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 | 1.17 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.00956 | −0.309782 | −0.154891 | − | 0.987932i | \(-0.549503\pi\) | ||||
−0.154891 | + | 0.987932i | \(0.549503\pi\) | |||||||
\(3\) | 248.596 | 1.77194 | 0.885969 | − | 0.463744i | \(-0.153494\pi\) | ||||
0.885969 | + | 0.463744i | \(0.153494\pi\) | |||||||
\(4\) | −462.866 | −0.904035 | ||||||||
\(5\) | −1624.49 | −1.16239 | −0.581194 | − | 0.813765i | \(-0.697414\pi\) | ||||
−0.581194 | + | 0.813765i | \(0.697414\pi\) | |||||||
\(6\) | −1742.55 | −0.548914 | ||||||||
\(7\) | −8782.15 | −1.38248 | −0.691242 | − | 0.722624i | \(-0.742936\pi\) | ||||
−0.691242 | + | 0.722624i | \(0.742936\pi\) | |||||||
\(8\) | 6833.38 | 0.589835 | ||||||||
\(9\) | 42117.0 | 2.13977 | ||||||||
\(10\) | 11386.9 | 0.360087 | ||||||||
\(11\) | −52453.2 | −1.08020 | −0.540101 | − | 0.841600i | \(-0.681614\pi\) | ||||
−0.540101 | + | 0.841600i | \(0.681614\pi\) | |||||||
\(12\) | −115067. | −1.60190 | ||||||||
\(13\) | 14453.2 | 0.140352 | 0.0701761 | − | 0.997535i | \(-0.477644\pi\) | ||||
0.0701761 | + | 0.997535i | \(0.477644\pi\) | |||||||
\(14\) | 61559.0 | 0.428268 | ||||||||
\(15\) | −403841. | −2.05968 | ||||||||
\(16\) | 189088. | 0.721315 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −295222. | −0.662861 | ||||||||
\(19\) | −931720. | −1.64019 | −0.820095 | − | 0.572227i | \(-0.806080\pi\) | ||||
−0.820095 | + | 0.572227i | \(0.806080\pi\) | |||||||
\(20\) | 751920. | 1.05084 | ||||||||
\(21\) | −2.18321e6 | −2.44968 | ||||||||
\(22\) | 367674. | 0.334627 | ||||||||
\(23\) | 1.37040e6 | 1.02111 | 0.510556 | − | 0.859845i | \(-0.329440\pi\) | ||||
0.510556 | + | 0.859845i | \(0.329440\pi\) | |||||||
\(24\) | 1.69875e6 | 1.04515 | ||||||||
\(25\) | 685836. | 0.351148 | ||||||||
\(26\) | −101311. | −0.0434786 | ||||||||
\(27\) | 5.57701e6 | 2.01960 | ||||||||
\(28\) | 4.06496e6 | 1.24981 | ||||||||
\(29\) | −4.42440e6 | −1.16162 | −0.580810 | − | 0.814039i | \(-0.697264\pi\) | ||||
−0.580810 | + | 0.814039i | \(0.697264\pi\) | |||||||
\(30\) | 2.83075e6 | 0.638052 | ||||||||
\(31\) | −2.02178e6 | −0.393194 | −0.196597 | − | 0.980484i | \(-0.562989\pi\) | ||||
−0.196597 | + | 0.980484i | \(0.562989\pi\) | |||||||
\(32\) | −4.82412e6 | −0.813286 | ||||||||
\(33\) | −1.30397e7 | −1.91405 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.42665e7 | 1.60698 | ||||||||
\(36\) | −1.94945e7 | −1.93442 | ||||||||
\(37\) | −1.55332e7 | −1.36255 | −0.681277 | − | 0.732026i | \(-0.738575\pi\) | ||||
−0.681277 | + | 0.732026i | \(0.738575\pi\) | |||||||
\(38\) | 6.53095e6 | 0.508101 | ||||||||
\(39\) | 3.59301e6 | 0.248696 | ||||||||
\(40\) | −1.11007e7 | −0.685618 | ||||||||
\(41\) | −8.35453e6 | −0.461737 | −0.230869 | − | 0.972985i | \(-0.574157\pi\) | ||||
−0.230869 | + | 0.972985i | \(0.574157\pi\) | |||||||
\(42\) | 1.53033e7 | 0.758865 | ||||||||
\(43\) | −2.42190e7 | −1.08031 | −0.540154 | − | 0.841566i | \(-0.681634\pi\) | ||||
−0.540154 | + | 0.841566i | \(0.681634\pi\) | |||||||
\(44\) | 2.42788e7 | 0.976541 | ||||||||
\(45\) | −6.84186e7 | −2.48724 | ||||||||
\(46\) | −9.60592e6 | −0.316322 | ||||||||
\(47\) | −2.77645e7 | −0.829945 | −0.414973 | − | 0.909834i | \(-0.636209\pi\) | ||||
−0.414973 | + | 0.909834i | \(0.636209\pi\) | |||||||
\(48\) | 4.70066e7 | 1.27813 | ||||||||
\(49\) | 3.67726e7 | 0.911260 | ||||||||
\(50\) | −4.80741e6 | −0.108779 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.68990e6 | −0.126883 | ||||||||
\(53\) | 1.77712e6 | 0.0309369 | 0.0154684 | − | 0.999880i | \(-0.495076\pi\) | ||||
0.0154684 | + | 0.999880i | \(0.495076\pi\) | |||||||
\(54\) | −3.90924e7 | −0.625634 | ||||||||
\(55\) | 8.52096e7 | 1.25561 | ||||||||
\(56\) | −6.00118e7 | −0.815437 | ||||||||
\(57\) | −2.31622e8 | −2.90632 | ||||||||
\(58\) | 3.10131e7 | 0.359848 | ||||||||
\(59\) | −1.56378e8 | −1.68012 | −0.840062 | − | 0.542491i | \(-0.817481\pi\) | ||||
−0.840062 | + | 0.542491i | \(0.817481\pi\) | |||||||
\(60\) | 1.86924e8 | 1.86203 | ||||||||
\(61\) | 2.14150e8 | 1.98031 | 0.990157 | − | 0.139959i | \(-0.0446971\pi\) | ||||
0.990157 | + | 0.139959i | \(0.0446971\pi\) | |||||||
\(62\) | 1.41718e7 | 0.121804 | ||||||||
\(63\) | −3.69878e8 | −2.95819 | ||||||||
\(64\) | −6.29983e7 | −0.469374 | ||||||||
\(65\) | −2.34791e7 | −0.163144 | ||||||||
\(66\) | 9.14023e7 | 0.592938 | ||||||||
\(67\) | 5.42382e7 | 0.328828 | 0.164414 | − | 0.986391i | \(-0.447427\pi\) | ||||
0.164414 | + | 0.986391i | \(0.447427\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.40677e8 | 1.80935 | ||||||||
\(70\) | −1.00002e8 | −0.497814 | ||||||||
\(71\) | 2.38979e8 | 1.11608 | 0.558042 | − | 0.829812i | \(-0.311553\pi\) | ||||
0.558042 | + | 0.829812i | \(0.311553\pi\) | |||||||
\(72\) | 2.87802e8 | 1.26211 | ||||||||
\(73\) | 3.24831e8 | 1.33876 | 0.669382 | − | 0.742918i | \(-0.266559\pi\) | ||||
0.669382 | + | 0.742918i | \(0.266559\pi\) | |||||||
\(74\) | 1.08881e8 | 0.422094 | ||||||||
\(75\) | 1.70496e8 | 0.622212 | ||||||||
\(76\) | 4.31262e8 | 1.48279 | ||||||||
\(77\) | 4.60652e8 | 1.49336 | ||||||||
\(78\) | −2.51854e7 | −0.0770414 | ||||||||
\(79\) | 3.05262e8 | 0.881760 | 0.440880 | − | 0.897566i | \(-0.354666\pi\) | ||||
0.440880 | + | 0.897566i | \(0.354666\pi\) | |||||||
\(80\) | −3.07172e8 | −0.838449 | ||||||||
\(81\) | 5.57434e8 | 1.43884 | ||||||||
\(82\) | 5.85616e7 | 0.143038 | ||||||||
\(83\) | 1.35790e8 | 0.314062 | 0.157031 | − | 0.987594i | \(-0.449808\pi\) | ||||
0.157031 | + | 0.987594i | \(0.449808\pi\) | |||||||
\(84\) | 1.01053e9 | 2.21459 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.69764e8 | 0.334660 | ||||||||
\(87\) | −1.09989e9 | −2.05832 | ||||||||
\(88\) | −3.58433e8 | −0.637141 | ||||||||
\(89\) | 1.08876e9 | 1.83941 | 0.919703 | − | 0.392616i | \(-0.128430\pi\) | ||||
0.919703 | + | 0.392616i | \(0.128430\pi\) | |||||||
\(90\) | 4.79584e8 | 0.770502 | ||||||||
\(91\) | −1.26930e8 | −0.194035 | ||||||||
\(92\) | −6.34313e8 | −0.923121 | ||||||||
\(93\) | −5.02607e8 | −0.696716 | ||||||||
\(94\) | 1.94617e8 | 0.257102 | ||||||||
\(95\) | 1.51357e9 | 1.90654 | ||||||||
\(96\) | −1.19926e9 | −1.44109 | ||||||||
\(97\) | 7.22732e8 | 0.828904 | 0.414452 | − | 0.910071i | \(-0.363973\pi\) | ||||
0.414452 | + | 0.910071i | \(0.363973\pi\) | |||||||
\(98\) | −2.57760e8 | −0.282292 | ||||||||
\(99\) | −2.20917e9 | −2.31138 | ||||||||
\(100\) | −3.17450e8 | −0.317450 | ||||||||
\(101\) | −2.47246e8 | −0.236420 | −0.118210 | − | 0.992989i | \(-0.537716\pi\) | ||||
−0.118210 | + | 0.992989i | \(0.537716\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.21679e9 | 1.06524 | 0.532621 | − | 0.846354i | \(-0.321207\pi\) | ||||
0.532621 | + | 0.846354i | \(0.321207\pi\) | |||||||
\(104\) | 9.87644e7 | 0.0827847 | ||||||||
\(105\) | 3.54660e9 | 2.84748 | ||||||||
\(106\) | −1.24569e7 | −0.00958368 | ||||||||
\(107\) | −4.94831e8 | −0.364947 | −0.182474 | − | 0.983211i | \(-0.558410\pi\) | ||||
−0.182474 | + | 0.983211i | \(0.558410\pi\) | |||||||
\(108\) | −2.58141e9 | −1.82579 | ||||||||
\(109\) | −8.73972e8 | −0.593032 | −0.296516 | − | 0.955028i | \(-0.595825\pi\) | ||||
−0.296516 | + | 0.955028i | \(0.595825\pi\) | |||||||
\(110\) | −5.97282e8 | −0.388966 | ||||||||
\(111\) | −3.86150e9 | −2.41436 | ||||||||
\(112\) | −1.66060e9 | −0.997206 | ||||||||
\(113\) | 1.44323e9 | 0.832691 | 0.416345 | − | 0.909207i | \(-0.363311\pi\) | ||||
