Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,10,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (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: | \(206.014334466\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.10.c.c.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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 174.000i | 1.24023i | 0.784509 | + | 0.620117i | \(0.212915\pi\) | ||||
−0.784509 | + | 0.620117i | \(0.787085\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4658.00i | − 0.733261i | −0.930367 | − | 0.366630i | \(-0.880511\pi\) | ||||
0.930367 | − | 0.366630i | \(-0.119489\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −10593.0 | −0.538180 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −28992.0 | −0.597051 | −0.298525 | − | 0.954402i | \(-0.596495\pi\) | ||||
−0.298525 | + | 0.954402i | \(0.596495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 164446.i | 1.59690i | 0.602060 | + | 0.798451i | \(0.294347\pi\) | ||||
−0.602060 | + | 0.798451i | \(0.705653\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 594822.i | − 1.72730i | −0.504095 | − | 0.863648i | \(-0.668174\pi\) | ||||
0.504095 | − | 0.863648i | \(-0.331826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −295780. | −0.520688 | −0.260344 | − | 0.965516i | \(-0.583836\pi\) | ||||
−0.260344 | + | 0.965516i | \(0.583836\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 810492. | 0.909415 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.54453e6i | 1.89598i | 0.318305 | + | 0.947988i | \(0.396886\pi\) | ||||
−0.318305 | + | 0.947988i | \(0.603114\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.58166e6i | 0.572765i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(-0.572934\pi\) | ||||
−0.227129 | + | 0.973865i | \(0.572934\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.04461e6i | − 0.740482i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.08404e7i | 0.950907i | 0.879741 | + | 0.475454i | \(0.157716\pi\) | ||||
−0.879741 | + | 0.475454i | \(0.842284\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.86136e7 | −1.98053 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.15939e7 | 1.19345 | 0.596723 | − | 0.802447i | \(-0.296469\pi\) | ||||
0.596723 | + | 0.802447i | \(0.296469\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.08323e7i | 0.483184i | 0.970378 | + | 0.241592i | \(0.0776695\pi\) | ||||
−0.970378 | + | 0.241592i | \(0.922330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.17214e6i | − 0.154607i | −0.997008 | − | 0.0773036i | \(-0.975369\pi\) | ||||
0.997008 | − | 0.0773036i | \(-0.0246311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.86566e7 | 0.462329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.03499e8 | 2.14225 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.81797e7i | − 1.70915i | −0.519328 | − | 0.854575i | \(-0.673818\pi\) | ||||
0.519328 | − | 0.854575i | \(-0.326182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 5.14657e7i | − 0.645775i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.61629e7 | 0.173654 | 0.0868269 | − | 0.996223i | \(-0.472327\pi\) | ||||
0.0868269 | + | 0.996223i | \(0.472327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.39282e7 | −0.406218 | −0.203109 | − | 0.979156i | \(-0.565105\pi\) | ||||
−0.203109 | + | 0.979156i | \(0.565105\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.93422e7i | 0.394626i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.15574e7i | 0.494455i | 0.968957 | + | 0.247228i | \(0.0795195\pi\) | ||||
−0.968957 | + | 0.247228i | \(0.920480\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.42749e8 | −2.35145 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.61308e8 | −0.753343 | −0.376671 | − | 0.926347i | \(-0.622931\pi\) | ||||
−0.376671 | + | 0.926347i | \(0.622931\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.47148e8i | 1.01860i | 0.860589 | + | 0.509301i | \(0.170096\pi\) | ||||
−0.860589 | + | 0.509301i | \(0.829904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.35045e8i | 0.437794i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.83346e8 | −1.68502 | −0.842508 | − | 0.538684i | \(-0.818922\pi\) | ||||
−0.842508 | + | 0.538684i | \(0.818922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.83711e8 | −1.24854 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.45718e7i | − 0.0337024i | −0.999858 | − | 0.0168512i | \(-0.994636\pi\) | ||||
0.999858 | − | 0.0168512i | \(-0.00536416\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.47797e8i | 1.21228i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 4.06424e8i | − 0.563386i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1.17838e8i | − 0.135149i | −0.997714 | − | 0.0675747i | \(-0.978474\pi\) | ||||
0.997714 | − | 0.0675747i | \(-0.0215261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.07112e8 | 0.321321 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.60927e7 | −0.0823228 | −0.0411614 | − | 0.999153i | \(-0.513106\pi\) | ||||
−0.0411614 | + | 0.999153i | \(0.513106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.92872e9i | 1.68850i | 0.535947 | + | 0.844252i | \(0.319955\pi\) | ||||
−0.535947 | + | 0.844252i | \(0.680045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.39685e9i | − 1.03020i | −0.857130 | − | 0.515100i | \(-0.827755\pi\) | ||||
