Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,26,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(19.7998389976\) |
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: | \( x^{12} + 71168091 x^{10} + \cdots + 10\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{20}\cdot 5^{29} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.8 | ||
Root | \(1460.97i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.26.b.a.4.5 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2921.94i | 0.504424i | 0.967672 | + | 0.252212i | \(0.0811581\pi\) | ||||
−0.967672 | + | 0.252212i | \(0.918842\pi\) | |||||||
\(3\) | − | 1.33312e6i | − | 1.44829i | −0.689650 | − | 0.724143i | \(-0.742235\pi\) | ||
0.689650 | − | 0.724143i | \(-0.257765\pi\) | |||||||
\(4\) | 2.50167e7 | 0.745556 | ||||||||
\(5\) | −5.18558e8 | + | 1.70647e8i | −0.949888 | + | 0.312589i | ||||
\(6\) | 3.89530e9 | 0.730551 | ||||||||
\(7\) | 4.60230e10i | 1.25675i | 0.777910 | + | 0.628375i | \(0.216280\pi\) | ||||
−0.777910 | + | 0.628375i | \(0.783720\pi\) | |||||||
\(8\) | 1.71141e11i | 0.880501i | ||||||||
\(9\) | −9.29927e11 | −1.09753 | ||||||||
\(10\) | −4.98620e11 | − | 1.51520e12i | −0.157678 | − | 0.479147i | ||||
\(11\) | 1.55304e13 | 1.49202 | 0.746010 | − | 0.665935i | \(-0.231967\pi\) | ||||
0.746010 | + | 0.665935i | \(0.231967\pi\) | |||||||
\(12\) | − | 3.33503e13i | − | 1.07978i | ||||||
\(13\) | − | 6.93016e13i | − | 0.824995i | −0.910959 | − | 0.412497i | \(-0.864657\pi\) | ||
0.910959 | − | 0.412497i | \(-0.135343\pi\) | |||||||
\(14\) | −1.34476e14 | −0.633936 | ||||||||
\(15\) | 2.27493e14 | + | 6.91302e14i | 0.452718 | + | 1.37571i | ||||
\(16\) | 3.39357e14 | 0.301410 | ||||||||
\(17\) | 1.00732e15i | 0.419328i | 0.977773 | + | 0.209664i | \(0.0672370\pi\) | ||||
−0.977773 | + | 0.209664i | \(0.932763\pi\) | |||||||
\(18\) | − | 2.71719e15i | − | 0.553623i | ||||||
\(19\) | 9.85510e15 | 1.02151 | 0.510753 | − | 0.859728i | \(-0.329367\pi\) | ||||
0.510753 | + | 0.859728i | \(0.329367\pi\) | |||||||
\(20\) | −1.29726e16 | + | 4.26903e15i | −0.708195 | + | 0.233053i | ||||
\(21\) | 6.13543e16 | 1.82014 | ||||||||
\(22\) | 4.53789e16i | 0.752611i | ||||||||
\(23\) | 3.90157e16i | 0.371229i | 0.982623 | + | 0.185614i | \(0.0594275\pi\) | ||||
−0.982623 | + | 0.185614i | \(0.940572\pi\) | |||||||
\(24\) | 2.28152e17 | 1.27522 | ||||||||
\(25\) | 2.39782e17 | − | 1.76981e17i | 0.804576 | − | 0.593849i | ||||
\(26\) | 2.02495e17 | 0.416148 | ||||||||
\(27\) | 1.10167e17i | 0.141256i | ||||||||
\(28\) | 1.15134e18i | 0.936978i | ||||||||
\(29\) | 2.60223e18 | 1.36575 | 0.682874 | − | 0.730536i | \(-0.260730\pi\) | ||||
0.682874 | + | 0.730536i | \(0.260730\pi\) | |||||||
\(30\) | −2.01994e18 | + | 6.64722e17i | −0.693942 | + | 0.228362i | ||||
\(31\) | −3.55337e18 | −0.810251 | −0.405126 | − | 0.914261i | \(-0.632772\pi\) | ||||
−0.405126 | + | 0.914261i | \(0.632772\pi\) | |||||||
\(32\) | 6.73413e18i | 1.03254i | ||||||||
\(33\) | − | 2.07039e19i | − | 2.16087i | ||||||
\(34\) | −2.94331e18 | −0.211519 | ||||||||
\(35\) | −7.85368e18 | − | 2.38656e19i | −0.392846 | − | 1.19377i | ||||
\(36\) | −2.32637e19 | −0.818272 | ||||||||
\(37\) | 5.55139e19i | 1.38637i | 0.720758 | + | 0.693187i | \(0.243794\pi\) | ||||
−0.720758 | + | 0.693187i | \(0.756206\pi\) | |||||||
\(38\) | 2.87960e19i | 0.515273i | ||||||||
\(39\) | −9.23875e19 | −1.19483 | ||||||||
\(40\) | −2.92047e19 | − | 8.87467e19i | −0.275235 | − | 0.836378i | ||||
\(41\) | 1.48547e20 | 1.02817 | 0.514085 | − | 0.857739i | \(-0.328132\pi\) | ||||
0.514085 | + | 0.857739i | \(0.328132\pi\) | |||||||
\(42\) | 1.79273e20i | 0.918121i | ||||||||
\(43\) | − | 2.65747e20i | − | 1.01417i | −0.861895 | − | 0.507087i | \(-0.830722\pi\) | ||
0.861895 | − | 0.507087i | \(-0.169278\pi\) | |||||||
\(44\) | 3.88520e20 | 1.11238 | ||||||||
\(45\) | 4.82222e20 | − | 1.58689e20i | 1.04253 | − | 0.343077i | ||||
\(46\) | −1.14002e20 | −0.187257 | ||||||||
\(47\) | 1.37381e21i | 1.72465i | 0.506352 | + | 0.862327i | \(0.330994\pi\) | ||||
−0.506352 | + | 0.862327i | \(0.669006\pi\) | |||||||
\(48\) | − | 4.52404e20i | − | 0.436527i | ||||||
\(49\) | −7.77046e20 | −0.579423 | ||||||||
\(50\) | 5.17127e20 | + | 7.00630e20i | 0.299552 | + | 0.405848i | ||||
\(51\) | 1.34288e21 | 0.607307 | ||||||||
\(52\) | − | 1.73370e21i | − | 0.615080i | ||||||
\(53\) | − | 1.71008e21i | − | 0.478153i | −0.971001 | − | 0.239077i | \(-0.923155\pi\) | ||
0.971001 | − | 0.239077i | \(-0.0768447\pi\) | |||||||
\(54\) | −3.21902e20 | −0.0712529 | ||||||||
\(55\) | −8.05343e21 | + | 2.65022e21i | −1.41725 | + | 0.466389i | ||||
\(56\) | −7.87643e21 | −1.10657 | ||||||||
\(57\) | − | 1.31381e22i | − | 1.47943i | ||||||
\(58\) | 7.60356e21i | 0.688917i | ||||||||
\(59\) | 5.13294e21 | 0.375592 | 0.187796 | − | 0.982208i | \(-0.439866\pi\) | ||||
0.187796 | + | 0.982208i | \(0.439866\pi\) | |||||||
\(60\) | 5.69114e21 | + | 1.72941e22i | 0.337527 | + | 1.02567i | ||||
\(61\) | −9.68041e19 | −0.00466951 | −0.00233475 | − | 0.999997i | \(-0.500743\pi\) | ||||
−0.00233475 | + | 0.999997i | \(0.500743\pi\) | |||||||
\(62\) | − | 1.03827e22i | − | 0.408711i | ||||||
\(63\) | − | 4.27980e22i | − | 1.37933i | ||||||
\(64\) | −8.28978e21 | −0.219429 | ||||||||
\(65\) | 1.18261e22 | + | 3.59369e22i | 0.257884 | + | 0.783653i | ||||
\(66\) | 6.04957e22 | 1.09000 | ||||||||
\(67\) | 9.29203e22i | 1.38732i | 0.720304 | + | 0.693658i | \(0.244002\pi\) | ||||
−0.720304 | + | 0.693658i | \(0.755998\pi\) | |||||||
\(68\) | 2.51997e22i | 0.312633i | ||||||||
\(69\) | 5.20127e22 | 0.537646 | ||||||||
\(70\) | 6.97338e22 | − | 2.29480e22i | 0.602168 | − | 0.198161i | ||||
\(71\) | −6.03387e22 | −0.436381 | −0.218191 | − | 0.975906i | \(-0.570015\pi\) | ||||
−0.218191 | + | 0.975906i | \(0.570015\pi\) | |||||||
\(72\) | − | 1.59149e23i | − | 0.966379i | ||||||
\(73\) | − | 3.38440e22i | − | 0.172960i | −0.996254 | − | 0.0864801i | \(-0.972438\pi\) | ||
0.996254 | − | 0.0864801i | \(-0.0275619\pi\) | |||||||
\(74\) | −1.62208e23 | −0.699321 | ||||||||
\(75\) | −2.35937e23 | − | 3.19659e23i | −0.860064 | − | 1.16526i | ||||
\(76\) | 2.46542e23 | 0.761590 | ||||||||
\(77\) | 7.14756e23i | 1.87510i | ||||||||
\(78\) | − | 2.69951e23i | − | 0.602701i | ||||||
\(79\) | −5.76376e23 | −1.09741 | −0.548703 | − | 0.836018i | \(-0.684878\pi\) | ||||
−0.548703 | + | 0.836018i | \(0.684878\pi\) | |||||||
\(80\) | −1.75976e23 | + | 5.79103e22i | −0.286305 | + | 0.0942173i | ||||
\(81\) | −6.41050e23 | −0.892954 | ||||||||
\(82\) | 4.34044e23i | 0.518634i | ||||||||
\(83\) | − | 2.45821e23i | − | 0.252431i | −0.992003 | − | 0.126216i | \(-0.959717\pi\) | ||
0.992003 | − | 0.126216i | \(-0.0402831\pi\) | |||||||
\(84\) | 1.53488e24 | 1.35701 | ||||||||
\(85\) | −1.71895e23 | − | 5.22352e23i | −0.131077 | − | 0.398315i | ||||
\(86\) | 7.76495e23 | 0.511574 | ||||||||
\(87\) | − | 3.46909e24i | − | 1.97800i | ||||||
\(88\) | 2.65789e24i | 1.31372i | ||||||||
\(89\) | 1.04517e24 | 0.448553 | 0.224276 | − | 0.974526i | \(-0.427998\pi\) | ||||
0.224276 | + | 0.974526i | \(0.427998\pi\) | |||||||
\(90\) | 4.63680e23 | + | 1.40902e24i | 0.173056 | + | 0.525880i | ||||
\(91\) | 3.18946e24 | 1.03681 | ||||||||
\(92\) | 9.76045e23i | 0.276772i | ||||||||
\(93\) | 4.73708e24i | 1.17348i | ||||||||
\(94\) | −4.01417e24 | −0.869958 | ||||||||
\(95\) | −5.11044e24 | + | 1.68174e24i | −0.970317 | + | 0.319312i | ||||
\(96\) | 8.97742e24 | 1.49541 | ||||||||
\(97\) | − | 8.72407e24i | − | 1.27665i | −0.769766 | − | 0.638326i | \(-0.779627\pi\) | ||
0.769766 | − | 0.638326i | \(-0.220373\pi\) | |||||||
\(98\) | − | 2.27048e24i | − | 0.292275i | ||||||
\(99\) | −1.44422e25 | −1.63754 | ||||||||
\(100\) | 5.99857e24 | − | 4.42748e24i | 0.599857 | − | 0.442748i | ||||
\(101\) | −5.47037e24 | −0.483058 | −0.241529 | − | 0.970394i | \(-0.577649\pi\) | ||||
−0.241529 | + | 0.970394i | \(0.577649\pi\) | |||||||
\(102\) | 3.92380e24i | 0.306341i | ||||||||
\(103\) | − | 1.52638e25i | − | 1.05487i | −0.849596 | − | 0.527434i | \(-0.823154\pi\) | ||
0.849596 | − | 0.527434i | \(-0.176846\pi\) | |||||||
\(104\) | 1.18604e25 | 0.726409 | ||||||||
\(105\) | −3.18158e25 | + | 1.04699e25i | −1.72893 | + | 0.568954i | ||||
\(106\) | 4.99674e24 | 0.241192 | ||||||||
\(107\) | 2.40394e25i | 1.03187i | 0.856627 | + | 0.515937i | \(0.172556\pi\) | ||||
−0.856627 | + | 0.515937i | \(0.827444\pi\) | |||||||
\(108\) | 2.75603e24i | 0.105314i | ||||||||
\(109\) | −2.25515e25 | −0.767970 | −0.383985 | − | 0.923339i | \(-0.625449\pi\) | ||||
