Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
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, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 81.6200 | 1.80356 | 0.901782 | − | 0.432192i | \(-0.142260\pi\) | ||||
0.901782 | + | 0.432192i | \(0.142260\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 4613.82 | 2.25284 | ||||||||
\(5\) | 4430.19 | 0.633997 | 0.316998 | − | 0.948426i | \(-0.397325\pi\) | ||||
0.316998 | + | 0.948426i | \(0.397325\pi\) | |||||||
\(6\) | 19833.6 | 1.04129 | ||||||||
\(7\) | −67642.9 | −1.52119 | −0.760595 | − | 0.649227i | \(-0.775092\pi\) | ||||
−0.760595 | + | 0.649227i | \(0.775092\pi\) | |||||||
\(8\) | 209422. | 2.25958 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 361592. | 1.14345 | ||||||||
\(11\) | −519775. | −0.973096 | −0.486548 | − | 0.873654i | \(-0.661744\pi\) | ||||
−0.486548 | + | 0.873654i | \(0.661744\pi\) | |||||||
\(12\) | 1.12116e6 | 1.30068 | ||||||||
\(13\) | −2.46231e6 | −1.83930 | −0.919652 | − | 0.392734i | \(-0.871529\pi\) | ||||
−0.919652 | + | 0.392734i | \(0.871529\pi\) | |||||||
\(14\) | −5.52101e6 | −2.74356 | ||||||||
\(15\) | 1.07654e6 | 0.366038 | ||||||||
\(16\) | 7.64391e6 | 1.82245 | ||||||||
\(17\) | −4.35544e6 | −0.743982 | −0.371991 | − | 0.928236i | \(-0.621325\pi\) | ||||
−0.371991 | + | 0.928236i | \(0.621325\pi\) | |||||||
\(18\) | 4.81958e6 | 0.601188 | ||||||||
\(19\) | 3.11830e6 | 0.288917 | 0.144459 | − | 0.989511i | \(-0.453856\pi\) | ||||
0.144459 | + | 0.989511i | \(0.453856\pi\) | |||||||
\(20\) | 2.04401e7 | 1.42829 | ||||||||
\(21\) | −1.64372e7 | −0.878259 | ||||||||
\(22\) | −4.24240e7 | −1.75504 | ||||||||
\(23\) | −1.04622e7 | −0.338936 | −0.169468 | − | 0.985536i | \(-0.554205\pi\) | ||||
−0.169468 | + | 0.985536i | \(0.554205\pi\) | |||||||
\(24\) | 5.08895e7 | 1.30457 | ||||||||
\(25\) | −2.92016e7 | −0.598048 | ||||||||
\(26\) | −2.00973e8 | −3.31730 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −3.12092e8 | −3.42700 | ||||||||
\(29\) | −2.13398e8 | −1.93197 | −0.965985 | − | 0.258596i | \(-0.916740\pi\) | ||||
−0.965985 | + | 0.258596i | \(0.916740\pi\) | |||||||
\(30\) | 8.78668e7 | 0.660173 | ||||||||
\(31\) | 1.99220e8 | 1.24981 | 0.624906 | − | 0.780700i | \(-0.285137\pi\) | ||||
0.624906 | + | 0.780700i | \(0.285137\pi\) | |||||||
\(32\) | 1.94999e8 | 1.02733 | ||||||||
\(33\) | −1.26305e8 | −0.561817 | ||||||||
\(34\) | −3.55491e8 | −1.34182 | ||||||||
\(35\) | −2.99671e8 | −0.964429 | ||||||||
\(36\) | 2.72441e8 | 0.750947 | ||||||||
\(37\) | 7.90601e8 | 1.87434 | 0.937169 | − | 0.348876i | \(-0.113436\pi\) | ||||
0.937169 | + | 0.348876i | \(0.113436\pi\) | |||||||
\(38\) | 2.54516e8 | 0.521080 | ||||||||
\(39\) | −5.98340e8 | −1.06192 | ||||||||
\(40\) | 9.27778e8 | 1.43256 | ||||||||
\(41\) | −4.32732e8 | −0.583321 | −0.291661 | − | 0.956522i | \(-0.594208\pi\) | ||||
−0.291661 | + | 0.956522i | \(0.594208\pi\) | |||||||
\(42\) | −1.34161e9 | −1.58400 | ||||||||
\(43\) | −4.93130e8 | −0.511546 | −0.255773 | − | 0.966737i | \(-0.582330\pi\) | ||||
−0.255773 | + | 0.966737i | \(0.582330\pi\) | |||||||
\(44\) | −2.39815e9 | −2.19223 | ||||||||
\(45\) | 2.61598e8 | 0.211332 | ||||||||
\(46\) | −8.53921e8 | −0.611293 | ||||||||
\(47\) | −3.47185e8 | −0.220812 | −0.110406 | − | 0.993887i | \(-0.535215\pi\) | ||||
−0.110406 | + | 0.993887i | \(0.535215\pi\) | |||||||
\(48\) | 1.85747e9 | 1.05219 | ||||||||
\(49\) | 2.59824e9 | 1.31402 | ||||||||
\(50\) | −2.38343e9 | −1.07862 | ||||||||
\(51\) | −1.05837e9 | −0.429538 | ||||||||
\(52\) | −1.13606e10 | −4.14366 | ||||||||
\(53\) | 6.14865e8 | 0.201959 | 0.100979 | − | 0.994889i | \(-0.467802\pi\) | ||||
0.100979 | + | 0.994889i | \(0.467802\pi\) | |||||||
\(54\) | 1.17116e9 | 0.347096 | ||||||||
\(55\) | −2.30270e9 | −0.616940 | ||||||||
\(56\) | −1.41659e10 | −3.43724 | ||||||||
\(57\) | 7.57747e8 | 0.166806 | ||||||||
\(58\) | −1.74175e10 | −3.48443 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | 4.96694e9 | 0.824626 | ||||||||
\(61\) | 9.09541e9 | 1.37882 | 0.689411 | − | 0.724370i | \(-0.257869\pi\) | ||||
0.689411 | + | 0.724370i | \(0.257869\pi\) | |||||||
\(62\) | 1.62604e10 | 2.25411 | ||||||||
\(63\) | −3.99425e9 | −0.507063 | ||||||||
\(64\) | 2.61119e8 | 0.0303983 | ||||||||
\(65\) | −1.09085e10 | −1.16611 | ||||||||
\(66\) | −1.03090e10 | −1.01327 | ||||||||
\(67\) | 2.20186e9 | 0.199241 | 0.0996203 | − | 0.995026i | \(-0.468237\pi\) | ||||
0.0996203 | + | 0.995026i | \(0.468237\pi\) | |||||||
\(68\) | −2.00952e10 | −1.67607 | ||||||||
\(69\) | −2.54230e9 | −0.195685 | ||||||||
\(70\) | −2.44591e10 | −1.73941 | ||||||||
\(71\) | 2.45387e10 | 1.61410 | 0.807051 | − | 0.590482i | \(-0.201062\pi\) | ||||
0.807051 | + | 0.590482i | \(0.201062\pi\) | |||||||
\(72\) | 1.23662e10 | 0.753192 | ||||||||
\(73\) | −8.48573e8 | −0.0479086 | −0.0239543 | − | 0.999713i | \(-0.507626\pi\) | ||||
−0.0239543 | + | 0.999713i | \(0.507626\pi\) | |||||||
\(74\) | 6.45288e10 | 3.38049 | ||||||||
\(75\) | −7.09598e9 | −0.345283 | ||||||||
\(76\) | 1.43873e10 | 0.650884 | ||||||||
\(77\) | 3.51591e10 | 1.48026 | ||||||||
\(78\) | −4.88365e10 | −1.91525 | ||||||||
\(79\) | −3.82381e10 | −1.39813 | −0.699065 | − | 0.715058i | \(-0.746400\pi\) | ||||
−0.699065 | + | 0.715058i | \(0.746400\pi\) | |||||||
\(80\) | 3.38639e10 | 1.15543 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −3.53196e10 | −1.05206 | ||||||||
\(83\) | 2.31641e10 | 0.645485 | 0.322743 | − | 0.946487i | \(-0.395395\pi\) | ||||
0.322743 | + | 0.946487i | \(0.395395\pi\) | |||||||
\(84\) | −7.58384e10 | −1.97858 | ||||||||
\(85\) | −1.92954e10 | −0.471682 | ||||||||
\(86\) | −4.02492e10 | −0.922606 | ||||||||
\(87\) | −5.18556e10 | −1.11542 | ||||||||
\(88\) | −1.08852e11 | −2.19878 | ||||||||
\(89\) | −2.16282e10 | −0.410559 | −0.205280 | − | 0.978703i | \(-0.565810\pi\) | ||||
−0.205280 | + | 0.978703i | \(0.565810\pi\) | |||||||
\(90\) | 2.13516e10 | 0.381151 | ||||||||
\(91\) | 1.66558e11 | 2.79793 | ||||||||
\(92\) | −4.82705e10 | −0.763569 | ||||||||
\(93\) | 4.84106e10 | 0.721579 | ||||||||
\(94\) | −2.83372e10 | −0.398248 | ||||||||
\(95\) | 1.38147e10 | 0.183172 | ||||||||
\(96\) | 4.73849e10 | 0.593127 | ||||||||
\(97\) | 8.63799e10 | 1.02134 | 0.510668 | − | 0.859778i | \(-0.329398\pi\) | ||||
0.510668 | + | 0.859778i | \(0.329398\pi\) | |||||||
\(98\) | 2.12068e11 | 2.36991 | ||||||||
\(99\) | −3.06922e10 | −0.324365 | ||||||||
\(100\) | −1.34731e11 | −1.34731 | ||||||||
\(101\) | −3.93356e10 | −0.372407 | −0.186204 | − | 0.982511i | \(-0.559618\pi\) | ||||
−0.186204 | + | 0.982511i | \(0.559618\pi\) | |||||||
\(102\) | −8.63842e10 | −0.774700 | ||||||||
\(103\) | 6.72298e10 | 0.571422 | 0.285711 | − | 0.958316i | \(-0.407770\pi\) | ||||
0.285711 | + | 0.958316i | \(0.407770\pi\) | |||||||
\(104\) | −5.15661e11 | −4.15605 | ||||||||
\(105\) | −7.28200e10 | −0.556813 | ||||||||
\(106\) | 5.01852e10 | 0.364245 | ||||||||
\(107\) | 1.33422e11 | 0.919637 | 0.459818 | − | 0.888013i | \(-0.347915\pi\) | ||||
0.459818 | + | 0.888013i | \(0.347915\pi\) | |||||||
\(108\) | 6.62032e10 | 0.433559 | ||||||||
\(109\) | −8.17691e10 | −0.509030 | −0.254515 | − | 0.967069i | \(-0.581916\pi\) | ||||
−0.254515 | + | 0.967069i | \(0.581916\pi\) | |||||||
\(110\) | −1.87946e11 | −1.11269 | ||||||||
\(111\) | 1.92116e11 | 1.08215 | ||||||||
\(112\) | −5.17056e11 | −2.77229 | ||||||||
\(113\) | −1.71104e11 | −0.873635 | −0.436817 | − | 0.899550i | \(-0.643894\pi\) | ||||
