Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,8,Mod(1,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(50.6063741284\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 162.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −165.000 | −0.590322 | −0.295161 | − | 0.955448i | \(-0.595373\pi\) | ||||
−0.295161 | + | 0.955448i | \(0.595373\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −508.000 | −0.559784 | −0.279892 | − | 0.960031i | \(-0.590299\pi\) | ||||
−0.279892 | + | 0.960031i | \(0.590299\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1320.00 | −0.417421 | ||||||||
\(11\) | 3024.00 | 0.685027 | 0.342513 | − | 0.939513i | \(-0.388722\pi\) | ||||
0.342513 | + | 0.939513i | \(0.388722\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5039.00 | 0.636125 | 0.318063 | − | 0.948070i | \(-0.396968\pi\) | ||||
0.318063 | + | 0.948070i | \(0.396968\pi\) | |||||||
\(14\) | −4064.00 | −0.395827 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −3189.00 | −0.157428 | −0.0787142 | − | 0.996897i | \(-0.525081\pi\) | ||||
−0.0787142 | + | 0.996897i | \(0.525081\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1508.00 | 0.0504387 | 0.0252193 | − | 0.999682i | \(-0.491972\pi\) | ||||
0.0252193 | + | 0.999682i | \(0.491972\pi\) | |||||||
\(20\) | −10560.0 | −0.295161 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 24192.0 | 0.484387 | ||||||||
\(23\) | −75600.0 | −1.29561 | −0.647805 | − | 0.761806i | \(-0.724313\pi\) | ||||
−0.647805 | + | 0.761806i | \(0.724313\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −50900.0 | −0.651520 | ||||||||
\(26\) | 40312.0 | 0.449808 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −32512.0 | −0.279892 | ||||||||
\(29\) | −82665.0 | −0.629403 | −0.314701 | − | 0.949191i | \(-0.601904\pi\) | ||||
−0.314701 | + | 0.949191i | \(0.601904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −174892. | −1.05440 | −0.527198 | − | 0.849742i | \(-0.676758\pi\) | ||||
−0.527198 | + | 0.849742i | \(0.676758\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −25512.0 | −0.111319 | ||||||||
\(35\) | 83820.0 | 0.330453 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −323569. | −1.05017 | −0.525087 | − | 0.851049i | \(-0.675967\pi\) | ||||
−0.525087 | + | 0.851049i | \(0.675967\pi\) | |||||||
\(38\) | 12064.0 | 0.0356655 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −84480.0 | −0.208710 | ||||||||
\(41\) | −308118. | −0.698190 | −0.349095 | − | 0.937087i | \(-0.613511\pi\) | ||||
−0.349095 | + | 0.937087i | \(0.613511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 336680. | 0.645770 | 0.322885 | − | 0.946438i | \(-0.395347\pi\) | ||||
0.322885 | + | 0.946438i | \(0.395347\pi\) | |||||||
\(44\) | 193536. | 0.342513 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −604800. | −0.916135 | ||||||||
\(47\) | −383196. | −0.538367 | −0.269184 | − | 0.963089i | \(-0.586754\pi\) | ||||
−0.269184 | + | 0.963089i | \(0.586754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −565479. | −0.686642 | ||||||||
\(50\) | −407200. | −0.460694 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 322496. | 0.318063 | ||||||||
\(53\) | 760206. | 0.701400 | 0.350700 | − | 0.936488i | \(-0.385944\pi\) | ||||
0.350700 | + | 0.936488i | \(0.385944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −498960. | −0.404386 | ||||||||
\(56\) | −260096. | −0.197914 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −661320. | −0.445055 | ||||||||
\(59\) | −2.22566e6 | −1.41084 | −0.705420 | − | 0.708790i | \(-0.749241\pi\) | ||||
−0.705420 | + | 0.708790i | \(0.749241\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.24482e6 | 1.26627 | 0.633135 | − | 0.774042i | \(-0.281768\pi\) | ||||
0.633135 | + | 0.774042i | \(0.281768\pi\) | |||||||
\(62\) | −1.39914e6 | −0.745571 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −831435. | −0.375519 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.47319e6 | 0.598407 | 0.299203 | − | 0.954189i | \(-0.403279\pi\) | ||||
0.299203 | + | 0.954189i | \(0.403279\pi\) | |||||||
\(68\) | −204096. | −0.0787142 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 670560. | 0.233665 | ||||||||
\(71\) | −5.00689e6 | −1.66021 | −0.830107 | − | 0.557604i | \(-0.811721\pi\) | ||||
−0.830107 | + | 0.557604i | \(0.811721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.89830e6 | −1.77459 | −0.887293 | − | 0.461207i | \(-0.847417\pi\) | ||||
−0.887293 | + | 0.461207i | \(0.847417\pi\) | |||||||
\(74\) | −2.58855e6 | −0.742584 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 96512.0 | 0.0252193 | ||||||||
\(77\) | −1.53619e6 | −0.383467 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.02877e6 | 1.60393 | 0.801963 | − | 0.597374i | \(-0.203789\pi\) | ||||
0.801963 | + | 0.597374i | \(0.203789\pi\) | |||||||
\(80\) | −675840. | −0.147580 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.46494e6 | −0.493695 | ||||||||
\(83\) | −2.65120e6 | −0.508942 | −0.254471 | − | 0.967080i | \(-0.581901\pi\) | ||||
−0.254471 | + | 0.967080i | \(0.581901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 526185. | 0.0929335 | ||||||||
\(86\) | 2.69344e6 | 0.456628 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.54829e6 | 0.242193 | ||||||||
\(89\) | −6.77090e6 | −1.01808 | −0.509039 | − | 0.860743i | \(-0.669999\pi\) | ||||
−0.509039 | + | 0.860743i | \(0.669999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.55981e6 | −0.356093 | ||||||||
\(92\) | −4.83840e6 | −0.647805 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.06557e6 | −0.380683 | ||||||||
\(95\) | −248820. | −0.0297751 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.61764e7 | 1.79962 | 0.899809 | − | 0.436284i | \(-0.143706\pi\) | ||||
0.899809 | + | 0.436284i | \(0.143706\pi\) | |||||||
\(98\) | −4.52383e6 | −0.485529 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.25760e6 | −0.325760 | ||||||||
\(101\) | 2.70161e6 | 0.260915 | 0.130457 | − | 0.991454i | \(-0.458355\pi\) | ||||
0.130457 | + | 0.991454i | \(0.458355\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.06892e6 | 0.186557 | 0.0932787 | − | 0.995640i | \(-0.470265\pi\) | ||||
0.0932787 | + | 0.995640i | \(0.470265\pi\) | |||||||
\(104\) | 2.57997e6 | 0.224904 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.08165e6 | 0.495965 | ||||||||
\(107\) | −9.15450e6 | −0.722423 | −0.361211 | − | 0.932484i | \(-0.617637\pi\) | ||||
−0.361211 | + | 0.932484i | \(0.617637\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.68645e6 | 0.642465 | 0.321233 | − | 0.947000i | \(-0.395903\pi\) | ||||
0.321233 | + | 0.947000i | \(0.395903\pi\) | |||||||
\(110\) | −3.99168e6 | −0.285944 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.08077e6 | −0.139946 | ||||||||
\(113\) | −2.49776e7 | −1.62845 | −0.814227 | − | 0.580547i | \(-0.802839\pi\) | ||||
