Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,19,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 19, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 19);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), 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: | \(10.2693068855\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1365649 x^{14} + 735328563216 x^{12} + \cdots + 22\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{12}\cdot 5^{25} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.7 | ||
Root | \(482.444i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.19.c.a.2.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 514.444 | − | 514.444i | 1.00477 | − | 1.00477i | 0.00478571 | − | 0.999989i | \(-0.498477\pi\) |
0.999989 | − | 0.00478571i | \(-0.00152335\pi\) | |||||||
\(3\) | 11708.2 | + | 11708.2i | 0.594836 | + | 0.594836i | 0.938934 | − | 0.344098i | \(-0.111815\pi\) |
−0.344098 | + | 0.938934i | \(0.611815\pi\) | |||||||
\(4\) | − | 267162.i | − | 1.01914i | ||||||
\(5\) | −1.06274e6 | − | 1.63869e6i | −0.544121 | − | 0.839007i | ||||
\(6\) | 1.20464e7 | 1.19535 | ||||||||
\(7\) | 4.54981e7 | − | 4.54981e7i | 1.12749 | − | 1.12749i | 0.136901 | − | 0.990585i | \(-0.456286\pi\) |
0.990585 | − | 0.136901i | \(-0.0437143\pi\) | |||||||
\(8\) | −2.58155e6 | − | 2.58155e6i | −0.0192340 | − | 0.0192340i | ||||
\(9\) | − | 1.13259e8i | − | 0.292340i | ||||||
\(10\) | −1.38973e9 | − | 2.96294e8i | −1.38973 | − | 0.296294i | ||||
\(11\) | 3.09896e8 | 0.131426 | 0.0657130 | − | 0.997839i | \(-0.479068\pi\) | ||||
0.0657130 | + | 0.997839i | \(0.479068\pi\) | |||||||
\(12\) | 3.12798e9 | − | 3.12798e9i | 0.606223 | − | 0.606223i | ||||
\(13\) | −8.68254e8 | − | 8.68254e8i | −0.0818760 | − | 0.0818760i | 0.664983 | − | 0.746859i | \(-0.268439\pi\) |
−0.746859 | + | 0.664983i | \(0.768439\pi\) | |||||||
\(14\) | − | 4.68125e10i | − | 2.26574i | ||||||
\(15\) | 6.74331e9 | − | 3.16287e10i | 0.175409 | − | 0.822734i | ||||
\(16\) | 6.73788e10 | 0.980491 | ||||||||
\(17\) | −1.22332e11 | + | 1.22332e11i | −1.03157 | + | 1.03157i | −0.0320833 | + | 0.999485i | \(0.510214\pi\) |
−0.999485 | + | 0.0320833i | \(0.989786\pi\) | |||||||
\(18\) | −5.82653e10 | − | 5.82653e10i | −0.293736 | − | 0.293736i | ||||
\(19\) | 3.40010e11i | 1.05368i | 0.849964 | + | 0.526841i | \(0.176624\pi\) | ||||
−0.849964 | + | 0.526841i | \(0.823376\pi\) | |||||||
\(20\) | −4.37795e11 | + | 2.83923e11i | −0.855068 | + | 0.554537i | ||||
\(21\) | 1.06540e12 | 1.34134 | ||||||||
\(22\) | 1.59424e11 | − | 1.59424e11i | 0.132054 | − | 0.132054i | ||||
\(23\) | 2.24314e10 | + | 2.24314e10i | 0.0124539 | + | 0.0124539i | 0.713306 | − | 0.700852i | \(-0.247197\pi\) |
−0.700852 | + | 0.713306i | \(0.747197\pi\) | |||||||
\(24\) | − | 6.04503e10i | − | 0.0228822i | ||||||
\(25\) | −1.55588e12 | + | 3.48298e12i | −0.407865 | + | 0.913042i | ||||
\(26\) | −8.93337e11 | −0.164534 | ||||||||
\(27\) | 5.86203e12 | − | 5.86203e12i | 0.768731 | − | 0.768731i | ||||
\(28\) | −1.21554e13 | − | 1.21554e13i | −1.14907 | − | 1.14907i | ||||
\(29\) | 1.17353e13i | 0.808930i | 0.914553 | + | 0.404465i | \(0.132542\pi\) | ||||
−0.914553 | + | 0.404465i | \(0.867458\pi\) | |||||||
\(30\) | −1.28021e13 | − | 1.97402e13i | −0.650415 | − | 1.00291i | ||||
\(31\) | 3.42479e13 | 1.29532 | 0.647662 | − | 0.761927i | \(-0.275747\pi\) | ||||
0.647662 | + | 0.761927i | \(0.275747\pi\) | |||||||
\(32\) | 3.53394e13 | − | 3.53394e13i | 1.00441 | − | 1.00441i | ||||
\(33\) | 3.62831e12 | + | 3.62831e12i | 0.0781769 | + | 0.0781769i | ||||
\(34\) | 1.25866e14i | 2.07299i | ||||||||
\(35\) | −1.22910e14 | − | 2.62046e13i | −1.55946 | − | 0.332480i | ||||
\(36\) | −3.02584e13 | −0.297937 | ||||||||
\(37\) | −7.33851e13 | + | 7.33851e13i | −0.564667 | + | 0.564667i | −0.930630 | − | 0.365963i | \(-0.880740\pi\) |
0.365963 | + | 0.930630i | \(0.380740\pi\) | |||||||
\(38\) | 1.74916e14 | + | 1.74916e14i | 1.05871 | + | 1.05871i | ||||
\(39\) | − | 2.03313e13i | − | 0.0974056i | ||||||
\(40\) | −1.48684e12 | + | 6.97384e12i | −0.00567185 | + | 0.0266031i | ||||
\(41\) | 9.80356e13 | 0.299453 | 0.149727 | − | 0.988727i | \(-0.452161\pi\) | ||||
0.149727 | + | 0.988727i | \(0.452161\pi\) | |||||||
\(42\) | 5.48088e14 | − | 5.48088e14i | 1.34774 | − | 1.34774i | ||||
\(43\) | −6.23419e14 | − | 6.23419e14i | −1.24041 | − | 1.24041i | −0.959833 | − | 0.280573i | \(-0.909476\pi\) |
−0.280573 | − | 0.959833i | \(-0.590524\pi\) | |||||||
\(44\) | − | 8.27924e13i | − | 0.133942i | ||||||
\(45\) | −1.85595e14 | + | 1.20364e14i | −0.245276 | + | 0.159068i | ||||
\(46\) | 2.30794e13 | 0.0250267 | ||||||||
\(47\) | −6.89773e14 | + | 6.89773e14i | −0.616347 | + | 0.616347i | −0.944593 | − | 0.328245i | \(-0.893543\pi\) |
0.328245 | + | 0.944593i | \(0.393543\pi\) | |||||||
\(48\) | 7.88882e14 | + | 7.88882e14i | 0.583231 | + | 0.583231i | ||||
\(49\) | − | 2.51174e15i | − | 1.54245i | ||||||
\(50\) | 9.91384e14 | + | 2.59221e15i | 0.507588 | + | 1.32721i | ||||
\(51\) | −2.86455e15 | −1.22723 | ||||||||
\(52\) | −2.31965e14 | + | 2.31965e14i | −0.0834433 | + | 0.0834433i | ||||
\(53\) | 4.54980e15 | + | 4.54980e15i | 1.37883 | + | 1.37883i | 0.846607 | + | 0.532219i | \(0.178642\pi\) |
0.532219 | + | 0.846607i | \(0.321358\pi\) | |||||||
\(54\) | − | 6.03138e15i | − | 1.54480i | ||||||
\(55\) | −3.29337e14 | − | 5.07822e14i | −0.0715116 | − | 0.110267i | ||||
\(56\) | −2.34911e14 | −0.0433722 | ||||||||
\(57\) | −3.98089e15 | + | 3.98089e15i | −0.626768 | + | 0.626768i | ||||
\(58\) | 6.03714e15 | + | 6.03714e15i | 0.812792 | + | 0.812792i | ||||
\(59\) | 2.86344e15i | 0.330537i | 0.986249 | + | 0.165268i | \(0.0528490\pi\) | ||||
−0.986249 | + | 0.165268i | \(0.947151\pi\) | |||||||
\(60\) | −8.44998e15 | − | 1.80156e15i | −0.838483 | − | 0.178767i | ||||
\(61\) | −1.35867e16 | −1.16184 | −0.580921 | − | 0.813960i | \(-0.697307\pi\) | ||||
−0.580921 | + | 0.813960i | \(0.697307\pi\) | |||||||
\(62\) | 1.76186e16 | − | 1.76186e16i | 1.30151 | − | 1.30151i | ||||
\(63\) | −5.15306e15 | − | 5.15306e15i | −0.329610 | − | 0.329610i | ||||
\(64\) | − | 1.86974e16i | − | 1.03791i | ||||||
\(65\) | −5.00071e14 | + | 2.34552e15i | −0.0241441 | + | 0.113245i | ||||
\(66\) | 3.73313e15 | 0.157100 | ||||||||
\(67\) | 2.72637e16 | − | 2.72637e16i | 1.00210 | − | 1.00210i | 0.00210466 | − | 0.999998i | \(-0.499330\pi\) |
0.999998 | − | 0.00210466i | \(-0.000669936\pi\) | |||||||
\(68\) | 3.26823e16 | + | 3.26823e16i | 1.05132 | + | 1.05132i | ||||
\(69\) | 5.25260e14i | 0.0148161i | ||||||||
\(70\) | −7.67110e16 | + | 4.97493e16i | −1.90097 | + | 1.23283i | ||||
\(71\) | −1.52953e16 | −0.333605 | −0.166802 | − | 0.985990i | \(-0.553344\pi\) | ||||
−0.166802 | + | 0.985990i | \(0.553344\pi\) | |||||||
\(72\) | −2.92383e14 | + | 2.92383e14i | −0.00562288 | + | 0.00562288i | ||||
\(73\) | 8.25139e15 | + | 8.25139e15i | 0.140159 | + | 0.140159i | 0.773705 | − | 0.633546i | \(-0.218401\pi\) |
−0.633546 | + | 0.773705i | \(0.718401\pi\) | |||||||
\(74\) | 7.55051e16i | 1.13473i | ||||||||
\(75\) | −5.89958e16 | + | 2.25627e16i | −0.785723 | + | 0.300497i | ||||
\(76\) | 9.08378e16 | 1.07385 | ||||||||
\(77\) | 1.40997e16 | − | 1.40997e16i | 0.148181 | − | 0.148181i | ||||
\(78\) | −1.04593e16 | − | 1.04593e16i | −0.0978706 | − | 0.0978706i | ||||
\(79\) | − | 9.97051e16i | − | 0.831904i | −0.909386 | − | 0.415952i | \(-0.863448\pi\) | ||
0.909386 | − | 0.415952i | \(-0.136552\pi\) | |||||||
\(80\) | −7.16059e16 | − | 1.10413e17i | −0.533505 | − | 0.822639i | ||||
\(81\) | 9.33884e16 | 0.622197 | ||||||||
\(82\) | 5.04339e16 | − | 5.04339e16i | 0.300883 | − | 0.300883i | ||||
\(83\) | 8.47982e16 | + | 8.47982e16i | 0.453611 | + | 0.453611i | 0.896551 | − | 0.442940i | \(-0.146064\pi\) |
−0.442940 | + | 0.896551i | \(0.646064\pi\) | |||||||
\(84\) | − | 2.84634e17i | − | 1.36701i | ||||||
\(85\) | 3.30469e17 | + | 7.04568e16i | 1.42679 | + | 0.304195i | ||||
\(86\) | −6.41429e17 | −2.49266 | ||||||||
\(87\) | −1.37398e17 | + | 1.37398e17i | −0.481181 | + | 0.481181i | ||||
\(88\) | −8.00010e14 | − | 8.00010e14i | −0.00252785 | − | 0.00252785i | ||||
\(89\) | − | 7.13356e16i | − | 0.203609i | −0.994804 | − | 0.101804i | \(-0.967538\pi\) | ||
0.994804 | − | 0.101804i | \(-0.0324616\pi\) | |||||||
\(90\) | −3.35579e16 | + | 1.57399e17i | −0.0866188 | + | 0.406275i | ||||
\(91\) | −7.90079e16 | −0.184628 | ||||||||
\(92\) | 5.99281e15 | − | 5.99281e15i | 0.0126923 | − | 0.0126923i | ||||
\(93\) | 4.00980e17 | + | 4.00980e17i | 0.770506 | + | 0.770506i | ||||
\(94\) | 7.09700e17i | 1.23858i | ||||||||
\(95\) | 5.57170e17 | − | 3.61341e17i | 0.884046 | − | 0.573330i | ||||
\(96\) | 8.27518e17 | 1.19491 | ||||||||
\(97\) | −1.73783e17 | + | 1.73783e17i | −0.228592 | + | 0.228592i | −0.812104 | − | 0.583512i | \(-0.801678\pi\) |
0.583512 | + | 0.812104i | \(0.301678\pi\) | |||||||
\(98\) | −1.29215e18 | − | 1.29215e18i | −1.54981 | − | 1.54981i | ||||
\(99\) | − | 3.50984e16i | − | 0.0384212i | ||||||
\(100\) | 9.30520e17 | + | 4.15673e17i | 0.930520 | + | 0.415673i | ||||
\(101\) | −1.06901e18 | −0.977440 | −0.488720 | − | 0.872441i | \(-0.662536\pi\) | ||||
−0.488720 | + | 0.872441i | \(0.662536\pi\) | |||||||
\(102\) | −1.47365e18 | + | 1.47365e18i | −1.23309 | + | 1.23309i | ||||
\(103\) | 7.71840e16 | + | 7.71840e16i | 0.0591551 | + | 0.0591551i | 0.736065 | − | 0.676910i | \(-0.236682\pi\) |
−0.676910 | + | 0.736065i | \(0.736682\pi\) | |||||||
\(104\) | 4.48288e15i | 0.00314961i | ||||||||
\(105\) | −1.13224e18 | − | 1.74585e18i | −0.729850 | − | 1.12539i | ||||
\(106\) | 4.68124e18 | 2.77082 | ||||||||
\(107\) | 2.95516e17 | − | 2.95516e17i | 0.160741 | − | 0.160741i | −0.622154 | − | 0.782895i | \(-0.713742\pi\) |
0.782895 | + | 0.622154i | \(0.213742\pi\) | |||||||
\(108\) | −1.56611e18 | − | 1.56611e18i | −0.783446 | − | 0.783446i | ||||
\(109\) | 5.03683e17i | 0.231910i | 0.993254 | + | 0.115955i | \(0.0369928\pi\) | ||||
−0.993254 | + | 0.115955i | \(0.963007\pi\) | |||||||
