Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,39,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.4390407101\) |
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: | \( x^{12} + 17353504902 x^{10} + \cdots + 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{75}\cdot 3^{91}\cdot 5^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.12 | ||
Root | \(81459.4i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.39.b.a.2.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 977513.i | 1.86446i | 0.361870 | + | 0.932229i | \(0.382138\pi\) | ||||
−0.361870 | + | 0.932229i | \(0.617862\pi\) | |||||||
\(3\) | −4.43499e8 | + | 1.07432e9i | −0.381583 | + | 0.924335i | ||||
\(4\) | −6.80653e11 | −2.47620 | ||||||||
\(5\) | − | 1.94075e13i | − | 1.01751i | −0.860910 | − | 0.508757i | \(-0.830105\pi\) | ||
0.860910 | − | 0.508757i | \(-0.169895\pi\) | |||||||
\(6\) | −1.05016e15 | − | 4.33526e14i | −1.72338 | − | 0.711445i | ||||
\(7\) | −1.85443e15 | −0.162685 | −0.0813426 | − | 0.996686i | \(-0.525921\pi\) | ||||
−0.0813426 | + | 0.996686i | \(0.525921\pi\) | |||||||
\(8\) | − | 3.96650e17i | − | 2.75231i | ||||||
\(9\) | −9.57469e17 | − | 9.52919e17i | −0.708789 | − | 0.705421i | ||||
\(10\) | 1.89711e19 | 1.89711 | ||||||||
\(11\) | 1.00331e20i | 1.64050i | 0.572007 | + | 0.820249i | \(0.306165\pi\) | ||||
−0.572007 | + | 0.820249i | \(0.693835\pi\) | |||||||
\(12\) | 3.01869e20 | − | 7.31238e20i | 0.944876 | − | 2.28884i | ||||
\(13\) | 5.34879e20 | 0.365875 | 0.182937 | − | 0.983125i | \(-0.441439\pi\) | ||||
0.182937 | + | 0.983125i | \(0.441439\pi\) | |||||||
\(14\) | − | 1.81273e21i | − | 0.303320i | ||||||
\(15\) | 2.08499e22 | + | 8.60722e21i | 0.940523 | + | 0.388266i | ||||
\(16\) | 2.00634e23 | 2.65537 | ||||||||
\(17\) | − | 2.93124e23i | − | 1.22609i | −0.790048 | − | 0.613045i | \(-0.789944\pi\) | ||
0.790048 | − | 0.613045i | \(-0.210056\pi\) | |||||||
\(18\) | 9.31490e23 | − | 9.35938e23i | 1.31523 | − | 1.32151i | ||||
\(19\) | −2.13221e24 | −1.07773 | −0.538866 | − | 0.842391i | \(-0.681147\pi\) | ||||
−0.538866 | + | 0.842391i | \(0.681147\pi\) | |||||||
\(20\) | 1.32098e25i | 2.51957i | ||||||||
\(21\) | 8.22439e23 | − | 1.99225e24i | 0.0620779 | − | 0.150376i | ||||
\(22\) | −9.80751e25 | −3.05864 | ||||||||
\(23\) | − | 6.81549e25i | − | 0.913416i | −0.889617 | − | 0.456708i | \(-0.849029\pi\) | ||
0.889617 | − | 0.456708i | \(-0.150971\pi\) | |||||||
\(24\) | 4.26128e26 | + | 1.75914e26i | 2.54406 | + | 1.05024i | ||||
\(25\) | −1.28546e25 | −0.0353344 | ||||||||
\(26\) | 5.22851e26i | 0.682157i | ||||||||
\(27\) | 1.44837e27 | − | 6.06008e26i | 0.922506 | − | 0.385982i | ||||
\(28\) | 1.26222e27 | 0.402841 | ||||||||
\(29\) | 4.43183e27i | 0.726141i | 0.931762 | + | 0.363071i | \(0.118272\pi\) | ||||
−0.931762 | + | 0.363071i | \(0.881728\pi\) | |||||||
\(30\) | −8.41367e27 | + | 2.03810e28i | −0.723905 | + | 1.75357i | ||||
\(31\) | 9.20206e27 | 0.424632 | 0.212316 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212316 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(32\) | 8.70919e28i | 2.19851i | ||||||||
\(33\) | −1.07788e29 | − | 4.44969e28i | −1.51637 | − | 0.625986i | ||||
\(34\) | 2.86533e29 | 2.28599 | ||||||||
\(35\) | 3.59900e28i | 0.165535i | ||||||||
\(36\) | 6.51704e29 | + | 6.48607e29i | 1.75510 | + | 1.74676i | ||||
\(37\) | −1.71160e29 | −0.273886 | −0.136943 | − | 0.990579i | \(-0.543728\pi\) | ||||
−0.136943 | + | 0.990579i | \(0.543728\pi\) | |||||||
\(38\) | − | 2.08426e30i | − | 2.00939i | ||||||
\(39\) | −2.37219e29 | + | 5.74631e29i | −0.139611 | + | 0.338190i | ||||
\(40\) | −7.69800e30 | −2.80052 | ||||||||
\(41\) | 3.25222e30i | 0.740093i | 0.929013 | + | 0.370046i | \(0.120658\pi\) | ||||
−0.929013 | + | 0.370046i | \(0.879342\pi\) | |||||||
\(42\) | 1.94745e30 | + | 8.03944e29i | 0.280369 | + | 0.115742i | ||||
\(43\) | 9.05664e30 | 0.833809 | 0.416904 | − | 0.908950i | \(-0.363115\pi\) | ||||
0.416904 | + | 0.908950i | \(0.363115\pi\) | |||||||
\(44\) | − | 6.82908e31i | − | 4.06220i | ||||||
\(45\) | −1.84938e31 | + | 1.85821e31i | −0.717775 | + | 0.721203i | ||||
\(46\) | 6.66223e31 | 1.70302 | ||||||||
\(47\) | − | 4.90800e31i | − | 0.833769i | −0.908960 | − | 0.416884i | \(-0.863122\pi\) | ||
0.908960 | − | 0.416884i | \(-0.136878\pi\) | |||||||
\(48\) | −8.89810e31 | + | 2.15545e32i | −1.01324 | + | 2.45445i | ||||
\(49\) | −1.26496e32 | −0.973534 | ||||||||
\(50\) | − | 1.25655e31i | − | 0.0658795i | ||||||
\(51\) | 3.14909e32 | + | 1.30000e32i | 1.13332 | + | 0.467855i | ||||
\(52\) | −3.64067e32 | −0.905979 | ||||||||
\(53\) | − | 3.19951e32i | − | 0.554425i | −0.960809 | − | 0.277212i | \(-0.910589\pi\) | ||
0.960809 | − | 0.277212i | \(-0.0894105\pi\) | |||||||
\(54\) | 5.92380e32 | + | 1.41580e33i | 0.719647 | + | 1.71997i | ||||
\(55\) | 1.94718e33 | 1.66923 | ||||||||
\(56\) | 7.35561e32i | 0.447761i | ||||||||
\(57\) | 9.45632e32 | − | 2.29067e33i | 0.411244 | − | 0.996186i | ||||
\(58\) | −4.33217e33 | −1.35386 | ||||||||
\(59\) | − | 2.55619e33i | − | 0.577304i | −0.957434 | − | 0.288652i | \(-0.906793\pi\) | ||
0.957434 | − | 0.288652i | \(-0.0932071\pi\) | |||||||
\(60\) | −1.41915e34 | − | 5.85853e33i | −2.32892 | − | 0.961424i | ||||
\(61\) | 1.24839e34 | 1.49653 | 0.748263 | − | 0.663403i | \(-0.230888\pi\) | ||||
0.748263 | + | 0.663403i | \(0.230888\pi\) | |||||||
\(62\) | 8.99513e33i | 0.791709i | ||||||||
\(63\) | 1.77556e33 | + | 1.76712e33i | 0.115310 | + | 0.114762i | ||||
\(64\) | −2.99835e34 | −1.44366 | ||||||||
\(65\) | − | 1.03807e34i | − | 0.372282i | ||||||
\(66\) | 4.34962e34 | − | 1.05364e35i | 1.16712 | − | 2.82720i | ||||
\(67\) | 4.69883e34 | 0.947476 | 0.473738 | − | 0.880666i | \(-0.342904\pi\) | ||||
0.473738 | + | 0.880666i | \(0.342904\pi\) | |||||||
\(68\) | 1.99516e35i | 3.03605i | ||||||||
\(69\) | 7.32201e34 | + | 3.02266e34i | 0.844302 | + | 0.348544i | ||||
\(70\) | −3.51806e34 | −0.308632 | ||||||||
\(71\) | − | 1.03720e35i | − | 0.694949i | −0.937689 | − | 0.347475i | \(-0.887039\pi\) | ||
0.937689 | − | 0.347475i | \(-0.112961\pi\) | |||||||
\(72\) | −3.77975e35 | + | 3.79780e35i | −1.94154 | + | 1.95081i | ||||
\(73\) | −1.12163e35 | −0.443317 | −0.221659 | − | 0.975124i | \(-0.571147\pi\) | ||||
−0.221659 | + | 0.975124i | \(0.571147\pi\) | |||||||
\(74\) | − | 1.67311e35i | − | 0.510649i | ||||||
\(75\) | 5.70100e33 | − | 1.38099e34i | 0.0134830 | − | 0.0326608i | ||||
\(76\) | 1.45129e36 | 2.66868 | ||||||||
\(77\) | − | 1.86058e35i | − | 0.266885i | ||||||
\(78\) | −5.61709e35 | − | 2.31884e35i | −0.630542 | − | 0.260300i | ||||
\(79\) | 5.18105e34 | 0.0456565 | 0.0228283 | − | 0.999739i | \(-0.492733\pi\) | ||||
0.0228283 | + | 0.999739i | \(0.492733\pi\) | |||||||
\(80\) | − | 3.89381e36i | − | 2.70187i | ||||||
\(81\) | 8.69280e33 | + | 1.82478e36i | 0.00476370 | + | 0.999989i | ||||
\(82\) | −3.17908e36 | −1.37987 | ||||||||
\(83\) | − | 1.87566e35i | − | 0.0646652i | −0.999477 | − | 0.0323326i | \(-0.989706\pi\) | ||
0.999477 | − | 0.0323326i | \(-0.0102936\pi\) | |||||||
\(84\) | −5.59795e35 | + | 1.35603e36i | −0.153717 | + | 0.372360i | ||||
\(85\) | −5.68882e36 | −1.24756 | ||||||||
\(86\) | 8.85298e36i | 1.55460i | ||||||||
\(87\) | −4.76120e36 | − | 1.96551e36i | −0.671197 | − | 0.277083i | ||||
\(88\) | 3.97964e37 | 4.51516 | ||||||||
\(89\) | − | 4.77590e36i | − | 0.437164i | −0.975819 | − | 0.218582i | \(-0.929857\pi\) | ||
0.975819 | − | 0.218582i | \(-0.0701432\pi\) | |||||||
\(90\) | −1.81642e37 | − | 1.80779e37i | −1.34465 | − | 1.33826i | ||||
\(91\) | −9.91898e35 | −0.0595224 | ||||||||
\(92\) | 4.63898e37i | 2.26180i | ||||||||
\(93\) | −4.08111e36 | + | 9.88595e36i | −0.162032 | + | 0.392502i | ||||
\(94\) | 4.79763e37 | 1.55453 | ||||||||
\(95\) | 4.13809e37i | 1.09661i | ||||||||
\(96\) | −9.35644e37 | − | 3.86252e37i | −2.03216 | − | 0.838913i | ||||
\(97\) | −7.67399e37 | −1.36886 | −0.684428 | − | 0.729080i | \(-0.739948\pi\) | ||||
−0.684428 | + | 0.729080i | \(0.739948\pi\) | |||||||
\(98\) | − | 1.23651e38i | − | 1.81511i | ||||||
\(99\) | 9.56076e37 | − | 9.60641e37i | 1.15724 | − | 1.16277i | ||||
\(100\) | 8.74951e36 | 0.0874951 | ||||||||
\(101\) | − | 4.54349e37i | − | 0.376083i | −0.982161 | − | 0.188041i | \(-0.939786\pi\) | ||
0.982161 | − | 0.188041i | \(-0.0602139\pi\) | |||||||
\(102\) | −1.27077e38 | + | 3.07828e38i | −0.872296 | + | 2.11302i | ||||
\(103\) | 2.67470e38 | 1.52535 | 0.762673 | − | 0.646785i | \(-0.223887\pi\) | ||||
0.762673 | + | 0.646785i | \(0.223887\pi\) | |||||||
\(104\) | − | 2.12160e38i | − | 1.00700i | ||||||
\(105\) | −3.86647e37 | − | 1.59615e37i | −0.153009 | − | 0.0631651i | ||||
\(106\) | 3.12756e38 | 1.03370 | ||||||||
\(107\) | − | 5.88759e38i | − | 1.62797i | −0.580887 | − | 0.813984i | \(-0.697294\pi\) | ||
0.580887 | − | 0.813984i | \(-0.302706\pi\) | |||||||
\(108\) | −9.85840e38 | + | 4.12481e38i | −2.28431 | + | 0.955768i | ||||
\(109\) | 3.21551e38 | 0.625383 | 0.312691 | − | 0.949855i | \(-0.398769\pi\) | ||||