−0.814227 | + | 0.580547i | \(0.802839\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.24740e7 | 0.764827 | ||||||||
\(116\) | −5.29056e6 | −0.314701 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.78053e7 | −0.997614 | ||||||||
\(119\) | 1.62001e6 | 0.0881260 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.03426e7 | −0.530739 | ||||||||
\(122\) | 1.79585e7 | 0.895388 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.11931e7 | −0.527198 | ||||||||
\(125\) | 2.12891e7 | 0.974929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.98659e6 | −0.216018 | −0.108009 | − | 0.994150i | \(-0.534448\pi\) | ||||
−0.108009 | + | 0.994150i | \(0.534448\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.65148e6 | −0.265532 | ||||||||
\(131\) | −2.23405e7 | −0.868246 | −0.434123 | − | 0.900854i | \(-0.642942\pi\) | ||||
−0.434123 | + | 0.900854i | \(0.642942\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −766064. | −0.0282348 | ||||||||
\(134\) | 1.17855e7 | 0.423137 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.63277e6 | −0.0556594 | ||||||||
\(137\) | 1.28631e7 | 0.427389 | 0.213694 | − | 0.976901i | \(-0.431450\pi\) | ||||
0.213694 | + | 0.976901i | \(0.431450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.41902e7 | 1.39564 | 0.697822 | − | 0.716271i | \(-0.254153\pi\) | ||||
0.697822 | + | 0.716271i | \(0.254153\pi\) | |||||||
\(140\) | 5.36448e6 | 0.165226 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00551e7 | −1.17395 | ||||||||
\(143\) | 1.52379e7 | 0.435763 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.36397e7 | 0.371550 | ||||||||
\(146\) | −4.71864e7 | −1.25482 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.07084e7 | −0.525087 | ||||||||
\(149\) | −2.62887e6 | −0.0651055 | −0.0325527 | − | 0.999470i | \(-0.510364\pi\) | ||||
−0.0325527 | + | 0.999470i | \(0.510364\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.53019e7 | −1.30714 | −0.653568 | − | 0.756868i | \(-0.726729\pi\) | ||||
−0.653568 | + | 0.756868i | \(0.726729\pi\) | |||||||
\(152\) | 772096. | 0.0178328 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.22895e7 | −0.271152 | ||||||||
\(155\) | 2.88572e7 | 0.622433 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.23711e7 | −0.461358 | −0.230679 | − | 0.973030i | \(-0.574095\pi\) | ||||
−0.230679 | + | 0.973030i | \(0.574095\pi\) | |||||||
\(158\) | 5.62301e7 | 1.13415 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.40672e6 | −0.104355 | ||||||||
\(161\) | 3.84048e7 | 0.725262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.23606e7 | 0.946995 | 0.473498 | − | 0.880795i | \(-0.342991\pi\) | ||||
0.473498 | + | 0.880795i | \(0.342991\pi\) | |||||||
\(164\) | −1.97196e7 | −0.349095 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.12096e7 | −0.359877 | ||||||||
\(167\) | −5.47957e7 | −0.910414 | −0.455207 | − | 0.890386i | \(-0.650435\pi\) | ||||
−0.455207 | + | 0.890386i | \(0.650435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.73570e7 | −0.595345 | ||||||||
\(170\) | 4.20948e6 | 0.0657139 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.15475e7 | 0.322885 | ||||||||
\(173\) | 1.23645e8 | 1.81558 | 0.907791 | − | 0.419424i | \(-0.137768\pi\) | ||||
0.907791 | + | 0.419424i | \(0.137768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.58572e7 | 0.364711 | ||||||||
\(176\) | 1.23863e7 | 0.171257 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.41672e7 | −0.719891 | ||||||||
\(179\) | 9.87297e7 | 1.28666 | 0.643328 | − | 0.765591i | \(-0.277553\pi\) | ||||
0.643328 | + | 0.765591i | \(0.277553\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.19855e7 | 1.15304 | 0.576520 | − | 0.817083i | \(-0.304410\pi\) | ||||
0.576520 | + | 0.817083i | \(0.304410\pi\) | |||||||
\(182\) | −2.04785e7 | −0.251796 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.87072e7 | −0.458067 | ||||||||
\(185\) | 5.33889e7 | 0.619940 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.64354e6 | −0.107843 | ||||||||
\(188\) | −2.45245e7 | −0.269184 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.99056e6 | −0.0210541 | ||||||||
\(191\) | 1.31979e8 | 1.37052 | 0.685262 | − | 0.728296i | \(-0.259688\pi\) | ||||
0.685262 | + | 0.728296i | \(0.259688\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.47907e8 | 1.48095 | 0.740473 | − | 0.672086i | \(-0.234602\pi\) | ||||
0.740473 | + | 0.672086i | \(0.234602\pi\) | |||||||
\(194\) | 1.29411e8 | 1.27252 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.61907e7 | −0.343321 | ||||||||
\(197\) | −2.69561e7 | −0.251203 | −0.125602 | − | 0.992081i | \(-0.540086\pi\) | ||||
−0.125602 | + | 0.992081i | \(0.540086\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.35831e8 | 1.22183 | 0.610916 | − | 0.791695i | \(-0.290801\pi\) | ||||
0.610916 | + | 0.791695i | \(0.290801\pi\) | |||||||
\(200\) | −2.60608e7 | −0.230347 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.16129e7 | 0.184495 | ||||||||
\(203\) | 4.19938e7 | 0.352330 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.08395e7 | 0.412157 | ||||||||
\(206\) | 1.65513e7 | 0.131916 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.06397e7 | 0.159031 | ||||||||
\(209\) | 4.56019e6 | 0.0345518 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.19340e6 | −0.0160742 | −0.00803710 | − | 0.999968i | \(-0.502558\pi\) | ||||
−0.00803710 | + | 0.999968i | \(0.502558\pi\) | |||||||
\(212\) | 4.86532e7 | 0.350700 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.32360e7 | −0.510830 | ||||||||
\(215\) | −5.55522e7 | −0.381212 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.88451e7 | 0.590234 | ||||||||
\(218\) | 6.94916e7 | 0.454292 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.19334e7 | −0.202193 | ||||||||
\(221\) | −1.60694e7 | −0.100144 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.99443e7 | 0.120435 | 0.0602174 | − | 0.998185i | \(-0.480821\pi\) | ||||
0.0602174 | + | 0.998185i | \(0.480821\pi\) | |||||||
\(224\) | −1.66461e7 | −0.0989568 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.99820e8 | −1.15149 | ||||||||
\(227\) | −1.25985e8 | −0.714872 | −0.357436 | − | 0.933938i | \(-0.616349\pi\) | ||||
−0.357436 | + | 0.933938i | \(0.616349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.35046e7 | 0.129339 | 0.0646693 | − | 0.997907i | \(-0.479401\pi\) | ||||
0.0646693 | + | 0.997907i | \(0.479401\pi\) | |||||||
\(230\) | 9.97920e7 | 0.540814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.23245e7 | −0.222527 | ||||||||
\(233\) | −1.27757e8 | −0.661665 | −0.330833 | − | 0.943689i | \(-0.607330\pi\) | ||||
−0.330833 | + | 0.943689i | \(0.607330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.32273e7 | 0.317810 | ||||||||
\(236\) | −1.42442e8 | −0.705420 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.29601e7 | 0.0623145 | ||||||||
\(239\) | −9.34878e7 | −0.442958 | −0.221479 | − | 0.975165i | \(-0.571088\pi\) | ||||
