Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −151.259 | −1.67120 | −0.835598 | − | 0.549342i | \(-0.814879\pi\) | ||||
−0.835598 | + | 0.549342i | \(0.814879\pi\) | |||||||
\(3\) | −729.000 | −0.577350 | ||||||||
\(4\) | 14687.4 | 1.79289 | ||||||||
\(5\) | 64912.3 | 1.85790 | 0.928949 | − | 0.370208i | \(-0.120714\pi\) | ||||
0.928949 | + | 0.370208i | \(0.120714\pi\) | |||||||
\(6\) | 110268. | 0.964865 | ||||||||
\(7\) | −35238.1 | −0.113208 | −0.0566038 | − | 0.998397i | \(-0.518027\pi\) | ||||
−0.0566038 | + | 0.998397i | \(0.518027\pi\) | |||||||
\(8\) | −982489. | −1.32508 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −9.81859e6 | −3.10491 | ||||||||
\(11\) | −846653. | −0.144096 | −0.0720482 | − | 0.997401i | \(-0.522954\pi\) | ||||
−0.0720482 | + | 0.997401i | \(0.522954\pi\) | |||||||
\(12\) | −1.07071e7 | −1.03513 | ||||||||
\(13\) | −6.32197e6 | −0.363263 | −0.181631 | − | 0.983367i | \(-0.558138\pi\) | ||||
−0.181631 | + | 0.983367i | \(0.558138\pi\) | |||||||
\(14\) | 5.33010e6 | 0.189192 | ||||||||
\(15\) | −4.73210e7 | −1.07266 | ||||||||
\(16\) | 2.82916e7 | 0.421577 | ||||||||
\(17\) | 8.25934e7 | 0.829903 | 0.414952 | − | 0.909844i | \(-0.363799\pi\) | ||||
0.414952 | + | 0.909844i | \(0.363799\pi\) | |||||||
\(18\) | −8.03854e7 | −0.557065 | ||||||||
\(19\) | 3.86792e8 | 1.88616 | 0.943080 | − | 0.332565i | \(-0.107914\pi\) | ||||
0.943080 | + | 0.332565i | \(0.107914\pi\) | |||||||
\(20\) | 9.53392e8 | 3.33102 | ||||||||
\(21\) | 2.56886e7 | 0.0653604 | ||||||||
\(22\) | 1.28064e8 | 0.240813 | ||||||||
\(23\) | −5.52943e8 | −0.778842 | −0.389421 | − | 0.921060i | \(-0.627325\pi\) | ||||
−0.389421 | + | 0.921060i | \(0.627325\pi\) | |||||||
\(24\) | 7.16235e8 | 0.765037 | ||||||||
\(25\) | 2.99290e9 | 2.45178 | ||||||||
\(26\) | 9.56257e8 | 0.607083 | ||||||||
\(27\) | −3.87420e8 | −0.192450 | ||||||||
\(28\) | −5.17556e8 | −0.202969 | ||||||||
\(29\) | −3.29886e9 | −1.02986 | −0.514929 | − | 0.857233i | \(-0.672182\pi\) | ||||
−0.514929 | + | 0.857233i | \(0.672182\pi\) | |||||||
\(30\) | 7.15775e9 | 1.79262 | ||||||||
\(31\) | −1.19195e9 | −0.241217 | −0.120608 | − | 0.992700i | \(-0.538485\pi\) | ||||
−0.120608 | + | 0.992700i | \(0.538485\pi\) | |||||||
\(32\) | 3.76919e9 | 0.620544 | ||||||||
\(33\) | 6.17210e8 | 0.0831941 | ||||||||
\(34\) | −1.24930e10 | −1.38693 | ||||||||
\(35\) | −2.28739e9 | −0.210328 | ||||||||
\(36\) | 7.80548e9 | 0.597632 | ||||||||
\(37\) | −2.10134e10 | −1.34644 | −0.673218 | − | 0.739444i | \(-0.735088\pi\) | ||||
−0.673218 | + | 0.739444i | \(0.735088\pi\) | |||||||
\(38\) | −5.85059e10 | −3.15214 | ||||||||
\(39\) | 4.60872e9 | 0.209730 | ||||||||
\(40\) | −6.37756e10 | −2.46187 | ||||||||
\(41\) | 5.49178e10 | 1.80559 | 0.902793 | − | 0.430076i | \(-0.141513\pi\) | ||||
0.902793 | + | 0.430076i | \(0.141513\pi\) | |||||||
\(42\) | −3.88564e9 | −0.109230 | ||||||||
\(43\) | −1.86354e9 | −0.0449565 | −0.0224783 | − | 0.999747i | \(-0.507156\pi\) | ||||
−0.0224783 | + | 0.999747i | \(0.507156\pi\) | |||||||
\(44\) | −1.24351e10 | −0.258350 | ||||||||
\(45\) | 3.44970e10 | 0.619299 | ||||||||
\(46\) | 8.36378e10 | 1.30160 | ||||||||
\(47\) | −1.24763e11 | −1.68830 | −0.844148 | − | 0.536110i | \(-0.819893\pi\) | ||||
−0.844148 | + | 0.536110i | \(0.819893\pi\) | |||||||
\(48\) | −2.06246e10 | −0.243398 | ||||||||
\(49\) | −9.56473e10 | −0.987184 | ||||||||
\(50\) | −4.52704e11 | −4.09741 | ||||||||
\(51\) | −6.02106e10 | −0.479145 | ||||||||
\(52\) | −9.28533e10 | −0.651292 | ||||||||
\(53\) | −2.31878e11 | −1.43703 | −0.718516 | − | 0.695511i | \(-0.755178\pi\) | ||||
−0.718516 | + | 0.695511i | \(0.755178\pi\) | |||||||
\(54\) | 5.86010e10 | 0.321622 | ||||||||
\(55\) | −5.49582e10 | −0.267716 | ||||||||
\(56\) | 3.46211e10 | 0.150009 | ||||||||
\(57\) | −2.81971e11 | −1.08898 | ||||||||
\(58\) | 4.98984e11 | 1.72109 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −6.95023e11 | −1.92316 | ||||||||
\(61\) | 2.65237e11 | 0.659159 | 0.329580 | − | 0.944128i | \(-0.393093\pi\) | ||||
0.329580 | + | 0.944128i | \(0.393093\pi\) | |||||||
\(62\) | 1.80294e11 | 0.403121 | ||||||||
\(63\) | −1.87270e10 | −0.0377359 | ||||||||
\(64\) | −8.01889e11 | −1.45863 | ||||||||
\(65\) | −4.10374e11 | −0.674905 | ||||||||
\(66\) | −9.33588e10 | −0.139034 | ||||||||
\(67\) | −6.42635e11 | −0.867917 | −0.433958 | − | 0.900933i | \(-0.642884\pi\) | ||||
−0.433958 | + | 0.900933i | \(0.642884\pi\) | |||||||
\(68\) | 1.21308e12 | 1.48793 | ||||||||
\(69\) | 4.03095e11 | 0.449665 | ||||||||
\(70\) | 3.45989e11 | 0.351499 | ||||||||
\(71\) | −1.49296e12 | −1.38315 | −0.691575 | − | 0.722305i | \(-0.743083\pi\) | ||||
−0.691575 | + | 0.722305i | \(0.743083\pi\) | |||||||
\(72\) | −5.22135e11 | −0.441694 | ||||||||
\(73\) | 8.05814e11 | 0.623212 | 0.311606 | − | 0.950211i | \(-0.399133\pi\) | ||||
0.311606 | + | 0.950211i | \(0.399133\pi\) | |||||||
\(74\) | 3.17848e12 | 2.25016 | ||||||||
\(75\) | −2.18182e12 | −1.41554 | ||||||||
\(76\) | 5.68096e12 | 3.38169 | ||||||||
\(77\) | 2.98345e10 | 0.0163128 | ||||||||
\(78\) | −6.97112e11 | −0.350500 | ||||||||
\(79\) | 2.72274e12 | 1.26017 | 0.630087 | − | 0.776525i | \(-0.283019\pi\) | ||||
0.630087 | + | 0.776525i | \(0.283019\pi\) | |||||||
\(80\) | 1.83647e12 | 0.783248 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −8.30683e12 | −3.01749 | ||||||||
\(83\) | −5.25906e12 | −1.76563 | −0.882817 | − | 0.469718i | \(-0.844356\pi\) | ||||
−0.882817 | + | 0.469718i | \(0.844356\pi\) | |||||||
\(84\) | 3.77299e11 | 0.117184 | ||||||||
\(85\) | 5.36133e12 | 1.54187 | ||||||||
\(86\) | 2.81877e11 | 0.0751311 | ||||||||
\(87\) | 2.40487e12 | 0.594589 | ||||||||
\(88\) | 8.31828e11 | 0.190940 | ||||||||
\(89\) | 2.96797e12 | 0.633030 | 0.316515 | − | 0.948587i | \(-0.397487\pi\) | ||||
0.316515 | + | 0.948587i | \(0.397487\pi\) | |||||||
\(90\) | −5.21800e12 | −1.03497 | ||||||||
\(91\) | 2.22774e11 | 0.0411241 | ||||||||
\(92\) | −8.12129e12 | −1.39638 | ||||||||
\(93\) | 8.68933e11 | 0.139267 | ||||||||
\(94\) | 1.88715e13 | 2.82147 | ||||||||
\(95\) | 2.51075e13 | 3.50429 | ||||||||
\(96\) | −2.74774e12 | −0.358271 | ||||||||
\(97\) | −1.05219e13 | −1.28256 | −0.641279 | − | 0.767308i | \(-0.721596\pi\) | ||||
−0.641279 | + | 0.767308i | \(0.721596\pi\) | |||||||
\(98\) | 1.44675e13 | 1.64978 | ||||||||
\(99\) | −4.49946e11 | −0.0480321 | ||||||||
\(100\) | 4.39579e13 | 4.39579 | ||||||||
\(101\) | −1.71707e13 | −1.60953 | −0.804764 | − | 0.593595i | \(-0.797708\pi\) | ||||
−0.804764 | + | 0.593595i | \(0.797708\pi\) | |||||||
\(102\) | 9.10742e12 | 0.800745 | ||||||||
\(103\) | −2.24871e13 | −1.85563 | −0.927813 | − | 0.373045i | \(-0.878314\pi\) | ||||
−0.927813 | + | 0.373045i | \(0.878314\pi\) | |||||||
\(104\) | 6.21127e12 | 0.481353 | ||||||||
\(105\) | 1.66751e12 | 0.121433 | ||||||||
\(106\) | 3.50737e13 | 2.40156 | ||||||||
\(107\) | 1.48950e13 | 0.959504 | 0.479752 | − | 0.877404i | \(-0.340727\pi\) | ||||
0.479752 | + | 0.877404i | \(0.340727\pi\) | |||||||
\(108\) | −5.69020e12 | −0.345043 | ||||||||
\(109\) | −6.24650e12 | −0.356751 | −0.178375 | − | 0.983963i | \(-0.557084\pi\) | ||||
−0.178375 | + | 0.983963i | \(0.557084\pi\) | |||||||
\(110\) | 8.31294e12 | 0.447406 | ||||||||
\(111\) | 1.53188e13 | 0.777365 | ||||||||
\(112\) | −9.96943e11 | −0.0477258 | ||||||||
\(113\) | 1.07703e13 | 0.486653 | 0.243327 | − | 0.969944i | \(-0.421761\pi\) | ||||
0.243327 | + | 0.969944i | \(0.421761\pi\) | |||||||
