Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,21,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.1405506041\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3 x^{7} + 41744 x^{6} - 12461904 x^{5} + 2339673984 x^{4} - 888904297728 x^{3} + 163438296621056 x^{2} + \cdots + 18\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{56}\cdot 3^{5}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.5 | ||
Root | \(77.2239 - 239.948i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.21.b.b.3.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 356.896 | − | 959.792i | 0.348531 | − | 0.937297i | ||||
\(3\) | − | 46975.6i | − | 0.795536i | −0.917486 | − | 0.397768i | \(-0.869785\pi\) | ||
0.917486 | − | 0.397768i | \(-0.130215\pi\) | |||||||
\(4\) | −793827. | − | 685091.i | −0.757052 | − | 0.653354i | ||||
\(5\) | −4.32154e6 | −0.442526 | −0.221263 | − | 0.975214i | \(-0.571018\pi\) | ||||
−0.221263 | + | 0.975214i | \(0.571018\pi\) | |||||||
\(6\) | −4.50868e7 | − | 1.67654e7i | −0.745654 | − | 0.277269i | ||||
\(7\) | − | 1.10972e8i | − | 0.392854i | −0.980518 | − | 0.196427i | \(-0.937066\pi\) | ||
0.980518 | − | 0.196427i | \(-0.0629339\pi\) | |||||||
\(8\) | −9.40859e8 | + | 5.17403e8i | −0.876243 | + | 0.481869i | ||||
\(9\) | 1.28008e9 | 0.367122 | ||||||||
\(10\) | −1.54234e9 | + | 4.14778e9i | −0.154234 | + | 0.414778i | ||||
\(11\) | 2.26825e10i | 0.874510i | 0.899337 | + | 0.437255i | \(0.144049\pi\) | ||||
−0.899337 | + | 0.437255i | \(0.855951\pi\) | |||||||
\(12\) | −3.21826e10 | + | 3.72905e10i | −0.519767 | + | 0.602263i | ||||
\(13\) | −2.51114e11 | −1.82154 | −0.910769 | − | 0.412916i | \(-0.864510\pi\) | ||||
−0.910769 | + | 0.412916i | \(0.864510\pi\) | |||||||
\(14\) | −1.06510e11 | − | 3.96053e10i | −0.368221 | − | 0.136922i | ||||
\(15\) | 2.03007e11i | 0.352045i | ||||||||
\(16\) | 1.60811e11 | + | 1.08769e12i | 0.146257 | + | 0.989247i | ||||
\(17\) | 1.40803e12 | 0.698430 | 0.349215 | − | 0.937043i | \(-0.386448\pi\) | ||||
0.349215 | + | 0.937043i | \(0.386448\pi\) | |||||||
\(18\) | 4.56853e11 | − | 1.22861e12i | 0.127953 | − | 0.344102i | ||||
\(19\) | − | 1.01893e13i | − | 1.66191i | −0.556339 | − | 0.830956i | \(-0.687794\pi\) | ||
0.556339 | − | 0.830956i | \(-0.312206\pi\) | |||||||
\(20\) | 3.43056e12 | + | 2.96065e12i | 0.335015 | + | 0.289126i | ||||
\(21\) | −5.21296e12 | −0.312530 | ||||||||
\(22\) | 2.17705e13 | + | 8.09530e12i | 0.819676 | + | 0.304794i | ||||
\(23\) | − | 4.06234e13i | − | 0.980613i | −0.871550 | − | 0.490307i | \(-0.836885\pi\) | ||
0.871550 | − | 0.490307i | \(-0.163115\pi\) | |||||||
\(24\) | 2.43053e13 | + | 4.41974e13i | 0.383344 | + | 0.697083i | ||||
\(25\) | −7.66917e13 | −0.804171 | ||||||||
\(26\) | −8.96217e13 | + | 2.41018e14i | −0.634862 | + | 1.70732i | ||||
\(27\) | − | 2.23926e14i | − | 1.08760i | ||||||
\(28\) | −7.60257e13 | + | 8.80923e13i | −0.256673 | + | 0.297411i | ||||
\(29\) | −2.78623e14 | −0.662273 | −0.331137 | − | 0.943583i | \(-0.607432\pi\) | ||||
−0.331137 | + | 0.943583i | \(0.607432\pi\) | |||||||
\(30\) | 1.94845e14 | + | 7.24523e13i | 0.329971 | + | 0.122699i | ||||
\(31\) | − | 5.16079e14i | − | 0.629650i | −0.949150 | − | 0.314825i | \(-0.898054\pi\) | ||
0.949150 | − | 0.314825i | \(-0.101946\pi\) | |||||||
\(32\) | 1.10135e15 | + | 2.33846e14i | 0.978193 | + | 0.207697i | ||||
\(33\) | 1.06553e15 | 0.695705 | ||||||||
\(34\) | 5.02520e14 | − | 1.35142e15i | 0.243424 | − | 0.654637i | ||||
\(35\) | 4.79568e14i | 0.173848i | ||||||||
\(36\) | −1.01616e15 | − | 8.76969e14i | −0.277931 | − | 0.239861i | ||||
\(37\) | 8.25764e14 | 0.171727 | 0.0858636 | − | 0.996307i | \(-0.472635\pi\) | ||||
0.0858636 | + | 0.996307i | \(0.472635\pi\) | |||||||
\(38\) | −9.77960e15 | − | 3.63651e15i | −1.55770 | − | 0.579227i | ||||
\(39\) | 1.17963e16i | 1.44910i | ||||||||
\(40\) | 4.06596e15 | − | 2.23598e15i | 0.387760 | − | 0.213240i | ||||
\(41\) | −2.23881e14 | −0.0166793 | −0.00833967 | − | 0.999965i | \(-0.502655\pi\) | ||||
−0.00833967 | + | 0.999965i | \(0.502655\pi\) | |||||||
\(42\) | −1.86048e15 | + | 5.00336e15i | −0.108926 | + | 0.292933i | ||||
\(43\) | 2.43150e16i | 1.12509i | 0.826765 | + | 0.562547i | \(0.190179\pi\) | ||||
−0.826765 | + | 0.562547i | \(0.809821\pi\) | |||||||
\(44\) | 1.55396e16 | − | 1.80060e16i | 0.571365 | − | 0.662050i | ||||
\(45\) | −5.53190e15 | −0.162461 | ||||||||
\(46\) | −3.89900e16 | − | 1.44983e16i | −0.919126 | − | 0.341774i | ||||
\(47\) | − | 7.49929e16i | − | 1.42574i | −0.701295 | − | 0.712872i | \(-0.747394\pi\) | ||
0.701295 | − | 0.712872i | \(-0.252606\pi\) | |||||||
\(48\) | 5.10948e16 | − | 7.55420e15i | 0.786982 | − | 0.116353i | ||||
\(49\) | 6.74776e16 | 0.845666 | ||||||||
\(50\) | −2.73709e16 | + | 7.36081e16i | −0.280278 | + | 0.753747i | ||||
\(51\) | − | 6.61431e16i | − | 0.555626i | ||||||
\(52\) | 1.99341e17 | + | 1.72036e17i | 1.37900 | + | 1.19011i | ||||
\(53\) | −1.39239e17 | −0.796162 | −0.398081 | − | 0.917350i | \(-0.630324\pi\) | ||||
−0.398081 | + | 0.917350i | \(0.630324\pi\) | |||||||
\(54\) | −2.14923e17 | − | 7.99183e16i | −1.01940 | − | 0.379061i | ||||
\(55\) | − | 9.80236e16i | − | 0.386993i | ||||||
\(56\) | 5.74171e16 | + | 1.04409e17i | 0.189304 | + | 0.344236i | ||||
\(57\) | −4.78648e17 | −1.32211 | ||||||||
\(58\) | −9.94394e16 | + | 2.67420e17i | −0.230823 | + | 0.620747i | ||||
\(59\) | 1.92225e17i | 0.376089i | 0.982160 | + | 0.188045i | \(0.0602150\pi\) | ||||
−0.982160 | + | 0.188045i | \(0.939785\pi\) | |||||||
\(60\) | 1.39078e17 | − | 1.61153e17i | 0.230010 | − | 0.266517i | ||||
\(61\) | 9.81172e17 | 1.37546 | 0.687728 | − | 0.725969i | \(-0.258608\pi\) | ||||
0.687728 | + | 0.725969i | \(0.258608\pi\) | |||||||
\(62\) | −4.95329e17 | − | 1.84186e17i | −0.590169 | − | 0.219452i | ||||
\(63\) | − | 1.42052e17i | − | 0.144225i | ||||||
\(64\) | 6.17510e17 | − | 9.73607e17i | 0.535604 | − | 0.844469i | ||||
\(65\) | 1.08520e18 | 0.806078 | ||||||||
\(66\) | 3.80282e17 | − | 1.02268e18i | 0.242475 | − | 0.652082i | ||||
\(67\) | 2.38323e18i | 1.30743i | 0.756740 | + | 0.653716i | \(0.226791\pi\) | ||||
−0.756740 | + | 0.653716i | \(0.773209\pi\) | |||||||
\(68\) | −1.11773e18 | − | 9.64630e17i | −0.528748 | − | 0.456322i | ||||
\(69\) | −1.90831e18 | −0.780113 | ||||||||
\(70\) | 4.60286e17 | + | 1.71156e17i | 0.162947 | + | 0.0605915i | ||||
\(71\) | − | 6.63259e17i | − | 0.203751i | −0.994797 | − | 0.101875i | \(-0.967516\pi\) | ||
0.994797 | − | 0.101875i | \(-0.0324843\pi\) | |||||||
\(72\) | −1.20437e18 | + | 6.62315e17i | −0.321688 | + | 0.176905i | ||||
\(73\) | −6.58097e17 | −0.153130 | −0.0765652 | − | 0.997065i | \(-0.524395\pi\) | ||||
−0.0765652 | + | 0.997065i | \(0.524395\pi\) | |||||||
\(74\) | 2.94712e17 | − | 7.92562e17i | 0.0598522 | − | 0.160959i | ||||
\(75\) | 3.60264e18i | 0.639747i | ||||||||
\(76\) | −6.98059e18 | + | 8.08853e18i | −1.08582 | + | 1.25815i | ||||
\(77\) | 2.51712e18 | 0.343555 | ||||||||
\(78\) | 1.13220e19 | + | 4.21003e18i | 1.35824 | + | 0.505056i | ||||
\(79\) | − | 1.44666e19i | − | 1.52790i | −0.645274 | − | 0.763951i | \(-0.723257\pi\) | ||
0.645274 | − | 0.763951i | \(-0.276743\pi\) | |||||||
\(80\) | −6.94952e17 | − | 4.70049e18i | −0.0647224 | − | 0.437767i | ||||
\(81\) | −6.05573e18 | −0.498099 | ||||||||
\(82\) | −7.99022e16 | + | 2.14880e17i | −0.00581327 | + | 0.0156335i | ||||
\(83\) | − | 1.67166e19i | − | 1.07737i | −0.842506 | − | 0.538687i | \(-0.818921\pi\) | ||
0.842506 | − | 0.538687i | \(-0.181079\pi\) | |||||||
\(84\) | 4.13819e18 | + | 3.57135e18i | 0.236601 | + | 0.204193i | ||||
\(85\) | −6.08486e18 | −0.309073 | ||||||||
\(86\) | 2.33373e19 | + | 8.67790e18i | 1.05455 | + | 0.392130i | ||||
\(87\) | 1.30885e19i | 0.526862i | ||||||||
\(88\) | −1.17360e19 | − | 2.13411e19i | −0.421400 | − | 0.766284i | ||||
\(89\) | 3.01212e19 | 0.965989 | 0.482994 | − | 0.875623i | \(-0.339549\pi\) | ||||
0.482994 | + | 0.875623i | \(0.339549\pi\) | |||||||
\(90\) | −1.97431e18 | + | 5.30947e18i | −0.0566227 | + | 0.152274i | ||||
\(91\) | 2.78666e19i | 0.715599i | ||||||||
\(92\) | −2.78307e19 | + | 3.22479e19i | −0.640688 | + | 0.742376i | ||||
\(93\) | −2.42431e19 | −0.500909 | ||||||||
\(94\) | −7.19776e19 | − | 2.67646e19i | −1.33635 | − | 0.496916i | ||||
\(95\) | 4.40334e19i | 0.735439i | ||||||||
\(96\) | 1.09851e19 | − | 5.17365e19i | 0.165230 | − | 0.778188i | ||||
\(97\) | −3.28404e19 | −0.445339 | −0.222669 | − | 0.974894i | \(-0.571477\pi\) | ||||
−0.222669 | + | 0.974894i | \(0.571477\pi\) | |||||||
\(98\) | 2.40824e19 | − | 6.47645e19i | 0.294741 | − | 0.792640i | ||||
\(99\) | 2.90354e19i | 0.321052i | ||||||||
\(100\) | 6.08800e19 | + | 5.25408e19i | 0.608800 | + | 0.525408i | ||||
\(101\) | 1.20372e20 | 1.08971 | 0.544857 | − | 0.838529i | \(-0.316584\pi\) | ||||
0.544857 | + | 0.838529i | \(0.316584\pi\) | |||||||
\(102\) | −6.34837e19 | − | 2.36062e19i | −0.520787 | − | 0.193653i | ||||
\(103\) | 5.38576e19i | 0.400751i | 0.979719 | + | 0.200375i | \(0.0642162\pi\) | ||||
−0.979719 | + | 0.200375i | \(0.935784\pi\) | |||||||
\(104\) | 2.36263e20 | − | 1.29927e20i | 1.59611 | − | 0.877743i | ||||
\(105\) | 2.25280e19 | 0.138303 | ||||||||
\(106\) | −4.96937e19 | + | 1.33640e20i | −0.277487 | + | 0.746240i | ||||
\(107\) | − | 3.68120e20i | − | 1.87134i | −0.352883 | − | 0.935668i | \(-0.614798\pi\) | ||
0.352883 | − | 0.935668i | \(-0.385202\pi\) | |||||||
\(108\) | −1.53410e20 | + | 1.77759e20i | −0.710585 | + | 0.823367i | ||||
\(109\) | −1.32963e20 | −0.561651 | −0.280826 | − | 0.959759i | \(-0.590608\pi\) | ||||
−0.280826 | + | 0.959759i | \(0.590608\pi\) | |||||||
