Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-13.7979\) of defining polynomial | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −12.7979 | −1.13119 | −0.565594 | − | 0.824684i | \(-0.691353\pi\) | ||||
−0.565594 | + | 0.824684i | \(0.691353\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 35.7870 | 0.279586 | ||||||||
\(5\) | −405.222 | −1.44977 | −0.724883 | − | 0.688872i | \(-0.758106\pi\) | ||||
−0.724883 | + | 0.688872i | \(0.758106\pi\) | |||||||
\(6\) | −345.544 | −0.653092 | ||||||||
\(7\) | −375.715 | −0.414014 | −0.207007 | − | 0.978339i | \(-0.566372\pi\) | ||||
−0.207007 | + | 0.978339i | \(0.566372\pi\) | |||||||
\(8\) | 1180.14 | 0.814924 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 5186.00 | 1.63996 | ||||||||
\(11\) | −1868.92 | −0.423366 | −0.211683 | − | 0.977338i | \(-0.567895\pi\) | ||||
−0.211683 | + | 0.977338i | \(0.567895\pi\) | |||||||
\(12\) | 966.249 | 0.161419 | ||||||||
\(13\) | 143.937 | 0.0181706 | 0.00908532 | − | 0.999959i | \(-0.497108\pi\) | ||||
0.00908532 | + | 0.999959i | \(0.497108\pi\) | |||||||
\(14\) | 4808.37 | 0.468328 | ||||||||
\(15\) | −10941.0 | −0.837023 | ||||||||
\(16\) | −19684.0 | −1.20142 | ||||||||
\(17\) | −7997.65 | −0.394813 | −0.197406 | − | 0.980322i | \(-0.563252\pi\) | ||||
−0.197406 | + | 0.980322i | \(0.563252\pi\) | |||||||
\(18\) | −9329.69 | −0.377063 | ||||||||
\(19\) | −54944.6 | −1.83776 | −0.918878 | − | 0.394543i | \(-0.870903\pi\) | ||||
−0.918878 | + | 0.394543i | \(0.870903\pi\) | |||||||
\(20\) | −14501.7 | −0.405334 | ||||||||
\(21\) | −10144.3 | −0.239031 | ||||||||
\(22\) | 23918.3 | 0.478907 | ||||||||
\(23\) | −57227.2 | −0.980743 | −0.490372 | − | 0.871513i | \(-0.663139\pi\) | ||||
−0.490372 | + | 0.871513i | \(0.663139\pi\) | |||||||
\(24\) | 31863.7 | 0.470496 | ||||||||
\(25\) | 86079.9 | 1.10182 | ||||||||
\(26\) | −1842.09 | −0.0205544 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −13445.7 | −0.115753 | ||||||||
\(29\) | 44123.3 | 0.335951 | 0.167975 | − | 0.985791i | \(-0.446277\pi\) | ||||
0.167975 | + | 0.985791i | \(0.446277\pi\) | |||||||
\(30\) | 140022. | 0.946830 | ||||||||
\(31\) | −127609. | −0.769333 | −0.384667 | − | 0.923056i | \(-0.625684\pi\) | ||||
−0.384667 | + | 0.923056i | \(0.625684\pi\) | |||||||
\(32\) | 100857. | 0.544105 | ||||||||
\(33\) | −50460.9 | −0.244431 | ||||||||
\(34\) | 102353. | 0.446607 | ||||||||
\(35\) | 152248. | 0.600224 | ||||||||
\(36\) | 26088.7 | 0.0931953 | ||||||||
\(37\) | −343781. | −1.11577 | −0.557886 | − | 0.829918i | \(-0.688387\pi\) | ||||
−0.557886 | + | 0.829918i | \(0.688387\pi\) | |||||||
\(38\) | 703178. | 2.07885 | ||||||||
\(39\) | 3886.30 | 0.0104908 | ||||||||
\(40\) | −478217. | −1.18145 | ||||||||
\(41\) | 57315.2 | 0.129875 | 0.0649376 | − | 0.997889i | \(-0.479315\pi\) | ||||
0.0649376 | + | 0.997889i | \(0.479315\pi\) | |||||||
\(42\) | 129826. | 0.270389 | ||||||||
\(43\) | 131635. | 0.252483 | 0.126241 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126241 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(44\) | −66883.0 | −0.118367 | ||||||||
\(45\) | −295407. | −0.483255 | ||||||||
\(46\) | 732390. | 1.10941 | ||||||||
\(47\) | 13310.0 | 0.0186998 | 0.00934989 | − | 0.999956i | \(-0.497024\pi\) | ||||
0.00934989 | + | 0.999956i | \(0.497024\pi\) | |||||||
\(48\) | −531469. | −0.693639 | ||||||||
\(49\) | −682381. | −0.828592 | ||||||||
\(50\) | −1.10164e6 | −1.24637 | ||||||||
\(51\) | −215937. | −0.227945 | ||||||||
\(52\) | 5151.07 | 0.00508026 | ||||||||
\(53\) | −642722. | −0.593004 | −0.296502 | − | 0.955032i | \(-0.595820\pi\) | ||||
−0.296502 | + | 0.955032i | \(0.595820\pi\) | |||||||
\(54\) | −251902. | −0.217697 | ||||||||
\(55\) | 757328. | 0.613782 | ||||||||
\(56\) | −443395. | −0.337390 | ||||||||
\(57\) | −1.48351e6 | −1.06103 | ||||||||
\(58\) | −564687. | −0.380023 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −391545. | −0.234020 | ||||||||
\(61\) | −1.24234e6 | −0.700785 | −0.350393 | − | 0.936603i | \(-0.613952\pi\) | ||||
−0.350393 | + | 0.936603i | \(0.613952\pi\) | |||||||
\(62\) | 1.63313e6 | 0.870261 | ||||||||
\(63\) | −273896. | −0.138005 | ||||||||
\(64\) | 1.22879e6 | 0.585932 | ||||||||
\(65\) | −58326.4 | −0.0263432 | ||||||||
\(66\) | 645794. | 0.276497 | ||||||||
\(67\) | 333473. | 0.135456 | 0.0677282 | − | 0.997704i | \(-0.478425\pi\) | ||||
0.0677282 | + | 0.997704i | \(0.478425\pi\) | |||||||
\(68\) | −286212. | −0.110384 | ||||||||
\(69\) | −1.54514e6 | −0.566233 | ||||||||
\(70\) | −1.94846e6 | −0.678966 | ||||||||
\(71\) | 4.40870e6 | 1.46186 | 0.730930 | − | 0.682452i | \(-0.239086\pi\) | ||||
0.730930 | + | 0.682452i | \(0.239086\pi\) | |||||||
\(72\) | 860319. | 0.271641 | ||||||||
\(73\) | −790210. | −0.237746 | −0.118873 | − | 0.992909i | \(-0.537928\pi\) | ||||
−0.118873 | + | 0.992909i | \(0.537928\pi\) | |||||||
\(74\) | 4.39968e6 | 1.26215 | ||||||||
\(75\) | 2.32416e6 | 0.636137 | ||||||||
\(76\) | −1.96630e6 | −0.513810 | ||||||||
\(77\) | 702181. | 0.175280 | ||||||||
\(78\) | −49736.5 | −0.0118671 | ||||||||
\(79\) | 1.80576e6 | 0.412065 | 0.206032 | − | 0.978545i | \(-0.433945\pi\) | ||||
0.206032 | + | 0.978545i | \(0.433945\pi\) | |||||||
\(80\) | 7.97640e6 | 1.74177 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −733516. | −0.146913 | ||||||||
\(83\) | 3.39335e6 | 0.651411 | 0.325705 | − | 0.945471i | \(-0.394398\pi\) | ||||
0.325705 | + | 0.945471i | \(0.394398\pi\) | |||||||
\(84\) | −363034. | −0.0668297 | ||||||||
\(85\) | 3.24082e6 | 0.572386 | ||||||||
\(86\) | −1.68465e6 | −0.285605 | ||||||||
\(87\) | 1.19133e6 | 0.193961 | ||||||||
\(88\) | −2.20558e6 | −0.345011 | ||||||||
\(89\) | 9.39299e6 | 1.41234 | 0.706169 | − | 0.708043i | \(-0.250422\pi\) | ||||
0.706169 | + | 0.708043i | \(0.250422\pi\) | |||||||
\(90\) | 3.78060e6 | 0.546653 | ||||||||
\(91\) | −54079.2 | −0.00752291 | ||||||||
\(92\) | −2.04799e6 | −0.274202 | ||||||||
\(93\) | −3.44544e6 | −0.444175 | ||||||||
\(94\) | −170341. | −0.0211530 | ||||||||
\(95\) | 2.22648e7 | 2.66432 | ||||||||
\(96\) | 2.72315e6 | 0.314139 | ||||||||
\(97\) | 773470. | 0.0860483 | 0.0430242 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430242 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(98\) | 8.73307e6 | 0.937293 | ||||||||
\(99\) | −1.36244e6 | −0.141122 | ||||||||
\(100\) | 3.08054e6 | 0.308054 | ||||||||
\(101\) | −654307. | −0.0631912 | −0.0315956 | − | 0.999501i | \(-0.510059\pi\) | ||||
−0.0315956 | + | 0.999501i | \(0.510059\pi\) | |||||||
\(102\) | 2.76354e6 | 0.257849 | ||||||||
\(103\) | 5.35811e6 | 0.483149 | 0.241574 | − | 0.970382i | \(-0.422336\pi\) | ||||
0.241574 | + | 0.970382i | \(0.422336\pi\) | |||||||
\(104\) | 169865. | 0.0148077 | ||||||||
\(105\) | 4.11069e6 | 0.346539 | ||||||||
\(106\) | 8.22551e6 | 0.670799 | ||||||||
\(107\) | −4.95592e6 | −0.391094 | −0.195547 | − | 0.980694i | \(-0.562648\pi\) | ||||
−0.195547 | + | 0.980694i | \(0.562648\pi\) | |||||||
\(108\) | 704395. | 0.0538063 | ||||||||
\(109\) | 1.10724e7 | 0.818931 | 0.409465 | − | 0.912326i | \(-0.365715\pi\) | ||||
0.409465 | + | 0.912326i | \(0.365715\pi\) | |||||||
\(110\) | −9.69223e6 | −0.694303 | ||||||||
\(111\) | −9.28208e6 | −0.644191 | ||||||||
\(112\) | 7.39558e6 | 0.497404 | ||||||||
\(113\) | 1.00502e7 | 0.655239 | 0.327619 | − | 0.944810i | \(-0.393754\pi\) | ||||
0.327619 | + | 0.944810i | \(0.393754\pi\) | |||||||
