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: | \(52\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −26.9890 | −1.19276 | −0.596379 | − | 0.802703i | \(-0.703395\pi\) | ||||
−0.596379 | + | 0.802703i | \(0.703395\pi\) | |||||||
\(3\) | −111.659 | −0.795878 | −0.397939 | − | 0.917412i | \(-0.630275\pi\) | ||||
−0.397939 | + | 0.917412i | \(0.630275\pi\) | |||||||
\(4\) | 216.409 | 0.422673 | ||||||||
\(5\) | −2126.40 | −1.52153 | −0.760764 | − | 0.649028i | \(-0.775176\pi\) | ||||
−0.760764 | + | 0.649028i | \(0.775176\pi\) | |||||||
\(6\) | 3013.56 | 0.949291 | ||||||||
\(7\) | −8475.21 | −1.33416 | −0.667082 | − | 0.744984i | \(-0.732457\pi\) | ||||
−0.667082 | + | 0.744984i | \(0.732457\pi\) | |||||||
\(8\) | 7977.73 | 0.688611 | ||||||||
\(9\) | −7215.34 | −0.366577 | ||||||||
\(10\) | 57389.5 | 1.81482 | ||||||||
\(11\) | −7768.93 | −0.159990 | −0.0799952 | − | 0.996795i | \(-0.525491\pi\) | ||||
−0.0799952 | + | 0.996795i | \(0.525491\pi\) | |||||||
\(12\) | −24163.9 | −0.336397 | ||||||||
\(13\) | 188698. | 1.83241 | 0.916205 | − | 0.400709i | \(-0.131236\pi\) | ||||
0.916205 | + | 0.400709i | \(0.131236\pi\) | |||||||
\(14\) | 228738. | 1.59134 | ||||||||
\(15\) | 237431. | 1.21095 | ||||||||
\(16\) | −326113. | −1.24402 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 194735. | 0.437238 | ||||||||
\(19\) | 117938. | 0.207616 | 0.103808 | − | 0.994597i | \(-0.466897\pi\) | ||||
0.103808 | + | 0.994597i | \(0.466897\pi\) | |||||||
\(20\) | −460172. | −0.643109 | ||||||||
\(21\) | 946331. | 1.06183 | ||||||||
\(22\) | 209676. | 0.190830 | ||||||||
\(23\) | 1.84165e6 | 1.37224 | 0.686122 | − | 0.727486i | \(-0.259311\pi\) | ||||
0.686122 | + | 0.727486i | \(0.259311\pi\) | |||||||
\(24\) | −890782. | −0.548051 | ||||||||
\(25\) | 2.56845e6 | 1.31505 | ||||||||
\(26\) | −5.09279e6 | −2.18562 | ||||||||
\(27\) | 3.00343e6 | 1.08763 | ||||||||
\(28\) | −1.83411e6 | −0.563916 | ||||||||
\(29\) | −5.18387e6 | −1.36101 | −0.680507 | − | 0.732741i | \(-0.738240\pi\) | ||||
−0.680507 | + | 0.732741i | \(0.738240\pi\) | |||||||
\(30\) | −6.40804e6 | −1.44437 | ||||||||
\(31\) | −4.70232e6 | −0.914501 | −0.457250 | − | 0.889338i | \(-0.651166\pi\) | ||||
−0.457250 | + | 0.889338i | \(0.651166\pi\) | |||||||
\(32\) | 4.71687e6 | 0.795205 | ||||||||
\(33\) | 867468. | 0.127333 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.80217e7 | 2.02997 | ||||||||
\(36\) | −1.56146e6 | −0.154942 | ||||||||
\(37\) | 337590. | 0.0296130 | 0.0148065 | − | 0.999890i | \(-0.495287\pi\) | ||||
0.0148065 | + | 0.999890i | \(0.495287\pi\) | |||||||
\(38\) | −3.18303e6 | −0.247636 | ||||||||
\(39\) | −2.10698e7 | −1.45838 | ||||||||
\(40\) | −1.69638e7 | −1.04774 | ||||||||
\(41\) | −1.68128e7 | −0.929205 | −0.464603 | − | 0.885519i | \(-0.653803\pi\) | ||||
−0.464603 | + | 0.885519i | \(0.653803\pi\) | |||||||
\(42\) | −2.55406e7 | −1.26651 | ||||||||
\(43\) | −1.06248e7 | −0.473929 | −0.236965 | − | 0.971518i | \(-0.576153\pi\) | ||||
−0.236965 | + | 0.971518i | \(0.576153\pi\) | |||||||
\(44\) | −1.68126e6 | −0.0676237 | ||||||||
\(45\) | 1.53427e7 | 0.557758 | ||||||||
\(46\) | −4.97043e7 | −1.63676 | ||||||||
\(47\) | 9.90984e6 | 0.296228 | 0.148114 | − | 0.988970i | \(-0.452680\pi\) | ||||
0.148114 | + | 0.988970i | \(0.452680\pi\) | |||||||
\(48\) | 3.64133e7 | 0.990089 | ||||||||
\(49\) | 3.14756e7 | 0.779995 | ||||||||
\(50\) | −6.93202e7 | −1.56854 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.08360e7 | 0.774511 | ||||||||
\(53\) | 8.09197e7 | 1.40868 | 0.704341 | − | 0.709862i | \(-0.251243\pi\) | ||||
0.704341 | + | 0.709862i | \(0.251243\pi\) | |||||||
\(54\) | −8.10598e7 | −1.29728 | ||||||||
\(55\) | 1.65199e7 | 0.243430 | ||||||||
\(56\) | −6.76129e7 | −0.918721 | ||||||||
\(57\) | −1.31688e7 | −0.165237 | ||||||||
\(58\) | 1.39908e8 | 1.62336 | ||||||||
\(59\) | 3.54248e7 | 0.380604 | 0.190302 | − | 0.981726i | \(-0.439053\pi\) | ||||
0.190302 | + | 0.981726i | \(0.439053\pi\) | |||||||
\(60\) | 5.13822e7 | 0.511837 | ||||||||
\(61\) | 1.51754e7 | 0.140331 | 0.0701657 | − | 0.997535i | \(-0.477647\pi\) | ||||
0.0701657 | + | 0.997535i | \(0.477647\pi\) | |||||||
\(62\) | 1.26911e8 | 1.09078 | ||||||||
\(63\) | 6.11516e7 | 0.489075 | ||||||||
\(64\) | 3.96658e7 | 0.295533 | ||||||||
\(65\) | −4.01248e8 | −2.78806 | ||||||||
\(66\) | −2.34121e7 | −0.151878 | ||||||||
\(67\) | −1.17520e8 | −0.712486 | −0.356243 | − | 0.934393i | \(-0.615943\pi\) | ||||
−0.356243 | + | 0.934393i | \(0.615943\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.05636e8 | −1.09214 | ||||||||
\(70\) | −4.86388e8 | −2.42126 | ||||||||
\(71\) | −3.17626e8 | −1.48338 | −0.741692 | − | 0.670740i | \(-0.765976\pi\) | ||||
−0.741692 | + | 0.670740i | \(0.765976\pi\) | |||||||
\(72\) | −5.75620e7 | −0.252429 | ||||||||
\(73\) | 1.04290e8 | 0.429824 | 0.214912 | − | 0.976633i | \(-0.431053\pi\) | ||||
0.214912 | + | 0.976633i | \(0.431053\pi\) | |||||||
\(74\) | −9.11124e6 | −0.0353211 | ||||||||
\(75\) | −2.86790e8 | −1.04662 | ||||||||
\(76\) | 2.55228e7 | 0.0877539 | ||||||||
\(77\) | 6.58433e7 | 0.213454 | ||||||||
\(78\) | 5.68654e8 | 1.73949 | ||||||||
\(79\) | −1.97824e8 | −0.571423 | −0.285712 | − | 0.958316i | \(-0.592230\pi\) | ||||
−0.285712 | + | 0.958316i | \(0.592230\pi\) | |||||||
\(80\) | 6.93446e8 | 1.89281 | ||||||||
\(81\) | −1.93340e8 | −0.499044 | ||||||||
\(82\) | 4.53760e8 | 1.10832 | ||||||||
\(83\) | 1.02741e7 | 0.0237626 | 0.0118813 | − | 0.999929i | \(-0.496218\pi\) | ||||
0.0118813 | + | 0.999929i | \(0.496218\pi\) | |||||||
\(84\) | 2.04794e8 | 0.448808 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.86754e8 | 0.565283 | ||||||||
\(87\) | 5.78823e8 | 1.08320 | ||||||||
\(88\) | −6.19784e7 | −0.110171 | ||||||||
\(89\) | −9.95387e8 | −1.68166 | −0.840828 | − | 0.541303i | \(-0.817931\pi\) | ||||
−0.840828 | + | 0.541303i | \(0.817931\pi\) | |||||||
\(90\) | −4.14085e8 | −0.665271 | ||||||||
\(91\) | −1.59926e9 | −2.44474 | ||||||||
\(92\) | 3.98549e8 | 0.580011 | ||||||||
\(93\) | 5.25054e8 | 0.727832 | ||||||||
\(94\) | −2.67457e8 | −0.353329 | ||||||||
\(95\) | −2.50783e8 | −0.315894 | ||||||||
\(96\) | −5.26679e8 | −0.632887 | ||||||||
\(97\) | 2.90283e8 | 0.332926 | 0.166463 | − | 0.986048i | \(-0.446765\pi\) | ||||
0.166463 | + | 0.986048i | \(0.446765\pi\) | |||||||
\(98\) | −8.49497e8 | −0.930346 | ||||||||
\(99\) | 5.60555e7 | 0.0586489 | ||||||||
\(100\) | 5.55836e8 | 0.555836 | ||||||||
\(101\) | −1.04616e8 | −0.100035 | −0.0500176 | − | 0.998748i | \(-0.515928\pi\) | ||||
−0.0500176 | + | 0.998748i | \(0.515928\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.89721e8 | −0.253637 | −0.126818 | − | 0.991926i | \(-0.540477\pi\) | ||||
−0.126818 | + | 0.991926i | \(0.540477\pi\) | |||||||
\(104\) | 1.50538e9 | 1.26182 | ||||||||
\(105\) | −2.01228e9 | −1.61561 | ||||||||
\(106\) | −2.18395e9 | −1.68022 | ||||||||
\(107\) | 2.59660e8 | 0.191504 | 0.0957520 | − | 0.995405i | \(-0.469474\pi\) | ||||
0.0957520 | + | 0.995405i | \(0.469474\pi\) | |||||||
\(108\) | 6.49969e8 | 0.459712 | ||||||||
\(109\) | −8.72678e8 | −0.592154 | −0.296077 | − | 0.955164i | \(-0.595679\pi\) | ||||
−0.296077 | + | 0.955164i | \(0.595679\pi\) | |||||||
\(110\) | −4.45855e8 | −0.290353 | ||||||||
\(111\) | −3.76949e7 | −0.0235683 | ||||||||
\(112\) | 2.76387e9 | 1.65973 | ||||||||
\(113\) | 1.61677e9 | 0.932815 | 0.466408 | − | 0.884570i | \(-0.345548\pi\) | ||||
