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 | 1.18 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.07469 | −0.135883 | −0.0679416 | − | 0.997689i | \(-0.521643\pi\) | ||||
−0.0679416 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(3\) | −18.6108 | −0.132653 | −0.0663267 | − | 0.997798i | \(-0.521128\pi\) | ||||
−0.0663267 | + | 0.997798i | \(0.521128\pi\) | |||||||
\(4\) | −502.546 | −0.981536 | ||||||||
\(5\) | 2540.06 | 1.81752 | 0.908760 | − | 0.417319i | \(-0.137030\pi\) | ||||
0.908760 | + | 0.417319i | \(0.137030\pi\) | |||||||
\(6\) | 57.2223 | 0.0180254 | ||||||||
\(7\) | 10949.3 | 1.72364 | 0.861821 | − | 0.507213i | \(-0.169324\pi\) | ||||
0.861821 | + | 0.507213i | \(0.169324\pi\) | |||||||
\(8\) | 3119.41 | 0.269258 | ||||||||
\(9\) | −19336.6 | −0.982403 | ||||||||
\(10\) | −7809.90 | −0.246971 | ||||||||
\(11\) | −55022.0 | −1.13310 | −0.566552 | − | 0.824026i | \(-0.691723\pi\) | ||||
−0.566552 | + | 0.824026i | \(0.691723\pi\) | |||||||
\(12\) | 9352.77 | 0.130204 | ||||||||
\(13\) | −101901. | −0.989539 | −0.494770 | − | 0.869024i | \(-0.664748\pi\) | ||||
−0.494770 | + | 0.869024i | \(0.664748\pi\) | |||||||
\(14\) | −33665.8 | −0.234214 | ||||||||
\(15\) | −47272.5 | −0.241100 | ||||||||
\(16\) | 247712. | 0.944948 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 59454.1 | 0.133492 | ||||||||
\(19\) | −243294. | −0.428292 | −0.214146 | − | 0.976802i | \(-0.568697\pi\) | ||||
−0.214146 | + | 0.976802i | \(0.568697\pi\) | |||||||
\(20\) | −1.27650e6 | −1.78396 | ||||||||
\(21\) | −203776. | −0.228647 | ||||||||
\(22\) | 169176. | 0.153970 | ||||||||
\(23\) | 799065. | 0.595397 | 0.297699 | − | 0.954660i | \(-0.403781\pi\) | ||||
0.297699 | + | 0.954660i | \(0.403781\pi\) | |||||||
\(24\) | −58054.7 | −0.0357180 | ||||||||
\(25\) | 4.49879e6 | 2.30338 | ||||||||
\(26\) | 313313. | 0.134462 | ||||||||
\(27\) | 726185. | 0.262973 | ||||||||
\(28\) | −5.50255e6 | −1.69182 | ||||||||
\(29\) | −1.08920e6 | −0.285967 | −0.142984 | − | 0.989725i | \(-0.545670\pi\) | ||||
−0.142984 | + | 0.989725i | \(0.545670\pi\) | |||||||
\(30\) | 145348. | 0.0327615 | ||||||||
\(31\) | 6.11921e6 | 1.19006 | 0.595028 | − | 0.803705i | \(-0.297141\pi\) | ||||
0.595028 | + | 0.803705i | \(0.297141\pi\) | |||||||
\(32\) | −2.35878e6 | −0.397660 | ||||||||
\(33\) | 1.02400e6 | 0.150310 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.78120e7 | 3.13275 | ||||||||
\(36\) | 9.71756e6 | 0.964264 | ||||||||
\(37\) | −1.09051e7 | −0.956578 | −0.478289 | − | 0.878203i | \(-0.658743\pi\) | ||||
−0.478289 | + | 0.878203i | \(0.658743\pi\) | |||||||
\(38\) | 748053. | 0.0581978 | ||||||||
\(39\) | 1.89645e6 | 0.131266 | ||||||||
\(40\) | 7.92350e6 | 0.489381 | ||||||||
\(41\) | −2.74132e6 | −0.151507 | −0.0757534 | − | 0.997127i | \(-0.524136\pi\) | ||||
−0.0757534 | + | 0.997127i | \(0.524136\pi\) | |||||||
\(42\) | 626547. | 0.0310693 | ||||||||
\(43\) | 3.55746e7 | 1.58684 | 0.793419 | − | 0.608676i | \(-0.208299\pi\) | ||||
0.793419 | + | 0.608676i | \(0.208299\pi\) | |||||||
\(44\) | 2.76511e7 | 1.11218 | ||||||||
\(45\) | −4.91163e7 | −1.78554 | ||||||||
\(46\) | −2.45687e6 | −0.0809045 | ||||||||
\(47\) | −1.19501e7 | −0.357215 | −0.178607 | − | 0.983920i | \(-0.557159\pi\) | ||||
−0.178607 | + | 0.983920i | \(0.557159\pi\) | |||||||
\(48\) | −4.61012e6 | −0.125351 | ||||||||
\(49\) | 7.95346e7 | 1.97094 | ||||||||
\(50\) | −1.38324e7 | −0.312991 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.12099e7 | 0.971268 | ||||||||
\(53\) | 6.12587e7 | 1.06641 | 0.533207 | − | 0.845985i | \(-0.320987\pi\) | ||||
0.533207 | + | 0.845985i | \(0.320987\pi\) | |||||||
\(54\) | −2.23279e6 | −0.0357336 | ||||||||
\(55\) | −1.39759e8 | −2.05944 | ||||||||
\(56\) | 3.41555e7 | 0.464104 | ||||||||
\(57\) | 4.52789e6 | 0.0568144 | ||||||||
\(58\) | 3.34895e6 | 0.0388582 | ||||||||
\(59\) | −7.89274e7 | −0.847996 | −0.423998 | − | 0.905663i | \(-0.639374\pi\) | ||||
−0.423998 | + | 0.905663i | \(0.639374\pi\) | |||||||
\(60\) | 2.37566e7 | 0.236649 | ||||||||
\(61\) | −5.32867e7 | −0.492759 | −0.246379 | − | 0.969173i | \(-0.579241\pi\) | ||||
−0.246379 | + | 0.969173i | \(0.579241\pi\) | |||||||
\(62\) | −1.88147e7 | −0.161709 | ||||||||
\(63\) | −2.11724e8 | −1.69331 | ||||||||
\(64\) | −1.19576e8 | −0.890913 | ||||||||
\(65\) | −2.58835e8 | −1.79851 | ||||||||
\(66\) | −3.14849e6 | −0.0204246 | ||||||||
\(67\) | −1.84553e8 | −1.11888 | −0.559441 | − | 0.828870i | \(-0.688984\pi\) | ||||
−0.559441 | + | 0.828870i | \(0.688984\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.48712e7 | −0.0789815 | ||||||||
\(70\) | −8.55133e7 | −0.425689 | ||||||||
\(71\) | 1.25020e8 | 0.583871 | 0.291935 | − | 0.956438i | \(-0.405701\pi\) | ||||
0.291935 | + | 0.956438i | \(0.405701\pi\) | |||||||
\(72\) | −6.03190e7 | −0.264520 | ||||||||
\(73\) | −9.89488e6 | −0.0407810 | −0.0203905 | − | 0.999792i | \(-0.506491\pi\) | ||||
−0.0203905 | + | 0.999792i | \(0.506491\pi\) | |||||||
\(74\) | 3.35297e7 | 0.129983 | ||||||||
\(75\) | −8.37259e7 | −0.305551 | ||||||||
\(76\) | 1.22267e8 | 0.420384 | ||||||||
\(77\) | −6.02455e8 | −1.95306 | ||||||||
\(78\) | −5.83100e6 | −0.0178368 | ||||||||
\(79\) | 3.48965e8 | 1.00800 | 0.504000 | − | 0.863704i | \(-0.331861\pi\) | ||||
0.504000 | + | 0.863704i | \(0.331861\pi\) | |||||||
\(80\) | 6.29205e8 | 1.71746 | ||||||||
\(81\) | 3.67088e8 | 0.947519 | ||||||||
\(82\) | 8.42870e6 | 0.0205872 | ||||||||
\(83\) | −1.63123e8 | −0.377281 | −0.188641 | − | 0.982046i | \(-0.560408\pi\) | ||||
−0.188641 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(84\) | 1.02407e8 | 0.224425 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.09381e8 | −0.215625 | ||||||||
\(87\) | 2.02708e7 | 0.0379346 | ||||||||
\(88\) | −1.71636e8 | −0.305097 | ||||||||
\(89\) | 1.08465e9 | 1.83246 | 0.916229 | − | 0.400656i | \(-0.131218\pi\) | ||||
0.916229 | + | 0.400656i | \(0.131218\pi\) | |||||||
\(90\) | 1.51017e8 | 0.242625 | ||||||||
\(91\) | −1.11575e9 | −1.70561 | ||||||||
\(92\) | −4.01567e8 | −0.584404 | ||||||||
\(93\) | −1.13883e8 | −0.157865 | ||||||||
\(94\) | 3.67427e7 | 0.0485395 | ||||||||
\(95\) | −6.17982e8 | −0.778430 | ||||||||
\(96\) | 4.38987e7 | 0.0527510 | ||||||||
\(97\) | 1.20151e8 | 0.137802 | 0.0689009 | − | 0.997624i | \(-0.478051\pi\) | ||||
0.0689009 | + | 0.997624i | \(0.478051\pi\) | |||||||
\(98\) | −2.44544e8 | −0.267818 | ||||||||
\(99\) | 1.06394e9 | 1.11316 | ||||||||
\(100\) | −2.26085e9 | −2.26085 | ||||||||
\(101\) | 1.08867e9 | 1.04100 | 0.520498 | − | 0.853863i | \(-0.325746\pi\) | ||||
0.520498 | + | 0.853863i | \(0.325746\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.18252e9 | −1.03524 | −0.517622 | − | 0.855610i | \(-0.673183\pi\) | ||||
−0.517622 | + | 0.855610i | \(0.673183\pi\) | |||||||
\(104\) | −3.17871e8 | −0.266441 | ||||||||
\(105\) | −5.17603e8 | −0.415571 | ||||||||
\(106\) | −1.88351e8 | −0.144908 | ||||||||
\(107\) | 1.49518e9 | 1.10272 | 0.551361 | − | 0.834267i | \(-0.314109\pi\) | ||||
0.551361 | + | 0.834267i | \(0.314109\pi\) | |||||||
\(108\) | −3.64942e8 | −0.258117 | ||||||||
\(109\) | 2.08481e9 | 1.41464 | 0.707321 | − | 0.706892i | \(-0.249903\pi\) | ||||
0.707321 | + | 0.706892i | \(0.249903\pi\) | |||||||
\(110\) | 4.29716e8 | 0.279843 | ||||||||
\(111\) | 2.02952e8 | 0.126893 | ||||||||
\(112\) | 2.71229e9 | 1.62875 | ||||||||
\(113\) | 7.38570e8 | 0.426126 | 0.213063 | − | 0.977038i | \(-0.431656\pi\) | ||||