−0.383985 | + | 0.923339i | \(0.625449\pi\) | |||||||
\(110\) | −7.74378e24 | − | 2.35316e25i | −0.235258 | − | 0.714897i | ||||
\(111\) | 7.40069e25 | 2.00787 | ||||||||
\(112\) | 1.56182e25i | 0.378797i | ||||||||
\(113\) | − | 1.47234e25i | − | 0.319541i | −0.987154 | − | 0.159771i | \(-0.948925\pi\) | ||
0.987154 | − | 0.159771i | \(-0.0510755\pi\) | |||||||
\(114\) | 3.83886e25 | 0.746262 | ||||||||
\(115\) | −6.65792e24 | − | 2.02319e25i | −0.116042 | − | 0.352626i | ||||
\(116\) | 6.50992e25 | 1.01824 | ||||||||
\(117\) | 6.44454e25i | 0.905459i | ||||||||
\(118\) | 1.49981e25i | 0.189458i | ||||||||
\(119\) | −4.63597e25 | −0.526991 | ||||||||
\(120\) | −1.18310e26 | + | 3.89335e25i | −1.21131 | + | 0.398619i | ||||
\(121\) | 1.32847e26 | 1.22612 | ||||||||
\(122\) | − | 2.82856e23i | − | 0.00235541i | ||||||
\(123\) | − | 1.98031e26i | − | 1.48908i | ||||||
\(124\) | −8.88937e25 | −0.604088 | ||||||||
\(125\) | −9.41399e25 | + | 1.32693e26i | −0.578627 | + | 0.815592i | ||||
\(126\) | 1.25053e26 | 0.695766 | ||||||||
\(127\) | − | 2.67225e26i | − | 1.34689i | −0.739240 | − | 0.673443i | \(-0.764815\pi\) | ||
0.739240 | − | 0.673443i | \(-0.235185\pi\) | |||||||
\(128\) | 2.01738e26i | 0.921854i | ||||||||
\(129\) | −3.54273e26 | −1.46881 | ||||||||
\(130\) | −1.05005e26 | + | 3.45552e25i | −0.395294 | + | 0.130083i | ||||
\(131\) | 1.69205e26 | 0.578790 | 0.289395 | − | 0.957210i | \(-0.406546\pi\) | ||||
0.289395 | + | 0.957210i | \(0.406546\pi\) | |||||||
\(132\) | − | 5.17944e26i | − | 1.61105i | ||||||
\(133\) | 4.53561e26i | 1.28378i | ||||||||
\(134\) | −2.71507e26 | −0.699796 | ||||||||
\(135\) | −1.87997e25 | − | 5.71282e25i | −0.0441550 | − | 0.134177i | ||||
\(136\) | −1.72393e26 | −0.369219 | ||||||||
\(137\) | 6.29711e26i | 1.23065i | 0.788274 | + | 0.615325i | \(0.210975\pi\) | ||||
−0.788274 | + | 0.615325i | \(0.789025\pi\) | |||||||
\(138\) | 1.51978e26i | 0.271202i | ||||||||
\(139\) | 9.76873e26 | 1.59277 | 0.796385 | − | 0.604790i | \(-0.206743\pi\) | ||||
0.796385 | + | 0.604790i | \(0.206743\pi\) | |||||||
\(140\) | −1.96473e26 | − | 5.97039e26i | −0.292889 | − | 0.890025i | ||||
\(141\) | 1.83145e27 | 2.49779 | ||||||||
\(142\) | − | 1.76306e26i | − | 0.220122i | ||||||
\(143\) | − | 1.07628e27i | − | 1.23091i | ||||||
\(144\) | −3.15577e26 | −0.330807 | ||||||||
\(145\) | −1.34941e27 | + | 4.44063e26i | −1.29731 | + | 0.426918i | ||||
\(146\) | 9.88901e25 | 0.0872453 | ||||||||
\(147\) | 1.03590e27i | 0.839170i | ||||||||
\(148\) | 1.38878e27i | 1.03362i | ||||||||
\(149\) | 8.38306e26 | 0.573554 | 0.286777 | − | 0.957997i | \(-0.407416\pi\) | ||||
0.286777 | + | 0.957997i | \(0.407416\pi\) | |||||||
\(150\) | 9.34025e26 | − | 6.89394e26i | 0.587784 | − | 0.433837i | ||||
\(151\) | −1.30894e27 | −0.758068 | −0.379034 | − | 0.925383i | \(-0.623744\pi\) | ||||
−0.379034 | + | 0.925383i | \(0.623744\pi\) | |||||||
\(152\) | 1.68661e27i | 0.899437i | ||||||||
\(153\) | − | 9.36730e26i | − | 0.460226i | ||||||
\(154\) | −2.08847e27 | −0.945845 | ||||||||
\(155\) | 1.84263e27 | − | 6.06373e26i | 0.769649 | − | 0.253276i | ||||
\(156\) | −2.31123e27 | −0.890811 | ||||||||
\(157\) | − | 1.73490e27i | − | 0.617344i | −0.951168 | − | 0.308672i | \(-0.900115\pi\) | ||
0.951168 | − | 0.308672i | \(-0.0998846\pi\) | |||||||
\(158\) | − | 1.68413e27i | − | 0.553558i | ||||||
\(159\) | −2.27974e27 | −0.692503 | ||||||||
\(160\) | −1.14916e27 | − | 3.49204e27i | −0.322760 | − | 0.980797i | ||||
\(161\) | −1.79562e27 | −0.466542 | ||||||||
\(162\) | − | 1.87311e27i | − | 0.450428i | ||||||
\(163\) | − | 2.32016e27i | − | 0.516623i | −0.966062 | − | 0.258311i | \(-0.916834\pi\) | ||
0.966062 | − | 0.258311i | \(-0.0831661\pi\) | |||||||
\(164\) | 3.71615e27 | 0.766558 | ||||||||
\(165\) | 3.53307e27 | + | 1.07362e28i | 0.675464 | + | 2.05259i | ||||
\(166\) | 7.18275e26 | 0.127333 | ||||||||
\(167\) | 1.85957e27i | 0.305814i | 0.988241 | + | 0.152907i | \(0.0488635\pi\) | ||||
−0.988241 | + | 0.152907i | \(0.951137\pi\) | |||||||
\(168\) | 1.05002e28i | 1.60263i | ||||||||
\(169\) | 2.25370e27 | 0.319384 | ||||||||
\(170\) | 1.52628e27 | − | 5.02268e26i | 0.200920 | − | 0.0661186i | ||||
\(171\) | −9.16452e27 | −1.12114 | ||||||||
\(172\) | − | 6.64811e27i | − | 0.756123i | ||||||
\(173\) | − | 1.33577e28i | − | 1.41304i | −0.707691 | − | 0.706522i | \(-0.750263\pi\) | ||
0.707691 | − | 0.706522i | \(-0.249737\pi\) | |||||||
\(174\) | 1.01365e28 | 0.997749 | ||||||||
\(175\) | 8.14519e27 | + | 1.10355e28i | 0.746321 | + | 1.01115i | ||||
\(176\) | 5.27035e27 | 0.449709 | ||||||||
\(177\) | − | 6.84283e27i | − | 0.543964i | ||||||
\(178\) | 3.05393e27i | 0.226261i | ||||||||
\(179\) | 9.48628e27 | 0.655289 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(180\) | 1.20636e28 | − | 3.96988e27i | 0.777267 | − | 0.255783i | ||||
\(181\) | −3.16510e28 | −1.90285 | −0.951427 | − | 0.307876i | \(-0.900382\pi\) | ||||
−0.951427 | + | 0.307876i | \(0.900382\pi\) | |||||||
\(182\) | 9.31942e27i | 0.522994i | ||||||||
\(183\) | 1.29052e26i | 0.00676278i | ||||||||
\(184\) | −6.67720e27 | −0.326867 | ||||||||
\(185\) | −9.47329e27 | − | 2.87872e28i | −0.433365 | − | 1.31690i | ||||
\(186\) | −1.38415e28 | −0.591930 | ||||||||
\(187\) | 1.56440e28i | 0.625646i | ||||||||
\(188\) | 3.43681e28i | 1.28583i | ||||||||
\(189\) | −5.07023e27 | −0.177523 | ||||||||
\(190\) | −4.91395e27 | − | 1.49324e28i | −0.161069 | − | 0.489452i | ||||
\(191\) | −3.69520e28 | −1.13428 | −0.567141 | − | 0.823621i | \(-0.691951\pi\) | ||||
−0.567141 | + | 0.823621i | \(0.691951\pi\) | |||||||
\(192\) | 1.10513e28i | 0.317796i | ||||||||
\(193\) | − | 4.44096e28i | − | 1.19677i | −0.801209 | − | 0.598385i | \(-0.795809\pi\) | ||
0.801209 | − | 0.598385i | \(-0.204191\pi\) | |||||||
\(194\) | 2.54912e28 | 0.643974 | ||||||||
\(195\) | 4.79083e28 | − | 1.57656e28i | 1.13495 | − | 0.373490i | ||||
\(196\) | −1.94391e28 | −0.431992 | ||||||||
\(197\) | 1.61228e28i | 0.336211i | 0.985769 | + | 0.168106i | \(0.0537650\pi\) | ||||
−0.985769 | + | 0.168106i | \(0.946235\pi\) | |||||||
\(198\) | − | 4.21991e28i | − | 0.826016i | ||||||
\(199\) | −8.59811e28 | −1.58030 | −0.790150 | − | 0.612913i | \(-0.789998\pi\) | ||||
−0.790150 | + | 0.612913i | \(0.789998\pi\) | |||||||
\(200\) | 3.02887e28 | + | 4.10367e28i | 0.522885 | + | 0.708430i | ||||
\(201\) | 1.23874e29 | 2.00923 | ||||||||
\(202\) | − | 1.59841e28i | − | 0.243666i | ||||||
\(203\) | 1.19762e29i | 1.71641i | ||||||||
\(204\) | 3.35943e28 | 0.452781 | ||||||||
\(205\) | −7.70301e28 | + | 2.53491e28i | −0.976647 | + | 0.321395i | ||||
\(206\) | 4.46000e28 | 0.532102 | ||||||||
\(207\) | − | 3.62818e28i | − | 0.407436i | ||||||
\(208\) | − | 2.35180e28i | − | 0.248661i | ||||||
\(209\) | 1.53054e29 | 1.52411 | ||||||||
\(210\) | −3.05925e28 | − | 9.29637e28i | −0.286994 | − | 0.872112i | ||||
\(211\) | −4.71369e28 | −0.416707 | −0.208353 | − | 0.978054i | \(-0.566810\pi\) | ||||
−0.208353 | + | 0.978054i | \(0.566810\pi\) | |||||||
\(212\) | − | 4.27805e28i | − | 0.356490i | ||||||
\(213\) | 8.04388e28i | 0.632005i | ||||||||
\(214\) | −7.02417e28 | −0.520502 | ||||||||
\(215\) | 4.53489e28 | + | 1.37805e29i | 0.317019 | + | 0.963351i | ||||
\(216\) | −1.88542e28 | −0.124376 | ||||||||
\(217\) | − | 1.63537e29i | − | 1.01828i | ||||||
\(218\) | − | 6.58941e28i | − | 0.387383i | ||||||
\(219\) | −4.51182e28 | −0.250496 | ||||||||
\(220\) | −2.01470e29 | + | 6.62997e28i | −1.05664 | + | 0.347719i | ||||
\(221\) | 6.98085e28 | 0.345943 | ||||||||
\(222\) | 2.16244e29i | 1.01282i | ||||||||
\(223\) | − | 9.50446e28i | − | 0.420840i | −0.977611 | − | 0.210420i | \(-0.932517\pi\) | ||
0.977611 | − | 0.210420i | \(-0.0674831\pi\) | |||||||
\(224\) | −3.09925e29 | −1.29765 | ||||||||
\(225\) | −2.22980e29 | + | 1.64579e29i | −0.883049 | + | 0.651769i | ||||
\(226\) | 4.30208e28 | 0.161184 | ||||||||
\(227\) | − | 3.76543e29i | − | 1.33503i | −0.744596 | − | 0.667516i | \(-0.767358\pi\) | ||
0.744596 | − | 0.667516i | \(-0.232642\pi\) | |||||||
\(228\) | − | 3.28671e29i | − | 1.10300i | ||||||
\(229\) | −8.92811e28 | −0.283672 | −0.141836 | − | 0.989890i | \(-0.545301\pi\) | ||||
−0.141836 | + | 0.989890i | \(0.545301\pi\) | |||||||
\(230\) | 5.91165e28 | − | 1.94540e28i | 0.177873 | − | 0.0585345i | ||||
\(231\) | 9.52857e29 | 2.71568 | ||||||||
\(232\) | 4.45349e29i | 1.20254i | ||||||||
\(233\) | 5.97595e28i | 0.152918i | 0.997073 | + | 0.0764589i | \(0.0243614\pi\) | ||||
−0.997073 | + | 0.0764589i | \(0.975639\pi\) | |||||||
\(234\) | −1.88306e29 | −0.456736 | ||||||||