0.466408 | + | 0.884570i | \(0.345548\pi\) | |||||||
\(114\) | 3.55413e8 | 0.197088 | ||||||||
\(115\) | −3.91608e9 | −2.08791 | ||||||||
\(116\) | −1.12183e9 | −0.575264 | ||||||||
\(117\) | −1.36152e9 | −0.671720 | ||||||||
\(118\) | −9.56082e8 | −0.453969 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.89416e9 | 0.833875 | ||||||||
\(121\) | −2.29759e9 | −0.974403 | ||||||||
\(122\) | −4.09569e8 | −0.167382 | ||||||||
\(123\) | 1.87729e9 | 0.739535 | ||||||||
\(124\) | −1.01762e9 | −0.386535 | ||||||||
\(125\) | −1.30844e9 | −0.479356 | ||||||||
\(126\) | −1.65042e9 | −0.583348 | ||||||||
\(127\) | −4.64829e9 | −1.58554 | −0.792769 | − | 0.609522i | \(-0.791361\pi\) | ||||
−0.792769 | + | 0.609522i | \(0.791361\pi\) | |||||||
\(128\) | −3.48558e9 | −1.14770 | ||||||||
\(129\) | 1.18635e9 | 0.377190 | ||||||||
\(130\) | 1.08293e10 | 3.32549 | ||||||||
\(131\) | 3.87389e9 | 1.14928 | 0.574641 | − | 0.818405i | \(-0.305142\pi\) | ||||
0.574641 | + | 0.818405i | \(0.305142\pi\) | |||||||
\(132\) | 1.87728e8 | 0.0538203 | ||||||||
\(133\) | −9.99547e8 | −0.276994 | ||||||||
\(134\) | 3.17176e9 | 0.849824 | ||||||||
\(135\) | −6.38650e9 | −1.65486 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.81827e9 | −0.683502 | −0.341751 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341751 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(138\) | 5.54992e9 | 1.30266 | ||||||||
\(139\) | −6.78367e9 | −1.54134 | −0.770670 | − | 0.637235i | \(-0.780078\pi\) | ||||
−0.770670 | + | 0.637235i | \(0.780078\pi\) | |||||||
\(140\) | 3.90005e9 | 0.858014 | ||||||||
\(141\) | −1.10652e9 | −0.235762 | ||||||||
\(142\) | 8.57243e9 | 1.76932 | ||||||||
\(143\) | −1.46598e9 | −0.293168 | ||||||||
\(144\) | 2.35301e9 | 0.456030 | ||||||||
\(145\) | 1.10230e10 | 2.07082 | ||||||||
\(146\) | −2.81469e9 | −0.512677 | ||||||||
\(147\) | −3.51453e9 | −0.620781 | ||||||||
\(148\) | 7.30575e7 | 0.0125166 | ||||||||
\(149\) | −8.91855e9 | −1.48237 | −0.741184 | − | 0.671302i | \(-0.765736\pi\) | ||||
−0.741184 | + | 0.671302i | \(0.765736\pi\) | |||||||
\(150\) | 7.74020e9 | 1.24836 | ||||||||
\(151\) | 9.82516e9 | 1.53795 | 0.768977 | − | 0.639276i | \(-0.220766\pi\) | ||||
0.768977 | + | 0.639276i | \(0.220766\pi\) | |||||||
\(152\) | 9.40875e8 | 0.142967 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.77705e9 | −0.254599 | ||||||||
\(155\) | 9.99901e9 | 1.39144 | ||||||||
\(156\) | −4.55969e9 | −0.616417 | ||||||||
\(157\) | −3.59938e8 | −0.0472802 | −0.0236401 | − | 0.999721i | \(-0.507526\pi\) | ||||
−0.0236401 | + | 0.999721i | \(0.507526\pi\) | |||||||
\(158\) | 5.33909e9 | 0.681570 | ||||||||
\(159\) | −9.03539e9 | −1.12114 | ||||||||
\(160\) | −1.00300e10 | −1.20993 | ||||||||
\(161\) | −1.56084e10 | −1.83080 | ||||||||
\(162\) | 5.21805e9 | 0.595239 | ||||||||
\(163\) | −2.33468e9 | −0.259050 | −0.129525 | − | 0.991576i | \(-0.541345\pi\) | ||||
−0.129525 | + | 0.991576i | \(0.541345\pi\) | |||||||
\(164\) | −3.63843e9 | −0.392750 | ||||||||
\(165\) | −1.84459e9 | −0.193741 | ||||||||
\(166\) | −2.77289e8 | −0.0283431 | ||||||||
\(167\) | −1.41903e10 | −1.41178 | −0.705891 | − | 0.708321i | \(-0.749453\pi\) | ||||
−0.705891 | + | 0.708321i | \(0.749453\pi\) | |||||||
\(168\) | 7.54957e9 | 0.731190 | ||||||||
\(169\) | 2.50025e10 | 2.35773 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.50961e8 | −0.0761075 | ||||||||
\(172\) | −2.29930e9 | −0.200317 | ||||||||
\(173\) | 1.14445e10 | 0.971380 | 0.485690 | − | 0.874131i | \(-0.338568\pi\) | ||||
0.485690 | + | 0.874131i | \(0.338568\pi\) | |||||||
\(174\) | −1.56219e10 | −1.29200 | ||||||||
\(175\) | −2.17682e10 | −1.75449 | ||||||||
\(176\) | 2.53355e9 | 0.199031 | ||||||||
\(177\) | −3.95549e9 | −0.302915 | ||||||||
\(178\) | 2.68645e10 | 2.00581 | ||||||||
\(179\) | 1.03273e10 | 0.751883 | 0.375941 | − | 0.926643i | \(-0.377319\pi\) | ||||
0.375941 | + | 0.926643i | \(0.377319\pi\) | |||||||
\(180\) | 3.32030e9 | 0.235749 | ||||||||
\(181\) | −7.53319e9 | −0.521706 | −0.260853 | − | 0.965379i | \(-0.584004\pi\) | ||||
−0.260853 | + | 0.965379i | \(0.584004\pi\) | |||||||
\(182\) | 4.31624e10 | 2.91598 | ||||||||
\(183\) | −1.69446e9 | −0.111687 | ||||||||
\(184\) | 1.46922e10 | 0.944943 | ||||||||
\(185\) | −7.17852e8 | −0.0450570 | ||||||||
\(186\) | −1.41707e10 | −0.868127 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.14458e9 | 0.125208 | ||||||||
\(189\) | −2.54547e10 | −1.45108 | ||||||||
\(190\) | 6.76839e9 | 0.376786 | ||||||||
\(191\) | 1.86443e10 | 1.01367 | 0.506834 | − | 0.862044i | \(-0.330816\pi\) | ||||
0.506834 | + | 0.862044i | \(0.330816\pi\) | |||||||
\(192\) | −4.42903e9 | −0.235208 | ||||||||
\(193\) | 2.71011e10 | 1.40598 | 0.702989 | − | 0.711200i | \(-0.251848\pi\) | ||||
0.702989 | + | 0.711200i | \(0.251848\pi\) | |||||||
\(194\) | −7.83445e9 | −0.397101 | ||||||||
\(195\) | 4.48028e10 | 2.21896 | ||||||||
\(196\) | 6.81160e9 | 0.329683 | ||||||||
\(197\) | −1.57089e9 | −0.0743101 | −0.0371551 | − | 0.999310i | \(-0.511830\pi\) | ||||
−0.0371551 | + | 0.999310i | \(0.511830\pi\) | |||||||
\(198\) | −1.51288e9 | −0.0699540 | ||||||||
\(199\) | −1.15986e10 | −0.524285 | −0.262143 | − | 0.965029i | \(-0.584429\pi\) | ||||
−0.262143 | + | 0.965029i | \(0.584429\pi\) | |||||||
\(200\) | 2.04904e10 | 0.905558 | ||||||||
\(201\) | 1.31222e10 | 0.567052 | ||||||||
\(202\) | 2.82349e9 | 0.119318 | ||||||||
\(203\) | 4.39344e10 | 1.81582 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.57507e10 | 1.41381 | ||||||||
\(206\) | 7.81928e9 | 0.302527 | ||||||||
\(207\) | −1.32881e10 | −0.503034 | ||||||||
\(208\) | −6.15369e10 | −2.27956 | ||||||||
\(209\) | −9.16250e8 | −0.0332166 | ||||||||
\(210\) | 5.43095e10 | 1.92703 | ||||||||
\(211\) | 3.17418e10 | 1.10246 | 0.551228 | − | 0.834355i | \(-0.314160\pi\) | ||||
0.551228 | + | 0.834355i | \(0.314160\pi\) | |||||||
\(212\) | 1.75117e10 | 0.595412 | ||||||||
\(213\) | 3.54657e10 | 1.18059 | ||||||||
\(214\) | −7.00797e9 | −0.228418 | ||||||||
\(215\) | 2.25926e10 | 0.721097 | ||||||||
\(216\) | 2.39606e10 | 0.748954 | ||||||||
\(217\) | 3.98531e10 | 1.22009 | ||||||||
\(218\) | 2.35527e10 | 0.706297 | ||||||||
\(219\) | −1.16449e10 | −0.342088 | ||||||||
\(220\) | 3.57504e9 | 0.102891 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.01735e9 | 0.0281113 | ||||||||
\(223\) | 4.39482e10 | 1.19006 | 0.595030 | − | 0.803704i | \(-0.297140\pi\) | ||||
0.595030 | + | 0.803704i | \(0.297140\pi\) | |||||||
\(224\) | −3.99765e10 | −1.06093 | ||||||||
\(225\) | −1.85323e10 | −0.482067 | ||||||||
\(226\) | −4.36351e10 | −1.11262 | ||||||||
\(227\) | 3.84258e10 | 0.960520 | 0.480260 | − | 0.877126i | \(-0.340542\pi\) | ||||
0.480260 | + | 0.877126i | \(0.340542\pi\) | |||||||
\(228\) | −2.84984e9 | −0.0698414 | ||||||||
\(229\) | −1.92884e10 | −0.463487 | −0.231744 | − | 0.972777i | \(-0.574443\pi\) | ||||
−0.231744 | + | 0.972777i | \(0.574443\pi\) | |||||||
\(230\) | 1.05691e11 | 2.49037 | ||||||||
\(231\) | −7.35198e9 | −0.169883 | ||||||||
\(232\) | −4.13555e10 | −0.937210 | ||||||||
\(233\) | −7.60123e10 | −1.68959 | −0.844797 | − | 0.535087i | \(-0.820279\pi\) | ||||
−0.844797 | + | 0.535087i | \(0.820279\pi\) | |||||||
\(234\) | 3.67462e10 | 0.801200 | ||||||||
\(235\) | −2.10723e10 | −0.450720 | ||||||||
\(236\) | 7.66624e9 | 0.160871 | ||||||||
\(237\) | 2.20888e10 | 0.454784 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.69458e10 | 0.534196 | 0.267098 | − | 0.963669i | \(-0.413935\pi\) | ||||
