Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,20,Mod(9,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("40.9");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.c (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: | \(91.5266786226\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 9.4 | ||
Character | \(\chi\) | \(=\) | 40.9 |
Dual form | 40.20.c.a.9.25 |
$q$-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 \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 51907.0i | − | 1.52256i | −0.648425 | − | 0.761279i | \(-0.724572\pi\) | ||
0.648425 | − | 0.761279i | \(-0.275428\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.18724e6 | + | 2.98580e6i | 0.729793 | + | 0.683668i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.49555e7i | 0.889382i | 0.895684 | + | 0.444691i | \(0.146687\pi\) | ||||
−0.895684 | + | 0.444691i | \(0.853313\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.53207e9 | −1.31818 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.75339e9 | −0.352077 | −0.176038 | − | 0.984383i | \(-0.556328\pi\) | ||||
−0.176038 | + | 0.984383i | \(0.556328\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.26869e10i | − | 1.63951i | −0.572712 | − | 0.819757i | \(-0.694108\pi\) | ||
0.572712 | − | 0.819757i | \(-0.305892\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.54984e11 | − | 1.65440e11i | 1.04092 | − | 1.11115i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.18891e11i | 1.26575i | 0.774252 | + | 0.632877i | \(0.218126\pi\) | ||||
−0.774252 | + | 0.632877i | \(0.781874\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.01733e11 | 0.356709 | 0.178354 | − | 0.983966i | \(-0.442923\pi\) | ||||
0.178354 | + | 0.983966i | \(0.442923\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.92885e12 | 1.35414 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 4.34747e12i | − | 0.503295i | −0.967819 | − | 0.251647i | \(-0.919028\pi\) | ||
0.967819 | − | 0.251647i | \(-0.0809723\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.24354e12 | + | 1.90329e13i | 0.0651971 | + | 0.997872i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.91957e13i | 0.484449i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.23271e14 | −1.57790 | −0.788952 | − | 0.614455i | \(-0.789376\pi\) | ||||
−0.788952 | + | 0.614455i | \(0.789376\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.11787e13 | 0.143868 | 0.0719340 | − | 0.997409i | \(-0.477083\pi\) | ||||
0.0719340 | + | 0.997409i | \(0.477083\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.42920e14i | 0.536057i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.83518e14 | + | 3.02646e14i | −0.608042 | + | 0.649065i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.81760e14i | 0.735915i | 0.929843 | + | 0.367958i | \(0.119943\pi\) | ||||
−0.929843 | + | 0.367958i | \(0.880057\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.25389e15 | −2.49625 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.73607e14 | −0.225929 | −0.112964 | − | 0.993599i | \(-0.536035\pi\) | ||||
−0.112964 | + | 0.993599i | \(0.536035\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.02442e15i | 1.52453i | 0.647266 | + | 0.762264i | \(0.275912\pi\) | ||||
−0.647266 | + | 0.762264i | \(0.724088\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.88308e15 | − | 4.57445e15i | −0.962000 | − | 0.901198i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.08473e16i | 1.41381i | 0.707309 | + | 0.706905i | \(0.249909\pi\) | ||||
−0.707309 | + | 0.706905i | \(0.750091\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.38236e15 | 0.208999 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.21248e16 | 1.92718 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.62044e16i | − | 0.674549i | −0.941406 | − | 0.337274i | \(-0.890495\pi\) | ||
0.941406 | − | 0.337274i | \(-0.109505\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.77572e15 | − | 8.22106e15i | −0.256943 | − | 0.240703i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.60434e16i | − | 0.543109i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.36470e16 | 0.806216 | 0.403108 | − | 0.915152i | \(-0.367930\pi\) | ||||
0.403108 | + | 0.915152i | \(0.367930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.07683e16 | −0.665340 | −0.332670 | − | 0.943043i | \(-0.607949\pi\) | ||||
−0.332670 | + | 0.943043i | \(0.607949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.45478e17i | − | 1.17237i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.87170e17 | − | 1.99798e17i | 1.12088 | − | 1.19651i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.31722e17i | 1.93863i | 0.245830 | + | 0.969313i | \(0.420939\pi\) | ||||
−0.245830 | + | 0.969313i | \(0.579061\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.25664e17 | −0.766295 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.10030e17 | 0.543660 | 0.271830 | − | 0.962345i | \(-0.412371\pi\) | ||||
0.271830 | + | 0.962345i | \(0.412371\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.63041e17i | 0.721752i | 0.932614 | + | 0.360876i | \(0.117522\pi\) | ||||
−0.932614 | + | 0.360876i | \(0.882478\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.87940e17 | − | 6.45482e16i | 1.51932 | − | 0.0992663i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.61449e17i | − | 0.313131i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.38309e17 | −0.599202 | −0.299601 | − | 0.954065i | \(-0.596854\pi\) | ||||
−0.299601 | + | 0.954065i | \(0.596854\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.84278e17 | −0.580580 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00531e18i | 0.590280i | 0.955454 | + | 0.295140i | \(0.0953663\pi\) | ||||
−0.955454 | + | 0.295140i | \(0.904634\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.84788e18 | + | 1.97256e18i | −0.865355 | + | 0.923739i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.39863e18i | 2.40245i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.24662e18 | −0.679713 | −0.339856 | − | 0.940477i | \(-0.610378\pi\) | ||||
−0.339856 | + | 0.940477i | \(0.610378\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.95247e18 | 1.45815 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1.09932e18i | − | 0.219047i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.59915e18 | + | 1.49807e18i | 0.260324 | + | 0.243870i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.27007e19i | − | 1.69627i | −0.529781 | − | 0.848135i | \(-0.677726\pi\) | ||
0.529781 | − | 0.848135i | \(-0.322274\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.21839e18 | 0.464101 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.86126e19 | 1.69338 | 0.846690 | − | 0.532087i | \(-0.178592\pi\) | ||||
0.846690 | + | 0.532087i | \(0.178592\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.72849e19i | 1.30531i | 0.757656 | + | 0.652654i | \(0.226344\pi\) | ||||
−0.757656 | + | 0.652654i | \(0.773656\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.57094e19 | + | 1.47165e19i | 0.988239 | + | 0.925779i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.53090e19i | − | 0.805008i | −0.915418 | − | 0.402504i | \(-0.868140\pi\) | ||