\(110\) | −9.40823e19 | − | 3.49842e19i | −0.362728 | − | 0.134879i | ||||
\(111\) | − | 3.87908e19i | − | 0.136615i | ||||||
\(112\) | 1.20703e20 | − | 1.78455e19i | 0.388630 | − | 0.0574576i | ||||
\(113\) | −1.19742e20 | −0.352746 | −0.176373 | − | 0.984323i | \(-0.556436\pi\) | ||||
−0.176373 | + | 0.984323i | \(0.556436\pi\) | |||||||
\(114\) | −1.70827e20 | + | 4.59403e20i | −0.460796 | + | 1.23921i | ||||
\(115\) | 1.75556e20i | 0.433947i | ||||||||
\(116\) | 2.21179e20 | + | 1.90882e20i | 0.501375 | + | 0.432699i | ||||
\(117\) | −3.21445e20 | −0.668727 | ||||||||
\(118\) | 1.84497e20 | + | 6.86044e19i | 0.352507 | + | 0.131079i | ||||
\(119\) | − | 1.56251e20i | − | 0.274381i | ||||||
\(120\) | −1.05036e20 | − | 1.91001e20i | −0.169640 | − | 0.308477i | ||||
\(121\) | 1.58252e20 | 0.235232 | ||||||||
\(122\) | 3.50176e20 | − | 9.41721e20i | 0.479389 | − | 1.28921i | ||||
\(123\) | 1.05170e19i | 0.0132690i | ||||||||
\(124\) | −3.53561e20 | + | 4.09677e20i | −0.411384 | + | 0.476678i | ||||
\(125\) | 7.43561e20 | 0.798392 | ||||||||
\(126\) | −1.36340e20 | − | 5.06977e19i | −0.135182 | − | 0.0502670i | ||||
\(127\) | 5.31218e20i | 0.486671i | 0.969942 | + | 0.243336i | \(0.0782416\pi\) | ||||
−0.969942 | + | 0.243336i | \(0.921758\pi\) | |||||||
\(128\) | −7.14074e20 | − | 9.40157e20i | −0.604844 | − | 0.796344i | ||||
\(129\) | 1.14221e21 | 0.895054 | ||||||||
\(130\) | 3.87304e20 | − | 1.04157e21i | 0.280943 | − | 0.755534i | ||||
\(131\) | 6.40485e20i | 0.430325i | 0.976578 | + | 0.215162i | \(0.0690281\pi\) | ||||
−0.976578 | + | 0.215162i | \(0.930972\pi\) | |||||||
\(132\) | −8.45844e20 | − | 7.29983e20i | −0.526685 | − | 0.454542i | ||||
\(133\) | −1.13072e21 | −0.652889 | ||||||||
\(134\) | 2.28741e21 | + | 8.50566e20i | 1.22545 | + | 0.455680i | ||||
\(135\) | 9.67706e20i | 0.481289i | ||||||||
\(136\) | −1.32476e21 | + | 7.28519e20i | −0.611995 | + | 0.336552i | ||||
\(137\) | −1.07755e20 | −0.0462630 | −0.0231315 | − | 0.999732i | \(-0.507364\pi\) | ||||
−0.0231315 | + | 0.999732i | \(0.507364\pi\) | |||||||
\(138\) | −6.81067e20 | + | 1.83158e21i | −0.271894 | + | 0.731198i | ||||
\(139\) | 1.98580e21i | 0.737542i | 0.929520 | + | 0.368771i | \(0.120221\pi\) | ||||
−0.929520 | + | 0.368771i | \(0.879779\pi\) | |||||||
\(140\) | 3.28548e20 | − | 3.80694e20i | 0.113584 | − | 0.131612i | ||||
\(141\) | −3.52284e21 | −1.13423 | ||||||||
\(142\) | −6.36591e20 | − | 2.36714e20i | −0.190975 | − | 0.0710135i | ||||
\(143\) | − | 5.69592e21i | − | 1.59295i | ||||||
\(144\) | 2.05850e20 | + | 1.39232e21i | 0.0536941 | + | 0.363174i | ||||
\(145\) | 1.20408e21 | 0.293073 | ||||||||
\(146\) | −2.34872e20 | + | 6.31637e20i | −0.0533707 | + | 0.143529i | ||||
\(147\) | − | 3.16980e21i | − | 0.672758i | ||||||
\(148\) | −6.55514e20 | − | 5.65724e20i | −0.130006 | − | 0.112199i | ||||
\(149\) | 4.30326e21 | 0.797875 | 0.398938 | − | 0.916978i | \(-0.369379\pi\) | ||||
0.398938 | + | 0.916978i | \(0.369379\pi\) | |||||||
\(150\) | 3.45779e21 | + | 1.28577e21i | 0.599633 | + | 0.222972i | ||||
\(151\) | − | 4.36918e21i | − | 0.708974i | −0.935061 | − | 0.354487i | \(-0.884656\pi\) | ||
0.935061 | − | 0.354487i | \(-0.115344\pi\) | |||||||
\(152\) | 5.27197e21 | + | 9.58668e21i | 0.800824 | + | 1.45624i | ||||
\(153\) | 1.80239e21 | 0.256409 | ||||||||
\(154\) | 8.98349e20 | − | 2.41591e21i | 0.119740 | − | 0.322013i | ||||
\(155\) | 2.23026e21i | 0.278636i | ||||||||
\(156\) | 8.08152e21 | − | 9.36419e21i | 0.946775 | − | 1.09704i | ||||
\(157\) | −7.25176e21 | −0.796980 | −0.398490 | − | 0.917173i | \(-0.630466\pi\) | ||||
−0.398490 | + | 0.917173i | \(0.630466\pi\) | |||||||
\(158\) | −1.38849e22 | − | 5.16307e21i | −1.43210 | − | 0.532521i | ||||
\(159\) | 6.54082e21i | 0.633375i | ||||||||
\(160\) | −4.75952e21 | − | 1.01057e21i | −0.432876 | − | 0.0919112i | ||||
\(161\) | −4.50804e21 | −0.385238 | ||||||||
\(162\) | −2.16126e21 | + | 5.81224e21i | −0.173603 | + | 0.466867i | ||||
\(163\) | 7.20508e21i | 0.544206i | 0.962268 | + | 0.272103i | \(0.0877191\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(164\) | 1.77723e20 | + | 1.53379e20i | 0.0126271 | + | 0.0108975i | ||||
\(165\) | −4.60472e21 | −0.307867 | ||||||||
\(166\) | −1.60444e22 | − | 5.96607e21i | −1.00982 | − | 0.375498i | ||||
\(167\) | 2.22940e22i | 1.32137i | 0.750665 | + | 0.660683i | \(0.229733\pi\) | ||||
−0.750665 | + | 0.660683i | \(0.770267\pi\) | |||||||
\(168\) | 4.90466e21 | − | 2.69720e21i | 0.273852 | − | 0.150598i | ||||
\(169\) | 4.40535e22 | 2.31800 | ||||||||
\(170\) | −2.17166e21 | + | 5.84020e21i | −0.107722 | + | 0.289694i | ||||
\(171\) | − | 1.30431e22i | − | 0.610124i | ||||||
\(172\) | 1.66580e22 | − | 1.93019e22i | 0.735085 | − | 0.851756i | ||||
\(173\) | −2.89860e22 | −1.20705 | −0.603527 | − | 0.797343i | \(-0.706238\pi\) | ||||
−0.603527 | + | 0.797343i | \(0.706238\pi\) | |||||||
\(174\) | 1.25622e22 | + | 4.67123e21i | 0.493827 | + | 0.183628i | ||||
\(175\) | 8.51060e21i | 0.315922i | ||||||||
\(176\) | −2.46715e22 | + | 3.64761e21i | −0.865106 | + | 0.127903i | ||||
\(177\) | 9.02991e21 | 0.299193 | ||||||||
\(178\) | 1.07501e22 | − | 2.89101e22i | 0.336677 | − | 0.905419i | ||||
\(179\) | − | 3.34229e22i | − | 0.989724i | −0.868972 | − | 0.494862i | \(-0.835219\pi\) | ||
0.868972 | − | 0.494862i | \(-0.164781\pi\) | |||||||
\(180\) | 4.39137e21 | + | 3.78986e21i | 0.122991 | + | 0.106145i | ||||
\(181\) | −1.78015e22 | −0.471705 | −0.235853 | − | 0.971789i | \(-0.575788\pi\) | ||||
−0.235853 | + | 0.971789i | \(0.575788\pi\) | |||||||
\(182\) | 2.67461e22 | + | 9.94546e21i | 0.670729 | + | 0.249408i | ||||
\(183\) | − | 4.60912e22i | − | 1.09423i | ||||||
\(184\) | 2.10187e22 | + | 3.82209e22i | 0.472527 | + | 0.859256i | ||||
\(185\) | −3.56857e21 | −0.0759937 | ||||||||
\(186\) | −8.65227e21 | + | 2.32684e22i | −0.174582 | + | 0.469501i | ||||
\(187\) | 3.19377e22i | 0.610784i | ||||||||
\(188\) | −5.13770e22 | + | 5.95314e22i | −0.931515 | + | 1.07936i | ||||
\(189\) | −2.48495e22 | −0.427266 | ||||||||
\(190\) | 4.22630e22 | + | 1.57153e22i | 0.689325 | + | 0.256323i | ||||
\(191\) | − | 7.50141e21i | − | 0.116094i | −0.998314 | − | 0.0580469i | \(-0.981513\pi\) | ||
0.998314 | − | 0.0580469i | \(-0.0184873\pi\) | |||||||
\(192\) | −4.57358e22 | − | 2.90079e22i | −0.671806 | − | 0.426093i | ||||
\(193\) | 6.42333e22 | 0.895751 | 0.447876 | − | 0.894096i | \(-0.352181\pi\) | ||||
0.447876 | + | 0.894096i | \(0.352181\pi\) | |||||||
\(194\) | −1.17206e22 | + | 3.15199e22i | −0.155214 | + | 0.417415i | ||||
\(195\) | − | 5.09780e22i | − | 0.641264i | ||||||
\(196\) | −5.35655e22 | − | 4.62283e22i | −0.640213 | − | 0.552519i | ||||
\(197\) | −1.51037e23 | −1.71562 | −0.857809 | − | 0.513968i | \(-0.828175\pi\) | ||||
−0.857809 | + | 0.513968i | \(0.828175\pi\) | |||||||
\(198\) | 2.78679e22 | + | 1.03626e22i | 0.300921 | + | 0.111897i | ||||
\(199\) | 9.57591e22i | 0.983217i | 0.870816 | + | 0.491608i | \(0.163591\pi\) | ||||
−0.870816 | + | 0.491608i | \(0.836409\pi\) | |||||||
\(200\) | 7.21561e22 | − | 3.96805e22i | 0.704649 | − | 0.387505i | ||||
\(201\) | 1.11954e23 | 1.04011 | ||||||||
\(202\) | 4.29603e22 | − | 1.15532e23i | 0.379799 | − | 1.02139i | ||||
\(203\) | 3.09193e22i | 0.260177i | ||||||||
\(204\) | −4.53141e22 | + | 5.25062e22i | −0.363021 | + | 0.420638i | ||||
\(205\) | 9.67512e20 | 0.00738104 | ||||||||
\(206\) | 5.16921e22 | + | 1.92215e22i | 0.375623 | + | 0.139674i | ||||
\(207\) | − | 5.20010e22i | − | 0.360005i | ||||||
\(208\) | −4.03820e22 | − | 2.73134e23i | −0.266412 | − | 1.80195i | ||||
\(209\) | 2.31119e23 | 1.45336 | ||||||||
\(210\) | 8.04015e21 | − | 2.16222e22i | 0.0482027 | − | 0.129631i | ||||
\(211\) | 2.46315e23i | 1.40821i | 0.710097 | + | 0.704104i | \(0.248651\pi\) | ||||
−0.710097 | + | 0.704104i | \(0.751349\pi\) | |||||||
\(212\) | 1.10531e23 | + | 9.53912e22i | 0.602736 | + | 0.520175i | ||||
\(213\) | −3.11570e22 | −0.162091 | ||||||||
\(214\) | −3.53319e23 | − | 1.31380e23i | −1.75400 | − | 0.652218i | ||||
\(215\) | − | 1.05078e23i | − | 0.497884i | ||||||
\(216\) | 1.15860e23 | + | 2.10683e23i | 0.524079 | + | 0.952998i | ||||
\(217\) | −5.72701e22 | −0.247361 | ||||||||
\(218\) | −4.74540e22 | + | 1.27617e23i | −0.195753 | + | 0.526434i | ||||
\(219\) | 3.09145e22i | 0.121821i | ||||||||
\(220\) | −6.71551e22 | + | 7.78138e22i | −0.252844 | + | 0.292974i | ||||
\(221\) | −3.53577e23 | −1.27222 | ||||||||
\(222\) | −3.72311e22 | − | 1.38443e22i | −0.128049 | − | 0.0476146i | ||||
\(223\) | − | 3.80877e21i | − | 0.0125238i | −0.999980 | − | 0.00626189i | \(-0.998007\pi\) | ||
0.999980 | − | 0.00626189i | \(-0.00199324\pi\) | |||||||
\(224\) | 2.59503e22 | − | 1.22218e23i | 0.0815946 | − | 0.384287i | ||||
\(225\) | −9.81712e22 | −0.295229 | ||||||||
\(226\) | −4.27354e22 | + | 1.14927e23i | −0.122943 | + | 0.330628i | ||||
\(227\) | − | 4.40164e23i | − | 1.21159i | −0.795621 | − | 0.605795i | \(-0.792855\pi\) | ||
0.795621 | − | 0.605795i | \(-0.207145\pi\) | |||||||
\(228\) | 3.79964e23 | + | 3.27918e23i | 1.00091 | + | 0.863806i | ||||
\(229\) | −1.47692e23 | −0.372395 | −0.186197 | − | 0.982512i | \(-0.559616\pi\) | ||||
−0.186197 | + | 0.982512i | \(0.559616\pi\) | |||||||
\(230\) | 1.68497e23 | + | 6.26550e22i | 0.406737 | + | 0.151244i | ||||
\(231\) | − | 1.18243e23i | − | 0.273311i | ||||||
\(232\) | 2.62145e23 | − | 1.44160e23i | 0.580312 | − | 0.319129i | ||||
\(233\) | 9.21685e23 | 1.95445 | 0.977223 | − | 0.212216i | \(-0.0680682\pi\) | ||||
0.977223 | + | 0.212216i | \(0.0680682\pi\) | |||||||
\(234\) | −1.14722e23 | + | 3.08521e23i | −0.233072 | + | 0.626796i | ||||
\(235\) | 3.24085e23i | 0.630928i | ||||||||
