Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,18,Mod(49,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(91.6110436723\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 41641x^{2} + 433472400 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-143.792i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.18.b.d.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 256.000i | − 0.707107i | ||||||||
\(3\) | − 8003.53i | − 0.704289i | −0.935946 | − | 0.352145i | \(-0.885452\pi\) | ||||
0.935946 | − | 0.352145i | \(-0.114548\pi\) | |||||||
\(4\) | −65536.0 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.04890e6 | −0.498008 | ||||||||
\(7\) | 2.54694e7i | 1.66988i | 0.550342 | + | 0.834939i | \(0.314497\pi\) | ||||
−0.550342 | + | 0.834939i | \(0.685503\pi\) | |||||||
\(8\) | 1.67772e7i | 0.353553i | ||||||||
\(9\) | 6.50836e7 | 0.503976 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.81089e8 | −0.395372 | −0.197686 | − | 0.980265i | \(-0.563343\pi\) | ||||
−0.197686 | + | 0.980265i | \(0.563343\pi\) | |||||||
\(12\) | 5.24520e8i | 0.352145i | ||||||||
\(13\) | 1.52610e9i | 0.518876i | 0.965760 | + | 0.259438i | \(0.0835373\pi\) | ||||
−0.965760 | + | 0.259438i | \(0.916463\pi\) | |||||||
\(14\) | 6.52016e9 | 1.18078 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | 5.46901e10i | 1.90148i | 0.309984 | + | 0.950742i | \(0.399676\pi\) | ||||
−0.309984 | + | 0.950742i | \(0.600324\pi\) | |||||||
\(18\) | − 1.66614e10i | − 0.356365i | ||||||||
\(19\) | −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 | ||||||||
\(22\) | 7.19587e10i | 0.279570i | ||||||||
\(23\) | − 3.91035e11i | − 1.04119i | −0.853804 | − | 0.520594i | \(-0.825710\pi\) | ||||
0.853804 | − | 0.520594i | \(-0.174290\pi\) | |||||||
\(24\) | 1.34277e11 | 0.249004 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.90681e11 | 0.366901 | ||||||||
\(27\) | − 1.55448e12i | − 1.05923i | ||||||||
\(28\) | − 1.66916e12i | − 0.834939i | ||||||||
\(29\) | −5.12259e12 | −1.90154 | −0.950772 | − | 0.309892i | \(-0.899707\pi\) | ||||
−0.950772 | + | 0.309892i | \(0.899707\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.31204e10 | −0.0153980 | −0.00769900 | − | 0.999970i | \(-0.502451\pi\) | ||||
−0.00769900 | + | 0.999970i | \(0.502451\pi\) | |||||||
\(32\) | − 1.09951e12i | − 0.176777i | ||||||||
\(33\) | 2.24970e12i | 0.278456i | ||||||||
\(34\) | 1.40007e13 | 1.34455 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.26532e12 | −0.251988 | ||||||||
\(37\) | − 6.81637e12i | − 0.319035i | −0.987195 | − | 0.159517i | \(-0.949006\pi\) | ||||
0.987195 | − | 0.159517i | \(-0.0509938\pi\) | |||||||
\(38\) | 1.76370e11i | 0.00658059i | ||||||||
\(39\) | 1.22142e13 | 0.365439 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.76386e13 | −1.12733 | −0.563665 | − | 0.826004i | \(-0.690609\pi\) | ||||
−0.563665 | + | 0.826004i | \(0.690609\pi\) | |||||||
\(42\) | − 5.21843e13i | − 0.831613i | ||||||||
\(43\) | − 7.57081e13i | − 0.987781i | −0.869524 | − | 0.493890i | \(-0.835574\pi\) | ||||
0.869524 | − | 0.493890i | \(-0.164426\pi\) | |||||||
\(44\) | 1.84214e13 | 0.197686 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00105e14 | −0.736231 | ||||||||
\(47\) | − 4.60351e13i | − 0.282006i | −0.990009 | − | 0.141003i | \(-0.954967\pi\) | ||||
0.990009 | − | 0.141003i | \(-0.0450327\pi\) | |||||||
\(48\) | − 3.43749e13i | − 0.176072i | ||||||||
\(49\) | −4.16059e14 | −1.78849 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.37714e14 | 1.33919 | ||||||||
\(52\) | − 1.00014e14i | − 0.259438i | ||||||||
\(53\) | − 6.58261e14i | − 1.45229i | −0.687541 | − | 0.726145i | \(-0.741310\pi\) | ||||
0.687541 | − | 0.726145i | \(-0.258690\pi\) | |||||||
\(54\) | −3.97946e14 | −0.748992 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.27305e14 | −0.590391 | ||||||||
\(57\) | 5.51401e12i | 0.00655437i | ||||||||
\(58\) | 1.31138e15i | 1.34459i | ||||||||
\(59\) | 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 | \(0.408320\pi\) | |||||||
\(62\) | 1.87188e13i | 0.0108880i | ||||||||
\(63\) | 1.65764e15i | 0.841580i | ||||||||
\(64\) | −2.81475e14 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.75924e14 | 0.196898 | ||||||||
\(67\) | − 6.12967e15i | − 1.84417i | −0.386987 | − | 0.922085i | \(-0.626484\pi\) | ||||
0.386987 | − | 0.922085i | \(-0.373516\pi\) | |||||||
\(68\) | − 3.58417e15i | − 0.950742i | ||||||||
\(69\) | −3.12966e15 | −0.733298 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.41472e14 | 0.0995131 | 0.0497565 | − | 0.998761i | \(-0.484155\pi\) | ||||
0.0497565 | + | 0.998761i | \(0.484155\pi\) | |||||||
\(72\) | 1.09192e15i | 0.178183i | ||||||||
\(73\) | 7.16849e15i | 1.04036i | 0.854057 | + | 0.520180i | \(0.174135\pi\) | ||||
−0.854057 | + | 0.520180i | \(0.825865\pi\) | |||||||
\(74\) | −1.74499e15 | −0.225592 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.51508e13 | 0.00465318 | ||||||||
\(77\) | − 7.15916e15i | − 0.660223i | ||||||||
\(78\) | − 3.12683e15i | − 0.258404i | ||||||||
\(79\) | −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 | ||||||||
\(82\) | 1.47555e16i | 0.797142i | ||||||||
\(83\) | 3.64723e15i | 0.177746i | 0.996043 | + | 0.0888728i | \(0.0283265\pi\) | ||||
−0.996043 | + | 0.0888728i | \(0.971674\pi\) | |||||||
\(84\) | −1.33592e16 | −0.588039 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.93813e16 | −0.698467 | ||||||||
\(87\) | 4.09988e16i | 1.33924i | ||||||||
\(88\) | − 4.71589e15i | − 0.139785i | ||||||||
\(89\) | −6.81792e14 | −0.0183585 | −0.00917925 | − | 0.999958i | \(-0.502922\pi\) | ||||
−0.00917925 | + | 0.999958i | \(0.502922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.88687e16 | −0.866460 | ||||||||
\(92\) | 2.56269e16i | 0.520594i | ||||||||
\(93\) | 5.85222e14i | 0.0108446i | ||||||||
\(94\) | −1.17850e16 | −0.199408 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.79998e15 | −0.124502 | ||||||||
\(97\) | − 1.20373e17i | − 1.55944i | −0.626129 | − | 0.779720i | \(-0.715362\pi\) | ||||
0.626129 | − | 0.779720i | \(-0.284638\pi\) | |||||||
\(98\) | 1.06511e17i | 1.26466i | ||||||||
\(99\) | −1.82943e16 | −0.199258 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.74092e16 | 0.711314 | 0.355657 | − | 0.934617i | \(-0.384257\pi\) | ||||
0.355657 | + | 0.934617i | \(0.384257\pi\) | |||||||
\(102\) | − 1.12055e17i | − 0.946954i | ||||||||
\(103\) | 1.39309e17i | 1.08359i | 0.840512 | + | 0.541793i | \(0.182254\pi\) | ||||
−0.840512 | + | 0.541793i | \(0.817746\pi\) | |||||||
\(104\) | −2.56037e16 | −0.183450 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.68515e17 | −1.02692 | ||||||||
\(107\) | 2.75662e17i | 1.55101i | 0.631341 | + | 0.775505i | \(0.282505\pi\) | ||||
−0.631341 | + | 0.775505i | \(0.717495\pi\) | |||||||
\(108\) | 1.01874e17i | 0.529617i | ||||||||
\(109\) | −1.37550e17 | −0.661202 | −0.330601 | − | 0.943771i | \(-0.607251\pi\) | ||||
−0.330601 | + | 0.943771i | \(0.607251\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.45550e16 | −0.224693 | ||||||||