0.915418 | − | 0.402504i | \(-0.131860\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.19011e19 | 1.84788 | 0.923940 | − | 0.382537i | \(-0.124950\pi\) | ||||
0.923940 | + | 0.382537i | \(0.124950\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.01974e19 | 1.12047 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.54178e19i | 1.10911i | 0.832146 | + | 0.554557i | \(0.187112\pi\) | ||||
−0.832146 | + | 0.554557i | \(0.812888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.29807e19 | − | 1.38564e19i | 0.344086 | − | 0.367301i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.60408e19i | 2.16118i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.87671e19 | −1.12574 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.35779e19 | −0.876042 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.45835e19i | 0.343989i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.28649e19 | + | 6.43754e19i | −0.634633 | + | 0.772814i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.80973e19i | 0.806308i | 0.915132 | + | 0.403154i | \(0.132086\pi\) | ||||
−0.915132 | + | 0.403154i | \(0.867914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.60802e20 | 2.32118 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.40863e19 | 0.108323 | 0.0541615 | − | 0.998532i | \(-0.482751\pi\) | ||||
0.0541615 | + | 0.998532i | \(0.482751\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.76423e19i | 0.317250i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.73144e19 | + | 6.11813e19i | −0.331202 | + | 0.353547i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.84488e20i | 1.42961i | 0.699323 | + | 0.714806i | \(0.253485\pi\) | ||||
−0.699323 | + | 0.714806i | \(0.746515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.56887e19 | 0.112487 | 0.0562434 | − | 0.998417i | \(-0.482088\pi\) | ||||
0.0562434 | + | 0.998417i | \(0.482088\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.63049e20 | 2.15261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.72602e20i | 0.577235i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.92895e20 | − | 3.68063e20i | −1.15154 | − | 1.07876i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.23661e20i | − | 0.318213i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.04560e19 | −0.136826 | −0.0684132 | − | 0.997657i | \(-0.521794\pi\) | ||||
−0.0684132 | + | 0.997657i | \(0.521794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.35785e20 | 1.86593 | 0.932964 | − | 0.359969i | \(-0.117213\pi\) | ||||
0.932964 | + | 0.359969i | \(0.117213\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 9.48185e20i | − | 1.66849i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.75018e19 | + | 6.32354e19i | 0.104994 | + | 0.0983578i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.63878e20i | − | 0.914201i | −0.889415 | − | 0.457101i | \(-0.848888\pi\) | ||
0.889415 | − | 0.457101i | \(-0.151112\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.41124e20 | −1.02704 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.12816e20 | 0.447622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.73165e20i | 0.938435i | 0.883083 | + | 0.469218i | \(0.155464\pi\) | ||||
−0.883083 | + | 0.469218i | \(0.844536\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.26730e20 | + | 4.55521e20i | −0.366485 | + | 0.391211i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.02768e20i | − | 0.0787137i | −0.999225 | − | 0.0393569i | \(-0.987469\pi\) | ||
0.999225 | − | 0.0393569i | \(-0.0125309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.46773e21 | −1.68801 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.68691e20 | −0.470207 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.57020e21i | − | 0.860039i | −0.902820 | − | 0.430020i | \(-0.858507\pi\) | ||
0.902820 | − | 0.430020i | \(-0.141493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.80728e21 | + | 1.18081e20i | −0.887490 | + | 0.0579851i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.78465e21i | − | 1.22751i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.88879e21 | −0.748308 | −0.374154 | − | 0.927367i | \(-0.622067\pi\) | ||||
−0.374154 | + | 0.927367i | \(0.622067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.78786e20 | 0.206334 | 0.103167 | − | 0.994664i | \(-0.467102\pi\) | ||||
0.103167 | + | 0.994664i | \(0.467102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.15430e21i | 1.01302i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.73702e21 | + | 1.85421e21i | −0.503121 | + | 0.537066i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.70405e21i | − | 0.445643i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.82273e21 | −0.430860 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.82963e21 | 1.03299 | 0.516495 | − | 0.856290i | \(-0.327236\pi\) | ||||
0.516495 | + | 0.856290i | \(0.327236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.40372e21i | − | 0.853149i | −0.904452 | − | 0.426575i | \(-0.859720\pi\) | ||
0.904452 | − | 0.426575i | \(-0.140280\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.03709e22 | − | 9.71544e21i | −1.82175 | − | 1.70661i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.23795e21i | − | 0.356797i | −0.983958 | − | 0.178399i | \(-0.942908\pi\) | ||
0.983958 | − | 0.178399i | \(-0.0570916\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.32253e22 | −1.91558 | −0.957789 | − | 0.287471i | \(-0.907186\pi\) | ||||
−0.957789 | + | 0.287471i | \(0.907186\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.24094e22 | 2.95167 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.17053e22i | − | 1.40336i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50950e21 | − | 1.41409e21i | −0.164881 | − | 0.154460i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.66064e21i | 0.663434i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.38147e21 | −0.125589 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.14422e21 | −0.0950221 | −0.0475110 | − | 0.998871i | \(-0.515129\pi\) | ||||
−0.0475110 | + | 0.998871i | \(0.515129\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.09020e22i | − | 0.827754i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.50019e22 | + | 1.60140e22i | −1.04227 | + | 1.11259i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.01104e21i | 0.127954i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.88443e22 | 1.09891 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.87964e22 | 2.07522 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.44066e22i | 1.19842i | 0.800591 | + | 0.599212i | \(0.204519\pi\) | ||||
−0.800591 | + | 0.599212i | \(0.795481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.90518e21 | − | 2.91598e22i | −0.0859416 | − | 1.31538i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.92778e22i | 0.799487i | 0.916627 | + | 0.399743i | \(0.130901\pi\) | ||||
−0.916627 | + | 0.399743i | \(0.869099\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.86172e22 | 0.710359 | 0.355180 | − | 0.934798i | \(-0.384420\pi\) | ||||
