Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.35 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 40.9577 | 1.81009 | 0.905045 | − | 0.425316i | \(-0.139837\pi\) | ||||
0.905045 | + | 0.425316i | \(0.139837\pi\) | |||||||
\(3\) | −105.034 | −0.748662 | −0.374331 | − | 0.927295i | \(-0.622128\pi\) | ||||
−0.374331 | + | 0.927295i | \(0.622128\pi\) | |||||||
\(4\) | 1165.53 | 2.27643 | ||||||||
\(5\) | 2072.52 | 1.48297 | 0.741487 | − | 0.670967i | \(-0.234121\pi\) | ||||
0.741487 | + | 0.670967i | \(0.234121\pi\) | |||||||
\(6\) | −4301.96 | −1.35515 | ||||||||
\(7\) | 5180.84 | 0.815566 | 0.407783 | − | 0.913079i | \(-0.366302\pi\) | ||||
0.407783 | + | 0.913079i | \(0.366302\pi\) | |||||||
\(8\) | 26767.1 | 2.31044 | ||||||||
\(9\) | −8650.78 | −0.439505 | ||||||||
\(10\) | 84885.6 | 2.68432 | ||||||||
\(11\) | −83913.5 | −1.72808 | −0.864042 | − | 0.503420i | \(-0.832075\pi\) | ||||
−0.864042 | + | 0.503420i | \(0.832075\pi\) | |||||||
\(12\) | −122421. | −1.70427 | ||||||||
\(13\) | −38456.2 | −0.373441 | −0.186720 | − | 0.982413i | \(-0.559786\pi\) | ||||
−0.186720 | + | 0.982413i | \(0.559786\pi\) | |||||||
\(14\) | 212195. | 1.47625 | ||||||||
\(15\) | −217686. | −1.11025 | ||||||||
\(16\) | 499564. | 1.90569 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −354316. | −0.795544 | ||||||||
\(19\) | 727879. | 1.28135 | 0.640675 | − | 0.767812i | \(-0.278655\pi\) | ||||
0.640675 | + | 0.767812i | \(0.278655\pi\) | |||||||
\(20\) | 2.41558e6 | 3.37588 | ||||||||
\(21\) | −544167. | −0.610584 | ||||||||
\(22\) | −3.43690e6 | −3.12799 | ||||||||
\(23\) | 2.28425e6 | 1.70203 | 0.851017 | − | 0.525139i | \(-0.175987\pi\) | ||||
0.851017 | + | 0.525139i | \(0.175987\pi\) | |||||||
\(24\) | −2.81146e6 | −1.72974 | ||||||||
\(25\) | 2.34222e6 | 1.19921 | ||||||||
\(26\) | −1.57508e6 | −0.675961 | ||||||||
\(27\) | 2.97602e6 | 1.07770 | ||||||||
\(28\) | 6.03843e6 | 1.85658 | ||||||||
\(29\) | 2.05994e6 | 0.540834 | 0.270417 | − | 0.962743i | \(-0.412838\pi\) | ||||
0.270417 | + | 0.962743i | \(0.412838\pi\) | |||||||
\(30\) | −8.91591e6 | −2.00965 | ||||||||
\(31\) | 2.10705e6 | 0.409778 | 0.204889 | − | 0.978785i | \(-0.434317\pi\) | ||||
0.204889 | + | 0.978785i | \(0.434317\pi\) | |||||||
\(32\) | 6.75626e6 | 1.13902 | ||||||||
\(33\) | 8.81380e6 | 1.29375 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.07374e7 | 1.20946 | ||||||||
\(36\) | −1.00827e7 | −1.00050 | ||||||||
\(37\) | 1.39359e7 | 1.22244 | 0.611220 | − | 0.791461i | \(-0.290679\pi\) | ||||
0.611220 | + | 0.791461i | \(0.290679\pi\) | |||||||
\(38\) | 2.98122e7 | 2.31936 | ||||||||
\(39\) | 4.03923e6 | 0.279581 | ||||||||
\(40\) | 5.54753e7 | 3.42633 | ||||||||
\(41\) | 2.53391e7 | 1.40044 | 0.700220 | − | 0.713927i | \(-0.253085\pi\) | ||||
0.700220 | + | 0.713927i | \(0.253085\pi\) | |||||||
\(42\) | −2.22878e7 | −1.10521 | ||||||||
\(43\) | −2.22102e7 | −0.990706 | −0.495353 | − | 0.868692i | \(-0.664961\pi\) | ||||
−0.495353 | + | 0.868692i | \(0.664961\pi\) | |||||||
\(44\) | −9.78037e7 | −3.93385 | ||||||||
\(45\) | −1.79289e7 | −0.651775 | ||||||||
\(46\) | 9.35575e7 | 3.08083 | ||||||||
\(47\) | 1.95036e7 | 0.583008 | 0.291504 | − | 0.956570i | \(-0.405844\pi\) | ||||
0.291504 | + | 0.956570i | \(0.405844\pi\) | |||||||
\(48\) | −5.24714e7 | −1.42672 | ||||||||
\(49\) | −1.35125e7 | −0.334851 | ||||||||
\(50\) | 9.59317e7 | 2.17069 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.48219e7 | −0.850110 | ||||||||
\(53\) | −3.74339e6 | −0.0651663 | −0.0325832 | − | 0.999469i | \(-0.510373\pi\) | ||||
−0.0325832 | + | 0.999469i | \(0.510373\pi\) | |||||||
\(54\) | 1.21891e8 | 1.95074 | ||||||||
\(55\) | −1.73912e8 | −2.56271 | ||||||||
\(56\) | 1.38676e8 | 1.88432 | ||||||||
\(57\) | −7.64523e7 | −0.959298 | ||||||||
\(58\) | 8.43705e7 | 0.978959 | ||||||||
\(59\) | −7.17696e7 | −0.771092 | −0.385546 | − | 0.922689i | \(-0.625987\pi\) | ||||
−0.385546 | + | 0.922689i | \(0.625987\pi\) | |||||||
\(60\) | −2.53719e8 | −2.52739 | ||||||||
\(61\) | −1.17343e7 | −0.108511 | −0.0542554 | − | 0.998527i | \(-0.517279\pi\) | ||||
−0.0542554 | + | 0.998527i | \(0.517279\pi\) | |||||||
\(62\) | 8.63000e7 | 0.741734 | ||||||||
\(63\) | −4.48183e7 | −0.358446 | ||||||||
\(64\) | 2.09436e7 | 0.156042 | ||||||||
\(65\) | −7.97013e7 | −0.553803 | ||||||||
\(66\) | 3.60993e8 | 2.34181 | ||||||||
\(67\) | 3.00544e8 | 1.82209 | 0.911047 | − | 0.412302i | \(-0.135275\pi\) | ||||
0.911047 | + | 0.412302i | \(0.135275\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.39925e8 | −1.27425 | ||||||||
\(70\) | 4.39779e8 | 2.18924 | ||||||||
\(71\) | 1.31667e8 | 0.614913 | 0.307457 | − | 0.951562i | \(-0.400522\pi\) | ||||
0.307457 | + | 0.951562i | \(0.400522\pi\) | |||||||
\(72\) | −2.31556e8 | −1.01545 | ||||||||
\(73\) | 3.21930e8 | 1.32681 | 0.663406 | − | 0.748260i | \(-0.269110\pi\) | ||||
0.663406 | + | 0.748260i | \(0.269110\pi\) | |||||||
\(74\) | 5.70782e8 | 2.21273 | ||||||||
\(75\) | −2.46013e8 | −0.897807 | ||||||||
\(76\) | 8.48364e8 | 2.91690 | ||||||||
\(77\) | −4.34743e8 | −1.40937 | ||||||||
\(78\) | 1.65437e8 | 0.506066 | ||||||||
\(79\) | 3.05655e8 | 0.882895 | 0.441448 | − | 0.897287i | \(-0.354465\pi\) | ||||
0.441448 | + | 0.897287i | \(0.354465\pi\) | |||||||
\(80\) | 1.03536e9 | 2.82609 | ||||||||
\(81\) | −1.42311e8 | −0.367330 | ||||||||
\(82\) | 1.03783e9 | 2.53492 | ||||||||
\(83\) | −4.83143e8 | −1.11744 | −0.558720 | − | 0.829356i | \(-0.688707\pi\) | ||||
−0.558720 | + | 0.829356i | \(0.688707\pi\) | |||||||
\(84\) | −6.34243e8 | −1.38995 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.09678e8 | −1.79327 | ||||||||
\(87\) | −2.16365e8 | −0.404902 | ||||||||
\(88\) | −2.24612e9 | −3.99264 | ||||||||
\(89\) | 1.76273e8 | 0.297803 | 0.148902 | − | 0.988852i | \(-0.452426\pi\) | ||||
0.148902 | + | 0.988852i | \(0.452426\pi\) | |||||||
\(90\) | −7.34326e8 | −1.17977 | ||||||||
\(91\) | −1.99236e8 | −0.304566 | ||||||||
\(92\) | 2.66236e9 | 3.87455 | ||||||||
\(93\) | −2.21313e8 | −0.306785 | ||||||||
\(94\) | 7.98822e8 | 1.05530 | ||||||||
\(95\) | 1.50854e9 | 1.90021 | ||||||||
\(96\) | −7.09640e8 | −0.852741 | ||||||||
\(97\) | −8.15034e8 | −0.934766 | −0.467383 | − | 0.884055i | \(-0.654803\pi\) | ||||
−0.467383 | + | 0.884055i | \(0.654803\pi\) | |||||||
\(98\) | −5.53439e8 | −0.606111 | ||||||||
\(99\) | 7.25917e8 | 0.759502 | ||||||||
\(100\) | 2.72992e9 | 2.72992 | ||||||||
\(101\) | 2.53858e8 | 0.242742 | 0.121371 | − | 0.992607i | \(-0.461271\pi\) | ||||
0.121371 | + | 0.992607i | \(0.461271\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.52399e9 | −1.33418 | −0.667090 | − | 0.744977i | \(-0.732460\pi\) | ||||
−0.667090 | + | 0.744977i | \(0.732460\pi\) | |||||||
\(104\) | −1.02936e9 | −0.862814 | ||||||||
\(105\) | −1.12780e9 | −0.905480 | ||||||||
\(106\) | −1.53320e8 | −0.117957 | ||||||||
\(107\) | −1.73003e9 | −1.27593 | −0.637966 | − | 0.770064i | \(-0.720224\pi\) | ||||
−0.637966 | + | 0.770064i | \(0.720224\pi\) | |||||||
\(108\) | 3.46864e9 | 2.45331 | ||||||||
\(109\) | −3.58188e8 | −0.243048 | −0.121524 | − | 0.992589i | \(-0.538778\pi\) | ||||
−0.121524 | + | 0.992589i | \(0.538778\pi\) | |||||||
\(110\) | −7.12305e9 | −4.63873 | ||||||||
\(111\) | −1.46375e9 | −0.915195 | ||||||||
\(112\) | 2.58817e9 | 1.55421 | ||||||||
\(113\) | −7.59574e8 | −0.438245 | −0.219123 | − | 0.975697i | \(-0.570319\pi\) | ||||