\(110\) | −4.30672e17 | − | 9.18203e16i | −0.182647 | − | 0.0389408i | ||||
\(111\) | −1.71841e18 | −0.671768 | ||||||||
\(112\) | 3.06561e18 | − | 3.06561e18i | 1.10549 | − | 1.10549i | ||||
\(113\) | −2.40642e18 | − | 2.40642e18i | −0.801059 | − | 0.801059i | 0.182202 | − | 0.983261i | \(-0.441678\pi\) |
−0.983261 | + | 0.182202i | \(0.941678\pi\) | |||||||
\(114\) | 4.09589e18i | 1.25952i | ||||||||
\(115\) | 1.29194e16 | − | 6.05966e16i | 0.00367249 | − | 0.0172253i | ||||
\(116\) | 3.13522e18 | 0.824415 | ||||||||
\(117\) | −9.83373e16 | + | 9.83373e16i | −0.0239357 | + | 0.0239357i | ||||
\(118\) | 1.47308e18 | + | 1.47308e18i | 0.332115 | + | 0.332115i | ||||
\(119\) | 1.11317e19i | 2.32616i | ||||||||
\(120\) | −9.90590e16 | + | 6.42427e16i | −0.0191983 | + | 0.0124507i | ||||
\(121\) | −5.46388e18 | −0.982727 | ||||||||
\(122\) | −6.98962e18 | + | 6.98962e18i | −1.16739 | + | 1.16739i | ||||
\(123\) | 1.14782e18 | + | 1.14782e18i | 0.178126 | + | 0.178126i | ||||
\(124\) | − | 9.14974e18i | − | 1.32012i | ||||||
\(125\) | 7.36100e18 | − | 1.15188e18i | 0.987977 | − | 0.154603i | ||||
\(126\) | −5.30192e18 | −0.662367 | ||||||||
\(127\) | 6.44985e18 | − | 6.44985e18i | 0.750440 | − | 0.750440i | −0.224121 | − | 0.974561i | \(-0.571951\pi\) |
0.974561 | + | 0.224121i | \(0.0719510\pi\) | |||||||
\(128\) | −3.54740e17 | − | 3.54740e17i | −0.0384610 | − | 0.0384610i | ||||
\(129\) | − | 1.45982e19i | − | 1.47568i | ||||||
\(130\) | 9.49381e17 | + | 1.46390e18i | 0.0895262 | + | 0.138045i | ||||
\(131\) | 2.34023e18 | 0.205976 | 0.102988 | − | 0.994683i | \(-0.467160\pi\) | ||||
0.102988 | + | 0.994683i | \(0.467160\pi\) | |||||||
\(132\) | 9.69346e17 | − | 9.69346e17i | 0.0796735 | − | 0.0796735i | ||||
\(133\) | 1.54698e19 | + | 1.54698e19i | 1.18801 | + | 1.18801i | ||||
\(134\) | − | 2.80514e19i | − | 2.01377i | ||||||
\(135\) | −1.58358e19 | − | 3.37624e18i | −1.06325 | − | 0.226688i | ||||
\(136\) | 6.31609e17 | 0.0396824 | ||||||||
\(137\) | −6.37189e18 | + | 6.37189e18i | −0.374786 | + | 0.374786i | −0.869217 | − | 0.494431i | \(-0.835376\pi\) |
0.494431 | + | 0.869217i | \(0.335376\pi\) | |||||||
\(138\) | 2.70217e17 | + | 2.70217e17i | 0.0148868 | + | 0.0148868i | ||||
\(139\) | 1.02362e19i | 0.528451i | 0.964461 | + | 0.264226i | \(0.0851164\pi\) | ||||
−0.964461 | + | 0.264226i | \(0.914884\pi\) | |||||||
\(140\) | −7.00089e18 | + | 3.28368e19i | −0.338845 | + | 1.58931i | ||||
\(141\) | −1.61519e19 | −0.733251 | ||||||||
\(142\) | −7.86857e18 | + | 7.86857e18i | −0.335198 | + | 0.335198i | ||||
\(143\) | −2.69068e17 | − | 2.69068e17i | −0.0107606 | − | 0.0107606i | ||||
\(144\) | − | 7.63124e18i | − | 0.286637i | ||||||
\(145\) | 1.92304e19 | − | 1.24715e19i | 0.678698 | − | 0.440156i | ||||
\(146\) | 8.48976e18 | 0.281657 | ||||||||
\(147\) | 2.94079e19 | − | 2.94079e19i | 0.917504 | − | 0.917504i | ||||
\(148\) | 1.96057e19 | + | 1.96057e19i | 0.575476 | + | 0.575476i | ||||
\(149\) | 1.72802e19i | 0.477390i | 0.971095 | + | 0.238695i | \(0.0767196\pi\) | ||||
−0.971095 | + | 0.238695i | \(0.923280\pi\) | |||||||
\(150\) | −1.87428e19 | + | 4.19573e19i | −0.487543 | + | 1.09141i | ||||
\(151\) | −1.21577e19 | −0.297893 | −0.148946 | − | 0.988845i | \(-0.547588\pi\) | ||||
−0.148946 | + | 0.988845i | \(0.547588\pi\) | |||||||
\(152\) | 8.77752e17 | − | 8.77752e17i | 0.0202665 | − | 0.0202665i | ||||
\(153\) | 1.38551e19 | + | 1.38551e19i | 0.301569 | + | 0.301569i | ||||
\(154\) | − | 1.45070e19i | − | 0.297777i | ||||||
\(155\) | −3.63965e19 | − | 5.61215e19i | −0.704813 | − | 1.08679i | ||||
\(156\) | −5.43175e18 | −0.0992702 | ||||||||
\(157\) | 5.29319e19 | − | 5.29319e19i | 0.913314 | − | 0.913314i | −0.0832172 | − | 0.996531i | \(-0.526520\pi\) |
0.996531 | + | 0.0832172i | \(0.0265195\pi\) | |||||||
\(158\) | −5.12927e19 | − | 5.12927e19i | −0.835876 | − | 0.835876i | ||||
\(159\) | 1.06539e20i | 1.64035i | ||||||||
\(160\) | −9.54666e19 | − | 2.03537e19i | −1.38922 | − | 0.296186i | ||||
\(161\) | 2.04117e18 | 0.0280832 | ||||||||
\(162\) | 4.80431e19 | − | 4.80431e19i | 0.625167 | − | 0.625167i | ||||
\(163\) | 3.07411e19 | + | 3.07411e19i | 0.378470 | + | 0.378470i | 0.870550 | − | 0.492080i | \(-0.163763\pi\) |
−0.492080 | + | 0.870550i | \(0.663763\pi\) | |||||||
\(164\) | − | 2.61914e19i | − | 0.305186i | ||||||
\(165\) | 2.08972e18 | − | 9.80159e18i | 0.0230533 | − | 0.108129i | ||||
\(166\) | 8.72480e19 | 0.911554 | ||||||||
\(167\) | −7.48607e19 | + | 7.48607e19i | −0.740979 | + | 0.740979i | −0.972766 | − | 0.231788i | \(-0.925543\pi\) |
0.231788 | + | 0.972766i | \(0.425543\pi\) | |||||||
\(168\) | −2.75037e18 | − | 2.75037e18i | −0.0257993 | − | 0.0257993i | ||||
\(169\) | − | 1.10948e20i | − | 0.986593i | ||||||
\(170\) | 2.06254e20 | − | 1.33762e20i | 1.73925 | − | 1.12795i | ||||
\(171\) | 3.85091e19 | 0.308034 | ||||||||
\(172\) | −1.66554e20 | + | 1.66554e20i | −1.26415 | + | 1.26415i | ||||
\(173\) | −7.97405e19 | − | 7.97405e19i | −0.574465 | − | 0.574465i | 0.358908 | − | 0.933373i | \(-0.383149\pi\) |
−0.933373 | + | 0.358908i | \(0.883149\pi\) | |||||||
\(174\) | 1.41368e20i | 0.966956i | ||||||||
\(175\) | 8.76792e19 | + | 2.29259e20i | 0.569579 | + | 1.48930i | ||||
\(176\) | 2.08804e19 | 0.128862 | ||||||||
\(177\) | −3.35256e19 | + | 3.35256e19i | −0.196615 | + | 0.196615i | ||||
\(178\) | −3.66982e19 | − | 3.66982e19i | −0.204581 | − | 0.204581i | ||||
\(179\) | 7.45354e19i | 0.395080i | 0.980295 | + | 0.197540i | \(0.0632953\pi\) | ||||
−0.980295 | + | 0.197540i | \(0.936705\pi\) | |||||||
\(180\) | 3.21567e19 | + | 4.95841e19i | 0.162113 | + | 0.249971i | ||||
\(181\) | −3.45032e20 | −1.65483 | −0.827413 | − | 0.561593i | \(-0.810189\pi\) | ||||
−0.827413 | + | 0.561593i | \(0.810189\pi\) | |||||||
\(182\) | −4.06451e19 | + | 4.06451e19i | −0.185510 | + | 0.185510i | ||||
\(183\) | −1.59076e20 | − | 1.59076e20i | −0.691105 | − | 0.691105i | ||||
\(184\) | − | 1.15815e17i | − | 0.000479077i | ||||||
\(185\) | 1.98244e20 | + | 4.22661e19i | 0.781006 | + | 0.166513i | ||||
\(186\) | 4.12564e20 | 1.54837 | ||||||||
\(187\) | −3.79100e19 | + | 3.79100e19i | −0.135575 | + | 0.135575i | ||||
\(188\) | 1.84281e20 | + | 1.84281e20i | 0.628146 | + | 0.628146i | ||||
\(189\) | − | 5.33423e20i | − | 1.73347i | ||||||
\(190\) | 1.00743e20 | − | 4.72523e20i | 0.312200 | − | 1.46433i | ||||
\(191\) | 3.52881e19 | 0.104311 | 0.0521553 | − | 0.998639i | \(-0.483391\pi\) | ||||
0.0521553 | + | 0.998639i | \(0.483391\pi\) | |||||||
\(192\) | 2.18912e20 | − | 2.18912e20i | 0.617387 | − | 0.617387i | ||||
\(193\) | −3.04873e20 | − | 3.04873e20i | −0.820545 | − | 0.820545i | 0.165641 | − | 0.986186i | \(-0.447031\pi\) |
−0.986186 | + | 0.165641i | \(0.947031\pi\) | |||||||
\(194\) | 1.78803e20i | 0.459367i | ||||||||
\(195\) | −3.33166e19 | + | 2.16068e19i | −0.0817240 | + | 0.0530004i | ||||
\(196\) | −6.71043e20 | −1.57198 | ||||||||
\(197\) | −3.42123e19 | + | 3.42123e19i | −0.0765572 | + | 0.0765572i | −0.744349 | − | 0.667791i | \(-0.767240\pi\) |
0.667791 | + | 0.744349i | \(0.267240\pi\) | |||||||
\(198\) | −1.80562e19 | − | 1.80562e19i | −0.0386046 | − | 0.0386046i | ||||
\(199\) | 4.00893e20i | 0.819127i | 0.912282 | + | 0.409564i | \(0.134319\pi\) | ||||
−0.912282 | + | 0.409564i | \(0.865681\pi\) | |||||||
\(200\) | 1.30081e19 | − | 4.97489e18i | 0.0254064 | − | 0.00971658i | ||||
\(201\) | 6.38416e20 | 1.19217 | ||||||||
\(202\) | −5.49947e20 | + | 5.49947e20i | −0.982106 | + | 0.982106i | ||||
\(203\) | 5.33933e20 | + | 5.33933e20i | 0.912057 | + | 0.912057i | ||||
\(204\) | 7.65300e20i | 1.25072i | ||||||||
\(205\) | −1.04186e20 | − | 1.60650e20i | −0.162939 | − | 0.251243i | ||||
\(206\) | 7.94138e19 | 0.118875 | ||||||||
\(207\) | 2.54055e18 | − | 2.54055e18i | 0.00364078 | − | 0.00364078i | ||||
\(208\) | −5.85019e19 | − | 5.85019e19i | −0.0802787 | − | 0.0802787i | ||||
\(209\) | 1.05368e20i | 0.138481i | ||||||||
\(210\) | −1.48062e21 | − | 3.15671e20i | −1.86410 | − | 0.397431i | ||||
\(211\) | 2.76408e20 | 0.333433 | 0.166716 | − | 0.986005i | \(-0.446684\pi\) | ||||
0.166716 | + | 0.986005i | \(0.446684\pi\) | |||||||
\(212\) | 1.21553e21 | − | 1.21553e21i | 1.40522 | − | 1.40522i | ||||
\(213\) | −1.79080e20 | − | 1.79080e20i | −0.198440 | − | 0.198440i | ||||
\(214\) | − | 3.04053e20i | − | 0.323017i | ||||||
\(215\) | −3.59058e20 | + | 1.68412e21i | −0.365779 | + | 1.71564i | ||||
\(216\) | −3.02662e19 | −0.0295716 | ||||||||
\(217\) | 1.55822e21 | − | 1.55822e21i | 1.46046 | − | 1.46046i | ||||
\(218\) | 2.59117e20 | + | 2.59117e20i | 0.233017 | + | 0.233017i | ||||
\(219\) | 1.93217e20i | 0.166743i | ||||||||
\(220\) | −1.35671e20 | + | 8.79865e19i | −0.112378 | + | 0.0728806i | ||||
\(221\) | 2.12430e20 | 0.168921 | ||||||||
\(222\) | −8.84025e20 | + | 8.84025e20i | −0.674975 | + | 0.674975i | ||||
\(223\) | 6.91582e19 | + | 6.91582e19i | 0.0507108 | + | 0.0507108i | 0.732007 | − | 0.681297i | \(-0.238584\pi\) |
−0.681297 | + | 0.732007i | \(0.738584\pi\) | |||||||
\(224\) | − | 3.21575e21i | − | 2.26491i | ||||||
\(225\) | 3.94478e20 | + | 1.76217e20i | 0.266919 | + | 0.119236i | ||||
\(226\) | −2.47593e21 | −1.60977 | ||||||||
\(227\) | −1.23387e21 | + | 1.23387e21i | −0.770971 | + | 0.770971i | −0.978276 | − | 0.207305i | \(-0.933531\pi\) |
0.207305 | + | 0.978276i | \(0.433531\pi\) | |||||||
\(228\) | 1.06354e21 | + | 1.06354e21i | 0.638766 | + | 0.638766i | ||||
\(229\) | − | 8.37298e20i | − | 0.483460i | −0.970343 | − | 0.241730i | \(-0.922285\pi\) | ||
0.970343 | − | 0.241730i | \(-0.0777149\pi\) | |||||||
\(230\) | −2.45273e19 | − | 3.78199e19i | −0.0136176 | − | 0.0209976i | ||||
\(231\) | 3.30162e20 | 0.176287 | ||||||||
\(232\) | 3.02951e19 | − | 3.02951e19i | 0.0155590 | − | 0.0155590i | ||||
\(233\) | −1.99651e21 | − | 1.99651e21i | −0.986432 | − | 0.986432i | 0.0134772 | − | 0.999909i | \(-0.495710\pi\) |
−0.999909 | + | 0.0134772i | \(0.995710\pi\) | |||||||
\(234\) | 1.01178e20i | 0.0480999i | ||||||||