0.416345 | + | 0.909207i | \(0.363311\pi\) | |||||||
\(114\) | 1.62357e9 | 0.900324 | ||||||||
\(115\) | −2.22620e9 | −1.18693 | ||||||||
\(116\) | 2.04791e9 | 1.05014 | ||||||||
\(117\) | 6.08727e8 | 0.300321 | ||||||||
\(118\) | 1.09614e9 | 0.520471 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.75960e9 | −1.21487 | ||||||||
\(121\) | 3.93390e8 | 0.166836 | ||||||||
\(122\) | −1.50110e9 | −0.613465 | ||||||||
\(123\) | −2.07690e9 | −0.818170 | ||||||||
\(124\) | 9.35815e8 | 0.355461 | ||||||||
\(125\) | 2.05870e9 | 0.754219 | ||||||||
\(126\) | 2.59268e9 | 0.916394 | ||||||||
\(127\) | 1.54660e9 | 0.527547 | 0.263774 | − | 0.964585i | \(-0.415033\pi\) | ||||
0.263774 | + | 0.964585i | \(0.415033\pi\) | |||||||
\(128\) | 2.91154e9 | 0.958689 | ||||||||
\(129\) | −6.02074e9 | −1.91424 | ||||||||
\(130\) | 1.64578e8 | 0.0505390 | ||||||||
\(131\) | 3.97813e8 | 0.118021 | 0.0590104 | − | 0.998257i | \(-0.481205\pi\) | ||||
0.0590104 | + | 0.998257i | \(0.481205\pi\) | |||||||
\(132\) | 6.03562e9 | 1.73037 | ||||||||
\(133\) | 8.18251e9 | 2.26754 | ||||||||
\(134\) | −3.80186e8 | −0.101865 | ||||||||
\(135\) | −9.05979e9 | −2.34756 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.76046e8 | 0.0426956 | 0.0213478 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213478 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(138\) | −2.38800e9 | −0.560503 | ||||||||
\(139\) | 1.08750e9 | 0.247094 | 0.123547 | − | 0.992339i | \(-0.460573\pi\) | ||||
0.123547 | + | 0.992339i | \(0.460573\pi\) | |||||||
\(140\) | −6.60348e9 | −1.45277 | ||||||||
\(141\) | −6.90215e9 | −1.47061 | ||||||||
\(142\) | −1.67514e9 | −0.345743 | ||||||||
\(143\) | −7.58117e8 | −0.151609 | ||||||||
\(144\) | 7.96384e9 | 1.54345 | ||||||||
\(145\) | 7.18739e9 | 1.35025 | ||||||||
\(146\) | −2.27692e9 | −0.414725 | ||||||||
\(147\) | 9.14153e9 | 1.61470 | ||||||||
\(148\) | 7.18980e9 | 1.23180 | ||||||||
\(149\) | −1.37802e9 | −0.229044 | −0.114522 | − | 0.993421i | \(-0.536534\pi\) | ||||
−0.114522 | + | 0.993421i | \(0.536534\pi\) | |||||||
\(150\) | −1.19510e9 | −0.192750 | ||||||||
\(151\) | 1.19046e9 | 0.186345 | 0.0931726 | − | 0.995650i | \(-0.470299\pi\) | ||||
0.0931726 | + | 0.995650i | \(0.470299\pi\) | |||||||
\(152\) | −6.36680e9 | −0.967442 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.22897e9 | −0.462616 | ||||||||
\(155\) | 3.28436e9 | 0.457044 | ||||||||
\(156\) | −1.66308e9 | −0.224830 | ||||||||
\(157\) | −5.46787e9 | −0.718240 | −0.359120 | − | 0.933291i | \(-0.616923\pi\) | ||||
−0.359120 | + | 0.933291i | \(0.616923\pi\) | |||||||
\(158\) | −2.13975e9 | −0.273153 | ||||||||
\(159\) | 4.41786e8 | 0.0548183 | ||||||||
\(160\) | 7.83672e9 | 0.945354 | ||||||||
\(161\) | −1.20351e10 | −1.41167 | ||||||||
\(162\) | −3.90737e9 | −0.445725 | ||||||||
\(163\) | −8.81919e8 | −0.0978553 | −0.0489276 | − | 0.998802i | \(-0.515580\pi\) | ||||
−0.0489276 | + | 0.998802i | \(0.515580\pi\) | |||||||
\(164\) | 3.86703e9 | 0.417427 | ||||||||
\(165\) | 2.11828e10 | 2.22487 | ||||||||
\(166\) | −9.51827e8 | −0.0972908 | ||||||||
\(167\) | −6.76444e8 | −0.0672988 | −0.0336494 | − | 0.999434i | \(-0.510713\pi\) | ||||
−0.0336494 | + | 0.999434i | \(0.510713\pi\) | |||||||
\(168\) | −1.49187e10 | −1.44491 | ||||||||
\(169\) | −1.03956e10 | −0.980301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.92413e10 | −3.50963 | ||||||||
\(172\) | 1.12101e10 | 0.976636 | ||||||||
\(173\) | 7.28714e9 | 0.618514 | 0.309257 | − | 0.950978i | \(-0.399920\pi\) | ||||
0.309257 | + | 0.950978i | \(0.399920\pi\) | |||||||
\(174\) | 7.70974e9 | 0.637629 | ||||||||
\(175\) | −6.02311e9 | −0.485456 | ||||||||
\(176\) | −9.91829e9 | −0.779166 | ||||||||
\(177\) | −3.88749e10 | −2.97708 | ||||||||
\(178\) | −7.63173e9 | −0.569814 | ||||||||
\(179\) | −7.99107e8 | −0.0581790 | −0.0290895 | − | 0.999577i | \(-0.509261\pi\) | ||||
−0.0290895 | + | 0.999577i | \(0.509261\pi\) | |||||||
\(180\) | 3.16687e10 | 2.24855 | ||||||||
\(181\) | −1.62217e10 | −1.12342 | −0.561711 | − | 0.827333i | \(-0.689857\pi\) | ||||
−0.561711 | + | 0.827333i | \(0.689857\pi\) | |||||||
\(182\) | 8.89726e8 | 0.0601084 | ||||||||
\(183\) | 5.32369e10 | 3.50900 | ||||||||
\(184\) | 9.36449e9 | 0.602288 | ||||||||
\(185\) | 2.52335e10 | 1.58382 | ||||||||
\(186\) | 3.52306e9 | 0.215830 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.28512e10 | 0.750300 | ||||||||
\(189\) | −4.89782e10 | −2.79206 | ||||||||
\(190\) | −1.06094e10 | −0.590611 | ||||||||
\(191\) | 2.65734e10 | 1.44476 | 0.722382 | − | 0.691494i | \(-0.243047\pi\) | ||||
0.722382 | + | 0.691494i | \(0.243047\pi\) | |||||||
\(192\) | −1.56611e10 | −0.831702 | ||||||||
\(193\) | 8.35519e8 | 0.0433460 | 0.0216730 | − | 0.999765i | \(-0.493101\pi\) | ||||
0.0216730 | + | 0.999765i | \(0.493101\pi\) | |||||||
\(194\) | −5.06603e9 | −0.256779 | ||||||||
\(195\) | −5.83681e9 | −0.289081 | ||||||||
\(196\) | −1.70208e10 | −0.823811 | ||||||||
\(197\) | −2.26220e10 | −1.07012 | −0.535061 | − | 0.844813i | \(-0.679712\pi\) | ||||
−0.535061 | + | 0.844813i | \(0.679712\pi\) | |||||||
\(198\) | 1.54853e10 | 0.716023 | ||||||||
\(199\) | −7.37113e9 | −0.333192 | −0.166596 | − | 0.986025i | \(-0.553278\pi\) | ||||
−0.166596 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(200\) | 4.68658e9 | 0.207119 | ||||||||
\(201\) | 1.34834e10 | 0.582663 | ||||||||
\(202\) | 1.73309e9 | 0.0732386 | ||||||||
\(203\) | 3.88558e10 | 1.60592 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.35718e10 | 0.536718 | ||||||||
\(206\) | −8.52916e9 | −0.329992 | ||||||||
\(207\) | 5.77173e10 | 2.18494 | ||||||||
\(208\) | 2.73294e9 | 0.101238 | ||||||||
\(209\) | 4.88717e10 | 1.77174 | ||||||||
\(210\) | −2.48601e10 | −0.882096 | ||||||||
\(211\) | 4.36911e10 | 1.51748 | 0.758739 | − | 0.651395i | \(-0.225816\pi\) | ||||
0.758739 | + | 0.651395i | \(0.225816\pi\) | |||||||
\(212\) | −8.22571e8 | −0.0279680 | ||||||||
\(213\) | 5.94093e10 | 1.97763 | ||||||||
\(214\) | 3.46855e9 | 0.113054 | ||||||||
\(215\) | 3.93434e10 | 1.25574 | ||||||||
\(216\) | 3.81099e10 | 1.19123 | ||||||||
\(217\) | 1.77556e10 | 0.543584 | ||||||||
\(218\) | 6.12616e9 | 0.183711 | ||||||||
\(219\) | 8.07516e10 | 2.37221 | ||||||||
\(220\) | −3.94406e10 | −1.13512 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.70674e10 | 0.747925 | ||||||||
\(223\) | −4.77247e10 | −1.29232 | −0.646162 | − | 0.763201i | \(-0.723627\pi\) | ||||
−0.646162 | + | 0.763201i | \(0.723627\pi\) | |||||||
\(224\) | 4.23661e10 | 1.12435 | ||||||||
\(225\) | 2.88854e10 | 0.751375 | ||||||||
\(226\) | −1.01164e10 | −0.257952 | ||||||||
\(227\) | 1.11533e10 | 0.278795 | 0.139398 | − | 0.990236i | \(-0.455483\pi\) | ||||
0.139398 | + | 0.990236i | \(0.455483\pi\) | |||||||
\(228\) | 1.07210e11 | 2.62741 | ||||||||
\(229\) | −3.24445e9 | −0.0779617 | −0.0389809 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389809 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(230\) | 1.56047e10 | 0.367689 | ||||||||
\(231\) | 1.14516e11 | 2.64614 | ||||||||
\(232\) | −3.02336e10 | −0.685164 | ||||||||
\(233\) | −3.64924e10 | −0.811149 | −0.405575 | − | 0.914062i | \(-0.632929\pi\) | ||||
−0.405575 | + | 0.914062i | \(0.632929\pi\) | |||||||
\(234\) | −4.26691e9 | −0.0930340 | ||||||||
\(235\) | 4.51031e10 | 0.964719 | ||||||||
\(236\) | 7.23820e10 | 1.51889 | ||||||||
