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 | 1.18 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −14.8865 | −0.657897 | −0.328949 | − | 0.944348i | \(-0.606694\pi\) | ||||
−0.328949 | + | 0.944348i | \(0.606694\pi\) | |||||||
\(3\) | 140.613 | 1.00226 | 0.501129 | − | 0.865372i | \(-0.332918\pi\) | ||||
0.501129 | + | 0.865372i | \(0.332918\pi\) | |||||||
\(4\) | −290.392 | −0.567171 | ||||||||
\(5\) | −1537.70 | −1.10029 | −0.550144 | − | 0.835070i | \(-0.685427\pi\) | ||||
−0.550144 | + | 0.835070i | \(0.685427\pi\) | |||||||
\(6\) | −2093.24 | −0.659383 | ||||||||
\(7\) | −2138.55 | −0.336650 | −0.168325 | − | 0.985732i | \(-0.553836\pi\) | ||||
−0.168325 | + | 0.985732i | \(0.553836\pi\) | |||||||
\(8\) | 11944.8 | 1.03104 | ||||||||
\(9\) | 89.0110 | 0.00452223 | ||||||||
\(10\) | 22891.0 | 0.723876 | ||||||||
\(11\) | 84061.4 | 1.73113 | 0.865565 | − | 0.500797i | \(-0.166960\pi\) | ||||
0.865565 | + | 0.500797i | \(0.166960\pi\) | |||||||
\(12\) | −40832.8 | −0.568452 | ||||||||
\(13\) | 12765.7 | 0.123965 | 0.0619826 | − | 0.998077i | \(-0.480258\pi\) | ||||
0.0619826 | + | 0.998077i | \(0.480258\pi\) | |||||||
\(14\) | 31835.6 | 0.221481 | ||||||||
\(15\) | −216220. | −1.10277 | ||||||||
\(16\) | −29136.1 | −0.111146 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1325.06 | −0.00297516 | ||||||||
\(19\) | 781004. | 1.37487 | 0.687436 | − | 0.726245i | \(-0.258736\pi\) | ||||
0.687436 | + | 0.726245i | \(0.258736\pi\) | |||||||
\(20\) | 446535. | 0.624052 | ||||||||
\(21\) | −300708. | −0.337411 | ||||||||
\(22\) | −1.25138e6 | −1.13891 | ||||||||
\(23\) | 1.32503e6 | 0.987303 | 0.493652 | − | 0.869660i | \(-0.335662\pi\) | ||||
0.493652 | + | 0.869660i | \(0.335662\pi\) | |||||||
\(24\) | 1.67960e6 | 1.03337 | ||||||||
\(25\) | 411393. | 0.210633 | ||||||||
\(26\) | −190037. | −0.0815564 | ||||||||
\(27\) | −2.75517e6 | −0.997726 | ||||||||
\(28\) | 621018. | 0.190938 | ||||||||
\(29\) | −2.18670e6 | −0.574114 | −0.287057 | − | 0.957914i | \(-0.592677\pi\) | ||||
−0.287057 | + | 0.957914i | \(0.592677\pi\) | |||||||
\(30\) | 3.21877e6 | 0.725511 | ||||||||
\(31\) | −2.91345e6 | −0.566605 | −0.283302 | − | 0.959031i | \(-0.591430\pi\) | ||||
−0.283302 | + | 0.959031i | \(0.591430\pi\) | |||||||
\(32\) | −5.68201e6 | −0.957915 | ||||||||
\(33\) | 1.18201e7 | 1.73504 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.28845e6 | 0.370412 | ||||||||
\(36\) | −25848.0 | −0.00256488 | ||||||||
\(37\) | −962092. | −0.0843935 | −0.0421968 | − | 0.999109i | \(-0.513436\pi\) | ||||
−0.0421968 | + | 0.999109i | \(0.513436\pi\) | |||||||
\(38\) | −1.16264e7 | −0.904524 | ||||||||
\(39\) | 1.79502e6 | 0.124245 | ||||||||
\(40\) | −1.83675e7 | −1.13444 | ||||||||
\(41\) | −2.92396e7 | −1.61601 | −0.808005 | − | 0.589176i | \(-0.799453\pi\) | ||||
−0.808005 | + | 0.589176i | \(0.799453\pi\) | |||||||
\(42\) | 4.47650e6 | 0.221982 | ||||||||
\(43\) | −9.73937e6 | −0.434433 | −0.217216 | − | 0.976123i | \(-0.569698\pi\) | ||||
−0.217216 | + | 0.976123i | \(0.569698\pi\) | |||||||
\(44\) | −2.44107e7 | −0.981847 | ||||||||
\(45\) | −136872. | −0.00497575 | ||||||||
\(46\) | −1.97251e7 | −0.649544 | ||||||||
\(47\) | −1.22741e7 | −0.366902 | −0.183451 | − | 0.983029i | \(-0.558727\pi\) | ||||
−0.183451 | + | 0.983029i | \(0.558727\pi\) | |||||||
\(48\) | −4.09692e6 | −0.111397 | ||||||||
\(49\) | −3.57802e7 | −0.886667 | ||||||||
\(50\) | −6.12420e6 | −0.138575 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.70706e6 | −0.0703095 | ||||||||
\(53\) | −5.42576e7 | −0.944537 | −0.472268 | − | 0.881455i | \(-0.656565\pi\) | ||||
−0.472268 | + | 0.881455i | \(0.656565\pi\) | |||||||
\(54\) | 4.10149e7 | 0.656401 | ||||||||
\(55\) | −1.29261e8 | −1.90474 | ||||||||
\(56\) | −2.55446e7 | −0.347099 | ||||||||
\(57\) | 1.09819e8 | 1.37798 | ||||||||
\(58\) | 3.25523e7 | 0.377708 | ||||||||
\(59\) | 1.10830e8 | 1.19076 | 0.595380 | − | 0.803444i | \(-0.297001\pi\) | ||||
0.595380 | + | 0.803444i | \(0.297001\pi\) | |||||||
\(60\) | 6.27886e7 | 0.625461 | ||||||||
\(61\) | 8.49900e7 | 0.785930 | 0.392965 | − | 0.919553i | \(-0.371449\pi\) | ||||
0.392965 | + | 0.919553i | \(0.371449\pi\) | |||||||
\(62\) | 4.33711e7 | 0.372768 | ||||||||
\(63\) | −190355. | −0.00152241 | ||||||||
\(64\) | 9.95030e7 | 0.741355 | ||||||||
\(65\) | −1.96298e7 | −0.136397 | ||||||||
\(66\) | −1.75960e8 | −1.14148 | ||||||||
\(67\) | −1.27439e8 | −0.772619 | −0.386310 | − | 0.922369i | \(-0.626250\pi\) | ||||
−0.386310 | + | 0.922369i | \(0.626250\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.86317e8 | 0.989533 | ||||||||
\(70\) | −4.89536e7 | −0.243693 | ||||||||
\(71\) | 3.50617e8 | 1.63746 | 0.818730 | − | 0.574179i | \(-0.194679\pi\) | ||||
0.818730 | + | 0.574179i | \(0.194679\pi\) | |||||||
\(72\) | 1.06322e6 | 0.00466259 | ||||||||
\(73\) | 2.51809e8 | 1.03781 | 0.518905 | − | 0.854832i | \(-0.326340\pi\) | ||||
0.518905 | + | 0.854832i | \(0.326340\pi\) | |||||||
\(74\) | 1.43222e7 | 0.0555223 | ||||||||
\(75\) | 5.78472e7 | 0.211109 | ||||||||
\(76\) | −2.26797e8 | −0.779787 | ||||||||
\(77\) | −1.79770e8 | −0.582785 | ||||||||
\(78\) | −2.67217e7 | −0.0817406 | ||||||||
\(79\) | 1.63817e8 | 0.473192 | 0.236596 | − | 0.971608i | \(-0.423968\pi\) | ||||
0.236596 | + | 0.971608i | \(0.423968\pi\) | |||||||
\(80\) | 4.48026e7 | 0.122292 | ||||||||
\(81\) | −3.89165e8 | −1.00450 | ||||||||
\(82\) | 4.35276e8 | 1.06317 | ||||||||
\(83\) | 7.86881e8 | 1.81994 | 0.909972 | − | 0.414671i | \(-0.136103\pi\) | ||||
0.909972 | + | 0.414671i | \(0.136103\pi\) | |||||||
\(84\) | 8.73232e7 | 0.191370 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.44985e8 | 0.285812 | ||||||||
\(87\) | −3.07478e8 | −0.575411 | ||||||||
\(88\) | 1.00410e9 | 1.78486 | ||||||||
\(89\) | −2.83737e8 | −0.479360 | −0.239680 | − | 0.970852i | \(-0.577042\pi\) | ||||
−0.239680 | + | 0.970852i | \(0.577042\pi\) | |||||||
\(90\) | 2.03755e6 | 0.00327353 | ||||||||
\(91\) | −2.73002e7 | −0.0417329 | ||||||||
\(92\) | −3.84778e8 | −0.559970 | ||||||||
\(93\) | −4.09669e8 | −0.567884 | ||||||||
\(94\) | 1.82719e8 | 0.241384 | ||||||||
\(95\) | −1.20095e9 | −1.51275 | ||||||||
\(96\) | −7.98964e8 | −0.960079 | ||||||||
\(97\) | 2.62185e8 | 0.300701 | 0.150350 | − | 0.988633i | \(-0.451960\pi\) | ||||
0.150350 | + | 0.988633i | \(0.451960\pi\) | |||||||
\(98\) | 5.32642e8 | 0.583335 | ||||||||
\(99\) | 7.48239e6 | 0.00782856 | ||||||||
\(100\) | −1.19465e8 | −0.119465 | ||||||||
\(101\) | −1.01701e9 | −0.972477 | −0.486238 | − | 0.873826i | \(-0.661631\pi\) | ||||
−0.486238 | + | 0.873826i | \(0.661631\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.11236e9 | 0.973814 | 0.486907 | − | 0.873454i | \(-0.338125\pi\) | ||||
0.486907 | + | 0.873454i | \(0.338125\pi\) | |||||||
\(104\) | 1.52484e8 | 0.127813 | ||||||||
\(105\) | 4.62399e8 | 0.371249 | ||||||||
\(106\) | 8.07706e8 | 0.621408 | ||||||||
\(107\) | 1.17459e9 | 0.866284 | 0.433142 | − | 0.901326i | \(-0.357405\pi\) | ||||
0.433142 | + | 0.901326i | \(0.357405\pi\) | |||||||
\(108\) | 8.00078e8 | 0.565882 | ||||||||
\(109\) | 1.13422e9 | 0.769625 | 0.384813 | − | 0.922995i | \(-0.374266\pi\) | ||||
0.384813 | + | 0.922995i | \(0.374266\pi\) | |||||||
\(110\) | 1.92425e9 | 1.25312 | ||||||||
\(111\) | −1.35283e8 | −0.0845841 | ||||||||
\(112\) | 6.23092e7 | 0.0374172 | ||||||||
\(113\) | −1.37503e9 | −0.793337 | −0.396668 | − | 0.917962i | \(-0.629834\pi\) | ||||
