Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,18,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(146.577669876\) |
Analytic rank: | \(1\) |
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: | no (minimal twist has level 10) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(144.792\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8003.53 | −0.704289 | −0.352145 | − | 0.935946i | \(-0.614548\pi\) | ||||
−0.352145 | + | 0.935946i | \(0.614548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 390625. | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.54694e7 | −1.66988 | −0.834939 | − | 0.550342i | \(-0.814497\pi\) | ||||
−0.834939 | + | 0.550342i | \(0.814497\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.50836e7 | −0.503976 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.81089e8 | 0.395372 | 0.197686 | − | 0.980265i | \(-0.436657\pi\) | ||||
0.197686 | + | 0.980265i | \(0.436657\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.52610e9 | −0.518876 | −0.259438 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259438 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.12638e9 | −0.314968 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.46901e10 | 1.90148 | 0.950742 | − | 0.309984i | \(-0.100324\pi\) | ||||
0.950742 | + | 0.309984i | \(0.100324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.88947e8 | −0.00930637 | −0.00465318 | − | 0.999989i | \(-0.501481\pi\) | ||||
−0.00465318 | + | 0.999989i | \(0.501481\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.03845e11 | 1.17608 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.91035e11 | −1.04119 | −0.520594 | − | 0.853804i | \(-0.674290\pi\) | ||||
−0.520594 | + | 0.853804i | \(0.674290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.55448e12 | 1.05923 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.12259e12 | 1.90154 | 0.950772 | − | 0.309892i | \(-0.100293\pi\) | ||||
0.950772 | + | 0.309892i | \(0.100293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.31204e10 | 0.0153980 | 0.00769900 | − | 0.999970i | \(-0.497549\pi\) | ||||
0.00769900 | + | 0.999970i | \(0.497549\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.24970e12 | −0.278456 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.94897e12 | −0.746792 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.81637e12 | −0.319035 | −0.159517 | − | 0.987195i | \(-0.550994\pi\) | ||||
−0.159517 | + | 0.987195i | \(0.550994\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.22142e13 | 0.365439 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.76386e13 | −1.12733 | −0.563665 | − | 0.826004i | \(-0.690609\pi\) | ||||
−0.563665 | + | 0.826004i | \(0.690609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.57081e13 | −0.987781 | −0.493890 | − | 0.869524i | \(-0.664426\pi\) | ||||
−0.493890 | + | 0.869524i | \(0.664426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.54233e13 | −0.225385 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.60351e13 | 0.282006 | 0.141003 | − | 0.990009i | \(-0.454967\pi\) | ||||
0.141003 | + | 0.990009i | \(0.454967\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.16059e14 | 1.78849 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.37714e14 | −1.33919 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.58261e14 | 1.45229 | 0.726145 | − | 0.687541i | \(-0.241310\pi\) | ||||
0.726145 | + | 0.687541i | \(0.241310\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.09800e14 | 0.176816 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.51401e12 | 0.00655437 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.98287e14 | 0.264479 | 0.132240 | − | 0.991218i | \(-0.457783\pi\) | ||||
0.132240 | + | 0.991218i | \(0.457783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.50623e14 | 0.568111 | 0.284056 | − | 0.958808i | \(-0.408320\pi\) | ||||
0.284056 | + | 0.958808i | \(0.408320\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.65764e15 | 0.841580 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.96131e14 | −0.232048 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.12967e15 | 1.84417 | 0.922085 | − | 0.386987i | \(-0.126484\pi\) | ||||
0.922085 | + | 0.386987i | \(0.126484\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.12966e15 | 0.733298 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.41472e14 | −0.0995131 | −0.0497565 | − | 0.998761i | \(-0.515845\pi\) | ||||
−0.0497565 | + | 0.998761i | \(0.515845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.16849e15 | −1.04036 | −0.520180 | − | 0.854057i | \(-0.674135\pi\) | ||||
−0.520180 | + | 0.854057i | \(0.674135\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.22124e15 | −0.140858 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.15916e15 | −0.660223 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.45373e15 | −0.404448 | −0.202224 | − | 0.979339i | \(-0.564817\pi\) | ||||
−0.202224 | + | 0.979339i | \(0.564817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.03640e15 | −0.242031 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.64723e15 | 0.177746 | 0.0888728 | − | 0.996043i | \(-0.471674\pi\) | ||||
0.0888728 | + | 0.996043i | \(0.471674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.13633e16 | 0.850369 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.09988e16 | −1.33924 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.81792e14 | 0.0183585 | 0.00917925 | − | 0.999958i | \(-0.497078\pi\) | ||||
0.00917925 | + | 0.999958i | \(0.497078\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.88687e16 | 0.866460 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.85222e14 | −0.0108446 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.69120e14 | −0.00416193 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.20373e17 | −1.55944 | −0.779720 | − | 0.626129i | \(-0.784638\pi\) | ||||
−0.779720 | + | 0.626129i | \(0.784638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.82943e16 | −0.199258 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.74092e16 | 0.711314 | 0.355657 | − | 0.934617i | \(-0.384257\pi\) | ||||
0.355657 | + | 0.934617i | \(0.384257\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.39309e17 | 1.08359 | 0.541793 | − | 0.840512i | \(-0.317746\pi\) | ||||
0.541793 | + | 0.840512i | \(0.317746\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.96270e16 | 0.525958 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.75662e17 | −1.55101 | −0.775505 | − | 0.631341i | \(-0.782505\pi\) | ||||
−0.775505 | + | 0.631341i | \(0.782505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.37550e17 | 0.661202 | 0.330601 | − | 0.943771i | \(-0.392749\pi\) | ||||