−0.219123 | + | 0.975697i | \(0.570319\pi\) | |||||||
\(114\) | −3.13131e9 | −1.73642 | ||||||||
\(115\) | 4.73415e9 | 2.52407 | ||||||||
\(116\) | 2.40093e9 | 1.23117 | ||||||||
\(117\) | 3.32676e8 | 0.164129 | ||||||||
\(118\) | −2.93951e9 | −1.39575 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.82681e9 | −2.56516 | ||||||||
\(121\) | 4.68353e9 | 1.98627 | ||||||||
\(122\) | −4.80610e8 | −0.196414 | ||||||||
\(123\) | −2.66148e9 | −1.04846 | ||||||||
\(124\) | 2.45583e9 | 0.932828 | ||||||||
\(125\) | 8.06399e8 | 0.295430 | ||||||||
\(126\) | −1.83565e9 | −0.648819 | ||||||||
\(127\) | 3.23828e9 | 1.10458 | 0.552291 | − | 0.833651i | \(-0.313754\pi\) | ||||
0.552291 | + | 0.833651i | \(0.313754\pi\) | |||||||
\(128\) | −2.60140e9 | −0.856570 | ||||||||
\(129\) | 2.33284e9 | 0.741704 | ||||||||
\(130\) | −3.26438e9 | −1.00243 | ||||||||
\(131\) | −2.74138e9 | −0.813294 | −0.406647 | − | 0.913585i | \(-0.633302\pi\) | ||||
−0.406647 | + | 0.913585i | \(0.633302\pi\) | |||||||
\(132\) | 1.02728e10 | 2.94513 | ||||||||
\(133\) | 3.77103e9 | 1.04503 | ||||||||
\(134\) | 1.23096e10 | 3.29815 | ||||||||
\(135\) | 6.16786e9 | 1.59821 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.82540e9 | 1.65533 | 0.827667 | − | 0.561220i | \(-0.189668\pi\) | ||||
0.827667 | + | 0.561220i | \(0.189668\pi\) | |||||||
\(138\) | −9.82675e9 | −2.30650 | ||||||||
\(139\) | −2.21726e9 | −0.503789 | −0.251895 | − | 0.967755i | \(-0.581054\pi\) | ||||
−0.251895 | + | 0.967755i | \(0.581054\pi\) | |||||||
\(140\) | 1.25148e10 | 2.75326 | ||||||||
\(141\) | −2.04855e9 | −0.436476 | ||||||||
\(142\) | 5.39277e9 | 1.11305 | ||||||||
\(143\) | 3.22700e9 | 0.645337 | ||||||||
\(144\) | −4.32162e9 | −0.837559 | ||||||||
\(145\) | 4.26928e9 | 0.802044 | ||||||||
\(146\) | 1.31855e10 | 2.40165 | ||||||||
\(147\) | 1.41927e9 | 0.250690 | ||||||||
\(148\) | 1.62427e10 | 2.78279 | ||||||||
\(149\) | −4.15025e9 | −0.689821 | −0.344910 | − | 0.938636i | \(-0.612091\pi\) | ||||
−0.344910 | + | 0.938636i | \(0.612091\pi\) | |||||||
\(150\) | −1.00761e10 | −1.62511 | ||||||||
\(151\) | 4.22098e8 | 0.0660719 | 0.0330359 | − | 0.999454i | \(-0.489482\pi\) | ||||
0.0330359 | + | 0.999454i | \(0.489482\pi\) | |||||||
\(152\) | 1.94832e10 | 2.96049 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.78061e10 | −2.55108 | ||||||||
\(155\) | 4.36691e9 | 0.607690 | ||||||||
\(156\) | 4.70784e9 | 0.636445 | ||||||||
\(157\) | 1.77965e9 | 0.233769 | 0.116885 | − | 0.993146i | \(-0.462709\pi\) | ||||
0.116885 | + | 0.993146i | \(0.462709\pi\) | |||||||
\(158\) | 1.25189e10 | 1.59812 | ||||||||
\(159\) | 3.93184e8 | 0.0487876 | ||||||||
\(160\) | 1.40025e10 | 1.68914 | ||||||||
\(161\) | 1.18343e10 | 1.38812 | ||||||||
\(162\) | −5.82874e9 | −0.664901 | ||||||||
\(163\) | −6.54651e9 | −0.726383 | −0.363192 | − | 0.931714i | \(-0.618313\pi\) | ||||
−0.363192 | + | 0.931714i | \(0.618313\pi\) | |||||||
\(164\) | 2.95335e10 | 3.18800 | ||||||||
\(165\) | 1.82668e10 | 1.91860 | ||||||||
\(166\) | −1.97884e10 | −2.02267 | ||||||||
\(167\) | 1.94448e9 | 0.193454 | 0.0967271 | − | 0.995311i | \(-0.469163\pi\) | ||||
0.0967271 | + | 0.995311i | \(0.469163\pi\) | |||||||
\(168\) | −1.45657e10 | −1.41072 | ||||||||
\(169\) | −9.12562e9 | −0.860542 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.29672e9 | −0.563160 | ||||||||
\(172\) | −2.58867e10 | −2.25527 | ||||||||
\(173\) | 1.57301e10 | 1.33513 | 0.667567 | − | 0.744550i | \(-0.267336\pi\) | ||||
0.667567 | + | 0.744550i | \(0.267336\pi\) | |||||||
\(174\) | −8.86180e9 | −0.732909 | ||||||||
\(175\) | 1.21347e10 | 0.978039 | ||||||||
\(176\) | −4.19202e10 | −3.29319 | ||||||||
\(177\) | 7.53828e9 | 0.577288 | ||||||||
\(178\) | 7.21971e9 | 0.539051 | ||||||||
\(179\) | 4.51445e9 | 0.328674 | 0.164337 | − | 0.986404i | \(-0.447451\pi\) | ||||
0.164337 | + | 0.986404i | \(0.447451\pi\) | |||||||
\(180\) | −2.08967e10 | −1.48372 | ||||||||
\(181\) | −2.26434e10 | −1.56815 | −0.784076 | − | 0.620665i | \(-0.786863\pi\) | ||||
−0.784076 | + | 0.620665i | \(0.786863\pi\) | |||||||
\(182\) | −8.16023e9 | −0.551291 | ||||||||
\(183\) | 1.23251e9 | 0.0812380 | ||||||||
\(184\) | 6.11426e10 | 3.93245 | ||||||||
\(185\) | 2.88825e10 | 1.81285 | ||||||||
\(186\) | −9.06447e9 | −0.555308 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.27320e10 | 1.32717 | ||||||||
\(189\) | 1.54183e10 | 0.878938 | ||||||||
\(190\) | 6.17864e10 | 3.43955 | ||||||||
\(191\) | −7.88641e9 | −0.428775 | −0.214387 | − | 0.976749i | \(-0.568776\pi\) | ||||
−0.214387 | + | 0.976749i | \(0.568776\pi\) | |||||||
\(192\) | −2.19980e9 | −0.116823 | ||||||||
\(193\) | −1.42449e10 | −0.739012 | −0.369506 | − | 0.929228i | \(-0.620473\pi\) | ||||
−0.369506 | + | 0.929228i | \(0.620473\pi\) | |||||||
\(194\) | −3.33819e10 | −1.69201 | ||||||||
\(195\) | 8.37138e9 | 0.414611 | ||||||||
\(196\) | −1.57492e10 | −0.762264 | ||||||||
\(197\) | 3.25891e9 | 0.154161 | 0.0770805 | − | 0.997025i | \(-0.475440\pi\) | ||||
0.0770805 | + | 0.997025i | \(0.475440\pi\) | |||||||
\(198\) | 2.97319e10 | 1.37477 | ||||||||
\(199\) | −7.31449e9 | −0.330632 | −0.165316 | − | 0.986241i | \(-0.552864\pi\) | ||||
−0.165316 | + | 0.986241i | \(0.552864\pi\) | |||||||
\(200\) | 6.26942e10 | 2.77072 | ||||||||
\(201\) | −3.15674e10 | −1.36413 | ||||||||
\(202\) | 1.03974e10 | 0.439385 | ||||||||
\(203\) | 1.06722e10 | 0.441086 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.25159e10 | 2.07682 | ||||||||
\(206\) | −6.24190e10 | −2.41499 | ||||||||
\(207\) | −1.97605e10 | −0.748052 | ||||||||
\(208\) | −1.92114e10 | −0.711661 | ||||||||
\(209\) | −6.10789e10 | −2.21428 | ||||||||
\(210\) | −4.61919e10 | −1.63900 | ||||||||
\(211\) | 8.04733e8 | 0.0279499 | 0.0139750 | − | 0.999902i | \(-0.495551\pi\) | ||||
0.0139750 | + | 0.999902i | \(0.495551\pi\) | |||||||
\(212\) | −4.36303e9 | −0.148346 | ||||||||
\(213\) | −1.38295e10 | −0.460362 | ||||||||
\(214\) | −7.08581e10 | −2.30955 | ||||||||
\(215\) | −4.60311e10 | −1.46919 | ||||||||
\(216\) | 7.96593e10 | 2.48997 | ||||||||
\(217\) | 1.09163e10 | 0.334201 | ||||||||
\(218\) | −1.46705e10 | −0.439938 | ||||||||
\(219\) | −3.38138e10 | −0.993333 | ||||||||
\(220\) | −2.02700e11 | −5.83381 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.99518e10 | −1.65658 | ||||||||
\(223\) | 2.06904e10 | 0.560268 | 0.280134 | − | 0.959961i | \(-0.409621\pi\) | ||||
0.280134 | + | 0.959961i | \(0.409621\pi\) | |||||||
\(224\) | 3.50031e10 | 0.928947 | ||||||||
\(225\) | −2.02620e10 | −0.527061 | ||||||||
\(226\) | −3.11104e10 | −0.793264 | ||||||||
\(227\) | −3.22296e10 | −0.805636 | −0.402818 | − | 0.915280i | \(-0.631969\pi\) | ||||
−0.402818 | + | 0.915280i | \(0.631969\pi\) | |||||||
\(228\) | −8.91074e10 | −2.18377 | ||||||||
\(229\) | −1.46098e10 | −0.351064 | −0.175532 | − | 0.984474i | \(-0.556165\pi\) | ||||
−0.175532 | + | 0.984474i | \(0.556165\pi\) | |||||||
\(230\) | 1.93900e11 | 4.56880 | ||||||||
\(231\) | 4.56630e10 | 1.05514 | ||||||||
\(232\) | 5.51386e10 | 1.24957 | ||||||||
\(233\) | 1.40255e10 | 0.311758 | 0.155879 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155879 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(234\) | 1.36256e10 | 0.297088 | ||||||||
\(235\) | 4.04216e10 | 0.864587 | ||||||||
\(236\) | −8.36496e10 | −1.75533 | ||||||||
