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: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −43.7427 | −1.93317 | −0.966586 | − | 0.256343i | \(-0.917482\pi\) | ||||
−0.966586 | + | 0.256343i | \(0.917482\pi\) | |||||||
\(3\) | −83.5916 | −0.595823 | −0.297911 | − | 0.954594i | \(-0.596290\pi\) | ||||
−0.297911 | + | 0.954594i | \(0.596290\pi\) | |||||||
\(4\) | 1401.42 | 2.73715 | ||||||||
\(5\) | 712.522 | 0.509839 | 0.254920 | − | 0.966962i | \(-0.417951\pi\) | ||||
0.254920 | + | 0.966962i | \(0.417951\pi\) | |||||||
\(6\) | 3656.52 | 1.15183 | ||||||||
\(7\) | −5542.36 | −0.872477 | −0.436238 | − | 0.899831i | \(-0.643690\pi\) | ||||
−0.436238 | + | 0.899831i | \(0.643690\pi\) | |||||||
\(8\) | −38905.7 | −3.35822 | ||||||||
\(9\) | −12695.4 | −0.644995 | ||||||||
\(10\) | −31167.6 | −0.985607 | ||||||||
\(11\) | −36089.6 | −0.743216 | −0.371608 | − | 0.928390i | \(-0.621193\pi\) | ||||
−0.371608 | + | 0.928390i | \(0.621193\pi\) | |||||||
\(12\) | −117147. | −1.63086 | ||||||||
\(13\) | −175561. | −1.70484 | −0.852419 | − | 0.522859i | \(-0.824865\pi\) | ||||
−0.852419 | + | 0.522859i | \(0.824865\pi\) | |||||||
\(14\) | 242438. | 1.68665 | ||||||||
\(15\) | −59560.8 | −0.303774 | ||||||||
\(16\) | 984313. | 3.75486 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 555333. | 1.24689 | ||||||||
\(19\) | −512948. | −0.902988 | −0.451494 | − | 0.892274i | \(-0.649109\pi\) | ||||
−0.451494 | + | 0.892274i | \(0.649109\pi\) | |||||||
\(20\) | 998544. | 1.39551 | ||||||||
\(21\) | 463295. | 0.519841 | ||||||||
\(22\) | 1.57866e6 | 1.43676 | ||||||||
\(23\) | 1.41122e6 | 1.05153 | 0.525764 | − | 0.850630i | \(-0.323779\pi\) | ||||
0.525764 | + | 0.850630i | \(0.323779\pi\) | |||||||
\(24\) | 3.25219e6 | 2.00090 | ||||||||
\(25\) | −1.44544e6 | −0.740064 | ||||||||
\(26\) | 7.67951e6 | 3.29574 | ||||||||
\(27\) | 2.70657e6 | 0.980126 | ||||||||
\(28\) | −7.76719e6 | −2.38810 | ||||||||
\(29\) | 6.23829e6 | 1.63785 | 0.818926 | − | 0.573899i | \(-0.194570\pi\) | ||||
0.818926 | + | 0.573899i | \(0.194570\pi\) | |||||||
\(30\) | 2.60535e6 | 0.587247 | ||||||||
\(31\) | 100038. | 0.0194553 | 0.00972767 | − | 0.999953i | \(-0.496904\pi\) | ||||
0.00972767 | + | 0.999953i | \(0.496904\pi\) | |||||||
\(32\) | −2.31367e7 | −3.90056 | ||||||||
\(33\) | 3.01679e6 | 0.442825 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.94906e6 | −0.444823 | ||||||||
\(36\) | −1.77917e7 | −1.76545 | ||||||||
\(37\) | 1.77417e7 | 1.55628 | 0.778141 | − | 0.628090i | \(-0.216163\pi\) | ||||
0.778141 | + | 0.628090i | \(0.216163\pi\) | |||||||
\(38\) | 2.24377e7 | 1.74563 | ||||||||
\(39\) | 1.46754e7 | 1.01578 | ||||||||
\(40\) | −2.77212e7 | −1.71215 | ||||||||
\(41\) | −2.70173e7 | −1.49319 | −0.746594 | − | 0.665280i | \(-0.768312\pi\) | ||||
−0.746594 | + | 0.665280i | \(0.768312\pi\) | |||||||
\(42\) | −2.02658e7 | −1.00494 | ||||||||
\(43\) | 778967. | 0.0347465 | 0.0173733 | − | 0.999849i | \(-0.494470\pi\) | ||||
0.0173733 | + | 0.999849i | \(0.494470\pi\) | |||||||
\(44\) | −5.05768e7 | −2.03430 | ||||||||
\(45\) | −9.04578e6 | −0.328844 | ||||||||
\(46\) | −6.17308e7 | −2.03278 | ||||||||
\(47\) | 1.03172e7 | 0.308406 | 0.154203 | − | 0.988039i | \(-0.450719\pi\) | ||||
0.154203 | + | 0.988039i | \(0.450719\pi\) | |||||||
\(48\) | −8.22803e7 | −2.23723 | ||||||||
\(49\) | −9.63580e6 | −0.238784 | ||||||||
\(50\) | 6.32273e7 | 1.43067 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.46035e8 | −4.66640 | ||||||||
\(53\) | 3.35090e7 | 0.583338 | 0.291669 | − | 0.956519i | \(-0.405789\pi\) | ||||
0.291669 | + | 0.956519i | \(0.405789\pi\) | |||||||
\(54\) | −1.18392e8 | −1.89475 | ||||||||
\(55\) | −2.57146e7 | −0.378921 | ||||||||
\(56\) | 2.15630e8 | 2.92997 | ||||||||
\(57\) | 4.28782e7 | 0.538021 | ||||||||
\(58\) | −2.72880e8 | −3.16625 | ||||||||
\(59\) | 1.32523e8 | 1.42383 | 0.711915 | − | 0.702265i | \(-0.247828\pi\) | ||||
0.711915 | + | 0.702265i | \(0.247828\pi\) | |||||||
\(60\) | −8.34699e7 | −0.831475 | ||||||||
\(61\) | 4.00552e7 | 0.370403 | 0.185202 | − | 0.982701i | \(-0.440706\pi\) | ||||
0.185202 | + | 0.982701i | \(0.440706\pi\) | |||||||
\(62\) | −4.37595e6 | −0.0376105 | ||||||||
\(63\) | 7.03628e7 | 0.562744 | ||||||||
\(64\) | 5.08095e8 | 3.78561 | ||||||||
\(65\) | −1.25091e8 | −0.869193 | ||||||||
\(66\) | −1.31962e8 | −0.856057 | ||||||||
\(67\) | 2.73645e8 | 1.65902 | 0.829509 | − | 0.558494i | \(-0.188621\pi\) | ||||
0.829509 | + | 0.558494i | \(0.188621\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.17967e8 | −0.626524 | ||||||||
\(70\) | 1.72742e8 | 0.859919 | ||||||||
\(71\) | −1.50488e8 | −0.702813 | −0.351406 | − | 0.936223i | \(-0.614296\pi\) | ||||
−0.351406 | + | 0.936223i | \(0.614296\pi\) | |||||||
\(72\) | 4.93925e8 | 2.16603 | ||||||||
\(73\) | −1.55653e7 | −0.0641511 | −0.0320755 | − | 0.999485i | \(-0.510212\pi\) | ||||
−0.0320755 | + | 0.999485i | \(0.510212\pi\) | |||||||
\(74\) | −7.76071e8 | −3.00856 | ||||||||
\(75\) | 1.20826e8 | 0.440947 | ||||||||
\(76\) | −7.18857e8 | −2.47162 | ||||||||
\(77\) | 2.00022e8 | 0.648439 | ||||||||
\(78\) | −6.41943e8 | −1.96368 | ||||||||
\(79\) | 4.95165e7 | 0.143030 | 0.0715152 | − | 0.997440i | \(-0.477217\pi\) | ||||
0.0715152 | + | 0.997440i | \(0.477217\pi\) | |||||||
\(80\) | 7.01344e8 | 1.91437 | ||||||||
\(81\) | 2.36382e7 | 0.0610143 | ||||||||
\(82\) | 1.18181e9 | 2.88659 | ||||||||
\(83\) | −2.23284e8 | −0.516423 | −0.258211 | − | 0.966088i | \(-0.583133\pi\) | ||||
−0.258211 | + | 0.966088i | \(0.583133\pi\) | |||||||
\(84\) | 6.49272e8 | 1.42289 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.40741e7 | −0.0671710 | ||||||||
\(87\) | −5.21469e8 | −0.975869 | ||||||||
\(88\) | 1.40409e9 | 2.49588 | ||||||||
\(89\) | 3.53228e7 | 0.0596761 | 0.0298380 | − | 0.999555i | \(-0.490501\pi\) | ||||
0.0298380 | + | 0.999555i | \(0.490501\pi\) | |||||||
\(90\) | 3.95687e8 | 0.635712 | ||||||||
\(91\) | 9.73023e8 | 1.48743 | ||||||||
\(92\) | 1.97772e9 | 2.87819 | ||||||||
\(93\) | −8.36237e6 | −0.0115919 | ||||||||
\(94\) | −4.51304e8 | −0.596203 | ||||||||
\(95\) | −3.65487e8 | −0.460379 | ||||||||
\(96\) | 1.93404e9 | 2.32404 | ||||||||
\(97\) | 1.41983e9 | 1.62841 | 0.814207 | − | 0.580575i | \(-0.197172\pi\) | ||||
0.814207 | + | 0.580575i | \(0.197172\pi\) | |||||||
\(98\) | 4.21496e8 | 0.461611 | ||||||||
\(99\) | 4.58174e8 | 0.479371 | ||||||||
\(100\) | −2.02567e9 | −2.02567 | ||||||||
\(101\) | −6.69672e8 | −0.640348 | −0.320174 | − | 0.947359i | \(-0.603741\pi\) | ||||
−0.320174 | + | 0.947359i | \(0.603741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.49559e8 | 0.743748 | 0.371874 | − | 0.928283i | \(-0.378715\pi\) | ||||
0.371874 | + | 0.928283i | \(0.378715\pi\) | |||||||
\(104\) | 6.83033e9 | 5.72521 | ||||||||
\(105\) | 3.30108e8 | 0.265036 | ||||||||
\(106\) | −1.46577e9 | −1.12769 | ||||||||
\(107\) | −1.20391e9 | −0.887905 | −0.443952 | − | 0.896050i | \(-0.646424\pi\) | ||||
−0.443952 | + | 0.896050i | \(0.646424\pi\) | |||||||
\(108\) | 3.79304e9 | 2.68275 | ||||||||
\(109\) | −1.20826e9 | −0.819861 | −0.409930 | − | 0.912117i | \(-0.634447\pi\) | ||||
−0.409930 | + | 0.912117i | \(0.634447\pi\) | |||||||
\(110\) | 1.12483e9 | 0.732519 | ||||||||
\(111\) | −1.48306e9 | −0.927268 | ||||||||
\(112\) | −5.45542e9 | −3.27602 | ||||||||
\(113\) | 2.90740e9 | 1.67746 | 0.838729 | − | 0.544549i | \(-0.183299\pi\) | ||||
