Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.90 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 53.2620i | 1.66444i | 0.554447 | + | 0.832219i | \(0.312930\pi\) | ||||
−0.554447 | + | 0.832219i | \(0.687070\pi\) | |||||||
\(3\) | −140.296 | −0.577350 | ||||||||
\(4\) | −1812.84 | −1.77035 | ||||||||
\(5\) | 3919.09 | 1.25411 | 0.627055 | − | 0.778975i | \(-0.284260\pi\) | ||||
0.627055 | + | 0.778975i | \(0.284260\pi\) | |||||||
\(6\) | − | 7472.46i | − | 0.960964i | ||||||
\(7\) | 33417.1 | 1.98829 | 0.994143 | − | 0.108074i | \(-0.0344684\pi\) | ||||
0.994143 | + | 0.108074i | \(0.0344684\pi\) | |||||||
\(8\) | − | 42015.4i | − | 1.28221i | ||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | 208739.i | 2.08739i | ||||||||
\(11\) | 106418.i | 0.660773i | 0.943846 | + | 0.330387i | \(0.107179\pi\) | ||||
−0.943846 | + | 0.330387i | \(0.892821\pi\) | |||||||
\(12\) | 254335. | 1.02211 | ||||||||
\(13\) | − | 359376.i | − | 0.967903i | −0.875095 | − | 0.483951i | \(-0.839201\pi\) | ||
0.875095 | − | 0.483951i | \(-0.160799\pi\) | |||||||
\(14\) | 1.77986e6i | 3.30938i | ||||||||
\(15\) | −549833. | −0.724060 | ||||||||
\(16\) | 381474. | 0.363802 | ||||||||
\(17\) | 20865.6 | 0.0146956 | 0.00734780 | − | 0.999973i | \(-0.497661\pi\) | ||||
0.00734780 | + | 0.999973i | \(0.497661\pi\) | |||||||
\(18\) | 1.04836e6i | 0.554813i | ||||||||
\(19\) | 2.00076e6 | 0.808029 | 0.404015 | − | 0.914753i | \(-0.367615\pi\) | ||||
0.404015 | + | 0.914753i | \(0.367615\pi\) | |||||||
\(20\) | −7.10470e6 | −2.22022 | ||||||||
\(21\) | −4.68829e6 | −1.14794 | ||||||||
\(22\) | −5.66805e6 | −1.09982 | ||||||||
\(23\) | − | 7.42032e6i | − | 1.15288i | −0.817140 | − | 0.576439i | \(-0.804442\pi\) | ||
0.817140 | − | 0.576439i | \(-0.195558\pi\) | |||||||
\(24\) | 5.89460e6i | 0.740283i | ||||||||
\(25\) | 5.59365e6 | 0.572790 | ||||||||
\(26\) | 1.91411e7 | 1.61101 | ||||||||
\(27\) | −2.76145e6 | −0.192450 | ||||||||
\(28\) | −6.05800e7 | −3.51997 | ||||||||
\(29\) | −1.04434e7 | −0.509158 | −0.254579 | − | 0.967052i | \(-0.581937\pi\) | ||||
−0.254579 | + | 0.967052i | \(0.581937\pi\) | |||||||
\(30\) | − | 2.92852e7i | − | 1.20515i | ||||||
\(31\) | 2.79714e7i | 0.977025i | 0.872557 | + | 0.488512i | \(0.162460\pi\) | ||||
−0.872557 | + | 0.488512i | \(0.837540\pi\) | |||||||
\(32\) | − | 2.27057e7i | − | 0.676683i | ||||||
\(33\) | − | 1.49301e7i | − | 0.381498i | ||||||
\(34\) | 1.11135e6i | 0.0244599i | ||||||||
\(35\) | 1.30965e8 | 2.49353 | ||||||||
\(36\) | −3.56822e7 | −0.590118 | ||||||||
\(37\) | 6.88027e7i | 0.992194i | 0.868267 | + | 0.496097i | \(0.165234\pi\) | ||||
−0.868267 | + | 0.496097i | \(0.834766\pi\) | |||||||
\(38\) | 1.06565e8i | 1.34491i | ||||||||
\(39\) | 5.04190e7i | 0.558819i | ||||||||
\(40\) | − | 1.64662e8i | − | 1.60803i | ||||||
\(41\) | 1.66483e8 | 1.43698 | 0.718491 | − | 0.695536i | \(-0.244833\pi\) | ||||
0.718491 | + | 0.695536i | \(0.244833\pi\) | |||||||
\(42\) | − | 2.49708e8i | − | 1.91067i | ||||||
\(43\) | − | 1.90640e8i | − | 1.29680i | −0.761302 | − | 0.648398i | \(-0.775439\pi\) | ||
0.761302 | − | 0.648398i | \(-0.224561\pi\) | |||||||
\(44\) | − | 1.92920e8i | − | 1.16980i | ||||||
\(45\) | 7.71395e7 | 0.418036 | ||||||||
\(46\) | 3.95221e8 | 1.91889 | ||||||||
\(47\) | 5.17915e7i | 0.225823i | 0.993605 | + | 0.112912i | \(0.0360177\pi\) | ||||
−0.993605 | + | 0.112912i | \(0.963982\pi\) | |||||||
\(48\) | −5.35193e7 | −0.210041 | ||||||||
\(49\) | 8.34228e8 | 2.95328 | ||||||||
\(50\) | 2.97929e8i | 0.953373i | ||||||||
\(51\) | −2.92737e6 | −0.00848450 | ||||||||
\(52\) | 6.51492e8i | 1.71353i | ||||||||
\(53\) | 7.24197e7 | 0.173172 | 0.0865860 | − | 0.996244i | \(-0.472404\pi\) | ||||
0.0865860 | + | 0.996244i | \(0.472404\pi\) | |||||||
\(54\) | − | 1.47080e8i | − | 0.320321i | ||||||
\(55\) | 4.17063e8i | 0.828682i | ||||||||
\(56\) | − | 1.40403e9i | − | 2.54940i | ||||||
\(57\) | −2.80699e8 | −0.466516 | ||||||||
\(58\) | − | 5.56237e8i | − | 0.847462i | ||||||
\(59\) | 4.01714e8 | + | 5.91390e8i | 0.561897 | + | 0.827207i | ||||
\(60\) | 9.96762e8 | 1.28184 | ||||||||
\(61\) | − | 8.18823e8i | − | 0.969484i | −0.874657 | − | 0.484742i | \(-0.838913\pi\) | ||
0.874657 | − | 0.484742i | \(-0.161087\pi\) | |||||||
\(62\) | −1.48981e9 | −1.62620 | ||||||||
\(63\) | 6.57749e8 | 0.662762 | ||||||||
\(64\) | 1.59998e9 | 1.49010 | ||||||||
\(65\) | − | 1.40843e9i | − | 1.21386i | ||||||
\(66\) | 7.95205e8 | 0.634979 | ||||||||
\(67\) | − | 7.49122e8i | − | 0.554854i | −0.960747 | − | 0.277427i | \(-0.910518\pi\) | ||
0.960747 | − | 0.277427i | \(-0.0894816\pi\) | |||||||
\(68\) | −3.78261e7 | −0.0260164 | ||||||||
\(69\) | 1.04104e9i | 0.665614i | ||||||||
\(70\) | 6.97545e9i | 4.15032i | ||||||||
\(71\) | −1.37407e9 | −0.761582 | −0.380791 | − | 0.924661i | \(-0.624348\pi\) | ||||
−0.380791 | + | 0.924661i | \(0.624348\pi\) | |||||||
\(72\) | − | 8.26989e8i | − | 0.427403i | ||||||
\(73\) | 2.48055e9i | 1.19656i | 0.801288 | + | 0.598279i | \(0.204149\pi\) | ||||
−0.801288 | + | 0.598279i | \(0.795851\pi\) | |||||||
\(74\) | −3.66457e9 | −1.65145 | ||||||||
\(75\) | −7.84767e8 | −0.330700 | ||||||||
\(76\) | −3.62706e9 | −1.43050 | ||||||||
\(77\) | 3.55619e9i | 1.31381i | ||||||||
\(78\) | −2.68542e9 | −0.930120 | ||||||||
\(79\) | 5.64088e9 | 1.83321 | 0.916604 | − | 0.399797i | \(-0.130919\pi\) | ||||
0.916604 | + | 0.399797i | \(0.130919\pi\) | |||||||
\(80\) | 1.49503e9 | 0.456247 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | 8.86723e9i | 2.39177i | ||||||||
\(83\) | 1.03817e9i | 0.263558i | 0.991279 | + | 0.131779i | \(0.0420690\pi\) | ||||
−0.991279 | + | 0.131779i | \(0.957931\pi\) | |||||||
\(84\) | 8.49914e9 | 2.03226 | ||||||||
\(85\) | 8.17743e7 | 0.0184299 | ||||||||
\(86\) | 1.01539e10 | 2.15844 | ||||||||
\(87\) | 1.46517e9 | 0.293962 | ||||||||
\(88\) | 4.47120e9 | 0.847249 | ||||||||
\(89\) | − | 4.10346e9i | − | 0.734853i | −0.930053 | − | 0.367426i | \(-0.880239\pi\) | ||
0.930053 | − | 0.367426i | \(-0.119761\pi\) | |||||||
\(90\) | 4.10860e9i | 0.695796i | ||||||||
\(91\) | − | 1.20093e10i | − | 1.92447i | ||||||
\(92\) | 1.34519e10i | 2.04100i | ||||||||
\(93\) | − | 3.92428e9i | − | 0.564085i | ||||||
\(94\) | −2.75852e9 | −0.375869 | ||||||||
\(95\) | 7.84116e9 | 1.01336 | ||||||||
\(96\) | 3.18552e9i | 0.390683i | ||||||||
\(97\) | − | 1.42779e10i | − | 1.66267i | −0.555769 | − | 0.831337i | \(-0.687576\pi\) | ||
0.555769 | − | 0.831337i | \(-0.312424\pi\) | |||||||
\(98\) | 4.44327e10i | 4.91555i | ||||||||
\(99\) | 2.09463e9i | 0.220258i | ||||||||
\(100\) | −1.01404e10 | −1.01404 | ||||||||
\(101\) | 1.51177e10i | 1.43840i | 0.694802 | + | 0.719201i | \(0.255492\pi\) | ||||
−0.694802 | + | 0.719201i | \(0.744508\pi\) | |||||||
\(102\) | − | 1.55918e8i | − | 0.0141219i | ||||||
\(103\) | − | 1.02128e10i | − | 0.880968i | −0.897760 | − | 0.440484i | \(-0.854807\pi\) | ||
0.897760 | − | 0.440484i | \(-0.145193\pi\) | |||||||
\(104\) | −1.50993e10 | −1.24105 | ||||||||
\(105\) | −1.83738e10 | −1.43964 | ||||||||
\(106\) | 3.85722e9i | 0.288234i | ||||||||
\(107\) | 8.79307e9 | 0.626933 | 0.313467 | − | 0.949599i | \(-0.398510\pi\) | ||||
0.313467 | + | 0.949599i | \(0.398510\pi\) | |||||||
\(108\) | 5.00607e9 | 0.340705 | ||||||||
\(109\) | − | 5.87428e9i | − | 0.381788i | −0.981611 | − | 0.190894i | \(-0.938861\pi\) | ||
0.981611 | − | 0.190894i | \(-0.0611387\pi\) | |||||||
\(110\) | −2.22136e10 | −1.37929 | ||||||||
\(111\) | − | 9.65275e9i | − | 0.572844i | ||||||
\(112\) | 1.27477e10 | 0.723341 | ||||||||
\(113\) | 8.58791e9i | 0.466117i | 0.972463 | + | 0.233059i | \(0.0748734\pi\) | ||||
−0.972463 | + | 0.233059i | \(0.925127\pi\) | |||||||
\(114\) | − | 1.49506e10i | − | 0.776487i | ||||||
\(115\) | − | 2.90809e10i | − | 1.44583i | ||||||