\(114\) | 1.89858e7 | 1.20022 | ||||||||
\(115\) | 2.31897e7 | 1.42185 | ||||||||
\(116\) | 1.57904e6 | 0.0939270 | ||||||||
\(117\) | 104930. | 0.00605688 | ||||||||
\(118\) | −2.62843e6 | −0.147268 | ||||||||
\(119\) | 3.00484e6 | 0.163458 | ||||||||
\(120\) | −1.29119e7 | −0.682110 | ||||||||
\(121\) | −1.59943e7 | −0.820761 | ||||||||
\(122\) | 1.58993e7 | 0.792720 | ||||||||
\(123\) | 1.54751e6 | 0.0749835 | ||||||||
\(124\) | −4.56673e6 | −0.215095 | ||||||||
\(125\) | −3.22348e6 | −0.147618 | ||||||||
\(126\) | 3.50530e6 | 0.156109 | ||||||||
\(127\) | −2.50572e7 | −1.08547 | −0.542737 | − | 0.839903i | \(-0.682612\pi\) | ||||
−0.542737 | + | 0.839903i | \(0.682612\pi\) | |||||||
\(128\) | −2.86357e7 | −1.20690 | ||||||||
\(129\) | 3.55414e6 | 0.145771 | ||||||||
\(130\) | 746457. | 0.0297991 | ||||||||
\(131\) | −1.29122e7 | −0.501823 | −0.250912 | − | 0.968010i | \(-0.580730\pi\) | ||||
−0.250912 | + | 0.968010i | \(0.580730\pi\) | |||||||
\(132\) | −1.80584e6 | −0.0683394 | ||||||||
\(133\) | 2.06435e7 | 0.760857 | ||||||||
\(134\) | −4.26777e6 | −0.153227 | ||||||||
\(135\) | −7.97598e6 | −0.279008 | ||||||||
\(136\) | −9.43831e6 | −0.321742 | ||||||||
\(137\) | 3.21499e6 | 0.106821 | 0.0534106 | − | 0.998573i | \(-0.482991\pi\) | ||||
0.0534106 | + | 0.998573i | \(0.482991\pi\) | |||||||
\(138\) | 1.97745e7 | 0.640515 | ||||||||
\(139\) | 1.39325e7 | 0.440025 | 0.220012 | − | 0.975497i | \(-0.429390\pi\) | ||||
0.220012 | + | 0.975497i | \(0.429390\pi\) | |||||||
\(140\) | 5.44849e6 | 0.167814 | ||||||||
\(141\) | 359371. | 0.0107963 | ||||||||
\(142\) | −5.64222e7 | −1.65364 | ||||||||
\(143\) | −269007. | −0.00769284 | ||||||||
\(144\) | −1.43497e7 | −0.400473 | ||||||||
\(145\) | −1.78797e7 | −0.487050 | ||||||||
\(146\) | 1.01130e7 | 0.268935 | ||||||||
\(147\) | −1.84243e7 | −0.478388 | ||||||||
\(148\) | −1.23029e7 | −0.311954 | ||||||||
\(149\) | 4.45947e7 | 1.10441 | 0.552206 | − | 0.833708i | \(-0.313786\pi\) | ||||
0.552206 | + | 0.833708i | \(0.313786\pi\) | |||||||
\(150\) | −2.97444e7 | −0.719591 | ||||||||
\(151\) | 3.86098e7 | 0.912595 | 0.456298 | − | 0.889827i | \(-0.349175\pi\) | ||||
0.456298 | + | 0.889827i | \(0.349175\pi\) | |||||||
\(152\) | −6.48421e7 | −1.49763 | ||||||||
\(153\) | −5.83029e6 | −0.131604 | ||||||||
\(154\) | −8.98647e6 | −0.198274 | ||||||||
\(155\) | 5.17099e7 | 1.11535 | ||||||||
\(156\) | 139079. | 0.00293309 | ||||||||
\(157\) | 6.75271e7 | 1.39261 | 0.696305 | − | 0.717746i | \(-0.254826\pi\) | ||||
0.696305 | + | 0.717746i | \(0.254826\pi\) | |||||||
\(158\) | −2.31100e7 | −0.466123 | ||||||||
\(159\) | −1.73535e7 | −0.342371 | ||||||||
\(160\) | −4.08696e7 | −0.788825 | ||||||||
\(161\) | 2.15011e7 | 0.406042 | ||||||||
\(162\) | −6.80134e6 | −0.125688 | ||||||||
\(163\) | −3.73402e7 | −0.675336 | −0.337668 | − | 0.941265i | \(-0.609638\pi\) | ||||
−0.337668 | + | 0.941265i | \(0.609638\pi\) | |||||||
\(164\) | 2.05114e6 | 0.0363113 | ||||||||
\(165\) | 2.04478e7 | 0.354367 | ||||||||
\(166\) | −4.34278e7 | −0.736868 | ||||||||
\(167\) | 4.08725e7 | 0.679085 | 0.339542 | − | 0.940591i | \(-0.389728\pi\) | ||||
0.339542 | + | 0.940591i | \(0.389728\pi\) | |||||||
\(168\) | −1.19717e7 | −0.194792 | ||||||||
\(169\) | −6.27278e7 | −0.999670 | ||||||||
\(170\) | −4.14758e7 | −0.647476 | ||||||||
\(171\) | −4.00546e7 | −0.612585 | ||||||||
\(172\) | 4.71082e6 | 0.0705906 | ||||||||
\(173\) | 3.92808e7 | 0.576791 | 0.288395 | − | 0.957511i | \(-0.406878\pi\) | ||||
0.288395 | + | 0.957511i | \(0.406878\pi\) | |||||||
\(174\) | −1.52466e7 | −0.219406 | ||||||||
\(175\) | −3.23415e7 | −0.456170 | ||||||||
\(176\) | 3.67879e7 | 0.508640 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −1.20211e8 | −1.59762 | ||||||||
\(179\) | −4.89222e7 | −0.637559 | −0.318780 | − | 0.947829i | \(-0.603273\pi\) | ||||
−0.318780 | + | 0.947829i | \(0.603273\pi\) | |||||||
\(180\) | −1.05717e7 | −0.135111 | ||||||||
\(181\) | −8.97873e7 | −1.12549 | −0.562743 | − | 0.826632i | \(-0.690254\pi\) | ||||
−0.562743 | + | 0.826632i | \(0.690254\pi\) | |||||||
\(182\) | 692102. | 0.00850982 | ||||||||
\(183\) | −3.35431e7 | −0.404599 | ||||||||
\(184\) | −6.75359e7 | −0.799231 | ||||||||
\(185\) | 1.39307e8 | 1.61761 | ||||||||
\(186\) | 4.40945e7 | 0.502445 | ||||||||
\(187\) | 1.49470e7 | 0.167150 | ||||||||
\(188\) | 476326. | 0.00522819 | ||||||||
\(189\) | −7.39520e6 | −0.0796771 | ||||||||
\(190\) | −2.84943e8 | −3.01384 | ||||||||
\(191\) | 1.17574e8 | 1.22094 | 0.610470 | − | 0.792040i | \(-0.290981\pi\) | ||||
0.610470 | + | 0.792040i | \(0.290981\pi\) | |||||||
\(192\) | 3.31773e7 | 0.338288 | ||||||||
\(193\) | −1.89578e8 | −1.89818 | −0.949092 | − | 0.314999i | \(-0.897996\pi\) | ||||
−0.949092 | + | 0.314999i | \(0.897996\pi\) | |||||||
\(194\) | −9.89881e6 | −0.0973368 | ||||||||
\(195\) | −1.57481e6 | −0.0152092 | ||||||||
\(196\) | −2.44204e7 | −0.231663 | ||||||||
\(197\) | 6.19268e7 | 0.577094 | 0.288547 | − | 0.957466i | \(-0.406828\pi\) | ||||
0.288547 | + | 0.957466i | \(0.406828\pi\) | |||||||
\(198\) | 1.74365e7 | 0.159636 | ||||||||
\(199\) | 1.68475e8 | 1.51548 | 0.757741 | − | 0.652556i | \(-0.226303\pi\) | ||||
0.757741 | + | 0.652556i | \(0.226303\pi\) | |||||||
\(200\) | 1.01586e8 | 0.897901 | ||||||||
\(201\) | 9.00378e6 | 0.0782058 | ||||||||
\(202\) | 8.37378e6 | 0.0714812 | ||||||||
\(203\) | −1.65778e7 | −0.139088 | ||||||||
\(204\) | −7.72772e6 | −0.0637303 | ||||||||
\(205\) | −2.32254e7 | −0.188289 | ||||||||
\(206\) | −6.85727e7 | −0.546532 | ||||||||
\(207\) | −4.17187e7 | −0.326914 | ||||||||
\(208\) | −2.83326e6 | −0.0218305 | ||||||||
\(209\) | 1.02687e8 | 0.778044 | ||||||||
\(210\) | −5.26084e7 | −0.392001 | ||||||||
\(211\) | 1.90058e7 | 0.139283 | 0.0696413 | − | 0.997572i | \(-0.477815\pi\) | ||||
0.0696413 | + | 0.997572i | \(0.477815\pi\) | |||||||
\(212\) | −2.30011e7 | −0.165796 | ||||||||
\(213\) | 1.19035e8 | 0.844006 | ||||||||
\(214\) | 6.34255e7 | 0.442401 | ||||||||
\(215\) | −5.33414e7 | −0.366041 | ||||||||
\(216\) | 2.32286e7 | 0.156832 | ||||||||
\(217\) | 4.79445e7 | 0.318515 | ||||||||
\(218\) | −1.41703e8 | −0.926364 | ||||||||
\(219\) | −2.13357e7 | −0.137262 | ||||||||
\(220\) | 2.71025e7 | 0.171605 | ||||||||
\(221\) | −1.15116e6 | −0.00717400 | ||||||||
\(222\) | 1.18791e8 | 0.728701 | ||||||||
\(223\) | −9.54195e7 | −0.576196 | −0.288098 | − | 0.957601i | \(-0.593023\pi\) | ||||
−0.288098 | + | 0.957601i | \(0.593023\pi\) | |||||||
\(224\) | −3.78936e7 | −0.225267 | ||||||||
\(225\) | 6.27522e7 | 0.367274 | ||||||||
\(226\) | −1.28622e8 | −0.741198 | ||||||||
\(227\) | 1.24600e7 | 0.0707012 | 0.0353506 | − | 0.999375i | \(-0.488745\pi\) | ||||
0.0353506 | + | 0.999375i | \(0.488745\pi\) | |||||||
\(228\) | −5.30902e7 | −0.296649 | ||||||||
\(229\) | −1.55581e8 | −0.856118 | −0.428059 | − | 0.903751i | \(-0.640802\pi\) | ||||
−0.428059 | + | 0.903751i | \(0.640802\pi\) | |||||||
\(230\) | −2.96781e8 | −1.60838 | ||||||||
\(231\) | 1.89589e7 | 0.101198 | ||||||||
\(232\) | 5.20715e7 | 0.273774 | ||||||||
\(233\) | −1.59313e8 | −0.825100 | −0.412550 | − | 0.910935i | \(-0.635362\pi\) | ||||
−0.412550 | + | 0.910935i | \(0.635362\pi\) | |||||||
\(234\) | −1.34289e6 | −0.00685147 | ||||||||
\(235\) | −5.39351e6 | −0.0271103 | ||||||||
\(236\) | 7.34990e6 | 0.0363990 | ||||||||
\(237\) | 4.87556e7 | 0.237906 | ||||||||
\(238\) | −3.84557e7 | −0.184902 | ||||||||
