Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,10,Mod(49,50)]
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([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(25.7517918082\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.10.b.d.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16.0000i | 0.707107i | ||||||||
\(3\) | − 174.000i | − 1.24023i | −0.784509 | − | 0.620117i | \(-0.787085\pi\) | ||||
0.784509 | − | 0.620117i | \(-0.212915\pi\) | |||||||
\(4\) | −256.000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2784.00 | 0.876978 | ||||||||
\(7\) | 4658.00i | 0.733261i | 0.930367 | + | 0.366630i | \(0.119489\pi\) | ||||
−0.930367 | + | 0.366630i | \(0.880511\pi\) | |||||||
\(8\) | − 4096.00i | − 0.353553i | ||||||||
\(9\) | −10593.0 | −0.538180 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28992.0 | 0.597051 | 0.298525 | − | 0.954402i | \(-0.403505\pi\) | ||||
0.298525 | + | 0.954402i | \(0.403505\pi\) | |||||||
\(12\) | 44544.0i | 0.620117i | ||||||||
\(13\) | 164446.i | 1.59690i | 0.602060 | + | 0.798451i | \(0.294347\pi\) | ||||
−0.602060 | + | 0.798451i | \(0.705653\pi\) | |||||||
\(14\) | −74528.0 | −0.518493 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | − 594822.i | − 1.72730i | −0.504095 | − | 0.863648i | \(-0.668174\pi\) | ||||
0.504095 | − | 0.863648i | \(-0.331826\pi\) | |||||||
\(18\) | − 169488.i | − 0.380551i | ||||||||
\(19\) | 295780. | 0.520688 | 0.260344 | − | 0.965516i | \(-0.416164\pi\) | ||||
0.260344 | + | 0.965516i | \(0.416164\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 810492. | 0.909415 | ||||||||
\(22\) | 463872.i | 0.422178i | ||||||||
\(23\) | − 2.54453e6i | − 1.89598i | −0.318305 | − | 0.947988i | \(-0.603114\pi\) | ||||
0.318305 | − | 0.947988i | \(-0.396886\pi\) | |||||||
\(24\) | −712704. | −0.438489 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.63114e6 | −1.12918 | ||||||||
\(27\) | − 1.58166e6i | − 0.572765i | ||||||||
\(28\) | − 1.19245e6i | − 0.366630i | ||||||||
\(29\) | 3.72297e6 | 0.977459 | 0.488729 | − | 0.872435i | \(-0.337461\pi\) | ||||
0.488729 | + | 0.872435i | \(0.337461\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.33577e6 | 0.454258 | 0.227129 | − | 0.973865i | \(-0.427066\pi\) | ||||
0.227129 | + | 0.973865i | \(0.427066\pi\) | |||||||
\(32\) | 1.04858e6i | 0.176777i | ||||||||
\(33\) | − 5.04461e6i | − 0.740482i | ||||||||
\(34\) | 9.51715e6 | 1.22138 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.71181e6 | 0.269090 | ||||||||
\(37\) | 1.08404e7i | 0.950907i | 0.879741 | + | 0.475454i | \(0.157716\pi\) | ||||
−0.879741 | + | 0.475454i | \(0.842284\pi\) | |||||||
\(38\) | 4.73248e6i | 0.368182i | ||||||||
\(39\) | 2.86136e7 | 1.98053 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.15939e7 | 1.19345 | 0.596723 | − | 0.802447i | \(-0.296469\pi\) | ||||
0.596723 | + | 0.802447i | \(0.296469\pi\) | |||||||
\(42\) | 1.29679e7i | 0.643053i | ||||||||
\(43\) | − 1.08323e7i | − 0.483184i | −0.970378 | − | 0.241592i | \(-0.922330\pi\) | ||||
0.970378 | − | 0.241592i | \(-0.0776695\pi\) | |||||||
\(44\) | −7.42195e6 | −0.298525 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.07125e7 | 1.34066 | ||||||||
\(47\) | 5.17214e6i | 0.154607i | 0.997008 | + | 0.0773036i | \(0.0246311\pi\) | ||||
−0.997008 | + | 0.0773036i | \(0.975369\pi\) | |||||||
\(48\) | − 1.14033e7i | − 0.310058i | ||||||||
\(49\) | 1.86566e7 | 0.462329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.03499e8 | −2.14225 | ||||||||
\(52\) | − 4.20982e7i | − 0.798451i | ||||||||
\(53\) | − 9.81797e7i | − 1.70915i | −0.519328 | − | 0.854575i | \(-0.673818\pi\) | ||||
0.519328 | − | 0.854575i | \(-0.326182\pi\) | |||||||
\(54\) | 2.53066e7 | 0.405006 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.90792e7 | 0.259247 | ||||||||
\(57\) | − 5.14657e7i | − 0.645775i | ||||||||
\(58\) | 5.95675e7i | 0.691168i | ||||||||
\(59\) | −1.61629e7 | −0.173654 | −0.0868269 | − | 0.996223i | \(-0.527673\pi\) | ||||
−0.0868269 | + | 0.996223i | \(0.527673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.39282e7 | −0.406218 | −0.203109 | − | 0.979156i | \(-0.565105\pi\) | ||||
−0.203109 | + | 0.979156i | \(0.565105\pi\) | |||||||
\(62\) | 3.73724e7i | 0.321209i | ||||||||
\(63\) | − 4.93422e7i | − 0.394626i | ||||||||
\(64\) | −1.67772e7 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.07137e7 | 0.523600 | ||||||||
\(67\) | − 8.15574e7i | − 0.494455i | −0.968957 | − | 0.247228i | \(-0.920480\pi\) | ||||
0.968957 | − | 0.247228i | \(-0.0795195\pi\) | |||||||
\(68\) | 1.52274e8i | 0.863648i | ||||||||
\(69\) | −4.42749e8 | −2.35145 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.61308e8 | 0.753343 | 0.376671 | − | 0.926347i | \(-0.377069\pi\) | ||||
0.376671 | + | 0.926347i | \(0.377069\pi\) | |||||||
\(72\) | 4.33889e7i | 0.190275i | ||||||||
\(73\) | 2.47148e8i | 1.01860i | 0.860589 | + | 0.509301i | \(0.170096\pi\) | ||||
−0.860589 | + | 0.509301i | \(0.829904\pi\) | |||||||
\(74\) | −1.73447e8 | −0.672393 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.57197e7 | −0.260344 | ||||||||
\(77\) | 1.35045e8i | 0.437794i | ||||||||
\(78\) | 4.57818e8i | 1.40045i | ||||||||
\(79\) | 5.83346e8 | 1.68502 | 0.842508 | − | 0.538684i | \(-0.181078\pi\) | ||||
0.842508 | + | 0.538684i | \(0.181078\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.83711e8 | −1.24854 | ||||||||
\(82\) | 3.45502e8i | 0.843894i | ||||||||
\(83\) | 1.45718e7i | 0.0337024i | 0.999858 | + | 0.0168512i | \(0.00536416\pi\) | ||||
−0.999858 | + | 0.0168512i | \(0.994636\pi\) | |||||||
\(84\) | −2.07486e8 | −0.454707 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.73317e8 | 0.341663 | ||||||||
\(87\) | − 6.47797e8i | − 1.21228i | ||||||||
\(88\) | − 1.18751e8i | − 0.211089i | ||||||||
\(89\) | −4.70134e8 | −0.794267 | −0.397133 | − | 0.917761i | \(-0.629995\pi\) | ||||
−0.397133 | + | 0.917761i | \(0.629995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.65989e8 | −1.17095 | ||||||||
\(92\) | 6.51401e8i | 0.947988i | ||||||||
\(93\) | − 4.06424e8i | − 0.563386i | ||||||||
\(94\) | −8.27542e7 | −0.109324 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.82452e8 | 0.219244 | ||||||||
\(97\) | − 1.17838e8i | − 0.135149i | −0.997714 | − | 0.0675747i | \(-0.978474\pi\) | ||||
0.997714 | − | 0.0675747i | \(-0.0215261\pi\) | |||||||
\(98\) | 2.98506e8i | 0.326916i | ||||||||
\(99\) | −3.07112e8 | −0.321321 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.60927e7 | −0.0823228 | −0.0411614 | − | 0.999153i | \(-0.513106\pi\) | ||||
−0.0411614 | + | 0.999153i | \(0.513106\pi\) | |||||||
\(102\) | − 1.65598e9i | − 1.51480i | ||||||||
\(103\) | − 1.92872e9i | − 1.68850i | −0.535947 | − | 0.844252i | \(-0.680045\pi\) | ||||
0.535947 | − | 0.844252i | \(-0.319955\pi\) | |||||||
\(104\) | 6.73571e8 | 0.564590 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.57087e9 | 1.20855 | ||||||||
\(107\) | 1.39685e9i | 1.03020i | 0.857130 | + | 0.515100i | \(0.172245\pi\) | ||||
−0.857130 | + | 0.515100i | \(0.827755\pi\) | |||||||
\(108\) | 4.04905e8i | 0.286382i | ||||||||
\(109\) | 6.04327e8 | 0.410065 | 0.205033 | − | 0.978755i | \(-0.434270\pi\) | ||||
0.205033 | + | 0.978755i | \(0.434270\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.88623e9 | 1.17935 | ||||||||
\(112\) | 3.05267e8i | 0.183315i | ||||||||
\(113\) | 1.68580e9i | 0.972643i | 0.873780 | + | 0.486322i | \(0.161662\pi\) | ||||