\(116\) | 1.89323e10 | 0.901390 | ||||||||
\(117\) | − | 7.07359e9i | − | 0.322634i | ||||||
\(118\) | −3.14987e10 | + | 2.13961e10i | −1.37684 | + | 0.935243i | ||||
\(119\) | 6.97270e8 | 0.0292190 | ||||||||
\(120\) | 2.31015e10i | 0.928396i | ||||||||
\(121\) | 1.46126e10 | 0.563379 | ||||||||
\(122\) | 4.36122e10 | 1.61365 | ||||||||
\(123\) | −2.33570e10 | −0.829642 | ||||||||
\(124\) | − | 5.07077e10i | − | 1.72968i | ||||||
\(125\) | −1.63504e10 | −0.535768 | ||||||||
\(126\) | 3.50331e10i | 1.10313i | ||||||||
\(127\) | 3.86487e8 | 0.0116981 | 0.00584907 | − | 0.999983i | \(-0.498138\pi\) | ||||
0.00584907 | + | 0.999983i | \(0.498138\pi\) | |||||||
\(128\) | 6.19676e10i | 1.80349i | ||||||||
\(129\) | 2.67460e10i | 0.748705i | ||||||||
\(130\) | 7.50156e10 | 2.02039 | ||||||||
\(131\) | − | 1.28381e10i | − | 0.332769i | −0.986061 | − | 0.166385i | \(-0.946791\pi\) | ||
0.986061 | − | 0.166385i | \(-0.0532094\pi\) | |||||||
\(132\) | 2.70659e10i | 0.675386i | ||||||||
\(133\) | 6.68596e10 | 1.60659 | ||||||||
\(134\) | 3.98997e10 | 0.923520 | ||||||||
\(135\) | −1.08224e10 | −0.241353 | ||||||||
\(136\) | − | 8.76678e8i | − | 0.0188428i | ||||||
\(137\) | 2.40665e10 | 0.498666 | 0.249333 | − | 0.968418i | \(-0.419789\pi\) | ||||
0.249333 | + | 0.968418i | \(0.419789\pi\) | |||||||
\(138\) | −5.54480e10 | −1.10787 | ||||||||
\(139\) | 6.39766e10 | 1.23295 | 0.616477 | − | 0.787373i | \(-0.288559\pi\) | ||||
0.616477 | + | 0.787373i | \(0.288559\pi\) | |||||||
\(140\) | −2.37419e11 | −4.41443 | ||||||||
\(141\) | − | 7.26614e9i | − | 0.130379i | ||||||
\(142\) | − | 7.31856e10i | − | 1.26761i | ||||||
\(143\) | 3.82441e10 | 0.639564 | ||||||||
\(144\) | 7.50855e9 | 0.121267 | ||||||||
\(145\) | −4.09287e10 | −0.638539 | ||||||||
\(146\) | −1.32119e11 | −1.99160 | ||||||||
\(147\) | −1.17039e11 | −1.70508 | ||||||||
\(148\) | − | 1.24728e11i | − | 1.75654i | ||||||
\(149\) | − | 1.48199e10i | − | 0.201796i | −0.994897 | − | 0.100898i | \(-0.967828\pi\) | ||
0.994897 | − | 0.100898i | \(-0.0321716\pi\) | |||||||
\(150\) | − | 4.17983e10i | − | 0.550430i | ||||||
\(151\) | − | 9.56084e9i | − | 0.121790i | −0.998144 | − | 0.0608950i | \(-0.980605\pi\) | ||
0.998144 | − | 0.0608950i | \(-0.0193955\pi\) | |||||||
\(152\) | − | 8.40627e10i | − | 1.03606i | ||||||
\(153\) | 4.10698e8 | 0.00489853 | ||||||||
\(154\) | −1.89410e11 | −2.18675 | ||||||||
\(155\) | 1.09622e11i | 1.22530i | ||||||||
\(156\) | − | 9.14017e10i | − | 0.989308i | ||||||
\(157\) | 1.61171e11i | 1.68961i | 0.535070 | + | 0.844807i | \(0.320285\pi\) | ||||
−0.535070 | + | 0.844807i | \(0.679715\pi\) | |||||||
\(158\) | 3.00445e11i | 3.05126i | ||||||||
\(159\) | −1.01602e10 | −0.0999809 | ||||||||
\(160\) | − | 8.89857e10i | − | 0.848634i | ||||||
\(161\) | − | 2.47966e11i | − | 2.29225i | ||||||
\(162\) | 2.06348e10i | 0.184938i | ||||||||
\(163\) | −2.19867e11 | −1.91083 | −0.955415 | − | 0.295266i | \(-0.904592\pi\) | ||||
−0.955415 | + | 0.295266i | \(0.904592\pi\) | |||||||
\(164\) | −3.01808e11 | −2.54397 | ||||||||
\(165\) | − | 5.85123e10i | − | 0.478440i | ||||||
\(166\) | −5.52949e10 | −0.438676 | ||||||||
\(167\) | −1.07295e11 | −0.826031 | −0.413016 | − | 0.910724i | \(-0.635525\pi\) | ||||
−0.413016 | + | 0.910724i | \(0.635525\pi\) | |||||||
\(168\) | 1.96980e11i | 1.47189i | ||||||||
\(169\) | 8.70774e9 | 0.0631643 | ||||||||
\(170\) | 4.35547e9i | 0.0306754i | ||||||||
\(171\) | 3.93810e10 | 0.269343 | ||||||||
\(172\) | 3.45600e11i | 2.29579i | ||||||||
\(173\) | 7.34928e9i | 0.0474258i | 0.999719 | + | 0.0237129i | \(0.00754875\pi\) | ||||
−0.999719 | + | 0.0237129i | \(0.992451\pi\) | |||||||
\(174\) | 7.80379e10i | 0.489282i | ||||||||
\(175\) | 1.86924e11 | 1.13887 | ||||||||
\(176\) | 4.05957e10i | 0.240390i | ||||||||
\(177\) | −5.63589e10 | − | 8.29698e10i | −0.324411 | − | 0.477588i | ||||
\(178\) | 2.18559e11 | 1.22312 | ||||||||
\(179\) | 2.35454e11i | 1.28127i | 0.767845 | + | 0.640636i | \(0.221329\pi\) | ||||
−0.767845 | + | 0.640636i | \(0.778671\pi\) | |||||||
\(180\) | −1.39842e11 | −0.740073 | ||||||||
\(181\) | −2.44056e11 | −1.25631 | −0.628156 | − | 0.778088i | \(-0.716190\pi\) | ||||
−0.628156 | + | 0.778088i | \(0.716190\pi\) | |||||||
\(182\) | 6.39639e11 | 3.20316 | ||||||||
\(183\) | 1.14878e11i | 0.559732i | ||||||||
\(184\) | −3.11768e11 | −1.47823 | ||||||||
\(185\) | 2.69644e11i | 1.24432i | ||||||||
\(186\) | 2.09015e11 | 0.938885 | ||||||||
\(187\) | 2.22048e9i | 0.00971046i | ||||||||
\(188\) | − | 9.38898e10i | − | 0.399787i | ||||||
\(189\) | −9.22796e10 | −0.382646 | ||||||||
\(190\) | 4.17636e11i | 1.68667i | ||||||||
\(191\) | 4.10598e10i | 0.161529i | 0.996733 | + | 0.0807643i | \(0.0257361\pi\) | ||||
−0.996733 | + | 0.0807643i | \(0.974264\pi\) | |||||||
\(192\) | −2.24471e11 | −0.860309 | ||||||||
\(193\) | −2.03753e11 | −0.760882 | −0.380441 | − | 0.924805i | \(-0.624228\pi\) | ||||
−0.380441 | + | 0.924805i | \(0.624228\pi\) | |||||||
\(194\) | 7.60472e11 | 2.76742 | ||||||||
\(195\) | 1.97597e11i | 0.700820i | ||||||||
\(196\) | −1.51233e12 | −5.22835 | ||||||||
\(197\) | 4.28827e11 | 1.44528 | 0.722639 | − | 0.691226i | \(-0.242929\pi\) | ||||
0.722639 | + | 0.691226i | \(0.242929\pi\) | |||||||
\(198\) | −1.11564e11 | −0.366605 | ||||||||
\(199\) | 3.84437e11 | 1.23185 | 0.615927 | − | 0.787803i | \(-0.288782\pi\) | ||||
0.615927 | + | 0.787803i | \(0.288782\pi\) | |||||||
\(200\) | − | 2.35019e11i | − | 0.734436i | ||||||
\(201\) | 1.05099e11i | 0.320345i | ||||||||
\(202\) | −8.05202e11 | −2.39413 | ||||||||
\(203\) | −3.48989e11 | −1.01235 | ||||||||
\(204\) | 5.30686e9 | 0.0150206 | ||||||||
\(205\) | 6.52463e11 | 1.80213 | ||||||||
\(206\) | 5.43956e11 | 1.46632 | ||||||||
\(207\) | − | 1.46054e11i | − | 0.384293i | ||||||
\(208\) | − | 1.37092e11i | − | 0.352125i | ||||||
\(209\) | 2.12917e11i | 0.533924i | ||||||||
\(210\) | − | 9.78628e11i | − | 2.39619i | ||||||
\(211\) | − | 4.71673e11i | − | 1.12779i | −0.825846 | − | 0.563895i | \(-0.809302\pi\) | ||
0.825846 | − | 0.563895i | \(-0.190698\pi\) | |||||||
\(212\) | −1.31286e11 | −0.306576 | ||||||||
\(213\) | 1.92776e11 | 0.439699 | ||||||||
\(214\) | 4.68337e11i | 1.04349i | ||||||||
\(215\) | − | 7.47135e11i | − | 1.62632i | ||||||
\(216\) | 1.16023e11i | 0.246761i | ||||||||
\(217\) | 9.34723e11i | 1.94260i | ||||||||
\(218\) | 3.12876e11 | 0.635463 | ||||||||
\(219\) | − | 3.48012e11i | − | 0.690834i | ||||||
\(220\) | − | 7.56069e11i | − | 1.46706i | ||||||
\(221\) | − | 7.49860e9i | − | 0.0142239i | ||||||
\(222\) | 5.14125e11 | 0.953463 | ||||||||
\(223\) | 1.68130e11 | 0.304874 | 0.152437 | − | 0.988313i | \(-0.451288\pi\) | ||||
0.152437 | + | 0.988313i | \(0.451288\pi\) | |||||||
\(224\) | − | 7.58759e11i | − | 1.34544i | ||||||
\(225\) | 1.10100e11 | 0.190930 | ||||||||
\(226\) | −4.57409e11 | −0.775823 | ||||||||
\(227\) | 9.48249e11i | 1.57323i | 0.617442 | + | 0.786616i | \(0.288169\pi\) | ||||
−0.617442 | + | 0.786616i | \(0.711831\pi\) | |||||||
\(228\) | 5.08863e11 | 0.825898 | ||||||||
\(229\) | 1.07967e12i | 1.71441i | 0.514978 | + | 0.857203i | \(0.327800\pi\) | ||||
−0.514978 | + | 0.857203i | \(0.672200\pi\) | |||||||
\(230\) | 1.54891e12 | 2.40650 | ||||||||
\(231\) | − | 4.98920e11i | − | 0.758526i | ||||||
\(232\) | 4.38784e11i | 0.652846i | ||||||||
\(233\) | 9.34518e11i | 1.36084i | 0.732821 | + | 0.680421i | \(0.238203\pi\) | ||||
−0.732821 | + | 0.680421i | \(0.761797\pi\) | |||||||
\(234\) | 3.76754e11 | 0.537005 | ||||||||
\(235\) | 2.02975e11i | 0.283207i | ||||||||
\(236\) | −7.28244e11 | − | 1.07210e12i | −0.994757 | − | 1.46445i | ||||
\(237\) | −7.91394e11 | −1.05840 | ||||||||
\(238\) | 3.71380e10i | 0.0486333i | ||||||||
\(239\) | −3.82544e11 | −0.490560 | −0.245280 | − | 0.969452i | \(-0.578880\pi\) | ||||
