Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,9,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.5172802326\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.11 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.9.b.b.42.18 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 10.2230i | − | 0.638938i | −0.947597 | − | 0.319469i | \(-0.896496\pi\) | ||
0.947597 | − | 0.319469i | \(-0.103504\pi\) | |||||||
\(3\) | − | 141.129i | − | 1.74234i | −0.490984 | − | 0.871168i | \(-0.663363\pi\) | ||
0.490984 | − | 0.871168i | \(-0.336637\pi\) | |||||||
\(4\) | 151.490 | 0.591759 | ||||||||
\(5\) | 508.524i | 0.813638i | 0.913509 | + | 0.406819i | \(0.133362\pi\) | ||||
−0.913509 | + | 0.406819i | \(0.866638\pi\) | |||||||
\(6\) | −1442.77 | −1.11324 | ||||||||
\(7\) | 610.830i | 0.254406i | 0.991877 | + | 0.127203i | \(0.0406000\pi\) | ||||
−0.991877 | + | 0.127203i | \(0.959400\pi\) | |||||||
\(8\) | − | 4165.77i | − | 1.01703i | ||||||
\(9\) | −13356.5 | −2.03574 | ||||||||
\(10\) | 5198.64 | 0.519864 | ||||||||
\(11\) | −23389.3 | −1.59752 | −0.798760 | − | 0.601650i | \(-0.794510\pi\) | ||||
−0.798760 | + | 0.601650i | \(0.794510\pi\) | |||||||
\(12\) | − | 21379.7i | − | 1.03104i | ||||||
\(13\) | −38247.2 | −1.33914 | −0.669570 | − | 0.742749i | \(-0.733522\pi\) | ||||
−0.669570 | + | 0.742749i | \(0.733522\pi\) | |||||||
\(14\) | 6244.51 | 0.162550 | ||||||||
\(15\) | 71767.6 | 1.41763 | ||||||||
\(16\) | −3805.23 | −0.0580631 | ||||||||
\(17\) | 8276.38 | 0.0990934 | 0.0495467 | − | 0.998772i | \(-0.484222\pi\) | ||||
0.0495467 | + | 0.998772i | \(0.484222\pi\) | |||||||
\(18\) | 136543.i | 1.30071i | ||||||||
\(19\) | 43946.0i | 0.337214i | 0.985683 | + | 0.168607i | \(0.0539268\pi\) | ||||
−0.985683 | + | 0.168607i | \(0.946073\pi\) | |||||||
\(20\) | 77036.4i | 0.481477i | ||||||||
\(21\) | 86206.0 | 0.443262 | ||||||||
\(22\) | 239109.i | 1.02072i | ||||||||
\(23\) | −109327. | −0.390676 | −0.195338 | − | 0.980736i | \(-0.562580\pi\) | ||||
−0.195338 | + | 0.980736i | \(0.562580\pi\) | |||||||
\(24\) | −587913. | −1.77202 | ||||||||
\(25\) | 132028. | 0.337993 | ||||||||
\(26\) | 391001.i | 0.855627i | ||||||||
\(27\) | 959041.i | 1.80460i | ||||||||
\(28\) | 92534.7i | 0.150547i | ||||||||
\(29\) | − | 1.33800e6i | − | 1.89175i | −0.324534 | − | 0.945874i | \(-0.605208\pi\) | ||
0.324534 | − | 0.945874i | \(-0.394792\pi\) | |||||||
\(30\) | − | 733681.i | − | 0.905778i | ||||||
\(31\) | −624882. | −0.676630 | −0.338315 | − | 0.941033i | \(-0.609857\pi\) | ||||
−0.338315 | + | 0.941033i | \(0.609857\pi\) | |||||||
\(32\) | − | 1.02754e6i | − | 0.979936i | ||||||
\(33\) | 3.30091e6i | 2.78342i | ||||||||
\(34\) | − | 84609.5i | − | 0.0633145i | ||||||
\(35\) | −310621. | −0.206995 | ||||||||
\(36\) | −2.02338e6 | −1.20467 | ||||||||
\(37\) | − | 12892.0i | − | 0.00687879i | −0.999994 | − | 0.00343939i | \(-0.998905\pi\) | ||
0.999994 | − | 0.00343939i | \(-0.00109480\pi\) | |||||||
\(38\) | 449260. | 0.215459 | ||||||||
\(39\) | 5.39780e6i | 2.33323i | ||||||||
\(40\) | 2.11840e6 | 0.827498 | ||||||||
\(41\) | 4.22110e6 | 1.49379 | 0.746895 | − | 0.664941i | \(-0.231544\pi\) | ||||
0.746895 | + | 0.664941i | \(0.231544\pi\) | |||||||
\(42\) | − | 881284.i | − | 0.283217i | ||||||
\(43\) | −1.81225e6 | − | 2.89896e6i | −0.530082 | − | 0.847946i | ||||
\(44\) | −3.54325e6 | −0.945346 | ||||||||
\(45\) | − | 6.79209e6i | − | 1.65635i | ||||||
\(46\) | 1.11765e6i | 0.249618i | ||||||||
\(47\) | 1.43455e6 | 0.293985 | 0.146992 | − | 0.989138i | \(-0.453041\pi\) | ||||
0.146992 | + | 0.989138i | \(0.453041\pi\) | |||||||
\(48\) | 537029.i | 0.101166i | ||||||||
\(49\) | 5.39169e6 | 0.935277 | ||||||||
\(50\) | − | 1.34973e6i | − | 0.215956i | ||||||
\(51\) | − | 1.16804e6i | − | 0.172654i | ||||||
\(52\) | −5.79407e6 | −0.792448 | ||||||||
\(53\) | −1.03918e7 | −1.31700 | −0.658500 | − | 0.752581i | \(-0.728809\pi\) | ||||
−0.658500 | + | 0.752581i | \(0.728809\pi\) | |||||||
\(54\) | 9.80428e6 | 1.15303 | ||||||||
\(55\) | − | 1.18940e7i | − | 1.29980i | ||||||
\(56\) | 2.54458e6 | 0.258740 | ||||||||
\(57\) | 6.20207e6 | 0.587540 | ||||||||
\(58\) | −1.36784e7 | −1.20871 | ||||||||
\(59\) | 8.60085e6 | 0.709796 | 0.354898 | − | 0.934905i | \(-0.384516\pi\) | ||||
0.354898 | + | 0.934905i | \(0.384516\pi\) | |||||||
\(60\) | 1.08721e7 | 0.838896 | ||||||||
\(61\) | − | 1.46732e7i | − | 1.05975i | −0.848075 | − | 0.529877i | \(-0.822238\pi\) | ||
0.848075 | − | 0.529877i | \(-0.177762\pi\) | |||||||
\(62\) | 6.38818e6i | 0.432325i | ||||||||
\(63\) | − | 8.15853e6i | − | 0.517905i | ||||||
\(64\) | −1.14787e7 | −0.684181 | ||||||||
\(65\) | − | 1.94496e7i | − | 1.08958i | ||||||
\(66\) | 3.37453e7 | 1.77843 | ||||||||
\(67\) | −9.05284e6 | −0.449247 | −0.224624 | − | 0.974446i | \(-0.572115\pi\) | ||||
−0.224624 | + | 0.974446i | \(0.572115\pi\) | |||||||
\(68\) | 1.25379e6 | 0.0586394 | ||||||||
\(69\) | 1.54293e7i | 0.680690i | ||||||||
\(70\) | 3.17548e6i | 0.132257i | ||||||||
\(71\) | − | 1.39287e7i | − | 0.548123i | −0.961712 | − | 0.274061i | \(-0.911633\pi\) | ||
0.961712 | − | 0.274061i | \(-0.0883672\pi\) | |||||||
\(72\) | 5.56401e7i | 2.07042i | ||||||||
\(73\) | 4.77368e7i | 1.68098i | 0.541828 | + | 0.840489i | \(0.317732\pi\) | ||||
−0.541828 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(74\) | −131795. | −0.00439512 | ||||||||
\(75\) | − | 1.86331e7i | − | 0.588897i | ||||||
\(76\) | 6.65739e6i | 0.199549i | ||||||||
\(77\) | − | 1.42869e7i | − | 0.406419i | ||||||
\(78\) | 5.51817e7 | 1.49079 | ||||||||
\(79\) | −2.98664e7 | −0.766788 | −0.383394 | − | 0.923585i | \(-0.625245\pi\) | ||||
−0.383394 | + | 0.923585i | \(0.625245\pi\) | |||||||
\(80\) | − | 1.93505e6i | − | 0.0472424i | ||||||
\(81\) | 4.77169e7 | 1.10849 | ||||||||
\(82\) | − | 4.31523e7i | − | 0.954439i | ||||||
\(83\) | −3.68875e7 | −0.777261 | −0.388631 | − | 0.921394i | \(-0.627052\pi\) | ||||
−0.388631 | + | 0.921394i | \(0.627052\pi\) | |||||||
\(84\) | 1.30594e7 | 0.262304 | ||||||||
\(85\) | 4.20874e6i | 0.0806262i | ||||||||
\(86\) | −2.96361e7 | + | 1.85266e7i | −0.541785 | + | 0.338689i | ||||
\(87\) | −1.88831e8 | −3.29606 | ||||||||
\(88\) | 9.74345e7i | 1.62473i | ||||||||
\(89\) | − | 9.08768e7i | − | 1.44841i | −0.689582 | − | 0.724207i | \(-0.742206\pi\) | ||
0.689582 | − | 0.724207i | \(-0.257794\pi\) | |||||||
\(90\) | −6.94355e7 | −1.05831 | ||||||||
\(91\) | − | 2.33625e7i | − | 0.340686i | ||||||
\(92\) | −1.65620e7 | −0.231186 | ||||||||
\(93\) | 8.81892e7i | 1.17892i | ||||||||
\(94\) | − | 1.46654e7i | − | 0.187838i | ||||||
\(95\) | −2.23476e7 | −0.274370 | ||||||||
\(96\) | −1.45016e8 | −1.70738 | ||||||||
\(97\) | −4.00745e7 | −0.452670 | −0.226335 | − | 0.974050i | \(-0.572674\pi\) | ||||
−0.226335 | + | 0.974050i | \(0.572674\pi\) | |||||||
\(98\) | − | 5.51192e7i | − | 0.597584i | ||||||
\(99\) | 3.12399e8 | 3.25213 | ||||||||
\(100\) | 2.00010e7 | 0.200010 | ||||||||
\(101\) | 2.84924e7 | 0.273807 | 0.136903 | − | 0.990584i | \(-0.456285\pi\) | ||||
0.136903 | + | 0.990584i | \(0.456285\pi\) | |||||||
\(102\) | −1.19409e7 | −0.110315 | ||||||||
\(103\) | 1.33245e8 | 1.18386 | 0.591932 | − | 0.805988i | \(-0.298365\pi\) | ||||
0.591932 | + | 0.805988i | \(0.298365\pi\) | |||||||
\(104\) | 1.59329e8i | 1.36195i | ||||||||
\(105\) | 4.38378e7i | 0.360655i | ||||||||
\(106\) | 1.06235e8i | 0.841481i | ||||||||
\(107\) | −1.39954e8 | −1.06770 | −0.533852 | − | 0.845578i | \(-0.679256\pi\) | ||||
−0.533852 | + | 0.845578i | \(0.679256\pi\) | |||||||
\(108\) | 1.45285e8i | 1.06789i | ||||||||
\(109\) | 2.11298e8 | 1.49689 | 0.748446 | − | 0.663196i | \(-0.230800\pi\) | ||||
0.748446 | + | 0.663196i | \(0.230800\pi\) | |||||||
\(110\) | −1.21593e8 | −0.830494 | ||||||||
\(111\) | −1.81943e6 | −0.0119852 | ||||||||
\(112\) | − | 2.32434e6i | − | 0.0147716i | ||||||