\(236\) | 1.31692e23 | − | 1.52594e23i | 0.245719 | − | 0.284719i | ||||
\(237\) | −6.79577e23 | −1.21550 | ||||||||
\(238\) | −1.49969e23 | − | 5.57655e22i | −0.257177 | − | 0.0956303i | ||||
\(239\) | − | 1.05038e24i | − | 1.72730i | −0.504092 | − | 0.863650i | \(-0.668173\pi\) | ||
0.504092 | − | 0.863650i | \(-0.331827\pi\) | |||||||
\(240\) | −2.20808e23 | + | 3.26458e22i | −0.348260 | + | 0.0514890i | ||||
\(241\) | 6.62860e23 | 1.00289 | 0.501443 | − | 0.865191i | \(-0.332803\pi\) | ||||
0.501443 | + | 0.865191i | \(0.332803\pi\) | |||||||
\(242\) | 5.64795e22 | − | 1.51889e23i | 0.0819855 | − | 0.220482i | ||||
\(243\) | − | 4.96311e23i | − | 0.691339i | ||||||
\(244\) | −7.78881e23 | − | 6.72192e23i | −1.04129 | − | 0.898660i | ||||
\(245\) | −2.91607e23 | −0.374229 | ||||||||
\(246\) | 1.00941e22 | + | 3.75346e21i | 0.0124370 | + | 0.00462467i | ||||
\(247\) | 2.55868e24i | 3.02723i | ||||||||
\(248\) | 2.67021e23 | + | 4.85558e23i | 0.303409 | + | 0.551727i | ||||
\(249\) | −7.85271e23 | −0.857090 | ||||||||
\(250\) | 2.65374e23 | − | 7.13664e23i | 0.278264 | − | 0.748331i | ||||
\(251\) | 7.10595e23i | 0.715954i | 0.933730 | + | 0.357977i | \(0.116533\pi\) | ||||
−0.933730 | + | 0.357977i | \(0.883467\pi\) | |||||||
\(252\) | −9.73186e22 | + | 1.12765e23i | −0.0942303 | + | 0.109186i | ||||
\(253\) | 9.21442e23 | 0.857556 | ||||||||
\(254\) | 5.09859e23 | + | 1.89589e23i | 0.456156 | + | 0.169620i | ||||
\(255\) | 2.85840e23i | 0.245879i | ||||||||
\(256\) | −1.15721e24 | + | 3.49825e23i | −0.957218 | + | 0.289368i | ||||
\(257\) | −1.74157e23 | −0.138551 | −0.0692757 | − | 0.997598i | \(-0.522069\pi\) | ||||
−0.0692757 | + | 0.997598i | \(0.522069\pi\) | |||||||
\(258\) | 4.07650e23 | − | 1.09629e24i | 0.311954 | − | 0.838931i | ||||
\(259\) | − | 9.16364e22i | − | 0.0674637i | ||||||
\(260\) | −8.61462e23 | − | 7.43462e23i | −0.610243 | − | 0.526654i | ||||
\(261\) | −3.56658e23 | −0.243135 | ||||||||
\(262\) | 6.14733e23 | + | 2.28586e23i | 0.403342 | + | 0.149981i | ||||
\(263\) | − | 1.12925e24i | − | 0.713236i | −0.934250 | − | 0.356618i | \(-0.883930\pi\) | ||
0.934250 | − | 0.356618i | \(-0.116070\pi\) | |||||||
\(264\) | −1.00251e24 | + | 5.51307e23i | −0.609607 | + | 0.335239i | ||||
\(265\) | 6.01726e23 | 0.352322 | ||||||||
\(266\) | −4.03550e23 | + | 1.08526e24i | −0.227552 | + | 0.611951i | ||||
\(267\) | − | 1.41496e24i | − | 0.768479i | ||||||
\(268\) | 1.63273e24 | − | 1.89188e24i | 0.854216 | − | 0.989794i | ||||
\(269\) | 6.44605e23 | 0.324916 | 0.162458 | − | 0.986715i | \(-0.448058\pi\) | ||||
0.162458 | + | 0.986715i | \(0.448058\pi\) | |||||||
\(270\) | 9.28797e23 | + | 3.45370e23i | 0.451111 | + | 0.167744i | ||||
\(271\) | − | 1.50436e23i | − | 0.0704139i | −0.999380 | − | 0.0352069i | \(-0.988791\pi\) | ||
0.999380 | − | 0.0352069i | \(-0.0112090\pi\) | |||||||
\(272\) | 2.26427e23 | + | 1.53150e24i | 0.102150 | + | 0.690920i | ||||
\(273\) | 1.30905e24 | 0.569285 | ||||||||
\(274\) | −3.84574e22 | + | 1.03423e23i | −0.0161241 | + | 0.0433621i | ||||
\(275\) | − | 1.73956e24i | − | 0.703256i | ||||||
\(276\) | 1.51487e24 | + | 1.30737e24i | 0.590587 | + | 0.509690i | ||||
\(277\) | −1.30317e24 | −0.490007 | −0.245003 | − | 0.969522i | \(-0.578789\pi\) | ||||
−0.245003 | + | 0.969522i | \(0.578789\pi\) | |||||||
\(278\) | 1.90595e24 | + | 7.08722e23i | 0.691296 | + | 0.257056i | ||||
\(279\) | − | 6.60620e23i | − | 0.231158i | ||||||
\(280\) | −2.48130e23 | − | 4.51206e23i | −0.0837721 | − | 0.152333i | ||||
\(281\) | −5.88408e24 | −1.91697 | −0.958484 | − | 0.285145i | \(-0.907958\pi\) | ||||
−0.958484 | + | 0.285145i | \(0.907958\pi\) | |||||||
\(282\) | −1.25728e24 | + | 3.38119e24i | −0.395314 | + | 1.06311i | ||||
\(283\) | 1.13806e24i | 0.345382i | 0.984976 | + | 0.172691i | \(0.0552463\pi\) | ||||
−0.984976 | + | 0.172691i | \(0.944754\pi\) | |||||||
\(284\) | −4.54393e23 | + | 5.26513e23i | −0.133121 | + | 0.154250i | ||||
\(285\) | 2.06850e24 | 0.585068 | ||||||||
\(286\) | −5.46690e24 | − | 2.03285e24i | −1.49307 | − | 0.555194i | ||||
\(287\) | 2.48445e22i | 0.00655255i | ||||||||
\(288\) | 1.40981e24 | + | 2.99340e23i | 0.359116 | + | 0.0762501i | ||||
\(289\) | −2.08168e24 | −0.512196 | ||||||||
\(290\) | 4.29731e23 | − | 1.15567e24i | 0.102145 | − | 0.274696i | ||||
\(291\) | 1.54270e24i | 0.354283i | ||||||||
\(292\) | 5.22415e23 | + | 4.50857e23i | 0.115928 | + | 0.100048i | ||||
\(293\) | 4.07125e24 | 0.873075 | 0.436537 | − | 0.899686i | \(-0.356205\pi\) | ||||
0.436537 | + | 0.899686i | \(0.356205\pi\) | |||||||
\(294\) | −3.04235e24 | − | 1.13129e24i | −0.630574 | − | 0.234477i | ||||
\(295\) | − | 8.30710e23i | − | 0.166429i | ||||||
\(296\) | −7.76928e23 | + | 4.27253e23i | −0.150475 | + | 0.0827500i | ||||
\(297\) | 5.07922e24 | 0.951113 | ||||||||
\(298\) | 1.53582e24 | − | 4.13024e24i | 0.278084 | − | 0.747846i | ||||
\(299\) | 1.02011e25i | 1.78622i | ||||||||
\(300\) | 2.46814e24 | − | 2.85987e24i | 0.417981 | − | 0.484322i | ||||
\(301\) | 2.69827e24 | 0.441998 | ||||||||
\(302\) | −4.19350e24 | − | 1.55934e24i | −0.664519 | − | 0.247099i | ||||
\(303\) | − | 5.65456e24i | − | 0.866907i | ||||||
\(304\) | 1.10828e25 | − | 1.63855e24i | 1.64404 | − | 0.243066i | ||||
\(305\) | −4.24017e24 | −0.608675 | ||||||||
\(306\) | 6.43263e23 | − | 1.72992e24i | 0.0893665 | − | 0.240331i | ||||
\(307\) | − | 3.43457e24i | − | 0.461837i | −0.972973 | − | 0.230918i | \(-0.925827\pi\) | ||
0.972973 | − | 0.230918i | \(-0.0741730\pi\) | |||||||
\(308\) | −1.99816e24 | − | 1.72446e24i | −0.260089 | − | 0.224463i | ||||
\(309\) | 2.52999e24 | 0.318812 | ||||||||
\(310\) | 2.14058e24 | + | 7.95969e23i | 0.261165 | + | 0.0971134i | ||||
\(311\) | 9.90915e24i | 1.17067i | 0.810793 | + | 0.585333i | \(0.199036\pi\) | ||||
−0.810793 | + | 0.585333i | \(0.800964\pi\) | |||||||
\(312\) | −6.10342e24 | − | 1.10986e25i | −0.698276 | − | 1.26976i | ||||
\(313\) | −4.23818e24 | −0.469609 | −0.234804 | − | 0.972043i | \(-0.575445\pi\) | ||||
−0.234804 | + | 0.972043i | \(0.575445\pi\) | |||||||
\(314\) | −2.58812e24 | + | 6.96019e24i | −0.277772 | + | 0.747007i | ||||
\(315\) | 6.13884e23i | 0.0638235i | ||||||||
\(316\) | −9.91094e24 | + | 1.14840e25i | −0.998261 | + | 1.15670i | ||||
\(317\) | 1.28467e24 | 0.125371 | 0.0626855 | − | 0.998033i | \(-0.480033\pi\) | ||||
0.0626855 | + | 0.998033i | \(0.480033\pi\) | |||||||
\(318\) | 6.27783e24 | + | 2.33439e24i | 0.593661 | + | 0.220751i | ||||
\(319\) | − | 6.31988e24i | − | 0.579165i | ||||||
\(320\) | −2.66859e24 | + | 4.20748e24i | −0.237019 | + | 0.373699i | ||||
\(321\) | −1.72927e25 | −1.48872 | ||||||||
\(322\) | −1.60890e24 | + | 4.32678e24i | −0.134267 | + | 0.361083i | ||||
\(323\) | − | 1.43468e25i | − | 1.16073i | ||||||
\(324\) | 4.80720e24 | + | 4.14873e24i | 0.377087 | + | 0.325435i | ||||
\(325\) | 1.92584e25 | 1.46483 | ||||||||
\(326\) | 6.91538e24 | + | 2.57146e24i | 0.510082 | + | 0.189672i | ||||
\(327\) | 6.24603e24i | 0.446814i | ||||||||
\(328\) | 2.10641e23 | − | 1.15837e23i | 0.0146152 | − | 0.00803726i | ||||
\(329\) | −8.32208e24 | −0.560109 | ||||||||
\(330\) | −1.64340e24 | + | 4.41957e24i | −0.107301 | + | 0.288563i | ||||
\(331\) | − | 6.47947e24i | − | 0.410449i | −0.978715 | − | 0.205225i | \(-0.934207\pi\) | ||
0.978715 | − | 0.205225i | \(-0.0657925\pi\) | |||||||
\(332\) | −1.14524e25 | + | 1.32701e25i | −0.703906 | + | 0.815628i | ||||
\(333\) | 1.05704e24 | 0.0630448 | ||||||||
\(334\) | 2.13976e25 | + | 7.95663e24i | 1.23851 | + | 0.460537i | ||||
\(335\) | − | 1.02992e25i | − | 0.578572i | ||||||
\(336\) | −8.38302e23 | − | 5.67008e24i | −0.0457096 | − | 0.309169i | ||||
\(337\) | −1.56644e25 | −0.829117 | −0.414559 | − | 0.910023i | \(-0.636064\pi\) | ||||
−0.414559 | + | 0.910023i | \(0.636064\pi\) | |||||||
\(338\) | 1.57225e25 | − | 4.22822e25i | 0.807895 | − | 2.17266i | ||||
\(339\) | 5.62496e24i | 0.280622i | ||||||||
\(340\) | 4.83033e24 | + | 4.16869e24i | 0.233985 | + | 0.201934i | ||||
\(341\) | 1.17060e25 | 0.550635 | ||||||||
\(342\) | −1.25186e25 | − | 4.65501e24i | −0.571868 | − | 0.212647i | ||||
\(343\) | − | 1.63428e25i | − | 0.725078i | ||||||
\(344\) | −1.25806e25 | − | 2.28770e25i | −0.542148 | − | 0.985857i | ||||
\(345\) | 8.24683e24 | 0.345220 | ||||||||
\(346\) | −1.03450e25 | + | 2.78205e25i | −0.420696 | + | 1.13137i | ||||
\(347\) | 7.41553e24i | 0.292987i | 0.989212 | + | 0.146493i | \(0.0467987\pi\) | ||||
−0.989212 | + | 0.146493i | \(0.953201\pi\) | |||||||
\(348\) | 8.96681e24 | − | 1.03900e25i | 0.344228 | − | 0.398862i | ||||
\(349\) | 5.41785e24 | 0.202103 | 0.101051 | − | 0.994881i | \(-0.467779\pi\) | ||||
0.101051 | + | 0.994881i | \(0.467779\pi\) | |||||||
\(350\) | 8.16841e24 | + | 3.03740e24i | 0.296113 | + | 0.110109i | ||||
\(351\) | 5.62311e25i | 1.98110i | ||||||||
\(352\) | −5.30422e24 | + | 2.49814e25i | −0.181633 | + | 0.855440i | ||||
\(353\) | 3.91060e25 | 1.30166 | 0.650828 | − | 0.759225i | \(-0.274422\pi\) | ||||
0.650828 | + | 0.759225i | \(0.274422\pi\) | |||||||
\(354\) | 3.22274e24 | − | 8.66684e24i | 0.104278 | − | 0.280432i | ||||
\(355\) | 2.86630e24i | 0.0901650i | ||||||||
\(356\) | −2.39110e25 | − | 2.06358e25i | −0.731304 | − | 0.631133i | ||||
\(357\) | −7.34001e24 | −0.218280 | ||||||||
\(358\) | −3.20791e25 | − | 1.19285e25i | −0.927665 | − | 0.344949i | ||||
\(359\) | 3.06864e25i | 0.862980i | 0.902118 | + | 0.431490i | \(0.142012\pi\) | ||||
−0.902118 | + | 0.431490i | \(0.857988\pi\) | |||||||
\(360\) | 5.20474e24 | − | 2.86222e24i | 0.142355 | − | 0.0782849i | ||||
\(361\) | −6.62316e25 | −1.76195 | ||||||||