\(239\) | 2.85477e8 | 1.35263 | 0.676314 | − | 0.736614i | \(-0.263576\pi\) | ||||
0.676314 | + | 0.736614i | \(0.263576\pi\) | |||||||
\(240\) | 2.15363e8 | 1.00561 | ||||||||
\(241\) | 2.08212e8 | 0.958177 | 0.479088 | − | 0.877767i | \(-0.340967\pi\) | ||||
0.479088 | + | 0.877767i | \(0.340967\pi\) | |||||||
\(242\) | 2.04694e8 | 0.928435 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −4.44595e7 | −0.195930 | ||||||||
\(245\) | 2.76516e8 | 1.20127 | ||||||||
\(246\) | −1.98049e7 | −0.0848204 | ||||||||
\(247\) | −7.90856e6 | −0.0333932 | ||||||||
\(248\) | −1.50596e8 | −0.626948 | ||||||||
\(249\) | 9.16203e7 | 0.376092 | ||||||||
\(250\) | 4.12539e7 | 0.166984 | ||||||||
\(251\) | −3.40393e8 | −1.35870 | −0.679348 | − | 0.733816i | \(-0.737737\pi\) | ||||
−0.679348 | + | 0.733816i | \(0.737737\pi\) | |||||||
\(252\) | −9.80192e6 | −0.0385842 | ||||||||
\(253\) | 1.06953e8 | 0.415214 | ||||||||
\(254\) | 3.20680e8 | 1.22788 | ||||||||
\(255\) | 8.75022e7 | 0.330467 | ||||||||
\(256\) | 2.09193e8 | 0.779304 | ||||||||
\(257\) | 1.59818e8 | 0.587298 | 0.293649 | − | 0.955913i | \(-0.405130\pi\) | ||||
0.293649 | + | 0.955913i | \(0.405130\pi\) | |||||||
\(258\) | −4.54857e7 | −0.164894 | ||||||||
\(259\) | 1.29164e8 | 0.461945 | ||||||||
\(260\) | −2.08733e6 | −0.00736518 | ||||||||
\(261\) | 3.21659e7 | 0.111984 | ||||||||
\(262\) | 1.65249e8 | 0.567656 | ||||||||
\(263\) | −7.73432e7 | −0.262166 | −0.131083 | − | 0.991371i | \(-0.541845\pi\) | ||||
−0.131083 | + | 0.991371i | \(0.541845\pi\) | |||||||
\(264\) | −5.95507e7 | −0.199192 | ||||||||
\(265\) | 2.60445e8 | 0.859717 | ||||||||
\(266\) | −2.64194e8 | −0.860672 | ||||||||
\(267\) | 2.53611e8 | 0.815414 | ||||||||
\(268\) | 1.19340e7 | 0.0378717 | ||||||||
\(269\) | −4.47623e8 | −1.40210 | −0.701050 | − | 0.713112i | \(-0.747285\pi\) | ||||
−0.701050 | + | 0.713112i | \(0.747285\pi\) | |||||||
\(270\) | 1.02076e8 | 0.315610 | ||||||||
\(271\) | −3.39469e8 | −1.03611 | −0.518056 | − | 0.855346i | \(-0.673344\pi\) | ||||
−0.518056 | + | 0.855346i | \(0.673344\pi\) | |||||||
\(272\) | 1.57426e8 | 0.474335 | ||||||||
\(273\) | −1.46014e6 | −0.00434335 | ||||||||
\(274\) | −4.11452e7 | −0.120835 | ||||||||
\(275\) | −1.60876e8 | −0.466475 | ||||||||
\(276\) | −5.52958e7 | −0.158311 | ||||||||
\(277\) | −3.30374e8 | −0.933957 | −0.466979 | − | 0.884269i | \(-0.654658\pi\) | ||||
−0.466979 | + | 0.884269i | \(0.654658\pi\) | |||||||
\(278\) | −1.78307e8 | −0.497751 | ||||||||
\(279\) | −9.30268e7 | −0.256444 | ||||||||
\(280\) | 1.79673e8 | 0.489137 | ||||||||
\(281\) | −5.59715e7 | −0.150486 | −0.0752428 | − | 0.997165i | \(-0.523973\pi\) | ||||
−0.0752428 | + | 0.997165i | \(0.523973\pi\) | |||||||
\(282\) | −4.59920e6 | −0.0122127 | ||||||||
\(283\) | −3.42839e8 | −0.899160 | −0.449580 | − | 0.893240i | \(-0.648426\pi\) | ||||
−0.449580 | + | 0.893240i | \(0.648426\pi\) | |||||||
\(284\) | 1.57774e8 | 0.408716 | ||||||||
\(285\) | 6.01149e8 | 1.53824 | ||||||||
\(286\) | 3.44273e6 | 0.00870205 | ||||||||
\(287\) | −2.15342e7 | −0.0537702 | ||||||||
\(288\) | 7.35251e7 | 0.181368 | ||||||||
\(289\) | −3.46376e8 | −0.844123 | ||||||||
\(290\) | 2.28824e8 | 0.550945 | ||||||||
\(291\) | 2.08837e7 | 0.0496800 | ||||||||
\(292\) | −2.82792e7 | −0.0664703 | ||||||||
\(293\) | 5.81815e8 | 1.35129 | 0.675644 | − | 0.737228i | \(-0.263865\pi\) | ||||
0.675644 | + | 0.737228i | \(0.263865\pi\) | |||||||
\(294\) | 2.35793e8 | 0.541147 | ||||||||
\(295\) | −8.32241e7 | −0.188743 | ||||||||
\(296\) | −4.05708e8 | −0.909269 | ||||||||
\(297\) | −3.67860e7 | −0.0814769 | ||||||||
\(298\) | −5.70719e8 | −1.24930 | ||||||||
\(299\) | −8.23711e6 | −0.0178207 | ||||||||
\(300\) | 8.31745e7 | 0.177855 | ||||||||
\(301\) | −4.94572e7 | −0.104531 | ||||||||
\(302\) | −4.94125e8 | −1.03232 | ||||||||
\(303\) | −1.76663e7 | −0.0364835 | ||||||||
\(304\) | 1.08153e9 | 2.20791 | ||||||||
\(305\) | 5.03422e8 | 1.01597 | ||||||||
\(306\) | 7.46156e7 | 0.148869 | ||||||||
\(307\) | −6.21817e8 | −1.22653 | −0.613265 | − | 0.789877i | \(-0.710144\pi\) | ||||
−0.613265 | + | 0.789877i | \(0.710144\pi\) | |||||||
\(308\) | 2.51290e7 | 0.0490057 | ||||||||
\(309\) | 1.44669e8 | 0.278946 | ||||||||
\(310\) | −6.61779e8 | −1.26167 | ||||||||
\(311\) | −7.86009e8 | −1.48172 | −0.740860 | − | 0.671659i | \(-0.765582\pi\) | ||||
−0.740860 | + | 0.671659i | \(0.765582\pi\) | |||||||
\(312\) | 4.58636e6 | 0.00854922 | ||||||||
\(313\) | −3.72650e8 | −0.686904 | −0.343452 | − | 0.939170i | \(-0.611596\pi\) | ||||
−0.343452 | + | 0.939170i | \(0.611596\pi\) | |||||||
\(314\) | −8.64207e8 | −1.57530 | ||||||||
\(315\) | 1.10989e8 | 0.200075 | ||||||||
\(316\) | 6.46228e7 | 0.115208 | ||||||||
\(317\) | 2.38136e8 | 0.419873 | 0.209936 | − | 0.977715i | \(-0.432674\pi\) | ||||
0.209936 | + | 0.977715i | \(0.432674\pi\) | |||||||
\(318\) | 2.22089e8 | 0.387286 | ||||||||
\(319\) | −8.24630e7 | −0.142230 | ||||||||
\(320\) | −4.97932e8 | −0.849465 | ||||||||
\(321\) | −1.33810e8 | −0.225798 | ||||||||
\(322\) | −2.75170e8 | −0.459309 | ||||||||
\(323\) | 4.39428e8 | 0.725569 | ||||||||
\(324\) | 1.90187e7 | 0.0310651 | ||||||||
\(325\) | 1.23901e7 | 0.0200208 | ||||||||
\(326\) | 4.77877e8 | 0.763932 | ||||||||
\(327\) | 2.98953e8 | 0.472810 | ||||||||
\(328\) | 6.76397e7 | 0.105838 | ||||||||
\(329\) | −5.00077e6 | −0.00774197 | ||||||||
\(330\) | −2.61690e8 | −0.400856 | ||||||||
\(331\) | 6.49978e8 | 0.985147 | 0.492573 | − | 0.870271i | \(-0.336056\pi\) | ||||
0.492573 | + | 0.870271i | \(0.336056\pi\) | |||||||
\(332\) | 1.21438e8 | 0.182125 | ||||||||
\(333\) | −2.50616e8 | −0.371924 | ||||||||
\(334\) | −5.23084e8 | −0.768172 | ||||||||
\(335\) | −1.35131e8 | −0.196380 | ||||||||
\(336\) | 1.99681e8 | 0.287176 | ||||||||
\(337\) | 6.65064e8 | 0.946583 | 0.473292 | − | 0.880906i | \(-0.343066\pi\) | ||||
0.473292 | + | 0.880906i | \(0.343066\pi\) | |||||||
\(338\) | 8.02786e8 | 1.13081 | ||||||||
\(339\) | 2.71355e8 | 0.378302 | ||||||||
\(340\) | 1.15979e8 | 0.160031 | ||||||||
\(341\) | 2.38491e8 | 0.325710 | ||||||||
\(342\) | 5.12616e8 | 0.692949 | ||||||||
\(343\) | 5.65798e8 | 0.757063 | ||||||||
\(344\) | 1.55347e8 | 0.205754 | ||||||||
\(345\) | 6.26123e8 | 0.820905 | ||||||||
\(346\) | −5.02712e8 | −0.652459 | ||||||||
\(347\) | 2.66064e8 | 0.341848 | 0.170924 | − | 0.985284i | \(-0.445325\pi\) | ||||
0.170924 | + | 0.985284i | \(0.445325\pi\) | |||||||
\(348\) | 4.26341e7 | 0.0542288 | ||||||||
\(349\) | 1.20795e9 | 1.52111 | 0.760556 | − | 0.649273i | \(-0.224927\pi\) | ||||
0.760556 | + | 0.649273i | \(0.224927\pi\) | |||||||
\(350\) | 4.13904e8 | 0.516014 | ||||||||
\(351\) | 2.83311e6 | 0.00349694 | ||||||||
\(352\) | −1.88494e8 | −0.230356 | ||||||||
\(353\) | 2.38306e8 | 0.288352 | 0.144176 | − | 0.989552i | \(-0.453947\pi\) | ||||
0.144176 | + | 0.989552i | \(0.453947\pi\) | |||||||
\(354\) | −7.09675e7 | −0.0850253 | ||||||||
\(355\) | −1.78650e9 | −2.11936 | ||||||||
\(356\) | 3.36147e8 | 0.394870 | ||||||||
\(357\) | 8.11306e7 | 0.0943726 | ||||||||
\(358\) | 6.26103e8 | 0.721199 | ||||||||
\(359\) | −1.03023e9 | −1.17518 | −0.587588 | − | 0.809160i | \(-0.699922\pi\) | ||||
−0.587588 | + | 0.809160i | \(0.699922\pi\) | |||||||
\(360\) | −3.48620e8 | −0.393816 | ||||||||
\(361\) | 2.12504e9 | 2.37734 | ||||||||
\(362\) | 1.14909e9 | 1.27314 | ||||||||
\(363\) | −4.31846e8 | −0.473866 | ||||||||
\(364\) | −1.93533e6 | −0.00210330 | ||||||||