\(114\) | 4.26508e13 | 1.81989 | ||||||||
\(115\) | −3.58928e13 | −1.44701 | ||||||||
\(116\) | −4.84517e13 | −1.84643 | ||||||||
\(117\) | −3.35976e12 | −0.121088 | ||||||||
\(118\) | 6.38020e12 | 0.217571 | ||||||||
\(119\) | −2.91044e12 | −0.0939513 | ||||||||
\(120\) | 4.64924e13 | 1.42136 | ||||||||
\(121\) | −3.38059e13 | −0.979236 | ||||||||
\(122\) | −4.01196e13 | −1.10158 | ||||||||
\(123\) | −4.00351e13 | −1.04246 | ||||||||
\(124\) | −1.75067e13 | −0.432476 | ||||||||
\(125\) | 1.15037e14 | 2.69726 | ||||||||
\(126\) | 2.83263e12 | 0.0630640 | ||||||||
\(127\) | 2.38612e13 | 0.504624 | 0.252312 | − | 0.967646i | \(-0.418809\pi\) | ||||
0.252312 | + | 0.967646i | \(0.418809\pi\) | |||||||
\(128\) | 9.04161e13 | 1.81711 | ||||||||
\(129\) | 1.35852e12 | 0.0259557 | ||||||||
\(130\) | 6.20728e13 | 1.12790 | ||||||||
\(131\) | −5.10666e13 | −0.882822 | −0.441411 | − | 0.897305i | \(-0.645522\pi\) | ||||
−0.441411 | + | 0.897305i | \(0.645522\pi\) | |||||||
\(132\) | 9.06521e12 | 0.149158 | ||||||||
\(133\) | −1.36298e13 | −0.213528 | ||||||||
\(134\) | 9.72046e13 | 1.45046 | ||||||||
\(135\) | −2.51483e13 | −0.357553 | ||||||||
\(136\) | −8.11472e13 | −1.09969 | ||||||||
\(137\) | 1.00612e14 | 1.30007 | 0.650035 | − | 0.759904i | \(-0.274754\pi\) | ||||
0.650035 | + | 0.759904i | \(0.274754\pi\) | |||||||
\(138\) | −6.09720e13 | −0.751478 | ||||||||
\(139\) | −6.63965e13 | −0.780817 | −0.390408 | − | 0.920642i | \(-0.627666\pi\) | ||||
−0.390408 | + | 0.920642i | \(0.627666\pi\) | |||||||
\(140\) | −3.35958e13 | −0.377096 | ||||||||
\(141\) | 9.09520e13 | 0.974738 | ||||||||
\(142\) | 2.25824e14 | 2.31151 | ||||||||
\(143\) | 5.35252e12 | 0.0523449 | ||||||||
\(144\) | 1.50353e13 | 0.140526 | ||||||||
\(145\) | −2.14137e14 | −1.91337 | ||||||||
\(146\) | −1.21887e14 | −1.04151 | ||||||||
\(147\) | 6.97269e13 | 0.569951 | ||||||||
\(148\) | −3.08632e14 | −2.41402 | ||||||||
\(149\) | 1.10223e14 | 0.825202 | 0.412601 | − | 0.910912i | \(-0.364620\pi\) | ||||
0.412601 | + | 0.910912i | \(0.364620\pi\) | |||||||
\(150\) | 3.30021e14 | 2.36564 | ||||||||
\(151\) | −9.61814e13 | −0.660299 | −0.330150 | − | 0.943929i | \(-0.607099\pi\) | ||||
−0.330150 | + | 0.943929i | \(0.607099\pi\) | |||||||
\(152\) | −3.80019e14 | −2.49932 | ||||||||
\(153\) | 4.38935e13 | 0.276634 | ||||||||
\(154\) | −4.51274e12 | −0.0272619 | ||||||||
\(155\) | −7.73723e13 | −0.448156 | ||||||||
\(156\) | 6.76901e13 | 0.376024 | ||||||||
\(157\) | 1.65060e14 | 0.879618 | 0.439809 | − | 0.898091i | \(-0.355046\pi\) | ||||
0.439809 | + | 0.898091i | \(0.355046\pi\) | |||||||
\(158\) | −4.11840e14 | −2.10600 | ||||||||
\(159\) | 1.69039e14 | 0.829670 | ||||||||
\(160\) | 2.44666e14 | 1.15291 | ||||||||
\(161\) | 1.94847e13 | 0.0881708 | ||||||||
\(162\) | −4.27201e13 | −0.185688 | ||||||||
\(163\) | 1.55380e14 | 0.648897 | 0.324448 | − | 0.945903i | \(-0.394821\pi\) | ||||
0.324448 | + | 0.945903i | \(0.394821\pi\) | |||||||
\(164\) | 8.06599e14 | 3.23723 | ||||||||
\(165\) | 4.00645e13 | 0.154566 | ||||||||
\(166\) | 7.95482e14 | 2.95072 | ||||||||
\(167\) | −3.80240e14 | −1.35644 | −0.678220 | − | 0.734859i | \(-0.737248\pi\) | ||||
−0.678220 | + | 0.734859i | \(0.737248\pi\) | |||||||
\(168\) | −2.52388e13 | −0.0866080 | ||||||||
\(169\) | −2.62908e14 | −0.868040 | ||||||||
\(170\) | −8.10951e14 | −2.57677 | ||||||||
\(171\) | 2.05557e14 | 0.628720 | ||||||||
\(172\) | −2.73705e13 | −0.0806023 | ||||||||
\(173\) | 1.73919e14 | 0.493228 | 0.246614 | − | 0.969114i | \(-0.420682\pi\) | ||||
0.246614 | + | 0.969114i | \(0.420682\pi\) | |||||||
\(174\) | −3.63759e14 | −0.993674 | ||||||||
\(175\) | −1.05464e14 | −0.277561 | ||||||||
\(176\) | −2.39532e13 | −0.0607478 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −4.48933e14 | −1.05792 | ||||||||
\(179\) | 3.26210e14 | 0.741230 | 0.370615 | − | 0.928787i | \(-0.379147\pi\) | ||||
0.370615 | + | 0.928787i | \(0.379147\pi\) | |||||||
\(180\) | 5.06672e14 | 1.11034 | ||||||||
\(181\) | −3.06032e14 | −0.646927 | −0.323464 | − | 0.946241i | \(-0.604847\pi\) | ||||
−0.323464 | + | 0.946241i | \(0.604847\pi\) | |||||||
\(182\) | −3.36967e13 | −0.0687264 | ||||||||
\(183\) | −1.93358e14 | −0.380566 | ||||||||
\(184\) | 5.43261e14 | 1.03203 | ||||||||
\(185\) | −1.36403e15 | −2.50154 | ||||||||
\(186\) | −1.31434e14 | −0.232742 | ||||||||
\(187\) | −6.99280e13 | −0.119586 | ||||||||
\(188\) | −1.83244e15 | −3.02694 | ||||||||
\(189\) | 1.36520e13 | 0.0217868 | ||||||||
\(190\) | −3.79775e15 | −5.85636 | ||||||||
\(191\) | 9.30763e14 | 1.38715 | 0.693573 | − | 0.720386i | \(-0.256035\pi\) | ||||
0.693573 | + | 0.720386i | \(0.256035\pi\) | |||||||
\(192\) | 5.84577e14 | 0.842139 | ||||||||
\(193\) | −2.42712e14 | −0.338040 | −0.169020 | − | 0.985613i | \(-0.554060\pi\) | ||||
−0.169020 | + | 0.985613i | \(0.554060\pi\) | |||||||
\(194\) | 1.59153e15 | 2.14341 | ||||||||
\(195\) | 2.99162e14 | 0.389656 | ||||||||
\(196\) | −1.40481e15 | −1.76992 | ||||||||
\(197\) | 8.35797e14 | 1.01876 | 0.509378 | − | 0.860543i | \(-0.329875\pi\) | ||||
0.509378 | + | 0.860543i | \(0.329875\pi\) | |||||||
\(198\) | 6.80586e13 | 0.0802711 | ||||||||
\(199\) | 6.29358e14 | 0.718377 | 0.359189 | − | 0.933265i | \(-0.383053\pi\) | ||||
0.359189 | + | 0.933265i | \(0.383053\pi\) | |||||||
\(200\) | −2.94049e15 | −3.24882 | ||||||||
\(201\) | 4.68481e14 | 0.501092 | ||||||||
\(202\) | 2.59723e15 | 2.68984 | ||||||||
\(203\) | 1.16246e14 | 0.116588 | ||||||||
\(204\) | −8.84337e14 | −0.859056 | ||||||||
\(205\) | 3.56484e15 | 3.35459 | ||||||||
\(206\) | 3.40138e15 | 3.10111 | ||||||||
\(207\) | −2.93857e14 | −0.259614 | ||||||||
\(208\) | −1.78859e14 | −0.153143 | ||||||||
\(209\) | −3.27478e14 | −0.271789 | ||||||||
\(210\) | −2.52226e14 | −0.202938 | ||||||||
\(211\) | −1.03086e15 | −0.804198 | −0.402099 | − | 0.915596i | \(-0.631719\pi\) | ||||
−0.402099 | + | 0.915596i | \(0.631719\pi\) | |||||||
\(212\) | −3.40568e15 | −2.57645 | ||||||||
\(213\) | 1.08837e15 | 0.798562 | ||||||||
\(214\) | −2.25301e15 | −1.60352 | ||||||||
\(215\) | −1.20966e14 | −0.0835246 | ||||||||
\(216\) | 3.80637e14 | 0.255012 | ||||||||
\(217\) | 4.20022e13 | 0.0273076 | ||||||||
\(218\) | 9.44842e14 | 0.596200 | ||||||||
\(219\) | −5.87438e14 | −0.359812 | ||||||||
\(220\) | −8.07193e14 | −0.479987 | ||||||||
\(221\) | −5.22153e14 | −0.301473 | ||||||||
\(222\) | −2.31711e15 | −1.29913 | ||||||||
\(223\) | −2.31105e15 | −1.25843 | −0.629214 | − | 0.777232i | \(-0.716623\pi\) | ||||
−0.629214 | + | 0.777232i | \(0.716623\pi\) | |||||||
\(224\) | −1.32819e14 | −0.0702503 | ||||||||
\(225\) | 1.59055e15 | 0.817261 | ||||||||
\(226\) | −1.62912e15 | −0.813293 | ||||||||
\(227\) | 3.55441e12 | 0.00172425 | 0.000862123 | − | 1.00000i | \(-0.499726\pi\) | ||||
0.000862123 | 1.00000i | \(0.499726\pi\) | ||||||||
\(228\) | −4.14142e15 | −1.95242 | ||||||||
\(229\) | −2.69927e15 | −1.23685 | −0.618423 | − | 0.785845i | \(-0.712228\pi\) | ||||
−0.618423 | + | 0.785845i | \(0.712228\pi\) | |||||||
\(230\) | 5.42912e15 | 2.41823 | ||||||||
\(231\) | −2.17493e13 | −0.00941821 | ||||||||
\(232\) | 3.24110e15 | 1.36465 | ||||||||
\(233\) | 1.99363e15 | 0.816265 | 0.408133 | − | 0.912923i | \(-0.366180\pi\) | ||||
0.408133 | + | 0.912923i | \(0.366180\pi\) | |||||||
\(234\) | 5.08194e14 | 0.202361 | ||||||||
\(235\) | −8.09863e15 | −3.13668 | ||||||||
\(236\) | −6.19522e14 | −0.233415 | ||||||||
\(237\) | −1.98488e15 | −0.727562 | ||||||||
\(238\) | 4.40231e14 | 0.157011 | ||||||||
