Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,8,Mod(4,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.4");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(4.68577538226\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 162x^{6} + 7361x^{4} + 87300x^{2} + 160000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{12}\cdot 5^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.3 | ||
Root | \(-3.83609i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.4 |
Dual form | 15.8.b.a.4.6 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 8.75511i | − | 0.773850i | −0.922111 | − | 0.386925i | \(-0.873537\pi\) | ||
0.922111 | − | 0.386925i | \(-0.126463\pi\) | |||||||
\(3\) | 27.0000i | 0.577350i | ||||||||
\(4\) | 51.3480 | 0.401156 | ||||||||
\(5\) | 231.605 | − | 156.474i | 0.828614 | − | 0.559820i | ||||
\(6\) | 236.388 | 0.446783 | ||||||||
\(7\) | − | 536.160i | − | 0.590814i | −0.955371 | − | 0.295407i | \(-0.904545\pi\) | ||
0.955371 | − | 0.295407i | \(-0.0954553\pi\) | |||||||
\(8\) | − | 1570.21i | − | 1.08428i | ||||||
\(9\) | −729.000 | −0.333333 | ||||||||
\(10\) | −1369.95 | − | 2027.73i | −0.433217 | − | 0.641223i | ||||
\(11\) | 5830.22 | 1.32072 | 0.660360 | − | 0.750949i | \(-0.270404\pi\) | ||||
0.660360 | + | 0.750949i | \(0.270404\pi\) | |||||||
\(12\) | 1386.40i | 0.231608i | ||||||||
\(13\) | 5815.44i | 0.734143i | 0.930193 | + | 0.367071i | \(0.119640\pi\) | ||||
−0.930193 | + | 0.367071i | \(0.880360\pi\) | |||||||
\(14\) | −4694.14 | −0.457202 | ||||||||
\(15\) | 4224.81 | + | 6253.33i | 0.323212 | + | 0.478401i | ||||
\(16\) | −7174.84 | −0.437918 | ||||||||
\(17\) | 9476.54i | 0.467820i | 0.972258 | + | 0.233910i | \(0.0751521\pi\) | ||||
−0.972258 | + | 0.233910i | \(0.924848\pi\) | |||||||
\(18\) | 6382.48i | 0.257950i | ||||||||
\(19\) | −52968.3 | −1.77165 | −0.885825 | − | 0.464019i | \(-0.846407\pi\) | ||||
−0.885825 | + | 0.464019i | \(0.846407\pi\) | |||||||
\(20\) | 11892.4 | − | 8034.65i | 0.332404 | − | 0.224575i | ||||
\(21\) | 14476.3 | 0.341107 | ||||||||
\(22\) | − | 51044.3i | − | 1.02204i | ||||||
\(23\) | 74966.7i | 1.28476i | 0.766387 | + | 0.642379i | \(0.222052\pi\) | ||||
−0.766387 | + | 0.642379i | \(0.777948\pi\) | |||||||
\(24\) | 42395.7 | 0.626012 | ||||||||
\(25\) | 29156.5 | − | 72480.4i | 0.373203 | − | 0.927750i | ||||
\(26\) | 50914.8 | 0.568117 | ||||||||
\(27\) | − | 19683.0i | − | 0.192450i | ||||||
\(28\) | − | 27530.7i | − | 0.237009i | ||||||
\(29\) | 22107.7 | 0.168326 | 0.0841628 | − | 0.996452i | \(-0.473178\pi\) | ||||
0.0841628 | + | 0.996452i | \(0.473178\pi\) | |||||||
\(30\) | 54748.6 | − | 36988.7i | 0.370210 | − | 0.250118i | ||||
\(31\) | −158843. | −0.957637 | −0.478819 | − | 0.877914i | \(-0.658935\pi\) | ||||
−0.478819 | + | 0.877914i | \(0.658935\pi\) | |||||||
\(32\) | − | 138171.i | − | 0.745402i | ||||||
\(33\) | 157416.i | 0.762518i | ||||||||
\(34\) | 82968.2 | 0.362022 | ||||||||
\(35\) | −83895.3 | − | 124177.i | −0.330750 | − | 0.489557i | ||||
\(36\) | −37432.7 | −0.133719 | ||||||||
\(37\) | 264554.i | 0.858636i | 0.903153 | + | 0.429318i | \(0.141246\pi\) | ||||
−0.903153 | + | 0.429318i | \(0.858754\pi\) | |||||||
\(38\) | 463743.i | 1.37099i | ||||||||
\(39\) | −157017. | −0.423858 | ||||||||
\(40\) | −245698. | − | 363668.i | −0.607004 | − | 0.898454i | ||||
\(41\) | −77139.7 | −0.174797 | −0.0873986 | − | 0.996173i | \(-0.527855\pi\) | ||||
−0.0873986 | + | 0.996173i | \(0.527855\pi\) | |||||||
\(42\) | − | 126742.i | − | 0.263966i | ||||||
\(43\) | 845105.i | 1.62096i | 0.585769 | + | 0.810478i | \(0.300793\pi\) | ||||
−0.585769 | + | 0.810478i | \(0.699207\pi\) | |||||||
\(44\) | 299370. | 0.529815 | ||||||||
\(45\) | −168840. | + | 114070.i | −0.276205 | + | 0.186607i | ||||
\(46\) | 656342. | 0.994209 | ||||||||
\(47\) | − | 893848.i | − | 1.25580i | −0.778293 | − | 0.627901i | \(-0.783914\pi\) | ||
0.778293 | − | 0.627901i | \(-0.216086\pi\) | |||||||
\(48\) | − | 193721.i | − | 0.252832i | ||||||
\(49\) | 536076. | 0.650938 | ||||||||
\(50\) | −634575. | − | 255268.i | −0.717939 | − | 0.288803i | ||||
\(51\) | −255867. | −0.270096 | ||||||||
\(52\) | 298611.i | 0.294506i | ||||||||
\(53\) | − | 153425.i | − | 0.141557i | −0.997492 | − | 0.0707784i | \(-0.977452\pi\) | ||
0.997492 | − | 0.0707784i | \(-0.0225483\pi\) | |||||||
\(54\) | −172327. | −0.148928 | ||||||||
\(55\) | 1.35031e6 | − | 912281.i | 1.09437 | − | 0.739366i | ||||
\(56\) | −841885. | −0.640611 | ||||||||
\(57\) | − | 1.43014e6i | − | 1.02286i | ||||||
\(58\) | − | 193555.i | − | 0.130259i | ||||||
\(59\) | 155813. | 0.0987690 | 0.0493845 | − | 0.998780i | \(-0.484274\pi\) | ||||
0.0493845 | + | 0.998780i | \(0.484274\pi\) | |||||||
\(60\) | 216935. | + | 321096.i | 0.129659 | + | 0.191913i | ||||
\(61\) | 721961. | 0.407248 | 0.203624 | − | 0.979049i | \(-0.434728\pi\) | ||||
0.203624 | + | 0.979049i | \(0.434728\pi\) | |||||||
\(62\) | 1.39068e6i | 0.741068i | ||||||||
\(63\) | 390861.i | 0.196938i | ||||||||
\(64\) | −2.12808e6 | −1.01475 | ||||||||
\(65\) | 909967. | + | 1.34688e6i | 0.410988 | + | 0.608321i | ||||
\(66\) | 1.37820e6 | 0.590075 | ||||||||
\(67\) | 2.87480e6i | 1.16774i | 0.811848 | + | 0.583869i | \(0.198462\pi\) | ||||
−0.811848 | + | 0.583869i | \(0.801538\pi\) | |||||||
\(68\) | 486601.i | 0.187669i | ||||||||
\(69\) | −2.02410e6 | −0.741755 | ||||||||
\(70\) | −1.08718e6 | + | 734513.i | −0.378844 | + | 0.255951i | ||||
\(71\) | −1.89425e6 | −0.628107 | −0.314053 | − | 0.949405i | \(-0.601687\pi\) | ||||
−0.314053 | + | 0.949405i | \(0.601687\pi\) | |||||||
\(72\) | 1.14468e6i | 0.361428i | ||||||||
\(73\) | − | 4.67419e6i | − | 1.40630i | −0.711044 | − | 0.703148i | \(-0.751777\pi\) | ||
0.711044 | − | 0.703148i | \(-0.248223\pi\) | |||||||
\(74\) | 2.31620e6 | 0.664455 | ||||||||
\(75\) | 1.95697e6 | + | 787225.i | 0.535637 | + | 0.215469i | ||||
\(76\) | −2.71981e6 | −0.710708 | ||||||||
\(77\) | − | 3.12593e6i | − | 0.780300i | ||||||
\(78\) | 1.37470e6i | 0.328002i | ||||||||
\(79\) | −2.70860e6 | −0.618087 | −0.309044 | − | 0.951048i | \(-0.600009\pi\) | ||||
−0.309044 | + | 0.951048i | \(0.600009\pi\) | |||||||
\(80\) | −1.66173e6 | + | 1.12268e6i | −0.362865 | + | 0.245155i | ||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 675367.i | 0.135267i | ||||||||
\(83\) | − | 4.54782e6i | − | 0.873031i | −0.899697 | − | 0.436515i | \(-0.856212\pi\) | ||
0.899697 | − | 0.436515i | \(-0.143788\pi\) | |||||||
\(84\) | 743330. | 0.136837 | ||||||||
\(85\) | 1.48284e6 | + | 2.19481e6i | 0.261895 | + | 0.387642i | ||||
\(86\) | 7.39899e6 | 1.25438 | ||||||||
\(87\) | 596908.i | 0.0971829i | ||||||||
\(88\) | − | 9.15469e6i | − | 1.43204i | ||||||
\(89\) | 1.17121e7 | 1.76104 | 0.880518 | − | 0.474012i | \(-0.157195\pi\) | ||||
0.880518 | + | 0.474012i | \(0.157195\pi\) | |||||||
\(90\) | 998695. | + | 1.47821e6i | 0.144406 | + | 0.213741i | ||||
\(91\) | 3.11800e6 | 0.433742 | ||||||||
\(92\) | 3.84939e6i | 0.515388i | ||||||||
\(93\) | − | 4.28875e6i | − | 0.552892i | ||||||
\(94\) | −7.82574e6 | −0.971802 | ||||||||
\(95\) | −1.22677e7 | + | 8.28818e6i | −1.46801 | + | 0.991805i | ||||
\(96\) | 3.73061e6 | 0.430358 | ||||||||
\(97\) | − | 4.83792e6i | − | 0.538217i | −0.963110 | − | 0.269109i | \(-0.913271\pi\) | ||
0.963110 | − | 0.269109i | \(-0.0867291\pi\) | |||||||
\(98\) | − | 4.69340e6i | − | 0.503729i | ||||||
\(99\) | −4.25023e6 | −0.440240 | ||||||||
\(100\) | 1.49713e6 | − | 3.72172e6i | 0.149713 | − | 0.372172i | ||||
\(101\) | −1.95309e7 | −1.88624 | −0.943121 | − | 0.332448i | \(-0.892125\pi\) | ||||
−0.943121 | + | 0.332448i | \(0.892125\pi\) | |||||||
\(102\) | 2.24014e6i | 0.209014i | ||||||||
\(103\) | 1.84497e7i | 1.66364i | 0.555044 | + | 0.831821i | \(0.312701\pi\) | ||||
−0.555044 | + | 0.831821i | \(0.687299\pi\) | |||||||
\(104\) | 9.13147e6 | 0.796020 | ||||||||
\(105\) | 3.35278e6 | − | 2.26517e6i | 0.282646 | − | 0.190958i | ||||
\(106\) | −1.34325e6 | −0.109544 | ||||||||
\(107\) | 1.06308e7i | 0.838923i | 0.907773 | + | 0.419462i | \(0.137781\pi\) | ||||
−0.907773 | + | 0.419462i | \(0.862219\pi\) | |||||||
\(108\) | − | 1.01068e6i | − | 0.0772025i | ||||||
\(109\) | 1.26870e7 | 0.938351 | 0.469176 | − | 0.883105i | \(-0.344551\pi\) | ||||
0.469176 | + | 0.883105i | \(0.344551\pi\) | |||||||
\(110\) | −7.98712e6 | − | 1.18221e7i | −0.572158 | − | 0.846876i | ||||
\(111\) | −7.14297e6 | −0.495734 | ||||||||
\(112\) | 3.84686e6i | 0.258728i | ||||||||