0.312691 | + | 0.949855i | \(0.398769\pi\) | |||||||
\(110\) | 1.90340e39i | 3.11221i | ||||||||
\(111\) | 7.59094e37 | − | 1.83881e38i | 0.104510 | − | 0.253163i | ||||
\(112\) | −3.72062e38 | −0.431989 | ||||||||
\(113\) | − | 8.86717e37i | − | 0.0869550i | −0.999054 | − | 0.0434775i | \(-0.986156\pi\) | ||
0.999054 | − | 0.0434775i | \(-0.0138437\pi\) | |||||||
\(114\) | 2.23916e39 | + | 9.24367e38i | 1.85735 | + | 0.766748i | ||||
\(115\) | −1.32272e39 | −0.929413 | ||||||||
\(116\) | − | 3.01654e39i | − | 1.79807i | ||||||
\(117\) | −5.12130e38 | − | 5.09696e38i | −0.259328 | − | 0.258095i | ||||
\(118\) | 2.49871e39 | 1.07636 | ||||||||
\(119\) | 5.43579e38i | 0.199467i | ||||||||
\(120\) | 3.41406e39 | − | 8.27010e39i | 1.06863 | − | 2.58861i | ||||
\(121\) | −6.32594e39 | −1.69123 | ||||||||
\(122\) | 1.22032e40i | 2.79021i | ||||||||
\(123\) | −3.49392e39 | − | 1.44236e39i | −0.684094 | − | 0.282407i | ||||
\(124\) | −6.26341e39 | −1.05147 | ||||||||
\(125\) | − | 6.81094e39i | − | 0.981561i | ||||||
\(126\) | −1.72738e39 | + | 1.73563e39i | −0.213968 | + | 0.214990i | ||||
\(127\) | 3.29072e39 | 0.350768 | 0.175384 | − | 0.984500i | \(-0.443883\pi\) | ||||
0.175384 | + | 0.984500i | \(0.443883\pi\) | |||||||
\(128\) | − | 5.36966e39i | − | 0.493125i | ||||||
\(129\) | −4.01661e39 | + | 9.72972e39i | −0.318167 | + | 0.770718i | ||||
\(130\) | 1.01473e40 | 0.694105 | ||||||||
\(131\) | − | 1.52248e40i | − | 0.900322i | −0.892947 | − | 0.450161i | \(-0.851367\pi\) | ||
0.892947 | − | 0.450161i | \(-0.148633\pi\) | |||||||
\(132\) | 7.33661e40 | + | 3.02869e40i | 3.75483 | + | 1.55007i | ||||
\(133\) | 3.95404e39 | 0.175331 | ||||||||
\(134\) | 4.59316e40i | 1.76653i | ||||||||
\(135\) | −1.17611e40 | − | 2.81094e40i | −0.392742 | − | 0.938663i | ||||
\(136\) | −1.16268e41 | −3.37458 | ||||||||
\(137\) | − | 7.34845e40i | − | 1.85569i | −0.372969 | − | 0.927844i | \(-0.621660\pi\) | ||
0.372969 | − | 0.927844i | \(-0.378340\pi\) | |||||||
\(138\) | −2.95469e40 | + | 7.15736e40i | −0.649845 | + | 1.57416i | ||||
\(139\) | 6.07971e38 | 0.0116574 | 0.00582870 | − | 0.999983i | \(-0.498145\pi\) | ||||
0.00582870 | + | 0.999983i | \(0.498145\pi\) | |||||||
\(140\) | − | 2.44967e40i | − | 0.409897i | ||||||
\(141\) | 5.27276e40 | + | 2.17669e40i | 0.770681 | + | 0.318152i | ||||
\(142\) | 1.01387e41 | 1.29570 | ||||||||
\(143\) | 5.36652e40i | 0.600216i | ||||||||
\(144\) | −1.92101e41 | − | 1.91188e41i | −1.88210 | − | 1.87315i | ||||
\(145\) | 8.60109e40 | 0.738859 | ||||||||
\(146\) | − | 1.09641e41i | − | 0.826546i | ||||||
\(147\) | 5.61008e40 | − | 1.35897e41i | 0.371484 | − | 0.899871i | ||||
\(148\) | 1.16501e41 | 0.678197 | ||||||||
\(149\) | 1.48174e40i | 0.0758983i | 0.999280 | + | 0.0379491i | \(0.0120825\pi\) | ||||
−0.999280 | + | 0.0379491i | \(0.987918\pi\) | |||||||
\(150\) | 1.34994e40 | + | 5.57280e39i | 0.0608947 | + | 0.0251385i | ||||
\(151\) | −1.38443e41 | −0.550438 | −0.275219 | − | 0.961382i | \(-0.588750\pi\) | ||||
−0.275219 | + | 0.961382i | \(0.588750\pi\) | |||||||
\(152\) | 8.45740e41i | 2.96626i | ||||||||
\(153\) | −2.79324e41 | + | 2.80658e41i | −0.864910 | + | 0.869040i | ||||
\(154\) | 1.81874e41 | 0.497595 | ||||||||
\(155\) | − | 1.78589e41i | − | 0.432069i | ||||||
\(156\) | 1.61463e41 | − | 3.91124e41i | 0.345706 | − | 0.837427i | ||||
\(157\) | −7.44067e41 | −1.41097 | −0.705486 | − | 0.708723i | \(-0.749271\pi\) | ||||
−0.705486 | + | 0.708723i | \(0.749271\pi\) | |||||||
\(158\) | 5.06454e40i | 0.0851247i | ||||||||
\(159\) | 3.43730e41 | + | 1.41898e41i | 0.512474 | + | 0.211559i | ||||
\(160\) | 1.69024e42 | 2.23701 | ||||||||
\(161\) | 1.26389e41i | 0.148599i | ||||||||
\(162\) | −1.78374e42 | + | 8.49732e39i | −1.86444 | + | 0.00888171i | ||||
\(163\) | 1.76036e42 | 1.63695 | 0.818477 | − | 0.574539i | \(-0.194819\pi\) | ||||
0.818477 | + | 0.574539i | \(0.194819\pi\) | |||||||
\(164\) | − | 2.21363e42i | − | 1.83262i | ||||||
\(165\) | −8.63574e41 | + | 2.09190e42i | −0.636949 | + | 1.54293i | ||||
\(166\) | 1.83348e41 | 0.120566 | ||||||||
\(167\) | − | 1.17329e42i | − | 0.688321i | −0.938911 | − | 0.344161i | \(-0.888164\pi\) | ||
0.938911 | − | 0.344161i | \(-0.111836\pi\) | |||||||
\(168\) | −7.90226e41 | − | 3.26220e41i | −0.413881 | − | 0.170858i | ||||
\(169\) | −1.85111e42 | −0.866136 | ||||||||
\(170\) | − | 5.56090e42i | − | 2.32603i | ||||||
\(171\) | 2.04152e42 | + | 2.03182e42i | 0.763885 | + | 0.760255i | ||||
\(172\) | −6.16443e42 | −2.06468 | ||||||||
\(173\) | 3.20663e42i | 0.961995i | 0.876722 | + | 0.480998i | \(0.159725\pi\) | ||||
−0.876722 | + | 0.480998i | \(0.840275\pi\) | |||||||
\(174\) | 1.92131e42 | − | 4.65413e42i | 0.516609 | − | 1.25142i | ||||
\(175\) | 2.38380e40 | 0.00574839 | ||||||||
\(176\) | 2.01299e43i | 4.35612i | ||||||||
\(177\) | 2.74616e42 | + | 1.13367e42i | 0.533622 | + | 0.220289i | ||||
\(178\) | 4.66850e42 | 0.815074 | ||||||||
\(179\) | − | 1.08485e43i | − | 1.70280i | −0.524520 | − | 0.851398i | \(-0.675755\pi\) | ||
0.524520 | − | 0.851398i | \(-0.324245\pi\) | |||||||
\(180\) | 1.25879e43 | − | 1.26480e43i | 1.77736 | − | 1.78584i | ||||
\(181\) | 7.21699e42 | 0.917199 | 0.458599 | − | 0.888643i | \(-0.348351\pi\) | ||||
0.458599 | + | 0.888643i | \(0.348351\pi\) | |||||||
\(182\) | − | 9.69592e41i | − | 0.110977i | ||||||
\(183\) | −5.53661e42 | + | 1.34117e43i | −0.571048 | + | 1.38329i | ||||
\(184\) | −2.70337e43 | −2.51400 | ||||||||
\(185\) | 3.32180e42i | 0.278683i | ||||||||
\(186\) | −9.66364e42 | − | 3.98933e42i | −0.731804 | − | 0.302102i | ||||
\(187\) | 2.94096e43 | 2.01140 | ||||||||
\(188\) | 3.34065e43i | 2.06458i | ||||||||
\(189\) | −2.68591e42 | + | 1.12380e42i | −0.150078 | + | 0.0627936i | ||||
\(190\) | −4.04504e43 | −2.04458 | ||||||||
\(191\) | − | 2.14694e43i | − | 0.982168i | −0.871112 | − | 0.491084i | \(-0.836601\pi\) | ||
0.871112 | − | 0.491084i | \(-0.163399\pi\) | |||||||
\(192\) | 1.32977e43 | − | 3.22119e43i | 0.550874 | − | 1.33442i | ||||
\(193\) | −3.76780e43 | −1.41416 | −0.707081 | − | 0.707133i | \(-0.749988\pi\) | ||||
−0.707081 | + | 0.707133i | \(0.749988\pi\) | |||||||
\(194\) | − | 7.50142e43i | − | 2.55218i | ||||||
\(195\) | 1.11522e43 | + | 4.60383e42i | 0.344113 | + | 0.142057i | ||||
\(196\) | 8.60998e43 | 2.41066 | ||||||||
\(197\) | − | 2.57608e43i | − | 0.654789i | −0.944888 | − | 0.327395i | \(-0.893829\pi\) | ||
0.944888 | − | 0.327395i | \(-0.106171\pi\) | |||||||
\(198\) | 9.39039e43 | + | 9.34576e43i | 2.16793 | + | 2.15763i | ||||
\(199\) | −9.03602e43 | −1.89570 | −0.947848 | − | 0.318722i | \(-0.896746\pi\) | ||||
−0.947848 | + | 0.318722i | \(0.896746\pi\) | |||||||
\(200\) | 5.09877e42i | 0.0972514i | ||||||||
\(201\) | −2.08393e43 | + | 5.04804e43i | −0.361541 | + | 0.875785i | ||||
\(202\) | 4.44131e43 | 0.701190 | ||||||||
\(203\) | − | 8.21853e42i | − | 0.118132i | ||||||
\(204\) | −2.14344e44 | − | 8.84852e43i | −2.80632 | − | 1.15850i | ||||
\(205\) | 6.31175e43 | 0.753055 | ||||||||
\(206\) | 2.61456e44i | 2.84394i | ||||||||
\(207\) | −6.49461e43 | + | 6.52562e43i | −0.644342 | + | 0.647419i | ||||
\(208\) | 1.07315e44 | 0.971532 | ||||||||
\(209\) | − | 2.13927e44i | − | 1.76802i | ||||||
\(210\) | 1.56026e43 | − | 3.77952e43i | 0.117769 | − | 0.285279i | ||||
\(211\) | −7.21399e43 | −0.497518 | −0.248759 | − | 0.968565i | \(-0.580023\pi\) | ||||
−0.248759 | + | 0.968565i | \(0.580023\pi\) | |||||||
\(212\) | 2.17776e44i | 1.37287i | ||||||||
\(213\) | 1.11428e44 | + | 4.59996e43i | 0.642366 | + | 0.265181i | ||||
\(214\) | 5.75519e44 | 3.03528 | ||||||||
\(215\) | − | 1.75767e44i | − | 0.848412i | ||||||
\(216\) | −2.40373e44 | − | 5.74498e44i | −1.06234 | − | 2.53903i | ||||
\(217\) | −1.70646e43 | −0.0690814 | ||||||||
\(218\) | 3.14320e44i | 1.16600i | ||||||||
\(219\) | 4.97441e43 | − | 1.20499e44i | 0.169162 | − | 0.409773i | ||||
\(220\) | −1.32536e45 | −4.13335 | ||||||||
\(221\) | − | 1.56786e44i | − | 0.448595i | ||||||
\(222\) | 1.79746e44 | + | 7.42024e43i | 0.472011 | + | 0.194855i | ||||
\(223\) | 5.48150e44 | 1.32162 | 0.660811 | − | 0.750552i | \(-0.270213\pi\) | ||||
0.660811 | + | 0.750552i | \(0.270213\pi\) | |||||||
\(224\) | − | 1.61506e44i | − | 0.357665i | ||||||
\(225\) | 1.23079e43 | + | 1.22494e43i | 0.0250447 | + | 0.0249256i | ||||
\(226\) | 8.66777e43 | 0.162124 | ||||||||
\(227\) | 2.52600e44i | 0.434452i | 0.976121 | + | 0.217226i | \(0.0697008\pi\) | ||||
−0.976121 | + | 0.217226i | \(0.930299\pi\) | |||||||
\(228\) | −6.43647e44 | + | 1.55915e45i | −1.01832 | + | 2.46676i | ||||
\(229\) | 6.92899e43 | 0.100878 | 0.0504389 | − | 0.998727i | \(-0.483938\pi\) | ||||
0.0504389 | + | 0.998727i | \(0.483938\pi\) | |||||||
\(230\) | − | 1.29297e45i | − | 1.73285i | ||||||
\(231\) | 1.99885e44 | + | 8.25164e43i | 0.246691 | + | 0.101839i | ||||
\(232\) | 1.75789e45 | 1.99857 | ||||||||
\(233\) | − | 4.70136e44i | − | 0.492563i | −0.969198 | − | 0.246281i | \(-0.920791\pi\) | ||
