Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(46.8682610909\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + \cdots - 24\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-34.2541\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 36.2541 | 1.60222 | 0.801110 | − | 0.598517i | \(-0.204243\pi\) | ||||
0.801110 | + | 0.598517i | \(0.204243\pi\) | |||||||
\(3\) | −166.815 | −1.18902 | −0.594511 | − | 0.804088i | \(-0.702654\pi\) | ||||
−0.594511 | + | 0.804088i | \(0.702654\pi\) | |||||||
\(4\) | 802.361 | 1.56711 | ||||||||
\(5\) | 2128.44 | 1.52299 | 0.761495 | − | 0.648170i | \(-0.224465\pi\) | ||||
0.761495 | + | 0.648170i | \(0.224465\pi\) | |||||||
\(6\) | −6047.74 | −1.90508 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | 10526.8 | 0.908636 | ||||||||
\(9\) | 8144.30 | 0.413773 | ||||||||
\(10\) | 77164.9 | 2.44017 | ||||||||
\(11\) | 43107.8 | 0.887745 | 0.443873 | − | 0.896090i | \(-0.353604\pi\) | ||||
0.443873 | + | 0.896090i | \(0.353604\pi\) | |||||||
\(12\) | −133846. | −1.86333 | ||||||||
\(13\) | −28561.0 | −0.277350 | ||||||||
\(14\) | 87046.1 | 0.605582 | ||||||||
\(15\) | −355057. | −1.81087 | ||||||||
\(16\) | −29170.1 | −0.111275 | ||||||||
\(17\) | 525481. | 1.52594 | 0.762969 | − | 0.646435i | \(-0.223741\pi\) | ||||
0.762969 | + | 0.646435i | \(0.223741\pi\) | |||||||
\(18\) | 295264. | 0.662956 | ||||||||
\(19\) | −730842. | −1.28657 | −0.643283 | − | 0.765628i | \(-0.722428\pi\) | ||||
−0.643283 | + | 0.765628i | \(0.722428\pi\) | |||||||
\(20\) | 1.70778e6 | 2.38670 | ||||||||
\(21\) | −400523. | −0.449408 | ||||||||
\(22\) | 1.56283e6 | 1.42236 | ||||||||
\(23\) | 1.94924e6 | 1.45241 | 0.726206 | − | 0.687477i | \(-0.241282\pi\) | ||||
0.726206 | + | 0.687477i | \(0.241282\pi\) | |||||||
\(24\) | −1.75602e6 | −1.08039 | ||||||||
\(25\) | 2.57715e6 | 1.31950 | ||||||||
\(26\) | −1.03545e6 | −0.444376 | ||||||||
\(27\) | 1.92483e6 | 0.697037 | ||||||||
\(28\) | 1.92647e6 | 0.592312 | ||||||||
\(29\) | −3.37235e6 | −0.885404 | −0.442702 | − | 0.896669i | \(-0.645980\pi\) | ||||
−0.442702 | + | 0.896669i | \(0.645980\pi\) | |||||||
\(30\) | −1.28723e7 | −2.90141 | ||||||||
\(31\) | 479891. | 0.0933286 | 0.0466643 | − | 0.998911i | \(-0.485141\pi\) | ||||
0.0466643 | + | 0.998911i | \(0.485141\pi\) | |||||||
\(32\) | −6.44724e6 | −1.08692 | ||||||||
\(33\) | −7.19103e6 | −1.05555 | ||||||||
\(34\) | 1.90509e7 | 2.44489 | ||||||||
\(35\) | 5.11040e6 | 0.575636 | ||||||||
\(36\) | 6.53466e6 | 0.648428 | ||||||||
\(37\) | 7.24197e6 | 0.635256 | 0.317628 | − | 0.948215i | \(-0.397114\pi\) | ||||
0.317628 | + | 0.948215i | \(0.397114\pi\) | |||||||
\(38\) | −2.64960e7 | −2.06136 | ||||||||
\(39\) | 4.76441e6 | 0.329775 | ||||||||
\(40\) | 2.24056e7 | 1.38384 | ||||||||
\(41\) | 2.74246e7 | 1.51570 | 0.757849 | − | 0.652430i | \(-0.226250\pi\) | ||||
0.757849 | + | 0.652430i | \(0.226250\pi\) | |||||||
\(42\) | −1.45206e7 | −0.720051 | ||||||||
\(43\) | 3.54975e7 | 1.58340 | 0.791698 | − | 0.610913i | \(-0.209197\pi\) | ||||
0.791698 | + | 0.610913i | \(0.209197\pi\) | |||||||
\(44\) | 3.45880e7 | 1.39119 | ||||||||
\(45\) | 1.73347e7 | 0.630173 | ||||||||
\(46\) | 7.06680e7 | 2.32709 | ||||||||
\(47\) | 1.65313e6 | 0.0494158 | 0.0247079 | − | 0.999695i | \(-0.492134\pi\) | ||||
0.0247079 | + | 0.999695i | \(0.492134\pi\) | |||||||
\(48\) | 4.86602e6 | 0.132309 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | 9.34323e7 | 2.11413 | ||||||||
\(51\) | −8.76582e7 | −1.81437 | ||||||||
\(52\) | −2.29162e7 | −0.434638 | ||||||||
\(53\) | 2.21254e7 | 0.385168 | 0.192584 | − | 0.981280i | \(-0.438313\pi\) | ||||
0.192584 | + | 0.981280i | \(0.438313\pi\) | |||||||
\(54\) | 6.97830e7 | 1.11681 | ||||||||
\(55\) | 9.17525e7 | 1.35203 | ||||||||
\(56\) | 2.52748e7 | 0.343432 | ||||||||
\(57\) | 1.21916e8 | 1.52976 | ||||||||
\(58\) | −1.22262e8 | −1.41861 | ||||||||
\(59\) | 1.15881e8 | 1.24503 | 0.622514 | − | 0.782608i | \(-0.286111\pi\) | ||||
0.622514 | + | 0.782608i | \(0.286111\pi\) | |||||||
\(60\) | −2.84884e8 | −2.83783 | ||||||||
\(61\) | 1.30109e8 | 1.20316 | 0.601578 | − | 0.798814i | \(-0.294539\pi\) | ||||
0.601578 | + | 0.798814i | \(0.294539\pi\) | |||||||
\(62\) | 1.73980e7 | 0.149533 | ||||||||
\(63\) | 1.95545e7 | 0.156392 | ||||||||
\(64\) | −2.18804e8 | −1.63022 | ||||||||
\(65\) | −6.07905e7 | −0.422402 | ||||||||
\(66\) | −2.60704e8 | −1.69122 | ||||||||
\(67\) | −2.46756e8 | −1.49600 | −0.747999 | − | 0.663700i | \(-0.768985\pi\) | ||||
−0.747999 | + | 0.663700i | \(0.768985\pi\) | |||||||
\(68\) | 4.21625e8 | 2.39131 | ||||||||
\(69\) | −3.25163e8 | −1.72695 | ||||||||
\(70\) | 1.85273e8 | 0.922297 | ||||||||
\(71\) | −4.10200e8 | −1.91572 | −0.957862 | − | 0.287228i | \(-0.907266\pi\) | ||||
−0.957862 | + | 0.287228i | \(0.907266\pi\) | |||||||
\(72\) | 8.57331e7 | 0.375969 | ||||||||
\(73\) | 2.58619e8 | 1.06588 | 0.532939 | − | 0.846153i | \(-0.321087\pi\) | ||||
0.532939 | + | 0.846153i | \(0.321087\pi\) | |||||||
\(74\) | 2.62551e8 | 1.01782 | ||||||||
\(75\) | −4.29908e8 | −1.56892 | ||||||||
\(76\) | −5.86399e8 | −2.01619 | ||||||||
\(77\) | 1.03502e8 | 0.335536 | ||||||||
\(78\) | 1.72729e8 | 0.528373 | ||||||||
\(79\) | −6.38704e8 | −1.84492 | −0.922461 | − | 0.386090i | \(-0.873825\pi\) | ||||
−0.922461 | + | 0.386090i | \(0.873825\pi\) | |||||||
\(80\) | −6.20870e7 | −0.169471 | ||||||||
\(81\) | −4.81395e8 | −1.24256 | ||||||||
\(82\) | 9.94254e8 | 2.42848 | ||||||||
\(83\) | 1.54980e8 | 0.358446 | 0.179223 | − | 0.983808i | \(-0.442642\pi\) | ||||
0.179223 | + | 0.983808i | \(0.442642\pi\) | |||||||
\(84\) | −3.21364e8 | −0.704272 | ||||||||
\(85\) | 1.11846e9 | 2.32399 | ||||||||
\(86\) | 1.28693e9 | 2.53695 | ||||||||
\(87\) | 5.62559e8 | 1.05276 | ||||||||
\(88\) | 4.53785e8 | 0.806637 | ||||||||
\(89\) | −3.37453e8 | −0.570110 | −0.285055 | − | 0.958511i | \(-0.592012\pi\) | ||||
−0.285055 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(90\) | 6.28454e8 | 1.00968 | ||||||||
\(91\) | −6.85750e7 | −0.104828 | ||||||||
\(92\) | 1.56399e9 | 2.27609 | ||||||||
\(93\) | −8.00530e7 | −0.110970 | ||||||||
\(94\) | 5.99326e7 | 0.0791749 | ||||||||
\(95\) | −1.55556e9 | −1.95943 | ||||||||
\(96\) | 1.07550e9 | 1.29238 | ||||||||
\(97\) | −5.42438e8 | −0.622125 | −0.311063 | − | 0.950389i | \(-0.600685\pi\) | ||||
−0.311063 | + | 0.950389i | \(0.600685\pi\) | |||||||
\(98\) | 2.08998e8 | 0.228889 | ||||||||
\(99\) | 3.51082e8 | 0.367325 | ||||||||
\(100\) | 2.06780e9 | 2.06780 | ||||||||
\(101\) | −1.26639e9 | −1.21094 | −0.605468 | − | 0.795870i | \(-0.707014\pi\) | ||||
−0.605468 | + | 0.795870i | \(0.707014\pi\) | |||||||
\(102\) | −3.17797e9 | −2.90703 | ||||||||
\(103\) | 3.72255e8 | 0.325891 | 0.162946 | − | 0.986635i | \(-0.447901\pi\) | ||||
0.162946 | + | 0.986635i | \(0.447901\pi\) | |||||||
\(104\) | −3.00655e8 | −0.252010 | ||||||||
\(105\) | −8.52491e8 | −0.684444 | ||||||||
\(106\) | 8.02138e8 | 0.617125 | ||||||||
\(107\) | −6.94990e8 | −0.512568 | −0.256284 | − | 0.966602i | \(-0.582498\pi\) | ||||
−0.256284 | + | 0.966602i | \(0.582498\pi\) | |||||||
\(108\) | 1.54441e9 | 1.09233 | ||||||||
\(109\) | −1.17208e9 | −0.795313 | −0.397656 | − | 0.917534i | \(-0.630176\pi\) | ||||
−0.397656 | + | 0.917534i | \(0.630176\pi\) | |||||||
\(110\) | 3.32640e9 | 2.16625 | ||||||||
\(111\) | −1.20807e9 | −0.755333 | ||||||||
\(112\) | −7.00375e7 | −0.0420581 | ||||||||