0.355180 | + | 0.934798i | \(0.384420\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.35710e22 | −0.476760 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.27033e22i | 0.734867i | 0.930050 | + | 0.367433i | \(0.119763\pi\) | ||||
−0.930050 | + | 0.367433i | \(0.880237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.23877e22 | + | 3.45729e22i | −0.966576 | + | 1.03179i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.31327e22i | 0.912320i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.52661e22 | −0.642329 | −0.321164 | − | 0.947023i | \(-0.604074\pi\) | ||||
−0.321164 | + | 0.947023i | \(0.604074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.86168e22 | −1.37677 | −0.688383 | − | 0.725347i | \(-0.741679\pi\) | ||||
−0.688383 | + | 0.725347i | \(0.741679\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.30199e22i | 1.36842i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.59315e21 | + | 7.11323e21i | 0.152526 | + | 0.142886i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.14521e22i | − | 0.584829i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.21826e22 | 0.898735 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.86574e22 | 1.41519 | 0.707595 | − | 0.706619i | \(-0.249780\pi\) | ||||
0.707595 | + | 0.706619i | \(0.249780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.19703e22i | 0.177198i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.02389e23 | + | 9.59180e22i | 1.40645 | + | 1.31755i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.04451e23i | − | 1.33213i | −0.745893 | − | 0.666065i | \(-0.767977\pi\) | ||
0.745893 | − | 0.666065i | \(-0.232023\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.52413e22 | −0.654510 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.88860e23 | 2.07996 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 1.57350e21i | − | 0.0161171i | −0.999968 | − | 0.00805855i | \(-0.997435\pi\) | ||
0.999968 | − | 0.00805855i | \(-0.00256515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.83832e22 | − | 5.16475e22i | 0.461167 | − | 0.492281i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.16615e23i | 1.03490i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.71828e22 | 0.803420 | 0.401710 | − | 0.915767i | \(-0.368416\pi\) | ||||
0.401710 | + | 0.915767i | \(0.368416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.57587e22 | −0.121427 | −0.0607133 | − | 0.998155i | \(-0.519338\pi\) | ||||
−0.0607133 | + | 0.998155i | \(0.519338\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 3.08974e23i | − | 2.22012i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.42394e21 | − | 5.24050e22i | −0.0229544 | − | 0.351328i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.05740e22i | 0.566821i | 0.958999 | + | 0.283411i | \(0.0914659\pi\) | ||||
−0.958999 | + | 0.283411i | \(0.908534\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.24473e22 | −0.189644 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.95756e23 | −1.06907 | −0.534534 | − | 0.845147i | \(-0.679513\pi\) | ||||
−0.534534 | + | 0.845147i | \(0.679513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.80289e23i | 0.920446i | 0.887803 | + | 0.460223i | \(0.152231\pi\) | ||||
−0.887803 | + | 0.460223i | \(0.847769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.77604e22 | − | 8.30068e22i | 0.371306 | − | 0.396358i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.49716e22i | − | 0.200937i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.43954e23 | −0.602135 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.59253e23 | −2.58267 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.98213e23i | 1.82883i | 0.404780 | + | 0.914414i | \(0.367348\pi\) | ||||
−0.404780 | + | 0.914414i | \(0.632652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.70986e23 | + | 1.60179e23i | 0.588371 | + | 0.551184i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.28532e22i | − | 0.170563i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.72530e23 | −0.825159 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.77096e23 | −1.35589 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.66124e23i | − | 2.57827i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.93683e23 | − | 1.81442e23i | −0.485561 | − | 0.454871i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.55902e22i | − | 0.178095i | −0.996027 | − | 0.0890473i | \(-0.971618\pi\) | ||
0.996027 | − | 0.0890473i | \(-0.0283822\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.97206e23 | 1.98741 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.02693e23 | −1.88069 | −0.940343 | − | 0.340228i | \(-0.889496\pi\) | ||||
−0.940343 | + | 0.340228i | \(0.889496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.36458e23i | − | 0.855601i | −0.903873 | − | 0.427801i | \(-0.859289\pi\) | ||
0.903873 | − | 0.427801i | \(-0.140711\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.34369e23 | − | 4.63675e23i | 0.801509 | − | 0.855586i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.56760e23i | 1.66242i | 0.555961 | + | 0.831208i | \(0.312350\pi\) | ||||
−0.555961 | + | 0.831208i | \(0.687650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.39414e23 | 0.555543 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.94642e23 | −1.22567 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.10518e23i | 0.451506i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.19311e24 | − | 7.79534e22i | 1.63603 | − | 0.106892i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.17496e24i | − | 2.81350i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.03001e24 | −1.25742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.98381e23 | 0.920120 | 0.460060 | − | 0.887888i | \(-0.347828\pi\) | ||||
0.460060 | + | 0.887888i | \(0.347828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.91298e23i | − | 0.970069i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.28903e24 | + | 1.37600e24i | −1.32538 | + | 1.41480i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.05297e23i | − | 0.102313i | −0.998691 | − | 0.0511567i | \(-0.983709\pi\) | ||
0.998691 | − | 0.0511567i | \(-0.0162908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.83843e24 | 1.68869 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.83133e22 | −0.0506525 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.30861e24i | 1.07526i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.19246e23 | − | 6.73787e23i | −0.559237 | − | 0.523891i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.22010e24i | − | 1.63397i | −0.576661 | − | 0.816983i | \(-0.695645\pi\) | ||
0.576661 | − | 0.816983i | \(-0.304355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.24343e24 | −1.56340 | −0.781700 | − | 0.623654i | \(-0.785647\pi\) | ||||
−0.781700 | + | 0.623654i | \(0.785647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.20332e24 | 0.794260 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.44469e24i | − | 0.903472i | −0.892152 | − | 0.451736i | \(-0.850805\pi\) | ||
0.892152 | − | 0.451736i | \(-0.149195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.69417e23 | + | 6.27108e23i | 0.396760 | + | 0.371683i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.05042e24i | 1.71400i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.47412e24 | 1.31833 | 0.659163 | − | 0.752000i | \(-0.270911\pi\) | ||||