0.857130 | − | 0.515100i | \(-0.172245\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 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 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.68580e9i | 0.972643i | 0.873780 | + | 0.486322i | \(0.161662\pi\) | ||||
−0.873780 | + | 0.486322i | \(0.838338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.74198e9i | − 0.859421i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.77068e9 | −1.26656 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.51741e9 | −0.643531 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.75733e9i | 1.48015i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.70716e9i | − 1.26452i | −0.774758 | − | 0.632258i | \(-0.782128\pi\) | ||||
0.774758 | − | 0.632258i | \(-0.217872\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.88482e9 | −0.599261 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.54080e9 | −0.753789 | −0.376895 | − | 0.926256i | \(-0.623008\pi\) | ||||
−0.376895 | + | 0.926256i | \(0.623008\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37774e9i | 0.381800i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1.15390e9i | − 0.279849i | −0.990162 | − | 0.139925i | \(-0.955314\pi\) | ||||
0.990162 | − | 0.139925i | \(-0.0446860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.62721e9 | −1.27858 | −0.639288 | − | 0.768968i | \(-0.720771\pi\) | ||||
−0.639288 | + | 0.768968i | \(0.720771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.99952e8 | 0.191749 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 4.76762e9i | − 0.953431i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.24626e9i | 0.573396i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 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 | \(-0.499759\pi\) | ||||
0.000757236 | 1.00000i | \(0.499759\pi\) | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.30095e9i | 0.929597i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 6.88488e8i | − 0.0904373i | −0.998977 | − | 0.0452187i | \(-0.985602\pi\) | ||||
0.998977 | − | 0.0452187i | \(-0.0143985\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.70833e10 | 2.11975 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.18524e10 | 1.39024 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 1.43082e10i | − 1.58759i | −0.608182 | − | 0.793797i | \(-0.708101\pi\) | ||||
0.608182 | − | 0.793797i | \(-0.291899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 9.98735e9i | − 0.993633i | −0.867856 | − | 0.496817i | \(-0.834502\pi\) | ||||
0.867856 | − | 0.496817i | \(-0.165498\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.64380e10 | −1.55010 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.13320e9 | 0.280224 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3.51396e9i | − 0.298256i | −0.988818 | − | 0.149128i | \(-0.952353\pi\) | ||||
0.988818 | − | 0.149128i | \(-0.0476466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.81234e9i | 0.215371i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.19502e9 | 0.0870038 | 0.0435019 | − | 0.999053i | \(-0.486149\pi\) | ||||
0.0435019 | + | 0.999053i | \(0.486149\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.12053e9 | −0.631635 | −0.315818 | − | 0.948820i | \(-0.602279\pi\) | ||||
−0.315818 | + | 0.948820i | \(0.602279\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 7.64350e9i | − 0.503805i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.72451e10i | 1.03128i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.36737e9 | 0.419986 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.37431e9 | 0.509670 | 0.254835 | − | 0.966985i | \(-0.417979\pi\) | ||||
0.254835 | + | 0.966985i | \(0.417979\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 2.40000e10i | − 1.24510i | −0.782580 | − | 0.622550i | \(-0.786097\pi\) | ||||
0.782580 | − | 0.622550i | \(-0.213903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5.56124e8i | − 0.0263071i | −0.999913 | − | 0.0131536i | \(-0.995813\pi\) | ||||
0.999913 | − | 0.0131536i | \(-0.00418703\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.51255e10 | −1.13573 | −0.567866 | − | 0.823121i | \(-0.692231\pi\) | ||||
−0.567866 | + | 0.823121i | \(0.692231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.41910e10 | −0.613240 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.73416e10i | − 0.716732i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.69542e10i | − 1.02038i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.57525e9 | 0.310877 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.63915e10 | 0.569309 | 0.284654 | − | 0.958630i | \(-0.408121\pi\) | ||||
0.284654 | + | 0.958630i | \(0.408121\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2.80675e10i | − 0.934321i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.08800e10i | 0.333090i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.30037e10 | −1.26330 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.78161e10 | 2.75832 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.65257e10i | 1.25986i | 0.776654 | + | 0.629928i | \(0.216916\pi\) | ||||
−0.776654 | + | 0.629928i | \(0.783084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.91415e9i | 0.0478475i | 0.999714 | + | 0.0239237i | \(0.00761589\pi\) | ||||
−0.999714 | + | 0.0239237i | \(0.992384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 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 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 4.12790e10i | − 0.917545i | −0.888554 | − | 0.458773i | \(-0.848289\pi\) | ||||