0.330601 | + | 0.943771i | \(0.392749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.45550e16 | 0.224693 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.90258e17 | −1.38097 | −0.690486 | − | 0.723345i | \(-0.742604\pi\) | ||||
−0.690486 | + | 0.723345i | \(0.742604\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.52748e17 | −0.465634 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.93239e16 | 0.261501 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.39292e18 | −3.17525 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.26436e17 | −0.843681 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.61313e17 | 0.793966 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.96046e16 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.37824e17 | 0.967433 | 0.483717 | − | 0.875225i | \(-0.339287\pi\) | ||||
0.483717 | + | 0.875225i | \(0.339287\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.05933e17 | 0.695684 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.45408e18 | 1.46482 | 0.732409 | − | 0.680865i | \(-0.238396\pi\) | ||||
0.732409 | + | 0.680865i | \(0.238396\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.75470e16 | 0.0155405 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.07217e17 | 0.473704 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.27534e18 | −1.56647 | −0.783236 | − | 0.621725i | \(-0.786432\pi\) | ||||
−0.783236 | + | 0.621725i | \(0.786432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.41598e17 | −0.0861849 | −0.0430924 | − | 0.999071i | \(-0.513721\pi\) | ||||
−0.0430924 | + | 0.999071i | \(0.513721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.68444e17 | −0.198614 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.28969e17 | −0.205149 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00101e18 | 0.850396 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.32994e18 | −1.25962 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.31089e18 | −0.442063 | −0.221032 | − | 0.975267i | \(-0.570942\pi\) | ||||
−0.221032 | + | 0.975267i | \(0.570942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.76548e18 | 0.832658 | 0.416329 | − | 0.909214i | \(-0.363316\pi\) | ||||
0.416329 | + | 0.909214i | \(0.363316\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.55943e18 | −0.958303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.85627e16 | 0.00688619 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.81235e18 | −0.824225 | −0.412112 | − | 0.911133i | \(-0.635209\pi\) | ||||
−0.412112 | + | 0.911133i | \(0.635209\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.26842e18 | −1.02283 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.95942e18 | 1.73866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.03773e19 | −1.63114 | −0.815570 | − | 0.578658i | \(-0.803577\pi\) | ||||
−0.815570 | + | 0.578658i | \(0.803577\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.78791e17 | −0.124529 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.21920e19 | −1.55949 | −0.779747 | − | 0.626095i | \(-0.784652\pi\) | ||||
−0.779747 | + | 0.626095i | \(0.784652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.32145e18 | −0.730768 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.48391e16 | 0.00469019 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.88210e18 | −0.367853 | −0.183927 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183927 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.88632e18 | −0.333976 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.38735e18 | −0.186270 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.62354e19 | 1.15136 | 0.575680 | − | 0.817675i | \(-0.304737\pi\) | ||||
0.575680 | + | 0.817675i | \(0.304737\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.32195e19 | −1.49825 | −0.749127 | − | 0.662427i | \(-0.769527\pi\) | ||||
−0.749127 | + | 0.662427i | \(0.769527\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.80799e18 | −0.400115 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.66264e18 | −0.142677 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.53728e19 | 0.751793 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.95915e19 | −1.76879 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.47928e19 | −1.82989 | −0.914944 | − | 0.403580i | \(-0.867766\pi\) | ||||
−0.914944 | + | 0.403580i | \(0.867766\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.61154e19 | 1.35038 | 0.675189 | − | 0.737645i | \(-0.264062\pi\) | ||||
0.675189 | + | 0.737645i | \(0.264062\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.77116e18 | 0.163429 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.80503e19 | −0.566920 | −0.283460 | − | 0.958984i | \(-0.591482\pi\) | ||||
−0.283460 | + | 0.958984i | \(0.591482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.39636e18 | 0.184366 | 0.0921832 | − | 0.995742i | \(-0.470615\pi\) | ||||
0.0921832 | + | 0.995742i | \(0.470615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.90590e19 | −1.29883 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.30469e20 | −3.17535 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.25151e19 | −0.504157 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.54500e19 | 0.524734 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.93655e17 | −0.00367948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.72101e18 | −0.135292 | −0.0676462 | − | 0.997709i | \(-0.521549\pi\) | ||||
−0.0676462 | + | 0.997709i | \(0.521549\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.33369e18 | 0.0700860 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.95735e19 | −0.441749 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.86233e18 | −0.0257128 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.73733e19 | 0.732715 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.34623e19 | −0.986634 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.08588e20 | 1.18902 | 0.594510 | − | 0.804088i | \(-0.297346\pi\) | ||||
0.594510 | + | 0.804088i | \(0.297346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.93097e18 | −0.100795 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.95539e19 | −0.184083 | −0.0920415 | − | 0.995755i | \(-0.529339\pi\) | ||||
−0.0920415 | + | 0.995755i | \(0.529339\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.20601e20 | 1.05378 | 0.526890 | − | 0.849933i | \(-0.323358\pi\) | ||||
0.526890 | + | 0.849933i | \(0.323358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.72986e19 | 0.464988 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.20388e19 | 0.543302 | 0.271651 | − | 0.962396i | \(-0.412430\pi\) | ||||
