Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,9,Mod(8,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.8");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.66640749055\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.8 |
Dual form | 9.9.b.a.8.1 |
$q$-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 \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.24264i | 0.265165i | 0.991172 | + | 0.132583i | \(0.0423270\pi\) | ||||
−0.991172 | + | 0.132583i | \(0.957673\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 238.000 | 0.929688 | ||||||||
\(5\) | 988.535i | 1.58166i | 0.612038 | + | 0.790828i | \(0.290350\pi\) | ||||
−0.612038 | + | 0.790828i | \(0.709650\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1652.00 | 0.688047 | 0.344023 | − | 0.938961i | \(-0.388210\pi\) | ||||
0.344023 | + | 0.938961i | \(0.388210\pi\) | |||||||
\(8\) | 2095.86i | 0.511686i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4194.00 | −0.419400 | ||||||||
\(11\) | − 21365.9i | − 1.45932i | −0.683809 | − | 0.729661i | \(-0.739678\pi\) | ||||
0.683809 | − | 0.729661i | \(-0.260322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26272.0 | −0.919856 | −0.459928 | − | 0.887956i | \(-0.652125\pi\) | ||||
−0.459928 | + | 0.887956i | \(0.652125\pi\) | |||||||
\(14\) | 7008.84i | 0.182446i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 52036.0 | 0.794006 | ||||||||
\(17\) | 15184.4i | 0.181804i | 0.995860 | + | 0.0909018i | \(0.0289749\pi\) | ||||
−0.995860 | + | 0.0909018i | \(0.971025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 46640.0 | 0.357886 | 0.178943 | − | 0.983859i | \(-0.442732\pi\) | ||||
0.178943 | + | 0.983859i | \(0.442732\pi\) | |||||||
\(20\) | 235271.i | 1.47045i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 90648.0 | 0.386961 | ||||||||
\(23\) | − 328092.i | − 1.17242i | −0.810158 | − | 0.586211i | \(-0.800619\pi\) | ||||
0.810158 | − | 0.586211i | \(-0.199381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −586577. | −1.50164 | ||||||||
\(26\) | − 111463.i | − 0.243914i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 393176. | 0.639668 | ||||||||
\(29\) | − 614983.i | − 0.869504i | −0.900550 | − | 0.434752i | \(-0.856836\pi\) | ||||
0.900550 | − | 0.434752i | \(-0.143164\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −196444. | −0.212712 | −0.106356 | − | 0.994328i | \(-0.533918\pi\) | ||||
−0.106356 | + | 0.994328i | \(0.533918\pi\) | |||||||
\(32\) | 757311.i | 0.722228i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −64422.0 | −0.0482079 | ||||||||
\(35\) | 1.63306e6i | 1.08825i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.81941e6 | 1.50436 | 0.752180 | − | 0.658957i | \(-0.229002\pi\) | ||||
0.752180 | + | 0.658957i | \(0.229002\pi\) | |||||||
\(38\) | 197877.i | 0.0948987i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.07184e6 | −0.809311 | ||||||||
\(41\) | − 706429.i | − 0.249996i | −0.992157 | − | 0.124998i | \(-0.960108\pi\) | ||||
0.992157 | − | 0.124998i | \(-0.0398925\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.21346e6 | −0.647439 | −0.323719 | − | 0.946153i | \(-0.604933\pi\) | ||||
−0.323719 | + | 0.946153i | \(0.604933\pi\) | |||||||
\(44\) | − 5.08509e6i | − 1.35671i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.39198e6 | 0.310885 | ||||||||
\(47\) | 1.63296e6i | 0.334645i | 0.985902 | + | 0.167322i | \(0.0535120\pi\) | ||||
−0.985902 | + | 0.167322i | \(0.946488\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.03570e6 | −0.526592 | ||||||||
\(50\) | − 2.48864e6i | − 0.398182i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.25274e6 | −0.855178 | ||||||||
\(53\) | 5.18868e6i | 0.657587i | 0.944402 | + | 0.328793i | \(0.106642\pi\) | ||||
−0.944402 | + | 0.328793i | \(0.893358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.11210e7 | 2.30815 | ||||||||
\(56\) | 3.46237e6i | 0.352064i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.60915e6 | 0.230562 | ||||||||
\(59\) | 1.17447e7i | 0.969250i | 0.874722 | + | 0.484625i | \(0.161044\pi\) | ||||
−0.874722 | + | 0.484625i | \(0.838956\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.74053e7 | −1.25708 | −0.628539 | − | 0.777778i | \(-0.716347\pi\) | ||||
−0.628539 | + | 0.777778i | \(0.716347\pi\) | |||||||
\(62\) | − 833441.i | − 0.0564038i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.01082e7 | 0.602497 | ||||||||
\(65\) | − 2.59708e7i | − 1.45490i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.43227e7 | −0.710763 | −0.355381 | − | 0.934721i | \(-0.615649\pi\) | ||||
−0.355381 | + | 0.934721i | \(0.615649\pi\) | |||||||
\(68\) | 3.61389e6i | 0.169020i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.92849e6 | −0.288567 | ||||||||
\(71\) | − 1.56456e7i | − 0.615686i | −0.951437 | − | 0.307843i | \(-0.900393\pi\) | ||||
0.951437 | − | 0.307843i | \(-0.0996072\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.90699e6 | −0.313646 | −0.156823 | − | 0.987627i | \(-0.550125\pi\) | ||||
−0.156823 | + | 0.987627i | \(0.550125\pi\) | |||||||
\(74\) | 1.19618e7i | 0.398904i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.11003e7 | 0.332722 | ||||||||
\(77\) | − 3.52965e7i | − 1.00408i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.27588e7 | 0.841047 | 0.420523 | − | 0.907282i | \(-0.361846\pi\) | ||||
