Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,21,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.11 | ||
Root | \(14907.4 + 4.14330e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.21.d.b.3.12 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 492.862 | − | 897.587i | 0.481311 | − | 0.876550i | ||||
\(3\) | 53283.8 | 0.902366 | 0.451183 | − | 0.892432i | \(-0.351002\pi\) | ||||
0.451183 | + | 0.892432i | \(0.351002\pi\) | |||||||
\(4\) | −562749. | − | 884774.i | −0.536680 | − | 0.843786i | ||||
\(5\) | − | 1.65732e7i | − | 1.69710i | −0.529118 | − | 0.848548i | \(-0.677477\pi\) | ||
0.529118 | − | 0.848548i | \(-0.322523\pi\) | |||||||
\(6\) | 2.62616e7 | − | 4.78269e7i | 0.434319 | − | 0.790969i | ||||
\(7\) | 1.30215e8i | 0.460979i | 0.973075 | + | 0.230490i | \(0.0740327\pi\) | ||||
−0.973075 | + | 0.230490i | \(0.925967\pi\) | |||||||
\(8\) | −1.07152e9 | + | 6.90447e7i | −0.997930 | + | 0.0643029i | ||||
\(9\) | −6.47621e8 | −0.185736 | ||||||||
\(10\) | −1.48759e10 | − | 8.16831e9i | −1.48759 | − | 0.816831i | ||||
\(11\) | 2.41984e10 | 0.932954 | 0.466477 | − | 0.884533i | \(-0.345523\pi\) | ||||
0.466477 | + | 0.884533i | \(0.345523\pi\) | |||||||
\(12\) | −2.99854e10 | − | 4.71441e10i | −0.484281 | − | 0.761404i | ||||
\(13\) | − | 6.71986e10i | − | 0.487446i | −0.969845 | − | 0.243723i | \(-0.921631\pi\) | ||
0.969845 | − | 0.243723i | \(-0.0783688\pi\) | |||||||
\(14\) | 1.16879e11 | + | 6.41782e10i | 0.404071 | + | 0.221874i | ||||
\(15\) | − | 8.83083e11i | − | 1.53140i | ||||||
\(16\) | −4.66138e11 | + | 9.95812e11i | −0.423950 | + | 0.905686i | ||||
\(17\) | −2.87376e12 | −1.42548 | −0.712741 | − | 0.701427i | \(-0.752547\pi\) | ||||
−0.712741 | + | 0.701427i | \(0.752547\pi\) | |||||||
\(18\) | −3.19188e11 | + | 5.81296e11i | −0.0893967 | + | 0.162807i | ||||
\(19\) | 7.21183e12 | 1.17628 | 0.588138 | − | 0.808761i | \(-0.299861\pi\) | ||||
0.588138 | + | 0.808761i | \(0.299861\pi\) | |||||||
\(20\) | −1.46635e13 | + | 9.32656e12i | −1.43199 | + | 0.910797i | ||||
\(21\) | 6.93836e12i | 0.415972i | ||||||||
\(22\) | 1.19265e13 | − | 2.17202e13i | 0.449041 | − | 0.817781i | ||||
\(23\) | − | 2.96291e12i | − | 0.0715221i | −0.999360 | − | 0.0357610i | \(-0.988614\pi\) | ||
0.999360 | − | 0.0357610i | \(-0.0113855\pi\) | |||||||
\(24\) | −5.70946e13 | + | 3.67896e12i | −0.900498 | + | 0.0580247i | ||||
\(25\) | −1.79304e14 | −1.88014 | ||||||||
\(26\) | −6.03166e13 | − | 3.31196e13i | −0.427271 | − | 0.234613i | ||||
\(27\) | −2.20297e14 | −1.06997 | ||||||||
\(28\) | 1.15211e14 | − | 7.32785e13i | 0.388968 | − | 0.247398i | ||||
\(29\) | − | 4.38340e14i | − | 1.04191i | −0.853583 | − | 0.520956i | \(-0.825575\pi\) | ||
0.853583 | − | 0.520956i | \(-0.174425\pi\) | |||||||
\(30\) | −7.92644e14 | − | 4.35239e14i | −1.34235 | − | 0.737080i | ||||
\(31\) | 9.28550e14i | 1.13289i | 0.824099 | + | 0.566446i | \(0.191682\pi\) | ||||
−0.824099 | + | 0.566446i | \(0.808318\pi\) | |||||||
\(32\) | 6.64086e14 | + | 9.09198e14i | 0.589827 | + | 0.807530i | ||||
\(33\) | 1.28938e15 | 0.841866 | ||||||||
\(34\) | −1.41637e15 | + | 2.57945e15i | −0.686100 | + | 1.24951i | ||||
\(35\) | 2.15808e15 | 0.782326 | ||||||||
\(36\) | 3.64448e14 | + | 5.72998e14i | 0.0996807 | + | 0.156721i | ||||
\(37\) | − | 7.26660e15i | − | 1.51117i | −0.655050 | − | 0.755586i | \(-0.727352\pi\) | ||
0.655050 | − | 0.755586i | \(-0.272648\pi\) | |||||||
\(38\) | 3.55444e15 | − | 6.47324e15i | 0.566155 | − | 1.03106i | ||||
\(39\) | − | 3.58059e15i | − | 0.439855i | ||||||
\(40\) | 1.14429e15 | + | 1.77585e16i | 0.109128 | + | 1.69358i | ||||
\(41\) | −1.47814e15 | −0.110123 | −0.0550616 | − | 0.998483i | \(-0.517536\pi\) | ||||
−0.0550616 | + | 0.998483i | \(0.517536\pi\) | |||||||
\(42\) | 6.22778e15 | + | 3.41966e15i | 0.364620 | + | 0.200212i | ||||
\(43\) | 3.77390e16 | 1.74625 | 0.873124 | − | 0.487498i | \(-0.162090\pi\) | ||||
0.873124 | + | 0.487498i | \(0.162090\pi\) | |||||||
\(44\) | −1.36177e16 | − | 2.14101e16i | −0.500698 | − | 0.787214i | ||||
\(45\) | 1.07332e16i | 0.315212i | ||||||||
\(46\) | −2.65947e15 | − | 1.46031e15i | −0.0626927 | − | 0.0344244i | ||||
\(47\) | − | 5.25428e16i | − | 0.998928i | −0.866335 | − | 0.499464i | \(-0.833530\pi\) | ||
0.866335 | − | 0.499464i | \(-0.166470\pi\) | |||||||
\(48\) | −2.48376e16 | + | 5.30606e16i | −0.382558 | + | 0.817260i | ||||
\(49\) | 6.28363e16 | 0.787498 | ||||||||
\(50\) | −8.83720e16 | + | 1.60941e17i | −0.904930 | + | 1.64803i | ||||
\(51\) | −1.53125e17 | −1.28631 | ||||||||
\(52\) | −5.94555e16 | + | 3.78159e16i | −0.411300 | + | 0.261602i | ||||
\(53\) | − | 2.49723e17i | − | 1.42790i | −0.700194 | − | 0.713952i | \(-0.746903\pi\) | ||
0.700194 | − | 0.713952i | \(-0.253097\pi\) | |||||||
\(54\) | −1.08576e17 | + | 1.97736e17i | −0.514987 | + | 0.937880i | ||||
\(55\) | − | 4.01046e17i | − | 1.58331i | ||||||
\(56\) | −8.99066e15 | − | 1.39528e17i | −0.0296423 | − | 0.460025i | ||||
\(57\) | 3.84274e17 | 1.06143 | ||||||||
\(58\) | −3.93448e17 | − | 2.16041e17i | −0.913288 | − | 0.501484i | ||||
\(59\) | 2.43410e17 | 0.476232 | 0.238116 | − | 0.971237i | \(-0.423470\pi\) | ||||
0.238116 | + | 0.971237i | \(0.423470\pi\) | |||||||
\(60\) | −7.81329e17 | + | 4.96954e17i | −1.29218 | + | 0.821872i | ||||
\(61\) | 5.14944e17i | 0.721874i | 0.932590 | + | 0.360937i | \(0.117543\pi\) | ||||
−0.932590 | + | 0.360937i | \(0.882457\pi\) | |||||||
\(62\) | 8.33455e17 | + | 4.57647e17i | 0.993036 | + | 0.545273i | ||||
\(63\) | − | 8.43301e16i | − | 0.0856204i | ||||||
\(64\) | 1.14339e18 | − | 1.47965e17i | 0.991730 | − | 0.128340i | ||||
\(65\) | −1.11370e18 | −0.827243 | ||||||||
\(66\) | 6.35489e17 | − | 1.15734e18i | 0.405199 | − | 0.737938i | ||||
\(67\) | 2.15425e18 | 1.18181 | 0.590906 | − | 0.806740i | \(-0.298770\pi\) | ||||
0.590906 | + | 0.806740i | \(0.298770\pi\) | |||||||
\(68\) | 1.61721e18 | + | 2.54263e18i | 0.765027 | + | 1.20280i | ||||
\(69\) | − | 1.57875e17i | − | 0.0645391i | ||||||
\(70\) | 1.06364e18 | − | 1.93707e18i | 0.376542 | − | 0.685748i | ||||
\(71\) | 1.26970e18i | 0.390048i | 0.980799 | + | 0.195024i | \(0.0624784\pi\) | ||||
−0.980799 | + | 0.195024i | \(0.937522\pi\) | |||||||
\(72\) | 6.93939e17 | − | 4.47148e16i | 0.185352 | − | 0.0119434i | ||||
\(73\) | 3.77047e18 | 0.877337 | 0.438668 | − | 0.898649i | \(-0.355450\pi\) | ||||
0.438668 | + | 0.898649i | \(0.355450\pi\) | |||||||
\(74\) | −6.52240e18 | − | 3.58143e18i | −1.32462 | − | 0.727344i | ||||
\(75\) | −9.55398e18 | −1.69657 | ||||||||
\(76\) | −4.05845e18 | − | 6.38084e18i | −0.631283 | − | 0.992526i | ||||
\(77\) | 3.15100e18i | 0.430072i | ||||||||
\(78\) | −3.21390e18 | − | 1.76474e18i | −0.385554 | − | 0.211707i | ||||
\(79\) | 2.34036e18i | 0.247179i | 0.992333 | + | 0.123590i | \(0.0394407\pi\) | ||||
−0.992333 | + | 0.123590i | \(0.960559\pi\) | |||||||
\(80\) | 1.65038e19 | + | 7.72540e18i | 1.53704 | + | 0.719484i | ||||
\(81\) | −9.48014e18 | −0.779766 | ||||||||
\(82\) | −7.28522e17 | + | 1.32676e18i | −0.0530035 | + | 0.0965284i | ||||
\(83\) | −1.71472e19 | −1.10513 | −0.552563 | − | 0.833471i | \(-0.686350\pi\) | ||||
−0.552563 | + | 0.833471i | \(0.686350\pi\) | |||||||
\(84\) | 6.13888e18 | − | 3.90456e18i | 0.350991 | − | 0.223244i | ||||
\(85\) | 4.76275e19i | 2.41918i | ||||||||
\(86\) | 1.86001e19 | − | 3.38740e19i | 0.840488 | − | 1.53067i | ||||
\(87\) | − | 2.33564e19i | − | 0.940186i | ||||||
\(88\) | −2.59291e19 | + | 1.67077e18i | −0.931024 | + | 0.0599916i | ||||
\(89\) | 6.55204e18 | 0.210124 | 0.105062 | − | 0.994466i | \(-0.466496\pi\) | ||||
0.105062 | + | 0.994466i | \(0.466496\pi\) | |||||||
\(90\) | 9.63394e18 | + | 5.28997e18i | 0.276299 | + | 0.151715i | ||||
\(91\) | 8.75027e18 | 0.224702 | ||||||||
\(92\) | −2.62150e18 | + | 1.66738e18i | −0.0603493 | + | 0.0383844i | ||||
\(93\) | 4.94767e19i | 1.02228i | ||||||||
\(94\) | −4.71617e19 | − | 2.58964e19i | −0.875611 | − | 0.480795i | ||||
\(95\) | − | 1.19523e20i | − | 1.99625i | ||||||
\(96\) | 3.53850e19 | + | 4.84455e19i | 0.532239 | + | 0.728687i | ||||
\(97\) | 1.29767e20 | 1.75973 | 0.879866 | − | 0.475221i | \(-0.157632\pi\) | ||||
0.879866 | + | 0.475221i | \(0.157632\pi\) | |||||||
\(98\) | 3.09696e19 | − | 5.64010e19i | 0.379032 | − | 0.690282i | ||||
\(99\) | −1.56714e19 | −0.173283 | ||||||||
\(100\) | 1.00903e20 | + | 1.58643e20i | 1.00903 | + | 1.58643i | ||||
\(101\) | − | 8.89506e19i | − | 0.805258i | −0.915363 | − | 0.402629i | \(-0.868096\pi\) | ||
0.915363 | − | 0.402629i | \(-0.131904\pi\) | |||||||
\(102\) | −7.54696e19 | + | 1.37443e20i | −0.619113 | + | 1.12751i | ||||
\(103\) | − | 2.01768e19i | − | 0.150135i | −0.997178 | − | 0.0750673i | \(-0.976083\pi\) | ||
0.997178 | − | 0.0750673i | \(-0.0239172\pi\) | |||||||
\(104\) | 4.63970e18 | + | 7.20046e19i | 0.0313442 | + | 0.486437i | ||||
\(105\) | 1.14991e20 | 0.705944 | ||||||||
\(106\) | −2.24148e20 | − | 1.23079e20i | −1.25163 | − | 0.687266i | ||||
\(107\) | −1.20079e20 | −0.610423 | −0.305211 | − | 0.952285i | \(-0.598727\pi\) | ||||
−0.305211 | + | 0.952285i | \(0.598727\pi\) | |||||||
\(108\) | 1.23972e20 | + | 1.94913e20i | 0.574230 | + | 0.902824i | ||||
\(109\) | 2.24102e20i | 0.946633i | 0.880893 | + | 0.473316i | \(0.156943\pi\) | ||||
−0.880893 | + | 0.473316i | \(0.843057\pi\) | |||||||
\(110\) | −3.59973e20 | − | 1.97660e20i | −1.38785 | − | 0.762066i | ||||
\(111\) | − | 3.87192e20i | − | 1.36363i | ||||||
\(112\) | −1.29670e20 | − | 6.06983e19i | −0.417502 | − | 0.195432i | ||||
\(113\) | −1.49362e20 | −0.440003 | −0.220001 | − | 0.975500i | \(-0.570606\pi\) | ||||