−0.221479 | + | 0.975165i | \(0.571088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.34780e8 | −0.620250 | −0.310125 | − | 0.950696i | \(-0.600371\pi\) | ||||
−0.310125 | + | 0.950696i | \(0.600371\pi\) | |||||||
\(242\) | −8.27408e7 | −0.375289 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.43668e8 | 0.633135 | ||||||||
\(245\) | 9.33040e7 | 0.405340 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.59881e6 | 0.0320853 | ||||||||
\(248\) | −8.95447e7 | −0.372786 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.70313e8 | 0.689379 | ||||||||
\(251\) | 1.31470e7 | 0.0524771 | 0.0262385 | − | 0.999656i | \(-0.491647\pi\) | ||||
0.0262385 | + | 0.999656i | \(0.491647\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.28614e8 | −0.887527 | ||||||||
\(254\) | −3.98927e7 | −0.152748 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −1.28471e8 | −0.472105 | −0.236053 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236053 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.64373e8 | 0.587870 | ||||||||
\(260\) | −5.32118e7 | −0.187759 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.78724e8 | −0.613942 | ||||||||
\(263\) | −9.77517e7 | −0.331344 | −0.165672 | − | 0.986181i | \(-0.552979\pi\) | ||||
−0.165672 | + | 0.986181i | \(0.552979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.25434e8 | −0.414052 | ||||||||
\(266\) | −6.12851e6 | −0.0199650 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.42840e7 | 0.299203 | ||||||||
\(269\) | 3.96851e7 | 0.124307 | 0.0621534 | − | 0.998067i | \(-0.480203\pi\) | ||||
0.0621534 | + | 0.998067i | \(0.480203\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.50733e8 | −1.07049 | −0.535246 | − | 0.844696i | \(-0.679781\pi\) | ||||
−0.535246 | + | 0.844696i | \(0.679781\pi\) | |||||||
\(272\) | −1.30621e7 | −0.0393571 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.02905e8 | 0.302209 | ||||||||
\(275\) | −1.53922e8 | −0.446308 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.39602e8 | 1.52544 | 0.762719 | − | 0.646730i | \(-0.223864\pi\) | ||||
0.762719 | + | 0.646730i | \(0.223864\pi\) | |||||||
\(278\) | 3.53522e8 | 0.986869 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.29158e7 | 0.116833 | ||||||||
\(281\) | −1.00852e8 | −0.271151 | −0.135576 | − | 0.990767i | \(-0.543288\pi\) | ||||
−0.135576 | + | 0.990767i | \(0.543288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.54112e8 | −0.666458 | −0.333229 | − | 0.942846i | \(-0.608138\pi\) | ||||
−0.333229 | + | 0.942846i | \(0.608138\pi\) | |||||||
\(284\) | −3.20441e8 | −0.830107 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.21903e8 | 0.308131 | ||||||||
\(287\) | 1.56524e8 | 0.390836 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00169e8 | −0.975216 | ||||||||
\(290\) | 1.09118e8 | 0.262726 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.77491e8 | −0.887293 | ||||||||
\(293\) | −5.43084e8 | −1.26134 | −0.630668 | − | 0.776053i | \(-0.717219\pi\) | ||||
−0.630668 | + | 0.776053i | \(0.717219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.67235e8 | 0.832849 | ||||||||
\(296\) | −1.65667e8 | −0.371292 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.10310e7 | −0.0460365 | ||||||||
\(299\) | −3.80948e8 | −0.824170 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.71033e8 | −0.361492 | ||||||||
\(302\) | −4.42415e8 | −0.924285 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.17677e6 | 0.0126097 | ||||||||
\(305\) | −3.70394e8 | −0.747507 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.29877e8 | −1.43968 | −0.719839 | − | 0.694141i | \(-0.755784\pi\) | ||||
−0.719839 | + | 0.694141i | \(0.755784\pi\) | |||||||
\(308\) | −9.83163e7 | −0.191733 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.30857e8 | 0.440127 | ||||||||
\(311\) | 6.38770e8 | 1.20416 | 0.602078 | − | 0.798437i | \(-0.294339\pi\) | ||||
0.602078 | + | 0.798437i | \(0.294339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.37761e8 | −1.17558 | −0.587790 | − | 0.809013i | \(-0.700002\pi\) | ||||
−0.587790 | + | 0.809013i | \(0.700002\pi\) | |||||||
\(314\) | −1.78968e8 | −0.326229 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.49841e8 | 0.801963 | ||||||||
\(317\) | −6.54377e8 | −1.15377 | −0.576887 | − | 0.816824i | \(-0.695733\pi\) | ||||
−0.576887 | + | 0.816824i | \(0.695733\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.49979e8 | −0.431158 | ||||||||
\(320\) | −4.32538e7 | −0.0737902 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.07238e8 | 0.512838 | ||||||||
\(323\) | −4.80901e6 | −0.00794049 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.56485e8 | −0.414448 | ||||||||
\(326\) | 4.18885e8 | 0.669627 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.57756e8 | −0.246847 | ||||||||
\(329\) | 1.94664e8 | 0.301369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.07689e8 | 1.22418 | 0.612091 | − | 0.790787i | \(-0.290329\pi\) | ||||
0.612091 | + | 0.790787i | \(0.290329\pi\) | |||||||
\(332\) | −1.69677e8 | −0.254471 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.38366e8 | −0.643760 | ||||||||
\(335\) | −2.43076e8 | −0.353253 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.87280e8 | −0.266555 | −0.133278 | − | 0.991079i | \(-0.542550\pi\) | ||||
−0.133278 | + | 0.991079i | \(0.542550\pi\) | |||||||
\(338\) | −2.98856e8 | −0.420972 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.36758e7 | 0.0464667 | ||||||||
\(341\) | −5.28873e8 | −0.722290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.05623e8 | 0.944155 | ||||||||
\(344\) | 1.72380e8 | 0.228314 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.89161e8 | 1.28381 | ||||||||
\(347\) | 2.82556e8 | 0.363037 | 0.181518 | − | 0.983388i | \(-0.441899\pi\) | ||||
0.181518 | + | 0.983388i | \(0.441899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.60612e8 | −0.957799 | −0.478899 | − | 0.877870i | \(-0.658964\pi\) | ||||
−0.478899 | + | 0.877870i | \(0.658964\pi\) | |||||||
\(350\) | 2.06858e8 | 0.257889 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.90904e7 | 0.121097 | ||||||||
\(353\) | −4.68893e8 | −0.567365 | −0.283683 | − | 0.958918i | \(-0.591556\pi\) | ||||
−0.283683 | + | 0.958918i | \(0.591556\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.26137e8 | 0.980061 | ||||||||
\(356\) | −4.33338e8 | −0.509039 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.89838e8 | 0.909803 | ||||||||
\(359\) | 1.53906e8 | 0.175560 | 0.0877802 | − | 0.996140i | \(-0.472023\pi\) | ||||
0.0877802 | + | 0.996140i | \(0.472023\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.91598e8 | −0.997456 | ||||||||
\(362\) | 7.35884e8 | 0.815323 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.63828e8 | −0.178046 | ||||||||
\(365\) | 9.73220e8 | 1.04758 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.49528e8 | −0.791510 | −0.395755 | − | 0.918356i | \(-0.629517\pi\) | ||||