\(113\) | −3.11053e8 | −0.179466 | −0.0897328 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897328 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(114\) | 4.41994e9 | 2.45101 | ||||||||
\(115\) | 4.14885e9 | 2.21201 | ||||||||
\(116\) | −2.70584e9 | −1.38753 | ||||||||
\(117\) | −2.32609e8 | −0.114760 | ||||||||
\(118\) | 4.20117e9 | 1.99481 | ||||||||
\(119\) | 1.26168e9 | 0.576751 | ||||||||
\(120\) | −3.73760e9 | −1.64542 | ||||||||
\(121\) | −4.99669e8 | −0.211908 | ||||||||
\(122\) | 4.71697e9 | 1.92772 | ||||||||
\(123\) | −4.57484e9 | −1.80220 | ||||||||
\(124\) | 3.85045e8 | 0.146256 | ||||||||
\(125\) | 1.32820e9 | 0.486598 | ||||||||
\(126\) | 7.08929e8 | 0.250574 | ||||||||
\(127\) | −7.17827e8 | −0.244852 | −0.122426 | − | 0.992478i | \(-0.539067\pi\) | ||||
−0.122426 | + | 0.992478i | \(0.539067\pi\) | |||||||
\(128\) | −4.63155e9 | −1.52504 | ||||||||
\(129\) | −5.92152e9 | −1.88269 | ||||||||
\(130\) | −2.20391e9 | −0.676781 | ||||||||
\(131\) | −1.59686e9 | −0.473746 | −0.236873 | − | 0.971541i | \(-0.576123\pi\) | ||||
−0.236873 | + | 0.971541i | \(0.576123\pi\) | |||||||
\(132\) | −5.76980e9 | −1.65416 | ||||||||
\(133\) | −1.75475e9 | −0.486276 | ||||||||
\(134\) | −8.94591e9 | −2.39692 | ||||||||
\(135\) | 4.09689e9 | 1.06158 | ||||||||
\(136\) | 5.53162e9 | 1.38652 | ||||||||
\(137\) | 3.27771e9 | 0.794929 | 0.397464 | − | 0.917618i | \(-0.369890\pi\) | ||||
0.397464 | + | 0.917618i | \(0.369890\pi\) | |||||||
\(138\) | −1.17885e10 | −2.76696 | ||||||||
\(139\) | −1.73472e9 | −0.394152 | −0.197076 | − | 0.980388i | \(-0.563145\pi\) | ||||
−0.197076 | + | 0.980388i | \(0.563145\pi\) | |||||||
\(140\) | 4.10038e9 | 0.902086 | ||||||||
\(141\) | −2.75766e8 | −0.0587564 | ||||||||
\(142\) | −1.48714e10 | −3.06941 | ||||||||
\(143\) | −1.23120e9 | −0.246216 | ||||||||
\(144\) | −2.37570e8 | −0.0460427 | ||||||||
\(145\) | −7.17786e9 | −1.34846 | ||||||||
\(146\) | 9.37601e9 | 1.70777 | ||||||||
\(147\) | −9.61656e8 | −0.169860 | ||||||||
\(148\) | 5.81067e9 | 0.995516 | ||||||||
\(149\) | 1.76392e9 | 0.293184 | 0.146592 | − | 0.989197i | \(-0.453169\pi\) | ||||
0.146592 | + | 0.989197i | \(0.453169\pi\) | |||||||
\(150\) | −1.55859e10 | −2.51375 | ||||||||
\(151\) | 7.95151e9 | 1.24467 | 0.622334 | − | 0.782752i | \(-0.286185\pi\) | ||||
0.622334 | + | 0.782752i | \(0.286185\pi\) | |||||||
\(152\) | −7.69340e9 | −1.16902 | ||||||||
\(153\) | 4.27967e9 | 0.631392 | ||||||||
\(154\) | 3.75236e9 | 0.537603 | ||||||||
\(155\) | 1.02142e9 | 0.142139 | ||||||||
\(156\) | 3.82277e9 | 0.516794 | ||||||||
\(157\) | 6.51392e9 | 0.855646 | 0.427823 | − | 0.903862i | \(-0.359281\pi\) | ||||
0.427823 | + | 0.903862i | \(0.359281\pi\) | |||||||
\(158\) | −2.31557e10 | −2.95597 | ||||||||
\(159\) | −3.69086e9 | −0.457974 | ||||||||
\(160\) | −1.37226e10 | −1.65537 | ||||||||
\(161\) | 4.68012e9 | 0.548960 | ||||||||
\(162\) | −1.74526e10 | −1.99086 | ||||||||
\(163\) | −2.09402e9 | −0.232347 | −0.116174 | − | 0.993229i | \(-0.537063\pi\) | ||||
−0.116174 | + | 0.993229i | \(0.537063\pi\) | |||||||
\(164\) | 2.20044e10 | 2.37527 | ||||||||
\(165\) | −1.53057e10 | −1.60759 | ||||||||
\(166\) | 5.61866e9 | 0.574310 | ||||||||
\(167\) | −1.57730e9 | −0.156924 | −0.0784620 | − | 0.996917i | \(-0.525001\pi\) | ||||
−0.0784620 | + | 0.996917i | \(0.525001\pi\) | |||||||
\(168\) | −4.21621e9 | −0.408348 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | 4.05487e10 | 3.72355 | ||||||||
\(171\) | −5.95219e9 | −0.532347 | ||||||||
\(172\) | 2.84818e10 | 2.48136 | ||||||||
\(173\) | 1.08098e10 | 0.917506 | 0.458753 | − | 0.888564i | \(-0.348296\pi\) | ||||
0.458753 | + | 0.888564i | \(0.348296\pi\) | |||||||
\(174\) | 2.03951e10 | 1.68676 | ||||||||
\(175\) | 6.18774e9 | 0.498725 | ||||||||
\(176\) | −1.25746e9 | −0.0987840 | ||||||||
\(177\) | −1.93308e10 | −1.48037 | ||||||||
\(178\) | −1.22341e10 | −0.913442 | ||||||||
\(179\) | −1.26967e10 | −0.924383 | −0.462192 | − | 0.886780i | \(-0.652937\pi\) | ||||
−0.462192 | + | 0.886780i | \(0.652937\pi\) | |||||||
\(180\) | 1.39087e10 | 0.987550 | ||||||||
\(181\) | 1.90915e10 | 1.32217 | 0.661084 | − | 0.750312i | \(-0.270097\pi\) | ||||
0.661084 | + | 0.750312i | \(0.270097\pi\) | |||||||
\(182\) | −2.48612e9 | −0.167958 | ||||||||
\(183\) | −2.17041e10 | −1.43058 | ||||||||
\(184\) | 2.05192e10 | 1.31971 | ||||||||
\(185\) | 1.54141e10 | 0.967489 | ||||||||
\(186\) | −2.90225e9 | −0.177798 | ||||||||
\(187\) | 2.26523e10 | 1.35464 | ||||||||
\(188\) | 1.32640e9 | 0.0774400 | ||||||||
\(189\) | 4.62152e9 | 0.263455 | ||||||||
\(190\) | −5.63953e10 | −3.13944 | ||||||||
\(191\) | −2.44449e10 | −1.32904 | −0.664521 | − | 0.747270i | \(-0.731364\pi\) | ||||
−0.664521 | + | 0.747270i | \(0.731364\pi\) | |||||||
\(192\) | 3.64998e10 | 1.93836 | ||||||||
\(193\) | 6.71475e9 | 0.348355 | 0.174177 | − | 0.984714i | \(-0.444273\pi\) | ||||
0.174177 | + | 0.984714i | \(0.444273\pi\) | |||||||
\(194\) | −1.96656e10 | −0.996781 | ||||||||
\(195\) | 1.01408e10 | 0.502245 | ||||||||
\(196\) | 4.62545e9 | 0.223873 | ||||||||
\(197\) | 1.16325e10 | 0.550268 | 0.275134 | − | 0.961406i | \(-0.411278\pi\) | ||||
0.275134 | + | 0.961406i | \(0.411278\pi\) | |||||||
\(198\) | 1.27282e10 | 0.588536 | ||||||||
\(199\) | −3.77740e10 | −1.70748 | −0.853738 | − | 0.520703i | \(-0.825670\pi\) | ||||
−0.853738 | + | 0.520703i | \(0.825670\pi\) | |||||||
\(200\) | 2.71291e10 | 1.19895 | ||||||||
\(201\) | 4.11626e10 | 1.77877 | ||||||||
\(202\) | −4.59118e10 | −1.94019 | ||||||||
\(203\) | −8.09701e9 | −0.334651 | ||||||||
\(204\) | −7.03335e10 | −2.84333 | ||||||||
\(205\) | 5.83717e10 | 2.30839 | ||||||||
\(206\) | 1.34958e10 | 0.522149 | ||||||||
\(207\) | 1.58752e10 | 0.600969 | ||||||||
\(208\) | 8.33128e8 | 0.0308622 | ||||||||
\(209\) | −3.15050e10 | −1.14214 | ||||||||
\(210\) | −3.09063e10 | −1.09663 | ||||||||
\(211\) | 2.79138e9 | 0.0969501 | 0.0484751 | − | 0.998824i | \(-0.484564\pi\) | ||||
0.0484751 | + | 0.998824i | \(0.484564\pi\) | |||||||
\(212\) | 1.77526e10 | 0.603601 | ||||||||
\(213\) | 6.84276e10 | 2.27784 | ||||||||
\(214\) | −2.51962e10 | −0.821247 | ||||||||
\(215\) | 7.55544e10 | 2.41150 | ||||||||
\(216\) | 2.02622e10 | 0.633353 | ||||||||
\(217\) | 1.15222e9 | 0.0352749 | ||||||||
\(218\) | −4.24927e10 | −1.27427 | ||||||||
\(219\) | −4.31416e10 | −1.26735 | ||||||||
\(220\) | 7.36186e10 | 2.11878 | ||||||||
\(221\) | −1.50083e10 | −0.423219 | ||||||||
\(222\) | −4.37975e10 | −1.21021 | ||||||||
\(223\) | −2.82013e10 | −0.763656 | −0.381828 | − | 0.924233i | \(-0.624705\pi\) | ||||
−0.381828 | + | 0.924233i | \(0.624705\pi\) | |||||||
\(224\) | −1.54798e10 | −0.410818 | ||||||||
\(225\) | 2.09891e10 | 0.545974 | ||||||||
\(226\) | −1.12769e10 | −0.287543 | ||||||||
\(227\) | −2.49158e10 | −0.622813 | −0.311407 | − | 0.950277i | \(-0.600800\pi\) | ||||
−0.311407 | + | 0.950277i | \(0.600800\pi\) | |||||||
\(228\) | 9.78202e10 | 2.39730 | ||||||||
\(229\) | 4.61661e9 | 0.110934 | 0.0554668 | − | 0.998461i | \(-0.482335\pi\) | ||||
0.0554668 | + | 0.998461i | \(0.482335\pi\) | |||||||
\(230\) | 1.50413e11 | 3.54413 | ||||||||
\(231\) | −1.72657e10 | −0.398960 | ||||||||
\(232\) | −3.54999e10 | −0.804510 | ||||||||
\(233\) | −3.52050e10 | −0.782534 | −0.391267 | − | 0.920277i | \(-0.627963\pi\) | ||||
−0.391267 | + | 0.920277i | \(0.627963\pi\) | |||||||
\(234\) | −8.43304e9 | −0.183871 | ||||||||
\(235\) | 3.51859e9 | 0.0752598 | ||||||||
\(236\) | 9.29786e10 | 1.95110 | ||||||||
\(237\) | 1.06546e11 | 2.19365 | ||||||||
