Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,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, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
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: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.11 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.24 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 29.9454i | − | 0.935795i | −0.883783 | − | 0.467897i | \(-0.845012\pi\) | ||
0.883783 | − | 0.467897i | \(-0.154988\pi\) | |||||||
\(3\) | 271.957i | 1.11916i | 0.828775 | + | 0.559581i | \(0.189038\pi\) | ||||
−0.828775 | + | 0.559581i | \(0.810962\pi\) | |||||||
\(4\) | 127.271 | 0.124288 | ||||||||
\(5\) | − | 203.516i | − | 0.0651250i | −0.999470 | − | 0.0325625i | \(-0.989633\pi\) | ||
0.999470 | − | 0.0325625i | \(-0.0103668\pi\) | |||||||
\(6\) | 8143.86 | 1.04731 | ||||||||
\(7\) | − | 3479.85i | − | 0.207048i | −0.994627 | − | 0.103524i | \(-0.966988\pi\) | ||
0.994627 | − | 0.103524i | \(-0.0330118\pi\) | |||||||
\(8\) | − | 34475.3i | − | 1.05210i | ||||||
\(9\) | −14911.3 | −0.252525 | ||||||||
\(10\) | −6094.37 | −0.0609437 | ||||||||
\(11\) | −186733. | −1.15946 | −0.579731 | − | 0.814808i | \(-0.696843\pi\) | ||||
−0.579731 | + | 0.814808i | \(0.696843\pi\) | |||||||
\(12\) | 34612.1i | 0.139098i | ||||||||
\(13\) | 180877. | 0.487155 | 0.243577 | − | 0.969881i | \(-0.421679\pi\) | ||||
0.243577 | + | 0.969881i | \(0.421679\pi\) | |||||||
\(14\) | −104206. | −0.193754 | ||||||||
\(15\) | 55347.4 | 0.0728855 | ||||||||
\(16\) | −902053. | −0.860265 | ||||||||
\(17\) | 2.31205e6 | 1.62837 | 0.814183 | − | 0.580608i | \(-0.197185\pi\) | ||||
0.814183 | + | 0.580608i | \(0.197185\pi\) | |||||||
\(18\) | 446527.i | 0.236311i | ||||||||
\(19\) | − | 1.81781e6i | − | 0.734143i | −0.930193 | − | 0.367072i | \(-0.880360\pi\) | ||
0.930193 | − | 0.367072i | \(-0.119640\pi\) | |||||||
\(20\) | − | 25901.6i | − | 0.00809425i | ||||||
\(21\) | 946367. | 0.231720 | ||||||||
\(22\) | 5.59179e6i | 1.08502i | ||||||||
\(23\) | 3.25182e6 | 0.505227 | 0.252614 | − | 0.967567i | \(-0.418710\pi\) | ||||
0.252614 | + | 0.967567i | \(0.418710\pi\) | |||||||
\(24\) | 9.37578e6 | 1.17747 | ||||||||
\(25\) | 9.72421e6 | 0.995759 | ||||||||
\(26\) | − | 5.41644e6i | − | 0.455877i | ||||||
\(27\) | 1.20035e7i | 0.836546i | ||||||||
\(28\) | − | 442883.i | − | 0.0257335i | ||||||
\(29\) | 1.93209e6i | 0.0941972i | 0.998890 | + | 0.0470986i | \(0.0149975\pi\) | ||||
−0.998890 | + | 0.0470986i | \(0.985002\pi\) | |||||||
\(30\) | − | 1.65740e6i | − | 0.0682059i | ||||||
\(31\) | 1.24335e7 | 0.434296 | 0.217148 | − | 0.976139i | \(-0.430325\pi\) | ||||
0.217148 | + | 0.976139i | \(0.430325\pi\) | |||||||
\(32\) | − | 8.29034e6i | − | 0.247071i | ||||||
\(33\) | − | 5.07832e7i | − | 1.29763i | ||||||
\(34\) | − | 6.92353e7i | − | 1.52382i | ||||||
\(35\) | −708204. | −0.0134840 | ||||||||
\(36\) | −1.89778e6 | −0.0313858 | ||||||||
\(37\) | − | 1.29307e8i | − | 1.86472i | −0.361535 | − | 0.932359i | \(-0.617747\pi\) | ||
0.361535 | − | 0.932359i | \(-0.382253\pi\) | |||||||
\(38\) | −5.44351e7 | −0.687007 | ||||||||
\(39\) | 4.91907e7i | 0.545205i | ||||||||
\(40\) | −7.01627e6 | −0.0685182 | ||||||||
\(41\) | 5.75466e7 | 0.496707 | 0.248354 | − | 0.968669i | \(-0.420111\pi\) | ||||
0.248354 | + | 0.968669i | \(0.420111\pi\) | |||||||
\(42\) | − | 2.83394e7i | − | 0.216842i | ||||||
\(43\) | −8.81905e7 | − | 1.17618e8i | −0.599901 | − | 0.800075i | ||||
\(44\) | −2.37656e7 | −0.144107 | ||||||||
\(45\) | 3.03469e6i | 0.0164457i | ||||||||
\(46\) | − | 9.73771e7i | − | 0.472789i | ||||||
\(47\) | 2.19743e8 | 0.958134 | 0.479067 | − | 0.877778i | \(-0.340975\pi\) | ||||
0.479067 | + | 0.877778i | \(0.340975\pi\) | |||||||
\(48\) | − | 2.45319e8i | − | 0.962776i | ||||||
\(49\) | 2.70366e8 | 0.957131 | ||||||||
\(50\) | − | 2.91196e8i | − | 0.931826i | ||||||
\(51\) | 6.28776e8i | 1.82241i | ||||||||
\(52\) | 2.30204e7 | 0.0605474 | ||||||||
\(53\) | 2.24365e8 | 0.536508 | 0.268254 | − | 0.963348i | \(-0.413553\pi\) | ||||
0.268254 | + | 0.963348i | \(0.413553\pi\) | |||||||
\(54\) | 3.59451e8 | 0.782836 | ||||||||
\(55\) | 3.80030e7i | 0.0755101i | ||||||||
\(56\) | −1.19969e8 | −0.217835 | ||||||||
\(57\) | 4.94366e8 | 0.821625 | ||||||||
\(58\) | 5.78574e7 | 0.0881493 | ||||||||
\(59\) | 4.63656e8 | 0.648538 | 0.324269 | − | 0.945965i | \(-0.394882\pi\) | ||||
0.324269 | + | 0.945965i | \(0.394882\pi\) | |||||||
\(60\) | 7.04411e6 | 0.00905878 | ||||||||
\(61\) | 1.32372e9i | 1.56729i | 0.621212 | + | 0.783643i | \(0.286641\pi\) | ||||
−0.621212 | + | 0.783643i | \(0.713359\pi\) | |||||||
\(62\) | − | 3.72327e8i | − | 0.406412i | ||||||
\(63\) | 5.18892e7i | 0.0522846i | ||||||||
\(64\) | −1.17196e9 | −1.09147 | ||||||||
\(65\) | − | 3.68113e7i | − | 0.0317260i | ||||||
\(66\) | −1.52072e9 | −1.21431 | ||||||||
\(67\) | −9.00383e8 | −0.666888 | −0.333444 | − | 0.942770i | \(-0.608211\pi\) | ||||
−0.333444 | + | 0.942770i | \(0.608211\pi\) | |||||||
\(68\) | 2.94256e8 | 0.202386 | ||||||||
\(69\) | 8.84353e8i | 0.565432i | ||||||||
\(70\) | 2.12075e7i | 0.0126182i | ||||||||
\(71\) | − | 5.54119e8i | − | 0.307122i | −0.988139 | − | 0.153561i | \(-0.950926\pi\) | ||
0.988139 | − | 0.153561i | \(-0.0490742\pi\) | |||||||
\(72\) | 5.14073e8i | 0.265682i | ||||||||
\(73\) | − | 2.21796e9i | − | 1.06989i | −0.844887 | − | 0.534944i | \(-0.820333\pi\) | ||
0.844887 | − | 0.534944i | \(-0.179667\pi\) | |||||||
\(74\) | −3.87215e9 | −1.74499 | ||||||||
\(75\) | 2.64456e9i | 1.11442i | ||||||||
\(76\) | − | 2.31354e8i | − | 0.0912450i | ||||||
\(77\) | 6.49801e8i | 0.240064i | ||||||||
\(78\) | 1.47304e9 | 0.510200 | ||||||||
\(79\) | 1.15303e9 | 0.374718 | 0.187359 | − | 0.982292i | \(-0.440007\pi\) | ||||
0.187359 | + | 0.982292i | \(0.440007\pi\) | |||||||
\(80\) | 1.83582e8i | 0.0560248i | ||||||||
\(81\) | −4.14494e9 | −1.18876 | ||||||||
\(82\) | − | 1.72326e9i | − | 0.464816i | ||||||
\(83\) | 1.02782e9 | 0.260931 | 0.130465 | − | 0.991453i | \(-0.458353\pi\) | ||||
0.130465 | + | 0.991453i | \(0.458353\pi\) | |||||||
\(84\) | 1.20445e8 | 0.0288000 | ||||||||
\(85\) | − | 4.70538e8i | − | 0.106047i | ||||||
\(86\) | −3.52211e9 | + | 2.64090e9i | −0.748706 | + | 0.561384i | ||||
\(87\) | −5.25445e8 | −0.105422 | ||||||||
\(88\) | 6.43767e9i | 1.21987i | ||||||||
\(89\) | 6.93215e9i | 1.24142i | 0.784041 | + | 0.620709i | \(0.213155\pi\) | ||||
−0.784041 | + | 0.620709i | \(0.786845\pi\) | |||||||
\(90\) | 9.08752e7 | 0.0153898 | ||||||||
\(91\) | − | 6.29425e8i | − | 0.100864i | ||||||
\(92\) | 4.13861e8 | 0.0627936 | ||||||||
\(93\) | 3.38138e9i | 0.486047i | ||||||||
\(94\) | − | 6.58031e9i | − | 0.896617i | ||||||
\(95\) | −3.69953e8 | −0.0478111 | ||||||||
\(96\) | 2.25461e9 | 0.276513 | ||||||||
\(97\) | 9.01632e9 | 1.04996 | 0.524978 | − | 0.851116i | \(-0.324074\pi\) | ||||
0.524978 | + | 0.851116i | \(0.324074\pi\) | |||||||
\(98\) | − | 8.09623e9i | − | 0.895679i | ||||||
\(99\) | 2.78443e9 | 0.292793 | ||||||||
\(100\) | 1.23761e9 | 0.123761 | ||||||||
\(101\) | 1.02554e9 | 0.0975768 | 0.0487884 | − | 0.998809i | \(-0.484464\pi\) | ||||
0.0487884 | + | 0.998809i | \(0.484464\pi\) | |||||||
\(102\) | 1.88290e10 | 1.70540 | ||||||||
\(103\) | −1.17742e10 | −1.01566 | −0.507828 | − | 0.861458i | \(-0.669552\pi\) | ||||
−0.507828 | + | 0.861458i | \(0.669552\pi\) | |||||||
\(104\) | − | 6.23579e9i | − | 0.512537i | ||||||
\(105\) | − | 1.92601e8i | − | 0.0150908i | ||||||
\(106\) | − | 6.71871e9i | − | 0.502061i | ||||||
\(107\) | −1.00033e10 | −0.713222 | −0.356611 | − | 0.934253i | \(-0.616068\pi\) | ||||
−0.356611 | + | 0.934253i | \(0.616068\pi\) | |||||||
\(108\) | 1.52770e9i | 0.103973i | ||||||||
\(109\) | −2.28161e10 | −1.48289 | −0.741444 | − | 0.671015i | \(-0.765858\pi\) | ||||
−0.741444 | + | 0.671015i | \(0.765858\pi\) | |||||||
\(110\) | 1.13802e9 | 0.0706619 | ||||||||