0.969198 | − | 0.246281i | \(-0.0792087\pi\) | |||||||
\(234\) | 4.98235e44 | − | 5.00614e44i | 0.481208 | − | 0.483506i | ||||
\(235\) | −9.52522e44 | −0.848371 | ||||||||
\(236\) | 1.73988e45i | 1.42952i | ||||||||
\(237\) | −2.29779e43 | + | 5.56610e43i | −0.0174218 | + | 0.0422019i | ||||
\(238\) | −5.31356e44 | −0.371897 | ||||||||
\(239\) | 2.79152e45i | 1.80418i | 0.431545 | + | 0.902092i | \(0.357969\pi\) | ||||
−0.431545 | + | 0.902092i | \(0.642031\pi\) | |||||||
\(240\) | 4.18319e45 | + | 1.72690e45i | 2.49744 | + | 1.03099i | ||||
\(241\) | −6.40166e44 | −0.353158 | −0.176579 | − | 0.984286i | \(-0.556503\pi\) | ||||
−0.176579 | + | 0.984286i | \(0.556503\pi\) | |||||||
\(242\) | − | 6.18369e45i | − | 3.15323i | ||||||
\(243\) | −1.96425e45 | − | 7.99949e44i | −0.926142 | − | 0.377175i | ||||
\(244\) | −8.49721e45 | −3.70570 | ||||||||
\(245\) | 2.45497e45i | 0.990584i | ||||||||
\(246\) | 1.40992e45 | − | 3.41535e45i | 0.526535 | − | 1.27546i | ||||
\(247\) | −1.14047e45 | −0.394315 | ||||||||
\(248\) | − | 3.65000e45i | − | 1.16872i | ||||||
\(249\) | 2.01506e44 | + | 8.31854e43i | 0.0597723 | + | 0.0246751i | ||||
\(250\) | 6.65778e45 | 1.83008 | ||||||||
\(251\) | 6.44255e45i | 1.64156i | 0.571243 | + | 0.820781i | \(0.306461\pi\) | ||||
−0.571243 | + | 0.820781i | \(0.693539\pi\) | |||||||
\(252\) | −1.20854e45 | − | 1.20280e45i | −0.285529 | − | 0.284173i | ||||
\(253\) | 6.83807e45 | 1.49846 | ||||||||
\(254\) | 3.21672e45i | 0.653991i | ||||||||
\(255\) | 2.52299e45 | − | 6.11161e45i | 0.476049 | − | 1.15317i | ||||
\(256\) | −2.99290e45 | −0.524244 | ||||||||
\(257\) | − | 3.63646e44i | − | 0.0591492i | −0.999563 | − | 0.0295746i | \(-0.990585\pi\) | ||
0.999563 | − | 0.0295746i | \(-0.00941527\pi\) | |||||||
\(258\) | −9.51092e45 | − | 3.92629e45i | −1.43697 | − | 0.593209i | ||||
\(259\) | 3.17405e44 | 0.0445572 | ||||||||
\(260\) | 7.06565e45i | 0.921846i | ||||||||
\(261\) | 4.22317e45 | − | 4.24334e45i | 0.512235 | − | 0.514681i | ||||
\(262\) | 1.48825e46 | 1.67861 | ||||||||
\(263\) | − | 9.58317e45i | − | 1.00543i | −0.864454 | − | 0.502713i | \(-0.832335\pi\) | ||
0.864454 | − | 0.502713i | \(-0.167665\pi\) | |||||||
\(264\) | −1.76497e46 | + | 4.27540e46i | −1.72291 | + | 4.17352i | ||||
\(265\) | −6.20947e45 | −0.564135 | ||||||||
\(266\) | 3.86512e45i | 0.326898i | ||||||||
\(267\) | 5.13083e45 | + | 2.11811e45i | 0.404086 | + | 0.166814i | ||||
\(268\) | −3.19827e46 | −2.34614 | ||||||||
\(269\) | 9.07840e45i | 0.620463i | 0.950661 | + | 0.310231i | \(0.100407\pi\) | ||||
−0.950661 | + | 0.310231i | \(0.899593\pi\) | |||||||
\(270\) | 2.74773e46 | − | 1.14966e46i | 1.75010 | − | 0.732250i | ||||
\(271\) | 1.17965e46 | 0.700383 | 0.350192 | − | 0.936678i | \(-0.386116\pi\) | ||||
0.350192 | + | 0.936678i | \(0.386116\pi\) | |||||||
\(272\) | − | 5.88107e46i | − | 3.25572i | ||||||
\(273\) | 4.39906e44 | − | 1.06561e45i | 0.0227127 | − | 0.0550186i | ||||
\(274\) | 7.18320e46 | 3.45985 | ||||||||
\(275\) | − | 1.28972e45i | − | 0.0579660i | ||||||
\(276\) | −4.98375e46 | − | 2.05739e46i | −2.09066 | − | 0.863064i | ||||
\(277\) | −3.13591e46 | −1.22814 | −0.614071 | − | 0.789251i | \(-0.710469\pi\) | ||||
−0.614071 | + | 0.789251i | \(0.710469\pi\) | |||||||
\(278\) | 5.94299e44i | 0.0217347i | ||||||||
\(279\) | −8.81069e45 | − | 8.76882e45i | −0.300975 | − | 0.299544i | ||||
\(280\) | 1.42754e46 | 0.455603 | ||||||||
\(281\) | 2.23453e45i | 0.0666447i | 0.999445 | + | 0.0333224i | \(0.0106088\pi\) | ||||
−0.999445 | + | 0.0333224i | \(0.989391\pi\) | |||||||
\(282\) | −2.12775e46 | + | 5.15419e46i | −0.593180 | + | 1.43690i | ||||
\(283\) | −1.42833e45 | −0.0372295 | −0.0186147 | − | 0.999827i | \(-0.505926\pi\) | ||||
−0.0186147 | + | 0.999827i | \(0.505926\pi\) | |||||||
\(284\) | 7.05972e46i | 1.72083i | ||||||||
\(285\) | −4.44563e46 | − | 1.83524e46i | −1.01363 | − | 0.418447i | ||||
\(286\) | −5.24584e46 | −1.11908 | ||||||||
\(287\) | − | 6.03102e45i | − | 0.120402i | ||||||
\(288\) | 8.29915e46 | − | 8.33877e46i | 1.55087 | − | 1.55828i | ||||
\(289\) | −2.87663e46 | −0.503298 | ||||||||
\(290\) | 8.40767e46i | 1.37757i | ||||||||
\(291\) | 3.40341e46 | − | 8.24431e46i | 0.522332 | − | 1.26528i | ||||
\(292\) | 7.63439e46 | 1.09774 | ||||||||
\(293\) | − | 8.13702e45i | − | 0.109643i | −0.998496 | − | 0.0548214i | \(-0.982541\pi\) | ||
0.998496 | − | 0.0548214i | \(-0.0174590\pi\) | |||||||
\(294\) | 1.32841e47 | + | 5.48392e46i | 1.67777 | + | 0.692615i | ||||
\(295\) | −4.96093e46 | −0.587415 | ||||||||
\(296\) | 6.78907e46i | 0.753820i | ||||||||
\(297\) | 6.08016e46 | + | 1.45317e47i | 0.633202 | + | 1.51337i | ||||
\(298\) | −1.44842e46 | −0.141509 | ||||||||
\(299\) | − | 3.64547e46i | − | 0.334195i | ||||||
\(300\) | −3.88040e45 | + | 9.39976e45i | −0.0333866 | + | 0.0808748i | ||||
\(301\) | −1.67949e46 | −0.135648 | ||||||||
\(302\) | − | 1.35330e47i | − | 1.02627i | ||||||
\(303\) | 4.88115e46 | + | 2.01503e46i | 0.347626 | + | 0.143507i | ||||
\(304\) | −4.27793e47 | −2.86178 | ||||||||
\(305\) | − | 2.42282e47i | − | 1.52274i | ||||||
\(306\) | −2.74346e47 | − | 2.73042e47i | −1.62029 | − | 1.61259i | ||||
\(307\) | 1.21487e47 | 0.674375 | 0.337188 | − | 0.941437i | \(-0.390524\pi\) | ||||
0.337188 | + | 0.941437i | \(0.390524\pi\) | |||||||
\(308\) | 1.26641e47i | 0.660860i | ||||||||
\(309\) | −1.18623e47 | + | 2.87348e47i | −0.582046 | + | 1.40993i | ||||
\(310\) | 1.74573e47 | 0.805575 | ||||||||
\(311\) | 2.51496e47i | 1.09165i | 0.837899 | + | 0.545825i | \(0.183784\pi\) | ||||
−0.837899 | + | 0.545825i | \(0.816216\pi\) | |||||||
\(312\) | 2.27927e47 | + | 9.40927e46i | 0.930806 | + | 0.384254i | ||||
\(313\) | 3.84707e47 | 1.47838 | 0.739192 | − | 0.673495i | \(-0.235208\pi\) | ||||
0.739192 | + | 0.673495i | \(0.235208\pi\) | |||||||
\(314\) | − | 7.27335e47i | − | 2.63070i | ||||||
\(315\) | 3.42955e46 | − | 3.44593e46i | 0.116771 | − | 0.117329i | ||||
\(316\) | −3.52650e46 | −0.113055 | ||||||||
\(317\) | − | 5.94628e47i | − | 1.79523i | −0.440784 | − | 0.897613i | \(-0.645299\pi\) | ||
0.440784 | − | 0.897613i | \(-0.354701\pi\) | |||||||
\(318\) | −1.38707e47 | + | 3.36000e47i | −0.394443 | + | 0.955485i | ||||
\(319\) | −4.44651e47 | −1.19123 | ||||||||
\(320\) | 5.81907e47i | 1.46894i | ||||||||
\(321\) | 6.32515e47 | + | 2.61114e47i | 1.50479 | + | 0.621205i | ||||
\(322\) | −1.23547e47 | −0.277057 | ||||||||
\(323\) | 6.25002e47i | 1.32140i | ||||||||
\(324\) | −5.91678e45 | − | 1.24204e48i | −0.0117959 | − | 2.47617i | ||||
\(325\) | −6.87565e45 | −0.0129280 | ||||||||
\(326\) | 1.72077e48i | 3.05203i | ||||||||
\(327\) | −1.42607e47 | + | 3.45448e47i | −0.238635 | + | 0.578063i | ||||
\(328\) | 1.28999e48 | 2.03697 | ||||||||
\(329\) | 9.10156e46i | 0.135642i | ||||||||
\(330\) | −2.04485e48 | − | 8.44155e47i | −2.87672 | − | 1.18756i | ||||
\(331\) | −5.89042e47 | −0.782374 | −0.391187 | − | 0.920311i | \(-0.627935\pi\) | ||||
−0.391187 | + | 0.920311i | \(0.627935\pi\) | |||||||
\(332\) | 1.27667e47i | 0.160124i | ||||||||
\(333\) | 1.63881e47 | + | 1.63102e47i | 0.194128 | + | 0.193205i | ||||
\(334\) | 1.14690e48 | 1.28335 | ||||||||
\(335\) | − | 9.11927e47i | − | 0.964070i | ||||||
\(336\) | 1.65009e47 | − | 3.99713e47i | 0.164840 | − | 0.399303i | ||||
\(337\) | −1.54032e48 | −1.45426 | −0.727132 | − | 0.686498i | \(-0.759147\pi\) | ||||
−0.727132 | + | 0.686498i | \(0.759147\pi\) | |||||||
\(338\) | − | 1.80949e48i | − | 1.61487i | ||||||
\(339\) | 9.52617e46 | + | 3.93258e46i | 0.0803755 | + | 0.0331806i | ||||
\(340\) | 3.87211e48 | 3.08922 | ||||||||
\(341\) | 9.23255e47i | 0.696608i | ||||||||
\(342\) | −1.98613e48 | + | 1.99561e48i | −1.41746 | + | 1.42423i | ||||
\(343\) | 4.75533e47 | 0.321065 | ||||||||
\(344\) | − | 3.59232e48i | − | 2.29490i | ||||||
\(345\) | 5.86625e47 | − | 1.42102e48i | 0.354648 | − | 0.859089i | ||||
\(346\) | −3.13452e48 | −1.79360 | ||||||||
\(347\) | 1.35408e48i | 0.733473i | 0.930325 | + | 0.366736i | \(0.119525\pi\) | ||||
−0.930325 | + | 0.366736i | \(0.880475\pi\) | |||||||
\(348\) | 3.24072e48 | + | 1.33783e48i | 1.66202 | + | 0.686113i | ||||
\(349\) | 2.81170e47 | 0.136548 | 0.0682740 | − | 0.997667i | \(-0.478251\pi\) | ||||
0.0682740 | + | 0.997667i | \(0.478251\pi\) | |||||||
\(350\) | 2.33019e46i | 0.0107176i | ||||||||
\(351\) | 7.74706e47 | − | 3.24141e47i | 0.337522 | − | 0.141221i | ||||
\(352\) | −8.73804e48 | −3.60665 | ||||||||
\(353\) | − | 1.03153e47i | − | 0.0403425i | −0.999797 | − | 0.0201712i | \(-0.993579\pi\) | ||
0.999797 | − | 0.0201712i | \(-0.00642114\pi\) | |||||||
\(354\) | −1.10817e48 | + | 2.68441e48i | −0.410720 | + | 0.994916i | ||||
\(355\) | −2.01295e48 | −0.707121 | ||||||||
\(356\) | 3.25073e48i | 1.08251i | ||||||||
\(357\) | −5.83978e47 | − | 2.41077e47i | −0.184374 | − | 0.0761131i | ||||
\(358\) | 1.06046e49 | 3.17479 | ||||||||
\(359\) | − | 4.39348e48i | − | 1.24742i | −0.781654 | − | 0.623712i | \(-0.785624\pi\) | ||
