Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(28.4270373191\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + 24331248 x^{3} + 727257184 x^{2} - 56397312 x - 7335224320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-6.95530\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.95530 | 0.614767 | 0.307384 | − | 0.951586i | \(-0.400547\pi\) | ||||
0.307384 | + | 0.951586i | \(0.400547\pi\) | |||||||
\(3\) | −32.1557 | −0.687595 | −0.343798 | − | 0.939044i | \(-0.611713\pi\) | ||||
−0.343798 | + | 0.939044i | \(0.611713\pi\) | |||||||
\(4\) | −79.6238 | −0.622061 | ||||||||
\(5\) | −381.581 | −1.36518 | −0.682592 | − | 0.730799i | \(-0.739148\pi\) | ||||
−0.682592 | + | 0.730799i | \(0.739148\pi\) | |||||||
\(6\) | −223.652 | −0.422711 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | −1444.09 | −0.997190 | ||||||||
\(9\) | −1153.01 | −0.527212 | ||||||||
\(10\) | −2654.01 | −0.839271 | ||||||||
\(11\) | 1248.93 | 0.282919 | 0.141460 | − | 0.989944i | \(-0.454820\pi\) | ||||
0.141460 | + | 0.989944i | \(0.454820\pi\) | |||||||
\(12\) | 2560.36 | 0.427727 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −2385.67 | −0.232360 | ||||||||
\(15\) | 12270.0 | 0.938695 | ||||||||
\(16\) | 147.808 | 0.00902148 | ||||||||
\(17\) | −12454.1 | −0.614812 | −0.307406 | − | 0.951578i | \(-0.599461\pi\) | ||||
−0.307406 | + | 0.951578i | \(0.599461\pi\) | |||||||
\(18\) | −8019.55 | −0.324113 | ||||||||
\(19\) | 7192.86 | 0.240582 | 0.120291 | − | 0.992739i | \(-0.461617\pi\) | ||||
0.120291 | + | 0.992739i | \(0.461617\pi\) | |||||||
\(20\) | 30382.9 | 0.849229 | ||||||||
\(21\) | 11029.4 | 0.259887 | ||||||||
\(22\) | 8686.66 | 0.173930 | ||||||||
\(23\) | 14380.5 | 0.246449 | 0.123225 | − | 0.992379i | \(-0.460676\pi\) | ||||
0.123225 | + | 0.992379i | \(0.460676\pi\) | |||||||
\(24\) | 46435.5 | 0.685663 | ||||||||
\(25\) | 67478.9 | 0.863730 | ||||||||
\(26\) | −15280.8 | −0.170506 | ||||||||
\(27\) | 107400. | 1.05010 | ||||||||
\(28\) | 27311.0 | 0.235117 | ||||||||
\(29\) | −13777.5 | −0.104900 | −0.0524502 | − | 0.998624i | \(-0.516703\pi\) | ||||
−0.0524502 | + | 0.998624i | \(0.516703\pi\) | |||||||
\(30\) | 85341.4 | 0.577079 | ||||||||
\(31\) | −87132.7 | −0.525309 | −0.262655 | − | 0.964890i | \(-0.584598\pi\) | ||||
−0.262655 | + | 0.964890i | \(0.584598\pi\) | |||||||
\(32\) | 185871. | 1.00274 | ||||||||
\(33\) | −40160.1 | −0.194534 | ||||||||
\(34\) | −86622.3 | −0.377966 | ||||||||
\(35\) | 130882. | 0.515991 | ||||||||
\(36\) | 91807.4 | 0.327958 | ||||||||
\(37\) | −107500. | −0.348902 | −0.174451 | − | 0.984666i | \(-0.555815\pi\) | ||||
−0.174451 | + | 0.984666i | \(0.555815\pi\) | |||||||
\(38\) | 50028.4 | 0.147902 | ||||||||
\(39\) | 70646.0 | 0.190705 | ||||||||
\(40\) | 551035. | 1.36135 | ||||||||
\(41\) | −451487. | −1.02306 | −0.511531 | − | 0.859265i | \(-0.670921\pi\) | ||||
−0.511531 | + | 0.859265i | \(0.670921\pi\) | |||||||
\(42\) | 76712.7 | 0.159770 | ||||||||
\(43\) | 145439. | 0.278960 | 0.139480 | − | 0.990225i | \(-0.455457\pi\) | ||||
0.139480 | + | 0.990225i | \(0.455457\pi\) | |||||||
\(44\) | −99444.4 | −0.175993 | ||||||||
\(45\) | 439968. | 0.719742 | ||||||||
\(46\) | 100021. | 0.151509 | ||||||||
\(47\) | 220745. | 0.310133 | 0.155067 | − | 0.987904i | \(-0.450441\pi\) | ||||
0.155067 | + | 0.987904i | \(0.450441\pi\) | |||||||
\(48\) | −4752.86 | −0.00620313 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 469336. | 0.530993 | ||||||||
\(51\) | 400471. | 0.422742 | ||||||||
\(52\) | 174934. | 0.172529 | ||||||||
\(53\) | −516722. | −0.476751 | −0.238375 | − | 0.971173i | \(-0.576615\pi\) | ||||
−0.238375 | + | 0.971173i | \(0.576615\pi\) | |||||||
\(54\) | 747001. | 0.645570 | ||||||||
\(55\) | −476567. | −0.386237 | ||||||||
\(56\) | 495321. | 0.376902 | ||||||||
\(57\) | −231291. | −0.165423 | ||||||||
\(58\) | −95826.6 | −0.0644893 | ||||||||
\(59\) | 384664. | 0.243837 | 0.121919 | − | 0.992540i | \(-0.461095\pi\) | ||||
0.121919 | + | 0.992540i | \(0.461095\pi\) | |||||||
\(60\) | −976983. | −0.583926 | ||||||||
\(61\) | −1.96831e6 | −1.11030 | −0.555148 | − | 0.831752i | \(-0.687338\pi\) | ||||
−0.555148 | + | 0.831752i | \(0.687338\pi\) | |||||||
\(62\) | −606034. | −0.322943 | ||||||||
\(63\) | 395484. | 0.199268 | ||||||||
\(64\) | 1.27387e6 | 0.607428 | ||||||||
\(65\) | 838333. | 0.378634 | ||||||||
\(66\) | −279325. | −0.119593 | ||||||||
\(67\) | −852766. | −0.346392 | −0.173196 | − | 0.984887i | \(-0.555409\pi\) | ||||
−0.173196 | + | 0.984887i | \(0.555409\pi\) | |||||||
\(68\) | 991647. | 0.382451 | ||||||||
\(69\) | −462415. | −0.169457 | ||||||||
\(70\) | 910325. | 0.317215 | ||||||||
\(71\) | 5.65372e6 | 1.87469 | 0.937346 | − | 0.348401i | \(-0.113275\pi\) | ||||
0.937346 | + | 0.348401i | \(0.113275\pi\) | |||||||
\(72\) | 1.66505e6 | 0.525731 | ||||||||
\(73\) | −1.67822e6 | −0.504917 | −0.252458 | − | 0.967608i | \(-0.581239\pi\) | ||||
−0.252458 | + | 0.967608i | \(0.581239\pi\) | |||||||
\(74\) | −747697. | −0.214494 | ||||||||
\(75\) | −2.16983e6 | −0.593897 | ||||||||
\(76\) | −572723. | −0.149657 | ||||||||
\(77\) | −428382. | −0.106933 | ||||||||
\(78\) | 491364. | 0.117239 | ||||||||
\(79\) | 3.43630e6 | 0.784145 | 0.392073 | − | 0.919934i | \(-0.371758\pi\) | ||||
0.392073 | + | 0.919934i | \(0.371758\pi\) | |||||||
\(80\) | −56400.7 | −0.0123160 | ||||||||
\(81\) | −931888. | −0.194835 | ||||||||
\(82\) | −3.14023e6 | −0.628945 | ||||||||
\(83\) | −1.39897e6 | −0.268555 | −0.134278 | − | 0.990944i | \(-0.542871\pi\) | ||||
−0.134278 | + | 0.990944i | \(0.542871\pi\) | |||||||
\(84\) | −878202. | −0.161665 | ||||||||
\(85\) | 4.75226e6 | 0.839333 | ||||||||
\(86\) | 1.01157e6 | 0.171496 | ||||||||
\(87\) | 443024. | 0.0721291 | ||||||||
\(88\) | −1.80356e6 | −0.282124 | ||||||||
\(89\) | 1.78133e6 | 0.267843 | 0.133921 | − | 0.990992i | \(-0.457243\pi\) | ||||
0.133921 | + | 0.990992i | \(0.457243\pi\) | |||||||
\(90\) | 3.06011e6 | 0.442474 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −1.14503e6 | −0.153306 | ||||||||
\(93\) | 2.80181e6 | 0.361200 | ||||||||
\(94\) | 1.53535e6 | 0.190660 | ||||||||
\(95\) | −2.74466e6 | −0.328439 | ||||||||
\(96\) | −5.97680e6 | −0.689477 | ||||||||
\(97\) | −6.05505e6 | −0.673623 | −0.336811 | − | 0.941572i | \(-0.609348\pi\) | ||||
−0.336811 | + | 0.941572i | \(0.609348\pi\) | |||||||
\(98\) | 818284. | 0.0878239 | ||||||||
\(99\) | −1.44003e6 | −0.149159 | ||||||||
\(100\) | −5.37293e6 | −0.537293 | ||||||||
\(101\) | −1.29334e7 | −1.24907 | −0.624534 | − | 0.780997i | \(-0.714711\pi\) | ||||
−0.624534 | + | 0.780997i | \(0.714711\pi\) | |||||||
\(102\) | 2.78540e6 | 0.259888 | ||||||||
\(103\) | −1.19105e7 | −1.07399 | −0.536995 | − | 0.843586i | \(-0.680440\pi\) | ||||
−0.536995 | + | 0.843586i | \(0.680440\pi\) | |||||||
\(104\) | 3.17266e6 | 0.276571 | ||||||||
\(105\) | −4.20860e6 | −0.354793 | ||||||||
\(106\) | −3.59396e6 | −0.293091 | ||||||||
\(107\) | −1.83303e7 | −1.44652 | −0.723262 | − | 0.690573i | \(-0.757358\pi\) | ||||
−0.723262 | + | 0.690573i | \(0.757358\pi\) | |||||||
\(108\) | −8.55163e6 | −0.653229 | ||||||||
\(109\) | −9.64748e6 | −0.713545 | −0.356772 | − | 0.934191i | \(-0.616123\pi\) | ||||
−0.356772 | + | 0.934191i | \(0.616123\pi\) | |||||||
\(110\) | −3.31466e6 | −0.237446 | ||||||||
\(111\) | 3.45674e6 | 0.239904 | ||||||||
\(112\) | −50698.1 | −0.00340980 | ||||||||