\(365\) | 3.20210e8 | 0.344675 | ||||||||
\(366\) | 4.29282e8 | 0.457677 | ||||||||
\(367\) | 1.50357e9 | 1.58779 | 0.793893 | − | 0.608058i | \(-0.208051\pi\) | ||||
0.793893 | + | 0.608058i | \(0.208051\pi\) | |||||||
\(368\) | 1.12646e9 | 1.17828 | ||||||||
\(369\) | 4.17828e7 | 0.0432917 | ||||||||
\(370\) | −1.78285e9 | −1.82982 | ||||||||
\(371\) | 2.41480e8 | 0.245512 | ||||||||
\(372\) | −1.23302e8 | −0.124185 | ||||||||
\(373\) | −5.53195e8 | −0.551947 | −0.275973 | − | 0.961165i | \(-0.589000\pi\) | ||||
−0.275973 | + | 0.961165i | \(0.589000\pi\) | |||||||
\(374\) | −1.91290e8 | −0.189079 | ||||||||
\(375\) | −8.70340e7 | −0.0852274 | ||||||||
\(376\) | 1.57076e7 | 0.0152389 | ||||||||
\(377\) | 6.35098e6 | 0.00610444 | ||||||||
\(378\) | 9.46432e7 | 0.0901297 | ||||||||
\(379\) | 1.05631e9 | 0.996680 | 0.498340 | − | 0.866982i | \(-0.333943\pi\) | ||||
0.498340 | + | 0.866982i | \(0.333943\pi\) | |||||||
\(380\) | 7.96789e8 | 0.744905 | ||||||||
\(381\) | −6.76544e8 | −0.626699 | ||||||||
\(382\) | −1.50470e9 | −1.38111 | ||||||||
\(383\) | −1.04319e8 | −0.0948782 | −0.0474391 | − | 0.998874i | \(-0.515106\pi\) | ||||
−0.0474391 | + | 0.998874i | \(0.515106\pi\) | |||||||
\(384\) | −7.73164e8 | −0.696807 | ||||||||
\(385\) | −2.84539e8 | −0.254115 | ||||||||
\(386\) | 2.42621e9 | 2.14720 | ||||||||
\(387\) | 9.59618e7 | 0.0841609 | ||||||||
\(388\) | 2.76802e7 | 0.0240579 | ||||||||
\(389\) | −1.52386e9 | −1.31257 | −0.656284 | − | 0.754514i | \(-0.727873\pi\) | ||||
−0.656284 | + | 0.754514i | \(0.727873\pi\) | |||||||
\(390\) | 2.01543e7 | 0.0172045 | ||||||||
\(391\) | 4.57683e8 | 0.387210 | ||||||||
\(392\) | −8.05302e8 | −0.675239 | ||||||||
\(393\) | −3.48629e8 | −0.289728 | ||||||||
\(394\) | −7.92534e8 | −0.652802 | ||||||||
\(395\) | −7.31734e8 | −0.597398 | ||||||||
\(396\) | −4.87577e7 | −0.0394558 | ||||||||
\(397\) | −2.77621e8 | −0.222683 | −0.111341 | − | 0.993782i | \(-0.535515\pi\) | ||||
−0.111341 | + | 0.993782i | \(0.535515\pi\) | |||||||
\(398\) | −2.15614e9 | −1.71429 | ||||||||
\(399\) | 5.57375e8 | 0.439281 | ||||||||
\(400\) | −1.69440e9 | −1.32375 | ||||||||
\(401\) | 3.39521e8 | 0.262943 | 0.131471 | − | 0.991320i | \(-0.458030\pi\) | ||||
0.131471 | + | 0.991320i | \(0.458030\pi\) | |||||||
\(402\) | −1.15230e8 | −0.0884654 | ||||||||
\(403\) | −1.83676e7 | −0.0139793 | ||||||||
\(404\) | −2.34157e7 | −0.0176674 | ||||||||
\(405\) | −2.15352e8 | −0.161085 | ||||||||
\(406\) | 2.12161e8 | 0.157335 | ||||||||
\(407\) | 6.42499e8 | 0.472380 | ||||||||
\(408\) | −2.54834e8 | −0.185758 | ||||||||
\(409\) | 2.23733e9 | 1.61696 | 0.808479 | − | 0.588525i | \(-0.200291\pi\) | ||||
0.808479 | + | 0.588525i | \(0.200291\pi\) | |||||||
\(410\) | 2.97237e8 | 0.212990 | ||||||||
\(411\) | 8.68047e7 | 0.0616733 | ||||||||
\(412\) | 1.91750e8 | 0.135082 | ||||||||
\(413\) | −7.71639e7 | −0.0539001 | ||||||||
\(414\) | 5.33912e8 | 0.369802 | ||||||||
\(415\) | −1.37506e9 | −0.944393 | ||||||||
\(416\) | 1.45171e7 | 0.00988674 | ||||||||
\(417\) | 3.76178e8 | 0.254049 | ||||||||
\(418\) | −1.31418e9 | −0.880114 | ||||||||
\(419\) | 1.72385e9 | 1.14485 | 0.572427 | − | 0.819955i | \(-0.306002\pi\) | ||||
0.572427 | + | 0.819955i | \(0.306002\pi\) | |||||||
\(420\) | 1.47109e8 | 0.0968875 | ||||||||
\(421\) | 2.37385e9 | 1.55048 | 0.775239 | − | 0.631668i | \(-0.217629\pi\) | ||||
0.775239 | + | 0.631668i | \(0.217629\pi\) | |||||||
\(422\) | −2.43234e8 | −0.157555 | ||||||||
\(423\) | 9.70301e6 | 0.00623326 | ||||||||
\(424\) | −7.58499e8 | −0.483253 | ||||||||
\(425\) | −6.88436e8 | −0.435013 | ||||||||
\(426\) | −1.52340e9 | −0.954729 | ||||||||
\(427\) | 4.66765e8 | 0.290135 | ||||||||
\(428\) | −1.77357e8 | −0.109344 | ||||||||
\(429\) | −7.26318e6 | −0.00444147 | ||||||||
\(430\) | 6.82659e8 | 0.414061 | ||||||||
\(431\) | −2.92636e9 | −1.76059 | −0.880294 | − | 0.474428i | \(-0.842655\pi\) | ||||
−0.880294 | + | 0.474428i | \(0.842655\pi\) | |||||||
\(432\) | −3.87441e8 | −0.231213 | ||||||||
\(433\) | −6.83606e8 | −0.404668 | −0.202334 | − | 0.979317i | \(-0.564853\pi\) | ||||
−0.202334 | + | 0.979317i | \(0.564853\pi\) | |||||||
\(434\) | −6.13591e8 | −0.360300 | ||||||||
\(435\) | −4.82753e8 | −0.281198 | ||||||||
\(436\) | 3.96246e8 | 0.228961 | ||||||||
\(437\) | 3.14433e9 | 1.80237 | ||||||||
\(438\) | 2.73052e8 | 0.155270 | ||||||||
\(439\) | −9.63693e8 | −0.543642 | −0.271821 | − | 0.962348i | \(-0.587626\pi\) | ||||
−0.271821 | + | 0.962348i | \(0.587626\pi\) | |||||||
\(440\) | 8.93749e8 | 0.500186 | ||||||||
\(441\) | −4.97456e8 | −0.276197 | ||||||||
\(442\) | 1.47324e7 | 0.00811514 | ||||||||
\(443\) | −1.22895e9 | −0.671616 | −0.335808 | − | 0.941930i | \(-0.609009\pi\) | ||||
−0.335808 | + | 0.941930i | \(0.609009\pi\) | |||||||
\(444\) | −3.32178e8 | −0.180107 | ||||||||
\(445\) | −3.80624e9 | −2.04756 | ||||||||
\(446\) | 1.22117e9 | 0.651786 | ||||||||
\(447\) | 1.20406e9 | 0.637632 | ||||||||
\(448\) | −4.61674e8 | −0.242584 | ||||||||
\(449\) | 2.87288e9 | 1.49781 | 0.748903 | − | 0.662679i | \(-0.230581\pi\) | ||||
0.748903 | + | 0.662679i | \(0.230581\pi\) | |||||||
\(450\) | −8.03098e8 | −0.415456 | ||||||||
\(451\) | −1.07118e8 | −0.0549848 | ||||||||
\(452\) | 3.59666e8 | 0.183196 | ||||||||
\(453\) | 1.04246e9 | 0.526887 | ||||||||
\(454\) | −1.59462e8 | −0.0799764 | ||||||||
\(455\) | 2.19141e7 | 0.0109065 | ||||||||
\(456\) | −1.75074e9 | −0.864657 | ||||||||
\(457\) | 5.34428e8 | 0.261929 | 0.130964 | − | 0.991387i | \(-0.458193\pi\) | ||||
0.130964 | + | 0.991387i | \(0.458193\pi\) | |||||||
\(458\) | 1.99112e9 | 0.968430 | ||||||||
\(459\) | −1.57418e8 | −0.0759817 | ||||||||
\(460\) | 8.29891e8 | 0.397529 | ||||||||
\(461\) | −2.83200e9 | −1.34629 | −0.673146 | − | 0.739510i | \(-0.735057\pi\) | ||||
−0.673146 | + | 0.739510i | \(0.735057\pi\) | |||||||
\(462\) | −2.42635e8 | −0.114474 | ||||||||
\(463\) | −2.92579e9 | −1.36997 | −0.684984 | − | 0.728558i | \(-0.740191\pi\) | ||||
−0.684984 | + | 0.728558i | \(0.740191\pi\) | |||||||
\(464\) | −8.68525e8 | −0.403617 | ||||||||
\(465\) | 1.39617e9 | 0.643950 | ||||||||
\(466\) | 2.03888e9 | 0.933343 | ||||||||
\(467\) | −1.22471e9 | −0.556449 | −0.278225 | − | 0.960516i | \(-0.589746\pi\) | ||||
−0.278225 | + | 0.960516i | \(0.589746\pi\) | |||||||
\(468\) | 3.75513e6 | 0.00169342 | ||||||||
\(469\) | −1.25291e8 | −0.0560809 | ||||||||
\(470\) | 6.90258e7 | 0.0306668 | ||||||||
\(471\) | 1.82323e9 | 0.804023 | ||||||||
\(472\) | 2.42375e8 | 0.106094 | ||||||||
\(473\) | −2.46015e8 | −0.106893 | ||||||||
\(474\) | −6.23970e8 | −0.269116 | ||||||||
\(475\) | −4.72963e9 | −2.02488 | ||||||||
\(476\) | 1.07534e8 | 0.0457006 | ||||||||
\(477\) | −4.68544e8 | −0.197668 | ||||||||
\(478\) | −3.65351e9 | −1.53008 | ||||||||
\(479\) | −1.72272e9 | −0.716211 | −0.358106 | − | 0.933681i | \(-0.616577\pi\) | ||||
−0.358106 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(480\) | −1.10348e9 | −0.455429 | ||||||||
\(481\) | −4.94827e7 | −0.0202743 | ||||||||
\(482\) | −2.66468e9 | −1.08388 | ||||||||
\(483\) | 5.80530e8 | 0.234428 | ||||||||
\(484\) | −5.72388e8 | −0.229473 | ||||||||
\(485\) | −3.13427e8 | −0.124750 | ||||||||
\(486\) | −1.83636e8 | −0.0725657 | ||||||||
\(487\) | 2.39061e9 | 0.937901 | 0.468950 | − | 0.883225i | \(-0.344632\pi\) | ||||
0.468950 | + | 0.883225i | \(0.344632\pi\) | |||||||
\(488\) | −1.46613e9 | −0.571087 | ||||||||
