Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,66,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 66, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 66);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 66 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(26.7572356472\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 10\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{12}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.39707e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.49786e9 | −1.23442 | −0.617209 | − | 0.786799i | \(-0.711737\pi\) | ||||
−0.617209 | + | 0.786799i | \(0.711737\pi\) | |||||||
\(3\) | −4.87294e15 | −1.51827 | −0.759137 | − | 0.650931i | \(-0.774379\pi\) | ||||
−0.759137 | + | 0.650931i | \(0.774379\pi\) | |||||||
\(4\) | 1.93244e19 | 0.523788 | ||||||||
\(5\) | −6.28165e22 | −1.20656 | −0.603279 | − | 0.797530i | \(-0.706140\pi\) | ||||
−0.603279 | + | 0.797530i | \(0.706140\pi\) | |||||||
\(6\) | 3.65366e25 | 1.87418 | ||||||||
\(7\) | −4.41462e27 | −1.51080 | −0.755399 | − | 0.655265i | \(-0.772557\pi\) | ||||
−0.755399 | + | 0.655265i | \(0.772557\pi\) | |||||||
\(8\) | 1.31731e29 | 0.587845 | ||||||||
\(9\) | 1.34445e31 | 1.30516 | ||||||||
\(10\) | 4.70989e32 | 1.48940 | ||||||||
\(11\) | 2.47205e33 | 0.353017 | 0.176508 | − | 0.984299i | \(-0.443520\pi\) | ||||
0.176508 | + | 0.984299i | \(0.443520\pi\) | |||||||
\(12\) | −9.41665e34 | −0.795254 | ||||||||
\(13\) | 8.18765e35 | 0.512862 | 0.256431 | − | 0.966563i | \(-0.417453\pi\) | ||||
0.256431 | + | 0.966563i | \(0.417453\pi\) | |||||||
\(14\) | 3.31002e37 | 1.86496 | ||||||||
\(15\) | 3.06101e38 | 1.83189 | ||||||||
\(16\) | −1.70064e39 | −1.24943 | ||||||||
\(17\) | 1.52850e40 | 1.56558 | 0.782789 | − | 0.622287i | \(-0.213796\pi\) | ||||
0.782789 | + | 0.622287i | \(0.213796\pi\) | |||||||
\(18\) | −1.00805e41 | −1.61111 | ||||||||
\(19\) | −1.62754e41 | −0.448785 | −0.224393 | − | 0.974499i | \(-0.572040\pi\) | ||||
−0.224393 | + | 0.974499i | \(0.572040\pi\) | |||||||
\(20\) | −1.21389e42 | −0.631981 | ||||||||
\(21\) | 2.15121e43 | 2.29381 | ||||||||
\(22\) | −1.85351e43 | −0.435770 | ||||||||
\(23\) | −1.77529e44 | −0.984269 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(24\) | −6.41916e44 | −0.892509 | ||||||||
\(25\) | 1.23540e45 | 0.455783 | ||||||||
\(26\) | −6.13898e45 | −0.633086 | ||||||||
\(27\) | −1.53177e46 | −0.463309 | ||||||||
\(28\) | −8.53097e46 | −0.791338 | ||||||||
\(29\) | −4.19469e47 | −1.24384 | −0.621921 | − | 0.783080i | \(-0.713647\pi\) | ||||
−0.621921 | + | 0.783080i | \(0.713647\pi\) | |||||||
\(30\) | −2.29510e48 | −2.26131 | ||||||||
\(31\) | −6.78523e47 | −0.230308 | −0.115154 | − | 0.993348i | \(-0.536736\pi\) | ||||
−0.115154 | + | 0.993348i | \(0.536736\pi\) | |||||||
\(32\) | 7.89116e48 | 0.954480 | ||||||||
\(33\) | −1.20462e49 | −0.535976 | ||||||||
\(34\) | −1.14605e50 | −1.93258 | ||||||||
\(35\) | 2.77311e50 | 1.82287 | ||||||||
\(36\) | 2.59806e50 | 0.683625 | ||||||||
\(37\) | 1.36074e51 | 1.46967 | 0.734833 | − | 0.678248i | \(-0.237260\pi\) | ||||
0.734833 | + | 0.678248i | \(0.237260\pi\) | |||||||
\(38\) | 1.22030e51 | 0.553988 | ||||||||
\(39\) | −3.98979e51 | −0.778665 | ||||||||
\(40\) | −8.27486e51 | −0.709269 | ||||||||
\(41\) | 3.18837e52 | 1.22488 | 0.612440 | − | 0.790517i | \(-0.290188\pi\) | ||||
0.612440 | + | 0.790517i | \(0.290188\pi\) | |||||||
\(42\) | −1.61295e53 | −2.83152 | ||||||||
\(43\) | 1.25486e53 | 1.02535 | 0.512674 | − | 0.858583i | \(-0.328655\pi\) | ||||
0.512674 | + | 0.858583i | \(0.328655\pi\) | |||||||
\(44\) | 4.77709e52 | 0.184906 | ||||||||
\(45\) | −8.44534e53 | −1.57475 | ||||||||
\(46\) | 1.33108e54 | 1.21500 | ||||||||
\(47\) | −9.94260e53 | −0.451149 | −0.225574 | − | 0.974226i | \(-0.572426\pi\) | ||||
−0.225574 | + | 0.974226i | \(0.572426\pi\) | |||||||
\(48\) | 8.28712e54 | 1.89698 | ||||||||
\(49\) | 1.09505e55 | 1.28251 | ||||||||
\(50\) | −9.26288e54 | −0.562627 | ||||||||
\(51\) | −7.44827e55 | −2.37698 | ||||||||
\(52\) | 1.58221e55 | 0.268631 | ||||||||
\(53\) | −1.30085e55 | −0.118922 | −0.0594608 | − | 0.998231i | \(-0.518938\pi\) | ||||
−0.0594608 | + | 0.998231i | \(0.518938\pi\) | |||||||
\(54\) | 1.14850e56 | 0.571917 | ||||||||
\(55\) | −1.55286e56 | −0.425935 | ||||||||
\(56\) | −5.81540e56 | −0.888115 | ||||||||
\(57\) | 7.93088e56 | 0.681379 | ||||||||
\(58\) | 3.14512e57 | 1.53542 | ||||||||
\(59\) | −1.98182e57 | −0.555103 | −0.277552 | − | 0.960711i | \(-0.589523\pi\) | ||||
−0.277552 | + | 0.960711i | \(0.589523\pi\) | |||||||
\(60\) | 5.91521e57 | 0.959520 | ||||||||
\(61\) | −5.55785e57 | −0.526850 | −0.263425 | − | 0.964680i | \(-0.584852\pi\) | ||||
−0.263425 | + | 0.964680i | \(0.584852\pi\) | |||||||
\(62\) | 5.08747e57 | 0.284297 | ||||||||
\(63\) | −5.93522e58 | −1.97183 | ||||||||
\(64\) | 3.57579e57 | 0.0712071 | ||||||||
\(65\) | −5.14319e58 | −0.618798 | ||||||||
\(66\) | 9.03203e58 | 0.661619 | ||||||||
\(67\) | 1.23347e59 | 0.554239 | 0.277119 | − | 0.960835i | \(-0.410620\pi\) | ||||
0.277119 | + | 0.960835i | \(0.410620\pi\) | |||||||
\(68\) | 2.95372e59 | 0.820031 | ||||||||
\(69\) | 8.65086e59 | 1.49439 | ||||||||
\(70\) | −2.07923e60 | −2.25018 | ||||||||
\(71\) | −5.36951e59 | −0.366470 | −0.183235 | − | 0.983069i | \(-0.558657\pi\) | ||||
−0.183235 | + | 0.983069i | \(0.558657\pi\) | |||||||
\(72\) | 1.77105e60 | 0.767228 | ||||||||
\(73\) | 5.21560e60 | 1.44315 | 0.721574 | − | 0.692337i | \(-0.243419\pi\) | ||||
0.721574 | + | 0.692337i | \(0.243419\pi\) | |||||||
\(74\) | −1.02026e61 | −1.81418 | ||||||||
\(75\) | −6.02004e60 | −0.692004 | ||||||||
\(76\) | −3.14511e60 | −0.235068 | ||||||||
\(77\) | −1.09132e61 | −0.533337 | ||||||||
\(78\) | 2.99149e61 | 0.961198 | ||||||||
\(79\) | 5.19565e61 | 1.10347 | 0.551734 | − | 0.834020i | \(-0.313967\pi\) | ||||
0.551734 | + | 0.834020i | \(0.313967\pi\) | |||||||
\(80\) | 1.06828e62 | 1.50752 | ||||||||
\(81\) | −6.38500e61 | −0.601725 | ||||||||
\(82\) | −2.39059e62 | −1.51201 | ||||||||
\(83\) | 8.74678e60 | 0.0373087 | 0.0186544 | − | 0.999826i | \(-0.494062\pi\) | ||||
0.0186544 | + | 0.999826i | \(0.494062\pi\) | |||||||
\(84\) | 4.15709e62 | 1.20147 | ||||||||
\(85\) | −9.60148e62 | −1.88896 | ||||||||
\(86\) | −9.40879e62 | −1.26571 | ||||||||
\(87\) | 2.04405e63 | 1.88849 | ||||||||
\(88\) | 3.25645e62 | 0.207519 | ||||||||
\(89\) | −1.81776e63 | −0.802344 | −0.401172 | − | 0.916003i | \(-0.631397\pi\) | ||||
−0.401172 | + | 0.916003i | \(0.631397\pi\) | |||||||
\(90\) | 6.33220e63 | 1.94390 | ||||||||
\(91\) | −3.61453e63 | −0.774831 | ||||||||
\(92\) | −3.43063e63 | −0.515548 | ||||||||
\(93\) | 3.30640e63 | 0.349671 | ||||||||
\(94\) | 7.45482e63 | 0.556906 | ||||||||
\(95\) | 1.02236e64 | 0.541485 | ||||||||
\(96\) | −3.84531e64 | −1.44916 | ||||||||
\(97\) | −1.86066e63 | −0.0500709 | −0.0250355 | − | 0.999687i | \(-0.507970\pi\) | ||||
−0.0250355 | + | 0.999687i | \(0.507970\pi\) | |||||||
\(98\) | −8.21053e64 | −1.58316 | ||||||||
\(99\) | 3.32354e64 | 0.460742 | ||||||||
\(100\) | 2.38734e64 | 0.238734 | ||||||||
\(101\) | 2.25012e64 | 0.162840 | 0.0814200 | − | 0.996680i | \(-0.474054\pi\) | ||||
0.0814200 | + | 0.996680i | \(0.474054\pi\) | |||||||
\(102\) | 5.58461e65 | 2.93418 | ||||||||
\(103\) | −1.05413e65 | −0.403352 | −0.201676 | − | 0.979452i | \(-0.564639\pi\) | ||||
−0.201676 | + | 0.979452i | \(0.564639\pi\) | |||||||
\(104\) | 1.07857e65 | 0.301483 | ||||||||
\(105\) | −1.35132e66 | −2.76761 | ||||||||
\(106\) | 9.75357e64 | 0.146799 | ||||||||