0.267098 | + | 0.963669i | \(0.413935\pi\) | |||||||
\(240\) | −7.74292e10 | −1.50645 | ||||||||
\(241\) | −7.71206e10 | −1.47263 | −0.736315 | − | 0.676639i | \(-0.763436\pi\) | ||||
−0.736315 | + | 0.676639i | \(0.763436\pi\) | |||||||
\(242\) | 6.20098e10 | 1.16223 | ||||||||
\(243\) | −3.75285e10 | −0.690452 | ||||||||
\(244\) | 3.28408e9 | 0.0593144 | ||||||||
\(245\) | −6.69298e10 | −1.18678 | ||||||||
\(246\) | −5.06663e10 | −0.882086 | ||||||||
\(247\) | 2.22546e10 | 0.380438 | ||||||||
\(248\) | −3.75138e10 | −0.629736 | ||||||||
\(249\) | −1.14720e9 | −0.0189122 | ||||||||
\(250\) | 3.53135e10 | 0.571756 | ||||||||
\(251\) | −2.37776e10 | −0.378125 | −0.189063 | − | 0.981965i | \(-0.560545\pi\) | ||||
−0.189063 | + | 0.981965i | \(0.560545\pi\) | |||||||
\(252\) | 1.32337e10 | 0.206719 | ||||||||
\(253\) | −1.43076e10 | −0.219546 | ||||||||
\(254\) | 1.25453e11 | 1.89116 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.37636e10 | 1.07340 | ||||||||
\(257\) | −4.21200e10 | −0.602267 | −0.301134 | − | 0.953582i | \(-0.597365\pi\) | ||||
−0.301134 | + | 0.953582i | \(0.597365\pi\) | |||||||
\(258\) | −3.20185e10 | −0.449897 | ||||||||
\(259\) | −2.86115e9 | −0.0395086 | ||||||||
\(260\) | −8.68336e10 | −1.17844 | ||||||||
\(261\) | 3.74034e10 | 0.498917 | ||||||||
\(262\) | −1.04553e11 | −1.37082 | ||||||||
\(263\) | 4.71166e10 | 0.607257 | 0.303629 | − | 0.952790i | \(-0.401802\pi\) | ||||
0.303629 | + | 0.952790i | \(0.401802\pi\) | |||||||
\(264\) | 6.92043e9 | 0.0876829 | ||||||||
\(265\) | −1.72068e11 | −2.14335 | ||||||||
\(266\) | 2.69768e10 | 0.330388 | ||||||||
\(267\) | 1.11144e11 | 1.33839 | ||||||||
\(268\) | −2.54324e10 | −0.301149 | ||||||||
\(269\) | −5.69389e9 | −0.0663015 | −0.0331508 | − | 0.999450i | \(-0.510554\pi\) | ||||
−0.0331508 | + | 0.999450i | \(0.510554\pi\) | |||||||
\(270\) | 1.72366e11 | 1.97385 | ||||||||
\(271\) | −1.51533e11 | −1.70666 | −0.853328 | − | 0.521375i | \(-0.825419\pi\) | ||||
−0.853328 | + | 0.521375i | \(0.825419\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.78571e11 | 1.94571 | ||||||||
\(274\) | 7.60624e10 | 0.815253 | ||||||||
\(275\) | −1.99541e10 | −0.210395 | ||||||||
\(276\) | −4.45014e10 | −0.461618 | ||||||||
\(277\) | 5.65276e10 | 0.576901 | 0.288451 | − | 0.957495i | \(-0.406860\pi\) | ||||
0.288451 | + | 0.957495i | \(0.406860\pi\) | |||||||
\(278\) | 1.83085e11 | 1.83845 | ||||||||
\(279\) | 3.39288e10 | 0.335235 | ||||||||
\(280\) | 1.43772e11 | 1.39786 | ||||||||
\(281\) | −3.63183e10 | −0.347493 | −0.173747 | − | 0.984790i | \(-0.555587\pi\) | ||||
−0.173747 | + | 0.984790i | \(0.555587\pi\) | |||||||
\(282\) | 2.98639e10 | 0.281207 | ||||||||
\(283\) | 2.29141e10 | 0.212355 | 0.106178 | − | 0.994347i | \(-0.466139\pi\) | ||||
0.106178 | + | 0.994347i | \(0.466139\pi\) | |||||||
\(284\) | −6.87371e10 | −0.626987 | ||||||||
\(285\) | 2.80021e10 | 0.251413 | ||||||||
\(286\) | 3.95655e10 | 0.349679 | ||||||||
\(287\) | 1.42492e11 | 1.23971 | ||||||||
\(288\) | −3.40338e10 | −0.291504 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −2.97500e11 | −2.46999 | ||||||||
\(291\) | −3.24126e10 | −0.264969 | ||||||||
\(292\) | 2.25693e10 | 0.181675 | ||||||||
\(293\) | 7.83040e10 | 0.620697 | 0.310348 | − | 0.950623i | \(-0.399554\pi\) | ||||
0.310348 | + | 0.950623i | \(0.399554\pi\) | |||||||
\(294\) | 9.48537e10 | 0.740442 | ||||||||
\(295\) | −7.53273e10 | −0.579100 | ||||||||
\(296\) | 2.69320e9 | 0.0203918 | ||||||||
\(297\) | −2.33335e10 | −0.174010 | ||||||||
\(298\) | 2.40703e11 | 1.76811 | ||||||||
\(299\) | 3.47516e11 | 2.51452 | ||||||||
\(300\) | −6.20639e10 | −0.442378 | ||||||||
\(301\) | 9.00476e10 | 0.632300 | ||||||||
\(302\) | −2.65172e11 | −1.83441 | ||||||||
\(303\) | 1.16813e10 | 0.0796158 | ||||||||
\(304\) | −3.84610e10 | −0.258279 | ||||||||
\(305\) | −3.22689e10 | −0.213518 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.62528e10 | −0.618430 | −0.309215 | − | 0.950992i | \(-0.600066\pi\) | ||||
−0.309215 | + | 0.950992i | \(0.600066\pi\) | |||||||
\(308\) | 1.42491e10 | 0.0902212 | ||||||||
\(309\) | 3.23498e10 | 0.201864 | ||||||||
\(310\) | −2.69864e11 | −1.65965 | ||||||||
\(311\) | −2.06836e11 | −1.25373 | −0.626865 | − | 0.779128i | \(-0.715662\pi\) | ||||
−0.626865 | + | 0.779128i | \(0.715662\pi\) | |||||||
\(312\) | −1.68089e11 | −1.00425 | ||||||||
\(313\) | −4.43872e10 | −0.261402 | −0.130701 | − | 0.991422i | \(-0.541723\pi\) | ||||
−0.130701 | + | 0.991422i | \(0.541723\pi\) | |||||||
\(314\) | 9.71439e9 | 0.0563939 | ||||||||
\(315\) | −1.30033e11 | −0.744141 | ||||||||
\(316\) | −4.28109e10 | −0.241525 | ||||||||
\(317\) | 1.67214e10 | 0.0930052 | 0.0465026 | − | 0.998918i | \(-0.485192\pi\) | ||||
0.0465026 | + | 0.998918i | \(0.485192\pi\) | |||||||
\(318\) | 2.43857e11 | 1.33725 | ||||||||
\(319\) | 4.02731e10 | 0.217749 | ||||||||
\(320\) | −8.43453e10 | −0.449662 | ||||||||
\(321\) | −2.89933e10 | −0.152414 | ||||||||
\(322\) | 4.21255e11 | 2.18370 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.18404e10 | −0.210932 | ||||||||
\(325\) | 4.84663e11 | 2.40971 | ||||||||
\(326\) | 6.30107e10 | 0.308984 | ||||||||
\(327\) | 9.74420e10 | 0.471283 | ||||||||
\(328\) | −1.34128e11 | −0.639861 | ||||||||
\(329\) | −8.39880e10 | −0.395217 | ||||||||
\(330\) | 4.97836e10 | 0.231086 | ||||||||
\(331\) | −2.85648e11 | −1.30799 | −0.653995 | − | 0.756499i | \(-0.726908\pi\) | ||||
−0.653995 | + | 0.756499i | \(0.726908\pi\) | |||||||
\(332\) | 2.22341e9 | 0.0100438 | ||||||||
\(333\) | −2.43583e9 | −0.0108554 | ||||||||
\(334\) | 3.82983e11 | 1.68391 | ||||||||
\(335\) | 2.49895e11 | 1.08407 | ||||||||
\(336\) | −3.08610e11 | −1.32094 | ||||||||
\(337\) | 1.51192e11 | 0.638549 | 0.319274 | − | 0.947662i | \(-0.396561\pi\) | ||||
0.319274 | + | 0.947662i | \(0.396561\pi\) | |||||||
\(338\) | −6.74795e11 | −2.81220 | ||||||||
\(339\) | −1.80526e11 | −0.742407 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.65320e10 | 0.146311 | ||||||||
\(342\) | 2.29666e10 | 0.0907779 | ||||||||
\(343\) | 7.52429e10 | 0.293523 | ||||||||
\(344\) | −8.47619e10 | −0.326353 | ||||||||
\(345\) | 4.37265e11 | 1.66172 | ||||||||
\(346\) | −3.08876e11 | −1.15862 | ||||||||
\(347\) | 3.16975e9 | 0.0117366 | 0.00586830 | − | 0.999983i | \(-0.498132\pi\) | ||||
0.00586830 | + | 0.999983i | \(0.498132\pi\) | |||||||
\(348\) | 1.25262e11 | 0.457841 | ||||||||
\(349\) | −1.16871e11 | −0.421689 | −0.210844 | − | 0.977520i | \(-0.567621\pi\) | ||||
−0.210844 | + | 0.977520i | \(0.567621\pi\) | |||||||
\(350\) | 5.87503e11 | 2.09269 | ||||||||
\(351\) | 5.66743e11 | 1.99298 | ||||||||
\(352\) | −3.66450e10 | −0.127225 | ||||||||
\(353\) | 6.42891e9 | 0.0220369 | 0.0110185 | − | 0.999939i | \(-0.496493\pi\) | ||||
0.0110185 | + | 0.999939i | \(0.496493\pi\) | |||||||
\(354\) | 1.06755e11 | 0.361304 | ||||||||
\(355\) | 6.75401e11 | 2.25701 | ||||||||
\(356\) | −2.15410e11 | −0.710791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.78725e11 | −0.896815 | ||||||||
\(359\) | −4.93384e10 | −0.156769 | −0.0783846 | − | 0.996923i | \(-0.524976\pi\) | ||||
−0.0783846 | + | 0.996923i | \(0.524976\pi\) | |||||||
\(360\) | 1.22400e11 | 0.384079 | ||||||||
\(361\) | −3.08778e11 | −0.956895 | ||||||||
\(362\) | 2.03314e11 | 0.622269 | ||||||||
\(363\) | 2.56546e11 | 0.775506 | ||||||||