0.213063 | + | 0.977038i | \(0.431656\pi\) | |||||||
\(114\) | −1.39218e7 | −0.00772013 | ||||||||
\(115\) | 2.02967e9 | 1.08215 | ||||||||
\(116\) | 5.47373e8 | 0.280687 | ||||||||
\(117\) | 1.97042e9 | 0.972126 | ||||||||
\(118\) | 2.42677e8 | 0.115229 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.47462e8 | −0.0649181 | ||||||||
\(121\) | 6.69477e8 | 0.283924 | ||||||||
\(122\) | 1.63840e8 | 0.0669577 | ||||||||
\(123\) | 5.10180e7 | 0.0200979 | ||||||||
\(124\) | −3.07519e9 | −1.16808 | ||||||||
\(125\) | 6.46614e9 | 2.36892 | ||||||||
\(126\) | 6.50984e8 | 0.230093 | ||||||||
\(127\) | −2.74828e9 | −0.937441 | −0.468721 | − | 0.883346i | \(-0.655285\pi\) | ||||
−0.468721 | + | 0.883346i | \(0.655285\pi\) | |||||||
\(128\) | 1.57535e9 | 0.518720 | ||||||||
\(129\) | −6.62071e8 | −0.210499 | ||||||||
\(130\) | 7.95836e8 | 0.244387 | ||||||||
\(131\) | −5.20552e9 | −1.54434 | −0.772170 | − | 0.635416i | \(-0.780829\pi\) | ||||
−0.772170 | + | 0.635416i | \(0.780829\pi\) | |||||||
\(132\) | −5.14609e8 | −0.147535 | ||||||||
\(133\) | −2.66391e9 | −0.738223 | ||||||||
\(134\) | 5.67442e8 | 0.152037 | ||||||||
\(135\) | 1.84456e9 | 0.477958 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.18810e9 | 1.50077 | 0.750386 | − | 0.661000i | \(-0.229868\pi\) | ||||
0.750386 | + | 0.661000i | \(0.229868\pi\) | |||||||
\(138\) | 4.57243e7 | 0.0107323 | ||||||||
\(139\) | −1.88233e9 | −0.427690 | −0.213845 | − | 0.976868i | \(-0.568599\pi\) | ||||
−0.213845 | + | 0.976868i | \(0.568599\pi\) | |||||||
\(140\) | −1.39768e10 | −3.07491 | ||||||||
\(141\) | 2.22400e8 | 0.0473858 | ||||||||
\(142\) | −3.84397e8 | −0.0793383 | ||||||||
\(143\) | 5.60680e9 | 1.12125 | ||||||||
\(144\) | −4.78993e9 | −0.928320 | ||||||||
\(145\) | −2.76663e9 | −0.519751 | ||||||||
\(146\) | 3.04237e7 | 0.00554146 | ||||||||
\(147\) | −1.48020e9 | −0.261452 | ||||||||
\(148\) | 5.48030e9 | 0.938915 | ||||||||
\(149\) | 8.74040e9 | 1.45276 | 0.726378 | − | 0.687295i | \(-0.241202\pi\) | ||||
0.726378 | + | 0.687295i | \(0.241202\pi\) | |||||||
\(150\) | 2.57431e8 | 0.0415193 | ||||||||
\(151\) | 4.41501e9 | 0.691091 | 0.345546 | − | 0.938402i | \(-0.387694\pi\) | ||||
0.345546 | + | 0.938402i | \(0.387694\pi\) | |||||||
\(152\) | −7.58935e8 | −0.115321 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.85236e9 | 0.265389 | ||||||||
\(155\) | 1.55432e10 | 2.16295 | ||||||||
\(156\) | −9.53056e8 | −0.128842 | ||||||||
\(157\) | 1.83214e9 | 0.240664 | 0.120332 | − | 0.992734i | \(-0.461604\pi\) | ||||
0.120332 | + | 0.992734i | \(0.461604\pi\) | |||||||
\(158\) | −1.07296e9 | −0.136970 | ||||||||
\(159\) | −1.14007e9 | −0.141464 | ||||||||
\(160\) | −5.99144e9 | −0.722756 | ||||||||
\(161\) | 8.74924e9 | 1.02625 | ||||||||
\(162\) | −1.12868e9 | −0.128752 | ||||||||
\(163\) | 3.05664e9 | 0.339156 | 0.169578 | − | 0.985517i | \(-0.445759\pi\) | ||||
0.169578 | + | 0.985517i | \(0.445759\pi\) | |||||||
\(164\) | 1.37764e9 | 0.148709 | ||||||||
\(165\) | 2.60103e9 | 0.273192 | ||||||||
\(166\) | 5.01554e8 | 0.0512662 | ||||||||
\(167\) | −5.54078e9 | −0.551248 | −0.275624 | − | 0.961266i | \(-0.588884\pi\) | ||||
−0.275624 | + | 0.961266i | \(0.588884\pi\) | |||||||
\(168\) | −6.35661e8 | −0.0615650 | ||||||||
\(169\) | −2.20706e8 | −0.0208124 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.70449e9 | 0.420756 | ||||||||
\(172\) | −1.78779e10 | −1.55754 | ||||||||
\(173\) | −2.19119e10 | −1.85983 | −0.929914 | − | 0.367778i | \(-0.880119\pi\) | ||||
−0.929914 | + | 0.367778i | \(0.880119\pi\) | |||||||
\(174\) | −6.23265e7 | −0.00515467 | ||||||||
\(175\) | 4.92588e10 | 3.97020 | ||||||||
\(176\) | −1.36296e10 | −1.07072 | ||||||||
\(177\) | 1.46890e9 | 0.112490 | ||||||||
\(178\) | −3.33495e9 | −0.249000 | ||||||||
\(179\) | −7.29594e9 | −0.531181 | −0.265591 | − | 0.964086i | \(-0.585567\pi\) | ||||
−0.265591 | + | 0.964086i | \(0.585567\pi\) | |||||||
\(180\) | 2.46832e10 | 1.75257 | ||||||||
\(181\) | 2.75510e10 | 1.90802 | 0.954011 | − | 0.299770i | \(-0.0969100\pi\) | ||||
0.954011 | + | 0.299770i | \(0.0969100\pi\) | |||||||
\(182\) | 3.43058e9 | 0.231764 | ||||||||
\(183\) | 9.91705e8 | 0.0653661 | ||||||||
\(184\) | 2.49261e9 | 0.160315 | ||||||||
\(185\) | −2.76995e10 | −1.73860 | ||||||||
\(186\) | 3.50155e8 | 0.0214512 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.00545e9 | 0.350619 | ||||||||
\(189\) | 7.95126e9 | 0.453271 | ||||||||
\(190\) | 1.90010e9 | 0.105776 | ||||||||
\(191\) | 8.40002e9 | 0.456699 | 0.228350 | − | 0.973579i | \(-0.426667\pi\) | ||||
0.228350 | + | 0.973579i | \(0.426667\pi\) | |||||||
\(192\) | 2.22541e9 | 0.118183 | ||||||||
\(193\) | −2.32479e10 | −1.20608 | −0.603040 | − | 0.797711i | \(-0.706044\pi\) | ||||
−0.603040 | + | 0.797711i | \(0.706044\pi\) | |||||||
\(194\) | −3.69427e8 | −0.0187250 | ||||||||
\(195\) | 4.81711e9 | 0.238578 | ||||||||
\(196\) | −3.99698e10 | −1.93455 | ||||||||
\(197\) | −2.22594e10 | −1.05297 | −0.526485 | − | 0.850185i | \(-0.676490\pi\) | ||||
−0.526485 | + | 0.850185i | \(0.676490\pi\) | |||||||
\(198\) | −3.27129e9 | −0.151260 | ||||||||
\(199\) | 1.96549e10 | 0.888447 | 0.444223 | − | 0.895916i | \(-0.353480\pi\) | ||||
0.444223 | + | 0.895916i | \(0.353480\pi\) | |||||||
\(200\) | 1.40336e10 | 0.620202 | ||||||||
\(201\) | 3.43467e9 | 0.148423 | ||||||||
\(202\) | −3.34731e9 | −0.141454 | ||||||||
\(203\) | −1.19260e10 | −0.492905 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.96312e9 | −0.275367 | ||||||||
\(206\) | 3.63589e9 | 0.140672 | ||||||||
\(207\) | −1.54512e10 | −0.584920 | ||||||||
\(208\) | −2.52421e10 | −0.935063 | ||||||||
\(209\) | 1.33865e10 | 0.485299 | ||||||||
\(210\) | 1.59147e9 | 0.0564691 | ||||||||
\(211\) | 2.13271e10 | 0.740730 | 0.370365 | − | 0.928886i | \(-0.379233\pi\) | ||||
0.370365 | + | 0.928886i | \(0.379233\pi\) | |||||||
\(212\) | −3.07853e10 | −1.04672 | ||||||||
\(213\) | −2.32672e9 | −0.0774525 | ||||||||
\(214\) | −4.59721e9 | −0.149842 | ||||||||
\(215\) | 9.03618e10 | 2.88411 | ||||||||
\(216\) | 2.26527e9 | 0.0708074 | ||||||||
\(217\) | 6.70013e10 | 2.05123 | ||||||||
\(218\) | −6.41013e9 | −0.192226 | ||||||||
\(219\) | 1.84151e8 | 0.00540974 | ||||||||
\(220\) | 7.02356e10 | 2.02141 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.24013e8 | −0.0172427 | ||||||||
\(223\) | 1.60477e10 | 0.434552 | 0.217276 | − | 0.976110i | \(-0.430283\pi\) | ||||
0.217276 | + | 0.976110i | \(0.430283\pi\) | |||||||
\(224\) | −2.58271e10 | −0.685424 | ||||||||
\(225\) | −8.69914e10 | −2.26285 | ||||||||
\(226\) | −2.27087e9 | −0.0579035 | ||||||||
\(227\) | 6.61656e10 | 1.65393 | 0.826963 | − | 0.562257i | \(-0.190067\pi\) | ||||
0.826963 | + | 0.562257i | \(0.190067\pi\) | |||||||
\(228\) | −2.27547e9 | −0.0557654 | ||||||||
\(229\) | −4.43447e10 | −1.06557 | −0.532786 | − | 0.846250i | \(-0.678855\pi\) | ||||
−0.532786 | + | 0.846250i | \(0.678855\pi\) | |||||||
\(230\) | −6.24061e9 | −0.147046 | ||||||||
\(231\) | 1.12122e10 | 0.259081 | ||||||||
\(232\) | −3.39766e9 | −0.0769989 | ||||||||
\(233\) | −5.39484e9 | −0.119916 | −0.0599579 | − | 0.998201i | \(-0.519097\pi\) | ||||
−0.0599579 | + | 0.998201i | \(0.519097\pi\) | |||||||
\(234\) | −6.05843e9 | −0.132096 | ||||||||
\(235\) | −3.03539e10 | −0.649245 | ||||||||
\(236\) | 3.96647e10 | 0.832339 | ||||||||
