Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −38.5064 | −0.850880 | −0.425440 | − | 0.904987i | \(-0.639881\pi\) | ||||
−0.425440 | + | 0.904987i | \(0.639881\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −565.255 | −0.276003 | ||||||||
\(5\) | −13229.8 | −1.89329 | −0.946644 | − | 0.322280i | \(-0.895551\pi\) | ||||
−0.946644 | + | 0.322280i | \(0.895551\pi\) | |||||||
\(6\) | 9357.06 | 0.491256 | ||||||||
\(7\) | −8923.95 | −0.200686 | −0.100343 | − | 0.994953i | \(-0.531994\pi\) | ||||
−0.100343 | + | 0.994953i | \(0.531994\pi\) | |||||||
\(8\) | 100627. | 1.08573 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 509431. | 1.61096 | ||||||||
\(11\) | −548740. | −1.02732 | −0.513662 | − | 0.857993i | \(-0.671711\pi\) | ||||
−0.513662 | + | 0.857993i | \(0.671711\pi\) | |||||||
\(12\) | 137357. | 0.159351 | ||||||||
\(13\) | 1.36786e6 | 1.02177 | 0.510884 | − | 0.859650i | \(-0.329318\pi\) | ||||
0.510884 | + | 0.859650i | \(0.329318\pi\) | |||||||
\(14\) | 343630. | 0.170760 | ||||||||
\(15\) | 3.21483e6 | 1.09309 | ||||||||
\(16\) | −2.71715e6 | −0.647819 | ||||||||
\(17\) | 5.04723e6 | 0.862152 | 0.431076 | − | 0.902316i | \(-0.358134\pi\) | ||||
0.431076 | + | 0.902316i | \(0.358134\pi\) | |||||||
\(18\) | −2.27377e6 | −0.283627 | ||||||||
\(19\) | −5.16583e6 | −0.478625 | −0.239312 | − | 0.970943i | \(-0.576922\pi\) | ||||
−0.239312 | + | 0.970943i | \(0.576922\pi\) | |||||||
\(20\) | 7.47818e6 | 0.522554 | ||||||||
\(21\) | 2.16852e6 | 0.115866 | ||||||||
\(22\) | 2.11300e7 | 0.874129 | ||||||||
\(23\) | −9.48085e6 | −0.307146 | −0.153573 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153573 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(24\) | −2.44524e7 | −0.626844 | ||||||||
\(25\) | 1.26198e8 | 2.58454 | ||||||||
\(26\) | −5.26712e7 | −0.869401 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 5.04431e6 | 0.0553901 | ||||||||
\(29\) | −1.29431e8 | −1.17179 | −0.585895 | − | 0.810387i | \(-0.699257\pi\) | ||||
−0.585895 | + | 0.810387i | \(0.699257\pi\) | |||||||
\(30\) | −1.23792e8 | −0.930089 | ||||||||
\(31\) | −9.27006e7 | −0.581558 | −0.290779 | − | 0.956790i | \(-0.593914\pi\) | ||||
−0.290779 | + | 0.956790i | \(0.593914\pi\) | |||||||
\(32\) | −1.01457e8 | −0.534510 | ||||||||
\(33\) | 1.33344e8 | 0.593125 | ||||||||
\(34\) | −1.94351e8 | −0.733588 | ||||||||
\(35\) | 1.18062e8 | 0.379957 | ||||||||
\(36\) | −3.33777e7 | −0.0920011 | ||||||||
\(37\) | −3.97993e7 | −0.0943552 | −0.0471776 | − | 0.998887i | \(-0.515023\pi\) | ||||
−0.0471776 | + | 0.998887i | \(0.515023\pi\) | |||||||
\(38\) | 1.98918e8 | 0.407252 | ||||||||
\(39\) | −3.32389e8 | −0.589918 | ||||||||
\(40\) | −1.33127e9 | −2.05559 | ||||||||
\(41\) | 9.65170e7 | 0.130105 | 0.0650523 | − | 0.997882i | \(-0.479279\pi\) | ||||
0.0650523 | + | 0.997882i | \(0.479279\pi\) | |||||||
\(42\) | −8.35020e7 | −0.0985884 | ||||||||
\(43\) | −6.50542e8 | −0.674837 | −0.337418 | − | 0.941355i | \(-0.609554\pi\) | ||||
−0.337418 | + | 0.941355i | \(0.609554\pi\) | |||||||
\(44\) | 3.10178e8 | 0.283545 | ||||||||
\(45\) | −7.81204e8 | −0.631096 | ||||||||
\(46\) | 3.65074e8 | 0.261344 | ||||||||
\(47\) | −1.60481e9 | −1.02067 | −0.510336 | − | 0.859975i | \(-0.670479\pi\) | ||||
−0.510336 | + | 0.859975i | \(0.670479\pi\) | |||||||
\(48\) | 6.60267e8 | 0.374018 | ||||||||
\(49\) | −1.89769e9 | −0.959725 | ||||||||
\(50\) | −4.85945e9 | −2.19914 | ||||||||
\(51\) | −1.22648e9 | −0.497763 | ||||||||
\(52\) | −7.73187e8 | −0.282011 | ||||||||
\(53\) | −3.48155e9 | −1.14355 | −0.571775 | − | 0.820411i | \(-0.693745\pi\) | ||||
−0.571775 | + | 0.820411i | \(0.693745\pi\) | |||||||
\(54\) | 5.52525e8 | 0.163752 | ||||||||
\(55\) | 7.25970e9 | 1.94502 | ||||||||
\(56\) | −8.97992e8 | −0.217890 | ||||||||
\(57\) | 1.25530e9 | 0.276334 | ||||||||
\(58\) | 4.98393e9 | 0.997053 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −1.81720e9 | −0.301697 | ||||||||
\(61\) | 5.15750e9 | 0.781853 | 0.390927 | − | 0.920422i | \(-0.372155\pi\) | ||||
0.390927 | + | 0.920422i | \(0.372155\pi\) | |||||||
\(62\) | 3.56957e9 | 0.494836 | ||||||||
\(63\) | −5.26950e8 | −0.0668955 | ||||||||
\(64\) | 9.47145e9 | 1.10262 | ||||||||
\(65\) | −1.80964e10 | −1.93450 | ||||||||
\(66\) | −5.13460e9 | −0.504678 | ||||||||
\(67\) | −5.22349e9 | −0.472661 | −0.236330 | − | 0.971673i | \(-0.575945\pi\) | ||||
−0.236330 | + | 0.971673i | \(0.575945\pi\) | |||||||
\(68\) | −2.85297e9 | −0.237957 | ||||||||
\(69\) | 2.30385e9 | 0.177331 | ||||||||
\(70\) | −4.54614e9 | −0.323298 | ||||||||
\(71\) | 1.67408e10 | 1.10117 | 0.550586 | − | 0.834779i | \(-0.314404\pi\) | ||||
0.550586 | + | 0.834779i | \(0.314404\pi\) | |||||||
\(72\) | 5.94193e9 | 0.361909 | ||||||||
\(73\) | 2.13806e10 | 1.20710 | 0.603552 | − | 0.797323i | \(-0.293751\pi\) | ||||
0.603552 | + | 0.797323i | \(0.293751\pi\) | |||||||
\(74\) | 1.53253e9 | 0.0802850 | ||||||||
\(75\) | −3.06662e10 | −1.49219 | ||||||||
\(76\) | 2.92001e9 | 0.132102 | ||||||||
\(77\) | 4.89693e9 | 0.206170 | ||||||||
\(78\) | 1.27991e10 | 0.501949 | ||||||||
\(79\) | −3.48354e10 | −1.27371 | −0.636857 | − | 0.770982i | \(-0.719766\pi\) | ||||
−0.636857 | + | 0.770982i | \(0.719766\pi\) | |||||||
\(80\) | 3.59472e10 | 1.22651 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −3.71653e9 | −0.110703 | ||||||||
\(83\) | −6.02784e10 | −1.67970 | −0.839850 | − | 0.542818i | \(-0.817357\pi\) | ||||
−0.839850 | + | 0.542818i | \(0.817357\pi\) | |||||||
\(84\) | −1.22577e9 | −0.0319795 | ||||||||
\(85\) | −6.67736e10 | −1.63230 | ||||||||
\(86\) | 2.50500e10 | 0.574205 | ||||||||
\(87\) | 3.14518e10 | 0.676533 | ||||||||
\(88\) | −5.52181e10 | −1.11539 | ||||||||
\(89\) | −5.21245e10 | −0.989458 | −0.494729 | − | 0.869047i | \(-0.664733\pi\) | ||||
−0.494729 | + | 0.869047i | \(0.664733\pi\) | |||||||
\(90\) | 3.00814e10 | 0.536987 | ||||||||
\(91\) | −1.22067e10 | −0.205055 | ||||||||
\(92\) | 5.35910e9 | 0.0847732 | ||||||||
\(93\) | 2.25262e10 | 0.335763 | ||||||||
\(94\) | 6.17956e10 | 0.868469 | ||||||||
\(95\) | 6.83426e10 | 0.906175 | ||||||||
\(96\) | 2.46540e10 | 0.308599 | ||||||||
\(97\) | −1.33295e11 | −1.57605 | −0.788024 | − | 0.615644i | \(-0.788896\pi\) | ||||
−0.788024 | + | 0.615644i | \(0.788896\pi\) | |||||||
\(98\) | 7.30733e10 | 0.816611 | ||||||||
\(99\) | −3.24026e10 | −0.342441 | ||||||||
\(100\) | −7.13342e10 | −0.713342 | ||||||||
\(101\) | −1.75528e11 | −1.66180 | −0.830902 | − | 0.556419i | \(-0.812175\pi\) | ||||
−0.830902 | + | 0.556419i | \(0.812175\pi\) | |||||||
\(102\) | 4.72272e10 | 0.423537 | ||||||||
\(103\) | 7.57783e10 | 0.644080 | 0.322040 | − | 0.946726i | \(-0.395631\pi\) | ||||
0.322040 | + | 0.946726i | \(0.395631\pi\) | |||||||
\(104\) | 1.37643e11 | 1.10936 | ||||||||
\(105\) | −2.86890e10 | −0.219369 | ||||||||
\(106\) | 1.34062e11 | 0.973023 | ||||||||
\(107\) | 2.53729e10 | 0.174887 | 0.0874437 | − | 0.996169i | \(-0.472130\pi\) | ||||
0.0874437 | + | 0.996169i | \(0.472130\pi\) | |||||||
\(108\) | 8.11079e9 | 0.0531169 | ||||||||
\(109\) | −1.49235e11 | −0.929018 | −0.464509 | − | 0.885568i | \(-0.653769\pi\) | ||||
−0.464509 | + | 0.885568i | \(0.653769\pi\) | |||||||
\(110\) | −2.79545e11 | −1.65498 | ||||||||
\(111\) | 9.67123e9 | 0.0544760 | ||||||||
\(112\) | 2.42477e10 | 0.130008 | ||||||||
\(113\) | −2.95296e11 | −1.50774 | −0.753869 | − | 0.657025i | \(-0.771815\pi\) | ||||
−0.753869 | + | 0.657025i | \(0.771815\pi\) | |||||||
\(114\) | −4.83370e10 | −0.235127 | ||||||||