0.420523 | + | 0.907282i | \(0.361846\pi\) | |||||||
\(80\) | 5.14394e7i | 1.25585i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.99713e6 | 0.0662902 | ||||||||
\(83\) | 8.50888e7i | 1.79292i | 0.443128 | + | 0.896458i | \(0.353869\pi\) | ||||
−0.443128 | + | 0.896458i | \(0.646131\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.50103e7 | −0.287551 | ||||||||
\(86\) | − 9.39093e6i | − 0.171678i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.47801e7 | 0.746714 | ||||||||
\(89\) | − 5.89361e7i | − 0.939337i | −0.882843 | − | 0.469668i | \(-0.844373\pi\) | ||||
0.882843 | − | 0.469668i | \(-0.155627\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.34013e7 | −0.632904 | ||||||||
\(92\) | − 7.80859e7i | − 1.08999i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.92806e6 | −0.0887360 | ||||||||
\(95\) | 4.61053e7i | 0.566052i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.44517e7 | −0.276200 | −0.138100 | − | 0.990418i | \(-0.544099\pi\) | ||||
−0.138100 | + | 0.990418i | \(0.544099\pi\) | |||||||
\(98\) | − 1.28794e7i | − 0.139634i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.39605e8 | −1.39605 | ||||||||
\(101\) | − 1.02159e8i | − 0.981733i | −0.871235 | − | 0.490866i | \(-0.836680\pi\) | ||||
0.871235 | − | 0.490866i | \(-0.163320\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.64259e8 | 1.45942 | 0.729708 | − | 0.683759i | \(-0.239656\pi\) | ||||
0.729708 | + | 0.683759i | \(0.239656\pi\) | |||||||
\(104\) | − 5.50626e7i | − 0.470677i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.20137e7 | −0.174369 | ||||||||
\(107\) | 1.73028e8i | 1.32002i | 0.751256 | + | 0.660011i | \(0.229449\pi\) | ||||
−0.751256 | + | 0.660011i | \(0.770551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.43430e7 | −0.526665 | −0.263332 | − | 0.964705i | \(-0.584822\pi\) | ||||
−0.263332 | + | 0.964705i | \(0.584822\pi\) | |||||||
\(110\) | 8.96087e7i | 0.612040i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.59635e7 | 0.546313 | ||||||||
\(113\) | 1.83570e8i | 1.12587i | 0.826501 | + | 0.562935i | \(0.190328\pi\) | ||||
−0.826501 | + | 0.562935i | \(0.809672\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.24330e8 | 1.85437 | ||||||||
\(116\) | − 1.46366e8i | − 0.808367i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.98288e7 | −0.257011 | ||||||||
\(119\) | 2.50846e7i | 0.125089i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.42144e8 | −1.12962 | ||||||||
\(122\) | − 7.38444e7i | − 0.333333i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.67537e7 | −0.197756 | ||||||||
\(125\) | − 1.93705e8i | − 0.793418i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.41939e8 | −0.930016 | −0.465008 | − | 0.885306i | \(-0.653949\pi\) | ||||
−0.465008 | + | 0.885306i | \(0.653949\pi\) | |||||||
\(128\) | 2.36757e8i | 0.881989i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.10185e8 | 0.385788 | ||||||||
\(131\) | − 3.76211e8i | − 1.27746i | −0.769432 | − | 0.638729i | \(-0.779461\pi\) | ||||
0.769432 | − | 0.638729i | \(-0.220539\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.70493e7 | 0.246242 | ||||||||
\(134\) | − 6.07659e7i | − 0.188469i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.18245e7 | −0.0930263 | ||||||||
\(137\) | − 3.29613e8i | − 0.935670i | −0.883816 | − | 0.467835i | \(-0.845034\pi\) | ||||
0.883816 | − | 0.467835i | \(-0.154966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.81930e8 | −0.755235 | −0.377618 | − | 0.925962i | \(-0.623257\pi\) | ||||
−0.377618 | + | 0.925962i | \(0.623257\pi\) | |||||||
\(140\) | 3.88668e8i | 1.01174i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.63787e7 | 0.163258 | ||||||||
\(143\) | 5.61326e8i | 1.34237i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.07933e8 | 1.37526 | ||||||||
\(146\) | − 3.77892e7i | − 0.0831679i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.71021e8 | 1.39859 | ||||||||
\(149\) | 2.86896e8i | 0.582075i | 0.956712 | + | 0.291037i | \(0.0940004\pi\) | ||||
−0.956712 | + | 0.291037i | \(0.906000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.90036e8 | −1.32729 | −0.663643 | − | 0.748050i | \(-0.730990\pi\) | ||||
−0.663643 | + | 0.748050i | \(0.730990\pi\) | |||||||
\(152\) | 9.77511e7i | 0.183125i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.49750e8 | 0.266247 | ||||||||
\(155\) | − 1.94192e8i | − 0.336437i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.38415e8 | −0.721584 | −0.360792 | − | 0.932646i | \(-0.617494\pi\) | ||||
−0.360792 | + | 0.932646i | \(0.617494\pi\) | |||||||
\(158\) | 1.38984e8i | 0.223016i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.48629e8 | −1.14232 | ||||||||
\(161\) | − 5.42008e8i | − 0.806681i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.20932e9 | 1.71313 | 0.856567 | − | 0.516036i | \(-0.172593\pi\) | ||||
0.856567 | + | 0.516036i | \(0.172593\pi\) | |||||||
\(164\) | − 1.68130e8i | − 0.232418i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.61001e8 | −0.475419 | ||||||||
\(167\) | − 1.24766e9i | − 1.60409i | −0.597262 | − | 0.802046i | \(-0.703745\pi\) | ||||
0.597262 | − | 0.802046i | \(-0.296255\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.25513e8 | −0.153865 | ||||||||
\(170\) | − 6.36834e7i | − 0.0762484i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.26804e8 | −0.601916 | ||||||||