0.781654 | − | 0.623712i | \(-0.214376\pi\) | |||||||
\(360\) | 7.37059e48 | + | 7.33557e48i | 1.98497 | + | 1.97554i | ||||
\(361\) | 6.32167e47 | 0.161508 | ||||||||
\(362\) | 7.05470e48i | 1.71008i | ||||||||
\(363\) | 2.80555e48 | − | 6.79608e48i | 0.645345 | − | 1.56326i | ||||
\(364\) | 6.75138e47 | 0.147389 | ||||||||
\(365\) | 2.17680e48i | 0.451081i | ||||||||
\(366\) | −1.31101e49 | − | 5.41210e48i | −2.57909 | − | 1.06470i | ||||
\(367\) | 2.89773e48 | 0.541257 | 0.270628 | − | 0.962684i | \(-0.412769\pi\) | ||||
0.270628 | + | 0.962684i | \(0.412769\pi\) | |||||||
\(368\) | − | 1.36742e49i | − | 2.42545i | ||||||
\(369\) | 3.09910e48 | − | 3.11390e48i | 0.522077 | − | 0.524570i | ||||
\(370\) | −3.24710e48 | −0.519593 | ||||||||
\(371\) | 5.93328e47i | 0.0901967i | ||||||||
\(372\) | 2.77782e48 | − | 6.72890e48i | 0.401225 | − | 0.971914i | ||||
\(373\) | −9.95641e48 | −1.36658 | −0.683290 | − | 0.730147i | \(-0.739452\pi\) | ||||
−0.683290 | + | 0.730147i | \(0.739452\pi\) | |||||||
\(374\) | 2.87482e49i | 3.75017i | ||||||||
\(375\) | 7.31712e48 | + | 3.02065e48i | 0.907290 | + | 0.374547i | ||||
\(376\) | −1.94676e49 | −2.29479 | ||||||||
\(377\) | 2.37049e48i | 0.265677i | ||||||||
\(378\) | −1.09853e48 | − | 2.62551e48i | −0.117076 | − | 0.279814i | ||||
\(379\) | −6.31988e48 | −0.640566 | −0.320283 | − | 0.947322i | \(-0.603778\pi\) | ||||
−0.320283 | + | 0.947322i | \(0.603778\pi\) | |||||||
\(380\) | − | 2.81660e49i | − | 2.71542i | ||||||
\(381\) | −1.45943e48 | + | 3.53528e48i | −0.133847 | + | 0.324227i | ||||
\(382\) | 2.09866e49 | 1.83121 | ||||||||
\(383\) | 4.72786e48i | 0.392544i | 0.980549 | + | 0.196272i | \(0.0628835\pi\) | ||||
−0.980549 | + | 0.196272i | \(0.937116\pi\) | |||||||
\(384\) | 5.76873e48 | + | 2.38144e48i | 0.455813 | + | 0.188168i | ||||
\(385\) | −3.61092e48 | −0.271559 | ||||||||
\(386\) | − | 3.68307e49i | − | 2.63664i | ||||||
\(387\) | −8.67145e48 | − | 8.63024e48i | −0.590994 | − | 0.588186i | ||||
\(388\) | 5.22332e49 | 3.38956 | ||||||||
\(389\) | 2.31399e49i | 1.42994i | 0.699153 | + | 0.714972i | \(0.253561\pi\) | ||||
−0.699153 | + | 0.714972i | \(0.746439\pi\) | |||||||
\(390\) | −4.50030e48 | + | 1.09014e49i | −0.264858 | + | 0.641585i | ||||
\(391\) | −1.99779e49 | −1.11993 | ||||||||
\(392\) | 5.01746e49i | 2.67947i | ||||||||
\(393\) | 1.63563e49 | + | 6.75220e48i | 0.832199 | + | 0.343547i | ||||
\(394\) | 2.51815e49 | 1.22083 | ||||||||
\(395\) | − | 1.00551e48i | − | 0.0464562i | ||||||
\(396\) | −6.50756e49 | + | 6.53863e49i | −2.86556 | + | 2.87924i | ||||
\(397\) | −9.52386e48 | −0.399755 | −0.199877 | − | 0.979821i | \(-0.564054\pi\) | ||||
−0.199877 | + | 0.979821i | \(0.564054\pi\) | |||||||
\(398\) | − | 8.83282e49i | − | 3.53444i | ||||||
\(399\) | −1.75361e48 | + | 4.24789e48i | −0.0669034 | + | 0.162065i | ||||
\(400\) | −2.57907e48 | −0.0938259 | ||||||||
\(401\) | 1.71356e48i | 0.0594506i | 0.999558 | + | 0.0297253i | \(0.00946325\pi\) | ||||
−0.999558 | + | 0.0297253i | \(0.990537\pi\) | |||||||
\(402\) | −4.93452e49 | − | 2.03706e49i | −1.63286 | − | 0.674077i | ||||
\(403\) | 4.92199e48 | 0.155362 | ||||||||
\(404\) | 3.09254e49i | 0.931256i | ||||||||
\(405\) | 3.54145e49 | − | 1.68706e47i | 1.01750 | − | 0.00484713i | ||||
\(406\) | 8.03371e48 | 0.220253 | ||||||||
\(407\) | − | 1.71727e49i | − | 0.449310i | ||||||
\(408\) | 5.15647e49 | − | 1.24909e50i | 1.28768 | − | 3.11925i | ||||
\(409\) | 5.80638e49 | 1.38408 | 0.692042 | − | 0.721857i | \(-0.256711\pi\) | ||||
0.692042 | + | 0.721857i | \(0.256711\pi\) | |||||||
\(410\) | 6.16982e49i | 1.40404i | ||||||||
\(411\) | 7.89457e49 | + | 3.25903e49i | 1.71528 | + | 0.708099i | ||||
\(412\) | −1.82054e50 | −3.77706 | ||||||||
\(413\) | 4.74028e48i | 0.0939189i | ||||||||
\(414\) | −6.37888e49 | − | 6.34856e49i | −1.20708 | − | 1.20135i | ||||
\(415\) | −3.64020e48 | −0.0657978 | ||||||||
\(416\) | 4.65836e49i | 0.804378i | ||||||||
\(417\) | −2.69635e47 | + | 6.53155e47i | −0.00444826 | + | 0.0107753i | ||||
\(418\) | 2.09117e50 | 3.29639 | ||||||||
\(419\) | − | 8.20553e49i | − | 1.23606i | −0.786154 | − | 0.618031i | \(-0.787931\pi\) | ||
0.786154 | − | 0.618031i | \(-0.212069\pi\) | |||||||
\(420\) | 2.63172e49 | + | 1.08642e49i | 0.378882 | + | 0.156410i | ||||
\(421\) | −1.10651e50 | −1.52263 | −0.761315 | − | 0.648382i | \(-0.775446\pi\) | ||||
−0.761315 | + | 0.648382i | \(0.775446\pi\) | |||||||
\(422\) | − | 7.05176e49i | − | 0.927601i | ||||||
\(423\) | −4.67693e49 | + | 4.69926e49i | −0.588157 | + | 0.590966i | ||||
\(424\) | −1.26909e50 | −1.52595 | ||||||||
\(425\) | 3.76799e48i | 0.0433232i | ||||||||
\(426\) | −4.49652e49 | + | 1.08922e50i | −0.494418 | + | 1.19766i | ||||
\(427\) | −2.31506e49 | −0.243463 | ||||||||
\(428\) | 4.00741e50i | 4.03118i | ||||||||
\(429\) | −5.76535e49 | − | 2.38004e49i | −0.554801 | − | 0.229032i | ||||
\(430\) | 1.71815e50 | 1.58183 | ||||||||
\(431\) | − | 1.46867e50i | − | 1.29377i | −0.762587 | − | 0.646885i | \(-0.776071\pi\) | ||
0.762587 | − | 0.646885i | \(-0.223929\pi\) | |||||||
\(432\) | 2.90593e50 | − | 1.21586e50i | 2.44959 | − | 1.02492i | ||||
\(433\) | 1.20647e50 | 0.973296 | 0.486648 | − | 0.873598i | \(-0.338219\pi\) | ||||
0.486648 | + | 0.873598i | \(0.338219\pi\) | |||||||
\(434\) | − | 1.66809e49i | − | 0.128799i | ||||||
\(435\) | −3.81458e49 | + | 9.24031e49i | −0.281936 | + | 0.682953i | ||||
\(436\) | −2.18864e50 | −1.54857 | ||||||||
\(437\) | 1.45320e50i | 0.984418i | ||||||||
\(438\) | 1.17789e50 | + | 4.86255e49i | 0.764005 | + | 0.315396i | ||||
\(439\) | −2.49606e50 | −1.55035 | −0.775175 | − | 0.631746i | \(-0.782338\pi\) | ||||
−0.775175 | + | 0.631746i | \(0.782338\pi\) | |||||||
\(440\) | − | 7.72351e50i | − | 4.59424i | ||||||
\(441\) | 1.21116e50 | + | 1.20540e50i | 0.690030 | + | 0.686751i | ||||
\(442\) | 1.53261e50 | 0.836387 | ||||||||
\(443\) | − | 1.99617e50i | − | 1.04358i | −0.853074 | − | 0.521790i | \(-0.825264\pi\) | ||
0.853074 | − | 0.521790i | \(-0.174736\pi\) | |||||||
\(444\) | −5.16680e49 | + | 1.25159e50i | −0.258788 | + | 0.626881i | ||||
\(445\) | −9.26884e49 | −0.444821 | ||||||||
\(446\) | 5.35824e50i | 2.46411i | ||||||||
\(447\) | −1.59186e49 | − | 6.57149e48i | −0.0701554 | − | 0.0289615i | ||||
\(448\) | 5.56025e49 | 0.234861 | ||||||||
\(449\) | − | 2.63311e50i | − | 1.06608i | −0.846090 | − | 0.533039i | \(-0.821050\pi\) | ||
0.846090 | − | 0.533039i | \(-0.178950\pi\) | |||||||
\(450\) | −1.19739e49 | + | 1.20311e49i | −0.0464728 | + | 0.0466947i | ||||
\(451\) | −3.26299e50 | −1.21412 | ||||||||
\(452\) | 6.03547e49i | 0.215318i | ||||||||
\(453\) | 6.13993e49 | − | 1.48732e50i | 0.210038 | − | 0.508789i | ||||
\(454\) | −2.46919e50 | −0.810016 | ||||||||
\(455\) | 1.92503e49i | 0.0605649i | ||||||||
\(456\) | −9.08595e50 | − | 3.75085e50i | −2.74181 | − | 1.13187i | ||||
\(457\) | 3.95099e50 | 1.14366 | 0.571832 | − | 0.820371i | \(-0.306233\pi\) | ||||
0.571832 | + | 0.820371i | \(0.306233\pi\) | |||||||
\(458\) | 6.77317e49i | 0.188082i | ||||||||
\(459\) | −1.77636e50 | − | 4.24554e50i | −0.473249 | − | 1.13108i | ||||
\(460\) | 9.00313e50 | 2.30141 | ||||||||
\(461\) | 5.51810e50i | 1.35354i | 0.736193 | + | 0.676771i | \(0.236621\pi\) | ||||
−0.736193 | + | 0.676771i | \(0.763379\pi\) | |||||||
\(462\) | −8.06608e49 | + | 1.95390e50i | −0.189874 | + | 0.459944i | ||||
\(463\) | 7.87996e50 | 1.78027 | 0.890133 | − | 0.455700i | \(-0.150611\pi\) | ||||
0.890133 | + | 0.455700i | \(0.150611\pi\) | |||||||
\(464\) | 8.89175e50i | 1.92817i | ||||||||
\(465\) | 1.91862e50 | + | 7.92042e49i | 0.399377 | + | 0.164870i | ||||
\(466\) | 4.59564e50 | 0.918362 | ||||||||
\(467\) | 2.60117e49i | 0.0499054i | 0.999689 | + | 0.0249527i | \(0.00794351\pi\) | ||||
−0.999689 | + | 0.0249527i | \(0.992056\pi\) | |||||||
\(468\) | 3.48583e50 | + | 3.46926e50i | 0.642148 | + | 0.639096i | ||||
\(469\) | −8.71366e49 | −0.154140 | ||||||||
\(470\) | − | 9.31103e50i | − | 1.58175i | ||||||
\(471\) | 3.29993e50 | − | 7.99365e50i | 0.538403 | − | 1.30421i | ||||
\(472\) | −1.01391e51 | −1.58892 | ||||||||
\(473\) | 9.08665e50i | 1.36786i | ||||||||
\(474\) | −5.44093e49 | − | 2.24612e49i | −0.0786837 | − | 0.0324821i | ||||
\(475\) | 2.74087e49 | 0.0380811 | ||||||||
\(476\) | − | 3.69989e50i | − | 0.493920i | ||||||
\(477\) | −3.04888e50 | + | 3.06343e50i | −0.391102 | + | 0.392970i | ||||
\(478\) | −2.72875e51 | −3.36382 | ||||||||
\(479\) | − | 3.83296e50i | − | 0.454108i | −0.973882 | − | 0.227054i | \(-0.927091\pi\) | ||
0.973882 | − | 0.227054i | \(-0.0729095\pi\) | |||||||
\(480\) | −7.49619e50 | + | 1.81585e51i | −0.853605 | + | 2.06775i | ||||
\(481\) | −9.15501e49 | −0.100208 | ||||||||
\(482\) | − | 6.25770e50i | − | 0.658448i | ||||||
\(483\) | −1.35782e50 | − | 5.60533e49i | −0.137355 | − | 0.0567029i | ||||
\(484\) | 4.30577e51 | 4.18783 | ||||||||
\(485\) | 1.48933e51i | 1.39283i | ||||||||
\(486\) | 7.81960e50 | − | 1.92008e51i | 0.703227 | − | 1.72675i | ||||