\(112\) | 1.09390e17i | 0.417470i | ||||||||
\(113\) | 3.90258e17i | 1.38097i | 0.723345 | + | 0.690486i | \(0.242604\pi\) | ||||
−0.723345 | + | 0.690486i | \(0.757396\pi\) | |||||||
\(114\) | 1.41159e15 | 0.00463464 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.35714e17 | 0.950772 | ||||||||
\(117\) | 9.93239e16i | 0.261501i | ||||||||
\(118\) | − 7.63614e16i | − 0.187015i | ||||||||
\(119\) | −1.39292e18 | −3.17525 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.26436e17 | −0.843681 | ||||||||
\(122\) | − 2.17759e17i | − 0.401715i | ||||||||
\(123\) | 4.61313e17i | 0.793966i | ||||||||
\(124\) | 4.79202e15 | 0.00769900 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.24355e17 | 0.595087 | ||||||||
\(127\) | − 7.37824e17i | − 0.967433i | −0.875225 | − | 0.483717i | \(-0.839287\pi\) | ||||
0.875225 | − | 0.483717i | \(-0.160713\pi\) | |||||||
\(128\) | 7.20576e16i | 0.0883883i | ||||||||
\(129\) | −6.05933e17 | −0.695684 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.45408e18 | −1.46482 | −0.732409 | − | 0.680865i | \(-0.761604\pi\) | ||||
−0.732409 | + | 0.680865i | \(0.761604\pi\) | |||||||
\(132\) | − 1.47437e17i | − 0.139228i | ||||||||
\(133\) | − 1.75470e16i | − 0.0155405i | ||||||||
\(134\) | −1.56919e18 | −1.30403 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.17547e17 | −0.672276 | ||||||||
\(137\) | − 2.27534e18i | − 1.56647i | −0.621725 | − | 0.783236i | \(-0.713568\pi\) | ||||
0.621725 | − | 0.783236i | \(-0.286432\pi\) | |||||||
\(138\) | 8.01194e17i | 0.518520i | ||||||||
\(139\) | −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 | ||||||||
\(142\) | − 1.38617e17i | − 0.0703664i | ||||||||
\(143\) | − 4.28969e17i | − 0.205149i | ||||||||
\(144\) | 2.79532e17 | 0.125994 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.83513e18 | 0.735646 | ||||||||
\(147\) | 3.32994e18i | 1.25962i | ||||||||
\(148\) | 4.46717e17i | 0.159517i | ||||||||
\(149\) | 1.31089e18 | 0.442063 | 0.221032 | − | 0.975267i | \(-0.429058\pi\) | ||||
0.221032 | + | 0.975267i | \(0.429058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.76548e18 | −0.832658 | −0.416329 | − | 0.909214i | \(-0.636684\pi\) | ||||
−0.416329 | + | 0.909214i | \(0.636684\pi\) | |||||||
\(152\) | − 1.15586e16i | − 0.00329030i | ||||||||
\(153\) | 3.55943e18i | 0.958303i | ||||||||
\(154\) | −1.83274e18 | −0.466848 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.00468e17 | −0.182719 | ||||||||
\(157\) | − 3.81235e18i | − 0.824225i | −0.911133 | − | 0.412112i | \(-0.864791\pi\) | ||||
0.911133 | − | 0.412112i | \(-0.135209\pi\) | |||||||
\(158\) | 1.39615e18i | 0.285988i | ||||||||
\(159\) | −5.26842e18 | −1.02283 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.95942e18 | 1.73866 | ||||||||
\(162\) | 1.03332e18i | 0.171142i | ||||||||
\(163\) | − 1.03773e19i | − 1.63114i | −0.578658 | − | 0.815570i | \(-0.696423\pi\) | ||||
0.578658 | − | 0.815570i | \(-0.303577\pi\) | |||||||
\(164\) | 3.77740e18 | 0.563665 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.33690e17 | 0.125685 | ||||||||
\(167\) | 1.21920e19i | 1.55949i | 0.626095 | + | 0.779747i | \(0.284652\pi\) | ||||
−0.626095 | + | 0.779747i | \(0.715348\pi\) | |||||||
\(168\) | 3.41995e18i | 0.415806i | ||||||||
\(169\) | 6.32145e18 | 0.730768 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.48391e16 | −0.00469019 | ||||||||
\(172\) | 4.96161e18i | 0.493890i | ||||||||
\(173\) | 3.88210e18i | 0.367853i | 0.982940 | + | 0.183927i | \(0.0588809\pi\) | ||||
−0.982940 | + | 0.183927i | \(0.941119\pi\) | |||||||
\(174\) | 1.04957e19 | 0.946983 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.20727e18 | −0.0988430 | ||||||||
\(177\) | − 2.38735e18i | − 0.186270i | ||||||||
\(178\) | 1.74539e17i | 0.0129814i | ||||||||
\(179\) | 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 | \(0.769527\pi\) | |||||||
\(182\) | 9.95039e18i | 0.612680i | ||||||||
\(183\) | − 6.80799e18i | − 0.400115i | ||||||||
\(184\) | 6.56048e18 | 0.368116 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.49817e17 | 0.00766832 | ||||||||
\(187\) | − 1.53728e19i | − 0.751793i | ||||||||
\(188\) | 3.01696e18i | 0.141003i | ||||||||
\(189\) | 3.95915e19 | 1.76879 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.47928e19 | 1.82989 | 0.914944 | − | 0.403580i | \(-0.132234\pi\) | ||||
0.914944 | + | 0.403580i | \(0.132234\pi\) | |||||||
\(192\) | 2.25279e18i | 0.0880362i | ||||||||
\(193\) | − 3.61154e19i | − 1.35038i | −0.737645 | − | 0.675189i | \(-0.764062\pi\) | ||||
0.737645 | − | 0.675189i | \(-0.235938\pi\) | |||||||
\(194\) | −3.08154e19 | −1.10269 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.72668e19 | 0.894247 | ||||||||
\(197\) | − 1.80503e19i | − 0.566920i | −0.958984 | − | 0.283460i | \(-0.908518\pi\) | ||||
0.958984 | − | 0.283460i | \(-0.0914823\pi\) | |||||||
\(198\) | 4.68333e18i | 0.140897i | ||||||||
\(199\) | 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 | ||||||||
\(202\) | − 1.98168e19i | − 0.502975i | ||||||||
\(203\) | − 1.30469e20i | − 3.17535i | ||||||||
\(204\) | −2.86860e19 | −0.669597 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.56631e19 | 0.766211 | ||||||||
\(207\) | − 2.54500e19i | − 0.524734i | ||||||||
\(208\) | 6.55453e18i | 0.129719i | ||||||||
\(209\) | 1.93655e17 | 0.00367948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.72101e18 | 0.135292 | 0.0676462 | − | 0.997709i | \(-0.478451\pi\) | ||||
0.0676462 | + | 0.997709i | \(0.478451\pi\) | |||||||
\(212\) | 4.31398e19i | 0.726145i | ||||||||
\(213\) | − 4.33369e18i | − 0.0700860i | ||||||||
\(214\) | 7.05695e19 | 1.09673 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.60798e19 | 0.374496 | ||||||||
\(217\) | − 1.86233e18i | − 0.0257128i | ||||||||
\(218\) | 3.52127e19i | 0.467541i | ||||||||
\(219\) | 5.73733e19 | 0.732715 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.34623e19 | −0.986634 | ||||||||
\(222\) | 1.39661e19i | 0.158882i | ||||||||
\(223\) | 1.08588e20i | 1.18902i | 0.804088 | + | 0.594510i | \(0.202654\pi\) | ||||
−0.804088 | + | 0.594510i | \(0.797346\pi\) | |||||||
\(224\) | 2.80039e19 | 0.295196 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.99061e19 | 0.976495 | ||||||||
\(227\) | 1.95539e19i | 0.184083i | 0.995755 | + | 0.0920415i | \(0.0293392\pi\) | ||||
−0.995755 | + | 0.0920415i | \(0.970661\pi\) | |||||||
\(228\) | − 3.61366e17i | − 0.00327719i | ||||||||
\(229\) | −1.20601e20 | −1.05378 | −0.526890 | − | 0.849933i | \(-0.676642\pi\) | ||||
−0.526890 | + | 0.849933i | \(0.676642\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.72986e19 | −0.464988 | ||||||||
\(232\) | − 8.59427e19i | − 0.672297i | ||||||||
\(233\) | − 7.20388e19i | − 0.543302i | −0.962396 | − | 0.271651i | \(-0.912430\pi\) | ||||
0.962396 | − | 0.271651i | \(-0.0875696\pi\) | |||||||
\(234\) | 2.54269e19 | 0.184909 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.95485e19 | −0.132240 | ||||||||