\(173\) | 1.56770e9i | 1.75016i | 0.483975 | + | 0.875082i | \(0.339192\pi\) | ||||
−0.483975 | + | 0.875082i | \(0.660808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.69025e8 | −1.03320 | ||||||||
\(176\) | − 1.11180e9i | − 1.15871i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.50045e8 | 0.249079 | ||||||||
\(179\) | 1.91059e8i | 0.186104i | 0.995661 | + | 0.0930520i | \(0.0296623\pi\) | ||||
−0.995661 | + | 0.0930520i | \(0.970338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.53680e9 | 1.43187 | 0.715936 | − | 0.698166i | \(-0.246000\pi\) | ||||
0.715936 | + | 0.698166i | \(0.246000\pi\) | |||||||
\(182\) | − 1.84136e8i | − 0.167824i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.87636e8 | 0.599912 | ||||||||
\(185\) | 2.78709e9i | 2.37938i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.24429e8 | 0.265310 | ||||||||
\(188\) | 3.88644e8i | 0.311115i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.95608e8 | −0.150097 | ||||||||
\(191\) | − 6.18990e8i | − 0.465104i | −0.972584 | − | 0.232552i | \(-0.925292\pi\) | ||||
0.972584 | − | 0.232552i | \(-0.0747076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.29048e6 | −0.00237154 | −0.00118577 | − | 0.999999i | \(-0.500377\pi\) | ||||
−0.00118577 | + | 0.999999i | \(0.500377\pi\) | |||||||
\(194\) | − 1.03740e8i | − 0.0732385i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.22496e8 | −0.489566 | ||||||||
\(197\) | − 4.55140e8i | − 0.302190i | −0.988519 | − | 0.151095i | \(-0.951720\pi\) | ||||
0.988519 | − | 0.151095i | \(-0.0482800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.01948e8 | −0.128774 | −0.0643869 | − | 0.997925i | \(-0.520509\pi\) | ||||
−0.0643869 | + | 0.997925i | \(0.520509\pi\) | |||||||
\(200\) | − 1.22939e9i | − 0.768366i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.33426e8 | 0.260321 | ||||||||
\(203\) | − 1.01595e9i | − 0.598259i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.98330e8 | 0.395408 | ||||||||
\(206\) | 6.96890e8i | 0.386986i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.36709e9 | −0.730371 | ||||||||
\(209\) | − 9.96507e8i | − 0.522270i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.02679e9 | −1.52705 | −0.763524 | − | 0.645780i | \(-0.776532\pi\) | ||||
−0.763524 | + | 0.645780i | \(0.776532\pi\) | |||||||
\(212\) | 1.23491e9i | 0.611350i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.34096e8 | −0.350024 | ||||||||
\(215\) | − 2.18809e9i | − 1.02403i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.24525e8 | −0.146356 | ||||||||
\(218\) | − 3.15411e8i | − 0.139653i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.02679e9 | 2.14586 | ||||||||
\(221\) | − 3.98925e8i | − 0.167233i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.21079e8 | 0.251147 | 0.125573 | − | 0.992084i | \(-0.459923\pi\) | ||||
0.125573 | + | 0.992084i | \(0.459923\pi\) | |||||||
\(224\) | 1.25108e9i | 0.496927i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.78822e8 | −0.298541 | ||||||||
\(227\) | 3.81091e9i | 1.43524i | 0.696434 | + | 0.717621i | \(0.254769\pi\) | ||||
−0.696434 | + | 0.717621i | \(0.745231\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.96529e8 | 0.362367 | 0.181183 | − | 0.983449i | \(-0.442007\pi\) | ||||
0.181183 | + | 0.983449i | \(0.442007\pi\) | |||||||
\(230\) | 1.37602e9i | 0.491714i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.28892e9 | 0.444913 | ||||||||
\(233\) | 7.27588e8i | 0.246866i | 0.992353 | + | 0.123433i | \(0.0393904\pi\) | ||||
−0.992353 | + | 0.123433i | \(0.960610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.61424e9 | −0.529293 | ||||||||
\(236\) | 2.79525e9i | 0.901099i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.06425e8 | −0.0331693 | ||||||||
\(239\) | − 3.98682e9i | − 1.22190i | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
0.791670 | − | 0.610949i | \(-0.209212\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.71314e9 | 1.10071 | 0.550355 | − | 0.834931i | \(-0.314492\pi\) | ||||
0.550355 | + | 0.834931i | \(0.314492\pi\) | |||||||
\(242\) | − 1.02733e9i | − 0.299536i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.14246e9 | −1.16869 | ||||||||
\(245\) | − 3.00089e9i | − 0.832887i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.22533e9 | −0.329203 | ||||||||
\(248\) | − 4.11720e8i | − 0.108842i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.21823e8 | 0.210387 | ||||||||
\(251\) | 2.55588e9i | 0.643940i | 0.946750 | + | 0.321970i | \(0.104345\pi\) | ||||
−0.946750 | + | 0.321970i | \(0.895655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.00999e9 | −1.71094 | ||||||||
\(254\) | − 1.02646e9i | − 0.246608i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.58323e9 | 0.368624 | ||||||||
\(257\) | − 7.81351e8i | − 0.179107i | −0.995982 | − | 0.0895537i | \(-0.971456\pi\) | ||||
0.995982 | − | 0.0895537i | \(-0.0285441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.65767e9 | 1.03507 | ||||||||
\(260\) | − 6.18105e9i | − 1.35260i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.59613e9 | 0.338737 | ||||||||
\(263\) | − 4.40922e9i | − 0.921593i | −0.887506 | − | 0.460796i | \(-0.847564\pi\) | ||||
0.887506 | − | 0.460796i | \(-0.152436\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.12919e9 | −1.04008 | ||||||||