\(115\) | 1.25429e11 | 0.581515 | ||||||||
\(116\) | 7.31616e10 | 0.323418 | ||||||||
\(117\) | 8.07705e10 | 0.340589 | ||||||||
\(118\) | 2.75292e10 | 0.110775 | ||||||||
\(119\) | −4.50412e10 | −0.173022 | ||||||||
\(120\) | 3.23499e11 | 1.18680 | ||||||||
\(121\) | 1.58041e10 | 0.0553926 | ||||||||
\(122\) | −1.98597e11 | −0.665263 | ||||||||
\(123\) | −2.34536e10 | −0.0751159 | ||||||||
\(124\) | 5.23994e10 | 0.160512 | ||||||||
\(125\) | −1.02359e12 | −3.00000 | ||||||||
\(126\) | 2.02910e10 | 0.0569200 | ||||||||
\(127\) | −7.67775e10 | −0.206212 | −0.103106 | − | 0.994670i | \(-0.532878\pi\) | ||||
−0.103106 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(128\) | −1.56929e11 | −0.403690 | ||||||||
\(129\) | 1.58082e11 | 0.389617 | ||||||||
\(130\) | 6.96828e11 | 1.64603 | ||||||||
\(131\) | 3.86066e11 | 0.874317 | 0.437159 | − | 0.899384i | \(-0.355985\pi\) | ||||
0.437159 | + | 0.899384i | \(0.355985\pi\) | |||||||
\(132\) | −7.53733e10 | −0.163705 | ||||||||
\(133\) | 4.60996e10 | 0.0960534 | ||||||||
\(134\) | 2.01138e11 | 0.402178 | ||||||||
\(135\) | 1.89833e11 | 0.364364 | ||||||||
\(136\) | 5.07888e11 | 0.936060 | ||||||||
\(137\) | 8.37523e11 | 1.48263 | 0.741317 | − | 0.671155i | \(-0.234202\pi\) | ||||
0.741317 | + | 0.671155i | \(0.234202\pi\) | |||||||
\(138\) | −8.87129e10 | −0.150887 | ||||||||
\(139\) | 7.87009e10 | 0.128647 | 0.0643233 | − | 0.997929i | \(-0.479511\pi\) | ||||
0.0643233 | + | 0.997929i | \(0.479511\pi\) | |||||||
\(140\) | −6.67350e10 | −0.104870 | ||||||||
\(141\) | 3.89969e11 | 0.589285 | ||||||||
\(142\) | −6.44628e11 | −0.936965 | ||||||||
\(143\) | −7.50598e11 | −1.04968 | ||||||||
\(144\) | −1.60445e11 | −0.215940 | ||||||||
\(145\) | 1.71234e12 | 2.21854 | ||||||||
\(146\) | −8.23292e11 | −1.02710 | ||||||||
\(147\) | 4.61139e11 | 0.554097 | ||||||||
\(148\) | 2.24968e10 | 0.0260424 | ||||||||
\(149\) | 4.99227e11 | 0.556896 | 0.278448 | − | 0.960451i | \(-0.410180\pi\) | ||||
0.278448 | + | 0.960451i | \(0.410180\pi\) | |||||||
\(150\) | 1.18085e12 | 1.26967 | ||||||||
\(151\) | 1.27434e12 | 1.32103 | 0.660514 | − | 0.750814i | \(-0.270338\pi\) | ||||
0.660514 | + | 0.750814i | \(0.270338\pi\) | |||||||
\(152\) | −5.19822e11 | −0.519655 | ||||||||
\(153\) | 2.98034e11 | 0.287384 | ||||||||
\(154\) | −1.88563e11 | −0.175426 | ||||||||
\(155\) | 1.22641e12 | 1.10106 | ||||||||
\(156\) | 1.87884e11 | 0.162819 | ||||||||
\(157\) | −5.95494e11 | −0.498229 | −0.249115 | − | 0.968474i | \(-0.580140\pi\) | ||||
−0.249115 | + | 0.968474i | \(0.580140\pi\) | |||||||
\(158\) | 1.34139e12 | 1.08378 | ||||||||
\(159\) | 8.46016e11 | 0.660228 | ||||||||
\(160\) | 1.34225e12 | 1.01198 | ||||||||
\(161\) | 8.46067e10 | 0.0616400 | ||||||||
\(162\) | −1.34264e11 | −0.0945422 | ||||||||
\(163\) | 6.18612e11 | 0.421101 | 0.210551 | − | 0.977583i | \(-0.432474\pi\) | ||||
0.210551 | + | 0.977583i | \(0.432474\pi\) | |||||||
\(164\) | −5.45567e10 | −0.0359093 | ||||||||
\(165\) | −1.76411e12 | −1.12296 | ||||||||
\(166\) | 2.32110e12 | 1.42922 | ||||||||
\(167\) | −1.69328e12 | −1.00876 | −0.504381 | − | 0.863481i | \(-0.668279\pi\) | ||||
−0.504381 | + | 0.863481i | \(0.668279\pi\) | |||||||
\(168\) | 2.18212e11 | 0.125799 | ||||||||
\(169\) | 7.88694e10 | 0.0440080 | ||||||||
\(170\) | 2.57121e12 | 1.38889 | ||||||||
\(171\) | −3.05037e11 | −0.159542 | ||||||||
\(172\) | 3.67722e11 | 0.186257 | ||||||||
\(173\) | −2.92929e12 | −1.43717 | −0.718587 | − | 0.695438i | \(-0.755211\pi\) | ||||
−0.718587 | + | 0.695438i | \(0.755211\pi\) | |||||||
\(174\) | −1.21110e12 | −0.575649 | ||||||||
\(175\) | −1.12619e12 | −0.518683 | ||||||||
\(176\) | 1.49101e12 | 0.665519 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 2.00713e12 | 0.841910 | ||||||||
\(179\) | 1.28881e12 | 0.524199 | 0.262099 | − | 0.965041i | \(-0.415585\pi\) | ||||
0.262099 | + | 0.965041i | \(0.415585\pi\) | |||||||
\(180\) | 4.41579e11 | 0.174185 | ||||||||
\(181\) | −1.05813e12 | −0.404860 | −0.202430 | − | 0.979297i | \(-0.564884\pi\) | ||||
−0.202430 | + | 0.979297i | \(0.564884\pi\) | |||||||
\(182\) | 4.70036e11 | 0.174477 | ||||||||
\(183\) | −1.25327e12 | −0.451403 | ||||||||
\(184\) | −9.54031e11 | −0.333476 | ||||||||
\(185\) | 5.26535e11 | 0.178642 | ||||||||
\(186\) | −8.67405e11 | −0.285694 | ||||||||
\(187\) | −2.76962e12 | −0.885708 | ||||||||
\(188\) | 9.07128e11 | 0.281709 | ||||||||
\(189\) | 1.28049e11 | 0.0386221 | ||||||||
\(190\) | −2.63163e12 | −0.771046 | ||||||||
\(191\) | 2.32669e12 | 0.662301 | 0.331150 | − | 0.943578i | \(-0.392563\pi\) | ||||
0.331150 | + | 0.943578i | \(0.392563\pi\) | |||||||
\(192\) | −2.30156e12 | −0.636599 | ||||||||
\(193\) | −2.14235e12 | −0.575872 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(194\) | 5.13272e12 | 1.34103 | ||||||||
\(195\) | 4.39743e12 | 1.11688 | ||||||||
\(196\) | 1.07268e12 | 0.264887 | ||||||||
\(197\) | −5.43248e12 | −1.30447 | −0.652235 | − | 0.758017i | \(-0.726168\pi\) | ||||
−0.652235 | + | 0.758017i | \(0.726168\pi\) | |||||||
\(198\) | 1.24771e12 | 0.291376 | ||||||||
\(199\) | 4.38801e12 | 0.996726 | 0.498363 | − | 0.866968i | \(-0.333935\pi\) | ||||
0.498363 | + | 0.866968i | \(0.333935\pi\) | |||||||
\(200\) | 1.26990e13 | 2.80610 | ||||||||
\(201\) | 1.26931e12 | 0.272891 | ||||||||
\(202\) | 6.75897e12 | 1.41399 | ||||||||
\(203\) | 1.15504e12 | 0.235162 | ||||||||
\(204\) | 6.93271e11 | 0.137384 | ||||||||
\(205\) | −1.27690e12 | −0.246326 | ||||||||
\(206\) | −2.91795e12 | −0.548035 | ||||||||
\(207\) | −5.59835e11 | −0.102382 | ||||||||
\(208\) | −3.71667e12 | −0.661920 | ||||||||
\(209\) | 2.83470e12 | 0.491702 | ||||||||
\(210\) | 1.10471e12 | 0.186656 | ||||||||
\(211\) | −2.77223e12 | −0.456327 | −0.228163 | − | 0.973623i | \(-0.573272\pi\) | ||||
−0.228163 | + | 0.973623i | \(0.573272\pi\) | |||||||
\(212\) | 1.96796e12 | 0.315623 | ||||||||
\(213\) | −4.06801e12 | −0.635762 | ||||||||
\(214\) | −9.77018e11 | −0.148808 | ||||||||
\(215\) | 8.60651e12 | 1.27766 | ||||||||
\(216\) | −1.44389e12 | −0.208948 | ||||||||
\(217\) | 8.27255e11 | 0.116711 | ||||||||
\(218\) | 5.74650e12 | 0.790483 | ||||||||
\(219\) | −5.19549e12 | −0.696922 | ||||||||
\(220\) | −4.10358e12 | −0.536832 | ||||||||
\(221\) | 6.90388e12 | 0.880918 | ||||||||
\(222\) | −3.72405e11 | −0.0463526 | ||||||||
\(223\) | 1.79436e12 | 0.217887 | 0.108944 | − | 0.994048i | \(-0.465253\pi\) | ||||
0.108944 | + | 0.994048i | \(0.465253\pi\) | |||||||
\(224\) | 9.05394e11 | 0.107269 | ||||||||
\(225\) | 7.45189e12 | 0.861514 | ||||||||
\(226\) | 1.13708e13 | 1.28290 | ||||||||
\(227\) | −1.07806e12 | −0.118713 | −0.0593567 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593567 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(228\) | −7.09562e11 | −0.0762691 | ||||||||
\(229\) | 9.89002e12 | 1.03777 | 0.518886 | − | 0.854843i | \(-0.326347\pi\) | ||||
0.518886 | + | 0.854843i | \(0.326347\pi\) | |||||||
\(230\) | −4.82984e12 | −0.494800 | ||||||||
\(231\) | −1.18995e12 | −0.119032 | ||||||||
\(232\) | −1.30243e13 | −1.27224 | ||||||||
\(233\) | −1.08290e13 | −1.03307 | −0.516534 | − | 0.856267i | \(-0.672778\pi\) | ||||
−0.516534 | + | 0.856267i | \(0.672778\pi\) | |||||||
\(234\) | −3.11018e12 | −0.289800 | ||||||||
\(235\) | 2.12313e13 | 1.93243 | ||||||||
\(236\) | 4.04114e11 | 0.0359326 | ||||||||
\(237\) | 8.46501e12 | 0.735380 | ||||||||
\(238\) | 1.73438e12 | 0.147221 | ||||||||
\(239\) | 1.53403e13 | 1.27247 | 0.636233 | − | 0.771497i | \(-0.280492\pi\) | ||||