\(237\) | −6.49451e9 | −0.133715 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.13971e10 | 0.820690 | 0.410345 | − | 0.911930i | \(-0.365408\pi\) | ||||
0.410345 | + | 0.911930i | \(0.365408\pi\) | |||||||
\(240\) | −1.17100e10 | −0.227827 | ||||||||
\(241\) | 1.66107e10 | 0.317183 | 0.158592 | − | 0.987344i | \(-0.449305\pi\) | ||||
0.158592 | + | 0.987344i | \(0.449305\pi\) | |||||||
\(242\) | −2.05843e9 | −0.0385805 | ||||||||
\(243\) | −2.11253e10 | −0.388664 | ||||||||
\(244\) | 2.67790e10 | 0.483660 | ||||||||
\(245\) | 2.02023e11 | 3.58223 | ||||||||
\(246\) | −1.56865e8 | −0.00273097 | ||||||||
\(247\) | 2.47919e10 | 0.423812 | ||||||||
\(248\) | 1.90883e10 | 0.320432 | ||||||||
\(249\) | 3.03585e9 | 0.0500476 | ||||||||
\(250\) | −1.98814e10 | −0.321896 | ||||||||
\(251\) | 3.10377e10 | 0.493581 | 0.246790 | − | 0.969069i | \(-0.420624\pi\) | ||||
0.246790 | + | 0.969069i | \(0.420624\pi\) | |||||||
\(252\) | 1.06401e11 | 1.66205 | ||||||||
\(253\) | −4.39662e10 | −0.674647 | ||||||||
\(254\) | 8.45010e9 | 0.127383 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.63793e10 | 0.820427 | ||||||||
\(257\) | 5.97981e10 | 0.855044 | 0.427522 | − | 0.904005i | \(-0.359387\pi\) | ||||
0.427522 | + | 0.904005i | \(0.359387\pi\) | |||||||
\(258\) | 2.03566e9 | 0.0286034 | ||||||||
\(259\) | −1.19403e11 | −1.64880 | ||||||||
\(260\) | 1.30076e11 | 1.76530 | ||||||||
\(261\) | 2.10615e10 | 0.280935 | ||||||||
\(262\) | 1.60053e10 | 0.209850 | ||||||||
\(263\) | −3.18665e10 | −0.410709 | −0.205354 | − | 0.978688i | \(-0.565835\pi\) | ||||
−0.205354 | + | 0.978688i | \(0.565835\pi\) | |||||||
\(264\) | 3.19429e9 | 0.0404721 | ||||||||
\(265\) | 1.55601e11 | 1.93823 | ||||||||
\(266\) | 8.19069e9 | 0.100312 | ||||||||
\(267\) | −2.01861e10 | −0.243082 | ||||||||
\(268\) | 9.27463e10 | 1.09822 | ||||||||
\(269\) | 3.97001e10 | 0.462281 | 0.231141 | − | 0.972920i | \(-0.425754\pi\) | ||||
0.231141 | + | 0.972920i | \(0.425754\pi\) | |||||||
\(270\) | −5.67143e9 | −0.0649465 | ||||||||
\(271\) | 7.58840e10 | 0.854650 | 0.427325 | − | 0.904098i | \(-0.359456\pi\) | ||||
0.427325 | + | 0.904098i | \(0.359456\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.07649e10 | 0.226255 | ||||||||
\(274\) | −1.90265e10 | −0.203930 | ||||||||
\(275\) | −2.47532e11 | −2.60997 | ||||||||
\(276\) | 7.47347e9 | 0.0775231 | ||||||||
\(277\) | 7.03115e10 | 0.717575 | 0.358788 | − | 0.933419i | \(-0.383190\pi\) | ||||
0.358788 | + | 0.933419i | \(0.383190\pi\) | |||||||
\(278\) | 5.78758e9 | 0.0581160 | ||||||||
\(279\) | −1.18325e11 | −1.16912 | ||||||||
\(280\) | 8.67572e10 | 0.843518 | ||||||||
\(281\) | 4.27010e10 | 0.408563 | 0.204282 | − | 0.978912i | \(-0.434514\pi\) | ||||
0.204282 | + | 0.978912i | \(0.434514\pi\) | |||||||
\(282\) | −6.83809e8 | −0.00643894 | ||||||||
\(283\) | 1.99849e10 | 0.185209 | 0.0926047 | − | 0.995703i | \(-0.470481\pi\) | ||||
0.0926047 | + | 0.995703i | \(0.470481\pi\) | |||||||
\(284\) | −6.28283e10 | −0.573090 | ||||||||
\(285\) | 1.15011e10 | 0.103261 | ||||||||
\(286\) | −1.72391e10 | −0.152359 | ||||||||
\(287\) | −3.00156e10 | −0.261143 | ||||||||
\(288\) | 4.56108e10 | 0.390663 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 8.50653e9 | 0.0706255 | ||||||||
\(291\) | −2.23610e9 | −0.0182799 | ||||||||
\(292\) | 4.97264e9 | 0.0400280 | ||||||||
\(293\) | 1.04039e11 | 0.824695 | 0.412347 | − | 0.911027i | \(-0.364709\pi\) | ||||
0.412347 | + | 0.911027i | \(0.364709\pi\) | |||||||
\(294\) | 4.55115e9 | 0.0355270 | ||||||||
\(295\) | −2.00481e11 | −1.54125 | ||||||||
\(296\) | −3.40174e10 | −0.257566 | ||||||||
\(297\) | −3.99562e10 | −0.297975 | ||||||||
\(298\) | −2.68740e10 | −0.197405 | ||||||||
\(299\) | −8.14254e10 | −0.589169 | ||||||||
\(300\) | 4.20761e10 | 0.299909 | ||||||||
\(301\) | 3.89519e11 | 2.73514 | ||||||||
\(302\) | −1.35748e10 | −0.0939077 | ||||||||
\(303\) | −2.02609e10 | −0.138092 | ||||||||
\(304\) | −6.02670e10 | −0.404714 | ||||||||
\(305\) | −1.35351e11 | −0.895599 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.84431e11 | 1.18498 | 0.592490 | − | 0.805578i | \(-0.298145\pi\) | ||||
0.592490 | + | 0.805578i | \(0.298145\pi\) | |||||||
\(308\) | 3.02762e11 | 1.91700 | ||||||||
\(309\) | 2.20077e10 | 0.137329 | ||||||||
\(310\) | −4.77904e10 | −0.293909 | ||||||||
\(311\) | 1.22863e11 | 0.744731 | 0.372365 | − | 0.928086i | \(-0.378547\pi\) | ||||
0.372365 | + | 0.928086i | \(0.378547\pi\) | |||||||
\(312\) | 5.91582e9 | 0.0353443 | ||||||||
\(313\) | −4.77009e10 | −0.280916 | −0.140458 | − | 0.990087i | \(-0.544858\pi\) | ||||
−0.140458 | + | 0.990087i | \(0.544858\pi\) | |||||||
\(314\) | −5.63327e9 | −0.0327022 | ||||||||
\(315\) | −5.37791e11 | −3.07763 | ||||||||
\(316\) | −1.75371e11 | −0.989388 | ||||||||
\(317\) | 2.10729e11 | 1.17208 | 0.586041 | − | 0.810281i | \(-0.300686\pi\) | ||||
0.586041 | + | 0.810281i | \(0.300686\pi\) | |||||||
\(318\) | 3.50536e9 | 0.0192225 | ||||||||
\(319\) | 5.99300e10 | 0.324031 | ||||||||
\(320\) | −3.03731e11 | −1.61925 | ||||||||
\(321\) | −2.78264e10 | −0.146280 | ||||||||
\(322\) | −2.69012e10 | −0.139450 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.84479e11 | −0.930024 | ||||||||
\(325\) | −4.58431e11 | −2.27928 | ||||||||
\(326\) | −9.39821e9 | −0.0460857 | ||||||||
\(327\) | −3.87999e10 | −0.187657 | ||||||||
\(328\) | −8.55130e9 | −0.0407944 | ||||||||
\(329\) | −1.30845e11 | −0.615710 | ||||||||
\(330\) | −7.99735e9 | −0.0371222 | ||||||||
\(331\) | −3.32123e10 | −0.152080 | −0.0760400 | − | 0.997105i | \(-0.524228\pi\) | ||||
−0.0760400 | + | 0.997105i | \(0.524228\pi\) | |||||||
\(332\) | 8.19771e10 | 0.370315 | ||||||||
\(333\) | 2.10867e11 | 0.939745 | ||||||||
\(334\) | 1.70362e10 | 0.0749054 | ||||||||
\(335\) | −4.68775e11 | −2.03359 | ||||||||
\(336\) | −5.04778e10 | −0.216060 | ||||||||
\(337\) | −3.00476e11 | −1.26904 | −0.634519 | − | 0.772907i | \(-0.718802\pi\) | ||||
−0.634519 | + | 0.772907i | \(0.718802\pi\) | |||||||
\(338\) | 6.78601e8 | 0.00282806 | ||||||||
\(339\) | −1.37453e10 | −0.0565271 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.36691e11 | −1.34846 | ||||||||
\(342\) | −1.44648e10 | −0.0571737 | ||||||||
\(343\) | 4.29006e11 | 1.67356 | ||||||||
\(344\) | 1.10972e11 | 0.427268 | ||||||||
\(345\) | −3.77738e10 | −0.143550 | ||||||||
\(346\) | 6.73723e10 | 0.252719 | ||||||||
\(347\) | −3.76252e11 | −1.39314 | −0.696571 | − | 0.717487i | \(-0.745292\pi\) | ||||
−0.696571 | + | 0.717487i | \(0.745292\pi\) | |||||||
\(348\) | −1.01870e10 | −0.0372341 | ||||||||
\(349\) | 2.25550e11 | 0.813819 | 0.406909 | − | 0.913469i | \(-0.366607\pi\) | ||||
0.406909 | + | 0.913469i | \(0.366607\pi\) | |||||||
\(350\) | −1.51455e11 | −0.539484 | ||||||||
\(351\) | −7.39989e10 | −0.260222 | ||||||||
\(352\) | 1.29785e11 | 0.450590 | ||||||||
\(353\) | 7.61898e9 | 0.0261162 | 0.0130581 | − | 0.999915i | \(-0.495843\pi\) | ||||
0.0130581 | + | 0.999915i | \(0.495843\pi\) | |||||||
\(354\) | −4.51641e9 | −0.0152855 | ||||||||
\(355\) | 3.17558e11 | 1.06120 | ||||||||
\(356\) | −5.45086e11 | −1.79862 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.24328e10 | 0.0721787 | ||||||||
\(359\) | 2.66775e11 | 0.847656 | 0.423828 | − | 0.905743i | \(-0.360686\pi\) | ||||
0.423828 | + | 0.905743i | \(0.360686\pi\) | |||||||
\(360\) | −1.53214e11 | −0.480770 | ||||||||
\(361\) | −2.63496e11 | −0.816566 | ||||||||
\(362\) | −8.47107e10 | −0.259268 | ||||||||
\(363\) | −1.24595e10 | −0.0376634 | ||||||||