\(364\) | −3.46093e11 | −1.03333 | ||||||||
\(365\) | −2.21763e11 | −0.653990 | ||||||||
\(366\) | 4.57319e10 | 0.133215 | ||||||||
\(367\) | −4.03374e11 | −1.16068 | −0.580338 | − | 0.814376i | \(-0.697079\pi\) | ||||
−0.580338 | + | 0.814376i | \(0.697079\pi\) | |||||||
\(368\) | −6.00585e11 | −1.70710 | ||||||||
\(369\) | 1.21310e11 | 0.340626 | ||||||||
\(370\) | 1.93741e10 | 0.0537421 | ||||||||
\(371\) | −6.85812e11 | −1.87941 | ||||||||
\(372\) | 1.13626e11 | 0.307635 | ||||||||
\(373\) | −4.66959e10 | −0.124908 | −0.0624538 | − | 0.998048i | \(-0.519893\pi\) | ||||
−0.0624538 | + | 0.998048i | \(0.519893\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.46098e11 | 0.381509 | ||||||||
\(376\) | 7.90580e10 | 0.203986 | ||||||||
\(377\) | −9.78186e11 | −2.49394 | ||||||||
\(378\) | 6.86999e11 | 1.73078 | ||||||||
\(379\) | 4.32289e10 | 0.107621 | 0.0538106 | − | 0.998551i | \(-0.482863\pi\) | ||||
0.0538106 | + | 0.998551i | \(0.482863\pi\) | |||||||
\(380\) | −5.42716e10 | −0.133520 | ||||||||
\(381\) | 5.19022e11 | 1.26190 | ||||||||
\(382\) | −5.03192e11 | −1.20906 | ||||||||
\(383\) | −6.63545e11 | −1.57571 | −0.787854 | − | 0.615862i | \(-0.788808\pi\) | ||||
−0.787854 | + | 0.615862i | \(0.788808\pi\) | |||||||
\(384\) | 3.89195e11 | 0.913433 | ||||||||
\(385\) | −1.40009e11 | −0.324776 | ||||||||
\(386\) | −7.31432e11 | −1.67699 | ||||||||
\(387\) | 7.66617e10 | 0.173732 | ||||||||
\(388\) | 6.28197e10 | 0.140719 | ||||||||
\(389\) | 3.77536e11 | 0.835959 | 0.417979 | − | 0.908456i | \(-0.362738\pi\) | ||||
0.417979 | + | 0.908456i | \(0.362738\pi\) | |||||||
\(390\) | −1.20919e12 | −2.64668 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.51104e11 | 0.537114 | ||||||||
\(393\) | −4.32554e11 | −0.914690 | ||||||||
\(394\) | 4.23969e10 | 0.0886341 | ||||||||
\(395\) | 4.20654e11 | 0.869437 | ||||||||
\(396\) | 1.21309e10 | 0.0247893 | ||||||||
\(397\) | −8.10743e11 | −1.63805 | −0.819023 | − | 0.573760i | \(-0.805484\pi\) | ||||
−0.819023 | + | 0.573760i | \(0.805484\pi\) | |||||||
\(398\) | 3.13036e11 | 0.625346 | ||||||||
\(399\) | 1.11608e11 | 0.220454 | ||||||||
\(400\) | −8.37605e11 | −1.63595 | ||||||||
\(401\) | −7.54539e11 | −1.45724 | −0.728622 | − | 0.684916i | \(-0.759839\pi\) | ||||
−0.728622 | + | 0.684916i | \(0.759839\pi\) | |||||||
\(402\) | −3.54155e11 | −0.676357 | ||||||||
\(403\) | −8.87319e11 | −1.67574 | ||||||||
\(404\) | −2.26398e10 | −0.0422822 | ||||||||
\(405\) | 4.11118e11 | 0.759309 | ||||||||
\(406\) | −1.18575e12 | −2.16583 | ||||||||
\(407\) | −2.62271e9 | −0.00473779 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.84207e11 | 0.855611 | 0.427805 | − | 0.903871i | \(-0.359287\pi\) | ||||
0.427805 | + | 0.903871i | \(0.359287\pi\) | |||||||
\(410\) | −9.64877e11 | −1.68634 | ||||||||
\(411\) | 3.14684e11 | 0.543985 | ||||||||
\(412\) | −6.26981e10 | −0.107205 | ||||||||
\(413\) | −3.00233e11 | −0.507788 | ||||||||
\(414\) | 3.58634e11 | 0.599998 | ||||||||
\(415\) | −2.18469e10 | −0.0361555 | ||||||||
\(416\) | 8.90065e11 | 1.45714 | ||||||||
\(417\) | 7.57456e11 | 1.22672 | ||||||||
\(418\) | 2.47287e10 | 0.0396194 | ||||||||
\(419\) | 7.47691e10 | 0.118511 | 0.0592555 | − | 0.998243i | \(-0.481127\pi\) | ||||
0.0592555 | + | 0.998243i | \(0.481127\pi\) | |||||||
\(420\) | −4.35475e11 | −0.682875 | ||||||||
\(421\) | −5.91134e11 | −0.917100 | −0.458550 | − | 0.888669i | \(-0.651631\pi\) | ||||
−0.458550 | + | 0.888669i | \(0.651631\pi\) | |||||||
\(422\) | −8.56682e11 | −1.31496 | ||||||||
\(423\) | −7.15029e10 | −0.108591 | ||||||||
\(424\) | 6.45556e11 | 0.970035 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.57186e11 | −1.40816 | ||||||||
\(427\) | −1.28614e11 | −0.187225 | ||||||||
\(428\) | 5.61927e10 | 0.0809436 | ||||||||
\(429\) | 1.63690e11 | 0.233326 | ||||||||
\(430\) | −6.09753e11 | −0.860094 | ||||||||
\(431\) | −4.74524e11 | −0.662386 | −0.331193 | − | 0.943563i | \(-0.607451\pi\) | ||||
−0.331193 | + | 0.943563i | \(0.607451\pi\) | |||||||
\(432\) | −9.79457e11 | −1.35303 | ||||||||
\(433\) | −1.35727e12 | −1.85554 | −0.927770 | − | 0.373153i | \(-0.878277\pi\) | ||||
−0.927770 | + | 0.373153i | \(0.878277\pi\) | |||||||
\(434\) | −1.07560e12 | −1.45528 | ||||||||
\(435\) | −1.23081e12 | −1.64812 | ||||||||
\(436\) | −1.88855e11 | −0.250288 | ||||||||
\(437\) | 2.17200e11 | 0.284900 | ||||||||
\(438\) | 3.14285e11 | 0.408028 | ||||||||
\(439\) | 5.54359e11 | 0.712362 | 0.356181 | − | 0.934417i | \(-0.384079\pi\) | ||||
0.356181 | + | 0.934417i | \(0.384079\pi\) | |||||||
\(440\) | 1.31791e11 | 0.167629 | ||||||||
\(441\) | −2.27107e11 | −0.285929 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.17232e12 | 1.44621 | 0.723103 | − | 0.690740i | \(-0.242715\pi\) | ||||
0.723103 | + | 0.690740i | \(0.242715\pi\) | |||||||
\(444\) | −8.15750e9 | −0.00996170 | ||||||||
\(445\) | 2.11659e12 | 2.55869 | ||||||||
\(446\) | −1.18612e12 | −1.41945 | ||||||||
\(447\) | 9.95834e11 | 1.17979 | ||||||||
\(448\) | −3.36176e11 | −0.394290 | ||||||||
\(449\) | 9.38348e11 | 1.08957 | 0.544786 | − | 0.838575i | \(-0.316611\pi\) | ||||
0.544786 | + | 0.838575i | \(0.316611\pi\) | |||||||
\(450\) | 5.00169e11 | 0.574990 | ||||||||
\(451\) | 1.30617e11 | 0.148664 | ||||||||
\(452\) | 3.49883e11 | 0.394276 | ||||||||
\(453\) | −1.09706e12 | −1.22402 | ||||||||
\(454\) | −1.03708e12 | −1.14567 | ||||||||
\(455\) | 3.40066e12 | 3.71974 | ||||||||
\(456\) | −1.05057e11 | −0.113784 | ||||||||
\(457\) | −1.33793e12 | −1.43487 | −0.717433 | − | 0.696628i | \(-0.754683\pi\) | ||||
−0.717433 | + | 0.696628i | \(0.754683\pi\) | |||||||
\(458\) | 5.20577e11 | 0.552828 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.47475e11 | −0.882504 | ||||||||
\(461\) | 8.45027e11 | 0.871398 | 0.435699 | − | 0.900092i | \(-0.356501\pi\) | ||||
0.435699 | + | 0.900092i | \(0.356501\pi\) | |||||||
\(462\) | 1.98423e11 | 0.202630 | ||||||||
\(463\) | −3.24656e11 | −0.328328 | −0.164164 | − | 0.986433i | \(-0.552493\pi\) | ||||
−0.164164 | + | 0.986433i | \(0.552493\pi\) | |||||||
\(464\) | 1.69052e12 | 1.69313 | ||||||||
\(465\) | −1.11648e12 | −1.10742 | ||||||||
\(466\) | 2.05150e12 | 2.01528 | ||||||||
\(467\) | 7.41373e11 | 0.721292 | 0.360646 | − | 0.932703i | \(-0.382556\pi\) | ||||
0.360646 | + | 0.932703i | \(0.382556\pi\) | |||||||
\(468\) | −2.94645e11 | −0.283918 | ||||||||
\(469\) | 9.96010e11 | 0.950574 | ||||||||
\(470\) | 5.68721e11 | 0.537600 | ||||||||
\(471\) | 4.01902e10 | 0.0376293 | ||||||||
\(472\) | 2.82609e11 | 0.262088 | ||||||||
\(473\) | 8.25435e10 | 0.0758242 | ||||||||
\(474\) | −5.96156e11 | −0.542447 | ||||||||
\(475\) | 3.02918e11 | 0.273026 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.83864e11 | −0.516391 | ||||||||
\(478\) | −7.27242e11 | −0.637167 | ||||||||
\(479\) | 3.31368e11 | 0.287608 | 0.143804 | − | 0.989606i | \(-0.454067\pi\) | ||||
0.143804 | + | 0.989606i | \(0.454067\pi\) | |||||||
\(480\) | 1.11993e12 | 0.962955 | ||||||||
\(481\) | 6.37027e10 | 0.0542631 | ||||||||
\(482\) | 2.08141e12 | 1.75649 | ||||||||
\(483\) | 1.74281e12 | 1.45709 | ||||||||
\(484\) | −4.97219e11 | −0.411854 | ||||||||
\(485\) | −6.17257e11 | −0.506557 | ||||||||
\(486\) | 1.01286e12 | 0.823542 | ||||||||
\(487\) | −1.84180e12 | −1.48375 | −0.741877 | − | 0.670536i | \(-0.766064\pi\) | ||||
−0.741877 | + | 0.670536i | \(0.766064\pi\) | |||||||
\(488\) | 1.21065e11 | 0.0966338 | ||||||||
\(489\) | 2.60687e11 | 0.206172 | ||||||||