0.636233 | + | 0.771497i | \(0.280492\pi\) | |||||||
\(240\) | −8.73518e12 | −0.708125 | ||||||||
\(241\) | −5.27094e12 | −0.417633 | −0.208816 | − | 0.977955i | \(-0.566961\pi\) | ||||
−0.208816 | + | 0.977955i | \(0.566961\pi\) | |||||||
\(242\) | −6.08561e11 | −0.0471324 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −2.91530e12 | −0.215794 | ||||||||
\(245\) | 2.51060e13 | 1.81704 | ||||||||
\(246\) | 9.03116e11 | 0.0639146 | ||||||||
\(247\) | −7.06611e12 | −0.489043 | ||||||||
\(248\) | −9.32819e12 | −0.631412 | ||||||||
\(249\) | 1.46476e13 | 0.969776 | ||||||||
\(250\) | 3.94148e13 | 2.55264 | ||||||||
\(251\) | −2.06077e13 | −1.30564 | −0.652820 | − | 0.757513i | \(-0.726414\pi\) | ||||
−0.652820 | + | 0.757513i | \(0.726414\pi\) | |||||||
\(252\) | 2.97861e11 | 0.0184634 | ||||||||
\(253\) | 5.20253e12 | 0.315538 | ||||||||
\(254\) | 2.95643e12 | 0.175462 | ||||||||
\(255\) | 1.62260e13 | 0.942410 | ||||||||
\(256\) | −1.33548e13 | −0.759131 | ||||||||
\(257\) | −2.21773e13 | −1.23389 | −0.616946 | − | 0.787006i | \(-0.711630\pi\) | ||||
−0.616946 | + | 0.787006i | \(0.711630\pi\) | |||||||
\(258\) | −6.08716e12 | −0.331517 | ||||||||
\(259\) | 3.55167e11 | 0.0189358 | ||||||||
\(260\) | 1.02291e13 | 0.533929 | ||||||||
\(261\) | −7.64278e12 | −0.390597 | ||||||||
\(262\) | −1.48660e13 | −0.743939 | ||||||||
\(263\) | −1.25777e12 | −0.0616375 | −0.0308188 | − | 0.999525i | \(-0.509811\pi\) | ||||
−0.0308188 | + | 0.999525i | \(0.509811\pi\) | |||||||
\(264\) | 1.34180e13 | 0.643971 | ||||||||
\(265\) | 4.60600e13 | 2.16507 | ||||||||
\(266\) | −1.77513e12 | −0.0817300 | ||||||||
\(267\) | 1.26663e13 | 0.571264 | ||||||||
\(268\) | 2.95260e12 | 0.130456 | ||||||||
\(269\) | −9.80514e12 | −0.424440 | −0.212220 | − | 0.977222i | \(-0.568069\pi\) | ||||
−0.212220 | + | 0.977222i | \(0.568069\pi\) | |||||||
\(270\) | −7.30978e12 | −0.310030 | ||||||||
\(271\) | −2.77249e13 | −1.15223 | −0.576114 | − | 0.817369i | \(-0.695432\pi\) | ||||
−0.576114 | + | 0.817369i | \(0.695432\pi\) | |||||||
\(272\) | −1.37141e13 | −0.558518 | ||||||||
\(273\) | 2.96622e12 | 0.118388 | ||||||||
\(274\) | −3.22500e13 | −1.26154 | ||||||||
\(275\) | −6.92501e13 | −2.65516 | ||||||||
\(276\) | −1.30226e12 | −0.0489438 | ||||||||
\(277\) | −1.02150e13 | −0.376358 | −0.188179 | − | 0.982135i | \(-0.560259\pi\) | ||||
−0.188179 | + | 0.982135i | \(0.560259\pi\) | |||||||
\(278\) | −3.03049e12 | −0.109463 | ||||||||
\(279\) | −5.47388e12 | −0.193853 | ||||||||
\(280\) | 1.18802e13 | 0.412529 | ||||||||
\(281\) | −2.51699e13 | −0.857031 | −0.428516 | − | 0.903534i | \(-0.640963\pi\) | ||||
−0.428516 | + | 0.903534i | \(0.640963\pi\) | |||||||
\(282\) | −1.50163e13 | −0.501411 | ||||||||
\(283\) | 4.75093e13 | 1.55580 | 0.777900 | − | 0.628388i | \(-0.216285\pi\) | ||||
0.777900 | + | 0.628388i | \(0.216285\pi\) | |||||||
\(284\) | −9.46281e12 | −0.303927 | ||||||||
\(285\) | −1.66073e13 | −0.523180 | ||||||||
\(286\) | 2.89028e13 | 0.893156 | ||||||||
\(287\) | −8.61313e11 | −0.0261102 | ||||||||
\(288\) | −5.99091e12 | −0.178170 | ||||||||
\(289\) | −8.79741e12 | −0.256695 | ||||||||
\(290\) | −6.59362e13 | −1.88771 | ||||||||
\(291\) | 3.23907e13 | 0.909932 | ||||||||
\(292\) | −1.20855e13 | −0.333165 | ||||||||
\(293\) | −2.75677e13 | −0.745811 | −0.372906 | − | 0.927869i | \(-0.621639\pi\) | ||||
−0.372906 | + | 0.927869i | \(0.621639\pi\) | |||||||
\(294\) | −1.77568e13 | −0.471470 | ||||||||
\(295\) | 9.45828e12 | 0.246485 | ||||||||
\(296\) | −4.00489e12 | −0.102444 | ||||||||
\(297\) | 7.87382e12 | 0.197708 | ||||||||
\(298\) | −1.92235e13 | −0.473851 | ||||||||
\(299\) | −1.29684e13 | −0.313831 | ||||||||
\(300\) | 1.73342e13 | 0.411848 | ||||||||
\(301\) | 5.80540e12 | 0.135431 | ||||||||
\(302\) | −4.90703e13 | −1.12404 | ||||||||
\(303\) | 4.26534e13 | 0.959442 | ||||||||
\(304\) | 1.40363e13 | 0.310062 | ||||||||
\(305\) | −6.82325e13 | −1.48027 | ||||||||
\(306\) | −1.14762e13 | −0.244529 | ||||||||
\(307\) | −2.04562e13 | −0.428118 | −0.214059 | − | 0.976821i | \(-0.568669\pi\) | ||||
−0.214059 | + | 0.976821i | \(0.568669\pi\) | |||||||
\(308\) | −2.76801e12 | −0.0569035 | ||||||||
\(309\) | −1.84141e13 | −0.371860 | ||||||||
\(310\) | −4.72245e13 | −0.936868 | ||||||||
\(311\) | 3.95899e13 | 0.771617 | 0.385809 | − | 0.922579i | \(-0.373923\pi\) | ||||
0.385809 | + | 0.922579i | \(0.373923\pi\) | |||||||
\(312\) | −3.34473e13 | −0.640489 | ||||||||
\(313\) | −7.17027e13 | −1.34909 | −0.674546 | − | 0.738233i | \(-0.735661\pi\) | ||||
−0.674546 | + | 0.738233i | \(0.735661\pi\) | |||||||
\(314\) | 2.29303e13 | 0.423933 | ||||||||
\(315\) | 6.97143e12 | 0.126652 | ||||||||
\(316\) | 1.96909e13 | 0.351550 | ||||||||
\(317\) | 5.35317e10 | 0.000939258 0 | 0.000469629 | − | 1.00000i | \(-0.499851\pi\) | ||||
0.000469629 | 1.00000i | \(0.499851\pi\) | ||||||||
\(318\) | −3.25770e13 | −0.561775 | ||||||||
\(319\) | 7.10241e13 | 1.20381 | ||||||||
\(320\) | −1.25305e14 | −2.08758 | ||||||||
\(321\) | −6.16560e12 | −0.100971 | ||||||||
\(322\) | −3.25790e12 | −0.0524482 | ||||||||
\(323\) | −2.60731e13 | −0.412647 | ||||||||
\(324\) | −1.97092e12 | −0.0306670 | ||||||||
\(325\) | 1.72621e14 | 2.64080 | ||||||||
\(326\) | −2.38205e13 | −0.358306 | ||||||||
\(327\) | 3.62640e13 | 0.536369 | ||||||||
\(328\) | 9.71223e12 | 0.141258 | ||||||||
\(329\) | 1.43213e13 | 0.204835 | ||||||||
\(330\) | 6.79295e13 | 0.955502 | ||||||||
\(331\) | −1.17536e14 | −1.62599 | −0.812996 | − | 0.582269i | \(-0.802165\pi\) | ||||
−0.812996 | + | 0.582269i | \(0.802165\pi\) | |||||||
\(332\) | 3.40726e13 | 0.463603 | ||||||||
\(333\) | −2.35011e12 | −0.0314517 | ||||||||
\(334\) | 6.52022e13 | 0.858335 | ||||||||
\(335\) | 6.91055e13 | 0.894883 | ||||||||
\(336\) | −5.89219e12 | −0.0750604 | ||||||||
\(337\) | 1.37448e14 | 1.72256 | 0.861279 | − | 0.508133i | \(-0.169664\pi\) | ||||
0.861279 | + | 0.508133i | \(0.169664\pi\) | |||||||
\(338\) | −3.03698e12 | −0.0374455 | ||||||||
\(339\) | 7.17569e13 | 0.870493 | ||||||||
\(340\) | 3.77441e13 | 0.450521 | ||||||||
\(341\) | 5.08685e13 | 0.597448 | ||||||||
\(342\) | 1.17459e13 | 0.135751 | ||||||||
\(343\) | 3.45805e13 | 0.393290 | ||||||||
\(344\) | −6.54621e13 | −0.732688 | ||||||||
\(345\) | −3.04793e13 | −0.335738 | ||||||||
\(346\) | 1.12797e14 | 1.22286 | ||||||||
\(347\) | 1.18508e14 | 1.26455 | 0.632276 | − | 0.774744i | \(-0.282121\pi\) | ||||
0.632276 | + | 0.774744i | \(0.282121\pi\) | |||||||
\(348\) | −1.77783e13 | −0.186725 | ||||||||
\(349\) | 5.65533e13 | 0.584680 | 0.292340 | − | 0.956314i | \(-0.405566\pi\) | ||||
0.292340 | + | 0.956314i | \(0.405566\pi\) | |||||||
\(350\) | 4.33655e13 | 0.441337 | ||||||||
\(351\) | −1.96272e13 | −0.196639 | ||||||||
\(352\) | 5.56733e13 | 0.549114 | ||||||||
\(353\) | −8.08290e13 | −0.784886 | −0.392443 | − | 0.919776i | \(-0.628370\pi\) | ||||
−0.392443 | + | 0.919776i | \(0.628370\pi\) | |||||||
\(354\) | −6.68959e12 | −0.0639561 | ||||||||
\(355\) | −2.21477e14 | −2.08484 | ||||||||
\(356\) | 2.94636e13 | 0.273094 | ||||||||
\(357\) | 1.09450e13 | 0.0998944 | ||||||||
\(358\) | −4.96273e13 | −0.446030 | ||||||||
\(359\) | 3.39630e13 | 0.300598 | 0.150299 | − | 0.988641i | \(-0.451976\pi\) | ||||
0.150299 | + | 0.988641i | \(0.451976\pi\) | |||||||
\(360\) | −7.86103e13 | −0.685197 | ||||||||
\(361\) | −8.98045e13 | −0.770919 | ||||||||
\(362\) | 4.07446e13 | 0.344487 | ||||||||
\(363\) | −3.84041e12 | −0.0319809 | ||||||||