−0.436817 | + | 0.899550i | \(0.643894\pi\) | |||||||
\(114\) | 6.18473e10 | 0.300846 | ||||||||
\(115\) | −4.63493e10 | −0.214885 | ||||||||
\(116\) | −9.84578e11 | −4.35242 | ||||||||
\(117\) | −1.45397e11 | −0.613102 | ||||||||
\(118\) | −5.83521e10 | −0.234804 | ||||||||
\(119\) | 2.94615e11 | 1.13174 | ||||||||
\(120\) | 2.25450e11 | 0.827092 | ||||||||
\(121\) | −1.51456e10 | −0.0530845 | ||||||||
\(122\) | 7.42367e11 | 2.48679 | ||||||||
\(123\) | −1.05154e11 | −0.336781 | ||||||||
\(124\) | 9.19167e11 | 2.81563 | ||||||||
\(125\) | −3.45686e11 | −1.01316 | ||||||||
\(126\) | −3.26010e11 | −0.914520 | ||||||||
\(127\) | 1.01955e11 | 0.273835 | 0.136917 | − | 0.990582i | \(-0.456281\pi\) | ||||
0.136917 | + | 0.990582i | \(0.456281\pi\) | |||||||
\(128\) | −3.78046e11 | −0.972501 | ||||||||
\(129\) | −1.19831e11 | −0.295341 | ||||||||
\(130\) | −8.90350e11 | −2.10316 | ||||||||
\(131\) | −8.49075e10 | −0.192289 | −0.0961444 | − | 0.995367i | \(-0.530651\pi\) | ||||
−0.0961444 | + | 0.995367i | \(0.530651\pi\) | |||||||
\(132\) | −5.82750e11 | −1.26568 | ||||||||
\(133\) | −2.10931e11 | −0.439497 | ||||||||
\(134\) | 1.79716e11 | 0.359343 | ||||||||
\(135\) | 6.35683e10 | 0.122013 | ||||||||
\(136\) | −9.12124e11 | −1.68109 | ||||||||
\(137\) | 1.31282e11 | 0.232404 | 0.116202 | − | 0.993226i | \(-0.462928\pi\) | ||||
0.116202 | + | 0.993226i | \(0.462928\pi\) | |||||||
\(138\) | −2.07503e11 | −0.352930 | ||||||||
\(139\) | −1.83692e11 | −0.300268 | −0.150134 | − | 0.988666i | \(-0.547971\pi\) | ||||
−0.150134 | + | 0.988666i | \(0.547971\pi\) | |||||||
\(140\) | −1.38263e12 | −2.17270 | ||||||||
\(141\) | −8.43658e10 | −0.127486 | ||||||||
\(142\) | 2.00285e12 | 2.91114 | ||||||||
\(143\) | 1.27985e12 | 1.78982 | ||||||||
\(144\) | 4.51365e11 | 0.607483 | ||||||||
\(145\) | −9.45391e11 | −1.22486 | ||||||||
\(146\) | −6.92605e10 | −0.0864062 | ||||||||
\(147\) | 6.31372e11 | 0.758648 | ||||||||
\(148\) | 3.64769e12 | 4.22258 | ||||||||
\(149\) | −1.31670e12 | −1.46880 | −0.734399 | − | 0.678718i | \(-0.762536\pi\) | ||||
−0.734399 | + | 0.678718i | \(0.762536\pi\) | |||||||
\(150\) | −5.79174e11 | −0.622740 | ||||||||
\(151\) | 1.34356e11 | 0.139279 | 0.0696395 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696395 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(152\) | 6.53040e11 | 0.652830 | ||||||||
\(153\) | −2.57184e11 | −0.247994 | ||||||||
\(154\) | 2.86968e12 | 2.66975 | ||||||||
\(155\) | 8.82584e11 | 0.792377 | ||||||||
\(156\) | −2.76063e12 | −2.39234 | ||||||||
\(157\) | −9.86879e11 | −0.825688 | −0.412844 | − | 0.910802i | \(-0.635465\pi\) | ||||
−0.412844 | + | 0.910802i | \(0.635465\pi\) | |||||||
\(158\) | −3.12100e12 | −2.52162 | ||||||||
\(159\) | 1.49412e11 | 0.116601 | ||||||||
\(160\) | 8.63884e11 | 0.651322 | ||||||||
\(161\) | 7.07691e11 | 0.515586 | ||||||||
\(162\) | 2.84591e11 | 0.200396 | ||||||||
\(163\) | −2.56794e12 | −1.74805 | −0.874024 | − | 0.485884i | \(-0.838498\pi\) | ||||
−0.874024 | + | 0.485884i | \(0.838498\pi\) | |||||||
\(164\) | −1.99655e12 | −1.31413 | ||||||||
\(165\) | −5.59556e11 | −0.356190 | ||||||||
\(166\) | 1.89065e12 | 1.16417 | ||||||||
\(167\) | −2.97952e11 | −0.177503 | −0.0887516 | − | 0.996054i | \(-0.528288\pi\) | ||||
−0.0887516 | + | 0.996054i | \(0.528288\pi\) | |||||||
\(168\) | −3.44232e12 | −1.98449 | ||||||||
\(169\) | 4.27079e12 | 2.38304 | ||||||||
\(170\) | −1.57489e12 | −0.850709 | ||||||||
\(171\) | 1.84133e11 | 0.0963057 | ||||||||
\(172\) | −2.27521e12 | −1.15243 | ||||||||
\(173\) | −3.28574e12 | −1.61205 | −0.806027 | − | 0.591879i | \(-0.798386\pi\) | ||||
−0.806027 | + | 0.591879i | \(0.798386\pi\) | |||||||
\(174\) | −4.23245e12 | −2.01174 | ||||||||
\(175\) | 1.97528e12 | 0.909744 | ||||||||
\(176\) | −3.97311e12 | −1.77342 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | −1.76529e12 | −0.740469 | ||||||||
\(179\) | −4.57859e12 | −1.86226 | −0.931130 | − | 0.364687i | \(-0.881176\pi\) | ||||
−0.931130 | + | 0.364687i | \(0.881176\pi\) | |||||||
\(180\) | 1.20697e12 | 0.476098 | ||||||||
\(181\) | 4.41485e12 | 1.68921 | 0.844606 | − | 0.535389i | \(-0.179835\pi\) | ||||
0.844606 | + | 0.535389i | \(0.179835\pi\) | |||||||
\(182\) | 1.35944e13 | 5.04624 | ||||||||
\(183\) | 2.21018e12 | 0.796063 | ||||||||
\(184\) | −2.19100e12 | −0.765853 | ||||||||
\(185\) | 3.50251e12 | 1.18832 | ||||||||
\(186\) | 3.95127e12 | 1.30141 | ||||||||
\(187\) | 2.26385e12 | 0.723966 | ||||||||
\(188\) | −1.60185e12 | −0.497454 | ||||||||
\(189\) | −9.70602e11 | −0.292753 | ||||||||
\(190\) | 1.12755e12 | 0.330363 | ||||||||
\(191\) | 6.22699e12 | 1.77253 | 0.886267 | − | 0.463175i | \(-0.153290\pi\) | ||||
0.886267 | + | 0.463175i | \(0.153290\pi\) | |||||||
\(192\) | 6.34520e10 | 0.0175504 | ||||||||
\(193\) | 2.20764e11 | 0.0593421 | 0.0296711 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296711 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(194\) | 7.05033e12 | 1.84204 | ||||||||
\(195\) | −2.65076e12 | −0.673256 | ||||||||
\(196\) | 1.19878e13 | 2.96027 | ||||||||
\(197\) | 3.23417e12 | 0.776603 | 0.388302 | − | 0.921532i | \(-0.373062\pi\) | ||||
0.388302 | + | 0.921532i | \(0.373062\pi\) | |||||||
\(198\) | −2.50510e12 | −0.585013 | ||||||||
\(199\) | −4.99865e12 | −1.13543 | −0.567716 | − | 0.823225i | \(-0.692173\pi\) | ||||
−0.567716 | + | 0.823225i | \(0.692173\pi\) | |||||||
\(200\) | −6.11545e12 | −1.35134 | ||||||||
\(201\) | 5.35051e11 | 0.115032 | ||||||||
\(202\) | −3.21057e12 | −0.671660 | ||||||||
\(203\) | 1.44348e13 | 2.93889 | ||||||||
\(204\) | −4.88313e12 | −0.967682 | ||||||||
\(205\) | −1.91708e12 | −0.369824 | ||||||||
\(206\) | 5.48729e12 | 1.03060 | ||||||||
\(207\) | −6.17780e11 | −0.112979 | ||||||||
\(208\) | −1.88216e13 | −3.35204 | ||||||||
\(209\) | −1.62081e12 | −0.281144 | ||||||||
\(210\) | −5.94357e12 | −1.00425 | ||||||||
\(211\) | −7.63999e12 | −1.25759 | −0.628796 | − | 0.777571i | \(-0.716452\pi\) | ||||
−0.628796 | + | 0.777571i | \(0.716452\pi\) | |||||||
\(212\) | 2.83687e12 | 0.454981 | ||||||||
\(213\) | 5.96291e12 | 0.931902 | ||||||||
\(214\) | 1.08899e13 | 1.65862 | ||||||||
\(215\) | −2.18466e12 | −0.324319 | ||||||||
\(216\) | 3.00498e12 | 0.434856 | ||||||||
\(217\) | −1.34759e13 | −1.90120 | ||||||||
\(218\) | −6.67399e12 | −0.918068 | ||||||||
\(219\) | −2.06203e11 | −0.0276601 | ||||||||
\(220\) | −1.06242e13 | −1.38987 | ||||||||
\(221\) | 1.07244e13 | 1.36841 | ||||||||
\(222\) | 1.56805e13 | 1.95173 | ||||||||
\(223\) | −1.31311e13 | −1.59450 | −0.797250 | − | 0.603649i | \(-0.793713\pi\) | ||||
−0.797250 | + | 0.603649i | \(0.793713\pi\) | |||||||
\(224\) | −1.31903e13 | −1.56276 | ||||||||
\(225\) | −1.72432e12 | −0.199349 | ||||||||
\(226\) | −1.39655e13 | −1.57566 | ||||||||
\(227\) | 6.16894e11 | 0.0679311 | 0.0339656 | − | 0.999423i | \(-0.489186\pi\) | ||||
0.0339656 | + | 0.999423i | \(0.489186\pi\) | |||||||
\(228\) | 3.49611e12 | 0.375788 | ||||||||
\(229\) | −1.04390e13 | −1.09538 | −0.547690 | − | 0.836682i | \(-0.684492\pi\) | ||||
−0.547690 | + | 0.836682i | \(0.684492\pi\) | |||||||
\(230\) | −3.78303e12 | −0.387558 | ||||||||
\(231\) | 8.54366e12 | 0.854630 | ||||||||
\(232\) | −4.46901e13 | −4.36544 | ||||||||
\(233\) | −1.43228e13 | −1.36637 | −0.683187 | − | 0.730243i | \(-0.739407\pi\) | ||||
−0.683187 | + | 0.730243i | \(0.739407\pi\) | |||||||
\(234\) | −1.18673e13 | −1.10577 | ||||||||
\(235\) | −1.53809e12 | −0.139994 | ||||||||
\(236\) | −3.29853e12 | −0.293295 | ||||||||