\(239\) | −8.90069e14 | −0.308914 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(240\) | −1.33879e15 | −0.452208 | ||||||||
\(241\) | −2.45265e15 | −0.806351 | −0.403176 | − | 0.915123i | \(-0.632094\pi\) | ||||
−0.403176 | + | 0.915123i | \(0.632094\pi\) | |||||||
\(242\) | 5.11346e15 | 1.63650 | ||||||||
\(243\) | −2.05891e14 | −0.0641500 | ||||||||
\(244\) | 3.89564e15 | 1.18180 | ||||||||
\(245\) | −6.20868e15 | −1.83409 | ||||||||
\(246\) | 6.05568e15 | 1.74215 | ||||||||
\(247\) | −2.44529e15 | −0.685172 | ||||||||
\(248\) | 1.17108e15 | 0.319632 | ||||||||
\(249\) | 3.83385e15 | 1.01939 | ||||||||
\(250\) | −1.74005e16 | −4.50766 | ||||||||
\(251\) | −1.12049e15 | −0.282832 | −0.141416 | − | 0.989950i | \(-0.545166\pi\) | ||||
−0.141416 | + | 0.989950i | \(0.545166\pi\) | |||||||
\(252\) | −2.75051e14 | −0.0676564 | ||||||||
\(253\) | 4.68151e14 | 0.112228 | ||||||||
\(254\) | −3.60923e15 | −0.843326 | ||||||||
\(255\) | −3.90841e15 | −0.890202 | ||||||||
\(256\) | −7.10721e15 | −1.57812 | ||||||||
\(257\) | −2.10640e15 | −0.456010 | −0.228005 | − | 0.973660i | \(-0.573220\pi\) | ||||
−0.228005 | + | 0.973660i | \(0.573220\pi\) | |||||||
\(258\) | −2.05488e14 | −0.0433770 | ||||||||
\(259\) | 7.40474e14 | 0.152427 | ||||||||
\(260\) | −6.02732e15 | −1.21003 | ||||||||
\(261\) | −1.75315e15 | −0.343286 | ||||||||
\(262\) | 7.72430e15 | 1.47537 | ||||||||
\(263\) | 7.69691e15 | 1.43418 | 0.717090 | − | 0.696980i | \(-0.245474\pi\) | ||||
0.717090 | + | 0.696980i | \(0.245474\pi\) | |||||||
\(264\) | −6.06403e14 | −0.110239 | ||||||||
\(265\) | −1.50517e16 | −2.66986 | ||||||||
\(266\) | 2.06164e15 | 0.356847 | ||||||||
\(267\) | −2.16365e15 | −0.365480 | ||||||||
\(268\) | −9.43863e15 | −1.55608 | ||||||||
\(269\) | 2.48086e15 | 0.399220 | 0.199610 | − | 0.979875i | \(-0.436032\pi\) | ||||
0.199610 | + | 0.979875i | \(0.436032\pi\) | |||||||
\(270\) | 3.80392e15 | 0.597540 | ||||||||
\(271\) | −5.84551e15 | −0.896442 | −0.448221 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448221 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(272\) | 2.33670e15 | 0.349868 | ||||||||
\(273\) | −1.62403e14 | −0.0237430 | ||||||||
\(274\) | −1.52185e16 | −2.17267 | ||||||||
\(275\) | −2.53395e15 | −0.353293 | ||||||||
\(276\) | 5.92042e15 | 0.806201 | ||||||||
\(277\) | 1.80975e15 | 0.240714 | 0.120357 | − | 0.992731i | \(-0.461596\pi\) | ||||
0.120357 | + | 0.992731i | \(0.461596\pi\) | |||||||
\(278\) | 1.00431e16 | 1.30490 | ||||||||
\(279\) | −6.33452e14 | −0.0804056 | ||||||||
\(280\) | 2.24733e15 | 0.278702 | ||||||||
\(281\) | 1.03992e15 | 0.126011 | 0.0630053 | − | 0.998013i | \(-0.479931\pi\) | ||||
0.0630053 | + | 0.998013i | \(0.479931\pi\) | |||||||
\(282\) | −1.37573e16 | −1.62898 | ||||||||
\(283\) | −3.26525e15 | −0.377837 | −0.188918 | − | 0.981993i | \(-0.560498\pi\) | ||||
−0.188918 | + | 0.981993i | \(0.560498\pi\) | |||||||
\(284\) | −2.19277e16 | −2.47984 | ||||||||
\(285\) | −1.83034e16 | −2.02320 | ||||||||
\(286\) | −8.09619e14 | −0.0874785 | ||||||||
\(287\) | −1.93520e15 | −0.204406 | ||||||||
\(288\) | 2.00310e15 | 0.206848 | ||||||||
\(289\) | −3.08291e15 | −0.311261 | ||||||||
\(290\) | 3.23902e16 | 3.19762 | ||||||||
\(291\) | 7.67045e15 | 0.740485 | ||||||||
\(292\) | 1.18353e16 | 1.11735 | ||||||||
\(293\) | 7.12460e15 | 0.657841 | 0.328920 | − | 0.944358i | \(-0.393315\pi\) | ||||
0.328920 | + | 0.944358i | \(0.393315\pi\) | |||||||
\(294\) | −1.05468e16 | −0.952500 | ||||||||
\(295\) | −2.73803e15 | −0.241878 | ||||||||
\(296\) | 2.06455e16 | 1.78414 | ||||||||
\(297\) | 3.28011e14 | 0.0277314 | ||||||||
\(298\) | −1.66722e16 | −1.37907 | ||||||||
\(299\) | 3.49569e15 | 0.282924 | ||||||||
\(300\) | −3.20453e16 | −2.53791 | ||||||||
\(301\) | 6.56675e13 | 0.00508942 | ||||||||
\(302\) | 1.45483e16 | 1.10349 | ||||||||
\(303\) | 1.25174e16 | 0.929262 | ||||||||
\(304\) | 1.09429e16 | 0.795163 | ||||||||
\(305\) | 1.72171e16 | 1.22465 | ||||||||
\(306\) | −6.63931e15 | −0.462310 | ||||||||
\(307\) | 1.28740e16 | 0.877637 | 0.438819 | − | 0.898576i | \(-0.355397\pi\) | ||||
0.438819 | + | 0.898576i | \(0.355397\pi\) | |||||||
\(308\) | 4.38191e14 | 0.0292472 | ||||||||
\(309\) | 1.63931e16 | 1.07135 | ||||||||
\(310\) | 1.17033e16 | 0.748957 | ||||||||
\(311\) | 1.89374e16 | 1.18680 | 0.593400 | − | 0.804908i | \(-0.297785\pi\) | ||||
0.593400 | + | 0.804908i | \(0.297785\pi\) | |||||||
\(312\) | −4.52802e15 | −0.277909 | ||||||||
\(313\) | 2.12357e16 | 1.27652 | 0.638261 | − | 0.769820i | \(-0.279654\pi\) | ||||
0.638261 | + | 0.769820i | \(0.279654\pi\) | |||||||
\(314\) | −2.49669e16 | −1.47001 | ||||||||
\(315\) | −1.21561e15 | −0.0701094 | ||||||||
\(316\) | 3.99900e16 | 2.25936 | ||||||||
\(317\) | −1.07565e16 | −0.595371 | −0.297685 | − | 0.954664i | \(-0.596215\pi\) | ||||
−0.297685 | + | 0.954664i | \(0.596215\pi\) | |||||||
\(318\) | −2.55687e16 | −1.38654 | ||||||||
\(319\) | 2.79299e15 | 0.148399 | ||||||||
\(320\) | −5.20525e16 | −2.70998 | ||||||||
\(321\) | −1.08585e16 | −0.553970 | ||||||||
\(322\) | −2.94724e15 | −0.147351 | ||||||||
\(323\) | 3.19464e16 | 1.56533 | ||||||||
\(324\) | 4.14815e15 | 0.199211 | ||||||||
\(325\) | −1.89210e16 | −0.890641 | ||||||||
\(326\) | −2.35027e16 | −1.08443 | ||||||||
\(327\) | 4.55370e15 | 0.205970 | ||||||||
\(328\) | −5.39562e16 | −2.39255 | ||||||||
\(329\) | 4.39640e15 | 0.191128 | ||||||||
\(330\) | −6.06013e15 | −0.258310 | ||||||||
\(331\) | 4.13197e16 | 1.72693 | 0.863466 | − | 0.504408i | \(-0.168289\pi\) | ||||
0.863466 | + | 0.504408i | \(0.168289\pi\) | |||||||
\(332\) | −7.72419e16 | −3.16559 | ||||||||
\(333\) | −1.11674e16 | −0.448812 | ||||||||
\(334\) | 5.75148e16 | 2.26688 | ||||||||
\(335\) | −4.17149e16 | −1.61250 | ||||||||
\(336\) | 7.26771e14 | 0.0275545 | ||||||||
\(337\) | −1.33796e16 | −0.497563 | −0.248781 | − | 0.968560i | \(-0.580030\pi\) | ||||
−0.248781 | + | 0.968560i | \(0.580030\pi\) | |||||||
\(338\) | 3.97673e16 | 1.45067 | ||||||||
\(339\) | −7.85158e15 | −0.280969 | ||||||||
\(340\) | 7.87439e16 | 2.76442 | ||||||||
\(341\) | 1.00917e15 | 0.0347585 | ||||||||
\(342\) | −3.10924e16 | −1.05071 | ||||||||
\(343\) | 6.78462e15 | 0.224964 | ||||||||
\(344\) | 1.83090e15 | 0.0595711 | ||||||||
\(345\) | 2.61658e16 | 0.835431 | ||||||||
\(346\) | −2.63069e16 | −0.824281 | ||||||||
\(347\) | −9.16237e15 | −0.281751 | −0.140876 | − | 0.990027i | \(-0.544992\pi\) | ||||
−0.140876 | + | 0.990027i | \(0.544992\pi\) | |||||||
\(348\) | 3.53213e16 | 1.06603 | ||||||||
\(349\) | 3.46463e16 | 1.02634 | 0.513170 | − | 0.858287i | \(-0.328471\pi\) | ||||
0.513170 | + | 0.858287i | \(0.328471\pi\) | |||||||
\(350\) | 1.59524e16 | 0.463858 | ||||||||
\(351\) | 2.44926e15 | 0.0699099 | ||||||||
\(352\) | −3.19119e15 | −0.0894182 | ||||||||
\(353\) | −4.07177e16 | −1.12008 | −0.560038 | − | 0.828467i | \(-0.689213\pi\) | ||||
−0.560038 | + | 0.828467i | \(0.689213\pi\) | |||||||
\(354\) | −4.65117e15 | −0.125615 | ||||||||
\(355\) | −9.69115e16 | −2.56975 | ||||||||
\(356\) | 4.35917e16 | 1.13496 | ||||||||
\(357\) | 2.12171e15 | 0.0542428 | ||||||||
\(358\) | −4.93424e16 | −1.23874 | ||||||||
\(359\) | 7.17437e16 | 1.76876 | 0.884382 | − | 0.466764i | \(-0.154580\pi\) | ||||
0.884382 | + | 0.466764i | \(0.154580\pi\) | |||||||
\(360\) | −3.38930e16 | −0.820623 | ||||||||
\(361\) | 1.07555e17 | 2.55760 | ||||||||
\(362\) | 4.62901e16 | 1.08114 | ||||||||
\(363\) | 2.46445e16 | 0.565362 | ||||||||
