Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,33,Mod(19,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 33, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36.19");
S:= CuspForms(chi, 33);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 33 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.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: | \(233.519958512\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + \cdots + 14\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{182}\cdot 3^{29}\cdot 5^{6} \) |
Twist minimal: | no (minimal twist has level 4) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.5 | ||
Root | \(-1.70126e9 - 1.38274e12i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 36.19 |
Dual form | 36.33.d.b.19.6 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32011.4 | − | 57186.0i | −0.488456 | − | 0.872589i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.24550e9 | + | 3.66121e9i | −0.522822 | + | 0.852442i | ||||
\(5\) | 4.45746e10 | 0.292124 | 0.146062 | − | 0.989275i | \(-0.453340\pi\) | ||||
0.146062 | + | 0.989275i | \(0.453340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.42477e13i | 1.33144i | 0.746201 | + | 0.665721i | \(0.231876\pi\) | ||||
−0.746201 | + | 0.665721i | \(0.768124\pi\) | |||||||
\(8\) | 2.81252e14 | + | 1.12108e13i | 0.999207 | + | 0.0398287i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.42690e15 | − | 2.54904e15i | −0.142690 | − | 0.254904i | ||||
\(11\) | 2.28722e16i | 0.497765i | 0.968534 | + | 0.248883i | \(0.0800633\pi\) | ||||
−0.968534 | + | 0.248883i | \(0.919937\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.09707e17 | −1.06656 | −0.533280 | − | 0.845939i | \(-0.679041\pi\) | ||||
−0.533280 | + | 0.845939i | \(0.679041\pi\) | |||||||
\(14\) | 2.53035e18 | − | 1.41643e18i | 1.16180 | − | 0.650350i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.36217e18 | − | 1.64425e19i | −0.453314 | − | 0.891351i | ||||
\(17\) | 5.13492e19 | 1.05524 | 0.527619 | − | 0.849481i | \(-0.323085\pi\) | ||||
0.527619 | + | 0.849481i | \(0.323085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 9.08704e19i | − | 0.315039i | −0.987516 | − | 0.157520i | \(-0.949650\pi\) | ||
0.987516 | − | 0.157520i | \(-0.0503498\pi\) | |||||||
\(20\) | −1.00093e20 | + | 1.63197e20i | −0.152729 | + | 0.249019i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.30797e21 | − | 7.32171e20i | 0.434344 | − | 0.243136i | ||||
\(23\) | 3.40920e21i | 0.555914i | 0.960594 | + | 0.277957i | \(0.0896573\pi\) | ||||
−0.960594 | + | 0.277957i | \(0.910343\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.12962e22 | −0.914663 | ||||||||
\(26\) | 2.27187e22 | + | 4.05853e22i | 0.520967 | + | 0.930668i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.62000e23 | − | 9.93584e22i | −1.13498 | − | 0.696107i | ||||
\(29\) | 9.75903e22 | 0.389977 | 0.194988 | − | 0.980806i | \(-0.437533\pi\) | ||||
0.194988 | + | 0.980806i | \(0.437533\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.90972e23i | − | 1.22483i | −0.790535 | − | 0.612416i | \(-0.790198\pi\) | ||
0.790535 | − | 0.612416i | \(-0.209802\pi\) | |||||||
\(32\) | −6.72597e23 | + | 1.00455e24i | −0.556359 | + | 0.830942i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.64376e24 | − | 2.93645e24i | −0.515437 | − | 0.920789i | ||||
\(35\) | 1.97232e24i | 0.388946i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.36985e25 | −1.11031 | −0.555155 | − | 0.831747i | \(-0.687341\pi\) | ||||
−0.555155 | + | 0.831747i | \(0.687341\pi\) | |||||||
\(38\) | −5.19651e24 | + | 2.90889e24i | −0.274900 | + | 0.153883i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.25367e25 | + | 4.99716e23i | 0.291892 | + | 0.0116349i | ||||
\(41\) | −9.45224e25 | −1.48249 | −0.741247 | − | 0.671232i | \(-0.765765\pi\) | ||||
−0.741247 | + | 0.671232i | \(0.765765\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.05450e26i | 1.50387i | 0.659235 | + | 0.751937i | \(0.270880\pi\) | ||||
−0.659235 | + | 0.751937i | \(0.729120\pi\) | |||||||
\(44\) | −8.37398e25 | − | 5.13596e25i | −0.424316 | − | 0.260243i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.94959e26 | − | 1.09133e26i | 0.485084 | − | 0.271539i | ||||
\(47\) | − | 6.70394e25i | − | 0.118240i | −0.998251 | − | 0.0591200i | \(-0.981171\pi\) | ||
0.998251 | − | 0.0591200i | \(-0.0188295\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.53431e26 | −0.772736 | ||||||||
\(50\) | 6.81721e26 | + | 1.21784e27i | 0.446773 | + | 0.798125i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.59365e27 | − | 2.59839e27i | 0.557621 | − | 0.909180i | ||||
\(53\) | 3.12663e27 | 0.806609 | 0.403305 | − | 0.915066i | \(-0.367861\pi\) | ||||
0.403305 | + | 0.915066i | \(0.367861\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.01952e27i | 0.145409i | ||||||||
\(56\) | −4.96051e26 | + | 1.24447e28i | −0.0530296 | + | 1.33038i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.12400e27 | − | 5.58079e27i | −0.190486 | − | 0.340289i | ||||
\(59\) | − | 4.03005e28i | − | 1.86930i | −0.355572 | − | 0.934649i | \(-0.615714\pi\) | ||
0.355572 | − | 0.934649i | \(-0.384286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.61340e28 | −1.25529 | −0.627644 | − | 0.778500i | \(-0.715981\pi\) | ||||
−0.627644 | + | 0.778500i | \(0.715981\pi\) | |||||||
\(62\) | −5.09511e28 | + | 2.85213e28i | −1.06878 | + | 0.598276i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.89768e28 | + | 6.30610e27i | 0.996827 | + | 0.0795942i | ||||
\(65\) | −3.16349e28 | −0.311568 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.83386e29i | 1.71863i | 0.511448 | + | 0.859314i | \(0.329109\pi\) | ||||
−0.511448 | + | 0.859314i | \(0.670891\pi\) | |||||||
\(68\) | −1.15305e29 | + | 1.88000e29i | −0.551702 | + | 0.899529i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.12789e29 | − | 6.31369e28i | 0.339390 | − | 0.189983i | ||||
\(71\) | 3.78115e29i | 0.906756i | 0.891318 | + | 0.453378i | \(0.149781\pi\) | ||||
−0.891318 | + | 0.453378i | \(0.850219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.28433e29 | −1.27377 | −0.636886 | − | 0.770958i | \(-0.719778\pi\) | ||||
−0.636886 | + | 0.770958i | \(0.719778\pi\) | |||||||
\(74\) | 4.38508e29 | + | 7.83360e29i | 0.542337 | + | 0.968845i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.32696e29 | + | 2.04050e29i | 0.268553 | + | 0.164710i | ||||
\(77\) | −1.01204e30 | −0.662745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.22124e30i | − | 1.39955i | −0.714362 | − | 0.699776i | \(-0.753283\pi\) | ||
0.714362 | − | 0.699776i | \(-0.246717\pi\) | |||||||
\(80\) | −3.72740e29 | − | 7.32919e29i | −0.132424 | − | 0.260385i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.02580e30 | + | 5.40536e30i | 0.724133 | + | 1.29361i | ||||
\(83\) | 3.96300e29i | 0.0781223i | 0.999237 | + | 0.0390611i | \(0.0124367\pi\) | ||||
−0.999237 | + | 0.0390611i | \(0.987563\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.28887e30 | 0.308261 | ||||||||
\(86\) | 1.17489e31 | − | 6.57676e30i | 1.31226 | − | 0.734576i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.56415e29 | + | 6.43284e30i | −0.0198253 | + | 0.497370i | ||||
\(89\) | −1.44641e31 | −0.933363 | −0.466682 | − | 0.884425i | \(-0.654551\pi\) | ||||
−0.466682 | + | 0.884425i | \(0.654551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.14029e31i | − | 1.42006i | ||||||
\(92\) | −1.24818e31 | − | 7.65538e30i | −0.473884 | − | 0.290644i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.83372e30 | + | 2.14603e30i | −0.103175 | + | 0.0577550i | ||||
\(95\) | − | 4.05052e30i | − | 0.0920307i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.69349e30 | 0.0926896 | 0.0463448 | − | 0.998926i | \(-0.485243\pi\) | ||||
0.0463448 | + | 0.998926i | \(0.485243\pi\) | |||||||
\(98\) | 2.73195e31 | + | 4.88043e31i | 0.377447 | + | 0.674280i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.78206e31 | − | 7.79697e31i | 0.478206 | − | 0.779697i | ||||
\(101\) | 1.45062e32 | 1.23712 | 0.618559 | − | 0.785738i | \(-0.287717\pi\) | ||||
0.618559 | + | 0.785738i | \(0.287717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.12151e32i | 1.32206i | 0.750362 | + | 0.661028i | \(0.229879\pi\) | ||||
−0.750362 | + | 0.661028i | \(0.770121\pi\) | |||||||
\(104\) | −1.99606e32 | − | 7.95637e30i | −1.06571 | − | 0.0424797i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.00088e32 | − | 1.78800e32i | −0.393993 | − | 0.703838i | ||||