\(266\) | 3.26892e8i | 0.0652948i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.40879e9 | −0.660787 | ||||||||
\(269\) | 8.30145e9i | 1.58542i | 0.609598 | + | 0.792711i | \(0.291331\pi\) | ||||
−0.609598 | + | 0.792711i | \(0.708669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.70047e9 | 1.42771 | 0.713855 | − | 0.700293i | \(-0.246947\pi\) | ||||
0.713855 | + | 0.700293i | \(0.246947\pi\) | |||||||
\(272\) | 7.90136e8i | 0.144353i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.39843e9 | 0.248107 | ||||||||
\(275\) | 1.25328e10i | 2.19137i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.65521e8 | 0.164000 | 0.0819998 | − | 0.996632i | \(-0.473869\pi\) | ||||
0.0819998 | + | 0.996632i | \(0.473869\pi\) | |||||||
\(278\) | − 1.19613e9i | − 0.200262i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.42267e9 | −0.556844 | ||||||||
\(281\) | 1.43642e9i | 0.230386i | 0.993343 | + | 0.115193i | \(0.0367486\pi\) | ||||
−0.993343 | + | 0.115193i | \(0.963251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.83057e9 | 1.22081 | 0.610405 | − | 0.792090i | \(-0.291007\pi\) | ||||
0.610405 | + | 0.792090i | \(0.291007\pi\) | |||||||
\(284\) | − 3.72366e9i | − 0.572396i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.38150e9 | −0.355949 | ||||||||
\(287\) | − 1.16702e9i | − 0.172009i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.74519e9 | 0.966947 | ||||||||
\(290\) | 2.57924e9i | 0.364670i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.11986e9 | −0.291593 | ||||||||
\(293\) | − 1.46462e10i | − 1.98726i | −0.112675 | − | 0.993632i | \(-0.535942\pi\) | ||||
0.112675 | − | 0.993632i | \(-0.464058\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.16101e10 | −1.53302 | ||||||||
\(296\) | 5.90911e9i | 0.769760i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.21719e9 | −0.154346 | ||||||||
\(299\) | 8.61963e9i | 1.07846i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.65664e9 | −0.445468 | ||||||||
\(302\) | − 2.92758e9i | − 0.351950i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.42696e9 | 0.284163 | ||||||||
\(305\) | − 1.72058e10i | − 1.98827i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.21094e9 | 0.586628 | 0.293314 | − | 0.956016i | \(-0.405242\pi\) | ||||
0.293314 | + | 0.956016i | \(0.405242\pi\) | |||||||
\(308\) | − 8.40057e9i | − 0.933482i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.23886e8 | 0.0892114 | ||||||||
\(311\) | 9.31283e9i | 0.995498i | 0.867321 | + | 0.497749i | \(0.165840\pi\) | ||||
−0.867321 | + | 0.497749i | \(0.834160\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.48794e10 | −1.55027 | −0.775137 | − | 0.631793i | \(-0.782319\pi\) | ||||
−0.775137 | + | 0.631793i | \(0.782319\pi\) | |||||||
\(314\) | − 1.86004e9i | − 0.191339i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.79660e9 | 0.781911 | ||||||||
\(317\) | − 4.30922e8i | − 0.0426739i | −0.999772 | − | 0.0213369i | \(-0.993208\pi\) | ||||
0.999772 | − | 0.0213369i | \(-0.00679227\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.31397e10 | −1.26889 | ||||||||
\(320\) | 9.99233e9i | 0.952943i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.29954e9 | 0.213904 | ||||||||
\(323\) | 7.08201e8i | 0.0650648i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.54106e10 | 1.38129 | ||||||||
\(326\) | 5.13072e9i | 0.454263i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.48058e9 | 0.127919 | ||||||||
\(329\) | 2.69765e9i | 0.230251i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.10236e10 | 1.75144 | 0.875718 | − | 0.482823i | \(-0.160389\pi\) | ||||
0.875718 | + | 0.482823i | \(0.160389\pi\) | |||||||
\(332\) | 2.02511e10i | 1.66685i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.29336e9 | 0.425349 | ||||||||
\(335\) | − 1.41585e10i | − 1.12418i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.29142e9 | −0.332722 | −0.166361 | − | 0.986065i | \(-0.553202\pi\) | ||||
−0.166361 | + | 0.986065i | \(0.553202\pi\) | |||||||
\(338\) | − 5.32505e8i | − 0.0407997i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.57246e9 | −0.267332 | ||||||||
\(341\) | 4.19721e9i | 0.310415i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.45384e10 | −1.05037 | ||||||||
\(344\) | − 4.63912e9i | − 0.331285i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.65119e9 | −0.464082 | ||||||||
\(347\) | 6.41858e8i | 0.0442712i | 0.999755 | + | 0.0221356i | \(0.00704656\pi\) | ||||
−0.999755 | + | 0.0221356i | \(0.992953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.90504e10 | −1.28411 | −0.642054 | − | 0.766660i | \(-0.721917\pi\) | ||||
−0.642054 | + | 0.766660i | \(0.721917\pi\) | |||||||
\(350\) | − 4.11123e9i | − 0.273968i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.61807e10 | 1.05396 | ||||||||
\(353\) | 2.10987e9i | 0.135880i | 0.997689 | + | 0.0679401i | \(0.0216427\pi\) | ||||
−0.997689 | + | 0.0679401i | \(0.978357\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.54662e10 | 0.973804 | ||||||||
\(356\) | − 1.40268e10i | − 0.873290i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.10595e8 | −0.0493483 | ||||||||
\(359\) | − 1.30698e10i | − 0.786846i | −0.919358 | − | 0.393423i | \(-0.871291\pi\) | ||||
0.919358 | − | 0.393423i | \(-0.128709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.48083e10 | −0.871918 | ||||||||