\(237\) | 4.36491e19i | 0.284849i | ||||||||
\(238\) | 3.56588e20i | 2.24524i | ||||||||
\(239\) | −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 | \(0.660940\pi\) | |||||||
\(242\) | 1.09168e20i | 0.596573i | ||||||||
\(243\) | − 1.68440e20i | − 0.888775i | ||||||||
\(244\) | −5.57464e19 | −0.284056 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.18096e20 | 0.561419 | ||||||||
\(247\) | − 1.05140e18i | − 0.00482885i | ||||||||
\(248\) | − 1.22676e18i | − 0.00544401i | ||||||||
\(249\) | 2.91907e19 | 0.125184 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.85831e20 | 0.744546 | 0.372273 | − | 0.928123i | \(-0.378578\pi\) | ||||
0.372273 | + | 0.928123i | \(0.378578\pi\) | |||||||
\(252\) | − 1.08635e20i | − 0.420790i | ||||||||
\(253\) | 1.09916e20i | 0.411657i | ||||||||
\(254\) | −1.88883e20 | −0.684078 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | 1.68273e19i | 0.0551547i | 0.999620 | + | 0.0275773i | \(0.00877925\pi\) | ||||
−0.999620 | + | 0.0275773i | \(0.991221\pi\) | |||||||
\(258\) | 1.55119e20i | 0.491923i | ||||||||
\(259\) | 1.73609e20 | 0.532750 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.33396e20 | −0.958333 | ||||||||
\(262\) | 3.72245e20i | 1.03578i | ||||||||
\(263\) | − 2.77268e20i | − 0.746924i | −0.927645 | − | 0.373462i | \(-0.878171\pi\) | ||||
0.927645 | − | 0.373462i | \(-0.121829\pi\) | |||||||
\(264\) | −3.77438e19 | −0.0984491 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.49204e18 | −0.0109888 | ||||||||
\(267\) | 5.45675e18i | 0.0129297i | ||||||||
\(268\) | 4.01714e20i | 0.922085i | ||||||||
\(269\) | −9.40799e19 | −0.209220 | −0.104610 | − | 0.994513i | \(-0.533359\pi\) | ||||
−0.104610 | + | 0.994513i | \(0.533359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.17628e20 | −1.28970 | −0.644849 | − | 0.764310i | \(-0.723080\pi\) | ||||
−0.644849 | + | 0.764310i | \(0.723080\pi\) | |||||||
\(272\) | 2.34892e20i | 0.475371i | ||||||||
\(273\) | 3.11087e20i | 0.610238i | ||||||||
\(274\) | −5.82488e20 | −1.10766 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.05106e20 | 0.366649 | ||||||||
\(277\) | − 6.67865e20i | − 1.15774i | −0.815420 | − | 0.578869i | \(-0.803494\pi\) | ||||
0.815420 | − | 0.578869i | \(-0.196506\pi\) | |||||||
\(278\) | 3.62491e19i | 0.0609419i | ||||||||
\(279\) | −4.75894e18 | −0.00776023 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.13640e20 | −0.174393 | −0.0871963 | − | 0.996191i | \(-0.527791\pi\) | ||||
−0.0871963 | + | 0.996191i | \(0.527791\pi\) | |||||||
\(282\) | 9.43216e19i | 0.140441i | ||||||||
\(283\) | 3.76957e20i | 0.544637i | 0.962207 | + | 0.272318i | \(0.0877904\pi\) | ||||
−0.962207 | + | 0.272318i | \(0.912210\pi\) | |||||||
\(284\) | −3.54859e19 | −0.0497565 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.09816e20 | −0.145062 | ||||||||
\(287\) | − 1.46802e21i | − 1.88250i | ||||||||
\(288\) | − 7.15602e19i | − 0.0890913i | ||||||||
\(289\) | −2.16376e21 | −2.61564 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.63408e20 | −1.09830 | ||||||||
\(292\) | − 4.69794e20i | − 0.520180i | ||||||||
\(293\) | 3.57350e20i | 0.384344i | 0.981361 | + | 0.192172i | \(0.0615531\pi\) | ||||
−0.981361 | + | 0.192172i | \(0.938447\pi\) | |||||||
\(294\) | 8.52464e20 | 0.890684 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.14360e20 | 0.112796 | ||||||||
\(297\) | 4.36946e20i | 0.418792i | ||||||||
\(298\) | − 3.35589e20i | − 0.312586i | ||||||||
\(299\) | 5.96757e20 | 0.540247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.92824e21 | 1.64947 | ||||||||
\(302\) | 7.07963e20i | 0.588778i | ||||||||
\(303\) | − 6.19547e20i | − 0.500971i | ||||||||
\(304\) | −2.95900e18 | −0.00232659 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.11213e20 | 0.677623 | ||||||||
\(307\) | 2.25658e21i | 1.63220i | 0.577908 | + | 0.816102i | \(0.303869\pi\) | ||||
−0.577908 | + | 0.816102i | \(0.696131\pi\) | |||||||
\(308\) | 4.69182e20i | 0.330112i | ||||||||
\(309\) | 1.11497e21 | 0.763158 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.76844e20 | 0.373762 | 0.186881 | − | 0.982383i | \(-0.440162\pi\) | ||||
0.186881 | + | 0.982383i | \(0.440162\pi\) | |||||||
\(312\) | 2.04920e20i | 0.129202i | ||||||||
\(313\) | − 2.63218e21i | − 1.61506i | −0.589827 | − | 0.807530i | \(-0.700804\pi\) | ||||
0.589827 | − | 0.807530i | \(-0.299196\pi\) | |||||||
\(314\) | −9.75961e20 | −0.582815 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.57415e20 | 0.202224 | ||||||||
\(317\) | − 9.95998e20i | − 0.548599i | −0.961644 | − | 0.274299i | \(-0.911554\pi\) | ||||
0.961644 | − | 0.274299i | \(-0.0884459\pi\) | |||||||
\(318\) | 1.34871e21i | 0.723252i | ||||||||
\(319\) | 1.43990e21 | 0.751817 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.20627e21 | 1.09236 | ||||||||
\(322\) | − 2.54961e21i | − 1.22942i | ||||||||
\(323\) | − 3.76786e19i | − 0.0176959i | ||||||||
\(324\) | 2.64529e20 | 0.121016 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.65660e21 | −1.15339 | ||||||||
\(327\) | 1.10088e21i | 0.465678i | ||||||||
\(328\) | − 9.67016e20i | − 0.398571i | ||||||||
\(329\) | 1.17249e21 | 0.470915 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.56520e21 | −1.36002 | −0.680011 | − | 0.733202i | \(-0.738025\pi\) | ||||
−0.680011 | + | 0.733202i | \(0.738025\pi\) | |||||||
\(332\) | − 2.39025e20i | − 0.0888728i | ||||||||
\(333\) | − 4.43634e20i | − 0.160786i | ||||||||
\(334\) | 3.12114e21 | 1.10273 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.75508e20 | 0.294019 | ||||||||
\(337\) | 3.65283e20i | 0.119612i | 0.998210 | + | 0.0598060i | \(0.0190482\pi\) | ||||
−0.998210 | + | 0.0598060i | \(0.980952\pi\) | |||||||
\(338\) | − 1.61829e21i | − 0.516731i | ||||||||
\(339\) | 3.12344e21 | 0.972605 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.05533e19 | 0.00608793 | ||||||||
\(342\) | 1.14788e19i | 0.00331646i | ||||||||
\(343\) | − 4.67180e21i | − 1.31669i | ||||||||
\(344\) | 1.27017e21 | 0.349233 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.93818e20 | 0.260112 | ||||||||
\(347\) | − 2.06934e21i | − 0.528483i | −0.964457 | − | 0.264242i | \(-0.914878\pi\) | ||||
0.964457 | − | 0.264242i | \(-0.0851217\pi\) | |||||||
\(348\) | − 2.68690e21i | − 0.669618i | ||||||||
\(349\) | −3.13803e20 | −0.0763204 | −0.0381602 | − | 0.999272i | \(-0.512150\pi\) | ||||
−0.0381602 | + | 0.999272i | \(0.512150\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.37228e21 | 0.549611 | ||||||||
\(352\) | 3.09060e20i | 0.0698925i | ||||||||
\(353\) | 6.87901e21i | 1.51859i | 0.650746 | + | 0.759296i | \(0.274456\pi\) | ||||
−0.650746 | + | 0.759296i | \(0.725544\pi\) | |||||||
\(354\) | −6.11161e20 | −0.131713 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.46820e19 | 0.00917925 | ||||||||
\(357\) | 1.11483e22i | 2.23629i | ||||||||
\(358\) | − 4.15625e21i | − 0.814134i | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 5.94420e21i | 1.05943i | ||||||||