0.659163 | + | 0.752000i | \(0.270911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.72668e24 | −0.872759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.78107e24i | 1.33382i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.08397e24 | + | 1.15710e24i | −0.493439 | + | 0.526730i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.79620e24i | 1.20848i | 0.796801 | + | 0.604241i | \(0.206524\pi\) | ||||
−0.796801 | + | 0.604241i | \(0.793476\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.25599e23 | 0.297815 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.53870e24 | 0.599932 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.66160e22i | 0.0172704i | 0.999963 | + | 0.00863518i | \(0.00274870\pi\) | ||||
−0.999963 | + | 0.00863518i | \(0.997251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.34153e24 | + | 2.74406e24i | 1.17665 | + | 0.966265i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.72749e24i | 2.58700i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.68682e24 | −1.49213 | −0.746063 | − | 0.665875i | \(-0.768058\pi\) | ||||
−0.746063 | + | 0.665875i | \(0.768058\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.05380e24 | 1.22765 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.47940e24i | − | 1.00257i | −0.865282 | − | 0.501286i | \(-0.832860\pi\) | ||
0.865282 | − | 0.501286i | \(-0.167140\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.80634e23 | − | 8.33303e23i | 0.214077 | − | 0.228521i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.69776e24i | − | 2.00960i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.55787e23 | −0.187879 | −0.0939395 | − | 0.995578i | \(-0.529946\pi\) | ||||
−0.0939395 | + | 0.995578i | \(0.529946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.69061e24 | 0.637048 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 7.31179e23i | − | 0.164928i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.03445e24 | − | 1.90586e24i | −0.437294 | − | 0.409655i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.54400e24i | 1.54558i | 0.634661 | + | 0.772791i | \(0.281140\pi\) | ||||
−0.634661 | + | 0.772791i | \(0.718860\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.47297e24 | 0.483032 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.32118e24 | 1.17741 | 0.588704 | − | 0.808349i | \(-0.299638\pi\) | ||||
0.588704 | + | 0.808349i | \(0.299638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.32763e24i | − | 0.235873i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.49968e24 | − | 2.34169e24i | −0.423704 | − | 0.396924i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.60181e24i | − | 0.259099i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00935e24 | −0.464624 | −0.232312 | − | 0.972641i | \(-0.574629\pi\) | ||||
−0.232312 | + | 0.972641i | \(0.574629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.47669e25 | 2.17667 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.09408e24i | 0.717034i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00165e24 | + | 3.20417e24i | −0.403555 | + | 0.430783i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.33342e24i | − | 0.171268i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.13195e23 | −0.0261663 | −0.0130832 | − | 0.999914i | \(-0.504165\pi\) | ||||
−0.0130832 | + | 0.999914i | \(0.504165\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.43076e24 | 0.637061 | 0.318530 | − | 0.947913i | \(-0.396811\pi\) | ||||
0.318530 | + | 0.947913i | \(0.396811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.66188e25i | − | 1.86366i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.17793e25 | + | 7.69613e23i | −1.26306 | + | 0.0825235i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5.77028e24i | − | 0.591742i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.95922e24 | 0.878873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.98233e24 | −0.843053 | −0.421527 | − | 0.906816i | \(-0.638506\pi\) | ||||
−0.421527 | + | 0.906816i | \(0.638506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.26267e24i | − | 0.293048i | −0.989207 | − | 0.146524i | \(-0.953192\pi\) | ||
0.989207 | − | 0.146524i | \(-0.0468085\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.91050e25 | + | 2.03940e25i | −1.64248 | + | 1.75329i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.18127e24i | − | 0.179530i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.11317e25 | −1.66541 | −0.832707 | − | 0.553714i | \(-0.813210\pi\) | ||||
−0.832707 | + | 0.553714i | \(0.813210\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.64994e24 | −0.275498 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.96861e24i | 0.576166i | 0.957606 | + | 0.288083i | \(0.0930178\pi\) | ||||
−0.957606 | + | 0.288083i | \(0.906982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.16054e24 | − | 6.70796e24i | −0.496050 | − | 0.464698i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.13809e24i | 0.208326i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.91113e24 | 0.439753 | 0.219877 | − | 0.975528i | \(-0.429435\pi\) | ||||
0.219877 | + | 0.975528i | \(0.429435\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.30402e24 | 0.0795442 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 4.85737e25i | − | 2.84098i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.89719e25 | + | 1.77728e25i | 1.06415 | + | 0.996893i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.29466e24i | 0.177258i | 0.996065 | + | 0.0886291i | \(0.0282486\pi\) | ||||
−0.996065 | + | 0.0886291i | \(0.971751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.18800e25 | −0.613193 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.23204e25 | −1.60073 | −0.800365 | − | 0.599513i | \(-0.795361\pi\) | ||||
−0.800365 | + | 0.599513i | \(0.795361\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.83832e24i | 0.229972i | 0.993367 | + | 0.114986i | \(0.0366823\pi\) | ||||
−0.993367 | + | 0.114986i | \(0.963318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.28236e24 | − | 3.50381e24i | 0.149755 | − | 0.159859i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.95292e25i | − | 1.29343i | −0.762734 | − | 0.646713i | \(-0.776143\pi\) | ||
0.762734 | − | 0.646713i | \(-0.223857\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.09944e25 | −1.72418 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.44599e25 | −1.39192 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.38342e25i | − | 0.536751i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.23923e23 | + | 9.54944e24i | 0.0232564 | + | 0.355950i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.48264e25i | 0.889178i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.00260e25 | 1.37770 | 0.688850 | − | 0.724904i | \(-0.258116\pi\) | ||||
0.688850 | + | 0.724904i | \(0.258116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.64688e25 | 1.20654 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 2.14280e25i | − | 0.681530i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.79216e25 | − | 4.04801e25i | 1.15968 | − | 1.23793i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.08371e24i | − | 0.0318704i | −0.999873 | − | 0.0159352i | \(-0.994927\pi\) | ||