−0.245280 | + | 0.969452i | \(0.578880\pi\) | |||||||
\(240\) | −2.09747e11 | −0.263414 | ||||||||
\(241\) | 9.57291e11 | 1.17749 | 0.588747 | − | 0.808317i | \(-0.299621\pi\) | ||||
0.588747 | + | 0.808317i | \(0.299621\pi\) | |||||||
\(242\) | 7.78296e11i | 0.937709i | ||||||||
\(243\) | −5.43536e10 | −0.0641500 | ||||||||
\(244\) | 1.48440e12i | 1.71633i | ||||||||
\(245\) | 3.26942e12 | 3.70374 | ||||||||
\(246\) | − | 1.24404e12i | − | 1.38089i | ||||||
\(247\) | − | 7.19024e11i | − | 0.782093i | ||||||
\(248\) | 1.17523e12 | 1.25275 | ||||||||
\(249\) | − | 1.45651e11i | − | 0.152165i | ||||||
\(250\) | − | 8.70853e11i | − | 0.891753i | ||||||
\(251\) | −4.55446e10 | −0.0457160 | −0.0228580 | − | 0.999739i | \(-0.507277\pi\) | ||||
−0.0228580 | + | 0.999739i | \(0.507277\pi\) | |||||||
\(252\) | −1.19240e12 | −1.17332 | ||||||||
\(253\) | 7.89657e11 | 0.761791 | ||||||||
\(254\) | 2.05851e10i | 0.0194708i | ||||||||
\(255\) | −1.14726e10 | −0.0106405 | ||||||||
\(256\) | −1.66214e12 | −1.51171 | ||||||||
\(257\) | −1.22550e12 | −1.09307 | −0.546536 | − | 0.837436i | \(-0.684054\pi\) | ||||
−0.546536 | + | 0.837436i | \(0.684054\pi\) | |||||||
\(258\) | −1.42455e12 | −1.24617 | ||||||||
\(259\) | 2.29919e12i | 1.97277i | ||||||||
\(260\) | 2.55325e12i | 2.14896i | ||||||||
\(261\) | −2.05558e11 | −0.169719 | ||||||||
\(262\) | 6.83782e11 | 0.553874 | ||||||||
\(263\) | −6.51338e11 | −0.517640 | −0.258820 | − | 0.965926i | \(-0.583334\pi\) | ||||
−0.258820 | + | 0.965926i | \(0.583334\pi\) | |||||||
\(264\) | −6.27292e11 | −0.489159 | ||||||||
\(265\) | 2.83820e11 | 0.217177 | ||||||||
\(266\) | 3.56108e12i | 2.67407i | ||||||||
\(267\) | 5.75700e11i | 0.424268i | ||||||||
\(268\) | 1.35804e12i | 0.982288i | ||||||||
\(269\) | − | 1.20428e11i | − | 0.0855000i | −0.999086 | − | 0.0427500i | \(-0.986388\pi\) | ||
0.999086 | − | 0.0427500i | \(-0.0136119\pi\) | |||||||
\(270\) | − | 5.76421e11i | − | 0.401718i | ||||||
\(271\) | −1.19542e12 | −0.817854 | −0.408927 | − | 0.912567i | \(-0.634097\pi\) | ||||
−0.408927 | + | 0.912567i | \(0.634097\pi\) | |||||||
\(272\) | 7.95969e9 | 0.00534628 | ||||||||
\(273\) | 1.68486e12i | 1.11109i | ||||||||
\(274\) | 1.28183e12i | 0.829998i | ||||||||
\(275\) | 5.95266e11i | 0.378484i | ||||||||
\(276\) | − | 1.88725e12i | − | 1.17837i | ||||||
\(277\) | 8.81594e11 | 0.540592 | 0.270296 | − | 0.962777i | \(-0.412878\pi\) | ||||
0.270296 | + | 0.962777i | \(0.412878\pi\) | |||||||
\(278\) | 3.40752e12i | 2.05218i | ||||||||
\(279\) | 5.50561e11i | 0.325675i | ||||||||
\(280\) | − | 5.50254e12i | − | 3.19722i | ||||||
\(281\) | −1.00101e12 | −0.571356 | −0.285678 | − | 0.958326i | \(-0.592219\pi\) | ||||
−0.285678 | + | 0.958326i | \(0.592219\pi\) | |||||||
\(282\) | 3.87009e11 | 0.217008 | ||||||||
\(283\) | − | 2.60213e12i | − | 1.43350i | −0.697332 | − | 0.716748i | \(-0.745630\pi\) | ||
0.697332 | − | 0.716748i | \(-0.254370\pi\) | |||||||
\(284\) | 2.49097e12 | 1.34827 | ||||||||
\(285\) | −1.10008e12 | −0.585062 | ||||||||
\(286\) | 2.03696e12i | 1.06452i | ||||||||
\(287\) | 5.56339e12 | 2.85713 | ||||||||
\(288\) | − | 4.46917e11i | − | 0.225561i | ||||||
\(289\) | −2.01556e12 | −0.999784 | ||||||||
\(290\) | − | 2.17994e12i | − | 1.06281i | ||||||
\(291\) | 2.00314e12i | 0.959945i | ||||||||
\(292\) | − | 4.49685e12i | − | 2.11833i | ||||||
\(293\) | 1.90454e12 | 0.881967 | 0.440984 | − | 0.897515i | \(-0.354630\pi\) | ||||
0.440984 | + | 0.897515i | \(0.354630\pi\) | |||||||
\(294\) | − | 6.23374e12i | − | 2.83800i | ||||||
\(295\) | 1.57435e12 | + | 2.31771e12i | 0.704680 | + | 1.03741i | ||||
\(296\) | 2.89077e12 | 1.27220 | ||||||||
\(297\) | − | 2.93868e11i | − | 0.127166i | ||||||
\(298\) | 7.89336e11 | 0.335877 | ||||||||
\(299\) | −2.66668e12 | −1.11587 | ||||||||
\(300\) | 1.42266e12 | 0.585457 | ||||||||
\(301\) | − | 6.37063e12i | − | 2.57840i | ||||||
\(302\) | 5.09230e11 | 0.202712 | ||||||||
\(303\) | − | 2.12096e12i | − | 0.830462i | ||||||
\(304\) | 7.63237e11 | 0.293962 | ||||||||
\(305\) | − | 3.20904e12i | − | 1.21584i | ||||||
\(306\) | 2.18746e10i | 0.00815330i | ||||||||
\(307\) | −3.59170e12 | −1.31707 | −0.658533 | − | 0.752552i | \(-0.728823\pi\) | ||||
−0.658533 | + | 0.752552i | \(0.728823\pi\) | |||||||
\(308\) | − | 6.44682e12i | − | 2.32590i | ||||||
\(309\) | 1.43282e12i | 0.508627i | ||||||||
\(310\) | −5.83871e12 | −2.03943 | ||||||||
\(311\) | −4.45288e12 | −1.53052 | −0.765261 | − | 0.643721i | \(-0.777390\pi\) | ||||
−0.765261 | + | 0.643721i | \(0.777390\pi\) | |||||||
\(312\) | 2.11837e12 | 0.716522 | ||||||||
\(313\) | − | 3.68117e12i | − | 1.22536i | −0.790330 | − | 0.612681i | \(-0.790091\pi\) | ||
0.790330 | − | 0.612681i | \(-0.209909\pi\) | |||||||
\(314\) | −8.58428e12 | −2.81226 | ||||||||
\(315\) | 2.57778e12 | 0.831176 | ||||||||
\(316\) | −1.02260e13 | −3.24543 | ||||||||
\(317\) | 2.44545e12 | 0.763947 | 0.381974 | − | 0.924173i | \(-0.375245\pi\) | ||||
0.381974 | + | 0.924173i | \(0.375245\pi\) | |||||||
\(318\) | − | 5.41153e11i | − | 0.166412i | ||||||
\(319\) | − | 1.11137e12i | − | 0.336438i | ||||||
\(320\) | 6.27047e12 | 1.86875 | ||||||||
\(321\) | −1.23363e12 | −0.361960 | ||||||||
\(322\) | 1.32072e13 | 3.81531 | ||||||||
\(323\) | 4.17471e10 | 0.0118745 | ||||||||
\(324\) | −7.02333e11 | −0.196706 | ||||||||
\(325\) | − | 2.01022e12i | − | 0.554405i | ||||||
\(326\) | − | 1.17106e13i | − | 3.18046i | ||||||
\(327\) | 8.24139e11i | 0.220426i | ||||||||
\(328\) | − | 6.99486e12i | − | 1.84251i | ||||||
\(329\) | 1.73072e12i | 0.449001i | ||||||||
\(330\) | 3.11648e12 | 0.796333 | ||||||||
\(331\) | 5.22488e11 | 0.131503 | 0.0657517 | − | 0.997836i | \(-0.479055\pi\) | ||||
0.0657517 | + | 0.997836i | \(0.479055\pi\) | |||||||
\(332\) | − | 1.88203e12i | − | 0.466592i | ||||||
\(333\) | 1.35424e12i | 0.330731i | ||||||||
\(334\) | − | 5.71474e12i | − | 1.37488i | ||||||
\(335\) | − | 2.93588e12i | − | 0.695847i | ||||||
\(336\) | −1.78846e12 | −0.417621 | ||||||||
\(337\) | 1.68684e12i | 0.388083i | 0.980993 | + | 0.194041i | \(0.0621596\pi\) | ||||
−0.980993 | + | 0.194041i | \(0.937840\pi\) | |||||||
\(338\) | 4.63792e11i | 0.105133i | ||||||||
\(339\) | − | 1.20485e12i | − | 0.269113i | ||||||
\(340\) | −1.48244e11 | −0.0326274 | ||||||||
\(341\) | −2.97666e12 | −0.645592 | ||||||||
\(342\) | 2.09751e12i | 0.448305i | ||||||||
\(343\) | 1.84380e13 | 3.88368 | ||||||||
\(344\) | −8.00981e12 | −1.66276 | ||||||||
\(345\) | 4.07994e12i | 0.834753i | ||||||||
\(346\) | −3.91438e11 | −0.0789372 | ||||||||
\(347\) | − | 3.48479e12i | − | 0.692674i | −0.938110 | − | 0.346337i | \(-0.887425\pi\) | ||
0.938110 | − | 0.346337i | \(-0.112575\pi\) | |||||||
\(348\) | −2.65612e12 | −0.520418 | ||||||||
\(349\) | 3.17418e12i | 0.613062i | 0.951861 | + | 0.306531i | \(0.0991684\pi\) | ||||
−0.951861 | + | 0.306531i | \(0.900832\pi\) | |||||||
\(350\) | 9.95593e12i | 1.89558i | ||||||||
\(351\) | 9.92397e11i | 0.186273i | ||||||||
\(352\) | 2.41630e12 | 0.447134 | ||||||||
\(353\) | 7.96464e12i | 1.45309i | 0.687118 | + | 0.726545i | \(0.258875\pi\) | ||||
−0.687118 | + | 0.726545i | \(0.741125\pi\) | |||||||
\(354\) | 4.41914e12 | − | 3.00179e12i | 0.794916 | − | 0.539963i | ||||
\(355\) | −5.38510e12 | −0.955106 | ||||||||
\(356\) | 7.43893e12i | 1.30095i | ||||||||
\(357\) | −9.78242e10 | −0.0168696 | ||||||||
\(358\) | −1.25408e13 | −2.13260 | ||||||||
\(359\) | 1.00989e13 | 1.69357 | 0.846783 | − | 0.531939i | \(-0.178536\pi\) | ||||
0.846783 | + | 0.531939i | \(0.178536\pi\) | |||||||
\(360\) | − | 3.24105e12i | − | 0.536010i | ||||||
\(361\) | −2.12803e12 | −0.347089 | ||||||||
\(362\) | − | 1.29989e13i | − | 2.09105i | ||||||
\(363\) | −2.05009e12 | −0.325267 | ||||||||
\(364\) | 2.17710e13i | 3.40699i | ||||||||