−0.873780 | + | 0.486322i | \(0.838338\pi\) | |||||||
\(114\) | 8.23452e8 | 0.456632 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.53080e8 | −0.488729 | ||||||||
\(117\) | − 1.74198e9i | − 0.859421i | ||||||||
\(118\) | − 2.58606e8i | − 0.122792i | ||||||||
\(119\) | 2.77068e9 | 1.26656 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.51741e9 | −0.643531 | ||||||||
\(122\) | − 7.02851e8i | − 0.287239i | ||||||||
\(123\) | − 3.75733e9i | − 1.48015i | ||||||||
\(124\) | −5.97958e8 | −0.227129 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.89475e8 | 0.279043 | ||||||||
\(127\) | 3.70716e9i | 1.26452i | 0.774758 | + | 0.632258i | \(0.217872\pi\) | ||||
−0.774758 | + | 0.632258i | \(0.782128\pi\) | |||||||
\(128\) | − 2.68435e8i | − 0.0883883i | ||||||||
\(129\) | −1.88482e9 | −0.599261 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.54080e9 | 0.753789 | 0.376895 | − | 0.926256i | \(-0.376992\pi\) | ||||
0.376895 | + | 0.926256i | \(0.376992\pi\) | |||||||
\(132\) | 1.29142e9i | 0.370241i | ||||||||
\(133\) | 1.37774e9i | 0.381800i | ||||||||
\(134\) | 1.30492e9 | 0.349633 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.43639e9 | −0.610692 | ||||||||
\(137\) | − 1.15390e9i | − 0.279849i | −0.990162 | − | 0.139925i | \(-0.955314\pi\) | ||||
0.990162 | − | 0.139925i | \(-0.0446860\pi\) | |||||||
\(138\) | − 7.08398e9i | − 1.66273i | ||||||||
\(139\) | 5.62721e9 | 1.27858 | 0.639288 | − | 0.768968i | \(-0.279229\pi\) | ||||
0.639288 | + | 0.768968i | \(0.279229\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.99952e8 | 0.191749 | ||||||||
\(142\) | 2.58092e9i | 0.532694i | ||||||||
\(143\) | 4.76762e9i | 0.953431i | ||||||||
\(144\) | −6.94223e8 | −0.134545 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.95437e9 | −0.720260 | ||||||||
\(147\) | − 3.24626e9i | − 0.573396i | ||||||||
\(148\) | − 2.77515e9i | − 0.475454i | ||||||||
\(149\) | 2.13688e9 | 0.355174 | 0.177587 | − | 0.984105i | \(-0.443171\pi\) | ||||
0.177587 | + | 0.984105i | \(0.443171\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.67515e6 | −0.00151447 | −0.000757236 | − | 1.00000i | \(-0.500241\pi\) | ||||
−0.000757236 | 1.00000i | \(0.500241\pi\) | ||||||||
\(152\) | − 1.21151e9i | − 0.184091i | ||||||||
\(153\) | 6.30095e9i | 0.929597i | ||||||||
\(154\) | −2.16072e9 | −0.309567 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.32508e9 | −0.990266 | ||||||||
\(157\) | − 6.88488e8i | − 0.0904373i | −0.998977 | − | 0.0452187i | \(-0.985602\pi\) | ||||
0.998977 | − | 0.0452187i | \(-0.0143985\pi\) | |||||||
\(158\) | 9.33353e9i | 1.19149i | ||||||||
\(159\) | −1.70833e10 | −2.11975 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.18524e10 | 1.39024 | ||||||||
\(162\) | − 7.73937e9i | − 0.882853i | ||||||||
\(163\) | 1.43082e10i | 1.58759i | 0.608182 | + | 0.793797i | \(0.291899\pi\) | ||||
−0.608182 | + | 0.793797i | \(0.708101\pi\) | |||||||
\(164\) | −5.52803e9 | −0.596723 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.33149e8 | −0.0238312 | ||||||||
\(167\) | 9.98735e9i | 0.993633i | 0.867856 | + | 0.496817i | \(0.165498\pi\) | ||||
−0.867856 | + | 0.496817i | \(0.834502\pi\) | |||||||
\(168\) | − 3.31978e9i | − 0.321527i | ||||||||
\(169\) | −1.64380e10 | −1.55010 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.13320e9 | −0.280224 | ||||||||
\(172\) | 2.77307e9i | 0.241592i | ||||||||
\(173\) | − 3.51396e9i | − 0.298256i | −0.988818 | − | 0.149128i | \(-0.952353\pi\) | ||||
0.988818 | − | 0.149128i | \(-0.0476466\pi\) | |||||||
\(174\) | 1.03647e10 | 0.857210 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.90002e9 | 0.149263 | ||||||||
\(177\) | 2.81234e9i | 0.215371i | ||||||||
\(178\) | − 7.52214e9i | − 0.561631i | ||||||||
\(179\) | −1.19502e9 | −0.0870038 | −0.0435019 | − | 0.999053i | \(-0.513851\pi\) | ||||
−0.0435019 | + | 0.999053i | \(0.513851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.12053e9 | −0.631635 | −0.315818 | − | 0.948820i | \(-0.602279\pi\) | ||||
−0.315818 | + | 0.948820i | \(0.602279\pi\) | |||||||
\(182\) | − 1.22558e10i | − 0.827983i | ||||||||
\(183\) | 7.64350e9i | 0.503805i | ||||||||
\(184\) | −1.04224e10 | −0.670329 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.50279e9 | 0.398374 | ||||||||
\(187\) | − 1.72451e10i | − 1.03128i | ||||||||
\(188\) | − 1.32407e9i | − 0.0773036i | ||||||||
\(189\) | 7.36737e9 | 0.419986 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.37431e9 | −0.509670 | −0.254835 | − | 0.966985i | \(-0.582021\pi\) | ||||
−0.254835 | + | 0.966985i | \(0.582021\pi\) | |||||||
\(192\) | 2.91924e9i | 0.155029i | ||||||||
\(193\) | − 2.40000e10i | − 1.24510i | −0.782580 | − | 0.622550i | \(-0.786097\pi\) | ||||
0.782580 | − | 0.622550i | \(-0.213903\pi\) | |||||||
\(194\) | 1.88542e9 | 0.0955651 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.77610e9 | −0.231165 | ||||||||
\(197\) | − 5.56124e8i | − 0.0263071i | −0.999913 | − | 0.0131536i | \(-0.995813\pi\) | ||||
0.999913 | − | 0.0131536i | \(-0.00418703\pi\) | |||||||
\(198\) | − 4.91380e9i | − 0.227208i | ||||||||
\(199\) | 2.51255e10 | 1.13573 | 0.567866 | − | 0.823121i | \(-0.307769\pi\) | ||||
0.567866 | + | 0.823121i | \(0.307769\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.41910e10 | −0.613240 | ||||||||
\(202\) | − 1.37748e9i | − 0.0582110i | ||||||||
\(203\) | 1.73416e10i | 0.716732i | ||||||||
\(204\) | 2.64958e10 | 1.07113 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.08595e10 | 1.19395 | ||||||||
\(207\) | 2.69542e10i | 1.02038i | ||||||||
\(208\) | 1.07771e10i | 0.399225i | ||||||||
\(209\) | 8.57525e9 | 0.310877 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.63915e10 | −0.569309 | −0.284654 | − | 0.958630i | \(-0.591879\pi\) | ||||
−0.284654 | + | 0.958630i | \(0.591879\pi\) | |||||||
\(212\) | 2.51340e10i | 0.854575i | ||||||||
\(213\) | − 2.80675e10i | − 0.934321i | ||||||||
\(214\) | −2.23495e10 | −0.728461 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.47848e9 | −0.202503 | ||||||||
\(217\) | 1.08800e10i | 0.333090i | ||||||||
\(218\) | 9.66924e9i | 0.289960i | ||||||||
\(219\) | 4.30037e10 | 1.26330 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.78161e10 | 2.75832 | ||||||||
\(222\) | 3.01797e10i | 0.833925i | ||||||||
\(223\) | − 4.65257e10i | − 1.25986i | −0.776654 | − | 0.629928i | \(-0.783084\pi\) | ||||
0.776654 | − | 0.629928i | \(-0.216916\pi\) | |||||||
\(224\) | −4.88427e9 | −0.129623 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.69728e10 | −0.687763 | ||||||||
\(227\) | − 1.91415e9i | − 0.0478475i | −0.999714 | − | 0.0239237i | \(-0.992384\pi\) | ||||
0.999714 | − | 0.0239237i | \(-0.00761589\pi\) | |||||||
\(228\) | 1.31752e10i | 0.322887i | ||||||||
\(229\) | 1.45825e10 | 0.350406 | 0.175203 | − | 0.984532i | \(-0.443942\pi\) | ||||
0.175203 | + | 0.984532i | \(0.443942\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.34978e10 | 0.542966 | ||||||||
\(232\) | − 1.52493e10i | − 0.345584i | ||||||||
\(233\) | − 4.12790e10i | − 0.917545i | −0.888554 | − | 0.458773i | \(-0.848289\pi\) | ||||
0.888554 | − | 0.458773i | \(-0.151711\pi\) | |||||||
\(234\) | 2.78716e10 | 0.607702 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.13769e9 | 0.0868269 | ||||||||
\(237\) | − 1.01502e11i | − 2.08981i | ||||||||
\(238\) | 4.43309e10i | 0.895592i | ||||||||
\(239\) | −3.65502e10 | −0.724602 | −0.362301 | − | 0.932061i | \(-0.618009\pi\) | ||||