\(237\) | 7.58869e10 | 1.56242 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.38967e10 | −1.66324 | −0.831619 | − | 0.555347i | \(-0.812586\pi\) | ||||
−0.831619 | + | 0.555347i | \(0.812586\pi\) | |||||||
\(240\) | −7.63617e10 | −1.48568 | ||||||||
\(241\) | 3.00413e10 | 0.573644 | 0.286822 | − | 0.957984i | \(-0.407401\pi\) | ||||
0.286822 | + | 0.957984i | \(0.407401\pi\) | |||||||
\(242\) | −2.75749e9 | −0.0516827 | ||||||||
\(243\) | 2.88037e10 | 0.529931 | ||||||||
\(244\) | −9.91229e10 | −1.79027 | ||||||||
\(245\) | −5.97367e10 | −1.05924 | ||||||||
\(246\) | 1.45582e10 | 0.253454 | ||||||||
\(247\) | −1.34664e10 | −0.230204 | ||||||||
\(248\) | −1.38156e10 | −0.231920 | ||||||||
\(249\) | 3.37568e10 | 0.556499 | ||||||||
\(250\) | −1.44306e10 | −0.233643 | ||||||||
\(251\) | −4.24314e10 | −0.674770 | −0.337385 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337385 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(252\) | 1.71204e11 | 2.67431 | ||||||||
\(253\) | −7.18820e10 | −1.10301 | ||||||||
\(254\) | −1.08410e10 | −0.163425 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.18465e10 | 0.172390 | ||||||||
\(257\) | −6.81051e10 | −0.973824 | −0.486912 | − | 0.873451i | \(-0.661877\pi\) | ||||
−0.486912 | + | 0.873451i | \(0.661877\pi\) | |||||||
\(258\) | 4.22027e10 | 0.592996 | ||||||||
\(259\) | 1.36415e11 | 1.88371 | ||||||||
\(260\) | 1.08677e10 | 0.147488 | ||||||||
\(261\) | −1.86343e11 | −2.48559 | ||||||||
\(262\) | −2.78850e9 | −0.0365607 | ||||||||
\(263\) | 5.16210e10 | 0.665313 | 0.332656 | − | 0.943048i | \(-0.392055\pi\) | ||||
0.332656 | + | 0.943048i | \(0.392055\pi\) | |||||||
\(264\) | −8.91050e10 | −1.12898 | ||||||||
\(265\) | −2.88692e9 | −0.0359607 | ||||||||
\(266\) | −5.73558e10 | −0.702441 | ||||||||
\(267\) | 2.70662e11 | 3.25931 | ||||||||
\(268\) | −2.51050e10 | −0.297272 | ||||||||
\(269\) | −9.39280e10 | −1.09373 | −0.546865 | − | 0.837221i | \(-0.684179\pi\) | ||||
−0.546865 | + | 0.837221i | \(0.684179\pi\) | |||||||
\(270\) | 6.35051e10 | 0.727230 | ||||||||
\(271\) | 5.18776e10 | 0.584276 | 0.292138 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292138 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.15544e10 | −0.343818 | ||||||||
\(274\) | −1.23400e9 | −0.0132263 | ||||||||
\(275\) | −3.59743e10 | −0.379311 | ||||||||
\(276\) | −1.57688e11 | −1.63571 | ||||||||
\(277\) | −3.86848e9 | −0.0394804 | −0.0197402 | − | 0.999805i | \(-0.506284\pi\) | ||||
−0.0197402 | + | 0.999805i | \(0.506284\pi\) | |||||||
\(278\) | −7.62288e9 | −0.0765451 | ||||||||
\(279\) | −8.51515e10 | −0.841343 | ||||||||
\(280\) | 9.74885e10 | 0.947855 | ||||||||
\(281\) | −8.99774e10 | −0.860904 | −0.430452 | − | 0.902613i | \(-0.641646\pi\) | ||||
−0.430452 | + | 0.902613i | \(0.641646\pi\) | |||||||
\(282\) | 4.83810e10 | 0.455569 | ||||||||
\(283\) | 1.82003e11 | 1.68671 | 0.843353 | − | 0.537360i | \(-0.180578\pi\) | ||||
0.843353 | + | 0.537360i | \(0.180578\pi\) | |||||||
\(284\) | −1.10615e11 | −1.00898 | ||||||||
\(285\) | 3.76267e11 | 3.37827 | ||||||||
\(286\) | 5.31407e9 | 0.0469656 | ||||||||
\(287\) | 7.33708e10 | 0.638344 | ||||||||
\(288\) | −2.03178e11 | −1.74024 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −5.03804e10 | −0.418284 | ||||||||
\(291\) | 1.79668e11 | 1.46877 | ||||||||
\(292\) | −1.50353e11 | −1.21029 | ||||||||
\(293\) | −2.62335e10 | −0.207947 | −0.103973 | − | 0.994580i | \(-0.533156\pi\) | ||||
−0.103973 | + | 0.994580i | \(0.533156\pi\) | |||||||
\(294\) | −6.40781e10 | −0.500203 | ||||||||
\(295\) | 2.54034e11 | 1.95296 | ||||||||
\(296\) | −1.06144e11 | −0.803682 | ||||||||
\(297\) | −2.92532e11 | −2.18157 | ||||||||
\(298\) | 9.65934e9 | 0.0709536 | ||||||||
\(299\) | 1.98067e10 | 0.143315 | ||||||||
\(300\) | −7.89169e10 | −0.562502 | ||||||||
\(301\) | 2.12695e11 | 1.49351 | ||||||||
\(302\) | −8.34459e9 | −0.0577263 | ||||||||
\(303\) | −6.14645e10 | −0.418922 | ||||||||
\(304\) | −1.76177e11 | −1.18309 | ||||||||
\(305\) | −3.47884e11 | −2.30190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.12502e11 | −0.722830 | −0.361415 | − | 0.932405i | \(-0.617706\pi\) | ||||
−0.361415 | + | 0.932405i | \(0.617706\pi\) | |||||||
\(308\) | −2.13220e11 | −1.35005 | ||||||||
\(309\) | 3.02489e11 | 1.88754 | ||||||||
\(310\) | −2.30219e10 | −0.141584 | ||||||||
\(311\) | −1.05036e11 | −0.636674 | −0.318337 | − | 0.947978i | \(-0.603124\pi\) | ||||
−0.318337 | + | 0.947978i | \(0.603124\pi\) | |||||||
\(312\) | 2.45524e10 | 0.146689 | ||||||||
\(313\) | 2.38828e11 | 1.40648 | 0.703242 | − | 0.710950i | \(-0.251735\pi\) | ||||
0.703242 | + | 0.710950i | \(0.251735\pi\) | |||||||
\(314\) | 3.83274e10 | 0.222498 | ||||||||
\(315\) | 6.00863e11 | 3.43857 | ||||||||
\(316\) | −1.41295e11 | −0.797142 | ||||||||
\(317\) | 8.68678e10 | 0.483161 | 0.241581 | − | 0.970381i | \(-0.422334\pi\) | ||||
0.241581 | + | 0.970381i | \(0.422334\pi\) | |||||||
\(318\) | −3.09673e9 | −0.0169817 | ||||||||
\(319\) | 2.32074e11 | 1.25478 | ||||||||
\(320\) | 1.02340e11 | 0.545595 | ||||||||
\(321\) | −1.23013e11 | −0.646664 | ||||||||
\(322\) | 8.43607e10 | 0.437309 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.58017e11 | −1.30076 | ||||||||
\(325\) | 9.91253e9 | 0.0492844 | ||||||||
\(326\) | 6.18186e9 | 0.0303138 | ||||||||
\(327\) | −2.17266e11 | −1.05082 | ||||||||
\(328\) | −5.70897e10 | −0.272349 | ||||||||
\(329\) | 2.43832e11 | 1.14739 | ||||||||
\(330\) | −1.48482e11 | −0.689225 | ||||||||
\(331\) | −2.31728e11 | −1.06109 | −0.530546 | − | 0.847656i | \(-0.678013\pi\) | ||||
−0.530546 | + | 0.847656i | \(0.678013\pi\) | |||||||
\(332\) | −6.28525e10 | −0.283923 | ||||||||
\(333\) | −6.54213e11 | −2.91555 | ||||||||
\(334\) | 4.74157e9 | 0.0208479 | ||||||||
\(335\) | −8.81093e10 | −0.382226 | ||||||||
\(336\) | −4.12820e11 | −1.76699 | ||||||||
\(337\) | −1.29186e11 | −0.545610 | −0.272805 | − | 0.962069i | \(-0.587951\pi\) | ||||
−0.272805 | + | 0.962069i | \(0.587951\pi\) | |||||||
\(338\) | 7.28686e10 | 0.303679 | ||||||||
\(339\) | 3.58782e11 | 1.47548 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.06049e11 | 0.424729 | ||||||||
\(342\) | 2.75064e11 | 1.08722 | ||||||||
\(343\) | 3.14488e10 | 0.122682 | ||||||||
\(344\) | −1.65497e11 | −0.637204 | ||||||||
\(345\) | −5.53426e11 | −2.10316 | ||||||||
\(346\) | −5.10796e10 | −0.191604 | ||||||||
\(347\) | −3.89281e11 | −1.44139 | −0.720693 | − | 0.693254i | \(-0.756176\pi\) | ||||
−0.720693 | + | 0.693254i | \(0.756176\pi\) | |||||||
\(348\) | 5.09102e11 | 1.86079 | ||||||||
\(349\) | −1.79089e11 | −0.646181 | −0.323090 | − | 0.946368i | \(-0.604722\pi\) | ||||
−0.323090 | + | 0.946368i | \(0.604722\pi\) | |||||||
\(350\) | 4.22194e10 | 0.150385 | ||||||||
\(351\) | 8.06058e10 | 0.283455 | ||||||||
\(352\) | 2.53040e11 | 0.878513 | ||||||||
\(353\) | 1.53076e11 | 0.524711 | 0.262355 | − | 0.964971i | \(-0.415501\pi\) | ||||
0.262355 | + | 0.964971i | \(0.415501\pi\) | |||||||
\(354\) | 2.72496e11 | 0.922244 | ||||||||
\(355\) | −3.88219e11 | −1.29732 | ||||||||
\(356\) | −5.03950e11 | −1.66289 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.60139e9 | 0.0180228 | ||||||||
\(359\) | 4.54830e11 | 1.44519 | 0.722593 | − | 0.691274i | \(-0.242950\pi\) | ||||
0.722593 | + | 0.691274i | \(0.242950\pi\) | |||||||
\(360\) | −4.67530e11 | −1.46706 | ||||||||
\(361\) | 5.45415e11 | 1.69022 | ||||||||
\(362\) | 1.13707e11 | 0.348016 | ||||||||