0.999873 | − | 0.0159352i | \(-0.00507254\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.05140e25 | 1.42882 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.29078e24 | −0.0623318 | −0.0311659 | − | 0.999514i | \(-0.509922\pi\) | ||||
−0.0311659 | + | 0.999514i | \(0.509922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.62914e25i | − | 1.99724i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.34450e25 | + | 1.25952e25i | 0.338698 | + | 0.317291i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.99435e25i | 0.483522i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.31509e25 | 0.540272 | 0.270136 | − | 0.962822i | \(-0.412931\pi\) | ||||
0.270136 | + | 0.962822i | \(0.412931\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.33436e24 | −0.119846 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 2.08813e25i | − | 0.451712i | −0.974161 | − | 0.225856i | \(-0.927482\pi\) | ||
0.974161 | − | 0.225856i | \(-0.0725179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.93229e25 | + | 5.55735e25i | 1.23582 | + | 1.15771i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.28092e26i | 2.57009i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.56854e25 | −0.303163 | −0.151581 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151581 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.44727e25 | −0.641914 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.63111e24i | 0.172807i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.16091e25 | + | 5.50911e25i | −0.892397 | + | 0.952605i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.98668e25i | − | 0.497769i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.15046e25 | −1.30946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.02646e25 | −0.313892 | −0.156946 | − | 0.987607i | \(-0.550165\pi\) | ||||
−0.156946 | + | 0.987607i | \(0.550165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.19165e25i | − | 0.327344i | −0.986515 | − | 0.163672i | \(-0.947666\pi\) | ||
0.986515 | − | 0.163672i | \(-0.0523338\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.12920e24 | + | 9.38103e25i | 0.0882857 | + | 1.35125i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.31073e25i | 0.182101i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.57149e25 | 0.746694 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.21910e25 | −1.06274 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.96890e25i | 0.370413i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.57094e25 | − | 4.87934e25i | 0.550358 | − | 0.587489i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.80415e25i | 1.13934i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.55956e24 | −0.0735836 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.03853e25 | 0.329071 | 0.164536 | − | 0.986371i | \(-0.447387\pi\) | ||||
0.164536 | + | 0.986371i | \(0.447387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 3.00430e25i | − | 0.314156i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.33549e26 | + | 1.25108e26i | 1.34857 | + | 1.26334i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.47601e26i | 1.43950i | 0.694235 | + | 0.719748i | \(0.255743\pi\) | ||||
−0.694235 | + | 0.719748i | \(0.744257\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.31013e25 | 0.877038 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.18493e25 | −0.562852 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.06109e25i | − | 0.532920i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.62464e25 | + | 9.01633e25i | 0.817714 | + | 0.766031i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.48048e26i | − | 1.21557i | −0.794103 | − | 0.607783i | \(-0.792059\pi\) | ||
0.794103 | − | 0.607783i | \(-0.207941\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.14965e26 | 2.49948 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.84520e25 | −0.678516 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.39040e26i | − | 1.77272i | −0.462994 | − | 0.886362i | \(-0.653225\pi\) | ||
0.462994 | − | 0.886362i | \(-0.346775\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.05750e26 | + | 1.12885e26i | −0.758265 | + | 0.809424i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 7.44714e25i | − | 0.516358i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.52796e25 | 0.370679 | 0.185340 | − | 0.982675i | \(-0.440662\pi\) | ||||
0.185340 | + | 0.982675i | \(0.440662\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.90520e26 | 1.23566 | 0.617830 | − | 0.786312i | \(-0.288012\pi\) | ||||
0.617830 | + | 0.786312i | \(0.288012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.50691e26i | − | 1.57279i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.27450e25 | − | 5.40624e24i | 0.502224 | − | 0.0328134i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.81877e26i | − | 1.65535i | −0.561208 | − | 0.827675i | \(-0.689663\pi\) | ||
0.561208 | − | 0.827675i | \(-0.310337\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.28584e26 | −1.29897 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.54597e25 | −0.524985 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.46172e25i | 0.237493i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.86758e26 | + | 3.06105e26i | −1.47753 | + | 1.57721i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.47526e26i | 0.735880i | 0.929850 | + | 0.367940i | \(0.119937\pi\) | ||||
−0.929850 | + | 0.367940i | \(0.880063\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.06261e25 | 0.0513189 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.16165e26 | −0.543244 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.42954e26i | − | 1.55316i | −0.630018 | − | 0.776580i | \(-0.716953\pi\) | ||
0.630018 | − | 0.776580i | \(-0.283047\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.87305e26 | − | 1.75467e26i | −0.821558 | − | 0.769632i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.86483e26i | 2.91658i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.08138e25 | 0.0445064 | 0.0222532 | − | 0.999752i | \(-0.492916\pi\) | ||||
0.0222532 | + | 0.999752i | \(0.492916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.33608e24 | 0.0133024 | 0.00665119 | − | 0.999978i | \(-0.497883\pi\) | ||||
0.00665119 | + | 0.999978i | \(0.497883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6.61429e26i | − | 2.55546i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.70766e26 | − | 1.59973e26i | −0.639330 | − | 0.598922i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.55206e26i | 0.925972i | 0.886366 | + | 0.462986i | \(0.153222\pi\) | ||||
−0.886366 | + | 0.462986i | \(0.846778\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.07585e26 | −2.13670 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.79982e26 | 2.31796 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.21928e26i | 0.402929i | 0.979496 | + | 0.201464i | \(0.0645701\pi\) | ||||