−0.396668 | + | 0.917962i | \(0.629834\pi\) | |||||||
\(114\) | −1.63483e9 | −0.906567 | ||||||||
\(115\) | −2.03750e9 | −1.08632 | ||||||||
\(116\) | 6.34999e8 | 0.325621 | ||||||||
\(117\) | 1.13629e6 | 0.000560599 0 | ||||||||
\(118\) | −1.64988e9 | −0.783398 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.58271e9 | −1.13700 | ||||||||
\(121\) | 4.70837e9 | 1.99681 | ||||||||
\(122\) | −1.26521e9 | −0.517061 | ||||||||
\(123\) | −4.11147e9 | −1.61966 | ||||||||
\(124\) | 8.46042e8 | 0.321362 | ||||||||
\(125\) | 2.37072e9 | 0.868531 | ||||||||
\(126\) | 2.83372e6 | 0.00100159 | ||||||||
\(127\) | −1.63757e9 | −0.558577 | −0.279289 | − | 0.960207i | \(-0.590099\pi\) | ||||
−0.279289 | + | 0.960207i | \(0.590099\pi\) | |||||||
\(128\) | 1.42794e9 | 0.470180 | ||||||||
\(129\) | −1.36948e9 | −0.435414 | ||||||||
\(130\) | 2.92220e8 | 0.0897355 | ||||||||
\(131\) | −4.89940e9 | −1.45352 | −0.726762 | − | 0.686890i | \(-0.758976\pi\) | ||||
−0.726762 | + | 0.686890i | \(0.758976\pi\) | |||||||
\(132\) | −3.43247e9 | −0.984064 | ||||||||
\(133\) | −1.67022e9 | −0.462851 | ||||||||
\(134\) | 1.89712e9 | 0.508304 | ||||||||
\(135\) | 4.23662e9 | 1.09779 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.10441e9 | −0.752899 | −0.376449 | − | 0.926437i | \(-0.622855\pi\) | ||||
−0.376449 | + | 0.926437i | \(0.622855\pi\) | |||||||
\(138\) | −2.77360e9 | −0.651011 | ||||||||
\(139\) | −2.82102e8 | −0.0640972 | −0.0320486 | − | 0.999486i | \(-0.510203\pi\) | ||||
−0.0320486 | + | 0.999486i | \(0.510203\pi\) | |||||||
\(140\) | −9.54939e8 | −0.210087 | ||||||||
\(141\) | −1.72590e9 | −0.367730 | ||||||||
\(142\) | −5.21947e9 | −1.07728 | ||||||||
\(143\) | 1.07310e9 | 0.214600 | ||||||||
\(144\) | −2.59344e6 | −0.000502625 0 | ||||||||
\(145\) | 3.36249e9 | 0.631691 | ||||||||
\(146\) | −3.74855e9 | −0.682772 | ||||||||
\(147\) | −5.03116e9 | −0.888669 | ||||||||
\(148\) | 2.79384e8 | 0.0478656 | ||||||||
\(149\) | −1.55842e9 | −0.259028 | −0.129514 | − | 0.991578i | \(-0.541342\pi\) | ||||
−0.129514 | + | 0.991578i | \(0.541342\pi\) | |||||||
\(150\) | −8.61142e8 | −0.138888 | ||||||||
\(151\) | 8.38462e9 | 1.31246 | 0.656231 | − | 0.754560i | \(-0.272150\pi\) | ||||
0.656231 | + | 0.754560i | \(0.272150\pi\) | |||||||
\(152\) | 9.32895e9 | 1.41754 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.67615e9 | 0.383413 | ||||||||
\(155\) | 4.48001e9 | 0.623428 | ||||||||
\(156\) | −5.21260e8 | −0.0704683 | ||||||||
\(157\) | 8.18273e9 | 1.07486 | 0.537428 | − | 0.843310i | \(-0.319396\pi\) | ||||
0.537428 | + | 0.843310i | \(0.319396\pi\) | |||||||
\(158\) | −2.43867e9 | −0.311312 | ||||||||
\(159\) | −7.62932e9 | −0.946670 | ||||||||
\(160\) | 8.73722e9 | 1.05398 | ||||||||
\(161\) | −2.83365e9 | −0.332376 | ||||||||
\(162\) | 5.79330e9 | 0.660859 | ||||||||
\(163\) | 9.23855e9 | 1.02508 | 0.512542 | − | 0.858662i | \(-0.328704\pi\) | ||||
0.512542 | + | 0.858662i | \(0.328704\pi\) | |||||||
\(164\) | 8.49093e9 | 0.916554 | ||||||||
\(165\) | −1.81758e10 | −1.90904 | ||||||||
\(166\) | −1.17139e10 | −1.19734 | ||||||||
\(167\) | −1.07606e10 | −1.07056 | −0.535279 | − | 0.844675i | \(-0.679794\pi\) | ||||
−0.535279 | + | 0.844675i | \(0.679794\pi\) | |||||||
\(168\) | −3.59191e9 | −0.347883 | ||||||||
\(169\) | −1.04415e10 | −0.984633 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.95179e7 | 0.00621748 | ||||||||
\(172\) | 2.82823e9 | 0.246398 | ||||||||
\(173\) | 1.65396e10 | 1.40384 | 0.701921 | − | 0.712255i | \(-0.252326\pi\) | ||||
0.701921 | + | 0.712255i | \(0.252326\pi\) | |||||||
\(174\) | 4.57728e9 | 0.378561 | ||||||||
\(175\) | −8.79785e8 | −0.0709097 | ||||||||
\(176\) | −2.44922e9 | −0.192407 | ||||||||
\(177\) | 1.55842e10 | 1.19345 | ||||||||
\(178\) | 4.22386e9 | 0.315369 | ||||||||
\(179\) | 1.20555e10 | 0.877699 | 0.438849 | − | 0.898561i | \(-0.355386\pi\) | ||||
0.438849 | + | 0.898561i | \(0.355386\pi\) | |||||||
\(180\) | 3.97465e7 | 0.00282210 | ||||||||
\(181\) | −2.05478e10 | −1.42302 | −0.711511 | − | 0.702675i | \(-0.751989\pi\) | ||||
−0.711511 | + | 0.702675i | \(0.751989\pi\) | |||||||
\(182\) | 4.06404e8 | 0.0274560 | ||||||||
\(183\) | 1.19507e10 | 0.787705 | ||||||||
\(184\) | 1.58272e10 | 1.01795 | ||||||||
\(185\) | 1.47941e9 | 0.0928571 | ||||||||
\(186\) | 6.09854e9 | 0.373610 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.56430e9 | 0.208096 | ||||||||
\(189\) | 5.89208e9 | 0.335885 | ||||||||
\(190\) | 1.78779e10 | 0.995236 | ||||||||
\(191\) | −3.26529e10 | −1.77530 | −0.887651 | − | 0.460517i | \(-0.847664\pi\) | ||||
−0.887651 | + | 0.460517i | \(0.847664\pi\) | |||||||
\(192\) | 1.39914e10 | 0.743030 | ||||||||
\(193\) | −2.78185e10 | −1.44320 | −0.721600 | − | 0.692310i | \(-0.756593\pi\) | ||||
−0.721600 | + | 0.692310i | \(0.756593\pi\) | |||||||
\(194\) | −3.90302e9 | −0.197830 | ||||||||
\(195\) | −2.76021e9 | −0.136705 | ||||||||
\(196\) | 1.03903e10 | 0.502892 | ||||||||
\(197\) | 2.76208e10 | 1.30659 | 0.653293 | − | 0.757105i | \(-0.273387\pi\) | ||||
0.653293 | + | 0.757105i | \(0.273387\pi\) | |||||||
\(198\) | −1.11387e8 | −0.00515039 | ||||||||
\(199\) | 3.75699e10 | 1.69825 | 0.849123 | − | 0.528195i | \(-0.177131\pi\) | ||||
0.849123 | + | 0.528195i | \(0.177131\pi\) | |||||||
\(200\) | 4.91401e9 | 0.217171 | ||||||||
\(201\) | −1.79196e10 | −0.774364 | ||||||||
\(202\) | 1.51397e10 | 0.639790 | ||||||||
\(203\) | 4.67638e9 | 0.193276 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.49617e10 | 1.77808 | ||||||||
\(206\) | −1.65591e10 | −0.640670 | ||||||||
\(207\) | 1.17942e8 | 0.00446481 | ||||||||
\(208\) | −3.71943e8 | −0.0137782 | ||||||||
\(209\) | 6.56523e10 | 2.38008 | ||||||||
\(210\) | −6.88351e9 | −0.244244 | ||||||||
\(211\) | 3.68658e9 | 0.128042 | 0.0640211 | − | 0.997949i | \(-0.479608\pi\) | ||||
0.0640211 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(212\) | 1.57559e10 | 0.535714 | ||||||||
\(213\) | 4.93013e10 | 1.64116 | ||||||||
\(214\) | −1.74856e10 | −0.569926 | ||||||||
\(215\) | 1.49762e10 | 0.478001 | ||||||||
\(216\) | −3.29100e10 | −1.02869 | ||||||||
\(217\) | 6.23057e9 | 0.190748 | ||||||||
\(218\) | −1.68846e10 | −0.506334 | ||||||||
\(219\) | 3.54076e10 | 1.04015 | ||||||||
\(220\) | 3.75363e10 | 1.08031 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 2.01389e9 | 0.0556477 | ||||||||
\(223\) | −1.26499e10 | −0.342544 | −0.171272 | − | 0.985224i | \(-0.554788\pi\) | ||||
−0.171272 | + | 0.985224i | \(0.554788\pi\) | |||||||
\(224\) | 1.21513e10 | 0.322483 | ||||||||
\(225\) | 3.66185e7 | 0.000952530 0 | ||||||||
\(226\) | 2.04693e10 | 0.521934 | ||||||||
\(227\) | −4.42724e10 | −1.10667 | −0.553333 | − | 0.832960i | \(-0.686644\pi\) | ||||
−0.553333 | + | 0.832960i | \(0.686644\pi\) | |||||||
\(228\) | −3.18906e10 | −0.781549 | ||||||||
\(229\) | 6.67619e10 | 1.60424 | 0.802119 | − | 0.597164i | \(-0.203706\pi\) | ||||
0.802119 | + | 0.597164i | \(0.203706\pi\) | |||||||
\(230\) | 3.03312e10 | 0.714685 | ||||||||
\(231\) | −2.52780e10 | −0.584101 | ||||||||
\(232\) | −2.61197e10 | −0.591933 | ||||||||
\(233\) | −6.22710e10 | −1.38415 | −0.692076 | − | 0.721824i | \(-0.743304\pi\) | ||||
−0.692076 | + | 0.721824i | \(0.743304\pi\) | |||||||
\(234\) | −1.69154e7 | −0.000368816 0 | ||||||||
\(235\) | 1.88739e10 | 0.403697 | ||||||||
\(236\) | −3.21842e10 | −0.675365 | ||||||||
\(237\) | 2.30348e10 | 0.474261 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.82772e10 | 1.35358 | 0.676792 | − | 0.736174i | \(-0.263370\pi\) | ||||