−0.362301 | + | 0.932061i | \(0.618009\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.66070e10 | −1.65377 | −0.826887 | − | 0.562368i | \(-0.809890\pi\) | ||||
−0.826887 | + | 0.562368i | \(0.809890\pi\) | |||||||
\(242\) | − 2.42786e10i | − 0.455045i | ||||||||
\(243\) | 5.30339e10i | 0.975720i | ||||||||
\(244\) | 1.12456e10 | 0.203109 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.01173e10 | 1.04663 | ||||||||
\(247\) | 4.86398e10i | 0.831488i | ||||||||
\(248\) | − 9.56732e9i | − 0.160605i | ||||||||
\(249\) | 2.53549e9 | 0.0417989 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.20769e10 | −1.14621 | −0.573105 | − | 0.819482i | \(-0.694261\pi\) | ||||
−0.573105 | + | 0.819482i | \(0.694261\pi\) | |||||||
\(252\) | 1.26316e10i | 0.197313i | ||||||||
\(253\) | − 7.37711e10i | − 1.13199i | ||||||||
\(254\) | −5.93145e10 | −0.894148 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | − 1.12729e11i | − 1.61190i | −0.591986 | − | 0.805948i | \(-0.701656\pi\) | ||||
0.591986 | − | 0.805948i | \(-0.298344\pi\) | |||||||
\(258\) | − 3.01571e10i | − 0.423741i | ||||||||
\(259\) | −5.04947e10 | −0.697263 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.94374e10 | −0.526049 | ||||||||
\(262\) | 4.06528e10i | 0.533009i | ||||||||
\(263\) | − 5.55225e10i | − 0.715596i | −0.933799 | − | 0.357798i | \(-0.883528\pi\) | ||||
0.933799 | − | 0.357798i | \(-0.116472\pi\) | |||||||
\(264\) | −2.06627e10 | −0.261800 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.20439e10 | −0.269973 | ||||||||
\(267\) | 8.18033e10i | 0.985076i | ||||||||
\(268\) | 2.08787e10i | 0.247228i | ||||||||
\(269\) | −2.79726e10 | −0.325722 | −0.162861 | − | 0.986649i | \(-0.552072\pi\) | ||||
−0.162861 | + | 0.986649i | \(0.552072\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.32884e10 | 0.374914 | 0.187457 | − | 0.982273i | \(-0.439975\pi\) | ||||
0.187457 | + | 0.982273i | \(0.439975\pi\) | |||||||
\(272\) | − 3.89823e10i | − 0.431824i | ||||||||
\(273\) | 1.33282e11i | 1.45225i | ||||||||
\(274\) | 1.84623e10 | 0.197883 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.13344e11 | 1.17573 | ||||||||
\(277\) | 5.46240e10i | 0.557474i | 0.960367 | + | 0.278737i | \(0.0899158\pi\) | ||||
−0.960367 | + | 0.278737i | \(0.910084\pi\) | |||||||
\(278\) | 9.00353e10i | 0.904090i | ||||||||
\(279\) | −2.47428e10 | −0.244473 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.37818e10 | −0.801625 | −0.400813 | − | 0.916160i | \(-0.631272\pi\) | ||||
−0.400813 | + | 0.916160i | \(0.631272\pi\) | |||||||
\(282\) | 1.43992e10i | 0.135587i | ||||||||
\(283\) | 8.36086e10i | 0.774840i | 0.921903 | + | 0.387420i | \(0.126634\pi\) | ||||
−0.921903 | + | 0.387420i | \(0.873366\pi\) | |||||||
\(284\) | −4.12948e10 | −0.376671 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.62819e10 | −0.674178 | ||||||||
\(287\) | 1.00584e11i | 0.875107i | ||||||||
\(288\) | − 1.11076e10i | − 0.0951377i | ||||||||
\(289\) | −2.35225e11 | −1.98355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.05039e10 | −0.167617 | ||||||||
\(292\) | − 6.32699e10i | − 0.509301i | ||||||||
\(293\) | 2.28547e11i | 1.81164i | 0.423666 | + | 0.905819i | \(0.360743\pi\) | ||||
−0.423666 | + | 0.905819i | \(0.639257\pi\) | |||||||
\(294\) | 5.19401e10 | 0.405452 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.44024e10 | 0.336197 | ||||||||
\(297\) | − 4.58555e10i | − 0.341969i | ||||||||
\(298\) | 3.41900e10i | 0.251146i | ||||||||
\(299\) | 4.18438e11 | 3.02769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.04568e10 | 0.354300 | ||||||||
\(302\) | − 1.54802e8i | − 0.00107089i | ||||||||
\(303\) | 1.49801e10i | 0.102100i | ||||||||
\(304\) | 1.93842e10 | 0.130172 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00815e11 | −0.657324 | ||||||||
\(307\) | 1.95064e11i | 1.25330i | 0.779302 | + | 0.626648i | \(0.215574\pi\) | ||||
−0.779302 | + | 0.626648i | \(0.784426\pi\) | |||||||
\(308\) | − 3.45715e10i | − 0.218897i | ||||||||
\(309\) | −3.35598e11 | −2.09414 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.15637e11 | 1.30708 | 0.653540 | − | 0.756892i | \(-0.273283\pi\) | ||||
0.653540 | + | 0.756892i | \(0.273283\pi\) | |||||||
\(312\) | − 1.17201e11i | − 0.700224i | ||||||||
\(313\) | − 1.91755e11i | − 1.12927i | −0.825341 | − | 0.564635i | \(-0.809017\pi\) | ||||
0.825341 | − | 0.564635i | \(-0.190983\pi\) | |||||||
\(314\) | 1.10158e10 | 0.0639488 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.49337e11 | −0.842508 | ||||||||
\(317\) | − 3.38886e11i | − 1.88489i | −0.334358 | − | 0.942446i | \(-0.608519\pi\) | ||||
0.334358 | − | 0.942446i | \(-0.391481\pi\) | |||||||
\(318\) | − 2.73332e11i | − 1.49889i | ||||||||
\(319\) | 1.07936e11 | 0.583592 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.43051e11 | 1.27769 | ||||||||
\(322\) | 1.89639e11i | 0.983052i | ||||||||
\(323\) | − 1.75936e11i | − 0.899383i | ||||||||
\(324\) | 1.23830e11 | 0.624271 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.28931e11 | −1.12260 | ||||||||
\(327\) | − 1.05153e11i | − 0.508577i | ||||||||
\(328\) | − 8.84485e10i | − 0.421947i | ||||||||
\(329\) | −2.40918e10 | −0.113367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.78427e11 | −0.817022 | −0.408511 | − | 0.912753i | \(-0.633952\pi\) | ||||
−0.408511 | + | 0.912753i | \(0.633952\pi\) | |||||||
\(332\) | − 3.73038e9i | − 0.0168512i | ||||||||
\(333\) | − 1.14833e11i | − 0.511760i | ||||||||
\(334\) | −1.59798e11 | −0.702605 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.31164e10 | 0.227354 | ||||||||
\(337\) | 2.64693e11i | 1.11791i | 0.829196 | + | 0.558957i | \(0.188798\pi\) | ||||
−0.829196 | + | 0.558957i | \(0.811202\pi\) | |||||||
\(338\) | − 2.63008e11i | − 1.09608i | ||||||||
\(339\) | 2.93330e11 | 1.20631 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.77187e10 | 0.271215 | ||||||||
\(342\) | − 5.01312e10i | − 0.198148i | ||||||||
\(343\) | 2.74870e11i | 1.07227i | ||||||||
\(344\) | −4.43691e10 | −0.170831 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.62233e10 | 0.210899 | ||||||||
\(347\) | − 8.11912e10i | − 0.300626i | −0.988638 | − | 0.150313i | \(-0.951972\pi\) | ||||
0.988638 | − | 0.150313i | \(-0.0480281\pi\) | |||||||
\(348\) | 1.65836e11i | 0.606139i | ||||||||
\(349\) | 2.26688e11 | 0.817926 | 0.408963 | − | 0.912551i | \(-0.365890\pi\) | ||||
0.408963 | + | 0.912551i | \(0.365890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.60098e11 | 0.914649 | ||||||||
\(352\) | 3.04003e10i | 0.105545i | ||||||||
\(353\) | − 3.28733e10i | − 0.112683i | −0.998412 | − | 0.0563413i | \(-0.982056\pi\) | ||||
0.998412 | − | 0.0563413i | \(-0.0179435\pi\) | |||||||
\(354\) | −4.49974e10 | −0.152290 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.20354e11 | 0.397133 | ||||||||
\(357\) | − 4.82098e11i | − 1.57083i | ||||||||
\(358\) | − 1.91204e10i | − 0.0615210i | ||||||||
\(359\) | 3.12096e11 | 0.991661 | 0.495831 | − | 0.868419i | \(-0.334864\pi\) | ||||
0.495831 | + | 0.868419i | \(0.334864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.35202e11 | −0.728884 | ||||||||
\(362\) | − 1.45928e11i | − 0.446634i | ||||||||
\(363\) | 2.64030e11i | 0.798129i | ||||||||
\(364\) | 1.96093e11 | 0.585473 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.22296e11 | −0.356244 | ||||||||
\(367\) | 6.28209e11i | 1.80762i | 0.427934 | + | 0.903810i | \(0.359241\pi\) | ||||