−0.220001 | + | 0.975500i | \(0.570606\pi\) | |||||||
\(114\) | 1.89394e20 | − | 3.44919e20i | 0.510879 | − | 0.930398i | ||||
\(115\) | −4.91049e19 | −0.121380 | ||||||||
\(116\) | −3.87832e20 | + | 2.46676e20i | −0.879151 | + | 0.559173i | ||||
\(117\) | 4.35192e19i | 0.0905362i | ||||||||
\(118\) | 1.19968e20 | − | 2.18482e20i | 0.229216 | − | 0.417441i | ||||
\(119\) | − | 3.74208e20i | − | 0.657118i | ||||||
\(120\) | 6.09722e19 | + | 9.46241e20i | 0.0984735 | + | 1.52823i | ||||
\(121\) | −8.71857e19 | −0.129596 | ||||||||
\(122\) | 4.62207e20 | + | 2.53797e20i | 0.632759 | + | 0.347446i | ||||
\(123\) | −7.87612e19 | −0.0993713 | ||||||||
\(124\) | 8.21557e20 | − | 5.22541e20i | 0.955918 | − | 0.608000i | ||||
\(125\) | 1.39109e21i | 1.49367i | ||||||||
\(126\) | −7.56936e19 | − | 4.15631e19i | −0.0750505 | − | 0.0412100i | ||||
\(127\) | − | 5.34974e20i | − | 0.490112i | −0.969509 | − | 0.245056i | \(-0.921194\pi\) | ||
0.969509 | − | 0.245056i | \(-0.0788063\pi\) | |||||||
\(128\) | 4.30721e20 | − | 1.09922e21i | 0.364835 | − | 0.931072i | ||||
\(129\) | 2.01088e21 | 1.57575 | ||||||||
\(130\) | −5.48899e20 | + | 9.99639e20i | −0.398161 | + | 0.725119i | ||||
\(131\) | −6.72549e20 | −0.451868 | −0.225934 | − | 0.974143i | \(-0.572543\pi\) | ||||
−0.225934 | + | 0.974143i | \(0.572543\pi\) | |||||||
\(132\) | −7.25600e20 | − | 1.14081e21i | −0.451812 | − | 0.710355i | ||||
\(133\) | 9.39089e20i | 0.542239i | ||||||||
\(134\) | 1.06175e21 | − | 1.93363e21i | 0.568819 | − | 1.03592i | ||||
\(135\) | 3.65102e21i | 1.81584i | ||||||||
\(136\) | 3.07929e21 | − | 1.98418e20i | 1.42253 | − | 0.0916626i | ||||
\(137\) | −1.70376e21 | −0.731479 | −0.365739 | − | 0.930717i | \(-0.619184\pi\) | ||||
−0.365739 | + | 0.930717i | \(0.619184\pi\) | |||||||
\(138\) | −1.41707e20 | − | 7.78107e19i | −0.0565717 | − | 0.0310634i | ||||
\(139\) | −1.86111e21 | −0.691231 | −0.345615 | − | 0.938376i | \(-0.612330\pi\) | ||||
−0.345615 | + | 0.938376i | \(0.612330\pi\) | |||||||
\(140\) | −1.21446e21 | − | 1.90942e21i | −0.419858 | − | 0.660116i | ||||
\(141\) | − | 2.79968e21i | − | 0.901399i | ||||||
\(142\) | 1.13967e21 | + | 6.25787e20i | 0.341896 | + | 0.187734i | ||||
\(143\) | − | 1.62610e21i | − | 0.454765i | ||||||
\(144\) | 3.01881e20 | − | 6.44909e20i | 0.0787428 | − | 0.168218i | ||||
\(145\) | −7.26470e21 | −1.76823 | ||||||||
\(146\) | 1.85832e21 | − | 3.38432e21i | 0.422272 | − | 0.769030i | ||||
\(147\) | 3.34816e21 | 0.710612 | ||||||||
\(148\) | −6.42930e21 | + | 4.08927e21i | −1.27511 | + | 0.811015i | ||||
\(149\) | − | 2.73667e21i | − | 0.507412i | −0.967281 | − | 0.253706i | \(-0.918350\pi\) | ||
0.967281 | − | 0.253706i | \(-0.0816495\pi\) | |||||||
\(150\) | −4.70880e21 | + | 8.57553e21i | −0.816578 | + | 1.48713i | ||||
\(151\) | 1.09639e22i | 1.77909i | 0.456852 | + | 0.889543i | \(0.348977\pi\) | ||||
−0.456852 | + | 0.889543i | \(0.651023\pi\) | |||||||
\(152\) | −7.72761e21 | + | 4.97938e20i | −1.17384 | + | 0.0756379i | ||||
\(153\) | 1.86111e21 | 0.264763 | ||||||||
\(154\) | 2.82830e21 | + | 1.55301e21i | 0.376980 | + | 0.206999i | ||||
\(155\) | 1.53890e22 | 1.92263 | ||||||||
\(156\) | −3.16802e21 | + | 2.01498e21i | −0.371143 | + | 0.236061i | ||||
\(157\) | − | 1.41430e22i | − | 1.55434i | −0.629294 | − | 0.777168i | \(-0.716656\pi\) | ||
0.629294 | − | 0.777168i | \(-0.283344\pi\) | |||||||
\(158\) | 2.10068e21 | + | 1.15348e21i | 0.216665 | + | 0.118970i | ||||
\(159\) | − | 1.33062e22i | − | 1.28849i | ||||||
\(160\) | 1.50683e22 | − | 1.10060e22i | 1.37046 | − | 1.00099i | ||||
\(161\) | 3.85816e20 | 0.0329702 | ||||||||
\(162\) | −4.67240e21 | + | 8.50925e21i | −0.375310 | + | 0.683504i | ||||
\(163\) | −7.62880e21 | −0.576209 | −0.288105 | − | 0.957599i | \(-0.593025\pi\) | ||||
−0.288105 | + | 0.957599i | \(0.593025\pi\) | |||||||
\(164\) | 8.31825e20 | + | 1.30782e21i | 0.0591008 | + | 0.0929203i | ||||
\(165\) | − | 2.13692e22i | − | 1.42873i | ||||||
\(166\) | −8.45120e21 | + | 1.53911e22i | −0.531909 | + | 0.968698i | ||||
\(167\) | 2.74529e22i | 1.62714i | 0.581469 | + | 0.813568i | \(0.302478\pi\) | ||||
−0.581469 | + | 0.813568i | \(0.697522\pi\) | |||||||
\(168\) | −4.79057e20 | − | 7.43459e21i | −0.0267482 | − | 0.415111i | ||||
\(169\) | 1.44893e22 | 0.762396 | ||||||||
\(170\) | 4.27498e22 | + | 2.34738e22i | 2.12053 | + | 1.16438i | ||||
\(171\) | −4.67053e21 | −0.218477 | ||||||||
\(172\) | −2.12376e22 | − | 3.33905e22i | −0.937175 | − | 1.47346i | ||||
\(173\) | 2.01546e22i | 0.839294i | 0.907687 | + | 0.419647i | \(0.137846\pi\) | ||||
−0.907687 | + | 0.419647i | \(0.862154\pi\) | |||||||
\(174\) | −2.09644e22 | − | 1.15115e22i | −0.824120 | − | 0.452522i | ||||
\(175\) | − | 2.33481e22i | − | 0.866703i | ||||||
\(176\) | −1.12798e22 | + | 2.40971e22i | −0.395526 | + | 0.844963i | ||||
\(177\) | 1.29698e22 | 0.429736 | ||||||||
\(178\) | 3.22926e21 | − | 5.88103e21i | 0.101135 | − | 0.184185i | ||||
\(179\) | 4.76803e22 | 1.41192 | 0.705958 | − | 0.708254i | \(-0.250517\pi\) | ||||
0.705958 | + | 0.708254i | \(0.250517\pi\) | |||||||
\(180\) | 9.49642e21 | − | 6.04008e21i | 0.265971 | − | 0.169168i | ||||
\(181\) | 1.72375e22i | 0.456761i | 0.973572 | + | 0.228380i | \(0.0733429\pi\) | ||||
−0.973572 | + | 0.228380i | \(0.926657\pi\) | |||||||
\(182\) | 4.31268e21 | − | 7.85413e21i | 0.108152 | − | 0.196963i | ||||
\(183\) | 2.74382e22i | 0.651395i | ||||||||
\(184\) | 2.04573e20 | + | 3.17482e21i | 0.00459907 | + | 0.0713740i | ||||
\(185\) | −1.20431e23 | −2.56460 | ||||||||
\(186\) | 4.44096e22 | + | 2.43852e22i | 0.896082 | + | 0.492036i | ||||
\(187\) | −6.95406e22 | −1.32991 | ||||||||
\(188\) | −4.64885e22 | + | 2.95684e22i | −0.842882 | + | 0.536104i | ||||
\(189\) | − | 2.86860e22i | − | 0.493233i | ||||||
\(190\) | −1.07282e23 | − | 5.89084e22i | −1.74982 | − | 0.960819i | ||||
\(191\) | − | 4.60627e22i | − | 0.712879i | −0.934318 | − | 0.356440i | \(-0.883991\pi\) | ||
0.934318 | − | 0.356440i | \(-0.116009\pi\) | |||||||
\(192\) | 6.09240e22 | − | 7.88416e21i | 0.894904 | − | 0.115809i | ||||
\(193\) | 3.15850e22 | 0.440462 | 0.220231 | − | 0.975448i | \(-0.429319\pi\) | ||||
0.220231 | + | 0.975448i | \(0.429319\pi\) | |||||||
\(194\) | 6.39572e22 | − | 1.16477e23i | 0.846979 | − | 1.54249i | ||||
\(195\) | −5.93419e22 | −0.746475 | ||||||||
\(196\) | −3.53611e22 | − | 5.55959e22i | −0.422634 | − | 0.664480i | ||||
\(197\) | 1.19350e23i | 1.35569i | 0.735205 | + | 0.677844i | \(0.237086\pi\) | ||||
−0.735205 | + | 0.677844i | \(0.762914\pi\) | |||||||
\(198\) | −7.72385e21 | + | 1.40665e22i | −0.0834031 | + | 0.151891i | ||||
\(199\) | 1.35757e23i | 1.39390i | 0.717121 | + | 0.696949i | \(0.245460\pi\) | ||||
−0.717121 | + | 0.696949i | \(0.754540\pi\) | |||||||
\(200\) | 1.92127e23 | − | 1.23800e22i | 1.87624 | − | 0.120898i | ||||
\(201\) | 1.14787e23 | 1.06643 | ||||||||
\(202\) | −7.98409e22 | − | 4.38404e22i | −0.705849 | − | 0.387580i | ||||
\(203\) | 5.70785e22 | 0.480300 | ||||||||
\(204\) | 8.61710e22 | + | 1.35481e23i | 0.690334 | + | 1.08537i | ||||
\(205\) | 2.44976e22i | 0.186889i | ||||||||
\(206\) | −1.81105e22 | − | 9.94441e21i | −0.131601 | − | 0.0722615i | ||||
\(207\) | 1.91884e21i | 0.0132842i | ||||||||
\(208\) | 6.69171e22 | + | 3.13238e22i | 0.441473 | + | 0.206653i | ||||
\(209\) | 1.74515e23 | 1.09741 | ||||||||
\(210\) | 5.66747e22 | − | 1.03214e23i | 0.339779 | − | 0.618795i | ||||
\(211\) | −1.62424e23 | −0.928594 | −0.464297 | − | 0.885680i | \(-0.653693\pi\) | ||||
−0.464297 | + | 0.885680i | \(0.653693\pi\) | |||||||
\(212\) | −2.20948e23 | + | 1.40531e23i | −1.20485 | + | 0.766327i | ||||
\(213\) | 6.76544e22i | 0.351966i | ||||||||
\(214\) | −5.91826e22 | + | 1.07782e23i | −0.293803 | + | 0.535066i | ||||
\(215\) | − | 6.25456e23i | − | 2.96355i | ||||||
\(216\) | 2.36052e23 | − | 1.52103e22i | 1.06775 | − | 0.0688020i | ||||
\(217\) | −1.20911e23 | −0.522239 | ||||||||
\(218\) | 2.01151e23 | + | 1.10452e23i | 0.829771 | + | 0.455625i | ||||
\(219\) | 2.00905e23 | 0.791679 | ||||||||
\(220\) | −3.54835e23 | + | 2.25688e23i | −1.33598 | + | 0.849732i | ||||
\(221\) | 1.93113e23i | 0.694846i | ||||||||
\(222\) | −3.47538e23 | − | 1.90832e23i | −1.19529 | − | 0.656330i | ||||
\(223\) | − | 4.02866e23i | − | 1.32468i | −0.749203 | − | 0.662341i | \(-0.769563\pi\) | ||
0.749203 | − | 0.662341i | \(-0.230437\pi\) | |||||||
\(224\) | −1.18391e23 | + | 8.64741e22i | −0.372254 | + | 0.271898i | ||||
\(225\) | 1.16121e23 | 0.349209 | ||||||||
\(226\) | −7.36149e22 | + | 1.34065e23i | −0.211778 | + | 0.385684i | ||||
\(227\) | 1.22521e23 | 0.337250 | 0.168625 | − | 0.985680i | \(-0.446067\pi\) | ||||
0.168625 | + | 0.985680i | \(0.446067\pi\) | |||||||
\(228\) | −2.16250e23 | − | 3.39995e23i | −0.569649 | − | 0.895621i | ||||
\(229\) | − | 1.04577e23i | − | 0.263681i | −0.991271 | − | 0.131841i | \(-0.957911\pi\) | ||
0.991271 | − | 0.131841i | \(-0.0420887\pi\) | |||||||
\(230\) | −2.42020e22 | + | 4.40759e22i | −0.0584214 | + | 0.106395i | ||||
\(231\) | 1.67897e23i | 0.388083i | ||||||||
\(232\) | 3.02650e22 | + | 4.69690e23i | 0.0669979 | + | 1.03976i | ||||
\(233\) | 1.59482e23 | 0.338185 | 0.169092 | − | 0.985600i | \(-0.445916\pi\) | ||||
0.169092 | + | 0.985600i | \(0.445916\pi\) | |||||||
\(234\) | 3.90623e22 | + | 2.14490e22i | 0.0793595 | + | 0.0435761i | ||||
\(235\) | −8.70802e23 | −1.69528 | ||||||||
\(236\) | −1.36979e23 | − | 2.15363e23i | −0.255584 | − | 0.401838i | ||||
\(237\) | 1.24703e23i | 0.223046i | ||||||||
\(238\) | −3.35884e23 | − | 1.84433e23i | −0.575996 | − | 0.316278i | ||||