\(113\) | 2.31706e7 | 1.51065 | 0.755323 | − | 0.655352i | \(-0.227480\pi\) | ||||
0.755323 | + | 0.655352i | \(0.227480\pi\) | |||||||
\(114\) | −1.60870e6 | −0.101697 | ||||||||
\(115\) | −5.48733e6 | −0.336449 | ||||||||
\(116\) | 1.09702e6 | 0.0652545 | ||||||||
\(117\) | 2.53317e6 | 0.146222 | ||||||||
\(118\) | 2.67545e6 | 0.149903 | ||||||||
\(119\) | 4.27177e6 | 0.232377 | ||||||||
\(120\) | −1.77189e7 | −0.936057 | ||||||||
\(121\) | −1.79274e7 | −0.919957 | ||||||||
\(122\) | −1.36902e7 | −0.682573 | ||||||||
\(123\) | 1.45179e7 | 0.703453 | ||||||||
\(124\) | 6.93784e6 | 0.326775 | ||||||||
\(125\) | 4.06236e6 | 0.186034 | ||||||||
\(126\) | 2.75071e6 | 0.122503 | ||||||||
\(127\) | 3.14779e7 | 1.36362 | 0.681808 | − | 0.731531i | \(-0.261194\pi\) | ||||
0.681808 | + | 0.731531i | \(0.261194\pi\) | |||||||
\(128\) | −1.49314e7 | −0.629309 | ||||||||
\(129\) | −4.67670e6 | −0.191812 | ||||||||
\(130\) | 5.83085e6 | 0.232772 | ||||||||
\(131\) | −1.65637e7 | −0.643736 | −0.321868 | − | 0.946785i | \(-0.604311\pi\) | ||||
−0.321868 | + | 0.946785i | \(0.604311\pi\) | |||||||
\(132\) | 3.19770e6 | 0.121012 | ||||||||
\(133\) | −2.46715e6 | −0.0909316 | ||||||||
\(134\) | −5.93124e6 | −0.212951 | ||||||||
\(135\) | −4.09819e7 | −1.43359 | ||||||||
\(136\) | 1.79848e7 | 0.613085 | ||||||||
\(137\) | 9.39642e6 | 0.312205 | 0.156103 | − | 0.987741i | \(-0.450107\pi\) | ||||
0.156103 | + | 0.987741i | \(0.450107\pi\) | |||||||
\(138\) | −3.21624e6 | −0.104177 | ||||||||
\(139\) | 6.18591e7 | 1.95367 | 0.976837 | − | 0.213986i | \(-0.0686448\pi\) | ||||
0.976837 | + | 0.213986i | \(0.0686448\pi\) | |||||||
\(140\) | −1.04213e7 | −0.320978 | ||||||||
\(141\) | −7.09820e6 | −0.213246 | ||||||||
\(142\) | 3.93233e7 | 1.15250 | ||||||||
\(143\) | −2.74389e6 | −0.0784677 | ||||||||
\(144\) | −170425. | −0.00475624 | ||||||||
\(145\) | 5.25723e6 | 0.143208 | ||||||||
\(146\) | −1.16725e7 | −0.310406 | ||||||||
\(147\) | −3.78308e6 | −0.0982279 | ||||||||
\(148\) | 8.55959e6 | 0.217039 | ||||||||
\(149\) | 2.15148e7 | 0.532827 | 0.266413 | − | 0.963859i | \(-0.414161\pi\) | ||||
0.266413 | + | 0.963859i | \(0.414161\pi\) | |||||||
\(150\) | −1.50918e7 | −0.365108 | ||||||||
\(151\) | 3.93596e7 | 0.930318 | 0.465159 | − | 0.885227i | \(-0.345997\pi\) | ||||
0.465159 | + | 0.885227i | \(0.345997\pi\) | |||||||
\(152\) | −1.03871e7 | −0.239906 | ||||||||
\(153\) | 1.43598e7 | 0.324137 | ||||||||
\(154\) | −2.97952e6 | −0.0657392 | ||||||||
\(155\) | 3.32481e7 | 0.717144 | ||||||||
\(156\) | −5.62510e6 | −0.118630 | ||||||||
\(157\) | 6.20466e7 | 1.27959 | 0.639793 | − | 0.768547i | \(-0.279020\pi\) | ||||
0.639793 | + | 0.768547i | \(0.279020\pi\) | |||||||
\(158\) | 2.39005e7 | 0.482067 | ||||||||
\(159\) | 1.66155e7 | 0.327812 | ||||||||
\(160\) | −7.09248e7 | −1.36892 | ||||||||
\(161\) | −4.93252e6 | −0.0931490 | ||||||||
\(162\) | −6.48156e6 | −0.119778 | ||||||||
\(163\) | 5.61916e7 | 1.01628 | 0.508141 | − | 0.861274i | \(-0.330333\pi\) | ||||
0.508141 | + | 0.861274i | \(0.330333\pi\) | |||||||
\(164\) | 3.59491e7 | 0.636407 | ||||||||
\(165\) | 1.53243e7 | 0.265575 | ||||||||
\(166\) | −9.73023e6 | −0.165099 | ||||||||
\(167\) | 2.13130e7 | 0.354109 | 0.177054 | − | 0.984201i | \(-0.443343\pi\) | ||||
0.177054 | + | 0.984201i | \(0.443343\pi\) | |||||||
\(168\) | −1.59274e7 | −0.259156 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 3.30534e7 | 0.515994 | ||||||||
\(171\) | −8.29346e6 | −0.126838 | ||||||||
\(172\) | −1.15804e7 | −0.173530 | ||||||||
\(173\) | −4.51220e7 | −0.662562 | −0.331281 | − | 0.943532i | \(-0.607481\pi\) | ||||
−0.331281 | + | 0.943532i | \(0.607481\pi\) | |||||||
\(174\) | 3.08137e6 | 0.0443426 | ||||||||
\(175\) | −2.31453e7 | −0.326459 | ||||||||
\(176\) | 184601. | 0.00255235 | ||||||||
\(177\) | −1.23691e7 | −0.167661 | ||||||||
\(178\) | 1.23897e7 | 0.164661 | ||||||||
\(179\) | 8.49518e7 | 1.10710 | 0.553550 | − | 0.832816i | \(-0.313273\pi\) | ||||
0.553550 | + | 0.832816i | \(0.313273\pi\) | |||||||
\(180\) | −3.50319e7 | −0.447724 | ||||||||
\(181\) | 6.90967e7 | 0.866128 | 0.433064 | − | 0.901363i | \(-0.357432\pi\) | ||||
0.433064 | + | 0.901363i | \(0.357432\pi\) | |||||||
\(182\) | 5.24131e6 | 0.0644451 | ||||||||
\(183\) | 6.32922e7 | 0.763434 | ||||||||
\(184\) | −2.07667e7 | −0.245757 | ||||||||
\(185\) | 4.10201e7 | 0.476316 | ||||||||
\(186\) | 1.94874e7 | 0.222054 | ||||||||
\(187\) | −1.55543e7 | −0.173942 | ||||||||
\(188\) | −1.75766e7 | −0.192922 | ||||||||
\(189\) | −3.68383e7 | −0.396902 | ||||||||
\(190\) | −1.90899e7 | −0.201914 | ||||||||
\(191\) | 1.05054e7 | 0.109092 | 0.0545462 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545462 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(192\) | −4.09621e7 | −0.417665 | ||||||||
\(193\) | −2.74699e7 | −0.275047 | −0.137523 | − | 0.990499i | \(-0.543914\pi\) | ||||
−0.137523 | + | 0.990499i | \(0.543914\pi\) | |||||||
\(194\) | −4.21147e7 | −0.414121 | ||||||||
\(195\) | −2.69571e7 | −0.260347 | ||||||||
\(196\) | −9.36767e6 | −0.0888659 | ||||||||
\(197\) | 9.00501e7 | 0.839174 | 0.419587 | − | 0.907715i | \(-0.362175\pi\) | ||||
0.419587 | + | 0.907715i | \(0.362175\pi\) | |||||||
\(198\) | −1.00158e7 | −0.0916978 | ||||||||
\(199\) | 1.82532e7 | 0.164193 | 0.0820964 | − | 0.996624i | \(-0.473838\pi\) | ||||
0.0820964 | + | 0.996624i | \(0.473838\pi\) | |||||||
\(200\) | −9.74453e7 | −0.861303 | ||||||||
\(201\) | 2.74213e7 | 0.238178 | ||||||||
\(202\) | −8.99553e7 | −0.767887 | ||||||||
\(203\) | 4.72568e6 | 0.0396486 | ||||||||
\(204\) | −3.18871e7 | −0.262972 | ||||||||
\(205\) | 1.72279e8 | 1.39667 | ||||||||
\(206\) | −8.28411e7 | −0.660253 | ||||||||
\(207\) | −1.65809e7 | −0.129931 | ||||||||
\(208\) | −324734. | −0.00250211 | ||||||||
\(209\) | 8.98335e6 | 0.0680654 | ||||||||
\(210\) | −2.92721e7 | −0.218115 | ||||||||
\(211\) | 1.16380e8 | 0.852880 | 0.426440 | − | 0.904516i | \(-0.359767\pi\) | ||||
0.426440 | + | 0.904516i | \(0.359767\pi\) | |||||||
\(212\) | 4.11434e7 | 0.296568 | ||||||||
\(213\) | −1.81799e8 | −1.28903 | ||||||||
\(214\) | −1.27493e8 | −0.889276 | ||||||||
\(215\) | −5.54968e7 | −0.380832 | ||||||||
\(216\) | −1.55095e8 | −1.04715 | ||||||||
\(217\) | 2.98865e7 | 0.198548 | ||||||||
\(218\) | −6.71011e7 | −0.438664 | ||||||||
\(219\) | 5.39644e7 | 0.347178 | ||||||||
\(220\) | 3.79461e7 | 0.240263 | ||||||||
\(221\) | 2.73618e7 | 0.170518 | ||||||||
\(222\) | 2.40427e7 | 0.147485 | ||||||||
\(223\) | −6.00297e7 | −0.362493 | −0.181246 | − | 0.983438i | \(-0.558013\pi\) | ||||
−0.181246 | + | 0.983438i | \(0.558013\pi\) | |||||||
\(224\) | −6.37538e7 | −0.378999 | ||||||||
\(225\) | −7.78041e7 | −0.455369 | ||||||||
\(226\) | 1.61158e8 | 0.928696 | ||||||||
\(227\) | −1.75709e8 | −0.997017 | −0.498508 | − | 0.866885i | \(-0.666119\pi\) | ||||
−0.498508 | + | 0.866885i | \(0.666119\pi\) | |||||||
\(228\) | 1.84163e7 | 0.102903 | ||||||||
\(229\) | −2.35858e8 | −1.29785 | −0.648927 | − | 0.760851i | \(-0.724782\pi\) | ||||
−0.648927 | + | 0.760851i | \(0.724782\pi\) | |||||||
\(230\) | −3.81660e7 | −0.206838 | ||||||||
\(231\) | 1.37749e7 | 0.0735270 | ||||||||
\(232\) | 1.98959e7 | 0.104606 | ||||||||
\(233\) | 3.05100e8 | 1.58014 | 0.790071 | − | 0.613015i | \(-0.210044\pi\) | ||||
0.790071 | + | 0.613015i | \(0.210044\pi\) | |||||||
\(234\) | 1.76190e7 | 0.0898928 | ||||||||
\(235\) | −8.42321e7 | −0.423389 | ||||||||
\(236\) | −3.06284e7 | −0.151682 | ||||||||