0.676792 | + | 0.736174i | \(0.263370\pi\) | |||||||
\(240\) | 6.29983e9 | 0.122568 | ||||||||
\(241\) | 6.20183e10 | 1.18425 | 0.592125 | − | 0.805846i | \(-0.298289\pi\) | ||||
0.592125 | + | 0.805846i | \(0.298289\pi\) | |||||||
\(242\) | −7.00912e10 | −1.31369 | ||||||||
\(243\) | −4.91595e8 | −0.00904438 | ||||||||
\(244\) | −2.46804e10 | −0.445757 | ||||||||
\(245\) | 5.50192e10 | 0.975588 | ||||||||
\(246\) | 6.12054e10 | 1.06557 | ||||||||
\(247\) | 9.97007e9 | 0.170436 | ||||||||
\(248\) | −3.48006e10 | −0.584191 | ||||||||
\(249\) | 1.10646e11 | 1.82405 | ||||||||
\(250\) | −3.52918e10 | −0.571404 | ||||||||
\(251\) | 8.72683e10 | 1.38779 | 0.693897 | − | 0.720074i | \(-0.255892\pi\) | ||||
0.693897 | + | 0.720074i | \(0.255892\pi\) | |||||||
\(252\) | 5.52774e7 | 0.000863467 0 | ||||||||
\(253\) | 1.11384e11 | 1.70915 | ||||||||
\(254\) | 2.43777e10 | 0.367486 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.22025e10 | −1.05069 | ||||||||
\(257\) | −2.32433e10 | −0.332353 | −0.166176 | − | 0.986096i | \(-0.553142\pi\) | ||||
−0.166176 | + | 0.986096i | \(0.553142\pi\) | |||||||
\(258\) | 2.03868e10 | 0.286458 | ||||||||
\(259\) | 2.05749e9 | 0.0284111 | ||||||||
\(260\) | 5.70033e9 | 0.0773607 | ||||||||
\(261\) | −1.94640e8 | −0.00259627 | ||||||||
\(262\) | 7.29350e10 | 0.956269 | ||||||||
\(263\) | 2.54583e10 | 0.328117 | 0.164058 | − | 0.986451i | \(-0.447541\pi\) | ||||
0.164058 | + | 0.986451i | \(0.447541\pi\) | |||||||
\(264\) | 1.41189e11 | 1.78889 | ||||||||
\(265\) | 8.34318e10 | 1.03926 | ||||||||
\(266\) | 2.48637e10 | 0.304508 | ||||||||
\(267\) | −3.98972e10 | −0.480442 | ||||||||
\(268\) | 3.70072e10 | 0.438207 | ||||||||
\(269\) | 1.66536e10 | 0.193921 | 0.0969603 | − | 0.995288i | \(-0.469088\pi\) | ||||
0.0969603 | + | 0.995288i | \(0.469088\pi\) | |||||||
\(270\) | −6.30685e10 | −0.722230 | ||||||||
\(271\) | 7.55383e10 | 0.850756 | 0.425378 | − | 0.905016i | \(-0.360141\pi\) | ||||
0.425378 | + | 0.905016i | \(0.360141\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.83876e9 | −0.0418272 | ||||||||
\(274\) | 4.62138e10 | 0.495330 | ||||||||
\(275\) | 3.45822e10 | 0.364633 | ||||||||
\(276\) | −5.41048e10 | −0.561235 | ||||||||
\(277\) | 3.08726e10 | 0.315076 | 0.157538 | − | 0.987513i | \(-0.449644\pi\) | ||||
0.157538 | + | 0.987513i | \(0.449644\pi\) | |||||||
\(278\) | 4.19951e9 | 0.0421694 | ||||||||
\(279\) | −2.59329e8 | −0.00256231 | ||||||||
\(280\) | 3.92800e10 | 0.381909 | ||||||||
\(281\) | 5.90092e10 | 0.564601 | 0.282300 | − | 0.959326i | \(-0.408903\pi\) | ||||
0.282300 | + | 0.959326i | \(0.408903\pi\) | |||||||
\(282\) | 2.56926e10 | 0.241929 | ||||||||
\(283\) | −1.83598e11 | −1.70149 | −0.850745 | − | 0.525579i | \(-0.823849\pi\) | ||||
−0.850745 | + | 0.525579i | \(0.823849\pi\) | |||||||
\(284\) | −1.01816e11 | −0.928720 | ||||||||
\(285\) | −1.68869e11 | −1.51617 | ||||||||
\(286\) | −1.59748e10 | −0.141185 | ||||||||
\(287\) | 6.25304e10 | 0.544030 | ||||||||
\(288\) | −5.05761e8 | −0.00433191 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −5.00557e10 | −0.415587 | ||||||||
\(291\) | 3.68666e10 | 0.301380 | ||||||||
\(292\) | −7.31231e10 | −0.588616 | ||||||||
\(293\) | 8.80276e10 | 0.697774 | 0.348887 | − | 0.937165i | \(-0.386560\pi\) | ||||
0.348887 | + | 0.937165i | \(0.386560\pi\) | |||||||
\(294\) | 7.48964e10 | 0.584653 | ||||||||
\(295\) | −1.70424e11 | −1.31018 | ||||||||
\(296\) | −1.14920e10 | −0.0870129 | ||||||||
\(297\) | −2.31603e11 | −1.72719 | ||||||||
\(298\) | 2.31995e10 | 0.170414 | ||||||||
\(299\) | 1.69150e10 | 0.122391 | ||||||||
\(300\) | −1.67983e10 | −0.119735 | ||||||||
\(301\) | 2.08282e10 | 0.146252 | ||||||||
\(302\) | −1.24818e11 | −0.863465 | ||||||||
\(303\) | −1.43005e11 | −0.974673 | ||||||||
\(304\) | −2.27554e10 | −0.152811 | ||||||||
\(305\) | −1.30689e11 | −0.864749 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.25066e11 | 0.803558 | 0.401779 | − | 0.915737i | \(-0.368392\pi\) | ||||
0.401779 | + | 0.915737i | \(0.368392\pi\) | |||||||
\(308\) | 5.22037e10 | 0.330539 | ||||||||
\(309\) | 1.56412e11 | 0.976014 | ||||||||
\(310\) | −6.66917e10 | −0.410152 | ||||||||
\(311\) | 1.23644e11 | 0.749466 | 0.374733 | − | 0.927133i | \(-0.377734\pi\) | ||||
0.374733 | + | 0.927133i | \(0.377734\pi\) | |||||||
\(312\) | 2.14412e10 | 0.128101 | ||||||||
\(313\) | −4.92496e10 | −0.290037 | −0.145018 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145018 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(314\) | −1.21812e11 | −0.707144 | ||||||||
\(315\) | 2.92708e8 | 0.00167509 | ||||||||
\(316\) | −4.75712e10 | −0.268381 | ||||||||
\(317\) | −2.94046e11 | −1.63549 | −0.817745 | − | 0.575580i | \(-0.804776\pi\) | ||||
−0.817745 | + | 0.575580i | \(0.804776\pi\) | |||||||
\(318\) | 1.13574e11 | 0.622812 | ||||||||
\(319\) | −1.83817e11 | −0.993865 | ||||||||
\(320\) | −1.53006e11 | −0.815704 | ||||||||
\(321\) | 1.65163e11 | 0.868240 | ||||||||
\(322\) | 4.21832e10 | 0.218669 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.13010e11 | 0.569725 | ||||||||
\(325\) | 5.25172e9 | 0.0261112 | ||||||||
\(326\) | −1.37530e11 | −0.674400 | ||||||||
\(327\) | 1.59487e11 | 0.771363 | ||||||||
\(328\) | −3.49262e11 | −1.66617 | ||||||||
\(329\) | 2.62488e10 | 0.123518 | ||||||||
\(330\) | 2.70574e11 | 1.25595 | ||||||||
\(331\) | 3.07114e10 | 0.140629 | 0.0703143 | − | 0.997525i | \(-0.477600\pi\) | ||||
0.0703143 | + | 0.997525i | \(0.477600\pi\) | |||||||
\(332\) | −2.28504e11 | −1.03222 | ||||||||
\(333\) | −8.56368e7 | −0.000381646 0 | ||||||||
\(334\) | 1.60187e11 | 0.704318 | ||||||||
\(335\) | 1.95963e11 | 0.850104 | ||||||||
\(336\) | 8.76148e9 | 0.0375017 | ||||||||
\(337\) | 4.27513e11 | 1.80557 | 0.902787 | − | 0.430088i | \(-0.141518\pi\) | ||||
0.902787 | + | 0.430088i | \(0.141518\pi\) | |||||||
\(338\) | 1.55438e11 | 0.647787 | ||||||||
\(339\) | −1.93346e11 | −0.795129 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.44909e11 | −0.980866 | ||||||||
\(342\) | −1.03488e9 | −0.00409046 | ||||||||
\(343\) | 1.62816e11 | 0.635147 | ||||||||
\(344\) | −1.16335e11 | −0.447917 | ||||||||
\(345\) | −2.86499e11 | −1.08877 | ||||||||
\(346\) | −2.46217e11 | −0.923584 | ||||||||
\(347\) | 1.31346e11 | 0.486335 | 0.243167 | − | 0.969984i | \(-0.421814\pi\) | ||||
0.243167 | + | 0.969984i | \(0.421814\pi\) | |||||||
\(348\) | 8.92892e10 | 0.326356 | ||||||||
\(349\) | −1.90494e11 | −0.687333 | −0.343666 | − | 0.939092i | \(-0.611669\pi\) | ||||
−0.343666 | + | 0.939092i | \(0.611669\pi\) | |||||||
\(350\) | 1.30969e10 | 0.0466513 | ||||||||
\(351\) | −3.51717e10 | −0.123683 | ||||||||
\(352\) | −4.77638e11 | −1.65828 | ||||||||
\(353\) | −5.20746e10 | −0.178501 | −0.0892503 | − | 0.996009i | \(-0.528447\pi\) | ||||
−0.0892503 | + | 0.996009i | \(0.528447\pi\) | |||||||
\(354\) | −2.31994e11 | −0.785167 | ||||||||
\(355\) | −5.39144e11 | −1.80168 | ||||||||
\(356\) | 8.23950e10 | 0.271879 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.79464e11 | −0.577435 | ||||||||
\(359\) | 6.15238e11 | 1.95487 | 0.977436 | − | 0.211232i | \(-0.0677474\pi\) | ||||
0.977436 | + | 0.211232i | \(0.0677474\pi\) | |||||||
\(360\) | −1.63491e9 | −0.00513019 | ||||||||
\(361\) | 2.87279e11 | 0.890271 | ||||||||
\(362\) | 3.05885e11 | 0.936202 | ||||||||
\(363\) | 6.62058e11 | 2.00132 | ||||||||
\(364\) | 7.92774e9 | 0.0236697 | ||||||||