\(487\) | −5.23031e50 | −0.452353 | −0.226176 | − | 0.974086i | \(-0.572623\pi\) | ||||
−0.226176 | + | 0.974086i | \(0.572623\pi\) | |||||||
\(488\) | − | 4.95175e51i | − | 4.11891i | ||||||
\(489\) | −7.80717e50 | + | 1.89119e51i | −0.624634 | + | 1.51309i | ||||
\(490\) | −2.39977e51 | −1.84690 | ||||||||
\(491\) | − | 2.96080e50i | − | 0.219210i | −0.993975 | − | 0.109605i | \(-0.965041\pi\) | ||
0.993975 | − | 0.109605i | \(-0.0349586\pi\) | |||||||
\(492\) | 2.37814e51 | + | 9.81743e50i | 1.69395 | + | 0.699296i | ||||
\(493\) | 1.29908e51 | 0.890315 | ||||||||
\(494\) | − | 1.11483e51i | − | 0.735183i | ||||||
\(495\) | −1.86437e51 | − | 1.85551e51i | −1.18313 | − | 1.17751i | ||||
\(496\) | 1.84625e51 | 1.12755 | ||||||||
\(497\) | 1.92341e50i | 0.113058i | ||||||||
\(498\) | −8.13148e49 | + | 1.96974e50i | −0.0460057 | + | 0.111443i | ||||
\(499\) | 5.15637e50 | 0.280823 | 0.140412 | − | 0.990093i | \(-0.455157\pi\) | ||||
0.140412 | + | 0.990093i | \(0.455157\pi\) | |||||||
\(500\) | 4.63589e51i | 2.43054i | ||||||||
\(501\) | 1.26048e51 | + | 5.20352e50i | 0.636239 | + | 0.262652i | ||||
\(502\) | −6.29767e51 | −3.06062 | ||||||||
\(503\) | 1.33918e51i | 0.626682i | 0.949641 | + | 0.313341i | \(0.101448\pi\) | ||||
−0.949641 | + | 0.313341i | \(0.898552\pi\) | |||||||
\(504\) | 7.00929e50 | − | 7.04276e50i | 0.315860 | − | 0.317368i | ||||
\(505\) | −8.81779e50 | −0.382669 | ||||||||
\(506\) | 6.68430e51i | 2.79381i | ||||||||
\(507\) | 8.20968e50 | − | 1.98869e51i | 0.330503 | − | 0.800599i | ||||
\(508\) | −2.23983e51 | −0.868571 | ||||||||
\(509\) | 7.06657e50i | 0.263980i | 0.991251 | + | 0.131990i | \(0.0421367\pi\) | ||||
−0.991251 | + | 0.131990i | \(0.957863\pi\) | |||||||
\(510\) | 5.97417e51 | + | 2.46625e51i | 2.15003 | + | 0.887573i | ||||
\(511\) | 2.07998e50 | 0.0721212 | ||||||||
\(512\) | − | 4.40160e51i | − | 1.47056i | ||||||
\(513\) | −3.08824e51 | + | 1.29214e51i | −0.994216 | + | 0.415985i | ||||
\(514\) | 3.55468e50 | 0.110281 | ||||||||
\(515\) | − | 5.19094e51i | − | 1.55206i | ||||||
\(516\) | 2.73392e51 | − | 6.62256e51i | 0.787846 | − | 1.90845i | ||||
\(517\) | 4.92426e51 | 1.36780 | ||||||||
\(518\) | 3.10267e50i | 0.0830751i | ||||||||
\(519\) | −3.44494e51 | − | 1.42214e51i | −0.889206 | − | 0.367081i | ||||
\(520\) | −4.11750e51 | −1.02464 | ||||||||
\(521\) | − | 3.23363e50i | − | 0.0775843i | −0.999247 | − | 0.0387922i | \(-0.987649\pi\) | ||
0.999247 | − | 0.0387922i | \(-0.0123510\pi\) | |||||||
\(522\) | 4.14792e51 | + | 4.12820e51i | 0.959600 | + | 0.955040i | ||||
\(523\) | 3.56990e51 | 0.796386 | 0.398193 | − | 0.917302i | \(-0.369637\pi\) | ||||
0.398193 | + | 0.917302i | \(0.369637\pi\) | |||||||
\(524\) | 1.03628e52i | 2.22938i | ||||||||
\(525\) | −1.05721e49 | + | 2.56096e49i | −0.00219349 | + | 0.00531344i | ||||
\(526\) | 9.36767e51 | 1.87457 | ||||||||
\(527\) | − | 2.69735e51i | − | 0.520638i | ||||||
\(528\) | −2.16259e52 | − | 8.92758e51i | −4.02652 | − | 1.66222i | ||||
\(529\) | 9.22374e50 | 0.165672 | ||||||||
\(530\) | − | 6.06983e51i | − | 1.05180i | ||||||
\(531\) | −2.43584e51 | + | 2.44747e51i | −0.407242 | + | 0.409187i | ||||
\(532\) | −2.69133e51 | −0.434155 | ||||||||
\(533\) | 1.73954e51i | 0.270781i | ||||||||
\(534\) | −2.07047e51 | + | 5.01545e51i | −0.311018 | + | 0.753401i | ||||
\(535\) | −1.14264e52 | −1.65648 | ||||||||
\(536\) | − | 1.86379e52i | − | 2.60775i | ||||||
\(537\) | 1.16548e52 | + | 4.81131e51i | 1.57395 | + | 0.649758i | ||||
\(538\) | −8.87425e51 | −1.15683 | ||||||||
\(539\) | − | 1.26915e52i | − | 1.59708i | ||||||
\(540\) | 8.00524e51 | + | 1.91327e52i | 0.972507 | + | 2.32432i | ||||
\(541\) | 1.47773e52 | 1.73319 | 0.866594 | − | 0.499014i | \(-0.166304\pi\) | ||||
0.866594 | + | 0.499014i | \(0.166304\pi\) | |||||||
\(542\) | 1.15312e52i | 1.30583i | ||||||||
\(543\) | −3.20073e51 | + | 7.75335e51i | −0.349987 | + | 0.847799i | ||||
\(544\) | 2.55288e52 | 2.69557 | ||||||||
\(545\) | − | 6.24051e51i | − | 0.636336i | ||||||
\(546\) | 1.04165e51 | + | 4.30013e50i | 0.102580 | + | 0.0423469i | ||||
\(547\) | −1.26863e52 | −1.20663 | −0.603317 | − | 0.797501i | \(-0.706155\pi\) | ||||
−0.603317 | + | 0.797501i | \(0.706155\pi\) | |||||||
\(548\) | 5.00174e52i | 4.59505i | ||||||||
\(549\) | −1.19530e52 | − | 1.18962e52i | −1.06072 | − | 1.05568i | ||||
\(550\) | 1.26072e51 | 0.108075 | ||||||||
\(551\) | − | 9.44958e51i | − | 0.782586i | ||||||
\(552\) | 1.19894e52 | − | 2.90428e52i | 0.959301 | − | 2.32378i | ||||
\(553\) | −9.60791e49 | −0.00742765 | ||||||||
\(554\) | − | 3.06539e52i | − | 2.28982i | ||||||
\(555\) | −3.56867e51 | − | 1.47321e51i | −0.257596 | − | 0.106341i | ||||
\(556\) | −4.13817e50 | −0.0288661 | ||||||||
\(557\) | 2.59652e52i | 1.75042i | 0.483740 | + | 0.875212i | \(0.339278\pi\) | ||||
−0.483740 | + | 0.875212i | \(0.660722\pi\) | |||||||
\(558\) | 8.57163e51 | − | 8.61256e51i | 0.558488 | − | 0.561154i | ||||
\(559\) | 4.84421e51 | 0.305069 | ||||||||
\(560\) | 7.22081e51i | 0.439555i | ||||||||
\(561\) | −1.30431e52 | + | 3.15952e52i | −0.767515 | + | 1.85921i | ||||
\(562\) | −2.18428e51 | −0.124256 | ||||||||
\(563\) | 3.13079e51i | 0.172184i | 0.996287 | + | 0.0860922i | \(0.0274380\pi\) | ||||
−0.996287 | + | 0.0860922i | \(0.972562\pi\) | |||||||
\(564\) | −3.58892e52 | − | 1.48157e52i | −1.90836 | − | 0.787808i | ||||
\(565\) | −1.72090e51 | −0.0884779 | ||||||||
\(566\) | − | 1.39621e51i | − | 0.0694127i | ||||||
\(567\) | −1.61202e49 | − | 3.38393e51i | −0.000774984 | − | 0.162683i | ||||
\(568\) | −4.11405e52 | −1.91272 | ||||||||
\(569\) | 1.09157e52i | 0.490816i | 0.969420 | + | 0.245408i | \(0.0789218\pi\) | ||||
−0.969420 | + | 0.245408i | \(0.921078\pi\) | |||||||
\(570\) | 1.79397e52 | − | 4.34566e52i | 0.780176 | − | 1.88988i | ||||
\(571\) | 2.15960e52 | 0.908422 | 0.454211 | − | 0.890894i | \(-0.349921\pi\) | ||||
0.454211 | + | 0.890894i | \(0.349921\pi\) | |||||||
\(572\) | − | 3.65273e52i | − | 1.48626i | ||||||
\(573\) | 2.30650e52 | + | 9.52165e51i | 0.907852 | + | 0.374778i | ||||
\(574\) | 5.89539e51 | 0.224485 | ||||||||
\(575\) | 8.76104e50i | 0.0322750i | ||||||||
\(576\) | 2.87083e52 | + | 2.85719e52i | 1.02325 | + | 1.01838i | ||||
\(577\) | −2.05789e52 | −0.709713 | −0.354856 | − | 0.934921i | \(-0.615470\pi\) | ||||
−0.354856 | + | 0.934921i | \(0.615470\pi\) | |||||||
\(578\) | − | 2.81195e52i | − | 0.938378i | ||||||
\(579\) | 1.67102e52 | − | 4.04782e52i | 0.539620 | − | 1.30716i | ||||
\(580\) | −5.85436e52 | −1.82956 | ||||||||
\(581\) | 3.47829e50i | 0.0105201i | ||||||||
\(582\) | 8.05891e52 | + | 3.32687e52i | 2.35906 | + | 0.973866i | ||||
\(583\) | 3.21011e52 | 0.909532 | ||||||||
\(584\) | 4.44894e52i | 1.22015i | ||||||||
\(585\) | −9.89195e51 | + | 9.93919e51i | −0.262616 | + | 0.263870i | ||||
\(586\) | 7.95404e51 | 0.204424 | ||||||||
\(587\) | − | 4.30984e51i | − | 0.107235i | −0.998562 | − | 0.0536176i | \(-0.982925\pi\) | ||
0.998562 | − | 0.0536176i | \(-0.0170752\pi\) | |||||||
\(588\) | −3.81852e52 | + | 9.24986e52i | −0.919868 | + | 2.22826i | ||||
\(589\) | −1.96207e52 | −0.457640 | ||||||||
\(590\) | − | 4.84937e52i | − | 1.09521i | ||||||
\(591\) | 2.76753e52 | + | 1.14249e52i | 0.605244 | + | 0.249856i | ||||
\(592\) | −3.43406e52 | −0.727269 | ||||||||
\(593\) | 4.71208e52i | 0.966437i | 0.875500 | + | 0.483218i | \(0.160532\pi\) | ||||
−0.875500 | + | 0.483218i | \(0.839468\pi\) | |||||||
\(594\) | −1.42050e53 | + | 5.94343e52i | −2.82161 | + | 1.18058i | ||||
\(595\) | 1.05495e52 | 0.202960 | ||||||||
\(596\) | − | 1.00855e52i | − | 0.187939i | ||||||
\(597\) | 4.00747e52 | − | 9.70756e52i | 0.723365 | − | 1.75226i | ||||
\(598\) | 3.56349e52 | 0.623093 | ||||||||
\(599\) | − | 2.00006e52i | − | 0.338793i | −0.985548 | − | 0.169396i | \(-0.945818\pi\) | ||
0.985548 | − | 0.169396i | \(-0.0541818\pi\) | |||||||
\(600\) | −5.47771e51 | − | 2.26130e51i | −0.0898928 | − | 0.0371095i | ||||
\(601\) | 5.78120e52 | 0.919185 | 0.459592 | − | 0.888130i | \(-0.347996\pi\) | ||||
0.459592 | + | 0.888130i | \(0.347996\pi\) | |||||||
\(602\) | − | 1.64172e52i | − | 0.252911i | ||||||
\(603\) | −4.49898e52 | − | 4.47760e52i | −0.671561 | − | 0.668369i | ||||
\(604\) | 9.42315e52 | 1.36300 | ||||||||
\(605\) | 1.22771e53i | 1.72085i | ||||||||
\(606\) | −1.96972e52 | + | 4.77139e52i | −0.267562 | + | 0.648134i | ||||
\(607\) | −1.31976e53 | −1.73744 | −0.868721 | − | 0.495301i | \(-0.835058\pi\) | ||||
−0.868721 | + | 0.495301i | \(0.835058\pi\) | |||||||
\(608\) | − | 1.85698e53i | − | 2.36940i | ||||||
\(609\) | 8.82932e51 | + | 3.64491e51i | 0.109194 | + | 0.0450773i | ||||
\(610\) | 2.36834e53 | 2.83907 | ||||||||
\(611\) | − | 2.62519e52i | − | 0.305055i | ||||||
\(612\) | 1.90122e53 | − | 1.91030e53i | 2.14169 | − | 2.15192i | ||||
\(613\) | −5.15273e52 | −0.562715 | −0.281357 | − | 0.959603i | \(-0.590785\pi\) | ||||
−0.281357 | + | 0.959603i | \(0.590785\pi\) | |||||||
\(614\) | 1.18755e53i | 1.25734i | ||||||||