\(237\) | −1.10497e8 | −0.539175 | ||||||||
\(238\) | 2.97114e7 | 0.142858 | ||||||||
\(239\) | 1.73701e8 | 0.823019 | 0.411509 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411509 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(240\) | 1.81360e6 | 0.00846842 | ||||||||
\(241\) | −4.92419e7 | −0.226608 | −0.113304 | − | 0.993560i | \(-0.536143\pi\) | ||||
−0.113304 | + | 0.993560i | \(0.536143\pi\) | |||||||
\(242\) | −1.24690e8 | −0.565559 | ||||||||
\(243\) | −2.04919e8 | −0.916137 | ||||||||
\(244\) | 1.56724e8 | 0.690672 | ||||||||
\(245\) | −4.48926e7 | −0.195026 | ||||||||
\(246\) | 1.00976e8 | 0.432460 | ||||||||
\(247\) | −1.58027e7 | −0.0667255 | ||||||||
\(248\) | 1.25827e8 | 0.523833 | ||||||||
\(249\) | 4.49847e7 | 0.184658 | ||||||||
\(250\) | 2.82549e7 | 0.114368 | ||||||||
\(251\) | −4.76583e7 | −0.190231 | −0.0951153 | − | 0.995466i | \(-0.530322\pi\) | ||||
−0.0951153 | + | 0.995466i | \(0.530322\pi\) | |||||||
\(252\) | −3.14899e7 | −0.123957 | ||||||||
\(253\) | 1.79602e7 | 0.0697253 | ||||||||
\(254\) | 2.18938e8 | 0.838306 | ||||||||
\(255\) | −1.52812e8 | −0.577121 | ||||||||
\(256\) | −2.66907e8 | −0.994307 | ||||||||
\(257\) | 3.83220e8 | 1.40826 | 0.704129 | − | 0.710072i | \(-0.251338\pi\) | ||||
0.704129 | + | 0.710072i | \(0.251338\pi\) | |||||||
\(258\) | −3.25278e7 | −0.117920 | ||||||||
\(259\) | 3.68726e7 | 0.131873 | ||||||||
\(260\) | −6.67513e7 | −0.235534 | ||||||||
\(261\) | 1.58856e7 | 0.0553048 | ||||||||
\(262\) | −1.15205e8 | −0.395748 | ||||||||
\(263\) | −5.15431e8 | −1.74713 | −0.873566 | − | 0.486707i | \(-0.838198\pi\) | ||||
−0.873566 | + | 0.486707i | \(0.838198\pi\) | |||||||
\(264\) | 5.79946e7 | 0.193987 | ||||||||
\(265\) | 1.97171e8 | 0.650853 | ||||||||
\(266\) | −1.71598e7 | −0.0559018 | ||||||||
\(267\) | −5.72799e7 | −0.184167 | ||||||||
\(268\) | 6.79005e7 | 0.215477 | ||||||||
\(269\) | −5.22355e7 | −0.163619 | −0.0818093 | − | 0.996648i | \(-0.526070\pi\) | ||||
−0.0818093 | + | 0.996648i | \(0.526070\pi\) | |||||||
\(270\) | −2.85041e8 | −0.881322 | ||||||||
\(271\) | −5.46494e8 | −1.66799 | −0.833994 | − | 0.551774i | \(-0.813951\pi\) | ||||
−0.833994 | + | 0.551774i | \(0.813951\pi\) | |||||||
\(272\) | −1.84082e6 | −0.00554652 | ||||||||
\(273\) | −2.42316e7 | −0.0720796 | ||||||||
\(274\) | 6.53549e7 | 0.191934 | ||||||||
\(275\) | 8.42762e7 | 0.244366 | ||||||||
\(276\) | 3.68193e7 | 0.105413 | ||||||||
\(277\) | 4.84372e7 | 0.136931 | 0.0684653 | − | 0.997654i | \(-0.478190\pi\) | ||||
0.0684653 | + | 0.997654i | \(0.478190\pi\) | |||||||
\(278\) | 4.30249e8 | 1.20105 | ||||||||
\(279\) | 1.00465e8 | 0.276950 | ||||||||
\(280\) | −1.89005e8 | −0.514541 | ||||||||
\(281\) | −2.46686e8 | −0.663244 | −0.331622 | − | 0.943412i | \(-0.607596\pi\) | ||||
−0.331622 | + | 0.943412i | \(0.607596\pi\) | |||||||
\(282\) | −4.93701e7 | −0.131097 | ||||||||
\(283\) | 4.15186e8 | 1.08890 | 0.544452 | − | 0.838792i | \(-0.316738\pi\) | ||||
0.544452 | + | 0.838792i | \(0.316738\pi\) | |||||||
\(284\) | −4.50171e8 | −1.16617 | ||||||||
\(285\) | 8.82562e7 | 0.225833 | ||||||||
\(286\) | −1.90846e7 | −0.0482394 | ||||||||
\(287\) | 1.54860e8 | 0.386681 | ||||||||
\(288\) | −2.14312e8 | −0.528655 | ||||||||
\(289\) | −2.55233e8 | −0.622006 | ||||||||
\(290\) | 3.65656e7 | 0.0880399 | ||||||||
\(291\) | 1.94704e8 | 0.463180 | ||||||||
\(292\) | 1.33627e8 | 0.314089 | ||||||||
\(293\) | 4.53635e8 | 1.05359 | 0.526793 | − | 0.849994i | \(-0.323394\pi\) | ||||
0.526793 | + | 0.849994i | \(0.323394\pi\) | |||||||
\(294\) | −2.63125e7 | −0.0603873 | ||||||||
\(295\) | −1.46780e8 | −0.332883 | ||||||||
\(296\) | 1.55240e8 | 0.347922 | ||||||||
\(297\) | 1.34135e8 | 0.297095 | ||||||||
\(298\) | 1.49642e8 | 0.327565 | ||||||||
\(299\) | −3.15940e7 | −0.0683527 | ||||||||
\(300\) | 1.72770e8 | 0.369440 | ||||||||
\(301\) | −4.98857e7 | −0.105437 | ||||||||
\(302\) | 2.73758e8 | 0.571929 | ||||||||
\(303\) | 4.15881e8 | 0.858854 | ||||||||
\(304\) | 1.06316e6 | 0.00217041 | ||||||||
\(305\) | 7.51069e8 | 1.51576 | ||||||||
\(306\) | 9.98767e7 | 0.199269 | ||||||||
\(307\) | 8.47339e7 | 0.167137 | 0.0835686 | − | 0.996502i | \(-0.473368\pi\) | ||||
0.0835686 | + | 0.996502i | \(0.473368\pi\) | |||||||
\(308\) | 3.41094e7 | 0.0665192 | ||||||||
\(309\) | 3.82990e8 | 0.738470 | ||||||||
\(310\) | 2.31251e8 | 0.440877 | ||||||||
\(311\) | −1.23785e8 | −0.233349 | −0.116674 | − | 0.993170i | \(-0.537223\pi\) | ||||
−0.116674 | + | 0.993170i | \(0.537223\pi\) | |||||||
\(312\) | −1.02019e8 | −0.190169 | ||||||||
\(313\) | −9.31573e8 | −1.71716 | −0.858582 | − | 0.512677i | \(-0.828654\pi\) | ||||
−0.858582 | + | 0.512677i | \(0.828654\pi\) | |||||||
\(314\) | 4.31553e8 | 0.786647 | ||||||||
\(315\) | −1.50909e8 | −0.272037 | ||||||||
\(316\) | −2.73612e8 | −0.487786 | ||||||||
\(317\) | 6.40816e8 | 1.12986 | 0.564932 | − | 0.825137i | \(-0.308902\pi\) | ||||
0.564932 | + | 0.825137i | \(0.308902\pi\) | |||||||
\(318\) | 1.15566e8 | 0.201528 | ||||||||
\(319\) | −1.72071e7 | −0.0296784 | ||||||||
\(320\) | −4.86084e8 | −0.829251 | ||||||||
\(321\) | 5.89422e8 | 0.994624 | ||||||||
\(322\) | −3.43071e7 | −0.0572650 | ||||||||
\(323\) | −8.95808e7 | −0.147913 | ||||||||
\(324\) | 7.42005e7 | 0.121199 | ||||||||
\(325\) | −1.48251e8 | −0.239556 | ||||||||
\(326\) | 3.90829e8 | 0.624777 | ||||||||
\(327\) | 3.10221e8 | 0.490630 | ||||||||
\(328\) | 6.51986e8 | 1.02019 | ||||||||
\(329\) | −7.57155e7 | −0.117219 | ||||||||
\(330\) | 1.06585e8 | 0.163267 | ||||||||
\(331\) | −4.01542e8 | −0.608601 | −0.304300 | − | 0.952576i | \(-0.598423\pi\) | ||||
−0.304300 | + | 0.952576i | \(0.598423\pi\) | |||||||
\(332\) | 1.11391e8 | 0.167058 | ||||||||
\(333\) | 1.23949e8 | 0.183946 | ||||||||
\(334\) | 1.48238e8 | 0.217695 | ||||||||
\(335\) | 3.25399e8 | 0.472890 | ||||||||
\(336\) | 1.63023e6 | 0.00234456 | ||||||||
\(337\) | 1.41278e8 | 0.201080 | 0.100540 | − | 0.994933i | \(-0.467943\pi\) | ||||
0.100540 | + | 0.994933i | \(0.467943\pi\) | |||||||
\(338\) | 3.35719e7 | 0.0472898 | ||||||||
\(339\) | −7.45066e8 | −1.03871 | ||||||||
\(340\) | −3.78393e8 | −0.522116 | ||||||||
\(341\) | −1.08822e8 | −0.148620 | ||||||||
\(342\) | −5.76835e7 | −0.0779759 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | −2.10027e8 | −0.278176 | ||||||||
\(345\) | 1.76449e8 | 0.231341 | ||||||||
\(346\) | −3.13837e8 | −0.407322 | ||||||||
\(347\) | −3.94593e8 | −0.506987 | −0.253493 | − | 0.967337i | \(-0.581580\pi\) | ||||
−0.253493 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(348\) | −3.52753e7 | −0.0448687 | ||||||||
\(349\) | 1.12883e9 | 1.42148 | 0.710739 | − | 0.703456i | \(-0.248361\pi\) | ||||
0.710739 | + | 0.703456i | \(0.248361\pi\) | |||||||
\(350\) | −1.60982e8 | −0.200696 | ||||||||
\(351\) | −2.35959e8 | −0.291247 | ||||||||
\(352\) | 2.32139e8 | 0.283694 | ||||||||
\(353\) | −1.16667e9 | −1.41168 | −0.705839 | − | 0.708372i | \(-0.749430\pi\) | ||||
−0.705839 | + | 0.708372i | \(0.749430\pi\) | |||||||
\(354\) | −8.60310e7 | −0.103073 | ||||||||
\(355\) | −2.15735e9 | −2.55930 | ||||||||
\(356\) | −1.41836e8 | −0.166615 | ||||||||
\(357\) | −1.37362e8 | −0.159782 | ||||||||
\(358\) | 5.90865e8 | 0.680609 | ||||||||
\(359\) | 1.52650e9 | 1.74127 | 0.870635 | − | 0.491929i | \(-0.163708\pi\) | ||||
0.870635 | + | 0.491929i | \(0.163708\pi\) | |||||||
\(360\) | −6.35351e8 | −0.717720 | ||||||||
