Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,43,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 43, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 43);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 43 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(33.5183121516\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 33864221333 x^{10} + \cdots + 25\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{73}\cdot 3^{104}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Root | \(-59345.7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.43.b.b.2.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.13644e6i | − | 1.01874i | −0.860549 | − | 0.509368i | \(-0.829879\pi\) | ||
0.860549 | − | 0.509368i | \(-0.170121\pi\) | |||||||
\(3\) | −3.48827e9 | − | 9.86159e9i | −0.333475 | − | 0.942759i | ||||
\(4\) | −1.66350e11 | −0.0378237 | ||||||||
\(5\) | 7.27116e14i | 1.52487i | 0.647063 | + | 0.762436i | \(0.275997\pi\) | ||||
−0.647063 | + | 0.762436i | \(0.724003\pi\) | |||||||
\(6\) | −2.10687e16 | + | 7.45250e15i | −0.960423 | + | 0.339723i | ||||
\(7\) | −7.17356e17 | −1.28433 | −0.642164 | − | 0.766567i | \(-0.721963\pi\) | ||||
−0.642164 | + | 0.766567i | \(0.721963\pi\) | |||||||
\(8\) | − | 9.04079e18i | − | 0.980204i | ||||||
\(9\) | −8.50829e19 | + | 6.87998e19i | −0.777588 | + | 0.628774i | ||||
\(10\) | 1.55344e21 | 1.55344 | ||||||||
\(11\) | 5.19263e21i | 0.701683i | 0.936435 | + | 0.350842i | \(0.114104\pi\) | ||||
−0.936435 | + | 0.350842i | \(0.885896\pi\) | |||||||
\(12\) | 5.80275e20 | + | 1.64048e21i | 0.0126133 | + | 0.0356586i | ||||
\(13\) | 2.30240e23 | 0.931900 | 0.465950 | − | 0.884811i | \(-0.345713\pi\) | ||||
0.465950 | + | 0.884811i | \(0.345713\pi\) | |||||||
\(14\) | 1.53259e24i | 1.30839i | ||||||||
\(15\) | 7.17052e24 | − | 2.53638e24i | 1.43759 | − | 0.508507i | ||||
\(16\) | −2.00468e25 | −1.03639 | ||||||||
\(17\) | − | 3.57260e25i | − | 0.517080i | −0.966001 | − | 0.258540i | \(-0.916759\pi\) | ||
0.966001 | − | 0.258540i | \(-0.0832413\pi\) | |||||||
\(18\) | 1.46987e26 | + | 1.81775e26i | 0.640555 | + | 0.792158i | ||||
\(19\) | 1.20200e27 | 1.68298 | 0.841491 | − | 0.540272i | \(-0.181679\pi\) | ||||
0.841491 | + | 0.540272i | \(0.181679\pi\) | |||||||
\(20\) | − | 1.20956e26i | − | 0.0576764i | ||||||
\(21\) | 2.50233e27 | + | 7.07428e27i | 0.428292 | + | 1.21081i | ||||
\(22\) | 1.10938e28 | 0.714830 | ||||||||
\(23\) | − | 4.53948e28i | − | 1.15006i | −0.818132 | − | 0.575031i | \(-0.804990\pi\) | ||
0.818132 | − | 0.575031i | \(-0.195010\pi\) | |||||||
\(24\) | −8.91565e28 | + | 3.15367e28i | −0.924096 | + | 0.326874i | ||||
\(25\) | −3.01324e29 | −1.32524 | ||||||||
\(26\) | − | 4.91894e29i | − | 0.949361i | ||||||
\(27\) | 9.75267e29 | + | 5.99061e29i | 0.852088 | + | 0.523398i | ||||
\(28\) | 1.19333e29 | 0.0485781 | ||||||||
\(29\) | 3.09807e30i | 0.603577i | 0.953375 | + | 0.301789i | \(0.0975837\pi\) | ||||
−0.953375 | + | 0.301789i | \(0.902416\pi\) | |||||||
\(30\) | −5.41883e30 | − | 1.53194e31i | −0.518035 | − | 1.46452i | ||||
\(31\) | 2.88102e31 | 1.38341 | 0.691705 | − | 0.722180i | \(-0.256860\pi\) | ||||
0.691705 | + | 0.722180i | \(0.256860\pi\) | |||||||
\(32\) | 3.06700e30i | 0.0756074i | ||||||||
\(33\) | 5.12076e31 | − | 1.81133e31i | 0.661518 | − | 0.233994i | ||||
\(34\) | −7.63267e31 | −0.526768 | ||||||||
\(35\) | − | 5.21601e32i | − | 1.95844i | ||||||
\(36\) | 1.41536e31 | − | 1.14449e31i | 0.0294113 | − | 0.0237826i | ||||
\(37\) | −7.76398e29 | −0.000907504 | −0.000453752 | − | 1.00000i | \(-0.500144\pi\) | ||||
−0.000453752 | 1.00000i | \(0.500144\pi\) | ||||||||
\(38\) | − | 2.56801e33i | − | 1.71451i | ||||||
\(39\) | −8.03138e32 | − | 2.27053e33i | −0.310766 | − | 0.878557i | ||||
\(40\) | 6.57370e33 | 1.49469 | ||||||||
\(41\) | − | 1.18439e33i | − | 0.160337i | −0.996781 | − | 0.0801686i | \(-0.974454\pi\) | ||
0.996781 | − | 0.0801686i | \(-0.0255459\pi\) | |||||||
\(42\) | 1.51138e34 | − | 5.34610e33i | 1.23350 | − | 0.436317i | ||||
\(43\) | 1.46050e33 | 0.0727215 | 0.0363608 | − | 0.999339i | \(-0.488423\pi\) | ||||
0.0363608 | + | 0.999339i | \(0.488423\pi\) | |||||||
\(44\) | − | 8.63796e32i | − | 0.0265403i | ||||||
\(45\) | −5.00254e34 | − | 6.18652e34i | −0.958800 | − | 1.18572i | ||||
\(46\) | −9.69834e34 | −1.17161 | ||||||||
\(47\) | 4.50924e34i | 0.346775i | 0.984854 | + | 0.173388i | \(0.0554713\pi\) | ||||
−0.984854 | + | 0.173388i | \(0.944529\pi\) | |||||||
\(48\) | 6.99285e34 | + | 1.97693e35i | 0.345612 | + | 0.977069i | ||||
\(49\) | 2.02627e35 | 0.649500 | ||||||||
\(50\) | 6.43762e35i | 1.35007i | ||||||||
\(51\) | −3.52316e35 | + | 1.24622e35i | −0.487481 | + | 0.172433i | ||||
\(52\) | −3.83005e34 | −0.0352479 | ||||||||
\(53\) | 2.22416e36i | 1.37206i | 0.727575 | + | 0.686028i | \(0.240647\pi\) | ||||
−0.727575 | + | 0.686028i | \(0.759353\pi\) | |||||||
\(54\) | 1.27986e36 | − | 2.08361e36i | 0.533204 | − | 0.868053i | ||||
\(55\) | −3.77564e36 | −1.06998 | ||||||||
\(56\) | 6.48547e36i | 1.25890i | ||||||||
\(57\) | −4.19290e36 | − | 1.18536e37i | −0.561233 | − | 1.58665i | ||||
\(58\) | 6.61885e36 | 0.614886 | ||||||||
\(59\) | − | 3.90010e36i | − | 0.253037i | −0.991964 | − | 0.126518i | \(-0.959620\pi\) | ||
0.991964 | − | 0.126518i | \(-0.0403802\pi\) | |||||||
\(60\) | −1.19282e36 | + | 4.21927e35i | −0.0543749 | + | 0.0192336i | ||||
\(61\) | 2.78638e37 | 0.897666 | 0.448833 | − | 0.893616i | \(-0.351840\pi\) | ||||
0.448833 | + | 0.893616i | \(0.351840\pi\) | |||||||
\(62\) | − | 6.15514e37i | − | 1.40933i | ||||||
\(63\) | 6.10348e37 | − | 4.93540e37i | 0.998679 | − | 0.807552i | ||||
\(64\) | −8.16141e37 | −0.959369 | ||||||||
\(65\) | 1.67411e38i | 1.42103i | ||||||||
\(66\) | −3.86981e37 | − | 1.09402e38i | −0.238378 | − | 0.673912i | ||||
\(67\) | 3.05468e38 | 1.37213 | 0.686064 | − | 0.727541i | \(-0.259337\pi\) | ||||
0.686064 | + | 0.727541i | \(0.259337\pi\) | |||||||
\(68\) | 5.94304e36i | 0.0195579i | ||||||||
\(69\) | −4.47665e38 | + | 1.58349e38i | −1.08423 | + | 0.383517i | ||||
\(70\) | −1.11437e39 | −1.99513 | ||||||||
\(71\) | 3.64924e38i | 0.485039i | 0.970147 | + | 0.242519i | \(0.0779738\pi\) | ||||
−0.970147 | + | 0.242519i | \(0.922026\pi\) | |||||||
\(72\) | 6.22004e38 | + | 7.69217e38i | 0.616326 | + | 0.762195i | ||||
\(73\) | 1.42617e39 | 1.05777 | 0.528885 | − | 0.848693i | \(-0.322610\pi\) | ||||
0.528885 | + | 0.848693i | \(0.322610\pi\) | |||||||
\(74\) | 1.65873e36i | 0.000924507i | ||||||||
\(75\) | 1.05110e39 | + | 2.97153e39i | 0.441934 | + | 1.24938i | ||||
\(76\) | −1.99953e38 | −0.0636566 | ||||||||
\(77\) | − | 3.72497e39i | − | 0.901192i | ||||||
\(78\) | −4.85086e39 | + | 1.71586e39i | −0.895018 | + | 0.316588i | ||||
\(79\) | 3.60695e38 | 0.0509298 | 0.0254649 | − | 0.999676i | \(-0.491893\pi\) | ||||
0.0254649 | + | 0.999676i | \(0.491893\pi\) | |||||||
\(80\) | − | 1.45763e40i | − | 1.58037i | ||||||
\(81\) | 2.50570e39 | − | 1.17074e40i | 0.209288 | − | 0.977854i | ||||
\(82\) | −2.53039e39 | −0.163341 | ||||||||
\(83\) | 7.96913e39i | 0.398815i | 0.979917 | + | 0.199407i | \(0.0639017\pi\) | ||||
−0.979917 | + | 0.199407i | \(0.936098\pi\) | |||||||
\(84\) | −4.16264e38 | − | 1.17681e39i | −0.0161996 | − | 0.0457974i | ||||
\(85\) | 2.59770e40 | 0.788481 | ||||||||
\(86\) | − | 3.12027e39i | − | 0.0740841i | ||||||
\(87\) | 3.05519e40 | − | 1.08069e40i | 0.569028 | − | 0.201278i | ||||
\(88\) | 4.69455e40 | 0.687792 | ||||||||
\(89\) | 6.40863e40i | 0.740585i | 0.928915 | + | 0.370292i | \(0.120743\pi\) | ||||
−0.928915 | + | 0.370292i | \(0.879257\pi\) | |||||||
\(90\) | −1.32172e41 | + | 1.06877e41i | −1.20794 | + | 0.976764i | ||||
\(91\) | −1.65164e41 | −1.19687 | ||||||||
\(92\) | 7.55144e39i | 0.0434996i | ||||||||
\(93\) | −1.00498e41 | − | 2.84114e41i | −0.461333 | − | 1.30422i | ||||
\(94\) | 9.63373e40 | 0.353272 | ||||||||
\(95\) | 8.73994e41i | 2.56633i | ||||||||
\(96\) | 3.02455e40 | − | 1.06985e40i | 0.0712795 | − | 0.0252132i | ||||
\(97\) | 5.27229e41 | 0.999523 | 0.499761 | − | 0.866163i | \(-0.333421\pi\) | ||||
0.499761 | + | 0.866163i | \(0.333421\pi\) | |||||||
\(98\) | − | 4.32901e41i | − | 0.661669i | ||||||
\(99\) | −3.57252e41 | − | 4.41804e41i | −0.441200 | − | 0.545621i | ||||
\(100\) | 5.01254e40 | 0.0501254 | ||||||||
\(101\) | − | 1.71112e42i | − | 1.38845i | −0.719756 | − | 0.694227i | \(-0.755746\pi\) | ||
0.719756 | − | 0.694227i | \(-0.244254\pi\) | |||||||
\(102\) | 2.66248e41 | + | 7.52703e41i | 0.175664 | + | 0.496615i | ||||
\(103\) | 2.09347e42 | 1.12535 | 0.562673 | − | 0.826680i | \(-0.309773\pi\) | ||||
0.562673 | + | 0.826680i | \(0.309773\pi\) | |||||||
\(104\) | − | 2.08155e42i | − | 0.913452i | ||||||
\(105\) | −5.14382e42 | + | 1.81949e42i | −1.84633 | + | 0.653091i | ||||
\(106\) | 4.75179e42 | 1.39776 | ||||||||
\(107\) | − | 3.85687e42i | − | 0.931486i | −0.884920 | − | 0.465743i | \(-0.845787\pi\) | ||
0.884920 | − | 0.465743i | \(-0.154213\pi\) | |||||||
\(108\) | −1.62236e41 | − | 9.96541e40i | −0.0322292 | − | 0.0197969i | ||||