0.838729 | + | 0.544549i | \(0.183299\pi\) | |||||||
\(114\) | −1.87561e9 | −1.04009 | ||||||||
\(115\) | 1.00553e9 | 0.536110 | ||||||||
\(116\) | 8.74248e9 | 4.48305 | ||||||||
\(117\) | 2.22883e9 | 1.09961 | ||||||||
\(118\) | −5.79693e9 | −2.75251 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.31726e9 | 1.02014 | ||||||||
\(121\) | −1.05549e9 | −0.447630 | ||||||||
\(122\) | −1.75212e9 | −0.716053 | ||||||||
\(123\) | 2.25842e9 | 0.889675 | ||||||||
\(124\) | 1.40196e8 | 0.0532523 | ||||||||
\(125\) | −2.42155e9 | −0.887153 | ||||||||
\(126\) | −3.07786e9 | −1.08788 | ||||||||
\(127\) | −1.75281e8 | −0.0597884 | −0.0298942 | − | 0.999553i | \(-0.509517\pi\) | ||||
−0.0298942 | + | 0.999553i | \(0.509517\pi\) | |||||||
\(128\) | −1.03794e10 | −3.41766 | ||||||||
\(129\) | −6.51151e7 | −0.0207028 | ||||||||
\(130\) | 5.47182e9 | 1.68030 | ||||||||
\(131\) | −4.29446e9 | −1.27405 | −0.637027 | − | 0.770841i | \(-0.719836\pi\) | ||||
−0.637027 | + | 0.770841i | \(0.719836\pi\) | |||||||
\(132\) | 4.22779e9 | 1.21208 | ||||||||
\(133\) | 2.84295e9 | 0.787837 | ||||||||
\(134\) | −1.19700e10 | −3.20717 | ||||||||
\(135\) | 1.92849e9 | 0.499706 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.83424e9 | −0.444850 | −0.222425 | − | 0.974950i | \(-0.571397\pi\) | ||||
−0.222425 | + | 0.974950i | \(0.571397\pi\) | |||||||
\(138\) | 5.16017e9 | 1.21118 | ||||||||
\(139\) | −3.09950e9 | −0.704247 | −0.352123 | − | 0.935954i | \(-0.614540\pi\) | ||||
−0.352123 | + | 0.935954i | \(0.614540\pi\) | |||||||
\(140\) | −5.53430e9 | −1.21755 | ||||||||
\(141\) | −8.62435e8 | −0.183756 | ||||||||
\(142\) | 6.58275e9 | 1.35866 | ||||||||
\(143\) | 6.33593e9 | 1.26706 | ||||||||
\(144\) | −1.24963e10 | −2.42186 | ||||||||
\(145\) | 4.44492e9 | 0.835041 | ||||||||
\(146\) | 6.80867e8 | 0.124015 | ||||||||
\(147\) | 8.05472e8 | 0.142273 | ||||||||
\(148\) | 2.48637e10 | 4.25978 | ||||||||
\(149\) | 2.53473e9 | 0.421302 | 0.210651 | − | 0.977561i | \(-0.432442\pi\) | ||||
0.210651 | + | 0.977561i | \(0.432442\pi\) | |||||||
\(150\) | −5.28527e9 | −0.852426 | ||||||||
\(151\) | −1.10620e9 | −0.173156 | −0.0865780 | − | 0.996245i | \(-0.527593\pi\) | ||||
−0.0865780 | + | 0.996245i | \(0.527593\pi\) | |||||||
\(152\) | 1.99566e10 | 3.03243 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.74949e9 | −1.25354 | ||||||||
\(155\) | 7.12795e7 | 0.00991909 | ||||||||
\(156\) | 2.05665e10 | 2.78035 | ||||||||
\(157\) | −1.70941e9 | −0.224542 | −0.112271 | − | 0.993678i | \(-0.535813\pi\) | ||||
−0.112271 | + | 0.993678i | \(0.535813\pi\) | |||||||
\(158\) | −2.16599e9 | −0.276502 | ||||||||
\(159\) | −2.80107e9 | −0.347566 | ||||||||
\(160\) | −1.64854e10 | −1.98866 | ||||||||
\(161\) | −7.82152e9 | −0.917434 | ||||||||
\(162\) | −1.03400e9 | −0.117951 | ||||||||
\(163\) | 4.74641e9 | 0.526649 | 0.263324 | − | 0.964707i | \(-0.415181\pi\) | ||||
0.263324 | + | 0.964707i | \(0.415181\pi\) | |||||||
\(164\) | −3.78626e10 | −4.08708 | ||||||||
\(165\) | 2.14953e9 | 0.225769 | ||||||||
\(166\) | 9.76703e9 | 0.998334 | ||||||||
\(167\) | −2.19497e8 | −0.0218376 | −0.0109188 | − | 0.999940i | \(-0.503476\pi\) | ||||
−0.0109188 | + | 0.999940i | \(0.503476\pi\) | |||||||
\(168\) | −1.80248e10 | −1.74574 | ||||||||
\(169\) | 2.02172e10 | 1.90647 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.51210e9 | 0.582423 | ||||||||
\(172\) | 1.09166e9 | 0.0951065 | ||||||||
\(173\) | −1.63408e10 | −1.38697 | −0.693485 | − | 0.720471i | \(-0.743926\pi\) | ||||
−0.693485 | + | 0.720471i | \(0.743926\pi\) | |||||||
\(174\) | 2.28104e10 | 1.88652 | ||||||||
\(175\) | 8.01114e9 | 0.645689 | ||||||||
\(176\) | −3.55235e10 | −2.79067 | ||||||||
\(177\) | −1.10778e10 | −0.848351 | ||||||||
\(178\) | −1.54512e9 | −0.115364 | ||||||||
\(179\) | 8.32078e9 | 0.605795 | 0.302897 | − | 0.953023i | \(-0.402046\pi\) | ||||
0.302897 | + | 0.953023i | \(0.402046\pi\) | |||||||
\(180\) | −1.26770e10 | −0.900096 | ||||||||
\(181\) | 5.65108e9 | 0.391361 | 0.195681 | − | 0.980668i | \(-0.437308\pi\) | ||||
0.195681 | + | 0.980668i | \(0.437308\pi\) | |||||||
\(182\) | −4.25627e10 | −2.87546 | ||||||||
\(183\) | −3.34828e9 | −0.220695 | ||||||||
\(184\) | −5.49047e10 | −3.53126 | ||||||||
\(185\) | 1.26414e10 | 0.793453 | ||||||||
\(186\) | 3.65792e8 | 0.0224092 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.44588e10 | 0.844156 | ||||||||
\(189\) | −1.50008e10 | −0.855137 | ||||||||
\(190\) | 1.59874e10 | 0.889991 | ||||||||
\(191\) | −4.52797e9 | −0.246180 | −0.123090 | − | 0.992395i | \(-0.539280\pi\) | ||||
−0.123090 | + | 0.992395i | \(0.539280\pi\) | |||||||
\(192\) | −4.24725e10 | −2.25555 | ||||||||
\(193\) | 2.74959e10 | 1.42646 | 0.713230 | − | 0.700931i | \(-0.247232\pi\) | ||||
0.713230 | + | 0.700931i | \(0.247232\pi\) | |||||||
\(194\) | −6.21073e10 | −3.14800 | ||||||||
\(195\) | 1.04566e10 | 0.517885 | ||||||||
\(196\) | −1.35038e10 | −0.653589 | ||||||||
\(197\) | −1.50301e10 | −0.710991 | −0.355495 | − | 0.934678i | \(-0.615688\pi\) | ||||
−0.355495 | + | 0.934678i | \(0.615688\pi\) | |||||||
\(198\) | −2.00417e10 | −0.926706 | ||||||||
\(199\) | 5.79615e9 | 0.262000 | 0.131000 | − | 0.991382i | \(-0.458181\pi\) | ||||
0.131000 | + | 0.991382i | \(0.458181\pi\) | |||||||
\(200\) | 5.62358e10 | 2.48529 | ||||||||
\(201\) | −2.28744e10 | −0.988480 | ||||||||
\(202\) | 2.92932e10 | 1.23790 | ||||||||
\(203\) | −3.45749e10 | −1.42899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.92504e10 | −0.761286 | ||||||||
\(206\) | −3.71620e10 | −1.43779 | ||||||||
\(207\) | −1.79161e10 | −0.678231 | ||||||||
\(208\) | −1.72807e11 | −6.40142 | ||||||||
\(209\) | 1.85121e10 | 0.671115 | ||||||||
\(210\) | −1.44398e10 | −0.512359 | ||||||||
\(211\) | 3.03732e10 | 1.05492 | 0.527460 | − | 0.849580i | \(-0.323144\pi\) | ||||
0.527460 | + | 0.849580i | \(0.323144\pi\) | |||||||
\(212\) | 4.69603e10 | 1.59669 | ||||||||
\(213\) | 1.25795e10 | 0.418752 | ||||||||
\(214\) | 5.26622e10 | 1.71647 | ||||||||
\(215\) | 5.55031e8 | 0.0177151 | ||||||||
\(216\) | −1.05301e11 | −3.29147 | ||||||||
\(217\) | −5.54449e8 | −0.0169743 | ||||||||
\(218\) | 5.28524e10 | 1.58493 | ||||||||
\(219\) | 1.30113e9 | 0.0382227 | ||||||||
\(220\) | −3.60371e10 | −1.03716 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.48730e10 | 1.79257 | ||||||||
\(223\) | 4.61309e10 | 1.24916 | 0.624582 | − | 0.780959i | \(-0.285269\pi\) | ||||
0.624582 | + | 0.780959i | \(0.285269\pi\) | |||||||
\(224\) | 1.28232e11 | 3.40315 | ||||||||
\(225\) | 1.83505e10 | 0.477338 | ||||||||
\(226\) | −1.27177e11 | −3.24282 | ||||||||
\(227\) | 1.32854e9 | 0.0332092 | 0.0166046 | − | 0.999862i | \(-0.494714\pi\) | ||||
0.0166046 | + | 0.999862i | \(0.494714\pi\) | |||||||
\(228\) | 6.00904e10 | 1.47265 | ||||||||
\(229\) | 1.58431e10 | 0.380699 | 0.190349 | − | 0.981716i | \(-0.439038\pi\) | ||||
0.190349 | + | 0.981716i | \(0.439038\pi\) | |||||||
\(230\) | −4.39845e10 | −1.03639 | ||||||||
\(231\) | −1.67201e10 | −0.386355 | ||||||||
\(232\) | −2.42705e11 | −5.50026 | ||||||||
\(233\) | 4.53578e8 | 0.0100821 | 0.00504104 | − | 0.999987i | \(-0.498395\pi\) | ||||
0.00504104 | + | 0.999987i | \(0.498395\pi\) | |||||||
\(234\) | −9.74948e10 | −2.12574 | ||||||||
\(235\) | 7.35126e9 | 0.157238 | ||||||||
\(236\) | 1.85721e11 | 3.89724 | ||||||||