\(107\) | 6.77694e65 | 0.751729 | 0.375864 | − | 0.926675i | \(-0.377346\pi\) | ||||
0.375864 | + | 0.926675i | \(0.377346\pi\) | |||||||
\(108\) | −2.96005e65 | −0.242676 | ||||||||
\(109\) | −2.43834e65 | −0.148161 | −0.0740805 | − | 0.997252i | \(-0.523602\pi\) | ||||
−0.0740805 | + | 0.997252i | \(0.523602\pi\) | |||||||
\(110\) | 1.16431e66 | 0.525782 | ||||||||
\(111\) | −6.63080e66 | −2.23136 | ||||||||
\(112\) | 7.50768e66 | 1.88764 | ||||||||
\(113\) | 3.56635e66 | 0.671699 | 0.335850 | − | 0.941916i | \(-0.390977\pi\) | ||||
0.335850 | + | 0.941916i | \(0.390977\pi\) | |||||||
\(114\) | −5.94646e66 | −0.841106 | ||||||||
\(115\) | 1.11517e67 | 1.18758 | ||||||||
\(116\) | −8.10597e66 | −0.651509 | ||||||||
\(117\) | 1.10079e67 | 0.669364 | ||||||||
\(118\) | 1.48594e67 | 0.685230 | ||||||||
\(119\) | −6.74773e67 | −2.36527 | ||||||||
\(120\) | 4.03229e67 | 1.07686 | ||||||||
\(121\) | −4.29260e67 | −0.875379 | ||||||||
\(122\) | 4.16719e67 | 0.650353 | ||||||||
\(123\) | −1.55367e68 | −1.85970 | ||||||||
\(124\) | −1.31120e67 | −0.120633 | ||||||||
\(125\) | 9.26607e67 | 0.656629 | ||||||||
\(126\) | 4.45014e68 | 2.43406 | ||||||||
\(127\) | 3.29671e68 | 1.39463 | 0.697317 | − | 0.716763i | \(-0.254377\pi\) | ||||
0.697317 | + | 0.716763i | \(0.254377\pi\) | |||||||
\(128\) | −3.17943e68 | −1.04238 | ||||||||
\(129\) | −6.11487e68 | −1.55676 | ||||||||
\(130\) | 3.85629e68 | 0.763855 | ||||||||
\(131\) | −8.62701e68 | −1.33212 | −0.666060 | − | 0.745898i | \(-0.732021\pi\) | ||||
−0.666060 | + | 0.745898i | \(0.732021\pi\) | |||||||
\(132\) | −2.32784e68 | −0.280738 | ||||||||
\(133\) | 7.18494e68 | 0.678024 | ||||||||
\(134\) | −9.24837e68 | −0.684163 | ||||||||
\(135\) | 9.62203e68 | 0.559010 | ||||||||
\(136\) | 2.01350e69 | 0.920316 | ||||||||
\(137\) | −8.40720e68 | −0.302854 | −0.151427 | − | 0.988468i | \(-0.548387\pi\) | ||||
−0.151427 | + | 0.988468i | \(0.548387\pi\) | |||||||
\(138\) | −6.48629e69 | −1.84470 | ||||||||
\(139\) | 3.55176e69 | 0.798845 | 0.399422 | − | 0.916767i | \(-0.369211\pi\) | ||||
0.399422 | + | 0.916767i | \(0.369211\pi\) | |||||||
\(140\) | 5.35885e69 | 0.954796 | ||||||||
\(141\) | 4.84497e69 | 0.684967 | ||||||||
\(142\) | 4.02598e69 | 0.452377 | ||||||||
\(143\) | 2.02403e69 | 0.181049 | ||||||||
\(144\) | −2.28642e70 | −1.63071 | ||||||||
\(145\) | 2.63496e70 | 1.50077 | ||||||||
\(146\) | −3.91058e70 | −1.78145 | ||||||||
\(147\) | −5.33611e70 | −1.94720 | ||||||||
\(148\) | 2.62954e70 | 0.769794 | ||||||||
\(149\) | 5.65978e70 | 1.33121 | 0.665604 | − | 0.746305i | \(-0.268174\pi\) | ||||
0.665604 | + | 0.746305i | \(0.268174\pi\) | |||||||
\(150\) | 4.51374e70 | 0.854222 | ||||||||
\(151\) | −1.02555e71 | −1.56390 | −0.781948 | − | 0.623343i | \(-0.785774\pi\) | ||||
−0.781948 | + | 0.623343i | \(0.785774\pi\) | |||||||
\(152\) | −2.14396e70 | −0.263816 | ||||||||
\(153\) | 2.05498e71 | 2.04332 | ||||||||
\(154\) | 8.18253e70 | 0.658361 | ||||||||
\(155\) | 4.26224e70 | 0.277880 | ||||||||
\(156\) | −7.71002e70 | −0.407855 | ||||||||
\(157\) | −2.01202e71 | −0.864755 | −0.432377 | − | 0.901693i | \(-0.642325\pi\) | ||||
−0.432377 | + | 0.901693i | \(0.642325\pi\) | |||||||
\(158\) | −3.89562e71 | −1.36214 | ||||||||
\(159\) | 6.33895e70 | 0.180555 | ||||||||
\(160\) | −4.95695e71 | −1.15164 | ||||||||
\(161\) | 7.83721e71 | 1.48703 | ||||||||
\(162\) | 4.78739e71 | 0.742780 | ||||||||
\(163\) | −8.87967e71 | −1.12798 | −0.563988 | − | 0.825783i | \(-0.690734\pi\) | ||||
−0.563988 | + | 0.825783i | \(0.690734\pi\) | |||||||
\(164\) | 6.16133e71 | 0.641578 | ||||||||
\(165\) | 7.56697e71 | 0.646686 | ||||||||
\(166\) | −6.55821e70 | −0.0460546 | ||||||||
\(167\) | −2.94357e72 | −1.70055 | −0.850276 | − | 0.526338i | \(-0.823565\pi\) | ||||
−0.850276 | + | 0.526338i | \(0.823565\pi\) | |||||||
\(168\) | 2.83381e72 | 1.34840 | ||||||||
\(169\) | −1.87832e72 | −0.736973 | ||||||||
\(170\) | 7.19905e72 | 2.33177 | ||||||||
\(171\) | −2.18814e72 | −0.585734 | ||||||||
\(172\) | 2.42494e72 | 0.537066 | ||||||||
\(173\) | −2.44850e72 | −0.449160 | −0.224580 | − | 0.974456i | \(-0.572101\pi\) | ||||
−0.224580 | + | 0.974456i | \(0.572101\pi\) | |||||||
\(174\) | −1.53260e73 | −2.33119 | ||||||||
\(175\) | −5.45383e72 | −0.688597 | ||||||||
\(176\) | −4.20407e72 | −0.441071 | ||||||||
\(177\) | 9.65728e72 | 0.842799 | ||||||||
\(178\) | 1.36293e73 | 0.990428 | ||||||||
\(179\) | 1.53155e73 | 0.927701 | 0.463850 | − | 0.885913i | \(-0.346467\pi\) | ||||
0.463850 | + | 0.885913i | \(0.346467\pi\) | |||||||
\(180\) | −1.63201e73 | −0.824833 | ||||||||
\(181\) | 1.32295e73 | 0.558459 | 0.279229 | − | 0.960224i | \(-0.409921\pi\) | ||||
0.279229 | + | 0.960224i | \(0.409921\pi\) | |||||||
\(182\) | 2.71013e73 | 0.956465 | ||||||||
\(183\) | 2.70830e73 | 0.799902 | ||||||||
\(184\) | −2.33860e73 | −0.578597 | ||||||||
\(185\) | −8.54768e73 | −1.77324 | ||||||||
\(186\) | −2.47909e73 | −0.431640 | ||||||||
\(187\) | 3.77852e73 | 0.552675 | ||||||||
\(188\) | −1.92135e73 | −0.236306 | ||||||||
\(189\) | 6.76217e73 | 0.699967 | ||||||||
\(190\) | −7.66551e73 | −0.668419 | ||||||||
\(191\) | −1.32871e74 | −0.976889 | −0.488444 | − | 0.872595i | \(-0.662435\pi\) | ||||
−0.488444 | + | 0.872595i | \(0.662435\pi\) | |||||||
\(192\) | −1.74246e73 | −0.108112 | ||||||||
\(193\) | 2.53755e74 | 1.32985 | 0.664925 | − | 0.746910i | \(-0.268464\pi\) | ||||
0.664925 | + | 0.746910i | \(0.268464\pi\) | |||||||
\(194\) | 1.39510e73 | 0.0618085 | ||||||||
\(195\) | 2.50625e74 | 0.939505 | ||||||||
\(196\) | 2.11612e74 | 0.671765 | ||||||||
\(197\) | −5.80730e74 | −1.56251 | −0.781253 | − | 0.624214i | \(-0.785419\pi\) | ||||
−0.781253 | + | 0.624214i | \(0.785419\pi\) | |||||||
\(198\) | −2.49195e74 | −0.568748 | ||||||||
\(199\) | 6.30427e74 | 1.22155 | 0.610773 | − | 0.791806i | \(-0.290859\pi\) | ||||
0.610773 | + | 0.791806i | \(0.290859\pi\) | |||||||
\(200\) | 1.62741e74 | 0.267930 | ||||||||
\(201\) | −6.01062e74 | −0.841486 | ||||||||
\(202\) | −1.68711e74 | −0.201013 | ||||||||
\(203\) | 1.85179e75 | 1.87919 | ||||||||
\(204\) | −1.43933e75 | −1.24503 | ||||||||
\(205\) | −2.00282e75 | −1.47789 | ||||||||
\(206\) | 7.90371e74 | 0.497905 | ||||||||
\(207\) | −2.38678e75 | −1.28462 | ||||||||
\(208\) | −1.39243e75 | −0.640787 | ||||||||
\(209\) | −4.02335e74 | −0.158429 | ||||||||
\(210\) | 1.01320e76 | 3.41639 | ||||||||
\(211\) | 3.20088e75 | 0.924890 | 0.462445 | − | 0.886648i | \(-0.346972\pi\) | ||||
0.462445 | + | 0.886648i | \(0.346972\pi\) | |||||||
\(212\) | −2.51381e74 | −0.0622897 | ||||||||
\(213\) | 2.61653e75 | 0.556402 | ||||||||
\(214\) | −5.08126e75 | −0.927948 | ||||||||
\(215\) | −7.88261e75 | −1.23714 | ||||||||
\(216\) | −2.01781e75 | −0.272354 | ||||||||
\(217\) | 2.99542e75 | 0.347949 | ||||||||
\(218\) | 1.82824e75 | 0.182893 | ||||||||
\(219\) | −2.54153e76 | −2.19110 | ||||||||
\(220\) | −3.00080e75 | −0.223100 | ||||||||
\(221\) | 1.25148e76 | 0.802925 | ||||||||
\(222\) | 4.97168e76 | 2.75443 | ||||||||
\(223\) | −1.64082e76 | −0.785514 | −0.392757 | − | 0.919642i | \(-0.628479\pi\) | ||||
−0.392757 | + | 0.919642i | \(0.628479\pi\) | |||||||
\(224\) | −3.48364e76 | −1.44203 | ||||||||
\(225\) | 1.66093e76 | 0.594868 | ||||||||
\(226\) | −2.67400e76 | −0.829158 | ||||||||
\(227\) | 3.31692e76 | 0.891036 | 0.445518 | − | 0.895273i | \(-0.353020\pi\) | ||||
0.445518 | + | 0.895273i | \(0.353020\pi\) | |||||||
\(228\) | 1.53259e76 | 0.356898 | ||||||||
\(229\) | 7.56824e76 | 1.52877 | 0.764384 | − | 0.644761i | \(-0.223043\pi\) | ||||
0.764384 | + | 0.644761i | \(0.223043\pi\) | |||||||
