Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,18,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
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: | yes |
Analytic conductor: | \(18.3222087345\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{83281}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 20820 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-143.792\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −256.000 | −0.707107 | ||||||||
\(3\) | 8003.53 | 0.704289 | 0.352145 | − | 0.935946i | \(-0.385452\pi\) | ||||
0.352145 | + | 0.935946i | \(0.385452\pi\) | |||||||
\(4\) | 65536.0 | 0.500000 | ||||||||
\(5\) | 390625. | 0.447214 | ||||||||
\(6\) | −2.04890e6 | −0.498008 | ||||||||
\(7\) | 2.54694e7 | 1.66988 | 0.834939 | − | 0.550342i | \(-0.185503\pi\) | ||||
0.834939 | + | 0.550342i | \(0.185503\pi\) | |||||||
\(8\) | −1.67772e7 | −0.353553 | ||||||||
\(9\) | −6.50836e7 | −0.503976 | ||||||||
\(10\) | −1.00000e8 | −0.316228 | ||||||||
\(11\) | −2.81089e8 | −0.395372 | −0.197686 | − | 0.980265i | \(-0.563343\pi\) | ||||
−0.197686 | + | 0.980265i | \(0.563343\pi\) | |||||||
\(12\) | 5.24520e8 | 0.352145 | ||||||||
\(13\) | −1.52610e9 | −0.518876 | −0.259438 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259438 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(14\) | −6.52016e9 | −1.18078 | ||||||||
\(15\) | 3.12638e9 | 0.314968 | ||||||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | 5.46901e10 | 1.90148 | 0.950742 | − | 0.309984i | \(-0.100324\pi\) | ||||
0.950742 | + | 0.309984i | \(0.100324\pi\) | |||||||
\(18\) | 1.66614e10 | 0.356365 | ||||||||
\(19\) | 6.88947e8 | 0.00930637 | 0.00465318 | − | 0.999989i | \(-0.498519\pi\) | ||||
0.00465318 | + | 0.999989i | \(0.498519\pi\) | |||||||
\(20\) | 2.56000e10 | 0.223607 | ||||||||
\(21\) | 2.03845e11 | 1.17608 | ||||||||
\(22\) | 7.19587e10 | 0.279570 | ||||||||
\(23\) | 3.91035e11 | 1.04119 | 0.520594 | − | 0.853804i | \(-0.325710\pi\) | ||||
0.520594 | + | 0.853804i | \(0.325710\pi\) | |||||||
\(24\) | −1.34277e11 | −0.249004 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | 3.90681e11 | 0.366901 | ||||||||
\(27\) | −1.55448e12 | −1.05923 | ||||||||
\(28\) | 1.66916e12 | 0.834939 | ||||||||
\(29\) | 5.12259e12 | 1.90154 | 0.950772 | − | 0.309892i | \(-0.100293\pi\) | ||||
0.950772 | + | 0.309892i | \(0.100293\pi\) | |||||||
\(30\) | −8.00353e11 | −0.222716 | ||||||||
\(31\) | −7.31204e10 | −0.0153980 | −0.00769900 | − | 0.999970i | \(-0.502451\pi\) | ||||
−0.00769900 | + | 0.999970i | \(0.502451\pi\) | |||||||
\(32\) | −1.09951e12 | −0.176777 | ||||||||
\(33\) | −2.24970e12 | −0.278456 | ||||||||
\(34\) | −1.40007e13 | −1.34455 | ||||||||
\(35\) | 9.94897e12 | 0.746792 | ||||||||
\(36\) | −4.26532e12 | −0.251988 | ||||||||
\(37\) | −6.81637e12 | −0.319035 | −0.159517 | − | 0.987195i | \(-0.550994\pi\) | ||||
−0.159517 | + | 0.987195i | \(0.550994\pi\) | |||||||
\(38\) | −1.76370e11 | −0.00658059 | ||||||||
\(39\) | −1.22142e13 | −0.365439 | ||||||||
\(40\) | −6.55360e12 | −0.158114 | ||||||||
\(41\) | −5.76386e13 | −1.12733 | −0.563665 | − | 0.826004i | \(-0.690609\pi\) | ||||
−0.563665 | + | 0.826004i | \(0.690609\pi\) | |||||||
\(42\) | −5.21843e13 | −0.831613 | ||||||||
\(43\) | 7.57081e13 | 0.987781 | 0.493890 | − | 0.869524i | \(-0.335574\pi\) | ||||
0.493890 | + | 0.869524i | \(0.335574\pi\) | |||||||
\(44\) | −1.84214e13 | −0.197686 | ||||||||
\(45\) | −2.54233e13 | −0.225385 | ||||||||
\(46\) | −1.00105e14 | −0.736231 | ||||||||
\(47\) | −4.60351e13 | −0.282006 | −0.141003 | − | 0.990009i | \(-0.545033\pi\) | ||||
−0.141003 | + | 0.990009i | \(0.545033\pi\) | |||||||
\(48\) | 3.43749e13 | 0.176072 | ||||||||
\(49\) | 4.16059e14 | 1.78849 | ||||||||
\(50\) | −3.90625e13 | −0.141421 | ||||||||
\(51\) | 4.37714e14 | 1.33919 | ||||||||
\(52\) | −1.00014e14 | −0.259438 | ||||||||
\(53\) | 6.58261e14 | 1.45229 | 0.726145 | − | 0.687541i | \(-0.241310\pi\) | ||||
0.726145 | + | 0.687541i | \(0.241310\pi\) | |||||||
\(54\) | 3.97946e14 | 0.748992 | ||||||||
\(55\) | −1.09800e14 | −0.176816 | ||||||||
\(56\) | −4.27305e14 | −0.590391 | ||||||||
\(57\) | 5.51401e12 | 0.00655437 | ||||||||
\(58\) | −1.31138e15 | −1.34459 | ||||||||
\(59\) | −2.98287e14 | −0.264479 | −0.132240 | − | 0.991218i | \(-0.542217\pi\) | ||||
−0.132240 | + | 0.991218i | \(0.542217\pi\) | |||||||
\(60\) | 2.04890e14 | 0.157484 | ||||||||
\(61\) | 8.50623e14 | 0.568111 | 0.284056 | − | 0.958808i | \(-0.408320\pi\) | ||||
0.284056 | + | 0.958808i | \(0.408320\pi\) | |||||||
\(62\) | 1.87188e13 | 0.0108880 | ||||||||
\(63\) | −1.65764e15 | −0.841580 | ||||||||
\(64\) | 2.81475e14 | 0.125000 | ||||||||
\(65\) | −5.96131e14 | −0.232048 | ||||||||
\(66\) | 5.75924e14 | 0.196898 | ||||||||
\(67\) | −6.12967e15 | −1.84417 | −0.922085 | − | 0.386987i | \(-0.873516\pi\) | ||||
−0.922085 | + | 0.386987i | \(0.873516\pi\) | |||||||
\(68\) | 3.58417e15 | 0.950742 | ||||||||
\(69\) | 3.12966e15 | 0.733298 | ||||||||
\(70\) | −2.54694e15 | −0.528062 | ||||||||
\(71\) | 5.41472e14 | 0.0995131 | 0.0497565 | − | 0.998761i | \(-0.484155\pi\) | ||||
0.0497565 | + | 0.998761i | \(0.484155\pi\) | |||||||
\(72\) | 1.09192e15 | 0.178183 | ||||||||
\(73\) | −7.16849e15 | −1.04036 | −0.520180 | − | 0.854057i | \(-0.674135\pi\) | ||||
−0.520180 | + | 0.854057i | \(0.674135\pi\) | |||||||
\(74\) | 1.74499e15 | 0.225592 | ||||||||
\(75\) | 1.22124e15 | 0.140858 | ||||||||
\(76\) | 4.51508e13 | 0.00465318 | ||||||||
\(77\) | −7.15916e15 | −0.660223 | ||||||||
\(78\) | 3.12683e15 | 0.258404 | ||||||||
\(79\) | 5.45373e15 | 0.404448 | 0.202224 | − | 0.979339i | \(-0.435183\pi\) | ||||
0.202224 | + | 0.979339i | \(0.435183\pi\) | |||||||
\(80\) | 1.67772e15 | 0.111803 | ||||||||
\(81\) | −4.03640e15 | −0.242031 | ||||||||
\(82\) | 1.47555e16 | 0.797142 | ||||||||
\(83\) | −3.64723e15 | −0.177746 | −0.0888728 | − | 0.996043i | \(-0.528326\pi\) | ||||
−0.0888728 | + | 0.996043i | \(0.528326\pi\) | |||||||
\(84\) | 1.33592e16 | 0.588039 | ||||||||
\(85\) | 2.13633e16 | 0.850369 | ||||||||
\(86\) | −1.93813e16 | −0.698467 | ||||||||
\(87\) | 4.09988e16 | 1.33924 | ||||||||
\(88\) | 4.71589e15 | 0.139785 | ||||||||
\(89\) | 6.81792e14 | 0.0183585 | 0.00917925 | − | 0.999958i | \(-0.497078\pi\) | ||||
0.00917925 | + | 0.999958i | \(0.497078\pi\) | |||||||
\(90\) | 6.50836e15 | 0.159371 | ||||||||
\(91\) | −3.88687e16 | −0.866460 | ||||||||
\(92\) | 2.56269e16 | 0.520594 | ||||||||
\(93\) | −5.85222e14 | −0.0108446 | ||||||||
\(94\) | 1.17850e16 | 0.199408 | ||||||||
\(95\) | 2.69120e14 | 0.00416193 | ||||||||
\(96\) | −8.79998e15 | −0.124502 | ||||||||
\(97\) | −1.20373e17 | −1.55944 | −0.779720 | − | 0.626129i | \(-0.784638\pi\) | ||||
−0.779720 | + | 0.626129i | \(0.784638\pi\) | |||||||
\(98\) | −1.06511e17 | −1.26466 | ||||||||
\(99\) | 1.82943e16 | 0.199258 | ||||||||
\(100\) | 1.00000e16 | 0.100000 | ||||||||
\(101\) | 7.74092e16 | 0.711314 | 0.355657 | − | 0.934617i | \(-0.384257\pi\) | ||||
0.355657 | + | 0.934617i | \(0.384257\pi\) | |||||||
\(102\) | −1.12055e17 | −0.946954 | ||||||||
\(103\) | −1.39309e17 | −1.08359 | −0.541793 | − | 0.840512i | \(-0.682254\pi\) | ||||
−0.541793 | + | 0.840512i | \(0.682254\pi\) | |||||||
\(104\) | 2.56037e16 | 0.183450 | ||||||||
\(105\) | 7.96270e16 | 0.525958 | ||||||||
\(106\) | −1.68515e17 | −1.02692 | ||||||||
\(107\) | 2.75662e17 | 1.55101 | 0.775505 | − | 0.631341i | \(-0.217495\pi\) | ||||
0.775505 | + | 0.631341i | \(0.217495\pi\) | |||||||
\(108\) | −1.01874e17 | −0.529617 | ||||||||
\(109\) | 1.37550e17 | 0.661202 | 0.330601 | − | 0.943771i | \(-0.392749\pi\) | ||||