−0.395755 | + | 0.918356i | \(0.629517\pi\) | |||||||
\(368\) | −3.09658e8 | −0.323903 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.27111e8 | 0.438364 | ||||||||
\(371\) | −3.86185e8 | −0.392633 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.41728e8 | −0.540506 | −0.270253 | − | 0.962789i | \(-0.587107\pi\) | ||||
−0.270253 | + | 0.962789i | \(0.587107\pi\) | |||||||
\(374\) | −7.71483e7 | −0.0762563 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.96196e8 | −0.190341 | ||||||||
\(377\) | −4.16549e8 | −0.400379 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.32974e9 | 1.25467 | 0.627334 | − | 0.778750i | \(-0.284146\pi\) | ||||
0.627334 | + | 0.778750i | \(0.284146\pi\) | |||||||
\(380\) | −1.59245e7 | −0.0148875 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.05583e9 | 0.969107 | ||||||||
\(383\) | 7.19949e8 | 0.654796 | 0.327398 | − | 0.944887i | \(-0.393828\pi\) | ||||
0.327398 | + | 0.944887i | \(0.393828\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.53472e8 | 0.226369 | ||||||||
\(386\) | 1.18326e9 | 1.04719 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.03529e9 | 0.899809 | ||||||||
\(389\) | 2.32067e9 | 1.99889 | 0.999447 | − | 0.0332482i | \(-0.0105852\pi\) | ||||
0.999447 | + | 0.0332482i | \(0.0105852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.41088e8 | 0.203966 | ||||||||
\(392\) | −2.89525e8 | −0.242765 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.15649e8 | −0.177628 | ||||||||
\(395\) | −1.15975e9 | −0.946833 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.18373e9 | 0.949477 | 0.474739 | − | 0.880127i | \(-0.342543\pi\) | ||||
0.474739 | + | 0.880127i | \(0.342543\pi\) | |||||||
\(398\) | 1.08664e9 | 0.863966 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.08486e8 | −0.162880 | ||||||||
\(401\) | 1.26764e9 | 0.981726 | 0.490863 | − | 0.871237i | \(-0.336681\pi\) | ||||
0.490863 | + | 0.871237i | \(0.336681\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.81281e8 | −0.670728 | ||||||||
\(404\) | 1.72903e8 | 0.130457 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.35951e8 | 0.249135 | ||||||||
\(407\) | −9.78473e8 | −0.719396 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.01949e9 | −0.736802 | −0.368401 | − | 0.929667i | \(-0.620095\pi\) | ||||
−0.368401 | + | 0.929667i | \(0.620095\pi\) | |||||||
\(410\) | 4.06716e8 | 0.291439 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.32411e8 | 0.0932787 | ||||||||
\(413\) | 1.13064e9 | 0.789765 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.37447e8 | 0.300440 | ||||||||
\(416\) | 1.65118e8 | 0.112452 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.64815e7 | 0.0244318 | ||||||||
\(419\) | 1.04129e9 | 0.691546 | 0.345773 | − | 0.938318i | \(-0.387617\pi\) | ||||
0.345773 | + | 0.938318i | \(0.387617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.95845e9 | −1.27916 | −0.639580 | − | 0.768725i | \(-0.720892\pi\) | ||||
−0.639580 | + | 0.768725i | \(0.720892\pi\) | |||||||
\(422\) | −1.75472e7 | −0.0113662 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.89225e8 | 0.247982 | ||||||||
\(425\) | 1.62320e8 | 0.102568 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.14037e9 | −0.708838 | ||||||||
\(428\) | −5.85888e8 | −0.361211 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.44418e8 | −0.269558 | ||||||||
\(431\) | 2.84256e9 | 1.71017 | 0.855084 | − | 0.518489i | \(-0.173505\pi\) | ||||
0.855084 | + | 0.518489i | \(0.173505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.41292e7 | −0.0498011 | −0.0249006 | − | 0.999690i | \(-0.507927\pi\) | ||||
−0.0249006 | + | 0.999690i | \(0.507927\pi\) | |||||||
\(434\) | 7.10761e8 | 0.417359 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.55933e8 | 0.321233 | ||||||||
\(437\) | −1.14005e8 | −0.0653489 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.87047e9 | −1.05517 | −0.527587 | − | 0.849501i | \(-0.676903\pi\) | ||||
−0.527587 | + | 0.849501i | \(0.676903\pi\) | |||||||
\(440\) | −2.55468e8 | −0.142972 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.28555e8 | −0.0708127 | ||||||||
\(443\) | −1.01333e9 | −0.553779 | −0.276889 | − | 0.960902i | \(-0.589304\pi\) | ||||
−0.276889 | + | 0.960902i | \(0.589304\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.11720e9 | 0.600994 | ||||||||
\(446\) | 1.59554e8 | 0.0851602 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.33169e8 | −0.0699730 | ||||||||
\(449\) | −1.65756e8 | −0.0864183 | −0.0432092 | − | 0.999066i | \(-0.513758\pi\) | ||||
−0.0432092 | + | 0.999066i | \(0.513758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.31749e8 | −0.478279 | ||||||||
\(452\) | −1.59856e9 | −0.814227 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.00788e9 | −0.505491 | ||||||||
\(455\) | 4.22369e8 | 0.210209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.38080e9 | −0.676742 | −0.338371 | − | 0.941013i | \(-0.609876\pi\) | ||||
−0.338371 | + | 0.941013i | \(0.609876\pi\) | |||||||
\(458\) | 1.88037e8 | 0.0914562 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.98336e8 | 0.382414 | ||||||||
\(461\) | 2.78491e9 | 1.32391 | 0.661955 | − | 0.749544i | \(-0.269727\pi\) | ||||
0.661955 | + | 0.749544i | \(0.269727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.78919e9 | 1.30600 | 0.653001 | − | 0.757357i | \(-0.273510\pi\) | ||||
0.653001 | + | 0.757357i | \(0.273510\pi\) | |||||||
\(464\) | −3.38596e8 | −0.157351 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.02205e9 | −0.467868 | ||||||||
\(467\) | 3.97258e9 | 1.80494 | 0.902471 | − | 0.430751i | \(-0.141751\pi\) | ||||
0.902471 | + | 0.430751i | \(0.141751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.48380e8 | −0.334979 | ||||||||
\(470\) | 5.05819e8 | 0.224726 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.13954e9 | −0.498807 | ||||||||
\(473\) | 1.01812e9 | 0.442369 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.67572e7 | −0.0328618 | ||||||||
\(476\) | 1.03681e8 | 0.0440630 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.47902e8 | −0.313218 | ||||||||
\(479\) | −2.34467e9 | −0.974782 | −0.487391 | − | 0.873184i | \(-0.662051\pi\) | ||||
−0.487391 | + | 0.873184i | \(0.662051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.63046e9 | −0.668042 | ||||||||
\(482\) | −1.07824e9 | −0.438583 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.61926e8 | −0.265369 | ||||||||
\(485\) | −2.66910e9 | −1.06235 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.08381e9 | 1.20986 | 0.604931 | − | 0.796278i | \(-0.293201\pi\) | ||||
0.604931 | + | 0.796278i | \(0.293201\pi\) | |||||||
\(488\) | 1.14935e9 | 0.447694 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.46432e8 | 0.286618 | ||||||||
\(491\) | −3.71851e9 | −1.41770 | −0.708848 | − | 0.705361i | \(-0.750785\pi\) | ||||