\(363\) | 3.41300e21i | 0.594196i | ||||||||
\(364\) | 2.54730e21 | 0.433230 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.74285e21 | −0.282924 | ||||||||
\(367\) | 1.88008e20i | 0.0298205i | 0.999889 | + | 0.0149103i | \(0.00474626\pi\) | ||||
−0.999889 | + | 0.0149103i | \(0.995254\pi\) | |||||||
\(368\) | − 1.67948e21i | − 0.260297i | ||||||||
\(369\) | −3.75133e21 | −0.568147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.67655e22 | 2.42515 | ||||||||
\(372\) | − 3.83531e19i | − 0.00542232i | ||||||||
\(373\) | − 9.66745e20i | − 0.133594i | −0.997767 | − | 0.0667970i | \(-0.978722\pi\) | ||||
0.997767 | − | 0.0667970i | \(-0.0212780\pi\) | |||||||
\(374\) | −3.93543e21 | −0.531598 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.72342e20 | 0.0997040 | ||||||||
\(377\) | − 7.81756e21i | − 0.986665i | ||||||||
\(378\) | − 1.01354e22i | − 1.25073i | ||||||||
\(379\) | −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 | ||||||||
\(382\) | − 1.14670e22i | − 1.29393i | ||||||||
\(383\) | 9.48135e21i | 1.04636i | 0.852223 | + | 0.523179i | \(0.175254\pi\) | ||||
−0.852223 | + | 0.523179i | \(0.824746\pi\) | |||||||
\(384\) | 5.76715e20 | 0.0622510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.24554e21 | −0.954861 | ||||||||
\(387\) | − 4.92736e21i | − 0.497818i | ||||||||
\(388\) | 7.88875e21i | 0.779720i | ||||||||
\(389\) | −8.68048e21 | −0.839406 | −0.419703 | − | 0.907661i | \(-0.637866\pi\) | ||||
−0.419703 | + | 0.907661i | \(0.637866\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.13857e22 | 1.97980 | ||||||||
\(392\) | − 6.98030e21i | − 0.632328i | ||||||||
\(393\) | 1.16378e22i | 1.03166i | ||||||||
\(394\) | −4.62088e21 | −0.400873 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.19893e21 | 0.0996291 | ||||||||
\(397\) | − 5.61938e21i | − 0.457055i | −0.973537 | − | 0.228528i | \(-0.926609\pi\) | ||||
0.973537 | − | 0.228528i | \(-0.0733911\pi\) | |||||||
\(398\) | − 1.63747e21i | − 0.130367i | ||||||||
\(399\) | −1.40438e20 | −0.0109450 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.97857e21 | −0.371858 | −0.185929 | − | 0.982563i | \(-0.559530\pi\) | ||||
−0.185929 | + | 0.982563i | \(0.559530\pi\) | |||||||
\(402\) | 1.25591e22i | 0.918411i | ||||||||
\(403\) | − 1.11589e20i | − 0.00798965i | ||||||||
\(404\) | −5.07309e21 | −0.355657 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.34001e22 | −2.24531 | ||||||||
\(407\) | 1.91600e21i | 0.126137i | ||||||||
\(408\) | 7.34362e21i | 0.473477i | ||||||||
\(409\) | −2.65693e20 | −0.0167777 | −0.00838883 | − | 0.999965i | \(-0.502670\pi\) | ||||
−0.00838883 | + | 0.999965i | \(0.502670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.82108e22 | −1.10325 | ||||||||
\(412\) | − 9.12977e21i | − 0.541793i | ||||||||
\(413\) | 7.59717e21i | 0.441648i | ||||||||
\(414\) | −6.51519e21 | −0.371043 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.67796e21 | 0.0917252 | ||||||||
\(417\) | 1.13328e21i | 0.0606991i | ||||||||
\(418\) | − 4.95757e19i | − 0.00260178i | ||||||||
\(419\) | −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 | \(0.265758\pi\) | |||||||
\(422\) | − 1.97658e21i | − 0.0956662i | ||||||||
\(423\) | − 2.99613e21i | − 0.142124i | ||||||||
\(424\) | 1.10438e22 | 0.513462 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.10942e21 | −0.0495583 | ||||||||
\(427\) | 2.16648e22i | 0.948677i | ||||||||
\(428\) | − 1.80658e22i | − 0.775505i | ||||||||
\(429\) | −3.43327e21 | −0.144484 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.34759e22 | −0.949656 | −0.474828 | − | 0.880079i | \(-0.657490\pi\) | ||||
−0.474828 | + | 0.880079i | \(0.657490\pi\) | |||||||
\(432\) | − 6.67643e21i | − 0.264809i | ||||||||
\(433\) | 1.88732e22i | 0.734003i | 0.930220 | + | 0.367002i | \(0.119616\pi\) | ||||
−0.930220 | + | 0.367002i | \(0.880384\pi\) | |||||||
\(434\) | −4.76757e20 | −0.0181817 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.01446e21 | 0.330601 | ||||||||
\(437\) | 2.69402e20i | 0.00968968i | ||||||||
\(438\) | − 1.46876e22i | − 0.518107i | ||||||||
\(439\) | −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 | ||||||||
\(442\) | 2.13664e22i | 0.697656i | ||||||||
\(443\) | 1.20735e22i | 0.386723i | 0.981128 | + | 0.193362i | \(0.0619391\pi\) | ||||
−0.981128 | + | 0.193362i | \(0.938061\pi\) | |||||||
\(444\) | 3.57532e21 | 0.112346 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.77984e22 | 0.840764 | ||||||||
\(447\) | − 1.04918e22i | − 0.311341i | ||||||||
\(448\) | − 7.16899e21i | − 0.208735i | ||||||||
\(449\) | −2.57466e22 | −0.735573 | −0.367787 | − | 0.929910i | \(-0.619884\pi\) | ||||
−0.367787 | + | 0.929910i | \(0.619884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.62016e22 | 0.445714 | ||||||||
\(452\) | − 2.55760e22i | − 0.690486i | ||||||||
\(453\) | 2.21336e22i | 0.586432i | ||||||||
\(454\) | 5.00580e21 | 0.130166 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.25097e19 | −0.00231732 | ||||||||
\(457\) | − 1.01069e22i | − 0.248503i | −0.992251 | − | 0.124252i | \(-0.960347\pi\) | ||||
0.992251 | − | 0.124252i | \(-0.0396530\pi\) | |||||||
\(458\) | 3.08739e22i | 0.745136i | ||||||||
\(459\) | 8.50144e22 | 2.01412 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.68599e21 | 0.0384942 | 0.0192471 | − | 0.999815i | \(-0.493873\pi\) | ||||
0.0192471 | + | 0.999815i | \(0.493873\pi\) | |||||||
\(462\) | 1.46684e22i | 0.328796i | ||||||||
\(463\) | 2.77945e22i | 0.611674i | 0.952084 | + | 0.305837i | \(0.0989363\pi\) | ||||
−0.952084 | + | 0.305837i | \(0.901064\pi\) | |||||||
\(464\) | −2.20013e22 | −0.475386 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.84419e22 | −0.384172 | ||||||||
\(467\) | 8.26643e22i | 1.69093i | 0.534034 | + | 0.845463i | \(0.320676\pi\) | ||||
−0.534034 | + | 0.845463i | \(0.679324\pi\) | |||||||
\(468\) | − 6.50929e21i | − 0.130751i | ||||||||
\(469\) | 1.56119e23 | 3.07954 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.05123e22 | −0.580493 | ||||||||
\(472\) | 5.00442e21i | 0.0935075i | ||||||||
\(473\) | 2.12807e22i | 0.390541i | ||||||||
\(474\) | 1.11742e22 | 0.201418 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.12865e22 | 1.58762 | ||||||||
\(477\) | − 4.28420e22i | − 0.731920i | ||||||||
\(478\) | 4.36287e22i | 0.732209i | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 4.38091e22i | 0.684960i | ||||||||
\(483\) | − 7.97106e22i | − 1.22452i | ||||||||
\(484\) | 2.79469e22 | 0.421841 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.31206e22 | −0.628459 | ||||||||
\(487\) | − 4.14828e22i | − 0.594116i | −0.954859 | − | 0.297058i | \(-0.903994\pi\) | ||||
0.954859 | − | 0.297058i | \(-0.0960055\pi\) | |||||||
\(488\) | 1.42711e22i | 0.200858i | ||||||||
\(489\) | −8.30554e22 | −1.14879 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.08644e22 | 0.412349 | 0.206174 | − | 0.978515i | \(-0.433899\pi\) | ||||
0.206174 | + | 0.978515i | \(0.433899\pi\) | |||||||
\(492\) | − 3.02326e22i | − 0.396983i | ||||||||