0.330601 | + | 0.943771i | \(0.392749\pi\) | |||||||
\(110\) | 2.81089e16 | 0.125028 | ||||||||
\(111\) | −5.45550e16 | −0.224693 | ||||||||
\(112\) | 1.09390e17 | 0.417470 | ||||||||
\(113\) | −3.90258e17 | −1.38097 | −0.690486 | − | 0.723345i | \(-0.742604\pi\) | ||||
−0.690486 | + | 0.723345i | \(0.742604\pi\) | |||||||
\(114\) | −1.41159e15 | −0.00463464 | ||||||||
\(115\) | 1.52748e17 | 0.465634 | ||||||||
\(116\) | 3.35714e17 | 0.950772 | ||||||||
\(117\) | 9.93239e16 | 0.261501 | ||||||||
\(118\) | 7.63614e16 | 0.187015 | ||||||||
\(119\) | 1.39292e18 | 3.17525 | ||||||||
\(120\) | −5.24520e16 | −0.111358 | ||||||||
\(121\) | −4.26436e17 | −0.843681 | ||||||||
\(122\) | −2.17759e17 | −0.401715 | ||||||||
\(123\) | −4.61313e17 | −0.793966 | ||||||||
\(124\) | −4.79202e15 | −0.00769900 | ||||||||
\(125\) | 5.96046e16 | 0.0894427 | ||||||||
\(126\) | 4.24355e17 | 0.595087 | ||||||||
\(127\) | −7.37824e17 | −0.967433 | −0.483717 | − | 0.875225i | \(-0.660713\pi\) | ||||
−0.483717 | + | 0.875225i | \(0.660713\pi\) | |||||||
\(128\) | −7.20576e16 | −0.0883883 | ||||||||
\(129\) | 6.05933e17 | 0.695684 | ||||||||
\(130\) | 1.52610e17 | 0.164083 | ||||||||
\(131\) | −1.45408e18 | −1.46482 | −0.732409 | − | 0.680865i | \(-0.761604\pi\) | ||||
−0.732409 | + | 0.680865i | \(0.761604\pi\) | |||||||
\(132\) | −1.47437e17 | −0.139228 | ||||||||
\(133\) | 1.75470e16 | 0.0155405 | ||||||||
\(134\) | 1.56919e18 | 1.30403 | ||||||||
\(135\) | −6.07217e17 | −0.473704 | ||||||||
\(136\) | −9.17547e17 | −0.672276 | ||||||||
\(137\) | −2.27534e18 | −1.56647 | −0.783236 | − | 0.621725i | \(-0.786432\pi\) | ||||
−0.783236 | + | 0.621725i | \(0.786432\pi\) | |||||||
\(138\) | −8.01194e17 | −0.518520 | ||||||||
\(139\) | 1.41598e17 | 0.0861849 | 0.0430924 | − | 0.999071i | \(-0.486279\pi\) | ||||
0.0430924 | + | 0.999071i | \(0.486279\pi\) | |||||||
\(140\) | 6.52016e17 | 0.373396 | ||||||||
\(141\) | −3.68444e17 | −0.198614 | ||||||||
\(142\) | −1.38617e17 | −0.0703664 | ||||||||
\(143\) | 4.28969e17 | 0.205149 | ||||||||
\(144\) | −2.79532e17 | −0.125994 | ||||||||
\(145\) | 2.00101e18 | 0.850396 | ||||||||
\(146\) | 1.83513e18 | 0.735646 | ||||||||
\(147\) | 3.32994e18 | 1.25962 | ||||||||
\(148\) | −4.46717e17 | −0.159517 | ||||||||
\(149\) | −1.31089e18 | −0.442063 | −0.221032 | − | 0.975267i | \(-0.570942\pi\) | ||||
−0.221032 | + | 0.975267i | \(0.570942\pi\) | |||||||
\(150\) | −3.12638e17 | −0.0996016 | ||||||||
\(151\) | −2.76548e18 | −0.832658 | −0.416329 | − | 0.909214i | \(-0.636684\pi\) | ||||
−0.416329 | + | 0.909214i | \(0.636684\pi\) | |||||||
\(152\) | −1.15586e16 | −0.00329030 | ||||||||
\(153\) | −3.55943e18 | −0.958303 | ||||||||
\(154\) | 1.83274e18 | 0.466848 | ||||||||
\(155\) | −2.85627e16 | −0.00688619 | ||||||||
\(156\) | −8.00468e17 | −0.182719 | ||||||||
\(157\) | −3.81235e18 | −0.824225 | −0.412112 | − | 0.911133i | \(-0.635209\pi\) | ||||
−0.412112 | + | 0.911133i | \(0.635209\pi\) | |||||||
\(158\) | −1.39615e18 | −0.285988 | ||||||||
\(159\) | 5.26842e18 | 1.02283 | ||||||||
\(160\) | −4.29497e17 | −0.0790569 | ||||||||
\(161\) | 9.95942e18 | 1.73866 | ||||||||
\(162\) | 1.03332e18 | 0.171142 | ||||||||
\(163\) | 1.03773e19 | 1.63114 | 0.815570 | − | 0.578658i | \(-0.196423\pi\) | ||||
0.815570 | + | 0.578658i | \(0.196423\pi\) | |||||||
\(164\) | −3.77740e18 | −0.563665 | ||||||||
\(165\) | −8.78791e17 | −0.124529 | ||||||||
\(166\) | 9.33690e17 | 0.125685 | ||||||||
\(167\) | 1.21920e19 | 1.55949 | 0.779747 | − | 0.626095i | \(-0.215348\pi\) | ||||
0.779747 | + | 0.626095i | \(0.215348\pi\) | |||||||
\(168\) | −3.41995e18 | −0.415806 | ||||||||
\(169\) | −6.32145e18 | −0.730768 | ||||||||
\(170\) | −5.46901e18 | −0.601302 | ||||||||
\(171\) | −4.48391e16 | −0.00469019 | ||||||||
\(172\) | 4.96161e18 | 0.493890 | ||||||||
\(173\) | −3.88210e18 | −0.367853 | −0.183927 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183927 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(174\) | −1.04957e19 | −0.946983 | ||||||||
\(175\) | 3.88632e18 | 0.333976 | ||||||||
\(176\) | −1.20727e18 | −0.0988430 | ||||||||
\(177\) | −2.38735e18 | −0.186270 | ||||||||
\(178\) | −1.74539e17 | −0.0129814 | ||||||||
\(179\) | −1.62354e19 | −1.15136 | −0.575680 | − | 0.817675i | \(-0.695263\pi\) | ||||
−0.575680 | + | 0.817675i | \(0.695263\pi\) | |||||||
\(180\) | −1.66614e18 | −0.112693 | ||||||||
\(181\) | −2.32195e19 | −1.49825 | −0.749127 | − | 0.662427i | \(-0.769527\pi\) | ||||
−0.749127 | + | 0.662427i | \(0.769527\pi\) | |||||||
\(182\) | 9.95039e18 | 0.612680 | ||||||||
\(183\) | 6.80799e18 | 0.400115 | ||||||||
\(184\) | −6.56048e18 | −0.368116 | ||||||||
\(185\) | −2.66264e18 | −0.142677 | ||||||||
\(186\) | 1.49817e17 | 0.00766832 | ||||||||
\(187\) | −1.53728e19 | −0.751793 | ||||||||
\(188\) | −3.01696e18 | −0.141003 | ||||||||
\(189\) | −3.95915e19 | −1.76879 | ||||||||
\(190\) | −6.88947e16 | −0.00294293 | ||||||||
\(191\) | 4.47928e19 | 1.82989 | 0.914944 | − | 0.403580i | \(-0.132234\pi\) | ||||
0.914944 | + | 0.403580i | \(0.132234\pi\) | |||||||
\(192\) | 2.25279e18 | 0.0880362 | ||||||||
\(193\) | 3.61154e19 | 1.35038 | 0.675189 | − | 0.737645i | \(-0.264062\pi\) | ||||
0.675189 | + | 0.737645i | \(0.264062\pi\) | |||||||
\(194\) | 3.08154e19 | 1.10269 | ||||||||
\(195\) | −4.77116e18 | −0.163429 | ||||||||
\(196\) | 2.72668e19 | 0.894247 | ||||||||
\(197\) | −1.80503e19 | −0.566920 | −0.283460 | − | 0.958984i | \(-0.591482\pi\) | ||||
−0.283460 | + | 0.958984i | \(0.591482\pi\) | |||||||
\(198\) | −4.68333e18 | −0.140897 | ||||||||
\(199\) | −6.39636e18 | −0.184366 | −0.0921832 | − | 0.995742i | \(-0.529385\pi\) | ||||
−0.0921832 | + | 0.995742i | \(0.529385\pi\) | |||||||
\(200\) | −2.56000e18 | −0.0707107 | ||||||||
\(201\) | −4.90590e19 | −1.29883 | ||||||||
\(202\) | −1.98168e19 | −0.502975 | ||||||||
\(203\) | 1.30469e20 | 3.17535 | ||||||||
\(204\) | 2.86860e19 | 0.669597 | ||||||||
\(205\) | −2.25151e19 | −0.504157 | ||||||||
\(206\) | 3.56631e19 | 0.766211 | ||||||||
\(207\) | −2.54500e19 | −0.524734 | ||||||||
\(208\) | −6.55453e18 | −0.129719 | ||||||||
\(209\) | −1.93655e17 | −0.00367948 | ||||||||
\(210\) | −2.03845e19 | −0.371908 | ||||||||
\(211\) | 7.72101e18 | 0.135292 | 0.0676462 | − | 0.997709i | \(-0.478451\pi\) | ||||
0.0676462 | + | 0.997709i | \(0.478451\pi\) | |||||||
\(212\) | 4.31398e19 | 0.726145 | ||||||||
\(213\) | 4.33369e18 | 0.0700860 | ||||||||
\(214\) | −7.05695e19 | −1.09673 | ||||||||
\(215\) | 2.95735e19 | 0.441749 | ||||||||
\(216\) | 2.60798e19 | 0.374496 | ||||||||
\(217\) | −1.86233e18 | −0.0257128 | ||||||||
\(218\) | −3.52127e19 | −0.467541 | ||||||||
\(219\) | −5.73733e19 | −0.732715 | ||||||||
\(220\) | −7.19587e18 | −0.0884078 | ||||||||
\(221\) | −8.34623e19 | −0.986634 | ||||||||
\(222\) | 1.39661e19 | 0.158882 | ||||||||
\(223\) | −1.08588e20 | −1.18902 | −0.594510 | − | 0.804088i | \(-0.702654\pi\) | ||||
−0.594510 | + | 0.804088i | \(0.702654\pi\) | |||||||
\(224\) | −2.80039e19 | −0.295196 | ||||||||
\(225\) | −9.93097e18 | −0.100795 | ||||||||
\(226\) | 9.99061e19 | 0.976495 | ||||||||
\(227\) | 1.95539e19 | 0.184083 | 0.0920415 | − | 0.995755i | \(-0.470661\pi\) | ||||
0.0920415 | + | 0.995755i | \(0.470661\pi\) | |||||||
\(228\) | 3.61366e17 | 0.00327719 | ||||||||
\(229\) | 1.20601e20 | 1.05378 | 0.526890 | − | 0.849933i | \(-0.323358\pi\) | ||||
0.526890 | + | 0.849933i | \(0.323358\pi\) | |||||||
\(230\) | −3.91035e19 | −0.329253 | ||||||||
\(231\) | −5.72986e19 | −0.464988 | ||||||||
\(232\) | −8.59427e19 | −0.672297 | ||||||||
\(233\) | 7.20388e19 | 0.543302 | 0.271651 | − | 0.962396i | \(-0.412430\pi\) | ||||