\(364\) | 3.27198e15 | 0.0737312 | ||||||||
\(365\) | 5.23072e16 | 1.15786 | ||||||||
\(366\) | 2.92472e16 | 0.636000 | ||||||||
\(367\) | 2.14448e16 | 0.458134 | 0.229067 | − | 0.973411i | \(-0.426432\pi\) | ||||
0.229067 | + | 0.973411i | \(0.426432\pi\) | |||||||
\(368\) | −1.56436e16 | −0.328342 | ||||||||
\(369\) | 2.91856e16 | 0.601862 | ||||||||
\(370\) | 2.06322e17 | 4.18056 | ||||||||
\(371\) | 8.17094e15 | 0.162683 | ||||||||
\(372\) | 1.27624e16 | 0.249690 | ||||||||
\(373\) | −7.93176e16 | −1.52497 | −0.762486 | − | 0.647004i | \(-0.776022\pi\) | ||||
−0.762486 | + | 0.647004i | \(0.776022\pi\) | |||||||
\(374\) | 1.05773e16 | 0.199852 | ||||||||
\(375\) | −8.38622e16 | −1.55727 | ||||||||
\(376\) | 1.22578e17 | 2.23713 | ||||||||
\(377\) | 2.08553e16 | 0.374109 | ||||||||
\(378\) | −2.06499e15 | −0.0364100 | ||||||||
\(379\) | 1.83872e15 | 0.0318685 | 0.0159342 | − | 0.999873i | \(-0.494928\pi\) | ||||
0.0159342 | + | 0.999873i | \(0.494928\pi\) | |||||||
\(380\) | 3.68764e17 | 6.28283 | ||||||||
\(381\) | −1.73948e16 | −0.291345 | ||||||||
\(382\) | −1.40787e17 | −2.31819 | ||||||||
\(383\) | −9.66850e16 | −1.56519 | −0.782595 | − | 0.622531i | \(-0.786105\pi\) | ||||
−0.782595 | + | 0.622531i | \(0.786105\pi\) | |||||||
\(384\) | −6.59133e16 | −1.04911 | ||||||||
\(385\) | 1.93662e15 | 0.0303075 | ||||||||
\(386\) | 3.67125e16 | 0.564932 | ||||||||
\(387\) | −9.90359e14 | −0.0149855 | ||||||||
\(388\) | −1.54539e17 | −2.29949 | ||||||||
\(389\) | −4.31007e16 | −0.630685 | −0.315342 | − | 0.948978i | \(-0.602119\pi\) | ||||
−0.315342 | + | 0.948978i | \(0.602119\pi\) | |||||||
\(390\) | −4.52511e16 | −0.651192 | ||||||||
\(391\) | −4.56694e16 | −0.646363 | ||||||||
\(392\) | 9.39724e16 | 1.30810 | ||||||||
\(393\) | 3.72275e16 | 0.509698 | ||||||||
\(394\) | −1.26422e17 | −1.70254 | ||||||||
\(395\) | 1.76739e17 | 2.34127 | ||||||||
\(396\) | −6.60854e15 | −0.0861166 | ||||||||
\(397\) | 1.16157e17 | 1.48904 | 0.744521 | − | 0.667599i | \(-0.232678\pi\) | ||||
0.744521 | + | 0.667599i | \(0.232678\pi\) | |||||||
\(398\) | −9.51962e16 | −1.20055 | ||||||||
\(399\) | 9.93613e15 | 0.123280 | ||||||||
\(400\) | 8.46739e16 | 1.03362 | ||||||||
\(401\) | 5.34610e16 | 0.642094 | 0.321047 | − | 0.947063i | \(-0.395965\pi\) | ||||
0.321047 | + | 0.947063i | \(0.395965\pi\) | |||||||
\(402\) | −7.08621e16 | −0.837423 | ||||||||
\(403\) | 7.53549e15 | 0.0876251 | ||||||||
\(404\) | −2.52193e17 | −2.88572 | ||||||||
\(405\) | 1.83331e16 | 0.206433 | ||||||||
\(406\) | −1.75833e16 | −0.194841 | ||||||||
\(407\) | 1.77911e16 | 0.194017 | ||||||||
\(408\) | 5.91563e16 | 0.634906 | ||||||||
\(409\) | 5.79161e16 | 0.611783 | 0.305892 | − | 0.952066i | \(-0.401045\pi\) | ||||
0.305892 | + | 0.952066i | \(0.401045\pi\) | |||||||
\(410\) | −5.39215e17 | −5.60618 | ||||||||
\(411\) | −7.33462e16 | −0.750596 | ||||||||
\(412\) | −3.30276e17 | −3.32694 | ||||||||
\(413\) | 1.48636e15 | 0.0147384 | ||||||||
\(414\) | 4.44486e16 | 0.433866 | ||||||||
\(415\) | −3.41377e17 | −3.28037 | ||||||||
\(416\) | −2.38287e16 | −0.225421 | ||||||||
\(417\) | 4.84031e16 | 0.450805 | ||||||||
\(418\) | 4.95342e16 | 0.454213 | ||||||||
\(419\) | −5.56422e16 | −0.502358 | −0.251179 | − | 0.967941i | \(-0.580818\pi\) | ||||
−0.251179 | + | 0.967941i | \(0.580818\pi\) | |||||||
\(420\) | 2.44913e16 | 0.217717 | ||||||||
\(421\) | −1.16772e17 | −1.02213 | −0.511066 | − | 0.859542i | \(-0.670749\pi\) | ||||
−0.511066 | + | 0.859542i | \(0.670749\pi\) | |||||||
\(422\) | 1.55927e17 | 1.34397 | ||||||||
\(423\) | −6.63040e16 | −0.562765 | ||||||||
\(424\) | 2.27818e17 | 1.90419 | ||||||||
\(425\) | 2.47194e17 | 2.03474 | ||||||||
\(426\) | −1.64626e17 | −1.33455 | ||||||||
\(427\) | −9.34646e15 | −0.0746218 | ||||||||
\(428\) | 2.18769e17 | 1.72029 | ||||||||
\(429\) | −3.90199e15 | −0.0302213 | ||||||||
\(430\) | 1.82973e16 | 0.139586 | ||||||||
\(431\) | −5.27394e16 | −0.396308 | −0.198154 | − | 0.980171i | \(-0.563495\pi\) | ||||
−0.198154 | + | 0.980171i | \(0.563495\pi\) | |||||||
\(432\) | −1.09607e16 | −0.0811326 | ||||||||
\(433\) | −2.11584e17 | −1.54281 | −0.771403 | − | 0.636347i | \(-0.780445\pi\) | ||||
−0.771403 | + | 0.636347i | \(0.780445\pi\) | |||||||
\(434\) | −6.35322e15 | −0.0456363 | ||||||||
\(435\) | 1.56106e17 | 1.10468 | ||||||||
\(436\) | −9.17449e16 | −0.639616 | ||||||||
\(437\) | −2.13874e17 | −1.46902 | ||||||||
\(438\) | 8.88555e16 | 0.601316 | ||||||||
\(439\) | −2.14705e17 | −1.43160 | −0.715802 | − | 0.698303i | \(-0.753939\pi\) | ||||
−0.715802 | + | 0.698303i | \(0.753939\pi\) | |||||||
\(440\) | 5.39958e16 | 0.354746 | ||||||||
\(441\) | −5.08309e16 | −0.329061 | ||||||||
\(442\) | 7.89806e16 | 0.503820 | ||||||||
\(443\) | −1.23709e17 | −0.777637 | −0.388818 | − | 0.921314i | \(-0.627117\pi\) | ||||
−0.388818 | + | 0.921314i | \(0.627117\pi\) | |||||||
\(444\) | 2.24993e17 | 1.39373 | ||||||||
\(445\) | 1.92658e17 | 1.17611 | ||||||||
\(446\) | 3.49569e17 | 2.10308 | ||||||||
\(447\) | −8.03523e16 | −0.476431 | ||||||||
\(448\) | 2.82571e16 | 0.165128 | ||||||||
\(449\) | 1.66258e16 | 0.0957592 | 0.0478796 | − | 0.998853i | \(-0.484754\pi\) | ||||
0.0478796 | + | 0.998853i | \(0.484754\pi\) | |||||||
\(450\) | −2.40586e17 | −1.36580 | ||||||||
\(451\) | −4.64963e16 | −0.260178 | ||||||||
\(452\) | 1.58188e17 | 0.872518 | ||||||||
\(453\) | 7.01162e16 | 0.381224 | ||||||||
\(454\) | −5.37637e14 | −0.00288155 | ||||||||
\(455\) | 1.44608e16 | 0.0764044 | ||||||||
\(456\) | 2.77034e17 | 1.44298 | ||||||||
\(457\) | −3.35081e17 | −1.72066 | −0.860329 | − | 0.509739i | \(-0.829742\pi\) | ||||
−0.860329 | + | 0.509739i | \(0.829742\pi\) | |||||||
\(458\) | 4.08290e17 | 2.06701 | ||||||||
\(459\) | −3.19984e16 | −0.159715 | ||||||||
\(460\) | −5.27171e17 | −2.59433 | ||||||||
\(461\) | 1.88360e16 | 0.0913972 | 0.0456986 | − | 0.998955i | \(-0.485449\pi\) | ||||
0.0456986 | + | 0.998955i | \(0.485449\pi\) | |||||||
\(462\) | 3.28979e15 | 0.0157397 | ||||||||
\(463\) | −3.49491e17 | −1.64877 | −0.824383 | − | 0.566032i | \(-0.808478\pi\) | ||||
−0.824383 | + | 0.566032i | \(0.808478\pi\) | |||||||
\(464\) | −9.33300e16 | −0.434165 | ||||||||
\(465\) | 5.64044e16 | 0.258743 | ||||||||
\(466\) | −3.01555e17 | −1.36414 | ||||||||
\(467\) | −1.43399e17 | −0.639714 | −0.319857 | − | 0.947466i | \(-0.603635\pi\) | ||||
−0.319857 | + | 0.947466i | \(0.603635\pi\) | |||||||
\(468\) | −4.93461e16 | −0.217097 | ||||||||
\(469\) | 2.26453e16 | 0.0982548 | ||||||||
\(470\) | 1.22499e18 | 5.24201 | ||||||||
\(471\) | −1.20329e17 | −0.507848 | ||||||||
\(472\) | 4.14419e16 | 0.172511 | ||||||||
\(473\) | 1.57777e15 | 0.00647807 | ||||||||
\(474\) | 3.00232e17 | 1.21590 | ||||||||
\(475\) | 1.15763e18 | 4.62446 | ||||||||
\(476\) | −4.27467e16 | −0.168445 | ||||||||
\(477\) | −1.23229e17 | −0.479010 | ||||||||
\(478\) | 1.34631e17 | 0.516256 | ||||||||
\(479\) | −3.49364e17 | −1.32159 | −0.660795 | − | 0.750566i | \(-0.729781\pi\) | ||||
−0.660795 | + | 0.750566i | \(0.729781\pi\) | |||||||
\(480\) | −1.78362e17 | −0.665632 | ||||||||
\(481\) | 1.32846e17 | 0.489110 | ||||||||
\(482\) | 3.70986e17 | 1.34757 | ||||||||
\(483\) | −1.42043e16 | −0.0509055 | ||||||||
\(484\) | −4.96520e17 | −1.75567 | ||||||||
\(485\) | −6.82999e17 | −2.38286 | ||||||||
\(486\) | 3.11430e16 | 0.107207 | ||||||||
\(487\) | 2.67667e17 | 0.909193 | 0.454597 | − | 0.890697i | \(-0.349783\pi\) | ||||
0.454597 | + | 0.890697i | \(0.349783\pi\) | |||||||