\(111\) | 3.51658e10 | 2.08692 | ||||||||
\(112\) | 3.13901e9i | 0.178116i | ||||||||
\(113\) | − | 5.09756e9i | − | 0.276675i | −0.990385 | − | 0.138338i | \(-0.955824\pi\) | ||
0.990385 | − | 0.138338i | \(-0.0441759\pi\) | |||||||
\(114\) | − | 1.48040e10i | − | 0.768873i | ||||||
\(115\) | − | 6.61796e8i | − | 0.0329029i | ||||||
\(116\) | 2.45899e8i | 0.0117076i | ||||||||
\(117\) | −2.69712e9 | −0.123019 | ||||||||
\(118\) | − | 1.38844e10i | − | 0.606899i | ||||||
\(119\) | − | 8.04557e9i | − | 0.337149i | ||||||
\(120\) | − | 1.90812e9i | − | 0.0766830i | ||||||
\(121\) | 8.93167e9 | 0.344354 | ||||||||
\(122\) | 3.96395e10 | 1.46666 | ||||||||
\(123\) | 1.56502e10i | 0.555896i | ||||||||
\(124\) | 1.58242e9 | 0.0539777 | ||||||||
\(125\) | − | 3.96649e9i | − | 0.129974i | ||||||
\(126\) | 1.55384e9 | 0.0489277 | ||||||||
\(127\) | −4.69853e10 | −1.42214 | −0.711072 | − | 0.703119i | \(-0.751790\pi\) | ||||
−0.711072 | + | 0.703119i | \(0.751790\pi\) | |||||||
\(128\) | 2.66055e10i | 0.774323i | ||||||||
\(129\) | 3.19869e10 | − | 2.39840e10i | 0.895413 | − | 0.671386i | ||||
\(130\) | −1.10233e9 | −0.0296890 | ||||||||
\(131\) | − | 4.29874e10i | − | 1.11426i | −0.830426 | − | 0.557128i | \(-0.811903\pi\) | ||
0.830426 | − | 0.557128i | \(-0.188097\pi\) | |||||||
\(132\) | − | 6.46321e9i | − | 0.161279i | ||||||
\(133\) | −6.32571e9 | −0.152003 | ||||||||
\(134\) | 2.69624e10i | 0.624071i | ||||||||
\(135\) | 2.44291e9 | 0.0544801 | ||||||||
\(136\) | − | 7.97086e10i | − | 1.71321i | ||||||
\(137\) | 3.02579e10i | 0.626954i | 0.949596 | + | 0.313477i | \(0.101494\pi\) | ||||
−0.949596 | + | 0.313477i | \(0.898506\pi\) | |||||||
\(138\) | 2.64823e10 | 0.529128 | ||||||||
\(139\) | −6.74771e10 | −1.30042 | −0.650208 | − | 0.759756i | \(-0.725318\pi\) | ||||
−0.650208 | + | 0.759756i | \(0.725318\pi\) | |||||||
\(140\) | −9.01336e7 | −0.00167589 | ||||||||
\(141\) | 5.97606e10i | 1.07231i | ||||||||
\(142\) | −1.65933e10 | −0.287403 | ||||||||
\(143\) | −3.37757e10 | −0.564838 | ||||||||
\(144\) | 1.34508e10 | 0.217238 | ||||||||
\(145\) | 3.93211e8 | 0.00613460 | ||||||||
\(146\) | −6.64176e10 | −1.00120 | ||||||||
\(147\) | 7.35278e10i | 1.07119i | ||||||||
\(148\) | − | 1.64570e10i | − | 0.231762i | ||||||
\(149\) | 6.07433e10i | 0.827117i | 0.910478 | + | 0.413558i | \(0.135714\pi\) | ||||
−0.910478 | + | 0.413558i | \(0.864286\pi\) | |||||||
\(150\) | 7.91925e10 | 1.04286 | ||||||||
\(151\) | − | 4.24289e10i | − | 0.540477i | −0.962793 | − | 0.270238i | \(-0.912898\pi\) | ||
0.962793 | − | 0.270238i | \(-0.0871025\pi\) | |||||||
\(152\) | −6.26696e10 | −0.772394 | ||||||||
\(153\) | −3.44757e10 | −0.411203 | ||||||||
\(154\) | 1.94586e10 | 0.224651 | ||||||||
\(155\) | − | 2.53042e9i | − | 0.0282835i | ||||||
\(156\) | 6.26054e9i | 0.0677624i | ||||||||
\(157\) | 6.74501e10i | 0.707105i | 0.935415 | + | 0.353553i | \(0.115027\pi\) | ||||
−0.935415 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(158\) | − | 3.45279e10i | − | 0.350659i | ||||||
\(159\) | 6.10175e10i | 0.600439i | ||||||||
\(160\) | −1.68721e9 | −0.0160905 | ||||||||
\(161\) | − | 1.13158e10i | − | 0.104606i | ||||||
\(162\) | 1.24122e11i | 1.11243i | ||||||||
\(163\) | 4.69429e10i | 0.407973i | 0.978974 | + | 0.203987i | \(0.0653899\pi\) | ||||
−0.978974 | + | 0.203987i | \(0.934610\pi\) | |||||||
\(164\) | 7.32400e9 | 0.0617346 | ||||||||
\(165\) | −1.03352e10 | −0.0845080 | ||||||||
\(166\) | − | 3.07784e10i | − | 0.244178i | ||||||
\(167\) | 2.47736e10 | 0.190725 | 0.0953623 | − | 0.995443i | \(-0.469599\pi\) | ||||
0.0953623 | + | 0.995443i | \(0.469599\pi\) | |||||||
\(168\) | − | 3.26263e10i | − | 0.243793i | ||||||
\(169\) | −1.05142e11 | −0.762680 | ||||||||
\(170\) | −1.40905e10 | −0.0992386 | ||||||||
\(171\) | 2.71060e10i | 0.185389i | ||||||||
\(172\) | −1.12241e10 | − | 1.49693e10i | −0.0745603 | − | 0.0994395i | ||||
\(173\) | 1.71294e11 | 1.10538 | 0.552690 | − | 0.833387i | \(-0.313601\pi\) | ||||
0.552690 | + | 0.833387i | \(0.313601\pi\) | |||||||
\(174\) | 1.57347e10i | 0.0986534i | ||||||||
\(175\) | − | 3.38388e10i | − | 0.206169i | ||||||
\(176\) | 1.68443e11 | 0.997445 | ||||||||
\(177\) | 1.26094e11i | 0.725820i | ||||||||
\(178\) | 2.07586e11 | 1.16171 | ||||||||
\(179\) | 2.81260e11i | 1.53054i | 0.643712 | + | 0.765268i | \(0.277394\pi\) | ||||
−0.643712 | + | 0.765268i | \(0.722606\pi\) | |||||||
\(180\) | 3.86227e8i | 0.00204400i | ||||||||
\(181\) | −9.21860e10 | −0.474539 | −0.237270 | − | 0.971444i | \(-0.576252\pi\) | ||||
−0.237270 | + | 0.971444i | \(0.576252\pi\) | |||||||
\(182\) | −1.88484e10 | −0.0943882 | ||||||||
\(183\) | −3.59995e11 | −1.75405 | ||||||||
\(184\) | − | 1.12107e11i | − | 0.531551i | ||||||
\(185\) | −2.63160e10 | −0.121440 | ||||||||
\(186\) | 1.01257e11 | 0.454841 | ||||||||
\(187\) | −4.31735e11 | −1.88803 | ||||||||
\(188\) | 2.79669e10 | 0.119084 | ||||||||
\(189\) | 4.17704e10 | 0.173205 | ||||||||
\(190\) | 1.10784e10i | 0.0447414i | ||||||||
\(191\) | − | 1.41848e11i | − | 0.558029i | −0.960287 | − | 0.279015i | \(-0.909992\pi\) | ||
0.960287 | − | 0.279015i | \(-0.0900078\pi\) | |||||||
\(192\) | − | 3.18722e11i | − | 1.22154i | ||||||
\(193\) | 3.49463e11 | 1.30501 | 0.652507 | − | 0.757783i | \(-0.273717\pi\) | ||||
0.652507 | + | 0.757783i | \(0.273717\pi\) | |||||||
\(194\) | − | 2.69998e11i | − | 0.982543i | ||||||
\(195\) | 1.00111e10 | 0.0355065 | ||||||||
\(196\) | 3.44097e10 | 0.118960 | ||||||||
\(197\) | −7.75830e10 | −0.261478 | −0.130739 | − | 0.991417i | \(-0.541735\pi\) | ||||
−0.130739 | + | 0.991417i | \(0.541735\pi\) | |||||||
\(198\) | − | 8.33811e10i | − | 0.273994i | ||||||
\(199\) | − | 5.02411e11i | − | 1.60988i | −0.593356 | − | 0.804940i | \(-0.702197\pi\) | ||
0.593356 | − | 0.804940i | \(-0.297803\pi\) | |||||||
\(200\) | − | 3.35245e11i | − | 1.04764i | ||||||
\(201\) | − | 2.44865e11i | − | 0.746357i | ||||||
\(202\) | − | 3.07103e10i | − | 0.0913119i | ||||||
\(203\) | 6.72339e9 | 0.0195033 | ||||||||
\(204\) | 8.00248e10i | 0.226503i | ||||||||
\(205\) | − | 1.17116e10i | − | 0.0323481i | ||||||
\(206\) | 3.52585e11i | 0.950446i | ||||||||
\(207\) | −4.84889e10 | −0.127582 | ||||||||
\(208\) | −1.63161e11 | −0.419082 | ||||||||
\(209\) | 3.39445e11i | 0.851212i | ||||||||
\(210\) | −5.76751e9 | −0.0141219 | ||||||||
\(211\) | − | 6.06724e11i | − | 1.45070i | −0.688378 | − | 0.725352i | \(-0.741677\pi\) | ||
0.688378 | − | 0.725352i | \(-0.258323\pi\) | |||||||
\(212\) | 2.85551e10 | 0.0666814 | ||||||||
\(213\) | 1.50696e11 | 0.343720 | ||||||||
\(214\) | 2.99553e11i | 0.667430i | ||||||||
\(215\) | −2.39370e10 | + | 1.79481e10i | −0.0521049 | + | 0.0390685i | ||||
\(216\) | 4.13825e11 | 0.880133 | ||||||||
\(217\) | − | 4.32667e10i | − | 0.0899199i | ||||||
\(218\) | 6.83237e11i | 1.38768i | ||||||||
\(219\) | 6.03187e11 | 1.19738 | ||||||||
\(220\) | 4.83667e9i | 0.00938498i | ||||||||
\(221\) | 4.18197e11 | 0.793266 | ||||||||
\(222\) | − | 1.05306e12i | − | 1.95293i | ||||||
\(223\) | 3.47401e11i | 0.629951i | 0.949100 | + | 0.314976i | \(0.101996\pi\) | ||||
−0.949100 | + | 0.314976i | \(0.898004\pi\) | |||||||
\(224\) | −2.88491e10 | −0.0511555 | ||||||||
\(225\) | −1.45001e11 | −0.251454 | ||||||||
\(226\) | −1.52649e11 | −0.258911 | ||||||||
\(227\) | 2.92541e11i | 0.485352i | 0.970107 | + | 0.242676i | \(0.0780252\pi\) | ||||
−0.970107 | + | 0.242676i | \(0.921975\pi\) | |||||||
\(228\) | 6.29183e10 | 0.102118 | ||||||||
\(229\) | 3.34745e11 | 0.531540 | 0.265770 | − | 0.964036i | \(-0.414374\pi\) | ||||
0.265770 | + | 0.964036i | \(0.414374\pi\) | |||||||
\(230\) | −1.98178e10 | −0.0307904 | ||||||||
\(231\) | −1.76718e11 | −0.268671 | ||||||||
\(232\) | 6.66095e10 | 0.0991052 | ||||||||
\(233\) | 9.55518e11i | 1.39142i | 0.718321 | + | 0.695711i | \(0.244911\pi\) | ||||
−0.718321 | + | 0.695711i | \(0.755089\pi\) | |||||||
\(234\) | 8.07664e10i | 0.115120i | ||||||||