\(364\) | 5.60715e11 | 1.67412 | ||||||||
\(365\) | −2.51336e10 | −0.0741203 | ||||||||
\(366\) | −3.04918e9 | −0.00888217 | ||||||||
\(367\) | 2.28618e11 | 0.657829 | 0.328914 | − | 0.944360i | \(-0.393317\pi\) | ||||
0.328914 | + | 0.944360i | \(0.393317\pi\) | |||||||
\(368\) | 1.97938e11 | 0.562619 | ||||||||
\(369\) | 5.30079e10 | 0.148841 | ||||||||
\(370\) | 8.51674e10 | 0.236247 | ||||||||
\(371\) | 6.70743e11 | 1.83812 | ||||||||
\(372\) | 5.72316e10 | 0.154950 | ||||||||
\(373\) | 6.18391e11 | 1.65415 | 0.827073 | − | 0.562095i | \(-0.190005\pi\) | ||||
0.827073 | + | 0.562095i | \(0.190005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.20340e11 | −0.314245 | ||||||||
\(376\) | −3.72771e10 | −0.0961828 | ||||||||
\(377\) | 1.10990e11 | 0.282976 | ||||||||
\(378\) | −2.44476e10 | −0.0615919 | ||||||||
\(379\) | −2.10741e11 | −0.524654 | −0.262327 | − | 0.964979i | \(-0.584490\pi\) | ||||
−0.262327 | + | 0.964979i | \(0.584490\pi\) | |||||||
\(380\) | 3.10564e11 | 0.764057 | ||||||||
\(381\) | 5.11476e10 | 0.124355 | ||||||||
\(382\) | −2.58274e10 | −0.0620578 | ||||||||
\(383\) | 3.03050e11 | 0.719648 | 0.359824 | − | 0.933020i | \(-0.382837\pi\) | ||||
0.359824 | + | 0.933020i | \(0.382837\pi\) | |||||||
\(384\) | −2.93185e10 | −0.0688101 | ||||||||
\(385\) | −1.53027e12 | −3.54973 | ||||||||
\(386\) | 7.14800e10 | 0.163886 | ||||||||
\(387\) | −6.87894e11 | −1.55891 | ||||||||
\(388\) | −6.03815e10 | −0.135257 | ||||||||
\(389\) | −3.07324e11 | −0.680491 | −0.340246 | − | 0.940337i | \(-0.610510\pi\) | ||||
−0.340246 | + | 0.940337i | \(0.610510\pi\) | |||||||
\(390\) | −1.48111e10 | −0.0324188 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.48101e11 | 0.530691 | ||||||||
\(393\) | 9.68787e10 | 0.204862 | ||||||||
\(394\) | 6.84408e10 | 0.143081 | ||||||||
\(395\) | 8.86394e11 | 1.83206 | ||||||||
\(396\) | −5.34680e11 | −1.09261 | ||||||||
\(397\) | 2.80841e11 | 0.567418 | 0.283709 | − | 0.958910i | \(-0.408435\pi\) | ||||
0.283709 | + | 0.958910i | \(0.408435\pi\) | |||||||
\(398\) | −6.04326e10 | −0.120725 | ||||||||
\(399\) | 4.95774e10 | 0.0979278 | ||||||||
\(400\) | 1.11441e12 | 2.17657 | ||||||||
\(401\) | −3.13411e11 | −0.605291 | −0.302645 | − | 0.953103i | \(-0.597870\pi\) | ||||
−0.302645 | + | 0.953103i | \(0.597870\pi\) | |||||||
\(402\) | −1.05605e10 | −0.0201683 | ||||||||
\(403\) | −6.23553e11 | −1.17761 | ||||||||
\(404\) | −5.47106e11 | −1.02177 | ||||||||
\(405\) | 9.32427e11 | 1.72213 | ||||||||
\(406\) | 3.66688e10 | 0.0669776 | ||||||||
\(407\) | 6.00019e11 | 1.08390 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.95263e11 | 1.05185 | 0.525926 | − | 0.850531i | \(-0.323719\pi\) | ||||
0.525926 | + | 0.850531i | \(0.323719\pi\) | |||||||
\(410\) | 2.14094e10 | 0.0374177 | ||||||||
\(411\) | −1.15165e11 | −0.199082 | ||||||||
\(412\) | 5.94273e11 | 1.01613 | ||||||||
\(413\) | −8.64204e11 | −1.46164 | ||||||||
\(414\) | 4.75077e10 | 0.0794808 | ||||||||
\(415\) | −4.14344e11 | −0.685716 | ||||||||
\(416\) | 2.40362e11 | 0.393500 | ||||||||
\(417\) | 3.50316e10 | 0.0567346 | ||||||||
\(418\) | −4.11594e10 | −0.0659441 | ||||||||
\(419\) | 3.62055e11 | 0.573867 | 0.286934 | − | 0.957950i | \(-0.407364\pi\) | ||||
0.286934 | + | 0.957950i | \(0.407364\pi\) | |||||||
\(420\) | 2.60119e11 | 0.407897 | ||||||||
\(421\) | 1.01670e12 | 1.57734 | 0.788668 | − | 0.614819i | \(-0.210771\pi\) | ||||
0.788668 | + | 0.614819i | \(0.210771\pi\) | |||||||
\(422\) | −6.55740e10 | −0.100653 | ||||||||
\(423\) | 2.31074e11 | 0.350929 | ||||||||
\(424\) | 1.91091e11 | 0.287140 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.15393e9 | 0.0105245 | ||||||||
\(427\) | −5.83454e11 | −0.849339 | ||||||||
\(428\) | −7.51397e11 | −1.08236 | ||||||||
\(429\) | −1.04347e11 | −0.148738 | ||||||||
\(430\) | −2.77834e11 | −0.391902 | ||||||||
\(431\) | 8.42323e11 | 1.17579 | 0.587897 | − | 0.808936i | \(-0.299956\pi\) | ||||
0.587897 | + | 0.808936i | \(0.299956\pi\) | |||||||
\(432\) | 1.79885e11 | 0.248495 | ||||||||
\(433\) | 1.18575e12 | 1.62106 | 0.810529 | − | 0.585698i | \(-0.199180\pi\) | ||||
0.810529 | + | 0.585698i | \(0.199180\pi\) | |||||||
\(434\) | −2.06008e11 | −0.278728 | ||||||||
\(435\) | 5.14892e10 | 0.0689468 | ||||||||
\(436\) | −1.04771e12 | −1.38852 | ||||||||
\(437\) | −1.94408e11 | −0.255004 | ||||||||
\(438\) | −5.66208e8 | −0.000735093 0 | ||||||||
\(439\) | −2.80153e11 | −0.360002 | −0.180001 | − | 0.983666i | \(-0.557610\pi\) | ||||
−0.180001 | + | 0.983666i | \(0.557610\pi\) | |||||||
\(440\) | −4.35967e11 | −0.554519 | ||||||||
\(441\) | −1.53793e12 | −1.93626 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.03647e12 | −1.27861 | −0.639307 | − | 0.768951i | \(-0.720779\pi\) | ||||
−0.639307 | + | 0.768951i | \(0.720779\pi\) | |||||||
\(444\) | −1.01993e11 | −0.124550 | ||||||||
\(445\) | 2.75507e12 | 3.33053 | ||||||||
\(446\) | −4.93418e10 | −0.0590484 | ||||||||
\(447\) | −1.62665e11 | −0.192713 | ||||||||
\(448\) | −1.30928e12 | −1.53561 | ||||||||
\(449\) | −9.51471e11 | −1.10481 | −0.552404 | − | 0.833576i | \(-0.686290\pi\) | ||||
−0.552404 | + | 0.833576i | \(0.686290\pi\) | |||||||
\(450\) | 2.67472e11 | 0.307483 | ||||||||
\(451\) | 1.50833e11 | 0.171673 | ||||||||
\(452\) | −3.71165e11 | −0.418258 | ||||||||
\(453\) | −8.21667e10 | −0.0916756 | ||||||||
\(454\) | −2.03439e11 | −0.224741 | ||||||||
\(455\) | −2.83407e12 | −3.09998 | ||||||||
\(456\) | 1.41244e10 | 0.0152977 | ||||||||
\(457\) | 5.23939e11 | 0.561899 | 0.280949 | − | 0.959723i | \(-0.409351\pi\) | ||||
0.280949 | + | 0.959723i | \(0.409351\pi\) | |||||||
\(458\) | 1.36346e11 | 0.144793 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.02000e12 | −1.06217 | ||||||||
\(461\) | −1.57356e12 | −1.62267 | −0.811333 | − | 0.584585i | \(-0.801257\pi\) | ||||
−0.811333 | + | 0.584585i | \(0.801257\pi\) | |||||||
\(462\) | −3.44739e10 | −0.0352048 | ||||||||
\(463\) | 8.11193e11 | 0.820370 | 0.410185 | − | 0.912002i | \(-0.365464\pi\) | ||||
0.410185 | + | 0.912002i | \(0.365464\pi\) | |||||||
\(464\) | −2.69808e11 | −0.270224 | ||||||||
\(465\) | −2.89270e11 | −0.286923 | ||||||||
\(466\) | 1.65874e10 | 0.0162946 | ||||||||
\(467\) | −1.43619e12 | −1.39729 | −0.698646 | − | 0.715467i | \(-0.746214\pi\) | ||||
−0.698646 | + | 0.715467i | \(0.746214\pi\) | |||||||
\(468\) | −9.90228e11 | −0.954177 | ||||||||
\(469\) | −2.02073e12 | −1.92855 | ||||||||
\(470\) | 9.33287e10 | 0.0882216 | ||||||||
\(471\) | −3.40976e10 | −0.0319249 | ||||||||
\(472\) | −2.46207e11 | −0.228329 | ||||||||
\(473\) | −1.95739e12 | −1.79805 | ||||||||
\(474\) | 1.99686e10 | 0.0181696 | ||||||||
\(475\) | −1.09453e12 | −0.986520 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.18454e12 | −1.04765 | ||||||||
\(478\) | −1.27283e11 | −0.111518 | ||||||||
\(479\) | 1.19894e11 | 0.104061 | 0.0520304 | − | 0.998646i | \(-0.483431\pi\) | ||||
0.0520304 | + | 0.998646i | \(0.483431\pi\) | |||||||
\(480\) | 1.11505e11 | 0.0958760 | ||||||||
\(481\) | 1.11124e12 | 0.946571 | ||||||||
\(482\) | −5.10726e10 | −0.0430999 | ||||||||
\(483\) | −1.62830e11 | −0.136136 | ||||||||
\(484\) | −3.36443e11 | −0.278681 | ||||||||
\(485\) | 3.05191e11 | 0.250458 | ||||||||
\(486\) | 6.49537e10 | 0.0528130 | ||||||||
\(487\) | 1.21696e12 | 0.980386 | 0.490193 | − | 0.871614i | \(-0.336926\pi\) | ||||
0.490193 | + | 0.871614i | \(0.336926\pi\) | |||||||