−0.979496 | + | 0.201464i | \(0.935430\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.34013e25 | + | 7.83535e25i | −0.235174 | + | 0.251041i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 4.20744e26i | − | 1.30710i | −0.756883 | − | 0.653550i | \(-0.773279\pi\) | ||
0.756883 | − | 0.653550i | \(-0.226721\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.15171e26 | −0.949478 | −0.474739 | − | 0.880127i | \(-0.657458\pi\) | ||||
−0.474739 | + | 0.880127i | \(0.657458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.34527e25 | 0.243820 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.13329e26i | − | 0.604525i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.60705e26 | + | 4.73362e25i | −0.991499 | + | 0.130117i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.17078e25i | 0.191216i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.60046e26 | −0.931488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.34376e26 | 0.839374 | 0.419687 | − | 0.907669i | \(-0.362140\pi\) | ||||
0.419687 | + | 0.907669i | \(0.362140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.93928e25i | 0.144677i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.33183e26 | + | 2.48915e26i | −0.551247 | + | 0.588438i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.49343e26i | − | 0.342657i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.21781e26 | −0.716643 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.13375e26 | −0.461309 | −0.230655 | − | 0.973036i | \(-0.574087\pi\) | ||||
−0.230655 | + | 0.973036i | \(0.574087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.78778e26i | − | 1.63459i | −0.576218 | − | 0.817296i | \(-0.695472\pi\) | ||
0.576218 | − | 0.817296i | \(-0.304528\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.31240e26 | + | 7.78702e26i | 1.69398 | + | 1.58692i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.74677e26i | 0.741423i | 0.928748 | + | 0.370711i | \(0.120886\pi\) | ||||
−0.928748 | + | 0.370711i | \(0.879114\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.47711e26 | −0.283850 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.04387e26 | 0.194817 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 8.45287e25i | − | 0.153225i | −0.997061 | − | 0.0766124i | \(-0.975590\pi\) | ||
0.997061 | − | 0.0766124i | \(-0.0244104\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.48966e25 | + | 4.20589e25i | 0.0790535 | + | 0.0740570i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 5.56204e26i | − | 0.951400i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.18088e25 | −0.0196243 | −0.00981216 | − | 0.999952i | \(-0.503123\pi\) | ||||
−0.00981216 | + | 0.999952i | \(0.503123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.62597e26 | 0.424009 | 0.212005 | − | 0.977269i | \(-0.432001\pi\) | ||||
0.212005 | + | 0.977269i | \(0.432001\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.01380e27i | − | 3.15964i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.42250e26 | + | 1.51848e26i | −0.216894 | + | 0.231527i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.35918e26i | 0.794151i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.26687e27 | 1.82467 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.67319e26 | 0.234251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.36213e26i | 0.321485i | 0.986996 | + | 0.160742i | \(0.0513888\pi\) | ||||
−0.986996 | + | 0.160742i | \(0.948611\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.65350e26 | + | 2.38705e25i | −0.483418 | + | 0.0315846i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.49049e26i | 0.834997i | 0.908678 | + | 0.417498i | \(0.137093\pi\) | ||||
−0.908678 | + | 0.417498i | \(0.862907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.20600e27 | 1.50863 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.00065e27 | 1.21726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.23990e26i | 0.974822i | 0.873173 | + | 0.487411i | \(0.162059\pi\) | ||||
−0.873173 | + | 0.487411i | \(0.837941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.49422e26 | + | 9.06731e26i | −0.977379 | + | 1.04332i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9.66364e26i | − | 1.08156i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.01581e27 | −1.10593 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.97671e26 | −0.738940 | −0.369470 | − | 0.929243i | \(-0.620461\pi\) | ||||
−0.369470 | + | 0.929243i | \(0.620461\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.00559e26i | 0.412763i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.18761e25 | + | 7.67012e25i | 0.0820921 | + | 0.0769036i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.93111e26i | − | 0.285970i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.17846e27 | 1.11888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.27862e26 | 0.580154 | 0.290077 | − | 0.957003i | \(-0.406319\pi\) | ||||
0.290077 | + | 0.957003i | \(0.406319\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.91888e26i | 0.262507i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.79457e27 | + | 1.68115e27i | 1.57096 | + | 1.47167i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.76737e27i | 1.50606i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.38698e26 | −0.446896 | −0.223448 | − | 0.974716i | \(-0.571731\pi\) | ||||
−0.223448 | + | 0.974716i | \(0.571731\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.77935e26 | 0.789857 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 9.20740e25i | − | 0.0724080i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.15353e26 | + | 5.50123e26i | −0.394637 | + | 0.421262i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.31148e27i | 0.977982i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.72365e26 | −0.633539 | −0.316770 | − | 0.948502i | \(-0.602598\pi\) | ||||
−0.316770 | + | 0.948502i | \(0.602598\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.64129e27 | −1.16092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.04262e27i | 2.09621i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.53292e26 | − | 2.34621e27i | −0.102875 | − | 1.57455i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.01357e27i | 1.97017i | 0.172065 | + | 0.985086i | \(0.444956\pi\) | ||||
−0.172065 | + | 0.985086i | \(0.555044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.35963e27 | 1.50291 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.10957e27 | −1.92968 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.19909e27i | − | 1.93437i | −0.254078 | − | 0.967184i | \(-0.581772\pi\) | ||
0.254078 | − | 0.967184i | \(-0.418228\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.69226e26 | − | 3.94137e26i | 0.217552 | − | 0.232230i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.18870e27i | − | 0.682545i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.17417e27 | −0.657068 | −0.328534 | − | 0.944492i | \(-0.606555\pi\) | ||||
−0.328534 | + | 0.944492i | \(0.606555\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.63258e27 | −0.890435 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.77571e27i | − | 0.944014i | −0.881595 | − | 0.472007i | \(-0.843530\pi\) | ||