\(235\) | 1.86337e21 | + | 3.97275e20i | 0.852487 | + | 0.181752i | ||||
\(236\) | 7.65003e20 | 0.336864 | ||||||||
\(237\) | 1.16736e21 | − | 1.16736e21i | 0.494847 | − | 0.494847i | ||||
\(238\) | 5.72665e21 | + | 5.72665e21i | 2.33726 | + | 2.33726i | ||||
\(239\) | − | 1.68704e21i | − | 0.663046i | −0.943447 | − | 0.331523i | \(-0.892438\pi\) | ||
0.943447 | − | 0.331523i | \(-0.107562\pi\) | |||||||
\(240\) | 4.54356e20 | − | 2.13110e21i | 0.171987 | − | 0.806683i | ||||
\(241\) | −1.62015e21 | −0.590747 | −0.295373 | − | 0.955382i | \(-0.595444\pi\) | ||||
−0.295373 | + | 0.955382i | \(0.595444\pi\) | |||||||
\(242\) | −2.81086e21 | + | 2.81086e21i | −0.987419 | + | 0.987419i | ||||
\(243\) | −1.17766e21 | − | 1.17766e21i | −0.398626 | − | 0.398626i | ||||
\(244\) | 3.62986e21i | 1.18408i | ||||||||
\(245\) | −4.11596e21 | + | 2.66932e21i | −1.29413 | + | 0.839278i | ||||
\(246\) | 1.18098e21 | 0.357952 | ||||||||
\(247\) | 2.95215e20 | − | 2.95215e20i | 0.0862712 | − | 0.0862712i | ||||
\(248\) | −8.84126e19 | − | 8.84126e19i | −0.0249143 | − | 0.0249143i | ||||
\(249\) | 1.98566e21i | 0.539649i | ||||||||
\(250\) | 3.19425e21 | − | 4.37940e21i | 0.837352 | − | 1.14803i | ||||
\(251\) | −6.23779e21 | −1.57749 | −0.788746 | − | 0.614719i | \(-0.789269\pi\) | ||||
−0.788746 | + | 0.614719i | \(0.789269\pi\) | |||||||
\(252\) | −1.37670e21 | + | 1.37670e21i | −0.335919 | + | 0.335919i | ||||
\(253\) | 6.95139e18 | + | 6.95139e18i | 0.00163677 | + | 0.00163677i | ||||
\(254\) | − | 6.63618e21i | − | 1.50805i | ||||||
\(255\) | 3.04426e21 | + | 4.69410e21i | 0.667760 | + | 1.02965i | ||||
\(256\) | 4.53641e21 | 0.960623 | ||||||||
\(257\) | 4.34881e21 | − | 4.34881e21i | 0.889145 | − | 0.889145i | −0.105296 | − | 0.994441i | \(-0.533579\pi\) |
0.994441 | + | 0.105296i | \(0.0335790\pi\) | |||||||
\(258\) | −7.50995e21 | − | 7.50995e21i | −1.48272 | − | 1.48272i | ||||
\(259\) | 6.67777e21i | 1.27331i | ||||||||
\(260\) | 6.26634e20 | + | 1.33600e20i | 0.115413 | + | 0.0246063i | ||||
\(261\) | 1.32912e21 | 0.236483 | ||||||||
\(262\) | 1.20392e21 | − | 1.20392e21i | 0.206959 | − | 0.206959i | ||||
\(263\) | −2.90958e21 | − | 2.90958e21i | −0.483313 | − | 0.483313i | 0.422875 | − | 0.906188i | \(-0.361021\pi\) |
−0.906188 | + | 0.422875i | \(0.861021\pi\) | |||||||
\(264\) | − | 1.87333e19i | − | 0.00300731i | ||||||
\(265\) | 2.62046e21 | − | 1.22909e22i | 0.406597 | − | 1.90709i | ||||
\(266\) | 1.59167e22 | 2.38737 | ||||||||
\(267\) | 8.35209e20 | − | 8.35209e20i | 0.121114 | − | 0.121114i | ||||
\(268\) | −7.28384e21 | − | 7.28384e21i | −1.02129 | − | 1.02129i | ||||
\(269\) | 1.40831e22i | 1.90953i | 0.297362 | + | 0.954765i | \(0.403893\pi\) | ||||
−0.297362 | + | 0.954765i | \(0.596107\pi\) | |||||||
\(270\) | −9.88353e21 | + | 6.40976e21i | −1.29610 | + | 0.840558i | ||||
\(271\) | −1.00083e20 | −0.0126951 | −0.00634756 | − | 0.999980i | \(-0.502021\pi\) | ||||
−0.00634756 | + | 0.999980i | \(0.502021\pi\) | |||||||
\(272\) | −8.24255e21 | + | 8.24255e21i | −1.01144 | + | 1.01144i | ||||
\(273\) | −9.25036e20 | − | 9.25036e20i | −0.109823 | − | 0.109823i | ||||
\(274\) | 6.55596e21i | 0.753150i | ||||||||
\(275\) | −4.82162e20 | + | 1.07936e21i | −0.0536042 | + | 0.119998i | ||||
\(276\) | 1.40330e20 | 0.0150997 | ||||||||
\(277\) | 1.67510e21 | − | 1.67510e21i | 0.174471 | − | 0.174471i | −0.614470 | − | 0.788940i | \(-0.710630\pi\) |
0.788940 | + | 0.614470i | \(0.210630\pi\) | |||||||
\(278\) | 5.26595e21 | + | 5.26595e21i | 0.530974 | + | 0.530974i | ||||
\(279\) | − | 3.87887e21i | − | 0.378676i | ||||||
\(280\) | 2.49648e20 | + | 3.84945e20i | 0.0235997 | + | 0.0363896i | ||||
\(281\) | −6.52949e21 | −0.597753 | −0.298877 | − | 0.954292i | \(-0.596612\pi\) | ||||
−0.298877 | + | 0.954292i | \(0.596612\pi\) | |||||||
\(282\) | −8.30927e21 | + | 8.30927e21i | −0.736752 | + | 0.736752i | ||||
\(283\) | 1.00354e22 | + | 1.00354e22i | 0.861897 | + | 0.861897i | 0.991558 | − | 0.129662i | \(-0.0413891\pi\) |
−0.129662 | + | 0.991558i | \(0.541389\pi\) | |||||||
\(284\) | 4.08632e21i | 0.339991i | ||||||||
\(285\) | 1.07541e22 | + | 2.29279e21i | 0.866900 | + | 0.184825i | ||||
\(286\) | −2.76841e20 | −0.0216240 | ||||||||
\(287\) | 4.46044e21 | − | 4.46044e21i | 0.337629 | − | 0.337629i | ||||
\(288\) | −4.00249e21 | − | 4.00249e21i | −0.293629 | − | 0.293629i | ||||
\(289\) | − | 1.58669e22i | − | 1.12827i | ||||||
\(290\) | 3.47709e21 | − | 1.63089e22i | 0.239681 | − | 1.12420i | ||||
\(291\) | −4.06935e21 | −0.271950 | ||||||||
\(292\) | 2.20446e21 | − | 2.20446e21i | 0.142842 | − | 0.142842i | ||||
\(293\) | 2.25541e21 | + | 2.25541e21i | 0.141716 | + | 0.141716i | 0.774405 | − | 0.632690i | \(-0.218049\pi\) |
−0.632690 | + | 0.774405i | \(0.718049\pi\) | |||||||
\(294\) | − | 3.02575e22i | − | 1.84377i | ||||||
\(295\) | 4.69228e21 | − | 3.04308e21i | 0.277323 | − | 0.179852i | ||||
\(296\) | 3.78894e20 | 0.0217216 | ||||||||
\(297\) | 1.81662e21 | − | 1.81662e21i | 0.101031 | − | 0.101031i | ||||
\(298\) | 8.88972e21 | + | 8.88972e21i | 0.479669 | + | 0.479669i | ||||
\(299\) | − | 3.89523e19i | − | 0.00203935i | ||||||
\(300\) | 6.02791e21 | + | 1.57614e22i | 0.306249 | + | 0.800764i | ||||
\(301\) | −5.67288e22 | −2.79708 | ||||||||
\(302\) | −6.25447e21 | + | 6.25447e21i | −0.299315 | + | 0.299315i | ||||
\(303\) | −1.25162e22 | − | 1.25162e22i | −0.581416 | − | 0.581416i | ||||
\(304\) | 2.29095e22i | 1.03313i | ||||||||
\(305\) | 1.44391e22 | + | 2.22644e22i | 0.632182 | + | 0.974793i | ||||
\(306\) | 1.42554e22 | 0.606018 | ||||||||
\(307\) | 2.09987e22 | − | 2.09987e22i | 0.866856 | − | 0.866856i | −0.125267 | − | 0.992123i | \(-0.539979\pi\) |
0.992123 | + | 0.125267i | \(0.0399787\pi\) | |||||||
\(308\) | −3.76690e21 | − | 3.76690e21i | −0.151018 | − | 0.151018i | ||||
\(309\) | 1.80736e21i | 0.0703752i | ||||||||
\(310\) | −4.75954e22 | − | 1.01475e22i | −1.80015 | − | 0.383797i | ||||
\(311\) | 4.48809e22 | 1.64899 | 0.824495 | − | 0.565869i | \(-0.191459\pi\) | ||||
0.824495 | + | 0.565869i | \(0.191459\pi\) | |||||||
\(312\) | −5.24862e19 | + | 5.24862e19i | −0.00187350 | + | 0.00187350i | ||||
\(313\) | 2.93050e22 | + | 2.93050e22i | 1.01635 | + | 1.01635i | 0.999864 | + | 0.0164840i | \(0.00524725\pi\) |
0.0164840 | + | 0.999864i | \(0.494753\pi\) | |||||||
\(314\) | − | 5.44610e22i | − | 1.83535i | ||||||
\(315\) | −2.96790e21 | + | 1.39206e22i | −0.0971974 | + | 0.455892i | ||||
\(316\) | −2.66374e22 | −0.847829 | ||||||||
\(317\) | −8.34466e21 | + | 8.34466e21i | −0.258152 | + | 0.258152i | −0.824302 | − | 0.566150i | \(-0.808432\pi\) |
0.566150 | + | 0.824302i | \(0.308432\pi\) | |||||||
\(318\) | 5.48086e22 | + | 5.48086e22i | 1.64818 | + | 1.64818i | ||||
\(319\) | 3.63671e21i | 0.106315i | ||||||||
\(320\) | −3.06391e22 | + | 1.98703e22i | −0.870815 | + | 0.564749i | ||||
\(321\) | 6.91990e21 | 0.191229 | ||||||||
\(322\) | 1.05007e21 | − | 1.05007e21i | 0.0282173 | − | 0.0282173i | ||||
\(323\) | −4.15939e22 | − | 4.15939e22i | −1.08694 | − | 1.08694i | ||||
\(324\) | − | 2.49498e22i | − | 0.634107i | ||||||
\(325\) | 4.37501e21 | − | 1.67321e21i | 0.108151 | − | 0.0413618i | ||||
\(326\) | 3.16292e22 | 0.760553 | ||||||||
\(327\) | −5.89720e21 | + | 5.89720e21i | −0.137948 | + | 0.137948i | ||||
\(328\) | −2.53084e20 | − | 2.53084e20i | −0.00575969 | − | 0.00575969i | ||||
\(329\) | 6.27668e22i | 1.38985i | ||||||||
\(330\) | −3.96733e21 | − | 6.11742e21i | −0.0854815 | − | 0.131808i | ||||
\(331\) | −3.83337e22 | −0.803765 | −0.401882 | − | 0.915691i | \(-0.631644\pi\) | ||||
−0.401882 | + | 0.915691i | \(0.631644\pi\) | |||||||
\(332\) | 2.26549e22 | − | 2.26549e22i | 0.462295 | − | 0.462295i | ||||
\(333\) | 8.31150e21 | + | 8.31150e21i | 0.165075 | + | 0.165075i | ||||
\(334\) | 7.70234e22i | 1.48903i | ||||||||
\(335\) | −7.36508e22 | − | 1.57025e22i | −1.38604 | − | 0.295506i | ||||
\(336\) | 7.17853e22 | 1.31517 | ||||||||
\(337\) | 2.54143e22 | − | 2.54143e22i | 0.453324 | − | 0.453324i | −0.443132 | − | 0.896456i | \(-0.646133\pi\) |
0.896456 | + | 0.443132i | \(0.146133\pi\) | |||||||
\(338\) | −5.70764e22 | − | 5.70764e22i | −0.991303 | − | 0.991303i | ||||
\(339\) | − | 5.63494e22i | − | 0.952998i | ||||||
\(340\) | 1.88234e22 | − | 8.82888e22i | 0.310019 | − | 1.45410i | ||||
\(341\) | 1.06133e22 | 0.170239 | ||||||||
\(342\) | 1.98108e22 | − | 1.98108e22i | 0.309504 | − | 0.309504i | ||||
\(343\) | −4.01899e22 | − | 4.01899e22i | −0.611603 | − | 0.611603i | ||||
\(344\) | 3.21877e21i | 0.0477160i | ||||||||
\(345\) | 8.60736e20 | − | 5.58213e20i | 0.0124308 | − | 0.00806172i | ||||
\(346\) | −8.20441e22 | −1.15442 | ||||||||
\(347\) | 3.62099e22 | − | 3.62099e22i | 0.496435 | − | 0.496435i | −0.413891 | − | 0.910326i | \(-0.635831\pi\) |
0.910326 | + | 0.413891i | \(0.135831\pi\) | |||||||
\(348\) | 3.67076e22 | + | 3.67076e22i | 0.490392 | + | 0.490392i | ||||
\(349\) | 4.97742e22i | 0.648001i | 0.946057 | + | 0.324000i | \(0.105028\pi\) | ||||
−0.946057 | + | 0.324000i | \(0.894972\pi\) | |||||||
\(350\) | 1.63047e23 | + | 7.28348e22i | 2.06871 | + | 0.924116i | ||||
\(351\) | −1.01795e22 | −0.125881 | ||||||||
\(352\) | 1.09515e22 | − | 1.09515e22i | 0.132005 | − | 0.132005i | ||||
\(353\) | 2.66903e22 | + | 2.66903e22i | 0.313604 | + | 0.313604i | 0.846304 | − | 0.532700i | \(-0.178823\pi\) |
−0.532700 | + | 0.846304i | \(0.678823\pi\) | |||||||
\(354\) | 3.44941e22i | 0.395108i | ||||||||
\(355\) | 1.62548e22 | + | 2.50642e22i | 0.181521 | + | 0.279897i | ||||
\(356\) | −1.90582e22 | −0.207506 | ||||||||
\(357\) | −1.30332e23 | + | 1.30332e23i | −1.38368 | + | 1.38368i | ||||
\(358\) | 3.83443e22 | + | 3.83443e22i | 0.396967 | + | 0.396967i | ||||
\(359\) | − | 1.03152e23i | − | 1.04142i | −0.853733 | − | 0.520711i | \(-0.825667\pi\) | ||
0.853733 | − | 0.520711i | \(-0.174333\pi\) | |||||||
\(360\) | 7.89849e20 | + | 1.68398e20i | 0.00777717 | + | 0.00165811i | ||||
\(361\) | −1.14795e22 | −0.110245 | ||||||||