\(107\) | − | 4.23255e32i | − | 1.43371i | −0.697222 | − | 0.716855i | \(-0.745581\pi\) | ||
0.697222 | − | 0.716855i | \(-0.254419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.59934e32 | 1.15844 | 0.579218 | − | 0.815173i | \(-0.303358\pi\) | ||||
0.579218 | + | 0.815173i | \(0.303358\pi\) | |||||||
\(110\) | 5.83022e31 | − | 3.26362e31i | 0.126883 | − | 0.0710260i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.27544e32 | − | 3.70007e32i | 1.18678 | − | 0.603561i | ||||
\(113\) | 5.97121e32 | 0.844904 | 0.422452 | − | 0.906385i | \(-0.361170\pi\) | ||||
0.422452 | + | 0.906385i | \(0.361170\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.51964e32i | 0.162396i | ||||||||
\(116\) | −2.19139e32 | + | 3.57298e32i | −0.203888 | + | 0.332432i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.30462e33 | + | 1.29008e33i | −1.63113 | + | 0.913069i | ||||
\(119\) | 2.27208e33i | 1.40499i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.58824e33 | 0.752230 | ||||||||
\(122\) | 1.47681e33 | + | 2.63822e33i | 0.613153 | + | 1.09535i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.26203e33 | + | 2.00068e33i | 1.04410 | + | 0.640370i | ||||
\(125\) | −1.98710e33 | −0.559320 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.79574e33i | − | 0.828775i | −0.910101 | − | 0.414387i | \(-0.863996\pi\) | ||
0.910101 | − | 0.414387i | \(-0.136004\pi\) | |||||||
\(128\) | −2.16754e33 | − | 4.71823e33i | −0.417453 | − | 0.908699i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.01268e33 | + | 1.80907e33i | 0.152187 | + | 0.271871i | ||||
\(131\) | − | 2.68711e33i | − | 0.357227i | −0.983919 | − | 0.178614i | \(-0.942839\pi\) | ||
0.983919 | − | 0.178614i | \(-0.0571612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.02081e33 | 0.419457 | ||||||||
\(134\) | 1.62057e34 | − | 9.07160e33i | 1.49966 | − | 0.839474i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.44420e34 | + | 5.75664e32i | 1.05440 | + | 0.0420288i | ||||
\(137\) | 1.03106e34 | 0.669509 | 0.334755 | − | 0.942305i | \(-0.391347\pi\) | ||||
0.334755 | + | 0.942305i | \(0.391347\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.16304e33i | − | 0.214375i | −0.994239 | − | 0.107188i | \(-0.965815\pi\) | ||
0.994239 | − | 0.107188i | \(-0.0341845\pi\) | |||||||
\(140\) | −7.22109e33 | − | 4.42886e33i | −0.331554 | − | 0.203350i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.16229e34 | − | 1.21040e34i | 0.791225 | − | 0.442910i | ||||
\(143\) | − | 1.62325e34i | − | 0.530896i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.35005e33 | 0.113922 | ||||||||
\(146\) | 2.65193e34 | + | 4.73748e34i | 0.622181 | + | 1.11148i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.07600e34 | − | 5.01530e34i | 0.580495 | − | 0.946475i | ||||
\(149\) | 6.24485e34 | 1.05814 | 0.529069 | − | 0.848579i | \(-0.322541\pi\) | ||||
0.529069 | + | 0.848579i | \(0.322541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.99336e34i | 0.409759i | 0.978787 | + | 0.204879i | \(0.0656802\pi\) | ||||
−0.978787 | + | 0.204879i | \(0.934320\pi\) | |||||||
\(152\) | 1.01873e33 | − | 2.55575e34i | 0.0125476 | − | 0.314789i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.23969e34 | + | 5.78745e34i | 0.323722 | + | 0.578304i | ||||
\(155\) | − | 3.97147e34i | − | 0.357803i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.31988e35 | 0.968593 | 0.484297 | − | 0.874904i | \(-0.339076\pi\) | ||||
0.484297 | + | 0.874904i | \(0.339076\pi\) | |||||||
\(158\) | −1.84210e35 | + | 1.03116e35i | −1.22123 | + | 0.683619i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.99807e34 | + | 4.47773e34i | −0.162526 | + | 0.242738i | ||||
\(161\) | −1.50849e35 | −0.740167 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.20065e35i | 0.483522i | 0.970336 | + | 0.241761i | \(0.0777250\pi\) | ||||
−0.970336 | + | 0.241761i | \(0.922275\pi\) | |||||||
\(164\) | 2.12250e35 | − | 3.46066e35i | 0.775081 | − | 1.26374i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.26628e34 | − | 1.26861e34i | 0.0681686 | − | 0.0381593i | ||||
\(167\) | 6.52369e35i | 1.78250i | 0.453511 | + | 0.891251i | \(0.350171\pi\) | ||||
−0.453511 | + | 0.891251i | \(0.649829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.09044e34 | 0.137550 | ||||||||
\(170\) | −7.32700e34 | − | 1.30891e35i | −0.150572 | − | 0.268985i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.52197e35 | − | 4.61340e35i | −1.28197 | − | 0.786259i | ||||
\(173\) | 2.42455e35 | 0.376611 | 0.188305 | − | 0.982111i | \(-0.439701\pi\) | ||||
0.188305 | + | 0.982111i | \(0.439701\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 9.42306e35i | − | 1.21782i | ||||||
\(176\) | 3.76076e35 | − | 1.91261e35i | 0.443683 | − | 0.225644i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.63016e35 | + | 8.27143e35i | 0.455907 | + | 0.814442i | ||||
\(179\) | − | 2.94586e35i | − | 0.265194i | −0.991170 | − | 0.132597i | \(-0.957668\pi\) | ||
0.991170 | − | 0.132597i | \(-0.0423316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.89528e35 | −0.670351 | −0.335176 | − | 0.942156i | \(-0.608796\pi\) | ||||
−0.335176 | + | 0.942156i | \(0.608796\pi\) | |||||||
\(182\) | −1.79580e36 | + | 1.00525e36i | −1.23913 | + | 0.693637i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.82198e34 | + | 9.58844e35i | −0.0221413 | + | 0.555473i | ||||
\(185\) | −6.10604e35 | −0.324349 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.17447e36i | 0.525261i | ||||||||
\(188\) | 2.45445e35 | + | 1.50537e35i | 0.100793 | + | 0.0618185i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.31633e35 | + | 1.29663e35i | −0.0803049 | + | 0.0449529i | ||||
\(191\) | − | 6.11925e36i | − | 1.95058i | −0.220924 | − | 0.975291i | \(-0.570907\pi\) | ||
0.220924 | − | 0.975291i | \(-0.429093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.19445e36 | −1.94125 | −0.970623 | − | 0.240607i | \(-0.922653\pi\) | ||||
−0.970623 | + | 0.240607i | \(0.922653\pi\) | |||||||
\(194\) | −1.82257e35 | − | 3.25588e35i | −0.0452748 | − | 0.0808799i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.91638e36 | − | 3.12459e36i | 0.404003 | − | 0.658712i | ||||
\(197\) | −8.26602e35 | −0.160634 | −0.0803169 | − | 0.996769i | \(-0.525593\pi\) | ||||
−0.0803169 | + | 0.996769i | \(0.525593\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.58369e36i | − | 0.261831i | −0.991394 | − | 0.130916i | \(-0.958208\pi\) | ||
0.991394 | − | 0.130916i | \(-0.0417917\pi\) | |||||||
\(200\) | −5.98958e36 | − | 2.38747e35i | −0.913938 | − | 0.0364298i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.64364e36 | − | 8.29550e36i | −0.604277 | − | 1.07950i | ||||
\(203\) | 4.31814e36i | 0.519231i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.21330e36 | −0.433073 | ||||||||
\(206\) | 1.21321e37 | − | 6.79126e36i | 1.15361 | − | 0.645765i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.93469e36 | + | 1.16694e37i | 0.483487 | + | 0.950679i | ||||
\(209\) | 2.07840e36 | 0.156816 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.90069e36i | − | 0.252710i | −0.991985 | − | 0.126355i | \(-0.959672\pi\) | ||
0.991985 | − | 0.126355i | \(-0.0403278\pi\) | |||||||
\(212\) | −7.02087e36 | + | 1.14473e37i | −0.421713 | + | 0.687588i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.42042e37 | + | 1.35490e37i | −1.25104 | + | 0.700304i | ||||
\(215\) | 9.15787e36i | 0.439318i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.94234e37 | 1.63079 | ||||||||
\(218\) | −1.47232e37 | − | 2.63018e37i | −0.565844 | − | 1.01084i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.73267e36 | − | 2.28933e36i | −0.123953 | − | 0.0760232i | ||||
\(221\) | −3.64428e37 | −1.12548 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.06246e37i | − | 0.284076i | −0.989861 | − | 0.142038i | \(-0.954635\pi\) | ||
0.989861 | − | 0.142038i | \(-0.0453655\pi\) | |||||||
\(224\) | −4.44489e37 | − | 2.97609e37i | −1.10635 | − | 0.740759i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.91147e37 | − | 3.41469e37i | −0.412698 | − | 0.737253i | ||||
\(227\) | 9.86501e36i | 0.198465i | 0.995064 | + | 0.0992325i | \(0.0316388\pi\) | ||||
−0.995064 | + | 0.0992325i | \(0.968361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.89076e37 | −0.505410 | −0.252705 | − | 0.967543i | \(-0.581320\pi\) | ||||
−0.252705 | + | 0.967543i | \(0.581320\pi\) | |||||||