\(365\) | 9.72151e12i | 1.50062i | ||||||||
\(366\) | −6.11862e12 | −0.931639 | ||||||||
\(367\) | − | 2.77661e12i | − | 0.417046i | −0.978017 | − | 0.208523i | \(-0.933134\pi\) | ||
0.978017 | − | 0.208523i | \(-0.0668657\pi\) | |||||||
\(368\) | − | 2.83066e12i | − | 0.419419i | ||||||
\(369\) | 3.27689e12 | 0.478994 | ||||||||
\(370\) | −1.43618e13 | −2.07109 | ||||||||
\(371\) | 2.42006e12 | 0.344315 | ||||||||
\(372\) | 7.11410e12i | 0.998631i | ||||||||
\(373\) | −1.13795e13 | −1.57608 | −0.788042 | − | 0.615621i | \(-0.788905\pi\) | ||||
−0.788042 | + | 0.615621i | \(0.788905\pi\) | |||||||
\(374\) | −1.18267e11 | −0.0161625 | ||||||||
\(375\) | 2.29389e12 | 0.309326 | ||||||||
\(376\) | 2.17604e12 | 0.289553 | ||||||||
\(377\) | 3.75311e12i | 0.492815i | ||||||||
\(378\) | − | 4.91500e12i | − | 0.636890i | ||||||
\(379\) | 8.15104e12 | 1.04236 | 0.521179 | − | 0.853447i | \(-0.325492\pi\) | ||||
0.521179 | + | 0.853447i | \(0.325492\pi\) | |||||||
\(380\) | −1.42148e13 | −1.79400 | ||||||||
\(381\) | −5.42227e10 | −0.00675392 | ||||||||
\(382\) | −2.18693e12 | −0.268854 | ||||||||
\(383\) | 7.96658e12 | 0.966670 | 0.483335 | − | 0.875435i | \(-0.339425\pi\) | ||||
0.483335 | + | 0.875435i | \(0.339425\pi\) | |||||||
\(384\) | − | 8.69381e12i | − | 1.04125i | ||||||
\(385\) | 1.39370e13i | 1.64766i | ||||||||
\(386\) | − | 1.08523e13i | − | 1.26644i | ||||||
\(387\) | − | 3.75236e12i | − | 0.432265i | ||||||
\(388\) | 2.58837e13i | 2.94352i | ||||||||
\(389\) | 9.34395e12 | 1.04902 | 0.524509 | − | 0.851405i | \(-0.324249\pi\) | ||||
0.524509 | + | 0.851405i | \(0.324249\pi\) | |||||||
\(390\) | −1.05244e13 | −1.16647 | ||||||||
\(391\) | − | 1.54830e11i | − | 0.0169422i | ||||||
\(392\) | − | 3.50504e13i | − | 3.78672i | ||||||
\(393\) | 1.80113e12i | 0.192125i | ||||||||
\(394\) | 2.28402e13i | 2.40557i | ||||||||
\(395\) | 2.21071e13 | 2.29904 | ||||||||
\(396\) | − | 3.79724e12i | − | 0.389934i | ||||||
\(397\) | − | 9.32716e12i | − | 0.945795i | −0.881118 | − | 0.472897i | \(-0.843208\pi\) | ||
0.881118 | − | 0.472897i | \(-0.156792\pi\) | |||||||
\(398\) | 2.04759e13i | 2.05035i | ||||||||
\(399\) | −9.38015e12 | −0.927567 | ||||||||
\(400\) | 2.13383e12 | 0.208382 | ||||||||
\(401\) | − | 1.61068e13i | − | 1.55342i | −0.629860 | − | 0.776709i | \(-0.716888\pi\) | ||
0.629860 | − | 0.776709i | \(-0.283112\pi\) | |||||||
\(402\) | −5.59778e12 | −0.533194 | ||||||||
\(403\) | 1.00522e13 | 0.945665 | ||||||||
\(404\) | − | 2.74061e13i | − | 2.54648i | ||||||
\(405\) | 1.51834e12 | 0.139345 | ||||||||
\(406\) | − | 1.85878e13i | − | 1.68500i | ||||||
\(407\) | −7.32186e12 | −0.655616 | ||||||||
\(408\) | 1.22995e11i | 0.0108789i | ||||||||
\(409\) | 2.87907e12i | 0.251557i | 0.992058 | + | 0.125778i | \(0.0401429\pi\) | ||||
−0.992058 | + | 0.125778i | \(0.959857\pi\) | |||||||
\(410\) | 3.47515e13i | 2.99954i | ||||||||
\(411\) | −3.37643e12 | −0.287905 | ||||||||
\(412\) | 1.85143e13i | 1.55963i | ||||||||
\(413\) | 1.34241e13 | + | 1.97626e13i | 1.11721 | + | 1.64472i | ||||
\(414\) | 7.77914e12 | 0.639631 | ||||||||
\(415\) | 4.06867e12i | 0.330531i | ||||||||
\(416\) | −8.15988e12 | −0.654963 | ||||||||
\(417\) | −8.97567e12 | −0.711847 | ||||||||
\(418\) | −1.13404e13 | −0.888684 | ||||||||
\(419\) | 2.00459e13i | 1.55223i | 0.630593 | + | 0.776114i | \(0.282812\pi\) | ||||
−0.630593 | + | 0.776114i | \(0.717188\pi\) | |||||||
\(420\) | 3.33089e13 | 2.54867 | ||||||||
\(421\) | − | 4.88487e12i | − | 0.369354i | −0.982799 | − | 0.184677i | \(-0.940876\pi\) | ||
0.982799 | − | 0.184677i | \(-0.0591239\pi\) | |||||||
\(422\) | 2.51223e13 | 1.87714 | ||||||||
\(423\) | 1.01941e12i | 0.0752745i | ||||||||
\(424\) | − | 3.04274e12i | − | 0.222043i | ||||||
\(425\) | 1.16715e11 | 0.00841748 | ||||||||
\(426\) | 1.02677e13i | 0.731852i | ||||||||
\(427\) | − | 2.73627e13i | − | 1.92761i | ||||||
\(428\) | −1.59405e13 | −1.10989 | ||||||||
\(429\) | −5.36550e12 | −0.369253 | ||||||||
\(430\) | 3.97939e13 | 2.70691 | ||||||||
\(431\) | − | 1.53241e13i | − | 1.03036i | −0.857083 | − | 0.515178i | \(-0.827726\pi\) | ||
0.857083 | − | 0.515178i | \(-0.172274\pi\) | |||||||
\(432\) | −1.05342e12 | −0.0700136 | ||||||||
\(433\) | −5.71238e12 | −0.375299 | −0.187649 | − | 0.982236i | \(-0.560087\pi\) | ||||
−0.187649 | + | 0.982236i | \(0.560087\pi\) | |||||||
\(434\) | −4.97852e13 | −3.23334 | ||||||||
\(435\) | 5.74213e12 | 0.368661 | ||||||||
\(436\) | 1.06492e13i | 0.675901i | ||||||||
\(437\) | − | 1.48463e13i | − | 0.931559i | ||||||
\(438\) | 1.85358e13 | 1.14985 | ||||||||
\(439\) | 4.08315e11 | 0.0250422 | 0.0125211 | − | 0.999922i | \(-0.496014\pi\) | ||||
0.0125211 | + | 0.999922i | \(0.496014\pi\) | |||||||
\(440\) | 1.75231e13 | 1.06254 | ||||||||
\(441\) | 1.64201e13 | 0.984427 | ||||||||
\(442\) | 3.99391e11 | 0.0236748 | ||||||||
\(443\) | 2.05868e13i | 1.20662i | 0.797507 | + | 0.603309i | \(0.206151\pi\) | ||||
−0.797507 | + | 0.603309i | \(0.793849\pi\) | |||||||
\(444\) | 1.74989e13i | 1.01414i | ||||||||
\(445\) | − | 1.60818e13i | − | 0.921586i | ||||||
\(446\) | 8.95494e12i | 0.507444i | ||||||||
\(447\) | 2.07917e12i | 0.116507i | ||||||||
\(448\) | 5.34668e13 | 2.96274 | ||||||||
\(449\) | 2.14624e13 | 1.17611 | 0.588053 | − | 0.808823i | \(-0.299895\pi\) | ||||
0.588053 | + | 0.808823i | \(0.299895\pi\) | |||||||
\(450\) | 5.86414e12i | 0.317791i | ||||||||
\(451\) | 1.77168e13i | 0.949519i | ||||||||
\(452\) | − | 1.55685e13i | − | 0.825193i | ||||||
\(453\) | 1.34135e12i | 0.0703154i | ||||||||
\(454\) | −5.05056e13 | −2.61855 | ||||||||
\(455\) | − | 4.70655e13i | − | 2.41349i | ||||||
\(456\) | 1.17937e13i | 0.598170i | ||||||||
\(457\) | 9.36974e12i | 0.470053i | 0.971989 | + | 0.235026i | \(0.0755176\pi\) | ||||
−0.971989 | + | 0.235026i | \(0.924482\pi\) | |||||||
\(458\) | −5.75054e13 | −2.85352 | ||||||||
\(459\) | −5.76194e10 | −0.00282817 | ||||||||
\(460\) | 5.27191e13i | 2.55964i | ||||||||
\(461\) | −1.08135e13 | −0.519352 | −0.259676 | − | 0.965696i | \(-0.583616\pi\) | ||||
−0.259676 | + | 0.965696i | \(0.583616\pi\) | |||||||
\(462\) | 2.65735e13 | 1.26252 | ||||||||
\(463\) | 3.90979e13i | 1.83759i | 0.394736 | + | 0.918794i | \(0.370836\pi\) | ||||
−0.394736 | + | 0.918794i | \(0.629164\pi\) | |||||||
\(464\) | −3.98389e12 | −0.185232 | ||||||||
\(465\) | − | 1.53796e13i | − | 0.707425i | ||||||
\(466\) | −4.97743e13 | −2.26504 | ||||||||
\(467\) | − | 3.31716e13i | − | 1.49342i | −0.665150 | − | 0.746710i | \(-0.731633\pi\) | ||
0.665150 | − | 0.746710i | \(-0.268367\pi\) | |||||||
\(468\) | 1.28233e13i | 0.571177i | ||||||||
\(469\) | − | 2.50335e13i | − | 1.10321i | ||||||
\(470\) | −1.08109e13 | −0.471381 | ||||||||
\(471\) | − | 2.26116e13i | − | 0.975500i | ||||||
\(472\) | 2.48475e13 | − | 1.68782e13i | 1.06065 | − | 0.720469i | ||||
\(473\) | 2.02875e13 | 0.856888 | ||||||||
\(474\) | − | 4.21512e13i | − | 1.76165i | ||||||
\(475\) | 1.11915e13 | 0.462831 | ||||||||
\(476\) | −1.26404e12 | −0.0517281 | ||||||||
\(477\) | 1.42544e12 | 0.0577240 | ||||||||
\(478\) | − | 2.03751e13i | − | 0.816507i | ||||||
\(479\) | 1.19299e12 | 0.0473106 | 0.0236553 | − | 0.999720i | \(-0.492470\pi\) | ||||
0.0236553 | + | 0.999720i | \(0.492470\pi\) | |||||||
\(480\) | 1.24844e13i | 0.489959i | ||||||||
\(481\) | 2.47260e13 | 0.960348 | ||||||||
\(482\) | 5.09873e13i | 1.95987i | ||||||||
\(483\) | 3.47886e13i | 1.32343i | ||||||||
\(484\) | −2.64903e13 | −0.997380 | ||||||||
\(485\) | − | 5.59565e13i | − | 2.08517i | ||||||
\(486\) | − | 2.89498e12i | − | 0.106774i | ||||||
\(487\) | −3.05250e13 | −1.11432 | −0.557162 | − | 0.830404i | \(-0.688110\pi\) | ||||
−0.557162 | + | 0.830404i | \(0.688110\pi\) | |||||||
\(488\) | −3.44032e13 | −1.24308 | ||||||||
\(489\) | 3.08465e13 | 1.10322 | ||||||||