\(363\) | 9.77953e10 | 0.295623 | ||||||||
\(364\) | 5.87518e10 | 0.175414 | ||||||||
\(365\) | −5.27683e11 | −1.55616 | ||||||||
\(366\) | −3.73167e11 | −1.08702 | ||||||||
\(367\) | 2.38622e11 | 0.686616 | 0.343308 | − | 0.939223i | \(-0.388453\pi\) | ||||
0.343308 | + | 0.939223i | \(0.388453\pi\) | |||||||
\(368\) | 2.59127e11 | 0.736543 | ||||||||
\(369\) | −3.51868e11 | −0.988010 | ||||||||
\(370\) | −1.76876e11 | −0.490638 | ||||||||
\(371\) | −1.56070e10 | −0.0427697 | ||||||||
\(372\) | 2.32640e11 | 0.629856 | ||||||||
\(373\) | 2.17508e11 | 0.581816 | 0.290908 | − | 0.956751i | \(-0.406043\pi\) | ||||
0.290908 | + | 0.956751i | \(0.406043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.11784e11 | 1.33643 | ||||||||
\(376\) | −1.89725e11 | −0.489531 | ||||||||
\(377\) | −6.39469e10 | −0.163036 | ||||||||
\(378\) | 3.43316e11 | 0.864929 | ||||||||
\(379\) | 1.13663e11 | 0.282972 | 0.141486 | − | 0.989940i | \(-0.454812\pi\) | ||||
0.141486 | + | 0.989940i | \(0.454812\pi\) | |||||||
\(380\) | −7.00579e11 | −1.72358 | ||||||||
\(381\) | 3.84479e11 | 0.934782 | ||||||||
\(382\) | −1.86268e11 | −0.447562 | ||||||||
\(383\) | −3.84471e11 | −0.912996 | −0.456498 | − | 0.889724i | \(-0.650896\pi\) | ||||
−0.456498 | + | 0.889724i | \(0.650896\pi\) | |||||||
\(384\) | 7.23797e11 | 1.69874 | ||||||||
\(385\) | −7.48324e11 | −1.73587 | ||||||||
\(386\) | −5.85662e9 | −0.0134278 | ||||||||
\(387\) | −1.02003e12 | −2.31161 | ||||||||
\(388\) | −3.34528e11 | −0.749359 | ||||||||
\(389\) | 4.29907e11 | 0.951921 | 0.475961 | − | 0.879467i | \(-0.342100\pi\) | ||||
0.475961 | + | 0.879467i | \(0.342100\pi\) | |||||||
\(390\) | 4.09135e10 | 0.0895520 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.51281e11 | 0.537493 | ||||||||
\(393\) | 9.88948e10 | 0.209126 | ||||||||
\(394\) | 1.58571e11 | 0.331504 | ||||||||
\(395\) | −4.95894e11 | −1.02495 | ||||||||
\(396\) | 1.02255e12 | 2.08957 | ||||||||
\(397\) | 7.51343e10 | 0.151803 | 0.0759017 | − | 0.997115i | \(-0.475816\pi\) | ||||
0.0759017 | + | 0.997115i | \(0.475816\pi\) | |||||||
\(398\) | 5.16683e10 | 0.103217 | ||||||||
\(399\) | 2.03414e12 | 4.01793 | ||||||||
\(400\) | 1.29684e11 | 0.253288 | ||||||||
\(401\) | −4.04002e11 | −0.780251 | −0.390125 | − | 0.920762i | \(-0.627568\pi\) | ||||
−0.390125 | + | 0.920762i | \(0.627568\pi\) | |||||||
\(402\) | −9.45128e10 | −0.180498 | ||||||||
\(403\) | −2.92213e10 | −0.0551857 | ||||||||
\(404\) | 1.14442e11 | 0.213732 | ||||||||
\(405\) | −9.05545e11 | −1.67249 | ||||||||
\(406\) | −2.72362e11 | −0.497484 | ||||||||
\(407\) | 8.14767e11 | 1.47183 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.13773e11 | 1.61467 | 0.807334 | − | 0.590094i | \(-0.200909\pi\) | ||||
0.807334 | + | 0.590094i | \(0.200909\pi\) | |||||||
\(410\) | −9.51326e10 | −0.166265 | ||||||||
\(411\) | 4.37643e10 | 0.0756541 | ||||||||
\(412\) | −5.63211e11 | −0.963016 | ||||||||
\(413\) | 1.37333e12 | 2.32274 | ||||||||
\(414\) | −4.04573e11 | −0.676855 | ||||||||
\(415\) | −2.20589e11 | −0.365063 | ||||||||
\(416\) | −6.97240e10 | −0.114146 | ||||||||
\(417\) | 2.70348e11 | 0.437835 | ||||||||
\(418\) | −3.42569e11 | −0.548852 | ||||||||
\(419\) | −1.00256e12 | −1.58909 | −0.794546 | − | 0.607204i | \(-0.792291\pi\) | ||||
−0.794546 | + | 0.607204i | \(0.792291\pi\) | |||||||
\(420\) | −1.64160e12 | −2.57422 | ||||||||
\(421\) | −2.42505e11 | −0.376229 | −0.188114 | − | 0.982147i | \(-0.560238\pi\) | ||||
−0.188114 | + | 0.982147i | \(0.560238\pi\) | |||||||
\(422\) | −3.06256e11 | −0.470087 | ||||||||
\(423\) | −1.16936e12 | −1.77589 | ||||||||
\(424\) | 1.21438e10 | 0.0182477 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.16433e11 | −0.612635 | ||||||||
\(427\) | −1.88070e12 | −2.73775 | ||||||||
\(428\) | 2.29040e11 | 0.329925 | ||||||||
\(429\) | −1.88465e11 | −0.268641 | ||||||||
\(430\) | −2.75780e11 | −0.389004 | ||||||||
\(431\) | 9.69783e11 | 1.35371 | 0.676857 | − | 0.736114i | \(-0.263341\pi\) | ||||
0.676857 | + | 0.736114i | \(0.263341\pi\) | |||||||
\(432\) | 1.05455e12 | 1.45677 | ||||||||
\(433\) | −1.45177e12 | −1.98473 | −0.992366 | − | 0.123330i | \(-0.960642\pi\) | ||||
−0.992366 | + | 0.123330i | \(0.960642\pi\) | |||||||
\(434\) | −1.24459e11 | −0.168392 | ||||||||
\(435\) | 1.78676e12 | 2.39257 | ||||||||
\(436\) | 4.04532e11 | 0.536122 | ||||||||
\(437\) | −1.27683e12 | −1.67482 | ||||||||
\(438\) | −5.66033e11 | −0.734867 | ||||||||
\(439\) | 4.81662e11 | 0.618945 | 0.309473 | − | 0.950908i | \(-0.399847\pi\) | ||||
0.309473 | + | 0.950908i | \(0.399847\pi\) | |||||||
\(440\) | 5.82270e11 | 0.740606 | ||||||||
\(441\) | 1.54875e12 | 1.94988 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.63906e11 | 0.942374 | 0.471187 | − | 0.882033i | \(-0.343826\pi\) | ||||
0.471187 | + | 0.882033i | \(0.343826\pi\) | |||||||
\(444\) | 1.78736e12 | 2.18267 | ||||||||
\(445\) | −1.76868e12 | −2.13810 | ||||||||
\(446\) | 3.34529e11 | 0.400338 | ||||||||
\(447\) | −3.42571e11 | −0.405852 | ||||||||
\(448\) | 5.53261e11 | 0.648902 | ||||||||
\(449\) | 6.18932e11 | 0.718678 | 0.359339 | − | 0.933207i | \(-0.383002\pi\) | ||||
0.359339 | + | 0.933207i | \(0.383002\pi\) | |||||||
\(450\) | −2.02474e11 | −0.232762 | ||||||||
\(451\) | 4.38222e11 | 0.498769 | ||||||||
\(452\) | −6.68024e11 | −0.752782 | ||||||||
\(453\) | 2.95943e11 | 0.330192 | ||||||||
\(454\) | −7.81795e10 | −0.0863657 | ||||||||
\(455\) | 2.06197e11 | 0.225544 | ||||||||
\(456\) | −1.58276e12 | −1.71425 | ||||||||
\(457\) | 7.94938e11 | 0.852532 | 0.426266 | − | 0.904598i | \(-0.359829\pi\) | ||||
0.426266 | + | 0.904598i | \(0.359829\pi\) | |||||||
\(458\) | 2.27422e10 | 0.0241511 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.03043e12 | 1.07303 | ||||||||
\(461\) | 1.01020e12 | 1.04173 | 0.520863 | − | 0.853640i | \(-0.325610\pi\) | ||||
0.520863 | + | 0.853640i | \(0.325610\pi\) | |||||||
\(462\) | −8.02709e11 | −0.819727 | ||||||||
\(463\) | 1.72927e12 | 1.74883 | 0.874414 | − | 0.485180i | \(-0.161246\pi\) | ||||
0.874414 | + | 0.485180i | \(0.161246\pi\) | |||||||
\(464\) | −8.36604e11 | −0.837893 | ||||||||
\(465\) | 8.16479e11 | 0.809854 | ||||||||
\(466\) | 2.55796e11 | 0.251279 | ||||||||
\(467\) | −6.73051e10 | −0.0654820 | −0.0327410 | − | 0.999464i | \(-0.510424\pi\) | ||||
−0.0327410 | + | 0.999464i | \(0.510424\pi\) | |||||||
\(468\) | −2.81759e11 | −0.271501 | ||||||||
\(469\) | −4.76328e11 | −0.454599 | ||||||||
\(470\) | −3.16153e11 | −0.298852 | ||||||||
\(471\) | −1.35929e12 | −1.27268 | ||||||||
\(472\) | −1.06859e12 | −0.990996 | ||||||||
\(473\) | 1.27036e12 | 1.16695 | ||||||||
\(474\) | −5.31934e11 | −0.484011 | ||||||||
\(475\) | −6.39007e11 | −0.575949 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.48472e10 | 0.0661977 | ||||||||
\(478\) | 5.88079e11 | 0.515241 | ||||||||
\(479\) | 2.10574e12 | 1.82766 | 0.913830 | − | 0.406097i | \(-0.133111\pi\) | ||||
0.913830 | + | 0.406097i | \(0.133111\pi\) | |||||||
\(480\) | 1.94818e12 | 1.67511 | ||||||||
\(481\) | −2.24505e11 | −0.191238 | ||||||||
\(482\) | −2.10577e11 | −0.177704 | ||||||||
\(483\) | −2.99188e12 | −2.50139 | ||||||||
\(484\) | −1.82087e11 | −0.150826 | ||||||||
\(485\) | −1.17407e12 | −0.963509 | ||||||||
\(486\) | −2.01901e11 | −0.164163 | ||||||||
\(487\) | 1.06942e12 | 0.861522 | 0.430761 | − | 0.902466i | \(-0.358245\pi\) | ||||
0.430761 | + | 0.902466i | \(0.358245\pi\) | |||||||