\(490\) | 1.80637e12 | 1.41555 | ||||||||
\(491\) | −1.63755e12 | −1.27153 | −0.635767 | − | 0.771881i | \(-0.719316\pi\) | ||||
−0.635767 | + | 0.771881i | \(0.719316\pi\) | |||||||
\(492\) | 4.06262e11 | 0.312582 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −6.00632e11 | −0.453771 | ||||||||
\(495\) | −1.19196e11 | −0.0892360 | ||||||||
\(496\) | 1.53348e12 | 1.13766 | ||||||||
\(497\) | 2.69195e12 | 1.97908 | ||||||||
\(498\) | 3.09618e10 | 0.0225576 | ||||||||
\(499\) | 8.40100e11 | 0.606567 | 0.303283 | − | 0.952900i | \(-0.401917\pi\) | ||||
0.303283 | + | 0.952900i | \(0.401917\pi\) | |||||||
\(500\) | −2.83157e11 | −0.202611 | ||||||||
\(501\) | 1.58447e12 | 1.12361 | ||||||||
\(502\) | 6.41734e11 | 0.451012 | ||||||||
\(503\) | 8.41199e11 | 0.585926 | 0.292963 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292963 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(504\) | 4.87850e11 | 0.336782 | ||||||||
\(505\) | 2.22456e11 | 0.152206 | ||||||||
\(506\) | 3.86150e11 | 0.261865 | ||||||||
\(507\) | −2.79175e12 | −1.87647 | ||||||||
\(508\) | −1.00593e12 | −0.670165 | ||||||||
\(509\) | 1.64594e12 | 1.08688 | 0.543442 | − | 0.839447i | \(-0.317121\pi\) | ||||
0.543442 | + | 0.839447i | \(0.317121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.83882e11 | −0.573456 | ||||||||
\(512\) | −2.06193e11 | −0.132605 | ||||||||
\(513\) | 3.54218e11 | 0.225810 | ||||||||
\(514\) | 1.13678e12 | 0.718359 | ||||||||
\(515\) | 6.16062e11 | 0.385915 | ||||||||
\(516\) | 2.56737e11 | 0.159428 | ||||||||
\(517\) | −7.69889e10 | −0.0473937 | ||||||||
\(518\) | 7.72197e10 | 0.0471242 | ||||||||
\(519\) | −1.27788e12 | −0.773101 | ||||||||
\(520\) | −3.20105e12 | −1.91989 | ||||||||
\(521\) | 3.51701e11 | 0.209124 | 0.104562 | − | 0.994518i | \(-0.466656\pi\) | ||||
0.104562 | + | 0.994518i | \(0.466656\pi\) | |||||||
\(522\) | −1.00948e12 | −0.595088 | ||||||||
\(523\) | 5.05119e11 | 0.295213 | 0.147607 | − | 0.989046i | \(-0.452843\pi\) | ||||
0.147607 | + | 0.989046i | \(0.452843\pi\) | |||||||
\(524\) | 8.38345e11 | 0.485771 | ||||||||
\(525\) | 2.43061e12 | 1.39636 | ||||||||
\(526\) | −1.27163e12 | −0.724311 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.82892e11 | −0.158405 | ||||||||
\(529\) | 1.59052e12 | 0.883055 | ||||||||
\(530\) | 4.64395e12 | 2.55650 | ||||||||
\(531\) | −2.55602e11 | −0.139521 | ||||||||
\(532\) | −2.16311e11 | −0.117078 | ||||||||
\(533\) | −3.17254e12 | −1.70269 | ||||||||
\(534\) | −2.99966e12 | −1.59638 | ||||||||
\(535\) | −5.52141e11 | −0.291379 | ||||||||
\(536\) | −9.37545e11 | −0.490626 | ||||||||
\(537\) | −1.15314e12 | −0.598407 | ||||||||
\(538\) | 1.53673e11 | 0.0790817 | ||||||||
\(539\) | −2.44532e11 | −0.124792 | ||||||||
\(540\) | −1.38209e12 | −0.699465 | ||||||||
\(541\) | −2.41525e11 | −0.121220 | −0.0606099 | − | 0.998162i | \(-0.519305\pi\) | ||||
−0.0606099 | + | 0.998162i | \(0.519305\pi\) | |||||||
\(542\) | 4.08974e12 | 2.03563 | ||||||||
\(543\) | 8.41146e11 | 0.415214 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.85566e12 | 0.900979 | ||||||||
\(546\) | −4.81946e12 | −2.32077 | ||||||||
\(547\) | −2.61893e12 | −1.25078 | −0.625389 | − | 0.780313i | \(-0.715060\pi\) | ||||
−0.625389 | + | 0.780313i | \(0.715060\pi\) | |||||||
\(548\) | −6.09898e11 | −0.288898 | ||||||||
\(549\) | −1.09495e11 | −0.0514423 | ||||||||
\(550\) | 5.38543e11 | 0.250951 | ||||||||
\(551\) | −6.11373e11 | −0.282569 | ||||||||
\(552\) | −1.64051e12 | −0.752060 | ||||||||
\(553\) | 1.67660e12 | 0.762373 | ||||||||
\(554\) | −1.52563e12 | −0.688104 | ||||||||
\(555\) | 8.01544e10 | 0.0358599 | ||||||||
\(556\) | −1.46805e12 | −0.651483 | ||||||||
\(557\) | −1.90268e12 | −0.837565 | −0.418782 | − | 0.908087i | \(-0.637543\pi\) | ||||
−0.418782 | + | 0.908087i | \(0.637543\pi\) | |||||||
\(558\) | −9.15707e11 | −0.399855 | ||||||||
\(559\) | −2.00488e12 | −0.868433 | ||||||||
\(560\) | −5.87710e12 | −2.52532 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.80195e11 | 0.414476 | ||||||||
\(563\) | 2.77945e12 | 1.16593 | 0.582964 | − | 0.812498i | \(-0.301893\pi\) | ||||
0.582964 | + | 0.812498i | \(0.301893\pi\) | |||||||
\(564\) | −2.39460e11 | −0.0996501 | ||||||||
\(565\) | −3.43790e12 | −1.41930 | ||||||||
\(566\) | −6.18429e11 | −0.253289 | ||||||||
\(567\) | 1.63860e12 | 0.665806 | ||||||||
\(568\) | −2.53394e12 | −1.02148 | ||||||||
\(569\) | −2.91719e12 | −1.16670 | −0.583350 | − | 0.812221i | \(-0.698258\pi\) | ||||
−0.583350 | + | 0.812221i | \(0.698258\pi\) | |||||||
\(570\) | −7.55750e11 | −0.299876 | ||||||||
\(571\) | −1.08718e12 | −0.427994 | −0.213997 | − | 0.976834i | \(-0.568648\pi\) | ||||
−0.213997 | + | 0.976834i | \(0.568648\pi\) | |||||||
\(572\) | −3.17252e11 | −0.123914 | ||||||||
\(573\) | −2.08180e12 | −0.806756 | ||||||||
\(574\) | −3.84572e12 | −1.47868 | ||||||||
\(575\) | 4.73019e12 | 1.80457 | ||||||||
\(576\) | −2.86202e11 | −0.108336 | ||||||||
\(577\) | 7.13293e11 | 0.267902 | 0.133951 | − | 0.990988i | \(-0.457233\pi\) | ||||
0.133951 | + | 0.990988i | \(0.457233\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.02607e12 | −1.11899 | ||||||||
\(580\) | 2.38547e12 | 0.875281 | ||||||||
\(581\) | −8.70755e10 | −0.0317032 | ||||||||
\(582\) | 8.74784e11 | 0.316044 | ||||||||
\(583\) | −6.28660e11 | −0.225376 | ||||||||
\(584\) | 8.31999e11 | 0.295982 | ||||||||
\(585\) | 2.89514e12 | 1.02204 | ||||||||
\(586\) | −2.11335e12 | −0.740341 | ||||||||
\(587\) | −6.12219e11 | −0.212831 | −0.106416 | − | 0.994322i | \(-0.533937\pi\) | ||||
−0.106416 | + | 0.994322i | \(0.533937\pi\) | |||||||
\(588\) | −7.60574e11 | −0.262388 | ||||||||
\(589\) | −5.54580e11 | −0.189865 | ||||||||
\(590\) | 2.03301e12 | 0.690726 | ||||||||
\(591\) | 1.75404e11 | 0.0591418 | ||||||||
\(592\) | −1.10092e11 | −0.0368391 | ||||||||
\(593\) | 1.86289e12 | 0.618643 | 0.309322 | − | 0.950957i | \(-0.399898\pi\) | ||||
0.309322 | + | 0.950957i | \(0.399898\pi\) | |||||||
\(594\) | 6.29748e11 | 0.207552 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.93005e12 | −0.626558 | ||||||||
\(597\) | 1.29509e12 | 0.417267 | ||||||||
\(598\) | −9.37912e12 | −2.99921 | ||||||||
\(599\) | 5.47380e12 | 1.73727 | 0.868637 | − | 0.495449i | \(-0.164996\pi\) | ||||
0.868637 | + | 0.495449i | \(0.164996\pi\) | |||||||
\(600\) | −2.28793e12 | −0.720714 | ||||||||
\(601\) | −4.44329e12 | −1.38921 | −0.694607 | − | 0.719389i | \(-0.744422\pi\) | ||||
−0.694607 | + | 0.719389i | \(0.744422\pi\) | |||||||
\(602\) | −2.43030e12 | −0.754181 | ||||||||
\(603\) | 8.47950e11 | 0.261181 | ||||||||
\(604\) | 2.12625e12 | 0.650052 | ||||||||
\(605\) | 4.88560e12 | 1.48258 | ||||||||
\(606\) | −3.15267e11 | −0.0949624 | ||||||||
\(607\) | 1.25061e12 | 0.373916 | 0.186958 | − | 0.982368i | \(-0.440137\pi\) | ||||
0.186958 | + | 0.982368i | \(0.440137\pi\) | |||||||
\(608\) | 5.56297e11 | 0.165098 | ||||||||
\(609\) | −4.90565e12 | −1.44517 | ||||||||
\(610\) | 8.70907e11 | 0.254676 | ||||||||
\(611\) | 1.86997e12 | 0.542812 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.34599e12 | 1.81521 | 0.907606 | − | 0.419823i | \(-0.137908\pi\) | ||||
0.907606 | + | 0.419823i | \(0.137908\pi\) | |||||||
\(614\) | 2.59777e12 | 0.737638 | ||||||||
\(615\) | −3.99187e12 | −1.12522 | ||||||||
\(616\) | 5.25280e11 | 0.146987 | ||||||||
\(617\) | 3.48028e12 | 0.966786 | 0.483393 | − | 0.875403i | \(-0.339404\pi\) | ||||