\(238\) | 4.57411e10 | 0.924082 | ||||||||
\(239\) | −3.07099e10 | −0.608818 | −0.304409 | − | 0.952541i | \(-0.598459\pi\) | ||||
−0.304409 | + | 0.952541i | \(0.598459\pi\) | |||||||
\(240\) | 1.03571e10 | 0.201505 | ||||||||
\(241\) | −6.56655e10 | −1.25389 | −0.626946 | − | 0.779063i | \(-0.715695\pi\) | ||||
−0.626946 | + | 0.779063i | \(0.715695\pi\) | |||||||
\(242\) | −1.81151e10 | −0.339524 | ||||||||
\(243\) | 4.24176e10 | 0.780400 | ||||||||
\(244\) | 1.04394e11 | 1.88548 | ||||||||
\(245\) | 1.22701e10 | 0.217570 | ||||||||
\(246\) | −1.65857e11 | −2.88752 | ||||||||
\(247\) | 2.08736e10 | 0.356829 | ||||||||
\(248\) | 5.05170e9 | 0.0848017 | ||||||||
\(249\) | −2.58530e10 | −0.426201 | ||||||||
\(250\) | 4.81529e10 | 0.779637 | ||||||||
\(251\) | −3.89631e10 | −0.619615 | −0.309808 | − | 0.950799i | \(-0.600265\pi\) | ||||
−0.309808 | + | 0.950799i | \(0.600265\pi\) | |||||||
\(252\) | 1.56897e10 | 0.245083 | ||||||||
\(253\) | 8.40274e10 | 1.28937 | ||||||||
\(254\) | −2.60242e10 | −0.392306 | ||||||||
\(255\) | −1.86576e11 | −2.76328 | ||||||||
\(256\) | −5.58852e10 | −0.813237 | ||||||||
\(257\) | 8.77992e10 | 1.25543 | 0.627713 | − | 0.778445i | \(-0.283991\pi\) | ||||
0.627713 | + | 0.778445i | \(0.283991\pi\) | |||||||
\(258\) | −2.14679e11 | −3.01649 | ||||||||
\(259\) | 1.73880e10 | 0.240104 | ||||||||
\(260\) | −4.87759e10 | −0.661950 | ||||||||
\(261\) | −2.74654e10 | −0.366356 | ||||||||
\(262\) | −5.78927e10 | −0.759046 | ||||||||
\(263\) | −9.79310e10 | −1.26217 | −0.631087 | − | 0.775712i | \(-0.717391\pi\) | ||||
−0.631087 | + | 0.775712i | \(0.717391\pi\) | |||||||
\(264\) | −7.56982e10 | −0.959109 | ||||||||
\(265\) | 4.70928e10 | 0.586608 | ||||||||
\(266\) | −6.36170e10 | −0.779122 | ||||||||
\(267\) | 5.62923e10 | 0.677873 | ||||||||
\(268\) | −1.97987e11 | −2.34439 | ||||||||
\(269\) | −7.73982e10 | −0.901251 | −0.450625 | − | 0.892713i | \(-0.648799\pi\) | ||||
−0.450625 | + | 0.892713i | \(0.648799\pi\) | |||||||
\(270\) | 1.48529e11 | 1.70089 | ||||||||
\(271\) | 9.39115e10 | 1.05769 | 0.528843 | − | 0.848719i | \(-0.322626\pi\) | ||||
0.528843 | + | 0.848719i | \(0.322626\pi\) | |||||||
\(272\) | −1.53284e10 | −0.169799 | ||||||||
\(273\) | 1.14393e10 | 0.124643 | ||||||||
\(274\) | 1.18831e11 | 1.27365 | ||||||||
\(275\) | 1.11095e11 | 1.17138 | ||||||||
\(276\) | −2.60898e11 | −2.70632 | ||||||||
\(277\) | 3.78054e10 | 0.385829 | 0.192914 | − | 0.981216i | \(-0.438206\pi\) | ||||
0.192914 | + | 0.981216i | \(0.438206\pi\) | |||||||
\(278\) | −6.28908e10 | −0.631518 | ||||||||
\(279\) | 3.90837e9 | 0.0386169 | ||||||||
\(280\) | 5.37959e10 | 0.523044 | ||||||||
\(281\) | −1.75269e11 | −1.67697 | −0.838487 | − | 0.544921i | \(-0.816559\pi\) | ||||
−0.838487 | + | 0.544921i | \(0.816559\pi\) | |||||||
\(282\) | −9.99767e9 | −0.0941407 | ||||||||
\(283\) | −1.66180e11 | −1.54007 | −0.770036 | − | 0.638000i | \(-0.779762\pi\) | ||||
−0.770036 | + | 0.638000i | \(0.779762\pi\) | |||||||
\(284\) | −3.29128e11 | −3.00215 | ||||||||
\(285\) | 2.59490e11 | 2.32980 | ||||||||
\(286\) | −4.46361e10 | −0.394493 | ||||||||
\(287\) | 6.58464e10 | 0.572880 | ||||||||
\(288\) | −5.25082e10 | −0.449740 | ||||||||
\(289\) | 1.57543e11 | 1.32849 | ||||||||
\(290\) | −2.60227e11 | −2.16053 | ||||||||
\(291\) | 9.04870e10 | 0.739720 | ||||||||
\(292\) | 2.07506e11 | 1.67035 | ||||||||
\(293\) | −1.62063e11 | −1.28464 | −0.642319 | − | 0.766438i | \(-0.722028\pi\) | ||||
−0.642319 | + | 0.766438i | \(0.722028\pi\) | |||||||
\(294\) | −3.48640e10 | −0.272154 | ||||||||
\(295\) | 2.46647e11 | 1.89617 | ||||||||
\(296\) | 7.62345e10 | 0.577216 | ||||||||
\(297\) | 8.29751e10 | 0.618791 | ||||||||
\(298\) | 6.39494e10 | 0.469746 | ||||||||
\(299\) | −5.56722e10 | −0.402827 | ||||||||
\(300\) | −3.44941e11 | −2.45866 | ||||||||
\(301\) | 8.52294e10 | 0.598467 | ||||||||
\(302\) | 2.88275e11 | 1.99423 | ||||||||
\(303\) | 2.11253e11 | 1.43983 | ||||||||
\(304\) | 2.13188e10 | 0.143163 | ||||||||
\(305\) | 2.76929e11 | 1.83239 | ||||||||
\(306\) | 1.55156e11 | 1.01163 | ||||||||
\(307\) | 1.82605e11 | 1.17325 | 0.586626 | − | 0.809858i | \(-0.300456\pi\) | ||||
0.586626 | + | 0.809858i | \(0.300456\pi\) | |||||||
\(308\) | 8.30457e10 | 0.525822 | ||||||||
\(309\) | −6.20977e10 | −0.387492 | ||||||||
\(310\) | 3.70307e10 | 0.227737 | ||||||||
\(311\) | 2.81282e11 | 1.70498 | 0.852491 | − | 0.522741i | \(-0.175091\pi\) | ||||
0.852491 | + | 0.522741i | \(0.175091\pi\) | |||||||
\(312\) | 5.01538e10 | 0.299646 | ||||||||
\(313\) | −2.00687e11 | −1.18187 | −0.590934 | − | 0.806720i | \(-0.701240\pi\) | ||||
−0.590934 | + | 0.806720i | \(0.701240\pi\) | |||||||
\(314\) | 2.36157e11 | 1.37093 | ||||||||
\(315\) | 4.16206e10 | 0.238183 | ||||||||
\(316\) | −5.12471e11 | −2.89120 | ||||||||
\(317\) | 8.92731e10 | 0.496540 | 0.248270 | − | 0.968691i | \(-0.420138\pi\) | ||||
0.248270 | + | 0.968691i | \(0.420138\pi\) | |||||||
\(318\) | −1.33809e11 | −0.733775 | ||||||||
\(319\) | −1.45374e11 | −0.786013 | ||||||||
\(320\) | −4.65712e11 | −2.48280 | ||||||||
\(321\) | 1.15935e11 | 0.609455 | ||||||||
\(322\) | 1.69674e11 | 0.879556 | ||||||||
\(323\) | −3.84044e11 | −1.96322 | ||||||||
\(324\) | −3.86252e11 | −1.94724 | ||||||||
\(325\) | −7.36060e10 | −0.365964 | ||||||||
\(326\) | −7.59169e10 | −0.372271 | ||||||||
\(327\) | 1.95521e11 | 0.945644 | ||||||||
\(328\) | 2.88692e11 | 1.37722 | ||||||||
\(329\) | 3.96915e9 | 0.0186774 | ||||||||
\(330\) | −5.54895e11 | −2.57571 | ||||||||
\(331\) | 2.08591e11 | 0.955147 | 0.477573 | − | 0.878592i | \(-0.341516\pi\) | ||||
0.477573 | + | 0.878592i | \(0.341516\pi\) | |||||||
\(332\) | 1.24350e11 | 0.561725 | ||||||||
\(333\) | 5.89807e10 | 0.262852 | ||||||||
\(334\) | −5.71835e10 | −0.251427 | ||||||||
\(335\) | −5.25206e11 | −2.27839 | ||||||||
\(336\) | 1.16833e10 | 0.0500080 | ||||||||
\(337\) | 3.64080e11 | 1.53767 | 0.768833 | − | 0.639449i | \(-0.220838\pi\) | ||||
0.768833 | + | 0.639449i | \(0.220838\pi\) | |||||||
\(338\) | 2.95736e10 | 0.123248 | ||||||||
\(339\) | 5.18883e10 | 0.213388 | ||||||||
\(340\) | 8.97406e11 | 3.64195 | ||||||||
\(341\) | 2.06870e10 | 0.0828520 | ||||||||
\(342\) | −2.15791e11 | −0.852937 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | 3.73674e11 | 1.43873 | ||||||||
\(345\) | −6.92091e11 | −2.63013 | ||||||||
\(346\) | 3.91899e11 | 1.47005 | ||||||||
\(347\) | −4.18976e11 | −1.55134 | −0.775670 | − | 0.631139i | \(-0.782588\pi\) | ||||
−0.775670 | + | 0.631139i | \(0.782588\pi\) | |||||||
\(348\) | 4.51375e11 | 1.64980 | ||||||||
\(349\) | 1.17690e11 | 0.424642 | 0.212321 | − | 0.977200i | \(-0.431898\pi\) | ||||
0.212321 | + | 0.977200i | \(0.431898\pi\) | |||||||
\(350\) | 2.24331e11 | 0.799067 | ||||||||
\(351\) | −5.49751e10 | −0.193323 | ||||||||
\(352\) | −2.77926e11 | −0.964911 | ||||||||
\(353\) | −9.49329e9 | −0.0325410 | −0.0162705 | − | 0.999868i | \(-0.505179\pi\) | ||||
−0.0162705 | + | 0.999868i | \(0.505179\pi\) | |||||||
\(354\) | −7.00820e11 | −2.37187 | ||||||||
\(355\) | −8.73088e11 | −2.91763 | ||||||||
\(356\) | −2.70759e11 | −0.893426 | ||||||||
\(357\) | −2.10467e11 | −0.685769 | ||||||||
\(358\) | −4.60307e11 | −1.48107 | ||||||||
\(359\) | 2.21163e11 | 0.702729 | 0.351364 | − | 0.936239i | \(-0.385718\pi\) | ||||
0.351364 | + | 0.936239i | \(0.385718\pi\) | |||||||
\(360\) | 1.82478e11 | 0.572598 | ||||||||
\(361\) | 2.11442e11 | 0.655253 | ||||||||
\(362\) | 6.92145e11 | 2.11840 | ||||||||