\(113\) | 6.54277e6i | 0.426567i | 0.976990 | + | 0.213284i | \(0.0684158\pi\) | ||||
−0.976990 | + | 0.213284i | \(0.931584\pi\) | |||||||
\(114\) | −1.25211e7 | −0.791543 | ||||||||
\(115\) | 1.17304e7 | + | 1.73626e7i | 0.719233 | + | 1.06457i | ||||
\(116\) | 1.13519e6 | 0.0675249 | ||||||||
\(117\) | − | 4.23945e6i | − | 0.244714i | ||||||
\(118\) | − | 1.36416e6i | − | 0.0764324i | ||||||
\(119\) | 5.08094e6 | 0.276395 | ||||||||
\(120\) | 9.81905e6 | − | 6.63385e6i | 0.518722 | − | 0.350454i | ||||
\(121\) | 1.45043e7 | 0.744301 | ||||||||
\(122\) | − | 6.32085e6i | − | 0.315149i | ||||||
\(123\) | − | 2.08277e6i | − | 0.100919i | ||||||
\(124\) | −8.15625e6 | −0.384162 | ||||||||
\(125\) | −4.58856e6 | − | 2.13491e7i | −0.210132 | − | 0.977673i | ||||
\(126\) | 3.42203e6 | 0.152401 | ||||||||
\(127\) | − | 3.28179e7i | − | 1.42167i | −0.703360 | − | 0.710834i | \(-0.748318\pi\) | ||
0.703360 | − | 0.710834i | \(-0.251682\pi\) | |||||||
\(128\) | 945743.i | 0.0398601i | ||||||||
\(129\) | −2.28178e7 | −0.935860 | ||||||||
\(130\) | 1.17921e7 | − | 7.96687e6i | 0.470749 | − | 0.318043i | ||||
\(131\) | 2.08304e6 | 0.0809557 | 0.0404778 | − | 0.999180i | \(-0.487112\pi\) | ||||
0.0404778 | + | 0.999180i | \(0.487112\pi\) | |||||||
\(132\) | 8.08299e6i | 0.305889i | ||||||||
\(133\) | 2.83994e7i | 1.04672i | ||||||||
\(134\) | 2.51692e7 | 0.903654 | ||||||||
\(135\) | −3.07989e6 | − | 4.55868e6i | −0.107737 | − | 0.159467i | ||||
\(136\) | 1.48802e7 | 0.507250 | ||||||||
\(137\) | − | 4.20215e7i | − | 1.39621i | −0.715997 | − | 0.698103i | \(-0.754028\pi\) | ||
0.715997 | − | 0.698103i | \(-0.245972\pi\) | |||||||
\(138\) | 1.77212e7i | 0.574007i | ||||||||
\(139\) | −4.89465e7 | −1.54586 | −0.772930 | − | 0.634492i | \(-0.781209\pi\) | ||||
−0.772930 | + | 0.634492i | \(0.781209\pi\) | |||||||
\(140\) | −4.30786e6 | − | 6.37624e6i | −0.132682 | − | 0.196389i | ||||
\(141\) | 2.41339e7 | 0.725037 | ||||||||
\(142\) | 1.65844e7i | 0.486060i | ||||||||
\(143\) | 3.39053e7i | 0.969597i | ||||||||
\(144\) | 5.23046e6 | 0.145973 | ||||||||
\(145\) | 5.12025e6 | − | 3.45929e6i | 0.139477 | − | 0.0942321i | ||||
\(146\) | −4.09231e7 | −1.08826 | ||||||||
\(147\) | 1.44740e7i | 0.375819i | ||||||||
\(148\) | 1.35843e7i | 0.344447i | ||||||||
\(149\) | 3.77290e7 | 0.934379 | 0.467189 | − | 0.884157i | \(-0.345267\pi\) | ||||
0.467189 | + | 0.884157i | \(0.345267\pi\) | |||||||
\(150\) | 6.89224e6 | − | 1.71335e7i | 0.166741 | − | 0.414502i | ||||
\(151\) | −6.39975e6 | −0.151267 | −0.0756334 | − | 0.997136i | \(-0.524098\pi\) | ||||
−0.0756334 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(152\) | 8.31714e7i | 1.92097i | ||||||||
\(153\) | − | 6.90840e6i | − | 0.155940i | ||||||
\(154\) | −2.73679e7 | −0.603836 | ||||||||
\(155\) | −3.67887e7 | + | 2.48548e7i | −0.793512 | + | 0.536105i | ||||
\(156\) | −8.06249e6 | −0.170033 | ||||||||
\(157\) | − | 6.53032e7i | − | 1.34675i | −0.739303 | − | 0.673373i | \(-0.764845\pi\) | ||
0.739303 | − | 0.673373i | \(-0.235155\pi\) | |||||||
\(158\) | 2.37141e7i | 0.478307i | ||||||||
\(159\) | 4.14248e6 | 0.0817279 | ||||||||
\(160\) | −2.16202e7 | − | 3.20010e7i | −0.417291 | − | 0.617651i | ||||
\(161\) | 4.01941e7 | 0.759053 | ||||||||
\(162\) | − | 4.65283e6i | − | 0.0859833i | ||||||
\(163\) | − | 3.69087e6i | − | 0.0667532i | −0.999443 | − | 0.0333766i | \(-0.989374\pi\) | ||
0.999443 | − | 0.0333766i | \(-0.0106261\pi\) | |||||||
\(164\) | −3.96097e6 | −0.0701210 | ||||||||
\(165\) | 2.46316e7 | + | 3.64583e7i | 0.426873 | + | 0.631833i | ||||
\(166\) | −3.98166e7 | −0.675595 | ||||||||
\(167\) | − | 3.63073e7i | − | 0.603235i | −0.953429 | − | 0.301618i | \(-0.902473\pi\) | ||
0.953429 | − | 0.301618i | \(-0.0975266\pi\) | |||||||
\(168\) | − | 2.27309e7i | − | 0.369857i | ||||||
\(169\) | 2.89292e7 | 0.461034 | ||||||||
\(170\) | 1.92158e7 | − | 1.29824e7i | 0.299977 | − | 0.202667i | ||||
\(171\) | 3.86139e7 | 0.590550 | ||||||||
\(172\) | 4.33945e7i | 0.650256i | ||||||||
\(173\) | − | 6.98352e7i | − | 1.02545i | −0.858554 | − | 0.512724i | \(-0.828637\pi\) | ||
0.858554 | − | 0.512724i | \(-0.171363\pi\) | |||||||
\(174\) | 5.22599e6 | 0.0752050 | ||||||||
\(175\) | −3.88611e7 | − | 1.56325e7i | −0.548128 | − | 0.220494i | ||||
\(176\) | −4.18309e7 | −0.578367 | ||||||||
\(177\) | 4.20694e6i | 0.0570243i | ||||||||
\(178\) | − | 1.02540e8i | − | 1.36278i | ||||||
\(179\) | 7.44273e7 | 0.969944 | 0.484972 | − | 0.874530i | \(-0.338830\pi\) | ||||
0.484972 | + | 0.874530i | \(0.338830\pi\) | |||||||
\(180\) | −8.66958e6 | + | 5.85726e6i | −0.110801 | + | 0.0748584i | ||||
\(181\) | −2.23241e7 | −0.279833 | −0.139917 | − | 0.990163i | \(-0.544683\pi\) | ||||
−0.139917 | + | 0.990163i | \(0.544683\pi\) | |||||||
\(182\) | − | 2.72985e7i | − | 0.335651i | ||||||
\(183\) | 1.94929e7i | 0.235125i | ||||||||
\(184\) | 1.17714e8 | 1.39304 | ||||||||
\(185\) | 4.13960e7 | + | 6.12720e7i | 0.480682 | + | 0.711478i | ||||
\(186\) | −3.75485e7 | −0.427856 | ||||||||
\(187\) | 5.52503e7i | 0.617859i | ||||||||
\(188\) | − | 4.58973e7i | − | 0.503772i | ||||||
\(189\) | −1.05532e7 | −0.113702 | ||||||||
\(190\) | 7.25640e7 | + | 1.07405e8i | 0.767509 | + | 1.13602i | ||||
\(191\) | −8.28691e6 | −0.0860550 | −0.0430275 | − | 0.999074i | \(-0.513700\pi\) | ||||
−0.0430275 | + | 0.999074i | \(0.513700\pi\) | |||||||
\(192\) | − | 5.74581e7i | − | 0.585865i | ||||||
\(193\) | − | 1.26638e7i | − | 0.126798i | −0.997988 | − | 0.0633990i | \(-0.979806\pi\) | ||
0.997988 | − | 0.0633990i | \(-0.0201941\pi\) | |||||||
\(194\) | −4.23565e7 | −0.416500 | ||||||||
\(195\) | −3.63658e7 | + | 2.45691e7i | −0.351214 | + | 0.237284i | ||||
\(196\) | 2.75264e7 | 0.261128 | ||||||||
\(197\) | 2.35528e7i | 0.219488i | 0.993960 | + | 0.109744i | \(0.0350031\pi\) | ||||
−0.993960 | + | 0.109744i | \(0.964997\pi\) | |||||||
\(198\) | 3.72113e7i | 0.340680i | ||||||||
\(199\) | −1.39990e8 | −1.25925 | −0.629626 | − | 0.776898i | \(-0.716792\pi\) | ||||
−0.629626 | + | 0.776898i | \(0.716792\pi\) | |||||||
\(200\) | −1.13810e8 | − | 4.57819e7i | −1.00594 | − | 0.404658i | ||||
\(201\) | −7.76195e7 | −0.674194 | ||||||||
\(202\) | 1.70995e8i | 1.45967i | ||||||||
\(203\) | − | 1.18533e7i | − | 0.0994493i | ||||||
\(204\) | −1.31382e7 | −0.108351 | ||||||||
\(205\) | −1.78659e7 | + | 1.20704e7i | −0.144839 | + | 0.0978550i | ||||
\(206\) | 1.61530e8 | 1.28741 | ||||||||
\(207\) | − | 5.46507e7i | − | 0.428252i | ||||||
\(208\) | − | 4.17248e7i | − | 0.321494i | ||||||
\(209\) | −3.08817e8 | −2.33985 | ||||||||
\(210\) | −1.98319e7 | − | 2.93540e7i | −0.147773 | − | 0.218726i | ||||
\(211\) | 1.10945e8 | 0.813055 | 0.406527 | − | 0.913639i | \(-0.366740\pi\) | ||||
0.406527 | + | 0.913639i | \(0.366740\pi\) | |||||||
\(212\) | − | 7.87807e6i | − | 0.0567864i | ||||||
\(213\) | − | 5.11448e7i | − | 0.362638i | ||||||
\(214\) | 9.30737e7 | 0.649201 | ||||||||
\(215\) | 1.32237e8 | + | 1.95730e8i | 0.907444 | + | 1.34315i | ||||
\(216\) | −3.09065e7 | −0.208671 | ||||||||
\(217\) | 8.51650e7i | 0.565786i | ||||||||
\(218\) | − | 1.11076e8i | − | 0.726143i | ||||||
\(219\) | 1.26203e8 | 0.811925 | ||||||||
\(220\) | 6.93355e7 | − | 4.68438e7i | 0.439012 | − | 0.296601i | ||||
\(221\) | −5.51102e7 | −0.343446 | ||||||||
\(222\) | 6.25375e7i | 0.383623i | ||||||||
\(223\) | − | 4.58840e7i | − | 0.277073i | −0.990357 | − | 0.138536i | \(-0.955760\pi\) | ||
0.990357 | − | 0.138536i | \(-0.0442398\pi\) | |||||||
\(224\) | −7.40815e7 | −0.440394 | ||||||||
\(225\) | −2.12551e7 | + | 5.28382e7i | −0.124401 | + | 0.309250i | ||||
\(226\) | 5.72827e7 | 0.330099 | ||||||||
\(227\) | − | 6.60981e7i | − | 0.375058i | −0.982259 | − | 0.187529i | \(-0.939952\pi\) | ||
0.982259 | − | 0.187529i | \(-0.0600479\pi\) | |||||||
\(228\) | − | 7.34349e7i | − | 0.410328i | ||||||
\(229\) | 1.41509e8 | 0.778684 | 0.389342 | − | 0.921093i | \(-0.372702\pi\) | ||||
0.389342 | + | 0.921093i | \(0.372702\pi\) | |||||||
\(230\) | 1.52012e8 | − | 1.02701e8i | 0.823816 | − | 0.556578i | ||||
\(231\) | 8.44001e7 | 0.450507 | ||||||||
\(232\) | − | 3.47138e7i | − | 0.182513i | ||||||
\(233\) | 1.55558e8i | 0.805651i | 0.915277 | + | 0.402826i | \(0.131972\pi\) | ||||
−0.915277 | + | 0.402826i | \(0.868028\pi\) | |||||||
\(234\) | −3.71169e7 | −0.189372 | ||||||||
\(235\) | −1.39864e8 | − | 2.07019e8i | −0.703023 | − | 1.04057i | ||||
\(236\) | 8.00066e6 | 0.0396218 | ||||||||
\(237\) | − | 7.31322e7i | − | 0.356853i | ||||||