\(615\) | −2.79926e52 | + | 6.78083e52i | −0.287353 | + | 0.696075i | ||||
\(616\) | −7.37998e52 | −0.734550 | ||||||||
\(617\) | − | 1.13864e53i | − | 1.09893i | −0.835517 | − | 0.549465i | \(-0.814832\pi\) | ||
0.835517 | − | 0.549465i | \(-0.185168\pi\) | |||||||
\(618\) | −2.80887e53 | − | 1.15955e53i | −2.62875 | − | 1.08520i | ||||
\(619\) | −6.36249e52 | −0.577437 | −0.288718 | − | 0.957414i | \(-0.593229\pi\) | ||||
−0.288718 | + | 0.957414i | \(0.593229\pi\) | |||||||
\(620\) | 1.21557e53i | 1.06989i | ||||||||
\(621\) | −4.13024e52 | − | 9.87139e52i | −0.352562 | − | 0.842632i | ||||
\(622\) | −2.45840e53 | −2.03534 | ||||||||
\(623\) | 8.85658e51i | 0.0711202i | ||||||||
\(624\) | −4.75941e52 | + | 1.15290e53i | −0.370720 | + | 0.898020i | ||||
\(625\) | −1.36860e53 | −1.03409 | ||||||||
\(626\) | 3.76056e53i | 2.75638i | ||||||||
\(627\) | 2.29826e53 | + | 9.48765e52i | 1.63424 | + | 0.674645i | ||||
\(628\) | 5.06451e53 | 3.49385 | ||||||||
\(629\) | 5.01713e52i | 0.335809i | ||||||||
\(630\) | 3.36844e52 | + | 3.35243e52i | 0.218755 | + | 0.217715i | ||||
\(631\) | −1.55428e53 | −0.979427 | −0.489713 | − | 0.871883i | \(-0.662899\pi\) | ||||
−0.489713 | + | 0.871883i | \(0.662899\pi\) | |||||||
\(632\) | − | 2.05506e52i | − | 0.125661i | ||||||
\(633\) | 3.19940e52 | − | 7.75012e52i | 0.189844 | − | 0.459873i | ||||
\(634\) | 5.81256e53 | 3.34712 | ||||||||
\(635\) | − | 6.38647e52i | − | 0.356911i | ||||||
\(636\) | −2.33961e53 | − | 9.65834e52i | −1.26899 | − | 0.523862i | ||||
\(637\) | −6.76600e52 | −0.356191 | ||||||||
\(638\) | − | 4.34652e53i | − | 2.22100i | ||||||
\(639\) | −9.88365e52 | + | 9.93085e52i | −0.490232 | + | 0.492572i | ||||
\(640\) | −1.04212e53 | −0.501762 | ||||||||
\(641\) | − | 3.62328e53i | − | 1.69356i | −0.531947 | − | 0.846778i | \(-0.678539\pi\) | ||
0.531947 | − | 0.846778i | \(-0.321461\pi\) | |||||||
\(642\) | −2.55242e53 | + | 6.18291e53i | −1.15821 | + | 2.80561i | ||||
\(643\) | 4.40218e53 | 1.93937 | 0.969683 | − | 0.244367i | \(-0.0785801\pi\) | ||||
0.969683 | + | 0.244367i | \(0.0785801\pi\) | |||||||
\(644\) | − | 8.60268e52i | − | 0.367962i | ||||||
\(645\) | 1.88830e53 | + | 7.79525e52i | 0.784217 | + | 0.323739i | ||||
\(646\) | −6.10948e53 | −2.46369 | ||||||||
\(647\) | 3.53960e53i | 1.38603i | 0.720923 | + | 0.693015i | \(0.243718\pi\) | ||||
−0.720923 | + | 0.693015i | \(0.756282\pi\) | |||||||
\(648\) | 7.23799e53 | − | 3.44800e51i | 2.75228 | − | 0.0131112i | ||||
\(649\) | 2.56466e53 | 0.947066 | ||||||||
\(650\) | − | 6.72104e51i | − | 0.0241036i | ||||||
\(651\) | 7.56814e51 | − | 1.83328e52i | 0.0263603 | − | 0.0638543i | ||||
\(652\) | −1.19819e54 | −4.05343 | ||||||||
\(653\) | − | 4.16045e53i | − | 1.36707i | −0.729919 | − | 0.683534i | \(-0.760442\pi\) | ||
0.729919 | − | 0.683534i | \(-0.239558\pi\) | |||||||
\(654\) | −3.37680e53 | − | 1.39401e53i | −1.07777 | − | 0.444926i | ||||
\(655\) | −2.95476e53 | −0.916090 | ||||||||
\(656\) | 6.52505e53i | 1.96522i | ||||||||
\(657\) | 1.07392e53 | + | 1.06882e53i | 0.314218 | + | 0.312725i | ||||
\(658\) | −8.89689e52 | −0.252898 | ||||||||
\(659\) | − | 1.42734e53i | − | 0.394189i | −0.980384 | − | 0.197095i | \(-0.936849\pi\) | ||
0.980384 | − | 0.197095i | \(-0.0631506\pi\) | |||||||
\(660\) | 5.87794e53 | − | 1.42385e54i | 1.57721 | − | 3.82059i | ||||
\(661\) | 7.90981e51 | 0.0206224 | 0.0103112 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103112 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(662\) | − | 5.75796e53i | − | 1.45870i | ||||||
\(663\) | 1.68438e53 | + | 6.95346e52i | 0.414652 | + | 0.171176i | ||||
\(664\) | −7.43981e52 | −0.177979 | ||||||||
\(665\) | − | 7.67381e52i | − | 0.178402i | ||||||
\(666\) | −1.59434e53 | + | 1.60195e53i | −0.360222 | + | 0.361942i | ||||
\(667\) | 3.02051e53 | 0.663269 | ||||||||
\(668\) | 7.98601e53i | 1.70442i | ||||||||
\(669\) | −2.43104e53 | + | 5.88888e53i | −0.504308 | + | 1.22162i | ||||
\(670\) | 8.91420e53 | 1.79747 | ||||||||
\(671\) | 1.25253e54i | 2.45505i | ||||||||
\(672\) | 1.73509e53 | + | 7.16277e52i | 0.330602 | + | 0.136479i | ||||
\(673\) | −3.96213e53 | −0.733910 | −0.366955 | − | 0.930239i | \(-0.619600\pi\) | ||||
−0.366955 | + | 0.930239i | \(0.619600\pi\) | |||||||
\(674\) | − | 1.50568e54i | − | 2.71141i | ||||||
\(675\) | −1.86183e52 | + | 7.78998e51i | −0.0325962 | + | 0.0136384i | ||||
\(676\) | 1.25997e54 | 2.14473 | ||||||||
\(677\) | − | 4.33082e53i | − | 0.716779i | −0.933572 | − | 0.358390i | \(-0.883326\pi\) | ||
0.933572 | − | 0.358390i | \(-0.116674\pi\) | |||||||
\(678\) | −3.84415e52 | + | 9.31195e52i | −0.0618637 | + | 0.149857i | ||||
\(679\) | 1.42309e53 | 0.222693 | ||||||||
\(680\) | 2.25647e54i | 3.43369i | ||||||||
\(681\) | −2.71372e53 | − | 1.12028e53i | −0.401579 | − | 0.165779i | ||||
\(682\) | −9.02493e53 | −1.29880 | ||||||||
\(683\) | 2.18362e53i | 0.305621i | 0.988255 | + | 0.152811i | \(0.0488325\pi\) | ||||
−0.988255 | + | 0.152811i | \(0.951168\pi\) | |||||||
\(684\) | −1.38957e54 | − | 1.38296e54i | −1.89153 | − | 1.88254i | ||||
\(685\) | −1.42615e54 | −1.88819 | ||||||||
\(686\) | 4.64840e53i | 0.598612i | ||||||||
\(687\) | −3.07300e52 | + | 7.44394e52i | −0.0384932 | + | 0.0932448i | ||||
\(688\) | 1.81707e54 | 2.21407 | ||||||||
\(689\) | − | 1.71135e53i | − | 0.202850i | ||||||
\(690\) | 1.38907e54 | + | 5.73433e53i | 1.60173 | + | 0.661226i | ||||
\(691\) | −8.19021e52 | −0.0918782 | −0.0459391 | − | 0.998944i | \(-0.514628\pi\) | ||||
−0.0459391 | + | 0.998944i | \(0.514628\pi\) | |||||||
\(692\) | − | 2.18260e54i | − | 2.38209i | ||||||
\(693\) | −1.77298e53 | + | 1.78144e53i | −0.188266 | + | 0.189165i | ||||
\(694\) | −1.32363e54 | −1.36753 | ||||||||
\(695\) | − | 1.17992e52i | − | 0.0118616i | ||||||
\(696\) | −7.79620e53 | + | 1.88853e54i | −0.762619 | + | 1.84735i | ||||
\(697\) | 9.53304e53 | 0.907421 | ||||||||
\(698\) | 2.74847e53i | 0.254588i | ||||||||
\(699\) | 5.05076e53 | + | 2.08505e53i | 0.455293 | + | 0.187953i | ||||
\(700\) | −1.62254e52 | −0.0142342 | ||||||||
\(701\) | − | 1.27469e54i | − | 1.08834i | −0.838976 | − | 0.544169i | \(-0.816845\pi\) | ||
0.838976 | − | 0.544169i | \(-0.183155\pi\) | |||||||
\(702\) | 3.16852e53 | + | 7.57285e53i | 0.263300 | + | 0.629295i | ||||
\(703\) | 3.64949e53 | 0.295176 | ||||||||
\(704\) | − | 3.00829e54i | − | 2.36831i | ||||||
\(705\) | 4.22443e53 | − | 1.02331e54i | 0.323724 | − | 0.784179i | ||||
\(706\) | 1.00833e53 | 0.0752168 | ||||||||
\(707\) | 8.42559e52i | 0.0611831i | ||||||||
\(708\) | −1.86918e54 | − | 7.71634e53i | −1.32136 | − | 0.545481i | ||||
\(709\) | 2.05256e54 | 1.41260 | 0.706298 | − | 0.707914i | \(-0.250364\pi\) | ||||
0.706298 | + | 0.707914i | \(0.250364\pi\) | |||||||
\(710\) | − | 1.96768e54i | − | 1.31840i | ||||||
\(711\) | −4.96069e52 | − | 4.93712e52i | −0.0323609 | − | 0.0322071i | ||||
\(712\) | −1.89436e54 | −1.20321 | ||||||||
\(713\) | − | 6.27166e53i | − | 0.387866i | ||||||
\(714\) | 2.35656e53 | − | 5.70845e53i | 0.141910 | − | 0.343758i | ||||
\(715\) | 1.04151e54 | 0.610728 | ||||||||
\(716\) | 7.38407e54i | 4.21647i | ||||||||
\(717\) | −2.99898e54 | − | 1.23804e54i | −1.66767 | − | 0.688445i | ||||
\(718\) | 4.29468e54 | 2.32577 | ||||||||
\(719\) | 1.72629e54i | 0.910469i | 0.890371 | + | 0.455235i | \(0.150445\pi\) | ||||
−0.890371 | + | 0.455235i | \(0.849555\pi\) | |||||||
\(720\) | −3.71048e54 | + | 3.72820e54i | −1.90596 | + | 1.91506i | ||||
\(721\) | −4.96005e53 | −0.248151 | ||||||||
\(722\) | 6.17951e53i | 0.301125i | ||||||||
\(723\) | 2.83913e53 | − | 6.87742e53i | 0.134759 | − | 0.326436i | ||||
\(724\) | −4.91227e54 | −2.27117 | ||||||||
\(725\) | − | 5.69693e52i | − | 0.0256578i | ||||||
\(726\) | 6.64325e54 | + | 2.74246e54i | 2.91464 | + | 1.20322i | ||||
\(727\) | −1.24366e53 | −0.0531555 | −0.0265778 | − | 0.999647i | \(-0.508461\pi\) | ||||
−0.0265778 | + | 0.999647i | \(0.508461\pi\) | |||||||
\(728\) | 3.93436e53i | 0.163824i | ||||||||
\(729\) | 1.73054e54 | − | 1.75545e54i | 0.702036 | − | 0.712141i | ||||
\(730\) | −2.12785e54 | −0.841022 | ||||||||
\(731\) | − | 2.65472e54i | − | 1.02233i | ||||||
\(732\) | 3.76851e54 | − | 9.12871e54i | 1.41403 | − | 3.42530i | ||||
\(733\) | −4.38973e54 | −1.60495 | −0.802476 | − | 0.596685i | \(-0.796484\pi\) | ||||
−0.802476 | + | 0.596685i | \(0.796484\pi\) | |||||||
\(734\) | 2.83257e54i | 1.00915i | ||||||||
\(735\) | −2.63742e54 | − | 1.08878e54i | −0.915631 | − | 0.377990i | ||||
\(736\) | 5.93574e54 | 2.00815 | ||||||||
\(737\) | 4.71440e54i | 1.55433i | ||||||||
\(738\) | 3.04387e54 | + | 3.02941e54i | 0.978038 | + | 0.973390i | ||||
\(739\) | 4.48590e54 | 1.40477 | 0.702384 | − | 0.711798i | \(-0.252119\pi\) | ||||
0.702384 | + | 0.711798i | \(0.252119\pi\) | |||||||
\(740\) | − | 2.26099e54i | − | 0.690075i | ||||||
\(741\) | 5.05799e53 | − | 1.22523e54i | 0.150464 | − | 0.364479i | ||||
\(742\) | −5.79986e53 | −0.168168 | ||||||||
\(743\) | 3.32855e54i | 0.940736i | 0.882470 | + | 0.470368i | \(0.155879\pi\) | ||||