\(490\) | 1.74136e14i | 6.16464i | ||||||||
\(491\) | −1.04431e13 | −0.365949 | −0.182975 | − | 0.983118i | \(-0.558573\pi\) | ||||
−0.182975 | + | 0.983118i | \(0.558573\pi\) | |||||||
\(492\) | 4.23425e13 | 1.46876 | ||||||||
\(493\) | −2.17908e11 | −0.00748238 | ||||||||
\(494\) | 3.82967e13 | 1.30175 | ||||||||
\(495\) | 8.20904e12i | 0.276227i | ||||||||
\(496\) | 1.06703e13i | 0.355443i | ||||||||
\(497\) | −4.59174e13 | −1.51424 | ||||||||
\(498\) | 7.75765e12 | 0.253270 | ||||||||
\(499\) | −2.85799e13 | −0.923759 | −0.461880 | − | 0.886943i | \(-0.652825\pi\) | ||||
−0.461880 | + | 0.886943i | \(0.652825\pi\) | |||||||
\(500\) | 2.96406e13 | 0.948500 | ||||||||
\(501\) | 1.50531e13 | 0.476909 | ||||||||
\(502\) | − | 2.42580e12i | − | 0.0760915i | ||||||
\(503\) | − | 3.67887e13i | − | 1.14255i | −0.820759 | − | 0.571275i | \(-0.806449\pi\) | ||
0.820759 | − | 0.571275i | \(-0.193551\pi\) | |||||||
\(504\) | − | 2.76356e13i | − | 0.849799i | ||||||
\(505\) | 5.92478e13i | 1.80391i | ||||||||
\(506\) | 4.20587e13i | 1.26795i | ||||||||
\(507\) | −1.22166e12 | −0.0364679 | ||||||||
\(508\) | −7.00641e11 | −0.0207099 | ||||||||
\(509\) | 2.57696e13i | 0.754257i | 0.926161 | + | 0.377128i | \(0.123088\pi\) | ||||
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(510\) | − | 6.11055e11i | − | 0.0177104i | ||||||
\(511\) | 8.28929e13i | 2.37910i | ||||||||
\(512\) | − | 2.50741e13i | − | 0.712648i | ||||||
\(513\) | −5.52500e12 | −0.155505 | ||||||||
\(514\) | − | 6.52727e13i | − | 1.81935i | ||||||
\(515\) | − | 4.00250e13i | − | 1.10483i | ||||||
\(516\) | − | 4.84864e13i | − | 1.32547i | ||||||
\(517\) | −5.51155e12 | −0.149218 | ||||||||
\(518\) | −1.22459e14 | −3.28355 | ||||||||
\(519\) | − | 1.03108e12i | − | 0.0273813i | ||||||
\(520\) | −5.91756e13 | −1.55642 | ||||||||
\(521\) | −1.98770e13 | −0.517801 | −0.258900 | − | 0.965904i | \(-0.583360\pi\) | ||||
−0.258900 | + | 0.965904i | \(0.583360\pi\) | |||||||
\(522\) | − | 1.09484e13i | − | 0.282487i | ||||||
\(523\) | −1.60013e13 | −0.408927 | −0.204463 | − | 0.978874i | \(-0.565545\pi\) | ||||
−0.204463 | + | 0.978874i | \(0.565545\pi\) | |||||||
\(524\) | 2.32734e13i | 0.589120i | ||||||||
\(525\) | −2.62247e13 | −0.657527 | ||||||||
\(526\) | − | 3.46916e13i | − | 0.861579i | ||||||
\(527\) | 5.83641e11i | 0.0143580i | ||||||||
\(528\) | − | 5.69542e12i | − | 0.138789i | ||||||
\(529\) | −1.36346e13 | −0.329127 | ||||||||
\(530\) | 1.51168e13i | 0.361477i | ||||||||
\(531\) | 7.90693e12 | + | 1.16403e13i | 0.187299 | + | 0.275736i | ||||
\(532\) | −1.21206e14 | −2.84424 | ||||||||
\(533\) | − | 5.98300e13i | − | 1.39086i | ||||||
\(534\) | −3.06629e13 | −0.706167 | ||||||||
\(535\) | 3.44608e13 | 0.786243 | ||||||||
\(536\) | −3.14747e13 | −0.711438 | ||||||||
\(537\) | − | 3.30333e13i | − | 0.739743i | ||||||
\(538\) | 6.41424e12 | 0.142309 | ||||||||
\(539\) | 8.87771e13i | 1.95145i | ||||||||
\(540\) | 1.96193e13 | 0.427281 | ||||||||
\(541\) | − | 7.78574e13i | − | 1.68002i | −0.542573 | − | 0.840008i | \(-0.682550\pi\) | ||
0.542573 | − | 0.840008i | \(-0.317450\pi\) | |||||||
\(542\) | − | 6.36707e13i | − | 1.36127i | ||||||
\(543\) | 3.42402e13 | 0.725332 | ||||||||
\(544\) | − | 4.73769e11i | − | 0.00994426i | ||||||
\(545\) | − | 2.30219e13i | − | 0.478804i | ||||||
\(546\) | −8.97389e13 | −1.84934 | ||||||||
\(547\) | −3.95256e13 | −0.807127 | −0.403563 | − | 0.914952i | \(-0.632229\pi\) | ||||
−0.403563 | + | 0.914952i | \(0.632229\pi\) | |||||||
\(548\) | −4.36287e13 | −0.882815 | ||||||||
\(549\) | − | 1.61169e13i | − | 0.323161i | ||||||
\(550\) | −3.17051e13 | −0.629964 | ||||||||
\(551\) | −2.08948e13 | −0.411414 | ||||||||
\(552\) | 4.37398e13 | 0.853456 | ||||||||
\(553\) | 1.88502e14 | 3.64494 | ||||||||
\(554\) | 4.69555e13i | 0.899782i | ||||||||
\(555\) | − | 3.78300e13i | − | 0.718408i | ||||||
\(556\) | −1.15980e14 | −2.18277 | ||||||||
\(557\) | −5.66900e13 | −1.05738 | −0.528689 | − | 0.848815i | \(-0.677316\pi\) | ||||
−0.528689 | + | 0.848815i | \(0.677316\pi\) | |||||||
\(558\) | −2.93240e13 | −0.542066 | ||||||||
\(559\) | −6.85113e13 | −1.25517 | ||||||||
\(560\) | 4.99596e13 | 0.907149 | ||||||||
\(561\) | − | 3.11525e11i | − | 0.00560633i | ||||||
\(562\) | − | 5.33158e13i | − | 0.950987i | ||||||
\(563\) | 2.79964e13i | 0.494949i | 0.968894 | + | 0.247475i | \(0.0796007\pi\) | ||||
−0.968894 | + | 0.247475i | \(0.920399\pi\) | |||||||
\(564\) | 1.31724e13i | 0.230817i | ||||||||
\(565\) | 3.36568e13i | 0.584562i | ||||||||
\(566\) | 1.38595e14 | 2.38597 | ||||||||
\(567\) | 1.29465e13 | 0.220921 | ||||||||
\(568\) | 5.77320e13i | 0.976506i | ||||||||
\(569\) | − | 8.11572e13i | − | 1.36071i | −0.732883 | − | 0.680355i | \(-0.761826\pi\) | ||
0.732883 | − | 0.680355i | \(-0.238174\pi\) | |||||||
\(570\) | − | 5.85927e13i | − | 0.973799i | ||||||
\(571\) | 4.68005e13i | 0.771027i | 0.922702 | + | 0.385514i | \(0.125976\pi\) | ||||
−0.922702 | + | 0.385514i | \(0.874024\pi\) | |||||||
\(572\) | −6.93306e13 | −1.13226 | ||||||||
\(573\) | − | 5.76052e12i | − | 0.0932586i | ||||||
\(574\) | 2.96317e14i | 4.75552i | ||||||||
\(575\) | − | 4.15066e13i | − | 0.660356i | ||||||
\(576\) | 3.14924e13 | 0.496700 | ||||||||
\(577\) | −2.26889e13 | −0.354759 | −0.177380 | − | 0.984143i | \(-0.556762\pi\) | ||||
−0.177380 | + | 0.984143i | \(0.556762\pi\) | |||||||
\(578\) | − | 1.07353e14i | − | 1.66408i | ||||||
\(579\) | 2.85857e13 | 0.439295 | ||||||||
\(580\) | 7.41973e13 | 1.13044 | ||||||||
\(581\) | 3.46925e13i | 0.524029i | ||||||||
\(582\) | −1.06691e14 | −1.59777 | ||||||||
\(583\) | 7.70678e12i | 0.114427i | ||||||||
\(584\) | 1.04221e14 | 1.53424 | ||||||||
\(585\) | − | 2.77220e13i | − | 0.404619i | ||||||
\(586\) | 1.01440e14i | 1.46798i | ||||||||
\(587\) | 6.53314e13i | 0.937415i | 0.883354 | + | 0.468707i | \(0.155280\pi\) | ||||
−0.883354 | + | 0.468707i | \(0.844720\pi\) | |||||||
\(588\) | 2.12173e14 | 3.01859 | ||||||||
\(589\) | 5.59640e13i | 0.789464i | ||||||||
\(590\) | −1.23446e14 | + | 8.38532e13i | −1.72670 | + | 1.17290i | ||||
\(591\) | −6.01628e13 | −0.834431 | ||||||||
\(592\) | 2.62464e13i | 0.360962i | ||||||||
\(593\) | −4.03338e13 | −0.550042 | −0.275021 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275021 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(594\) | 1.56520e13 | 0.211660 | ||||||||
\(595\) | 2.73266e12 | 0.0366439 | ||||||||
\(596\) | 2.68661e13i | 0.357251i | ||||||||
\(597\) | −5.39350e13 | −0.711211 | ||||||||
\(598\) | − | 1.42033e14i | − | 1.85730i | ||||||
\(599\) | 1.23104e13 | 0.159639 | 0.0798195 | − | 0.996809i | \(-0.474566\pi\) | ||||
0.0798195 | + | 0.996809i | \(0.474566\pi\) | |||||||
\(600\) | 3.29723e13i | 0.424027i | ||||||||
\(601\) | − | 1.21795e14i | − | 1.55331i | −0.629926 | − | 0.776655i | \(-0.716915\pi\) | ||
0.629926 | − | 0.776655i | \(-0.283085\pi\) | |||||||
\(602\) | 3.39313e14 | 4.29159 | ||||||||
\(603\) | − | 1.47450e13i | − | 0.184951i | ||||||
\(604\) | 1.73323e13i | 0.215611i | ||||||||
\(605\) | 5.72681e13 | 0.706538 | ||||||||
\(606\) | 1.12967e14 | 1.38225 | ||||||||
\(607\) | −6.22812e13 | −0.755811 | −0.377906 | − | 0.925844i | \(-0.623356\pi\) | ||||
−0.377906 | + | 0.925844i | \(0.623356\pi\) | |||||||
\(608\) | − | 4.54287e13i | − | 0.546779i | ||||||
\(609\) | 4.89618e13 | 0.584481 | ||||||||
\(610\) | 1.70920e14 | 2.02369 | ||||||||
\(611\) | 1.86126e13 | 0.218575 | ||||||||
\(612\) | −7.44532e11 | −0.00867214 | ||||||||
\(613\) | − | 8.79024e13i | − | 1.01554i | −0.861492 | − | 0.507772i | \(-0.830469\pi\) | ||
0.861492 | − | 0.507772i | \(-0.169531\pi\) | |||||||
\(614\) | − | 1.91301e14i | − | 2.19218i | ||||||
\(615\) | −9.15380e13 | −1.04046 | ||||||||
\(616\) | 1.49415e14 | 1.68457 | ||||||||