\(237\) | −9.29187e12 | −0.807211 | ||||||||
\(238\) | 2.40464e13 | 2.04116 | ||||||||
\(239\) | −5.85963e11 | −0.0486051 | −0.0243025 | − | 0.999705i | \(-0.507737\pi\) | ||||
−0.0243025 | + | 0.999705i | \(0.507737\pi\) | |||||||
\(240\) | 8.22894e12 | 0.667086 | ||||||||
\(241\) | −5.63661e12 | −0.446606 | −0.223303 | − | 0.974749i | \(-0.571684\pi\) | ||||
−0.223303 | + | 0.974749i | \(0.571684\pi\) | |||||||
\(242\) | −1.23619e12 | −0.0957413 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | 4.19646e13 | 3.10627 | ||||||||
\(245\) | 1.15107e13 | 0.833082 | ||||||||
\(246\) | −8.58265e12 | −0.607405 | ||||||||
\(247\) | −7.67821e12 | −0.531406 | ||||||||
\(248\) | 4.17211e13 | 2.82405 | ||||||||
\(249\) | 5.62888e12 | 0.372671 | ||||||||
\(250\) | −2.82149e13 | −1.82729 | ||||||||
\(251\) | −1.30318e13 | −0.825659 | −0.412829 | − | 0.910808i | \(-0.635459\pi\) | ||||
−0.412829 | + | 0.910808i | \(0.635459\pi\) | |||||||
\(252\) | −1.84287e13 | −1.14233 | ||||||||
\(253\) | 5.43797e12 | 0.329818 | ||||||||
\(254\) | 8.32157e12 | 0.493878 | ||||||||
\(255\) | −4.68878e12 | −0.272326 | ||||||||
\(256\) | −3.13909e13 | −1.78437 | ||||||||
\(257\) | 2.06055e12 | 0.114644 | 0.0573218 | − | 0.998356i | \(-0.481744\pi\) | ||||
0.0573218 | + | 0.998356i | \(0.481744\pi\) | |||||||
\(258\) | −9.78056e12 | −0.532667 | ||||||||
\(259\) | −5.34786e13 | −2.85122 | ||||||||
\(260\) | −5.03297e13 | −2.62707 | ||||||||
\(261\) | −1.26009e13 | −0.643990 | ||||||||
\(262\) | −6.93015e12 | −0.346805 | ||||||||
\(263\) | −4.23790e12 | −0.207680 | −0.103840 | − | 0.994594i | \(-0.533113\pi\) | ||||
−0.103840 | + | 0.994594i | \(0.533113\pi\) | |||||||
\(264\) | −2.64511e13 | −1.26947 | ||||||||
\(265\) | 2.72397e12 | 0.128041 | ||||||||
\(266\) | −1.72162e13 | −0.792661 | ||||||||
\(267\) | −5.25566e12 | −0.237036 | ||||||||
\(268\) | 1.01590e13 | 0.448857 | ||||||||
\(269\) | 1.56676e13 | 0.678211 | 0.339105 | − | 0.940748i | \(-0.389876\pi\) | ||||
0.339105 | + | 0.940748i | \(0.389876\pi\) | |||||||
\(270\) | 5.18845e12 | 0.220058 | ||||||||
\(271\) | 4.51306e13 | 1.87560 | 0.937800 | − | 0.347176i | \(-0.112859\pi\) | ||||
0.937800 | + | 0.347176i | \(0.112859\pi\) | |||||||
\(272\) | −3.32926e13 | −1.35587 | ||||||||
\(273\) | 4.04735e13 | 1.61539 | ||||||||
\(274\) | 1.07153e13 | 0.419155 | ||||||||
\(275\) | 1.51782e13 | 0.581958 | ||||||||
\(276\) | −1.17297e13 | −0.440847 | ||||||||
\(277\) | −2.57908e13 | −0.950226 | −0.475113 | − | 0.879925i | \(-0.657593\pi\) | ||||
−0.475113 | + | 0.879925i | \(0.657593\pi\) | |||||||
\(278\) | −1.49929e13 | −0.541553 | ||||||||
\(279\) | 1.17638e13 | 0.416604 | ||||||||
\(280\) | −6.27576e13 | −2.17920 | ||||||||
\(281\) | −4.46980e13 | −1.52196 | −0.760980 | − | 0.648775i | \(-0.775282\pi\) | ||||
−0.760980 | + | 0.648775i | \(0.775282\pi\) | |||||||
\(282\) | −6.88594e12 | −0.229929 | ||||||||
\(283\) | 3.44164e13 | 1.12704 | 0.563521 | − | 0.826102i | \(-0.309446\pi\) | ||||
0.563521 | + | 0.826102i | \(0.309446\pi\) | |||||||
\(284\) | 1.13217e14 | 3.63632 | ||||||||
\(285\) | 3.35696e12 | 0.105755 | ||||||||
\(286\) | 1.04461e14 | 3.22805 | ||||||||
\(287\) | 2.92712e13 | 0.887342 | ||||||||
\(288\) | 1.15145e13 | 0.342442 | ||||||||
\(289\) | −1.53021e13 | −0.446490 | ||||||||
\(290\) | −7.71628e13 | −2.20912 | ||||||||
\(291\) | 2.09903e13 | 0.589668 | ||||||||
\(292\) | −3.91516e12 | −0.107930 | ||||||||
\(293\) | 2.91846e13 | 0.789554 | 0.394777 | − | 0.918777i | \(-0.370822\pi\) | ||||
0.394777 | + | 0.918777i | \(0.370822\pi\) | |||||||
\(294\) | 5.15326e13 | 1.36827 | ||||||||
\(295\) | −3.16725e12 | −0.0825394 | ||||||||
\(296\) | 1.65569e14 | 4.23521 | ||||||||
\(297\) | −7.45820e12 | −0.187272 | ||||||||
\(298\) | −1.07469e14 | −2.64907 | ||||||||
\(299\) | 2.57610e13 | 0.623407 | ||||||||
\(300\) | −3.27396e13 | −0.777868 | ||||||||
\(301\) | 3.33567e13 | 0.778158 | ||||||||
\(302\) | 1.09662e13 | 0.251198 | ||||||||
\(303\) | −9.55854e12 | −0.215009 | ||||||||
\(304\) | 2.38360e13 | 0.526537 | ||||||||
\(305\) | 4.02944e13 | 0.874169 | ||||||||
\(306\) | −2.09914e13 | −0.447273 | ||||||||
\(307\) | −1.28328e13 | −0.268572 | −0.134286 | − | 0.990943i | \(-0.542874\pi\) | ||||
−0.134286 | + | 0.990943i | \(0.542874\pi\) | |||||||
\(308\) | 1.62218e14 | 3.33480 | ||||||||
\(309\) | 1.63368e13 | 0.329911 | ||||||||
\(310\) | 7.20365e13 | 1.42910 | ||||||||
\(311\) | −7.63079e13 | −1.48726 | −0.743631 | − | 0.668590i | \(-0.766898\pi\) | ||||
−0.743631 | + | 0.668590i | \(0.766898\pi\) | |||||||
\(312\) | −1.25306e14 | −2.39950 | ||||||||
\(313\) | −4.98603e13 | −0.938126 | −0.469063 | − | 0.883165i | \(-0.655408\pi\) | ||||
−0.469063 | + | 0.883165i | \(0.655408\pi\) | |||||||
\(314\) | −8.05490e13 | −1.48918 | ||||||||
\(315\) | −1.76953e13 | −0.321476 | ||||||||
\(316\) | −1.76424e14 | −3.14977 | ||||||||
\(317\) | 9.01966e13 | 1.58257 | 0.791287 | − | 0.611444i | \(-0.209411\pi\) | ||||
0.791287 | + | 0.611444i | \(0.209411\pi\) | |||||||
\(318\) | 1.21950e13 | 0.210297 | ||||||||
\(319\) | 1.10919e14 | 1.87999 | ||||||||
\(320\) | 1.15681e12 | 0.0192724 | ||||||||
\(321\) | 3.24215e13 | 0.530952 | ||||||||
\(322\) | 5.77617e13 | 0.929892 | ||||||||
\(323\) | −1.35816e13 | −0.214949 | ||||||||
\(324\) | 1.60874e13 | 0.250316 | ||||||||
\(325\) | 7.19032e13 | 1.09999 | ||||||||
\(326\) | −2.09595e14 | −3.15271 | ||||||||
\(327\) | −1.98699e13 | −0.293889 | ||||||||
\(328\) | −9.06235e13 | −1.31806 | ||||||||
\(329\) | 2.34846e13 | 0.335896 | ||||||||
\(330\) | −4.56710e13 | −0.642412 | ||||||||
\(331\) | 4.61834e13 | 0.638899 | 0.319449 | − | 0.947603i | \(-0.396502\pi\) | ||||
0.319449 | + | 0.947603i | \(0.396502\pi\) | |||||||
\(332\) | 1.06875e14 | 1.45417 | ||||||||
\(333\) | 4.66842e13 | 0.624779 | ||||||||
\(334\) | −2.43189e13 | −0.320138 | ||||||||
\(335\) | 9.75464e12 | 0.126318 | ||||||||
\(336\) | −1.25645e14 | −1.60058 | ||||||||
\(337\) | 1.14155e14 | 1.43065 | 0.715323 | − | 0.698794i | \(-0.246279\pi\) | ||||
0.715323 | + | 0.698794i | \(0.246279\pi\) | |||||||
\(338\) | 3.48582e14 | 4.29797 | ||||||||
\(339\) | −4.15784e13 | −0.504393 | ||||||||
\(340\) | −8.90255e13 | −1.06263 | ||||||||
\(341\) | −1.03550e14 | −1.21619 | ||||||||
\(342\) | 1.50289e13 | 0.173693 | ||||||||
\(343\) | −4.20003e13 | −0.477678 | ||||||||
\(344\) | −1.03272e14 | −1.15588 | ||||||||
\(345\) | −1.12629e13 | −0.124064 | ||||||||
\(346\) | −2.68182e14 | −2.90744 | ||||||||
\(347\) | 1.57017e14 | 1.67546 | 0.837728 | − | 0.546087i | \(-0.183883\pi\) | ||||
0.837728 | + | 0.546087i | \(0.183883\pi\) | |||||||
\(348\) | −2.39252e14 | −2.51287 | ||||||||
\(349\) | −4.41868e13 | −0.456828 | −0.228414 | − | 0.973564i | \(-0.573354\pi\) | ||||
−0.228414 | + | 0.973564i | \(0.573354\pi\) | |||||||
\(350\) | 1.61222e14 | 1.64078 | ||||||||
\(351\) | −3.53314e13 | −0.353974 | ||||||||
\(352\) | −1.01356e14 | −0.999687 | ||||||||
\(353\) | 2.97334e12 | 0.0288724 | 0.0144362 | − | 0.999896i | \(-0.495405\pi\) | ||||
0.0144362 | + | 0.999896i | \(0.495405\pi\) | |||||||
\(354\) | −1.41796e13 | −0.135564 | ||||||||
\(355\) | 1.08711e14 | 1.02334 | ||||||||
\(356\) | −9.97886e13 | −0.924924 | ||||||||
\(357\) | 7.15913e13 | 0.653409 | ||||||||
\(358\) | −3.73705e14 | −3.35870 | ||||||||
\(359\) | 5.01767e13 | 0.444101 | 0.222051 | − | 0.975035i | \(-0.428725\pi\) | ||||
0.222051 | + | 0.975035i | \(0.428725\pi\) | |||||||
\(360\) | 5.47844e13 | 0.477522 | ||||||||
\(361\) | −1.06766e14 | −0.916527 | ||||||||