0.271651 | + | 0.962396i | \(0.412430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.79825e19 | 0.126117 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.36491e19 | 0.284849 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.70425e20 | −1.03550 | −0.517750 | − | 0.855532i | \(-0.673230\pi\) | ||||
−0.517750 | + | 0.855532i | \(0.673230\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.71129e20 | −0.968679 | −0.484340 | − | 0.874880i | \(-0.660940\pi\) | ||||
−0.484340 | + | 0.874880i | \(0.660940\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.68440e20 | −0.888775 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.62523e20 | 0.799839 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.05140e18 | 0.00482885 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.91907e19 | −0.125184 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.85831e20 | −0.744546 | −0.372273 | − | 0.928123i | \(-0.621422\pi\) | ||||
−0.372273 | + | 0.928123i | \(0.621422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.09916e20 | −0.411657 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.70982e20 | −0.598906 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.68273e19 | 0.0551547 | 0.0275773 | − | 0.999620i | \(-0.491221\pi\) | ||||
0.0275773 | + | 0.999620i | \(0.491221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.73609e20 | 0.532750 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.33396e20 | −0.958333 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.77268e20 | −0.746924 | −0.373462 | − | 0.927645i | \(-0.621829\pi\) | ||||
−0.373462 | + | 0.927645i | \(0.621829\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.57133e20 | 0.649484 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.45675e18 | −0.0129297 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.40799e19 | 0.209220 | 0.104610 | − | 0.994513i | \(-0.466641\pi\) | ||||
0.104610 | + | 0.994513i | \(0.466641\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.17628e20 | 1.28970 | 0.644849 | − | 0.764310i | \(-0.276920\pi\) | ||||
0.644849 | + | 0.764310i | \(0.276920\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.11087e20 | −0.610238 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.28907e19 | 0.0790744 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.67865e20 | −1.15774 | −0.578869 | − | 0.815420i | \(-0.696506\pi\) | ||||
−0.578869 | + | 0.815420i | \(0.696506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.75894e18 | −0.00776023 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.13640e20 | −0.174393 | −0.0871963 | − | 0.996191i | \(-0.527791\pi\) | ||||
−0.0871963 | + | 0.996191i | \(0.527791\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.76957e20 | 0.544637 | 0.272318 | − | 0.962207i | \(-0.412210\pi\) | ||||
0.272318 | + | 0.962207i | \(0.412210\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.15391e18 | 0.00293121 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.46802e21 | 1.88250 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.16376e21 | 2.61564 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.63408e20 | 1.09830 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.57350e20 | −0.384344 | −0.192172 | − | 0.981361i | \(-0.561553\pi\) | ||||
−0.192172 | + | 0.981361i | \(0.561553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.16518e20 | 0.118279 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.36946e20 | 0.418792 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.96757e20 | 0.540247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.92824e21 | 1.64947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.19547e20 | −0.500971 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.32275e20 | 0.254067 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.25658e21 | −1.63220 | −0.816102 | − | 0.577908i | \(-0.803869\pi\) | ||||
−0.816102 | + | 0.577908i | \(0.803869\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.11497e21 | −0.763158 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.76844e20 | −0.373762 | −0.186881 | − | 0.982383i | \(-0.559838\pi\) | ||||
−0.186881 | + | 0.982383i | \(0.559838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.63218e21 | 1.61506 | 0.807530 | − | 0.589827i | \(-0.200804\pi\) | ||||
0.807530 | + | 0.589827i | \(0.200804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.47515e20 | 0.376366 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.95998e20 | −0.548599 | −0.274299 | − | 0.961644i | \(-0.588446\pi\) | ||||
−0.274299 | + | 0.961644i | \(0.588446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.43990e21 | 0.751817 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.20627e21 | 1.09236 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.76786e19 | −0.0176959 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.32864e20 | −0.103775 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.10088e21 | −0.465678 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.17249e21 | −0.470915 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.56520e21 | 1.36002 | 0.680011 | − | 0.733202i | \(-0.261975\pi\) | ||||
0.680011 | + | 0.733202i | \(0.261975\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.43634e20 | 0.160786 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.39440e21 | 0.824738 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.65283e20 | 0.119612 | 0.0598060 | − | 0.998210i | \(-0.480952\pi\) | ||||
0.0598060 | + | 0.998210i | \(0.480952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.12344e21 | 0.972605 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.05533e19 | 0.00608793 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.67180e21 | −1.31669 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.22252e21 | 0.327941 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.06934e21 | 0.528483 | 0.264242 | − | 0.964457i | \(-0.414878\pi\) | ||||
0.264242 | + | 0.964457i | \(0.414878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.13803e20 | 0.0763204 | 0.0381602 | − | 0.999272i | \(-0.487850\pi\) | ||||
0.0381602 | + | 0.999272i | \(0.487850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.37228e21 | −0.549611 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.87901e21 | −1.51859 | −0.759296 | − | 0.650746i | \(-0.774456\pi\) | ||||
−0.759296 | + | 0.650746i | \(0.774456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.11513e20 | −0.0445036 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.11483e22 | 2.23629 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.50907e21 | 1.81901 | 0.909505 | − | 0.415693i | \(-0.136461\pi\) | ||||