\(488\) | −2.60593e17 | −0.873440 | ||||||||
\(489\) | −1.13272e17 | −0.374641 | ||||||||
\(490\) | 9.39121e17 | 3.06512 | ||||||||
\(491\) | 2.79936e17 | 0.901630 | 0.450815 | − | 0.892617i | \(-0.351133\pi\) | ||||
0.450815 | + | 0.892617i | \(0.351133\pi\) | |||||||
\(492\) | −5.88011e17 | −1.86901 | ||||||||
\(493\) | −2.72464e17 | −0.854682 | ||||||||
\(494\) | 3.69872e17 | 1.14506 | ||||||||
\(495\) | −2.92070e16 | −0.0892388 | ||||||||
\(496\) | −3.37222e16 | −0.101692 | ||||||||
\(497\) | 5.26092e16 | 0.156583 | ||||||||
\(498\) | −5.79906e17 | −1.70360 | ||||||||
\(499\) | 1.78178e17 | 0.516655 | 0.258328 | − | 0.966057i | \(-0.416829\pi\) | ||||
0.258328 | + | 0.966057i | \(0.416829\pi\) | |||||||
\(500\) | 1.68960e18 | 4.83591 | ||||||||
\(501\) | 2.77195e17 | 0.783141 | ||||||||
\(502\) | 1.69485e17 | 0.472668 | ||||||||
\(503\) | −1.20853e17 | −0.332711 | −0.166355 | − | 0.986066i | \(-0.553200\pi\) | ||||
−0.166355 | + | 0.986066i | \(0.553200\pi\) | |||||||
\(504\) | 1.83991e16 | 0.0500031 | ||||||||
\(505\) | −1.11459e18 | −2.99034 | ||||||||
\(506\) | −7.08122e16 | −0.187556 | ||||||||
\(507\) | 1.91660e17 | 0.501163 | ||||||||
\(508\) | 3.50459e17 | 0.904739 | ||||||||
\(509\) | 4.48694e17 | 1.14363 | 0.571814 | − | 0.820383i | \(-0.306240\pi\) | ||||
0.571814 | + | 0.820383i | \(0.306240\pi\) | |||||||
\(510\) | 5.91183e17 | 1.48770 | ||||||||
\(511\) | −2.83954e16 | −0.0705524 | ||||||||
\(512\) | 3.34343e17 | 0.820232 | ||||||||
\(513\) | −1.49851e17 | −0.362992 | ||||||||
\(514\) | 3.18612e17 | 0.762083 | ||||||||
\(515\) | −1.45969e18 | −3.44756 | ||||||||
\(516\) | 1.99531e16 | 0.0465358 | ||||||||
\(517\) | 1.05631e17 | 0.243277 | ||||||||
\(518\) | −1.12004e17 | −0.254735 | ||||||||
\(519\) | −1.26787e17 | −0.284766 | ||||||||
\(520\) | 4.03188e17 | 0.894305 | ||||||||
\(521\) | 2.63047e17 | 0.576219 | 0.288109 | − | 0.957597i | \(-0.406973\pi\) | ||||
0.288109 | + | 0.957597i | \(0.406973\pi\) | |||||||
\(522\) | 2.65180e17 | 0.573698 | ||||||||
\(523\) | −1.31320e17 | −0.280588 | −0.140294 | − | 0.990110i | \(-0.544805\pi\) | ||||
−0.140294 | + | 0.990110i | \(0.544805\pi\) | |||||||
\(524\) | −7.50035e17 | −1.58281 | ||||||||
\(525\) | 7.68834e16 | 0.160250 | ||||||||
\(526\) | −1.16423e18 | −2.39680 | ||||||||
\(527\) | −9.84474e16 | −0.200187 | ||||||||
\(528\) | 1.74619e16 | 0.0350728 | ||||||||
\(529\) | −1.98290e17 | −0.393405 | ||||||||
\(530\) | 2.27671e18 | 4.46185 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −2.00186e17 | −0.382833 | ||||||||
\(533\) | −3.47189e17 | −0.655902 | ||||||||
\(534\) | 3.27272e17 | 0.610789 | ||||||||
\(535\) | 9.66871e17 | 1.78266 | ||||||||
\(536\) | 6.31382e17 | 1.15006 | ||||||||
\(537\) | −2.37807e17 | −0.427949 | ||||||||
\(538\) | −3.75253e17 | −0.667175 | ||||||||
\(539\) | 8.09801e16 | 0.142250 | ||||||||
\(540\) | −3.69364e17 | −0.641054 | ||||||||
\(541\) | 2.10937e17 | 0.361718 | 0.180859 | − | 0.983509i | \(-0.442112\pi\) | ||||
0.180859 | + | 0.983509i | \(0.442112\pi\) | |||||||
\(542\) | 8.84188e17 | 1.49813 | ||||||||
\(543\) | 2.23097e17 | 0.373504 | ||||||||
\(544\) | 3.11310e17 | 0.514992 | ||||||||
\(545\) | −4.05475e17 | −0.662806 | ||||||||
\(546\) | 2.45649e16 | 0.0396792 | ||||||||
\(547\) | −6.27933e17 | −1.00230 | −0.501148 | − | 0.865362i | \(-0.667089\pi\) | ||||
−0.501148 | + | 0.865362i | \(0.667089\pi\) | |||||||
\(548\) | 1.47773e18 | 2.33089 | ||||||||
\(549\) | 1.40958e17 | 0.219720 | ||||||||
\(550\) | 3.83283e17 | 0.590422 | ||||||||
\(551\) | −1.27597e18 | −1.94248 | ||||||||
\(552\) | −3.96037e17 | −0.595843 | ||||||||
\(553\) | −9.59444e16 | −0.142661 | ||||||||
\(554\) | −2.73742e17 | −0.402280 | ||||||||
\(555\) | 9.94377e17 | 1.44426 | ||||||||
\(556\) | −9.75192e17 | −1.39992 | ||||||||
\(557\) | 5.59177e17 | 0.793396 | 0.396698 | − | 0.917949i | \(-0.370156\pi\) | ||||
0.396698 | + | 0.917949i | \(0.370156\pi\) | |||||||
\(558\) | 9.58156e16 | 0.134374 | ||||||||
\(559\) | 1.17812e16 | 0.0163310 | ||||||||
\(560\) | −6.47138e16 | −0.0886696 | ||||||||
\(561\) | 5.09775e16 | 0.0690431 | ||||||||
\(562\) | −1.57297e17 | −0.210588 | ||||||||
\(563\) | 4.12831e17 | 0.546346 | 0.273173 | − | 0.961965i | \(-0.411927\pi\) | ||||
0.273173 | + | 0.961965i | \(0.411927\pi\) | |||||||
\(564\) | 1.33585e18 | 1.74760 | ||||||||
\(565\) | 6.99127e17 | 0.904152 | ||||||||
\(566\) | 4.93899e17 | 0.631439 | ||||||||
\(567\) | −9.95229e15 | −0.0125786 | ||||||||
\(568\) | 1.46682e18 | 1.83279 | ||||||||
\(569\) | 4.35537e17 | 0.538016 | 0.269008 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269008 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(570\) | 2.76856e18 | 3.38117 | ||||||||
\(571\) | 1.13189e17 | 0.136668 | 0.0683342 | − | 0.997662i | \(-0.478232\pi\) | ||||
0.0683342 | + | 0.997662i | \(0.478232\pi\) | |||||||
\(572\) | 7.86146e16 | 0.0938488 | ||||||||
\(573\) | −6.78526e17 | −0.800870 | ||||||||
\(574\) | 2.92717e17 | 0.341602 | ||||||||
\(575\) | −1.65490e18 | −1.90955 | ||||||||
\(576\) | −4.26157e17 | −0.486209 | ||||||||
\(577\) | −3.48334e17 | −0.392965 | −0.196482 | − | 0.980507i | \(-0.562952\pi\) | ||||
−0.196482 | + | 0.980507i | \(0.562952\pi\) | |||||||
\(578\) | 4.66319e17 | 0.520178 | ||||||||
\(579\) | 1.76937e17 | 0.195168 | ||||||||
\(580\) | −3.14511e18 | −3.43047 | ||||||||
\(581\) | 1.85319e17 | 0.199883 | ||||||||
\(582\) | −1.16023e18 | −1.23750 | ||||||||
\(583\) | 1.96320e17 | 0.207071 | ||||||||
\(584\) | −7.91704e17 | −0.825808 | ||||||||
\(585\) | −2.18089e17 | −0.224968 | ||||||||
\(586\) | −1.07766e18 | −1.09938 | ||||||||
\(587\) | 3.23634e17 | 0.326518 | 0.163259 | − | 0.986583i | \(-0.447799\pi\) | ||||
0.163259 | + | 0.986583i | \(0.447799\pi\) | |||||||
\(588\) | 1.02411e18 | 1.02186 | ||||||||
\(589\) | −4.61037e17 | −0.454974 | ||||||||
\(590\) | 4.14153e17 | 0.404225 | ||||||||
\(591\) | −6.09296e17 | −0.588179 | ||||||||
\(592\) | −5.94503e17 | −0.567627 | ||||||||
\(593\) | −4.53247e17 | −0.428035 | −0.214017 | − | 0.976830i | \(-0.568655\pi\) | ||||
−0.214017 | + | 0.976830i | \(0.568655\pi\) | |||||||
\(594\) | −4.96147e16 | −0.0463445 | ||||||||
\(595\) | −1.88923e17 | −0.174552 | ||||||||
\(596\) | 1.61888e18 | 1.47950 | ||||||||
\(597\) | −4.58802e17 | −0.414755 | ||||||||
\(598\) | −5.28756e17 | −0.472822 | ||||||||
\(599\) | −8.02630e17 | −0.709972 | −0.354986 | − | 0.934872i | \(-0.615514\pi\) | ||||
−0.354986 | + | 0.934872i | \(0.615514\pi\) | |||||||
\(600\) | 2.14362e18 | 1.87570 | ||||||||
\(601\) | 1.19626e18 | 1.03548 | 0.517741 | − | 0.855537i | \(-0.326773\pi\) | ||||
0.517741 | + | 0.855537i | \(0.326773\pi\) | |||||||
\(602\) | −9.93282e15 | −0.00850542 | ||||||||
\(603\) | −3.41523e17 | −0.289306 | ||||||||
\(604\) | −1.41265e18 | −1.18385 | ||||||||
\(605\) | −2.19442e18 | −1.81932 | ||||||||
\(606\) | −1.89338e18 | −1.55298 | ||||||||
\(607\) | −2.42333e18 | −1.96646 | −0.983232 | − | 0.182361i | \(-0.941626\pi\) | ||||
−0.983232 | + | 0.182361i | \(0.941626\pi\) | |||||||
\(608\) | 1.45789e18 | 1.17045 | ||||||||
\(609\) | −8.47431e16 | −0.0673119 | ||||||||
\(610\) | −2.60425e18 | −2.04663 | ||||||||
\(611\) | 7.88746e17 | 0.613295 | ||||||||
\(612\) | 6.44682e17 | 0.495976 | ||||||||
\(613\) | −2.15648e18 | −1.64154 | −0.820771 | − | 0.571257i | \(-0.806456\pi\) | ||||
−0.820771 | + | 0.571257i | \(0.806456\pi\) | |||||||
\(614\) | −1.94732e18 | −1.46670 | ||||||||
\(615\) | −2.59877e18 | −1.93678 | ||||||||
\(616\) | −2.93121e16 | −0.0216158 | ||||||||