\(237\) | −3.21043e10 | −0.660990 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.43516e9 | −0.0879264 | −0.0439632 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439632 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(240\) | −1.08748e11 | −2.11578 | ||||||||
\(241\) | 1.91454e10 | 0.365584 | 0.182792 | − | 0.983152i | \(-0.441487\pi\) | ||||
0.182792 | + | 0.983152i | \(0.441487\pi\) | |||||||
\(242\) | 1.91826e11 | 3.59533 | ||||||||
\(243\) | −4.36294e10 | −0.802697 | ||||||||
\(244\) | −1.36767e10 | −0.247017 | ||||||||
\(245\) | −2.80048e10 | −0.496576 | ||||||||
\(246\) | −1.09008e11 | −1.89780 | ||||||||
\(247\) | −2.79915e10 | −0.478508 | ||||||||
\(248\) | 5.63996e10 | 0.946768 | ||||||||
\(249\) | 5.07467e10 | 0.836585 | ||||||||
\(250\) | 3.30282e10 | 0.534755 | ||||||||
\(251\) | −8.63881e9 | −0.137380 | −0.0686898 | − | 0.997638i | \(-0.521882\pi\) | ||||
−0.0686898 | + | 0.997638i | \(0.521882\pi\) | |||||||
\(252\) | −5.22371e10 | −0.815975 | ||||||||
\(253\) | −1.91679e11 | −2.94126 | ||||||||
\(254\) | 1.32633e11 | 1.99939 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.17271e11 | −1.70651 | ||||||||
\(257\) | −1.14783e11 | −1.64127 | −0.820634 | − | 0.571455i | \(-0.806379\pi\) | ||||
−0.820634 | + | 0.571455i | \(0.806379\pi\) | |||||||
\(258\) | 9.55475e10 | 1.34255 | ||||||||
\(259\) | 7.21998e10 | 0.996981 | ||||||||
\(260\) | −9.28942e10 | −1.26069 | ||||||||
\(261\) | −1.78201e10 | −0.237699 | ||||||||
\(262\) | −1.12280e11 | −1.47214 | ||||||||
\(263\) | 3.42476e10 | 0.441397 | 0.220699 | − | 0.975342i | \(-0.429166\pi\) | ||||
0.220699 | + | 0.975342i | \(0.429166\pi\) | |||||||
\(264\) | 2.35920e11 | 2.98914 | ||||||||
\(265\) | −7.75825e9 | −0.0966400 | ||||||||
\(266\) | 1.54452e11 | 1.89159 | ||||||||
\(267\) | −1.85147e10 | −0.222954 | ||||||||
\(268\) | 3.50293e11 | 4.14786 | ||||||||
\(269\) | 6.94696e10 | 0.808927 | 0.404464 | − | 0.914554i | \(-0.367458\pi\) | ||||
0.404464 | + | 0.914554i | \(0.367458\pi\) | |||||||
\(270\) | 2.52621e11 | 2.89290 | ||||||||
\(271\) | −1.06575e9 | −0.0120031 | −0.00600154 | − | 0.999982i | \(-0.501910\pi\) | ||||
−0.00600154 | + | 0.999982i | \(0.501910\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.09266e10 | 0.228017 | ||||||||
\(274\) | 2.79552e11 | 2.99630 | ||||||||
\(275\) | −1.96544e11 | −2.07234 | ||||||||
\(276\) | −2.79639e11 | −2.90073 | ||||||||
\(277\) | 9.88531e10 | 1.00886 | 0.504431 | − | 0.863452i | \(-0.331702\pi\) | ||||
0.504431 | + | 0.863452i | \(0.331702\pi\) | |||||||
\(278\) | −9.08136e10 | −0.911904 | ||||||||
\(279\) | −1.82277e10 | −0.180099 | ||||||||
\(280\) | 2.87409e11 | 2.79440 | ||||||||
\(281\) | −1.79379e11 | −1.71630 | −0.858151 | − | 0.513398i | \(-0.828386\pi\) | ||||
−0.858151 | + | 0.513398i | \(0.828386\pi\) | |||||||
\(282\) | −8.39038e10 | −0.790061 | ||||||||
\(283\) | 3.09384e10 | 0.286720 | 0.143360 | − | 0.989671i | \(-0.454209\pi\) | ||||
0.143360 | + | 0.989671i | \(0.454209\pi\) | |||||||
\(284\) | 1.53462e11 | 1.39980 | ||||||||
\(285\) | −1.58449e11 | −1.42262 | ||||||||
\(286\) | 1.32170e11 | 1.16812 | ||||||||
\(287\) | 1.31278e11 | 1.14215 | ||||||||
\(288\) | −5.84469e10 | −0.500605 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 1.74860e11 | 1.45177 | ||||||||
\(291\) | 8.56066e10 | 0.699824 | ||||||||
\(292\) | 3.75219e11 | 3.02039 | ||||||||
\(293\) | 1.72026e10 | 0.136361 | 0.0681803 | − | 0.997673i | \(-0.478281\pi\) | ||||
0.0681803 | + | 0.997673i | \(0.478281\pi\) | |||||||
\(294\) | 5.81301e10 | 0.453772 | ||||||||
\(295\) | −1.48744e11 | −1.14351 | ||||||||
\(296\) | 3.73023e11 | 2.82438 | ||||||||
\(297\) | −2.49728e11 | −1.86236 | ||||||||
\(298\) | −1.69985e11 | −1.24864 | ||||||||
\(299\) | −8.78436e10 | −0.635608 | ||||||||
\(300\) | −2.86736e11 | −2.04379 | ||||||||
\(301\) | −1.15068e11 | −0.807986 | ||||||||
\(302\) | 1.72881e10 | 0.119596 | ||||||||
\(303\) | −2.66638e10 | −0.181732 | ||||||||
\(304\) | 3.63622e11 | 2.44185 | ||||||||
\(305\) | −2.43196e10 | −0.160919 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.84456e11 | −1.18514 | −0.592570 | − | 0.805519i | \(-0.701887\pi\) | ||||
−0.592570 | + | 0.805519i | \(0.701887\pi\) | |||||||
\(308\) | −5.06706e11 | −3.20832 | ||||||||
\(309\) | 1.60071e11 | 0.998850 | ||||||||
\(310\) | 1.78859e11 | 1.09997 | ||||||||
\(311\) | 1.97872e11 | 1.19939 | 0.599697 | − | 0.800227i | \(-0.295288\pi\) | ||||
0.599697 | + | 0.800227i | \(0.295288\pi\) | |||||||
\(312\) | 1.08118e11 | 0.645956 | ||||||||
\(313\) | −8.05381e10 | −0.474299 | −0.237149 | − | 0.971473i | \(-0.576213\pi\) | ||||
−0.237149 | + | 0.971473i | \(0.576213\pi\) | |||||||
\(314\) | 7.28905e10 | 0.423143 | ||||||||
\(315\) | −9.28869e10 | −0.531566 | ||||||||
\(316\) | 3.56250e11 | 2.00985 | ||||||||
\(317\) | −1.37985e11 | −0.767475 | −0.383738 | − | 0.923442i | \(-0.625363\pi\) | ||||
−0.383738 | + | 0.923442i | \(0.625363\pi\) | |||||||
\(318\) | 1.61039e10 | 0.0883099 | ||||||||
\(319\) | −1.72857e11 | −0.934607 | ||||||||
\(320\) | 4.34061e10 | 0.231407 | ||||||||
\(321\) | 1.81713e11 | 0.955242 | ||||||||
\(322\) | 4.84707e11 | 2.51262 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.65868e11 | −0.836200 | ||||||||
\(325\) | −9.00728e10 | −0.447835 | ||||||||
\(326\) | −2.68130e11 | −1.31482 | ||||||||
\(327\) | 3.76220e10 | 0.181961 | ||||||||
\(328\) | 6.78254e11 | 3.23564 | ||||||||
\(329\) | 1.01045e11 | 0.475482 | ||||||||
\(330\) | 7.48165e11 | 3.47284 | ||||||||
\(331\) | −1.12292e11 | −0.514189 | −0.257095 | − | 0.966386i | \(-0.582765\pi\) | ||||
−0.257095 | + | 0.966386i | \(0.582765\pi\) | |||||||
\(332\) | −5.63118e11 | −2.54377 | ||||||||
\(333\) | −1.20556e11 | −0.537269 | ||||||||
\(334\) | 7.96412e10 | 0.350170 | ||||||||
\(335\) | 6.22883e11 | 2.70212 | ||||||||
\(336\) | −2.71846e11 | −1.16358 | ||||||||
\(337\) | 2.22819e11 | 0.941063 | 0.470531 | − | 0.882383i | \(-0.344062\pi\) | ||||
0.470531 | + | 0.882383i | \(0.344062\pi\) | |||||||
\(338\) | −3.73764e11 | −1.55766 | ||||||||
\(339\) | 7.97814e10 | 0.328098 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.76810e11 | −0.708130 | ||||||||
\(342\) | −2.57899e11 | −1.01937 | ||||||||
\(343\) | −2.79072e11 | −1.08866 | ||||||||
\(344\) | −5.94502e11 | −2.28897 | ||||||||
\(345\) | −4.97249e11 | −1.88968 | ||||||||
\(346\) | 6.44269e11 | 2.41671 | ||||||||
\(347\) | 8.77169e10 | 0.324788 | 0.162394 | − | 0.986726i | \(-0.448078\pi\) | ||||
0.162394 | + | 0.986726i | \(0.448078\pi\) | |||||||
\(348\) | −2.52180e11 | −0.921730 | ||||||||
\(349\) | −3.18539e11 | −1.14934 | −0.574669 | − | 0.818386i | \(-0.694869\pi\) | ||||
−0.574669 | + | 0.818386i | \(0.694869\pi\) | |||||||
\(350\) | 4.97007e11 | 1.77034 | ||||||||
\(351\) | −1.14447e11 | −0.402458 | ||||||||
\(352\) | −5.66942e11 | −1.96832 | ||||||||
\(353\) | −5.28579e11 | −1.81186 | −0.905928 | − | 0.423432i | \(-0.860825\pi\) | ||||
−0.905928 | + | 0.423432i | \(0.860825\pi\) | |||||||
\(354\) | 3.08750e11 | 1.04494 | ||||||||
\(355\) | 2.72882e11 | 0.911901 | ||||||||
\(356\) | 2.05451e11 | 0.677927 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.84901e11 | 0.594930 | ||||||||
\(359\) | 4.14566e11 | 1.31725 | 0.658625 | − | 0.752471i | \(-0.271138\pi\) | ||||
0.658625 | + | 0.752471i | \(0.271138\pi\) | |||||||
\(360\) | −4.79904e11 | −1.50589 | ||||||||
\(361\) | 2.07120e11 | 0.641858 | ||||||||