\(363\) | 8.33524e10 | 0.251964 | ||||||||
\(364\) | −5.50218e10 | −0.164278 | ||||||||
\(365\) | 5.50456e11 | 1.62332 | ||||||||
\(366\) | −7.86862e11 | −2.29210 | ||||||||
\(367\) | 5.16287e11 | 1.48557 | 0.742786 | − | 0.669529i | \(-0.233504\pi\) | ||||
0.742786 | + | 0.669529i | \(0.233504\pi\) | |||||||
\(368\) | −5.68596e10 | −0.161618 | ||||||||
\(369\) | 2.23354e11 | 0.627155 | ||||||||
\(370\) | 5.58825e11 | 1.55013 | ||||||||
\(371\) | 5.31232e10 | 0.145580 | ||||||||
\(372\) | −6.42314e10 | −0.173902 | ||||||||
\(373\) | 3.32716e11 | 0.889986 | 0.444993 | − | 0.895534i | \(-0.353206\pi\) | ||||
0.444993 | + | 0.895534i | \(0.353206\pi\) | |||||||
\(374\) | 8.21240e11 | 2.17044 | ||||||||
\(375\) | −2.21565e11 | −0.578575 | ||||||||
\(376\) | 1.74021e10 | 0.0449009 | ||||||||
\(377\) | 9.63177e10 | 0.245567 | ||||||||
\(378\) | 1.67549e11 | 0.422113 | ||||||||
\(379\) | −4.11081e11 | −1.02341 | −0.511706 | − | 0.859161i | \(-0.670986\pi\) | ||||
−0.511706 | + | 0.859161i | \(0.670986\pi\) | |||||||
\(380\) | −1.24812e12 | −3.07064 | ||||||||
\(381\) | 1.19744e11 | 0.291134 | ||||||||
\(382\) | −8.86229e11 | −2.12942 | ||||||||
\(383\) | −7.34558e11 | −1.74434 | −0.872171 | − | 0.489201i | \(-0.837288\pi\) | ||||
−0.872171 | + | 0.489201i | \(0.837288\pi\) | |||||||
\(384\) | 7.72613e11 | 1.81331 | ||||||||
\(385\) | 2.20298e11 | 0.511018 | ||||||||
\(386\) | 2.43437e11 | 0.558141 | ||||||||
\(387\) | 2.89102e11 | 0.655167 | ||||||||
\(388\) | −4.35231e11 | −0.974939 | ||||||||
\(389\) | 7.93230e11 | 1.75641 | 0.878205 | − | 0.478284i | \(-0.158741\pi\) | ||||
0.878205 | + | 0.478284i | \(0.158741\pi\) | |||||||
\(390\) | 3.67645e11 | 0.804707 | ||||||||
\(391\) | 1.02429e12 | 2.21629 | ||||||||
\(392\) | 6.06847e10 | 0.129805 | ||||||||
\(393\) | 2.66380e11 | 0.563295 | ||||||||
\(394\) | 4.21725e11 | 0.881651 | ||||||||
\(395\) | −1.35945e12 | −2.80980 | ||||||||
\(396\) | 2.81695e11 | 0.575639 | ||||||||
\(397\) | 2.72888e10 | 0.0551349 | 0.0275674 | − | 0.999620i | \(-0.491224\pi\) | ||||
0.0275674 | + | 0.999620i | \(0.491224\pi\) | |||||||
\(398\) | −1.36946e12 | −2.73575 | ||||||||
\(399\) | 2.92719e11 | 0.578193 | ||||||||
\(400\) | −7.51758e10 | −0.146828 | ||||||||
\(401\) | −3.99757e11 | −0.772053 | −0.386026 | − | 0.922488i | \(-0.626153\pi\) | ||||
−0.386026 | + | 0.922488i | \(0.626153\pi\) | |||||||
\(402\) | 1.49231e12 | 2.84999 | ||||||||
\(403\) | −1.37062e10 | −0.0258847 | ||||||||
\(404\) | −1.01610e12 | −1.89767 | ||||||||
\(405\) | −1.02462e12 | −1.89242 | ||||||||
\(406\) | −2.93550e11 | −0.536185 | ||||||||
\(407\) | 3.12185e11 | 0.563945 | ||||||||
\(408\) | −9.22757e11 | −1.64861 | ||||||||
\(409\) | −2.63237e11 | −0.465148 | −0.232574 | − | 0.972579i | \(-0.574715\pi\) | ||||
−0.232574 | + | 0.972579i | \(0.574715\pi\) | |||||||
\(410\) | 2.11621e12 | 3.69856 | ||||||||
\(411\) | −5.46772e11 | −0.945188 | ||||||||
\(412\) | 2.98682e11 | 0.510707 | ||||||||
\(413\) | 2.78231e11 | 0.470577 | ||||||||
\(414\) | 5.75541e11 | 0.962885 | ||||||||
\(415\) | 3.29866e11 | 0.545911 | ||||||||
\(416\) | 1.84140e11 | 0.301458 | ||||||||
\(417\) | 2.89378e11 | 0.468655 | ||||||||
\(418\) | −1.14218e12 | −1.82997 | ||||||||
\(419\) | −1.14730e12 | −1.81850 | −0.909248 | − | 0.416254i | \(-0.863343\pi\) | ||||
−0.909248 | + | 0.416254i | \(0.863343\pi\) | |||||||
\(420\) | −6.84005e11 | −1.07260 | ||||||||
\(421\) | 2.85921e11 | 0.443585 | 0.221792 | − | 0.975094i | \(-0.428809\pi\) | ||||
0.221792 | + | 0.975094i | \(0.428809\pi\) | |||||||
\(422\) | 1.01199e11 | 0.155336 | ||||||||
\(423\) | 1.34635e10 | 0.0204469 | ||||||||
\(424\) | 2.32909e11 | 0.349978 | ||||||||
\(425\) | 1.35424e12 | 2.01348 | ||||||||
\(426\) | 2.48078e12 | 3.64960 | ||||||||
\(427\) | 3.12391e11 | 0.454750 | ||||||||
\(428\) | −5.57632e11 | −0.803251 | ||||||||
\(429\) | 2.05383e11 | 0.292756 | ||||||||
\(430\) | 2.73916e12 | 3.86375 | ||||||||
\(431\) | −9.10442e11 | −1.27088 | −0.635440 | − | 0.772150i | \(-0.719181\pi\) | ||||
−0.635440 | + | 0.772150i | \(0.719181\pi\) | |||||||
\(432\) | −5.61476e10 | −0.0775629 | ||||||||
\(433\) | 6.62331e9 | 0.00905481 | 0.00452741 | − | 0.999990i | \(-0.498559\pi\) | ||||
0.00452741 | + | 0.999990i | \(0.498559\pi\) | |||||||
\(434\) | 4.17726e10 | 0.0565181 | ||||||||
\(435\) | 1.19738e12 | 1.60335 | ||||||||
\(436\) | −9.40431e11 | −1.24634 | ||||||||
\(437\) | −1.42459e12 | −1.86863 | ||||||||
\(438\) | −1.56406e12 | −2.03058 | ||||||||
\(439\) | 2.02207e11 | 0.259840 | 0.129920 | − | 0.991524i | \(-0.458528\pi\) | ||||
0.129920 | + | 0.991524i | \(0.458528\pi\) | |||||||
\(440\) | 9.65857e11 | 1.22850 | ||||||||
\(441\) | 4.69503e10 | 0.0591105 | ||||||||
\(442\) | −5.44111e11 | −0.678090 | ||||||||
\(443\) | 1.03584e11 | 0.127784 | 0.0638922 | − | 0.997957i | \(-0.479649\pi\) | ||||
0.0638922 | + | 0.997957i | \(0.479649\pi\) | |||||||
\(444\) | −9.69308e11 | −1.18369 | ||||||||
\(445\) | −7.18251e11 | −0.868272 | ||||||||
\(446\) | −1.02241e12 | −1.22354 | ||||||||
\(447\) | −2.94249e11 | −0.348603 | ||||||||
\(448\) | −5.25348e11 | −0.616164 | ||||||||
\(449\) | 9.35615e11 | 1.08640 | 0.543198 | − | 0.839604i | \(-0.317213\pi\) | ||||
0.543198 | + | 0.839604i | \(0.317213\pi\) | |||||||
\(450\) | 7.60941e11 | 0.874771 | ||||||||
\(451\) | 1.18221e12 | 1.34555 | ||||||||
\(452\) | −2.49576e11 | −0.281242 | ||||||||
\(453\) | −1.32643e12 | −1.47994 | ||||||||
\(454\) | −9.03299e11 | −0.997884 | ||||||||
\(455\) | −1.45958e11 | −0.159653 | ||||||||
\(456\) | 1.28338e12 | 1.38999 | ||||||||
\(457\) | −1.53349e12 | −1.64459 | −0.822296 | − | 0.569060i | \(-0.807307\pi\) | ||||
−0.822296 | + | 0.569060i | \(0.807307\pi\) | |||||||
\(458\) | 1.67371e11 | 0.177740 | ||||||||
\(459\) | 1.01146e12 | 1.06363 | ||||||||
\(460\) | 3.32887e12 | 3.46647 | ||||||||
\(461\) | 2.62636e11 | 0.270832 | 0.135416 | − | 0.990789i | \(-0.456763\pi\) | ||||
0.135416 | + | 0.990789i | \(0.456763\pi\) | |||||||
\(462\) | −6.25951e11 | −0.639222 | ||||||||
\(463\) | 8.78762e11 | 0.888703 | 0.444351 | − | 0.895853i | \(-0.353434\pi\) | ||||
0.444351 | + | 0.895853i | \(0.353434\pi\) | |||||||
\(464\) | 9.83719e10 | 0.0985235 | ||||||||
\(465\) | −1.70388e11 | −0.169006 | ||||||||
\(466\) | −1.27633e12 | −1.25379 | ||||||||
\(467\) | 8.84893e11 | 0.860924 | 0.430462 | − | 0.902609i | \(-0.358351\pi\) | ||||
0.430462 | + | 0.902609i | \(0.358351\pi\) | |||||||
\(468\) | −1.86637e11 | −0.179842 | ||||||||
\(469\) | −5.92461e11 | −0.565434 | ||||||||
\(470\) | 1.27563e11 | 0.120583 | ||||||||
\(471\) | −1.08662e12 | −1.01738 | ||||||||
\(472\) | 1.21986e12 | 1.13128 | ||||||||
\(473\) | 1.53022e12 | 1.40565 | ||||||||
\(474\) | 3.86272e12 | 3.51472 | ||||||||
\(475\) | −1.88349e12 | −1.69763 | ||||||||
\(476\) | 1.01232e12 | 0.903832 | ||||||||
\(477\) | 1.80196e11 | 0.159372 | ||||||||
\(478\) | −1.11336e12 | −0.975460 | ||||||||
\(479\) | 5.98750e10 | 0.0519679 | 0.0259840 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259840 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(480\) | 2.28914e12 | 1.96828 | ||||||||
\(481\) | −2.06838e11 | −0.176188 | ||||||||
\(482\) | −2.38064e12 | −2.00901 | ||||||||
\(483\) | −7.80716e11 | −0.652726 | ||||||||
\(484\) | −4.00915e11 | −0.332084 | ||||||||
\(485\) | −1.15455e12 | −0.947491 | ||||||||
\(486\) | 1.53781e12 | 1.25037 | ||||||||
\(487\) | 3.16083e11 | 0.254637 | 0.127318 | − | 0.991862i | \(-0.459363\pi\) | ||||
