Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,40,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 40, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 40);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 40 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(19.2679102779\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 524288. | 0.707107 | ||||||||
\(3\) | −7.35458e8 | −0.365337 | −0.182668 | − | 0.983175i | \(-0.558473\pi\) | ||||
−0.182668 | + | 0.983175i | \(0.558473\pi\) | |||||||
\(4\) | 2.74878e11 | 0.500000 | ||||||||
\(5\) | −1.62262e13 | −0.380453 | −0.190227 | − | 0.981740i | \(-0.560922\pi\) | ||||
−0.190227 | + | 0.981740i | \(0.560922\pi\) | |||||||
\(6\) | −3.85592e14 | −0.258332 | ||||||||
\(7\) | 1.60501e16 | 0.532188 | 0.266094 | − | 0.963947i | \(-0.414267\pi\) | ||||
0.266094 | + | 0.963947i | \(0.414267\pi\) | |||||||
\(8\) | 1.44115e17 | 0.353553 | ||||||||
\(9\) | −3.51166e18 | −0.866529 | ||||||||
\(10\) | −8.50719e18 | −0.269021 | ||||||||
\(11\) | −1.67430e20 | −0.825421 | −0.412710 | − | 0.910862i | \(-0.635418\pi\) | ||||
−0.412710 | + | 0.910862i | \(0.635418\pi\) | |||||||
\(12\) | −2.02161e20 | −0.182668 | ||||||||
\(13\) | −1.32369e21 | −0.251126 | −0.125563 | − | 0.992086i | \(-0.540074\pi\) | ||||
−0.125563 | + | 0.992086i | \(0.540074\pi\) | |||||||
\(14\) | 8.41486e21 | 0.376314 | ||||||||
\(15\) | 1.19337e22 | 0.138994 | ||||||||
\(16\) | 7.55579e22 | 0.250000 | ||||||||
\(17\) | −4.96481e23 | −0.503673 | −0.251836 | − | 0.967770i | \(-0.581034\pi\) | ||||
−0.251836 | + | 0.967770i | \(0.581034\pi\) | |||||||
\(18\) | −1.84112e24 | −0.612728 | ||||||||
\(19\) | −1.14998e25 | −1.33350 | −0.666752 | − | 0.745280i | \(-0.732316\pi\) | ||||
−0.666752 | + | 0.745280i | \(0.732316\pi\) | |||||||
\(20\) | −4.46022e24 | −0.190227 | ||||||||
\(21\) | −1.18042e25 | −0.194428 | ||||||||
\(22\) | −8.77814e25 | −0.583660 | ||||||||
\(23\) | −6.66242e26 | −1.86183 | −0.930913 | − | 0.365241i | \(-0.880987\pi\) | ||||
−0.930913 | + | 0.365241i | \(0.880987\pi\) | |||||||
\(24\) | −1.05991e26 | −0.129166 | ||||||||
\(25\) | −1.55570e27 | −0.855255 | ||||||||
\(26\) | −6.93995e26 | −0.177573 | ||||||||
\(27\) | 5.56316e27 | 0.681912 | ||||||||
\(28\) | 4.41181e27 | 0.266094 | ||||||||
\(29\) | 4.40183e28 | 1.33928 | 0.669641 | − | 0.742685i | \(-0.266448\pi\) | ||||
0.669641 | + | 0.742685i | \(0.266448\pi\) | |||||||
\(30\) | 6.25668e27 | 0.0982833 | ||||||||
\(31\) | 1.58310e28 | 0.131207 | 0.0656033 | − | 0.997846i | \(-0.479103\pi\) | ||||
0.0656033 | + | 0.997846i | \(0.479103\pi\) | |||||||
\(32\) | 3.96141e28 | 0.176777 | ||||||||
\(33\) | 1.23138e29 | 0.301557 | ||||||||
\(34\) | −2.60299e29 | −0.356150 | ||||||||
\(35\) | −2.60431e29 | −0.202473 | ||||||||
\(36\) | −9.65277e29 | −0.433264 | ||||||||
\(37\) | −2.58657e30 | −0.680440 | −0.340220 | − | 0.940346i | \(-0.610502\pi\) | ||||
−0.340220 | + | 0.940346i | \(0.610502\pi\) | |||||||
\(38\) | −6.02920e30 | −0.942930 | ||||||||
\(39\) | 9.73520e29 | 0.0917455 | ||||||||
\(40\) | −2.33844e30 | −0.134510 | ||||||||
\(41\) | 5.12373e31 | 1.82096 | 0.910482 | − | 0.413550i | \(-0.135711\pi\) | ||||
0.910482 | + | 0.413550i | \(0.135711\pi\) | |||||||
\(42\) | −6.18878e30 | −0.137481 | ||||||||
\(43\) | 7.87984e31 | 1.10632 | 0.553162 | − | 0.833074i | \(-0.313421\pi\) | ||||
0.553162 | + | 0.833074i | \(0.313421\pi\) | |||||||
\(44\) | −4.60227e31 | −0.412710 | ||||||||
\(45\) | 5.69808e31 | 0.329674 | ||||||||
\(46\) | −3.49303e32 | −1.31651 | ||||||||
\(47\) | 2.42751e32 | 0.601524 | 0.300762 | − | 0.953699i | \(-0.402759\pi\) | ||||
0.300762 | + | 0.953699i | \(0.402759\pi\) | |||||||
\(48\) | −5.55697e31 | −0.0913342 | ||||||||
\(49\) | −6.51939e32 | −0.716776 | ||||||||
\(50\) | −8.15635e32 | −0.604757 | ||||||||
\(51\) | 3.65141e32 | 0.184010 | ||||||||
\(52\) | −3.63853e32 | −0.125563 | ||||||||
\(53\) | 6.95517e32 | 0.165550 | 0.0827748 | − | 0.996568i | \(-0.473622\pi\) | ||||
0.0827748 | + | 0.996568i | \(0.473622\pi\) | |||||||
\(54\) | 2.91670e33 | 0.482185 | ||||||||
\(55\) | 2.71675e33 | 0.314034 | ||||||||
\(56\) | 2.31306e33 | 0.188157 | ||||||||
\(57\) | 8.45761e33 | 0.487178 | ||||||||
\(58\) | 2.30783e34 | 0.947016 | ||||||||
\(59\) | −2.01815e34 | −0.593389 | −0.296695 | − | 0.954972i | \(-0.595884\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595884\pi\) | |||||||
\(60\) | 3.28030e33 | 0.0694968 | ||||||||
\(61\) | −1.28433e35 | −1.97127 | −0.985635 | − | 0.168890i | \(-0.945982\pi\) | ||||
−0.985635 | + | 0.168890i | \(0.945982\pi\) | |||||||
\(62\) | 8.30001e33 | 0.0927770 | ||||||||
\(63\) | −5.63623e34 | −0.461156 | ||||||||
\(64\) | 2.07692e34 | 0.125000 | ||||||||
\(65\) | 2.14784e34 | 0.0955416 | ||||||||
\(66\) | 6.45596e34 | 0.213233 | ||||||||
\(67\) | 4.56918e35 | 1.12559 | 0.562794 | − | 0.826597i | \(-0.309726\pi\) | ||||
0.562794 | + | 0.826597i | \(0.309726\pi\) | |||||||
\(68\) | −1.36472e35 | −0.251836 | ||||||||
\(69\) | 4.89993e35 | 0.680194 | ||||||||
\(70\) | −1.36541e35 | −0.143170 | ||||||||
\(71\) | −9.94586e34 | −0.0790869 | −0.0395434 | − | 0.999218i | \(-0.512590\pi\) | ||||
−0.0395434 | + | 0.999218i | \(0.512590\pi\) | |||||||
\(72\) | −5.06083e35 | −0.306364 | ||||||||
\(73\) | 8.12888e35 | 0.376041 | 0.188020 | − | 0.982165i | \(-0.439793\pi\) | ||||
0.188020 | + | 0.982165i | \(0.439793\pi\) | |||||||
\(74\) | −1.35611e36 | −0.481144 | ||||||||
\(75\) | 1.14415e36 | 0.312456 | ||||||||
\(76\) | −3.16104e36 | −0.666752 | ||||||||
\(77\) | −2.68726e36 | −0.439279 | ||||||||
\(78\) | 5.10405e35 | 0.0648739 | ||||||||
\(79\) | −8.57275e36 | −0.849947 | −0.424973 | − | 0.905206i | \(-0.639717\pi\) | ||||
−0.424973 | + | 0.905206i | \(0.639717\pi\) | |||||||
\(80\) | −1.22602e36 | −0.0951133 | ||||||||
\(81\) | 1.01397e37 | 0.617401 | ||||||||
\(82\) | 2.68631e37 | 1.28762 | ||||||||
\(83\) | 7.12589e36 | 0.269660 | 0.134830 | − | 0.990869i | \(-0.456951\pi\) | ||||
0.134830 | + | 0.990869i | \(0.456951\pi\) | |||||||
\(84\) | −3.24470e36 | −0.0972140 | ||||||||
\(85\) | 8.05599e36 | 0.191624 | ||||||||
\(86\) | 4.13131e37 | 0.782290 | ||||||||
\(87\) | −3.23736e37 | −0.489290 | ||||||||
\(88\) | −2.41292e37 | −0.291830 | ||||||||
\(89\) | −1.30970e38 | −1.27076 | −0.635382 | − | 0.772198i | \(-0.719157\pi\) | ||||
−0.635382 | + | 0.772198i | \(0.719157\pi\) | |||||||
\(90\) | 2.98743e37 | 0.233114 | ||||||||
\(91\) | −2.12453e37 | −0.133646 | ||||||||
\(92\) | −1.83135e38 | −0.930913 | ||||||||
\(93\) | −1.16430e37 | −0.0479346 | ||||||||
\(94\) | 1.27271e38 | 0.425342 | ||||||||
\(95\) | 1.86598e38 | 0.507336 | ||||||||
\(96\) | −2.91345e37 | −0.0645831 | ||||||||
\(97\) | 7.61043e38 | 1.37835 | 0.689176 | − | 0.724594i | \(-0.257973\pi\) | ||||
0.689176 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(98\) | −3.41804e38 | −0.506837 | ||||||||
\(99\) | 5.87956e38 | 0.715251 | ||||||||
\(100\) | −4.27628e38 | −0.427628 | ||||||||
\(101\) | −7.14964e38 | −0.588868 | −0.294434 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294434 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(102\) | 1.91439e38 | 0.130115 | ||||||||
\(103\) | 6.55259e38 | 0.368203 | 0.184101 | − | 0.982907i | \(-0.441063\pi\) | ||||
0.184101 | + | 0.982907i | \(0.441063\pi\) | |||||||
\(104\) | −1.90764e38 | −0.0887864 | ||||||||
\(105\) | 1.91536e38 | 0.0739707 | ||||||||
\(106\) | 3.64651e38 | 0.117061 | ||||||||
\(107\) | −5.91456e39 | −1.58103 | −0.790513 | − | 0.612445i | \(-0.790186\pi\) | ||||
−0.790513 | + | 0.612445i | \(0.790186\pi\) | |||||||
\(108\) | 1.52919e39 | 0.340956 | ||||||||