\(362\) | 6.52010e9i | 0.379682i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.03295e10 | −0.588403 | ||||||||
\(365\) | − 8.80488e9i | − 0.496080i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.66221e9 | −0.477490 | −0.238745 | − | 0.971082i | \(-0.576736\pi\) | ||||
−0.238745 | + | 0.971082i | \(0.576736\pi\) | |||||||
\(368\) | − 1.70726e10i | − 0.930911i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.18246e10 | −0.630929 | ||||||||
\(371\) | 8.57170e9i | 0.452451i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.28526e10 | 1.18060 | 0.590298 | − | 0.807186i | \(-0.299010\pi\) | ||||
0.590298 | + | 0.807186i | \(0.299010\pi\) | |||||||
\(374\) | 1.37644e9i | 0.0703509i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.42246e9 | −0.171233 | ||||||||
\(377\) | 1.61568e10i | 0.799818i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.19395e10 | 0.578668 | 0.289334 | − | 0.957228i | \(-0.406566\pi\) | ||||
0.289334 | + | 0.957228i | \(0.406566\pi\) | |||||||
\(380\) | 1.09731e10i | 0.526251i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.62615e9 | 0.123329 | ||||||||
\(383\) | 2.82543e9i | 0.131308i | 0.997842 | + | 0.0656538i | \(0.0209133\pi\) | ||||
−0.997842 | + | 0.0656538i | \(0.979087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.48919e10 | 1.58811 | ||||||||
\(386\) | − 1.39603e7i | 0 0.000628849i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.81952e9 | −0.256779 | ||||||||
\(389\) | 2.51686e10i | 1.09916i | 0.835441 | + | 0.549580i | \(0.185212\pi\) | ||||
−0.835441 | + | 0.549580i | \(0.814788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.98188e9 | 0.213151 | ||||||||
\(392\) | − 6.36241e9i | − 0.269449i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.93100e9 | 0.0801303 | ||||||||
\(395\) | 3.23833e10i | 1.33025i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.22833e10 | −0.897052 | −0.448526 | − | 0.893770i | \(-0.648051\pi\) | ||||
−0.448526 | + | 0.893770i | \(0.648051\pi\) | |||||||
\(398\) | − 8.56793e8i | − 0.0341463i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.05231e10 | −1.19231 | ||||||||
\(401\) | 5.87601e9i | 0.227251i | 0.993524 | + | 0.113625i | \(0.0362463\pi\) | ||||
−0.993524 | + | 0.113625i | \(0.963754\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.16098e9 | 0.195664 | ||||||||
\(404\) | − 2.43140e10i | − 0.912705i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.31032e9 | 0.158637 | ||||||||
\(407\) | − 6.02394e10i | − 2.19535i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.11930e10 | 1.47208 | 0.736039 | − | 0.676940i | \(-0.236694\pi\) | ||||
0.736039 | + | 0.676940i | \(0.236694\pi\) | |||||||
\(410\) | 2.96276e9i | 0.104848i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.90935e10 | 1.35680 | ||||||||
\(413\) | 1.94023e10i | 0.666889i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.41133e10 | −2.83578 | ||||||||
\(416\) | − 1.98961e10i | − 0.664346i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.22782e9 | 0.138488 | ||||||||
\(419\) | 5.63009e9i | 0.182666i | 0.995820 | + | 0.0913332i | \(0.0291128\pi\) | ||||
−0.995820 | + | 0.0913332i | \(0.970887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.82721e9 | −0.312825 | −0.156413 | − | 0.987692i | \(-0.549993\pi\) | ||||
−0.156413 | + | 0.987692i | \(0.549993\pi\) | |||||||
\(422\) | − 1.28416e10i | − 0.404920i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.08748e10 | −0.336478 | ||||||||
\(425\) | − 8.90683e9i | − 0.273003i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.87536e10 | −0.864928 | ||||||||
\(428\) | 4.11807e10i | 1.22721i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.28327e9 | 0.271536 | ||||||||
\(431\) | − 6.62106e10i | − 1.91875i | −0.282135 | − | 0.959375i | \(-0.591043\pi\) | ||||
0.282135 | − | 0.959375i | \(-0.408957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.02313e10 | 0.575537 | 0.287768 | − | 0.957700i | \(-0.407087\pi\) | ||||
0.287768 | + | 0.957700i | \(0.407087\pi\) | |||||||
\(434\) | − 1.37685e9i | − 0.0388084i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.76936e10 | −0.489634 | ||||||||
\(437\) | − 1.53022e10i | − 0.419593i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.82267e10 | 0.759981 | 0.379990 | − | 0.924990i | \(-0.375927\pi\) | ||||
0.379990 | + | 0.924990i | \(0.375927\pi\) | |||||||
\(440\) | 4.42667e10i | 1.18105i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.69249e9 | 0.0443443 | ||||||||
\(443\) | 6.41109e10i | 1.66463i | 0.554305 | + | 0.832314i | \(0.312984\pi\) | ||||
−0.554305 | + | 0.832314i | \(0.687016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.82604e10 | 1.48571 | ||||||||
\(446\) | 2.63501e9i | 0.0665953i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.66988e10 | 0.414546 | ||||||||
\(449\) | 3.14738e10i | 0.774398i | 0.921996 | + | 0.387199i | \(0.126557\pi\) | ||||
−0.921996 | + | 0.387199i | \(0.873443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.50935e10 | −0.364825 | ||||||||
\(452\) | 4.36897e10i | 1.04671i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.61683e10 | −0.380576 | ||||||||
\(455\) | − 4.29038e10i | − 1.00104i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.49162e10 | −1.48829 | −0.744146 | − | 0.668017i | \(-0.767143\pi\) | ||||