0.271651 | + | 0.962396i | \(0.412430\pi\) | |||||||
\(234\) | −2.54269e19 | −0.184909 | ||||||||
\(235\) | −1.79825e19 | −0.126117 | ||||||||
\(236\) | −1.95485e19 | −0.132240 | ||||||||
\(237\) | 4.36491e19 | 0.284849 | ||||||||
\(238\) | −3.56588e20 | −2.24524 | ||||||||
\(239\) | 1.70425e20 | 1.03550 | 0.517750 | − | 0.855532i | \(-0.326770\pi\) | ||||
0.517750 | + | 0.855532i | \(0.326770\pi\) | |||||||
\(240\) | 1.34277e19 | 0.0787419 | ||||||||
\(241\) | −1.71129e20 | −0.968679 | −0.484340 | − | 0.874880i | \(-0.660940\pi\) | ||||
−0.484340 | + | 0.874880i | \(0.660940\pi\) | |||||||
\(242\) | 1.09168e20 | 0.596573 | ||||||||
\(243\) | 1.68440e20 | 0.888775 | ||||||||
\(244\) | 5.57464e19 | 0.284056 | ||||||||
\(245\) | 1.62523e20 | 0.799839 | ||||||||
\(246\) | 1.18096e20 | 0.561419 | ||||||||
\(247\) | −1.05140e18 | −0.00482885 | ||||||||
\(248\) | 1.22676e18 | 0.00544401 | ||||||||
\(249\) | −2.91907e19 | −0.125184 | ||||||||
\(250\) | −1.52588e19 | −0.0632456 | ||||||||
\(251\) | 1.85831e20 | 0.744546 | 0.372273 | − | 0.928123i | \(-0.378578\pi\) | ||||
0.372273 | + | 0.928123i | \(0.378578\pi\) | |||||||
\(252\) | −1.08635e20 | −0.420790 | ||||||||
\(253\) | −1.09916e20 | −0.411657 | ||||||||
\(254\) | 1.88883e20 | 0.684078 | ||||||||
\(255\) | 1.70982e20 | 0.598906 | ||||||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | 1.68273e19 | 0.0551547 | 0.0275773 | − | 0.999620i | \(-0.491221\pi\) | ||||
0.0275773 | + | 0.999620i | \(0.491221\pi\) | |||||||
\(258\) | −1.55119e20 | −0.491923 | ||||||||
\(259\) | −1.73609e20 | −0.532750 | ||||||||
\(260\) | −3.90681e19 | −0.116024 | ||||||||
\(261\) | −3.33396e20 | −0.958333 | ||||||||
\(262\) | 3.72245e20 | 1.03578 | ||||||||
\(263\) | 2.77268e20 | 0.746924 | 0.373462 | − | 0.927645i | \(-0.378171\pi\) | ||||
0.373462 | + | 0.927645i | \(0.378171\pi\) | |||||||
\(264\) | 3.77438e19 | 0.0984491 | ||||||||
\(265\) | 2.57133e20 | 0.649484 | ||||||||
\(266\) | −4.49204e18 | −0.0109888 | ||||||||
\(267\) | 5.45675e18 | 0.0129297 | ||||||||
\(268\) | −4.01714e20 | −0.922085 | ||||||||
\(269\) | 9.40799e19 | 0.209220 | 0.104610 | − | 0.994513i | \(-0.466641\pi\) | ||||
0.104610 | + | 0.994513i | \(0.466641\pi\) | |||||||
\(270\) | 1.55448e20 | 0.334959 | ||||||||
\(271\) | −6.17628e20 | −1.28970 | −0.644849 | − | 0.764310i | \(-0.723080\pi\) | ||||
−0.644849 | + | 0.764310i | \(0.723080\pi\) | |||||||
\(272\) | 2.34892e20 | 0.475371 | ||||||||
\(273\) | −3.11087e20 | −0.610238 | ||||||||
\(274\) | 5.82488e20 | 1.10766 | ||||||||
\(275\) | −4.28907e19 | −0.0790744 | ||||||||
\(276\) | 2.05106e20 | 0.366649 | ||||||||
\(277\) | −6.67865e20 | −1.15774 | −0.578869 | − | 0.815420i | \(-0.696506\pi\) | ||||
−0.578869 | + | 0.815420i | \(0.696506\pi\) | |||||||
\(278\) | −3.62491e19 | −0.0609419 | ||||||||
\(279\) | 4.75894e18 | 0.00776023 | ||||||||
\(280\) | −1.66916e20 | −0.264031 | ||||||||
\(281\) | −1.13640e20 | −0.174393 | −0.0871963 | − | 0.996191i | \(-0.527791\pi\) | ||||
−0.0871963 | + | 0.996191i | \(0.527791\pi\) | |||||||
\(282\) | 9.43216e19 | 0.140441 | ||||||||
\(283\) | −3.76957e20 | −0.544637 | −0.272318 | − | 0.962207i | \(-0.587790\pi\) | ||||
−0.272318 | + | 0.962207i | \(0.587790\pi\) | |||||||
\(284\) | 3.54859e19 | 0.0497565 | ||||||||
\(285\) | 2.15391e18 | 0.00293121 | ||||||||
\(286\) | −1.09816e20 | −0.145062 | ||||||||
\(287\) | −1.46802e21 | −1.88250 | ||||||||
\(288\) | 7.15602e19 | 0.0890913 | ||||||||
\(289\) | 2.16376e21 | 2.61564 | ||||||||
\(290\) | −5.12259e20 | −0.601321 | ||||||||
\(291\) | −9.63408e20 | −1.09830 | ||||||||
\(292\) | −4.69794e20 | −0.520180 | ||||||||
\(293\) | −3.57350e20 | −0.384344 | −0.192172 | − | 0.981361i | \(-0.561553\pi\) | ||||
−0.192172 | + | 0.981361i | \(0.561553\pi\) | |||||||
\(294\) | −8.52464e20 | −0.890684 | ||||||||
\(295\) | −1.16518e20 | −0.118279 | ||||||||
\(296\) | 1.14360e20 | 0.112796 | ||||||||
\(297\) | 4.36946e20 | 0.418792 | ||||||||
\(298\) | 3.35589e20 | 0.312586 | ||||||||
\(299\) | −5.96757e20 | −0.540247 | ||||||||
\(300\) | 8.00353e19 | 0.0704289 | ||||||||
\(301\) | 1.92824e21 | 1.64947 | ||||||||
\(302\) | 7.07963e20 | 0.588778 | ||||||||
\(303\) | 6.19547e20 | 0.500971 | ||||||||
\(304\) | 2.95900e18 | 0.00232659 | ||||||||
\(305\) | 3.32275e20 | 0.254067 | ||||||||
\(306\) | 9.11213e20 | 0.677623 | ||||||||
\(307\) | 2.25658e21 | 1.63220 | 0.816102 | − | 0.577908i | \(-0.196131\pi\) | ||||
0.816102 | + | 0.577908i | \(0.196131\pi\) | |||||||
\(308\) | −4.69182e20 | −0.330112 | ||||||||
\(309\) | −1.11497e21 | −0.763158 | ||||||||
\(310\) | 7.31204e18 | 0.00486927 | ||||||||
\(311\) | 5.76844e20 | 0.373762 | 0.186881 | − | 0.982383i | \(-0.440162\pi\) | ||||
0.186881 | + | 0.982383i | \(0.440162\pi\) | |||||||
\(312\) | 2.04920e20 | 0.129202 | ||||||||
\(313\) | 2.63218e21 | 1.61506 | 0.807530 | − | 0.589827i | \(-0.200804\pi\) | ||||
0.807530 | + | 0.589827i | \(0.200804\pi\) | |||||||
\(314\) | 9.75961e20 | 0.582815 | ||||||||
\(315\) | −6.47515e20 | −0.376366 | ||||||||
\(316\) | 3.57415e20 | 0.202224 | ||||||||
\(317\) | −9.95998e20 | −0.548599 | −0.274299 | − | 0.961644i | \(-0.588446\pi\) | ||||
−0.274299 | + | 0.961644i | \(0.588446\pi\) | |||||||
\(318\) | −1.34871e21 | −0.723252 | ||||||||
\(319\) | −1.43990e21 | −0.751817 | ||||||||
\(320\) | 1.09951e20 | 0.0559017 | ||||||||
\(321\) | 2.20627e21 | 1.09236 | ||||||||
\(322\) | −2.54961e21 | −1.22942 | ||||||||
\(323\) | 3.76786e19 | 0.0176959 | ||||||||
\(324\) | −2.64529e20 | −0.121016 | ||||||||
\(325\) | −2.32864e20 | −0.103775 | ||||||||
\(326\) | −2.65660e21 | −1.15339 | ||||||||
\(327\) | 1.10088e21 | 0.465678 | ||||||||
\(328\) | 9.67016e20 | 0.398571 | ||||||||
\(329\) | −1.17249e21 | −0.470915 | ||||||||
\(330\) | 2.24970e20 | 0.0880556 | ||||||||
\(331\) | −3.56520e21 | −1.36002 | −0.680011 | − | 0.733202i | \(-0.738025\pi\) | ||||
−0.680011 | + | 0.733202i | \(0.738025\pi\) | |||||||
\(332\) | −2.39025e20 | −0.0888728 | ||||||||
\(333\) | 4.43634e20 | 0.160786 | ||||||||
\(334\) | −3.12114e21 | −1.10273 | ||||||||
\(335\) | −2.39440e21 | −0.824738 | ||||||||
\(336\) | 8.75508e20 | 0.294019 | ||||||||
\(337\) | 3.65283e20 | 0.119612 | 0.0598060 | − | 0.998210i | \(-0.480952\pi\) | ||||
0.0598060 | + | 0.998210i | \(0.480952\pi\) | |||||||
\(338\) | 1.61829e21 | 0.516731 | ||||||||
\(339\) | −3.12344e21 | −0.972605 | ||||||||
\(340\) | 1.40007e21 | 0.425185 | ||||||||
\(341\) | 2.05533e19 | 0.00608793 | ||||||||
\(342\) | 1.14788e19 | 0.00331646 | ||||||||
\(343\) | 4.67180e21 | 1.31669 | ||||||||
\(344\) | −1.27017e21 | −0.349233 | ||||||||
\(345\) | 1.22252e21 | 0.327941 | ||||||||
\(346\) | 9.93818e20 | 0.260112 | ||||||||
\(347\) | −2.06934e21 | −0.528483 | −0.264242 | − | 0.964457i | \(-0.585122\pi\) | ||||
−0.264242 | + | 0.964457i | \(0.585122\pi\) | |||||||
\(348\) | 2.68690e21 | 0.669618 | ||||||||
\(349\) | 3.13803e20 | 0.0763204 | 0.0381602 | − | 0.999272i | \(-0.487850\pi\) | ||||
0.0381602 | + | 0.999272i | \(0.487850\pi\) | |||||||
\(350\) | −9.94897e20 | −0.236157 | ||||||||
\(351\) | 2.37228e21 | 0.549611 | ||||||||
\(352\) | 3.09060e20 | 0.0698925 | ||||||||
\(353\) | −6.87901e21 | −1.51859 | −0.759296 | − | 0.650746i | \(-0.774456\pi\) | ||||
−0.759296 | + | 0.650746i | \(0.774456\pi\) | |||||||
\(354\) | 6.11161e20 | 0.131713 | ||||||||
\(355\) | 2.11513e20 | 0.0445036 | ||||||||
\(356\) | 4.46820e19 | 0.00917925 | ||||||||
\(357\) | 1.11483e22 | 2.23629 | ||||||||
\(358\) | 4.15625e21 | 0.814134 | ||||||||
\(359\) | −9.50907e21 | −1.81901 | −0.909505 | − | 0.415693i | \(-0.863539\pi\) | ||||
−0.909505 | + | 0.415693i | \(0.863539\pi\) | |||||||
