Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,11,Mod(14,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.14");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.d (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: | \(9.53035879011\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 17880 x^{14} + 140656106 x^{12} + 568287997200 x^{10} + \cdots + 16\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24}\cdot 3^{32}\cdot 5^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 14.3 | ||
Root | \(6.53233 + 63.3725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.14 |
Dual form | 15.11.d.c.14.4 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −36.7249 | −1.14765 | −0.573827 | − | 0.818977i | \(-0.694542\pi\) | ||||
−0.573827 | + | 0.818977i | \(0.694542\pi\) | |||||||
\(3\) | 151.342 | − | 190.117i | 0.622806 | − | 0.782376i | ||||
\(4\) | 324.720 | 0.317110 | ||||||||
\(5\) | 2839.18 | − | 1305.64i | 0.908537 | − | 0.417804i | ||||
\(6\) | −5558.02 | + | 6982.05i | −0.714766 | + | 0.897897i | ||||
\(7\) | 17185.2i | 1.02250i | 0.859432 | + | 0.511250i | \(0.170818\pi\) | ||||
−0.859432 | + | 0.511250i | \(0.829182\pi\) | |||||||
\(8\) | 25681.0 | 0.783722 | ||||||||
\(9\) | −13240.3 | − | 57545.5i | −0.224225 | − | 0.974537i | ||||
\(10\) | −104269. | + | 47949.4i | −1.04269 | + | 0.479494i | ||||
\(11\) | − | 57743.7i | − | 0.358543i | −0.983800 | − | 0.179271i | \(-0.942626\pi\) | ||
0.983800 | − | 0.179271i | \(-0.0573740\pi\) | |||||||
\(12\) | 49143.8 | − | 61735.0i | 0.197498 | − | 0.248099i | ||||
\(13\) | − | 726186.i | − | 1.95583i | −0.209002 | − | 0.977915i | \(-0.567021\pi\) | ||
0.209002 | − | 0.977915i | \(-0.432979\pi\) | |||||||
\(14\) | − | 631124.i | − | 1.17348i | ||||||
\(15\) | 181462. | − | 737375.i | 0.238963 | − | 0.971029i | ||||
\(16\) | −1.27565e6 | −1.21655 | ||||||||
\(17\) | 853907. | 0.601404 | 0.300702 | − | 0.953718i | \(-0.402779\pi\) | ||||
0.300702 | + | 0.953718i | \(0.402779\pi\) | |||||||
\(18\) | 486248. | + | 2.11335e6i | 0.257333 | + | 1.11843i | ||||
\(19\) | −3.02605e6 | −1.22210 | −0.611051 | − | 0.791591i | \(-0.709253\pi\) | ||||
−0.611051 | + | 0.791591i | \(0.709253\pi\) | |||||||
\(20\) | 921940. | − | 423967.i | 0.288106 | − | 0.132490i | ||||
\(21\) | 3.26720e6 | + | 2.60084e6i | 0.799980 | + | 0.636820i | ||||
\(22\) | 2.12063e6i | 0.411483i | ||||||||
\(23\) | −1.73585e6 | −0.269694 | −0.134847 | − | 0.990866i | \(-0.543054\pi\) | ||||
−0.134847 | + | 0.990866i | \(0.543054\pi\) | |||||||
\(24\) | 3.88661e6 | − | 4.88240e6i | 0.488107 | − | 0.613165i | ||||
\(25\) | 6.35625e6 | − | 7.41388e6i | 0.650880 | − | 0.759181i | ||||
\(26\) | 2.66691e7i | 2.24462i | ||||||||
\(27\) | −1.29442e7 | − | 6.19183e6i | −0.902104 | − | 0.431519i | ||||
\(28\) | 5.58038e6i | 0.324245i | ||||||||
\(29\) | − | 2.25917e7i | − | 1.10144i | −0.834691 | − | 0.550718i | \(-0.814354\pi\) | ||
0.834691 | − | 0.550718i | \(-0.185646\pi\) | |||||||
\(30\) | −6.66419e6 | + | 2.70800e7i | −0.274246 | + | 1.11441i | ||||
\(31\) | 1.06363e7 | 0.371519 | 0.185760 | − | 0.982595i | \(-0.440525\pi\) | ||||
0.185760 | + | 0.982595i | \(0.440525\pi\) | |||||||
\(32\) | 2.05507e7 | 0.612458 | ||||||||
\(33\) | −1.09781e7 | − | 8.73903e6i | −0.280515 | − | 0.223303i | ||||
\(34\) | −3.13597e7 | −0.690204 | ||||||||
\(35\) | 2.24376e7 | + | 4.87918e7i | 0.427205 | + | 0.928980i | ||||
\(36\) | −4.29939e6 | − | 1.86862e7i | −0.0711040 | − | 0.309035i | ||||
\(37\) | 1.97180e7i | 0.284351i | 0.989841 | + | 0.142175i | \(0.0454097\pi\) | ||||
−0.989841 | + | 0.142175i | \(0.954590\pi\) | |||||||
\(38\) | 1.11131e8 | 1.40255 | ||||||||
\(39\) | −1.38061e8 | − | 1.09902e8i | −1.53020 | − | 1.21810i | ||||
\(40\) | 7.29129e7 | − | 3.35301e7i | 0.712040 | − | 0.327442i | ||||
\(41\) | − | 8.40244e7i | − | 0.725248i | −0.931936 | − | 0.362624i | \(-0.881881\pi\) | ||
0.931936 | − | 0.362624i | \(-0.118119\pi\) | |||||||
\(42\) | −1.19988e8 | − | 9.55155e7i | −0.918101 | − | 0.730849i | ||||
\(43\) | 7.92041e7i | 0.538773i | 0.963032 | + | 0.269386i | \(0.0868208\pi\) | ||||
−0.963032 | + | 0.269386i | \(0.913179\pi\) | |||||||
\(44\) | − | 1.87506e7i | − | 0.113697i | ||||||
\(45\) | −1.12725e8 | − | 1.46095e8i | −0.610882 | − | 0.791721i | ||||
\(46\) | 6.37488e7 | 0.309516 | ||||||||
\(47\) | 1.87387e8 | 0.817054 | 0.408527 | − | 0.912746i | \(-0.366043\pi\) | ||||
0.408527 | + | 0.912746i | \(0.366043\pi\) | |||||||
\(48\) | −1.93059e8 | + | 2.42523e8i | −0.757676 | + | 0.951801i | ||||
\(49\) | −1.28549e7 | −0.0455080 | ||||||||
\(50\) | −2.33433e8 | + | 2.72274e8i | −0.746985 | + | 0.871277i | ||||
\(51\) | 1.29232e8 | − | 1.62343e8i | 0.374558 | − | 0.470524i | ||||
\(52\) | − | 2.35808e8i | − | 0.620213i | ||||||
\(53\) | 5.59650e8 | 1.33825 | 0.669125 | − | 0.743149i | \(-0.266669\pi\) | ||||
0.669125 | + | 0.743149i | \(0.266669\pi\) | |||||||
\(54\) | 4.75375e8 | + | 2.27395e8i | 1.03530 | + | 0.495235i | ||||
\(55\) | −7.53923e7 | − | 1.63945e8i | −0.149801 | − | 0.325749i | ||||
\(56\) | 4.41332e8i | 0.801356i | ||||||||
\(57\) | −4.57968e8 | + | 5.75304e8i | −0.761133 | + | 0.956144i | ||||
\(58\) | 8.29680e8i | 1.26407i | ||||||||
\(59\) | 6.70180e8i | 0.937414i | 0.883354 | + | 0.468707i | \(0.155280\pi\) | ||||
−0.883354 | + | 0.468707i | \(0.844720\pi\) | |||||||
\(60\) | 5.89245e7 | − | 2.39441e8i | 0.0757774 | − | 0.307923i | ||||
\(61\) | −7.73815e8 | −0.916195 | −0.458097 | − | 0.888902i | \(-0.651469\pi\) | ||||
−0.458097 | + | 0.888902i | \(0.651469\pi\) | |||||||
\(62\) | −3.90616e8 | −0.426375 | ||||||||
\(63\) | 9.88929e8 | − | 2.27536e8i | 0.996465 | − | 0.229270i | ||||
\(64\) | 5.51539e8 | 0.513661 | ||||||||
\(65\) | −9.48136e8 | − | 2.06177e9i | −0.817154 | − | 1.77694i | ||||
\(66\) | 4.03169e8 | + | 3.20940e8i | 0.321935 | + | 0.256274i | ||||
\(67\) | − | 1.72739e9i | − | 1.27943i | −0.768612 | − | 0.639715i | \(-0.779052\pi\) | ||
0.768612 | − | 0.639715i | \(-0.220948\pi\) | |||||||
\(68\) | 2.77281e8 | 0.190711 | ||||||||
\(69\) | −2.62706e8 | + | 3.30015e8i | −0.167967 | + | 0.211003i | ||||
\(70\) | −8.24019e8 | − | 1.79187e9i | −0.490283 | − | 1.06615i | ||||
\(71\) | − | 9.90045e8i | − | 0.548736i | −0.961625 | − | 0.274368i | \(-0.911531\pi\) | ||
0.961625 | − | 0.274368i | \(-0.0884686\pi\) | |||||||
\(72\) | −3.40023e8 | − | 1.47782e9i | −0.175730 | − | 0.763766i | ||||
\(73\) | 3.12724e9i | 1.50851i | 0.656584 | + | 0.754253i | \(0.272001\pi\) | ||||
−0.656584 | + | 0.754253i | \(0.727999\pi\) | |||||||
\(74\) | − | 7.24143e8i | − | 0.326337i | ||||||
\(75\) | −4.47540e8 | − | 2.33046e9i | −0.188593 | − | 0.982055i | ||||
\(76\) | −9.82620e8 | −0.387541 | ||||||||
\(77\) | 9.92335e8 | 0.366610 | ||||||||
\(78\) | 5.07027e9 | + | 4.03616e9i | 1.75613 | + | 1.39796i | ||||
\(79\) | 1.32376e9 | 0.430203 | 0.215102 | − | 0.976592i | \(-0.430992\pi\) | ||||
0.215102 | + | 0.976592i | \(0.430992\pi\) | |||||||
\(80\) | −3.62179e9 | + | 1.66553e9i | −1.10528 | + | 0.508280i | ||||
\(81\) | −3.13617e9 | + | 1.52383e9i | −0.899446 | + | 0.437032i | ||||
\(82\) | 3.08579e9i | 0.832333i | ||||||||
\(83\) | −1.92072e9 | −0.487612 | −0.243806 | − | 0.969824i | \(-0.578396\pi\) | ||||
−0.243806 | + | 0.969824i | \(0.578396\pi\) | |||||||
\(84\) | 1.06093e9 | + | 8.44545e8i | 0.253682 | + | 0.201942i | ||||
\(85\) | 2.42440e9 | − | 1.11489e9i | 0.546398 | − | 0.251269i | ||||
\(86\) | − | 2.90877e9i | − | 0.618325i | ||||||
\(87\) | −4.29508e9 | − | 3.41908e9i | −0.861738 | − | 0.685982i | ||||
\(88\) | − | 1.48291e9i | − | 0.280998i | ||||||
\(89\) | 1.80622e9i | 0.323460i | 0.986835 | + | 0.161730i | \(0.0517074\pi\) | ||||
−0.986835 | + | 0.161730i | \(0.948293\pi\) | |||||||
\(90\) | 4.13982e9 | + | 5.36532e9i | 0.701082 | + | 0.908622i | ||||
\(91\) | 1.24796e10 | 1.99984 | ||||||||
\(92\) | −5.63665e8 | −0.0855228 | ||||||||
\(93\) | 1.60971e9 | − | 2.02214e9i | 0.231384 | − | 0.290668i | ||||
\(94\) | −6.88179e9 | −0.937696 | ||||||||
\(95\) | −8.59149e9 | + | 3.95092e9i | −1.11033 | + | 0.510599i | ||||
\(96\) | 3.11018e9 | − | 3.90704e9i | 0.381443 | − | 0.479173i | ||||
\(97\) | 7.72264e8i | 0.0899305i | 0.998989 | + | 0.0449653i | \(0.0143177\pi\) | ||||
−0.998989 | + | 0.0449653i | \(0.985682\pi\) | |||||||
\(98\) | 4.72095e8 | 0.0522275 | ||||||||
\(99\) | −3.32289e9 | + | 7.64542e8i | −0.349413 | + | 0.0803943i | ||||
\(100\) | 2.06400e9 | − | 2.40744e9i | 0.206400 | − | 0.240744i | ||||
\(101\) | 8.59370e9i | 0.817661i | 0.912610 | + | 0.408830i | \(0.134063\pi\) | ||||
−0.912610 | + | 0.408830i | \(0.865937\pi\) | |||||||
\(102\) | −4.74603e9 | + | 5.96202e9i | −0.429863 | + | 0.539999i | ||||
\(103\) | 8.48204e9i | 0.731668i | 0.930680 | + | 0.365834i | \(0.119216\pi\) | ||||
−0.930680 | + | 0.365834i | \(0.880784\pi\) | |||||||
\(104\) | − | 1.86492e10i | − | 1.53283i | ||||||
\(105\) | 1.26719e10 | + | 3.11846e9i | 0.992878 | + | 0.244340i | ||||
\(106\) | −2.05531e10 | −1.53585 | ||||||||
\(107\) | 2.59046e10 | 1.84696 | 0.923482 | − | 0.383642i | \(-0.125330\pi\) | ||||
0.923482 | + | 0.383642i | \(0.125330\pi\) | |||||||
\(108\) | −4.20325e9 | − | 2.01061e9i | −0.286066 | − | 0.136839i | ||||
\(109\) | −1.71341e10 | −1.11360 | −0.556800 | − | 0.830647i | \(-0.687971\pi\) | ||||
−0.556800 | + | 0.830647i | \(0.687971\pi\) | |||||||
\(110\) | 2.76878e9 | + | 6.02085e9i | 0.171919 | + | 0.373848i | ||||
\(111\) | 3.74874e9 | + | 2.98416e9i | 0.222469 | + | 0.177096i | ||||
\(112\) | − | 2.19222e10i | − | 1.24392i | ||||||