\(109\) | −8.60429e42 | −1.40851 | −0.704253 | − | 0.709949i | \(-0.748718\pi\) | ||||
−0.704253 | + | 0.709949i | \(0.748718\pi\) | |||||||
\(110\) | 8.06646e42i | 1.09002i | ||||||||
\(111\) | 2.70829e39 | + | 7.65652e39i | 0.000302630 | + | 0.000855557i | ||||
\(112\) | 1.43807e43 | 1.33107 | ||||||||
\(113\) | 8.77386e42i | 0.673819i | 0.941537 | + | 0.336909i | \(0.109382\pi\) | ||||
−0.941537 | + | 0.336909i | \(0.890618\pi\) | |||||||
\(114\) | −2.53247e43 | + | 8.95791e42i | −1.61637 | + | 0.571748i | ||||
\(115\) | 3.30073e43 | 1.75370 | ||||||||
\(116\) | − | 5.15365e41i | − | 0.0228295i | ||||||
\(117\) | −1.95895e43 | + | 1.58404e43i | −0.724635 | + | 0.585954i | ||||
\(118\) | −8.33234e42 | −0.257778 | ||||||||
\(119\) | 2.56283e43i | 0.664100i | ||||||||
\(120\) | −2.29308e43 | − | 6.48271e43i | −0.498441 | − | 1.40913i | ||||
\(121\) | 2.78003e43 | 0.507641 | ||||||||
\(122\) | − | 5.95296e43i | − | 0.914484i | ||||||
\(123\) | −1.16800e43 | + | 4.13148e42i | −0.151159 | + | 0.0534685i | ||||
\(124\) | −4.79259e42 | −0.0523257 | ||||||||
\(125\) | − | 5.37704e43i | − | 0.495944i | ||||||
\(126\) | −1.05442e44 | − | 1.30397e44i | −0.822683 | − | 1.01739i | ||||
\(127\) | 2.84926e44 | 1.88301 | 0.941507 | − | 0.336994i | \(-0.109410\pi\) | ||||
0.941507 | + | 0.336994i | \(0.109410\pi\) | |||||||
\(128\) | 1.87853e44i | 1.05295i | ||||||||
\(129\) | −5.09461e42 | − | 1.44028e43i | −0.0242508 | − | 0.0685589i | ||||
\(130\) | 3.57664e44 | 1.44765 | ||||||||
\(131\) | 1.92184e44i | 0.662247i | 0.943587 | + | 0.331123i | \(0.107428\pi\) | ||||
−0.943587 | + | 0.331123i | \(0.892572\pi\) | |||||||
\(132\) | −8.51841e42 | + | 3.01316e42i | −0.0250211 | + | 0.00885052i | ||||
\(133\) | −8.62263e44 | −2.16150 | ||||||||
\(134\) | − | 6.52615e44i | − | 1.39784i | ||||||
\(135\) | −4.35587e44 | + | 7.09132e44i | −0.798115 | + | 1.29933i | ||||
\(136\) | −3.22991e44 | −0.506844 | ||||||||
\(137\) | 8.44852e43i | 0.113671i | 0.998384 | + | 0.0568354i | \(0.0181010\pi\) | ||||
−0.998384 | + | 0.0568354i | \(0.981899\pi\) | |||||||
\(138\) | 3.38304e44 | + | 9.56411e44i | 0.390703 | + | 1.10455i | ||||
\(139\) | 5.21481e44 | 0.517520 | 0.258760 | − | 0.965942i | \(-0.416686\pi\) | ||||
0.258760 | + | 0.965942i | \(0.416686\pi\) | |||||||
\(140\) | 8.67686e43i | 0.0740754i | ||||||||
\(141\) | 4.44682e44 | − | 1.57294e44i | 0.326925 | − | 0.115641i | ||||
\(142\) | 7.79639e44 | 0.494127 | ||||||||
\(143\) | 1.19555e45i | 0.653899i | ||||||||
\(144\) | 1.70564e45 | − | 1.37921e45i | 0.805887 | − | 0.651657i | ||||
\(145\) | −2.25265e45 | −0.920378 | ||||||||
\(146\) | − | 3.04693e45i | − | 1.07759i | ||||||
\(147\) | −7.06817e44 | − | 1.99822e45i | −0.216592 | − | 0.612322i | ||||
\(148\) | 1.29154e41 | 3.43252e−5 | ||||||||
\(149\) | 1.48633e45i | 0.342927i | 0.985190 | + | 0.171464i | \(0.0548496\pi\) | ||||
−0.985190 | + | 0.171464i | \(0.945150\pi\) | |||||||
\(150\) | 6.34852e45 | − | 2.24562e45i | 1.27279 | − | 0.450214i | ||||
\(151\) | −6.65776e45 | −1.16095 | −0.580473 | − | 0.814279i | \(-0.697132\pi\) | ||||
−0.580473 | + | 0.814279i | \(0.697132\pi\) | |||||||
\(152\) | − | 1.08670e46i | − | 1.64966i | ||||||
\(153\) | 2.45794e45 | + | 3.03968e45i | 0.325126 | + | 0.402075i | ||||
\(154\) | −7.95819e45 | −0.918077 | ||||||||
\(155\) | 2.09484e46i | 2.10952i | ||||||||
\(156\) | 1.33602e44 | + | 3.77703e44i | 0.0117543 | + | 0.0332303i | ||||
\(157\) | 7.07911e45 | 0.544610 | 0.272305 | − | 0.962211i | \(-0.412214\pi\) | ||||
0.272305 | + | 0.962211i | \(0.412214\pi\) | |||||||
\(158\) | − | 7.70606e44i | − | 0.0518840i | ||||||
\(159\) | 2.19337e46 | − | 7.75846e45i | 1.29352 | − | 0.457547i | ||||
\(160\) | −2.23006e45 | −0.115292 | ||||||||
\(161\) | 3.25642e46i | 1.47706i | ||||||||
\(162\) | −2.50122e46 | − | 5.35329e45i | −0.996176 | − | 0.213209i | ||||
\(163\) | −4.31606e46 | −1.51059 | −0.755297 | − | 0.655382i | \(-0.772508\pi\) | ||||
−0.755297 | + | 0.655382i | \(0.772508\pi\) | |||||||
\(164\) | 1.97024e44i | 0.00606455i | ||||||||
\(165\) | 1.31705e46 | + | 3.72339e46i | 0.356811 | + | 1.00873i | ||||
\(166\) | 1.70256e46 | 0.406287 | ||||||||
\(167\) | − | 5.67100e46i | − | 1.19293i | −0.802640 | − | 0.596464i | \(-0.796572\pi\) | ||
0.802640 | − | 0.596464i | \(-0.203428\pi\) | |||||||
\(168\) | 6.39570e46 | − | 2.26231e46i | 1.18684 | − | 0.419813i | ||||
\(169\) | −8.03065e45 | −0.131562 | ||||||||
\(170\) | − | 5.54984e46i | − | 0.803254i | ||||||
\(171\) | −1.02270e47 | + | 8.26974e46i | −1.30867 | + | 1.05821i | ||||
\(172\) | −2.42954e44 | −0.00275060 | ||||||||
\(173\) | − | 1.07288e47i | − | 1.07543i | −0.843127 | − | 0.537714i | \(-0.819288\pi\) | ||
0.843127 | − | 0.537714i | \(-0.180712\pi\) | |||||||
\(174\) | −2.30883e46 | − | 6.52724e46i | −0.205049 | − | 0.579689i | ||||
\(175\) | 2.16157e47 | 1.70204 | ||||||||
\(176\) | − | 1.04095e47i | − | 0.727219i | ||||||
\(177\) | −3.84612e46 | + | 1.36046e46i | −0.238552 | + | 0.0843814i | ||||
\(178\) | 1.36917e47 | 0.754461 | ||||||||
\(179\) | 2.70557e47i | 1.32540i | 0.748887 | + | 0.662698i | \(0.230589\pi\) | ||||
−0.748887 | + | 0.662698i | \(0.769411\pi\) | |||||||
\(180\) | 8.32175e45 | + | 1.02913e46i | 0.0362654 | + | 0.0448485i | ||||
\(181\) | −4.69197e46 | −0.182014 | −0.0910070 | − | 0.995850i | \(-0.529009\pi\) | ||||
−0.0910070 | + | 0.995850i | \(0.529009\pi\) | |||||||
\(182\) | 3.52863e47i | 1.21929i | ||||||||
\(183\) | −9.71966e46 | − | 2.74782e47i | −0.299349 | − | 0.846282i | ||||
\(184\) | −4.10404e47 | −1.12730 | ||||||||
\(185\) | − | 5.64532e44i | − | 0.00138383i | ||||||
\(186\) | −6.06995e47 | + | 2.14708e47i | −1.32866 | + | 0.469977i | ||||
\(187\) | 1.85512e47 | 0.362826 | ||||||||
\(188\) | − | 7.50114e45i | − | 0.0131163i | ||||||
\(189\) | −6.99614e47 | − | 4.29740e47i | −1.09436 | − | 0.672215i | ||||
\(190\) | 1.86724e48 | 2.61442 | ||||||||
\(191\) | 1.26327e48i | 1.58415i | 0.610422 | + | 0.792076i | \(0.291000\pi\) | ||||
−0.610422 | + | 0.792076i | \(0.709000\pi\) | |||||||
\(192\) | 2.84692e47 | + | 8.04845e47i | 0.319926 | + | 0.904454i | ||||
\(193\) | −1.04891e48 | −1.05690 | −0.528452 | − | 0.848963i | \(-0.677227\pi\) | ||||
−0.528452 | + | 0.848963i | \(0.677227\pi\) | |||||||
\(194\) | − | 1.12640e48i | − | 1.01825i | ||||||
\(195\) | 1.65094e48 | − | 5.83974e47i | 1.33969 | − | 0.473878i | ||||
\(196\) | −3.37071e46 | −0.0245665 | ||||||||
\(197\) | − | 2.93719e48i | − | 1.92372i | −0.273545 | − | 0.961859i | \(-0.588196\pi\) | ||
0.273545 | − | 0.961859i | \(-0.411804\pi\) | |||||||
\(198\) | −9.43890e47 | + | 7.63249e47i | −0.555844 | + | 0.449466i | ||||
\(199\) | 1.88201e48 | 0.997028 | 0.498514 | − | 0.866882i | \(-0.333879\pi\) | ||||
0.498514 | + | 0.866882i | \(0.333879\pi\) | |||||||
\(200\) | 2.72420e48i | 1.29900i | ||||||||
\(201\) | −1.06555e48 | − | 3.01240e48i | −0.457571 | − | 1.29359i | ||||
\(202\) | −3.65571e48 | −1.41447 | ||||||||
\(203\) | − | 2.22242e48i | − | 0.775191i | ||||||
\(204\) | 5.86079e46 | − | 2.07309e46i | 0.0184384 | − | 0.00652207i | ||||
\(205\) | 8.61190e47 | 0.244494 | ||||||||
\(206\) | − | 4.47259e48i | − | 1.14643i | ||||||
\(207\) | 3.12315e48 | + | 3.86232e48i | 0.723129 | + | 0.894275i | ||||
\(208\) | −4.61556e48 | −0.965815 | ||||||||
\(209\) | 6.24155e48i | 1.18092i | ||||||||
\(210\) | 3.88723e48 | + | 1.09895e49i | 0.665327 | + | 1.88093i | ||||
\(211\) | 6.01374e48 | 0.931564 | 0.465782 | − | 0.884899i | \(-0.345773\pi\) | ||||
0.465782 | + | 0.884899i | \(0.345773\pi\) | |||||||
\(212\) | − | 3.69989e47i | − | 0.0518963i | ||||||
\(213\) | 3.59873e48 | − | 1.27295e48i | 0.457275 | − | 0.161749i | ||||
\(214\) | −8.24000e48 | −0.948938 | ||||||||
\(215\) | 1.06195e48i | 0.110891i | ||||||||
\(216\) | 5.41598e48 | − | 8.81718e48i | 0.513037 | − | 0.835220i | ||||
\(217\) | −2.06672e49 | −1.77675 | ||||||||
\(218\) | 1.83826e49i | 1.43490i | ||||||||
\(219\) | −4.97487e48 | − | 1.40643e49i | −0.352740 | − | 0.997222i | ||||
\(220\) | 6.28080e47 | 0.0404705 | ||||||||
\(221\) | − | 8.22554e48i | − | 0.481867i | ||||||
\(222\) | 1.63577e46 | − | 5.78610e45i | 0.000871587 | − | 0.000308300i | ||||
\(223\) | 5.63802e48 | 0.273353 | 0.136677 | − | 0.990616i | \(-0.456358\pi\) | ||||
0.136677 | + | 0.990616i | \(0.456358\pi\) | |||||||
\(224\) | − | 2.20013e48i | − | 0.0971047i | ||||||
\(225\) | 2.56375e49 | − | 2.07310e49i | 1.03049 | − | 0.833274i | ||||
\(226\) | 1.87449e49 | 0.686444 | ||||||||
\(227\) | 1.22643e49i | 0.409353i | 0.978830 | + | 0.204677i | \(0.0656143\pi\) | ||||
−0.978830 | + | 0.204677i | \(0.934386\pi\) | |||||||
\(228\) | 6.97492e47 | + | 1.97186e48i | 0.0212279 | + | 0.0600128i | ||||
\(229\) | −1.00652e49 | −0.279432 | −0.139716 | − | 0.990192i | \(-0.544619\pi\) | ||||
−0.139716 | + | 0.990192i | \(0.544619\pi\) | |||||||
\(230\) | − | 7.05182e49i | − | 1.78656i | ||||||
\(231\) | −3.67341e49 | + | 1.29937e49i | −0.849606 | + | 0.300525i | ||||
\(232\) | 2.80090e49 | 0.591629 | ||||||||
\(233\) | 1.30888e49i | 0.252595i | 0.991992 | + | 0.126298i | \(0.0403094\pi\) | ||||