\(360\) | 4.26532e20 | 0.0796857 | ||||||||
\(361\) | −5.47991e21 | −0.999913 | ||||||||
\(362\) | 5.94420e21 | 1.05943 | ||||||||
\(363\) | −3.41300e21 | −0.594196 | ||||||||
\(364\) | −2.54730e21 | −0.433230 | ||||||||
\(365\) | −2.80019e21 | −0.465263 | ||||||||
\(366\) | −1.74285e21 | −0.282924 | ||||||||
\(367\) | 1.88008e20 | 0.0298205 | 0.0149103 | − | 0.999889i | \(-0.495254\pi\) | ||||
0.0149103 | + | 0.999889i | \(0.495254\pi\) | |||||||
\(368\) | 1.67948e21 | 0.260297 | ||||||||
\(369\) | 3.75133e21 | 0.568147 | ||||||||
\(370\) | 6.81637e20 | 0.100888 | ||||||||
\(371\) | 1.67655e22 | 2.42515 | ||||||||
\(372\) | −3.83531e19 | −0.00542232 | ||||||||
\(373\) | 9.66745e20 | 0.133594 | 0.0667970 | − | 0.997767i | \(-0.478722\pi\) | ||||
0.0667970 | + | 0.997767i | \(0.478722\pi\) | |||||||
\(374\) | 3.93543e21 | 0.531598 | ||||||||
\(375\) | 4.77048e20 | 0.0629936 | ||||||||
\(376\) | 7.72342e20 | 0.0997040 | ||||||||
\(377\) | −7.81756e21 | −0.986665 | ||||||||
\(378\) | 1.01354e22 | 1.25073 | ||||||||
\(379\) | 1.09478e22 | 1.32097 | 0.660484 | − | 0.750840i | \(-0.270351\pi\) | ||||
0.660484 | + | 0.750840i | \(0.270351\pi\) | |||||||
\(380\) | 1.76370e19 | 0.00208097 | ||||||||
\(381\) | −5.90520e21 | −0.681353 | ||||||||
\(382\) | −1.14670e22 | −1.29393 | ||||||||
\(383\) | −9.48135e21 | −1.04636 | −0.523179 | − | 0.852223i | \(-0.675254\pi\) | ||||
−0.523179 | + | 0.852223i | \(0.675254\pi\) | |||||||
\(384\) | −5.76715e20 | −0.0622510 | ||||||||
\(385\) | −2.79655e21 | −0.295261 | ||||||||
\(386\) | −9.24554e21 | −0.954861 | ||||||||
\(387\) | −4.92736e21 | −0.497818 | ||||||||
\(388\) | −7.88875e21 | −0.779720 | ||||||||
\(389\) | 8.68048e21 | 0.839406 | 0.419703 | − | 0.907661i | \(-0.362134\pi\) | ||||
0.419703 | + | 0.907661i | \(0.362134\pi\) | |||||||
\(390\) | 1.22142e21 | 0.115562 | ||||||||
\(391\) | 2.13857e22 | 1.97980 | ||||||||
\(392\) | −6.98030e21 | −0.632328 | ||||||||
\(393\) | −1.16378e22 | −1.03166 | ||||||||
\(394\) | 4.62088e21 | 0.400873 | ||||||||
\(395\) | 2.13036e21 | 0.180875 | ||||||||
\(396\) | 1.19893e21 | 0.0996291 | ||||||||
\(397\) | −5.61938e21 | −0.457055 | −0.228528 | − | 0.973537i | \(-0.573391\pi\) | ||||
−0.228528 | + | 0.973537i | \(0.573391\pi\) | |||||||
\(398\) | 1.63747e21 | 0.130367 | ||||||||
\(399\) | 1.40438e20 | 0.0109450 | ||||||||
\(400\) | 6.55360e20 | 0.0500000 | ||||||||
\(401\) | −4.97857e21 | −0.371858 | −0.185929 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185929 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(402\) | 1.25591e22 | 0.918411 | ||||||||
\(403\) | 1.11589e20 | 0.00798965 | ||||||||
\(404\) | 5.07309e21 | 0.355657 | ||||||||
\(405\) | −1.57672e21 | −0.108240 | ||||||||
\(406\) | −3.34001e22 | −2.24531 | ||||||||
\(407\) | 1.91600e21 | 0.126137 | ||||||||
\(408\) | −7.34362e21 | −0.473477 | ||||||||
\(409\) | 2.65693e20 | 0.0167777 | 0.00838883 | − | 0.999965i | \(-0.497330\pi\) | ||||
0.00838883 | + | 0.999965i | \(0.497330\pi\) | |||||||
\(410\) | 5.76386e21 | 0.356493 | ||||||||
\(411\) | −1.82108e22 | −1.10325 | ||||||||
\(412\) | −9.12977e21 | −0.541793 | ||||||||
\(413\) | −7.59717e21 | −0.441648 | ||||||||
\(414\) | 6.51519e21 | 0.371043 | ||||||||
\(415\) | −1.42470e21 | −0.0794903 | ||||||||
\(416\) | 1.67796e21 | 0.0917252 | ||||||||
\(417\) | 1.13328e21 | 0.0606991 | ||||||||
\(418\) | 4.95757e19 | 0.00260178 | ||||||||
\(419\) | 1.71242e22 | 0.880626 | 0.440313 | − | 0.897844i | \(-0.354867\pi\) | ||||
0.440313 | + | 0.897844i | \(0.354867\pi\) | |||||||
\(420\) | 5.21843e21 | 0.262979 | ||||||||
\(421\) | 2.71839e22 | 1.34250 | 0.671249 | − | 0.741231i | \(-0.265758\pi\) | ||||
0.671249 | + | 0.741231i | \(0.265758\pi\) | |||||||
\(422\) | −1.97658e21 | −0.0956662 | ||||||||
\(423\) | 2.99613e21 | 0.142124 | ||||||||
\(424\) | −1.10438e22 | −0.513462 | ||||||||
\(425\) | 8.34504e21 | 0.380297 | ||||||||
\(426\) | −1.10942e21 | −0.0495583 | ||||||||
\(427\) | 2.16648e22 | 0.948677 | ||||||||
\(428\) | 1.80658e22 | 0.775505 | ||||||||
\(429\) | 3.43327e21 | 0.144484 | ||||||||
\(430\) | −7.57081e21 | −0.312364 | ||||||||
\(431\) | −2.34759e22 | −0.949656 | −0.474828 | − | 0.880079i | \(-0.657490\pi\) | ||||
−0.474828 | + | 0.880079i | \(0.657490\pi\) | |||||||
\(432\) | −6.67643e21 | −0.264809 | ||||||||
\(433\) | −1.88732e22 | −0.734003 | −0.367002 | − | 0.930220i | \(-0.619616\pi\) | ||||
−0.367002 | + | 0.930220i | \(0.619616\pi\) | |||||||
\(434\) | 4.76757e20 | 0.0181817 | ||||||||
\(435\) | 1.60152e22 | 0.598925 | ||||||||
\(436\) | 9.01446e21 | 0.330601 | ||||||||
\(437\) | 2.69402e20 | 0.00968968 | ||||||||
\(438\) | 1.46876e22 | 0.518107 | ||||||||
\(439\) | 5.51895e22 | 1.90945 | 0.954724 | − | 0.297494i | \(-0.0961509\pi\) | ||||
0.954724 | + | 0.297494i | \(0.0961509\pi\) | |||||||
\(440\) | 1.84214e21 | 0.0625138 | ||||||||
\(441\) | −2.70786e22 | −0.901359 | ||||||||
\(442\) | 2.13664e22 | 0.697656 | ||||||||
\(443\) | −1.20735e22 | −0.386723 | −0.193362 | − | 0.981128i | \(-0.561939\pi\) | ||||
−0.193362 | + | 0.981128i | \(0.561939\pi\) | |||||||
\(444\) | −3.57532e21 | −0.112346 | ||||||||
\(445\) | 2.66325e20 | 0.00821017 | ||||||||
\(446\) | 2.77984e22 | 0.840764 | ||||||||
\(447\) | −1.04918e22 | −0.311341 | ||||||||
\(448\) | 7.16899e21 | 0.208735 | ||||||||
\(449\) | 2.57466e22 | 0.735573 | 0.367787 | − | 0.929910i | \(-0.380116\pi\) | ||||
0.367787 | + | 0.929910i | \(0.380116\pi\) | |||||||
\(450\) | 2.54233e21 | 0.0712730 | ||||||||
\(451\) | 1.62016e22 | 0.445714 | ||||||||
\(452\) | −2.55760e22 | −0.690486 | ||||||||
\(453\) | −2.21336e22 | −0.586432 | ||||||||
\(454\) | −5.00580e21 | −0.130166 | ||||||||
\(455\) | −1.51831e22 | −0.387493 | ||||||||
\(456\) | −9.25097e19 | −0.00231732 | ||||||||
\(457\) | −1.01069e22 | −0.248503 | −0.124252 | − | 0.992251i | \(-0.539653\pi\) | ||||
−0.124252 | + | 0.992251i | \(0.539653\pi\) | |||||||
\(458\) | −3.08739e22 | −0.745136 | ||||||||
\(459\) | −8.50144e22 | −2.01412 | ||||||||
\(460\) | 1.00105e22 | 0.232817 | ||||||||
\(461\) | 1.68599e21 | 0.0384942 | 0.0192471 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192471 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(462\) | 1.46684e22 | 0.328796 | ||||||||
\(463\) | −2.77945e22 | −0.611674 | −0.305837 | − | 0.952084i | \(-0.598936\pi\) | ||||
−0.305837 | + | 0.952084i | \(0.598936\pi\) | |||||||
\(464\) | 2.20013e22 | 0.475386 | ||||||||
\(465\) | −2.28602e20 | −0.00484987 | ||||||||
\(466\) | −1.84419e22 | −0.384172 | ||||||||
\(467\) | 8.26643e22 | 1.69093 | 0.845463 | − | 0.534034i | \(-0.179324\pi\) | ||||
0.845463 | + | 0.534034i | \(0.179324\pi\) | |||||||
\(468\) | 6.50929e21 | 0.130751 | ||||||||
\(469\) | −1.56119e23 | −3.07954 | ||||||||
\(470\) | 4.60351e21 | 0.0891780 | ||||||||
\(471\) | −3.05123e22 | −0.580493 | ||||||||
\(472\) | 5.00442e21 | 0.0935075 | ||||||||
\(473\) | −2.12807e22 | −0.390541 | ||||||||
\(474\) | −1.11742e22 | −0.201418 | ||||||||
\(475\) | 1.05125e20 | 0.00186127 | ||||||||
\(476\) | 9.12865e22 | 1.58762 | ||||||||
\(477\) | −4.28420e22 | −0.731920 | ||||||||
\(478\) | −4.36287e22 | −0.732209 | ||||||||
\(479\) | 2.59191e22 | 0.427335 | 0.213667 | − | 0.976906i | \(-0.431459\pi\) | ||||
0.213667 | + | 0.976906i | \(0.431459\pi\) | |||||||
\(480\) | −3.43749e21 | −0.0556790 | ||||||||
\(481\) | 1.04024e22 | 0.165540 | ||||||||
\(482\) | 4.38091e22 | 0.684960 | ||||||||
\(483\) | 7.97106e22 | 1.22452 | ||||||||
\(484\) | −2.79469e22 | −0.421841 | ||||||||
\(485\) | −4.70206e22 | −0.697403 | ||||||||
\(486\) | −4.31206e22 | −0.628459 | ||||||||
\(487\) | −4.14828e22 | −0.594116 | −0.297058 | − | 0.954859i | \(-0.596006\pi\) | ||||