\(109\) | −4.18504e39 | −0.779620 | −0.389810 | − | 0.920895i | \(-0.627459\pi\) | ||||
−0.389810 | + | 0.920895i | \(0.627459\pi\) | |||||||
\(110\) | 1.42436e39 | 0.222055 | ||||||||
\(111\) | 1.90231e39 | 0.248590 | ||||||||
\(112\) | 1.21271e39 | 0.133047 | ||||||||
\(113\) | 3.82469e39 | 0.352831 | 0.176415 | − | 0.984316i | \(-0.443550\pi\) | ||||
0.176415 | + | 0.984316i | \(0.443550\pi\) | |||||||
\(114\) | 4.43422e39 | 0.344487 | ||||||||
\(115\) | 1.08106e40 | 0.708338 | ||||||||
\(116\) | 1.20997e40 | 0.669641 | ||||||||
\(117\) | 4.64835e39 | 0.217608 | ||||||||
\(118\) | −1.05809e40 | −0.419590 | ||||||||
\(119\) | −7.96855e39 | −0.268049 | ||||||||
\(120\) | 1.71982e39 | 0.0491417 | ||||||||
\(121\) | −1.31121e40 | −0.318681 | ||||||||
\(122\) | −6.73361e40 | −1.39390 | ||||||||
\(123\) | −3.76829e40 | −0.665265 | ||||||||
\(124\) | 4.35159e39 | 0.0656033 | ||||||||
\(125\) | 5.47583e40 | 0.705838 | ||||||||
\(126\) | −2.95501e40 | −0.326087 | ||||||||
\(127\) | 8.14150e40 | 0.770073 | 0.385037 | − | 0.922901i | \(-0.374189\pi\) | ||||
0.385037 | + | 0.922901i | \(0.374189\pi\) | |||||||
\(128\) | 1.08890e40 | 0.0883883 | ||||||||
\(129\) | −5.79529e40 | −0.404181 | ||||||||
\(130\) | 1.12609e40 | 0.0675581 | ||||||||
\(131\) | 2.55072e41 | 1.31787 | 0.658936 | − | 0.752199i | \(-0.271007\pi\) | ||||
0.658936 | + | 0.752199i | \(0.271007\pi\) | |||||||
\(132\) | 3.38478e40 | 0.150778 | ||||||||
\(133\) | −1.84572e41 | −0.709675 | ||||||||
\(134\) | 2.39556e41 | 0.795911 | ||||||||
\(135\) | −9.02689e40 | −0.259436 | ||||||||
\(136\) | −7.15504e40 | −0.178075 | ||||||||
\(137\) | −1.57560e41 | −0.339933 | −0.169967 | − | 0.985450i | \(-0.554366\pi\) | ||||
−0.169967 | + | 0.985450i | \(0.554366\pi\) | |||||||
\(138\) | 2.56898e41 | 0.480970 | ||||||||
\(139\) | −5.88829e41 | −0.957637 | −0.478819 | − | 0.877914i | \(-0.658935\pi\) | ||||
−0.478819 | + | 0.877914i | \(0.658935\pi\) | |||||||
\(140\) | −7.15868e40 | −0.101236 | ||||||||
\(141\) | −1.78533e41 | −0.219759 | ||||||||
\(142\) | −5.21449e40 | −0.0559229 | ||||||||
\(143\) | 2.21625e41 | 0.207284 | ||||||||
\(144\) | −2.65333e41 | −0.216632 | ||||||||
\(145\) | −7.14249e41 | −0.509534 | ||||||||
\(146\) | 4.26187e41 | 0.265901 | ||||||||
\(147\) | 4.79474e41 | 0.261865 | ||||||||
\(148\) | −7.10990e41 | −0.340220 | ||||||||
\(149\) | 1.20747e42 | 0.506691 | 0.253346 | − | 0.967376i | \(-0.418469\pi\) | ||||
0.253346 | + | 0.967376i | \(0.418469\pi\) | |||||||
\(150\) | 5.99866e41 | 0.220940 | ||||||||
\(151\) | 5.68508e42 | 1.83944 | 0.919721 | − | 0.392573i | \(-0.128415\pi\) | ||||
0.919721 | + | 0.392573i | \(0.128415\pi\) | |||||||
\(152\) | −1.65729e42 | −0.471465 | ||||||||
\(153\) | 1.74347e42 | 0.436447 | ||||||||
\(154\) | −1.40890e42 | −0.310617 | ||||||||
\(155\) | −2.56877e41 | −0.0499179 | ||||||||
\(156\) | 2.67599e41 | 0.0458728 | ||||||||
\(157\) | −9.75064e42 | −1.47567 | −0.737836 | − | 0.674980i | \(-0.764152\pi\) | ||||
−0.737836 | + | 0.674980i | \(0.764152\pi\) | |||||||
\(158\) | −4.49459e42 | −0.601003 | ||||||||
\(159\) | −5.11524e41 | −0.0604814 | ||||||||
\(160\) | −6.42785e41 | −0.0672552 | ||||||||
\(161\) | −1.06932e43 | −0.990842 | ||||||||
\(162\) | 5.31613e42 | 0.436569 | ||||||||
\(163\) | 4.57034e42 | 0.332882 | 0.166441 | − | 0.986051i | \(-0.446773\pi\) | ||||
0.166441 | + | 0.986051i | \(0.446773\pi\) | |||||||
\(164\) | 1.40840e43 | 0.910482 | ||||||||
\(165\) | −1.99805e42 | −0.114728 | ||||||||
\(166\) | 3.73602e42 | 0.190678 | ||||||||
\(167\) | 2.16180e43 | 0.981397 | 0.490699 | − | 0.871329i | \(-0.336742\pi\) | ||||
0.490699 | + | 0.871329i | \(0.336742\pi\) | |||||||
\(168\) | −1.70116e42 | −0.0687406 | ||||||||
\(169\) | −2.60316e43 | −0.936936 | ||||||||
\(170\) | 4.22366e42 | 0.135499 | ||||||||
\(171\) | 4.03833e43 | 1.15552 | ||||||||
\(172\) | 2.16599e43 | 0.553162 | ||||||||
\(173\) | −3.61908e43 | −0.825467 | −0.412733 | − | 0.910852i | \(-0.635426\pi\) | ||||
−0.412733 | + | 0.910852i | \(0.635426\pi\) | |||||||
\(174\) | −1.69731e43 | −0.345980 | ||||||||
\(175\) | −2.49691e43 | −0.455157 | ||||||||
\(176\) | −1.26506e43 | −0.206355 | ||||||||
\(177\) | 1.48427e43 | 0.216787 | ||||||||
\(178\) | −6.86657e43 | −0.898566 | ||||||||
\(179\) | 8.73010e43 | 1.02420 | 0.512100 | − | 0.858926i | \(-0.328868\pi\) | ||||
0.512100 | + | 0.858926i | \(0.328868\pi\) | |||||||
\(180\) | 1.56628e43 | 0.164837 | ||||||||
\(181\) | −1.51508e44 | −1.43121 | −0.715607 | − | 0.698504i | \(-0.753850\pi\) | ||||
−0.715607 | + | 0.698504i | \(0.753850\pi\) | |||||||
\(182\) | −1.11387e43 | −0.0945021 | ||||||||
\(183\) | 9.44574e43 | 0.720178 | ||||||||
\(184\) | −9.60156e43 | −0.658255 | ||||||||
\(185\) | 4.19701e43 | 0.258876 | ||||||||
\(186\) | −6.10431e42 | −0.0338949 | ||||||||
\(187\) | 8.31257e43 | 0.415742 | ||||||||
\(188\) | 6.67269e43 | 0.300762 | ||||||||
\(189\) | 8.92891e43 | 0.362905 | ||||||||
\(190\) | 9.78308e43 | 0.358741 | ||||||||
\(191\) | 4.32591e44 | 1.43195 | 0.715974 | − | 0.698127i | \(-0.245983\pi\) | ||||
0.715974 | + | 0.698127i | \(0.245983\pi\) | |||||||
\(192\) | −1.52749e43 | −0.0456671 | ||||||||
\(193\) | −7.04390e44 | −1.90303 | −0.951515 | − | 0.307601i | \(-0.900474\pi\) | ||||
−0.951515 | + | 0.307601i | \(0.900474\pi\) | |||||||
\(194\) | 3.99006e44 | 0.974643 | ||||||||
\(195\) | −1.57965e43 | −0.0349049 | ||||||||
\(196\) | −1.79204e44 | −0.358388 | ||||||||
\(197\) | −1.81044e44 | −0.327864 | −0.163932 | − | 0.986472i | \(-0.552418\pi\) | ||||
−0.163932 | + | 0.986472i | \(0.552418\pi\) | |||||||
\(198\) | 3.08258e44 | 0.505759 | ||||||||
\(199\) | −9.78460e44 | −1.45515 | −0.727575 | − | 0.686028i | \(-0.759353\pi\) | ||||
−0.727575 | + | 0.686028i | \(0.759353\pi\) | |||||||
\(200\) | −2.24200e44 | −0.302378 | ||||||||
\(201\) | −3.36044e44 | −0.411219 | ||||||||
\(202\) | −3.74847e44 | −0.416392 | ||||||||
\(203\) | 7.06497e44 | 0.712750 | ||||||||
\(204\) | 1.00369e44 | 0.0920051 | ||||||||
\(205\) | −8.31386e44 | −0.692791 | ||||||||
\(206\) | 3.43544e44 | 0.260359 | ||||||||
\(207\) | 2.33961e45 | 1.61333 | ||||||||
\(208\) | −1.00015e44 | −0.0627814 | ||||||||
\(209\) | 1.92541e45 | 1.10070 | ||||||||
\(210\) | 1.00420e44 | 0.0523052 | ||||||||
\(211\) | 1.87844e44 | 0.0891843 | 0.0445922 | − | 0.999005i | \(-0.485801\pi\) | ||||
0.0445922 | + | 0.999005i | \(0.485801\pi\) | |||||||
\(212\) | 1.91182e44 | 0.0827748 | ||||||||
\(213\) | 7.31476e43 | 0.0288934 | ||||||||
\(214\) | −3.10093e45 | −1.11795 | ||||||||
\(215\) | −1.27860e45 | −0.420905 | ||||||||
\(216\) | 8.01736e44 | 0.241092 | ||||||||
\(217\) | 2.54089e44 | 0.0698265 | ||||||||
\(218\) | −2.19417e45 | −0.551275 | ||||||||
\(219\) | −5.97845e44 | −0.137382 | ||||||||
\(220\) | 7.46773e44 | 0.157017 | ||||||||
\(221\) | 6.57187e44 | 0.126485 | ||||||||
\(222\) | 9.97359e44 | 0.175780 | ||||||||
\(223\) | −7.17839e45 | −1.15900 | −0.579498 | − | 0.814974i | \(-0.696751\pi\) | ||||
−0.579498 | + | 0.814974i | \(0.696751\pi\) | |||||||
\(224\) | 6.35809e44 | 0.0940784 | ||||||||
\(225\) | 5.46309e45 | 0.741104 | ||||||||
\(226\) | 2.00524e45 | 0.249489 | ||||||||
\(227\) | −7.82184e45 | −0.892904 | −0.446452 | − | 0.894808i | \(-0.647313\pi\) | ||||
−0.446452 | + | 0.894808i | \(0.647313\pi\) | |||||||
\(228\) | 2.32481e45 | 0.243589 | ||||||||
\(229\) | −4.60714e45 | −0.443240 | −0.221620 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221620 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(230\) | 5.66785e45 | 0.500870 | ||||||||
\(231\) | 1.97637e45 | 0.160485 | ||||||||
\(232\) | 6.34371e45 | 0.473508 | ||||||||