\(235\) | −2.34436e29 | − | 7.12398e29i | −0.539108 | − | 1.63823i | ||||
\(236\) | 1.28409e29 | 0.280024 | ||||||||
\(237\) | 7.68380e29i | 1.58936i | ||||||||
\(238\) | − | 1.35460e29i | − | 0.265827i | ||||||
\(239\) | 4.35621e29 | 0.811214 | 0.405607 | − | 0.914048i | \(-0.367060\pi\) | ||||
0.405607 | + | 0.914048i | \(0.367060\pi\) | |||||||
\(240\) | 7.72015e28 | + | 2.34598e29i | 0.136454 | + | 0.414652i | ||||
\(241\) | −3.34058e29 | −0.560543 | −0.280271 | − | 0.959921i | \(-0.590424\pi\) | ||||
−0.280271 | + | 0.959921i | \(0.590424\pi\) | |||||||
\(242\) | 3.88170e29i | 0.618486i | ||||||||
\(243\) | 9.47942e29i | 1.43451i | ||||||||
\(244\) | −2.42172e27 | −0.00348138 | ||||||||
\(245\) | 4.02944e29 | − | 1.32601e29i | 0.550387 | − | 0.181121i | ||||
\(246\) | 5.78634e29 | 0.751131 | ||||||||
\(247\) | − | 6.82974e29i | − | 0.842737i | ||||||
\(248\) | − | 6.08129e29i | − | 0.713427i | ||||||
\(249\) | −3.27710e29 | −0.365593 | ||||||||
\(250\) | −3.87721e29 | − | 2.75071e29i | −0.411405 | − | 0.291874i | ||||
\(251\) | 2.73598e29 | 0.276179 | 0.138090 | − | 0.990420i | \(-0.455904\pi\) | ||||
0.138090 | + | 0.990420i | \(0.455904\pi\) | |||||||
\(252\) | − | 1.07067e30i | − | 1.02836i | ||||||
\(253\) | 6.05930e29i | 0.553881i | ||||||||
\(254\) | 7.80815e29 | 0.679402 | ||||||||
\(255\) | −6.96359e29 | + | 2.29158e29i | −0.576874 | + | 0.189838i | ||||
\(256\) | −8.67624e29 | −0.684435 | ||||||||
\(257\) | − | 8.97420e29i | − | 0.674267i | −0.941457 | − | 0.337133i | \(-0.890543\pi\) | ||
0.941457 | − | 0.337133i | \(-0.109457\pi\) | |||||||
\(258\) | − | 1.03516e30i | − | 0.740905i | ||||||
\(259\) | −2.55492e30 | −1.74233 | ||||||||
\(260\) | 2.95850e29 | + | 8.99023e29i | 0.192267 | + | 0.584257i | ||||
\(261\) | −2.41989e30 | −1.49895 | ||||||||
\(262\) | 4.94405e29i | 0.291956i | ||||||||
\(263\) | 1.70766e30i | 0.961510i | 0.876855 | + | 0.480755i | \(0.159637\pi\) | ||||
−0.876855 | + | 0.480755i | \(0.840363\pi\) | |||||||
\(264\) | 3.54330e30 | 1.90265 | ||||||||
\(265\) | 2.91819e29 | + | 8.86774e29i | 0.149465 | + | 0.454192i | ||||
\(266\) | −1.32528e30 | −0.647569 | ||||||||
\(267\) | − | 1.39334e30i | − | 0.649633i | ||||||
\(268\) | 2.32456e30i | 1.03432i | ||||||||
\(269\) | 3.03624e29 | 0.128953 | 0.0644766 | − | 0.997919i | \(-0.479462\pi\) | ||||
0.0644766 | + | 0.997919i | \(0.479462\pi\) | |||||||
\(270\) | 1.66925e29 | − | 5.49317e28i | 0.0676823 | − | 0.0222729i | ||||
\(271\) | 1.57356e30 | 0.609210 | 0.304605 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304605 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(272\) | 3.41840e29i | 0.126390i | ||||||||
\(273\) | − | 4.25195e30i | − | 1.50160i | ||||||
\(274\) | −1.83998e30 | −0.620770 | ||||||||
\(275\) | 3.72392e30 | − | 2.74859e30i | 1.20044 | − | 0.886035i | ||||
\(276\) | 1.30119e30 | 0.400845 | ||||||||
\(277\) | − | 1.53940e30i | − | 0.453267i | −0.973980 | − | 0.226633i | \(-0.927228\pi\) | ||
0.973980 | − | 0.226633i | \(-0.0727719\pi\) | |||||||
\(278\) | 2.85436e30i | 0.803432i | ||||||||
\(279\) | 3.30438e30 | 0.889278 | ||||||||
\(280\) | 4.08439e30 | − | 1.34409e30i | 1.05112 | − | 0.345902i | ||||
\(281\) | −6.95030e30 | −1.71070 | −0.855351 | − | 0.518049i | \(-0.826659\pi\) | ||||
−0.855351 | + | 0.518049i | \(0.826659\pi\) | |||||||
\(282\) | 5.35139e30i | 1.25995i | ||||||||
\(283\) | 2.34367e28i | 0.00527917i | 0.999997 | + | 0.00263958i | \(0.000840206\pi\) | ||||
−0.999997 | + | 0.00263958i | \(0.999160\pi\) | |||||||
\(284\) | −1.50947e30 | −0.325347 | ||||||||
\(285\) | 2.24197e30 | + | 6.81285e30i | 0.462454 | + | 1.40530i | ||||
\(286\) | 3.14483e30 | 0.620900 | ||||||||
\(287\) | 6.83656e30i | 1.29215i | ||||||||
\(288\) | − | 6.26225e30i | − | 1.13325i | ||||||
\(289\) | 4.75594e30 | 0.824164 | ||||||||
\(290\) | −1.29752e30 | − | 3.94289e30i | −0.215348 | − | 0.654394i | ||||
\(291\) | −1.16302e31 | −1.84896 | ||||||||
\(292\) | − | 8.46666e29i | − | 0.128951i | ||||||
\(293\) | − | 1.03650e31i | − | 1.51260i | −0.654226 | − | 0.756299i | \(-0.727006\pi\) | ||
0.654226 | − | 0.756299i | \(-0.272994\pi\) | |||||||
\(294\) | −3.02683e30 | −0.423298 | ||||||||
\(295\) | −2.66173e30 | + | 8.75920e29i | −0.356770 | + | 0.117406i | ||||
\(296\) | −9.50073e30 | −1.22070 | ||||||||
\(297\) | 1.71095e30i | 0.210756i | ||||||||
\(298\) | 2.44948e30i | 0.289315i | ||||||||
\(299\) | 2.70385e30 | 0.306262 | ||||||||
\(300\) | −5.90237e30 | − | 7.99682e30i | −0.641226 | − | 0.868764i | ||||
\(301\) | 1.22305e31 | 1.27456 | ||||||||
\(302\) | − | 3.82465e30i | − | 0.382388i | ||||||
\(303\) | 7.29268e30i | 0.699607i | ||||||||
\(304\) | 3.34440e30 | 0.307892 | ||||||||
\(305\) | 5.01986e28 | − | 1.65193e28i | 0.00443551 | − | 0.00145964i | ||||
\(306\) | 2.73707e30 | 0.232150 | ||||||||
\(307\) | − | 6.56613e30i | − | 0.534663i | −0.963605 | − | 0.267331i | \(-0.913858\pi\) | ||
0.963605 | − | 0.267331i | \(-0.0861418\pi\) | |||||||
\(308\) | 1.78808e31i | 1.39799i | ||||||||
\(309\) | −2.03486e31 | −1.52775 | ||||||||
\(310\) | 1.77178e30 | + | 5.38406e30i | 0.127758 | + | 0.388230i | ||||
\(311\) | 1.09459e31 | 0.758138 | 0.379069 | − | 0.925368i | \(-0.376244\pi\) | ||||
0.379069 | + | 0.925368i | \(0.376244\pi\) | |||||||
\(312\) | − | 1.58113e31i | − | 1.05205i | ||||||
\(313\) | − | 1.19799e30i | − | 0.0765861i | −0.999267 | − | 0.0382930i | \(-0.987808\pi\) | ||
0.999267 | − | 0.0382930i | \(-0.0121920\pi\) | |||||||
\(314\) | 5.06926e30 | 0.311404 | ||||||||
\(315\) | 7.30335e30 | + | 2.21933e31i | 0.431162 | + | 1.31021i | ||||
\(316\) | −1.44190e31 | −0.818177 | ||||||||
\(317\) | − | 8.57599e30i | − | 0.467782i | −0.972263 | − | 0.233891i | \(-0.924854\pi\) | ||
0.972263 | − | 0.233891i | \(-0.0751459\pi\) | |||||||
\(318\) | − | 6.66126e30i | − | 0.349315i | ||||||
\(319\) | 4.04137e31 | 2.03772 | ||||||||
\(320\) | 4.29874e30 | − | 1.41463e30i | 0.208433 | − | 0.0685910i | ||||
\(321\) | 3.20475e31 | 1.49445 | ||||||||
\(322\) | − | 5.24669e30i | − | 0.235335i | ||||||
\(323\) | 9.92719e30i | 0.428346i | ||||||||
\(324\) | −1.60370e31 | −0.665747 | ||||||||
\(325\) | −1.22651e31 | − | 1.66173e31i | −0.489923 | − | 0.663771i | ||||
\(326\) | 6.77938e30 | 0.260597 | ||||||||
\(327\) | 3.00639e31i | 1.11224i | ||||||||
\(328\) | 2.54225e31i | 0.905305i | ||||||||
\(329\) | −6.32266e31 | −2.16746 | ||||||||
\(330\) | −3.13705e31 | + | 1.03234e31i | −1.03537 | + | 0.340721i | ||||
\(331\) | 4.51780e31 | 1.43575 | 0.717873 | − | 0.696174i | \(-0.245116\pi\) | ||||
0.717873 | + | 0.696174i | \(0.245116\pi\) | |||||||
\(332\) | − | 6.14964e30i | − | 0.188202i | ||||||
\(333\) | − | 5.16239e31i | − | 1.52159i | ||||||
\(334\) | −5.43356e30 | −0.154260 | ||||||||
\(335\) | −1.58566e31 | − | 4.81846e31i | −0.433660 | − | 1.31780i | ||||
\(336\) | 2.08210e31 | 0.548606 | ||||||||
\(337\) | 3.65657e31i | 0.928325i | 0.885750 | + | 0.464163i | \(0.153645\pi\) | ||||
−0.885750 | + | 0.464163i | \(0.846355\pi\) | |||||||
\(338\) | 6.58518e30i | 0.161105i | ||||||||
\(339\) | −1.96281e31 | −0.462787 | ||||||||
\(340\) | −4.30026e30 | − | 1.30675e31i | −0.0977255 | − | 0.296966i | ||||
\(341\) | −5.51854e31 | −1.20891 | ||||||||
\(342\) | − | 2.67782e31i | − | 0.565529i | ||||||
\(343\) | 2.59580e31i | 0.528561i | ||||||||
\(344\) | 4.54802e31 | 0.892981 | ||||||||
\(345\) | −2.69716e31 | + | 8.87582e30i | −0.510703 | + | 0.168062i | ||||
\(346\) | 3.90304e31 | 0.712774 | ||||||||
\(347\) | − | 1.69385e31i | − | 0.298370i | −0.988809 | − | 0.149185i | \(-0.952335\pi\) | ||
0.988809 | − | 0.149185i | \(-0.0476651\pi\) | |||||||
\(348\) | − | 8.67853e31i | − | 1.47471i | ||||||
\(349\) | −2.49178e31 | −0.408500 | −0.204250 | − | 0.978919i | \(-0.565476\pi\) | ||||
−0.204250 | + | 0.978919i | \(0.565476\pi\) | |||||||
\(350\) | −3.22451e31 | + | 2.37997e31i | −0.510050 | + | 0.376462i | ||||
\(351\) | 7.63478e30 | 0.116535 | ||||||||
\(352\) | 1.04584e32i | 1.54057i | ||||||||
\(353\) | 5.75445e31i | 0.818125i | 0.912506 | + | 0.409063i | \(0.134144\pi\) | ||||
−0.912506 | + | 0.409063i | \(0.865856\pi\) | |||||||
\(354\) | 1.99943e31 | 0.274389 | ||||||||
\(355\) | 3.12891e31 | − | 1.02966e31i | 0.414514 | − | 0.136408i | ||||
\(356\) | 2.61468e31 | 0.334421 | ||||||||
\(357\) | 6.18031e31i | 0.763234i | ||||||||
\(358\) | 2.77183e31i | 0.330544i | ||||||||
\(359\) | 6.95546e31 | 0.801024 | 0.400512 | − | 0.916292i | \(-0.368832\pi\) | ||||
0.400512 | + | 0.916292i | \(0.368832\pi\) | |||||||
\(360\) | 2.71583e31 | + | 8.25280e31i | 0.302079 | + | 0.917952i | ||||
\(361\) | 4.04645e30 | 0.0434745 | ||||||||