−0.744146 | + | 0.668017i | \(0.767143\pi\) | |||||||
\(458\) | 4.22792e9i | 0.0960870i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.71906e10 | 1.72398 | ||||||||
\(461\) | − 3.31042e9i | − 0.0732959i | −0.999328 | − | 0.0366480i | \(-0.988332\pi\) | ||||
0.999328 | − | 0.0366480i | \(-0.0116680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.98533e10 | 0.867243 | 0.433621 | − | 0.901095i | \(-0.357236\pi\) | ||||
0.433621 | + | 0.901095i | \(0.357236\pi\) | |||||||
\(464\) | − 3.20013e10i | − 0.690392i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.08689e9 | −0.0654603 | ||||||||
\(467\) | − 4.81612e10i | − 1.01258i | −0.862363 | − | 0.506291i | \(-0.831016\pi\) | ||||
0.862363 | − | 0.506291i | \(-0.168984\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.36610e10 | −0.489038 | ||||||||
\(470\) | − 6.84863e9i | − 0.140350i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.46154e10 | −0.495951 | ||||||||
\(473\) | 4.72927e10i | 0.944822i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.73580e10 | −0.537414 | ||||||||
\(476\) | 5.97015e9i | 0.116294i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.69146e10 | 0.324005 | ||||||||
\(479\) | − 4.57029e10i | − 0.868164i | −0.900873 | − | 0.434082i | \(-0.857073\pi\) | ||||
0.900873 | − | 0.434082i | \(-0.142927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.40716e10 | −1.38379 | ||||||||
\(482\) | 1.57535e10i | 0.291870i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.76304e10 | −1.05020 | ||||||||
\(485\) | − 2.41714e10i | − 0.436853i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.67295e10 | 0.652978 | 0.326489 | − | 0.945201i | \(-0.394134\pi\) | ||||
0.326489 | + | 0.945201i | \(0.394134\pi\) | |||||||
\(488\) | − 3.64792e10i | − 0.643229i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.27317e10 | 0.220853 | ||||||||
\(491\) | − 1.16241e10i | − 0.200001i | −0.994987 | − | 0.100001i | \(-0.968116\pi\) | ||||
0.994987 | − | 0.100001i | \(-0.0318845\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.33816e9 | 0.158079 | ||||||||
\(494\) | − 5.19862e9i | − 0.0872931i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.02222e10 | −0.168895 | ||||||||
\(497\) | − 2.58466e10i | − 0.423621i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.46311e10 | 0.558552 | 0.279276 | − | 0.960211i | \(-0.409905\pi\) | ||||
0.279276 | + | 0.960211i | \(0.409905\pi\) | |||||||
\(500\) | − 4.61019e10i | − 0.737630i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.08437e10 | −0.170750 | ||||||||
\(503\) | 8.31882e10i | 1.29954i | 0.760130 | + | 0.649770i | \(0.225135\pi\) | ||||
−0.760130 | + | 0.649770i | \(0.774865\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00988e11 | 1.55276 | ||||||||
\(506\) | − 2.97409e10i | − 0.453682i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.75814e10 | −0.864624 | ||||||||
\(509\) | 6.07300e10i | 0.904758i | 0.891826 | + | 0.452379i | \(0.149425\pi\) | ||||
−0.891826 | + | 0.452379i | \(0.850575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.47144e10 | −0.215803 | ||||||||
\(512\) | 6.73269e10i | 0.979736i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.31499e9 | 0.0474930 | ||||||||
\(515\) | 1.62375e11i | 2.30829i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.48897e10 | 0.488354 | ||||||||
\(518\) | 1.97608e10i | 0.274464i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.44313e10 | 0.744449 | ||||||||
\(521\) | − 6.81755e10i | − 0.925289i | −0.886544 | − | 0.462644i | \(-0.846901\pi\) | ||||
0.886544 | − | 0.462644i | \(-0.153099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.73708e10 | 0.633147 | 0.316573 | − | 0.948568i | \(-0.397468\pi\) | ||||
0.316573 | + | 0.948568i | \(0.397468\pi\) | |||||||
\(524\) | − 8.95382e10i | − 1.18764i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.87067e10 | 0.244374 | ||||||||
\(527\) | − 2.98289e9i | − 0.0386718i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.93333e10 | −0.374575 | ||||||||
\(530\) | − 2.17613e10i | − 0.275792i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.83377e10 | 0.228928 | ||||||||
\(533\) | 1.85593e10i | 0.229960i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.71044e11 | −2.08782 | ||||||||
\(536\) | − 3.00184e10i | − 0.363687i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.52201e10 | −0.420398 | ||||||||
\(539\) | 6.48605e10i | 0.768467i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.63796e10 | 0.191212 | 0.0956059 | − | 0.995419i | \(-0.469521\pi\) | ||||
0.0956059 | + | 0.995419i | \(0.469521\pi\) | |||||||
\(542\) | 3.26703e10i | 0.378579i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.14993e10 | −0.131304 | ||||||||
\(545\) | − 7.34907e10i | − 0.833003i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.48606e10 | 0.836188 | 0.418094 | − | 0.908404i | \(-0.362698\pi\) | ||||
0.418094 | + | 0.908404i | \(0.362698\pi\) | |||||||
\(548\) | − 7.84480e10i | − 0.869881i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.31720e10 | −0.581075 | ||||||||
\(551\) | − 2.86828e10i | − 0.311183i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.41176e10 | 0.578679 | ||||||||
\(554\) | 4.09636e9i | 0.0434869i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.70994e10 | −0.702133 | ||||||||
\(557\) | − 1.58080e11i | − 1.64231i | −0.570705 | − | 0.821155i | \(-0.693330\pi\) | ||||
0.570705 | − | 0.821155i | \(-0.306670\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.81521e10 | 0.595550 | ||||||||
\(560\) | 8.49779e10i | 0.864080i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.09421e9 | −0.0610902 | ||||||||
\(563\) | − 1.27798e11i | − 1.27201i | −0.771687 | − | 0.636003i | \(-0.780587\pi\) | ||||
0.771687 | − | 0.636003i | \(-0.219413\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.81465e11 | −1.78074 | ||||||||
\(566\) | 3.32223e10i | 0.323716i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.27911e10 | 0.315038 | ||||||||
\(569\) | − 5.42832e10i | − 0.517865i | −0.965895 | − | 0.258933i | \(-0.916629\pi\) | ||||
0.965895 | − | 0.258933i | \(-0.0833707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.20161e11 | 1.13037 | 0.565184 | − | 0.824965i | \(-0.308805\pi\) | ||||
0.565184 | + | 0.824965i | \(0.308805\pi\) | |||||||
\(572\) | 1.33596e11i | 1.24798i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.95125e9 | 0.0456108 | ||||||||
\(575\) | 1.92451e11i | 1.76055i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.83000e11 | −1.65101 | −0.825503 | − | 0.564398i | \(-0.809109\pi\) | ||||
−0.825503 | + | 0.564398i | \(0.809109\pi\) | |||||||
\(578\) | 2.86174e10i | 0.256401i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.44688e11 | 1.27856 | ||||||||
\(581\) | 1.40567e11i | 1.23361i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.10861e11 | 0.959631 | ||||||||
\(584\) | − 1.86678e10i | − 0.160488i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.21387e10 | 0.526953 | ||||||||
\(587\) | − 7.16104e10i | − 0.603148i | −0.953443 | − | 0.301574i | \(-0.902488\pi\) | ||||
0.953443 | − | 0.301574i | \(-0.0975120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.16215e9 | −0.0761265 | ||||||||
\(590\) | − 4.92575e10i | − 0.406503i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.46711e11 | 1.19447 | ||||||||
\(593\) | − 6.84140e9i | − 0.0553256i | −0.999617 | − | 0.0276628i | \(-0.991194\pi\) | ||||
0.999617 | − | 0.0276628i | \(-0.00880647\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47971e10 | −0.197848 | ||||||||
\(596\) | 6.82812e10i | 0.541148i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.65700e10 | −0.285970 | ||||||||
\(599\) | 1.61467e11i | 1.25423i | 0.778927 | + | 0.627115i | \(0.215764\pi\) | ||||
−0.778927 | + | 0.627115i | \(0.784236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.14207e10 | 0.317482 | 0.158741 | − | 0.987320i | \(-0.449257\pi\) | ||||
0.158741 | + | 0.987320i | \(0.449257\pi\) | |||||||
\(602\) | − 1.55138e10i | − 0.118123i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.64229e11 | −1.23396 | ||||||||
\(605\) | − 2.39368e11i | − 1.78667i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.14644e11 | −0.844492 | −0.422246 | − | 0.906481i | \(-0.638758\pi\) | ||||
−0.422246 | + | 0.906481i | \(0.638758\pi\) | |||||||
\(608\) | 3.53210e10i | 0.258475i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.29978e10 | 0.527219 | ||||||||
\(611\) | − 4.29011e10i | − 0.307825i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.23749e11 | −0.876397 | −0.438198 | − | 0.898878i | \(-0.644383\pi\) | ||||
−0.438198 | + | 0.898878i | \(0.644383\pi\) | |||||||
\(614\) | 2.21082e10i | 0.155553i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.39767e10 | 0.513774 | ||||||||
\(617\) | − 6.29138e10i | − 0.434116i | −0.976159 | − | 0.217058i | \(-0.930354\pi\) | ||||
0.976159 | − | 0.217058i | \(-0.0696460\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.39495e11 | 0.950156 | 0.475078 | − | 0.879944i | \(-0.342420\pi\) | ||||
0.475078 | + | 0.879944i | \(0.342420\pi\) | |||||||
\(620\) | − 4.62177e10i | − 0.312782i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.95110e10 | −0.263971 | ||||||||
\(623\) | − 9.73624e10i | − 0.646308i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.76470e10 | −0.246723 | ||||||||
\(626\) | − 6.31280e10i | − 0.411079i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.04343e11 | −0.670848 | ||||||||
\(629\) | 4.28111e10i | 0.273498i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.25299e10 | −0.520588 | −0.260294 | − | 0.965529i | \(-0.583819\pi\) | ||||
−0.260294 | + | 0.965529i | \(0.583819\pi\) | |||||||
\(632\) | 6.86581e10i | 0.430352i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.82825e9 | 0.0113156 | ||||||||
\(635\) | − 2.39165e11i | − 1.47097i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.97538e10 | 0.484389 | ||||||||
\(638\) | − 5.57470e10i | − 0.336464i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.34043e11 | −1.39500 | ||||||||
\(641\) | 3.04379e11i | 1.80295i | 0.432836 | + | 0.901473i | \(0.357513\pi\) | ||||
−0.432836 | + | 0.901473i | \(0.642487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.29544e11 | −1.34283 | −0.671416 | − | 0.741080i | \(-0.734314\pi\) | ||||
−0.671416 | + | 0.741080i | \(0.734314\pi\) | |||||||
\(644\) | − 1.28998e11i | − 0.749962i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.00464e9 | −0.0172529 | ||||||||
\(647\) | 1.03124e11i | 0.588494i | 0.955729 | + | 0.294247i | \(0.0950688\pi\) | ||||
−0.955729 | + | 0.294247i | \(0.904931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.50938e11 | 1.41445 | ||||||||