−0.882470 | + | 0.470368i | \(0.844121\pi\) | |||||||
\(744\) | 3.92126e54 | + | 1.61877e54i | 1.08029 | + | 0.445964i | ||||
\(745\) | 2.87569e53 | 0.0772275 | ||||||||
\(746\) | − | 9.73252e54i | − | 2.54793i | ||||||
\(747\) | −1.78735e53 | + | 1.79589e53i | −0.0456162 | + | 0.0458340i | ||||
\(748\) | −2.00177e55 | −4.98063 | ||||||||
\(749\) | 1.09181e54i | 0.264846i | ||||||||
\(750\) | −2.95272e54 | + | 7.15258e54i | −0.698326 | + | 1.69160i | ||||
\(751\) | −1.83280e54 | −0.422627 | −0.211313 | − | 0.977418i | \(-0.567774\pi\) | ||||
−0.211313 | + | 0.977418i | \(0.567774\pi\) | |||||||
\(752\) | − | 9.84712e54i | − | 2.21396i | ||||||
\(753\) | −6.92135e54 | − | 2.85727e54i | −1.51735 | − | 0.626392i | ||||
\(754\) | −2.31719e54 | −0.495343 | ||||||||
\(755\) | 2.68683e54i | 0.560078i | ||||||||
\(756\) | 1.82817e54 | − | 7.64918e53i | 0.371624 | − | 0.155489i | ||||
\(757\) | 7.97431e54 | 1.58078 | 0.790390 | − | 0.612604i | \(-0.209878\pi\) | ||||
0.790390 | + | 0.612604i | \(0.209878\pi\) | |||||||
\(758\) | − | 6.17776e54i | − | 1.19431i | ||||||
\(759\) | −3.03268e54 | + | 7.34627e54i | −0.571785 | + | 1.38507i | ||||
\(760\) | 1.64137e55 | 3.01821 | ||||||||
\(761\) | − | 4.06921e54i | − | 0.729796i | −0.931048 | − | 0.364898i | \(-0.881104\pi\) | ||
0.931048 | − | 0.364898i | \(-0.118896\pi\) | |||||||
\(762\) | −3.45578e54 | − | 1.42661e54i | −0.604507 | − | 0.249552i | ||||
\(763\) | −5.96294e53 | −0.101741 | ||||||||
\(764\) | 1.46132e55i | 2.43204i | ||||||||
\(765\) | 5.44687e54 | + | 5.42099e54i | 0.884260 | + | 0.880057i | ||||
\(766\) | −4.62155e54 | −0.731881 | ||||||||
\(767\) | − | 1.36725e54i | − | 0.211221i | ||||||
\(768\) | 1.32735e54 | − | 3.21533e54i | 0.200042 | − | 0.484577i | ||||
\(769\) | −4.87719e54 | −0.717082 | −0.358541 | − | 0.933514i | \(-0.616726\pi\) | ||||
−0.358541 | + | 0.933514i | \(0.616726\pi\) | |||||||
\(770\) | − | 3.52972e54i | − | 0.506310i | ||||||
\(771\) | 3.90671e53 | + | 1.61277e53i | 0.0546737 | + | 0.0225703i | ||||
\(772\) | 2.56456e55 | 3.50175 | ||||||||
\(773\) | − | 7.25727e54i | − | 0.966858i | −0.875384 | − | 0.483429i | \(-0.839391\pi\) | ||
0.875384 | − | 0.483429i | \(-0.160609\pi\) | |||||||
\(774\) | 8.43617e54 | − | 8.47645e54i | 1.09665 | − | 1.10188i | ||||
\(775\) | −1.18289e53 | −0.0150041 | ||||||||
\(776\) | 3.04389e55i | 3.76752i | ||||||||
\(777\) | −1.40769e53 | + | 3.40994e53i | −0.0170023 | + | 0.0411858i | ||||
\(778\) | −2.26195e55 | −2.66607 | ||||||||
\(779\) | − | 6.93440e54i | − | 0.797623i | ||||||
\(780\) | −7.59075e54 | − | 3.13361e54i | −0.852094 | − | 0.351761i | ||||
\(781\) | 1.04063e55 | 1.14006 | ||||||||
\(782\) | − | 1.95286e55i | − | 2.08806i | ||||||
\(783\) | 2.68572e54 | + | 6.41895e54i | 0.280277 | + | 0.669870i | ||||
\(784\) | −2.53794e55 | −2.58509 | ||||||||
\(785\) | 1.44405e55i | 1.43568i | ||||||||
\(786\) | −6.60036e54 | + | 1.59885e55i | −0.640529 | + | 1.55160i | ||||
\(787\) | 1.12718e54 | 0.106776 | 0.0533880 | − | 0.998574i | \(-0.482998\pi\) | ||||
0.0533880 | + | 0.998574i | \(0.482998\pi\) | |||||||
\(788\) | 1.75342e55i | 1.62139i | ||||||||
\(789\) | 1.02954e55 | + | 4.25013e54i | 0.929350 | + | 0.383653i | ||||
\(790\) | 9.82903e53 | 0.0866155 | ||||||||
\(791\) | 1.64436e53i | 0.0141463i | ||||||||
\(792\) | −3.81038e55 | − | 3.79228e55i | −3.20030 | − | 3.18509i | ||||
\(793\) | 6.67739e54 | 0.547540 | ||||||||
\(794\) | − | 9.30969e54i | − | 0.745325i | ||||||
\(795\) | 2.75389e54 | − | 6.67095e54i | 0.215264 | − | 0.521449i | ||||
\(796\) | 6.15039e55 | 4.69412 | ||||||||
\(797\) | − | 4.35977e54i | − | 0.324904i | −0.986716 | − | 0.162452i | \(-0.948060\pi\) | ||
0.986716 | − | 0.162452i | \(-0.0519403\pi\) | |||||||
\(798\) | −4.15237e54 | − | 1.71418e54i | −0.302163 | − | 0.124739i | ||||
\(799\) | −1.43866e55 | −1.02228 | ||||||||
\(800\) | − | 1.11953e54i | − | 0.0776830i | ||||||
\(801\) | −4.55104e54 | + | 4.57277e54i | −0.308385 | + | 0.309857i | ||||
\(802\) | −1.67503e54 | −0.110843 | ||||||||
\(803\) | − | 1.12534e55i | − | 0.727261i | ||||||
\(804\) | 1.41843e55 | − | 3.43596e55i | 0.895247 | − | 2.16862i | ||||
\(805\) | 2.45289e54 | 0.151202 | ||||||||
\(806\) | 4.81131e54i | 0.289666i | ||||||||
\(807\) | −9.75309e54 | − | 4.02626e54i | −0.573515 | − | 0.236758i | ||||
\(808\) | −1.80217e55 | −1.03510 | ||||||||
\(809\) | − | 4.16420e54i | − | 0.233620i | −0.993154 | − | 0.116810i | \(-0.962733\pi\) | ||
0.993154 | − | 0.116810i | \(-0.0372668\pi\) | |||||||
\(810\) | 1.64912e53 | + | 3.46181e55i | 0.00903726 | + | 1.89709i | ||||
\(811\) | −8.66827e54 | −0.464019 | −0.232010 | − | 0.972713i | \(-0.574530\pi\) | ||||
−0.232010 | + | 0.972713i | \(0.574530\pi\) | |||||||
\(812\) | 5.59396e54i | 0.292520i | ||||||||
\(813\) | −5.23173e54 | + | 1.26732e55i | −0.267254 | + | 0.647389i | ||||
\(814\) | 1.67866e55 | 0.837719 | ||||||||
\(815\) | − | 3.41642e55i | − | 1.66562i | ||||||
\(816\) | 6.31814e55 | + | 2.60825e55i | 3.00938 | + | 1.24233i | ||||
\(817\) | −1.93106e55 | −0.898623 | ||||||||
\(818\) | 5.67581e55i | 2.58057i | ||||||||
\(819\) | 9.49711e53 | + | 9.45198e53i | 0.0421888 | + | 0.0419883i | ||||
\(820\) | −4.29611e55 | −1.86471 | ||||||||
\(821\) | 1.22436e55i | 0.519267i | 0.965707 | + | 0.259634i | \(0.0836018\pi\) | ||||
−0.965707 | + | 0.259634i | \(0.916398\pi\) | |||||||
\(822\) | −3.18574e55 | + | 7.71705e55i | −1.32022 | + | 3.19806i | ||||
\(823\) | 1.60452e55 | 0.649755 | 0.324877 | − | 0.945756i | \(-0.394677\pi\) | ||||
0.324877 | + | 0.945756i | \(0.394677\pi\) | |||||||
\(824\) | − | 1.06092e56i | − | 4.19823i | ||||||
\(825\) | 1.38557e54 | + | 5.71989e53i | 0.0535800 | + | 0.0221188i | ||||
\(826\) | −4.63368e54 | −0.175108 | ||||||||
\(827\) | 3.02976e54i | 0.111893i | 0.998434 | + | 0.0559465i | \(0.0178176\pi\) | ||||
−0.998434 | + | 0.0559465i | \(0.982182\pi\) | |||||||
\(828\) | 4.42057e55 | − | 4.44168e55i | 1.59552 | − | 1.60314i | ||||
\(829\) | −3.83145e55 | −1.35153 | −0.675767 | − | 0.737116i | \(-0.736187\pi\) | ||||
−0.675767 | + | 0.737116i | \(0.736187\pi\) | |||||||
\(830\) | − | 3.55834e54i | − | 0.122677i | ||||||
\(831\) | 1.39077e55 | − | 3.36897e55i | 0.468638 | − | 1.13521i | ||||
\(832\) | −1.60376e55 | −0.528197 | ||||||||
\(833\) | 3.70790e55i | 1.19364i | ||||||||
\(834\) | −6.38467e53 | − | 2.63571e53i | −0.0200902 | − | 0.00829360i | ||||
\(835\) | −2.27706e55 | −0.700376 | ||||||||
\(836\) | 1.45610e56i | 4.37797i | ||||||||
\(837\) | 1.33280e55 | − | 5.57652e54i | 0.391726 | − | 0.163900i | ||||
\(838\) | 8.02101e55 | 2.30459 | ||||||||
\(839\) | − | 3.56264e55i | − | 1.00068i | −0.865829 | − | 0.500339i | \(-0.833209\pi\) | ||
0.865829 | − | 0.500339i | \(-0.166791\pi\) | |||||||
\(840\) | −6.33114e54 | + | 1.53363e55i | −0.173850 | + | 0.421129i | ||||
\(841\) | 1.76087e55 | 0.472719 | ||||||||
\(842\) | − | 1.08163e56i | − | 2.83888i | ||||||
\(843\) | −2.40059e54 | − | 9.91011e53i | −0.0616020 | − | 0.0254305i | ||||
\(844\) | 4.91022e55 | 1.23195 | ||||||||
\(845\) | 3.59256e55i | 0.881305i | ||||||||
\(846\) | −4.59359e55 | − | 4.57175e55i | −1.10183 | − | 1.09659i | ||||
\(847\) | 1.17310e55 | 0.275138 | ||||||||
\(848\) | − | 6.41931e55i | − | 1.47220i | ||||||
\(849\) | 6.33464e53 | − | 1.53448e54i | 0.0142061 | − | 0.0344125i | ||||
\(850\) | −3.68326e54 | −0.0807743 | ||||||||
\(851\) | 1.16654e55i | 0.250172i | ||||||||
\(852\) | −7.58439e55 | − | 3.13098e55i | −1.59063 | − | 0.656641i | ||||
\(853\) | −1.55865e55 | −0.319681 | −0.159841 | − | 0.987143i | \(-0.551098\pi\) | ||||
−0.159841 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(854\) | − | 2.26300e55i | − | 0.453926i | ||||||
\(855\) | 3.94326e55 | − | 3.96209e55i | 0.773570 | − | 0.777264i | ||||
\(856\) | −2.33531e56 | −4.48068 | ||||||||
\(857\) | 3.51881e55i | 0.660329i | 0.943923 | + | 0.330165i | \(0.107104\pi\) | ||||
−0.943923 | + | 0.330165i | \(0.892896\pi\) | |||||||
\(858\) | 2.32652e55 | − | 5.63570e55i | 0.427021 | − | 1.03440i | ||||
\(859\) | −3.48134e55 | −0.624995 | −0.312498 | − | 0.949919i | \(-0.601166\pi\) | ||||
−0.312498 | + | 0.949919i | \(0.601166\pi\) | |||||||
\(860\) | 1.19636e56i | 2.10084i | ||||||||
\(861\) | 6.47923e54 | + | 2.67475e54i | 0.111292 | + | 0.0459434i | ||||
\(862\) | 1.43565e56 | 2.41218 | ||||||||
\(863\) | − | 6.24240e54i | − | 0.102600i | −0.998683 | − | 0.0512999i | \(-0.983664\pi\) | ||
0.998683 | − | 0.0512999i | \(-0.0163364\pi\) | |||||||
\(864\) | 5.27784e55 | + | 1.26142e56i | 0.848584 | + | 2.02814i | ||||
\(865\) | 6.22328e55 | 0.978844 | ||||||||
\(866\) | 1.17934e56i | 1.81467i | ||||||||
\(867\) | 1.27578e55 | − | 3.09042e55i | 0.192050 | − | 0.465216i | ||||
\(868\) | 1.16151e55 | 0.171059 | ||||||||
\(869\) | 5.19822e54i | 0.0748994i | ||||||||
\(870\) | −9.03252e55 | − | 3.72879e55i | −1.27334 | − | 0.525657i | ||||
\(871\) | 2.51331e55 | 0.346657 | ||||||||
\(872\) | − | 1.27543e56i | − | 1.72125i | ||||||