\(113\) | 5.53627e7i | 0.339550i | 0.985483 | + | 0.169775i | \(0.0543041\pi\) | ||||
−0.985483 | + | 0.169775i | \(0.945696\pi\) | |||||||
\(114\) | − | 6.34038e7i | − | 0.375401i | ||||||
\(115\) | − | 5.55955e7i | − | 0.317869i | ||||||
\(116\) | − | 2.02693e8i | − | 1.11946i | ||||||
\(117\) | 5.10848e8 | 2.72614 | ||||||||
\(118\) | − | 8.79265e7i | − | 0.453515i | ||||||
\(119\) | 5.05546e6i | 0.0252100i | ||||||||
\(120\) | − | 2.98968e8i | − | 1.44178i | ||||||
\(121\) | 3.32700e8 | 1.55207 | ||||||||
\(122\) | −1.50004e8 | −0.677117 | ||||||||
\(123\) | − | 5.95720e8i | − | 2.60269i | ||||||
\(124\) | −9.46636e7 | −0.400402 | ||||||||
\(125\) | 2.65782e8i | 1.08864i | ||||||||
\(126\) | −8.34047e7 | −0.330909 | ||||||||
\(127\) | −8.40413e7 | −0.323056 | −0.161528 | − | 0.986868i | \(-0.551642\pi\) | ||||
−0.161528 | + | 0.986868i | \(0.551642\pi\) | |||||||
\(128\) | − | 1.45703e8i | − | 0.542787i | ||||||
\(129\) | −4.09128e8 | + | 2.55761e8i | −1.47741 | + | 0.923582i | ||||
\(130\) | −1.98833e8 | −0.696171 | ||||||||
\(131\) | − | 5.12788e8i | − | 1.74122i | −0.491978 | − | 0.870608i | \(-0.663726\pi\) | ||
0.491978 | − | 0.870608i | \(-0.336274\pi\) | |||||||
\(132\) | 5.00056e8i | 1.64711i | ||||||||
\(133\) | −2.68435e7 | −0.0857893 | ||||||||
\(134\) | 9.25472e7i | 0.287041i | ||||||||
\(135\) | −4.87695e8 | −1.46830 | ||||||||
\(136\) | − | 3.44775e7i | − | 0.100781i | ||||||
\(137\) | − | 2.04952e8i | − | 0.581794i | −0.956754 | − | 0.290897i | \(-0.906046\pi\) | ||
0.956754 | − | 0.290897i | \(-0.0939538\pi\) | |||||||
\(138\) | 1.57734e8 | 0.434918 | ||||||||
\(139\) | −4.64854e8 | −1.24525 | −0.622626 | − | 0.782520i | \(-0.713934\pi\) | ||||
−0.622626 | + | 0.782520i | \(0.713934\pi\) | |||||||
\(140\) | −4.70561e7 | −0.122491 | ||||||||
\(141\) | − | 2.02457e8i | − | 0.512221i | ||||||
\(142\) | −1.42393e8 | −0.350216 | ||||||||
\(143\) | 8.94575e8 | 2.13930 | ||||||||
\(144\) | 5.08244e7 | 0.118201 | ||||||||
\(145\) | 6.80404e8 | 1.53920 | ||||||||
\(146\) | 4.88014e8 | 1.07404 | ||||||||
\(147\) | − | 7.60925e8i | − | 1.62957i | ||||||
\(148\) | − | 1.95301e6i | − | 0.00407058i | ||||||
\(149\) | 7.12509e6i | 0.0144559i | 0.999974 | + | 0.00722795i | \(0.00230075\pi\) | ||||
−0.999974 | + | 0.00722795i | \(0.997699\pi\) | |||||||
\(150\) | −1.90486e8 | −0.376269 | ||||||||
\(151\) | 4.53627e8i | 0.872552i | 0.899813 | + | 0.436276i | \(0.143703\pi\) | ||||
−0.899813 | + | 0.436276i | \(0.856297\pi\) | |||||||
\(152\) | 1.83069e8 | 0.342958 | ||||||||
\(153\) | −1.10543e8 | −0.201728 | ||||||||
\(154\) | −1.46055e8 | −0.259677 | ||||||||
\(155\) | − | 3.17768e8i | − | 0.550532i | ||||||
\(156\) | 8.17714e8i | 1.38071i | ||||||||
\(157\) | 4.62842e8i | 0.761789i | 0.924619 | + | 0.380894i | \(0.124384\pi\) | ||||
−0.924619 | + | 0.380894i | \(0.875616\pi\) | |||||||
\(158\) | 3.05325e8i | 0.489930i | ||||||||
\(159\) | 1.46658e9i | 2.29466i | ||||||||
\(160\) | 5.22527e8 | 0.797313 | ||||||||
\(161\) | − | 6.67803e7i | − | 0.0993905i | ||||||
\(162\) | − | 4.87810e8i | − | 0.708257i | ||||||
\(163\) | 3.93979e8i | 0.558113i | 0.960275 | + | 0.279057i | \(0.0900217\pi\) | ||||
−0.960275 | + | 0.279057i | \(0.909978\pi\) | |||||||
\(164\) | 6.39455e8 | 0.883964 | ||||||||
\(165\) | −1.67859e9 | −2.26470 | ||||||||
\(166\) | 3.77101e8i | 0.496622i | ||||||||
\(167\) | −1.50142e9 | −1.93035 | −0.965173 | − | 0.261614i | \(-0.915745\pi\) | ||||
−0.965173 | + | 0.261614i | \(0.915745\pi\) | |||||||
\(168\) | − | 3.59114e8i | − | 0.450812i | ||||||
\(169\) | 6.47117e8 | 0.793297 | ||||||||
\(170\) | 4.30260e7 | 0.0515151 | ||||||||
\(171\) | − | 5.86964e8i | − | 0.686479i | ||||||
\(172\) | −2.74537e8 | − | 4.39164e8i | −0.313681 | − | 0.501780i | ||||
\(173\) | 1.15836e9 | 1.29318 | 0.646591 | − | 0.762837i | \(-0.276194\pi\) | ||||
0.646591 | + | 0.762837i | \(0.276194\pi\) | |||||||
\(174\) | 1.93042e9i | 2.10598i | ||||||||
\(175\) | 8.06469e7i | 0.0859875i | ||||||||
\(176\) | 8.90015e7 | 0.0927570 | ||||||||
\(177\) | − | 1.21383e9i | − | 1.23670i | ||||||
\(178\) | −9.29034e8 | −0.925447 | ||||||||
\(179\) | 1.24575e9i | 1.21344i | 0.794916 | + | 0.606719i | \(0.207515\pi\) | ||||
−0.794916 | + | 0.606719i | \(0.792485\pi\) | |||||||
\(180\) | − | 1.02893e9i | − | 0.980162i | ||||||
\(181\) | −2.15685e8 | −0.200958 | −0.100479 | − | 0.994939i | \(-0.532037\pi\) | ||||
−0.100479 | + | 0.994939i | \(0.532037\pi\) | |||||||
\(182\) | −2.38835e8 | −0.217677 | ||||||||
\(183\) | −2.07082e9 | −1.84645 | ||||||||
\(184\) | 4.55433e8i | 0.397331i | ||||||||
\(185\) | 6.55587e6 | 0.00559685 | ||||||||
\(186\) | 9.01559e8 | 0.753255 | ||||||||
\(187\) | −1.93579e8 | −0.158304 | ||||||||
\(188\) | 2.17321e8 | 0.173968 | ||||||||
\(189\) | −5.85811e8 | −0.459103 | ||||||||
\(190\) | 2.28460e8i | 0.175305i | ||||||||
\(191\) | − | 1.65296e9i | − | 1.24202i | −0.783803 | − | 0.621009i | \(-0.786723\pi\) | ||
0.783803 | − | 0.621009i | \(-0.213277\pi\) | |||||||
\(192\) | 1.61997e9i | 1.19207i | ||||||||
\(193\) | 1.26825e9 | 0.914065 | 0.457033 | − | 0.889450i | \(-0.348912\pi\) | ||||
0.457033 | + | 0.889450i | \(0.348912\pi\) | |||||||
\(194\) | 4.09682e8i | 0.289228i | ||||||||
\(195\) | −2.74491e9 | −1.89841 | ||||||||
\(196\) | 8.16788e8 | 0.553458 | ||||||||
\(197\) | 1.60703e9 | 1.06699 | 0.533494 | − | 0.845804i | \(-0.320879\pi\) | ||||
0.533494 | + | 0.845804i | \(0.320879\pi\) | |||||||
\(198\) | − | 3.19365e9i | − | 2.07791i | ||||||
\(199\) | − | 1.63024e9i | − | 1.03953i | −0.854309 | − | 0.519766i | \(-0.826019\pi\) | ||
0.854309 | − | 0.519766i | \(-0.173981\pi\) | |||||||
\(200\) | − | 5.50001e8i | − | 0.343750i | ||||||
\(201\) | 1.27762e9i | 0.782740i | ||||||||
\(202\) | − | 2.91278e8i | − | 0.174945i | ||||||
\(203\) | 8.17288e8 | 0.481273 | ||||||||
\(204\) | − | 1.76947e8i | − | 0.102170i | ||||||
\(205\) | 2.14653e9i | 1.21541i | ||||||||
\(206\) | − | 1.36216e9i | − | 0.756415i | ||||||
\(207\) | 1.46023e9 | 0.795314 | ||||||||
\(208\) | 1.45539e8 | 0.0777547 | ||||||||
\(209\) | − | 1.02787e9i | − | 0.538706i | ||||||
\(210\) | 4.48154e8 | 0.230436 | ||||||||
\(211\) | 2.53499e9i | 1.27893i | 0.768821 | + | 0.639464i | \(0.220844\pi\) | ||||
−0.768821 | + | 0.639464i | \(0.779156\pi\) | |||||||
\(212\) | −1.57425e9 | −0.779346 | ||||||||
\(213\) | −1.96575e9 | −0.955015 | ||||||||
\(214\) | 1.43075e9i | 0.682197i | ||||||||
\(215\) | 1.47419e9 | − | 9.21570e8i | 0.689922 | − | 0.431295i | ||||
\(216\) | 3.99515e9 | 1.83535 | ||||||||
\(217\) | − | 3.81697e8i | − | 0.172139i | ||||||
\(218\) | − | 2.16010e9i | − | 0.956420i | ||||||
\(219\) | 6.73707e9 | 2.92883 | ||||||||
\(220\) | − | 1.80183e9i | − | 0.769170i | ||||||
\(221\) | −3.16548e8 | −0.132700 | ||||||||
\(222\) | 1.86001e7i | 0.00765778i | ||||||||
\(223\) | 3.90361e9i | 1.57851i | 0.614067 | + | 0.789254i | \(0.289532\pi\) | ||||
−0.614067 | + | 0.789254i | \(0.710468\pi\) | |||||||
\(224\) | 6.27650e8 | 0.249302 | ||||||||
\(225\) | −1.76343e9 | −0.688065 | ||||||||
\(226\) | 5.65974e8 | 0.216951 | ||||||||
\(227\) | − | 4.89808e9i | − | 1.84469i | −0.386373 | − | 0.922343i | \(-0.626272\pi\) | ||
0.386373 | − | 0.922343i | \(-0.373728\pi\) | |||||||
\(228\) | 9.39553e8 | 0.347682 | ||||||||
\(229\) | −4.85451e9 | −1.76524 | −0.882619 | − | 0.470089i | \(-0.844222\pi\) | ||||
−0.882619 | + | 0.470089i | \(0.844222\pi\) | |||||||
\(230\) | −5.68353e8 | −0.203099 | ||||||||
\(231\) | −2.01630e9 | −0.708119 | ||||||||
\(232\) | −5.57379e9 | −1.92397 | ||||||||
\(233\) | − | 2.29736e8i | − | 0.0779480i | −0.999240 | − | 0.0389740i | \(-0.987591\pi\) | ||
0.999240 | − | 0.0389740i | \(-0.0124089\pi\) | |||||||
\(234\) | − | 5.22240e9i | − | 1.74183i | ||||||
\(235\) | 7.29504e8i | 0.239197i | ||||||||
\(236\) | 1.30294e9 | 0.420028 | ||||||||