\(488\) | 1.46337e12 | 1.16806 | ||||||||
\(489\) | −2.19242e11 | −0.173394 | ||||||||
\(490\) | 4.18728e11 | 0.328133 | ||||||||
\(491\) | 3.63691e10 | 0.0282400 | 0.0141200 | − | 0.999900i | \(-0.495505\pi\) | ||||
0.0141200 | + | 0.999900i | \(0.495505\pi\) | |||||||
\(492\) | 9.61329e11 | 0.739654 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 9.43932e10 | 0.0713131 | ||||||||
\(495\) | 3.58877e12 | 2.68672 | ||||||||
\(496\) | −3.82296e11 | −0.283617 | ||||||||
\(497\) | −2.09875e12 | −1.54297 | ||||||||
\(498\) | −2.36621e11 | −0.172393 | ||||||||
\(499\) | 1.51766e12 | 1.09578 | 0.547888 | − | 0.836552i | \(-0.315432\pi\) | ||||
0.547888 | + | 0.836552i | \(0.315432\pi\) | |||||||
\(500\) | −9.52901e11 | −0.681840 | ||||||||
\(501\) | −1.68161e11 | −0.119249 | ||||||||
\(502\) | 2.97426e11 | 0.209031 | ||||||||
\(503\) | −1.28396e12 | −0.894328 | −0.447164 | − | 0.894452i | \(-0.647566\pi\) | ||||
−0.447164 | + | 0.894452i | \(0.647566\pi\) | |||||||
\(504\) | −2.52752e12 | −1.74485 | ||||||||
\(505\) | 4.01649e11 | 0.274812 | ||||||||
\(506\) | 5.03861e11 | 0.341691 | ||||||||
\(507\) | −2.58431e12 | −1.73703 | ||||||||
\(508\) | −7.15869e11 | −0.476921 | ||||||||
\(509\) | −1.62951e12 | −1.07604 | −0.538018 | − | 0.842934i | \(-0.680827\pi\) | ||||
−0.538018 | + | 0.842934i | \(0.680827\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.85271e12 | −1.85082 | ||||||||
\(512\) | −1.57375e12 | −1.01209 | ||||||||
\(513\) | −5.19622e12 | −3.31252 | ||||||||
\(514\) | 4.77387e11 | 0.301673 | ||||||||
\(515\) | −1.97666e12 | −1.23822 | ||||||||
\(516\) | 2.78680e12 | 1.73054 | ||||||||
\(517\) | 1.45634e12 | 0.896509 | ||||||||
\(518\) | −9.56210e11 | −0.583538 | ||||||||
\(519\) | 1.81155e12 | 1.09597 | ||||||||
\(520\) | −1.60442e11 | −0.0962280 | ||||||||
\(521\) | −2.49853e12 | −1.48565 | −0.742823 | − | 0.669488i | \(-0.766513\pi\) | ||||
−0.742823 | + | 0.669488i | \(0.766513\pi\) | |||||||
\(522\) | 1.30618e12 | 0.769992 | ||||||||
\(523\) | −2.86852e12 | −1.67649 | −0.838244 | − | 0.545295i | \(-0.816417\pi\) | ||||
−0.838244 | + | 0.545295i | \(0.816417\pi\) | |||||||
\(524\) | −1.84134e11 | −0.106695 | ||||||||
\(525\) | −1.49732e12 | −0.860198 | ||||||||
\(526\) | −3.61841e11 | −0.206102 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.46565e12 | −1.38063 | ||||||||
\(529\) | 7.68525e10 | 0.0426685 | ||||||||
\(530\) | 2.02360e10 | 0.0111400 | ||||||||
\(531\) | −6.58617e12 | −3.59507 | ||||||||
\(532\) | −3.78741e12 | −2.04993 | ||||||||
\(533\) | −1.20750e11 | −0.0648059 | ||||||||
\(534\) | −1.89722e12 | −1.00968 | ||||||||
\(535\) | 8.03847e11 | 0.424210 | ||||||||
\(536\) | 3.70630e11 | 0.193954 | ||||||||
\(537\) | −1.98655e11 | −0.103090 | ||||||||
\(538\) | 6.58394e11 | 0.338817 | ||||||||
\(539\) | −1.92884e12 | −0.984344 | ||||||||
\(540\) | 4.19347e12 | 2.12227 | ||||||||
\(541\) | 5.94020e11 | 0.298135 | 0.149068 | − | 0.988827i | \(-0.452373\pi\) | ||||
0.149068 | + | 0.988827i | \(0.452373\pi\) | |||||||
\(542\) | −3.63639e11 | −0.180998 | ||||||||
\(543\) | −4.03266e12 | −1.99064 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.41976e12 | 0.689334 | ||||||||
\(546\) | 2.21182e11 | 0.106508 | ||||||||
\(547\) | 6.01511e11 | 0.287277 | 0.143639 | − | 0.989630i | \(-0.454120\pi\) | ||||
0.143639 | + | 0.989630i | \(0.454120\pi\) | |||||||
\(548\) | −8.14857e10 | −0.0385984 | ||||||||
\(549\) | 9.01937e12 | 4.23741 | ||||||||
\(550\) | 2.52164e11 | 0.117503 | ||||||||
\(551\) | 4.12231e12 | 1.90528 | ||||||||
\(552\) | 2.32798e12 | 1.06722 | ||||||||
\(553\) | −2.68085e12 | −1.21902 | ||||||||
\(554\) | 2.71163e10 | 0.0122303 | ||||||||
\(555\) | 6.27296e12 | 2.80643 | ||||||||
\(556\) | −5.03366e11 | −0.223382 | ||||||||
\(557\) | 2.06033e12 | 0.906959 | 0.453480 | − | 0.891267i | \(-0.350182\pi\) | ||||
0.453480 | + | 0.891267i | \(0.350182\pi\) | |||||||
\(558\) | 5.96874e11 | 0.260633 | ||||||||
\(559\) | −3.50042e11 | −0.151624 | ||||||||
\(560\) | 2.69763e12 | 1.15914 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.30702e11 | 0.266692 | ||||||||
\(563\) | 2.45629e12 | 1.03037 | 0.515183 | − | 0.857080i | \(-0.327724\pi\) | ||||
0.515183 | + | 0.857080i | \(0.327724\pi\) | |||||||
\(564\) | 3.19477e12 | 1.32949 | ||||||||
\(565\) | −2.34452e12 | −0.967910 | ||||||||
\(566\) | −1.27576e12 | −0.522511 | ||||||||
\(567\) | −4.89547e12 | −1.98917 | ||||||||
\(568\) | 1.63304e12 | 0.658306 | ||||||||
\(569\) | −3.63389e11 | −0.145334 | −0.0726669 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726669 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(570\) | −2.63747e12 | −1.04653 | ||||||||
\(571\) | 2.95458e11 | 0.116314 | 0.0581572 | − | 0.998307i | \(-0.481478\pi\) | ||||
0.0581572 | + | 0.998307i | \(0.481478\pi\) | |||||||
\(572\) | 3.50907e11 | 0.137060 | ||||||||
\(573\) | 6.60605e12 | 2.56003 | ||||||||
\(574\) | −5.14297e11 | −0.197747 | ||||||||
\(575\) | 9.39871e11 | 0.358561 | ||||||||
\(576\) | −2.65330e12 | −1.00435 | ||||||||
\(577\) | −3.92296e12 | −1.47341 | −0.736703 | − | 0.676217i | \(-0.763618\pi\) | ||||
−0.736703 | + | 0.676217i | \(0.763618\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.07707e11 | 0.0768064 | ||||||||
\(580\) | −3.32680e12 | −1.22068 | ||||||||
\(581\) | −1.19253e12 | −0.434186 | ||||||||
\(582\) | −1.25940e12 | −0.454997 | ||||||||
\(583\) | −9.32159e10 | −0.0334181 | ||||||||
\(584\) | 2.21969e12 | 0.789650 | ||||||||
\(585\) | −9.88869e11 | −0.349090 | ||||||||
\(586\) | 1.83885e11 | 0.0644181 | ||||||||
\(587\) | −9.38917e11 | −0.326404 | −0.163202 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163202 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(588\) | −4.23130e12 | −1.45974 | ||||||||
\(589\) | 1.88374e12 | 0.644913 | ||||||||
\(590\) | −1.78067e12 | −0.604990 | ||||||||
\(591\) | −5.62375e12 | −1.89619 | ||||||||
\(592\) | −2.93715e12 | −0.982831 | ||||||||
\(593\) | −1.11640e12 | −0.370743 | −0.185372 | − | 0.982668i | \(-0.559349\pi\) | ||||
−0.185372 | + | 0.982668i | \(0.559349\pi\) | |||||||
\(594\) | 2.05052e12 | 0.675811 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.37841e11 | 0.207064 | ||||||||
\(597\) | −1.83243e12 | −0.590396 | ||||||||
\(598\) | −1.38837e11 | −0.0443965 | ||||||||
\(599\) | 3.47623e12 | 1.10329 | 0.551643 | − | 0.834080i | \(-0.314001\pi\) | ||||
0.551643 | + | 0.834080i | \(0.314001\pi\) | |||||||
\(600\) | 1.16506e12 | 0.367003 | ||||||||
\(601\) | −2.69936e12 | −0.843969 | −0.421984 | − | 0.906603i | \(-0.638666\pi\) | ||||
−0.421984 | + | 0.906603i | \(0.638666\pi\) | |||||||
\(602\) | −1.49090e12 | −0.462661 | ||||||||
\(603\) | 2.28435e12 | 0.703615 | ||||||||
\(604\) | −5.51023e11 | −0.168463 | ||||||||
\(605\) | −6.39058e11 | −0.193928 | ||||||||
\(606\) | 4.30839e11 | 0.129774 | ||||||||
\(607\) | 2.93363e10 | 0.00877114 | 0.00438557 | − | 0.999990i | \(-0.498604\pi\) | ||||
0.00438557 | + | 0.999990i | \(0.498604\pi\) | |||||||
\(608\) | 4.49473e12 | 1.33394 | ||||||||
\(609\) | 9.65940e12 | 2.84559 | ||||||||
\(610\) | 2.43852e12 | 0.713085 | ||||||||
\(611\) | −4.01286e11 | −0.116485 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.08148e11 | 0.231163 | 0.115582 | − | 0.993298i | \(-0.463127\pi\) | ||||
0.115582 | + | 0.993298i | \(0.463127\pi\) | |||||||
\(614\) | 7.88587e11 | 0.223919 | ||||||||
\(615\) | 3.37391e12 | 0.951032 | ||||||||
\(616\) | 3.14781e12 | 0.880837 | ||||||||