\(239\) | 8.73131e23i | 1.43582i | 0.696136 | + | 0.717910i | \(0.254901\pi\) | ||||
−0.696136 | + | 0.717910i | \(0.745099\pi\) | |||||||
\(240\) | 8.79385e23 | + | 4.11639e23i | 1.38697 | + | 0.649238i | ||||
\(241\) | 6.52500e22 | 0.0987211 | 0.0493605 | − | 0.998781i | \(-0.484282\pi\) | ||||
0.0493605 | + | 0.998781i | \(0.484282\pi\) | |||||||
\(242\) | −4.29705e22 | + | 7.82567e22i | −0.0623759 | + | 0.113597i | ||||
\(243\) | 2.62990e23 | 0.366333 | ||||||||
\(244\) | 4.55609e23 | − | 2.89784e23i | 0.609108 | − | 0.387415i | ||||
\(245\) | − | 1.04140e24i | − | 1.33646i | ||||||
\(246\) | −3.88184e22 | + | 7.06950e22i | −0.0478285 | + | 0.0871039i | ||||
\(247\) | − | 4.84624e23i | − | 0.573371i | ||||||
\(248\) | −6.41114e22 | − | 9.94960e23i | −0.0728482 | − | 1.13055i | ||||
\(249\) | −9.13667e23 | −0.997228 | ||||||||
\(250\) | 1.24863e24 | + | 6.85617e23i | 1.30928 | + | 0.718922i | ||||
\(251\) | 1.14171e24 | 1.15032 | 0.575162 | − | 0.818040i | \(-0.304939\pi\) | ||||
0.575162 | + | 0.818040i | \(0.304939\pi\) | |||||||
\(252\) | −7.46131e22 | + | 4.74567e22i | −0.0722453 | + | 0.0459507i | ||||
\(253\) | − | 7.16978e22i | − | 0.0667268i | ||||||
\(254\) | −4.80185e23 | − | 2.63668e23i | −0.429607 | − | 0.235896i | ||||
\(255\) | 2.53777e24i | 2.18299i | ||||||||
\(256\) | −7.74356e23 | − | 9.28372e23i | −0.640532 | − | 0.767931i | ||||
\(257\) | 1.02107e24 | 0.812318 | 0.406159 | − | 0.913802i | \(-0.366868\pi\) | ||||
0.406159 | + | 0.913802i | \(0.366868\pi\) | |||||||
\(258\) | 9.91086e23 | − | 1.80494e24i | 0.758428 | − | 1.38123i | ||||
\(259\) | 9.46221e23 | 0.696619 | ||||||||
\(260\) | 6.26731e23 | + | 9.85369e23i | 0.443964 | + | 0.698016i | ||||
\(261\) | 2.83878e23i | 0.193521i | ||||||||
\(262\) | −3.31474e23 | + | 6.03672e23i | −0.217489 | + | 0.396085i | ||||
\(263\) | − | 3.41230e23i | − | 0.215521i | −0.994177 | − | 0.107761i | \(-0.965632\pi\) | ||
0.994177 | − | 0.107761i | \(-0.0343680\pi\) | |||||||
\(264\) | −1.38160e24 | + | 8.90251e22i | −0.840124 | + | 0.0541344i | ||||
\(265\) | −4.13870e24 | −2.42329 | ||||||||
\(266\) | 8.42915e23 | + | 4.62842e23i | 0.475299 | + | 0.260985i | ||||
\(267\) | 3.49118e23 | 0.189609 | ||||||||
\(268\) | −1.21230e24 | − | 1.90603e24i | −0.634255 | − | 0.997197i | ||||
\(269\) | − | 2.76279e23i | − | 0.139259i | −0.997573 | − | 0.0696297i | \(-0.977818\pi\) | ||
0.997573 | − | 0.0696297i | \(-0.0221818\pi\) | |||||||
\(270\) | 3.27711e24 | + | 1.79945e24i | 1.59167 | + | 0.873983i | ||||
\(271\) | 1.80384e24i | 0.844318i | 0.906522 | + | 0.422159i | \(0.138728\pi\) | ||||
−0.906522 | + | 0.422159i | \(0.861272\pi\) | |||||||
\(272\) | 1.33957e24 | − | 2.86173e24i | 0.604333 | − | 1.29104i | ||||
\(273\) | 4.66248e23 | 0.202764 | ||||||||
\(274\) | −8.39717e23 | + | 1.52927e24i | −0.352069 | + | 0.641178i | ||||
\(275\) | −4.33887e24 | −1.75408 | ||||||||
\(276\) | −1.39684e23 | + | 8.88441e22i | −0.0544572 | + | 0.0346368i | ||||
\(277\) | 1.40813e24i | 0.529476i | 0.964320 | + | 0.264738i | \(0.0852854\pi\) | ||||
−0.964320 | + | 0.264738i | \(0.914715\pi\) | |||||||
\(278\) | −9.17269e23 | + | 1.67050e24i | −0.332697 | + | 0.605898i | ||||
\(279\) | − | 6.01349e23i | − | 0.210419i | ||||||
\(280\) | −2.31243e24 | + | 1.49004e23i | −0.780707 | + | 0.0503058i | ||||
\(281\) | 1.85060e24 | 0.602906 | 0.301453 | − | 0.953481i | \(-0.402528\pi\) | ||||
0.301453 | + | 0.953481i | \(0.402528\pi\) | |||||||
\(282\) | −2.51296e24 | − | 1.37986e24i | −0.790121 | − | 0.433853i | ||||
\(283\) | 8.04995e22 | 0.0244303 | 0.0122152 | − | 0.999925i | \(-0.496112\pi\) | ||||
0.0122152 | + | 0.999925i | \(0.496112\pi\) | |||||||
\(284\) | 1.12340e24 | − | 7.14523e23i | 0.329117 | − | 0.209331i | ||||
\(285\) | − | 6.36864e24i | − | 1.80135i | ||||||
\(286\) | −1.45957e24 | − | 8.01444e23i | −0.398624 | − | 0.218883i | ||||
\(287\) | − | 1.92477e23i | − | 0.0507644i | ||||||
\(288\) | −4.30076e23 | − | 5.88816e23i | −0.109552 | − | 0.149987i | ||||
\(289\) | 4.19429e24 | 1.03200 | ||||||||
\(290\) | −3.58050e24 | + | 6.52070e24i | −0.851066 | + | 1.54994i | ||||
\(291\) | 6.91448e24 | 1.58792 | ||||||||
\(292\) | −2.12183e24 | − | 3.33601e24i | −0.470849 | − | 0.740285i | ||||
\(293\) | − | 2.22935e24i | − | 0.478082i | −0.971009 | − | 0.239041i | \(-0.923167\pi\) | ||
0.971009 | − | 0.239041i | \(-0.0768331\pi\) | |||||||
\(294\) | 1.65018e24 | − | 3.00526e24i | 0.342025 | − | 0.622886i | ||||
\(295\) | − | 4.03409e24i | − | 0.808212i | ||||||
\(296\) | 5.01720e23 | + | 7.78630e24i | 0.0971727 | + | 1.50804i | ||||
\(297\) | −5.33084e24 | −0.998231 | ||||||||
\(298\) | −2.45640e24 | − | 1.34880e24i | −0.444772 | − | 0.244223i | ||||
\(299\) | −1.99103e23 | −0.0348631 | ||||||||
\(300\) | 5.37650e24 | + | 8.45311e24i | 0.910514 | + | 1.43154i | ||||
\(301\) | 4.91419e24i | 0.804984i | ||||||||
\(302\) | 9.84108e24 | + | 5.40371e24i | 1.55946 | + | 0.856293i | ||||
\(303\) | − | 4.73963e24i | − | 0.726637i | ||||||
\(304\) | −3.36171e24 | + | 7.18162e24i | −0.498683 | + | 1.06534i | ||||
\(305\) | 8.53427e24 | 1.22509 | ||||||||
\(306\) | 9.17271e23 | − | 1.67051e24i | 0.127433 | − | 0.232078i | ||||
\(307\) | 4.70697e24 | 0.632933 | 0.316466 | − | 0.948604i | \(-0.397504\pi\) | ||||
0.316466 | + | 0.948604i | \(0.397504\pi\) | |||||||
\(308\) | 2.78793e24 | − | 1.77323e24i | 0.362889 | − | 0.230811i | ||||
\(309\) | − | 1.07510e24i | − | 0.135476i | ||||||
\(310\) | 7.58468e24 | − | 1.38130e25i | 0.925381 | − | 1.68528i | ||||
\(311\) | 5.93399e24i | 0.701040i | 0.936555 | + | 0.350520i | \(0.113995\pi\) | ||||
−0.936555 | + | 0.350520i | \(0.886005\pi\) | |||||||
\(312\) | 2.47221e23 | + | 3.83668e24i | 0.0282839 | + | 0.438944i | ||||
\(313\) | −3.32332e24 | −0.368239 | −0.184119 | − | 0.982904i | \(-0.558943\pi\) | ||||
−0.184119 | + | 0.982904i | \(0.558943\pi\) | |||||||
\(314\) | −1.26946e25 | − | 6.97055e24i | −1.36245 | − | 0.748119i | ||||
\(315\) | −1.39762e24 | −0.145306 | ||||||||
\(316\) | 2.07069e24 | − | 1.31704e24i | 0.208567 | − | 0.132656i | ||||
\(317\) | 9.92638e24i | 0.968720i | 0.874869 | + | 0.484360i | \(0.160947\pi\) | ||||
−0.874869 | + | 0.484360i | \(0.839053\pi\) | |||||||
\(318\) | −1.19434e25 | − | 6.55811e24i | −1.12943 | − | 0.620165i | ||||
\(319\) | − | 1.06071e25i | − | 0.972057i | ||||||
\(320\) | −2.45226e24 | − | 1.89496e25i | −0.217805 | − | 1.68306i | ||||
\(321\) | −6.39828e24 | −0.550824 | ||||||||
\(322\) | 1.90154e23 | − | 3.46303e23i | 0.0158689 | − | 0.0289000i | ||||
\(323\) | −2.07251e25 | −1.67676 | ||||||||
\(324\) | 5.33494e24 | + | 8.38778e24i | 0.418485 | + | 0.657956i | ||||
\(325\) | 1.20489e25i | 0.916464i | ||||||||
\(326\) | −3.75995e24 | + | 6.84751e24i | −0.277336 | + | 0.505076i | ||||
\(327\) | 1.19410e25i | 0.854209i | ||||||||
\(328\) | 1.58386e24 | − | 1.02058e23i | 0.109895 | − | 0.00708123i | ||||
\(329\) | 6.84187e24 | 0.460485 | ||||||||
\(330\) | −1.91807e25 | − | 1.05321e25i | −1.25235 | − | 0.687662i | ||||
\(331\) | −2.33153e25 | −1.47693 | −0.738466 | − | 0.674290i | \(-0.764450\pi\) | ||||
−0.738466 | + | 0.674290i | \(0.764450\pi\) | |||||||
\(332\) | 9.64956e24 | + | 1.51714e25i | 0.593099 | + | 0.932490i | ||||
\(333\) | 4.70600e24i | 0.280679i | ||||||||
\(334\) | 2.46414e25 | + | 1.35305e25i | 1.42627 | + | 0.783159i | ||||
\(335\) | − | 3.57029e25i | − | 2.00565i | ||||||
\(336\) | −6.90930e24 | − | 3.23423e24i | −0.376740 | − | 0.176351i | ||||
\(337\) | 1.72473e25 | 0.912899 | 0.456449 | − | 0.889749i | \(-0.349121\pi\) | ||||
0.456449 | + | 0.889749i | \(0.349121\pi\) | |||||||
\(338\) | 7.14124e24 | − | 1.30054e25i | 0.366950 | − | 0.668279i | ||||
\(339\) | −7.95857e24 | −0.397043 | ||||||||
\(340\) | 4.21395e25 | − | 2.68023e25i | 2.04127 | − | 1.29832i | ||||
\(341\) | 2.24695e25i | 1.05694i | ||||||||
\(342\) | −2.30193e24 | + | 4.19221e24i | −0.105155 | + | 0.191506i | ||||
\(343\) | 1.85724e25i | 0.823999i | ||||||||
\(344\) | −4.04381e25 | + | 2.60568e24i | −1.74263 | + | 0.112289i | ||||
\(345\) | −2.61650e24 | −0.109529 | ||||||||
\(346\) | 1.80905e25 | + | 9.93346e24i | 0.735683 | + | 0.403961i | ||||
\(347\) | 3.94050e25 | 1.55688 | 0.778442 | − | 0.627716i | \(-0.216010\pi\) | ||||
0.778442 | + | 0.627716i | \(0.216010\pi\) | |||||||
\(348\) | −2.06652e25 | + | 1.31438e25i | −0.793316 | + | 0.504579i | ||||
\(349\) | 1.08315e25i | 0.404049i | 0.979380 | + | 0.202025i | \(0.0647521\pi\) | ||||
−0.979380 | + | 0.202025i | \(0.935248\pi\) | |||||||
\(350\) | −2.09569e25 | − | 1.15074e25i | −0.759708 | − | 0.417154i | ||||
\(351\) | 1.48036e25i | 0.521551i | ||||||||
\(352\) | 1.60698e25 | + | 2.20012e25i | 0.550281 | + | 0.753389i | ||||
\(353\) | −2.90728e25 | −0.967697 | −0.483849 | − | 0.875152i | \(-0.660761\pi\) | ||||
−0.483849 | + | 0.875152i | \(0.660761\pi\) | |||||||
\(354\) | 6.39234e24 | − | 1.16415e25i | 0.206836 | − | 0.376685i | ||||
\(355\) | 2.10430e25 | 0.661948 | ||||||||
\(356\) | −3.68716e24 | − | 5.79708e24i | −0.112770 | − | 0.177300i | ||||
\(357\) | − | 1.99392e25i | − | 0.592960i | ||||||
\(358\) | 2.34998e25 | − | 4.27972e25i | 0.679570 | − | 1.23761i | ||||
\(359\) | − | 2.47565e25i | − | 0.696218i | −0.937454 | − | 0.348109i | \(-0.886824\pi\) | ||
0.937454 | − | 0.348109i | \(-0.113176\pi\) | |||||||
\(360\) | −7.41067e23 | − | 1.15008e25i | −0.0202690 | − | 0.314559i | ||||
\(361\) | 1.44205e25 | 0.383626 | ||||||||
\(362\) | 1.54722e25 | + | 8.49572e24i | 0.400373 | + | 0.219844i | ||||
\(363\) | −4.64558e24 | −0.116943 | ||||||||
\(364\) | −4.92421e24 | − | 7.74201e24i | −0.120593 | − | 0.189601i | ||||
\(365\) | − | 6.24887e25i | − | 1.48892i | ||||||