\(364\) | 6.89988e12 | 0.0565958 | ||||||||
\(365\) | −2.82861e14 | −2.28540 | ||||||||
\(366\) | 4.82590e13 | 0.384090 | ||||||||
\(367\) | −7.35188e13 | −0.576415 | −0.288207 | − | 0.957568i | \(-0.593059\pi\) | ||||
−0.288207 | + | 0.957568i | \(0.593059\pi\) | |||||||
\(368\) | 2.57609e13 | 0.198975 | ||||||||
\(369\) | 5.69923e12 | 0.0433682 | ||||||||
\(370\) | −2.02750e13 | −0.152003 | ||||||||
\(371\) | 3.10691e13 | 0.229495 | ||||||||
\(372\) | −1.27331e13 | −0.0926716 | ||||||||
\(373\) | −1.36850e14 | −0.981398 | −0.490699 | − | 0.871329i | \(-0.663258\pi\) | ||||
−0.490699 | + | 0.871329i | \(0.663258\pi\) | |||||||
\(374\) | 1.06648e14 | 0.753631 | ||||||||
\(375\) | 2.48732e14 | 1.73205 | ||||||||
\(376\) | −1.61488e14 | −1.10817 | ||||||||
\(377\) | −1.77043e14 | −1.19730 | ||||||||
\(378\) | −4.93071e12 | −0.0328628 | ||||||||
\(379\) | −1.56486e14 | −1.02792 | −0.513960 | − | 0.857814i | \(-0.671822\pi\) | ||||
−0.513960 | + | 0.857814i | \(0.671822\pi\) | |||||||
\(380\) | −3.86310e13 | −0.250107 | ||||||||
\(381\) | 1.86569e13 | 0.119056 | ||||||||
\(382\) | −8.95926e13 | −0.563538 | ||||||||
\(383\) | −2.72767e14 | −1.69121 | −0.845607 | − | 0.533806i | \(-0.820761\pi\) | ||||
−0.845607 | + | 0.533806i | \(0.820761\pi\) | |||||||
\(384\) | 3.81337e13 | 0.233070 | ||||||||
\(385\) | −6.47852e13 | −0.390339 | ||||||||
\(386\) | 8.24944e13 | 0.489998 | ||||||||
\(387\) | −3.84138e13 | −0.224946 | ||||||||
\(388\) | 7.53457e13 | 0.434995 | ||||||||
\(389\) | −3.21230e14 | −1.82849 | −0.914247 | − | 0.405157i | \(-0.867217\pi\) | ||||
−0.914247 | + | 0.405157i | \(0.867217\pi\) | |||||||
\(390\) | −1.69329e14 | −0.950334 | ||||||||
\(391\) | −4.78520e13 | −0.264806 | ||||||||
\(392\) | −1.90959e14 | −1.04200 | ||||||||
\(393\) | −9.38139e13 | −0.504787 | ||||||||
\(394\) | 2.09185e14 | 1.10995 | ||||||||
\(395\) | 4.60864e14 | 2.41151 | ||||||||
\(396\) | 1.83157e13 | 0.0945149 | ||||||||
\(397\) | 3.76608e14 | 1.91664 | 0.958322 | − | 0.285690i | \(-0.0922227\pi\) | ||||
0.958322 | + | 0.285690i | \(0.0922227\pi\) | |||||||
\(398\) | −1.68967e14 | −0.848094 | ||||||||
\(399\) | −1.12022e13 | −0.0554565 | ||||||||
\(400\) | −3.42900e14 | −1.67432 | ||||||||
\(401\) | −6.97557e13 | −0.335958 | −0.167979 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167979 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(402\) | −4.88765e13 | −0.232197 | ||||||||
\(403\) | −1.26801e14 | −0.594217 | ||||||||
\(404\) | 9.92182e13 | 0.458663 | ||||||||
\(405\) | −4.61293e13 | −0.210365 | ||||||||
\(406\) | −4.44764e13 | −0.200095 | ||||||||
\(407\) | 2.18395e13 | 0.0969333 | ||||||||
\(408\) | −1.23417e14 | −0.540435 | ||||||||
\(409\) | 3.30559e14 | 1.42814 | 0.714069 | − | 0.700075i | \(-0.246850\pi\) | ||||
0.714069 | + | 0.700075i | \(0.246850\pi\) | |||||||
\(410\) | 4.91687e13 | 0.209594 | ||||||||
\(411\) | −2.03518e14 | −0.855999 | ||||||||
\(412\) | −4.28340e13 | −0.177768 | ||||||||
\(413\) | 6.37995e12 | 0.0261271 | ||||||||
\(414\) | 2.15572e13 | 0.0871147 | ||||||||
\(415\) | 7.97468e14 | 3.18016 | ||||||||
\(416\) | −1.38778e14 | −0.546144 | ||||||||
\(417\) | −1.91243e13 | −0.0742742 | ||||||||
\(418\) | −1.09154e14 | −0.418379 | ||||||||
\(419\) | −3.91370e14 | −1.48051 | −0.740254 | − | 0.672327i | \(-0.765295\pi\) | ||||
−0.740254 | + | 0.672327i | \(0.765295\pi\) | |||||||
\(420\) | 1.62166e13 | 0.0605464 | ||||||||
\(421\) | 2.19574e14 | 0.809150 | 0.404575 | − | 0.914505i | \(-0.367419\pi\) | ||||
0.404575 | + | 0.914505i | \(0.367419\pi\) | |||||||
\(422\) | 1.06749e14 | 0.388279 | ||||||||
\(423\) | −9.47625e13 | −0.340224 | ||||||||
\(424\) | −3.50338e14 | −1.24158 | ||||||||
\(425\) | 6.36952e14 | 2.22827 | ||||||||
\(426\) | 1.56645e14 | 0.540957 | ||||||||
\(427\) | −4.60253e13 | −0.156907 | ||||||||
\(428\) | −1.43421e13 | −0.0482695 | ||||||||
\(429\) | 1.82395e14 | 0.606036 | ||||||||
\(430\) | −3.31406e14 | −1.08714 | ||||||||
\(431\) | 1.17139e14 | 0.379382 | 0.189691 | − | 0.981844i | \(-0.439251\pi\) | ||||
0.189691 | + | 0.981844i | \(0.439251\pi\) | |||||||
\(432\) | 3.89881e13 | 0.124673 | ||||||||
\(433\) | 1.68180e14 | 0.530995 | 0.265497 | − | 0.964112i | \(-0.414464\pi\) | ||||
0.265497 | + | 0.964112i | \(0.414464\pi\) | |||||||
\(434\) | −3.18546e13 | −0.0993069 | ||||||||
\(435\) | −4.16099e14 | −1.28087 | ||||||||
\(436\) | 8.43556e13 | 0.256412 | ||||||||
\(437\) | 4.89764e13 | 0.147007 | ||||||||
\(438\) | 2.00060e14 | 0.592997 | ||||||||
\(439\) | 4.29459e14 | 1.25709 | 0.628546 | − | 0.777772i | \(-0.283650\pi\) | ||||
0.628546 | + | 0.777772i | \(0.283650\pi\) | |||||||
\(440\) | 7.30523e14 | 2.11176 | ||||||||
\(441\) | −1.12057e14 | −0.319908 | ||||||||
\(442\) | −2.65844e14 | −0.749556 | ||||||||
\(443\) | −4.46499e14 | −1.24337 | −0.621684 | − | 0.783268i | \(-0.713551\pi\) | ||||
−0.621684 | + | 0.783268i | \(0.713551\pi\) | |||||||
\(444\) | −5.46671e12 | −0.0150356 | ||||||||
\(445\) | 6.89595e14 | 1.87333 | ||||||||
\(446\) | −6.90942e13 | −0.185396 | ||||||||
\(447\) | −1.21312e14 | −0.321524 | ||||||||
\(448\) | −8.45228e13 | −0.221281 | ||||||||
\(449\) | −2.27812e14 | −0.589145 | −0.294573 | − | 0.955629i | \(-0.595177\pi\) | ||||
−0.294573 | + | 0.955629i | \(0.595177\pi\) | |||||||
\(450\) | −2.86946e14 | −0.733045 | ||||||||
\(451\) | −5.29628e13 | −0.133659 | ||||||||
\(452\) | 1.66917e14 | 0.416141 | ||||||||
\(453\) | −3.09665e14 | −0.762696 | ||||||||
\(454\) | 4.15122e13 | 0.101011 | ||||||||
\(455\) | 1.61491e14 | 0.388228 | ||||||||
\(456\) | 1.26317e14 | 0.300023 | ||||||||
\(457\) | 4.70956e13 | 0.110520 | 0.0552600 | − | 0.998472i | \(-0.482401\pi\) | ||||
0.0552600 | + | 0.998472i | \(0.482401\pi\) | |||||||
\(458\) | −3.80830e14 | −0.883020 | ||||||||
\(459\) | −7.24222e13 | −0.165921 | ||||||||
\(460\) | −7.08996e13 | −0.160500 | ||||||||
\(461\) | −7.29447e13 | −0.163169 | −0.0815847 | − | 0.996666i | \(-0.525998\pi\) | ||||
−0.0815847 | + | 0.996666i | \(0.525998\pi\) | |||||||
\(462\) | 4.58209e13 | 0.101282 | ||||||||
\(463\) | −3.70200e14 | −0.808613 | −0.404306 | − | 0.914624i | \(-0.632487\pi\) | ||||
−0.404306 | + | 0.914624i | \(0.632487\pi\) | |||||||
\(464\) | 3.51684e14 | 0.759108 | ||||||||
\(465\) | −2.98017e14 | −0.635696 | ||||||||
\(466\) | 4.16984e14 | 0.879017 | ||||||||
\(467\) | −3.41187e14 | −0.710803 | −0.355402 | − | 0.934714i | \(-0.615656\pi\) | ||||
−0.355402 | + | 0.934714i | \(0.615656\pi\) | |||||||
\(468\) | −4.56559e13 | −0.0940037 | ||||||||
\(469\) | 4.66142e13 | 0.0948566 | ||||||||
\(470\) | −8.17541e14 | −1.64426 | ||||||||
\(471\) | 1.44705e14 | 0.287653 | ||||||||
\(472\) | −7.19408e13 | −0.141349 | ||||||||
\(473\) | 3.56978e14 | 0.693275 | ||||||||
\(474\) | −3.25957e14 | −0.625720 | ||||||||
\(475\) | −6.51919e14 | −1.23703 | ||||||||
\(476\) | 2.54598e13 | 0.0477547 | ||||||||
\(477\) | −2.05582e14 | −0.381183 | ||||||||
\(478\) | −5.90701e14 | −1.08272 | ||||||||
\(479\) | −3.09598e14 | −0.560986 | −0.280493 | − | 0.959856i | \(-0.590498\pi\) | ||||
−0.280493 | + | 0.959856i | \(0.590498\pi\) | |||||||
\(480\) | −3.26166e14 | −0.584268 | ||||||||
\(481\) | −5.44397e13 | −0.0964091 | ||||||||
\(482\) | 2.02965e14 | 0.355355 | ||||||||
\(483\) | −2.05594e13 | −0.0355878 | ||||||||
\(484\) | −8.93337e12 | −0.0152885 | ||||||||
\(485\) | 1.76346e15 | 2.98392 | ||||||||
\(486\) | 3.26261e13 | 0.0545840 | ||||||||
\(487\) | 9.11010e14 | 1.50700 | 0.753501 | − | 0.657447i | \(-0.228364\pi\) | ||||