0.909505 | + | 0.415693i | \(0.136461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.47991e21 | −0.999913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.41300e21 | 0.594196 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.80019e21 | −0.465263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.88008e20 | −0.0298205 | −0.0149103 | − | 0.999889i | \(-0.504746\pi\) | ||||
−0.0149103 | + | 0.999889i | \(0.504746\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.75133e21 | 0.568147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.67655e22 | −2.42515 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.66745e20 | 0.133594 | 0.0667970 | − | 0.997767i | \(-0.478722\pi\) | ||||
0.0667970 | + | 0.997767i | \(0.478722\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.77048e20 | −0.0629936 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.81756e21 | −0.986665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.09478e22 | −1.32097 | −0.660484 | − | 0.750840i | \(-0.729649\pi\) | ||||
−0.660484 | + | 0.750840i | \(0.729649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.90520e21 | −0.681353 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.48135e21 | 1.04636 | 0.523179 | − | 0.852223i | \(-0.324746\pi\) | ||||
0.523179 | + | 0.852223i | \(0.324746\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.79655e21 | −0.295261 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.92736e21 | 0.497818 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.68048e21 | 0.839406 | 0.419703 | − | 0.907661i | \(-0.362134\pi\) | ||||
0.419703 | + | 0.907661i | \(0.362134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.13857e22 | −1.97980 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.16378e22 | −1.03166 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.13036e21 | −0.180875 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.61938e21 | −0.457055 | −0.228528 | − | 0.973537i | \(-0.573391\pi\) | ||||
−0.228528 | + | 0.973537i | \(0.573391\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.40438e20 | −0.0109450 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.97857e21 | −0.371858 | −0.185929 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185929 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.11589e20 | −0.00798965 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.57672e21 | −0.108240 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.91600e21 | −0.126137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.65693e20 | 0.0167777 | 0.00838883 | − | 0.999965i | \(-0.497330\pi\) | ||||
0.00838883 | + | 0.999965i | \(0.497330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.82108e22 | 1.10325 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.59717e21 | −0.441648 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.42470e21 | 0.0794903 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.13328e21 | 0.0606991 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.71242e22 | −0.880626 | −0.440313 | − | 0.897844i | \(-0.645133\pi\) | ||||
−0.440313 | + | 0.897844i | \(0.645133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.71839e22 | 1.34250 | 0.671249 | − | 0.741231i | \(-0.265758\pi\) | ||||
0.671249 | + | 0.741231i | \(0.265758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.99613e21 | −0.142124 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.34504e21 | 0.380297 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.16648e22 | −0.948677 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.43327e21 | 0.144484 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.34759e22 | 0.949656 | 0.474828 | − | 0.880079i | \(-0.342510\pi\) | ||||
0.474828 | + | 0.880079i | \(0.342510\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.88732e22 | −0.734003 | −0.367002 | − | 0.930220i | \(-0.619616\pi\) | ||||
−0.367002 | + | 0.930220i | \(0.619616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.60152e22 | −0.598925 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.69402e20 | 0.00968968 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.51895e22 | −1.90945 | −0.954724 | − | 0.297494i | \(-0.903849\pi\) | ||||
−0.954724 | + | 0.297494i | \(0.903849\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.70786e22 | −0.901359 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.20735e22 | 0.386723 | 0.193362 | − | 0.981128i | \(-0.438061\pi\) | ||||
0.193362 | + | 0.981128i | \(0.438061\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.66325e20 | 0.00821017 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.04918e22 | 0.311341 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.57466e22 | 0.735573 | 0.367787 | − | 0.929910i | \(-0.380116\pi\) | ||||
0.367787 | + | 0.929910i | \(0.380116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.62016e22 | −0.445714 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.21336e22 | −0.586432 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.51831e22 | 0.387493 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.01069e22 | −0.248503 | −0.124252 | − | 0.992251i | \(-0.539653\pi\) | ||||
−0.124252 | + | 0.992251i | \(0.539653\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.50144e22 | 2.01412 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.68599e21 | 0.0384942 | 0.0192471 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192471 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.77945e22 | 0.611674 | 0.305837 | − | 0.952084i | \(-0.401064\pi\) | ||||
0.305837 | + | 0.952084i | \(0.401064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.28602e20 | −0.00484987 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.26643e22 | −1.69093 | −0.845463 | − | 0.534034i | \(-0.820676\pi\) | ||||
−0.845463 | + | 0.534034i | \(0.820676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.56119e23 | −3.07954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.05123e22 | 0.580493 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.12807e22 | −0.390541 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.05125e20 | −0.00186127 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.28420e22 | −0.731920 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.59191e22 | −0.427335 | −0.213667 | − | 0.976906i | \(-0.568541\pi\) | ||||
−0.213667 | + | 0.976906i | \(0.568541\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.04024e22 | 0.165540 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.97106e22 | −1.22452 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.70206e22 | −0.697403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.14828e22 | 0.594116 | 0.297058 | − | 0.954859i | \(-0.403994\pi\) | ||||