\(362\) | −9.27421e11 | −2.83850 | ||||||||
\(363\) | −4.91932e11 | −1.48705 | ||||||||
\(364\) | −2.32215e11 | −0.693321 | ||||||||
\(365\) | 6.67207e11 | 1.96763 | ||||||||
\(366\) | 5.04805e10 | 0.147048 | ||||||||
\(367\) | 2.91075e11 | 0.837543 | 0.418771 | − | 0.908092i | \(-0.362461\pi\) | ||||
0.418771 | + | 0.908092i | \(0.362461\pi\) | |||||||
\(368\) | 1.14113e12 | 3.24354 | ||||||||
\(369\) | −2.19203e11 | −0.615500 | ||||||||
\(370\) | 1.18296e12 | 3.28142 | ||||||||
\(371\) | −1.93939e10 | −0.0531475 | ||||||||
\(372\) | −2.57947e11 | −0.698373 | ||||||||
\(373\) | −8.23127e10 | −0.220180 | −0.110090 | − | 0.993922i | \(-0.535114\pi\) | ||||
−0.110090 | + | 0.993922i | \(0.535114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.46997e10 | −0.221177 | ||||||||
\(376\) | 5.22054e11 | 1.34701 | ||||||||
\(377\) | −7.92176e10 | −0.201970 | ||||||||
\(378\) | 6.31498e11 | 1.59096 | ||||||||
\(379\) | 5.54877e11 | 1.38140 | 0.690701 | − | 0.723140i | \(-0.257302\pi\) | ||||
0.690701 | + | 0.723140i | \(0.257302\pi\) | |||||||
\(380\) | 1.75825e12 | 4.32569 | ||||||||
\(381\) | −3.40131e11 | −0.826959 | ||||||||
\(382\) | −3.23009e11 | −0.776121 | ||||||||
\(383\) | 5.79022e11 | 1.37499 | 0.687496 | − | 0.726188i | \(-0.258710\pi\) | ||||
0.687496 | + | 0.726188i | \(0.258710\pi\) | |||||||
\(384\) | 2.73237e11 | 0.641282 | ||||||||
\(385\) | −9.01014e11 | −2.09006 | ||||||||
\(386\) | −5.83438e11 | −1.33768 | ||||||||
\(387\) | 1.92136e11 | 0.435420 | ||||||||
\(388\) | −9.49946e11 | −2.12792 | ||||||||
\(389\) | 5.29321e11 | 1.17205 | 0.586025 | − | 0.810293i | \(-0.300692\pi\) | ||||
0.586025 | + | 0.810293i | \(0.300692\pi\) | |||||||
\(390\) | 3.42872e11 | 0.750484 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.61689e11 | −0.773655 | ||||||||
\(393\) | 2.87939e11 | 0.608883 | ||||||||
\(394\) | 1.33477e11 | 0.279045 | ||||||||
\(395\) | 6.33476e11 | 1.30931 | ||||||||
\(396\) | 8.46078e11 | 1.72895 | ||||||||
\(397\) | −4.75199e10 | −0.0960105 | −0.0480052 | − | 0.998847i | \(-0.515286\pi\) | ||||
−0.0480052 | + | 0.998847i | \(0.515286\pi\) | |||||||
\(398\) | −2.99584e11 | −0.598474 | ||||||||
\(399\) | −3.96087e11 | −0.782372 | ||||||||
\(400\) | 1.17009e12 | 2.28533 | ||||||||
\(401\) | 5.62820e11 | 1.08697 | 0.543487 | − | 0.839417i | \(-0.317104\pi\) | ||||
0.543487 | + | 0.839417i | \(0.317104\pi\) | |||||||
\(402\) | −1.29293e12 | −2.46920 | ||||||||
\(403\) | −8.10293e10 | −0.153028 | ||||||||
\(404\) | 2.95879e11 | 0.552584 | ||||||||
\(405\) | −2.94943e11 | −0.544742 | ||||||||
\(406\) | 4.37110e11 | 0.798406 | ||||||||
\(407\) | −1.16941e12 | −2.11248 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.86774e11 | −0.330037 | −0.165018 | − | 0.986290i | \(-0.552768\pi\) | ||||
−0.165018 | + | 0.986290i | \(0.552768\pi\) | |||||||
\(410\) | 2.15093e12 | 3.75923 | ||||||||
\(411\) | −7.16902e11 | −1.23929 | ||||||||
\(412\) | −1.77626e12 | −3.03716 | ||||||||
\(413\) | −3.71827e11 | −0.628877 | ||||||||
\(414\) | −8.09345e11 | −1.35404 | ||||||||
\(415\) | −1.00132e12 | −1.65714 | ||||||||
\(416\) | −2.59820e11 | −0.425356 | ||||||||
\(417\) | 2.32888e11 | 0.377168 | ||||||||
\(418\) | −2.50165e12 | −4.00805 | ||||||||
\(419\) | 5.54170e11 | 0.878375 | 0.439187 | − | 0.898395i | \(-0.355266\pi\) | ||||
0.439187 | + | 0.898395i | \(0.355266\pi\) | |||||||
\(420\) | −1.31448e12 | −2.06126 | ||||||||
\(421\) | −4.58096e11 | −0.710701 | −0.355351 | − | 0.934733i | \(-0.615639\pi\) | ||||
−0.355351 | + | 0.934733i | \(0.615639\pi\) | |||||||
\(422\) | 3.29600e10 | 0.0505919 | ||||||||
\(423\) | −1.68721e11 | −0.256235 | ||||||||
\(424\) | −1.00199e11 | −0.150563 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.66426e11 | −0.833297 | ||||||||
\(427\) | −6.07936e10 | −0.0884978 | ||||||||
\(428\) | −2.01641e12 | −2.90456 | ||||||||
\(429\) | −3.38946e11 | −0.483139 | ||||||||
\(430\) | −1.88533e12 | −2.65937 | ||||||||
\(431\) | −3.33640e11 | −0.465726 | −0.232863 | − | 0.972510i | \(-0.574809\pi\) | ||||
−0.232863 | + | 0.972510i | \(0.574809\pi\) | |||||||
\(432\) | 1.48671e12 | 2.05376 | ||||||||
\(433\) | −7.14343e11 | −0.976588 | −0.488294 | − | 0.872679i | \(-0.662381\pi\) | ||||
−0.488294 | + | 0.872679i | \(0.662381\pi\) | |||||||
\(434\) | 4.47107e11 | 0.604934 | ||||||||
\(435\) | −4.48421e11 | −0.600460 | ||||||||
\(436\) | −4.17478e11 | −0.553280 | ||||||||
\(437\) | 1.66266e12 | 2.18090 | ||||||||
\(438\) | −1.38493e12 | −1.79802 | ||||||||
\(439\) | −5.11066e11 | −0.656729 | −0.328365 | − | 0.944551i | \(-0.606497\pi\) | ||||
−0.328365 | + | 0.944551i | \(0.606497\pi\) | |||||||
\(440\) | −4.65512e12 | −5.92099 | ||||||||
\(441\) | 1.16893e11 | 0.147169 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.01063e11 | 0.618124 | 0.309062 | − | 0.951042i | \(-0.399985\pi\) | ||||
0.309062 | + | 0.951042i | \(0.399985\pi\) | |||||||
\(444\) | −1.70604e12 | −2.08337 | ||||||||
\(445\) | 3.65328e11 | 0.441635 | ||||||||
\(446\) | 8.47428e11 | 1.01414 | ||||||||
\(447\) | 4.35919e11 | 0.516443 | ||||||||
\(448\) | 1.08506e11 | 0.127263 | ||||||||
\(449\) | −1.40379e12 | −1.63002 | −0.815011 | − | 0.579445i | \(-0.803269\pi\) | ||||
−0.815011 | + | 0.579445i | \(0.803269\pi\) | |||||||
\(450\) | −8.29884e11 | −0.954028 | ||||||||
\(451\) | −2.12630e12 | −2.42008 | ||||||||
\(452\) | −8.85307e11 | −0.997633 | ||||||||
\(453\) | −4.43348e10 | −0.0494655 | ||||||||
\(454\) | −1.32005e12 | −1.45827 | ||||||||
\(455\) | −4.12920e11 | −0.451663 | ||||||||
\(456\) | −2.04640e12 | −2.21641 | ||||||||
\(457\) | 1.21248e12 | 1.30032 | 0.650161 | − | 0.759797i | \(-0.274702\pi\) | ||||
0.650161 | + | 0.759797i | \(0.274702\pi\) | |||||||
\(458\) | −5.98385e11 | −0.635457 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.51779e12 | 5.74586 | ||||||||
\(461\) | 9.45438e10 | 0.0974942 | 0.0487471 | − | 0.998811i | \(-0.484477\pi\) | ||||
0.0487471 | + | 0.998811i | \(0.484477\pi\) | |||||||
\(462\) | 1.87025e12 | 1.90990 | ||||||||
\(463\) | 6.27192e11 | 0.634287 | 0.317144 | − | 0.948378i | \(-0.397276\pi\) | ||||
0.317144 | + | 0.948378i | \(0.397276\pi\) | |||||||
\(464\) | 1.02907e12 | 1.03066 | ||||||||
\(465\) | −4.58676e11 | −0.454954 | ||||||||
\(466\) | 5.74453e11 | 0.564310 | ||||||||
\(467\) | 1.46476e12 | 1.42508 | 0.712542 | − | 0.701630i | \(-0.247544\pi\) | ||||
0.712542 | + | 0.701630i | \(0.247544\pi\) | |||||||
\(468\) | 3.87744e11 | 0.373627 | ||||||||
\(469\) | 1.55707e12 | 1.48604 | ||||||||
\(470\) | 1.65558e12 | 1.56498 | ||||||||
\(471\) | −1.86925e11 | −0.175014 | ||||||||
\(472\) | −1.92106e12 | −1.78157 | ||||||||
\(473\) | 1.86374e12 | 1.71202 | ||||||||
\(474\) | −1.31492e12 | −1.19645 | ||||||||
\(475\) | 1.70485e12 | 1.53661 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.23832e10 | 0.0286409 | ||||||||
\(478\) | −1.81654e11 | −0.159155 | ||||||||
\(479\) | 1.19999e12 | 1.04152 | 0.520761 | − | 0.853703i | \(-0.325648\pi\) | ||||
0.520761 | + | 0.853703i | \(0.325648\pi\) | |||||||
\(480\) | −1.47074e12 | −1.26459 | ||||||||
\(481\) | −5.35922e11 | −0.456509 | ||||||||
\(482\) | 7.84149e11 | 0.661740 | ||||||||
\(483\) | −1.24301e12 | −1.03923 | ||||||||
\(484\) | 5.45879e12 | 4.52160 | ||||||||
\(485\) | −1.68917e12 | −1.38623 | ||||||||
\(486\) | −1.78696e12 | −1.45295 | ||||||||
\(487\) | 2.37860e11 | 0.191620 | 0.0958100 | − | 0.995400i | \(-0.469456\pi\) | ||||
