 | ||||||||
\(842\) | −3.03953e36 | −0.824907 | ||||||||
\(843\) | −6.40996e36 | −1.71400 | ||||||||
\(844\) | 1.52839e36 | 0.402675 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.29891e35 | −0.161115 | ||||||||
\(847\) | −1.12405e36 | −0.283297 | ||||||||
\(848\) | −7.16563e35 | −0.177953 | ||||||||
\(849\) | 1.72094e36 | 0.421134 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.31153e36 | 1.97497 | ||||||||
\(852\) | 6.54749e35 | 0.153313 | ||||||||
\(853\) | 2.49788e36 | 0.576379 | 0.288189 | − | 0.957573i | \(-0.406947\pi\) | ||||
0.288189 | + | 0.957573i | \(0.406947\pi\) | |||||||
\(854\) | −1.48809e36 | −0.338381 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.06928e35 | 0.0677820 | ||||||||
\(857\) | −5.58799e36 | −1.21617 | −0.608086 | − | 0.793871i | \(-0.708062\pi\) | ||||
−0.608086 | + | 0.793871i | \(0.708062\pi\) | |||||||
\(858\) | 6.53389e36 | 1.40146 | ||||||||
\(859\) | 4.00214e36 | 0.846015 | 0.423007 | − | 0.906126i | \(-0.360974\pi\) | ||||
0.423007 | + | 0.906126i | \(0.360974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.24755e35 | 0.0461497 | ||||||||
\(862\) | 4.35896e36 | 0.882149 | ||||||||
\(863\) | 1.01320e36 | 0.202097 | 0.101048 | − | 0.994882i | \(-0.467780\pi\) | ||||
0.101048 | + | 0.994882i | \(0.467780\pi\) | |||||||
\(864\) | −6.42981e35 | −0.126409 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.76971e36 | 0.720003 | ||||||||
\(867\) | 9.32618e36 | 1.75576 | ||||||||
\(868\) | −2.38071e36 | −0.441783 | ||||||||
\(869\) | −8.98952e36 | −1.64433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.69915e36 | 1.36841 | ||||||||
\(872\) | −3.09117e36 | −0.541586 | ||||||||
\(873\) | 2.91113e36 | 0.502786 | ||||||||
\(874\) | 7.62083e36 | 1.29751 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.61729e36 | −0.598524 | ||||||||
\(877\) | −1.04808e37 | −1.70962 | −0.854808 | − | 0.518944i | \(-0.826325\pi\) | ||||
−0.854808 | + | 0.518944i | \(0.826325\pi\) | |||||||
\(878\) | −1.57662e36 | −0.253539 | ||||||||
\(879\) | 5.39529e36 | 0.855370 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.82632e36 | −1.20603 | −0.603016 | − | 0.797729i | \(-0.706035\pi\) | ||||
−0.603016 | + | 0.797729i | \(0.706035\pi\) | |||||||
\(882\) | 1.44884e36 | 0.220122 | ||||||||
\(883\) | −1.14075e37 | −1.70876 | −0.854379 | − | 0.519651i | \(-0.826062\pi\) | ||||
−0.854379 | + | 0.519651i | \(0.826062\pi\) | |||||||
\(884\) | −8.14005e36 | −1.20219 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.49590e36 | −0.501924 | ||||||||
\(887\) | −2.08825e35 | −0.0295622 | −0.0147811 | − | 0.999891i | \(-0.504705\pi\) | ||||
−0.0147811 | + | 0.999891i | \(0.504705\pi\) | |||||||
\(888\) | −3.41122e36 | −0.476155 | ||||||||
\(889\) | 9.38744e36 | 1.29204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.01908e37 | −1.36375 | ||||||||
\(892\) | 1.77848e36 | 0.234687 | ||||||||
\(893\) | 4.70388e36 | 0.612086 | ||||||||
\(894\) | −8.54783e36 | −1.09682 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.47490e35 | −0.118229 | ||||||||