0.483393 | + | 0.875403i | \(0.339404\pi\) | |||||||
\(618\) | −8.73091e11 | −0.240775 | ||||||||
\(619\) | 2.75090e12 | 0.753125 | 0.376563 | − | 0.926391i | \(-0.377106\pi\) | ||||
0.376563 | + | 0.926391i | \(0.377106\pi\) | |||||||
\(620\) | 2.16387e12 | 0.588124 | ||||||||
\(621\) | 5.53127e12 | 1.49249 | ||||||||
\(622\) | 5.58230e12 | 1.49540 | ||||||||
\(623\) | 8.43612e12 | 2.24360 | ||||||||
\(624\) | 6.87112e12 | 1.81425 | ||||||||
\(625\) | −2.23425e12 | −0.585695 | ||||||||
\(626\) | 1.19797e12 | 0.311789 | ||||||||
\(627\) | 1.02307e11 | 0.0264364 | ||||||||
\(628\) | −7.78938e10 | −0.0199841 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 3.50946e12 | 0.887581 | ||||||||
\(631\) | −3.13630e12 | −0.787563 | −0.393782 | − | 0.919204i | \(-0.628833\pi\) | ||||
−0.393782 | + | 0.919204i | \(0.628833\pi\) | |||||||
\(632\) | −1.57819e12 | −0.393489 | ||||||||
\(633\) | −3.54425e12 | −0.877421 | ||||||||
\(634\) | −4.51296e11 | −0.110933 | ||||||||
\(635\) | 9.88413e12 | 2.41244 | ||||||||
\(636\) | −1.95534e12 | −0.473876 | ||||||||
\(637\) | 5.93939e12 | 1.42927 | ||||||||
\(638\) | −1.08693e12 | −0.259722 | ||||||||
\(639\) | 2.29178e12 | 0.543775 | ||||||||
\(640\) | 7.41174e12 | 1.74627 | ||||||||
\(641\) | 3.99573e12 | 0.934836 | 0.467418 | − | 0.884036i | \(-0.345184\pi\) | ||||
0.467418 | + | 0.884036i | \(0.345184\pi\) | |||||||
\(642\) | 7.82501e11 | 0.181793 | ||||||||
\(643\) | −4.46811e12 | −1.03080 | −0.515400 | − | 0.856950i | \(-0.672357\pi\) | ||||
−0.515400 | + | 0.856950i | \(0.672357\pi\) | |||||||
\(644\) | −3.37779e12 | −0.773830 | ||||||||
\(645\) | −2.52266e12 | −0.573905 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.65786e12 | −0.596297 | −0.298148 | − | 0.954520i | \(-0.596369\pi\) | ||||
−0.298148 | + | 0.954520i | \(0.596369\pi\) | |||||||
\(648\) | −1.54241e12 | −0.343647 | ||||||||
\(649\) | −2.75213e11 | −0.0608930 | ||||||||
\(650\) | −1.30806e13 | −2.87420 | ||||||||
\(651\) | −4.44995e12 | −0.971047 | ||||||||
\(652\) | −5.05245e11 | −0.109493 | ||||||||
\(653\) | 1.39817e12 | 0.300919 | 0.150459 | − | 0.988616i | \(-0.451925\pi\) | ||||
0.150459 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(654\) | −2.62987e12 | −0.562126 | ||||||||
\(655\) | −8.23745e12 | −1.74867 | ||||||||
\(656\) | 5.48285e12 | 1.15595 | ||||||||
\(657\) | −7.52490e11 | −0.157564 | ||||||||
\(658\) | 2.26676e12 | 0.471399 | ||||||||
\(659\) | −3.25916e12 | −0.673165 | −0.336582 | − | 0.941654i | \(-0.609271\pi\) | ||||
−0.336582 | + | 0.941654i | \(0.609271\pi\) | |||||||
\(660\) | −3.99184e11 | −0.0818890 | ||||||||
\(661\) | −3.38834e12 | −0.690368 | −0.345184 | − | 0.938535i | \(-0.612183\pi\) | ||||
−0.345184 | + | 0.938535i | \(0.612183\pi\) | |||||||
\(662\) | 7.70936e12 | 1.56012 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.19643e10 | 0.0163632 | ||||||||
\(665\) | 2.12544e12 | 0.421455 | ||||||||
\(666\) | 6.57407e10 | 0.0129479 | ||||||||
\(667\) | −9.54686e12 | −1.86764 | ||||||||
\(668\) | −3.07090e12 | −0.596722 | ||||||||
\(669\) | −4.90719e12 | −0.947143 | ||||||||
\(670\) | −6.74444e12 | −1.29303 | ||||||||
\(671\) | −1.17896e11 | −0.0224517 | ||||||||
\(672\) | 4.46372e12 | 0.844375 | ||||||||
\(673\) | 3.81702e12 | 0.717228 | 0.358614 | − | 0.933486i | \(-0.383250\pi\) | ||||
0.358614 | + | 0.933486i | \(0.383250\pi\) | |||||||
\(674\) | −4.08052e12 | −0.761634 | ||||||||
\(675\) | 7.71418e12 | 1.43029 | ||||||||
\(676\) | 5.41077e12 | 0.996549 | ||||||||
\(677\) | 9.52051e12 | 1.74185 | 0.870926 | − | 0.491414i | \(-0.163520\pi\) | ||||
0.870926 | + | 0.491414i | \(0.163520\pi\) | |||||||
\(678\) | 4.87224e12 | 0.885513 | ||||||||
\(679\) | −2.46021e12 | −0.444178 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.29057e12 | −0.764457 | ||||||||
\(682\) | −9.85963e11 | −0.174514 | ||||||||
\(683\) | −3.65262e12 | −0.642260 | −0.321130 | − | 0.947035i | \(-0.604063\pi\) | ||||
−0.321130 | + | 0.947035i | \(0.604063\pi\) | |||||||
\(684\) | −1.84155e11 | −0.0321686 | ||||||||
\(685\) | 5.99277e12 | 1.03997 | ||||||||
\(686\) | −2.03073e12 | −0.350102 | ||||||||
\(687\) | 2.15372e12 | 0.368879 | ||||||||
\(688\) | 3.46489e12 | 0.589578 | ||||||||
\(689\) | 1.52694e13 | 2.58128 | ||||||||
\(690\) | −1.18014e13 | −1.98203 | ||||||||
\(691\) | −7.17157e12 | −1.19664 | −0.598320 | − | 0.801258i | \(-0.704165\pi\) | ||||
−0.598320 | + | 0.801258i | \(0.704165\pi\) | |||||||
\(692\) | 2.47669e12 | 0.410577 | ||||||||
\(693\) | −4.75082e11 | −0.0782473 | ||||||||
\(694\) | −8.55485e10 | −0.0139989 | ||||||||
\(695\) | 1.44248e13 | 2.34519 | ||||||||
\(696\) | 4.61770e12 | 0.745905 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.15424e12 | 0.502973 | ||||||||
\(699\) | 8.48743e12 | 1.34471 | ||||||||
\(700\) | −4.71083e12 | −0.741577 | ||||||||
\(701\) | 2.77953e12 | 0.434750 | 0.217375 | − | 0.976088i | \(-0.430251\pi\) | ||||
0.217375 | + | 0.976088i | \(0.430251\pi\) | |||||||
\(702\) | −1.52958e13 | −2.37715 | ||||||||
\(703\) | 3.98146e10 | 0.00614814 | ||||||||
\(704\) | −3.08161e11 | −0.0472825 | ||||||||
\(705\) | 2.35290e12 | 0.358718 | ||||||||
\(706\) | −1.73510e11 | −0.0262847 | ||||||||
\(707\) | 8.86644e11 | 0.133463 | ||||||||
\(708\) | −8.56002e11 | −0.128034 | ||||||||
\(709\) | 2.42496e12 | 0.360410 | 0.180205 | − | 0.983629i | \(-0.442324\pi\) | ||||
0.180205 | + | 0.983629i | \(0.442324\pi\) | |||||||
\(710\) | −1.82284e13 | −2.69207 | ||||||||
\(711\) | 1.42737e12 | 0.209471 | ||||||||
\(712\) | −7.94093e12 | −1.15801 | ||||||||
\(713\) | −8.66001e12 | −1.25492 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.11727e12 | 0.446064 | ||||||||
\(716\) | 2.23493e12 | 0.317801 | ||||||||
\(717\) | −3.00874e12 | −0.425155 | ||||||||
\(718\) | 1.33160e12 | 0.186988 | ||||||||
\(719\) | −1.26802e13 | −1.76948 | −0.884742 | − | 0.466081i | \(-0.845666\pi\) | ||||
−0.884742 | + | 0.466081i | \(0.845666\pi\) | |||||||
\(720\) | −5.00345e12 | −0.693862 | ||||||||
\(721\) | 2.45544e12 | 0.338393 | ||||||||
\(722\) | 8.33363e12 | 1.14135 | ||||||||
\(723\) | 8.61118e12 | 1.17203 | ||||||||
\(724\) | −1.63025e12 | −0.220511 | ||||||||
\(725\) | −1.33145e13 | −1.78980 | ||||||||
\(726\) | −6.92393e12 | −0.924992 | ||||||||
\(727\) | 3.80482e12 | 0.505160 | 0.252580 | − | 0.967576i | \(-0.418721\pi\) | ||||
0.252580 | + | 0.967576i | \(0.418721\pi\) | |||||||
\(728\) | −1.27584e13 | −1.68347 | ||||||||
\(729\) | 7.99589e12 | 1.04856 | ||||||||
\(730\) | 5.98517e12 | 0.780052 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.66696e11 | −0.0472070 | ||||||||
\(733\) | −1.10980e13 | −1.41996 | −0.709979 | − | 0.704223i | \(-0.751296\pi\) | ||||
−0.709979 | + | 0.704223i | \(0.751296\pi\) | |||||||
\(734\) | 1.08867e13 | 1.38441 | ||||||||
\(735\) | 7.47329e12 | 0.944537 | ||||||||
\(736\) | 8.68682e12 | 1.09122 | ||||||||
\(737\) | 9.13007e11 | 0.113991 | ||||||||
\(738\) | −3.27404e12 | −0.406284 | ||||||||
\(739\) | 2.33123e12 | 0.287531 | 0.143765 | − | 0.989612i | \(-0.454079\pi\) | ||||
0.143765 | + | 0.989612i | \(0.454079\pi\) | |||||||
\(740\) | −1.55349e11 | −0.0190444 | ||||||||
\(741\) | −2.48492e12 | −0.302783 | ||||||||
\(742\) | 1.85094e13 | 2.24169 | ||||||||
\(743\) | −1.09510e13 | −1.31827 | −0.659136 | − | 0.752024i | \(-0.729078\pi\) | ||||
−0.659136 | + | 0.752024i | \(0.729078\pi\) | |||||||
\(744\) | 4.18874e12 | 0.501193 | ||||||||
\(745\) | 1.89644e13 | 2.25547 | ||||||||