\(237\) | 4.21503e9i | 1.33600i | ||||||||
\(238\) | 5.16820e7 | 0.0161076 | ||||||||
\(239\) | 5.01758e9 | 1.53781 | 0.768905 | − | 0.639363i | \(-0.220802\pi\) | ||||
0.768905 | + | 0.639363i | \(0.220802\pi\) | |||||||
\(240\) | −2.73092e8 | −0.0823122 | ||||||||
\(241\) | − | 8.41073e8i | − | 0.249325i | −0.992199 | − | 0.124662i | \(-0.960215\pi\) | ||
0.992199 | − | 0.124662i | \(-0.0397848\pi\) | |||||||
\(242\) | − | 3.40120e9i | − | 0.991677i | ||||||
\(243\) | − | 4.41986e8i | − | 0.126760i | ||||||
\(244\) | − | 2.22284e9i | − | 0.627118i | ||||||
\(245\) | 2.74180e9i | 0.760977i | ||||||||
\(246\) | −6.09005e9 | −1.66295 | ||||||||
\(247\) | − | 1.68081e9i | − | 0.451577i | ||||||
\(248\) | 2.60312e9i | 0.688157i | ||||||||
\(249\) | 5.20591e9i | 1.35425i | ||||||||
\(250\) | 2.71709e9 | 0.695574 | ||||||||
\(251\) | 6.10592e8 | 0.153835 | 0.0769177 | − | 0.997037i | \(-0.475492\pi\) | ||||
0.0769177 | + | 0.997037i | \(0.475492\pi\) | |||||||
\(252\) | − | 1.23594e9i | − | 0.306475i | ||||||
\(253\) | 2.55709e9 | 0.624113 | ||||||||
\(254\) | 8.59154e8i | 0.206413i | ||||||||
\(255\) | 5.93976e8 | 0.140478 | ||||||||
\(256\) | −4.42806e9 | −1.03099 | ||||||||
\(257\) | − | 2.83448e9i | − | 0.649743i | −0.945758 | − | 0.324871i | \(-0.894679\pi\) | ||
0.945758 | − | 0.324871i | \(-0.105321\pi\) | |||||||
\(258\) | 2.61464e9 | + | 4.18252e9i | 0.590111 | + | 0.943972i | ||||
\(259\) | 7.87479e6 | 0.00175001 | ||||||||
\(260\) | − | 2.94643e9i | − | 0.644766i | ||||||
\(261\) | 1.78709e10i | 3.85110i | ||||||||
\(262\) | −5.24223e9 | −1.11253 | ||||||||
\(263\) | − | 3.92497e9i | − | 0.820378i | −0.912001 | − | 0.410189i | \(-0.865463\pi\) | ||
0.912001 | − | 0.410189i | \(-0.134537\pi\) | |||||||
\(264\) | 1.37509e10 | 2.83083 | ||||||||
\(265\) | − | 5.28446e9i | − | 1.07156i | ||||||
\(266\) | 2.74422e8i | 0.0548140i | ||||||||
\(267\) | −1.28254e10 | −2.52363 | ||||||||
\(268\) | −1.37142e9 | −0.265846 | ||||||||
\(269\) | 5.01380e9 | 0.957543 | 0.478771 | − | 0.877940i | \(-0.341082\pi\) | ||||
0.478771 | + | 0.877940i | \(0.341082\pi\) | |||||||
\(270\) | 4.98571e9i | 0.938149i | ||||||||
\(271\) | 5.99686e9 | 1.11185 | 0.555926 | − | 0.831232i | \(-0.312364\pi\) | ||||
0.555926 | + | 0.831232i | \(0.312364\pi\) | |||||||
\(272\) | −3.14935e7 | −0.00575368 | ||||||||
\(273\) | −3.29714e9 | −0.593589 | ||||||||
\(274\) | −2.09522e9 | −0.371730 | ||||||||
\(275\) | −3.08805e9 | −0.539950 | ||||||||
\(276\) | 2.33738e9i | 0.402804i | ||||||||
\(277\) | − | 3.81516e9i | − | 0.648027i | −0.946052 | − | 0.324014i | \(-0.894968\pi\) | ||
0.946052 | − | 0.324014i | \(-0.105032\pi\) | |||||||
\(278\) | 4.75220e9i | 0.795638i | ||||||||
\(279\) | 8.34623e9 | 1.37744 | ||||||||
\(280\) | 1.29398e9i | 0.210521i | ||||||||
\(281\) | −9.65432e9 | −1.54845 | −0.774224 | − | 0.632912i | \(-0.781859\pi\) | ||||
−0.774224 | + | 0.632912i | \(0.781859\pi\) | |||||||
\(282\) | −2.06972e9 | −0.327277 | ||||||||
\(283\) | −2.68907e9 | −0.419234 | −0.209617 | − | 0.977784i | \(-0.567222\pi\) | ||||
−0.209617 | + | 0.977784i | \(0.567222\pi\) | |||||||
\(284\) | − | 2.11006e9i | − | 0.324356i | ||||||
\(285\) | 3.15390e9i | 0.478045i | ||||||||
\(286\) | − | 9.14524e9i | − | 1.36688i | ||||||
\(287\) | 2.57837e9i | 0.380030i | ||||||||
\(288\) | 1.37243e10i | 1.99489i | ||||||||
\(289\) | −6.90726e9 | −0.990180 | ||||||||
\(290\) | − | 6.95577e9i | − | 0.983452i | ||||||
\(291\) | 5.65569e9i | 0.788703i | ||||||||
\(292\) | 7.23166e9i | 0.994734i | ||||||||
\(293\) | −8.49101e9 | −1.15210 | −0.576049 | − | 0.817415i | \(-0.695406\pi\) | ||||
−0.576049 | + | 0.817415i | \(0.695406\pi\) | |||||||
\(294\) | −7.77894e9 | −1.04119 | ||||||||
\(295\) | 4.37374e9i | 0.577517i | ||||||||
\(296\) | −5.37050e7 | −0.00699597 | ||||||||
\(297\) | − | 2.24313e10i | − | 2.88289i | ||||||
\(298\) | 7.28398e7 | 0.00923642 | ||||||||
\(299\) | 4.18146e9 | 0.523170 | ||||||||
\(300\) | − | 2.82273e9i | − | 0.348485i | ||||||
\(301\) | 1.77077e9 | − | 1.10697e9i | 0.215723 | − | 0.134856i | ||||
\(302\) | 4.63743e9 | 0.557507 | ||||||||
\(303\) | − | 4.02112e9i | − | 0.477064i | ||||||
\(304\) | − | 1.67225e8i | − | 0.0195797i | ||||||
\(305\) | 7.46166e9 | 0.862256 | ||||||||
\(306\) | 1.13008e9i | 0.128892i | ||||||||
\(307\) | −8.44085e9 | −0.950239 | −0.475120 | − | 0.879921i | \(-0.657595\pi\) | ||||
−0.475120 | + | 0.879921i | \(0.657595\pi\) | |||||||
\(308\) | − | 2.16432e9i | − | 0.240502i | ||||||
\(309\) | − | 1.88048e10i | − | 2.06269i | ||||||
\(310\) | −3.24854e9 | −0.351756 | ||||||||
\(311\) | 6.75741e9 | 0.722335 | 0.361168 | − | 0.932501i | \(-0.382378\pi\) | ||||
0.361168 | + | 0.932501i | \(0.382378\pi\) | |||||||
\(312\) | 2.24860e10 | 2.37298 | ||||||||
\(313\) | − | 8.86708e9i | − | 0.923854i | −0.886918 | − | 0.461927i | \(-0.847158\pi\) | ||
0.886918 | − | 0.461927i | \(-0.152842\pi\) | |||||||
\(314\) | 4.73164e9 | 0.486735 | ||||||||
\(315\) | 4.14881e9 | 0.421387 | ||||||||
\(316\) | −4.52447e9 | −0.453753 | ||||||||
\(317\) | −3.54232e9 | −0.350793 | −0.175397 | − | 0.984498i | \(-0.556121\pi\) | ||||
−0.175397 | + | 0.984498i | \(0.556121\pi\) | |||||||
\(318\) | 1.49929e10 | 1.46614 | ||||||||
\(319\) | 3.12948e10i | 3.02211i | ||||||||
\(320\) | − | 5.83717e9i | − | 0.556676i | ||||||
\(321\) | 1.97516e10i | 1.86030i | ||||||||
\(322\) | −6.82695e8 | −0.0635044 | ||||||||
\(323\) | 3.63714e8i | 0.0334157i | ||||||||
\(324\) | 7.22864e9 | 0.655959 | ||||||||
\(325\) | −5.04972e9 | −0.452620 | ||||||||
\(326\) | 4.02765e9 | 0.356600 | ||||||||
\(327\) | − | 2.98204e10i | − | 2.60809i | ||||||
\(328\) | − | 1.75841e10i | − | 1.51924i | ||||||
\(329\) | 8.76267e8i | 0.0747916i | ||||||||
\(330\) | 1.71603e10i | 1.44700i | ||||||||
\(331\) | 8.57562e9i | 0.714420i | 0.934024 | + | 0.357210i | \(0.116272\pi\) | ||||
−0.934024 | + | 0.357210i | \(0.883728\pi\) | |||||||
\(332\) | −5.58810e9 | −0.459951 | ||||||||
\(333\) | 1.72191e8i | 0.0140034i | ||||||||
\(334\) | 1.53490e10i | 1.23337i | ||||||||
\(335\) | − | 4.60359e9i | − | 0.365525i | ||||||
\(336\) | −3.28033e8 | −0.0257372 | ||||||||
\(337\) | 1.16877e10 | 0.906166 | 0.453083 | − | 0.891468i | \(-0.350324\pi\) | ||||
0.453083 | + | 0.891468i | \(0.350324\pi\) | |||||||
\(338\) | − | 6.61548e9i | − | 0.506867i | ||||||
\(339\) | 7.81331e9 | 0.591611 | ||||||||
\(340\) | 6.37583e8i | 0.0477113i | ||||||||
\(341\) | 1.46156e10 | 1.08093 | ||||||||
\(342\) | −6.00054e9 | −0.438617 | ||||||||
\(343\) | 6.81471e9i | 0.492347i | ||||||||
\(344\) | −1.20764e10 | + | 7.54940e9i | −0.862391 | + | 0.539112i | ||||
\(345\) | −7.84616e9 | −0.553835 | ||||||||
\(346\) | − | 1.18419e10i | − | 0.826262i | ||||||
\(347\) | − | 1.00908e10i | − | 0.695995i | −0.937495 | − | 0.347998i | \(-0.886862\pi\) | ||
0.937495 | − | 0.347998i | \(-0.113138\pi\) | |||||||
\(348\) | −2.86060e10 | −1.95047 | ||||||||
\(349\) | − | 1.53839e10i | − | 1.03697i | −0.855088 | − | 0.518483i | \(-0.826497\pi\) | ||
0.855088 | − | 0.518483i | \(-0.173503\pi\) | |||||||
\(350\) | 8.24453e8 | 0.0549407 | ||||||||
\(351\) | − | 3.66806e10i | − | 2.41662i | ||||||
\(352\) | 2.40334e10i | 1.56547i | ||||||||
\(353\) | 8.54458e9 | 0.550290 | 0.275145 | − | 0.961403i | \(-0.411274\pi\) | ||||
0.275145 | + | 0.961403i | \(0.411274\pi\) | |||||||
\(354\) | −1.24090e10 | −0.790177 | ||||||||
\(355\) | 7.08309e9 | 0.445974 | ||||||||
\(356\) | − | 1.37669e10i | − | 0.857112i | ||||||
\(357\) | 7.13474e8 | 0.0439243 | ||||||||
\(358\) | 1.27353e10 | 0.775312 | ||||||||
\(359\) | 2.58791e10 | 1.55801 | 0.779006 | − | 0.627016i | \(-0.215724\pi\) | ||||
0.779006 | + | 0.627016i | \(0.215724\pi\) | |||||||
\(360\) | −2.82943e10 | −1.68457 | ||||||||
\(361\) | 1.50523e10 | 0.886287 | ||||||||
\(362\) | 2.20494e9i | 0.128400i | ||||||||
\(363\) | − | 4.69538e10i | − | 2.70423i | ||||||