\(113\) | 2.06259e9 | 0.111949 | 0.0559745 | − | 0.998432i | \(-0.482173\pi\) | ||||
0.0559745 | + | 0.998432i | \(0.482173\pi\) | |||||||
\(114\) | 1.68188e10 | − | 2.11280e10i | 0.873517 | − | 1.09732i | ||||
\(115\) | −4.92838e9 | + | 2.26639e9i | −0.245027 | + | 0.112679i | ||||
\(116\) | − | 7.33600e9i | − | 0.349277i | ||||||
\(117\) | −4.17887e10 | + | 9.61490e9i | −1.90603 | + | 0.438546i | ||||
\(118\) | − | 2.46123e10i | − | 1.07583i | ||||||
\(119\) | 1.46745e10i | 0.614936i | ||||||||
\(120\) | 4.66013e9 | − | 1.89365e10i | 0.187280 | − | 0.761016i | ||||
\(121\) | 2.26031e10 | 0.871447 | ||||||||
\(122\) | 2.84183e10 | 1.05147 | ||||||||
\(123\) | −1.59745e10 | − | 1.27164e10i | −0.567416 | − | 0.451689i | ||||
\(124\) | 3.45382e9 | 0.117812 | ||||||||
\(125\) | 8.36669e9 | − | 2.93483e10i | 0.274160 | − | 0.961684i | ||||
\(126\) | −3.63183e10 | + | 8.35625e9i | −1.14360 | + | 0.263123i | ||||
\(127\) | 4.05289e10i | 1.22672i | 0.789803 | + | 0.613361i | \(0.210183\pi\) | ||||
−0.789803 | + | 0.613361i | \(0.789817\pi\) | |||||||
\(128\) | −4.12991e10 | −1.20196 | ||||||||
\(129\) | 1.50581e10 | + | 1.19869e10i | 0.421523 | + | 0.335551i | ||||
\(130\) | 3.48202e10 | + | 7.57184e10i | 0.937810 | + | 2.03932i | ||||
\(131\) | 5.25628e10i | 1.36245i | 0.732072 | + | 0.681227i | \(0.238553\pi\) | ||||
−0.732072 | + | 0.681227i | \(0.761447\pi\) | |||||||
\(132\) | −3.56481e9 | − | 2.83774e9i | −0.0889542 | − | 0.0708115i | ||||
\(133\) | − | 5.20031e10i | − | 1.24960i | ||||||
\(134\) | 6.34383e10i | 1.46834i | ||||||||
\(135\) | −4.48352e10 | − | 6.79287e8i | −0.999885 | − | 0.0151490i | ||||
\(136\) | 2.19292e10 | 0.471333 | ||||||||
\(137\) | 5.48676e10 | 1.13688 | 0.568438 | − | 0.822726i | \(-0.307548\pi\) | ||||
0.568438 | + | 0.822726i | \(0.307548\pi\) | |||||||
\(138\) | 9.64787e9 | − | 1.21198e10i | 0.192768 | − | 0.242158i | ||||
\(139\) | 3.59765e10 | 0.693338 | 0.346669 | − | 0.937988i | \(-0.387313\pi\) | ||||
0.346669 | + | 0.937988i | \(0.387313\pi\) | |||||||
\(140\) | 7.28595e9 | + | 1.58437e10i | 0.135471 | + | 0.294589i | ||||
\(141\) | 2.83595e10 | − | 3.56256e10i | 0.508866 | − | 0.639244i | ||||
\(142\) | 3.63593e10i | 0.629759i | ||||||||
\(143\) | −4.19327e10 | −0.701249 | ||||||||
\(144\) | 1.68899e10 | + | 7.34077e10i | 0.272781 | + | 1.18557i | ||||
\(145\) | −2.94966e10 | − | 6.41420e10i | −0.460185 | − | 1.00070i | ||||
\(146\) | − | 1.14848e11i | − | 1.73124i | ||||||
\(147\) | −1.94548e9 | + | 2.44394e9i | −0.0283427 | + | 0.0356044i | ||||
\(148\) | 6.40285e9i | 0.0901705i | ||||||||
\(149\) | − | 4.09955e10i | − | 0.558219i | −0.960259 | − | 0.279110i | \(-0.909961\pi\) | ||
0.960259 | − | 0.279110i | \(-0.0900393\pi\) | |||||||
\(150\) | 1.64359e10 | + | 8.55861e10i | 0.216440 | + | 1.12706i | ||||
\(151\) | −6.68405e10 | −0.851442 | −0.425721 | − | 0.904855i | \(-0.639979\pi\) | ||||
−0.425721 | + | 0.904855i | \(0.639979\pi\) | |||||||
\(152\) | −7.77119e10 | −0.957788 | ||||||||
\(153\) | −1.13060e10 | − | 4.91385e10i | −0.134850 | − | 0.586091i | ||||
\(154\) | −3.64434e10 | −0.420742 | ||||||||
\(155\) | 3.01983e10 | − | 1.38871e10i | 0.337539 | − | 0.155222i | ||||
\(156\) | −4.48311e10 | − | 3.56876e10i | −0.485240 | − | 0.386273i | ||||
\(157\) | − | 4.61509e10i | − | 0.483817i | −0.970299 | − | 0.241909i | \(-0.922227\pi\) | ||
0.970299 | − | 0.241909i | \(-0.0777735\pi\) | |||||||
\(158\) | −4.86150e10 | −0.493724 | ||||||||
\(159\) | 8.46986e10 | − | 1.06399e11i | 0.833471 | − | 1.04702i | ||||
\(160\) | 5.83471e10 | − | 2.68317e10i | 0.556441 | − | 0.255887i | ||||
\(161\) | − | 2.98308e10i | − | 0.275763i | ||||||
\(162\) | 1.15176e11 | − | 5.59627e10i | 1.03225 | − | 0.501561i | ||||
\(163\) | 6.09521e9i | 0.0529725i | 0.999649 | + | 0.0264862i | \(0.00843182\pi\) | ||||
−0.999649 | + | 0.0264862i | \(0.991568\pi\) | |||||||
\(164\) | − | 2.72845e10i | − | 0.229983i | ||||||
\(165\) | −4.25787e10 | − | 1.04783e10i | −0.348155 | − | 0.0856783i | ||||
\(166\) | 7.05384e10 | 0.559610 | ||||||||
\(167\) | −2.17918e9 | −0.0167768 | −0.00838842 | − | 0.999965i | \(-0.502670\pi\) | ||||
−0.00838842 | + | 0.999965i | \(0.502670\pi\) | |||||||
\(168\) | 8.39050e10 | + | 6.67921e10i | 0.626962 | + | 0.499089i | ||||
\(169\) | −3.89488e11 | −2.82527 | ||||||||
\(170\) | −8.90358e10 | + | 4.09444e10i | −0.627076 | + | 0.288370i | ||||
\(171\) | 4.00657e10 | + | 1.74135e11i | 0.274026 | + | 1.19098i | ||||
\(172\) | 2.57192e10i | 0.170850i | ||||||||
\(173\) | 1.35971e11 | 0.877433 | 0.438717 | − | 0.898625i | \(-0.355433\pi\) | ||||
0.438717 | + | 0.898625i | \(0.355433\pi\) | |||||||
\(174\) | 1.57737e11 | + | 1.25565e11i | 0.988977 | + | 0.787270i | ||||
\(175\) | 1.27409e11 | + | 1.09233e11i | 0.776263 | + | 0.665525i | ||||
\(176\) | 7.36605e10i | 0.436186i | ||||||||
\(177\) | 1.27413e11 | + | 1.01426e11i | 0.733411 | + | 0.583827i | ||||
\(178\) | − | 6.63334e10i | − | 0.371220i | ||||||
\(179\) | − | 1.70509e11i | − | 0.927858i | −0.885872 | − | 0.463929i | \(-0.846439\pi\) | ||
0.885872 | − | 0.463929i | \(-0.153561\pi\) | |||||||
\(180\) | −3.66041e10 | − | 4.74400e10i | −0.193717 | − | 0.251063i | ||||
\(181\) | 1.47301e11 | 0.758250 | 0.379125 | − | 0.925346i | \(-0.376225\pi\) | ||||
0.379125 | + | 0.925346i | \(0.376225\pi\) | |||||||
\(182\) | −4.58314e11 | −2.29512 | ||||||||
\(183\) | −1.17111e11 | + | 1.47116e11i | −0.570612 | + | 0.716809i | ||||
\(184\) | −4.45782e10 | −0.211365 | ||||||||
\(185\) | 2.57446e10 | + | 5.59830e10i | 0.118803 | + | 0.258343i | ||||
\(186\) | −5.91166e10 | + | 7.42630e10i | −0.265549 | + | 0.333586i | ||||
\(187\) | − | 4.93077e10i | − | 0.215629i | ||||||
\(188\) | 6.08485e10 | 0.259096 | ||||||||
\(189\) | 1.06408e11 | − | 2.22448e11i | 0.441229 | − | 0.922402i | ||||
\(190\) | 3.15522e11 | − | 1.45097e11i | 1.27427 | − | 0.585991i | ||||
\(191\) | 4.11947e11i | 1.62059i | 0.586019 | + | 0.810297i | \(0.300694\pi\) | ||||
−0.586019 | + | 0.810297i | \(0.699306\pi\) | |||||||
\(192\) | 8.34710e10 | − | 1.04857e11i | 0.319911 | − | 0.401876i | ||||
\(193\) | 2.80177e11i | 1.04628i | 0.852248 | + | 0.523138i | \(0.175239\pi\) | ||||
−0.852248 | + | 0.523138i | \(0.824761\pi\) | |||||||
\(194\) | − | 2.83613e10i | − | 0.103209i | ||||||
\(195\) | −5.35472e11 | − | 1.31775e11i | −1.89917 | − | 0.467370i | ||||
\(196\) | −4.17425e9 | −0.0144310 | ||||||||
\(197\) | 5.11823e10 | 0.172500 | 0.0862499 | − | 0.996274i | \(-0.472512\pi\) | ||||
0.0862499 | + | 0.996274i | \(0.472512\pi\) | |||||||
\(198\) | 1.22033e11 | − | 2.80777e10i | 0.401006 | − | 0.0922648i | ||||
\(199\) | 1.20927e11 | 0.387487 | 0.193743 | − | 0.981052i | \(-0.437937\pi\) | ||||
0.193743 | + | 0.981052i | \(0.437937\pi\) | |||||||
\(200\) | 1.63235e11 | − | 1.90396e11i | 0.510109 | − | 0.594986i | ||||
\(201\) | −3.28407e11 | − | 2.61427e11i | −1.00100 | − | 0.796837i | ||||
\(202\) | − | 3.15603e11i | − | 0.938392i | ||||||
\(203\) | 3.88243e11 | 1.12622 | ||||||||
\(204\) | 4.19643e10 | − | 5.27160e10i | 0.118776 | − | 0.149208i | ||||
\(205\) | −1.09705e11 | − | 2.38560e11i | −0.303011 | − | 0.658914i | ||||
\(206\) | − | 3.11502e11i | − | 0.839702i | ||||||
\(207\) | 2.29831e10 | + | 9.98901e10i | 0.0604723 | + | 0.262827i | ||||
\(208\) | 9.26357e11i | 2.37937i | ||||||||
\(209\) | 1.74735e11i | 0.438176i | ||||||||
\(210\) | −4.65375e11 | − | 1.14525e11i | −1.13948 | − | 0.280417i | ||||
\(211\) | 4.63289e11 | 1.10775 | 0.553873 | − | 0.832601i | \(-0.313149\pi\) | ||||
0.553873 | + | 0.832601i | \(0.313149\pi\) | |||||||
\(212\) | 1.81730e11 | 0.424373 | ||||||||
\(213\) | −1.88225e11 | − | 1.49835e11i | −0.429318 | − | 0.341756i | ||||
\(214\) | −9.51346e11 | −2.11968 | ||||||||
\(215\) | 1.03412e11 | + | 2.24875e11i | 0.225101 | + | 0.489495i | ||||
\(216\) | −3.32420e11 | − | 1.59012e11i | −0.706998 | − | 0.338191i | ||||
\(217\) | 1.82786e11i | 0.379879i | ||||||||
\(218\) | 6.29249e11 | 1.27803 | ||||||||
\(219\) | 5.94543e11 | + | 4.73282e11i | 1.18022 | + | 0.939506i | ||||
\(220\) | −2.44814e10 | − | 5.32362e10i | −0.0475032 | − | 0.103298i | ||||
\(221\) | − | 6.20096e11i | − | 1.17624i | ||||||
\(222\) | −1.37672e11 | − | 1.09593e11i | −0.255318 | − | 0.203244i | ||||
\(223\) | − | 7.27823e11i | − | 1.31978i | −0.751362 | − | 0.659890i | \(-0.770603\pi\) | ||
0.751362 | − | 0.659890i | \(-0.229397\pi\) | |||||||
\(224\) | 3.53167e11i | 0.626239i | ||||||||
\(225\) | −5.10793e11 | − | 2.67611e11i | −0.885794 | − | 0.464079i | ||||
\(226\) | −7.57484e10 | −0.128479 | ||||||||
\(227\) | −4.05951e11 | −0.673510 | −0.336755 | − | 0.941592i | \(-0.609329\pi\) | ||||
−0.336755 | + | 0.941592i | \(0.609329\pi\) | |||||||
\(228\) | −1.48711e11 | + | 1.86813e11i | −0.241363 | + | 0.303203i | ||||
\(229\) | 8.19857e10 | 0.130185 | 0.0650924 | − | 0.997879i | \(-0.479266\pi\) | ||||
0.0650924 | + | 0.997879i | \(0.479266\pi\) | |||||||
\(230\) | 1.80994e11 | − | 8.32328e10i | 0.281207 | − | 0.129317i | ||||
\(231\) | 1.50182e11 | − | 1.88660e11i | 0.228327 | − | 0.286827i | ||||
\(232\) | − | 5.80178e11i | − | 0.863220i | ||||||
\(233\) | −3.36869e11 | −0.490548 | −0.245274 | − | 0.969454i | \(-0.578878\pi\) | ||||
−0.245274 | + | 0.969454i | \(0.578878\pi\) | |||||||
\(234\) | 1.53469e12 | − | 3.53107e11i | 2.18746 | − | 0.503299i | ||||
\(235\) | 5.32026e11 | − | 2.44660e11i | 0.742324 | − | 0.341368i | ||||
\(236\) | 2.17621e11i | 0.297263i | ||||||||
\(237\) | 2.00340e11 | − | 2.51670e11i | 0.267933 | − | 0.336581i | ||||
\(238\) | − | 5.38922e11i | − | 0.705734i | ||||||