−0.991992 | + | 0.126298i | \(0.959691\pi\) | |||||||
\(234\) | 3.38422e49 | + | 4.18518e49i | 0.596933 | + | 0.738212i | ||||
\(235\) | −3.27874e49 | −0.528788 | ||||||||
\(236\) | 6.48783e47i | 0.00957078i | ||||||||
\(237\) | −1.25820e48 | − | 3.55703e48i | −0.0169838 | − | 0.0480145i | ||||
\(238\) | 5.47535e49 | 0.676543 | ||||||||
\(239\) | 9.12653e49i | 1.03264i | 0.856395 | + | 0.516321i | \(0.172699\pi\) | ||||
−0.856395 | + | 0.516321i | \(0.827301\pi\) | |||||||
\(240\) | −1.43746e50 | + | 5.08461e49i | −1.48991 | + | 0.527014i | ||||
\(241\) | −1.31700e49 | −0.125092 | −0.0625458 | − | 0.998042i | \(-0.519922\pi\) | ||||
−0.0625458 | + | 0.998042i | \(0.519922\pi\) | |||||||
\(242\) | − | 5.93938e49i | − | 0.517152i | ||||||
\(243\) | −1.24194e50 | + | 1.61283e49i | −0.991673 | + | 0.128783i | ||||
\(244\) | −4.63516e48 | −0.0339530 | ||||||||
\(245\) | 1.47333e50i | 0.990405i | ||||||||
\(246\) | 8.82667e48 | + | 2.49536e49i | 0.0544703 | + | 0.153992i | ||||
\(247\) | 2.76748e50 | 1.56837 | ||||||||
\(248\) | − | 2.60467e50i | − | 1.35602i | ||||||
\(249\) | 7.85883e49 | − | 2.77985e49i | 0.375986 | − | 0.132995i | ||||
\(250\) | −1.14877e50 | −0.505236 | ||||||||
\(251\) | 2.45524e50i | 0.992994i | 0.868039 | + | 0.496497i | \(0.165381\pi\) | ||||
−0.868039 | + | 0.496497i | \(0.834619\pi\) | |||||||
\(252\) | −1.01532e49 | + | 8.21006e48i | −0.0377738 | + | 0.0305446i | ||||
\(253\) | 2.35718e50 | 0.806979 | ||||||||
\(254\) | − | 6.08728e50i | − | 1.91829i | ||||||
\(255\) | −9.06147e49 | − | 2.56174e50i | −0.262939 | − | 0.743347i | ||||
\(256\) | 4.23946e49 | 0.113311 | ||||||||
\(257\) | 4.52151e50i | 1.11349i | 0.830682 | + | 0.556747i | \(0.187951\pi\) | ||||
−0.830682 | + | 0.556747i | \(0.812049\pi\) | |||||||
\(258\) | −3.07708e49 | + | 1.08843e49i | −0.0698434 | + | 0.0247052i | ||||
\(259\) | 5.56954e47 | 0.00116553 | ||||||||
\(260\) | − | 2.78489e49i | − | 0.0537486i | ||||||
\(261\) | −2.13146e50 | − | 2.63593e50i | −0.379513 | − | 0.469335i | ||||
\(262\) | 4.10590e50 | 0.674655 | ||||||||
\(263\) | − | 6.20036e50i | − | 0.940473i | −0.882541 | − | 0.470236i | \(-0.844169\pi\) | ||
0.882541 | − | 0.470236i | \(-0.155831\pi\) | |||||||
\(264\) | −1.63758e50 | − | 4.62957e50i | −0.229362 | − | 0.648422i | ||||
\(265\) | −1.61722e51 | −2.09221 | ||||||||
\(266\) | 1.84218e51i | 2.20200i | ||||||||
\(267\) | 6.31993e50 | − | 2.23550e50i | 0.698193 | − | 0.246967i | ||||
\(268\) | −5.08147e49 | −0.0518990 | ||||||||
\(269\) | 2.78786e50i | 0.263314i | 0.991295 | + | 0.131657i | \(0.0420297\pi\) | ||||
−0.991295 | + | 0.131657i | \(0.957970\pi\) | |||||||
\(270\) | 1.51502e51 | + | 9.30607e50i | 1.32367 | + | 0.813069i | ||||
\(271\) | −2.02394e50 | −0.163623 | −0.0818113 | − | 0.996648i | \(-0.526070\pi\) | ||||
−0.0818113 | + | 0.996648i | \(0.526070\pi\) | |||||||
\(272\) | 7.16191e50i | 0.535898i | ||||||||
\(273\) | 5.76136e50 | + | 1.62878e51i | 0.399125 | + | 1.12836i | ||||
\(274\) | 1.80498e50 | 0.115801 | ||||||||
\(275\) | − | 1.56466e51i | − | 0.929896i | ||||||
\(276\) | 7.44692e49 | − | 2.63415e49i | 0.0410097 | − | 0.0145061i | ||||
\(277\) | 8.83785e50 | 0.451098 | 0.225549 | − | 0.974232i | \(-0.427582\pi\) | ||||
0.225549 | + | 0.974232i | \(0.427582\pi\) | |||||||
\(278\) | − | 1.11411e51i | − | 0.527217i | ||||||
\(279\) | −2.45126e51 | + | 1.98214e51i | −1.07572 | + | 0.869851i | ||||
\(280\) | −4.71569e51 | −1.91967 | ||||||||
\(281\) | − | 4.53059e51i | − | 1.71128i | −0.517569 | − | 0.855642i | \(-0.673163\pi\) | ||
0.517569 | − | 0.855642i | \(-0.326837\pi\) | |||||||
\(282\) | −3.36051e50 | − | 9.50039e50i | −0.117808 | − | 0.333051i | ||||
\(283\) | −2.02053e51 | −0.657581 | −0.328791 | − | 0.944403i | \(-0.606641\pi\) | ||||
−0.328791 | + | 0.944403i | \(0.606641\pi\) | |||||||
\(284\) | − | 6.07052e49i | − | 0.0183460i | ||||||
\(285\) | 8.61897e51 | − | 3.04873e51i | 2.41943 | − | 0.855808i | ||||
\(286\) | 2.55422e51 | 0.666150 | ||||||||
\(287\) | 8.49631e50i | 0.205926i | ||||||||
\(288\) | −2.11009e50 | − | 2.60949e50i | −0.0475399 | − | 0.0587914i | ||||
\(289\) | 3.49735e51 | 0.732629 | ||||||||
\(290\) | 4.81267e51i | 0.937623i | ||||||||
\(291\) | −1.83912e51 | − | 5.19932e51i | −0.333316 | − | 0.942309i | ||||
\(292\) | −2.37244e50 | −0.0400088 | ||||||||
\(293\) | 2.82430e51i | 0.443294i | 0.975127 | + | 0.221647i | \(0.0711432\pi\) | ||||
−0.975127 | + | 0.221647i | \(0.928857\pi\) | |||||||
\(294\) | −4.26909e51 | + | 1.51008e51i | −0.623795 | + | 0.220650i | ||||
\(295\) | 2.83582e51 | 0.385848 | ||||||||
\(296\) | 7.01925e48i | 0.000889539i | ||||||||
\(297\) | −3.11070e51 | + | 5.06420e51i | −0.367259 | + | 0.597896i | ||||
\(298\) | 3.17545e51 | 0.349353 | ||||||||
\(299\) | − | 1.04517e52i | − | 1.07174i | ||||||
\(300\) | −1.74851e50 | − | 4.94316e50i | −0.0167156 | − | 0.0472561i | ||||
\(301\) | −1.04770e51 | −0.0933983 | ||||||||
\(302\) | 1.42239e52i | 1.18270i | ||||||||
\(303\) | −1.68744e52 | + | 5.96885e51i | −1.30898 | + | 0.463015i | ||||
\(304\) | −2.40962e52 | −1.74423 | ||||||||
\(305\) | 2.02602e52i | 1.36883i | ||||||||
\(306\) | 6.49410e51 | − | 5.25126e51i | 0.409609 | − | 0.331218i | ||||
\(307\) | 2.15551e52 | 1.26953 | 0.634766 | − | 0.772705i | \(-0.281097\pi\) | ||||
0.634766 | + | 0.772705i | \(0.281097\pi\) | |||||||
\(308\) | 6.19650e50i | 0.0340864i | ||||||||
\(309\) | −7.30260e51 | − | 2.06450e52i | −0.375275 | − | 1.06093i | ||||
\(310\) | 4.47550e52 | 2.14905 | ||||||||
\(311\) | − | 1.35097e52i | − | 0.606284i | −0.952945 | − | 0.303142i | \(-0.901964\pi\) | ||
0.952945 | − | 0.303142i | \(-0.0980356\pi\) | |||||||
\(312\) | −2.05274e52 | + | 7.26099e51i | −0.861165 | + | 0.304614i | ||||
\(313\) | −6.40636e51 | −0.251293 | −0.125646 | − | 0.992075i | \(-0.540100\pi\) | ||||
−0.125646 | + | 0.992075i | \(0.540100\pi\) | |||||||
\(314\) | − | 1.51241e52i | − | 0.554814i | ||||||
\(315\) | 3.58861e52 | + | 4.43794e52i | 1.23141 | + | 1.52286i | ||||
\(316\) | −6.00018e49 | −0.00192635 | ||||||||
\(317\) | − | 1.49860e52i | − | 0.450237i | −0.974331 | − | 0.225118i | \(-0.927723\pi\) | ||
0.974331 | − | 0.225118i | \(-0.0722769\pi\) | |||||||
\(318\) | −1.65755e52 | − | 4.68602e52i | −0.466120 | − | 1.31775i | ||||
\(319\) | −1.60871e52 | −0.423520 | ||||||||
\(320\) | − | 5.93429e52i | − | 1.46292i | ||||||
\(321\) | −3.80349e52 | + | 1.34538e52i | −0.878166 | + | 0.310628i | ||||
\(322\) | 6.95717e52 | 1.50473 | ||||||||
\(323\) | − | 4.29427e52i | − | 0.870235i | ||||||
\(324\) | −4.16824e50 | + | 1.94753e51i | −0.00791603 | + | 0.0369861i | ||||
\(325\) | −6.93767e52 | −1.23499 | ||||||||
\(326\) | 9.22103e52i | 1.53890i | ||||||||
\(327\) | 3.00141e52 | + | 8.48520e52i | 0.469702 | + | 1.32788i | ||||
\(328\) | −1.07078e52 | −0.157163 | ||||||||
\(329\) | − | 3.23473e52i | − | 0.445373i | ||||||
\(330\) | 7.95481e52 | − | 2.81380e52i | 1.02763 | − | 0.363496i | ||||
\(331\) | −4.37137e52 | −0.529944 | −0.264972 | − | 0.964256i | \(-0.585363\pi\) | ||||
−0.264972 | + | 0.964256i | \(0.585363\pi\) | |||||||
\(332\) | − | 1.32567e51i | − | 0.0150847i | ||||||
\(333\) | 6.60582e49 | − | 5.34160e49i | 0.000705664 | − | 0.000570614i | ||||
\(334\) | −1.21158e53 | −1.21528 | ||||||||
\(335\) | 2.22110e53i | 2.09232i | ||||||||
\(336\) | −5.01637e52 | − | 1.41816e53i | −0.443879 | − | 1.25488i | ||||
\(337\) | 6.31139e52 | 0.524683 | 0.262342 | − | 0.964975i | \(-0.415505\pi\) | ||||
0.262342 | + | 0.964975i | \(0.415505\pi\) | |||||||
\(338\) | 1.71570e52i | 0.134027i | ||||||||
\(339\) | 8.65242e52 | − | 3.06056e52i | 0.635249 | − | 0.224702i | ||||
\(340\) | −4.32128e51 | −0.0298233 | ||||||||
\(341\) | 1.49601e53i | 0.970715i | ||||||||
\(342\) | 1.76678e53 | + | 2.18494e53i | 1.07804 | + | 1.33319i | ||||
\(343\) | 7.84405e52 | 0.450157 | ||||||||
\(344\) | − | 1.32040e52i | − | 0.0712819i | ||||||
\(345\) | −1.15138e53 | − | 3.25504e53i | −0.584815 | − | 1.65331i | ||||
\(346\) | −2.29214e53 | −1.09558 | ||||||||
\(347\) | − | 2.10203e53i | − | 0.945627i | −0.881162 | − | 0.472814i | \(-0.843238\pi\) | ||
0.881162 | − | 0.472814i | \(-0.156762\pi\) | |||||||
\(348\) | −5.08232e51 | + | 1.79773e51i | −0.0215227 | + | 0.00761308i | ||||
\(349\) | −1.71927e53 | −0.685504 | −0.342752 | − | 0.939426i | \(-0.611359\pi\) | ||||
−0.342752 | + | 0.939426i | \(0.611359\pi\) | |||||||
\(350\) | − | 4.61807e53i | − | 1.73393i | ||||||
\(351\) | 2.24545e53 | + | 1.37927e53i | 0.794061 | + | 0.487755i | ||||
\(352\) | −1.59258e52 | −0.0530524 | ||||||||
\(353\) | − | 1.77688e52i | − | 0.0557686i | −0.999611 | − | 0.0278843i | \(-0.991123\pi\) | ||
0.999611 | − | 0.0278843i | \(-0.00887700\pi\) | |||||||
\(354\) | 2.90655e52 | + | 8.21702e52i | 0.0859624 | + | 0.243022i | ||||
\(355\) | −2.65342e53 | −0.739623 | ||||||||
\(356\) | − | 1.06608e52i | − | 0.0280117i | ||||||
\(357\) | 2.52736e53 | − | 8.93984e52i | 0.626086 | − | 0.221461i | ||||
\(358\) | 5.78031e53 | 1.35023 | ||||||||
\(359\) | − | 2.55854e53i | − | 0.563649i | −0.959466 | − | 0.281825i | \(-0.909060\pi\) | ||