\(362\) | −1.77500e23 | + | 1.77500e23i | −1.66273 | + | 1.66273i | ||||
\(363\) | −6.39720e22 | − | 6.39720e22i | −0.584561 | − | 0.584561i | ||||
\(364\) | 2.11079e22i | 0.188162i | ||||||||
\(365\) | 4.75239e21 | − | 2.22905e22i | 0.0413310 | − | 0.193858i | ||||
\(366\) | −1.63671e23 | −1.38881 | ||||||||
\(367\) | −4.77233e22 | + | 4.77233e22i | −0.395127 | + | 0.395127i | −0.876510 | − | 0.481384i | \(-0.840134\pi\) |
0.481384 | + | 0.876510i | \(0.340134\pi\) | |||||||
\(368\) | 1.51140e21 | + | 1.51140e21i | 0.0122109 | + | 0.0122109i | ||||
\(369\) | − | 1.11034e22i | − | 0.0875423i | ||||||
\(370\) | 1.23729e23 | − | 8.02419e22i | 0.952042 | − | 0.617427i | ||||
\(371\) | 4.14015e23 | 3.10921 | ||||||||
\(372\) | 1.07127e23 | − | 1.07127e23i | 0.785255 | − | 0.785255i | ||||
\(373\) | −1.41044e22 | − | 1.41044e22i | −0.100920 | − | 0.100920i | 0.654844 | − | 0.755764i | \(-0.272734\pi\) |
−0.755764 | + | 0.654844i | \(0.772734\pi\) | |||||||
\(374\) | 3.90052e22i | 0.272445i | ||||||||
\(375\) | 9.96701e22 | + | 7.26973e22i | 0.679647 | + | 0.495721i | ||||
\(376\) | 3.56136e21 | 0.0237097 | ||||||||
\(377\) | 1.01892e22 | − | 1.01892e22i | 0.0662320 | − | 0.0662320i | ||||
\(378\) | −2.74416e23 | − | 2.74416e23i | −1.74174 | − | 1.74174i | ||||
\(379\) | − | 1.16384e23i | − | 0.721341i | −0.932693 | − | 0.360671i | \(-0.882548\pi\) | ||
0.932693 | − | 0.360671i | \(-0.117452\pi\) | |||||||
\(380\) | −9.65366e22 | − | 1.48855e23i | −0.584305 | − | 0.900969i | ||||
\(381\) | 1.51032e23 | 0.892778 | ||||||||
\(382\) | 1.81538e22 | − | 1.81538e22i | 0.104809 | − | 0.104809i | ||||
\(383\) | 8.23735e22 | + | 8.23735e22i | 0.464514 | + | 0.464514i | 0.900132 | − | 0.435618i | \(-0.143470\pi\) |
−0.435618 | + | 0.900132i | \(0.643470\pi\) | |||||||
\(384\) | − | 8.30670e21i | − | 0.0457560i | ||||||
\(385\) | −3.80892e22 | − | 8.12071e21i | −0.204953 | − | 0.0436966i | ||||
\(386\) | −3.13680e23 | −1.64893 | ||||||||
\(387\) | −7.06076e22 | + | 7.06076e22i | −0.362621 | + | 0.362621i | ||||
\(388\) | 4.64282e22 | + | 4.64282e22i | 0.232968 | + | 0.232968i | ||||
\(389\) | 1.22594e22i | 0.0601066i | 0.999548 | + | 0.0300533i | \(0.00956771\pi\) | ||||
−0.999548 | + | 0.0300533i | \(0.990432\pi\) | |||||||
\(390\) | −6.02405e21 | + | 2.82550e22i | −0.0288607 | + | 0.135368i | ||||
\(391\) | −5.48813e21 | −0.0256941 | ||||||||
\(392\) | −6.48419e21 | + | 6.48419e21i | −0.0296675 | + | 0.0296675i | ||||
\(393\) | 2.73998e22 | + | 2.73998e22i | 0.122522 | + | 0.122522i | ||||
\(394\) | 3.52006e22i | 0.153845i | ||||||||
\(395\) | −1.63385e23 | + | 1.05960e23i | −0.697974 | + | 0.452656i | ||||
\(396\) | −9.37696e21 | −0.0391566 | ||||||||
\(397\) | 2.14140e23 | − | 2.14140e23i | 0.874146 | − | 0.874146i | −0.118775 | − | 0.992921i | \(-0.537897\pi\) |
0.992921 | + | 0.118775i | \(0.0378967\pi\) | |||||||
\(398\) | 2.06237e23 | + | 2.06237e23i | 0.823038 | + | 0.823038i | ||||
\(399\) | 3.62246e23i | 1.41334i | ||||||||
\(400\) | −1.04834e23 | + | 2.34679e23i | −0.399908 | + | 0.895229i | ||||
\(401\) | −3.97111e23 | −1.48120 | −0.740598 | − | 0.671948i | \(-0.765458\pi\) | ||||
−0.740598 | + | 0.671948i | \(0.765458\pi\) | |||||||
\(402\) | 3.28430e23 | − | 3.28430e23i | 1.19786 | − | 1.19786i | ||||
\(403\) | −2.97359e22 | − | 2.97359e22i | −0.106056 | − | 0.106056i | ||||
\(404\) | 2.85599e23i | 0.996151i | ||||||||
\(405\) | −9.92471e22 | − | 1.53034e23i | −0.338550 | − | 0.522027i | ||||
\(406\) | 5.49357e23 | 1.83282 | ||||||||
\(407\) | −2.27417e22 | + | 2.27417e22i | −0.0742119 | + | 0.0742119i | ||||
\(408\) | 7.39498e21 | + | 7.39498e21i | 0.0236045 | + | 0.0236045i | ||||
\(409\) | − | 1.10759e23i | − | 0.345836i | −0.984936 | − | 0.172918i | \(-0.944680\pi\) | ||
0.984936 | − | 0.172918i | \(-0.0553196\pi\) | |||||||
\(410\) | −1.36243e23 | − | 2.90474e22i | −0.416160 | − | 0.0887263i | ||||
\(411\) | −1.49206e23 | −0.445872 | ||||||||
\(412\) | 2.06206e22 | − | 2.06206e22i | 0.0602875 | − | 0.0602875i | ||||
\(413\) | 1.30281e23 | + | 1.30281e23i | 0.372676 | + | 0.372676i | ||||
\(414\) | − | 2.61394e21i | − | 0.00731632i | ||||||
\(415\) | 4.88395e22 | − | 2.29076e23i | 0.133764 | − | 0.627403i | ||||
\(416\) | −6.13671e22 | −0.164474 | ||||||||
\(417\) | −1.19847e23 | + | 1.19847e23i | −0.314342 | + | 0.314342i | ||||
\(418\) | 5.42058e22 | + | 5.42058e22i | 0.139142 | + | 0.139142i | ||||
\(419\) | − | 6.06052e23i | − | 1.52259i | −0.648405 | − | 0.761296i | \(-0.724564\pi\) | ||
0.648405 | − | 0.761296i | \(-0.275436\pi\) | |||||||
\(420\) | −4.66426e23 | + | 3.02491e23i | −1.14694 | + | 0.743821i | ||||
\(421\) | 3.29882e23 | 0.793999 | 0.397000 | − | 0.917819i | \(-0.370051\pi\) | ||||
0.397000 | + | 0.917819i | \(0.370051\pi\) | |||||||
\(422\) | 1.42196e23 | − | 1.42196e23i | 0.335025 | − | 0.335025i | ||||
\(423\) | 7.81228e22 | + | 7.81228e22i | 0.180183 | + | 0.180183i | ||||
\(424\) | − | 2.34910e22i | − | 0.0530407i | ||||||
\(425\) | −2.35745e23 | − | 6.16412e23i | −0.521124 | − | 1.36261i | ||||
\(426\) | −1.84253e23 | −0.398775 | ||||||||
\(427\) | −6.18171e23 | + | 6.18171e23i | −1.30996 | + | 1.30996i | ||||
\(428\) | −7.89508e22 | − | 7.89508e22i | −0.163818 | − | 0.163818i | ||||
\(429\) | − | 6.30059e21i | − | 0.0128016i | ||||||
\(430\) | 6.81669e23 | + | 1.05110e24i | 1.35631 | + | 2.09136i | ||||
\(431\) | −5.90484e23 | −1.15057 | −0.575284 | − | 0.817954i | \(-0.695109\pi\) | ||||
−0.575284 | + | 0.817954i | \(0.695109\pi\) | |||||||
\(432\) | 3.94977e23 | − | 3.94977e23i | 0.753733 | − | 0.753733i | ||||
\(433\) | 1.62662e23 | + | 1.62662e23i | 0.304016 | + | 0.304016i | 0.842583 | − | 0.538567i | \(-0.181034\pi\) |
−0.538567 | + | 0.842583i | \(0.681034\pi\) | |||||||
\(434\) | − | 1.60323e24i | − | 2.93487i | ||||||
\(435\) | 3.71171e23 | + | 7.91346e22i | 0.665534 | + | 0.141894i | ||||
\(436\) | 1.34565e23 | 0.236349 | ||||||||
\(437\) | −7.62689e21 | + | 7.62689e21i | −0.0131224 | + | 0.0131224i | ||||
\(438\) | 9.93995e22 | + | 9.93995e22i | 0.167539 | + | 0.167539i | ||||
\(439\) | − | 7.48498e23i | − | 1.23598i | −0.786188 | − | 0.617988i | \(-0.787948\pi\) | ||
0.786188 | − | 0.617988i | \(-0.212052\pi\) | |||||||
\(440\) | −4.60766e20 | + | 2.16117e21i | −0.000745429 | + | 0.00349634i | ||||
\(441\) | −2.84477e23 | −0.450920 | ||||||||
\(442\) | 1.09283e23 | − | 1.09283e23i | 0.169728 | − | 0.169728i | ||||
\(443\) | 8.56187e23 | + | 8.56187e23i | 1.30297 | + | 1.30297i | 0.926379 | + | 0.376592i | \(0.122904\pi\) |
0.376592 | + | 0.926379i | \(0.377096\pi\) | |||||||
\(444\) | 4.59093e23i | 0.684628i | ||||||||
\(445\) | −1.16897e23 | + | 7.58109e22i | −0.170829 | + | 0.110788i | ||||
\(446\) | 7.11561e22 | 0.101906 | ||||||||
\(447\) | −2.02320e23 | + | 2.02320e23i | −0.283969 | + | 0.283969i | ||||
\(448\) | −8.50695e23 | − | 8.50695e23i | −1.17023 | − | 1.17023i | ||||
\(449\) | 1.02420e24i | 1.38091i | 0.723375 | + | 0.690455i | \(0.242590\pi\) | ||||
−0.723375 | + | 0.690455i | \(0.757410\pi\) | |||||||
\(450\) | 2.93591e23 | − | 1.12283e23i | 0.387998 | − | 0.148389i | ||||
\(451\) | 3.03808e22 | 0.0393560 | ||||||||
\(452\) | −6.42903e23 | + | 6.42903e23i | −0.816394 | + | 0.816394i | ||||
\(453\) | −1.42345e23 | − | 1.42345e23i | −0.177197 | − | 0.177197i | ||||
\(454\) | 1.26952e24i | 1.54930i | ||||||||
\(455\) | 8.39645e22 | + | 1.29469e23i | 0.100460 | + | 0.154904i | ||||
\(456\) | 2.05537e22 | 0.0241105 | ||||||||
\(457\) | 2.93797e23 | − | 2.93797e23i | 0.337911 | − | 0.337911i | −0.517670 | − | 0.855581i | \(-0.673200\pi\) |
0.855581 | + | 0.517670i | \(0.173200\pi\) | |||||||
\(458\) | −4.30744e23 | − | 4.30744e23i | −0.485769 | − | 0.485769i | ||||
\(459\) | 1.43422e24i | 1.58600i | ||||||||
\(460\) | −1.61891e22 | − | 3.45156e21i | −0.0175551 | − | 0.00374279i | ||||
\(461\) | 7.81447e23 | 0.830982 | 0.415491 | − | 0.909597i | \(-0.363610\pi\) | ||||
0.415491 | + | 0.909597i | \(0.363610\pi\) | |||||||
\(462\) | 1.69850e23 | − | 1.69850e23i | 0.177128 | − | 0.177128i | ||||
\(463\) | −2.86591e23 | − | 2.86591e23i | −0.293112 | − | 0.293112i | 0.545196 | − | 0.838308i | \(-0.316455\pi\) |
−0.838308 | + | 0.545196i | \(0.816455\pi\) | |||||||
\(464\) | 7.90709e23i | 0.793149i | ||||||||
\(465\) | 2.30944e23 | − | 1.08322e24i | 0.227212 | − | 1.06571i | ||||
\(466\) | −2.05418e24 | −1.98228 | ||||||||
\(467\) | −1.08185e23 | + | 1.08185e23i | −0.102403 | + | 0.102403i | −0.756452 | − | 0.654049i | \(-0.773069\pi\) |
0.654049 | + | 0.756452i | \(0.273069\pi\) | |||||||
\(468\) | 2.62720e22 | + | 2.62720e22i | 0.0243939 | + | 0.0243939i | ||||
\(469\) | − | 2.48090e24i | − | 2.25971i | ||||||
\(470\) | 1.16297e24 | − | 7.54223e23i | 1.03918 | − | 0.673937i | ||||
\(471\) | 1.23947e24 | 1.08654 | ||||||||
\(472\) | 7.39210e21 | − | 7.39210e21i | 0.00635755 | − | 0.00635755i | ||||
\(473\) | −1.93195e23 | − | 1.93195e23i | −0.163022 | − | 0.163022i | ||||
\(474\) | − | 1.20109e24i | − | 0.994418i | ||||||
\(475\) | −1.18425e24 | − | 5.29016e23i | −0.962056 | − | 0.429760i | ||||
\(476\) | 2.97397e24 | 2.37069 | ||||||||
\(477\) | 5.15304e23 | − | 5.15304e23i | 0.403087 | − | 0.403087i | ||||
\(478\) | −8.67887e23 | − | 8.67887e23i | −0.666211 | − | 0.666211i | ||||
\(479\) | 2.16217e24i | 1.62881i | 0.580299 | + | 0.814404i | \(0.302936\pi\) | ||||
−0.580299 | + | 0.814404i | \(0.697064\pi\) | |||||||
\(480\) | −8.79433e23 | − | 1.35604e24i | −0.650177 | − | 1.00254i | ||||
\(481\) | 1.27434e23 | 0.0924653 | ||||||||
\(482\) | −8.33476e23 | + | 8.33476e23i | −0.593567 | + | 0.593567i | ||||
\(483\) | 2.38983e22 | + | 2.38983e22i | 0.0167049 | + | 0.0167049i | ||||
\(484\) | 1.45974e24i | 1.00154i | ||||||||
\(485\) | 4.69461e23 | + | 1.00090e23i | 0.316172 | + | 0.0674087i | ||||
\(486\) | −1.21169e24 | −0.801058 | ||||||||
\(487\) | 8.70611e23 | − | 8.70611e23i | 0.565020 | − | 0.565020i | −0.365709 | − | 0.930729i | \(-0.619174\pi\) |
0.930729 | + | 0.365709i | \(0.119174\pi\) | |||||||
\(488\) | 3.50748e22 | + | 3.50748e22i | 0.0223469 | + | 0.0223469i | ||||