\(239\) | 1.30858e12i | 1.67808i | 0.544072 | + | 0.839038i | \(0.316882\pi\) | ||||
−0.544072 | + | 0.839038i | \(0.683118\pi\) | |||||||
\(240\) | −2.31482e11 | + | 9.40630e11i | −0.290710 | + | 1.18131i | ||||
\(241\) | −5.45295e11 | −0.670728 | −0.335364 | − | 0.942089i | \(-0.608859\pi\) | ||||
−0.335364 | + | 0.942089i | \(0.608859\pi\) | |||||||
\(242\) | −8.30097e11 | −1.00012 | ||||||||
\(243\) | −1.84927e11 | + | 8.26862e11i | −0.218258 | + | 0.975891i | ||||
\(244\) | −2.51273e11 | −0.290534 | ||||||||
\(245\) | −3.64973e10 | + | 1.67838e10i | −0.0413457 | + | 0.0190134i | ||||
\(246\) | 5.86663e11 | + | 4.67009e11i | 0.651198 | + | 0.518382i | ||||
\(247\) | 2.19747e12i | 2.39023i | ||||||||
\(248\) | 2.73150e11 | 0.291168 | ||||||||
\(249\) | −2.90686e11 | + | 3.65163e11i | −0.303688 | + | 0.381496i | ||||
\(250\) | −3.07266e11 | + | 1.07781e12i | −0.314641 | + | 1.10368i | ||||
\(251\) | 3.22417e11i | 0.323630i | 0.986821 | + | 0.161815i | \(0.0517348\pi\) | ||||
−0.986821 | + | 0.161815i | \(0.948265\pi\) | |||||||
\(252\) | 3.21125e11 | − | 7.38857e10i | 0.315989 | − | 0.0727039i | ||||
\(253\) | 1.00234e11i | 0.0966970i | ||||||||
\(254\) | − | 1.48842e12i | − | 1.40785i | ||||||
\(255\) | 1.54952e11 | − | 6.29650e11i | 0.143713 | − | 0.583980i | ||||
\(256\) | 9.51932e11 | 0.865777 | ||||||||
\(257\) | 2.01099e12 | 1.79368 | 0.896839 | − | 0.442358i | \(-0.145858\pi\) | ||||
0.896839 | + | 0.442358i | \(0.145858\pi\) | |||||||
\(258\) | −5.53007e11 | − | 4.40218e11i | −0.483762 | − | 0.385096i | ||||
\(259\) | −3.38858e11 | −0.290749 | ||||||||
\(260\) | −3.07879e11 | − | 6.69500e11i | −0.259127 | − | 0.563487i | ||||
\(261\) | −1.30005e12 | + | 2.99121e11i | −1.07339 | + | 0.246970i | ||||
\(262\) | − | 1.93036e12i | − | 1.56363i | ||||||
\(263\) | −2.08594e12 | −1.65776 | −0.828882 | − | 0.559424i | \(-0.811022\pi\) | ||||
−0.828882 | + | 0.559424i | \(0.811022\pi\) | |||||||
\(264\) | −2.81928e11 | − | 2.24427e11i | −0.219846 | − | 0.175007i | ||||
\(265\) | 1.58895e12 | − | 7.30701e11i | 1.21585 | − | 0.559126i | ||||
\(266\) | 1.90981e12i | 1.43411i | ||||||||
\(267\) | 3.43394e11 | + | 2.73357e11i | 0.253068 | + | 0.201453i | ||||
\(268\) | − | 5.60919e11i | − | 0.405720i | ||||||
\(269\) | − | 2.14609e12i | − | 1.52365i | −0.647781 | − | 0.761826i | \(-0.724303\pi\) | ||
0.647781 | − | 0.761826i | \(-0.275697\pi\) | |||||||
\(270\) | 1.64657e12 | + | 2.49468e10i | 1.14752 | + | 0.0173858i | ||||
\(271\) | −2.87177e11 | −0.196473 | −0.0982364 | − | 0.995163i | \(-0.531320\pi\) | ||||
−0.0982364 | + | 0.995163i | \(0.531320\pi\) | |||||||
\(272\) | −1.08928e12 | −0.731639 | ||||||||
\(273\) | 1.88869e12 | − | 2.37260e12i | 1.24551 | − | 1.56463i | ||||
\(274\) | −2.01501e12 | −1.30474 | ||||||||
\(275\) | −4.28104e11 | − | 3.67033e11i | −0.272199 | − | 0.233368i | ||||
\(276\) | −8.53061e10 | + | 1.07162e11i | −0.0532641 | + | 0.0669110i | ||||
\(277\) | 8.41910e11i | 0.516258i | 0.966110 | + | 0.258129i | \(0.0831059\pi\) | ||||
−0.966110 | + | 0.258129i | \(0.916894\pi\) | |||||||
\(278\) | −1.32123e12 | −0.795712 | ||||||||
\(279\) | −1.40827e11 | − | 6.12069e11i | −0.0833039 | − | 0.362059i | ||||
\(280\) | 5.76220e11 | + | 1.25302e12i | 0.334810 | + | 0.728062i | ||||
\(281\) | − | 3.00772e12i | − | 1.71675i | −0.513025 | − | 0.858374i | \(-0.671475\pi\) | ||
0.513025 | − | 0.858374i | \(-0.328525\pi\) | |||||||
\(282\) | −1.04150e12 | + | 1.30835e12i | −0.584003 | + | 0.733631i | ||||
\(283\) | − | 2.02042e12i | − | 1.11304i | −0.830835 | − | 0.556519i | \(-0.812137\pi\) | ||
0.830835 | − | 0.556519i | \(-0.187863\pi\) | |||||||
\(284\) | − | 3.21488e11i | − | 0.174009i | ||||||
\(285\) | −5.49113e11 | + | 2.23133e12i | −0.292037 | + | 1.18670i | ||||
\(286\) | 1.53997e12 | 0.804791 | ||||||||
\(287\) | 1.44397e12 | 0.741566 | ||||||||
\(288\) | −2.72097e11 | − | 1.18260e12i | −0.137329 | − | 0.596863i | ||||
\(289\) | −1.28684e12 | −0.638313 | ||||||||
\(290\) | 1.08326e12 | + | 2.35561e12i | 0.528133 | + | 1.14845i | ||||
\(291\) | 1.46821e11 | + | 1.16876e11i | 0.0703595 | + | 0.0560093i | ||||
\(292\) | 1.01548e12i | 0.478362i | ||||||||
\(293\) | −1.85878e12 | −0.860774 | −0.430387 | − | 0.902644i | \(-0.641623\pi\) | ||||
−0.430387 | + | 0.902644i | \(0.641623\pi\) | |||||||
\(294\) | 7.14477e10 | − | 8.97535e10i | 0.0325276 | − | 0.0408615i | ||||
\(295\) | 8.75012e11 | + | 1.90276e12i | 0.391655 | + | 0.851676i | ||||
\(296\) | 5.06378e11i | 0.222852i | ||||||||
\(297\) | −3.57539e11 | + | 7.47446e11i | −0.154718 | + | 0.323443i | ||||
\(298\) | 1.50556e12i | 0.640643i | ||||||||
\(299\) | 1.26055e12i | 0.527477i | ||||||||
\(300\) | −1.45326e11 | − | 7.56749e11i | −0.0598047 | − | 0.311419i | ||||
\(301\) | −1.36114e12 | −0.550895 | ||||||||
\(302\) | 2.45471e12 | 0.977160 | ||||||||
\(303\) | 1.63381e12 | + | 1.30059e12i | 0.639718 | + | 0.509244i | ||||
\(304\) | 3.86017e12 | 1.48675 | ||||||||
\(305\) | −2.19700e12 | + | 1.01032e12i | −0.832397 | + | 0.382790i | ||||
\(306\) | 4.15211e11 | + | 1.80461e12i | 0.154761 | + | 0.672629i | ||||
\(307\) | − | 2.24705e12i | − | 0.823988i | −0.911187 | − | 0.411994i | \(-0.864832\pi\) | ||
0.911187 | − | 0.411994i | \(-0.135168\pi\) | |||||||
\(308\) | 3.22231e11 | 0.116256 | ||||||||
\(309\) | 1.61258e12 | + | 1.28369e12i | 0.572440 | + | 0.455688i | ||||
\(310\) | −1.10903e12 | + | 5.10003e11i | −0.387378 | + | 0.178141i | ||||
\(311\) | 4.03605e11i | 0.138725i | 0.997592 | + | 0.0693625i | \(0.0220965\pi\) | ||||
−0.997592 | + | 0.0693625i | \(0.977903\pi\) | |||||||
\(312\) | −3.54553e12 | − | 2.82240e12i | −1.19925 | − | 0.954654i | ||||
\(313\) | − | 8.52934e11i | − | 0.283918i | −0.989873 | − | 0.141959i | \(-0.954660\pi\) | ||
0.989873 | − | 0.141959i | \(-0.0453402\pi\) | |||||||
\(314\) | 1.69489e12i | 0.555255i | ||||||||
\(315\) | 2.51067e12 | − | 1.93720e12i | 0.809536 | − | 0.624628i | ||||
\(316\) | 4.29852e11 | 0.136422 | ||||||||
\(317\) | 1.62693e12 | 0.508246 | 0.254123 | − | 0.967172i | \(-0.418213\pi\) | ||||
0.254123 | + | 0.967172i | \(0.418213\pi\) | |||||||
\(318\) | −3.11055e12 | + | 3.90751e12i | −0.956536 | + | 1.20161i | ||||
\(319\) | −1.30453e12 | −0.394912 | ||||||||
\(320\) | 1.56592e12 | − | 7.20110e11i | 0.466680 | − | 0.214610i | ||||
\(321\) | 3.92046e12 | − | 4.92492e12i | 1.15030 | − | 1.44502i | ||||
\(322\) | 1.09553e12i | 0.316480i | ||||||||
\(323\) | −2.58396e12 | −0.734977 | ||||||||
\(324\) | −1.01838e12 | + | 4.94820e11i | −0.285223 | + | 0.138587i | ||||
\(325\) | −5.38385e12 | − | 4.61582e12i | −1.48483 | − | 1.27301i | ||||
\(326\) | − | 2.23846e11i | − | 0.0607941i | ||||||
\(327\) | −2.59311e12 | + | 3.25749e12i | −0.693557 | + | 0.871254i | ||||
\(328\) | − | 2.15783e12i | − | 0.568392i | ||||||
\(329\) | 3.22028e12i | 0.835439i | ||||||||
\(330\) | 1.56370e12 | + | 3.84815e11i | 0.399562 | + | 0.0983291i | ||||
\(331\) | −9.37645e11 | −0.235993 | −0.117996 | − | 0.993014i | \(-0.537647\pi\) | ||||
−0.117996 | + | 0.993014i | \(0.537647\pi\) | |||||||
\(332\) | −6.23698e11 | −0.154627 | ||||||||
\(333\) | 1.13468e12 | − | 2.61072e11i | 0.277111 | − | 0.0637586i | ||||
\(334\) | 8.00301e10 | 0.0192540 | ||||||||
\(335\) | −2.25535e12 | − | 4.90437e12i | −0.534551 | − | 1.16241i | ||||
\(336\) | −4.16779e12 | − | 3.31775e12i | −0.973217 | − | 0.774724i | ||||
\(337\) | 1.28553e12i | 0.295755i | 0.989006 | + | 0.147877i | \(0.0472441\pi\) | ||||
−0.989006 | + | 0.147877i | \(0.952756\pi\) | |||||||
\(338\) | 1.43039e13 | 3.24244 | ||||||||
\(339\) | 3.12156e11 | − | 3.92134e11i | 0.0697225 | − | 0.0875862i | ||||
\(340\) | 7.87251e11 | − | 3.62029e11i | 0.173268 | − | 0.0796798i | ||||
\(341\) | − | 6.14177e11i | − | 0.133205i | ||||||
\(342\) | −1.47141e12 | − | 6.39511e12i | −0.314487 | − | 1.36684i | ||||
\(343\) | 4.63347e12i | 0.975969i | ||||||||
\(344\) | 2.03404e12i | 0.422248i | ||||||||
\(345\) | −3.14991e11 | + | 1.27997e12i | −0.0644469 | + | 0.261881i | ||||
\(346\) | −4.99351e12 | −1.00699 | ||||||||
\(347\) | 6.96146e12 | 1.38374 | 0.691868 | − | 0.722024i | \(-0.256788\pi\) | ||||
0.691868 | + | 0.722024i | \(0.256788\pi\) | |||||||
\(348\) | −1.39470e12 | − | 1.11024e12i | −0.273266 | − | 0.217532i | ||||
\(349\) | 7.62023e12 | 1.47177 | 0.735887 | − | 0.677105i | \(-0.236766\pi\) | ||||
0.735887 | + | 0.677105i | \(0.236766\pi\) | |||||||
\(350\) | −4.67908e12 | − | 4.01158e12i | −0.890881 | − | 0.763793i | ||||
\(351\) | −4.49642e12 | + | 9.39990e12i | −0.843979 | + | 1.76436i | ||||
\(352\) | − | 1.18667e12i | − | 0.219592i | ||||||
\(353\) | −3.03938e12 | −0.554513 | −0.277256 | − | 0.960796i | \(-0.589425\pi\) | ||||
−0.277256 | + | 0.960796i | \(0.589425\pi\) | |||||||
\(354\) | −4.67923e12 | − | 3.72488e12i | −0.841702 | − | 0.670032i | ||||
\(355\) | −1.29264e12 | − | 2.81091e12i | −0.229264 | − | 0.498547i | ||||
\(356\) | 5.86517e11i | 0.102572i | ||||||||
\(357\) | 2.78989e12 | + | 2.22087e12i | 0.481111 | + | 0.382986i | ||||
\(358\) | 6.26192e12i | 1.06486i | ||||||||
\(359\) | − | 6.57631e12i | − | 1.10283i | −0.834230 | − | 0.551417i | \(-0.814087\pi\) | ||
0.834230 | − | 0.551417i | \(-0.185913\pi\) | |||||||
\(360\) | −2.89489e12 | − | 3.75186e12i | −0.478762 | − | 0.620489i | ||||
\(361\) | 3.02590e12 | 0.493535 | ||||||||
\(362\) | −5.40961e12 | −0.870208 | ||||||||
\(363\) | 3.42079e12 | − | 4.29724e12i | 0.542743 | − | 0.681800i | ||||
\(364\) | 4.05239e12 | 0.634168 | ||||||||
\(365\) | 4.08304e12 | + | 8.87879e12i | 0.630260 | + | 1.37053i | ||||