0.888554 | − | 0.458773i | \(-0.151711\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.01502e11i | − 2.08981i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.65502e10 | 0.724602 | 0.362301 | − | 0.932061i | \(-0.381991\pi\) | ||||
0.362301 | + | 0.932061i | \(0.381991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.66070e10 | −1.65377 | −0.826887 | − | 0.562368i | \(-0.809890\pi\) | ||||
−0.826887 | + | 0.562368i | \(0.809890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 5.30339e10i | − 0.975720i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 4.86398e10i | − 0.831488i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.53549e9 | 0.0417989 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.20769e10 | 1.14621 | 0.573105 | − | 0.819482i | \(-0.305739\pi\) | ||||
0.573105 | + | 0.819482i | \(0.305739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7.37711e10i | − 1.13199i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.12729e11i | − 1.61190i | −0.591986 | − | 0.805948i | \(-0.701656\pi\) | ||||
0.591986 | − | 0.805948i | \(-0.298344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.04947e10 | 0.697263 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.94374e10 | −0.526049 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.55225e10i | 0.715596i | 0.933799 | + | 0.357798i | \(0.116472\pi\) | ||||
−0.933799 | + | 0.357798i | \(0.883528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 8.18033e10i | − 0.985076i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −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 | \(-0.560025\pi\) | ||||
−0.187457 | + | 0.982273i | \(0.560025\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.33282e11i | 1.45225i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.46240e10i | 0.557474i | 0.960367 | + | 0.278737i | \(0.0899158\pi\) | ||||
−0.960367 | + | 0.278737i | \(0.910084\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.47428e10 | 0.244473 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.37818e10 | −0.801625 | −0.400813 | − | 0.916160i | \(-0.631272\pi\) | ||||
−0.400813 | + | 0.916160i | \(0.631272\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8.36086e10i | − 0.774840i | −0.921903 | − | 0.387420i | \(-0.873366\pi\) | ||||
0.921903 | − | 0.387420i | \(-0.126634\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.00584e11i | − 0.875107i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.35225e11 | −1.98355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.05039e10 | 0.167617 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.28547e11i | 1.81164i | 0.423666 | + | 0.905819i | \(0.360743\pi\) | ||||
−0.423666 | + | 0.905819i | \(0.639257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 4.58555e10i | − 0.341969i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.18438e11 | −3.02769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.04568e10 | 0.354300 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 1.49801e10i | − 0.102100i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.95064e11i | − 1.25330i | −0.779302 | − | 0.626648i | \(-0.784426\pi\) | ||||
0.779302 | − | 0.626648i | \(-0.215574\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.35598e11 | −2.09414 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.15637e11 | −1.30708 | −0.653540 | − | 0.756892i | \(-0.726717\pi\) | ||||
−0.653540 | + | 0.756892i | \(0.726717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.91755e11i | − 1.12927i | −0.825341 | − | 0.564635i | \(-0.809017\pi\) | ||||
0.825341 | − | 0.564635i | \(-0.190983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.38886e11i | − 1.88489i | −0.334358 | − | 0.942446i | \(-0.608519\pi\) | ||||
0.334358 | − | 0.942446i | \(-0.391481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07936e11 | −0.583592 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.43051e11 | 1.27769 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.75936e11i | 0.899383i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.05153e11i | 0.508577i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.40918e10 | −0.113367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.78427e11 | 0.817022 | 0.408511 | − | 0.912753i | \(-0.366048\pi\) | ||||
0.408511 | + | 0.912753i | \(0.366048\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.14833e11i | − 0.511760i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.64693e11i | 1.11791i | 0.829196 | + | 0.558957i | \(0.188798\pi\) | ||||
−0.829196 | + | 0.558957i | \(0.811202\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.93330e11 | −1.20631 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.77187e10 | 0.271215 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.74870e11i | − 1.07227i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.11912e10i | 0.300626i | 0.988638 | + | 0.150313i | \(0.0480281\pi\) | ||||
−0.988638 | + | 0.150313i | \(0.951972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 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 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 3.28733e10i | − 0.112683i | −0.998412 | − | 0.0563413i | \(-0.982056\pi\) | ||||
0.998412 | − | 0.0563413i | \(-0.0179435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 4.82098e11i | − 1.57083i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.12096e11 | −0.991661 | −0.495831 | − | 0.868419i | \(-0.665136\pi\) | ||||