\(362\) | −6.35327e24 | + | 1.70857e25i | −0.164404 | + | 0.442128i | ||||
\(363\) | − | 7.43399e24i | − | 0.187135i | ||||||
\(364\) | 1.90912e25 | − | 2.21212e25i | 0.467540 | − | 0.541746i | ||||
\(365\) | 2.84399e24 | 0.0677642 | ||||||||
\(366\) | −4.42379e25 | − | 1.64497e25i | −1.02561 | − | 0.381371i | ||||
\(367\) | − | 3.23632e25i | − | 0.730113i | −0.930985 | − | 0.365057i | \(-0.881050\pi\) | ||
0.930985 | − | 0.365057i | \(-0.118950\pi\) | |||||||
\(368\) | 4.41856e25 | − | 6.53269e24i | 0.970068 | − | 0.143421i | ||||
\(369\) | −2.86585e23 | −0.00612336 | ||||||||
\(370\) | −1.27361e24 | + | 3.42509e24i | −0.0264861 | + | 0.0712287i | ||||
\(371\) | 1.54515e25i | 0.312776i | ||||||||
\(372\) | 1.92449e25 | + | 1.66088e25i | 0.379215 | + | 0.327271i | ||||
\(373\) | −6.42747e24 | −0.123297 | −0.0616484 | − | 0.998098i | \(-0.519636\pi\) | ||||
−0.0616484 | + | 0.998098i | \(0.519636\pi\) | |||||||
\(374\) | 3.06536e25 | + | 1.13984e25i | 0.572486 | + | 0.212877i | ||||
\(375\) | − | 3.49292e25i | − | 0.635150i | ||||||
\(376\) | 3.88015e25 | + | 7.05577e25i | 0.687022 | + | 1.24930i | ||||
\(377\) | 6.99663e25 | 1.20636 | ||||||||
\(378\) | −8.86866e24 | + | 2.38503e25i | −0.148916 | + | 0.400476i | ||||
\(379\) | − | 7.60895e25i | − | 1.24432i | −0.782889 | − | 0.622161i | \(-0.786255\pi\) | ||
0.782889 | − | 0.622161i | \(-0.213745\pi\) | |||||||
\(380\) | 3.01669e25 | − | 3.49549e25i | 0.480502 | − | 0.556766i | ||||
\(381\) | 2.49543e25 | 0.387165 | ||||||||
\(382\) | −7.19980e24 | − | 2.67722e24i | −0.108814 | − | 0.0404623i | ||||
\(383\) | − | 4.45029e25i | − | 0.655241i | −0.944809 | − | 0.327620i | \(-0.893753\pi\) | ||
0.944809 | − | 0.327620i | \(-0.106247\pi\) | |||||||
\(384\) | −4.41645e25 | + | 3.35441e25i | −0.633521 | + | 0.481175i | ||||
\(385\) | −1.08778e25 | −0.152032 | ||||||||
\(386\) | 2.29246e25 | − | 6.16507e25i | 0.312197 | − | 0.839585i | ||||
\(387\) | 3.11250e25i | 0.413047i | ||||||||
\(388\) | 2.60696e25 | + | 2.24986e25i | 0.337145 | + | 0.290964i | ||||
\(389\) | −9.57190e25 | −1.20643 | −0.603215 | − | 0.797579i | \(-0.706114\pi\) | ||||
−0.603215 | + | 0.797579i | \(0.706114\pi\) | |||||||
\(390\) | −4.89283e25 | − | 1.81938e25i | −0.601055 | − | 0.223500i | ||||
\(391\) | − | 5.71990e25i | − | 0.684890i | ||||||
\(392\) | −6.34869e25 | + | 3.49131e25i | −0.741009 | + | 0.407500i | ||||
\(393\) | 3.00872e25 | 0.342339 | ||||||||
\(394\) | −5.39044e25 | + | 1.44964e26i | −0.597946 | + | 1.60804i | ||||
\(395\) | 6.25180e25i | 0.676136i | ||||||||
\(396\) | 1.98919e25 | − | 2.30491e25i | 0.209761 | − | 0.243053i | ||||
\(397\) | −1.10405e26 | −1.13523 | −0.567616 | − | 0.823294i | \(-0.692134\pi\) | ||||
−0.567616 | + | 0.823294i | \(0.692134\pi\) | |||||||
\(398\) | 9.19088e25 | + | 3.41760e25i | 0.921566 | + | 0.342681i | ||||
\(399\) | 5.31164e25i | 0.519397i | ||||||||
\(400\) | −1.23329e25 | − | 8.34167e25i | −0.117615 | − | 0.795523i | ||||
\(401\) | 2.17511e24 | 0.0202319 | 0.0101160 | − | 0.999949i | \(-0.496780\pi\) | ||||
0.0101160 | + | 0.999949i | \(0.496780\pi\) | |||||||
\(402\) | 3.99559e25 | − | 1.07453e26i | 0.362510 | − | 0.974891i | ||||
\(403\) | 1.29595e26i | 1.14693i | ||||||||
\(404\) | −9.55547e25 | − | 8.24660e25i | −0.824971 | − | 0.711969i | ||||
\(405\) | 2.61701e25 | 0.220422 | ||||||||
\(406\) | 2.96761e25 | + | 1.10349e25i | 0.243863 | + | 0.0906797i | ||||
\(407\) | 1.87304e25i | 0.150177i | ||||||||
\(408\) | 3.42226e25 | + | 6.22313e25i | 0.267739 | + | 0.486864i | ||||
\(409\) | 1.56984e26 | 1.19846 | 0.599228 | − | 0.800578i | \(-0.295474\pi\) | ||||
0.599228 | + | 0.800578i | \(0.295474\pi\) | |||||||
\(410\) | 3.45301e23 | − | 9.28611e23i | 0.00257252 | − | 0.00691823i | ||||
\(411\) | 5.06188e24i | 0.0368039i | ||||||||
\(412\) | 3.68974e25 | − | 4.27536e25i | 0.261832 | − | 0.303389i | ||||
\(413\) | 2.13316e25 | 0.147748 | ||||||||
\(414\) | −4.99101e25 | − | 1.85589e25i | −0.337431 | − | 0.125473i | ||||
\(415\) | 7.22414e25i | 0.476766i | ||||||||
\(416\) | −2.76564e26 | − | 5.87221e25i | −1.78182 | − | 0.378328i | ||||
\(417\) | 9.32841e25 | 0.586742 | ||||||||
\(418\) | 8.24854e25 | − | 2.21826e26i | 0.506540 | − | 1.36223i | ||||
\(419\) | − | 8.81451e25i | − | 0.528516i | −0.964452 | − | 0.264258i | \(-0.914873\pi\) | ||
0.964452 | − | 0.264258i | \(-0.0851270\pi\) | |||||||
\(420\) | −1.78834e25 | − | 1.54338e25i | −0.104702 | − | 0.0903605i | ||||
\(421\) | 9.14206e25 | 0.522665 | 0.261332 | − | 0.965249i | \(-0.415838\pi\) | ||||
0.261332 | + | 0.965249i | \(0.415838\pi\) | |||||||
\(422\) | 2.36411e26 | + | 8.79088e25i | 1.31991 | + | 0.490804i | ||||
\(423\) | − | 9.59965e25i | − | 0.523422i | ||||||
\(424\) | 1.31004e26 | − | 7.20425e25i | 0.697631 | − | 0.383646i | ||||
\(425\) | −1.07984e26 | −0.561657 | ||||||||
\(426\) | −1.11198e25 | + | 2.99042e25i | −0.0564938 | + | 0.151928i | ||||
\(427\) | − | 1.08882e26i | − | 0.540354i | ||||||
\(428\) | −2.52196e26 | + | 2.92224e26i | −1.22264 | + | 1.41670i | ||||
\(429\) | −2.67569e26 | −1.26725 | ||||||||
\(430\) | −1.00853e26 | − | 3.75019e25i | −0.466665 | − | 0.173528i | ||||
\(431\) | 2.07549e26i | 0.938315i | 0.883114 | + | 0.469158i | \(0.155442\pi\) | ||||
−0.883114 | + | 0.469158i | \(0.844558\pi\) | |||||||
\(432\) | 2.43562e26 | − | 3.60098e25i | 1.07590 | − | 0.159068i | ||||
\(433\) | 2.42954e26 | 1.04869 | 0.524343 | − | 0.851507i | \(-0.324311\pi\) | ||||
0.524343 | + | 0.851507i | \(0.324311\pi\) | |||||||
\(434\) | −2.04395e25 | + | 5.49674e25i | −0.0862128 | + | 0.231851i | ||||
\(435\) | − | 5.65625e25i | − | 0.233150i | ||||||
\(436\) | 1.05550e26 | + | 9.10920e25i | 0.425200 | + | 0.366957i | ||||
\(437\) | −4.13923e26 | −1.62969 | ||||||||
\(438\) | 2.96715e25 | + | 1.10333e25i | 0.114182 | + | 0.0424583i | ||||
\(439\) | − | 5.15067e25i | − | 0.193740i | −0.995297 | − | 0.0968699i | \(-0.969117\pi\) | ||
0.995297 | − | 0.0968699i | \(-0.0308831\pi\) | |||||||
\(440\) | 5.07177e25 | + | 9.22264e25i | 0.186480 | + | 0.339100i | ||||
\(441\) | 8.63764e25 | 0.310462 | ||||||||
\(442\) | −1.26190e26 | + | 3.39360e26i | −0.443407 | + | 1.19245i | ||||
\(443\) | − | 1.24024e26i | − | 0.426059i | −0.977046 | − | 0.213029i | \(-0.931667\pi\) | ||
0.977046 | − | 0.213029i | \(-0.0683330\pi\) | |||||||
\(444\) | −2.65752e25 | + | 3.07932e25i | −0.0892581 | + | 0.103425i | ||||
\(445\) | −1.30170e26 | −0.427475 | ||||||||
\(446\) | −3.65562e24 | − | 1.35933e24i | −0.0117385 | − | 0.00436493i | ||||
\(447\) | − | 2.02148e26i | − | 0.634739i | ||||||
\(448\) | −1.08043e26 | − | 6.85260e25i | −0.331753 | − | 0.210414i | ||||
\(449\) | 2.51952e26 | 0.756579 | 0.378289 | − | 0.925687i | \(-0.376512\pi\) | ||||
0.378289 | + | 0.925687i | \(0.376512\pi\) | |||||||
\(450\) | −3.50369e25 | + | 9.42239e25i | −0.102896 | + | 0.276717i | ||||
\(451\) | − | 5.07820e24i | − | 0.0145863i | ||||||
\(452\) | 9.50545e25 | + | 8.20342e25i | 0.267047 | + | 0.230468i | ||||
\(453\) | −2.05245e26 | −0.564014 | ||||||||
\(454\) | −4.22466e26 | − | 1.57092e26i | −1.13562 | − | 0.422276i | ||||
\(455\) | − | 1.20427e26i | − | 0.316671i | ||||||
\(456\) | 4.50340e26 | − | 2.47654e26i | 1.15849 | − | 0.637084i | ||||
\(457\) | 2.63098e25 | 0.0662150 | 0.0331075 | − | 0.999452i | \(-0.489460\pi\) | ||||
0.0331075 | + | 0.999452i | \(0.489460\pi\) | |||||||
\(458\) | −5.27108e25 | + | 1.41754e26i | −0.129791 | + | 0.349045i | ||||
\(459\) | − | 3.15295e26i | − | 0.759609i | ||||||
\(460\) | 1.20272e26 | − | 1.39361e26i | 0.283521 | − | 0.328520i | ||||
\(461\) | 5.55492e26 | 1.28135 | 0.640677 | − | 0.767811i | \(-0.278654\pi\) | ||||
0.640677 | + | 0.767811i | \(0.278654\pi\) | |||||||
\(462\) | −1.13489e26 | − | 4.22005e25i | −0.256173 | − | 0.0952572i | ||||
\(463\) | 6.62902e26i | 1.46433i | 0.681126 | + | 0.732166i | \(0.261491\pi\) | ||||
−0.681126 | + | 0.732166i | \(0.738509\pi\) | |||||||
\(464\) | −4.48057e25 | − | 3.03055e26i | −0.0968620 | − | 0.655151i | ||||
\(465\) | 1.04768e26 | 0.221665 | ||||||||
\(466\) | 3.28946e26 | − | 8.84627e26i | 0.681185 | − | 1.83190i | ||||
\(467\) | 1.84071e26i | 0.373092i | 0.982446 | + | 0.186546i | \(0.0597294\pi\) | ||||
−0.982446 | + | 0.186546i | \(0.940271\pi\) | |||||||
\(468\) | 2.55172e26 | + | 2.20219e26i | 0.506261 | + | 0.436915i | ||||
\(469\) | 2.64471e26 | 0.513630 | ||||||||
\(470\) | 3.11054e26 | + | 1.15664e26i | 0.591367 | + | 0.219898i | ||||
\(471\) | 3.40656e26i | 0.634026i | ||||||||
\(472\) | −9.94581e25 | − | 1.80857e26i | −0.181226 | − | 0.329546i | ||||
\(473\) | −5.51525e26 | −0.983907 | ||||||||
\(474\) | −2.42538e26 | + | 6.52253e26i | −0.423640 | + | 1.13929i | ||||
\(475\) | 7.81434e26i | 1.33646i | ||||||||
\(476\) | −1.07047e26 | + | 1.24037e26i | −0.179268 | + | 0.207721i | ||||
\(477\) | −1.78236e26 | −0.292288 | ||||||||
\(478\) | −1.00815e27 | − | 3.74876e26i | −1.61899 | − | 0.602018i | ||||
\(479\) | − | 6.01355e26i | − | 0.945749i | −0.881130 | − | 0.472874i | \(-0.843216\pi\) | ||
0.881130 | − | 0.472874i | \(-0.156784\pi\) | |||||||
\(480\) | −4.74724e25 | + | 2.23581e26i | −0.0731187 | + | 0.344368i | ||||
\(481\) | −2.07361e26 | −0.312807 | ||||||||
\(482\) | 2.36572e26 | − | 6.36208e26i | 0.349537 | − | 0.940002i | ||||
\(483\) | 2.11768e26i | 0.306471i | ||||||||
\(484\) | −1.25625e26 | − | 1.08417e26i | −0.178083 | − | 0.153690i | ||||
\(485\) | 1.41921e26 | 0.197074 | ||||||||
\(486\) | −4.76355e26 | − | 1.77131e26i | −0.647990 | − | 0.240953i | ||||
\(487\) | − | 2.56966e26i | − | 0.342441i | −0.985233 | − | 0.171220i | \(-0.945229\pi\) | ||
0.985233 | − | 0.171220i | \(-0.0547710\pi\) | |||||||
\(488\) | −9.23144e26 | + | 5.07661e26i | −1.20523 | + | 0.662790i | ||||