\(364\) | − | 3.53919e9i | − | 0.201604i | ||||||
\(365\) | −2.42753e10 | −1.36771 | ||||||||
\(366\) | 2.11700e10i | 1.17977i | ||||||||
\(367\) | 2.44465e9 | 0.134757 | 0.0673786 | − | 0.997727i | \(-0.478536\pi\) | ||||
0.0673786 | + | 0.997727i | \(0.478536\pi\) | |||||||
\(368\) | 4.16015e8 | 0.0226839 | ||||||||
\(369\) | −5.63790e10 | −3.04097 | ||||||||
\(370\) | − | 6.70207e7i | − | 0.00357604i | ||||||
\(371\) | − | 6.34760e9i | − | 0.335053i | ||||||
\(372\) | 1.33598e10i | 0.697635i | ||||||||
\(373\) | 7.22158e9i | 0.373076i | 0.982448 | + | 0.186538i | \(0.0597267\pi\) | ||||
−0.982448 | + | 0.186538i | \(0.940273\pi\) | |||||||
\(374\) | 1.97896e9i | 0.101146i | ||||||||
\(375\) | 3.75096e10 | 1.89678 | ||||||||
\(376\) | − | 5.97602e9i | − | 0.298993i | ||||||
\(377\) | 5.11746e10i | 2.53332i | ||||||||
\(378\) | 5.98874e9i | 0.293338i | ||||||||
\(379\) | 4.92413e9 | 0.238656 | 0.119328 | − | 0.992855i | \(-0.461926\pi\) | ||||
0.119328 | + | 0.992855i | \(0.461926\pi\) | |||||||
\(380\) | −3.38544e9 | −0.162361 | ||||||||
\(381\) | 1.18607e10i | 0.562872i | ||||||||
\(382\) | −1.68982e10 | −0.793572 | ||||||||
\(383\) | 2.26540e10i | 1.05281i | 0.850234 | + | 0.526404i | \(0.176460\pi\) | ||||
−0.850234 | + | 0.526404i | \(0.823540\pi\) | |||||||
\(384\) | −2.05630e10 | −0.945717 | ||||||||
\(385\) | 7.26522e9 | 0.330678 | ||||||||
\(386\) | − | 1.29654e10i | − | 0.584031i | ||||||
\(387\) | 2.42052e10 | + | 3.87199e10i | 1.07911 | + | 1.72620i | ||||
\(388\) | −6.07090e9 | −0.267871 | ||||||||
\(389\) | 4.06348e9i | 0.177460i | 0.996056 | + | 0.0887299i | \(0.0282808\pi\) | ||||
−0.996056 | + | 0.0887299i | \(0.971719\pi\) | |||||||
\(390\) | 2.80612e10i | 1.21296i | ||||||||
\(391\) | −9.04834e8 | −0.0387135 | ||||||||
\(392\) | − | 2.24606e10i | − | 0.951209i | ||||||
\(393\) | −7.23694e10 | −3.03378 | ||||||||
\(394\) | − | 1.64287e10i | − | 0.681739i | ||||||
\(395\) | − | 1.51878e10i | − | 0.623888i | ||||||
\(396\) | 4.73253e10 | 1.92448 | ||||||||
\(397\) | 3.30903e10 | 1.33211 | 0.666053 | − | 0.745905i | \(-0.267983\pi\) | ||||
0.666053 | + | 0.745905i | \(0.267983\pi\) | |||||||
\(398\) | −1.66659e10 | −0.664196 | ||||||||
\(399\) | 3.78841e9i | 0.149474i | ||||||||
\(400\) | −5.02398e8 | −0.0196249 | ||||||||
\(401\) | 8.53281e9 | 0.330001 | 0.165000 | − | 0.986294i | \(-0.447237\pi\) | ||||
0.165000 | + | 0.986294i | \(0.447237\pi\) | |||||||
\(402\) | 1.30611e10 | 0.500122 | ||||||||
\(403\) | 2.39000e10 | 0.906103 | ||||||||
\(404\) | 4.31633e9 | 0.162028 | ||||||||
\(405\) | 2.42652e10i | 0.901911i | ||||||||
\(406\) | − | 8.35514e9i | − | 0.307503i | ||||||
\(407\) | 3.01534e8i | 0.0109890i | ||||||||
\(408\) | −4.86579e9 | −0.175595 | ||||||||
\(409\) | 2.02511e10i | 0.723694i | 0.932237 | + | 0.361847i | \(0.117854\pi\) | ||||
−0.932237 | + | 0.361847i | \(0.882146\pi\) | |||||||
\(410\) | 2.19440e10 | 0.776568 | ||||||||
\(411\) | −2.89247e10 | −1.01368 | ||||||||
\(412\) | 2.01853e10 | 0.700562 | ||||||||
\(413\) | 5.25366e9i | 0.180577i | ||||||||
\(414\) | − | 1.49279e10i | − | 0.508156i | ||||||
\(415\) | − | 1.87582e10i | − | 0.632410i | ||||||
\(416\) | 3.93004e10i | 1.31227i | ||||||||
\(417\) | 6.56045e10i | 2.16965i | ||||||||
\(418\) | −1.05079e10 | −0.344199 | ||||||||
\(419\) | − | 4.85618e10i | − | 1.57557i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) | ||
0.615948 | − | 0.787787i | \(-0.288773\pi\) | |||||||
\(420\) | 6.64100e9i | 0.213420i | ||||||||
\(421\) | 5.23909e10i | 1.66774i | 0.551964 | + | 0.833868i | \(0.313879\pi\) | ||||
−0.551964 | + | 0.833868i | \(0.686121\pi\) | |||||||
\(422\) | 2.59152e10 | 0.817155 | ||||||||
\(423\) | −1.91606e10 | −0.598476 | ||||||||
\(424\) | 4.32897e10i | 1.33943i | ||||||||
\(425\) | 1.09272e9 | 0.0334929 | ||||||||
\(426\) | 2.00959e10i | 0.610195i | ||||||||
\(427\) | 8.96282e9 | 0.269608 | ||||||||
\(428\) | −2.12017e10 | −0.631823 | ||||||||
\(429\) | − | 1.26251e11i | − | 3.72739i | ||||||
\(430\) | −9.42121e9 | − | 1.50707e10i | −0.275571 | − | 0.440817i | ||||
\(431\) | −8.47294e9 | −0.245542 | −0.122771 | − | 0.992435i | \(-0.539178\pi\) | ||||
−0.122771 | + | 0.992435i | \(0.539178\pi\) | |||||||
\(432\) | − | 3.64937e9i | − | 0.104781i | ||||||
\(433\) | 1.82972e10i | 0.520516i | 0.965539 | + | 0.260258i | \(0.0838076\pi\) | ||||
−0.965539 | + | 0.260258i | \(0.916192\pi\) | |||||||
\(434\) | −3.90209e9 | −0.109986 | ||||||||
\(435\) | − | 9.60249e10i | − | 2.68180i | ||||||
\(436\) | 3.20096e10 | 0.885798 | ||||||||
\(437\) | − | 4.80450e9i | − | 0.131741i | ||||||
\(438\) | − | 6.88731e10i | − | 1.87134i | ||||||
\(439\) | 4.05234e10 | 1.09106 | 0.545529 | − | 0.838092i | \(-0.316329\pi\) | ||||
0.545529 | + | 0.838092i | \(0.316329\pi\) | |||||||
\(440\) | −4.95478e10 | −1.32195 | ||||||||
\(441\) | −7.20140e10 | −1.90398 | ||||||||
\(442\) | 3.23608e9i | 0.0847871i | ||||||||
\(443\) | −5.19815e10 | −1.34969 | −0.674845 | − | 0.737960i | \(-0.735789\pi\) | ||||
−0.674845 | + | 0.737960i | \(0.735789\pi\) | |||||||
\(444\) | −2.75626e8 | −0.00709233 | ||||||||
\(445\) | 4.62130e10 | 1.17849 | ||||||||
\(446\) | 3.99066e10 | 1.00857 | ||||||||
\(447\) | 1.00556e9 | 0.0251870 | ||||||||
\(448\) | − | 7.01150e9i | − | 0.174060i | ||||||
\(449\) | − | 1.28565e10i | − | 0.316328i | −0.987413 | − | 0.158164i | \(-0.949443\pi\) | ||
0.987413 | − | 0.158164i | \(-0.0505575\pi\) | |||||||
\(450\) | 1.80276e10i | 0.439631i | ||||||||
\(451\) | −9.87285e10 | −2.38636 | ||||||||
\(452\) | 8.38691e9i | 0.200932i | ||||||||
\(453\) | 6.40201e10 | 1.52028 | ||||||||
\(454\) | −5.00731e10 | −1.17864 | ||||||||
\(455\) | 1.18804e10 | 0.277195 | ||||||||
\(456\) | − | 2.58364e10i | − | 0.597549i | ||||||
\(457\) | − | 5.62798e10i | − | 1.29029i | −0.764060 | − | 0.645146i | \(-0.776797\pi\) | ||
0.764060 | − | 0.645146i | \(-0.223203\pi\) | |||||||
\(458\) | 4.96277e10i | 1.12788i | ||||||||
\(459\) | 7.93739e9i | 0.178824i | ||||||||
\(460\) | − | 8.42218e9i | − | 0.188102i | ||||||
\(461\) | −4.05469e10 | −0.897746 | −0.448873 | − | 0.893596i | \(-0.648174\pi\) | ||||
−0.448873 | + | 0.893596i | \(0.648174\pi\) | |||||||
\(462\) | 2.06126e10i | 0.452444i | ||||||||
\(463\) | − | 1.79105e9i | − | 0.0389748i | −0.999810 | − | 0.0194874i | \(-0.993797\pi\) | ||
0.999810 | − | 0.0194874i | \(-0.00620342\pi\) | |||||||
\(464\) | 5.09138e9i | 0.109841i | ||||||||
\(465\) | −4.48463e10 | −0.959213 | ||||||||
\(466\) | −2.34859e9 | −0.0498039 | ||||||||
\(467\) | − | 6.60966e9i | − | 0.138967i | −0.997583 | − | 0.0694835i | \(-0.977865\pi\) | ||
0.997583 | − | 0.0694835i | \(-0.0221351\pi\) | |||||||
\(468\) | 7.73884e10 | 1.61322 | ||||||||
\(469\) | − | 5.52974e9i | − | 0.114291i | ||||||
\(470\) | 7.45773e9 | 0.152832 | ||||||||
\(471\) | 6.53206e10 | 1.32729 | ||||||||
\(472\) | − | 3.58292e10i | − | 0.721887i | ||||||
\(473\) | 4.23871e10 | + | 6.78046e10i | 0.846817 | + | 1.35461i | ||||
\(474\) | 4.30903e10 | 0.853623 | ||||||||
\(475\) | 5.80213e9i | 0.113976i | ||||||||
\(476\) | 7.65853e8i | 0.0149182i | ||||||||
\(477\) | 1.38797e11 | 2.68107 | ||||||||
\(478\) | − | 5.12947e10i | − | 0.982564i | ||||||
\(479\) | −5.75458e10 | −1.09313 | −0.546565 | − | 0.837417i | \(-0.684065\pi\) | ||||
−0.546565 | + | 0.837417i | \(0.684065\pi\) | |||||||
\(480\) | − | 7.37439e10i | − | 1.38919i | ||||||
\(481\) | 4.93081e8i | 0.00921166i | ||||||||
\(482\) | −8.59829e9 | −0.159303 | ||||||||
\(483\) | −9.42466e9 | −0.173172 | ||||||||
\(484\) | 5.04008e10 | 0.918452 | ||||||||
\(485\) | − | 2.03789e10i | − | 0.368309i | ||||||
\(486\) | −4.51842e9 | −0.0809919 | ||||||||
\(487\) | 1.42045e10 | 0.252528 | 0.126264 | − | 0.991997i | \(-0.459701\pi\) | ||||
0.126264 | + | 0.991997i | \(0.459701\pi\) | |||||||
\(488\) | −6.11252e10 | −1.07781 | ||||||||
\(489\) | 5.56019e10 | 0.972421 | ||||||||