0.0958100 | + | 0.995400i | \(0.469456\pi\) | |||||||
\(488\) | −3.14093e11 | −0.250708 | ||||||||
\(489\) | 6.87609e11 | 0.543816 | ||||||||
\(490\) | −1.14701e12 | −0.898847 | ||||||||
\(491\) | −2.34046e12 | −1.81734 | −0.908668 | − | 0.417520i | \(-0.862899\pi\) | ||||
−0.908668 | + | 0.417520i | \(0.862899\pi\) | |||||||
\(492\) | −3.10204e12 | −2.38673 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −1.14646e12 | −0.866143 | ||||||||
\(495\) | 1.50448e12 | 1.12632 | ||||||||
\(496\) | 1.05261e12 | 0.780908 | ||||||||
\(497\) | 6.82146e11 | 0.501503 | ||||||||
\(498\) | 2.07846e12 | 1.51429 | ||||||||
\(499\) | −1.92746e12 | −1.39166 | −0.695829 | − | 0.718207i | \(-0.744963\pi\) | ||||
−0.695829 | + | 0.718207i | \(0.744963\pi\) | |||||||
\(500\) | 9.39882e11 | 0.672525 | ||||||||
\(501\) | −2.04237e11 | −0.144832 | ||||||||
\(502\) | −3.53825e11 | −0.248669 | ||||||||
\(503\) | −5.96651e11 | −0.415589 | −0.207795 | − | 0.978172i | \(-0.566629\pi\) | ||||
−0.207795 | + | 0.978172i | \(0.566629\pi\) | |||||||
\(504\) | −1.19965e12 | −0.828169 | ||||||||
\(505\) | 5.26126e11 | 0.359980 | ||||||||
\(506\) | −7.85074e12 | −5.32394 | ||||||||
\(507\) | 9.58504e11 | 0.644255 | ||||||||
\(508\) | 3.77432e12 | 2.51450 | ||||||||
\(509\) | 1.05883e12 | 0.699190 | 0.349595 | − | 0.936901i | \(-0.386319\pi\) | ||||
0.349595 | + | 0.936901i | \(0.386319\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.66787e12 | 1.08210 | ||||||||
\(512\) | −3.47121e12 | −2.23237 | ||||||||
\(513\) | 2.16618e12 | 1.38091 | ||||||||
\(514\) | −4.70125e12 | −2.97084 | ||||||||
\(515\) | −3.15850e12 | −1.97856 | ||||||||
\(516\) | 2.71899e12 | 1.68843 | ||||||||
\(517\) | −1.63662e12 | −1.00749 | ||||||||
\(518\) | 2.95713e12 | 1.80463 | ||||||||
\(519\) | −1.65220e12 | −0.999564 | ||||||||
\(520\) | −2.13337e12 | −1.27953 | ||||||||
\(521\) | −3.10824e12 | −1.84818 | −0.924091 | − | 0.382172i | \(-0.875176\pi\) | ||||
−0.924091 | + | 0.382172i | \(0.875176\pi\) | |||||||
\(522\) | −7.29870e11 | −0.430257 | ||||||||
\(523\) | 1.18130e12 | 0.690400 | 0.345200 | − | 0.938529i | \(-0.387811\pi\) | ||||
0.345200 | + | 0.938529i | \(0.387811\pi\) | |||||||
\(524\) | −3.19516e12 | −1.85140 | ||||||||
\(525\) | −1.27456e12 | −0.732221 | ||||||||
\(526\) | 1.40270e12 | 0.798968 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 4.40306e12 | 2.46548 | ||||||||
\(529\) | 3.41664e12 | 1.89692 | ||||||||
\(530\) | −3.17760e11 | −0.174927 | ||||||||
\(531\) | 6.20863e11 | 0.338899 | ||||||||
\(532\) | 4.39524e12 | 2.37892 | ||||||||
\(533\) | −9.74447e11 | −0.522981 | ||||||||
\(534\) | −7.58318e11 | −0.403567 | ||||||||
\(535\) | −3.58553e12 | −1.89218 | ||||||||
\(536\) | 8.04467e12 | 4.20985 | ||||||||
\(537\) | −4.74172e11 | −0.246066 | ||||||||
\(538\) | 2.84531e12 | 1.46423 | ||||||||
\(539\) | 1.13388e12 | 0.578651 | ||||||||
\(540\) | 7.18883e12 | 3.63820 | ||||||||
\(541\) | −3.43819e12 | −1.72561 | −0.862803 | − | 0.505540i | \(-0.831293\pi\) | ||||
−0.862803 | + | 0.505540i | \(0.831293\pi\) | |||||||
\(542\) | −4.36506e10 | −0.0217267 | ||||||||
\(543\) | 2.37834e12 | 1.17402 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.42351e11 | −0.360433 | ||||||||
\(546\) | 8.57104e11 | 0.412731 | ||||||||
\(547\) | −1.60640e12 | −0.767201 | −0.383601 | − | 0.923499i | \(-0.625316\pi\) | ||||
−0.383601 | + | 0.923499i | \(0.625316\pi\) | |||||||
\(548\) | 7.95521e12 | 3.76824 | ||||||||
\(549\) | 1.01511e11 | 0.0476911 | ||||||||
\(550\) | −8.04997e12 | −3.75113 | ||||||||
\(551\) | 1.49939e12 | 0.692998 | ||||||||
\(552\) | −6.42207e12 | −2.94408 | ||||||||
\(553\) | 1.58355e12 | 0.720060 | ||||||||
\(554\) | 4.04879e12 | 1.82613 | ||||||||
\(555\) | −3.03365e12 | −1.35721 | ||||||||
\(556\) | −2.58428e12 | −1.14684 | ||||||||
\(557\) | −1.82680e12 | −0.804160 | −0.402080 | − | 0.915604i | \(-0.631713\pi\) | ||||
−0.402080 | + | 0.915604i | \(0.631713\pi\) | |||||||
\(558\) | −7.46562e11 | −0.325996 | ||||||||
\(559\) | 8.54121e11 | 0.369970 | ||||||||
\(560\) | 5.36403e12 | 2.30486 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.34695e12 | −3.10666 | ||||||||
\(563\) | −2.07582e12 | −0.870768 | −0.435384 | − | 0.900245i | \(-0.643387\pi\) | ||||
−0.435384 | + | 0.900245i | \(0.643387\pi\) | |||||||
\(564\) | −2.38765e12 | −0.993606 | ||||||||
\(565\) | −1.57423e12 | −0.649907 | ||||||||
\(566\) | 1.26716e12 | 0.518989 | ||||||||
\(567\) | −7.37293e11 | −0.299582 | ||||||||
\(568\) | 3.52433e12 | 1.42072 | ||||||||
\(569\) | −2.00630e12 | −0.802398 | −0.401199 | − | 0.915991i | \(-0.631406\pi\) | ||||
−0.401199 | + | 0.915991i | \(0.631406\pi\) | |||||||
\(570\) | −6.48970e12 | −2.57506 | ||||||||
\(571\) | −4.13921e12 | −1.62950 | −0.814750 | − | 0.579812i | \(-0.803126\pi\) | ||||
−0.814750 | + | 0.579812i | \(0.803126\pi\) | |||||||
\(572\) | 3.76116e12 | 1.46906 | ||||||||
\(573\) | 8.28345e11 | 0.321008 | ||||||||
\(574\) | 5.37684e12 | 2.06740 | ||||||||
\(575\) | 5.35020e12 | 2.04110 | ||||||||
\(576\) | −1.81179e11 | −0.0685814 | ||||||||
\(577\) | −1.32648e12 | −0.498207 | −0.249103 | − | 0.968477i | \(-0.580136\pi\) | ||||
−0.249103 | + | 0.968477i | \(0.580136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.49620e12 | 0.553270 | ||||||||
\(580\) | 4.97597e12 | 1.82579 | ||||||||
\(581\) | −2.50309e12 | −0.911347 | ||||||||
\(582\) | 3.50624e12 | 1.26674 | ||||||||
\(583\) | 3.14121e11 | 0.112613 | ||||||||
\(584\) | 8.61713e12 | 3.06552 | ||||||||
\(585\) | 6.89478e11 | 0.243399 | ||||||||
\(586\) | 7.04576e11 | 0.246825 | ||||||||
\(587\) | 1.74995e12 | 0.608350 | 0.304175 | − | 0.952616i | \(-0.401619\pi\) | ||||
0.304175 | + | 0.952616i | \(0.401619\pi\) | |||||||
\(588\) | 1.65420e12 | 0.570678 | ||||||||
\(589\) | 1.53368e12 | 0.525068 | ||||||||
\(590\) | −6.09220e12 | −2.06986 | ||||||||
\(591\) | −3.42298e11 | −0.115415 | ||||||||
\(592\) | 6.96189e12 | 2.32959 | ||||||||
\(593\) | 1.45962e12 | 0.484723 | 0.242361 | − | 0.970186i | \(-0.422078\pi\) | ||||
0.242361 | + | 0.970186i | \(0.422078\pi\) | |||||||
\(594\) | −1.02283e13 | −3.37104 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.83724e12 | −1.57033 | ||||||||
\(597\) | 7.68272e11 | 0.247532 | ||||||||
\(598\) | −3.59787e12 | −1.15051 | ||||||||
\(599\) | 5.09467e12 | 1.61695 | 0.808473 | − | 0.588534i | \(-0.200295\pi\) | ||||
0.808473 | + | 0.588534i | \(0.200295\pi\) | |||||||
\(600\) | −6.58505e12 | −2.07433 | ||||||||
\(601\) | 3.21832e12 | 1.00622 | 0.503111 | − | 0.864222i | \(-0.332189\pi\) | ||||
0.503111 | + | 0.864222i | \(0.332189\pi\) | |||||||
\(602\) | −4.71290e12 | −1.46253 | ||||||||
\(603\) | −2.59994e12 | −0.800820 | ||||||||
\(604\) | 4.91968e11 | 0.150408 | ||||||||
\(605\) | 9.70671e12 | 2.94559 | ||||||||
\(606\) | −1.09209e12 | −0.328951 | ||||||||
\(607\) | 6.15206e12 | 1.83938 | 0.919690 | − | 0.392645i | \(-0.128440\pi\) | ||||
0.919690 | + | 0.392645i | \(0.128440\pi\) | |||||||
\(608\) | 4.91774e12 | 1.45948 | ||||||||
\(609\) | −1.12095e12 | −0.330225 | ||||||||
\(610\) | −9.96073e11 | −0.291278 | ||||||||
\(611\) | −7.50035e11 | −0.217719 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.67903e12 | −1.33839 | −0.669196 | − | 0.743086i | \(-0.733361\pi\) | ||||
−0.669196 | + | 0.743086i | \(0.733361\pi\) | |||||||
\(614\) | −7.55488e12 | −2.14521 | ||||||||
\(615\) | −5.51597e12 | −1.55483 | ||||||||