\(366\) | 2.46282e25 | + | 1.35232e25i | 0.570980 | + | 0.313523i | ||||
\(367\) | 9.71830e24i | 0.219245i | 0.993973 | + | 0.109623i | \(0.0349642\pi\) | ||||
−0.993973 | + | 0.109623i | \(0.965036\pi\) | |||||||
\(368\) | 2.95050e24 | + | 1.38113e24i | 0.0647765 | + | 0.0303218i | ||||
\(369\) | 9.57278e23 | 0.0204538 | ||||||||
\(370\) | −5.93558e25 | + | 1.08097e26i | −1.23437 | + | 2.24800i | ||||
\(371\) | 3.25177e25 | 0.658234 | ||||||||
\(372\) | 4.37757e25 | − | 2.78430e25i | 0.862588 | − | 0.548638i | ||||
\(373\) | − | 6.08237e25i | − | 1.16677i | −0.812197 | − | 0.583384i | \(-0.801728\pi\) | ||
0.812197 | − | 0.583384i | \(-0.198272\pi\) | |||||||
\(374\) | −3.42739e25 | + | 6.24187e25i | −0.640100 | + | 1.16573i | ||||
\(375\) | 7.41227e25i | 1.34784i | ||||||||
\(376\) | 3.62780e24 | + | 5.63006e25i | 0.0642340 | + | 0.996861i | ||||
\(377\) | −2.94558e25 | −0.507876 | ||||||||
\(378\) | −2.57482e25 | − | 1.41382e25i | −0.432343 | − | 0.237398i | ||||
\(379\) | −8.22232e24 | −0.134463 | −0.0672314 | − | 0.997737i | \(-0.521417\pi\) | ||||
−0.0672314 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(380\) | −1.05751e26 | + | 6.72615e25i | −1.68441 | + | 1.07135i | ||||
\(381\) | − | 2.85054e25i | − | 0.442260i | ||||||
\(382\) | −4.13453e25 | − | 2.27026e25i | −0.624874 | − | 0.343117i | ||||
\(383\) | − | 4.32837e24i | − | 0.0637289i | −0.999492 | − | 0.0318645i | \(-0.989856\pi\) | ||
0.999492 | − | 0.0318645i | \(-0.0101445\pi\) | |||||||
\(384\) | 2.29504e25 | − | 5.85704e25i | 0.329214 | − | 0.840168i | ||||
\(385\) | 5.22222e25 | 0.729874 | ||||||||
\(386\) | 1.55671e25 | − | 2.83503e25i | 0.211999 | − | 0.386087i | ||||
\(387\) | −2.44406e25 | −0.324341 | ||||||||
\(388\) | −7.30262e25 | − | 1.14814e26i | −0.944413 | − | 1.48484i | ||||
\(389\) | − | 1.07897e26i | − | 1.35993i | −0.733247 | − | 0.679963i | \(-0.761996\pi\) | ||
0.733247 | − | 0.679963i | \(-0.238004\pi\) | |||||||
\(390\) | −2.92474e25 | + | 5.32646e25i | −0.359287 | + | 0.654323i | ||||
\(391\) | 8.51470e24i | 0.101953i | ||||||||
\(392\) | −6.73303e25 | + | 4.33851e24i | −0.785869 | + | 0.0506384i | ||||
\(393\) | −3.58360e25 | −0.407750 | ||||||||
\(394\) | 1.07127e26 | + | 5.88231e25i | 1.18833 | + | 0.652508i | ||||
\(395\) | 3.87873e25 | 0.419487 | ||||||||
\(396\) | 8.81908e24 | + | 1.38657e25i | 0.0929975 | + | 0.146214i | ||||
\(397\) | 1.05083e26i | 1.08051i | 0.841502 | + | 0.540254i | \(0.181672\pi\) | ||||
−0.841502 | + | 0.540254i | \(0.818328\pi\) | |||||||
\(398\) | 1.21854e26 | + | 6.69095e25i | 1.22182 | + | 0.670898i | ||||
\(399\) | 5.00383e25i | 0.489298i | ||||||||
\(400\) | 8.35803e25 | − | 1.78553e26i | 0.797084 | − | 1.70281i | ||||
\(401\) | −1.57729e26 | −1.46713 | −0.733563 | − | 0.679622i | \(-0.762144\pi\) | ||||
−0.733563 | + | 0.679622i | \(0.762144\pi\) | |||||||
\(402\) | 5.65741e25 | − | 1.03031e26i | 0.513283 | − | 0.934777i | ||||
\(403\) | 6.23972e25 | 0.552223 | ||||||||
\(404\) | −7.87012e25 | + | 5.00569e25i | −0.679466 | + | 0.432166i | ||||
\(405\) | 1.57116e26i | 1.32334i | ||||||||
\(406\) | 2.81319e25 | − | 5.12330e25i | 0.231174 | − | 0.421007i | ||||
\(407\) | − | 1.75840e26i | − | 1.40985i | ||||||
\(408\) | 1.64076e26 | − | 1.05725e25i | 1.28364 | − | 0.0827132i | ||||
\(409\) | 6.00717e25 | 0.458603 | 0.229301 | − | 0.973355i | \(-0.426356\pi\) | ||||
0.229301 | + | 0.973355i | \(0.426356\pi\) | |||||||
\(410\) | 2.19887e25 | + | 1.20739e25i | 0.163818 | + | 0.0899520i | ||||
\(411\) | −9.07826e25 | −0.660062 | ||||||||
\(412\) | −1.78519e25 | + | 1.13545e25i | −0.126682 | + | 0.0805742i | ||||
\(413\) | 3.16957e25i | 0.219533i | ||||||||
\(414\) | 1.72233e24 | + | 9.45726e23i | 0.0116443 | + | 0.00639384i | ||||
\(415\) | 2.84184e26i | 1.87551i | ||||||||
\(416\) | 6.10968e25 | − | 4.46256e25i | 0.393627 | − | 0.287509i | ||||
\(417\) | −9.91668e25 | −0.623743 | ||||||||
\(418\) | 8.60119e25 | − | 1.56642e26i | 0.528197 | − | 0.961937i | ||||
\(419\) | 9.17104e25 | 0.549893 | 0.274947 | − | 0.961460i | \(-0.411340\pi\) | ||||
0.274947 | + | 0.961460i | \(0.411340\pi\) | |||||||
\(420\) | −6.47110e25 | − | 1.01741e26i | −0.378866 | − | 0.595666i | ||||
\(421\) | 2.84776e25i | 0.162811i | 0.996681 | + | 0.0814054i | \(0.0259408\pi\) | ||||
−0.996681 | + | 0.0814054i | \(0.974059\pi\) | |||||||
\(422\) | −8.00527e25 | + | 1.45790e26i | −0.446942 | + | 0.813959i | ||||
\(423\) | 3.40278e25i | 0.185537i | ||||||||
\(424\) | 1.72420e25 | + | 2.67583e26i | 0.0918183 | + | 1.42495i | ||||
\(425\) | 5.15276e26 | 2.68010 | ||||||||
\(426\) | 6.07257e25 | + | 3.33443e25i | 0.308515 | + | 0.169405i | ||||
\(427\) | −6.70535e25 | −0.332769 | ||||||||
\(428\) | 6.75746e25 | + | 1.06243e26i | 0.327601 | + | 0.515066i | ||||
\(429\) | − | 8.66448e25i | − | 0.410364i | ||||||
\(430\) | −5.61401e26 | − | 3.08264e26i | −2.59770 | − | 1.42639i | ||||
\(431\) | 1.53210e25i | 0.0692652i | 0.999400 | + | 0.0346326i | \(0.0110261\pi\) | ||||
−0.999400 | + | 0.0346326i | \(0.988974\pi\) | |||||||
\(432\) | 1.02689e26 | − | 2.19374e26i | 0.453613 | − | 0.969054i | ||||
\(433\) | −3.33355e26 | −1.43889 | −0.719447 | − | 0.694548i | \(-0.755604\pi\) | ||||
−0.719447 | + | 0.694548i | \(0.755604\pi\) | |||||||
\(434\) | −5.95926e25 | + | 1.08528e26i | −0.251360 | + | 0.457769i | ||||
\(435\) | −3.87091e26 | −1.59559 | ||||||||
\(436\) | 1.98280e26 | − | 1.26113e26i | 0.798756 | − | 0.508038i | ||||
\(437\) | − | 2.13680e25i | − | 0.0841297i | ||||||
\(438\) | 9.90184e25 | − | 1.80329e26i | 0.381044 | − | 0.693946i | ||||
\(439\) | − | 4.20421e26i | − | 1.58139i | −0.612210 | − | 0.790695i | \(-0.709719\pi\) | ||
0.612210 | − | 0.790695i | \(-0.290281\pi\) | |||||||
\(440\) | 2.76901e25 | + | 4.29728e26i | 0.101812 | + | 1.58004i | ||||
\(441\) | −4.06941e25 | −0.146267 | ||||||||
\(442\) | 1.73336e26 | + | 9.51780e25i | 0.609067 | + | 0.334437i | ||||
\(443\) | −1.38603e25 | −0.0476141 | −0.0238070 | − | 0.999717i | \(-0.507579\pi\) | ||||
−0.0238070 | + | 0.999717i | \(0.507579\pi\) | |||||||
\(444\) | −3.42577e26 | + | 2.17892e26i | −1.15061 | + | 0.731832i | ||||
\(445\) | − | 1.08588e26i | − | 0.356601i | ||||||
\(446\) | −3.61607e26 | − | 1.98557e26i | −1.16115 | − | 0.637584i | ||||
\(447\) | − | 1.45820e26i | − | 0.457871i | ||||||
\(448\) | 1.92673e25 | + | 1.48886e26i | 0.0591619 | + | 0.457167i | ||||
\(449\) | 8.14375e25 | 0.244546 | 0.122273 | − | 0.992496i | \(-0.460982\pi\) | ||||
0.122273 | + | 0.992496i | \(0.460982\pi\) | |||||||
\(450\) | 5.72316e25 | − | 1.04229e26i | 0.168078 | − | 0.306099i | ||||
\(451\) | −3.57688e25 | −0.102740 | ||||||||
\(452\) | 8.40533e25 | + | 1.32151e26i | 0.236140 | + | 0.371268i | ||||
\(453\) | 5.84200e26i | 1.60539i | ||||||||
\(454\) | 6.03860e25 | − | 1.09973e26i | 0.162322 | − | 0.295617i | ||||
\(455\) | − | 1.45020e26i | − | 0.381342i | ||||||
\(456\) | −4.11757e26 | + | 2.65320e25i | −1.05923 | + | 0.0682531i | ||||
\(457\) | −3.19651e26 | −0.804478 | −0.402239 | − | 0.915535i | \(-0.631768\pi\) | ||||
−0.402239 | + | 0.915535i | \(0.631768\pi\) | |||||||
\(458\) | −9.38665e25 | − | 5.15418e25i | −0.231130 | − | 0.126913i | ||||
\(459\) | 6.33081e26 | 1.52522 | ||||||||
\(460\) | 2.76337e25 | + | 4.34467e25i | 0.0651421 | + | 0.102419i | ||||
\(461\) | 1.06243e25i | 0.0245071i | 0.999925 | + | 0.0122535i | \(0.00390052\pi\) | ||||
−0.999925 | + | 0.0122535i | \(0.996099\pi\) | |||||||
\(462\) | 1.50703e26 | + | 8.27503e25i | 0.340174 | + | 0.186788i | ||||
\(463\) | − | 1.83285e26i | − | 0.404872i | −0.979296 | − | 0.202436i | \(-0.935114\pi\) | ||
0.979296 | − | 0.202436i | \(-0.0648858\pi\) | |||||||
\(464\) | 4.36504e26 | + | 2.04327e26i | 0.943645 | + | 0.441719i | ||||
\(465\) | 8.19987e26 | 1.73491 | ||||||||
\(466\) | 7.86029e25 | − | 1.43149e26i | 0.162772 | − | 0.296436i | ||||
\(467\) | 5.41789e26 | 1.09815 | 0.549075 | − | 0.835773i | \(-0.314980\pi\) | ||||
0.549075 | + | 0.835773i | \(0.314980\pi\) | |||||||
\(468\) | 3.85047e25 | − | 2.44904e25i | 0.0763932 | − | 0.0485889i | ||||
\(469\) | 2.80516e26i | 0.544791i | ||||||||
\(470\) | −4.29186e26 | + | 7.81621e26i | −0.815956 | + | 1.48600i | ||||
\(471\) | − | 7.53592e26i | − | 1.40258i | ||||||
\(472\) | −2.60819e26 | + | 1.68062e25i | −0.475247 | + | 0.0306231i | ||||
\(473\) | 9.13225e26 | 1.62917 | ||||||||
\(474\) | 1.11932e26 | + | 6.14617e25i | 0.195511 | + | 0.107355i | ||||
\(475\) | −1.29311e27 | −2.21156 | ||||||||
\(476\) | −3.31089e26 | + | 2.10585e26i | −0.554467 | + | 0.352662i | ||||
\(477\) | 1.61726e26i | 0.265213i | ||||||||
\(478\) | 7.83711e26 | + | 4.30333e26i | 1.25857 | + | 0.691076i | ||||
\(479\) | − | 3.43182e26i | − | 0.539721i | −0.962899 | − | 0.269861i | \(-0.913022\pi\) | ||
0.962899 | − | 0.269861i | \(-0.0869776\pi\) | |||||||
\(480\) | 8.02897e26 | − | 5.86443e26i | 1.23665 | − | 0.903261i | ||||
\(481\) | −4.88305e26 | −0.736615 | ||||||||
\(482\) | 3.21593e25 | − | 5.85675e25i | 0.0475155 | − | 0.0865340i | ||||
\(483\) | 2.05577e25 | 0.0297512 | ||||||||
\(484\) | 4.90637e25 | + | 7.71396e25i | 0.0695515 | + | 0.109351i | ||||
\(485\) | − | 2.15065e27i | − | 2.98644i | ||||||
\(486\) | 1.29618e26 | − | 2.36056e26i | 0.176320 | − | 0.321109i | ||||
\(487\) | 1.33645e27i | 1.78099i | 0.454992 | + | 0.890496i | \(0.349642\pi\) | ||||
−0.454992 | + | 0.890496i | \(0.650358\pi\) | |||||||
\(488\) | −3.55541e25 | − | 5.51773e26i | −0.0464186 | − | 0.720380i | ||||
\(489\) | −4.06491e26 | −0.519951 | ||||||||
\(490\) | −9.34746e26 | − | 5.13266e26i | −1.17147 | − | 0.643253i | ||||