\(489\) | 7.19843e23i | 0.450255i | ||||||||
\(490\) | −7.44215e23 | + | 3.49065e24i | −0.457019 | + | 2.14359i | ||||
\(491\) | −1.00188e23 | −0.0604064 | −0.0302032 | − | 0.999544i | \(-0.509615\pi\) | ||||
−0.0302032 | + | 0.999544i | \(0.509615\pi\) | |||||||
\(492\) | 3.06653e23 | − | 3.06653e23i | 0.181535 | − | 0.181535i | ||||
\(493\) | −1.43559e24 | − | 1.43559e24i | −0.834467 | − | 0.834467i | ||||
\(494\) | − | 3.03744e23i | − | 0.173366i | ||||||
\(495\) | −5.75152e22 | + | 3.73003e22i | −0.0322356 | + | 0.0209057i | ||||
\(496\) | 2.30758e24 | 1.27005 | ||||||||
\(497\) | −6.95907e23 | + | 6.95907e23i | −0.376135 | + | 0.376135i | ||||
\(498\) | 1.02151e24 | + | 1.02151e24i | 0.542225 | + | 0.542225i | ||||
\(499\) | 1.48372e24i | 0.773477i | 0.922189 | + | 0.386738i | \(0.126398\pi\) | ||||
−0.922189 | + | 0.386738i | \(0.873602\pi\) | |||||||
\(500\) | −3.07739e23 | − | 1.96658e24i | −0.157563 | − | 1.00689i | ||||
\(501\) | −1.75296e24 | −0.881522 | ||||||||
\(502\) | −3.20900e24 | + | 3.20900e24i | −1.58502 | + | 1.58502i | ||||
\(503\) | 1.41462e23 | + | 1.41462e23i | 0.0686320 | + | 0.0686320i | 0.740590 | − | 0.671958i | \(-0.234546\pi\) |
−0.671958 | + | 0.740590i | \(0.734546\pi\) | |||||||
\(504\) | 2.66057e22i | 0.0126794i | ||||||||
\(505\) | 1.13608e24 | + | 1.75177e24i | 0.531845 | + | 0.820079i | ||||
\(506\) | 7.15221e21 | 0.00328916 | ||||||||
\(507\) | 1.29899e24 | − | 1.29899e24i | 0.586861 | − | 0.586861i | ||||
\(508\) | −1.72316e24 | − | 1.72316e24i | −0.764806 | − | 0.764806i | ||||
\(509\) | − | 2.04253e24i | − | 0.890653i | −0.895368 | − | 0.445327i | \(-0.853088\pi\) | ||
0.895368 | − | 0.445327i | \(-0.146912\pi\) | |||||||
\(510\) | 3.98096e24 | + | 8.48750e23i | 1.70552 | + | 0.363621i | ||||
\(511\) | 7.50845e23 | 0.316055 | ||||||||
\(512\) | 2.42672e24 | − | 2.42672e24i | 1.00367 | − | 1.00367i | ||||
\(513\) | 1.99315e24 | + | 1.99315e24i | 0.809997 | + | 0.809997i | ||||
\(514\) | − | 4.47444e24i | − | 1.78678i | ||||||
\(515\) | 4.44541e22 | − | 2.08507e23i | 0.0174440 | − | 0.0818191i | ||||
\(516\) | −3.90008e24 | −1.50392 | ||||||||
\(517\) | −2.13758e23 | + | 2.13758e23i | −0.0810041 | + | 0.0810041i | ||||
\(518\) | 3.43534e24 | + | 3.43534e24i | 1.27939 | + | 1.27939i | ||||
\(519\) | − | 1.86723e24i | − | 0.683425i | ||||||
\(520\) | 7.34603e21 | − | 4.76411e21i | 0.00264254 | − | 0.00171377i | ||||
\(521\) | −2.17020e24 | −0.767292 | −0.383646 | − | 0.923480i | \(-0.625332\pi\) | ||||
−0.383646 | + | 0.923480i | \(0.625332\pi\) | |||||||
\(522\) | 6.83759e23 | − | 6.83759e23i | 0.237612 | − | 0.237612i | ||||
\(523\) | −2.79500e22 | − | 2.79500e22i | −0.00954701 | − | 0.00954701i | 0.702317 | − | 0.711864i | \(-0.252149\pi\) |
−0.711864 | + | 0.702317i | \(0.752149\pi\) | |||||||
\(524\) | − | 6.25221e23i | − | 0.209919i | ||||||
\(525\) | −1.65764e24 | + | 3.71076e24i | −0.547085 | + | 1.22470i | ||||
\(526\) | −2.99363e24 | −0.971241 | ||||||||
\(527\) | −4.18960e24 | + | 4.18960e24i | −1.33622 | + | 1.33622i | ||||
\(528\) | 2.44471e23 | + | 2.44471e23i | 0.0766518 | + | 0.0766518i | ||||
\(529\) | − | 3.24314e24i | − | 0.999690i | ||||||
\(530\) | −4.97492e24 | − | 7.67108e24i | −1.50766 | − | 2.32473i | ||||
\(531\) | 3.24309e23 | 0.0966293 | ||||||||
\(532\) | 4.13295e24 | − | 4.13295e24i | 1.21075 | − | 1.21075i | ||||
\(533\) | −8.51198e22 | − | 8.51198e22i | −0.0245180 | − | 0.0245180i | ||||
\(534\) | − | 8.59337e23i | − | 0.243384i | ||||||
\(535\) | −7.98314e23 | − | 1.70203e23i | −0.222326 | − | 0.0474004i | ||||
\(536\) | −1.40765e23 | −0.0385489 | ||||||||
\(537\) | −8.72673e23 | + | 8.72673e23i | −0.235008 | + | 0.235008i | ||||
\(538\) | 7.24495e24 | + | 7.24495e24i | 1.91865 | + | 1.91865i | ||||
\(539\) | − | 7.78379e23i | − | 0.202718i | ||||||
\(540\) | −9.02002e23 | + | 4.23073e24i | −0.231028 | + | 1.08361i | ||||
\(541\) | 7.18172e24 | 1.80906 | 0.904530 | − | 0.426409i | \(-0.140222\pi\) | ||||
0.904530 | + | 0.426409i | \(0.140222\pi\) | |||||||
\(542\) | −5.14871e22 | + | 5.14871e22i | −0.0127557 | + | 0.0127557i | ||||
\(543\) | −4.03969e24 | − | 4.03969e24i | −0.984350 | − | 0.984350i | ||||
\(544\) | 8.64624e24i | 2.07223i | ||||||||
\(545\) | 8.25378e23 | − | 5.35282e23i | 0.194574 | − | 0.126187i | ||||
\(546\) | −9.51759e23 | −0.220695 | ||||||||
\(547\) | 6.03797e24 | − | 6.03797e24i | 1.37723 | − | 1.37723i | 0.527950 | − | 0.849275i | \(-0.322961\pi\) |
0.849275 | − | 0.527950i | \(-0.177039\pi\) | |||||||
\(548\) | 1.70233e24 | + | 1.70233e24i | 0.381960 | + | 0.381960i | ||||
\(549\) | 1.53882e24i | 0.339653i | ||||||||
\(550\) | 3.07226e23 | + | 8.03316e23i | 0.0667103 | + | 0.174430i | ||||
\(551\) | −3.99011e24 | −0.852355 | ||||||||
\(552\) | 1.35598e21 | − | 1.35598e21i | 0.000284972 | − | 0.000284972i | ||||
\(553\) | −4.53639e24 | − | 4.53639e24i | −0.937960 | − | 0.937960i | ||||
\(554\) | − | 1.72349e24i | − | 0.350607i | ||||||
\(555\) | 1.82621e24 | + | 2.81593e24i | 0.365523 | + | 0.563618i | ||||
\(556\) | 2.73472e24 | 0.538567 | ||||||||
\(557\) | −4.27906e24 | + | 4.27906e24i | −0.829185 | + | 0.829185i | −0.987404 | − | 0.158219i | \(-0.949425\pi\) |
0.158219 | + | 0.987404i | \(0.449425\pi\) | |||||||
\(558\) | −1.99546e24 | − | 1.99546e24i | −0.380484 | − | 0.380484i | ||||
\(559\) | 1.08257e24i | 0.203119i | ||||||||
\(560\) | −8.28150e24 | − | 1.76564e24i | −1.52903 | − | 0.325994i | ||||
\(561\) | −8.87713e23 | −0.161290 | ||||||||
\(562\) | −3.35906e24 | + | 3.35906e24i | −0.600607 | + | 0.600607i | ||||
\(563\) | 5.52381e23 | + | 5.52381e23i | 0.0971993 | + | 0.0971993i | 0.754034 | − | 0.656835i | \(-0.228105\pi\) |
−0.656835 | + | 0.754034i | \(0.728105\pi\) | |||||||
\(564\) | 4.31519e24i | 0.747287i | ||||||||
\(565\) | −1.38597e24 | + | 6.50074e24i | −0.236221 | + | 1.10797i | ||||
\(566\) | 1.03253e25 | 1.73202 | ||||||||
\(567\) | 4.24899e24 | − | 4.24899e24i | 0.701518 | − | 0.701518i | ||||
\(568\) | 3.94855e22 | + | 3.94855e22i | 0.00641656 | + | 0.00641656i | ||||
\(569\) | 3.53272e24i | 0.565066i | 0.959258 | + | 0.282533i | \(0.0911746\pi\) | ||||
−0.959258 | + | 0.282533i | \(0.908825\pi\) | |||||||
\(570\) | 6.71188e24 | − | 4.35285e24i | 1.05675 | − | 0.685331i | ||||
\(571\) | −7.27280e24 | −1.12714 | −0.563569 | − | 0.826069i | \(-0.690572\pi\) | ||||
−0.563569 | + | 0.826069i | \(0.690572\pi\) | |||||||
\(572\) | −7.18849e22 | + | 7.18849e22i | −0.0109666 | + | 0.0109666i | ||||
\(573\) | 4.13159e23 | + | 4.13159e23i | 0.0620476 | + | 0.0620476i | ||||
\(574\) | − | 4.58929e24i | − | 0.678483i | ||||||
\(575\) | −1.13029e23 | + | 4.32274e22i | −0.0164505 | + | 0.00629142i | ||||
\(576\) | −2.11764e24 | −0.303424 | ||||||||
\(577\) | 6.81728e24 | − | 6.81728e24i | 0.961676 | − | 0.961676i | −0.0376159 | − | 0.999292i | \(-0.511976\pi\) |
0.999292 | + | 0.0376159i | \(0.0119763\pi\) | |||||||
\(578\) | −8.16265e24 | − | 8.16265e24i | −1.13365 | − | 1.13365i | ||||
\(579\) | − | 7.13899e24i | − | 0.976180i | ||||||
\(580\) | −3.33191e24 | − | 5.13764e24i | −0.448581 | − | 0.691690i | ||||
\(581\) | 7.71632e24 | 1.02288 | ||||||||
\(582\) | −2.09346e24 | + | 2.09346e24i | −0.273248 | + | 0.273248i | ||||
\(583\) | 1.40996e24 | + | 1.40996e24i | 0.181214 | + | 0.181214i | ||||
\(584\) | − | 4.26027e22i | − | 0.00539165i | ||||||
\(585\) | 2.65651e23 | + | 5.66374e22i | 0.0331061 | + | 0.00705830i | ||||
\(586\) | 2.32057e24 | 0.284784 | ||||||||
\(587\) | 2.55631e24 | − | 2.55631e24i | 0.308938 | − | 0.308938i | −0.535560 | − | 0.844497i | \(-0.679899\pi\) |
0.844497 | + | 0.535560i | \(0.179899\pi\) | |||||||
\(588\) | −7.85667e24 | − | 7.85667e24i | −0.935067 | − | 0.935067i | ||||
\(589\) | 1.16446e25i | 1.36486i | ||||||||
\(590\) | 8.48420e23 | − | 3.97941e24i | 0.0979362 | − | 0.459357i | ||||
\(591\) | −8.01126e23 | −0.0910780 | ||||||||
\(592\) | −4.94460e24 | + | 4.94460e24i | −0.553651 | + | 0.553651i | ||||
\(593\) | 1.05028e25 | + | 1.05028e25i | 1.15828 | + | 1.15828i | 0.984845 | + | 0.173438i | \(0.0554876\pi\) |
0.173438 | + | 0.984845i | \(0.444512\pi\) | |||||||
\(594\) | − | 1.86910e24i | − | 0.203027i | ||||||
\(595\) | 1.82414e25 | − | 1.18301e25i | 1.95166 | − | 1.26571i | ||||
\(596\) | 4.61662e24 | 0.486528 | ||||||||
\(597\) | −4.69372e24 | + | 4.69372e24i | −0.487246 | + | 0.487246i | ||||
\(598\) | −2.00388e22 | − | 2.00388e22i | −0.00204909 | − | 0.00204909i | ||||
\(599\) | − | 4.15761e24i | − | 0.418796i | −0.977830 | − | 0.209398i | \(-0.932850\pi\) | ||
0.977830 | − | 0.209398i | \(-0.0671505\pi\) | |||||||
\(600\) | 2.10547e23 | + | 9.40536e22i | 0.0208924 | + | 0.00933285i | ||||
\(601\) | −1.22302e25 | −1.19554 | −0.597770 | − | 0.801668i | \(-0.703946\pi\) | ||||
−0.597770 | + | 0.801668i | \(0.703946\pi\) | |||||||
\(602\) | −2.91838e25 | + | 2.91838e25i | −2.81043 | + | 2.81043i | ||||
\(603\) | −3.08786e24 | − | 3.08786e24i | −0.292955 | − | 0.292955i | ||||
\(604\) | 3.24808e24i | 0.303595i | ||||||||
\(605\) | 5.80666e24 | + | 8.95358e24i | 0.534722 | + | 0.824515i | ||||
\(606\) | −1.28777e25 | −1.16838 | ||||||||
\(607\) | −4.32512e24 | + | 4.32512e24i | −0.386633 | + | 0.386633i | −0.873485 | − | 0.486851i | \(-0.838145\pi\) |
0.486851 | + | 0.873485i | \(0.338145\pi\) | |||||||
\(608\) | 1.20158e25 | + | 1.20158e25i | 1.05832 | + | 1.05832i | ||||
\(609\) | 1.25027e25i | 1.08505i | ||||||||
\(610\) | 1.88819e25 | + | 4.02567e24i | 1.61465 | + | 0.344247i | ||||
\(611\) | 1.19780e24 | 0.100928 | ||||||||
\(612\) | 3.70156e24 | − | 3.70156e24i | 0.307342 | − | 0.307342i | ||||
\(613\) | −9.48466e24 | − | 9.48466e24i | −0.776028 | − | 0.776028i | 0.203125 | − | 0.979153i | \(-0.434890\pi\) |
−0.979153 | + | 0.203125i | \(0.934890\pi\) | |||||||
\(614\) | − | 2.16053e25i | − | 1.74199i | ||||||
\(615\) | 6.61085e23 | − | 3.10074e24i | 0.0525268 | − | 0.246370i | ||||
\(616\) | −7.27979e22 | −0.00570023 | ||||||||
\(617\) | 1.21871e25 | − | 1.21871e25i | 0.940444 | − | 0.940444i | −0.0578795 | − | 0.998324i | \(-0.518434\pi\) |