\(616\) | −1.16368e13 | −3.25627 | ||||||||
\(617\) | −1.42170e12 | −0.394933 | −0.197467 | − | 0.980310i | \(-0.563271\pi\) | ||||
−0.197467 | + | 0.980310i | \(0.563271\pi\) | |||||||
\(618\) | 6.55615e12 | 1.80801 | ||||||||
\(619\) | −2.99905e12 | −0.821061 | −0.410531 | − | 0.911847i | \(-0.634656\pi\) | ||||
−0.410531 | + | 0.911847i | \(0.634656\pi\) | |||||||
\(620\) | 5.08977e12 | 1.38336 | ||||||||
\(621\) | 6.79797e12 | 1.83429 | ||||||||
\(622\) | 8.10436e12 | 2.17101 | ||||||||
\(623\) | 9.13240e11 | 0.242878 | ||||||||
\(624\) | 2.01785e12 | 0.532794 | ||||||||
\(625\) | −2.90336e12 | −0.761099 | ||||||||
\(626\) | −3.29865e12 | −0.858523 | ||||||||
\(627\) | 6.41538e12 | 1.65775 | ||||||||
\(628\) | 2.07424e12 | 0.532158 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −3.80443e12 | −0.962182 | ||||||||
\(631\) | −3.26952e12 | −0.821017 | −0.410508 | − | 0.911857i | \(-0.634649\pi\) | ||||
−0.410508 | + | 0.911857i | \(0.634649\pi\) | |||||||
\(632\) | 8.18148e12 | 2.03988 | ||||||||
\(633\) | −8.45246e10 | −0.0209251 | ||||||||
\(634\) | −5.65153e12 | −1.38920 | ||||||||
\(635\) | 6.71141e12 | 1.63807 | ||||||||
\(636\) | 4.58268e11 | 0.111061 | ||||||||
\(637\) | 5.19638e11 | 0.125047 | ||||||||
\(638\) | −7.07982e12 | −1.69172 | ||||||||
\(639\) | −1.13902e12 | −0.270258 | ||||||||
\(640\) | −5.39146e12 | −1.27027 | ||||||||
\(641\) | −2.29784e12 | −0.537598 | −0.268799 | − | 0.963196i | \(-0.586627\pi\) | ||||
−0.268799 | + | 0.963196i | \(0.586627\pi\) | |||||||
\(642\) | 7.44254e12 | 1.72907 | ||||||||
\(643\) | −1.34089e12 | −0.309345 | −0.154673 | − | 0.987966i | \(-0.549432\pi\) | ||||
−0.154673 | + | 0.987966i | \(0.549432\pi\) | |||||||
\(644\) | 1.37933e13 | 3.15995 | ||||||||
\(645\) | 4.83485e12 | 1.09993 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.20336e12 | 1.39174 | 0.695869 | − | 0.718168i | \(-0.255019\pi\) | ||||
0.695869 | + | 0.718168i | \(0.255019\pi\) | |||||||
\(648\) | −3.80925e12 | −0.848696 | ||||||||
\(649\) | 6.02244e12 | 1.33251 | ||||||||
\(650\) | −3.68917e12 | −0.810622 | ||||||||
\(651\) | −1.14659e12 | −0.250203 | ||||||||
\(652\) | −7.63016e12 | −1.65356 | ||||||||
\(653\) | 5.36324e11 | 0.115430 | 0.0577149 | − | 0.998333i | \(-0.481619\pi\) | ||||
0.0577149 | + | 0.998333i | \(0.481619\pi\) | |||||||
\(654\) | 1.54091e12 | 0.329365 | ||||||||
\(655\) | −5.68156e12 | −1.20610 | ||||||||
\(656\) | 1.26585e13 | 2.66880 | ||||||||
\(657\) | −2.78495e12 | −0.583140 | ||||||||
\(658\) | 4.13857e12 | 0.860665 | ||||||||
\(659\) | 3.60641e11 | 0.0744887 | 0.0372443 | − | 0.999306i | \(-0.488142\pi\) | ||||
0.0372443 | + | 0.999306i | \(0.488142\pi\) | |||||||
\(660\) | 2.12905e13 | 4.36755 | ||||||||
\(661\) | −6.10771e12 | −1.24443 | −0.622216 | − | 0.782845i | \(-0.713768\pi\) | ||||
−0.622216 | + | 0.782845i | \(0.713768\pi\) | |||||||
\(662\) | −4.59922e12 | −0.930729 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.29323e13 | −2.58178 | ||||||||
\(665\) | 7.81553e12 | 1.54975 | ||||||||
\(666\) | −4.93771e12 | −0.972504 | ||||||||
\(667\) | 4.70542e12 | 0.920518 | ||||||||
\(668\) | 2.26634e12 | 0.440384 | ||||||||
\(669\) | −2.17320e12 | −0.419452 | ||||||||
\(670\) | 2.55118e13 | 4.89108 | ||||||||
\(671\) | 9.84667e11 | 0.187516 | ||||||||
\(672\) | −3.67653e12 | −0.695467 | ||||||||
\(673\) | −5.35107e12 | −1.00548 | −0.502739 | − | 0.864438i | \(-0.667674\pi\) | ||||
−0.502739 | + | 0.864438i | \(0.667674\pi\) | |||||||
\(674\) | 9.12616e12 | 1.70341 | ||||||||
\(675\) | 6.97048e12 | 1.29240 | ||||||||
\(676\) | −1.06362e13 | −1.95896 | ||||||||
\(677\) | 2.46559e12 | 0.451099 | 0.225550 | − | 0.974232i | \(-0.427582\pi\) | ||||
0.225550 | + | 0.974232i | \(0.427582\pi\) | |||||||
\(678\) | 3.26766e12 | 0.593886 | ||||||||
\(679\) | −4.22256e12 | −0.762364 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.38522e12 | 0.603149 | ||||||||
\(682\) | −7.24174e12 | −1.28178 | ||||||||
\(683\) | −8.41114e12 | −1.47898 | −0.739489 | − | 0.673169i | \(-0.764933\pi\) | ||||
−0.739489 | + | 0.673169i | \(0.764933\pi\) | |||||||
\(684\) | −7.33901e12 | −1.28199 | ||||||||
\(685\) | 1.41458e13 | 2.45482 | ||||||||
\(686\) | −1.14301e13 | −1.97057 | ||||||||
\(687\) | 1.53454e12 | 0.262828 | ||||||||
\(688\) | −1.10954e13 | −1.88797 | ||||||||
\(689\) | 1.43957e11 | 0.0243358 | ||||||||
\(690\) | −2.03661e13 | −3.42049 | ||||||||
\(691\) | −3.08875e12 | −0.515384 | −0.257692 | − | 0.966227i | \(-0.582962\pi\) | ||||
−0.257692 | + | 0.966227i | \(0.582962\pi\) | |||||||
\(692\) | 1.83339e13 | 3.03933 | ||||||||
\(693\) | 3.76086e12 | 0.619424 | ||||||||
\(694\) | 3.59268e12 | 0.587896 | ||||||||
\(695\) | −4.59531e12 | −0.747107 | ||||||||
\(696\) | −5.79145e12 | −0.935504 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.30466e13 | −2.08040 | ||||||||
\(699\) | −1.47316e12 | −0.233401 | ||||||||
\(700\) | 1.41433e13 | 2.22643 | ||||||||
\(701\) | −9.89703e12 | −1.54801 | −0.774005 | − | 0.633180i | \(-0.781749\pi\) | ||||
−0.774005 | + | 0.633180i | \(0.781749\pi\) | |||||||
\(702\) | −4.68746e12 | −0.728485 | ||||||||
\(703\) | 1.01437e13 | 1.56637 | ||||||||
\(704\) | −1.75745e12 | −0.269654 | ||||||||
\(705\) | −4.24566e12 | −0.647283 | ||||||||
\(706\) | −2.16494e13 | −3.27962 | ||||||||
\(707\) | 1.31520e12 | 0.197972 | ||||||||
\(708\) | 8.78608e12 | 1.31415 | ||||||||
\(709\) | 6.74854e12 | 1.00300 | 0.501501 | − | 0.865157i | \(-0.332781\pi\) | ||||
0.501501 | + | 0.865157i | \(0.332781\pi\) | |||||||
\(710\) | 1.11766e13 | 1.65062 | ||||||||
\(711\) | −2.64415e12 | −0.388037 | ||||||||
\(712\) | 4.71830e12 | 0.688058 | ||||||||
\(713\) | 4.81304e12 | 0.697455 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.68802e12 | 0.957018 | ||||||||
\(716\) | 5.26172e12 | 0.748203 | ||||||||
\(717\) | 4.65845e11 | 0.0658272 | ||||||||
\(718\) | 1.69796e13 | 2.38434 | ||||||||
\(719\) | 8.19160e12 | 1.14311 | 0.571556 | − | 0.820563i | \(-0.306340\pi\) | ||||
0.571556 | + | 0.820563i | \(0.306340\pi\) | |||||||
\(720\) | −8.95665e12 | −1.24208 | ||||||||
\(721\) | −7.89555e12 | −1.08811 | ||||||||
\(722\) | 8.48314e12 | 1.16182 | ||||||||
\(723\) | −2.01092e12 | −0.273699 | ||||||||
\(724\) | −2.63916e13 | −3.56978 | ||||||||
\(725\) | 4.82483e12 | 0.648577 | ||||||||
\(726\) | −2.01484e13 | −2.69169 | ||||||||
\(727\) | 5.33262e12 | 0.708004 | 0.354002 | − | 0.935245i | \(-0.384821\pi\) | ||||
0.354002 | + | 0.935245i | \(0.384821\pi\) | |||||||
\(728\) | −5.33295e12 | −0.703682 | ||||||||
\(729\) | 7.38370e12 | 0.968279 | ||||||||
\(730\) | 2.73272e13 | 3.56158 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.43652e12 | 0.184932 | ||||||||
\(733\) | −7.95146e12 | −1.01737 | −0.508685 | − | 0.860953i | \(-0.669868\pi\) | ||||
−0.508685 | + | 0.860953i | \(0.669868\pi\) | |||||||
\(734\) | 1.19217e13 | 1.51603 | ||||||||
\(735\) | 2.94147e12 | 0.371768 | ||||||||
\(736\) | 1.54330e13 | 1.93865 | ||||||||
\(737\) | −2.52197e13 | −3.14873 | ||||||||
\(738\) | −8.97805e12 | −1.11411 | ||||||||
\(739\) | −2.28266e11 | −0.0281541 | −0.0140770 | − | 0.999901i | \(-0.504481\pi\) | ||||
−0.0140770 | + | 0.999901i | \(0.504481\pi\) | |||||||
\(740\) | 3.36634e13 | 4.12681 | ||||||||
\(741\) | 2.94007e12 | 0.358241 | ||||||||
\(742\) | −7.94329e11 | −0.0962017 | ||||||||
\(743\) | −8.49426e12 | −1.02253 | −0.511265 | − | 0.859423i | \(-0.670823\pi\) | ||||