\(366\) | 4.30088e12 | − | 5.40281e12i | 0.654865 | − | 0.822649i | ||||
\(367\) | 2.32215e12i | 0.348786i | 0.984676 | + | 0.174393i | \(0.0557963\pi\) | ||||
−0.984676 | + | 0.174393i | \(0.944204\pi\) | |||||||
\(368\) | 2.21433e12 | 0.328097 | ||||||||
\(369\) | −4.83522e12 | + | 1.11251e12i | −0.706781 | + | 0.162619i | ||||
\(370\) | −9.45468e11 | − | 2.05597e12i | −0.136345 | − | 0.296489i | ||||
\(371\) | 9.61769e12i | 1.36836i | ||||||||
\(372\) | 5.22707e11 | − | 6.56631e11i | 0.0733743 | − | 0.0921736i | ||||
\(373\) | 6.74020e12i | 0.933531i | 0.884381 | + | 0.466766i | \(0.154581\pi\) | ||||
−0.884381 | + | 0.466766i | \(0.845419\pi\) | |||||||
\(374\) | 1.81082e12i | 0.247467i | ||||||||
\(375\) | −4.31339e12 | − | 6.03228e12i | −0.581650 | − | 0.813439i | ||||
\(376\) | 4.81229e12 | 0.640343 | ||||||||
\(377\) | −1.64058e13 | −2.15422 | ||||||||
\(378\) | −3.90782e12 | + | 8.16940e12i | −0.506378 | + | 1.05860i | ||||
\(379\) | 4.47192e12 | 0.571871 | 0.285936 | − | 0.958249i | \(-0.407696\pi\) | ||||
0.285936 | + | 0.958249i | \(0.407696\pi\) | |||||||
\(380\) | −2.78983e12 | + | 1.28294e12i | −0.352095 | + | 0.161916i | ||||
\(381\) | 7.70525e12 | + | 6.13372e12i | 0.959758 | + | 0.764010i | ||||
\(382\) | − | 1.51287e13i | − | 1.85988i | ||||||
\(383\) | 2.03208e12 | 0.246574 | 0.123287 | − | 0.992371i | \(-0.460656\pi\) | ||||
0.123287 | + | 0.992371i | \(0.460656\pi\) | |||||||
\(384\) | −6.25029e12 | + | 7.85169e12i | −0.748590 | + | 0.940388i | ||||
\(385\) | 2.81742e12 | − | 1.29563e12i | 0.333079 | − | 0.153171i | ||||
\(386\) | − | 1.02895e13i | − | 1.20076i | ||||||
\(387\) | 4.55784e12 | − | 1.04868e12i | 0.525054 | − | 0.120806i | ||||
\(388\) | 2.50770e11i | 0.0285179i | ||||||||
\(389\) | − | 5.60385e12i | − | 0.629128i | −0.949236 | − | 0.314564i | \(-0.898142\pi\) | ||
0.949236 | − | 0.314564i | \(-0.101858\pi\) | |||||||
\(390\) | 1.96652e13 | + | 4.83944e12i | 2.17959 | + | 0.536380i | ||||
\(391\) | −1.48225e12 | −0.162195 | ||||||||
\(392\) | −3.30126e11 | −0.0356656 | ||||||||
\(393\) | 9.99310e12 | + | 7.95495e12i | 1.06595 | + | 0.848545i | ||||
\(394\) | −1.87967e12 | −0.197970 | ||||||||
\(395\) | 3.75839e12 | − | 1.72835e12i | 0.390856 | − | 0.179741i | ||||
\(396\) | −1.07901e12 | + | 2.48262e11i | −0.110802 | + | 0.0254938i | ||||
\(397\) | 8.63100e12i | 0.875203i | 0.899169 | + | 0.437602i | \(0.144172\pi\) | ||||
−0.899169 | + | 0.437602i | \(0.855828\pi\) | |||||||
\(398\) | −4.44103e12 | −0.444701 | ||||||||
\(399\) | −9.88670e12 | − | 7.87025e12i | −0.977658 | − | 0.778259i | ||||
\(400\) | −8.10832e12 | + | 9.45748e12i | −0.791829 | + | 0.923582i | ||||
\(401\) | 2.34497e12i | 0.226160i | 0.993586 | + | 0.113080i | \(0.0360716\pi\) | ||||
−0.993586 | + | 0.113080i | \(0.963928\pi\) | |||||||
\(402\) | 1.20607e13 | + | 9.60087e12i | 1.14880 | + | 0.914493i | ||||
\(403\) | − | 7.72392e12i | − | 0.726628i | ||||||
\(404\) | 2.79055e12i | 0.259288i | ||||||||
\(405\) | −6.91459e12 | + | 8.42115e12i | −0.634587 | + | 0.772852i | ||||
\(406\) | −1.42582e13 | −1.29251 | ||||||||
\(407\) | 1.13859e12 | 0.101952 | ||||||||
\(408\) | 3.31880e12 | − | 4.16912e12i | 0.293549 | − | 0.368760i | ||||
\(409\) | −7.52569e12 | −0.657552 | −0.328776 | − | 0.944408i | \(-0.606636\pi\) | ||||
−0.328776 | + | 0.944408i | \(0.606636\pi\) | |||||||
\(410\) | 4.02892e12 | + | 8.76111e12i | 0.347752 | + | 0.756206i | ||||
\(411\) | 8.30377e12 | − | 1.04313e13i | 0.708054 | − | 0.889465i | ||||
\(412\) | 2.75429e12i | 0.232019i | ||||||||
\(413\) | −1.15172e13 | −0.958507 | ||||||||
\(414\) | −8.44052e11 | − | 3.66846e12i | −0.0694012 | − | 0.301635i | ||||
\(415\) | −5.45328e12 | + | 2.50777e12i | −0.443014 | + | 0.203726i | ||||
\(416\) | − | 1.49236e13i | − | 1.19786i | ||||||
\(417\) | 5.44475e12 | − | 6.83976e12i | 0.431815 | − | 0.542451i | ||||
\(418\) | − | 6.41713e12i | − | 0.502875i | ||||||
\(419\) | − | 1.38946e13i | − | 1.07591i | −0.842974 | − | 0.537955i | \(-0.819197\pi\) | ||
0.842974 | − | 0.537955i | \(-0.180803\pi\) | |||||||
\(420\) | 4.11483e12 | + | 1.01263e12i | 0.314851 | + | 0.0774825i | ||||
\(421\) | −9.62790e11 | −0.0727983 | −0.0363991 | − | 0.999337i | \(-0.511589\pi\) | ||||
−0.0363991 | + | 0.999337i | \(0.511589\pi\) | |||||||
\(422\) | −1.70143e13 | −1.27131 | ||||||||
\(423\) | −2.48106e12 | − | 1.07833e13i | −0.183204 | − | 0.796250i | ||||
\(424\) | 1.43724e13 | 1.04882 | ||||||||
\(425\) | 5.42765e12 | − | 6.33076e12i | 0.391442 | − | 0.456574i | ||||
\(426\) | 6.91254e12 | + | 5.50269e12i | 0.492708 | + | 0.392218i | ||||
\(427\) | − | 1.32981e13i | − | 0.936810i | ||||||
\(428\) | 8.41176e12 | 0.585691 | ||||||||
\(429\) | −6.34617e12 | + | 7.97213e12i | −0.436742 | + | 0.548640i | ||||
\(430\) | −3.79779e12 | − | 8.25851e12i | −0.258338 | − | 0.561771i | ||||
\(431\) | 9.24299e11i | 0.0621479i | 0.999517 | + | 0.0310739i | \(0.00989273\pi\) | ||||
−0.999517 | + | 0.0310739i | \(0.990107\pi\) | |||||||
\(432\) | 1.65122e13 | + | 7.89859e12i | 1.09746 | + | 0.524965i | ||||
\(433\) | − | 1.60295e13i | − | 1.05313i | −0.850135 | − | 0.526564i | \(-0.823480\pi\) | ||
0.850135 | − | 0.526564i | \(-0.176520\pi\) | |||||||
\(434\) | − | 6.71281e12i | − | 0.435969i | ||||||
\(435\) | −1.66586e13 | − | 4.09955e12i | −1.06953 | − | 0.263202i | ||||
\(436\) | −5.56380e12 | −0.353133 | ||||||||
\(437\) | 5.25275e12 | 0.329594 | ||||||||
\(438\) | −2.18345e13 | − | 1.73813e13i | −1.35448 | − | 1.07823i | ||||
\(439\) | 1.19822e13 | 0.734874 | 0.367437 | − | 0.930048i | \(-0.380235\pi\) | ||||
0.367437 | + | 0.930048i | \(0.380235\pi\) | |||||||
\(440\) | −1.93615e12 | − | 4.21026e12i | −0.117402 | − | 0.255297i | ||||
\(441\) | 1.70202e11 | + | 7.39741e11i | 0.0102040 | + | 0.0443493i | ||||
\(442\) | 2.27730e13i | 1.34992i | ||||||||
\(443\) | −1.12721e12 | −0.0660672 | −0.0330336 | − | 0.999454i | \(-0.510517\pi\) | ||||
−0.0330336 | + | 0.999454i | \(0.510517\pi\) | |||||||
\(444\) | 1.21729e12 | + | 9.69019e11i | 0.0705473 | + | 0.0561587i | ||||
\(445\) | 2.35827e12 | + | 5.12819e12i | 0.135143 | + | 0.293876i | ||||
\(446\) | 2.67293e13i | 1.51465i | ||||||||
\(447\) | −7.79396e12 | − | 6.20434e12i | −0.436738 | − | 0.347663i | ||||
\(448\) | 9.47830e12i | 0.525219i | ||||||||
\(449\) | 3.07134e13i | 1.68305i | 0.540221 | + | 0.841523i | \(0.318341\pi\) | ||||
−0.540221 | + | 0.841523i | \(0.681659\pi\) | |||||||
\(450\) | 1.87588e13 | + | 9.82801e12i | 1.01658 | + | 0.532602i | ||||
\(451\) | −4.85188e12 | −0.260032 | ||||||||
\(452\) | 6.69765e11 | 0.0355001 | ||||||||
\(453\) | −1.01158e13 | + | 1.27075e13i | −0.530283 | + | 0.666148i | ||||
\(454\) | 1.49085e13 | 0.772956 | ||||||||
\(455\) | 3.54319e13 | − | 1.62939e13i | 1.81693 | − | 0.835540i | ||||
\(456\) | −1.17611e13 | + | 1.47744e13i | −0.596516 | + | 0.749351i | ||||
\(457\) | 7.89556e12i | 0.396097i | 0.980192 | + | 0.198049i | \(0.0634604\pi\) | ||||
−0.980192 | + | 0.198049i | \(0.936540\pi\) | |||||||
\(458\) | −3.01092e12 | −0.149407 | ||||||||
\(459\) | −1.10532e13 | − | 5.28725e12i | −0.542529 | − | 0.259517i | ||||
\(460\) | −1.60035e12 | + | 7.35942e11i | −0.0777006 | + | 0.0357317i | ||||
\(461\) | − | 9.79629e12i | − | 0.470497i | −0.971935 | − | 0.235249i | \(-0.924410\pi\) | ||
0.971935 | − | 0.235249i | \(-0.0755904\pi\) | |||||||
\(462\) | −5.51542e12 | + | 6.92853e12i | −0.262041 | + | 0.329178i | ||||
\(463\) | 1.24871e13i | 0.586891i | 0.955976 | + | 0.293445i | \(0.0948018\pi\) | ||||
−0.955976 | + | 0.293445i | \(0.905198\pi\) | |||||||
\(464\) | 2.88191e13i | 1.33995i | ||||||||
\(465\) | 1.93008e12 | − | 7.84292e12i | 0.0887792 | − | 0.360756i | ||||
\(466\) | 1.23715e13 | 0.562980 | ||||||||
\(467\) | 7.82498e12 | 0.352289 | 0.176144 | − | 0.984364i | \(-0.443637\pi\) | ||||
0.176144 | + | 0.984364i | \(0.443637\pi\) | |||||||
\(468\) | −1.35697e13 | + | 3.12216e12i | −0.604421 | + | 0.139067i | ||||
\(469\) | 2.96855e13 | 1.30822 | ||||||||
\(470\) | −1.95386e13 | + | 8.98512e12i | −0.851931 | + | 0.391773i | ||||
\(471\) | −8.77408e12 | − | 6.98456e12i | −0.378527 | − | 0.301324i | ||||
\(472\) | 1.72109e13i | 0.734672i | ||||||||
\(473\) | 4.57354e12 | 0.193173 | ||||||||
\(474\) | −7.35748e12 | + | 9.24255e12i | −0.307495 | + | 0.386278i | ||||
\(475\) | −1.92343e13 | + | 2.24347e13i | −0.795442 | + | 0.927797i | ||||
\(476\) | 4.76513e12i | 0.195002i | ||||||||
\(477\) | −7.40992e12 | − | 3.22053e13i | −0.300069 | − | 1.30418i | ||||
\(478\) | − | 4.80576e13i | − | 1.92585i | ||||||
\(479\) | 1.27765e13i | 0.506679i | 0.967377 | + | 0.253339i | \(0.0815289\pi\) | ||||
−0.967377 | + | 0.253339i | \(0.918471\pi\) | |||||||
\(480\) | 3.72917e12 | − | 1.51536e13i | 0.146355 | − | 0.594715i | ||||
\(481\) | 1.43190e13 | 0.556142 | ||||||||
\(482\) | 2.00259e13 | 0.769763 | ||||||||
\(483\) | −5.67136e12 | − | 4.51465e12i | −0.215750 | − | 0.171747i | ||||
\(484\) | 7.33969e12 | 0.276344 | ||||||||
\(485\) | 1.00830e12 | + | 2.19260e12i | 0.0375733 | + | 0.0817052i | ||||
\(486\) | 6.79144e12 | − | 3.03664e13i | 0.250484 | − | 1.11999i | ||||
\(487\) | − | 1.60149e13i | − | 0.584627i | −0.956323 | − | 0.292314i | \(-0.905575\pi\) | ||
0.956323 | − | 0.292314i | \(-0.0944251\pi\) | |||||||
\(488\) | −1.98723e13 | −0.718042 | ||||||||
\(489\) | 1.15881e12 | + | 9.22460e11i | 0.0414444 | + | 0.0329916i | ||||
\(490\) | 1.34036e12 | − | 6.16385e11i | 0.0474506 | − | 0.0218208i | ||||
\(491\) | 2.98492e12i | 0.104598i | 0.998631 | + | 0.0522992i | \(0.0166550\pi\) | ||||