\(617\) | −6.66373e12 | −1.85112 | −0.925559 | − | 0.378603i | \(-0.876405\pi\) | ||||
−0.925559 | + | 0.378603i | \(0.876405\pi\) | |||||||
\(618\) | −2.12032e12 | −0.584726 | ||||||||
\(619\) | −3.87308e12 | −1.06035 | −0.530175 | − | 0.847888i | \(-0.677874\pi\) | ||||
−0.530175 | + | 0.847888i | \(0.677874\pi\) | |||||||
\(620\) | −1.52022e12 | −0.413184 | ||||||||
\(621\) | 7.64276e12 | 2.06223 | ||||||||
\(622\) | 7.36257e11 | 0.197230 | ||||||||
\(623\) | −9.56166e12 | −2.54295 | ||||||||
\(624\) | 6.79397e11 | 0.179388 | ||||||||
\(625\) | −4.68385e12 | −1.22784 | ||||||||
\(626\) | −1.67408e12 | −0.435703 | ||||||||
\(627\) | 1.21493e13 | 3.13941 | ||||||||
\(628\) | 2.53089e12 | 0.649315 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4.21178e12 | −1.06521 | ||||||||
\(631\) | −5.76051e12 | −1.44653 | −0.723267 | − | 0.690568i | \(-0.757360\pi\) | ||||
−0.723267 | + | 0.690568i | \(0.757360\pi\) | |||||||
\(632\) | 2.08597e12 | 0.520093 | ||||||||
\(633\) | 1.08614e13 | 2.68888 | ||||||||
\(634\) | −6.08905e11 | −0.149674 | ||||||||
\(635\) | −2.51243e12 | −0.613215 | ||||||||
\(636\) | −2.04488e11 | −0.0495576 | ||||||||
\(637\) | 5.31483e11 | 0.127897 | ||||||||
\(638\) | −1.62674e12 | −0.388709 | ||||||||
\(639\) | 1.00651e13 | 2.38816 | ||||||||
\(640\) | −4.72976e12 | −1.11437 | ||||||||
\(641\) | 2.94103e12 | 0.688079 | 0.344039 | − | 0.938955i | \(-0.388205\pi\) | ||||
0.344039 | + | 0.938955i | \(0.388205\pi\) | |||||||
\(642\) | 8.62267e11 | 0.200325 | ||||||||
\(643\) | 4.08339e12 | 0.942044 | 0.471022 | − | 0.882122i | \(-0.343885\pi\) | ||||
0.471022 | + | 0.882122i | \(0.343885\pi\) | |||||||
\(644\) | 5.57064e12 | 1.27620 | ||||||||
\(645\) | 9.78062e12 | 2.22509 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.11077e12 | 0.922262 | 0.461131 | − | 0.887332i | \(-0.347444\pi\) | ||||
0.461131 | + | 0.887332i | \(0.347444\pi\) | |||||||
\(648\) | 3.80916e12 | 0.848676 | ||||||||
\(649\) | 8.20252e12 | 1.81487 | ||||||||
\(650\) | −6.94825e10 | −0.0152674 | ||||||||
\(651\) | 4.41397e12 | 0.963198 | ||||||||
\(652\) | 4.08210e11 | 0.0884646 | ||||||||
\(653\) | 4.38279e12 | 0.943282 | 0.471641 | − | 0.881791i | \(-0.343662\pi\) | ||||
0.471641 | + | 0.881791i | \(0.343662\pi\) | |||||||
\(654\) | 1.52294e12 | 0.325524 | ||||||||
\(655\) | −6.46243e11 | −0.137186 | ||||||||
\(656\) | −1.57975e12 | −0.333058 | ||||||||
\(657\) | 1.36809e13 | 2.86464 | ||||||||
\(658\) | −1.70916e12 | −0.355439 | ||||||||
\(659\) | 1.21956e12 | 0.251894 | 0.125947 | − | 0.992037i | \(-0.459803\pi\) | ||||
0.125947 | + | 0.992037i | \(0.459803\pi\) | |||||||
\(660\) | −9.80479e12 | −2.01136 | ||||||||
\(661\) | −6.37742e12 | −1.29939 | −0.649694 | − | 0.760196i | \(-0.725103\pi\) | ||||
−0.649694 | + | 0.760196i | \(0.725103\pi\) | |||||||
\(662\) | 1.62431e12 | 0.328707 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.27904e11 | 0.185245 | ||||||||
\(665\) | −1.32924e13 | −2.63576 | ||||||||
\(666\) | 4.58574e12 | 0.903183 | ||||||||
\(667\) | −6.06322e12 | −1.18614 | ||||||||
\(668\) | 3.13103e11 | 0.0608405 | ||||||||
\(669\) | −1.18642e13 | −2.28992 | ||||||||
\(670\) | 6.17608e11 | 0.118407 | ||||||||
\(671\) | −1.12329e13 | −2.13914 | ||||||||
\(672\) | 1.05321e13 | 1.99229 | ||||||||
\(673\) | 1.25663e12 | 0.236124 | 0.118062 | − | 0.993006i | \(-0.462332\pi\) | ||||
0.118062 | + | 0.993006i | \(0.462332\pi\) | |||||||
\(674\) | 9.05539e11 | 0.169020 | ||||||||
\(675\) | 3.82491e12 | 0.709177 | ||||||||
\(676\) | 4.81177e12 | 0.886227 | ||||||||
\(677\) | −9.83587e11 | −0.179955 | −0.0899775 | − | 0.995944i | \(-0.528679\pi\) | ||||
−0.0899775 | + | 0.995944i | \(0.528679\pi\) | |||||||
\(678\) | −2.51491e12 | −0.457076 | ||||||||
\(679\) | −6.34714e12 | −1.14595 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.77266e12 | 0.494008 | ||||||||
\(682\) | −7.43357e11 | −0.131573 | ||||||||
\(683\) | 5.43786e12 | 0.956169 | 0.478084 | − | 0.878314i | \(-0.341331\pi\) | ||||
0.478084 | + | 0.878314i | \(0.341331\pi\) | |||||||
\(684\) | 1.81635e13 | 3.17283 | ||||||||
\(685\) | −2.85985e11 | −0.0496289 | ||||||||
\(686\) | −2.20443e11 | −0.0380047 | ||||||||
\(687\) | −8.06558e11 | −0.138143 | ||||||||
\(688\) | −4.57952e12 | −0.779242 | ||||||||
\(689\) | 2.56852e10 | 0.00434206 | ||||||||
\(690\) | 3.87927e12 | 0.651522 | ||||||||
\(691\) | −7.35157e12 | −1.22667 | −0.613337 | − | 0.789821i | \(-0.710173\pi\) | ||||
−0.613337 | + | 0.789821i | \(0.710173\pi\) | |||||||
\(692\) | −3.37297e12 | −0.559159 | ||||||||
\(693\) | 1.94013e13 | 3.19544 | ||||||||
\(694\) | 2.72869e12 | 0.446515 | ||||||||
\(695\) | −1.76663e12 | −0.287219 | ||||||||
\(696\) | −7.51597e12 | −1.21407 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.25533e12 | 0.200175 | ||||||||
\(699\) | −9.07187e12 | −1.43731 | ||||||||
\(700\) | 2.78790e12 | 0.438869 | ||||||||
\(701\) | −2.91902e12 | −0.456568 | −0.228284 | − | 0.973595i | \(-0.573311\pi\) | ||||
−0.228284 | + | 0.973595i | \(0.573311\pi\) | |||||||
\(702\) | −5.65011e11 | −0.0878092 | ||||||||
\(703\) | 1.44726e13 | 2.23485 | ||||||||
\(704\) | 3.30446e12 | 0.507019 | ||||||||
\(705\) | 1.12125e13 | 1.70942 | ||||||||
\(706\) | −1.07299e12 | −0.162546 | ||||||||
\(707\) | 2.17136e12 | 0.326846 | ||||||||
\(708\) | 1.79939e13 | 2.69138 | ||||||||
\(709\) | −1.06024e13 | −1.57577 | −0.787887 | − | 0.615819i | \(-0.788825\pi\) | ||||
−0.787887 | + | 0.615819i | \(0.788825\pi\) | |||||||
\(710\) | 2.72124e12 | 0.401887 | ||||||||
\(711\) | 1.28567e13 | 1.88676 | ||||||||
\(712\) | 7.43992e12 | 1.08495 | ||||||||
\(713\) | −2.77066e12 | −0.401495 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.23155e12 | 0.176228 | ||||||||
\(716\) | 3.69880e11 | 0.0525959 | ||||||||
\(717\) | −2.08564e13 | −2.94716 | ||||||||
\(718\) | −3.18816e12 | −0.447692 | ||||||||
\(719\) | 1.29087e13 | 1.80137 | 0.900683 | − | 0.434477i | \(-0.143067\pi\) | ||||
0.900683 | + | 0.434477i | \(0.143067\pi\) | |||||||
\(720\) | −1.29372e13 | −1.79408 | ||||||||
\(721\) | −1.06860e13 | −1.47268 | ||||||||
\(722\) | −3.82312e12 | −0.523601 | ||||||||
\(723\) | 7.46816e12 | 1.01646 | ||||||||
\(724\) | 7.50848e12 | 1.01561 | ||||||||
\(725\) | −3.03441e12 | −0.407900 | ||||||||
\(726\) | −6.85502e11 | −0.0915786 | ||||||||
\(727\) | 9.77625e12 | 1.29798 | 0.648989 | − | 0.760797i | \(-0.275192\pi\) | ||||
0.648989 | + | 0.760797i | \(0.275192\pi\) | |||||||
\(728\) | −8.67364e11 | −0.114448 | ||||||||
\(729\) | −3.81150e12 | −0.499830 | ||||||||
\(730\) | 3.69883e12 | 0.482071 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.46416e13 | −3.17226 | ||||||||
\(733\) | 4.87882e11 | 0.0624233 | 0.0312116 | − | 0.999513i | \(-0.490063\pi\) | ||||
0.0312116 | + | 0.999513i | \(0.490063\pi\) | |||||||
\(734\) | −1.67264e12 | −0.212701 | ||||||||
\(735\) | −1.48503e13 | −1.87690 | ||||||||
\(736\) | −6.61099e12 | −0.830455 | ||||||||
\(737\) | −2.84497e12 | −0.355201 | ||||||||
\(738\) | 2.46644e12 | 0.306067 | ||||||||
\(739\) | −1.08646e13 | −1.34003 | −0.670017 | − | 0.742346i | \(-0.733713\pi\) | ||||
−0.670017 | + | 0.742346i | \(0.733713\pi\) | |||||||
\(740\) | −1.16797e13 | −1.43183 | ||||||||
\(741\) | −3.34768e12 | −0.407908 | ||||||||
\(742\) | 1.09398e11 | 0.0132493 | ||||||||
\(743\) | 1.10195e13 | 1.32651 | 0.663257 | − | 0.748392i | \(-0.269174\pi\) | ||||
0.663257 | + | 0.748392i | \(0.269174\pi\) | |||||||