0.881595 | − | 0.472007i | \(-0.156470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.92688e26 | − | 1.80509e26i | −0.0998550 | − | 0.0935438i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.54021e27i | − | 0.778096i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.45367e27 | 0.715960 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.75649e27 | 1.80386 | 0.901930 | − | 0.431882i | \(-0.142150\pi\) | ||||
0.901930 | + | 0.431882i | \(0.142150\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.60194e27i | − | 2.15471i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.98257e27 | + | 2.79406e27i | 1.36174 | + | 1.27568i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.52038e26i | 0.423880i | 0.977283 | + | 0.211940i | \(0.0679782\pi\) | ||||
−0.977283 | + | 0.211940i | \(0.932022\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.21341e26 | 0.269795 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.69849e27 | −1.56628 | −0.783141 | − | 0.621845i | \(-0.786384\pi\) | ||||
−0.783141 | + | 0.621845i | \(0.786384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.97874e27i | 1.64347i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.83109e27 | − | 3.02209e27i | 1.14069 | − | 1.21766i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.36297e27i | − | 1.32180i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.80215e27 | 1.07446 | 0.537232 | − | 0.843435i | \(-0.319470\pi\) | ||||
0.537232 | + | 0.843435i | \(0.319470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.42172e27 | −2.02825 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.21422e26i | 0.0808194i | 0.999183 | + | 0.0404097i | \(0.0128663\pi\) | ||||
−0.999183 | + | 0.0404097i | \(0.987134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.63365e25 | + | 4.03093e26i | 0.00937977 | + | 0.143562i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.86741e27i | 0.996529i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.37624e26 | −0.0805907 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.78295e26 | −0.191410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.36627e27i | − | 0.764413i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.98221e27 | − | 2.11594e27i | 0.625010 | − | 0.667178i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.93703e27i | − | 1.82730i | −0.406504 | − | 0.913649i | \(-0.633252\pi\) | ||
0.406504 | − | 0.913649i | \(-0.366748\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.16756e25 | −0.0245392 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.36311e27 | −0.986426 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.80938e27i | 1.09083i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.68086e27 | − | 2.51142e27i | −0.749527 | − | 0.702154i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.92749e27i | − | 0.526185i | −0.964771 | − | 0.263093i | \(-0.915258\pi\) | ||
0.964771 | − | 0.263093i | \(-0.0847425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.71328e27 | −1.78954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.44199e27 | 0.895984 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 9.99593e26i | − | 0.254112i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.31575e27 | + | 1.23259e27i | 0.326671 | + | 0.306024i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 5.04446e27i | − | 1.22325i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.43062e27 | −0.812572 | −0.406286 | − | 0.913746i | \(-0.633176\pi\) | ||||
−0.406286 | + | 0.913746i | \(0.633176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.59172e27 | 0.368272 | 0.184136 | − | 0.982901i | \(-0.441051\pi\) | ||||
0.184136 | + | 0.982901i | \(0.441051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.17989e26i | 0.184879i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.90567e27 | + | 3.10171e27i | −0.641578 | + | 0.684864i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.52092e27i | 0.543812i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.11960e27 | −1.92211 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.09546e27 | −1.46124 | −0.730618 | − | 0.682786i | \(-0.760768\pi\) | ||||
−0.730618 | + | 0.682786i | \(0.760768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.62780e27i | 1.13251i | 0.824232 | + | 0.566253i | \(0.191607\pi\) | ||||
−0.824232 | + | 0.566253i | \(0.808393\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.72018e27 | + | 1.77726e26i | −0.534916 | + | 0.0349493i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.11492e27i | 0.214260i | 0.994245 | + | 0.107130i | \(0.0341661\pi\) | ||||
−0.994245 | + | 0.107130i | \(0.965834\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.95026e27 | −0.554105 | −0.277052 | − | 0.960855i | \(-0.589358\pi\) | ||||
−0.277052 | + | 0.960855i | \(0.589358\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.70142e27 | 0.863018 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.47442e27i | 0.264541i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.06844e26 | − | 3.27546e26i | 0.0538140 | − | 0.0574448i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.06540e26i | 0.0696966i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.78383e27 | 1.13694 | 0.568469 | − | 0.822705i | \(-0.307536\pi\) | ||||
0.568469 | + | 0.822705i | \(0.307536\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.09252e27 | 1.48978 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.01611e28i | 1.62772i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.86525e27 | − | 7.36814e27i | −1.23190 | − | 1.15404i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.08752e27i | − | 0.779136i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.35826e27 | 1.40143 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.52919e27 | 0.370382 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.09040e27i | − | 0.299374i | −0.988733 | − | 0.149687i | \(-0.952173\pi\) | ||
0.988733 | − | 0.149687i | \(-0.0478265\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.45000e27 | − | 2.29515e27i | −0.343154 | − | 0.321465i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.53040e27i | − | 0.209646i | −0.994491 | − | 0.104823i | \(-0.966572\pi\) | ||
0.994491 | − | 0.104823i | \(-0.0334276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.08735e27 | 0.279679 | 0.139839 | − | 0.990174i | \(-0.455341\pi\) | ||||
0.139839 | + | 0.990174i | \(0.455341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.33434e27 | −0.305938 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 8.71784e27i | − | 1.11765i | −0.829285 | − | 0.558826i | \(-0.811252\pi\) | ||
0.829285 | − | 0.558826i | \(-0.188748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.68831e27 | − | 5.00462e27i | 0.587981 | − | 0.627651i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.47220e27i | 0.916784i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75751e27 | 0.210965 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.70634e28 | 3.17840 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.94583e28i | 2.23599i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.11280e27 | − | 5.01981e27i | −0.687327 | − | 0.564431i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.82930e26i | 0.0421331i | 0.999778 | + | 0.0210665i | \(0.00670618\pi\) | ||||