\(230\) | −8.36140e76 | −1.46597 | ||||||||
\(231\) | 5.31791e76 | 0.809752 | ||||||||
\(232\) | −5.52569e76 | −0.731185 | ||||||||
\(233\) | −7.85150e74 | −0.00903410 | −0.00451705 | − | 0.999990i | \(-0.501438\pi\) | ||||
−0.00451705 | + | 0.999990i | \(0.501438\pi\) | |||||||
\(234\) | −8.25354e76 | −0.826276 | ||||||||
\(235\) | 6.24559e76 | 0.544337 | ||||||||
\(236\) | −3.82974e76 | −0.290757 | ||||||||
\(237\) | −2.53181e77 | −1.67537 | ||||||||
\(238\) | 5.05935e77 | 2.91974 | ||||||||
\(239\) | −3.24479e77 | −1.63401 | −0.817006 | − | 0.576629i | \(-0.804368\pi\) | ||||
−0.817006 | + | 0.576629i | \(0.804368\pi\) | |||||||
\(240\) | −5.20568e77 | −2.28882 | ||||||||
\(241\) | 4.35995e77 | 1.67466 | 0.837332 | − | 0.546694i | \(-0.184114\pi\) | ||||
0.837332 | + | 0.546694i | \(0.184114\pi\) | |||||||
\(242\) | 3.21853e77 | 1.08058 | ||||||||
\(243\) | 4.68926e77 | 1.37689 | ||||||||
\(244\) | −1.07402e77 | −0.275958 | ||||||||
\(245\) | −6.87872e77 | −1.54743 | ||||||||
\(246\) | 1.16492e78 | 2.29565 | ||||||||
\(247\) | −1.33257e77 | −0.230165 | ||||||||
\(248\) | −8.93823e76 | −0.135385 | ||||||||
\(249\) | −4.26225e76 | −0.0566448 | ||||||||
\(250\) | −6.94757e77 | −0.810555 | ||||||||
\(251\) | −1.07974e78 | −1.10642 | −0.553212 | − | 0.833040i | \(-0.686598\pi\) | ||||
−0.553212 | + | 0.833040i | \(0.686598\pi\) | |||||||
\(252\) | −1.14694e78 | −1.03282 | ||||||||
\(253\) | −4.38860e77 | −0.347463 | ||||||||
\(254\) | −2.47183e78 | −1.72156 | ||||||||
\(255\) | 4.67874e78 | 2.86796 | ||||||||
\(256\) | 2.25197e78 | 1.21552 | ||||||||
\(257\) | 8.71232e77 | 0.414293 | 0.207146 | − | 0.978310i | \(-0.433582\pi\) | ||||
0.207146 | + | 0.978310i | \(0.433582\pi\) | |||||||
\(258\) | 4.58484e78 | 1.92169 | ||||||||
\(259\) | −6.00714e78 | −2.22037 | ||||||||
\(260\) | −9.93890e77 | −0.324119 | ||||||||
\(261\) | −5.63954e78 | −1.62341 | ||||||||
\(262\) | 6.46841e78 | 1.64439 | ||||||||
\(263\) | 2.13751e78 | 0.480116 | 0.240058 | − | 0.970759i | \(-0.422834\pi\) | ||||
0.240058 | + | 0.970759i | \(0.422834\pi\) | |||||||
\(264\) | −1.58685e78 | −0.315071 | ||||||||
\(265\) | 8.17146e77 | 0.143486 | ||||||||
\(266\) | −5.38717e78 | −0.836965 | ||||||||
\(267\) | 8.85781e78 | 1.21818 | ||||||||
\(268\) | 2.38360e78 | 0.290304 | ||||||||
\(269\) | −7.76436e78 | −0.837831 | −0.418916 | − | 0.908025i | \(-0.637590\pi\) | ||||
−0.418916 | + | 0.908025i | \(0.637590\pi\) | |||||||
\(270\) | −7.21446e78 | −0.690052 | ||||||||
\(271\) | −2.75336e78 | −0.233540 | −0.116770 | − | 0.993159i | \(-0.537254\pi\) | ||||
−0.116770 | + | 0.993159i | \(0.537254\pi\) | |||||||
\(272\) | −2.59943e79 | −1.95609 | ||||||||
\(273\) | 1.76134e79 | 1.17641 | ||||||||
\(274\) | 6.30360e78 | 0.373848 | ||||||||
\(275\) | 3.05398e78 | 0.160899 | ||||||||
\(276\) | 1.67172e79 | 0.782744 | ||||||||
\(277\) | 3.41655e79 | 1.42231 | 0.711157 | − | 0.703033i | \(-0.248171\pi\) | ||||
0.711157 | + | 0.703033i | \(0.248171\pi\) | |||||||
\(278\) | −2.66306e79 | −0.986108 | ||||||||
\(279\) | −9.12238e78 | −0.300588 | ||||||||
\(280\) | 3.65303e79 | 1.07156 | ||||||||
\(281\) | 2.92641e79 | 0.764503 | 0.382252 | − | 0.924058i | \(-0.375149\pi\) | ||||
0.382252 | + | 0.924058i | \(0.375149\pi\) | |||||||
\(282\) | −3.63269e79 | −0.845536 | ||||||||
\(283\) | −1.48186e79 | −0.307431 | −0.153715 | − | 0.988115i | \(-0.549124\pi\) | ||||
−0.153715 | + | 0.988115i | \(0.549124\pi\) | |||||||
\(284\) | −1.03762e79 | −0.191953 | ||||||||
\(285\) | −4.98190e79 | −0.822123 | ||||||||
\(286\) | −1.51759e79 | −0.223490 | ||||||||
\(287\) | −1.40754e80 | −1.85055 | ||||||||
\(288\) | 1.06093e80 | 1.24574 | ||||||||
\(289\) | 1.38311e80 | 1.45103 | ||||||||
\(290\) | −1.97565e80 | −1.85257 | ||||||||
\(291\) | 9.06688e78 | 0.0760214 | ||||||||
\(292\) | 1.00788e80 | 0.755904 | ||||||||
\(293\) | −1.37981e80 | −0.926021 | −0.463010 | − | 0.886353i | \(-0.653231\pi\) | ||||
−0.463010 | + | 0.886353i | \(0.653231\pi\) | |||||||
\(294\) | 4.00094e80 | 2.40366 | ||||||||
\(295\) | 1.24491e80 | 0.669765 | ||||||||
\(296\) | 1.79251e80 | 0.863936 | ||||||||
\(297\) | −3.78661e79 | −0.163556 | ||||||||
\(298\) | −4.24362e80 | −1.64327 | ||||||||
\(299\) | −1.45354e80 | −0.504794 | ||||||||
\(300\) | −1.16334e80 | −0.362464 | ||||||||
\(301\) | −5.53974e80 | −1.54910 | ||||||||
\(302\) | 7.68946e80 | 1.93050 | ||||||||
\(303\) | −1.09647e80 | −0.247236 | ||||||||
\(304\) | 2.76785e80 | 0.560727 | ||||||||
\(305\) | 3.49124e80 | 0.635675 | ||||||||
\(306\) | −1.54080e81 | −2.52231 | ||||||||
\(307\) | 8.32934e80 | 1.22635 | 0.613174 | − | 0.789948i | \(-0.289893\pi\) | ||||
0.613174 | + | 0.789948i | \(0.289893\pi\) | |||||||
\(308\) | −2.10890e80 | −0.279356 | ||||||||
\(309\) | 5.13671e80 | 0.612399 | ||||||||
\(310\) | −3.19577e80 | −0.343020 | ||||||||
\(311\) | −2.02227e79 | −0.0195491 | −0.00977455 | − | 0.999952i | \(-0.503111\pi\) | ||||
−0.00977455 | + | 0.999952i | \(0.503111\pi\) | |||||||
\(312\) | −5.25578e80 | −0.457734 | ||||||||
\(313\) | −2.05669e81 | −1.61428 | −0.807139 | − | 0.590361i | \(-0.798985\pi\) | ||||
−0.807139 | + | 0.590361i | \(0.798985\pi\) | |||||||
\(314\) | 1.50858e81 | 1.06747 | ||||||||
\(315\) | 3.72829e81 | 2.37912 | ||||||||
\(316\) | 1.00403e81 | 0.577983 | ||||||||
\(317\) | 1.39661e81 | 0.725517 | 0.362758 | − | 0.931883i | \(-0.381835\pi\) | ||||
0.362758 | + | 0.931883i | \(0.381835\pi\) | |||||||
\(318\) | −4.75285e80 | −0.222881 | ||||||||
\(319\) | −1.03695e81 | −0.439097 | ||||||||
\(320\) | −2.24619e80 | −0.0859155 | ||||||||
\(321\) | −3.30236e81 | −1.14133 | ||||||||
\(322\) | −5.87623e81 | −1.83562 | ||||||||
\(323\) | −2.48768e81 | −0.702608 | ||||||||
\(324\) | −1.23386e81 | −0.315176 | ||||||||
\(325\) | 1.01151e81 | 0.233754 | ||||||||
\(326\) | 6.65785e81 | 1.39239 | ||||||||
\(327\) | 1.18819e81 | 0.224949 | ||||||||
\(328\) | 4.20006e81 | 0.720039 | ||||||||
\(329\) | 4.38928e81 | 0.681595 | ||||||||
\(330\) | −5.67361e81 | −0.798282 | ||||||||
\(331\) | −8.98103e81 | −1.14529 | −0.572646 | − | 0.819803i | \(-0.694083\pi\) | ||||
−0.572646 | + | 0.819803i | \(0.694083\pi\) | |||||||
\(332\) | 1.69026e80 | 0.0195419 | ||||||||
\(333\) | 1.82944e82 | 1.91814 | ||||||||
\(334\) | 2.20705e82 | 2.09919 | ||||||||
\(335\) | −7.74821e81 | −0.668722 | ||||||||
\(336\) | −3.65844e82 | −2.86596 | ||||||||
\(337\) | 1.09804e82 | 0.780990 | 0.390495 | − | 0.920605i | \(-0.372304\pi\) | ||||
0.390495 | + | 0.920605i | \(0.372304\pi\) | |||||||
\(338\) | 1.40834e82 | 0.909732 | ||||||||
\(339\) | −1.73786e82 | −1.01982 | ||||||||
\(340\) | −1.85543e82 | −0.989415 | ||||||||
\(341\) | −1.67734e81 | −0.0813026 | ||||||||
\(342\) | 1.64063e82 | 0.723041 | ||||||||
\(343\) | −1.06488e82 | −0.426819 | ||||||||
\(344\) | 1.65304e82 | 0.602746 | ||||||||
\(345\) | −5.43416e82 | −1.80307 | ||||||||
\(346\) | 1.83585e82 | 0.554452 | ||||||||
\(347\) | 5.19171e82 | 1.42759 | 0.713793 | − | 0.700357i | \(-0.246976\pi\) | ||||
0.713793 | + | 0.700357i | \(0.246976\pi\) | |||||||
\(348\) | 3.94999e82 | 0.989169 | ||||||||
\(349\) | −7.56370e82 | −1.72547 | −0.862735 | − | 0.505656i | \(-0.831251\pi\) | ||||
−0.862735 | + | 0.505656i | \(0.831251\pi\) | |||||||
\(350\) | 4.08920e82 | 0.850017 | ||||||||
\(351\) | −1.25416e82 | −0.237614 | ||||||||
\(352\) | 1.95074e82 | 0.336947 | ||||||||
\(353\) | 5.18406e81 | 0.0816567 | 0.0408284 | − | 0.999166i | \(-0.487000\pi\) | ||||
0.0408284 | + | 0.999166i | \(0.487000\pi\) | |||||||
\(354\) | −7.24089e82 | −1.04037 | ||||||||
\(355\) | 3.37294e82 | 0.442167 | ||||||||