0.959466 | − | 0.281825i | \(-0.0909396\pi\) | |||||||
\(360\) | −5.59310e53 | + | 4.52269e53i | −1.16225 | + | 0.939819i | ||||
\(361\) | 9.34712e53 | 1.83243 | ||||||||
\(362\) | 1.00241e53i | 0.185424i | ||||||||
\(363\) | −9.69749e52 | − | 2.74155e53i | −0.169286 | − | 0.478583i | ||||
\(364\) | 2.74751e52 | 0.0452699 | ||||||||
\(365\) | 1.03699e54i | 1.61297i | ||||||||
\(366\) | −5.87056e53 | + | 2.07655e53i | −0.862138 | + | 0.304958i | ||||
\(367\) | −9.25599e53 | −1.28362 | −0.641808 | − | 0.766865i | \(-0.721816\pi\) | ||||
−0.641808 | + | 0.766865i | \(0.721816\pi\) | |||||||
\(368\) | 9.10018e53i | 1.19192i | ||||||||
\(369\) | 8.14859e52 | + | 1.00772e53i | 0.100816 | + | 0.124676i | ||||
\(370\) | −1.20609e51 | −0.00140976 | ||||||||
\(371\) | − | 1.59551e54i | − | 1.76217i | ||||||
\(372\) | 1.67179e52 | + | 4.72626e52i | 0.0174493 | + | 0.0493305i | ||||
\(373\) | −2.80838e53 | −0.277058 | −0.138529 | − | 0.990358i | \(-0.544237\pi\) | ||||
−0.138529 | + | 0.990358i | \(0.544237\pi\) | |||||||
\(374\) | − | 3.96336e53i | − | 0.369624i | ||||||
\(375\) | −5.30262e53 | + | 1.87566e53i | −0.467556 | + | 0.165385i | ||||
\(376\) | 4.07670e53 | 0.339910 | ||||||||
\(377\) | 7.13297e53i | 0.562474i | ||||||||
\(378\) | −9.18116e53 | + | 1.49469e54i | −0.684810 | + | 1.11487i | ||||
\(379\) | 2.57918e53 | 0.181995 | 0.0909973 | − | 0.995851i | \(-0.470995\pi\) | ||||
0.0909973 | + | 0.995851i | \(0.470995\pi\) | |||||||
\(380\) | − | 1.45389e53i | − | 0.0970682i | ||||||
\(381\) | −9.93898e53 | − | 2.80982e54i | −0.627939 | − | 1.77523i | ||||
\(382\) | 2.69892e54 | 1.61383 | ||||||||
\(383\) | − | 4.26971e53i | − | 0.241671i | −0.992673 | − | 0.120835i | \(-0.961443\pi\) | ||
0.992673 | − | 0.120835i | \(-0.0385573\pi\) | |||||||
\(384\) | 1.85253e54 | − | 6.55281e53i | 0.992679 | − | 0.351133i | ||||
\(385\) | 2.70848e54 | 1.37420 | ||||||||
\(386\) | 2.24094e54i | 1.07671i | ||||||||
\(387\) | −1.24263e53 | + | 1.00482e53i | −0.0565474 | + | 0.0457254i | ||||
\(388\) | −8.77048e52 | −0.0378057 | ||||||||
\(389\) | − | 1.11523e53i | − | 0.0455430i | −0.999741 | − | 0.0227715i | \(-0.992751\pi\) | ||
0.999741 | − | 0.0227715i | \(-0.00724902\pi\) | |||||||
\(390\) | −1.24763e54 | − | 3.52714e54i | −0.482757 | − | 1.36479i | ||||
\(391\) | −1.62178e54 | −0.594674 | ||||||||
\(392\) | − | 1.83191e54i | − | 0.636643i | ||||||
\(393\) | 1.89524e54 | − | 6.70389e53i | 0.624339 | − | 0.220843i | ||||
\(394\) | −6.27515e54 | −1.95976 | ||||||||
\(395\) | 2.62267e53i | 0.0776614i | ||||||||
\(396\) | 5.94290e52 | + | 7.34943e52i | 0.0166878 | + | 0.0206374i | ||||
\(397\) | −5.82360e54 | −1.55093 | −0.775463 | − | 0.631394i | \(-0.782483\pi\) | ||||
−0.775463 | + | 0.631394i | \(0.782483\pi\) | |||||||
\(398\) | − | 4.02081e54i | − | 1.01571i | ||||||
\(399\) | 3.00781e54 | + | 8.50329e54i | 0.720807 | + | 2.03777i | ||||
\(400\) | 6.04057e54 | 1.37347 | ||||||||
\(401\) | 4.43513e54i | 0.956918i | 0.878110 | + | 0.478459i | \(0.158804\pi\) | ||||
−0.878110 | + | 0.478459i | \(0.841196\pi\) | |||||||
\(402\) | −6.43582e54 | + | 2.27650e54i | −1.31782 | + | 0.466144i | ||||
\(403\) | 6.63325e54 | 1.28920 | ||||||||
\(404\) | 2.84646e53i | 0.0525165i | ||||||||
\(405\) | 8.51262e54 | + | 1.82193e54i | 1.49110 | + | 0.319137i | ||||
\(406\) | −4.74807e54 | −0.789716 | ||||||||
\(407\) | − | 4.03155e51i | − | 0.000636780i | ||||||
\(408\) | 1.12668e54 | + | 3.18521e54i | 0.169020 | + | 0.477831i | ||||
\(409\) | −1.10033e55 | −1.56796 | −0.783980 | − | 0.620786i | \(-0.786814\pi\) | ||||
−0.783980 | + | 0.620786i | \(0.786814\pi\) | |||||||
\(410\) | − | 1.83989e54i | − | 0.249075i | ||||||
\(411\) | 8.33158e53 | − | 2.94707e53i | 0.107164 | − | 0.0379064i | ||||
\(412\) | −3.48250e53 | −0.0425648 | ||||||||
\(413\) | 2.79776e54i | 0.324982i | ||||||||
\(414\) | 8.25164e54 | − | 6.67244e54i | 0.911030 | − | 0.736678i | ||||
\(415\) | −5.79448e54 | −0.608142 | ||||||||
\(416\) | 7.06144e53i | 0.0704585i | ||||||||
\(417\) | −1.81907e54 | − | 5.14263e54i | −0.172580 | − | 0.487897i | ||||
\(418\) | 1.33347e55 | 1.20305 | ||||||||
\(419\) | − | 5.67630e54i | − | 0.487047i | −0.969895 | − | 0.243524i | \(-0.921697\pi\) | ||
0.969895 | − | 0.243524i | \(-0.0783033\pi\) | |||||||
\(420\) | 8.55677e53 | − | 3.02672e53i | 0.0698352 | − | 0.0247023i | ||||
\(421\) | −1.72259e55 | −1.33739 | −0.668693 | − | 0.743538i | \(-0.733146\pi\) | ||||
−0.668693 | + | 0.743538i | \(0.733146\pi\) | |||||||
\(422\) | − | 1.28480e55i | − | 0.949018i | ||||||
\(423\) | −3.10234e54 | − | 3.83659e54i | −0.218043 | − | 0.269648i | ||||
\(424\) | 2.01081e55 | 1.34490 | ||||||||
\(425\) | 1.07651e55i | 0.685253i | ||||||||
\(426\) | −2.71959e54 | − | 7.68848e54i | −0.164779 | − | 0.465842i | ||||
\(427\) | −1.99883e55 | −1.15290 | ||||||||
\(428\) | 6.41593e53i | 0.0352323i | ||||||||
\(429\) | 1.17900e55 | − | 4.17040e54i | 0.616469 | − | 0.218059i | ||||
\(430\) | 2.26880e54 | 0.112969 | ||||||||
\(431\) | − | 5.94563e54i | − | 0.281952i | −0.990013 | − | 0.140976i | \(-0.954976\pi\) | ||
0.990013 | − | 0.140976i | \(-0.0450241\pi\) | |||||||
\(432\) | −1.95509e55 | − | 1.20092e55i | −0.883099 | − | 0.542446i | ||||
\(433\) | 4.34540e55 | 1.86975 | 0.934877 | − | 0.354972i | \(-0.115510\pi\) | ||||
0.934877 | + | 0.354972i | \(0.115510\pi\) | |||||||
\(434\) | 4.41543e55i | 1.81004i | ||||||||
\(435\) | 7.85786e54 | + | 2.22147e55i | 0.306923 | + | 0.867695i | ||||
\(436\) | 1.43133e54 | 0.0532749 | ||||||||
\(437\) | − | 5.45646e55i | − | 1.93553i | ||||||
\(438\) | −3.00476e55 | + | 1.06285e55i | −1.01591 | + | 0.359349i | ||||
\(439\) | 1.23238e55 | 0.397182 | 0.198591 | − | 0.980082i | \(-0.436363\pi\) | ||||
0.198591 | + | 0.980082i | \(0.436363\pi\) | |||||||
\(440\) | 3.41348e55i | 1.04880i | ||||||||
\(441\) | −1.72401e55 | + | 1.39407e55i | −0.505044 | + | 0.408389i | ||||
\(442\) | −1.75734e55 | −0.490895 | ||||||||
\(443\) | 5.56284e55i | 1.48190i | 0.671562 | + | 0.740948i | \(0.265624\pi\) | ||||
−0.671562 | + | 0.740948i | \(0.734376\pi\) | |||||||
\(444\) | −4.50525e50 | − | 1.27367e51i | −1.14466e−5 | − | 3.23603e-5i | ||||
\(445\) | −4.65981e55 | −1.12930 | ||||||||
\(446\) | − | 1.20453e55i | − | 0.278475i | ||||||
\(447\) | 1.46575e55 | − | 5.18470e54i | 0.323298 | − | 0.114358i | ||||
\(448\) | 5.85464e55 | 1.23215 | ||||||||
\(449\) | − | 1.31335e55i | − | 0.263758i | −0.991266 | − | 0.131879i | \(-0.957899\pi\) | ||
0.991266 | − | 0.131879i | \(-0.0421010\pi\) | |||||||
\(450\) | −4.42907e55 | − | 5.47732e55i | −0.848886 | − | 1.04980i | ||||
\(451\) | 6.15011e54 | 0.112506 | ||||||||
\(452\) | − | 1.45954e54i | − | 0.0254863i | ||||||
\(453\) | 2.32241e55 | + | 6.56561e55i | 0.387147 | + | 1.09449i | ||||
\(454\) | 2.62019e55 | 0.417023 | ||||||||
\(455\) | − | 1.20093e56i | − | 1.82507i | ||||||
\(456\) | −1.07166e56 | + | 3.79071e55i | −1.55524 | + | 0.550122i | ||||
\(457\) | 1.77206e55 | 0.245606 | 0.122803 | − | 0.992431i | \(-0.460812\pi\) | ||||
0.122803 | + | 0.992431i | \(0.460812\pi\) | |||||||
\(458\) | 2.15037e55i | 0.284667i | ||||||||
\(459\) | 2.14021e55 | − | 3.48424e55i | 0.270638 | − | 0.440598i | ||||
\(460\) | −5.49077e54 | −0.0663314 | ||||||||
\(461\) | − | 1.44665e56i | − | 1.66972i | −0.550460 | − | 0.834861i | \(-0.685548\pi\) | ||
0.550460 | − | 0.834861i | \(-0.314452\pi\) | |||||||
\(462\) | 2.77603e55 | + | 7.84804e55i | 0.306156 | + | 0.865525i | ||||
\(463\) | 1.12959e56 | 1.19048 | 0.595238 | − | 0.803549i | \(-0.297058\pi\) | ||||
0.595238 | + | 0.803549i | \(0.297058\pi\) | |||||||
\(464\) | − | 6.21062e55i | − | 0.625543i | ||||||
\(465\) | 2.06584e56 | − | 7.30735e55i | 1.98877 | − | 0.703474i | ||||
\(466\) | 2.79635e55 | 0.257328 | ||||||||
\(467\) | 2.05563e56i | 1.80838i | 0.427131 | + | 0.904190i | \(0.359524\pi\) | ||||
−0.427131 | + | 0.904190i | \(0.640476\pi\) | |||||||
\(468\) | 3.25872e54 | − | 2.63506e54i | 0.0274084 | − | 0.0221630i | ||||
\(469\) | −2.19129e56 | −1.76226 | ||||||||
\(470\) | 7.00484e55i | 0.538695i | ||||||||
\(471\) | −2.46938e55 | − | 6.98113e55i | −0.181614 | − | 0.513436i | ||||
\(472\) | −3.52599e55 | −0.248027 | ||||||||
\(473\) | 7.58382e54i | 0.0510275i | ||||||||
\(474\) | −7.59940e54 | + | 2.68808e54i | −0.0489141 | + | 0.0173020i | ||||
\(475\) | −3.62192e56 | −2.23035 | ||||||||
\(476\) | − | 4.26328e54i | − | 0.0251187i | ||||||
\(477\) | −1.53021e56 | − | 1.89238e56i | −0.862713 | − | 1.06690i | ||||
\(478\) | 1.94983e56 | 1.05199 | ||||||||
\(479\) | 2.80412e56i | 1.44794i | 0.689830 | + | 0.723972i | \(0.257685\pi\) | ||||
−0.689830 | + | 0.723972i | \(0.742315\pi\) | |||||||
\(480\) | 7.77906e54 | + | 2.19920e55i | 0.0384469 | + | 0.108692i | ||||
\(481\) | −1.78758e53 | −0.000845703 | ||||||||
\(482\) | 2.81370e55i | 0.127435i | ||||||||
\(483\) | 3.21135e56 | − | 1.13593e56i | 1.39251 | − | 0.492562i | ||||
\(484\) | −4.62459e54 | −0.0192009 | ||||||||
\(485\) | 3.83357e56i | 1.52415i | ||||||||