\(362\) | − | 9.24823e31i | − | 0.959846i | ||||||
\(363\) | − | 1.77101e32i | − | 1.77577i | ||||||
\(364\) | 7.97899e31 | 0.773002 | ||||||||
\(365\) | 5.77538e30 | + | 1.75501e31i | 0.0540654 | + | 0.164293i | ||||
\(366\) | −3.77081e29 | −0.00341131 | ||||||||
\(367\) | − | 1.92271e32i | − | 1.68107i | −0.541754 | − | 0.840537i | \(-0.682240\pi\) | ||
0.541754 | − | 0.840537i | \(-0.317760\pi\) | |||||||
\(368\) | 1.32403e31i | 0.111892i | ||||||||
\(369\) | −1.38138e32 | −1.12845 | ||||||||
\(370\) | 8.41145e31 | − | 2.76804e31i | 0.664277 | − | 0.218600i | ||||
\(371\) | 7.87028e31 | 0.600919 | ||||||||
\(372\) | 1.18506e32i | 0.874892i | ||||||||
\(373\) | 2.12399e32i | 1.51632i | 0.652068 | + | 0.758161i | \(0.273902\pi\) | ||||
−0.652068 | + | 0.758161i | \(0.726098\pi\) | |||||||
\(374\) | −4.57109e31 | −0.315591 | ||||||||
\(375\) | 1.76896e32 | + | 1.25500e32i | 1.18121 | + | 0.838018i | ||||
\(376\) | −2.35115e32 | −1.51856 | ||||||||
\(377\) | − | 1.80339e32i | − | 1.12674i | ||||||
\(378\) | − | 1.48149e31i | − | 0.0895471i | ||||||
\(379\) | −2.03719e32 | −1.19136 | −0.595679 | − | 0.803223i | \(-0.703117\pi\) | ||||
−0.595679 | + | 0.803223i | \(0.703117\pi\) | |||||||
\(380\) | −1.27846e32 | + | 4.20717e31i | −0.723425 | + | 0.238065i | ||||
\(381\) | −3.56244e32 | −1.95068 | ||||||||
\(382\) | − | 1.07972e32i | − | 0.572160i | ||||||
\(383\) | 3.00431e32i | 1.54085i | 0.637531 | + | 0.770424i | \(0.279956\pi\) | ||||
−0.637531 | + | 0.770424i | \(0.720044\pi\) | |||||||
\(384\) | 2.68941e32 | 1.33511 | ||||||||
\(385\) | −1.21971e32 | − | 3.70643e32i | −0.586135 | − | 1.78113i | ||||
\(386\) | 1.29762e32 | 0.603680 | ||||||||
\(387\) | 2.47125e32i | 1.11309i | ||||||||
\(388\) | − | 2.18247e32i | − | 0.951815i | ||||||
\(389\) | 1.14176e32 | 0.482177 | 0.241088 | − | 0.970503i | \(-0.422496\pi\) | ||||
0.241088 | + | 0.970503i | \(0.422496\pi\) | |||||||
\(390\) | 4.60663e31 | + | 1.39985e32i | 0.188398 | + | 0.572498i | ||||
\(391\) | −3.93011e31 | −0.155667 | ||||||||
\(392\) | − | 1.32985e32i | − | 0.510183i | ||||||
\(393\) | − | 2.25570e32i | − | 0.838253i | ||||||
\(394\) | −4.71098e31 | −0.169593 | ||||||||
\(395\) | 2.98885e32 | − | 9.83568e31i | 1.04241 | − | 0.343037i | ||||
\(396\) | −3.61295e32 | −1.22088 | ||||||||
\(397\) | 1.58269e32i | 0.518221i | 0.965848 | + | 0.259111i | \(0.0834294\pi\) | ||||
−0.965848 | + | 0.259111i | \(0.916571\pi\) | |||||||
\(398\) | − | 2.51232e32i | − | 0.797142i | ||||||
\(399\) | 6.04652e32 | 1.85928 | ||||||||
\(400\) | 8.13718e31 | − | 6.00597e31i | 0.242507 | − | 0.178992i | ||||
\(401\) | −1.50822e32 | −0.435671 | −0.217836 | − | 0.975985i | \(-0.569900\pi\) | ||||
−0.217836 | + | 0.975985i | \(0.569900\pi\) | |||||||
\(402\) | 3.61953e32i | 1.01351i | ||||||||
\(403\) | 2.46254e32i | 0.668453i | ||||||||
\(404\) | −1.36851e32 | −0.360147 | ||||||||
\(405\) | 3.32422e32 | − | 1.09393e32i | 0.848207 | − | 0.279128i | ||||
\(406\) | −3.49938e32 | −0.865797 | ||||||||
\(407\) | 8.62154e32i | 2.06850i | ||||||||
\(408\) | 2.29821e32i | 0.534735i | ||||||||
\(409\) | −4.78027e31 | −0.107873 | −0.0539363 | − | 0.998544i | \(-0.517177\pi\) | ||||
−0.0539363 | + | 0.998544i | \(0.517177\pi\) | |||||||
\(410\) | −7.40684e31 | − | 2.25077e32i | −0.162119 | − | 0.492645i | ||||
\(411\) | 8.39483e32 | 1.78233 | ||||||||
\(412\) | − | 3.81851e32i | − | 0.786464i | ||||||
\(413\) | 2.36233e32i | 0.472025i | ||||||||
\(414\) | 1.06013e32 | 0.205521 | ||||||||
\(415\) | 4.19487e31 | + | 1.27473e32i | 0.0789073 | + | 0.239782i | ||||
\(416\) | 4.66686e32 | 0.851840 | ||||||||
\(417\) | − | 1.30229e33i | − | 2.30679i | ||||||
\(418\) | 4.47214e32i | 0.768797i | ||||||||
\(419\) | −5.50053e32 | −0.917760 | −0.458880 | − | 0.888498i | \(-0.651749\pi\) | ||||
−0.458880 | + | 0.888498i | \(0.651749\pi\) | |||||||
\(420\) | −7.95926e32 | + | 2.61923e32i | −1.28901 | + | 0.424187i | ||||
\(421\) | −6.24373e32 | −0.981563 | −0.490781 | − | 0.871283i | \(-0.663289\pi\) | ||||
−0.490781 | + | 0.871283i | \(0.663289\pi\) | |||||||
\(422\) | − | 1.37731e32i | − | 0.210197i | ||||||
\(423\) | − | 1.27754e33i | − | 1.89286i | ||||||
\(424\) | 2.92665e32 | 0.421014 | ||||||||
\(425\) | 1.78276e32 | + | 2.41537e32i | 0.249018 | + | 0.337381i | ||||
\(426\) | −2.35037e32 | −0.318799 | ||||||||
\(427\) | − | 4.45521e30i | − | 0.00586841i | ||||||
\(428\) | 6.01387e32i | 0.769319i | ||||||||
\(429\) | −1.43482e33 | −1.78271 | ||||||||
\(430\) | −4.02658e32 | + | 1.32507e32i | −0.485938 | + | 0.159912i | ||||
\(431\) | 9.95413e32 | 1.16691 | 0.583455 | − | 0.812146i | \(-0.301701\pi\) | ||||
0.583455 | + | 0.812146i | \(0.301701\pi\) | |||||||
\(432\) | 3.73861e31i | 0.0425758i | ||||||||
\(433\) | − | 1.01179e33i | − | 1.11942i | −0.828688 | − | 0.559711i | \(-0.810912\pi\) | ||
0.828688 | − | 0.559711i | \(-0.189088\pi\) | |||||||
\(434\) | 4.77845e32 | 0.513648 | ||||||||
\(435\) | 5.91990e32 | + | 1.79893e33i | 0.618299 | + | 1.87887i | ||||
\(436\) | −5.64164e32 | −0.572565 | ||||||||
\(437\) | 3.84504e32i | 0.379213i | ||||||||
\(438\) | − | 1.31833e32i | − | 0.126356i | ||||||
\(439\) | −1.31957e33 | −1.22921 | −0.614606 | − | 0.788834i | \(-0.710685\pi\) | ||||
−0.614606 | + | 0.788834i | \(0.710685\pi\) | |||||||
\(440\) | −4.53562e32 | − | 1.37827e33i | −0.410656 | − | 1.24789i | ||||
\(441\) | 7.22596e32 | 0.635936 | ||||||||
\(442\) | 2.03976e32i | 0.174502i | ||||||||
\(443\) | 7.07458e32i | 0.588375i | 0.955748 | + | 0.294188i | \(0.0950490\pi\) | ||||
−0.955748 | + | 0.294188i | \(0.904951\pi\) | |||||||
\(444\) | 1.85141e33 | 1.49698 | ||||||||
\(445\) | −5.41984e32 | + | 1.78356e32i | −0.426075 | + | 0.140213i | ||||
\(446\) | 2.77715e32 | 0.212282 | ||||||||
\(447\) | − | 1.11757e33i | − | 0.830671i | ||||||
\(448\) | − | 3.81520e32i | − | 0.275767i | ||||||
\(449\) | −1.43255e32 | −0.100701 | −0.0503503 | − | 0.998732i | \(-0.516034\pi\) | ||||
−0.0503503 | + | 0.998732i | \(0.516034\pi\) | |||||||
\(450\) | −4.80891e32 | − | 6.51534e32i | −0.328768 | − | 0.445432i | ||||
\(451\) | 2.30699e33 | 1.53405 | ||||||||
\(452\) | − | 3.68330e32i | − | 0.238236i | ||||||
\(453\) | 1.74498e33i | 1.09790i | ||||||||
\(454\) | 1.10024e33 | 0.673423 | ||||||||
\(455\) | −1.65392e33 | + | 5.44273e32i | −0.984857 | + | 0.324096i | ||||
\(456\) | 2.24846e33 | 1.30264 | ||||||||
\(457\) | 2.29124e33i | 1.29157i | 0.763519 | + | 0.645785i | \(0.223470\pi\) | ||||
−0.763519 | + | 0.645785i | \(0.776530\pi\) | |||||||
\(458\) | − | 2.60874e32i | − | 0.143091i | ||||||
\(459\) | −1.10973e32 | −0.0592325 | ||||||||
\(460\) | −1.66559e32 | − | 5.06136e32i | −0.0865158 | − | 0.262902i | ||||
\(461\) | −5.28423e30 | −0.00267129 | −0.00133564 | − | 0.999999i | \(-0.500425\pi\) | ||||
−0.00133564 | + | 0.999999i | \(0.500425\pi\) | |||||||
\(462\) | 2.78419e33i | 1.36985i | ||||||||
\(463\) | − | 9.84320e32i | − | 0.471383i | −0.971828 | − | 0.235692i | \(-0.924264\pi\) | ||
0.971828 | − | 0.235692i | \(-0.0757355\pi\) | |||||||
\(464\) | 8.83085e32 | 0.411650 | ||||||||
\(465\) | −8.08369e32 | − | 2.45645e33i | −0.366816 | − | 1.11467i | ||||
\(466\) | −1.74614e32 | −0.0771355 | ||||||||
\(467\) | − | 2.70720e33i | − | 1.16428i | −0.813087 | − | 0.582142i | \(-0.802215\pi\) | ||
0.813087 | − | 0.582142i | \(-0.197785\pi\) | |||||||
\(468\) | 1.61221e33i | 0.675070i | ||||||||
\(469\) | −4.27647e33 | −1.74351 | ||||||||
\(470\) | 2.08158e33 | − | 6.85007e32i | 0.826363 | − | 0.271939i | ||||
\(471\) | −2.31283e33 | −0.894092 | ||||||||
\(472\) | 8.78457e32i | 0.330709i | ||||||||
\(473\) | − | 4.12715e33i | − | 1.51317i | ||||||
\(474\) | −2.24516e33 | −0.801711 | ||||||||
\(475\) | 2.36308e33 | − | 1.74416e33i | 0.821879 | − | 0.606621i | ||||
\(476\) | −1.15977e33 | −0.392901 | ||||||||
\(477\) | 1.59025e33i | 0.524789i | ||||||||
\(478\) | 1.27286e33i | 0.409196i | ||||||||
\(479\) | −6.97657e32 | −0.218498 | −0.109249 | − | 0.994014i | \(-0.534845\pi\) | ||||
−0.109249 | + | 0.994014i | \(0.534845\pi\) | |||||||
\(480\) | −4.65532e33 | + | 1.53197e33i | −1.42048 | + | 0.467450i | ||||
\(481\) | 3.84720e33 | 1.14375 | ||||||||
\(482\) | − | 9.76097e32i | − | 0.282752i | ||||||
\(483\) | 2.39378e33i | 0.675687i | ||||||||
\(484\) | 3.32339e33 | 0.914142 | ||||||||
\(485\) | 1.48874e33 | + | 4.52394e33i | 0.399067 | + | 1.21268i | ||||
\(486\) | −2.76983e33 | −0.723602 | ||||||||
\(487\) | − | 2.67547e33i | − | 0.681222i | −0.940204 | − | 0.340611i | \(-0.889366\pi\) | ||
0.940204 | − | 0.340611i | \(-0.110634\pi\) | |||||||