0.753501 | + | 0.657447i | \(0.228364\pi\) | |||||||
\(488\) | 5.18984e14 | 0.848878 | ||||||||
\(489\) | −1.50323e14 | −0.243123 | ||||||||
\(490\) | −9.66742e14 | −1.54608 | ||||||||
\(491\) | −4.54520e14 | −0.718795 | −0.359398 | − | 0.933185i | \(-0.617018\pi\) | ||||
−0.359398 | + | 0.933185i | \(0.617018\pi\) | |||||||
\(492\) | 1.32573e13 | 0.0207322 | ||||||||
\(493\) | −6.53268e14 | −1.01026 | ||||||||
\(494\) | 2.72091e14 | 0.416117 | ||||||||
\(495\) | 4.28678e14 | 0.648340 | ||||||||
\(496\) | 2.51881e14 | 0.376744 | ||||||||
\(497\) | −1.49394e14 | −0.220990 | ||||||||
\(498\) | −5.64028e14 | −0.825163 | ||||||||
\(499\) | 4.96092e14 | 0.717809 | 0.358904 | − | 0.933374i | \(-0.383150\pi\) | ||||
0.358904 | + | 0.933374i | \(0.383150\pi\) | |||||||
\(500\) | 5.78589e14 | 0.828009 | ||||||||
\(501\) | 4.11467e14 | 0.582409 | ||||||||
\(502\) | 7.93528e14 | 1.11094 | ||||||||
\(503\) | −7.22327e14 | −1.00025 | −0.500126 | − | 0.865952i | \(-0.666713\pi\) | ||||
−0.500126 | + | 0.865952i | \(0.666713\pi\) | |||||||
\(504\) | −5.30255e13 | −0.0726301 | ||||||||
\(505\) | 2.32220e15 | 3.14627 | ||||||||
\(506\) | −2.00331e14 | −0.268485 | ||||||||
\(507\) | −1.91653e13 | −0.0254080 | ||||||||
\(508\) | 4.33989e13 | 0.0569152 | ||||||||
\(509\) | −5.21265e14 | −0.676256 | −0.338128 | − | 0.941100i | \(-0.609794\pi\) | ||||
−0.338128 | + | 0.941100i | \(0.609794\pi\) | |||||||
\(510\) | −6.24805e14 | −0.801878 | ||||||||
\(511\) | −1.90800e14 | −0.242249 | ||||||||
\(512\) | 8.35635e14 | 1.04962 | ||||||||
\(513\) | 7.41240e13 | 0.0921113 | ||||||||
\(514\) | 8.53970e14 | 1.04989 | ||||||||
\(515\) | −1.00253e15 | −1.21943 | ||||||||
\(516\) | −8.93564e13 | −0.107536 | ||||||||
\(517\) | 8.80625e14 | 1.04856 | ||||||||
\(518\) | −1.36762e13 | −0.0161121 | ||||||||
\(519\) | 7.11818e14 | 0.829752 | ||||||||
\(520\) | −1.82099e15 | −2.10034 | ||||||||
\(521\) | 9.18931e14 | 1.04876 | 0.524379 | − | 0.851485i | \(-0.324297\pi\) | ||||
0.524379 | + | 0.851485i | \(0.324297\pi\) | |||||||
\(522\) | 2.94296e14 | 0.332351 | ||||||||
\(523\) | 6.36992e13 | 0.0711827 | 0.0355913 | − | 0.999366i | \(-0.488669\pi\) | ||||
0.0355913 | + | 0.999366i | \(0.488669\pi\) | |||||||
\(524\) | −2.18225e14 | −0.241314 | ||||||||
\(525\) | 2.73664e14 | 0.299462 | ||||||||
\(526\) | 4.84323e13 | 0.0524461 | ||||||||
\(527\) | −4.67881e14 | −0.501391 | ||||||||
\(528\) | −3.62315e14 | −0.384238 | ||||||||
\(529\) | −8.62923e14 | −0.905662 | ||||||||
\(530\) | −1.77361e15 | −1.84221 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | −2.60580e13 | −0.0265111 | ||||||||
\(533\) | 1.32021e14 | 0.132937 | ||||||||
\(534\) | −4.87733e14 | −0.486077 | ||||||||
\(535\) | −3.35677e14 | −0.331112 | ||||||||
\(536\) | −5.25625e14 | −0.513180 | ||||||||
\(537\) | −3.13180e14 | −0.302646 | ||||||||
\(538\) | 3.77561e14 | 0.361147 | ||||||||
\(539\) | 1.04134e15 | 0.985948 | ||||||||
\(540\) | −1.07304e14 | −0.100566 | ||||||||
\(541\) | −1.62321e15 | −1.50588 | −0.752939 | − | 0.658090i | \(-0.771365\pi\) | ||||
−0.752939 | + | 0.658090i | \(0.771365\pi\) | |||||||
\(542\) | 1.06759e15 | 0.980408 | ||||||||
\(543\) | 2.57124e14 | 0.233746 | ||||||||
\(544\) | −5.12074e14 | −0.460828 | ||||||||
\(545\) | 1.97434e15 | 1.75890 | ||||||||
\(546\) | −1.14219e14 | −0.100734 | ||||||||
\(547\) | 1.15177e15 | 1.00562 | 0.502810 | − | 0.864397i | \(-0.332299\pi\) | ||||
0.502810 | + | 0.864397i | \(0.332299\pi\) | |||||||
\(548\) | −4.73414e14 | −0.409212 | ||||||||
\(549\) | 3.04545e14 | 0.260618 | ||||||||
\(550\) | 2.66658e15 | 2.25922 | ||||||||
\(551\) | 6.68619e14 | 0.560847 | ||||||||
\(552\) | 2.31830e14 | 0.192532 | ||||||||
\(553\) | 3.10870e14 | 0.255617 | ||||||||
\(554\) | 3.93345e14 | 0.320236 | ||||||||
\(555\) | −1.27948e14 | −0.103139 | ||||||||
\(556\) | −4.44861e13 | −0.0355069 | ||||||||
\(557\) | −3.76631e14 | −0.297654 | −0.148827 | − | 0.988863i | \(-0.547550\pi\) | ||||
−0.148827 | + | 0.988863i | \(0.547550\pi\) | |||||||
\(558\) | 2.10779e14 | 0.164945 | ||||||||
\(559\) | −8.89847e14 | −0.689526 | ||||||||
\(560\) | −3.20791e14 | −0.246144 | ||||||||
\(561\) | 6.73017e14 | 0.511364 | ||||||||
\(562\) | 9.69203e14 | 0.729231 | ||||||||
\(563\) | 5.16229e14 | 0.384632 | 0.192316 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192316 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(564\) | −2.20432e14 | −0.162645 | ||||||||
\(565\) | 3.90669e15 | 2.85458 | ||||||||
\(566\) | −1.82942e15 | −1.32380 | ||||||||
\(567\) | −3.11159e13 | −0.0222985 | ||||||||
\(568\) | 1.68458e15 | 1.19557 | ||||||||
\(569\) | 1.67695e14 | 0.117870 | 0.0589349 | − | 0.998262i | \(-0.481230\pi\) | ||||
0.0589349 | + | 0.998262i | \(0.481230\pi\) | |||||||
\(570\) | 6.39486e14 | 0.445163 | ||||||||
\(571\) | 2.56075e15 | 1.76550 | 0.882752 | − | 0.469839i | \(-0.155688\pi\) | ||||
0.882752 | + | 0.469839i | \(0.155688\pi\) | |||||||
\(572\) | 4.24279e14 | 0.289717 | ||||||||
\(573\) | −5.65386e14 | −0.382379 | ||||||||
\(574\) | 3.31661e13 | 0.0222167 | ||||||||
\(575\) | −1.19647e15 | −0.793831 | ||||||||
\(576\) | 5.59280e14 | 0.367541 | ||||||||
\(577\) | 1.11755e15 | 0.727442 | 0.363721 | − | 0.931508i | \(-0.381506\pi\) | ||||
0.363721 | + | 0.931508i | \(0.381506\pi\) | |||||||
\(578\) | 3.38757e14 | 0.218416 | ||||||||
\(579\) | 5.20592e14 | 0.332480 | ||||||||
\(580\) | −9.67910e14 | −0.612324 | ||||||||
\(581\) | 5.37921e14 | 0.337093 | ||||||||
\(582\) | −1.24725e15 | −0.774243 | ||||||||
\(583\) | 1.91046e15 | 1.17479 | ||||||||
\(584\) | 2.15147e15 | 1.31058 | ||||||||
\(585\) | −1.06857e15 | −0.644833 | ||||||||
\(586\) | 1.06153e15 | 0.634596 | ||||||||
\(587\) | −3.26597e15 | −1.93420 | −0.967102 | − | 0.254390i | \(-0.918125\pi\) | ||||
−0.967102 | + | 0.254390i | \(0.918125\pi\) | |||||||
\(588\) | −2.60661e14 | −0.152933 | ||||||||
\(589\) | 4.78875e14 | 0.278348 | ||||||||
\(590\) | −3.64204e14 | −0.209729 | ||||||||
\(591\) | 1.32009e15 | 0.753136 | ||||||||
\(592\) | 1.08141e14 | 0.0611251 | ||||||||
\(593\) | 1.98254e15 | 1.11025 | 0.555125 | − | 0.831767i | \(-0.312671\pi\) | ||||
0.555125 | + | 0.831767i | \(0.312671\pi\) | |||||||
\(594\) | −3.03193e14 | −0.168226 | ||||||||
\(595\) | 5.95884e14 | 0.327581 | ||||||||
\(596\) | −2.82191e14 | −0.153705 | ||||||||
\(597\) | −1.06629e15 | −0.575460 | ||||||||
\(598\) | 4.99368e14 | 0.267033 | ||||||||
\(599\) | −3.00851e14 | −0.159406 | −0.0797028 | − | 0.996819i | \(-0.525397\pi\) | ||||
−0.0797028 | + | 0.996819i | \(0.525397\pi\) | |||||||
\(600\) | −3.08585e15 | −1.62011 | ||||||||
\(601\) | −4.02711e14 | −0.209500 | −0.104750 | − | 0.994499i | \(-0.533404\pi\) | ||||
−0.104750 | + | 0.994499i | \(0.533404\pi\) | |||||||
\(602\) | −2.23545e14 | −0.115235 | ||||||||
\(603\) | −3.08442e14 | −0.157554 | ||||||||
\(604\) | −7.20327e14 | −0.364608 | ||||||||
\(605\) | −2.09085e14 | −0.104874 | ||||||||
\(606\) | −1.64243e15 | −0.816370 | ||||||||
\(607\) | 1.62300e14 | 0.0799431 | 0.0399715 | − | 0.999201i | \(-0.487273\pi\) | ||||
0.0399715 | + | 0.999201i | \(0.487273\pi\) | |||||||
\(608\) | 5.24107e14 | 0.255829 | ||||||||
\(609\) | −2.80674e14 | −0.135771 | ||||||||
\(610\) | 2.62739e15 | 1.25954 | ||||||||
\(611\) | −2.19515e15 | −1.04289 | ||||||||
\(612\) | −1.68465e14 | −0.0793189 | ||||||||
\(613\) | 2.80499e15 | 1.30888 | 0.654439 | − | 0.756114i | \(-0.272905\pi\) | ||||
0.654439 | + | 0.756114i | \(0.272905\pi\) | |||||||
\(614\) | 7.87695e14 | 0.364277 | ||||||||
\(615\) | 3.10286e14 | 0.142216 | ||||||||