\(235\) | − | 4.47212e10i | − | 0.0623985i | ||||||
\(236\) | 5.90098e10 | 0.0806054 | ||||||||
\(237\) | 3.13573e11i | 0.419370i | ||||||||
\(238\) | −2.40928e11 | −0.315503 | ||||||||
\(239\) | 1.01652e12 | 1.30355 | 0.651773 | − | 0.758414i | \(-0.274026\pi\) | ||||
0.651773 | + | 0.758414i | \(0.274026\pi\) | |||||||
\(240\) | −4.99263e10 | −0.0627008 | ||||||||
\(241\) | 4.87485e11i | 0.599620i | 0.953999 | + | 0.299810i | \(0.0969233\pi\) | ||||
−0.953999 | + | 0.299810i | \(0.903077\pi\) | |||||||
\(242\) | − | 2.67463e11i | − | 0.322245i | ||||||
\(243\) | − | 4.18446e11i | − | 0.493865i | ||||||
\(244\) | 1.68471e11i | 0.194795i | ||||||||
\(245\) | − | 5.50237e10i | − | 0.0623332i | ||||||
\(246\) | 4.68651e11 | 0.520205 | ||||||||
\(247\) | − | 3.28800e11i | − | 0.357641i | ||||||
\(248\) | − | 4.28649e11i | − | 0.456924i | ||||||
\(249\) | 2.79521e11i | 0.292024i | ||||||||
\(250\) | −1.18778e11 | −0.121629 | ||||||||
\(251\) | −1.82489e12 | −1.83176 | −0.915880 | − | 0.401453i | \(-0.868505\pi\) | ||||
−0.915880 | + | 0.401453i | \(0.868505\pi\) | |||||||
\(252\) | 6.60398e9i | 0.00649834i | ||||||||
\(253\) | −6.07220e11 | −0.585792 | ||||||||
\(254\) | 1.40700e12i | 1.33084i | ||||||||
\(255\) | 1.27966e11 | 0.118684 | ||||||||
\(256\) | −4.03372e11 | −0.366865 | ||||||||
\(257\) | 2.84410e11i | 0.253676i | 0.991923 | + | 0.126838i | \(0.0404828\pi\) | ||||
−0.991923 | + | 0.126838i | \(0.959517\pi\) | |||||||
\(258\) | −7.18210e11 | − | 9.57862e11i | −0.628280 | − | 0.837923i | ||||
\(259\) | −4.49968e11 | −0.386085 | ||||||||
\(260\) | − | 4.68500e9i | − | 0.00394315i | ||||||
\(261\) | − | 2.88101e10i | − | 0.0237871i | ||||||
\(262\) | −1.28728e12 | −1.04272 | ||||||||
\(263\) | 3.79504e11i | 0.301604i | 0.988564 | + | 0.150802i | \(0.0481856\pi\) | ||||
−0.988564 | + | 0.150802i | \(0.951814\pi\) | |||||||
\(264\) | −1.75077e12 | −1.36524 | ||||||||
\(265\) | − | 4.56618e10i | − | 0.0349401i | ||||||
\(266\) | 1.89426e11i | 0.142243i | ||||||||
\(267\) | −1.88524e12 | −1.38935 | ||||||||
\(268\) | −1.14592e11 | −0.0828861 | ||||||||
\(269\) | 4.04745e11 | 0.287356 | 0.143678 | − | 0.989625i | \(-0.454107\pi\) | ||||
0.143678 | + | 0.989625i | \(0.454107\pi\) | |||||||
\(270\) | − | 7.31539e10i | − | 0.0509822i | ||||||
\(271\) | 2.37135e12 | 1.62237 | 0.811183 | − | 0.584793i | \(-0.198824\pi\) | ||||
0.811183 | + | 0.584793i | \(0.198824\pi\) | |||||||
\(272\) | −2.08559e12 | −1.40083 | ||||||||
\(273\) | 1.71176e11 | 0.112883 | ||||||||
\(274\) | 9.06085e11 | 0.586700 | ||||||||
\(275\) | −1.81583e12 | −1.15455 | ||||||||
\(276\) | 1.12552e11i | 0.0702763i | ||||||||
\(277\) | − | 2.24997e12i | − | 1.37968i | −0.723964 | − | 0.689838i | \(-0.757682\pi\) | ||
0.723964 | − | 0.689838i | \(-0.242318\pi\) | |||||||
\(278\) | 2.02063e12i | 1.21692i | ||||||||
\(279\) | −1.85400e11 | −0.109670 | ||||||||
\(280\) | 2.44155e10i | 0.0141865i | ||||||||
\(281\) | −7.18647e11 | −0.410189 | −0.205094 | − | 0.978742i | \(-0.565750\pi\) | ||||
−0.205094 | + | 0.978742i | \(0.565750\pi\) | |||||||
\(282\) | 1.78956e12 | 1.00346 | ||||||||
\(283\) | 2.12573e12 | 1.17105 | 0.585527 | − | 0.810653i | \(-0.300888\pi\) | ||||
0.585527 | + | 0.810653i | \(0.300888\pi\) | |||||||
\(284\) | − | 7.05231e10i | − | 0.0381715i | ||||||
\(285\) | − | 1.00611e11i | − | 0.0535084i | ||||||
\(286\) | 1.01143e12i | 0.528572i | ||||||||
\(287\) | − | 2.00253e11i | − | 0.102842i | ||||||
\(288\) | 1.23620e11i | 0.0623917i | ||||||||
\(289\) | 3.32957e12 | 1.65158 | ||||||||
\(290\) | − | 1.17749e10i | − | 0.00574072i | ||||||
\(291\) | 2.45205e12i | 1.17507i | ||||||||
\(292\) | − | 2.82281e11i | − | 0.132974i | ||||||
\(293\) | 3.97847e12 | 1.84237 | 0.921187 | − | 0.389121i | \(-0.127221\pi\) | ||||
0.921187 | + | 0.389121i | \(0.127221\pi\) | |||||||
\(294\) | 2.20182e12 | 1.00241 | ||||||||
\(295\) | − | 9.43612e10i | − | 0.0422361i | ||||||
\(296\) | −4.45789e12 | −1.96187 | ||||||||
\(297\) | − | 2.24145e12i | − | 0.969944i | ||||||
\(298\) | 1.81898e12 | 0.774012 | ||||||||
\(299\) | 5.88179e11 | 0.246124 | ||||||||
\(300\) | 3.36575e11i | 0.138508i | ||||||||
\(301\) | −4.09292e11 | + | 3.06889e11i | −0.165653 | + | 0.124208i | ||||
\(302\) | −1.27055e12 | −0.505775 | ||||||||
\(303\) | 2.78903e11i | 0.109204i | ||||||||
\(304\) | 1.63976e12i | 0.631557i | ||||||||
\(305\) | 2.69399e11 | 0.102070 | ||||||||
\(306\) | 1.03239e12i | 0.384802i | ||||||||
\(307\) | 2.68118e11 | 0.0983183 | 0.0491591 | − | 0.998791i | \(-0.484346\pi\) | ||||
0.0491591 | + | 0.998791i | \(0.484346\pi\) | |||||||
\(308\) | 8.27007e10i | 0.0298370i | ||||||||
\(309\) | − | 3.20208e12i | − | 1.13668i | ||||||
\(310\) | −7.57744e10 | −0.0264676 | ||||||||
\(311\) | −1.56641e12 | −0.538399 | −0.269199 | − | 0.963084i | \(-0.586759\pi\) | ||||
−0.269199 | + | 0.963084i | \(0.586759\pi\) | |||||||
\(312\) | 1.69586e12 | 0.573612 | ||||||||
\(313\) | − | 2.16661e11i | − | 0.0721205i | −0.999350 | − | 0.0360602i | \(-0.988519\pi\) | ||
0.999350 | − | 0.0360602i | \(-0.0114808\pi\) | |||||||
\(314\) | 2.01982e12 | 0.661706 | ||||||||
\(315\) | 1.05603e10 | 0.00340504 | ||||||||
\(316\) | 1.46747e11 | 0.0465729 | ||||||||
\(317\) | −4.92724e11 | −0.153924 | −0.0769622 | − | 0.997034i | \(-0.524522\pi\) | ||||
−0.0769622 | + | 0.997034i | \(0.524522\pi\) | |||||||
\(318\) | 1.82720e12 | 0.561888 | ||||||||
\(319\) | − | 3.60785e11i | − | 0.109218i | ||||||
\(320\) | 2.38512e11i | 0.0710822i | ||||||||
\(321\) | − | 2.72046e12i | − | 0.798211i | ||||||
\(322\) | −3.38857e11 | −0.0978898 | ||||||||
\(323\) | − | 4.20287e12i | − | 1.19545i | ||||||
\(324\) | −5.27529e11 | −0.147748 | ||||||||
\(325\) | 1.75889e12 | 0.485089 | ||||||||
\(326\) | 1.40572e12 | 0.381779 | ||||||||
\(327\) | − | 6.20497e12i | − | 1.65959i | ||||||
\(328\) | − | 1.98394e12i | − | 0.522587i | ||||||
\(329\) | − | 7.64673e11i | − | 0.198379i | ||||||
\(330\) | 3.09491e11i | 0.0790822i | ||||||||
\(331\) | 9.92385e11i | 0.249770i | 0.992171 | + | 0.124885i | \(0.0398562\pi\) | ||||
−0.992171 | + | 0.124885i | \(0.960144\pi\) | |||||||
\(332\) | 1.30811e11 | 0.0324305 | ||||||||
\(333\) | 1.92814e12i | 0.470887i | ||||||||
\(334\) | − | 7.41856e11i | − | 0.178479i | ||||||
\(335\) | 1.83242e11i | 0.0434311i | ||||||||
\(336\) | −8.53673e11 | −0.199340 | ||||||||
\(337\) | −5.53124e12 | −1.27254 | −0.636272 | − | 0.771465i | \(-0.719524\pi\) | ||||
−0.636272 | + | 0.771465i | \(0.719524\pi\) | |||||||
\(338\) | 3.14852e12i | 0.713712i | ||||||||
\(339\) | 1.38632e12 | 0.309645 | ||||||||
\(340\) | − | 5.98857e10i | − | 0.0131804i | ||||||
\(341\) | −2.32174e12 | −0.503550 | ||||||||
\(342\) | 8.11701e11 | 0.173486 | ||||||||
\(343\) | − | 1.92380e12i | − | 0.405219i | ||||||
\(344\) | −4.05491e12 | + | 3.04039e12i | −0.841761 | + | 0.631157i | ||||
\(345\) | 1.79980e11 | 0.0368237 | ||||||||
\(346\) | − | 5.12947e12i | − | 1.03441i | ||||||
\(347\) | − | 1.35809e12i | − | 0.269948i | −0.990849 | − | 0.134974i | \(-0.956905\pi\) | ||
0.990849 | − | 0.134974i | \(-0.0430951\pi\) | |||||||
\(348\) | −6.68738e10 | −0.0131027 | ||||||||
\(349\) | − | 5.27222e12i | − | 1.01828i | −0.860684 | − | 0.509139i | \(-0.829964\pi\) | ||
0.860684 | − | 0.509139i | \(-0.170036\pi\) | |||||||
\(350\) | −1.01332e12 | −0.192932 | ||||||||
\(351\) | 2.17116e12i | 0.407527i | ||||||||
\(352\) | 1.54808e12i | 0.286470i | ||||||||
\(353\) | −7.41122e12 | −1.35212 | −0.676062 | − | 0.736845i | \(-0.736315\pi\) | ||||
−0.676062 | + | 0.736845i | \(0.736315\pi\) | |||||||
\(354\) | 3.77595e12 | 0.679218 | ||||||||
\(355\) | −1.12772e11 | −0.0200013 | ||||||||
\(356\) | 8.82259e11i | 0.154293i | ||||||||
\(357\) | 2.18805e12 | 0.377325 | ||||||||
\(358\) | 8.42247e12 | 1.43227 | ||||||||
\(359\) | −6.00592e12 | −1.00718 | −0.503591 | − | 0.863942i | \(-0.667988\pi\) | ||||
−0.503591 | + | 0.863942i | \(0.667988\pi\) | |||||||
\(360\) | 1.04622e11 | 0.0173026 | ||||||||