\(897\) | −2.53371e37 | −3.11782 | ||||||||
\(898\) | 1.40350e36 | 0.170317 | ||||||||
\(899\) | 6.34849e36 | 0.759756 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.64384e36 | 1.12251 | ||||||||
\(902\) | −1.98116e35 | −0.0227425 | ||||||||
\(903\) | −6.53693e35 | −0.0740077 | ||||||||
\(904\) | −1.91754e36 | −0.214111 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.36097e36 | −0.582292 | ||||||||
\(907\) | −1.26800e37 | −1.35841 | −0.679203 | − | 0.733950i | \(-0.737674\pi\) | ||||
−0.679203 | + | 0.733950i | \(0.737674\pi\) | |||||||
\(908\) | −8.40614e36 | −0.888226 | ||||||||
\(909\) | 2.61173e36 | 0.272195 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.78070e36 | −0.991722 | −0.495861 | − | 0.868402i | \(-0.665148\pi\) | ||||
−0.495861 | + | 0.868402i | \(0.665148\pi\) | |||||||
\(912\) | −3.12774e36 | −0.312821 | ||||||||
\(913\) | −5.27586e36 | −0.520486 | ||||||||
\(914\) | 1.85175e36 | 0.180200 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.37053e35 | −0.0508538 | ||||||||
\(917\) | 1.09108e37 | 1.01916 | ||||||||
\(918\) | 8.65354e36 | 0.797370 | ||||||||
\(919\) | −7.03823e36 | −0.639764 | −0.319882 | − | 0.947457i | \(-0.603643\pi\) | ||||
−0.319882 | + | 0.947457i | \(0.603643\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.40596e37 | 1.24373 | ||||||||
\(922\) | 1.01236e37 | 0.883485 | ||||||||
\(923\) | 4.59843e36 | 0.395903 | ||||||||
\(924\) | −1.02356e37 | −0.869391 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.07085e36 | −0.584567 | ||||||||
\(927\) | −3.53185e36 | −0.288075 | ||||||||
\(928\) | 2.52661e36 | 0.203324 | ||||||||
\(929\) | 2.91517e36 | 0.231455 | 0.115728 | − | 0.993281i | \(-0.463080\pi\) | ||||
0.115728 | + | 0.993281i | \(0.463080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.08196e37 | −0.836258 | ||||||||
\(932\) | −1.03956e37 | −0.792778 | ||||||||
\(933\) | −1.83303e36 | −0.137927 | ||||||||
\(934\) | −7.71244e36 | −0.572606 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.94154e36 | 0.212631 | ||||||||
\(937\) | −1.15106e37 | −0.821016 | −0.410508 | − | 0.911857i | \(-0.634649\pi\) | ||||
−0.410508 | + | 0.911857i | \(0.634649\pi\) | |||||||
\(938\) | −1.20611e37 | −0.848888 | ||||||||
\(939\) | 2.93889e36 | 0.204110 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.44936e37 | 0.980179 | 0.490090 | − | 0.871672i | \(-0.336964\pi\) | ||||
0.490090 | + | 0.871672i | \(0.336964\pi\) | |||||||
\(942\) | −1.92774e37 | −1.28651 | ||||||||
\(943\) | 7.68253e35 | 0.0505951 | ||||||||
\(944\) | −6.19733e35 | −0.0402768 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.76215e35 | 0.0364708 | ||||||||
\(947\) | 2.53109e37 | 1.58100 | 0.790502 | − | 0.612459i | \(-0.209820\pi\) | ||||
0.790502 | + | 0.612459i | \(0.209820\pi\) | |||||||
\(948\) | −1.43071e37 | −0.881956 | ||||||||
\(949\) | −2.54049e37 | −1.54557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.57728e37 | 2.11981 | ||||||||
\(952\) | 1.27518e37 | 0.745775 | ||||||||