\(233\) | 1.80888e46 | 1.24157 | 0.620784 | − | 0.783982i | \(-0.286814\pi\) | ||||
0.620784 | + | 0.783982i | \(0.286814\pi\) | |||||||
\(234\) | 2.43707e45 | 0.153872 | ||||||||
\(235\) | −3.93892e45 | −0.228852 | ||||||||
\(236\) | −5.54746e45 | −0.296695 | ||||||||
\(237\) | 6.30490e45 | 0.310517 | ||||||||
\(238\) | −4.17781e45 | −0.189539 | ||||||||
\(239\) | −8.37506e45 | −0.350129 | −0.175065 | − | 0.984557i | \(-0.556013\pi\) | ||||
−0.175065 | + | 0.984557i | \(0.556013\pi\) | |||||||
\(240\) | 9.01683e44 | 0.0347484 | ||||||||
\(241\) | 1.67167e45 | 0.0594044 | 0.0297022 | − | 0.999559i | \(-0.490544\pi\) | ||||
0.0297022 | + | 0.999559i | \(0.490544\pi\) | |||||||
\(242\) | −6.87449e45 | −0.225341 | ||||||||
\(243\) | −3.00024e46 | −0.907471 | ||||||||
\(244\) | −3.53035e46 | −0.985635 | ||||||||
\(245\) | 1.05785e46 | 0.272700 | ||||||||
\(246\) | −1.97567e46 | −0.470413 | ||||||||
\(247\) | 1.52222e46 | 0.334877 | ||||||||
\(248\) | 2.28149e45 | 0.0463885 | ||||||||
\(249\) | −5.24080e45 | −0.0985167 | ||||||||
\(250\) | 2.87091e46 | 0.499103 | ||||||||
\(251\) | −7.60545e45 | −0.122317 | −0.0611586 | − | 0.998128i | \(-0.519480\pi\) | ||||
−0.0611586 | + | 0.998128i | \(0.519480\pi\) | |||||||
\(252\) | −1.54928e46 | −0.230578 | ||||||||
\(253\) | 1.11549e47 | 1.53679 | ||||||||
\(254\) | 4.26849e46 | 0.544524 | ||||||||
\(255\) | −5.92484e45 | −0.0700073 | ||||||||
\(256\) | 5.70899e45 | 0.0625000 | ||||||||
\(257\) | 9.64642e46 | 0.978747 | 0.489373 | − | 0.872074i | \(-0.337226\pi\) | ||||
0.489373 | + | 0.872074i | \(0.337226\pi\) | |||||||
\(258\) | −3.03840e46 | −0.285799 | ||||||||
\(259\) | −4.15146e46 | −0.362122 | ||||||||
\(260\) | 5.90395e45 | 0.0477708 | ||||||||
\(261\) | −1.54577e47 | −1.16053 | ||||||||
\(262\) | 1.33731e47 | 0.931876 | ||||||||
\(263\) | −2.38043e47 | −1.53999 | −0.769997 | − | 0.638048i | \(-0.779742\pi\) | ||||
−0.769997 | + | 0.638048i | \(0.779742\pi\) | |||||||
\(264\) | 1.77460e46 | 0.106616 | ||||||||
\(265\) | −1.12856e46 | −0.0629839 | ||||||||
\(266\) | −9.67690e46 | −0.501816 | ||||||||
\(267\) | 9.63226e46 | 0.464257 | ||||||||
\(268\) | 1.25597e47 | 0.562794 | ||||||||
\(269\) | −3.43730e47 | −1.43235 | −0.716173 | − | 0.697923i | \(-0.754108\pi\) | ||||
−0.716173 | + | 0.697923i | \(0.754108\pi\) | |||||||
\(270\) | −4.73269e46 | −0.183449 | ||||||||
\(271\) | 2.34239e47 | 0.844809 | 0.422404 | − | 0.906408i | \(-0.361186\pi\) | ||||
0.422404 | + | 0.906408i | \(0.361186\pi\) | |||||||
\(272\) | −3.75130e46 | −0.125918 | ||||||||
\(273\) | 1.56251e46 | 0.0488259 | ||||||||
\(274\) | −8.26066e46 | −0.240369 | ||||||||
\(275\) | 2.60471e47 | 0.705945 | ||||||||
\(276\) | 1.34688e47 | 0.340097 | ||||||||
\(277\) | 4.97473e47 | 1.17062 | 0.585308 | − | 0.810811i | \(-0.300974\pi\) | ||||
0.585308 | + | 0.810811i | \(0.300974\pi\) | |||||||
\(278\) | −3.08716e47 | −0.677152 | ||||||||
\(279\) | −5.55931e46 | −0.113694 | ||||||||
\(280\) | −3.75321e46 | −0.0715849 | ||||||||
\(281\) | −2.28343e47 | −0.406270 | −0.203135 | − | 0.979151i | \(-0.565113\pi\) | ||||
−0.203135 | + | 0.979151i | \(0.565113\pi\) | |||||||
\(282\) | −9.36029e46 | −0.155393 | ||||||||
\(283\) | 6.09891e47 | 0.944968 | 0.472484 | − | 0.881339i | \(-0.343358\pi\) | ||||
0.472484 | + | 0.881339i | \(0.343358\pi\) | |||||||
\(284\) | −2.73390e46 | −0.0395434 | ||||||||
\(285\) | −1.37235e47 | −0.185349 | ||||||||
\(286\) | 1.16195e47 | 0.146572 | ||||||||
\(287\) | 8.22362e47 | 0.969095 | ||||||||
\(288\) | −1.39111e47 | −0.153182 | ||||||||
\(289\) | −7.25153e47 | −0.746314 | ||||||||
\(290\) | −3.74472e47 | −0.360295 | ||||||||
\(291\) | −5.59715e47 | −0.503563 | ||||||||
\(292\) | 2.23445e47 | 0.188020 | ||||||||
\(293\) | −2.18536e48 | −1.72030 | −0.860149 | − | 0.510043i | \(-0.829630\pi\) | ||||
−0.860149 | + | 0.510043i | \(0.829630\pi\) | |||||||
\(294\) | 2.51382e47 | 0.185166 | ||||||||
\(295\) | 3.27469e47 | 0.225757 | ||||||||
\(296\) | −3.72763e47 | −0.240572 | ||||||||
\(297\) | −9.31439e47 | −0.562864 | ||||||||
\(298\) | 6.33061e47 | 0.358285 | ||||||||
\(299\) | 8.81898e47 | 0.467553 | ||||||||
\(300\) | 3.14502e47 | 0.156228 | ||||||||
\(301\) | 1.26472e48 | 0.588773 | ||||||||
\(302\) | 2.98062e48 | 1.30068 | ||||||||
\(303\) | 5.25827e47 | 0.215135 | ||||||||
\(304\) | −8.68899e47 | −0.333376 | ||||||||
\(305\) | 2.08398e48 | 0.749976 | ||||||||
\(306\) | 9.14080e47 | 0.308615 | ||||||||
\(307\) | −1.84711e48 | −0.585187 | −0.292594 | − | 0.956237i | \(-0.594518\pi\) | ||||
−0.292594 | + | 0.956237i | \(0.594518\pi\) | |||||||
\(308\) | −7.38668e47 | −0.219639 | ||||||||
\(309\) | −4.81915e47 | −0.134518 | ||||||||
\(310\) | −1.34677e47 | −0.0352973 | ||||||||
\(311\) | 3.22674e48 | 0.794211 | 0.397105 | − | 0.917773i | \(-0.370015\pi\) | ||||
0.397105 | + | 0.917773i | \(0.370015\pi\) | |||||||
\(312\) | 1.40299e47 | 0.0324369 | ||||||||
\(313\) | −6.99390e48 | −1.51916 | −0.759582 | − | 0.650411i | \(-0.774597\pi\) | ||||
−0.759582 | + | 0.650411i | \(0.774597\pi\) | |||||||
\(314\) | −5.11215e48 | −1.04346 | ||||||||
\(315\) | 9.14545e47 | 0.175448 | ||||||||
\(316\) | −2.35646e48 | −0.424973 | ||||||||
\(317\) | 5.37916e48 | 0.912135 | 0.456067 | − | 0.889945i | \(-0.349258\pi\) | ||||
0.456067 | + | 0.889945i | \(0.349258\pi\) | |||||||
\(318\) | −2.68186e47 | −0.0427668 | ||||||||
\(319\) | −7.36997e48 | −1.10547 | ||||||||
\(320\) | −3.37005e47 | −0.0475566 | ||||||||
\(321\) | 4.34991e48 | 0.577607 | ||||||||
\(322\) | −5.60633e48 | −0.700631 | ||||||||
\(323\) | 5.70942e48 | 0.671650 | ||||||||
\(324\) | 2.78718e48 | 0.308701 | ||||||||
\(325\) | 2.05927e48 | 0.214777 | ||||||||
\(326\) | 2.39617e48 | 0.235383 | ||||||||
\(327\) | 3.07792e48 | 0.284824 | ||||||||
\(328\) | 7.38408e48 | 0.643808 | ||||||||
\(329\) | 3.89617e48 | 0.320124 | ||||||||
\(330\) | −1.04756e48 | −0.0811251 | ||||||||
\(331\) | −1.40018e49 | −1.02220 | −0.511102 | − | 0.859520i | \(-0.670762\pi\) | ||||
−0.511102 | + | 0.859520i | \(0.670762\pi\) | |||||||
\(332\) | 1.95875e48 | 0.134830 | ||||||||
\(333\) | 9.08313e48 | 0.589621 | ||||||||
\(334\) | 1.13341e49 | 0.693953 | ||||||||
\(335\) | −7.41403e48 | −0.428233 | ||||||||
\(336\) | −8.91897e47 | −0.0486070 | ||||||||
\(337\) | −3.35577e48 | −0.172587 | −0.0862936 | − | 0.996270i | \(-0.527502\pi\) | ||||
−0.0862936 | + | 0.996270i | \(0.527502\pi\) | |||||||
\(338\) | −1.36480e49 | −0.662514 | ||||||||
\(339\) | −2.81290e48 | −0.128902 | ||||||||
\(340\) | 2.21441e48 | 0.0958119 | ||||||||
\(341\) | −2.65058e48 | −0.108301 | ||||||||
\(342\) | 2.11725e49 | 0.817076 | ||||||||
\(343\) | −2.50619e49 | −0.913647 | ||||||||
\(344\) | 1.13560e49 | 0.391145 | ||||||||
\(345\) | −7.95072e48 | −0.258782 | ||||||||
\(346\) | −1.89744e49 | −0.583693 | ||||||||
\(347\) | −2.60839e49 | −0.758486 | −0.379243 | − | 0.925297i | \(-0.623816\pi\) | ||||
−0.379243 | + | 0.925297i | \(0.623816\pi\) | |||||||
\(348\) | −8.89879e48 | −0.244645 | ||||||||
\(349\) | 2.03635e49 | 0.529366 | 0.264683 | − | 0.964335i | \(-0.414733\pi\) | ||||
0.264683 | + | 0.964335i | \(0.414733\pi\) | |||||||
\(350\) | −1.30910e49 | −0.321844 | ||||||||
\(351\) | −7.36391e48 | −0.171246 | ||||||||
\(352\) | −6.63258e48 | −0.145915 | ||||||||
\(353\) | 8.08319e49 | 1.68258 | 0.841291 | − | 0.540583i | \(-0.181796\pi\) | ||||
0.841291 | + | 0.540583i | \(0.181796\pi\) | |||||||
\(354\) | 7.78183e48 | 0.153292 | ||||||||
\(355\) | 1.61383e48 | 0.0300888 | ||||||||
\(356\) | −3.60006e49 | −0.635382 | ||||||||
\(357\) | 5.86054e48 | 0.0979281 | ||||||||
\(358\) | 4.57709e49 | 0.724219 | ||||||||