−0.495831 | + | 0.868419i | \(0.665136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.35202e11 | −0.728884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.64030e11i | − 0.798129i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 6.28209e11i | − 1.80762i | −0.427934 | − | 0.903810i | \(-0.640759\pi\) | ||||
0.427934 | − | 0.903810i | \(-0.359241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.28744e11 | −0.642289 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.57321e11 | −1.25325 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.84770e10i | 0.263418i | 0.991288 | + | 0.131709i | \(0.0420464\pi\) | ||||
−0.991288 | + | 0.131709i | \(0.957954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.12228e11i | 1.56091i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.89024e11 | 0.719544 | 0.359772 | − | 0.933040i | \(-0.382855\pi\) | ||||
0.359772 | + | 0.933040i | \(0.382855\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.45046e11 | 1.56830 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.01350e11i | 0.478141i | 0.971002 | + | 0.239071i | \(0.0768427\pi\) | ||||
−0.971002 | + | 0.239071i | \(0.923157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.14746e11i | − 0.260040i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 4.42099e11i | − 0.934875i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.15625e11i | − 1.04178i | −0.853623 | − | 0.520891i | \(-0.825600\pi\) | ||||
0.853623 | − | 0.520891i | \(-0.174400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.39727e11 | −0.473521 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.43309e11 | −1.62869 | −0.814343 | − | 0.580384i | \(-0.802902\pi\) | ||||
−0.814343 | + | 0.580384i | \(0.802902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 3.84108e11i | − 0.725406i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 3.14285e11i | − 0.567740i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −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 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7.52866e10i | − 0.127333i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 9.79134e11i | − 1.58573i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.92475e11 | 1.09759 | 0.548796 | − | 0.835956i | \(-0.315086\pi\) | ||||
0.548796 | + | 0.835956i | \(0.315086\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.08125e11 | 0.633176 | 0.316588 | − | 0.948563i | \(-0.397463\pi\) | ||||
0.316588 | + | 0.948563i | \(0.397463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.47885e10i | 0.0832065i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.04617e11i | 0.297863i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.29566e11 | 1.18248 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.41055e11 | −0.615665 | −0.307833 | − | 0.951441i | \(-0.599604\pi\) | ||||
−0.307833 | + | 0.951441i | \(0.599604\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.15390e10i | 0.0978019i | 0.998804 | + | 0.0489009i | \(0.0155719\pi\) | ||||
−0.998804 | + | 0.0489009i | \(0.984428\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 7.52622e11i | − 0.987212i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.74967e11 | 0.610342 | 0.305171 | − | 0.952298i | \(-0.401286\pi\) | ||||
0.305171 | + | 0.952298i | \(0.401286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.97630e11 | −0.248816 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1.97072e11i | − 0.243113i | −0.992585 | − | 0.121556i | \(-0.961211\pi\) | ||||
0.992585 | − | 0.121556i | \(-0.0387885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.71817e11i | 0.440499i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.68348e9i | 0.00187830i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.88006e11i | 0.845097i | 0.906340 | + | 0.422549i | \(0.138864\pi\) | ||||
−0.906340 | + | 0.422549i | \(0.861136\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.40806e11 | 0.989334 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.53496e10 | 0.0158286 | 0.00791429 | − | 0.999969i | \(-0.497481\pi\) | ||||
0.00791429 | + | 0.999969i | \(0.497481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.94494e11i | 0.196694i | 0.995152 | + | 0.0983471i | \(0.0313555\pi\) | ||||
−0.995152 | + | 0.0983471i | \(0.968644\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.06503e11i | − 0.103618i | −0.998657 | − | 0.0518089i | \(-0.983501\pi\) | ||||
0.998657 | − | 0.0518089i | \(-0.0164987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.79894e11 | 0.362564 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.19797e11 | 0.112163 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.14050e11i | − 0.288485i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.04002e12i | 0.919831i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.31146e11 | −0.721386 | −0.360693 | − | 0.932685i | \(-0.617460\pi\) | ||||
−0.360693 | + | 0.932685i | \(0.617460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.78266e12 | −1.51851 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.06232e12i | 1.72423i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.38566e12i | 1.11629i | 0.829743 | + | 0.558146i | \(0.188487\pi\) | ||||
−0.829743 | + | 0.558146i | \(0.811513\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.48962e12 | 1.96899 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.92804e11 | −0.305007 | −0.152503 | − | 0.988303i | \(-0.548734\pi\) | ||||