\(490\) | 2.80295e10 | 0.486217 | ||||||||
\(491\) | 6.76583e10i | 1.16411i | 0.813149 | + | 0.582056i | \(0.197752\pi\) | ||||
−0.813149 | + | 0.582056i | \(0.802248\pi\) | |||||||
\(492\) | − | 9.02458e10i | − | 1.54016i | ||||||
\(493\) | − | 1.10738e10i | − | 0.187460i | ||||||
\(494\) | −1.71829e10 | −0.288529 | ||||||||
\(495\) | 1.58862e11i | 2.64606i | ||||||||
\(496\) | 2.37782e9 | 0.0392873 | ||||||||
\(497\) | 8.50808e9 | 0.139446 | ||||||||
\(498\) | 5.32200e10 | 0.865282 | ||||||||
\(499\) | − | 6.92061e10i | − | 1.11620i | −0.829773 | − | 0.558100i | \(-0.811530\pi\) | ||
0.829773 | − | 0.558100i | \(-0.188470\pi\) | |||||||
\(500\) | 4.02633e10i | 0.644213i | ||||||||
\(501\) | 2.11894e11i | 3.36331i | ||||||||
\(502\) | − | 6.24209e9i | − | 0.0982913i | ||||||
\(503\) | 6.26497e10i | 0.978695i | 0.872089 | + | 0.489348i | \(0.162765\pi\) | ||||
−0.872089 | + | 0.489348i | \(0.837235\pi\) | |||||||
\(504\) | −3.39866e10 | −0.526727 | ||||||||
\(505\) | 1.44891e10i | 0.222780i | ||||||||
\(506\) | − | 2.61411e10i | − | 0.398770i | ||||||
\(507\) | − | 9.13271e10i | − | 1.38219i | ||||||
\(508\) | −1.27314e10 | −0.191171 | ||||||||
\(509\) | 3.06030e10 | 0.455924 | 0.227962 | − | 0.973670i | \(-0.426794\pi\) | ||||
0.227962 | + | 0.973670i | \(0.426794\pi\) | |||||||
\(510\) | − | 6.07222e9i | − | 0.0897567i | ||||||
\(511\) | −2.91591e10 | −0.427652 | ||||||||
\(512\) | 7.96805e9i | 0.115950i | ||||||||
\(513\) | −4.21460e10 | −0.608537 | ||||||||
\(514\) | −2.89769e10 | −0.415145 | ||||||||
\(515\) | 6.77582e10i | 0.963237i | ||||||||
\(516\) | −6.19789e10 | + | 3.87453e10i | −0.874269 | + | 0.546537i | ||||
\(517\) | −3.35532e10 | −0.469647 | ||||||||
\(518\) | − | 8.05040e7i | − | 0.00111815i | ||||||
\(519\) | − | 1.63479e11i | − | 2.25316i | ||||||
\(520\) | −8.10227e10 | −1.10814 | ||||||||
\(521\) | 6.05568e10i | 0.821886i | 0.911661 | + | 0.410943i | \(0.134801\pi\) | ||||
−0.911661 | + | 0.410943i | \(0.865199\pi\) | |||||||
\(522\) | 1.82695e11 | 2.46061 | ||||||||
\(523\) | − | 1.12688e11i | − | 1.50616i | −0.657931 | − | 0.753078i | \(-0.728568\pi\) | ||
0.657931 | − | 0.753078i | \(-0.271432\pi\) | |||||||
\(524\) | − | 7.76823e10i | − | 1.03038i | ||||||
\(525\) | 1.13816e10 | 0.149819 | ||||||||
\(526\) | −4.01250e10 | −0.524170 | ||||||||
\(527\) | −5.17177e9 | −0.0670496 | ||||||||
\(528\) | − | 1.25607e10i | − | 0.161614i | ||||||
\(529\) | −6.63585e10 | −0.847372 | ||||||||
\(530\) | −5.40231e10 | −0.684661 | ||||||||
\(531\) | −1.14877e11 | −1.44496 | ||||||||
\(532\) | −4.06653e9 | −0.0507666 | ||||||||
\(533\) | −1.61445e11 | −2.00040 | ||||||||
\(534\) | 1.31114e11i | 1.61244i | ||||||||
\(535\) | − | 7.11701e10i | − | 0.868725i | ||||||
\(536\) | 3.77121e10i | 0.456900i | ||||||||
\(537\) | 1.75811e11 | 2.11422 | ||||||||
\(538\) | − | 5.12561e10i | − | 0.611810i | ||||||
\(539\) | −1.26108e11 | −1.49412 | ||||||||
\(540\) | −7.38810e10 | −0.868876 | ||||||||
\(541\) | −1.14693e9 | −0.0133890 | −0.00669451 | − | 0.999978i | \(-0.502131\pi\) | ||||
−0.00669451 | + | 0.999978i | \(0.502131\pi\) | |||||||
\(542\) | − | 6.13059e10i | − | 0.710404i | ||||||
\(543\) | 3.04394e10i | 0.350136i | ||||||||
\(544\) | − | 8.50429e9i | − | 0.0971052i | ||||||
\(545\) | 1.07450e11i | 1.21793i | ||||||||
\(546\) | 3.37066e10i | 0.379267i | ||||||||
\(547\) | −2.05760e10 | −0.229833 | −0.114916 | − | 0.993375i | \(-0.536660\pi\) | ||||
−0.114916 | + | 0.993375i | \(0.536660\pi\) | |||||||
\(548\) | − | 3.10482e10i | − | 0.344282i | ||||||
\(549\) | 1.95982e11i | 2.15738i | ||||||||
\(550\) | 3.15692e10i | 0.344995i | ||||||||
\(551\) | 5.87997e10 | 0.637923 | ||||||||
\(552\) | 6.42749e10 | 0.692285 | ||||||||
\(553\) | − | 1.82433e10i | − | 0.195076i | ||||||
\(554\) | −3.90024e10 | −0.414049 | ||||||||
\(555\) | − | 9.25225e8i | − | 0.00975159i | ||||||
\(556\) | −7.04208e10 | −0.736888 | ||||||||
\(557\) | −5.52422e10 | −0.573919 | −0.286959 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286959 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(558\) | − | 8.53235e10i | − | 0.880100i | ||||||
\(559\) | 6.93133e10 | + | 1.10877e11i | 0.709854 | + | 1.13552i | ||||
\(560\) | 1.18198e9 | 0.0120188 | ||||||||
\(561\) | 2.73196e10i | 0.275819i | ||||||||
\(562\) | 9.86962e10i | 0.989361i | ||||||||
\(563\) | 6.10219e10 | 0.607368 | 0.303684 | − | 0.952773i | \(-0.401783\pi\) | ||||
0.303684 | + | 0.952773i | \(0.401783\pi\) | |||||||
\(564\) | − | 3.06703e10i | − | 0.303111i | ||||||
\(565\) | −2.81533e10 | −0.276271 | ||||||||
\(566\) | 2.74904e10i | 0.267865i | ||||||||
\(567\) | 2.91469e10i | 0.282007i | ||||||||
\(568\) | −5.80239e10 | −0.557460 | ||||||||
\(569\) | 1.19187e11 | 1.13705 | 0.568525 | − | 0.822666i | \(-0.307514\pi\) | ||||
0.568525 | + | 0.822666i | \(0.307514\pi\) | |||||||
\(570\) | 3.22424e10 | 0.305441 | ||||||||
\(571\) | 5.18835e10i | 0.488073i | 0.969766 | + | 0.244036i | \(0.0784716\pi\) | ||||
−0.969766 | + | 0.244036i | \(0.921528\pi\) | |||||||
\(572\) | 1.35519e11 | 1.26595 | ||||||||
\(573\) | −2.33281e11 | −2.16401 | ||||||||
\(574\) | 2.63587e10 | 0.242815 | ||||||||
\(575\) | −1.44343e10 | −0.132046 | ||||||||
\(576\) | 1.53314e11 | 1.39281 | ||||||||
\(577\) | − | 1.07678e11i | − | 0.971460i | −0.874109 | − | 0.485730i | \(-0.838554\pi\) | ||
0.874109 | − | 0.485730i | \(-0.161446\pi\) | |||||||
\(578\) | 7.06129e10i | 0.632664i | ||||||||
\(579\) | − | 1.78988e11i | − | 1.59261i | ||||||
\(580\) | 1.03074e11 | 0.910834 | ||||||||
\(581\) | − | 2.25320e10i | − | 0.197740i | ||||||
\(582\) | 5.78181e10 | 0.503932 | ||||||||
\(583\) | 2.43056e11 | 2.10393 | ||||||||
\(584\) | 1.98861e11 | 1.70961 | ||||||||
\(585\) | 2.59778e11i | 2.21809i | ||||||||
\(586\) | 8.68037e10i | 0.736118i | ||||||||
\(587\) | − | 1.96919e11i | − | 1.65858i | −0.558819 | − | 0.829289i | \(-0.688746\pi\) | ||
0.558819 | − | 0.829289i | \(-0.311254\pi\) | |||||||
\(588\) | − | 1.15273e11i | − | 0.964311i | ||||||
\(589\) | − | 2.74611e10i | − | 0.228169i | ||||||
\(590\) | 4.47127e10 | 0.368997 | ||||||||
\(591\) | − | 2.26799e11i | − | 1.85905i | ||||||
\(592\) | 4.90568e7i | 0.000399404i | ||||||||
\(593\) | − | 4.01305e10i | − | 0.324530i | −0.986747 | − | 0.162265i | \(-0.948120\pi\) | ||
0.986747 | − | 0.162265i | \(-0.0518800\pi\) | |||||||
\(594\) | −2.29315e11 | −1.84199 | ||||||||
\(595\) | −2.57082e9 | −0.0205118 | ||||||||
\(596\) | 1.07938e9i | 0.00855440i | ||||||||
\(597\) | −2.30074e11 | −1.81122 | ||||||||
\(598\) | − | 4.27471e10i | − | 0.334273i | ||||||
\(599\) | −1.50298e11 | −1.16747 | −0.583734 | − | 0.811945i | \(-0.698409\pi\) | ||||
−0.583734 | + | 0.811945i | \(0.698409\pi\) | |||||||
\(600\) | −7.76212e10 | −0.598929 | ||||||||
\(601\) | − | 9.06889e10i | − | 0.695114i | −0.937659 | − | 0.347557i | \(-0.887011\pi\) | ||
0.937659 | − | 0.347557i | \(-0.112989\pi\) | |||||||
\(602\) | −1.13166e10 | − | 1.81026e10i | −0.0861647 | − | 0.137834i | ||||
\(603\) | 1.20914e11 | 0.914550 | ||||||||
\(604\) | 6.87201e10i | 0.516340i | ||||||||
\(605\) | 1.69186e11i | 1.26282i | ||||||||
\(606\) | −4.11079e10 | −0.304814 | ||||||||
\(607\) | − | 5.62467e9i | − | 0.0414326i | −0.999785 | − | 0.0207163i | \(-0.993405\pi\) | ||
0.999785 | − | 0.0207163i | \(-0.00659468\pi\) | |||||||
\(608\) | 4.51562e10 | 0.330448 | ||||||||
\(609\) | − | 1.15343e11i | − | 0.838539i | ||||||
\(610\) | − | 7.62806e10i | − | 0.550928i | ||||||
\(611\) | −5.48676e10 | −0.393687 | ||||||||
\(612\) | −1.67462e10 | −0.119374 | ||||||||
\(613\) | 2.46512e11 | 1.74581 | 0.872905 | − | 0.487891i | \(-0.162234\pi\) | ||||
0.872905 | + | 0.487891i | \(0.162234\pi\) | |||||||
\(614\) | 8.62909e10i | 0.607144i | ||||||||
\(615\) | 3.02938e11 | 2.11765 | ||||||||
\(616\) | −5.95159e10 | −0.413343 | ||||||||