\(359\) | 7.35363e49 | 1.10194 | 0.550972 | − | 0.834524i | \(-0.314257\pi\) | ||||
0.550972 | + | 0.834524i | \(0.314257\pi\) | |||||||
\(360\) | 8.21179e48 | 0.116557 | ||||||||
\(361\) | 5.78763e49 | 0.778234 | ||||||||
\(362\) | −7.94340e49 | −1.01202 | ||||||||
\(363\) | 9.64337e48 | 0.116426 | ||||||||
\(364\) | −5.83987e48 | −0.0668231 | ||||||||
\(365\) | −1.31901e49 | −0.143066 | ||||||||
\(366\) | 4.95229e49 | 0.509243 | ||||||||
\(367\) | −9.99437e49 | −0.974467 | −0.487233 | − | 0.873272i | \(-0.661994\pi\) | ||||
−0.487233 | + | 0.873272i | \(0.661994\pi\) | |||||||
\(368\) | −5.03398e49 | −0.465457 | ||||||||
\(369\) | −1.79928e50 | −1.57792 | ||||||||
\(370\) | 2.20044e49 | 0.183053 | ||||||||
\(371\) | 1.11631e49 | 0.0881036 | ||||||||
\(372\) | −3.20042e48 | −0.0239673 | ||||||||
\(373\) | −1.06368e50 | −0.755944 | −0.377972 | − | 0.925817i | \(-0.623378\pi\) | ||||
−0.377972 | + | 0.925817i | \(0.623378\pi\) | |||||||
\(374\) | 4.35818e49 | 0.293974 | ||||||||
\(375\) | −4.02725e49 | −0.257869 | ||||||||
\(376\) | 3.49841e49 | 0.212671 | ||||||||
\(377\) | −5.82666e49 | −0.336328 | ||||||||
\(378\) | 4.68132e49 | 0.256613 | ||||||||
\(379\) | 3.09568e50 | 1.61173 | 0.805864 | − | 0.592101i | \(-0.201701\pi\) | ||||
0.805864 | + | 0.592101i | \(0.201701\pi\) | |||||||
\(380\) | 5.12915e49 | 0.253668 | ||||||||
\(381\) | −5.98773e49 | −0.281336 | ||||||||
\(382\) | 2.26802e50 | 1.01254 | ||||||||
\(383\) | 1.31362e50 | 0.557304 | 0.278652 | − | 0.960392i | \(-0.410112\pi\) | ||||
0.278652 | + | 0.960392i | \(0.410112\pi\) | |||||||
\(384\) | −8.00843e48 | −0.0322915 | ||||||||
\(385\) | 4.36039e49 | 0.167125 | ||||||||
\(386\) | −3.69303e50 | −1.34565 | ||||||||
\(387\) | −2.76713e50 | −0.958662 | ||||||||
\(388\) | 2.09194e50 | 0.689176 | ||||||||
\(389\) | 1.27217e50 | 0.398592 | 0.199296 | − | 0.979939i | \(-0.436134\pi\) | ||||
0.199296 | + | 0.979939i | \(0.436134\pi\) | |||||||
\(390\) | −8.28192e48 | −0.0246815 | ||||||||
\(391\) | 3.30776e50 | 0.937751 | ||||||||
\(392\) | −9.39543e49 | −0.253419 | ||||||||
\(393\) | −1.87595e50 | −0.481467 | ||||||||
\(394\) | −9.49193e49 | −0.231835 | ||||||||
\(395\) | 1.39103e50 | 0.323365 | ||||||||
\(396\) | 1.61616e50 | 0.357625 | ||||||||
\(397\) | −4.10443e50 | −0.864646 | −0.432323 | − | 0.901719i | \(-0.642306\pi\) | ||||
−0.432323 | + | 0.901719i | \(0.642306\pi\) | |||||||
\(398\) | −5.12995e50 | −1.02895 | ||||||||
\(399\) | 1.35745e50 | 0.259270 | ||||||||
\(400\) | −1.17545e50 | −0.213814 | ||||||||
\(401\) | 7.58787e49 | 0.131463 | 0.0657317 | − | 0.997837i | \(-0.479062\pi\) | ||||
0.0657317 | + | 0.997837i | \(0.479062\pi\) | |||||||
\(402\) | −1.76184e50 | −0.290776 | ||||||||
\(403\) | −2.09554e49 | −0.0329493 | ||||||||
\(404\) | −1.96528e50 | −0.294434 | ||||||||
\(405\) | −1.64529e50 | −0.234892 | ||||||||
\(406\) | 3.70408e50 | 0.503991 | ||||||||
\(407\) | 4.33068e50 | 0.561649 | ||||||||
\(408\) | 5.26224e49 | 0.0650575 | ||||||||
\(409\) | 2.10087e50 | 0.247626 | 0.123813 | − | 0.992306i | \(-0.460488\pi\) | ||||
0.123813 | + | 0.992306i | \(0.460488\pi\) | |||||||
\(410\) | −4.35886e50 | −0.489877 | ||||||||
\(411\) | 1.15879e50 | 0.124190 | ||||||||
\(412\) | 1.80116e50 | 0.184101 | ||||||||
\(413\) | −3.23915e50 | −0.315795 | ||||||||
\(414\) | 1.22663e51 | 1.14079 | ||||||||
\(415\) | −1.15626e50 | −0.102593 | ||||||||
\(416\) | −5.24368e49 | −0.0443932 | ||||||||
\(417\) | 4.33060e50 | 0.349860 | ||||||||
\(418\) | 1.00947e51 | 0.778314 | ||||||||
\(419\) | 1.77773e50 | 0.130826 | 0.0654129 | − | 0.997858i | \(-0.479164\pi\) | ||||
0.0654129 | + | 0.997858i | \(0.479164\pi\) | |||||||
\(420\) | 5.26491e49 | 0.0369854 | ||||||||
\(421\) | −7.65653e50 | −0.513489 | −0.256744 | − | 0.966479i | \(-0.582650\pi\) | ||||
−0.256744 | + | 0.966479i | \(0.582650\pi\) | |||||||
\(422\) | 9.84841e49 | 0.0630628 | ||||||||
\(423\) | −8.52458e50 | −0.521238 | ||||||||
\(424\) | 1.00235e50 | 0.0585307 | ||||||||
\(425\) | 7.72375e50 | 0.430769 | ||||||||
\(426\) | 3.83504e49 | 0.0204307 | ||||||||
\(427\) | −2.06136e51 | −1.04909 | ||||||||
\(428\) | −1.62578e51 | −0.790513 | ||||||||
\(429\) | −1.62996e50 | −0.0757286 | ||||||||
\(430\) | −6.70353e50 | −0.297625 | ||||||||
\(431\) | −9.06012e50 | −0.384439 | −0.192219 | − | 0.981352i | \(-0.561569\pi\) | ||||
−0.192219 | + | 0.981352i | \(0.561569\pi\) | |||||||
\(432\) | 4.20341e50 | 0.170478 | ||||||||
\(433\) | −2.95958e51 | −1.14740 | −0.573702 | − | 0.819064i | \(-0.694493\pi\) | ||||
−0.573702 | + | 0.819064i | \(0.694493\pi\) | |||||||
\(434\) | 1.33216e50 | 0.0493748 | ||||||||
\(435\) | 5.25300e50 | 0.186152 | ||||||||
\(436\) | −1.15038e51 | −0.389810 | ||||||||
\(437\) | 7.66164e51 | 2.48275 | ||||||||
\(438\) | −3.13443e50 | −0.0971434 | ||||||||
\(439\) | −1.93285e51 | −0.572982 | −0.286491 | − | 0.958083i | \(-0.592489\pi\) | ||||
−0.286491 | + | 0.958083i | \(0.592489\pi\) | |||||||
\(440\) | 3.91524e50 | 0.111028 | ||||||||
\(441\) | 2.28939e51 | 0.621107 | ||||||||
\(442\) | 3.44555e50 | 0.0894386 | ||||||||
\(443\) | 5.23473e51 | 1.30023 | 0.650117 | − | 0.759834i | \(-0.274720\pi\) | ||||
0.650117 | + | 0.759834i | \(0.274720\pi\) | |||||||
\(444\) | 5.22903e50 | 0.124295 | ||||||||
\(445\) | 2.12513e51 | 0.483466 | ||||||||
\(446\) | −3.76354e51 | −0.819534 | ||||||||
\(447\) | −8.88042e50 | −0.185113 | ||||||||
\(448\) | 3.33347e50 | 0.0665235 | ||||||||
\(449\) | 2.64498e51 | 0.505380 | 0.252690 | − | 0.967547i | \(-0.418685\pi\) | ||||
0.252690 | + | 0.967547i | \(0.418685\pi\) | |||||||
\(450\) | 2.86423e51 | 0.524039 | ||||||||
\(451\) | −8.57865e51 | −1.50306 | ||||||||
\(452\) | 1.05132e51 | 0.176415 | ||||||||
\(453\) | −4.18114e51 | −0.672016 | ||||||||
\(454\) | −4.10090e51 | −0.631378 | ||||||||
\(455\) | 3.44731e50 | 0.0508461 | ||||||||
\(456\) | 1.21887e51 | 0.172244 | ||||||||
\(457\) | 3.37218e49 | 0.00456610 | 0.00228305 | − | 0.999997i | \(-0.499273\pi\) | ||||
0.00228305 | + | 0.999997i | \(0.499273\pi\) | |||||||
\(458\) | −2.41547e51 | −0.313418 | ||||||||
\(459\) | −2.76200e51 | −0.343460 | ||||||||
\(460\) | 2.97158e51 | 0.354169 | ||||||||
\(461\) | −7.93487e50 | −0.0906508 | −0.0453254 | − | 0.998972i | \(-0.514432\pi\) | ||||
−0.0453254 | + | 0.998972i | \(0.514432\pi\) | |||||||
\(462\) | 1.03619e51 | 0.113480 | ||||||||
\(463\) | −7.37575e51 | −0.774420 | −0.387210 | − | 0.921992i | \(-0.626561\pi\) | ||||
−0.387210 | + | 0.921992i | \(0.626561\pi\) | |||||||
\(464\) | 3.32593e51 | 0.334821 | ||||||||
\(465\) | 1.88922e50 | 0.0182369 | ||||||||
\(466\) | 9.48376e51 | 0.877921 | ||||||||
\(467\) | −8.02286e51 | −0.712279 | −0.356139 | − | 0.934433i | \(-0.615907\pi\) | ||||
−0.356139 | + | 0.934433i | \(0.615907\pi\) | |||||||
\(468\) | 1.27773e51 | 0.108804 | ||||||||
\(469\) | 7.33356e51 | 0.599024 | ||||||||
\(470\) | −2.06513e51 | −0.161823 | ||||||||
\(471\) | 7.17119e51 | 0.539118 | ||||||||
\(472\) | −2.90846e51 | −0.209795 | ||||||||
\(473\) | −1.31932e52 | −0.913183 | ||||||||
\(474\) | 3.30558e51 | 0.219569 | ||||||||
\(475\) | 1.78902e52 | 1.14049 | ||||||||
\(476\) | −2.19038e51 | −0.134024 | ||||||||
\(477\) | −2.44242e51 | −0.143454 | ||||||||
\(478\) | −4.39094e51 | −0.247579 | ||||||||
\(479\) | 2.10871e52 | 1.14150 | 0.570748 | − | 0.821125i | \(-0.306653\pi\) | ||||
0.570748 | + | 0.821125i | \(0.306653\pi\) | |||||||
\(480\) | 4.72742e50 | 0.0245708 | ||||||||
\(481\) | 3.42381e51 | 0.170876 | ||||||||
\(482\) | 8.76438e50 | 0.0420053 | ||||||||
\(483\) | 7.86442e51 | 0.361991 | ||||||||
\(484\) | −3.60421e51 | −0.159340 | ||||||||
\(485\) | −1.23488e52 | −0.524399 | ||||||||