0.127318 | + | 0.991862i | \(0.459363\pi\) | |||||||
\(488\) | 1.36962e12 | 1.09323 | ||||||||
\(489\) | 3.49315e11 | 0.276266 | ||||||||
\(490\) | 4.44840e11 | 0.348595 | ||||||||
\(491\) | 6.15781e11 | 0.478145 | 0.239072 | − | 0.971002i | \(-0.423157\pi\) | ||||
0.239072 | + | 0.971002i | \(0.423157\pi\) | |||||||
\(492\) | −3.67067e12 | −2.82424 | ||||||||
\(493\) | −1.77211e12 | −1.35107 | ||||||||
\(494\) | 7.56753e11 | 0.571719 | ||||||||
\(495\) | 7.47259e11 | 0.559433 | ||||||||
\(496\) | −1.39985e10 | −0.0103852 | ||||||||
\(497\) | −9.84890e11 | −0.724076 | ||||||||
\(498\) | −9.37278e11 | −0.682867 | ||||||||
\(499\) | −2.42258e12 | −1.74915 | −0.874573 | − | 0.484894i | \(-0.838858\pi\) | ||||
−0.874573 | + | 0.484894i | \(0.838858\pi\) | |||||||
\(500\) | 1.06570e12 | 0.762552 | ||||||||
\(501\) | 2.63117e11 | 0.186586 | ||||||||
\(502\) | −1.41257e12 | −0.992760 | ||||||||
\(503\) | −4.11652e11 | −0.286731 | −0.143365 | − | 0.989670i | \(-0.545792\pi\) | ||||
−0.143365 | + | 0.989670i | \(0.545792\pi\) | |||||||
\(504\) | 2.05845e11 | 0.142103 | ||||||||
\(505\) | −2.69544e12 | −1.84424 | ||||||||
\(506\) | 3.04634e12 | 2.06586 | ||||||||
\(507\) | −1.36076e11 | −0.0914632 | ||||||||
\(508\) | −5.75956e11 | −0.383710 | ||||||||
\(509\) | 2.25798e12 | 1.49104 | 0.745520 | − | 0.666483i | \(-0.232201\pi\) | ||||
0.745520 | + | 0.666483i | \(0.232201\pi\) | |||||||
\(510\) | −6.76414e12 | −4.42738 | ||||||||
\(511\) | 6.20945e11 | 0.402864 | ||||||||
\(512\) | 3.45285e11 | 0.222056 | ||||||||
\(513\) | −1.40675e12 | −0.896784 | ||||||||
\(514\) | 3.18308e12 | 2.01147 | ||||||||
\(515\) | 7.92323e11 | 0.496329 | ||||||||
\(516\) | −4.75119e12 | −2.95039 | ||||||||
\(517\) | 7.12625e10 | 0.0438686 | ||||||||
\(518\) | 6.30385e11 | 0.384700 | ||||||||
\(519\) | −1.80323e12 | −1.09094 | ||||||||
\(520\) | −6.39927e11 | −0.383809 | ||||||||
\(521\) | 4.60392e11 | 0.273752 | 0.136876 | − | 0.990588i | \(-0.456294\pi\) | ||||
0.136876 | + | 0.990588i | \(0.456294\pi\) | |||||||
\(522\) | −9.95734e11 | −0.586984 | ||||||||
\(523\) | −2.63675e12 | −1.54103 | −0.770516 | − | 0.637421i | \(-0.780001\pi\) | ||||
−0.770516 | + | 0.637421i | \(0.780001\pi\) | |||||||
\(524\) | −1.28126e12 | −0.742413 | ||||||||
\(525\) | −1.03221e12 | −0.592994 | ||||||||
\(526\) | −3.55040e12 | −2.02228 | ||||||||
\(527\) | 2.52173e11 | 0.142414 | ||||||||
\(528\) | 2.09763e11 | 0.117456 | ||||||||
\(529\) | 1.99838e12 | 1.10950 | ||||||||
\(530\) | 1.70731e12 | 0.939875 | ||||||||
\(531\) | 9.43772e11 | 0.515160 | ||||||||
\(532\) | −1.40794e12 | −0.762049 | ||||||||
\(533\) | −7.83273e11 | −0.420379 | ||||||||
\(534\) | 2.04083e12 | 1.08610 | ||||||||
\(535\) | −1.47925e12 | −0.780636 | ||||||||
\(536\) | −2.59754e12 | −1.35932 | ||||||||
\(537\) | 2.11800e12 | 1.09911 | ||||||||
\(538\) | −2.80600e12 | −1.44400 | ||||||||
\(539\) | 2.48508e11 | 0.126821 | ||||||||
\(540\) | 3.28719e12 | 1.66361 | ||||||||
\(541\) | −2.33082e11 | −0.116982 | −0.0584912 | − | 0.998288i | \(-0.518629\pi\) | ||||
−0.0584912 | + | 0.998288i | \(0.518629\pi\) | |||||||
\(542\) | 3.40468e12 | 1.69465 | ||||||||
\(543\) | −3.18475e12 | −1.57209 | ||||||||
\(544\) | −3.38790e12 | −1.65858 | ||||||||
\(545\) | −2.49471e12 | −1.21125 | ||||||||
\(546\) | 4.14723e11 | 0.199706 | ||||||||
\(547\) | 1.82746e12 | 0.872782 | 0.436391 | − | 0.899757i | \(-0.356256\pi\) | ||||
0.436391 | + | 0.899757i | \(0.356256\pi\) | |||||||
\(548\) | 2.62991e12 | 1.24574 | ||||||||
\(549\) | 1.05964e12 | 0.497833 | ||||||||
\(550\) | 4.02766e12 | 1.87681 | ||||||||
\(551\) | 2.46465e12 | 1.13913 | ||||||||
\(552\) | −3.42291e12 | −1.56917 | ||||||||
\(553\) | −1.53353e12 | −0.697315 | ||||||||
\(554\) | 1.37060e12 | 0.618182 | ||||||||
\(555\) | −2.57131e12 | −1.15037 | ||||||||
\(556\) | −1.39187e12 | −0.617679 | ||||||||
\(557\) | −1.31844e12 | −0.580379 | −0.290190 | − | 0.956969i | \(-0.593718\pi\) | ||||
−0.290190 | + | 0.956969i | \(0.593718\pi\) | |||||||
\(558\) | 1.41695e11 | 0.0618727 | ||||||||
\(559\) | −1.01384e12 | −0.439155 | ||||||||
\(560\) | −1.49071e11 | −0.0640541 | ||||||||
\(561\) | −3.77875e12 | −1.61070 | ||||||||
\(562\) | −6.35422e12 | −2.68688 | ||||||||
\(563\) | 3.22229e12 | 1.35169 | 0.675845 | − | 0.737043i | \(-0.263779\pi\) | ||||
0.675845 | + | 0.737043i | \(0.263779\pi\) | |||||||
\(564\) | −2.21264e11 | −0.0920778 | ||||||||
\(565\) | −6.62059e11 | −0.273324 | ||||||||
\(566\) | −6.02473e12 | −2.46753 | ||||||||
\(567\) | −1.15583e12 | −0.469645 | ||||||||
\(568\) | −4.31808e12 | −1.74070 | ||||||||
\(569\) | 7.01148e11 | 0.280417 | 0.140209 | − | 0.990122i | \(-0.455223\pi\) | ||||
0.140209 | + | 0.990122i | \(0.455223\pi\) | |||||||
\(570\) | 9.40759e12 | 3.73286 | ||||||||
\(571\) | 2.49034e12 | 0.980385 | 0.490193 | − | 0.871614i | \(-0.336926\pi\) | ||||
0.490193 | + | 0.871614i | \(0.336926\pi\) | |||||||
\(572\) | −9.87867e11 | −0.385848 | ||||||||
\(573\) | 4.07778e12 | 1.58026 | ||||||||
\(574\) | 2.38720e12 | 0.917880 | ||||||||
\(575\) | 5.02349e12 | 1.91646 | ||||||||
\(576\) | −1.78200e12 | −0.674540 | ||||||||
\(577\) | −1.62515e12 | −0.610384 | −0.305192 | − | 0.952291i | \(-0.598721\pi\) | ||||
−0.305192 | + | 0.952291i | \(0.598721\pi\) | |||||||
\(578\) | 5.71157e12 | 2.12853 | ||||||||
\(579\) | −1.12012e12 | −0.414202 | ||||||||
\(580\) | −5.75923e12 | −2.11319 | ||||||||
\(581\) | 3.72107e11 | 0.135480 | ||||||||
\(582\) | 3.28052e12 | 1.18519 | ||||||||
\(583\) | 9.53778e11 | 0.341931 | ||||||||
\(584\) | 2.72242e12 | 0.968496 | ||||||||
\(585\) | −4.95096e11 | −0.174778 | ||||||||
\(586\) | −5.87546e12 | −2.05827 | ||||||||
\(587\) | 3.20635e12 | 1.11465 | 0.557326 | − | 0.830294i | \(-0.311827\pi\) | ||||
0.557326 | + | 0.830294i | \(0.311827\pi\) | |||||||
\(588\) | −7.71595e11 | −0.266190 | ||||||||
\(589\) | −3.50724e11 | −0.120073 | ||||||||
\(590\) | 8.94197e12 | 3.03808 | ||||||||
\(591\) | −1.94047e12 | −0.654281 | ||||||||
\(592\) | −2.11249e11 | −0.0706882 | ||||||||
\(593\) | 5.88754e12 | 1.95518 | 0.977592 | − | 0.210510i | \(-0.0675123\pi\) | ||||
0.977592 | + | 0.210510i | \(0.0675123\pi\) | |||||||
\(594\) | 3.00819e12 | 0.991439 | ||||||||
\(595\) | 2.68542e12 | 0.878386 | ||||||||
\(596\) | 1.41530e12 | 0.459452 | ||||||||
\(597\) | 6.30128e12 | 2.03023 | ||||||||
\(598\) | −2.01835e12 | −0.645417 | ||||||||
\(599\) | −2.71579e12 | −0.861938 | −0.430969 | − | 0.902367i | \(-0.641828\pi\) | ||||
−0.430969 | + | 0.902367i | \(0.641828\pi\) | |||||||
\(600\) | −4.52554e12 | −1.42557 | ||||||||
\(601\) | 2.54821e12 | 0.796709 | 0.398355 | − | 0.917232i | \(-0.369581\pi\) | ||||
0.398355 | + | 0.917232i | \(0.369581\pi\) | |||||||
\(602\) | 3.08992e12 | 0.958876 | ||||||||
\(603\) | −2.00965e12 | −0.619004 | ||||||||
\(604\) | 6.37998e12 | 1.95053 | ||||||||
\(605\) | −1.06352e12 | −0.322735 | ||||||||
\(606\) | 7.65879e12 | 2.30692 | ||||||||
\(607\) | 4.56076e11 | 0.136360 | 0.0681802 | − | 0.997673i | \(-0.478281\pi\) | ||||
0.0681802 | + | 0.997673i | \(0.478281\pi\) | |||||||
\(608\) | 4.71191e12 | 1.39840 | ||||||||
\(609\) | 1.35070e12 | 0.397908 | ||||||||
\(610\) | 1.00398e13 | 2.93590 | ||||||||
\(611\) | −4.72149e10 | −0.0137055 | ||||||||
\(612\) | 3.43384e12 | 0.989462 | ||||||||
\(613\) | −2.43450e12 | −0.696365 | −0.348183 | − | 0.937427i | \(-0.613201\pi\) | ||||
−0.348183 | + | 0.937427i | \(0.613201\pi\) | |||||||
\(614\) | 6.62020e12 | 1.87981 | ||||||||
\(615\) | −9.73728e12 | −2.74473 | ||||||||