\(489\) | −1.00818e9 | −0.389905 | ||||||||
\(490\) | −3.53883e9 | −1.35886 | ||||||||
\(491\) | 5.12479e8 | 0.195385 | 0.0976924 | − | 0.995217i | \(-0.468854\pi\) | ||||
0.0976924 | + | 0.995217i | \(0.468854\pi\) | |||||||
\(492\) | 5.53807e7 | 0.0209643 | ||||||||
\(493\) | −3.52883e8 | −0.132638 | ||||||||
\(494\) | 1.01213e8 | 0.0377740 | ||||||||
\(495\) | 5.52092e8 | 0.204594 | ||||||||
\(496\) | 2.51185e9 | 0.924291 | ||||||||
\(497\) | −1.65641e9 | −0.605231 | ||||||||
\(498\) | −1.17255e9 | −0.425431 | ||||||||
\(499\) | 3.61805e9 | 1.30354 | 0.651768 | − | 0.758418i | \(-0.274028\pi\) | ||||
0.651768 | + | 0.758418i | \(0.274028\pi\) | |||||||
\(500\) | −1.15359e8 | −0.0412720 | ||||||||
\(501\) | 1.10356e9 | 0.392070 | ||||||||
\(502\) | 4.35632e9 | 1.53694 | ||||||||
\(503\) | 3.85817e9 | 1.35174 | 0.675870 | − | 0.737021i | \(-0.263768\pi\) | ||||
0.675870 | + | 0.737021i | \(0.263768\pi\) | |||||||
\(504\) | −3.23235e8 | −0.112463 | ||||||||
\(505\) | 2.65140e8 | 0.0916125 | ||||||||
\(506\) | −1.36878e9 | −0.469685 | ||||||||
\(507\) | −1.69365e9 | −0.577160 | ||||||||
\(508\) | −8.96722e8 | −0.303483 | ||||||||
\(509\) | 5.17337e9 | 1.73885 | 0.869423 | − | 0.494068i | \(-0.164491\pi\) | ||||
0.869423 | + | 0.494068i | \(0.164491\pi\) | |||||||
\(510\) | −1.11985e9 | −0.373821 | ||||||||
\(511\) | 2.96894e8 | 0.0984300 | ||||||||
\(512\) | 9.88137e8 | 0.325366 | ||||||||
\(513\) | −1.08148e9 | −0.353676 | ||||||||
\(514\) | −2.04533e9 | −0.664345 | ||||||||
\(515\) | −2.17122e9 | −0.700453 | ||||||||
\(516\) | 1.27192e8 | 0.0407555 | ||||||||
\(517\) | −2.48754e7 | −0.00791686 | ||||||||
\(518\) | −1.65303e9 | −0.522547 | ||||||||
\(519\) | 1.06058e9 | 0.333010 | ||||||||
\(520\) | −6.88331e7 | −0.0214677 | ||||||||
\(521\) | −5.01575e9 | −1.55383 | −0.776916 | − | 0.629604i | \(-0.783217\pi\) | ||||
−0.776916 | + | 0.629604i | \(0.783217\pi\) | |||||||
\(522\) | −4.11657e8 | −0.126674 | ||||||||
\(523\) | 3.72739e9 | 1.13933 | 0.569664 | − | 0.821878i | \(-0.307073\pi\) | ||||
0.569664 | + | 0.821878i | \(0.307073\pi\) | |||||||
\(524\) | −4.62089e8 | −0.140303 | ||||||||
\(525\) | −8.73220e8 | −0.263370 | ||||||||
\(526\) | 9.89832e8 | 0.296559 | ||||||||
\(527\) | 1.02057e9 | 0.303743 | ||||||||
\(528\) | 9.93273e8 | 0.293663 | ||||||||
\(529\) | −1.29868e8 | −0.0381422 | ||||||||
\(530\) | −3.33316e9 | −0.972501 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 7.38769e8 | 0.212725 | ||||||||
\(533\) | 8.24977e6 | 0.00235992 | ||||||||
\(534\) | −3.24569e9 | −0.922386 | ||||||||
\(535\) | 2.00825e9 | 0.566995 | ||||||||
\(536\) | 3.93544e8 | 0.110387 | ||||||||
\(537\) | −1.32090e9 | −0.368095 | ||||||||
\(538\) | 5.72864e9 | 1.58604 | ||||||||
\(539\) | 1.27532e9 | 0.350798 | ||||||||
\(540\) | −2.85436e8 | −0.0780066 | ||||||||
\(541\) | −7.61357e8 | −0.206727 | −0.103364 | − | 0.994644i | \(-0.532961\pi\) | ||||
−0.103364 | + | 0.994644i | \(0.532961\pi\) | |||||||
\(542\) | 4.34449e9 | 1.17204 | ||||||||
\(543\) | −2.42426e9 | −0.649799 | ||||||||
\(544\) | −8.06622e8 | −0.214820 | ||||||||
\(545\) | −4.48676e9 | −1.18726 | ||||||||
\(546\) | 1.86868e7 | 0.00491315 | ||||||||
\(547\) | −1.94954e9 | −0.509304 | −0.254652 | − | 0.967033i | \(-0.581961\pi\) | ||||
−0.254652 | + | 0.967033i | \(0.581961\pi\) | |||||||
\(548\) | 1.15055e8 | 0.0298657 | ||||||||
\(549\) | −9.05664e8 | −0.233595 | ||||||||
\(550\) | 2.05888e9 | 0.527670 | ||||||||
\(551\) | −2.42434e9 | −0.617395 | ||||||||
\(552\) | −1.82347e9 | −0.461436 | ||||||||
\(553\) | −6.78452e8 | −0.170601 | ||||||||
\(554\) | 4.22811e9 | 1.05648 | ||||||||
\(555\) | 3.76130e9 | 0.933927 | ||||||||
\(556\) | 4.98602e8 | 0.123025 | ||||||||
\(557\) | −4.11925e9 | −1.01001 | −0.505004 | − | 0.863117i | \(-0.668509\pi\) | ||||
−0.505004 | + | 0.863117i | \(0.668509\pi\) | |||||||
\(558\) | 1.19055e9 | 0.290087 | ||||||||
\(559\) | 1.89471e7 | 0.00458777 | ||||||||
\(560\) | −2.99685e9 | −0.721119 | ||||||||
\(561\) | 4.03568e8 | 0.0965044 | ||||||||
\(562\) | 7.16319e8 | 0.170227 | ||||||||
\(563\) | −1.25233e9 | −0.295760 | −0.147880 | − | 0.989005i | \(-0.547245\pi\) | ||||
−0.147880 | + | 0.989005i | \(0.547245\pi\) | |||||||
\(564\) | 1.28608e7 | 0.00301850 | ||||||||
\(565\) | −4.07256e9 | −0.949943 | ||||||||
\(566\) | 4.38762e9 | 1.01712 | ||||||||
\(567\) | −1.99670e8 | −0.0460016 | ||||||||
\(568\) | 5.20286e9 | 1.19130 | ||||||||
\(569\) | −1.82236e9 | −0.414708 | −0.207354 | − | 0.978266i | \(-0.566485\pi\) | ||||
−0.207354 | + | 0.978266i | \(0.566485\pi\) | |||||||
\(570\) | −7.69346e9 | −1.74004 | ||||||||
\(571\) | −2.71123e9 | −0.609453 | −0.304727 | − | 0.952440i | \(-0.598565\pi\) | ||||
−0.304727 | + | 0.952440i | \(0.598565\pi\) | |||||||
\(572\) | −9.62694e6 | −0.00215081 | ||||||||
\(573\) | 3.17450e9 | 0.704910 | ||||||||
\(574\) | 2.75593e8 | 0.0608242 | ||||||||
\(575\) | −4.92611e9 | −1.08060 | ||||||||
\(576\) | 8.95787e8 | 0.195311 | ||||||||
\(577\) | −6.72315e8 | −0.145699 | −0.0728496 | − | 0.997343i | \(-0.523209\pi\) | ||||
−0.0728496 | + | 0.997343i | \(0.523209\pi\) | |||||||
\(578\) | 4.43290e9 | 0.954862 | ||||||||
\(579\) | −5.11862e9 | −1.09592 | ||||||||
\(580\) | −6.39862e8 | −0.136172 | ||||||||
\(581\) | −1.27493e9 | −0.269693 | ||||||||
\(582\) | −2.67268e8 | −0.0561974 | ||||||||
\(583\) | 1.20120e9 | 0.251058 | ||||||||
\(584\) | −9.32555e8 | −0.193744 | ||||||||
\(585\) | −4.25199e7 | −0.00878106 | ||||||||
\(586\) | −7.44603e9 | −1.52856 | ||||||||
\(587\) | −2.63538e9 | −0.537786 | −0.268893 | − | 0.963170i | \(-0.586658\pi\) | ||||
−0.268893 | + | 0.963170i | \(0.586658\pi\) | |||||||
\(588\) | −6.59350e8 | −0.133750 | ||||||||
\(589\) | 7.01142e9 | 1.41385 | ||||||||
\(590\) | 1.06510e9 | 0.213504 | ||||||||
\(591\) | 1.67202e9 | 0.333185 | ||||||||
\(592\) | 6.76699e9 | 1.34051 | ||||||||
\(593\) | 1.67193e9 | 0.329251 | 0.164625 | − | 0.986356i | \(-0.447359\pi\) | ||||
0.164625 | + | 0.986356i | \(0.447359\pi\) | |||||||
\(594\) | 4.70784e8 | 0.0921657 | ||||||||
\(595\) | −1.21763e9 | −0.236976 | ||||||||
\(596\) | 1.59591e9 | 0.308778 | ||||||||
\(597\) | 4.54883e9 | 0.874963 | ||||||||
\(598\) | 1.05418e8 | 0.0201586 | ||||||||
\(599\) | 1.58648e9 | 0.301607 | 0.150803 | − | 0.988564i | \(-0.451814\pi\) | ||||
0.150803 | + | 0.988564i | \(0.451814\pi\) | |||||||
\(600\) | 2.74282e9 | 0.518403 | ||||||||
\(601\) | 1.06586e9 | 0.200280 | 0.100140 | − | 0.994973i | \(-0.468071\pi\) | ||||
0.100140 | + | 0.994973i | \(0.468071\pi\) | |||||||
\(602\) | 6.32950e8 | 0.118245 | ||||||||
\(603\) | 2.43102e8 | 0.0451521 | ||||||||
\(604\) | 1.38173e9 | 0.255149 | ||||||||
\(605\) | 6.48124e9 | 1.18991 | ||||||||
\(606\) | 2.26092e8 | 0.0412697 | ||||||||
\(607\) | 9.08916e9 | 1.64954 | 0.824771 | − | 0.565467i | \(-0.191304\pi\) | ||||
0.824771 | + | 0.565467i | \(0.191304\pi\) | |||||||
\(608\) | −5.54157e9 | −0.999932 | ||||||||
\(609\) | −4.47600e8 | −0.0803027 | ||||||||
\(610\) | −6.44276e9 | −1.14926 | ||||||||
\(611\) | 1.91580e6 | 0.000339787 0 | ||||||||
\(612\) | −2.08648e8 | −0.0367947 | ||||||||
\(613\) | −3.73946e9 | −0.655688 | −0.327844 | − | 0.944732i | \(-0.606322\pi\) | ||||
−0.327844 | + | 0.944732i | \(0.606322\pi\) | |||||||
\(614\) | 7.95797e9 | 1.38744 | ||||||||
\(615\) | −6.27085e8 | −0.108709 | ||||||||
\(616\) | 8.28669e8 | 0.142840 | ||||||||
\(617\) | 5.49157e9 | 0.941236 | 0.470618 | − | 0.882337i | \(-0.344031\pi\) | ||||