\(617\) | 5.58242e12 | 0.0624304 | 0.0312152 | − | 0.999513i | \(-0.490062\pi\) | ||||
0.0312152 | + | 0.999513i | \(0.490062\pi\) | |||||||
\(618\) | −7.63149e13 | −0.846578 | ||||||||
\(619\) | −5.46830e13 | −0.601726 | −0.300863 | − | 0.953667i | \(-0.597275\pi\) | ||||
−0.300863 | + | 0.953667i | \(0.597275\pi\) | |||||||
\(620\) | − | 1.98728e14i | − | 2.16921i | ||||||
\(621\) | 2.04908e13i | 0.221871i | ||||||||
\(622\) | − | 2.37170e14i | − | 2.54746i | ||||||
\(623\) | − | 1.37126e14i | − | 1.46110i | ||||||
\(624\) | 1.92335e13i | 0.203299i | ||||||||
\(625\) | −1.18704e14 | −1.24470 | ||||||||
\(626\) | 1.96067e14 | 2.03954 | ||||||||
\(627\) | − | 2.98715e13i | − | 0.308261i | ||||||
\(628\) | − | 2.92177e14i | − | 2.99122i | ||||||
\(629\) | 1.43561e12i | 0.0145809i | ||||||||
\(630\) | 1.37298e14i | 1.38344i | ||||||||
\(631\) | 3.18938e13 | 0.318830 | 0.159415 | − | 0.987212i | \(-0.449039\pi\) | ||||
0.159415 | + | 0.987212i | \(0.449039\pi\) | |||||||
\(632\) | − | 2.37004e14i | − | 2.35055i | ||||||
\(633\) | 6.61739e13i | 0.651130i | ||||||||
\(634\) | 1.30250e14i | 1.27154i | ||||||||
\(635\) | 1.51468e12 | 0.0146707 | ||||||||
\(636\) | 1.84189e13 | 0.177002 | ||||||||
\(637\) | − | 2.99801e14i | − | 2.85849i | ||||||
\(638\) | 5.91938e13 | 0.559980 | ||||||||
\(639\) | −2.70458e13 | −0.253861 | ||||||||
\(640\) | 2.42857e14i | 2.26178i | ||||||||
\(641\) | −5.15106e13 | −0.475999 | −0.238000 | − | 0.971265i | \(-0.576492\pi\) | ||||
−0.238000 | + | 0.971265i | \(0.576492\pi\) | |||||||
\(642\) | − | 6.57058e13i | − | 0.602460i | ||||||
\(643\) | −1.34620e14 | −1.22477 | −0.612387 | − | 0.790558i | \(-0.709791\pi\) | ||||
−0.612387 | + | 0.790558i | \(0.709791\pi\) | |||||||
\(644\) | 4.49523e14i | 4.05810i | ||||||||
\(645\) | 1.04820e14i | 0.938958i | ||||||||
\(646\) | 2.22354e12i | 0.0197643i | ||||||||
\(647\) | −1.82590e14 | −1.61048 | −0.805238 | − | 0.592951i | \(-0.797963\pi\) | ||||
−0.805238 | + | 0.592951i | \(0.797963\pi\) | |||||||
\(648\) | − | 1.62776e13i | − | 0.142468i | ||||||
\(649\) | −6.29347e13 | + | 4.27497e13i | −0.546596 | + | 0.371287i | ||||
\(650\) | 1.07068e14 | 0.922772 | ||||||||
\(651\) | − | 1.31138e14i | − | 1.12156i | ||||||
\(652\) | 3.98585e14 | 3.38285 | ||||||||
\(653\) | −1.37386e14 | −1.15712 | −0.578559 | − | 0.815640i | \(-0.696385\pi\) | ||||
−0.578559 | + | 0.815640i | \(0.696385\pi\) | |||||||
\(654\) | −4.38953e13 | −0.366885 | ||||||||
\(655\) | − | 5.03136e13i | − | 0.417329i | ||||||
\(656\) | 6.35090e13 | 0.522776 | ||||||||
\(657\) | 4.88247e13i | 0.398853i | ||||||||
\(658\) | −9.21817e13 | −0.747335 | ||||||||
\(659\) | − | 8.92668e13i | − | 0.718229i | −0.933294 | − | 0.359114i | \(-0.883079\pi\) | ||
0.933294 | − | 0.359114i | \(-0.116921\pi\) | |||||||
\(660\) | 1.06074e14i | 0.847008i | ||||||||
\(661\) | 1.21953e14 | 0.966461 | 0.483230 | − | 0.875493i | \(-0.339463\pi\) | ||||
0.483230 | + | 0.875493i | \(0.339463\pi\) | |||||||
\(662\) | 2.78288e13i | 0.218879i | ||||||||
\(663\) | 1.05202e12i | 0.00821217i | ||||||||
\(664\) | 4.36190e13 | 0.337937 | ||||||||
\(665\) | 2.62029e14 | 2.01484 | ||||||||
\(666\) | −7.21297e13 | −0.550482 | ||||||||
\(667\) | 7.74934e13i | 0.586997i | ||||||||
\(668\) | 1.94509e14 | 1.46237 | ||||||||
\(669\) | −2.35880e13 | −0.176019 | ||||||||
\(670\) | 1.56371e14 | 1.15819 | ||||||||
\(671\) | 8.71377e13 | 0.640609 | ||||||||
\(672\) | 1.06451e14i | 0.776790i | ||||||||
\(673\) | 4.70316e12i | 0.0340655i | 0.999855 | + | 0.0170327i | \(0.00542195\pi\) | ||||
−0.999855 | + | 0.0170327i | \(0.994578\pi\) | |||||||
\(674\) | −8.98445e13 | −0.645940 | ||||||||
\(675\) | −1.54466e13 | −0.110233 | ||||||||
\(676\) | −1.57858e13 | −0.111823 | ||||||||
\(677\) | 2.28104e14 | 1.60395 | 0.801974 | − | 0.597359i | \(-0.203783\pi\) | ||||
0.801974 | + | 0.597359i | \(0.203783\pi\) | |||||||
\(678\) | 6.41728e13 | 0.447922 | ||||||||
\(679\) | − | 4.77128e14i | − | 3.30587i | ||||||
\(680\) | − | 3.43578e12i | − | 0.0236309i | ||||||
\(681\) | − | 1.33036e14i | − | 0.908306i | ||||||
\(682\) | − | 1.58543e14i | − | 1.07455i | ||||||
\(683\) | 2.29139e14i | 1.54168i | 0.637028 | + | 0.770841i | \(0.280164\pi\) | ||||
−0.637028 | + | 0.770841i | \(0.719836\pi\) | |||||||
\(684\) | −7.13915e13 | −0.476833 | ||||||||
\(685\) | 9.43187e13 | 0.625381 | ||||||||
\(686\) | 9.82045e14i | 6.46414i | ||||||||
\(687\) | − | 1.51474e14i | − | 0.989813i | ||||||
\(688\) | − | 7.27241e13i | − | 0.471776i | ||||||
\(689\) | − | 2.60259e13i | − | 0.167614i | ||||||
\(690\) | −2.17306e14 | −1.38939 | ||||||||
\(691\) | 2.46227e14i | 1.56295i | 0.623937 | + | 0.781474i | \(0.285532\pi\) | ||||
−0.623937 | + | 0.781474i | \(0.714468\pi\) | |||||||
\(692\) | − | 1.33231e13i | − | 0.0839604i | ||||||
\(693\) | 6.99965e13i | 0.437935i | ||||||||
\(694\) | 1.85607e14 | 1.15291 | ||||||||
\(695\) | 2.50730e14 | 1.54626 | ||||||||
\(696\) | − | 6.15597e13i | − | 0.376921i | ||||||
\(697\) | 3.47378e12 | 0.0211173 | ||||||||
\(698\) | −1.69063e14 | −1.02040 | ||||||||
\(699\) | − | 1.31109e14i | − | 0.785683i | ||||||
\(700\) | −3.38863e14 | −2.01620 | ||||||||
\(701\) | − | 1.24494e14i | − | 0.735462i | −0.929932 | − | 0.367731i | \(-0.880135\pi\) | ||
0.929932 | − | 0.367731i | \(-0.119865\pi\) | |||||||
\(702\) | −5.28571e13 | −0.310040 | ||||||||
\(703\) | 1.37658e14i | 0.801722i | ||||||||
\(704\) | 1.70267e14i | 0.984617i | ||||||||
\(705\) | − | 2.84767e13i | − | 0.163510i | ||||||
\(706\) | −4.24213e14 | −2.41858 | ||||||||
\(707\) | 5.05192e14i | 2.85995i | ||||||||
\(708\) | 1.02170e14 | + | 1.50411e14i | 0.574323 | + | 0.845501i | ||||
\(709\) | 5.03176e13 | 0.280859 | 0.140430 | − | 0.990091i | \(-0.455152\pi\) | ||||
0.140430 | + | 0.990091i | \(0.455152\pi\) | |||||||
\(710\) | − | 2.86821e14i | − | 1.58972i | ||||||
\(711\) | 1.11029e14 | 0.611069 | ||||||||
\(712\) | −1.72409e14 | −0.942234 | ||||||||
\(713\) | 2.07557e14 | 1.12639 | ||||||||
\(714\) | − | 5.21032e12i | − | 0.0280784i | ||||||
\(715\) | 1.49882e14 | 0.802083 | ||||||||
\(716\) | − | 4.26842e14i | − | 2.26831i | ||||||
\(717\) | 5.36695e13 | 0.283225 | ||||||||
\(718\) | 5.37888e14i | 2.81884i | ||||||||
\(719\) | 2.68377e14i | 1.39669i | 0.715760 | + | 0.698346i | \(0.246080\pi\) | ||||
−0.715760 | + | 0.698346i | \(0.753920\pi\) | |||||||
\(720\) | 2.94267e13 | 0.152082 | ||||||||
\(721\) | − | 3.41283e14i | − | 1.75162i | ||||||
\(722\) | − | 1.13343e14i | − | 0.577708i | ||||||
\(723\) | −1.34304e14 | −0.679827 | ||||||||
\(724\) | 4.42436e14 | 2.22412 | ||||||||
\(725\) | −5.84168e13 | −0.291640 | ||||||||
\(726\) | − | 1.09192e14i | − | 0.541386i | ||||||
\(727\) | 4.13444e13 | 0.203585 | 0.101792 | − | 0.994806i | \(-0.467542\pi\) | ||||
0.101792 | + | 0.994806i | \(0.467542\pi\) | |||||||
\(728\) | −5.04575e14 | −2.46757 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | −5.17787e14 | −2.49768 | ||||||||
\(731\) | − | 3.97782e12i | − | 0.0190572i | ||||||
\(732\) | − | 2.08255e14i | − | 0.990924i | ||||||
\(733\) | −1.84839e14 | −0.873522 | −0.436761 | − | 0.899578i | \(-0.643874\pi\) | ||||
−0.436761 | + | 0.899578i | \(0.643874\pi\) | |||||||
\(734\) | 1.47888e14 | 0.694148 | ||||||||
\(735\) | −4.58687e14 | −2.13835 | ||||||||
\(736\) | −1.68484e14 | −0.780133 | ||||||||
\(737\) | 7.97202e13 | 0.366632 | ||||||||
\(738\) | 1.74534e14i | 0.797256i | ||||||||
\(739\) | − | 2.88722e14i | − | 1.30996i | −0.755648 | − | 0.654978i | \(-0.772678\pi\) | ||
0.755648 | − | 0.654978i | \(-0.227322\pi\) | |||||||
\(740\) | − | 4.88822e14i | − | 2.20289i | ||||||
\(741\) | 1.00876e14i | 0.451542i | ||||||||
\(742\) | 1.28897e14i | 0.573092i | ||||||||
\(743\) | 1.09253e13 | 0.0482489 | 0.0241245 | − | 0.999709i | \(-0.492320\pi\) | ||||
0.0241245 | + | 0.999709i | \(0.492320\pi\) | |||||||