\(488\) | −1.66223e11 | −0.132679 | ||||||||
\(489\) | −5.68864e10 | −0.0449902 | ||||||||
\(490\) | −6.21157e11 | −0.486765 | ||||||||
\(491\) | 1.10228e12 | 0.855904 | 0.427952 | − | 0.903802i | \(-0.359235\pi\) | ||||
0.427952 | + | 0.903802i | \(0.359235\pi\) | |||||||
\(492\) | −2.56389e10 | −0.0197268 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −7.62273e10 | −0.0575890 | ||||||||
\(495\) | 2.70248e12 | 2.02320 | ||||||||
\(496\) | 1.51580e12 | 1.12454 | ||||||||
\(497\) | 1.36889e12 | 1.00638 | ||||||||
\(498\) | −9.33430e9 | −0.00680064 | ||||||||
\(499\) | −1.83821e12 | −1.32722 | −0.663610 | − | 0.748078i | \(-0.730977\pi\) | ||||
−0.663610 | + | 0.748078i | \(0.730977\pi\) | |||||||
\(500\) | −3.24953e12 | −2.32518 | ||||||||
\(501\) | 1.03118e11 | 0.0731250 | ||||||||
\(502\) | −9.54314e10 | −0.0670694 | ||||||||
\(503\) | 1.35686e12 | 0.945104 | 0.472552 | − | 0.881303i | \(-0.343333\pi\) | ||||
0.472552 | + | 0.881303i | \(0.343333\pi\) | |||||||
\(504\) | −6.60453e11 | −0.455937 | ||||||||
\(505\) | 2.76528e12 | 1.89203 | ||||||||
\(506\) | 1.35182e11 | 0.0916732 | ||||||||
\(507\) | 4.10750e9 | 0.00276084 | ||||||||
\(508\) | 1.38114e12 | 0.920132 | ||||||||
\(509\) | −1.97514e12 | −1.30427 | −0.652137 | − | 0.758101i | \(-0.726127\pi\) | ||||
−0.652137 | + | 0.758101i | \(0.726127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.08342e11 | −0.0702918 | ||||||||
\(512\) | −9.79930e11 | −0.630203 | ||||||||
\(513\) | −1.76677e11 | −0.112629 | ||||||||
\(514\) | −1.83861e11 | −0.116186 | ||||||||
\(515\) | −3.00368e12 | −1.88158 | ||||||||
\(516\) | 3.32721e11 | 0.206613 | ||||||||
\(517\) | 6.57516e11 | 0.404761 | ||||||||
\(518\) | 3.67128e11 | 0.224044 | ||||||||
\(519\) | 4.07797e11 | 0.246713 | ||||||||
\(520\) | −8.07412e11 | −0.484262 | ||||||||
\(521\) | −1.99095e12 | −1.18383 | −0.591917 | − | 0.805999i | \(-0.701629\pi\) | ||||
−0.591917 | + | 0.805999i | \(0.701629\pi\) | |||||||
\(522\) | −6.47574e10 | −0.0381744 | ||||||||
\(523\) | −3.10464e11 | −0.181448 | −0.0907242 | − | 0.995876i | \(-0.528918\pi\) | ||||
−0.0907242 | + | 0.995876i | \(0.528918\pi\) | |||||||
\(524\) | 2.61601e12 | 1.51583 | ||||||||
\(525\) | −9.16744e11 | −0.526661 | ||||||||
\(526\) | 9.79796e10 | 0.0558084 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.53658e11 | 0.142035 | ||||||||
\(529\) | −1.16265e12 | −0.645502 | ||||||||
\(530\) | −4.78424e11 | −0.263373 | ||||||||
\(531\) | 1.52619e12 | 0.833074 | ||||||||
\(532\) | 1.33874e12 | 0.724592 | ||||||||
\(533\) | 2.79343e11 | 0.149922 | ||||||||
\(534\) | 6.20661e10 | 0.0330308 | ||||||||
\(535\) | 3.79785e12 | 2.00422 | ||||||||
\(536\) | −5.75696e11 | −0.301267 | ||||||||
\(537\) | 1.35783e11 | 0.0704630 | ||||||||
\(538\) | −1.22065e11 | −0.0628163 | ||||||||
\(539\) | −4.37616e12 | −2.23328 | ||||||||
\(540\) | −9.26975e11 | −0.469133 | ||||||||
\(541\) | −8.59585e11 | −0.431421 | −0.215711 | − | 0.976457i | \(-0.569207\pi\) | ||||
−0.215711 | + | 0.976457i | \(0.569207\pi\) | |||||||
\(542\) | −2.33320e11 | −0.116133 | ||||||||
\(543\) | −5.12745e11 | −0.253106 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.29554e12 | 2.57114 | ||||||||
\(546\) | −6.38457e10 | −0.0307443 | ||||||||
\(547\) | −2.41617e12 | −1.15394 | −0.576971 | − | 0.816765i | \(-0.695765\pi\) | ||||
−0.576971 | + | 0.816765i | \(0.695765\pi\) | |||||||
\(548\) | −3.10980e12 | −1.47306 | ||||||||
\(549\) | 1.03038e12 | 0.484088 | ||||||||
\(550\) | 7.61085e11 | 0.354651 | ||||||||
\(551\) | 2.64996e11 | 0.122478 | ||||||||
\(552\) | −4.63894e10 | −0.0212664 | ||||||||
\(553\) | 3.82094e12 | 1.73743 | ||||||||
\(554\) | −2.16186e11 | −0.0975065 | ||||||||
\(555\) | 5.15509e11 | 0.230631 | ||||||||
\(556\) | 9.45958e11 | 0.419793 | ||||||||
\(557\) | 1.61258e12 | 0.709859 | 0.354929 | − | 0.934893i | \(-0.384505\pi\) | ||||
0.354929 | + | 0.934893i | \(0.384505\pi\) | |||||||
\(558\) | 3.63812e11 | 0.158863 | ||||||||
\(559\) | −3.62509e12 | −1.57024 | ||||||||
\(560\) | 6.88938e12 | 2.96029 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.31292e11 | −0.0555169 | ||||||||
\(563\) | 4.85659e10 | 0.0203725 | 0.0101862 | − | 0.999948i | \(-0.496758\pi\) | ||||
0.0101862 | + | 0.999948i | \(0.496758\pi\) | |||||||
\(564\) | −1.11766e11 | −0.0465108 | ||||||||
\(565\) | 1.87601e12 | 0.774493 | ||||||||
\(566\) | −6.14473e10 | −0.0251669 | ||||||||
\(567\) | 4.01938e12 | 1.63318 | ||||||||
\(568\) | 3.89989e11 | 0.157212 | ||||||||
\(569\) | −2.08971e12 | −0.835758 | −0.417879 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417879 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(570\) | −3.53623e10 | −0.0140315 | ||||||||
\(571\) | 1.98387e12 | 0.780999 | 0.390500 | − | 0.920603i | \(-0.372302\pi\) | ||||
0.390500 | + | 0.920603i | \(0.372302\pi\) | |||||||
\(572\) | −2.81767e12 | −1.10055 | ||||||||
\(573\) | −1.56331e11 | −0.0605827 | ||||||||
\(574\) | 9.22887e10 | 0.0354850 | ||||||||
\(575\) | 3.59482e12 | 1.37143 | ||||||||
\(576\) | 2.31220e12 | 0.875235 | ||||||||
\(577\) | −1.30195e12 | −0.488992 | −0.244496 | − | 0.969650i | \(-0.578623\pi\) | ||||
−0.244496 | + | 0.969650i | \(0.578623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.32661e11 | 0.159991 | ||||||||
\(580\) | 1.39036e12 | 0.510155 | ||||||||
\(581\) | −1.78610e12 | −0.650297 | ||||||||
\(582\) | 6.87532e9 | 0.00248393 | ||||||||
\(583\) | −3.37058e12 | −1.20836 | ||||||||
\(584\) | −3.08662e10 | −0.0109806 | ||||||||
\(585\) | 5.00499e12 | 1.76686 | ||||||||
\(586\) | −3.19888e11 | −0.112062 | ||||||||
\(587\) | 8.77295e11 | 0.304982 | 0.152491 | − | 0.988305i | \(-0.451270\pi\) | ||||
0.152491 | + | 0.988305i | \(0.451270\pi\) | |||||||
\(588\) | 7.43869e11 | 0.256625 | ||||||||
\(589\) | −1.48877e12 | −0.509692 | ||||||||
\(590\) | 6.16415e11 | 0.209430 | ||||||||
\(591\) | 4.14265e11 | 0.139680 | ||||||||
\(592\) | −2.70132e12 | −0.903917 | ||||||||
\(593\) | 1.76865e12 | 0.587348 | 0.293674 | − | 0.955906i | \(-0.405122\pi\) | ||||
0.293674 | + | 0.955906i | \(0.405122\pi\) | |||||||
\(594\) | 1.22853e11 | 0.0404899 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.39245e12 | −1.42593 | ||||||||
\(597\) | −3.65792e11 | −0.117856 | ||||||||
\(598\) | 2.50358e11 | 0.0800582 | ||||||||
\(599\) | −4.78571e12 | −1.51889 | −0.759444 | − | 0.650573i | \(-0.774529\pi\) | ||||
−0.759444 | + | 0.650573i | \(0.774529\pi\) | |||||||
\(600\) | −2.61176e11 | −0.0822720 | ||||||||
\(601\) | 2.40341e12 | 0.751439 | 0.375719 | − | 0.926734i | \(-0.377396\pi\) | ||||
0.375719 | + | 0.926734i | \(0.377396\pi\) | |||||||
\(602\) | −1.19765e12 | −0.371660 | ||||||||
\(603\) | 3.56863e12 | 1.09919 | ||||||||
\(604\) | −2.21875e12 | −0.678331 | ||||||||
\(605\) | 1.70051e12 | 0.516037 | ||||||||
\(606\) | 6.22960e10 | 0.0187644 | ||||||||
\(607\) | 3.97836e11 | 0.118947 | 0.0594737 | − | 0.998230i | \(-0.481058\pi\) | ||||
0.0594737 | + | 0.998230i | \(0.481058\pi\) | |||||||
\(608\) | 5.73877e11 | 0.170315 | ||||||||
\(609\) | 2.21952e11 | 0.0653856 | ||||||||
\(610\) | 4.16163e11 | 0.121697 | ||||||||
\(611\) | 1.21772e12 | 0.353478 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.43845e12 | −0.697497 | −0.348748 | − | 0.937216i | \(-0.613393\pi\) | ||||
−0.348748 | + | 0.937216i | \(0.613393\pi\) | |||||||
\(614\) | −5.67068e11 | −0.161019 | ||||||||
\(615\) | 1.29589e11 | 0.0365283 | ||||||||
\(616\) | −1.87931e12 | −0.525878 | ||||||||