−0.998631 | + | 0.0522992i | \(0.983345\pi\) | |||||||
\(492\) | −5.18725e12 | − | 4.12928e12i | −0.179933 | − | 0.143235i | ||||
\(493\) | − | 1.92913e13i | − | 0.662408i | ||||||
\(494\) | − | 8.07021e13i | − | 2.74315i | ||||||
\(495\) | −8.43605e12 | + | 6.50915e12i | −0.283866 | + | 0.219027i | ||||
\(496\) | −1.35681e13 | −0.451972 | ||||||||
\(497\) | 1.70141e13 | 0.561083 | ||||||||
\(498\) | 1.06754e13 | − | 1.34106e13i | 0.348528 | − | 0.437825i | ||||
\(499\) | −3.21812e13 | −1.04016 | −0.520080 | − | 0.854118i | \(-0.674098\pi\) | ||||
−0.520080 | + | 0.854118i | \(0.674098\pi\) | |||||||
\(500\) | 2.71684e12 | − | 9.52999e12i | 0.0869388 | − | 0.304960i | ||||
\(501\) | −3.29801e11 | + | 4.14299e11i | −0.0104487 | + | 0.0131258i | ||||
\(502\) | − | 1.18407e13i | − | 0.371415i | ||||||
\(503\) | 2.05869e13 | 0.639367 | 0.319683 | − | 0.947524i | \(-0.396423\pi\) | ||||
0.319683 | + | 0.947524i | \(0.396423\pi\) | |||||||
\(504\) | 2.53967e13 | − | 5.84336e12i | 0.780951 | − | 0.179684i | ||||
\(505\) | 1.12203e13 | + | 2.43990e13i | 0.341622 | + | 0.742875i | ||||
\(506\) | − | 3.68109e12i | − | 0.110975i | ||||||
\(507\) | −5.89458e13 | + | 7.40484e13i | −1.75960 | + | 2.21043i | ||||
\(508\) | 1.31606e13i | 0.389006i | ||||||||
\(509\) | 2.17795e13i | 0.637468i | 0.947844 | + | 0.318734i | \(0.103258\pi\) | ||||
−0.947844 | + | 0.318734i | \(0.896742\pi\) | |||||||
\(510\) | −5.69060e12 | + | 2.31239e13i | −0.164933 | + | 0.670208i | ||||
\(511\) | −5.37422e13 | −1.54245 | ||||||||
\(512\) | 7.33069e12 | 0.208351 | ||||||||
\(513\) | 3.91698e13 | + | 1.87368e13i | 1.10246 | + | 0.527361i | ||||
\(514\) | −7.38535e13 | −2.05852 | ||||||||
\(515\) | 1.10745e13 | + | 2.40820e13i | 0.305694 | + | 0.664748i | ||||
\(516\) | 4.88967e12 | + | 3.89239e12i | 0.133669 | + | 0.106406i | ||||
\(517\) | − | 1.08204e13i | − | 0.292949i | ||||||
\(518\) | 1.24445e13 | 0.333679 | ||||||||
\(519\) | 2.05780e13 | − | 2.58504e13i | 0.546471 | − | 0.686483i | ||||
\(520\) | −2.43491e13 | − | 5.29484e13i | −0.640421 | − | 1.39263i | ||||
\(521\) | − | 2.84879e13i | − | 0.742115i | −0.928610 | − | 0.371057i | \(-0.878995\pi\) | ||
0.928610 | − | 0.371057i | \(-0.121005\pi\) | |||||||
\(522\) | 4.77443e13 | − | 1.09852e13i | 1.23188 | − | 0.283436i | ||||
\(523\) | 4.35895e13i | 1.11397i | 0.830522 | + | 0.556985i | \(0.188042\pi\) | ||||
−0.830522 | + | 0.556985i | \(0.811958\pi\) | |||||||
\(524\) | 1.70682e13i | 0.432048i | ||||||||
\(525\) | 4.00494e13 | − | 7.69106e12i | 1.00415 | − | 0.192837i | ||||
\(526\) | 7.66059e13 | 1.90254 | ||||||||
\(527\) | 9.08239e12 | 0.223433 | ||||||||
\(528\) | 1.40041e13 | + | 1.11479e13i | 0.341261 | + | 0.271659i | ||||
\(529\) | −3.84133e13 | −0.927265 | ||||||||
\(530\) | −5.83540e13 | + | 2.68349e13i | −1.39538 | + | 0.641684i | ||||
\(531\) | 3.85658e13 | − | 8.87337e12i | 0.913545 | − | 0.210192i | ||||
\(532\) | − | 1.68865e13i | − | 0.396261i | ||||||
\(533\) | −6.10174e13 | −1.41846 | ||||||||
\(534\) | −1.26111e13 | − | 1.00390e13i | −0.290434 | − | 0.231198i | ||||
\(535\) | 7.35479e13 | − | 3.38220e13i | 1.67804 | − | 0.771669i | ||||
\(536\) | − | 4.43611e13i | − | 1.00272i | ||||||
\(537\) | −3.24167e13 | − | 2.58051e13i | −0.725934 | − | 0.577875i | ||||
\(538\) | 7.88149e13i | 1.74863i | ||||||||
\(539\) | 7.42288e11i | 0.0163166i | ||||||||
\(540\) | −1.45589e13 | − | 2.20578e11i | −0.317073 | − | 0.00480390i | ||||
\(541\) | 2.73506e13 | 0.590175 | 0.295087 | − | 0.955470i | \(-0.404651\pi\) | ||||
0.295087 | + | 0.955470i | \(0.404651\pi\) | |||||||
\(542\) | 1.05465e13 | 0.225483 | ||||||||
\(543\) | 2.22928e13 | − | 2.80045e13i | 0.472243 | − | 0.593237i | ||||
\(544\) | 1.75484e13 | 0.368335 | ||||||||
\(545\) | −4.86468e13 | + | 2.23709e13i | −1.01175 | + | 0.465266i | ||||
\(546\) | −6.93621e13 | + | 8.71334e13i | −1.42942 | + | 1.79565i | ||||
\(547\) | − | 6.95316e13i | − | 1.41986i | −0.704272 | − | 0.709930i | \(-0.748727\pi\) | ||
0.704272 | − | 0.709930i | \(-0.251273\pi\) | |||||||
\(548\) | 1.78166e13 | 0.360515 | ||||||||
\(549\) | 1.02455e13 | + | 4.45295e13i | 0.205434 | + | 0.892866i | ||||
\(550\) | 1.57221e13 | + | 1.34793e13i | 0.312390 | + | 0.267826i | ||||
\(551\) | 6.83637e13i | 1.34607i | ||||||||
\(552\) | −6.74656e12 | + | 8.47510e12i | −0.131640 | + | 0.165367i | ||||
\(553\) | 2.27490e13i | 0.439883i | ||||||||
\(554\) | − | 3.09191e13i | − | 0.592485i | ||||||
\(555\) | 1.45396e13 | + | 3.57808e12i | 0.276113 | + | 0.0679493i | ||||
\(556\) | 1.16823e13 | 0.219864 | ||||||||
\(557\) | −5.31234e13 | −0.990854 | −0.495427 | − | 0.868650i | \(-0.664988\pi\) | ||||
−0.495427 | + | 0.868650i | \(0.664988\pi\) | |||||||
\(558\) | 5.17187e12 | + | 2.24782e13i | 0.0956041 | + | 0.415519i | ||||
\(559\) | 5.75169e13 | 1.05375 | ||||||||
\(560\) | −2.86224e13 | − | 6.22411e13i | −0.519717 | − | 1.13015i | ||||
\(561\) | −9.37426e12 | − | 7.46233e12i | −0.168703 | − | 0.134295i | ||||
\(562\) | 1.10458e14i | 1.97023i | ||||||||
\(563\) | −4.21423e12 | −0.0745034 | −0.0372517 | − | 0.999306i | \(-0.511860\pi\) | ||||
−0.0372517 | + | 0.999306i | \(0.511860\pi\) | |||||||
\(564\) | 9.20893e12 | − | 1.15684e13i | 0.161367 | − | 0.202711i | ||||
\(565\) | 5.85606e12 | − | 2.69299e12i | 0.101710 | − | 0.0467727i | ||||
\(566\) | 7.41999e13i | 1.27738i | ||||||||
\(567\) | −2.61874e13 | − | 5.38957e13i | −0.446865 | − | 0.919685i | ||||
\(568\) | − | 2.54253e13i | − | 0.430056i | ||||||
\(569\) | − | 1.06431e14i | − | 1.78446i | −0.451577 | − | 0.892232i | \(-0.649138\pi\) | ||
0.451577 | − | 0.892232i | \(-0.350862\pi\) | |||||||
\(570\) | 2.01662e13 | − | 8.19455e13i | 0.335157 | − | 1.36192i | ||||
\(571\) | −3.51947e13 | −0.579824 | −0.289912 | − | 0.957053i | \(-0.593626\pi\) | ||||
−0.289912 | + | 0.957053i | \(0.593626\pi\) | |||||||
\(572\) | −1.36164e13 | −0.222373 | ||||||||
\(573\) | 7.83183e13 | + | 6.23448e13i | 1.26791 | + | 1.00932i | ||||
\(574\) | −5.30299e13 | −0.851062 | ||||||||
\(575\) | −1.10335e13 | + | 1.28693e13i | −0.175539 | + | 0.204747i | ||||
\(576\) | −7.30253e12 | − | 3.17386e13i | −0.115176 | − | 0.500582i | ||||
\(577\) | 1.84177e12i | 0.0287976i | 0.999896 | + | 0.0143988i | \(0.00458343\pi\) | ||||
−0.999896 | + | 0.0143988i | \(0.995417\pi\) | |||||||
\(578\) | 4.72590e13 | 0.732563 | ||||||||
\(579\) | 5.32665e13 | + | 4.24025e13i | 0.818581 | + | 0.651627i | ||||
\(580\) | −9.57816e12 | − | 2.08282e13i | −0.145929 | − | 0.317331i | ||||
\(581\) | − | 3.30080e13i | − | 0.498584i | ||||||
\(582\) | −5.39199e12 | − | 4.29226e12i | −0.0807484 | − | 0.0642793i | ||||
\(583\) | − | 3.23163e13i | − | 0.479820i | ||||||
\(584\) | 8.03106e13i | 1.18225i | ||||||||
\(585\) | −1.06092e14 | + | 8.18593e13i | −1.54847 | + | 1.19478i | ||||
\(586\) | 6.82635e13 | 0.987871 | ||||||||
\(587\) | 4.23190e13 | 0.607218 | 0.303609 | − | 0.952797i | \(-0.401808\pi\) | ||||
0.303609 | + | 0.952797i | \(0.401808\pi\) | |||||||
\(588\) | −6.31738e11 | + | 7.93597e11i | −0.00898774 | + | 0.0112905i | ||||
\(589\) | −3.21859e13 | −0.454034 | ||||||||
\(590\) | −3.21348e13 | − | 6.98788e13i | −0.449485 | − | 0.977429i | ||||
\(591\) | 7.74603e12 | − | 9.73065e12i | 0.107434 | − | 0.134960i | ||||
\(592\) | − | 2.51532e13i | − | 0.345928i | ||||||
\(593\) | 8.58099e13 | 1.17021 | 0.585105 | − | 0.810958i | \(-0.301053\pi\) | ||||
0.585105 | + | 0.810958i | \(0.301053\pi\) | |||||||
\(594\) | 1.31306e13 | − | 2.74499e13i | 0.177563 | − | 0.371200i | ||||
\(595\) | 1.91596e13 | + | 4.16637e13i | 0.256923 | + | 0.558692i | ||||
\(596\) | − | 1.33121e13i | − | 0.177017i | ||||||
\(597\) | 1.83013e13 | − | 2.29903e13i | 0.241329 | − | 0.303161i | ||||
\(598\) | − | 4.62935e13i | − | 0.605361i | ||||||
\(599\) | 6.43173e13i | 0.834053i | 0.908894 | + | 0.417027i | \(0.136928\pi\) | ||||
−0.908894 | + | 0.417027i | \(0.863072\pi\) | |||||||
\(600\) | −1.14933e13 | − | 5.98486e13i | −0.147805 | − | 0.769658i | ||||
\(601\) | −1.46385e14 | −1.86692 | −0.933459 | − | 0.358684i | \(-0.883225\pi\) | ||||
−0.933459 | + | 0.358684i | \(0.883225\pi\) | |||||||
\(602\) | 4.99876e13 | 0.632237 | ||||||||
\(603\) | −9.94035e13 | + | 2.28711e13i | −1.24685 | + | 0.286880i | ||||
\(604\) | −2.17045e13 | −0.270001 | ||||||||
\(605\) | 6.41742e13 | − | 2.95114e13i | 0.791742 | − | 0.364094i | ||||
\(606\) | −6.00016e13 | − | 4.77639e13i | −0.734175 | − | 0.584436i | ||||
\(607\) | − | 5.84050e12i | − | 0.0708772i | −0.999372 | − | 0.0354386i | \(-0.988717\pi\) | ||
0.999372 | − | 0.0354386i | \(-0.0112828\pi\) | |||||||
\(608\) | −6.21874e13 | −0.748487 | ||||||||
\(609\) | 5.87574e13 | − | 7.38117e13i | 0.701417 | − | 0.881128i | ||||
\(610\) | 8.06846e13 | − | 3.71040e13i | 0.955304 | − | 0.439310i | ||||
\(611\) | − | 1.36078e14i | − | 1.59802i | ||||||
\(612\) | −3.67128e12 | − | 1.59563e13i | −0.0427622 | − | 0.185855i | ||||
\(613\) | 9.69115e13i | 1.11963i | 0.828619 | + | 0.559813i | \(0.189127\pi\) | ||||
−0.828619 | + | 0.559813i | \(0.810873\pi\) | |||||||
\(614\) | 8.25228e13i | 0.945653i | ||||||||
\(615\) | −6.19575e13 | − | 1.52473e13i | −0.704236 | − | 0.173307i | ||||
\(616\) | 2.54841e13 | 0.287320 | ||||||||
\(617\) | −4.73194e13 | −0.529193 | −0.264596 | − | 0.964359i | \(-0.585239\pi\) | ||||
−0.264596 | + | 0.964359i | \(0.585239\pi\) | |||||||
\(618\) | −5.92220e13 | − | 4.71434e13i | −0.656963 | − | 0.522972i | ||||
\(619\) | −6.28987e13 | −0.692131 | −0.346065 | − | 0.938210i | \(-0.612482\pi\) | ||||
−0.346065 | + | 0.938210i | \(0.612482\pi\) | |||||||