\(746\) | 1.26028e12 | 0.148985 | ||||||||
\(747\) | −7.41315e10 | −0.00871084 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.20067e12 | −0.255498 | ||||||||
\(750\) | −3.94306e12 | −0.455048 | ||||||||
\(751\) | −4.36338e12 | −0.500545 | −0.250272 | − | 0.968175i | \(-0.580520\pi\) | ||||
−0.250272 | + | 0.968175i | \(0.580520\pi\) | |||||||
\(752\) | −3.23172e12 | −0.368514 | ||||||||
\(753\) | 2.65497e12 | 0.300942 | ||||||||
\(754\) | 2.64003e13 | 2.97467 | ||||||||
\(755\) | −2.08922e13 | −2.34004 | ||||||||
\(756\) | −5.50863e12 | −0.613331 | ||||||||
\(757\) | 5.31168e12 | 0.587896 | 0.293948 | − | 0.955821i | \(-0.405031\pi\) | ||||
0.293948 | + | 0.955821i | \(0.405031\pi\) | |||||||
\(758\) | −1.16671e12 | −0.128366 | ||||||||
\(759\) | 1.59757e12 | 0.174732 | ||||||||
\(760\) | −2.00068e12 | −0.217528 | ||||||||
\(761\) | 1.63902e13 | 1.77155 | 0.885777 | − | 0.464111i | \(-0.153626\pi\) | ||||
0.885777 | + | 0.464111i | \(0.153626\pi\) | |||||||
\(762\) | −1.40079e13 | −1.50514 | ||||||||
\(763\) | 7.39613e12 | 0.790031 | ||||||||
\(764\) | 4.03479e12 | 0.428450 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.79084e13 | 1.87944 | ||||||||
\(767\) | 6.68460e12 | 0.697423 | ||||||||
\(768\) | −8.23634e12 | −0.854297 | ||||||||
\(769\) | 1.34189e13 | 1.38372 | 0.691859 | − | 0.722033i | \(-0.256792\pi\) | ||||
0.691859 | + | 0.722033i | \(0.256792\pi\) | |||||||
\(770\) | 3.77872e12 | 0.387379 | ||||||||
\(771\) | 4.70306e12 | 0.479331 | ||||||||
\(772\) | 5.86491e12 | 0.594270 | ||||||||
\(773\) | −5.22917e12 | −0.526775 | −0.263387 | − | 0.964690i | \(-0.584840\pi\) | ||||
−0.263387 | + | 0.964690i | \(0.584840\pi\) | |||||||
\(774\) | −2.06903e12 | −0.207220 | ||||||||
\(775\) | −1.20777e13 | −1.20261 | ||||||||
\(776\) | 2.31579e12 | 0.229257 | ||||||||
\(777\) | 3.19472e11 | 0.0314440 | ||||||||
\(778\) | −1.01893e13 | −0.997097 | ||||||||
\(779\) | −1.98286e12 | −0.192918 | ||||||||
\(780\) | 9.69572e12 | 0.937896 | ||||||||
\(781\) | 2.46762e12 | 0.237327 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.55694e13 | −1.48028 | ||||||||
\(784\) | −1.02646e13 | −0.970330 | ||||||||
\(785\) | 7.65373e11 | 0.0719382 | ||||||||
\(786\) | 1.16742e13 | 1.09100 | ||||||||
\(787\) | 6.84661e12 | 0.636194 | 0.318097 | − | 0.948058i | \(-0.396956\pi\) | ||||
0.318097 | + | 0.948058i | \(0.396956\pi\) | |||||||
\(788\) | −3.39955e11 | −0.0314089 | ||||||||
\(789\) | −5.26097e12 | −0.483303 | ||||||||
\(790\) | −1.13531e13 | −1.03703 | ||||||||
\(791\) | −1.37025e13 | −1.24453 | ||||||||
\(792\) | 4.47195e11 | 0.0403863 | ||||||||
\(793\) | 2.86357e12 | 0.257145 | ||||||||
\(794\) | 2.18812e13 | 1.95379 | ||||||||
\(795\) | 1.92129e13 | 1.70585 | ||||||||
\(796\) | −2.51004e12 | −0.221601 | ||||||||
\(797\) | −1.71243e13 | −1.50332 | −0.751658 | − | 0.659553i | \(-0.770745\pi\) | ||||
−0.751658 | + | 0.659553i | \(0.770745\pi\) | |||||||
\(798\) | −3.01220e12 | −0.262948 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.21151e13 | 1.04573 | ||||||||
\(801\) | 7.18206e12 | 0.616457 | ||||||||
\(802\) | 2.03643e13 | 1.73814 | ||||||||
\(803\) | −8.10224e11 | −0.0687678 | ||||||||
\(804\) | 2.83975e12 | 0.239678 | ||||||||
\(805\) | 3.31896e13 | 2.78561 | ||||||||
\(806\) | 2.39479e13 | 1.99875 | ||||||||
\(807\) | 6.35772e11 | 0.0527680 | ||||||||
\(808\) | −8.34599e11 | −0.0688853 | ||||||||
\(809\) | −1.37472e13 | −1.12836 | −0.564178 | − | 0.825653i | \(-0.690807\pi\) | ||||
−0.564178 | + | 0.825653i | \(0.690807\pi\) | |||||||
\(810\) | −1.10957e13 | −0.905672 | ||||||||
\(811\) | −4.44088e12 | −0.360475 | −0.180237 | − | 0.983623i | \(-0.557687\pi\) | ||||
−0.180237 | + | 0.983623i | \(0.557687\pi\) | |||||||
\(812\) | 9.50778e12 | 0.767497 | ||||||||
\(813\) | 1.69200e13 | 1.35829 | ||||||||
\(814\) | 7.07846e10 | 0.00565104 | ||||||||
\(815\) | 4.96446e12 | 0.394151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.25307e12 | −0.0983955 | ||||||||
\(818\) | −1.30683e13 | −1.02054 | ||||||||
\(819\) | 1.15392e13 | 0.896185 | ||||||||
\(820\) | 7.73676e12 | 0.597581 | ||||||||
\(821\) | −3.20955e12 | −0.246547 | −0.123274 | − | 0.992373i | \(-0.539339\pi\) | ||||
−0.123274 | + | 0.992373i | \(0.539339\pi\) | |||||||
\(822\) | −8.49303e12 | −0.648843 | ||||||||
\(823\) | 1.82964e12 | 0.139016 | 0.0695081 | − | 0.997581i | \(-0.477857\pi\) | ||||
0.0695081 | + | 0.997581i | \(0.477857\pi\) | |||||||
\(824\) | −2.31131e12 | −0.174657 | ||||||||
\(825\) | 2.22805e12 | 0.167449 | ||||||||
\(826\) | 8.10299e12 | 0.605669 | ||||||||
\(827\) | 4.67524e12 | 0.347560 | 0.173780 | − | 0.984785i | \(-0.444402\pi\) | ||||
0.173780 | + | 0.984785i | \(0.444402\pi\) | |||||||
\(828\) | −2.87567e12 | −0.212619 | ||||||||
\(829\) | −2.09218e13 | −1.53852 | −0.769260 | − | 0.638936i | \(-0.779375\pi\) | ||||
−0.769260 | + | 0.638936i | \(0.779375\pi\) | |||||||
\(830\) | 5.89628e11 | 0.0431248 | ||||||||
\(831\) | −6.31179e12 | −0.459143 | ||||||||
\(832\) | 7.48486e12 | 0.541538 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.04430e13 | −1.46318 | ||||||||
\(835\) | 3.01743e13 | 2.14807 | ||||||||
\(836\) | −1.98285e11 | −0.0140398 | ||||||||
\(837\) | −1.41231e13 | −0.994638 | ||||||||
\(838\) | −2.01795e12 | −0.141355 | ||||||||
\(839\) | −2.22899e13 | −1.55303 | −0.776515 | − | 0.630098i | \(-0.783015\pi\) | ||||
−0.776515 | + | 0.630098i | \(0.783015\pi\) | |||||||
\(840\) | −1.60534e13 | −1.11253 | ||||||||
\(841\) | 1.23653e13 | 0.852360 | ||||||||
\(842\) | 1.59541e13 | 1.09388 | ||||||||
\(843\) | 4.05525e12 | 0.276563 | ||||||||
\(844\) | 6.86921e12 | 0.465979 | ||||||||
\(845\) | −5.31654e13 | −3.58735 | ||||||||
\(846\) | 1.92980e12 | 0.129522 | ||||||||
\(847\) | 1.94726e13 | 1.30001 | ||||||||
\(848\) | −2.63889e13 | −1.75243 | ||||||||
\(849\) | −2.55855e12 | −0.169009 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.21722e11 | 0.0406362 | ||||||||
\(852\) | 7.67509e12 | 0.499006 | ||||||||
\(853\) | −1.82969e13 | −1.18333 | −0.591666 | − | 0.806183i | \(-0.701530\pi\) | ||||
−0.591666 | + | 0.806183i | \(0.701530\pi\) | |||||||
\(854\) | 3.47118e12 | 0.223315 | ||||||||
\(855\) | 1.80948e12 | 0.115800 | ||||||||
\(856\) | 2.07150e12 | 0.131872 | ||||||||
\(857\) | 2.46088e13 | 1.55839 | 0.779197 | − | 0.626780i | \(-0.215627\pi\) | ||||
0.779197 | + | 0.626780i | \(0.215627\pi\) | |||||||
\(858\) | −4.41783e12 | −0.278302 | ||||||||
\(859\) | 9.01006e12 | 0.564623 | 0.282311 | − | 0.959323i | \(-0.408899\pi\) | ||||
0.282311 | + | 0.959323i | \(0.408899\pi\) | |||||||
\(860\) | 4.88924e12 | 0.304788 | ||||||||
\(861\) | −1.59104e13 | −0.986661 | ||||||||
\(862\) | 1.28070e13 | 0.790066 | ||||||||
\(863\) | 2.76290e13 | 1.69557 | 0.847785 | − | 0.530339i | \(-0.177935\pi\) | ||||
0.847785 | + | 0.530339i | \(0.177935\pi\) | |||||||
\(864\) | 1.41668e13 | 0.864888 | ||||||||
\(865\) | −2.43356e13 | −1.47798 | ||||||||
\(866\) | 3.66314e13 | 2.21321 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.62456e12 | 0.515701 | ||||||||
\(869\) | 1.53688e12 | 0.0914223 | ||||||||
\(870\) | 3.32184e13 | 1.96581 | ||||||||
\(871\) | −2.21759e13 | −1.30557 | ||||||||
\(872\) | −6.96198e12 | −0.407764 | ||||||||
\(873\) | −2.09449e12 | −0.122043 | ||||||||
\(874\) | −5.86202e12 | −0.339817 | ||||||||
\(875\) | 1.10893e13 | 0.639540 | ||||||||
\(876\) | −2.52006e12 | −0.144591 | ||||||||
\(877\) | 1.67098e12 | 0.0953833 | 0.0476916 | − | 0.998862i | \(-0.484814\pi\) | ||||