\(486\) | −1.57299e52 | −0.641679 | ||||||||
\(487\) | 2.17331e52 | 0.851738 | 0.425869 | − | 0.904785i | \(-0.359968\pi\) | ||||
0.425869 | + | 0.904785i | \(0.359968\pi\) | |||||||
\(488\) | −1.85092e52 | −0.696949 | ||||||||
\(489\) | −3.36129e51 | −0.121614 | ||||||||
\(490\) | 5.54617e51 | 0.192828 | ||||||||
\(491\) | −4.64580e52 | −1.55228 | −0.776142 | − | 0.630558i | \(-0.782826\pi\) | ||||
−0.776142 | + | 0.630558i | \(0.782826\pi\) | |||||||
\(492\) | −1.03582e52 | −0.332633 | ||||||||
\(493\) | −2.18542e52 | −0.674560 | ||||||||
\(494\) | 7.98080e51 | 0.236794 | ||||||||
\(495\) | −9.54027e51 | −0.272119 | ||||||||
\(496\) | 1.19616e51 | 0.0328016 | ||||||||
\(497\) | −1.59632e51 | −0.0420891 | ||||||||
\(498\) | −2.74769e51 | −0.0696618 | ||||||||
\(499\) | 7.18834e52 | 1.75254 | 0.876270 | − | 0.481820i | \(-0.160024\pi\) | ||||
0.876270 | + | 0.481820i | \(0.160024\pi\) | |||||||
\(500\) | 1.50519e52 | 0.352919 | ||||||||
\(501\) | −1.58992e52 | −0.358541 | ||||||||
\(502\) | −3.98745e51 | −0.0864913 | ||||||||
\(503\) | −1.23248e52 | −0.257161 | −0.128581 | − | 0.991699i | \(-0.541042\pi\) | ||||
−0.128581 | + | 0.991699i | \(0.541042\pi\) | |||||||
\(504\) | −8.12267e51 | −0.163043 | ||||||||
\(505\) | 1.16011e52 | 0.224037 | ||||||||
\(506\) | 5.84837e52 | 1.08667 | ||||||||
\(507\) | 1.91451e52 | 0.342297 | ||||||||
\(508\) | 2.23792e52 | 0.385037 | ||||||||
\(509\) | 2.18738e52 | 0.362182 | 0.181091 | − | 0.983466i | \(-0.442037\pi\) | ||||
0.181091 | + | 0.983466i | \(0.442037\pi\) | |||||||
\(510\) | −3.10632e51 | −0.0495026 | ||||||||
\(511\) | 1.30469e52 | 0.200124 | ||||||||
\(512\) | 2.99316e51 | 0.0441942 | ||||||||
\(513\) | −6.39752e52 | −0.909333 | ||||||||
\(514\) | 5.05750e52 | 0.692079 | ||||||||
\(515\) | −1.06323e52 | −0.140084 | ||||||||
\(516\) | −1.59300e52 | −0.202091 | ||||||||
\(517\) | −4.06438e52 | −0.496510 | ||||||||
\(518\) | −2.17656e52 | −0.256059 | ||||||||
\(519\) | 2.66169e52 | 0.301574 | ||||||||
\(520\) | 3.09537e51 | 0.0337791 | ||||||||
\(521\) | −7.50925e52 | −0.789334 | −0.394667 | − | 0.918824i | \(-0.629140\pi\) | ||||
−0.394667 | + | 0.918824i | \(0.629140\pi\) | |||||||
\(522\) | −8.10429e52 | −0.820617 | ||||||||
\(523\) | −1.56095e53 | −1.52267 | −0.761337 | − | 0.648356i | \(-0.775457\pi\) | ||||
−0.761337 | + | 0.648356i | \(0.775457\pi\) | |||||||
\(524\) | 7.01138e52 | 0.658936 | ||||||||
\(525\) | 1.83637e52 | 0.166286 | ||||||||
\(526\) | −1.24803e53 | −1.08894 | ||||||||
\(527\) | −7.85979e51 | −0.0660852 | ||||||||
\(528\) | 9.30401e51 | 0.0753892 | ||||||||
\(529\) | 3.15827e53 | 2.46640 | ||||||||
\(530\) | −5.91690e51 | −0.0445363 | ||||||||
\(531\) | 7.08706e52 | 0.514189 | ||||||||
\(532\) | −5.07348e52 | −0.354837 | ||||||||
\(533\) | −6.78224e52 | −0.457291 | ||||||||
\(534\) | 5.05008e52 | 0.328279 | ||||||||
\(535\) | 9.59708e52 | 0.601506 | ||||||||
\(536\) | 6.58488e52 | 0.397955 | ||||||||
\(537\) | −6.42063e52 | −0.374178 | ||||||||
\(538\) | −1.80213e53 | −1.01282 | ||||||||
\(539\) | 1.09154e53 | 0.591642 | ||||||||
\(540\) | −2.48129e52 | −0.129718 | ||||||||
\(541\) | 2.61710e52 | 0.131969 | 0.0659847 | − | 0.997821i | \(-0.478981\pi\) | ||||
0.0659847 | + | 0.997821i | \(0.478981\pi\) | |||||||
\(542\) | 1.22809e53 | 0.597370 | ||||||||
\(543\) | 1.11428e53 | 0.522875 | ||||||||
\(544\) | −1.96676e52 | −0.0890376 | ||||||||
\(545\) | 6.79072e52 | 0.296609 | ||||||||
\(546\) | 8.19203e51 | 0.0345251 | ||||||||
\(547\) | −4.07795e53 | −1.65840 | −0.829199 | − | 0.558953i | \(-0.811203\pi\) | ||||
−0.829199 | + | 0.558953i | \(0.811203\pi\) | |||||||
\(548\) | −4.33096e52 | −0.169967 | ||||||||
\(549\) | 4.51014e53 | 1.70816 | ||||||||
\(550\) | 1.36562e53 | 0.499179 | ||||||||
\(551\) | −5.06201e53 | −1.78594 | ||||||||
\(552\) | 7.06155e52 | 0.240485 | ||||||||
\(553\) | −1.37593e53 | −0.452331 | ||||||||
\(554\) | 2.60819e53 | 0.827750 | ||||||||
\(555\) | −3.08672e52 | −0.0945768 | ||||||||
\(556\) | −1.61856e53 | −0.478819 | ||||||||
\(557\) | −6.72948e52 | −0.192223 | −0.0961115 | − | 0.995371i | \(-0.530641\pi\) | ||||
−0.0961115 | + | 0.995371i | \(0.530641\pi\) | |||||||
\(558\) | −2.91468e52 | −0.0803940 | ||||||||
\(559\) | −1.04305e53 | −0.277827 | ||||||||
\(560\) | −1.96776e52 | −0.0506181 | ||||||||
\(561\) | −6.11355e52 | −0.151886 | ||||||||
\(562\) | −1.19717e53 | −0.287276 | ||||||||
\(563\) | −4.55904e53 | −1.05672 | −0.528360 | − | 0.849020i | \(-0.677193\pi\) | ||||
−0.528360 | + | 0.849020i | \(0.677193\pi\) | |||||||
\(564\) | −4.90749e52 | −0.109879 | ||||||||
\(565\) | −6.20601e52 | −0.134236 | ||||||||
\(566\) | 3.19759e53 | 0.668193 | ||||||||
\(567\) | 1.62743e53 | 0.328574 | ||||||||
\(568\) | −1.43335e52 | −0.0279614 | ||||||||
\(569\) | 5.98039e53 | 1.12730 | 0.563651 | − | 0.826013i | \(-0.309396\pi\) | ||||
0.563651 | + | 0.826013i | \(0.309396\pi\) | |||||||
\(570\) | −7.19505e52 | −0.131061 | ||||||||
\(571\) | 3.54056e52 | 0.0623258 | 0.0311629 | − | 0.999514i | \(-0.490079\pi\) | ||||
0.0311629 | + | 0.999514i | \(0.490079\pi\) | |||||||
\(572\) | 6.09199e52 | 0.103642 | ||||||||
\(573\) | −3.18153e53 | −0.523143 | ||||||||
\(574\) | 4.31155e53 | 0.685253 | ||||||||
\(575\) | 1.03647e54 | 1.59234 | ||||||||
\(576\) | −7.29342e52 | −0.108316 | ||||||||
\(577\) | 2.71624e53 | 0.389978 | 0.194989 | − | 0.980805i | \(-0.437533\pi\) | ||||
0.194989 | + | 0.980805i | \(0.437533\pi\) | |||||||
\(578\) | −3.80189e53 | −0.527723 | ||||||||
\(579\) | 5.18050e53 | 0.695247 | ||||||||
\(580\) | −1.96331e53 | −0.254767 | ||||||||
\(581\) | 1.14371e53 | 0.143510 | ||||||||
\(582\) | −2.93452e53 | −0.356073 | ||||||||
\(583\) | −1.16450e53 | −0.136648 | ||||||||
\(584\) | 1.17149e53 | 0.132950 | ||||||||
\(585\) | −7.54249e52 | −0.0827895 | ||||||||
\(586\) | −1.14576e54 | −1.21643 | ||||||||
\(587\) | −9.17025e53 | −0.941755 | −0.470878 | − | 0.882199i | \(-0.656063\pi\) | ||||
−0.470878 | + | 0.882199i | \(0.656063\pi\) | |||||||
\(588\) | 1.31797e53 | 0.130932 | ||||||||
\(589\) | −1.82053e53 | −0.174964 | ||||||||
\(590\) | 1.71688e53 | 0.159634 | ||||||||
\(591\) | 1.33151e53 | 0.119781 | ||||||||
\(592\) | −1.95435e53 | −0.170110 | ||||||||
\(593\) | −1.82661e54 | −1.53844 | −0.769219 | − | 0.638985i | \(-0.779355\pi\) | ||||
−0.769219 | + | 0.638985i | \(0.779355\pi\) | |||||||
\(594\) | −4.88342e53 | −0.398005 | ||||||||
\(595\) | 1.29299e53 | 0.101980 | ||||||||
\(596\) | 3.31906e53 | 0.253346 | ||||||||
\(597\) | 7.19616e53 | 0.531620 | ||||||||
\(598\) | 4.62369e53 | 0.330610 | ||||||||
\(599\) | 2.02996e54 | 1.40496 | 0.702482 | − | 0.711702i | \(-0.252075\pi\) | ||||
0.702482 | + | 0.711702i | \(0.252075\pi\) | |||||||
\(600\) | 1.64890e53 | 0.110470 | ||||||||
\(601\) | −1.35173e54 | −0.876673 | −0.438337 | − | 0.898811i | \(-0.644432\pi\) | ||||
−0.438337 | + | 0.898811i | \(0.644432\pi\) | |||||||
\(602\) | 6.63077e53 | 0.416325 | ||||||||
\(603\) | −1.60454e54 | −0.975354 | ||||||||
\(604\) | 1.56270e54 | 0.919721 | ||||||||
\(605\) | 2.12759e53 | 0.121243 | ||||||||
\(606\) | 2.75685e53 | 0.152123 | ||||||||
\(607\) | 2.31650e54 | 1.23781 | 0.618903 | − | 0.785468i | \(-0.287578\pi\) | ||||
0.618903 | + | 0.785468i | \(0.287578\pi\) | |||||||
\(608\) | −4.55553e53 | −0.235732 | ||||||||
\(609\) | −5.19599e53 | −0.260394 | ||||||||
\(610\) | 1.09261e54 | 0.530313 | ||||||||
\(611\) | −3.21327e53 | −0.151058 | ||||||||
\(612\) | 4.79241e53 | 0.218224 | ||||||||
\(613\) | −2.04561e53 | −0.0902284 | −0.0451142 | − | 0.998982i | \(-0.514365\pi\) | ||||
−0.0451142 | + | 0.998982i | \(0.514365\pi\) | |||||||