\(617\) | 1.89909e17 | 0.138577 | 0.0692887 | − | 0.997597i | \(-0.477927\pi\) | ||||
0.0692887 | + | 0.997597i | \(0.477927\pi\) | |||||||
\(618\) | −2.47960e18 | −1.79043 | ||||||||
\(619\) | 1.00865e18 | 0.720697 | 0.360348 | − | 0.932818i | \(-0.382658\pi\) | ||||
0.360348 | + | 0.932818i | \(0.382658\pi\) | |||||||
\(620\) | −1.13640e18 | −0.803497 | ||||||||
\(621\) | 2.14221e17 | 0.149888 | ||||||||
\(622\) | −2.86446e18 | −1.98337 | ||||||||
\(623\) | −1.04586e17 | −0.0716638 | ||||||||
\(624\) | 1.30388e17 | 0.0884174 | ||||||||
\(625\) | 3.81389e18 | 2.55946 | ||||||||
\(626\) | −3.21210e18 | −2.13332 | ||||||||
\(627\) | 2.38732e17 | 0.156917 | ||||||||
\(628\) | 2.42430e18 | 1.57706 | ||||||||
\(629\) | −1.73557e18 | −1.11741 | ||||||||
\(630\) | 1.83873e17 | 0.117166 | ||||||||
\(631\) | −8.15155e17 | −0.514102 | −0.257051 | − | 0.966398i | \(-0.582751\pi\) | ||||
−0.257051 | + | 0.966398i | \(0.582751\pi\) | |||||||
\(632\) | −2.67507e18 | −1.66983 | ||||||||
\(633\) | 7.51496e17 | 0.464304 | ||||||||
\(634\) | 1.62703e18 | 0.994981 | ||||||||
\(635\) | 1.54889e18 | 0.937540 | ||||||||
\(636\) | 2.48274e18 | 1.48751 | ||||||||
\(637\) | 6.04679e17 | 0.358607 | ||||||||
\(638\) | −4.22466e17 | −0.248003 | ||||||||
\(639\) | −7.93421e17 | −0.461050 | ||||||||
\(640\) | 5.86911e18 | 3.37600 | ||||||||
\(641\) | −2.00287e18 | −1.14045 | −0.570225 | − | 0.821489i | \(-0.693144\pi\) | ||||
−0.570225 | + | 0.821489i | \(0.693144\pi\) | |||||||
\(642\) | 1.64245e18 | 0.925793 | ||||||||
\(643\) | −6.60505e17 | −0.368557 | −0.184279 | − | 0.982874i | \(-0.558995\pi\) | ||||
−0.184279 | + | 0.982874i | \(0.558995\pi\) | |||||||
\(644\) | 2.86179e17 | 0.158081 | ||||||||
\(645\) | 8.81844e16 | 0.0482229 | ||||||||
\(646\) | −4.83220e18 | −2.61597 | ||||||||
\(647\) | 1.50934e18 | 0.808925 | 0.404462 | − | 0.914555i | \(-0.367459\pi\) | ||||
0.404462 | + | 0.914555i | \(0.367459\pi\) | |||||||
\(648\) | −2.77484e17 | −0.147231 | ||||||||
\(649\) | 3.57123e16 | 0.0187598 | ||||||||
\(650\) | 2.86198e18 | 1.48844 | ||||||||
\(651\) | −3.06196e16 | −0.0157660 | ||||||||
\(652\) | 2.28213e18 | 1.16340 | ||||||||
\(653\) | −3.08451e18 | −1.55686 | −0.778432 | − | 0.627729i | \(-0.783984\pi\) | ||||
−0.778432 | + | 0.627729i | \(0.783984\pi\) | |||||||
\(654\) | −6.88790e17 | −0.344216 | ||||||||
\(655\) | −3.31485e18 | −1.64019 | ||||||||
\(656\) | 1.55371e18 | 0.761194 | ||||||||
\(657\) | 4.28243e17 | 0.207737 | ||||||||
\(658\) | −6.64997e17 | −0.319412 | ||||||||
\(659\) | −2.30137e18 | −1.09454 | −0.547268 | − | 0.836957i | \(-0.684332\pi\) | ||||
−0.547268 | + | 0.836957i | \(0.684332\pi\) | |||||||
\(660\) | 5.88444e17 | 0.277121 | ||||||||
\(661\) | 3.33324e18 | 1.55438 | 0.777191 | − | 0.629265i | \(-0.216644\pi\) | ||||
0.777191 | + | 0.629265i | \(0.216644\pi\) | |||||||
\(662\) | −6.24999e18 | −2.88604 | ||||||||
\(663\) | 3.80650e17 | 0.174055 | ||||||||
\(664\) | 5.16697e18 | 2.33961 | ||||||||
\(665\) | −8.84742e17 | −0.396713 | ||||||||
\(666\) | 1.68917e18 | 0.750052 | ||||||||
\(667\) | 1.82408e18 | 0.802096 | ||||||||
\(668\) | −5.58473e18 | −2.43195 | ||||||||
\(669\) | 1.68476e18 | 0.726554 | ||||||||
\(670\) | 6.30977e18 | 2.69480 | ||||||||
\(671\) | −2.24564e17 | −0.0949825 | ||||||||
\(672\) | 9.68251e16 | 0.0405590 | ||||||||
\(673\) | 1.34611e18 | 0.558448 | 0.279224 | − | 0.960226i | \(-0.409923\pi\) | ||||
0.279224 | + | 0.960226i | \(0.409923\pi\) | |||||||
\(674\) | 2.02379e18 | 0.831525 | ||||||||
\(675\) | −1.15951e18 | −0.471846 | ||||||||
\(676\) | −3.86143e18 | −1.55630 | ||||||||
\(677\) | −4.97872e18 | −1.98743 | −0.993715 | − | 0.111942i | \(-0.964293\pi\) | ||||
−0.993715 | + | 0.111942i | \(0.964293\pi\) | |||||||
\(678\) | 1.18762e18 | 0.469555 | ||||||||
\(679\) | 3.70771e17 | 0.145195 | ||||||||
\(680\) | −5.26745e18 | −2.04311 | ||||||||
\(681\) | −2.59116e15 | −0.000995494 0 | ||||||||
\(682\) | −1.52646e17 | −0.0580882 | ||||||||
\(683\) | −3.99309e18 | −1.50513 | −0.752566 | − | 0.658517i | \(-0.771184\pi\) | ||||
−0.752566 | + | 0.658517i | \(0.771184\pi\) | |||||||
\(684\) | 3.01910e18 | 1.12723 | ||||||||
\(685\) | 6.53096e18 | 2.41540 | ||||||||
\(686\) | −1.02624e18 | −0.375959 | ||||||||
\(687\) | 1.96777e18 | 0.714094 | ||||||||
\(688\) | −5.27224e16 | −0.0189527 | ||||||||
\(689\) | 1.46593e18 | 0.522020 | ||||||||
\(690\) | −3.95783e18 | −1.39617 | ||||||||
\(691\) | −2.83371e18 | −0.990256 | −0.495128 | − | 0.868820i | \(-0.664879\pi\) | ||||
−0.495128 | + | 0.868820i | \(0.664879\pi\) | |||||||
\(692\) | 2.55442e18 | 0.884307 | ||||||||
\(693\) | 1.58553e16 | 0.00543760 | ||||||||
\(694\) | 1.38589e18 | 0.470862 | ||||||||
\(695\) | −4.30995e18 | −1.45068 | ||||||||
\(696\) | −2.36276e18 | −0.787879 | ||||||||
\(697\) | 4.53585e18 | 1.49846 | ||||||||
\(698\) | −5.24057e18 | −1.71521 | ||||||||
\(699\) | −1.45336e18 | −0.471271 | ||||||||
\(700\) | −1.54899e18 | −0.497637 | ||||||||
\(701\) | 2.78936e18 | 0.887845 | 0.443923 | − | 0.896065i | \(-0.353586\pi\) | ||||
0.443923 | + | 0.896065i | \(0.353586\pi\) | |||||||
\(702\) | −3.70474e17 | −0.116833 | ||||||||
\(703\) | −8.12782e18 | −2.53959 | ||||||||
\(704\) | 6.78922e17 | 0.210183 | ||||||||
\(705\) | 5.90390e18 | 1.81096 | ||||||||
\(706\) | 6.15893e18 | 1.87187 | ||||||||
\(707\) | 6.05063e17 | 0.182211 | ||||||||
\(708\) | 4.51632e17 | 0.134762 | ||||||||
\(709\) | 8.97213e16 | 0.0265274 | 0.0132637 | − | 0.999912i | \(-0.495778\pi\) | ||||
0.0132637 | + | 0.999912i | \(0.495778\pi\) | |||||||
\(710\) | 1.46588e19 | 4.29456 | ||||||||
\(711\) | 1.44698e18 | 0.420058 | ||||||||
\(712\) | −2.91600e18 | −0.838817 | ||||||||
\(713\) | 6.59081e17 | 0.187870 | ||||||||
\(714\) | −3.20928e17 | −0.0906504 | ||||||||
\(715\) | 3.47444e17 | 0.0972514 | ||||||||
\(716\) | 4.79118e18 | 1.32895 | ||||||||
\(717\) | 6.48860e17 | 0.178352 | ||||||||
\(718\) | −1.08519e19 | −2.95595 | ||||||||
\(719\) | −2.39931e18 | −0.647662 | −0.323831 | − | 0.946115i | \(-0.604971\pi\) | ||||
−0.323831 | + | 0.946115i | \(0.604971\pi\) | |||||||
\(720\) | 9.75976e17 | 0.261083 | ||||||||
\(721\) | 7.92402e17 | 0.210071 | ||||||||
\(722\) | −1.62687e19 | −4.27425 | ||||||||
\(723\) | 1.78798e18 | 0.465547 | ||||||||
\(724\) | −4.49481e18 | −1.15987 | ||||||||
\(725\) | −9.87316e18 | −2.52499 | ||||||||
\(726\) | −3.72771e18 | −0.944831 | ||||||||
\(727\) | 9.93810e17 | 0.249649 | 0.124824 | − | 0.992179i | \(-0.460163\pi\) | ||||
0.124824 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(728\) | −2.18874e17 | −0.0544928 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −7.91195e18 | −1.93502 | ||||||||
\(731\) | −1.53916e17 | −0.0373095 | ||||||||
\(732\) | −2.83992e18 | −0.682314 | ||||||||
\(733\) | −3.93573e18 | −0.937237 | −0.468619 | − | 0.883401i | \(-0.655248\pi\) | ||||
−0.468619 | + | 0.883401i | \(0.655248\pi\) | |||||||
\(734\) | −3.24373e18 | −0.765632 | ||||||||
\(735\) | 4.52613e18 | 1.05891 | ||||||||
\(736\) | −2.08415e18 | −0.483306 | ||||||||
\(737\) | 5.44089e17 | 0.125064 | ||||||||
\(738\) | −4.41459e18 | −1.00583 | ||||||||
\(739\) | −7.49608e18 | −1.69295 | −0.846477 | − | 0.532426i | \(-0.821281\pi\) | ||||
−0.846477 | + | 0.532426i | \(0.821281\pi\) | |||||||
\(740\) | −2.00340e19 | −4.48500 | ||||||||
\(741\) | 1.78261e18 | 0.395584 | ||||||||
\(742\) | −1.23593e18 | −0.271875 | ||||||||
\(743\) | −7.38140e17 | −0.160958 | −0.0804788 | − | 0.996756i | \(-0.525645\pi\) | ||||