\(365\) | −3.87206e11 | −1.14189 | ||||||||
\(366\) | −1.77904e11 | −0.518229 | ||||||||
\(367\) | −5.60031e11 | −1.61144 | −0.805721 | − | 0.592295i | \(-0.798222\pi\) | ||||
−0.805721 | + | 0.592295i | \(0.798222\pi\) | |||||||
\(368\) | −3.86063e10 | −0.109734 | ||||||||
\(369\) | −2.60264e9 | −0.00730796 | ||||||||
\(370\) | −2.20232e10 | −0.0610904 | ||||||||
\(371\) | 1.16033e11 | 0.317979 | ||||||||
\(372\) | 1.18964e11 | 0.322088 | ||||||||
\(373\) | −2.00817e10 | −0.0537169 | −0.0268585 | − | 0.999639i | \(-0.508550\pi\) | ||||
−0.0268585 | + | 0.999639i | \(0.508550\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.33354e11 | 0.870492 | ||||||||
\(376\) | −1.46612e11 | −0.378289 | ||||||||
\(377\) | −2.79148e10 | −0.0711702 | ||||||||
\(378\) | −8.77125e10 | −0.220978 | ||||||||
\(379\) | 2.22361e10 | 0.0553581 | 0.0276791 | − | 0.999617i | \(-0.491188\pi\) | ||||
0.0276791 | + | 0.999617i | \(0.491188\pi\) | |||||||
\(380\) | 3.48746e11 | 0.857990 | ||||||||
\(381\) | −2.30264e11 | −0.559839 | ||||||||
\(382\) | 4.86089e11 | 1.16797 | ||||||||
\(383\) | 1.05889e11 | 0.251453 | 0.125726 | − | 0.992065i | \(-0.459874\pi\) | ||||
0.125726 | + | 0.992065i | \(0.459874\pi\) | |||||||
\(384\) | 2.00786e11 | 0.471242 | ||||||||
\(385\) | 2.76432e11 | 0.641231 | ||||||||
\(386\) | 4.14121e11 | 0.949477 | ||||||||
\(387\) | −8.66911e8 | −0.00196460 | ||||||||
\(388\) | −7.61363e10 | −0.170549 | ||||||||
\(389\) | 6.41740e10 | 0.142097 | 0.0710486 | − | 0.997473i | \(-0.477365\pi\) | ||||
0.0710486 | + | 0.997473i | \(0.477365\pi\) | |||||||
\(390\) | 4.10899e10 | 0.0899381 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.27388e11 | −0.914187 | ||||||||
\(393\) | −6.88919e11 | −1.45681 | ||||||||
\(394\) | −4.11177e11 | −0.859600 | ||||||||
\(395\) | −2.51902e11 | −0.520648 | ||||||||
\(396\) | −2.17282e9 | −0.00444013 | ||||||||
\(397\) | 1.37059e11 | 0.276917 | 0.138458 | − | 0.990368i | \(-0.455785\pi\) | ||||
0.138458 | + | 0.990368i | \(0.455785\pi\) | |||||||
\(398\) | −5.59284e11 | −1.11727 | ||||||||
\(399\) | −2.34854e11 | −0.463896 | ||||||||
\(400\) | −1.19864e10 | −0.0234109 | ||||||||
\(401\) | 4.83309e11 | 0.933415 | 0.466708 | − | 0.884412i | \(-0.345440\pi\) | ||||
0.466708 | + | 0.884412i | \(0.345440\pi\) | |||||||
\(402\) | 2.66760e11 | 0.509452 | ||||||||
\(403\) | −3.71923e10 | −0.0702393 | ||||||||
\(404\) | 2.95331e11 | 0.551561 | ||||||||
\(405\) | 5.98418e11 | 1.10524 | ||||||||
\(406\) | −6.96149e10 | −0.127156 | ||||||||
\(407\) | −8.08748e10 | −0.146096 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.08768e11 | −0.368900 | −0.184450 | − | 0.982842i | \(-0.559050\pi\) | ||||
−0.184450 | + | 0.982842i | \(0.559050\pi\) | |||||||
\(410\) | −6.69323e11 | −1.16979 | ||||||||
\(411\) | −4.36520e11 | −0.754599 | ||||||||
\(412\) | −3.23019e11 | −0.552319 | ||||||||
\(413\) | −2.37016e11 | −0.400870 | ||||||||
\(414\) | −1.75575e9 | −0.00293739 | ||||||||
\(415\) | −1.20999e12 | −2.00246 | ||||||||
\(416\) | −7.25349e10 | −0.118748 | ||||||||
\(417\) | −3.96672e10 | −0.0642420 | ||||||||
\(418\) | −9.77333e11 | −1.56585 | ||||||||
\(419\) | 1.79984e11 | 0.285280 | 0.142640 | − | 0.989775i | \(-0.454441\pi\) | ||||
0.142640 | + | 0.989775i | \(0.454441\pi\) | |||||||
\(420\) | −1.34277e11 | −0.210562 | ||||||||
\(421\) | 1.24378e12 | 1.92963 | 0.964813 | − | 0.262937i | \(-0.0846912\pi\) | ||||
0.964813 | + | 0.262937i | \(0.0846912\pi\) | |||||||
\(422\) | −5.48804e10 | −0.0842386 | ||||||||
\(423\) | −1.09253e9 | −0.00165921 | ||||||||
\(424\) | −6.48097e11 | −0.973853 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.33925e11 | −1.07971 | ||||||||
\(427\) | −1.81756e11 | −0.264584 | ||||||||
\(428\) | −3.41092e11 | −0.491331 | ||||||||
\(429\) | 1.50892e11 | 0.215084 | ||||||||
\(430\) | −2.22944e11 | −0.314476 | ||||||||
\(431\) | 8.50306e11 | 1.18694 | 0.593468 | − | 0.804857i | \(-0.297758\pi\) | ||||
0.593468 | + | 0.804857i | \(0.297758\pi\) | |||||||
\(432\) | 8.02750e10 | 0.110893 | ||||||||
\(433\) | 6.91161e11 | 0.944895 | 0.472448 | − | 0.881359i | \(-0.343371\pi\) | ||||
0.472448 | + | 0.881359i | \(0.343371\pi\) | |||||||
\(434\) | −9.27515e10 | −0.125492 | ||||||||
\(435\) | 4.72809e11 | 0.633117 | ||||||||
\(436\) | −3.29369e11 | −0.436509 | ||||||||
\(437\) | 1.03485e12 | 1.35741 | ||||||||
\(438\) | −5.27095e11 | −0.684314 | ||||||||
\(439\) | −1.98550e11 | −0.255140 | −0.127570 | − | 0.991830i | \(-0.540718\pi\) | ||||
−0.127570 | + | 0.991830i | \(0.540718\pi\) | |||||||
\(440\) | −1.54400e12 | −1.96386 | ||||||||
\(441\) | −3.18483e9 | −0.00400971 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.17901e12 | 1.45445 | 0.727227 | − | 0.686397i | \(-0.240809\pi\) | ||||
0.727227 | + | 0.686397i | \(0.240809\pi\) | |||||||
\(444\) | 3.92850e10 | 0.0479737 | ||||||||
\(445\) | 4.36303e11 | 0.527434 | ||||||||
\(446\) | 1.88313e11 | 0.225359 | ||||||||
\(447\) | −2.19134e11 | −0.259613 | ||||||||
\(448\) | −2.12793e11 | −0.249578 | ||||||||
\(449\) | 7.72876e10 | 0.0897432 | 0.0448716 | − | 0.998993i | \(-0.485712\pi\) | ||||
0.0448716 | + | 0.998993i | \(0.485712\pi\) | |||||||
\(450\) | −5.45121e8 | −0.000626667 0 | ||||||||
\(451\) | −2.45792e12 | −2.79752 | ||||||||
\(452\) | 3.99296e11 | 0.449958 | ||||||||
\(453\) | 1.17899e12 | 1.31543 | ||||||||
\(454\) | 6.59062e11 | 0.728073 | ||||||||
\(455\) | 4.19794e10 | 0.0459182 | ||||||||
\(456\) | 1.31177e12 | 1.42075 | ||||||||
\(457\) | −2.62124e11 | −0.281115 | −0.140558 | − | 0.990073i | \(-0.544890\pi\) | ||||
−0.140558 | + | 0.990073i | \(0.544890\pi\) | |||||||
\(458\) | −9.93851e11 | −1.05542 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.91672e11 | 0.616128 | ||||||||
\(461\) | 7.85754e11 | 0.810275 | 0.405138 | − | 0.914256i | \(-0.367224\pi\) | ||||
0.405138 | + | 0.914256i | \(0.367224\pi\) | |||||||
\(462\) | 3.76301e11 | 0.384279 | ||||||||
\(463\) | 1.23202e12 | 1.24596 | 0.622981 | − | 0.782237i | \(-0.285921\pi\) | ||||
0.622981 | + | 0.782237i | \(0.285921\pi\) | |||||||
\(464\) | 6.37120e10 | 0.0638102 | ||||||||
\(465\) | 6.29948e11 | 0.624836 | ||||||||
\(466\) | 9.26998e11 | 0.910630 | ||||||||
\(467\) | 5.56830e10 | 0.0541747 | 0.0270874 | − | 0.999633i | \(-0.491377\pi\) | ||||
0.0270874 | + | 0.999633i | \(0.491377\pi\) | |||||||
\(468\) | −3.29969e8 | −0.000317955 0 | ||||||||
\(469\) | 2.72535e11 | 0.260103 | ||||||||
\(470\) | −2.80966e11 | −0.265591 | ||||||||
\(471\) | 1.15060e12 | 1.07728 | ||||||||
\(472\) | 1.32385e12 | 1.22772 | ||||||||
\(473\) | −8.18705e11 | −0.752059 | ||||||||
\(474\) | −3.42908e11 | −0.312015 | ||||||||
\(475\) | 3.21299e11 | 0.289593 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.82952e9 | −0.00427141 | ||||||||
\(478\) | −1.01641e12 | −0.890519 | ||||||||
\(479\) | −1.63312e12 | −1.41745 | −0.708726 | − | 0.705484i | \(-0.750730\pi\) | ||||
−0.708726 | + | 0.705484i | \(0.750730\pi\) | |||||||
\(480\) | 1.22857e12 | 1.05636 | ||||||||
\(481\) | −1.22818e10 | −0.0104619 | ||||||||
\(482\) | −9.23237e11 | −0.779115 | ||||||||
\(483\) | −3.98448e11 | −0.333127 | ||||||||
\(484\) | −1.36727e12 | −1.13253 | ||||||||
\(485\) | −4.03161e11 | −0.330857 | ||||||||
\(486\) | 7.31813e9 | 0.00595027 | ||||||||
\(487\) | 6.96278e11 | 0.560922 | 0.280461 | − | 0.959865i | \(-0.409513\pi\) | ||||
0.280461 | + | 0.959865i | \(0.409513\pi\) | |||||||
\(488\) | 1.01519e12 | 0.810323 | ||||||||
\(489\) | 1.29906e12 | 1.02740 | ||||||||