\(616\) | 1.08954e12 | 0.304880 | ||||||||
\(617\) | 2.93769e12 | 0.816062 | 0.408031 | − | 0.912968i | \(-0.366216\pi\) | ||||
0.408031 | + | 0.912968i | \(0.366216\pi\) | |||||||
\(618\) | −2.25130e12 | −0.620847 | ||||||||
\(619\) | 2.29646e12 | 0.628710 | 0.314355 | − | 0.949305i | \(-0.398212\pi\) | ||||
0.314355 | + | 0.949305i | \(0.398212\pi\) | |||||||
\(620\) | 8.19548e11 | 0.222747 | ||||||||
\(621\) | 3.75196e12 | 1.01238 | ||||||||
\(622\) | 1.01976e13 | 2.73176 | ||||||||
\(623\) | −8.10226e11 | −0.215481 | ||||||||
\(624\) | −1.38978e11 | −0.0366958 | ||||||||
\(625\) | −2.20649e12 | −0.578418 | ||||||||
\(626\) | −7.27571e12 | −1.89361 | ||||||||
\(627\) | 5.25550e12 | 1.35803 | ||||||||
\(628\) | 5.22652e12 | 1.34089 | ||||||||
\(629\) | 3.80552e12 | 0.969361 | ||||||||
\(630\) | 1.50892e12 | 0.381622 | ||||||||
\(631\) | 6.09950e12 | 1.53166 | 0.765829 | − | 0.643044i | \(-0.222329\pi\) | ||||
0.765829 | + | 0.643044i | \(0.222329\pi\) | |||||||
\(632\) | −6.72349e12 | −1.67636 | ||||||||
\(633\) | −4.65645e11 | −0.115276 | ||||||||
\(634\) | 3.23652e12 | 0.795566 | ||||||||
\(635\) | −1.52786e12 | −0.372907 | ||||||||
\(636\) | −2.96140e12 | −0.717695 | ||||||||
\(637\) | −1.64648e11 | −0.0396214 | ||||||||
\(638\) | −5.27042e12 | −1.25937 | ||||||||
\(639\) | −3.34079e12 | −0.792675 | ||||||||
\(640\) | −9.85800e12 | −2.32262 | ||||||||
\(641\) | −1.88700e12 | −0.441480 | −0.220740 | − | 0.975333i | \(-0.570847\pi\) | ||||
−0.220740 | + | 0.975333i | \(0.570847\pi\) | |||||||
\(642\) | 4.20311e12 | 0.976481 | ||||||||
\(643\) | −5.70855e12 | −1.31697 | −0.658485 | − | 0.752594i | \(-0.728803\pi\) | ||||
−0.658485 | + | 0.752594i | \(0.728803\pi\) | |||||||
\(644\) | 3.75515e12 | 0.860282 | ||||||||
\(645\) | −1.26036e13 | −2.86732 | ||||||||
\(646\) | −1.39232e13 | −3.14551 | ||||||||
\(647\) | −6.03413e12 | −1.35377 | −0.676886 | − | 0.736088i | \(-0.736671\pi\) | ||||
−0.676886 | + | 0.736088i | \(0.736671\pi\) | |||||||
\(648\) | −5.06753e12 | −1.12904 | ||||||||
\(649\) | 4.99538e12 | 1.10527 | ||||||||
\(650\) | −2.66852e12 | −0.586355 | ||||||||
\(651\) | −1.92207e11 | −0.0419426 | ||||||||
\(652\) | −1.68016e12 | −0.364113 | ||||||||
\(653\) | −3.28882e12 | −0.707833 | −0.353917 | − | 0.935277i | \(-0.615150\pi\) | ||||
−0.353917 | + | 0.935277i | \(0.615150\pi\) | |||||||
\(654\) | 7.08843e12 | 1.51513 | ||||||||
\(655\) | −3.39883e12 | −0.721511 | ||||||||
\(656\) | −7.99979e11 | −0.168660 | ||||||||
\(657\) | 2.10627e12 | 0.441032 | ||||||||
\(658\) | 1.43898e11 | 0.0299253 | ||||||||
\(659\) | −1.29201e12 | −0.266859 | −0.133430 | − | 0.991058i | \(-0.542599\pi\) | ||||
−0.133430 | + | 0.991058i | \(0.542599\pi\) | |||||||
\(660\) | −1.22807e13 | −2.51927 | ||||||||
\(661\) | −4.91713e12 | −1.00186 | −0.500928 | − | 0.865489i | \(-0.667008\pi\) | ||||
−0.500928 | + | 0.865489i | \(0.667008\pi\) | |||||||
\(662\) | 7.56229e12 | 1.53036 | ||||||||
\(663\) | 2.50361e12 | 0.503217 | ||||||||
\(664\) | 1.63144e12 | 0.325697 | ||||||||
\(665\) | −3.73489e12 | −0.740595 | ||||||||
\(666\) | 2.13829e12 | 0.421147 | ||||||||
\(667\) | −6.57352e12 | −1.28597 | ||||||||
\(668\) | −1.26556e12 | −0.245917 | ||||||||
\(669\) | 4.70441e12 | 0.908003 | ||||||||
\(670\) | −1.90409e13 | −3.65048 | ||||||||
\(671\) | 5.60869e12 | 1.06810 | ||||||||
\(672\) | 2.58227e12 | 0.488472 | ||||||||
\(673\) | 7.81572e12 | 1.46859 | 0.734296 | − | 0.678830i | \(-0.237513\pi\) | ||||
0.734296 | + | 0.678830i | \(0.237513\pi\) | |||||||
\(674\) | 1.31994e13 | 2.46368 | ||||||||
\(675\) | 4.96058e12 | 0.919741 | ||||||||
\(676\) | 6.54510e11 | 0.120547 | ||||||||
\(677\) | −8.00743e12 | −1.46502 | −0.732511 | − | 0.680755i | \(-0.761652\pi\) | ||||
−0.732511 | + | 0.680755i | \(0.761652\pi\) | |||||||
\(678\) | 1.88116e12 | 0.341895 | ||||||||
\(679\) | −1.30239e12 | −0.235141 | ||||||||
\(680\) | 1.17737e13 | 2.11166 | ||||||||
\(681\) | 4.15633e12 | 0.740538 | ||||||||
\(682\) | 7.49989e11 | 0.132747 | ||||||||
\(683\) | −6.26724e11 | −0.110200 | −0.0551002 | − | 0.998481i | \(-0.517548\pi\) | ||||
−0.0551002 | + | 0.998481i | \(0.517548\pi\) | |||||||
\(684\) | −4.77581e12 | −0.834246 | ||||||||
\(685\) | 6.97643e12 | 1.21067 | ||||||||
\(686\) | 5.01804e11 | 0.0865118 | ||||||||
\(687\) | −7.70120e11 | −0.131903 | ||||||||
\(688\) | −1.03547e12 | −0.176193 | ||||||||
\(689\) | −6.31925e11 | −0.106826 | ||||||||
\(690\) | −2.50911e13 | −4.21405 | ||||||||
\(691\) | 6.81882e12 | 1.13778 | 0.568890 | − | 0.822414i | \(-0.307373\pi\) | ||||
0.568890 | + | 0.822414i | \(0.307373\pi\) | |||||||
\(692\) | 8.67334e12 | 1.43783 | ||||||||
\(693\) | 8.42949e11 | 0.138836 | ||||||||
\(694\) | −1.51896e13 | −2.48559 | ||||||||
\(695\) | −3.69226e12 | −0.600289 | ||||||||
\(696\) | 5.92193e12 | 0.956580 | ||||||||
\(697\) | 1.44111e13 | 2.31286 | ||||||||
\(698\) | 4.26673e12 | 0.680371 | ||||||||
\(699\) | 5.87273e12 | 0.930450 | ||||||||
\(700\) | 4.96480e12 | 0.781557 | ||||||||
\(701\) | −6.80541e12 | −1.06444 | −0.532222 | − | 0.846605i | \(-0.678643\pi\) | ||||
−0.532222 | + | 0.846605i | \(0.678643\pi\) | |||||||
\(702\) | −1.99307e12 | −0.309746 | ||||||||
\(703\) | −5.29273e12 | −0.817299 | ||||||||
\(704\) | −9.43214e12 | −1.44722 | ||||||||
\(705\) | −5.86953e11 | −0.0894855 | ||||||||
\(706\) | −3.44171e11 | −0.0521378 | ||||||||
\(707\) | −3.04060e12 | −0.457691 | ||||||||
\(708\) | −1.55102e13 | −2.31990 | ||||||||
\(709\) | 8.21818e12 | 1.22143 | 0.610714 | − | 0.791851i | \(-0.290883\pi\) | ||||
0.610714 | + | 0.791851i | \(0.290883\pi\) | |||||||
\(710\) | −3.16530e13 | −4.67469 | ||||||||
\(711\) | −5.20180e12 | −0.763379 | ||||||||
\(712\) | −3.55229e12 | −0.518023 | ||||||||
\(713\) | 9.35422e11 | 0.135552 | ||||||||
\(714\) | −7.63031e12 | −1.09875 | ||||||||
\(715\) | −2.62054e12 | −0.374985 | ||||||||
\(716\) | −1.01873e13 | −1.44861 | ||||||||
\(717\) | 5.12287e12 | 0.723898 | ||||||||
\(718\) | 8.01807e12 | 1.12593 | ||||||||
\(719\) | −5.58560e12 | −0.779453 | −0.389726 | − | 0.920931i | \(-0.627430\pi\) | ||||
−0.389726 | + | 0.920931i | \(0.627430\pi\) | |||||||
\(720\) | −5.05655e11 | −0.0701226 | ||||||||
\(721\) | 8.93783e11 | 0.123175 | ||||||||
\(722\) | 7.66565e12 | 1.04986 | ||||||||
\(723\) | 1.09540e13 | 1.49091 | ||||||||
\(724\) | 1.53183e13 | 2.07198 | ||||||||
\(725\) | −8.69105e12 | −1.16829 | ||||||||
\(726\) | 3.02187e12 | 0.403702 | ||||||||
\(727\) | 1.11646e13 | 1.48231 | 0.741157 | − | 0.671332i | \(-0.234278\pi\) | ||||
0.741157 | + | 0.671332i | \(0.234278\pi\) | |||||||
\(728\) | −7.21872e11 | −0.0952509 | ||||||||
\(729\) | 2.39941e12 | 0.314652 | ||||||||
\(730\) | 1.99563e13 | 2.60092 | ||||||||
\(731\) | 1.86533e13 | 2.41616 | ||||||||
\(732\) | −1.74145e13 | −2.24187 | ||||||||
\(733\) | 3.62658e12 | 0.464013 | 0.232006 | − | 0.972714i | \(-0.425471\pi\) | ||||
0.232006 | + | 0.972714i | \(0.425471\pi\) | |||||||
\(734\) | 1.87175e13 | 2.38021 | ||||||||
\(735\) | −2.04683e12 | −0.258696 | ||||||||
\(736\) | −1.25672e13 | −1.57866 | ||||||||
\(737\) | −1.06371e13 | −1.32806 | ||||||||
\(738\) | 8.09750e12 | 1.00484 | ||||||||
\(739\) | −6.28280e12 | −0.774914 | −0.387457 | − | 0.921888i | \(-0.626646\pi\) | ||||
−0.387457 | + | 0.921888i | \(0.626646\pi\) | |||||||
\(740\) | 1.23677e13 | 1.51616 | ||||||||
\(741\) | −3.48203e12 | −0.424278 | ||||||||
\(742\) | 1.92593e12 | 0.233251 | ||||||||
\(743\) | −1.19933e13 | −1.44374 | −0.721872 | − | 0.692026i | \(-0.756718\pi\) | ||||