\(617\) | −1.65485e11 | −1.14187 | −0.570936 | − | 0.820994i | \(-0.693420\pi\) | ||||
−0.570936 | + | 0.820994i | \(0.693420\pi\) | |||||||
\(618\) | −1.92241e11 | −1.31793 | ||||||||
\(619\) | −1.66265e10 | −0.113250 | −0.0566250 | − | 0.998396i | \(-0.518034\pi\) | ||||
−0.0566250 | + | 0.998396i | \(0.518034\pi\) | |||||||
\(620\) | − | 4.81387e10i | − | 0.325782i | ||||||
\(621\) | − | 1.04849e11i | − | 0.705016i | ||||||
\(622\) | − | 6.90811e10i | − | 0.461527i | ||||||
\(623\) | 5.55102e10 | 0.368486 | ||||||||
\(624\) | − | 2.05398e10i | − | 0.135475i | ||||||
\(625\) | −8.35828e10 | −0.547768 | ||||||||
\(626\) | −9.06482e10 | −0.590285 | ||||||||
\(627\) | −1.45062e11 | −0.938607 | ||||||||
\(628\) | 7.01161e10i | 0.450795i | ||||||||
\(629\) | − | 1.06699e8i | − | 0.000681643i | ||||||
\(630\) | − | 4.24133e10i | − | 0.269240i | ||||||
\(631\) | − | 7.50263e10i | − | 0.473256i | −0.971600 | − | 0.236628i | \(-0.923958\pi\) | ||
0.971600 | − | 0.236628i | \(-0.0760423\pi\) | |||||||
\(632\) | 1.24417e11i | 0.779850i | ||||||||
\(633\) | 3.57761e11 | 2.22832 | ||||||||
\(634\) | 3.62132e10i | 0.224135i | ||||||||
\(635\) | − | 4.27370e10i | − | 0.262851i | ||||||
\(636\) | 2.22173e11i | 1.35788i | ||||||||
\(637\) | −2.06217e11 | −1.25247 | ||||||||
\(638\) | 3.19927e11 | 1.93094 | ||||||||
\(639\) | 1.86039e11i | 1.11583i | ||||||||
\(640\) | 7.40936e10 | 0.441632 | ||||||||
\(641\) | − | 2.82104e11i | − | 1.67100i | −0.549489 | − | 0.835501i | \(-0.685178\pi\) | ||
0.549489 | − | 0.835501i | \(-0.314822\pi\) | |||||||
\(642\) | 2.01921e11 | 1.18862 | ||||||||
\(643\) | 1.95960e11 | 1.14637 | 0.573183 | − | 0.819427i | \(-0.305708\pi\) | ||||
0.573183 | + | 0.819427i | \(0.305708\pi\) | |||||||
\(644\) | − | 1.01166e10i | − | 0.0588152i | ||||||
\(645\) | −1.30061e11 | − | 2.08051e11i | −0.751461 | − | 1.20208i | ||||
\(646\) | 3.71825e9 | 0.0213505 | ||||||||
\(647\) | 2.37614e9i | 0.0135598i | 0.999977 | + | 0.00677992i | \(0.00215813\pi\) | ||||
−0.999977 | + | 0.00677992i | \(0.997842\pi\) | |||||||
\(648\) | − | 1.98778e11i | − | 1.12737i | ||||||
\(649\) | −2.01168e11 | −1.13391 | ||||||||
\(650\) | 5.16233e10i | 0.289196i | ||||||||
\(651\) | −5.38686e10 | −0.299924 | ||||||||
\(652\) | 5.96839e10i | 0.330268i | ||||||||
\(653\) | 1.28525e11i | 0.706862i | 0.935461 | + | 0.353431i | \(0.114985\pi\) | ||||
−0.935461 | + | 0.353431i | \(0.885015\pi\) | |||||||
\(654\) | −3.04854e11 | −1.66641 | ||||||||
\(655\) | 2.60765e11 | 1.41672 | ||||||||
\(656\) | −1.60622e10 | −0.0867342 | ||||||||
\(657\) | − | 6.37596e11i | − | 3.42203i | ||||||
\(658\) | 8.95809e9 | 0.0477872 | ||||||||
\(659\) | 1.48704e11 | 0.788464 | 0.394232 | − | 0.919011i | \(-0.371011\pi\) | ||||
0.394232 | + | 0.919011i | \(0.371011\pi\) | |||||||
\(660\) | −2.54291e11 | −1.34015 | ||||||||
\(661\) | −5.70041e10 | −0.298607 | −0.149304 | − | 0.988791i | \(-0.547703\pi\) | ||||
−0.149304 | + | 0.988791i | \(0.547703\pi\) | |||||||
\(662\) | 8.76686e10 | 0.456470 | ||||||||
\(663\) | 4.46743e10i | 0.231208i | ||||||||
\(664\) | 1.53665e11i | 0.790502i | ||||||||
\(665\) | − | 1.36506e10i | − | 0.0698015i | ||||||
\(666\) | 1.76031e9 | 0.00894731 | ||||||||
\(667\) | 1.46280e11i | 0.739061i | ||||||||
\(668\) | −2.27450e11 | −1.14230 | ||||||||
\(669\) | 5.50913e11 | 2.75029 | ||||||||
\(670\) | −4.70625e10 | −0.233548 | ||||||||
\(671\) | 3.43195e11i | 1.69298i | ||||||||
\(672\) | − | 8.85798e10i | − | 0.434368i | ||||||
\(673\) | 2.33498e11i | 1.13821i | 0.822264 | + | 0.569106i | \(0.192711\pi\) | ||||
−0.822264 | + | 0.569106i | \(0.807289\pi\) | |||||||
\(674\) | − | 1.19483e11i | − | 0.578983i | ||||||
\(675\) | 1.26621e11i | 0.609943i | ||||||||
\(676\) | 9.80318e10 | 0.469440 | ||||||||
\(677\) | 7.17939e10i | 0.341769i | 0.985291 | + | 0.170885i | \(0.0546625\pi\) | ||||
−0.985291 | + | 0.170885i | \(0.945337\pi\) | |||||||
\(678\) | − | 7.98754e10i | − | 0.378002i | ||||||
\(679\) | − | 2.44787e10i | − | 0.115162i | ||||||
\(680\) | 1.75327e10 | 0.0819996 | ||||||||
\(681\) | −6.91262e11 | −3.21406 | ||||||||
\(682\) | − | 1.49415e11i | − | 0.690648i | ||||||
\(683\) | −3.60964e11 | −1.65875 | −0.829374 | − | 0.558694i | \(-0.811303\pi\) | ||||
−0.829374 | + | 0.558694i | \(0.811303\pi\) | |||||||
\(684\) | − | 8.89193e10i | − | 0.406230i | ||||||
\(685\) | 1.04223e11 | 0.473370 | ||||||||
\(686\) | 6.96668e10 | 0.314579 | ||||||||
\(687\) | 6.85113e11i | 3.07564i | ||||||||
\(688\) | 6.89600e9 | + | 1.10312e10i | 0.0307782 | + | 0.0492344i | ||||
\(689\) | 3.97456e11 | 1.76365 | ||||||||
\(690\) | 8.02113e10i | 0.353866i | ||||||||
\(691\) | − | 2.51135e11i | − | 1.10153i | −0.834662 | − | 0.550763i | \(-0.814337\pi\) | ||
0.834662 | − | 0.550763i | \(-0.185663\pi\) | |||||||
\(692\) | 1.75480e11 | 0.765251 | ||||||||
\(693\) | 1.90822e11i | 0.827363i | ||||||||
\(694\) | −1.03158e11 | −0.444697 | ||||||||
\(695\) | − | 2.36389e11i | − | 1.01318i | ||||||
\(696\) | 7.86626e11i | 3.35221i | ||||||||
\(697\) | 3.49354e10 | 0.148025 | ||||||||
\(698\) | −1.57270e11 | −0.662557 | ||||||||
\(699\) | −3.24224e10 | −0.135812 | ||||||||
\(700\) | 1.22172e10i | 0.0508839i | ||||||||
\(701\) | −9.21164e10 | −0.381474 | −0.190737 | − | 0.981641i | \(-0.561088\pi\) | ||||
−0.190737 | + | 0.981641i | \(0.561088\pi\) | |||||||
\(702\) | −3.74986e11 | −1.54407 | ||||||||
\(703\) | 5.66550e8 | 0.00231962 | ||||||||
\(704\) | 2.68478e11 | 1.09299 | ||||||||
\(705\) | 1.02954e11 | 0.416763 | ||||||||
\(706\) | − | 8.73513e10i | − | 0.351601i | ||||||
\(707\) | 1.74040e10i | 0.0696582i | ||||||||
\(708\) | − | 1.83884e11i | − | 0.731830i | ||||||
\(709\) | −4.42941e11 | −1.75291 | −0.876457 | − | 0.481480i | \(-0.840100\pi\) | ||||
−0.876457 | + | 0.481480i | \(0.840100\pi\) | |||||||
\(710\) | − | 7.24104e10i | − | 0.284949i | ||||||
\(711\) | 3.98911e11 | 1.56098 | ||||||||
\(712\) | −3.78572e11 | −1.47309 | ||||||||
\(713\) | 6.83167e10 | 0.264343 | ||||||||
\(714\) | − | 7.29384e9i | − | 0.0280649i | ||||||
\(715\) | 4.54913e11i | 1.74062i | ||||||||
\(716\) | 1.88718e11i | 0.718063i | ||||||||
\(717\) | − | 7.08127e11i | − | 2.67938i | ||||||
\(718\) | − | 2.64562e11i | − | 0.995473i | ||||||
\(719\) | −5.11725e10 | −0.191479 | −0.0957395 | − | 0.995406i | \(-0.530522\pi\) | ||||
−0.0957395 | + | 0.995406i | \(0.530522\pi\) | |||||||
\(720\) | 2.58454e10i | 0.0961731i | ||||||||
\(721\) | 8.13900e10i | 0.301183i | ||||||||
\(722\) | − | 1.53880e11i | − | 0.566282i | ||||||
\(723\) | −1.18700e11 | −0.434408 | ||||||||
\(724\) | −3.26741e10 | −0.118919 | ||||||||
\(725\) | − | 1.76654e11i | − | 0.639397i | ||||||
\(726\) | −4.80008e11 | −1.72784 | ||||||||
\(727\) | − | 1.66037e11i | − | 0.594385i | −0.954818 | − | 0.297192i | \(-0.903950\pi\) | ||
0.954818 | − | 0.297192i | \(-0.0960502\pi\) | |||||||
\(728\) | −9.73230e10 | −0.346489 | ||||||||
\(729\) | 2.50693e11 | 0.887632 | ||||||||
\(730\) | 2.48167e11i | 0.873881i | ||||||||
\(731\) | −1.49988e10 | − | 2.39929e10i | −0.0525277 | − | 0.0840259i | ||||
\(732\) | −3.13708e11 | −1.09265 | ||||||||
\(733\) | 2.79590e11i | 0.968513i | 0.874926 | + | 0.484257i | \(0.160910\pi\) | ||||
−0.874926 | + | 0.484257i | \(0.839090\pi\) | |||||||
\(734\) | − | 2.49916e10i | − | 0.0861014i | ||||||
\(735\) | 3.86949e11 | 1.32588 | ||||||||
\(736\) | 1.12338e11i | 0.382838i | ||||||||
\(737\) | 2.11740e11 | 0.717682 | ||||||||
\(738\) | 5.76362e11i | 1.94299i | ||||||||
\(739\) | − | 1.64286e11i | − | 0.550837i | −0.961324 | − | 0.275418i | \(-0.911184\pi\) | ||
0.961324 | − | 0.275418i | \(-0.0888163\pi\) | |||||||
\(740\) | 9.93150e8 | 0.00331198 | ||||||||
\(741\) | −2.37212e11 | −0.786799 | ||||||||
\(742\) | −6.48915e10 | −0.214078 | ||||||||
\(743\) | 4.46894e11i | 1.46639i | 0.680019 | + | 0.733195i | \(0.261972\pi\) | ||||
−0.680019 | + | 0.733195i | \(0.738028\pi\) | |||||||