\(238\) | − | 4.44842e7i | − | 0.213888i | ||||||
\(239\) | 8.55969e6 | 0.0405570 | 0.0202785 | − | 0.999794i | \(-0.493545\pi\) | ||||
0.0202785 | + | 0.999794i | \(0.493545\pi\) | |||||||
\(240\) | −3.03124e7 | − | 4.48666e7i | −0.141540 | − | 0.209500i | ||||
\(241\) | −2.16028e8 | −0.994147 | −0.497073 | − | 0.867708i | \(-0.665592\pi\) | ||||
−0.497073 | + | 0.867708i | \(0.665592\pi\) | |||||||
\(242\) | − | 1.26987e8i | − | 0.575978i | ||||||
\(243\) | 1.43489e7i | 0.0641500i | ||||||||
\(244\) | 3.70712e7 | 0.163370 | ||||||||
\(245\) | 1.24158e8 | − | 8.38822e7i | 0.539377 | − | 0.364408i | ||||
\(246\) | −1.82349e7 | −0.0780963 | ||||||||
\(247\) | − | 3.08034e8i | − | 1.30064i | ||||||
\(248\) | 2.49417e8i | 1.03835i | ||||||||
\(249\) | 1.22791e8 | 0.504045 | ||||||||
\(250\) | −1.86913e8 | + | 4.01734e7i | −0.756572 | + | 0.162610i | ||||
\(251\) | 7.51840e7 | 0.300101 | 0.150051 | − | 0.988678i | \(-0.452056\pi\) | ||||
0.150051 | + | 0.988678i | \(0.452056\pi\) | |||||||
\(252\) | 2.00699e7i | 0.0790029i | ||||||||
\(253\) | 4.37073e8i | 1.69680i | ||||||||
\(254\) | −2.87325e8 | −1.10016 | ||||||||
\(255\) | −5.92599e7 | + | 4.00366e7i | −0.223805 | + | 0.151205i | ||||
\(256\) | −2.64114e8 | −0.983901 | ||||||||
\(257\) | 2.50348e8i | 0.919981i | 0.887924 | + | 0.459991i | \(0.152147\pi\) | ||||
−0.887924 | + | 0.459991i | \(0.847853\pi\) | |||||||
\(258\) | 1.99773e8i | 0.724215i | ||||||||
\(259\) | 1.41843e8 | 0.507294 | ||||||||
\(260\) | 4.67250e7 | + | 6.91597e7i | 0.164870 | + | 0.244032i | ||||
\(261\) | −1.61165e7 | −0.0561086 | ||||||||
\(262\) | − | 1.82372e7i | − | 0.0626476i | ||||||
\(263\) | − | 2.25906e8i | − | 0.765743i | −0.923802 | − | 0.382872i | \(-0.874935\pi\) | ||
0.923802 | − | 0.382872i | \(-0.125065\pi\) | |||||||
\(264\) | 2.47177e8 | 0.826787 | ||||||||
\(265\) | −2.40071e7 | − | 3.55340e7i | −0.0792464 | − | 0.117296i | ||||
\(266\) | 2.48640e8 | 0.810002 | ||||||||
\(267\) | 3.16226e8i | 1.01674i | ||||||||
\(268\) | 1.47615e8i | 0.468445i | ||||||||
\(269\) | 2.55932e8 | 0.801662 | 0.400831 | − | 0.916152i | \(-0.368721\pi\) | ||||
0.400831 | + | 0.916152i | \(0.368721\pi\) | |||||||
\(270\) | −3.99117e7 | + | 2.69648e7i | −0.123403 | + | 0.0833726i | ||||
\(271\) | −1.62476e8 | −0.495903 | −0.247951 | − | 0.968772i | \(-0.579757\pi\) | ||||
−0.247951 | + | 0.968772i | \(0.579757\pi\) | |||||||
\(272\) | − | 6.79927e7i | − | 0.204867i | ||||||
\(273\) | 8.41861e7i | 0.250421i | ||||||||
\(274\) | −3.67903e8 | −1.08045 | ||||||||
\(275\) | 1.69989e8 | − | 4.22577e8i | 0.492897 | − | 1.22530i | ||||
\(276\) | −1.03934e8 | −0.297560 | ||||||||
\(277\) | − | 2.30349e8i | − | 0.651190i | −0.945509 | − | 0.325595i | \(-0.894435\pi\) | ||
0.945509 | − | 0.325595i | \(-0.105565\pi\) | |||||||
\(278\) | 4.28532e8i | 1.19626i | ||||||||
\(279\) | 1.15796e8 | 0.319212 | ||||||||
\(280\) | −1.94984e8 | + | 1.31733e8i | −0.530819 | + | 0.358627i | ||||
\(281\) | −4.07719e8 | −1.09620 | −0.548098 | − | 0.836414i | \(-0.684648\pi\) | ||||
−0.548098 | + | 0.836414i | \(0.684648\pi\) | |||||||
\(282\) | − | 2.11295e8i | − | 0.561070i | ||||||
\(283\) | − | 2.04032e8i | − | 0.535113i | −0.963542 | − | 0.267556i | \(-0.913784\pi\) | ||
0.963542 | − | 0.267556i | \(-0.0862162\pi\) | |||||||
\(284\) | −9.72660e7 | −0.251969 | ||||||||
\(285\) | −2.23781e8 | − | 3.31228e8i | −0.572619 | − | 0.847559i | ||||
\(286\) | 2.96845e8 | 0.750323 | ||||||||
\(287\) | 4.13592e7i | 0.103273i | ||||||||
\(288\) | 1.00726e8i | 0.248467i | ||||||||
\(289\) | 3.20534e8 | 0.781145 | ||||||||
\(290\) | −3.02865e7 | − | 4.48283e7i | −0.0729215 | − | 0.107934i | ||||
\(291\) | 1.30624e8 | 0.310740 | ||||||||
\(292\) | − | 2.40010e8i | − | 0.564144i | ||||||
\(293\) | − | 9.60811e6i | − | 0.0223152i | −0.999938 | − | 0.0111576i | \(-0.996448\pi\) | ||
0.999938 | − | 0.0111576i | \(-0.00355165\pi\) | |||||||
\(294\) | 1.26722e8 | 0.290828 | ||||||||
\(295\) | 3.60869e7 | − | 2.43807e7i | 0.0818414 | − | 0.0552929i | ||||
\(296\) | 4.15407e8 | 0.931006 | ||||||||
\(297\) | − | 1.14756e8i | − | 0.254173i | ||||||
\(298\) | − | 3.30321e8i | − | 0.723069i | ||||||
\(299\) | −4.35964e8 | −0.943195 | ||||||||
\(300\) | 1.00487e8 | + | 4.04224e7i | 0.214874 | + | 0.0864366i | ||||
\(301\) | 4.53112e8 | 0.957684 | ||||||||
\(302\) | 5.60305e7i | 0.117058i | ||||||||
\(303\) | − | 5.27335e8i | − | 1.08902i | ||||||
\(304\) | 3.80039e8 | 0.775837 | ||||||||
\(305\) | 1.67210e8 | − | 1.12968e8i | 0.337452 | − | 0.227986i | ||||
\(306\) | −6.04838e7 | −0.120674 | ||||||||
\(307\) | 1.74442e8i | 0.344085i | 0.985090 | + | 0.172043i | \(0.0550367\pi\) | ||||
−0.985090 | + | 0.172043i | \(0.944963\pi\) | |||||||
\(308\) | − | 1.60510e8i | − | 0.313022i | ||||||
\(309\) | −4.98143e8 | −0.960504 | ||||||||
\(310\) | 2.17607e8 | + | 3.22089e8i | 0.414865 | + | 0.614059i | ||||
\(311\) | 1.93660e8 | 0.365072 | 0.182536 | − | 0.983199i | \(-0.441569\pi\) | ||||
0.182536 | + | 0.983199i | \(0.441569\pi\) | |||||||
\(312\) | 2.46550e8i | 0.459582i | ||||||||
\(313\) | 8.09094e8i | 1.49140i | 0.666282 | + | 0.745700i | \(0.267885\pi\) | ||||
−0.666282 | + | 0.745700i | \(0.732115\pi\) | |||||||
\(314\) | −5.71737e8 | −1.04218 | ||||||||
\(315\) | 6.11597e7 | + | 9.05251e7i | 0.110250 | + | 0.163186i | ||||
\(316\) | −1.39081e8 | −0.247950 | ||||||||
\(317\) | 2.03639e8i | 0.359049i | 0.983754 | + | 0.179524i | \(0.0574559\pi\) | ||||
−0.983754 | + | 0.179524i | \(0.942544\pi\) | |||||||
\(318\) | − | 3.62679e7i | − | 0.0632451i | ||||||
\(319\) | 1.28893e8 | 0.222311 | ||||||||
\(320\) | −4.92873e8 | + | 3.32990e8i | −0.840834 | + | 0.568076i | ||||
\(321\) | −2.87031e8 | −0.484352 | ||||||||
\(322\) | − | 3.51904e8i | − | 0.587393i | ||||||
\(323\) | − | 5.01956e8i | − | 0.828813i | ||||||
\(324\) | 2.72884e7 | 0.0445729 | ||||||||
\(325\) | 4.21505e8 | + | 1.69558e8i | 0.681101 | + | 0.273984i | ||||
\(326\) | −3.23140e7 | −0.0516569 | ||||||||
\(327\) | 3.42548e8i | 0.541757i | ||||||||
\(328\) | 1.21126e8i | 0.189530i | ||||||||
\(329\) | −4.79245e8 | −0.741946 | ||||||||
\(330\) | 3.19196e8 | − | 2.15652e8i | 0.488944 | − | 0.330336i | ||||
\(331\) | −2.04595e8 | −0.310097 | −0.155049 | − | 0.987907i | \(-0.549553\pi\) | ||||
−0.155049 | + | 0.987907i | \(0.549553\pi\) | |||||||
\(332\) | − | 2.33521e8i | − | 0.350222i | ||||||
\(333\) | − | 1.92860e8i | − | 0.286212i | ||||||
\(334\) | −3.17875e8 | −0.466813 | ||||||||
\(335\) | 4.49832e8 | + | 6.65816e8i | 0.653723 | + | 0.967604i | ||||
\(336\) | −1.03865e8 | −0.149377 | ||||||||
\(337\) | 1.27274e9i | 1.81149i | 0.423823 | + | 0.905745i | \(0.360688\pi\) | ||||
−0.423823 | + | 0.905745i | \(0.639312\pi\) | |||||||
\(338\) | − | 2.53279e8i | − | 0.356771i | ||||||
\(339\) | −1.76655e8 | −0.246279 | ||||||||
\(340\) | 7.61406e7 | + | 1.12699e8i | 0.105061 | + | 0.155505i | ||||
\(341\) | −9.26088e8 | −1.26477 | ||||||||
\(342\) | − | 3.38069e8i | − | 0.456997i | ||||||
\(343\) | − | 7.28973e8i | − | 0.975398i | ||||||
\(344\) | 1.32699e9 | 1.75758 | ||||||||
\(345\) | −4.68791e8 | + | 3.16720e8i | −0.614629 | + | 0.415249i | ||||
\(346\) | −6.11416e8 | −0.793542 | ||||||||
\(347\) | 1.14893e8i | 0.147618i | 0.997272 | + | 0.0738091i | \(0.0235156\pi\) | ||||
−0.997272 | + | 0.0738091i | \(0.976484\pi\) | |||||||
\(348\) | 3.06500e7i | 0.0389855i | ||||||||
\(349\) | −4.53912e8 | −0.571587 | −0.285794 | − | 0.958291i | \(-0.592257\pi\) | ||||
−0.285794 | + | 0.958291i | \(0.592257\pi\) | |||||||
\(350\) | −1.36865e8 | + | 3.40233e8i | −0.170629 | + | 0.424169i | ||||
\(351\) | 1.14465e8 | 0.141286 | ||||||||
\(352\) | − | 8.05565e8i | − | 0.984467i | ||||||
\(353\) | − | 8.07883e8i | − | 0.977546i | −0.872411 | − | 0.488773i | \(-0.837445\pi\) | ||
0.872411 | − | 0.488773i | \(-0.162555\pi\) | |||||||
\(354\) | 3.68322e7 | 0.0441283 | ||||||||
\(355\) | −4.38718e8 | + | 2.96402e8i | −0.520458 | + | 0.351627i | ||||
\(356\) | 6.01391e8 | 0.706451 | ||||||||
\(357\) | 1.37185e8i | 0.159577i | ||||||||
\(358\) | − | 6.51620e8i | − | 0.750591i | ||||||
\(359\) | 1.05589e9 | 1.20445 | 0.602225 | − | 0.798327i | \(-0.294281\pi\) | ||||
0.602225 | + | 0.798327i | \(0.294281\pi\) | |||||||
\(360\) | 1.79114e8 | + | 2.65114e8i | 0.202335 | + | 0.299485i | ||||
\(361\) | 1.91176e9 | 2.13875 | ||||||||
\(362\) | 1.95450e8i | 0.216549i | ||||||||
\(363\) | 3.91617e8i | 0.429723i | ||||||||
\(364\) | 1.60103e8 | 0.173998 | ||||||||
\(365\) | −7.31392e8 | − | 1.08257e9i | −0.787273 | − | 1.16528i | ||||