\(617\) | 5.95149e12 | 1.65326 | 0.826632 | − | 0.562743i | \(-0.190254\pi\) | ||||
0.826632 | + | 0.562743i | \(0.190254\pi\) | |||||||
\(618\) | −6.76667e10 | −0.0186607 | ||||||||
\(619\) | 5.90632e12 | 1.61700 | 0.808499 | − | 0.588498i | \(-0.200280\pi\) | ||||
0.808499 | + | 0.588498i | \(0.200280\pi\) | |||||||
\(620\) | −7.81116e12 | −2.12301 | ||||||||
\(621\) | 5.80269e11 | 0.156573 | ||||||||
\(622\) | −3.77765e11 | −0.101196 | ||||||||
\(623\) | 1.18762e13 | 3.15850 | ||||||||
\(624\) | 4.69775e11 | 0.124039 | ||||||||
\(625\) | 7.63770e12 | 2.00218 | ||||||||
\(626\) | 1.46665e11 | 0.0381718 | ||||||||
\(627\) | −2.49134e11 | −0.0643767 | ||||||||
\(628\) | −9.20737e11 | −0.236220 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.65354e12 | 0.418198 | ||||||||
\(631\) | 5.67619e12 | 1.42536 | 0.712680 | − | 0.701489i | \(-0.247481\pi\) | ||||
0.712680 | + | 0.701489i | \(0.247481\pi\) | |||||||
\(632\) | 1.08857e12 | 0.271412 | ||||||||
\(633\) | −3.96913e11 | −0.0982604 | ||||||||
\(634\) | −6.47926e11 | −0.159266 | ||||||||
\(635\) | −6.98080e12 | −1.70382 | ||||||||
\(636\) | 5.72938e11 | 0.138852 | ||||||||
\(637\) | −8.10465e12 | −1.95032 | ||||||||
\(638\) | −1.84266e11 | −0.0440303 | ||||||||
\(639\) | −2.41747e12 | −0.573597 | ||||||||
\(640\) | 4.00150e12 | 0.942785 | ||||||||
\(641\) | −1.49036e12 | −0.348681 | −0.174341 | − | 0.984685i | \(-0.555779\pi\) | ||||
−0.174341 | + | 0.984685i | \(0.555779\pi\) | |||||||
\(642\) | 8.55576e10 | 0.0198770 | ||||||||
\(643\) | 8.89423e11 | 0.205191 | 0.102596 | − | 0.994723i | \(-0.467285\pi\) | ||||
0.102596 | + | 0.994723i | \(0.467285\pi\) | |||||||
\(644\) | −4.39690e12 | −1.00730 | ||||||||
\(645\) | −1.68170e12 | −0.382587 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.62659e12 | 0.364929 | 0.182465 | − | 0.983212i | \(-0.441593\pi\) | ||||
0.182465 | + | 0.983212i | \(0.441593\pi\) | |||||||
\(648\) | 1.14510e12 | 0.255127 | ||||||||
\(649\) | 4.34275e12 | 0.960867 | ||||||||
\(650\) | 1.40953e12 | 0.309717 | ||||||||
\(651\) | −1.24695e12 | −0.272103 | ||||||||
\(652\) | −1.53610e12 | −0.332894 | ||||||||
\(653\) | −5.76853e12 | −1.24153 | −0.620763 | − | 0.783998i | \(-0.713177\pi\) | ||||
−0.620763 | + | 0.783998i | \(0.713177\pi\) | |||||||
\(654\) | 1.19297e11 | 0.0254995 | ||||||||
\(655\) | −1.32223e13 | −2.80687 | ||||||||
\(656\) | −6.79059e11 | −0.143166 | ||||||||
\(657\) | 1.91334e11 | 0.0400634 | ||||||||
\(658\) | 4.02308e11 | 0.0836648 | ||||||||
\(659\) | −2.19347e12 | −0.453050 | −0.226525 | − | 0.974005i | \(-0.572737\pi\) | ||||
−0.226525 | + | 0.974005i | \(0.572737\pi\) | |||||||
\(660\) | −1.30714e12 | −0.268147 | ||||||||
\(661\) | −3.13563e12 | −0.638879 | −0.319439 | − | 0.947607i | \(-0.603495\pi\) | ||||
−0.319439 | + | 0.947607i | \(0.603495\pi\) | |||||||
\(662\) | 1.02117e11 | 0.0206651 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.08850e11 | −0.101586 | ||||||||
\(665\) | −6.76650e12 | −1.34173 | ||||||||
\(666\) | −6.48351e11 | −0.127696 | ||||||||
\(667\) | −8.70341e11 | −0.170264 | ||||||||
\(668\) | 2.78450e12 | 0.541070 | ||||||||
\(669\) | −2.98661e11 | −0.0576449 | ||||||||
\(670\) | 1.44134e12 | 0.276331 | ||||||||
\(671\) | 2.93194e12 | 0.558346 | ||||||||
\(672\) | 4.80662e11 | 0.0909239 | ||||||||
\(673\) | 3.23212e12 | 0.607323 | 0.303662 | − | 0.952780i | \(-0.401791\pi\) | ||||
0.303662 | + | 0.952780i | \(0.401791\pi\) | |||||||
\(674\) | 9.23869e11 | 0.172441 | ||||||||
\(675\) | 3.26695e12 | 0.605726 | ||||||||
\(676\) | 1.10915e11 | 0.0204282 | ||||||||
\(677\) | −6.52077e12 | −1.19303 | −0.596513 | − | 0.802603i | \(-0.703448\pi\) | ||||
−0.596513 | + | 0.802603i | \(0.703448\pi\) | |||||||
\(678\) | 4.22626e10 | 0.00768109 | ||||||||
\(679\) | 1.31558e12 | 0.237521 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.23139e12 | −0.219399 | ||||||||
\(682\) | 1.03522e12 | 0.183233 | ||||||||
\(683\) | −2.88073e11 | −0.0506534 | −0.0253267 | − | 0.999679i | \(-0.508063\pi\) | ||||
−0.0253267 | + | 0.999679i | \(0.508063\pi\) | |||||||
\(684\) | −2.36422e12 | −0.412987 | ||||||||
\(685\) | 1.57181e13 | 2.72768 | ||||||||
\(686\) | −1.31906e12 | −0.227408 | ||||||||
\(687\) | 8.25290e11 | 0.141352 | ||||||||
\(688\) | 8.81228e12 | 1.49948 | ||||||||
\(689\) | −6.24231e12 | −1.05526 | ||||||||
\(690\) | 1.16143e11 | 0.0195061 | ||||||||
\(691\) | 6.08618e12 | 1.01553 | 0.507766 | − | 0.861495i | \(-0.330471\pi\) | ||||
0.507766 | + | 0.861495i | \(0.330471\pi\) | |||||||
\(692\) | 1.10117e13 | 1.82549 | ||||||||
\(693\) | 1.16495e13 | 1.91870 | ||||||||
\(694\) | 1.15686e12 | 0.189305 | ||||||||
\(695\) | −4.78124e12 | −0.777335 | ||||||||
\(696\) | 6.32331e10 | 0.0102142 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −6.93495e11 | −0.110584 | ||||||||
\(699\) | 1.00402e11 | 0.0159073 | ||||||||
\(700\) | −2.47548e13 | −3.89689 | ||||||||
\(701\) | −1.78933e12 | −0.279872 | −0.139936 | − | 0.990161i | \(-0.544690\pi\) | ||||
−0.139936 | + | 0.990161i | \(0.544690\pi\) | |||||||
\(702\) | 2.27524e11 | 0.0353598 | ||||||||
\(703\) | 2.65314e12 | 0.409695 | ||||||||
\(704\) | 6.57933e12 | 1.00950 | ||||||||
\(705\) | 5.64909e11 | 0.0861246 | ||||||||
\(706\) | −2.34260e10 | −0.00354876 | ||||||||
\(707\) | 1.19202e13 | 1.79430 | ||||||||
\(708\) | −7.38190e11 | −0.110413 | ||||||||
\(709\) | −7.74406e12 | −1.15096 | −0.575481 | − | 0.817815i | \(-0.695185\pi\) | ||||
−0.575481 | + | 0.817815i | \(0.695185\pi\) | |||||||
\(710\) | −9.76393e11 | −0.144199 | ||||||||
\(711\) | −6.74782e12 | −0.990262 | ||||||||
\(712\) | 3.38347e12 | 0.493403 | ||||||||
\(713\) | 4.88964e12 | 0.708556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.42416e13 | 2.03789 | ||||||||
\(716\) | 3.66655e12 | 0.521373 | ||||||||
\(717\) | −7.70432e11 | −0.108867 | ||||||||
\(718\) | −8.20249e11 | −0.115182 | ||||||||
\(719\) | 7.67138e12 | 1.07052 | 0.535258 | − | 0.844688i | \(-0.320214\pi\) | ||||
0.535258 | + | 0.844688i | \(0.320214\pi\) | |||||||
\(720\) | −1.21667e13 | −1.68724 | ||||||||
\(721\) | −1.29479e13 | −1.78439 | ||||||||
\(722\) | 8.10167e11 | 0.110958 | ||||||||
\(723\) | −3.09137e11 | −0.0420755 | ||||||||
\(724\) | −1.38456e13 | −1.87279 | ||||||||
\(725\) | −4.90008e12 | −0.658691 | ||||||||
\(726\) | 3.83090e10 | 0.00511783 | ||||||||
\(727\) | −8.22639e12 | −1.09221 | −0.546103 | − | 0.837718i | \(-0.683889\pi\) | ||||
−0.546103 | + | 0.837718i | \(0.683889\pi\) | |||||||
\(728\) | −3.48048e12 | −0.459249 | ||||||||
\(729\) | −6.83224e12 | −0.895961 | ||||||||
\(730\) | 7.72780e10 | 0.0100717 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.98378e11 | −0.0641592 | ||||||||
\(733\) | 9.55042e11 | 0.122195 | 0.0610977 | − | 0.998132i | \(-0.480540\pi\) | ||||
0.0610977 | + | 0.998132i | \(0.480540\pi\) | |||||||
\(734\) | −7.02929e11 | −0.0893880 | ||||||||
\(735\) | −3.75980e12 | −0.475195 | ||||||||
\(736\) | −1.88482e12 | −0.236766 | ||||||||
\(737\) | 1.01545e13 | 1.26781 | ||||||||
\(738\) | −1.62983e11 | −0.0202250 | ||||||||
\(739\) | −3.28401e12 | −0.405046 | −0.202523 | − | 0.979278i | \(-0.564914\pi\) | ||||
−0.202523 | + | 0.979278i | \(0.564914\pi\) | |||||||
\(740\) | 1.39203e13 | 1.70650 | ||||||||
\(741\) | −4.61396e11 | −0.0562201 | ||||||||
\(742\) | −2.06232e12 | −0.249769 | ||||||||
\(743\) | −2.11148e12 | −0.254178 | −0.127089 | − | 0.991891i | \(-0.540563\pi\) | ||||
−0.127089 | + | 0.991891i | \(0.540563\pi\) | |||||||