\(489\) | 3.38463e26 | 0.432935 | ||||||||
\(490\) | −1.04073e26 | + | 2.79882e26i | −0.130430 | + | 0.350764i | ||||
\(491\) | − | 1.07454e26i | − | 0.131949i | −0.997821 | − | 0.0659744i | \(-0.978984\pi\) | ||
0.997821 | − | 0.0659744i | \(-0.0210156\pi\) | |||||||
\(492\) | 7.20508e24 | − | 8.34865e24i | 0.00866937 | − | 0.0100454i | ||||
\(493\) | −3.92310e26 | −0.462551 | ||||||||
\(494\) | 2.45580e27 | + | 9.13181e26i | 2.83742 | + | 1.05508i | ||||
\(495\) | − | 1.25478e26i | − | 0.142074i | ||||||
\(496\) | 5.61333e26 | − | 8.29912e25i | 0.622879 | − | 0.0920906i | ||||
\(497\) | −7.36029e25 | −0.0800444 | ||||||||
\(498\) | −2.80260e26 | + | 7.53698e26i | −0.298722 | + | 0.803348i | ||||
\(499\) | 4.56847e26i | 0.477271i | 0.971109 | + | 0.238636i | \(0.0767001\pi\) | ||||
−0.971109 | + | 0.238636i | \(0.923300\pi\) | |||||||
\(500\) | −5.90259e26 | − | 5.09407e26i | −0.604425 | − | 0.521633i | ||||
\(501\) | 1.04727e27 | 1.05119 | ||||||||
\(502\) | 6.82024e26 | + | 2.53608e26i | 0.671062 | + | 0.249532i | ||||
\(503\) | − | 1.36768e27i | − | 1.31918i | −0.751626 | − | 0.659590i | \(-0.770730\pi\) | ||
0.751626 | − | 0.659590i | \(-0.229270\pi\) | |||||||
\(504\) | 7.34981e25 | + | 1.33651e26i | 0.0694978 | + | 0.126377i | ||||
\(505\) | −5.20194e26 | −0.482227 | ||||||||
\(506\) | 3.28859e26 | − | 8.84393e26i | 0.298885 | − | 0.803785i | ||||
\(507\) | − | 2.06944e27i | − | 1.84405i | ||||||
\(508\) | 3.63933e26 | − | 4.21695e26i | 0.317969 | − | 0.368436i | ||||
\(509\) | −2.65638e26 | −0.227569 | −0.113784 | − | 0.993505i | \(-0.536297\pi\) | ||||
−0.113784 | + | 0.993505i | \(0.536297\pi\) | |||||||
\(510\) | 2.74347e26 | + | 1.02015e26i | 0.230462 | + | 0.0856964i | ||||
\(511\) | 7.30301e25i | 0.0601580i | ||||||||
\(512\) | −7.72425e25 | + | 1.23553e27i | −0.0623960 | + | 0.998051i | ||||
\(513\) | −2.28165e27 | −1.80749 | ||||||||
\(514\) | −6.21560e25 | + | 1.67155e26i | −0.0482894 | + | 0.129864i | ||||
\(515\) | − | 2.32748e26i | − | 0.177343i | ||||||
\(516\) | −9.06718e26 | − | 7.82519e26i | −0.677603 | − | 0.584787i | ||||
\(517\) | 1.70103e27 | 1.24683 | ||||||||
\(518\) | −8.79519e25 | − | 3.27046e25i | −0.0632336 | − | 0.0235132i | ||||
\(519\) | 1.36163e27i | 0.960255i | ||||||||
\(520\) | −1.02102e27 | + | 5.61487e26i | −0.706320 | + | 0.388424i | ||||
\(521\) | 6.73621e26 | 0.457129 | 0.228564 | − | 0.973529i | \(-0.426597\pi\) | ||||
0.228564 | + | 0.973529i | \(0.426597\pi\) | |||||||
\(522\) | −1.27290e26 | + | 3.42318e26i | −0.0847401 | + | 0.227890i | ||||
\(523\) | 2.31489e27i | 1.51187i | 0.654648 | + | 0.755934i | \(0.272817\pi\) | ||||
−0.654648 | + | 0.755934i | \(0.727183\pi\) | |||||||
\(524\) | 4.38791e26 | − | 5.08435e26i | 0.281154 | − | 0.325778i | ||||
\(525\) | 3.99791e26 | 0.251327 | ||||||||
\(526\) | −1.08385e27 | − | 4.03025e26i | −0.668514 | − | 0.248585i | ||||
\(527\) | − | 7.26655e26i | − | 0.439766i | ||||||
\(528\) | 1.71349e26 | + | 1.15896e27i | 0.101752 | + | 0.688224i | ||||
\(529\) | 6.58969e25 | 0.0383980 | ||||||||
\(530\) | 2.14753e26 | − | 5.77532e26i | 0.122795 | − | 0.330231i | ||||
\(531\) | 2.46063e26i | 0.138071i | ||||||||
\(532\) | 8.97597e26 | + | 7.74648e26i | 0.494271 | + | 0.426568i | ||||
\(533\) | 5.62198e25 | 0.0303821 | ||||||||
\(534\) | −1.35807e27 | − | 5.04994e26i | −0.720293 | − | 0.267839i | ||||
\(535\) | 1.59085e27i | 0.828114i | ||||||||
\(536\) | −1.23309e27 | − | 2.24229e27i | −0.630011 | − | 1.14563i | ||||
\(537\) | −1.57006e27 | −0.787361 | ||||||||
\(538\) | 2.30057e26 | − | 6.18687e26i | 0.113243 | − | 0.304543i | ||||
\(539\) | 1.53056e27i | 0.739543i | ||||||||
\(540\) | 6.62967e26 | − | 7.68191e26i | 0.314452 | − | 0.364361i | ||||
\(541\) | 2.78485e26 | 0.129667 | 0.0648333 | − | 0.997896i | \(-0.479348\pi\) | ||||
0.0648333 | + | 0.997896i | \(0.479348\pi\) | |||||||
\(542\) | −1.44387e26 | − | 5.36899e25i | −0.0659987 | − | 0.0245414i | ||||
\(543\) | 8.36236e26i | 0.375258i | ||||||||
\(544\) | 1.55073e27 | + | 3.29262e26i | 0.683199 | + | 0.145062i | ||||
\(545\) | 5.74606e26 | 0.248545 | ||||||||
\(546\) | 4.67194e26 | − | 1.25642e27i | 0.198413 | − | 0.533589i | ||||
\(547\) | − | 3.92778e27i | − | 1.63785i | −0.573901 | − | 0.818924i | \(-0.694571\pi\) | ||
0.573901 | − | 0.818924i | \(-0.305429\pi\) | |||||||
\(548\) | 8.55392e25 | + | 7.38223e25i | 0.0350235 | + | 0.0302261i | ||||
\(549\) | 1.25597e27 | 0.504960 | ||||||||
\(550\) | −1.66962e27 | − | 6.20843e26i | −0.659160 | − | 0.245106i | ||||
\(551\) | 2.83897e27i | 1.10064i | ||||||||
\(552\) | 1.79545e27 | − | 9.87365e26i | 0.683569 | − | 0.375913i | ||||
\(553\) | −1.60538e27 | −0.600243 | ||||||||
\(554\) | −4.65094e26 | + | 1.25077e27i | −0.170783 | + | 0.459282i | ||||
\(555\) | 1.67636e26i | 0.0604557i | ||||||||
\(556\) | 1.36045e27 | − | 1.57638e27i | 0.481876 | − | 0.558358i | ||||
\(557\) | 3.16206e27 | 1.10007 | 0.550033 | − | 0.835143i | \(-0.314615\pi\) | ||||
0.550033 | + | 0.835143i | \(0.314615\pi\) | |||||||
\(558\) | −6.34058e26 | − | 2.35772e26i | −0.216664 | − | 0.0805658i | ||||
\(559\) | − | 6.10584e27i | − | 2.04940i | ||||||
\(560\) | −5.21621e26 | + | 7.71199e25i | −0.171979 | + | 0.0254265i | ||||
\(561\) | 1.50029e27 | 0.485901 | ||||||||
\(562\) | −2.10000e27 | + | 5.64749e27i | −0.668123 | + | 1.79677i | ||||
\(563\) | − | 8.24040e26i | − | 0.257552i | −0.991674 | − | 0.128776i | \(-0.958895\pi\) | ||
0.991674 | − | 0.128776i | \(-0.0411048\pi\) | |||||||
\(564\) | 2.79652e27 | + | 2.41346e27i | 0.858672 | + | 0.741054i | ||||
\(565\) | 5.17470e26 | 0.156099 | ||||||||
\(566\) | 1.09230e27 | + | 4.06168e26i | 0.323726 | + | 0.120376i | ||||
\(567\) | 6.72014e26i | 0.195681i | ||||||||
\(568\) | 3.43172e26 | + | 6.24033e26i | 0.0981813 | + | 0.178535i | ||||
\(569\) | −6.59416e27 | −1.85369 | −0.926844 | − | 0.375446i | \(-0.877489\pi\) | ||||
−0.926844 | + | 0.375446i | \(0.877489\pi\) | |||||||
\(570\) | 7.38238e26 | − | 1.98533e27i | 0.203914 | − | 0.548383i | ||||
\(571\) | − | 7.51186e25i | − | 0.0203886i | −0.999948 | − | 0.0101943i | \(-0.996755\pi\) | ||
0.999948 | − | 0.0101943i | \(-0.00324500\pi\) | |||||||
\(572\) | −3.90222e27 | + | 4.52157e27i | −1.04076 | + | 1.20595i | ||||
\(573\) | −3.52383e26 | −0.0923569 | ||||||||
\(574\) | 2.38455e25 | + | 8.86688e24i | 0.00614169 | + | 0.00228377i | ||||
\(575\) | 3.11548e27i | 0.788580i | ||||||||
\(576\) | 7.90459e26 | − | 1.24629e27i | 0.196632 | − | 0.310023i | ||||
\(577\) | −2.15646e27 | −0.527209 | −0.263605 | − | 0.964631i | \(-0.584911\pi\) | ||||
−0.263605 | + | 0.964631i | \(0.584911\pi\) | |||||||
\(578\) | −7.42943e26 | + | 1.99798e27i | −0.178516 | + | 0.480080i | ||||
\(579\) | − | 3.01740e27i | − | 0.712603i | ||||||
\(580\) | −9.55832e26 | − | 8.24906e26i | −0.221872 | − | 0.191480i | ||||
\(581\) | −1.85507e27 | −0.423251 | ||||||||
\(582\) | 1.48067e27 | + | 5.50581e26i | 0.332069 | + | 0.123479i | ||||
\(583\) | − | 3.15829e27i | − | 0.696252i | ||||||
\(584\) | 6.19177e26 | − | 3.40502e26i | 0.134180 | − | 0.0737888i | ||||
\(585\) | 1.38914e27 | 0.295929 | ||||||||
\(586\) | 1.45301e27 | − | 3.90755e27i | 0.304293 | − | 0.818330i | ||||
\(587\) | − | 2.34361e25i | − | 0.00482508i | −0.999997 | − | 0.00241254i | \(-0.999232\pi\) | ||
0.999997 | − | 0.00241254i | \(-0.000767936\pi\) | |||||||
\(588\) | −2.17160e27 | + | 2.51627e27i | −0.439549 | + | 0.509313i | ||||
\(589\) | −5.25848e27 | −1.04642 | ||||||||
\(590\) | −7.97310e26 | − | 2.96477e26i | −0.155994 | − | 0.0580057i | ||||
\(591\) | 7.09505e27i | 1.36484i | ||||||||
\(592\) | 1.32792e26 | + | 8.98174e26i | 0.0251163 | + | 0.169880i | ||||
\(593\) | 7.67293e27 | 1.42697 | 0.713484 | − | 0.700672i | \(-0.247116\pi\) | ||||
0.713484 | + | 0.700672i | \(0.247116\pi\) | |||||||
\(594\) | 1.81275e27 | − | 4.87499e27i | 0.331492 | − | 0.891476i | ||||
\(595\) | 6.75247e26i | 0.121421i | ||||||||
\(596\) | −3.41604e27 | − | 2.94813e27i | −0.604033 | − | 0.521295i | ||||
\(597\) | 4.49834e27 | 0.782185 | ||||||||
\(598\) | 9.79096e27 | + | 3.64073e27i | 1.67422 | + | 0.622554i | ||||
\(599\) | − | 3.68287e27i | − | 0.619324i | −0.950847 | − | 0.309662i | \(-0.899784\pi\) | ||
0.950847 | − | 0.309662i | \(-0.100216\pi\) | |||||||
\(600\) | −1.86402e27 | − | 3.38958e27i | −0.308274 | − | 0.560574i | ||||
\(601\) | 8.99774e27 | 1.46349 | 0.731743 | − | 0.681581i | \(-0.238707\pi\) | ||||
0.731743 | + | 0.681581i | \(0.238707\pi\) | |||||||
\(602\) | 9.63001e26 | − | 2.58978e27i | 0.154050 | − | 0.414284i | ||||
\(603\) | 3.05072e27i | 0.479987i | ||||||||
\(604\) | −2.99329e27 | + | 3.46837e27i | −0.463211 | + | 0.536730i | ||||
\(605\) | −6.83893e26 | −0.104096 | ||||||||
\(606\) | −5.42720e27 | − | 2.01809e27i | −0.812550 | − | 0.302144i | ||||
\(607\) | − | 7.57570e27i | − | 1.11567i | −0.829952 | − | 0.557835i | \(-0.811632\pi\) | ||
0.829952 | − | 0.557835i | \(-0.188368\pi\) | |||||||
\(608\) | 2.38272e27 | − | 1.12219e28i | 0.345174 | − | 1.62567i | ||||
\(609\) | 1.45245e27 | 0.206980 | ||||||||
\(610\) | −1.51330e27 | + | 4.06969e27i | −0.212142 | + | 0.570509i | ||||
\(611\) | 1.88318e28i | 2.59705i | ||||||||
\(612\) | −1.43078e27 | − | 1.23480e27i | −0.194115 | − | 0.167526i | ||||
\(613\) | −2.13003e25 | −0.00284302 | −0.00142151 | − | 0.999999i | \(-0.500452\pi\) | ||||
−0.00142151 | + | 0.999999i | \(0.500452\pi\) | |||||||
\(614\) | −3.29647e27 | − | 1.22578e27i | −0.432878 | − | 0.160964i | ||||
\(615\) | − | 4.54495e25i | − | 0.00587189i | ||||||
\(616\) | −2.36825e27 | + | 1.30237e27i | −0.301038 | + | 0.165549i | ||||
\(617\) | −1.43698e28 | −1.79721 | −0.898605 | − | 0.438759i | \(-0.855418\pi\) | ||||