0.470618 | + | 0.882337i | \(0.344031\pi\) | |||||||
\(618\) | −1.85146e9 | −0.315540 | ||||||||
\(619\) | 6.71900e9 | 1.13864 | 0.569321 | − | 0.822115i | \(-0.307206\pi\) | ||||
0.569321 | + | 0.822115i | \(0.307206\pi\) | |||||||
\(620\) | 1.85054e9 | 0.311837 | ||||||||
\(621\) | −1.12640e9 | −0.188744 | ||||||||
\(622\) | 1.00593e10 | 1.67610 | ||||||||
\(623\) | −3.52908e9 | −0.584728 | ||||||||
\(624\) | −7.64980e7 | −0.0126039 | ||||||||
\(625\) | −5.41876e9 | −0.887810 | ||||||||
\(626\) | 4.76915e9 | 0.777018 | ||||||||
\(627\) | 2.77255e9 | 0.449204 | ||||||||
\(628\) | 2.41659e9 | 0.389354 | ||||||||
\(629\) | 2.74944e9 | 0.440521 | ||||||||
\(630\) | −1.42043e9 | −0.226322 | ||||||||
\(631\) | 3.57282e9 | 0.566119 | 0.283060 | − | 0.959102i | \(-0.408651\pi\) | ||||
0.283060 | + | 0.959102i | \(0.408651\pi\) | |||||||
\(632\) | 2.13104e9 | 0.335801 | ||||||||
\(633\) | 5.13155e8 | 0.0804148 | ||||||||
\(634\) | −3.04765e9 | −0.474955 | ||||||||
\(635\) | 1.01537e10 | 1.57368 | ||||||||
\(636\) | −6.21029e8 | −0.0957221 | ||||||||
\(637\) | −9.82199e7 | −0.0150561 | ||||||||
\(638\) | 1.05536e9 | 0.160889 | ||||||||
\(639\) | 3.21394e9 | 0.487287 | ||||||||
\(640\) | 1.16038e10 | 1.74973 | ||||||||
\(641\) | −9.37478e8 | −0.140591 | −0.0702956 | − | 0.997526i | \(-0.522394\pi\) | ||||
−0.0702956 | + | 0.997526i | \(0.522394\pi\) | |||||||
\(642\) | 1.71249e9 | 0.255420 | ||||||||
\(643\) | 8.40132e9 | 1.24626 | 0.623131 | − | 0.782118i | \(-0.285860\pi\) | ||||
0.623131 | + | 0.782118i | \(0.285860\pi\) | |||||||
\(644\) | 7.69461e8 | 0.113524 | ||||||||
\(645\) | −1.44022e9 | −0.211334 | ||||||||
\(646\) | −5.62377e9 | −0.820755 | ||||||||
\(647\) | 1.33915e10 | 1.94386 | 0.971931 | − | 0.235264i | \(-0.0755956\pi\) | ||||
0.971931 | + | 0.235264i | \(0.0755956\pi\) | |||||||
\(648\) | 6.27172e8 | 0.0905471 | ||||||||
\(649\) | −3.83837e8 | −0.0551176 | ||||||||
\(650\) | −1.58567e8 | −0.0226473 | ||||||||
\(651\) | 1.29450e9 | 0.183895 | ||||||||
\(652\) | −1.33629e9 | −0.188814 | ||||||||
\(653\) | −7.85725e9 | −1.10427 | −0.552134 | − | 0.833756i | \(-0.686186\pi\) | ||||
−0.552134 | + | 0.833756i | \(0.686186\pi\) | |||||||
\(654\) | −3.82599e9 | −0.534837 | ||||||||
\(655\) | 5.23231e9 | 0.727526 | ||||||||
\(656\) | −1.12819e9 | −0.156034 | ||||||||
\(657\) | −5.76063e8 | −0.0792485 | ||||||||
\(658\) | 6.39995e7 | 0.00875762 | ||||||||
\(659\) | 3.05094e9 | 0.415273 | 0.207637 | − | 0.978206i | \(-0.433423\pi\) | ||||
0.207637 | + | 0.978206i | \(0.433423\pi\) | |||||||
\(660\) | 7.31767e8 | 0.0990761 | ||||||||
\(661\) | 1.41136e10 | 1.90079 | 0.950395 | − | 0.311045i | \(-0.100679\pi\) | ||||
0.950395 | + | 0.311045i | \(0.100679\pi\) | |||||||
\(662\) | −8.31838e9 | −1.11439 | ||||||||
\(663\) | −3.10812e7 | −0.00414191 | ||||||||
\(664\) | 4.00461e9 | 0.530850 | ||||||||
\(665\) | −8.36521e9 | −1.10306 | ||||||||
\(666\) | 3.20737e9 | 0.420716 | ||||||||
\(667\) | −2.52506e9 | −0.329481 | ||||||||
\(668\) | 1.46270e9 | 0.189862 | ||||||||
\(669\) | −2.57633e9 | −0.332667 | ||||||||
\(670\) | 1.72939e9 | 0.222143 | ||||||||
\(671\) | 2.32183e9 | 0.296689 | ||||||||
\(672\) | −1.02313e9 | −0.130058 | ||||||||
\(673\) | 1.56465e10 | 1.97863 | 0.989313 | − | 0.145809i | \(-0.0465786\pi\) | ||||
0.989313 | + | 0.145809i | \(0.0465786\pi\) | |||||||
\(674\) | −8.51144e9 | −1.07076 | ||||||||
\(675\) | 1.69431e9 | 0.212046 | ||||||||
\(676\) | −2.24484e9 | −0.279494 | ||||||||
\(677\) | 5.00729e9 | 0.620215 | 0.310107 | − | 0.950702i | \(-0.399635\pi\) | ||||
0.310107 | + | 0.950702i | \(0.399635\pi\) | |||||||
\(678\) | −3.47278e9 | −0.427931 | ||||||||
\(679\) | −2.90604e8 | −0.0356252 | ||||||||
\(680\) | 3.82461e9 | 0.466451 | ||||||||
\(681\) | 3.36420e8 | 0.0408194 | ||||||||
\(682\) | −3.05219e9 | −0.368439 | ||||||||
\(683\) | −1.48727e10 | −1.78615 | −0.893073 | − | 0.449911i | \(-0.851456\pi\) | ||||
−0.893073 | + | 0.449911i | \(0.851456\pi\) | |||||||
\(684\) | −1.43343e9 | −0.171270 | ||||||||
\(685\) | −1.30278e9 | −0.154866 | ||||||||
\(686\) | −7.24105e9 | −0.856381 | ||||||||
\(687\) | −4.20070e9 | −0.494280 | ||||||||
\(688\) | −2.59110e9 | −0.303337 | ||||||||
\(689\) | −9.25114e7 | −0.0107753 | ||||||||
\(690\) | −8.01308e9 | −0.928597 | ||||||||
\(691\) | −1.34895e8 | −0.0155532 | −0.00777662 | − | 0.999970i | \(-0.502475\pi\) | ||||
−0.00777662 | + | 0.999970i | \(0.502475\pi\) | |||||||
\(692\) | 1.40574e9 | 0.161263 | ||||||||
\(693\) | 5.11890e8 | 0.0584266 | ||||||||
\(694\) | −3.40507e9 | −0.386695 | ||||||||
\(695\) | −5.64576e9 | −0.637933 | ||||||||
\(696\) | 1.40593e9 | 0.158064 | ||||||||
\(697\) | −4.58387e8 | −0.0512764 | ||||||||
\(698\) | −1.54593e10 | −1.72066 | ||||||||
\(699\) | −4.30146e9 | −0.476372 | ||||||||
\(700\) | −1.15740e9 | −0.127539 | ||||||||
\(701\) | −8.34830e9 | −0.915345 | −0.457672 | − | 0.889121i | \(-0.651317\pi\) | ||||
−0.457672 | + | 0.889121i | \(0.651317\pi\) | |||||||
\(702\) | −3.62579e7 | −0.00395570 | ||||||||
\(703\) | 1.88889e10 | 2.05052 | ||||||||
\(704\) | −2.29651e9 | −0.248064 | ||||||||
\(705\) | −1.45625e8 | −0.0156521 | ||||||||
\(706\) | −3.04982e9 | −0.326180 | ||||||||
\(707\) | 2.45833e8 | 0.0261621 | ||||||||
\(708\) | 1.98447e8 | 0.0210150 | ||||||||
\(709\) | −1.42535e9 | −0.150197 | −0.0750983 | − | 0.997176i | \(-0.523927\pi\) | ||||
−0.0750983 | + | 0.997176i | \(0.523927\pi\) | |||||||
\(710\) | 2.28635e10 | 2.39739 | ||||||||
\(711\) | 1.31640e9 | 0.137355 | ||||||||
\(712\) | 1.10850e10 | 1.15095 | ||||||||
\(713\) | 7.30270e9 | 0.754519 | ||||||||
\(714\) | −1.03830e9 | −0.106753 | ||||||||
\(715\) | 1.09007e8 | 0.0111528 | ||||||||
\(716\) | −1.75078e9 | −0.178253 | ||||||||
\(717\) | 7.70788e9 | 0.780940 | ||||||||
\(718\) | 1.31848e10 | 1.32935 | ||||||||
\(719\) | −5.22232e9 | −0.523978 | −0.261989 | − | 0.965071i | \(-0.584378\pi\) | ||||
−0.261989 | + | 0.965071i | \(0.584378\pi\) | |||||||
\(720\) | 5.81480e9 | 0.580592 | ||||||||
\(721\) | −2.01312e9 | −0.200031 | ||||||||
\(722\) | −2.71961e10 | −2.68922 | ||||||||
\(723\) | 5.62172e9 | 0.553204 | ||||||||
\(724\) | −3.21322e9 | −0.314670 | ||||||||
\(725\) | 3.79813e9 | 0.370158 | ||||||||
\(726\) | 5.52674e9 | 0.536032 | ||||||||
\(727\) | 1.04981e10 | 1.01330 | 0.506652 | − | 0.862150i | \(-0.330883\pi\) | ||||
0.506652 | + | 0.862150i | \(0.330883\pi\) | |||||||
\(728\) | −6.38208e7 | −0.00613060 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −4.09803e9 | −0.389893 | ||||||||
\(731\) | −1.05277e9 | −0.0996833 | ||||||||
\(732\) | −1.20041e9 | −0.113120 | ||||||||
\(733\) | −1.91930e10 | −1.80003 | −0.900014 | − | 0.435862i | \(-0.856444\pi\) | ||||
−0.900014 | + | 0.435862i | \(0.856444\pi\) | |||||||
\(734\) | −1.92426e10 | −1.79608 | ||||||||
\(735\) | 7.46593e9 | 0.693551 | ||||||||
\(736\) | −5.77179e9 | −0.533628 | ||||||||
\(737\) | −6.23235e8 | −0.0573477 | ||||||||
\(738\) | −5.34733e8 | −0.0489711 | ||||||||
\(739\) | −1.50672e10 | −1.37334 | −0.686669 | − | 0.726970i | \(-0.740928\pi\) | ||||
−0.686669 | + | 0.726970i | \(0.740928\pi\) | |||||||
\(740\) | 4.98539e9 | 0.452260 | ||||||||
\(741\) | −2.13531e8 | −0.0192796 | ||||||||
\(742\) | −3.09045e9 | −0.277720 | ||||||||
\(743\) | −1.35355e10 | −1.21064 | −0.605318 | − | 0.795984i | \(-0.706954\pi\) | ||||
−0.605318 | + | 0.795984i | \(0.706954\pi\) | |||||||
\(744\) | −4.06608e9 | −0.361969 | ||||||||