\(490\) | −8.19044e11 | −0.641837 | ||||||||
\(491\) | 7.38660e10 | 0.0573559 | 0.0286779 | − | 0.999589i | \(-0.490870\pi\) | ||||
0.0286779 | + | 0.999589i | \(0.490870\pi\) | |||||||
\(492\) | 1.19394e12 | 0.918624 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.48420e11 | −0.112129 | ||||||||
\(495\) | −1.15057e10 | −0.00861367 | ||||||||
\(496\) | 8.48867e10 | 0.0629756 | ||||||||
\(497\) | −7.49814e11 | −0.551251 | ||||||||
\(498\) | −1.64713e12 | −1.20004 | ||||||||
\(499\) | −4.42678e11 | −0.319621 | −0.159811 | − | 0.987148i | \(-0.551088\pi\) | ||||
−0.159811 | + | 0.987148i | \(0.551088\pi\) | |||||||
\(500\) | −6.88437e11 | −0.492606 | ||||||||
\(501\) | −1.51307e12 | −1.07298 | ||||||||
\(502\) | −1.29912e12 | −0.913026 | ||||||||
\(503\) | 7.67499e11 | 0.534591 | 0.267296 | − | 0.963615i | \(-0.413870\pi\) | ||||
0.267296 | + | 0.963615i | \(0.413870\pi\) | |||||||
\(504\) | −2.27375e9 | −0.00156966 | ||||||||
\(505\) | 1.56386e12 | 1.07000 | ||||||||
\(506\) | −1.65812e12 | −1.12444 | ||||||||
\(507\) | −1.46822e12 | −0.986856 | ||||||||
\(508\) | 4.75537e11 | 0.316809 | ||||||||
\(509\) | 1.23640e12 | 0.816452 | 0.408226 | − | 0.912881i | \(-0.366148\pi\) | ||||
0.408226 | + | 0.912881i | \(0.366148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.38506e11 | −0.349379 | ||||||||
\(512\) | 3.43741e11 | 0.221063 | ||||||||
\(513\) | −2.15180e12 | −1.37174 | ||||||||
\(514\) | 3.46012e11 | 0.218654 | ||||||||
\(515\) | −1.71047e12 | −1.07148 | ||||||||
\(516\) | 3.97686e11 | 0.246954 | ||||||||
\(517\) | −1.03178e12 | −0.635154 | ||||||||
\(518\) | −3.06288e10 | −0.0186916 | ||||||||
\(519\) | 2.32569e12 | 1.40701 | ||||||||
\(520\) | −2.34474e11 | −0.140631 | ||||||||
\(521\) | −6.77564e11 | −0.402885 | −0.201442 | − | 0.979500i | \(-0.564563\pi\) | ||||
−0.201442 | + | 0.979500i | \(0.564563\pi\) | |||||||
\(522\) | 2.89751e9 | 0.00170808 | ||||||||
\(523\) | −1.65170e12 | −0.965324 | −0.482662 | − | 0.875807i | \(-0.660330\pi\) | ||||
−0.482662 | + | 0.875807i | \(0.660330\pi\) | |||||||
\(524\) | 1.42274e12 | 0.824397 | ||||||||
\(525\) | −1.23709e11 | −0.0710698 | ||||||||
\(526\) | −3.78985e11 | −0.215867 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.44393e11 | −0.192842 | ||||||||
\(529\) | −4.54466e10 | −0.0252320 | ||||||||
\(530\) | −1.24201e12 | −0.683728 | ||||||||
\(531\) | 9.86511e9 | 0.00538489 | ||||||||
\(532\) | 4.85018e11 | 0.262516 | ||||||||
\(533\) | −3.73264e11 | −0.200329 | ||||||||
\(534\) | 5.93930e11 | 0.316082 | ||||||||
\(535\) | −1.80617e12 | −0.953161 | ||||||||
\(536\) | −1.52223e12 | −0.796600 | ||||||||
\(537\) | 1.69516e12 | 0.879681 | ||||||||
\(538\) | −2.47915e11 | −0.127580 | ||||||||
\(539\) | −3.00773e12 | −1.53493 | ||||||||
\(540\) | −1.23028e12 | −0.622633 | ||||||||
\(541\) | −9.85219e10 | −0.0494476 | −0.0247238 | − | 0.999694i | \(-0.507871\pi\) | ||||
−0.0247238 | + | 0.999694i | \(0.507871\pi\) | |||||||
\(542\) | −1.12450e12 | −0.559710 | ||||||||
\(543\) | −2.88929e12 | −1.42624 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.74409e12 | −0.846809 | ||||||||
\(546\) | 5.71457e10 | 0.0275180 | ||||||||
\(547\) | 1.58944e11 | 0.0759102 | 0.0379551 | − | 0.999279i | \(-0.487916\pi\) | ||||
0.0379551 | + | 0.999279i | \(0.487916\pi\) | |||||||
\(548\) | 9.01495e11 | 0.427022 | ||||||||
\(549\) | 7.56505e9 | 0.00355415 | ||||||||
\(550\) | −5.14809e11 | −0.239891 | ||||||||
\(551\) | −1.70782e12 | −0.789333 | ||||||||
\(552\) | 2.22552e12 | 1.02025 | ||||||||
\(553\) | −3.50332e11 | −0.159300 | ||||||||
\(554\) | −4.59586e11 | −0.207287 | ||||||||
\(555\) | 2.08024e11 | 0.0930669 | ||||||||
\(556\) | 8.19200e10 | 0.0363541 | ||||||||
\(557\) | 2.80868e12 | 1.23639 | 0.618194 | − | 0.786026i | \(-0.287865\pi\) | ||||
0.618194 | + | 0.786026i | \(0.287865\pi\) | |||||||
\(558\) | 3.86051e9 | 0.00168574 | ||||||||
\(559\) | −1.24330e11 | −0.0538546 | ||||||||
\(560\) | −9.58128e10 | −0.0411697 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.78442e11 | −0.371449 | ||||||||
\(563\) | 3.00188e11 | 0.125923 | 0.0629616 | − | 0.998016i | \(-0.479945\pi\) | ||||
0.0629616 | + | 0.998016i | \(0.479945\pi\) | |||||||
\(564\) | 5.01187e11 | 0.208566 | ||||||||
\(565\) | 2.11437e12 | 0.872899 | ||||||||
\(566\) | 2.73314e12 | 1.11940 | ||||||||
\(567\) | 8.32249e11 | 0.338166 | ||||||||
\(568\) | 4.18806e12 | 1.68828 | ||||||||
\(569\) | 4.28791e12 | 1.71491 | 0.857454 | − | 0.514561i | \(-0.172045\pi\) | ||||
0.857454 | + | 0.514561i | \(0.172045\pi\) | |||||||
\(570\) | 2.51387e12 | 0.997484 | ||||||||
\(571\) | −1.67794e11 | −0.0660562 | −0.0330281 | − | 0.999454i | \(-0.510515\pi\) | ||||
−0.0330281 | + | 0.999454i | \(0.510515\pi\) | |||||||
\(572\) | −3.11620e11 | −0.121715 | ||||||||
\(573\) | −4.59143e12 | −1.77931 | ||||||||
\(574\) | −9.30860e11 | −0.357916 | ||||||||
\(575\) | 5.45108e11 | 0.207959 | ||||||||
\(576\) | 8.85686e9 | 0.00335258 | ||||||||
\(577\) | 7.33555e11 | 0.275513 | 0.137756 | − | 0.990466i | \(-0.456011\pi\) | ||||
0.137756 | + | 0.990466i | \(0.456011\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.91165e12 | −1.44646 | ||||||||
\(580\) | −9.76438e11 | −0.358277 | ||||||||
\(581\) | −1.68279e12 | −0.612684 | ||||||||
\(582\) | −5.48815e11 | −0.198277 | ||||||||
\(583\) | −4.56097e12 | −1.63512 | ||||||||
\(584\) | 3.00781e12 | 1.07002 | ||||||||
\(585\) | −1.74727e9 | −0.000616820 0 | ||||||||
\(586\) | −1.31042e12 | −0.459064 | ||||||||
\(587\) | 3.71592e12 | 1.29180 | 0.645899 | − | 0.763423i | \(-0.276483\pi\) | ||||
0.645899 | + | 0.763423i | \(0.276483\pi\) | |||||||
\(588\) | 1.46101e12 | 0.504028 | ||||||||
\(589\) | −2.27542e12 | −0.779008 | ||||||||
\(590\) | 2.53701e12 | 0.861963 | ||||||||
\(591\) | 3.88384e12 | 1.30954 | ||||||||
\(592\) | 2.80316e10 | 0.00937996 | ||||||||
\(593\) | 2.82729e11 | 0.0938910 | 0.0469455 | − | 0.998897i | \(-0.485051\pi\) | ||||
0.0469455 | + | 0.998897i | \(0.485051\pi\) | |||||||
\(594\) | 3.44777e12 | 1.13632 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.52553e11 | 0.146913 | ||||||||
\(597\) | 5.28281e12 | 1.70208 | ||||||||
\(598\) | −2.51805e11 | −0.0805209 | ||||||||
\(599\) | −5.50565e12 | −1.74738 | −0.873691 | − | 0.486482i | \(-0.838280\pi\) | ||||
−0.873691 | + | 0.486482i | \(0.838280\pi\) | |||||||
\(600\) | 6.90974e11 | 0.217661 | ||||||||
\(601\) | −1.54272e12 | −0.482338 | −0.241169 | − | 0.970483i | \(-0.577531\pi\) | ||||
−0.241169 | + | 0.970483i | \(0.577531\pi\) | |||||||
\(602\) | −3.10059e11 | −0.0962188 | ||||||||
\(603\) | −1.13435e10 | −0.00349396 | ||||||||
\(604\) | −2.43482e12 | −0.744391 | ||||||||
\(605\) | −7.24005e12 | −2.19706 | ||||||||
\(606\) | 2.12884e12 | 0.641235 | ||||||||
\(607\) | −3.59153e12 | −1.07382 | −0.536909 | − | 0.843640i | \(-0.680408\pi\) | ||||
−0.536909 | + | 0.843640i | \(0.680408\pi\) | |||||||
\(608\) | −4.43767e12 | −1.31701 | ||||||||
\(609\) | 6.57559e11 | 0.193712 | ||||||||
\(610\) | 1.94551e12 | 0.568916 | ||||||||
\(611\) | −1.56688e11 | −0.0454830 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.79969e12 | 1.65895 | 0.829474 | − | 0.558546i | \(-0.188641\pi\) | ||||
0.829474 | + | 0.558546i | \(0.188641\pi\) | |||||||
\(614\) | −1.86180e12 | −0.528658 | ||||||||
\(615\) | 6.32220e12 | 1.78209 | ||||||||
\(616\) | −2.14732e12 | −0.600873 | ||||||||
\(617\) | 5.14222e12 | 1.42846 | 0.714229 | − | 0.699912i | \(-0.246778\pi\) | ||||
0.714229 | + | 0.699912i | \(0.246778\pi\) | |||||||