\(237\) | −4.13917e9 | −0.0852208 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.02131e10 | 1.19371 | 0.596857 | − | 0.802348i | \(-0.296416\pi\) | ||||
0.596857 | + | 0.802348i | \(0.296416\pi\) | |||||||
\(240\) | −5.86265e10 | −1.14063 | ||||||||
\(241\) | 1.95681e10 | 0.373656 | 0.186828 | − | 0.982393i | \(-0.440179\pi\) | ||||
0.186828 | + | 0.982393i | \(0.440179\pi\) | |||||||
\(242\) | 4.61699e10 | 0.865346 | ||||||||
\(243\) | −5.52493e10 | −1.01648 | ||||||||
\(244\) | 5.61343e10 | 1.01385 | ||||||||
\(245\) | −6.86572e9 | −0.121741 | ||||||||
\(246\) | −9.87893e10 | −1.71989 | ||||||||
\(247\) | 9.00537e10 | 1.53945 | ||||||||
\(248\) | −3.89206e9 | −0.0653352 | ||||||||
\(249\) | 1.86646e10 | 0.307696 | ||||||||
\(250\) | 1.05925e11 | 1.71502 | ||||||||
\(251\) | −1.06749e11 | −1.69759 | −0.848794 | − | 0.528724i | \(-0.822671\pi\) | ||||
−0.848794 | + | 0.528724i | \(0.822671\pi\) | |||||||
\(252\) | 9.86080e10 | 1.54032 | ||||||||
\(253\) | −5.09305e10 | −0.781513 | ||||||||
\(254\) | 7.66724e9 | 0.115581 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.93880e11 | 2.82132 | ||||||||
\(257\) | −1.35700e10 | −0.194035 | −0.0970176 | − | 0.995283i | \(-0.530930\pi\) | ||||
−0.0970176 | + | 0.995283i | \(0.530930\pi\) | |||||||
\(258\) | 2.84831e9 | 0.0400220 | ||||||||
\(259\) | −9.83311e10 | −1.35782 | ||||||||
\(260\) | −1.75305e11 | −2.37911 | ||||||||
\(261\) | −7.91979e10 | −1.05641 | ||||||||
\(262\) | 1.87851e11 | 2.46297 | ||||||||
\(263\) | −4.47087e10 | −0.576224 | −0.288112 | − | 0.957597i | \(-0.593027\pi\) | ||||
−0.288112 | + | 0.957597i | \(0.593027\pi\) | |||||||
\(264\) | −1.17370e11 | −1.48710 | ||||||||
\(265\) | 2.38759e10 | 0.297409 | ||||||||
\(266\) | −1.24358e11 | −1.52302 | ||||||||
\(267\) | −2.95269e9 | −0.0355564 | ||||||||
\(268\) | 3.83492e11 | 4.54098 | ||||||||
\(269\) | −9.73705e10 | −1.13381 | −0.566907 | − | 0.823782i | \(-0.691860\pi\) | ||||
−0.566907 | + | 0.823782i | \(0.691860\pi\) | |||||||
\(270\) | −8.43572e10 | −0.966018 | ||||||||
\(271\) | −8.62013e10 | −0.970850 | −0.485425 | − | 0.874278i | \(-0.661335\pi\) | ||||
−0.485425 | + | 0.874278i | \(0.661335\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.13366e10 | −0.886245 | ||||||||
\(274\) | 8.02346e10 | 0.859971 | ||||||||
\(275\) | 5.21653e10 | 0.550027 | ||||||||
\(276\) | −1.65321e11 | −1.71489 | ||||||||
\(277\) | 1.81712e10 | 0.185449 | 0.0927243 | − | 0.995692i | \(-0.470442\pi\) | ||||
0.0927243 | + | 0.995692i | \(0.470442\pi\) | |||||||
\(278\) | 1.35580e11 | 1.36143 | ||||||||
\(279\) | −1.27003e9 | −0.0125486 | ||||||||
\(280\) | 1.53641e11 | 1.49381 | ||||||||
\(281\) | −3.90556e10 | −0.373684 | −0.186842 | − | 0.982390i | \(-0.559825\pi\) | ||||
−0.186842 | + | 0.982390i | \(0.559825\pi\) | |||||||
\(282\) | 3.77252e10 | 0.355231 | ||||||||
\(283\) | 1.56085e11 | 1.44651 | 0.723255 | − | 0.690581i | \(-0.242645\pi\) | ||||
0.723255 | + | 0.690581i | \(0.242645\pi\) | |||||||
\(284\) | −2.10897e11 | −1.92371 | ||||||||
\(285\) | 3.05516e10 | 0.274304 | ||||||||
\(286\) | −2.77151e11 | −2.44945 | ||||||||
\(287\) | 1.49740e11 | 1.30277 | ||||||||
\(288\) | 2.93731e11 | 2.51585 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1.94433e11 | −1.61428 | ||||||||
\(291\) | −1.18686e11 | −0.970246 | ||||||||
\(292\) | −2.18135e10 | −0.175591 | ||||||||
\(293\) | 1.99350e11 | 1.58020 | 0.790099 | − | 0.612980i | \(-0.210029\pi\) | ||||
0.790099 | + | 0.612980i | \(0.210029\pi\) | |||||||
\(294\) | −3.52335e10 | −0.275038 | ||||||||
\(295\) | 9.44258e10 | 0.725925 | ||||||||
\(296\) | −6.90255e11 | −5.22633 | ||||||||
\(297\) | −9.76789e10 | −0.728445 | ||||||||
\(298\) | −1.10876e11 | −0.814449 | ||||||||
\(299\) | −2.47756e11 | −1.79269 | ||||||||
\(300\) | 1.69329e11 | 1.20694 | ||||||||
\(301\) | −4.31732e9 | −0.0303155 | ||||||||
\(302\) | 4.83882e10 | 0.334740 | ||||||||
\(303\) | 5.59789e10 | 0.381534 | ||||||||
\(304\) | −5.04901e11 | −3.39059 | ||||||||
\(305\) | 2.85402e10 | 0.188846 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.45882e11 | −0.937298 | −0.468649 | − | 0.883384i | \(-0.655259\pi\) | ||||
−0.468649 | + | 0.883384i | \(0.655259\pi\) | |||||||
\(308\) | 2.80315e11 | 1.77488 | ||||||||
\(309\) | −7.10160e10 | −0.443142 | ||||||||
\(310\) | −3.11796e9 | −0.0191753 | ||||||||
\(311\) | 5.10899e10 | 0.309680 | 0.154840 | − | 0.987940i | \(-0.450514\pi\) | ||||
0.154840 | + | 0.987940i | \(0.450514\pi\) | |||||||
\(312\) | −5.70958e11 | −3.41121 | ||||||||
\(313\) | −2.60411e11 | −1.53359 | −0.766797 | − | 0.641890i | \(-0.778151\pi\) | ||||
−0.766797 | + | 0.641890i | \(0.778151\pi\) | |||||||
\(314\) | 7.47742e10 | 0.434079 | ||||||||
\(315\) | 5.01350e10 | 0.286909 | ||||||||
\(316\) | 6.93936e10 | 0.391496 | ||||||||
\(317\) | −6.41873e8 | −0.00357012 | −0.00178506 | − | 0.999998i | \(-0.500568\pi\) | ||||
−0.00178506 | + | 0.999998i | \(0.500568\pi\) | |||||||
\(318\) | 1.22526e11 | 0.671905 | ||||||||
\(319\) | −2.25137e11 | −1.21728 | ||||||||
\(320\) | 3.62029e11 | 1.93005 | ||||||||
\(321\) | 1.00637e11 | 0.529034 | ||||||||
\(322\) | 3.42134e11 | 1.77356 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.31271e10 | 0.167006 | ||||||||
\(325\) | 2.53763e11 | 1.26169 | ||||||||
\(326\) | −2.07621e11 | −1.01810 | ||||||||
\(327\) | 1.01000e11 | 0.488492 | ||||||||
\(328\) | 1.05113e12 | 5.01445 | ||||||||
\(329\) | −5.71819e10 | −0.269077 | ||||||||
\(330\) | −9.40261e10 | −0.436451 | ||||||||
\(331\) | −2.52438e11 | −1.15592 | −0.577962 | − | 0.816063i | \(-0.696152\pi\) | ||||
−0.577962 | + | 0.816063i | \(0.696152\pi\) | |||||||
\(332\) | −3.12915e11 | −1.41353 | ||||||||
\(333\) | −2.25239e11 | −1.00379 | ||||||||
\(334\) | 9.60139e9 | 0.0422158 | ||||||||
\(335\) | 1.94978e11 | 0.845832 | ||||||||
\(336\) | 4.56027e11 | 1.95193 | ||||||||
\(337\) | −2.71455e11 | −1.14647 | −0.573235 | − | 0.819391i | \(-0.694312\pi\) | ||||
−0.573235 | + | 0.819391i | \(0.694312\pi\) | |||||||
\(338\) | −8.84354e11 | −3.68554 | ||||||||
\(339\) | −2.43034e11 | −0.999468 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.61034e9 | −0.0144595 | ||||||||
\(342\) | −2.84857e11 | −1.12592 | ||||||||
\(343\) | 2.77060e11 | 1.08081 | ||||||||
\(344\) | −3.03063e10 | −0.116686 | ||||||||
\(345\) | −8.40537e10 | −0.319427 | ||||||||
\(346\) | 7.14792e11 | 2.68125 | ||||||||
\(347\) | 1.21278e11 | 0.449053 | 0.224527 | − | 0.974468i | \(-0.427916\pi\) | ||||
0.224527 | + | 0.974468i | \(0.427916\pi\) | |||||||
\(348\) | −7.30798e11 | −2.67110 | ||||||||
\(349\) | 4.94486e11 | 1.78418 | 0.892092 | − | 0.451854i | \(-0.149237\pi\) | ||||
0.892092 | + | 0.451854i | \(0.149237\pi\) | |||||||
\(350\) | −3.50429e11 | −1.24823 | ||||||||
\(351\) | −4.75168e11 | −1.67096 | ||||||||
\(352\) | 8.34996e11 | 2.89896 | ||||||||
\(353\) | 2.59580e11 | 0.889785 | 0.444893 | − | 0.895584i | \(-0.353242\pi\) | ||||
0.444893 | + | 0.895584i | \(0.353242\pi\) | |||||||
\(354\) | 4.84574e11 | 1.64001 | ||||||||
\(355\) | −1.07226e11 | −0.358321 | ||||||||
\(356\) | 4.95022e10 | 0.163343 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.63973e11 | −1.17111 | ||||||||
\(359\) | 5.64703e11 | 1.79430 | 0.897150 | − | 0.441725i | \(-0.145633\pi\) | ||||
0.897150 | + | 0.441725i | \(0.145633\pi\) | |||||||
\(360\) | 3.51933e11 | 1.10433 | ||||||||
\(361\) | −5.95720e10 | −0.184612 | ||||||||
\(362\) | −2.47193e11 | −0.756569 | ||||||||