−0.297058 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(488\) | −1.42711e22 | −0.200858 | ||||||||
\(489\) | 8.30554e22 | 1.14879 | ||||||||
\(490\) | −4.16059e22 | −0.565572 | ||||||||
\(491\) | 3.08644e22 | 0.412349 | 0.206174 | − | 0.978515i | \(-0.433899\pi\) | ||||
0.206174 | + | 0.978515i | \(0.433899\pi\) | |||||||
\(492\) | −3.02326e22 | −0.396983 | ||||||||
\(493\) | 2.80155e23 | 3.61575 | ||||||||
\(494\) | 2.69158e20 | 0.00341451 | ||||||||
\(495\) | 7.14620e21 | 0.0891109 | ||||||||
\(496\) | −3.14050e20 | −0.00384950 | ||||||||
\(497\) | 1.37910e22 | 0.166175 | ||||||||
\(498\) | 7.47282e21 | 0.0885187 | ||||||||
\(499\) | 3.24182e22 | 0.377516 | 0.188758 | − | 0.982024i | \(-0.439554\pi\) | ||||
0.188758 | + | 0.982024i | \(0.439554\pi\) | |||||||
\(500\) | 3.90625e21 | 0.0447214 | ||||||||
\(501\) | 9.75788e22 | 1.09833 | ||||||||
\(502\) | −4.75728e22 | −0.526474 | ||||||||
\(503\) | 6.39324e22 | 0.695654 | 0.347827 | − | 0.937559i | \(-0.386920\pi\) | ||||
0.347827 | + | 0.937559i | \(0.386920\pi\) | |||||||
\(504\) | 2.78106e22 | 0.297543 | ||||||||
\(505\) | 3.02380e22 | 0.318109 | ||||||||
\(506\) | 2.81384e22 | 0.291085 | ||||||||
\(507\) | −5.05939e22 | −0.514672 | ||||||||
\(508\) | −4.83540e22 | −0.483717 | ||||||||
\(509\) | −9.33355e22 | −0.918218 | −0.459109 | − | 0.888380i | \(-0.651831\pi\) | ||||
−0.459109 | + | 0.888380i | \(0.651831\pi\) | |||||||
\(510\) | −4.37714e22 | −0.423491 | ||||||||
\(511\) | −1.82577e23 | −1.73728 | ||||||||
\(512\) | −4.72237e21 | −0.0441942 | ||||||||
\(513\) | −1.07095e21 | −0.00985763 | ||||||||
\(514\) | −4.30778e21 | −0.0390003 | ||||||||
\(515\) | −5.44176e22 | −0.484594 | ||||||||
\(516\) | 3.97104e22 | 0.347842 | ||||||||
\(517\) | 1.29400e22 | 0.111497 | ||||||||
\(518\) | 4.44438e22 | 0.376711 | ||||||||
\(519\) | −3.10705e22 | −0.259075 | ||||||||
\(520\) | 1.00014e22 | 0.0820415 | ||||||||
\(521\) | 3.30201e22 | 0.266476 | 0.133238 | − | 0.991084i | \(-0.457463\pi\) | ||||
0.133238 | + | 0.991084i | \(0.457463\pi\) | |||||||
\(522\) | 8.53495e22 | 0.677644 | ||||||||
\(523\) | 4.06002e22 | 0.317149 | 0.158575 | − | 0.987347i | \(-0.449310\pi\) | ||||
0.158575 | + | 0.987347i | \(0.449310\pi\) | |||||||
\(524\) | −9.52948e22 | −0.732409 | ||||||||
\(525\) | 3.11043e22 | 0.235216 | ||||||||
\(526\) | −7.09807e22 | −0.528155 | ||||||||
\(527\) | −3.99896e21 | −0.0292790 | ||||||||
\(528\) | −9.66240e21 | −0.0696140 | ||||||||
\(529\) | 1.18585e22 | 0.0840729 | ||||||||
\(530\) | −6.58261e22 | −0.459255 | ||||||||
\(531\) | 1.94136e22 | 0.133291 | ||||||||
\(532\) | 1.14996e21 | 0.00777025 | ||||||||
\(533\) | 8.79621e22 | 0.584944 | ||||||||
\(534\) | −1.39693e21 | −0.00914268 | ||||||||
\(535\) | 1.07680e23 | 0.693633 | ||||||||
\(536\) | 1.02839e23 | 0.652013 | ||||||||
\(537\) | −1.29940e23 | −0.810890 | ||||||||
\(538\) | −2.40844e22 | −0.147941 | ||||||||
\(539\) | −1.16949e23 | −0.707121 | ||||||||
\(540\) | −3.97946e22 | −0.236852 | ||||||||
\(541\) | −4.20460e22 | −0.246347 | −0.123174 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123174 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(542\) | 1.58113e23 | 0.911954 | ||||||||
\(543\) | −1.85838e23 | −1.05520 | ||||||||
\(544\) | −6.01324e22 | −0.336138 | ||||||||
\(545\) | 5.37303e22 | 0.295699 | ||||||||
\(546\) | 7.96383e22 | 0.431504 | ||||||||
\(547\) | −2.01110e23 | −1.07285 | −0.536427 | − | 0.843947i | \(-0.680226\pi\) | ||||
−0.536427 | + | 0.843947i | \(0.680226\pi\) | |||||||
\(548\) | −1.49117e23 | −0.783236 | ||||||||
\(549\) | −5.53616e22 | −0.286315 | ||||||||
\(550\) | 1.09800e22 | 0.0559140 | ||||||||
\(551\) | 3.52919e21 | 0.0176965 | ||||||||
\(552\) | −5.25070e22 | −0.259260 | ||||||||
\(553\) | 1.38903e23 | 0.675380 | ||||||||
\(554\) | 1.70973e23 | 0.818645 | ||||||||
\(555\) | −2.13106e22 | −0.100486 | ||||||||
\(556\) | 9.27976e21 | 0.0430924 | ||||||||
\(557\) | 1.46727e23 | 0.671030 | 0.335515 | − | 0.942035i | \(-0.391090\pi\) | ||||
0.335515 | + | 0.942035i | \(0.391090\pi\) | |||||||
\(558\) | −1.21829e21 | −0.00548731 | ||||||||
\(559\) | −1.15538e23 | −0.512536 | ||||||||
\(560\) | 4.27305e22 | 0.186698 | ||||||||
\(561\) | −1.23036e23 | −0.529480 | ||||||||
\(562\) | 2.90919e22 | 0.123314 | ||||||||
\(563\) | −3.39706e23 | −1.41834 | −0.709172 | − | 0.705036i | \(-0.750931\pi\) | ||||
−0.709172 | + | 0.705036i | \(0.750931\pi\) | |||||||
\(564\) | −2.41463e22 | −0.0993068 | ||||||||
\(565\) | −1.52445e23 | −0.617590 | ||||||||
\(566\) | 9.65010e22 | 0.385116 | ||||||||
\(567\) | −1.02805e23 | −0.404163 | ||||||||
\(568\) | −9.08439e21 | −0.0351832 | ||||||||
\(569\) | 2.72602e23 | 1.04010 | 0.520050 | − | 0.854136i | \(-0.325913\pi\) | ||||
0.520050 | + | 0.854136i | \(0.325913\pi\) | |||||||
\(570\) | −5.51401e20 | −0.00207268 | ||||||||
\(571\) | −2.79882e22 | −0.103650 | −0.0518249 | − | 0.998656i | \(-0.516504\pi\) | ||||
−0.0518249 | + | 0.998656i | \(0.516504\pi\) | |||||||
\(572\) | 2.81129e22 | 0.102574 | ||||||||
\(573\) | 3.58501e23 | 1.28877 | ||||||||
\(574\) | 3.75813e23 | 1.33113 | ||||||||
\(575\) | 5.96672e22 | 0.208238 | ||||||||
\(576\) | −1.83194e22 | −0.0629971 | ||||||||
\(577\) | 3.86678e23 | 1.31025 | 0.655127 | − | 0.755519i | \(-0.272615\pi\) | ||||
0.655127 | + | 0.755519i | \(0.272615\pi\) | |||||||
\(578\) | −5.53923e23 | −1.84954 | ||||||||
\(579\) | 2.89051e23 | 0.951056 | ||||||||
\(580\) | 1.31138e23 | 0.425198 | ||||||||
\(581\) | −9.28926e22 | −0.296814 | ||||||||
\(582\) | 2.46632e23 | 0.776613 | ||||||||
\(583\) | −1.85030e23 | −0.574195 | ||||||||
\(584\) | 1.20267e23 | 0.367823 | ||||||||
\(585\) | 3.87984e22 | 0.116947 | ||||||||
\(586\) | 9.14817e22 | 0.271772 | ||||||||
\(587\) | 3.64152e23 | 1.06625 | 0.533125 | − | 0.846036i | \(-0.321017\pi\) | ||||
0.533125 | + | 0.846036i | \(0.321017\pi\) | |||||||
\(588\) | 2.18231e23 | 0.629809 | ||||||||
\(589\) | −5.03761e19 | −0.000143299 0 | ||||||||
\(590\) | 2.98287e22 | 0.0836357 | ||||||||
\(591\) | −1.44466e23 | −0.399276 | ||||||||
\(592\) | −2.92761e22 | −0.0797587 | ||||||||
\(593\) | −6.86689e23 | −1.84415 | −0.922073 | − | 0.387017i | \(-0.873506\pi\) | ||||
−0.922073 | + | 0.387017i | \(0.873506\pi\) | |||||||
\(594\) | −1.11858e23 | −0.296130 | ||||||||
\(595\) | 5.44110e23 | 1.42001 | ||||||||
\(596\) | −8.59108e22 | −0.221032 | ||||||||
\(597\) | −5.11935e22 | −0.129847 | ||||||||
\(598\) | 1.52770e23 | 0.382013 | ||||||||
\(599\) | −3.82850e23 | −0.943846 | −0.471923 | − | 0.881640i | \(-0.656440\pi\) | ||||
−0.471923 | + | 0.881640i | \(0.656440\pi\) | |||||||
\(600\) | −2.04890e22 | −0.0498008 | ||||||||
\(601\) | −2.66402e23 | −0.638417 | −0.319209 | − | 0.947684i | \(-0.603417\pi\) | ||||
−0.319209 | + | 0.947684i | \(0.603417\pi\) | |||||||
\(602\) | −4.93629e23 | −1.16635 | ||||||||
\(603\) | 3.98941e23 | 0.929418 | ||||||||
\(604\) | −1.81239e23 | −0.416329 | ||||||||
\(605\) | −1.66577e23 | −0.377306 | ||||||||
\(606\) | −1.58604e23 | −0.354240 | ||||||||
\(607\) | −1.11277e23 | −0.245076 | −0.122538 | − | 0.992464i | \(-0.539103\pi\) | ||||
−0.122538 | + | 0.992464i | \(0.539103\pi\) | |||||||
\(608\) | −7.57505e20 | −0.00164515 | ||||||||
\(609\) | 1.04421e24 | 2.23636 | ||||||||
\(610\) | −8.50623e22 | −0.179653 | ||||||||
\(611\) | 7.02541e22 | 0.146326 | ||||||||
\(612\) | −2.33271e23 | −0.479152 | ||||||||
\(613\) | −3.91229e23 | −0.792532 | −0.396266 | − | 0.918136i | \(-0.629694\pi\) | ||||
−0.396266 | + | 0.918136i | \(0.629694\pi\) | |||||||
\(614\) | −5.77684e23 | −1.15414 | ||||||||
\(615\) | −1.80200e23 | −0.355072 | ||||||||
\(616\) | 1.20111e23 | 0.233424 | ||||||||