\(361\) | −8.42135e8 | −0.942120 | ||||||||
\(362\) | 4.80588e8 | 0.532467 | ||||||||
\(363\) | 5.76466e8 | 0.632558 | ||||||||
\(364\) | −6.00022e7 | −0.0652097 | ||||||||
\(365\) | 6.40378e8 | 0.689305 | ||||||||
\(366\) | 4.40216e8 | 0.469334 | ||||||||
\(367\) | −1.56116e9 | −1.64860 | −0.824302 | − | 0.566150i | \(-0.808432\pi\) | ||||
−0.824302 | + | 0.566150i | \(0.808432\pi\) | |||||||
\(368\) | 2.12556e6 | 0.00222334 | ||||||||
\(369\) | 5.20571e8 | 0.539371 | ||||||||
\(370\) | 2.85307e8 | 0.292823 | ||||||||
\(371\) | 1.77236e8 | 0.180195 | ||||||||
\(372\) | −2.23091e8 | −0.224689 | ||||||||
\(373\) | 6.30670e8 | 0.629247 | 0.314623 | − | 0.949217i | \(-0.398122\pi\) | ||||
0.314623 | + | 0.949217i | \(0.398122\pi\) | |||||||
\(374\) | −1.08185e8 | −0.106934 | ||||||||
\(375\) | −1.30628e8 | −0.127916 | ||||||||
\(376\) | −3.18775e8 | −0.309262 | ||||||||
\(377\) | 3.02692e7 | 0.0290941 | ||||||||
\(378\) | −2.56221e8 | −0.244002 | ||||||||
\(379\) | −1.03258e9 | −0.974283 | −0.487141 | − | 0.873323i | \(-0.661960\pi\) | ||||
−0.487141 | + | 0.873323i | \(0.661960\pi\) | |||||||
\(380\) | 2.18540e8 | 0.204309 | ||||||||
\(381\) | −1.01219e9 | −0.937616 | ||||||||
\(382\) | 7.30680e7 | 0.0670664 | ||||||||
\(383\) | 2.21286e8 | 0.201261 | 0.100630 | − | 0.994924i | \(-0.467914\pi\) | ||||
0.100630 | + | 0.994924i | \(0.467914\pi\) | |||||||
\(384\) | 4.80127e8 | 0.432710 | ||||||||
\(385\) | 1.63462e8 | 0.145984 | ||||||||
\(386\) | −1.91061e8 | −0.169090 | ||||||||
\(387\) | −1.67693e8 | −0.147071 | ||||||||
\(388\) | 4.82127e8 | 0.419035 | ||||||||
\(389\) | 1.89442e9 | 1.63175 | 0.815873 | − | 0.578231i | \(-0.196257\pi\) | ||||
0.815873 | + | 0.578231i | \(0.196257\pi\) | |||||||
\(390\) | −1.87495e8 | −0.160053 | ||||||||
\(391\) | −1.79097e8 | −0.151520 | ||||||||
\(392\) | −1.69895e8 | −0.142456 | ||||||||
\(393\) | 5.32617e8 | 0.442630 | ||||||||
\(394\) | 6.26325e8 | 0.515897 | ||||||||
\(395\) | −1.31123e9 | −1.07050 | ||||||||
\(396\) | 1.14661e8 | 0.0927858 | ||||||||
\(397\) | −4.13478e8 | −0.331654 | −0.165827 | − | 0.986155i | \(-0.553029\pi\) | ||||
−0.165827 | + | 0.986155i | \(0.553029\pi\) | |||||||
\(398\) | 1.26957e8 | 0.100940 | ||||||||
\(399\) | 7.93328e7 | 0.0625241 | ||||||||
\(400\) | 9.97392e6 | 0.00779212 | ||||||||
\(401\) | 1.29463e9 | 1.00263 | 0.501314 | − | 0.865265i | \(-0.332850\pi\) | ||||
0.501314 | + | 0.865265i | \(0.332850\pi\) | |||||||
\(402\) | 1.90723e8 | 0.146424 | ||||||||
\(403\) | 1.91430e8 | 0.145695 | ||||||||
\(404\) | 1.02980e9 | 0.776997 | ||||||||
\(405\) | 3.55590e8 | 0.265985 | ||||||||
\(406\) | 3.28685e7 | 0.0243747 | ||||||||
\(407\) | −1.34260e8 | −0.0987112 | ||||||||
\(408\) | −5.78315e8 | −0.421554 | ||||||||
\(409\) | 1.53435e8 | 0.110890 | 0.0554449 | − | 0.998462i | \(-0.482342\pi\) | ||||
0.0554449 | + | 0.998462i | \(0.482342\pi\) | |||||||
\(410\) | 1.19825e9 | 0.858626 | ||||||||
\(411\) | −3.02148e8 | −0.214671 | ||||||||
\(412\) | 9.48360e8 | 0.668087 | ||||||||
\(413\) | −1.31940e8 | −0.0921617 | ||||||||
\(414\) | −1.15325e8 | −0.0798774 | ||||||||
\(415\) | 5.33819e8 | 0.366628 | ||||||||
\(416\) | −4.08359e8 | −0.278109 | ||||||||
\(417\) | −1.98912e9 | −1.34334 | ||||||||
\(418\) | 6.24819e7 | 0.0418444 | ||||||||
\(419\) | −1.34262e9 | −0.891667 | −0.445833 | − | 0.895116i | \(-0.647093\pi\) | ||||
−0.445833 | + | 0.895116i | \(0.647093\pi\) | |||||||
\(420\) | 3.35105e8 | 0.220703 | ||||||||
\(421\) | −1.80068e9 | −1.17611 | −0.588055 | − | 0.808821i | \(-0.700106\pi\) | ||||
−0.588055 | + | 0.808821i | \(0.700106\pi\) | |||||||
\(422\) | 8.09454e8 | 0.524323 | ||||||||
\(423\) | −2.54522e8 | −0.163506 | ||||||||
\(424\) | 7.46191e8 | 0.475411 | ||||||||
\(425\) | −8.40392e8 | −0.531032 | ||||||||
\(426\) | −1.26447e9 | −0.792453 | ||||||||
\(427\) | 6.75130e8 | 0.419652 | ||||||||
\(428\) | 1.45953e9 | 0.899827 | ||||||||
\(429\) | 8.82317e7 | 0.0539541 | ||||||||
\(430\) | −3.85997e8 | −0.234123 | ||||||||
\(431\) | −2.86118e9 | −1.72137 | −0.860686 | − | 0.509137i | \(-0.829965\pi\) | ||||
−0.860686 | + | 0.509137i | \(0.829965\pi\) | |||||||
\(432\) | 1.58746e7 | 0.00947350 | ||||||||
\(433\) | −2.21570e9 | −1.31160 | −0.655802 | − | 0.754933i | \(-0.727669\pi\) | ||||
−0.655802 | + | 0.754933i | \(0.727669\pi\) | |||||||
\(434\) | 2.07869e8 | 0.122061 | ||||||||
\(435\) | −1.69050e8 | −0.0984695 | ||||||||
\(436\) | 7.68170e8 | 0.443869 | ||||||||
\(437\) | 1.03437e8 | 0.0592913 | ||||||||
\(438\) | 3.75338e8 | 0.213434 | ||||||||
\(439\) | −6.24237e8 | −0.352147 | −0.176073 | − | 0.984377i | \(-0.556340\pi\) | ||||
−0.176073 | + | 0.984377i | \(0.556340\pi\) | |||||||
\(440\) | 6.88203e8 | 0.385152 | ||||||||
\(441\) | −1.35651e8 | −0.0753161 | ||||||||
\(442\) | 1.90309e8 | 0.104829 | ||||||||
\(443\) | −1.35040e9 | −0.737987 | −0.368993 | − | 0.929432i | \(-0.620298\pi\) | ||||
−0.368993 | + | 0.929432i | \(0.620298\pi\) | |||||||
\(444\) | −2.75239e8 | −0.149235 | ||||||||
\(445\) | −6.79722e8 | −0.365655 | ||||||||
\(446\) | −4.17525e8 | −0.222849 | ||||||||
\(447\) | −6.91824e8 | −0.366369 | ||||||||
\(448\) | −4.36937e8 | −0.229586 | ||||||||
\(449\) | 8.40873e7 | 0.0438397 | 0.0219199 | − | 0.999760i | \(-0.493022\pi\) | ||||
0.0219199 | + | 0.999760i | \(0.493022\pi\) | |||||||
\(450\) | −5.41150e8 | −0.279946 | ||||||||
\(451\) | −5.63875e8 | −0.289444 | ||||||||
\(452\) | −1.84493e9 | −0.939715 | ||||||||
\(453\) | −1.26563e9 | −0.639682 | ||||||||
\(454\) | −1.22211e9 | −0.612933 | ||||||||
\(455\) | −2.87548e8 | −0.143110 | ||||||||
\(456\) | 3.34004e8 | 0.164959 | ||||||||
\(457\) | −5.67963e8 | −0.278364 | −0.139182 | − | 0.990267i | \(-0.544447\pi\) | ||||
−0.139182 | + | 0.990267i | \(0.544447\pi\) | |||||||
\(458\) | −1.64046e9 | −0.797878 | ||||||||
\(459\) | −1.33758e9 | −0.645617 | ||||||||
\(460\) | 4.36923e8 | 0.209292 | ||||||||
\(461\) | −8.22112e8 | −0.390821 | −0.195410 | − | 0.980722i | \(-0.562604\pi\) | ||||
−0.195410 | + | 0.980722i | \(0.562604\pi\) | |||||||
\(462\) | 9.58086e7 | 0.0452020 | ||||||||
\(463\) | −1.87940e9 | −0.880006 | −0.440003 | − | 0.897996i | \(-0.645023\pi\) | ||||
−0.440003 | + | 0.897996i | \(0.645023\pi\) | |||||||
\(464\) | −2.03642e6 | −0.000946357 0 | ||||||||
\(465\) | −1.06912e9 | −0.493105 | ||||||||
\(466\) | 2.12206e9 | 0.971420 | ||||||||
\(467\) | 3.08803e9 | 1.40305 | 0.701524 | − | 0.712646i | \(-0.252503\pi\) | ||||
0.701524 | + | 0.712646i | \(0.252503\pi\) | |||||||
\(468\) | −2.01701e8 | −0.0909593 | ||||||||
\(469\) | 2.92499e8 | 0.130924 | ||||||||
\(470\) | −5.85859e8 | −0.260286 | ||||||||
\(471\) | −1.99515e9 | −0.879837 | ||||||||
\(472\) | −5.55488e8 | −0.243152 | ||||||||
\(473\) | 1.81643e8 | 0.0789232 | ||||||||
\(474\) | −7.68536e8 | −0.331467 | ||||||||
\(475\) | 4.85366e8 | 0.207798 | ||||||||
\(476\) | −3.40135e8 | −0.144553 | ||||||||
\(477\) | 5.95788e8 | 0.251349 | ||||||||
\(478\) | 1.20814e9 | 0.505965 | ||||||||
\(479\) | 4.41054e9 | 1.83366 | 0.916828 | − | 0.399282i | \(-0.130741\pi\) | ||||
0.916828 | + | 0.399282i | \(0.130741\pi\) | |||||||
\(480\) | 2.28063e9 | 0.941263 | ||||||||
\(481\) | 2.36178e8 | 0.0967681 | ||||||||
\(482\) | −3.42492e8 | −0.139311 | ||||||||
\(483\) | 1.58608e8 | 0.0640489 | ||||||||
\(484\) | 1.42744e9 | 0.572269 | ||||||||
\(485\) | 2.31049e9 | 0.919620 | ||||||||
\(486\) | −1.42527e9 | −0.563211 | ||||||||
\(487\) | −8.06410e8 | −0.316377 | −0.158188 | − | 0.987409i | \(-0.550565\pi\) | ||||