−0.0804788 | + | 0.996756i | \(0.525645\pi\) | |||||||
\(744\) | −8.53717e17 | −0.184540 | ||||||||
\(745\) | 7.15480e18 | 1.53314 | ||||||||
\(746\) | 1.19975e19 | 2.54853 | ||||||||
\(747\) | −2.79488e18 | −0.588544 | ||||||||
\(748\) | −1.02706e18 | −0.214405 | ||||||||
\(749\) | −5.24873e17 | −0.108623 | ||||||||
\(750\) | 1.26849e19 | 2.60250 | ||||||||
\(751\) | 1.18812e18 | 0.241657 | 0.120829 | − | 0.992673i | \(-0.461445\pi\) | ||||
0.120829 | + | 0.992673i | \(0.461445\pi\) | |||||||
\(752\) | −3.52973e18 | −0.711748 | ||||||||
\(753\) | 8.16838e17 | 0.163293 | ||||||||
\(754\) | −3.15456e18 | −0.625209 | ||||||||
\(755\) | −6.24335e18 | −1.22677 | ||||||||
\(756\) | 2.00512e17 | 0.0390615 | ||||||||
\(757\) | 1.06498e17 | 0.0205692 | 0.0102846 | − | 0.999947i | \(-0.496726\pi\) | ||||
0.0102846 | + | 0.999947i | \(0.496726\pi\) | |||||||
\(758\) | −2.78124e17 | −0.0532585 | ||||||||
\(759\) | −3.41282e17 | −0.0647951 | ||||||||
\(760\) | −2.46679e19 | −4.64348 | ||||||||
\(761\) | 1.38713e18 | 0.258891 | 0.129445 | − | 0.991587i | \(-0.458680\pi\) | ||||
0.129445 | + | 0.991587i | \(0.458680\pi\) | |||||||
\(762\) | 2.63113e18 | 0.486895 | ||||||||
\(763\) | 2.20115e17 | 0.0403869 | ||||||||
\(764\) | 1.36705e19 | 2.48701 | ||||||||
\(765\) | 2.84923e18 | 0.513958 | ||||||||
\(766\) | 1.46245e19 | 2.61574 | ||||||||
\(767\) | 2.66664e17 | 0.0472928 | ||||||||
\(768\) | 5.18115e18 | 0.911126 | ||||||||
\(769\) | 7.71703e16 | 0.0134564 | 0.00672820 | − | 0.999977i | \(-0.497858\pi\) | ||||
0.00672820 | + | 0.999977i | \(0.497858\pi\) | |||||||
\(770\) | −2.92933e17 | −0.0506498 | ||||||||
\(771\) | 1.53556e18 | 0.263278 | ||||||||
\(772\) | −3.56481e18 | −0.606071 | ||||||||
\(773\) | 6.74644e18 | 1.13739 | 0.568693 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568693 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(774\) | 1.49801e17 | 0.0250437 | ||||||||
\(775\) | −3.56739e18 | −0.591411 | ||||||||
\(776\) | 1.03376e19 | 1.69950 | ||||||||
\(777\) | −5.39805e17 | −0.0880036 | ||||||||
\(778\) | 6.51939e18 | 1.05400 | ||||||||
\(779\) | 2.12417e19 | 3.40562 | ||||||||
\(780\) | 4.39392e18 | 0.698613 | ||||||||
\(781\) | 1.26402e18 | 0.199307 | ||||||||
\(782\) | 6.90793e18 | 1.08020 | ||||||||
\(783\) | 1.27805e18 | 0.198196 | ||||||||
\(784\) | −2.70601e18 | −0.416175 | ||||||||
\(785\) | 1.07144e19 | 1.63424 | ||||||||
\(786\) | −5.63101e18 | −0.851805 | ||||||||
\(787\) | −6.61858e18 | −0.992954 | −0.496477 | − | 0.868050i | \(-0.665373\pi\) | ||||
−0.496477 | + | 0.868050i | \(0.665373\pi\) | |||||||
\(788\) | 1.22757e19 | 1.82652 | ||||||||
\(789\) | −5.61104e18 | −0.828024 | ||||||||
\(790\) | −2.67335e19 | −3.91273 | ||||||||
\(791\) | −3.79527e17 | −0.0550928 | ||||||||
\(792\) | 4.42068e17 | 0.0636466 | ||||||||
\(793\) | −1.67682e18 | −0.239448 | ||||||||
\(794\) | −1.75698e19 | −2.48848 | ||||||||
\(795\) | 1.09727e19 | 1.54144 | ||||||||
\(796\) | 9.24363e18 | 1.28797 | ||||||||
\(797\) | 1.10316e19 | 1.52462 | 0.762308 | − | 0.647214i | \(-0.224066\pi\) | ||||
0.762308 | + | 0.647214i | \(0.224066\pi\) | |||||||
\(798\) | −1.50293e18 | −0.206025 | ||||||||
\(799\) | −1.03046e19 | −1.40112 | ||||||||
\(800\) | 1.12808e19 | 1.52144 | ||||||||
\(801\) | 1.57730e18 | 0.211010 | ||||||||
\(802\) | −8.08647e18 | −1.07306 | ||||||||
\(803\) | −6.82245e17 | −0.0898027 | ||||||||
\(804\) | 6.88076e18 | 0.898405 | ||||||||
\(805\) | 1.26479e18 | 0.163812 | ||||||||
\(806\) | −1.13981e18 | −0.146439 | ||||||||
\(807\) | −1.80855e18 | −0.230490 | ||||||||
\(808\) | 1.68700e19 | 2.13276 | ||||||||
\(809\) | 2.41246e18 | 0.302549 | 0.151274 | − | 0.988492i | \(-0.451662\pi\) | ||||
0.151274 | + | 0.988492i | \(0.451662\pi\) | |||||||
\(810\) | −2.77306e18 | −0.344990 | ||||||||
\(811\) | −2.50278e18 | −0.308878 | −0.154439 | − | 0.988002i | \(-0.549357\pi\) | ||||
−0.154439 | + | 0.988002i | \(0.549357\pi\) | |||||||
\(812\) | 1.70735e18 | 0.209030 | ||||||||
\(813\) | 4.26138e18 | 0.517561 | ||||||||
\(814\) | −2.69107e18 | −0.324240 | ||||||||
\(815\) | 1.00861e19 | 1.20558 | ||||||||
\(816\) | −1.70345e18 | −0.201997 | ||||||||
\(817\) | −7.20800e17 | −0.0847952 | ||||||||
\(818\) | −8.76035e18 | −1.02241 | ||||||||
\(819\) | 1.18391e17 | 0.0137080 | ||||||||
\(820\) | 5.23582e19 | 6.01443 | ||||||||
\(821\) | −4.69298e17 | −0.0534833 | −0.0267416 | − | 0.999642i | \(-0.508513\pi\) | ||||
−0.0267416 | + | 0.999642i | \(0.508513\pi\) | |||||||
\(822\) | 1.10943e19 | 1.25439 | ||||||||
\(823\) | −5.97438e18 | −0.670184 | −0.335092 | − | 0.942185i | \(-0.608767\pi\) | ||||
−0.335092 | + | 0.942185i | \(0.608767\pi\) | |||||||
\(824\) | 2.20933e19 | 2.45886 | ||||||||
\(825\) | 1.84725e18 | 0.203974 | ||||||||
\(826\) | −2.24826e17 | −0.0246307 | ||||||||
\(827\) | 6.24146e18 | 0.678423 | 0.339212 | − | 0.940710i | \(-0.389840\pi\) | ||||
0.339212 | + | 0.940710i | \(0.389840\pi\) | |||||||
\(828\) | −4.31599e18 | −0.465461 | ||||||||
\(829\) | 1.19846e19 | 1.28239 | 0.641195 | − | 0.767378i | \(-0.278439\pi\) | ||||
0.641195 | + | 0.767378i | \(0.278439\pi\) | |||||||
\(830\) | 5.16365e19 | 5.48213 | ||||||||
\(831\) | −1.31931e18 | −0.138976 | ||||||||
\(832\) | 5.06952e18 | 0.529865 | ||||||||
\(833\) | −7.89984e18 | −0.819267 | ||||||||
\(834\) | −7.32142e18 | −0.753383 | ||||||||
\(835\) | −2.46822e19 | −2.52013 | ||||||||
\(836\) | −4.80981e18 | −0.487289 | ||||||||
\(837\) | 4.61787e17 | 0.0464222 | ||||||||
\(838\) | 8.41641e18 | 0.839539 | ||||||||
\(839\) | −1.31942e19 | −1.30596 | −0.652979 | − | 0.757376i | \(-0.726481\pi\) | ||||
−0.652979 | + | 0.757376i | \(0.726481\pi\) | |||||||
\(840\) | −1.63831e18 | −0.160909 | ||||||||
\(841\) | 6.21862e17 | 0.0606066 | ||||||||
\(842\) | 1.76629e19 | 1.70818 | ||||||||
\(843\) | −7.58099e17 | −0.0727523 | ||||||||
\(844\) | −1.51406e19 | −1.44184 | ||||||||
\(845\) | −1.70659e19 | −1.61273 | ||||||||
\(846\) | 1.00291e19 | 0.940491 | ||||||||
\(847\) | 1.19126e18 | 0.110857 | ||||||||
\(848\) | −6.56019e18 | −0.605820 | ||||||||
\(849\) | 2.38037e18 | 0.218144 | ||||||||
\(850\) | −3.73904e19 | −3.40045 | ||||||||
\(851\) | 1.16192e19 | 1.04866 | ||||||||
\(852\) | 1.59853e19 | 1.43174 | ||||||||
\(853\) | 9.01253e18 | 0.801084 | 0.400542 | − | 0.916278i | \(-0.368822\pi\) | ||||
0.400542 | + | 0.916278i | \(0.368822\pi\) | |||||||
\(854\) | 1.41374e18 | 0.124708 | ||||||||
\(855\) | 1.33432e19 | 1.16810 | ||||||||
\(856\) | −1.46342e19 | −1.27142 | ||||||||
\(857\) | 1.75382e19 | 1.51221 | 0.756103 | − | 0.654453i | \(-0.227101\pi\) | ||||
0.756103 | + | 0.654453i | \(0.227101\pi\) | |||||||
\(858\) | 5.90212e17 | 0.0505057 | ||||||||
\(859\) | −3.38176e18 | −0.287202 | −0.143601 | − | 0.989636i | \(-0.545868\pi\) | ||||
−0.143601 | + | 0.989636i | \(0.545868\pi\) | |||||||
\(860\) | −1.77668e18 | −0.149751 | ||||||||
\(861\) | 1.41076e18 | 0.118014 | ||||||||
\(862\) | 7.97733e18 | 0.662309 | ||||||||
\(863\) | −1.64437e18 | −0.135497 | −0.0677486 | − | 0.997702i | \(-0.521582\pi\) | ||||
−0.0677486 | + | 0.997702i | \(0.521582\pi\) | |||||||
\(864\) | −1.46026e18 | −0.119424 | ||||||||
\(865\) | 1.12895e19 | 0.916368 | ||||||||
\(866\) | 3.20040e19 | 2.57833 | ||||||||
\(867\) | 2.24744e18 | 0.179707 | ||||||||
\(868\) | 6.16902e17 | 0.0489596 | ||||||||
\(869\) | −2.30522e18 | −0.181587 | ||||||||
\(870\) | −2.36124e19 | −1.84614 | ||||||||
\(871\) | 4.06272e18 | 0.315282 | ||||||||
\(872\) | 6.13712e18 | 0.472724 | ||||||||