\(616\) | 4.92764e14 | 0.223844 | ||||||||
\(617\) | 2.73536e15 | 1.23153 | 0.615766 | − | 0.787929i | \(-0.288847\pi\) | ||||
0.615766 | + | 0.787929i | \(0.288847\pi\) | |||||||
\(618\) | 7.09062e14 | 0.316408 | ||||||||
\(619\) | −3.03415e14 | −0.134196 | −0.0670979 | − | 0.997746i | \(-0.521374\pi\) | ||||
−0.0670979 | + | 0.997746i | \(0.521374\pi\) | |||||||
\(620\) | −6.93232e14 | −0.303895 | ||||||||
\(621\) | 1.36040e14 | 0.0591102 | ||||||||
\(622\) | −1.52446e15 | −0.656554 | ||||||||
\(623\) | 4.65157e14 | 0.198571 | ||||||||
\(624\) | 9.03150e14 | 0.382160 | ||||||||
\(625\) | 7.37982e15 | 3.09532 | ||||||||
\(626\) | 2.76101e15 | 1.14792 | ||||||||
\(627\) | −6.88831e14 | −0.283884 | ||||||||
\(628\) | 3.36606e14 | 0.137513 | ||||||||
\(629\) | −2.00876e14 | −0.0813485 | ||||||||
\(630\) | −2.68445e14 | −0.107766 | ||||||||
\(631\) | 1.28691e15 | 0.512137 | 0.256068 | − | 0.966659i | \(-0.417573\pi\) | ||||
0.256068 | + | 0.966659i | \(0.417573\pi\) | |||||||
\(632\) | −3.50539e15 | −1.38290 | ||||||||
\(633\) | 6.73652e14 | 0.263460 | ||||||||
\(634\) | −2.06131e12 | −0.000799196 0 | ||||||||
\(635\) | 1.01575e15 | 0.390419 | ||||||||
\(636\) | −4.78214e14 | −0.182225 | ||||||||
\(637\) | −2.59577e15 | −0.980615 | ||||||||
\(638\) | −2.73488e15 | −1.02430 | ||||||||
\(639\) | 9.88527e14 | 0.367057 | ||||||||
\(640\) | 2.07613e15 | 0.764301 | ||||||||
\(641\) | 2.70651e15 | 0.987848 | 0.493924 | − | 0.869505i | \(-0.335562\pi\) | ||||
0.493924 | + | 0.869505i | \(0.335562\pi\) | |||||||
\(642\) | 2.37415e14 | 0.0859145 | ||||||||
\(643\) | −5.18247e15 | −1.85942 | −0.929708 | − | 0.368298i | \(-0.879941\pi\) | ||||
−0.929708 | + | 0.368298i | \(0.879941\pi\) | |||||||
\(644\) | −4.78243e13 | −0.0170128 | ||||||||
\(645\) | −2.09138e15 | −0.737658 | ||||||||
\(646\) | 1.00398e15 | 0.351113 | ||||||||
\(647\) | 3.11247e15 | 1.07927 | 0.539637 | − | 0.841898i | \(-0.318561\pi\) | ||||
0.539637 | + | 0.841898i | \(0.318561\pi\) | |||||||
\(648\) | 3.50865e14 | 0.120636 | ||||||||
\(649\) | 3.92308e14 | 0.133746 | ||||||||
\(650\) | −6.64703e15 | −2.24700 | ||||||||
\(651\) | −2.01023e14 | −0.0673830 | ||||||||
\(652\) | −3.49673e14 | −0.116225 | ||||||||
\(653\) | −1.22125e15 | −0.402516 | −0.201258 | − | 0.979538i | \(-0.564503\pi\) | ||||
−0.201258 | + | 0.979538i | \(0.564503\pi\) | |||||||
\(654\) | −1.39640e15 | −0.456385 | ||||||||
\(655\) | −5.10755e15 | −1.65533 | ||||||||
\(656\) | −2.62251e14 | −0.0842842 | ||||||||
\(657\) | 1.26251e15 | 0.402368 | ||||||||
\(658\) | −5.51461e14 | −0.174290 | ||||||||
\(659\) | 4.37350e14 | 0.137075 | 0.0685377 | − | 0.997649i | \(-0.478167\pi\) | ||||
0.0685377 | + | 0.997649i | \(0.478167\pi\) | |||||||
\(660\) | 9.97170e14 | 0.309940 | ||||||||
\(661\) | −1.38090e15 | −0.425650 | −0.212825 | − | 0.977090i | \(-0.568266\pi\) | ||||
−0.212825 | + | 0.977090i | \(0.568266\pi\) | |||||||
\(662\) | 4.52591e15 | 1.38352 | ||||||||
\(663\) | −1.67764e15 | −0.508598 | ||||||||
\(664\) | −6.06564e15 | −1.82369 | ||||||||
\(665\) | −6.09886e14 | −0.181857 | ||||||||
\(666\) | 9.04943e13 | 0.0267617 | ||||||||
\(667\) | 1.22712e15 | 0.359910 | ||||||||
\(668\) | 9.57135e14 | 0.278422 | ||||||||
\(669\) | −4.36028e14 | −0.125797 | ||||||||
\(670\) | −2.66101e15 | −0.761438 | ||||||||
\(671\) | −2.83013e15 | −0.803216 | ||||||||
\(672\) | −2.20011e14 | −0.0619317 | ||||||||
\(673\) | −4.15651e15 | −1.16050 | −0.580252 | − | 0.814437i | \(-0.697046\pi\) | ||||
−0.580252 | + | 0.814437i | \(0.697046\pi\) | |||||||
\(674\) | −5.29263e15 | −1.46569 | ||||||||
\(675\) | −1.81081e15 | −0.497396 | ||||||||
\(676\) | −4.45813e13 | −0.0121464 | ||||||||
\(677\) | 1.94680e15 | 0.526119 | 0.263060 | − | 0.964780i | \(-0.415268\pi\) | ||||
0.263060 | + | 0.964780i | \(0.415268\pi\) | |||||||
\(678\) | −2.76310e15 | −0.740685 | ||||||||
\(679\) | 1.18952e15 | 0.316292 | ||||||||
\(680\) | −6.71923e15 | −1.77223 | ||||||||
\(681\) | 2.61968e14 | 0.0685393 | ||||||||
\(682\) | −1.95877e15 | −0.508356 | ||||||||
\(683\) | −3.57495e15 | −0.920358 | −0.460179 | − | 0.887826i | \(-0.652215\pi\) | ||||
−0.460179 | + | 0.887826i | \(0.652215\pi\) | |||||||
\(684\) | 1.72424e14 | 0.0440340 | ||||||||
\(685\) | −1.10802e16 | −2.80705 | ||||||||
\(686\) | −1.33157e15 | −0.334643 | ||||||||
\(687\) | −2.40328e15 | −0.599158 | ||||||||
\(688\) | 1.76762e15 | 0.437172 | ||||||||
\(689\) | −4.76225e15 | −1.16844 | ||||||||
\(690\) | 1.17365e15 | 0.285673 | ||||||||
\(691\) | −2.73596e15 | −0.660663 | −0.330331 | − | 0.943865i | \(-0.607160\pi\) | ||||
−0.330331 | + | 0.943865i | \(0.607160\pi\) | |||||||
\(692\) | 1.65580e15 | 0.396665 | ||||||||
\(693\) | 2.89159e14 | 0.0687233 | ||||||||
\(694\) | −4.56333e15 | −1.07598 | ||||||||
\(695\) | −1.04119e15 | −0.243565 | ||||||||
\(696\) | 3.16490e15 | 0.734529 | ||||||||
\(697\) | 4.87143e14 | 0.112170 | ||||||||
\(698\) | −2.17767e15 | −0.497492 | ||||||||
\(699\) | 2.63144e15 | 0.596442 | ||||||||
\(700\) | 6.36583e14 | 0.143158 | ||||||||
\(701\) | 3.17495e15 | 0.708415 | 0.354208 | − | 0.935167i | \(-0.384751\pi\) | ||||
0.354208 | + | 0.935167i | \(0.384751\pi\) | |||||||
\(702\) | 7.55775e14 | 0.167316 | ||||||||
\(703\) | 2.05596e14 | 0.0451607 | ||||||||
\(704\) | −5.19737e15 | −1.13275 | ||||||||
\(705\) | −5.15920e15 | −1.11569 | ||||||||
\(706\) | 3.11244e15 | 0.667844 | ||||||||
\(707\) | 1.56641e15 | 0.333501 | ||||||||
\(708\) | −9.81998e13 | −0.0207457 | ||||||||
\(709\) | 4.33573e15 | 0.908883 | 0.454441 | − | 0.890777i | \(-0.349839\pi\) | ||||
0.454441 | + | 0.890777i | \(0.349839\pi\) | |||||||
\(710\) | 8.52827e15 | 1.77395 | ||||||||
\(711\) | −2.05700e15 | −0.424572 | ||||||||
\(712\) | −5.24514e15 | −1.07428 | ||||||||
\(713\) | 8.78880e14 | 0.178623 | ||||||||
\(714\) | −4.21453e14 | −0.0849981 | ||||||||
\(715\) | 9.93022e15 | 1.98736 | ||||||||
\(716\) | −7.28504e14 | −0.144681 | ||||||||
\(717\) | −3.72770e15 | −0.734659 | ||||||||
\(718\) | −1.30779e15 | −0.255773 | ||||||||
\(719\) | 5.63989e15 | 1.09462 | 0.547308 | − | 0.836931i | \(-0.315653\pi\) | ||||
0.547308 | + | 0.836931i | \(0.315653\pi\) | |||||||
\(720\) | 2.12265e15 | 0.408836 | ||||||||
\(721\) | −6.76242e14 | −0.129258 | ||||||||
\(722\) | 3.45805e15 | 0.655959 | ||||||||
\(723\) | 1.28084e15 | 0.241120 | ||||||||
\(724\) | 5.98110e14 | 0.111743 | ||||||||
\(725\) | −1.63340e16 | −3.02854 | ||||||||
\(726\) | 1.47880e14 | 0.0272119 | ||||||||
\(727\) | −5.36267e15 | −0.979358 | −0.489679 | − | 0.871903i | \(-0.662886\pi\) | ||||
−0.489679 | + | 0.871903i | \(0.662886\pi\) | |||||||
\(728\) | −1.22832e15 | −0.222633 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 1.08920e16 | 1.94460 | ||||||||
\(731\) | −3.28343e15 | −0.581812 | ||||||||
\(732\) | 7.08418e14 | 0.124589 | ||||||||
\(733\) | 4.25039e15 | 0.741920 | 0.370960 | − | 0.928649i | \(-0.379029\pi\) | ||||
0.370960 | + | 0.928649i | \(0.379029\pi\) | |||||||
\(734\) | 2.83095e15 | 0.490460 | ||||||||
\(735\) | −6.10075e15 | −1.04907 | ||||||||
\(736\) | 9.61895e14 | 0.164172 | ||||||||
\(737\) | 2.86634e15 | 0.485575 | ||||||||
\(738\) | −2.19457e14 | −0.0369011 | ||||||||
\(739\) | −1.19448e16 | −1.99358 | −0.996790 | − | 0.0800612i | \(-0.974488\pi\) | ||||
−0.996790 | + | 0.0800612i | \(0.974488\pi\) | |||||||
\(740\) | −2.97627e14 | −0.0493057 | ||||||||
\(741\) | 1.71706e15 | 0.282349 | ||||||||
\(742\) | −1.19636e15 | −0.195273 | ||||||||