\(493\) | − 2.80155e23i | − 3.61575i | ||||||||
\(494\) | −2.69158e20 | −0.00341451 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.14050e20 | −0.00384950 | ||||||||
\(497\) | 1.37910e22i | 0.166175i | ||||||||
\(498\) | − 7.47282e21i | − 0.0885187i | ||||||||
\(499\) | −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 | ||||||||
\(502\) | − 4.75728e22i | − 0.526474i | ||||||||
\(503\) | − 6.39324e22i | − 0.695654i | −0.937559 | − | 0.347827i | \(-0.886920\pi\) | ||||
0.937559 | − | 0.347827i | \(-0.113080\pi\) | |||||||
\(504\) | −2.78106e22 | −0.297543 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.81384e22 | 0.291085 | ||||||||
\(507\) | − 5.05939e22i | − 0.514672i | ||||||||
\(508\) | 4.83540e22i | 0.483717i | ||||||||
\(509\) | 9.33355e22 | 0.918218 | 0.459109 | − | 0.888380i | \(-0.348169\pi\) | ||||
0.459109 | + | 0.888380i | \(0.348169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.82577e23 | −1.73728 | ||||||||
\(512\) | − 4.72237e21i | − 0.0441942i | ||||||||
\(513\) | 1.07095e21i | 0.00985763i | ||||||||
\(514\) | 4.30778e21 | 0.0390003 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.97104e22 | 0.347842 | ||||||||
\(517\) | 1.29400e22i | 0.111497i | ||||||||
\(518\) | − 4.44438e22i | − 0.376711i | ||||||||
\(519\) | 3.10705e22 | 0.259075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.30201e22 | 0.266476 | 0.133238 | − | 0.991084i | \(-0.457463\pi\) | ||||
0.133238 | + | 0.991084i | \(0.457463\pi\) | |||||||
\(522\) | 8.53495e22i | 0.677644i | ||||||||
\(523\) | − 4.06002e22i | − 0.317149i | −0.987347 | − | 0.158575i | \(-0.949310\pi\) | ||||
0.987347 | − | 0.158575i | \(-0.0506898\pi\) | |||||||
\(524\) | 9.52948e22 | 0.732409 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.09807e22 | −0.528155 | ||||||||
\(527\) | − 3.99896e21i | − 0.0292790i | ||||||||
\(528\) | 9.66240e21i | 0.0696140i | ||||||||
\(529\) | −1.18585e22 | −0.0840729 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.94136e22 | 0.133291 | ||||||||
\(532\) | 1.14996e21i | 0.00777025i | ||||||||
\(533\) | − 8.79621e22i | − 0.584944i | ||||||||
\(534\) | 1.39693e21 | 0.00914268 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.02839e23 | 0.652013 | ||||||||
\(537\) | − 1.29940e23i | − 0.810890i | ||||||||
\(538\) | 2.40844e22i | 0.147941i | ||||||||
\(539\) | 1.16949e23 | 0.707121 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.20460e22 | −0.246347 | −0.123174 | − | 0.992385i | \(-0.539307\pi\) | ||||
−0.123174 | + | 0.992385i | \(0.539307\pi\) | |||||||
\(542\) | 1.58113e23i | 0.911954i | ||||||||
\(543\) | 1.85838e23i | 1.05520i | ||||||||
\(544\) | 6.01324e22 | 0.336138 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.96383e22 | 0.431504 | ||||||||
\(547\) | − 2.01110e23i | − 1.07285i | −0.843947 | − | 0.536427i | \(-0.819774\pi\) | ||||
0.843947 | − | 0.536427i | \(-0.180226\pi\) | |||||||
\(548\) | 1.49117e23i | 0.783236i | ||||||||
\(549\) | 5.53616e22 | 0.286315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.52919e21 | 0.0176965 | ||||||||
\(552\) | − 5.25070e22i | − 0.259260i | ||||||||
\(553\) | − 1.38903e23i | − 0.675380i | ||||||||
\(554\) | −1.70973e23 | −0.818645 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.27976e21 | 0.0430924 | ||||||||
\(557\) | 1.46727e23i | 0.671030i | 0.942035 | + | 0.335515i | \(0.108910\pi\) | ||||
−0.942035 | + | 0.335515i | \(0.891090\pi\) | |||||||
\(558\) | 1.21829e21i | 0.00548731i | ||||||||
\(559\) | 1.15538e23 | 0.512536 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23036e23 | −0.529480 | ||||||||
\(562\) | 2.90919e22i | 0.123314i | ||||||||
\(563\) | 3.39706e23i | 1.41834i | 0.705036 | + | 0.709172i | \(0.250931\pi\) | ||||
−0.705036 | + | 0.709172i | \(0.749069\pi\) | |||||||
\(564\) | 2.41463e22 | 0.0993068 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.65010e22 | 0.385116 | ||||||||
\(567\) | − 1.02805e23i | − 0.404163i | ||||||||
\(568\) | 9.08439e21i | 0.0351832i | ||||||||
\(569\) | −2.72602e23 | −1.04010 | −0.520050 | − | 0.854136i | \(-0.674087\pi\) | ||||
−0.520050 | + | 0.854136i | \(0.674087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.79882e22 | −0.103650 | −0.0518249 | − | 0.998656i | \(-0.516504\pi\) | ||||
−0.0518249 | + | 0.998656i | \(0.516504\pi\) | |||||||
\(572\) | 2.81129e22i | 0.102574i | ||||||||
\(573\) | − 3.58501e23i | − 1.28877i | ||||||||
\(574\) | −3.75813e23 | −1.33113 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.83194e22 | −0.0629971 | ||||||||
\(577\) | 3.86678e23i | 1.31025i | 0.755519 | + | 0.655127i | \(0.227385\pi\) | ||||
−0.755519 | + | 0.655127i | \(0.772615\pi\) | |||||||
\(578\) | 5.53923e23i | 1.84954i | ||||||||
\(579\) | −2.89051e23 | −0.951056 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.28926e22 | −0.296814 | ||||||||
\(582\) | 2.46632e23i | 0.776613i | ||||||||
\(583\) | 1.85030e23i | 0.574195i | ||||||||
\(584\) | −1.20267e23 | −0.367823 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.14817e22 | 0.271772 | ||||||||
\(587\) | 3.64152e23i | 1.06625i | 0.846036 | + | 0.533125i | \(0.178983\pi\) | ||||
−0.846036 | + | 0.533125i | \(0.821017\pi\) | |||||||
\(588\) | − 2.18231e23i | − 0.629809i | ||||||||
\(589\) | 5.03761e19 | 0.000143299 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.44466e23 | −0.399276 | ||||||||
\(592\) | − 2.92761e22i | − 0.0797587i | ||||||||
\(593\) | 6.86689e23i | 1.84415i | 0.387017 | + | 0.922073i | \(0.373506\pi\) | ||||
−0.387017 | + | 0.922073i | \(0.626494\pi\) | |||||||
\(594\) | 1.11858e23 | 0.296130 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.59108e22 | −0.221032 | ||||||||
\(597\) | − 5.11935e22i | − 0.129847i | ||||||||
\(598\) | − 1.52770e23i | − 0.382013i | ||||||||
\(599\) | 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 | \(0.603417\pi\) | |||||||
\(602\) | − 4.93629e23i | − 1.16635i | ||||||||
\(603\) | − 3.98941e23i | − 0.929418i | ||||||||
\(604\) | 1.81239e23 | 0.416329 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.58604e23 | −0.354240 | ||||||||
\(607\) | − 1.11277e23i | − 0.245076i | −0.992464 | − | 0.122538i | \(-0.960897\pi\) | ||||
0.992464 | − | 0.122538i | \(-0.0391034\pi\) | |||||||
\(608\) | 7.57505e20i | 0.00164515i | ||||||||
\(609\) | −1.04421e24 | −2.23636 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.02541e22 | 0.146326 | ||||||||
\(612\) | − 2.33271e23i | − 0.479152i | ||||||||
\(613\) | 3.91229e23i | 0.792532i | 0.918136 | + | 0.396266i | \(0.129694\pi\) | ||||
−0.918136 | + | 0.396266i | \(0.870306\pi\) | |||||||
\(614\) | 5.77684e23 | 1.15414 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.20111e23 | 0.233424 | ||||||||
\(617\) | − 5.72626e23i | − 1.09761i | −0.835951 | − | 0.548804i | \(-0.815083\pi\) | ||||
0.835951 | − | 0.548804i | \(-0.184917\pi\) | |||||||
\(618\) | − 2.85431e23i | − 0.539634i | ||||||||
\(619\) | −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 | ||||||||
\(622\) | − 1.47672e23i | − 0.264290i | ||||||||