\(744\) | 3.67376e11 | 1.19900 | ||||||||
\(745\) | −3.62328e9 | −0.0117619 | ||||||||
\(746\) | 7.38263e10 | 0.238372 | ||||||||
\(747\) | 4.92687e11 | 1.58230 | ||||||||
\(748\) | −2.93253e10 | −0.0936776 | ||||||||
\(749\) | − | 8.54882e10i | − | 0.271631i | ||||||
\(750\) | − | 3.83461e11i | − | 1.21193i | ||||||
\(751\) | 1.65073e11i | 0.518939i | 0.965751 | + | 0.259469i | \(0.0835477\pi\) | ||||
−0.965751 | + | 0.259469i | \(0.916452\pi\) | |||||||
\(752\) | −5.45880e9 | −0.0170697 | ||||||||
\(753\) | − | 8.61725e10i | − | 0.268033i | ||||||
\(754\) | 5.23158e11 | 1.61863 | ||||||||
\(755\) | −2.30680e11 | −0.709942 | ||||||||
\(756\) | −8.87446e10 | −0.271678 | ||||||||
\(757\) | − | 4.16379e11i | − | 1.26796i | −0.773350 | − | 0.633979i | \(-0.781420\pi\) | ||
0.773350 | − | 0.633979i | \(-0.218580\pi\) | |||||||
\(758\) | − | 5.03394e10i | − | 0.152487i | ||||||
\(759\) | − | 3.60880e11i | − | 1.08742i | ||||||
\(760\) | 9.30951e10i | 0.279044i | ||||||||
\(761\) | − | 5.59476e11i | − | 1.66818i | −0.551628 | − | 0.834090i | \(-0.685993\pi\) | ||
0.551628 | − | 0.834090i | \(-0.314007\pi\) | |||||||
\(762\) | 1.21252e11 | 0.359640 | ||||||||
\(763\) | 1.29067e11i | 0.380819i | ||||||||
\(764\) | − | 2.50407e11i | − | 0.734975i | ||||||
\(765\) | − | 5.62139e10i | − | 0.164134i | ||||||
\(766\) | 2.31592e11 | 0.672679 | ||||||||
\(767\) | −3.28958e11 | −0.950516 | ||||||||
\(768\) | 6.24929e11i | 1.79633i | ||||||||
\(769\) | 3.83384e11 | 1.09630 | 0.548150 | − | 0.836380i | \(-0.315332\pi\) | ||||
0.548150 | + | 0.836380i | \(0.315332\pi\) | |||||||
\(770\) | − | 7.42723e10i | − | 0.211283i | ||||||
\(771\) | −4.00029e11 | −1.13207 | ||||||||
\(772\) | 1.92128e11 | 0.540906 | ||||||||
\(773\) | 1.08957e11i | 0.305168i | 0.988291 | + | 0.152584i | \(0.0487594\pi\) | ||||
−0.988291 | + | 0.152584i | \(0.951241\pi\) | |||||||
\(774\) | 3.95834e11 | − | 2.47450e11i | 1.10293 | − | 0.689483i | ||||
\(775\) | −8.25023e10 | −0.228696 | ||||||||
\(776\) | 1.66941e11i | 0.460381i | ||||||||
\(777\) | − | 1.11136e9i | − | 0.00304910i | ||||||
\(778\) | 4.15410e10 | 0.113386 | ||||||||
\(779\) | 1.85500e11i | 0.503727i | ||||||||
\(780\) | −4.15827e11 | −1.12340 | ||||||||
\(781\) | 3.25783e11i | 0.875637i | ||||||||
\(782\) | 9.25012e9i | 0.0247355i | ||||||||
\(783\) | 1.28319e12 | 3.41386 | ||||||||
\(784\) | −2.05166e10 | −0.0543051 | ||||||||
\(785\) | −2.35366e11 | −0.619820 | ||||||||
\(786\) | 7.39832e11i | 1.93840i | ||||||||
\(787\) | 3.10785e9 | 0.00810141 | 0.00405071 | − | 0.999992i | \(-0.498711\pi\) | ||||
0.00405071 | + | 0.999992i | \(0.498711\pi\) | |||||||
\(788\) | 2.43450e11 | 0.631400 | ||||||||
\(789\) | −5.53929e11 | −1.42937 | ||||||||
\(790\) | −1.55265e11 | −0.398626 | ||||||||
\(791\) | −3.38172e10 | −0.0863837 | ||||||||
\(792\) | − | 1.30138e12i | − | 3.30753i | ||||||
\(793\) | 5.61208e11i | 1.41916i | ||||||||
\(794\) | − | 3.38282e11i | − | 0.851132i | ||||||
\(795\) | −7.45792e11 | −1.86702 | ||||||||
\(796\) | − | 2.46965e11i | − | 0.615152i | ||||||
\(797\) | −1.39632e11 | −0.346060 | −0.173030 | − | 0.984917i | \(-0.555356\pi\) | ||||
−0.173030 | + | 0.984917i | \(0.555356\pi\) | |||||||
\(798\) | 3.87289e10 | 0.0955045 | ||||||||
\(799\) | 1.18729e10 | 0.0291320 | ||||||||
\(800\) | − | 1.35664e11i | − | 0.331211i | ||||||
\(801\) | 1.21379e12i | 2.94859i | ||||||||
\(802\) | − | 8.72310e10i | − | 0.210850i | ||||||
\(803\) | − | 1.11653e12i | − | 2.68540i | ||||||
\(804\) | 1.93547e11i | 0.463193i | ||||||||
\(805\) | 3.39594e10 | 0.0808679 | ||||||||
\(806\) | − | 2.44330e11i | − | 0.578943i | ||||||
\(807\) | − | 7.07594e11i | − | 1.66836i | ||||||
\(808\) | − | 1.18693e11i | − | 0.278471i | ||||||
\(809\) | 2.09300e11 | 0.488623 | 0.244312 | − | 0.969697i | \(-0.421438\pi\) | ||||
0.244312 | + | 0.969697i | \(0.421438\pi\) | |||||||
\(810\) | 2.48063e11 | 0.576265 | ||||||||
\(811\) | − | 5.69929e11i | − | 1.31746i | −0.752379 | − | 0.658730i | \(-0.771094\pi\) | ||
0.752379 | − | 0.658730i | \(-0.228906\pi\) | |||||||
\(812\) | 1.23811e11 | 0.284797 | ||||||||
\(813\) | − | 8.46332e11i | − | 1.93722i | ||||||
\(814\) | 3.08258e9 | 0.00702129 | ||||||||
\(815\) | −2.00348e11 | −0.454102 | ||||||||
\(816\) | 4.44466e9i | 0.0100248i | ||||||||
\(817\) | 1.27398e11 | − | 7.96410e10i | 0.285939 | − | 0.178751i | ||||
\(818\) | 2.07027e11 | 0.462396 | ||||||||
\(819\) | 3.12041e11i | 0.693547i | ||||||||
\(820\) | 3.25178e11i | 0.719227i | ||||||||
\(821\) | 4.64555e11 | 1.02250 | 0.511252 | − | 0.859431i | \(-0.329182\pi\) | ||||
0.511252 | + | 0.859431i | \(0.329182\pi\) | |||||||
\(822\) | 2.95697e11i | 0.647680i | ||||||||
\(823\) | −7.12381e11 | −1.55279 | −0.776395 | − | 0.630246i | \(-0.782954\pi\) | ||||
−0.776395 | + | 0.630246i | \(0.782954\pi\) | |||||||
\(824\) | − | 5.55068e11i | − | 1.20403i | ||||||
\(825\) | 4.35815e11i | 0.940776i | ||||||||
\(826\) | 5.37081e10 | 0.115377 | ||||||||
\(827\) | −6.92473e11 | −1.48041 | −0.740203 | − | 0.672383i | \(-0.765271\pi\) | ||||
−0.740203 | + | 0.672383i | \(0.765271\pi\) | |||||||
\(828\) | 2.21210e11 | 0.470634 | ||||||||
\(829\) | − | 3.05973e11i | − | 0.647836i | −0.946085 | − | 0.323918i | \(-0.895000\pi\) | ||
0.946085 | − | 0.323918i | \(-0.105000\pi\) | |||||||
\(830\) | −1.91765e11 | −0.404070 | ||||||||
\(831\) | −5.38430e11 | −1.12908 | ||||||||
\(832\) | 4.39026e11 | 0.916215 | ||||||||
\(833\) | 4.46237e10 | 0.0926799 | ||||||||
\(834\) | 6.70675e11 | 1.38627 | ||||||||
\(835\) | − | 7.63506e11i | − | 1.57060i | ||||||
\(836\) | − | 1.55712e11i | − | 0.318784i | ||||||
\(837\) | − | 5.99288e11i | − | 1.22105i | ||||||
\(838\) | −4.96448e11 | −1.00669 | ||||||||
\(839\) | 2.00550e11i | 0.404739i | 0.979309 | + | 0.202370i | \(0.0648642\pi\) | ||||
−0.979309 | + | 0.202370i | \(0.935136\pi\) | |||||||
\(840\) | 1.82618e11 | 0.366798 | ||||||||
\(841\) | −1.28999e12 | −2.57871 | ||||||||
\(842\) | 5.35592e11 | 1.06558 | ||||||||
\(843\) | 1.36251e12i | 2.69792i | ||||||||
\(844\) | 3.84026e11i | 0.756816i | ||||||||
\(845\) | 3.29074e11i | 0.645457i | ||||||||
\(846\) | 1.95879e11i | 0.382389i | ||||||||
\(847\) | 2.03223e11i | 0.394857i | ||||||||
\(848\) | 3.95430e10 | 0.0764692 | ||||||||
\(849\) | 3.79507e11i | 0.730448i | ||||||||
\(850\) | − | 1.11709e10i | − | 0.0213999i | ||||||
\(851\) | 1.40944e9i | 0.00268738i | ||||||||
\(852\) | −2.97792e11 | −0.565138 | ||||||||
\(853\) | 9.68289e11 | 1.82898 | 0.914490 | − | 0.404609i | \(-0.132592\pi\) | ||||
0.914490 | + | 0.404609i | \(0.132592\pi\) | |||||||
\(854\) | − | 9.16269e10i | − | 0.172263i | ||||||
\(855\) | 2.98485e11 | 0.558545 | ||||||||
\(856\) | 5.83018e11i | 1.08589i | ||||||||
\(857\) | −9.03629e11 | −1.67520 | −0.837600 | − | 0.546284i | \(-0.816042\pi\) | ||||
−0.837600 | + | 0.546284i | \(0.816042\pi\) | |||||||
\(858\) | −1.29066e12 | −2.38157 | ||||||||
\(859\) | − | 1.38859e11i | − | 0.255036i | −0.991836 | − | 0.127518i | \(-0.959299\pi\) | ||
0.991836 | − | 0.127518i | \(-0.0407011\pi\) | |||||||
\(860\) | 2.23325e11 | − | 1.39609e11i | 0.408267 | − | 0.255223i | ||||
\(861\) | 3.63884e11 | 0.662140 | ||||||||
\(862\) | 8.66189e10i | 0.156886i | ||||||||
\(863\) | − | 2.95981e11i | − | 0.533605i | −0.963751 | − | 0.266803i | \(-0.914033\pi\) | ||
0.963751 | − | 0.266803i | \(-0.0859672\pi\) | |||||||
\(864\) | 9.85450e11 | 1.76840 | ||||||||
\(865\) | 5.89054e11i | 1.05218i | ||||||||
\(866\) | 1.87053e11 | 0.332577 | ||||||||
\(867\) | 9.74817e11i | 1.72523i | ||||||||
\(868\) | − | 5.78233e10i | − | 0.101865i | ||||||
\(869\) | 6.98555e11 | 1.22496 | ||||||||
\(870\) | −9.81663e11 | −1.71350 | ||||||||
\(871\) | 3.46246e11 | 0.601605 | ||||||||
\(872\) | − | 8.80222e11i | − | 1.52239i | ||||||
\(873\) | 5.35255e11 | 0.921517 | ||||||||
\(874\) | −4.91164e10 | −0.0841746 | ||||||||
\(875\) | −1.62347e11 | −0.276957 | ||||||||