\(486\) | 3.44572e55 | + | 2.65333e56i | 0.131195 | + | 1.01025i | ||||
\(487\) | −2.41714e56 | −0.881440 | −0.440720 | − | 0.897645i | \(-0.645277\pi\) | ||||
−0.440720 | + | 0.897645i | \(0.645277\pi\) | |||||||
\(488\) | − | 2.51911e56i | − | 0.879895i | ||||||
\(489\) | 1.50556e56 | + | 4.25632e56i | 0.503746 | + | 1.42413i | ||||
\(490\) | 3.14769e56 | 1.00896 | ||||||||
\(491\) | − | 2.68654e56i | − | 0.825053i | −0.910946 | − | 0.412526i | \(-0.864646\pi\) | ||
0.910946 | − | 0.412526i | \(-0.135354\pi\) | |||||||
\(492\) | 1.94297e54 | − | 6.87273e53i | 0.00571741 | − | 0.00202238i | ||||
\(493\) | 1.10682e56 | 0.312097 | ||||||||
\(494\) | − | 5.91257e56i | − | 1.59776i | ||||||
\(495\) | 3.21243e56 | − | 2.59763e56i | 0.832002 | − | 0.672773i | ||||
\(496\) | −5.77551e56 | −1.43376 | ||||||||
\(497\) | − | 2.61780e56i | − | 0.622949i | ||||||
\(498\) | −5.93899e55 | − | 1.67900e56i | −0.135487 | − | 0.383031i | ||||
\(499\) | −4.16921e56 | −0.911890 | −0.455945 | − | 0.890008i | \(-0.650699\pi\) | ||||
−0.455945 | + | 0.890008i | \(0.650699\pi\) | |||||||
\(500\) | 8.94473e54i | 0.0187585i | ||||||||
\(501\) | −5.59251e56 | + | 1.97820e56i | −1.12464 | + | 0.397812i | ||||
\(502\) | 5.24549e56 | 1.01160 | ||||||||
\(503\) | 5.45303e56i | 1.00858i | 0.863535 | + | 0.504290i | \(0.168246\pi\) | ||||
−0.863535 | + | 0.504290i | \(0.831754\pi\) | |||||||
\(504\) | −4.46199e56 | − | 5.51803e56i | −0.791566 | − | 0.978909i | ||||
\(505\) | 1.24418e57 | 2.11722 | ||||||||
\(506\) | − | 5.03599e56i | − | 0.822099i | ||||||
\(507\) | 2.80131e55 | + | 7.91950e55i | 0.0438726 | + | 0.124031i | ||||
\(508\) | −4.73975e55 | −0.0712226 | ||||||||
\(509\) | − | 9.31700e56i | − | 1.34339i | −0.740827 | − | 0.671696i | \(-0.765566\pi\) | ||
0.740827 | − | 0.671696i | \(-0.234434\pi\) | |||||||
\(510\) | −5.47302e56 | + | 1.93593e56i | −0.757275 | + | 0.267865i | ||||
\(511\) | −1.02307e57 | −1.35852 | ||||||||
\(512\) | 7.35612e56i | 0.937518i | ||||||||
\(513\) | 1.17227e57 | + | 7.20072e56i | 1.43405 | + | 0.880869i | ||||
\(514\) | 9.65996e56 | 1.13436 | ||||||||
\(515\) | 1.52220e57i | 1.71601i | ||||||||
\(516\) | 8.47490e53 | + | 2.39592e54i | 0.000917257 | + | 0.00259315i | ||||
\(517\) | −2.34148e56 | −0.243326 | ||||||||
\(518\) | − | 1.18990e54i | − | 0.00118737i | ||||||
\(519\) | −1.05803e57 | + | 3.74248e56i | −1.01387 | + | 0.358629i | ||||
\(520\) | 1.51353e57 | 1.39290 | ||||||||
\(521\) | 6.71722e55i | 0.0593742i | 0.999559 | + | 0.0296871i | \(0.00945108\pi\) | ||||
−0.999559 | + | 0.0296871i | \(0.990549\pi\) | |||||||
\(522\) | −5.63151e56 | + | 4.55375e56i | −0.478128 | + | 0.386624i | ||||
\(523\) | −5.13804e54 | −0.00419046 | −0.00209523 | − | 0.999998i | \(-0.500667\pi\) | ||||
−0.00209523 | + | 0.999998i | \(0.500667\pi\) | |||||||
\(524\) | − | 3.19699e55i | − | 0.0250486i | ||||||
\(525\) | −7.54013e56 | − | 2.13165e57i | −0.567588 | − | 1.60461i | ||||
\(526\) | −1.32467e57 | −0.958094 | ||||||||
\(527\) | − | 1.02927e57i | − | 0.715333i | ||||||
\(528\) | −1.02655e57 | + | 3.63113e56i | −0.685593 | + | 0.242510i | ||||
\(529\) | −5.02680e56 | −0.322643 | ||||||||
\(530\) | 3.45510e57i | 2.13141i | ||||||||
\(531\) | 2.68326e56 | + | 3.31832e56i | 0.159103 | + | 0.196758i | ||||
\(532\) | 1.43438e56 | 0.0817560 | ||||||||
\(533\) | − | 2.72694e56i | − | 0.149418i | ||||||
\(534\) | −4.77603e56 | − | 1.35022e57i | −0.251594 | − | 0.711275i | ||||
\(535\) | 2.80440e57 | 1.42040 | ||||||||
\(536\) | − | 2.76167e57i | − | 1.34497i | ||||||
\(537\) | 2.66812e57 | − | 9.43777e56i | 1.24953 | − | 0.441987i | ||||
\(538\) | 5.95611e56 | 0.268247 | ||||||||
\(539\) | 1.05217e57i | 0.455743i | ||||||||
\(540\) | 7.24601e55 | − | 1.17965e56i | 0.0301877 | − | 0.0491454i | ||||
\(541\) | −2.83251e57 | −1.13508 | −0.567542 | − | 0.823344i | \(-0.692106\pi\) | ||||
−0.567542 | + | 0.823344i | \(0.692106\pi\) | |||||||
\(542\) | 4.32405e56i | 0.166688i | ||||||||
\(543\) | 1.63668e56 | + | 4.62702e56i | 0.0606972 | + | 0.171595i | ||||
\(544\) | 1.09572e56 | 0.0390950 | ||||||||
\(545\) | − | 6.25632e57i | − | 2.14779i | ||||||
\(546\) | 3.47979e57 | − | 1.23088e57i | 1.14950 | − | 0.406604i | ||||
\(547\) | 9.20507e56 | 0.292613 | 0.146306 | − | 0.989239i | \(-0.453261\pi\) | ||||
0.146306 | + | 0.989239i | \(0.453261\pi\) | |||||||
\(548\) | − | 1.40542e55i | − | 0.00429945i | ||||||
\(549\) | −2.37074e57 | + | 1.91703e57i | −0.698014 | + | 0.564428i | ||||
\(550\) | −3.34282e57 | −0.947319 | ||||||||
\(551\) | 3.72388e57i | 1.01581i | ||||||||
\(552\) | 1.43160e57 | + | 4.04724e57i | 0.375925 | + | 1.06277i | ||||
\(553\) | −2.58747e56 | −0.0654105 | ||||||||
\(554\) | − | 1.88816e57i | − | 0.459550i | ||||||
\(555\) | −5.56718e54 | + | 1.96924e54i | −0.00130462 | + | 0.000461472i | ||||
\(556\) | −8.67486e55 | −0.0195745 | ||||||||
\(557\) | − | 6.21919e57i | − | 1.35137i | −0.737190 | − | 0.675686i | \(-0.763848\pi\) | ||
0.737190 | − | 0.675686i | \(-0.236152\pi\) | |||||||
\(558\) | 4.23472e57 | + | 5.23698e57i | 0.886149 | + | 1.09588i | ||||
\(559\) | 3.36264e56 | 0.0677692 | ||||||||
\(560\) | 1.04564e58i | 2.02971i | ||||||||
\(561\) | −6.47116e56 | − | 1.82944e57i | −0.120994 | − | 0.342057i | ||||
\(562\) | −9.67935e57 | −1.74335 | ||||||||
\(563\) | − | 4.91519e57i | − | 0.852834i | −0.904527 | − | 0.426417i | \(-0.859776\pi\) | ||
0.904527 | − | 0.426417i | \(-0.140224\pi\) | |||||||
\(564\) | −7.39731e55 | + | 2.61660e55i | −0.0123655 | + | 0.00437397i | ||||
\(565\) | −6.37961e57 | −1.02749 | ||||||||
\(566\) | 4.31674e57i | 0.669902i | ||||||||
\(567\) | −1.79748e57 | + | 8.39836e57i | −0.268794 | + | 1.25589i | ||||
\(568\) | 3.29920e57 | 0.475437 | ||||||||
\(569\) | 4.79293e57i | 0.665646i | 0.942989 | + | 0.332823i | \(0.108001\pi\) | ||||
−0.942989 | + | 0.332823i | \(0.891999\pi\) | |||||||
\(570\) | −6.51344e57 | − | 1.84140e58i | −0.871843 | − | 2.46476i | ||||
\(571\) | 6.89407e57 | 0.889442 | 0.444721 | − | 0.895669i | \(-0.353303\pi\) | ||||
0.444721 | + | 0.895669i | \(0.353303\pi\) | |||||||
\(572\) | − | 1.98880e56i | − | 0.0247329i | ||||||
\(573\) | 1.24579e58 | − | 4.40664e57i | 1.49347 | − | 0.528276i | ||||
\(574\) | 1.81519e57 | 0.209784 | ||||||||
\(575\) | 1.36785e58i | 1.52410i | ||||||||
\(576\) | 6.94397e57 | − | 5.61503e57i | 0.745994 | − | 0.603226i | ||||
\(577\) | 5.24748e57 | 0.543574 | 0.271787 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271787 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(578\) | − | 7.47189e57i | − | 0.746355i | ||||||
\(579\) | 3.65889e57 | + | 1.03439e58i | 0.352451 | + | 0.996405i | ||||
\(580\) | 3.74730e56 | 0.0348121 | ||||||||
\(581\) | − | 5.71671e57i | − | 0.512209i | ||||||
\(582\) | −1.11081e58 | + | 3.92917e57i | −0.959965 | + | 0.339561i | ||||
\(583\) | −1.15492e58 | −0.962749 | ||||||||
\(584\) | − | 1.28937e58i | − | 1.03683i | ||||||
\(585\) | −1.15178e58 | − | 1.42438e58i | −0.893506 | − | 1.10498i | ||||
\(586\) | 6.03397e57 | 0.451599 | ||||||||
\(587\) | − | 8.91021e57i | − | 0.643410i | −0.946840 | − | 0.321705i | \(-0.895744\pi\) | ||
0.946840 | − | 0.321705i | \(-0.104256\pi\) | |||||||
\(588\) | 1.17579e56 | + | 3.32405e56i | 0.00819233 | + | 0.0231603i | ||||
\(589\) | 3.46299e58 | 2.32825 | ||||||||
\(590\) | − | 6.05858e57i | − | 0.393078i | ||||||
\(591\) | −2.89654e58 | + | 1.02457e58i | −1.81360 | + | 0.641513i | ||||
\(592\) | 1.55643e55 | 0.000940530 | ||||||||
\(593\) | 1.08094e58i | 0.630451i | 0.949017 | + | 0.315226i | \(0.102080\pi\) | ||||
−0.949017 | + | 0.315226i | \(0.897920\pi\) | |||||||
\(594\) | 1.08194e58 | + | 6.64584e57i | 0.609098 | + | 0.374141i | ||||
\(595\) | −1.86347e58 | −1.01267 | ||||||||
\(596\) | − | 2.47251e56i | − | 0.0129708i | ||||||
\(597\) | −6.56496e57 | − | 1.85596e58i | −0.332484 | − | 0.939957i | ||||
\(598\) | −2.23294e58 | −1.09182 | ||||||||
\(599\) | 1.89633e58i | 0.895261i | 0.894219 | + | 0.447630i | \(0.147732\pi\) | ||||
−0.894219 | + | 0.447630i | \(0.852268\pi\) | |||||||
\(600\) | 2.68650e58 | − | 9.50276e57i | 1.22465 | − | 0.433185i | ||||
\(601\) | 2.88502e58 | 1.26994 | 0.634972 | − | 0.772535i | \(-0.281012\pi\) | ||||
0.634972 | + | 0.772535i | \(0.281012\pi\) | |||||||
\(602\) | 2.23835e57i | 0.0951483i | ||||||||
\(603\) | −2.59901e58 | + | 2.10161e58i | −1.06695 | + | 0.862758i | ||||
\(604\) | 1.10752e57 | 0.0439113 | ||||||||
\(605\) | 2.02140e58i | 0.774088i | ||||||||
\(606\) | 1.27521e58 | + | 3.60512e58i | 0.471690 | + | 1.33350i | ||||
\(607\) | 6.03978e57 | 0.215804 | 0.107902 | − | 0.994162i | \(-0.465587\pi\) | ||||
0.107902 | + | 0.994162i | \(0.465587\pi\) | |||||||
\(608\) | 3.68654e57i | 0.127246i | ||||||||
\(609\) | −2.19166e58 | + | 7.75239e57i | −0.730818 | + | 0.258507i | ||||
\(610\) | 4.32849e58 | 1.39447 | ||||||||
\(611\) | 1.03820e58i | 0.323160i | ||||||||
\(612\) | −4.08880e56 | − | 5.05652e56i | −0.0122975 | − | 0.0152080i | ||||
\(613\) | 1.31791e58 | 0.383015 | 0.191507 | − | 0.981491i | \(-0.438662\pi\) | ||||
0.191507 | + | 0.981491i | \(0.438662\pi\) | |||||||