\(362\) | 3.60340e14 | 3.04660 | ||||||||
\(363\) | −3.68039e12 | −0.0306484 | ||||||||
\(364\) | 7.68466e14 | 6.30329 | ||||||||
\(365\) | −3.75934e12 | −0.0303739 | ||||||||
\(366\) | 1.80395e14 | 1.43575 | ||||||||
\(367\) | −2.52774e14 | −1.98184 | −0.990922 | − | 0.134440i | \(-0.957076\pi\) | ||||
−0.990922 | + | 0.134440i | \(0.957076\pi\) | |||||||
\(368\) | −7.99718e13 | −0.617694 | ||||||||
\(369\) | −2.55524e13 | −0.194440 | ||||||||
\(370\) | 2.85875e14 | 2.14322 | ||||||||
\(371\) | −4.15913e13 | −0.307217 | ||||||||
\(372\) | 2.23358e14 | 1.62560 | ||||||||
\(373\) | 2.51671e14 | 1.80483 | 0.902413 | − | 0.430873i | \(-0.141794\pi\) | ||||
0.902413 | + | 0.430873i | \(0.141794\pi\) | |||||||
\(374\) | 1.84775e14 | 1.30572 | ||||||||
\(375\) | −8.40017e13 | −0.584947 | ||||||||
\(376\) | −7.27080e13 | −0.498941 | ||||||||
\(377\) | 5.25450e14 | 3.55348 | ||||||||
\(378\) | −7.92205e13 | −0.527999 | ||||||||
\(379\) | −9.29507e12 | −0.0610572 | −0.0305286 | − | 0.999534i | \(-0.509719\pi\) | ||||
−0.0305286 | + | 0.999534i | \(0.509719\pi\) | |||||||
\(380\) | 6.37383e13 | 0.412658 | ||||||||
\(381\) | 2.47751e13 | 0.158098 | ||||||||
\(382\) | 5.08246e14 | 3.19688 | ||||||||
\(383\) | −1.92786e13 | −0.119532 | −0.0597658 | − | 0.998212i | \(-0.519035\pi\) | ||||
−0.0597658 | + | 0.998212i | \(0.519035\pi\) | |||||||
\(384\) | −9.18652e13 | −0.561474 | ||||||||
\(385\) | 1.55761e14 | 0.938482 | ||||||||
\(386\) | 1.80187e13 | 0.107027 | ||||||||
\(387\) | −2.91188e13 | −0.170515 | ||||||||
\(388\) | 3.98541e14 | 2.30091 | ||||||||
\(389\) | −7.46505e13 | −0.424923 | −0.212461 | − | 0.977169i | \(-0.568148\pi\) | ||||
−0.212461 | + | 0.977169i | \(0.568148\pi\) | |||||||
\(390\) | −2.16355e14 | −1.21426 | ||||||||
\(391\) | 4.55673e13 | 0.252163 | ||||||||
\(392\) | 5.44128e14 | 2.96912 | ||||||||
\(393\) | −2.06325e13 | −0.111018 | ||||||||
\(394\) | 2.63973e14 | 1.40065 | ||||||||
\(395\) | −1.69402e14 | −0.886410 | ||||||||
\(396\) | −1.41608e14 | −0.730743 | ||||||||
\(397\) | 2.36210e14 | 1.20213 | 0.601064 | − | 0.799201i | \(-0.294744\pi\) | ||||
0.601064 | + | 0.799201i | \(0.294744\pi\) | |||||||
\(398\) | −4.07990e14 | −2.04782 | ||||||||
\(399\) | −5.12562e13 | −0.253744 | ||||||||
\(400\) | −2.23214e14 | −1.08991 | ||||||||
\(401\) | 2.20343e14 | 1.06122 | 0.530609 | − | 0.847616i | \(-0.321963\pi\) | ||||
0.530609 | + | 0.847616i | \(0.321963\pi\) | |||||||
\(402\) | 4.36709e13 | 0.207467 | ||||||||
\(403\) | −4.90542e14 | −2.29878 | ||||||||
\(404\) | −1.81487e14 | −0.838974 | ||||||||
\(405\) | 1.54471e13 | 0.0704441 | ||||||||
\(406\) | 1.17817e15 | 5.30048 | ||||||||
\(407\) | −4.10935e14 | −1.82391 | ||||||||
\(408\) | −2.21646e14 | −0.970575 | ||||||||
\(409\) | 3.88815e13 | 0.167983 | 0.0839915 | − | 0.996466i | \(-0.473233\pi\) | ||||
0.0839915 | + | 0.996466i | \(0.473233\pi\) | |||||||
\(410\) | −1.56472e14 | −0.667000 | ||||||||
\(411\) | 3.19016e13 | 0.134178 | ||||||||
\(412\) | 3.10186e14 | 1.28732 | ||||||||
\(413\) | 4.83596e13 | 0.198042 | ||||||||
\(414\) | −5.04232e13 | −0.203764 | ||||||||
\(415\) | 1.02621e14 | 0.409235 | ||||||||
\(416\) | −4.80148e14 | −1.88957 | ||||||||
\(417\) | −4.46372e13 | −0.173360 | ||||||||
\(418\) | −1.32291e14 | −0.507061 | ||||||||
\(419\) | −3.55079e14 | −1.34322 | −0.671611 | − | 0.740904i | \(-0.734398\pi\) | ||||
−0.671611 | + | 0.740904i | \(0.734398\pi\) | |||||||
\(420\) | −3.35978e14 | −1.25441 | ||||||||
\(421\) | −1.71850e14 | −0.633282 | −0.316641 | − | 0.948545i | \(-0.602555\pi\) | ||||
−0.316641 | + | 0.948545i | \(0.602555\pi\) | |||||||
\(422\) | −6.23576e14 | −2.26815 | ||||||||
\(423\) | −2.05009e13 | −0.0736039 | ||||||||
\(424\) | 1.28766e14 | 0.456341 | ||||||||
\(425\) | 1.27186e14 | 0.444937 | ||||||||
\(426\) | 4.86692e14 | 1.68074 | ||||||||
\(427\) | −6.15240e14 | −2.09745 | ||||||||
\(428\) | 6.15584e14 | 2.07179 | ||||||||
\(429\) | 3.11002e14 | 1.03335 | ||||||||
\(430\) | −1.78312e14 | −0.584929 | ||||||||
\(431\) | −6.14914e13 | −0.199154 | −0.0995771 | − | 0.995030i | \(-0.531749\pi\) | ||||
−0.0995771 | + | 0.995030i | \(0.531749\pi\) | |||||||
\(432\) | 1.09682e14 | 0.350731 | ||||||||
\(433\) | −7.82609e13 | −0.247094 | −0.123547 | − | 0.992339i | \(-0.539427\pi\) | ||||
−0.123547 | + | 0.992339i | \(0.539427\pi\) | |||||||
\(434\) | −1.09990e15 | −3.42893 | ||||||||
\(435\) | −2.29730e14 | −0.707175 | ||||||||
\(436\) | −3.77268e14 | −1.14676 | ||||||||
\(437\) | −3.26241e13 | −0.0979245 | ||||||||
\(438\) | −1.68303e13 | −0.0498867 | ||||||||
\(439\) | 3.28708e14 | 0.962179 | 0.481089 | − | 0.876672i | \(-0.340241\pi\) | ||||
0.481089 | + | 0.876672i | \(0.340241\pi\) | |||||||
\(440\) | −4.82236e14 | −1.39402 | ||||||||
\(441\) | 1.53423e14 | 0.438005 | ||||||||
\(442\) | 8.75327e14 | 2.46801 | ||||||||
\(443\) | 4.77298e14 | 1.32914 | 0.664568 | − | 0.747228i | \(-0.268616\pi\) | ||||
0.664568 | + | 0.747228i | \(0.268616\pi\) | |||||||
\(444\) | 8.86388e14 | 2.43791 | ||||||||
\(445\) | −9.58170e13 | −0.260293 | ||||||||
\(446\) | −1.07176e15 | −2.87578 | ||||||||
\(447\) | −3.19958e14 | −0.848011 | ||||||||
\(448\) | −1.76629e13 | −0.0462415 | ||||||||
\(449\) | 5.08724e14 | 1.31561 | 0.657806 | − | 0.753187i | \(-0.271485\pi\) | ||||
0.657806 | + | 0.753187i | \(0.271485\pi\) | |||||||
\(450\) | −1.40739e14 | −0.359539 | ||||||||
\(451\) | 2.24923e14 | 0.567627 | ||||||||
\(452\) | −7.89445e14 | −1.96816 | ||||||||
\(453\) | 3.26486e13 | 0.0804127 | ||||||||
\(454\) | 5.03509e13 | 0.122518 | ||||||||
\(455\) | 7.37881e14 | 1.77388 | ||||||||
\(456\) | 1.58689e14 | 0.376912 | ||||||||
\(457\) | 3.88523e14 | 0.911754 | 0.455877 | − | 0.890043i | \(-0.349326\pi\) | ||||
0.455877 | + | 0.890043i | \(0.349326\pi\) | |||||||
\(458\) | −8.52032e14 | −1.97559 | ||||||||
\(459\) | −6.24958e13 | −0.143179 | ||||||||
\(460\) | −2.13847e14 | −0.484101 | ||||||||
\(461\) | 6.82062e12 | 0.0152570 | 0.00762849 | − | 0.999971i | \(-0.497572\pi\) | ||||
0.00762849 | + | 0.999971i | \(0.497572\pi\) | |||||||
\(462\) | 6.97333e14 | 1.54138 | ||||||||
\(463\) | 1.72115e14 | 0.375943 | 0.187972 | − | 0.982174i | \(-0.439809\pi\) | ||||
0.187972 | + | 0.982174i | \(0.439809\pi\) | |||||||
\(464\) | −1.63119e15 | −3.52092 | ||||||||
\(465\) | 2.14468e14 | 0.457479 | ||||||||
\(466\) | −1.16902e15 | −2.46434 | ||||||||
\(467\) | 7.08424e14 | 1.47588 | 0.737939 | − | 0.674868i | \(-0.235799\pi\) | ||||
0.737939 | + | 0.674868i | \(0.235799\pi\) | |||||||
\(468\) | −6.70834e14 | −1.38122 | ||||||||
\(469\) | −1.48940e14 | −0.303083 | ||||||||
\(470\) | −1.25539e14 | −0.252488 | ||||||||
\(471\) | −2.39812e14 | −0.476711 | ||||||||
\(472\) | −1.49721e14 | −0.294172 | ||||||||
\(473\) | 2.56317e14 | 0.497783 | ||||||||
\(474\) | −7.58402e14 | −1.45586 | ||||||||
\(475\) | −9.10593e13 | −0.172786 | ||||||||
\(476\) | 1.35930e15 | 2.54963 | ||||||||
\(477\) | 3.63072e13 | 0.0673195 | ||||||||
\(478\) | −4.78263e13 | −0.0876623 | ||||||||
\(479\) | −8.72334e13 | −0.158066 | −0.0790328 | − | 0.996872i | \(-0.525183\pi\) | ||||
−0.0790328 | + | 0.996872i | \(0.525183\pi\) | |||||||
\(480\) | 2.09924e14 | 0.376041 | ||||||||
\(481\) | −1.94670e15 | −3.44748 | ||||||||
\(482\) | −4.60060e14 | −0.805482 | ||||||||
\(483\) | 1.71969e14 | 0.297674 | ||||||||
\(484\) | −6.98792e13 | −0.119591 | ||||||||
\(485\) | 3.82679e14 | 0.647523 | ||||||||
\(486\) | 6.91557e13 | 0.115699 | ||||||||
\(487\) | 4.43086e14 | 0.732958 | 0.366479 | − | 0.930426i | \(-0.380563\pi\) | ||||