\(491\) | −3.05224e26 | −0.374803 | −0.187402 | − | 0.982283i | \(-0.560007\pi\) | ||||
−0.187402 | + | 0.982283i | \(0.560007\pi\) | |||||||
\(492\) | 4.43228e25 | + | 6.96858e25i | 0.0533306 | + | 0.0838481i | ||||
\(493\) | 1.25969e27i | 1.48523i | ||||||||
\(494\) | −4.34993e26 | − | 2.38853e26i | −0.502588 | − | 0.275970i | ||||
\(495\) | 2.59726e26i | 0.294078i | ||||||||
\(496\) | −9.24661e26 | − | 4.32833e26i | −1.02604 | − | 0.480290i | ||||
\(497\) | −1.65334e26 | −0.179804 | ||||||||
\(498\) | −4.50312e26 | + | 8.20096e26i | −0.479977 | + | 0.874120i | ||||
\(499\) | 4.76885e26 | 0.498206 | 0.249103 | − | 0.968477i | \(-0.419864\pi\) | ||||
0.249103 | + | 0.968477i | \(0.419864\pi\) | |||||||
\(500\) | 1.23080e27 | − | 7.82836e26i | 1.26034 | − | 0.801624i | ||||
\(501\) | 1.46280e27i | 1.46827i | ||||||||
\(502\) | 5.62708e26 | − | 1.02479e27i | 0.553663 | − | 1.00832i | ||||
\(503\) | 1.99413e27i | 1.92341i | 0.274080 | + | 0.961707i | \(0.411627\pi\) | ||||
−0.274080 | + | 0.961707i | \(0.588373\pi\) | |||||||
\(504\) | 5.82254e24 | + | 9.03614e25i | 0.00550564 | + | 0.0854432i | ||||
\(505\) | −1.47420e27 | −1.36660 | ||||||||
\(506\) | −6.43550e25 | − | 3.53371e25i | −0.0584894 | − | 0.0321164i | ||||
\(507\) | 7.72046e26 | 0.687960 | ||||||||
\(508\) | −4.73331e26 | + | 3.01056e26i | −0.413549 | + | 0.263033i | ||||
\(509\) | − | 1.26697e27i | − | 1.08539i | −0.839929 | − | 0.542696i | \(-0.817403\pi\) | ||
0.839929 | − | 0.542696i | \(-0.182597\pi\) | |||||||
\(510\) | 2.27787e27 | + | 1.25077e27i | 1.91350 | + | 1.05069i | ||||
\(511\) | 4.90972e26i | 0.404434i | ||||||||
\(512\) | −1.21495e27 | + | 2.37493e26i | −0.981425 | + | 0.191845i | ||||
\(513\) | −1.58874e27 | −1.25858 | ||||||||
\(514\) | 5.03249e26 | − | 9.16503e26i | 0.390977 | − | 0.712037i | ||||
\(515\) | −3.34395e26 | −0.254793 | ||||||||
\(516\) | −1.13162e27 | − | 1.77917e27i | −0.845675 | − | 1.32960i | ||||
\(517\) | − | 1.27145e27i | − | 0.931955i | ||||||
\(518\) | 4.66357e26 | − | 8.49316e26i | 0.335290 | − | 0.610621i | ||||
\(519\) | 1.07392e27i | 0.757350i | ||||||||
\(520\) | 1.19335e27 | − | 7.68947e25i | 0.825531 | − | 0.0531941i | ||||
\(521\) | −1.34331e27 | −0.911592 | −0.455796 | − | 0.890084i | \(-0.650645\pi\) | ||||
−0.455796 | + | 0.890084i | \(0.650645\pi\) | |||||||
\(522\) | 2.54806e26 | + | 1.39913e26i | 0.169630 | + | 0.0931436i | ||||
\(523\) | 8.25533e26 | 0.539160 | 0.269580 | − | 0.962978i | \(-0.413115\pi\) | ||||
0.269580 | + | 0.962978i | \(0.413115\pi\) | |||||||
\(524\) | 3.78477e26 | + | 5.95054e26i | 0.242508 | + | 0.381280i | ||||
\(525\) | − | 1.24407e27i | − | 0.782083i | ||||||
\(526\) | −3.06284e26 | − | 1.68180e26i | −0.188915 | − | 0.103733i | ||||
\(527\) | − | 2.66843e27i | − | 1.61492i | ||||||
\(528\) | −6.01031e26 | + | 1.28398e27i | −0.356909 | + | 0.762466i | ||||
\(529\) | 1.70738e27 | 0.994885 | ||||||||
\(530\) | −2.03981e27 | + | 3.71485e27i | −1.16636 | + | 2.12414i | ||||
\(531\) | −1.57638e26 | −0.0884534 | ||||||||
\(532\) | 8.30882e26 | − | 5.28472e26i | 0.457534 | − | 0.291008i | ||||
\(533\) | 9.93292e25i | 0.0536791i | ||||||||
\(534\) | 1.72067e26 | − | 3.13364e26i | 0.0912610 | − | 0.166202i | ||||
\(535\) | 1.99010e27i | 1.03595i | ||||||||
\(536\) | −2.30832e27 | + | 1.48740e26i | −1.17937 | + | 0.0759939i | ||||
\(537\) | 2.54059e27 | 1.27406 | ||||||||
\(538\) | −2.47984e26 | − | 1.36167e26i | −0.122068 | − | 0.0670271i | ||||
\(539\) | 1.52054e27 | 0.734700 | ||||||||
\(540\) | 3.23033e27 | − | 2.05461e27i | 1.53218 | − | 0.974523i | ||||
\(541\) | − | 1.08634e27i | − | 0.505816i | −0.967490 | − | 0.252908i | \(-0.918613\pi\) | ||
0.967490 | − | 0.252908i | \(-0.0813869\pi\) | |||||||
\(542\) | 1.61911e27 | + | 8.89047e26i | 0.740087 | + | 0.406380i | ||||
\(543\) | 9.18480e26i | 0.412165i | ||||||||
\(544\) | −1.90843e27 | − | 2.61282e27i | −0.840788 | − | 1.15112i | ||||
\(545\) | 3.71409e27 | 1.60653 | ||||||||
\(546\) | 2.29796e26 | − | 4.18498e26i | 0.0975924 | − | 0.177733i | ||||
\(547\) | 1.79834e27 | 0.749890 | 0.374945 | − | 0.927047i | \(-0.377662\pi\) | ||||
0.374945 | + | 0.927047i | \(0.377662\pi\) | |||||||
\(548\) | 9.58788e26 | + | 1.50744e27i | 0.392570 | + | 0.617212i | ||||
\(549\) | − | 3.33489e26i | − | 0.134078i | ||||||
\(550\) | −2.13847e27 | + | 3.89451e27i | −0.844258 | + | 1.53754i | ||||
\(551\) | − | 3.16123e27i | − | 1.22558i | ||||||
\(552\) | 1.09004e25 | + | 1.69166e26i | 0.00415005 | + | 0.0644055i | ||||
\(553\) | −3.04751e26 | −0.113945 | ||||||||
\(554\) | 1.26392e27 | + | 6.94016e26i | 0.464112 | + | 0.254842i | ||||
\(555\) | −6.41701e27 | −2.31421 | ||||||||
\(556\) | 1.04734e27 | + | 1.64666e27i | 0.370969 | + | 0.583251i | ||||
\(557\) | 2.52076e27i | 0.876959i | 0.898741 | + | 0.438479i | \(0.144483\pi\) | ||||
−0.898741 | + | 0.438479i | \(0.855517\pi\) | |||||||
\(558\) | −5.39763e26 | − | 2.96382e26i | −0.184442 | − | 0.101277i | ||||
\(559\) | − | 2.53601e27i | − | 0.851201i | ||||||
\(560\) | −1.00596e27 | + | 2.14904e27i | −0.331667 | + | 0.708541i | ||||
\(561\) | −3.70539e27 | −1.20007 | ||||||||
\(562\) | 9.12092e26 | − | 1.66108e27i | 0.290185 | − | 0.528477i | ||||
\(563\) | 3.61466e27 | 1.12975 | 0.564876 | − | 0.825176i | \(-0.308924\pi\) | ||||
0.564876 | + | 0.825176i | \(0.308924\pi\) | |||||||
\(564\) | −2.47708e27 | + | 1.57552e27i | −0.760588 | + | 0.483762i | ||||
\(565\) | 2.47540e27i | 0.746727i | ||||||||
\(566\) | 3.96752e25 | − | 7.22553e25i | 0.0117586 | − | 0.0214144i | ||||
\(567\) | − | 1.23446e27i | − | 0.359456i | ||||||
\(568\) | −8.76660e25 | − | 1.36051e27i | −0.0250812 | − | 0.389240i | ||||
\(569\) | −5.56745e27 | −1.56507 | −0.782535 | − | 0.622607i | \(-0.786074\pi\) | ||||
−0.782535 | + | 0.622607i | \(0.786074\pi\) | |||||||
\(570\) | −5.71641e27 | − | 3.13887e27i | −1.57897 | − | 0.867010i | ||||
\(571\) | −2.37197e27 | −0.643795 | −0.321897 | − | 0.946775i | \(-0.604321\pi\) | ||||
−0.321897 | + | 0.946775i | \(0.604321\pi\) | |||||||
\(572\) | −1.43873e27 | + | 9.15087e26i | −0.383724 | + | 0.244063i | ||||
\(573\) | − | 2.45440e27i | − | 0.643278i | ||||||
\(574\) | −1.72765e26 | − | 9.48646e25i | −0.0444976 | − | 0.0244335i | ||||
\(575\) | 5.31261e26i | 0.134471i | ||||||||
\(576\) | −7.40482e26 | + | 9.58256e25i | −0.184200 | + | 0.0238373i | ||||
\(577\) | 6.44852e27 | 1.57653 | 0.788264 | − | 0.615337i | \(-0.210980\pi\) | ||||
0.788264 | + | 0.615337i | \(0.210980\pi\) | |||||||
\(578\) | 2.06721e27 | − | 3.76474e27i | 0.496713 | − | 0.904599i | ||||
\(579\) | 1.68297e27 | 0.397458 | ||||||||
\(580\) | 4.08820e27 | + | 6.42762e27i | 0.948970 | + | 1.49200i | ||||
\(581\) | − | 2.23282e27i | − | 0.509440i | ||||||
\(582\) | 3.40789e27 | − | 6.20634e27i | 0.764285 | − | 1.39189i | ||||
\(583\) | − | 6.04290e27i | − | 1.33217i | ||||||
\(584\) | −4.04013e27 | + | 2.60331e26i | −0.875521 | + | 0.0564153i | ||||
\(585\) | 7.21253e26 | 0.153649 | ||||||||
\(586\) | −2.00104e27 | − | 1.09876e27i | −0.419063 | − | 0.230106i | ||||
\(587\) | 1.54560e27 | 0.318211 | 0.159106 | − | 0.987262i | \(-0.449139\pi\) | ||||
0.159106 | + | 0.987262i | \(0.449139\pi\) | |||||||
\(588\) | −1.88417e27 | − | 2.96236e27i | −0.381371 | − | 0.599604i | ||||
\(589\) | 6.69654e27i | 1.33259i | ||||||||
\(590\) | −3.62094e27 | − | 1.98825e27i | −0.708438 | − | 0.389001i | ||||
\(591\) | 6.35942e27i | 1.22333i | ||||||||
\(592\) | 7.23616e27 | + | 3.38724e27i | 1.36865 | + | 0.640662i | ||||
\(593\) | 6.71123e26 | 0.124812 | 0.0624058 | − | 0.998051i | \(-0.480123\pi\) | ||||
0.0624058 | + | 0.998051i | \(0.480123\pi\) | |||||||
\(594\) | −2.62737e27 | + | 4.78489e27i | −0.480460 | + | 0.874999i | ||||
\(595\) | −6.20182e27 | −1.11519 | ||||||||
\(596\) | −2.42134e27 | + | 1.54006e27i | −0.428147 | + | 0.272317i | ||||
\(597\) | 7.23364e27i | 1.25781i | ||||||||
\(598\) | −9.81305e25 | + | 1.78713e26i | −0.0167800 | + | 0.0305593i | ||||
\(599\) | 2.61339e26i | 0.0439476i | 0.999759 | + | 0.0219738i | \(0.00699504\pi\) | ||||
−0.999759 | + | 0.0219738i | \(0.993005\pi\) | |||||||
\(600\) | 1.02373e28 | − | 6.59651e26i | 1.69306 | − | 0.109094i | ||||
\(601\) | −2.17843e26 | −0.0354323 | −0.0177161 | − | 0.999843i | \(-0.505640\pi\) | ||||
−0.0177161 | + | 0.999843i | \(0.505640\pi\) | |||||||
\(602\) | 4.41091e27 | + | 2.42202e27i | 0.705608 | + | 0.387447i | ||||
\(603\) | −1.39514e27 | −0.219505 | ||||||||
\(604\) | 9.70060e27 | − | 6.16994e27i | 1.50117 | − | 0.954799i | ||||
\(605\) | 1.44495e27i | 0.219937i | ||||||||
\(606\) | −4.25423e27 | − | 2.33598e27i | −0.636934 | − | 0.349739i | ||||
\(607\) | 2.74208e27i | 0.403824i | 0.979404 | + | 0.201912i | \(0.0647155\pi\) | ||||
−0.979404 | + | 0.201912i | \(0.935284\pi\) | |||||||
\(608\) | 4.78927e27 | + | 6.55698e27i | 0.693799 | + | 0.949878i | ||||
\(609\) | 3.04136e27 | 0.433406 | ||||||||
\(610\) | 4.20622e27 | − | 7.66025e27i | 0.589649 | − | 1.07385i | ||||
\(611\) | −3.53080e27 | −0.486924 | ||||||||
\(612\) | −1.04734e27 | − | 1.64666e27i | −0.142093 | − | 0.223404i | ||||
\(613\) | − | 5.68816e27i | − | 0.759218i | −0.925147 | − | 0.379609i | \(-0.876058\pi\) | ||
0.925147 | − | 0.379609i | \(-0.123942\pi\) | |||||||
\(614\) | 2.31989e27 | − | 4.22491e27i | 0.304637 | − | 0.554797i | ||||
\(615\) | 1.30532e27i | 0.168643i | ||||||||
\(616\) | −2.17560e26 | − | 3.37636e27i | −0.0276549 | − | 0.429182i | ||||
\(617\) | 3.78592e26 | 0.0473500 | 0.0236750 | − | 0.999720i | \(-0.492463\pi\) | ||||
0.0236750 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(618\) | −9.64995e26 | − | 5.29876e26i | −0.118752 | − | 0.0652063i | ||||