\(488\) | − | 1.65672e31i | − | 0.00411151i | ||||||
\(489\) | −3.09306e33 | −0.748218 | ||||||||
\(490\) | 3.87451e32 | + | 1.17738e33i | 0.0913620 | + | 0.277629i | ||||
\(491\) | −6.76932e33 | −1.55606 | −0.778030 | − | 0.628227i | \(-0.783781\pi\) | ||||
−0.778030 | + | 0.628227i | \(0.783781\pi\) | |||||||
\(492\) | − | 4.95408e33i | − | 1.11020i | ||||||
\(493\) | 2.62127e33i | 0.572697i | ||||||||
\(494\) | 1.99561e33 | 0.425097 | ||||||||
\(495\) | 7.48910e33 | − | 2.46451e33i | 1.55548 | − | 0.511877i | ||||
\(496\) | −1.20586e33 | −0.244218 | ||||||||
\(497\) | − | 2.77696e33i | − | 0.548423i | ||||||
\(498\) | − | 9.57548e32i | − | 0.184414i | ||||||
\(499\) | 9.92600e33 | 1.86431 | 0.932153 | − | 0.362064i | \(-0.117928\pi\) | ||||
0.932153 | + | 0.362064i | \(0.117928\pi\) | |||||||
\(500\) | −2.35507e33 | + | 3.31954e33i | −0.431399 | + | 0.608070i | ||||
\(501\) | 2.47904e33 | 0.442906 | ||||||||
\(502\) | 7.99436e32i | 0.139312i | ||||||||
\(503\) | 5.51083e33i | 0.936736i | 0.883534 | + | 0.468368i | \(0.155158\pi\) | ||||
−0.883534 | + | 0.468368i | \(0.844842\pi\) | |||||||
\(504\) | 7.32451e33 | 1.21450 | ||||||||
\(505\) | 2.83671e33 | − | 9.33503e32i | 0.458852 | − | 0.150999i | ||||
\(506\) | −1.77049e33 | −0.279391 | ||||||||
\(507\) | − | 3.00446e33i | − | 0.462559i | ||||||
\(508\) | − | 6.68509e33i | − | 1.00418i | ||||||
\(509\) | −3.51385e33 | −0.515004 | −0.257502 | − | 0.966278i | \(-0.582899\pi\) | ||||
−0.257502 | + | 0.966278i | \(0.582899\pi\) | |||||||
\(510\) | −6.69585e32 | − | 2.03472e33i | −0.0957587 | − | 0.290989i | ||||
\(511\) | 1.55760e33 | 0.217368 | ||||||||
\(512\) | 4.23405e33i | 0.576609i | ||||||||
\(513\) | 1.08571e33i | 0.144294i | ||||||||
\(514\) | 2.62221e33 | 0.340117 | ||||||||
\(515\) | 2.60473e33 | + | 7.91519e33i | 0.329740 | + | 1.00201i | ||||
\(516\) | −8.86274e33 | −1.09508 | ||||||||
\(517\) | 2.13358e34i | 2.57322i | ||||||||
\(518\) | − | 7.46531e33i | − | 0.878873i | ||||||
\(519\) | −1.78075e34 | −2.04649 | ||||||||
\(520\) | −6.15029e33 | + | 2.02393e33i | −0.690007 | + | 0.227067i | ||||
\(521\) | −4.44244e33 | −0.486575 | −0.243288 | − | 0.969954i | \(-0.578226\pi\) | ||||
−0.243288 | + | 0.969954i | \(0.578226\pi\) | |||||||
\(522\) | − | 7.07076e33i | − | 0.756109i | ||||||
\(523\) | − | 3.50209e33i | − | 0.365642i | −0.983146 | − | 0.182821i | \(-0.941477\pi\) | ||
0.983146 | − | 0.182821i | \(-0.0585229\pi\) | |||||||
\(524\) | 4.23294e33 | 0.431520 | ||||||||
\(525\) | 1.47117e34 | − | 1.08585e34i | 1.46444 | − | 1.08089i | ||||
\(526\) | −4.98967e33 | −0.485009 | ||||||||
\(527\) | − | 3.57937e33i | − | 0.339761i | ||||||
\(528\) | − | 7.02603e33i | − | 0.651307i | ||||||
\(529\) | 9.52354e33 | 0.862189 | ||||||||
\(530\) | −2.59110e33 | + | 8.52678e32i | −0.229106 | + | 0.0753940i | ||||
\(531\) | −4.77326e33 | −0.412224 | ||||||||
\(532\) | 1.13466e34i | 0.957129i | ||||||||
\(533\) | − | 1.02945e34i | − | 0.848235i | ||||||
\(534\) | 4.07127e33 | 0.327691 | ||||||||
\(535\) | −4.10225e33 | − | 1.24658e34i | −0.322552 | − | 0.980165i | ||||
\(536\) | −1.59025e34 | −1.22153 | ||||||||
\(537\) | − | 1.26464e34i | − | 0.949046i | ||||||
\(538\) | 8.87170e32i | 0.0650472i | ||||||||
\(539\) | −1.20678e34 | −0.864510 | ||||||||
\(540\) | −4.70308e32 | − | 1.42916e33i | −0.0329200 | − | 0.100037i | ||||
\(541\) | 8.58091e33 | 0.586905 | 0.293452 | − | 0.955974i | \(-0.405196\pi\) | ||||
0.293452 | + | 0.955974i | \(0.405196\pi\) | |||||||
\(542\) | 4.59784e33i | 0.307300i | ||||||||
\(543\) | 4.21947e34i | 2.75588i | ||||||||
\(544\) | −6.78339e33 | −0.432973 | ||||||||
\(545\) | 1.16943e34 | − | 3.84835e33i | 0.729486 | − | 0.240059i | ||||
\(546\) | 1.24239e34 | 0.757445 | ||||||||
\(547\) | − | 7.19024e33i | − | 0.428452i | −0.976784 | − | 0.214226i | \(-0.931277\pi\) | ||
0.976784 | − | 0.214226i | \(-0.0687229\pi\) | |||||||
\(548\) | 1.57533e34i | 0.917518i | ||||||||
\(549\) | 9.00208e31 | 0.00512494 | ||||||||
\(550\) | 8.03120e33 | + | 1.08811e34i | 0.446938 | + | 0.605533i | ||||
\(551\) | 2.56452e34 | 1.39512 | ||||||||
\(552\) | 8.90153e33i | 0.473398i | ||||||||
\(553\) | − | 2.65265e34i | − | 1.37917i | ||||||
\(554\) | 4.49803e33 | 0.228639 | ||||||||
\(555\) | −3.83769e34 | + | 1.26291e34i | −1.90725 | + | 0.627637i | ||||
\(556\) | 2.44381e34 | 1.18750 | ||||||||
\(557\) | 6.67160e33i | 0.316986i | 0.987360 | + | 0.158493i | \(0.0506635\pi\) | ||||
−0.987360 | + | 0.158493i | \(0.949336\pi\) | |||||||
\(558\) | 9.65520e33i | 0.448573i | ||||||||
\(559\) | −1.84167e34 | −0.836687 | ||||||||
\(560\) | −2.66520e33 | − | 8.09896e33i | −0.118408 | − | 0.359815i | ||||
\(561\) | 2.08554e34 | 0.906114 | ||||||||
\(562\) | − | 2.03083e34i | − | 0.862920i | ||||||
\(563\) | − | 2.00429e34i | − | 0.832925i | −0.909153 | − | 0.416462i | \(-0.863270\pi\) | ||
0.909153 | − | 0.416462i | \(-0.136730\pi\) | |||||||
\(564\) | 4.58169e34 | 1.86224 | ||||||||
\(565\) | 2.51250e33 | + | 7.63493e33i | 0.0998851 | + | 0.303529i | ||||
\(566\) | −6.84805e31 | −0.00266294 | ||||||||
\(567\) | − | 2.95030e34i | − | 1.12222i | ||||||
\(568\) | − | 1.03264e34i | − | 0.384234i | ||||||
\(569\) | 1.35074e34 | 0.491664 | 0.245832 | − | 0.969312i | \(-0.420939\pi\) | ||||
0.245832 | + | 0.969312i | \(0.420939\pi\) | |||||||
\(570\) | −1.99067e34 | + | 6.55090e33i | −0.708866 | + | 0.233273i | ||||
\(571\) | −4.31121e34 | −1.50192 | −0.750961 | − | 0.660346i | \(-0.770410\pi\) | ||||
−0.750961 | + | 0.660346i | \(0.770410\pi\) | |||||||
\(572\) | − | 2.69250e34i | − | 0.917711i | ||||||
\(573\) | 4.92616e34i | 1.64276i | ||||||||
\(574\) | −1.99760e34 | −0.651794 | ||||||||
\(575\) | 6.90504e33 | + | 9.35528e33i | 0.220454 | + | 0.298682i | ||||
\(576\) | 7.70889e33 | 0.240830 | ||||||||
\(577\) | 3.54921e34i | 1.08501i | 0.840052 | + | 0.542505i | \(0.182524\pi\) | ||||
−0.840052 | + | 0.542505i | \(0.817476\pi\) | |||||||
\(578\) | 1.38966e34i | 0.415728i | ||||||||
\(579\) | −5.92034e34 | −1.73326 | ||||||||
\(580\) | −3.37578e34 | + | 1.11090e34i | −0.967216 | + | 0.318291i | ||||
\(581\) | 1.13134e34 | 0.317243 | ||||||||
\(582\) | − | 3.39829e34i | − | 0.932659i | ||||||
\(583\) | − | 2.65582e34i | − | 0.713414i | ||||||
\(584\) | 5.79211e33 | 0.152292 | ||||||||
\(585\) | −1.09974e34 | − | 3.34187e34i | −0.283036 | − | 0.860085i | ||||
\(586\) | 3.02859e34 | 0.762991 | ||||||||
\(587\) | 1.24414e34i | 0.306827i | 0.988162 | + | 0.153413i | \(0.0490266\pi\) | ||||
−0.988162 | + | 0.153413i | \(0.950973\pi\) | |||||||
\(588\) | 2.59147e34i | 0.625648i | ||||||||
\(589\) | −3.50189e34 | −0.827677 | ||||||||
\(590\) | −2.55939e33 | − | 7.77741e33i | −0.0592223 | − | 0.179964i | ||||
\(591\) | 2.14937e34 | 0.486930 | ||||||||
\(592\) | 1.88390e34i | 0.417867i | ||||||||
\(593\) | − | 8.64628e34i | − | 1.87778i | −0.344212 | − | 0.938892i | \(-0.611854\pi\) | ||
0.344212 | − | 0.938892i | \(-0.388146\pi\) | |||||||
\(594\) | −4.99928e33 | −0.106311 | ||||||||
\(595\) | 2.40402e34 | − | 7.91114e33i | 0.500583 | − | 0.164732i | ||||
\(596\) | 2.09717e34 | 0.427617 | ||||||||
\(597\) | 1.14623e35i | 2.28873i | ||||||||
\(598\) | 7.90049e33i | 0.154486i | ||||||||
\(599\) | −1.88641e34 | −0.361243 | −0.180622 | − | 0.983553i | \(-0.557811\pi\) | ||||
−0.180622 | + | 0.983553i | \(0.557811\pi\) | |||||||
\(600\) | 5.47069e34 | − | 4.03786e34i | 1.02601 | − | 0.757287i | ||||
\(601\) | 7.66027e33 | 0.140706 | 0.0703531 | − | 0.997522i | \(-0.477587\pi\) | ||||
0.0703531 | + | 0.997522i | \(0.477587\pi\) | |||||||
\(602\) | 3.57366e34i | 0.642921i | ||||||||
\(603\) | − | 8.64091e34i | − | 1.52263i | ||||||
\(604\) | −3.27454e34 | −0.565182 | ||||||||
\(605\) | −6.88888e34 | + | 2.26699e34i | −1.16468 | + | 0.383272i | ||||
\(606\) | −2.13088e34 | −0.352899 | ||||||||
\(607\) | − | 3.80410e34i | − | 0.617154i | −0.951199 | − | 0.308577i | \(-0.900147\pi\) | ||
0.951199 | − | 0.308577i | \(-0.0998527\pi\) | |||||||
\(608\) | 6.63655e34i | 1.05475i | ||||||||
\(609\) | 1.59658e35 | 2.48585 | ||||||||
\(610\) | 4.82685e31 | + | 1.46677e32i | 0.000736276 | + | 0.00223738i | ||||
\(611\) | 9.52069e34 | 1.42283 | ||||||||
\(612\) | − | 2.34339e34i | − | 0.343125i | ||||||
\(613\) | 2.90088e34i | 0.416172i | 0.978111 | + | 0.208086i | \(0.0667234\pi\) | ||||
−0.978111 | + | 0.208086i | \(0.933277\pi\) | |||||||
\(614\) | 1.91858e34 | 0.269697 | ||||||||
\(615\) | 3.37934e34 | + | 1.02691e35i | 0.465471 | + | 1.41446i | ||||
\(616\) | −1.22324e35 | −1.65102 | ||||||||
\(617\) | 4.91805e34i | 0.650472i | 0.945633 | + | 0.325236i | \(0.105444\pi\) | ||||