0.366479 | + | 0.930426i | \(0.380563\pi\) | |||||||
\(488\) | 1.90478e15 | 3.11555 | ||||||||
\(489\) | −6.24010e14 | −1.00924 | ||||||||
\(490\) | 9.39502e14 | 1.50252 | ||||||||
\(491\) | −2.84084e14 | −0.449260 | −0.224630 | − | 0.974444i | \(-0.572117\pi\) | ||||
−0.224630 | + | 0.974444i | \(0.572117\pi\) | |||||||
\(492\) | −4.85161e14 | −0.758713 | ||||||||
\(493\) | 9.29440e14 | 1.43735 | ||||||||
\(494\) | −6.26695e14 | −0.958425 | ||||||||
\(495\) | −1.35972e14 | −0.205647 | ||||||||
\(496\) | 1.52282e15 | 2.27772 | ||||||||
\(497\) | −1.65987e15 | −2.45535 | ||||||||
\(498\) | 4.59429e14 | 0.672136 | ||||||||
\(499\) | 9.50905e14 | 1.37589 | 0.687946 | − | 0.725762i | \(-0.258513\pi\) | ||||
0.687946 | + | 0.725762i | \(0.258513\pi\) | |||||||
\(500\) | −1.59493e15 | −2.28248 | ||||||||
\(501\) | −7.24024e13 | −0.102482 | ||||||||
\(502\) | −1.06366e15 | −1.48913 | ||||||||
\(503\) | −1.16004e15 | −1.60638 | −0.803188 | − | 0.595725i | \(-0.796865\pi\) | ||||
−0.803188 | + | 0.595725i | \(0.796865\pi\) | |||||||
\(504\) | −8.36483e14 | −1.14575 | ||||||||
\(505\) | −1.74264e14 | −0.236105 | ||||||||
\(506\) | 4.43847e14 | 0.594847 | ||||||||
\(507\) | 1.03780e15 | 1.37585 | ||||||||
\(508\) | 4.70402e14 | 0.616906 | ||||||||
\(509\) | 7.97015e14 | 1.03400 | 0.516998 | − | 0.855987i | \(-0.327050\pi\) | ||||
0.516998 | + | 0.855987i | \(0.327050\pi\) | |||||||
\(510\) | −3.82698e14 | −0.491157 | ||||||||
\(511\) | 5.74000e13 | 0.0728781 | ||||||||
\(512\) | −1.78788e15 | −2.24572 | ||||||||
\(513\) | 4.47442e13 | 0.0556021 | ||||||||
\(514\) | 1.68182e14 | 0.206767 | ||||||||
\(515\) | 2.97841e14 | 0.362280 | ||||||||
\(516\) | −5.52876e14 | −0.665357 | ||||||||
\(517\) | 1.80458e14 | 0.214871 | ||||||||
\(518\) | −4.36492e15 | −5.14236 | ||||||||
\(519\) | −7.98434e14 | −0.930719 | ||||||||
\(520\) | −2.28447e15 | −2.63492 | ||||||||
\(521\) | 1.25262e15 | 1.42960 | 0.714798 | − | 0.699331i | \(-0.246519\pi\) | ||||
0.714798 | + | 0.699331i | \(0.246519\pi\) | |||||||
\(522\) | −1.02849e15 | −1.16148 | ||||||||
\(523\) | −8.79438e14 | −0.982756 | −0.491378 | − | 0.870946i | \(-0.663507\pi\) | ||||
−0.491378 | + | 0.870946i | \(0.663507\pi\) | |||||||
\(524\) | −3.91748e14 | −0.433196 | ||||||||
\(525\) | 4.79993e14 | 0.525241 | ||||||||
\(526\) | −3.45897e14 | −0.374564 | ||||||||
\(527\) | −8.67692e14 | −0.929838 | ||||||||
\(528\) | −9.65466e14 | −1.02388 | ||||||||
\(529\) | −8.43353e14 | −0.885122 | ||||||||
\(530\) | 2.22330e14 | 0.230930 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | −9.73197e14 | −0.990118 | ||||||||
\(533\) | 1.06552e15 | 1.07291 | ||||||||
\(534\) | −4.28966e14 | −0.427510 | ||||||||
\(535\) | 5.91084e14 | 0.583047 | ||||||||
\(536\) | 4.61117e14 | 0.450200 | ||||||||
\(537\) | −1.11260e15 | −1.07518 | ||||||||
\(538\) | 1.27879e15 | 1.22320 | ||||||||
\(539\) | −1.35050e15 | −1.27866 | ||||||||
\(540\) | 2.93293e14 | 0.274875 | ||||||||
\(541\) | −4.33896e14 | −0.402533 | −0.201266 | − | 0.979537i | \(-0.564506\pi\) | ||||
−0.201266 | + | 0.979537i | \(0.564506\pi\) | |||||||
\(542\) | 3.68356e15 | 3.38276 | ||||||||
\(543\) | 1.07281e15 | 0.975267 | ||||||||
\(544\) | −8.49308e14 | −0.764313 | ||||||||
\(545\) | −3.62252e14 | −0.322723 | ||||||||
\(546\) | 3.30345e15 | 2.91345 | ||||||||
\(547\) | −1.45755e15 | −1.27260 | −0.636302 | − | 0.771440i | \(-0.719537\pi\) | ||||
−0.636302 | + | 0.771440i | \(0.719537\pi\) | |||||||
\(548\) | 6.05713e14 | 0.523569 | ||||||||
\(549\) | 5.37075e14 | 0.459607 | ||||||||
\(550\) | 1.23885e15 | 1.04960 | ||||||||
\(551\) | −6.65438e14 | −0.558179 | ||||||||
\(552\) | −5.32414e14 | −0.442165 | ||||||||
\(553\) | 2.58654e15 | 2.12682 | ||||||||
\(554\) | −2.10505e15 | −1.71379 | ||||||||
\(555\) | 8.51110e14 | 0.686079 | ||||||||
\(556\) | −8.47522e14 | −0.676456 | ||||||||
\(557\) | −1.26701e15 | −1.00133 | −0.500666 | − | 0.865641i | \(-0.666912\pi\) | ||||
−0.500666 | + | 0.865641i | \(0.666912\pi\) | |||||||
\(558\) | 9.60158e14 | 0.751371 | ||||||||
\(559\) | 1.21424e15 | 0.940889 | ||||||||
\(560\) | −2.29066e15 | −1.75762 | ||||||||
\(561\) | 5.50115e14 | 0.417982 | ||||||||
\(562\) | −3.64825e15 | −2.74495 | ||||||||
\(563\) | 2.07754e15 | 1.54794 | 0.773969 | − | 0.633224i | \(-0.218269\pi\) | ||||
0.773969 | + | 0.633224i | \(0.218269\pi\) | |||||||
\(564\) | −3.89249e14 | −0.287205 | ||||||||
\(565\) | −7.58025e14 | −0.553882 | ||||||||
\(566\) | 2.80906e15 | 2.03269 | ||||||||
\(567\) | −2.35856e14 | −0.169021 | ||||||||
\(568\) | 5.13895e15 | 3.64719 | ||||||||
\(569\) | 1.41887e15 | 0.997301 | 0.498650 | − | 0.866803i | \(-0.333829\pi\) | ||||
0.498650 | + | 0.866803i | \(0.333829\pi\) | |||||||
\(570\) | 2.73995e14 | 0.190735 | ||||||||
\(571\) | 1.21211e15 | 0.835686 | 0.417843 | − | 0.908519i | \(-0.362786\pi\) | ||||
0.417843 | + | 0.908519i | \(0.362786\pi\) | |||||||
\(572\) | 5.90497e15 | 4.03218 | ||||||||
\(573\) | 1.51316e15 | 1.02337 | ||||||||
\(574\) | 2.38912e15 | 1.60038 | ||||||||
\(575\) | 3.05511e14 | 0.202700 | ||||||||
\(576\) | 1.54188e13 | 0.0101328 | ||||||||
\(577\) | −1.12144e15 | −0.729974 | −0.364987 | − | 0.931013i | \(-0.618927\pi\) | ||||
−0.364987 | + | 0.931013i | \(0.618927\pi\) | |||||||
\(578\) | −1.24895e15 | −0.805273 | ||||||||
\(579\) | 5.36457e13 | 0.0342612 | ||||||||
\(580\) | −4.36186e15 | −2.75942 | ||||||||
\(581\) | −1.56689e15 | −0.981905 | ||||||||
\(582\) | 1.71323e15 | 1.06350 | ||||||||
\(583\) | −3.19591e14 | −0.196525 | ||||||||
\(584\) | −1.77710e14 | −0.108253 | ||||||||
\(585\) | −6.44135e14 | −0.388704 | ||||||||
\(586\) | 2.38205e15 | 1.42401 | ||||||||
\(587\) | −4.87270e14 | −0.288576 | −0.144288 | − | 0.989536i | \(-0.546089\pi\) | ||||
−0.144288 | + | 0.989536i | \(0.546089\pi\) | |||||||
\(588\) | 2.91304e15 | 1.70911 | ||||||||
\(589\) | 6.21229e14 | 0.361092 | ||||||||
\(590\) | −2.58511e14 | −0.148865 | ||||||||
\(591\) | 7.85904e14 | 0.448372 | ||||||||
\(592\) | 6.04328e15 | 3.41589 | ||||||||
\(593\) | 1.61540e14 | 0.0904648 | 0.0452324 | − | 0.998976i | \(-0.485597\pi\) | ||||
0.0452324 | + | 0.998976i | \(0.485597\pi\) | |||||||
\(594\) | −6.08738e14 | −0.337758 | ||||||||
\(595\) | 1.30520e15 | 0.717518 | ||||||||
\(596\) | −6.07501e15 | −3.30897 | ||||||||
\(597\) | −1.21467e15 | −0.655542 | ||||||||
\(598\) | 2.10261e15 | 1.12435 | ||||||||
\(599\) | −3.16140e15 | −1.67507 | −0.837533 | − | 0.546386i | \(-0.816003\pi\) | ||||
−0.837533 | + | 0.546386i | \(0.816003\pi\) | |||||||
\(600\) | −1.48605e15 | −0.780194 | ||||||||
\(601\) | 3.23614e15 | 1.68352 | 0.841759 | − | 0.539853i | \(-0.181520\pi\) | ||||
0.841759 | + | 0.539853i | \(0.181520\pi\) | |||||||
\(602\) | 2.72258e15 | 1.40346 | ||||||||
\(603\) | 1.30018e14 | 0.0664135 | ||||||||
\(604\) | 6.19896e14 | 0.313773 | ||||||||
\(605\) | −6.70980e13 | −0.0336554 | ||||||||
\(606\) | −7.80168e14 | −0.387783 | ||||||||
\(607\) | −2.17513e15 | −1.07139 | −0.535695 | − | 0.844412i | \(-0.679950\pi\) | ||||
−0.535695 | + | 0.844412i | \(0.679950\pi\) | |||||||
\(608\) | 6.08067e14 | 0.296812 | ||||||||
\(609\) | 3.50767e15 | 1.69677 | ||||||||
\(610\) | 3.28883e15 | 1.57662 | ||||||||
\(611\) | 8.54875e14 | 0.406140 | ||||||||
\(612\) | −1.18660e15 | −0.558691 | ||||||||
\(613\) | 2.25791e15 | 1.05359 | 0.526797 | − | 0.849991i | \(-0.323393\pi\) | ||||
0.526797 | + | 0.849991i | \(0.323393\pi\) | |||||||
\(614\) | −1.04741e15 | −0.484387 | ||||||||
\(615\) | −4.65851e14 | −0.213518 | ||||||||