\(230\) | 8.69021e36 | − | 4.86458e36i | 0.141705 | − | 0.0793232i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.74474e37 | + | 1.09406e36i | 0.389667 | + | 0.0155323i | ||||
\(233\) | 5.22180e37 | 0.692031 | 0.346015 | − | 0.938229i | \(-0.387535\pi\) | ||||
0.346015 | + | 0.938229i | \(0.387535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.98826e36i | − | 0.0345408i | ||||||
\(236\) | 1.47549e38 | + | 9.04950e37i | 1.59347 | + | 0.977310i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.29931e38 | − | 7.27326e37i | 1.22598 | − | 0.686274i | ||||
\(239\) | − | 2.02819e38i | − | 1.78955i | −0.446522 | − | 0.894773i | \(-0.647337\pi\) | ||
0.446522 | − | 0.894773i | \(-0.352663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.98788e37 | 0.230723 | 0.115361 | − | 0.993324i | \(-0.463197\pi\) | ||||
0.115361 | + | 0.993324i | \(0.463197\pi\) | |||||||
\(242\) | −5.08419e37 | − | 9.08251e37i | −0.367431 | − | 0.656387i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.03594e38 | − | 1.68906e38i | 0.656293 | − | 1.07006i | ||||
\(245\) | −3.80413e37 | −0.225735 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.44914e37i | 0.336009i | ||||||||
\(248\) | 9.98849e36 | − | 2.50587e38i | 0.0487835 | − | 1.22386i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.36100e37 | + | 1.13634e38i | 0.273203 | + | 0.488056i | ||||
\(251\) | − | 4.02684e38i | − | 1.62250i | −0.584698 | − | 0.811251i | \(-0.698787\pi\) | ||
0.584698 | − | 0.811251i | \(-0.301213\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.79759e37 | −0.276715 | ||||||||
\(254\) | −2.17063e38 | + | 1.21507e38i | −0.723180 | + | 0.404820i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.00431e38 | + | 2.74990e38i | −0.589013 | + | 0.808124i | ||||
\(257\) | −2.02522e38 | −0.559167 | −0.279583 | − | 0.960121i | \(-0.590196\pi\) | ||||
−0.279583 | + | 0.960121i | \(0.590196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6.06126e38i | − | 1.47831i | ||||||
\(260\) | 7.10363e37 | − | 1.15822e38i | 0.162895 | − | 0.265594i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.53665e38 | + | 8.60182e37i | −0.311713 | + | 0.174490i | ||||
\(263\) | 4.37514e38i | 0.835027i | 0.908671 | + | 0.417513i | \(0.137098\pi\) | ||||
−0.908671 | + | 0.417513i | \(0.862902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.39369e38 | 0.235630 | ||||||||
\(266\) | −1.28712e38 | − | 2.29934e38i | −0.204886 | − | 0.366013i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.03754e39 | − | 6.36345e38i | −1.46503 | − | 0.898537i | ||||
\(269\) | −9.84294e38 | −1.30945 | −0.654724 | − | 0.755868i | \(-0.727215\pi\) | ||||
−0.654724 | + | 0.755868i | \(0.727215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.82572e38i | − | 0.688400i | −0.938896 | − | 0.344200i | \(-0.888150\pi\) | ||
0.938896 | − | 0.344200i | \(-0.111850\pi\) | |||||||
\(272\) | −4.29390e38 | − | 8.44310e38i | −0.478354 | − | 0.940588i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.30058e38 | − | 5.89624e38i | −0.327026 | − | 0.584206i | ||||
\(275\) | − | 4.87090e38i | − | 0.455288i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.68908e38 | −0.640027 | −0.320013 | − | 0.947413i | \(-0.603687\pi\) | ||||
−0.320013 | + | 0.947413i | \(0.603687\pi\) | |||||||
\(278\) | −2.38068e38 | + | 1.33265e38i | −0.187061 | + | 0.104713i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.21113e37 | + | 5.54719e38i | −0.0154912 | + | 0.388638i | ||||
\(281\) | 3.37707e38 | 0.223480 | 0.111740 | − | 0.993737i | \(-0.464358\pi\) | ||||
0.111740 | + | 0.993737i | \(0.464358\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.20946e39i | 1.30528i | 0.757668 | + | 0.652641i | \(0.226339\pi\) | ||||
−0.757668 | + | 0.652641i | \(0.773661\pi\) | |||||||
\(284\) | −1.38436e39 | − | 8.49059e38i | −0.772956 | − | 0.474072i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.28273e38 | + | 5.19627e38i | −0.463254 | + | 0.259319i | ||||
\(287\) | − | 4.18240e39i | − | 1.97385i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.68825e38 | 0.113528 | ||||||||
\(290\) | −1.39251e38 | − | 2.48762e38i | −0.0556457 | − | 0.0994067i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.86025e39 | − | 3.03307e39i | 0.665956 | − | 1.08582i | ||||
\(293\) | −2.28152e39 | −0.773291 | −0.386646 | − | 0.922228i | \(-0.626366\pi\) | ||||
−0.386646 | + | 0.922228i | \(0.626366\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.79638e39i | − | 0.546067i | ||||||
\(296\) | −3.85272e39 | − | 1.53571e38i | −1.10943 | − | 0.0442222i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.99907e39 | − | 3.57118e39i | −0.516853 | − | 0.923319i | ||||
\(299\) | − | 2.41953e39i | − | 0.592916i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.09070e39 | −2.00232 | ||||||||
\(302\) | 1.71178e39 | − | 9.58218e38i | 0.357551 | − | 0.200149i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.49414e39 | + | 7.59874e38i | −0.280811 | + | 0.142812i | ||||
\(305\) | −2.05641e39 | −0.366700 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.88725e39i | − | 1.58804i | −0.607892 | − | 0.794020i | \(-0.707984\pi\) | ||
0.607892 | − | 0.794020i | \(-0.292016\pi\) | |||||||
\(308\) | 2.27254e39 | − | 3.70529e39i | 0.346498 | − | 0.564952i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.27113e39 | + | 1.27133e39i | −0.312215 | + | 0.174771i | ||||
\(311\) | 2.75970e39i | 0.360326i | 0.983637 | + | 0.180163i | \(0.0576625\pi\) | ||||
−0.983637 | + | 0.180163i | \(0.942337\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.86301e39 | 0.455215 | 0.227607 | − | 0.973753i | \(-0.426910\pi\) | ||||
0.227607 | + | 0.973753i | \(0.426910\pi\) | |||||||
\(314\) | −4.22514e39 | − | 7.54789e39i | −0.473115 | − | 0.845183i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.17936e40 | + | 7.23330e39i | 1.19304 | + | 0.731717i | ||||
\(317\) | −2.74902e39 | −0.264381 | −0.132190 | − | 0.991224i | \(-0.542201\pi\) | ||||
−0.132190 | + | 0.991224i | \(0.542201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.23210e39i | 0.194117i | ||||||||
\(320\) | 3.52036e39 | + | 2.81092e38i | 0.291197 | + | 0.0232514i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.82890e39 | + | 8.62647e39i | 0.361539 | + | 0.645861i | ||||
\(323\) | − | 4.66612e39i | − | 0.332442i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.51140e40 | 0.975543 | ||||||||
\(326\) | 6.86606e39 | − | 3.84347e39i | 0.421916 | − | 0.236179i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.65846e40 | − | 1.05967e39i | −1.48132 | − | 0.0590458i | ||||
\(329\) | 2.96634e39 | 0.157430 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.88587e39i | 0.139005i | 0.997582 | + | 0.0695023i | \(0.0221411\pi\) | ||||
−0.997582 | + | 0.0695023i | \(0.977859\pi\) | |||||||
\(332\) | −1.45094e39 | − | 8.89894e38i | −0.0665947 | − | 0.0408441i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.73064e40 | − | 2.08833e40i | 1.55539 | − | 0.870673i | ||||
\(335\) | 1.26318e40i | 0.502053i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.46962e39 | −0.125373 | −0.0626865 | − | 0.998033i | \(-0.519967\pi\) | ||||
−0.0626865 | + | 0.998033i | \(0.519967\pi\) | |||||||
\(338\) | −1.94964e39 | − | 3.48288e39i | −0.0671873 | − | 0.120025i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.13967e39 | + | 8.38003e39i | −0.161166 | + | 0.262774i | ||||
\(341\) | 2.03785e40 | 0.609679 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.11060e40i | 0.302589i | ||||||||
\(344\) | −2.30326e39 | + | 5.77832e40i | −0.0598973 | + | 1.50268i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.76132e39 | − | 1.38650e40i | −0.183958 | − | 0.328626i | ||||
\(347\) | − | 6.04708e39i | − | 0.136859i | −0.997656 | − | 0.0684296i | \(-0.978201\pi\) | ||
0.997656 | − | 0.0684296i | \(-0.0217989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.56362e40 | 0.529232 | 0.264616 | − | 0.964354i | \(-0.414755\pi\) | ||||
0.264616 | + | 0.964354i | \(0.414755\pi\) | |||||||
\(350\) | −5.38867e40 | + | 3.01646e40i | −1.06266 | + | 0.594851i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.29762e40 | − | 1.53837e40i | −0.413614 | − | 0.276936i | ||||
\(353\) | 6.22211e40 | 1.07039 | 0.535195 | − | 0.844728i | \(-0.320238\pi\) | ||||
0.535195 | + | 0.844728i | \(0.320238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.68543e40i | 0.264885i | ||||||||
\(356\) | 3.24792e40 | − | 5.29560e40i | 0.487983 | − | 0.795638i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.68462e40 | + | 9.43012e39i | −0.231405 | + | 0.129535i | ||||