\(366\) | 1.70663e8 | 0.181951 | ||||||||
\(367\) | 6.63835e8i | 0.701018i | 0.936559 | + | 0.350509i | \(0.113991\pi\) | ||||
−0.936559 | + | 0.350509i | \(0.886009\pi\) | |||||||
\(368\) | − | 5.37874e8i | − | 0.562618i | ||||||
\(369\) | 5.62348e7 | 0.0582657 | ||||||||
\(370\) | 5.36444e8 | − | 3.62427e8i | 0.550577 | − | 0.371975i | ||||
\(371\) | −8.22604e7 | −0.0836338 | ||||||||
\(372\) | − | 2.20219e8i | − | 0.221796i | ||||||
\(373\) | − | 8.17776e8i | − | 0.815931i | −0.912997 | − | 0.407966i | \(-0.866238\pi\) | ||
0.912997 | − | 0.407966i | \(-0.133762\pi\) | |||||||
\(374\) | 4.83723e8 | 0.478130 | ||||||||
\(375\) | 5.76425e8 | − | 1.23891e8i | 0.564460 | − | 0.121320i | ||||
\(376\) | −1.40353e9 | −1.36165 | ||||||||
\(377\) | 1.28566e8i | 0.123575i | ||||||||
\(378\) | 9.23948e7i | 0.0879885i | ||||||||
\(379\) | −1.24877e9 | −1.17827 | −0.589137 | − | 0.808033i | \(-0.700532\pi\) | ||||
−0.589137 | + | 0.808033i | \(0.700532\pi\) | |||||||
\(380\) | −6.29921e8 | + | 4.25581e8i | −0.588903 | + | 0.397869i | ||||
\(381\) | 8.86084e8 | 0.820801 | ||||||||
\(382\) | 7.25529e7i | 0.0665937i | ||||||||
\(383\) | 1.76845e9i | 1.60841i | 0.594349 | + | 0.804207i | \(0.297410\pi\) | ||||
−0.594349 | + | 0.804207i | \(0.702590\pi\) | |||||||
\(384\) | −2.55351e7 | −0.0230132 | ||||||||
\(385\) | −4.89128e8 | − | 7.23980e8i | −0.436828 | − | 0.646568i | ||||
\(386\) | −1.10873e8 | −0.0981226 | ||||||||
\(387\) | − | 6.16082e8i | − | 0.540319i | ||||||
\(388\) | − | 2.48417e8i | − | 0.215909i | ||||||
\(389\) | 1.64047e9 | 1.41301 | 0.706506 | − | 0.707707i | \(-0.250270\pi\) | ||||
0.706506 | + | 0.707707i | \(0.250270\pi\) | |||||||
\(390\) | 2.15105e8 | + | 3.18387e8i | 0.183622 | + | 0.271787i | ||||
\(391\) | −7.10425e8 | −0.601035 | ||||||||
\(392\) | − | 8.41752e8i | − | 0.705802i | ||||||
\(393\) | 5.62420e7i | 0.0467398i | ||||||||
\(394\) | 2.06208e8 | 0.169851 | ||||||||
\(395\) | −6.27324e8 | + | 4.23827e8i | −0.512156 | + | 0.346018i | ||||
\(396\) | −2.18241e8 | −0.176605 | ||||||||
\(397\) | − | 2.89394e8i | − | 0.232126i | −0.993242 | − | 0.116063i | \(-0.962973\pi\) | ||
0.993242 | − | 0.116063i | \(-0.0370274\pi\) | |||||||
\(398\) | 1.22563e9i | 0.974472i | ||||||||
\(399\) | −7.66785e8 | −0.604322 | ||||||||
\(400\) | −2.09193e8 | + | 5.20036e8i | −0.163432 | + | 0.406278i | ||||
\(401\) | −1.40144e9 | −1.08535 | −0.542673 | − | 0.839944i | \(-0.682588\pi\) | ||||
−0.542673 | + | 0.839944i | \(0.682588\pi\) | |||||||
\(402\) | 6.79568e8i | 0.521725i | ||||||||
\(403\) | − | 9.23739e8i | − | 0.703043i | ||||||
\(404\) | −1.00287e9 | −0.756678 | ||||||||
\(405\) | 1.23084e8 | − | 8.31569e7i | 0.0920682 | − | 0.0622022i | ||||
\(406\) | −1.03777e8 | −0.0769588 | ||||||||
\(407\) | 1.54241e9i | 1.13402i | ||||||||
\(408\) | 4.01765e8i | 0.292861i | ||||||||
\(409\) | −2.85819e8 | −0.206566 | −0.103283 | − | 0.994652i | \(-0.532935\pi\) | ||||
−0.103283 | + | 0.994652i | \(0.532935\pi\) | |||||||
\(410\) | 1.05678e8 | + | 1.56418e8i | 0.0757251 | + | 0.112084i | ||||
\(411\) | 1.13458e9 | 0.806100 | ||||||||
\(412\) | 9.47356e8i | 0.667380i | ||||||||
\(413\) | − | 8.35405e7i | − | 0.0583541i | ||||||
\(414\) | −4.78473e8 | −0.331403 | ||||||||
\(415\) | −7.11617e8 | − | 1.05330e9i | −0.488740 | − | 0.723406i | ||||
\(416\) | 8.03522e8 | 0.547232 | ||||||||
\(417\) | − | 1.32156e9i | − | 0.892502i | ||||||
\(418\) | 2.70373e9i | 1.81070i | ||||||||
\(419\) | 1.44224e9 | 0.957827 | 0.478914 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478914 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(420\) | 1.72159e8 | − | 1.16312e8i | 0.113385 | − | 0.0766042i | ||||
\(421\) | 2.04694e9 | 1.33696 | 0.668480 | − | 0.743730i | \(-0.266945\pi\) | ||||
0.668480 | + | 0.743730i | \(0.266945\pi\) | |||||||
\(422\) | − | 9.71338e8i | − | 0.629183i | ||||||
\(423\) | 6.51615e8i | 0.418601i | ||||||||
\(424\) | −2.40910e8 | −0.153488 | ||||||||
\(425\) | 6.86864e8 | + | 2.76303e8i | 0.434020 | + | 0.174592i | ||||
\(426\) | −4.47778e8 | −0.280627 | ||||||||
\(427\) | − | 3.87086e8i | − | 0.240608i | ||||||
\(428\) | 5.45869e8i | 0.336539i | ||||||||
\(429\) | −9.15443e8 | −0.559797 | ||||||||
\(430\) | 1.71364e9 | − | 1.15775e9i | 1.03939 | − | 0.702225i | ||||
\(431\) | −1.83156e9 | −1.10192 | −0.550961 | − | 0.834531i | \(-0.685739\pi\) | ||||
−0.550961 | + | 0.834531i | \(0.685739\pi\) | |||||||
\(432\) | 1.41222e8i | 0.0842773i | ||||||||
\(433\) | 2.10470e9i | 1.24590i | 0.782262 | + | 0.622950i | \(0.214066\pi\) | ||||
−0.782262 | + | 0.622950i | \(0.785934\pi\) | |||||||
\(434\) | 7.45629e8 | 0.437833 | ||||||||
\(435\) | 9.34008e7 | + | 1.38247e8i | 0.0544049 | + | 0.0805271i | ||||
\(436\) | 6.51451e8 | 0.376425 | ||||||||
\(437\) | − | 3.97086e9i | − | 2.27614i | ||||||
\(438\) | − | 1.10492e9i | − | 0.628309i | ||||||
\(439\) | −1.23565e9 | −0.697059 | −0.348529 | − | 0.937298i | \(-0.613319\pi\) | ||||
−0.348529 | + | 0.937298i | \(0.613319\pi\) | |||||||
\(440\) | −1.43247e9 | − | 2.12027e9i | −0.801683 | − | 1.18661i | ||||
\(441\) | −3.90799e8 | −0.216979 | ||||||||
\(442\) | 4.82496e8i | 0.265776i | ||||||||
\(443\) | − | 1.12007e9i | − | 0.612114i | −0.952013 | − | 0.306057i | \(-0.900990\pi\) | ||
0.952013 | − | 0.306057i | \(-0.0990098\pi\) | |||||||
\(444\) | −3.66777e8 | −0.198867 | ||||||||
\(445\) | 2.71257e9 | − | 1.83264e9i | 1.45922 | − | 0.985864i | ||||
\(446\) | −4.01720e8 | −0.214413 | ||||||||
\(447\) | 1.01868e9i | 0.539464i | ||||||||
\(448\) | 1.14099e9i | 0.599527i | ||||||||
\(449\) | −1.60454e8 | −0.0836542 | −0.0418271 | − | 0.999125i | \(-0.513318\pi\) | ||||
−0.0418271 | + | 0.999125i | \(0.513318\pi\) | |||||||
\(450\) | 4.62605e8 | + | 1.86091e8i | 0.239313 | + | 0.0962677i | ||||
\(451\) | −4.49742e8 | −0.230858 | ||||||||
\(452\) | 3.35958e8i | 0.171120i | ||||||||
\(453\) | − | 1.72793e8i | − | 0.0873340i | ||||||
\(454\) | −5.78697e8 | −0.290239 | ||||||||
\(455\) | 7.22144e8 | − | 4.87888e8i | 0.359405 | − | 0.242818i | ||||
\(456\) | −2.24563e9 | −1.10907 | ||||||||
\(457\) | − | 1.05598e8i | − | 0.0517544i | −0.999665 | − | 0.0258772i | \(-0.991762\pi\) | ||
0.999665 | − | 0.0258772i | \(-0.00823789\pi\) | |||||||
\(458\) | − | 1.23893e9i | − | 0.602585i | ||||||
\(459\) | 1.86527e8 | 0.0900319 | ||||||||
\(460\) | 6.02331e8 | + | 8.91537e8i | 0.288525 | + | 0.427058i | ||||
\(461\) | 2.40108e9 | 1.14144 | 0.570721 | − | 0.821144i | \(-0.306664\pi\) | ||||
0.570721 | + | 0.821144i | \(0.306664\pi\) | |||||||
\(462\) | − | 7.38933e8i | − | 0.348625i | ||||||
\(463\) | − | 1.64082e9i | − | 0.768295i | −0.923272 | − | 0.384147i | \(-0.874495\pi\) | ||
0.923272 | − | 0.384147i | \(-0.125505\pi\) | |||||||
\(464\) | −1.58619e8 | −0.0737128 | ||||||||
\(465\) | −6.71080e8 | − | 9.93295e8i | −0.309520 | − | 0.458134i | ||||
\(466\) | 1.36193e9 | 0.623453 | ||||||||
\(467\) | 1.58089e9i | 0.718277i | 0.933284 | + | 0.359139i | \(0.116929\pi\) | ||||
−0.933284 | + | 0.359139i | \(0.883071\pi\) | |||||||
\(468\) | − | 2.17687e8i | − | 0.0981686i | ||||||
\(469\) | 1.54135e9 | 0.689916 | ||||||||
\(470\) | −1.81248e9 | + | 1.22453e9i | −0.805249 | + | 0.544034i | ||||
\(471\) | 1.76319e9 | 0.777544 | ||||||||
\(472\) | − | 2.44659e8i | − | 0.107094i | ||||||
\(473\) | 4.92715e9i | 2.14083i | ||||||||
\(474\) | −6.40281e8 | −0.276151 | ||||||||
\(475\) | −1.54437e9 | + | 3.83916e9i | −0.661185 | + | 1.64365i | ||||
\(476\) | 2.60896e8 | 0.110877 | ||||||||
\(477\) | 1.11847e8i | 0.0471856i | ||||||||
\(478\) | − | 7.49411e7i | − | 0.0313850i | ||||||
\(479\) | 7.41778e8 | 0.308389 | 0.154195 | − | 0.988040i | \(-0.450722\pi\) | ||||
0.154195 | + | 0.988040i | \(0.450722\pi\) | |||||||
\(480\) | 8.64026e8 | − | 5.83744e8i | 0.356601 | − | 0.240923i | ||||
\(481\) | −1.53850e9 | −0.630361 | ||||||||
\(482\) | 1.89135e9i | 0.769321i | ||||||||
\(483\) | 1.08524e9i | 0.438240i | ||||||||
\(484\) | 7.44768e8 | 0.298581 | ||||||||
\(485\) | −7.57011e8 | − | 1.12049e9i | −0.301305 | − | 0.445975i | ||||
\(486\) | 1.25626e8 | 0.0496425 | ||||||||
\(487\) | 6.33772e7i | 0.0248646i | 0.999923 | + | 0.0124323i | \(0.00395743\pi\) | ||||
−0.999923 | + | 0.0124323i | \(0.996043\pi\) | |||||||
\(488\) | − | 1.13363e9i | − | 0.441573i | ||||||
\(489\) | 9.96534e7 | 0.0385400 | ||||||||
\(490\) | −7.34398e8 | − | 1.08701e9i | −0.281997 | − | 0.417397i | ||||
\(491\) | −3.94003e9 | −1.50215 | −0.751077 | − | 0.660215i | \(-0.770465\pi\) | ||||
−0.751077 | + | 0.660215i | \(0.770465\pi\) | |||||||