\(614\) | −9.68418e53 | −0.413790 | ||||||||
\(615\) | 6.11450e53 | 0.253102 | ||||||||
\(616\) | −3.87275e53 | −0.155309 | ||||||||
\(617\) | −5.94190e53 | −0.230869 | −0.115434 | − | 0.993315i | \(-0.536826\pi\) | ||||
−0.115434 | + | 0.993315i | \(0.536826\pi\) | |||||||
\(618\) | −2.52662e53 | −0.0951186 | ||||||||
\(619\) | 1.60053e54 | 0.583845 | 0.291922 | − | 0.956442i | \(-0.405705\pi\) | ||||
0.291922 | + | 0.956442i | \(0.405705\pi\) | |||||||
\(620\) | −7.06097e52 | −0.0249590 | ||||||||
\(621\) | −3.70641e54 | −1.26960 | ||||||||
\(622\) | 1.69174e54 | 0.561592 | ||||||||
\(623\) | −2.10207e54 | −0.676286 | ||||||||
\(624\) | 7.35571e52 | 0.0229364 | ||||||||
\(625\) | 1.94128e54 | 0.586717 | ||||||||
\(626\) | −3.66682e54 | −1.07421 | ||||||||
\(627\) | −1.41606e54 | −0.402127 | ||||||||
\(628\) | −2.68024e54 | −0.737836 | ||||||||
\(629\) | 1.28418e54 | 0.342719 | ||||||||
\(630\) | 4.79485e53 | 0.124061 | ||||||||
\(631\) | 3.92756e54 | 0.985260 | 0.492630 | − | 0.870239i | \(-0.336036\pi\) | ||||
0.492630 | + | 0.870239i | \(0.336036\pi\) | |||||||
\(632\) | −1.23546e54 | −0.300502 | ||||||||
\(633\) | −1.38151e53 | −0.0325823 | ||||||||
\(634\) | 2.82023e54 | 0.644977 | ||||||||
\(635\) | −1.32105e54 | −0.292977 | ||||||||
\(636\) | −1.40607e53 | −0.0302407 | ||||||||
\(637\) | 8.62966e53 | 0.180001 | ||||||||
\(638\) | −3.86399e54 | −0.781686 | ||||||||
\(639\) | 3.49264e53 | 0.0685311 | ||||||||
\(640\) | −1.76687e53 | −0.0336276 | ||||||||
\(641\) | 3.85006e54 | 0.710781 | 0.355390 | − | 0.934718i | \(-0.384348\pi\) | ||||
0.355390 | + | 0.934718i | \(0.384348\pi\) | |||||||
\(642\) | 2.28061e54 | 0.408430 | ||||||||
\(643\) | −3.53258e54 | −0.613732 | −0.306866 | − | 0.951753i | \(-0.599280\pi\) | ||||
−0.306866 | + | 0.951753i | \(0.599280\pi\) | |||||||
\(644\) | −2.93933e54 | −0.495421 | ||||||||
\(645\) | 9.40355e53 | 0.153772 | ||||||||
\(646\) | 2.99338e54 | 0.474928 | ||||||||
\(647\) | 6.40779e54 | 0.986449 | 0.493225 | − | 0.869902i | \(-0.335818\pi\) | ||||
0.493225 | + | 0.869902i | \(0.335818\pi\) | |||||||
\(648\) | 1.46129e54 | 0.218284 | ||||||||
\(649\) | 3.37899e54 | 0.489796 | ||||||||
\(650\) | 1.07965e54 | 0.151870 | ||||||||
\(651\) | −1.86872e53 | −0.0255102 | ||||||||
\(652\) | 1.25628e54 | 0.166441 | ||||||||
\(653\) | 1.99210e54 | 0.256156 | 0.128078 | − | 0.991764i | \(-0.459119\pi\) | ||||
0.128078 | + | 0.991764i | \(0.459119\pi\) | |||||||
\(654\) | 1.61372e54 | 0.201401 | ||||||||
\(655\) | −4.13885e54 | −0.501389 | ||||||||
\(656\) | 3.87138e54 | 0.455241 | ||||||||
\(657\) | −2.85458e54 | −0.325850 | ||||||||
\(658\) | 2.04272e54 | 0.226362 | ||||||||
\(659\) | −1.17248e55 | −1.26137 | −0.630684 | − | 0.776040i | \(-0.717225\pi\) | ||||
−0.630684 | + | 0.776040i | \(0.717225\pi\) | |||||||
\(660\) | −5.49221e53 | −0.0573641 | ||||||||
\(661\) | −1.31406e55 | −1.33256 | −0.666282 | − | 0.745700i | \(-0.732115\pi\) | ||||
−0.666282 | + | 0.745700i | \(0.732115\pi\) | |||||||
\(662\) | −7.34096e54 | −0.722807 | ||||||||
\(663\) | −4.83334e53 | −0.0462097 | ||||||||
\(664\) | 1.02695e54 | 0.0953392 | ||||||||
\(665\) | 2.99490e54 | 0.269998 | ||||||||
\(666\) | 4.76218e54 | 0.416925 | ||||||||
\(667\) | −2.93268e55 | −2.49351 | ||||||||
\(668\) | 5.94232e54 | 0.490699 | ||||||||
\(669\) | 5.27940e54 | 0.423424 | ||||||||
\(670\) | −3.88709e54 | −0.302807 | ||||||||
\(671\) | 2.15036e55 | 1.62713 | ||||||||
\(672\) | −4.67611e53 | −0.0343703 | ||||||||
\(673\) | 9.01981e54 | 0.644027 | 0.322013 | − | 0.946735i | \(-0.395640\pi\) | ||||
0.322013 | + | 0.946735i | \(0.395640\pi\) | |||||||
\(674\) | −1.75939e54 | −0.122038 | ||||||||
\(675\) | −8.65461e54 | −0.583209 | ||||||||
\(676\) | −7.15551e54 | −0.468468 | ||||||||
\(677\) | 2.47399e55 | 1.57369 | 0.786844 | − | 0.617153i | \(-0.211714\pi\) | ||||
0.786844 | + | 0.617153i | \(0.211714\pi\) | |||||||
\(678\) | −1.47477e54 | −0.0911476 | ||||||||
\(679\) | 1.22148e55 | 0.733543 | ||||||||
\(680\) | 1.16099e54 | 0.0677493 | ||||||||
\(681\) | 5.75264e54 | 0.326211 | ||||||||
\(682\) | −1.38967e54 | −0.0765801 | ||||||||
\(683\) | 3.20867e54 | 0.171839 | 0.0859195 | − | 0.996302i | \(-0.472617\pi\) | ||||
0.0859195 | + | 0.996302i | \(0.472617\pi\) | |||||||
\(684\) | 1.11005e55 | 0.577760 | ||||||||
\(685\) | 2.55659e54 | 0.129329 | ||||||||
\(686\) | −1.31397e55 | −0.646046 | ||||||||
\(687\) | 3.38836e54 | 0.161932 | ||||||||
\(688\) | 5.95384e54 | 0.276581 | ||||||||
\(689\) | −9.20650e53 | −0.0415738 | ||||||||
\(690\) | −4.16847e54 | −0.182986 | ||||||||
\(691\) | −2.16393e55 | −0.923468 | −0.461734 | − | 0.887019i | \(-0.652772\pi\) | ||||
−0.461734 | + | 0.887019i | \(0.652772\pi\) | |||||||
\(692\) | −9.94806e54 | −0.412733 | ||||||||
\(693\) | 9.43673e54 | 0.380648 | ||||||||
\(694\) | −1.36755e55 | −0.536331 | ||||||||
\(695\) | 9.55445e54 | 0.364336 | ||||||||
\(696\) | −4.66553e54 | −0.172990 | ||||||||
\(697\) | −2.54383e55 | −0.917170 | ||||||||
\(698\) | 1.06763e55 | 0.374319 | ||||||||
\(699\) | −1.33036e55 | −0.453590 | ||||||||
\(700\) | −6.86345e54 | −0.227578 | ||||||||
\(701\) | −1.92533e55 | −0.620876 | −0.310438 | − | 0.950594i | \(-0.600476\pi\) | ||||
−0.310438 | + | 0.950594i | \(0.600476\pi\) | |||||||
\(702\) | −3.86081e54 | −0.121089 | ||||||||
\(703\) | 2.97449e55 | 0.907370 | ||||||||
\(704\) | −3.47738e54 | −0.103178 | ||||||||
\(705\) | 2.89691e54 | 0.0836080 | ||||||||
\(706\) | 4.23792e55 | 1.18976 | ||||||||
\(707\) | −1.14752e55 | −0.313388 | ||||||||
\(708\) | 4.07992e54 | 0.108394 | ||||||||
\(709\) | −5.00428e55 | −1.29342 | −0.646711 | − | 0.762735i | \(-0.723856\pi\) | ||||
−0.646711 | + | 0.762735i | \(0.723856\pi\) | |||||||
\(710\) | 8.46113e53 | 0.0212760 | ||||||||
\(711\) | 3.01045e55 | 0.736503 | ||||||||
\(712\) | −1.88747e55 | −0.449283 | ||||||||
\(713\) | −1.05473e55 | −0.244284 | ||||||||
\(714\) | 3.07261e54 | 0.0692456 | ||||||||
\(715\) | −3.59613e54 | −0.0788620 | ||||||||
\(716\) | 2.39971e55 | 0.512100 | ||||||||
\(717\) | 6.15950e54 | 0.127915 | ||||||||
\(718\) | 3.85542e55 | 0.779192 | ||||||||
\(719\) | 2.94837e55 | 0.579921 | 0.289961 | − | 0.957039i | \(-0.406358\pi\) | ||||
0.289961 | + | 0.957039i | \(0.406358\pi\) | |||||||
\(720\) | 4.30534e54 | 0.0824184 | ||||||||
\(721\) | 1.05169e55 | 0.195953 | ||||||||
\(722\) | 3.03438e55 | 0.550294 | ||||||||
\(723\) | −1.22945e54 | −0.0217026 | ||||||||
\(724\) | −4.16463e55 | −0.715607 | ||||||||
\(725\) | −6.84793e55 | −1.14543 | ||||||||
\(726\) | 5.05590e54 | 0.0823256 | ||||||||
\(727\) | 9.06551e55 | 1.43705 | 0.718524 | − | 0.695502i | \(-0.244818\pi\) | ||||
0.718524 | + | 0.695502i | \(0.244818\pi\) | |||||||
\(728\) | −3.06177e54 | −0.0472510 | ||||||||
\(729\) | −1.90262e55 | −0.285868 | ||||||||
\(730\) | −6.91539e54 | −0.101163 | ||||||||
\(731\) | −3.91219e55 | −0.557226 | ||||||||
\(732\) | 2.59642e55 | 0.360089 | ||||||||
\(733\) | 1.21737e56 | 1.64397 | 0.821987 | − | 0.569507i | \(-0.192866\pi\) | ||||
0.821987 | + | 0.569507i | \(0.192866\pi\) | |||||||
\(734\) | −5.23993e55 | −0.689052 | ||||||||
\(735\) | −7.78003e54 | −0.0996273 | ||||||||
\(736\) | −2.63926e55 | −0.329128 | ||||||||
\(737\) | −7.65016e55 | −0.929083 | ||||||||
\(738\) | −9.43340e55 | −1.11576 | ||||||||
\(739\) | −7.42605e55 | −0.855444 | −0.427722 | − | 0.903910i | \(-0.640684\pi\) | ||||
−0.427722 | + | 0.903910i | \(0.640684\pi\) | |||||||
\(740\) | 1.15366e55 | 0.129438 | ||||||||
\(741\) | −1.11953e55 | −0.122343 | ||||||||
\(742\) | 5.85268e54 | 0.0622986 | ||||||||
\(743\) | 9.86558e55 | 1.02292 | 0.511459 | − | 0.859308i | \(-0.329105\pi\) | ||||