−0.427934 | + | 0.903810i | \(0.640759\pi\) | |||||||
\(368\) | − 1.66759e11i | − 0.473994i | ||||||||
\(369\) | −2.28744e11 | −0.642289 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.57321e11 | 1.25325 | ||||||||
\(372\) | 1.04045e11i | 0.281693i | ||||||||
\(373\) | 9.84770e10i | 0.263418i | 0.991288 | + | 0.131709i | \(0.0420464\pi\) | ||||
−0.991288 | + | 0.131709i | \(0.957954\pi\) | |||||||
\(374\) | 2.75921e11 | 0.729227 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.11851e10 | 0.0546619 | ||||||||
\(377\) | 6.12228e11i | 1.56091i | ||||||||
\(378\) | 1.17878e11i | 0.296975i | ||||||||
\(379\) | −2.89024e11 | −0.719544 | −0.359772 | − | 0.933040i | \(-0.617145\pi\) | ||||
−0.359772 | + | 0.933040i | \(0.617145\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.45046e11 | 1.56830 | ||||||||
\(382\) | − 1.49989e11i | − 0.360391i | ||||||||
\(383\) | − 2.01350e11i | − 0.478141i | −0.971002 | − | 0.239071i | \(-0.923157\pi\) | ||||
0.971002 | − | 0.239071i | \(-0.0768427\pi\) | |||||||
\(384\) | −4.67078e10 | −0.109622 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.84001e11 | 0.880418 | ||||||||
\(387\) | 1.14746e11i | 0.260040i | ||||||||
\(388\) | 3.01666e10i | 0.0675747i | ||||||||
\(389\) | −3.93769e11 | −0.871904 | −0.435952 | − | 0.899970i | \(-0.643588\pi\) | ||||
−0.435952 | + | 0.899970i | \(0.643588\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.51354e12 | −3.27491 | ||||||||
\(392\) | − 7.64176e10i | − 0.163458i | ||||||||
\(393\) | − 4.42099e11i | − 0.934875i | ||||||||
\(394\) | 8.89798e9 | 0.0186019 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.86207e10 | 0.160660 | ||||||||
\(397\) | − 5.15625e11i | − 1.04178i | −0.853623 | − | 0.520891i | \(-0.825600\pi\) | ||||
0.853623 | − | 0.520891i | \(-0.174400\pi\) | |||||||
\(398\) | 4.02008e11i | 0.803084i | ||||||||
\(399\) | 2.39727e11 | 0.473521 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.43309e11 | −1.62869 | −0.814343 | − | 0.580384i | \(-0.802902\pi\) | ||||
−0.814343 | + | 0.580384i | \(0.802902\pi\) | |||||||
\(402\) | − 2.27056e11i | − 0.433626i | ||||||||
\(403\) | 3.84108e11i | 0.725406i | ||||||||
\(404\) | 2.20397e10 | 0.0411614 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.77466e11 | −0.506806 | ||||||||
\(407\) | 3.14285e11i | 0.567740i | ||||||||
\(408\) | 4.23932e11i | 0.757400i | ||||||||
\(409\) | −5.64549e11 | −0.997577 | −0.498789 | − | 0.866724i | \(-0.666222\pi\) | ||||
−0.498789 | + | 0.866724i | \(0.666222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00778e11 | −0.347078 | ||||||||
\(412\) | 4.93753e11i | 0.844252i | ||||||||
\(413\) | − 7.52866e10i | − 0.127333i | ||||||||
\(414\) | −4.31268e11 | −0.721516 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.72434e11 | −0.282295 | ||||||||
\(417\) | − 9.79134e11i | − 1.58573i | ||||||||
\(418\) | 1.37204e11i | 0.219823i | ||||||||
\(419\) | −6.92475e11 | −1.09759 | −0.548796 | − | 0.835956i | \(-0.684914\pi\) | ||||
−0.548796 | + | 0.835956i | \(0.684914\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.08125e11 | 0.633176 | 0.316588 | − | 0.948563i | \(-0.397463\pi\) | ||||
0.316588 | + | 0.948563i | \(0.397463\pi\) | |||||||
\(422\) | − 2.62264e11i | − 0.402562i | ||||||||
\(423\) | − 5.47885e10i | − 0.0832065i | ||||||||
\(424\) | −4.02144e11 | −0.604276 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.49081e11 | 0.660665 | ||||||||
\(427\) | − 2.04617e11i | − 0.297863i | ||||||||
\(428\) | − 3.57592e11i | − 0.515100i | ||||||||
\(429\) | 8.29566e11 | 1.18248 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.41055e11 | 0.615665 | 0.307833 | − | 0.951441i | \(-0.400396\pi\) | ||||
0.307833 | + | 0.951441i | \(0.400396\pi\) | |||||||
\(432\) | − 1.03656e11i | − 0.143191i | ||||||||
\(433\) | 7.15390e10i | 0.0978019i | 0.998804 | + | 0.0489009i | \(0.0155719\pi\) | ||||
−0.998804 | + | 0.0489009i | \(0.984428\pi\) | |||||||
\(434\) | −1.74080e11 | −0.235530 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.54708e11 | −0.205033 | ||||||||
\(437\) | − 7.52622e11i | − 0.987212i | ||||||||
\(438\) | 6.88060e11i | 0.893291i | ||||||||
\(439\) | −4.74967e11 | −0.610342 | −0.305171 | − | 0.952298i | \(-0.598714\pi\) | ||||
−0.305171 | + | 0.952298i | \(0.598714\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.97630e11 | −0.248816 | ||||||||
\(442\) | 1.56506e12i | 1.95043i | ||||||||
\(443\) | 1.97072e11i | 0.243113i | 0.992585 | + | 0.121556i | \(0.0387885\pi\) | ||||
−0.992585 | + | 0.121556i | \(0.961211\pi\) | |||||||
\(444\) | −4.82876e11 | −0.589674 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.44411e11 | 0.890853 | ||||||||
\(447\) | − 3.71817e11i | − 0.440499i | ||||||||
\(448\) | − 7.81483e10i | − 0.0916576i | ||||||||
\(449\) | 6.20156e11 | 0.720100 | 0.360050 | − | 0.932933i | \(-0.382760\pi\) | ||||
0.360050 | + | 0.932933i | \(0.382760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.26049e11 | 0.712548 | ||||||||
\(452\) | − 4.31565e11i | − 0.486322i | ||||||||
\(453\) | 1.68348e9i | 0.00187830i | ||||||||
\(454\) | 3.06264e10 | 0.0338333 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.10804e11 | −0.228316 | ||||||||
\(457\) | 7.88006e11i | 0.845097i | 0.906340 | + | 0.422549i | \(0.138864\pi\) | ||||
−0.906340 | + | 0.422549i | \(0.861136\pi\) | |||||||
\(458\) | 2.33319e11i | 0.247774i | ||||||||
\(459\) | −9.40806e11 | −0.989334 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.53496e10 | 0.0158286 | 0.00791429 | − | 0.999969i | \(-0.497481\pi\) | ||||
0.00791429 | + | 0.999969i | \(0.497481\pi\) | |||||||
\(462\) | 3.75965e11i | 0.383935i | ||||||||
\(463\) | − 1.94494e11i | − 0.196694i | −0.995152 | − | 0.0983471i | \(-0.968644\pi\) | ||||
0.995152 | − | 0.0983471i | \(-0.0313555\pi\) | |||||||
\(464\) | 2.43989e11 | 0.244365 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.60464e11 | 0.648802 | ||||||||
\(467\) | 1.06503e11i | 0.103618i | 0.998657 | + | 0.0518089i | \(0.0164987\pi\) | ||||
−0.998657 | + | 0.0518089i | \(0.983501\pi\) | |||||||
\(468\) | 4.45946e11i | 0.429710i | ||||||||
\(469\) | 3.79894e11 | 0.362564 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.19797e11 | −0.112163 | ||||||||
\(472\) | 6.62031e10i | 0.0613959i | ||||||||
\(473\) | − 3.14050e11i | − 0.288485i | ||||||||
\(474\) | 1.62403e12 | 1.47772 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.09294e11 | −0.633279 | ||||||||
\(477\) | 1.04002e12i | 0.919831i | ||||||||
\(478\) | − 5.84803e11i | − 0.512371i | ||||||||
\(479\) | 8.31146e11 | 0.721386 | 0.360693 | − | 0.932685i | \(-0.382540\pi\) | ||||
0.360693 | + | 0.932685i | \(0.382540\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.78266e12 | −1.51851 | ||||||||
\(482\) | − 1.38571e12i | − 1.16939i | ||||||||
\(483\) | − 2.06232e12i | − 1.72423i | ||||||||
\(484\) | 3.88457e11 | 0.321765 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.48542e11 | −0.689938 | ||||||||
\(487\) | − 1.38566e12i | − 1.11629i | −0.829743 | − | 0.558146i | \(-0.811513\pi\) | ||||
0.829743 | − | 0.558146i | \(-0.188487\pi\) | |||||||
\(488\) | 1.79930e11i | 0.143620i | ||||||||
\(489\) | 2.48962e12 | 1.96899 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.92804e11 | 0.305007 | 0.152503 | − | 0.988303i | \(-0.451266\pi\) | ||||
0.152503 | + | 0.988303i | \(0.451266\pi\) | |||||||
\(492\) | 9.61877e11i | 0.740076i | ||||||||