\(492\) | − | 1.06946e8i | − | 0.0404844i | ||||||
\(493\) | 2.09504e8i | 0.0787461i | ||||||||
\(494\) | −2.69687e9 | −1.00650 | ||||||||
\(495\) | −9.84374e8 | + | 6.65053e8i | −0.364789 | + | 0.246455i | ||||
\(496\) | 1.13967e9 | 0.419366 | ||||||||
\(497\) | 1.01562e9i | 0.371095i | ||||||||
\(498\) | − | 1.07505e9i | − | 0.390055i | ||||||
\(499\) | 3.16502e8 | 0.114031 | 0.0570157 | − | 0.998373i | \(-0.481841\pi\) | ||||
0.0570157 | + | 0.998373i | \(0.481841\pi\) | |||||||
\(500\) | −2.35613e8 | − | 1.09623e9i | −0.0842956 | − | 0.392200i | ||||
\(501\) | 9.80298e8 | 0.348278 | ||||||||
\(502\) | − | 6.58245e8i | − | 0.232233i | ||||||
\(503\) | − | 3.82978e9i | − | 1.34179i | −0.741551 | − | 0.670896i | \(-0.765910\pi\) | ||
0.741551 | − | 0.670896i | \(-0.234090\pi\) | |||||||
\(504\) | 6.13734e8 | 0.213537 | ||||||||
\(505\) | −4.52345e9 | + | 3.05609e9i | −1.56297 | + | 1.05596i | ||||
\(506\) | 3.82662e9 | 1.31307 | ||||||||
\(507\) | 7.81089e8i | 0.266178i | ||||||||
\(508\) | − | 1.68513e9i | − | 0.570311i | ||||||
\(509\) | 2.44585e8 | 0.0822085 | 0.0411043 | − | 0.999155i | \(-0.486912\pi\) | ||||
0.0411043 | + | 0.999155i | \(0.486912\pi\) | |||||||
\(510\) | 3.50525e8 | + | 5.18827e8i | 0.117010 | + | 0.173192i | ||||
\(511\) | −2.50612e9 | −0.830860 | ||||||||
\(512\) | 2.43340e9i | 0.801252i | ||||||||
\(513\) | 1.04257e9i | 0.340954i | ||||||||
\(514\) | 2.19183e9 | 0.711928 | ||||||||
\(515\) | 2.88691e9 | + | 4.27304e9i | 0.931340 | + | 1.37852i | ||||
\(516\) | −1.17165e9 | −0.375426 | ||||||||
\(517\) | − | 5.21133e9i | − | 1.65856i | ||||||
\(518\) | − | 1.24186e9i | − | 0.392570i | ||||||
\(519\) | 1.88555e9 | 0.592042 | ||||||||
\(520\) | 2.11489e9 | − | 1.42884e9i | 0.659593 | − | 0.445628i | ||||
\(521\) | −7.10895e8 | −0.220229 | −0.110114 | − | 0.993919i | \(-0.535122\pi\) | ||||
−0.110114 | + | 0.993919i | \(0.535122\pi\) | |||||||
\(522\) | 1.41102e8i | 0.0434196i | ||||||||
\(523\) | − | 3.12678e9i | − | 0.955744i | −0.878429 | − | 0.477872i | \(-0.841408\pi\) | ||
0.878429 | − | 0.477872i | \(-0.158592\pi\) | |||||||
\(524\) | 1.06960e8 | 0.0324759 | ||||||||
\(525\) | 4.22078e8 | − | 1.04925e9i | 0.127302 | − | 0.316462i | ||||
\(526\) | −1.97783e9 | −0.592570 | ||||||||
\(527\) | − | 1.50528e9i | − | 0.448002i | ||||||
\(528\) | − | 1.12944e9i | − | 0.333920i | ||||||
\(529\) | −2.21518e9 | −0.650601 | ||||||||
\(530\) | −3.11104e8 | + | 2.10185e8i | −0.0907695 | + | 0.0613248i | ||||
\(531\) | −1.13587e8 | −0.0329230 | ||||||||
\(532\) | 1.45825e9i | 0.419897i | ||||||||
\(533\) | − | 4.48601e8i | − | 0.128326i | ||||||
\(534\) | 2.76859e9 | 0.786801 | ||||||||
\(535\) | 1.66345e9 | + | 2.46214e9i | 0.469646 | + | 0.695144i | ||||
\(536\) | 4.51404e9 | 1.26616 | ||||||||
\(537\) | 2.00954e9i | 0.559997i | ||||||||
\(538\) | − | 2.24071e9i | − | 0.620366i | ||||||
\(539\) | 3.12544e9 | 0.859707 | ||||||||
\(540\) | −1.58146e8 | − | 2.34079e8i | −0.0432195 | − | 0.0639711i | ||||
\(541\) | 1.36632e7 | 0.00370991 | 0.00185495 | − | 0.999998i | \(-0.499410\pi\) | ||||
0.00185495 | + | 0.999998i | \(0.499410\pi\) | |||||||
\(542\) | 1.42250e9i | 0.383755i | ||||||||
\(543\) | − | 6.02751e8i | − | 0.161562i | ||||||
\(544\) | 1.30938e9 | 0.348714 | ||||||||
\(545\) | 2.93836e9 | − | 1.98519e9i | 0.777531 | − | 0.525308i | ||||
\(546\) | 7.37059e8 | 0.193788 | ||||||||
\(547\) | − | 2.64940e9i | − | 0.692136i | −0.938209 | − | 0.346068i | \(-0.887517\pi\) | ||
0.938209 | − | 0.346068i | \(-0.112483\pi\) | |||||||
\(548\) | − | 2.15772e9i | − | 0.560097i | ||||||
\(549\) | −5.26309e8 | −0.135749 | ||||||||
\(550\) | −3.69971e9 | − | 1.48827e9i | −0.948197 | − | 0.381428i | ||||
\(551\) | −1.17101e9 | −0.298214 | ||||||||
\(552\) | 3.17827e9i | 0.804274i | ||||||||
\(553\) | 1.45224e9i | 0.365175i | ||||||||
\(554\) | −2.01673e9 | −0.503923 | ||||||||
\(555\) | −1.65435e9 | + | 1.11769e9i | −0.410772 | + | 0.277522i | ||||
\(556\) | −2.51330e9 | −0.620131 | ||||||||
\(557\) | − | 1.23692e9i | − | 0.303284i | −0.988435 | − | 0.151642i | \(-0.951544\pi\) | ||
0.988435 | − | 0.151642i | \(-0.0484561\pi\) | |||||||
\(558\) | − | 1.01381e9i | − | 0.247023i | ||||||
\(559\) | −4.91466e9 | −1.19001 | ||||||||
\(560\) | 6.01936e8 | + | 8.90952e8i | 0.144841 | + | 0.214386i | ||||
\(561\) | −1.49176e9 | −0.356721 | ||||||||
\(562\) | 3.56962e9i | 0.848292i | ||||||||
\(563\) | − | 1.73095e9i | − | 0.408795i | −0.978888 | − | 0.204397i | \(-0.934477\pi\) | ||
0.978888 | − | 0.204397i | \(-0.0655234\pi\) | |||||||
\(564\) | 1.23923e9 | 0.290853 | ||||||||
\(565\) | 1.02378e9 | + | 1.51534e9i | 0.238801 | + | 0.353460i | ||||
\(566\) | −1.78632e9 | −0.414097 | ||||||||
\(567\) | − | 2.84937e8i | − | 0.0656461i | ||||||
\(568\) | 2.97438e9i | 0.681046i | ||||||||
\(569\) | −5.70834e9 | −1.29902 | −0.649511 | − | 0.760352i | \(-0.725027\pi\) | ||||
−0.649511 | + | 0.760352i | \(0.725027\pi\) | |||||||
\(570\) | −2.89994e9 | + | 1.95923e9i | −0.655883 | + | 0.443121i | ||||
\(571\) | 3.41952e9 | 0.768668 | 0.384334 | − | 0.923194i | \(-0.374431\pi\) | ||||
0.384334 | + | 0.923194i | \(0.374431\pi\) | |||||||
\(572\) | 1.74097e9i | 0.388960i | ||||||||
\(573\) | − | 2.23747e8i | − | 0.0496839i | ||||||
\(574\) | 3.62105e8 | 0.0799176 | ||||||||
\(575\) | 5.43362e9 | + | 2.18577e9i | 1.19193 | + | 0.479475i | ||||
\(576\) | 1.55137e9 | 0.338249 | ||||||||
\(577\) | 3.59458e9i | 0.778991i | 0.921028 | + | 0.389496i | \(0.127351\pi\) | ||||
−0.921028 | + | 0.389496i | \(0.872649\pi\) | |||||||
\(578\) | − | 2.80631e9i | − | 0.604489i | ||||||
\(579\) | 3.41922e8 | 0.0732068 | ||||||||
\(580\) | 2.62914e8 | − | 1.77628e8i | 0.0559521 | − | 0.0378018i | ||||
\(581\) | −2.43836e9 | −0.515799 | ||||||||
\(582\) | − | 1.14363e9i | − | 0.240466i | ||||||
\(583\) | − | 8.94502e8i | − | 0.186957i | ||||||
\(584\) | −7.33948e9 | −1.52483 | ||||||||
\(585\) | −6.63366e8 | − | 9.81877e8i | −0.136996 | − | 0.202774i | ||||
\(586\) | −8.41201e7 | −0.0172686 | ||||||||
\(587\) | 6.09879e8i | 0.124454i | 0.998062 | + | 0.0622272i | \(0.0198204\pi\) | ||||
−0.998062 | + | 0.0622272i | \(0.980180\pi\) | |||||||
\(588\) | 7.43213e8i | 0.150762i | ||||||||
\(589\) | 8.41361e9 | 1.69660 | ||||||||
\(590\) | −2.13456e8 | − | 3.15945e8i | −0.0427884 | − | 0.0633330i | ||||
\(591\) | −6.35926e8 | −0.126722 | ||||||||
\(592\) | − | 1.89814e9i | − | 0.376012i | ||||||
\(593\) | 8.96159e9i | 1.76479i | 0.470507 | + | 0.882396i | \(0.344071\pi\) | ||||
−0.470507 | + | 0.882396i | \(0.655929\pi\) | |||||||
\(594\) | −1.00470e9 | −0.196692 | ||||||||
\(595\) | 1.17677e9 | − | 7.95037e8i | 0.229025 | − | 0.154731i | ||||
\(596\) | 1.93731e9 | 0.374832 | ||||||||
\(597\) | − | 3.77974e9i | − | 0.727030i | ||||||
\(598\) | 3.81692e9i | 0.729892i | ||||||||
\(599\) | −7.37621e9 | −1.40230 | −0.701148 | − | 0.713016i | \(-0.747329\pi\) | ||||
−0.701148 | + | 0.713016i | \(0.747329\pi\) | |||||||
\(600\) | 1.23611e9 | − | 3.07286e9i | 0.233630 | − | 0.580783i | ||||
\(601\) | 4.41191e9 | 0.829022 | 0.414511 | − | 0.910044i | \(-0.363953\pi\) | ||||
0.414511 | + | 0.910044i | \(0.363953\pi\) | |||||||
\(602\) | − | 3.96704e9i | − | 0.741104i | ||||||
\(603\) | − | 2.09573e9i | − | 0.389246i | ||||||
\(604\) | −3.28614e8 | −0.0606816 | ||||||||
\(605\) | 3.35927e9 | − | 2.26956e9i | 0.616739 | − | 0.416675i | ||||
\(606\) | −4.61687e9 | −0.842740 | ||||||||
\(607\) | 2.08098e9i | 0.377666i | 0.982009 | + | 0.188833i | \(0.0604704\pi\) | ||||
−0.982009 | + | 0.188833i | \(0.939530\pi\) | |||||||
\(608\) | 7.31865e9i | 1.32059i | ||||||||
\(609\) | 3.20038e8 | 0.0574171 | ||||||||
\(610\) | −9.89051e8 | − | 1.46394e9i | −0.176427 | − | 0.261137i | ||||
\(611\) | 5.19811e9 | 0.921938 | ||||||||
\(612\) | − | 3.54732e8i | − | 0.0625562i | ||||||
\(613\) | 7.91735e8i | 0.138825i | 0.997588 | + | 0.0694126i | \(0.0221125\pi\) | ||||
−0.997588 | + | 0.0694126i | \(0.977888\pi\) | |||||||
\(614\) | 1.52726e9 | 0.266270 | ||||||||
\(615\) | −3.25901e8 | − | 4.82380e8i | −0.0564966 | − | 0.0836231i | ||||
\(616\) | −4.90837e9 | −0.846068 | ||||||||
\(617\) | − | 6.13159e9i | − | 1.05093i | −0.850814 | − | 0.525467i | \(-0.823891\pi\) | ||
0.850814 | − | 0.525467i | \(-0.176109\pi\) | |||||||
\(618\) | 4.36130e9i | 0.743286i | ||||||||
\(619\) | 7.99222e9 | 1.35441 | 0.677205 | − | 0.735795i | \(-0.263191\pi\) | ||||
0.677205 | + | 0.735795i | \(0.263191\pi\) | |||||||
\(620\) | −1.88902e9 | + | 1.27624e9i | −0.318322 | + | 0.215062i | ||||