−0.721872 | + | 0.692026i | \(0.756718\pi\) | |||||||
\(744\) | −8.42699e11 | −0.100831 | ||||||||
\(745\) | 3.75441e12 | 0.446517 | ||||||||
\(746\) | 1.20623e13 | 1.42595 | ||||||||
\(747\) | 1.26220e12 | 0.148316 | ||||||||
\(748\) | 1.81753e13 | 2.12288 | ||||||||
\(749\) | −1.66867e12 | −0.193732 | ||||||||
\(750\) | −8.03263e12 | −0.927005 | ||||||||
\(751\) | −1.51642e13 | −1.73956 | −0.869779 | − | 0.493441i | \(-0.835739\pi\) | ||||
−0.869779 | + | 0.493441i | \(0.835739\pi\) | |||||||
\(752\) | −4.82219e10 | −0.00549875 | ||||||||
\(753\) | 6.49964e12 | 0.736736 | ||||||||
\(754\) | 3.49191e12 | 0.393452 | ||||||||
\(755\) | 1.69243e13 | 1.89562 | ||||||||
\(756\) | 3.70812e12 | 0.412863 | ||||||||
\(757\) | −9.26562e11 | −0.102552 | −0.0512758 | − | 0.998685i | \(-0.516329\pi\) | ||||
−0.0512758 | + | 0.998685i | \(0.516329\pi\) | |||||||
\(758\) | −1.49034e13 | −1.63973 | ||||||||
\(759\) | −1.40170e13 | −1.53309 | ||||||||
\(760\) | −1.63750e13 | −1.78041 | ||||||||
\(761\) | 1.47223e13 | 1.59128 | 0.795638 | − | 0.605772i | \(-0.207136\pi\) | ||||
0.795638 | + | 0.605772i | \(0.207136\pi\) | |||||||
\(762\) | 4.34123e12 | 0.466461 | ||||||||
\(763\) | −2.81416e12 | −0.300600 | ||||||||
\(764\) | −1.96136e13 | −2.08275 | ||||||||
\(765\) | 9.10905e12 | 0.961605 | ||||||||
\(766\) | −2.66308e13 | −2.79482 | ||||||||
\(767\) | −3.30969e12 | −0.345309 | ||||||||
\(768\) | 9.32251e12 | 0.966957 | ||||||||
\(769\) | −5.00088e12 | −0.515677 | −0.257839 | − | 0.966188i | \(-0.583010\pi\) | ||||
−0.257839 | + | 0.966188i | \(0.583010\pi\) | |||||||
\(770\) | 7.98670e12 | 0.818764 | ||||||||
\(771\) | −1.46462e13 | −1.49273 | ||||||||
\(772\) | 5.38765e12 | 0.545911 | ||||||||
\(773\) | −8.46485e12 | −0.852730 | −0.426365 | − | 0.904551i | \(-0.640206\pi\) | ||||
−0.426365 | + | 0.904551i | \(0.640206\pi\) | |||||||
\(774\) | 1.04811e13 | 1.04972 | ||||||||
\(775\) | 1.23675e12 | 0.123147 | ||||||||
\(776\) | −5.71012e12 | −0.565285 | ||||||||
\(777\) | −2.90058e12 | −0.285489 | ||||||||
\(778\) | 2.87578e13 | 2.81416 | ||||||||
\(779\) | −2.00430e13 | −1.95005 | ||||||||
\(780\) | 8.13656e12 | 0.787073 | ||||||||
\(781\) | −1.76828e13 | −1.70067 | ||||||||
\(782\) | 3.71347e13 | 3.55099 | ||||||||
\(783\) | −6.49120e12 | −0.617159 | ||||||||
\(784\) | −1.68160e11 | −0.0158965 | ||||||||
\(785\) | 1.38645e13 | 1.30314 | ||||||||
\(786\) | 9.65738e12 | 0.902522 | ||||||||
\(787\) | 4.37741e12 | 0.406753 | 0.203376 | − | 0.979101i | \(-0.434808\pi\) | ||||
0.203376 | + | 0.979101i | \(0.434808\pi\) | |||||||
\(788\) | 9.33344e12 | 0.862331 | ||||||||
\(789\) | 1.63364e13 | 1.50075 | ||||||||
\(790\) | −4.92855e13 | −4.50192 | ||||||||
\(791\) | −7.46838e11 | −0.0678316 | ||||||||
\(792\) | 3.69576e12 | 0.333765 | ||||||||
\(793\) | −3.71603e12 | −0.333695 | ||||||||
\(794\) | 9.89330e11 | 0.0883382 | ||||||||
\(795\) | −7.85579e12 | −0.697490 | ||||||||
\(796\) | −3.03084e13 | −2.67580 | ||||||||
\(797\) | −4.41467e11 | −0.0387558 | −0.0193779 | − | 0.999812i | \(-0.506169\pi\) | ||||
−0.0193779 | + | 0.999812i | \(0.506169\pi\) | |||||||
\(798\) | 1.06123e13 | 0.926393 | ||||||||
\(799\) | 8.68686e11 | 0.0754054 | ||||||||
\(800\) | −1.66155e13 | −1.43420 | ||||||||
\(801\) | −2.74832e12 | −0.235896 | ||||||||
\(802\) | −1.44929e13 | −1.23700 | ||||||||
\(803\) | 1.11485e13 | 0.946229 | ||||||||
\(804\) | 3.30273e13 | 2.78753 | ||||||||
\(805\) | 9.96139e12 | 0.836062 | ||||||||
\(806\) | −4.96904e11 | −0.0414730 | ||||||||
\(807\) | 1.29112e13 | 1.07161 | ||||||||
\(808\) | −1.33310e13 | −1.10030 | ||||||||
\(809\) | 9.18962e12 | 0.754274 | 0.377137 | − | 0.926157i | \(-0.376909\pi\) | ||||
0.377137 | + | 0.926157i | \(0.376909\pi\) | |||||||
\(810\) | −3.71468e13 | −3.03207 | ||||||||
\(811\) | −2.42346e13 | −1.96717 | −0.983585 | − | 0.180447i | \(-0.942246\pi\) | ||||
−0.983585 | + | 0.180447i | \(0.942246\pi\) | |||||||
\(812\) | −6.49672e12 | −0.524436 | ||||||||
\(813\) | −1.56659e13 | −1.25761 | ||||||||
\(814\) | 1.13180e13 | 0.903565 | ||||||||
\(815\) | −4.45701e12 | −0.353862 | ||||||||
\(816\) | 2.55700e12 | 0.201895 | ||||||||
\(817\) | −2.59430e13 | −2.03714 | ||||||||
\(818\) | −9.54341e12 | −0.745270 | ||||||||
\(819\) | −5.58495e11 | −0.0433752 | ||||||||
\(820\) | 4.68351e13 | 3.61751 | ||||||||
\(821\) | 9.59483e12 | 0.737043 | 0.368522 | − | 0.929619i | \(-0.379864\pi\) | ||||
0.368522 | + | 0.929619i | \(0.379864\pi\) | |||||||
\(822\) | −1.98227e13 | −1.51440 | ||||||||
\(823\) | 8.78641e12 | 0.667594 | 0.333797 | − | 0.942645i | \(-0.391670\pi\) | ||||
0.333797 | + | 0.942645i | \(0.391670\pi\) | |||||||
\(824\) | 3.91864e12 | 0.296116 | ||||||||
\(825\) | −1.85324e13 | −1.39280 | ||||||||
\(826\) | 1.00870e13 | 0.753968 | ||||||||
\(827\) | 1.76469e13 | 1.31188 | 0.655941 | − | 0.754812i | \(-0.272272\pi\) | ||||
0.655941 | + | 0.754812i | \(0.272272\pi\) | |||||||
\(828\) | 1.27376e13 | 0.941785 | ||||||||
\(829\) | −9.87352e12 | −0.726067 | −0.363033 | − | 0.931776i | \(-0.618259\pi\) | ||||
−0.363033 | + | 0.931776i | \(0.618259\pi\) | |||||||
\(830\) | 1.19590e13 | 0.874669 | ||||||||
\(831\) | −6.30651e12 | −0.458759 | ||||||||
\(832\) | 6.24926e12 | 0.452141 | ||||||||
\(833\) | 3.02929e12 | 0.217991 | ||||||||
\(834\) | 1.04911e13 | 0.750889 | ||||||||
\(835\) | −3.35719e12 | −0.238994 | ||||||||
\(836\) | −2.52783e13 | −1.78986 | ||||||||
\(837\) | 9.23708e11 | 0.0650534 | ||||||||
\(838\) | −4.15942e13 | −2.91363 | ||||||||
\(839\) | 5.54138e12 | 0.386090 | 0.193045 | − | 0.981190i | \(-0.438164\pi\) | ||||
0.193045 | + | 0.981190i | \(0.438164\pi\) | |||||||
\(840\) | −8.97398e12 | −0.621911 | ||||||||
\(841\) | −3.13441e12 | −0.216060 | ||||||||
\(842\) | 1.03658e13 | 0.710721 | ||||||||
\(843\) | 2.92375e13 | 1.99396 | ||||||||
\(844\) | 2.23970e12 | 0.151932 | ||||||||
\(845\) | 1.73624e12 | 0.117153 | ||||||||
\(846\) | 4.88109e11 | 0.0327605 | ||||||||
\(847\) | −1.19971e12 | −0.0800939 | ||||||||
\(848\) | −6.45402e11 | −0.0428597 | ||||||||
\(849\) | 2.77214e13 | 1.83118 | ||||||||
\(850\) | 4.90969e13 | 3.22604 | ||||||||
\(851\) | 1.41163e13 | 0.922654 | ||||||||
\(852\) | 5.49036e13 | 3.56962 | ||||||||
\(853\) | −8.98490e12 | −0.581089 | −0.290545 | − | 0.956861i | \(-0.593836\pi\) | ||||
−0.290545 | + | 0.956861i | \(0.593836\pi\) | |||||||
\(854\) | 1.13254e13 | 0.728610 | ||||||||
\(855\) | −1.26689e13 | −0.810759 | ||||||||
\(856\) | −7.31599e12 | −0.465738 | ||||||||
\(857\) | −2.42067e13 | −1.53293 | −0.766465 | − | 0.642287i | \(-0.777986\pi\) | ||||
−0.766465 | + | 0.642287i | \(0.777986\pi\) | |||||||
\(858\) | 7.44598e12 | 0.469060 | ||||||||
\(859\) | 2.19676e13 | 1.37662 | 0.688308 | − | 0.725418i | \(-0.258354\pi\) | ||||
0.688308 | + | 0.725418i | \(0.258354\pi\) | |||||||
\(860\) | 6.06219e13 | 3.77908 | ||||||||
\(861\) | −1.09842e13 | −0.681167 | ||||||||
\(862\) | −3.30073e13 | −2.03623 | ||||||||
\(863\) | 2.60407e13 | 1.59810 | 0.799050 | − | 0.601265i | \(-0.205336\pi\) | ||||
0.799050 | + | 0.601265i | \(0.205336\pi\) | |||||||
\(864\) | −1.24098e13 | −0.757625 | ||||||||
\(865\) | 2.30080e13 | 1.39735 | ||||||||
\(866\) | 2.40122e11 | 0.0145078 | ||||||||
\(867\) | −2.62805e13 | −1.57960 | ||||||||
\(868\) | 9.24494e11 | 0.0552796 | ||||||||
\(869\) | −2.75331e13 | −1.63782 | ||||||||
\(870\) | 4.34098e13 | 2.56892 | ||||||||
\(871\) | 7.04759e12 | 0.414915 | ||||||||
\(872\) | −1.23382e13 | −0.722650 | ||||||||