\(618\) | −2.32842e12 | −0.642117 | ||||||||
\(619\) | −1.66025e11 | −0.0454534 | −0.0227267 | − | 0.999742i | \(-0.507235\pi\) | ||||
−0.0227267 | + | 0.999742i | \(0.507235\pi\) | |||||||
\(620\) | −1.30096e12 | −0.353591 | ||||||||
\(621\) | −3.65068e12 | −0.985058 | ||||||||
\(622\) | −1.84063e12 | −0.493071 | ||||||||
\(623\) | 6.06788e11 | 0.161377 | ||||||||
\(624\) | −5.23001e10 | −0.0138093 | ||||||||
\(625\) | −4.44895e12 | −1.16627 | ||||||||
\(626\) | 7.33155e11 | 0.190815 | ||||||||
\(627\) | 9.23156e12 | 2.38546 | ||||||||
\(628\) | −2.37620e12 | −0.609627 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4.35741e9 | −0.00110204 | ||||||||
\(631\) | 2.14564e12 | 0.538796 | 0.269398 | − | 0.963029i | \(-0.413175\pi\) | ||||
0.269398 | + | 0.963029i | \(0.413175\pi\) | |||||||
\(632\) | 1.95677e12 | 0.487879 | ||||||||
\(633\) | 5.18382e11 | 0.128331 | ||||||||
\(634\) | 4.37731e12 | 1.07598 | ||||||||
\(635\) | 2.51809e12 | 0.614595 | ||||||||
\(636\) | 2.21549e12 | 0.536924 | ||||||||
\(637\) | −4.56759e11 | −0.109916 | ||||||||
\(638\) | 2.73639e12 | 0.653861 | ||||||||
\(639\) | 3.12088e10 | 0.00740496 | ||||||||
\(640\) | −2.19574e12 | −0.517333 | ||||||||
\(641\) | 6.35807e11 | 0.148752 | 0.0743762 | − | 0.997230i | \(-0.476303\pi\) | ||||
0.0743762 | + | 0.997230i | \(0.476303\pi\) | |||||||
\(642\) | −2.45870e12 | −0.571213 | ||||||||
\(643\) | −4.36286e12 | −1.00652 | −0.503259 | − | 0.864135i | \(-0.667866\pi\) | ||||
−0.503259 | + | 0.864135i | \(0.667866\pi\) | |||||||
\(644\) | 8.22868e11 | 0.188514 | ||||||||
\(645\) | 2.10585e12 | 0.479081 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.37030e12 | 1.20484 | 0.602419 | − | 0.798180i | \(-0.294204\pi\) | ||||
0.602419 | + | 0.798180i | \(0.294204\pi\) | |||||||
\(648\) | −4.64850e12 | −1.03568 | ||||||||
\(649\) | 9.31655e12 | 2.06136 | ||||||||
\(650\) | −7.81798e10 | −0.0171785 | ||||||||
\(651\) | 8.76099e11 | 0.191178 | ||||||||
\(652\) | −2.68280e12 | −0.581399 | ||||||||
\(653\) | −1.91038e12 | −0.411160 | −0.205580 | − | 0.978640i | \(-0.565908\pi\) | ||||
−0.205580 | + | 0.978640i | \(0.565908\pi\) | |||||||
\(654\) | −2.37420e12 | −0.507478 | ||||||||
\(655\) | 7.53380e12 | 1.59929 | ||||||||
\(656\) | 8.51928e11 | 0.179612 | ||||||||
\(657\) | 2.24137e10 | 0.00469321 | ||||||||
\(658\) | −3.90754e11 | −0.0812619 | ||||||||
\(659\) | −4.74561e11 | −0.0980184 | −0.0490092 | − | 0.998798i | \(-0.515606\pi\) | ||||
−0.0490092 | + | 0.998798i | \(0.515606\pi\) | |||||||
\(660\) | 5.27810e12 | 1.08275 | ||||||||
\(661\) | −6.60336e12 | −1.34542 | −0.672710 | − | 0.739906i | \(-0.734870\pi\) | ||||
−0.672710 | + | 0.739906i | \(0.734870\pi\) | |||||||
\(662\) | −4.57186e11 | −0.0925192 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.39915e12 | 1.87643 | ||||||||
\(665\) | 2.56829e12 | 0.509269 | ||||||||
\(666\) | 1.27483e9 | 0.000251084 0 | ||||||||
\(667\) | −2.89744e12 | −0.566825 | ||||||||
\(668\) | 3.12478e12 | 0.607190 | ||||||||
\(669\) | −1.77874e12 | −0.343317 | ||||||||
\(670\) | −2.91720e12 | −0.559281 | ||||||||
\(671\) | 7.14438e12 | 1.36055 | ||||||||
\(672\) | 1.70863e12 | 0.323211 | ||||||||
\(673\) | −2.74504e12 | −0.515800 | −0.257900 | − | 0.966172i | \(-0.583031\pi\) | ||||
−0.257900 | + | 0.966172i | \(0.583031\pi\) | |||||||
\(674\) | −6.36418e12 | −1.18788 | ||||||||
\(675\) | −1.13346e12 | −0.210154 | ||||||||
\(676\) | 3.03214e12 | 0.558455 | ||||||||
\(677\) | −1.15812e12 | −0.211887 | −0.105943 | − | 0.994372i | \(-0.533786\pi\) | ||||
−0.105943 | + | 0.994372i | \(0.533786\pi\) | |||||||
\(678\) | 2.87825e12 | 0.523113 | ||||||||
\(679\) | −5.60696e11 | −0.101231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.22527e12 | −1.10917 | ||||||||
\(682\) | 3.64584e12 | 0.645309 | ||||||||
\(683\) | 6.11786e12 | 1.07574 | 0.537869 | − | 0.843029i | \(-0.319230\pi\) | ||||
0.537869 | + | 0.843029i | \(0.319230\pi\) | |||||||
\(684\) | −2.01874e10 | −0.00352637 | ||||||||
\(685\) | 4.77365e12 | 0.828405 | ||||||||
\(686\) | −2.42377e12 | −0.417861 | ||||||||
\(687\) | 9.38758e12 | 1.60786 | ||||||||
\(688\) | 2.83767e11 | 0.0482853 | ||||||||
\(689\) | −6.92636e11 | −0.117090 | ||||||||
\(690\) | 4.26497e12 | 0.716300 | ||||||||
\(691\) | 2.38401e12 | 0.397793 | 0.198897 | − | 0.980020i | \(-0.436264\pi\) | ||||
0.198897 | + | 0.980020i | \(0.436264\pi\) | |||||||
\(692\) | −4.80297e12 | −0.796219 | ||||||||
\(693\) | −1.60015e10 | −0.00263549 | ||||||||
\(694\) | −1.95529e12 | −0.319958 | ||||||||
\(695\) | 4.33787e11 | 0.0705253 | ||||||||
\(696\) | −3.67277e12 | −0.593270 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.83579e12 | 0.452194 | ||||||||
\(699\) | −8.75611e12 | −1.38728 | ||||||||
\(700\) | 2.55482e11 | 0.0402179 | ||||||||
\(701\) | −3.30170e12 | −0.516424 | −0.258212 | − | 0.966088i | \(-0.583133\pi\) | ||||
−0.258212 | + | 0.966088i | \(0.583133\pi\) | |||||||
\(702\) | 5.23584e11 | 0.0813709 | ||||||||
\(703\) | −7.51398e11 | −0.116030 | ||||||||
\(704\) | 8.36436e12 | 1.28338 | ||||||||
\(705\) | 2.65391e12 | 0.404609 | ||||||||
\(706\) | 7.75209e11 | 0.117435 | ||||||||
\(707\) | 2.17493e12 | 0.327385 | ||||||||
\(708\) | −4.52551e12 | −0.676890 | ||||||||
\(709\) | 6.50115e12 | 0.966234 | 0.483117 | − | 0.875556i | \(-0.339505\pi\) | ||||
0.483117 | + | 0.875556i | \(0.339505\pi\) | |||||||
\(710\) | 8.02597e12 | 1.18532 | ||||||||
\(711\) | 1.45815e10 | 0.00213988 | ||||||||
\(712\) | −3.38919e12 | −0.494238 | ||||||||
\(713\) | −3.86041e12 | −0.559411 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.65011e12 | −0.236122 | ||||||||
\(716\) | −3.50081e12 | −0.497805 | ||||||||
\(717\) | 9.60066e12 | 1.35664 | ||||||||
\(718\) | −9.15875e12 | −1.28610 | ||||||||
\(719\) | −2.37012e12 | −0.330742 | −0.165371 | − | 0.986231i | \(-0.552882\pi\) | ||||
−0.165371 | + | 0.986231i | \(0.552882\pi\) | |||||||
\(720\) | 3.98792e9 | 0.000553032 0 | ||||||||
\(721\) | −2.37883e12 | −0.327835 | ||||||||
\(722\) | −4.27659e12 | −0.585706 | ||||||||
\(723\) | 8.72058e12 | 1.18692 | ||||||||
\(724\) | 5.96691e12 | 0.807097 | ||||||||
\(725\) | −8.99592e11 | −0.120927 | ||||||||
\(726\) | −9.85573e12 | −1.31666 | ||||||||
\(727\) | −6.84668e12 | −0.909023 | −0.454512 | − | 0.890741i | \(-0.650186\pi\) | ||||
−0.454512 | + | 0.890741i | \(0.650186\pi\) | |||||||
\(728\) | −3.26095e11 | −0.0430282 | ||||||||
\(729\) | 7.59080e12 | 0.995437 | ||||||||
\(730\) | 5.76414e12 | 0.751246 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.47039e12 | −0.446764 | ||||||||
\(733\) | 1.22017e13 | 1.56118 | 0.780592 | − | 0.625041i | \(-0.214918\pi\) | ||||
0.780592 | + | 0.625041i | \(0.214918\pi\) | |||||||
\(734\) | 8.33691e12 | 1.06016 | ||||||||
\(735\) | 7.73641e12 | 0.977792 | ||||||||
\(736\) | −7.52884e12 | −0.945753 | ||||||||
\(737\) | −1.07127e13 | −1.33750 | ||||||||
\(738\) | 3.87443e10 | 0.00480789 | ||||||||
\(739\) | 6.41729e12 | 0.791501 | 0.395751 | − | 0.918358i | \(-0.370484\pi\) | ||||
0.395751 | + | 0.918358i | \(0.370484\pi\) | |||||||
\(740\) | −4.29608e11 | −0.0526659 | ||||||||
\(741\) | 1.40192e12 | 0.170821 | ||||||||
\(742\) | −1.72732e12 | −0.209197 | ||||||||
\(743\) | −1.87182e11 | −0.0225327 | −0.0112664 | − | 0.999937i | \(-0.503586\pi\) | ||||
−0.0112664 | + | 0.999937i | \(0.503586\pi\) | |||||||
\(744\) | −4.89342e12 | −0.585510 | ||||||||
\(745\) | 2.39638e12 | 0.285005 | ||||||||
\(746\) | 2.98947e11 | 0.0353402 | ||||||||