\(359\) | − | 6.52926e40i | − | 0.857735i | −0.903367 | − | 0.428867i | \(-0.858913\pi\) | ||
0.903367 | − | 0.428867i | \(-0.141087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.49410e40 | 0.900750 | ||||||||
\(362\) | 2.84751e40 | + | 5.08685e40i | 0.327437 | + | 0.584941i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.14973e41 | + | 7.05153e40i | 1.21052 | + | 0.742440i | ||||
\(365\) | −3.69271e40 | −0.372100 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.37914e39i | − | 0.0219666i | −0.999940 | − | 0.0109833i | \(-0.996504\pi\) | ||
0.999940 | − | 0.0109833i | \(-0.00349617\pi\) | |||||||
\(368\) | 5.60559e40 | − | 2.85083e40i | 0.495514 | − | 0.252004i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.95463e40 | + | 3.49180e40i | 0.158430 | + | 0.283023i | ||||
\(371\) | 1.38346e41i | 1.07395i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.72340e41 | −1.22756 | −0.613782 | − | 0.789476i | \(-0.710352\pi\) | ||||
−0.613782 | + | 0.789476i | \(0.710352\pi\) | |||||||
\(374\) | 6.71630e40 | − | 3.75964e40i | 0.458337 | − | 0.256567i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.51564e38 | − | 1.88549e40i | 0.00470935 | − | 0.118146i | ||||
\(377\) | −6.92605e40 | −0.415933 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.76915e41i | − | 0.976199i | −0.872788 | − | 0.488099i | \(-0.837690\pi\) | ||
0.872788 | − | 0.488099i | \(-0.162310\pi\) | |||||||
\(380\) | 1.48298e40 | + | 9.09545e39i | 0.0784508 | + | 0.0481157i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.49935e41 | + | 1.95886e41i | −1.70206 | + | 0.952773i | ||||
\(383\) | 4.14172e41i | 1.93197i | 0.258600 | + | 0.965984i | \(0.416739\pi\) | ||||
−0.258600 | + | 0.965984i | \(0.583261\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.51113e40 | −0.193604 | ||||||||
\(386\) | 2.30304e41 | + | 4.11421e41i | 0.948212 | + | 1.69391i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.27848e40 | + | 2.08451e40i | −0.0484602 | + | 0.0790125i | ||||
\(389\) | −9.84662e40 | −0.358174 | −0.179087 | − | 0.983833i | \(-0.557314\pi\) | ||||
−0.179087 | + | 0.983833i | \(0.557314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.75060e41i | 0.586622i | ||||||||
\(392\) | −2.40029e41 | − | 9.56762e39i | −0.772122 | − | 0.0307770i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.64607e40 | + | 4.72701e40i | 0.0784625 | + | 0.140167i | ||||
\(395\) | − | 1.43585e41i | − | 0.408843i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.57975e40 | 0.0677530 | 0.0338765 | − | 0.999426i | \(-0.489215\pi\) | ||||
0.0338765 | + | 0.999426i | \(0.489215\pi\) | |||||||
\(398\) | −9.05649e40 | + | 5.06962e40i | −0.228471 | + | 0.127893i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.78082e41 | + | 3.50163e41i | 0.414630 | + | 0.815286i | ||||
\(401\) | 1.27557e41 | 0.285360 | 0.142680 | − | 0.989769i | \(-0.454428\pi\) | ||||
0.142680 | + | 0.989769i | \(0.454428\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.32329e41i | 1.30636i | ||||||||
\(404\) | −3.25737e41 | + | 5.31102e41i | −0.646793 | + | 1.05457i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.46937e41 | − | 1.38230e41i | 0.453075 | − | 0.253621i | ||||
\(407\) | − | 3.13314e41i | − | 0.552674i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.78521e41 | 1.26969 | 0.634844 | − | 0.772640i | \(-0.281064\pi\) | ||||
0.634844 | + | 0.772640i | \(0.281064\pi\) | |||||||
\(410\) | 1.34874e41 | + | 2.40942e41i | 0.211537 | + | 0.377894i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.76729e41 | − | 4.76386e41i | −1.12698 | − | 0.691200i | ||||
\(413\) | 1.78321e42 | 2.48886 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.76649e40i | 0.0228214i | ||||||||
\(416\) | 4.77346e41 | − | 7.12934e41i | 0.593390 | − | 0.886250i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.65327e40 | − | 1.18856e41i | −0.0765975 | − | 0.136836i | ||||
\(419\) | 4.49421e41i | 0.498000i | 0.968503 | + | 0.249000i | \(0.0801019\pi\) | ||||
−0.968503 | + | 0.249000i | \(0.919898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.94700e40 | −0.0507959 | −0.0253979 | − | 0.999677i | \(-0.508085\pi\) | ||||
−0.0253979 | + | 0.999677i | \(0.508085\pi\) | |||||||
\(422\) | −2.23065e41 | + | 1.24867e41i | −0.220512 | + | 0.123438i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.79371e41 | + | 3.50520e40i | 0.805969 | + | 0.0321262i | ||||
\(425\) | −1.09354e42 | −0.965188 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2.04132e42i | − | 1.67134i | ||||||
\(428\) | 1.54963e42 | + | 9.50421e41i | 1.22216 | + | 0.749576i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.23702e41 | − | 2.93157e41i | 0.383344 | − | 0.214587i | ||||
\(431\) | − | 2.94290e41i | − | 0.207558i | −0.994600 | − | 0.103779i | \(-0.966907\pi\) | ||
0.994600 | − | 0.103779i | \(-0.0330934\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.53346e42 | 1.00431 | 0.502153 | − | 0.864779i | \(-0.332542\pi\) | ||||
0.502153 | + | 0.864779i | \(0.332542\pi\) | |||||||
\(434\) | −1.26200e42 | − | 2.25447e42i | −0.796570 | − | 1.42301i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.03278e42 | + | 1.68392e42i | −0.605656 | + | 0.987499i | ||||
\(437\) | 3.09796e41 | 0.175135 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.32023e42i | − | 0.693771i | −0.937907 | − | 0.346886i | \(-0.887239\pi\) | ||
0.937907 | − | 0.346886i | \(-0.112761\pi\) | |||||||
\(440\) | −1.14296e40 | + | 2.86741e41i | −0.00579146 | + | 0.145294i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.16659e42 | + | 2.08402e42i | 0.549745 | + | 0.982077i | ||||
\(443\) | − | 1.15073e42i | − | 0.523016i | −0.965201 | − | 0.261508i | \(-0.915780\pi\) | ||
0.965201 | − | 0.261508i | \(-0.0842198\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.44731e41 | −0.272658 | ||||||||
\(446\) | −6.07577e41 | + | 3.40108e41i | −0.247881 | + | 0.138758i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.79030e41 | + | 3.49454e42i | −0.105975 | + | 1.32722i | ||||
\(449\) | −2.92673e42 | −1.07261 | −0.536303 | − | 0.844025i | \(-0.680180\pi\) | ||||
−0.536303 | + | 0.844025i | \(0.680180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.16193e42i | − | 0.737934i | ||||||
\(452\) | −1.34084e42 | + | 2.18619e42i | −0.441734 | + | 0.720231i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.64140e41 | − | 3.15793e41i | 0.173178 | − | 0.0969414i | ||||
\(455\) | − | 1.39977e42i | − | 0.414835i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.62955e42 | 1.00275 | 0.501376 | − | 0.865230i | \(-0.332827\pi\) | ||||
0.501376 | + | 0.865230i | \(0.332827\pi\) | |||||||
\(458\) | 9.25372e41 | + | 1.65311e42i | 0.246870 | + | 0.441015i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.56372e41 | − | 3.41236e41i | −0.138433 | − | 0.0849042i | ||||
\(461\) | 5.81945e42 | 1.39852 | 0.699258 | − | 0.714870i | \(-0.253514\pi\) | ||||
0.699258 | + | 0.714870i | \(0.253514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.14237e42i | − | 0.480396i | −0.970724 | − | 0.240198i | \(-0.922788\pi\) | ||
0.970724 | − | 0.240198i | \(-0.0772123\pi\) | |||||||
\(464\) | −8.16066e41 | − | 1.60463e42i | −0.176782 | − | 0.347606i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.67157e42 | − | 2.98614e42i | −0.338026 | − | 0.603858i | ||||
\(467\) | − | 2.32316e42i | − | 0.453951i | −0.973900 | − | 0.226975i | \(-0.927116\pi\) | ||
0.973900 | − | 0.226975i | \(-0.0728837\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.25392e43 | −2.28825 | ||||||||
\(470\) | −1.70886e41 | + | 9.56584e40i | −0.0301399 | + | 0.0168716i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.51800e41 | − | 1.13346e43i | 0.0744517 | − | 1.86781i | ||||
\(473\) | −4.69910e42 | −0.748576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.93519e42i | 0.288155i | ||||||||
\(476\) | −8.31857e42 | − | 5.10197e42i | −1.19767 | − | 0.734559i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.15984e43 | + | 6.49253e42i | −1.56154 | + | 0.874114i | ||||
\(479\) | − | 1.10819e43i | − | 1.44294i | −0.692447 | − | 0.721469i | \(-0.743467\pi\) | ||
0.692447 | − | 0.721469i | \(-0.256533\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.72190e42 | 1.18421 | ||||||||
\(482\) | −9.56464e41 | − | 1.70865e42i | −0.112698 | − | 0.201326i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.56640e42 | + | 5.81488e42i | −0.393282 | + | 0.641232i | ||||