\(363\) | 8.82299e10 | 0.266708 | ||||||||
\(364\) | 1.36362e12 | 4.07133 | ||||||||
\(365\) | −1.10906e10 | −0.0327067 | ||||||||
\(366\) | 1.46463e11 | 0.426641 | ||||||||
\(367\) | −5.01887e10 | −0.144414 | −0.0722069 | − | 0.997390i | \(-0.523004\pi\) | ||||
−0.0722069 | + | 0.997390i | \(0.523004\pi\) | |||||||
\(368\) | 1.38909e12 | 3.94834 | ||||||||
\(369\) | 3.42996e11 | 0.963099 | ||||||||
\(370\) | −5.52967e11 | −1.53388 | ||||||||
\(371\) | −1.85719e11 | −0.508949 | ||||||||
\(372\) | −1.17192e10 | −0.0317289 | ||||||||
\(373\) | 2.42202e11 | 0.647870 | 0.323935 | − | 0.946079i | \(-0.394994\pi\) | ||||
0.323935 | + | 0.946079i | \(0.394994\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.02421e11 | 0.528586 | ||||||||
\(376\) | −4.01400e11 | −1.03570 | ||||||||
\(377\) | −1.09520e12 | −2.79227 | ||||||||
\(378\) | 6.56174e11 | 1.65313 | ||||||||
\(379\) | −6.36704e11 | −1.58512 | −0.792559 | − | 0.609796i | \(-0.791251\pi\) | ||||
−0.792559 | + | 0.609796i | \(0.791251\pi\) | |||||||
\(380\) | −5.12201e11 | −1.26013 | ||||||||
\(381\) | 1.46520e10 | 0.0356233 | ||||||||
\(382\) | 1.98066e11 | 0.475909 | ||||||||
\(383\) | 4.29691e10 | 0.102038 | 0.0510190 | − | 0.998698i | \(-0.483753\pi\) | ||||
0.0510190 | + | 0.998698i | \(0.483753\pi\) | |||||||
\(384\) | 8.67634e11 | 2.03632 | ||||||||
\(385\) | 1.42520e11 | 0.330599 | ||||||||
\(386\) | −1.20274e12 | −2.75759 | ||||||||
\(387\) | −9.88934e9 | −0.0224113 | ||||||||
\(388\) | 1.98979e12 | 4.45722 | ||||||||
\(389\) | 5.97037e11 | 1.32199 | 0.660995 | − | 0.750391i | \(-0.270135\pi\) | ||||
0.660995 | + | 0.750391i | \(0.270135\pi\) | |||||||
\(390\) | −4.57398e11 | −1.00116 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.74888e11 | 0.801889 | ||||||||
\(393\) | 3.58981e11 | 0.759110 | ||||||||
\(394\) | 6.57457e11 | 1.37447 | ||||||||
\(395\) | 3.52816e10 | 0.0729225 | ||||||||
\(396\) | 6.42095e11 | 1.31211 | ||||||||
\(397\) | 4.91474e11 | 0.992986 | 0.496493 | − | 0.868041i | \(-0.334621\pi\) | ||||
0.496493 | + | 0.868041i | \(0.334621\pi\) | |||||||
\(398\) | −2.53539e11 | −0.506491 | ||||||||
\(399\) | −2.37646e11 | −0.469411 | ||||||||
\(400\) | −1.42276e12 | −2.77883 | ||||||||
\(401\) | −2.34902e11 | −0.453668 | −0.226834 | − | 0.973933i | \(-0.572837\pi\) | ||||
−0.226834 | + | 0.973933i | \(0.572837\pi\) | |||||||
\(402\) | 1.00059e12 | 1.91090 | ||||||||
\(403\) | −1.75628e10 | −0.0331682 | ||||||||
\(404\) | −9.38493e11 | −1.75273 | ||||||||
\(405\) | 1.68427e10 | 0.0311075 | ||||||||
\(406\) | 1.51240e12 | 2.76248 | ||||||||
\(407\) | −6.40292e11 | −1.15665 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.31401e11 | 0.232191 | 0.116095 | − | 0.993238i | \(-0.462962\pi\) | ||||
0.116095 | + | 0.993238i | \(0.462962\pi\) | |||||||
\(410\) | 8.42065e11 | 1.47170 | ||||||||
\(411\) | 1.53327e11 | 0.265052 | ||||||||
\(412\) | 1.19059e12 | 2.03575 | ||||||||
\(413\) | −7.34493e11 | −1.24226 | ||||||||
\(414\) | 7.83699e11 | 1.31114 | ||||||||
\(415\) | −1.59094e11 | −0.263293 | ||||||||
\(416\) | 4.06191e12 | 6.64983 | ||||||||
\(417\) | 2.59092e11 | 0.419606 | ||||||||
\(418\) | −8.09769e11 | −1.29738 | ||||||||
\(419\) | 6.01297e11 | 0.953072 | 0.476536 | − | 0.879155i | \(-0.341892\pi\) | ||||
0.476536 | + | 0.879155i | \(0.341892\pi\) | |||||||
\(420\) | 4.62621e11 | 0.725443 | ||||||||
\(421\) | 1.16288e11 | 0.180412 | 0.0902062 | − | 0.995923i | \(-0.471247\pi\) | ||||
0.0902062 | + | 0.995923i | \(0.471247\pi\) | |||||||
\(422\) | −1.32861e12 | −2.03934 | ||||||||
\(423\) | −1.30982e11 | −0.198921 | ||||||||
\(424\) | −1.30369e12 | −1.95898 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.50263e11 | −0.809519 | ||||||||
\(427\) | −2.22001e11 | −0.323168 | ||||||||
\(428\) | −1.68718e12 | −2.43033 | ||||||||
\(429\) | −5.29630e11 | −0.754945 | ||||||||
\(430\) | −2.42786e10 | −0.0342464 | ||||||||
\(431\) | 9.23955e11 | 1.28974 | 0.644871 | − | 0.764291i | \(-0.276911\pi\) | ||||
0.644871 | + | 0.764291i | \(0.276911\pi\) | |||||||
\(432\) | 2.66411e12 | 3.68023 | ||||||||
\(433\) | −3.64410e11 | −0.498189 | −0.249095 | − | 0.968479i | \(-0.580133\pi\) | ||||
−0.249095 | + | 0.968479i | \(0.580133\pi\) | |||||||
\(434\) | 2.42531e10 | 0.0328143 | ||||||||
\(435\) | −3.71558e11 | −0.497536 | ||||||||
\(436\) | −1.69328e12 | −2.24408 | ||||||||
\(437\) | −7.23885e11 | −0.949518 | ||||||||
\(438\) | −5.69148e10 | −0.0738910 | ||||||||
\(439\) | −6.78960e11 | −0.872476 | −0.436238 | − | 0.899831i | \(-0.643689\pi\) | ||||
−0.436238 | + | 0.899831i | \(0.643689\pi\) | |||||||
\(440\) | 1.00045e12 | 1.27250 | ||||||||
\(441\) | 1.22331e11 | 0.154015 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.20909e11 | −0.642607 | −0.321303 | − | 0.946976i | \(-0.604121\pi\) | ||||
−0.321303 | + | 0.946976i | \(0.604121\pi\) | |||||||
\(444\) | −2.07839e12 | −2.53807 | ||||||||
\(445\) | 2.51683e10 | 0.0304252 | ||||||||
\(446\) | −2.01789e12 | −2.41485 | ||||||||
\(447\) | −2.11882e11 | −0.251021 | ||||||||
\(448\) | −2.81605e12 | −3.30285 | ||||||||
\(449\) | −8.95134e11 | −1.03939 | −0.519696 | − | 0.854351i | \(-0.673955\pi\) | ||||
−0.519696 | + | 0.854351i | \(0.673955\pi\) | |||||||
\(450\) | −8.02699e11 | −0.922776 | ||||||||
\(451\) | 9.75043e11 | 1.10976 | ||||||||
\(452\) | 4.07450e12 | 4.59146 | ||||||||
\(453\) | 9.24690e10 | 0.103170 | ||||||||
\(454\) | −5.81139e10 | −0.0641991 | ||||||||
\(455\) | 6.93300e11 | 0.758351 | ||||||||
\(456\) | −1.66821e12 | −1.80679 | ||||||||
\(457\) | 1.95511e11 | 0.209675 | 0.104838 | − | 0.994489i | \(-0.466568\pi\) | ||||
0.104838 | + | 0.994489i | \(0.466568\pi\) | |||||||
\(458\) | −6.93021e11 | −0.735956 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.40917e12 | 1.46742 | ||||||||
\(461\) | −6.94628e11 | −0.716305 | −0.358153 | − | 0.933663i | \(-0.616593\pi\) | ||||
−0.358153 | + | 0.933663i | \(0.616593\pi\) | |||||||
\(462\) | 7.31384e11 | 0.746890 | ||||||||
\(463\) | 1.44310e12 | 1.45943 | 0.729713 | − | 0.683753i | \(-0.239654\pi\) | ||||
0.729713 | + | 0.683753i | \(0.239654\pi\) | |||||||
\(464\) | 6.14043e12 | 6.14990 | ||||||||
\(465\) | −5.95837e9 | −0.00591002 | ||||||||
\(466\) | −1.98407e10 | −0.0194904 | ||||||||
\(467\) | −1.73333e12 | −1.68637 | −0.843187 | − | 0.537620i | \(-0.819324\pi\) | ||||
−0.843187 | + | 0.537620i | \(0.819324\pi\) | |||||||
\(468\) | 3.12353e12 | 3.00981 | ||||||||
\(469\) | −1.51664e12 | −1.44745 | ||||||||
\(470\) | −3.21564e11 | −0.303967 | ||||||||
\(471\) | 1.42892e11 | 0.133787 | ||||||||
\(472\) | −5.15592e12 | −4.78153 | ||||||||
\(473\) | −2.81126e10 | −0.0258242 | ||||||||
\(474\) | 1.81058e11 | 0.164746 | ||||||||
\(475\) | 7.41434e11 | 0.668269 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.25412e11 | −0.376250 | ||||||||
\(478\) | −2.63388e12 | −2.30765 | ||||||||
\(479\) | −4.61090e11 | −0.400199 | −0.200100 | − | 0.979776i | \(-0.564127\pi\) | ||||
−0.200100 | + | 0.979776i | \(0.564127\pi\) | |||||||
\(480\) | 1.37804e12 | 1.18489 | ||||||||
\(481\) | −3.11476e12 | −2.65321 | ||||||||
\(482\) | −8.55961e11 | −0.722341 | ||||||||
\(483\) | 6.53814e11 | 0.546628 | ||||||||
\(484\) | −1.47918e12 | −1.22523 | ||||||||
\(485\) | 1.01166e12 | 0.830229 | ||||||||
\(486\) | 2.41675e12 | 1.96503 | ||||||||
\(487\) | −1.31130e12 | −1.05638 | −0.528191 | − | 0.849126i | \(-0.677129\pi\) | ||||
−0.528191 | + | 0.849126i | \(0.677129\pi\) | |||||||