\(614\) | − | 4.60512e58i | − | 1.29332i | ||||||
\(615\) | −3.00406e57 | − | 8.49270e57i | −0.0815327 | − | 0.230499i | ||||
\(616\) | −3.36766e58 | −0.883352 | ||||||||
\(617\) | − | 3.27470e58i | − | 0.830202i | −0.909775 | − | 0.415101i | \(-0.863746\pi\) | ||
0.909775 | − | 0.415101i | \(-0.136254\pi\) | |||||||
\(618\) | −4.41069e58 | + | 1.56016e58i | −1.08081 | + | 0.382306i | ||||
\(619\) | −5.06522e58 | −1.19976 | −0.599880 | − | 0.800090i | \(-0.704785\pi\) | ||||
−0.599880 | + | 0.800090i | \(0.704785\pi\) | |||||||
\(620\) | − | 3.48477e57i | − | 0.0797900i | ||||||
\(621\) | 2.71942e58 | − | 4.42720e58i | 0.601940 | − | 0.979955i | ||||
\(622\) | −2.88626e58 | −0.617643 | ||||||||
\(623\) | − | 4.59727e58i | − | 0.951154i | ||||||
\(624\) | 1.61003e58 | + | 4.55167e58i | 0.322075 | + | 0.910531i | ||||
\(625\) | −2.94158e58 | −0.568985 | ||||||||
\(626\) | 1.36868e58i | 0.256001i | ||||||||
\(627\) | 6.15516e58 | − | 2.17722e58i | 1.11332 | − | 0.393807i | ||||
\(628\) | −1.17761e57 | −0.0205992 | ||||||||
\(629\) | 2.77376e55i | 0.000469252i | ||||||||
\(630\) | 9.48141e58 | − | 7.66686e58i | 1.55139 | − | 1.25449i | ||||
\(631\) | 1.15422e59 | 1.82672 | 0.913362 | − | 0.407148i | \(-0.133477\pi\) | ||||
0.913362 | + | 0.407148i | \(0.133477\pi\) | |||||||
\(632\) | − | 3.26097e57i | − | 0.0499215i | ||||||
\(633\) | −2.09775e58 | − | 5.93050e58i | −0.310654 | − | 0.878240i | ||||
\(634\) | −3.20167e58 | −0.458673 | ||||||||
\(635\) | 2.07174e59i | 2.87136i | ||||||||
\(636\) | −3.64868e57 | + | 1.29062e57i | −0.0489257 | + | 0.0173061i | ||||
\(637\) | 4.66527e58 | 0.605269 | ||||||||
\(638\) | 3.43692e58i | 0.431455i | ||||||||
\(639\) | −2.51067e58 | − | 3.10488e58i | −0.304980 | − | 0.377161i | ||||
\(640\) | −1.36591e59 | −1.60562 | ||||||||
\(641\) | − | 1.46357e59i | − | 1.66493i | −0.554078 | − | 0.832465i | \(-0.686929\pi\) | ||
0.554078 | − | 0.832465i | \(-0.313071\pi\) | |||||||
\(642\) | 2.87433e58 | + | 8.12595e58i | 0.316448 | + | 0.894620i | ||||
\(643\) | −2.32480e58 | −0.247717 | −0.123858 | − | 0.992300i | \(-0.539527\pi\) | ||||
−0.123858 | + | 0.992300i | \(0.539527\pi\) | |||||||
\(644\) | − | 5.41708e57i | − | 0.0558678i | ||||||
\(645\) | 1.04725e58 | − | 3.70437e57i | 0.104544 | − | 0.0369794i | ||||
\(646\) | −9.17448e58 | −0.886540 | ||||||||
\(647\) | 1.03073e58i | 0.0964176i | 0.998837 | + | 0.0482088i | \(0.0153513\pi\) | ||||
−0.998837 | + | 0.0482088i | \(0.984649\pi\) | |||||||
\(648\) | −1.05844e59 | − | 2.26535e58i | −0.958496 | − | 0.205144i | ||||
\(649\) | 2.02518e58 | 0.177551 | ||||||||
\(650\) | 1.48219e59i | 1.25813i | ||||||||
\(651\) | 7.20927e58 | + | 2.03811e59i | 0.592503 | + | 1.67505i | ||||
\(652\) | 7.17979e57 | 0.0571363 | ||||||||
\(653\) | − | 1.68043e59i | − | 1.29492i | −0.762100 | − | 0.647460i | \(-0.775831\pi\) | ||
0.762100 | − | 0.647460i | \(-0.224169\pi\) | |||||||
\(654\) | 1.81282e59 | − | 6.41234e58i | 1.35276 | − | 0.478502i | ||||
\(655\) | −1.39740e59 | −1.00984 | ||||||||
\(656\) | 2.37432e58i | 0.166172i | ||||||||
\(657\) | −1.21343e59 | + | 9.81202e58i | −0.822510 | + | 0.665098i | ||||
\(658\) | −6.91082e58 | −0.453718 | ||||||||
\(659\) | 1.35087e59i | 0.859055i | 0.903054 | + | 0.429528i | \(0.141320\pi\) | ||||
−0.903054 | + | 0.429528i | \(0.858680\pi\) | |||||||
\(660\) | −2.19091e57 | − | 6.19387e57i | −0.0134959 | − | 0.0381539i | ||||
\(661\) | 1.83751e59 | 1.09648 | 0.548238 | − | 0.836322i | \(-0.315299\pi\) | ||||
0.548238 | + | 0.836322i | \(0.315299\pi\) | |||||||
\(662\) | 9.33920e58i | 0.539873i | ||||||||
\(663\) | −8.11170e58 | + | 2.86929e58i | −0.454284 | + | 0.160691i | ||||
\(664\) | 7.20472e58 | 0.390920 | ||||||||
\(665\) | − | 6.26965e59i | − | 3.29601i | ||||||
\(666\) | −1.14120e56 | − | 1.41130e56i | −0.000581306 | − | 0.000718886i | ||||
\(667\) | 1.40636e59 | 0.694151 | ||||||||
\(668\) | 9.43374e57i | 0.0451210i | ||||||||
\(669\) | −1.96669e58 | − | 5.55998e58i | −0.0911566 | − | 0.257706i | ||||
\(670\) | 4.74527e59 | 2.13152 | ||||||||
\(671\) | 1.44687e59i | 0.629877i | ||||||||
\(672\) | −2.16968e58 | + | 7.67465e57i | −0.0915463 | + | 0.0323820i | ||||
\(673\) | −1.14509e59 | −0.468298 | −0.234149 | − | 0.972201i | \(-0.575230\pi\) | ||||
−0.234149 | + | 0.972201i | \(0.575230\pi\) | |||||||
\(674\) | − | 1.34839e59i | − | 0.534514i | ||||||
\(675\) | −2.93871e59 | − | 1.80511e59i | −1.12922 | − | 0.693626i | ||||
\(676\) | 1.33590e57 | 0.00497616 | ||||||||
\(677\) | 3.43532e59i | 1.24052i | 0.784395 | + | 0.620262i | \(0.212974\pi\) | ||||
−0.784395 | + | 0.620262i | \(0.787026\pi\) | |||||||
\(678\) | −6.53871e58 | − | 1.84854e59i | −0.228912 | − | 0.647151i | ||||
\(679\) | −3.78211e59 | −1.28372 | ||||||||
\(680\) | − | 2.34852e59i | − | 0.772872i | ||||||
\(681\) | 1.20945e59 | − | 4.27811e58i | 0.385922 | − | 0.136509i | ||||
\(682\) | 3.19614e59 | 0.988903 | ||||||||
\(683\) | 3.14711e58i | 0.0944227i | 0.998885 | + | 0.0472114i | \(0.0150334\pi\) | ||||
−0.998885 | + | 0.0472114i | \(0.984967\pi\) | |||||||
\(684\) | 1.70126e58 | − | 1.37568e58i | 0.0494986 | − | 0.0400256i | ||||
\(685\) | −6.14305e58 | −0.173333 | ||||||||
\(686\) | − | 1.67584e59i | − | 0.458591i | ||||||
\(687\) | 3.51100e58 | + | 9.92586e58i | 0.0931836 | + | 0.263437i | ||||
\(688\) | −2.92782e58 | −0.0753681 | ||||||||
\(689\) | 5.12089e59i | 1.27862i | ||||||||
\(690\) | −6.95422e59 | + | 2.45987e59i | −1.68429 | + | 0.595772i | ||||
\(691\) | 5.83430e59 | 1.37072 | 0.685362 | − | 0.728203i | \(-0.259644\pi\) | ||||
0.685362 | + | 0.728203i | \(0.259644\pi\) | |||||||
\(692\) | 1.78474e58i | 0.0406767i | ||||||||
\(693\) | 2.56277e59 | + | 3.16931e59i | 0.566646 | + | 0.700756i | ||||
\(694\) | −4.49087e59 | −0.963345 | ||||||||
\(695\) | 3.79177e59i | 0.789153i | ||||||||
\(696\) | −9.77028e58 | − | 2.76213e59i | −0.197294 | − | 0.557763i | ||||
\(697\) | −4.23136e58 | −0.0829071 | ||||||||
\(698\) | 3.67313e59i | 0.698348i | ||||||||
\(699\) | 1.29076e59 | − | 4.56572e58i | 0.238136 | − | 0.0842343i | ||||
\(700\) | −3.59578e58 | −0.0643775 | ||||||||
\(701\) | − | 3.33564e59i | − | 0.579563i | −0.957093 | − | 0.289781i | \(-0.906417\pi\) | ||
0.957093 | − | 0.289781i | \(-0.0935826\pi\) | |||||||
\(702\) | 2.94675e59 | − | 4.79728e59i | 0.496893 | − | 0.808939i | ||||
\(703\) | −9.33232e56 | −0.00152731 | ||||||||
\(704\) | − | 4.23792e59i | − | 0.673173i | ||||||
\(705\) | 1.14371e59 | + | 3.23336e59i | 0.176338 | + | 0.498519i | ||||
\(706\) | −3.79621e58 | −0.0568135 | ||||||||
\(707\) | 1.22748e60i | 1.78323i | ||||||||
\(708\) | 6.39803e57 | − | 2.26313e57i | 0.00902294 | − | 0.00319162i | ||||
\(709\) | 1.41570e58 | 0.0193821 | 0.00969106 | − | 0.999953i | \(-0.496915\pi\) | ||||
0.00969106 | + | 0.999953i | \(0.496915\pi\) | |||||||
\(710\) | 5.66888e59i | 0.753480i | ||||||||
\(711\) | −3.06890e58 | + | 2.48158e58i | −0.0396024 | + | 0.0320233i | ||||
\(712\) | 5.79390e59 | 0.725924 | ||||||||
\(713\) | − | 1.30783e60i | − | 1.59101i | ||||||
\(714\) | −1.90995e59 | − | 5.39956e59i | −0.225610 | − | 0.637817i | ||||
\(715\) | −8.69302e59 | −0.997112 | ||||||||
\(716\) | − | 4.50073e58i | − | 0.0501314i | ||||||
\(717\) | 9.00021e59 | − | 3.18358e59i | 0.973532 | − | 0.344361i | ||||
\(718\) | −5.46618e59 | −0.574210 | ||||||||
\(719\) | − | 1.87268e60i | − | 1.91054i | −0.295729 | − | 0.955272i | \(-0.595563\pi\) | ||
0.295729 | − | 0.955272i | \(-0.404437\pi\) | |||||||
\(720\) | 1.00285e60 | + | 1.24020e60i | 0.993693 | + | 1.22888i | ||||
\(721\) | −1.50177e60 | −1.44531 | ||||||||
\(722\) | − | 1.99696e60i | − | 1.86676i | ||||||
\(723\) | 4.59406e58 | + | 1.29877e59i | 0.0417150 | + | 0.117931i | ||||
\(724\) | 7.80511e57 | 0.00688445 | ||||||||
\(725\) | − | 9.33521e59i | − | 0.799882i | ||||||
\(726\) | −5.85717e59 | + | 2.07182e59i | −0.487550 | + | 0.172458i | ||||
\(727\) | −1.13110e60 | −0.914700 | −0.457350 | − | 0.889287i | \(-0.651201\pi\) | ||||
−0.457350 | + | 0.889287i | \(0.651201\pi\) | |||||||
\(728\) | 1.49321e60i | 1.17317i | ||||||||
\(729\) | 5.92273e59 | + | 1.16849e60i | 0.452109 | + | 0.891963i | ||||
\(730\) | 2.21547e60 | 1.64319 | ||||||||
\(731\) | − | 5.21777e58i | − | 0.0376028i | ||||||
\(732\) | 1.61687e58 | + | 4.57101e58i | 0.0113225 | + | 0.0320095i | ||||
\(733\) | 1.19118e60 | 0.810575 | 0.405287 | − | 0.914189i | \(-0.367172\pi\) | ||||
0.405287 | + | 0.914189i | \(0.367172\pi\) | |||||||
\(734\) | 1.97749e60i | 1.30767i | ||||||||
\(735\) | 1.45294e60 | − | 5.13938e59i | 0.933713 | − | 0.330276i | ||||
\(736\) | 1.39226e59 | 0.0869532 | ||||||||
\(737\) | 1.58618e60i | 0.962799i | ||||||||
\(738\) | 2.15293e59 | − | 1.74090e59i | 0.127012 | − | 0.102705i | ||||
\(739\) | 1.01276e60 | 0.580731 | 0.290366 | − | 0.956916i | \(-0.406223\pi\) | ||||
0.290366 | + | 0.956916i | \(0.406223\pi\) | |||||||
\(740\) | 9.39101e55i | 5.23415e-5i | ||||||||
\(741\) | −9.65372e59 | − | 2.72918e60i | −0.523013 | − | 1.47860i | ||||
\(742\) | −3.40873e60 | −1.79519 | ||||||||
\(743\) | 1.88526e60i | 0.965177i | 0.875847 | + | 0.482589i | \(0.160303\pi\) | ||||