−0.898605 | + | 0.438759i | \(0.855418\pi\) | |||||||
\(618\) | 9.02943e26 | − | 2.42827e27i | 0.111116 | − | 0.298822i | ||||
\(619\) | 1.69027e25i | 0.00204667i | 0.999999 | + | 0.00102334i | \(0.000325738\pi\) | ||||
−0.999999 | + | 0.00102334i | \(0.999674\pi\) | |||||||
\(620\) | 1.52793e27 | − | 1.77044e27i | 0.182048 | − | 0.210942i | ||||
\(621\) | −9.09664e27 | −1.06651 | ||||||||
\(622\) | 9.51073e27 | + | 3.53653e27i | 1.09726 | + | 0.408013i | ||||
\(623\) | − | 3.34260e27i | − | 0.379493i | ||||||
\(624\) | −1.28307e28 | + | 1.89697e27i | −1.43352 | + | 0.211941i | ||||
\(625\) | 4.10056e27 | 0.450862 | ||||||||
\(626\) | −1.51259e27 | + | 4.06778e27i | −0.163673 | + | 0.440163i | ||||
\(627\) | − | 1.08570e28i | − | 1.15620i | ||||||
\(628\) | 5.75665e27 | + | 4.96812e27i | 0.603355 | + | 0.520710i | ||||
\(629\) | 1.16270e27 | 0.119939 | ||||||||
\(630\) | 5.89201e26 | + | 2.19092e26i | 0.0598216 | + | 0.0222445i | ||||
\(631\) | 1.22788e28i | 1.22706i | 0.789673 | + | 0.613528i | \(0.210250\pi\) | ||||
−0.789673 | + | 0.613528i | \(0.789750\pi\) | |||||||
\(632\) | 7.48506e27 | + | 1.36110e28i | 0.736249 | + | 1.33881i | ||||
\(633\) | 1.15708e28 | 1.12028 | ||||||||
\(634\) | 4.58491e26 | − | 1.23301e27i | 0.0436957 | − | 0.117510i | ||||
\(635\) | − | 2.29568e27i | − | 0.215365i | ||||||
\(636\) | 4.48106e27 | − | 5.19228e27i | 0.413818 | − | 0.479498i | ||||
\(637\) | −1.69446e28 | −1.54041 | ||||||||
\(638\) | −6.06577e27 | − | 2.25554e27i | −0.542849 | − | 0.201857i | ||||
\(639\) | − | 8.49021e26i | − | 0.0748014i | ||||||
\(640\) | 3.08590e27 | + | 4.06293e27i | 0.267659 | + | 0.352403i | ||||
\(641\) | 1.84865e28 | 1.57861 | 0.789306 | − | 0.614000i | \(-0.210441\pi\) | ||||
0.789306 | + | 0.614000i | \(0.210441\pi\) | |||||||
\(642\) | −6.17168e27 | + | 1.65974e28i | −0.518863 | + | 1.39537i | ||||
\(643\) | − | 1.89929e28i | − | 1.57211i | −0.618159 | − | 0.786053i | \(-0.712121\pi\) | ||
0.618159 | − | 0.786053i | \(-0.287879\pi\) | |||||||
\(644\) | 3.57861e27 | + | 3.08842e27i | 0.291645 | + | 0.251697i | ||||
\(645\) | −4.93611e27 | −0.396084 | ||||||||
\(646\) | −1.37700e28 | − | 5.12032e27i | −1.08795 | − | 0.404550i | ||||
\(647\) | − | 1.85495e28i | − | 1.44308i | −0.692375 | − | 0.721538i | \(-0.743436\pi\) | ||
0.692375 | − | 0.721538i | \(-0.256564\pi\) | |||||||
\(648\) | 5.69758e27 | − | 3.13325e27i | 0.436456 | − | 0.240019i | ||||
\(649\) | −4.36016e27 | −0.328894 | ||||||||
\(650\) | 6.87324e27 | − | 1.84841e28i | 0.510538 | − | 1.37298i | ||||
\(651\) | 2.69030e27i | 0.196784i | ||||||||
\(652\) | 4.93614e27 | − | 5.71959e27i | 0.355559 | − | 0.411992i | ||||
\(653\) | 7.10570e26 | 0.0504052 | 0.0252026 | − | 0.999682i | \(-0.491977\pi\) | ||||
0.0252026 | + | 0.999682i | \(0.491977\pi\) | |||||||
\(654\) | 5.99490e27 | + | 2.22918e27i | 0.418798 | + | 0.155729i | ||||
\(655\) | − | 2.76788e27i | − | 0.190430i | ||||||
\(656\) | −3.60026e25 | − | 2.43513e26i | −0.00243947 | − | 0.0165000i | ||||
\(657\) | −8.42414e26 | −0.0562176 | ||||||||
\(658\) | −2.97011e27 | + | 7.98747e27i | −0.195215 | + | 0.524989i | ||||
\(659\) | − | 7.25237e26i | − | 0.0469490i | −0.999724 | − | 0.0234745i | \(-0.992527\pi\) | ||
0.999724 | − | 0.0234745i | \(-0.00747284\pi\) | |||||||
\(660\) | 3.65535e27 | + | 3.15465e27i | 0.233072 | + | 0.201146i | ||||
\(661\) | −1.64602e27 | −0.103376 | −0.0516880 | − | 0.998663i | \(-0.516460\pi\) | ||||
−0.0516880 | + | 0.998663i | \(0.516460\pi\) | |||||||
\(662\) | −6.21895e27 | − | 2.31250e27i | −0.384713 | − | 0.143054i | ||||
\(663\) | 1.66095e28i | 1.01209i | ||||||||
\(664\) | 8.64921e27 | + | 1.57279e28i | 0.519153 | + | 0.944041i | ||||
\(665\) | 4.88646e27 | 0.288920 | ||||||||
\(666\) | 3.77253e26 | − | 1.01454e27i | 0.0219731 | − | 0.0590917i | ||||
\(667\) | 1.13186e28i | 0.649434i | ||||||||
\(668\) | 1.52734e28 | − | 1.76976e28i | 0.863320 | − | 1.00034i | ||||
\(669\) | −1.78919e26 | −0.00996313 | ||||||||
\(670\) | −9.88514e27 | − | 3.67576e27i | −0.542294 | − | 0.201650i | ||||
\(671\) | 2.22555e28i | 1.20285i | ||||||||
\(672\) | −5.74128e27 | − | 1.21903e27i | −0.305715 | − | 0.0649115i | ||||
\(673\) | 4.79262e27 | 0.251433 | 0.125716 | − | 0.992066i | \(-0.459877\pi\) | ||||
0.125716 | + | 0.992066i | \(0.459877\pi\) | |||||||
\(674\) | −5.59057e27 | + | 1.50346e28i | −0.288973 | + | 0.777129i | ||||
\(675\) | 1.71733e28i | 0.874612i | ||||||||
\(676\) | −3.49709e28 | − | 3.01807e28i | −1.75485 | − | 1.51447i | ||||
\(677\) | −9.21148e26 | −0.0455452 | −0.0227726 | − | 0.999741i | \(-0.507249\pi\) | ||||
−0.0227726 | + | 0.999741i | \(0.507249\pi\) | |||||||
\(678\) | 5.39879e27 | + | 2.00752e27i | 0.263026 | + | 0.0978055i | ||||
\(679\) | 3.64435e27i | 0.174953i | ||||||||
\(680\) | 5.72500e27 | − | 3.14833e27i | 0.270823 | − | 0.148933i | ||||
\(681\) | −2.06770e28 | −0.963863 | ||||||||
\(682\) | 4.17781e27 | − | 1.12353e28i | 0.191913 | − | 0.516109i | ||||
\(683\) | − | 3.26558e28i | − | 1.47827i | −0.673558 | − | 0.739135i | \(-0.735235\pi\) | ||
0.673558 | − | 0.739135i | \(-0.264765\pi\) | |||||||
\(684\) | −8.93569e27 | + | 1.03539e28i | −0.398627 | + | 0.461896i | ||||
\(685\) | 4.65669e26 | 0.0204726 | ||||||||
\(686\) | −1.56857e28 | − | 5.83266e27i | −0.679613 | − | 0.252712i | ||||
\(687\) | 6.93795e27i | 0.296254i | ||||||||
\(688\) | −2.64471e28 | + | 3.91012e27i | −1.11300 | + | 0.164553i | ||||
\(689\) | 3.49648e28 | 1.45024 | ||||||||
\(690\) | 2.94326e27 | − | 7.91525e27i | 0.120320 | − | 0.323574i | ||||
\(691\) | 4.19194e28i | 1.68902i | 0.535541 | + | 0.844509i | \(0.320108\pi\) | ||||
−0.535541 | + | 0.844509i | \(0.679892\pi\) | |||||||
\(692\) | 2.30098e28 | + | 1.98580e28i | 0.913803 | + | 0.788634i | ||||
\(693\) | 3.22210e27 | 0.126127 | ||||||||
\(694\) | 7.11737e27 | + | 2.64657e27i | 0.274616 | + | 0.102115i | ||||
\(695\) | − | 8.58170e27i | − | 0.326381i | ||||||
\(696\) | −6.77203e27 | − | 1.23144e28i | −0.253879 | − | 0.461659i | ||||
\(697\) | −3.15232e26 | −0.0116494 | ||||||||
\(698\) | 1.93361e27 | − | 5.20001e27i | 0.0704391 | − | 0.189430i | ||||
\(699\) | − | 4.32967e28i | − | 1.55483i | ||||||
\(700\) | 5.83054e27 | − | 6.75595e27i | 0.206409 | − | 0.239170i | ||||
\(701\) | −3.11179e28 | −1.08600 | −0.543000 | − | 0.839732i | \(-0.682712\pi\) | ||||
−0.543000 | + | 0.839732i | \(0.682712\pi\) | |||||||
\(702\) | 5.39702e28 | + | 2.00686e28i | 1.85688 | + | 0.690473i | ||||
\(703\) | − | 8.41395e27i | − | 0.285395i | ||||||
\(704\) | 2.20839e28 | + | 1.40067e28i | 0.738497 | + | 0.468392i | ||||
\(705\) | 1.52241e28 | 0.501926 | ||||||||
\(706\) | 1.39568e28 | − | 3.75336e28i | 0.453667 | − | 1.22004i | ||||
\(707\) | − | 1.33579e28i | − | 0.428099i | ||||||
\(708\) | −7.16819e27 | − | 6.18632e27i | −0.226504 | − | 0.195479i | ||||
\(709\) | 3.43808e28 | 1.07116 | 0.535580 | − | 0.844485i | \(-0.320093\pi\) | ||||
0.535580 | + | 0.844485i | \(0.320093\pi\) | |||||||
\(710\) | 2.75105e27 | + | 1.02297e27i | 0.0845114 | + | 0.0314253i | ||||
\(711\) | − | 1.85183e28i | − | 0.560926i | ||||||
\(712\) | −2.83398e28 | + | 1.55848e28i | −0.846441 | + | 0.465480i | ||||
\(713\) | −2.09649e28 | −0.617443 | ||||||||
\(714\) | −2.61962e27 | + | 7.04488e27i | −0.0760774 | + | 0.204593i | ||||
\(715\) | 2.46151e28i | 0.704923i | ||||||||
\(716\) | −2.28978e28 | + | 2.65320e28i | −0.646640 | + | 0.749273i | ||||
\(717\) | −4.93423e28 | −1.37413 | ||||||||
\(718\) | 2.94525e28 | + | 1.09518e28i | 0.808869 | + | 0.300775i | ||||
\(719\) | − | 8.43616e27i | − | 0.228484i | −0.993453 | − | 0.114242i | \(-0.963556\pi\) | ||
0.993453 | − | 0.114242i | \(-0.0364439\pi\) | |||||||
\(720\) | −8.89591e26 | − | 6.01698e27i | −0.0237610 | − | 0.160714i | ||||
\(721\) | 5.97666e27 | 0.157437 | ||||||||
\(722\) | −2.36378e28 | + | 6.35686e28i | −0.614094 | + | 1.65147i | ||||
\(723\) | − | 3.11383e28i | − | 0.797832i | ||||||
\(724\) | 1.41313e28 | + | 1.21956e28i | 0.357105 | + | 0.308190i | ||||
\(725\) | 2.13681e28 | 0.532581 | ||||||||
\(726\) | −7.13509e27 | − | 2.65316e27i | −0.175401 | − | 0.0652224i | ||||
\(727\) | − | 4.05297e28i | − | 0.982718i | −0.870957 | − | 0.491359i | \(-0.836500\pi\) | ||
0.870957 | − | 0.491359i | \(-0.163500\pi\) | |||||||
\(728\) | −1.44183e28 | − | 2.62185e28i | −0.344825 | − | 0.627039i | ||||
\(729\) | −4.44295e28 | −1.04808 | ||||||||
\(730\) | 1.01501e27 | − | 2.72964e27i | 0.0236179 | − | 0.0635152i | ||||
\(731\) | 3.42362e28i | 0.785800i | ||||||||
\(732\) | −3.15767e28 | + | 3.65884e28i | −0.714916 | + | 0.828386i | ||||
\(733\) | 1.18252e28 | 0.264101 | 0.132050 | − | 0.991243i | \(-0.457844\pi\) | ||||
0.132050 | + | 0.991243i | \(0.457844\pi\) | |||||||
\(734\) | −3.10619e28 | − | 1.15503e28i | −0.684333 | − | 0.254467i | ||||
\(735\) | 1.36984e28i | 0.297713i | ||||||||
\(736\) | 9.49961e27 | − | 4.47405e28i | 0.203670 | − | 0.959229i | ||||
\(737\) | −5.40578e28 | −1.14336 | ||||||||
\(738\) | −1.02281e26 | + | 2.75062e26i | −0.00213418 | + | 0.00573941i | ||||
\(739\) | 5.26424e28i | 1.08366i | 0.840490 | + | 0.541828i | \(0.182267\pi\) | ||||
−0.840490 | + | 0.541828i | \(0.817733\pi\) | |||||||
\(740\) | 2.83283e27 | + | 2.44480e27i | 0.0575312 | + | 0.0496508i | ||||
\(741\) | 1.20195e29 | 2.40827 | ||||||||
\(742\) | 1.48303e28 | + | 5.51459e27i | 0.293164 | + | 0.109012i | ||||
\(743\) | 1.23546e28i | 0.240957i | 0.992716 | + | 0.120478i | \(0.0384428\pi\) | ||||
−0.992716 | + | 0.120478i | \(0.961557\pi\) | |||||||
\(744\) | 2.28094e28 | − | 1.25435e28i | 0.438918 | − | 0.241373i | ||||
\(745\) | −1.85967e28 | −0.353080 | ||||||||
\(746\) | −2.29394e27 | + | 6.16904e27i | −0.0429728 | + | 0.115566i | ||||