\(488\) | −1.55838e12 | −1.24389 | ||||||||
\(489\) | −3.96760e11 | −0.313789 | ||||||||
\(490\) | 3.00325e11 | 0.235347 | ||||||||
\(491\) | −2.42631e11 | −0.188399 | −0.0941997 | − | 0.995553i | \(-0.530029\pi\) | ||||
−0.0941997 | + | 0.995553i | \(0.530029\pi\) | |||||||
\(492\) | 3.16500e12 | 2.43518 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3.93919e12 | −2.97602 | ||||||||
\(495\) | 3.26459e11 | 0.244402 | ||||||||
\(496\) | 9.84690e10 | 0.0730520 | ||||||||
\(497\) | 8.34060e11 | 0.613188 | ||||||||
\(498\) | −8.16441e11 | −0.594830 | ||||||||
\(499\) | −1.85899e12 | −1.34223 | −0.671113 | − | 0.741355i | \(-0.734184\pi\) | ||||
−0.671113 | + | 0.741355i | \(0.734184\pi\) | |||||||
\(500\) | −3.39361e12 | −2.42827 | ||||||||
\(501\) | 1.83481e10 | 0.0130113 | ||||||||
\(502\) | 4.66949e12 | 3.28173 | ||||||||
\(503\) | −1.96267e12 | −1.36707 | −0.683537 | − | 0.729916i | \(-0.739559\pi\) | ||||
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(504\) | −2.73752e12 | −1.88981 | ||||||||
\(505\) | −4.77156e11 | −0.326474 | ||||||||
\(506\) | 2.22784e12 | 1.51080 | ||||||||
\(507\) | −1.68999e12 | −1.13592 | ||||||||
\(508\) | −2.45642e11 | −0.163650 | ||||||||
\(509\) | −1.96893e12 | −1.30017 | −0.650085 | − | 0.759861i | \(-0.725267\pi\) | ||||
−0.650085 | + | 0.759861i | \(0.725267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.62684e10 | 0.0559703 | ||||||||
\(512\) | −3.16655e12 | −2.03644 | ||||||||
\(513\) | −1.38833e12 | −0.885042 | ||||||||
\(514\) | 5.93588e11 | 0.375103 | ||||||||
\(515\) | 6.05329e11 | 0.379192 | ||||||||
\(516\) | −9.12538e10 | −0.0566666 | ||||||||
\(517\) | −3.72345e11 | −0.229213 | ||||||||
\(518\) | 4.30127e12 | 2.62490 | ||||||||
\(519\) | 1.36596e12 | 0.826388 | ||||||||
\(520\) | 4.86676e12 | 2.91894 | ||||||||
\(521\) | −7.98293e11 | −0.474671 | −0.237335 | − | 0.971428i | \(-0.576274\pi\) | ||||
−0.237335 | + | 0.971428i | \(0.576274\pi\) | |||||||
\(522\) | 3.46433e12 | 2.04222 | ||||||||
\(523\) | −1.48202e12 | −0.866158 | −0.433079 | − | 0.901356i | \(-0.642573\pi\) | ||||
−0.433079 | + | 0.901356i | \(0.642573\pi\) | |||||||
\(524\) | −6.01835e12 | −3.48728 | ||||||||
\(525\) | −6.69664e11 | −0.384716 | ||||||||
\(526\) | 1.95568e12 | 1.11394 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.96946e12 | 1.66274 | ||||||||
\(529\) | 1.90403e11 | 0.105712 | ||||||||
\(530\) | −1.04440e12 | −0.574942 | ||||||||
\(531\) | −1.68244e12 | −0.918364 | ||||||||
\(532\) | 3.98417e12 | 2.15643 | ||||||||
\(533\) | 4.74318e12 | 2.54564 | ||||||||
\(534\) | 1.29159e11 | 0.0687366 | ||||||||
\(535\) | −8.57811e11 | −0.452689 | ||||||||
\(536\) | −1.06464e13 | −5.57134 | ||||||||
\(537\) | −6.95547e11 | −0.360946 | ||||||||
\(538\) | 4.25925e12 | 2.19186 | ||||||||
\(539\) | 3.47752e11 | 0.177468 | ||||||||
\(540\) | 2.70263e12 | 1.36777 | ||||||||
\(541\) | 1.28357e12 | 0.644219 | 0.322109 | − | 0.946702i | \(-0.395608\pi\) | ||||
0.322109 | + | 0.946702i | \(0.395608\pi\) | |||||||
\(542\) | 3.77068e12 | 1.87682 | ||||||||
\(543\) | −4.72383e11 | −0.233182 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.60909e11 | −0.417997 | ||||||||
\(546\) | 3.55788e12 | 1.71326 | ||||||||
\(547\) | −2.44820e12 | −1.16924 | −0.584619 | − | 0.811308i | \(-0.698756\pi\) | ||||
−0.584619 | + | 0.811308i | \(0.698756\pi\) | |||||||
\(548\) | −2.57054e12 | −1.21762 | ||||||||
\(549\) | −5.08519e11 | −0.238908 | ||||||||
\(550\) | −2.28185e12 | −1.06330 | ||||||||
\(551\) | −3.19992e12 | −1.47896 | ||||||||
\(552\) | 4.58957e12 | 2.10400 | ||||||||
\(553\) | −2.74439e11 | −0.124791 | ||||||||
\(554\) | −7.94855e11 | −0.358504 | ||||||||
\(555\) | −1.05671e12 | −0.472757 | ||||||||
\(556\) | −4.34371e12 | −1.92763 | ||||||||
\(557\) | −2.37115e11 | −0.104378 | −0.0521892 | − | 0.998637i | \(-0.516620\pi\) | ||||
−0.0521892 | + | 0.998637i | \(0.516620\pi\) | |||||||
\(558\) | 5.55546e10 | 0.0242586 | ||||||||
\(559\) | −1.36756e11 | −0.0592372 | ||||||||
\(560\) | −3.88711e12 | −1.67025 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.70840e12 | 0.722396 | ||||||||
\(563\) | −1.25277e12 | −0.525512 | −0.262756 | − | 0.964862i | \(-0.584631\pi\) | ||||
−0.262756 | + | 0.964862i | \(0.584631\pi\) | |||||||
\(564\) | −1.20864e12 | −0.502967 | ||||||||
\(565\) | 2.07159e12 | 0.855234 | ||||||||
\(566\) | −6.82756e12 | −2.79635 | ||||||||
\(567\) | −1.31012e11 | −0.0532336 | ||||||||
\(568\) | 5.85485e12 | 2.36020 | ||||||||
\(569\) | 9.49810e11 | 0.379867 | 0.189933 | − | 0.981797i | \(-0.439173\pi\) | ||||
0.189933 | + | 0.981797i | \(0.439173\pi\) | |||||||
\(570\) | −1.33641e12 | −0.530277 | ||||||||
\(571\) | −4.03177e12 | −1.58721 | −0.793604 | − | 0.608435i | \(-0.791798\pi\) | ||||
−0.793604 | + | 0.608435i | \(0.791798\pi\) | |||||||
\(572\) | 8.87931e12 | 3.46815 | ||||||||
\(573\) | 3.78500e11 | 0.146680 | ||||||||
\(574\) | −6.55002e12 | −2.51848 | ||||||||
\(575\) | −2.03984e12 | −0.778198 | ||||||||
\(576\) | −6.45050e12 | −2.44170 | ||||||||
\(577\) | −2.32183e12 | −0.872045 | −0.436023 | − | 0.899936i | \(-0.643613\pi\) | ||||
−0.436023 | + | 0.899936i | \(0.643613\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.29842e12 | −0.849917 | ||||||||
\(580\) | 6.22921e12 | 2.28564 | ||||||||
\(581\) | 1.23752e12 | 0.450567 | ||||||||
\(582\) | 5.19165e12 | 1.87565 | ||||||||
\(583\) | −1.20933e12 | −0.433546 | ||||||||
\(584\) | 6.05578e11 | 0.215433 | ||||||||
\(585\) | 1.58809e12 | 0.560625 | ||||||||
\(586\) | −8.72009e12 | −3.05479 | ||||||||
\(587\) | −3.45750e12 | −1.20196 | −0.600982 | − | 0.799263i | \(-0.705224\pi\) | ||||
−0.600982 | + | 0.799263i | \(0.705224\pi\) | |||||||
\(588\) | 1.12881e12 | 0.389423 | ||||||||
\(589\) | −5.13145e10 | −0.0175679 | ||||||||
\(590\) | −4.13044e12 | −1.40334 | ||||||||
\(591\) | 1.25639e12 | 0.423624 | ||||||||
\(592\) | 1.74634e13 | 5.84361 | ||||||||
\(593\) | 4.64446e12 | 1.54237 | 0.771186 | − | 0.636610i | \(-0.219664\pi\) | ||||
0.771186 | + | 0.636610i | \(0.219664\pi\) | |||||||
\(594\) | 4.27274e12 | 1.40821 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.55223e12 | 1.15317 | ||||||||
\(597\) | −4.84510e11 | −0.156105 | ||||||||
\(598\) | 1.08375e13 | 3.46557 | ||||||||
\(599\) | −2.82740e10 | −0.00897358 | −0.00448679 | − | 0.999990i | \(-0.501428\pi\) | ||||
−0.00448679 | + | 0.999990i | \(0.501428\pi\) | |||||||
\(600\) | −4.70084e12 | −1.48080 | ||||||||
\(601\) | 4.13809e12 | 1.29379 | 0.646896 | − | 0.762578i | \(-0.276067\pi\) | ||||
0.646896 | + | 0.762578i | \(0.276067\pi\) | |||||||
\(602\) | 1.88851e11 | 0.0586051 | ||||||||
\(603\) | −3.47404e12 | −1.07006 | ||||||||
\(604\) | −1.55025e12 | −0.473954 | ||||||||
\(605\) | −7.52058e11 | −0.228219 | ||||||||
\(606\) | −2.44867e12 | −0.737570 | ||||||||
\(607\) | 4.30595e12 | 1.28742 | 0.643709 | − | 0.765270i | \(-0.277395\pi\) | ||||
0.643709 | + | 0.765270i | \(0.277395\pi\) | |||||||
\(608\) | 1.18680e13 | 3.52216 | ||||||||
\(609\) | 2.89017e12 | 0.851423 | ||||||||
\(610\) | −1.24843e12 | −0.365072 | ||||||||
\(611\) | −1.81131e12 | −0.525783 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.41377e12 | 1.83460 | 0.917300 | − | 0.398197i | \(-0.130364\pi\) | ||||
0.917300 | + | 0.398197i | \(0.130364\pi\) | |||||||
\(614\) | 6.38125e12 | 1.81196 | ||||||||
\(615\) | 1.60917e12 | 0.453591 | ||||||||
\(616\) | −7.78199e12 | −2.17760 | ||||||||