−0.945633 | + | 0.325236i | \(0.894556\pi\) | |||||||
\(618\) | − | 5.94573e34i | − | 0.770635i | ||||||
\(619\) | 2.55433e34 | 0.324447 | 0.162223 | − | 0.986754i | \(-0.448133\pi\) | ||||
0.162223 | + | 0.986754i | \(0.448133\pi\) | |||||||
\(620\) | 4.60966e34 | − | 1.51694e34i | 0.573816 | − | 0.188831i | ||||
\(621\) | −4.29826e33 | −0.0524382 | ||||||||
\(622\) | 3.19834e34i | 0.382424i | ||||||||
\(623\) | 4.81020e34i | 0.563719i | ||||||||
\(624\) | −3.13523e34 | −0.360133 | ||||||||
\(625\) | 2.61734e34 | − | 8.48738e34i | 0.294686 | − | 0.955594i | ||||
\(626\) | 3.50046e33 | 0.0386319 | ||||||||
\(627\) | − | 2.04039e35i | − | 2.20734i | ||||||
\(628\) | − | 4.34014e34i | − | 0.460265i | ||||||
\(629\) | −5.59201e34 | −0.581346 | ||||||||
\(630\) | −6.48474e34 | + | 2.13400e34i | −0.660900 | + | 0.217489i | ||||
\(631\) | −1.79226e35 | −1.79075 | −0.895375 | − | 0.445314i | \(-0.853092\pi\) | ||||
−0.895375 | + | 0.445314i | \(0.853092\pi\) | |||||||
\(632\) | − | 9.86417e34i | − | 0.966267i | ||||||
\(633\) | 6.28393e34i | 0.603510i | ||||||||
\(634\) | 2.50585e34 | 0.235961 | ||||||||
\(635\) | 4.56011e34 | + | 1.38572e35i | 0.421021 | + | 1.27939i | ||||
\(636\) | −5.70316e34 | −0.516299 | ||||||||
\(637\) | 5.38505e34i | 0.478021i | ||||||||
\(638\) | 1.18086e35i | 1.02788i | ||||||||
\(639\) | 5.61106e34 | 0.478943 | ||||||||
\(640\) | −3.44259e34 | − | 1.04613e35i | −0.288161 | − | 0.875659i | ||||
\(641\) | −1.08126e35 | −0.887575 | −0.443787 | − | 0.896132i | \(-0.646365\pi\) | ||||
−0.443787 | + | 0.896132i | \(0.646365\pi\) | |||||||
\(642\) | 9.36407e34i | 0.753836i | ||||||||
\(643\) | 1.53840e35i | 1.21459i | 0.794475 | + | 0.607297i | \(0.207746\pi\) | ||||
−0.794475 | + | 0.607297i | \(0.792254\pi\) | |||||||
\(644\) | −4.49205e34 | −0.347833 | ||||||||
\(645\) | 1.83711e35 | − | 6.04556e34i | 1.39521 | − | 0.459135i | ||||
\(646\) | −2.90066e34 | −0.216068 | ||||||||
\(647\) | − | 2.04770e35i | − | 1.49611i | −0.663639 | − | 0.748053i | \(-0.730989\pi\) | ||
0.663639 | − | 0.748053i | \(-0.269011\pi\) | |||||||
\(648\) | − | 1.09710e35i | − | 0.786247i | ||||||
\(649\) | 7.97166e34 | 0.560390 | ||||||||
\(650\) | 4.85547e34 | − | 3.58377e34i | 0.334822 | − | 0.247129i | ||||
\(651\) | −2.18015e35 | −1.47477 | ||||||||
\(652\) | − | 5.80429e34i | − | 0.385171i | ||||||
\(653\) | 6.07692e33i | 0.0395611i | 0.999804 | + | 0.0197806i | \(0.00629676\pi\) | ||||
−0.999804 | + | 0.0197806i | \(0.993703\pi\) | |||||||
\(654\) | −8.78449e34 | −0.561041 | ||||||||
\(655\) | −8.77424e34 | + | 2.88743e34i | −0.549786 | + | 0.180923i | ||||
\(656\) | 5.04104e34 | 0.309900 | ||||||||
\(657\) | 3.14725e34i | 0.189829i | ||||||||
\(658\) | − | 1.84744e35i | − | 1.09332i | ||||||
\(659\) | 1.25296e35 | 0.727559 | 0.363780 | − | 0.931485i | \(-0.381486\pi\) | ||||
0.363780 | + | 0.931485i | \(0.381486\pi\) | |||||||
\(660\) | 8.83857e34 | + | 2.68584e35i | 0.503597 | + | 1.53032i | ||||
\(661\) | 3.27675e35 | 1.83200 | 0.915998 | − | 0.401183i | \(-0.131401\pi\) | ||||
0.915998 | + | 0.401183i | \(0.131401\pi\) | |||||||
\(662\) | 1.32007e35i | 0.724225i | ||||||||
\(663\) | − | 9.30633e34i | − | 0.501025i | ||||||
\(664\) | 4.20702e34 | 0.222266 | ||||||||
\(665\) | −7.73988e34 | − | 2.35198e35i | −0.401295 | − | 1.21945i | ||||
\(666\) | 1.50842e35 | 0.767528 | ||||||||
\(667\) | 1.01528e35i | 0.507005i | ||||||||
\(668\) | 4.65204e34i | 0.228001i | ||||||||
\(669\) | −1.26706e35 | −0.609496 | ||||||||
\(670\) | 1.40792e35 | − | 4.63319e34i | 0.664728 | − | 0.218749i | ||||
\(671\) | −1.50341e33 | −0.00696699 | ||||||||
\(672\) | 4.13168e35i | 1.87936i | ||||||||
\(673\) | 2.70609e35i | 1.20824i | 0.796892 | + | 0.604122i | \(0.206476\pi\) | ||||
−0.796892 | + | 0.604122i | \(0.793524\pi\) | |||||||
\(674\) | −1.06843e35 | −0.468270 | ||||||||
\(675\) | 1.94975e34 | + | 2.64162e34i | 0.0838846 | + | 0.113651i | ||||
\(676\) | 5.63802e34 | 0.238119 | ||||||||
\(677\) | 5.21912e33i | 0.0216391i | 0.999941 | + | 0.0108196i | \(0.00344404\pi\) | ||||
−0.999941 | + | 0.0108196i | \(0.996556\pi\) | |||||||
\(678\) | − | 5.73520e34i | − | 0.233441i | ||||||
\(679\) | 4.01507e35 | 1.60443 | ||||||||
\(680\) | 8.93960e34 | − | 2.94184e34i | 0.350717 | − | 0.115414i | ||||
\(681\) | −5.01978e35 | −1.93351 | ||||||||
\(682\) | − | 1.61248e35i | − | 0.609804i | ||||||
\(683\) | 3.69358e34i | 0.137148i | 0.997646 | + | 0.0685739i | \(0.0218449\pi\) | ||||
−0.997646 | + | 0.0685739i | \(0.978155\pi\) | |||||||
\(684\) | −2.29266e35 | −0.835870 | ||||||||
\(685\) | −1.07458e35 | − | 3.26542e35i | −0.384688 | − | 1.16898i | ||||
\(686\) | −7.58477e34 | −0.266619 | ||||||||
\(687\) | 1.19023e35i | 0.410838i | ||||||||
\(688\) | − | 9.01830e34i | − | 0.305681i | ||||||
\(689\) | −1.18511e35 | −0.394474 | ||||||||
\(690\) | −2.59346e34 | − | 7.88095e34i | −0.0847746 | − | 0.257611i | ||||
\(691\) | 1.05074e35 | 0.337304 | 0.168652 | − | 0.985676i | \(-0.446059\pi\) | ||||
0.168652 | + | 0.985676i | \(0.446059\pi\) | |||||||
\(692\) | − | 3.34166e35i | − | 1.05350i | ||||||
\(693\) | − | 6.64671e35i | − | 2.05798i | ||||||
\(694\) | 4.94932e34 | 0.150505 | ||||||||
\(695\) | −5.06566e35 | + | 1.66700e35i | −1.51295 | + | 0.497882i | ||||
\(696\) | 5.93705e35 | 1.74163 | ||||||||
\(697\) | 1.49633e35i | 0.431141i | ||||||||
\(698\) | − | 7.28083e34i | − | 0.206057i | ||||||
\(699\) | 7.96667e34 | 0.221469 | ||||||||
\(700\) | 2.03766e35 | + | 2.76072e35i | 0.556424 | + | 0.753870i | ||||
\(701\) | −1.02093e35 | −0.273855 | −0.136928 | − | 0.990581i | \(-0.543723\pi\) | ||||
−0.136928 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(702\) | 2.23083e34i | 0.0587832i | ||||||||
\(703\) | 5.47095e35i | 1.41619i | ||||||||
\(704\) | −1.28744e35 | −0.327392 | ||||||||
\(705\) | −9.49714e35 | + | 3.12532e35i | −2.37262 | + | 0.780782i | ||||
\(706\) | −1.68141e35 | −0.412682 | ||||||||
\(707\) | − | 2.51763e35i | − | 0.607084i | ||||||
\(708\) | − | 1.71185e35i | − | 0.405556i | ||||||
\(709\) | −2.46590e35 | −0.573981 | −0.286990 | − | 0.957933i | \(-0.592655\pi\) | ||||
−0.286990 | + | 0.957933i | \(0.592655\pi\) | |||||||
\(710\) | 3.00861e34 | + | 9.14249e34i | 0.0688076 | + | 0.209091i | ||||
\(711\) | 5.35988e35 | 1.20444 | ||||||||
\(712\) | 1.78872e35i | 0.394951i | ||||||||
\(713\) | − | 1.38637e35i | − | 0.300789i | ||||||
\(714\) | −1.80585e35 | −0.384994 | ||||||||
\(715\) | 1.83664e35 | + | 5.58115e35i | 0.384768 | + | 1.16923i | ||||
\(716\) | 2.37315e35 | 0.488555 | ||||||||
\(717\) | − | 5.80736e35i | − | 1.17487i | ||||||
\(718\) | 2.03234e35i | 0.404056i | ||||||||
\(719\) | −8.52137e34 | −0.166494 | −0.0832470 | − | 0.996529i | \(-0.526529\pi\) | ||||
−0.0832470 | + | 0.996529i | \(0.526529\pi\) | |||||||
\(720\) | 1.63645e35 | − | 5.38523e34i | 0.314230 | − | 0.103407i | ||||
\(721\) | 7.02487e35 | 1.32571 | ||||||||
\(722\) | 1.18235e34i | 0.0219296i | ||||||||
\(723\) | 4.45340e35i | 0.811827i | ||||||||
\(724\) | −7.91804e35 | −1.41868 | ||||||||
\(725\) | 6.23969e35 | − | 4.60545e35i | 1.09885 | − | 0.811049i | ||||
\(726\) | 5.17478e35 | 0.895744 | ||||||||
\(727\) | − | 9.18354e35i | − | 1.56254i | −0.624196 | − | 0.781268i | \(-0.714573\pi\) | ||
0.624196 | − | 0.781268i | \(-0.285427\pi\) | |||||||
\(728\) | 5.45849e35i | 0.912915i | ||||||||
\(729\) | 7.20568e35 | 1.18463 | ||||||||
\(730\) | −5.12803e34 | + | 1.68753e34i | −0.0828733 | + | 0.0272719i | ||||
\(731\) | 2.67691e35 | 0.425271 | ||||||||
\(732\) | 3.22845e33i | 0.00504203i | ||||||||
\(733\) | − | 2.21685e35i | − | 0.340358i | −0.985413 | − | 0.170179i | \(-0.945565\pi\) | ||
0.985413 | − | 0.170179i | \(-0.0544347\pi\) | |||||||
\(734\) | 5.61803e35 | 0.847975 | ||||||||
\(735\) | −1.76773e35 | − | 5.37173e35i | −0.262315 | − | 0.797118i | ||||
\(736\) | −2.62737e35 | −0.383308 | ||||||||
\(737\) | 1.44309e36i | 2.06990i | ||||||||
\(738\) | − | 4.03630e35i | − | 0.569218i | ||||||
\(739\) | 6.47256e35 | 0.897472 | 0.448736 | − | 0.893664i | \(-0.351874\pi\) | ||||
0.448736 | + | 0.893664i | \(0.351874\pi\) | |||||||
\(740\) | −2.36990e35 | − | 7.20161e35i | −0.323098 | − | 0.981823i | ||||
\(741\) | −9.10488e35 | −1.22052 | ||||||||
\(742\) | 2.29965e35i | 0.303119i | ||||||||
\(743\) | 3.13033e35i | 0.405723i | 0.979207 | + | 0.202861i | \(0.0650241\pi\) | ||||
−0.979207 | + | 0.202861i | \(0.934976\pi\) | |||||||
\(744\) | −8.10711e35 | −1.03325 | ||||||||
\(745\) | −4.34711e35 | + | 1.43054e35i | −0.544813 | + | 0.179287i | ||||
\(746\) | −6.20616e35 | −0.764870 | ||||||||
\(747\) | 2.28596e35i | 0.277052i | ||||||||