0.297058 | + | 0.954859i | \(0.403994\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.30554e22 | 1.14879 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.08644e22 | −0.412349 | −0.206174 | − | 0.978515i | \(-0.566101\pi\) | ||||
−0.206174 | + | 0.978515i | \(0.566101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.80155e23 | 3.61575 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.14620e21 | −0.0891109 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.37910e22 | 0.166175 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.24182e22 | −0.377516 | −0.188758 | − | 0.982024i | \(-0.560446\pi\) | ||||
−0.188758 | + | 0.982024i | \(0.560446\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.75788e22 | 1.09833 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.39324e22 | −0.695654 | −0.347827 | − | 0.937559i | \(-0.613080\pi\) | ||||
−0.347827 | + | 0.937559i | \(0.613080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.02380e22 | 0.318109 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.05939e22 | 0.514672 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.33355e22 | −0.918218 | −0.459109 | − | 0.888380i | \(-0.651831\pi\) | ||||
−0.459109 | + | 0.888380i | \(0.651831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.82577e23 | 1.73728 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.07095e21 | −0.00985763 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.44176e22 | 0.484594 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.29400e22 | 0.111497 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.10705e22 | 0.259075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.30201e22 | 0.266476 | 0.133238 | − | 0.991084i | \(-0.457463\pi\) | ||||
0.133238 | + | 0.991084i | \(0.457463\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.06002e22 | −0.317149 | −0.158575 | − | 0.987347i | \(-0.550690\pi\) | ||||
−0.158575 | + | 0.987347i | \(0.550690\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.11043e22 | 0.235216 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.99896e21 | 0.0292790 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.18585e22 | 0.0840729 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.94136e22 | −0.133291 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.79621e22 | 0.584944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.07680e23 | −0.693633 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.29940e23 | −0.810890 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.16949e23 | 0.707121 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.20460e22 | −0.246347 | −0.123174 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123174 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.85838e23 | 1.05520 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.37303e22 | 0.295699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.01110e23 | 1.07285 | 0.536427 | − | 0.843947i | \(-0.319774\pi\) | ||||
0.536427 | + | 0.843947i | \(0.319774\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.53616e22 | −0.286315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.52919e21 | −0.0176965 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.38903e23 | 0.675380 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.13106e22 | 0.100486 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.46727e23 | 0.671030 | 0.335515 | − | 0.942035i | \(-0.391090\pi\) | ||||
0.335515 | + | 0.942035i | \(0.391090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.15538e23 | 0.512536 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23036e23 | −0.529480 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.39706e23 | 1.41834 | 0.709172 | − | 0.705036i | \(-0.249069\pi\) | ||||
0.709172 | + | 0.705036i | \(0.249069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.52445e23 | −0.617590 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.02805e23 | 0.404163 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.72602e23 | 1.04010 | 0.520050 | − | 0.854136i | \(-0.325913\pi\) | ||||
0.520050 | + | 0.854136i | \(0.325913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.79882e22 | 0.103650 | 0.0518249 | − | 0.998656i | \(-0.483496\pi\) | ||||
0.0518249 | + | 0.998656i | \(0.483496\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.58501e23 | 1.28877 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.96672e22 | −0.208238 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.86678e23 | 1.31025 | 0.655127 | − | 0.755519i | \(-0.272615\pi\) | ||||
0.655127 | + | 0.755519i | \(0.272615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.89051e23 | −0.951056 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.28926e22 | −0.296814 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.85030e23 | 0.574195 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.87984e22 | 0.116947 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.64152e23 | −1.06625 | −0.533125 | − | 0.846036i | \(-0.678983\pi\) | ||||
−0.533125 | + | 0.846036i | \(0.678983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.03761e19 | −0.000143299 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.44466e23 | 0.399276 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.86689e23 | −1.84415 | −0.922073 | − | 0.387017i | \(-0.873506\pi\) | ||||
−0.922073 | + | 0.387017i | \(0.873506\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.44110e23 | −1.42001 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.11935e22 | −0.129847 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.82850e23 | 0.943846 | 0.471923 | − | 0.881640i | \(-0.343560\pi\) | ||||
0.471923 | + | 0.881640i | \(0.343560\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.66402e23 | −0.638417 | −0.319209 | − | 0.947684i | \(-0.603417\pi\) | ||||
−0.319209 | + | 0.947684i | \(0.603417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.98941e23 | −0.929418 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.66577e23 | −0.377306 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.11277e23 | 0.245076 | 0.122538 | − | 0.992464i | \(-0.460897\pi\) | ||||
0.122538 | + | 0.992464i | \(0.460897\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.04421e24 | 2.23636 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.02541e22 | −0.146326 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.91229e23 | −0.792532 | −0.396266 | − | 0.918136i | \(-0.629694\pi\) | ||||
−0.396266 | + | 0.918136i | \(0.629694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.80200e23 | 0.355072 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.72626e23 | −1.09761 | −0.548804 | − | 0.835951i | \(-0.684917\pi\) | ||||