\(747\) | 7.00411e10 | 0.00823019 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.51193e12 | −0.291635 | ||||||||
\(750\) | −4.96248e12 | −0.572695 | ||||||||
\(751\) | −1.47873e13 | −1.69633 | −0.848163 | − | 0.529735i | \(-0.822291\pi\) | ||||
−0.848163 | + | 0.529735i | \(0.822291\pi\) | |||||||
\(752\) | 3.57620e11 | 0.0407795 | ||||||||
\(753\) | 1.22711e13 | 1.39093 | ||||||||
\(754\) | 4.15554e11 | 0.0468226 | ||||||||
\(755\) | −1.28930e13 | −1.44409 | ||||||||
\(756\) | −1.71101e12 | −0.190504 | ||||||||
\(757\) | 1.41642e13 | 1.56770 | 0.783848 | − | 0.620952i | \(-0.213254\pi\) | ||||
0.783848 | + | 0.620952i | \(0.213254\pi\) | |||||||
\(758\) | −3.31017e11 | −0.0364200 | ||||||||
\(759\) | 1.56620e13 | 1.71301 | ||||||||
\(760\) | −1.43451e13 | −1.55971 | ||||||||
\(761\) | −1.94664e12 | −0.210404 | −0.105202 | − | 0.994451i | \(-0.533549\pi\) | ||||
−0.105202 | + | 0.994451i | \(0.533549\pi\) | |||||||
\(762\) | 3.42782e12 | 0.368316 | ||||||||
\(763\) | −2.42560e12 | −0.259095 | ||||||||
\(764\) | 9.48215e12 | 1.00690 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.57632e12 | −0.165430 | ||||||||
\(767\) | 1.41483e12 | 0.147613 | ||||||||
\(768\) | −1.01526e13 | −1.05306 | ||||||||
\(769\) | −9.54772e12 | −0.984535 | −0.492267 | − | 0.870444i | \(-0.663832\pi\) | ||||
−0.492267 | + | 0.870444i | \(0.663832\pi\) | |||||||
\(770\) | −4.11511e12 | −0.421864 | ||||||||
\(771\) | −3.26831e12 | −0.333103 | ||||||||
\(772\) | 8.07827e12 | 0.818542 | ||||||||
\(773\) | −6.14763e12 | −0.619298 | −0.309649 | − | 0.950851i | \(-0.600212\pi\) | ||||
−0.309649 | + | 0.950851i | \(0.600212\pi\) | |||||||
\(774\) | 1.29053e10 | 0.00129251 | ||||||||
\(775\) | −1.19857e12 | −0.119346 | ||||||||
\(776\) | 3.13175e12 | 0.310034 | ||||||||
\(777\) | 2.89309e11 | 0.0284753 | ||||||||
\(778\) | −9.55327e11 | −0.0934854 | ||||||||
\(779\) | −2.28362e13 | −2.22180 | ||||||||
\(780\) | 8.01541e11 | 0.0775354 | ||||||||
\(781\) | 2.94734e13 | 2.83465 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.02473e12 | 0.572808 | ||||||||
\(784\) | 1.04250e12 | 0.0985490 | ||||||||
\(785\) | −1.25826e13 | −1.18265 | ||||||||
\(786\) | 1.02556e13 | 0.958429 | ||||||||
\(787\) | −9.50792e12 | −0.883485 | −0.441742 | − | 0.897142i | \(-0.645639\pi\) | ||||
−0.441742 | + | 0.897142i | \(0.645639\pi\) | |||||||
\(788\) | −8.02085e12 | −0.741058 | ||||||||
\(789\) | 3.57977e12 | 0.328858 | ||||||||
\(790\) | 3.74994e12 | 0.342533 | ||||||||
\(791\) | 2.94057e12 | 0.267077 | ||||||||
\(792\) | 8.93757e10 | 0.00807154 | ||||||||
\(793\) | 1.08496e12 | 0.0974280 | ||||||||
\(794\) | −2.04033e12 | −0.182183 | ||||||||
\(795\) | 1.17316e13 | 1.04161 | ||||||||
\(796\) | −1.09100e13 | −0.963196 | ||||||||
\(797\) | 4.57017e12 | 0.401208 | 0.200604 | − | 0.979672i | \(-0.435710\pi\) | ||||
0.200604 | + | 0.979672i | \(0.435710\pi\) | |||||||
\(798\) | 3.49616e12 | 0.305196 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2.33754e12 | −0.201769 | ||||||||
\(801\) | −2.52557e10 | −0.00216777 | ||||||||
\(802\) | −7.19478e12 | −0.614091 | ||||||||
\(803\) | 2.11674e13 | 1.79658 | ||||||||
\(804\) | 5.20369e12 | 0.439197 | ||||||||
\(805\) | 4.35730e12 | 0.365709 | ||||||||
\(806\) | 5.53663e11 | 0.0462102 | ||||||||
\(807\) | 2.34172e12 | 0.194359 | ||||||||
\(808\) | −1.21480e13 | −1.00266 | ||||||||
\(809\) | −1.08135e13 | −0.887560 | −0.443780 | − | 0.896136i | \(-0.646363\pi\) | ||||
−0.443780 | + | 0.896136i | \(0.646363\pi\) | |||||||
\(810\) | −8.90836e12 | −0.727135 | ||||||||
\(811\) | 1.66684e13 | 1.35301 | 0.676504 | − | 0.736439i | \(-0.263494\pi\) | ||||
0.676504 | + | 0.736439i | \(0.263494\pi\) | |||||||
\(812\) | −1.35798e12 | −0.109620 | ||||||||
\(813\) | 1.06217e13 | 0.852678 | ||||||||
\(814\) | 1.20394e12 | 0.0961162 | ||||||||
\(815\) | −1.42061e13 | −1.12789 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.60648e12 | −0.597289 | ||||||||
\(818\) | 3.10782e12 | 0.242698 | ||||||||
\(819\) | −2.43001e9 | −0.000188726 0 | ||||||||
\(820\) | −1.30565e13 | −1.00847 | ||||||||
\(821\) | −7.04533e12 | −0.541199 | −0.270600 | − | 0.962692i | \(-0.587222\pi\) | ||||
−0.270600 | + | 0.962692i | \(0.587222\pi\) | |||||||
\(822\) | 6.49827e12 | 0.496449 | ||||||||
\(823\) | 4.13230e12 | 0.313973 | 0.156986 | − | 0.987601i | \(-0.449822\pi\) | ||||
0.156986 | + | 0.987601i | \(0.449822\pi\) | |||||||
\(824\) | 1.32869e13 | 1.00404 | ||||||||
\(825\) | 4.86271e12 | 0.365457 | ||||||||
\(826\) | 3.52835e12 | 0.263731 | ||||||||
\(827\) | −3.87796e12 | −0.288289 | −0.144145 | − | 0.989557i | \(-0.546043\pi\) | ||||
−0.144145 | + | 0.989557i | \(0.546043\pi\) | |||||||
\(828\) | −3.42495e10 | −0.00253231 | ||||||||
\(829\) | 2.77616e12 | 0.204150 | 0.102075 | − | 0.994777i | \(-0.467452\pi\) | ||||
0.102075 | + | 0.994777i | \(0.467452\pi\) | |||||||
\(830\) | 1.80125e13 | 1.31741 | ||||||||
\(831\) | 4.34109e12 | 0.315787 | ||||||||
\(832\) | 1.27023e12 | 0.0919023 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.90506e11 | 0.0422646 | ||||||||
\(835\) | 1.65465e13 | 1.17792 | ||||||||
\(836\) | −1.90649e13 | −1.34991 | ||||||||
\(837\) | 8.02705e12 | 0.565316 | ||||||||
\(838\) | −2.67934e12 | −0.187685 | ||||||||
\(839\) | −1.10624e13 | −0.770760 | −0.385380 | − | 0.922758i | \(-0.625930\pi\) | ||||
−0.385380 | + | 0.922758i | \(0.625930\pi\) | |||||||
\(840\) | 5.52327e12 | 0.382771 | ||||||||
\(841\) | −9.72549e12 | −0.670393 | ||||||||
\(842\) | −1.85155e13 | −1.26950 | ||||||||
\(843\) | 8.29746e12 | 0.565876 | ||||||||
\(844\) | −1.07055e12 | −0.0726218 | ||||||||
\(845\) | 1.60559e13 | 1.08338 | ||||||||
\(846\) | 1.62640e10 | 0.00109159 | ||||||||
\(847\) | −1.00691e13 | −0.672226 | ||||||||
\(848\) | 1.58086e12 | 0.104981 | ||||||||
\(849\) | −2.58163e13 | −1.70533 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.27480e12 | −0.0833220 | ||||||||
\(852\) | −1.43167e13 | −0.930818 | ||||||||
\(853\) | 2.50474e13 | 1.61992 | 0.809958 | − | 0.586488i | \(-0.199490\pi\) | ||||
0.809958 | + | 0.586488i | \(0.199490\pi\) | |||||||
\(854\) | 2.70571e12 | 0.174069 | ||||||||
\(855\) | −1.06898e11 | −0.00684101 | ||||||||
\(856\) | 1.40303e13 | 0.893171 | ||||||||
\(857\) | −2.13270e12 | −0.135057 | −0.0675284 | − | 0.997717i | \(-0.521511\pi\) | ||||
−0.0675284 | + | 0.997717i | \(0.521511\pi\) | |||||||
\(858\) | −2.24626e12 | −0.141503 | ||||||||
\(859\) | 4.78118e11 | 0.0299617 | 0.0149808 | − | 0.999888i | \(-0.495231\pi\) | ||||
0.0149808 | + | 0.999888i | \(0.495231\pi\) | |||||||
\(860\) | −4.34897e12 | −0.271109 | ||||||||
\(861\) | 8.79259e12 | 0.545259 | ||||||||
\(862\) | −1.26581e13 | −0.780882 | ||||||||
\(863\) | 8.51279e12 | 0.522424 | 0.261212 | − | 0.965281i | \(-0.415878\pi\) | ||||
0.261212 | + | 0.965281i | \(0.415878\pi\) | |||||||
\(864\) | 1.56549e13 | 0.955737 | ||||||||
\(865\) | −2.54330e13 | −1.54463 | ||||||||
\(866\) | −1.02890e13 | −0.621644 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.80931e12 | −0.108187 | ||||||||
\(869\) | 1.37707e13 | 0.819157 | ||||||||
\(870\) | −7.03848e12 | −0.416526 | ||||||||
\(871\) | −1.62685e12 | −0.0957779 | ||||||||
\(872\) | 1.35481e13 | 0.793512 | ||||||||
\(873\) | 2.33373e10 | 0.00135984 | ||||||||
\(874\) | −1.54054e13 | −0.893039 | ||||||||
\(875\) | −5.06991e12 | −0.292391 | ||||||||
\(876\) | −1.02821e13 | −0.589945 | ||||||||
\(877\) | 1.88647e13 | 1.07684 | 0.538421 | − | 0.842676i | \(-0.319021\pi\) | ||||