\(873\) | −4.41778e12 | −0.257419 | ||||||||
\(874\) | −5.16471e13 | −2.99395 | ||||||||
\(875\) | 3.18902e12 | 0.183917 | ||||||||
\(876\) | −3.46151e13 | −1.98608 | ||||||||
\(877\) | 2.27235e13 | 1.29711 | 0.648555 | − | 0.761168i | \(-0.275374\pi\) | ||||
0.648555 | + | 0.761168i | \(0.275374\pi\) | |||||||
\(878\) | 7.33083e12 | 0.416321 | ||||||||
\(879\) | 2.70346e13 | 1.52746 | ||||||||
\(880\) | −2.67643e12 | −0.150447 | ||||||||
\(881\) | 9.48493e12 | 0.530447 | 0.265224 | − | 0.964187i | \(-0.414554\pi\) | ||||
0.265224 | + | 0.964187i | \(0.414554\pi\) | |||||||
\(882\) | 1.70214e12 | 0.0947080 | ||||||||
\(883\) | −1.50500e13 | −0.833130 | −0.416565 | − | 0.909106i | \(-0.636766\pi\) | ||||
−0.416565 | + | 0.909106i | \(0.636766\pi\) | |||||||
\(884\) | −1.20420e13 | −0.663231 | ||||||||
\(885\) | −4.11445e13 | −2.25459 | ||||||||
\(886\) | 3.75536e12 | 0.204739 | ||||||||
\(887\) | 1.05055e13 | 0.569851 | 0.284926 | − | 0.958550i | \(-0.408031\pi\) | ||||
0.284926 | + | 0.958550i | \(0.408031\pi\) | |||||||
\(888\) | −1.27171e13 | −0.686323 | ||||||||
\(889\) | −1.72350e12 | −0.0925452 | ||||||||
\(890\) | −2.60395e13 | −1.39116 | ||||||||
\(891\) | −2.07519e13 | −1.10308 | ||||||||
\(892\) | −2.26276e13 | −1.19673 | ||||||||
\(893\) | −1.20817e12 | −0.0635767 | ||||||||
\(894\) | −1.06677e13 | −0.558539 | ||||||||
\(895\) | −2.70242e13 | −1.40783 | ||||||||
\(896\) | −1.11204e13 | −0.576412 | ||||||||
\(897\) | 9.28697e12 | 0.478970 | ||||||||
\(898\) | 3.39199e13 | 1.74065 | ||||||||
\(899\) | −1.61836e12 | −0.0826335 | ||||||||
\(900\) | 1.68408e13 | 0.855602 | ||||||||
\(901\) | 1.16265e13 | 0.587743 | ||||||||
\(902\) | 4.28600e13 | 2.15587 | ||||||||
\(903\) | −1.42176e13 | −0.711591 | ||||||||
\(904\) | −3.27438e12 | −0.163069 | ||||||||
\(905\) | 4.06352e13 | 2.01365 | ||||||||
\(906\) | −4.80886e13 | −2.37119 | ||||||||
\(907\) | 2.00145e13 | 0.982001 | 0.491001 | − | 0.871159i | \(-0.336631\pi\) | ||||
0.491001 | + | 0.871159i | \(0.336631\pi\) | |||||||
\(908\) | −1.99914e13 | −0.976017 | ||||||||
\(909\) | −1.03139e13 | −0.501053 | ||||||||
\(910\) | −5.29158e12 | −0.255799 | ||||||||
\(911\) | −1.18505e13 | −0.570038 | −0.285019 | − | 0.958522i | \(-0.592000\pi\) | ||||
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(912\) | −3.55629e12 | −0.170224 | ||||||||
\(913\) | 6.68084e12 | 0.318209 | ||||||||
\(914\) | −5.55953e13 | −2.63500 | ||||||||
\(915\) | −4.61959e13 | −2.17876 | ||||||||
\(916\) | 3.70419e12 | 0.173845 | ||||||||
\(917\) | −3.83406e12 | −0.179059 | ||||||||
\(918\) | 3.66697e13 | 1.70418 | ||||||||
\(919\) | 2.15844e13 | 0.998206 | 0.499103 | − | 0.866543i | \(-0.333663\pi\) | ||||
0.499103 | + | 0.866543i | \(0.333663\pi\) | |||||||
\(920\) | 4.36740e13 | 2.00991 | ||||||||
\(921\) | −3.04614e13 | −1.39502 | ||||||||
\(922\) | 9.52163e12 | 0.433933 | ||||||||
\(923\) | 1.17157e13 | 0.531326 | ||||||||
\(924\) | −1.38533e13 | −0.625214 | ||||||||
\(925\) | 1.86636e13 | 0.838221 | ||||||||
\(926\) | 3.18587e13 | 1.42390 | ||||||||
\(927\) | 3.03175e12 | 0.134845 | ||||||||
\(928\) | 2.17423e13 | 0.962367 | ||||||||
\(929\) | −1.61104e13 | −0.709638 | −0.354819 | − | 0.934935i | \(-0.615457\pi\) | ||||
−0.354819 | + | 0.934935i | \(0.615457\pi\) | |||||||
\(930\) | −6.17728e12 | −0.270785 | ||||||||
\(931\) | −4.21316e12 | −0.183795 | ||||||||
\(932\) | −2.82471e13 | −1.22632 | ||||||||
\(933\) | −4.69221e13 | −2.02726 | ||||||||
\(934\) | 3.20810e13 | 1.37939 | ||||||||
\(935\) | 4.82142e13 | 2.06311 | ||||||||
\(936\) | −2.44862e12 | −0.104275 | ||||||||
\(937\) | 2.92171e13 | 1.23825 | 0.619126 | − | 0.785291i | \(-0.287487\pi\) | ||||
0.619126 | + | 0.785291i | \(0.287487\pi\) | |||||||
\(938\) | −2.14791e13 | −0.905950 | ||||||||
\(939\) | 3.34776e13 | 1.40527 | ||||||||
\(940\) | 2.82317e12 | 0.117940 | ||||||||
\(941\) | 1.55829e13 | 0.647882 | 0.323941 | − | 0.946077i | \(-0.394992\pi\) | ||||
0.323941 | + | 0.946077i | \(0.394992\pi\) | |||||||
\(942\) | −3.93945e13 | −1.63007 | ||||||||
\(943\) | 5.34571e13 | 2.20142 | ||||||||
\(944\) | −3.38027e12 | −0.138541 | ||||||||
\(945\) | 9.83664e12 | 0.401240 | ||||||||
\(946\) | 5.54766e13 | 2.25216 | ||||||||
\(947\) | 3.01152e13 | 1.21677 | 0.608387 | − | 0.793640i | \(-0.291817\pi\) | ||||
0.608387 | + | 0.793640i | \(0.291817\pi\) | |||||||
\(948\) | 8.54880e13 | 3.43770 | ||||||||
\(949\) | −7.38642e12 | −0.295622 | ||||||||
\(950\) | −6.82842e13 | −2.71997 | ||||||||
\(951\) | −1.48921e13 | −0.590397 | ||||||||
\(952\) | 1.32814e13 | 0.524056 | ||||||||
\(953\) | −2.09287e13 | −0.821908 | −0.410954 | − | 0.911656i | \(-0.634804\pi\) | ||||
−0.410954 | + | 0.911656i | \(0.634804\pi\) | |||||||
\(954\) | 6.53285e12 | 0.255350 | ||||||||
\(955\) | −5.20296e13 | −2.02412 | ||||||||
\(956\) | −2.46404e13 | −0.954085 | ||||||||
\(957\) | 2.42507e13 | 0.934587 | ||||||||
\(958\) | 2.17071e12 | 0.0832641 | ||||||||
\(959\) | 7.86979e12 | 0.300455 | ||||||||
\(960\) | 7.76878e13 | 2.95211 | ||||||||
\(961\) | −2.62093e13 | −0.991290 | ||||||||
\(962\) | −7.49872e12 | −0.282292 | ||||||||
\(963\) | −5.66020e12 | −0.212087 | ||||||||
\(964\) | −5.26874e13 | −1.96499 | ||||||||
\(965\) | 1.42920e13 | 0.530541 | ||||||||
\(966\) | −2.83042e13 | −1.04581 | ||||||||
\(967\) | −2.49667e13 | −0.918209 | −0.459104 | − | 0.888382i | \(-0.651830\pi\) | ||||
−0.459104 | + | 0.888382i | \(0.651830\pi\) | |||||||
\(968\) | −5.25990e12 | −0.192548 | ||||||||
\(969\) | 6.40643e13 | 2.33431 | ||||||||
\(970\) | −4.18572e13 | −1.51809 | ||||||||
\(971\) | 1.46151e13 | 0.527614 | 0.263807 | − | 0.964575i | \(-0.415022\pi\) | ||||
0.263807 | + | 0.964575i | \(0.415022\pi\) | |||||||
\(972\) | 3.40342e13 | 1.22297 | ||||||||
\(973\) | −4.16507e12 | −0.148975 | ||||||||
\(974\) | 1.14593e13 | 0.407984 | ||||||||
\(975\) | 1.22786e13 | 0.435139 | ||||||||
\(976\) | −3.79528e12 | −0.133881 | ||||||||
\(977\) | 1.49672e13 | 0.525552 | 0.262776 | − | 0.964857i | \(-0.415362\pi\) | ||||
0.262776 | + | 0.964857i | \(0.415362\pi\) | |||||||
\(978\) | 1.26641e13 | 0.442639 | ||||||||
\(979\) | −1.45469e13 | −0.506112 | ||||||||
\(980\) | 9.84501e12 | 0.340956 | ||||||||
\(981\) | −9.54577e12 | −0.329079 | ||||||||
\(982\) | 2.23246e13 | 0.766094 | ||||||||
\(983\) | −5.93014e12 | −0.202570 | −0.101285 | − | 0.994857i | \(-0.532295\pi\) | ||||
−0.101285 | + | 0.994857i | \(0.532295\pi\) | |||||||
\(984\) | −4.81582e13 | −1.63754 | ||||||||
\(985\) | 2.47591e13 | 0.838053 | ||||||||
\(986\) | −6.42461e13 | −2.16472 | ||||||||
\(987\) | −6.62115e11 | −0.0222078 | ||||||||
\(988\) | 1.67481e13 | 0.559191 | ||||||||
\(989\) | 6.91931e13 | 2.29974 | ||||||||
\(990\) | 2.70912e13 | 0.896335 | ||||||||
\(991\) | −2.39086e12 | −0.0787451 | −0.0393725 | − | 0.999225i | \(-0.512536\pi\) | ||||
−0.0393725 | + | 0.999225i | \(0.512536\pi\) | |||||||
\(992\) | −3.09397e12 | −0.101441 | ||||||||
\(993\) | −3.47962e13 | −1.13569 | ||||||||
\(994\) | −3.57063e13 | −1.16013 | ||||||||
\(995\) | −8.03999e13 | −2.60047 | ||||||||
\(996\) | −2.07434e13 | −0.667904 | ||||||||
\(997\) | −1.77355e13 | −0.568481 | −0.284241 | − | 0.958753i | \(-0.591741\pi\) | ||||
−0.284241 | + | 0.958753i | \(0.591741\pi\) | |||||||
\(998\) | −8.78285e13 | −2.80252 | ||||||||
\(999\) | 1.39396e13 | 0.442797 |
(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 | 91.10.a.c.1.13 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.c.1.13 | ✓ | 14 | 1.1 | even | 1 | trivial |