\(743\) | 6.10708e15 | 0.989453 | 0.494727 | − | 0.869049i | \(-0.335268\pi\) | ||||
0.494727 | + | 0.869049i | \(0.335268\pi\) | |||||||
\(744\) | 2.26675e15 | 0.364546 | ||||||||
\(745\) | −6.60466e15 | −1.05436 | ||||||||
\(746\) | 5.26959e15 | 0.835052 | ||||||||
\(747\) | −3.55938e15 | −0.559900 | ||||||||
\(748\) | 1.56554e15 | 0.244458 | ||||||||
\(749\) | −2.26426e14 | −0.0350975 | ||||||||
\(750\) | −9.57780e15 | −1.47377 | ||||||||
\(751\) | 1.08674e15 | 0.165999 | 0.0829996 | − | 0.996550i | \(-0.473550\pi\) | ||||
0.0829996 | + | 0.996550i | \(0.473550\pi\) | |||||||
\(752\) | 4.36051e15 | 0.661210 | ||||||||
\(753\) | 5.00766e15 | 0.753811 | ||||||||
\(754\) | 6.81730e15 | 1.01876 | ||||||||
\(755\) | −1.68592e16 | −2.50109 | ||||||||
\(756\) | −7.23803e13 | −0.0106598 | ||||||||
\(757\) | 8.46368e15 | 1.23746 | 0.618731 | − | 0.785603i | \(-0.287647\pi\) | ||||
0.618731 | + | 0.785603i | \(0.287647\pi\) | |||||||
\(758\) | 6.02570e15 | 0.874636 | ||||||||
\(759\) | −1.26421e15 | −0.182176 | ||||||||
\(760\) | 6.87712e15 | 0.983857 | ||||||||
\(761\) | −2.19644e15 | −0.311963 | −0.155982 | − | 0.987760i | \(-0.549854\pi\) | ||||
−0.155982 | + | 0.987760i | \(0.549854\pi\) | |||||||
\(762\) | −7.18412e14 | −0.101303 | ||||||||
\(763\) | 1.33176e15 | 0.186441 | ||||||||
\(764\) | −1.31517e15 | −0.182797 | ||||||||
\(765\) | −3.94291e15 | −0.544101 | ||||||||
\(766\) | 1.05033e16 | 1.43902 | ||||||||
\(767\) | −9.77913e14 | −0.133023 | ||||||||
\(768\) | 3.24521e15 | 0.438284 | ||||||||
\(769\) | 5.08350e15 | 0.681661 | 0.340830 | − | 0.940125i | \(-0.389292\pi\) | ||||
0.340830 | + | 0.940125i | \(0.389292\pi\) | |||||||
\(770\) | 2.49465e15 | 0.332132 | ||||||||
\(771\) | 5.38909e15 | 0.712388 | ||||||||
\(772\) | 1.21098e15 | 0.158943 | ||||||||
\(773\) | 1.19595e16 | 1.55856 | 0.779282 | − | 0.626674i | \(-0.215584\pi\) | ||||
0.779282 | + | 0.626674i | \(0.215584\pi\) | |||||||
\(774\) | 1.47918e15 | 0.191402 | ||||||||
\(775\) | −1.16987e16 | −1.50306 | ||||||||
\(776\) | −1.34131e16 | −1.71116 | ||||||||
\(777\) | −8.63056e13 | −0.0109326 | ||||||||
\(778\) | 1.23694e16 | 1.55583 | ||||||||
\(779\) | −4.98590e14 | −0.0622713 | ||||||||
\(780\) | −2.48567e15 | −0.308264 | ||||||||
\(781\) | −9.18634e15 | −1.13126 | ||||||||
\(782\) | 1.84261e15 | 0.225318 | ||||||||
\(783\) | 1.85720e15 | 0.225511 | ||||||||
\(784\) | 5.15631e15 | 0.621728 | ||||||||
\(785\) | 7.87824e15 | 0.943292 | ||||||||
\(786\) | 3.61244e15 | 0.429513 | ||||||||
\(787\) | 1.14735e16 | 1.35467 | 0.677335 | − | 0.735675i | \(-0.263135\pi\) | ||||
0.677335 | + | 0.735675i | \(0.263135\pi\) | |||||||
\(788\) | 3.07074e15 | 0.360038 | ||||||||
\(789\) | 3.05639e14 | 0.0355864 | ||||||||
\(790\) | −1.77462e16 | −2.05191 | ||||||||
\(791\) | 2.63520e15 | 0.302582 | ||||||||
\(792\) | −3.26058e15 | −0.371797 | ||||||||
\(793\) | 7.05472e15 | 0.798872 | ||||||||
\(794\) | −1.45018e16 | −1.63083 | ||||||||
\(795\) | −1.11926e16 | −1.25000 | ||||||||
\(796\) | −2.48034e15 | −0.275100 | ||||||||
\(797\) | −1.37704e16 | −1.51679 | −0.758393 | − | 0.651798i | \(-0.774015\pi\) | ||||
−0.758393 | + | 0.651798i | \(0.774015\pi\) | |||||||
\(798\) | 4.31357e14 | 0.0471868 | ||||||||
\(799\) | −8.09985e15 | −0.879973 | ||||||||
\(800\) | −1.28037e16 | −1.38146 | ||||||||
\(801\) | −3.07790e15 | −0.329819 | ||||||||
\(802\) | 2.68604e15 | 0.285860 | ||||||||
\(803\) | −1.17324e16 | −1.24009 | ||||||||
\(804\) | −7.17483e14 | −0.0753188 | ||||||||
\(805\) | −1.11933e15 | −0.116702 | ||||||||
\(806\) | 4.88265e15 | 0.505607 | ||||||||
\(807\) | 2.38265e15 | 0.245050 | ||||||||
\(808\) | −1.76629e16 | −1.80426 | ||||||||
\(809\) | 4.97789e15 | 0.505043 | 0.252521 | − | 0.967591i | \(-0.418740\pi\) | ||||
0.252521 | + | 0.967591i | \(0.418740\pi\) | |||||||
\(810\) | 1.77628e15 | 0.178996 | ||||||||
\(811\) | 9.30004e15 | 0.930830 | 0.465415 | − | 0.885093i | \(-0.345905\pi\) | ||||
0.465415 | + | 0.885093i | \(0.345905\pi\) | |||||||
\(812\) | −6.52890e14 | −0.0649056 | ||||||||
\(813\) | 6.73715e15 | 0.665240 | ||||||||
\(814\) | −8.40960e14 | −0.0824786 | ||||||||
\(815\) | −8.18408e15 | −0.797266 | ||||||||
\(816\) | 3.33252e15 | 0.322461 | ||||||||
\(817\) | 3.36059e15 | 0.322993 | ||||||||
\(818\) | −1.27286e16 | −1.21517 | ||||||||
\(819\) | −7.20792e14 | −0.0683516 | ||||||||
\(820\) | 7.21772e14 | 0.0679867 | ||||||||
\(821\) | 1.83634e16 | 1.71817 | 0.859085 | − | 0.511834i | \(-0.171034\pi\) | ||||
0.859085 | + | 0.511834i | \(0.171034\pi\) | |||||||
\(822\) | 7.83676e15 | 0.728352 | ||||||||
\(823\) | 1.65501e16 | 1.52793 | 0.763964 | − | 0.645259i | \(-0.223251\pi\) | ||||
0.763964 | + | 0.645259i | \(0.223251\pi\) | |||||||
\(824\) | 7.62535e15 | 0.699294 | ||||||||
\(825\) | 1.68278e16 | 1.53296 | ||||||||
\(826\) | −2.45669e14 | −0.0222311 | ||||||||
\(827\) | 1.94784e16 | 1.75094 | 0.875471 | − | 0.483270i | \(-0.160551\pi\) | ||||
0.875471 | + | 0.483270i | \(0.160551\pi\) | |||||||
\(828\) | 3.16449e14 | 0.0282577 | ||||||||
\(829\) | −9.00331e15 | −0.798643 | −0.399321 | − | 0.916811i | \(-0.630754\pi\) | ||||
−0.399321 | + | 0.916811i | \(0.630754\pi\) | |||||||
\(830\) | −3.07077e16 | −2.70593 | ||||||||
\(831\) | 2.48226e15 | 0.217291 | ||||||||
\(832\) | 1.29556e16 | 1.12662 | ||||||||
\(833\) | −9.57807e15 | −0.827428 | ||||||||
\(834\) | 7.36409e14 | 0.0631984 | ||||||||
\(835\) | 2.24017e16 | 1.90988 | ||||||||
\(836\) | −1.60233e15 | −0.135711 | ||||||||
\(837\) | 1.33015e15 | 0.111921 | ||||||||
\(838\) | 1.50703e16 | 1.25973 | ||||||||
\(839\) | 8.51024e15 | 0.706726 | 0.353363 | − | 0.935486i | \(-0.385038\pi\) | ||||
0.353363 | + | 0.935486i | \(0.385038\pi\) | |||||||
\(840\) | −2.88689e15 | −0.238174 | ||||||||
\(841\) | 4.55191e15 | 0.373092 | ||||||||
\(842\) | −8.45500e15 | −0.688489 | ||||||||
\(843\) | 6.11628e15 | 0.494807 | ||||||||
\(844\) | 1.56702e15 | 0.125948 | ||||||||
\(845\) | −1.04342e15 | −0.0833199 | ||||||||
\(846\) | 3.64897e15 | 0.289490 | ||||||||
\(847\) | −1.41035e14 | −0.0111165 | ||||||||
\(848\) | 9.45988e15 | 0.740813 | ||||||||
\(849\) | −1.15448e16 | −0.898241 | ||||||||
\(850\) | −2.45267e16 | −1.89599 | ||||||||
\(851\) | 3.77331e14 | 0.0289808 | ||||||||
\(852\) | 2.29946e15 | 0.175472 | ||||||||
\(853\) | −1.47084e16 | −1.11519 | −0.557593 | − | 0.830115i | \(-0.688275\pi\) | ||||
−0.557593 | + | 0.830115i | \(0.688275\pi\) | |||||||
\(854\) | 1.77227e15 | 0.133509 | ||||||||
\(855\) | 4.03556e15 | 0.302058 | ||||||||
\(856\) | 2.55320e15 | 0.189880 | ||||||||
\(857\) | −5.31834e15 | −0.392990 | −0.196495 | − | 0.980505i | \(-0.562956\pi\) | ||||
−0.196495 | + | 0.980505i | \(0.562956\pi\) | |||||||
\(858\) | −7.02339e15 | −0.515664 | ||||||||
\(859\) | 1.44436e16 | 1.05369 | 0.526845 | − | 0.849962i | \(-0.323375\pi\) | ||||
0.526845 | + | 0.849962i | \(0.323375\pi\) | |||||||
\(860\) | −4.86487e15 | −0.352639 | ||||||||
\(861\) | 2.09299e14 | 0.0150747 | ||||||||
\(862\) | −4.51061e15 | −0.322809 | ||||||||
\(863\) | −1.88206e16 | −1.33836 | −0.669180 | − | 0.743100i | \(-0.733355\pi\) | ||||
−0.669180 | + | 0.743100i | \(0.733355\pi\) | |||||||
\(864\) | 1.45579e15 | 0.102866 | ||||||||
\(865\) | 3.87538e16 | 2.72098 | ||||||||
\(866\) | −6.47600e15 | −0.451813 | ||||||||
\(867\) | 2.13777e15 | 0.148203 | ||||||||
\(868\) | −4.67610e14 | −0.0322126 | ||||||||
\(869\) | 1.91156e16 | 1.30852 | ||||||||
\(870\) | 1.60225e16 | 1.08987 | ||||||||
\(871\) | −7.14498e15 | −0.482949 | ||||||||
\(872\) | −1.50171e16 | −1.00866 | ||||||||