−0.152503 | + | 0.988303i | \(0.548734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 2.21450e12i | − 1.68836i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.51371e11i | 0.552397i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.52029e11 | −0.542978 | −0.271489 | − | 0.962442i | \(-0.587516\pi\) | ||||
−0.271489 | + | 0.962442i | \(0.587516\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.73780e12 | 1.23234 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 1.83429e12i | − 1.27765i | −0.769351 | − | 0.638826i | \(-0.779420\pi\) | ||||
0.769351 | − | 0.638826i | \(-0.220580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2.86021e12i | − 1.92248i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.67823e11i | − 0.298232i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.49951e11i | 0.0923083i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.11428e11 | 0.369907 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.25683e11 | 0.312575 | 0.156287 | − | 0.987712i | \(-0.450047\pi\) | ||||
0.156287 | + | 0.987712i | \(0.450047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.68426e11i | 0.0984353i | 0.998788 | + | 0.0492177i | \(0.0156728\pi\) | ||||
−0.998788 | + | 0.0492177i | \(0.984327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.38937e12i | 0.784639i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.67350e12 | −2.59473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.71213e11 | −0.0934570 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.55102e12i | 1.90582i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.07934e11i | 0.107905i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.40893e11 | −0.276034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.20612e12 | 1.10724 | 0.553620 | − | 0.832769i | \(-0.313246\pi\) | ||||
0.553620 | + | 0.832769i | \(0.313246\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.58697e12i | − 0.783375i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.51639e12i | 1.67940i | 0.543049 | + | 0.839701i | \(0.317270\pi\) | ||||
−0.543049 | + | 0.839701i | \(0.682730\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.65331e11 | 0.218618 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.10118e12 | −0.508951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.71722e12i | 1.23556i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.29996e11i | 0.277325i | 0.990340 | + | 0.138663i | \(0.0442803\pi\) | ||||
−0.990340 | + | 0.138663i | \(0.955720\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.78133e12 | −0.771597 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.00064e12 | −1.27903 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.02619e11i | 0.168891i | 0.996428 | + | 0.0844455i | \(0.0269119\pi\) | ||||
−0.996428 | + | 0.0844455i | \(0.973088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.25313e12i | 0.915507i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −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 | \(-0.573484\pi\) | ||||
−0.228810 | + | 0.973471i | \(0.573484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.63113e12i | 0.632110i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.66332e12i | 1.75148i | 0.482787 | + | 0.875738i | \(0.339625\pi\) | ||||
−0.482787 | + | 0.875738i | \(0.660375\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.17601e12 | 1.54421 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.78754e10 | −0.0247127 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.84643e12i | 1.02045i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 3.88422e12i | − 1.35030i | −0.737678 | − | 0.675152i | \(-0.764078\pi\) | ||||
0.737678 | − | 0.675152i | \(-0.235922\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.90875e11 | 0.236527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.67655e10 | 0.0326270 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.01341e12i | 0.668631i | 0.942461 | + | 0.334315i | \(0.108505\pi\) | ||||
−0.942461 | + | 0.334315i | \(0.891495\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 4.37184e12i | − 1.40857i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.10578e12 | 0.668333 | 0.334166 | − | 0.942514i | \(-0.391545\pi\) | ||||
0.334166 | + | 0.942514i | \(0.391545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.74058e12 | 1.48216 | 0.741082 | − | 0.671415i | \(-0.234313\pi\) | ||||
0.741082 | + | 0.671415i | \(0.234313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8.63938e11i | − 0.266106i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.01476e12i | 1.20036i | 0.799866 | + | 0.600179i | \(0.204904\pi\) | ||||
−0.799866 | + | 0.600179i | \(0.795096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.01744e12 | 0.888915 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.50537e11 | 0.246893 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.30399e12i | − 0.372993i | −0.982456 | − | 0.186496i | \(-0.940287\pi\) | ||||
0.982456 | − | 0.186496i | \(-0.0597133\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.10164e12i | 1.41719i | 0.705618 | + | 0.708593i | \(0.250670\pi\) | ||||
−0.705618 | + | 0.708593i | \(0.749330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.50630e11 | −0.123371 | −0.0616854 | − | 0.998096i | \(-0.519648\pi\) | ||||
−0.0616854 | + | 0.998096i | \(0.519648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.02459e12 | −1.08595 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.18988e12i | 0.582404i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.49209e12i | 0.385560i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.44812e12 | 1.64250 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.97105e10 | −0.0200163 | −0.0100081 | − | 0.999950i | \(-0.503186\pi\) | ||||