−0.511265 | + | 0.859423i | \(0.670823\pi\) | |||||||
\(744\) | −5.92390e12 | −0.708810 | ||||||||
\(745\) | −8.60148e12 | −1.02299 | ||||||||
\(746\) | −3.37134e12 | −0.398545 | ||||||||
\(747\) | 4.17956e12 | 0.491121 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.96304e12 | −1.04061 | ||||||||
\(750\) | −3.46910e12 | −0.400351 | ||||||||
\(751\) | 7.62165e12 | 0.874318 | 0.437159 | − | 0.899384i | \(-0.355985\pi\) | ||||
0.437159 | + | 0.899384i | \(0.355985\pi\) | |||||||
\(752\) | 9.74331e12 | 1.11103 | ||||||||
\(753\) | 9.07372e11 | 0.102851 | ||||||||
\(754\) | −3.24457e12 | −0.365583 | ||||||||
\(755\) | 8.74806e11 | 0.0979830 | ||||||||
\(756\) | 1.79705e13 | 2.00084 | ||||||||
\(757\) | 1.21708e13 | 1.34706 | 0.673532 | − | 0.739158i | \(-0.264776\pi\) | ||||
0.673532 | + | 0.739158i | \(0.264776\pi\) | |||||||
\(758\) | 2.27265e13 | 2.50046 | ||||||||
\(759\) | 2.01329e13 | 2.20201 | ||||||||
\(760\) | 4.03793e13 | 4.39033 | ||||||||
\(761\) | −1.72056e13 | −1.85968 | −0.929840 | − | 0.367964i | \(-0.880055\pi\) | ||||
−0.929840 | + | 0.367964i | \(0.880055\pi\) | |||||||
\(762\) | −1.39310e13 | −1.49687 | ||||||||
\(763\) | −1.85571e12 | −0.198221 | ||||||||
\(764\) | −9.19185e12 | −0.976074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.37154e13 | 2.48886 | ||||||||
\(767\) | 2.75999e12 | 0.287957 | ||||||||
\(768\) | 1.23174e13 | 1.27760 | ||||||||
\(769\) | −1.42533e13 | −1.46976 | −0.734879 | − | 0.678198i | \(-0.762761\pi\) | ||||
−0.734879 | + | 0.678198i | \(0.762761\pi\) | |||||||
\(770\) | −3.69034e13 | −3.78319 | ||||||||
\(771\) | 1.20562e13 | 1.22875 | ||||||||
\(772\) | −1.66029e13 | −1.68231 | ||||||||
\(773\) | −3.75655e12 | −0.378426 | −0.189213 | − | 0.981936i | \(-0.560594\pi\) | ||||
−0.189213 | + | 0.981936i | \(0.560594\pi\) | |||||||
\(774\) | 7.86942e12 | 0.788150 | ||||||||
\(775\) | 4.93518e12 | 0.491411 | ||||||||
\(776\) | −2.18160e13 | −2.15972 | ||||||||
\(777\) | −7.58346e12 | −0.746402 | ||||||||
\(778\) | 2.16798e13 | 2.12152 | ||||||||
\(779\) | 1.84438e13 | 1.79445 | ||||||||
\(780\) | 9.75709e12 | 0.943832 | ||||||||
\(781\) | −1.10486e13 | −1.06262 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.13044e12 | 0.582859 | ||||||||
\(784\) | −6.75034e12 | −0.638122 | ||||||||
\(785\) | 3.68837e12 | 0.346674 | ||||||||
\(786\) | 1.17933e13 | 1.10213 | ||||||||
\(787\) | 1.53858e13 | 1.42967 | 0.714833 | − | 0.699296i | \(-0.246503\pi\) | ||||
0.714833 | + | 0.699296i | \(0.246503\pi\) | |||||||
\(788\) | 3.79836e12 | 0.350936 | ||||||||
\(789\) | −3.59718e12 | −0.330457 | ||||||||
\(790\) | 2.59457e13 | 2.36997 | ||||||||
\(791\) | −3.93524e12 | −0.357418 | ||||||||
\(792\) | 1.94307e13 | 1.75479 | ||||||||
\(793\) | 4.51257e11 | 0.0405224 | ||||||||
\(794\) | −1.94631e12 | −0.173788 | ||||||||
\(795\) | 8.14883e11 | 0.0723507 | ||||||||
\(796\) | −8.52525e12 | −0.752659 | ||||||||
\(797\) | −1.86441e13 | −1.63674 | −0.818370 | − | 0.574692i | \(-0.805122\pi\) | ||||
−0.818370 | + | 0.574692i | \(0.805122\pi\) | |||||||
\(798\) | −1.62228e13 | −1.41616 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.58246e13 | 1.36593 | ||||||||
\(801\) | −1.52489e12 | −0.130886 | ||||||||
\(802\) | 2.30518e13 | 1.96752 | ||||||||
\(803\) | −2.70143e13 | −2.29284 | ||||||||
\(804\) | −3.67928e13 | −3.10535 | ||||||||
\(805\) | 2.45269e13 | 2.05855 | ||||||||
\(806\) | −3.31877e12 | −0.276994 | ||||||||
\(807\) | −7.29670e12 | −0.605613 | ||||||||
\(808\) | 6.79503e12 | 0.560842 | ||||||||
\(809\) | −1.03571e13 | −0.850099 | −0.425050 | − | 0.905170i | \(-0.639743\pi\) | ||||
−0.425050 | + | 0.905170i | \(0.639743\pi\) | |||||||
\(810\) | −1.20802e13 | −0.986031 | ||||||||
\(811\) | −1.65829e13 | −1.34607 | −0.673035 | − | 0.739611i | \(-0.735010\pi\) | ||||
−0.673035 | + | 0.739611i | \(0.735010\pi\) | |||||||
\(812\) | 1.24388e13 | 1.00410 | ||||||||
\(813\) | 1.11940e11 | 0.00898626 | ||||||||
\(814\) | −4.78963e13 | −3.82378 | ||||||||
\(815\) | −1.35678e13 | −1.07721 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.61663e13 | −1.26944 | ||||||||
\(818\) | −7.64984e12 | −0.597396 | ||||||||
\(819\) | 1.72354e12 | 0.133858 | ||||||||
\(820\) | 6.12088e13 | 4.72772 | ||||||||
\(821\) | −4.69704e11 | −0.0360811 | −0.0180406 | − | 0.999837i | \(-0.505743\pi\) | ||||
−0.0180406 | + | 0.999837i | \(0.505743\pi\) | |||||||
\(822\) | −2.93626e13 | −2.24322 | ||||||||
\(823\) | −9.83346e12 | −0.747149 | −0.373574 | − | 0.927600i | \(-0.621868\pi\) | ||||
−0.373574 | + | 0.927600i | \(0.621868\pi\) | |||||||
\(824\) | −4.07927e13 | −3.08255 | ||||||||
\(825\) | 2.06438e13 | 1.55149 | ||||||||
\(826\) | −1.52292e13 | −1.13832 | ||||||||
\(827\) | 1.86474e13 | 1.38625 | 0.693126 | − | 0.720816i | \(-0.256233\pi\) | ||||
0.693126 | + | 0.720816i | \(0.256233\pi\) | |||||||
\(828\) | −2.30315e13 | −1.70289 | ||||||||
\(829\) | −1.30982e13 | −0.963202 | −0.481601 | − | 0.876391i | \(-0.659945\pi\) | ||||
−0.481601 | + | 0.876391i | \(0.659945\pi\) | |||||||
\(830\) | −4.10119e13 | −2.99957 | ||||||||
\(831\) | −1.03830e13 | −0.755296 | ||||||||
\(832\) | −8.05413e11 | −0.0582725 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.53855e12 | 0.682708 | ||||||||
\(835\) | 4.02997e12 | 0.286888 | ||||||||
\(836\) | −7.11892e13 | −5.04064 | ||||||||
\(837\) | 6.27064e12 | 0.441618 | ||||||||
\(838\) | 2.26975e13 | 1.58994 | ||||||||
\(839\) | −1.02237e13 | −0.712325 | −0.356163 | − | 0.934424i | \(-0.615915\pi\) | ||||
−0.356163 | + | 0.934424i | \(0.615915\pi\) | |||||||
\(840\) | −3.01878e13 | −2.09206 | ||||||||
\(841\) | −1.02638e13 | −0.707498 | ||||||||
\(842\) | −1.87625e13 | −1.28643 | ||||||||
\(843\) | 1.88410e13 | 1.28493 | ||||||||
\(844\) | 9.37940e11 | 0.0636259 | ||||||||
\(845\) | −1.89130e13 | −1.27616 | ||||||||
\(846\) | −6.91044e12 | −0.463809 | ||||||||
\(847\) | 2.42646e13 | 1.61994 | ||||||||
\(848\) | −1.87006e12 | −0.124187 | ||||||||
\(849\) | −3.24959e12 | −0.214657 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.18331e13 | 2.08063 | ||||||||
\(852\) | −1.61188e13 | −1.04798 | ||||||||
\(853\) | 2.01132e13 | 1.30080 | 0.650399 | − | 0.759593i | \(-0.274602\pi\) | ||||
0.650399 | + | 0.759593i | \(0.274602\pi\) | |||||||
\(854\) | −2.48996e12 | −0.160189 | ||||||||
\(855\) | −1.30501e13 | −0.835152 | ||||||||
\(856\) | −4.63079e13 | −2.94797 | ||||||||
\(857\) | −1.09459e13 | −0.693168 | −0.346584 | − | 0.938019i | \(-0.612658\pi\) | ||||
−0.346584 | + | 0.938019i | \(0.612658\pi\) | |||||||
\(858\) | −1.38824e13 | −0.874525 | ||||||||
\(859\) | 2.56259e13 | 1.60587 | 0.802935 | − | 0.596066i | \(-0.203270\pi\) | ||||
0.802935 | + | 0.596066i | \(0.203270\pi\) | |||||||
\(860\) | −5.36506e13 | −3.34450 | ||||||||
\(861\) | −1.37887e13 | −0.855086 | ||||||||
\(862\) | −1.36651e13 | −0.843006 | ||||||||
\(863\) | 2.79069e13 | 1.71263 | 0.856313 | − | 0.516456i | \(-0.172749\pi\) | ||||
0.856313 | + | 0.516456i | \(0.172749\pi\) | |||||||
\(864\) | 2.01068e13 | 1.22753 | ||||||||
\(865\) | 3.26010e13 | 1.97997 | ||||||||
\(866\) | −2.92578e13 | −1.76771 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.27233e13 | 0.760783 | ||||||||
\(869\) | −2.56486e13 | −1.52572 | ||||||||
\(870\) | −1.83663e13 | −1.08689 | ||||||||
\(871\) | −1.15578e13 | −0.680444 | ||||||||
\(872\) | −9.58763e12 | −0.561548 | ||||||||
\(873\) | 7.05068e12 | 0.410834 | ||||||||