\(623\) | − 1.73648e22i | − 0.0306565i | ||||||||
\(624\) | 5.24594e22 | 0.0913597 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.73838e23 | −1.14202 | ||||||||
\(627\) | − 1.54993e21i | − 0.00259142i | ||||||||
\(628\) | 2.49846e23i | 0.412112i | ||||||||
\(629\) | 3.72788e23 | 0.606640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.52712e23 | 1.03389 | 0.516943 | − | 0.856020i | \(-0.327070\pi\) | ||||
0.516943 | + | 0.856020i | \(0.327070\pi\) | |||||||
\(632\) | − 9.14983e22i | − 0.142994i | ||||||||
\(633\) | − 6.17954e22i | − 0.0952850i | ||||||||
\(634\) | −2.54975e23 | −0.387918 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.45271e23 | 0.511416 | ||||||||
\(637\) | − 6.34945e23i | − 0.928007i | ||||||||
\(638\) | − 3.68615e23i | − 0.531615i | ||||||||
\(639\) | 3.52410e22 | 0.0501522 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.10734e23 | 0.984950 | 0.492475 | − | 0.870327i | \(-0.336092\pi\) | ||||
0.492475 | + | 0.870327i | \(0.336092\pi\) | |||||||
\(642\) | − 5.64805e23i | − 0.772415i | ||||||||
\(643\) | − 2.34278e23i | − 0.316183i | −0.987424 | − | 0.158092i | \(-0.949466\pi\) | ||||
0.987424 | − | 0.158092i | \(-0.0505341\pi\) | |||||||
\(644\) | −6.52701e23 | −0.869329 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.64571e21 | −0.0125129 | ||||||||
\(647\) | 1.50806e23i | 0.193078i | 0.995329 | + | 0.0965391i | \(0.0307773\pi\) | ||||
−0.995329 | + | 0.0965391i | \(0.969223\pi\) | |||||||
\(648\) | − 6.77195e22i | − 0.0855710i | ||||||||
\(649\) | −8.38450e22 | −0.104568 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.49052e22 | −0.0181092 | ||||||||
\(652\) | 6.80089e23i | 0.815570i | ||||||||
\(653\) | − 6.74375e22i | − 0.0798251i | −0.999203 | − | 0.0399126i | \(-0.987292\pi\) | ||||
0.999203 | − | 0.0399126i | \(-0.0127079\pi\) | |||||||
\(654\) | 2.81826e23 | 0.329284 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.47556e23 | −0.281832 | ||||||||
\(657\) | 4.66551e23i | 0.524317i | ||||||||
\(658\) | − 3.00157e23i | − 0.332987i | ||||||||
\(659\) | −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 | \(0.138997\pi\) | |||||||
\(662\) | 9.12691e23i | 0.961680i | ||||||||
\(663\) | 6.67994e23i | 0.694876i | ||||||||
\(664\) | −6.11903e22 | −0.0628426 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.13570e23 | −0.113693 | ||||||||
\(667\) | 2.00311e24i | 1.97986i | ||||||||
\(668\) | − 7.99012e23i | − 0.779747i | ||||||||
\(669\) | 8.69085e23 | 0.837414 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.39101e23 | −0.224615 | ||||||||
\(672\) | − 2.24130e23i | − 0.207903i | ||||||||
\(673\) | 1.39848e24i | 1.28094i | 0.767984 | + | 0.640469i | \(0.221260\pi\) | ||||
−0.767984 | + | 0.640469i | \(0.778740\pi\) | |||||||
\(674\) | 9.35124e22 | 0.0845785 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.14282e23 | −0.365384 | ||||||||
\(677\) | − 9.38639e23i | − 0.817514i | −0.912643 | − | 0.408757i | \(-0.865962\pi\) | ||||
0.912643 | − | 0.408757i | \(-0.134038\pi\) | |||||||
\(678\) | − 7.99602e23i | − 0.687735i | ||||||||
\(679\) | 3.06582e24 | 2.60408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.56500e23 | 0.129648 | ||||||||
\(682\) | − 5.26165e21i | − 0.00430482i | ||||||||
\(683\) | − 1.23254e24i | − 0.995922i | −0.867199 | − | 0.497961i | \(-0.834082\pi\) | ||||
0.867199 | − | 0.497961i | \(-0.165918\pi\) | |||||||
\(684\) | 2.93858e21 | 0.00234509 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.19598e24 | −0.931041 | ||||||||
\(687\) | 9.65236e23i | 0.742167i | ||||||||
\(688\) | − 3.25164e23i | − 0.246945i | ||||||||
\(689\) | 1.00457e24 | 0.753559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.83055e23 | 0.280348 | 0.140174 | − | 0.990127i | \(-0.455234\pi\) | ||||
0.140174 | + | 0.990127i | \(0.455234\pi\) | |||||||
\(692\) | − 2.54417e23i | − 0.183927i | ||||||||
\(693\) | − 4.65944e23i | − 0.332737i | ||||||||
\(694\) | −5.29751e23 | −0.373694 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.87845e23 | −0.473492 | ||||||||
\(697\) | − 3.15226e24i | − 2.14360i | ||||||||
\(698\) | 8.03335e22i | 0.0539667i | ||||||||
\(699\) | −5.76565e23 | −0.382642 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.63235e24 | 1.05733 | 0.528665 | − | 0.848831i | \(-0.322693\pi\) | ||||
0.528665 | + | 0.848831i | \(0.322693\pi\) | |||||||
\(702\) | − 6.07304e23i | − 0.388634i | ||||||||
\(703\) | 4.69611e21i | 0.00296906i | ||||||||
\(704\) | 7.91195e22 | 0.0494215 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.76103e24 | 1.07381 | ||||||||
\(707\) | 1.97156e24i | 1.18781i | ||||||||
\(708\) | 1.56457e23i | 0.0931350i | ||||||||
\(709\) | 6.09431e23 | 0.358453 | 0.179226 | − | 0.983808i | \(-0.442641\pi\) | ||||
0.179226 | + | 0.983808i | \(0.442641\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.54948e23 | −0.203832 | ||||||||
\(712\) | − 1.14386e22i | − 0.00649071i | ||||||||
\(713\) | 2.85926e22i | 0.0160322i | ||||||||
\(714\) | 2.85396e24 | 1.58130 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.06400e24 | −0.575680 | ||||||||
\(717\) | 1.36400e24i | 0.729292i | ||||||||
\(718\) | − 2.43432e24i | − 1.28623i | ||||||||
\(719\) | 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 | ||||||||
\(722\) | 1.40286e24i | 0.707046i | ||||||||
\(723\) | 1.36964e24i | 0.682230i | ||||||||
\(724\) | 1.52171e24 | 0.749127 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.73727e23 | 0.420160 | ||||||||
\(727\) | − 5.00713e23i | − 0.237983i | −0.992895 | − | 0.118992i | \(-0.962034\pi\) | ||||
0.992895 | − | 0.118992i | \(-0.0379662\pi\) | |||||||
\(728\) | − 6.52109e23i | − 0.306340i | ||||||||
\(729\) | −1.86938e24 | −0.867986 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.14048e24 | 1.87825 | ||||||||
\(732\) | 4.46168e23i | 0.200057i | ||||||||
\(733\) | − 1.20329e24i | − 0.533320i | −0.963791 | − | 0.266660i | \(-0.914080\pi\) | ||||
0.963791 | − | 0.266660i | \(-0.0859201\pi\) | |||||||
\(734\) | 4.81301e22 | 0.0210863 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.29948e23 | −0.184058 | ||||||||
\(737\) | 1.72298e24i | 0.729133i | ||||||||
\(738\) | 9.60340e23i | 0.401741i | ||||||||
\(739\) | 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 | ||||||||
\(742\) | − 4.29197e24i | − 1.71484i | ||||||||
\(743\) | 9.89633e22i | 0.0390903i | 0.999809 | + | 0.0195452i | \(0.00622181\pi\) | ||||
−0.999809 | + | 0.0195452i | \(0.993778\pi\) | |||||||
\(744\) | −9.81839e21 | −0.00383416 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.47487e23 | −0.0944652 | ||||||||
\(747\) | 2.37375e23i | 0.0895796i | ||||||||
\(748\) | 1.00747e24i | 0.375897i | ||||||||
\(749\) | −7.02094e24 | −2.59000 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.01856e24 | −0.367322 | −0.183661 | − | 0.982990i | \(-0.558795\pi\) | ||||
−0.183661 | + | 0.982990i | \(0.558795\pi\) | |||||||
\(752\) | − 1.97719e23i | − 0.0705014i | ||||||||
\(753\) | − 1.48731e24i | − 0.524376i | ||||||||