\(356\) | −3.51270e82 | −0.420258 | ||||||||
\(357\) | 3.28812e83 | 3.59113 | ||||||||
\(358\) | −1.14834e83 | −1.14517 | ||||||||
\(359\) | −6.01244e82 | −0.547622 | −0.273811 | − | 0.961784i | \(-0.588284\pi\) | ||||
−0.273811 | + | 0.961784i | \(0.588284\pi\) | |||||||
\(360\) | −1.11251e83 | −0.925706 | ||||||||
\(361\) | −1.05029e83 | −0.798592 | ||||||||
\(362\) | −9.91932e82 | −0.689372 | ||||||||
\(363\) | 2.09176e83 | 1.32907 | ||||||||
\(364\) | −6.98486e82 | −0.405847 | ||||||||
\(365\) | −3.27625e83 | −1.74124 | ||||||||
\(366\) | −2.03065e83 | −0.987414 | ||||||||
\(367\) | −5.84299e82 | −0.260009 | −0.130004 | − | 0.991513i | \(-0.541499\pi\) | ||||
−0.130004 | + | 0.991513i | \(0.541499\pi\) | |||||||
\(368\) | 3.01913e83 | 1.22978 | ||||||||
\(369\) | 4.28660e83 | 1.59866 | ||||||||
\(370\) | 6.40893e83 | 2.18892 | ||||||||
\(371\) | 5.74274e82 | 0.179666 | ||||||||
\(372\) | 6.38941e82 | 0.183153 | ||||||||
\(373\) | 3.39596e82 | 0.0892124 | 0.0446062 | − | 0.999005i | \(-0.485797\pi\) | ||||
0.0446062 | + | 0.999005i | \(0.485797\pi\) | |||||||
\(374\) | −2.83308e83 | −0.682232 | ||||||||
\(375\) | −4.51530e83 | −0.996943 | ||||||||
\(376\) | −1.30975e83 | −0.265205 | ||||||||
\(377\) | −3.43447e83 | −0.637919 | ||||||||
\(378\) | −5.07018e83 | −0.864052 | ||||||||
\(379\) | 8.27047e83 | 1.29347 | 0.646734 | − | 0.762715i | \(-0.276134\pi\) | ||||
0.646734 | + | 0.762715i | \(0.276134\pi\) | |||||||
\(380\) | 1.97565e83 | 0.283624 | ||||||||
\(381\) | −1.60647e84 | −2.11744 | ||||||||
\(382\) | 9.96246e83 | 1.20589 | ||||||||
\(383\) | −1.10487e84 | −1.22844 | −0.614218 | − | 0.789136i | \(-0.710528\pi\) | ||||
−0.614218 | + | 0.789136i | \(0.710528\pi\) | |||||||
\(384\) | 1.54932e84 | 1.58262 | ||||||||
\(385\) | 6.85526e83 | 0.643502 | ||||||||
\(386\) | −1.90262e84 | −1.64159 | ||||||||
\(387\) | 1.68710e84 | 1.33824 | ||||||||
\(388\) | −3.59561e82 | −0.0262266 | ||||||||
\(389\) | 6.97054e83 | 0.467632 | 0.233816 | − | 0.972281i | \(-0.424879\pi\) | ||||
0.233816 | + | 0.972281i | \(0.424879\pi\) | |||||||
\(390\) | −1.87915e84 | −1.15974 | ||||||||
\(391\) | −2.71352e84 | −1.54095 | ||||||||
\(392\) | 1.44252e84 | 0.753918 | ||||||||
\(393\) | 4.20389e84 | 2.02252 | ||||||||
\(394\) | 4.35423e84 | 1.92879 | ||||||||
\(395\) | −3.26372e84 | −1.33140 | ||||||||
\(396\) | 6.42254e83 | 0.241331 | ||||||||
\(397\) | 6.86328e83 | 0.237596 | 0.118798 | − | 0.992918i | \(-0.462096\pi\) | ||||
0.118798 | + | 0.992918i | \(0.462096\pi\) | |||||||
\(398\) | −4.72685e84 | −1.50790 | ||||||||
\(399\) | −3.50118e84 | −1.02943 | ||||||||
\(400\) | −2.10098e84 | −0.569471 | ||||||||
\(401\) | 1.98012e84 | 0.494879 | 0.247439 | − | 0.968903i | \(-0.420411\pi\) | ||||
0.247439 | + | 0.968903i | \(0.420411\pi\) | |||||||
\(402\) | 4.50667e84 | 1.03875 | ||||||||
\(403\) | −5.55551e83 | −0.118116 | ||||||||
\(404\) | 4.34822e83 | 0.0852937 | ||||||||
\(405\) | 4.01083e84 | 0.726016 | ||||||||
\(406\) | −1.38845e85 | −2.31971 | ||||||||
\(407\) | 3.36382e84 | 0.518817 | ||||||||
\(408\) | −9.81166e84 | −1.39729 | ||||||||
\(409\) | −1.24288e84 | −0.163463 | −0.0817316 | − | 0.996654i | \(-0.526045\pi\) | ||||
−0.0817316 | + | 0.996654i | \(0.526045\pi\) | |||||||
\(410\) | 1.50169e85 | 1.82433 | ||||||||
\(411\) | 4.09678e84 | 0.459815 | ||||||||
\(412\) | −2.03704e84 | −0.211271 | ||||||||
\(413\) | 8.74897e84 | 0.838649 | ||||||||
\(414\) | 1.78957e85 | 1.58576 | ||||||||
\(415\) | −5.49442e83 | −0.0450151 | ||||||||
\(416\) | 6.46101e84 | 0.489516 | ||||||||
\(417\) | −1.73075e85 | −1.21286 | ||||||||
\(418\) | 3.01665e84 | 0.195567 | ||||||||
\(419\) | −2.85264e84 | −0.171116 | −0.0855580 | − | 0.996333i | \(-0.527267\pi\) | ||||
−0.0855580 | + | 0.996333i | \(0.527267\pi\) | |||||||
\(420\) | −2.61134e85 | −1.44964 | ||||||||
\(421\) | 6.27821e83 | 0.0322602 | 0.0161301 | − | 0.999870i | \(-0.494865\pi\) | ||||
0.0161301 | + | 0.999870i | \(0.494865\pi\) | |||||||
\(422\) | −2.39998e85 | −1.14170 | ||||||||
\(423\) | −1.33673e85 | −0.588819 | ||||||||
\(424\) | −1.71362e84 | −0.0699074 | ||||||||
\(425\) | 1.88831e85 | 0.713564 | ||||||||
\(426\) | −1.96184e85 | −0.686832 | ||||||||
\(427\) | 2.45357e85 | 0.795964 | ||||||||
\(428\) | 1.30960e85 | 0.393747 | ||||||||
\(429\) | −9.86297e84 | −0.274882 | ||||||||
\(430\) | 5.91027e85 | 1.52715 | ||||||||
\(431\) | 5.37189e85 | 1.28711 | 0.643555 | − | 0.765400i | \(-0.277459\pi\) | ||||
0.643555 | + | 0.765400i | \(0.277459\pi\) | |||||||
\(432\) | 2.60499e85 | 0.578874 | ||||||||
\(433\) | −5.31909e85 | −1.09643 | −0.548215 | − | 0.836338i | \(-0.684692\pi\) | ||||
−0.548215 | + | 0.836338i | \(0.684692\pi\) | |||||||
\(434\) | −2.24592e85 | −0.429515 | ||||||||
\(435\) | −1.28400e86 | −2.27858 | ||||||||
\(436\) | −4.71195e84 | −0.0776050 | ||||||||
\(437\) | 2.88934e85 | 0.441725 | ||||||||
\(438\) | 1.90560e86 | 2.70473 | ||||||||
\(439\) | −1.02401e86 | −1.34961 | −0.674806 | − | 0.737995i | \(-0.735773\pi\) | ||||
−0.674806 | + | 0.737995i | \(0.735773\pi\) | |||||||
\(440\) | −2.04559e85 | −0.250384 | ||||||||
\(441\) | 1.47224e86 | 1.67388 | ||||||||
\(442\) | −9.38342e85 | −0.991145 | ||||||||
\(443\) | −3.98853e85 | −0.391464 | −0.195732 | − | 0.980657i | \(-0.562708\pi\) | ||||
−0.195732 | + | 0.980657i | \(0.562708\pi\) | |||||||
\(444\) | −1.28136e86 | −1.16876 | ||||||||
\(445\) | 1.14185e86 | 0.968075 | ||||||||
\(446\) | 1.23027e86 | 0.969653 | ||||||||
\(447\) | −2.75798e86 | −2.02114 | ||||||||
\(448\) | −1.57858e85 | −0.107580 | ||||||||
\(449\) | −1.07852e86 | −0.683634 | −0.341817 | − | 0.939766i | \(-0.611042\pi\) | ||||
−0.341817 | + | 0.939766i | \(0.611042\pi\) | |||||||
\(450\) | −1.24535e86 | −0.734316 | ||||||||
\(451\) | 7.88182e85 | 0.432403 | ||||||||
\(452\) | 6.89175e85 | 0.351828 | ||||||||
\(453\) | 4.99746e86 | 2.37442 | ||||||||
\(454\) | −2.48698e86 | −1.09991 | ||||||||
\(455\) | 2.27052e86 | 0.934879 | ||||||||
\(456\) | 1.04474e86 | 0.400545 | ||||||||
\(457\) | 4.87620e86 | 1.74103 | 0.870513 | − | 0.492146i | \(-0.163787\pi\) | ||||
0.870513 | + | 0.492146i | \(0.163787\pi\) | |||||||
\(458\) | −5.67456e86 | −1.88714 | ||||||||
\(459\) | −2.34130e86 | −0.725347 | ||||||||
\(460\) | 2.15500e86 | 0.622039 | ||||||||
\(461\) | 4.13101e86 | 1.11116 | 0.555579 | − | 0.831464i | \(-0.312497\pi\) | ||||
0.555579 | + | 0.831464i | \(0.312497\pi\) | |||||||
\(462\) | −3.98730e86 | −0.999572 | ||||||||
\(463\) | −6.31593e86 | −1.47589 | −0.737947 | − | 0.674859i | \(-0.764204\pi\) | ||||
−0.737947 | + | 0.674859i | \(0.764204\pi\) | |||||||
\(464\) | 7.13366e86 | 1.55410 | ||||||||
\(465\) | −2.07696e86 | −0.421898 | ||||||||
\(466\) | 5.88694e84 | 0.0111519 | ||||||||
\(467\) | −1.06959e87 | −1.88981 | −0.944904 | − | 0.327348i | \(-0.893845\pi\) | ||||
−0.944904 | + | 0.327348i | \(0.893845\pi\) | |||||||
\(468\) | 2.12720e86 | 0.350605 | ||||||||
\(469\) | −5.44529e86 | −0.837343 | ||||||||
\(470\) | −4.68286e86 | −0.671940 | ||||||||
\(471\) | 9.80443e86 | 1.31293 | ||||||||
\(472\) | −2.61067e86 | −0.326314 | ||||||||
\(473\) | 3.10209e86 | 0.361965 | ||||||||
\(474\) | 1.89831e87 | 2.06810 | ||||||||
\(475\) | −2.01066e86 | −0.204549 | ||||||||
\(476\) | −1.30396e87 | −1.23890 | ||||||||
\(477\) | −1.74892e86 | −0.155211 | ||||||||
\(478\) | 2.43290e87 | 2.01705 | ||||||||
\(479\) | −7.36945e85 | −0.0570862 | −0.0285431 | − | 0.999593i | \(-0.509087\pi\) | ||||
−0.0285431 | + | 0.999593i | \(0.509087\pi\) | |||||||
\(480\) | 2.41549e87 | 1.74850 | ||||||||
\(481\) | 1.11413e87 | 0.753736 | ||||||||
\(482\) | −3.26903e87 | −2.06724 | ||||||||