\(744\) | −3.43451e12 | −0.410947 | ||||||||
\(745\) | 2.23858e12 | 0.266238 | ||||||||
\(746\) | −1.52464e12 | −0.180236 | ||||||||
\(747\) | 5.71907e12 | 0.672020 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.34568e12 | 0.504533 | ||||||||
\(750\) | −3.58738e12 | −0.414001 | ||||||||
\(751\) | 3.58977e12 | 0.411801 | 0.205900 | − | 0.978573i | \(-0.433988\pi\) | ||||
0.205900 | + | 0.978573i | \(0.433988\pi\) | |||||||
\(752\) | −5.24995e12 | −0.598652 | ||||||||
\(753\) | −1.05483e13 | −1.19565 | ||||||||
\(754\) | 4.48239e11 | 0.0505055 | ||||||||
\(755\) | −1.93389e12 | −0.216606 | ||||||||
\(756\) | 2.26703e13 | 2.52412 | ||||||||
\(757\) | −2.28696e12 | −0.253120 | −0.126560 | − | 0.991959i | \(-0.540394\pi\) | ||||
−0.126560 | + | 0.991959i | \(0.540394\pi\) | |||||||
\(758\) | −7.96729e11 | −0.0876596 | ||||||||
\(759\) | −1.78696e13 | −1.95446 | ||||||||
\(760\) | 1.03428e13 | 1.12454 | ||||||||
\(761\) | −1.64862e13 | −1.78193 | −0.890963 | − | 0.454075i | \(-0.849970\pi\) | ||||
−0.890963 | + | 0.454075i | \(0.849970\pi\) | |||||||
\(762\) | −2.69503e12 | −0.289578 | ||||||||
\(763\) | 7.67536e12 | 0.819857 | ||||||||
\(764\) | −1.22999e13 | −1.30612 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.69497e12 | 0.282829 | ||||||||
\(767\) | −2.26016e12 | −0.235809 | ||||||||
\(768\) | 2.94500e12 | 0.305464 | ||||||||
\(769\) | 1.24332e13 | 1.28208 | 0.641041 | − | 0.767507i | \(-0.278503\pi\) | ||||
0.641041 | + | 0.767507i | \(0.278503\pi\) | |||||||
\(770\) | 5.24542e12 | 0.537740 | ||||||||
\(771\) | −1.69307e13 | −1.72556 | ||||||||
\(772\) | −3.86734e11 | −0.0391863 | ||||||||
\(773\) | 1.06939e12 | 0.107728 | 0.0538642 | − | 0.998548i | \(-0.482846\pi\) | ||||
0.0538642 | + | 0.998548i | \(0.482846\pi\) | |||||||
\(774\) | 7.14997e12 | 0.716093 | ||||||||
\(775\) | −1.38661e12 | −0.138069 | ||||||||
\(776\) | 4.93870e12 | 0.488917 | ||||||||
\(777\) | 3.39123e13 | 3.33781 | ||||||||
\(778\) | −3.01346e12 | −0.294888 | ||||||||
\(779\) | 7.78409e12 | 0.757337 | ||||||||
\(780\) | 2.70166e12 | 0.261339 | ||||||||
\(781\) | −1.25352e13 | −1.20560 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.46750e13 | −2.34600 | ||||||||
\(784\) | 6.95328e12 | 0.657305 | ||||||||
\(785\) | 8.88249e12 | 0.834875 | ||||||||
\(786\) | −6.93209e11 | −0.0647833 | ||||||||
\(787\) | −1.51542e13 | −1.40815 | −0.704073 | − | 0.710128i | \(-0.748637\pi\) | ||||
−0.704073 | + | 0.710128i | \(0.748637\pi\) | |||||||
\(788\) | 1.04710e13 | 0.967429 | ||||||||
\(789\) | 1.28328e13 | 1.17889 | ||||||||
\(790\) | 3.47600e12 | 0.317510 | ||||||||
\(791\) | −1.26747e13 | −1.15118 | ||||||||
\(792\) | −1.50961e13 | −1.36333 | ||||||||
\(793\) | 3.09516e12 | 0.277942 | ||||||||
\(794\) | −5.26659e11 | −0.0470259 | ||||||||
\(795\) | −7.17677e11 | −0.0637201 | ||||||||
\(796\) | 3.41184e12 | 0.301218 | ||||||||
\(797\) | 1.45731e12 | 0.127935 | 0.0639675 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639675 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(798\) | −1.42584e13 | −1.24468 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −3.30855e12 | −0.285583 | ||||||||
\(801\) | 4.58554e13 | 3.93590 | ||||||||
\(802\) | 2.83188e12 | 0.241707 | ||||||||
\(803\) | −1.70384e13 | −1.44614 | ||||||||
\(804\) | −6.24101e12 | −0.526748 | ||||||||
\(805\) | 1.95509e13 | 1.64091 | ||||||||
\(806\) | 2.04828e11 | 0.0170955 | ||||||||
\(807\) | −2.33501e13 | −1.93802 | ||||||||
\(808\) | −1.68953e12 | −0.139449 | ||||||||
\(809\) | 3.25669e12 | 0.267306 | 0.133653 | − | 0.991028i | \(-0.457329\pi\) | ||||
0.133653 | + | 0.991028i | \(0.457329\pi\) | |||||||
\(810\) | 6.34747e12 | 0.518106 | ||||||||
\(811\) | −3.09214e12 | −0.250995 | −0.125498 | − | 0.992094i | \(-0.540053\pi\) | ||||
−0.125498 | + | 0.992094i | \(0.540053\pi\) | |||||||
\(812\) | −1.79850e13 | −1.45181 | ||||||||
\(813\) | 1.28966e13 | 1.03530 | ||||||||
\(814\) | −5.71116e12 | −0.455947 | ||||||||
\(815\) | 1.43267e12 | 0.113746 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.25653e13 | 1.77191 | ||||||||
\(818\) | −6.40515e12 | −0.500195 | ||||||||
\(819\) | −5.34593e12 | −0.415189 | ||||||||
\(820\) | −6.28194e12 | −0.485212 | ||||||||
\(821\) | −2.16404e13 | −1.66235 | −0.831173 | − | 0.556014i | \(-0.812330\pi\) | ||||
−0.831173 | + | 0.556014i | \(0.812330\pi\) | |||||||
\(822\) | −3.06769e11 | −0.0234362 | ||||||||
\(823\) | −1.30860e13 | −0.994274 | −0.497137 | − | 0.867672i | \(-0.665615\pi\) | ||||
−0.497137 | + | 0.867672i | \(0.665615\pi\) | |||||||
\(824\) | 8.31479e12 | 0.628317 | ||||||||
\(825\) | −8.94306e12 | −0.672115 | ||||||||
\(826\) | −9.62647e12 | −0.719543 | ||||||||
\(827\) | 2.09145e13 | 1.55479 | 0.777395 | − | 0.629012i | \(-0.216541\pi\) | ||||
0.777395 | + | 0.629012i | \(0.216541\pi\) | |||||||
\(828\) | −2.67154e13 | −1.97526 | ||||||||
\(829\) | 1.62798e13 | 1.19716 | 0.598582 | − | 0.801062i | \(-0.295731\pi\) | ||||
0.598582 | + | 0.801062i | \(0.295731\pi\) | |||||||
\(830\) | 1.54623e12 | 0.113090 | ||||||||
\(831\) | −9.61688e11 | −0.0699568 | ||||||||
\(832\) | −9.10529e11 | −0.0658777 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.89502e12 | −0.135633 | ||||||||
\(835\) | 1.09887e12 | 0.0782274 | ||||||||
\(836\) | −2.26211e13 | −1.60171 | ||||||||
\(837\) | −1.12755e13 | −0.794093 | ||||||||
\(838\) | 7.02753e12 | 0.492271 | ||||||||
\(839\) | 1.90100e13 | 1.32450 | 0.662250 | − | 0.749283i | \(-0.269601\pi\) | ||||
0.662250 | + | 0.749283i | \(0.269601\pi\) | |||||||
\(840\) | 2.42353e13 | 1.67954 | ||||||||
\(841\) | 5.06820e12 | 0.349359 | ||||||||
\(842\) | 1.69986e12 | 0.116549 | ||||||||
\(843\) | −2.23680e13 | −1.52547 | ||||||||
\(844\) | −2.02231e13 | −1.37185 | ||||||||
\(845\) | 1.68875e13 | 1.13949 | ||||||||
\(846\) | 8.19669e12 | 0.550138 | ||||||||
\(847\) | −3.45481e12 | −0.230648 | ||||||||
\(848\) | 3.36034e11 | 0.0223152 | ||||||||
\(849\) | 4.52452e13 | 2.98874 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.12868e13 | −1.39132 | ||||||||
\(852\) | −2.74985e13 | −1.78785 | ||||||||
\(853\) | 2.05191e13 | 1.32705 | 0.663526 | − | 0.748153i | \(-0.269059\pi\) | ||||
0.663526 | + | 0.748153i | \(0.269059\pi\) | |||||||
\(854\) | 1.31829e13 | 0.848105 | ||||||||
\(855\) | 6.37470e13 | 4.07955 | ||||||||
\(856\) | −3.38137e12 | −0.215259 | ||||||||
\(857\) | −2.96637e12 | −0.187850 | −0.0939250 | − | 0.995579i | \(-0.529941\pi\) | ||||
−0.0939250 | + | 0.995579i | \(0.529941\pi\) | |||||||
\(858\) | 1.32106e12 | 0.0832202 | ||||||||
\(859\) | 1.06159e13 | 0.665257 | 0.332628 | − | 0.943058i | \(-0.392065\pi\) | ||||
0.332628 | + | 0.943058i | \(0.392065\pi\) | |||||||
\(860\) | −1.82107e13 | −1.13523 | ||||||||
\(861\) | 1.82397e13 | 1.13111 | ||||||||
\(862\) | −6.79775e12 | −0.419356 | ||||||||
\(863\) | −1.32698e13 | −0.814356 | −0.407178 | − | 0.913349i | \(-0.633487\pi\) | ||||
−0.407178 | + | 0.913349i | \(0.633487\pi\) | |||||||
\(864\) | −2.69042e13 | −1.64251 | ||||||||
\(865\) | −1.18379e13 | −0.718954 | ||||||||
\(866\) | 1.01763e13 | 0.614833 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.21847e12 | −0.491419 | ||||||||
\(869\) | −1.60120e13 | −0.952479 | ||||||||
\(870\) | −1.25244e13 | −0.741173 | ||||||||
\(871\) | 7.83917e11 | 0.0461518 | ||||||||
\(872\) | −5.97218e12 | −0.349791 | ||||||||
\(873\) | 3.04393e13 | 1.77366 | ||||||||
\(874\) | 8.95003e12 | 0.518828 | ||||||||