0.998324 | + | 0.0578795i | \(0.0184339\pi\) | |||||||
\(618\) | 9.29789e23 | + | 9.29789e23i | 0.0707112 | + | 0.0707112i | ||||
\(619\) | 1.24532e25i | 0.933392i | 0.884418 | + | 0.466696i | \(0.154556\pi\) | ||||
−0.884418 | + | 0.466696i | \(0.845444\pi\) | |||||||
\(620\) | −1.49935e25 | + | 9.72376e24i | −1.10759 | + | 0.718305i | ||||
\(621\) | 2.62987e23 | 0.0191474 | ||||||||
\(622\) | 2.30887e25 | − | 2.30887e25i | 1.65686 | − | 1.65686i | ||||
\(623\) | −3.24564e24 | − | 3.24564e24i | −0.229566 | − | 0.229566i | ||||
\(624\) | − | 1.36990e24i | − | 0.0955053i | ||||||
\(625\) | −9.71037e24 | − | 1.08382e25i | −0.667292 | − | 0.744797i | ||||
\(626\) | 3.01516e25 | 2.04240 | ||||||||
\(627\) | −1.23366e24 | + | 1.23366e24i | −0.0823736 | + | 0.0823736i | ||||
\(628\) | −1.41414e25 | − | 1.41414e25i | −0.930797 | − | 0.930797i | ||||
\(629\) | − | 1.79546e25i | − | 1.16498i | ||||||
\(630\) | 5.63454e24 | + | 8.68819e24i | 0.360407 | + | 0.555730i | ||||
\(631\) | −2.82220e25 | −1.77960 | −0.889802 | − | 0.456348i | \(-0.849157\pi\) | ||||
−0.889802 | + | 0.456348i | \(0.849157\pi\) | |||||||
\(632\) | −2.57393e23 | + | 2.57393e23i | −0.0160009 | + | 0.0160009i | ||||
\(633\) | 3.23623e24 | + | 3.23623e24i | 0.198338 | + | 0.198338i | ||||
\(634\) | 8.58573e24i | 0.518769i | ||||||||
\(635\) | −1.74238e25 | − | 3.71479e24i | −1.03795 | − | 0.221295i | ||||
\(636\) | 2.84633e25 | 1.67175 | ||||||||
\(637\) | −2.18083e24 | + | 2.18083e24i | −0.126290 | + | 0.126290i | ||||
\(638\) | 1.87089e24 | + | 1.87089e24i | 0.106822 | + | 0.106822i | ||||
\(639\) | 1.73232e24i | 0.0975262i | ||||||||
\(640\) | −2.04313e23 | + | 9.58302e23i | −0.0113416 | + | 0.0531965i | ||||
\(641\) | 3.08248e24 | 0.168724 | 0.0843622 | − | 0.996435i | \(-0.473115\pi\) | ||||
0.0843622 | + | 0.996435i | \(0.473115\pi\) | |||||||
\(642\) | 3.55990e24 | − | 3.55990e24i | 0.192142 | − | 0.192142i | ||||
\(643\) | 1.11895e25 | + | 1.11895e25i | 0.595539 | + | 0.595539i | 0.939122 | − | 0.343583i | \(-0.111641\pi\) |
−0.343583 | + | 0.939122i | \(0.611641\pi\) | |||||||
\(644\) | − | 5.45324e23i | − | 0.0286208i | ||||||
\(645\) | −2.39218e25 | + | 1.55140e25i | −1.23810 | + | 0.802946i | ||||
\(646\) | −4.27955e25 | −2.18427 | ||||||||
\(647\) | −6.46529e23 | + | 6.46529e23i | −0.0325424 | + | 0.0325424i | −0.723191 | − | 0.690648i | \(-0.757325\pi\) |
0.690648 | + | 0.723191i | \(0.257325\pi\) | |||||||
\(648\) | −2.41086e23 | − | 2.41086e23i | −0.0119673 | − | 0.0119673i | ||||
\(649\) | 8.87368e23i | 0.0434412i | ||||||||
\(650\) | 1.38993e24 | − | 3.11147e24i | 0.0671077 | − | 0.150226i | ||||
\(651\) | 3.64876e25 | 1.73747 | ||||||||
\(652\) | 8.21286e24 | − | 8.21286e24i | 0.385715 | − | 0.385715i | ||||
\(653\) | −2.12074e25 | − | 2.12074e25i | −0.982357 | − | 0.982357i | 0.0174899 | − | 0.999847i | \(-0.494433\pi\) |
−0.999847 | + | 0.0174899i | \(0.994433\pi\) | |||||||
\(654\) | 6.06756e24i | 0.277214i | ||||||||
\(655\) | −2.48705e24 | − | 3.83490e24i | −0.112076 | − | 0.172815i | ||||
\(656\) | 6.60552e24 | 0.293611 | ||||||||
\(657\) | 9.34542e23 | − | 9.34542e23i | 0.0409742 | − | 0.0409742i | ||||
\(658\) | 3.22900e25 | + | 3.22900e25i | 1.39648 | + | 1.39648i | ||||
\(659\) | 8.76231e24i | 0.373809i | 0.982378 | + | 0.186905i | \(0.0598455\pi\) | ||||
−0.982378 | + | 0.186905i | \(0.940155\pi\) | |||||||
\(660\) | −2.61861e24 | − | 5.58295e23i | −0.110199 | − | 0.0234946i | ||||
\(661\) | −7.04682e24 | −0.292536 | −0.146268 | − | 0.989245i | \(-0.546726\pi\) | ||||
−0.146268 | + | 0.989245i | \(0.546726\pi\) | |||||||
\(662\) | −1.97206e25 | + | 1.97206e25i | −0.807602 | + | 0.807602i | ||||
\(663\) | 2.48716e24 | + | 2.48716e24i | 0.100481 | + | 0.100481i | ||||
\(664\) | − | 4.37821e23i | − | 0.0174495i | ||||||
\(665\) | 8.90984e24 | − | 4.17905e25i | 0.350328 | − | 1.64317i | ||||
\(666\) | 8.55161e24 | 0.331726 | ||||||||
\(667\) | −2.63238e23 | + | 2.63238e23i | −0.0100743 | + | 0.0100743i | ||||
\(668\) | 2.00000e25 | + | 2.00000e25i | 0.755163 | + | 0.755163i | ||||
\(669\) | 1.61943e24i | 0.0603292i | ||||||||
\(670\) | −4.59673e25 | + | 2.98112e25i | −1.68957 | + | 1.09574i | ||||
\(671\) | −4.21047e24 | −0.152696 | ||||||||
\(672\) | 3.76505e25 | − | 3.76505e25i | 1.34725 | − | 1.34725i | ||||
\(673\) | 3.91313e25 | + | 3.91313e25i | 1.38162 | + | 1.38162i | 0.841743 | + | 0.539878i | \(0.181530\pi\) |
0.539878 | + | 0.841743i | \(0.318470\pi\) | |||||||
\(674\) | − | 2.61485e25i | − | 0.910977i | ||||||
\(675\) | 1.12967e25 | + | 2.95380e25i | 0.388345 | + | 1.01542i | ||||
\(676\) | −2.96410e25 | −1.00548 | ||||||||
\(677\) | 2.07331e24 | − | 2.07331e24i | 0.0694010 | − | 0.0694010i | −0.671554 | − | 0.740955i | \(-0.734373\pi\) |
0.740955 | + | 0.671554i | \(0.234373\pi\) | |||||||
\(678\) | −2.89886e25 | − | 2.89886e25i | −0.957547 | − | 0.957547i | ||||
\(679\) | 1.58136e25i | 0.515469i | ||||||||
\(680\) | −6.71233e23 | − | 1.03501e24i | −0.0215920 | − | 0.0332938i | ||||
\(681\) | −2.88928e25 | −0.917203 | ||||||||
\(682\) | 5.45994e24 | − | 5.45994e24i | 0.171052 | − | 0.171052i | ||||
\(683\) | 1.44974e25 | + | 1.44974e25i | 0.448234 | + | 0.448234i | 0.894767 | − | 0.446533i | \(-0.147342\pi\) |
−0.446533 | + | 0.894767i | \(0.647342\pi\) | |||||||
\(684\) | − | 1.02882e25i | − | 0.313930i | ||||||
\(685\) | 1.72131e25 | + | 3.66989e24i | 0.518376 | + | 0.110519i | ||||
\(686\) | −4.13509e25 | −1.22905 | ||||||||
\(687\) | 9.80322e24 | − | 9.80322e24i | 0.287580 | − | 0.287580i | ||||
\(688\) | −4.20052e25 | − | 4.20052e25i | −1.21621 | − | 1.21621i | ||||
\(689\) | − | 7.90076e24i | − | 0.225785i | ||||||
\(690\) | 1.55632e23 | − | 7.29970e23i | 0.00438991 | − | 0.0205903i | ||||
\(691\) | 1.75229e24 | 0.0487869 | 0.0243934 | − | 0.999702i | \(-0.492235\pi\) | ||||
0.0243934 | + | 0.999702i | \(0.492235\pi\) | |||||||
\(692\) | −2.13036e25 | + | 2.13036e25i | −0.585462 | + | 0.585462i | ||||
\(693\) | −1.59691e24 | − | 1.59691e24i | −0.0433193 | − | 0.0433193i | ||||
\(694\) | − | 3.72560e25i | − | 0.997610i | ||||||
\(695\) | 1.67739e25 | − | 1.08784e25i | 0.443374 | − | 0.287541i | ||||
\(696\) | 7.09401e23 | 0.0185101 | ||||||||
\(697\) | −1.19928e25 | + | 1.19928e25i | −0.308907 | + | 0.308907i | ||||
\(698\) | 2.56061e25 | + | 2.56061e25i | 0.651095 | + | 0.651095i | ||||
\(699\) | − | 4.67508e25i | − | 1.17353i | ||||||
\(700\) | 6.12493e25 | − | 2.34246e25i | 1.51781 | − | 0.580483i | ||||
\(701\) | 4.99793e25 | 1.22272 | 0.611361 | − | 0.791352i | \(-0.290622\pi\) | ||||
0.611361 | + | 0.791352i | \(0.290622\pi\) | |||||||
\(702\) | −5.23677e24 | + | 5.23677e24i | −0.126482 | + | 0.126482i | ||||
\(703\) | −2.49517e25 | − | 2.49517e25i | −0.594979 | − | 0.594979i | ||||
\(704\) | − | 5.79423e24i | − | 0.136409i | ||||||
\(705\) | 1.71652e25 | + | 2.64679e25i | 0.398977 | + | 0.615203i | ||||
\(706\) | 2.74614e25 | 0.630203 | ||||||||
\(707\) | −4.86380e25 | + | 4.86380e25i | −1.10205 | + | 1.10205i | ||||
\(708\) | 8.95677e24 | + | 8.95677e24i | 0.200379 | + | 0.200379i | ||||
\(709\) | − | 8.07324e25i | − | 1.78333i | −0.452695 | − | 0.891665i | \(-0.649537\pi\) | ||
0.452695 | − | 0.891665i | \(-0.350463\pi\) | |||||||
\(710\) | 2.12563e25 | + | 4.53190e24i | 0.463621 | + | 0.0988452i | ||||
\(711\) | −1.12925e25 | −0.243199 | ||||||||
\(712\) | −1.84156e23 | + | 1.84156e23i | −0.00391622 | + | 0.00391622i | ||||
\(713\) | 7.68228e23 | + | 7.68228e23i | 0.0161318 | + | 0.0161318i | ||||
\(714\) | 1.34097e26i | 2.78058i | ||||||||
\(715\) | −1.54970e23 | + | 7.26867e23i | −0.00317317 | + | 0.0148833i | ||||
\(716\) | 1.99130e25 | 0.402643 | ||||||||
\(717\) | 1.97521e25 | − | 1.97521e25i | 0.394403 | − | 0.394403i | ||||
\(718\) | −5.30658e25 | − | 5.30658e25i | −1.04639 | − | 1.04639i | ||||
\(719\) | 4.57638e25i | 0.891173i | 0.895239 | + | 0.445586i | \(0.147005\pi\) | ||||
−0.895239 | + | 0.445586i | \(0.852995\pi\) | |||||||
\(720\) | −1.25052e25 | + | 8.10999e24i | −0.240491 | + | 0.155965i | ||||
\(721\) | 7.02346e24 | 0.133393 | ||||||||
\(722\) | −5.90556e24 | + | 5.90556e24i | −0.110771 | + | 0.110771i | ||||
\(723\) | −1.89689e25 | − | 1.89689e25i | −0.351397 | − | 0.351397i | ||||
\(724\) | 9.21795e25i | 1.68650i | ||||||||
\(725\) | −4.08737e25 | − | 1.82587e25i | −0.738587 | − | 0.329935i | ||||
\(726\) | −6.58201e25 | −1.17470 | ||||||||
\(727\) | −7.47038e25 | + | 7.47038e25i | −1.31684 | + | 1.31684i | −0.400578 | + | 0.916263i | \(0.631191\pi\) |
−0.916263 | + | 0.400578i | \(0.868809\pi\) | |||||||
\(728\) | 2.03962e23 | + | 2.03962e23i | 0.00355114 | + | 0.00355114i | ||||
\(729\) | − | 6.37571e25i | − | 1.09643i | ||||||
\(730\) | −9.02237e24 | − | 1.39121e25i | −0.153255 | − | 0.236312i | ||||
\(731\) | 1.52528e26 | 2.55913 | ||||||||
\(732\) | −4.24990e25 | + | 4.24990e25i | −0.704334 | + | 0.704334i | ||||
\(733\) | 5.83039e25 | + | 5.83039e25i | 0.954470 | + | 0.954470i | 0.999008 | − | 0.0445380i | \(-0.0141816\pi\) |
−0.0445380 | + | 0.999008i | \(0.514182\pi\) | |||||||
\(734\) | 4.91020e25i | 0.794026i | ||||||||
\(735\) | −7.94431e25 | − | 1.69375e25i | −1.26902 | − | 0.270559i | ||||
\(736\) | 1.58542e24 | 0.0250175 | ||||||||
\(737\) | 8.44892e24 | − | 8.44892e24i | 0.131702 | − | 0.131702i | ||||
\(738\) | −5.71208e24 | − | 5.71208e24i | −0.0879603 | − | 0.0879603i | ||||
\(739\) | 7.38335e25i | 1.12319i | 0.827412 | + | 0.561596i | \(0.189812\pi\) | ||||
−0.827412 | + | 0.561596i | \(0.810188\pi\) | |||||||
\(740\) | 1.12919e25 | − | 5.29633e25i | 0.169700 | − | 0.795957i | ||||
\(741\) | 6.91285e24 | 0.102634 | ||||||||
\(742\) | 2.12987e26 | − | 2.12987e26i | 3.12406 | − | 3.12406i | ||||
\(743\) | −6.71150e25 | − | 6.71150e25i | −0.972568 | − | 0.972568i | 0.0270652 | − | 0.999634i | \(-0.491384\pi\) |
−0.999634 | + | 0.0270652i | \(0.991384\pi\) | |||||||
\(744\) | − | 2.07030e24i | − | 0.0296398i | ||||||
\(745\) | 2.83169e25 | − | 1.83643e25i | 0.400533 | − | 0.259758i | ||||
\(746\) | −1.45119e25 | −0.202803 | ||||||||