−0.875847 | + | 0.482589i | \(0.839697\pi\) | |||||||
\(744\) | −2.56862e60 | + | 9.08579e59i | −1.27840 | + | 0.452200i | ||||
\(745\) | −1.08073e60 | −0.522921 | ||||||||
\(746\) | 5.99994e59i | 0.282249i | ||||||||
\(747\) | −5.48275e59 | − | 6.78037e59i | −0.250764 | − | 0.310114i | ||||
\(748\) | −3.08600e58 | −0.0137234 | ||||||||
\(749\) | 2.76675e60i | 1.19633i | ||||||||
\(750\) | 4.00724e59 | + | 1.13287e60i | 0.168484 | + | 0.476316i | ||||
\(751\) | −1.65912e60 | −0.678327 | −0.339163 | − | 0.940727i | \(-0.610144\pi\) | ||||
−0.339163 | + | 0.940727i | \(0.610144\pi\) | |||||||
\(752\) | − | 9.03956e59i | − | 0.359395i | ||||||
\(753\) | 2.42126e60 | − | 8.56455e59i | 0.936153 | − | 0.331139i | ||||
\(754\) | 1.52392e60 | 0.573012 | ||||||||
\(755\) | − | 4.84096e60i | − | 1.77030i | ||||||
\(756\) | 1.16381e59 | + | 7.14875e58i | 0.0413928 | + | 0.0254257i | ||||
\(757\) | −3.17570e60 | −1.09856 | −0.549282 | − | 0.835637i | \(-0.685099\pi\) | ||||
−0.549282 | + | 0.835637i | \(0.685099\pi\) | |||||||
\(758\) | − | 5.51028e59i | − | 0.185404i | ||||||
\(759\) | −8.22249e59 | − | 2.32456e60i | −0.269108 | − | 0.760787i | ||||
\(760\) | 7.90159e60 | 2.51553 | ||||||||
\(761\) | 2.25357e60i | 0.697901i | 0.937141 | + | 0.348951i | \(0.113462\pi\) | ||||
−0.937141 | + | 0.348951i | \(0.886538\pi\) | |||||||
\(762\) | −6.00303e60 | + | 2.12341e60i | −1.80849 | + | 0.639704i | ||||
\(763\) | 6.17234e60 | 1.80898 | ||||||||
\(764\) | − | 2.10146e59i | − | 0.0599185i | ||||||
\(765\) | −2.21020e60 | + | 1.78721e60i | −0.613113 | + | 0.495776i | ||||
\(766\) | −9.12200e59 | −0.246199 | ||||||||
\(767\) | − | 8.97957e59i | − | 0.235805i | ||||||
\(768\) | −1.47884e59 | − | 4.18078e59i | −0.0377864 | − | 0.106825i | ||||
\(769\) | 6.98979e60 | 1.73784 | 0.868922 | − | 0.494948i | \(-0.164813\pi\) | ||||
0.868922 | + | 0.494948i | \(0.164813\pi\) | |||||||
\(770\) | − | 5.78652e60i | − | 1.39995i | ||||||
\(771\) | 4.45893e60 | − | 1.57722e60i | 1.04976 | − | 0.371323i | ||||
\(772\) | 1.74487e59 | 0.0399760 | ||||||||
\(773\) | 2.04748e60i | 0.456511i | 0.973601 | + | 0.228255i | \(0.0733021\pi\) | ||||
−0.973601 | + | 0.228255i | \(0.926698\pi\) | |||||||
\(774\) | 2.14674e59 | + | 2.65482e59i | 0.0465821 | + | 0.0576069i | ||||
\(775\) | −8.68120e60 | −1.83335 | ||||||||
\(776\) | − | 4.76656e60i | − | 0.979736i | ||||||
\(777\) | −1.94281e57 | − | 5.49246e57i | −0.000388676 | − | 0.00109882i | ||||
\(778\) | −2.38262e59 | −0.0463963 | ||||||||
\(779\) | − | 1.42364e60i | − | 0.269845i | ||||||
\(780\) | −2.74634e59 | + | 9.71444e58i | −0.0506720 | + | 0.0179238i | ||||
\(781\) | −1.89491e60 | −0.340344 | ||||||||
\(782\) | 3.46483e60i | 0.605816i | ||||||||
\(783\) | −1.85593e60 | + | 3.02144e60i | −0.315911 | + | 0.514301i | ||||
\(784\) | −4.06201e60 | −0.673138 | ||||||||
\(785\) | 5.14733e60i | 0.830461i | ||||||||
\(786\) | −1.43225e60 | − | 4.04907e60i | −0.224981 | − | 0.636037i | ||||
\(787\) | −9.53164e57 | −0.00145780 | −0.000728900 | − | 1.00000i | \(-0.500232\pi\) | ||||
−0.000728900 | 1.00000i | \(0.500232\pi\) | ||||||||
\(788\) | 4.88603e59i | 0.0727622i | ||||||||
\(789\) | −6.11454e60 | + | 2.16285e60i | −0.886639 | + | 0.313624i | ||||
\(790\) | 5.60320e59 | 0.0791165 | ||||||||
\(791\) | − | 6.29398e60i | − | 0.865405i | ||||||
\(792\) | −3.99426e60 | + | 3.22984e60i | −0.534819 | + | 0.432466i | ||||
\(793\) | 6.41536e60 | 0.836535 | ||||||||
\(794\) | 1.24418e61i | 1.57998i | ||||||||
\(795\) | 5.64130e60 | + | 1.59484e61i | 0.697701 | + | 1.97245i | ||||
\(796\) | −3.13073e59 | −0.0377113 | ||||||||
\(797\) | − | 5.56964e59i | − | 0.0653435i | −0.999466 | − | 0.0326718i | \(-0.989598\pi\) | ||
0.999466 | − | 0.0326718i | \(-0.0104016\pi\) | |||||||
\(798\) | 1.81668e61 | − | 6.42601e60i | 2.07595 | − | 0.734313i | ||||
\(799\) | 1.61097e60 | 0.179310 | ||||||||
\(800\) | − | 9.24160e59i | − | 0.100198i | ||||||
\(801\) | −4.40912e60 | − | 5.45265e60i | −0.465660 | − | 0.575870i | ||||
\(802\) | 9.47541e60 | 0.974847 | ||||||||
\(803\) | 7.40558e60i | 0.742220i | ||||||||
\(804\) | 1.77255e59 | + | 5.01114e59i | 0.0173070 | + | 0.0489282i | ||||
\(805\) | −2.36780e61 | −2.25233 | ||||||||
\(806\) | − | 1.41716e61i | − | 1.31335i | ||||||
\(807\) | 2.74927e60 | − | 9.72481e59i | 0.248241 | − | 0.0878086i | ||||
\(808\) | −1.54699e61 | −1.36097 | ||||||||
\(809\) | 1.17085e61i | 1.00365i | 0.864969 | + | 0.501826i | \(0.167338\pi\) | ||||
−0.864969 | + | 0.501826i | \(0.832662\pi\) | |||||||
\(810\) | 3.89246e60 | − | 1.81867e61i | 0.325116 | − | 1.51904i | ||||
\(811\) | 2.34143e60 | 0.190565 | 0.0952823 | − | 0.995450i | \(-0.469625\pi\) | ||||
0.0952823 | + | 0.995450i | \(0.469625\pi\) | |||||||
\(812\) | 3.69700e59i | 0.0293206i | ||||||||
\(813\) | 7.06006e59 | + | 1.99593e60i | 0.0545641 | + | 0.154257i | ||||
\(814\) | −8.61318e57 | −0.000648711 | ||||||||
\(815\) | − | 3.13828e61i | − | 2.30346i | ||||||
\(816\) | 7.06278e60 | − | 2.49827e60i | 0.505222 | − | 0.178709i | ||||
\(817\) | 1.75552e60 | 0.122389 | ||||||||
\(818\) | 2.35080e61i | 1.59734i | ||||||||
\(819\) | 1.40526e61 | − | 1.13632e61i | 0.930669 | − | 0.752558i | ||||
\(820\) | −1.43259e59 | −0.00924767 | ||||||||
\(821\) | 1.15239e61i | 0.725090i | 0.931966 | + | 0.362545i | \(0.118092\pi\) | ||||
−0.931966 | + | 0.362545i | \(0.881908\pi\) | |||||||
\(822\) | −6.29626e59 | − | 1.78000e60i | −0.0386166 | − | 0.109172i | ||||
\(823\) | 8.97873e60 | 0.536807 | 0.268404 | − | 0.963307i | \(-0.413504\pi\) | ||||
0.268404 | + | 0.963307i | \(0.413504\pi\) | |||||||
\(824\) | − | 1.89267e61i | − | 1.10307i | ||||||
\(825\) | −1.54301e61 | + | 5.45797e60i | −0.876668 | + | 0.310097i | ||||
\(826\) | 5.97726e60 | 0.331071 | ||||||||
\(827\) | 2.40762e60i | 0.130009i | 0.997885 | + | 0.0650044i | \(0.0207062\pi\) | ||||
−0.997885 | + | 0.0650044i | \(0.979294\pi\) | |||||||
\(828\) | −5.19538e59 | − | 6.42499e59i | −0.0273514 | − | 0.0338248i | ||||
\(829\) | −2.02726e61 | −1.04055 | −0.520276 | − | 0.853998i | \(-0.674171\pi\) | ||||
−0.520276 | + | 0.853998i | \(0.674171\pi\) | |||||||
\(830\) | 1.23796e61i | 0.619536i | ||||||||
\(831\) | −3.08288e60 | − | 8.71552e60i | −0.150430 | − | 0.425277i | ||||
\(832\) | −1.87908e61 | −0.894036 | ||||||||
\(833\) | − | 7.23905e60i | − | 0.335843i | ||||||
\(834\) | −1.09869e61 | + | 3.88633e60i | −0.497038 | + | 0.175814i | ||||
\(835\) | 4.12348e61 | 1.81906 | ||||||||
\(836\) | − | 1.03828e60i | − | 0.0446668i | ||||||
\(837\) | 2.80977e61 | + | 1.72591e61i | 1.17879 | + | 0.724074i | ||||
\(838\) | −1.21271e61 | −0.496173 | ||||||||
\(839\) | − | 2.77679e61i | − | 1.10801i | −0.832515 | − | 0.554003i | \(-0.813100\pi\) | ||
0.832515 | − | 0.554003i | \(-0.186900\pi\) | |||||||
\(840\) | 1.64496e61 | + | 4.65042e61i | 0.640162 | + | 1.80978i | ||||
\(841\) | 1.67481e61 | 0.635695 | ||||||||
\(842\) | 3.68021e61i | 1.36244i | ||||||||
\(843\) | −4.46788e61 | + | 1.58039e61i | −1.61333 | + | 0.570671i | ||||
\(844\) | −1.00039e60 | −0.0352352 | ||||||||
\(845\) | − | 5.83921e60i | − | 0.200615i | ||||||
\(846\) | −8.19666e60 | + | 6.62799e60i | −0.274701 | + | 0.222128i | ||||
\(847\) | −1.99427e61 | −0.651978 | ||||||||
\(848\) | − | 4.45871e61i | − | 1.42199i | ||||||
\(849\) | 7.04814e60 | + | 1.99256e61i | 0.219287 | + | 0.619941i | ||||
\(850\) | 2.29991e61 | 0.698092 | ||||||||
\(851\) | 3.52444e58i | 0.00104369i | ||||||||
\(852\) | −5.98650e59 | + | 2.11756e59i | −0.0172958 | + | 0.00611793i | ||||
\(853\) | 1.30625e61 | 0.368210 | 0.184105 | − | 0.982907i | \(-0.441061\pi\) | ||||
0.184105 | + | 0.982907i | \(0.441061\pi\) | |||||||
\(854\) | 4.27039e61i | 1.17450i | ||||||||
\(855\) | −6.01306e61 | − | 7.43620e61i | −1.61364 | − | 1.99555i | ||||
\(856\) | −3.48692e61 | −0.913046 | ||||||||
\(857\) | 6.41360e61i | 1.63872i | 0.573280 | + | 0.819360i | \(0.305671\pi\) | ||||
−0.573280 | + | 0.819360i | \(0.694329\pi\) | |||||||
\(858\) | −8.90982e60 | − | 2.51887e61i | −0.222145 | − | 0.628019i | ||||
\(859\) | 3.48827e61 | 0.848699 | 0.424350 | − | 0.905498i | \(-0.360503\pi\) | ||||
0.424350 | + | 0.905498i | \(0.360503\pi\) | |||||||
\(860\) | − | 1.76656e59i | − | 0.00419431i | ||||||
\(861\) | 8.37871e60 | − | 2.96374e60i | 0.194138 | − | 0.0686711i | ||||
\(862\) | −1.27025e61 | −0.287235 | ||||||||
\(863\) | − | 5.40809e61i | − | 1.19349i | −0.802432 | − | 0.596743i | \(-0.796461\pi\) | ||
0.802432 | − | 0.596743i | \(-0.203539\pi\) | |||||||
\(864\) | −1.83732e60 | + | 2.99114e60i | −0.0395727 | + | 0.0644242i | ||||
\(865\) | 7.80106e61 | 1.63989 | ||||||||
\(866\) | − | 9.28372e61i | − | 1.90479i | ||||||
\(867\) | −1.21997e61 | − | 3.44894e61i | −0.244314 | − | 0.690692i | ||||
\(868\) | 3.43800e60 | 0.0672034 | ||||||||
\(869\) | 1.87296e60i | 0.0357365i | ||||||||
\(870\) | 4.74606e61 | − | 1.67879e61i | 0.883952 | − | 0.312674i | ||||
\(871\) | 7.03308e61 | 1.27869 | ||||||||
\(872\) | 7.77895e61i | 1.38062i | ||||||||
\(873\) | −4.48582e61 | + | 3.62732e61i | −0.777217 | + | 0.628474i | ||||