0.511459 | + | 0.859308i | \(0.329105\pi\) | |||||||
\(744\) | −1.67794e54 | −0.0169474 | ||||||||
\(745\) | −1.95926e55 | −0.192772 | ||||||||
\(746\) | −5.57676e55 | −0.534533 | ||||||||
\(747\) | −2.50237e55 | −0.233668 | ||||||||
\(748\) | 2.28494e55 | 0.207871 | ||||||||
\(749\) | −9.49291e55 | −0.841403 | ||||||||
\(750\) | −2.11144e55 | −0.182341 | ||||||||
\(751\) | 1.97249e56 | 1.65972 | 0.829861 | − | 0.557971i | \(-0.188420\pi\) | ||||
0.829861 | + | 0.557971i | \(0.188420\pi\) | |||||||
\(752\) | 1.83418e55 | 0.150381 | ||||||||
\(753\) | 5.59349e54 | 0.0446870 | ||||||||
\(754\) | −3.05485e55 | −0.237820 | ||||||||
\(755\) | −9.22471e55 | −0.699821 | ||||||||
\(756\) | 2.45436e55 | 0.181453 | ||||||||
\(757\) | 1.98251e56 | 1.42839 | 0.714193 | − | 0.699949i | \(-0.246794\pi\) | ||||
0.714193 | + | 0.699949i | \(0.246794\pi\) | |||||||
\(758\) | 1.62303e56 | 1.13966 | ||||||||
\(759\) | −8.20394e55 | −0.561446 | ||||||||
\(760\) | 2.68915e55 | 0.179370 | ||||||||
\(761\) | 1.83095e56 | 1.19035 | 0.595175 | − | 0.803596i | \(-0.297083\pi\) | ||||
0.595175 | + | 0.803596i | \(0.297083\pi\) | |||||||
\(762\) | −3.13930e55 | −0.198935 | ||||||||
\(763\) | −6.71702e55 | −0.414904 | ||||||||
\(764\) | 1.18910e56 | 0.715974 | ||||||||
\(765\) | −2.82899e55 | −0.166048 | ||||||||
\(766\) | 6.88713e55 | 0.394074 | ||||||||
\(767\) | 2.67141e55 | 0.149015 | ||||||||
\(768\) | −4.19872e54 | −0.0228336 | ||||||||
\(769\) | −2.06387e56 | −1.09425 | −0.547126 | − | 0.837050i | \(-0.684278\pi\) | ||||
−0.547126 | + | 0.837050i | \(0.684278\pi\) | |||||||
\(770\) | 2.28610e55 | 0.118175 | ||||||||
\(771\) | −7.09454e55 | −0.357572 | ||||||||
\(772\) | −1.93621e56 | −0.951515 | ||||||||
\(773\) | −1.30613e56 | −0.625871 | −0.312936 | − | 0.949774i | \(-0.601312\pi\) | ||||
−0.312936 | + | 0.949774i | \(0.601312\pi\) | |||||||
\(774\) | −1.45077e56 | −0.677877 | ||||||||
\(775\) | −2.46283e55 | −0.112215 | ||||||||
\(776\) | 1.09678e56 | 0.487321 | ||||||||
\(777\) | 3.05322e55 | 0.132297 | ||||||||
\(778\) | 6.66985e55 | 0.281847 | ||||||||
\(779\) | −5.89218e56 | −2.42826 | ||||||||
\(780\) | −4.34211e54 | −0.0174524 | ||||||||
\(781\) | 1.66523e55 | 0.0652799 | ||||||||
\(782\) | 1.73422e56 | 0.663090 | ||||||||
\(783\) | 2.44881e56 | 0.913273 | ||||||||
\(784\) | −4.92591e55 | −0.179194 | ||||||||
\(785\) | 1.58216e56 | 0.561424 | ||||||||
\(786\) | −9.83539e55 | −0.340449 | ||||||||
\(787\) | 1.04231e56 | 0.351956 | 0.175978 | − | 0.984394i | \(-0.443691\pi\) | ||||
0.175978 | + | 0.984394i | \(0.443691\pi\) | |||||||
\(788\) | −4.97651e55 | −0.163932 | ||||||||
\(789\) | 1.75071e56 | 0.562617 | ||||||||
\(790\) | 7.29300e55 | 0.228653 | ||||||||
\(791\) | 6.13865e55 | 0.187772 | ||||||||
\(792\) | 8.47333e55 | 0.252879 | ||||||||
\(793\) | 1.70006e56 | 0.495037 | ||||||||
\(794\) | −2.15191e56 | −0.611397 | ||||||||
\(795\) | 8.30008e54 | 0.0230103 | ||||||||
\(796\) | −2.68957e56 | −0.727575 | ||||||||
\(797\) | 1.94067e56 | 0.512289 | 0.256145 | − | 0.966638i | \(-0.417548\pi\) | ||||
0.256145 | + | 0.966638i | \(0.417548\pi\) | |||||||
\(798\) | 7.11696e55 | 0.183332 | ||||||||
\(799\) | −1.20521e56 | −0.302971 | ||||||||
\(800\) | −6.16276e55 | −0.151189 | ||||||||
\(801\) | 4.59920e56 | 1.10115 | ||||||||
\(802\) | 3.97823e55 | 0.0929587 | ||||||||
\(803\) | −1.36102e56 | −0.310392 | ||||||||
\(804\) | −9.23711e55 | −0.205609 | ||||||||
\(805\) | 1.73510e56 | 0.376969 | ||||||||
\(806\) | −1.09866e55 | −0.0232987 | ||||||||
\(807\) | 2.52799e56 | 0.523289 | ||||||||
\(808\) | −1.03037e56 | −0.208196 | ||||||||
\(809\) | 2.23938e56 | 0.441705 | 0.220852 | − | 0.975307i | \(-0.429116\pi\) | ||||
0.220852 | + | 0.975307i | \(0.429116\pi\) | |||||||
\(810\) | −8.62604e55 | −0.166094 | ||||||||
\(811\) | −5.47814e56 | −1.02974 | −0.514869 | − | 0.857269i | \(-0.672159\pi\) | ||||
−0.514869 | + | 0.857269i | \(0.672159\pi\) | |||||||
\(812\) | 1.94200e56 | 0.356375 | ||||||||
\(813\) | −1.72273e56 | −0.308640 | ||||||||
\(814\) | 2.27052e56 | 0.397146 | ||||||||
\(815\) | −7.41591e55 | −0.126646 | ||||||||
\(816\) | 2.75893e55 | 0.0460026 | ||||||||
\(817\) | −9.06165e56 | −1.47529 | ||||||||
\(818\) | 1.10146e56 | 0.175098 | ||||||||
\(819\) | 7.46063e55 | 0.115808 | ||||||||
\(820\) | −2.28530e56 | −0.346396 | ||||||||
\(821\) | −4.98980e56 | −0.738569 | −0.369285 | − | 0.929316i | \(-0.620397\pi\) | ||||
−0.369285 | + | 0.929316i | \(0.620397\pi\) | |||||||
\(822\) | 6.07537e55 | 0.0878157 | ||||||||
\(823\) | 4.03098e56 | 0.569003 | 0.284501 | − | 0.958676i | \(-0.408172\pi\) | ||||
0.284501 | + | 0.958676i | \(0.408172\pi\) | |||||||
\(824\) | 9.44327e55 | 0.130179 | ||||||||
\(825\) | −1.91565e56 | −0.257908 | ||||||||
\(826\) | −1.69825e56 | −0.223301 | ||||||||
\(827\) | 5.98393e54 | 0.00768474 | 0.00384237 | − | 0.999993i | \(-0.498777\pi\) | ||||
0.00384237 | + | 0.999993i | \(0.498777\pi\) | |||||||
\(828\) | 6.43108e56 | 0.806663 | ||||||||
\(829\) | −6.22265e56 | −0.762363 | −0.381182 | − | 0.924500i | \(-0.624483\pi\) | ||||
−0.381182 | + | 0.924500i | \(0.624483\pi\) | |||||||
\(830\) | −6.06213e55 | −0.0725442 | ||||||||
\(831\) | −3.65871e56 | −0.427669 | ||||||||
\(832\) | −2.74920e55 | −0.0313907 | ||||||||
\(833\) | 3.23675e56 | 0.361021 | ||||||||
\(834\) | 2.27048e56 | 0.247389 | ||||||||
\(835\) | −3.50778e56 | −0.373376 | ||||||||
\(836\) | 5.29251e56 | 0.550351 | ||||||||
\(837\) | 8.80705e55 | 0.0894713 | ||||||||
\(838\) | 9.32045e55 | 0.0925078 | ||||||||
\(839\) | 1.71925e57 | 1.66717 | 0.833586 | − | 0.552389i | \(-0.186284\pi\) | ||||
0.833586 | + | 0.552389i | \(0.186284\pi\) | |||||||
\(840\) | 2.76033e55 | 0.0261526 | ||||||||
\(841\) | 8.57367e56 | 0.793679 | ||||||||
\(842\) | −4.01423e56 | −0.363092 | ||||||||
\(843\) | 1.67937e56 | 0.148425 | ||||||||
\(844\) | 5.16341e55 | 0.0445922 | ||||||||
\(845\) | 4.22393e56 | 0.356460 | ||||||||
\(846\) | −4.46934e56 | −0.368571 | ||||||||
\(847\) | −2.10449e56 | −0.169598 | ||||||||
\(848\) | 5.25518e55 | 0.0413874 | ||||||||
\(849\) | −4.48550e56 | −0.345232 | ||||||||
\(850\) | 4.04947e56 | 0.304600 | ||||||||
\(851\) | 1.72328e57 | 1.26686 | ||||||||
\(852\) | 2.01067e55 | 0.0144467 | ||||||||
\(853\) | −1.47498e57 | −1.03581 | −0.517906 | − | 0.855438i | \(-0.673288\pi\) | ||||
−0.517906 | + | 0.855438i | \(0.673288\pi\) | |||||||
\(854\) | −1.08075e57 | −0.741816 | ||||||||
\(855\) | −6.55266e56 | −0.439621 | ||||||||
\(856\) | −8.52378e56 | −0.558977 | ||||||||
\(857\) | −2.25922e57 | −1.44822 | −0.724108 | − | 0.689687i | \(-0.757748\pi\) | ||||
−0.724108 | + | 0.689687i | \(0.757748\pi\) | |||||||
\(858\) | −8.54569e55 | −0.0535482 | ||||||||
\(859\) | 1.62602e57 | 0.996002 | 0.498001 | − | 0.867177i | \(-0.334068\pi\) | ||||
0.498001 | + | 0.867177i | \(0.334068\pi\) | |||||||
\(860\) | −3.51458e56 | −0.210452 | ||||||||
\(861\) | −6.04813e56 | −0.354046 | ||||||||
\(862\) | −4.75011e56 | −0.271839 | ||||||||
\(863\) | −4.93931e56 | −0.276347 | −0.138174 | − | 0.990408i | \(-0.544123\pi\) | ||||
−0.138174 | + | 0.990408i | \(0.544123\pi\) | |||||||
\(864\) | 2.20380e56 | 0.120546 | ||||||||
\(865\) | 5.87239e56 | 0.314051 | ||||||||
\(866\) | −1.55167e57 | −0.811336 | ||||||||
\(867\) | 5.33319e56 | 0.272656 | ||||||||
\(868\) | 6.98434e55 | 0.0349133 | ||||||||
\(869\) | 1.43533e57 | 0.701563 | ||||||||
\(870\) | 2.75409e56 | 0.131629 | ||||||||
\(871\) | −6.04818e56 | −0.282664 | ||||||||
\(872\) | −6.03128e56 | −0.275637 | ||||||||
\(873\) | −2.67252e57 | −1.19438 | ||||||||
\(874\) | 4.01690e57 | 1.75557 | ||||||||
\(875\) | 8.78875e56 | 0.375638 | ||||||||