\(621\) | 1.47557e9 | 0.247252 | ||||||||
\(622\) | − | 1.69552e9i | − | 0.282511i | ||||||
\(623\) | − | 6.27954e9i | − | 1.04045i | ||||||
\(624\) | 1.12657e9 | 0.185615 | ||||||||
\(625\) | −4.40331e9 | − | 4.22655e9i | −0.721439 | − | 0.692478i | ||||
\(626\) | 7.08371e9 | 1.15412 | ||||||||
\(627\) | − | 8.33805e9i | − | 1.35092i | ||||||
\(628\) | − | 3.35319e9i | − | 0.540255i | ||||||
\(629\) | −2.50706e9 | −0.401687 | ||||||||
\(630\) | 7.92558e8 | − | 5.35460e8i | 0.126281 | − | 0.0853169i | ||||
\(631\) | 1.14433e10 | 1.81322 | 0.906609 | − | 0.421973i | \(-0.138662\pi\) | ||||
0.906609 | + | 0.421973i | \(0.138662\pi\) | |||||||
\(632\) | 4.25307e9i | 0.670183i | ||||||||
\(633\) | 2.99552e9i | 0.469417i | ||||||||
\(634\) | 1.78288e9 | 0.277850 | ||||||||
\(635\) | −5.13517e9 | − | 7.60079e9i | −0.795878 | − | 1.17801i | ||||
\(636\) | 2.12708e8 | 0.0327856 | ||||||||
\(637\) | 3.11751e9i | 0.477882i | ||||||||
\(638\) | − | 1.12847e9i | − | 0.172035i | ||||||
\(639\) | 1.38091e9 | 0.209369 | ||||||||
\(640\) | 1.47985e8 | + | 2.19038e8i | 0.0223145 | + | 0.0330286i | ||||
\(641\) | −1.08654e10 | −1.62945 | −0.814726 | − | 0.579846i | \(-0.803113\pi\) | ||||
−0.814726 | + | 0.579846i | \(0.803113\pi\) | |||||||
\(642\) | 2.51299e9i | 0.374816i | ||||||||
\(643\) | − | 1.73452e7i | − | 0.00257301i | −0.999999 | − | 0.00128651i | \(-0.999590\pi\) | ||
0.999999 | − | 0.00128651i | \(-0.000409508\pi\) | |||||||
\(644\) | 2.06389e9 | 0.304499 | ||||||||
\(645\) | −5.28472e9 | + | 3.57041e9i | −0.775466 | + | 0.523913i | ||||
\(646\) | −4.39468e9 | −0.641377 | ||||||||
\(647\) | − | 4.60457e9i | − | 0.668381i | −0.942506 | − | 0.334190i | \(-0.891537\pi\) | ||
0.942506 | − | 0.334190i | \(-0.108463\pi\) | |||||||
\(648\) | − | 8.34475e8i | − | 0.120476i | ||||||
\(649\) | 9.08422e8 | 0.130446 | ||||||||
\(650\) | 1.48450e9 | − | 3.69033e9i | 0.212023 | − | 0.527070i | ||||
\(651\) | −2.29946e9 | −0.326657 | ||||||||
\(652\) | − | 1.89519e8i | − | 0.0267784i | ||||||
\(653\) | 8.69457e9i | 1.22195i | 0.791652 | + | 0.610973i | \(0.209222\pi\) | ||||
−0.791652 | + | 0.610973i | \(0.790778\pi\) | |||||||
\(654\) | 2.99905e9 | 0.419239 | ||||||||
\(655\) | 4.82441e8 | − | 3.25942e8i | 0.0670810 | − | 0.0453206i | ||||
\(656\) | 5.53465e8 | 0.0765468 | ||||||||
\(657\) | 3.40749e9i | 0.468765i | ||||||||
\(658\) | 4.19585e9i | 0.574155i | ||||||||
\(659\) | 6.26635e8 | 0.0852934 | 0.0426467 | − | 0.999090i | \(-0.486421\pi\) | ||||
0.0426467 | + | 0.999090i | \(0.486421\pi\) | |||||||
\(660\) | 1.26478e9 | + | 1.87206e9i | 0.171243 | + | 0.253464i | ||||
\(661\) | −1.43479e10 | −1.93234 | −0.966170 | − | 0.257906i | \(-0.916968\pi\) | ||||
−0.966170 | + | 0.257906i | \(0.916968\pi\) | |||||||
\(662\) | 1.79126e9i | 0.239969i | ||||||||
\(663\) | − | 1.48798e9i | − | 0.198289i | ||||||
\(664\) | −7.14104e9 | −0.946614 | ||||||||
\(665\) | 4.44379e9 | + | 6.57745e9i | 0.585973 | + | 0.867324i | ||||
\(666\) | −1.68851e9 | −0.221485 | ||||||||
\(667\) | 1.65734e9i | 0.216258i | ||||||||
\(668\) | − | 1.86431e9i | − | 0.241991i | ||||||
\(669\) | 1.23887e9 | 0.159968 | ||||||||
\(670\) | 5.82930e9 | − | 3.93833e9i | 0.748780 | − | 0.505884i | ||||
\(671\) | 4.20919e9 | 0.537861 | ||||||||
\(672\) | − | 2.00020e9i | − | 0.254262i | ||||||
\(673\) | 1.39752e10i | 1.76728i | 0.468169 | + | 0.883639i | \(0.344914\pi\) | ||||
−0.468169 | + | 0.883639i | \(0.655086\pi\) | |||||||
\(674\) | 1.11430e10 | 1.40182 | ||||||||
\(675\) | −1.42663e9 | − | 5.73887e8i | −0.178546 | − | 0.0718229i | ||||
\(676\) | 1.48546e9 | 0.184947 | ||||||||
\(677\) | − | 1.74930e9i | − | 0.216672i | −0.994114 | − | 0.108336i | \(-0.965448\pi\) | ||
0.994114 | − | 0.108336i | \(-0.0345523\pi\) | |||||||
\(678\) | 1.54663e9i | 0.190583i | ||||||||
\(679\) | −2.59390e9 | −0.317987 | ||||||||
\(680\) | 3.44632e9 | − | 2.32837e9i | 0.420314 | − | 0.283969i | ||||
\(681\) | 1.78465e9 | 0.216540 | ||||||||
\(682\) | 8.10800e9i | 0.978743i | ||||||||
\(683\) | 5.25111e9i | 0.630636i | 0.948986 | + | 0.315318i | \(0.102111\pi\) | ||||
−0.948986 | + | 0.315318i | \(0.897889\pi\) | |||||||
\(684\) | 1.98274e9 | 0.236903 | ||||||||
\(685\) | −6.57529e9 | − | 9.73238e9i | −0.781625 | − | 1.15692i | ||||
\(686\) | −6.38224e9 | −0.754812 | ||||||||
\(687\) | 3.82075e9i | 0.449573i | ||||||||
\(688\) | − | 6.06350e9i | − | 0.709845i | ||||||
\(689\) | 8.92234e8 | 0.103923 | ||||||||
\(690\) | 2.77292e9 | + | 4.10432e9i | 0.321341 | + | 0.475630i | ||||
\(691\) | −3.17886e9 | −0.366521 | −0.183260 | − | 0.983064i | \(-0.558665\pi\) | ||||
−0.183260 | + | 0.983064i | \(0.558665\pi\) | |||||||
\(692\) | − | 3.58590e9i | − | 0.411364i | ||||||
\(693\) | 2.27880e9i | 0.260100i | ||||||||
\(694\) | 1.00590e9 | 0.114234 | ||||||||
\(695\) | −1.13362e10 | + | 7.65888e9i | −1.28092 | + | 0.865403i | ||||
\(696\) | 9.37272e8 | 0.105374 | ||||||||
\(697\) | − | 7.31017e8i | − | 0.0817736i | ||||||
\(698\) | 3.97405e9i | 0.442323i | ||||||||
\(699\) | −4.20007e9 | −0.465143 | ||||||||
\(700\) | −1.99544e9 | − | 8.02699e8i | −0.219885 | − | 0.0884524i | ||||
\(701\) | 1.19964e10 | 1.31534 | 0.657672 | − | 0.753304i | \(-0.271541\pi\) | ||||
0.657672 | + | 0.753304i | \(0.271541\pi\) | |||||||
\(702\) | − | 1.00216e9i | − | 0.109334i | ||||||
\(703\) | − | 1.40130e10i | − | 1.52120i | ||||||
\(704\) | −1.24072e10 | −1.34020 | ||||||||
\(705\) | 5.58952e9 | − | 3.77634e9i | 0.600776 | − | 0.405890i | ||||
\(706\) | −7.07311e9 | −0.756474 | ||||||||
\(707\) | 1.04717e10i | 1.11442i | ||||||||
\(708\) | 2.16018e8i | 0.0228756i | ||||||||
\(709\) | −6.04187e9 | −0.636663 | −0.318332 | − | 0.947979i | \(-0.603123\pi\) | ||||
−0.318332 | + | 0.947979i | \(0.603123\pi\) | |||||||
\(710\) | 2.59503e9 | + | 3.84102e9i | 0.272106 | + | 0.402757i | ||||
\(711\) | 1.97457e9 | 0.206029 | ||||||||
\(712\) | − | 1.83904e10i | − | 1.90947i | ||||||
\(713\) | − | 1.19079e10i | − | 1.23033i | ||||||
\(714\) | 1.20107e9 | 0.123488 | ||||||||
\(715\) | 5.30531e9 | + | 7.85263e9i | 0.542800 | + | 0.803422i | ||||
\(716\) | 3.82169e9 | 0.389099 | ||||||||
\(717\) | 2.31112e8i | 0.0234156i | ||||||||
\(718\) | − | 9.24445e9i | − | 0.932063i | ||||||
\(719\) | 7.33783e9 | 0.736235 | 0.368118 | − | 0.929779i | \(-0.380002\pi\) | ||||
0.368118 | + | 0.929779i | \(0.380002\pi\) | |||||||
\(720\) | 1.21140e9 | − | 8.18434e8i | 0.120955 | − | 0.0817184i | ||||
\(721\) | 9.89200e9 | 0.982903 | ||||||||
\(722\) | − | 1.67377e10i | − | 1.65507i | ||||||
\(723\) | − | 5.83276e9i | − | 0.573971i | ||||||
\(724\) | −1.14630e9 | −0.112257 | ||||||||
\(725\) | 6.44583e8 | − | 1.60238e9i | 0.0628196 | − | 0.156164i | ||||
\(726\) | 3.42865e9 | 0.332541 | ||||||||
\(727\) | 5.42358e9i | 0.523499i | 0.965136 | + | 0.261749i | \(0.0842994\pi\) | ||||
−0.965136 | + | 0.261749i | \(0.915701\pi\) | |||||||
\(728\) | − | 4.89593e9i | − | 0.470300i | ||||||
\(729\) | −3.87420e8 | −0.0370370 | ||||||||
\(730\) | −9.47798e9 | + | 6.40342e9i | −0.901750 | + | 0.609231i | ||||
\(731\) | −8.00867e9 | −0.758315 | ||||||||
\(732\) | 1.00092e9i | 0.0943218i | ||||||||
\(733\) | 2.45352e9i | 0.230104i | 0.993359 | + | 0.115052i | \(0.0367035\pi\) | ||||
−0.993359 | + | 0.115052i | \(0.963296\pi\) | |||||||
\(734\) | 5.81195e9 | 0.542483 | ||||||||
\(735\) | 2.26482e9 | + | 3.35226e9i | 0.210391 | + | 0.311409i | ||||
\(736\) | 1.03582e10 | 0.957661 | ||||||||
\(737\) | 1.67607e10i | 1.54225i | ||||||||
\(738\) | − | 4.92342e8i | − | 0.0450889i | ||||||
\(739\) | −1.09881e9 | −0.100154 | −0.0500770 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500770 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(740\) | 2.12560e9 | + | 3.14620e9i | 0.192828 | + | 0.285414i | ||||
\(741\) | 8.31691e9 | 0.750928 | ||||||||
\(742\) | 7.20199e8i | 0.0647200i | ||||||||
\(743\) | − | 1.26814e10i | − | 1.13425i | −0.823633 | − | 0.567123i | \(-0.808056\pi\) | ||
0.823633 | − | 0.567123i | \(-0.191944\pi\) | |||||||
\(744\) | −6.73425e9 | −0.599492 | ||||||||
\(745\) | 8.73821e9 | − | 5.90362e9i | 0.774240 | − | 0.523084i | ||||
\(746\) | −7.15972e9 | −0.631408 | ||||||||
\(747\) | 3.31536e9i | 0.291010i | ||||||||
\(748\) | 2.83699e9i | 0.247858i | ||||||||
\(749\) | 5.69980e9 | 0.495648 | ||||||||
\(750\) | −1.08468e9 | − | 5.04666e9i | −0.0938831 | − | 0.436807i | ||||
\(751\) | 1.42471e9 | 0.122740 | 0.0613699 | − | 0.998115i | \(-0.480453\pi\) | ||||
0.0613699 | + | 0.998115i | \(0.480453\pi\) | |||||||