−0.0100081 | + | 0.999950i | \(0.503186\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.85212e12i | 0.706076i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.06801e12i | 0.738294i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.70873e12 | 0.405434 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.12648e12 | −0.731468 | −0.365734 | − | 0.930719i | \(-0.619182\pi\) | ||||
−0.365734 | + | 0.930719i | \(0.619182\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.94982e12i | − 1.37263i | −0.727303 | − | 0.686316i | \(-0.759227\pi\) | ||||
0.727303 | − | 0.686316i | \(-0.240773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 3.56187e12i | − 0.799115i | −0.916708 | − | 0.399557i | \(-0.869164\pi\) | ||||
0.916708 | − | 0.399557i | \(-0.130836\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.68594e11 | −0.103680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.89312e12 | −0.413109 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.37883e11i | 0.0296757i | 0.999890 | + | 0.0148379i | \(0.00472321\pi\) | ||||
−0.999890 | + | 0.0148379i | \(0.995277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 2.61804e12i | − 0.548191i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.16654e12 | −0.860581 | −0.430290 | − | 0.902691i | \(-0.641589\pi\) | ||||
−0.430290 | + | 0.902691i | \(0.641589\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.29083e12 | −0.670500 | −0.335250 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335250 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.70200e13i | 3.42097i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.47322e12i | 1.85324i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.09547e12 | −1.56252 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.27357e12 | 0.242532 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 5.74732e12i | − 1.07993i | −0.841686 | − | 0.539967i | \(-0.818437\pi\) | ||||
0.841686 | − | 0.539967i | \(-0.181563\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.31245e12i | 1.70379i | 0.523716 | + | 0.851893i | \(0.324545\pi\) | ||||
−0.523716 | + | 0.851893i | \(0.675455\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.48892e11 | −0.0990998 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.33062e11 | −0.0593421 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.19967e12i | 1.61763i | 0.588063 | + | 0.808815i | \(0.299891\pi\) | ||||
−0.588063 | + | 0.808815i | \(0.700109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.53735e12i | 0.434585i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.61453e13 | 2.72934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.03125e13 | −1.72074 | −0.860369 | − | 0.509672i | \(-0.829767\pi\) | ||||
−0.860369 | + | 0.509672i | \(0.829767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.43053e12i | − 0.235612i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.28445e13i | − 2.06144i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.18255e12 | 1.13797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.52566e12 | −1.48992 | −0.744961 | − | 0.667108i | \(-0.767532\pi\) | ||||
−0.744961 | + | 0.667108i | \(0.767532\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 3.20638e12i | − 0.495126i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.01020e11i | 0.0603641i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 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 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 5.94345e12i | − 0.861263i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.35974e12i | 0.898676i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.94013e12 | 0.968473 | 0.484236 | − | 0.874937i | \(-0.339097\pi\) | ||||
0.484236 | + | 0.874937i | \(0.339097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.98398e12 | 1.23811 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.50696e13i | − 2.05107i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.74984e12i | − 1.02893i | −0.857510 | − | 0.514467i | \(-0.827990\pi\) | ||||
0.857510 | − | 0.514467i | \(-0.172010\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.92986e11 | −0.0384214 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.44329e12 | 0.834602 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.12555e12i | − 0.527854i | −0.964543 | − | 0.263927i | \(-0.914982\pi\) | ||||
0.964543 | − | 0.263927i | \(-0.0850178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.36451e12i | − 0.295215i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.33931e12 | 0.411867 | 0.205933 | − | 0.978566i | \(-0.433977\pi\) | ||||
0.205933 | + | 0.978566i | \(0.433977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.46333e12 | 1.03124 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.26471e13i | − 1.52245i | −0.648489 | − | 0.761224i | \(-0.724599\pi\) | ||||
0.648489 | − | 0.761224i | \(-0.275401\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.54359e11i | 0.0181380i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.50651e12 | −0.755405 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.56552e12 | −0.179588 | −0.0897941 | − | 0.995960i | \(-0.528621\pi\) | ||||