\(485\) | 2.53785e41 | 0.0270769 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.03406e42i | − | 0.702656i | −0.936252 | − | 0.351328i | \(-0.885730\pi\) | ||
0.936252 | − | 0.351328i | \(-0.114270\pi\) | |||||||
\(488\) | −1.29753e43 | − | 5.17198e41i | −1.25429 | − | 0.0499965i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.21776e42 | + | 2.17543e42i | 0.110261 | + | 0.196974i | ||||
\(491\) | − | 8.92602e42i | − | 0.782265i | −0.920334 | − | 0.391132i | \(-0.872083\pi\) | ||
0.920334 | − | 0.391132i | \(-0.127917\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.01118e42 | 0.411518 | ||||||||
\(494\) | 3.68800e42 | − | 2.06446e42i | 0.293197 | − | 0.164125i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.46498e43 | + | 7.45045e42i | −1.09176 | + | 0.555234i | ||||
\(497\) | −1.67307e43 | −1.20729 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.62413e43i | − | 1.77573i | −0.460102 | − | 0.887866i | \(-0.652187\pi\) | ||
0.460102 | − | 0.887866i | \(-0.347813\pi\) | |||||||
\(500\) | 4.46205e42 | − | 7.27520e42i | 0.292425 | − | 0.476787i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.30279e43 | + | 1.28905e43i | −1.41578 | + | 0.792520i | ||||
\(503\) | − | 4.05670e42i | − | 0.241593i | −0.992677 | − | 0.120797i | \(-0.961455\pi\) | ||
0.992677 | − | 0.120797i | \(-0.0385449\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.46608e42 | 0.361392 | ||||||||
\(506\) | 2.49612e42 | + | 4.45913e42i | 0.135163 | + | 0.241458i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.38970e43 | + | 8.52334e42i | 0.706482 | + | 0.433302i | ||||
\(509\) | 2.68863e43 | 1.32449 | 0.662243 | − | 0.749289i | \(-0.269605\pi\) | ||||
0.662243 | + | 0.749289i | \(0.269605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.66563e43i | − | 1.69595i | ||||||
\(512\) | 2.21417e43 | + | 2.65899e42i | 0.992866 | + | 0.119233i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.48300e42 | + | 1.15814e43i | 0.273128 | + | 0.487923i | ||||
\(515\) | 9.45655e42i | 0.386204i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.53334e42 | 0.0588558 | ||||||||
\(518\) | −3.46619e43 | + | 1.94030e43i | −1.28996 | + | 0.722090i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.89737e42 | − | 3.54652e41i | −0.311321 | − | 0.0124093i | ||||
\(521\) | −3.82848e43 | −1.29904 | −0.649520 | − | 0.760344i | \(-0.725030\pi\) | ||||
−0.649520 | + | 0.760344i | \(0.725030\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.05305e43i | 0.336065i | 0.985781 | + | 0.168033i | \(0.0537414\pi\) | ||||
−0.985781 | + | 0.168033i | \(0.946259\pi\) | |||||||
\(524\) | 9.83807e42 | + | 6.03392e42i | 0.304516 | + | 0.186766i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.50197e43 | − | 1.40055e43i | 0.728635 | − | 0.407873i | ||||
\(527\) | − | 4.57506e43i | − | 1.29249i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.59862e43 | 0.690960 | ||||||||
\(530\) | −4.46139e42 | − | 7.96993e42i | −0.115095 | − | 0.205608i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.02874e42 | + | 1.47210e43i | −0.219301 | + | 0.357562i | ||||
\(533\) | 6.70832e43 | 1.58117 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.88664e43i | − | 0.418822i | ||||||
\(536\) | −3.17698e42 | + | 7.97029e43i | −0.0684507 | + | 1.71726i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.15087e43 | + | 5.62878e43i | 0.639608 | + | 1.14261i | ||||
\(539\) | − | 1.95198e43i | − | 0.384641i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.27835e43 | 0.237408 | 0.118704 | − | 0.992930i | \(-0.462126\pi\) | ||||
0.118704 | + | 0.992930i | \(0.462126\pi\) | |||||||
\(542\) | −3.33149e43 | + | 1.86490e43i | −0.600690 | + | 0.336253i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.45373e43 | + | 5.15827e43i | −0.587091 | + | 0.876842i | ||||
\(545\) | 2.05014e43 | 0.338407 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.15299e43i | 0.179485i | 0.995965 | + | 0.0897424i | \(0.0286044\pi\) | ||||
−0.995965 | + | 0.0897424i | \(0.971396\pi\) | |||||||
\(548\) | −2.31526e43 | + | 3.77494e43i | −0.350034 | + | 0.570718i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.78547e43 | + | 1.55924e43i | −0.397279 | + | 0.222388i | ||||
\(551\) | − | 8.86807e42i | − | 0.122858i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.42532e44 | 1.86342 | ||||||||
\(554\) | 2.46138e43 | + | 4.39707e43i | 0.312625 | + | 0.558480i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.52418e43 | + | 9.34813e42i | 0.182742 | + | 0.112080i | ||||
\(557\) | 6.49038e43 | 0.756114 | 0.378057 | − | 0.925782i | \(-0.376592\pi\) | ||||
0.378057 | + | 0.925782i | \(0.376592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.45809e44i | − | 1.60397i | ||||||
\(560\) | 3.24300e43 | − | 1.64929e43i | 0.346688 | − | 0.176315i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.08105e43 | − | 1.93121e43i | −0.109160 | − | 0.195006i | ||||
\(563\) | 1.15419e44i | 1.13277i | 0.824140 | + | 0.566387i | \(0.191659\pi\) | ||||
−0.824140 | + | 0.566387i | \(0.808341\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.66164e43 | 0.246817 | ||||||||
\(566\) | 1.26350e44 | − | 7.07281e43i | 1.13897 | − | 0.637572i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.23896e42 | + | 1.06345e44i | −0.0361149 | + | 0.906036i | ||||
\(569\) | 1.20494e44 | 0.998091 | 0.499045 | − | 0.866576i | \(-0.333684\pi\) | ||||
0.499045 | + | 0.866576i | \(0.333684\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.72878e44i | − | 1.35382i | −0.736064 | − | 0.676911i | \(-0.763318\pi\) | ||
0.736064 | − | 0.676911i | \(-0.236682\pi\) | |||||||
\(572\) | 5.94307e43 | + | 3.64502e43i | 0.452558 | + | 0.277564i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.39175e44 | + | 1.33885e44i | −1.72236 | + | 0.964140i | ||||
\(575\) | − | 7.26030e43i | − | 0.508474i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.82754e44 | 1.21075 | 0.605375 | − | 0.795941i | \(-0.293023\pi\) | ||||
0.605375 | + | 0.795941i | \(0.293023\pi\) | |||||||
\(578\) | −8.60547e42 | − | 1.53730e43i | −0.0554535 | − | 0.0990635i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.76805e42 | + | 1.59264e43i | −0.0595608 | + | 0.0971116i | ||||
\(581\) | −1.75354e43 | −0.104015 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.15129e43i | 0.401502i | ||||||||
\(584\) | −2.32998e44 | − | 9.28738e42i | −1.27276 | − | 0.0507327i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.30348e43 | + | 1.30471e44i | 0.377718 | + | 0.674765i | ||||
\(587\) | 1.97836e44i | 0.995624i | 0.867285 | + | 0.497812i | \(0.165863\pi\) | ||||
−0.867285 | + | 0.497812i | \(0.834137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.09630e43 | −0.385871 | ||||||||
\(590\) | −1.02728e44 | + | 5.75047e43i | −0.476492 | + | 0.266730i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.14549e44 | + | 2.25237e44i | 0.503319 | + | 0.989676i | ||||
\(593\) | −6.82693e43 | −0.291978 | −0.145989 | − | 0.989286i | \(-0.546636\pi\) | ||||
−0.145989 | + | 0.989286i | \(0.546636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01277e44i | 0.410431i | ||||||||
\(596\) | −1.40228e44 | + | 2.28637e44i | −0.553218 | + | 0.902000i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.38363e44 | + | 7.74528e43i | −0.517371 | + | 0.289613i | ||||
\(599\) | − | 2.54468e44i | − | 0.926413i | −0.886250 | − | 0.463206i | \(-0.846699\pi\) | ||
0.886250 | − | 0.463206i | \(-0.153301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.10791e44 | −1.41785 | −0.708924 | − | 0.705285i | \(-0.750819\pi\) | ||||
−0.708924 | + | 0.705285i | \(0.750819\pi\) | |||||||
\(602\) | 2.91006e44 | + | 5.19861e44i | 0.978045 | + | 1.74720i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.09593e44 | − | 6.72161e43i | −0.349295 | − | 0.214231i | ||||
\(605\) | 7.07953e43 | 0.219745 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.36172e44i | − | 1.87308i | −0.350565 | − | 0.936538i | \(-0.614010\pi\) | ||
0.350565 | − | 0.936538i | \(-0.385990\pi\) | |||||||
\(608\) | 9.12836e43 | + | 6.11192e43i | 0.261780 | + | 0.175275i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.58285e43 | + | 1.17598e44i | 0.179117 | + | 0.319979i | ||||
\(611\) | 4.75783e43i | 0.126110i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.83540e43 | 0.146792 | 0.0733961 | − | 0.997303i | \(-0.476616\pi\) | ||||
0.0733961 | + | 0.997303i | \(0.476616\pi\) | |||||||