\(616\) | 7.36309e15 | 3.34477 | ||||||||
\(617\) | −3.28604e14 | −0.147946 | −0.0739732 | − | 0.997260i | \(-0.523568\pi\) | ||||
−0.0739732 | + | 0.997260i | \(0.523568\pi\) | |||||||
\(618\) | 1.33341e15 | 0.595015 | ||||||||
\(619\) | 4.52186e14 | 0.199995 | 0.0999974 | − | 0.994988i | \(-0.468117\pi\) | ||||
0.0999974 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(620\) | 4.07208e15 | 1.78510 | ||||||||
\(621\) | −1.50121e14 | −0.0652283 | ||||||||
\(622\) | −6.22825e15 | −2.68237 | ||||||||
\(623\) | 1.46300e15 | 0.624538 | ||||||||
\(624\) | −4.57366e15 | −1.93530 | ||||||||
\(625\) | −1.05597e14 | −0.0442904 | ||||||||
\(626\) | −4.06960e15 | −1.69197 | ||||||||
\(627\) | −3.93858e14 | −0.162319 | ||||||||
\(628\) | −4.55328e15 | −1.86014 | ||||||||
\(629\) | −3.44341e15 | −1.39447 | ||||||||
\(630\) | −1.44429e15 | −0.579803 | ||||||||
\(631\) | −2.72204e15 | −1.08326 | −0.541630 | − | 0.840617i | \(-0.682192\pi\) | ||||
−0.541630 | + | 0.840617i | \(0.682192\pi\) | |||||||
\(632\) | −8.00790e15 | −3.15918 | ||||||||
\(633\) | −1.85652e15 | −0.726071 | ||||||||
\(634\) | 7.36184e15 | 2.85427 | ||||||||
\(635\) | 4.51680e14 | 0.173610 | ||||||||
\(636\) | 6.89360e14 | 0.262683 | ||||||||
\(637\) | −6.39766e15 | −2.41688 | ||||||||
\(638\) | 9.05318e15 | 3.39069 | ||||||||
\(639\) | 1.44899e15 | 0.538034 | ||||||||
\(640\) | −1.67482e15 | −0.616563 | ||||||||
\(641\) | −2.25361e15 | −0.822544 | −0.411272 | − | 0.911513i | \(-0.634915\pi\) | ||||
−0.411272 | + | 0.911513i | \(0.634915\pi\) | |||||||
\(642\) | 2.64624e15 | 0.957606 | ||||||||
\(643\) | 2.05762e15 | 0.738252 | 0.369126 | − | 0.929379i | \(-0.379657\pi\) | ||||
0.369126 | + | 0.929379i | \(0.379657\pi\) | |||||||
\(644\) | 3.26516e15 | 1.16153 | ||||||||
\(645\) | −5.30872e14 | −0.187245 | ||||||||
\(646\) | −1.10853e15 | −0.387674 | ||||||||
\(647\) | −4.94916e15 | −1.71616 | −0.858081 | − | 0.513515i | \(-0.828343\pi\) | ||||
−0.858081 | + | 0.513515i | \(0.828343\pi\) | |||||||
\(648\) | 7.30209e14 | 0.251064 | ||||||||
\(649\) | 3.71600e14 | 0.126686 | ||||||||
\(650\) | 5.86874e15 | 1.98391 | ||||||||
\(651\) | −3.27463e15 | −1.09766 | ||||||||
\(652\) | −1.18480e16 | −3.93807 | ||||||||
\(653\) | 3.07508e14 | 0.101352 | 0.0506762 | − | 0.998715i | \(-0.483862\pi\) | ||||
0.0506762 | + | 0.998715i | \(0.483862\pi\) | |||||||
\(654\) | −1.62178e15 | −0.530047 | ||||||||
\(655\) | −3.76156e14 | −0.121910 | ||||||||
\(656\) | −3.30776e15 | −1.06307 | ||||||||
\(657\) | −5.01074e13 | −0.0159695 | ||||||||
\(658\) | 1.91681e15 | 0.605810 | ||||||||
\(659\) | −5.82789e15 | −1.82659 | −0.913297 | − | 0.407295i | \(-0.866472\pi\) | ||||
−0.913297 | + | 0.407295i | \(0.866472\pi\) | |||||||
\(660\) | −2.58169e15 | −0.802440 | ||||||||
\(661\) | 1.33207e15 | 0.410601 | 0.205300 | − | 0.978699i | \(-0.434183\pi\) | ||||
0.205300 | + | 0.978699i | \(0.434183\pi\) | |||||||
\(662\) | 3.76949e15 | 1.15229 | ||||||||
\(663\) | 2.60603e15 | 0.790052 | ||||||||
\(664\) | 4.85107e15 | 1.45852 | ||||||||
\(665\) | −9.34464e14 | −0.278640 | ||||||||
\(666\) | 3.81036e15 | 1.12683 | ||||||||
\(667\) | 2.23260e15 | 0.654815 | ||||||||
\(668\) | −1.37470e15 | −0.399887 | ||||||||
\(669\) | −3.19086e15 | −0.920585 | ||||||||
\(670\) | 7.96174e14 | 0.227822 | ||||||||
\(671\) | −4.72757e15 | −1.34173 | ||||||||
\(672\) | −3.20525e15 | −0.902258 | ||||||||
\(673\) | −1.52829e15 | −0.426700 | −0.213350 | − | 0.976976i | \(-0.568437\pi\) | ||||
−0.213350 | + | 0.976976i | \(0.568437\pi\) | |||||||
\(674\) | 9.31737e15 | 2.58026 | ||||||||
\(675\) | −4.19011e14 | −0.115094 | ||||||||
\(676\) | 1.97047e16 | 5.36861 | ||||||||
\(677\) | −5.12640e15 | −1.38540 | −0.692700 | − | 0.721226i | \(-0.743579\pi\) | ||||
−0.692700 | + | 0.721226i | \(0.743579\pi\) | |||||||
\(678\) | −3.39363e15 | −0.909705 | ||||||||
\(679\) | −5.84299e15 | −1.55364 | ||||||||
\(680\) | −4.04088e15 | −1.06580 | ||||||||
\(681\) | 1.49905e14 | 0.0392200 | ||||||||
\(682\) | −8.45173e15 | −2.19347 | ||||||||
\(683\) | 1.46991e14 | 0.0378423 | 0.0189211 | − | 0.999821i | \(-0.493977\pi\) | ||||
0.0189211 | + | 0.999821i | \(0.493977\pi\) | |||||||
\(684\) | 8.49554e14 | 0.216961 | ||||||||
\(685\) | 5.81605e14 | 0.147343 | ||||||||
\(686\) | −3.42807e15 | −0.861522 | ||||||||
\(687\) | −2.53668e15 | −0.632417 | ||||||||
\(688\) | −3.76944e15 | −0.932267 | ||||||||
\(689\) | −1.51399e15 | −0.371463 | ||||||||
\(690\) | −9.19276e14 | −0.223757 | ||||||||
\(691\) | −1.07587e15 | −0.259796 | −0.129898 | − | 0.991527i | \(-0.541465\pi\) | ||||
−0.129898 | + | 0.991527i | \(0.541465\pi\) | |||||||
\(692\) | −1.51598e16 | −3.63170 | ||||||||
\(693\) | 2.07611e15 | 0.493421 | ||||||||
\(694\) | 1.28157e16 | 3.02179 | ||||||||
\(695\) | −8.13791e14 | −0.190369 | ||||||||
\(696\) | −1.08597e16 | −2.52039 | ||||||||
\(697\) | 1.88474e15 | 0.433981 | ||||||||
\(698\) | −3.60653e15 | −0.823919 | ||||||||
\(699\) | −3.48044e15 | −0.788877 | ||||||||
\(700\) | 9.11358e15 | 2.04951 | ||||||||
\(701\) | 2.38968e15 | 0.533201 | 0.266600 | − | 0.963807i | \(-0.414100\pi\) | ||||
0.266600 | + | 0.963807i | \(0.414100\pi\) | |||||||
\(702\) | −2.88375e15 | −0.638415 | ||||||||
\(703\) | 2.46533e15 | 0.541528 | ||||||||
\(704\) | −1.35723e14 | −0.0295804 | ||||||||
\(705\) | −3.73757e14 | −0.0808255 | ||||||||
\(706\) | 2.42684e14 | 0.0520732 | ||||||||
\(707\) | 2.66077e15 | 0.566501 | ||||||||
\(708\) | −8.01543e14 | −0.169334 | ||||||||
\(709\) | −7.42029e15 | −1.55549 | −0.777743 | − | 0.628582i | \(-0.783636\pi\) | ||||
−0.777743 | + | 0.628582i | \(0.783636\pi\) | |||||||
\(710\) | 8.87300e15 | 1.84565 | ||||||||
\(711\) | −2.25792e15 | −0.466044 | ||||||||
\(712\) | −4.52942e15 | −0.927690 | ||||||||
\(713\) | −2.08428e15 | −0.423607 | ||||||||
\(714\) | 5.84328e15 | 1.17846 | ||||||||
\(715\) | 5.66995e15 | 1.13474 | ||||||||
\(716\) | −2.11248e16 | −4.19538 | ||||||||
\(717\) | −1.42389e14 | −0.0280622 | ||||||||
\(718\) | 4.09542e15 | 0.800965 | ||||||||
\(719\) | −7.33878e15 | −1.42434 | −0.712172 | − | 0.702005i | \(-0.752288\pi\) | ||||
−0.712172 | + | 0.702005i | \(0.752288\pi\) | |||||||
\(720\) | 1.99963e15 | 0.385142 | ||||||||
\(721\) | −4.54762e15 | −0.869241 | ||||||||
\(722\) | −8.71427e15 | −1.65301 | ||||||||
\(723\) | −1.36970e15 | −0.257848 | ||||||||
\(724\) | 2.03693e16 | 3.80552 | ||||||||
\(725\) | 6.23154e15 | 1.15541 | ||||||||
\(726\) | −3.00393e14 | −0.0552763 | ||||||||
\(727\) | −5.82793e15 | −1.06433 | −0.532163 | − | 0.846642i | \(-0.678621\pi\) | ||||
−0.532163 | + | 0.846642i | \(0.678621\pi\) | |||||||
\(728\) | 3.48808e16 | 6.32214 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −3.06837e14 | −0.0547813 | ||||||||
\(731\) | 2.14780e15 | 0.380581 | ||||||||
\(732\) | 1.01974e16 | 1.79340 | ||||||||
\(733\) | −6.11773e15 | −1.06787 | −0.533935 | − | 0.845525i | \(-0.679287\pi\) | ||||
−0.533935 | + | 0.845525i | \(0.679287\pi\) | |||||||
\(734\) | −2.06314e16 | −3.57438 | ||||||||
\(735\) | 2.79710e15 | 0.480980 | ||||||||
\(736\) | −2.04011e15 | −0.348198 | ||||||||
\(737\) | −1.14447e15 | −0.193880 | ||||||||
\(738\) | −2.08558e15 | −0.350685 | ||||||||
\(739\) | 1.98400e13 | 0.00331128 | 0.00165564 | − | 0.999999i | \(-0.499473\pi\) | ||||
0.00165564 | + | 0.999999i | \(0.499473\pi\) | |||||||
\(740\) | 1.61599e16 | 2.67710 | ||||||||
\(741\) | −1.86581e15 | −0.306808 | ||||||||
\(742\) | −3.39468e15 | −0.554086 | ||||||||