\(876\) | 1.02060e12 | 1.73316 | ||||||||
\(877\) | 2.10271e11 | 0.355452 | 0.177726 | − | 0.984080i | \(-0.443126\pi\) | ||||
0.177726 | + | 0.984080i | \(0.443126\pi\) | |||||||
\(878\) | − | 4.14271e11i | − | 0.697119i | ||||||
\(879\) | 1.19833e12i | 2.00734i | ||||||||
\(880\) | 4.52594e10i | 0.0754707i | ||||||||
\(881\) | 6.57140e11 | 1.09082 | 0.545412 | − | 0.838168i | \(-0.316373\pi\) | ||||
0.545412 | + | 0.838168i | \(0.316373\pi\) | |||||||
\(882\) | 7.36199e11i | 1.21652i | ||||||||
\(883\) | 4.57073e11 | 0.751869 | 0.375935 | − | 0.926646i | \(-0.377322\pi\) | ||||
0.375935 | + | 0.926646i | \(0.377322\pi\) | |||||||
\(884\) | −4.79540e10 | −0.0785264 | ||||||||
\(885\) | 6.17263e11 | 1.00623 | ||||||||
\(886\) | 5.31407e11i | 0.862367i | ||||||||
\(887\) | − | 2.15040e11i | − | 0.347395i | −0.984799 | − | 0.173698i | \(-0.944428\pi\) | ||
0.984799 | − | 0.173698i | \(-0.0555716\pi\) | |||||||
\(888\) | 7.57935e9i | 0.0121893i | ||||||||
\(889\) | − | 5.13349e10i | − | 0.0821875i | ||||||
\(890\) | − | 4.72436e11i | − | 0.752979i | ||||||
\(891\) | −1.11606e12 | −1.77084 | ||||||||
\(892\) | 5.91358e11i | 0.934095i | ||||||||
\(893\) | 6.30429e10i | 0.0991358i | ||||||||
\(894\) | − | 1.02798e10i | − | 0.0160930i | ||||||
\(895\) | −6.33492e11 | −0.987300 | ||||||||
\(896\) | 8.89998e10 | 0.138088 | ||||||||
\(897\) | − | 5.90126e11i | − | 0.911539i | ||||||
\(898\) | −1.31432e11 | −0.202114 | ||||||||
\(899\) | 8.36091e11i | 1.28001i | ||||||||
\(900\) | −2.67143e11 | −0.407168 | ||||||||
\(901\) | −8.60062e10 | −0.130506 | ||||||||
\(902\) | 1.00930e12i | 1.52474i | ||||||||
\(903\) | −1.56226e11 | − | 2.49908e11i | −0.234965 | − | 0.375862i | ||||
\(904\) | 2.30629e11 | 0.345334 | ||||||||
\(905\) | − | 1.09681e11i | − | 0.163507i | ||||||
\(906\) | − | 6.54478e11i | − | 0.971364i | ||||||
\(907\) | −1.16366e12 | −1.71948 | −0.859738 | − | 0.510735i | \(-0.829373\pi\) | ||||
−0.859738 | + | 0.510735i | \(0.829373\pi\) | |||||||
\(908\) | − | 7.42011e11i | − | 1.09161i | ||||||
\(909\) | −3.80559e11 | −0.557399 | ||||||||
\(910\) | − | 1.21453e11i | − | 0.177110i | ||||||
\(911\) | 1.03563e12i | 1.50359i | 0.659395 | + | 0.751797i | \(0.270813\pi\) | ||||
−0.659395 | + | 0.751797i | \(0.729187\pi\) | |||||||
\(912\) | −2.36003e10 | −0.0341144 | ||||||||
\(913\) | 8.62773e11 | 1.24169 | ||||||||
\(914\) | −5.75349e11 | −0.824416 | ||||||||
\(915\) | − | 1.05306e12i | − | 1.50234i | ||||||
\(916\) | −7.35411e11 | −1.04460 | ||||||||
\(917\) | 3.13226e11 | 0.442976 | ||||||||
\(918\) | 8.11440e10 | 0.114258 | ||||||||
\(919\) | −4.00458e11 | −0.561428 | −0.280714 | − | 0.959791i | \(-0.590571\pi\) | ||||
−0.280714 | + | 0.959791i | \(0.590571\pi\) | |||||||
\(920\) | −2.31598e11 | −0.323284 | ||||||||
\(921\) | 1.19125e12i | 1.65564i | ||||||||
\(922\) | 4.14511e11i | 0.573604i | ||||||||
\(923\) | 5.32734e11i | 0.734013i | ||||||||
\(924\) | −3.05449e11 | −0.419036 | ||||||||
\(925\) | − | 1.70211e9i | − | 0.00232498i | ||||||
\(926\) | −1.83099e10 | −0.0249025 | ||||||||
\(927\) | −1.77968e12 | −2.41004 | ||||||||
\(928\) | −1.37484e12 | −1.85379 | ||||||||
\(929\) | − | 1.01464e11i | − | 0.136223i | −0.997678 | − | 0.0681113i | \(-0.978303\pi\) | ||
0.997678 | − | 0.0681113i | \(-0.0216973\pi\) | |||||||
\(930\) | 4.58464e11i | 0.612877i | ||||||||
\(931\) | 2.36943e11i | 0.315388i | ||||||||
\(932\) | − | 3.48027e10i | − | 0.0461264i | ||||||
\(933\) | − | 9.53669e11i | − | 1.25855i | ||||||
\(934\) | −6.75706e10 | −0.0887913 | ||||||||
\(935\) | − | 9.84394e10i | − | 0.128802i | ||||||
\(936\) | − | 2.12808e12i | − | 2.77258i | ||||||
\(937\) | − | 1.08546e12i | − | 1.40817i | −0.710115 | − | 0.704085i | \(-0.751357\pi\) | ||
0.710115 | − | 0.704085i | \(-0.248643\pi\) | |||||||
\(938\) | −5.65306e10 | −0.0730251 | ||||||||
\(939\) | −1.25141e12 | −1.60967 | ||||||||
\(940\) | 1.10513e11i | 0.141547i | ||||||||
\(941\) | 8.11626e9 | 0.0103514 | 0.00517568 | − | 0.999987i | \(-0.498353\pi\) | ||||
0.00517568 | + | 0.999987i | \(0.498353\pi\) | |||||||
\(942\) | − | 6.67773e11i | − | 0.848057i | ||||||
\(943\) | −4.61481e11 | −0.583589 | ||||||||
\(944\) | −3.27282e10 | −0.0412130 | ||||||||
\(945\) | − | 2.97899e11i | − | 0.373544i | ||||||
\(946\) | 6.93167e11 | − | 4.33324e11i | 0.865512 | − | 0.541063i | ||||
\(947\) | 1.10138e12 | 1.36943 | 0.684713 | − | 0.728813i | \(-0.259928\pi\) | ||||
0.684713 | + | 0.728813i | \(0.259928\pi\) | |||||||
\(948\) | 6.38536e11i | 0.790591i | ||||||||
\(949\) | − | 1.82580e12i | − | 2.25107i | ||||||
\(950\) | 5.93152e10 | 0.0728235 | ||||||||
\(951\) | 4.99926e11i | 0.611200i | ||||||||
\(952\) | 2.10599e10 | 0.0256394 | ||||||||
\(953\) | 1.42579e12i | 1.72855i | 0.503017 | + | 0.864277i | \(0.332223\pi\) | ||||
−0.503017 | + | 0.864277i | \(0.667777\pi\) | |||||||
\(954\) | − | 1.41893e12i | − | 1.71304i | ||||||
\(955\) | 8.40568e11 | 1.01055 | ||||||||
\(956\) | 7.60114e11 | 0.910012 | ||||||||
\(957\) | 4.41661e12 | 5.26553 | ||||||||
\(958\) | 5.88291e11i | 0.698442i | ||||||||
\(959\) | 1.25191e11 | 0.148012 | ||||||||
\(960\) | −8.23796e11 | −0.969917 | ||||||||
\(961\) | −4.62413e11 | −0.542171 | ||||||||
\(962\) | 5.04077e9 | 0.00588568 | ||||||||
\(963\) | 1.86930e12 | 2.17357 | ||||||||
\(964\) | − | 1.27414e11i | − | 0.147540i | ||||||
\(965\) | 6.44938e11i | 0.743719i | ||||||||
\(966\) | 9.63483e10i | 0.110646i | ||||||||
\(967\) | 2.21670e10 | 0.0253513 | 0.0126756 | − | 0.999920i | \(-0.495965\pi\) | ||||
0.0126756 | + | 0.999920i | \(0.495965\pi\) | |||||||
\(968\) | − | 1.38595e12i | − | 1.57851i | ||||||
\(969\) | 5.13307e10 | 0.0582214 | ||||||||
\(970\) | −2.08333e11 | −0.235327 | ||||||||
\(971\) | −1.94301e11 | −0.218574 | −0.109287 | − | 0.994010i | \(-0.534857\pi\) | ||||
−0.109287 | + | 0.994010i | \(0.534857\pi\) | |||||||
\(972\) | − | 6.69565e10i | − | 0.0750115i | ||||||
\(973\) | − | 2.83946e11i | − | 0.316800i | ||||||
\(974\) | − | 1.45212e11i | − | 0.161350i | ||||||
\(975\) | 7.12663e11i | 0.788616i | ||||||||
\(976\) | 5.58348e10i | 0.0615326i | ||||||||
\(977\) | 5.07790e10 | 0.0557321 | 0.0278661 | − | 0.999612i | \(-0.491129\pi\) | ||||
0.0278661 | + | 0.999612i | \(0.491129\pi\) | |||||||
\(978\) | − | 5.68419e11i | − | 0.621317i | ||||||
\(979\) | 2.12554e12i | 2.31387i | ||||||||
\(980\) | 4.15356e11i | 0.450315i | ||||||||
\(981\) | −2.82220e12 | −3.04728 | ||||||||
\(982\) | 6.91671e11 | 0.743795 | ||||||||
\(983\) | − | 3.96924e11i | − | 0.425103i | −0.977150 | − | 0.212551i | \(-0.931823\pi\) | ||
0.977150 | − | 0.212551i | \(-0.0681773\pi\) | |||||||
\(984\) | −2.48164e12 | −2.64702 | ||||||||
\(985\) | 8.17214e11i | 0.868143i | ||||||||
\(986\) | −1.13207e11 | −0.119775 | ||||||||
\(987\) | 1.23667e11 | 0.130312 | ||||||||
\(988\) | − | 2.54627e11i | − | 0.267224i | ||||||
\(989\) | 1.98128e11 | + | 3.16935e11i | 0.207091 | + | 0.331273i | ||||
\(990\) | 1.62405e12 | 1.69067 | ||||||||
\(991\) | 4.78133e10i | 0.0495740i | 0.999693 | + | 0.0247870i | \(0.00789076\pi\) | ||||
−0.999693 | + | 0.0247870i | \(0.992109\pi\) | |||||||
\(992\) | 6.42090e11i | 0.663054i | ||||||||
\(993\) | 1.21027e12 | 1.24476 | ||||||||
\(994\) | − | 8.69781e10i | − | 0.0890973i | ||||||
\(995\) | 8.29014e11 | 0.845803 | ||||||||
\(996\) | 7.88644e11i | 0.801390i | ||||||||
\(997\) | 3.74693e11i | 0.379223i | 0.981859 | + | 0.189612i | \(0.0607229\pi\) | ||||
−0.981859 | + | 0.189612i | \(0.939277\pi\) | |||||||
\(998\) | −7.07494e11 | −0.713183 | ||||||||
\(999\) | 1.23639e10 | 0.0124135 |
(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 | 43.9.b.b.42.11 | ✓ | 28 | |
43.42 | odd | 2 | inner | 43.9.b.b.42.18 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.9.b.b.42.11 | ✓ | 28 | 1.1 | even | 1 | trivial | |
43.9.b.b.42.18 | yes | 28 | 43.42 | odd | 2 | inner |