−0.158188 | + | 0.987409i | \(0.550565\pi\) | |||||||
\(488\) | 2.84241e9 | 1.10718 | ||||||||
\(489\) | −1.80688e9 | −0.698792 | ||||||||
\(490\) | −3.12241e8 | −0.119896 | ||||||||
\(491\) | 1.88312e9 | 0.717948 | 0.358974 | − | 0.933348i | \(-0.383127\pi\) | ||||
0.358974 | + | 0.933348i | \(0.383127\pi\) | |||||||
\(492\) | −1.15597e9 | −0.437591 | ||||||||
\(493\) | 1.71587e8 | 0.0644941 | ||||||||
\(494\) | −1.09913e8 | −0.0410207 | ||||||||
\(495\) | 5.49488e8 | 0.203629 | ||||||||
\(496\) | −1.28789e7 | −0.00473907 | ||||||||
\(497\) | −1.93922e9 | −0.708567 | ||||||||
\(498\) | 3.12882e8 | 0.113521 | ||||||||
\(499\) | 4.27934e9 | 1.54179 | 0.770895 | − | 0.636962i | \(-0.219809\pi\) | ||||
0.770895 | + | 0.636962i | \(0.219809\pi\) | |||||||
\(500\) | −3.23460e8 | −0.115725 | ||||||||
\(501\) | −6.85334e8 | −0.243484 | ||||||||
\(502\) | −3.31477e8 | −0.116947 | ||||||||
\(503\) | 2.89029e9 | 1.01263 | 0.506317 | − | 0.862347i | \(-0.331006\pi\) | ||||
0.506317 | + | 0.862347i | \(0.331006\pi\) | |||||||
\(504\) | −5.71112e8 | −0.198708 | ||||||||
\(505\) | 4.93512e9 | 1.70521 | ||||||||
\(506\) | 1.24919e8 | 0.0428648 | ||||||||
\(507\) | −1.55209e8 | −0.0528920 | ||||||||
\(508\) | −2.50639e9 | −0.848253 | ||||||||
\(509\) | 4.52661e9 | 1.52146 | 0.760731 | − | 0.649067i | \(-0.224840\pi\) | ||||
0.760731 | + | 0.649067i | \(0.224840\pi\) | |||||||
\(510\) | −1.06285e9 | −0.354795 | ||||||||
\(511\) | 5.75631e8 | 0.190841 | ||||||||
\(512\) | 5.47945e7 | 0.0180423 | ||||||||
\(513\) | 7.72515e8 | 0.252637 | ||||||||
\(514\) | 2.66541e9 | 0.865751 | ||||||||
\(515\) | 4.54482e9 | 1.46619 | ||||||||
\(516\) | 3.72376e8 | 0.119319 | ||||||||
\(517\) | 2.75694e8 | 0.0877427 | ||||||||
\(518\) | 2.56460e8 | 0.0810710 | ||||||||
\(519\) | 1.45093e9 | 0.455575 | ||||||||
\(520\) | −1.21062e9 | −0.377570 | ||||||||
\(521\) | 4.03795e9 | 1.25092 | 0.625459 | − | 0.780257i | \(-0.284912\pi\) | ||||
0.625459 | + | 0.780257i | \(0.284912\pi\) | |||||||
\(522\) | 1.10489e8 | 0.0339996 | ||||||||
\(523\) | −5.83872e9 | −1.78469 | −0.892343 | − | 0.451358i | \(-0.850940\pi\) | ||||
−0.892343 | + | 0.451358i | \(0.850940\pi\) | |||||||
\(524\) | 1.31887e9 | 0.400443 | ||||||||
\(525\) | 7.44251e8 | 0.224472 | ||||||||
\(526\) | −3.58498e9 | −1.07408 | ||||||||
\(527\) | 1.08516e9 | 0.322967 | ||||||||
\(528\) | −5.93598e6 | −0.00175499 | ||||||||
\(529\) | −3.19803e9 | −0.939263 | ||||||||
\(530\) | 1.37138e9 | 0.400123 | ||||||||
\(531\) | −4.43523e8 | −0.128554 | ||||||||
\(532\) | 1.96444e8 | 0.0565650 | ||||||||
\(533\) | 9.91917e8 | 0.283746 | ||||||||
\(534\) | −3.98399e8 | −0.113220 | ||||||||
\(535\) | 6.99448e9 | 1.97477 | ||||||||
\(536\) | 1.23147e9 | 0.345419 | ||||||||
\(537\) | −2.73168e9 | −0.761237 | ||||||||
\(538\) | −3.63313e8 | −0.100587 | ||||||||
\(539\) | 1.46935e8 | 0.0404171 | ||||||||
\(540\) | 3.26314e9 | 0.891779 | ||||||||
\(541\) | 3.67872e8 | 0.0998863 | 0.0499432 | − | 0.998752i | \(-0.484096\pi\) | ||||
0.0499432 | + | 0.998752i | \(0.484096\pi\) | |||||||
\(542\) | −3.80103e9 | −1.02542 | ||||||||
\(543\) | −2.22185e9 | −0.595546 | ||||||||
\(544\) | −2.31486e9 | −0.616495 | ||||||||
\(545\) | 3.68129e9 | 0.974121 | ||||||||
\(546\) | −1.68538e8 | −0.0443122 | ||||||||
\(547\) | 1.47383e9 | 0.385028 | 0.192514 | − | 0.981294i | \(-0.438336\pi\) | ||||
0.192514 | + | 0.981294i | \(0.438336\pi\) | |||||||
\(548\) | −7.48179e8 | −0.194211 | ||||||||
\(549\) | 2.26949e9 | 0.585362 | ||||||||
\(550\) | 5.86166e8 | 0.150228 | ||||||||
\(551\) | −9.90995e7 | −0.0252372 | ||||||||
\(552\) | 6.67767e8 | 0.168981 | ||||||||
\(553\) | −1.17865e9 | −0.296379 | ||||||||
\(554\) | 3.36895e8 | 0.0841804 | ||||||||
\(555\) | −1.31903e9 | −0.327513 | ||||||||
\(556\) | −4.92546e9 | −1.21530 | ||||||||
\(557\) | 3.10977e9 | 0.762491 | 0.381246 | − | 0.924474i | \(-0.375495\pi\) | ||||
0.381246 | + | 0.924474i | \(0.375495\pi\) | |||||||
\(558\) | 6.98765e8 | 0.170260 | ||||||||
\(559\) | −3.19530e8 | −0.0773696 | ||||||||
\(560\) | 1.93454e7 | 0.00465501 | ||||||||
\(561\) | 5.00159e8 | 0.119602 | ||||||||
\(562\) | −1.71578e9 | −0.407741 | ||||||||
\(563\) | 4.68729e9 | 1.10699 | 0.553493 | − | 0.832854i | \(-0.313294\pi\) | ||||
0.553493 | + | 0.832854i | \(0.313294\pi\) | |||||||
\(564\) | 5.65186e8 | 0.132652 | ||||||||
\(565\) | −8.84146e9 | −2.06231 | ||||||||
\(566\) | 2.88774e9 | 0.669423 | ||||||||
\(567\) | 3.19637e8 | 0.0736405 | ||||||||
\(568\) | −8.16445e9 | −1.86942 | ||||||||
\(569\) | −4.16238e9 | −0.947216 | −0.473608 | − | 0.880736i | \(-0.657049\pi\) | ||||
−0.473608 | + | 0.880736i | \(0.657049\pi\) | |||||||
\(570\) | 6.13848e8 | 0.138835 | ||||||||
\(571\) | 1.08668e9 | 0.244273 | 0.122137 | − | 0.992513i | \(-0.461025\pi\) | ||||
0.122137 | + | 0.992513i | \(0.461025\pi\) | |||||||
\(572\) | 2.18479e8 | 0.0488117 | ||||||||
\(573\) | −3.37807e8 | −0.0750115 | ||||||||
\(574\) | 1.07710e9 | 0.237719 | ||||||||
\(575\) | 9.70382e8 | 0.212865 | ||||||||
\(576\) | −1.46879e9 | −0.320244 | ||||||||
\(577\) | 4.80319e9 | 1.04091 | 0.520456 | − | 0.853888i | \(-0.325762\pi\) | ||||
0.520456 | + | 0.853888i | \(0.325762\pi\) | |||||||
\(578\) | −1.77522e9 | −0.382389 | ||||||||
\(579\) | 8.83312e8 | 0.189121 | ||||||||
\(580\) | −4.18601e8 | −0.0890844 | ||||||||
\(581\) | 4.79846e8 | 0.101504 | ||||||||
\(582\) | 1.35423e9 | 0.284748 | ||||||||
\(583\) | −6.45348e8 | −0.134882 | ||||||||
\(584\) | 2.42350e9 | 0.503498 | ||||||||
\(585\) | −9.66609e8 | −0.199621 | ||||||||
\(586\) | 3.15516e9 | 0.647710 | ||||||||
\(587\) | 5.36662e9 | 1.09513 | 0.547567 | − | 0.836762i | \(-0.315554\pi\) | ||||
0.547567 | + | 0.836762i | \(0.315554\pi\) | |||||||
\(588\) | 3.01223e8 | 0.0611038 | ||||||||
\(589\) | −6.26733e8 | −0.126380 | ||||||||
\(590\) | −1.02090e9 | −0.204645 | ||||||||
\(591\) | −2.89562e9 | −0.577012 | ||||||||
\(592\) | −1.58894e7 | −0.00314762 | ||||||||
\(593\) | 4.81236e9 | 0.947691 | 0.473845 | − | 0.880608i | \(-0.342866\pi\) | ||||
0.473845 | + | 0.880608i | \(0.342866\pi\) | |||||||
\(594\) | 9.32950e8 | 0.182644 | ||||||||
\(595\) | −1.63003e9 | −0.317238 | ||||||||
\(596\) | −1.71309e9 | −0.331451 | ||||||||
\(597\) | −5.86945e8 | −0.112898 | ||||||||
\(598\) | −2.19746e8 | −0.0420210 | ||||||||
\(599\) | 1.29580e9 | 0.246345 | 0.123173 | − | 0.992385i | \(-0.460693\pi\) | ||||
0.123173 | + | 0.992385i | \(0.460693\pi\) | |||||||
\(600\) | 3.13342e9 | 0.592228 | ||||||||
\(601\) | −6.01433e9 | −1.13012 | −0.565062 | − | 0.825048i | \(-0.691148\pi\) | ||||
−0.565062 | + | 0.825048i | \(0.691148\pi\) | |||||||
\(602\) | −3.46970e8 | −0.0648192 | ||||||||
\(603\) | 9.83251e8 | 0.182622 | ||||||||
\(604\) | −3.13396e9 | −0.578715 | ||||||||
\(605\) | 6.84073e9 | 1.25591 | ||||||||
\(606\) | 2.89257e9 | 0.527995 | ||||||||
\(607\) | −4.04454e9 | −0.734021 | −0.367010 | − | 0.930217i | \(-0.619619\pi\) | ||||
−0.367010 | + | 0.930217i | \(0.619619\pi\) | |||||||
\(608\) | 1.33694e9 | 0.241241 | ||||||||
\(609\) | −1.51957e8 | −0.0272622 | ||||||||
\(610\) | 5.22390e9 | 0.931839 | ||||||||
\(611\) | −4.84977e8 | −0.0860155 | ||||||||
\(612\) | −1.14338e9 | −0.201633 | ||||||||
\(613\) | −1.01120e9 | −0.177308 | −0.0886538 | − | 0.996062i | \(-0.528256\pi\) | ||||
−0.0886538 | + | 0.996062i | \(0.528256\pi\) | |||||||
\(614\) | 5.89350e8 | 0.102750 | ||||||||
\(615\) | −5.53974e9 | −0.960343 | ||||||||