\(619\) | −3.37929e27 | −0.409184 | −0.204592 | − | 0.978847i | \(-0.565587\pi\) | ||||
−0.204592 | + | 0.978847i | \(0.565587\pi\) | |||||||
\(620\) | −8.66018e27 | − | 1.36158e28i | −1.03183 | − | 1.62229i | ||||
\(621\) | 6.52720e26i | 0.0765263i | ||||||||
\(622\) | 5.32627e27 | + | 2.92464e27i | 0.614497 | + | 0.337418i | ||||
\(623\) | 8.53175e26i | 0.0968630i | ||||||||
\(624\) | 3.56560e27 | + | 1.66905e27i | 0.398370 | + | 0.186476i | ||||
\(625\) | 5.95513e27 | 0.654773 | ||||||||
\(626\) | −1.63794e27 | + | 2.98297e27i | −0.177237 | + | 0.322780i | ||||
\(627\) | 9.29882e27 | 0.990267 | ||||||||
\(628\) | −1.25133e28 | + | 7.95896e27i | −1.31153 | + | 0.834180i | ||||
\(629\) | 2.08825e28i | 2.15415i | ||||||||
\(630\) | −6.88834e26 | + | 1.25449e27i | −0.0699374 | + | 0.127368i | ||||
\(631\) | − | 1.77177e28i | − | 1.77058i | −0.465043 | − | 0.885288i | \(-0.653961\pi\) | ||
0.465043 | − | 0.885288i | \(-0.346039\pi\) | |||||||
\(632\) | −1.61590e26 | − | 2.50775e27i | −0.0158943 | − | 0.246668i | ||||
\(633\) | −8.65457e27 | −0.837931 | ||||||||
\(634\) | 8.90979e27 | + | 4.89234e27i | 0.849131 | + | 0.466256i | ||||
\(635\) | −8.86623e27 | −0.831767 | ||||||||
\(636\) | −1.17730e28 | + | 7.48804e27i | −1.08721 | + | 0.691507i | ||||
\(637\) | − | 4.22251e27i | − | 0.383863i | ||||||
\(638\) | −9.52084e27 | − | 5.22786e27i | −0.852056 | − | 0.467862i | ||||
\(639\) | − | 8.22284e26i | − | 0.0724458i | ||||||
\(640\) | −1.82175e28 | − | 7.13842e27i | −1.58012 | − | 0.619159i | ||||
\(641\) | −1.53543e28 | −1.31114 | −0.655571 | − | 0.755134i | \(-0.727572\pi\) | ||||
−0.655571 | + | 0.755134i | \(0.727572\pi\) | |||||||
\(642\) | −3.15347e27 | + | 5.74302e27i | −0.265118 | + | 0.482825i | ||||
\(643\) | 2.16089e28 | 1.78864 | 0.894321 | − | 0.447425i | \(-0.147659\pi\) | ||||
0.894321 | + | 0.447425i | \(0.147659\pi\) | |||||||
\(644\) | −2.17118e26 | − | 3.41360e26i | −0.0176944 | − | 0.0278198i | ||||
\(645\) | − | 3.33267e28i | − | 2.67421i | ||||||
\(646\) | −1.02146e28 | + | 1.86026e28i | −0.807043 | + | 1.46976i | ||||
\(647\) | 2.76915e27i | 0.215429i | 0.994182 | + | 0.107714i | \(0.0343532\pi\) | ||||
−0.994182 | + | 0.107714i | \(0.965647\pi\) | |||||||
\(648\) | 1.01582e28 | − | 6.54553e26i | 0.778152 | − | 0.0501412i | ||||
\(649\) | 5.89015e27 | 0.444303 | ||||||||
\(650\) | 1.08150e28 | + | 5.93847e27i | 0.803327 | + | 0.441104i | ||||
\(651\) | −6.44261e27 | −0.471251 | ||||||||
\(652\) | 4.29310e27 | + | 6.74976e27i | 0.309240 | + | 0.486197i | ||||
\(653\) | − | 1.65324e28i | − | 1.17275i | −0.810041 | − | 0.586374i | \(-0.800555\pi\) | ||
0.810041 | − | 0.586374i | \(-0.199445\pi\) | |||||||
\(654\) | 1.07181e28 | + | 5.88528e27i | 0.748757 | + | 0.411140i | ||||
\(655\) | 1.11463e28i | 0.766863i | ||||||||
\(656\) | 6.89020e26 | − | 1.47195e27i | 0.0466867 | − | 0.0997369i | ||||
\(657\) | −2.44183e27 | −0.162953 | ||||||||
\(658\) | 3.37210e27 | − | 6.14117e27i | 0.221637 | − | 0.403638i | ||||
\(659\) | 2.52135e27 | 0.163222 | 0.0816112 | − | 0.996664i | \(-0.473993\pi\) | ||||
0.0816112 | + | 0.996664i | \(0.473993\pi\) | |||||||
\(660\) | −1.89069e28 | + | 1.20255e28i | −1.20554 | + | 0.766769i | ||||
\(661\) | 1.53460e28i | 0.963783i | 0.876231 | + | 0.481892i | \(0.160050\pi\) | ||||
−0.876231 | + | 0.481892i | \(0.839950\pi\) | |||||||
\(662\) | −1.14912e28 | + | 2.09275e28i | −0.710864 | + | 1.29461i | ||||
\(663\) | 1.02898e28i | 0.627005i | ||||||||
\(664\) | 1.83735e28 | − | 1.18392e27i | 1.10284 | − | 0.0710628i | ||||
\(665\) | 1.55637e28 | 0.920231 | ||||||||
\(666\) | 4.22405e27 | + | 2.31941e27i | 0.246029 | + | 0.135094i | ||||
\(667\) | −1.29876e27 | −0.0745197 | ||||||||
\(668\) | 2.42896e28 | − | 1.54491e28i | 1.37296 | − | 0.873251i | ||||
\(669\) | − | 2.14662e28i | − | 1.19535i | ||||||
\(670\) | −3.20464e28 | − | 1.75966e28i | −1.75805 | − | 0.965341i | ||||
\(671\) | 1.24608e28i | 0.673476i | ||||||||
\(672\) | −6.30834e27 | + | 4.60767e27i | −0.335910 | + | 0.245351i | ||||
\(673\) | −5.30782e27 | −0.278462 | −0.139231 | − | 0.990260i | \(-0.544463\pi\) | ||||
−0.139231 | + | 0.990260i | \(0.544463\pi\) | |||||||
\(674\) | 8.50056e27 | − | 1.54810e28i | 0.439388 | − | 0.800201i | ||||
\(675\) | 3.95000e28 | 2.01168 | ||||||||
\(676\) | −8.15385e27 | − | 1.28198e28i | −0.409163 | − | 0.643300i | ||||
\(677\) | − | 3.58407e28i | − | 1.77211i | −0.463581 | − | 0.886054i | \(-0.653436\pi\) | ||
0.463581 | − | 0.886054i | \(-0.346564\pi\) | |||||||
\(678\) | −3.92248e27 | + | 7.14351e27i | −0.191101 | + | 0.348028i | ||||
\(679\) | 1.68976e28i | 0.811200i | ||||||||
\(680\) | −3.28842e27 | − | 5.10338e28i | −0.155560 | − | 2.41417i | ||||
\(681\) | 6.52839e27 | 0.304323 | ||||||||
\(682\) | 2.01683e28 | + | 1.10744e28i | 0.926457 | + | 0.508715i | ||||
\(683\) | −2.36613e28 | −1.07111 | −0.535553 | − | 0.844502i | \(-0.679897\pi\) | ||||
−0.535553 | + | 0.844502i | \(0.679897\pi\) | |||||||
\(684\) | 2.62834e27 | + | 4.13237e27i | 0.117252 | + | 0.184348i | ||||
\(685\) | 2.82367e28i | 1.24139i | ||||||||
\(686\) | 1.66703e28 | + | 9.15364e27i | 0.722277 | + | 0.396600i | ||||
\(687\) | − | 5.57223e27i | − | 0.237937i | ||||||
\(688\) | −1.75916e28 | + | 3.75809e28i | −0.740322 | + | 1.58155i | ||||
\(689\) | −1.67810e28 | −0.696026 | ||||||||
\(690\) | −1.28957e27 | + | 2.34853e27i | −0.0527175 | + | 0.0960076i | ||||
\(691\) | −7.90476e27 | −0.318499 | −0.159250 | − | 0.987238i | \(-0.550907\pi\) | ||||
−0.159250 | + | 0.987238i | \(0.550907\pi\) | |||||||
\(692\) | 1.78323e28 | − | 1.13420e28i | 0.708184 | − | 0.450432i | ||||
\(693\) | − | 2.04066e27i | − | 0.0798799i | ||||||
\(694\) | 1.94212e28 | − | 3.53694e28i | 0.749345 | − | 1.36469i | ||||
\(695\) | 3.08445e28i | 1.17309i | ||||||||
\(696\) | 1.61264e27 | + | 2.50269e28i | 0.0604567 | + | 0.938240i | ||||
\(697\) | 4.24784e27 | 0.156979 | ||||||||
\(698\) | 9.72221e27 | + | 5.33844e27i | 0.354169 | + | 0.194473i | ||||
\(699\) | 8.49783e27 | 0.305166 | ||||||||
\(700\) | −2.06578e28 | + | 1.31391e28i | −0.731312 | + | 0.465142i | ||||
\(701\) | 2.73811e28i | 0.955586i | 0.878472 | + | 0.477793i | \(0.158563\pi\) | ||||
−0.878472 | + | 0.477793i | \(0.841437\pi\) | |||||||
\(702\) | 1.32875e28 | + | 7.29615e27i | 0.457166 | + | 0.251028i | ||||
\(703\) | − | 5.24054e28i | − | 1.77756i | ||||||
\(704\) | 2.76682e28 | − | 3.58053e27i | 0.925239 | − | 0.119735i | ||||
\(705\) | −4.63996e28 | −1.52976 | ||||||||
\(706\) | −1.43289e28 | + | 2.60953e28i | −0.465763 | + | 0.848235i | ||||
\(707\) | 1.15827e28 | 0.371207 | ||||||||
\(708\) | −7.29876e27 | − | 1.14754e28i | −0.230630 | − | 0.362605i | ||||
\(709\) | 1.71589e27i | 0.0534597i | 0.999643 | + | 0.0267299i | \(0.00850939\pi\) | ||||
−0.999643 | + | 0.0267299i | \(0.991491\pi\) | |||||||
\(710\) | 1.03713e28 | − | 1.88879e28i | 0.318603 | − | 0.580231i | ||||
\(711\) | − | 1.51567e27i | − | 0.0459101i | ||||||
\(712\) | −7.02064e27 | + | 4.52384e26i | −0.209690 | + | 0.0135116i | ||||
\(713\) | 2.75121e27 | 0.0810267 | ||||||||
\(714\) | −1.78972e28 | − | 9.82728e27i | −0.519759 | − | 0.285398i | ||||
\(715\) | −2.69497e28 | −0.771780 | ||||||||
\(716\) | −2.68321e28 | − | 4.21863e28i | −0.757746 | − | 1.19135i | ||||
\(717\) | 4.65237e28i | 1.29564i | ||||||||
\(718\) | −2.22211e28 | − | 1.22016e28i | −0.610270 | − | 0.335097i | ||||
\(719\) | 1.73205e28i | 0.469106i | 0.972103 | + | 0.234553i | \(0.0753626\pi\) | ||||
−0.972103 | + | 0.234553i | \(0.924637\pi\) | |||||||
\(720\) | −1.06882e28 | − | 5.00313e27i | −0.285483 | − | 0.133634i | ||||
\(721\) | 2.62733e27 | 0.0692089 | ||||||||
\(722\) | 7.10731e27 | − | 1.29436e28i | 0.184643 | − | 0.336267i | ||||
\(723\) | 3.47677e27 | 0.0890825 | ||||||||
\(724\) | 1.52513e28 | − | 9.70039e27i | 0.385408 | − | 0.245134i | ||||
\(725\) | 7.85960e28i | 1.95894i | ||||||||
\(726\) | −2.28963e27 | + | 4.16982e27i | −0.0562859 | + | 0.102506i | ||||
\(727\) | − | 2.91046e28i | − | 0.705697i | −0.935680 | − | 0.352848i | \(-0.885213\pi\) | ||
0.935680 | − | 0.352848i | \(-0.114787\pi\) | |||||||
\(728\) | −9.37609e27 | + | 6.04160e26i | −0.224237 | + | 0.0144490i | ||||
\(729\) | 4.70683e28 | 1.11033 | ||||||||
\(730\) | −5.60890e28 | − | 3.07983e28i | −1.30512 | − | 0.716636i | ||||
\(731\) | −1.08453e29 | −2.48925 | ||||||||
\(732\) | 2.42766e28 | − | 1.54408e28i | 0.549638 | − | 0.349590i | ||||
\(733\) | − | 6.11377e28i | − | 1.36543i | −0.730685 | − | 0.682714i | \(-0.760799\pi\) | ||
0.730685 | − | 0.682714i | \(-0.239201\pi\) | |||||||
\(734\) | 8.72302e27 | + | 4.78979e27i | 0.192179 | + | 0.105525i | ||||
\(735\) | − | 5.54897e28i | − | 1.20598i | ||||||
\(736\) | 2.69387e27 | − | 1.96763e27i | 0.0577562 | − | 0.0421856i | ||||
\(737\) | 5.21295e28 | 1.10258 | ||||||||
\(738\) | 4.71806e26 | − | 8.59240e26i | 0.00984465 | − | 0.0179288i | ||||
\(739\) | −3.00879e28 | −0.619367 | −0.309683 | − | 0.950840i | \(-0.600223\pi\) | ||||
−0.309683 | + | 0.950840i | \(0.600223\pi\) | |||||||
\(740\) | 6.77723e28 | + | 1.06554e29i | 1.37637 | + | 2.16398i | ||||
\(741\) | − | 2.58226e28i | − | 0.517390i | ||||||
\(742\) | 1.60267e28 | − | 2.91874e28i | 0.316815 | − | 0.576975i | ||||
\(743\) | 8.91348e28i | 1.73844i | 0.494428 | + | 0.869218i | \(0.335377\pi\) | ||||
−0.494428 | + | 0.869218i | \(0.664623\pi\) | |||||||
\(744\) | −3.41610e27 | − | 5.30152e28i | −0.0657357 | − | 1.02017i | ||||
\(745\) | −4.53555e28 | −0.861126 | ||||||||
\(746\) | −5.45946e28 | − | 2.99777e28i | −1.02273 | − | 0.561578i | ||||
\(747\) | 1.11049e28 | 0.205262 | ||||||||
\(748\) | 3.91339e28 | + | 6.15277e28i | 0.713736 | + | 1.12216i | ||||