\(614\) | −5.65412e44 | + | 3.16505e44i | −1.38571 | + | 0.775687i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.84638e44 | − | 1.13458e43i | −0.662219 | − | 0.0263963i | ||||
\(617\) | 2.60007e44 | 0.589417 | 0.294709 | − | 0.955587i | \(-0.404777\pi\) | ||||
0.294709 | + | 0.955587i | \(0.404777\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.93411e44i | 0.416324i | 0.978094 | + | 0.208162i | \(0.0667481\pi\) | ||||
−0.978094 | + | 0.208162i | \(0.933252\pi\) | |||||||
\(620\) | 1.45404e44 | + | 8.91796e43i | 0.305007 | + | 0.187067i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.57816e44 | − | 8.83419e43i | 0.314416 | − | 0.176003i | ||||
\(623\) | − | 6.40002e44i | − | 1.24272i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.07266e44 | 0.751273 | ||||||||
\(626\) | −1.23660e44 | − | 2.20910e44i | −0.222352 | − | 0.397215i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.96381e44 | + | 4.83237e44i | −0.506402 | + | 0.825669i | ||||
\(629\) | −7.03405e44 | −1.17164 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.02399e44i | − | 0.953707i | −0.878983 | − | 0.476853i | \(-0.841777\pi\) | ||
0.878983 | − | 0.476853i | \(-0.158223\pi\) | |||||||
\(632\) | 3.61126e43 | − | 9.05978e44i | 0.0557423 | − | 1.39844i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.80001e43 | + | 1.57205e44i | 0.129138 | + | 0.230696i | ||||
\(635\) | − | 1.69194e44i | − | 0.242105i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.05685e44 | 0.824169 | ||||||||
\(638\) | 1.27645e44 | − | 7.14528e43i | 0.169384 | − | 0.0948174i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.66173e43 | − | 2.10313e44i | −0.121948 | − | 0.265453i | ||||
\(641\) | 1.17050e45 | 1.44093 | 0.720465 | − | 0.693491i | \(-0.243928\pi\) | ||||
0.720465 | + | 0.693491i | \(0.243928\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 6.41412e44i | − | 0.751210i | −0.926780 | − | 0.375605i | \(-0.877435\pi\) | ||
0.926780 | − | 0.375605i | \(-0.122565\pi\) | |||||||
\(644\) | 3.38733e44 | − | 5.52291e44i | 0.386976 | − | 0.630949i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.66837e44 | + | 1.49369e44i | −0.290085 | + | 0.162383i | ||||
\(647\) | − | 6.68917e44i | − | 0.709421i | −0.934976 | − | 0.354710i | \(-0.884579\pi\) | ||
0.934976 | − | 0.354710i | \(-0.115421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.21761e44 | 0.930471 | ||||||||
\(650\) | −4.83822e44 | − | 8.64311e44i | −0.476510 | − | 0.851248i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.39585e44 | − | 2.69608e44i | −0.412175 | − | 0.252796i | ||||
\(653\) | −9.73888e44 | −0.891042 | −0.445521 | − | 0.895271i | \(-0.646982\pi\) | ||||
−0.445521 | + | 0.895271i | \(0.646982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.19777e44i | − | 0.104355i | ||||||
\(656\) | 7.90412e44 | + | 1.55419e45i | 0.672036 | + | 1.32142i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.49568e43 | − | 1.69633e44i | −0.0768974 | − | 0.137371i | ||||
\(659\) | 1.33156e45i | 1.05243i | 0.850352 | + | 0.526215i | \(0.176389\pi\) | ||||
−0.850352 | + | 0.526215i | \(0.823611\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.18916e45 | 0.895398 | 0.447699 | − | 0.894184i | \(-0.352244\pi\) | ||||
0.447699 | + | 0.894184i | \(0.352244\pi\) | |||||||
\(662\) | 1.65031e44 | − | 9.23808e43i | 0.121294 | − | 0.0678975i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.44284e42 | + | 1.11460e44i | −0.00311151 | + | 0.0780603i | ||||
\(665\) | 1.79226e44 | 0.122533 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.32705e44i | 0.216793i | ||||||||
\(668\) | −2.38846e45 | − | 1.46490e45i | −1.51948 | − | 0.931931i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.22364e44 | − | 4.04363e44i | 0.438086 | − | 0.245231i | ||||
\(671\) | − | 1.05518e45i | − | 0.624839i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.07010e45 | −1.73345 | −0.866726 | − | 0.498784i | \(-0.833780\pi\) | ||||
−0.866726 | + | 0.498784i | \(0.833780\pi\) | |||||||
\(674\) | 1.11068e44 | + | 1.98414e44i | 0.0612392 | + | 0.109399i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.36761e44 | + | 2.22984e44i | −0.0719144 | + | 0.117254i | ||||
\(677\) | 1.15491e44 | 0.0593100 | 0.0296550 | − | 0.999560i | \(-0.490559\pi\) | ||||
0.0296550 | + | 0.999560i | \(0.490559\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.51924e44i | 0.123411i | ||||||||
\(680\) | 6.43748e44 | + | 2.56600e43i | 0.308016 | + | 0.0122776i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.52344e44 | − | 1.16536e45i | −0.297801 | − | 0.531999i | ||||
\(683\) | − | 4.36205e45i | − | 1.94518i | −0.232530 | − | 0.972589i | \(-0.574700\pi\) | ||
0.232530 | − | 0.972589i | \(-0.425300\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.59593e44 | 0.195580 | ||||||||
\(686\) | 6.35110e44 | − | 3.55520e44i | 0.264036 | − | 0.147801i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.37812e45 | − | 1.71801e45i | 1.34048 | − | 0.681727i | ||||
\(689\) | −2.21899e45 | −0.860297 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.13389e43i | 0.00419684i | 0.999998 | + | 0.00209842i | \(0.000667948\pi\) | ||||
−0.999998 | + | 0.00209842i | \(0.999332\pi\) | |||||||
\(692\) | −5.44433e44 | + | 8.87677e44i | −0.196900 | + | 0.321039i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.45808e44 | + | 1.93576e44i | −0.119422 | + | 0.0668496i | ||||
\(695\) | − | 1.85566e44i | − | 0.0626242i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.85365e45 | −1.56439 | ||||||||
\(698\) | −8.20650e44 | − | 1.46603e45i | −0.258506 | − | 0.461802i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.44998e45 | + | 2.11595e45i | 1.03812 | + | 0.636704i | ||||
\(701\) | −2.51171e45 | −0.738722 | −0.369361 | − | 0.929286i | \(-0.620423\pi\) | ||||
−0.369361 | + | 0.929286i | \(0.620423\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.24479e45i | 0.349792i | ||||||||
\(704\) | −1.44234e44 | + | 1.80637e45i | −0.0396192 | + | 0.496186i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.99179e45 | − | 3.55817e45i | −0.522838 | − | 0.934011i | ||||
\(707\) | 6.41865e45i | 1.64715i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.49801e45 | 0.612710 | 0.306355 | − | 0.951917i | \(-0.400891\pi\) | ||||
0.306355 | + | 0.951917i | \(0.400891\pi\) | |||||||
\(710\) | 9.63831e44 | − | 5.39531e44i | 0.231136 | − | 0.129385i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.06805e45 | − | 1.62154e44i | −0.932623 | − | 0.0371746i | ||||
\(713\) | 3.03750e45 | 0.680901 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 7.23559e44i | − | 0.155088i | ||||||
\(716\) | 1.07854e45 | + | 6.61494e44i | 0.226062 | + | 0.138649i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.73382e45 | + | 2.09011e45i | −0.748450 | + | 0.418965i | ||||
\(719\) | 1.24854e45i | 0.244759i | 0.992483 | + | 0.122380i | \(0.0390526\pi\) | ||||
−0.992483 | + | 0.122380i | \(0.960947\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.38719e45 | −1.76024 | ||||||||
\(722\) | −2.39897e45 | − | 4.28557e45i | −0.439976 | − | 0.785984i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.99744e45 | − | 3.25675e45i | 0.350474 | − | 0.571435i | ||||
\(725\) | −2.07830e45 | −0.356697 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.70587e45i | 0.444382i | 0.975003 | + | 0.222191i | \(0.0713209\pi\) | ||||
−0.975003 | + | 0.222191i | \(0.928679\pi\) | |||||||
\(728\) | 3.52051e44 | − | 8.83211e45i | 0.0565592 | − | 1.41894i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.18209e45 | + | 2.11171e45i | 0.181754 | + | 0.324690i | ||||
\(731\) | 1.05497e46i | 1.58695i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.08091e46 | 1.55642 | 0.778212 | − | 0.628002i | \(-0.216127\pi\) | ||||
0.778212 | + | 0.628002i | \(0.216127\pi\) | |||||||
\(734\) | −1.36054e44 | + | 7.61598e43i | −0.0191678 | + | 0.0107297i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.42471e45 | − | 2.29302e45i | −0.461932 | − | 0.309288i | ||||
\(737\) | −6.48166e45 | −0.855473 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.01661e46i | 1.28482i | 0.766360 | + | 0.642412i | \(0.222066\pi\) | ||||
−0.766360 | + | 0.642412i | \(0.777934\pi\) | |||||||
\(740\) | 1.37111e45 | − | 2.23555e45i | 0.169577 | − | 0.276488i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.91147e45 | − | 4.42867e45i | 0.937119 | − | 0.524578i | ||||
\(743\) | − | 1.12410e46i | − | 1.30312i | −0.758596 | − | 0.651562i | \(-0.774114\pi\) | ||