\(617\) | −5.72626e23 | −1.09761 | −0.548804 | − | 0.835951i | \(-0.684917\pi\) | ||||
−0.548804 | + | 0.835951i | \(0.684917\pi\) | |||||||
\(618\) | 2.85431e23 | 0.539634 | ||||||||
\(619\) | 7.86155e23 | 1.46601 | 0.733007 | − | 0.680222i | \(-0.238116\pi\) | ||||
0.733007 | + | 0.680222i | \(0.238116\pi\) | |||||||
\(620\) | −1.87188e21 | −0.00344310 | ||||||||
\(621\) | −6.07855e23 | −1.10286 | ||||||||
\(622\) | −1.47672e23 | −0.264290 | ||||||||
\(623\) | 1.73648e22 | 0.0306565 | ||||||||
\(624\) | −5.24594e22 | −0.0913597 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | −6.73838e23 | −1.14202 | ||||||||
\(627\) | −1.54993e21 | −0.00259142 | ||||||||
\(628\) | −2.49846e23 | −0.412112 | ||||||||
\(629\) | −3.72788e23 | −0.606640 | ||||||||
\(630\) | 1.65764e23 | 0.266131 | ||||||||
\(631\) | 6.52712e23 | 1.03389 | 0.516943 | − | 0.856020i | \(-0.327070\pi\) | ||||
0.516943 | + | 0.856020i | \(0.327070\pi\) | |||||||
\(632\) | −9.14983e22 | −0.142994 | ||||||||
\(633\) | 6.17954e22 | 0.0952850 | ||||||||
\(634\) | 2.54975e23 | 0.387918 | ||||||||
\(635\) | −2.88212e23 | −0.432649 | ||||||||
\(636\) | 3.45271e23 | 0.511416 | ||||||||
\(637\) | −6.34945e23 | −0.928007 | ||||||||
\(638\) | 3.68615e23 | 0.531615 | ||||||||
\(639\) | −3.52410e22 | −0.0501522 | ||||||||
\(640\) | −2.81475e22 | −0.0395285 | ||||||||
\(641\) | 7.10734e23 | 0.984950 | 0.492475 | − | 0.870327i | \(-0.336092\pi\) | ||||
0.492475 | + | 0.870327i | \(0.336092\pi\) | |||||||
\(642\) | −5.64805e23 | −0.772415 | ||||||||
\(643\) | 2.34278e23 | 0.316183 | 0.158092 | − | 0.987424i | \(-0.449466\pi\) | ||||
0.158092 | + | 0.987424i | \(0.449466\pi\) | |||||||
\(644\) | 6.52701e23 | 0.869329 | ||||||||
\(645\) | 2.36692e23 | 0.311119 | ||||||||
\(646\) | −9.64571e21 | −0.0125129 | ||||||||
\(647\) | 1.50806e23 | 0.193078 | 0.0965391 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965391 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(648\) | 6.77195e22 | 0.0855710 | ||||||||
\(649\) | 8.38450e22 | 0.104568 | ||||||||
\(650\) | 5.96131e22 | 0.0733801 | ||||||||
\(651\) | −1.49052e22 | −0.0181092 | ||||||||
\(652\) | 6.80089e23 | 0.815570 | ||||||||
\(653\) | 6.74375e22 | 0.0798251 | 0.0399126 | − | 0.999203i | \(-0.487292\pi\) | ||||
0.0399126 | + | 0.999203i | \(0.487292\pi\) | |||||||
\(654\) | −2.81826e23 | −0.329284 | ||||||||
\(655\) | −5.68001e23 | −0.655086 | ||||||||
\(656\) | −2.47556e23 | −0.281832 | ||||||||
\(657\) | 4.66551e23 | 0.524317 | ||||||||
\(658\) | 3.00157e23 | 0.332987 | ||||||||
\(659\) | 7.11301e22 | 0.0778981 | 0.0389491 | − | 0.999241i | \(-0.487599\pi\) | ||||
0.0389491 | + | 0.999241i | \(0.487599\pi\) | |||||||
\(660\) | −5.75924e22 | −0.0622647 | ||||||||
\(661\) | 1.69805e24 | 1.81233 | 0.906164 | − | 0.422926i | \(-0.138997\pi\) | ||||
0.906164 | + | 0.422926i | \(0.138997\pi\) | |||||||
\(662\) | 9.12691e23 | 0.961680 | ||||||||
\(663\) | −6.67994e23 | −0.694876 | ||||||||
\(664\) | 6.11903e22 | 0.0628426 | ||||||||
\(665\) | 6.85431e21 | 0.00694992 | ||||||||
\(666\) | −1.13570e23 | −0.113693 | ||||||||
\(667\) | 2.00311e24 | 1.97986 | ||||||||
\(668\) | 7.99012e23 | 0.779747 | ||||||||
\(669\) | −8.69085e23 | −0.837414 | ||||||||
\(670\) | 6.12967e23 | 0.583178 | ||||||||
\(671\) | −2.39101e23 | −0.224615 | ||||||||
\(672\) | −2.24130e23 | −0.207903 | ||||||||
\(673\) | −1.39848e24 | −1.28094 | −0.640469 | − | 0.767984i | \(-0.721260\pi\) | ||||
−0.640469 | + | 0.767984i | \(0.721260\pi\) | |||||||
\(674\) | −9.35124e22 | −0.0845785 | ||||||||
\(675\) | −2.37194e23 | −0.211847 | ||||||||
\(676\) | −4.14282e23 | −0.365384 | ||||||||
\(677\) | −9.38639e23 | −0.817514 | −0.408757 | − | 0.912643i | \(-0.634038\pi\) | ||||
−0.408757 | + | 0.912643i | \(0.634038\pi\) | |||||||
\(678\) | 7.99602e23 | 0.687735 | ||||||||
\(679\) | −3.06582e24 | −2.60408 | ||||||||
\(680\) | −3.58417e23 | −0.300651 | ||||||||
\(681\) | 1.56500e23 | 0.129648 | ||||||||
\(682\) | −5.26165e21 | −0.00430482 | ||||||||
\(683\) | 1.23254e24 | 0.995922 | 0.497961 | − | 0.867199i | \(-0.334082\pi\) | ||||
0.497961 | + | 0.867199i | \(0.334082\pi\) | |||||||
\(684\) | −2.93858e21 | −0.00234509 | ||||||||
\(685\) | −8.88807e23 | −0.700547 | ||||||||
\(686\) | −1.19598e24 | −0.931041 | ||||||||
\(687\) | 9.65236e23 | 0.742167 | ||||||||
\(688\) | 3.25164e23 | 0.246945 | ||||||||
\(689\) | −1.00457e24 | −0.753559 | ||||||||
\(690\) | −3.12966e23 | −0.231889 | ||||||||
\(691\) | 3.83055e23 | 0.280348 | 0.140174 | − | 0.990127i | \(-0.455234\pi\) | ||||
0.140174 | + | 0.990127i | \(0.455234\pi\) | |||||||
\(692\) | −2.54417e23 | −0.183927 | ||||||||
\(693\) | 4.65944e23 | 0.332737 | ||||||||
\(694\) | 5.29751e23 | 0.373694 | ||||||||
\(695\) | 5.53117e22 | 0.0385431 | ||||||||
\(696\) | −6.87845e23 | −0.473492 | ||||||||
\(697\) | −3.15226e24 | −2.14360 | ||||||||
\(698\) | −8.03335e22 | −0.0539667 | ||||||||
\(699\) | 5.76565e23 | 0.382642 | ||||||||
\(700\) | 2.54694e23 | 0.166988 | ||||||||
\(701\) | 1.63235e24 | 1.05733 | 0.528665 | − | 0.848831i | \(-0.322693\pi\) | ||||
0.528665 | + | 0.848831i | \(0.322693\pi\) | |||||||
\(702\) | −6.07304e23 | −0.388634 | ||||||||
\(703\) | −4.69611e21 | −0.00296906 | ||||||||
\(704\) | −7.91195e22 | −0.0494215 | ||||||||
\(705\) | −1.43923e23 | −0.0888227 | ||||||||
\(706\) | 1.76103e24 | 1.07381 | ||||||||
\(707\) | 1.97156e24 | 1.18781 | ||||||||
\(708\) | −1.56457e23 | −0.0931350 | ||||||||
\(709\) | −6.09431e23 | −0.358453 | −0.179226 | − | 0.983808i | \(-0.557359\pi\) | ||||
−0.179226 | + | 0.983808i | \(0.557359\pi\) | |||||||
\(710\) | −5.41472e22 | −0.0314688 | ||||||||
\(711\) | −3.54948e23 | −0.203832 | ||||||||
\(712\) | −1.14386e22 | −0.00649071 | ||||||||
\(713\) | −2.85926e22 | −0.0160322 | ||||||||
\(714\) | −2.85396e24 | −1.58130 | ||||||||
\(715\) | 1.67566e23 | 0.0917454 | ||||||||
\(716\) | −1.06400e24 | −0.575680 | ||||||||
\(717\) | 1.36400e24 | 0.729292 | ||||||||
\(718\) | 2.43432e24 | 1.28623 | ||||||||
\(719\) | −4.49148e23 | −0.234527 | −0.117264 | − | 0.993101i | \(-0.537412\pi\) | ||||
−0.117264 | + | 0.993101i | \(0.537412\pi\) | |||||||
\(720\) | −1.09192e23 | −0.0563463 | ||||||||
\(721\) | −3.54812e24 | −1.80946 | ||||||||
\(722\) | 1.40286e24 | 0.707046 | ||||||||
\(723\) | −1.36964e24 | −0.682230 | ||||||||
\(724\) | −1.52171e24 | −0.749127 | ||||||||
\(725\) | 7.81644e23 | 0.380309 | ||||||||
\(726\) | 8.73727e23 | 0.420160 | ||||||||
\(727\) | −5.00713e23 | −0.237983 | −0.118992 | − | 0.992895i | \(-0.537966\pi\) | ||||
−0.118992 | + | 0.992895i | \(0.537966\pi\) | |||||||
\(728\) | 6.52109e23 | 0.306340 | ||||||||
\(729\) | 1.86938e24 | 0.867986 | ||||||||
\(730\) | 7.16849e23 | 0.328991 | ||||||||
\(731\) | 4.14048e24 | 1.87825 | ||||||||
\(732\) | 4.46168e23 | 0.200057 | ||||||||
\(733\) | 1.20329e24 | 0.533320 | 0.266660 | − | 0.963791i | \(-0.414080\pi\) | ||||
0.266660 | + | 0.963791i | \(0.414080\pi\) | |||||||
\(734\) | −4.81301e22 | −0.0210863 | ||||||||
\(735\) | 1.30076e24 | 0.563318 | ||||||||
\(736\) | −4.29948e23 | −0.184058 | ||||||||
\(737\) | 1.72298e24 | 0.729133 | ||||||||
\(738\) | −9.60340e23 | −0.401741 | ||||||||
\(739\) | −2.19426e24 | −0.907426 | −0.453713 | − | 0.891148i | \(-0.649901\pi\) | ||||
−0.453713 | + | 0.891148i | \(0.649901\pi\) | |||||||
\(740\) | −1.74499e23 | −0.0713384 | ||||||||
\(741\) | −8.41491e21 | −0.00340091 | ||||||||
\(742\) | −4.29197e24 | −1.71484 | ||||||||
\(743\) | −9.89633e22 | −0.0390903 | −0.0195452 | − | 0.999809i | \(-0.506222\pi\) | ||||
−0.0195452 | + | 0.999809i | \(0.506222\pi\) | |||||||
\(744\) | 9.81839e21 | 0.00383416 | ||||||||
\(745\) | −5.12068e23 | −0.197697 | ||||||||