\(873\) | −7.87094e15 | −0.525350 | ||||||||
\(874\) | −1.88591e15 | −0.125086 | ||||||||
\(875\) | 9.13447e15 | 0.602059 | ||||||||
\(876\) | 2.93678e15 | 0.192353 | ||||||||
\(877\) | −1.11677e16 | −0.726885 | −0.363443 | − | 0.931617i | \(-0.618399\pi\) | ||||
−0.363443 | + | 0.931617i | \(0.618399\pi\) | |||||||
\(878\) | −1.65370e16 | −1.06964 | ||||||||
\(879\) | 6.69896e15 | 0.430594 | ||||||||
\(880\) | −1.97257e16 | −1.26002 | ||||||||
\(881\) | −2.25647e16 | −1.43239 | −0.716195 | − | 0.697900i | \(-0.754118\pi\) | ||||
−0.716195 | + | 0.697900i | \(0.754118\pi\) | |||||||
\(882\) | 4.31490e15 | 0.272204 | ||||||||
\(883\) | 1.02568e16 | 0.643026 | 0.321513 | − | 0.946905i | \(-0.395809\pi\) | ||||
0.321513 | + | 0.946905i | \(0.395809\pi\) | |||||||
\(884\) | −3.90245e15 | −0.243136 | ||||||||
\(885\) | −2.29836e15 | −0.142308 | ||||||||
\(886\) | 1.71931e16 | 1.05796 | ||||||||
\(887\) | −4.84262e15 | −0.296143 | −0.148071 | − | 0.988977i | \(-0.547307\pi\) | ||||
−0.148071 | + | 0.988977i | \(0.547307\pi\) | |||||||
\(888\) | 9.73188e14 | 0.0591460 | ||||||||
\(889\) | 6.85159e14 | 0.0413839 | ||||||||
\(890\) | −2.65538e16 | −1.59398 | ||||||||
\(891\) | −1.91334e15 | −0.114147 | ||||||||
\(892\) | −1.01427e15 | −0.0601376 | ||||||||
\(893\) | 8.29018e15 | 0.488518 | ||||||||
\(894\) | 4.67130e15 | 0.273578 | ||||||||
\(895\) | −1.70506e16 | −0.992460 | ||||||||
\(896\) | 1.40042e15 | 0.0810150 | ||||||||
\(897\) | 3.15133e15 | 0.181191 | ||||||||
\(898\) | 8.77224e15 | 0.501292 | ||||||||
\(899\) | 1.19983e16 | 0.681464 | ||||||||
\(900\) | −4.21222e15 | −0.237781 | ||||||||
\(901\) | −1.75721e16 | −0.985913 | ||||||||
\(902\) | 2.03941e15 | 0.113728 | ||||||||
\(903\) | −1.41071e15 | −0.0781909 | ||||||||
\(904\) | −2.97148e16 | −1.63699 | ||||||||
\(905\) | 1.39987e16 | 0.766517 | ||||||||
\(906\) | 1.19241e16 | 0.648963 | ||||||||
\(907\) | 2.75849e16 | 1.49222 | 0.746108 | − | 0.665825i | \(-0.231920\pi\) | ||||
0.746108 | + | 0.665825i | \(0.231920\pi\) | |||||||
\(908\) | 6.09378e14 | 0.0327653 | ||||||||
\(909\) | −1.03648e16 | −0.553934 | ||||||||
\(910\) | −6.21846e15 | −0.330335 | ||||||||
\(911\) | 3.00066e16 | 1.58440 | 0.792202 | − | 0.610259i | \(-0.208934\pi\) | ||||
0.792202 | + | 0.610259i | \(0.208934\pi\) | |||||||
\(912\) | −3.41083e15 | −0.179014 | ||||||||
\(913\) | 3.30772e16 | 1.72560 | ||||||||
\(914\) | −1.81348e15 | −0.0940392 | ||||||||
\(915\) | 1.65805e16 | 0.854636 | ||||||||
\(916\) | −5.59038e15 | −0.286429 | ||||||||
\(917\) | −3.44523e15 | −0.175464 | ||||||||
\(918\) | 2.78872e15 | 0.141179 | ||||||||
\(919\) | −1.72784e16 | −0.869495 | −0.434748 | − | 0.900552i | \(-0.643162\pi\) | ||||
−0.434748 | + | 0.900552i | \(0.643162\pi\) | |||||||
\(920\) | 1.26216e16 | 0.631366 | ||||||||
\(921\) | 4.97086e15 | 0.247174 | ||||||||
\(922\) | 2.80884e15 | 0.138838 | ||||||||
\(923\) | 2.28990e16 | 1.12514 | ||||||||
\(924\) | 6.72627e14 | 0.0328533 | ||||||||
\(925\) | −5.02261e15 | −0.243865 | ||||||||
\(926\) | 1.42551e16 | 0.688032 | ||||||||
\(927\) | 4.47463e15 | 0.214693 | ||||||||
\(928\) | 1.31316e16 | 0.626333 | ||||||||
\(929\) | −2.08626e16 | −0.989194 | −0.494597 | − | 0.869122i | \(-0.664684\pi\) | ||||
−0.494597 | + | 0.869122i | \(0.664684\pi\) | |||||||
\(930\) | 1.14756e16 | 0.540901 | ||||||||
\(931\) | 9.80314e15 | 0.459348 | ||||||||
\(932\) | 6.12112e15 | 0.285130 | ||||||||
\(933\) | −9.62034e15 | −0.445493 | ||||||||
\(934\) | 1.31379e16 | 0.604808 | ||||||||
\(935\) | 3.66413e16 | 1.67690 | ||||||||
\(936\) | 8.12770e15 | 0.369786 | ||||||||
\(937\) | −1.02457e16 | −0.463418 | −0.231709 | − | 0.972785i | \(-0.574432\pi\) | ||||
−0.231709 | + | 0.972785i | \(0.574432\pi\) | |||||||
\(938\) | −1.79495e15 | −0.0807116 | ||||||||
\(939\) | 1.74238e16 | 0.778899 | ||||||||
\(940\) | −1.20011e16 | −0.533356 | ||||||||
\(941\) | 2.75473e16 | 1.21713 | 0.608565 | − | 0.793504i | \(-0.291746\pi\) | ||||
0.608565 | + | 0.793504i | \(0.291746\pi\) | |||||||
\(942\) | −5.57207e15 | −0.244758 | ||||||||
\(943\) | −9.15064e14 | −0.0399611 | ||||||||
\(944\) | 1.94256e15 | 0.0843388 | ||||||||
\(945\) | −1.69406e15 | −0.0731228 | ||||||||
\(946\) | −1.37460e16 | −0.589894 | ||||||||
\(947\) | 4.25827e16 | 1.81681 | 0.908403 | − | 0.418095i | \(-0.137302\pi\) | ||||
0.908403 | + | 0.418095i | \(0.137302\pi\) | |||||||
\(948\) | −4.78489e15 | −0.202967 | ||||||||
\(949\) | 2.92456e16 | 1.23338 | ||||||||
\(950\) | 2.51031e16 | 1.05256 | ||||||||
\(951\) | −1.30082e13 | −0.000542281 0 | ||||||||
\(952\) | −4.53237e15 | −0.187855 | ||||||||
\(953\) | 2.07111e16 | 0.853476 | 0.426738 | − | 0.904375i | \(-0.359663\pi\) | ||||
0.426738 | + | 0.904375i | \(0.359663\pi\) | |||||||
\(954\) | 7.91622e15 | 0.324341 | ||||||||
\(955\) | −3.07816e16 | −1.25393 | ||||||||
\(956\) | −8.67120e15 | −0.351205 | ||||||||
\(957\) | −1.72588e16 | −0.695018 | ||||||||
\(958\) | 1.19215e16 | 0.477332 | ||||||||
\(959\) | −7.47402e15 | −0.297544 | ||||||||
\(960\) | 3.04491e16 | 1.20527 | ||||||||
\(961\) | −1.68151e16 | −0.661790 | ||||||||
\(962\) | 2.09628e15 | 0.0820326 | ||||||||
\(963\) | 1.49824e15 | 0.0582958 | ||||||||
\(964\) | 2.97942e15 | 0.115268 | ||||||||
\(965\) | 2.83428e16 | 1.09029 | ||||||||
\(966\) | 7.91670e14 | 0.0302810 | ||||||||
\(967\) | −5.37393e14 | −0.0204384 | −0.0102192 | − | 0.999948i | \(-0.503253\pi\) | ||||
−0.0102192 | + | 0.999948i | \(0.503253\pi\) | |||||||
\(968\) | 1.59033e15 | 0.0601411 | ||||||||
\(969\) | 6.33576e15 | 0.238242 | ||||||||
\(970\) | −6.79046e16 | −2.53895 | ||||||||
\(971\) | 1.89251e16 | 0.703612 | 0.351806 | − | 0.936073i | \(-0.385568\pi\) | ||||
0.351806 | + | 0.936073i | \(0.385568\pi\) | |||||||
\(972\) | 4.78934e14 | 0.0177056 | ||||||||
\(973\) | −7.02323e14 | −0.0258176 | ||||||||
\(974\) | −3.50797e16 | −1.28228 | ||||||||
\(975\) | −4.19470e16 | −1.52467 | ||||||||
\(976\) | −1.40137e16 | −0.506499 | ||||||||
\(977\) | −5.54836e15 | −0.199409 | −0.0997044 | − | 0.995017i | \(-0.531790\pi\) | ||||
−0.0997044 | + | 0.995017i | \(0.531790\pi\) | |||||||
\(978\) | 5.78839e15 | 0.206868 | ||||||||
\(979\) | 2.86028e16 | 1.01649 | ||||||||
\(980\) | −1.41913e16 | −0.501508 | ||||||||
\(981\) | −8.81216e15 | −0.309673 | ||||||||
\(982\) | 1.75020e16 | 0.611608 | ||||||||
\(983\) | 4.72330e16 | 1.64135 | 0.820675 | − | 0.571396i | \(-0.193598\pi\) | ||||
0.820675 | + | 0.571396i | \(0.193598\pi\) | |||||||
\(984\) | −2.36007e15 | −0.0815553 | ||||||||
\(985\) | 7.18704e16 | 2.46974 | ||||||||
\(986\) | 2.51550e16 | 0.859610 | ||||||||
\(987\) | −3.48007e15 | −0.118261 | ||||||||
\(988\) | 3.99415e15 | 0.134977 | ||||||||
\(989\) | 6.16769e15 | 0.207273 | ||||||||
\(990\) | −1.65069e16 | −0.551659 | ||||||||
\(991\) | −6.68696e15 | −0.222241 | −0.111120 | − | 0.993807i | \(-0.535444\pi\) | ||||
−0.111120 | + | 0.993807i | \(0.535444\pi\) | |||||||
\(992\) | 9.40508e15 | 0.310848 | ||||||||
\(993\) | 2.85614e16 | 0.938767 | ||||||||
\(994\) | 5.75263e15 | 0.188036 | ||||||||
\(995\) | −5.80523e16 | −1.88709 | ||||||||
\(996\) | −8.27965e15 | −0.267661 | ||||||||
\(997\) | 8.23312e15 | 0.264692 | 0.132346 | − | 0.991204i | \(-0.457749\pi\) | ||||
0.132346 | + | 0.991204i | \(0.457749\pi\) | |||||||
\(998\) | −1.91027e16 | −0.610769 | ||||||||
\(999\) | 5.71077e14 | 0.0181587 |
(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 | 177.12.a.c.1.10 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.c.1.10 | ✓ | 27 | 1.1 | even | 1 | trivial |