\(873\) | −5.59176e18 | −0.427519 | ||||||||
\(874\) | 3.23504e19 | 2.45502 | ||||||||
\(875\) | −4.05370e18 | −0.305351 | ||||||||
\(876\) | −8.62794e18 | −0.645105 | ||||||||
\(877\) | 1.31534e18 | 0.0976203 | 0.0488102 | − | 0.998808i | \(-0.484457\pi\) | ||||
0.0488102 | + | 0.998808i | \(0.484457\pi\) | |||||||
\(878\) | 3.24762e19 | 2.39249 | ||||||||
\(879\) | −5.19383e18 | −0.379805 | ||||||||
\(880\) | −1.55485e18 | −0.112863 | ||||||||
\(881\) | 1.37999e19 | 0.994334 | 0.497167 | − | 0.867655i | \(-0.334374\pi\) | ||||
0.497167 | + | 0.867655i | \(0.334374\pi\) | |||||||
\(882\) | 7.68865e18 | 0.549926 | ||||||||
\(883\) | 1.45218e19 | 1.03104 | 0.515520 | − | 0.856877i | \(-0.327599\pi\) | ||||
0.515520 | + | 0.856877i | \(0.327599\pi\) | |||||||
\(884\) | −7.66907e18 | −0.540509 | ||||||||
\(885\) | 1.99603e18 | 0.139648 | ||||||||
\(886\) | 1.87121e19 | 1.29958 | ||||||||
\(887\) | 3.56456e18 | 0.245755 | 0.122878 | − | 0.992422i | \(-0.460788\pi\) | ||||
0.122878 | + | 0.992422i | \(0.460788\pi\) | |||||||
\(888\) | −1.50505e19 | −1.03007 | ||||||||
\(889\) | −8.40824e17 | −0.0571273 | ||||||||
\(890\) | −2.91413e19 | −1.96550 | ||||||||
\(891\) | −2.39120e17 | −0.0160107 | ||||||||
\(892\) | −3.39434e19 | −2.25623 | ||||||||
\(893\) | −4.82572e19 | −3.18440 | ||||||||
\(894\) | 1.21540e19 | 0.796209 | ||||||||
\(895\) | 2.11750e19 | 1.37713 | ||||||||
\(896\) | −3.18609e18 | −0.205711 | ||||||||
\(897\) | −2.54836e18 | −0.163346 | ||||||||
\(898\) | −2.51480e18 | −0.160032 | ||||||||
\(899\) | 3.93208e18 | 0.248419 | ||||||||
\(900\) | 2.33610e19 | 1.46526 | ||||||||
\(901\) | −1.91516e19 | −1.19260 | ||||||||
\(902\) | 7.03301e18 | 0.434809 | ||||||||
\(903\) | −4.78716e16 | −0.00293838 | ||||||||
\(904\) | −1.05817e19 | −0.644856 | ||||||||
\(905\) | −1.98652e19 | −1.20192 | ||||||||
\(906\) | −1.06057e19 | −0.637100 | ||||||||
\(907\) | −1.61526e19 | −0.963372 | −0.481686 | − | 0.876344i | \(-0.659975\pi\) | ||||
−0.481686 | + | 0.876344i | \(0.659975\pi\) | |||||||
\(908\) | 5.22050e16 | 0.00309139 | ||||||||
\(909\) | −9.12521e18 | −0.536509 | ||||||||
\(910\) | −2.18733e18 | −0.127687 | ||||||||
\(911\) | −2.26254e19 | −1.31138 | −0.655688 | − | 0.755032i | \(-0.727621\pi\) | ||||
−0.655688 | + | 0.755032i | \(0.727621\pi\) | |||||||
\(912\) | −7.97741e18 | −0.459087 | ||||||||
\(913\) | 4.45260e18 | 0.254421 | ||||||||
\(914\) | 5.06841e19 | 2.87556 | ||||||||
\(915\) | −1.25513e19 | −0.707052 | ||||||||
\(916\) | −3.96453e19 | −2.21754 | ||||||||
\(917\) | 1.79949e18 | 0.0999422 | ||||||||
\(918\) | 4.84005e18 | 0.266915 | ||||||||
\(919\) | 1.71301e19 | 0.938013 | 0.469007 | − | 0.883195i | \(-0.344612\pi\) | ||||
0.469007 | + | 0.883195i | \(0.344612\pi\) | |||||||
\(920\) | 3.52643e19 | 1.91741 | ||||||||
\(921\) | −9.38517e18 | −0.506704 | ||||||||
\(922\) | −2.84912e18 | −0.152743 | ||||||||
\(923\) | 9.43846e18 | 0.502447 | ||||||||
\(924\) | −3.19441e17 | −0.0168859 | ||||||||
\(925\) | −6.28911e19 | −3.30117 | ||||||||
\(926\) | 5.28637e19 | 2.75541 | ||||||||
\(927\) | −1.19505e19 | −0.618542 | ||||||||
\(928\) | −1.24340e19 | −0.639072 | ||||||||
\(929\) | −3.94107e17 | −0.0201146 | −0.0100573 | − | 0.999949i | \(-0.503201\pi\) | ||||
−0.0100573 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(930\) | −8.53169e18 | −0.432410 | ||||||||
\(931\) | −3.69956e19 | −1.86199 | ||||||||
\(932\) | 2.92813e19 | 1.46348 | ||||||||
\(933\) | −1.38054e19 | −0.685199 | ||||||||
\(934\) | 2.16904e19 | 1.06909 | ||||||||
\(935\) | −4.53918e18 | −0.222179 | ||||||||
\(936\) | 3.30092e18 | 0.160451 | ||||||||
\(937\) | 3.20171e19 | 1.54552 | 0.772760 | − | 0.634698i | \(-0.218876\pi\) | ||||
0.772760 | + | 0.634698i | \(0.218876\pi\) | |||||||
\(938\) | −3.42531e18 | −0.164203 | ||||||||
\(939\) | −1.54808e19 | −0.737001 | ||||||||
\(940\) | −1.18948e20 | −5.62374 | ||||||||
\(941\) | 3.00723e18 | 0.141200 | 0.0706000 | − | 0.997505i | \(-0.477509\pi\) | ||||
0.0706000 | + | 0.997505i | \(0.477509\pi\) | |||||||
\(942\) | 1.82008e19 | 0.848713 | ||||||||
\(943\) | −3.03664e19 | −1.40627 | ||||||||
\(944\) | −1.19335e18 | −0.0548847 | ||||||||
\(945\) | 8.86181e17 | 0.0404777 | ||||||||
\(946\) | −2.38652e17 | −0.0108261 | ||||||||
\(947\) | 1.83503e18 | 0.0826738 | 0.0413369 | − | 0.999145i | \(-0.486838\pi\) | ||||
0.0413369 | + | 0.999145i | \(0.486838\pi\) | |||||||
\(948\) | −2.91527e19 | −1.30444 | ||||||||
\(949\) | −5.09433e18 | −0.226390 | ||||||||
\(950\) | −1.75102e20 | −7.72837 | ||||||||
\(951\) | 7.84152e18 | 0.343737 | ||||||||
\(952\) | 2.85947e18 | 0.124493 | ||||||||
\(953\) | −2.15614e19 | −0.932340 | −0.466170 | − | 0.884695i | \(-0.654366\pi\) | ||||
−0.466170 | + | 0.884695i | \(0.654366\pi\) | |||||||
\(954\) | 1.86396e19 | 0.800520 | ||||||||
\(955\) | 6.04180e19 | 2.57718 | ||||||||
\(956\) | −1.30728e19 | −0.553850 | ||||||||
\(957\) | −2.03609e18 | −0.0856781 | ||||||||
\(958\) | 5.28445e19 | 2.20864 | ||||||||
\(959\) | −3.54538e18 | −0.147178 | ||||||||
\(960\) | 3.79462e19 | 1.56461 | ||||||||
\(961\) | −2.29968e19 | −0.941814 | ||||||||
\(962\) | −2.00942e19 | −0.817398 | ||||||||
\(963\) | 7.91583e18 | 0.319835 | ||||||||
\(964\) | −3.60230e19 | −1.44570 | ||||||||
\(965\) | −1.57550e19 | −0.628044 | ||||||||
\(966\) | 2.14854e18 | 0.0850730 | ||||||||
\(967\) | −2.27525e19 | −0.894865 | −0.447432 | − | 0.894318i | \(-0.647662\pi\) | ||||
−0.447432 | + | 0.894318i | \(0.647662\pi\) | |||||||
\(968\) | 3.32139e19 | 1.29757 | ||||||||
\(969\) | −2.32890e19 | −0.903744 | ||||||||
\(970\) | 1.03310e20 | 3.98223 | ||||||||
\(971\) | −8.61735e18 | −0.329950 | −0.164975 | − | 0.986298i | \(-0.552754\pi\) | ||||
−0.164975 | + | 0.986298i | \(0.552754\pi\) | |||||||
\(972\) | −3.02400e18 | −0.115014 | ||||||||
\(973\) | 2.33969e18 | 0.0883944 | ||||||||
\(974\) | −4.04871e19 | −1.51944 | ||||||||
\(975\) | 1.37934e19 | 0.514212 | ||||||||
\(976\) | 7.50398e18 | 0.277887 | ||||||||
\(977\) | 3.20669e19 | 1.17962 | 0.589810 | − | 0.807542i | \(-0.299202\pi\) | ||||
0.589810 | + | 0.807542i | \(0.299202\pi\) | |||||||
\(978\) | 1.71334e19 | 0.626098 | ||||||||
\(979\) | −2.51284e18 | −0.0912174 | ||||||||
\(980\) | −9.11894e19 | −3.28833 | ||||||||
\(981\) | −3.31965e18 | −0.118917 | ||||||||
\(982\) | −4.23429e19 | −1.50680 | ||||||||
\(983\) | 5.11263e18 | 0.180737 | 0.0903683 | − | 0.995908i | \(-0.471196\pi\) | ||||
0.0903683 | + | 0.995908i | \(0.471196\pi\) | |||||||
\(984\) | 3.93340e19 | 1.38134 | ||||||||
\(985\) | 5.42535e19 | 1.89274 | ||||||||
\(986\) | 4.12128e19 | 1.42834 | ||||||||
\(987\) | −3.20498e18 | −0.110348 | ||||||||
\(988\) | −3.59149e19 | −1.22844 | ||||||||
\(989\) | 1.03043e18 | 0.0350140 | ||||||||
\(990\) | 4.41784e18 | 0.149135 | ||||||||
\(991\) | 4.91293e19 | 1.64764 | 0.823819 | − | 0.566853i | \(-0.191839\pi\) | ||||
0.823819 | + | 0.566853i | \(0.191839\pi\) | |||||||
\(992\) | −4.49269e18 | −0.149686 | ||||||||
\(993\) | −3.01220e19 | −0.997044 | ||||||||
\(994\) | −7.95763e18 | −0.261681 | ||||||||
\(995\) | 4.08530e19 | 1.33467 | ||||||||
\(996\) | 5.63093e19 | 1.82766 | ||||||||
\(997\) | 5.73498e19 | 1.84933 | 0.924663 | − | 0.380787i | \(-0.124347\pi\) | ||||
0.924663 | + | 0.380787i | \(0.124347\pi\) | |||||||
\(998\) | −2.69511e19 | −0.863432 | ||||||||
\(999\) | 8.14103e18 | 0.259122 |
(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 | 177.14.a.b.1.4 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.b.1.4 | ✓ | 31 | 1.1 | even | 1 | trivial |