\(749\) | − | 1.56362e28i | − | 0.281392i | ||||||
\(750\) | 6.65316e28 | + | 3.65323e28i | 1.18145 | + | 0.648730i | ||||
\(751\) | − | 8.75074e28i | − | 1.53336i | −0.642026 | − | 0.766682i | \(-0.721906\pi\) | ||
0.642026 | − | 0.766682i | \(-0.278094\pi\) | |||||||
\(752\) | 5.23227e28 | + | 2.44922e28i | 0.904715 | + | 0.423496i | ||||
\(753\) | 6.08348e28 | 1.03801 | ||||||||
\(754\) | −1.45177e28 | + | 2.64392e28i | −0.244446 | + | 0.445179i | ||||
\(755\) | 1.81707e29 | 3.01928 | ||||||||
\(756\) | −2.53806e28 | + | 1.61430e28i | −0.416183 | + | 0.264708i | ||||
\(757\) | 6.81060e28i | 1.10211i | 0.834468 | + | 0.551057i | \(0.185775\pi\) | ||||
−0.834468 | + | 0.551057i | \(0.814225\pi\) | |||||||
\(758\) | −4.05247e27 | + | 7.38024e27i | −0.0647184 | + | 0.117863i | ||||
\(759\) | − | 3.82033e27i | − | 0.0602120i | ||||||
\(760\) | 8.25243e27 | + | 1.28071e29i | 0.128365 | + | 1.99212i | ||||
\(761\) | 1.69559e28 | 0.260300 | 0.130150 | − | 0.991494i | \(-0.458454\pi\) | ||||
0.130150 | + | 0.991494i | \(0.458454\pi\) | |||||||
\(762\) | −2.55861e28 | − | 1.40493e28i | −0.387663 | − | 0.212865i | ||||
\(763\) | −2.91815e28 | −0.436378 | ||||||||
\(764\) | −4.07551e28 | + | 2.59218e28i | −0.601518 | + | 0.382588i | ||||
\(765\) | − | 3.08446e28i | − | 0.449329i | ||||||
\(766\) | −3.88509e27 | − | 2.13329e27i | −0.0558616 | − | 0.0306734i | ||||
\(767\) | − | 1.63568e28i | − | 0.232137i | ||||||
\(768\) | −4.12606e28 | − | 4.94672e28i | −0.577995 | − | 0.692955i | ||||
\(769\) | 2.31433e28 | 0.320008 | 0.160004 | − | 0.987116i | \(-0.448849\pi\) | ||||
0.160004 | + | 0.987116i | \(0.448849\pi\) | |||||||
\(770\) | 2.57384e28 | − | 4.68740e28i | 0.351297 | − | 0.639771i | ||||
\(771\) | 5.44067e28 | 0.733008 | ||||||||
\(772\) | −1.77744e28 | − | 2.79456e28i | −0.236387 | − | 0.371655i | ||||
\(773\) | − | 4.49830e28i | − | 0.590546i | −0.955413 | − | 0.295273i | \(-0.904589\pi\) | ||
0.955413 | − | 0.295273i | \(-0.0954106\pi\) | |||||||
\(774\) | −1.20458e28 | + | 2.19375e28i | −0.156109 | + | 0.284301i | ||||
\(775\) | − | 1.66492e29i | − | 2.12999i | ||||||
\(776\) | −1.39048e29 | + | 8.95972e27i | −1.75609 | + | 0.113156i | ||||
\(777\) | 5.04183e28 | 0.628605 | ||||||||
\(778\) | −9.68473e28 | − | 5.31786e28i | −1.19204 | − | 0.654547i | ||||
\(779\) | −1.06601e28 | −0.129535 | ||||||||
\(780\) | 3.33946e28 | + | 5.25042e28i | 0.400618 | + | 0.629866i | ||||
\(781\) | 3.07247e28i | 0.363897i | ||||||||
\(782\) | 7.64269e27 | + | 4.19658e27i | 0.0893673 | + | 0.0490713i | ||||
\(783\) | 9.65649e28i | 1.11481i | ||||||||
\(784\) | −2.92904e28 | + | 6.25731e28i | −0.333860 | + | 0.713226i | ||||
\(785\) | −2.34395e29 | −2.63786 | ||||||||
\(786\) | −1.76622e28 | + | 3.21659e28i | −0.196254 | + | 0.357413i | ||||
\(787\) | 2.22980e27 | 0.0244635 | 0.0122317 | − | 0.999925i | \(-0.496106\pi\) | ||||
0.0122317 | + | 0.999925i | \(0.496106\pi\) | |||||||
\(788\) | 1.05598e29 | − | 6.71641e28i | 1.14391 | − | 0.727570i | ||||
\(789\) | − | 1.81820e28i | − | 0.194479i | ||||||
\(790\) | 1.91168e28 | − | 3.48150e28i | 0.201904 | − | 0.367702i | ||||
\(791\) | − | 1.94492e28i | − | 0.202832i | ||||||
\(792\) | 1.67922e28 | − | 1.08203e27i | 0.172925 | − | 0.0111426i | ||||
\(793\) | 3.46035e28 | 0.351875 | ||||||||
\(794\) | 9.43212e28 | + | 5.17915e28i | 0.947119 | + | 0.520060i | ||||
\(795\) | −2.20526e29 | −2.18670 | ||||||||
\(796\) | 1.20114e29 | − | 7.63971e28i | 1.17615 | − | 0.748077i | ||||
\(797\) | − | 3.29774e28i | − | 0.318884i | −0.987207 | − | 0.159442i | \(-0.949030\pi\) | ||
0.987207 | − | 0.159442i | \(-0.0509696\pi\) | |||||||
\(798\) | 4.49137e28 | + | 2.46620e28i | 0.428894 | + | 0.235504i | ||||
\(799\) | 1.50995e29i | 1.42395i | ||||||||
\(800\) | −1.19073e29 | − | 1.63022e29i | −1.10895 | − | 1.51827i | ||||
\(801\) | −4.24324e27 | −0.0390277 | ||||||||
\(802\) | −7.77386e28 | + | 1.41575e29i | −0.706143 | + | 1.28601i | ||||
\(803\) | 9.12394e28 | 0.818515 | ||||||||
\(804\) | −6.45962e28 | − | 1.01560e29i | −0.572330 | − | 0.899837i | ||||
\(805\) | − | 6.39420e27i | − | 0.0559536i | ||||||
\(806\) | 3.07532e28 | − | 5.60069e28i | 0.265791 | − | 0.484051i | ||||
\(807\) | − | 1.47212e28i | − | 0.125663i | ||||||
\(808\) | 6.14157e27 | + | 9.53123e28i | 0.0517804 | + | 0.803592i | ||||
\(809\) | 2.71776e27 | 0.0226322 | 0.0113161 | − | 0.999936i | \(-0.496398\pi\) | ||||
0.0113161 | + | 0.999936i | \(0.496398\pi\) | |||||||
\(810\) | 1.41026e29 | + | 7.74367e28i | 1.15997 | + | 0.636937i | ||||
\(811\) | −1.44694e29 | −1.17555 | −0.587775 | − | 0.809024i | \(-0.699996\pi\) | ||||
−0.587775 | + | 0.809024i | \(0.699996\pi\) | |||||||
\(812\) | −3.21209e28 | − | 5.05016e28i | −0.257767 | − | 0.405270i | ||||
\(813\) | 9.61157e28i | 0.761884i | ||||||||
\(814\) | −1.57832e29 | − | 8.66651e28i | −1.23581 | − | 0.678578i | ||||
\(815\) | 1.26434e29i | 0.977882i | ||||||||
\(816\) | 7.13774e28 | − | 1.52484e29i | 0.545330 | − | 1.16499i | ||||
\(817\) | 2.72167e29 | 2.05407 | ||||||||
\(818\) | 2.96071e28 | − | 5.39196e28i | 0.220731 | − | 0.401988i | ||||
\(819\) | −5.66686e27 | −0.0417353 | ||||||||
\(820\) | 2.16748e28 | − | 1.37860e28i | 0.157695 | − | 0.100300i | ||||
\(821\) | − | 1.63132e28i | − | 0.117248i | −0.998280 | − | 0.0586242i | \(-0.981329\pi\) | ||
0.998280 | − | 0.0586242i | \(-0.0186714\pi\) | |||||||
\(822\) | −4.47433e28 | + | 8.14853e28i | −0.317695 | + | 0.578577i | ||||
\(823\) | 1.60847e29i | 1.12828i | 0.825681 | + | 0.564138i | \(0.190791\pi\) | ||||
−0.825681 | + | 0.564138i | \(0.809209\pi\) | |||||||
\(824\) | 1.39310e27 | + | 2.16199e28i | 0.00965409 | + | 0.149824i | ||||
\(825\) | −2.31191e29 | −1.58282 | ||||||||
\(826\) | 2.84497e28 | + | 1.56216e28i | 0.192432 | + | 0.105664i | ||||
\(827\) | 2.68295e28 | 0.179291 | 0.0896453 | − | 0.995974i | \(-0.471427\pi\) | ||||
0.0896453 | + | 0.995974i | \(0.471427\pi\) | |||||||
\(828\) | 1.69774e27 | − | 1.07983e27i | 0.0112090 | − | 0.00712937i | ||||
\(829\) | 8.25928e28i | 0.538762i | 0.963034 | + | 0.269381i | \(0.0868191\pi\) | ||||
−0.963034 | + | 0.269381i | \(0.913181\pi\) | |||||||
\(830\) | 2.55080e29 | + | 1.40063e29i | 1.64397 | + | 0.902701i | ||||
\(831\) | 7.50307e28i | 0.477781i | ||||||||
\(832\) | −9.94307e27 | − | 7.68340e28i | −0.0625586 | − | 0.483415i | ||||
\(833\) | −1.80577e29 | −1.12256 | ||||||||
\(834\) | −4.88756e28 | + | 8.90108e28i | −0.300214 | + | 0.546742i | ||||
\(835\) | 4.54983e29 | 2.76141 | ||||||||
\(836\) | −9.82082e28 | − | 1.54406e29i | −0.588959 | − | 0.925981i | ||||
\(837\) | − | 2.04557e29i | − | 1.21216i | ||||||
\(838\) | 4.52006e28 | − | 8.23180e28i | 0.264670 | − | 0.482009i | ||||
\(839\) | − | 1.70706e29i | − | 0.987709i | −0.869545 | − | 0.493855i | \(-0.835588\pi\) | ||
0.869545 | − | 0.493855i | \(-0.164412\pi\) | |||||||
\(840\) | −1.23215e29 | + | 7.93951e27i | −0.704483 | + | 0.0453942i | ||||
\(841\) | −1.51474e28 | −0.0855813 | ||||||||
\(842\) | 2.55612e28 | + | 1.40356e28i | 0.142712 | + | 0.0783626i | ||||
\(843\) | 9.86070e28 | 0.544042 | ||||||||
\(844\) | 9.14040e28 | + | 1.43709e29i | 0.498357 | + | 0.783535i | ||||
\(845\) | − | 2.40134e29i | − | 1.29386i | ||||||
\(846\) | 3.05429e28 | + | 1.67710e28i | 0.162632 | + | 0.0893009i | ||||
\(847\) | − | 1.13529e28i | − | 0.0597410i | ||||||
\(848\) | 2.48677e29 | + | 1.16405e29i | 1.29323 | + | 0.605360i | ||||
\(849\) | 4.28932e27 | 0.0220451 | ||||||||
\(850\) | 2.53960e29 | − | 4.62505e29i | 1.28996 | − | 2.34924i | ||||
\(851\) | −2.15303e28 | −0.108082 | ||||||||
\(852\) | 5.98589e28 | − | 3.80725e28i | 0.296984 | − | 0.188893i | ||||
\(853\) | 8.71573e27i | 0.0427379i | 0.999772 | + | 0.0213690i | \(0.00680247\pi\) | ||||
−0.999772 | + | 0.0213690i | \(0.993198\pi\) | |||||||
\(854\) | −3.30482e28 | + | 6.01864e28i | −0.160165 | + | 0.291689i | ||||
\(855\) | 7.74057e28i | 0.370776i | ||||||||
\(856\) | 1.28667e29 | − | 8.29084e27i | 0.609159 | − | 0.0392519i | ||||
\(857\) | −3.22623e29 | −1.50969 | −0.754844 | − | 0.655904i | \(-0.772288\pi\) | ||||
−0.754844 | + | 0.655904i | \(0.772288\pi\) | |||||||
\(858\) | −7.77713e28 | − | 4.27040e28i | −0.359705 | − | 0.197513i | ||||
\(859\) | −3.05560e29 | −1.39690 | −0.698450 | − | 0.715659i | \(-0.746127\pi\) | ||||
−0.698450 | + | 0.715659i | \(0.746127\pi\) | |||||||
\(860\) | −5.53387e29 | + | 3.51975e29i | −2.50060 | + | 1.59048i | ||||
\(861\) | − | 1.02559e28i | − | 0.0458081i | ||||||
\(862\) | 1.37519e28 | + | 7.55115e27i | 0.0607144 | + | 0.0333381i | ||||
\(863\) | 3.95432e29i | 1.72570i | 0.505463 | + | 0.862848i | \(0.331322\pi\) | ||||
−0.505463 | + | 0.862848i | \(0.668678\pi\) | |||||||
\(864\) | −1.46296e29 | − | 2.00293e29i | −0.631095 | − | 0.864031i | ||||
\(865\) | 3.34027e29 | 1.42436 | ||||||||
\(866\) | −1.64298e29 | + | 2.99216e29i | −0.692555 | + | 1.26126i | ||||
\(867\) | 2.23487e29 | 0.931241 | ||||||||
\(868\) | 6.80427e28 | + | 1.06979e29i | 0.280275 | + | 0.440658i | ||||
\(869\) | 5.66331e28i | 0.230607i | ||||||||
\(870\) | −1.90782e29 | + | 3.47448e29i | −0.767973 | + | 1.39861i | ||||
\(871\) | − | 1.44763e29i | − | 0.576070i | ||||||
\(872\) | −1.54731e28 | − | 2.40130e29i | −0.0608712 | − | 0.944674i | ||||
\(873\) | −8.40398e28 | −0.326846 | ||||||||
\(874\) | −1.91796e28 | − | 1.05315e28i | −0.0737439 | − | 0.0404925i | ||||
\(875\) | −1.81141e29 | −0.688552 | ||||||||
\(876\) | −1.13059e29 | − | 1.77755e29i | −0.424878 | − | 0.668008i | ||||
\(877\) | 1.07850e29i | 0.400704i | 0.979724 | + | 0.200352i | \(0.0642085\pi\) | ||||
−0.979724 | + | 0.200352i | \(0.935791\pi\) | |||||||