\(746\) | −2.47487e23 | −0.0944652 | ||||||||
\(747\) | 2.37375e23 | 0.0895796 | ||||||||
\(748\) | −1.00747e24 | −0.375897 | ||||||||
\(749\) | 7.02094e24 | 2.59000 | ||||||||
\(750\) | −1.22124e23 | −0.0445432 | ||||||||
\(751\) | −1.01856e24 | −0.367322 | −0.183661 | − | 0.982990i | \(-0.558795\pi\) | ||||
−0.183661 | + | 0.982990i | \(0.558795\pi\) | |||||||
\(752\) | −1.97719e23 | −0.0705014 | ||||||||
\(753\) | 1.48731e24 | 0.524376 | ||||||||
\(754\) | 2.00130e24 | 0.697677 | ||||||||
\(755\) | −1.08027e24 | −0.372376 | ||||||||
\(756\) | −2.59467e24 | −0.884397 | ||||||||
\(757\) | −1.43989e24 | −0.485305 | −0.242653 | − | 0.970113i | \(-0.578018\pi\) | ||||
−0.242653 | + | 0.970113i | \(0.578018\pi\) | |||||||
\(758\) | −2.80263e24 | −0.934066 | ||||||||
\(759\) | −8.79713e23 | −0.289925 | ||||||||
\(760\) | −4.51508e21 | −0.00147147 | ||||||||
\(761\) | −7.15424e23 | −0.230565 | −0.115283 | − | 0.993333i | \(-0.536777\pi\) | ||||
−0.115283 | + | 0.993333i | \(0.536777\pi\) | |||||||
\(762\) | 1.51173e24 | 0.481789 | ||||||||
\(763\) | 3.50330e24 | 1.10413 | ||||||||
\(764\) | 2.93554e24 | 0.914944 | ||||||||
\(765\) | −1.39040e24 | −0.428566 | ||||||||
\(766\) | 2.42722e24 | 0.739887 | ||||||||
\(767\) | 4.55214e23 | 0.137232 | ||||||||
\(768\) | 1.47639e23 | 0.0440181 | ||||||||
\(769\) | 1.87177e24 | 0.551922 | 0.275961 | − | 0.961169i | \(-0.411004\pi\) | ||||
0.275961 | + | 0.961169i | \(0.411004\pi\) | |||||||
\(770\) | 7.15916e23 | 0.208781 | ||||||||
\(771\) | 1.34678e23 | 0.0388449 | ||||||||
\(772\) | 2.36686e24 | 0.675189 | ||||||||
\(773\) | −1.86999e24 | −0.527611 | −0.263805 | − | 0.964576i | \(-0.584978\pi\) | ||||
−0.263805 | + | 0.964576i | \(0.584978\pi\) | |||||||
\(774\) | 1.26140e24 | 0.352011 | ||||||||
\(775\) | −1.11573e22 | −0.00307960 | ||||||||
\(776\) | 2.01952e24 | 0.551345 | ||||||||
\(777\) | −1.38948e24 | −0.375210 | ||||||||
\(778\) | −2.22220e24 | −0.593550 | ||||||||
\(779\) | −3.97099e22 | −0.0104913 | ||||||||
\(780\) | −3.12683e23 | −0.0817146 | ||||||||
\(781\) | −1.52202e23 | −0.0393447 | ||||||||
\(782\) | −5.47475e24 | −1.39993 | ||||||||
\(783\) | −7.96294e24 | −2.01418 | ||||||||
\(784\) | 1.78696e24 | 0.447124 | ||||||||
\(785\) | −1.48920e24 | −0.368604 | ||||||||
\(786\) | 2.97928e24 | 0.729490 | ||||||||
\(787\) | −3.29304e24 | −0.797648 | −0.398824 | − | 0.917027i | \(-0.630582\pi\) | ||||
−0.398824 | + | 0.917027i | \(0.630582\pi\) | |||||||
\(788\) | −1.18295e24 | −0.283460 | ||||||||
\(789\) | 2.21913e24 | 0.526051 | ||||||||
\(790\) | −5.45373e23 | −0.127898 | ||||||||
\(791\) | −9.93963e24 | −2.30606 | ||||||||
\(792\) | −3.06927e23 | −0.0704484 | ||||||||
\(793\) | −1.29813e24 | −0.294779 | ||||||||
\(794\) | 1.43856e24 | 0.323187 | ||||||||
\(795\) | 2.05798e24 | 0.457425 | ||||||||
\(796\) | −4.19192e23 | −0.0921832 | ||||||||
\(797\) | −3.80089e24 | −0.826969 | −0.413485 | − | 0.910511i | \(-0.635688\pi\) | ||||
−0.413485 | + | 0.910511i | \(0.635688\pi\) | |||||||
\(798\) | −3.59522e22 | −0.00773929 | ||||||||
\(799\) | −2.51767e24 | −0.536229 | ||||||||
\(800\) | −1.67772e23 | −0.0353553 | ||||||||
\(801\) | −4.43735e22 | −0.00925225 | ||||||||
\(802\) | 1.27451e24 | 0.262944 | ||||||||
\(803\) | 2.01498e24 | 0.411329 | ||||||||
\(804\) | −3.21513e24 | −0.649415 | ||||||||
\(805\) | 3.89040e24 | 0.777552 | ||||||||
\(806\) | −2.85667e22 | −0.00564953 | ||||||||
\(807\) | 7.52972e23 | 0.147351 | ||||||||
\(808\) | −1.29871e24 | −0.251487 | ||||||||
\(809\) | 1.38713e24 | 0.265799 | 0.132900 | − | 0.991129i | \(-0.457571\pi\) | ||||
0.132900 | + | 0.991129i | \(0.457571\pi\) | |||||||
\(810\) | 4.03640e23 | 0.0765370 | ||||||||
\(811\) | 2.43418e24 | 0.456747 | 0.228374 | − | 0.973574i | \(-0.426659\pi\) | ||||
0.228374 | + | 0.973574i | \(0.426659\pi\) | |||||||
\(812\) | 8.55042e24 | 1.58767 | ||||||||
\(813\) | −4.94321e24 | −0.908321 | ||||||||
\(814\) | −4.90497e23 | −0.0891926 | ||||||||
\(815\) | 4.05365e24 | 0.729468 | ||||||||
\(816\) | 1.87997e24 | 0.334799 | ||||||||
\(817\) | 5.21589e22 | 0.00919265 | ||||||||
\(818\) | −6.80174e22 | −0.0118636 | ||||||||
\(819\) | 2.52972e24 | 0.436675 | ||||||||
\(820\) | −1.47555e24 | −0.252078 | ||||||||
\(821\) | −7.07675e24 | −1.19651 | −0.598256 | − | 0.801305i | \(-0.704140\pi\) | ||||
−0.598256 | + | 0.801305i | \(0.704140\pi\) | |||||||
\(822\) | 4.66196e24 | 0.780115 | ||||||||
\(823\) | −5.31425e24 | −0.880124 | −0.440062 | − | 0.897968i | \(-0.645043\pi\) | ||||
−0.440062 | + | 0.897968i | \(0.645043\pi\) | |||||||
\(824\) | 2.33722e24 | 0.383105 | ||||||||
\(825\) | −3.43278e23 | −0.0556912 | ||||||||
\(826\) | 1.94488e24 | 0.312292 | ||||||||
\(827\) | 5.13487e24 | 0.816080 | 0.408040 | − | 0.912964i | \(-0.366212\pi\) | ||||
0.408040 | + | 0.912964i | \(0.366212\pi\) | |||||||
\(828\) | −1.66789e24 | −0.262367 | ||||||||
\(829\) | 1.06738e25 | 1.66191 | 0.830954 | − | 0.556341i | \(-0.187795\pi\) | ||||
0.830954 | + | 0.556341i | \(0.187795\pi\) | |||||||
\(830\) | 3.64723e23 | 0.0562081 | ||||||||
\(831\) | −5.34528e24 | −0.815383 | ||||||||
\(832\) | −4.29558e23 | −0.0648595 | ||||||||
\(833\) | 2.27543e25 | 3.40079 | ||||||||
\(834\) | −2.90121e23 | −0.0429208 | ||||||||
\(835\) | 4.76248e24 | 0.697427 | ||||||||
\(836\) | −1.26914e22 | −0.00183974 | ||||||||
\(837\) | 1.13664e23 | 0.0163101 | ||||||||
\(838\) | −4.38380e24 | −0.622697 | ||||||||
\(839\) | −6.47302e24 | −0.910186 | −0.455093 | − | 0.890444i | \(-0.650394\pi\) | ||||
−0.455093 | + | 0.890444i | \(0.650394\pi\) | |||||||
\(840\) | −1.33592e24 | −0.185954 | ||||||||
\(841\) | 1.89837e25 | 2.61587 | ||||||||
\(842\) | −6.95908e24 | −0.949290 | ||||||||
\(843\) | −9.09523e23 | −0.122823 | ||||||||
\(844\) | 5.06004e23 | 0.0676462 | ||||||||
\(845\) | −2.46931e24 | −0.326809 | ||||||||
\(846\) | −7.67010e23 | −0.100497 | ||||||||
\(847\) | −1.08611e25 | −1.40885 | ||||||||
\(848\) | 2.82721e24 | 0.363073 | ||||||||
\(849\) | −3.01699e24 | −0.383582 | ||||||||
\(850\) | −2.13633e24 | −0.268910 | ||||||||
\(851\) | −2.66544e24 | −0.332175 | ||||||||
\(852\) | 2.84013e23 | 0.0350430 | ||||||||
\(853\) | 2.69306e24 | 0.328988 | 0.164494 | − | 0.986378i | \(-0.447401\pi\) | ||||
0.164494 | + | 0.986378i | \(0.447401\pi\) | |||||||
\(854\) | −5.54620e24 | −0.670816 | ||||||||
\(855\) | −1.75153e22 | −0.00209752 | ||||||||
\(856\) | −4.62484e24 | −0.548365 | ||||||||
\(857\) | −1.86785e24 | −0.219283 | −0.109641 | − | 0.993971i | \(-0.534970\pi\) | ||||
−0.109641 | + | 0.993971i | \(0.534970\pi\) | |||||||
\(858\) | −8.78916e23 | −0.102166 | ||||||||
\(859\) | −1.13124e25 | −1.30200 | −0.651000 | − | 0.759077i | \(-0.725650\pi\) | ||||
−0.651000 | + | 0.759077i | \(0.725650\pi\) | |||||||
\(860\) | 1.93813e24 | 0.220875 | ||||||||
\(861\) | −1.17493e25 | −1.32583 | ||||||||
\(862\) | 6.00984e24 | 0.671508 | ||||||||
\(863\) | −2.37061e24 | −0.262282 | −0.131141 | − | 0.991364i | \(-0.541864\pi\) | ||||
−0.131141 | + | 0.991364i | \(0.541864\pi\) | |||||||
\(864\) | 1.70917e24 | 0.187248 | ||||||||
\(865\) | −1.51645e24 | −0.164509 | ||||||||
\(866\) | 4.83153e24 | 0.519019 | ||||||||
\(867\) | 1.73178e25 | 1.84217 | ||||||||
\(868\) | −1.22050e23 | −0.0128564 | ||||||||
\(869\) | −1.53298e24 | −0.159907 | ||||||||
\(870\) | −4.09988e24 | −0.423504 | ||||||||
\(871\) | 9.35446e24 | 0.956895 | ||||||||
\(872\) | −2.30770e24 | −0.233770 | ||||||||
\(873\) | 7.83429e24 | 0.785921 | ||||||||
\(874\) | −6.89670e22 | −0.00685164 | ||||||||
\(875\) | 1.51809e24 | 0.149358 | ||||||||
\(876\) | −3.76002e24 | −0.366357 | ||||||||
\(877\) | −6.79534e24 | −0.655714 | −0.327857 | − | 0.944727i | \(-0.606326\pi\) | ||||