\(617\) | 5.16320e12 | 1.43429 | 0.717143 | − | 0.696926i | \(-0.245449\pi\) | ||||
0.717143 | + | 0.696926i | \(0.245449\pi\) | |||||||
\(618\) | 3.10643e12 | 0.856670 | ||||||||
\(619\) | 6.94645e12 | 1.90176 | 0.950878 | − | 0.309566i | \(-0.100184\pi\) | ||||
0.950878 | + | 0.309566i | \(0.100184\pi\) | |||||||
\(620\) | 9.98927e10 | 0.0271501 | ||||||||
\(621\) | 3.81957e12 | 1.03063 | ||||||||
\(622\) | −2.23481e12 | −0.598665 | ||||||||
\(623\) | −1.95772e11 | −0.0520660 | ||||||||
\(624\) | 1.44452e13 | 3.81411 | ||||||||
\(625\) | 1.09771e12 | 0.287759 | ||||||||
\(626\) | 1.13911e13 | 2.96470 | ||||||||
\(627\) | −1.54746e12 | −0.399866 | ||||||||
\(628\) | −2.39561e12 | −0.614607 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −2.19304e12 | −0.554644 | ||||||||
\(631\) | 2.70305e12 | 0.678770 | 0.339385 | − | 0.940648i | \(-0.389781\pi\) | ||||
0.339385 | + | 0.940648i | \(0.389781\pi\) | |||||||
\(632\) | −1.92648e12 | −0.480327 | ||||||||
\(633\) | −2.53895e12 | −0.628545 | ||||||||
\(634\) | 2.80772e10 | 0.00690165 | ||||||||
\(635\) | −1.24891e11 | −0.0304825 | ||||||||
\(636\) | −3.92549e12 | −0.951342 | ||||||||
\(637\) | 1.69167e12 | 0.407088 | ||||||||
\(638\) | 9.84812e12 | 2.35321 | ||||||||
\(639\) | 1.91051e12 | 0.453311 | ||||||||
\(640\) | −7.39558e12 | −1.74246 | ||||||||
\(641\) | −2.11271e10 | −0.00494286 | −0.00247143 | − | 0.999997i | \(-0.500787\pi\) | ||||
−0.00247143 | + | 0.999997i | \(0.500787\pi\) | |||||||
\(642\) | −4.40212e12 | −1.02271 | ||||||||
\(643\) | −6.38463e12 | −1.47294 | −0.736472 | − | 0.676468i | \(-0.763510\pi\) | ||||
−0.736472 | + | 0.676468i | \(0.763510\pi\) | |||||||
\(644\) | −1.09613e13 | −2.51116 | ||||||||
\(645\) | −4.63960e10 | −0.0105551 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.90284e12 | −1.54867 | −0.774334 | − | 0.632777i | \(-0.781915\pi\) | ||||
−0.774334 | + | 0.632777i | \(0.781915\pi\) | |||||||
\(648\) | −9.19662e11 | −0.204899 | ||||||||
\(649\) | −4.78271e12 | −1.05821 | ||||||||
\(650\) | −1.11003e13 | −2.43906 | ||||||||
\(651\) | 4.63473e10 | 0.0101137 | ||||||||
\(652\) | 6.65172e12 | 1.44152 | ||||||||
\(653\) | 6.56358e11 | 0.141264 | 0.0706319 | − | 0.997502i | \(-0.477498\pi\) | ||||
0.0706319 | + | 0.997502i | \(0.477498\pi\) | |||||||
\(654\) | −4.41802e12 | −0.944338 | ||||||||
\(655\) | −3.05990e12 | −0.649563 | ||||||||
\(656\) | −2.65935e13 | −5.60670 | ||||||||
\(657\) | 1.97608e11 | 0.0413771 | ||||||||
\(658\) | 2.50129e12 | 0.520173 | ||||||||
\(659\) | −4.39856e12 | −0.908503 | −0.454251 | − | 0.890874i | \(-0.650093\pi\) | ||||
−0.454251 | + | 0.890874i | \(0.650093\pi\) | |||||||
\(660\) | 3.01240e12 | 0.617966 | ||||||||
\(661\) | −8.91098e12 | −1.81559 | −0.907797 | − | 0.419410i | \(-0.862237\pi\) | ||||
−0.907797 | + | 0.419410i | \(0.862237\pi\) | |||||||
\(662\) | 1.10423e13 | 2.23460 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.68701e12 | 1.73426 | ||||||||
\(665\) | 2.02566e12 | 0.401670 | ||||||||
\(666\) | 9.85256e12 | 1.94051 | ||||||||
\(667\) | 8.80363e12 | 1.72225 | ||||||||
\(668\) | −3.07608e11 | −0.0597728 | ||||||||
\(669\) | −3.85615e12 | −0.744281 | ||||||||
\(670\) | −8.52886e12 | −1.63514 | ||||||||
\(671\) | −1.44558e12 | −0.275290 | ||||||||
\(672\) | −1.07191e13 | −2.02768 | ||||||||
\(673\) | −1.29085e11 | −0.0242554 | −0.0121277 | − | 0.999926i | \(-0.503860\pi\) | ||||
−0.0121277 | + | 0.999926i | \(0.503860\pi\) | |||||||
\(674\) | 1.18742e13 | 2.21632 | ||||||||
\(675\) | −3.91217e12 | −0.725356 | ||||||||
\(676\) | 2.83328e13 | 5.21831 | ||||||||
\(677\) | −2.61666e12 | −0.478738 | −0.239369 | − | 0.970929i | \(-0.576941\pi\) | ||||
−0.239369 | + | 0.970929i | \(0.576941\pi\) | |||||||
\(678\) | 1.06310e13 | 1.93214 | ||||||||
\(679\) | −7.86924e12 | −1.42075 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.11055e11 | −0.0197868 | ||||||||
\(682\) | 1.57926e11 | 0.0279527 | ||||||||
\(683\) | −5.88812e12 | −1.03534 | −0.517671 | − | 0.855580i | \(-0.673201\pi\) | ||||
−0.517671 | + | 0.855580i | \(0.673201\pi\) | |||||||
\(684\) | 9.12621e12 | 1.59418 | ||||||||
\(685\) | −1.30694e12 | −0.226802 | ||||||||
\(686\) | −1.21193e13 | −2.08939 | ||||||||
\(687\) | −1.32435e12 | −0.226829 | ||||||||
\(688\) | 7.66748e11 | 0.130468 | ||||||||
\(689\) | −5.88288e12 | −0.994497 | ||||||||
\(690\) | 3.67674e12 | 0.617507 | ||||||||
\(691\) | 1.46603e12 | 0.244620 | 0.122310 | − | 0.992492i | \(-0.460970\pi\) | ||||
0.122310 | + | 0.992492i | \(0.460970\pi\) | |||||||
\(692\) | −2.29004e13 | −3.79635 | ||||||||
\(693\) | −2.53936e12 | −0.418240 | ||||||||
\(694\) | −5.30500e12 | −0.868097 | ||||||||
\(695\) | −2.20846e12 | −0.359053 | ||||||||
\(696\) | 2.02881e13 | 3.27718 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2.16302e13 | −3.44913 | ||||||||
\(699\) | −3.79153e10 | −0.00600713 | ||||||||
\(700\) | 1.12270e13 | 1.76735 | ||||||||
\(701\) | 6.32038e12 | 0.988580 | 0.494290 | − | 0.869297i | \(-0.335428\pi\) | ||||
0.494290 | + | 0.869297i | \(0.335428\pi\) | |||||||
\(702\) | 2.07851e13 | 3.23024 | ||||||||
\(703\) | −9.10058e12 | −1.40530 | ||||||||
\(704\) | −1.83370e13 | −2.81352 | ||||||||
\(705\) | −6.14504e11 | −0.0936858 | ||||||||
\(706\) | −1.13547e13 | −1.72011 | ||||||||
\(707\) | 3.71156e12 | 0.558688 | ||||||||
\(708\) | −1.55247e13 | −2.32207 | ||||||||
\(709\) | 3.78053e12 | 0.561882 | 0.280941 | − | 0.959725i | \(-0.409354\pi\) | ||||
0.280941 | + | 0.959725i | \(0.409354\pi\) | |||||||
\(710\) | 4.69036e12 | 0.692697 | ||||||||
\(711\) | −6.28634e11 | −0.0922539 | ||||||||
\(712\) | −1.37426e12 | −0.200405 | ||||||||
\(713\) | 1.41177e11 | 0.0204578 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.51449e12 | 0.645998 | ||||||||
\(716\) | 1.16609e13 | 1.65815 | ||||||||
\(717\) | −5.03331e12 | −0.711242 | ||||||||
\(718\) | −2.47016e13 | −3.46869 | ||||||||
\(719\) | −9.62888e12 | −1.34368 | −0.671840 | − | 0.740696i | \(-0.734496\pi\) | ||||
−0.671840 | + | 0.740696i | \(0.734496\pi\) | |||||||
\(720\) | −8.90388e12 | −1.23476 | ||||||||
\(721\) | −4.70857e12 | −0.648903 | ||||||||
\(722\) | 2.60584e12 | 0.356886 | ||||||||
\(723\) | −1.63573e12 | −0.222633 | ||||||||
\(724\) | 7.91955e12 | 1.07122 | ||||||||
\(725\) | −9.01706e12 | −1.21212 | ||||||||
\(726\) | −3.85941e12 | −0.515593 | ||||||||
\(727\) | 9.26284e12 | 1.22981 | 0.614907 | − | 0.788600i | \(-0.289194\pi\) | ||||
0.614907 | + | 0.788600i | \(0.289194\pi\) | |||||||
\(728\) | −3.78562e13 | −4.99512 | ||||||||
\(729\) | 4.15311e12 | 0.544627 | ||||||||
\(730\) | 4.85133e11 | 0.0632277 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −4.69236e12 | −0.604075 | ||||||||
\(733\) | −3.26111e12 | −0.417251 | −0.208625 | − | 0.977996i | \(-0.566899\pi\) | ||||
−0.208625 | + | 0.977996i | \(0.566899\pi\) | |||||||
\(734\) | 2.19539e12 | 0.279177 | ||||||||
\(735\) | 5.73916e11 | 0.0725363 | ||||||||
\(736\) | −3.26512e13 | −4.10155 | ||||||||
\(737\) | −9.87574e12 | −1.23301 | ||||||||
\(738\) | −1.50036e13 | −1.86184 | ||||||||
\(739\) | 1.43463e13 | 1.76946 | 0.884731 | − | 0.466101i | \(-0.154342\pi\) | ||||
0.884731 | + | 0.466101i | \(0.154342\pi\) | |||||||
\(740\) | 1.77159e13 | 2.17180 | ||||||||
\(741\) | −7.52773e12 | −0.917239 | ||||||||
\(742\) | 8.12386e12 | 0.983886 | ||||||||
\(743\) | 5.86395e12 | 0.705896 | 0.352948 | − | 0.935643i | \(-0.385179\pi\) | ||||