\(747\) | 9.60414e24 | − | 9.60414e24i | 0.132609 | − | 0.132609i | ||||
\(748\) | 1.01281e25 | + | 1.01281e25i | 0.138170 | + | 0.138170i | ||||
\(749\) | − | 2.68909e25i | − | 0.362467i | ||||||
\(750\) | 8.86735e25 | − | 1.38760e25i | 1.18098 | − | 0.184805i | ||||
\(751\) | 5.68691e25 | 0.748371 | 0.374186 | − | 0.927354i | \(-0.377922\pi\) | ||||
0.374186 | + | 0.927354i | \(0.377922\pi\) | |||||||
\(752\) | −4.64761e25 | + | 4.64761e25i | −0.604323 | + | 0.604323i | ||||
\(753\) | −7.30330e25 | − | 7.30330e25i | −0.938349 | − | 0.938349i | ||||
\(754\) | − | 1.04835e25i | − | 0.133096i | ||||||
\(755\) | 1.29204e25 | + | 1.99227e25i | 0.162090 | + | 0.249934i | ||||
\(756\) | −1.42510e26 | −1.76665 | ||||||||
\(757\) | −4.37454e25 | + | 4.37454e25i | −0.535883 | + | 0.535883i | −0.922317 | − | 0.386434i | \(-0.873707\pi\) |
0.386434 | + | 0.922317i | \(0.373707\pi\) | |||||||
\(758\) | −5.98732e25 | − | 5.98732e25i | −0.724785 | − | 0.724785i | ||||
\(759\) | 1.62776e23i | 0.00194722i | ||||||||
\(760\) | −2.37118e24 | − | 5.05541e23i | −0.0280312 | − | 0.00597632i | ||||
\(761\) | −1.29060e26 | −1.50775 | −0.753874 | − | 0.657019i | \(-0.771817\pi\) | ||||
−0.753874 | + | 0.657019i | \(0.771817\pi\) | |||||||
\(762\) | 7.76974e25 | − | 7.76974e25i | 0.897040 | − | 0.897040i | ||||
\(763\) | 2.29166e25 | + | 2.29166e25i | 0.261475 | + | 0.261475i | ||||
\(764\) | − | 9.42765e24i | − | 0.106307i | ||||||
\(765\) | 7.97985e24 | − | 3.74285e25i | 0.0889287 | − | 0.417109i | ||||
\(766\) | 8.47532e25 | 0.933463 | ||||||||
\(767\) | 2.48619e24 | − | 2.48619e24i | 0.0270630 | − | 0.0270630i | ||||
\(768\) | 5.31130e25 | + | 5.31130e25i | 0.571413 | + | 0.571413i | ||||
\(769\) | 4.12094e25i | 0.438187i | 0.975704 | + | 0.219094i | \(0.0703100\pi\) | ||||
−0.975704 | + | 0.219094i | \(0.929690\pi\) | |||||||
\(770\) | −2.37724e25 | + | 1.54171e25i | −0.249837 | + | 0.162027i | ||||
\(771\) | 1.01833e26 | 1.05779 | ||||||||
\(772\) | −8.14504e25 | + | 8.14504e25i | −0.836253 | + | 0.836253i | ||||
\(773\) | 6.57712e25 | + | 6.57712e25i | 0.667453 | + | 0.667453i | 0.957126 | − | 0.289673i | \(-0.0935466\pi\) |
−0.289673 | + | 0.957126i | \(0.593547\pi\) | |||||||
\(774\) | 7.26474e25i | 0.728704i | ||||||||
\(775\) | −5.32857e25 | + | 1.19285e26i | −0.528318 | + | 1.18269i | ||||
\(776\) | 8.97257e23 | 0.00879349 | ||||||||
\(777\) | −7.81843e25 | + | 7.81843e25i | −0.757409 | + | 0.757409i | ||||
\(778\) | 6.30677e24 | + | 6.30677e24i | 0.0603936 | + | 0.0603936i | ||||
\(779\) | 3.33331e25i | 0.315528i | ||||||||
\(780\) | 5.77252e24 | + | 8.90094e24i | 0.0540150 | + | 0.0832884i | ||||
\(781\) | −4.73994e24 | −0.0438444 | ||||||||
\(782\) | −2.82334e24 | + | 2.82334e24i | −0.0258168 | + | 0.0258168i | ||||
\(783\) | 6.87925e25 | + | 6.87925e25i | 0.621849 | + | 0.621849i | ||||
\(784\) | − | 1.69238e26i | − | 1.51236i | ||||||
\(785\) | −1.42991e26 | − | 3.04861e25i | −1.26323 | − | 0.269324i | ||||
\(786\) | 2.81913e25 | 0.246214 | ||||||||
\(787\) | 8.32552e25 | − | 8.32552e25i | 0.718851 | − | 0.718851i | −0.249519 | − | 0.968370i | \(-0.580272\pi\) |
0.968370 | + | 0.249519i | \(0.0802724\pi\) | |||||||
\(788\) | 9.14023e24 | + | 9.14023e24i | 0.0780227 | + | 0.0780227i | ||||
\(789\) | − | 6.81316e25i | − | 0.574984i | ||||||
\(790\) | −2.95420e25 | + | 1.38563e26i | −0.246488 | + | 1.15612i | ||||
\(791\) | −2.18975e26 | −1.80637 | ||||||||
\(792\) | −9.06081e22 | + | 9.06081e22i | −0.000738993 | + | 0.000738993i | ||||
\(793\) | 1.17967e25 | + | 1.17967e25i | 0.0951269 | + | 0.0951269i | ||||
\(794\) | − | 2.20327e26i | − | 1.75664i | ||||||
\(795\) | 1.74585e26 | − | 1.13223e26i | 1.37627 | − | 0.892548i | ||||
\(796\) | 1.07104e26 | 0.834807 | ||||||||
\(797\) | 1.00222e26 | − | 1.00222e26i | 0.772395 | − | 0.772395i | −0.206130 | − | 0.978525i | \(-0.566087\pi\) |
0.978525 | + | 0.206130i | \(0.0660869\pi\) | |||||||
\(798\) | 1.86355e26 | + | 1.86355e26i | 1.42009 | + | 1.42009i | ||||
\(799\) | − | 1.68762e26i | − | 1.27161i | ||||||
\(800\) | 6.81024e25 | + | 1.78070e26i | 0.507402 | + | 1.32673i | ||||
\(801\) | −8.07938e24 | −0.0595231 | ||||||||
\(802\) | −2.04292e26 | + | 2.04292e26i | −1.48827 | + | 1.48827i | ||||
\(803\) | 2.55707e24 | + | 2.55707e24i | 0.0184206 | + | 0.0184206i | ||||
\(804\) | − | 1.70561e26i | − | 1.21499i | ||||||
\(805\) | −2.16923e24 | − | 3.34484e24i | −0.0152806 | − | 0.0235620i | ||||
\(806\) | −3.05949e25 | −0.213125 | ||||||||
\(807\) | −1.64887e26 | + | 1.64887e26i | −1.13586 | + | 1.13586i | ||||
\(808\) | 2.75970e24 | + | 2.75970e24i | 0.0188001 | + | 0.0188001i | ||||
\(809\) | 1.13885e26i | 0.767240i | 0.923491 | + | 0.383620i | \(0.125323\pi\) | ||||
−0.923491 | + | 0.383620i | \(0.874677\pi\) | |||||||
\(810\) | −1.29785e26 | − | 2.76704e25i | −0.864686 | − | 0.184353i | ||||
\(811\) | −1.82302e25 | −0.120117 | −0.0600583 | − | 0.998195i | \(-0.519129\pi\) | ||||
−0.0600583 | + | 0.998195i | \(0.519129\pi\) | |||||||
\(812\) | 1.42647e26 | − | 1.42647e26i | 0.929517 | − | 0.929517i | ||||
\(813\) | −1.17179e24 | − | 1.17179e24i | −0.00755151 | − | 0.00755151i | ||||
\(814\) | 2.33987e25i | 0.149132i | ||||||||
\(815\) | 1.77053e25 | − | 8.30447e25i | 0.111606 | − | 0.523472i | ||||
\(816\) | −1.93010e26 | −1.20329 | ||||||||
\(817\) | 2.11969e26 | − | 2.11969e26i | 1.30699 | − | 1.30699i | ||||
\(818\) | −5.69795e25 | − | 5.69795e25i | −0.347488 | − | 0.347488i | ||||
\(819\) | 8.94833e24i | 0.0539743i | ||||||||
\(820\) | −4.29195e25 | + | 2.78345e25i | −0.256053 | + | 0.166058i | ||||
\(821\) | −7.75019e25 | −0.457324 | −0.228662 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228662 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(822\) | −7.67582e25 | + | 7.67582e25i | −0.448001 | + | 0.448001i | ||||
\(823\) | −1.94271e26 | − | 1.94271e26i | −1.12152 | − | 1.12152i | −0.991512 | − | 0.130013i | \(-0.958498\pi\) |
−0.130013 | − | 0.991512i | \(-0.541502\pi\) | |||||||
\(824\) | − | 3.98508e23i | − | 0.00227558i | ||||||
\(825\) | −1.82825e25 | + | 6.99210e24i | −0.103265 | + | 0.0394932i | ||||
\(826\) | 1.34045e26 | 0.748910 | ||||||||
\(827\) | 1.62207e26 | − | 1.62207e26i | 0.896438 | − | 0.896438i | −0.0986809 | − | 0.995119i | \(-0.531462\pi\) |
0.995119 | + | 0.0986809i | \(0.0314623\pi\) | |||||||
\(828\) | −6.78738e23 | − | 6.78738e23i | −0.00371047 | − | 0.00371047i | ||||
\(829\) | 3.29834e26i | 1.78363i | 0.452398 | + | 0.891816i | \(0.350569\pi\) | ||||
−0.452398 | + | 0.891816i | \(0.649431\pi\) | |||||||
\(830\) | −9.27215e25 | − | 1.42972e26i | −0.495995 | − | 0.764800i | ||||
\(831\) | 3.92246e25 | 0.207563 | ||||||||
\(832\) | −1.62341e25 | + | 1.62341e25i | −0.0849801 | + | 0.0849801i | ||||
\(833\) | 3.07265e26 | + | 3.07265e26i | 1.59114 | + | 1.59114i | ||||
\(834\) | 1.23309e26i | 0.631685i | ||||||||
\(835\) | 2.02230e26 | + | 4.31160e25i | 1.02487 | + | 0.218505i | ||||
\(836\) | 2.81503e25 | 0.141132 | ||||||||
\(837\) | 2.00762e26 | − | 2.00762e26i | 0.995756 | − | 0.995756i | ||||
\(838\) | −3.11780e26 | − | 3.11780e26i | −1.52986 | − | 1.52986i | ||||
\(839\) | 3.41571e24i | 0.0165815i | 0.999966 | + | 0.00829075i | \(0.00263906\pi\) | ||||
−0.999966 | + | 0.00829075i | \(0.997361\pi\) | |||||||
\(840\) | −1.58408e24 | + | 7.42992e24i | −0.00760787 | + | 0.0356838i | ||||
\(841\) | 7.27407e25 | 0.345632 | ||||||||
\(842\) | 1.69706e26 | − | 1.69706e26i | 0.797790 | − | 0.797790i | ||||
\(843\) | −7.64482e25 | − | 7.64482e25i | −0.355565 | − | 0.355565i | ||||
\(844\) | − | 7.38457e25i | − | 0.339816i | ||||||
\(845\) | −1.81808e26 | + | 1.17908e26i | −0.827758 | + | 0.536825i | ||||
\(846\) | 8.03797e25 | 0.362087 | ||||||||
\(847\) | −2.48596e26 | + | 2.48596e26i | −1.10801 | + | 1.10801i | ||||
\(848\) | 3.06560e26 | + | 3.06560e26i | 1.35193 | + | 1.35193i | ||||
\(849\) | 2.34991e26i | 1.02537i | ||||||||
\(850\) | −4.38387e26 | − | 1.95832e26i | −1.89272 | − | 0.845500i | ||||
\(851\) | −3.29226e24 | −0.0140646 | ||||||||
\(852\) | −4.78433e25 | + | 4.78433e25i | −0.202239 | + | 0.202239i | ||||
\(853\) | 6.73088e25 | + | 6.73088e25i | 0.281534 | + | 0.281534i | 0.833720 | − | 0.552187i | \(-0.186206\pi\) |
−0.552187 | + | 0.833720i | \(0.686206\pi\) | |||||||
\(854\) | 6.36029e26i | 2.63243i | ||||||||
\(855\) | −4.09250e25 | − | 6.31043e25i | −0.167608 | − | 0.258442i | ||||
\(856\) | −1.52578e24 | −0.00618340 | ||||||||
\(857\) | −1.87254e26 | + | 1.87254e26i | −0.750935 | + | 0.750935i | −0.974654 | − | 0.223718i | \(-0.928180\pi\) |
0.223718 | + | 0.974654i | \(0.428180\pi\) | |||||||
\(858\) | −3.24130e24 | − | 3.24130e24i | −0.0128627 | − | 0.0128627i | ||||
\(859\) | − | 2.23551e26i | − | 0.877884i | −0.898515 | − | 0.438942i | \(-0.855353\pi\) | ||
0.898515 | − | 0.438942i | \(-0.144647\pi\) | |||||||
\(860\) | 4.49932e26 | + | 9.59267e25i | 1.74848 | + | 0.372781i | ||||
\(861\) | 1.04447e26 | 0.401668 | ||||||||
\(862\) | −3.03771e26 | + | 3.03771e26i | −1.15606 | + | 1.15606i | ||||
\(863\) | −1.57856e26 | − | 1.57856e26i | −0.594517 | − | 0.594517i | 0.344331 | − | 0.938848i | \(-0.388106\pi\) |
−0.938848 | + | 0.344331i | \(0.888106\pi\) | |||||||
\(864\) | − | 4.14321e26i | − | 1.54424i | ||||||
\(865\) | −4.59265e25 | + | 2.15413e26i | −0.169402 | + | 0.794559i | ||||
\(866\) | 1.67362e26 | 0.610935 | ||||||||
\(867\) | 1.85772e26 | − | 1.85772e26i | 0.671134 | − | 0.671134i | ||||
\(868\) | −4.16296e26 | − | 4.16296e26i | −1.48842 | − | 1.48842i | ||||
\(869\) | − | 3.08982e25i | − | 0.109334i | ||||||
\(870\) | 2.31657e26 | − | 1.50236e26i | 0.811283 | − | 0.526141i | ||||
\(871\) | −4.73437e25 | −0.164096 | ||||||||
\(872\) | 1.30028e24 | − | 1.30028e24i | 0.00446056 | − | 0.00446056i | ||||
\(873\) | 1.96824e25 | + | 1.96824e25i | 0.0668268 | + | 0.0668268i | ||||
\(874\) | 7.84723e24i | 0.0263702i | ||||||||
\(875\) | 2.82503e26 | − | 3.87320e26i | 0.939617 | − | 1.28824i | ||||
\(876\) | 5.16203e25 | 0.169935 | ||||||||
\(877\) | −1.32860e26 | + | 1.32860e26i | −0.432909 | + | 0.432909i | −0.889617 | − | 0.456708i | \(-0.849029\pi\) |