\(483\) | −3.81902e87 | −2.25772 | ||||||||
\(484\) | −8.29519e86 | −0.458513 | ||||||||
\(485\) | 1.16880e86 | 0.0604135 | ||||||||
\(486\) | −3.51594e87 | −1.69966 | ||||||||
\(487\) | 3.08739e87 | 1.39605 | 0.698024 | − | 0.716074i | \(-0.254063\pi\) | ||||
0.698024 | + | 0.716074i | \(0.254063\pi\) | |||||||
\(488\) | −7.32139e86 | −0.309706 | ||||||||
\(489\) | 4.32701e87 | 1.71258 | ||||||||
\(490\) | 5.15757e87 | 1.91017 | ||||||||
\(491\) | −7.58213e86 | −0.262810 | −0.131405 | − | 0.991329i | \(-0.541949\pi\) | ||||
−0.131405 | + | 0.991329i | \(0.541949\pi\) | |||||||
\(492\) | −3.00238e87 | −0.974090 | ||||||||
\(493\) | −6.41157e87 | −1.94733 | ||||||||
\(494\) | 9.99141e86 | 0.284120 | ||||||||
\(495\) | −2.08773e87 | −0.555912 | ||||||||
\(496\) | 1.15392e87 | 0.287755 | ||||||||
\(497\) | 2.37043e87 | 0.553662 | ||||||||
\(498\) | 3.19578e86 | 0.0699234 | ||||||||
\(499\) | −7.04288e87 | −1.44372 | −0.721859 | − | 0.692040i | \(-0.756712\pi\) | ||||
−0.721859 | + | 0.692040i | \(0.756712\pi\) | |||||||
\(500\) | 1.79061e87 | 0.343935 | ||||||||
\(501\) | 1.43439e88 | 2.58190 | ||||||||
\(502\) | 8.09571e87 | 1.36579 | ||||||||
\(503\) | −5.74552e87 | −0.908594 | −0.454297 | − | 0.890850i | \(-0.650110\pi\) | ||||
−0.454297 | + | 0.890850i | \(0.650110\pi\) | |||||||
\(504\) | −7.81850e87 | −1.15913 | ||||||||
\(505\) | −1.41345e87 | −0.196476 | ||||||||
\(506\) | 3.29051e87 | 0.428915 | ||||||||
\(507\) | 9.15293e87 | 1.11893 | ||||||||
\(508\) | 6.37069e87 | 0.730493 | ||||||||
\(509\) | 1.76018e88 | 1.89334 | 0.946671 | − | 0.322202i | \(-0.104423\pi\) | ||||
0.946671 | + | 0.322202i | \(0.104423\pi\) | |||||||
\(510\) | −3.50805e88 | −3.54026 | ||||||||
\(511\) | −2.30249e88 | −2.18031 | ||||||||
\(512\) | −5.15491e87 | −0.458086 | ||||||||
\(513\) | 2.49301e87 | 0.207926 | ||||||||
\(514\) | −6.53237e87 | −0.511410 | ||||||||
\(515\) | 6.62167e87 | 0.486668 | ||||||||
\(516\) | −1.18166e88 | −0.815413 | ||||||||
\(517\) | −2.45786e87 | −0.159263 | ||||||||
\(518\) | 4.50407e88 | 2.74087 | ||||||||
\(519\) | 1.19314e88 | 0.681948 | ||||||||
\(520\) | −6.77517e87 | −0.363757 | ||||||||
\(521\) | −1.77119e88 | −0.893386 | −0.446693 | − | 0.894687i | \(-0.647398\pi\) | ||||
−0.446693 | + | 0.894687i | \(0.647398\pi\) | |||||||
\(522\) | 4.22845e88 | 2.00396 | ||||||||
\(523\) | −1.01782e88 | −0.453281 | −0.226640 | − | 0.973978i | \(-0.572774\pi\) | ||||
−0.226640 | + | 0.973978i | \(0.572774\pi\) | |||||||
\(524\) | −1.66712e88 | −0.697749 | ||||||||
\(525\) | 2.65762e88 | 1.04548 | ||||||||
\(526\) | −1.60267e88 | −0.592663 | ||||||||
\(527\) | −1.03712e88 | −0.360565 | ||||||||
\(528\) | 2.04862e88 | 0.669667 | ||||||||
\(529\) | −1.01548e87 | −0.0312148 | ||||||||
\(530\) | −6.12685e87 | −0.177121 | ||||||||
\(531\) | −2.66445e88 | −0.724496 | ||||||||
\(532\) | 1.38844e88 | 0.355141 | ||||||||
\(533\) | 2.61053e88 | 0.628194 | ||||||||
\(534\) | −6.64146e88 | −1.50374 | ||||||||
\(535\) | −4.25704e88 | −0.907005 | ||||||||
\(536\) | 1.62486e88 | 0.325806 | ||||||||
\(537\) | −7.46315e88 | −1.40850 | ||||||||
\(538\) | 5.82161e88 | 1.03423 | ||||||||
\(539\) | 2.70702e88 | 0.452748 | ||||||||
\(540\) | 1.85940e88 | 0.292803 | ||||||||
\(541\) | 2.29885e88 | 0.340879 | 0.170440 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170440 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(542\) | 2.06443e88 | 0.288286 | ||||||||
\(543\) | −6.44667e88 | −0.847893 | ||||||||
\(544\) | 1.20616e89 | 1.49431 | ||||||||
\(545\) | 1.53168e88 | 0.178765 | ||||||||
\(546\) | −1.32063e89 | −1.45218 | ||||||||
\(547\) | 1.50750e89 | 1.56195 | 0.780976 | − | 0.624561i | \(-0.214722\pi\) | ||||
0.780976 | + | 0.624561i | \(0.214722\pi\) | |||||||
\(548\) | −1.62464e88 | −0.158631 | ||||||||
\(549\) | −7.47223e88 | −0.687621 | ||||||||
\(550\) | −2.28983e88 | −0.198617 | ||||||||
\(551\) | 6.82700e88 | 0.558217 | ||||||||
\(552\) | 1.13958e89 | 0.878469 | ||||||||
\(553\) | −2.29368e89 | −1.66712 | ||||||||
\(554\) | −2.56168e89 | −1.75573 | ||||||||
\(555\) | 4.16523e89 | 2.69226 | ||||||||
\(556\) | 6.86355e88 | 0.418425 | ||||||||
\(557\) | 1.01681e89 | 0.584715 | 0.292357 | − | 0.956309i | \(-0.405560\pi\) | ||||
0.292357 | + | 0.956309i | \(0.405560\pi\) | |||||||
\(558\) | 6.83983e88 | 0.371051 | ||||||||
\(559\) | 1.02744e89 | 0.525862 | ||||||||
\(560\) | −4.71606e89 | −2.27755 | ||||||||
\(561\) | −1.84125e89 | −0.839112 | ||||||||
\(562\) | −2.19418e89 | −0.943717 | ||||||||
\(563\) | −1.75906e89 | −0.714097 | −0.357048 | − | 0.934086i | \(-0.616217\pi\) | ||||
−0.357048 | + | 0.934086i | \(0.616217\pi\) | |||||||
\(564\) | 9.36260e88 | 0.358778 | ||||||||
\(565\) | −2.24026e89 | −0.810444 | ||||||||
\(566\) | 1.11108e89 | 0.379498 | ||||||||
\(567\) | 2.81873e89 | 0.909085 | ||||||||
\(568\) | −7.07329e88 | −0.215427 | ||||||||
\(569\) | 4.73652e89 | 1.36242 | 0.681209 | − | 0.732089i | \(-0.261454\pi\) | ||||
0.681209 | + | 0.732089i | \(0.261454\pi\) | |||||||
\(570\) | 3.73536e89 | 1.01484 | ||||||||
\(571\) | −3.10204e89 | −0.796113 | −0.398056 | − | 0.917361i | \(-0.630315\pi\) | ||||
−0.398056 | + | 0.917361i | \(0.630315\pi\) | |||||||
\(572\) | 3.91131e88 | 0.0948312 | ||||||||
\(573\) | 6.47471e89 | 1.48318 | ||||||||
\(574\) | 1.05536e90 | 2.28435 | ||||||||
\(575\) | −2.19319e89 | −0.448613 | ||||||||
\(576\) | 4.80747e88 | 0.0929363 | ||||||||
\(577\) | −8.08841e89 | −1.47791 | −0.738957 | − | 0.673752i | \(-0.764681\pi\) | ||||
−0.738957 | + | 0.673752i | \(0.764681\pi\) | |||||||
\(578\) | −1.03704e90 | −1.79118 | ||||||||
\(579\) | −1.23653e90 | −2.01908 | ||||||||
\(580\) | 5.09189e89 | 0.786084 | ||||||||
\(581\) | −3.86137e88 | −0.0563659 | ||||||||
\(582\) | −6.79822e88 | −0.0938422 | ||||||||
\(583\) | −3.21576e88 | −0.0419813 | ||||||||
\(584\) | 6.87054e89 | 0.848347 | ||||||||
\(585\) | −6.91475e89 | −0.807627 | ||||||||
\(586\) | 1.03456e90 | 1.14310 | ||||||||
\(587\) | 2.04373e89 | 0.213641 | 0.106820 | − | 0.994278i | \(-0.465933\pi\) | ||||
0.106820 | + | 0.994278i | \(0.465933\pi\) | |||||||
\(588\) | −1.03117e90 | −1.01992 | ||||||||
\(589\) | 1.10432e89 | 0.103359 | ||||||||
\(590\) | −9.33415e89 | −0.826770 | ||||||||
\(591\) | 2.82986e90 | 2.37231 | ||||||||
\(592\) | −2.31413e90 | −1.83625 | ||||||||
\(593\) | −3.01234e89 | −0.226270 | −0.113135 | − | 0.993580i | \(-0.536089\pi\) | ||||
−0.113135 | + | 0.993580i | \(0.536089\pi\) | |||||||
\(594\) | 2.83915e89 | 0.201896 | ||||||||
\(595\) | 4.23868e90 | 2.85384 | ||||||||
\(596\) | 1.09372e90 | 0.697271 | ||||||||
\(597\) | −3.07203e90 | −1.85464 | ||||||||
\(598\) | 1.08985e90 | 0.623127 | ||||||||
\(599\) | −2.20682e90 | −1.19507 | −0.597537 | − | 0.801841i | \(-0.703854\pi\) | ||||
−0.597537 | + | 0.801841i | \(0.703854\pi\) | |||||||
\(600\) | −7.93025e89 | −0.406791 | ||||||||
\(601\) | −2.25821e90 | −1.09735 | −0.548673 | − | 0.836037i | \(-0.684867\pi\) | ||||
−0.548673 | + | 0.836037i | \(0.684867\pi\) | |||||||
\(602\) | 4.15362e90 | 1.91223 | ||||||||
\(603\) | 1.65833e90 | 0.723368 | ||||||||
\(604\) | −1.98182e90 | −0.819151 | ||||||||
\(605\) | 2.69646e90 | 1.05620 | ||||||||
\(606\) | 8.22118e89 | 0.305192 | ||||||||
\(607\) | −1.94001e89 | −0.0682610 | −0.0341305 | − | 0.999417i | \(-0.510866\pi\) | ||||
−0.0341305 | + | 0.999417i | \(0.510866\pi\) | |||||||
\(608\) | −1.28431e90 | −0.428356 | ||||||||
\(609\) | −9.02368e90 | −2.85313 | ||||||||
\(610\) | −2.61768e90 | −0.784689 | ||||||||
\(611\) | −8.14066e89 | −0.231377 | ||||||||
\(612\) | 3.97113e90 | 1.07027 | ||||||||