−0.548804 | + | 0.835951i | \(0.684917\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.86155e23 | −1.46601 | −0.733007 | − | 0.680222i | \(-0.761884\pi\) | ||||
−0.733007 | + | 0.680222i | \(0.761884\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.07855e23 | −1.10286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73648e22 | −0.0306565 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.54993e21 | 0.00259142 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.72788e23 | −0.606640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.52712e23 | −1.03389 | −0.516943 | − | 0.856020i | \(-0.672930\pi\) | ||||
−0.516943 | + | 0.856020i | \(0.672930\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.17954e22 | 0.0952850 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.88212e23 | 0.432649 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.34945e23 | −0.928007 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.52410e22 | 0.0501522 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.10734e23 | 0.984950 | 0.492475 | − | 0.870327i | \(-0.336092\pi\) | ||||
0.492475 | + | 0.870327i | \(0.336092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.34278e23 | −0.316183 | −0.158092 | − | 0.987424i | \(-0.550534\pi\) | ||||
−0.158092 | + | 0.987424i | \(0.550534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.36692e23 | 0.311119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.50806e23 | −0.193078 | −0.0965391 | − | 0.995329i | \(-0.530777\pi\) | ||||
−0.0965391 | + | 0.995329i | \(0.530777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.38450e22 | 0.104568 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.49052e22 | 0.0181092 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.74375e22 | 0.0798251 | 0.0399126 | − | 0.999203i | \(-0.487292\pi\) | ||||
0.0399126 | + | 0.999203i | \(0.487292\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.68001e23 | 0.655086 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.66551e23 | 0.524317 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.11301e22 | −0.0778981 | −0.0389491 | − | 0.999241i | \(-0.512401\pi\) | ||||
−0.0389491 | + | 0.999241i | \(0.512401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.69805e24 | 1.81233 | 0.906164 | − | 0.422926i | \(-0.138997\pi\) | ||||
0.906164 | + | 0.422926i | \(0.138997\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.67994e23 | 0.694876 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.85431e21 | 0.00694992 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00311e24 | −1.97986 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.69085e23 | −0.837414 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.39101e23 | 0.224615 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.39848e24 | −1.28094 | −0.640469 | − | 0.767984i | \(-0.721260\pi\) | ||||
−0.640469 | + | 0.767984i | \(0.721260\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.37194e23 | 0.211847 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.38639e23 | −0.817514 | −0.408757 | − | 0.912643i | \(-0.634038\pi\) | ||||
−0.408757 | + | 0.912643i | \(0.634038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.06582e24 | 2.60408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.56500e23 | 0.129648 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.23254e24 | −0.995922 | −0.497961 | − | 0.867199i | \(-0.665918\pi\) | ||||
−0.497961 | + | 0.867199i | \(0.665918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.88807e23 | −0.700547 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.65236e23 | −0.742167 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.00457e24 | −0.753559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.83055e23 | −0.280348 | −0.140174 | − | 0.990127i | \(-0.544766\pi\) | ||||
−0.140174 | + | 0.990127i | \(0.544766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.65944e23 | 0.332737 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.53117e22 | −0.0385431 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.15226e24 | −2.14360 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.76565e23 | −0.382642 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.63235e24 | 1.05733 | 0.528665 | − | 0.848831i | \(-0.322693\pi\) | ||||
0.528665 | + | 0.848831i | \(0.322693\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.69611e21 | 0.00296906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.43923e23 | −0.0888227 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.97156e24 | −1.18781 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.09431e23 | −0.358453 | −0.179226 | − | 0.983808i | \(-0.557359\pi\) | ||||
−0.179226 | + | 0.983808i | \(0.557359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.54948e23 | 0.203832 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.85926e22 | −0.0160322 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.67566e23 | −0.0917454 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.36400e24 | 0.729292 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.49148e23 | 0.234527 | 0.117264 | − | 0.993101i | \(-0.462588\pi\) | ||||
0.117264 | + | 0.993101i | \(0.462588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.54812e24 | −1.80946 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.36964e24 | 0.682230 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.81644e23 | 0.380309 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.00713e23 | 0.237983 | 0.118992 | − | 0.992895i | \(-0.462034\pi\) | ||||
0.118992 | + | 0.992895i | \(0.462034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.86938e24 | 0.867986 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.14048e24 | −1.87825 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.20329e24 | 0.533320 | 0.266660 | − | 0.963791i | \(-0.414080\pi\) | ||||
0.266660 | + | 0.963791i | \(0.414080\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.30076e24 | −0.563318 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.72298e24 | 0.729133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.19426e24 | 0.907426 | 0.453713 | − | 0.891148i | \(-0.350099\pi\) | ||||
0.453713 | + | 0.891148i | \(0.350099\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.41491e21 | −0.00340091 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.89633e22 | 0.0390903 | 0.0195452 | − | 0.999809i | \(-0.493778\pi\) | ||||