−0.708848 | + | 0.705361i | \(0.750785\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.63619e8 | 0.0990859 | ||||||||
\(494\) | 6.07905e7 | 0.0226877 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.16358e8 | −0.263599 | ||||||||
\(497\) | 2.54350e9 | 0.929361 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.36426e8 | 0.157238 | 0.0786192 | − | 0.996905i | \(-0.474949\pi\) | ||||
0.0786192 | + | 0.996905i | \(0.474949\pi\) | |||||||
\(500\) | 1.36250e9 | 0.487464 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.05176e8 | 0.0371069 | ||||||||
\(503\) | −5.04603e8 | −0.176792 | −0.0883958 | − | 0.996085i | \(-0.528174\pi\) | ||||
−0.0883958 | + | 0.996085i | \(0.528174\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.45766e8 | −0.154024 | ||||||||
\(506\) | −1.82892e9 | −0.627577 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.19142e8 | −0.108009 | ||||||||
\(509\) | −4.60085e9 | −1.54642 | −0.773208 | − | 0.634153i | \(-0.781349\pi\) | ||||
−0.773208 | + | 0.634153i | \(0.781349\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.99634e9 | 0.993385 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.02777e9 | −0.333829 | ||||||||
\(515\) | −3.41371e8 | −0.110129 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.15878e9 | −0.368796 | ||||||||
\(518\) | 1.31498e9 | 0.415687 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.25695e8 | −0.132766 | ||||||||
\(521\) | 7.14937e7 | 0.0221481 | 0.0110740 | − | 0.999939i | \(-0.496475\pi\) | ||||
0.0110740 | + | 0.999939i | \(0.496475\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.12182e9 | −0.648563 | −0.324281 | − | 0.945961i | \(-0.605122\pi\) | ||||
−0.324281 | + | 0.945961i | \(0.605122\pi\) | |||||||
\(524\) | −1.42979e9 | −0.434123 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.82013e8 | −0.234296 | ||||||||
\(527\) | 5.57731e8 | 0.165992 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.31053e9 | 0.678606 | ||||||||
\(530\) | −1.00347e9 | −0.292779 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.90281e7 | −0.0141174 | ||||||||
\(533\) | −1.55261e9 | −0.444136 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.51049e9 | 0.426462 | ||||||||
\(536\) | 7.54272e8 | 0.211569 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.17481e8 | 0.0878981 | ||||||||
\(539\) | −1.71001e9 | −0.470368 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.11351e9 | −0.573870 | −0.286935 | − | 0.957950i | \(-0.592636\pi\) | ||||
−0.286935 | + | 0.957950i | \(0.592636\pi\) | |||||||
\(542\) | −2.80586e9 | −0.756953 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.04497e8 | −0.0278297 | ||||||||
\(545\) | −1.43326e9 | −0.379261 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.25553e9 | 1.63421 | 0.817107 | − | 0.576487i | \(-0.195577\pi\) | ||||
0.817107 | + | 0.576487i | \(0.195577\pi\) | |||||||
\(548\) | 8.23237e8 | 0.213694 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.23137e9 | −0.315588 | ||||||||
\(551\) | −1.24659e8 | −0.0317462 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.57061e9 | −0.897852 | ||||||||
\(554\) | 4.31682e9 | 1.07865 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.82818e9 | 0.697822 | ||||||||
\(557\) | −6.50846e9 | −1.59583 | −0.797913 | − | 0.602773i | \(-0.794062\pi\) | ||||
−0.797913 | + | 0.602773i | \(0.794062\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.69653e9 | 0.410790 | ||||||||
\(560\) | 3.43327e8 | 0.0826132 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.06815e8 | −0.191733 | ||||||||
\(563\) | −1.73249e8 | −0.0409158 | −0.0204579 | − | 0.999791i | \(-0.506512\pi\) | ||||
−0.0204579 | + | 0.999791i | \(0.506512\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.12130e9 | 0.961312 | ||||||||
\(566\) | −2.03290e9 | −0.471257 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.56353e9 | −0.586974 | ||||||||
\(569\) | 7.28881e9 | 1.65869 | 0.829343 | − | 0.558740i | \(-0.188715\pi\) | ||||
0.829343 | + | 0.558740i | \(0.188715\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.29036e9 | 0.964423 | 0.482212 | − | 0.876055i | \(-0.339834\pi\) | ||||
0.482212 | + | 0.876055i | \(0.339834\pi\) | |||||||
\(572\) | 9.75228e8 | 0.217881 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.25219e9 | 0.276363 | ||||||||
\(575\) | 3.84804e9 | 0.844116 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.28378e8 | 0.136178 | 0.0680888 | − | 0.997679i | \(-0.478310\pi\) | ||||
0.0680888 | + | 0.997679i | \(0.478310\pi\) | |||||||
\(578\) | −3.20135e9 | −0.689582 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.72942e8 | 0.185775 | ||||||||
\(581\) | 1.34681e9 | 0.284898 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.29886e9 | 0.480478 | ||||||||
\(584\) | −3.01993e9 | −0.627411 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.34467e9 | −0.891899 | ||||||||
\(587\) | −8.96802e9 | −1.83005 | −0.915026 | − | 0.403395i | \(-0.867830\pi\) | ||||
−0.915026 | + | 0.403395i | \(0.867830\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.63737e8 | −0.0531824 | ||||||||
\(590\) | 2.93788e9 | 0.588913 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.32534e9 | −0.262543 | ||||||||
\(593\) | −7.57484e9 | −1.49170 | −0.745851 | − | 0.666112i | \(-0.767957\pi\) | ||||
−0.745851 | + | 0.666112i | \(0.767957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.67302e8 | −0.0520227 | ||||||||
\(596\) | −1.68248e8 | −0.0325527 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.04759e9 | −0.582776 | ||||||||
\(599\) | −6.05946e9 | −1.15197 | −0.575984 | − | 0.817461i | \(-0.695381\pi\) | ||||
−0.575984 | + | 0.817461i | \(0.695381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.55797e8 | −0.123228 | −0.0616139 | − | 0.998100i | \(-0.519625\pi\) | ||||
−0.0616139 | + | 0.998100i | \(0.519625\pi\) | |||||||
\(602\) | −1.36827e9 | −0.255613 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.53932e9 | −0.653568 | ||||||||
\(605\) | 1.70653e9 | 0.313307 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.85611e9 | 0.699825 | 0.349913 | − | 0.936782i | \(-0.386211\pi\) | ||||
0.349913 | + | 0.936782i | \(0.386211\pi\) | |||||||
\(608\) | 4.94141e7 | 0.00891638 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.96316e9 | −0.528567 | ||||||||
\(611\) | −1.93092e9 | −0.342469 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.89889e9 | −0.858986 | −0.429493 | − | 0.903070i | \(-0.641308\pi\) | ||||
−0.429493 | + | 0.903070i | \(0.641308\pi\) | |||||||
\(614\) | −5.83902e9 | −1.01801 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.86530e8 | −0.135576 | ||||||||
\(617\) | −6.65456e9 | −1.14057 | −0.570284 | − | 0.821448i | \(-0.693167\pi\) | ||||
−0.570284 | + | 0.821448i | \(0.693167\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.05531e10 | 1.78840 | 0.894199 | − | 0.447669i | \(-0.147746\pi\) | ||||