\(493\) | − 2.21450e12i | − 1.68836i | ||||||||
\(494\) | −7.78237e11 | −0.587951 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.53077e11 | 0.113565 | ||||||||
\(497\) | 7.51371e11i | 0.552397i | ||||||||
\(498\) | 4.05679e10i | 0.0295563i | ||||||||
\(499\) | 7.52029e11 | 0.542978 | 0.271489 | − | 0.962442i | \(-0.412484\pi\) | ||||
0.271489 | + | 0.962442i | \(0.412484\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.73780e12 | 1.23234 | ||||||||
\(502\) | − 1.15323e12i | − 0.810493i | ||||||||
\(503\) | 1.83429e12i | 1.27765i | 0.769351 | + | 0.638826i | \(0.220580\pi\) | ||||
−0.769351 | + | 0.638826i | \(0.779420\pi\) | |||||||
\(504\) | −2.02106e11 | −0.139521 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.18034e12 | 0.800441 | ||||||||
\(507\) | 2.86021e12i | 1.92248i | ||||||||
\(508\) | − 9.49033e11i | − 0.632258i | ||||||||
\(509\) | 6.19864e11 | 0.409323 | 0.204662 | − | 0.978833i | \(-0.434391\pi\) | ||||
0.204662 | + | 0.978833i | \(0.434391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.15122e12 | −0.746900 | ||||||||
\(512\) | 6.87195e10i | 0.0441942i | ||||||||
\(513\) | − 4.67823e11i | − 0.298232i | ||||||||
\(514\) | 1.80367e12 | 1.13978 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.82514e11 | 0.299630 | ||||||||
\(517\) | 1.49951e11i | 0.0923083i | ||||||||
\(518\) | − 8.07915e11i | − 0.493039i | ||||||||
\(519\) | −6.11428e11 | −0.369907 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.25683e11 | 0.312575 | 0.156287 | − | 0.987712i | \(-0.450047\pi\) | ||||
0.156287 | + | 0.987712i | \(0.450047\pi\) | |||||||
\(522\) | − 6.30999e11i | − 0.371973i | ||||||||
\(523\) | − 1.68426e11i | − 0.0984353i | −0.998788 | − | 0.0492177i | \(-0.984327\pi\) | ||||
0.998788 | − | 0.0492177i | \(-0.0156728\pi\) | |||||||
\(524\) | −6.50445e11 | −0.376895 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.88360e11 | 0.506003 | ||||||||
\(527\) | − 1.38937e12i | − 0.784639i | ||||||||
\(528\) | − 3.30603e11i | − 0.185121i | ||||||||
\(529\) | −4.67350e12 | −2.59473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.71213e11 | 0.0934570 | ||||||||
\(532\) | − 3.52702e11i | − 0.190900i | ||||||||
\(533\) | 3.55102e12i | 1.90582i | ||||||||
\(534\) | −1.30885e12 | −0.696554 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.34059e11 | −0.174816 | ||||||||
\(537\) | 2.07934e11i | 0.107905i | ||||||||
\(538\) | − 4.47561e11i | − 0.230320i | ||||||||
\(539\) | 5.40893e11 | 0.276034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.20612e12 | 1.10724 | 0.553620 | − | 0.832769i | \(-0.313246\pi\) | ||||
0.553620 | + | 0.832769i | \(0.313246\pi\) | |||||||
\(542\) | 5.32615e11i | 0.265104i | ||||||||
\(543\) | 1.58697e12i | 0.783375i | ||||||||
\(544\) | 6.23716e11 | 0.305346 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.13251e12 | −1.02689 | ||||||||
\(547\) | − 3.51639e12i | − 1.67940i | −0.543049 | − | 0.839701i | \(-0.682730\pi\) | ||||
0.543049 | − | 0.839701i | \(-0.317270\pi\) | |||||||
\(548\) | 2.95397e11i | 0.139925i | ||||||||
\(549\) | 4.65331e11 | 0.218618 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10118e12 | 0.508951 | ||||||||
\(552\) | 1.81350e12i | 0.831365i | ||||||||
\(553\) | 2.71722e12i | 1.23556i | ||||||||
\(554\) | −8.73985e11 | −0.394194 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.44057e12 | −0.639288 | ||||||||
\(557\) | 6.29996e11i | 0.277325i | 0.990340 | + | 0.138663i | \(0.0442803\pi\) | ||||
−0.990340 | + | 0.138663i | \(0.955720\pi\) | |||||||
\(558\) | − 3.95885e11i | − 0.172868i | ||||||||
\(559\) | 1.78133e12 | 0.771597 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.00064e12 | −1.27903 | ||||||||
\(562\) | − 1.34051e12i | − 0.566835i | ||||||||
\(563\) | − 4.02619e11i | − 0.168891i | −0.996428 | − | 0.0844455i | \(-0.973088\pi\) | ||||
0.996428 | − | 0.0844455i | \(-0.0269119\pi\) | |||||||
\(564\) | −2.30388e11 | −0.0958746 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.33774e12 | −0.547894 | ||||||||
\(567\) | − 2.25313e12i | − 0.915507i | ||||||||
\(568\) | − 6.60716e11i | − 0.266347i | ||||||||
\(569\) | −2.55482e12 | −1.02177 | −0.510887 | − | 0.859648i | \(-0.670683\pi\) | ||||
−0.510887 | + | 0.859648i | \(0.670683\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.16243e12 | 0.457620 | 0.228810 | − | 0.973471i | \(-0.426516\pi\) | ||||
0.228810 | + | 0.973471i | \(0.426516\pi\) | |||||||
\(572\) | − 1.22051e12i | − 0.476716i | ||||||||
\(573\) | 1.63113e12i | 0.632110i | ||||||||
\(574\) | −1.60935e12 | −0.618794 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.77721e11 | 0.0672725 | ||||||||
\(577\) | 4.66332e12i | 1.75148i | 0.482787 | + | 0.875738i | \(0.339625\pi\) | ||||
−0.482787 | + | 0.875738i | \(0.660375\pi\) | |||||||
\(578\) | − 3.76361e12i | − 1.40258i | ||||||||
\(579\) | −4.17601e12 | −1.54421 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.78754e10 | −0.0247127 | ||||||||
\(582\) | − 3.28062e11i | − 0.118523i | ||||||||
\(583\) | − 2.84643e12i | − 1.02045i | ||||||||
\(584\) | 1.01232e12 | 0.360130 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.65675e12 | −1.28102 | ||||||||
\(587\) | 3.88422e12i | 1.35030i | 0.737678 | + | 0.675152i | \(0.235922\pi\) | ||||
−0.737678 | + | 0.675152i | \(0.764078\pi\) | |||||||
\(588\) | 8.31042e11i | 0.286698i | ||||||||
\(589\) | 6.90875e11 | 0.236527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.67655e10 | −0.0326270 | ||||||||
\(592\) | 7.10438e11i | 0.237727i | ||||||||
\(593\) | 2.01341e12i | 0.668631i | 0.942461 | + | 0.334315i | \(0.108505\pi\) | ||||
−0.942461 | + | 0.334315i | \(0.891495\pi\) | |||||||
\(594\) | 7.33688e11 | 0.241809 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.47041e11 | −0.177587 | ||||||||
\(597\) | − 4.37184e12i | − 1.40857i | ||||||||
\(598\) | 6.69502e12i | 2.14090i | ||||||||
\(599\) | −2.10578e12 | −0.668333 | −0.334166 | − | 0.942514i | \(-0.608455\pi\) | ||||
−0.334166 | + | 0.942514i | \(0.608455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.74058e12 | 1.48216 | 0.741082 | − | 0.671415i | \(-0.234313\pi\) | ||||
0.741082 | + | 0.671415i | \(0.234313\pi\) | |||||||
\(602\) | 8.07309e11i | 0.250528i | ||||||||
\(603\) | 8.63938e11i | 0.266106i | ||||||||
\(604\) | 2.47684e9 | 0.000757236 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.39682e11 | −0.0721953 | ||||||||
\(607\) | − 4.01476e12i | − 1.20036i | −0.799866 | − | 0.600179i | \(-0.795096\pi\) | ||||
0.799866 | − | 0.600179i | \(-0.204904\pi\) | |||||||
\(608\) | 3.10148e11i | 0.0920455i | ||||||||
\(609\) | 3.01744e12 | 0.888915 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.50537e11 | −0.246893 | ||||||||
\(612\) | − 1.61304e12i | − 0.464798i | ||||||||
\(613\) | − 1.30399e12i | − 0.372993i | −0.982456 | − | 0.186496i | \(-0.940287\pi\) | ||||
0.982456 | − | 0.186496i | \(-0.0597133\pi\) | |||||||
\(614\) | −3.12102e12 | −0.886214 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.53143e11 | 0.154783 | ||||||||
\(617\) | 5.10164e12i | 1.41719i | 0.705618 | + | 0.708593i | \(0.250670\pi\) | ||||
−0.705618 | + | 0.708593i | \(0.749330\pi\) | |||||||
\(618\) | − 5.36956e12i | − 1.48078i | ||||||||
\(619\) | 4.50630e11 | 0.123371 | 0.0616854 | − | 0.998096i | \(-0.480352\pi\) | ||||
0.0616854 | + | 0.998096i | \(0.480352\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.02459e12 | −1.08595 | ||||||||
\(622\) | 3.45020e12i | 0.924246i | ||||||||