\(878\) | −3.77364e29 | − | 2.07210e29i | −1.38617 | − | 0.761140i | ||||
\(879\) | − | 1.18788e29i | − | 0.431405i | ||||||
\(880\) | 3.99366e29 | + | 1.86943e29i | 1.43398 | + | 0.671246i | ||||
\(881\) | 3.88787e29 | 1.38023 | 0.690117 | − | 0.723698i | \(-0.257559\pi\) | ||||
0.690117 | + | 0.723698i | \(0.257559\pi\) | |||||||
\(882\) | −2.00566e28 | + | 3.65265e28i | −0.0703998 | + | 0.128210i | ||||
\(883\) | −9.39171e28 | −0.325940 | −0.162970 | − | 0.986631i | \(-0.552107\pi\) | ||||
−0.162970 | + | 0.986631i | \(0.552107\pi\) | |||||||
\(884\) | 1.70861e29 | − | 1.08674e29i | 0.586301 | − | 0.372909i | ||||
\(885\) | − | 2.14951e29i | − | 0.729303i | ||||||
\(886\) | −6.83122e27 | + | 1.24408e28i | −0.0229172 | + | 0.0417361i | ||||
\(887\) | − | 2.07007e29i | − | 0.686673i | −0.939213 | − | 0.343336i | \(-0.888443\pi\) | ||
0.939213 | − | 0.343336i | \(-0.111557\pi\) | |||||||
\(888\) | 2.67335e28 | + | 4.14884e29i | 0.0876853 | + | 1.36081i | ||||
\(889\) | 6.96617e28 | 0.225931 | ||||||||
\(890\) | −9.74675e28 | − | 5.35191e28i | −0.312579 | − | 0.171636i | ||||
\(891\) | −2.29404e29 | −0.727486 | ||||||||
\(892\) | −3.56445e29 | + | 2.26712e29i | −1.11775 | + | 0.710930i | ||||
\(893\) | − | 3.78929e29i | − | 1.17502i | ||||||
\(894\) | −1.30887e29 | − | 7.18694e28i | −0.401347 | − | 0.220378i | ||||
\(895\) | − | 7.90215e29i | − | 2.39616i | ||||||
\(896\) | 1.43135e29 | + | 5.60864e28i | 0.429205 | + | 0.168181i | ||||
\(897\) | −1.06090e28 | −0.0314593 | ||||||||
\(898\) | 4.01375e28 | − | 7.30973e28i | 0.117703 | − | 0.214357i | ||||
\(899\) | 4.07021e29 | 1.18037 | ||||||||
\(900\) | −6.53469e28 | − | 1.02741e29i | −0.187413 | − | 0.294657i | ||||
\(901\) | 7.17644e29i | 2.03545i | ||||||||
\(902\) | −1.76291e28 | + | 3.21056e28i | −0.0494498 | + | 0.0900566i | ||||
\(903\) | 2.61847e29i | 0.726390i | ||||||||
\(904\) | 1.60044e29 | − | 1.03126e28i | 0.439092 | − | 0.0282934i | ||||
\(905\) | 2.85681e29 | 0.775167 | ||||||||
\(906\) | 5.24370e29 | + | 2.87930e29i | 1.40720 | + | 0.772690i | ||||
\(907\) | −7.13860e29 | −1.89470 | −0.947350 | − | 0.320201i | \(-0.896250\pi\) | ||||
−0.947350 | + | 0.320201i | \(0.896250\pi\) | |||||||
\(908\) | −6.89486e28 | − | 1.08403e29i | −0.180995 | − | 0.284567i | ||||
\(909\) | 5.76063e28i | 0.149565i | ||||||||
\(910\) | −1.30168e29 | − | 7.14749e28i | −0.334265 | − | 0.183544i | ||||
\(911\) | − | 4.56065e29i | − | 1.15836i | −0.815201 | − | 0.579179i | \(-0.803373\pi\) | ||
0.815201 | − | 0.579179i | \(-0.196627\pi\) | |||||||
\(912\) | −1.79125e29 | + | 3.82664e29i | −0.449994 | + | 0.961323i | ||||
\(913\) | −4.14935e29 | −1.03103 | ||||||||
\(914\) | −1.57544e29 | + | 2.86915e29i | −0.387204 | + | 0.705165i | ||||
\(915\) | 4.54738e29 | 1.10548 | ||||||||
\(916\) | −9.25266e28 | + | 5.88504e28i | −0.222491 | + | 0.141512i | ||||
\(917\) | − | 8.75761e28i | − | 0.208302i | ||||||
\(918\) | 3.12022e29 | − | 5.68245e29i | 0.734105 | − | 1.33693i | ||||
\(919\) | − | 4.59527e29i | − | 1.06944i | −0.845030 | − | 0.534719i | \(-0.820417\pi\) | ||
0.845030 | − | 0.534719i | \(-0.179583\pi\) | |||||||
\(920\) | 5.26169e28 | − | 3.39043e27i | 0.121129 | − | 0.00780507i | ||||
\(921\) | 2.50805e29 | 0.571137 | ||||||||
\(922\) | 9.53625e27 | + | 5.23633e27i | 0.0214817 | + | 0.0117955i | ||||
\(923\) | 8.53220e28 | 0.190127 | ||||||||
\(924\) | 1.48551e29 | − | 9.44842e28i | 0.327459 | − | 0.208276i | ||||
\(925\) | 1.30293e30i | 2.84121i | ||||||||
\(926\) | −1.64514e29 | − | 9.03344e28i | −0.354890 | − | 0.194869i | ||||
\(927\) | 1.30669e28i | 0.0278854i | ||||||||
\(928\) | 3.98538e29 | − | 2.91095e29i | 0.841375 | − | 0.614548i | ||||
\(929\) | 4.91360e29 | 1.02623 | 0.513113 | − | 0.858321i | \(-0.328492\pi\) | ||||
0.513113 | + | 0.858321i | \(0.328492\pi\) | |||||||
\(930\) | 4.04141e29 | − | 7.36010e29i | 0.835032 | − | 1.52074i | ||||
\(931\) | 4.53164e29 | 0.926316 | ||||||||
\(932\) | −8.97487e28 | − | 1.41106e29i | −0.181497 | − | 0.285355i | ||||
\(933\) | 3.16186e29i | 0.632595i | ||||||||
\(934\) | 2.67027e29 | − | 4.86303e29i | 0.528551 | − | 0.962583i | ||||
\(935\) | 1.15251e30i | 2.25699i | ||||||||
\(936\) | −3.00477e27 | − | 4.66317e28i | −0.00582174 | − | 0.0903489i | ||||
\(937\) | −2.07933e29 | −0.398590 | −0.199295 | − | 0.979940i | \(-0.563865\pi\) | ||||
−0.199295 | + | 0.979940i | \(0.563865\pi\) | |||||||
\(938\) | 2.51788e29 | + | 1.38256e29i | 0.477536 | + | 0.262214i | ||||
\(939\) | −1.77079e29 | −0.332286 | ||||||||
\(940\) | 4.90043e29 | + | 7.70463e29i | 0.909821 | + | 1.43045i | ||||
\(941\) | − | 1.19882e29i | − | 0.220221i | −0.993919 | − | 0.110111i | \(-0.964880\pi\) | ||
0.993919 | − | 0.110111i | \(-0.0351205\pi\) | |||||||
\(942\) | −6.76415e29 | − | 3.71417e29i | −1.22943 | − | 0.675077i | ||||
\(943\) | 4.37961e27i | 0.00787623i | ||||||||
\(944\) | −1.13463e29 | + | 2.42391e29i | −0.201899 | + | 0.431317i | ||||
\(945\) | −4.75419e29 | −0.837063 | ||||||||
\(946\) | 4.50094e29 | − | 8.19699e29i | 0.784137 | − | 1.42805i | ||||
\(947\) | −9.55513e29 | −1.64716 | −0.823582 | − | 0.567197i | \(-0.808028\pi\) | ||||
−0.823582 | + | 0.567197i | \(0.808028\pi\) | |||||||
\(948\) | 1.10334e29 | − | 7.01768e28i | 0.188203 | − | 0.119704i | ||||
\(949\) | − | 2.53370e29i | − | 0.427654i | ||||||
\(950\) | −6.37324e29 | + | 1.16068e30i | −1.06445 | + | 1.93854i | ||||
\(951\) | 5.28915e29i | 0.874140i | ||||||||
\(952\) | 2.58370e28 | + | 4.00971e29i | 0.0422545 | + | 0.655758i | ||||
\(953\) | 3.81494e28 | 0.0617389 | 0.0308695 | − | 0.999523i | \(-0.490172\pi\) | ||||
0.0308695 | + | 0.999523i | \(0.490172\pi\) | |||||||
\(954\) | 1.45163e29 | + | 7.97085e28i | 0.232473 | + | 0.127650i | ||||
\(955\) | −7.63407e29 | −1.20982 | ||||||||
\(956\) | 7.72523e29 | − | 4.91354e29i | 1.21153 | − | 0.770576i | ||||
\(957\) | − | 5.65189e29i | − | 0.877151i | ||||||
\(958\) | −3.08036e29 | − | 1.69142e29i | −0.473092 | − | 0.259774i | ||||
\(959\) | − | 2.21855e29i | − | 0.337196i | ||||||
\(960\) | −1.30666e29 | − | 1.00971e30i | −0.196539 | − | 1.51874i | ||||
\(961\) | −1.90415e29 | −0.283443 | ||||||||
\(962\) | −2.40667e29 | + | 4.38296e29i | −0.354541 | + | 0.645679i | ||||
\(963\) | 7.77659e28 | 0.113377 | ||||||||
\(964\) | −3.67194e28 | − | 5.77315e28i | −0.0529816 | − | 0.0832995i | ||||
\(965\) | − | 5.23465e29i | − | 0.747506i | ||||||
\(966\) | 1.01321e28 | − | 1.84524e28i | 0.0143196 | − | 0.0260784i | ||||
\(967\) | − | 5.25367e29i | − | 0.734849i | −0.930053 | − | 0.367424i | \(-0.880240\pi\) | ||
0.930053 | − | 0.367424i | \(-0.119760\pi\) | |||||||
\(968\) | 9.34212e28 | − | 6.01971e27i | 0.129328 | − | 0.00833339i | ||||
\(969\) | −1.10431e30 | −1.51305 | ||||||||
\(970\) | −1.93040e30 | − | 1.05998e30i | −2.61776 | − | 1.43740i | ||||
\(971\) | 3.77736e29 | 0.506986 | 0.253493 | − | 0.967337i | \(-0.418420\pi\) | ||||
0.253493 | + | 0.967337i | \(0.418420\pi\) | |||||||
\(972\) | −1.47997e29 | − | 2.32687e29i | −0.196604 | − | 0.309107i | ||||
\(973\) | − | 2.42344e29i | − | 0.318643i | ||||||
\(974\) | 1.19958e30 | + | 6.58684e29i | 1.56113 | + | 0.857211i | ||||
\(975\) | 6.42014e29i | 0.826986i | ||||||||
\(976\) | −5.12787e29 | − | 2.40035e29i | −0.653791 | − | 0.306039i | ||||
\(977\) | 3.46580e29 | 0.437379 | 0.218689 | − | 0.975795i | \(-0.429822\pi\) | ||||
0.218689 | + | 0.975795i | \(0.429822\pi\) | |||||||
\(978\) | −2.00344e29 | + | 3.64861e29i | −0.250258 | + | 0.455763i | ||||
\(979\) | 1.58549e29 | 0.196037 | ||||||||
\(980\) | −9.21402e29 | + | 5.86046e29i | −1.12769 | + | 0.717251i | ||||
\(981\) | − | 1.45133e29i | − | 0.175824i | ||||||
\(982\) | −1.50433e29 | + | 2.73965e29i | −0.180397 | + | 0.328534i | ||||
\(983\) | − | 1.93685e29i | − | 0.229911i | −0.993371 | − | 0.114955i | \(-0.963327\pi\) | ||
0.993371 | − | 0.114955i | \(-0.0366725\pi\) | |||||||
\(984\) | 8.43941e28 | − | 5.43804e27i | 0.0991657 | − | 0.00638986i | ||||
\(985\) | 1.97801e30 | 2.30073 | ||||||||
\(986\) | 1.13068e30 | + | 6.20852e29i | 1.30188 | + | 0.714856i | ||||
\(987\) | 3.64561e29 | 0.415526 | ||||||||
\(988\) | −4.28783e29 | + | 2.72722e29i | −0.483803 | + | 0.307717i | ||||
\(989\) | − | 1.11817e29i | − | 0.124895i | ||||||
\(990\) | 2.33126e29 | + | 1.28009e29i | 0.257774 | + | 0.141543i | ||||
\(991\) | − | 4.01836e28i | − | 0.0439858i | −0.999758 | − | 0.0219929i | \(-0.992999\pi\) | ||
0.999758 | − | 0.0219929i | \(-0.00700113\pi\) | |||||||
\(992\) | −8.44236e29 | + | 6.16637e29i | −0.914844 | + | 0.668210i | ||||
\(993\) | −1.24233e30 | −1.33273 | ||||||||
\(994\) | −8.14870e28 | + | 1.48402e29i | −0.0865415 | + | 0.157607i | ||||
\(995\) | 2.24993e30 | 2.36558 | ||||||||
\(996\) | 5.14165e29 | + | 8.08389e29i | 0.535192 | + | 0.841447i | ||||
\(997\) | 1.61307e30i | 1.66227i | 0.556073 | + | 0.831133i | \(0.312307\pi\) | ||||
−0.556073 | + | 0.831133i | \(0.687693\pi\) | |||||||
\(998\) | 2.35039e29 | − | 4.28046e29i | 0.239792 | − | 0.436702i | ||||
\(999\) | 1.60081e30i | 1.61690i |
(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 | 8.21.d.b.3.11 | ✓ | 18 | |
3.2 | odd | 2 | 72.21.b.b.19.8 | 18 | |||
4.3 | odd | 2 | 32.21.d.b.15.5 | 18 | |||
8.3 | odd | 2 | inner | 8.21.d.b.3.12 | yes | 18 | |
8.5 | even | 2 | 32.21.d.b.15.6 | 18 | |||
24.11 | even | 2 | 72.21.b.b.19.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.21.d.b.3.11 | ✓ | 18 | 1.1 | even | 1 | trivial | |
8.21.d.b.3.12 | yes | 18 | 8.3 | odd | 2 | inner | |
32.21.d.b.15.5 | 18 | 4.3 | odd | 2 | |||
32.21.d.b.15.6 | 18 | 8.5 | even | 2 | |||
72.21.b.b.19.7 | 18 | 24.11 | even | 2 | |||
72.21.b.b.19.8 | 18 | 3.2 | odd | 2 |