\(620\) | 9.80600e12 | − | 4.50943e12i | 0.107037 | − | 0.0492225i | ||||
\(621\) | 2.24691e13 | + | 1.07481e13i | 0.243292 | + | 0.116378i | ||||
\(622\) | − | 1.48224e13i | − | 0.159208i | ||||||
\(623\) | −3.10402e13 | −0.330738 | ||||||||
\(624\) | 1.76117e14 | + | 1.40197e14i | 1.86156 | + | 1.48188i | ||||
\(625\) | −1.45637e13 | − | 9.42489e13i | −0.152711 | − | 0.988271i | ||||
\(626\) | 3.13239e13i | 0.325840i | ||||||||
\(627\) | 3.32202e13 | + | 2.64447e13i | 0.342819 | + | 0.272899i | ||||
\(628\) | − | 1.49861e13i | − | 0.153423i | ||||||
\(629\) | 1.68374e13i | 0.171010i | ||||||||
\(630\) | −9.22040e13 | + | 7.11435e13i | −0.929067 | + | 0.716857i | ||||
\(631\) | 1.04836e14 | 1.04800 | 0.524001 | − | 0.851718i | \(-0.324439\pi\) | ||||
0.524001 | + | 0.851718i | \(0.324439\pi\) | |||||||
\(632\) | 3.39955e13 | 0.337160 | ||||||||
\(633\) | 7.01151e13 | − | 8.80794e13i | 0.689911 | − | 0.866674i | ||||
\(634\) | −5.97490e13 | −0.583290 | ||||||||
\(635\) | 5.29160e13 | + | 1.15069e14i | 0.512529 | + | 1.11452i | ||||
\(636\) | 2.75034e13 | − | 3.45500e13i | 0.264302 | − | 0.332019i | ||||
\(637\) | 9.33504e12i | 0.0890060i | ||||||||
\(638\) | 4.79088e13 | 0.453223 | ||||||||
\(639\) | −5.69726e13 | + | 1.31085e13i | −0.534763 | + | 0.123040i | ||||
\(640\) | −1.17256e14 | + | 5.39217e13i | −1.09203 | + | 0.502185i | ||||
\(641\) | 5.73253e12i | 0.0529732i | 0.999649 | + | 0.0264866i | \(0.00843193\pi\) | ||||
−0.999649 | + | 0.0264866i | \(0.991568\pi\) | |||||||
\(642\) | −1.43978e14 | + | 1.80867e14i | −1.32015 | + | 1.65838i | ||||
\(643\) | − | 1.19706e13i | − | 0.108909i | −0.998516 | − | 0.0544544i | \(-0.982658\pi\) | ||
0.998516 | − | 0.0544544i | \(-0.0173419\pi\) | |||||||
\(644\) | − | 9.68668e12i | − | 0.0874471i | ||||||
\(645\) | 5.84031e13 | + | 1.43726e13i | 0.523164 | + | 0.128747i | ||||
\(646\) | 9.48959e13 | 0.843500 | ||||||||
\(647\) | 7.29754e12 | 0.0643658 | 0.0321829 | − | 0.999482i | \(-0.489754\pi\) | ||||
0.0321829 | + | 0.999482i | \(0.489754\pi\) | |||||||
\(648\) | −8.05401e13 | + | 3.91336e13i | −0.704915 | + | 0.342511i | ||||
\(649\) | 3.86987e13 | 0.336103 | ||||||||
\(650\) | 1.97722e14 | + | 1.69516e14i | 1.70407 | + | 1.46098i | ||||
\(651\) | 3.47508e13 | + | 2.76632e13i | 0.297208 | + | 0.236591i | ||||
\(652\) | 1.97924e12i | 0.0167981i | ||||||||
\(653\) | −1.25949e14 | −1.06079 | −0.530395 | − | 0.847751i | \(-0.677956\pi\) | ||||
−0.530395 | + | 0.847751i | \(0.677956\pi\) | |||||||
\(654\) | 9.52317e13 | − | 1.19631e14i | 0.795963 | − | 0.999898i | ||||
\(655\) | 6.86279e13 | + | 1.49235e14i | 0.569239 | + | 1.23784i | ||||
\(656\) | 1.07185e14i | 0.882301i | ||||||||
\(657\) | 1.79958e14 | − | 4.14055e13i | 1.47009 | − | 0.338245i | ||||
\(658\) | − | 1.18265e14i | − | 0.958795i | ||||||
\(659\) | 5.00896e13i | 0.403014i | 0.979487 | + | 0.201507i | \(0.0645839\pi\) | ||||
−0.979487 | + | 0.201507i | \(0.935416\pi\) | |||||||
\(660\) | −1.38262e13 | − | 3.40252e12i | −0.110403 | − | 0.0271694i | ||||
\(661\) | −7.45774e13 | −0.591017 | −0.295509 | − | 0.955340i | \(-0.595489\pi\) | ||||
−0.295509 | + | 0.955340i | \(0.595489\pi\) | |||||||
\(662\) | 3.44349e13 | 0.270838 | ||||||||
\(663\) | −1.17891e14 | − | 9.38465e13i | −0.920265 | − | 0.732572i | ||||
\(664\) | −4.93261e13 | −0.382152 | ||||||||
\(665\) | −6.78972e13 | − | 1.47646e14i | −0.522088 | − | 1.13531i | ||||
\(666\) | −4.16711e13 | + | 9.58785e12i | −0.318027 | + | 0.0731729i | ||||
\(667\) | 3.92158e13i | 0.297051i | ||||||||
\(668\) | −7.07623e11 | −0.00532010 | ||||||||
\(669\) | −1.38372e14 | − | 1.10150e14i | −1.03256 | − | 0.821967i | ||||
\(670\) | 8.28274e13 | + | 1.80113e14i | 0.613480 | + | 1.33404i | ||||
\(671\) | 4.46829e13i | 0.328495i | ||||||||
\(672\) | 6.71432e13 | + | 5.34490e13i | 0.489955 | + | 0.390026i | ||||
\(673\) | − | 1.40113e14i | − | 1.01486i | −0.861694 | − | 0.507428i | \(-0.830596\pi\) | ||
0.861694 | − | 0.507428i | \(-0.169404\pi\) | |||||||
\(674\) | − | 4.72109e13i | − | 0.339424i | ||||||
\(675\) | −1.28182e14 | + | 5.66099e13i | −0.914762 | + | 0.403993i | ||||
\(676\) | −1.26475e14 | −0.895922 | ||||||||
\(677\) | −1.95148e14 | −1.37221 | −0.686105 | − | 0.727502i | \(-0.740681\pi\) | ||||
−0.686105 | + | 0.727502i | \(0.740681\pi\) | |||||||
\(678\) | −1.14639e13 | + | 1.44011e13i | −0.0800173 | + | 0.100519i | ||||
\(679\) | −1.32715e13 | −0.0919540 | ||||||||
\(680\) | 6.22609e13 | − | 2.86316e13i | 0.428224 | − | 0.196925i | ||||
\(681\) | −6.14373e13 | + | 7.71783e13i | −0.419466 | + | 0.526938i | ||||
\(682\) | 2.25556e13i | 0.152874i | ||||||||
\(683\) | 1.95137e14 | 1.31291 | 0.656456 | − | 0.754364i | \(-0.272055\pi\) | ||||
0.656456 | + | 0.754364i | \(0.272055\pi\) | |||||||
\(684\) | 1.30101e13 | + | 5.65453e13i | 0.0868964 | + | 0.377673i | ||||
\(685\) | 1.55779e14 | − | 7.16372e13i | 1.03290 | − | 0.474992i | ||||
\(686\) | − | 1.70164e14i | − | 1.12007i | ||||||
\(687\) | 1.24079e13 | − | 1.55869e13i | 0.0810799 | − | 0.101854i | ||||
\(688\) | − | 1.01036e14i | − | 0.655444i | ||||||
\(689\) | − | 4.06410e14i | − | 2.61739i | ||||||
\(690\) | 1.15680e13 | − | 4.70068e13i | 0.0739628 | − | 0.300549i | ||||
\(691\) | 2.59159e14 | 1.64504 | 0.822520 | − | 0.568737i | \(-0.192568\pi\) | ||||
0.822520 | + | 0.568737i | \(0.192568\pi\) | |||||||
\(692\) | 4.41524e13 | 0.278243 | ||||||||
\(693\) | −1.31388e13 | − | 5.71044e13i | −0.0822032 | − | 0.357275i | ||||
\(694\) | −2.55659e14 | −1.58805 | ||||||||
\(695\) | 1.02144e14 | − | 4.69722e13i | 0.629923 | − | 0.289679i | ||||
\(696\) | −1.10302e14 | − | 8.78053e13i | −0.675363 | − | 0.537619i | ||||
\(697\) | − | 7.17491e13i | − | 0.436167i | ||||||
\(698\) | −2.79852e14 | −1.68909 | ||||||||
\(699\) | −5.09824e13 | + | 6.40447e13i | −0.305516 | + | 0.383793i | ||||
\(700\) | 4.13722e13 | + | 3.54703e13i | 0.246161 | + | 0.211045i | ||||
\(701\) | 2.90918e14i | 1.71862i | 0.511451 | + | 0.859312i | \(0.329108\pi\) | ||||
−0.511451 | + | 0.859312i | \(0.670892\pi\) | |||||||
\(702\) | 1.65131e14 | − | 3.45211e14i | 0.968596 | − | 2.02488i | ||||
\(703\) | − | 5.96677e13i | − | 0.347506i | ||||||
\(704\) | − | 3.18479e13i | − | 0.184169i | ||||||
\(705\) | 3.40037e13 | − | 1.38175e14i | 0.195245 | − | 0.793383i | ||||
\(706\) | 1.11621e14 | 0.636389 | ||||||||
\(707\) | −1.47684e14 | −0.836059 | ||||||||
\(708\) | 4.13736e13 | + | 3.29352e13i | 0.232572 | + | 0.185137i | ||||
\(709\) | 8.43977e13 | 0.471085 | 0.235543 | − | 0.971864i | \(-0.424313\pi\) | ||||
0.235543 | + | 0.971864i | \(0.424313\pi\) | |||||||
\(710\) | 4.74721e13 | + | 1.03231e14i | 0.263116 | + | 0.572159i | ||||
\(711\) | −1.75269e13 | − | 7.61763e13i | −0.0964624 | − | 0.419249i | ||||
\(712\) | 4.63856e13i | 0.253503i | ||||||||
\(713\) | −1.84629e13 | −0.100197 | ||||||||
\(714\) | −1.02458e14 | − | 8.15614e13i | −0.552149 | − | 0.439535i | ||||
\(715\) | −1.19054e14 | + | 5.47488e13i | −0.637111 | + | 0.292985i | ||||
\(716\) | − | 5.53677e13i | − | 0.294233i | ||||||
\(717\) | 2.48784e14 | + | 1.98043e14i | 1.31289 | + | 1.04512i | ||||
\(718\) | 2.41514e14i | 1.26567i | ||||||||
\(719\) | 1.24176e14i | 0.646237i | 0.946358 | + | 0.323119i | \(0.104731\pi\) | ||||
−0.946358 | + | 0.323119i | \(0.895269\pi\) | |||||||
\(720\) | 1.43797e14 | + | 1.86365e14i | 0.743170 | + | 0.963170i | ||||
\(721\) | −1.45765e14 | −0.748132 | ||||||||
\(722\) | −1.11126e14 | −0.566408 | ||||||||
\(723\) | −8.25260e13 | + | 1.03670e14i | −0.417733 | + | 0.524761i | ||||
\(724\) | 4.78316e13 | 0.240448 | ||||||||
\(725\) | −1.67492e14 | − | 1.43599e14i | −0.836190 | − | 0.716903i | ||||
\(726\) | −1.25628e14 | + | 1.57816e14i | −0.622881 | + | 0.782470i | ||||
\(727\) | 3.84408e14i | 1.89287i | 0.322900 | + | 0.946433i | \(0.395342\pi\) | ||||
−0.322900 | + | 0.946433i | \(0.604658\pi\) | |||||||
\(728\) | 3.20489e14 | 1.56732 | ||||||||
\(729\) | 1.29214e14 | + | 1.60297e14i | 0.627582 | + | 0.778550i | ||||
\(730\) | −1.49949e14 | − | 3.26073e14i | −0.723320 | − | 1.57290i | ||||
\(731\) | 6.76330e13i | 0.324020i | ||||||||
\(732\) | −3.80282e13 | + | 4.77715e13i | −0.180947 | + | 0.227307i | ||||
\(733\) | 1.65534e14i | 0.782291i | 0.920329 | + | 0.391146i | \(0.127921\pi\) | ||||
−0.920329 | + | 0.391146i | \(0.872079\pi\) | |||||||
\(734\) | − | 8.52806e13i | − | 0.400286i | ||||||
\(735\) | −2.33268e12 | + | 9.47887e12i | −0.0108747 | + | 0.0441896i | ||||
\(736\) | −3.56728e13 | −0.165177 | ||||||||
\(737\) | −9.97459e13 | −0.458730 | ||||||||
\(738\) | 1.77573e14 | − | 4.08567e13i | 0.811140 | − | 0.186630i | ||||
\(739\) | 7.39498e13 | 0.335517 | 0.167759 | − | 0.985828i | \(-0.446347\pi\) | ||||
0.167759 | + | 0.985828i | \(0.446347\pi\) | |||||||
\(740\) | 8.35979e12 | + | 1.81788e13i | 0.0376736 | + | 0.0819233i | ||||
\(741\) | 4.17778e14 | + | 3.32570e14i | 1.87006 | + | 1.48865i | ||||
\(742\) | − | 3.53209e14i | − | 1.57041i | ||||||
\(743\) | −3.00169e14 | −1.32563 | −0.662813 | − | 0.748785i | \(-0.730638\pi\) | ||||
−0.662813 | + | 0.748785i | \(0.730638\pi\) | |||||||
\(744\) | 4.13390e13 | − | 5.19306e13i | 0.181341 | − | 0.227803i | ||||
\(745\) | −5.35253e13 | − | 1.16394e14i | −0.233226 | − | 0.507163i | ||||
\(746\) | − | 2.47534e14i | − | 1.07137i | ||||||
\(747\) | 2.54309e13 | + | 1.10529e14i | 0.109335 | + | 0.475196i | ||||
\(748\) | − | 1.60112e13i | − | 0.0683781i | ||||||
\(749\) | 4.45175e14i | 1.88852i | ||||||||
\(750\) | 1.58409e14 | + | 2.21535e14i | 0.667534 | + | 0.933546i | ||||