\(743\) | −1.16649e15 | −0.188992 | −0.0944959 | − | 0.995525i | \(-0.530124\pi\) | ||||
−0.0944959 | + | 0.995525i | \(0.530124\pi\) | |||||||
\(744\) | 1.01382e16 | 1.63046 | ||||||||
\(745\) | −5.83322e15 | −0.931213 | ||||||||
\(746\) | 2.05414e16 | 3.25512 | ||||||||
\(747\) | 1.36782e15 | 0.215162 | ||||||||
\(748\) | 1.04450e16 | 1.63098 | ||||||||
\(749\) | −9.02505e15 | −1.39894 | ||||||||
\(750\) | −6.85622e15 | −1.05499 | ||||||||
\(751\) | 7.85668e15 | 1.20010 | 0.600052 | − | 0.799961i | \(-0.295146\pi\) | ||||
0.600052 | + | 0.799961i | \(0.295146\pi\) | |||||||
\(752\) | −2.65385e15 | −0.402418 | ||||||||
\(753\) | −3.16674e15 | −0.476694 | ||||||||
\(754\) | 4.28872e16 | 6.40893 | ||||||||
\(755\) | 5.95224e14 | 0.0883024 | ||||||||
\(756\) | −4.47818e15 | −0.659526 | ||||||||
\(757\) | −9.69063e15 | −1.41685 | −0.708427 | − | 0.705784i | \(-0.750595\pi\) | ||||
−0.708427 | + | 0.705784i | \(0.750595\pi\) | |||||||
\(758\) | −7.58663e14 | −0.110121 | ||||||||
\(759\) | 1.32143e15 | 0.190420 | ||||||||
\(760\) | 2.89309e15 | 0.413892 | ||||||||
\(761\) | −3.74357e15 | −0.531704 | −0.265852 | − | 0.964014i | \(-0.585653\pi\) | ||||
−0.265852 | + | 0.964014i | \(0.585653\pi\) | |||||||
\(762\) | 2.02214e15 | 0.285141 | ||||||||
\(763\) | 5.53110e15 | 0.774331 | ||||||||
\(764\) | 2.87302e16 | 3.99324 | ||||||||
\(765\) | −1.13937e15 | −0.157227 | ||||||||
\(766\) | −1.57352e15 | −0.215583 | ||||||||
\(767\) | 1.76036e15 | 0.239457 | ||||||||
\(768\) | −7.62799e15 | −1.03020 | ||||||||
\(769\) | 9.86595e15 | 1.32295 | 0.661476 | − | 0.749967i | \(-0.269930\pi\) | ||||
0.661476 | + | 0.749967i | \(0.269930\pi\) | |||||||
\(770\) | 1.27132e16 | 1.69261 | ||||||||
\(771\) | 5.00713e14 | 0.0661896 | ||||||||
\(772\) | 1.01856e15 | 0.133688 | ||||||||
\(773\) | −1.10280e16 | −1.43717 | −0.718585 | − | 0.695439i | \(-0.755210\pi\) | ||||
−0.718585 | + | 0.695439i | \(0.755210\pi\) | |||||||
\(774\) | −2.37668e15 | −0.307535 | ||||||||
\(775\) | −5.81755e15 | −0.747447 | ||||||||
\(776\) | 1.80899e16 | 2.30779 | ||||||||
\(777\) | −1.29953e16 | −1.64615 | ||||||||
\(778\) | −6.09297e15 | −0.766375 | ||||||||
\(779\) | −1.34939e15 | −0.168531 | ||||||||
\(780\) | −1.22301e16 | −1.51674 | ||||||||
\(781\) | −1.27546e16 | −1.57068 | ||||||||
\(782\) | 3.71920e15 | 0.454791 | ||||||||
\(783\) | −3.06202e15 | −0.371808 | ||||||||
\(784\) | 1.98607e16 | 2.39473 | ||||||||
\(785\) | −4.37206e15 | −0.523483 | ||||||||
\(786\) | −1.68403e15 | −0.200228 | ||||||||
\(787\) | −8.72132e15 | −1.02972 | −0.514862 | − | 0.857273i | \(-0.672157\pi\) | ||||
−0.514862 | + | 0.857273i | \(0.672157\pi\) | |||||||
\(788\) | 1.49219e16 | 1.74956 | ||||||||
\(789\) | −1.02981e15 | −0.119904 | ||||||||
\(790\) | −1.38266e16 | −1.59870 | ||||||||
\(791\) | 1.15740e16 | 1.32896 | ||||||||
\(792\) | −6.42762e15 | −0.732928 | ||||||||
\(793\) | −2.23957e16 | −2.53607 | ||||||||
\(794\) | 1.92795e16 | 2.16811 | ||||||||
\(795\) | 6.61924e14 | 0.0739246 | ||||||||
\(796\) | −2.30629e16 | −2.55795 | ||||||||
\(797\) | 4.87124e15 | 0.536561 | 0.268280 | − | 0.963341i | \(-0.413545\pi\) | ||||
0.268280 | + | 0.963341i | \(0.413545\pi\) | |||||||
\(798\) | −4.18353e15 | −0.457643 | ||||||||
\(799\) | 1.51214e15 | 0.164280 | ||||||||
\(800\) | −5.69429e15 | −0.614391 | ||||||||
\(801\) | −1.27712e15 | −0.136853 | ||||||||
\(802\) | 1.79844e16 | 1.91398 | ||||||||
\(803\) | 4.41067e14 | 0.0466197 | ||||||||
\(804\) | 2.46863e15 | 0.259148 | ||||||||
\(805\) | 3.13520e15 | 0.326880 | ||||||||
\(806\) | −4.00380e16 | −4.14600 | ||||||||
\(807\) | 3.80723e15 | 0.391565 | ||||||||
\(808\) | −8.23773e15 | −0.841482 | ||||||||
\(809\) | 1.27539e16 | 1.29398 | 0.646989 | − | 0.762499i | \(-0.276028\pi\) | ||||
0.646989 | + | 0.762499i | \(0.276028\pi\) | |||||||
\(810\) | 1.26079e15 | 0.127050 | ||||||||
\(811\) | 6.39555e15 | 0.640123 | 0.320061 | − | 0.947397i | \(-0.396296\pi\) | ||||
0.320061 | + | 0.947397i | \(0.396296\pi\) | |||||||
\(812\) | 6.65997e16 | 6.62086 | ||||||||
\(813\) | 1.09667e16 | 1.08288 | ||||||||
\(814\) | −3.35405e16 | −3.28954 | ||||||||
\(815\) | −1.13765e16 | −1.10826 | ||||||||
\(816\) | −8.09009e15 | −0.782812 | ||||||||
\(817\) | −1.53773e15 | −0.147794 | ||||||||
\(818\) | 3.17351e15 | 0.302968 | ||||||||
\(819\) | 9.83506e15 | 0.932643 | ||||||||
\(820\) | −8.84507e15 | −0.833154 | ||||||||
\(821\) | 3.80524e15 | 0.356036 | 0.178018 | − | 0.984027i | \(-0.443031\pi\) | ||||
0.178018 | + | 0.984027i | \(0.443031\pi\) | |||||||
\(822\) | 2.60381e15 | 0.241999 | ||||||||
\(823\) | 8.80374e15 | 0.812771 | 0.406386 | − | 0.913702i | \(-0.366789\pi\) | ||||
0.406386 | + | 0.913702i | \(0.366789\pi\) | |||||||
\(824\) | 1.40794e16 | 1.29117 | ||||||||
\(825\) | 3.68831e15 | 0.335994 | ||||||||
\(826\) | 3.94711e15 | 0.357181 | ||||||||
\(827\) | −1.45550e16 | −1.30838 | −0.654188 | − | 0.756332i | \(-0.726990\pi\) | ||||
−0.654188 | + | 0.756332i | \(0.726990\pi\) | |||||||
\(828\) | −2.85032e15 | −0.254523 | ||||||||
\(829\) | 1.55479e16 | 1.37918 | 0.689590 | − | 0.724200i | \(-0.257791\pi\) | ||||
0.689590 | + | 0.724200i | \(0.257791\pi\) | |||||||
\(830\) | 8.37595e15 | 0.738082 | ||||||||
\(831\) | −6.26717e15 | −0.548613 | ||||||||
\(832\) | −6.42955e14 | −0.0559117 | ||||||||
\(833\) | −1.13165e16 | −0.977605 | ||||||||
\(834\) | −3.64329e15 | −0.312666 | ||||||||
\(835\) | −1.31998e15 | −0.112536 | ||||||||
\(836\) | −7.47814e15 | −0.633372 | ||||||||
\(837\) | 2.85860e15 | 0.240526 | ||||||||
\(838\) | −2.89815e16 | −2.42259 | ||||||||
\(839\) | 1.35558e15 | 0.112573 | 0.0562863 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562863 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(840\) | −1.52501e16 | −1.25816 | ||||||||
\(841\) | 3.33380e16 | 2.73251 | ||||||||
\(842\) | −1.40264e16 | −1.14216 | ||||||||
\(843\) | −1.08616e16 | −0.878704 | ||||||||
\(844\) | −3.52495e16 | −2.83315 | ||||||||
\(845\) | 1.89204e16 | 1.51084 | ||||||||
\(846\) | −1.67328e15 | −0.132749 | ||||||||
\(847\) | 1.02450e15 | 0.0807516 | ||||||||
\(848\) | 4.69997e15 | 0.368059 | ||||||||
\(849\) | 8.36318e15 | 0.650698 | ||||||||
\(850\) | 1.03809e16 | 0.802473 | ||||||||
\(851\) | −8.27139e15 | −0.635281 | ||||||||
\(852\) | 2.75118e16 | 2.09943 | ||||||||
\(853\) | 1.78055e15 | 0.135000 | 0.0675002 | − | 0.997719i | \(-0.478498\pi\) | ||||
0.0675002 | + | 0.997719i | \(0.478498\pi\) | |||||||
\(854\) | −5.02159e16 | −3.78288 | ||||||||
\(855\) | 8.15741e14 | 0.0610575 | ||||||||
\(856\) | 2.79415e16 | 2.07799 | ||||||||
\(857\) | −1.27734e16 | −0.943867 | −0.471934 | − | 0.881634i | \(-0.656444\pi\) | ||||
−0.471934 | + | 0.881634i | \(0.656444\pi\) | |||||||
\(858\) | 2.53840e16 | 1.86372 | ||||||||
\(859\) | −8.71174e15 | −0.635539 | −0.317770 | − | 0.948168i | \(-0.602934\pi\) | ||||
−0.317770 | + | 0.948168i | \(0.602934\pi\) | |||||||
\(860\) | −1.00796e16 | −0.730638 | ||||||||
\(861\) | 7.11291e15 | 0.512307 | ||||||||
\(862\) | −5.01893e15 | −0.359187 | ||||||||
\(863\) | −7.36490e15 | −0.523730 | −0.261865 | − | 0.965104i | \(-0.584338\pi\) | ||||
−0.261865 | + | 0.965104i | \(0.584338\pi\) | |||||||
\(864\) | 2.79803e15 | 0.197709 | ||||||||
\(865\) | −1.45564e16 | −1.02204 | ||||||||
\(866\) | −6.38765e15 | −0.445649 | ||||||||
\(867\) | −3.71840e15 | −0.257781 | ||||||||
\(868\) | −6.21751e16 | −4.28310 | ||||||||
\(869\) | 1.98752e16 | 1.36052 | ||||||||
\(870\) | −1.87506e16 | −1.27544 | ||||||||
\(871\) | −5.42165e15 | −0.366464 | ||||||||