0.352948 | + | 0.935643i | \(0.385179\pi\) | |||||||
\(744\) | 3.25344e11 | 0.0389282 | ||||||||
\(745\) | 1.80605e12 | 0.214796 | ||||||||
\(746\) | −1.05946e13 | −1.25244 | ||||||||
\(747\) | 2.83468e12 | 0.333090 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.67250e12 | 0.774676 | ||||||||
\(750\) | −8.85445e12 | −1.02185 | ||||||||
\(751\) | 7.70810e12 | 0.884234 | 0.442117 | − | 0.896957i | \(-0.354228\pi\) | ||||
0.442117 | + | 0.896957i | \(0.354228\pi\) | |||||||
\(752\) | 1.01554e13 | 1.15802 | ||||||||
\(753\) | 8.92332e12 | 1.01146 | ||||||||
\(754\) | 4.79070e13 | 5.39794 | ||||||||
\(755\) | −7.88192e11 | −0.0882817 | ||||||||
\(756\) | −2.10224e13 | −2.34064 | ||||||||
\(757\) | 9.90551e12 | 1.09634 | 0.548170 | − | 0.836367i | \(-0.315325\pi\) | ||||
0.548170 | + | 0.836367i | \(0.315325\pi\) | |||||||
\(758\) | 2.78512e13 | 3.06430 | ||||||||
\(759\) | 4.25737e12 | 0.465643 | ||||||||
\(760\) | 1.42195e13 | 1.54605 | ||||||||
\(761\) | 2.67093e12 | 0.288690 | 0.144345 | − | 0.989527i | \(-0.453893\pi\) | ||||
0.144345 | + | 0.989527i | \(0.453893\pi\) | |||||||
\(762\) | −6.40917e11 | −0.0688659 | ||||||||
\(763\) | 6.69660e12 | 0.715309 | ||||||||
\(764\) | −6.34560e12 | −0.673834 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.87959e12 | −0.197257 | ||||||||
\(767\) | −2.32659e13 | −2.42740 | ||||||||
\(768\) | −1.62067e13 | −1.68101 | ||||||||
\(769\) | 2.81525e12 | 0.290301 | 0.145151 | − | 0.989410i | \(-0.453633\pi\) | ||||
0.145151 | + | 0.989410i | \(0.453633\pi\) | |||||||
\(770\) | −6.23420e12 | −0.639106 | ||||||||
\(771\) | 1.13434e12 | 0.115611 | ||||||||
\(772\) | 3.85333e13 | 3.90444 | ||||||||
\(773\) | 1.90214e12 | 0.191617 | 0.0958085 | − | 0.995400i | \(-0.469456\pi\) | ||||
0.0958085 | + | 0.995400i | \(0.469456\pi\) | |||||||
\(774\) | 4.32586e11 | 0.0433250 | ||||||||
\(775\) | −1.44599e11 | −0.0143982 | ||||||||
\(776\) | −5.52397e13 | −5.46856 | ||||||||
\(777\) | 8.21966e12 | 0.809020 | ||||||||
\(778\) | −2.61160e13 | −2.55563 | ||||||||
\(779\) | 1.38585e13 | 1.34833 | ||||||||
\(780\) | 1.46541e13 | 1.41753 | ||||||||
\(781\) | 5.43106e12 | 0.522342 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.68843e13 | 1.60530 | ||||||||
\(784\) | −9.48464e12 | −0.896600 | ||||||||
\(785\) | −1.21799e12 | −0.114480 | ||||||||
\(786\) | −1.57028e13 | −1.46749 | ||||||||
\(787\) | 1.30989e13 | 1.21716 | 0.608580 | − | 0.793493i | \(-0.291740\pi\) | ||||
0.608580 | + | 0.793493i | \(0.291740\pi\) | |||||||
\(788\) | −2.10635e13 | −1.94609 | ||||||||
\(789\) | 3.73727e12 | 0.343327 | ||||||||
\(790\) | −1.54331e12 | −0.140972 | ||||||||
\(791\) | −1.61139e13 | −1.46354 | ||||||||
\(792\) | −1.78256e13 | −1.60983 | ||||||||
\(793\) | −7.03214e12 | −0.631478 | ||||||||
\(794\) | −2.14984e13 | −1.91961 | ||||||||
\(795\) | −1.99583e12 | −0.177203 | ||||||||
\(796\) | 8.12286e12 | 0.717134 | ||||||||
\(797\) | −9.57855e12 | −0.840886 | −0.420443 | − | 0.907319i | \(-0.638125\pi\) | ||||
−0.420443 | + | 0.907319i | \(0.638125\pi\) | |||||||
\(798\) | 1.03953e13 | 0.907452 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.34427e13 | 2.88667 | ||||||||
\(801\) | −4.48439e11 | −0.0384908 | ||||||||
\(802\) | 1.02753e13 | 0.877017 | ||||||||
\(803\) | 5.61745e11 | 0.0476781 | ||||||||
\(804\) | −3.20567e13 | −2.70562 | ||||||||
\(805\) | −5.57301e12 | −0.467744 | ||||||||
\(806\) | 7.68246e11 | 0.0641198 | ||||||||
\(807\) | 8.13935e12 | 0.675552 | ||||||||
\(808\) | 2.60541e13 | 2.15043 | ||||||||
\(809\) | 2.70995e12 | 0.222430 | 0.111215 | − | 0.993796i | \(-0.464526\pi\) | ||||
0.111215 | + | 0.993796i | \(0.464526\pi\) | |||||||
\(810\) | −7.36747e11 | −0.0601361 | ||||||||
\(811\) | −8.05231e11 | −0.0653622 | −0.0326811 | − | 0.999466i | \(-0.510405\pi\) | ||||
−0.0326811 | + | 0.999466i | \(0.510405\pi\) | |||||||
\(812\) | −4.84540e13 | −3.91136 | ||||||||
\(813\) | 7.20571e12 | 0.578455 | ||||||||
\(814\) | 2.80081e13 | 2.23601 | ||||||||
\(815\) | 3.38192e12 | 0.268506 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.99570e11 | −0.0313757 | ||||||||
\(818\) | −5.74785e12 | −0.448865 | ||||||||
\(819\) | −1.23530e13 | −0.959386 | ||||||||
\(820\) | −2.69780e13 | −2.08376 | ||||||||
\(821\) | 3.07077e12 | 0.235886 | 0.117943 | − | 0.993020i | \(-0.462370\pi\) | ||||
0.117943 | + | 0.993020i | \(0.462370\pi\) | |||||||
\(822\) | −6.70694e12 | −0.512390 | ||||||||
\(823\) | 1.09157e13 | 0.829375 | 0.414688 | − | 0.909964i | \(-0.363891\pi\) | ||||
0.414688 | + | 0.909964i | \(0.363891\pi\) | |||||||
\(824\) | −3.30527e13 | −2.49767 | ||||||||
\(825\) | −4.36058e12 | −0.327719 | ||||||||
\(826\) | 3.21287e13 | 2.40150 | ||||||||
\(827\) | 4.38102e12 | 0.325687 | 0.162844 | − | 0.986652i | \(-0.447933\pi\) | ||||
0.162844 | + | 0.986652i | \(0.447933\pi\) | |||||||
\(828\) | −2.51081e13 | −1.85642 | ||||||||
\(829\) | −9.43248e11 | −0.0693634 | −0.0346817 | − | 0.999398i | \(-0.511042\pi\) | ||||
−0.0346817 | + | 0.999398i | \(0.511042\pi\) | |||||||
\(830\) | 6.95922e12 | 0.508990 | ||||||||
\(831\) | −1.51896e12 | −0.110494 | ||||||||
\(832\) | −8.92018e13 | −6.45384 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.13334e13 | −0.811171 | ||||||||
\(835\) | −1.56396e11 | −0.0111336 | ||||||||
\(836\) | 2.59433e13 | 1.83695 | ||||||||
\(837\) | 2.70760e11 | 0.0190687 | ||||||||
\(838\) | −2.63023e13 | −1.84245 | ||||||||
\(839\) | 1.06739e13 | 0.743695 | 0.371847 | − | 0.928294i | \(-0.378724\pi\) | ||||
0.371847 | + | 0.928294i | \(0.378724\pi\) | |||||||
\(840\) | −1.28431e13 | −0.890047 | ||||||||
\(841\) | 2.44091e13 | 1.68256 | ||||||||
\(842\) | −5.08676e12 | −0.348768 | ||||||||
\(843\) | 3.26472e12 | 0.222650 | ||||||||
\(844\) | 4.25657e13 | 2.88748 | ||||||||
\(845\) | 1.44052e13 | 0.971994 | ||||||||
\(846\) | 5.72950e12 | 0.384548 | ||||||||
\(847\) | 5.84990e12 | 0.390547 | ||||||||
\(848\) | 3.29834e13 | 2.19035 | ||||||||
\(849\) | −1.30474e13 | −0.861863 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.50376e13 | 1.63647 | ||||||||
\(852\) | 1.76293e13 | 1.14619 | ||||||||
\(853\) | −1.66067e11 | −0.0107402 | −0.00537012 | − | 0.999986i | \(-0.501709\pi\) | ||||
−0.00537012 | + | 0.999986i | \(0.501709\pi\) | |||||||
\(854\) | 9.71091e12 | 0.624740 | ||||||||
\(855\) | 4.64002e12 | 0.296942 | ||||||||
\(856\) | 4.68389e13 | 2.98178 | ||||||||
\(857\) | −1.03151e13 | −0.653223 | −0.326611 | − | 0.945159i | \(-0.605907\pi\) | ||||
−0.326611 | + | 0.945159i | \(0.605907\pi\) | |||||||
\(858\) | 2.31675e13 | 1.45944 | ||||||||
\(859\) | 1.10331e12 | 0.0691398 | 0.0345699 | − | 0.999402i | \(-0.488994\pi\) | ||||
0.0345699 | + | 0.999402i | \(0.488994\pi\) | |||||||
\(860\) | 7.77833e11 | 0.0484890 | ||||||||
\(861\) | −1.25170e13 | −0.776221 | ||||||||
\(862\) | −4.04163e13 | −2.49329 | ||||||||
\(863\) | 1.58469e13 | 0.972514 | 0.486257 | − | 0.873816i | \(-0.338362\pi\) | ||||
0.486257 | + | 0.873816i | \(0.338362\pi\) | |||||||
\(864\) | −6.26211e13 | −3.82304 | ||||||||
\(865\) | −1.16432e13 | −0.707131 | ||||||||
\(866\) | 1.59403e13 | 0.963086 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.77017e11 | −0.0464614 | ||||||||
\(869\) | −1.78703e12 | −0.106302 | ||||||||
\(870\) | 1.62529e13 | 0.961823 | ||||||||
\(871\) | −4.80414e13 | −2.82836 | ||||||||
\(872\) | 4.70081e13 | 2.75327 | ||||||||
\(873\) | −1.80254e13 | −1.05032 | ||||||||