\(751\) | −2.13746e14 | −0.894742 | −0.447371 | − | 0.894348i | \(-0.647640\pi\) | ||||
−0.447371 | + | 0.894348i | \(0.647640\pi\) | |||||||
\(752\) | −2.39040e14 | −0.993988 | ||||||||
\(753\) | 6.12970e13 | + | 4.87951e13i | 0.253200 | + | 0.201559i | ||||
\(754\) | 6.02502e14 | 2.47230 | ||||||||
\(755\) | −1.89772e14 | + | 8.72694e13i | −0.773566 | + | 0.355736i | ||||
\(756\) | 3.45528e13 | − | 7.22335e13i | 0.139918 | − | 0.292503i | ||||
\(757\) | − | 1.39360e14i | − | 0.560608i | −0.959911 | − | 0.280304i | \(-0.909565\pi\) | ||
0.959911 | − | 0.280304i | \(-0.0904352\pi\) | |||||||
\(758\) | −1.64231e14 | −0.656310 | ||||||||
\(759\) | 1.90563e13 | + | 1.51696e13i | 0.0756534 | + | 0.0602235i | ||||
\(760\) | −2.20638e14 | + | 1.01464e14i | −0.870186 | + | 0.400168i | ||||
\(761\) | − | 3.76303e14i | − | 1.47440i | −0.675676 | − | 0.737198i | \(-0.736148\pi\) | ||
0.675676 | − | 0.737198i | \(-0.263852\pi\) | |||||||
\(762\) | −2.82975e14 | − | 2.25260e14i | −1.10147 | − | 0.876819i | ||||
\(763\) | − | 2.94453e14i | − | 1.13866i | ||||||
\(764\) | 1.33768e14i | 0.513907i | ||||||||
\(765\) | −9.62567e13 | − | 1.24751e14i | −0.367387 | − | 0.476144i | ||||
\(766\) | −7.46280e13 | −0.282981 | ||||||||
\(767\) | 4.86676e14 | 1.83342 | ||||||||
\(768\) | 1.44067e14 | − | 1.80979e14i | 0.539211 | − | 0.677363i | ||||
\(769\) | −1.23191e14 | −0.458085 | −0.229043 | − | 0.973416i | \(-0.573560\pi\) | ||||
−0.229043 | + | 0.973416i | \(0.573560\pi\) | |||||||
\(770\) | −1.03469e14 | + | 4.75819e13i | −0.382260 | + | 0.175788i | ||||
\(771\) | 3.04347e14 | − | 3.82324e14i | 1.11711 | − | 1.40333i | ||||
\(772\) | 9.09792e13i | 0.331784i | ||||||||
\(773\) | 4.52781e14 | 1.64056 | 0.820278 | − | 0.571965i | \(-0.193819\pi\) | ||||
0.820278 | + | 0.571965i | \(0.193819\pi\) | |||||||
\(774\) | −1.67386e14 | + | 3.85128e13i | −0.602580 | + | 0.138644i | ||||
\(775\) | 6.76068e13 | − | 7.88560e13i | 0.241814 | − | 0.282050i | ||||
\(776\) | 1.98325e13i | 0.0704805i | ||||||||
\(777\) | −5.12833e13 | + | 6.44227e13i | −0.181080 | + | 0.227475i | ||||
\(778\) | 2.05801e14i | 0.722021i | ||||||||
\(779\) | 2.54262e14i | 0.886327i | ||||||||
\(780\) | −1.73879e14 | − | 4.27902e13i | −0.602245 | − | 0.148208i | ||||
\(781\) | −5.71688e13 | −0.196745 | ||||||||
\(782\) | 5.44356e13 | 0.186144 | ||||||||
\(783\) | −1.39884e14 | + | 2.92432e14i | −0.475291 | + | 0.993610i | ||||
\(784\) | 1.63983e13 | 0.0553628 | ||||||||
\(785\) | −6.02563e13 | − | 1.31031e14i | −0.202141 | − | 0.439566i | ||||
\(786\) | −3.66996e14 | − | 2.92145e14i | −1.22334 | − | 0.973836i | ||||
\(787\) | 3.31476e12i | 0.0109794i | 0.999985 | + | 0.00548970i | \(0.00174743\pi\) | ||||
−0.999985 | + | 0.00548970i | \(0.998253\pi\) | |||||||
\(788\) | 1.66199e13 | 0.0547014 | ||||||||
\(789\) | −3.15690e14 | + | 3.96573e14i | −1.03247 | + | 1.29699i | ||||
\(790\) | −1.38027e14 | + | 6.34735e13i | −0.448567 | + | 0.206280i | ||||
\(791\) | 3.54459e13i | 0.114468i | ||||||||
\(792\) | −8.53350e13 | + | 1.96342e13i | −0.273843 | + | 0.0630067i | ||||
\(793\) | 5.61933e14i | 1.79192i | ||||||||
\(794\) | − | 3.16973e14i | − | 1.00443i | ||||||
\(795\) | 1.01555e14 | − | 4.12672e14i | 0.319792 | − | 1.29948i | ||||
\(796\) | 3.92674e13 | 0.122876 | ||||||||
\(797\) | 3.09187e13 | 0.0961455 | 0.0480727 | − | 0.998844i | \(-0.484692\pi\) | ||||
0.0480727 | + | 0.998844i | \(0.484692\pi\) | |||||||
\(798\) | 3.63089e14 | + | 2.89035e14i | 1.12201 | + | 0.893172i | ||||
\(799\) | 1.60011e14 | 0.491380 | ||||||||
\(800\) | 1.30625e14 | − | 1.52360e14i | 0.398637 | − | 0.464967i | ||||
\(801\) | 1.03940e14 | − | 2.39149e13i | 0.315224 | − | 0.0725279i | ||||
\(802\) | − | 8.61188e13i | − | 0.259553i | ||||||
\(803\) | 1.80578e14 | 0.540864 | ||||||||
\(804\) | −1.06641e14 | − | 8.48906e13i | −0.317426 | − | 0.252685i | ||||
\(805\) | −3.89482e13 | − | 8.46950e13i | −0.115215 | − | 0.250541i | ||||
\(806\) | 2.83660e14i | 0.833918i | ||||||||
\(807\) | −4.08009e14 | − | 3.24793e14i | −1.19207 | − | 0.948940i | ||||
\(808\) | 2.20695e14i | 0.640818i | ||||||||
\(809\) | − | 2.79430e14i | − | 0.806363i | −0.915120 | − | 0.403181i | \(-0.867904\pi\) | ||
0.915120 | − | 0.403181i | \(-0.132096\pi\) | |||||||
\(810\) | 2.53938e14 | − | 3.09266e14i | 0.728286 | − | 0.886966i | ||||
\(811\) | −4.13858e14 | −1.17963 | −0.589816 | − | 0.807537i | \(-0.700800\pi\) | ||||
−0.589816 | + | 0.807537i | \(0.700800\pi\) | |||||||
\(812\) | 1.26070e14 | 0.357136 | ||||||||
\(813\) | −4.34618e13 | + | 5.45973e13i | −0.122364 | + | 0.153716i | ||||
\(814\) | −4.18147e13 | −0.117006 | ||||||||
\(815\) | 7.95813e12 | + | 1.73054e13i | 0.0221321 | + | 0.0481275i | ||||
\(816\) | −1.64854e14 | + | 2.07092e14i | −0.455669 | + | 0.572417i | ||||
\(817\) | − | 2.39675e14i | − | 0.658435i | ||||||
\(818\) | 2.76381e14 | 0.754642 | ||||||||
\(819\) | −1.65234e14 | − | 7.18146e14i | −0.448414 | − | 1.94892i | ||||
\(820\) | −3.56236e13 | − | 7.74654e13i | −0.0960879 | − | 0.208948i | ||||
\(821\) | 2.71361e14i | 0.727497i | 0.931497 | + | 0.363749i | \(0.118503\pi\) | ||||
−0.931497 | + | 0.363749i | \(0.881497\pi\) | |||||||
\(822\) | −3.04955e14 | + | 3.83089e14i | −0.812601 | + | 1.02080i | ||||
\(823\) | − | 6.14560e14i | − | 1.62767i | −0.581099 | − | 0.813833i | \(-0.697377\pi\) | ||
0.581099 | − | 0.813833i | \(-0.302623\pi\) | |||||||
\(824\) | 2.17827e14i | 0.573424i | ||||||||
\(825\) | −1.34569e14 | + | 2.58426e13i | −0.352109 | + | 0.0676187i | ||||
\(826\) | 4.22967e14 | 1.10003 | ||||||||
\(827\) | 4.23837e14 | 1.09565 | 0.547825 | − | 0.836593i | \(-0.315456\pi\) | ||||
0.547825 | + | 0.836593i | \(0.315456\pi\) | |||||||
\(828\) | 7.46307e12 | + | 3.24363e13i | 0.0191764 | + | 0.0833451i | ||||
\(829\) | 5.18512e14 | 1.32430 | 0.662149 | − | 0.749372i | \(-0.269645\pi\) | ||||
0.662149 | + | 0.749372i | \(0.269645\pi\) | |||||||
\(830\) | 2.00271e14 | − | 9.20976e13i | 0.508426 | − | 0.233807i | ||||
\(831\) | 1.60062e14 | + | 1.27416e14i | 0.403908 | + | 0.321529i | ||||
\(832\) | − | 4.00520e14i | − | 1.00463i | ||||||
\(833\) | −1.09769e13 | −0.0273687 | ||||||||
\(834\) | −1.99958e14 | + | 2.51190e14i | −0.495574 | + | 0.622546i | ||||
\(835\) | −6.18707e12 | + | 2.84521e12i | −0.0152424 | + | 0.00700943i | ||||
\(836\) | 5.67401e13i | 0.138950i | ||||||||
\(837\) | −1.37678e14 | − | 6.58580e13i | −0.335149 | − | 0.160318i | ||||
\(838\) | 5.10278e14i | 1.23477i | ||||||||
\(839\) | − | 6.00279e14i | − | 1.44392i | −0.691934 | − | 0.721960i | \(-0.743241\pi\) | ||
0.691934 | − | 0.721960i | \(-0.256759\pi\) | |||||||
\(840\) | 3.25427e14 | + | 8.00852e13i | 0.778140 | + | 0.191494i | ||||
\(841\) | −8.96794e13 | −0.213163 | ||||||||
\(842\) | 3.53584e13 | 0.0835473 | ||||||||
\(843\) | −5.71821e14 | − | 4.55195e14i | −1.34314 | − | 1.06920i | ||||
\(844\) | 1.50440e14 | 0.351277 | ||||||||
\(845\) | −1.10583e15 | + | 5.08530e14i | −2.56687 | + | 1.18041i | ||||
\(846\) | 9.11167e13 | + | 3.96015e14i | 0.210255 | + | 0.913819i | ||||
\(847\) | 3.88438e14i | 0.891055i | ||||||||
\(848\) | −7.13916e14 | −1.62805 | ||||||||
\(849\) | −3.84117e14 | − | 3.05774e14i | −0.870814 | − | 0.693207i | ||||
\(850\) | −1.99330e14 | + | 2.32497e14i | −0.449240 | + | 0.523989i | ||||
\(851\) | − | 3.42275e13i | − | 0.0766879i | ||||||
\(852\) | −6.11204e13 | − | 4.86546e13i | −0.136141 | − | 0.108374i | ||||
\(853\) | 1.51930e14i | 0.336433i | 0.985750 | + | 0.168216i | \(0.0538007\pi\) | ||||
−0.985750 | + | 0.168216i | \(0.946199\pi\) | |||||||
\(854\) | 4.88373e14i | 1.07513i | ||||||||
\(855\) | 3.41111e14 | + | 4.42090e14i | 0.746561 | + | 0.967565i | ||||
\(856\) | 6.65257e14 | 1.44751 | ||||||||
\(857\) | 4.95461e14 | 1.07178 | 0.535889 | − | 0.844288i | \(-0.319976\pi\) | ||||
0.535889 | + | 0.844288i | \(0.319976\pi\) | |||||||
\(858\) | 2.33063e14 | − | 2.92776e14i | 0.501229 | − | 0.629649i | ||||
\(859\) | 3.38503e14 | 0.723763 | 0.361882 | − | 0.932224i | \(-0.382134\pi\) | ||||
0.361882 | + | 0.932224i | \(0.382134\pi\) | |||||||
\(860\) | 3.35799e13 | + | 7.30214e13i | 0.0713818 | + | 0.155224i | ||||
\(861\) | 2.18534e14 | − | 2.74525e14i | 0.461852 | − | 0.580184i | ||||
\(862\) | − | 3.39448e13i | − | 0.0713243i | ||||||
\(863\) | 8.08631e14 | 1.68926 | 0.844629 | − | 0.535351i | \(-0.179821\pi\) | ||||
0.844629 | + | 0.535351i | \(0.179821\pi\) | |||||||
\(864\) | −2.66012e14 | − | 1.27246e14i | −0.552501 | − | 0.264288i | ||||
\(865\) | 3.86045e14 | − | 1.77528e14i | 0.797181 | − | 0.366595i | ||||
\(866\) | 5.88683e14i | 1.20863i | ||||||||
\(867\) | −1.94752e14 | + | 2.44650e14i | −0.397545 | + | 0.499401i | ||||
\(868\) | 5.93544e13i | 0.120463i | ||||||||
\(869\) | − | 7.64387e13i | − | 0.154246i | ||||||
\(870\) | 6.11785e14 | + | 1.50556e14i | 1.22745 | + | 0.302065i | ||||
\(871\) | −1.25441e15 | −2.50235 | ||||||||
\(872\) | −4.40021e14 | −0.872752 | ||||||||
\(873\) | 4.44403e13 | − | 1.02250e13i | 0.0876407 | − | 0.0201647i | ||||
\(874\) | −1.92907e14 | −0.378260 | ||||||||
\(875\) | 5.04355e14 | + | 1.43783e14i | 0.983323 | + | 0.280329i | ||||
\(876\) | 1.93060e14 | + | 1.53684e14i | 0.374259 | + | 0.297927i | ||||
\(877\) | 9.66772e14i | 1.86349i | 0.363118 | + | 0.931743i | \(0.381712\pi\) | ||||
−0.363118 | + | 0.931743i | \(0.618288\pi\) | |||||||
\(878\) | −4.40045e14 | −0.843381 | ||||||||
\(879\) | −2.81311e14 | + | 3.53386e14i | −0.536096 | + | 0.673449i | ||||
\(880\) | 9.61739e13 | + | 2.09135e14i | 0.182240 | + | 0.396291i | ||||