\(616\) | 6.18620e8 | 0.106633 | ||||||||
\(617\) | −9.03950e9 | −1.54934 | −0.774669 | − | 0.632367i | \(-0.782083\pi\) | ||||
−0.774669 | + | 0.632367i | \(0.782083\pi\) | |||||||
\(618\) | 2.66381e9 | 0.453987 | ||||||||
\(619\) | 1.24718e9 | 0.211355 | 0.105678 | − | 0.994400i | \(-0.466299\pi\) | ||||
0.105678 | + | 0.994400i | \(0.466299\pi\) | |||||||
\(620\) | −2.64735e9 | −0.446108 | ||||||||
\(621\) | 1.54447e9 | 0.258797 | ||||||||
\(622\) | −8.60959e8 | −0.143455 | ||||||||
\(623\) | −6.10997e8 | −0.101235 | ||||||||
\(624\) | 1.04420e7 | 0.00172044 | ||||||||
\(625\) | −6.82190e9 | −1.11770 | ||||||||
\(626\) | −6.47937e9 | −1.05566 | ||||||||
\(627\) | −2.88866e8 | −0.0468015 | ||||||||
\(628\) | −4.94039e9 | −0.795981 | ||||||||
\(629\) | 1.33882e9 | 0.214509 | ||||||||
\(630\) | −1.04962e9 | −0.167239 | ||||||||
\(631\) | −1.02219e10 | −1.61968 | −0.809839 | − | 0.586652i | \(-0.800446\pi\) | ||||
−0.809839 | + | 0.586652i | \(0.800446\pi\) | |||||||
\(632\) | −4.96231e9 | −0.781942 | ||||||||
\(633\) | −3.74226e9 | −0.586437 | ||||||||
\(634\) | 4.45707e9 | 0.694603 | ||||||||
\(635\) | −1.20113e10 | −1.86159 | ||||||||
\(636\) | −1.32299e9 | −0.203919 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −1.19680e8 | −0.0182453 | ||||||||
\(639\) | −6.51881e9 | −0.988361 | ||||||||
\(640\) | 5.69752e9 | 0.859124 | ||||||||
\(641\) | −8.10582e9 | −1.21561 | −0.607804 | − | 0.794087i | \(-0.707949\pi\) | ||||
−0.607804 | + | 0.794087i | \(0.707949\pi\) | |||||||
\(642\) | 4.09961e9 | 0.611462 | ||||||||
\(643\) | −1.03980e10 | −1.54245 | −0.771225 | − | 0.636563i | \(-0.780356\pi\) | ||||
−0.771225 | + | 0.636563i | \(0.780356\pi\) | |||||||
\(644\) | 3.92746e8 | 0.0579444 | ||||||||
\(645\) | 1.78454e9 | 0.261858 | ||||||||
\(646\) | −6.23061e8 | −0.0909321 | ||||||||
\(647\) | 5.54098e9 | 0.804306 | 0.402153 | − | 0.915572i | \(-0.368262\pi\) | ||||
0.402153 | + | 0.915572i | \(0.368262\pi\) | |||||||
\(648\) | 1.34573e9 | 0.194287 | ||||||||
\(649\) | 4.80418e8 | 0.0689862 | ||||||||
\(650\) | −1.03113e9 | −0.147271 | ||||||||
\(651\) | −9.61020e8 | −0.136521 | ||||||||
\(652\) | −4.47419e9 | −0.632190 | ||||||||
\(653\) | −5.05858e9 | −0.710939 | −0.355469 | − | 0.934688i | \(-0.615679\pi\) | ||||
−0.355469 | + | 0.934688i | \(0.615679\pi\) | |||||||
\(654\) | 2.15768e9 | 0.301623 | ||||||||
\(655\) | 6.32039e9 | 0.878819 | ||||||||
\(656\) | −6.67334e7 | −0.00922954 | ||||||||
\(657\) | 1.93501e9 | 0.266198 | ||||||||
\(658\) | −5.26624e8 | −0.0720626 | ||||||||
\(659\) | −8.78170e9 | −1.19531 | −0.597653 | − | 0.801755i | \(-0.703900\pi\) | ||||
−0.597653 | + | 0.801755i | \(0.703900\pi\) | |||||||
\(660\) | −1.22018e9 | −0.165204 | ||||||||
\(661\) | 1.14547e10 | 1.54269 | 0.771347 | − | 0.636415i | \(-0.219583\pi\) | ||||
0.771347 | + | 0.636415i | \(0.219583\pi\) | |||||||
\(662\) | −2.79284e9 | −0.374148 | ||||||||
\(663\) | −8.79835e8 | −0.117248 | ||||||||
\(664\) | 2.02023e9 | 0.267801 | ||||||||
\(665\) | 9.41417e8 | 0.124138 | ||||||||
\(666\) | 8.62105e8 | 0.113084 | ||||||||
\(667\) | −1.98128e8 | −0.0258526 | ||||||||
\(668\) | −1.69702e9 | −0.220277 | ||||||||
\(669\) | 1.93029e9 | 0.249248 | ||||||||
\(670\) | 2.26325e9 | 0.290717 | ||||||||
\(671\) | −2.45827e9 | −0.314124 | ||||||||
\(672\) | 2.05004e9 | 0.260598 | ||||||||
\(673\) | 1.16861e10 | 1.47780 | 0.738902 | − | 0.673813i | \(-0.235345\pi\) | ||||
0.738902 | + | 0.673813i | \(0.235345\pi\) | |||||||
\(674\) | 9.82630e8 | 0.123618 | ||||||||
\(675\) | 7.24725e9 | 0.907006 | ||||||||
\(676\) | −3.84329e8 | −0.0478509 | ||||||||
\(677\) | 9.29654e9 | 1.15149 | 0.575746 | − | 0.817629i | \(-0.304712\pi\) | ||||
0.575746 | + | 0.817629i | \(0.304712\pi\) | |||||||
\(678\) | −5.18216e9 | −0.638567 | ||||||||
\(679\) | 2.07688e9 | 0.254606 | ||||||||
\(680\) | −6.86267e9 | −0.836974 | ||||||||
\(681\) | 5.65002e9 | 0.685544 | ||||||||
\(682\) | −7.56892e8 | −0.0913668 | ||||||||
\(683\) | 3.85605e9 | 0.463095 | 0.231547 | − | 0.972824i | \(-0.425621\pi\) | ||||
0.231547 | + | 0.972824i | \(0.425621\pi\) | |||||||
\(684\) | 6.60357e8 | 0.0789010 | ||||||||
\(685\) | −3.58549e9 | −0.426218 | ||||||||
\(686\) | −2.80671e8 | −0.0331943 | ||||||||
\(687\) | 7.58415e9 | 0.892398 | ||||||||
\(688\) | 2.14971e7 | 0.00251663 | ||||||||
\(689\) | 1.13524e9 | 0.132227 | ||||||||
\(690\) | 1.22725e9 | 0.142221 | ||||||||
\(691\) | 1.52193e10 | 1.75477 | 0.877386 | − | 0.479785i | \(-0.159286\pi\) | ||||
0.877386 | + | 0.479785i | \(0.159286\pi\) | |||||||
\(692\) | 3.59278e9 | 0.412154 | ||||||||
\(693\) | 4.93930e8 | 0.0563767 | ||||||||
\(694\) | −2.74451e9 | −0.311679 | ||||||||
\(695\) | −2.36043e10 | −2.66713 | ||||||||
\(696\) | −6.39765e8 | −0.0719264 | ||||||||
\(697\) | 5.62289e9 | 0.628991 | ||||||||
\(698\) | 7.85136e9 | 0.873878 | ||||||||
\(699\) | −9.81068e9 | −1.08650 | ||||||||
\(700\) | 1.84291e9 | 0.203078 | ||||||||
\(701\) | 1.74595e10 | 1.91434 | 0.957170 | − | 0.289527i | \(-0.0934980\pi\) | ||||
0.957170 | + | 0.289527i | \(0.0934980\pi\) | |||||||
\(702\) | −1.64116e9 | −0.179049 | ||||||||
\(703\) | −7.73234e8 | −0.0839397 | ||||||||
\(704\) | 1.59097e9 | 0.171853 | ||||||||
\(705\) | 2.70854e9 | 0.291121 | ||||||||
\(706\) | −8.11452e9 | −0.867854 | ||||||||
\(707\) | 4.43614e9 | 0.472104 | ||||||||
\(708\) | 9.84877e8 | 0.104296 | ||||||||
\(709\) | 1.06434e10 | 1.12155 | 0.560777 | − | 0.827967i | \(-0.310502\pi\) | ||||
0.560777 | + | 0.827967i | \(0.310502\pi\) | |||||||
\(710\) | −1.50050e10 | −1.57337 | ||||||||
\(711\) | −3.96210e9 | −0.413411 | ||||||||
\(712\) | −2.57240e9 | −0.267090 | ||||||||
\(713\) | −1.25301e9 | −0.129462 | ||||||||
\(714\) | −9.55391e8 | −0.0982284 | ||||||||
\(715\) | 1.04702e9 | 0.107123 | ||||||||
\(716\) | −6.76419e9 | −0.688684 | ||||||||
\(717\) | −5.58547e9 | −0.565904 | ||||||||
\(718\) | 1.06173e10 | 1.07048 | ||||||||
\(719\) | −3.93718e9 | −0.395034 | −0.197517 | − | 0.980299i | \(-0.563288\pi\) | ||||
−0.197517 | + | 0.980299i | \(0.563288\pi\) | |||||||
\(720\) | 6.50307e7 | 0.00649314 | ||||||||
\(721\) | 4.08530e9 | 0.405930 | ||||||||
\(722\) | −5.85730e9 | −0.579185 | ||||||||
\(723\) | 1.58341e9 | 0.155815 | ||||||||
\(724\) | −5.50174e9 | −0.538785 | ||||||||
\(725\) | −9.29690e8 | −0.0906056 | ||||||||
\(726\) | 4.00949e9 | 0.388876 | ||||||||
\(727\) | 1.76816e8 | 0.0170668 | 0.00853339 | − | 0.999964i | \(-0.497284\pi\) | ||||
0.00853339 | + | 0.999964i | \(0.497284\pi\) | |||||||
\(728\) | −1.08822e9 | −0.104534 | ||||||||
\(729\) | 8.62735e9 | 0.824766 | ||||||||
\(730\) | 4.45402e9 | 0.423762 | ||||||||
\(731\) | −1.81132e9 | −0.171508 | ||||||||
\(732\) | −5.03957e9 | −0.474903 | ||||||||
\(733\) | 5.88295e9 | 0.551736 | 0.275868 | − | 0.961195i | \(-0.411035\pi\) | ||||
0.275868 | + | 0.961195i | \(0.411035\pi\) | |||||||
\(734\) | −1.08583e10 | −1.01351 | ||||||||
\(735\) | 1.44355e9 | 0.134099 | ||||||||
\(736\) | 2.67292e9 | 0.247124 | ||||||||
\(737\) | −1.06504e9 | −0.0980011 | ||||||||
\(738\) | 3.62073e9 | 0.331588 | ||||||||
\(739\) | 1.68753e10 | 1.53814 | 0.769069 | − | 0.639166i | \(-0.220720\pi\) | ||||
0.769069 | + | 0.639166i | \(0.220720\pi\) | |||||||
\(740\) | −3.26617e9 | −0.296298 | ||||||||
\(741\) | 5.08146e8 | 0.0458802 | ||||||||
\(742\) | 1.23273e9 | 0.110778 | ||||||||
\(743\) | −5.61136e9 | −0.501888 | −0.250944 | − | 0.968002i | \(-0.580741\pi\) | ||||