−0.0897941 | + | 0.995960i | \(0.528621\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.25414e13i | 1.42157i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.54781e11i | 0.105675i | 0.998603 | + | 0.0528375i | \(0.0168265\pi\) | ||||
−0.998603 | + | 0.0528375i | \(0.983173\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.28362e13 | 1.40394 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.27330e12 | 0.569969 | 0.284985 | − | 0.958532i | \(-0.408012\pi\) | ||||
0.284985 | + | 0.958532i | \(0.408012\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 2.81496e12i | − 0.300685i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.65792e12i | 0.277308i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.79383e12i | 0.382182i | 0.981572 | + | 0.191091i | \(0.0612025\pi\) | ||||
−0.981572 | + | 0.191091i | \(0.938797\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.78607e12i | 0.864769i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.38703e12 | −0.621413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.67663e12 | 0.449784 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.88847e12i | 0.559854i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.05939e13i | 1.91361i | 0.290736 | + | 0.956803i | \(0.406100\pi\) | ||||
−0.290736 | + | 0.956803i | \(0.593900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.66092e12 | −0.887507 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.85247e12 | 0.713201 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 7.22381e12i | − 0.648690i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.45507e12i | 0.127738i | 0.997958 | + | 0.0638690i | \(0.0203440\pi\) | ||||
−0.997958 | + | 0.0638690i | \(0.979656\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.07650e12 | −0.267052 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.98013e12 | 0.427459 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.16531e12i | − 0.608156i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 4.86722e12i | − 0.403971i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −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 | \(-0.632722\pi\) | ||||
−0.404980 | + | 0.914325i | \(0.632722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 5.79219e12i | − 0.464981i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3.20398e12i | − 0.251588i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.11413e12 | −0.630179 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.80913e13 | −1.38972 | −0.694859 | − | 0.719146i | \(-0.744533\pi\) | ||||
−0.694859 | + | 0.719146i | \(0.744533\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.39801e12i | 0.106221i | 0.998589 | + | 0.0531107i | \(0.0169136\pi\) | ||||
−0.998589 | + | 0.0531107i | \(0.983086\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.26201e13i | − 1.68159i | −0.541354 | − | 0.840794i | \(-0.682088\pi\) | ||||
0.541354 | − | 0.840794i | \(-0.317912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −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 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.10974e13i | − 0.798579i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.69440e12i | − 0.260183i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.76607e12 | −0.123049 | −0.0615245 | − | 0.998106i | \(-0.519596\pi\) | ||||
−0.0615245 | + | 0.998106i | \(0.519596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.46640e11 | −0.0445739 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.45780e13i | − 0.994203i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.06810e12i | 0.471876i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.45479e13 | 0.960983 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.75838e13 | −1.80290 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.37844e13i | 1.53823i | 0.639109 | + | 0.769116i | \(0.279303\pi\) | ||||
−0.639109 | + | 0.769116i | \(0.720697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.61941e12i | 0.482511i | 0.970462 | + | 0.241256i | \(0.0775593\pi\) | ||||
−0.970462 | + | 0.241256i | \(0.922441\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.27695e13 | −0.800212 | −0.400106 | − | 0.916469i | \(-0.631027\pi\) | ||||
−0.400106 | + | 0.916469i | \(0.631027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.75017e13 | 1.08534 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.63038e13i | 1.61425i | 0.590382 | + | 0.807124i | \(0.298977\pi\) | ||||
−0.590382 | + | 0.807124i | \(0.701023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 4.09292e13i | − 2.46007i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.69124e13 | 1.00604 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.34118e13 | −0.789596 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.24826e12i | 0.0727347i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.76832e11i | 0.0272187i | 0.999907 | + | 0.0136093i | \(0.00433212\pi\) | ||||
−0.999907 | + | 0.0136093i | \(0.995668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.97672e13 | −2.24685 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.74839e13 | 0.977791 | 0.488896 | − | 0.872342i | \(-0.337400\pi\) | ||||
0.488896 | + | 0.872342i | \(0.337400\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 6.48321e12i | − 0.358894i | −0.983768 | − | 0.179447i | \(-0.942569\pi\) | ||||
0.983768 | − | 0.179447i | \(-0.0574309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.92450e12i | 0.538335i | 0.963093 | + | 0.269167i | \(0.0867485\pi\) | ||||