\(754\) | −2.00130e24 | −0.697677 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.59467e24 | −0.884397 | ||||||||
\(757\) | − 1.43989e24i | − 0.485305i | −0.970113 | − | 0.242653i | \(-0.921982\pi\) | ||||
0.970113 | − | 0.242653i | \(-0.0780175\pi\) | |||||||
\(758\) | 2.80263e24i | 0.934066i | ||||||||
\(759\) | 8.79713e23 | 0.289925 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.15424e23 | −0.230565 | −0.115283 | − | 0.993333i | \(-0.536777\pi\) | ||||
−0.115283 | + | 0.993333i | \(0.536777\pi\) | |||||||
\(762\) | 1.51173e24i | 0.481789i | ||||||||
\(763\) | − 3.50330e24i | − 1.10413i | ||||||||
\(764\) | −2.93554e24 | −0.914944 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.42722e24 | 0.739887 | ||||||||
\(767\) | 4.55214e23i | 0.137232i | ||||||||
\(768\) | − 1.47639e23i | − 0.0440181i | ||||||||
\(769\) | −1.87177e24 | −0.551922 | −0.275961 | − | 0.961169i | \(-0.588996\pi\) | ||||
−0.275961 | + | 0.961169i | \(0.588996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.34678e23 | 0.0388449 | ||||||||
\(772\) | 2.36686e24i | 0.675189i | ||||||||
\(773\) | 1.86999e24i | 0.527611i | 0.964576 | + | 0.263805i | \(0.0849777\pi\) | ||||
−0.964576 | + | 0.263805i | \(0.915022\pi\) | |||||||
\(774\) | −1.26140e24 | −0.352011 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.01952e24 | 0.551345 | ||||||||
\(777\) | − 1.38948e24i | − 0.375210i | ||||||||
\(778\) | 2.22220e24i | 0.593550i | ||||||||
\(779\) | 3.97099e22 | 0.0104913 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.52202e23 | −0.0393447 | ||||||||
\(782\) | − 5.47475e24i | − 1.39993i | ||||||||
\(783\) | 7.96294e24i | 2.01418i | ||||||||
\(784\) | −1.78696e24 | −0.447124 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.97928e24 | 0.729490 | ||||||||
\(787\) | − 3.29304e24i | − 0.797648i | −0.917027 | − | 0.398824i | \(-0.869418\pi\) | ||||
0.917027 | − | 0.398824i | \(-0.130582\pi\) | |||||||
\(788\) | 1.18295e24i | 0.283460i | ||||||||
\(789\) | −2.21913e24 | −0.526051 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.93963e24 | −2.30606 | ||||||||
\(792\) | − 3.06927e23i | − 0.0704484i | ||||||||
\(793\) | 1.29813e24i | 0.294779i | ||||||||
\(794\) | −1.43856e24 | −0.323187 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.19192e23 | −0.0921832 | ||||||||
\(797\) | − 3.80089e24i | − 0.826969i | −0.910511 | − | 0.413485i | \(-0.864312\pi\) | ||||
0.910511 | − | 0.413485i | \(-0.135688\pi\) | |||||||
\(798\) | 3.59522e22i | 0.00773929i | ||||||||
\(799\) | 2.51767e24 | 0.536229 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.43735e22 | −0.00925225 | ||||||||
\(802\) | 1.27451e24i | 0.262944i | ||||||||
\(803\) | − 2.01498e24i | − 0.411329i | ||||||||
\(804\) | 3.21513e24 | 0.649415 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.85667e22 | −0.00564953 | ||||||||
\(807\) | 7.52972e23i | 0.147351i | ||||||||
\(808\) | 1.29871e24i | 0.251487i | ||||||||
\(809\) | −1.38713e24 | −0.265799 | −0.132900 | − | 0.991129i | \(-0.542429\pi\) | ||||
−0.132900 | + | 0.991129i | \(0.542429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.43418e24 | 0.456747 | 0.228374 | − | 0.973574i | \(-0.426659\pi\) | ||||
0.228374 | + | 0.973574i | \(0.426659\pi\) | |||||||
\(812\) | 8.55042e24i | 1.58767i | ||||||||
\(813\) | 4.94321e24i | 0.908321i | ||||||||
\(814\) | 4.90497e23 | 0.0891926 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.87997e24 | 0.334799 | ||||||||
\(817\) | 5.21589e22i | 0.00919265i | ||||||||
\(818\) | 6.80174e22i | 0.0118636i | ||||||||
\(819\) | −2.52972e24 | −0.436675 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.07675e24 | −1.19651 | −0.598256 | − | 0.801305i | \(-0.704140\pi\) | ||||
−0.598256 | + | 0.801305i | \(0.704140\pi\) | |||||||
\(822\) | 4.66196e24i | 0.780115i | ||||||||
\(823\) | 5.31425e24i | 0.880124i | 0.897968 | + | 0.440062i | \(0.145043\pi\) | ||||
−0.897968 | + | 0.440062i | \(0.854957\pi\) | |||||||
\(824\) | −2.33722e24 | −0.383105 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.94488e24 | 0.312292 | ||||||||
\(827\) | 5.13487e24i | 0.816080i | 0.912964 | + | 0.408040i | \(0.133788\pi\) | ||||
−0.912964 | + | 0.408040i | \(0.866212\pi\) | |||||||
\(828\) | 1.66789e24i | 0.262367i | ||||||||
\(829\) | −1.06738e25 | −1.66191 | −0.830954 | − | 0.556341i | \(-0.812205\pi\) | ||||
−0.830954 | + | 0.556341i | \(0.812205\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.34528e24 | −0.815383 | ||||||||
\(832\) | − 4.29558e23i | − 0.0648595i | ||||||||
\(833\) | − 2.27543e25i | − 3.40079i | ||||||||
\(834\) | 2.90121e23 | 0.0429208 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.26914e22 | −0.00183974 | ||||||||
\(837\) | 1.13664e23i | 0.0163101i | ||||||||
\(838\) | 4.38380e24i | 0.622697i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | − 6.95908e24i | − 0.949290i | ||||||||
\(843\) | 9.09523e23i | 0.122823i | ||||||||
\(844\) | −5.06004e23 | −0.0676462 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.67010e23 | −0.100497 | ||||||||
\(847\) | − 1.08611e25i | − 1.40885i | ||||||||
\(848\) | − 2.82721e24i | − 0.363073i | ||||||||
\(849\) | 3.01699e24 | 0.383582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.66544e24 | −0.332175 | ||||||||
\(852\) | 2.84013e23i | 0.0350430i | ||||||||
\(853\) | − 2.69306e24i | − 0.328988i | −0.986378 | − | 0.164494i | \(-0.947401\pi\) | ||||
0.986378 | − | 0.164494i | \(-0.0525991\pi\) | |||||||
\(854\) | 5.54620e24 | 0.670816 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.62484e24 | −0.548365 | ||||||||
\(857\) | − 1.86785e24i | − 0.219283i | −0.993971 | − | 0.109641i | \(-0.965030\pi\) | ||||
0.993971 | − | 0.109641i | \(-0.0349702\pi\) | |||||||
\(858\) | 8.78916e23i | 0.102166i | ||||||||
\(859\) | 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 | ||||||||
\(862\) | 6.00984e24i | 0.671508i | ||||||||
\(863\) | 2.37061e24i | 0.262282i | 0.991364 | + | 0.131141i | \(0.0418640\pi\) | ||||
−0.991364 | + | 0.131141i | \(0.958136\pi\) | |||||||
\(864\) | −1.70917e24 | −0.187248 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.83153e24 | 0.519019 | ||||||||
\(867\) | 1.73178e25i | 1.84217i | ||||||||
\(868\) | 1.22050e23i | 0.0128564i | ||||||||
\(869\) | 1.53298e24 | 0.159907 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.35446e24 | 0.956895 | ||||||||
\(872\) | − 2.30770e24i | − 0.233770i | ||||||||
\(873\) | − 7.83429e24i | − 0.785921i | ||||||||
\(874\) | 6.89670e22 | 0.00685164 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.76002e24 | −0.366357 | ||||||||
\(877\) | − 6.79534e24i | − 0.655714i | −0.944727 | − | 0.327857i | \(-0.893674\pi\) | ||||
0.944727 | − | 0.327857i | \(-0.106326\pi\) | |||||||
\(878\) | 1.41285e25i | 1.35018i | ||||||||
\(879\) | 2.86007e24 | 0.270689 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.88402e25 | −1.74900 | −0.874501 | − | 0.485024i | \(-0.838811\pi\) | ||||
−0.874501 | + | 0.485024i | \(0.838811\pi\) | |||||||
\(882\) | 6.93212e24i | 0.637357i | ||||||||
\(883\) | − 3.85491e24i | − 0.351033i | −0.984476 | − | 0.175517i | \(-0.943840\pi\) | ||||
0.984476 | − | 0.175517i | \(-0.0561596\pi\) | |||||||
\(884\) | 5.46979e24 | 0.493317 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.09081e24 | 0.273455 | ||||||||
\(887\) | 8.32727e24i | 0.729712i | 0.931064 | + | 0.364856i | \(0.118882\pi\) | ||||
−0.931064 | + | 0.364856i | \(0.881118\pi\) | |||||||
\(888\) | − 9.15281e23i | − 0.0794410i | ||||||||
\(889\) | 1.87919e25 | 1.61550 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.13459e24 | 0.0956924 | ||||||||
\(892\) | − 7.11640e24i | − 0.594510i | ||||||||
\(893\) | 3.17158e22i | 0.00262445i | ||||||||
\(894\) | −2.68590e24 | −0.220151 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.83526e24 | −0.147598 | ||||||||
\(897\) | − 4.77617e24i | − 0.380491i | ||||||||
\(898\) | 6.59113e24i | 0.520129i | ||||||||
\(899\) | 3.74565e23 | 0.0292799 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.60004e25 | 2.76151 | ||||||||
\(902\) | − 4.14760e24i | − 0.315168i | ||||||||
\(903\) | − 1.54327e25i | − 1.16171i | ||||||||
\(904\) | −6.54744e24 | −0.488248 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.66621e24 | 0.414670 | ||||||||
\(907\) | 1.92435e25i | 1.39515i | 0.716511 | + | 0.697576i | \(0.245738\pi\) | ||||
−0.716511 | + | 0.697576i | \(0.754262\pi\) | |||||||
\(908\) | − 1.28148e24i | − 0.0920415i | ||||||||
\(909\) | 5.03807e24 | 0.358485 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.57682e25 | −1.10123 | −0.550613 | − | 0.834761i | \(-0.685606\pi\) | ||||
−0.550613 | + | 0.834761i | \(0.685606\pi\) | |||||||
\(912\) | 2.36825e22i | 0.00163859i | ||||||||
\(913\) | − 1.02519e24i | − 0.0702756i | ||||||||
\(914\) | −2.58738e24 | −0.175718 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.90373e24 | 0.526890 | ||||||||
\(917\) | − 3.70346e25i | − 2.44607i | ||||||||
\(918\) | − 2.17637e25i | − 1.42420i | ||||||||
\(919\) | −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 | ||||||||
\(922\) | − 4.31612e23i | − 0.0272195i | ||||||||
\(923\) | 8.26339e23i | 0.0516349i | ||||||||
\(924\) | 3.75512e24 | 0.232494 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.11539e24 | 0.432519 | ||||||||
\(927\) | 9.06674e24i | 0.546102i | ||||||||
\(928\) | 5.63234e24i | 0.336149i | ||||||||
\(929\) | −9.73688e24 | −0.575819 | −0.287910 | − | 0.957658i | \(-0.592960\pi\) | ||||
−0.287910 | + | 0.957658i | \(0.592960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.86642e23 | 0.0166444 | ||||||||
\(932\) | 4.72113e24i | 0.271651i | ||||||||
\(933\) | − 4.61679e24i | − 0.263236i | ||||||||
\(934\) | 2.11621e25 | 1.19567 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.66638e24 | −0.0924547 | ||||||||
\(937\) | − 3.22145e25i | − 1.77119i | −0.464459 | − | 0.885594i | \(-0.653751\pi\) | ||||
0.464459 | − | 0.885594i | \(-0.346249\pi\) | |||||||
\(938\) | − 3.99664e25i | − 2.17756i | ||||||||
\(939\) | −2.10667e25 | −1.13747 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.90374e24 | −0.419103 | −0.209552 | − | 0.977798i | \(-0.567200\pi\) | ||||
−0.209552 | + | 0.977798i | \(0.567200\pi\) | |||||||
\(942\) | 7.81114e24i | 0.410470i | ||||||||
\(943\) | 2.25387e25i | 1.17376i | ||||||||
\(944\) | 1.28113e24 | 0.0661198 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.44786e24 | 0.276154 | ||||||||
\(947\) | 2.36682e25i | 1.18902i | 0.804086 | + | 0.594512i | \(0.202655\pi\) | ||||
−0.804086 | + | 0.594512i | \(0.797345\pi\) | |||||||
\(948\) | − 2.86059e24i | − 0.142424i | ||||||||
\(949\) | −1.09398e25 | −0.539818 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.97150e24 | −0.386372 | ||||||||
\(952\) | − 2.33693e25i | − 1.12262i | ||||||||
\(953\) | − 9.09477e24i | − 0.433014i | −0.976281 | − | 0.216507i | \(-0.930534\pi\) | ||||
0.976281 | − | 0.216507i | \(-0.0694664\pi\) | |||||||
\(954\) | −1.09676e25 | −0.517546 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.11690e25 | 0.517750 | ||||||||
\(957\) | − 1.15243e25i | − 0.529496i | ||||||||
\(958\) | 6.63529e24i | 0.302171i | ||||||||
\(959\) | 5.79516e25 | 2.61582 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.25448e25 | −0.999763 | ||||||||
\(962\) | − 2.66302e24i | − 0.117054i | ||||||||
\(963\) | 1.79411e25i | 0.781673i | ||||||||
\(964\) | 1.12151e25 | 0.484340 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.04059e25 | −0.865865 | ||||||||
\(967\) | 3.62970e25i | 1.52667i | 0.646001 | + | 0.763337i | \(0.276440\pi\) | ||||
−0.646001 | + | 0.763337i | \(0.723560\pi\) | |||||||
\(968\) | − 7.15441e24i | − 0.298286i | ||||||||
\(969\) | −3.01562e23 | −0.0124630 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.70396e24 | −0.394081 | −0.197040 | − | 0.980395i | \(-0.563133\pi\) | ||||
−0.197040 | + | 0.980395i | \(0.563133\pi\) | |||||||
\(972\) | 1.10389e25i | 0.444387i | ||||||||
\(973\) | − 3.60641e24i | − 0.143918i | ||||||||
\(974\) | −1.06196e25 | −0.420104 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.65340e24 | 0.142028 | ||||||||
\(977\) | 3.70141e25i | 1.42647i | 0.700924 | + | 0.713236i | \(0.252771\pi\) | ||||
−0.700924 | + | 0.713236i | \(0.747229\pi\) | |||||||
\(978\) | 2.12622e25i | 0.812321i | ||||||||
\(979\) | 1.91644e23 | 0.00725843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.95223e24 | −0.333230 | ||||||||
\(982\) | − 7.90127e24i | − 0.291574i | ||||||||
\(983\) | 6.43184e24i | 0.235305i | 0.993055 | + | 0.117652i | \(0.0375368\pi\) | ||||
−0.993055 | + | 0.117652i | \(0.962463\pi\) | |||||||
\(984\) | −7.73954e24 | −0.280709 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.17196e25 | −2.55672 | ||||||||
\(987\) | − 9.38403e24i | − 0.331661i | ||||||||
\(988\) | 6.89045e22i | 0.00241442i | ||||||||
\(989\) | −2.96045e25 | −1.02847 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.17070e25 | 1.76573 | 0.882863 | − | 0.469631i | \(-0.155613\pi\) | ||||
0.882863 | + | 0.469631i | \(0.155613\pi\) | |||||||
\(992\) | 8.03967e22i | 0.00272201i | ||||||||
\(993\) | 2.85342e25i | 0.957848i | ||||||||
\(994\) | 3.53048e24 | 0.117503 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.91304e24 | −0.0625922 | ||||||||
\(997\) | − 2.77457e25i | − 0.900093i | −0.893005 | − | 0.450047i | \(-0.851407\pi\) | ||||
0.893005 | − | 0.450047i | \(-0.148593\pi\) | |||||||
\(998\) | 8.29907e24i | 0.266944i | ||||||||
\(999\) | −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 | 50.18.b.d.49.1 | 4 | ||
5.2 | odd | 4 | 50.18.a.f.1.1 | 2 | |||
5.3 | odd | 4 | 10.18.a.c.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 50.18.b.d.49.4 | 4 | ||
15.8 | even | 4 | 90.18.a.k.1.2 | 2 | |||
20.3 | even | 4 | 80.18.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.c.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
50.18.a.f.1.1 | 2 | 5.2 | odd | 4 | |||
50.18.b.d.49.1 | 4 | 1.1 | even | 1 | trivial | ||
50.18.b.d.49.4 | 4 | 5.4 | even | 2 | inner | ||
80.18.a.d.1.1 | 2 | 20.3 | even | 4 | |||
90.18.a.k.1.2 | 2 | 15.8 | even | 4 |