0.538421 | + | 0.842676i | \(0.319021\pi\) | |||||||
\(878\) | 2.95571e12 | 0.167856 | ||||||||
\(879\) | 1.23778e13 | 0.699350 | ||||||||
\(880\) | 3.76617e12 | 0.211703 | ||||||||
\(881\) | 2.99720e12 | 0.167619 | 0.0838095 | − | 0.996482i | \(-0.473291\pi\) | ||||
0.0838095 | + | 0.996482i | \(0.473291\pi\) | |||||||
\(882\) | 4.74110e10 | 0.00263797 | ||||||||
\(883\) | −9.35302e12 | −0.517760 | −0.258880 | − | 0.965909i | \(-0.583353\pi\) | ||||
−0.258880 | + | 0.965909i | \(0.583353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.39638e13 | −1.31314 | ||||||||
\(886\) | −1.75513e13 | −0.956881 | ||||||||
\(887\) | −1.00237e13 | −0.543716 | −0.271858 | − | 0.962337i | \(-0.587638\pi\) | ||||
−0.271858 | + | 0.962337i | \(0.587638\pi\) | |||||||
\(888\) | −1.61593e12 | −0.0872094 | ||||||||
\(889\) | 3.50203e12 | 0.188045 | ||||||||
\(890\) | −6.49502e12 | −0.346997 | ||||||||
\(891\) | −3.27137e13 | −1.73892 | ||||||||
\(892\) | 3.67343e12 | 0.194281 | ||||||||
\(893\) | −9.58613e12 | −0.504442 | ||||||||
\(894\) | 3.26215e12 | 0.170799 | ||||||||
\(895\) | −1.85377e13 | −0.965721 | ||||||||
\(896\) | −3.05372e12 | −0.158286 | ||||||||
\(897\) | 2.37846e12 | 0.122668 | ||||||||
\(898\) | −1.15054e12 | −0.0590418 | ||||||||
\(899\) | 6.37084e12 | 0.325296 | ||||||||
\(900\) | −1.06337e10 | −0.000540248 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.65899e13 | 1.84048 | ||||||||
\(903\) | 2.92871e12 | 0.146582 | ||||||||
\(904\) | −1.64244e13 | −0.817960 | ||||||||
\(905\) | 3.15963e13 | 1.56573 | ||||||||
\(906\) | −1.75510e13 | −0.865416 | ||||||||
\(907\) | 9.97808e12 | 0.489569 | 0.244785 | − | 0.969577i | \(-0.421283\pi\) | ||||
0.244785 | + | 0.969577i | \(0.421283\pi\) | |||||||
\(908\) | 1.28563e13 | 0.627669 | ||||||||
\(909\) | −9.05251e10 | −0.00439776 | ||||||||
\(910\) | −6.24927e11 | −0.0302095 | ||||||||
\(911\) | −2.06967e13 | −0.995562 | −0.497781 | − | 0.867303i | \(-0.665852\pi\) | ||||
−0.497781 | + | 0.867303i | \(0.665852\pi\) | |||||||
\(912\) | −3.19971e12 | −0.153156 | ||||||||
\(913\) | 6.61463e13 | 3.15056 | ||||||||
\(914\) | 3.90212e12 | 0.184945 | ||||||||
\(915\) | −1.83766e13 | −0.866702 | ||||||||
\(916\) | −1.93871e13 | −0.909878 | ||||||||
\(917\) | 1.04776e13 | 0.489329 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.75832e13 | 0.813164 | 0.406582 | − | 0.913614i | \(-0.366721\pi\) | ||||
0.406582 | + | 0.913614i | \(0.366721\pi\) | |||||||
\(920\) | −2.43375e13 | −1.12003 | ||||||||
\(921\) | 1.75859e13 | 0.805373 | ||||||||
\(922\) | −1.16971e13 | −0.533078 | ||||||||
\(923\) | 4.47588e12 | 0.202988 | ||||||||
\(924\) | 7.34051e12 | 0.331286 | ||||||||
\(925\) | −3.95798e11 | −0.0177761 | ||||||||
\(926\) | −1.83405e13 | −0.819715 | ||||||||
\(927\) | 9.90119e10 | 0.00440381 | ||||||||
\(928\) | 1.24248e13 | 0.549953 | ||||||||
\(929\) | 2.50697e13 | 1.10428 | 0.552138 | − | 0.833753i | \(-0.313812\pi\) | ||||
0.552138 | + | 0.833753i | \(0.313812\pi\) | |||||||
\(930\) | −9.37772e12 | −0.411078 | ||||||||
\(931\) | −2.79445e13 | −1.21905 | ||||||||
\(932\) | 1.80830e13 | 0.785052 | ||||||||
\(933\) | 1.73860e13 | 0.751158 | ||||||||
\(934\) | −8.28926e11 | −0.0356414 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.35728e10 | 0.000577998 0 | ||||||||
\(937\) | −3.59638e13 | −1.52418 | −0.762091 | − | 0.647470i | \(-0.775827\pi\) | ||||
−0.762091 | + | 0.647470i | \(0.775827\pi\) | |||||||
\(938\) | −4.05710e12 | −0.171121 | ||||||||
\(939\) | −6.92514e12 | −0.290692 | ||||||||
\(940\) | −5.48082e12 | −0.228966 | ||||||||
\(941\) | 4.41801e13 | 1.83685 | 0.918425 | − | 0.395596i | \(-0.129462\pi\) | ||||
0.918425 | + | 0.395596i | \(0.129462\pi\) | |||||||
\(942\) | −1.71284e13 | −0.708741 | ||||||||
\(943\) | −3.87434e13 | −1.59549 | ||||||||
\(944\) | −3.22916e12 | −0.132348 | ||||||||
\(945\) | −9.06024e12 | −0.369570 | ||||||||
\(946\) | 1.21877e13 | 0.494778 | ||||||||
\(947\) | −1.28335e13 | −0.518527 | −0.259263 | − | 0.965807i | \(-0.583480\pi\) | ||||
−0.259263 | + | 0.965807i | \(0.583480\pi\) | |||||||
\(948\) | −6.68912e12 | −0.268987 | ||||||||
\(949\) | 3.21451e12 | 0.128652 | ||||||||
\(950\) | −4.78303e12 | −0.190523 | ||||||||
\(951\) | −4.13466e13 | −1.63918 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.92880e13 | −1.54291 | −0.771457 | − | 0.636281i | \(-0.780472\pi\) | ||||
−0.771457 | + | 0.636281i | \(0.780472\pi\) | |||||||
\(954\) | 7.18947e10 | 0.00281015 | ||||||||
\(955\) | 5.02104e13 | 1.95334 | ||||||||
\(956\) | −1.98271e13 | −0.767714 | ||||||||
\(957\) | −2.58471e13 | −0.996110 | ||||||||
\(958\) | 2.43115e13 | 0.932537 | ||||||||
\(959\) | 6.63895e12 | 0.253464 | ||||||||
\(960\) | −2.15146e13 | −0.817546 | ||||||||
\(961\) | −1.79514e13 | −0.678959 | ||||||||
\(962\) | 1.82833e11 | 0.00688283 | ||||||||
\(963\) | 1.04552e11 | 0.00391753 | ||||||||
\(964\) | −1.80096e13 | −0.671673 | ||||||||
\(965\) | 4.27765e13 | 1.58794 | ||||||||
\(966\) | 5.93150e12 | 0.219163 | ||||||||
\(967\) | −1.46165e13 | −0.537556 | −0.268778 | − | 0.963202i | \(-0.586620\pi\) | ||||
−0.268778 | + | 0.963202i | \(0.586620\pi\) | |||||||
\(968\) | 5.62406e13 | 2.05878 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.00167e12 | 0.217670 | ||||||||
\(971\) | 2.39472e13 | 0.864508 | 0.432254 | − | 0.901752i | \(-0.357718\pi\) | ||||
0.432254 | + | 0.901752i | \(0.357718\pi\) | |||||||
\(972\) | 1.42755e11 | 0.00512971 | ||||||||
\(973\) | 6.03290e11 | 0.0215783 | ||||||||
\(974\) | −1.03652e13 | −0.369029 | ||||||||
\(975\) | 7.38460e11 | 0.0261701 | ||||||||
\(976\) | −2.47628e12 | −0.0873526 | ||||||||
\(977\) | 4.54828e13 | 1.59706 | 0.798530 | − | 0.601954i | \(-0.205611\pi\) | ||||
0.798530 | + | 0.601954i | \(0.205611\pi\) | |||||||
\(978\) | −1.93385e13 | −0.675923 | ||||||||
\(979\) | −2.38514e13 | −0.829833 | ||||||||
\(980\) | −1.59771e13 | −0.553326 | ||||||||
\(981\) | 1.00958e11 | 0.00348042 | ||||||||
\(982\) | −1.09961e12 | −0.0377343 | ||||||||
\(983\) | −3.89910e12 | −0.133191 | −0.0665954 | − | 0.997780i | \(-0.521214\pi\) | ||||
−0.0665954 | + | 0.997780i | \(0.521214\pi\) | |||||||
\(984\) | −4.91107e13 | −1.66993 | ||||||||
\(985\) | −4.24725e13 | −1.43762 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.69093e12 | 0.123797 | ||||||||
\(988\) | −2.89522e12 | −0.0966665 | ||||||||
\(989\) | −1.29050e13 | −0.428917 | ||||||||
\(990\) | 1.71279e11 | 0.00566691 | ||||||||
\(991\) | −1.86771e13 | −0.615147 | −0.307574 | − | 0.951524i | \(-0.599517\pi\) | ||||
−0.307574 | + | 0.951524i | \(0.599517\pi\) | |||||||
\(992\) | 1.65543e13 | 0.542759 | ||||||||
\(993\) | 4.31842e12 | 0.140946 | ||||||||
\(994\) | 1.11621e13 | 0.362667 | ||||||||
\(995\) | −5.77711e13 | −1.86856 | ||||||||
\(996\) | −3.21306e13 | −1.03455 | ||||||||
\(997\) | 4.71408e13 | 1.51101 | 0.755507 | − | 0.655140i | \(-0.227390\pi\) | ||||
0.755507 | + | 0.655140i | \(0.227390\pi\) | |||||||
\(998\) | 6.58993e12 | 0.210278 | ||||||||
\(999\) | 2.65073e12 | 0.0842016 |
(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.1.18 | 52 | ||
17.11 | odd | 16 | 17.10.d.a.2.5 | ✓ | 52 | ||
17.14 | odd | 16 | 17.10.d.a.9.5 | yes | 52 | ||
17.16 | even | 2 | inner | 289.10.a.i.1.17 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.d.a.2.5 | ✓ | 52 | 17.11 | odd | 16 | ||
17.10.d.a.9.5 | yes | 52 | 17.14 | odd | 16 | ||
289.10.a.i.1.17 | 52 | 17.16 | even | 2 | inner | ||
289.10.a.i.1.18 | 52 | 1.1 | even | 1 | trivial |