\(745\) | −1.80707e10 | −1.60114 | ||||||||
\(746\) | 7.07975e9 | 0.624355 | ||||||||
\(747\) | 2.47375e9 | 0.217137 | ||||||||
\(748\) | 5.34907e8 | 0.0467329 | ||||||||
\(749\) | 1.86201e9 | 0.161918 | ||||||||
\(750\) | 1.11385e9 | 0.0964082 | ||||||||
\(751\) | −4.44209e9 | −0.382690 | −0.191345 | − | 0.981523i | \(-0.561285\pi\) | ||||
−0.191345 | + | 0.981523i | \(0.561285\pi\) | |||||||
\(752\) | −2.61995e8 | −0.0224662 | ||||||||
\(753\) | −9.19061e9 | −0.784444 | ||||||||
\(754\) | −8.12793e7 | −0.00690527 | ||||||||
\(755\) | −1.56455e10 | −1.32305 | ||||||||
\(756\) | −2.64652e8 | −0.0222766 | ||||||||
\(757\) | −1.96167e10 | −1.64358 | −0.821789 | − | 0.569792i | \(-0.807024\pi\) | ||||
−0.821789 | + | 0.569792i | \(0.807024\pi\) | |||||||
\(758\) | −1.35186e10 | −1.12743 | ||||||||
\(759\) | 2.88774e9 | 0.239724 | ||||||||
\(760\) | 2.62755e10 | 2.17121 | ||||||||
\(761\) | −8.13676e9 | −0.669276 | −0.334638 | − | 0.942347i | \(-0.608614\pi\) | ||||
−0.334638 | + | 0.942347i | \(0.608614\pi\) | |||||||
\(762\) | 8.65837e9 | 0.708914 | ||||||||
\(763\) | −4.16005e9 | −0.339049 | ||||||||
\(764\) | 4.20762e9 | 0.341357 | ||||||||
\(765\) | 2.36256e9 | 0.190795 | ||||||||
\(766\) | 1.33506e9 | 0.107325 | ||||||||
\(767\) | 2.95616e7 | 0.00236562 | ||||||||
\(768\) | 5.64820e9 | 0.449931 | ||||||||
\(769\) | −1.79213e10 | −1.42111 | −0.710554 | − | 0.703642i | \(-0.751556\pi\) | ||||
−0.710554 | + | 0.703642i | \(0.751556\pi\) | |||||||
\(770\) | 3.64151e9 | 0.287451 | ||||||||
\(771\) | 4.31508e9 | 0.339077 | ||||||||
\(772\) | −6.78444e9 | −0.530705 | ||||||||
\(773\) | 1.39926e10 | 1.08961 | 0.544804 | − | 0.838563i | \(-0.316604\pi\) | ||||
0.544804 | + | 0.838563i | \(0.316604\pi\) | |||||||
\(774\) | −1.22811e9 | −0.0952017 | ||||||||
\(775\) | −1.09845e10 | −0.847669 | ||||||||
\(776\) | 9.12799e8 | 0.0701228 | ||||||||
\(777\) | 3.48741e9 | 0.266704 | ||||||||
\(778\) | 1.95023e10 | 1.48476 | ||||||||
\(779\) | −3.14916e9 | −0.238679 | ||||||||
\(780\) | −5.63578e7 | −0.00425229 | ||||||||
\(781\) | −8.23950e9 | −0.618903 | ||||||||
\(782\) | −5.85740e9 | −0.438007 | ||||||||
\(783\) | 8.68480e8 | 0.0646537 | ||||||||
\(784\) | 1.34320e10 | 0.995485 | ||||||||
\(785\) | −2.73635e10 | −2.01896 | ||||||||
\(786\) | 4.46174e9 | 0.327737 | ||||||||
\(787\) | 7.87847e9 | 0.576143 | 0.288071 | − | 0.957609i | \(-0.406986\pi\) | ||||
0.288071 | + | 0.957609i | \(0.406986\pi\) | |||||||
\(788\) | 2.21617e9 | 0.161347 | ||||||||
\(789\) | −2.08827e9 | −0.151362 | ||||||||
\(790\) | 9.36468e9 | 0.675769 | ||||||||
\(791\) | −3.77601e9 | −0.271278 | ||||||||
\(792\) | −1.60787e9 | −0.115004 | ||||||||
\(793\) | −1.78818e8 | −0.0127337 | ||||||||
\(794\) | 3.55298e9 | 0.251896 | ||||||||
\(795\) | 7.03202e9 | 0.496358 | ||||||||
\(796\) | 6.02922e9 | 0.423707 | ||||||||
\(797\) | −7.12267e9 | −0.498355 | −0.249178 | − | 0.968458i | \(-0.580160\pi\) | ||||
−0.249178 | + | 0.968458i | \(0.580160\pi\) | |||||||
\(798\) | −7.13325e9 | −0.496909 | ||||||||
\(799\) | −1.06449e8 | −0.00738291 | ||||||||
\(800\) | 8.68179e9 | 0.599507 | ||||||||
\(801\) | 6.84749e9 | 0.470779 | ||||||||
\(802\) | −4.34517e9 | −0.297438 | ||||||||
\(803\) | 1.47684e9 | 0.100653 | ||||||||
\(804\) | 3.22218e8 | 0.0218652 | ||||||||
\(805\) | −8.71273e9 | −0.588666 | ||||||||
\(806\) | 2.35067e8 | 0.0158132 | ||||||||
\(807\) | −1.20858e10 | −0.809503 | ||||||||
\(808\) | −7.72171e8 | −0.0514960 | ||||||||
\(809\) | −1.13613e10 | −0.754412 | −0.377206 | − | 0.926129i | \(-0.623115\pi\) | ||||
−0.377206 | + | 0.926129i | \(0.623115\pi\) | |||||||
\(810\) | 2.75605e9 | 0.182218 | ||||||||
\(811\) | −1.58411e10 | −1.04283 | −0.521413 | − | 0.853304i | \(-0.674595\pi\) | ||||
−0.521413 | + | 0.853304i | \(0.674595\pi\) | |||||||
\(812\) | −5.93269e8 | −0.0388871 | ||||||||
\(813\) | −9.16565e9 | −0.598200 | ||||||||
\(814\) | −8.22265e9 | −0.534351 | ||||||||
\(815\) | 1.51311e10 | 0.979079 | ||||||||
\(816\) | 4.25050e9 | 0.273857 | ||||||||
\(817\) | −7.23263e9 | −0.464001 | ||||||||
\(818\) | −2.86332e10 | −1.82908 | ||||||||
\(819\) | −3.94238e7 | −0.00250764 | ||||||||
\(820\) | −8.31166e8 | −0.0526429 | ||||||||
\(821\) | 2.50210e10 | 1.57799 | 0.788993 | − | 0.614402i | \(-0.210603\pi\) | ||||
0.788993 | + | 0.614402i | \(0.210603\pi\) | |||||||
\(822\) | −1.11092e9 | −0.0697640 | ||||||||
\(823\) | 1.51409e10 | 0.946790 | 0.473395 | − | 0.880850i | \(-0.343028\pi\) | ||||
0.473395 | + | 0.880850i | \(0.343028\pi\) | |||||||
\(824\) | 6.32329e9 | 0.393730 | ||||||||
\(825\) | −4.34366e9 | −0.269319 | ||||||||
\(826\) | 9.87539e8 | 0.0609711 | ||||||||
\(827\) | −7.61883e9 | −0.468402 | −0.234201 | − | 0.972188i | \(-0.575247\pi\) | ||||
−0.234201 | + | 0.972188i | \(0.575247\pi\) | |||||||
\(828\) | −1.49299e9 | −0.0914007 | ||||||||
\(829\) | −1.04307e10 | −0.635879 | −0.317940 | − | 0.948111i | \(-0.602991\pi\) | ||||
−0.317940 | + | 0.948111i | \(0.602991\pi\) | |||||||
\(830\) | 1.75979e10 | 1.06829 | ||||||||
\(831\) | −8.92011e9 | −0.539221 | ||||||||
\(832\) | 1.76868e8 | 0.0106468 | ||||||||
\(833\) | 5.45745e9 | 0.327139 | ||||||||
\(834\) | −4.81429e9 | −0.287377 | ||||||||
\(835\) | −1.65624e10 | −0.984514 | ||||||||
\(836\) | 3.67486e9 | 0.217530 | ||||||||
\(837\) | −2.51172e9 | −0.148058 | ||||||||
\(838\) | −2.20617e10 | −1.29505 | ||||||||
\(839\) | −8.81723e9 | −0.515425 | −0.257712 | − | 0.966222i | \(-0.582969\pi\) | ||||
−0.257712 | + | 0.966222i | \(0.582969\pi\) | |||||||
\(840\) | 4.85118e9 | 0.282403 | ||||||||
\(841\) | −1.53030e10 | −0.887137 | ||||||||
\(842\) | −3.03804e10 | −1.75388 | ||||||||
\(843\) | −1.51123e9 | −0.0868829 | ||||||||
\(844\) | 6.80159e8 | 0.0389414 | ||||||||
\(845\) | 2.54187e10 | 1.44929 | ||||||||
\(846\) | −1.24178e8 | −0.00705098 | ||||||||
\(847\) | 6.00930e9 | 0.339807 | ||||||||
\(848\) | 1.26514e10 | 0.712445 | ||||||||
\(849\) | −9.25664e9 | −0.519130 | ||||||||
\(850\) | 8.81056e9 | 0.492082 | ||||||||
\(851\) | 1.96736e10 | 1.09429 | ||||||||
\(852\) | 4.25990e9 | 0.235972 | ||||||||
\(853\) | 6.88811e9 | 0.379995 | 0.189998 | − | 0.981785i | \(-0.439152\pi\) | ||||
0.189998 | + | 0.981785i | \(0.439152\pi\) | |||||||
\(854\) | −5.97362e9 | −0.328197 | ||||||||
\(855\) | 1.62310e10 | 0.888105 | ||||||||
\(856\) | −5.84866e9 | −0.318712 | ||||||||
\(857\) | 7.74166e9 | 0.420147 | 0.210074 | − | 0.977686i | \(-0.432630\pi\) | ||||
0.210074 | + | 0.977686i | \(0.432630\pi\) | |||||||
\(858\) | 9.29537e7 | 0.00502413 | ||||||||
\(859\) | −7.99776e9 | −0.430519 | −0.215259 | − | 0.976557i | \(-0.569060\pi\) | ||||
−0.215259 | + | 0.976557i | \(0.569060\pi\) | |||||||
\(860\) | −1.90893e9 | −0.102340 | ||||||||
\(861\) | −5.81423e8 | −0.0310442 | ||||||||
\(862\) | 3.74514e10 | 1.99156 | ||||||||
\(863\) | −2.16260e10 | −1.14535 | −0.572675 | − | 0.819782i | \(-0.694094\pi\) | ||||
−0.572675 | + | 0.819782i | \(0.694094\pi\) | |||||||
\(864\) | 1.98518e9 | 0.104713 | ||||||||
\(865\) | −1.59174e10 | −0.836212 | ||||||||
\(866\) | 8.74875e9 | 0.457755 | ||||||||
\(867\) | −9.35216e9 | −0.487355 | ||||||||
\(868\) | 1.71579e9 | 0.0890523 | ||||||||
\(869\) | −3.37483e9 | −0.174454 | ||||||||
\(870\) | 6.17824e9 | 0.318088 | ||||||||
\(871\) | 4.79991e7 | 0.00246133 | ||||||||
\(872\) | 1.30669e10 | 0.667366 | ||||||||
\(873\) | 5.63859e8 | 0.0286828 | ||||||||
\(874\) | −4.02409e10 | −2.03882 | ||||||||
\(875\) | 1.21111e9 | 0.0611160 | ||||||||