0.758596 | − | 0.651562i | \(-0.225886\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.78362e45 | 0.309108 | ||||||||
\(746\) | 5.51684e45 | + | 9.85541e45i | 0.599610 | + | 1.07116i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.29997e45 | − | 2.63727e45i | −0.447754 | − | 0.274618i | ||||
\(749\) | 1.87281e46 | 1.90890 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.21834e45i | 0.216665i | 0.994115 | + | 0.108332i | \(0.0345511\pi\) | ||||
−0.994115 | + | 0.108332i | \(0.965449\pi\) | |||||||
\(752\) | −1.10230e45 | + | 5.60595e44i | −0.105393 | + | 0.0535999i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.21713e45 | + | 3.96073e45i | 0.203165 | + | 0.362939i | ||||
\(755\) | 1.33428e45i | 0.119700i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.67388e46 | −1.43943 | −0.719716 | − | 0.694268i | \(-0.755728\pi\) | ||||
−0.719716 | + | 0.694268i | \(0.755728\pi\) | |||||||
\(758\) | −1.01171e46 | + | 5.66331e45i | −0.851820 | + | 0.476830i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.54094e43 | − | 1.13921e45i | 0.00366546 | − | 0.0919577i | ||||
\(761\) | 1.04245e46 | 0.823948 | 0.411974 | − | 0.911196i | \(-0.364839\pi\) | ||||
0.411974 | + | 0.911196i | \(0.364839\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03510e46i | 1.54239i | ||||||||
\(764\) | 2.24039e46 | + | 1.37408e46i | 1.66276 | + | 1.01981i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.36848e46 | − | 1.32582e46i | 1.68581 | − | 0.943681i | ||||
\(767\) | 2.86016e46i | 1.99372i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.62732e45 | −0.443115 | −0.221557 | − | 0.975147i | \(-0.571114\pi\) | ||||
−0.221557 | + | 0.975147i | \(0.571114\pi\) | |||||||
\(770\) | 1.44408e45 | + | 2.57974e45i | 0.0945669 | + | 0.168937i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.61552e46 | − | 2.63404e46i | 1.01493 | − | 1.65480i | ||||
\(773\) | −3.08742e46 | −1.89987 | −0.949934 | − | 0.312451i | \(-0.898850\pi\) | ||||
−0.949934 | + | 0.312451i | \(0.898850\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.89743e46i | 1.12031i | ||||||||
\(776\) | 1.60130e45 | + | 6.38285e43i | 0.0926161 | + | 0.00369171i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.15204e45 | + | 5.63089e45i | 0.174952 | + | 0.312538i | ||||
\(779\) | 8.58929e45i | 0.467044i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.64831e45 | −0.451351 | ||||||||
\(782\) | 1.00110e46 | − | 5.60391e45i | 0.511880 | − | 0.286539i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.13653e45 | + | 1.40326e46i | 0.350292 | + | 0.688779i | ||||
\(785\) | 5.88333e45 | 0.282950 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.29987e46i | 0.600213i | 0.953906 | + | 0.300107i | \(0.0970222\pi\) | ||||
−0.953906 | + | 0.300107i | \(0.902978\pi\) | |||||||
\(788\) | 1.85614e45 | − | 3.02636e45i | 0.0839829 | − | 0.136931i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.21107e45 | + | 4.59637e45i | −0.356752 | + | 0.199702i | ||||
\(791\) | 2.64212e46i | 1.12494i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.27416e46 | 1.33884 | ||||||||
\(794\) | −8.25814e44 | − | 1.47525e45i | −0.0330944 | − | 0.0591205i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.79822e45 | + | 3.55618e45i | 0.223196 | + | 0.136891i | ||||
\(797\) | 9.76951e44 | 0.0368587 | 0.0184293 | − | 0.999830i | \(-0.494133\pi\) | ||||
0.0184293 | + | 0.999830i | \(0.494133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.44242e45i | − | 0.124771i | ||||||
\(800\) | 1.43237e46 | − | 2.13930e46i | 0.508881 | − | 0.760032i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.08327e45 | − | 7.29445e45i | −0.139386 | − | 0.249002i | ||||
\(803\) | − | 1.89481e46i | − | 0.634039i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.72405e45 | −0.216221 | ||||||||
\(806\) | 3.61603e46 | − | 2.02417e46i | 1.13991 | − | 0.638098i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.07989e46 | + | 1.62626e45i | 1.23614 | + | 0.0492728i | ||||
\(809\) | −1.11267e46 | −0.330515 | −0.165258 | − | 0.986250i | \(-0.552846\pi\) | ||||
−0.165258 | + | 0.986250i | \(0.552846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.33104e46i | − | 0.951145i | −0.879677 | − | 0.475573i | \(-0.842241\pi\) | ||
0.879677 | − | 0.475573i | \(-0.157759\pi\) | |||||||
\(812\) | −1.58096e46 | − | 9.69641e45i | −0.442614 | − | 0.271465i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.79172e46 | + | 1.00296e46i | −0.482257 | + | 0.269957i | ||||
\(815\) | 5.35187e45i | 0.141249i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.86694e46 | 0.473780 | ||||||||
\(818\) | −2.49216e46 | − | 4.45205e46i | −0.620186 | − | 1.10792i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.46099e45 | − | 1.54258e46i | 0.226420 | − | 0.369169i | ||||
\(821\) | 3.68247e46 | 0.864269 | 0.432134 | − | 0.901809i | \(-0.357761\pi\) | ||||
0.432134 | + | 0.901809i | \(0.357761\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.28307e46i | 0.966848i | 0.875386 | + | 0.483424i | \(0.160607\pi\) | ||||
−0.875386 | + | 0.483424i | \(0.839393\pi\) | |||||||
\(824\) | −2.37838e45 | + | 5.96678e46i | −0.0526557 | + | 1.32101i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.70829e46 | − | 1.01974e47i | −1.21570 | − | 2.17175i | ||||
\(827\) | 2.53823e45i | 0.0530203i | 0.999649 | + | 0.0265102i | \(0.00843944\pi\) | ||||
−0.999649 | + | 0.0265102i | \(0.991561\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.61887e46 | −0.727278 | −0.363639 | − | 0.931540i | \(-0.618466\pi\) | ||||
−0.363639 | + | 0.931540i | \(0.618466\pi\) | |||||||
\(830\) | 1.01019e45 | − | 5.65480e44i | 0.0199137 | − | 0.0111472i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.60504e46 | − | 4.47548e45i | −1.06318 | − | 0.0848920i | ||||
\(833\) | −4.38229e46 | −0.815420 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.90791e46i | 0.520712i | ||||||||
\(836\) | −4.66707e45 | + | 7.60947e45i | −0.0819867 | + | 0.133676i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.57006e46 | − | 1.43866e46i | 0.434549 | − | 0.243251i | ||||
\(839\) | − | 1.24041e46i | − | 0.205767i | −0.994693 | − | 0.102883i | \(-0.967193\pi\) | ||
0.994693 | − | 0.102883i | \(-0.0328068\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.30994e46 | −0.847918 | ||||||||
\(842\) | 1.58361e45 | + | 2.82899e45i | 0.0248115 | + | 0.0443239i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.42812e46 | + | 8.75901e45i | 0.215420 | + | 0.132122i | ||||
\(845\) | 2.71479e45 | 0.0401818 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.02760e46i | 1.00155i | ||||||||
\(848\) | −2.61454e46 | − | 5.14098e46i | −0.365647 | − | 0.718972i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.50058e46 | + | 6.25352e46i | 0.471452 | + | 0.842212i | ||||
\(851\) | − | 4.67009e46i | − | 0.617237i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.73958e46 | −1.11252 | −0.556258 | − | 0.831010i | \(-0.687763\pi\) | ||||
−0.556258 | + | 0.831010i | \(0.687763\pi\) | |||||||
\(854\) | −1.16735e47 | + | 6.53457e46i | −1.45840 | + | 0.816377i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.74502e45 | − | 1.19041e47i | 0.0571028 | − | 1.43257i | ||||
\(857\) | −1.34006e47 | −1.58282 | −0.791412 | − | 0.611283i | \(-0.790654\pi\) | ||||
−0.791412 | + | 0.611283i | \(0.790654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.58120e46i | 0.179927i | 0.995945 | + | 0.0899637i | \(0.0286751\pi\) | ||||
−0.995945 | + | 0.0899637i | \(0.971325\pi\) | |||||||
\(860\) | −3.35289e46 | − | 2.05640e46i | −0.374493 | − | 0.229685i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.68293e46 | + | 9.42064e45i | −0.181113 | + | 0.101383i | ||||
\(863\) | − | 6.77128e46i | − | 0.715316i | −0.933853 | − | 0.357658i | \(-0.883575\pi\) | ||
0.933853 | − | 0.357658i | \(-0.116425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.08073e46 | 0.110017 | ||||||||
\(866\) | −4.90882e46 | − | 8.76923e46i | −0.490559 | − | 0.876346i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.85255e46 | + | 1.44337e47i | −0.852614 | + | 1.39016i | ||||
\(869\) | 7.36767e46 | 0.696648 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.01121e47i | − | 1.83302i | ||||||
\(872\) | 1.29357e47 | + | 5.15622e45i | 1.15752 | + | 0.0461390i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.91701e45 | − | 1.77160e46i | −0.0855456 | − | 0.152821i | ||||