0.894199 | + | 0.447669i | \(0.147746\pi\) | |||||||
\(620\) | 1.84686e9 | 0.311217 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.11016e9 | 0.851468 | ||||||||
\(623\) | 3.43962e9 | 0.569904 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.63857e8 | 0.0759983 | ||||||||
\(626\) | −5.10208e9 | −0.831261 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.43175e9 | −0.230679 | ||||||||
\(629\) | 1.03186e9 | 0.165327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.37775e9 | 1.01057 | 0.505283 | − | 0.862954i | \(-0.331388\pi\) | ||||
0.505283 | + | 0.862954i | \(0.331388\pi\) | |||||||
\(632\) | 3.59873e9 | 0.567074 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.23502e9 | −0.815842 | ||||||||
\(635\) | 8.22788e8 | 0.127520 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.84945e9 | −0.436790 | ||||||||
\(638\) | −1.99983e9 | −0.304874 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.46030e8 | −0.0521776 | ||||||||
\(641\) | 6.68703e8 | 0.100284 | 0.0501418 | − | 0.998742i | \(-0.484033\pi\) | ||||
0.0501418 | + | 0.998742i | \(0.484033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.24632e9 | 0.481564 | 0.240782 | − | 0.970579i | \(-0.422596\pi\) | ||||
0.240782 | + | 0.970579i | \(0.422596\pi\) | |||||||
\(644\) | 2.45791e9 | 0.362631 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.84721e7 | −0.00561477 | ||||||||
\(647\) | 7.46321e9 | 1.08333 | 0.541665 | − | 0.840595i | \(-0.317794\pi\) | ||||
0.541665 | + | 0.840595i | \(0.317794\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.73041e9 | −0.966462 | ||||||||
\(650\) | −2.05188e9 | −0.293059 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.35108e9 | 0.473498 | ||||||||
\(653\) | −1.01630e10 | −1.42832 | −0.714160 | − | 0.699982i | \(-0.753191\pi\) | ||||
−0.714160 | + | 0.699982i | \(0.753191\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.68618e9 | 0.512544 | ||||||||
\(656\) | −1.26205e9 | −0.174547 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.55731e9 | 0.213100 | ||||||||
\(659\) | −2.83068e9 | −0.385294 | −0.192647 | − | 0.981268i | \(-0.561707\pi\) | ||||
−0.192647 | + | 0.981268i | \(0.561707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.96275e9 | 0.533693 | 0.266846 | − | 0.963739i | \(-0.414018\pi\) | ||||
0.266846 | + | 0.963739i | \(0.414018\pi\) | |||||||
\(662\) | 6.46151e9 | 0.865628 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.35741e9 | −0.179938 | ||||||||
\(665\) | 1.26401e8 | 0.0166676 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.24947e9 | 0.815461 | ||||||||
\(668\) | −3.50693e9 | −0.455207 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.94461e9 | −0.249787 | ||||||||
\(671\) | 6.78832e9 | 0.867428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.18615e10 | −1.49999 | −0.749995 | − | 0.661443i | \(-0.769944\pi\) | ||||
−0.749995 | + | 0.661443i | \(0.769944\pi\) | |||||||
\(674\) | −1.49824e9 | −0.188483 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.39085e9 | −0.297672 | ||||||||
\(677\) | 9.86836e9 | 1.22232 | 0.611159 | − | 0.791508i | \(-0.290703\pi\) | ||||
0.611159 | + | 0.791508i | \(0.290703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.21760e9 | −1.00740 | ||||||||
\(680\) | 2.69407e8 | 0.0328569 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.23099e9 | −0.510736 | ||||||||
\(683\) | 1.36287e10 | 1.63674 | 0.818372 | − | 0.574689i | \(-0.194877\pi\) | ||||
0.818372 | + | 0.574689i | \(0.194877\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.12241e9 | −0.252297 | ||||||||
\(686\) | 5.64499e9 | 0.667619 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.37904e9 | 0.161442 | ||||||||
\(689\) | 3.83068e9 | 0.446178 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.16270e9 | −0.249357 | −0.124679 | − | 0.992197i | \(-0.539790\pi\) | ||||
−0.124679 | + | 0.992197i | \(0.539790\pi\) | |||||||
\(692\) | 7.91329e9 | 0.907791 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.26045e9 | 0.256706 | ||||||||
\(695\) | −7.29139e9 | −0.823879 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.82588e8 | 0.109915 | ||||||||
\(698\) | −6.08490e9 | −0.677266 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.65486e9 | 0.182355 | ||||||||
\(701\) | 2.93914e9 | 0.322260 | 0.161130 | − | 0.986933i | \(-0.448486\pi\) | ||||
0.161130 | + | 0.986933i | \(0.448486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.87942e8 | −0.0529693 | ||||||||
\(704\) | 7.92723e8 | 0.0856283 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.75115e9 | −0.401188 | ||||||||
\(707\) | −1.37242e9 | −0.146056 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.30914e10 | −1.37951 | −0.689756 | − | 0.724041i | \(-0.742282\pi\) | ||||
−0.689756 | + | 0.724041i | \(0.742282\pi\) | |||||||
\(710\) | 6.60910e9 | 0.693007 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.46670e9 | −0.359945 | ||||||||
\(713\) | 1.32218e10 | 1.36609 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.51426e9 | −0.257240 | ||||||||
\(716\) | 6.31870e9 | 0.643328 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.23125e9 | 0.124140 | ||||||||
\(719\) | −3.03015e9 | −0.304027 | −0.152014 | − | 0.988378i | \(-0.548576\pi\) | ||||
−0.152014 | + | 0.988378i | \(0.548576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.05101e9 | −0.104432 | ||||||||
\(722\) | −7.13278e9 | −0.705308 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.88707e9 | 0.576520 | ||||||||
\(725\) | 4.20765e9 | 0.410069 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.06848e10 | −1.03132 | −0.515661 | − | 0.856793i | \(-0.672454\pi\) | ||||
−0.515661 | + | 0.856793i | \(0.672454\pi\) | |||||||
\(728\) | −1.31062e9 | −0.125898 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.78576e9 | 0.740749 | ||||||||
\(731\) | −1.07367e9 | −0.101663 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.67705e10 | −1.57283 | −0.786414 | − | 0.617699i | \(-0.788065\pi\) | ||||
−0.786414 | + | 0.617699i | \(0.788065\pi\) | |||||||
\(734\) | −5.99622e9 | −0.559682 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.47726e9 | −0.229034 | ||||||||
\(737\) | 4.45492e9 | 0.409924 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.68052e10 | 1.53175 | 0.765877 | − | 0.642987i | \(-0.222305\pi\) | ||||
0.765877 | + | 0.642987i | \(0.222305\pi\) | |||||||
\(740\) | 3.41689e9 | 0.309970 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.08948e9 | −0.277633 | ||||||||
\(743\) | 2.07834e10 | 1.85890 | 0.929448 | − | 0.368952i | \(-0.120283\pi\) | ||||
0.929448 | + | 0.368952i | \(0.120283\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.33764e8 | 0.0384332 | ||||||||
\(746\) | −4.33382e9 | −0.382195 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.17186e8 | −0.0539213 | ||||||||
\(749\) | 4.65049e9 | 0.404401 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00601e10 | 0.866689 | 0.433344 | − | 0.901228i | \(-0.357333\pi\) | ||||