0.456708 | + | 0.889617i | \(0.349029\pi\) | |||||||
\(878\) | −3.85060e26 | − | 3.85060e26i | −1.24188 | − | 1.24188i | ||||
\(879\) | 5.28135e25i | 0.168595i | ||||||||
\(880\) | −2.21904e25 | − | 3.42164e25i | −0.0701165 | − | 0.108116i | ||||
\(881\) | −1.97429e26 | −0.617486 | −0.308743 | − | 0.951145i | \(-0.599908\pi\) | ||||
−0.308743 | + | 0.951145i | \(0.599908\pi\) | |||||||
\(882\) | −1.46348e26 | + | 1.46348e26i | −0.453073 | + | 0.453073i | ||||
\(883\) | 2.23309e26 | + | 2.23309e26i | 0.684320 | + | 0.684320i | 0.960970 | − | 0.276651i | \(-0.0892246\pi\) |
−0.276651 | + | 0.960970i | \(0.589225\pi\) | |||||||
\(884\) | − | 5.67532e25i | − | 0.172155i | ||||||
\(885\) | 9.05667e25 | + | 1.93091e25i | 0.271944 | + | 0.0579791i | ||||
\(886\) | 8.80921e26 | 2.61838 | ||||||||
\(887\) | 1.76217e26 | − | 1.76217e26i | 0.518483 | − | 0.518483i | −0.398629 | − | 0.917112i | \(-0.630514\pi\) |
0.917112 | + | 0.398629i | \(0.130514\pi\) | |||||||
\(888\) | 4.43615e24 | + | 4.43615e24i | 0.0129208 | + | 0.0129208i | ||||
\(889\) | − | 5.86912e26i | − | 1.69222i | ||||||
\(890\) | −2.11363e25 | + | 9.91373e25i | −0.0603281 | + | 0.282961i | ||||
\(891\) | 2.89407e25 | 0.0817728 | ||||||||
\(892\) | 1.84765e25 | − | 1.84765e25i | 0.0516815 | − | 0.0516815i | ||||
\(893\) | −2.34530e26 | − | 2.34530e26i | −0.649434 | − | 0.649434i | ||||
\(894\) | 2.08164e26i | 0.570649i | ||||||||
\(895\) | 1.22140e26 | − | 7.92115e25i | 0.331475 | − | 0.214971i | ||||
\(896\) | −3.22800e25 | −0.0867285 | ||||||||
\(897\) | 4.56059e23 | − | 4.56059e23i | 0.00121308 | − | 0.00121308i | ||||
\(898\) | 5.26891e26 | + | 5.26891e26i | 1.38750 | + | 1.38750i | ||||
\(899\) | 4.01908e26i | 1.04783i | ||||||||
\(900\) | 4.70786e25 | − | 1.05389e26i | 0.121518 | − | 0.272029i | ||||
\(901\) | −1.11317e27 | −2.84471 | ||||||||
\(902\) | 1.56292e25 | − | 1.56292e25i | 0.0395439 | − | 0.0395439i | ||||
\(903\) | −6.64189e26 | − | 6.64189e26i | −1.66380 | − | 1.66380i | ||||
\(904\) | 1.24245e25i | 0.0308152i | ||||||||
\(905\) | 3.66678e26 | + | 5.65399e26i | 0.900425 | + | 1.38841i | ||||
\(906\) | −1.46457e26 | −0.356086 | ||||||||
\(907\) | −2.67834e26 | + | 2.67834e26i | −0.644763 | + | 0.644763i | −0.951723 | − | 0.306960i | \(-0.900688\pi\) |
0.306960 | + | 0.951723i | \(0.400688\pi\) | |||||||
\(908\) | 3.29644e26 | + | 3.29644e26i | 0.785730 | + | 0.785730i | ||||
\(909\) | 1.21075e26i | 0.285745i | ||||||||
\(910\) | 1.09800e26 | + | 2.34096e25i | 0.256583 | + | 0.0547042i | ||||
\(911\) | −5.76143e26 | −1.33311 | −0.666553 | − | 0.745457i | \(-0.732231\pi\) | ||||
−0.666553 | + | 0.745457i | \(0.732231\pi\) | |||||||
\(912\) | −2.68228e26 | + | 2.68228e26i | −0.614540 | + | 0.614540i | ||||
\(913\) | 2.62786e25 | + | 2.62786e25i | 0.0596164 | + | 0.0596164i | ||||
\(914\) | − | 3.02285e26i | − | 0.679048i | ||||||
\(915\) | −9.16196e25 | + | 4.29730e26i | −0.203797 | + | 0.955886i | ||||
\(916\) | −2.23694e26 | −0.492715 | ||||||||
\(917\) | 1.06476e26 | − | 1.06476e26i | 0.232235 | − | 0.232235i | ||||
\(918\) | 7.37827e26 | + | 7.37827e26i | 1.59357 | + | 1.59357i | ||||
\(919\) | 2.42026e26i | 0.517633i | 0.965927 | + | 0.258817i | \(0.0833325\pi\) | ||||
−0.965927 | + | 0.258817i | \(0.916667\pi\) | |||||||
\(920\) | −1.89785e23 | + | 1.23081e23i | −0.000401949 | + | 0.000260676i | ||||
\(921\) | 4.91712e26 | 1.03127 | ||||||||
\(922\) | 4.02011e26 | − | 4.02011e26i | 0.834949 | − | 0.834949i | ||||
\(923\) | 1.32802e25 | + | 1.32802e25i | 0.0273142 | + | 0.0273142i | ||||
\(924\) | − | 8.82069e25i | − | 0.179661i | ||||||
\(925\) | −1.41420e26 | − | 3.69777e26i | −0.285256 | − | 0.745873i | ||||
\(926\) | −2.94871e26 | −0.589023 | ||||||||
\(927\) | 8.74176e24 | − | 8.74176e24i | 0.0172934 | − | 0.0172934i | ||||
\(928\) | 4.14717e26 | + | 4.14717e26i | 0.812494 | + | 0.812494i | ||||
\(929\) | − | 8.98057e26i | − | 1.74246i | −0.490877 | − | 0.871229i | \(-0.663323\pi\) | ||
0.490877 | − | 0.871229i | \(-0.336677\pi\) | |||||||
\(930\) | −4.38446e26 | − | 6.76062e26i | −0.842499 | − | 1.29909i | ||||
\(931\) | 8.54018e26 | 1.62525 | ||||||||
\(932\) | −5.33391e26 | + | 5.33391e26i | −1.00531 | + | 1.00531i | ||||
\(933\) | 5.25473e26 | + | 5.25473e26i | 0.980879 | + | 0.980879i | ||||
\(934\) | 1.11310e26i | 0.205784i | ||||||||
\(935\) | 1.02411e26 | + | 2.18343e25i | 0.187518 | + | 0.0399792i | ||||
\(936\) | 5.07725e23 | 0.000920758 | ||||||||
\(937\) | 3.02375e26 | − | 3.02375e26i | 0.543112 | − | 0.543112i | −0.381328 | − | 0.924440i | \(-0.624533\pi\) |
0.924440 | + | 0.381328i | \(0.124533\pi\) | |||||||
\(938\) | −1.27628e27 | − | 1.27628e27i | −2.27050 | − | 2.27050i | ||||
\(939\) | 6.86215e26i | 1.20912i | ||||||||
\(940\) | 1.06137e26 | − | 4.97821e26i | 0.185232 | − | 0.868806i | ||||
\(941\) | 6.92218e26 | 1.19657 | 0.598283 | − | 0.801285i | \(-0.295850\pi\) | ||||
0.598283 | + | 0.801285i | \(0.295850\pi\) | |||||||
\(942\) | 6.37638e26 | − | 6.37638e26i | 1.09173 | − | 1.09173i | ||||
\(943\) | 2.19907e24 | + | 2.19907e24i | 0.00372936 | + | 0.00372936i | ||||
\(944\) | 1.92935e26i | 0.324088i | ||||||||
\(945\) | −8.74112e26 | + | 5.66887e26i | −1.45439 | + | 0.943214i | ||||
\(946\) | −1.98776e26 | −0.327600 | ||||||||
\(947\) | 4.30648e26 | − | 4.30648e26i | 0.703028 | − | 0.703028i | −0.262032 | − | 0.965059i | \(-0.584392\pi\) |
0.965059 | + | 0.262032i | \(0.0843925\pi\) | |||||||
\(948\) | −3.11875e26 | − | 3.11875e26i | −0.504319 | − | 0.504319i | ||||
\(949\) | − | 1.43286e25i | − | 0.0229513i | ||||||
\(950\) | −8.81379e26 | + | 3.37080e26i | −1.39846 | + | 0.534837i | ||||
\(951\) | −1.95401e26 | −0.307116 | ||||||||
\(952\) | 2.87370e25 | − | 2.87370e25i | 0.0447414 | − | 0.0447414i | ||||
\(953\) | −4.88115e26 | − | 4.88115e26i | −0.752810 | − | 0.752810i | 0.222192 | − | 0.975003i | \(-0.428679\pi\) |
−0.975003 | + | 0.222192i | \(0.928679\pi\) | |||||||
\(954\) | − | 5.30191e26i | − | 0.810022i | ||||||
\(955\) | −3.75019e25 | − | 5.78261e25i | −0.0567575 | − | 0.0875173i | ||||
\(956\) | −4.50712e26 | −0.675738 | ||||||||
\(957\) | −4.25792e25 | + | 4.25792e25i | −0.0632397 | + | 0.0632397i | ||||
\(958\) | 1.11232e27 | + | 1.11232e27i | 1.63658 | + | 1.63658i | ||||
\(959\) | 5.79818e26i | 0.845131i | ||||||||
\(960\) | −5.91372e26 | − | 1.26082e26i | −0.853925 | − | 0.182059i | ||||
\(961\) | 4.73865e26 | 0.677866 | ||||||||
\(962\) | 6.55576e25 | − | 6.55576e25i | 0.0929068 | − | 0.0929068i | ||||
\(963\) | −3.34698e25 | − | 3.34698e25i | −0.0469912 | − | 0.0469912i | ||||
\(964\) | 4.32842e26i | 0.602055i | ||||||||
\(965\) | −1.75591e26 | + | 8.23589e26i | −0.241968 | + | 1.13492i | ||||
\(966\) | 2.45887e25 | 0.0335693 | ||||||||
\(967\) | 2.74723e26 | − | 2.74723e26i | 0.371584 | − | 0.371584i | −0.496470 | − | 0.868054i | \(-0.665371\pi\) |
0.868054 | + | 0.496470i | \(0.165371\pi\) | |||||||
\(968\) | 1.41053e25 | + | 1.41053e25i | 0.0189018 | + | 0.0189018i | ||||
\(969\) | − | 9.73977e26i | − | 1.29311i | ||||||
\(970\) | 2.93002e26 | − | 1.90021e26i | 0.385412 | − | 0.249951i | ||||
\(971\) | 1.00811e27 | 1.31382 | 0.656912 | − | 0.753968i | \(-0.271862\pi\) | ||||
0.656912 | + | 0.753968i | \(0.271862\pi\) | |||||||
\(972\) | −3.14627e26 | + | 3.14627e26i | −0.406256 | + | 0.406256i | ||||
\(973\) | 4.65727e26 | + | 4.65727e26i | 0.595821 | + | 0.595821i | ||||
\(974\) | − | 8.95762e26i | − | 1.13543i | ||||||
\(975\) | 7.08135e25 | + | 3.16331e25i | 0.0889354 | + | 0.0397284i | ||||
\(976\) | −9.15459e26 | −1.13917 | ||||||||
\(977\) | 2.87323e26 | − | 2.87323e26i | 0.354258 | − | 0.354258i | −0.507433 | − | 0.861691i | \(-0.669406\pi\) |
0.861691 | + | 0.507433i | \(0.169406\pi\) | |||||||
\(978\) | 3.70319e26 | + | 3.70319e26i | 0.452404 | + | 0.452404i | ||||
\(979\) | − | 2.21066e25i | − | 0.0267595i | ||||||
\(980\) | 7.13141e26 | + | 1.09963e27i | 0.855344 | + | 1.31890i | ||||
\(981\) | 5.70465e25 | 0.0677966 | ||||||||
\(982\) | −5.15413e25 | + | 5.15413e25i | −0.0606948 | + | 0.0606948i | ||||
\(983\) | −2.47845e26 | − | 2.47845e26i | −0.289200 | − | 0.289200i | 0.547564 | − | 0.836764i | \(-0.315555\pi\) |
−0.836764 | + | 0.547564i | \(0.815555\pi\) | |||||||
\(984\) | − | 5.92628e24i | − | 0.00685214i | ||||||
\(985\) | 9.24218e25 | + | 1.97046e25i | 0.105888 | + | 0.0225757i | ||||
\(986\) | −1.47707e27 | −1.67690 | ||||||||
\(987\) | −7.34883e26 | + | 7.34883e26i | −0.826730 | + | 0.826730i | ||||
\(988\) | −7.88703e25 | − | 7.88703e25i | −0.0879227 | − | 0.0879227i | ||||
\(989\) | − | 2.79683e25i | − | 0.0308958i | ||||||
\(990\) | −1.03995e25 | + | 4.87773e25i | −0.0113840 | + | 0.0533951i | ||||
\(991\) | −3.81522e26 | −0.413863 | −0.206931 | − | 0.978355i | \(-0.566348\pi\) | ||||
−0.206931 | + | 0.978355i | \(0.566348\pi\) | |||||||
\(992\) | 1.21030e27 | − | 1.21030e27i | 1.30103 | − | 1.30103i | ||||
\(993\) | −4.48817e26 | − | 4.48817e26i | −0.478108 | − | 0.478108i | ||||
\(994\) | 7.16011e26i | 0.755861i | ||||||||
\(995\) | 6.56938e26 | − | 4.26044e26i | 0.687253 | − | 0.445704i | ||||
\(996\) | 5.30494e26 | 0.549979 | ||||||||
\(997\) | −2.39641e25 | + | 2.39641e25i | −0.0246210 | + | 0.0246210i | −0.719310 | − | 0.694689i | \(-0.755542\pi\) |
0.694689 | + | 0.719310i | \(0.255542\pi\) | |||||||
\(998\) | 7.63292e26 | + | 7.63292e26i | 0.777170 | + | 0.777170i | ||||
\(999\) | 8.60371e26i | 0.868153i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5.19.c.a.3.7 | yes | 16 | |
3.2 | odd | 2 | 45.19.g.a.28.2 | 16 | |||
5.2 | odd | 4 | inner | 5.19.c.a.2.7 | ✓ | 16 | |
5.3 | odd | 4 | 25.19.c.b.7.2 | 16 | |||
5.4 | even | 2 | 25.19.c.b.18.2 | 16 | |||
15.2 | even | 4 | 45.19.g.a.37.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.19.c.a.2.7 | ✓ | 16 | 5.2 | odd | 4 | inner | |
5.19.c.a.3.7 | yes | 16 | 1.1 | even | 1 | trivial | |
25.19.c.b.7.2 | 16 | 5.3 | odd | 4 | |||
25.19.c.b.18.2 | 16 | 5.4 | even | 2 | |||
45.19.g.a.28.2 | 16 | 3.2 | odd | 2 | |||
45.19.g.a.37.2 | 16 | 15.2 | even | 4 |