\(744\) | −1.64880e14 | −0.723275 | ||||||||
\(745\) | − | 5.80804e13i | − | 0.253074i | ||||||
\(746\) | − | 6.06096e14i | − | 2.62330i | ||||||
\(747\) | 2.04342e13i | 0.0878528i | ||||||||
\(748\) | − | 4.02539e12i | − | 0.0171910i | ||||||
\(749\) | 2.93839e14 | 1.24652 | ||||||||
\(750\) | 1.22177e14i | 0.514854i | ||||||||
\(751\) | 2.52489e14i | 1.05692i | 0.848957 | + | 0.528462i | \(0.177231\pi\) | ||||
−0.848957 | + | 0.528462i | \(0.822769\pi\) | |||||||
\(752\) | 1.97571e13i | 0.0821549i | ||||||||
\(753\) | 6.38974e12 | 0.0263942 | ||||||||
\(754\) | −1.99898e14 | −0.820261 | ||||||||
\(755\) | − | 3.74698e13i | − | 0.152738i | ||||||
\(756\) | 1.67289e14 | 0.677419 | ||||||||
\(757\) | 2.01417e14 | 0.810245 | 0.405122 | − | 0.914262i | \(-0.367229\pi\) | ||||
0.405122 | + | 0.914262i | \(0.367229\pi\) | |||||||
\(758\) | 4.34141e14i | 1.73494i | ||||||||
\(759\) | −1.10786e14 | −0.439820 | ||||||||
\(760\) | − | 3.29449e14i | − | 1.29933i | ||||||
\(761\) | 2.30842e14 | 0.904464 | 0.452232 | − | 0.891900i | \(-0.350628\pi\) | ||||
0.452232 | + | 0.891900i | \(0.350628\pi\) | |||||||
\(762\) | − | 2.88801e12i | − | 0.0112415i | ||||||
\(763\) | − | 1.96302e14i | − | 0.759104i | ||||||
\(764\) | − | 7.44349e13i | − | 0.285963i | ||||||
\(765\) | 1.60956e12 | 0.00614329 | ||||||||
\(766\) | 4.24316e14i | 1.60896i | ||||||||
\(767\) | 2.12531e14 | − | 1.44366e14i | 0.800656 | − | 0.543862i | ||||
\(768\) | 2.33192e14 | 0.872784 | ||||||||
\(769\) | − | 2.24358e14i | − | 0.834274i | −0.908844 | − | 0.417137i | \(-0.863033\pi\) | ||
0.908844 | − | 0.417137i | \(-0.136967\pi\) | |||||||
\(770\) | −7.42315e14 | −2.74242 | ||||||||
\(771\) | 1.71933e14 | 0.631085 | ||||||||
\(772\) | 3.69372e14 | 1.34703 | ||||||||
\(773\) | − | 4.66834e14i | − | 1.69147i | −0.533601 | − | 0.845737i | \(-0.679161\pi\) | ||
0.533601 | − | 0.845737i | \(-0.320839\pi\) | |||||||
\(774\) | 1.99859e14 | 0.719479 | ||||||||
\(775\) | 1.56462e14i | 0.559630i | ||||||||
\(776\) | −5.99893e14 | −2.13189 | ||||||||
\(777\) | − | 3.22567e14i | − | 1.13898i | ||||||
\(778\) | 4.97678e14i | 1.74602i | ||||||||
\(779\) | 3.33093e14 | 1.16112 | ||||||||
\(780\) | − | 3.58212e14i | − | 1.24070i | ||||||
\(781\) | − | 1.46226e14i | − | 0.503233i | ||||||
\(782\) | 8.24654e12 | 0.0281993 | ||||||||
\(783\) | 2.88389e13 | 0.0979875 | ||||||||
\(784\) | 3.18236e14 | 1.07441 | ||||||||
\(785\) | 6.31642e14i | 2.11896i | ||||||||
\(786\) | −9.59319e13 | −0.319779 | ||||||||
\(787\) | −4.35024e14 | −1.44092 | −0.720460 | − | 0.693496i | \(-0.756069\pi\) | ||||
−0.720460 | + | 0.693496i | \(0.756069\pi\) | |||||||
\(788\) | −7.77397e14 | −2.55865 | ||||||||
\(789\) | 9.13801e13 | 0.298859 | ||||||||
\(790\) | 1.17747e15i | 3.82661i | ||||||||
\(791\) | 2.86983e14i | 0.926774i | ||||||||
\(792\) | 8.80067e13 | 0.282416 | ||||||||
\(793\) | −2.94265e14 | −0.938366 | ||||||||
\(794\) | 4.96783e14 | 1.57422 | ||||||||
\(795\) | −3.98188e13 | −0.125387 | ||||||||
\(796\) | −6.96923e14 | −2.18082 | ||||||||
\(797\) | − | 4.75169e14i | − | 1.47760i | −0.673925 | − | 0.738800i | \(-0.735393\pi\) | ||
0.673925 | − | 0.738800i | \(-0.264607\pi\) | |||||||
\(798\) | − | 4.99606e14i | − | 1.54388i | ||||||
\(799\) | 1.08066e12i | 0.00331861i | ||||||||
\(800\) | − | 1.27008e14i | − | 0.387597i | ||||||
\(801\) | − | 8.07684e13i | − | 0.244951i | ||||||
\(802\) | 8.57883e14 | 2.58557 | ||||||||
\(803\) | −2.63976e14 | −0.790654 | ||||||||
\(804\) | − | 1.90528e14i | − | 0.567124i | ||||||
\(805\) | − | 9.71800e14i | − | 2.87473i | ||||||
\(806\) | 5.35402e14i | 1.57400i | ||||||||
\(807\) | 1.68956e13i | 0.0493634i | ||||||||
\(808\) | 6.35178e14 | 1.84433 | ||||||||
\(809\) | 2.54070e14i | 0.733180i | 0.930383 | + | 0.366590i | \(0.119475\pi\) | ||||
−0.930383 | + | 0.366590i | \(0.880525\pi\) | |||||||
\(810\) | 8.08697e13i | 0.231932i | ||||||||
\(811\) | − | 4.46779e14i | − | 1.27347i | −0.771083 | − | 0.636734i | \(-0.780285\pi\) | ||
0.771083 | − | 0.636734i | \(-0.219715\pi\) | |||||||
\(812\) | 6.32662e14 | 1.79222 | ||||||||
\(813\) | 1.67713e14 | 0.472188 | ||||||||
\(814\) | − | 3.89977e14i | − | 1.09123i | ||||||
\(815\) | −8.61679e14 | −2.39639 | ||||||||
\(816\) | −1.11671e12 | −0.00308668 | ||||||||
\(817\) | − | 3.81425e14i | − | 1.04785i | ||||||
\(818\) | −1.53345e14 | −0.418701 | ||||||||
\(819\) | − | 2.36379e14i | − | 0.641489i | ||||||
\(820\) | −1.18281e15 | −3.19041 | ||||||||
\(821\) | 1.60914e14i | 0.431399i | 0.976460 | + | 0.215699i | \(0.0692031\pi\) | ||||
−0.976460 | + | 0.215699i | \(0.930797\pi\) | |||||||
\(822\) | − | 1.79836e14i | − | 0.479200i | ||||||
\(823\) | 5.10025e14i | 1.35080i | 0.737449 | + | 0.675402i | \(0.236030\pi\) | ||||
−0.737449 | + | 0.675402i | \(0.763970\pi\) | |||||||
\(824\) | −4.29096e14 | −1.12958 | ||||||||
\(825\) | − | 8.35135e13i | − | 0.218518i | ||||||
\(826\) | −1.05259e15 | + | 7.14996e14i | −2.73754 | + | 1.85953i | ||||
\(827\) | 5.27881e14 | 1.36461 | 0.682304 | − | 0.731068i | \(-0.260978\pi\) | ||||
0.682304 | + | 0.731068i | \(0.260978\pi\) | |||||||
\(828\) | 2.64773e14i | 0.680334i | ||||||||
\(829\) | 2.73340e14 | 0.698120 | 0.349060 | − | 0.937100i | \(-0.386501\pi\) | ||||
0.349060 | + | 0.937100i | \(0.386501\pi\) | |||||||
\(830\) | −2.16706e14 | −0.550148 | ||||||||
\(831\) | −1.23684e14 | −0.312111 | ||||||||
\(832\) | − | 5.74994e14i | − | 1.44227i | ||||||
\(833\) | 1.74067e13 | 0.0434002 | ||||||||
\(834\) | − | 4.78062e14i | − | 1.18483i | ||||||
\(835\) | −4.20498e14 | −1.03593 | ||||||||
\(836\) | − | 3.85986e14i | − | 0.945235i | ||||||
\(837\) | − | 7.72415e13i | − | 0.188028i | ||||||
\(838\) | −1.06769e15 | −2.58359 | ||||||||
\(839\) | 3.16463e12i | 0.00761224i | 0.999993 | + | 0.00380612i | \(0.00121153\pi\) | ||||
−0.999993 | + | 0.00380612i | \(0.998788\pi\) | |||||||
\(840\) | 7.71984e14i | 1.84592i | ||||||||
\(841\) | −3.11642e14 | −0.740758 | ||||||||
\(842\) | 2.60178e14 | 0.614767 | ||||||||
\(843\) | 1.40438e14 | 0.329873 | ||||||||
\(844\) | 8.55069e14i | 1.99659i | ||||||||
\(845\) | 3.41264e13 | 0.0792149 | ||||||||
\(846\) | −5.42959e13 | −0.125290 | ||||||||
\(847\) | 4.88311e14 | 1.12016 | ||||||||
\(848\) | 2.76262e13 | 0.0630002 | ||||||||
\(849\) | 3.65068e14i | 0.827629i | ||||||||
\(850\) | 6.21648e12i | 0.0140104i | ||||||||
\(851\) | 5.10538e14 | 1.14388 | ||||||||
\(852\) | −3.49473e14 | −0.778424 | ||||||||
\(853\) | 1.09027e14 | 0.241429 | 0.120714 | − | 0.992687i | \(-0.461482\pi\) | ||||
0.120714 | + | 0.992687i | \(0.461482\pi\) | |||||||
\(854\) | 1.45739e15 | 3.20839 | ||||||||
\(855\) | 1.54338e14 | 0.337786 | ||||||||
\(856\) | − | 3.69444e14i | − | 0.803859i | ||||||
\(857\) | 3.16897e14i | 0.685509i | 0.939425 | + | 0.342755i | \(0.111360\pi\) | ||||
−0.939425 | + | 0.342755i | \(0.888640\pi\) | |||||||
\(858\) | − | 2.85777e14i | − | 0.614598i | ||||||
\(859\) | 2.57916e14i | 0.551458i | 0.961235 | + | 0.275729i | \(0.0889193\pi\) | ||||
−0.961235 | + | 0.275729i | \(0.911081\pi\) | |||||||
\(860\) | 1.35444e15i | 2.87917i | ||||||||
\(861\) | −7.80522e14 | −1.64956 | ||||||||
\(862\) | 8.16190e14 | 1.71496 | ||||||||
\(863\) | 2.39772e14i | 0.500893i | 0.968130 | + | 0.250447i | \(0.0805775\pi\) | ||||
−0.968130 | + | 0.250447i | \(0.919423\pi\) | |||||||
\(864\) | 6.27007e13i | 0.130228i | ||||||||
\(865\) | 2.88025e13i | 0.0594771i | ||||||||
\(866\) | − | 3.04253e14i | − | 0.624662i | ||||||
\(867\) | 2.82775e14 | 0.577226 | ||||||||
\(868\) | − | 1.69451e15i | − | 3.43910i | ||||||
\(869\) | 6.00293e14i | 1.21133i | ||||||||
\(870\) | 3.05838e14i | 0.613613i | ||||||||
\(871\) | −2.69216e14 | −0.537044 | ||||||||
\(872\) | −2.46810e14 | −0.489532 | ||||||||
\(873\) | − | 2.81033e14i | − | 0.554224i | ||||||
\(874\) | 7.90743e14 | 1.55052 | ||||||||