\(623\) | − 2.18988e12i | − 0.582404i | ||||||||
\(624\) | 1.87522e12 | 0.495133 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.06808e12 | 0.798514 | ||||||||
\(627\) | − 1.49209e12i | − 0.385560i | ||||||||
\(628\) | 1.76253e11i | 0.0452187i | ||||||||
\(629\) | 6.44812e12 | 1.64250 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.97105e10 | 0.0200163 | 0.0100081 | − | 0.999950i | \(-0.496814\pi\) | ||||
0.0100081 | + | 0.999950i | \(0.496814\pi\) | |||||||
\(632\) | − 2.38938e12i | − 0.595743i | ||||||||
\(633\) | 2.85212e12i | 0.706076i | ||||||||
\(634\) | 5.42217e12 | 1.33282 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.37332e12 | 1.05987 | ||||||||
\(637\) | 3.06801e12i | 0.738294i | ||||||||
\(638\) | 1.72698e12i | 0.412662i | ||||||||
\(639\) | −1.70873e12 | −0.405434 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.12648e12 | −0.731468 | −0.365734 | − | 0.930719i | \(-0.619182\pi\) | ||||
−0.365734 | + | 0.930719i | \(0.619182\pi\) | |||||||
\(642\) | 3.88882e12i | 0.903462i | ||||||||
\(643\) | 5.94982e12i | 1.37263i | 0.727303 | + | 0.686316i | \(0.240773\pi\) | ||||
−0.727303 | + | 0.686316i | \(0.759227\pi\) | |||||||
\(644\) | −3.03422e12 | −0.695122 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.81498e12 | 0.635960 | ||||||||
\(647\) | 3.56187e12i | 0.799115i | 0.916708 | + | 0.399557i | \(0.130836\pi\) | ||||
−0.916708 | + | 0.399557i | \(0.869164\pi\) | |||||||
\(648\) | 1.98128e12i | 0.441426i | ||||||||
\(649\) | −4.68594e11 | −0.103680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.89312e12 | 0.413109 | ||||||||
\(652\) | − 3.66289e12i | − 0.793797i | ||||||||
\(653\) | 1.37883e11i | 0.0296757i | 0.999890 | + | 0.0148379i | \(0.00472321\pi\) | ||||
−0.999890 | + | 0.0148379i | \(0.995277\pi\) | |||||||
\(654\) | 1.68245e12 | 0.359618 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.41518e12 | 0.298362 | ||||||||
\(657\) | − 2.61804e12i | − 0.548191i | ||||||||
\(658\) | − 3.85469e11i | − 0.0801628i | ||||||||
\(659\) | 4.16654e12 | 0.860581 | 0.430290 | − | 0.902691i | \(-0.358411\pi\) | ||||
0.430290 | + | 0.902691i | \(0.358411\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.29083e12 | −0.670500 | −0.335250 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335250 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(662\) | − 2.85483e12i | − 0.577722i | ||||||||
\(663\) | − 1.70200e13i | − 3.42097i | ||||||||
\(664\) | 5.96860e10 | 0.0119156 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.83732e12 | 0.361869 | ||||||||
\(667\) | − 9.47322e12i | − 1.85324i | ||||||||
\(668\) | − 2.55676e12i | − 0.496817i | ||||||||
\(669\) | −8.09547e12 | −1.56252 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.27357e12 | −0.242532 | ||||||||
\(672\) | 8.49862e11i | 0.160763i | ||||||||
\(673\) | − 5.74732e12i | − 1.07993i | −0.841686 | − | 0.539967i | \(-0.818437\pi\) | ||||
0.841686 | − | 0.539967i | \(-0.181563\pi\) | |||||||
\(674\) | −4.23510e12 | −0.790485 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.20812e12 | 0.775048 | ||||||||
\(677\) | 9.31245e12i | 1.70379i | 0.523716 | + | 0.851893i | \(0.324545\pi\) | ||||
−0.523716 | + | 0.851893i | \(0.675455\pi\) | |||||||
\(678\) | 4.69327e12i | 0.852987i | ||||||||
\(679\) | 5.48892e11 | 0.0990998 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.33062e11 | −0.0593421 | ||||||||
\(682\) | 1.08350e12i | 0.191778i | ||||||||
\(683\) | − 9.19967e12i | − 1.61763i | −0.588063 | − | 0.808815i | \(-0.700109\pi\) | ||||
0.588063 | − | 0.808815i | \(-0.299891\pi\) | |||||||
\(684\) | 8.02099e11 | 0.140112 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.39792e12 | −0.758208 | ||||||||
\(687\) | − 2.53735e12i | − 0.434585i | ||||||||
\(688\) | − 7.09905e11i | − 0.120796i | ||||||||
\(689\) | 1.61453e13 | 2.72934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.03125e13 | 1.72074 | 0.860369 | − | 0.509672i | \(-0.170233\pi\) | ||||
0.860369 | + | 0.509672i | \(0.170233\pi\) | |||||||
\(692\) | 8.99573e11i | 0.149128i | ||||||||
\(693\) | − 1.43053e12i | − 0.235612i | ||||||||
\(694\) | 1.29906e12 | 0.212574 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.65338e12 | −0.428605 | ||||||||
\(697\) | − 1.28445e13i | − 2.06144i | ||||||||
\(698\) | 3.62701e12i | 0.578361i | ||||||||
\(699\) | −7.18255e12 | −1.13797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.52566e12 | −1.48992 | −0.744961 | − | 0.667108i | \(-0.767532\pi\) | ||||
−0.744961 | + | 0.667108i | \(0.767532\pi\) | |||||||
\(702\) | 4.16156e12i | 0.646754i | ||||||||
\(703\) | 3.20638e12i | 0.495126i | ||||||||
\(704\) | −4.86405e11 | −0.0746313 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.25973e11 | 0.0796787 | ||||||||
\(707\) | − 4.01020e11i | − 0.0603641i | ||||||||
\(708\) | − 7.19958e11i | − 0.107686i | ||||||||
\(709\) | 8.38537e12 | 1.24628 | 0.623138 | − | 0.782112i | \(-0.285858\pi\) | ||||
0.623138 | + | 0.782112i | \(0.285858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.17938e12 | −0.906842 | ||||||||
\(712\) | 1.92567e12i | 0.280816i | ||||||||
\(713\) | − 5.94345e12i | − 0.861263i | ||||||||
\(714\) | 7.71358e12 | 1.11074 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.05926e11 | 0.0435019 | ||||||||
\(717\) | 6.35974e12i | 0.898676i | ||||||||
\(718\) | 4.99354e12i | 0.701211i | ||||||||
\(719\) | −6.94013e12 | −0.968473 | −0.484236 | − | 0.874937i | \(-0.660903\pi\) | ||||
−0.484236 | + | 0.874937i | \(0.660903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.98398e12 | 1.23811 | ||||||||
\(722\) | − 3.76323e12i | − 0.515399i | ||||||||
\(723\) | 1.50696e13i | 2.05107i | ||||||||
\(724\) | 2.33485e12 | 0.315818 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.22447e12 | −0.564362 | ||||||||
\(727\) | 7.74984e12i | 1.02893i | 0.857510 | + | 0.514467i | \(0.172010\pi\) | ||||
−0.857510 | + | 0.514467i | \(0.827990\pi\) | |||||||
\(728\) | 3.13749e12i | 0.413992i | ||||||||
\(729\) | −2.92986e11 | −0.0384214 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.44329e12 | −0.834602 | ||||||||
\(732\) | − 1.95674e12i | − 0.251902i | ||||||||
\(733\) | − 4.12555e12i | − 0.527854i | −0.964543 | − | 0.263927i | \(-0.914982\pi\) | ||||
0.964543 | − | 0.263927i | \(-0.0850178\pi\) | |||||||
\(734\) | −1.00513e13 | −1.27818 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.66814e12 | 0.335164 | ||||||||
\(737\) | − 2.36451e12i | − 0.295215i | ||||||||
\(738\) | − 3.65990e12i | − 0.454167i | ||||||||
\(739\) | −3.33931e12 | −0.411867 | −0.205933 | − | 0.978566i | \(-0.566023\pi\) | ||||
−0.205933 | + | 0.978566i | \(0.566023\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.46333e12 | 1.03124 | ||||||||
\(742\) | 7.31713e12i | 0.886183i | ||||||||
\(743\) | 1.26471e13i | 1.52245i | 0.648489 | + | 0.761224i | \(0.275401\pi\) | ||||
−0.648489 | + | 0.761224i | \(0.724599\pi\) | |||||||
\(744\) | −1.66471e12 | −0.199187 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.57563e12 | −0.186265 | ||||||||
\(747\) | − 1.54359e11i | − 0.0181380i | ||||||||
\(748\) | 4.41474e12i | 0.515642i | ||||||||
\(749\) | −6.50651e12 | −0.755405 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.56552e12 | 0.179588 | 0.0897941 | − | 0.995960i | \(-0.471379\pi\) | ||||
0.0897941 | + | 0.995960i | \(0.471379\pi\) | |||||||
\(752\) | 3.38961e11i | 0.0386518i | ||||||||
\(753\) | 1.25414e13i | 1.42157i | ||||||||