0.433344 | + | 0.901228i | \(0.357333\pi\) | |||||||
\(752\) | −1.56957e9 | −0.134592 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.33239e9 | −0.283111 | ||||||||
\(755\) | 9.12481e9 | 0.771631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.59893e9 | 0.552889 | 0.276445 | − | 0.961030i | \(-0.410844\pi\) | ||||
0.276445 | + | 0.961030i | \(0.410844\pi\) | |||||||
\(758\) | 1.06379e10 | 0.887185 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.27396e8 | −0.0105271 | ||||||||
\(761\) | −6.07925e9 | −0.500039 | −0.250019 | − | 0.968241i | \(-0.580437\pi\) | ||||
−0.250019 | + | 0.968241i | \(0.580437\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.41272e9 | −0.359642 | ||||||||
\(764\) | 8.44663e9 | 0.685262 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.75959e9 | 0.463011 | ||||||||
\(767\) | −1.12151e10 | −0.897471 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.85049e9 | 0.384630 | 0.192315 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192315 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(770\) | 2.02777e9 | 0.160067 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.46607e9 | 0.740473 | ||||||||
\(773\) | −2.33466e10 | −1.81800 | −0.909002 | − | 0.416792i | \(-0.863154\pi\) | ||||
−0.909002 | + | 0.416792i | \(0.863154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.90200e9 | 0.686961 | ||||||||
\(776\) | 8.28231e9 | 0.636261 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.85654e10 | 1.41343 | ||||||||
\(779\) | −4.64642e8 | −0.0352158 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.51408e10 | −1.13729 | ||||||||
\(782\) | 1.92871e9 | 0.144226 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.31620e9 | −0.171660 | ||||||||
\(785\) | 3.69123e9 | 0.272350 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.36056e9 | 0.684526 | 0.342263 | − | 0.939604i | \(-0.388807\pi\) | ||||
0.342263 | + | 0.939604i | \(0.388807\pi\) | |||||||
\(788\) | −1.72519e9 | −0.125602 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.27797e9 | −0.669512 | ||||||||
\(791\) | 1.26886e10 | 0.911582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.13116e10 | 0.805506 | ||||||||
\(794\) | 9.46981e9 | 0.671382 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.69315e9 | 0.610916 | ||||||||
\(797\) | 2.62373e10 | 1.83576 | 0.917878 | − | 0.396864i | \(-0.129901\pi\) | ||||
0.917878 | + | 0.396864i | \(0.129901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.22201e9 | 0.0847543 | ||||||||
\(800\) | −1.66789e9 | −0.115174 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.01411e10 | 0.694185 | ||||||||
\(803\) | −1.78365e10 | −1.21564 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.33679e9 | −0.428138 | ||||||||
\(806\) | −7.05025e9 | −0.474277 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.38323e9 | 0.0922473 | ||||||||
\(809\) | −1.59304e10 | −1.05780 | −0.528902 | − | 0.848683i | \(-0.677396\pi\) | ||||
−0.528902 | + | 0.848683i | \(0.677396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.69281e10 | −1.11438 | −0.557191 | − | 0.830384i | \(-0.688121\pi\) | ||||
−0.557191 | + | 0.830384i | \(0.688121\pi\) | |||||||
\(812\) | 2.68760e9 | 0.176165 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.82778e9 | −0.508690 | ||||||||
\(815\) | −8.63949e9 | −0.559032 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.07713e8 | 0.0325718 | ||||||||
\(818\) | −8.15591e9 | −0.520997 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.25373e9 | 0.206078 | ||||||||
\(821\) | 8.73592e9 | 0.550944 | 0.275472 | − | 0.961309i | \(-0.411166\pi\) | ||||
0.275472 | + | 0.961309i | \(0.411166\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.44369e10 | 0.902767 | 0.451384 | − | 0.892330i | \(-0.350931\pi\) | ||||
0.451384 | + | 0.892330i | \(0.350931\pi\) | |||||||
\(824\) | 1.05928e9 | 0.0659580 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.04510e9 | 0.558449 | ||||||||
\(827\) | 5.56666e9 | 0.342236 | 0.171118 | − | 0.985251i | \(-0.445262\pi\) | ||||
0.171118 | + | 0.985251i | \(0.445262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.50766e10 | −0.919101 | −0.459550 | − | 0.888152i | \(-0.651989\pi\) | ||||
−0.459550 | + | 0.888152i | \(0.651989\pi\) | |||||||
\(830\) | 3.49958e9 | 0.212443 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.32094e9 | 0.0795157 | ||||||||
\(833\) | 1.80331e9 | 0.108097 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.04130e9 | 0.537438 | ||||||||
\(836\) | 2.91852e8 | 0.0172759 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.33029e9 | 0.488997 | ||||||||
\(839\) | 1.20004e10 | 0.701502 | 0.350751 | − | 0.936469i | \(-0.385926\pi\) | ||||
0.350751 | + | 0.936469i | \(0.385926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.04164e10 | −0.603852 | ||||||||
\(842\) | −1.56676e10 | −0.904503 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.40378e8 | −0.00803710 | ||||||||
\(845\) | 6.16390e9 | 0.351445 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.25404e9 | 0.297099 | ||||||||
\(848\) | 3.11380e9 | 0.175350 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.29856e9 | 0.0725264 | ||||||||
\(851\) | 2.44618e10 | 1.36061 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.01661e8 | −0.0497418 | −0.0248709 | − | 0.999691i | \(-0.507917\pi\) | ||||
−0.0248709 | + | 0.999691i | \(0.507917\pi\) | |||||||
\(854\) | −9.12293e9 | −0.501224 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.68710e9 | −0.255415 | ||||||||
\(857\) | −2.81436e10 | −1.52738 | −0.763690 | − | 0.645583i | \(-0.776614\pi\) | ||||
−0.763690 | + | 0.645583i | \(0.776614\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.51543e9 | −0.512215 | −0.256107 | − | 0.966648i | \(-0.582440\pi\) | ||||
−0.256107 | + | 0.966648i | \(0.582440\pi\) | |||||||
\(860\) | −3.55534e9 | −0.190606 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.27405e10 | 1.20927 | ||||||||
\(863\) | −1.24682e10 | −0.660336 | −0.330168 | − | 0.943922i | \(-0.607105\pi\) | ||||
−0.330168 | + | 0.943922i | \(0.607105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.04014e10 | −1.07178 | ||||||||
\(866\) | −6.73033e8 | −0.0352147 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.68609e9 | 0.295117 | ||||||||
\(869\) | 2.12550e10 | 1.09873 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.42339e9 | 0.380662 | ||||||||
\(872\) | 4.44746e9 | 0.227146 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.12038e8 | −0.0462086 | ||||||||
\(875\) | −1.08149e10 | −0.545749 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.71074e9 | −0.335948 | −0.167974 | − | 0.985791i | \(-0.553722\pi\) | ||||
−0.167974 | + | 0.985791i | \(0.553722\pi\) | |||||||
\(878\) | −1.49637e10 | −0.746120 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.04374e9 | −0.101097 | ||||||||