\(752\) | 6.41322e9i | 0.549938i | ||||||||
\(753\) | 2.02997e9i | 0.173263i | ||||||||
\(754\) | 1.12561e9 | 0.0956286 | ||||||||
\(755\) | −1.48221e9 | + | 1.00140e9i | −0.125342 | + | 0.0846822i | ||||
\(756\) | −5.41887e8 | −0.0456124 | ||||||||
\(757\) | 1.25591e9i | 0.105226i | 0.998615 | + | 0.0526128i | \(0.0167549\pi\) | ||||
−0.998615 | + | 0.0526128i | \(0.983245\pi\) | |||||||
\(758\) | 1.09332e10i | 0.911808i | ||||||||
\(759\) | −1.18010e10 | −0.979651 | ||||||||
\(760\) | 1.30142e10 | + | 1.92629e10i | 1.07540 | + | 1.59175i | ||||
\(761\) | −6.61122e9 | −0.543795 | −0.271897 | − | 0.962326i | \(-0.587651\pi\) | ||||
−0.271897 | + | 0.962326i | \(0.587651\pi\) | |||||||
\(762\) | − | 7.75777e9i | − | 0.635177i | ||||||
\(763\) | − | 6.80225e9i | − | 0.554392i | ||||||
\(764\) | −4.25516e8 | −0.0345215 | ||||||||
\(765\) | −1.08099e9 | − | 1.60002e9i | −0.0872983 | − | 0.129214i | ||||
\(766\) | 1.54830e10 | 1.24467 | ||||||||
\(767\) | 9.06118e8i | 0.0725106i | ||||||||
\(768\) | − | 7.13108e9i | − | 0.568056i | ||||||
\(769\) | −1.61751e10 | −1.28264 | −0.641320 | − | 0.767273i | \(-0.721613\pi\) | ||||
−0.641320 | + | 0.767273i | \(0.721613\pi\) | |||||||
\(770\) | −6.33853e9 | + | 4.28238e9i | −0.500347 | + | 0.338039i | ||||
\(771\) | −6.75941e9 | −0.531151 | ||||||||
\(772\) | − | 6.50259e8i | − | 0.0508658i | ||||||
\(773\) | − | 2.10944e9i | − | 0.164263i | −0.996622 | − | 0.0821313i | \(-0.973827\pi\) | ||
0.996622 | − | 0.0821313i | \(-0.0261727\pi\) | |||||||
\(774\) | −5.39387e9 | −0.418126 | ||||||||
\(775\) | −4.63129e9 | + | 1.15130e10i | −0.357393 | + | 0.888448i | ||||
\(776\) | −7.59656e9 | −0.583581 | ||||||||
\(777\) | 3.82977e9i | 0.292887i | ||||||||
\(778\) | − | 1.43625e10i | − | 1.09346i | ||||||
\(779\) | 4.08595e9 | 0.309680 | ||||||||
\(780\) | −1.86731e9 | + | 1.26157e9i | −0.140892 | + | 0.0951879i | ||||
\(781\) | −1.10439e10 | −0.829553 | ||||||||
\(782\) | 6.21985e9i | 0.465111i | ||||||||
\(783\) | − | 4.35146e8i | − | 0.0323943i | ||||||
\(784\) | −3.84626e9 | −0.285057 | ||||||||
\(785\) | −1.02183e10 | − | 1.51245e10i | −0.753935 | − | 1.11593i | ||||
\(786\) | 4.92405e8 | 0.0361696 | ||||||||
\(787\) | 1.72091e10i | 1.25848i | 0.777211 | + | 0.629240i | \(0.216634\pi\) | ||||
−0.777211 | + | 0.629240i | \(0.783366\pi\) | |||||||
\(788\) | 1.20939e9i | 0.0880491i | ||||||||
\(789\) | 6.09947e9 | 0.442102 | ||||||||
\(790\) | 3.71065e9 | + | 5.49230e9i | 0.267766 | + | 0.396332i | ||||
\(791\) | 3.50797e9 | 0.252022 | ||||||||
\(792\) | 6.67377e9i | 0.477346i | ||||||||
\(793\) | 4.19852e9i | 0.298978i | ||||||||
\(794\) | −2.53368e9 | −0.179630 | ||||||||
\(795\) | 9.59417e8 | − | 6.48192e8i | 0.0677209 | − | 0.0457529i | ||||
\(796\) | −7.18823e9 | −0.505157 | ||||||||
\(797\) | − | 9.52182e9i | − | 0.666217i | −0.942889 | − | 0.333108i | \(-0.891902\pi\) | ||
0.942889 | − | 0.333108i | \(-0.108098\pi\) | |||||||
\(798\) | 6.71329e9i | 0.467655i | ||||||||
\(799\) | 8.47058e9 | 0.587489 | ||||||||
\(800\) | −1.00147e10 | − | 4.02857e9i | −0.691547 | − | 0.278186i | ||||
\(801\) | −8.53810e9 | −0.587012 | ||||||||
\(802\) | 1.22697e10i | 0.839895i | ||||||||
\(803\) | − | 2.72516e10i | − | 1.85732i | ||||||
\(804\) | −3.98560e9 | −0.270457 | ||||||||
\(805\) | 9.30915e9 | − | 6.28936e9i | 0.628962 | − | 0.424933i | ||||
\(806\) | −8.08744e9 | −0.544050 | ||||||||
\(807\) | 6.91016e9i | 0.462840i | ||||||||
\(808\) | 3.06677e10i | 2.04522i | ||||||||
\(809\) | 2.68450e10 | 1.78256 | 0.891278 | − | 0.453458i | \(-0.149810\pi\) | ||||
0.891278 | + | 0.453458i | \(0.149810\pi\) | |||||||
\(810\) | −7.28049e8 | − | 1.07762e9i | −0.0481352 | − | 0.0712470i | ||||
\(811\) | 1.76621e10 | 1.16270 | 0.581351 | − | 0.813653i | \(-0.302524\pi\) | ||||
0.581351 | + | 0.813653i | \(0.302524\pi\) | |||||||
\(812\) | − | 6.08641e8i | − | 0.0398947i | ||||||
\(813\) | − | 4.38685e9i | − | 0.286310i | ||||||
\(814\) | 1.35040e10 | 0.877559 | ||||||||
\(815\) | −5.77526e8 | − | 8.54822e8i | −0.0373698 | − | 0.0553126i | ||||
\(816\) | 1.83580e9 | 0.118280 | ||||||||
\(817\) | − | 4.47638e10i | − | 2.87177i | ||||||
\(818\) | 2.50238e9i | 0.159851i | ||||||||
\(819\) | −2.27302e9 | −0.144581 | ||||||||
\(820\) | −9.17379e8 | + | 6.19790e8i | −0.0581032 | + | 0.0392551i | ||||
\(821\) | 7.60914e9 | 0.479882 | 0.239941 | − | 0.970787i | \(-0.422872\pi\) | ||||
0.239941 | + | 0.970787i | \(0.422872\pi\) | |||||||
\(822\) | − | 9.93339e9i | − | 0.623801i | ||||||
\(823\) | 2.14232e10i | 1.33963i | 0.742529 | + | 0.669814i | \(0.233626\pi\) | ||||
−0.742529 | + | 0.669814i | \(0.766374\pi\) | |||||||
\(824\) | 2.89700e10 | 1.80386 | ||||||||
\(825\) | 1.14096e10 | + | 4.58970e9i | 0.707426 | + | 0.284574i | ||||
\(826\) | −7.31406e8 | −0.0451574 | ||||||||
\(827\) | 1.41079e10i | 0.867345i | 0.901071 | + | 0.433673i | \(0.142783\pi\) | ||||
−0.901071 | + | 0.433673i | \(0.857217\pi\) | |||||||
\(828\) | − | 2.80620e9i | − | 0.171796i | ||||||
\(829\) | −6.92118e9 | −0.421929 | −0.210965 | − | 0.977494i | \(-0.567660\pi\) | ||||
−0.210965 | + | 0.977494i | \(0.567660\pi\) | |||||||
\(830\) | −9.22172e9 | + | 6.23029e9i | −0.559808 | + | 0.378212i | ||||
\(831\) | 6.21943e9 | 0.375965 | ||||||||
\(832\) | − | 1.23757e10i | − | 0.744969i | ||||||
\(833\) | 5.08014e9i | 0.304522i | ||||||||
\(834\) | −1.15704e10 | −0.690663 | ||||||||
\(835\) | −5.68117e9 | − | 8.40895e9i | −0.337703 | − | 0.499849i | ||||
\(836\) | −1.58571e10 | −0.938647 | ||||||||
\(837\) | 3.12650e9i | 0.184297i | ||||||||
\(838\) | − | 1.26269e10i | − | 0.741215i | ||||||
\(839\) | −2.84396e9 | −0.166248 | −0.0831240 | − | 0.996539i | \(-0.526490\pi\) | ||||
−0.0831240 | + | 0.996539i | \(0.526490\pi\) | |||||||
\(840\) | −3.55680e9 | − | 5.26458e9i | −0.207053 | − | 0.306469i | ||||
\(841\) | −1.67611e10 | −0.971666 | ||||||||
\(842\) | − | 1.79212e10i | − | 1.03461i | ||||||
\(843\) | − | 1.10084e10i | − | 0.632889i | ||||||
\(844\) | 5.69681e9 | 0.326162 | ||||||||
\(845\) | 6.70014e9 | − | 4.52668e9i | 0.382020 | − | 0.258096i | ||||
\(846\) | 5.70496e9 | 0.323934 | ||||||||
\(847\) | − | 7.77664e9i | − | 0.439744i | ||||||
\(848\) | 1.10080e9i | 0.0619902i | ||||||||
\(849\) | 5.50886e9 | 0.308948 | ||||||||
\(850\) | 2.41906e9 | − | 6.01357e9i | 0.135108 | − | 0.335866i | ||||
\(851\) | −1.98328e10 | −1.10314 | ||||||||
\(852\) | − | 2.62618e9i | − | 0.145474i | ||||||
\(853\) | − | 1.54319e10i | − | 0.851330i | −0.904881 | − | 0.425665i | \(-0.860040\pi\) | ||
0.904881 | − | 0.425665i | \(-0.139960\pi\) | |||||||
\(854\) | −3.38899e9 | −0.186195 | ||||||||
\(855\) | 8.94315e9 | − | 6.04208e9i | 0.489338 | − | 0.330602i | ||||
\(856\) | 1.66926e10 | 0.909631 | ||||||||
\(857\) | 1.53742e10i | 0.834373i | 0.908821 | + | 0.417186i | \(0.136984\pi\) | ||||
−0.908821 | + | 0.417186i | \(0.863016\pi\) | |||||||
\(858\) | 8.01481e9i | 0.433199i | ||||||||
\(859\) | 1.32076e10 | 0.710966 | 0.355483 | − | 0.934683i | \(-0.384316\pi\) | ||||
0.355483 | + | 0.934683i | \(0.384316\pi\) | |||||||
\(860\) | 6.79012e9 | + | 1.00504e10i | 0.364027 | + | 0.538812i | ||||
\(861\) | −1.11670e9 | −0.0596245 | ||||||||
\(862\) | 1.60355e10i | 0.852722i | ||||||||
\(863\) | 2.37085e10i | 1.25564i | 0.778357 | + | 0.627822i | \(0.216053\pi\) | ||||
−0.778357 | + | 0.627822i | \(0.783947\pi\) | |||||||
\(864\) | −2.71961e9 | −0.143453 | ||||||||
\(865\) | −1.09274e10 | − | 1.61742e10i | −0.574066 | − | 0.849700i | ||||
\(866\) | 1.84269e10 | 0.964139 | ||||||||
\(867\) | 8.65442e9i | 0.450994i | ||||||||
\(868\) | 4.37305e9i | 0.226968i | ||||||||
\(869\) | −1.57917e10 | −0.816320 | ||||||||
\(870\) | 1.21036e9 | − | 8.17735e8i | 0.0623159 | − | 0.0421013i | ||||
\(871\) | −1.67182e10 | −0.857286 | ||||||||
\(872\) | − | 1.99212e10i | − | 1.01744i | ||||||
\(873\) | 3.52684e9i | 0.179406i | ||||||||
\(874\) | −3.47653e10 | −1.76139 | ||||||||
\(875\) | −1.14465e10 | + | 2.46020e9i | −0.577623 | + | 0.124149i | ||||
\(876\) | 6.48028e9 | 0.325709 | ||||||||
\(877\) | − | 3.40371e9i | − | 0.170394i | −0.996364 | − | 0.0851970i | \(-0.972848\pi\) | ||
0.996364 | − | 0.0851970i | \(-0.0271520\pi\) | |||||||
\(878\) | 1.08182e10i | 0.539419i | ||||||||
\(879\) | 2.59419e8 | 0.0128837 | ||||||||
\(880\) | −9.68824e9 | + | 6.54547e9i | −0.479243 | + | 0.323781i | ||||
\(881\) | 3.81831e10 | 1.88129 | 0.940644 | − | 0.339395i | \(-0.110222\pi\) | ||||
0.940644 | + | 0.339395i | \(0.110222\pi\) | |||||||
\(882\) | 3.42149e9i | 0.167910i | ||||||||