\(613\) | 6.13649e90 | 1.56839 | 0.784196 | − | 0.620514i | \(-0.213076\pi\) | ||||
0.784196 | + | 0.620514i | \(0.213076\pi\) | |||||||
\(614\) | −6.24522e90 | −1.51383 | ||||||||
\(615\) | 9.75963e90 | 2.24384 | ||||||||
\(616\) | −1.43760e90 | −0.313519 | ||||||||
\(617\) | −5.08036e89 | −0.105106 | −0.0525529 | − | 0.998618i | \(-0.516736\pi\) | ||||
−0.0525529 | + | 0.998618i | \(0.516736\pi\) | |||||||
\(618\) | −3.85143e90 | −0.755956 | ||||||||
\(619\) | −5.67982e90 | −1.05776 | −0.528882 | − | 0.848696i | \(-0.677389\pi\) | ||||
−0.528882 | + | 0.848696i | \(0.677389\pi\) | |||||||
\(620\) | 8.23651e89 | 0.145550 | ||||||||
\(621\) | 2.71933e90 | 0.456021 | ||||||||
\(622\) | 1.51627e89 | 0.0241318 | ||||||||
\(623\) | 8.02469e90 | 1.21218 | ||||||||
\(624\) | 6.78521e90 | 0.972890 | ||||||||
\(625\) | −9.16919e90 | −1.24804 | ||||||||
\(626\) | 1.54208e91 | 1.99270 | ||||||||
\(627\) | 1.96055e90 | 0.240538 | ||||||||
\(628\) | −3.88810e90 | −0.452948 | ||||||||
\(629\) | 2.07989e91 | 2.30088 | ||||||||
\(630\) | −2.79542e91 | −2.93683 | ||||||||
\(631\) | −7.67702e90 | −0.766017 | −0.383009 | − | 0.923745i | \(-0.625112\pi\) | ||||
−0.383009 | + | 0.923745i | \(0.625112\pi\) | |||||||
\(632\) | 6.84427e90 | 0.648667 | ||||||||
\(633\) | −1.55977e91 | −1.40424 | ||||||||
\(634\) | −1.04715e91 | −0.895591 | ||||||||
\(635\) | −2.07088e91 | −1.68271 | ||||||||
\(636\) | 1.22496e90 | 0.0945728 | ||||||||
\(637\) | 8.96589e90 | 0.657752 | ||||||||
\(638\) | 7.77490e90 | 0.542029 | ||||||||
\(639\) | −7.21902e90 | −0.478300 | ||||||||
\(640\) | 1.99721e91 | 1.25769 | ||||||||
\(641\) | −2.19458e91 | −1.31361 | −0.656804 | − | 0.754061i | \(-0.728092\pi\) | ||||
−0.656804 | + | 0.754061i | \(0.728092\pi\) | |||||||
\(642\) | 2.47606e91 | 1.40888 | ||||||||
\(643\) | 7.55485e90 | 0.408667 | 0.204333 | − | 0.978901i | \(-0.434497\pi\) | ||||
0.204333 | + | 0.978901i | \(0.434497\pi\) | |||||||
\(644\) | 1.51449e91 | 0.778890 | ||||||||
\(645\) | 3.84115e91 | 1.87832 | ||||||||
\(646\) | 1.86523e91 | 0.867312 | ||||||||
\(647\) | −3.77147e91 | −1.66771 | −0.833856 | − | 0.551982i | \(-0.813872\pi\) | ||||
−0.833856 | + | 0.551982i | \(0.813872\pi\) | |||||||
\(648\) | −8.41101e90 | −0.353721 | ||||||||
\(649\) | −4.89916e90 | −0.195961 | ||||||||
\(650\) | −7.58412e90 | −0.288550 | ||||||||
\(651\) | −1.45965e91 | −0.528282 | ||||||||
\(652\) | −1.71594e91 | −0.590820 | ||||||||
\(653\) | −8.24655e90 | −0.270143 | −0.135072 | − | 0.990836i | \(-0.543126\pi\) | ||||
−0.135072 | + | 0.990836i | \(0.543126\pi\) | |||||||
\(654\) | −8.90888e90 | −0.277681 | ||||||||
\(655\) | 5.41919e91 | 1.60728 | ||||||||
\(656\) | −5.42228e91 | −1.53041 | ||||||||
\(657\) | 7.01210e91 | 1.88353 | ||||||||
\(658\) | −3.29102e91 | −0.841373 | ||||||||
\(659\) | −1.36580e91 | −0.332361 | −0.166180 | − | 0.986095i | \(-0.553143\pi\) | ||||
−0.166180 | + | 0.986095i | \(0.553143\pi\) | |||||||
\(660\) | 1.46227e91 | 0.338727 | ||||||||
\(661\) | −5.25207e90 | −0.115820 | −0.0579099 | − | 0.998322i | \(-0.518444\pi\) | ||||
−0.0579099 | + | 0.998322i | \(0.518444\pi\) | |||||||
\(662\) | 6.73385e91 | 1.41377 | ||||||||
\(663\) | −6.09838e91 | −1.21906 | ||||||||
\(664\) | 1.15222e90 | 0.0219317 | ||||||||
\(665\) | −4.51333e91 | −0.818075 | ||||||||
\(666\) | −1.37169e92 | −2.36779 | ||||||||
\(667\) | 7.44677e91 | 1.22427 | ||||||||
\(668\) | −5.68827e91 | −0.890729 | ||||||||
\(669\) | 7.99563e91 | 1.19263 | ||||||||
\(670\) | 5.80950e91 | 0.825482 | ||||||||
\(671\) | −1.37393e91 | −0.185987 | ||||||||
\(672\) | 1.69756e92 | 2.18939 | ||||||||
\(673\) | −2.81696e91 | −0.346171 | −0.173086 | − | 0.984907i | \(-0.555374\pi\) | ||||
−0.173086 | + | 0.984907i | \(0.555374\pi\) | |||||||
\(674\) | −8.23293e91 | −0.964068 | ||||||||
\(675\) | −1.89235e91 | −0.211169 | ||||||||
\(676\) | −3.62973e91 | −0.386018 | ||||||||
\(677\) | 1.70699e92 | 1.73021 | 0.865106 | − | 0.501589i | \(-0.167251\pi\) | ||||
0.865106 | + | 0.501589i | \(0.167251\pi\) | |||||||
\(678\) | 1.30302e92 | 1.25889 | ||||||||
\(679\) | 8.21410e90 | 0.0756471 | ||||||||
\(680\) | −1.26481e92 | −1.11042 | ||||||||
\(681\) | −1.61632e92 | −1.35284 | ||||||||
\(682\) | 1.25765e91 | 0.100361 | ||||||||
\(683\) | 5.51499e91 | 0.419636 | 0.209818 | − | 0.977741i | \(-0.432713\pi\) | ||||
0.209818 | + | 0.977741i | \(0.432713\pi\) | |||||||
\(684\) | −4.22843e91 | −0.306801 | ||||||||
\(685\) | 5.28111e91 | 0.365411 | ||||||||
\(686\) | 7.98435e91 | 0.526873 | ||||||||
\(687\) | −3.68796e92 | −2.32109 | ||||||||
\(688\) | −2.13407e92 | −1.28111 | ||||||||
\(689\) | −1.06509e91 | −0.0609903 | ||||||||
\(690\) | 4.07446e92 | 2.22574 | ||||||||
\(691\) | 3.73079e91 | 0.194430 | 0.0972152 | − | 0.995263i | \(-0.469006\pi\) | ||||
0.0972152 | + | 0.995263i | \(0.469006\pi\) | |||||||
\(692\) | −4.73157e91 | −0.235265 | ||||||||
\(693\) | −1.46722e92 | −0.696088 | ||||||||
\(694\) | −3.89267e92 | −1.76224 | ||||||||
\(695\) | −2.23109e92 | −0.963853 | ||||||||
\(696\) | 2.69264e92 | 1.11014 | ||||||||
\(697\) | 4.87341e92 | 1.91764 | ||||||||
\(698\) | 5.67115e92 | 2.12995 | ||||||||
\(699\) | 3.82599e90 | 0.0137162 | ||||||||
\(700\) | −1.05392e92 | −0.360679 | ||||||||
\(701\) | 2.66904e92 | 0.872005 | 0.436003 | − | 0.899945i | \(-0.356394\pi\) | ||||
0.436003 | + | 0.899945i | \(0.356394\pi\) | |||||||
\(702\) | 9.40351e91 | 0.293315 | ||||||||
\(703\) | −2.21465e92 | −0.659564 | ||||||||
\(704\) | 8.83955e90 | 0.0251373 | ||||||||
\(705\) | −3.04344e92 | −0.826453 | ||||||||
\(706\) | −3.88693e91 | −0.100799 | ||||||||
\(707\) | −9.93342e91 | −0.246019 | ||||||||
\(708\) | 1.86621e92 | 0.441448 | ||||||||
\(709\) | −3.84583e92 | −0.868936 | −0.434468 | − | 0.900687i | \(-0.643064\pi\) | ||||
−0.434468 | + | 0.900687i | \(0.643064\pi\) | |||||||
\(710\) | −2.52898e92 | −0.545819 | ||||||||
\(711\) | 6.98528e92 | 1.44020 | ||||||||
\(712\) | −2.39454e92 | −0.471653 | ||||||||
\(713\) | 1.20457e92 | 0.226685 | ||||||||
\(714\) | −2.46539e93 | −4.43296 | ||||||||
\(715\) | −1.27142e92 | −0.218446 | ||||||||
\(716\) | 2.95963e92 | 0.485919 | ||||||||
\(717\) | 1.58117e93 | 2.48088 | ||||||||
\(718\) | 4.50804e92 | 0.675995 | ||||||||
\(719\) | −2.82885e92 | −0.405434 | −0.202717 | − | 0.979237i | \(-0.564977\pi\) | ||||
−0.202717 | + | 0.979237i | \(0.564977\pi\) | |||||||
\(720\) | 1.43625e93 | 1.96754 | ||||||||
\(721\) | 4.65358e92 | 0.609383 | ||||||||
\(722\) | 7.87492e92 | 0.985796 | ||||||||
\(723\) | −2.12458e93 | −2.54260 | ||||||||
\(724\) | 2.55653e92 | 0.292514 | ||||||||
\(725\) | −5.18213e92 | −0.566922 | ||||||||
\(726\) | −1.56837e93 | −1.64062 | ||||||||
\(727\) | 5.75312e92 | 0.575487 | 0.287743 | − | 0.957708i | \(-0.407095\pi\) | ||||
0.287743 | + | 0.957708i | \(0.407095\pi\) | |||||||
\(728\) | −4.76145e92 | −0.455480 | ||||||||
\(729\) | −1.62732e93 | −1.48877 | ||||||||
\(730\) | 2.45649e93 | 2.14942 | ||||||||
\(731\) | 1.91805e93 | 1.60526 | ||||||||
\(732\) | 5.23363e92 | 0.418979 | ||||||||
\(733\) | −4.37341e92 | −0.334920 | −0.167460 | − | 0.985879i | \(-0.553556\pi\) | ||||
−0.167460 | + | 0.985879i | \(0.553556\pi\) | |||||||
\(734\) | 4.38099e92 | 0.320959 | ||||||||
\(735\) | 3.35196e93 | 2.34942 | ||||||||
\(736\) | −1.40091e93 | −0.939465 | ||||||||
\(737\) | 3.04920e92 | 0.195656 | ||||||||
\(738\) | −3.21403e93 | −1.97341 | ||||||||
\(739\) | −1.48307e93 | −0.871399 | −0.435699 | − | 0.900092i | \(-0.643499\pi\) | ||||
−0.435699 | + | 0.900092i | \(0.643499\pi\) | |||||||
\(740\) | −1.65179e93 | −0.928802 | ||||||||
\(741\) | 6.49353e92 | 0.349453 | ||||||||