\(881\) | −3.59350e10 | −1.77053 | −0.885263 | − | 0.465091i | \(-0.846022\pi\) | ||||
−0.885263 | + | 0.465091i | \(0.846022\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.40241e9 | −0.0685509 | −0.0342754 | − | 0.999412i | \(-0.510912\pi\) | ||||
−0.0342754 | + | 0.999412i | \(0.510912\pi\) | |||||||
\(884\) | −1.02844e9 | −0.0500721 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.10661e9 | −0.391581 | ||||||||
\(887\) | −8.19690e8 | −0.0394382 | −0.0197191 | − | 0.999806i | \(-0.506277\pi\) | ||||
−0.0197191 | + | 0.999806i | \(0.506277\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.53319e9 | 0.120924 | ||||||||
\(890\) | 8.93759e9 | 0.424967 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.27643e9 | 0.0602174 | ||||||||
\(893\) | −5.77860e8 | −0.0271545 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.62904e10 | −0.759541 | ||||||||
\(896\) | −1.06535e9 | −0.0494784 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.32604e9 | −0.0611070 | ||||||||
\(899\) | 1.44574e10 | 0.663640 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.42430e9 | −0.110420 | ||||||||
\(902\) | −7.45399e9 | −0.338194 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.27885e10 | −0.575745 | ||||||||
\(905\) | −1.51776e10 | −0.680665 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.84506e9 | 0.126609 | 0.0633047 | − | 0.997994i | \(-0.479836\pi\) | ||||
0.0633047 | + | 0.997994i | \(0.479836\pi\) | |||||||
\(908\) | −8.06304e9 | −0.357436 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.37895e9 | 0.148640 | ||||||||
\(911\) | −4.32996e10 | −1.89745 | −0.948723 | − | 0.316108i | \(-0.897624\pi\) | ||||
−0.948723 | + | 0.316108i | \(0.897624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.01722e9 | −0.348639 | ||||||||
\(914\) | −1.10464e10 | −0.478529 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.50429e9 | 0.0646693 | ||||||||
\(917\) | 1.13490e10 | 0.486030 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.26317e10 | −1.38687 | −0.693435 | − | 0.720520i | \(-0.743903\pi\) | ||||
−0.693435 | + | 0.720520i | \(0.743903\pi\) | |||||||
\(920\) | 6.38669e9 | 0.270407 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.22793e10 | 0.936146 | ||||||||
\(923\) | −2.52297e10 | −1.05610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.64697e10 | 0.684209 | ||||||||
\(926\) | 2.23135e10 | 0.923483 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.70877e9 | −0.111264 | ||||||||
\(929\) | 4.69546e10 | 1.92142 | 0.960712 | − | 0.277546i | \(-0.0895211\pi\) | ||||
0.960712 | + | 0.277546i | \(0.0895211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.52742e8 | −0.0346333 | ||||||||
\(932\) | −8.17644e9 | −0.330833 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.17806e10 | 1.27629 | ||||||||
\(935\) | 1.59118e9 | 0.0636619 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.80951e10 | −1.11569 | −0.557843 | − | 0.829947i | \(-0.688371\pi\) | ||||
−0.557843 | + | 0.829947i | \(0.688371\pi\) | |||||||
\(938\) | −5.98704e9 | −0.236866 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.04655e9 | 0.158905 | ||||||||
\(941\) | −2.72197e10 | −1.06493 | −0.532464 | − | 0.846453i | \(-0.678734\pi\) | ||||
−0.532464 | + | 0.846453i | \(0.678734\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.32937e10 | 0.904582 | ||||||||
\(944\) | −9.11632e9 | −0.352710 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.14496e9 | 0.312802 | ||||||||
\(947\) | −2.30441e10 | −0.881729 | −0.440864 | − | 0.897574i | \(-0.645328\pi\) | ||||
−0.440864 | + | 0.897574i | \(0.645328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.97215e10 | −1.12886 | ||||||||
\(950\) | −6.14058e8 | −0.0232368 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.29446e8 | 0.0311572 | ||||||||
\(953\) | 2.22131e10 | 0.831352 | 0.415676 | − | 0.909513i | \(-0.363545\pi\) | ||||
0.415676 | + | 0.909513i | \(0.363545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.17765e10 | −0.809051 | ||||||||
\(956\) | −5.98322e9 | −0.221479 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.87574e10 | −0.689275 | ||||||||
\(959\) | −6.53444e9 | −0.239245 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.07460e9 | 0.111752 | ||||||||
\(962\) | −1.30437e10 | −0.472377 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.62593e9 | −0.310125 | ||||||||
\(965\) | −2.44047e10 | −0.874235 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.70771e10 | 0.962962 | 0.481481 | − | 0.876457i | \(-0.340099\pi\) | ||||
0.481481 | + | 0.876457i | \(0.340099\pi\) | |||||||
\(968\) | −5.29541e9 | −0.187644 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.13528e10 | −0.751198 | ||||||||
\(971\) | −2.57664e10 | −0.903204 | −0.451602 | − | 0.892220i | \(-0.649147\pi\) | ||||
−0.451602 | + | 0.892220i | \(0.649147\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.24486e10 | −0.781259 | ||||||||
\(974\) | 2.46705e10 | 0.855502 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.19476e9 | 0.316567 | ||||||||
\(977\) | −9.51873e9 | −0.326549 | −0.163274 | − | 0.986581i | \(-0.552206\pi\) | ||||
−0.163274 | + | 0.986581i | \(0.552206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.04752e10 | −0.697411 | ||||||||
\(980\) | 5.97146e9 | 0.202670 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.97481e10 | −1.00246 | ||||||||
\(983\) | −5.51917e9 | −0.185326 | −0.0926631 | − | 0.995698i | \(-0.529538\pi\) | ||||
−0.0926631 | + | 0.995698i | \(0.529538\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.44776e9 | 0.148291 | ||||||||
\(986\) | 2.10895e9 | 0.0700643 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.86324e8 | 0.0160427 | ||||||||
\(989\) | −2.54530e10 | −0.836666 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.65440e10 | 0.539987 | 0.269994 | − | 0.962862i | \(-0.412978\pi\) | ||||
0.269994 | + | 0.962862i | \(0.412978\pi\) | |||||||
\(992\) | −5.73086e9 | −0.186393 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.03480e10 | 0.657158 | ||||||||
\(995\) | −2.24120e10 | −0.721274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.10055e10 | 1.31042 | 0.655208 | − | 0.755448i | \(-0.272581\pi\) | ||||
0.655208 | + | 0.755448i | \(0.272581\pi\) | |||||||
\(998\) | 3.49141e9 | 0.111184 | ||||||||
\(999\) | 0 | 0 |
(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 | 162.8.a.b.1.1 | yes | 1 | |
3.2 | odd | 2 | 162.8.a.a.1.1 | ✓ | 1 | ||
9.2 | odd | 6 | 162.8.c.h.109.1 | 2 | |||
9.4 | even | 3 | 162.8.c.e.55.1 | 2 | |||
9.5 | odd | 6 | 162.8.c.h.55.1 | 2 | |||
9.7 | even | 3 | 162.8.c.e.109.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.8.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
162.8.a.b.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
162.8.c.e.55.1 | 2 | 9.4 | even | 3 | |||
162.8.c.e.109.1 | 2 | 9.7 | even | 3 | |||
162.8.c.h.55.1 | 2 | 9.5 | odd | 6 | |||
162.8.c.h.109.1 | 2 | 9.2 | odd | 6 |