−0.963093 | + | 0.269167i | \(0.913252\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.72679e13 | −0.927220 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.40237e13 | 0.745443 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.52981e12i | 0.0805021i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 7.28083e13i | − 3.75504i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.69601e12 | −0.444019 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.83994e13 | −2.95221 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.77949e12i | 0.439414i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.40768e12i | − 0.0690671i | −0.999404 | − | 0.0345335i | \(-0.989005\pi\) | ||||
0.999404 | − | 0.0345335i | \(-0.0109946\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.11980e11 | 0.0443045 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.91343e12 | −0.332553 | −0.166277 | − | 0.986079i | \(-0.553174\pi\) | ||||
−0.166277 | + | 0.986079i | \(0.553174\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.22465e11i | 0.0201221i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.18351e13i | 0.552724i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.50189e12 | −0.393184 | −0.196592 | − | 0.980485i | \(-0.562987\pi\) | ||||
−0.196592 | + | 0.980485i | \(0.562987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.39411e13 | 1.55438 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 2.65264e13i | − 1.20301i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.04309e13i | − 0.908719i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3.75209e13i | − 1.62109i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.40064e12i | 0.313647i | 0.987627 | + | 0.156824i | \(0.0501254\pi\) | ||||
−0.987627 | + | 0.156824i | \(0.949875\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.33654e13 | 1.40056 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.13867e12 | −0.338377 | −0.169188 | − | 0.985584i | \(-0.554115\pi\) | ||||
−0.169188 | + | 0.985584i | \(0.554115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.49463e13i | 2.26275i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.16975e13i | 0.472627i | 0.971677 | + | 0.236313i | \(0.0759392\pi\) | ||||
−0.971677 | + | 0.236313i | \(0.924061\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.06425e13 | −1.62661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.89661e13 | 2.33771 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.50410e13i | 0.983406i | 0.870763 | + | 0.491703i | \(0.163625\pi\) | ||||
−0.870763 | + | 0.491703i | \(0.836375\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1.87809e13i | − 0.723791i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.37485e12 | −0.205202 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.09838e13 | −0.793649 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.47968e13i | 0.554433i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2.68904e13i | − 0.988960i | −0.869189 | − | 0.494480i | \(-0.835359\pi\) | ||||
0.869189 | − | 0.494480i | \(-0.164641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.06129e13 | −1.11544 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.28780e13 | −1.18691 | −0.593456 | − | 0.804866i | \(-0.702237\pi\) | ||||
−0.593456 | + | 0.804866i | \(0.702237\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.62115e13i | 0.937529i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 8.13505e11i | − 0.0285650i | −0.999898 | − | 0.0142825i | \(-0.995454\pi\) | ||||
0.999898 | − | 0.0142825i | \(-0.00454642\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.36301e13 | 0.474217 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.40164e12 | −0.220689 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 4.13240e13i | − 1.41160i | −0.708412 | − | 0.705800i | \(-0.750588\pi\) | ||||
0.708412 | − | 0.705800i | \(-0.249412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 4.19198e12i | − 0.140602i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.75631e13 | −0.916105 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.61227e13 | 1.18973 | 0.594866 | − | 0.803825i | \(-0.297205\pi\) | ||||
0.594866 | + | 0.803825i | \(0.297205\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.10462e13i | 1.01330i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.07166e13i | − 0.984565i | −0.870435 | − | 0.492283i | \(-0.836163\pi\) | ||||
0.870435 | − | 0.492283i | \(-0.163837\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 400.10.c.c.49.2 | 2 | ||
4.3 | odd | 2 | 50.10.b.d.49.2 | 2 | |||
5.2 | odd | 4 | 400.10.a.j.1.1 | 1 | |||
5.3 | odd | 4 | 80.10.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 400.10.c.c.49.1 | 2 | ||
20.3 | even | 4 | 10.10.a.c.1.1 | ✓ | 1 | ||
20.7 | even | 4 | 50.10.a.a.1.1 | 1 | |||
20.19 | odd | 2 | 50.10.b.d.49.1 | 2 | |||
40.3 | even | 4 | 320.10.a.b.1.1 | 1 | |||
40.13 | odd | 4 | 320.10.a.i.1.1 | 1 | |||
60.23 | odd | 4 | 90.10.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.10.a.c.1.1 | ✓ | 1 | 20.3 | even | 4 | ||
50.10.a.a.1.1 | 1 | 20.7 | even | 4 | |||
50.10.b.d.49.1 | 2 | 20.19 | odd | 2 | |||
50.10.b.d.49.2 | 2 | 4.3 | odd | 2 | |||
80.10.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
90.10.a.e.1.1 | 1 | 60.23 | odd | 4 | |||
320.10.a.b.1.1 | 1 | 40.3 | even | 4 | |||
320.10.a.i.1.1 | 1 | 40.13 | odd | 4 | |||
400.10.a.j.1.1 | 1 | 5.2 | odd | 4 | |||
400.10.c.c.49.1 | 2 | 5.4 | even | 2 | inner | ||
400.10.c.c.49.2 | 2 | 1.1 | even | 1 | trivial |