\(881\) | 7.33479e13i | 0.138200i | 0.997610 | + | 0.0691000i | \(0.0220128\pi\) | ||||
−0.997610 | + | 0.0691000i | \(0.977987\pi\) | |||||||
\(882\) | −6.25066e12 | − | 2.71669e13i | −0.0117107 | − | 0.0508976i | ||||
\(883\) | − | 6.11724e14i | − | 1.13960i | −0.821784 | − | 0.569800i | \(-0.807021\pi\) | ||
0.821784 | − | 0.569800i | \(-0.192979\pi\) | |||||||
\(884\) | − | 2.01358e14i | − | 0.372999i | ||||||
\(885\) | 4.94174e14 | + | 1.21612e14i | 0.910256 | + | 0.224007i | ||||
\(886\) | 4.13967e13 | 0.0758223 | ||||||||
\(887\) | 3.47616e14 | 0.633113 | 0.316557 | − | 0.948574i | \(-0.397473\pi\) | ||||
0.316557 | + | 0.948574i | \(0.397473\pi\) | |||||||
\(888\) | 9.62713e13 | + | 7.66363e13i | 0.174354 | + | 0.138794i | ||||
\(889\) | −6.96496e14 | −1.25432 | ||||||||
\(890\) | −8.66073e13 | − | 1.88332e14i | −0.155097 | − | 0.337268i | ||||
\(891\) | 8.79918e13 | + | 1.81094e14i | 0.156694 | + | 0.322490i | ||||
\(892\) | − | 2.36339e14i | − | 0.418515i | ||||||
\(893\) | −5.67043e14 | −0.998524 | ||||||||
\(894\) | 2.86233e14 | + | 2.27854e14i | 0.501224 | + | 0.398996i | ||||
\(895\) | −2.22623e14 | − | 4.84105e14i | −0.387663 | − | 0.842993i | ||||
\(896\) | − | 7.09733e14i | − | 1.22901i | ||||||
\(897\) | 2.39652e14 | + | 1.90774e14i | 0.412685 | + | 0.328516i | ||||
\(898\) | − | 1.12795e15i | − | 1.93155i | ||||||
\(899\) | − | 2.40292e14i | − | 0.409205i | ||||||
\(900\) | −1.65865e14 | − | 8.68989e13i | −0.280894 | − | 0.147164i | ||||
\(901\) | 4.77890e14 | 0.804829 | ||||||||
\(902\) | 1.78185e14 | 0.298427 | ||||||||
\(903\) | −2.05997e14 | + | 2.58776e14i | −0.343101 | + | 0.431007i | ||||
\(904\) | 5.29693e13 | 0.0877369 | ||||||||
\(905\) | 4.18213e14 | − | 1.92321e14i | 0.688898 | − | 0.316800i | ||||
\(906\) | 3.71501e14 | − | 4.66684e14i | 0.608581 | − | 0.764507i | ||||
\(907\) | − | 3.37948e14i | − | 0.550571i | −0.961362 | − | 0.275286i | \(-0.911228\pi\) | ||
0.961362 | − | 0.275286i | \(-0.0887724\pi\) | |||||||
\(908\) | −1.31820e14 | −0.213577 | ||||||||
\(909\) | 4.94528e14 | − | 1.13783e14i | 0.796841 | − | 0.183340i | ||||
\(910\) | −1.30123e15 | + | 5.98391e14i | −2.08520 | + | 0.958911i | ||||
\(911\) | − | 9.70578e14i | − | 1.54682i | −0.633908 | − | 0.773408i | \(-0.718550\pi\) | ||
0.633908 | − | 0.773408i | \(-0.281450\pi\) | |||||||
\(912\) | 5.84205e14 | − | 7.33885e14i | 0.925957 | − | 1.16320i | ||||
\(913\) | 1.10910e14i | 0.174830i | ||||||||
\(914\) | − | 2.89964e14i | − | 0.454583i | ||||||
\(915\) | −1.40418e14 | + | 5.70592e14i | −0.218936 | + | 0.889651i | ||||
\(916\) | 2.66224e13 | 0.0412829 | ||||||||
\(917\) | −9.03301e14 | −1.39311 | ||||||||
\(918\) | 4.05926e14 | + | 1.94174e14i | 0.622635 | + | 0.297836i | ||||
\(919\) | −4.30146e13 | −0.0656204 | −0.0328102 | − | 0.999462i | \(-0.510446\pi\) | ||||
−0.0328102 | + | 0.999462i | \(0.510446\pi\) | |||||||
\(920\) | −1.26566e14 | + | 5.82030e13i | −0.192033 | + | 0.0883093i | ||||
\(921\) | −4.27203e14 | − | 3.40073e14i | −0.644669 | − | 0.513185i | ||||
\(922\) | 3.59768e14i | 0.539968i | ||||||||
\(923\) | −7.18957e14 | −1.07323 | ||||||||
\(924\) | 4.87671e13 | − | 6.12618e13i | 0.0724048 | − | 0.0909557i | ||||
\(925\) | 1.46187e14 | + | 1.25333e14i | 0.215874 | + | 0.185078i | ||||
\(926\) | − | 4.58588e14i | − | 0.673547i | ||||||
\(927\) | 4.88103e14 | − | 1.12305e14i | 0.713038 | − | 0.164058i | ||||
\(928\) | − | 4.64276e14i | − | 0.674584i | ||||||
\(929\) | 1.14012e15i | 1.64768i | 0.566825 | + | 0.823838i | \(0.308172\pi\) | ||||
−0.566825 | + | 0.823838i | \(0.691828\pi\) | |||||||
\(930\) | −7.08821e13 | + | 2.88031e14i | −0.101888 | + | 0.414023i | ||||
\(931\) | 3.88995e13 | 0.0556155 | ||||||||
\(932\) | −1.09388e14 | −0.155558 | ||||||||
\(933\) | 7.67324e13 | + | 6.10824e13i | 0.108535 | + | 0.0863988i | ||||
\(934\) | −2.87372e14 | −0.404306 | ||||||||
\(935\) | −6.43780e13 | − | 1.39994e14i | −0.0900906 | − | 0.195907i | ||||
\(936\) | −1.07318e15 | + | 2.46920e14i | −1.49380 | + | 0.343698i | ||||
\(937\) | − | 4.74829e14i | − | 0.657414i | −0.944432 | − | 0.328707i | \(-0.893387\pi\) | ||
0.944432 | − | 0.328707i | \(-0.106613\pi\) | |||||||
\(938\) | −1.09020e15 | −1.50138 | ||||||||
\(939\) | −1.62158e14 | − | 1.29085e14i | −0.222131 | − | 0.176826i | ||||
\(940\) | 1.72760e14 | − | 7.94461e13i | 0.235398 | − | 0.108251i | ||||
\(941\) | 5.41591e14i | 0.734046i | 0.930212 | + | 0.367023i | \(0.119623\pi\) | ||||
−0.930212 | + | 0.367023i | \(0.880377\pi\) | |||||||
\(942\) | 3.22228e14 | + | 2.56507e14i | 0.434418 | + | 0.345816i | ||||
\(943\) | 1.45853e14i | 0.195595i | ||||||||
\(944\) | − | 8.54913e14i | − | 1.14041i | ||||||
\(945\) | 1.16737e13 | − | 7.70500e14i | 0.0154899 | − | 1.02238i | ||||
\(946\) | −1.67963e14 | −0.221696 | ||||||||
\(947\) | 4.19418e14 | 0.550678 | 0.275339 | − | 0.961347i | \(-0.411210\pi\) | ||||
0.275339 | + | 0.961347i | \(0.411210\pi\) | |||||||
\(948\) | 6.50546e13 | − | 8.17223e13i | 0.0849642 | − | 0.106733i | ||||
\(949\) | 2.27096e15 | 2.95038 | ||||||||
\(950\) | 7.06379e14 | − | 8.23914e14i | 0.912892 | − | 1.06479i | ||||
\(951\) | 2.46223e14 | − | 3.09308e14i | 0.316538 | − | 0.397639i | ||||
\(952\) | 3.76857e14i | 0.481939i | ||||||||
\(953\) | 8.57043e14 | 1.09028 | 0.545140 | − | 0.838345i | \(-0.316477\pi\) | ||||
0.545140 | + | 0.838345i | \(0.316477\pi\) | |||||||
\(954\) | 2.72129e14 | + | 1.18274e15i | 0.344376 | + | 1.49674i | ||||
\(955\) | 5.37853e14 | + | 1.16959e15i | 0.677091 | + | 1.47237i | ||||
\(956\) | 4.24924e14i | 0.532135i | ||||||||
\(957\) | −1.97430e14 | + | 2.48014e14i | −0.245954 | + | 0.308970i | ||||
\(958\) | − | 4.69214e14i | − | 0.581492i | ||||||
\(959\) | 9.42910e14i | 1.16246i | ||||||||
\(960\) | 1.00084e14 | − | 4.06691e14i | 0.122746 | − | 0.498780i | ||||
\(961\) | −7.06498e14 | −0.861974 | ||||||||
\(962\) | −5.25863e14 | −0.638259 | ||||||||
\(963\) | −3.42984e14 | − | 1.49069e15i | −0.414136 | − | 1.79994i | ||||
\(964\) | −1.77068e14 | −0.212694 | ||||||||
\(965\) | 3.65810e14 | + | 7.95473e14i | 0.437138 | + | 0.950580i | ||||
\(966\) | 2.08280e14 | + | 1.65800e14i | 0.247607 | + | 0.197106i | ||||
\(967\) | 1.14967e15i | 1.35969i | 0.733356 | + | 0.679845i | \(0.237953\pi\) | ||||
−0.733356 | + | 0.679845i | \(0.762047\pi\) | |||||||
\(968\) | 5.80470e14 | 0.682972 | ||||||||
\(969\) | −3.91062e14 | + | 4.91257e14i | −0.457748 | + | 0.575029i | ||||
\(970\) | −3.70296e13 | − | 8.05229e13i | −0.0431212 | − | 0.0937693i | ||||
\(971\) | − | 9.55627e13i | − | 0.110711i | −0.998467 | − | 0.0553557i | \(-0.982371\pi\) | ||
0.998467 | − | 0.0553557i | \(-0.0176293\pi\) | |||||||
\(972\) | −6.00496e13 | + | 2.68499e14i | −0.0692116 | + | 0.309465i | ||||
\(973\) | 6.18262e14i | 0.708938i | ||||||||
\(974\) | 5.88146e14i | 0.670950i | ||||||||
\(975\) | −1.69235e15 | + | 3.24998e14i | −1.92073 | + | 0.368856i | ||||
\(976\) | 9.87114e14 | 1.11460 | ||||||||
\(977\) | −5.87672e14 | −0.660179 | −0.330090 | − | 0.943950i | \(-0.607079\pi\) | ||||
−0.330090 | + | 0.943950i | \(0.607079\pi\) | |||||||
\(978\) | −4.25570e13 | − | 3.38773e13i | −0.0475639 | − | 0.0378629i | ||||
\(979\) | 1.04298e14 | 0.115974 | ||||||||
\(980\) | −1.18514e13 | + | 5.45005e12i | −0.0131111 | + | 0.00602935i | ||||
\(981\) | 2.26860e14 | + | 9.85990e14i | 0.249697 | + | 1.08524i | ||||
\(982\) | − | 1.09621e14i | − | 0.120043i | ||||||
\(983\) | −1.10930e15 | −1.20860 | −0.604300 | − | 0.796757i | \(-0.706547\pi\) | ||||
−0.604300 | + | 0.796757i | \(0.706547\pi\) | |||||||
\(984\) | −4.10241e14 | − | 3.26570e14i | −0.444697 | − | 0.353998i | ||||
\(985\) | 1.45316e14 | − | 6.68255e13i | 0.156723 | − | 0.0720711i | ||||
\(986\) | 7.08470e14i | 0.760216i | ||||||||
\(987\) | 6.12232e14 | + | 4.87364e14i | 0.653627 | + | 0.520316i | ||||
\(988\) | 7.13565e14i | 0.757964i | ||||||||
\(989\) | − | 1.37486e14i | − | 0.145304i | ||||||
\(990\) | 3.09813e14 | − | 2.39048e14i | 0.325780 | − | 0.251368i | ||||
\(991\) | 1.00801e15 | 1.05462 | 0.527312 | − | 0.849671i | \(-0.323200\pi\) | ||||
0.527312 | + | 0.849671i | \(0.323200\pi\) | |||||||
\(992\) | 2.18583e14 | 0.227540 | ||||||||
\(993\) | −1.41905e14 | + | 1.78263e14i | −0.146978 | + | 0.184635i | ||||
\(994\) | −6.24841e14 | −0.643929 | ||||||||
\(995\) | 3.43333e14 | − | 1.57886e14i | 0.352046 | − | 0.161894i | ||||
\(996\) | −9.43917e13 | + | 1.18576e14i | −0.0963024 | + | 0.120976i | ||||
\(997\) | − | 1.85313e15i | − | 1.88118i | −0.339542 | − | 0.940591i | \(-0.610272\pi\) | ||
0.339542 | − | 0.940591i | \(-0.389728\pi\) | |||||||
\(998\) | 1.18185e15 | 1.19374 | ||||||||
\(999\) | 1.22091e14 | − | 2.55234e14i | 0.122703 | − | 0.256514i |
(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 | 15.11.d.c.14.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 15.11.d.c.14.13 | yes | 16 | |
5.2 | odd | 4 | 75.11.c.h.26.3 | 16 | |||
5.3 | odd | 4 | 75.11.c.h.26.14 | 16 | |||
5.4 | even | 2 | inner | 15.11.d.c.14.14 | yes | 16 | |
15.2 | even | 4 | 75.11.c.h.26.13 | 16 | |||
15.8 | even | 4 | 75.11.c.h.26.4 | 16 | |||
15.14 | odd | 2 | inner | 15.11.d.c.14.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.11.d.c.14.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
15.11.d.c.14.4 | yes | 16 | 15.14 | odd | 2 | inner | |
15.11.d.c.14.13 | yes | 16 | 3.2 | odd | 2 | inner | |
15.11.d.c.14.14 | yes | 16 | 5.4 | even | 2 | inner | |
75.11.c.h.26.3 | 16 | 5.2 | odd | 4 | |||
75.11.c.h.26.4 | 16 | 15.8 | even | 4 | |||
75.11.c.h.26.13 | 16 | 15.2 | even | 4 | |||
75.11.c.h.26.14 | 16 | 5.3 | odd | 4 |