\(953\) | 8.20660e36 | 0.473698 | 0.236849 | − | 0.971546i | \(-0.423885\pi\) | ||||
0.236849 | + | 0.971546i | \(0.423885\pi\) | |||||||
\(954\) | −3.48496e36 | −0.198538 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.63622e36 | 0.201803 | ||||||||
\(957\) | 2.72948e37 | 1.49513 | ||||||||
\(958\) | 4.39513e36 | 0.237631 | ||||||||
\(959\) | 1.76313e37 | 0.940917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.08408e37 | −0.563665 | ||||||||
\(962\) | −2.39577e37 | −1.22958 | ||||||||
\(963\) | 1.49273e36 | 0.0756226 | ||||||||
\(964\) | 1.25216e37 | 0.626178 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.96917e37 | 1.93413 | ||||||||
\(967\) | 2.92106e37 | 1.40511 | 0.702555 | − | 0.711630i | \(-0.252043\pi\) | ||||
0.702555 | + | 0.711630i | \(0.252043\pi\) | |||||||
\(968\) | 1.57692e36 | 0.0748804 | ||||||||
\(969\) | 4.20946e37 | 1.97324 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.97325e36 | 0.455613 | 0.227807 | − | 0.973706i | \(-0.426845\pi\) | ||||
0.227807 | + | 0.973706i | \(0.426845\pi\) | |||||||
\(972\) | −8.29117e36 | −0.373928 | ||||||||
\(973\) | 2.53810e37 | 1.13005 | ||||||||
\(974\) | −2.56529e37 | −1.12759 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.08763e36 | 0.0894399 | ||||||||
\(977\) | −3.07257e37 | −1.29963 | −0.649816 | − | 0.760092i | \(-0.725154\pi\) | ||||
−0.649816 | + | 0.760092i | \(0.725154\pi\) | |||||||
\(978\) | 2.23600e37 | 0.933760 | ||||||||
\(979\) | 6.80658e36 | 0.280637 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.50337e37 | −0.604233 | ||||||||
\(982\) | 1.27153e37 | 0.504582 | ||||||||
\(983\) | 5.34152e36 | 0.209289 | 0.104644 | − | 0.994510i | \(-0.466630\pi\) | ||||
0.104644 | + | 0.994510i | \(0.466630\pi\) | |||||||
\(984\) | −3.15307e35 | −0.0121982 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.40043e37 | −1.28255 | ||||||||
\(987\) | 2.44993e37 | 0.912409 | ||||||||
\(988\) | −2.19667e37 | −0.807800 | ||||||||
\(989\) | −2.23445e36 | −0.0811365 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.37784e36 | −0.155003 | −0.0775013 | − | 0.996992i | \(-0.524694\pi\) | ||||
−0.0775013 | + | 0.996992i | \(0.524694\pi\) | |||||||
\(992\) | 3.33988e36 | 0.116771 | ||||||||
\(993\) | −3.37359e37 | −1.16473 | ||||||||
\(994\) | −7.20365e36 | −0.245597 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.39668e36 | −0.279168 | ||||||||
\(997\) | 2.23560e37 | 0.734015 | 0.367008 | − | 0.930218i | \(-0.380382\pi\) | ||||
0.367008 | + | 0.930218i | \(0.380382\pi\) | |||||||
\(998\) | 2.91817e37 | 0.946190 | ||||||||
\(999\) | 2.54690e37 | 0.815535 |
(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 | 50.26.a.l.1.6 | 6 | ||
5.2 | odd | 4 | 10.26.b.a.9.7 | yes | 12 | ||
5.3 | odd | 4 | 10.26.b.a.9.6 | ✓ | 12 | ||
5.4 | even | 2 | 50.26.a.k.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.b.a.9.6 | ✓ | 12 | 5.3 | odd | 4 | ||
10.26.b.a.9.7 | yes | 12 | 5.2 | odd | 4 | ||
50.26.a.k.1.1 | 6 | 5.4 | even | 2 | |||
50.26.a.l.1.6 | 6 | 1.1 | even | 1 | trivial |