\(744\) | −3.55249e11 | −0.0425064 | ||||||||
\(745\) | 2.22011e13 | 2.64041 | ||||||||
\(746\) | −1.90136e12 | −0.224771 | ||||||||
\(747\) | 3.15426e12 | 0.370642 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.63712e13 | 1.90070 | ||||||||
\(750\) | 3.70007e11 | 0.0427007 | ||||||||
\(751\) | 3.55572e12 | 0.407895 | 0.203947 | − | 0.978982i | \(-0.434623\pi\) | ||||
0.203947 | + | 0.978982i | \(0.434623\pi\) | |||||||
\(752\) | −2.96018e12 | −0.337549 | ||||||||
\(753\) | −5.77636e11 | −0.0654752 | ||||||||
\(754\) | −3.41261e11 | −0.0384517 | ||||||||
\(755\) | 1.12144e13 | 1.25607 | ||||||||
\(756\) | −3.99587e12 | −0.444901 | ||||||||
\(757\) | −8.12210e12 | −0.898953 | −0.449476 | − | 0.893292i | \(-0.648389\pi\) | ||||
−0.449476 | + | 0.893292i | \(0.648389\pi\) | |||||||
\(758\) | 6.47963e11 | 0.0712917 | ||||||||
\(759\) | 8.18244e11 | 0.0894942 | ||||||||
\(760\) | −1.92774e12 | −0.209598 | ||||||||
\(761\) | 1.55670e13 | 1.68258 | 0.841289 | − | 0.540586i | \(-0.181797\pi\) | ||||
0.841289 | + | 0.540586i | \(0.181797\pi\) | |||||||
\(762\) | −1.57263e11 | −0.0168977 | ||||||||
\(763\) | 2.28273e13 | 2.43834 | ||||||||
\(764\) | −4.22140e12 | −0.448267 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.31785e11 | −0.0977881 | ||||||||
\(767\) | 8.04278e12 | 0.839125 | ||||||||
\(768\) | −1.04926e12 | −0.108833 | ||||||||
\(769\) | −1.59487e13 | −1.64458 | −0.822292 | − | 0.569066i | \(-0.807305\pi\) | ||||
−0.822292 | + | 0.569066i | \(0.807305\pi\) | |||||||
\(770\) | 4.70511e12 | 0.482350 | ||||||||
\(771\) | −1.11289e12 | −0.113425 | ||||||||
\(772\) | 1.16831e13 | 1.18381 | ||||||||
\(773\) | −4.36572e12 | −0.439793 | −0.219896 | − | 0.975523i | \(-0.570572\pi\) | ||||
−0.219896 | + | 0.975523i | \(0.570572\pi\) | |||||||
\(774\) | 2.11506e12 | 0.211830 | ||||||||
\(775\) | 2.75290e13 | 2.74115 | ||||||||
\(776\) | 3.74801e11 | 0.0371042 | ||||||||
\(777\) | 2.22219e12 | 0.218719 | ||||||||
\(778\) | 9.44924e11 | 0.0924674 | ||||||||
\(779\) | 6.66946e11 | 0.0648892 | ||||||||
\(780\) | −2.42082e12 | −0.234173 | ||||||||
\(781\) | −6.87885e12 | −0.661586 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.90961e11 | −0.0752016 | ||||||||
\(784\) | 1.97017e13 | 1.86244 | ||||||||
\(785\) | 4.65376e12 | 0.437411 | ||||||||
\(786\) | −2.97872e11 | −0.0278373 | ||||||||
\(787\) | −1.29316e13 | −1.20162 | −0.600808 | − | 0.799393i | \(-0.705154\pi\) | ||||
−0.600808 | + | 0.799393i | \(0.705154\pi\) | |||||||
\(788\) | 1.11864e13 | 1.03353 | ||||||||
\(789\) | 5.93060e11 | 0.0544819 | ||||||||
\(790\) | −2.72538e12 | −0.248946 | ||||||||
\(791\) | 8.08685e12 | 0.734489 | ||||||||
\(792\) | 3.31887e12 | 0.299728 | ||||||||
\(793\) | 5.42996e12 | 0.487604 | ||||||||
\(794\) | −8.63499e11 | −0.0771027 | ||||||||
\(795\) | −2.89585e12 | −0.257113 | ||||||||
\(796\) | −9.87748e12 | −0.872042 | ||||||||
\(797\) | 7.30256e12 | 0.641081 | 0.320540 | − | 0.947235i | \(-0.396135\pi\) | ||||
0.320540 | + | 0.947235i | \(0.396135\pi\) | |||||||
\(798\) | −1.52435e11 | −0.0133067 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.06116e13 | −0.915962 | ||||||||
\(801\) | −2.09734e13 | −1.80021 | ||||||||
\(802\) | 9.63640e11 | 0.0822489 | ||||||||
\(803\) | 5.44437e11 | 0.0462091 | ||||||||
\(804\) | −1.72608e12 | −0.145683 | ||||||||
\(805\) | 2.22236e13 | 1.86523 | ||||||||
\(806\) | 1.91723e12 | 0.160017 | ||||||||
\(807\) | −7.38849e11 | −0.0613232 | ||||||||
\(808\) | 3.39600e12 | 0.280296 | ||||||||
\(809\) | −2.08963e13 | −1.71514 | −0.857571 | − | 0.514365i | \(-0.828027\pi\) | ||||
−0.857571 | + | 0.514365i | \(0.828027\pi\) | |||||||
\(810\) | −2.86692e12 | −0.234009 | ||||||||
\(811\) | −8.60451e12 | −0.698445 | −0.349222 | − | 0.937040i | \(-0.613554\pi\) | ||||
−0.349222 | + | 0.937040i | \(0.613554\pi\) | |||||||
\(812\) | 5.99338e12 | 0.483804 | ||||||||
\(813\) | −1.41226e12 | −0.113372 | ||||||||
\(814\) | −1.84487e12 | −0.147284 | ||||||||
\(815\) | 7.76405e12 | 0.616423 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.65509e12 | −0.679630 | ||||||||
\(818\) | −1.83025e12 | −0.142929 | ||||||||
\(819\) | 2.15748e13 | 1.67560 | ||||||||
\(820\) | 3.49929e12 | 0.270282 | ||||||||
\(821\) | −1.33422e13 | −1.02491 | −0.512453 | − | 0.858716i | \(-0.671263\pi\) | ||||
−0.512453 | + | 0.858716i | \(0.671263\pi\) | |||||||
\(822\) | 3.54097e11 | 0.0270520 | ||||||||
\(823\) | −9.21038e12 | −0.699807 | −0.349903 | − | 0.936786i | \(-0.613786\pi\) | ||||
−0.349903 | + | 0.936786i | \(0.613786\pi\) | |||||||
\(824\) | −3.68878e12 | −0.278747 | ||||||||
\(825\) | 4.60677e12 | 0.346221 | ||||||||
\(826\) | 2.65716e12 | 0.198613 | ||||||||
\(827\) | 1.73042e13 | 1.28640 | 0.643202 | − | 0.765696i | \(-0.277605\pi\) | ||||
0.643202 | + | 0.765696i | \(0.277605\pi\) | |||||||
\(828\) | 7.76496e12 | 0.574120 | ||||||||
\(829\) | −1.69425e13 | −1.24590 | −0.622949 | − | 0.782263i | \(-0.714065\pi\) | ||||
−0.622949 | + | 0.782263i | \(0.714065\pi\) | |||||||
\(830\) | 1.27398e12 | 0.0931773 | ||||||||
\(831\) | −1.30855e12 | −0.0951889 | ||||||||
\(832\) | 1.21849e13 | 0.881593 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.07711e11 | −0.00770928 | ||||||||
\(835\) | −1.40739e13 | −1.00190 | ||||||||
\(836\) | −6.72735e12 | −0.476339 | ||||||||
\(837\) | 4.44368e12 | 0.312952 | ||||||||
\(838\) | −1.11321e12 | −0.0779790 | ||||||||
\(839\) | −2.51719e13 | −1.75383 | −0.876915 | − | 0.480645i | \(-0.840402\pi\) | ||||
−0.876915 | + | 0.480645i | \(0.840402\pi\) | |||||||
\(840\) | −1.61462e12 | −0.111896 | ||||||||
\(841\) | −1.33208e13 | −0.918223 | ||||||||
\(842\) | −3.12604e12 | −0.214334 | ||||||||
\(843\) | −7.94698e11 | −0.0541973 | ||||||||
\(844\) | −1.07178e13 | −0.727053 | ||||||||
\(845\) | −5.60606e11 | −0.0378270 | ||||||||
\(846\) | −7.10480e11 | −0.0476854 | ||||||||
\(847\) | 7.33034e12 | 0.489383 | ||||||||
\(848\) | 1.51745e13 | 1.00771 | ||||||||
\(849\) | −3.71934e11 | −0.0245687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.71385e12 | −0.569544 | ||||||||
\(852\) | 1.16928e12 | 0.0760224 | ||||||||
\(853\) | −1.68384e13 | −1.08901 | −0.544503 | − | 0.838759i | \(-0.683282\pi\) | ||||
−0.544503 | + | 0.838759i | \(0.683282\pi\) | |||||||
\(854\) | 1.79394e12 | 0.115411 | ||||||||
\(855\) | 1.19497e13 | 0.764732 | ||||||||
\(856\) | 4.66408e12 | 0.296916 | ||||||||
\(857\) | 1.45946e13 | 0.924225 | 0.462113 | − | 0.886821i | \(-0.347092\pi\) | ||||
0.462113 | + | 0.886821i | \(0.347092\pi\) | |||||||
\(858\) | 3.20834e11 | 0.0202110 | ||||||||
\(859\) | −2.05283e13 | −1.28642 | −0.643211 | − | 0.765689i | \(-0.722398\pi\) | ||||
−0.643211 | + | 0.765689i | \(0.722398\pi\) | |||||||
\(860\) | −4.54110e13 | −2.83086 | ||||||||
\(861\) | 5.58614e11 | 0.0346416 | ||||||||
\(862\) | −2.58988e12 | −0.159771 | ||||||||
\(863\) | 2.15891e13 | 1.32491 | 0.662453 | − | 0.749104i | \(-0.269515\pi\) | ||||
0.662453 | + | 0.749104i | \(0.269515\pi\) | |||||||
\(864\) | −1.71291e12 | −0.104574 | ||||||||
\(865\) | −5.56576e13 | −3.38027 | ||||||||
\(866\) | −3.64582e12 | −0.220275 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.36713e13 | −2.01336 | ||||||||
\(869\) | −1.92008e13 | −1.14217 | ||||||||
\(870\) | −1.58313e11 | −0.00936872 | ||||||||
\(871\) | 1.88061e13 | 1.10718 | ||||||||
\(872\) | 6.50338e12 | 0.380903 | ||||||||
\(873\) | −2.32332e12 | −0.135377 | ||||||||