\(361\) | 2.82663e12 | 0.461034 | ||||||||
\(362\) | 2.76055e12i | 0.444071i | ||||||||
\(363\) | 2.42902e12i | 0.385389i | ||||||||
\(364\) | − | 8.01074e10i | − | 0.0125362i | ||||||
\(365\) | −4.51389e11 | −0.0696765 | ||||||||
\(366\) | 1.07802e13i | 1.64143i | ||||||||
\(367\) | 9.10870e11 | 0.136813 | 0.0684063 | − | 0.997658i | \(-0.478209\pi\) | ||||
0.0684063 | + | 0.997658i | \(0.478209\pi\) | |||||||
\(368\) | −2.93331e12 | −0.434629 | ||||||||
\(369\) | −8.58097e11 | −0.125431 | ||||||||
\(370\) | 7.88043e11i | 0.113643i | ||||||||
\(371\) | − | 7.80756e11i | − | 0.111083i | ||||||
\(372\) | 4.30350e11i | 0.0604098i | ||||||||
\(373\) | 1.18703e13i | 1.64406i | 0.569443 | + | 0.822031i | \(0.307159\pi\) | ||||
−0.569443 | + | 0.822031i | \(0.692841\pi\) | |||||||
\(374\) | 1.29285e13i | 1.76681i | ||||||||
\(375\) | 1.07871e12 | 0.145462 | ||||||||
\(376\) | − | 7.57572e12i | − | 1.00806i | ||||||
\(377\) | 3.49471e11i | 0.0458886i | ||||||||
\(378\) | − | 1.25083e12i | − | 0.162084i | ||||||
\(379\) | 6.13117e12 | 0.784056 | 0.392028 | − | 0.919953i | \(-0.371774\pi\) | ||||
0.392028 | + | 0.919953i | \(0.371774\pi\) | |||||||
\(380\) | −4.70842e10 | −0.00594234 | ||||||||
\(381\) | − | 1.27780e13i | − | 1.59161i | ||||||
\(382\) | −4.24771e12 | −0.522201 | ||||||||
\(383\) | 1.63650e13i | 1.98574i | 0.119205 | + | 0.992870i | \(0.461965\pi\) | ||||
−0.119205 | + | 0.992870i | \(0.538035\pi\) | |||||||
\(384\) | −7.23555e12 | −0.866594 | ||||||||
\(385\) | 1.32245e11 | 0.0156342 | ||||||||
\(386\) | − | 1.04648e13i | − | 1.22123i | ||||||
\(387\) | 1.31504e12 | + | 1.75384e12i | 0.151490 | + | 0.202039i | ||||
\(388\) | 1.14751e12 | 0.130497 | ||||||||
\(389\) | 7.49710e12i | 0.841677i | 0.907136 | + | 0.420839i | \(0.138264\pi\) | ||||
−0.907136 | + | 0.420839i | \(0.861736\pi\) | |||||||
\(390\) | − | 2.99786e11i | − | 0.0332268i | ||||||
\(391\) | 7.51836e12 | 0.822695 | ||||||||
\(392\) | − | 9.32095e12i | − | 1.00700i | ||||||
\(393\) | 1.16907e13 | 1.24703 | ||||||||
\(394\) | 2.32326e12i | 0.244690i | ||||||||
\(395\) | − | 2.34659e11i | − | 0.0244035i | ||||||
\(396\) | 3.54377e11 | 0.0363906 | ||||||||
\(397\) | −1.07340e13 | −1.08845 | −0.544227 | − | 0.838938i | \(-0.683177\pi\) | ||||
−0.544227 | + | 0.838938i | \(0.683177\pi\) | |||||||
\(398\) | −1.50449e13 | −1.50652 | ||||||||
\(399\) | − | 1.72032e12i | − | 0.170116i | ||||||
\(400\) | −8.77175e12 | −0.856616 | ||||||||
\(401\) | −8.46435e12 | −0.816341 | −0.408171 | − | 0.912906i | \(-0.633833\pi\) | ||||
−0.408171 | + | 0.912906i | \(0.633833\pi\) | |||||||
\(402\) | −7.33259e12 | −0.698437 | ||||||||
\(403\) | 2.24894e12 | 0.211569 | ||||||||
\(404\) | 1.30521e11 | 0.0121276 | ||||||||
\(405\) | 8.43560e11i | 0.0774178i | ||||||||
\(406\) | − | 2.01335e11i | − | 0.0182511i | ||||||
\(407\) | 2.41458e13i | 2.16207i | ||||||||
\(408\) | 2.16773e13 | 1.91736 | ||||||||
\(409\) | 6.90427e12i | 0.603255i | 0.953426 | + | 0.301628i | \(0.0975299\pi\) | ||||
−0.953426 | + | 0.301628i | \(0.902470\pi\) | |||||||
\(410\) | −3.50710e11 | −0.0302711 | ||||||||
\(411\) | −8.22882e12 | −0.701663 | ||||||||
\(412\) | −1.49852e12 | −0.126234 | ||||||||
\(413\) | − | 1.61345e12i | − | 0.134278i | ||||||
\(414\) | 1.45202e12i | 0.119391i | ||||||||
\(415\) | − | 2.09177e11i | − | 0.0169931i | ||||||
\(416\) | − | 1.49953e12i | − | 0.120362i | ||||||
\(417\) | − | 1.83508e13i | − | 1.45538i | ||||||
\(418\) | 1.01648e13 | 0.796560 | ||||||||
\(419\) | 3.78990e12i | 0.293466i | 0.989176 | + | 0.146733i | \(0.0468758\pi\) | ||||
−0.989176 | + | 0.146733i | \(0.953124\pi\) | |||||||
\(420\) | − | 2.45124e10i | − | 0.00187560i | ||||||
\(421\) | 2.61396e12i | 0.197646i | 0.995105 | + | 0.0988229i | \(0.0315077\pi\) | ||||
−0.995105 | + | 0.0988229i | \(0.968492\pi\) | |||||||
\(422\) | −1.81686e13 | −1.35756 | ||||||||
\(423\) | −3.27667e12 | −0.241953 | ||||||||
\(424\) | − | 7.73505e12i | − | 0.564461i | ||||||
\(425\) | 2.24828e13 | 1.62146 | ||||||||
\(426\) | − | 4.51266e12i | − | 0.321651i | ||||||
\(427\) | 4.60636e12 | 0.324503 | ||||||||
\(428\) | −1.27313e12 | −0.0886448 | ||||||||
\(429\) | − | 9.18551e12i | − | 0.632145i | ||||||
\(430\) | 5.37465e11 | + | 7.16805e11i | 0.0365601 | + | 0.0487595i | ||||
\(431\) | 5.30690e12 | 0.356824 | 0.178412 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178412 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(432\) | − | 1.08278e13i | − | 0.719651i | ||||||
\(433\) | 9.50518e12i | 0.624484i | 0.950003 | + | 0.312242i | \(0.101080\pi\) | ||||
−0.950003 | + | 0.312242i | \(0.898920\pi\) | |||||||
\(434\) | −1.29564e12 | −0.0841465 | ||||||||
\(435\) | 1.06936e11i | 0.00686561i | ||||||||
\(436\) | −2.90382e12 | −0.184305 | ||||||||
\(437\) | − | 5.91119e12i | − | 0.370909i | ||||||
\(438\) | − | 1.80627e13i | − | 1.12050i | ||||||
\(439\) | 2.23920e13 | 1.37332 | 0.686658 | − | 0.726980i | \(-0.259077\pi\) | ||||
0.686658 | + | 0.726980i | \(0.259077\pi\) | |||||||
\(440\) | 1.31017e12 | 0.0794443 | ||||||||
\(441\) | −4.03152e12 | −0.241699 | ||||||||
\(442\) | − | 1.25231e13i | − | 0.742335i | ||||||
\(443\) | −1.73807e12 | −0.101870 | −0.0509352 | − | 0.998702i | \(-0.516220\pi\) | ||||
−0.0509352 | + | 0.998702i | \(0.516220\pi\) | |||||||
\(444\) | 4.47558e12 | 0.259379 | ||||||||
\(445\) | 1.41080e12 | 0.0808473 | ||||||||
\(446\) | 1.04031e13 | 0.589505 | ||||||||
\(447\) | −1.65195e13 | −0.925678 | ||||||||
\(448\) | 4.07824e12i | 0.225987i | ||||||||
\(449\) | − | 1.71473e13i | − | 0.939647i | −0.882760 | − | 0.469823i | \(-0.844318\pi\) | ||
0.882760 | − | 0.469823i | \(-0.155682\pi\) | |||||||
\(450\) | 4.34212e12i | 0.235309i | ||||||||
\(451\) | −1.07458e13 | −0.575913 | ||||||||
\(452\) | − | 6.48770e11i | − | 0.0343874i | ||||||
\(453\) | 1.15388e13 | 0.604881 | ||||||||
\(454\) | 8.76025e12 | 0.454190 | ||||||||
\(455\) | −1.28098e11 | −0.00656878 | ||||||||
\(456\) | − | 1.70434e13i | − | 0.864435i | ||||||
\(457\) | − | 2.13148e13i | − | 1.06930i | −0.845073 | − | 0.534651i | \(-0.820443\pi\) | ||
0.845073 | − | 0.534651i | \(-0.179557\pi\) | |||||||
\(458\) | − | 1.00241e13i | − | 0.497413i | ||||||
\(459\) | 2.77527e13i | 1.36220i | ||||||||
\(460\) | − | 8.42272e10i | − | 0.00408944i | ||||||
\(461\) | −2.53916e13 | −1.21951 | −0.609754 | − | 0.792590i | \(-0.708732\pi\) | ||||
−0.609754 | + | 0.792590i | \(0.708732\pi\) | |||||||
\(462\) | 5.29189e12i | 0.251421i | ||||||||
\(463\) | 1.86225e13i | 0.875254i | 0.899157 | + | 0.437627i | \(0.144181\pi\) | ||||
−0.899157 | + | 0.437627i | \(0.855819\pi\) | |||||||
\(464\) | − | 1.74285e12i | − | 0.0810346i | ||||||
\(465\) | 6.88163e11 | 0.0316539 | ||||||||
\(466\) | 2.86134e13 | 1.30209 | ||||||||
\(467\) | 2.68346e13i | 1.20812i | 0.796938 | + | 0.604062i | \(0.206452\pi\) | ||||
−0.796938 | + | 0.604062i | \(0.793548\pi\) | |||||||
\(468\) | −3.43264e11 | −0.0152897 | ||||||||
\(469\) | 3.13320e12i | 0.138078i | ||||||||
\(470\) | −1.33920e12 | −0.0583922 | ||||||||
\(471\) | −1.83435e13 | −0.791366 | ||||||||
\(472\) | − | 1.59847e13i | − | 0.682329i | ||||||
\(473\) | 1.64680e13 | + | 2.19631e13i | 0.695563 | + | 0.927657i | ||||
\(474\) | 9.39009e12 | 0.392444 | ||||||||
\(475\) | − | 1.76768e13i | − | 0.731029i | ||||||
\(476\) | − | 1.02397e12i | − | 0.0419035i | ||||||
\(477\) | −3.34558e12 | −0.135482 | ||||||||
\(478\) | − | 3.04401e13i | − | 1.21985i | ||||||
\(479\) | −7.59261e12 | −0.301102 | −0.150551 | − | 0.988602i | \(-0.548105\pi\) | ||||
−0.150551 | + | 0.988602i | \(0.548105\pi\) | |||||||
\(480\) | − | 4.58849e11i | − | 0.0180079i | ||||||
\(481\) | − | 2.33887e13i | − | 0.908406i | ||||||
\(482\) | 1.45980e13 | 0.561121 | ||||||||
\(483\) | 3.07741e12 | 0.117071 | ||||||||
\(484\) | 1.13674e12 | 0.0427991 | ||||||||
\(485\) | − | 1.83496e12i | − | 0.0683784i | ||||||
\(486\) | −1.25306e13 | −0.462156 | ||||||||
\(487\) | −2.06304e13 | −0.753116 | −0.376558 | − | 0.926393i | \(-0.622892\pi\) | ||||
−0.376558 | + | 0.926393i | \(0.622892\pi\) | |||||||
\(488\) | 4.56358e13 | 1.64895 | ||||||||
\(489\) | −1.27664e13 | −0.456588 | ||||||||
\(490\) | −1.64771e12 | −0.0583311 | ||||||||
\(491\) | 5.74792e10i | 0.00201420i | 0.999999 | + | 0.00100710i | \(0.000320570\pi\) | ||||
−0.999999 | + | 0.00100710i | \(0.999679\pi\) | |||||||
\(492\) | 1.99181e12i | 0.0690911i | ||||||||
\(493\) | 4.46709e12i | 0.153388i | ||||||||
\(494\) | −9.84607e12 | −0.334679 | ||||||||
\(495\) | − | 5.66676e11i | − | 0.0190682i | ||||||
\(496\) | −1.12157e13 | −0.373609 | ||||||||
\(497\) | −1.92825e12 | −0.0635889 | ||||||||
\(498\) | 8.37039e12 | 0.273274 | ||||||||
\(499\) | − | 3.88299e13i | − | 1.25506i | −0.778594 | − | 0.627528i | \(-0.784067\pi\) | ||
0.778594 | − | 0.627528i | \(-0.215933\pi\) | |||||||
\(500\) | − | 5.04818e11i | − | 0.0161542i | ||||||
\(501\) | 6.73734e12i | 0.213452i | ||||||||
\(502\) | 5.46472e13i | 1.71415i | ||||||||
\(503\) | 5.96465e13i | 1.85244i | 0.376978 | + | 0.926222i | \(0.376963\pi\) | ||||
−0.376978 | + | 0.926222i | \(0.623037\pi\) | |||||||
\(504\) | 1.78890e12 | 0.0550088 | ||||||||
\(505\) | − | 2.08714e11i | − | 0.00635469i | ||||||
\(506\) | 1.81835e13i | 0.548182i | ||||||||
\(507\) | − | 2.85940e13i | − | 0.853563i | ||||||
\(508\) | −5.97986e12 | −0.176755 | ||||||||
\(509\) | 9.68042e12 | 0.283338 | 0.141669 | − | 0.989914i | \(-0.454753\pi\) | ||||
0.141669 | + | 0.989914i | \(0.454753\pi\) | |||||||
\(510\) | − | 3.83199e12i | − | 0.111064i | ||||||
\(511\) | −7.71815e12 | −0.221518 | ||||||||
\(512\) | 3.93232e13i | 1.11763i | ||||||||
\(513\) | 2.18201e13 | 0.614145 | ||||||||
\(514\) | 8.51677e12 | 0.237388 | ||||||||
\(515\) | 2.39624e12i | 0.0661446i | ||||||||
\(516\) | 4.07100e12 | − | 3.05246e12i | 0.111289 | − | 0.0834451i | ||||
\(517\) | −4.10333e13 | −1.11092 | ||||||||
\(518\) | 1.34745e13i | 0.361297i | ||||||||
\(519\) | 4.65845e13i | 1.23710i | ||||||||
\(520\) | −1.26908e12 | −0.0333790 | ||||||||
\(521\) | − | 2.61386e13i | − | 0.680916i | −0.940260 | − | 0.340458i | \(-0.889418\pi\) | ||
0.940260 | − | 0.340458i | \(-0.110582\pi\) | |||||||
\(522\) | −8.62731e11 | −0.0222599 | ||||||||
\(523\) | 4.15936e12i | 0.106296i | 0.998587 | + | 0.0531482i | \(0.0169256\pi\) | ||||
−0.998587 | + | 0.0531482i | \(0.983074\pi\) | |||||||
\(524\) | − | 5.47104e12i | − | 0.138489i | ||||||
\(525\) | 9.20267e12 | 0.230737 | ||||||||
\(526\) | 1.13644e13 | 0.282239 | ||||||||
\(527\) | 2.87469e13 | 0.707193 | ||||||||
\(528\) | 4.58091e13i | 1.11630i | ||||||||
\(529\) | −3.08522e13 | −0.744745 | ||||||||
\(530\) | −1.36736e12 | −0.0326967 | ||||||||
\(531\) | −6.91373e12 | −0.163772 | ||||||||
\(532\) | −8.05077e11 | −0.0188921 | ||||||||
\(533\) | 1.04089e13 | 0.241973 | ||||||||
\(534\) | 5.64544e13i | 1.30014i | ||||||||
\(535\) | 2.03583e12i | 0.0464486i | ||||||||
\(536\) | 3.10410e13i | 0.701635i | ||||||||
\(537\) | −7.64906e13 | −1.71292 | ||||||||
\(538\) | − | 1.21203e13i | − | 0.268906i | ||||||
\(539\) | −5.04861e13 | −1.10976 | ||||||||
\(540\) | 3.10910e11 | 0.00677121 | ||||||||
\(541\) | 2.48861e13 | 0.536995 | 0.268497 | − | 0.963280i | \(-0.413473\pi\) | ||||
0.268497 | + | 0.963280i | \(0.413473\pi\) | |||||||
\(542\) | − | 7.10110e13i | − | 1.51820i | ||||||
\(543\) | − | 2.50706e13i | − | 0.531086i | ||||||
\(544\) | − | 1.91677e13i | − | 0.402323i | ||||||
\(545\) | 4.64343e12i | 0.0965731i | ||||||||
\(546\) | − | 5.12595e12i | − | 0.105636i | ||||||
\(547\) | −8.18220e13 | −1.67083 | −0.835417 | − | 0.549616i | \(-0.814774\pi\) | ||||
−0.835417 | + | 0.549616i | \(0.814774\pi\) | |||||||
\(548\) | 3.85094e12i | 0.0779227i | ||||||||
\(549\) | − | 1.97385e13i | − | 0.395779i | ||||||
\(550\) | 5.43757e13i | 1.08042i | ||||||||
\(551\) | 3.51218e12 | 0.0691542 | ||||||||
\(552\) | 3.04883e13 | 0.594892 | ||||||||
\(553\) | − | 4.01236e12i | − | 0.0775844i | ||||||
\(554\) | −6.73762e13 | −1.29109 | ||||||||
\(555\) | − | 7.15680e12i | − | 0.135911i | ||||||
\(556\) | −8.58786e12 | −0.161626 | ||||||||
\(557\) | 4.67918e13 | 0.872758 | 0.436379 | − | 0.899763i | \(-0.356261\pi\) | ||||
0.436379 | + | 0.899763i | \(0.356261\pi\) | |||||||
\(558\) | 5.55190e12i | 0.102629i | ||||||||
\(559\) | −1.59516e13 | − | 2.12744e13i | −0.292244 | − | 0.389760i | ||||
\(560\) | 6.38837e11 | 0.0115998 | ||||||||
\(561\) | − | 1.17413e14i | − | 2.11301i | ||||||
\(562\) | 2.15202e13i | 0.383853i | ||||||||
\(563\) | −5.92155e13 | −1.04687 | −0.523436 | − | 0.852065i | \(-0.675350\pi\) | ||||
−0.523436 | + | 0.852065i | \(0.675350\pi\) | |||||||
\(564\) | 7.60578e12i | 0.133275i | ||||||||
\(565\) | −1.03743e12 | −0.0180185 | ||||||||
\(566\) | − | 6.36560e13i | − | 1.09587i | ||||||
\(567\) | 1.44237e13i | 0.246129i | ||||||||
\(568\) | −1.91034e13 | −0.323124 | ||||||||
\(569\) | 1.03745e14 | 1.73943 | 0.869714 | − | 0.493556i | \(-0.164303\pi\) | ||||
0.869714 | + | 0.493556i | \(0.164303\pi\) | |||||||
\(570\) | −3.01284e12 | −0.0500729 | ||||||||
\(571\) | − | 5.54780e12i | − | 0.0913988i | −0.998955 | − | 0.0456994i | \(-0.985448\pi\) | ||
0.998955 | − | 0.0456994i | \(-0.0145516\pi\) | |||||||
\(572\) | −4.29865e12 | −0.0702025 | ||||||||
\(573\) | 3.85765e13 | 0.624525 | ||||||||
\(574\) | −5.99668e12 | −0.0962390 | ||||||||
\(575\) | 3.16213e13 | 0.503085 | ||||||||
\(576\) | 1.74755e13 | 0.275624 | ||||||||
\(577\) | 1.06287e14i | 1.66189i | 0.556355 | + | 0.830945i | \(0.312200\pi\) | ||||
−0.556355 | + | 0.830945i | \(0.687800\pi\) | |||||||
\(578\) | − | 9.97055e13i | − | 1.54554i | ||||||
\(579\) | 9.50388e13i | 1.46052i | ||||||||
\(580\) | 5.00443e10 | 0.000762456 | ||||||||
\(581\) | − | 3.57665e12i | − | 0.0540251i | ||||||
\(582\) | 7.34276e13 | 1.09963 | ||||||||
\(583\) | −4.18963e13 | −0.622061 | ||||||||
\(584\) | −7.64647e13 | −1.12563 | ||||||||
\(585\) | 5.48906e11i | 0.00801159i | ||||||||
\(586\) | − | 1.19137e14i | − | 1.72408i | ||||||
\(587\) | − | 5.54347e13i | − | 0.795411i | −0.917513 | − | 0.397705i | \(-0.869807\pi\) | ||
0.917513 | − | 0.397705i | \(-0.130193\pi\) | |||||||
\(588\) | 9.35793e12i | 0.133135i | ||||||||
\(589\) | − | 2.26018e13i | − | 0.318835i | ||||||
\(590\) | −2.82569e12 | −0.0395243 | ||||||||
\(591\) | − | 2.10992e13i | − | 0.292637i | ||||||
\(592\) | 1.16642e14i | 1.60415i | ||||||||
\(593\) | 1.23403e14i | 1.68288i | 0.540349 | + | 0.841441i | \(0.318292\pi\) | ||||
−0.540349 | + | 0.841441i | \(0.681708\pi\) | |||||||
\(594\) | −6.71212e13 | −0.907669 | ||||||||
\(595\) | −1.63740e12 | −0.0219569 | ||||||||
\(596\) | 7.73084e12i | 0.102801i | ||||||||
\(597\) | 1.36634e14 | 1.80172 | ||||||||
\(598\) | − | 1.76133e13i | − | 0.230321i | ||||||
\(599\) | 5.75412e13 | 0.746182 | 0.373091 | − | 0.927795i | \(-0.378298\pi\) | ||||
0.373091 | + | 0.927795i | \(0.378298\pi\) | |||||||
\(600\) | 9.11721e13 | 1.17248 | ||||||||
\(601\) | − | 1.12470e14i | − | 1.43437i | −0.696881 | − | 0.717187i | \(-0.745429\pi\) | ||
0.696881 | − | 0.717187i | \(-0.254571\pi\) | |||||||
\(602\) | 9.18994e12 | + | 1.22564e13i | 0.116233 | + | 0.155018i | ||||
\(603\) | 1.34259e13 | 0.168406 | ||||||||
\(604\) | − | 5.39996e12i | − | 0.0671747i | ||||||
\(605\) | − | 1.81773e12i | − | 0.0224261i | ||||||
\(606\) | 8.35187e12 | 0.102193 | ||||||||
\(607\) | 1.14155e13i | 0.138532i | 0.997598 | + | 0.0692659i | \(0.0220657\pi\) | ||||
−0.997598 | + | 0.0692659i | \(0.977934\pi\) | |||||||
\(608\) | −1.50703e13 | −0.181386 | ||||||||
\(609\) | 1.82847e12i | 0.0218274i | ||||||||
\(610\) | − | 8.06726e12i | − | 0.0955161i | ||||||
\(611\) | 3.97465e13 | 0.466760 | ||||||||
\(612\) | −4.38775e12 | −0.0511075 | ||||||||
\(613\) | 1.42106e14 | 1.64177 | 0.820883 | − | 0.571096i | \(-0.193482\pi\) | ||||
0.820883 | + | 0.571096i | \(0.193482\pi\) | |||||||
\(614\) | − | 8.02892e12i | − | 0.0920058i | ||||||
\(615\) | 3.18506e12 | 0.0362027 | ||||||||
\(616\) | 2.24021e13 | 0.252572 | ||||||||
\(617\) | 6.74557e13 | 0.754384 | 0.377192 | − | 0.926135i | \(-0.376890\pi\) | ||||
0.377192 | + | 0.926135i | \(0.376890\pi\) | |||||||
\(618\) | −9.58877e13 | −1.06370 | ||||||||
\(619\) | 2.48391e13 | 0.273327 | 0.136664 | − | 0.990618i | \(-0.456362\pi\) | ||||
0.136664 | + | 0.990618i | \(0.456362\pi\) | |||||||
\(620\) | − | 3.22048e11i | − | 0.00351530i | ||||||
\(621\) | 3.90333e13i | 0.422646i | ||||||||
\(622\) | 4.69069e13i | 0.503831i | ||||||||
\(623\) | 2.41228e13 | 0.257032 | ||||||||
\(624\) | − | 4.43726e13i | − | 0.469021i | ||||||
\(625\) | 9.41557e13 | 0.987294 | ||||||||
\(626\) | −6.48800e12 | −0.0674900 | ||||||||
\(627\) | −9.23142e13 | −0.952644 | ||||||||
\(628\) | 8.58442e12i | 0.0878846i | ||||||||
\(629\) | − | 2.98964e14i | − | 3.03644i | ||||||
\(630\) | − | 3.16232e11i | − | 0.00318642i | ||||||
\(631\) | 6.71070e13i | 0.670843i | 0.942068 | + | 0.335422i | \(0.108879\pi\) | ||||
−0.942068 | + | 0.335422i | \(0.891121\pi\) | |||||||
\(632\) | − | 3.97510e13i | − | 0.394242i | ||||||
\(633\) | 1.65003e14 | 1.62357 | ||||||||
\(634\) | 1.47548e13i | 0.144042i | ||||||||
\(635\) | 9.56225e12i | 0.0926172i | ||||||||
\(636\) | 7.76575e12i | 0.0746273i | ||||||||
\(637\) | 4.89030e13 | 0.466271 | ||||||||
\(638\) | −1.08039e13 | −0.102206 | ||||||||
\(639\) | 8.26265e12i | 0.0775560i | ||||||||
\(640\) | 5.41465e12 | 0.0504278 | ||||||||
\(641\) | 1.30587e14i | 1.20673i | 0.797465 | + | 0.603365i | \(0.206174\pi\) | ||||
−0.797465 | + | 0.603365i | \(0.793826\pi\) | |||||||
\(642\) | −8.14655e13 | −0.746962 | ||||||||
\(643\) | −8.09113e13 | −0.736130 | −0.368065 | − | 0.929800i | \(-0.619980\pi\) | ||||
−0.368065 | + | 0.929800i | \(0.619980\pi\) | |||||||
\(644\) | − | 1.44017e12i | − | 0.0130013i | ||||||
\(645\) | −4.88111e12 | − | 6.50984e12i | −0.0437240 | − | 0.0583138i | ||||
\(646\) | −1.25857e14 | −1.11870 | ||||||||
\(647\) | − | 8.55615e13i | − | 0.754669i | −0.926077 | − | 0.377335i | \(-0.876841\pi\) | ||
0.926077 | − | 0.377335i | \(-0.123159\pi\) | |||||||
\(648\) | 1.42898e14i | 1.25069i | ||||||||
\(649\) | −8.65797e13 | −0.751956 | ||||||||
\(650\) | − | 5.26706e13i | − | 0.453943i | ||||||
\(651\) | 1.17667e13 | 0.100635 | ||||||||
\(652\) | 5.97445e12i | 0.0507061i | ||||||||
\(653\) | − | 1.61973e14i | − | 1.36420i | −0.731259 | − | 0.682100i | \(-0.761067\pi\) | ||
0.731259 | − | 0.682100i | \(-0.238933\pi\) | |||||||
\(654\) | −1.85811e14 | −1.55304 | ||||||||
\(655\) | −8.74862e12 | −0.0725660 | ||||||||
\(656\) | −5.19101e13 | −0.427300 | ||||||||
\(657\) | 3.30727e13i | 0.270173i | ||||||||
\(658\) | −2.28985e13 | −0.185642 | ||||||||
\(659\) | −8.60337e13 | −0.692216 | −0.346108 | − | 0.938195i | \(-0.612497\pi\) | ||||
−0.346108 | + | 0.938195i | \(0.612497\pi\) | |||||||
\(660\) | −1.31536e12 | −0.0105033 | ||||||||
\(661\) | −1.67477e14 | −1.32723 | −0.663617 | − | 0.748073i | \(-0.730979\pi\) | ||||
−0.663617 | + | 0.748073i | \(0.730979\pi\) | |||||||
\(662\) | 2.97174e13 | 0.233734 | ||||||||
\(663\) | 1.13731e14i | 0.887794i | ||||||||
\(664\) | − | 3.54343e13i | − | 0.274526i | ||||||
\(665\) | 1.28738e12i | 0.00989917i | ||||||||
\(666\) | 5.77390e13 | 0.440654 | ||||||||
\(667\) | 6.28281e12i | 0.0475910i | ||||||||
\(668\) | 3.15295e12 | 0.0237047 | ||||||||
\(669\) | −9.44780e13 | −0.705018 | ||||||||
\(670\) | 5.48726e12 | 0.0406426 | ||||||||
\(671\) | − | 2.47182e14i | − | 1.81721i | ||||||
\(672\) | − | 7.84571e12i | − | 0.0572514i | ||||||
\(673\) | − | 2.30784e14i | − | 1.67159i | −0.549039 | − | 0.835797i | \(-0.685006\pi\) | ||
0.549039 | − | 0.835797i | \(-0.314994\pi\) | |||||||
\(674\) | 1.65635e14i | 1.19084i | ||||||||
\(675\) | 1.16725e14i | 0.832998i | ||||||||
\(676\) | −1.33815e13 | −0.0947919 | ||||||||
\(677\) | 8.43691e13i | 0.593253i | 0.954994 | + | 0.296627i | \(0.0958617\pi\) | ||||
−0.954994 | + | 0.296627i | \(0.904138\pi\) | |||||||
\(678\) | − | 4.15138e13i | − | 0.289764i | ||||||
\(679\) | − | 3.13754e13i | − | 0.217391i | ||||||
\(680\) | −1.62219e13 | −0.111573 | ||||||||
\(681\) | −7.95583e13 | −0.543188 | ||||||||
\(682\) | 6.95256e13i | 0.471219i | ||||||||
\(683\) | 1.33475e14 | 0.898038 | 0.449019 | − | 0.893522i | \(-0.351773\pi\) | ||||
0.449019 | + | 0.893522i | \(0.351773\pi\) | |||||||
\(684\) | 3.44980e12i | 0.0230416i | ||||||||
\(685\) | 6.15795e12 | 0.0408304 | ||||||||
\(686\) | −5.76091e13 | −0.379202 | ||||||||
\(687\) | 9.10360e13i | 0.594880i | ||||||||
\(688\) | 7.95525e13 | + | 1.06097e14i | 0.516073 | + | 0.688276i | ||||
\(689\) | 4.05825e13 | 0.261362 | ||||||||
\(690\) | − | 5.38957e12i | − | 0.0344595i | ||||||
\(691\) | 2.31962e14i | 1.47240i | 0.676764 | + | 0.736200i | \(0.263382\pi\) | ||||
−0.676764 | + | 0.736200i | \(0.736618\pi\) | |||||||
\(692\) | 2.18007e13 | 0.137385 | ||||||||
\(693\) | − | 9.68941e12i | − | 0.0606221i | ||||||
\(694\) | −4.06685e13 | −0.252616 | ||||||||
\(695\) | 1.37327e13i | 0.0846897i | ||||||||
\(696\) | 1.81149e13i | 0.110915i | ||||||||
\(697\) | 1.33050e14 | 0.808821 | ||||||||
\(698\) | −1.57879e14 | −0.952900 | ||||||||
\(699\) | −2.59859e14 | −1.55723 | ||||||||
\(700\) | − | 4.30668e12i | − | 0.0256243i | ||||||
\(701\) | 5.99175e13 | 0.353968 | 0.176984 | − | 0.984214i | \(-0.443366\pi\) | ||||
0.176984 | + | 0.984214i | \(0.443366\pi\) | |||||||
\(702\) | 6.50164e13 | 0.381362 | ||||||||
\(703\) | −2.35055e14 | −1.36897 | ||||||||
\(704\) | 2.18843e14 | 1.26552 | ||||||||
\(705\) | 1.21622e13 | 0.0698341 | ||||||||
\(706\) | 2.21932e14i | 1.26531i | ||||||||
\(707\) | − | 3.56873e12i | − | 0.0202030i | ||||||
\(708\) | 1.60481e13i | 0.0902106i | ||||||||
\(709\) | 2.44977e14 | 1.36740 | 0.683698 | − | 0.729765i | \(-0.260370\pi\) | ||||
0.683698 | + | 0.729765i | \(0.260370\pi\) | |||||||
\(710\) | 3.37700e12i | 0.0187171i | ||||||||
\(711\) | −1.71932e13 | −0.0946256 | ||||||||
\(712\) | 2.38988e14 | 1.30610 | ||||||||
\(713\) | 4.04315e13 | 0.219418 | ||||||||
\(714\) | − | 6.55220e13i | − | 0.353099i | ||||||
\(715\) | 6.87388e12i | 0.0367851i | ||||||||
\(716\) | 3.57962e13i | 0.190227i | ||||||||
\(717\) | 2.76449e14i | 1.45888i | ||||||||
\(718\) | 1.79850e14i | 0.942515i | ||||||||
\(719\) | 1.12367e14 | 0.584785 | 0.292392 | − | 0.956298i | \(-0.405549\pi\) | ||||
0.292392 | + | 0.956298i | \(0.405549\pi\) | |||||||
\(720\) | − | 2.73745e12i | − | 0.0141476i | ||||||
\(721\) | 4.09726e13i | 0.210289i | ||||||||
\(722\) | − | 8.46447e13i | − | 0.431433i | ||||||
\(723\) | −1.32575e14 | −0.671072 | ||||||||
\(724\) | −1.17326e13 | −0.0589794 | ||||||||
\(725\) | 1.87881e13i | 0.0937977i | ||||||||
\(726\) | 7.27382e13 | 0.360645 | ||||||||
\(727\) | 2.03887e14i | 1.00396i | 0.864878 | + | 0.501982i | \(0.167396\pi\) | ||||
−0.864878 | + | 0.501982i | \(0.832604\pi\) | |||||||
\(728\) | −2.16996e13 | −0.106119 | ||||||||
\(729\) | −1.30955e14 | −0.636041 | ||||||||
\(730\) | 1.35170e13i | 0.0652029i | ||||||||
\(731\) | −2.03901e14 | − | 2.71938e14i | −0.976858 | − | 1.30281i | ||||
\(732\) | −4.58169e13 | −0.218007 | ||||||||
\(733\) | − | 1.40792e14i | − | 0.665362i | −0.943039 | − | 0.332681i | \(-0.892047\pi\) | ||
0.943039 | − | 0.332681i | \(-0.107953\pi\) | |||||||
\(734\) | − | 2.72764e13i | − | 0.128028i | ||||||
\(735\) | 1.49641e13 | 0.0697610 | ||||||||
\(736\) | − | 2.69587e13i | − | 0.124827i | ||||||
\(737\) | 1.68131e14 | 0.773233 | ||||||||
\(738\) | 2.56961e13i | 0.117378i | ||||||||
\(739\) | − | 5.06958e13i | − | 0.230012i | −0.993365 | − | 0.115006i | \(-0.963311\pi\) | ||
0.993365 | − | 0.115006i | \(-0.0366887\pi\) | |||||||
\(740\) | −3.34925e12 | −0.0150935 | ||||||||
\(741\) | 8.94194e13 | 0.400259 | ||||||||
\(742\) | −2.33801e13 | −0.103951 | ||||||||
\(743\) | 3.77080e14i | 1.66529i | 0.553810 | + | 0.832643i | \(0.313173\pi\) | ||||
−0.553810 | + | 0.832643i | \(0.686827\pi\) | |||||||
\(744\) | 1.16574e14 | 0.511372 | ||||||||
\(745\) | 1.23622e13 | 0.0538660 | ||||||||
\(746\) | 3.55462e14 | 1.53850 | ||||||||
\(747\) | −1.53261e13 | −0.0658915 | ||||||||
\(748\) | −5.49472e13 | −0.234659 | ||||||||
\(749\) | 3.48100e13i | 0.147671i | ||||||||
\(750\) | − | 3.23025e13i | − | 0.136122i | ||||||
\(751\) | 3.16255e14i | 1.32385i | 0.749571 | + | 0.661923i | \(0.230260\pi\) | ||||
−0.749571 | + | 0.661923i | \(0.769740\pi\) | |||||||
\(752\) | −1.98220e14 | −0.824249 | ||||||||
\(753\) | − | 4.96291e14i | − | 2.05004i | ||||||
\(754\) | 1.04651e13 | 0.0429423 | ||||||||
\(755\) | −8.63494e12 | −0.0351985 | ||||||||
\(756\) | 5.31615e12 | 0.0215273 | ||||||||
\(757\) | − | 1.69500e14i | − | 0.681853i | −0.940090 | − | 0.340927i | \(-0.889259\pi\) | ||
0.940090 | − | 0.340927i | \(-0.110741\pi\) | |||||||
\(758\) | − | 1.83601e14i | − | 0.733716i | ||||||
\(759\) | − | 1.65138e14i | − | 0.655597i | ||||||
\(760\) | 1.27542e13i | 0.0503022i | ||||||||
\(761\) | − | 4.88591e14i | − | 1.91435i | −0.289507 | − | 0.957176i | \(-0.593491\pi\) | ||
0.289507 | − | 0.957176i | \(-0.406509\pi\) | |||||||
\(762\) | −3.82642e14 | −1.48942 | ||||||||
\(763\) | 7.93964e13i | 0.307028i | ||||||||
\(764\) | − | 1.80531e13i | − | 0.0693562i | ||||||
\(765\) | 7.01635e12i | 0.0267796i | ||||||||
\(766\) | 4.90057e14 | 1.85824 | ||||||||
\(767\) | 8.38647e13 | 0.315938 | ||||||||
\(768\) | − | 1.09700e14i | − | 0.410582i | ||||||
\(769\) | −5.11989e14 | −1.90383 | −0.951917 | − | 0.306356i | \(-0.900890\pi\) | ||||
−0.951917 | + | 0.306356i | \(0.900890\pi\) | |||||||
\(770\) | − | 3.96013e12i | − | 0.0146304i | ||||||
\(771\) | −7.73470e13 | −0.283904 | ||||||||
\(772\) | 4.44764e13 | 0.162197 | ||||||||
\(773\) | − | 1.45115e14i | − | 0.525792i | −0.964824 | − | 0.262896i | \(-0.915322\pi\) | ||
0.964824 | − | 0.262896i | \(-0.0846777\pi\) | |||||||
\(774\) | 5.25194e13 | − | 3.93794e13i | 0.189067 | − | 0.141763i | ||||
\(775\) | 1.20906e14 | 0.432454 | ||||||||
\(776\) | − | 3.10840e14i | − | 1.10466i | ||||||
\(777\) | − | 1.22372e14i | − | 0.432092i | ||||||
\(778\) | 2.24504e14 | 0.787637 | ||||||||
\(779\) | − | 1.04609e14i | − | 0.364654i | ||||||
\(780\) | 1.27412e12 | 0.00441303 | ||||||||
\(781\) | 1.03472e14i | 0.356097i | ||||||||
\(782\) | − | 2.25140e14i | − | 0.769874i | ||||||
\(783\) | −2.31919e13 | −0.0788003 | ||||||||
\(784\) | −2.43884e14 | −0.823386 | ||||||||
\(785\) | 1.37271e13 | 0.0460503 | ||||||||
\(786\) | − | 3.50084e14i | − | 1.16697i | ||||||
\(787\) | −1.46059e14 | −0.483789 | −0.241894 | − | 0.970303i | \(-0.577769\pi\) | ||||
−0.241894 | + | 0.970303i | \(0.577769\pi\) | |||||||
\(788\) | −9.87404e12 | −0.0324985 | ||||||||
\(789\) | −1.03208e14 | −0.337544 | ||||||||
\(790\) | −7.02697e12 | −0.0228367 | ||||||||
\(791\) | −1.77387e13 | −0.0572849 | ||||||||
\(792\) | − | 9.59942e13i | − | 0.308049i | ||||||
\(793\) | 2.39431e14i | 0.763510i | ||||||||
\(794\) | 3.21435e14i | 1.01857i | ||||||||
\(795\) | 1.24180e13 | 0.0391036 | ||||||||
\(796\) | − | 6.39422e13i | − | 0.200088i | ||||||
\(797\) | −5.63988e14 | −1.75379 | −0.876896 | − | 0.480680i | \(-0.840390\pi\) | ||||
−0.876896 | + | 0.480680i | \(0.840390\pi\) | |||||||
\(798\) | −5.15156e13 | −0.159193 | ||||||||
\(799\) | 5.08057e14 | 1.56019 | ||||||||
\(800\) | − | 8.06170e13i | − | 0.246024i | ||||||
\(801\) | − | 1.03368e14i | − | 0.313489i | ||||||
\(802\) | 2.53469e14i | 0.763928i | ||||||||
\(803\) | 4.14165e14i | 1.24050i | ||||||||
\(804\) | − | 3.11641e13i | − | 0.0927630i | ||||||
\(805\) | −2.30295e12 | −0.00681247 | ||||||||
\(806\) | − | 6.73455e13i | − | 0.197985i | ||||||
\(807\) | 1.10073e14i | 0.321598i | ||||||||
\(808\) | − | 3.53559e13i | − | 0.102661i | ||||||
\(809\) | 3.18933e14 | 0.920359 | 0.460180 | − | 0.887826i | \(-0.347785\pi\) | ||||
0.460180 | + | 0.887826i | \(0.347785\pi\) | |||||||
\(810\) | 2.52608e13 | 0.0724471 | ||||||||
\(811\) | − | 4.60416e14i | − | 1.31234i | −0.754614 | − | 0.656169i | \(-0.772176\pi\) | ||
0.754614 | − | 0.656169i | \(-0.227824\pi\) | |||||||
\(812\) | 8.55691e11 | 0.00242402 | ||||||||
\(813\) | 6.44903e14i | 1.81569i | ||||||||
\(814\) | 7.23057e14 | 2.02325 | ||||||||
\(815\) | 9.55361e12 | 0.0265693 | ||||||||
\(816\) | − | 5.67190e14i | − | 1.56775i | ||||||
\(817\) | −2.13807e14 | + | 1.60314e14i | −0.587369 | + | 0.440413i | ||||
\(818\) | 2.06751e14 | 0.564523 | ||||||||
\(819\) | 9.38557e12i | 0.0254707i | ||||||||
\(820\) | − | 1.49055e12i | − | 0.00402047i | ||||||
\(821\) | 2.17005e14 | 0.581772 | 0.290886 | − | 0.956758i | \(-0.406050\pi\) | ||||
0.290886 | + | 0.956758i | \(0.406050\pi\) | |||||||
\(822\) | 2.46416e14i | 0.656613i | ||||||||
\(823\) | −1.74147e14 | −0.461230 | −0.230615 | − | 0.973045i | \(-0.574074\pi\) | ||||
−0.230615 | + | 0.973045i | \(0.574074\pi\) | |||||||
\(824\) | 4.05921e14i | 1.06858i | ||||||||
\(825\) | − | 4.93826e14i | − | 1.29212i | ||||||
\(826\) | −4.83155e13 | −0.125657 | ||||||||
\(827\) | −8.11856e13 | −0.209870 | −0.104935 | − | 0.994479i | \(-0.533464\pi\) | ||||
−0.104935 | + | 0.994479i | \(0.533464\pi\) | |||||||
\(828\) | −6.17122e12 | −0.0158569 | ||||||||
\(829\) | − | 1.27790e14i | − | 0.326381i | −0.986595 | − | 0.163190i | \(-0.947822\pi\) | ||
0.986595 | − | 0.163190i | \(-0.0521785\pi\) | |||||||
\(830\) | −6.26389e12 | −0.0159021 | ||||||||
\(831\) | 6.11893e14 | 1.54408 | ||||||||
\(832\) | −2.11981e14 | −0.531716 | ||||||||
\(833\) | 6.25099e14 | 1.55856 | ||||||||
\(834\) | −5.49524e14 | −1.36194 | ||||||||
\(835\) | − | 5.04182e12i | − | 0.0124209i | ||||||
\(836\) | 4.32014e13i | 0.105795i | ||||||||
\(837\) | 1.49246e14i | 0.363308i | ||||||||
\(838\) | 1.13490e14 | 0.274624 | ||||||||
\(839\) | 5.42822e14i | 1.30571i | 0.757481 | + | 0.652857i | \(0.226430\pi\) | ||||
−0.757481 | + | 0.652857i | \(0.773570\pi\) | |||||||
\(840\) | −6.63996e12 | −0.0158770 | ||||||||
\(841\) | 4.16974e14 | 0.991127 | ||||||||
\(842\) | 7.82760e13 | 0.184956 | ||||||||
\(843\) | − | 1.95441e14i | − | 0.459068i | ||||||
\(844\) | − | 7.72182e13i | − | 0.180305i | ||||||
\(845\) | 2.13980e13i | 0.0496696i | ||||||||
\(846\) | 9.81212e13i | 0.226418i | ||||||||
\(847\) | − | 3.10808e13i | − | 0.0712977i | ||||||
\(848\) | −2.02389e14 | −0.461539 | ||||||||
\(849\) | 5.78107e14i | 1.31060i | ||||||||
\(850\) | − | 6.73258e14i | − | 1.51735i | ||||||
\(851\) | − | 4.20482e14i | − | 0.942106i | ||||||
\(852\) | 1.91792e13 | 0.0427202 | ||||||||
\(853\) | −5.87310e14 | −1.30053 | −0.650267 | − | 0.759706i | \(-0.725343\pi\) | ||||
−0.650267 | + | 0.759706i | \(0.725343\pi\) | |||||||
\(854\) | − | 1.37939e14i | − | 0.303668i | ||||||
\(855\) | 5.51650e12 | 0.0120735 | ||||||||
\(856\) | 3.44867e14i | 0.750383i | ||||||||
\(857\) | −5.55311e14 | −1.20125 | −0.600623 | − | 0.799532i | \(-0.705081\pi\) | ||||
−0.600623 | + | 0.799532i | \(0.705081\pi\) | |||||||
\(858\) | −2.75064e14 | −0.591558 | ||||||||
\(859\) | 2.54422e14i | 0.543988i | 0.962299 | + | 0.271994i | \(0.0876831\pi\) | ||||
−0.962299 | + | 0.271994i | \(0.912317\pi\) | |||||||
\(860\) | −3.04649e12 | + | 2.28427e12i | −0.00647600 | + | 0.00485574i | ||||
\(861\) | 5.44602e13 | 0.115097 | ||||||||
\(862\) | − | 1.58917e14i | − | 0.333914i | ||||||
\(863\) | 5.36575e14i | 1.12093i | 0.828180 | + | 0.560463i | \(0.189377\pi\) | ||||
−0.828180 | + | 0.560463i | \(0.810623\pi\) | |||||||
\(864\) | 9.95133e13 | 0.206687 | ||||||||
\(865\) | − | 3.48610e13i | − | 0.0719879i | ||||||
\(866\) | 2.84637e14 | 0.584389 | ||||||||
\(867\) | 9.05498e14i | 1.84838i | ||||||||
\(868\) | − | 5.50659e12i | − | 0.0111759i | ||||||
\(869\) | −2.15308e14 | −0.434471 | ||||||||
\(870\) | 3.20226e12 | 0.00642480 | ||||||||
\(871\) | −1.62859e14 | −0.324878 | ||||||||
\(872\) | 7.86591e14i | 1.56015i | ||||||||
\(873\) | −1.34445e14 | −0.265140 | ||||||||
\(874\) | −1.77013e14 | −0.347095 | ||||||||
\(875\) | −1.38028e13 | −0.0269108 | ||||||||
\(876\) | 7.67681e13 | 0.148820 | ||||||||
\(877\) | −4.93296e14 | −0.950844 | −0.475422 | − | 0.879758i | \(-0.657705\pi\) | ||||
−0.475422 | + | 0.879758i | \(0.657705\pi\) | |||||||
\(878\) | − | 6.70539e14i | − | 1.28514i | ||||||
\(879\) | 1.08197e15i | 2.06192i | ||||||||
\(880\) | − | 3.42807e13i | − | 0.0649586i | ||||||
\(881\) | 9.18966e13 | 0.173149 | 0.0865744 | − | 0.996245i | \(-0.472408\pi\) | ||||
0.0865744 | + | 0.996245i | \(0.472408\pi\) | |||||||
\(882\) | 1.20726e14i | 0.226181i | ||||||||
\(883\) | −9.39719e14 | −1.75063 | −0.875315 | − | 0.483553i | \(-0.839346\pi\) | ||||
−0.875315 | + | 0.483553i | \(0.839346\pi\) | |||||||
\(884\) | 5.32242e13 | 0.0985933 | ||||||||
\(885\) | 2.56621e13 | 0.0472690 | ||||||||
\(886\) | 5.20472e13i | 0.0953298i | ||||||||
\(887\) | − | 5.78866e14i | − | 1.05429i | −0.849776 | − | 0.527145i | \(-0.823263\pi\) | ||
0.849776 | − | 0.527145i | \(-0.176737\pi\) | |||||||
\(888\) | − | 1.21235e15i | − | 2.19566i | ||||||
\(889\) | 1.63502e14i | 0.294452i | ||||||||
\(890\) | − | 4.22470e13i | − | 0.0756565i | ||||||
\(891\) | 7.73995e14 | 1.37832 | ||||||||
\(892\) | 4.42140e13i | 0.0782953i | ||||||||
\(893\) | − | 3.99452e14i | − | 0.703408i | ||||||
\(894\) | 4.94684e14i | 0.866245i | ||||||||
\(895\) | 5.72409e13 | 0.0996762 | ||||||||
\(896\) | 9.25833e13 | 0.160322 | ||||||||
\(897\) | 1.59959e14i | 0.275453i | ||||||||
\(898\) | −5.13484e14 | −0.879317 | ||||||||
\(899\) | 2.40227e13i | 0.0409095i | ||||||||
\(900\) | −1.84544e13 | −0.0312526 | ||||||||
\(901\) | 5.18743e14 | 0.873631 | ||||||||
\(902\) | 3.21789e14i | 0.538937i | ||||||||
\(903\) | −8.34606e13 | − | 1.11310e14i | −0.139009 | − | 0.185393i | ||||
\(904\) | −1.75740e14 | −0.291091 | ||||||||
\(905\) | 1.87613e13i | 0.0309044i | ||||||||
\(906\) | − | 3.45535e14i | − | 0.566045i | ||||||
\(907\) | −5.34411e14 | −0.870641 | −0.435321 | − | 0.900275i | \(-0.643365\pi\) | ||||
−0.435321 | + | 0.900275i | \(0.643365\pi\) | |||||||
\(908\) | 3.72318e13i | 0.0603233i | ||||||||
\(909\) | −1.52922e13 | −0.0246406 | ||||||||
\(910\) | 3.83595e12i | 0.00614703i | ||||||||
\(911\) | 8.04949e14i | 1.28285i | 0.767185 | + | 0.641426i | \(0.221657\pi\) | ||||
−0.767185 | + | 0.641426i | \(0.778343\pi\) | |||||||
\(912\) | −4.45944e14 | −0.706815 | ||||||||
\(913\) | −1.91927e14 | −0.302539 | ||||||||
\(914\) | −6.38282e14 | −1.00065 | ||||||||
\(915\) | 7.32647e13i | 0.114232i | ||||||||
\(916\) | 4.26032e13 | 0.0660640 | ||||||||
\(917\) | −1.49590e14 | −0.230704 | ||||||||
\(918\) | 8.31067e14 | 1.27474 | ||||||||
\(919\) | −8.09171e14 | −1.23442 | −0.617209 | − | 0.786799i | \(-0.711737\pi\) | ||||
−0.617209 | + | 0.786799i | \(0.711737\pi\) | |||||||
\(920\) | −2.28156e13 | −0.0346173 | ||||||||
\(921\) | 7.29165e13i | 0.110034i | ||||||||
\(922\) | 7.60362e14i | 1.14121i | ||||||||
\(923\) | − | 1.00227e14i | − | 0.149616i | ||||||
\(924\) | −2.24910e13 | −0.0333925 | ||||||||
\(925\) | − | 1.25741e15i | − | 1.85681i | ||||||
\(926\) | 5.57660e14 | 0.819058 | ||||||||
\(927\) | 1.75570e14 | 0.256478 | ||||||||
\(928\) | 1.60177e13 | 0.0232734 | ||||||||
\(929\) | − | 1.50256e14i | − | 0.217146i | −0.994088 | − | 0.108573i | \(-0.965372\pi\) | ||
0.994088 | − | 0.108573i | \(-0.0346282\pi\) | |||||||
\(930\) | − | 2.06073e13i | − | 0.0296215i | ||||||
\(931\) | − | 4.91474e14i | − | 0.702671i | ||||||
\(932\) | 1.21609e14i | 0.172937i | ||||||||
\(933\) | − | 4.25996e14i | − | 0.602556i | ||||||
\(934\) | 8.03575e14 | 1.13056 | ||||||||
\(935\) | 8.78648e13i | 0.122958i | ||||||||
\(936\) | 9.29840e13i | 0.129428i | ||||||||
\(937\) | − | 5.48073e14i | − | 0.758822i | −0.925228 | − | 0.379411i | \(-0.876127\pi\) | ||
0.925228 | − | 0.379411i | \(-0.123873\pi\) | |||||||
\(938\) | 9.38249e13 | 0.129212 | ||||||||
\(939\) | 5.89223e13 | 0.0807145 | ||||||||
\(940\) | − | 5.69170e12i | − | 0.00775538i | ||||||
\(941\) | 1.40204e15 | 1.90026 | 0.950131 | − | 0.311851i | \(-0.100949\pi\) | ||||
0.950131 | + | 0.311851i | \(0.100949\pi\) | |||||||
\(942\) | 5.49304e14i | 0.740556i | ||||||||
\(943\) | 1.87131e14 | 0.250950 | ||||||||
\(944\) | −4.18242e14 | −0.557915 | ||||||||
\(945\) | − | 8.50094e12i | − | 0.0112800i | ||||||
\(946\) | 6.57694e14 | − | 4.93143e14i | 0.868097 | − | 0.650904i | ||||
\(947\) | −3.00078e13 | −0.0393989 | −0.0196995 | − | 0.999806i | \(-0.506271\pi\) | ||||
−0.0196995 | + | 0.999806i | \(0.506271\pi\) | |||||||
\(948\) | 3.99087e13i | 0.0521226i | ||||||||
\(949\) | − | 4.01177e14i | − | 0.521201i | ||||||
\(950\) | −5.29339e14 | −0.684094 | ||||||||
\(951\) | − | 1.33999e14i | − | 0.172266i | ||||||
\(952\) | −2.77374e14 | −0.354716 | ||||||||
\(953\) | 8.16681e14i | 1.03893i | 0.854490 | + | 0.519467i | \(0.173870\pi\) | ||||
−0.854490 | + | 0.519467i | \(0.826130\pi\) | |||||||
\(954\) | 1.00185e14i | 0.126783i | ||||||||
\(955\) | −2.88683e13 | −0.0363417 | ||||||||
\(956\) | 1.29373e14 | 0.162015 | ||||||||
\(957\) | 9.81178e13 | 0.122233 | ||||||||
\(958\) | 2.27364e14i | 0.281770i | ||||||||
\(959\) | 1.05293e14 | 0.129809 | ||||||||
\(960\) | −6.48650e13 | −0.0795525 | ||||||||
\(961\) | −6.65036e14 | −0.811387 | ||||||||
\(962\) | −7.00384e14 | −0.850081 | ||||||||
\(963\) | 1.49163e14 | 0.180106 | ||||||||
\(964\) | 6.20426e13i | 0.0745254i | ||||||||
\(965\) | − | 7.11213e13i | − | 0.0849890i | ||||||
\(966\) | − | 9.21545e13i | − | 0.109555i | ||||||
\(967\) | 1.31271e15 | 1.55251 | 0.776257 | − | 0.630417i | \(-0.217116\pi\) | ||||
0.776257 | + | 0.630417i | \(0.217116\pi\) | |||||||
\(968\) | − | 3.07922e14i | − | 0.362296i | ||||||
\(969\) | 1.14300e15 | 1.33791 | ||||||||
\(970\) | −5.49488e13 | −0.0639881 | ||||||||
\(971\) | −1.04586e15 | −1.21165 | −0.605827 | − | 0.795596i | \(-0.707158\pi\) | ||||
−0.605827 | + | 0.795596i | \(0.707158\pi\) | |||||||
\(972\) | − | 5.32560e13i | − | 0.0613814i | ||||||
\(973\) | 2.34810e14i | 0.269248i | ||||||||
\(974\) | 6.17785e14i | 0.704762i | ||||||||
\(975\) | 4.78341e14i | 0.542893i | ||||||||
\(976\) | − | 1.19407e15i | − | 1.34828i | ||||||
\(977\) | −6.00194e14 | −0.674247 | −0.337123 | − | 0.941460i | \(-0.609454\pi\) | ||||
−0.337123 | + | 0.941460i | \(0.609454\pi\) | |||||||
\(978\) | 3.82296e14i | 0.427273i | ||||||||
\(979\) | − | 1.29446e15i | − | 1.43938i | ||||||
\(980\) | − | 7.00291e12i | − | 0.00774726i | ||||||
\(981\) | 3.40218e14 | 0.374466 | ||||||||
\(982\) | 1.72124e12 | 0.00188488 | ||||||||
\(983\) | − | 2.00636e14i | − | 0.218595i | −0.994009 | − | 0.109298i | \(-0.965140\pi\) | ||
0.994009 | − | 0.109298i | \(-0.0348601\pi\) | |||||||
\(984\) | 5.39544e14 | 0.584860 | ||||||||
\(985\) | 1.57894e13i | 0.0170288i | ||||||||
\(986\) | 1.33769e14 | 0.143539 | ||||||||
\(987\) | 2.07958e14 | 0.222019 | ||||||||
\(988\) | − | 4.18467e13i | − | 0.0444504i | ||||||
\(989\) | −2.86779e14 | − | 3.82471e14i | −0.303086 | − | 0.404220i | ||||
\(990\) | −1.69694e13 | −0.0178439 | ||||||||
\(991\) | − | 1.24930e15i | − | 1.30707i | −0.756896 | − | 0.653535i | \(-0.773285\pi\) | ||
0.756896 | − | 0.653535i | \(-0.226715\pi\) | |||||||
\(992\) | − | 1.03078e14i | − | 0.107302i | ||||||
\(993\) | −2.69886e14 | −0.279533 | ||||||||
\(994\) | 5.77423e13i | 0.0595062i | ||||||||
\(995\) | −1.02248e14 | −0.104843 | ||||||||
\(996\) | 3.55749e13i | 0.0362950i | ||||||||
\(997\) | − | 7.32543e14i | − | 0.743631i | −0.928307 | − | 0.371815i | \(-0.878735\pi\) | ||
0.928307 | − | 0.371815i | \(-0.121265\pi\) | |||||||
\(998\) | −1.16278e15 | −1.17448 | ||||||||
\(999\) | 1.55214e15 | 1.55992 |
(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 | 43.11.b.b.42.11 | ✓ | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.24 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.11 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.11.b.b.42.24 | yes | 34 | 43.42 | odd | 2 | inner |