0.0195452 | + | 0.999809i | \(0.493778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.12068e23 | −0.197697 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.37375e23 | −0.0895796 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.02094e24 | 2.59000 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.01856e24 | 0.367322 | 0.183661 | − | 0.982990i | \(-0.441205\pi\) | ||||
0.183661 | + | 0.982990i | \(0.441205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.48731e24 | 0.524376 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.08027e24 | 0.372376 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.43989e24 | −0.485305 | −0.242653 | − | 0.970113i | \(-0.578018\pi\) | ||||
−0.242653 | + | 0.970113i | \(0.578018\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.79713e23 | 0.289925 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.15424e23 | −0.230565 | −0.115283 | − | 0.993333i | \(-0.536777\pi\) | ||||
−0.115283 | + | 0.993333i | \(0.536777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.50330e24 | −1.10413 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.39040e24 | −0.428566 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.55214e23 | −0.137232 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.87177e24 | 0.551922 | 0.275961 | − | 0.961169i | \(-0.411004\pi\) | ||||
0.275961 | + | 0.961169i | \(0.411004\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.34678e23 | −0.0388449 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.86999e24 | −0.527611 | −0.263805 | − | 0.964576i | \(-0.584978\pi\) | ||||
−0.263805 | + | 0.964576i | \(0.584978\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.11573e22 | 0.00307960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.38948e24 | −0.375210 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.97099e22 | 0.0104913 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.52202e23 | −0.0393447 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.96294e24 | 2.01418 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.48920e24 | −0.368604 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.29304e24 | 0.797648 | 0.398824 | − | 0.917027i | \(-0.369418\pi\) | ||||
0.398824 | + | 0.917027i | \(0.369418\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.21913e24 | 0.526051 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.93963e24 | 2.30606 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.29813e24 | −0.294779 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.05798e24 | −0.457425 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.80089e24 | −0.826969 | −0.413485 | − | 0.910511i | \(-0.635688\pi\) | ||||
−0.413485 | + | 0.910511i | \(0.635688\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.51767e24 | 0.536229 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.43735e22 | −0.00925225 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.01498e24 | −0.411329 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.89040e24 | 0.777552 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.52972e23 | −0.147351 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.38713e24 | 0.265799 | 0.132900 | − | 0.991129i | \(-0.457571\pi\) | ||||
0.132900 | + | 0.991129i | \(0.457571\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.43418e24 | −0.456747 | −0.228374 | − | 0.973574i | \(-0.573341\pi\) | ||||
−0.228374 | + | 0.973574i | \(0.573341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.94321e24 | −0.908321 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.05365e24 | −0.729468 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.21589e22 | 0.00919265 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.52972e24 | −0.436675 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.07675e24 | −1.19651 | −0.598256 | − | 0.801305i | \(-0.704140\pi\) | ||||
−0.598256 | + | 0.801305i | \(0.704140\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.31425e24 | 0.880124 | 0.440062 | − | 0.897968i | \(-0.354957\pi\) | ||||
0.440062 | + | 0.897968i | \(0.354957\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.43278e23 | −0.0556912 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.13487e24 | −0.816080 | −0.408040 | − | 0.912964i | \(-0.633788\pi\) | ||||
−0.408040 | + | 0.912964i | \(0.633788\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.06738e25 | 1.66191 | 0.830954 | − | 0.556341i | \(-0.187795\pi\) | ||||
0.830954 | + | 0.556341i | \(0.187795\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.34528e24 | 0.815383 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.27543e25 | 3.40079 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.76248e24 | −0.697427 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.13664e23 | 0.0163101 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.47302e24 | 0.910186 | 0.455093 | − | 0.890444i | \(-0.349606\pi\) | ||||
0.455093 | + | 0.890444i | \(0.349606\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.89837e25 | 2.61587 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.09523e23 | 0.122823 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.46931e24 | −0.326809 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.08611e25 | 1.40885 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.01699e24 | −0.383582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.66544e24 | 0.332175 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.69306e24 | 0.328988 | 0.164494 | − | 0.986378i | \(-0.447401\pi\) | ||||
0.164494 | + | 0.986378i | \(0.447401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.75153e22 | 0.00209752 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.86785e24 | −0.219283 | −0.109641 | − | 0.993971i | \(-0.534970\pi\) | ||||
−0.109641 | + | 0.993971i | \(0.534970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.13124e25 | 1.30200 | 0.651000 | − | 0.759077i | \(-0.274350\pi\) | ||||
0.651000 | + | 0.759077i | \(0.274350\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.17493e25 | −1.32583 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.37061e24 | 0.262282 | 0.131141 | − | 0.991364i | \(-0.458136\pi\) | ||||
0.131141 | + | 0.991364i | \(0.458136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.51645e24 | −0.164509 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.73178e25 | −1.84217 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.53298e24 | −0.159907 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.35446e24 | −0.956895 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.83429e24 | 0.785921 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.51809e24 | −0.149358 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.79534e24 | −0.655714 | −0.327857 | − | 0.944727i | \(-0.606326\pi\) | ||||