\(747\) | − | 2.13985e28i | − | 0.395528i | ||||||
\(748\) | 2.18803e28 | − | 2.53530e28i | 0.399058 | − | 0.462396i | ||||
\(749\) | −4.08509e28 | −0.735162 | ||||||||
\(750\) | −3.35248e28 | − | 1.24661e28i | −0.595324 | − | 0.221369i | ||||
\(751\) | 6.50823e28i | 1.14042i | 0.821500 | + | 0.570208i | \(0.193138\pi\) | ||||
−0.821500 | + | 0.570208i | \(0.806862\pi\) | |||||||
\(752\) | 8.15688e28 | − | 1.20597e28i | 1.41041 | − | 0.208525i | ||||
\(753\) | 3.33807e28 | 0.569567 | ||||||||
\(754\) | 2.49707e28 | − | 6.71531e28i | 0.420452 | − | 1.13071i | ||||
\(755\) | 1.88816e28i | 0.313739i | ||||||||
\(756\) | 1.97262e28 | + | 1.70241e28i | 0.323463 | + | 0.279156i | ||||
\(757\) | 8.59189e28 | 1.39037 | 0.695184 | − | 0.718832i | \(-0.255323\pi\) | ||||
0.695184 | + | 0.718832i | \(0.255323\pi\) | |||||||
\(758\) | −7.30301e28 | − | 2.71560e28i | −1.16630 | − | 0.433685i | ||||
\(759\) | − | 4.32853e28i | − | 0.682217i | ||||||
\(760\) | −2.27830e28 | − | 4.14292e28i | −0.354385 | − | 0.644423i | ||||
\(761\) | −5.28034e28 | −0.810616 | −0.405308 | − | 0.914180i | \(-0.632836\pi\) | ||||
−0.405308 | + | 0.914180i | \(0.632836\pi\) | |||||||
\(762\) | 8.90608e27 | − | 2.39509e28i | 0.134939 | − | 0.362888i | ||||
\(763\) | 1.47552e28i | 0.220647i | ||||||||
\(764\) | −5.13915e27 | + | 5.95482e27i | −0.0758504 | + | 0.0878891i | ||||
\(765\) | −7.78908e27 | −0.113468 | ||||||||
\(766\) | −4.27136e28 | − | 1.58829e28i | −0.614156 | − | 0.228372i | ||||
\(767\) | − | 4.82706e28i | − | 0.685061i | ||||||
\(768\) | 1.64332e28 | + | 5.43604e28i | 0.230203 | + | 0.761502i | ||||
\(769\) | −7.68587e26 | −0.0106275 | −0.00531373 | − | 0.999986i | \(-0.501691\pi\) | ||||
−0.00531373 | + | 0.999986i | \(0.501691\pi\) | |||||||
\(770\) | −3.88225e27 | + | 1.04405e28i | −0.0529879 | + | 0.142499i | ||||
\(771\) | 8.18116e27i | 0.110223i | ||||||||
\(772\) | −5.09902e28 | − | 4.40057e28i | −0.678131 | − | 0.585243i | ||||
\(773\) | 1.94609e28 | 0.255486 | 0.127743 | − | 0.991807i | \(-0.459227\pi\) | ||||
0.127743 | + | 0.991807i | \(0.459227\pi\) | |||||||
\(774\) | 2.98735e28 | + | 1.11084e28i | 0.387148 | + | 0.143960i | ||||
\(775\) | 3.95790e28i | 0.506346i | ||||||||
\(776\) | 3.08981e28 | − | 1.69917e28i | 0.390225 | − | 0.214595i | ||||
\(777\) | −4.30468e27 | −0.0536699 | ||||||||
\(778\) | −3.41617e28 | + | 9.18703e28i | −0.420478 | + | 1.13078i | ||||
\(779\) | 2.28119e27i | 0.0277196i | ||||||||
\(780\) | −3.49246e28 | + | 4.04677e28i | −0.418972 | + | 0.485470i | ||||
\(781\) | 1.50444e28 | 0.178182 | ||||||||
\(782\) | −5.48991e28 | − | 2.04141e28i | −0.641945 | − | 0.238705i | ||||
\(783\) | 6.23910e28i | 0.720285i | ||||||||
\(784\) | 1.08511e28 | + | 7.33946e28i | 0.123684 | + | 0.836572i | ||||
\(785\) | 3.13388e28 | 0.352684 | ||||||||
\(786\) | 1.07380e28 | − | 2.88775e28i | 0.119316 | − | 0.320873i | ||||
\(787\) | − | 1.09776e29i | − | 1.20437i | −0.798356 | − | 0.602186i | \(-0.794297\pi\) | ||
0.798356 | − | 0.602186i | \(-0.205703\pi\) | |||||||
\(788\) | 1.19897e29 | + | 1.03474e29i | 1.29881 | + | 1.12091i | ||||
\(789\) | −5.30473e28 | −0.567405 | ||||||||
\(790\) | 6.00043e28 | + | 2.23124e28i | 0.633741 | + | 0.235654i | ||||
\(791\) | 1.32880e28i | 0.138578i | ||||||||
\(792\) | −1.50230e28 | − | 2.73182e28i | −0.154705 | − | 0.281320i | ||||
\(793\) | −2.46386e29 | −2.50544 | ||||||||
\(794\) | −3.94031e28 | + | 1.05966e29i | −0.395663 | + | 1.06405i | ||||
\(795\) | − | 2.82664e28i | − | 0.280285i | ||||||
\(796\) | 6.56037e28 | − | 7.60161e28i | 0.642389 | − | 0.744347i | ||||
\(797\) | 4.82089e28 | 0.466170 | 0.233085 | − | 0.972456i | \(-0.425118\pi\) | ||||
0.233085 | + | 0.972456i | \(0.425118\pi\) | |||||||
\(798\) | 5.09807e28 | + | 1.89570e28i | 0.486829 | + | 0.181026i | ||||
\(799\) | − | 1.05592e29i | − | 0.995782i | ||||||
\(800\) | −8.44642e28 | − | 1.79340e28i | −0.786635 | − | 0.167024i | ||||
\(801\) | 3.85574e28 | 0.354636 | ||||||||
\(802\) | 7.76287e26 | − | 2.08765e27i | 0.00705145 | − | 0.0189633i | ||||
\(803\) | − | 1.49273e28i | − | 0.133914i | ||||||
\(804\) | −8.88721e28 | − | 7.66987e28i | −0.787417 | − | 0.679559i | ||||
\(805\) | 1.94817e28 | 0.170478 | ||||||||
\(806\) | 1.24384e29 | + | 4.62518e28i | 1.07502 | + | 0.399741i | ||||
\(807\) | − | 3.02807e28i | − | 0.258483i | ||||||
\(808\) | −1.13253e29 | + | 6.22810e28i | −0.954854 | + | 0.525100i | ||||
\(809\) | −5.78152e28 | −0.481456 | −0.240728 | − | 0.970593i | \(-0.577386\pi\) | ||||
−0.240728 | + | 0.970593i | \(0.577386\pi\) | |||||||
\(810\) | 9.33998e27 | − | 2.51178e28i | 0.0768238 | − | 0.206601i | ||||
\(811\) | − | 7.59855e28i | − | 0.617337i | −0.951170 | − | 0.308668i | \(-0.900117\pi\) | ||
0.951170 | − | 0.308668i | \(-0.0998833\pi\) | |||||||
\(812\) | 2.11825e28 | − | 2.45445e28i | 0.169988 | − | 0.196967i | ||||
\(813\) | −7.06681e27 | −0.0560168 | ||||||||
\(814\) | 1.79773e28 | + | 6.68481e27i | 0.140761 | + | 0.0523414i | ||||
\(815\) | − | 3.11371e28i | − | 0.240825i | ||||||
\(816\) | 7.19431e28 | − | 1.06365e28i | 0.549652 | − | 0.0812642i | ||||
\(817\) | 2.47752e29 | 1.86981 | ||||||||
\(818\) | 5.60269e28 | − | 1.50672e29i | 0.417699 | − | 1.12331i | ||||
\(819\) | 3.56713e28i | 0.262712i | ||||||||
\(820\) | −7.68037e26 | − | 6.62834e26i | −0.00558784 | − | 0.00482243i | ||||
\(821\) | 2.52919e29 | 1.81782 | 0.908908 | − | 0.416997i | \(-0.136917\pi\) | ||||
0.908908 | + | 0.416997i | \(0.136917\pi\) | |||||||
\(822\) | 4.85835e27 | + | 1.80656e27i | 0.0344962 | + | 0.0128273i | ||||
\(823\) | 2.11620e29i | 1.48443i | 0.670163 | + | 0.742214i | \(0.266224\pi\) | ||||
−0.670163 | + | 0.742214i | \(0.733776\pi\) | |||||||
\(824\) | −2.78661e28 | − | 5.06724e28i | −0.193110 | − | 0.351155i | ||||
\(825\) | −8.17171e28 | −0.559466 | ||||||||
\(826\) | 7.61314e27 | − | 2.04739e28i | 0.0514948 | − | 0.138484i | ||||
\(827\) | 5.82890e28i | 0.389521i | 0.980851 | + | 0.194761i | \(0.0623930\pi\) | ||||
−0.980851 | + | 0.194761i | \(0.937607\pi\) | |||||||
\(828\) | −3.56254e28 | + | 4.12798e28i | −0.235211 | + | 0.272542i | ||||
\(829\) | −1.85843e29 | −1.21228 | −0.606138 | − | 0.795359i | \(-0.707282\pi\) | ||||
−0.606138 | + | 0.795359i | \(0.707282\pi\) | |||||||
\(830\) | 6.93367e28 | + | 2.57826e28i | 0.446871 | + | 0.166168i | ||||
\(831\) | 6.12170e28i | 0.389818i | ||||||||
\(832\) | −1.55066e29 | + | 2.44487e29i | −0.975623 | + | 1.53823i | ||||
\(833\) | 9.50105e28 | 0.590638 | ||||||||
\(834\) | 3.32927e28 | − | 8.95333e28i | 0.204498 | − | 0.549951i | ||||
\(835\) | − | 9.63444e28i | − | 0.584739i | ||||||
\(836\) | −1.83469e29 | − | 1.58338e29i | −1.10027 | − | 0.949558i | ||||
\(837\) | −1.15564e29 | −0.684804 | ||||||||
\(838\) | −8.46010e28 | − | 3.14586e28i | −0.495377 | − | 0.184204i | ||||
\(839\) | 1.00427e29i | 0.581071i | 0.956864 | + | 0.290536i | \(0.0938335\pi\) | ||||
−0.956864 | + | 0.290536i | \(0.906167\pi\) | |||||||
\(840\) | −2.11957e28 | + | 1.16561e28i | −0.121187 | + | 0.0666437i | ||||
\(841\) | −9.93638e28 | −0.561394 | ||||||||
\(842\) | 3.26276e28 | − | 8.77448e28i | 0.182165 | − | 0.489892i | ||||
\(843\) | 2.76408e29i | 1.52502i | ||||||||
\(844\) | 1.68748e29 | − | 1.95532e29i | 0.920058 | − | 1.06609i | ||||
\(845\) | −1.90379e29 | −1.02577 | ||||||||
\(846\) | −9.21367e28 | − | 3.42607e28i | −0.490602 | − | 0.182429i | ||||
\(847\) | − | 1.75615e28i | − | 0.0924117i | ||||||
\(848\) | −2.23911e28 | − | 1.51448e29i | −0.116444 | − | 0.787600i | ||||
\(849\) | 5.34610e28 | 0.274764 | ||||||||
\(850\) | −3.85391e28 | + | 1.03642e29i | −0.195755 | + | 0.526440i | ||||
\(851\) | − | 3.35453e28i | − | 0.168398i | ||||||
\(852\) | 2.47333e28 | + | 2.13454e28i | 0.122712 | + | 0.105903i | ||||
\(853\) | 7.73820e28 | 0.379446 | 0.189723 | − | 0.981838i | \(-0.439241\pi\) | ||||
0.189723 | + | 0.981838i | \(0.439241\pi\) | |||||||
\(854\) | −1.04504e29 | − | 3.88596e28i | −0.506472 | − | 0.188330i | ||||
\(855\) | 5.63661e28i | 0.269996i | ||||||||
\(856\) | 1.90466e29 | + | 3.46349e29i | 0.901739 | + | 1.63974i | ||||
\(857\) | 8.40785e28 | 0.393439 | 0.196719 | − | 0.980460i | \(-0.436971\pi\) | ||||
0.196719 | + | 0.980460i | \(0.436971\pi\) | |||||||
\(858\) | −9.54943e28 | + | 2.56811e29i | −0.441677 | + | 1.18779i | ||||
\(859\) | 1.74941e28i | 0.0799759i | 0.999200 | + | 0.0399880i | \(0.0127320\pi\) | ||||
−0.999200 | + | 0.0399880i | \(0.987268\pi\) | |||||||
\(860\) | −7.19881e28 | + | 8.34139e28i | −0.325294 | + | 0.376924i | ||||
\(861\) | 1.16708e27 | 0.00521279 | ||||||||
\(862\) | 1.99204e29 | + | 7.40735e28i | 0.879480 | + | 0.327032i | ||||
\(863\) | − | 2.78339e29i | − | 1.21469i | −0.794437 | − | 0.607346i | \(-0.792234\pi\) | ||
0.794437 | − | 0.607346i | \(-0.207766\pi\) | |||||||
\(864\) | 5.23642e28 | − | 2.46621e29i | 0.225890 | − | 1.06388i | ||||
\(865\) | 1.25264e29 | 0.534153 | ||||||||
\(866\) | 8.67092e28 | − | 2.33185e29i | 0.365499 | − | 0.982930i | ||||
\(867\) | 9.77883e28i | 0.407470i | ||||||||
\(868\) | 4.54626e28 | + | 3.92353e28i | 0.187265 | + | 0.161614i | ||||
\(869\) | 3.28139e29 | 1.33617 | ||||||||
\(870\) | −5.42882e28 | − | 2.01869e28i | −0.218531 | − | 0.0812600i | ||||
\(871\) | − | 5.98465e29i | − | 2.38154i | ||||||
\(872\) | 1.25100e29 | − | 6.87956e28i | 0.492143 | − | 0.270642i | ||||
\(873\) | −4.20381e28 | −0.163494 | ||||||||
\(874\) | −1.47727e29 | + | 3.97280e29i | −0.567998 | + | 1.52751i | ||||
\(875\) | − | 8.25141e28i | − | 0.313652i | ||||||
\(876\) | 2.11793e28 | − | 2.45408e28i | 0.0795921 | − | 0.0922248i | ||||
\(877\) | −3.40612e29 | −1.26550 | −0.632752 | − | 0.774355i | \(-0.718075\pi\) | ||||