\(742\) | −4.30582e92 | −0.221784 | ||||||||
\(743\) | 7.24601e92 | 0.357242 | 0.178621 | − | 0.983918i | \(-0.442836\pi\) | ||||
0.178621 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(744\) | 4.35554e92 | 0.205552 | ||||||||
\(745\) | −3.55528e93 | −1.60618 | ||||||||
\(746\) | −2.54624e92 | −0.110125 | ||||||||
\(747\) | 1.17596e92 | 0.0486937 | ||||||||
\(748\) | 7.30176e92 | 0.289485 | ||||||||
\(749\) | −2.99176e93 | −1.13571 | ||||||||
\(750\) | 3.38551e93 | 1.23064 | ||||||||
\(751\) | −4.54486e92 | −0.158206 | −0.0791030 | − | 0.996866i | \(-0.525206\pi\) | ||||
−0.0791030 | + | 0.996866i | \(0.525206\pi\) | |||||||
\(752\) | 1.69088e93 | 0.563681 | ||||||||
\(753\) | 5.26149e93 | 1.67985 | ||||||||
\(754\) | 2.57511e93 | 0.787458 | ||||||||
\(755\) | 6.44217e93 | 1.88693 | ||||||||
\(756\) | 1.30675e93 | 0.366634 | ||||||||
\(757\) | −7.28700e93 | −1.95854 | −0.979270 | − | 0.202559i | \(-0.935074\pi\) | ||||
−0.979270 | + | 0.202559i | \(0.935074\pi\) | |||||||
\(758\) | −6.20108e93 | −1.59668 | ||||||||
\(759\) | 2.13854e93 | 0.527545 | ||||||||
\(760\) | 1.34676e93 | 0.318309 | ||||||||
\(761\) | −7.53622e93 | −1.70668 | −0.853341 | − | 0.521354i | \(-0.825427\pi\) | ||||
−0.853341 | + | 0.521354i | \(0.825427\pi\) | |||||||
\(762\) | 1.20451e94 | 2.61380 | ||||||||
\(763\) | 1.07644e93 | 0.223841 | ||||||||
\(764\) | −2.56764e93 | −0.511683 | ||||||||
\(765\) | −1.29087e94 | −2.46539 | ||||||||
\(766\) | 8.28419e93 | 1.51640 | ||||||||
\(767\) | −1.62265e93 | −0.284691 | ||||||||
\(768\) | −1.09737e94 | −1.84550 | ||||||||
\(769\) | 1.01482e94 | 1.63600 | 0.818001 | − | 0.575217i | \(-0.195082\pi\) | ||||
0.818001 | + | 0.575217i | \(0.195082\pi\) | |||||||
\(770\) | −5.13998e93 | −0.794351 | ||||||||
\(771\) | −4.24546e93 | −0.629010 | ||||||||
\(772\) | 4.90366e93 | 0.696560 | ||||||||
\(773\) | −1.13392e93 | −0.154436 | −0.0772179 | − | 0.997014i | \(-0.524604\pi\) | ||||
−0.0772179 | + | 0.997014i | \(0.524604\pi\) | |||||||
\(774\) | −1.26496e94 | −1.65195 | ||||||||
\(775\) | −8.38249e92 | −0.104971 | ||||||||
\(776\) | −2.45106e92 | −0.0294339 | ||||||||
\(777\) | 2.92724e94 | 3.37113 | ||||||||
\(778\) | −5.22641e93 | −0.577254 | ||||||||
\(779\) | −5.18919e93 | −0.549708 | ||||||||
\(780\) | 4.84316e93 | 0.492101 | ||||||||
\(781\) | −1.32737e93 | −0.129370 | ||||||||
\(782\) | 2.03456e94 | 1.90218 | ||||||||
\(783\) | 6.42529e93 | 0.576283 | ||||||||
\(784\) | −1.86229e94 | −1.60241 | ||||||||
\(785\) | 1.26388e94 | 1.04338 | ||||||||
\(786\) | −3.15202e94 | −2.49664 | ||||||||
\(787\) | 2.00701e94 | 1.52535 | 0.762676 | − | 0.646781i | \(-0.223885\pi\) | ||||
0.762676 | + | 0.646781i | \(0.223885\pi\) | |||||||
\(788\) | −1.12222e94 | −0.818423 | ||||||||
\(789\) | −1.04159e94 | −0.728947 | ||||||||
\(790\) | 2.44709e94 | 1.64350 | ||||||||
\(791\) | −1.57441e94 | −1.01480 | ||||||||
\(792\) | 4.37813e93 | 0.270844 | ||||||||
\(793\) | −4.55057e93 | −0.270201 | ||||||||
\(794\) | −5.14599e93 | −0.293293 | ||||||||
\(795\) | −3.98190e93 | −0.217851 | ||||||||
\(796\) | 1.21826e94 | 0.639832 | ||||||||
\(797\) | −4.77501e93 | −0.240757 | −0.120378 | − | 0.992728i | \(-0.538411\pi\) | ||||
−0.120378 | + | 0.992728i | \(0.538411\pi\) | |||||||
\(798\) | 2.62513e94 | 1.27074 | ||||||||
\(799\) | −1.51972e94 | −0.706308 | ||||||||
\(800\) | 9.74877e93 | 0.435036 | ||||||||
\(801\) | −2.44388e94 | −1.04718 | ||||||||
\(802\) | −1.48466e94 | −0.610887 | ||||||||
\(803\) | 1.28932e94 | 0.509456 | ||||||||
\(804\) | −1.16151e94 | −0.440761 | ||||||||
\(805\) | −4.92306e94 | −1.79419 | ||||||||
\(806\) | 4.16544e93 | 0.145805 | ||||||||
\(807\) | 3.78352e94 | 1.27206 | ||||||||
\(808\) | 2.96410e93 | 0.0957246 | ||||||||
\(809\) | 5.87211e93 | 0.182166 | 0.0910829 | − | 0.995843i | \(-0.470967\pi\) | ||||
0.0910829 | + | 0.995843i | \(0.470967\pi\) | |||||||
\(810\) | −3.00727e94 | −0.896208 | ||||||||
\(811\) | 1.43057e94 | 0.409573 | 0.204786 | − | 0.978807i | \(-0.434350\pi\) | ||||
0.204786 | + | 0.978807i | \(0.434350\pi\) | |||||||
\(812\) | 3.57848e94 | 0.984299 | ||||||||
\(813\) | 1.34170e94 | 0.354578 | ||||||||
\(814\) | −2.52214e94 | −0.640437 | ||||||||
\(815\) | 5.57790e94 | 1.36097 | ||||||||
\(816\) | 1.26668e95 | 2.96987 | ||||||||
\(817\) | −2.04233e94 | −0.460161 | ||||||||
\(818\) | 9.31890e93 | 0.201782 | ||||||||
\(819\) | −4.85955e94 | −1.01127 | ||||||||
\(820\) | −3.87033e94 | −0.774101 | ||||||||
\(821\) | 8.34931e93 | 0.160508 | 0.0802542 | − | 0.996774i | \(-0.474427\pi\) | ||||
0.0802542 | + | 0.996774i | \(0.474427\pi\) | |||||||
\(822\) | −3.07170e94 | −0.567604 | ||||||||
\(823\) | −7.51066e94 | −1.33408 | −0.667042 | − | 0.745020i | \(-0.732440\pi\) | ||||
−0.667042 | + | 0.745020i | \(0.732440\pi\) | |||||||
\(824\) | −1.38861e94 | −0.237108 | ||||||||
\(825\) | −1.48819e94 | −0.244289 | ||||||||
\(826\) | −6.55985e94 | −1.03524 | ||||||||
\(827\) | −3.46296e94 | −0.525434 | −0.262717 | − | 0.964873i | \(-0.584618\pi\) | ||||
−0.262717 | + | 0.964873i | \(0.584618\pi\) | |||||||
\(828\) | −4.61230e94 | −0.672871 | ||||||||
\(829\) | 8.40749e94 | 1.17935 | 0.589677 | − | 0.807639i | \(-0.299255\pi\) | ||||
0.589677 | + | 0.807639i | \(0.299255\pi\) | |||||||
\(830\) | 4.11964e93 | 0.0555675 | ||||||||
\(831\) | −1.66487e95 | −2.15946 | ||||||||
\(832\) | 2.92774e93 | 0.0365194 | ||||||||
\(833\) | 1.67378e95 | 2.00787 | ||||||||
\(834\) | 1.29769e95 | 1.49718 | ||||||||
\(835\) | 1.84905e95 | 2.05181 | ||||||||
\(836\) | −7.77487e93 | −0.0829830 | ||||||||
\(837\) | 1.03934e94 | 0.106704 | ||||||||
\(838\) | 2.13886e94 | 0.211229 | ||||||||
\(839\) | −1.27529e95 | −1.21156 | −0.605780 | − | 0.795632i | \(-0.707139\pi\) | ||||
−0.605780 | + | 0.795632i | \(0.707139\pi\) | |||||||
\(840\) | −1.78010e95 | −1.62692 | ||||||||
\(841\) | 6.22255e94 | 0.547140 | ||||||||
\(842\) | −4.70731e93 | −0.0398226 | ||||||||
\(843\) | −1.42602e95 | −1.16073 | ||||||||
\(844\) | 6.18551e94 | 0.484447 | ||||||||
\(845\) | 1.17989e95 | 0.889201 | ||||||||
\(846\) | 1.00226e95 | 0.726849 | ||||||||
\(847\) | 1.89502e95 | 1.32252 | ||||||||
\(848\) | 2.21227e94 | 0.148585 | ||||||||
\(849\) | 7.22100e94 | 0.466764 | ||||||||
\(850\) | −1.41583e95 | −0.880837 | ||||||||
\(851\) | −2.41570e95 | −1.44655 | ||||||||
\(852\) | 5.05628e94 | 0.291437 | ||||||||
\(853\) | −2.73020e95 | −1.51479 | −0.757394 | − | 0.652959i | \(-0.773528\pi\) | ||||
−0.757394 | + | 0.652959i | \(0.773528\pi\) | |||||||
\(854\) | −1.83966e95 | −0.982552 | ||||||||
\(855\) | 1.37451e95 | 0.706723 | ||||||||
\(856\) | 8.92732e94 | 0.441900 | ||||||||
\(857\) | −2.34418e95 | −1.11716 | −0.558578 | − | 0.829452i | \(-0.688653\pi\) | ||||
−0.558578 | + | 0.829452i | \(0.688653\pi\) | |||||||
\(858\) | 7.39512e94 | 0.339319 | ||||||||
\(859\) | 3.16987e95 | 1.40044 | 0.700218 | − | 0.713930i | \(-0.253086\pi\) | ||||
0.700218 | + | 0.713930i | \(0.253086\pi\) | |||||||
\(860\) | −1.52326e95 | −0.648001 | ||||||||
\(861\) | 6.85887e95 | 2.80964 | ||||||||
\(862\) | −4.02777e95 | −1.58883 | ||||||||
\(863\) | −4.68316e95 | −1.77905 | −0.889525 | − | 0.456886i | \(-0.848965\pi\) | ||||
−0.889525 | + | 0.456886i | \(0.848965\pi\) | |||||||
\(864\) | −1.20874e95 | −0.442219 | ||||||||
\(865\) | 1.53806e95 | 0.541938 | ||||||||
\(866\) | 3.98818e95 | 1.35345 | ||||||||
\(867\) | −6.73982e95 | −2.20307 | ||||||||
\(868\) | 5.78845e94 | 0.182252 | ||||||||
\(869\) | 1.28439e95 | 0.389542 | ||||||||
\(870\) | 9.62723e95 | 2.81271 | ||||||||
\(871\) | 1.00992e95 | 0.284248 | ||||||||
\(872\) | −3.21205e94 | −0.0870956 | ||||||||