\(874\) | −1.16574e62 | −1.97180 | ||||||||
\(875\) | 3.85725e61i | 0.636956i | ||||||||
\(876\) | 8.27572e59 | + | 2.33960e60i | 0.0133420 | + | 0.0377187i | ||||
\(877\) | 5.70025e61 | 0.897227 | 0.448613 | − | 0.893726i | \(-0.351918\pi\) | ||||
0.448613 | + | 0.893726i | \(0.351918\pi\) | |||||||
\(878\) | − | 2.63291e61i | − | 0.404624i | ||||||
\(879\) | 2.78521e61 | − | 9.85193e60i | 0.417919 | − | 0.147827i | ||||
\(880\) | 7.56894e61 | 1.10892 | ||||||||
\(881\) | − | 1.05231e62i | − | 1.50539i | −0.658369 | − | 0.752696i | \(-0.728753\pi\) | ||
0.658369 | − | 0.752696i | \(-0.271247\pi\) | |||||||
\(882\) | 2.97835e61 | + | 3.68325e61i | 0.416040 | + | 0.514507i | ||||
\(883\) | −1.12382e62 | −1.53292 | −0.766462 | − | 0.642290i | \(-0.777985\pi\) | ||||
−0.766462 | + | 0.642290i | \(0.777985\pi\) | |||||||
\(884\) | 1.36832e60i | 0.0182260i | ||||||||
\(885\) | −9.89212e60 | − | 2.79657e61i | −0.128671 | − | 0.363762i | ||||
\(886\) | 1.18847e62 | 1.50966 | ||||||||
\(887\) | 1.08353e62i | 1.34414i | 0.740490 | + | 0.672068i | \(0.234594\pi\) | ||||
−0.740490 | + | 0.672068i | \(0.765406\pi\) | |||||||
\(888\) | 6.92210e58 | − | 2.44850e58i | 0.000838620 | − | 0.000296639i | ||||
\(889\) | −2.04393e62 | −2.41841 | ||||||||
\(890\) | 9.95544e61i | 1.15046i | ||||||||
\(891\) | 6.07921e61 | + | 1.30112e61i | 0.686144 | + | 0.146853i | ||||
\(892\) | −9.37887e59 | −0.0103392 | ||||||||
\(893\) | 5.42011e61i | 0.583616i | ||||||||
\(894\) | −1.10768e61 | − | 3.13150e61i | −0.116500 | − | 0.329355i | ||||
\(895\) | −1.96726e62 | −2.02106 | ||||||||
\(896\) | − | 1.34757e62i | − | 1.35234i | ||||||
\(897\) | −1.03070e62 | + | 3.64582e61i | −1.01040 | + | 0.357400i | ||||
\(898\) | −2.80589e61 | −0.268700 | ||||||||
\(899\) | 8.92559e61i | 0.834994i | ||||||||
\(900\) | −4.26481e60 | + | 3.44861e60i | −0.0389769 | + | 0.0315175i | ||||
\(901\) | 7.94603e61 | 0.709463 | ||||||||
\(902\) | − | 1.31394e61i | − | 0.114614i | ||||||
\(903\) | 3.65465e60 | + | 1.03320e61i | 0.0311460 | + | 0.0880521i | ||||
\(904\) | 7.93226e61 | 0.660480 | ||||||||
\(905\) | − | 3.41160e61i | − | 0.277548i | ||||||
\(906\) | 1.40271e62 | − | 4.96169e61i | 1.11500 | − | 0.394401i | ||||
\(907\) | 2.30658e62 | 1.79149 | 0.895747 | − | 0.444563i | \(-0.146641\pi\) | ||||
0.895747 | + | 0.444563i | \(0.146641\pi\) | |||||||
\(908\) | − | 2.04017e60i | − | 0.0154833i | ||||||
\(909\) | 1.17725e62 | + | 1.45587e62i | 0.873023 | + | 1.07965i | ||||
\(910\) | −2.56573e62 | −1.85926 | ||||||||
\(911\) | − | 5.09186e60i | − | 0.0360571i | −0.999837 | − | 0.0180285i | \(-0.994261\pi\) | ||
0.999837 | − | 0.0180285i | \(-0.00573898\pi\) | |||||||
\(912\) | 8.40541e61 | + | 2.37627e62i | 0.581658 | + | 1.64439i | ||||
\(913\) | −4.13808e61 | −0.279842 | ||||||||
\(914\) | − | 3.78591e61i | − | 0.250208i | ||||||
\(915\) | 1.99798e62 | − | 7.06732e61i | 1.29047 | − | 0.456470i | ||||
\(916\) | 1.67435e60 | 0.0105692 | ||||||||
\(917\) | − | 1.37864e62i | − | 0.850542i | ||||||
\(918\) | −7.44389e61 | − | 4.57243e61i | −0.448853 | − | 0.275709i | ||||
\(919\) | 8.15286e61 | 0.480490 | 0.240245 | − | 0.970712i | \(-0.422772\pi\) | ||||
0.240245 | + | 0.970712i | \(0.422772\pi\) | |||||||
\(920\) | − | 2.98412e62i | − | 1.71898i | ||||||
\(921\) | −7.51899e61 | − | 2.12567e62i | −0.423357 | − | 1.19686i | ||||
\(922\) | −3.09069e62 | −1.70101 | ||||||||
\(923\) | 8.40198e61i | 0.452008i | ||||||||
\(924\) | 6.11073e60 | − | 2.16151e60i | 0.0321353 | − | 0.0113670i | ||||
\(925\) | 2.33947e59 | 0.00120266 | ||||||||
\(926\) | − | 2.41331e62i | − | 1.21278i | ||||||
\(927\) | −1.78119e62 | + | 1.44031e62i | −0.875056 | + | 0.707588i | ||||
\(928\) | −9.50176e60 | −0.0456349 | ||||||||
\(929\) | 2.00651e62i | 0.942130i | 0.882098 | + | 0.471065i | \(0.156130\pi\) | ||||
−0.882098 | + | 0.471065i | \(0.843870\pi\) | |||||||
\(930\) | −1.56118e62 | − | 4.41356e62i | −0.716655 | − | 2.02603i | ||||
\(931\) | 2.43558e62 | 1.09310 | ||||||||
\(932\) | − | 2.17733e60i | − | 0.00955409i | ||||||
\(933\) | −1.33227e62 | + | 4.71253e61i | −0.571579 | + | 0.202181i | ||||
\(934\) | 4.39173e62 | 1.84226 | ||||||||
\(935\) | 1.34889e62i | 0.553263i | ||||||||
\(936\) | 1.43210e62 | + | 1.77104e62i | 0.574355 | + | 0.710290i | ||||
\(937\) | −2.70506e62 | −1.06083 | −0.530416 | − | 0.847738i | \(-0.677964\pi\) | ||||
−0.530416 | + | 0.847738i | \(0.677964\pi\) | |||||||
\(938\) | 4.68158e62i | 1.79528i | ||||||||
\(939\) | 2.23471e61 | + | 6.31768e61i | 0.0837999 | + | 0.236908i | ||||
\(940\) | 5.45420e60 | 0.0200007 | ||||||||
\(941\) | 2.30368e61i | 0.0826113i | 0.999147 | + | 0.0413057i | \(0.0131517\pi\) | ||||
−0.999147 | + | 0.0413057i | \(0.986848\pi\) | |||||||
\(942\) | −1.49148e62 | + | 5.27570e61i | −0.523056 | + | 0.185017i | ||||
\(943\) | −5.37652e61 | −0.184398 | ||||||||
\(944\) | 7.81843e61i | 0.262245i | ||||||||
\(945\) | 3.12471e62 | − | 5.08701e62i | 1.02504 | − | 1.66876i | ||||
\(946\) | 1.62024e61 | 0.0519835 | ||||||||
\(947\) | 1.12155e62i | 0.351940i | 0.984396 | + | 0.175970i | \(0.0563062\pi\) | ||||
−0.984396 | + | 0.175970i | \(0.943694\pi\) | |||||||
\(948\) | 2.09303e59 | + | 5.91714e59i | 0.000642391 | + | 0.00181609i | ||||
\(949\) | 3.28361e62 | 0.985737 | ||||||||
\(950\) | 7.73803e62i | 2.27214i | ||||||||
\(951\) | −1.47786e62 | + | 5.22752e61i | −0.424465 | + | 0.150143i | ||||
\(952\) | 2.31700e62 | 0.650954 | ||||||||
\(953\) | − | 5.87297e62i | − | 1.61401i | −0.590542 | − | 0.807007i | \(-0.701086\pi\) | ||
0.590542 | − | 0.807007i | \(-0.298914\pi\) | |||||||
\(954\) | −4.04296e62 | + | 3.26922e62i | −1.08688 | + | 0.878877i | ||||
\(955\) | −9.18547e62 | −2.41563 | ||||||||
\(956\) | − | 1.51820e61i | − | 0.0390584i | ||||||
\(957\) | 5.61162e61 | + | 1.58644e62i | 0.141233 | + | 0.399277i | ||||
\(958\) | 5.99086e62 | 1.47507 | ||||||||
\(959\) | − | 6.06060e61i | − | 0.145991i | ||||||
\(960\) | −5.85215e62 | + | 2.07004e62i | −1.37918 | + | 0.487846i | ||||
\(961\) | 3.96326e62 | 0.913822 | ||||||||
\(962\) | 3.81906e59i | 0.000861548i | ||||||||
\(963\) | 2.65352e62 | + | 3.28154e62i | 0.585694 | + | 0.724313i | ||||
\(964\) | 2.19084e60 | 0.00473143 | ||||||||
\(965\) | − | 7.62680e62i | − | 1.61164i | ||||||
\(966\) | −2.42685e62 | − | 6.86088e62i | −0.501791 | − | 1.41860i | ||||
\(967\) | −1.68585e62 | −0.341086 | −0.170543 | − | 0.985350i | \(-0.554552\pi\) | ||||
−0.170543 | + | 0.985350i | \(0.554552\pi\) | |||||||
\(968\) | − | 2.51336e62i | − | 0.497592i | ||||||
\(969\) | −4.23484e62 | + | 1.49796e62i | −0.820422 | + | 0.290202i | ||||
\(970\) | 8.19020e62 | 1.55270 | ||||||||
\(971\) | − | 9.90017e62i | − | 1.83670i | −0.395766 | − | 0.918351i | \(-0.629521\pi\) | ||
0.395766 | − | 0.918351i | \(-0.370479\pi\) | |||||||
\(972\) | 2.06597e61 | − | 2.68295e60i | 0.0375088 | − | 0.00487104i | ||||
\(973\) | −3.74088e62 | −0.664666 | ||||||||
\(974\) | 5.16408e62i | 0.897955i | ||||||||
\(975\) | 2.42005e62 | + | 6.84164e62i | 0.411838 | + | 1.16430i | ||||
\(976\) | −5.58580e62 | −0.930334 | ||||||||
\(977\) | 6.54803e62i | 1.06739i | 0.845676 | + | 0.533697i | \(0.179198\pi\) | ||||
−0.845676 | + | 0.533697i | \(0.820802\pi\) | |||||||
\(978\) | 9.09340e62 | − | 3.21654e62i | 1.45081 | − | 0.513184i | ||||
\(979\) | −3.32776e62 | −0.519656 | ||||||||
\(980\) | − | 2.45089e61i | − | 0.0374608i | ||||||
\(981\) | 7.32078e62 | − | 5.91973e62i | 1.09524 | − | 0.885631i | ||||
\(982\) | −5.73964e62 | −0.840511 | ||||||||
\(983\) | − | 6.63799e62i | − | 0.951509i | −0.879578 | − | 0.475754i | \(-0.842175\pi\) | ||
0.879578 | − | 0.475754i | \(-0.157825\pi\) | |||||||
\(984\) | 3.73518e61 | + | 1.05596e62i | 0.0524100 | + | 0.148167i | ||||
\(985\) | 2.13568e63 | 2.93343 | ||||||||
\(986\) | − | 2.36465e62i | − | 0.317945i | ||||||
\(987\) | −3.18996e62 | + | 1.12836e62i | −0.419880 | + | 0.148521i | ||||
\(988\) | −4.60372e61 | −0.0593216 | ||||||||
\(989\) | − | 6.62989e61i | − | 0.0836343i | ||||||
\(990\) | −5.54970e62 | − | 6.86318e62i | −0.685379 | − | 0.847591i | ||||
\(991\) | −5.83179e62 | −0.705108 | −0.352554 | − | 0.935792i | \(-0.614687\pi\) | ||||
−0.352554 | + | 0.935792i | \(0.614687\pi\) | |||||||
\(992\) | 8.83609e61i | 0.104596i | ||||||||
\(993\) | 1.52485e62 | + | 4.31087e62i | 0.176723 | + | 0.499610i | ||||
\(994\) | −5.59279e62 | −0.634621 | ||||||||
\(995\) | 1.36844e63i | 1.52034i | ||||||||
\(996\) | −1.30732e61 | + | 4.62429e60i | −0.0142212 | + | 0.00503036i | ||||
\(997\) | −1.50217e63 | −1.60000 | −0.800001 | − | 0.599999i | \(-0.795168\pi\) | ||||
−0.800001 | + | 0.599999i | \(0.795168\pi\) | |||||||
\(998\) | 8.90729e62i | 0.928976i | ||||||||
\(999\) | −7.57196e59 | − | 4.65110e59i | −0.000773273 | − | 0.000474985i |
(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 | 3.43.b.b.2.4 | ✓ | 12 | |
3.2 | odd | 2 | inner | 3.43.b.b.2.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.43.b.b.2.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
3.43.b.b.2.9 | yes | 12 | 3.2 | odd | 2 | inner |