−0.632752 | + | 0.774355i | \(0.718075\pi\) | |||||||
\(878\) | −4.94358e28 | − | 1.83825e28i | −0.181592 | − | 0.0675243i | ||||
\(879\) | − | 1.91249e29i | − | 0.694562i | ||||||
\(880\) | 1.06619e29 | − | 1.57633e28i | 0.382832 | − | 0.0566004i | ||||
\(881\) | −2.52780e28 | −0.0897394 | −0.0448697 | − | 0.998993i | \(-0.514287\pi\) | ||||
−0.0448697 | + | 0.998993i | \(0.514287\pi\) | |||||||
\(882\) | 3.08273e28 | − | 8.29034e28i | 0.108206 | − | 0.290996i | ||||
\(883\) | − | 8.39810e28i | − | 0.291457i | −0.989325 | − | 0.145728i | \(-0.953447\pi\) | ||
0.989325 | − | 0.145728i | \(-0.0465526\pi\) | |||||||
\(884\) | 2.80679e29 | + | 2.42232e29i | 0.963135 | + | 0.831208i | ||||
\(885\) | −3.90231e28 | −0.132400 | ||||||||
\(886\) | −1.19038e29 | − | 4.42637e28i | −0.399344 | − | 0.148495i | ||||
\(887\) | 4.81109e29i | 1.59591i | 0.602720 | + | 0.797953i | \(0.294084\pi\) | ||||
−0.602720 | + | 0.797953i | \(0.705916\pi\) | |||||||
\(888\) | 2.00705e28 | + | 3.64967e28i | 0.0658306 | + | 0.119708i | ||||
\(889\) | 5.89501e28 | 0.191191 | ||||||||
\(890\) | −4.64571e28 | + | 1.24936e29i | −0.148988 | + | 0.400671i | ||||
\(891\) | − | 1.37359e29i | − | 0.435593i | ||||||
\(892\) | −2.60935e27 | + | 3.02350e27i | −0.00818247 | + | 0.00948116i | ||||
\(893\) | −7.64124e29 | −2.36946 | ||||||||
\(894\) | −1.94020e29 | − | 7.21459e28i | −0.594939 | − | 0.221226i | ||||
\(895\) | 1.44439e29i | 0.437978i | ||||||||
\(896\) | −1.04331e29 | + | 7.92419e28i | −0.312847 | + | 0.237616i | ||||
\(897\) | 4.79204e29 | 1.42101 | ||||||||
\(898\) | 8.99205e28 | − | 2.41821e29i | 0.263691 | − | 0.709139i | ||||
\(899\) | 1.43791e29i | 0.417000i | ||||||||
\(900\) | 7.79309e28 | + | 6.72562e28i | 0.223504 | + | 0.192889i | ||||
\(901\) | −1.96052e29 | −0.556063 | ||||||||
\(902\) | −4.87401e27 | − | 1.81239e27i | −0.0136717 | − | 0.00508376i | ||||
\(903\) | − | 1.26753e29i | − | 0.351626i | ||||||
\(904\) | 1.12660e29 | − | 6.19549e28i | 0.309091 | − | 0.169977i | ||||
\(905\) | 7.69299e28 | 0.208742 | ||||||||
\(906\) | −7.32510e28 | + | 1.96992e29i | −0.196576 | + | 0.528649i | ||||
\(907\) | 4.31861e28i | 0.114623i | 0.998356 | + | 0.0573115i | \(0.0182528\pi\) | ||||
−0.998356 | + | 0.0573115i | \(0.981747\pi\) | |||||||
\(908\) | −3.01552e29 | + | 3.49414e29i | −0.791597 | + | 0.917237i | ||||
\(909\) | 1.54085e29 | 0.400058 | ||||||||
\(910\) | −1.15585e29 | − | 4.29797e28i | −0.296815 | − | 0.110370i | ||||
\(911\) | 2.79697e29i | 0.710402i | 0.934790 | + | 0.355201i | \(0.115588\pi\) | ||||
−0.934790 | + | 0.355201i | \(0.884412\pi\) | |||||||
\(912\) | −7.69719e28 | − | 5.20620e29i | −0.193368 | − | 1.30789i | ||||
\(913\) | 3.79174e29 | 0.942174 | ||||||||
\(914\) | 9.38987e27 | − | 2.52520e28i | 0.0230780 | − | 0.0620631i | ||||
\(915\) | 1.99185e29i | 0.484223i | ||||||||
\(916\) | 1.17242e29 | + | 1.01183e29i | 0.281922 | + | 0.243306i | ||||
\(917\) | 7.10757e28 | 0.169055 | ||||||||
\(918\) | −3.02618e29 | − | 1.12527e29i | −0.711980 | − | 0.264747i | ||||
\(919\) | 3.42266e29i | 0.796541i | 0.917268 | + | 0.398270i | \(0.130389\pi\) | ||||
−0.917268 | + | 0.398270i | \(0.869611\pi\) | |||||||
\(920\) | −9.08330e28 | − | 1.65173e29i | −0.209105 | − | 0.380243i | ||||
\(921\) | −1.61341e29 | −0.367408 | ||||||||
\(922\) | 1.98253e29 | − | 5.33157e29i | 0.446591 | − | 1.20101i | ||||
\(923\) | 1.66554e29i | 0.371140i | ||||||||
\(924\) | −8.10074e28 | + | 9.38647e28i | −0.178569 | + | 0.206910i | ||||
\(925\) | −6.33293e28 | −0.138098 | ||||||||
\(926\) | 6.36249e29 | + | 2.36587e29i | 1.37251 | + | 0.510365i | ||||
\(927\) | 6.89418e28i | 0.147124i | ||||||||
\(928\) | −3.06861e29 | − | 6.51549e28i | −0.647831 | − | 0.137552i | ||||
\(929\) | 5.60736e29 | 1.17112 | 0.585560 | − | 0.810629i | \(-0.300875\pi\) | ||||
0.585560 | + | 0.810629i | \(0.300875\pi\) | |||||||
\(930\) | 3.73911e28 | − | 1.00555e29i | 0.0772572 | − | 0.207766i | ||||
\(931\) | − | 6.87548e29i | − | 1.40542i | ||||||
\(932\) | −7.31659e29 | − | 6.31439e29i | −1.47962 | − | 1.27694i | ||||
\(933\) | 4.65489e29 | 0.931307 | ||||||||
\(934\) | 1.76670e29 | + | 6.56941e28i | 0.349698 | + | 0.130034i | ||||
\(935\) | − | 1.38020e29i | − | 0.270288i | ||||||
\(936\) | 3.02435e29 | − | 1.66317e29i | 0.585967 | − | 0.322239i | ||||
\(937\) | −5.90326e29 | −1.13161 | −0.565804 | − | 0.824540i | \(-0.691434\pi\) | ||||
−0.565804 | + | 0.824540i | \(0.691434\pi\) | |||||||
\(938\) | 9.43887e28 | − | 2.53838e29i | 0.179016 | − | 0.481424i | ||||
\(939\) | 1.99091e29i | 0.373591i | ||||||||
\(940\) | 2.22028e29 | − | 2.57267e29i | 0.412220 | − | 0.477646i | ||||
\(941\) | −5.80808e29 | −1.06693 | −0.533466 | − | 0.845822i | \(-0.679111\pi\) | ||||
−0.533466 | + | 0.845822i | \(0.679111\pi\) | |||||||
\(942\) | 3.26959e29 | + | 1.21579e29i | 0.594271 | + | 0.220978i | ||||
\(943\) | 9.09481e27i | 0.0163560i | ||||||||
\(944\) | −2.09081e29 | + | 3.09120e28i | −0.372045 | + | 0.0550056i | ||||
\(945\) | 1.07388e29 | 0.189076 | ||||||||
\(946\) | −1.96837e29 | + | 5.29350e29i | −0.342922 | + | 0.922213i | ||||
\(947\) | − | 1.14663e28i | − | 0.0197661i | −0.999951 | − | 0.00988307i | \(-0.996854\pi\) | ||
0.999951 | − | 0.00988307i | \(-0.00314593\pi\) | |||||||
\(948\) | 5.39467e29 | + | 4.65573e29i | 0.920198 | + | 0.794153i | ||||
\(949\) | 1.65258e29 | 0.278933 | ||||||||
\(950\) | 7.50014e29 | + | 2.78890e29i | 1.25266 | + | 0.465798i | ||||
\(951\) | − | 6.03480e28i | − | 0.0997372i | ||||||
\(952\) | 8.08450e28 | + | 1.47011e29i | 0.132216 | + | 0.240425i | ||||
\(953\) | 4.04399e28 | 0.0654457 | 0.0327228 | − | 0.999464i | \(-0.489582\pi\) | ||||
0.0327228 | + | 0.999464i | \(0.489582\pi\) | |||||||
\(954\) | −6.36116e28 | + | 1.71070e29i | −0.101872 | + | 0.273961i | ||||
\(955\) | 3.24177e28i | 0.0513745i | ||||||||
\(956\) | −7.19607e29 | + | 8.33821e29i | −1.12854 | + | 1.30766i | ||||
\(957\) | −2.96880e29 | −0.460747 | ||||||||
\(958\) | −5.77176e29 | − | 2.14621e29i | −0.886448 | − | 0.329623i | ||||
\(959\) | 1.19578e28i | 0.0181746i | ||||||||
\(960\) | 1.97649e29 | + | 1.25359e29i | 0.297291 | + | 0.188557i | ||||
\(961\) | 4.05453e29 | 0.603541 | ||||||||
\(962\) | −7.40064e28 | + | 1.99024e29i | −0.109023 | + | 0.293194i | ||||
\(963\) | − | 4.71221e29i | − | 0.687008i | ||||||
\(964\) | −5.26196e29 | − | 4.54120e29i | −0.759237 | − | 0.655239i | ||||
\(965\) | −2.77587e29 | −0.396393 | ||||||||
\(966\) | 2.03253e29 | + | 7.55791e28i | 0.287254 | + | 0.106815i | ||||
\(967\) | 1.79373e29i | 0.250895i | 0.992100 | + | 0.125448i | \(0.0400367\pi\) | ||||
−0.992100 | + | 0.125448i | \(0.959963\pi\) | |||||||
\(968\) | −1.48893e29 | + | 8.18801e28i | −0.206120 | + | 0.113351i | ||||
\(969\) | −6.73951e29 | −0.923402 | ||||||||
\(970\) | 5.06510e28 | − | 1.36215e29i | 0.0686863 | − | 0.184717i | ||||
\(971\) | − | 7.65855e29i | − | 1.02791i | −0.857818 | − | 0.513954i | \(-0.828180\pi\) | ||
0.857818 | − | 0.513954i | \(-0.171820\pi\) | |||||||
\(972\) | −3.40018e29 | + | 3.93985e29i | −0.451689 | + | 0.523380i | ||||
\(973\) | 2.20367e29 | 0.289747 | ||||||||
\(974\) | −2.46634e29 | − | 9.17100e28i | −0.320969 | − | 0.119351i | ||||
\(975\) | − | 9.04675e29i | − | 1.16532i | ||||||
\(976\) | 1.57783e29 | + | 1.06721e30i | 0.201170 | + | 1.36067i | ||||
\(977\) | −9.46713e29 | −1.19474 | −0.597369 | − | 0.801967i | \(-0.703787\pi\) | ||||
−0.597369 | + | 0.801967i | \(0.703787\pi\) | |||||||
\(978\) | 1.20796e29 | − | 3.24854e29i | 0.150891 | − | 0.405789i | ||||
\(979\) | 6.83225e29i | 0.844767i | ||||||||
\(980\) | 2.31486e29 | + | 1.99778e29i | 0.283311 | + | 0.244504i | ||||
\(981\) | −1.70203e29 | −0.206195 | ||||||||
\(982\) | −1.03133e29 | − | 3.83497e28i | −0.123675 | − | 0.0459883i | ||||
\(983\) | − | 1.69036e29i | − | 0.200652i | −0.994955 | − | 0.100326i | \(-0.968011\pi\) | ||
0.994955 | − | 0.100326i | \(-0.0319885\pi\) | |||||||
\(984\) | −5.44151e27 | − | 9.89498e27i | −0.00639394 | − | 0.0116269i | ||||
\(985\) | 6.52712e29 | 0.759205 | ||||||||
\(986\) | −1.40014e29 | + | 3.76536e29i | −0.161213 | + | 0.433548i | ||||
\(987\) | 3.90935e29i | 0.445587i | ||||||||
\(988\) | 1.75293e30 | − | 2.03115e30i | 1.97786 | − | 2.29178i | ||||
\(989\) | 9.87756e29 | 1.10328 | ||||||||
\(990\) | −1.20432e29 | − | 4.47824e28i | −0.133165 | − | 0.0495171i | ||||
\(991\) | 6.84335e29i | 0.749087i | 0.927209 | + | 0.374543i | \(0.122201\pi\) | ||||
−0.927209 | + | 0.374543i | \(0.877799\pi\) | |||||||
\(992\) | 1.20683e29 | − | 5.68382e29i | 0.130776 | − | 0.615919i | ||||
\(993\) | −3.04377e29 | −0.326527 | ||||||||
\(994\) | −2.62686e28 | + | 7.06435e28i | −0.0278979 | + | 0.0750254i | ||||
\(995\) | − | 4.13827e29i | − | 0.435099i | ||||||
\(996\) | 6.23370e29 | + | 5.37983e29i | 0.648862 | + | 0.559983i | ||||
\(997\) | 1.75083e30 | 1.80423 | 0.902114 | − | 0.431497i | \(-0.142015\pi\) | ||||
0.902114 | + | 0.431497i | \(0.142015\pi\) | |||||||
\(998\) | 4.38478e29 | + | 1.63047e29i | 0.447345 | + | 0.166344i | ||||
\(999\) | − | 1.84910e29i | − | 0.186770i |
(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 | 4.21.b.b.3.5 | ✓ | 8 | |
3.2 | odd | 2 | 36.21.d.b.19.4 | 8 | |||
4.3 | odd | 2 | inner | 4.21.b.b.3.6 | yes | 8 | |
8.3 | odd | 2 | 64.21.c.d.63.3 | 8 | |||
8.5 | even | 2 | 64.21.c.d.63.6 | 8 | |||
12.11 | even | 2 | 36.21.d.b.19.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.21.b.b.3.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4.21.b.b.3.6 | yes | 8 | 4.3 | odd | 2 | inner | |
36.21.d.b.19.3 | 8 | 12.11 | even | 2 | |||
36.21.d.b.19.4 | 8 | 3.2 | odd | 2 | |||
64.21.c.d.63.3 | 8 | 8.3 | odd | 2 | |||
64.21.c.d.63.6 | 8 | 8.5 | even | 2 |