\(874\) | 6.80985e13 | 3.94763 | ||||||||
\(875\) | 4.17783e12 | 0.240943 | ||||||||
\(876\) | −3.94109e13 | −2.26125 | ||||||||
\(877\) | 3.22173e12 | 0.183904 | 0.0919520 | − | 0.995763i | \(-0.470689\pi\) | ||||
0.0919520 | + | 0.995763i | \(0.470689\pi\) | |||||||
\(878\) | −2.09321e13 | −1.18874 | ||||||||
\(879\) | −1.80686e12 | −0.102088 | ||||||||
\(880\) | −8.68805e13 | −4.88371 | ||||||||
\(881\) | 2.98527e13 | 1.66952 | 0.834762 | − | 0.550611i | \(-0.185605\pi\) | ||||
0.834762 | + | 0.550611i | \(0.185605\pi\) | |||||||
\(882\) | 4.78767e12 | 0.266389 | ||||||||
\(883\) | 2.33030e13 | 1.29000 | 0.644998 | − | 0.764184i | \(-0.276858\pi\) | ||||
0.644998 | + | 0.764184i | \(0.276858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.56232e13 | 0.856103 | ||||||||
\(886\) | 2.05224e13 | 1.11886 | ||||||||
\(887\) | −1.81953e13 | −0.986966 | −0.493483 | − | 0.869755i | \(-0.664276\pi\) | ||||
−0.493483 | + | 0.869755i | \(0.664276\pi\) | |||||||
\(888\) | −3.91803e13 | −2.11451 | ||||||||
\(889\) | 1.67770e13 | 0.900860 | ||||||||
\(890\) | 1.49630e13 | 0.799399 | ||||||||
\(891\) | 1.19418e13 | 0.634777 | ||||||||
\(892\) | 2.41152e13 | 1.27541 | ||||||||
\(893\) | 1.41963e13 | 0.747038 | ||||||||
\(894\) | 1.78542e13 | 0.934807 | ||||||||
\(895\) | 9.35628e12 | 0.487416 | ||||||||
\(896\) | −1.34775e13 | −0.698590 | ||||||||
\(897\) | 9.22659e12 | 0.475856 | ||||||||
\(898\) | −5.74959e13 | −2.95049 | ||||||||
\(899\) | 4.34041e12 | 0.221622 | ||||||||
\(900\) | −2.36160e13 | −1.19981 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −8.70881e13 | −4.38056 | ||||||||
\(903\) | 1.20861e13 | 0.604909 | ||||||||
\(904\) | −2.03316e13 | −1.01254 | ||||||||
\(905\) | −4.69289e13 | −2.32553 | ||||||||
\(906\) | −1.81585e12 | −0.0895371 | ||||||||
\(907\) | −8.29665e12 | −0.407071 | −0.203535 | − | 0.979068i | \(-0.565243\pi\) | ||||
−0.203535 | + | 0.979068i | \(0.565243\pi\) | |||||||
\(908\) | −3.75646e13 | −1.83397 | ||||||||
\(909\) | −2.19607e12 | −0.106686 | ||||||||
\(910\) | −1.69122e13 | −0.817551 | ||||||||
\(911\) | −1.97513e13 | −0.950089 | −0.475044 | − | 0.879962i | \(-0.657568\pi\) | ||||
−0.475044 | + | 0.879962i | \(0.657568\pi\) | |||||||
\(912\) | −3.81929e13 | −1.82812 | ||||||||
\(913\) | 4.05422e13 | 1.93103 | ||||||||
\(914\) | 4.96602e13 | 2.35370 | ||||||||
\(915\) | 2.55439e12 | 0.120474 | ||||||||
\(916\) | −1.70282e13 | −0.799170 | ||||||||
\(917\) | −1.42026e13 | −0.663296 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.17107e13 | 1.00405 | 0.502023 | − | 0.864854i | \(-0.332589\pi\) | ||||
0.502023 | + | 0.864854i | \(0.332589\pi\) | |||||||
\(920\) | 1.26719e14 | 5.83173 | ||||||||
\(921\) | 1.93742e13 | 0.887270 | ||||||||
\(922\) | 3.87229e12 | 0.176473 | ||||||||
\(923\) | −5.06341e12 | −0.229634 | ||||||||
\(924\) | 5.32215e13 | 2.40195 | ||||||||
\(925\) | 3.26409e13 | 1.46597 | ||||||||
\(926\) | 2.56883e13 | 1.14812 | ||||||||
\(927\) | 1.31837e13 | 0.586379 | ||||||||
\(928\) | 1.39175e13 | 0.616022 | ||||||||
\(929\) | −2.57045e13 | −1.13224 | −0.566119 | − | 0.824324i | \(-0.691556\pi\) | ||||
−0.566119 | + | 0.824324i | \(0.691556\pi\) | |||||||
\(930\) | −1.87863e13 | −0.823508 | ||||||||
\(931\) | −9.83543e12 | −0.429062 | ||||||||
\(932\) | 1.63472e13 | 0.709694 | ||||||||
\(933\) | −2.07833e13 | −0.897941 | ||||||||
\(934\) | 5.99931e13 | 2.57953 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.90476e12 | 0.379211 | ||||||||
\(937\) | 6.39027e12 | 0.270827 | 0.135413 | − | 0.990789i | \(-0.456764\pi\) | ||||
0.135413 | + | 0.990789i | \(0.456764\pi\) | |||||||
\(938\) | 6.37739e13 | 2.68986 | ||||||||
\(939\) | 8.45927e12 | 0.355089 | ||||||||
\(940\) | 4.71126e13 | 1.96817 | ||||||||
\(941\) | 4.18227e13 | 1.73884 | 0.869419 | − | 0.494076i | \(-0.164493\pi\) | ||||
0.869419 | + | 0.494076i | \(0.164493\pi\) | |||||||
\(942\) | −7.65600e12 | −0.316791 | ||||||||
\(943\) | 5.78809e13 | 2.38360 | ||||||||
\(944\) | −3.58535e13 | −1.46946 | ||||||||
\(945\) | 3.19547e13 | 1.30344 | ||||||||
\(946\) | 7.63343e13 | 3.09891 | ||||||||
\(947\) | 2.86239e13 | 1.15652 | 0.578260 | − | 0.815852i | \(-0.303732\pi\) | ||||
0.578260 | + | 0.815852i | \(0.303732\pi\) | |||||||
\(948\) | −3.74185e13 | −1.50470 | ||||||||
\(949\) | −1.23802e13 | −0.495485 | ||||||||
\(950\) | 6.98266e13 | 2.78141 | ||||||||
\(951\) | 1.44931e13 | 0.574580 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.18770e13 | 1.64459 | 0.822295 | − | 0.569062i | \(-0.192693\pi\) | ||||
0.822295 | + | 0.569062i | \(0.192693\pi\) | |||||||
\(954\) | 1.32634e12 | 0.0518427 | ||||||||
\(955\) | −1.63448e13 | −0.635862 | ||||||||
\(956\) | −5.16932e12 | −0.200158 | ||||||||
\(957\) | 1.81559e13 | 0.699705 | ||||||||
\(958\) | 4.91488e13 | 1.88525 | ||||||||
\(959\) | 3.53613e13 | 1.35003 | ||||||||
\(960\) | −4.55913e12 | −0.173245 | ||||||||
\(961\) | −2.19999e13 | −0.832082 | ||||||||
\(962\) | −2.19501e13 | −0.826322 | ||||||||
\(963\) | 1.49661e13 | 0.560779 | ||||||||
\(964\) | 2.23145e13 | 0.832224 | ||||||||
\(965\) | −2.95228e13 | −1.09594 | ||||||||
\(966\) | −5.09109e13 | −1.88111 | ||||||||
\(967\) | 1.10971e13 | 0.408124 | 0.204062 | − | 0.978958i | \(-0.434586\pi\) | ||||
0.204062 | + | 0.978958i | \(0.434586\pi\) | |||||||
\(968\) | 1.25364e14 | 4.58918 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.91846e13 | −2.50921 | ||||||||
\(971\) | −1.62887e12 | −0.0588029 | −0.0294015 | − | 0.999568i | \(-0.509360\pi\) | ||||
−0.0294015 | + | 0.999568i | \(0.509360\pi\) | |||||||
\(972\) | −5.08514e13 | −1.82728 | ||||||||
\(973\) | −1.14873e13 | −0.410874 | ||||||||
\(974\) | 9.74219e12 | 0.346850 | ||||||||
\(975\) | 9.46074e12 | 0.335277 | ||||||||
\(976\) | −5.86204e12 | −0.206788 | ||||||||
\(977\) | −4.55973e12 | −0.160108 | −0.0800541 | − | 0.996791i | \(-0.525509\pi\) | ||||
−0.0800541 | + | 0.996791i | \(0.525509\pi\) | |||||||
\(978\) | 2.81629e13 | 0.984355 | ||||||||
\(979\) | −1.47916e13 | −0.514629 | ||||||||
\(980\) | −3.26405e13 | −1.13042 | ||||||||
\(981\) | 3.09860e12 | 0.106821 | ||||||||
\(982\) | −9.58599e13 | −3.28954 | ||||||||
\(983\) | 1.34574e13 | 0.459694 | 0.229847 | − | 0.973227i | \(-0.426177\pi\) | ||||
0.229847 | + | 0.973227i | \(0.426177\pi\) | |||||||
\(984\) | −7.12400e13 | −2.42240 | ||||||||
\(985\) | 6.75416e12 | 0.228617 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.06132e13 | −0.355975 | ||||||||
\(988\) | −3.26249e13 | −1.08929 | ||||||||
\(989\) | −5.07336e13 | −1.68621 | ||||||||
\(990\) | 6.16199e13 | 2.03874 | ||||||||
\(991\) | 1.26466e13 | 0.416525 | 0.208262 | − | 0.978073i | \(-0.433219\pi\) | ||||
0.208262 | + | 0.978073i | \(0.433219\pi\) | |||||||
\(992\) | 1.42358e13 | 0.466745 | ||||||||
\(993\) | 1.17945e13 | 0.384954 | ||||||||
\(994\) | 2.79391e13 | 0.907765 | ||||||||
\(995\) | −1.51594e13 | −0.490319 | ||||||||
\(996\) | 5.91467e13 | 1.90442 | ||||||||
\(997\) | 4.22854e13 | 1.35538 | 0.677692 | − | 0.735346i | \(-0.262980\pi\) | ||||
0.677692 | + | 0.735346i | \(0.262980\pi\) | |||||||
\(998\) | −7.89442e13 | −2.51903 | ||||||||
\(999\) | 4.14736e13 | 1.31743 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 289.10.a.h.1.35 | yes | 36 | |
17.16 | even | 2 | 289.10.a.g.1.35 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.35 | ✓ | 36 | 17.16 | even | 2 | ||
289.10.a.h.1.35 | yes | 36 | 1.1 | even | 1 | trivial |