\(872\) | −1.71242e16 | −1.15019 | ||||||||
\(873\) | 5.10065e15 | 0.340445 | ||||||||
\(874\) | −2.66278e15 | −0.176613 | ||||||||
\(875\) | 2.33832e16 | 1.54120 | ||||||||
\(876\) | −9.51384e14 | −0.0623137 | ||||||||
\(877\) | −5.63043e15 | −0.366475 | −0.183237 | − | 0.983069i | \(-0.558658\pi\) | ||||
−0.183237 | + | 0.983069i | \(0.558658\pi\) | |||||||
\(878\) | 2.68291e16 | 1.73535 | ||||||||
\(879\) | 7.09186e15 | 0.455849 | ||||||||
\(880\) | −1.76016e16 | −1.12434 | ||||||||
\(881\) | −9.45939e15 | −0.600476 | −0.300238 | − | 0.953864i | \(-0.597066\pi\) | ||||
−0.300238 | + | 0.953864i | \(0.597066\pi\) | |||||||
\(882\) | 1.25224e16 | 0.789970 | ||||||||
\(883\) | 5.51462e15 | 0.345725 | 0.172863 | − | 0.984946i | \(-0.444698\pi\) | ||||
0.172863 | + | 0.984946i | \(0.444698\pi\) | |||||||
\(884\) | 4.94805e16 | 3.08281 | ||||||||
\(885\) | −7.69641e14 | −0.0476541 | ||||||||
\(886\) | 3.89571e16 | 2.39718 | ||||||||
\(887\) | 4.65928e14 | 0.0284931 | 0.0142465 | − | 0.999899i | \(-0.495465\pi\) | ||||
0.0142465 | + | 0.999899i | \(0.495465\pi\) | |||||||
\(888\) | 4.02333e16 | 2.44520 | ||||||||
\(889\) | −6.89654e15 | −0.416554 | ||||||||
\(890\) | −7.82058e15 | −0.469455 | ||||||||
\(891\) | −1.81234e15 | −0.108122 | ||||||||
\(892\) | −6.05845e16 | −3.59215 | ||||||||
\(893\) | −1.08263e15 | −0.0637963 | ||||||||
\(894\) | −2.61149e16 | −1.52944 | ||||||||
\(895\) | −2.02840e16 | −1.18067 | ||||||||
\(896\) | 2.55722e16 | 1.47936 | ||||||||
\(897\) | 6.25993e15 | 0.359924 | ||||||||
\(898\) | 4.15221e16 | 2.37279 | ||||||||
\(899\) | −4.25132e16 | −2.41460 | ||||||||
\(900\) | −7.95571e15 | −0.449102 | ||||||||
\(901\) | −2.67801e15 | −0.150254 | ||||||||
\(902\) | 1.83582e16 | 1.02375 | ||||||||
\(903\) | 8.10569e15 | 0.449270 | ||||||||
\(904\) | −3.58330e16 | −1.97404 | ||||||||
\(905\) | 1.95586e16 | 1.07095 | ||||||||
\(906\) | 2.66478e15 | 0.145029 | ||||||||
\(907\) | −1.01609e16 | −0.549657 | −0.274829 | − | 0.961493i | \(-0.588621\pi\) | ||||
−0.274829 | + | 0.961493i | \(0.588621\pi\) | |||||||
\(908\) | 2.84624e15 | 0.153038 | ||||||||
\(909\) | −2.32273e15 | −0.124136 | ||||||||
\(910\) | 6.02259e16 | 3.19930 | ||||||||
\(911\) | 2.38551e16 | 1.25959 | 0.629796 | − | 0.776761i | \(-0.283139\pi\) | ||||
0.629796 | + | 0.776761i | \(0.283139\pi\) | |||||||
\(912\) | 5.79215e15 | 0.303996 | ||||||||
\(913\) | −1.20401e16 | −0.628119 | ||||||||
\(914\) | 3.17112e16 | 1.64441 | ||||||||
\(915\) | 9.79153e15 | 0.504702 | ||||||||
\(916\) | −4.81637e16 | −2.46771 | ||||||||
\(917\) | 5.74339e15 | 0.292508 | ||||||||
\(918\) | −5.10090e15 | −0.258233 | ||||||||
\(919\) | −1.02830e16 | −0.517469 | −0.258734 | − | 0.965949i | \(-0.583305\pi\) | ||||
−0.258734 | + | 0.965949i | \(0.583305\pi\) | |||||||
\(920\) | −9.70656e15 | −0.485548 | ||||||||
\(921\) | −3.11838e15 | −0.155060 | ||||||||
\(922\) | 5.56698e14 | 0.0275169 | ||||||||
\(923\) | −6.04219e16 | −2.96883 | ||||||||
\(924\) | 3.94189e16 | 1.92535 | ||||||||
\(925\) | −2.30868e16 | −1.12094 | ||||||||
\(926\) | 1.40480e16 | 0.678037 | ||||||||
\(927\) | 3.96985e15 | 0.190474 | ||||||||
\(928\) | −4.16124e16 | −1.98476 | ||||||||
\(929\) | 1.53630e16 | 0.728433 | 0.364217 | − | 0.931314i | \(-0.381337\pi\) | ||||
0.364217 | + | 0.931314i | \(0.381337\pi\) | |||||||
\(930\) | 1.75049e16 | 0.825092 | ||||||||
\(931\) | 8.10209e15 | 0.379642 | ||||||||
\(932\) | −6.60827e16 | −3.07822 | ||||||||
\(933\) | −1.85428e16 | −0.858671 | ||||||||
\(934\) | 5.78215e16 | 2.66184 | ||||||||
\(935\) | 1.00293e16 | 0.458992 | ||||||||
\(936\) | −3.04493e16 | −1.38535 | ||||||||
\(937\) | −4.34110e16 | −1.96351 | −0.981753 | − | 0.190163i | \(-0.939099\pi\) | ||||
−0.981753 | + | 0.190163i | \(0.939099\pi\) | |||||||
\(938\) | −1.21565e16 | −0.546629 | ||||||||
\(939\) | −1.21161e16 | −0.541627 | ||||||||
\(940\) | −7.09648e15 | −0.315384 | ||||||||
\(941\) | −1.63325e16 | −0.721624 | −0.360812 | − | 0.932639i | \(-0.617500\pi\) | ||||
−0.360812 | + | 0.932639i | \(0.617500\pi\) | |||||||
\(942\) | −1.95734e16 | −0.859779 | ||||||||
\(943\) | 4.52731e15 | 0.197709 | ||||||||
\(944\) | −5.46482e15 | −0.237263 | ||||||||
\(945\) | −4.29995e15 | −0.185604 | ||||||||
\(946\) | 2.09205e16 | 0.897784 | ||||||||
\(947\) | 2.61485e16 | 1.11563 | 0.557817 | − | 0.829964i | \(-0.311639\pi\) | ||||
0.557817 | + | 0.829964i | \(0.311639\pi\) | |||||||
\(948\) | −4.28710e16 | −1.81852 | ||||||||
\(949\) | 2.08945e15 | 0.0881185 | ||||||||
\(950\) | −7.43225e15 | −0.311631 | ||||||||
\(951\) | 2.19178e16 | 0.913700 | ||||||||
\(952\) | 6.16987e16 | 2.55725 | ||||||||
\(953\) | −1.41902e16 | −0.584761 | −0.292380 | − | 0.956302i | \(-0.594447\pi\) | ||||
−0.292380 | + | 0.956302i | \(0.594447\pi\) | |||||||
\(954\) | 2.96339e15 | 0.121415 | ||||||||
\(955\) | 2.75867e16 | 1.12378 | ||||||||
\(956\) | −2.70353e15 | −0.109499 | ||||||||
\(957\) | 2.69533e16 | 1.08541 | ||||||||
\(958\) | −7.11999e15 | −0.285081 | ||||||||
\(959\) | −8.88032e15 | −0.353530 | ||||||||
\(960\) | 2.81104e14 | 0.0111269 | ||||||||
\(961\) | 1.42803e16 | 0.562029 | ||||||||
\(962\) | −1.58890e17 | −6.21775 | ||||||||
\(963\) | 7.87843e15 | 0.306546 | ||||||||
\(964\) | −2.60063e16 | −1.00613 | ||||||||
\(965\) | 9.78026e14 | 0.0376227 | ||||||||
\(966\) | 1.40361e16 | 0.536874 | ||||||||
\(967\) | 1.42672e16 | 0.542618 | 0.271309 | − | 0.962492i | \(-0.412544\pi\) | ||||
0.271309 | + | 0.962492i | \(0.412544\pi\) | |||||||
\(968\) | −3.17183e15 | −0.119949 | ||||||||
\(969\) | −3.30032e15 | −0.124101 | ||||||||
\(970\) | 3.12343e16 | 1.16785 | ||||||||
\(971\) | 4.02883e16 | 1.49787 | 0.748933 | − | 0.662645i | \(-0.230566\pi\) | ||||
0.748933 | + | 0.662645i | \(0.230566\pi\) | |||||||
\(972\) | 3.90923e15 | 0.144520 | ||||||||
\(973\) | 1.24255e16 | 0.456765 | ||||||||
\(974\) | 3.61647e16 | 1.32194 | ||||||||
\(975\) | 1.74725e16 | 0.635081 | ||||||||
\(976\) | 6.95245e16 | 2.51283 | ||||||||
\(977\) | −3.48577e16 | −1.25279 | −0.626396 | − | 0.779505i | \(-0.715471\pi\) | ||||
−0.626396 | + | 0.779505i | \(0.715471\pi\) | |||||||
\(978\) | −5.09316e16 | −1.82022 | ||||||||
\(979\) | 1.12418e16 | 0.399513 | ||||||||
\(980\) | 5.31082e16 | 1.87680 | ||||||||
\(981\) | −4.82838e15 | −0.169677 | ||||||||
\(982\) | −2.31869e16 | −0.810270 | ||||||||
\(983\) | −1.36013e15 | −0.0472645 | −0.0236323 | − | 0.999721i | \(-0.507523\pi\) | ||||
−0.0236323 | + | 0.999721i | \(0.507523\pi\) | |||||||
\(984\) | −2.20215e16 | −0.760982 | ||||||||
\(985\) | 1.43280e16 | 0.492364 | ||||||||
\(986\) | 7.58608e16 | 2.59236 | ||||||||
\(987\) | 5.70675e15 | 0.193930 | ||||||||
\(988\) | −3.54259e16 | −1.19717 | ||||||||
\(989\) | 5.15920e15 | 0.173382 | ||||||||
\(990\) | −1.10980e16 | −0.370897 | ||||||||
\(991\) | −4.70157e16 | −1.56256 | −0.781282 | − | 0.624178i | \(-0.785434\pi\) | ||||
−0.781282 | + | 0.624178i | \(0.785434\pi\) | |||||||
\(992\) | 3.88479e16 | 1.28396 | ||||||||
\(993\) | 1.12226e16 | 0.368868 | ||||||||
\(994\) | −1.35479e17 | −4.42839 | ||||||||
\(995\) | −2.21450e16 | −0.719860 | ||||||||
\(996\) | 2.59706e16 | 0.839568 | ||||||||
\(997\) | −1.00204e16 | −0.322154 | −0.161077 | − | 0.986942i | \(-0.551497\pi\) | ||||
−0.161077 | + | 0.986942i | \(0.551497\pi\) | |||||||
\(998\) | 7.76129e16 | 2.48151 | ||||||||
\(999\) | 1.13443e16 | 0.360717 |
(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 | 177.12.a.b.1.26 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.b.1.26 | ✓ | 27 | 1.1 | even | 1 | trivial |