\(754\) | −9.79564e12 | −1.10373 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.88605e12 | −0.209993 | ||||||||
\(757\) | 9.54781e11i | 0.105675i | 0.998603 | + | 0.0528375i | \(0.0168265\pi\) | ||||
−0.998603 | + | 0.0528375i | \(0.983173\pi\) | |||||||
\(758\) | − 4.62438e12i | − 0.508794i | ||||||||
\(759\) | −1.28362e13 | −1.40394 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.27330e12 | 0.569969 | 0.284985 | − | 0.958532i | \(-0.408012\pi\) | ||||
0.284985 | + | 0.958532i | \(0.408012\pi\) | |||||||
\(762\) | 1.03207e13i | 1.10895i | ||||||||
\(763\) | 2.81496e12i | 0.300685i | ||||||||
\(764\) | 2.39982e12 | 0.254835 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.22159e12 | 0.338097 | ||||||||
\(767\) | − 2.65792e12i | − 0.277308i | ||||||||
\(768\) | − 7.47324e11i | − 0.0775146i | ||||||||
\(769\) | 6.96923e12 | 0.718648 | 0.359324 | − | 0.933213i | \(-0.383007\pi\) | ||||
0.359324 | + | 0.933213i | \(0.383007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.96149e13 | −1.99913 | ||||||||
\(772\) | 6.14401e12i | 0.622550i | ||||||||
\(773\) | 3.79383e12i | 0.382182i | 0.981572 | + | 0.191091i | \(0.0612025\pi\) | ||||
−0.981572 | + | 0.191091i | \(0.938797\pi\) | |||||||
\(774\) | −1.83594e12 | −0.183876 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.82666e11 | −0.0477825 | ||||||||
\(777\) | 8.78607e12i | 0.864769i | ||||||||
\(778\) | − 6.30031e12i | − 0.616530i | ||||||||
\(779\) | 6.38703e12 | 0.621413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.67663e12 | 0.449784 | ||||||||
\(782\) | − 2.42167e13i | − 2.31571i | ||||||||
\(783\) | − 5.88847e12i | − 0.559854i | ||||||||
\(784\) | 1.22268e12 | 0.115582 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.07359e12 | 0.661056 | ||||||||
\(787\) | − 2.05939e13i | − 1.91361i | −0.290736 | − | 0.956803i | \(-0.593900\pi\) | ||||
0.290736 | − | 0.956803i | \(-0.406100\pi\) | |||||||
\(788\) | 1.42368e11i | 0.0131536i | ||||||||
\(789\) | −9.66092e12 | −0.887507 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.85247e12 | −0.713201 | ||||||||
\(792\) | 1.25793e12i | 0.113604i | ||||||||
\(793\) | − 7.22381e12i | − 0.648690i | ||||||||
\(794\) | 8.25000e12 | 0.736651 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.43213e12 | −0.567866 | ||||||||
\(797\) | 1.45507e12i | 0.127738i | 0.997958 | + | 0.0638690i | \(0.0203440\pi\) | ||||
−0.997958 | + | 0.0638690i | \(0.979656\pi\) | |||||||
\(798\) | 3.83564e12i | 0.334830i | ||||||||
\(799\) | 3.07650e12 | 0.267052 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.98013e12 | 0.427459 | ||||||||
\(802\) | − 1.34929e13i | − 1.15165i | ||||||||
\(803\) | 7.16531e12i | 0.608156i | ||||||||
\(804\) | 3.63289e12 | 0.306620 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.14573e12 | −0.512939 | ||||||||
\(807\) | 4.86722e12i | 0.403971i | ||||||||
\(808\) | 3.52636e11i | 0.0291055i | ||||||||
\(809\) | −1.31749e13 | −1.08138 | −0.540690 | − | 0.841222i | \(-0.681837\pi\) | ||||
−0.540690 | + | 0.841222i | \(0.681837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.97833e12 | 0.809961 | 0.404980 | − | 0.914325i | \(-0.367278\pi\) | ||||
0.404980 | + | 0.914325i | \(0.367278\pi\) | |||||||
\(812\) | − 4.43945e12i | − 0.358366i | ||||||||
\(813\) | − 5.79219e12i | − 0.464981i | ||||||||
\(814\) | −5.02857e12 | −0.401453 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.78291e12 | −0.535563 | ||||||||
\(817\) | − 3.20398e12i | − 0.251588i | ||||||||
\(818\) | − 9.03278e12i | − 0.705394i | ||||||||
\(819\) | 8.11413e12 | 0.630179 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.80913e13 | −1.38972 | −0.694859 | − | 0.719146i | \(-0.744533\pi\) | ||||
−0.694859 | + | 0.719146i | \(0.744533\pi\) | |||||||
\(822\) | − 3.21245e12i | − 0.245422i | ||||||||
\(823\) | − 1.39801e12i | − 0.106221i | −0.998589 | − | 0.0531107i | \(-0.983086\pi\) | ||||
0.998589 | − | 0.0531107i | \(-0.0169136\pi\) | |||||||
\(824\) | −7.90004e12 | −0.596976 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.20459e12 | 0.0900383 | ||||||||
\(827\) | 2.26201e13i | 1.68159i | 0.541354 | + | 0.840794i | \(0.317912\pi\) | ||||
−0.541354 | + | 0.840794i | \(0.682088\pi\) | |||||||
\(828\) | − 6.90029e12i | − 0.510189i | ||||||||
\(829\) | −1.72646e13 | −1.26959 | −0.634793 | − | 0.772682i | \(-0.718915\pi\) | ||||
−0.634793 | + | 0.772682i | \(0.718915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.50458e12 | 0.691398 | ||||||||
\(832\) | − 2.75895e12i | − 0.199613i | ||||||||
\(833\) | − 1.10974e13i | − 0.798579i | ||||||||
\(834\) | 1.56662e13 | 1.12128 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.19526e12 | −0.155439 | ||||||||
\(837\) | − 3.69440e12i | − 0.260183i | ||||||||
\(838\) | − 1.10796e13i | − 0.776115i | ||||||||
\(839\) | 1.76607e12 | 0.123049 | 0.0615245 | − | 0.998106i | \(-0.480404\pi\) | ||||
0.0615245 | + | 0.998106i | \(0.480404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.46640e11 | −0.0445739 | ||||||||
\(842\) | 6.53001e12i | 0.447723i | ||||||||
\(843\) | 1.45780e13i | 0.994203i | ||||||||
\(844\) | 4.19622e12 | 0.284654 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.76615e11 | 0.0588359 | ||||||||
\(847\) | − 7.06810e12i | − 0.471876i | ||||||||
\(848\) | − 6.43430e12i | − 0.427287i | ||||||||
\(849\) | 1.45479e13 | 0.960983 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.75838e13 | 1.80290 | ||||||||
\(852\) | 7.18529e12i | 0.467161i | ||||||||
\(853\) | 2.37844e13i | 1.53823i | 0.639109 | + | 0.769116i | \(0.279303\pi\) | ||||
−0.639109 | + | 0.769116i | \(0.720697\pi\) | |||||||
\(854\) | 3.27388e12 | 0.210621 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.72148e12 | 0.364230 | ||||||||
\(857\) | 7.61941e12i | 0.482511i | 0.970462 | + | 0.241256i | \(0.0775593\pi\) | ||||
−0.970462 | + | 0.241256i | \(0.922441\pi\) | |||||||
\(858\) | 1.32730e13i | 0.836138i | ||||||||
\(859\) | 1.27695e13 | 0.800212 | 0.400106 | − | 0.916469i | \(-0.368973\pi\) | ||||
0.400106 | + | 0.916469i | \(0.368973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.75017e13 | 1.08534 | ||||||||
\(862\) | 7.05687e12i | 0.435341i | ||||||||
\(863\) | − 2.63038e13i | − 1.61425i | −0.590382 | − | 0.807124i | \(-0.701023\pi\) | ||||
0.590382 | − | 0.807124i | \(-0.298977\pi\) | |||||||
\(864\) | 1.65849e12 | 0.101251 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.14462e12 | −0.0691564 | ||||||||
\(867\) | 4.09292e13i | 2.46007i | ||||||||
\(868\) | − 2.78529e12i | − 0.166545i | ||||||||
\(869\) | 1.69124e13 | 1.00604 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.34118e13 | 0.789596 | ||||||||
\(872\) | − 2.47532e12i | − 0.144980i | ||||||||
\(873\) | 1.24826e12i | 0.0727347i | ||||||||
\(874\) | 1.20420e13 | 0.698065 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.10090e13 | −0.631652 | ||||||||
\(877\) | 4.76832e11i | 0.0272187i | 0.999907 | + | 0.0136093i | \(0.00433212\pi\) | ||||
−0.999907 | + | 0.0136093i | \(0.995668\pi\) | |||||||
\(878\) | − 7.59947e12i | − 0.431577i | ||||||||
\(879\) | 3.97672e13 | 2.24685 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.74839e13 | 0.977791 | 0.488896 | − | 0.872342i | \(-0.337400\pi\) | ||||
0.488896 | + | 0.872342i | \(0.337400\pi\) | |||||||
\(882\) | − 3.16208e12i | − 0.175940i | ||||||||
\(883\) | 6.48321e12i | 0.358894i | 0.983768 | + | 0.179447i | \(0.0574309\pi\) | ||||
−0.983768 | + | 0.179447i | \(0.942569\pi\) | |||||||