\(875\) | −1.80798e13 | −1.04269 | ||||||||
\(876\) | −3.73772e13 | −2.14456 | ||||||||
\(877\) | 1.84228e13 | 1.05162 | 0.525808 | − | 0.850603i | \(-0.323763\pi\) | ||||
0.525808 | + | 0.850603i | \(0.323763\pi\) | |||||||
\(878\) | −3.37624e12 | −0.191738 | ||||||||
\(879\) | −6.52155e12 | −0.368469 | ||||||||
\(880\) | 1.61121e13 | 0.905694 | ||||||||
\(881\) | −1.68763e12 | −0.0943813 | −0.0471907 | − | 0.998886i | \(-0.515027\pi\) | ||||
−0.0471907 | + | 0.998886i | \(0.515027\pi\) | |||||||
\(882\) | −1.08561e13 | −0.604038 | ||||||||
\(883\) | 4.77050e12 | 0.264083 | 0.132042 | − | 0.991244i | \(-0.457847\pi\) | ||||
0.132042 | + | 0.991244i | \(0.457847\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.31518e13 | 3.46052 | ||||||||
\(886\) | −5.35464e12 | −0.291930 | ||||||||
\(887\) | 1.25350e13 | 0.679936 | 0.339968 | − | 0.940437i | \(-0.389584\pi\) | ||||
0.339968 | + | 0.940437i | \(0.389584\pi\) | |||||||
\(888\) | −2.63871e13 | −1.42408 | ||||||||
\(889\) | −1.35825e13 | −0.729325 | ||||||||
\(890\) | 1.23977e13 | 0.662346 | ||||||||
\(891\) | −2.92392e13 | −1.55423 | ||||||||
\(892\) | 2.20901e13 | 1.16831 | ||||||||
\(893\) | 2.58687e13 | 1.36127 | ||||||||
\(894\) | 2.40128e12 | 0.125725 | ||||||||
\(895\) | 1.29814e12 | 0.0676266 | ||||||||
\(896\) | −2.55696e13 | −1.32537 | ||||||||
\(897\) | 4.92388e12 | 0.253946 | ||||||||
\(898\) | −4.33844e12 | −0.222633 | ||||||||
\(899\) | 8.94518e12 | 0.456742 | ||||||||
\(900\) | −1.33701e13 | −0.679269 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3.07174e12 | −0.154510 | ||||||||
\(903\) | 5.28751e13 | 2.64640 | ||||||||
\(904\) | 9.86217e12 | 0.491150 | ||||||||
\(905\) | 2.63520e13 | 1.30585 | ||||||||
\(906\) | −2.07443e12 | −0.102288 | ||||||||
\(907\) | −1.39545e13 | −0.684668 | −0.342334 | − | 0.939578i | \(-0.611217\pi\) | ||||
−0.342334 | + | 0.939578i | \(0.611217\pi\) | |||||||
\(908\) | −5.16247e12 | −0.252041 | ||||||||
\(909\) | −1.04133e13 | −0.505883 | ||||||||
\(910\) | −1.44535e12 | −0.0698693 | ||||||||
\(911\) | 1.75468e13 | 0.844045 | 0.422022 | − | 0.906585i | \(-0.361320\pi\) | ||||
0.422022 | + | 0.906585i | \(0.361320\pi\) | |||||||
\(912\) | −4.37970e13 | −2.09637 | ||||||||
\(913\) | −7.12261e12 | −0.339251 | ||||||||
\(914\) | −5.57217e12 | −0.264099 | ||||||||
\(915\) | −8.64827e13 | −4.07882 | ||||||||
\(916\) | 1.50175e12 | 0.0704801 | ||||||||
\(917\) | −3.49366e12 | −0.163162 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.57783e12 | 0.257956 | 0.128978 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128978 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(920\) | −1.52125e13 | −0.700092 | ||||||||
\(921\) | −2.79675e13 | −1.28081 | ||||||||
\(922\) | −7.08106e12 | −0.322708 | ||||||||
\(923\) | 3.45402e12 | 0.156645 | ||||||||
\(924\) | −5.30057e13 | −2.39221 | ||||||||
\(925\) | −1.06532e13 | −0.478458 | ||||||||
\(926\) | −1.21214e13 | −0.541755 | ||||||||
\(927\) | 5.12476e13 | 2.27937 | ||||||||
\(928\) | 2.13438e13 | 0.944728 | ||||||||
\(929\) | −2.46767e13 | −1.08697 | −0.543483 | − | 0.839420i | \(-0.682895\pi\) | ||||
−0.543483 | + | 0.839420i | \(0.682895\pi\) | |||||||
\(930\) | −5.72316e12 | −0.250878 | ||||||||
\(931\) | −3.42618e13 | −1.49464 | ||||||||
\(932\) | 1.68911e13 | 0.733308 | ||||||||
\(933\) | −2.61116e13 | −1.12815 | ||||||||
\(934\) | 4.71779e11 | 0.0202851 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.15966e12 | 0.177140 | ||||||||
\(937\) | 3.72310e13 | 1.57789 | 0.788944 | − | 0.614465i | \(-0.210628\pi\) | ||||
0.788944 | + | 0.614465i | \(0.210628\pi\) | |||||||
\(938\) | 3.33885e12 | 0.140827 | ||||||||
\(939\) | 5.93716e13 | 2.49220 | ||||||||
\(940\) | −2.08767e13 | −0.872140 | ||||||||
\(941\) | 2.09390e13 | 0.870569 | 0.435284 | − | 0.900293i | \(-0.356648\pi\) | ||||
0.435284 | + | 0.900293i | \(0.356648\pi\) | |||||||
\(942\) | 9.52803e12 | 0.394252 | ||||||||
\(943\) | −1.14491e13 | −0.471485 | ||||||||
\(944\) | −2.95692e13 | −1.21190 | ||||||||
\(945\) | 7.95645e13 | 3.24546 | ||||||||
\(946\) | −8.90468e12 | −0.361500 | ||||||||
\(947\) | −3.50065e13 | −1.41440 | −0.707202 | − | 0.707011i | \(-0.750043\pi\) | ||||
−0.707202 | + | 0.707011i | \(0.750043\pi\) | |||||||
\(948\) | −3.51255e13 | −1.41249 | ||||||||
\(949\) | 4.69485e12 | 0.187899 | ||||||||
\(950\) | 4.47916e12 | 0.178419 | ||||||||
\(951\) | 2.15950e13 | 0.856132 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.83362e12 | 0.189825 | 0.0949127 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949127 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(954\) | −5.24646e11 | −0.0205068 | ||||||||
\(955\) | −4.31682e13 | −1.67938 | ||||||||
\(956\) | 3.88329e13 | 1.50363 | ||||||||
\(957\) | 5.76927e13 | 2.22340 | ||||||||
\(958\) | −1.47603e13 | −0.566176 | ||||||||
\(959\) | −1.54606e12 | −0.0590260 | ||||||||
\(960\) | 2.54413e13 | 0.966761 | ||||||||
\(961\) | −2.23520e13 | −0.845399 | ||||||||
\(962\) | 1.57368e12 | 0.0592419 | ||||||||
\(963\) | −2.08408e13 | −0.780902 | ||||||||
\(964\) | −1.39051e13 | −0.518595 | ||||||||
\(965\) | −1.35729e12 | −0.0503849 | ||||||||
\(966\) | 2.09717e13 | 0.774885 | ||||||||
\(967\) | 2.43474e13 | 0.895436 | 0.447718 | − | 0.894175i | \(-0.352237\pi\) | ||||
0.447718 | + | 0.894175i | \(0.352237\pi\) | |||||||
\(968\) | 2.68819e12 | 0.0984057 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.22971e12 | 0.298478 | ||||||||
\(971\) | −1.35465e13 | −0.489034 | −0.244517 | − | 0.969645i | \(-0.578629\pi\) | ||||
−0.244517 | + | 0.969645i | \(0.578629\pi\) | |||||||
\(972\) | −1.33322e13 | −0.479076 | ||||||||
\(973\) | −9.55057e12 | −0.341603 | ||||||||
\(974\) | −7.49614e12 | −0.266884 | ||||||||
\(975\) | 2.46422e12 | 0.0873289 | ||||||||
\(976\) | 4.04933e13 | 1.42843 | ||||||||
\(977\) | 3.05916e13 | 1.07418 | 0.537090 | − | 0.843525i | \(-0.319524\pi\) | ||||
0.537090 | + | 0.843525i | \(0.319524\pi\) | |||||||
\(978\) | 1.53679e12 | 0.0537142 | ||||||||
\(979\) | −5.71090e13 | −1.98693 | ||||||||
\(980\) | 2.76501e13 | 0.957589 | ||||||||
\(981\) | −3.68091e13 | −1.26895 | ||||||||
\(982\) | −2.54931e11 | −0.00874825 | ||||||||
\(983\) | −8.75389e12 | −0.299027 | −0.149514 | − | 0.988760i | \(-0.547771\pi\) | ||||
−0.149514 | + | 0.988760i | \(0.547771\pi\) | |||||||
\(984\) | −1.41923e13 | −0.482585 | ||||||||
\(985\) | 3.67492e13 | 1.24390 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.06157e13 | 2.03310 | ||||||||
\(988\) | 6.23312e12 | 0.208113 | ||||||||
\(989\) | −3.31897e13 | −1.10311 | ||||||||
\(990\) | −2.51557e13 | −0.832297 | ||||||||
\(991\) | 9.06157e12 | 0.298450 | 0.149225 | − | 0.988803i | \(-0.452322\pi\) | ||||
0.149225 | + | 0.988803i | \(0.452322\pi\) | |||||||
\(992\) | 9.75332e12 | 0.319779 | ||||||||
\(993\) | −5.76068e13 | −1.88019 | ||||||||
\(994\) | 1.47113e13 | 0.477983 | ||||||||
\(995\) | 1.19743e13 | 0.387299 | ||||||||
\(996\) | −1.56249e13 | −0.503095 | ||||||||
\(997\) | −1.22306e13 | −0.392030 | −0.196015 | − | 0.980601i | \(-0.562800\pi\) | ||||
−0.196015 | + | 0.980601i | \(0.562800\pi\) | |||||||
\(998\) | −1.06381e13 | −0.339451 | ||||||||
\(999\) | −8.66290e13 | −2.75181 |
(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.1.17 | yes | 36 | |
17.16 | even | 2 | 289.10.a.g.1.17 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.17 | ✓ | 36 | 17.16 | even | 2 | ||
289.10.a.h.1.17 | yes | 36 | 1.1 | even | 1 | trivial |