0.0476916 | + | 0.998862i | \(0.484814\pi\) | |||||||
\(878\) | −1.49616e13 | −0.849677 | ||||||||
\(879\) | −8.74332e12 | −0.493999 | ||||||||
\(880\) | −5.38733e12 | −0.302832 | ||||||||
\(881\) | −2.17946e13 | −1.21887 | −0.609434 | − | 0.792837i | \(-0.708603\pi\) | ||||
−0.609434 | + | 0.792837i | \(0.708603\pi\) | |||||||
\(882\) | 6.12941e12 | 0.341044 | ||||||||
\(883\) | −2.01668e13 | −1.11639 | −0.558193 | − | 0.829711i | \(-0.688505\pi\) | ||||
−0.558193 | + | 0.829711i | \(0.688505\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.41095e12 | 0.460893 | ||||||||
\(886\) | −3.16399e13 | −1.72497 | ||||||||
\(887\) | 1.66457e13 | 0.902914 | 0.451457 | − | 0.892293i | \(-0.350904\pi\) | ||||
0.451457 | + | 0.892293i | \(0.350904\pi\) | |||||||
\(888\) | −3.00719e11 | −0.0162294 | ||||||||
\(889\) | 3.93953e13 | 2.11537 | ||||||||
\(890\) | −5.71248e13 | −3.05190 | ||||||||
\(891\) | 1.50204e12 | 0.0798422 | ||||||||
\(892\) | 9.51077e12 | 0.503007 | ||||||||
\(893\) | 1.16874e12 | 0.0615018 | ||||||||
\(894\) | −2.68766e13 | −1.40720 | ||||||||
\(895\) | −2.19601e13 | −1.14401 | ||||||||
\(896\) | 2.95410e13 | 1.53123 | ||||||||
\(897\) | −3.88032e13 | −2.00125 | ||||||||
\(898\) | −2.53251e13 | −1.29960 | ||||||||
\(899\) | 2.43762e13 | 1.24465 | ||||||||
\(900\) | −4.01055e12 | −0.203757 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3.52523e12 | −0.177320 | ||||||||
\(903\) | −1.00546e13 | −0.503234 | ||||||||
\(904\) | 1.28982e13 | 0.642347 | ||||||||
\(905\) | 1.60186e13 | 0.793790 | ||||||||
\(906\) | 2.96087e13 | 1.45997 | ||||||||
\(907\) | 2.83791e13 | 1.39241 | 0.696204 | − | 0.717844i | \(-0.254871\pi\) | ||||
0.696204 | + | 0.717844i | \(0.254871\pi\) | |||||||
\(908\) | 8.31568e12 | 0.405986 | ||||||||
\(909\) | 7.54841e11 | 0.0366706 | ||||||||
\(910\) | −9.17807e13 | −4.43675 | ||||||||
\(911\) | 2.64888e13 | 1.27418 | 0.637088 | − | 0.770791i | \(-0.280139\pi\) | ||||
0.637088 | + | 0.770791i | \(0.280139\pi\) | |||||||
\(912\) | 4.29450e12 | 0.205559 | ||||||||
\(913\) | −7.98191e10 | −0.00380179 | ||||||||
\(914\) | 3.61095e13 | 1.71145 | ||||||||
\(915\) | 3.60310e12 | 0.169935 | ||||||||
\(916\) | −4.17419e12 | −0.195904 | ||||||||
\(917\) | −3.28321e13 | −1.53333 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.71751e13 | −1.71922 | −0.859612 | − | 0.510947i | \(-0.829295\pi\) | ||||
−0.859612 | + | 0.510947i | \(0.829295\pi\) | |||||||
\(920\) | −3.12414e13 | −1.43776 | ||||||||
\(921\) | 1.07475e13 | 0.492195 | ||||||||
\(922\) | −2.28065e13 | −1.03937 | ||||||||
\(923\) | −5.99355e13 | −2.71817 | ||||||||
\(924\) | −1.59103e12 | −0.0718051 | ||||||||
\(925\) | 8.67085e11 | 0.0389425 | ||||||||
\(926\) | 8.76214e12 | 0.391616 | ||||||||
\(927\) | 2.09043e12 | 0.0929774 | ||||||||
\(928\) | −2.44516e13 | −1.08229 | ||||||||
\(929\) | 1.56182e13 | 0.687953 | 0.343977 | − | 0.938978i | \(-0.388226\pi\) | ||||
0.343977 | + | 0.938978i | \(0.388226\pi\) | |||||||
\(930\) | 3.01326e13 | 1.32088 | ||||||||
\(931\) | 3.71216e12 | 0.161940 | ||||||||
\(932\) | −1.64497e13 | −0.714146 | ||||||||
\(933\) | 2.30950e13 | 0.997816 | ||||||||
\(934\) | −2.00090e13 | −0.860327 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.08619e13 | −0.462554 | ||||||||
\(937\) | −1.17488e13 | −0.497927 | −0.248964 | − | 0.968513i | \(-0.580090\pi\) | ||||
−0.248964 | + | 0.968513i | \(0.580090\pi\) | |||||||
\(938\) | −2.68814e13 | −1.13381 | ||||||||
\(939\) | 4.95621e12 | 0.208044 | ||||||||
\(940\) | −4.56023e12 | −0.190507 | ||||||||
\(941\) | −6.72829e12 | −0.279738 | −0.139869 | − | 0.990170i | \(-0.544668\pi\) | ||||
−0.139869 | + | 0.990170i | \(0.544668\pi\) | |||||||
\(942\) | −1.08470e12 | −0.0448827 | ||||||||
\(943\) | −3.09632e13 | −1.27510 | ||||||||
\(944\) | −1.15525e13 | −0.473479 | ||||||||
\(945\) | 5.41270e13 | 2.20785 | ||||||||
\(946\) | −2.22777e12 | −0.0904399 | ||||||||
\(947\) | −3.08477e13 | −1.24637 | −0.623186 | − | 0.782074i | \(-0.714162\pi\) | ||||
−0.623186 | + | 0.782074i | \(0.714162\pi\) | |||||||
\(948\) | 4.78021e12 | 0.192225 | ||||||||
\(949\) | 1.96794e13 | 0.787614 | ||||||||
\(950\) | −8.17546e12 | −0.325654 | ||||||||
\(951\) | −1.86709e12 | −0.0740208 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.93554e13 | 0.760123 | 0.380062 | − | 0.924961i | \(-0.375903\pi\) | ||||
0.380062 | + | 0.924961i | \(0.375903\pi\) | |||||||
\(954\) | 1.57579e13 | 0.615930 | ||||||||
\(955\) | −3.96452e13 | −1.54232 | ||||||||
\(956\) | 5.83131e12 | 0.225791 | ||||||||
\(957\) | −4.49684e12 | −0.173302 | ||||||||
\(958\) | −8.94330e12 | −0.343047 | ||||||||
\(959\) | 2.38854e13 | 0.911905 | ||||||||
\(960\) | 9.41788e12 | 0.357876 | ||||||||
\(961\) | −4.32785e12 | −0.163688 | ||||||||
\(962\) | −1.71927e12 | −0.0647228 | ||||||||
\(963\) | −1.87354e12 | −0.0702010 | ||||||||
\(964\) | −1.66896e13 | −0.622441 | ||||||||
\(965\) | −5.76278e13 | −2.13924 | ||||||||
\(966\) | −4.70368e13 | −1.73796 | ||||||||
\(967\) | −3.72066e13 | −1.36836 | −0.684181 | − | 0.729312i | \(-0.739840\pi\) | ||||
−0.684181 | + | 0.729312i | \(0.739840\pi\) | |||||||
\(968\) | −1.83296e13 | −0.670985 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.66592e13 | 0.604200 | ||||||||
\(971\) | 4.17404e13 | 1.50685 | 0.753426 | − | 0.657533i | \(-0.228400\pi\) | ||||
0.753426 | + | 0.657533i | \(0.228400\pi\) | |||||||
\(972\) | −8.12150e12 | −0.291835 | ||||||||
\(973\) | 5.74931e13 | 2.05640 | ||||||||
\(974\) | 4.97084e13 | 1.76976 | ||||||||
\(975\) | −5.41168e13 | −1.91784 | ||||||||
\(976\) | −4.94888e12 | −0.174575 | ||||||||
\(977\) | −3.20906e12 | −0.112681 | −0.0563407 | − | 0.998412i | \(-0.517943\pi\) | ||||
−0.0563407 | + | 0.998412i | \(0.517943\pi\) | |||||||
\(978\) | −7.03569e12 | −0.245913 | ||||||||
\(979\) | 7.73309e12 | 0.269049 | ||||||||
\(980\) | −1.44842e13 | −0.501622 | ||||||||
\(981\) | 6.29667e12 | 0.217070 | ||||||||
\(982\) | 4.41959e13 | 1.51663 | ||||||||
\(983\) | −7.14967e12 | −0.244228 | −0.122114 | − | 0.992516i | \(-0.538967\pi\) | ||||
−0.122114 | + | 0.992516i | \(0.538967\pi\) | |||||||
\(984\) | 1.49765e13 | 0.509252 | ||||||||
\(985\) | 3.34034e12 | 0.113065 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.37799e12 | 0.314545 | ||||||||
\(988\) | 4.81610e12 | 0.160801 | ||||||||
\(989\) | −1.95672e13 | −0.650347 | ||||||||
\(990\) | 3.21700e12 | 0.106437 | ||||||||
\(991\) | 4.53035e13 | 1.49211 | 0.746053 | − | 0.665886i | \(-0.231946\pi\) | ||||
0.746053 | + | 0.665886i | \(0.231946\pi\) | |||||||
\(992\) | −2.21802e13 | −0.727216 | ||||||||
\(993\) | 3.18950e13 | 1.04100 | ||||||||
\(994\) | −7.26532e13 | −2.36056 | ||||||||
\(995\) | 2.46633e13 | 0.797715 | ||||||||
\(996\) | −2.48263e11 | −0.00799366 | ||||||||
\(997\) | 1.60620e13 | 0.514838 | 0.257419 | − | 0.966300i | \(-0.417128\pi\) | ||||
0.257419 | + | 0.966300i | \(0.417128\pi\) | |||||||
\(998\) | −2.26735e13 | −0.723488 | ||||||||
\(999\) | 1.01393e12 | 0.0322079 |
(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.i.1.11 | 52 | ||
17.3 | odd | 16 | 17.10.d.a.9.4 | yes | 52 | ||
17.6 | odd | 16 | 17.10.d.a.2.4 | ✓ | 52 | ||
17.16 | even | 2 | inner | 289.10.a.i.1.12 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.d.a.2.4 | ✓ | 52 | 17.6 | odd | 16 | ||
17.10.d.a.9.4 | yes | 52 | 17.3 | odd | 16 | ||
289.10.a.i.1.11 | 52 | 1.1 | even | 1 | trivial | ||
289.10.a.i.1.12 | 52 | 17.16 | even | 2 | inner |