−0.999778 | + | 0.0210665i | \(0.993294\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.58607e28 | 2.78450 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.11821e28 | −1.17829 | −0.589143 | − | 0.808029i | \(-0.700534\pi\) | ||||
−0.589143 | + | 0.808029i | \(0.700534\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.48578e27i | 0.668861i | 0.942420 | + | 0.334430i | \(0.108544\pi\) | ||||
−0.942420 | + | 0.334430i | \(0.891456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.31440e27 | − | 8.87536e27i | 0.839209 | − | 0.895829i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 9.49846e27i | − | 0.938380i | −0.883097 | − | 0.469190i | \(-0.844546\pi\) | ||
0.883097 | − | 0.469190i | \(-0.155454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.41577e27 | −0.717116 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.15942e27 | 0.204409 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.44244e27i | 0.504318i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.02004e27 | − | 5.63955e27i | −0.546111 | − | 0.511594i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.41462e28i | 1.25635i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.61073e27 | −0.227010 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00288e28 | 0.853813 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.47646e28i | 2.06442i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.84473e27 | + | 1.72814e27i | 0.150581 | + | 0.141064i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.45654e28i | 1.16427i | 0.813093 | + | 0.582134i | \(0.197782\pi\) | ||||
−0.813093 | + | 0.582134i | \(0.802218\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.85158e28 | −2.23218 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.31168e27 | 0.713844 | 0.356922 | − | 0.934134i | \(-0.383826\pi\) | ||||
0.356922 | + | 0.934134i | \(0.383826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.76801e27i | − | 0.207824i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.41808e27 | + | 1.00535e28i | −0.692568 | + | 0.739294i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.33758e27i | 0.0963406i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.77093e27 | −0.124941 | −0.0624705 | − | 0.998047i | \(-0.519898\pi\) | ||||
−0.0624705 | + | 0.998047i | \(0.519898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.92366e27 | −0.271159 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.31662e28i | − | 0.891339i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.10726e28 | + | 7.23440e26i | −0.734349 | + | 0.0479795i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.64817e28i | − | 1.72063i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.17089e27 | −0.0745359 | −0.0372680 | − | 0.999305i | \(-0.511866\pi\) | ||||
−0.0372680 | + | 0.999305i | \(0.511866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.19531e27 | 0.0745517 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.68560e28i | 2.86345i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.08794e27 | − | 5.43122e27i | 0.304671 | − | 0.325227i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.69183e27i | 0.451340i | 0.974204 | + | 0.225670i | \(0.0724571\pi\) | ||||
−0.974204 | + | 0.225670i | \(0.927543\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.26552e28 | −1.30270 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.18799e28 | 0.669440 | 0.334720 | − | 0.942318i | \(-0.391358\pi\) | ||||
0.334720 | + | 0.942318i | \(0.391358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.05899e27i | 0.113709i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.80950e27 | − | 5.44231e27i | −0.314439 | − | 0.294565i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.13232e28i | − | 1.13117i | −0.824690 | − | 0.565586i | \(-0.808650\pi\) | ||
0.824690 | − | 0.565586i | \(-0.191350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.27579e28 | 1.18332 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.96625e28 | 2.53112 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.15954e28i | 0.579299i | 0.957133 | + | 0.289650i | \(0.0935387\pi\) | ||||
−0.957133 | + | 0.289650i | \(0.906461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.53932e28 | + | 1.44203e28i | 0.753870 | + | 0.706222i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.76179e28i | − | 0.845846i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.70137e28 | −1.27147 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.12221e28 | −0.979302 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.34544e28i | 1.06115i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.31486e28 | − | 1.40357e28i | 0.583270 | − | 0.622623i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.71941e28i | − | 1.18283i | −0.806366 | − | 0.591417i | \(-0.798569\pi\) | ||
0.806366 | − | 0.591417i | \(-0.201431\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.61181e28 | 0.687443 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.13235e28 | −0.891818 | −0.445909 | − | 0.895078i | \(-0.647120\pi\) | ||||
−0.445909 | + | 0.895078i | \(0.647120\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.43928e27i | 0.100044i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.04633e27 | − | 6.19309e28i | −0.162748 | − | 2.49094i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.37913e28i | − | 1.72739i | −0.504019 | − | 0.863693i | \(-0.668146\pi\) | ||
0.504019 | − | 0.863693i | \(-0.331854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.18583e27 | 0.239311 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.41955e28 | −2.43584 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.29758e28i | − | 0.855091i | −0.903994 | − | 0.427546i | \(-0.859378\pi\) | ||
0.903994 | − | 0.427546i | \(-0.140622\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.68206e27 | − | 7.13289e27i | 0.243931 | − | 0.260388i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.34646e28i | 1.91449i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.18435e28 | 0.767287 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.81722e28 | −1.65996 | −0.829978 | − | 0.557796i | \(-0.811647\pi\) | ||||
−0.829978 | + | 0.557796i | \(0.811647\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 4.14415e28i | − | 1.40094i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.21521e28 | − | 3.94879e28i | −1.39798 | − | 1.30962i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.18301e28i | − | 0.384933i | −0.981304 | − | 0.192466i | \(-0.938351\pi\) | ||
0.981304 | − | 0.192466i | \(-0.0616487\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.11673e28 | −0.356513 |
(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 | 40.20.c.a.9.4 | ✓ | 28 | |
4.3 | odd | 2 | 80.20.c.d.49.25 | 28 | |||
5.4 | even | 2 | inner | 40.20.c.a.9.25 | yes | 28 | |
20.19 | odd | 2 | 80.20.c.d.49.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.20.c.a.9.4 | ✓ | 28 | 1.1 | even | 1 | trivial | |
40.20.c.a.9.25 | yes | 28 | 5.4 | even | 2 | inner | |
80.20.c.d.49.4 | 28 | 20.19 | odd | 2 | |||
80.20.c.d.49.25 | 28 | 4.3 | odd | 2 |