−0.327857 | + | 0.944727i | \(0.606326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.86007e24 | 0.270689 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.88402e25 | −1.74900 | −0.874501 | − | 0.485024i | \(-0.838811\pi\) | ||||
−0.874501 | + | 0.485024i | \(0.838811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.85491e24 | −0.351033 | −0.175517 | − | 0.984476i | \(-0.556160\pi\) | ||||
−0.175517 | + | 0.984476i | \(0.556160\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.32557e23 | −0.0833024 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.32727e24 | −0.729712 | −0.364856 | − | 0.931064i | \(-0.618882\pi\) | ||||
−0.364856 | + | 0.931064i | \(0.618882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.87919e25 | −1.61550 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.13459e24 | −0.0956924 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.17158e22 | −0.00262445 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.34194e24 | 0.514904 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.77617e24 | −0.380491 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.74565e23 | 0.0292799 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.60004e25 | 2.76151 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.54327e25 | −1.16171 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.07012e24 | −0.670039 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.92435e25 | −1.39515 | −0.697576 | − | 0.716511i | \(-0.745738\pi\) | ||||
−0.697576 | + | 0.716511i | \(0.745738\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.03807e24 | −0.358485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.57682e25 | 1.10123 | 0.550613 | − | 0.834761i | \(-0.314394\pi\) | ||||
0.550613 | + | 0.834761i | \(0.314394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.02519e24 | 0.0702756 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.65937e24 | −0.178937 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.70346e25 | −2.44607 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.03058e25 | −0.668189 | −0.334094 | − | 0.942540i | \(-0.608430\pi\) | ||||
−0.334094 | + | 0.942540i | \(0.608430\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.80606e25 | 1.14954 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.26339e23 | 0.0516349 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.04010e24 | −0.0638070 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.06674e24 | −0.546102 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.73688e24 | 0.575819 | 0.287910 | − | 0.957658i | \(-0.407040\pi\) | ||||
0.287910 | + | 0.957658i | \(0.407040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.86642e23 | −0.0166444 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.61679e24 | 0.263236 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.00499e24 | 0.336212 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.22145e25 | −1.77119 | −0.885594 | − | 0.464459i | \(-0.846249\pi\) | ||||
−0.885594 | + | 0.464459i | \(0.846249\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.10667e25 | −1.13747 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.90374e24 | −0.419103 | −0.209552 | − | 0.977798i | \(-0.567200\pi\) | ||||
−0.209552 | + | 0.977798i | \(0.567200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.25387e25 | 1.17376 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.54654e25 | −0.791028 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.36682e25 | −1.18902 | −0.594512 | − | 0.804086i | \(-0.702655\pi\) | ||||
−0.594512 | + | 0.804086i | \(0.702655\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.09398e25 | 0.539818 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.97150e24 | 0.386372 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.09477e24 | 0.433014 | 0.216507 | − | 0.976281i | \(-0.430534\pi\) | ||||
0.216507 | + | 0.976281i | \(0.430534\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.74972e25 | −0.818351 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.15243e25 | −0.529496 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.79516e25 | 2.61582 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.25448e25 | −0.999763 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.79411e25 | 0.781673 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.41076e25 | 0.603907 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.62970e25 | −1.52667 | −0.763337 | − | 0.646001i | \(-0.776440\pi\) | ||||
−0.763337 | + | 0.646001i | \(0.776440\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.01562e23 | 0.0124630 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.70396e24 | 0.394081 | 0.197040 | − | 0.980395i | \(-0.436867\pi\) | ||||
0.197040 | + | 0.980395i | \(0.436867\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.60641e24 | 0.143918 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.86373e24 | 0.0730878 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.70141e25 | 1.42647 | 0.713236 | − | 0.700924i | \(-0.247229\pi\) | ||||
0.713236 | + | 0.700924i | \(0.247229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.91644e23 | 0.00725843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.95223e24 | −0.333230 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.43184e24 | 0.235305 | 0.117652 | − | 0.993055i | \(-0.462463\pi\) | ||||
0.117652 | + | 0.993055i | \(0.462463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.05090e24 | −0.253534 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.38403e24 | 0.331661 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.96045e25 | 1.02847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.17070e25 | −1.76573 | −0.882863 | − | 0.469631i | \(-0.844387\pi\) | ||||
−0.882863 | + | 0.469631i | \(0.844387\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.85342e25 | −0.957848 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.49858e24 | 0.0824512 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.77457e25 | −0.900093 | −0.450047 | − | 0.893005i | \(-0.648593\pi\) | ||||
−0.450047 | + | 0.893005i | \(0.648593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 80.18.a.d.1.1 | 2 | ||
4.3 | odd | 2 | 10.18.a.c.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 90.18.a.k.1.2 | 2 | |||
20.3 | even | 4 | 50.18.b.d.49.4 | 4 | |||
20.7 | even | 4 | 50.18.b.d.49.1 | 4 | |||
20.19 | odd | 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 | 4.3 | odd | 2 | ||
50.18.a.f.1.1 | 2 | 20.19 | odd | 2 | |||
50.18.b.d.49.1 | 4 | 20.7 | even | 4 | |||
50.18.b.d.49.4 | 4 | 20.3 | even | 4 | |||
80.18.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
90.18.a.k.1.2 | 2 | 12.11 | even | 2 |