\(883\) | 2.44534e10i | 1.19530i | 0.801758 | + | 0.597649i | \(0.203898\pi\) | ||||
−0.801758 | + | 0.597649i | \(0.796102\pi\) | |||||||
\(884\) | −2.82980e9 | −0.137776 | ||||||||
\(885\) | 6.58279e8 | + | 9.74347e8i | 0.0319233 | + | 0.0472511i | ||||
\(886\) | −9.80635e9 | −0.473685 | ||||||||
\(887\) | 1.85474e8i | 0.00892383i | 0.999990 | + | 0.00446192i | \(0.00142028\pi\) | ||||
−0.999990 | + | 0.00446192i | \(0.998580\pi\) | |||||||
\(888\) | 1.12160e10i | 0.537516i | ||||||||
\(889\) | −1.75957e10 | −0.839942 | ||||||||
\(890\) | −1.60450e10 | − | 2.37489e10i | −0.762911 | − | 1.12922i | ||||
\(891\) | 3.09842e9 | 0.146747 | ||||||||
\(892\) | − | 2.35605e9i | − | 0.111150i | ||||||
\(893\) | 4.73455e10i | 2.22484i | ||||||||
\(894\) | 8.91868e9 | 0.417464 | ||||||||
\(895\) | 1.72377e10 | − | 1.16460e10i | 0.803709 | − | 0.542994i | ||||
\(896\) | 5.07069e8 | 0.0235499 | ||||||||
\(897\) | − | 1.17710e10i | − | 0.544554i | ||||||
\(898\) | 1.40479e9i | 0.0647358i | ||||||||
\(899\) | −3.51164e9 | −0.161195 | ||||||||
\(900\) | −1.09141e9 | + | 2.71314e9i | −0.0499042 | + | 0.124057i | ||||
\(901\) | 1.45394e9 | 0.0662231 | ||||||||
\(902\) | 3.93754e9i | 0.178650i | ||||||||
\(903\) | 1.22340e10i | 0.552919i | ||||||||
\(904\) | 1.02735e10 | 0.462520 | ||||||||
\(905\) | −5.17037e9 | + | 3.49316e9i | −0.231874 | + | 0.156656i | ||||
\(906\) | −1.51282e9 | −0.0675834 | ||||||||
\(907\) | 2.45453e10i | 1.09230i | 0.837686 | + | 0.546152i | \(0.183908\pi\) | ||||
−0.837686 | + | 0.546152i | \(0.816092\pi\) | |||||||
\(908\) | − | 3.39401e9i | − | 0.150457i | ||||||
\(909\) | 1.42380e10 | 0.628748 | ||||||||
\(910\) | −4.27151e9 | − | 6.32246e9i | −0.187904 | − | 0.278126i | ||||
\(911\) | 2.83465e9 | 0.124218 | 0.0621092 | − | 0.998069i | \(-0.480217\pi\) | ||||
0.0621092 | + | 0.998069i | \(0.480217\pi\) | |||||||
\(912\) | 1.02611e10i | 0.447930i | ||||||||
\(913\) | − | 2.65148e10i | − | 1.15303i | ||||||
\(914\) | −9.24519e8 | −0.0400501 | ||||||||
\(915\) | 3.05015e9 | + | 4.51466e9i | 0.131628 | + | 0.194828i | ||||
\(916\) | 7.26622e9 | 0.312374 | ||||||||
\(917\) | − | 1.11684e9i | − | 0.0478298i | ||||||
\(918\) | − | 1.63306e9i | − | 0.0696712i | ||||||
\(919\) | −4.04874e10 | −1.72074 | −0.860370 | − | 0.509669i | \(-0.829768\pi\) | ||||
−0.860370 | + | 0.509669i | \(0.829768\pi\) | |||||||
\(920\) | 2.72630e10 | − | 1.84192e10i | 1.15429 | − | 0.779853i | ||||
\(921\) | −4.70992e9 | −0.198658 | ||||||||
\(922\) | − | 2.10218e10i | − | 0.883305i | ||||||
\(923\) | − | 1.10159e10i | − | 0.461120i | ||||||
\(924\) | 4.33378e9 | 0.180723 | ||||||||
\(925\) | 1.91750e10 | + | 7.71348e9i | 0.796599 | + | 0.320445i | ||||
\(926\) | −1.43656e10 | −0.594545 | ||||||||
\(927\) | − | 1.34499e10i | − | 0.554547i | ||||||
\(928\) | − | 3.05463e9i | − | 0.125470i | ||||||
\(929\) | 1.05190e10 | 0.430447 | 0.215223 | − | 0.976565i | \(-0.430952\pi\) | ||||
0.215223 | + | 0.976565i | \(0.430952\pi\) | |||||||
\(930\) | −8.69641e9 | + | 5.87538e9i | −0.354527 | + | 0.239522i | ||||
\(931\) | −2.83950e10 | −1.15324 | ||||||||
\(932\) | 7.98760e9i | 0.323192i | ||||||||
\(933\) | 5.22882e9i | 0.210775i | ||||||||
\(934\) | 1.38409e10 | 0.555839 | ||||||||
\(935\) | 8.64527e9 | + | 1.27962e10i | 0.345890 | + | 0.511967i | ||||
\(936\) | −6.65684e9 | −0.265340 | ||||||||
\(937\) | 3.07454e10i | 1.22093i | 0.792043 | + | 0.610466i | \(0.209018\pi\) | ||||
−0.792043 | + | 0.610466i | \(0.790982\pi\) | |||||||
\(938\) | − | 1.34947e10i | − | 0.533892i | ||||||
\(939\) | −2.18456e10 | −0.861060 | ||||||||
\(940\) | −7.18175e9 | − | 1.06300e10i | −0.282022 | − | 0.417433i | ||||
\(941\) | −8.99712e7 | −0.00351998 | −0.00175999 | − | 0.999998i | \(-0.500560\pi\) | ||||
−0.00175999 | + | 0.999998i | \(0.500560\pi\) | |||||||
\(942\) | − | 1.54369e10i | − | 0.601703i | ||||||
\(943\) | − | 5.78291e9i | − | 0.224572i | ||||||
\(944\) | −1.11793e9 | −0.0432527 | ||||||||
\(945\) | −2.44418e9 | + | 1.65131e9i | −0.0942153 | + | 0.0636528i | ||||
\(946\) | 4.31378e10 | 1.65668 | ||||||||
\(947\) | − | 4.18307e10i | − | 1.60055i | −0.599630 | − | 0.800277i | \(-0.704686\pi\) | ||
0.599630 | − | 0.800277i | \(-0.295314\pi\) | |||||||
\(948\) | − | 3.75519e9i | − | 0.143154i | ||||||
\(949\) | 2.71825e10 | 1.03242 | ||||||||
\(950\) | 3.36123e10 | + | 1.35211e10i | 1.27194 | + | 0.511658i | ||||
\(951\) | −5.49825e9 | −0.207297 | ||||||||
\(952\) | − | 7.97815e9i | − | 0.299690i | ||||||
\(953\) | − | 3.89523e10i | − | 1.45783i | −0.684602 | − | 0.728917i | \(-0.740024\pi\) | ||
0.684602 | − | 0.728917i | \(-0.259976\pi\) | |||||||
\(954\) | 9.79232e8 | 0.0365146 | ||||||||
\(955\) | −1.91929e9 | + | 1.29669e9i | −0.0713064 | + | 0.0481753i | ||||
\(956\) | 4.39523e8 | 0.0162697 | ||||||||
\(957\) | 3.48010e9i | 0.128351i | ||||||||
\(958\) | − | 6.49435e9i | − | 0.238647i | ||||||
\(959\) | −2.25302e10 | −0.824899 | ||||||||
\(960\) | −8.99073e9 | − | 1.33076e10i | −0.327979 | − | 0.485456i | ||||
\(961\) | −2.28165e9 | −0.0829309 | ||||||||
\(962\) | 1.34697e10i | 0.487805i | ||||||||
\(963\) | − | 7.74984e9i | − | 0.279641i | ||||||
\(964\) | −1.10926e10 | −0.398808 | ||||||||
\(965\) | −1.98156e9 | − | 2.93299e9i | −0.0709840 | − | 0.105067i | ||||
\(966\) | 9.50142e9 | 0.339132 | ||||||||
\(967\) | − | 2.21029e9i | − | 0.0786060i | −0.999227 | − | 0.0393030i | \(-0.987486\pi\) | ||
0.999227 | − | 0.0393030i | \(-0.0125138\pi\) | |||||||
\(968\) | − | 2.27749e10i | − | 0.807035i | ||||||
\(969\) | 1.35528e10 | 0.478515 | ||||||||
\(970\) | −9.80998e9 | + | 6.62772e9i | −0.345117 | + | 0.233165i | ||||
\(971\) | −1.45215e10 | −0.509029 | −0.254515 | − | 0.967069i | \(-0.581916\pi\) | ||||
−0.254515 | + | 0.967069i | \(0.581916\pi\) | |||||||
\(972\) | 7.36787e8i | 0.0257342i | ||||||||
\(973\) | 2.62432e10i | 0.913316i | ||||||||
\(974\) | 5.54875e8 | 0.0192415 | ||||||||
\(975\) | −4.57806e9 | + | 1.13806e10i | −0.158185 | + | 0.393234i | ||||
\(976\) | −5.17996e9 | −0.178341 | ||||||||
\(977\) | − | 1.45088e10i | − | 0.497739i | −0.968537 | − | 0.248870i | \(-0.919941\pi\) | ||
0.968537 | − | 0.248870i | \(-0.0800591\pi\) | |||||||
\(978\) | − | 8.72477e8i | − | 0.0298241i | ||||||
\(979\) | 6.82840e10 | 2.32584 | ||||||||
\(980\) | 6.37524e9 | − | 4.30718e9i | 0.216374 | − | 0.146185i | ||||
\(981\) | −9.24881e9 | −0.312784 | ||||||||
\(982\) | 3.44954e10i | 1.16244i | ||||||||
\(983\) | 3.73720e10i | 1.25490i | 0.778657 | + | 0.627450i | \(0.215901\pi\) | ||||
−0.778657 | + | 0.627450i | \(0.784099\pi\) | |||||||
\(984\) | −3.27039e9 | −0.109425 | ||||||||
\(985\) | 3.68542e9 | + | 5.45495e9i | 0.122874 | + | 0.181871i | ||||
\(986\) | 1.83423e9 | 0.0609376 | ||||||||
\(987\) | − | 1.29396e10i | − | 0.428363i | ||||||
\(988\) | − | 1.58169e10i | − | 0.521761i | ||||||
\(989\) | −6.33548e10 | −2.08254 | ||||||||
\(990\) | 5.82261e9 | + | 8.61831e9i | 0.190719 | + | 0.282292i | ||||
\(991\) | 3.20279e10 | 1.04537 | 0.522687 | − | 0.852525i | \(-0.324930\pi\) | ||||
0.522687 | + | 0.852525i | \(0.324930\pi\) | |||||||
\(992\) | 2.19474e10i | 0.713825i | ||||||||
\(993\) | − | 5.52407e9i | − | 0.179035i | ||||||
\(994\) | 8.89188e9 | 0.287172 | ||||||||
\(995\) | −3.24225e10 | + | 2.19049e10i | −1.04343 | + | 0.704955i | ||||
\(996\) | 6.30507e9 | 0.202201 | ||||||||
\(997\) | 1.33254e10i | 0.425841i | 0.977070 | + | 0.212920i | \(0.0682975\pi\) | ||||
−0.977070 | + | 0.212920i | \(0.931703\pi\) | |||||||
\(998\) | − | 2.77101e9i | − | 0.0882432i | ||||||
\(999\) | 5.20722e9 | 0.165245 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 15.8.b.a.4.3 | ✓ | 8 | |
3.2 | odd | 2 | 45.8.b.d.19.6 | 8 | |||
4.3 | odd | 2 | 240.8.f.e.49.4 | 8 | |||
5.2 | odd | 4 | 75.8.a.j.1.3 | 4 | |||
5.3 | odd | 4 | 75.8.a.i.1.2 | 4 | |||
5.4 | even | 2 | inner | 15.8.b.a.4.6 | yes | 8 | |
15.2 | even | 4 | 225.8.a.z.1.2 | 4 | |||
15.8 | even | 4 | 225.8.a.bb.1.3 | 4 | |||
15.14 | odd | 2 | 45.8.b.d.19.3 | 8 | |||
20.19 | odd | 2 | 240.8.f.e.49.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.8.b.a.4.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
15.8.b.a.4.6 | yes | 8 | 5.4 | even | 2 | inner | |
45.8.b.d.19.3 | 8 | 15.14 | odd | 2 | |||
45.8.b.d.19.6 | 8 | 3.2 | odd | 2 | |||
75.8.a.i.1.2 | 4 | 5.3 | odd | 4 | |||
75.8.a.j.1.3 | 4 | 5.2 | odd | 4 | |||
225.8.a.z.1.2 | 4 | 15.2 | even | 4 | |||
225.8.a.bb.1.3 | 4 | 15.8 | even | 4 | |||
240.8.f.e.49.4 | 8 | 4.3 | odd | 2 | |||
240.8.f.e.49.8 | 8 | 20.19 | odd | 2 |