\(748\) | 3.91362e35i | 0.466454i | ||||||||
\(749\) | −1.10636e36 | −1.29681 | ||||||||
\(750\) | −3.66704e35 | + | 5.16880e35i | −0.422717 | + | 0.595832i | ||||
\(751\) | 1.24295e36 | 1.40914 | 0.704569 | − | 0.709635i | \(-0.251140\pi\) | ||||
0.704569 | + | 0.709635i | \(0.251140\pi\) | |||||||
\(752\) | 4.66210e35i | 0.519827i | ||||||||
\(753\) | − | 3.64739e35i | − | 0.399987i | ||||||
\(754\) | 5.26938e35 | 0.568353 | ||||||||
\(755\) | 6.78763e35 | − | 2.23367e35i | 0.720080 | − | 0.236964i | ||||
\(756\) | −1.26841e35 | −0.132354 | ||||||||
\(757\) | 2.50689e35i | 0.257298i | 0.991690 | + | 0.128649i | \(0.0410641\pi\) | ||||
−0.991690 | + | 0.128649i | \(0.958936\pi\) | |||||||
\(758\) | − | 5.95255e35i | − | 0.600950i | ||||||
\(759\) | 8.07779e35 | 0.802178 | ||||||||
\(760\) | −2.87816e35 | − | 8.74608e35i | −0.281154 | − | 0.854365i | ||||
\(761\) | −1.75153e36 | −1.68309 | −0.841547 | − | 0.540183i | \(-0.818355\pi\) | ||||
−0.841547 | + | 0.540183i | \(0.818355\pi\) | |||||||
\(762\) | − | 1.04092e36i | − | 0.983968i | ||||||
\(763\) | − | 1.03789e36i | − | 0.965147i | ||||||
\(764\) | −9.24418e35 | −0.845670 | ||||||||
\(765\) | 1.59850e35 | + | 4.85749e35i | 0.143862 | + | 0.437164i | ||||
\(766\) | −8.77841e35 | −0.777242 | ||||||||
\(767\) | − | 3.55721e35i | − | 0.309861i | ||||||
\(768\) | 1.15665e36i | 0.991257i | ||||||||
\(769\) | 1.03505e36 | 0.872731 | 0.436366 | − | 0.899769i | \(-0.356265\pi\) | ||||
0.436366 | + | 0.899769i | \(0.356265\pi\) | |||||||
\(770\) | 1.08300e36 | − | 3.56392e35i | 0.898447 | − | 0.295661i | ||||
\(771\) | −1.19637e36 | −0.976531 | ||||||||
\(772\) | − | 1.11098e36i | − | 0.892258i | ||||||
\(773\) | − | 8.74798e35i | − | 0.691296i | −0.938364 | − | 0.345648i | \(-0.887659\pi\) | ||
0.938364 | − | 0.345648i | \(-0.112341\pi\) | |||||||
\(774\) | −7.22084e35 | −0.561469 | ||||||||
\(775\) | −8.52037e35 | + | 6.28879e35i | −0.651909 | + | 0.481167i | ||||
\(776\) | 1.49305e36 | 1.12409 | ||||||||
\(777\) | 3.40602e36i | 2.52339i | ||||||||
\(778\) | 3.33616e35i | 0.243222i | ||||||||
\(779\) | 1.46394e36 | 1.05028 | ||||||||
\(780\) | 1.19851e36 | − | 3.94405e35i | 0.846171 | − | 0.278458i | ||||
\(781\) | −9.37084e35 | −0.651090 | ||||||||
\(782\) | − | 1.14836e35i | − | 0.0785221i | ||||||
\(783\) | 2.86681e35i | 0.192920i | ||||||||
\(784\) | −2.63696e35 | −0.174644 | ||||||||
\(785\) | 2.96055e35 | + | 8.99644e35i | 0.192975 | + | 0.586408i | ||||
\(786\) | 6.59103e35 | 0.422835 | ||||||||
\(787\) | − | 5.62209e35i | − | 0.354988i | −0.984122 | − | 0.177494i | \(-0.943201\pi\) | ||
0.984122 | − | 0.177494i | \(-0.0567990\pi\) | |||||||
\(788\) | 4.03339e35i | 0.250664i | ||||||||
\(789\) | 2.27652e36 | 1.39254 | ||||||||
\(790\) | 2.87393e35 | + | 8.73322e35i | 0.173036 | + | 0.525819i | ||||
\(791\) | 6.77614e35 | 0.401584 | ||||||||
\(792\) | − | 2.47165e36i | − | 1.44186i | ||||||
\(793\) | 6.70868e33i | 0.00385232i | ||||||||
\(794\) | −4.62453e35 | −0.261403 | ||||||||
\(795\) | 1.18218e36 | − | 3.89031e35i | 0.657800 | − | 0.216469i | ||||
\(796\) | −2.15096e36 | −1.17820 | ||||||||
\(797\) | − | 1.39898e36i | − | 0.754369i | −0.926138 | − | 0.377184i | \(-0.876892\pi\) | ||
0.926138 | − | 0.377184i | \(-0.123108\pi\) | |||||||
\(798\) | 1.76676e36i | 0.937866i | ||||||||
\(799\) | −1.38386e36 | −0.723196 | ||||||||
\(800\) | 1.19181e36 | + | 1.61473e36i | 0.613173 | + | 0.830757i | ||||
\(801\) | −9.71936e35 | −0.492301 | ||||||||
\(802\) | − | 4.40692e35i | − | 0.219763i | ||||||
\(803\) | − | 5.25611e35i | − | 0.258060i | ||||||
\(804\) | 3.09892e36 | 1.49799 | ||||||||
\(805\) | 9.31134e35 | − | 3.06417e35i | 0.443163 | − | 0.145836i | ||||
\(806\) | −7.19540e35 | −0.337184 | ||||||||
\(807\) | − | 4.04768e35i | − | 0.186761i | ||||||
\(808\) | − | 9.36206e35i | − | 0.425333i | ||||||
\(809\) | −1.99727e36 | −0.893469 | −0.446734 | − | 0.894667i | \(-0.647413\pi\) | ||||
−0.446734 | + | 0.894667i | \(0.647413\pi\) | |||||||
\(810\) | 3.19640e35 | + | 9.71316e35i | 0.140799 | + | 0.427856i | ||||
\(811\) | −1.75537e36 | −0.761393 | −0.380696 | − | 0.924700i | \(-0.624316\pi\) | ||||
−0.380696 | + | 0.924700i | \(0.624316\pi\) | |||||||
\(812\) | 2.99606e36i | 1.27968i | ||||||||
\(813\) | − | 2.09775e36i | − | 0.882310i | ||||||
\(814\) | −2.51916e36 | −1.04340 | ||||||||
\(815\) | 3.95929e35 | + | 1.20314e36i | 0.161491 | + | 0.490734i | ||||
\(816\) | 4.55714e35 | 0.183048 | ||||||||
\(817\) | − | 2.61896e36i | − | 1.03598i | ||||||
\(818\) | − | 1.39677e35i | − | 0.0544136i | ||||||
\(819\) | −2.96597e36 | −1.13794 | ||||||||
\(820\) | −1.92704e36 | + | 6.34150e35i | −0.728145 | + | 0.239618i | ||||
\(821\) | 1.90029e36 | 0.707181 | 0.353591 | − | 0.935400i | \(-0.384961\pi\) | ||||
0.353591 | + | 0.935400i | \(0.384961\pi\) | |||||||
\(822\) | 2.45292e36i | 0.899052i | ||||||||
\(823\) | − | 1.45322e35i | − | 0.0524606i | −0.999656 | − | 0.0262303i | \(-0.991650\pi\) | ||
0.999656 | − | 0.0262303i | \(-0.00835033\pi\) | |||||||
\(824\) | 2.61227e36 | 0.928813 | ||||||||
\(825\) | −3.66420e36 | − | 4.96444e36i | −1.28323 | − | 1.73859i | ||||
\(826\) | −6.90259e35 | −0.238101 | ||||||||
\(827\) | 1.69798e36i | 0.576918i | 0.957492 | + | 0.288459i | \(0.0931428\pi\) | ||||
−0.957492 | + | 0.288459i | \(0.906857\pi\) | |||||||
\(828\) | − | 9.07651e35i | − | 0.303766i | ||||||
\(829\) | 1.42211e35 | 0.0468816 | 0.0234408 | − | 0.999725i | \(-0.492538\pi\) | ||||
0.0234408 | + | 0.999725i | \(0.492538\pi\) | |||||||
\(830\) | −3.72467e35 | + | 1.22571e35i | −0.120952 | + | 0.0398028i | ||||
\(831\) | −2.05221e36 | −0.656460 | ||||||||
\(832\) | 5.74495e35i | 0.181027i | ||||||||
\(833\) | − | 7.82730e35i | − | 0.242968i | ||||||
\(834\) | 3.80521e36 | 1.16360 | ||||||||
\(835\) | −3.17330e35 | − | 9.64297e35i | −0.0955940 | − | 0.290489i | ||||
\(836\) | 3.82890e36 | 1.13631 | ||||||||
\(837\) | − | 3.91466e35i | − | 0.114453i | ||||||
\(838\) | − | 1.60722e36i | − | 0.462941i | ||||||
\(839\) | −1.73838e36 | −0.493311 | −0.246656 | − | 0.969103i | \(-0.579332\pi\) | ||||
−0.246656 | + | 0.969103i | \(0.579332\pi\) | |||||||
\(840\) | −1.79184e36 | − | 5.44499e36i | −0.500965 | − | 1.52232i | ||||
\(841\) | 3.14124e36 | 0.865269 | ||||||||
\(842\) | − | 1.82438e36i | − | 0.495124i | ||||||
\(843\) | 9.26560e36i | 2.47759i | ||||||||
\(844\) | −1.17921e36 | −0.310678 | ||||||||
\(845\) | −1.16868e36 | + | 3.84588e35i | −0.303379 | + | 0.0998359i | ||||
\(846\) | 3.73289e36 | 0.954807 | ||||||||
\(847\) | 6.11400e36i | 1.54093i | ||||||||
\(848\) | − | 5.80326e35i | − | 0.144120i | ||||||
\(849\) | 3.12439e34 | 0.00764574 | ||||||||
\(850\) | −7.05755e35 | + | 5.20910e35i | −0.170183 | + | 0.125611i | ||||
\(851\) | −2.16592e36 | −0.514662 | ||||||||
\(852\) | 2.01231e36i | 0.471195i | ||||||||
\(853\) | 5.78242e36i | 1.33428i | 0.744933 | + | 0.667139i | \(0.232481\pi\) | ||||
−0.744933 | + | 0.667139i | \(0.767519\pi\) | |||||||
\(854\) | 1.30179e34 | 0.00296017 | ||||||||
\(855\) | 4.75234e36 | − | 1.56390e36i | 1.06495 | − | 0.350455i | ||||
\(856\) | −4.11413e36 | −0.908566 | ||||||||
\(857\) | − | 4.03252e36i | − | 0.877640i | −0.898575 | − | 0.438820i | \(-0.855397\pi\) | ||
0.898575 | − | 0.438820i | \(-0.144603\pi\) | |||||||
\(858\) | − | 4.19244e36i | − | 0.899241i | ||||||
\(859\) | 5.20623e36 | 1.10055 | 0.550274 | − | 0.834984i | \(-0.314523\pi\) | ||||
0.550274 | + | 0.834984i | \(0.314523\pi\) | |||||||
\(860\) | 1.13448e36 | + | 3.44743e36i | 0.236356 | + | 0.718232i | ||||
\(861\) | 9.11398e36 | 1.87141 | ||||||||
\(862\) | 2.90853e36i | 0.588618i | ||||||||
\(863\) | − | 5.25366e36i | − | 1.04792i | −0.851744 | − | 0.523958i | \(-0.824455\pi\) | ||
0.851744 | − | 0.523958i | \(-0.175545\pi\) | |||||||
\(864\) | −7.41882e35 | −0.145852 | ||||||||
\(865\) | 2.27945e36 | + | 6.92676e36i | 0.441702 | + | 1.34223i | ||||
\(866\) | 2.95640e36 | 0.564664 | ||||||||
\(867\) | − | 6.34025e36i | − | 1.19363i | ||||||
\(868\) | − | 4.09115e36i | − | 0.759188i | ||||||
\(869\) | −8.95135e36 | −1.63735 | ||||||||
\(870\) | −5.25635e36 | + | 1.72976e36i | −0.947750 | + | 0.311885i | ||||
\(871\) | 6.43952e36 | 1.14453 | ||||||||
\(872\) | − | 3.85949e36i | − | 0.676199i | ||||||
\(873\) | 8.11275e36i | 1.40117i | ||||||||
\(874\) | −1.12350e36 | −0.191284 | ||||||||
\(875\) | −6.10693e36 | − | 4.33260e36i | −1.02500 | − | 0.727190i | ||||
\(876\) | −1.12871e36 | −0.186759 | ||||||||
\(877\) | − | 8.98820e36i | − | 1.46615i | −0.680149 | − | 0.733074i | \(-0.738085\pi\) | ||