−0.250944 | + | 0.968002i | \(0.580741\pi\) | |||||||
\(744\) | −4.04605e9 | −0.360185 | ||||||||
\(745\) | −8.20965e9 | −0.727407 | ||||||||
\(746\) | 4.38649e9 | 0.386840 | ||||||||
\(747\) | 1.61303e9 | 0.141586 | ||||||||
\(748\) | 1.23849e9 | 0.108203 | ||||||||
\(749\) | 6.28729e9 | 0.546735 | ||||||||
\(750\) | −9.08555e8 | −0.0786387 | ||||||||
\(751\) | −9.05348e9 | −0.779966 | −0.389983 | − | 0.920822i | \(-0.627519\pi\) | ||||
−0.389983 | + | 0.920822i | \(0.627519\pi\) | |||||||
\(752\) | 3.26279e7 | 0.00279786 | ||||||||
\(753\) | 1.53248e9 | 0.130802 | ||||||||
\(754\) | 2.10531e8 | 0.0178861 | ||||||||
\(755\) | −1.50189e10 | −1.27006 | ||||||||
\(756\) | 2.93321e9 | 0.246897 | ||||||||
\(757\) | 1.51419e10 | 1.26866 | 0.634329 | − | 0.773063i | \(-0.281277\pi\) | ||||
0.634329 | + | 0.773063i | \(0.281277\pi\) | |||||||
\(758\) | −7.18188e9 | −0.598957 | ||||||||
\(759\) | −5.77523e8 | −0.0479428 | ||||||||
\(760\) | 3.96352e9 | 0.327516 | ||||||||
\(761\) | 1.28555e10 | 1.05741 | 0.528703 | − | 0.848807i | \(-0.322679\pi\) | ||||
0.528703 | + | 0.848807i | \(0.322679\pi\) | |||||||
\(762\) | −7.04009e9 | −0.576416 | ||||||||
\(763\) | 3.30909e9 | 0.269695 | ||||||||
\(764\) | −8.36478e8 | −0.0678622 | ||||||||
\(765\) | −5.47942e9 | −0.442507 | ||||||||
\(766\) | 1.53911e9 | 0.123728 | ||||||||
\(767\) | −8.45107e8 | −0.0676282 | ||||||||
\(768\) | 8.58258e9 | 0.683681 | ||||||||
\(769\) | 2.32284e10 | 1.84194 | 0.920972 | − | 0.389629i | \(-0.127397\pi\) | ||||
0.920972 | + | 0.389629i | \(0.127397\pi\) | |||||||
\(770\) | 1.13693e9 | 0.0897462 | ||||||||
\(771\) | −1.23227e10 | −0.968311 | ||||||||
\(772\) | 2.18726e9 | 0.171096 | ||||||||
\(773\) | 1.44242e10 | 1.12321 | 0.561607 | − | 0.827404i | \(-0.310183\pi\) | ||||
0.561607 | + | 0.827404i | \(0.310183\pi\) | |||||||
\(774\) | −1.16636e9 | −0.0904146 | ||||||||
\(775\) | −5.87961e9 | −0.453725 | ||||||||
\(776\) | 8.74401e9 | 0.671730 | ||||||||
\(777\) | −1.18566e9 | −0.0906750 | ||||||||
\(778\) | 1.31763e10 | 1.00314 | ||||||||
\(779\) | −3.24748e9 | −0.246131 | ||||||||
\(780\) | 2.14643e9 | 0.161952 | ||||||||
\(781\) | 7.06108e9 | 0.530387 | ||||||||
\(782\) | −1.24567e9 | −0.0931495 | ||||||||
\(783\) | −1.47971e9 | −0.110156 | ||||||||
\(784\) | 1.73895e7 | 0.00128878 | ||||||||
\(785\) | −2.36758e10 | −1.74687 | ||||||||
\(786\) | 3.70451e9 | 0.272115 | ||||||||
\(787\) | −1.09086e10 | −0.797735 | −0.398867 | − | 0.917009i | \(-0.630597\pi\) | ||||
−0.398867 | + | 0.917009i | \(0.630597\pi\) | |||||||
\(788\) | −7.17013e9 | −0.522018 | ||||||||
\(789\) | 1.65740e10 | 1.20132 | ||||||||
\(790\) | −9.11997e9 | −0.658110 | ||||||||
\(791\) | −7.94752e9 | −0.570971 | ||||||||
\(792\) | 2.07953e9 | 0.148740 | ||||||||
\(793\) | 4.32437e9 | 0.307941 | ||||||||
\(794\) | −2.87586e9 | −0.203890 | ||||||||
\(795\) | −6.34017e9 | −0.447524 | ||||||||
\(796\) | −1.45339e9 | −0.102138 | ||||||||
\(797\) | 1.69316e9 | 0.118466 | 0.0592330 | − | 0.998244i | \(-0.481135\pi\) | ||||
0.0592330 | + | 0.998244i | \(0.481135\pi\) | |||||||
\(798\) | 5.51783e8 | 0.0384378 | ||||||||
\(799\) | −2.74919e9 | −0.190674 | ||||||||
\(800\) | 1.25424e10 | 0.866093 | ||||||||
\(801\) | −2.05390e9 | −0.141210 | ||||||||
\(802\) | 9.00453e9 | 0.616383 | ||||||||
\(803\) | −2.09598e9 | −0.142851 | ||||||||
\(804\) | −2.18339e9 | −0.148161 | ||||||||
\(805\) | 1.88216e9 | 0.127166 | ||||||||
\(806\) | 1.33146e9 | 0.0895682 | ||||||||
\(807\) | 1.67967e9 | 0.112503 | ||||||||
\(808\) | 1.86769e10 | 1.24556 | ||||||||
\(809\) | −1.36657e10 | −0.907429 | −0.453715 | − | 0.891147i | \(-0.649901\pi\) | ||||
−0.453715 | + | 0.891147i | \(0.649901\pi\) | |||||||
\(810\) | 2.47324e9 | 0.163519 | ||||||||
\(811\) | 1.83163e10 | 1.20577 | 0.602885 | − | 0.797828i | \(-0.294018\pi\) | ||||
0.602885 | + | 0.797828i | \(0.294018\pi\) | |||||||
\(812\) | −3.76277e8 | −0.0246639 | ||||||||
\(813\) | 1.75729e10 | 1.14690 | ||||||||
\(814\) | −9.33819e8 | −0.0606844 | ||||||||
\(815\) | −2.14416e10 | −1.38741 | ||||||||
\(816\) | 5.91928e7 | 0.00381376 | ||||||||
\(817\) | 1.04612e9 | 0.0671129 | ||||||||
\(818\) | 1.06718e9 | 0.0681714 | ||||||||
\(819\) | −8.68878e8 | −0.0552669 | ||||||||
\(820\) | −1.37175e10 | −0.868814 | ||||||||
\(821\) | 1.34510e10 | 0.848307 | 0.424153 | − | 0.905590i | \(-0.360572\pi\) | ||||
0.424153 | + | 0.905590i | \(0.360572\pi\) | |||||||
\(822\) | −2.10153e9 | −0.131973 | ||||||||
\(823\) | 1.06821e9 | 0.0667968 | 0.0333984 | − | 0.999442i | \(-0.489367\pi\) | ||||
0.0333984 | + | 0.999442i | \(0.489367\pi\) | |||||||
\(824\) | 1.71998e10 | 1.07097 | ||||||||
\(825\) | −2.70996e9 | −0.168025 | ||||||||
\(826\) | −9.17680e8 | −0.0566580 | ||||||||
\(827\) | −1.47731e9 | −0.0908245 | −0.0454123 | − | 0.998968i | \(-0.514460\pi\) | ||||
−0.0454123 | + | 0.998968i | \(0.514460\pi\) | |||||||
\(828\) | 1.32024e9 | 0.0808251 | ||||||||
\(829\) | −5.54603e9 | −0.338097 | −0.169048 | − | 0.985608i | \(-0.554069\pi\) | ||||
−0.169048 | + | 0.985608i | \(0.554069\pi\) | |||||||
\(830\) | 3.71287e9 | 0.225391 | ||||||||
\(831\) | −1.55753e9 | −0.0941528 | ||||||||
\(832\) | −2.79869e9 | −0.168470 | ||||||||
\(833\) | −1.46522e9 | −0.0878303 | ||||||||
\(834\) | −1.38349e10 | −0.825839 | ||||||||
\(835\) | −8.13263e9 | −0.483424 | ||||||||
\(836\) | −7.15289e8 | −0.0423409 | ||||||||
\(837\) | −9.35808e9 | −0.551630 | ||||||||
\(838\) | −9.33829e9 | −0.548168 | ||||||||
\(839\) | 2.04818e10 | 1.19729 | 0.598646 | − | 0.801013i | \(-0.295705\pi\) | ||||
0.598646 | + | 0.801013i | \(0.295705\pi\) | |||||||
\(840\) | 6.07758e9 | 0.353796 | ||||||||
\(841\) | −1.70601e10 | −0.988996 | ||||||||
\(842\) | −1.25242e10 | −0.723034 | ||||||||
\(843\) | 7.93237e9 | 0.456043 | ||||||||
\(844\) | −9.26659e9 | −0.530544 | ||||||||
\(845\) | −1.84182e9 | −0.105014 | ||||||||
\(846\) | −1.77028e9 | −0.100518 | ||||||||
\(847\) | 6.14908e9 | 0.347711 | ||||||||
\(848\) | −7.63756e7 | −0.00430100 | ||||||||
\(849\) | −1.33506e10 | −0.748726 | ||||||||
\(850\) | −5.84517e9 | −0.326461 | ||||||||
\(851\) | −1.54591e9 | −0.0859867 | ||||||||
\(852\) | 1.44755e10 | 0.801855 | ||||||||
\(853\) | 2.15373e10 | 1.18814 | 0.594072 | − | 0.804412i | \(-0.297519\pi\) | ||||
0.594072 | + | 0.804412i | \(0.297519\pi\) | |||||||
\(854\) | 4.69573e9 | 0.257989 | ||||||||
\(855\) | 3.16463e9 | 0.173157 | ||||||||
\(856\) | 2.64705e10 | 1.44246 | ||||||||
\(857\) | 1.35756e10 | 0.736760 | 0.368380 | − | 0.929675i | \(-0.379913\pi\) | ||||
0.368380 | + | 0.929675i | \(0.379913\pi\) | |||||||
\(858\) | 6.13678e8 | 0.0331692 | ||||||||
\(859\) | −1.21787e10 | −0.655581 | −0.327790 | − | 0.944750i | \(-0.606304\pi\) | ||||
−0.327790 | + | 0.944750i | \(0.606304\pi\) | |||||||
\(860\) | 4.41887e9 | 0.236901 | ||||||||
\(861\) | −4.97963e9 | −0.265880 | ||||||||
\(862\) | −1.99004e10 | −1.05824 | ||||||||
\(863\) | −6.53280e9 | −0.345988 | −0.172994 | − | 0.984923i | \(-0.555344\pi\) | ||||
−0.172994 | + | 0.984923i | \(0.555344\pi\) | |||||||
\(864\) | 1.99626e10 | 1.05298 | ||||||||
\(865\) | 1.72177e10 | 0.904520 | ||||||||
\(866\) | −1.54108e10 | −0.806331 | ||||||||
\(867\) | 8.20719e9 | 0.427688 | ||||||||
\(868\) | −2.37968e9 | −0.123509 | ||||||||
\(869\) | 4.29169e9 | 0.221850 | ||||||||
\(870\) | −1.17579e9 | −0.0605358 | ||||||||
\(871\) | 1.87353e9 | 0.0960720 | ||||||||
\(872\) | 1.39318e10 | 0.711540 | ||||||||
\(873\) | 6.98156e9 | 0.355142 | ||||||||