\(884\) | −2.50409e13 | −1.37916 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.15315e12 | −0.171907 | ||||||||
\(887\) | − 9.92450e12i | − 0.538335i | −0.963093 | − | 0.269167i | \(-0.913252\pi\) | ||||
0.963093 | − | 0.269167i | \(-0.0867485\pi\) | |||||||
\(888\) | − 7.72601e12i | − 0.416962i | ||||||||
\(889\) | −1.72679e13 | −0.927220 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.40237e13 | −0.745443 | ||||||||
\(892\) | 1.19106e13i | 0.629928i | ||||||||
\(893\) | 1.52981e12i | 0.0805021i | ||||||||
\(894\) | 5.94907e12 | 0.311480 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.25037e12 | 0.0648117 | ||||||||
\(897\) | − 7.28083e13i | − 3.75504i | ||||||||
\(898\) | 9.92250e12i | 0.509187i | ||||||||
\(899\) | 8.69601e12 | 0.444019 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.83994e13 | −2.95221 | ||||||||
\(902\) | 1.00168e13i | 0.503847i | ||||||||
\(903\) | − 8.77949e12i | − 0.439414i | ||||||||
\(904\) | 6.90505e12 | 0.343881 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.69356e10 | −0.00132816 | ||||||||
\(907\) | 1.40768e12i | 0.0690671i | 0.999404 | + | 0.0345335i | \(0.0109946\pi\) | ||||
−0.999404 | + | 0.0345335i | \(0.989005\pi\) | |||||||
\(908\) | 4.90022e11i | 0.0239237i | ||||||||
\(909\) | 9.11980e11 | 0.0443045 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.91343e12 | 0.332553 | 0.166277 | − | 0.986079i | \(-0.446826\pi\) | ||||
0.166277 | + | 0.986079i | \(0.446826\pi\) | |||||||
\(912\) | − 3.37286e12i | − 0.161444i | ||||||||
\(913\) | 4.22465e11i | 0.0201221i | ||||||||
\(914\) | −1.26081e13 | −0.597574 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.73311e12 | −0.175203 | ||||||||
\(917\) | 1.18351e13i | 0.552724i | ||||||||
\(918\) | − 1.50529e13i | − 0.699565i | ||||||||
\(919\) | 8.50189e12 | 0.393184 | 0.196592 | − | 0.980485i | \(-0.437013\pi\) | ||||
0.196592 | + | 0.980485i | \(0.437013\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.39411e13 | 1.55438 | ||||||||
\(922\) | 2.45593e11i | 0.0111925i | ||||||||
\(923\) | 2.65264e13i | 1.20301i | ||||||||
\(924\) | −6.01543e12 | −0.271483 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.11190e12 | 0.139084 | ||||||||
\(927\) | 2.04309e13i | 0.908719i | ||||||||
\(928\) | 3.90382e12i | 0.172792i | ||||||||
\(929\) | −8.90639e12 | −0.392311 | −0.196156 | − | 0.980573i | \(-0.562846\pi\) | ||||
−0.196156 | + | 0.980573i | \(0.562846\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.51826e12 | 0.240729 | ||||||||
\(932\) | 1.05674e13i | 0.458773i | ||||||||
\(933\) | − 3.75209e13i | − 1.62109i | ||||||||
\(934\) | −1.70404e12 | −0.0732689 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.13514e12 | −0.303851 | ||||||||
\(937\) | 7.40064e12i | 0.313647i | 0.987627 | + | 0.156824i | \(0.0501254\pi\) | ||||
−0.987627 | + | 0.156824i | \(0.949875\pi\) | |||||||
\(938\) | 6.07831e12i | 0.256372i | ||||||||
\(939\) | −3.33654e13 | −1.40056 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.13867e12 | −0.338377 | −0.169188 | − | 0.985584i | \(-0.554115\pi\) | ||||
−0.169188 | + | 0.985584i | \(0.554115\pi\) | |||||||
\(942\) | − 1.91675e12i | − 0.0793115i | ||||||||
\(943\) | − 5.49463e13i | − 2.26275i | ||||||||
\(944\) | −1.05925e12 | −0.0434134 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.02480e12 | 0.203990 | ||||||||
\(947\) | − 1.16975e13i | − 0.472627i | −0.971677 | − | 0.236313i | \(-0.924061\pi\) | ||||
0.971677 | − | 0.236313i | \(-0.0759392\pi\) | |||||||
\(948\) | 2.59846e13i | 1.04491i | ||||||||
\(949\) | −4.06425e13 | −1.62661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.89661e13 | −2.33771 | ||||||||
\(952\) | − 1.13487e13i | − 0.447796i | ||||||||
\(953\) | 2.50410e13i | 0.983406i | 0.870763 | + | 0.491703i | \(0.163625\pi\) | ||||
−0.870763 | + | 0.491703i | \(0.836375\pi\) | |||||||
\(954\) | −1.66403e13 | −0.650418 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.35686e12 | 0.362301 | ||||||||
\(957\) | − 1.87809e13i | − 0.723791i | ||||||||
\(958\) | 1.32983e13i | 0.510097i | ||||||||
\(959\) | 5.37485e12 | 0.205202 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09838e13 | −0.793649 | ||||||||
\(962\) | − 2.85226e13i | − 1.07375i | ||||||||
\(963\) | − 1.47968e13i | − 0.554433i | ||||||||
\(964\) | 2.21714e13 | 0.826887 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.29972e13 | 1.21921 | ||||||||
\(967\) | 2.68904e13i | 0.988960i | 0.869189 | + | 0.494480i | \(0.164641\pi\) | ||||
−0.869189 | + | 0.494480i | \(0.835359\pi\) | |||||||
\(968\) | 6.21532e12i | 0.227522i | ||||||||
\(969\) | −3.06129e13 | −1.11544 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.28780e13 | 1.18691 | 0.593456 | − | 0.804866i | \(-0.297763\pi\) | ||||
0.593456 | + | 0.804866i | \(0.297763\pi\) | |||||||
\(972\) | − 1.35767e13i | − 0.487860i | ||||||||
\(973\) | 2.62115e13i | 0.937529i | ||||||||
\(974\) | 2.21706e13 | 0.789338 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.87888e12 | −0.101554 | ||||||||
\(977\) | − 8.13505e11i | − 0.0285650i | −0.999898 | − | 0.0142825i | \(-0.995454\pi\) | ||||
0.999898 | − | 0.0142825i | \(-0.00454642\pi\) | |||||||
\(978\) | 3.98339e13i | 1.39229i | ||||||||
\(979\) | −1.36301e13 | −0.474217 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.40164e12 | −0.220689 | ||||||||
\(982\) | 6.28487e12i | 0.215672i | ||||||||
\(983\) | 4.13240e13i | 1.41160i | 0.708412 | + | 0.705800i | \(0.249412\pi\) | ||||
−0.708412 | + | 0.705800i | \(0.750588\pi\) | |||||||
\(984\) | −1.53900e13 | −0.523313 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.54321e13 | 1.19385 | ||||||||
\(987\) | 4.19198e12i | 0.140602i | ||||||||
\(988\) | − 1.24518e13i | − 0.415744i | ||||||||
\(989\) | −2.75631e13 | −0.916105 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.61227e13 | −1.18973 | −0.594866 | − | 0.803825i | \(-0.702795\pi\) | ||||
−0.594866 | + | 0.803825i | \(0.702795\pi\) | |||||||
\(992\) | 2.44923e12i | 0.0803023i | ||||||||
\(993\) | 3.10462e13i | 1.01330i | ||||||||
\(994\) | −1.20219e13 | −0.390603 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.49086e11 | −0.0208995 | ||||||||
\(997\) | − 3.07166e13i | − 0.984565i | −0.870435 | − | 0.492283i | \(-0.836163\pi\) | ||||
0.870435 | − | 0.492283i | \(-0.163837\pi\) | |||||||
\(998\) | 1.20325e13i | 0.383944i | ||||||||
\(999\) | 1.71459e13 | 0.544646 |
(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 | 50.10.b.d.49.2 | 2 | ||
4.3 | odd | 2 | 400.10.c.c.49.2 | 2 | |||
5.2 | odd | 4 | 50.10.a.a.1.1 | 1 | |||
5.3 | odd | 4 | 10.10.a.c.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 50.10.b.d.49.1 | 2 | ||
15.8 | even | 4 | 90.10.a.e.1.1 | 1 | |||
20.3 | even | 4 | 80.10.a.a.1.1 | 1 | |||
20.7 | even | 4 | 400.10.a.j.1.1 | 1 | |||
20.19 | odd | 2 | 400.10.c.c.49.1 | 2 | |||
40.3 | even | 4 | 320.10.a.i.1.1 | 1 | |||
40.13 | odd | 4 | 320.10.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.10.a.c.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
50.10.a.a.1.1 | 1 | 5.2 | odd | 4 | |||
50.10.b.d.49.1 | 2 | 5.4 | even | 2 | inner | ||
50.10.b.d.49.2 | 2 | 1.1 | even | 1 | trivial | ||
80.10.a.a.1.1 | 1 | 20.3 | even | 4 | |||
90.10.a.e.1.1 | 1 | 15.8 | even | 4 | |||
320.10.a.b.1.1 | 1 | 40.13 | odd | 4 | |||
320.10.a.i.1.1 | 1 | 40.3 | even | 4 | |||
400.10.a.j.1.1 | 1 | 20.7 | even | 4 | |||
400.10.c.c.49.1 | 2 | 20.19 | odd | 2 | |||
400.10.c.c.49.2 | 2 | 4.3 | odd | 2 |