\(875\) | − | 8.79247e46i | − | 0.744701i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.77276e46 | −0.716378 | −0.358189 | − | 0.933649i | \(-0.616606\pi\) | ||||
−0.358189 | + | 0.933649i | \(0.616606\pi\) | |||||||
\(878\) | −7.54985e46 | + | 4.22624e46i | −0.605377 | + | 0.338877i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.67635e46 | − | 8.52539e45i | 0.129611 | − | 0.0659161i | ||||
\(881\) | 7.45226e43 | 0.000565814 | 0.000282907 | − | 1.00000i | \(-0.499910\pi\) | ||||
0.000282907 | 1.00000i | \(0.499910\pi\) | ||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.02137e47i | − | 1.48004i | −0.672584 | − | 0.740021i | \(-0.734815\pi\) | ||
0.672584 | − | 0.740021i | \(-0.265185\pi\) | |||||||
\(884\) | 8.18326e46 | − | 1.33425e47i | 0.588423 | − | 0.959402i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.58058e46 | + | 3.68366e46i | −0.456378 | + | 0.255470i | ||||
\(887\) | 1.65088e47i | 1.12445i | 0.826985 | + | 0.562223i | \(0.190054\pi\) | ||||
−0.826985 | + | 0.562223i | \(0.809946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.67953e47 | 1.10346 | ||||||||
\(890\) | 2.06388e46 | + | 3.68696e46i | 0.133181 | + | 0.237918i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.88988e46 | + | 2.38576e46i | 0.242158 | + | 0.148521i | ||||
\(893\) | −6.09190e45 | −0.0372503 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.31311e46i | − | 0.0774696i | ||||||
\(896\) | 2.08771e47 | − | 9.59086e46i | 1.20988 | − | 0.555814i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.36887e46 | + | 1.67368e47i | 0.523921 | + | 0.935945i | ||||
\(899\) | − | 8.69502e46i | − | 0.477656i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.60550e47 | 0.851165 | ||||||||
\(902\) | −1.23632e47 | + | 6.92066e46i | −0.643913 | + | 0.360448i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.67941e47 | + | 6.69419e45i | 0.844233 | + | 0.0336514i | ||||
\(905\) | −3.96504e46 | −0.195826 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9.68064e46i | − | 0.461517i | −0.973011 | − | 0.230758i | \(-0.925879\pi\) | ||
0.973011 | − | 0.230758i | \(-0.0741207\pi\) | |||||||
\(908\) | −3.61179e46 | − | 2.21519e46i | −0.169180 | − | 0.103762i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.00473e46 | + | 4.48087e46i | −0.361980 | + | 0.202628i | ||||
\(911\) | − | 7.98730e46i | − | 0.354900i | −0.984130 | − | 0.177450i | \(-0.943215\pi\) | ||
0.984130 | − | 0.177450i | \(-0.0567848\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.06425e45 | −0.0388866 | ||||||||
\(914\) | −1.16187e47 | − | 2.07559e47i | −0.489800 | − | 0.874990i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.49120e46 | − | 1.05837e47i | 0.264239 | − | 0.430833i | ||||
\(917\) | 1.18898e47 | 0.475627 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.59603e47i | 0.616585i | 0.951292 | + | 0.308292i | \(0.0997575\pi\) | ||||
−0.951292 | + | 0.308292i | \(0.900242\pi\) | |||||||
\(920\) | −1.70363e45 | + | 4.27401e46i | −0.00646802 | + | 0.162267i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.86289e47 | − | 3.32791e47i | −0.683113 | − | 1.22033i | ||||
\(923\) | − | 2.68351e47i | − | 0.967109i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.91725e47 | 1.01556 | ||||||||
\(926\) | −1.22514e47 | + | 6.85804e46i | −0.419188 | + | 0.234652i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.56389e46 | + | 9.80340e46i | −0.216967 | + | 0.324048i | ||||
\(929\) | −2.29442e46 | −0.0745455 | −0.0372728 | − | 0.999305i | \(-0.511867\pi\) | ||||
−0.0372728 | + | 0.999305i | \(0.511867\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.75516e46i | 0.243442i | ||||||||
\(932\) | −1.17256e47 | + | 1.91181e47i | −0.361809 | + | 0.589916i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.32852e47 | + | 7.43676e46i | −0.396112 | + | 0.221735i | ||||
\(935\) | 5.23514e46i | 0.153441i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.64376e46 | −0.0465591 | −0.0232795 | − | 0.999729i | \(-0.507411\pi\) | ||||
−0.0232795 | + | 0.999729i | \(0.507411\pi\) | |||||||
\(938\) | 4.01397e47 | + | 7.17066e47i | 1.11771 | + | 1.99670i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.09406e46 | + | 6.71014e45i | 0.0294440 | + | 0.0180587i | ||||
\(941\) | 5.50564e47 | 1.45671 | 0.728356 | − | 0.685199i | \(-0.240285\pi\) | ||||
0.728356 | + | 0.685199i | \(0.240285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.22246e47i | − | 0.824139i | ||||||
\(944\) | −6.62642e47 | + | 3.37000e47i | −1.66620 | + | 0.847379i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.50425e47 | + | 2.68722e47i | 0.365646 | + | 0.653199i | ||||
\(947\) | − | 5.04243e46i | − | 0.120515i | −0.998183 | − | 0.0602574i | \(-0.980808\pi\) | ||
0.998183 | − | 0.0602574i | \(-0.0191922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.87945e47 | 1.35855 | ||||||||
\(950\) | 1.10666e47 | − | 6.19483e46i | 0.251441 | − | 0.140751i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.54718e46 | + | 6.39027e47i | −0.0559588 | + | 1.40387i | ||||
\(953\) | 3.90363e47 | 0.843299 | 0.421650 | − | 0.906759i | \(-0.361451\pi\) | ||||
0.421650 | + | 0.906759i | \(0.361451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 2.72763e47i | − | 0.569812i | ||||||
\(956\) | 7.42564e47 | + | 4.55431e47i | 1.52548 | + | 0.935614i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.33732e47 | + | 3.54749e47i | −1.25909 | + | 0.704811i | ||||
\(959\) | 4.56222e47i | 0.891412i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.64686e47 | −0.500215 | ||||||||
\(962\) | −3.11212e47 | − | 5.55956e47i | −0.578436 | − | 1.03333i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.70930e46 | + | 1.09393e47i | −0.120627 | + | 0.196678i | ||||
\(965\) | −3.20690e47 | −0.567085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.20852e47i | − | 0.377814i | −0.981995 | − | 0.188907i | \(-0.939506\pi\) | ||
0.981995 | − | 0.188907i | \(-0.0604944\pi\) | |||||||
\(968\) | 4.46695e47 | + | 1.78054e46i | 0.751633 | + | 0.0299603i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.12403e45 | − | 1.45130e46i | −0.0132259 | − | 0.0236270i | ||||
\(971\) | 1.34172e47i | 0.214860i | 0.994213 | + | 0.107430i | \(0.0342622\pi\) | ||||
−0.994213 | + | 0.107430i | \(0.965738\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.84205e47 | 0.285428 | ||||||||
\(974\) | −4.02250e47 | + | 2.25170e47i | −0.613130 | + | 0.343216i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.85780e47 | + | 7.58559e47i | 0.569040 | + | 1.11890i | ||||
\(977\) | −3.59875e47 | −0.522202 | −0.261101 | − | 0.965312i | \(-0.584085\pi\) | ||||
−0.261101 | + | 0.965312i | \(0.584085\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.30825e47i | − | 0.464596i | ||||||
\(980\) | 8.54220e46 | − | 1.39277e47i | 0.118019 | − | 0.192426i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.10443e47 | + | 2.85735e47i | −0.682596 | + | 0.382102i | ||||
\(983\) | − | 5.51865e46i | − | 0.0726067i | −0.999341 | − | 0.0363034i | \(-0.988442\pi\) | ||
0.999341 | − | 0.0363034i | \(-0.0115583\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.68455e46 | −0.0469250 | ||||||||
\(986\) | −1.60415e47 | − | 2.86569e47i | −0.201008 | − | 0.359086i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.36116e47 | − | 1.44816e47i | −0.286428 | − | 0.175673i | ||||
\(989\) | −7.00422e47 | −0.836025 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.22322e47i | 0.372488i | 0.982504 | + | 0.186244i | \(0.0596314\pi\) | ||||
−0.982504 | + | 0.186244i | \(0.940369\pi\) | |||||||
\(992\) | 8.95023e47 | + | 5.99265e47i | 1.01776 | + | 0.681447i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.35574e47 | + | 9.56762e47i | 0.589708 | + | 1.05347i | ||||
\(995\) | − | 7.05924e46i | − | 0.0764872i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.66475e47 | −0.489447 | −0.244724 | − | 0.969593i | \(-0.578697\pi\) | ||||
−0.244724 | + | 0.969593i | \(0.578697\pi\) | |||||||
\(998\) | −1.50064e48 | + | 8.40023e47i | −1.54948 | + | 0.867366i | ||||
\(999\) | 0 | 0 |
(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 | 36.33.d.b.19.5 | 14 | ||
3.2 | odd | 2 | 4.33.b.b.3.10 | yes | 14 | ||
4.3 | odd | 2 | inner | 36.33.d.b.19.6 | 14 | ||
12.11 | even | 2 | 4.33.b.b.3.9 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.33.b.b.3.9 | ✓ | 14 | 12.11 | even | 2 | ||
4.33.b.b.3.10 | yes | 14 | 3.2 | odd | 2 | ||
36.33.d.b.19.5 | 14 | 1.1 | even | 1 | trivial | ||
36.33.d.b.19.6 | 14 | 4.3 | odd | 2 | inner |