\(873\) | 7.34760e55 | + | 7.31268e55i | 0.970231 | + | 0.965620i | ||||
\(874\) | −1.42053e56 | −1.83541 | ||||||||
\(875\) | 1.26304e55i | 0.159685i | ||||||||
\(876\) | −3.38585e55 | + | 8.20177e55i | −0.418880 | + | 1.01468i | ||||
\(877\) | 5.20887e55 | 0.630597 | 0.315298 | − | 0.948993i | \(-0.397895\pi\) | ||||
0.315298 | + | 0.948993i | \(0.397895\pi\) | |||||||
\(878\) | − | 2.43993e56i | − | 2.89056i | ||||||
\(879\) | 8.74175e54 | + | 3.60876e54i | 0.101347 | + | 0.0418378i | ||||
\(880\) | 3.90671e56 | 4.43242 | ||||||||
\(881\) | − | 7.60630e55i | − | 0.844562i | −0.906465 | − | 0.422281i | \(-0.861230\pi\) | ||
0.906465 | − | 0.422281i | \(-0.138770\pi\) | |||||||
\(882\) | −1.17830e56 | + | 1.18392e56i | −1.28042 | + | 1.28653i | ||||
\(883\) | −4.82205e55 | −0.512836 | −0.256418 | − | 0.966566i | \(-0.582542\pi\) | ||||
−0.256418 | + | 0.966566i | \(0.582542\pi\) | |||||||
\(884\) | 1.06717e56i | 1.11081i | ||||||||
\(885\) | 2.20017e55 | − | 5.32962e55i | 0.224148 | − | 0.542968i | ||||
\(886\) | 1.95128e56 | 1.94571 | ||||||||
\(887\) | 1.72116e56i | 1.67986i | 0.542693 | + | 0.839931i | \(0.317405\pi\) | ||||
−0.542693 | + | 0.839931i | \(0.682595\pi\) | |||||||
\(888\) | −7.29363e55 | − | 3.01095e55i | −0.696782 | − | 0.287645i | ||||
\(889\) | −6.10241e54 | −0.0570647 | ||||||||
\(890\) | − | 9.06041e55i | − | 0.829349i | ||||||
\(891\) | −1.83083e56 | + | 8.72160e53i | −1.64048 | + | 0.00781483i | ||||
\(892\) | −3.73100e56 | −3.27260 | ||||||||
\(893\) | 1.04649e56i | 0.898580i | ||||||||
\(894\) | 6.42371e54 | − | 1.55606e55i | 0.0539974 | − | 0.130802i | ||||
\(895\) | −2.10543e56 | −1.73262 | ||||||||
\(896\) | 9.95767e54i | 0.0802242i | ||||||||
\(897\) | 3.91639e55 | + | 1.61676e55i | 0.308908 | + | 0.127523i | ||||
\(898\) | 2.57390e56 | 1.98766 | ||||||||
\(899\) | 4.07820e55i | 0.308343i | ||||||||
\(900\) | −8.37739e54 | − | 8.33757e54i | −0.0620156 | − | 0.0617209i | ||||
\(901\) | −9.37856e55 | −0.679775 | ||||||||
\(902\) | − | 3.18962e56i | − | 2.26368i | ||||||
\(903\) | 7.44853e54 | − | 1.80431e55i | 0.0517611 | − | 0.125385i | ||||
\(904\) | −3.51716e55 | −0.239327 | ||||||||
\(905\) | − | 1.40064e56i | − | 0.933262i | ||||||
\(906\) | 1.45387e56 | + | 6.00186e55i | 0.948615 | + | 0.391606i | ||||
\(907\) | −3.53652e55 | −0.225963 | −0.112982 | − | 0.993597i | \(-0.536040\pi\) | ||||
−0.112982 | + | 0.993597i | \(0.536040\pi\) | |||||||
\(908\) | − | 1.71933e56i | − | 1.07579i | ||||||
\(909\) | −4.32957e55 | + | 4.35025e55i | −0.265296 | + | 0.266563i | ||||
\(910\) | −1.88174e55 | −0.112921 | ||||||||
\(911\) | − | 1.65257e55i | − | 0.0971205i | −0.998820 | − | 0.0485603i | \(-0.984537\pi\) | ||
0.998820 | − | 0.0485603i | \(-0.0154633\pi\) | |||||||
\(912\) | 1.89726e56 | − | 4.59586e56i | 1.09201 | − | 2.64524i | ||||
\(913\) | 1.88188e55 | 0.106083 | ||||||||
\(914\) | 3.86214e56i | 2.13231i | ||||||||
\(915\) | 2.60288e56 | + | 1.07452e56i | 1.40752 | + | 0.581050i | ||||
\(916\) | −4.71623e55 | −0.249794 | ||||||||
\(917\) | 2.82334e55i | 0.146469i | ||||||||
\(918\) | 4.15007e56 | − | 1.73641e56i | 2.10884 | − | 0.882352i | ||||
\(919\) | 3.29364e56 | 1.63939 | 0.819694 | − | 0.572802i | \(-0.194143\pi\) | ||||
0.819694 | + | 0.572802i | \(0.194143\pi\) | |||||||
\(920\) | 5.24657e56i | 2.55803i | ||||||||
\(921\) | −5.38795e55 | + | 1.30516e56i | −0.257330 | + | 0.623348i | ||||
\(922\) | −5.39401e56 | −2.52362 | ||||||||
\(923\) | − | 5.54776e55i | − | 0.254264i | ||||||
\(924\) | −1.36052e56 | − | 5.61650e55i | −0.610856 | − | 0.252173i | ||||
\(925\) | 2.20019e54 | 0.00967761 | ||||||||
\(926\) | 7.70276e56i | 3.31923i | ||||||||
\(927\) | −2.56094e56 | − | 2.54877e56i | −1.08115 | − | 1.07601i | ||||
\(928\) | −3.85976e56 | −1.59643 | ||||||||
\(929\) | − | 4.60431e56i | − | 1.86580i | −0.360130 | − | 0.932902i | \(-0.617268\pi\) | ||
0.360130 | − | 0.932902i | \(-0.382732\pi\) | |||||||
\(930\) | −7.74231e55 | + | 1.87547e56i | −0.307393 | + | 0.744620i | ||||
\(931\) | 2.69716e56 | 1.04921 | ||||||||
\(932\) | 3.20000e56i | 1.21968i | ||||||||
\(933\) | −2.70187e56 | − | 1.11538e56i | −1.00905 | − | 0.416555i | ||||
\(934\) | −2.54267e55 | −0.0930464 | ||||||||
\(935\) | − | 5.70767e56i | − | 2.04663i | ||||||
\(936\) | −2.02171e56 | + | 2.03137e56i | −0.710359 | + | 0.713751i | ||||
\(937\) | 1.45541e56 | 0.501109 | 0.250555 | − | 0.968102i | \(-0.419387\pi\) | ||||
0.250555 | + | 0.968102i | \(0.419387\pi\) | |||||||
\(938\) | − | 8.51771e55i | − | 0.287388i | ||||||
\(939\) | −1.70617e56 | + | 4.13297e56i | −0.564126 | + | 1.36652i | ||||
\(940\) | 6.48337e56 | 2.10074 | ||||||||
\(941\) | − | 1.33855e56i | − | 0.425042i | −0.977157 | − | 0.212521i | \(-0.931833\pi\) | ||
0.977157 | − | 0.212521i | \(-0.0681673\pi\) | |||||||
\(942\) | 7.81389e56 | + | 3.22572e56i | 2.43165 | + | 1.00383i | ||||
\(943\) | 2.21655e56 | 0.676012 | ||||||||
\(944\) | − | 5.12858e56i | − | 1.53296i | ||||||
\(945\) | 2.18102e55 | + | 5.21269e55i | 0.0638933 | + | 0.152707i | ||||
\(946\) | −8.88231e56 | −2.55032 | ||||||||
\(947\) | 1.51962e55i | 0.0427647i | 0.999771 | + | 0.0213823i | \(0.00680673\pi\) | ||||
−0.999771 | + | 0.0213823i | \(0.993193\pi\) | |||||||
\(948\) | 1.56400e55 | − | 3.78858e55i | 0.0431398 | − | 0.104500i | ||||
\(949\) | −5.99936e55 | −0.162198 | ||||||||
\(950\) | 2.67923e55i | 0.0710005i | ||||||||
\(951\) | 6.38820e56 | + | 2.63717e56i | 1.65939 | + | 0.685028i | ||||
\(952\) | 2.15611e56 | 0.548995 | ||||||||
\(953\) | 1.88445e56i | 0.470349i | 0.971953 | + | 0.235175i | \(0.0755662\pi\) | ||||
−0.971953 | + | 0.235175i | \(0.924434\pi\) | |||||||
\(954\) | −2.99455e56 | − | 2.98031e56i | −0.732676 | − | 0.729194i | ||||
\(955\) | −4.16668e56 | −0.999369 | ||||||||
\(956\) | − | 1.90006e57i | − | 4.46752i | ||||||
\(957\) | 1.97202e56 | − | 4.77697e56i | 0.454554 | − | 1.10110i | ||||
\(958\) | 3.74677e56 | 0.846666 | ||||||||
\(959\) | 1.36272e56i | 0.301893i | ||||||||
\(960\) | −6.25153e56 | − | 2.58075e56i | −1.35779 | − | 0.560522i | ||||
\(961\) | −3.84940e56 | −0.819687 | ||||||||
\(962\) | − | 8.94914e55i | − | 0.186833i | ||||||
\(963\) | −5.61040e56 | + | 5.63719e56i | −1.14840 | + | 1.15389i | ||||
\(964\) | 4.35731e56 | 0.874489 | ||||||||
\(965\) | 7.31237e56i | 1.43893i | ||||||||
\(966\) | 5.47928e55 | − | 1.32728e56i | 0.105720 | − | 0.256093i | ||||
\(967\) | 1.89028e56 | 0.357621 | 0.178810 | − | 0.983884i | \(-0.442775\pi\) | ||||
0.178810 | + | 0.983884i | \(0.442775\pi\) | |||||||
\(968\) | 2.50918e57i | 4.65480i | ||||||||
\(969\) | −6.71452e56 | − | 2.77188e56i | −1.22141 | − | 0.504223i | ||||
\(970\) | −1.45584e57 | −2.59687 | ||||||||
\(971\) | − | 3.38305e56i | − | 0.591757i | −0.955226 | − | 0.295878i | \(-0.904388\pi\) | ||
0.955226 | − | 0.295878i | \(-0.0956123\pi\) | |||||||
\(972\) | 1.33697e57 | + | 5.44488e56i | 2.29331 | + | 0.933962i | ||||
\(973\) | −1.12744e54 | −0.00189649 | ||||||||
\(974\) | − | 5.11270e56i | − | 0.843393i | ||||||
\(975\) | 3.04935e54 | − | 7.38664e54i | 0.00493309 | − | 0.0119498i | ||||
\(976\) | 2.50470e57 | 3.97383 | ||||||||
\(977\) | 2.50646e56i | 0.389999i | 0.980803 | + | 0.194999i | \(0.0624705\pi\) | ||||
−0.980803 | + | 0.194999i | \(0.937529\pi\) | |||||||
\(978\) | −1.84866e57 | − | 7.63161e56i | −2.82110 | − | 1.16460i | ||||
\(979\) | 4.79172e56 | 0.717167 | ||||||||
\(980\) | − | 1.67098e57i | − | 2.45288i | ||||||
\(981\) | −3.07875e56 | − | 3.06412e56i | −0.443265 | − | 0.441158i | ||||
\(982\) | 2.89422e56 | 0.408708 | ||||||||
\(983\) | 9.01690e56i | 1.24894i | 0.781050 | + | 0.624468i | \(0.214684\pi\) | ||||
−0.781050 | + | 0.624468i | \(0.785316\pi\) | |||||||
\(984\) | −5.72110e56 | + | 1.38586e57i | −0.777272 | + | 1.88284i | ||||
\(985\) | −4.99954e56 | −0.666257 | ||||||||
\(986\) | 1.26986e57i | 1.65995i | ||||||||
\(987\) | −9.77797e55 | − | 4.03653e55i | −0.125378 | − | 0.0517586i | ||||
\(988\) | 7.76267e56 | 0.976403 | ||||||||
\(989\) | − | 6.17255e56i | − | 0.761614i | ||||||
\(990\) | 1.81378e57 | − | 1.82244e57i | 2.19541 | − | 2.20590i | ||||
\(991\) | 1.10910e57 | 1.31696 | 0.658480 | − | 0.752598i | \(-0.271200\pi\) | ||||
0.658480 | + | 0.752598i | \(0.271200\pi\) | |||||||
\(992\) | 8.01425e56i | 0.933557i | ||||||||
\(993\) | 2.61240e56 | − | 6.32819e56i | 0.298541 | − | 0.723175i | ||||
\(994\) | −1.88016e56 | −0.210792 | ||||||||
\(995\) | 1.75367e57i | 1.92890i | ||||||||
\(996\) | −1.37155e56 | − | 5.66204e55i | −0.148008 | − | 0.0611006i | ||||
\(997\) | 2.04331e56 | 0.216335 | 0.108168 | − | 0.994133i | \(-0.465502\pi\) | ||||
0.108168 | + | 0.994133i | \(0.465502\pi\) | |||||||
\(998\) | 5.04041e56i | 0.523583i | ||||||||
\(999\) | −2.47904e56 | + | 1.03724e56i | −0.252662 | + | 0.105715i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3.39.b.a.2.12 | yes | 12 | |
3.2 | odd | 2 | inner | 3.39.b.a.2.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.39.b.a.2.1 | ✓ | 12 | 3.2 | odd | 2 | inner | |
3.39.b.a.2.12 | yes | 12 | 1.1 | even | 1 | trivial |