0.680149 | − | 0.733074i | \(-0.261915\pi\) | |||||||
\(878\) | − | 3.85571e36i | − | 0.620045i | ||||||
\(879\) | −1.38178e37 | −2.19067 | ||||||||
\(880\) | −2.73299e36 | + | 8.99370e35i | −0.427173 | + | 0.140574i | ||||
\(881\) | 7.27878e36 | 1.12166 | 0.560828 | − | 0.827933i | \(-0.310483\pi\) | ||||
0.560828 | + | 0.827933i | \(0.310483\pi\) | |||||||
\(882\) | 2.11138e36i | 0.320782i | ||||||||
\(883\) | − | 1.06302e37i | − | 1.59233i | −0.605078 | − | 0.796166i | \(-0.706858\pi\) | ||
0.605078 | − | 0.796166i | \(-0.293142\pi\) | |||||||
\(884\) | 1.74638e36 | 0.257920 | ||||||||
\(885\) | 1.16771e36 | + | 3.54841e36i | 0.170037 | + | 0.516705i | ||||
\(886\) | −2.06715e36 | −0.296791 | ||||||||
\(887\) | 7.11036e36i | 1.00658i | 0.864119 | + | 0.503288i | \(0.167876\pi\) | ||||
−0.864119 | + | 0.503288i | \(0.832124\pi\) | |||||||
\(888\) | 1.26656e37i | 1.76793i | ||||||||
\(889\) | 1.22985e37 | 1.69270 | ||||||||
\(890\) | −5.21145e35 | − | 1.58364e36i | −0.0707267 | − | 0.214923i | ||||
\(891\) | −9.95577e36 | −1.33230 | ||||||||
\(892\) | − | 2.37770e36i | − | 0.313760i | ||||||
\(893\) | 1.35390e37i | 1.76174i | ||||||||
\(894\) | 3.26546e36 | 0.419011 | ||||||||
\(895\) | −4.91919e36 | + | 1.61880e36i | −0.622451 | + | 0.204836i | ||||
\(896\) | −9.28457e36 | −1.15854 | ||||||||
\(897\) | − | 3.60456e36i | − | 0.443555i | ||||||
\(898\) | − | 4.18583e35i | − | 0.0507958i | ||||||
\(899\) | −9.24670e36 | −1.10660 | ||||||||
\(900\) | −5.57823e36 | + | 4.11723e36i | −0.658362 | + | 0.485930i | ||||
\(901\) | 1.72259e36 | 0.200503 | ||||||||
\(902\) | 6.74089e36i | 0.773812i | ||||||||
\(903\) | − | 1.63047e37i | − | 1.84593i | ||||||
\(904\) | 2.51978e36 | 0.281356 | ||||||||
\(905\) | 1.64129e37 | − | 5.40115e36i | 1.80750 | − | 0.594811i | ||||
\(906\) | −5.09872e36 | −0.553808 | ||||||||
\(907\) | 2.31903e35i | 0.0248437i | 0.999923 | + | 0.0124218i | \(0.00395409\pi\) | ||||
−0.999923 | + | 0.0124218i | \(0.996046\pi\) | |||||||
\(908\) | − | 9.41987e36i | − | 0.995341i | ||||||
\(909\) | 5.08705e36 | 0.530173 | ||||||||
\(910\) | −1.59033e36 | − | 4.83266e36i | −0.163482 | − | 0.496786i | ||||
\(911\) | 1.71872e37 | 1.74271 | 0.871353 | − | 0.490656i | \(-0.163243\pi\) | ||||
0.871353 | + | 0.490656i | \(0.163243\pi\) | |||||||
\(912\) | − | 4.45849e36i | − | 0.445915i | ||||||
\(913\) | − | 3.81771e36i | − | 0.376632i | ||||||
\(914\) | −6.69486e36 | −0.651500 | ||||||||
\(915\) | −2.20223e34 | − | 6.69209e34i | −0.00211397 | − | 0.00642389i | ||||
\(916\) | −2.23352e36 | −0.211493 | ||||||||
\(917\) | 7.78730e36i | 0.727395i | ||||||||
\(918\) | − | 3.24257e35i | − | 0.0298783i | ||||||
\(919\) | 1.57745e37 | 1.43387 | 0.716937 | − | 0.697138i | \(-0.245543\pi\) | ||||
0.716937 | + | 0.697138i | \(0.245543\pi\) | |||||||
\(920\) | 3.46252e36 | − | 1.13944e36i | 0.310488 | − | 0.102175i | ||||
\(921\) | −8.75346e36 | −0.774344 | ||||||||
\(922\) | − | 1.54402e34i | − | 0.00134746i | ||||||
\(923\) | 4.18156e36i | 0.360012i | ||||||||
\(924\) | 2.38373e37 | 2.02469 | ||||||||
\(925\) | 9.82491e36 | + | 1.33113e37i | 0.823297 | + | 1.11544i | ||||
\(926\) | 2.87612e36 | 0.237777 | ||||||||
\(927\) | 1.41943e37i | 1.15775i | ||||||||
\(928\) | 1.75238e37i | 1.41019i | ||||||||
\(929\) | −2.16681e37 | −1.72038 | −0.860189 | − | 0.509975i | \(-0.829655\pi\) | ||||
−0.860189 | + | 0.509975i | \(0.829655\pi\) | |||||||
\(930\) | 7.17761e36 | − | 2.36201e36i | 0.562268 | − | 0.185031i | ||||
\(931\) | −7.65786e36 | −0.591884 | ||||||||
\(932\) | 1.49499e36i | 0.114009i | ||||||||
\(933\) | − | 1.45923e37i | − | 1.09800i | ||||||
\(934\) | 7.91026e36 | 0.587293 | ||||||||
\(935\) | −2.66961e36 | − | 8.11234e36i | −0.195570 | − | 0.594294i | ||||
\(936\) | −1.10293e37 | −0.797258 | ||||||||
\(937\) | 2.38865e37i | 1.70376i | 0.523740 | + | 0.851878i | \(0.324536\pi\) | ||||
−0.523740 | + | 0.851878i | \(0.675464\pi\) | |||||||
\(938\) | − | 1.24956e37i | − | 0.879470i | ||||||
\(939\) | −1.59707e36 | −0.110919 | ||||||||
\(940\) | −5.86481e36 | − | 1.78219e37i | −0.401935 | − | 1.22139i | ||||
\(941\) | −2.60228e37 | −1.75989 | −0.879943 | − | 0.475080i | \(-0.842419\pi\) | ||||
−0.879943 | + | 0.475080i | \(0.842419\pi\) | |||||||
\(942\) | − | 6.75794e36i | − | 0.451002i | ||||||
\(943\) | 5.79566e36i | 0.381686i | ||||||||
\(944\) | 1.74190e36 | 0.113207 | ||||||||
\(945\) | 2.62921e36 | − | 8.65220e35i | 0.168627 | − | 0.0554918i | ||||
\(946\) | 1.20593e37 | 0.763278 | ||||||||
\(947\) | − | 6.01381e36i | − | 0.375643i | −0.982203 | − | 0.187821i | \(-0.939857\pi\) | ||
0.982203 | − | 0.187821i | \(-0.0601426\pi\) | |||||||
\(948\) | 1.92223e37i | 1.18495i | ||||||||
\(949\) | −2.34544e36 | −0.142691 | ||||||||
\(950\) | 5.09634e36 | + | 6.90477e36i | 0.305994 | + | 0.414576i | ||||
\(951\) | −1.14328e37 | −0.677482 | ||||||||
\(952\) | − | 7.93405e36i | − | 0.464016i | ||||||
\(953\) | 7.32290e36i | 0.422690i | 0.977412 | + | 0.211345i | \(0.0677843\pi\) | ||||
−0.977412 | + | 0.211345i | \(0.932216\pi\) | |||||||
\(954\) | −4.64660e36 | −0.264716 | ||||||||
\(955\) | 1.91618e37 | − | 6.30575e36i | 1.07744 | − | 0.354564i | ||||
\(956\) | 1.08978e37 | 0.604805 | ||||||||
\(957\) | − | 5.38764e37i | − | 2.95121i | ||||||
\(958\) | − | 2.03851e36i | − | 0.110216i | ||||||
\(959\) | −2.89812e37 | −1.54662 | ||||||||
\(960\) | −1.88587e36 | − | 5.73074e36i | −0.0993394 | − | 0.301870i | ||||
\(961\) | −6.60632e36 | −0.343493 | ||||||||
\(962\) | 1.12413e37i | 0.576936i | ||||||||
\(963\) | − | 2.23549e37i | − | 1.13252i | ||||||
\(964\) | −8.35703e36 | −0.417916 | ||||||||
\(965\) | 7.57837e36 | + | 2.30290e37i | 0.374097 | + | 1.13680i | ||||
\(966\) | −6.99448e36 | −0.340833 | ||||||||
\(967\) | − | 1.82355e37i | − | 0.877174i | −0.898689 | − | 0.438587i | \(-0.855479\pi\) | ||
0.898689 | − | 0.438587i | \(-0.144521\pi\) | |||||||
\(968\) | 2.27355e37i | 1.07960i | ||||||||
\(969\) | 1.32342e37 | 0.620368 | ||||||||
\(970\) | −1.32187e37 | + | 4.34999e36i | −0.611704 | + | 0.201299i | ||||
\(971\) | −1.93748e37 | −0.885111 | −0.442555 | − | 0.896741i | \(-0.645928\pi\) | ||||
−0.442555 | + | 0.896741i | \(0.645928\pi\) | |||||||
\(972\) | 2.37144e37i | 1.06951i | ||||||||
\(973\) | 4.49586e37i | 2.00171i | ||||||||
\(974\) | 7.81757e36 | 0.343625 | ||||||||
\(975\) | −2.21529e37 | + | 1.63508e37i | −0.961331 | + | 0.709548i | ||||
\(976\) | −3.28512e34 | −0.00140743 | ||||||||
\(977\) | − | 4.13548e37i | − | 1.74922i | −0.484828 | − | 0.874610i | \(-0.661118\pi\) | ||
0.484828 | − | 0.874610i | \(-0.338882\pi\) | |||||||
\(978\) | − | 9.03774e36i | − | 0.377419i | ||||||
\(979\) | 1.62320e37 | 0.669249 | ||||||||
\(980\) | 1.00803e37 | − | 3.31723e36i | 0.410344 | − | 0.135036i | ||||
\(981\) | 2.09713e37 | 0.842872 | ||||||||
\(982\) | − | 1.97795e37i | − | 0.784915i | ||||||
\(983\) | − | 8.53182e36i | − | 0.334289i | −0.985932 | − | 0.167145i | \(-0.946545\pi\) | ||
0.985932 | − | 0.167145i | \(-0.0534547\pi\) | |||||||
\(984\) | 3.38913e37 | 1.31114 | ||||||||
\(985\) | −2.75131e36 | − | 8.36061e36i | −0.105096 | − | 0.319363i | ||||
\(986\) | −7.65918e36 | −0.288882 | ||||||||
\(987\) | 8.42888e37i | 3.13910i | ||||||||
\(988\) | − | 1.70858e37i | − | 0.628308i | ||||||
\(989\) | 1.03683e37 | 0.376490 | ||||||||
\(990\) | 7.20115e36 | + | 2.18827e37i | 0.258203 | + | 0.784623i | ||||
\(991\) | 9.57286e36 | 0.338939 | 0.169469 | − | 0.985535i | \(-0.445795\pi\) | ||||
0.169469 | + | 0.985535i | \(0.445795\pi\) | |||||||
\(992\) | − | 2.39289e37i | − | 0.836617i | ||||||
\(993\) | − | 6.02279e37i | − | 2.07937i | ||||||
\(994\) | 8.11412e36 | 0.276638 | ||||||||
\(995\) | 4.45862e37 | − | 1.46724e37i | 1.50111 | − | 0.493985i | ||||
\(996\) | −8.19822e36 | −0.272570 | ||||||||
\(997\) | 3.61670e37i | 1.18747i | 0.804660 | + | 0.593736i | \(0.202347\pi\) | ||||
−0.804660 | + | 0.593736i | \(0.797653\pi\) | |||||||
\(998\) | 2.90032e37i | 0.940402i | ||||||||
\(999\) | −6.11583e36 | −0.195833 |
(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 | 5.26.b.a.4.8 | yes | 12 | |
3.2 | odd | 2 | 45.26.b.b.19.5 | 12 | |||
5.2 | odd | 4 | 25.26.a.f.1.5 | 12 | |||
5.3 | odd | 4 | 25.26.a.f.1.8 | 12 | |||
5.4 | even | 2 | inner | 5.26.b.a.4.5 | ✓ | 12 | |
15.14 | odd | 2 | 45.26.b.b.19.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.26.b.a.4.5 | ✓ | 12 | 5.4 | even | 2 | inner | |
5.26.b.a.4.8 | yes | 12 | 1.1 | even | 1 | trivial | |
25.26.a.f.1.5 | 12 | 5.2 | odd | 4 | |||
25.26.a.f.1.8 | 12 | 5.3 | odd | 4 | |||
45.26.b.b.19.5 | 12 | 3.2 | odd | 2 | |||
45.26.b.b.19.8 | 12 | 15.14 | odd | 2 |