\(875\) | −5.46382e14 | −1.06526 | ||||||||
\(876\) | 6.30891e14i | 1.22302i | ||||||||
\(877\) | 5.90921e13 | 0.113902 | 0.0569510 | − | 0.998377i | \(-0.481862\pi\) | ||||
0.0569510 | + | 0.998377i | \(0.481862\pi\) | |||||||
\(878\) | 2.17477e13i | 0.0416812i | ||||||||
\(879\) | −2.67200e14 | −0.509204 | ||||||||
\(880\) | 1.59098e14i | 0.301476i | ||||||||
\(881\) | − | 6.09408e14i | − | 1.14823i | −0.818775 | − | 0.574115i | \(-0.805346\pi\) | ||
0.818775 | − | 0.574115i | \(-0.194654\pi\) | |||||||
\(882\) | 8.74569e14i | 1.63852i | ||||||||
\(883\) | 7.00235e14 | 1.30449 | 0.652244 | − | 0.758009i | \(-0.273828\pi\) | ||||
0.652244 | + | 0.758009i | \(0.273828\pi\) | |||||||
\(884\) | 1.35938e13i | 0.0251814i | ||||||||
\(885\) | −2.20876e14 | − | 3.25166e14i | −0.406847 | − | 0.598948i | ||||
\(886\) | −1.09649e15 | −2.00834 | ||||||||
\(887\) | − | 3.34243e14i | − | 0.608757i | −0.952551 | − | 0.304379i | \(-0.901551\pi\) | ||
0.952551 | − | 0.304379i | \(-0.0984488\pi\) | |||||||
\(888\) | −4.05564e14 | −0.734505 | ||||||||
\(889\) | 1.29153e13 | 0.0232592 | ||||||||
\(890\) | 8.56551e14 | 1.53392 | ||||||||
\(891\) | 4.12286e13i | 0.0734193i | ||||||||
\(892\) | −3.04793e14 | −0.539735 | ||||||||
\(893\) | 1.03622e14i | 0.182472i | ||||||||
\(894\) | −1.10741e14 | −0.193919 | ||||||||
\(895\) | 9.22767e14i | 1.60686i | ||||||||
\(896\) | 2.07078e15i | 3.58586i | ||||||||
\(897\) | 3.74125e14 | 0.644250 | ||||||||
\(898\) | 1.14313e15i | 1.95755i | ||||||||
\(899\) | − | 2.92117e14i | − | 0.497460i | ||||||
\(900\) | −1.99594e14 | −0.338014 | ||||||||
\(901\) | 1.51108e12 | 0.00254487 | ||||||||
\(902\) | −9.43635e14 | −1.58042 | ||||||||
\(903\) | 8.93775e14i | 1.48864i | ||||||||
\(904\) | 3.60824e14 | 0.597659 | ||||||||
\(905\) | −9.56479e14 | −1.57555 | ||||||||
\(906\) | −7.14430e13 | −0.117036 | ||||||||
\(907\) | −1.03495e15 | −1.68610 | −0.843052 | − | 0.537831i | \(-0.819244\pi\) | ||||
−0.843052 | + | 0.537831i | \(0.819244\pi\) | |||||||
\(908\) | − | 1.71903e15i | − | 2.78518i | ||||||
\(909\) | 2.97563e14i | 0.479467i | ||||||||
\(910\) | 2.50680e15 | 4.01711 | ||||||||
\(911\) | 3.72003e14 | 0.592863 | 0.296432 | − | 0.955054i | \(-0.404203\pi\) | ||||
0.296432 | + | 0.955054i | \(0.404203\pi\) | |||||||
\(912\) | −1.07079e14 | −0.169719 | ||||||||
\(913\) | −1.10480e14 | −0.174152 | ||||||||
\(914\) | −4.99051e14 | −0.782374 | ||||||||
\(915\) | 4.50216e14i | 0.701965i | ||||||||
\(916\) | − | 1.95727e15i | − | 3.03511i | ||||||
\(917\) | − | 4.29011e14i | − | 0.661641i | ||||||
\(918\) | − | 3.06893e12i | − | 0.00470731i | ||||||
\(919\) | 1.47429e14i | 0.224908i | 0.993657 | + | 0.112454i | \(0.0358711\pi\) | ||||
−0.993657 | + | 0.112454i | \(0.964129\pi\) | |||||||
\(920\) | −1.22185e15 | −1.85386 | ||||||||
\(921\) | 5.03901e14 | 0.760409 | ||||||||
\(922\) | − | 5.75949e14i | − | 0.864430i | ||||||
\(923\) | 4.93806e14i | 0.737137i | ||||||||
\(924\) | 9.04463e14i | 1.34286i | ||||||||
\(925\) | 3.84858e14i | 0.568319i | ||||||||
\(926\) | −2.08243e15 | −3.05855 | ||||||||
\(927\) | − | 2.01019e14i | − | 0.293656i | ||||||
\(928\) | 2.37125e14i | 0.344538i | ||||||||
\(929\) | 1.17709e14i | 0.170111i | 0.996376 | + | 0.0850556i | \(0.0271068\pi\) | ||||
−0.996376 | + | 0.0850556i | \(0.972893\pi\) | |||||||
\(930\) | 8.19149e14 | 1.17746 | ||||||||
\(931\) | 1.66909e15 | 2.38634 | ||||||||
\(932\) | − | 1.69413e15i | − | 2.40917i | ||||||
\(933\) | 6.24722e14 | 0.883647 | ||||||||
\(934\) | 1.76679e15 | 2.48570 | ||||||||
\(935\) | 8.70228e12i | 0.0121780i | ||||||||
\(936\) | −2.97200e14 | −0.413684 | ||||||||
\(937\) | 5.99925e14i | 0.830613i | 0.909681 | + | 0.415307i | \(0.136326\pi\) | ||||
−0.909681 | + | 0.415307i | \(0.863674\pi\) | |||||||
\(938\) | 1.33333e15 | 1.83622 | ||||||||
\(939\) | 5.16454e14i | 0.707463i | ||||||||
\(940\) | − | 3.67963e14i | − | 0.501377i | ||||||
\(941\) | 1.34013e15i | 1.81634i | 0.418597 | + | 0.908172i | \(0.362522\pi\) | ||||
−0.418597 | + | 0.908172i | \(0.637478\pi\) | |||||||
\(942\) | 1.20434e15 | 1.62366 | ||||||||
\(943\) | − | 1.23536e15i | − | 1.65666i | ||||||
\(944\) | 1.53243e14 | + | 2.25600e14i | 0.204419 | + | 0.300939i | ||||
\(945\) | −3.61652e14 | −0.479880 | ||||||||
\(946\) | 1.08056e15i | 1.42624i | ||||||||
\(947\) | 3.79409e14 | 0.498147 | 0.249074 | − | 0.968485i | \(-0.419874\pi\) | ||||
0.249074 | + | 0.968485i | \(0.419874\pi\) | |||||||
\(948\) | 1.43467e15 | 1.87375 | ||||||||
\(949\) | 8.91450e14 | 1.15815 | ||||||||
\(950\) | 5.96085e14i | 0.770353i | ||||||||
\(951\) | −3.43088e14 | −0.441065 | ||||||||
\(952\) | − | 2.92961e13i | − | 0.0374649i | ||||||
\(953\) | −1.09728e14 | −0.139589 | −0.0697947 | − | 0.997561i | \(-0.522234\pi\) | ||||
−0.0697947 | + | 0.997561i | \(0.522234\pi\) | |||||||
\(954\) | 7.59217e13i | 0.0960780i | ||||||||
\(955\) | 1.60917e14i | 0.202575i | ||||||||
\(956\) | 6.93493e14 | 0.868466 | ||||||||
\(957\) | 1.55921e14i | 0.194243i | ||||||||
\(958\) | 6.35409e13i | 0.0787456i | ||||||||
\(959\) | 8.04232e14 | 0.991490 | ||||||||
\(960\) | −8.79723e14 | −1.07892 | ||||||||
\(961\) | 3.72298e13 | 0.0454227 | ||||||||
\(962\) | 1.31696e15i | 1.59844i | ||||||||
\(963\) | 1.73074e14 | 0.208978 | ||||||||
\(964\) | −1.73542e15 | −2.08458 | ||||||||
\(965\) | −7.98526e14 | −0.954229 | ||||||||
\(966\) | −1.85291e15 | −2.20277 | ||||||||
\(967\) | 6.17351e14i | 0.730130i | 0.930982 | + | 0.365065i | \(0.118953\pi\) | ||||
−0.930982 | + | 0.365065i | \(0.881047\pi\) | |||||||
\(968\) | − | 6.13954e14i | − | 0.722369i | ||||||
\(969\) | −5.85696e12 | −0.00685573 | ||||||||
\(970\) | 2.98036e15 | 3.47064 | ||||||||
\(971\) | −3.92563e14 | −0.454793 | −0.227396 | − | 0.973802i | \(-0.573021\pi\) | ||||
−0.227396 | + | 0.973802i | \(0.573021\pi\) | |||||||
\(972\) | 9.85345e13 | 0.113568 | ||||||||
\(973\) | 2.13791e15 | 2.45147 | ||||||||
\(974\) | − | 1.62582e15i | − | 1.85472i | ||||||
\(975\) | 2.82026e14i | 0.320086i | ||||||||
\(976\) | − | 3.12359e14i | − | 0.352700i | ||||||
\(977\) | 1.37731e15i | 1.54725i | 0.633645 | + | 0.773624i | \(0.281558\pi\) | ||||
−0.633645 | + | 0.773624i | \(0.718442\pi\) | |||||||
\(978\) | 1.64295e15i | 1.83624i | ||||||||
\(979\) | 4.36683e14 | 0.485571 | ||||||||
\(980\) | −5.92694e15 | −6.55693 | ||||||||
\(981\) | − | 1.15624e14i | − | 0.127263i | ||||||
\(982\) | − | 5.56219e14i | − | 0.609100i | ||||||
\(983\) | − | 9.78937e14i | − | 1.06656i | −0.845938 | − | 0.533282i | \(-0.820958\pi\) | ||
0.845938 | − | 0.533282i | \(-0.179042\pi\) | |||||||
\(984\) | 9.81352e14i | 1.06377i | ||||||||
\(985\) | 1.68061e15 | 1.81254 | ||||||||
\(986\) | − | 1.16062e13i | − | 0.0124540i | ||||||
\(987\) | − | 2.42813e14i | − | 0.259231i | ||||||
\(988\) | 1.30348e15i | 1.38458i | ||||||||
\(989\) | −1.41461e15 | −1.49505 | ||||||||
\(990\) | −4.37230e14 | −0.459763 | ||||||||
\(991\) | 4.54987e14i | 0.476026i | 0.971262 | + | 0.238013i | \(0.0764961\pi\) | ||||
−0.971262 | + | 0.238013i | \(0.923504\pi\) | |||||||
\(992\) | 6.35110e14 | 0.661136 | ||||||||
\(993\) | −7.33031e13 | −0.0759235 | ||||||||
\(994\) | − | 2.44565e15i | − | 2.52036i | ||||||
\(995\) | 1.50664e15 | 1.54488 | ||||||||
\(996\) | 2.64042e14i | 0.269387i | ||||||||
\(997\) | 3.09664e14 | 0.314351 | 0.157175 | − | 0.987571i | \(-0.449761\pi\) | ||||
0.157175 | + | 0.987571i | \(0.449761\pi\) | |||||||
\(998\) | − | 1.52223e15i | − | 1.53754i | ||||||
\(999\) | − | 1.89995e14i | − | 0.190948i |
(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 | 177.11.c.a.58.90 | yes | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.11 | ✓ | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.11 | ✓ | 100 | 59.58 | odd | 2 | inner | |
177.11.c.a.58.90 | yes | 100 | 1.1 | even | 1 | trivial |