\(874\) | 5.97743e11 | 0.0346508 | ||||||||
\(875\) | 7.08000e13 | 4.08317 | ||||||||
\(876\) | −9.25446e10 | −0.00530985 | ||||||||
\(877\) | 1.82834e13 | 1.04366 | 0.521830 | − | 0.853049i | \(-0.325250\pi\) | ||||
0.521830 | + | 0.853049i | \(0.325250\pi\) | |||||||
\(878\) | 8.61383e11 | 0.0489182 | ||||||||
\(879\) | −1.93625e12 | −0.109399 | ||||||||
\(880\) | −3.46201e13 | −1.94606 | ||||||||
\(881\) | 1.70514e12 | 0.0953604 | 0.0476802 | − | 0.998863i | \(-0.484817\pi\) | ||||
0.0476802 | + | 0.998863i | \(0.484817\pi\) | |||||||
\(882\) | 4.72866e12 | 0.263105 | ||||||||
\(883\) | −2.21871e13 | −1.22822 | −0.614112 | − | 0.789219i | \(-0.710486\pi\) | ||||
−0.614112 | + | 0.789219i | \(0.710486\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.73110e12 | 0.204452 | ||||||||
\(886\) | 3.18682e12 | 0.173742 | ||||||||
\(887\) | 2.47842e13 | 1.34437 | 0.672186 | − | 0.740382i | \(-0.265356\pi\) | ||||
0.672186 | + | 0.740382i | \(0.265356\pi\) | |||||||
\(888\) | 6.33090e11 | 0.0341670 | ||||||||
\(889\) | −3.00919e13 | −1.61581 | ||||||||
\(890\) | −8.47099e12 | −0.452563 | ||||||||
\(891\) | −2.01979e13 | −1.07364 | ||||||||
\(892\) | −8.06474e12 | −0.426529 | ||||||||
\(893\) | 2.90738e12 | 0.152992 | ||||||||
\(894\) | 5.00145e11 | 0.0261865 | ||||||||
\(895\) | −1.85321e13 | −0.965433 | ||||||||
\(896\) | 1.72491e13 | 0.894088 | ||||||||
\(897\) | 1.51539e12 | 0.0781553 | ||||||||
\(898\) | 2.92548e12 | 0.150125 | ||||||||
\(899\) | −6.66504e12 | −0.340317 | ||||||||
\(900\) | 4.37172e13 | 2.22107 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4.63764e11 | −0.0233275 | ||||||||
\(903\) | −7.24925e12 | −0.362826 | ||||||||
\(904\) | 2.30390e12 | 0.114738 | ||||||||
\(905\) | 6.99812e13 | 3.46787 | ||||||||
\(906\) | 2.52637e11 | 0.0124572 | ||||||||
\(907\) | −2.81679e13 | −1.38204 | −0.691021 | − | 0.722835i | \(-0.742839\pi\) | ||||
−0.691021 | + | 0.722835i | \(0.742839\pi\) | |||||||
\(908\) | −3.32513e13 | −1.62339 | ||||||||
\(909\) | −2.10512e13 | −1.02268 | ||||||||
\(910\) | 8.71388e12 | 0.421236 | ||||||||
\(911\) | 2.22649e12 | 0.107100 | 0.0535498 | − | 0.998565i | \(-0.482946\pi\) | ||||
0.0535498 | + | 0.998565i | \(0.482946\pi\) | |||||||
\(912\) | 1.12161e12 | 0.0536867 | ||||||||
\(913\) | 8.97539e12 | 0.427499 | ||||||||
\(914\) | −1.61095e12 | −0.0763527 | ||||||||
\(915\) | 2.51899e12 | 0.118804 | ||||||||
\(916\) | 2.22853e13 | 1.04590 | ||||||||
\(917\) | −5.69970e13 | −2.66189 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.93520e13 | 1.35743 | 0.678715 | − | 0.734402i | \(-0.262537\pi\) | ||||
0.678715 | + | 0.734402i | \(0.262537\pi\) | |||||||
\(920\) | 6.33139e12 | 0.291376 | ||||||||
\(921\) | −3.43240e12 | −0.157192 | ||||||||
\(922\) | 4.83820e12 | 0.220493 | ||||||||
\(923\) | −1.27396e13 | −0.577763 | ||||||||
\(924\) | −5.63463e12 | −0.254297 | ||||||||
\(925\) | −4.90596e13 | −2.20336 | ||||||||
\(926\) | −2.49416e12 | −0.111475 | ||||||||
\(927\) | 2.28660e13 | 1.01703 | ||||||||
\(928\) | 2.56918e12 | 0.113718 | ||||||||
\(929\) | −7.11576e12 | −0.313437 | −0.156719 | − | 0.987643i | \(-0.550092\pi\) | ||||
−0.156719 | + | 0.987643i | \(0.550092\pi\) | |||||||
\(930\) | 8.89416e11 | 0.0389881 | ||||||||
\(931\) | −1.93503e13 | −0.844139 | ||||||||
\(932\) | 2.71115e12 | 0.117702 | ||||||||
\(933\) | −2.28657e12 | −0.0987911 | ||||||||
\(934\) | 4.41585e12 | 0.189869 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.14656e12 | 0.261752 | ||||||||
\(937\) | 1.06889e13 | 0.453007 | 0.226503 | − | 0.974010i | \(-0.427271\pi\) | ||||
0.226503 | + | 0.974010i | \(0.427271\pi\) | |||||||
\(938\) | 6.21312e12 | 0.262058 | ||||||||
\(939\) | 8.87750e11 | 0.0372645 | ||||||||
\(940\) | 1.52542e13 | 0.637257 | ||||||||
\(941\) | 1.96244e13 | 0.815910 | 0.407955 | − | 0.913002i | \(-0.366242\pi\) | ||||
0.407955 | + | 0.913002i | \(0.366242\pi\) | |||||||
\(942\) | 1.04839e11 | 0.00433806 | ||||||||
\(943\) | −2.19049e12 | −0.0902067 | ||||||||
\(944\) | −1.95513e13 | −0.801312 | ||||||||
\(945\) | 2.01967e13 | 0.823829 | ||||||||
\(946\) | 6.01836e12 | 0.244325 | ||||||||
\(947\) | −1.29410e13 | −0.522870 | −0.261435 | − | 0.965221i | \(-0.584196\pi\) | ||||
−0.261435 | + | 0.965221i | \(0.584196\pi\) | |||||||
\(948\) | 3.26379e12 | 0.131246 | ||||||||
\(949\) | 1.00830e12 | 0.0403544 | ||||||||
\(950\) | 3.36533e12 | 0.134052 | ||||||||
\(951\) | −3.92183e12 | −0.155481 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.09666e13 | −0.430680 | −0.215340 | − | 0.976539i | \(-0.569086\pi\) | ||||
−0.215340 | + | 0.976539i | \(0.569086\pi\) | |||||||
\(954\) | 3.64208e12 | 0.142358 | ||||||||
\(955\) | 2.13366e13 | 0.830060 | ||||||||
\(956\) | −2.08040e13 | −0.805537 | ||||||||
\(957\) | −1.11534e12 | −0.0429838 | ||||||||
\(958\) | −3.68636e11 | −0.0141401 | ||||||||
\(959\) | 6.77556e13 | 2.58679 | ||||||||
\(960\) | 5.65267e12 | 0.214799 | ||||||||
\(961\) | 1.10051e13 | 0.416235 | ||||||||
\(962\) | −3.41670e12 | −0.128623 | ||||||||
\(963\) | −2.89117e13 | −1.08332 | ||||||||
\(964\) | −8.34763e12 | −0.311327 | ||||||||
\(965\) | −5.90511e13 | −2.19207 | ||||||||
\(966\) | 5.00651e11 | 0.0184986 | ||||||||
\(967\) | 3.26302e13 | 1.20005 | 0.600027 | − | 0.799980i | \(-0.295157\pi\) | ||||
0.600027 | + | 0.799980i | \(0.295157\pi\) | |||||||
\(968\) | 2.08838e12 | 0.0764486 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.38368e11 | −0.0340330 | ||||||||
\(971\) | 1.49723e13 | 0.540507 | 0.270253 | − | 0.962789i | \(-0.412893\pi\) | ||||
0.270253 | + | 0.962789i | \(0.412893\pi\) | |||||||
\(972\) | 1.06164e13 | 0.381488 | ||||||||
\(973\) | −2.06103e13 | −0.737185 | ||||||||
\(974\) | −3.74178e12 | −0.133218 | ||||||||
\(975\) | 8.53174e12 | 0.302355 | ||||||||
\(976\) | −1.31998e13 | −0.465631 | ||||||||
\(977\) | 1.12933e13 | 0.396548 | 0.198274 | − | 0.980147i | \(-0.436466\pi\) | ||||
0.198274 | + | 0.980147i | \(0.436466\pi\) | |||||||
\(978\) | 1.74908e11 | 0.00611342 | ||||||||
\(979\) | −5.96795e13 | −2.07636 | ||||||||
\(980\) | −1.01526e14 | −3.51608 | ||||||||
\(981\) | −4.03132e13 | −1.38975 | ||||||||
\(982\) | −3.38916e12 | −0.116303 | ||||||||
\(983\) | −5.44159e13 | −1.85881 | −0.929404 | − | 0.369063i | \(-0.879679\pi\) | ||||
−0.929404 | + | 0.369063i | \(0.879679\pi\) | |||||||
\(984\) | 1.59146e11 | 0.00541151 | ||||||||
\(985\) | −5.65403e13 | −1.91379 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.43513e12 | 0.0816761 | ||||||||
\(988\) | −1.24591e13 | −0.415987 | ||||||||
\(989\) | 2.84264e13 | 0.944798 | ||||||||
\(990\) | −8.30927e12 | −0.274919 | ||||||||
\(991\) | −3.13975e13 | −1.03410 | −0.517052 | − | 0.855954i | \(-0.672971\pi\) | ||||
−0.517052 | + | 0.855954i | \(0.672971\pi\) | |||||||
\(992\) | −1.44339e13 | −0.473238 | ||||||||
\(993\) | 6.18105e11 | 0.0201740 | ||||||||
\(994\) | −4.20890e12 | −0.136751 | ||||||||
\(995\) | 4.99246e13 | 1.61477 | ||||||||
\(996\) | −1.52566e12 | −0.0491235 | ||||||||
\(997\) | 3.75262e11 | 0.0120284 | 0.00601419 | − | 0.999982i | \(-0.498086\pi\) | ||||
0.00601419 | + | 0.999982i | \(0.498086\pi\) | |||||||
\(998\) | 5.65193e12 | 0.180347 | ||||||||
\(999\) | −7.91910e12 | −0.251554 |
(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.1.18 | yes | 36 | |
17.16 | even | 2 | 289.10.a.g.1.18 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.18 | ✓ | 36 | 17.16 | even | 2 | ||
289.10.a.h.1.18 | yes | 36 | 1.1 | even | 1 | trivial |