\(876\) | −7.63539e8 | −0.0383766 | ||||||||
\(877\) | −2.67027e10 | −1.33677 | −0.668385 | − | 0.743816i | \(-0.733014\pi\) | ||||
−0.668385 | + | 0.743816i | \(0.733014\pi\) | |||||||
\(878\) | 1.23333e10 | 0.614961 | ||||||||
\(879\) | 1.57090e10 | 0.780167 | ||||||||
\(880\) | −1.49073e10 | −0.737409 | ||||||||
\(881\) | −1.15396e10 | −0.568559 | −0.284279 | − | 0.958741i | \(-0.591754\pi\) | ||||
−0.284279 | + | 0.958741i | \(0.591754\pi\) | |||||||
\(882\) | 6.36641e9 | 0.312431 | ||||||||
\(883\) | −3.23054e10 | −1.57911 | −0.789555 | − | 0.613679i | \(-0.789689\pi\) | ||||
−0.789555 | + | 0.613679i | \(0.789689\pi\) | |||||||
\(884\) | −4.11964e7 | −0.00200575 | ||||||||
\(885\) | −2.24705e9 | −0.108971 | ||||||||
\(886\) | 1.57280e10 | 0.759724 | ||||||||
\(887\) | 1.57129e10 | 0.756005 | 0.378002 | − | 0.925805i | \(-0.376611\pi\) | ||||
0.378002 | + | 0.925805i | \(0.376611\pi\) | |||||||
\(888\) | −1.09541e10 | −0.524967 | ||||||||
\(889\) | 9.41436e9 | 0.449402 | ||||||||
\(890\) | 4.87120e10 | 2.31617 | ||||||||
\(891\) | −9.93221e8 | −0.0470407 | ||||||||
\(892\) | −3.41478e9 | −0.161096 | ||||||||
\(893\) | −7.31314e8 | −0.0343656 | ||||||||
\(894\) | −1.54094e10 | −0.721282 | ||||||||
\(895\) | 1.98244e10 | 0.924312 | ||||||||
\(896\) | 1.07589e10 | 0.499676 | ||||||||
\(897\) | −2.22402e8 | −0.0102888 | ||||||||
\(898\) | −3.67670e10 | −1.69430 | ||||||||
\(899\) | −5.63053e9 | −0.258458 | ||||||||
\(900\) | 2.24571e9 | 0.102685 | ||||||||
\(901\) | 5.14026e9 | 0.234125 | ||||||||
\(902\) | 1.37088e9 | 0.0621982 | ||||||||
\(903\) | −1.33534e9 | −0.0603512 | ||||||||
\(904\) | 1.18606e10 | 0.533970 | ||||||||
\(905\) | 3.63838e10 | 1.63169 | ||||||||
\(906\) | −1.33414e10 | −0.596008 | ||||||||
\(907\) | −6.98597e9 | −0.310886 | −0.155443 | − | 0.987845i | \(-0.549681\pi\) | ||||
−0.155443 | + | 0.987845i | \(0.549681\pi\) | |||||||
\(908\) | 4.45905e8 | 0.0197671 | ||||||||
\(909\) | −4.76990e8 | −0.0210637 | ||||||||
\(910\) | −2.80455e8 | −0.0123372 | ||||||||
\(911\) | −4.32364e9 | −0.189468 | −0.0947339 | − | 0.995503i | \(-0.530200\pi\) | ||||
−0.0947339 | + | 0.995503i | \(0.530200\pi\) | |||||||
\(912\) | 2.92014e10 | 1.27474 | ||||||||
\(913\) | −6.34189e9 | −0.275785 | ||||||||
\(914\) | −6.83958e9 | −0.296290 | ||||||||
\(915\) | 1.35924e10 | 0.586573 | ||||||||
\(916\) | −5.56779e9 | −0.239358 | ||||||||
\(917\) | 4.85131e9 | 0.207762 | ||||||||
\(918\) | 2.01462e9 | 0.0859496 | ||||||||
\(919\) | −2.41430e10 | −1.02609 | −0.513046 | − | 0.858361i | \(-0.671483\pi\) | ||||
−0.513046 | + | 0.858361i | \(0.671483\pi\) | |||||||
\(920\) | 2.73670e10 | 1.15870 | ||||||||
\(921\) | −1.67891e10 | −0.708138 | ||||||||
\(922\) | 3.62437e10 | 1.52291 | ||||||||
\(923\) | 6.34574e8 | 0.0265630 | ||||||||
\(924\) | 6.78482e8 | 0.0282935 | ||||||||
\(925\) | −2.95926e10 | −1.22938 | ||||||||
\(926\) | 3.74441e10 | 1.54969 | ||||||||
\(927\) | 3.90606e9 | 0.161050 | ||||||||
\(928\) | 4.45017e9 | 0.182792 | ||||||||
\(929\) | 2.15464e10 | 0.881699 | 0.440850 | − | 0.897581i | \(-0.354677\pi\) | ||||
0.440850 | + | 0.897581i | \(0.354677\pi\) | |||||||
\(930\) | −1.78680e10 | −0.728428 | ||||||||
\(931\) | 3.74932e10 | 1.52275 | ||||||||
\(932\) | −5.70135e9 | −0.230686 | ||||||||
\(933\) | −2.12222e10 | −0.855471 | ||||||||
\(934\) | 1.56738e10 | 0.629449 | ||||||||
\(935\) | −6.05684e9 | −0.242329 | ||||||||
\(936\) | 1.23832e8 | 0.00493590 | ||||||||
\(937\) | 3.83047e10 | 1.52112 | 0.760561 | − | 0.649267i | \(-0.224924\pi\) | ||||
0.760561 | + | 0.649267i | \(0.224924\pi\) | |||||||
\(938\) | 1.60346e9 | 0.0634380 | ||||||||
\(939\) | −1.00616e10 | −0.396584 | ||||||||
\(940\) | −1.93018e8 | −0.00757966 | ||||||||
\(941\) | −2.56605e10 | −1.00392 | −0.501962 | − | 0.864890i | \(-0.667388\pi\) | ||||
−0.501962 | + | 0.864890i | \(0.667388\pi\) | |||||||
\(942\) | −2.33336e10 | −0.909502 | ||||||||
\(943\) | −3.27999e9 | −0.127374 | ||||||||
\(944\) | −4.04269e9 | −0.156411 | ||||||||
\(945\) | 2.99670e9 | 0.115513 | ||||||||
\(946\) | 3.14848e9 | 0.120916 | ||||||||
\(947\) | 4.39924e10 | 1.68326 | 0.841632 | − | 0.540051i | \(-0.181595\pi\) | ||||
0.841632 | + | 0.540051i | \(0.181595\pi\) | |||||||
\(948\) | 1.74481e9 | 0.0665151 | ||||||||
\(949\) | −1.13740e8 | −0.00431999 | ||||||||
\(950\) | 6.05294e10 | 2.29052 | ||||||||
\(951\) | 6.42967e9 | 0.242414 | ||||||||
\(952\) | 3.54611e9 | 0.133206 | ||||||||
\(953\) | −4.24635e8 | −0.0158924 | −0.00794622 | − | 0.999968i | \(-0.502529\pi\) | ||||
−0.00794622 | + | 0.999968i | \(0.502529\pi\) | |||||||
\(954\) | 5.99640e9 | 0.223600 | ||||||||
\(955\) | −4.76435e10 | −1.77008 | ||||||||
\(956\) | 1.02164e10 | 0.378176 | ||||||||
\(957\) | −2.22650e9 | −0.0821166 | ||||||||
\(958\) | 2.20473e10 | 0.810170 | ||||||||
\(959\) | −1.20792e9 | −0.0442255 | ||||||||
\(960\) | −1.34442e10 | −0.490439 | ||||||||
\(961\) | −1.12286e10 | −0.408126 | ||||||||
\(962\) | 6.33276e8 | 0.0229340 | ||||||||
\(963\) | −3.61287e9 | −0.130365 | ||||||||
\(964\) | 7.45127e9 | 0.267893 | ||||||||
\(965\) | 7.68213e10 | 2.75192 | ||||||||
\(966\) | −7.42959e9 | −0.265182 | ||||||||
\(967\) | 4.76260e10 | 1.69376 | 0.846879 | − | 0.531786i | \(-0.178479\pi\) | ||||
0.846879 | + | 0.531786i | \(0.178479\pi\) | |||||||
\(968\) | −1.88755e10 | −0.668857 | ||||||||
\(969\) | 1.18646e10 | 0.418908 | ||||||||
\(970\) | 4.01122e9 | 0.141116 | ||||||||
\(971\) | −1.01771e10 | −0.356744 | −0.178372 | − | 0.983963i | \(-0.557083\pi\) | ||||
−0.178372 | + | 0.983963i | \(0.557083\pi\) | |||||||
\(972\) | 5.13504e8 | 0.0179354 | ||||||||
\(973\) | −5.23465e9 | −0.182177 | ||||||||
\(974\) | −3.05948e10 | −1.06094 | ||||||||
\(975\) | 3.34532e8 | 0.0115590 | ||||||||
\(976\) | 2.44542e10 | 0.841936 | ||||||||
\(977\) | 5.07713e10 | 1.74176 | 0.870878 | − | 0.491499i | \(-0.163551\pi\) | ||||
0.870878 | + | 0.491499i | \(0.163551\pi\) | |||||||
\(978\) | 1.29027e10 | 0.441056 | ||||||||
\(979\) | −1.75547e10 | −0.597937 | ||||||||
\(980\) | 9.89567e9 | 0.335857 | ||||||||
\(981\) | 8.07174e9 | 0.272977 | ||||||||
\(982\) | −6.55867e9 | −0.221017 | ||||||||
\(983\) | 3.69088e10 | 1.23934 | 0.619672 | − | 0.784861i | \(-0.287266\pi\) | ||||
0.619672 | + | 0.784861i | \(0.287266\pi\) | |||||||
\(984\) | 1.82627e9 | 0.0611058 | ||||||||
\(985\) | −2.50941e10 | −0.836651 | ||||||||
\(986\) | 4.51617e9 | 0.150038 | ||||||||
\(987\) | −1.35021e8 | −0.00446983 | ||||||||
\(988\) | −2.83024e8 | −0.00933627 | ||||||||
\(989\) | −7.53310e9 | −0.247621 | ||||||||
\(990\) | −7.06563e9 | −0.231434 | ||||||||
\(991\) | 5.58119e10 | 1.82167 | 0.910833 | − | 0.412774i | \(-0.135440\pi\) | ||||
0.910833 | + | 0.412774i | \(0.135440\pi\) | |||||||
\(992\) | −1.28703e10 | −0.418598 | ||||||||
\(993\) | 1.75494e10 | 0.568775 | ||||||||
\(994\) | 2.11987e10 | 0.684630 | ||||||||
\(995\) | −6.82699e10 | −2.19709 | ||||||||
\(996\) | 3.27882e9 | 0.105150 | ||||||||
\(997\) | −4.81978e9 | −0.154026 | −0.0770130 | − | 0.997030i | \(-0.524538\pi\) | ||||
−0.0770130 | + | 0.997030i | \(0.524538\pi\) | |||||||
\(998\) | −4.63036e10 | −1.47454 | ||||||||
\(999\) | −6.76663e9 | −0.214730 |
(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 | 177.8.a.d.1.5 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.14 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.5 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.14 | 18 | 3.2 | odd | 2 |