−0.327857 | + | 0.944727i | \(0.606326\pi\) | |||||||
\(878\) | −1.41285e25 | −1.35018 | ||||||||
\(879\) | −2.86007e24 | −0.270689 | ||||||||
\(880\) | −4.71589e23 | −0.0442039 | ||||||||
\(881\) | −1.88402e25 | −1.74900 | −0.874501 | − | 0.485024i | \(-0.838811\pi\) | ||||
−0.874501 | + | 0.485024i | \(0.838811\pi\) | |||||||
\(882\) | 6.93212e24 | 0.637357 | ||||||||
\(883\) | 3.85491e24 | 0.351033 | 0.175517 | − | 0.984476i | \(-0.443840\pi\) | ||||
0.175517 | + | 0.984476i | \(0.443840\pi\) | |||||||
\(884\) | −5.46979e24 | −0.493317 | ||||||||
\(885\) | −9.32557e23 | −0.0833024 | ||||||||
\(886\) | 3.09081e24 | 0.273455 | ||||||||
\(887\) | 8.32727e24 | 0.729712 | 0.364856 | − | 0.931064i | \(-0.381118\pi\) | ||||
0.364856 | + | 0.931064i | \(0.381118\pi\) | |||||||
\(888\) | 9.15281e23 | 0.0794410 | ||||||||
\(889\) | −1.87919e25 | −1.61550 | ||||||||
\(890\) | −6.81792e22 | −0.00580547 | ||||||||
\(891\) | 1.13459e24 | 0.0956924 | ||||||||
\(892\) | −7.11640e24 | −0.594510 | ||||||||
\(893\) | −3.17158e22 | −0.00262445 | ||||||||
\(894\) | 2.68590e24 | 0.220151 | ||||||||
\(895\) | −6.34194e24 | −0.514904 | ||||||||
\(896\) | −1.83526e24 | −0.147598 | ||||||||
\(897\) | −4.77617e24 | −0.380491 | ||||||||
\(898\) | −6.59113e24 | −0.520129 | ||||||||
\(899\) | −3.74565e23 | −0.0292799 | ||||||||
\(900\) | −6.50836e23 | −0.0503976 | ||||||||
\(901\) | 3.60004e25 | 2.76151 | ||||||||
\(902\) | −4.14760e24 | −0.315168 | ||||||||
\(903\) | 1.54327e25 | 1.16171 | ||||||||
\(904\) | 6.54744e24 | 0.488248 | ||||||||
\(905\) | −9.07012e24 | −0.670039 | ||||||||
\(906\) | 5.66621e24 | 0.414670 | ||||||||
\(907\) | 1.92435e25 | 1.39515 | 0.697576 | − | 0.716511i | \(-0.254262\pi\) | ||||
0.697576 | + | 0.716511i | \(0.254262\pi\) | |||||||
\(908\) | 1.28148e24 | 0.0920415 | ||||||||
\(909\) | −5.03807e24 | −0.358485 | ||||||||
\(910\) | 3.88687e24 | 0.273999 | ||||||||
\(911\) | −1.57682e25 | −1.10123 | −0.550613 | − | 0.834761i | \(-0.685606\pi\) | ||||
−0.550613 | + | 0.834761i | \(0.685606\pi\) | |||||||
\(912\) | 2.36825e22 | 0.00163859 | ||||||||
\(913\) | 1.02519e24 | 0.0702756 | ||||||||
\(914\) | 2.58738e24 | 0.175718 | ||||||||
\(915\) | 2.65937e24 | 0.178937 | ||||||||
\(916\) | 7.90373e24 | 0.526890 | ||||||||
\(917\) | −3.70346e25 | −2.44607 | ||||||||
\(918\) | 2.17637e25 | 1.42420 | ||||||||
\(919\) | 1.03058e25 | 0.668189 | 0.334094 | − | 0.942540i | \(-0.391570\pi\) | ||||
0.334094 | + | 0.942540i | \(0.391570\pi\) | |||||||
\(920\) | −2.56269e24 | −0.164626 | ||||||||
\(921\) | 1.80606e25 | 1.14954 | ||||||||
\(922\) | −4.31612e23 | −0.0272195 | ||||||||
\(923\) | −8.26339e23 | −0.0516349 | ||||||||
\(924\) | −3.75512e24 | −0.232494 | ||||||||
\(925\) | −1.04010e24 | −0.0638070 | ||||||||
\(926\) | 7.11539e24 | 0.432519 | ||||||||
\(927\) | 9.06674e24 | 0.546102 | ||||||||
\(928\) | −5.63234e24 | −0.336149 | ||||||||
\(929\) | 9.73688e24 | 0.575819 | 0.287910 | − | 0.957658i | \(-0.407040\pi\) | ||||
0.287910 | + | 0.957658i | \(0.407040\pi\) | |||||||
\(930\) | 5.85222e22 | 0.00342938 | ||||||||
\(931\) | 2.86642e23 | 0.0166444 | ||||||||
\(932\) | 4.72113e24 | 0.271651 | ||||||||
\(933\) | 4.61679e24 | 0.263236 | ||||||||
\(934\) | −2.11621e25 | −1.19567 | ||||||||
\(935\) | −6.00499e24 | −0.336212 | ||||||||
\(936\) | −1.66638e24 | −0.0924547 | ||||||||
\(937\) | −3.22145e25 | −1.77119 | −0.885594 | − | 0.464459i | \(-0.846249\pi\) | ||||
−0.885594 | + | 0.464459i | \(0.846249\pi\) | |||||||
\(938\) | 3.99664e25 | 2.17756 | ||||||||
\(939\) | 2.10667e25 | 1.13747 | ||||||||
\(940\) | −1.17850e24 | −0.0630584 | ||||||||
\(941\) | −7.90374e24 | −0.419103 | −0.209552 | − | 0.977798i | \(-0.567200\pi\) | ||||
−0.209552 | + | 0.977798i | \(0.567200\pi\) | |||||||
\(942\) | 7.81114e24 | 0.410470 | ||||||||
\(943\) | −2.25387e25 | −1.17376 | ||||||||
\(944\) | −1.28113e24 | −0.0661198 | ||||||||
\(945\) | −1.54654e25 | −0.791028 | ||||||||
\(946\) | 5.44786e24 | 0.276154 | ||||||||
\(947\) | 2.36682e25 | 1.18902 | 0.594512 | − | 0.804086i | \(-0.297345\pi\) | ||||
0.594512 | + | 0.804086i | \(0.297345\pi\) | |||||||
\(948\) | 2.86059e24 | 0.142424 | ||||||||
\(949\) | 1.09398e25 | 0.539818 | ||||||||
\(950\) | −2.69120e22 | −0.00131612 | ||||||||
\(951\) | −7.97150e24 | −0.386372 | ||||||||
\(952\) | −2.33693e25 | −1.12262 | ||||||||
\(953\) | 9.09477e24 | 0.433014 | 0.216507 | − | 0.976281i | \(-0.430534\pi\) | ||||
0.216507 | + | 0.976281i | \(0.430534\pi\) | |||||||
\(954\) | 1.09676e25 | 0.517546 | ||||||||
\(955\) | 1.74972e25 | 0.818351 | ||||||||
\(956\) | 1.11690e25 | 0.517750 | ||||||||
\(957\) | −1.15243e25 | −0.529496 | ||||||||
\(958\) | −6.63529e24 | −0.302171 | ||||||||
\(959\) | −5.79516e25 | −2.61582 | ||||||||
\(960\) | 8.79998e23 | 0.0393710 | ||||||||
\(961\) | −2.25448e25 | −0.999763 | ||||||||
\(962\) | −2.66302e24 | −0.117054 | ||||||||
\(963\) | −1.79411e25 | −0.781673 | ||||||||
\(964\) | −1.12151e25 | −0.484340 | ||||||||
\(965\) | 1.41076e25 | 0.603907 | ||||||||
\(966\) | −2.04059e25 | −0.865865 | ||||||||
\(967\) | 3.62970e25 | 1.52667 | 0.763337 | − | 0.646001i | \(-0.223560\pi\) | ||||
0.763337 | + | 0.646001i | \(0.223560\pi\) | |||||||
\(968\) | 7.15441e24 | 0.298286 | ||||||||
\(969\) | 3.01562e23 | 0.0124630 | ||||||||
\(970\) | 1.20373e25 | 0.493138 | ||||||||
\(971\) | −9.70396e24 | −0.394081 | −0.197040 | − | 0.980395i | \(-0.563133\pi\) | ||||
−0.197040 | + | 0.980395i | \(0.563133\pi\) | |||||||
\(972\) | 1.10389e25 | 0.444387 | ||||||||
\(973\) | 3.60641e24 | 0.143918 | ||||||||
\(974\) | 1.06196e25 | 0.420104 | ||||||||
\(975\) | −1.86373e24 | −0.0730878 | ||||||||
\(976\) | 3.65340e24 | 0.142028 | ||||||||
\(977\) | 3.70141e25 | 1.42647 | 0.713236 | − | 0.700924i | \(-0.247229\pi\) | ||||
0.713236 | + | 0.700924i | \(0.247229\pi\) | |||||||
\(978\) | −2.12622e25 | −0.812321 | ||||||||
\(979\) | −1.91644e23 | −0.00725843 | ||||||||
\(980\) | 1.06511e25 | 0.399920 | ||||||||
\(981\) | −8.95223e24 | −0.333230 | ||||||||
\(982\) | −7.90127e24 | −0.291574 | ||||||||
\(983\) | −6.43184e24 | −0.235305 | −0.117652 | − | 0.993055i | \(-0.537537\pi\) | ||||
−0.117652 | + | 0.993055i | \(0.537537\pi\) | |||||||
\(984\) | 7.73954e24 | 0.280709 | ||||||||
\(985\) | −7.05090e24 | −0.253534 | ||||||||
\(986\) | −7.17196e25 | −2.55672 | ||||||||
\(987\) | −9.38403e24 | −0.331661 | ||||||||
\(988\) | −6.89045e22 | −0.00241442 | ||||||||
\(989\) | 2.96045e25 | 1.02847 | ||||||||
\(990\) | −1.82943e24 | −0.0630109 | ||||||||
\(991\) | 5.17070e25 | 1.76573 | 0.882863 | − | 0.469631i | \(-0.155613\pi\) | ||||
0.882863 | + | 0.469631i | \(0.155613\pi\) | |||||||
\(992\) | 8.03967e22 | 0.00272201 | ||||||||
\(993\) | −2.85342e25 | −0.957848 | ||||||||
\(994\) | −3.53048e24 | −0.117503 | ||||||||
\(995\) | −2.49858e24 | −0.0824512 | ||||||||
\(996\) | −1.91304e24 | −0.0625922 | ||||||||
\(997\) | −2.77457e25 | −0.900093 | −0.450047 | − | 0.893005i | \(-0.648593\pi\) | ||||
−0.450047 | + | 0.893005i | \(0.648593\pi\) | |||||||
\(998\) | −8.29907e24 | −0.266944 | ||||||||
\(999\) | 1.05959e25 | 0.337933 |
(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 | 10.18.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 90.18.a.k.1.2 | 2 | |||
4.3 | odd | 2 | 80.18.a.d.1.1 | 2 | |||
5.2 | odd | 4 | 50.18.b.d.49.1 | 4 | |||
5.3 | odd | 4 | 50.18.b.d.49.4 | 4 | |||
5.4 | even | 2 | 50.18.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.18.a.f.1.1 | 2 | 5.4 | even | 2 | |||
50.18.b.d.49.1 | 4 | 5.2 | odd | 4 | |||
50.18.b.d.49.4 | 4 | 5.3 | odd | 4 | |||
80.18.a.d.1.1 | 2 | 4.3 | odd | 2 | |||
90.18.a.k.1.2 | 2 | 3.2 | odd | 2 |