\(876\) | −1.64334e56 | −0.0686908 | ||||||||
\(877\) | 3.26253e57 | 1.33371 | 0.666857 | − | 0.745186i | \(-0.267639\pi\) | ||||
0.666857 | + | 0.745186i | \(0.267639\pi\) | |||||||
\(878\) | −1.01337e57 | −0.405160 | ||||||||
\(879\) | 1.60724e57 | 0.628488 | ||||||||
\(880\) | 2.05271e56 | 0.0785085 | ||||||||
\(881\) | 1.49144e57 | 0.557925 | 0.278963 | − | 0.960302i | \(-0.410009\pi\) | ||||
0.278963 | + | 0.960302i | \(0.410009\pi\) | |||||||
\(882\) | 1.20030e57 | 0.439189 | ||||||||
\(883\) | −1.82576e57 | −0.653446 | −0.326723 | − | 0.945120i | \(-0.605944\pi\) | ||||
−0.326723 | + | 0.945120i | \(0.605944\pi\) | |||||||
\(884\) | 1.80646e56 | 0.0632426 | ||||||||
\(885\) | −2.40840e56 | −0.0824773 | ||||||||
\(886\) | 2.74451e57 | 0.919405 | ||||||||
\(887\) | −3.77183e57 | −1.23607 | −0.618034 | − | 0.786152i | \(-0.712070\pi\) | ||||
−0.618034 | + | 0.786152i | \(0.712070\pi\) | |||||||
\(888\) | 2.74152e56 | 0.0878898 | ||||||||
\(889\) | 1.30672e57 | 0.409824 | ||||||||
\(890\) | 1.11418e57 | 0.341862 | ||||||||
\(891\) | −1.69769e57 | −0.509616 | ||||||||
\(892\) | −1.97318e57 | −0.579498 | ||||||||
\(893\) | −2.79158e57 | −0.802135 | ||||||||
\(894\) | −4.65590e56 | −0.130895 | ||||||||
\(895\) | −1.41656e57 | −0.389660 | ||||||||
\(896\) | 1.74770e56 | 0.0470392 | ||||||||
\(897\) | −6.48600e56 | −0.170814 | ||||||||
\(898\) | 1.38673e57 | 0.357358 | ||||||||
\(899\) | 6.96854e56 | 0.175723 | ||||||||
\(900\) | 1.50168e57 | 0.370552 | ||||||||
\(901\) | −3.45311e56 | −0.0833829 | ||||||||
\(902\) | −4.49768e57 | −1.06282 | ||||||||
\(903\) | −9.30149e56 | −0.215100 | ||||||||
\(904\) | 5.51196e56 | 0.124745 | ||||||||
\(905\) | 2.45840e57 | 0.544510 | ||||||||
\(906\) | −2.19212e57 | −0.475187 | ||||||||
\(907\) | 3.05905e57 | 0.649000 | 0.324500 | − | 0.945886i | \(-0.394804\pi\) | ||||
0.324500 | + | 0.945886i | \(0.394804\pi\) | |||||||
\(908\) | −2.15005e57 | −0.446452 | ||||||||
\(909\) | 2.51071e57 | 0.510271 | ||||||||
\(910\) | 1.80738e56 | 0.0359536 | ||||||||
\(911\) | −3.49012e57 | −0.679566 | −0.339783 | − | 0.940504i | \(-0.610354\pi\) | ||||
−0.339783 | + | 0.940504i | \(0.610354\pi\) | |||||||
\(912\) | 6.39039e56 | 0.121795 | ||||||||
\(913\) | −1.19309e57 | −0.222583 | ||||||||
\(914\) | 1.76800e55 | 0.00322872 | ||||||||
\(915\) | −1.53268e57 | −0.273994 | ||||||||
\(916\) | −1.26640e57 | −0.221620 | ||||||||
\(917\) | 4.09393e57 | 0.701356 | ||||||||
\(918\) | −1.44809e57 | −0.242863 | ||||||||
\(919\) | 1.50067e57 | 0.246395 | 0.123198 | − | 0.992382i | \(-0.460685\pi\) | ||||
0.123198 | + | 0.992382i | \(0.460685\pi\) | |||||||
\(920\) | 1.55797e57 | 0.250435 | ||||||||
\(921\) | 1.35847e57 | 0.213790 | ||||||||
\(922\) | −4.16015e56 | −0.0640998 | ||||||||
\(923\) | 1.31652e56 | 0.0198608 | ||||||||
\(924\) | 5.43259e56 | 0.0802424 | ||||||||
\(925\) | 4.02392e57 | 0.581950 | ||||||||
\(926\) | −3.86702e57 | −0.547598 | ||||||||
\(927\) | −2.30104e57 | −0.319058 | ||||||||
\(928\) | 1.74374e57 | 0.236754 | ||||||||
\(929\) | 1.07229e58 | 1.42563 | 0.712817 | − | 0.701351i | \(-0.247419\pi\) | ||||
0.712817 | + | 0.701351i | \(0.247419\pi\) | |||||||
\(930\) | 9.90496e55 | 0.0128954 | ||||||||
\(931\) | 7.49716e57 | 0.955824 | ||||||||
\(932\) | 4.97222e57 | 0.620784 | ||||||||
\(933\) | −2.37313e57 | −0.290155 | ||||||||
\(934\) | −4.20629e57 | −0.503657 | ||||||||
\(935\) | −1.34881e57 | −0.158170 | ||||||||
\(936\) | 6.69898e56 | 0.0769360 | ||||||||
\(937\) | −2.19037e57 | −0.246374 | −0.123187 | − | 0.992383i | \(-0.539311\pi\) | ||||
−0.123187 | + | 0.992383i | \(0.539311\pi\) | |||||||
\(938\) | 3.84490e57 | 0.423574 | ||||||||
\(939\) | 5.14372e57 | 0.555007 | ||||||||
\(940\) | −1.08272e57 | −0.114426 | ||||||||
\(941\) | −1.08101e58 | −1.11901 | −0.559505 | − | 0.828827i | \(-0.689009\pi\) | ||||
−0.559505 | + | 0.828827i | \(0.689009\pi\) | |||||||
\(942\) | 3.75977e57 | 0.381214 | ||||||||
\(943\) | −3.41364e58 | −3.39032 | ||||||||
\(944\) | −1.52487e57 | −0.148347 | ||||||||
\(945\) | −1.44882e57 | −0.138068 | ||||||||
\(946\) | −6.91703e57 | −0.645718 | ||||||||
\(947\) | 1.01364e58 | 0.926956 | 0.463478 | − | 0.886108i | \(-0.346601\pi\) | ||||
0.463478 | + | 0.886108i | \(0.346601\pi\) | |||||||
\(948\) | 1.73308e57 | 0.155258 | ||||||||
\(949\) | −1.07601e57 | −0.0944335 | ||||||||
\(950\) | 9.37963e57 | 0.806446 | ||||||||
\(951\) | −3.95615e57 | −0.333237 | ||||||||
\(952\) | −1.14839e57 | −0.0947695 | ||||||||
\(953\) | −3.31702e55 | −0.00268186 | −0.00134093 | − | 0.999999i | \(-0.500427\pi\) | ||||
−0.00134093 | + | 0.999999i | \(0.500427\pi\) | |||||||
\(954\) | −1.28053e57 | −0.101437 | ||||||||
\(955\) | −7.01930e57 | −0.544789 | ||||||||
\(956\) | −2.30212e57 | −0.175065 | ||||||||
\(957\) | 5.42031e57 | 0.403870 | ||||||||
\(958\) | 1.10557e58 | 0.807160 | ||||||||
\(959\) | −2.52884e57 | −0.180908 | ||||||||
\(960\) | 2.47853e56 | 0.0173742 | ||||||||
\(961\) | −1.43075e58 | −0.982785 | ||||||||
\(962\) | 1.79506e57 | 0.120828 | ||||||||
\(963\) | 2.07699e58 | 1.37000 | ||||||||
\(964\) | 4.59506e56 | 0.0297022 | ||||||||
\(965\) | 1.14296e58 | 0.724014 | ||||||||
\(966\) | 4.12322e57 | 0.255966 | ||||||||
\(967\) | 2.19730e58 | 1.33682 | 0.668411 | − | 0.743793i | \(-0.266975\pi\) | ||||
0.668411 | + | 0.743793i | \(0.266975\pi\) | |||||||
\(968\) | −1.88965e57 | −0.112671 | ||||||||
\(969\) | −4.19904e57 | −0.245378 | ||||||||
\(970\) | −6.47434e57 | −0.370806 | ||||||||
\(971\) | 1.76835e58 | 0.992646 | 0.496323 | − | 0.868138i | \(-0.334683\pi\) | ||||
0.496323 | + | 0.868138i | \(0.334683\pi\) | |||||||
\(972\) | −8.24698e57 | −0.453736 | ||||||||
\(973\) | −9.45075e57 | −0.509643 | ||||||||
\(974\) | 1.13944e58 | 0.602270 | ||||||||
\(975\) | −1.51450e57 | −0.0784658 | ||||||||
\(976\) | −9.70415e57 | −0.492817 | ||||||||
\(977\) | −5.66963e57 | −0.282235 | −0.141118 | − | 0.989993i | \(-0.545070\pi\) | ||||
−0.141118 | + | 0.989993i | \(0.545070\pi\) | |||||||
\(978\) | −1.76229e57 | −0.0859941 | ||||||||
\(979\) | 2.19282e58 | 1.04892 | ||||||||
\(980\) | 2.90779e57 | 0.136350 | ||||||||
\(981\) | 1.46964e58 | 0.675563 | ||||||||
\(982\) | −2.43574e58 | −1.09763 | ||||||||
\(983\) | −3.22545e58 | −1.42494 | −0.712469 | − | 0.701703i | \(-0.752423\pi\) | ||||
−0.712469 | + | 0.701703i | \(0.752423\pi\) | |||||||
\(984\) | −5.43068e57 | −0.235207 | ||||||||
\(985\) | 2.93766e57 | 0.124737 | ||||||||
\(986\) | −1.14579e58 | −0.476986 | ||||||||
\(987\) | −2.86547e57 | −0.116953 | ||||||||
\(988\) | 4.18424e57 | 0.167439 | ||||||||
\(989\) | −5.24988e58 | −2.05978 | ||||||||
\(990\) | −5.00185e57 | −0.192417 | ||||||||
\(991\) | 2.73974e58 | 1.03341 | 0.516706 | − | 0.856163i | \(-0.327158\pi\) | ||||
0.516706 | + | 0.856163i | \(0.327158\pi\) | |||||||
\(992\) | 6.27131e56 | 0.0231943 | ||||||||
\(993\) | 1.02977e58 | 0.373449 | ||||||||
\(994\) | −8.36930e56 | −0.0297615 | ||||||||
\(995\) | 1.58767e58 | 0.553617 | ||||||||
\(996\) | −1.44058e57 | −0.0492584 | ||||||||
\(997\) | −2.71260e58 | −0.909559 | −0.454779 | − | 0.890604i | \(-0.650282\pi\) | ||||
−0.454779 | + | 0.890604i | \(0.650282\pi\) | |||||||
\(998\) | 3.76876e58 | 1.23923 | ||||||||
\(999\) | −1.43895e58 | −0.464000 |
(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 | 2.40.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.40.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 16.40.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.40.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
16.40.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
18.40.a.a.1.1 | 1 | 3.2 | odd | 2 |