\(874\) | 7.19435e8 | 0.0364504 | ||||||||
\(875\) | −1.39339e9 | −0.0703143 | ||||||||
\(876\) | −4.29685e9 | −0.215966 | ||||||||
\(877\) | −1.56638e10 | −0.784151 | −0.392075 | − | 0.919933i | \(-0.628243\pi\) | ||||
−0.392075 | + | 0.919933i | \(0.628243\pi\) | |||||||
\(878\) | −4.34175e9 | −0.216488 | ||||||||
\(879\) | −1.45869e10 | −0.724440 | ||||||||
\(880\) | −7.04403e7 | −0.00348443 | ||||||||
\(881\) | 3.73448e9 | 0.183998 | 0.0919992 | − | 0.995759i | \(-0.470674\pi\) | ||||
0.0919992 | + | 0.995759i | \(0.470674\pi\) | |||||||
\(882\) | −9.43492e8 | −0.0463018 | ||||||||
\(883\) | 9.21741e9 | 0.450554 | 0.225277 | − | 0.974295i | \(-0.427671\pi\) | ||||
0.225277 | + | 0.974295i | \(0.427671\pi\) | |||||||
\(884\) | −2.17865e9 | −0.106073 | ||||||||
\(885\) | 4.71982e9 | 0.228889 | ||||||||
\(886\) | −9.39242e9 | −0.453690 | ||||||||
\(887\) | −3.72046e10 | −1.79004 | −0.895022 | − | 0.446023i | \(-0.852840\pi\) | ||||
−0.895022 | + | 0.446023i | \(0.852840\pi\) | |||||||
\(888\) | −4.99183e9 | −0.239229 | ||||||||
\(889\) | −1.07969e10 | −0.515398 | ||||||||
\(890\) | −4.72767e9 | −0.224793 | ||||||||
\(891\) | −1.16386e9 | −0.0551225 | ||||||||
\(892\) | 4.77980e9 | 0.225493 | ||||||||
\(893\) | 1.58779e9 | 0.0746126 | ||||||||
\(894\) | −4.81184e9 | −0.225232 | ||||||||
\(895\) | −3.24160e10 | −1.51140 | ||||||||
\(896\) | 5.12145e9 | 0.237857 | ||||||||
\(897\) | 1.01593e9 | 0.0469990 | ||||||||
\(898\) | 5.84852e8 | 0.0269512 | ||||||||
\(899\) | 1.20047e9 | 0.0551052 | ||||||||
\(900\) | 6.19506e9 | 0.283267 | ||||||||
\(901\) | 6.43533e9 | 0.293112 | ||||||||
\(902\) | −3.92192e9 | −0.177941 | ||||||||
\(903\) | 1.60411e9 | 0.0724980 | ||||||||
\(904\) | −3.34603e10 | −1.50640 | ||||||||
\(905\) | −2.63660e10 | −1.18243 | ||||||||
\(906\) | −8.80286e9 | −0.393256 | ||||||||
\(907\) | −2.49092e9 | −0.110849 | −0.0554247 | − | 0.998463i | \(-0.517651\pi\) | ||||
−0.0554247 | + | 0.998463i | \(0.517651\pi\) | |||||||
\(908\) | 1.39906e10 | 0.620205 | ||||||||
\(909\) | 1.49123e10 | 0.658525 | ||||||||
\(910\) | −1.99998e9 | −0.0879795 | ||||||||
\(911\) | −2.57216e10 | −1.12715 | −0.563576 | − | 0.826064i | \(-0.690575\pi\) | ||||
−0.563576 | + | 0.826064i | \(0.690575\pi\) | |||||||
\(912\) | −3.41867e7 | −0.00149236 | ||||||||
\(913\) | −1.74721e9 | −0.0759796 | ||||||||
\(914\) | −3.95035e9 | −0.171129 | ||||||||
\(915\) | −2.41511e10 | −1.04223 | ||||||||
\(916\) | 1.87799e10 | 0.807344 | ||||||||
\(917\) | 5.68135e9 | 0.243309 | ||||||||
\(918\) | −9.30326e9 | −0.396904 | ||||||||
\(919\) | 5.43149e9 | 0.230842 | 0.115421 | − | 0.993317i | \(-0.463178\pi\) | ||||
0.115421 | + | 0.993317i | \(0.463178\pi\) | |||||||
\(920\) | 7.92418e9 | 0.335503 | ||||||||
\(921\) | −2.72467e9 | −0.114923 | ||||||||
\(922\) | −5.71803e9 | −0.240264 | ||||||||
\(923\) | −1.24212e10 | −0.519946 | ||||||||
\(924\) | −1.09681e9 | −0.0457383 | ||||||||
\(925\) | −7.25400e9 | −0.301357 | ||||||||
\(926\) | −1.30718e10 | −0.540999 | ||||||||
\(927\) | 1.37330e10 | 0.566220 | ||||||||
\(928\) | −2.56084e9 | −0.105187 | ||||||||
\(929\) | 4.77407e10 | 1.95359 | 0.976797 | − | 0.214169i | \(-0.0687044\pi\) | ||||
0.976797 | + | 0.214169i | \(0.0687044\pi\) | |||||||
\(930\) | −7.43602e9 | −0.303145 | ||||||||
\(931\) | 8.46232e8 | 0.0343689 | ||||||||
\(932\) | −2.42932e10 | −0.982945 | ||||||||
\(933\) | 3.98038e9 | 0.160450 | ||||||||
\(934\) | 2.14782e10 | 0.862548 | ||||||||
\(935\) | 5.93523e9 | 0.237463 | ||||||||
\(936\) | −3.65812e9 | −0.145812 | ||||||||
\(937\) | −2.24030e10 | −0.889648 | −0.444824 | − | 0.895618i | \(-0.646734\pi\) | ||||
−0.444824 | + | 0.895618i | \(0.646734\pi\) | |||||||
\(938\) | 2.03442e9 | 0.0804878 | ||||||||
\(939\) | 2.99553e10 | 1.18071 | ||||||||
\(940\) | 6.70688e9 | 0.263374 | ||||||||
\(941\) | −1.06797e10 | −0.417826 | −0.208913 | − | 0.977934i | \(-0.566993\pi\) | ||||
−0.208913 | + | 0.977934i | \(0.566993\pi\) | |||||||
\(942\) | −1.38769e10 | −0.540895 | ||||||||
\(943\) | −6.49262e9 | −0.252133 | ||||||||
\(944\) | 5.68564e7 | 0.00219977 | ||||||||
\(945\) | 1.40568e10 | 0.541845 | ||||||||
\(946\) | 1.26338e9 | 0.0485194 | ||||||||
\(947\) | −3.66166e10 | −1.40105 | −0.700525 | − | 0.713628i | \(-0.747051\pi\) | ||||
−0.700525 | + | 0.713628i | \(0.747051\pi\) | |||||||
\(948\) | 8.79816e9 | 0.335400 | ||||||||
\(949\) | 3.68706e9 | 0.140039 | ||||||||
\(950\) | 3.37586e9 | 0.127747 | ||||||||
\(951\) | −2.06059e10 | −0.776889 | ||||||||
\(952\) | −6.16880e9 | −0.231724 | ||||||||
\(953\) | 3.67810e10 | 1.37657 | 0.688285 | − | 0.725440i | \(-0.258364\pi\) | ||||
0.688285 | + | 0.725440i | \(0.258364\pi\) | |||||||
\(954\) | 4.14388e9 | 0.154521 | ||||||||
\(955\) | −4.00865e9 | −0.148931 | ||||||||
\(956\) | −1.38307e10 | −0.511968 | ||||||||
\(957\) | 5.53305e8 | 0.0204067 | ||||||||
\(958\) | 3.06766e10 | 1.12727 | ||||||||
\(959\) | −3.22297e9 | −0.118003 | ||||||||
\(960\) | 1.56303e10 | 0.570189 | ||||||||
\(961\) | −1.99205e10 | −0.724050 | ||||||||
\(962\) | 1.64269e9 | 0.0594898 | ||||||||
\(963\) | 2.11351e10 | 0.762626 | ||||||||
\(964\) | 3.92083e9 | 0.140964 | ||||||||
\(965\) | 1.04820e10 | 0.375489 | ||||||||
\(966\) | 1.10317e9 | 0.0393751 | ||||||||
\(967\) | −2.03570e10 | −0.723971 | −0.361986 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361986 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(968\) | 2.58886e10 | 0.917372 | ||||||||
\(969\) | 2.88053e9 | 0.101704 | ||||||||
\(970\) | 1.60702e10 | 0.565352 | ||||||||
\(971\) | 9.34911e9 | 0.327720 | 0.163860 | − | 0.986484i | \(-0.447605\pi\) | ||||
0.163860 | + | 0.986484i | \(0.447605\pi\) | |||||||
\(972\) | 1.63164e10 | 0.569893 | ||||||||
\(973\) | −2.12177e10 | −0.738419 | ||||||||
\(974\) | −5.60882e9 | −0.194498 | ||||||||
\(975\) | 4.76711e9 | 0.164717 | ||||||||
\(976\) | −2.90932e8 | −0.0100165 | ||||||||
\(977\) | −4.95354e10 | −1.69936 | −0.849679 | − | 0.527300i | \(-0.823204\pi\) | ||||
−0.849679 | + | 0.527300i | \(0.823204\pi\) | |||||||
\(978\) | −1.25674e10 | −0.429594 | ||||||||
\(979\) | 2.22475e9 | 0.0757779 | ||||||||
\(980\) | 3.57452e9 | 0.121318 | ||||||||
\(981\) | 1.11237e10 | 0.376190 | ||||||||
\(982\) | 1.30977e10 | 0.441371 | ||||||||
\(983\) | 8.29372e9 | 0.278492 | 0.139246 | − | 0.990258i | \(-0.455532\pi\) | ||||
0.139246 | + | 0.990258i | \(0.455532\pi\) | |||||||
\(984\) | −2.09650e10 | −0.701476 | ||||||||
\(985\) | −3.43614e10 | −1.14563 | ||||||||
\(986\) | 1.19344e9 | 0.0396488 | ||||||||
\(987\) | 2.43468e9 | 0.0805995 | ||||||||
\(988\) | 1.25827e9 | 0.0415074 | ||||||||
\(989\) | 2.09149e9 | 0.0687495 | ||||||||
\(990\) | 3.82185e9 | 0.125185 | ||||||||
\(991\) | 3.81642e9 | 0.124566 | 0.0622829 | − | 0.998059i | \(-0.480162\pi\) | ||||
0.0622829 | + | 0.998059i | \(0.480162\pi\) | |||||||
\(992\) | −1.61954e10 | −0.526747 | ||||||||
\(993\) | 1.29118e10 | 0.418471 | ||||||||
\(994\) | −1.34879e10 | −0.435604 | ||||||||
\(995\) | −6.96508e9 | −0.224153 | ||||||||
\(996\) | −3.58185e9 | −0.114868 | ||||||||
\(997\) | −4.67648e10 | −1.49447 | −0.747234 | − | 0.664562i | \(-0.768618\pi\) | ||||
−0.747234 | + | 0.664562i | \(0.768618\pi\) | |||||||
\(998\) | 2.97641e10 | 0.947842 | ||||||||
\(999\) | −1.15456e10 | −0.366384 |
(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 | 91.8.a.d.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.d.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial |