Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.41399 | 0.239267 | 0.119633 | − | 0.992818i | \(-0.461828\pi\) | ||||
0.119633 | + | 0.992818i | \(0.461828\pi\) | |||||||
\(3\) | −128.596 | −0.916602 | −0.458301 | − | 0.888797i | \(-0.651542\pi\) | ||||
−0.458301 | + | 0.888797i | \(0.651542\pi\) | |||||||
\(4\) | −482.689 | −0.942751 | ||||||||
\(5\) | −1448.98 | −1.03680 | −0.518402 | − | 0.855137i | \(-0.673473\pi\) | ||||
−0.518402 | + | 0.855137i | \(0.673473\pi\) | |||||||
\(6\) | −696.216 | −0.219313 | ||||||||
\(7\) | 9443.95 | 1.48666 | 0.743332 | − | 0.668923i | \(-0.233244\pi\) | ||||
0.743332 | + | 0.668923i | \(0.233244\pi\) | |||||||
\(8\) | −5385.24 | −0.464836 | ||||||||
\(9\) | −3146.14 | −0.159841 | ||||||||
\(10\) | −7844.76 | −0.248073 | ||||||||
\(11\) | −53314.9 | −1.09795 | −0.548973 | − | 0.835840i | \(-0.684981\pi\) | ||||
−0.548973 | + | 0.835840i | \(0.684981\pi\) | |||||||
\(12\) | 62071.7 | 0.864128 | ||||||||
\(13\) | 50477.7 | 0.490179 | 0.245090 | − | 0.969500i | \(-0.421183\pi\) | ||||
0.245090 | + | 0.969500i | \(0.421183\pi\) | |||||||
\(14\) | 51129.5 | 0.355709 | ||||||||
\(15\) | 186332. | 0.950337 | ||||||||
\(16\) | 217981. | 0.831531 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −17033.2 | −0.0382446 | ||||||||
\(19\) | −361216. | −0.635881 | −0.317940 | − | 0.948111i | \(-0.602991\pi\) | ||||
−0.317940 | + | 0.948111i | \(0.602991\pi\) | |||||||
\(20\) | 699405. | 0.977448 | ||||||||
\(21\) | −1.21445e6 | −1.36268 | ||||||||
\(22\) | −288646. | −0.262702 | ||||||||
\(23\) | −378125. | −0.281748 | −0.140874 | − | 0.990028i | \(-0.544991\pi\) | ||||
−0.140874 | + | 0.990028i | \(0.544991\pi\) | |||||||
\(24\) | 692518. | 0.426070 | ||||||||
\(25\) | 146411. | 0.0749627 | ||||||||
\(26\) | 273286. | 0.117284 | ||||||||
\(27\) | 2.93573e6 | 1.06311 | ||||||||
\(28\) | −4.55849e6 | −1.40155 | ||||||||
\(29\) | −4.53701e6 | −1.19118 | −0.595592 | − | 0.803287i | \(-0.703082\pi\) | ||||
−0.595592 | + | 0.803287i | \(0.703082\pi\) | |||||||
\(30\) | 1.00880e6 | 0.227384 | ||||||||
\(31\) | −7.59551e6 | −1.47717 | −0.738583 | − | 0.674162i | \(-0.764505\pi\) | ||||
−0.738583 | + | 0.674162i | \(0.764505\pi\) | |||||||
\(32\) | 3.93739e6 | 0.663794 | ||||||||
\(33\) | 6.85606e6 | 1.00638 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.36841e7 | −1.54138 | ||||||||
\(36\) | 1.51861e6 | 0.150690 | ||||||||
\(37\) | −1.33174e7 | −1.16819 | −0.584093 | − | 0.811687i | \(-0.698550\pi\) | ||||
−0.584093 | + | 0.811687i | \(0.698550\pi\) | |||||||
\(38\) | −1.95562e6 | −0.152145 | ||||||||
\(39\) | −6.49122e6 | −0.449299 | ||||||||
\(40\) | 7.80309e6 | 0.481944 | ||||||||
\(41\) | 1.88813e7 | 1.04353 | 0.521765 | − | 0.853089i | \(-0.325274\pi\) | ||||
0.521765 | + | 0.853089i | \(0.325274\pi\) | |||||||
\(42\) | −6.57503e6 | −0.326044 | ||||||||
\(43\) | −1.12895e7 | −0.503578 | −0.251789 | − | 0.967782i | \(-0.581019\pi\) | ||||
−0.251789 | + | 0.967782i | \(0.581019\pi\) | |||||||
\(44\) | 2.57345e7 | 1.03509 | ||||||||
\(45\) | 4.55869e6 | 0.165724 | ||||||||
\(46\) | −2.04717e6 | −0.0674129 | ||||||||
\(47\) | −2.82338e7 | −0.843973 | −0.421986 | − | 0.906602i | \(-0.638667\pi\) | ||||
−0.421986 | + | 0.906602i | \(0.638667\pi\) | |||||||
\(48\) | −2.80314e7 | −0.762183 | ||||||||
\(49\) | 4.88347e7 | 1.21017 | ||||||||
\(50\) | 792671. | 0.0179361 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.43650e7 | −0.462117 | ||||||||
\(53\) | −1.10817e8 | −1.92914 | −0.964570 | − | 0.263828i | \(-0.915015\pi\) | ||||
−0.964570 | + | 0.263828i | \(0.915015\pi\) | |||||||
\(54\) | 1.58940e7 | 0.254368 | ||||||||
\(55\) | 7.72520e7 | 1.13836 | ||||||||
\(56\) | −5.08579e7 | −0.691055 | ||||||||
\(57\) | 4.64508e7 | 0.582850 | ||||||||
\(58\) | −2.45633e7 | −0.285011 | ||||||||
\(59\) | −1.66374e8 | −1.78752 | −0.893761 | − | 0.448543i | \(-0.851943\pi\) | ||||
−0.893761 | + | 0.448543i | \(0.851943\pi\) | |||||||
\(60\) | −8.99405e7 | −0.895931 | ||||||||
\(61\) | −1.24581e8 | −1.15204 | −0.576019 | − | 0.817436i | \(-0.695395\pi\) | ||||
−0.576019 | + | 0.817436i | \(0.695395\pi\) | |||||||
\(62\) | −4.11221e7 | −0.353437 | ||||||||
\(63\) | −2.97120e7 | −0.237629 | ||||||||
\(64\) | −9.02893e7 | −0.672707 | ||||||||
\(65\) | −7.31411e7 | −0.508220 | ||||||||
\(66\) | 3.71187e7 | 0.240793 | ||||||||
\(67\) | −2.73657e8 | −1.65909 | −0.829543 | − | 0.558442i | \(-0.811399\pi\) | ||||
−0.829543 | + | 0.558442i | \(0.811399\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.86253e7 | 0.258250 | ||||||||
\(70\) | −7.40855e7 | −0.368801 | ||||||||
\(71\) | 1.28257e8 | 0.598990 | 0.299495 | − | 0.954098i | \(-0.403182\pi\) | ||||
0.299495 | + | 0.954098i | \(0.403182\pi\) | |||||||
\(72\) | 1.69427e7 | 0.0742998 | ||||||||
\(73\) | −1.38744e8 | −0.571825 | −0.285912 | − | 0.958256i | \(-0.592297\pi\) | ||||
−0.285912 | + | 0.958256i | \(0.592297\pi\) | |||||||
\(74\) | −7.21004e7 | −0.279508 | ||||||||
\(75\) | −1.88279e7 | −0.0687109 | ||||||||
\(76\) | 1.74355e8 | 0.599477 | ||||||||
\(77\) | −5.03503e8 | −1.63228 | ||||||||
\(78\) | −3.51434e7 | −0.107502 | ||||||||
\(79\) | 6.51178e8 | 1.88095 | 0.940476 | − | 0.339861i | \(-0.110380\pi\) | ||||
0.940476 | + | 0.339861i | \(0.110380\pi\) | |||||||
\(80\) | −3.15850e8 | −0.862135 | ||||||||
\(81\) | −3.15597e8 | −0.814610 | ||||||||
\(82\) | 1.02223e8 | 0.249682 | ||||||||
\(83\) | 2.90303e8 | 0.671430 | 0.335715 | − | 0.941964i | \(-0.391022\pi\) | ||||
0.335715 | + | 0.941964i | \(0.391022\pi\) | |||||||
\(84\) | 5.86202e8 | 1.28467 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.11212e7 | −0.120489 | ||||||||
\(87\) | 5.83440e8 | 1.09184 | ||||||||
\(88\) | 2.87113e8 | 0.510365 | ||||||||
\(89\) | −8.64347e7 | −0.146027 | −0.0730135 | − | 0.997331i | \(-0.523262\pi\) | ||||
−0.0730135 | + | 0.997331i | \(0.523262\pi\) | |||||||
\(90\) | 2.46807e7 | 0.0396522 | ||||||||
\(91\) | 4.76709e8 | 0.728731 | ||||||||
\(92\) | 1.82517e8 | 0.265618 | ||||||||
\(93\) | 9.76750e8 | 1.35397 | ||||||||
\(94\) | −1.52857e8 | −0.201935 | ||||||||
\(95\) | 5.23394e8 | 0.659284 | ||||||||
\(96\) | −5.06331e8 | −0.608435 | ||||||||
\(97\) | −9.69081e8 | −1.11144 | −0.555722 | − | 0.831368i | \(-0.687558\pi\) | ||||
−0.555722 | + | 0.831368i | \(0.687558\pi\) | |||||||
\(98\) | 2.64391e8 | 0.289553 | ||||||||
\(99\) | 1.67736e8 | 0.175497 | ||||||||
\(100\) | −7.06712e7 | −0.0706712 | ||||||||
\(101\) | −1.61123e8 | −0.154068 | −0.0770340 | − | 0.997028i | \(-0.524545\pi\) | ||||
−0.0770340 | + | 0.997028i | \(0.524545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.13713e8 | 0.537276 | 0.268638 | − | 0.963241i | \(-0.413426\pi\) | ||||
0.268638 | + | 0.963241i | \(0.413426\pi\) | |||||||
\(104\) | −2.71835e8 | −0.227853 | ||||||||
\(105\) | 1.75971e9 | 1.41283 | ||||||||
\(106\) | −5.99961e8 | −0.461579 | ||||||||
\(107\) | 3.82243e8 | 0.281911 | 0.140956 | − | 0.990016i | \(-0.454983\pi\) | ||||
0.140956 | + | 0.990016i | \(0.454983\pi\) | |||||||
\(108\) | −1.41704e9 | −1.00225 | ||||||||
\(109\) | −7.12993e8 | −0.483800 | −0.241900 | − | 0.970301i | \(-0.577771\pi\) | ||||
−0.241900 | + | 0.970301i | \(0.577771\pi\) | |||||||
\(110\) | 4.18242e8 | 0.272371 | ||||||||
\(111\) | 1.71256e9 | 1.07076 | ||||||||
\(112\) | 2.05860e9 | 1.23621 | ||||||||
\(113\) | 1.25446e9 | 0.723775 | 0.361888 | − | 0.932222i | \(-0.382132\pi\) | ||||
0.361888 | + | 0.932222i | \(0.382132\pi\) | |||||||
\(114\) | 2.51484e8 | 0.139457 | ||||||||
\(115\) | 5.47895e8 | 0.292117 | ||||||||
\(116\) | 2.18996e9 | 1.12299 | ||||||||
\(117\) | −1.58810e8 | −0.0783506 | ||||||||
\(118\) | −9.00748e8 | −0.427695 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00344e9 | −0.441751 | ||||||||
\(121\) | 4.84527e8 | 0.205487 | ||||||||
\(122\) | −6.74480e8 | −0.275645 | ||||||||
\(123\) | −2.42805e9 | −0.956501 | ||||||||
\(124\) | 3.66627e9 | 1.39260 | ||||||||
\(125\) | 2.61789e9 | 0.959082 | ||||||||
\(126\) | −1.60861e8 | −0.0568569 | ||||||||
\(127\) | −4.71287e9 | −1.60757 | −0.803783 | − | 0.594923i | \(-0.797183\pi\) | ||||
−0.803783 | + | 0.594923i | \(0.797183\pi\) | |||||||
\(128\) | −2.50477e9 | −0.824751 | ||||||||
\(129\) | 1.45178e9 | 0.461580 | ||||||||
\(130\) | −3.95986e8 | −0.121600 | ||||||||
\(131\) | 5.24689e9 | 1.55661 | 0.778307 | − | 0.627884i | \(-0.216079\pi\) | ||||
0.778307 | + | 0.627884i | \(0.216079\pi\) | |||||||
\(132\) | −3.30934e9 | −0.948766 | ||||||||
\(133\) | −3.41131e9 | −0.945341 | ||||||||
\(134\) | −1.48157e9 | −0.396965 | ||||||||
\(135\) | −4.25381e9 | −1.10224 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50319e9 | 0.849613 | 0.424806 | − | 0.905284i | \(-0.360342\pi\) | ||||
0.424806 | + | 0.905284i | \(0.360342\pi\) | |||||||
\(138\) | 2.63257e8 | 0.0617908 | ||||||||
\(139\) | −5.88400e9 | −1.33692 | −0.668461 | − | 0.743747i | \(-0.733047\pi\) | ||||
−0.668461 | + | 0.743747i | \(0.733047\pi\) | |||||||
\(140\) | 6.60515e9 | 1.45314 | ||||||||
\(141\) | 3.63074e9 | 0.773587 | ||||||||
\(142\) | 6.94384e8 | 0.143319 | ||||||||
\(143\) | −2.69121e9 | −0.538190 | ||||||||
\(144\) | −6.85800e8 | −0.132913 | ||||||||
\(145\) | 6.57402e9 | 1.23502 | ||||||||
\(146\) | −7.51162e8 | −0.136819 | ||||||||
\(147\) | −6.27993e9 | −1.10924 | ||||||||
\(148\) | 6.42816e9 | 1.10131 | ||||||||
\(149\) | 5.04607e8 | 0.0838716 | 0.0419358 | − | 0.999120i | \(-0.486648\pi\) | ||||
0.0419358 | + | 0.999120i | \(0.486648\pi\) | |||||||
\(150\) | −1.01934e8 | −0.0164403 | ||||||||
\(151\) | 4.88828e9 | 0.765174 | 0.382587 | − | 0.923920i | \(-0.375033\pi\) | ||||
0.382587 | + | 0.923920i | \(0.375033\pi\) | |||||||
\(152\) | 1.94523e9 | 0.295580 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.72596e9 | −0.390550 | ||||||||
\(155\) | 1.10057e10 | 1.53153 | ||||||||
\(156\) | 3.13324e9 | 0.423577 | ||||||||
\(157\) | −8.97747e8 | −0.117925 | −0.0589624 | − | 0.998260i | \(-0.518779\pi\) | ||||
−0.0589624 | + | 0.998260i | \(0.518779\pi\) | |||||||
\(158\) | 3.52547e9 | 0.450050 | ||||||||
\(159\) | 1.42505e10 | 1.76825 | ||||||||
\(160\) | −5.70519e9 | −0.688225 | ||||||||
\(161\) | −3.57100e9 | −0.418864 | ||||||||
\(162\) | −1.70864e9 | −0.194909 | ||||||||
\(163\) | 8.17404e9 | 0.906970 | 0.453485 | − | 0.891264i | \(-0.350181\pi\) | ||||
0.453485 | + | 0.891264i | \(0.350181\pi\) | |||||||
\(164\) | −9.11379e9 | −0.983789 | ||||||||
\(165\) | −9.93428e9 | −1.04342 | ||||||||
\(166\) | 1.57170e9 | 0.160651 | ||||||||
\(167\) | −2.12188e9 | −0.211104 | −0.105552 | − | 0.994414i | \(-0.533661\pi\) | ||||
−0.105552 | + | 0.994414i | \(0.533661\pi\) | |||||||
\(168\) | 6.54011e9 | 0.633422 | ||||||||
\(169\) | −8.05650e9 | −0.759724 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.13644e9 | 0.101640 | ||||||||
\(172\) | 5.44931e9 | 0.474748 | ||||||||
\(173\) | 1.36572e10 | 1.15919 | 0.579594 | − | 0.814905i | \(-0.303211\pi\) | ||||
0.579594 | + | 0.814905i | \(0.303211\pi\) | |||||||
\(174\) | 3.15874e9 | 0.261241 | ||||||||
\(175\) | 1.38270e9 | 0.111444 | ||||||||
\(176\) | −1.16216e10 | −0.912977 | ||||||||
\(177\) | 2.13950e10 | 1.63845 | ||||||||
\(178\) | −4.67957e8 | −0.0349394 | ||||||||
\(179\) | −2.02667e10 | −1.47552 | −0.737759 | − | 0.675064i | \(-0.764116\pi\) | ||||
−0.737759 | + | 0.675064i | \(0.764116\pi\) | |||||||
\(180\) | −2.20043e9 | −0.156236 | ||||||||
\(181\) | −2.65298e10 | −1.83730 | −0.918651 | − | 0.395070i | \(-0.870720\pi\) | ||||
−0.918651 | + | 0.395070i | \(0.870720\pi\) | |||||||
\(182\) | 2.58090e9 | 0.174361 | ||||||||
\(183\) | 1.60206e10 | 1.05596 | ||||||||
\(184\) | 2.03629e9 | 0.130966 | ||||||||
\(185\) | 1.92966e10 | 1.21118 | ||||||||
\(186\) | 5.28812e9 | 0.323961 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.36281e10 | 0.795656 | ||||||||
\(189\) | 2.77249e10 | 1.58049 | ||||||||
\(190\) | 2.83365e9 | 0.157745 | ||||||||
\(191\) | 2.39093e9 | 0.129992 | 0.0649960 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649960 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(192\) | 1.16108e10 | 0.616605 | ||||||||
\(193\) | 3.20320e10 | 1.66179 | 0.830896 | − | 0.556427i | \(-0.187828\pi\) | ||||
0.830896 | + | 0.556427i | \(0.187828\pi\) | |||||||
\(194\) | −5.24660e9 | −0.265932 | ||||||||
\(195\) | 9.40563e9 | 0.465835 | ||||||||
\(196\) | −2.35719e10 | −1.14089 | ||||||||
\(197\) | 2.47491e10 | 1.17074 | 0.585370 | − | 0.810766i | \(-0.300949\pi\) | ||||
0.585370 | + | 0.810766i | \(0.300949\pi\) | |||||||
\(198\) | 9.08123e8 | 0.0419905 | ||||||||
\(199\) | −1.05656e10 | −0.477591 | −0.238796 | − | 0.971070i | \(-0.576753\pi\) | ||||
−0.238796 | + | 0.971070i | \(0.576753\pi\) | |||||||
\(200\) | −7.88461e8 | −0.0348454 | ||||||||
\(201\) | 3.51911e10 | 1.52072 | ||||||||
\(202\) | −8.72321e8 | −0.0368634 | ||||||||
\(203\) | −4.28473e10 | −1.77089 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.73586e10 | −1.08194 | ||||||||
\(206\) | 3.32264e9 | 0.128552 | ||||||||
\(207\) | 1.18964e9 | 0.0450347 | ||||||||
\(208\) | 1.10032e10 | 0.407599 | ||||||||
\(209\) | 1.92582e10 | 0.698163 | ||||||||
\(210\) | 9.52708e9 | 0.338044 | ||||||||
\(211\) | −4.57152e10 | −1.58778 | −0.793889 | − | 0.608062i | \(-0.791947\pi\) | ||||
−0.793889 | + | 0.608062i | \(0.791947\pi\) | |||||||
\(212\) | 5.34899e10 | 1.81870 | ||||||||
\(213\) | −1.64933e10 | −0.549035 | ||||||||
\(214\) | 2.06946e9 | 0.0674520 | ||||||||
\(215\) | 1.63582e10 | 0.522111 | ||||||||
\(216\) | −1.58096e10 | −0.494173 | ||||||||
\(217\) | −7.17317e10 | −2.19605 | ||||||||
\(218\) | −3.86014e9 | −0.115757 | ||||||||
\(219\) | 1.78419e10 | 0.524136 | ||||||||
\(220\) | −3.72887e10 | −1.07319 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.27180e9 | 0.256198 | ||||||||
\(223\) | −1.06039e10 | −0.287141 | −0.143571 | − | 0.989640i | \(-0.545858\pi\) | ||||
−0.143571 | + | 0.989640i | \(0.545858\pi\) | |||||||
\(224\) | 3.71845e10 | 0.986839 | ||||||||
\(225\) | −4.60632e8 | −0.0119821 | ||||||||
\(226\) | 6.79164e9 | 0.173175 | ||||||||
\(227\) | 3.17793e9 | 0.0794379 | 0.0397190 | − | 0.999211i | \(-0.487354\pi\) | ||||
0.0397190 | + | 0.999211i | \(0.487354\pi\) | |||||||
\(228\) | −2.24213e10 | −0.549482 | ||||||||
\(229\) | −5.66623e10 | −1.36155 | −0.680777 | − | 0.732491i | \(-0.738358\pi\) | ||||
−0.680777 | + | 0.732491i | \(0.738358\pi\) | |||||||
\(230\) | 2.96630e9 | 0.0698940 | ||||||||
\(231\) | 6.47483e10 | 1.49615 | ||||||||
\(232\) | 2.44329e10 | 0.553705 | ||||||||
\(233\) | 6.44249e10 | 1.43203 | 0.716015 | − | 0.698085i | \(-0.245964\pi\) | ||||
0.716015 | + | 0.698085i | \(0.245964\pi\) | |||||||
\(234\) | −8.59798e8 | −0.0187467 | ||||||||
\(235\) | 4.09101e10 | 0.875034 | ||||||||
\(236\) | 8.03069e10 | 1.68519 | ||||||||
\(237\) | −8.37387e10 | −1.72408 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.83304e10 | −0.759894 | −0.379947 | − | 0.925008i | \(-0.624058\pi\) | ||||
−0.379947 | + | 0.925008i | \(0.624058\pi\) | |||||||
\(240\) | 4.06169e10 | 0.790235 | ||||||||
\(241\) | 7.17784e9 | 0.137062 | 0.0685310 | − | 0.997649i | \(-0.478169\pi\) | ||||
0.0685310 | + | 0.997649i | \(0.478169\pi\) | |||||||
\(242\) | 2.62322e9 | 0.0491661 | ||||||||
\(243\) | −1.71996e10 | −0.316439 | ||||||||
\(244\) | 6.01338e10 | 1.08609 | ||||||||
\(245\) | −7.07603e10 | −1.25471 | ||||||||
\(246\) | −1.31455e10 | −0.228859 | ||||||||
\(247\) | −1.82334e10 | −0.311695 | ||||||||
\(248\) | 4.09036e10 | 0.686640 | ||||||||
\(249\) | −3.73318e10 | −0.615434 | ||||||||
\(250\) | 1.41732e10 | 0.229477 | ||||||||
\(251\) | −6.44186e10 | −1.02442 | −0.512212 | − | 0.858859i | \(-0.671174\pi\) | ||||
−0.512212 | + | 0.858859i | \(0.671174\pi\) | |||||||
\(252\) | 1.43417e10 | 0.224025 | ||||||||
\(253\) | 2.01597e10 | 0.309344 | ||||||||
\(254\) | −2.55155e10 | −0.384637 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.26673e10 | 0.475372 | ||||||||
\(257\) | −1.76291e10 | −0.252076 | −0.126038 | − | 0.992025i | \(-0.540226\pi\) | ||||
−0.126038 | + | 0.992025i | \(0.540226\pi\) | |||||||
\(258\) | 7.85993e9 | 0.110441 | ||||||||
\(259\) | −1.25769e11 | −1.73670 | ||||||||
\(260\) | 3.53044e10 | 0.479125 | ||||||||
\(261\) | 1.42741e10 | 0.190400 | ||||||||
\(262\) | 2.84066e10 | 0.372446 | ||||||||
\(263\) | 7.05351e10 | 0.909084 | 0.454542 | − | 0.890725i | \(-0.349803\pi\) | ||||
0.454542 | + | 0.890725i | \(0.349803\pi\) | |||||||
\(264\) | −3.69215e10 | −0.467802 | ||||||||
\(265\) | 1.60571e11 | 2.00014 | ||||||||
\(266\) | −1.84688e10 | −0.226189 | ||||||||
\(267\) | 1.11151e10 | 0.133849 | ||||||||
\(268\) | 1.32091e11 | 1.56411 | ||||||||
\(269\) | −5.82993e10 | −0.678857 | −0.339428 | − | 0.940632i | \(-0.610234\pi\) | ||||
−0.339428 | + | 0.940632i | \(0.610234\pi\) | |||||||
\(270\) | −2.30301e10 | −0.263729 | ||||||||
\(271\) | −5.65565e10 | −0.636973 | −0.318486 | − | 0.947927i | \(-0.603175\pi\) | ||||
−0.318486 | + | 0.947927i | \(0.603175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.13028e10 | −0.667957 | ||||||||
\(274\) | 1.89662e10 | 0.203284 | ||||||||
\(275\) | −7.80591e9 | −0.0823050 | ||||||||
\(276\) | −2.34709e10 | −0.243466 | ||||||||
\(277\) | 1.21584e11 | 1.24085 | 0.620423 | − | 0.784268i | \(-0.286961\pi\) | ||||
0.620423 | + | 0.784268i | \(0.286961\pi\) | |||||||
\(278\) | −3.18559e10 | −0.319881 | ||||||||
\(279\) | 2.38966e10 | 0.236111 | ||||||||
\(280\) | 7.36920e10 | 0.716489 | ||||||||
\(281\) | −1.34239e10 | −0.128440 | −0.0642202 | − | 0.997936i | \(-0.520456\pi\) | ||||
−0.0642202 | + | 0.997936i | \(0.520456\pi\) | |||||||
\(282\) | 1.96568e10 | 0.185094 | ||||||||
\(283\) | −1.50629e11 | −1.39595 | −0.697975 | − | 0.716122i | \(-0.745916\pi\) | ||||
−0.697975 | + | 0.716122i | \(0.745916\pi\) | |||||||
\(284\) | −6.19084e10 | −0.564699 | ||||||||
\(285\) | −6.73062e10 | −0.604301 | ||||||||
\(286\) | −1.45702e10 | −0.128771 | ||||||||
\(287\) | 1.78314e11 | 1.55138 | ||||||||
\(288\) | −1.23876e10 | −0.106101 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 3.55917e10 | 0.295500 | ||||||||
\(291\) | 1.24620e11 | 1.01875 | ||||||||
\(292\) | 6.69704e10 | 0.539088 | ||||||||
\(293\) | 2.31251e11 | 1.83307 | 0.916535 | − | 0.399954i | \(-0.130974\pi\) | ||||
0.916535 | + | 0.399954i | \(0.130974\pi\) | |||||||
\(294\) | −3.39995e10 | −0.265405 | ||||||||
\(295\) | 2.41072e11 | 1.85331 | ||||||||
\(296\) | 7.17174e10 | 0.543015 | ||||||||
\(297\) | −1.56518e11 | −1.16724 | ||||||||
\(298\) | 2.73194e9 | 0.0200677 | ||||||||
\(299\) | −1.90869e10 | −0.138107 | ||||||||
\(300\) | 9.08801e9 | 0.0647773 | ||||||||
\(301\) | −1.06617e11 | −0.748650 | ||||||||
\(302\) | 2.64651e10 | 0.183081 | ||||||||
\(303\) | 2.07198e10 | 0.141219 | ||||||||
\(304\) | −7.87382e10 | −0.528755 | ||||||||
\(305\) | 1.80515e11 | 1.19444 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.24870e10 | −0.208731 | −0.104365 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104365 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(308\) | 2.43035e11 | 1.53883 | ||||||||
\(309\) | −7.89208e10 | −0.492469 | ||||||||
\(310\) | 5.95849e10 | 0.366445 | ||||||||
\(311\) | 2.43533e11 | 1.47617 | 0.738086 | − | 0.674707i | \(-0.235730\pi\) | ||||
0.738086 | + | 0.674707i | \(0.235730\pi\) | |||||||
\(312\) | 3.49568e10 | 0.208851 | ||||||||
\(313\) | −1.00730e9 | −0.00593212 | −0.00296606 | − | 0.999996i | \(-0.500944\pi\) | ||||
−0.00296606 | + | 0.999996i | \(0.500944\pi\) | |||||||
\(314\) | −4.86039e9 | −0.0282155 | ||||||||
\(315\) | 4.30521e10 | 0.246375 | ||||||||
\(316\) | −3.14316e11 | −1.77327 | ||||||||
\(317\) | −2.11430e11 | −1.17598 | −0.587991 | − | 0.808868i | \(-0.700081\pi\) | ||||
−0.587991 | + | 0.808868i | \(0.700081\pi\) | |||||||
\(318\) | 7.71523e10 | 0.423084 | ||||||||
\(319\) | 2.41890e11 | 1.30786 | ||||||||
\(320\) | 1.30827e11 | 0.697466 | ||||||||
\(321\) | −4.91548e10 | −0.258400 | ||||||||
\(322\) | −1.93333e10 | −0.100220 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.52335e11 | 0.767975 | ||||||||
\(325\) | 7.39052e9 | 0.0367451 | ||||||||
\(326\) | 4.42542e10 | 0.217008 | ||||||||
\(327\) | 9.16878e10 | 0.443452 | ||||||||
\(328\) | −1.01680e11 | −0.485070 | ||||||||
\(329\) | −2.66638e11 | −1.25470 | ||||||||
\(330\) | −5.37841e10 | −0.249656 | ||||||||
\(331\) | −1.05381e11 | −0.482543 | −0.241271 | − | 0.970458i | \(-0.577564\pi\) | ||||
−0.241271 | + | 0.970458i | \(0.577564\pi\) | |||||||
\(332\) | −1.40126e11 | −0.632992 | ||||||||
\(333\) | 4.18985e10 | 0.186724 | ||||||||
\(334\) | −1.14878e10 | −0.0505102 | ||||||||
\(335\) | 3.96522e11 | 1.72015 | ||||||||
\(336\) | −2.64727e11 | −1.13311 | ||||||||
\(337\) | 2.53745e10 | 0.107167 | 0.0535836 | − | 0.998563i | \(-0.482936\pi\) | ||||
0.0535836 | + | 0.998563i | \(0.482936\pi\) | |||||||
\(338\) | −4.36178e10 | −0.181777 | ||||||||
\(339\) | −1.61318e11 | −0.663414 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.04954e11 | 1.62185 | ||||||||
\(342\) | 6.15267e9 | 0.0243190 | ||||||||
\(343\) | 8.00947e10 | 0.312450 | ||||||||
\(344\) | 6.07966e10 | 0.234081 | ||||||||
\(345\) | −7.04569e10 | −0.267755 | ||||||||
\(346\) | 7.39400e10 | 0.277356 | ||||||||
\(347\) | −1.47329e9 | −0.00545515 | −0.00272757 | − | 0.999996i | \(-0.500868\pi\) | ||||
−0.00272757 | + | 0.999996i | \(0.500868\pi\) | |||||||
\(348\) | −2.81620e11 | −1.02933 | ||||||||
\(349\) | −4.79754e10 | −0.173103 | −0.0865513 | − | 0.996247i | \(-0.527585\pi\) | ||||
−0.0865513 | + | 0.996247i | \(0.527585\pi\) | |||||||
\(350\) | 7.48595e9 | 0.0266649 | ||||||||
\(351\) | 1.48189e11 | 0.521115 | ||||||||
\(352\) | −2.09921e11 | −0.728811 | ||||||||
\(353\) | −1.19962e11 | −0.411203 | −0.205601 | − | 0.978636i | \(-0.565915\pi\) | ||||
−0.205601 | + | 0.978636i | \(0.565915\pi\) | |||||||
\(354\) | 1.15832e11 | 0.392026 | ||||||||
\(355\) | −1.85842e11 | −0.621035 | ||||||||
\(356\) | 4.17210e10 | 0.137667 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.09724e11 | −0.353043 | ||||||||
\(359\) | −3.49206e11 | −1.10958 | −0.554788 | − | 0.831992i | \(-0.687201\pi\) | ||||
−0.554788 | + | 0.831992i | \(0.687201\pi\) | |||||||
\(360\) | −2.45497e10 | −0.0770343 | ||||||||
\(361\) | −1.92211e11 | −0.595656 | ||||||||
\(362\) | −1.43632e11 | −0.439606 | ||||||||
\(363\) | −6.23080e10 | −0.188349 | ||||||||
\(364\) | −2.30102e11 | −0.687012 | ||||||||
\(365\) | 2.01038e11 | 0.592870 | ||||||||
\(366\) | 8.67352e10 | 0.252657 | ||||||||
\(367\) | −3.99938e11 | −1.15079 | −0.575395 | − | 0.817876i | \(-0.695152\pi\) | ||||
−0.575395 | + | 0.817876i | \(0.695152\pi\) | |||||||
\(368\) | −8.24241e10 | −0.234282 | ||||||||
\(369\) | −5.94033e10 | −0.166798 | ||||||||
\(370\) | 1.04472e11 | 0.289795 | ||||||||
\(371\) | −1.04655e12 | −2.86798 | ||||||||
\(372\) | −4.71466e11 | −1.27646 | ||||||||
\(373\) | 2.53082e11 | 0.676973 | 0.338487 | − | 0.940971i | \(-0.390085\pi\) | ||||
0.338487 | + | 0.940971i | \(0.390085\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.36649e11 | −0.879097 | ||||||||
\(376\) | 1.52046e11 | 0.392309 | ||||||||
\(377\) | −2.29018e11 | −0.583893 | ||||||||
\(378\) | 1.50102e11 | 0.378159 | ||||||||
\(379\) | 3.64607e11 | 0.907714 | 0.453857 | − | 0.891075i | \(-0.350048\pi\) | ||||
0.453857 | + | 0.891075i | \(0.350048\pi\) | |||||||
\(380\) | −2.52636e11 | −0.621541 | ||||||||
\(381\) | 6.06055e11 | 1.47350 | ||||||||
\(382\) | 1.29445e10 | 0.0311028 | ||||||||
\(383\) | 5.96099e11 | 1.41555 | 0.707773 | − | 0.706440i | \(-0.249700\pi\) | ||||
0.707773 | + | 0.706440i | \(0.249700\pi\) | |||||||
\(384\) | 3.22102e11 | 0.755968 | ||||||||
\(385\) | 7.29565e11 | 1.69235 | ||||||||
\(386\) | 1.73421e11 | 0.397612 | ||||||||
\(387\) | 3.55184e10 | 0.0804922 | ||||||||
\(388\) | 4.67765e11 | 1.04781 | ||||||||
\(389\) | 5.78216e11 | 1.28032 | 0.640158 | − | 0.768243i | \(-0.278869\pi\) | ||||
0.640158 | + | 0.768243i | \(0.278869\pi\) | |||||||
\(390\) | 5.09220e10 | 0.111459 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.62986e11 | −0.562530 | ||||||||
\(393\) | −6.74727e11 | −1.42680 | ||||||||
\(394\) | 1.33991e11 | 0.280120 | ||||||||
\(395\) | −9.43542e11 | −1.95018 | ||||||||
\(396\) | −8.09644e10 | −0.165450 | ||||||||
\(397\) | −9.41819e10 | −0.190288 | −0.0951438 | − | 0.995464i | \(-0.530331\pi\) | ||||
−0.0951438 | + | 0.995464i | \(0.530331\pi\) | |||||||
\(398\) | −5.72022e10 | −0.114272 | ||||||||
\(399\) | 4.38679e11 | 0.866501 | ||||||||
\(400\) | 3.19149e10 | 0.0623338 | ||||||||
\(401\) | 5.33397e11 | 1.03015 | 0.515075 | − | 0.857145i | \(-0.327764\pi\) | ||||
0.515075 | + | 0.857145i | \(0.327764\pi\) | |||||||
\(402\) | 1.90524e11 | 0.363859 | ||||||||
\(403\) | −3.83404e11 | −0.724076 | ||||||||
\(404\) | 7.77724e10 | 0.145248 | ||||||||
\(405\) | 4.57293e11 | 0.844591 | ||||||||
\(406\) | −2.31975e11 | −0.423715 | ||||||||
\(407\) | 7.10016e11 | 1.28261 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.13190e11 | −0.553418 | −0.276709 | − | 0.960954i | \(-0.589244\pi\) | ||||
−0.276709 | + | 0.960954i | \(0.589244\pi\) | |||||||
\(410\) | −1.48119e11 | −0.258871 | ||||||||
\(411\) | −4.50495e11 | −0.778757 | ||||||||
\(412\) | −2.96232e11 | −0.506518 | ||||||||
\(413\) | −1.57123e12 | −2.65745 | ||||||||
\(414\) | 6.44068e9 | 0.0107753 | ||||||||
\(415\) | −4.20643e11 | −0.696142 | ||||||||
\(416\) | 1.98750e11 | 0.325378 | ||||||||
\(417\) | 7.56657e11 | 1.22542 | ||||||||
\(418\) | 1.04264e11 | 0.167047 | ||||||||
\(419\) | 9.82119e11 | 1.55669 | 0.778343 | − | 0.627839i | \(-0.216060\pi\) | ||||
0.778343 | + | 0.627839i | \(0.216060\pi\) | |||||||
\(420\) | −8.49394e11 | −1.33195 | ||||||||
\(421\) | 1.73588e11 | 0.269308 | 0.134654 | − | 0.990893i | \(-0.457008\pi\) | ||||
0.134654 | + | 0.990893i | \(0.457008\pi\) | |||||||
\(422\) | −2.47502e11 | −0.379903 | ||||||||
\(423\) | 8.88275e10 | 0.134901 | ||||||||
\(424\) | 5.96774e11 | 0.896734 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.92948e10 | −0.131366 | ||||||||
\(427\) | −1.17654e12 | −1.71269 | ||||||||
\(428\) | −1.84504e11 | −0.265772 | ||||||||
\(429\) | 3.46078e11 | 0.493306 | ||||||||
\(430\) | 8.85633e10 | 0.124924 | ||||||||
\(431\) | −3.54330e11 | −0.494606 | −0.247303 | − | 0.968938i | \(-0.579544\pi\) | ||||
−0.247303 | + | 0.968938i | \(0.579544\pi\) | |||||||
\(432\) | 6.39933e11 | 0.884011 | ||||||||
\(433\) | 6.69890e7 | 9.15815e−5 0 | 4.57907e−5 | − | 1.00000i | \(-0.499985\pi\) | ||||
4.57907e−5 | 1.00000i | \(0.499985\pi\) | ||||||||
\(434\) | −3.88355e11 | −0.525442 | ||||||||
\(435\) | −8.45391e11 | −1.13203 | ||||||||
\(436\) | 3.44154e11 | 0.456103 | ||||||||
\(437\) | 1.36585e11 | 0.179158 | ||||||||
\(438\) | 9.65962e10 | 0.125408 | ||||||||
\(439\) | −4.51683e11 | −0.580422 | −0.290211 | − | 0.956963i | \(-0.593725\pi\) | ||||
−0.290211 | + | 0.956963i | \(0.593725\pi\) | |||||||
\(440\) | −4.16021e11 | −0.529149 | ||||||||
\(441\) | −1.53641e11 | −0.193434 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.61003e11 | 0.938792 | 0.469396 | − | 0.882988i | \(-0.344472\pi\) | ||||
0.469396 | + | 0.882988i | \(0.344472\pi\) | |||||||
\(444\) | −8.26634e11 | −1.00946 | ||||||||
\(445\) | 1.25242e11 | 0.151401 | ||||||||
\(446\) | −5.74097e10 | −0.0687034 | ||||||||
\(447\) | −6.48903e10 | −0.0768769 | ||||||||
\(448\) | −8.52688e11 | −1.00009 | ||||||||
\(449\) | −5.03740e9 | −0.00584921 | −0.00292461 | − | 0.999996i | \(-0.500931\pi\) | ||||
−0.00292461 | + | 0.999996i | \(0.500931\pi\) | |||||||
\(450\) | −2.49386e9 | −0.00286692 | ||||||||
\(451\) | −1.00665e12 | −1.14574 | ||||||||
\(452\) | −6.05513e11 | −0.682340 | ||||||||
\(453\) | −6.28612e11 | −0.701360 | ||||||||
\(454\) | 1.72053e10 | 0.0190069 | ||||||||
\(455\) | −6.90741e11 | −0.755552 | ||||||||
\(456\) | −2.50149e11 | −0.270930 | ||||||||
\(457\) | −7.31493e11 | −0.784490 | −0.392245 | − | 0.919861i | \(-0.628301\pi\) | ||||
−0.392245 | + | 0.919861i | \(0.628301\pi\) | |||||||
\(458\) | −3.06769e11 | −0.325775 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.64463e11 | −0.275394 | ||||||||
\(461\) | 7.48760e11 | 0.772126 | 0.386063 | − | 0.922472i | \(-0.373835\pi\) | ||||
0.386063 | + | 0.922472i | \(0.373835\pi\) | |||||||
\(462\) | 3.50547e11 | 0.357979 | ||||||||
\(463\) | 1.32071e11 | 0.133565 | 0.0667827 | − | 0.997768i | \(-0.478727\pi\) | ||||
0.0667827 | + | 0.997768i | \(0.478727\pi\) | |||||||
\(464\) | −9.88981e11 | −0.990506 | ||||||||
\(465\) | −1.41529e12 | −1.40381 | ||||||||
\(466\) | 3.48796e11 | 0.342637 | ||||||||
\(467\) | −1.16300e11 | −0.113150 | −0.0565750 | − | 0.998398i | \(-0.518018\pi\) | ||||
−0.0565750 | + | 0.998398i | \(0.518018\pi\) | |||||||
\(468\) | 7.66559e10 | 0.0738651 | ||||||||
\(469\) | −2.58440e12 | −2.46650 | ||||||||
\(470\) | 2.21487e11 | 0.209367 | ||||||||
\(471\) | 1.15446e11 | 0.108090 | ||||||||
\(472\) | 8.95964e11 | 0.830905 | ||||||||
\(473\) | 6.01898e11 | 0.552901 | ||||||||
\(474\) | −4.53361e11 | −0.412516 | ||||||||
\(475\) | −5.28862e10 | −0.0476673 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.48645e11 | 0.308355 | ||||||||
\(478\) | −2.07521e11 | −0.181818 | ||||||||
\(479\) | 2.63575e11 | 0.228768 | 0.114384 | − | 0.993437i | \(-0.463511\pi\) | ||||
0.114384 | + | 0.993437i | \(0.463511\pi\) | |||||||
\(480\) | 7.33663e11 | 0.630828 | ||||||||
\(481\) | −6.72233e11 | −0.572620 | ||||||||
\(482\) | 3.88608e10 | 0.0327944 | ||||||||
\(483\) | 4.59215e11 | 0.383931 | ||||||||
\(484\) | −2.33876e11 | −0.193723 | ||||||||
\(485\) | 1.40418e12 | 1.15235 | ||||||||
\(486\) | −9.31185e10 | −0.0757134 | ||||||||
\(487\) | 5.21302e11 | 0.419961 | 0.209981 | − | 0.977706i | \(-0.432660\pi\) | ||||
0.209981 | + | 0.977706i | \(0.432660\pi\) | |||||||
\(488\) | 6.70898e11 | 0.535509 | ||||||||
\(489\) | −1.05115e12 | −0.831330 | ||||||||
\(490\) | −3.83096e11 | −0.300210 | ||||||||
\(491\) | −2.46427e12 | −1.91347 | −0.956737 | − | 0.290955i | \(-0.906027\pi\) | ||||
−0.956737 | + | 0.290955i | \(0.906027\pi\) | |||||||
\(492\) | 1.17199e12 | 0.901743 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −9.87153e10 | −0.0745784 | ||||||||
\(495\) | −2.43046e11 | −0.181956 | ||||||||
\(496\) | −1.65568e12 | −1.22831 | ||||||||
\(497\) | 1.21126e12 | 0.890497 | ||||||||
\(498\) | −2.02114e11 | −0.147253 | ||||||||
\(499\) | 1.19804e12 | 0.865009 | 0.432505 | − | 0.901632i | \(-0.357630\pi\) | ||||
0.432505 | + | 0.901632i | \(0.357630\pi\) | |||||||
\(500\) | −1.26362e12 | −0.904176 | ||||||||
\(501\) | 2.72865e11 | 0.193498 | ||||||||
\(502\) | −3.48762e11 | −0.245111 | ||||||||
\(503\) | −2.80910e12 | −1.95664 | −0.978322 | − | 0.207090i | \(-0.933601\pi\) | ||||
−0.978322 | + | 0.207090i | \(0.933601\pi\) | |||||||
\(504\) | 1.60006e11 | 0.110459 | ||||||||
\(505\) | 2.33464e11 | 0.159738 | ||||||||
\(506\) | 1.09144e11 | 0.0740158 | ||||||||
\(507\) | 1.03603e12 | 0.696365 | ||||||||
\(508\) | 2.27485e12 | 1.51553 | ||||||||
\(509\) | 1.29541e12 | 0.855416 | 0.427708 | − | 0.903917i | \(-0.359321\pi\) | ||||
0.427708 | + | 0.903917i | \(0.359321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.31030e12 | −0.850111 | ||||||||
\(512\) | 1.45930e12 | 0.938492 | ||||||||
\(513\) | −1.06043e12 | −0.676013 | ||||||||
\(514\) | −9.54439e10 | −0.0603134 | ||||||||
\(515\) | −8.89256e11 | −0.557050 | ||||||||
\(516\) | −7.00758e11 | −0.435155 | ||||||||
\(517\) | 1.50528e12 | 0.926637 | ||||||||
\(518\) | −6.80913e11 | −0.415535 | ||||||||
\(519\) | −1.75626e12 | −1.06251 | ||||||||
\(520\) | 3.93882e11 | 0.236239 | ||||||||
\(521\) | −2.01682e12 | −1.19922 | −0.599609 | − | 0.800293i | \(-0.704677\pi\) | ||||
−0.599609 | + | 0.800293i | \(0.704677\pi\) | |||||||
\(522\) | 7.72798e10 | 0.0455563 | ||||||||
\(523\) | 2.41603e12 | 1.41203 | 0.706017 | − | 0.708195i | \(-0.250490\pi\) | ||||
0.706017 | + | 0.708195i | \(0.250490\pi\) | |||||||
\(524\) | −2.53261e12 | −1.46750 | ||||||||
\(525\) | −1.77810e11 | −0.102150 | ||||||||
\(526\) | 3.81876e11 | 0.217514 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.49449e12 | 0.836837 | ||||||||
\(529\) | −1.65817e12 | −0.920618 | ||||||||
\(530\) | 8.69329e11 | 0.478567 | ||||||||
\(531\) | 5.23437e11 | 0.285719 | ||||||||
\(532\) | 1.64660e12 | 0.891221 | ||||||||
\(533\) | 9.53086e11 | 0.511516 | ||||||||
\(534\) | 6.01772e10 | 0.0320255 | ||||||||
\(535\) | −5.53861e11 | −0.292287 | ||||||||
\(536\) | 1.47371e12 | 0.771204 | ||||||||
\(537\) | 2.60621e12 | 1.35246 | ||||||||
\(538\) | −3.15632e11 | −0.162428 | ||||||||
\(539\) | −2.60361e12 | −1.32870 | ||||||||
\(540\) | 2.05326e12 | 1.03914 | ||||||||
\(541\) | 5.24241e11 | 0.263114 | 0.131557 | − | 0.991309i | \(-0.458002\pi\) | ||||
0.131557 | + | 0.991309i | \(0.458002\pi\) | |||||||
\(542\) | −3.06197e11 | −0.152407 | ||||||||
\(543\) | 3.41162e12 | 1.68407 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.03311e12 | 0.501606 | ||||||||
\(546\) | −3.31893e11 | −0.159820 | ||||||||
\(547\) | −1.39403e12 | −0.665777 | −0.332888 | − | 0.942966i | \(-0.608023\pi\) | ||||
−0.332888 | + | 0.942966i | \(0.608023\pi\) | |||||||
\(548\) | −1.69095e12 | −0.800973 | ||||||||
\(549\) | 3.91950e11 | 0.184143 | ||||||||
\(550\) | −4.22611e10 | −0.0196929 | ||||||||
\(551\) | 1.63884e12 | 0.757451 | ||||||||
\(552\) | −2.61859e11 | −0.120044 | ||||||||
\(553\) | 6.14969e12 | 2.79634 | ||||||||
\(554\) | 6.58255e11 | 0.296893 | ||||||||
\(555\) | −2.48146e12 | −1.11017 | ||||||||
\(556\) | 2.84014e12 | 1.26038 | ||||||||
\(557\) | −3.95429e11 | −0.174069 | −0.0870343 | − | 0.996205i | \(-0.527739\pi\) | ||||
−0.0870343 | + | 0.996205i | \(0.527739\pi\) | |||||||
\(558\) | 1.29376e11 | 0.0564936 | ||||||||
\(559\) | −5.69868e11 | −0.246843 | ||||||||
\(560\) | −2.98287e12 | −1.28170 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.26772e10 | −0.0307316 | ||||||||
\(563\) | 2.92242e12 | 1.22590 | 0.612951 | − | 0.790121i | \(-0.289982\pi\) | ||||
0.612951 | + | 0.790121i | \(0.289982\pi\) | |||||||
\(564\) | −1.75252e12 | −0.729300 | ||||||||
\(565\) | −1.81768e12 | −0.750413 | ||||||||
\(566\) | −8.15505e11 | −0.334005 | ||||||||
\(567\) | −2.98048e12 | −1.21105 | ||||||||
\(568\) | −6.90696e11 | −0.278432 | ||||||||
\(569\) | 6.55993e11 | 0.262358 | 0.131179 | − | 0.991359i | \(-0.458124\pi\) | ||||
0.131179 | + | 0.991359i | \(0.458124\pi\) | |||||||
\(570\) | −3.64395e11 | −0.144589 | ||||||||
\(571\) | 1.68512e12 | 0.663391 | 0.331695 | − | 0.943387i | \(-0.392379\pi\) | ||||
0.331695 | + | 0.943387i | \(0.392379\pi\) | |||||||
\(572\) | 1.29902e12 | 0.507380 | ||||||||
\(573\) | −3.07463e11 | −0.119151 | ||||||||
\(574\) | 9.65392e11 | 0.371193 | ||||||||
\(575\) | −5.53619e10 | −0.0211206 | ||||||||
\(576\) | 2.84063e11 | 0.107526 | ||||||||
\(577\) | −3.07782e12 | −1.15599 | −0.577993 | − | 0.816042i | \(-0.696164\pi\) | ||||
−0.577993 | + | 0.816042i | \(0.696164\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.11918e12 | −1.52320 | ||||||||
\(580\) | −3.17321e12 | −1.16432 | ||||||||
\(581\) | 2.74161e12 | 0.998191 | ||||||||
\(582\) | 6.74690e11 | 0.243754 | ||||||||
\(583\) | 5.90817e12 | 2.11809 | ||||||||
\(584\) | 7.47172e11 | 0.265805 | ||||||||
\(585\) | 2.30113e11 | 0.0812342 | ||||||||
\(586\) | 1.25199e12 | 0.438593 | ||||||||
\(587\) | −1.96540e12 | −0.683250 | −0.341625 | − | 0.939836i | \(-0.610977\pi\) | ||||
−0.341625 | + | 0.939836i | \(0.610977\pi\) | |||||||
\(588\) | 3.03125e12 | 1.04574 | ||||||||
\(589\) | 2.74362e12 | 0.939302 | ||||||||
\(590\) | 1.30516e12 | 0.443436 | ||||||||
\(591\) | −3.18262e12 | −1.07310 | ||||||||
\(592\) | −2.90294e12 | −0.971383 | ||||||||
\(593\) | 1.10021e12 | 0.365367 | 0.182683 | − | 0.983172i | \(-0.441522\pi\) | ||||
0.182683 | + | 0.983172i | \(0.441522\pi\) | |||||||
\(594\) | −8.47388e11 | −0.279282 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.43568e11 | −0.0790700 | ||||||||
\(597\) | 1.35869e12 | 0.437761 | ||||||||
\(598\) | −1.03336e11 | −0.0330444 | ||||||||
\(599\) | −5.63562e12 | −1.78863 | −0.894315 | − | 0.447437i | \(-0.852337\pi\) | ||||
−0.894315 | + | 0.447437i | \(0.852337\pi\) | |||||||
\(600\) | 1.01393e11 | 0.0319393 | ||||||||
\(601\) | 3.46470e12 | 1.08325 | 0.541627 | − | 0.840619i | \(-0.317809\pi\) | ||||
0.541627 | + | 0.840619i | \(0.317809\pi\) | |||||||
\(602\) | −5.77226e11 | −0.179127 | ||||||||
\(603\) | 8.60963e11 | 0.265190 | ||||||||
\(604\) | −2.35952e12 | −0.721368 | ||||||||
\(605\) | −7.02068e11 | −0.213049 | ||||||||
\(606\) | 1.12177e11 | 0.0337890 | ||||||||
\(607\) | 2.58507e12 | 0.772900 | 0.386450 | − | 0.922310i | \(-0.373701\pi\) | ||||
0.386450 | + | 0.922310i | \(0.373701\pi\) | |||||||
\(608\) | −1.42225e12 | −0.422094 | ||||||||
\(609\) | 5.50998e12 | 1.62320 | ||||||||
\(610\) | 9.77307e11 | 0.285790 | ||||||||
\(611\) | −1.42518e12 | −0.413698 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.46982e12 | 1.56459 | 0.782296 | − | 0.622906i | \(-0.214048\pi\) | ||||
0.782296 | + | 0.622906i | \(0.214048\pi\) | |||||||
\(614\) | −1.75884e11 | −0.0499424 | ||||||||
\(615\) | 3.51820e12 | 0.991704 | ||||||||
\(616\) | 2.71148e12 | 0.758741 | ||||||||
\(617\) | −4.06569e12 | −1.12941 | −0.564704 | − | 0.825294i | \(-0.691010\pi\) | ||||
−0.564704 | + | 0.825294i | \(0.691010\pi\) | |||||||
\(618\) | −4.27277e11 | −0.117831 | ||||||||
\(619\) | −2.50487e12 | −0.685767 | −0.342883 | − | 0.939378i | \(-0.611404\pi\) | ||||
−0.342883 | + | 0.939378i | \(0.611404\pi\) | |||||||
\(620\) | −5.31234e12 | −1.44385 | ||||||||
\(621\) | −1.11007e12 | −0.299529 | ||||||||
\(622\) | 1.31849e12 | 0.353199 | ||||||||
\(623\) | −8.16285e11 | −0.217093 | ||||||||
\(624\) | −1.41496e12 | −0.373606 | ||||||||
\(625\) | −4.07922e12 | −1.06934 | ||||||||
\(626\) | −5.45352e9 | −0.00141936 | ||||||||
\(627\) | −2.47652e12 | −0.639938 | ||||||||
\(628\) | 4.33332e11 | 0.111174 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.33084e11 | 0.0589494 | ||||||||
\(631\) | 3.07145e12 | 0.771279 | 0.385640 | − | 0.922650i | \(-0.373981\pi\) | ||||
0.385640 | + | 0.922650i | \(0.373981\pi\) | |||||||
\(632\) | −3.50675e12 | −0.874334 | ||||||||
\(633\) | 5.87878e12 | 1.45536 | ||||||||
\(634\) | −1.14468e12 | −0.281374 | ||||||||
\(635\) | 6.82885e12 | 1.66673 | ||||||||
\(636\) | −6.87858e12 | −1.66702 | ||||||||
\(637\) | 2.46506e12 | 0.593199 | ||||||||
\(638\) | 1.30959e12 | 0.312927 | ||||||||
\(639\) | −4.03516e11 | −0.0957430 | ||||||||
\(640\) | 3.62935e12 | 0.855105 | ||||||||
\(641\) | −1.02073e12 | −0.238809 | −0.119404 | − | 0.992846i | \(-0.538098\pi\) | ||||
−0.119404 | + | 0.992846i | \(0.538098\pi\) | |||||||
\(642\) | −2.66124e11 | −0.0618266 | ||||||||
\(643\) | 1.45556e12 | 0.335801 | 0.167900 | − | 0.985804i | \(-0.446301\pi\) | ||||
0.167900 | + | 0.985804i | \(0.446301\pi\) | |||||||
\(644\) | 1.72368e12 | 0.394884 | ||||||||
\(645\) | −2.10360e12 | −0.478568 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.55404e11 | −0.0797357 | −0.0398679 | − | 0.999205i | \(-0.512694\pi\) | ||||
−0.0398679 | + | 0.999205i | \(0.512694\pi\) | |||||||
\(648\) | 1.69956e12 | 0.378660 | ||||||||
\(649\) | 8.87021e12 | 1.96260 | ||||||||
\(650\) | 4.00122e10 | 0.00879190 | ||||||||
\(651\) | 9.22438e12 | 2.01290 | ||||||||
\(652\) | −3.94552e12 | −0.855047 | ||||||||
\(653\) | −4.75410e12 | −1.02320 | −0.511598 | − | 0.859225i | \(-0.670946\pi\) | ||||
−0.511598 | + | 0.859225i | \(0.670946\pi\) | |||||||
\(654\) | 4.96397e11 | 0.106103 | ||||||||
\(655\) | −7.60262e12 | −1.61390 | ||||||||
\(656\) | 4.11577e12 | 0.867727 | ||||||||
\(657\) | 4.36510e11 | 0.0914009 | ||||||||
\(658\) | −1.44358e12 | −0.300209 | ||||||||
\(659\) | −5.01255e12 | −1.03532 | −0.517660 | − | 0.855586i | \(-0.673197\pi\) | ||||
−0.517660 | + | 0.855586i | \(0.673197\pi\) | |||||||
\(660\) | 4.79517e12 | 0.983685 | ||||||||
\(661\) | 7.92167e12 | 1.61402 | 0.807012 | − | 0.590534i | \(-0.201083\pi\) | ||||
0.807012 | + | 0.590534i | \(0.201083\pi\) | |||||||
\(662\) | −5.70531e11 | −0.115457 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.56335e12 | −0.312105 | ||||||||
\(665\) | 4.94291e12 | 0.980133 | ||||||||
\(666\) | 2.26838e11 | 0.0446768 | ||||||||
\(667\) | 1.71556e12 | 0.335613 | ||||||||
\(668\) | 1.02421e12 | 0.199019 | ||||||||
\(669\) | 1.36362e12 | 0.263194 | ||||||||
\(670\) | 2.14677e12 | 0.411575 | ||||||||
\(671\) | 6.64201e12 | 1.26488 | ||||||||
\(672\) | −4.78177e12 | −0.904538 | ||||||||
\(673\) | 9.72451e11 | 0.182726 | 0.0913629 | − | 0.995818i | \(-0.470878\pi\) | ||||
0.0913629 | + | 0.995818i | \(0.470878\pi\) | |||||||
\(674\) | 1.37377e11 | 0.0256416 | ||||||||
\(675\) | 4.29825e11 | 0.0796938 | ||||||||
\(676\) | 3.88878e12 | 0.716231 | ||||||||
\(677\) | −2.68897e12 | −0.491968 | −0.245984 | − | 0.969274i | \(-0.579111\pi\) | ||||
−0.245984 | + | 0.969274i | \(0.579111\pi\) | |||||||
\(678\) | −8.73375e11 | −0.158733 | ||||||||
\(679\) | −9.15196e12 | −1.65234 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.08668e11 | −0.0728129 | ||||||||
\(682\) | 2.19242e12 | 0.388055 | ||||||||
\(683\) | 5.44998e12 | 0.958300 | 0.479150 | − | 0.877733i | \(-0.340945\pi\) | ||||
0.479150 | + | 0.877733i | \(0.340945\pi\) | |||||||
\(684\) | −5.48546e11 | −0.0958209 | ||||||||
\(685\) | −5.07604e12 | −0.880882 | ||||||||
\(686\) | 4.33632e11 | 0.0747589 | ||||||||
\(687\) | 7.28653e12 | 1.24800 | ||||||||
\(688\) | −2.46089e12 | −0.418741 | ||||||||
\(689\) | −5.59377e12 | −0.945624 | ||||||||
\(690\) | −3.81453e11 | −0.0640649 | ||||||||
\(691\) | −6.45907e12 | −1.07775 | −0.538876 | − | 0.842385i | \(-0.681151\pi\) | ||||
−0.538876 | + | 0.842385i | \(0.681151\pi\) | |||||||
\(692\) | −6.59218e12 | −1.09283 | ||||||||
\(693\) | 1.58409e12 | 0.260904 | ||||||||
\(694\) | −7.97640e9 | −0.00130524 | ||||||||
\(695\) | 8.52578e12 | 1.38613 | ||||||||
\(696\) | −3.14196e12 | −0.507527 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2.59738e11 | −0.0414178 | ||||||||
\(699\) | −8.28476e12 | −1.31260 | ||||||||
\(700\) | −6.67415e11 | −0.105064 | ||||||||
\(701\) | −1.69528e12 | −0.265161 | −0.132580 | − | 0.991172i | \(-0.542326\pi\) | ||||
−0.132580 | + | 0.991172i | \(0.542326\pi\) | |||||||
\(702\) | 8.02294e11 | 0.124686 | ||||||||
\(703\) | 4.81046e12 | 0.742827 | ||||||||
\(704\) | 4.81376e12 | 0.738597 | ||||||||
\(705\) | −5.26086e12 | −0.802058 | ||||||||
\(706\) | −6.49472e11 | −0.0983873 | ||||||||
\(707\) | −1.52164e12 | −0.229047 | ||||||||
\(708\) | −1.03271e13 | −1.54465 | ||||||||
\(709\) | −8.47386e12 | −1.25943 | −0.629714 | − | 0.776827i | \(-0.716828\pi\) | ||||
−0.629714 | + | 0.776827i | \(0.716828\pi\) | |||||||
\(710\) | −1.00615e12 | −0.148593 | ||||||||
\(711\) | −2.04870e12 | −0.300653 | ||||||||
\(712\) | 4.65471e11 | 0.0678786 | ||||||||
\(713\) | 2.87205e12 | 0.416188 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.89951e12 | 0.557998 | ||||||||
\(716\) | 9.78252e12 | 1.39105 | ||||||||
\(717\) | 4.92913e12 | 0.696521 | ||||||||
\(718\) | −1.89060e12 | −0.265485 | ||||||||
\(719\) | 4.90262e12 | 0.684145 | 0.342072 | − | 0.939674i | \(-0.388871\pi\) | ||||
0.342072 | + | 0.939674i | \(0.388871\pi\) | |||||||
\(720\) | 9.93709e11 | 0.137804 | ||||||||
\(721\) | 5.79588e12 | 0.798749 | ||||||||
\(722\) | −1.04063e12 | −0.142521 | ||||||||
\(723\) | −9.23040e11 | −0.125631 | ||||||||
\(724\) | 1.28056e13 | 1.73212 | ||||||||
\(725\) | −6.64270e11 | −0.0892943 | ||||||||
\(726\) | −3.37335e11 | −0.0450658 | ||||||||
\(727\) | 1.95230e12 | 0.259204 | 0.129602 | − | 0.991566i | \(-0.458630\pi\) | ||||
0.129602 | + | 0.991566i | \(0.458630\pi\) | |||||||
\(728\) | −2.56719e12 | −0.338741 | ||||||||
\(729\) | 8.42368e12 | 1.10466 | ||||||||
\(730\) | 1.08842e12 | 0.141854 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −7.73295e12 | −0.995509 | ||||||||
\(733\) | 7.11010e12 | 0.909720 | 0.454860 | − | 0.890563i | \(-0.349689\pi\) | ||||
0.454860 | + | 0.890563i | \(0.349689\pi\) | |||||||
\(734\) | −2.16526e12 | −0.275346 | ||||||||
\(735\) | 9.09947e12 | 1.15007 | ||||||||
\(736\) | −1.48883e12 | −0.187022 | ||||||||
\(737\) | 1.45900e13 | 1.82159 | ||||||||
\(738\) | −3.21609e11 | −0.0399094 | ||||||||
\(739\) | 1.39531e13 | 1.72096 | 0.860479 | − | 0.509486i | \(-0.170164\pi\) | ||||
0.860479 | + | 0.509486i | \(0.170164\pi\) | |||||||
\(740\) | −9.31427e12 | −1.14184 | ||||||||
\(741\) | 2.34473e12 | 0.285701 | ||||||||
\(742\) | −5.66600e12 | −0.686213 | ||||||||
\(743\) | 1.59226e13 | 1.91674 | 0.958371 | − | 0.285525i | \(-0.0921679\pi\) | ||||
0.958371 | + | 0.285525i | \(0.0921679\pi\) | |||||||
\(744\) | −5.26003e12 | −0.629376 | ||||||||
\(745\) | −7.31164e11 | −0.0869584 | ||||||||
\(746\) | 1.37018e12 | 0.161977 | ||||||||
\(747\) | −9.13337e11 | −0.107322 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.60988e12 | 0.419107 | ||||||||
\(750\) | −1.82262e12 | −0.210339 | ||||||||
\(751\) | −1.25896e13 | −1.44421 | −0.722107 | − | 0.691781i | \(-0.756826\pi\) | ||||
−0.722107 | + | 0.691781i | \(0.756826\pi\) | |||||||
\(752\) | −6.15442e12 | −0.701790 | ||||||||
\(753\) | 8.28395e12 | 0.938988 | ||||||||
\(754\) | −1.23990e12 | −0.139706 | ||||||||
\(755\) | −7.08301e12 | −0.793335 | ||||||||
\(756\) | −1.33825e13 | −1.49001 | ||||||||
\(757\) | 1.73721e13 | 1.92275 | 0.961373 | − | 0.275249i | \(-0.0887602\pi\) | ||||
0.961373 | + | 0.275249i | \(0.0887602\pi\) | |||||||
\(758\) | 1.97398e12 | 0.217186 | ||||||||
\(759\) | −2.59245e12 | −0.283545 | ||||||||
\(760\) | −2.81860e12 | −0.306459 | ||||||||
\(761\) | 1.03599e13 | 1.11976 | 0.559882 | − | 0.828572i | \(-0.310846\pi\) | ||||
0.559882 | + | 0.828572i | \(0.310846\pi\) | |||||||
\(762\) | 3.28118e12 | 0.352559 | ||||||||
\(763\) | −6.73347e12 | −0.719248 | ||||||||
\(764\) | −1.15408e12 | −0.122550 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.22728e12 | 0.338694 | ||||||||
\(767\) | −8.39819e12 | −0.876206 | ||||||||
\(768\) | −4.20087e12 | −0.435727 | ||||||||
\(769\) | 4.12658e11 | 0.0425522 | 0.0212761 | − | 0.999774i | \(-0.493227\pi\) | ||||
0.0212761 | + | 0.999774i | \(0.493227\pi\) | |||||||
\(770\) | 3.94986e12 | 0.404924 | ||||||||
\(771\) | 2.26703e12 | 0.231053 | ||||||||
\(772\) | −1.54615e13 | −1.56666 | ||||||||
\(773\) | −6.07702e12 | −0.612185 | −0.306093 | − | 0.952002i | \(-0.599022\pi\) | ||||
−0.306093 | + | 0.952002i | \(0.599022\pi\) | |||||||
\(774\) | 1.92296e11 | 0.0192591 | ||||||||
\(775\) | −1.11207e12 | −0.110732 | ||||||||
\(776\) | 5.21873e12 | 0.516639 | ||||||||
\(777\) | 1.61734e13 | 1.59186 | ||||||||
\(778\) | 3.13046e12 | 0.306337 | ||||||||
\(779\) | −6.82023e12 | −0.663560 | ||||||||
\(780\) | −4.53999e12 | −0.439167 | ||||||||
\(781\) | −6.83802e12 | −0.657659 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.33194e13 | −1.26636 | ||||||||
\(784\) | 1.06450e13 | 1.00629 | ||||||||
\(785\) | 1.30081e12 | 0.122265 | ||||||||
\(786\) | −3.65297e12 | −0.341385 | ||||||||
\(787\) | −1.63722e12 | −0.152132 | −0.0760660 | − | 0.997103i | \(-0.524236\pi\) | ||||
−0.0760660 | + | 0.997103i | \(0.524236\pi\) | |||||||
\(788\) | −1.19461e13 | −1.10372 | ||||||||
\(789\) | −9.07051e12 | −0.833269 | ||||||||
\(790\) | −5.10833e12 | −0.466613 | ||||||||
\(791\) | 1.18471e13 | 1.07601 | ||||||||
\(792\) | −9.03300e11 | −0.0815772 | ||||||||
\(793\) | −6.28856e12 | −0.564705 | ||||||||
\(794\) | −5.09900e11 | −0.0455295 | ||||||||
\(795\) | −2.06487e13 | −1.83333 | ||||||||
\(796\) | 5.09991e12 | 0.450250 | ||||||||
\(797\) | 6.48377e12 | 0.569200 | 0.284600 | − | 0.958646i | \(-0.408139\pi\) | ||||
0.284600 | + | 0.958646i | \(0.408139\pi\) | |||||||
\(798\) | 2.37501e12 | 0.207325 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 5.76479e11 | 0.0497598 | ||||||||
\(801\) | 2.71936e11 | 0.0233411 | ||||||||
\(802\) | 2.88781e12 | 0.246481 | ||||||||
\(803\) | 7.39714e12 | 0.627833 | ||||||||
\(804\) | −1.69863e13 | −1.43366 | ||||||||
\(805\) | 5.17429e12 | 0.434280 | ||||||||
\(806\) | −2.07575e12 | −0.173247 | ||||||||
\(807\) | 7.49704e12 | 0.622241 | ||||||||
\(808\) | 8.67688e11 | 0.0716164 | ||||||||
\(809\) | −1.49241e12 | −0.122496 | −0.0612478 | − | 0.998123i | \(-0.519508\pi\) | ||||
−0.0612478 | + | 0.998123i | \(0.519508\pi\) | |||||||
\(810\) | 2.47578e12 | 0.202083 | ||||||||
\(811\) | 1.02148e13 | 0.829153 | 0.414576 | − | 0.910015i | \(-0.363930\pi\) | ||||
0.414576 | + | 0.910015i | \(0.363930\pi\) | |||||||
\(812\) | 2.06819e13 | 1.66951 | ||||||||
\(813\) | 7.27293e12 | 0.583851 | ||||||||
\(814\) | 3.84402e12 | 0.306885 | ||||||||
\(815\) | −1.18440e13 | −0.940350 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.07794e12 | 0.320215 | ||||||||
\(818\) | −1.69561e12 | −0.132415 | ||||||||
\(819\) | −1.49980e12 | −0.116481 | ||||||||
\(820\) | 1.32057e13 | 1.02000 | ||||||||
\(821\) | 2.08043e13 | 1.59812 | 0.799060 | − | 0.601251i | \(-0.205331\pi\) | ||||
0.799060 | + | 0.601251i | \(0.205331\pi\) | |||||||
\(822\) | −2.43898e12 | −0.186331 | ||||||||
\(823\) | 1.92775e13 | 1.46471 | 0.732354 | − | 0.680924i | \(-0.238422\pi\) | ||||
0.732354 | + | 0.680924i | \(0.238422\pi\) | |||||||
\(824\) | −3.30499e12 | −0.249746 | ||||||||
\(825\) | 1.00381e12 | 0.0754409 | ||||||||
\(826\) | −8.50662e12 | −0.635839 | ||||||||
\(827\) | −1.99779e11 | −0.0148517 | −0.00742583 | − | 0.999972i | \(-0.502364\pi\) | ||||
−0.00742583 | + | 0.999972i | \(0.502364\pi\) | |||||||
\(828\) | −5.74224e11 | −0.0424566 | ||||||||
\(829\) | −1.49162e13 | −1.09689 | −0.548446 | − | 0.836186i | \(-0.684780\pi\) | ||||
−0.548446 | + | 0.836186i | \(0.684780\pi\) | |||||||
\(830\) | −2.27736e12 | −0.166564 | ||||||||
\(831\) | −1.56352e13 | −1.13736 | ||||||||
\(832\) | −4.55760e12 | −0.329747 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.09653e12 | 0.293204 | ||||||||
\(835\) | 3.07456e12 | 0.218874 | ||||||||
\(836\) | −9.29570e12 | −0.658194 | ||||||||
\(837\) | −2.22984e13 | −1.57039 | ||||||||
\(838\) | 5.31719e12 | 0.372464 | ||||||||
\(839\) | −1.89640e13 | −1.32130 | −0.660649 | − | 0.750695i | \(-0.729719\pi\) | ||||
−0.660649 | + | 0.750695i | \(0.729719\pi\) | |||||||
\(840\) | −9.47648e12 | −0.656735 | ||||||||
\(841\) | 6.07730e12 | 0.418918 | ||||||||
\(842\) | 9.39803e11 | 0.0644366 | ||||||||
\(843\) | 1.72626e12 | 0.117729 | ||||||||
\(844\) | 2.20662e13 | 1.49688 | ||||||||
\(845\) | 1.16737e13 | 0.787685 | ||||||||
\(846\) | 4.80912e11 | 0.0322774 | ||||||||
\(847\) | 4.57585e12 | 0.305489 | ||||||||
\(848\) | −2.41559e13 | −1.60414 | ||||||||
\(849\) | 1.93703e13 | 1.27953 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.03565e12 | 0.329134 | ||||||||
\(852\) | 7.96115e12 | 0.517604 | ||||||||
\(853\) | 4.00742e12 | 0.259176 | 0.129588 | − | 0.991568i | \(-0.458635\pi\) | ||||
0.129588 | + | 0.991568i | \(0.458635\pi\) | |||||||
\(854\) | −6.36976e12 | −0.409791 | ||||||||
\(855\) | −1.64667e12 | −0.105380 | ||||||||
\(856\) | −2.05847e12 | −0.131042 | ||||||||
\(857\) | 1.02490e13 | 0.649033 | 0.324517 | − | 0.945880i | \(-0.394798\pi\) | ||||
0.324517 | + | 0.945880i | \(0.394798\pi\) | |||||||
\(858\) | 1.87367e12 | 0.118032 | ||||||||
\(859\) | 9.08859e12 | 0.569544 | 0.284772 | − | 0.958595i | \(-0.408082\pi\) | ||||
0.284772 | + | 0.958595i | \(0.408082\pi\) | |||||||
\(860\) | −7.89593e12 | −0.492221 | ||||||||
\(861\) | −2.29304e13 | −1.42200 | ||||||||
\(862\) | −1.91834e12 | −0.118343 | ||||||||
\(863\) | 1.47122e13 | 0.902878 | 0.451439 | − | 0.892302i | \(-0.350911\pi\) | ||||
0.451439 | + | 0.892302i | \(0.350911\pi\) | |||||||
\(864\) | 1.15591e13 | 0.705688 | ||||||||
\(865\) | −1.97890e13 | −1.20185 | ||||||||
\(866\) | 3.62678e8 | 2.19124e−5 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.46241e13 | 2.07033 | ||||||||
\(869\) | −3.47175e13 | −2.06518 | ||||||||
\(870\) | −4.57694e12 | −0.270856 | ||||||||
\(871\) | −1.38136e13 | −0.813250 | ||||||||
\(872\) | 3.83964e12 | 0.224888 | ||||||||
\(873\) | 3.04887e12 | 0.177654 | ||||||||
\(874\) | 7.39469e11 | 0.0428666 | ||||||||
\(875\) | 2.47232e13 | 1.42583 | ||||||||
\(876\) | −8.61211e12 | −0.494130 | ||||||||
\(877\) | −2.05098e12 | −0.117075 | −0.0585373 | − | 0.998285i | \(-0.518644\pi\) | ||||
−0.0585373 | + | 0.998285i | \(0.518644\pi\) | |||||||
\(878\) | −2.44541e12 | −0.138876 | ||||||||
\(879\) | −2.97379e13 | −1.68020 | ||||||||
\(880\) | 1.68395e13 | 0.946578 | ||||||||
\(881\) | 1.10960e13 | 0.620550 | 0.310275 | − | 0.950647i | \(-0.399579\pi\) | ||||
0.310275 | + | 0.950647i | \(0.399579\pi\) | |||||||
\(882\) | −8.31811e11 | −0.0462824 | ||||||||
\(883\) | 1.24270e13 | 0.687931 | 0.343965 | − | 0.938982i | \(-0.388230\pi\) | ||||
0.343965 | + | 0.938982i | \(0.388230\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.10009e13 | −1.69875 | ||||||||
\(886\) | 4.12006e12 | 0.224622 | ||||||||
\(887\) | 1.86959e13 | 1.01412 | 0.507061 | − | 0.861910i | \(-0.330732\pi\) | ||||
0.507061 | + | 0.861910i | \(0.330732\pi\) | |||||||
\(888\) | −9.22255e12 | −0.497729 | ||||||||
\(889\) | −4.45081e13 | −2.38991 | ||||||||
\(890\) | 6.78059e11 | 0.0362253 | ||||||||
\(891\) | 1.68260e13 | 0.894398 | ||||||||
\(892\) | 5.11840e12 | 0.270703 | ||||||||
\(893\) | 1.01985e13 | 0.536666 | ||||||||
\(894\) | −3.51315e11 | −0.0183941 | ||||||||
\(895\) | 2.93660e13 | 1.52982 | ||||||||
\(896\) | −2.36549e13 | −1.22613 | ||||||||
\(897\) | 2.45449e12 | 0.126589 | ||||||||
\(898\) | −2.72724e10 | −0.00139952 | ||||||||
\(899\) | 3.44609e13 | 1.75958 | ||||||||
\(900\) | 2.22342e11 | 0.0112961 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −5.45002e12 | −0.274138 | ||||||||
\(903\) | 1.37105e13 | 0.686214 | ||||||||
\(904\) | −6.75556e12 | −0.336437 | ||||||||
\(905\) | 3.84411e13 | 1.90492 | ||||||||
\(906\) | −3.40330e12 | −0.167812 | ||||||||
\(907\) | −1.01605e13 | −0.498519 | −0.249259 | − | 0.968437i | \(-0.580187\pi\) | ||||
−0.249259 | + | 0.968437i | \(0.580187\pi\) | |||||||
\(908\) | −1.53395e12 | −0.0748902 | ||||||||
\(909\) | 5.06917e11 | 0.0246263 | ||||||||
\(910\) | −3.73967e12 | −0.180779 | ||||||||
\(911\) | −4.35827e12 | −0.209644 | −0.104822 | − | 0.994491i | \(-0.533427\pi\) | ||||
−0.104822 | + | 0.994491i | \(0.533427\pi\) | |||||||
\(912\) | 1.01254e13 | 0.484658 | ||||||||
\(913\) | −1.54775e13 | −0.737194 | ||||||||
\(914\) | −3.96030e12 | −0.187702 | ||||||||
\(915\) | −2.32134e13 | −1.09482 | ||||||||
\(916\) | 2.73503e13 | 1.28361 | ||||||||
\(917\) | 4.95514e13 | 2.31416 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.96170e12 | −0.460695 | −0.230348 | − | 0.973108i | \(-0.573986\pi\) | ||||
−0.230348 | + | 0.973108i | \(0.573986\pi\) | |||||||
\(920\) | −2.95054e12 | −0.135787 | ||||||||
\(921\) | 4.17768e12 | 0.191323 | ||||||||
\(922\) | 4.05378e12 | 0.184744 | ||||||||
\(923\) | 6.47414e12 | 0.293612 | ||||||||
\(924\) | −3.12533e13 | −1.41050 | ||||||||
\(925\) | −1.94982e12 | −0.0875704 | ||||||||
\(926\) | 7.15033e11 | 0.0319578 | ||||||||
\(927\) | −1.93083e12 | −0.0858786 | ||||||||
\(928\) | −1.78640e13 | −0.790701 | ||||||||
\(929\) | 1.47335e13 | 0.648985 | 0.324492 | − | 0.945888i | \(-0.394807\pi\) | ||||
0.324492 | + | 0.945888i | \(0.394807\pi\) | |||||||
\(930\) | −7.66237e12 | −0.335884 | ||||||||
\(931\) | −1.76399e13 | −0.769523 | ||||||||
\(932\) | −3.10972e13 | −1.35005 | ||||||||
\(933\) | −3.13173e13 | −1.35306 | ||||||||
\(934\) | −6.29649e11 | −0.0270731 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.55231e11 | 0.0364202 | ||||||||
\(937\) | −3.24887e13 | −1.37691 | −0.688453 | − | 0.725280i | \(-0.741710\pi\) | ||||
−0.688453 | + | 0.725280i | \(0.741710\pi\) | |||||||
\(938\) | −1.39919e13 | −0.590153 | ||||||||
\(939\) | 1.29535e11 | 0.00543739 | ||||||||
\(940\) | −1.97468e13 | −0.824940 | ||||||||
\(941\) | 1.89258e13 | 0.786868 | 0.393434 | − | 0.919353i | \(-0.371287\pi\) | ||||
0.393434 | + | 0.919353i | \(0.371287\pi\) | |||||||
\(942\) | 6.25026e11 | 0.0258624 | ||||||||
\(943\) | −7.13950e12 | −0.294012 | ||||||||
\(944\) | −3.62664e13 | −1.48638 | ||||||||
\(945\) | −4.01728e13 | −1.63866 | ||||||||
\(946\) | 3.25867e12 | 0.132291 | ||||||||
\(947\) | 1.03479e13 | 0.418097 | 0.209049 | − | 0.977905i | \(-0.432963\pi\) | ||||
0.209049 | + | 0.977905i | \(0.432963\pi\) | |||||||
\(948\) | 4.04197e13 | 1.62538 | ||||||||
\(949\) | −7.00351e12 | −0.280297 | ||||||||
\(950\) | −2.86325e11 | −0.0114052 | ||||||||
\(951\) | 2.71890e13 | 1.07791 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.52060e13 | −0.989888 | −0.494944 | − | 0.868925i | \(-0.664811\pi\) | ||||
−0.494944 | + | 0.868925i | \(0.664811\pi\) | |||||||
\(954\) | 1.88756e12 | 0.0737792 | ||||||||
\(955\) | −3.46441e12 | −0.134776 | ||||||||
\(956\) | 1.85017e13 | 0.716391 | ||||||||
\(957\) | −3.11060e13 | −1.19878 | ||||||||
\(958\) | 1.42700e12 | 0.0547366 | ||||||||
\(959\) | 3.30839e13 | 1.26309 | ||||||||
\(960\) | −1.68238e13 | −0.639299 | ||||||||
\(961\) | 3.12522e13 | 1.18202 | ||||||||
\(962\) | −3.63946e12 | −0.137009 | ||||||||
\(963\) | −1.20259e12 | −0.0450609 | ||||||||
\(964\) | −3.46466e12 | −0.129215 | ||||||||
\(965\) | −4.64137e13 | −1.72295 | ||||||||
\(966\) | 2.48619e12 | 0.0918621 | ||||||||
\(967\) | −2.89363e13 | −1.06420 | −0.532101 | − | 0.846681i | \(-0.678597\pi\) | ||||
−0.532101 | + | 0.846681i | \(0.678597\pi\) | |||||||
\(968\) | −2.60929e12 | −0.0955176 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.60221e12 | 0.275719 | ||||||||
\(971\) | −5.37388e13 | −1.94000 | −0.969999 | − | 0.243110i | \(-0.921833\pi\) | ||||
−0.969999 | + | 0.243110i | \(0.921833\pi\) | |||||||
\(972\) | 8.30205e12 | 0.298323 | ||||||||
\(973\) | −5.55682e13 | −1.98755 | ||||||||
\(974\) | 2.82233e12 | 0.100483 | ||||||||
\(975\) | −9.50389e11 | −0.0336807 | ||||||||
\(976\) | −2.71563e13 | −0.957956 | ||||||||
\(977\) | −4.64572e13 | −1.63128 | −0.815638 | − | 0.578562i | \(-0.803614\pi\) | ||||
−0.815638 | + | 0.578562i | \(0.803614\pi\) | |||||||
\(978\) | −5.69090e12 | −0.198910 | ||||||||
\(979\) | 4.60825e12 | 0.160330 | ||||||||
\(980\) | 3.41552e13 | 1.18288 | ||||||||
\(981\) | 2.24318e12 | 0.0773310 | ||||||||
\(982\) | −1.33416e13 | −0.457831 | ||||||||
\(983\) | −2.41824e13 | −0.826055 | −0.413027 | − | 0.910719i | \(-0.635529\pi\) | ||||
−0.413027 | + | 0.910719i | \(0.635529\pi\) | |||||||
\(984\) | 1.30757e13 | 0.444616 | ||||||||
\(985\) | −3.58608e13 | −1.21383 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.42885e13 | 1.15006 | ||||||||
\(988\) | 8.80104e12 | 0.293851 | ||||||||
\(989\) | 4.26884e12 | 0.141882 | ||||||||
\(990\) | −1.31585e12 | −0.0435360 | ||||||||
\(991\) | −2.08758e13 | −0.687563 | −0.343781 | − | 0.939050i | \(-0.611708\pi\) | ||||
−0.343781 | + | 0.939050i | \(0.611708\pi\) | |||||||
\(992\) | −2.99065e13 | −0.980534 | ||||||||
\(993\) | 1.35515e13 | 0.442300 | ||||||||
\(994\) | 6.55773e12 | 0.213066 | ||||||||
\(995\) | 1.53094e13 | 0.495169 | ||||||||
\(996\) | 1.80196e13 | 0.580201 | ||||||||
\(997\) | −1.59134e13 | −0.510075 | −0.255038 | − | 0.966931i | \(-0.582088\pi\) | ||||
−0.255038 | + | 0.966931i | \(0.582088\pi\) | |||||||
\(998\) | 6.48621e12 | 0.206968 | ||||||||
\(999\) | −3.90963e13 | −1.24191 |
(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 | 289.10.a.h.1.21 | yes | 36 | |
17.16 | even | 2 | 289.10.a.g.1.21 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.21 | ✓ | 36 | 17.16 | even | 2 | ||
289.10.a.h.1.21 | yes | 36 | 1.1 | even | 1 | trivial |