\(873\) | −2.50156e94 | −0.0653503 | ||||||||
\(874\) | −2.16639e95 | −0.545274 | ||||||||
\(875\) | −4.09061e95 | −0.992034 | ||||||||
\(876\) | −4.91134e95 | −1.14767 | ||||||||
\(877\) | −1.75364e94 | −0.0394870 | −0.0197435 | − | 0.999805i | \(-0.506285\pi\) | ||||
−0.0197435 | + | 0.999805i | \(0.506285\pi\) | |||||||
\(878\) | 7.67791e95 | 1.66599 | ||||||||
\(879\) | 6.72371e95 | 1.40595 | ||||||||
\(880\) | 2.64085e95 | 0.532178 | ||||||||
\(881\) | −7.68400e94 | −0.149235 | −0.0746174 | − | 0.997212i | \(-0.523774\pi\) | ||||
−0.0746174 | + | 0.997212i | \(0.523774\pi\) | |||||||
\(882\) | −1.10386e96 | −2.06626 | ||||||||
\(883\) | 6.26629e95 | 1.13054 | 0.565272 | − | 0.824904i | \(-0.308771\pi\) | ||||
0.565272 | + | 0.824904i | \(0.308771\pi\) | |||||||
\(884\) | 2.41841e95 | 0.420563 | ||||||||
\(885\) | −6.06637e95 | −1.01689 | ||||||||
\(886\) | 2.99055e95 | 0.483231 | ||||||||
\(887\) | 5.78744e94 | 0.0901507 | 0.0450753 | − | 0.998984i | \(-0.485647\pi\) | ||||
0.0450753 | + | 0.998984i | \(0.485647\pi\) | |||||||
\(888\) | −8.73480e95 | −1.31169 | ||||||||
\(889\) | −1.45537e96 | −2.10701 | ||||||||
\(890\) | −8.56143e95 | −1.19501 | ||||||||
\(891\) | −1.57841e95 | −0.212419 | ||||||||
\(892\) | −3.17079e95 | −0.411443 | ||||||||
\(893\) | 1.61819e95 | 0.202469 | ||||||||
\(894\) | 2.06789e96 | 2.49493 | ||||||||
\(895\) | −9.62066e95 | −1.11933 | ||||||||
\(896\) | 1.40360e96 | 1.57482 | ||||||||
\(897\) | 7.08302e95 | 0.766415 | ||||||||
\(898\) | 8.08662e95 | 0.843891 | ||||||||
\(899\) | 2.84619e95 | 0.286467 | ||||||||
\(900\) | 3.20965e95 | 0.311585 | ||||||||
\(901\) | −1.98834e95 | −0.186181 | ||||||||
\(902\) | −5.90967e95 | −0.533766 | ||||||||
\(903\) | 2.69948e96 | 2.35195 | ||||||||
\(904\) | 4.69798e95 | 0.394855 | ||||||||
\(905\) | −8.31033e95 | −0.673813 | ||||||||
\(906\) | −3.74703e96 | −2.93103 | ||||||||
\(907\) | 1.32052e96 | 0.996572 | 0.498286 | − | 0.867013i | \(-0.333963\pi\) | ||||
0.498286 | + | 0.867013i | \(0.333963\pi\) | |||||||
\(908\) | 6.40975e95 | 0.466714 | ||||||||
\(909\) | 3.02517e95 | 0.212532 | ||||||||
\(910\) | −1.70241e96 | −1.15403 | ||||||||
\(911\) | 1.65330e95 | 0.108144 | 0.0540721 | − | 0.998537i | \(-0.482780\pi\) | ||||
0.0540721 | + | 0.998537i | \(0.482780\pi\) | |||||||
\(912\) | −1.34876e96 | −0.851338 | ||||||||
\(913\) | 2.16225e94 | 0.0131706 | ||||||||
\(914\) | −3.65611e96 | −2.14915 | ||||||||
\(915\) | −1.70126e96 | −0.965129 | ||||||||
\(916\) | 1.46251e96 | 0.800751 | ||||||||
\(917\) | 3.80849e96 | 2.01257 | ||||||||
\(918\) | 1.75548e96 | 0.895381 | ||||||||
\(919\) | 2.04368e96 | 1.00614 | 0.503069 | − | 0.864246i | \(-0.332204\pi\) | ||||
0.503069 | + | 0.864246i | \(0.332204\pi\) | |||||||
\(920\) | 1.46902e96 | 0.698111 | ||||||||
\(921\) | −4.05884e96 | −1.86193 | ||||||||
\(922\) | −3.09737e96 | −1.37163 | ||||||||
\(923\) | −4.39637e95 | −0.187948 | ||||||||
\(924\) | 1.02765e96 | 0.424138 | ||||||||
\(925\) | 1.68106e96 | 0.669850 | ||||||||
\(926\) | 4.73559e96 | 1.82187 | ||||||||
\(927\) | −1.41722e96 | −0.526437 | ||||||||
\(928\) | −3.31010e96 | −1.18722 | ||||||||
\(929\) | −2.46989e96 | −0.855396 | −0.427698 | − | 0.903922i | \(-0.640675\pi\) | ||||
−0.427698 | + | 0.903922i | \(0.640675\pi\) | |||||||
\(930\) | 1.55728e96 | 0.520799 | ||||||||
\(931\) | −1.78223e96 | −0.575572 | ||||||||
\(932\) | −1.51725e94 | −0.00473196 | ||||||||
\(933\) | 9.85441e94 | 0.0296809 | ||||||||
\(934\) | 8.01961e96 | 2.33281 | ||||||||
\(935\) | −2.37354e96 | −0.666835 | ||||||||
\(936\) | 1.45007e96 | 0.393482 | ||||||||
\(937\) | −4.67372e96 | −1.22497 | −0.612486 | − | 0.790481i | \(-0.709831\pi\) | ||||
−0.612486 | + | 0.790481i | \(0.709831\pi\) | |||||||
\(938\) | 4.08280e96 | 1.03363 | ||||||||
\(939\) | 1.00221e97 | 2.45092 | ||||||||
\(940\) | 1.20692e96 | 0.285117 | ||||||||
\(941\) | −2.71979e96 | −0.620688 | −0.310344 | − | 0.950624i | \(-0.600444\pi\) | ||||
−0.310344 | + | 0.950624i | \(0.600444\pi\) | |||||||
\(942\) | −7.35122e96 | −1.62071 | ||||||||
\(943\) | −5.66027e96 | −1.20561 | ||||||||
\(944\) | 3.37037e96 | 0.693565 | ||||||||
\(945\) | −4.24776e96 | −0.844551 | ||||||||
\(946\) | −2.32590e96 | −0.446817 | ||||||||
\(947\) | 1.54092e96 | 0.286026 | 0.143013 | − | 0.989721i | \(-0.454321\pi\) | ||||
0.143013 | + | 0.989721i | \(0.454321\pi\) | |||||||
\(948\) | −4.89256e96 | −0.877537 | ||||||||
\(949\) | 4.27035e96 | 0.740136 | ||||||||
\(950\) | 1.50757e96 | 0.252499 | ||||||||
\(951\) | −6.80557e96 | −1.10153 | ||||||||
\(952\) | −8.88883e96 | −1.39041 | ||||||||
\(953\) | 7.16977e96 | 1.08389 | 0.541946 | − | 0.840413i | \(-0.317688\pi\) | ||||
0.541946 | + | 0.840413i | \(0.317688\pi\) | |||||||
\(954\) | 1.31132e96 | 0.191595 | ||||||||
\(955\) | 8.34647e96 | 1.17867 | ||||||||
\(956\) | −6.27036e96 | −0.855876 | ||||||||
\(957\) | 5.05299e96 | 0.666669 | ||||||||
\(958\) | 5.52551e95 | 0.0704682 | ||||||||
\(959\) | 3.71146e96 | 0.457551 | ||||||||
\(960\) | 1.09455e96 | 0.130443 | ||||||||
\(961\) | −8.21941e96 | −0.946958 | ||||||||
\(962\) | −8.35356e96 | −0.930425 | ||||||||
\(963\) | 9.11124e96 | 0.981123 | ||||||||
\(964\) | 8.42534e96 | 0.877170 | ||||||||
\(965\) | −1.59400e97 | −1.60454 | ||||||||
\(966\) | 2.86345e97 | 2.78697 | ||||||||
\(967\) | 1.00835e97 | 0.948962 | 0.474481 | − | 0.880266i | \(-0.342636\pi\) | ||||
0.474481 | + | 0.880266i | \(0.342636\pi\) | |||||||
\(968\) | −5.65468e96 | −0.514587 | ||||||||
\(969\) | 1.21223e97 | 1.06675 | ||||||||
\(970\) | −8.76350e95 | −0.0745755 | ||||||||
\(971\) | −3.00015e96 | −0.246898 | −0.123449 | − | 0.992351i | \(-0.539396\pi\) | ||||
−0.123449 | + | 0.992351i | \(0.539396\pi\) | |||||||
\(972\) | 9.06169e96 | 0.721200 | ||||||||
\(973\) | −1.56796e97 | −1.20689 | ||||||||
\(974\) | −2.31488e97 | −1.72331 | ||||||||
\(975\) | −4.92900e96 | −0.354903 | ||||||||
\(976\) | 9.45190e96 | 0.658264 | ||||||||
\(977\) | −7.90349e96 | −0.532409 | −0.266205 | − | 0.963917i | \(-0.585770\pi\) | ||||
−0.266205 | + | 0.963917i | \(0.585770\pi\) | |||||||
\(978\) | −3.24433e97 | −2.11403 | ||||||||
\(979\) | −4.49359e96 | −0.283241 | ||||||||
\(980\) | −1.32927e97 | −0.810523 | ||||||||
\(981\) | −3.27823e96 | −0.193373 | ||||||||
\(982\) | 5.68497e96 | 0.324418 | ||||||||
\(983\) | 2.35570e97 | 1.30056 | 0.650281 | − | 0.759694i | \(-0.274651\pi\) | ||||
0.650281 | + | 0.759694i | \(0.274651\pi\) | |||||||
\(984\) | −2.04666e97 | −1.09322 | ||||||||
\(985\) | 3.64794e97 | 1.88526 | ||||||||
\(986\) | 4.80730e97 | 2.40382 | ||||||||
\(987\) | −2.13887e97 | −1.03485 | ||||||||
\(988\) | −2.57511e96 | −0.120558 | ||||||||
\(989\) | −2.22774e97 | −1.00922 | ||||||||
\(990\) | 1.56535e97 | 0.686228 | ||||||||
\(991\) | 8.80715e96 | 0.373630 | 0.186815 | − | 0.982395i | \(-0.440184\pi\) | ||||
0.186815 | + | 0.982395i | \(0.440184\pi\) | |||||||
\(992\) | −5.35433e96 | −0.219824 | ||||||||
\(993\) | 4.37640e97 | 1.73887 | ||||||||
\(994\) | −1.77732e97 | −0.683451 | ||||||||
\(995\) | −3.96012e97 | −1.47387 | ||||||||
\(996\) | −8.23653e95 | −0.0296699 | ||||||||
\(997\) | 2.37020e97 | 0.826402 | 0.413201 | − | 0.910640i | \(-0.364411\pi\) | ||||
0.413201 | + | 0.910640i | \(0.364411\pi\) | |||||||
\(998\) | 5.28065e97 | 1.78215 | ||||||||
\(999\) | −2.08434e97 | −0.680910 |
(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 | 1.66.a.a.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 9.66.a.b.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.66.a.a.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.66.a.b.1.4 | 5 | 3.2 | odd | 2 |