\(874\) | 3.16647e13 | 1.83558 | ||||||||
\(875\) | 1.34211e13 | 0.774020 | ||||||||
\(876\) | 1.82343e12 | 0.104621 | ||||||||
\(877\) | 3.07621e13 | 1.75597 | 0.877987 | − | 0.478684i | \(-0.158886\pi\) | ||||
0.877987 | + | 0.478684i | \(0.158886\pi\) | |||||||
\(878\) | 2.96995e13 | 1.68665 | ||||||||
\(879\) | −1.66640e13 | −0.941517 | ||||||||
\(880\) | −2.53112e13 | −1.42279 | ||||||||
\(881\) | 7.14002e10 | 0.00399308 | 0.00199654 | − | 0.999998i | \(-0.499364\pi\) | ||||
0.00199654 | + | 0.999998i | \(0.499364\pi\) | |||||||
\(882\) | −5.35108e12 | −0.297737 | ||||||||
\(883\) | −2.91216e13 | −1.61210 | −0.806050 | − | 0.591847i | \(-0.798399\pi\) | ||||
−0.806050 | + | 0.591847i | \(0.798399\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.89320e12 | −0.432522 | ||||||||
\(886\) | 2.27860e13 | 1.24227 | ||||||||
\(887\) | −5.81157e12 | −0.315237 | −0.157618 | − | 0.987500i | \(-0.550382\pi\) | ||||
−0.157618 | + | 0.987500i | \(0.550382\pi\) | |||||||
\(888\) | 5.76995e13 | 3.11397 | ||||||||
\(889\) | 9.71469e11 | 0.0521640 | ||||||||
\(890\) | −1.10093e12 | −0.0588171 | ||||||||
\(891\) | −8.53094e11 | −0.0453468 | ||||||||
\(892\) | 6.46488e13 | 3.41916 | ||||||||
\(893\) | −5.29221e12 | −0.278487 | ||||||||
\(894\) | 9.26829e12 | 0.485267 | ||||||||
\(895\) | 5.92874e12 | 0.308858 | ||||||||
\(896\) | 5.75267e13 | 2.98183 | ||||||||
\(897\) | 2.07103e13 | 1.06812 | ||||||||
\(898\) | 3.91555e13 | 2.00932 | ||||||||
\(899\) | 6.24068e11 | 0.0318650 | ||||||||
\(900\) | 2.57168e13 | 1.30655 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4.26510e13 | −2.14536 | ||||||||
\(903\) | 3.60892e11 | 0.0180627 | ||||||||
\(904\) | −1.13115e14 | −5.63327 | ||||||||
\(905\) | 4.02652e12 | 0.199531 | ||||||||
\(906\) | −4.04484e12 | −0.199446 | ||||||||
\(907\) | −2.77171e13 | −1.35993 | −0.679963 | − | 0.733246i | \(-0.738004\pi\) | ||||
−0.679963 | + | 0.733246i | \(0.738004\pi\) | |||||||
\(908\) | 1.86185e12 | 0.0908987 | ||||||||
\(909\) | 8.50178e12 | 0.413021 | ||||||||
\(910\) | −3.03268e13 | −1.46602 | ||||||||
\(911\) | −2.12590e13 | −1.02261 | −0.511305 | − | 0.859399i | \(-0.670838\pi\) | ||||
−0.511305 | + | 0.859399i | \(0.670838\pi\) | |||||||
\(912\) | 4.22055e13 | 2.02019 | ||||||||
\(913\) | 8.05822e12 | 0.383814 | ||||||||
\(914\) | −8.55216e12 | −0.405339 | ||||||||
\(915\) | −2.38572e12 | −0.112519 | ||||||||
\(916\) | 2.22029e13 | 1.04203 | ||||||||
\(917\) | 2.38015e13 | 1.11158 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.16408e13 | 1.46328 | 0.731641 | − | 0.681690i | \(-0.238755\pi\) | ||||
0.731641 | + | 0.681690i | \(0.238755\pi\) | |||||||
\(920\) | −3.91208e13 | −1.80037 | ||||||||
\(921\) | 1.21945e13 | 0.558464 | ||||||||
\(922\) | 3.03849e13 | 1.38474 | ||||||||
\(923\) | 2.64198e13 | 1.19818 | ||||||||
\(924\) | −2.34320e13 | −1.05751 | ||||||||
\(925\) | −2.56446e13 | −1.15175 | ||||||||
\(926\) | −6.31251e13 | −2.82132 | ||||||||
\(927\) | −1.07855e13 | −0.479714 | ||||||||
\(928\) | −1.44334e14 | −6.38855 | ||||||||
\(929\) | −2.81954e13 | −1.24196 | −0.620980 | − | 0.783827i | \(-0.713265\pi\) | ||||
−0.620980 | + | 0.783827i | \(0.713265\pi\) | |||||||
\(930\) | 2.60635e11 | 0.0114251 | ||||||||
\(931\) | 4.94267e12 | 0.215619 | ||||||||
\(932\) | 6.35654e11 | 0.0275962 | ||||||||
\(933\) | −4.27069e12 | −0.184515 | ||||||||
\(934\) | 7.58203e13 | 3.26005 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.67141e13 | −3.69274 | ||||||||
\(937\) | −1.91653e13 | −0.812244 | −0.406122 | − | 0.913819i | \(-0.633119\pi\) | ||||
−0.406122 | + | 0.913819i | \(0.633119\pi\) | |||||||
\(938\) | 6.63419e13 | 2.79818 | ||||||||
\(939\) | 2.17682e13 | 0.913750 | ||||||||
\(940\) | 1.03022e13 | 0.430384 | ||||||||
\(941\) | −5.92110e11 | −0.0246178 | −0.0123089 | − | 0.999924i | \(-0.503918\pi\) | ||||
−0.0123089 | + | 0.999924i | \(0.503918\pi\) | |||||||
\(942\) | −6.25050e12 | −0.258634 | ||||||||
\(943\) | −3.81275e13 | −1.57013 | ||||||||
\(944\) | 1.30444e14 | 5.34628 | ||||||||
\(945\) | −1.06884e13 | −0.435982 | ||||||||
\(946\) | 1.22972e12 | 0.0499226 | ||||||||
\(947\) | 2.32692e13 | 0.940171 | 0.470085 | − | 0.882621i | \(-0.344223\pi\) | ||||
0.470085 | + | 0.882621i | \(0.344223\pi\) | |||||||
\(948\) | −5.80072e12 | −0.233262 | ||||||||
\(949\) | 2.73266e12 | 0.109367 | ||||||||
\(950\) | −3.24323e13 | −1.29188 | ||||||||
\(951\) | 5.36552e10 | 0.00212716 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.58962e13 | 1.40971 | 0.704856 | − | 0.709351i | \(-0.251012\pi\) | ||||
0.704856 | + | 0.709351i | \(0.251012\pi\) | |||||||
\(954\) | 1.86087e13 | 0.727357 | ||||||||
\(955\) | −3.22628e12 | −0.125512 | ||||||||
\(956\) | 8.43840e13 | 3.26738 | ||||||||
\(957\) | 1.88196e13 | 0.725282 | ||||||||
\(958\) | 2.01693e13 | 0.773654 | ||||||||
\(959\) | 1.01660e13 | 0.388121 | ||||||||
\(960\) | −3.02626e13 | −1.14997 | ||||||||
\(961\) | −2.64296e13 | −0.999621 | ||||||||
\(962\) | 1.36248e14 | 5.12911 | ||||||||
\(963\) | 1.52841e13 | 0.572694 | ||||||||
\(964\) | 2.74232e13 | 1.02275 | ||||||||
\(965\) | 1.95914e13 | 0.727265 | ||||||||
\(966\) | −2.85996e13 | −1.05673 | ||||||||
\(967\) | −2.74118e13 | −1.00813 | −0.504067 | − | 0.863664i | \(-0.668164\pi\) | ||||
−0.504067 | + | 0.863664i | \(0.668164\pi\) | |||||||
\(968\) | 4.10645e13 | 1.50324 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.42528e13 | −1.60497 | ||||||||
\(971\) | −4.52819e13 | −1.63470 | −0.817350 | − | 0.576141i | \(-0.804558\pi\) | ||||
−0.817350 | + | 0.576141i | \(0.804558\pi\) | |||||||
\(972\) | −7.74276e13 | −2.78226 | ||||||||
\(973\) | 1.71786e13 | 0.614439 | ||||||||
\(974\) | 5.73596e13 | 2.04217 | ||||||||
\(975\) | −2.12124e13 | −0.751743 | ||||||||
\(976\) | 3.94269e13 | 1.39081 | ||||||||
\(977\) | 9.97230e12 | 0.350163 | 0.175081 | − | 0.984554i | \(-0.443981\pi\) | ||||
0.175081 | + | 0.984554i | \(0.443981\pi\) | |||||||
\(978\) | 1.73553e13 | 0.606608 | ||||||||
\(979\) | −1.27479e12 | −0.0443522 | ||||||||
\(980\) | −9.62177e12 | −0.333225 | ||||||||
\(981\) | 1.53394e13 | 0.528806 | ||||||||
\(982\) | 1.06133e13 | 0.364208 | ||||||||
\(983\) | 1.25146e13 | 0.427491 | 0.213745 | − | 0.976889i | \(-0.431434\pi\) | ||||
0.213745 | + | 0.976889i | \(0.431434\pi\) | |||||||
\(984\) | −8.78654e13 | −2.98772 | ||||||||
\(985\) | −1.07093e13 | −0.362491 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.77993e12 | 0.160322 | ||||||||
\(988\) | 1.26203e14 | 4.21371 | ||||||||
\(989\) | 1.09930e12 | 0.0365369 | ||||||||
\(990\) | −1.42802e13 | −0.472471 | ||||||||
\(991\) | 2.64145e12 | 0.0869982 | 0.0434991 | − | 0.999053i | \(-0.486149\pi\) | ||||
0.0434991 | + | 0.999053i | \(0.486149\pi\) | |||||||
\(992\) | −2.31456e12 | −0.0758868 | ||||||||
\(993\) | 2.11017e13 | 0.688726 | ||||||||
\(994\) | −3.64840e13 | −1.18540 | ||||||||
\(995\) | 4.12989e12 | 0.133578 | ||||||||
\(996\) | 2.61570e13 | 0.842212 | ||||||||
\(997\) | 1.22459e13 | 0.392520 | 0.196260 | − | 0.980552i | \(-0.437120\pi\) | ||||
0.196260 | + | 0.980552i | \(0.437120\pi\) | |||||||
\(998\) | 8.13174e13 | 2.59475 | ||||||||
\(999\) | 4.80192e13 | 1.52535 |
(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.g.1.2 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.2 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.2 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.2 | yes | 36 | 17.16 | even | 2 |