\(650\) | 6.53814e10i | 0.366270i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.87818e11 | 1.59268 | ||||||||
\(653\) | − 1.38484e10i | − 0.0761633i | −0.999275 | − | 0.0380816i | \(-0.987875\pi\) | ||||
0.999275 | − | 0.0380816i | \(-0.0121247\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.71898e11 | 2.02050 | ||||||||
\(656\) | − 3.67598e10i | − 0.198499i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.14451e10 | −0.0610545 | ||||||||
\(659\) | 2.78234e11i | 1.47526i | 0.675205 | + | 0.737630i | \(0.264055\pi\) | ||||
−0.675205 | + | 0.737630i | \(0.735945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00656e11 | 1.05111 | 0.525554 | − | 0.850761i | \(-0.323858\pi\) | ||||
0.525554 | + | 0.850761i | \(0.323858\pi\) | |||||||
\(662\) | 8.91954e10i | 0.464419i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.78335e11 | −0.917410 | ||||||||
\(665\) | 7.61659e10i | 0.389470i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.01771e11 | −1.01943 | ||||||||
\(668\) | − 2.96942e11i | − 1.49130i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.00693e10 | 0.298094 | ||||||||
\(671\) | 3.71881e11i | 1.83448i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.93202e11 | −0.941784 | −0.470892 | − | 0.882191i | \(-0.656068\pi\) | ||||
−0.470892 | + | 0.882191i | \(0.656068\pi\) | |||||||
\(674\) | − 1.82070e10i | − 0.0882263i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.98720e10 | −0.143047 | ||||||||
\(677\) | 9.03093e9i | 0.0429910i | 0.999769 | + | 0.0214955i | \(0.00684276\pi\) | ||||
−0.999769 | + | 0.0214955i | \(0.993157\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.03943e10 | −0.190038 | ||||||||
\(680\) | − 3.14596e10i | − 0.147136i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.78073e10 | −0.0823113 | ||||||||
\(683\) | − 2.79267e11i | − 1.28333i | −0.766987 | − | 0.641663i | \(-0.778245\pi\) | ||||
0.766987 | − | 0.641663i | \(-0.221755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.25835e11 | 1.47991 | ||||||||
\(686\) | − 6.16813e10i | − 0.278520i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.15180e11 | −0.514070 | ||||||||
\(689\) | − 1.36317e11i | − 0.604885i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.41810e11 | −0.622006 | −0.311003 | − | 0.950409i | \(-0.600665\pi\) | ||||
−0.311003 | + | 0.950409i | \(0.600665\pi\) | |||||||
\(692\) | 3.73113e11i | 1.62710i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.72317e9 | −0.0117392 | ||||||||
\(695\) | − 2.78698e11i | − 1.19452i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.07267e10 | 0.0454502 | ||||||||
\(698\) | − 8.08238e10i | − 0.340500i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.30628e11 | −0.960550 | ||||||||
\(701\) | 1.72900e10i | 0.0716017i | 0.999359 | + | 0.0358008i | \(0.0113982\pi\) | ||||
−0.999359 | + | 0.0358008i | \(0.988602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.31497e11 | 0.538389 | ||||||||
\(704\) | − 2.15972e11i | − 0.879237i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.95141e9 | −0.0360307 | ||||||||
\(707\) | − 1.68767e11i | − 0.675478i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.29325e11 | −0.907541 | −0.453771 | − | 0.891118i | \(-0.649921\pi\) | ||||
−0.453771 | + | 0.891118i | \(0.649921\pi\) | |||||||
\(710\) | 6.56177e10i | 0.258219i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.23522e11 | 0.480645 | ||||||||
\(713\) | 6.44517e10i | 0.249388i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.54890e11 | −2.12316 | ||||||||
\(716\) | 4.54721e10i | 0.173019i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.54503e10 | 0.208644 | ||||||||
\(719\) | − 2.34118e11i | − 0.876030i | −0.898968 | − | 0.438015i | \(-0.855682\pi\) | ||||
0.898968 | − | 0.438015i | \(-0.144318\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.71355e11 | 1.00415 | ||||||||
\(722\) | − 6.28262e10i | − 0.231202i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.65759e11 | 1.33119 | ||||||||
\(725\) | 3.60735e11i | 1.30568i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.62995e11 | 0.941479 | 0.470740 | − | 0.882272i | \(-0.343987\pi\) | ||||
0.470740 | + | 0.882272i | \(0.343987\pi\) | |||||||
\(728\) | − 9.09633e10i | − 0.323848i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.73559e10 | 0.131543 | ||||||||
\(731\) | − 3.36101e10i | − 0.117707i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.39665e11 | −0.830213 | −0.415106 | − | 0.909773i | \(-0.636256\pi\) | ||||
−0.415106 | + | 0.909773i | \(0.636256\pi\) | |||||||
\(734\) | − 3.67506e10i | − 0.126614i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.48468e11 | 0.846757 | ||||||||
\(737\) | 3.06017e11i | 1.03723i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.01061e10 | 0.134472 | 0.0672361 | − | 0.997737i | \(-0.478582\pi\) | ||||
0.0672361 | + | 0.997737i | \(0.478582\pi\) | |||||||
\(740\) | 6.63327e11i | 2.21208i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.63666e10 | −0.119974 | ||||||||
\(743\) | 5.15417e10i | 0.169123i | 0.996418 | + | 0.0845617i | \(0.0269490\pi\) | ||||
−0.996418 | + | 0.0845617i | \(0.973051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.83606e11 | −0.920642 | ||||||||
\(746\) | 9.69556e10i | 0.313053i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.72141e10 | 0.246655 | ||||||||
\(749\) | 2.85842e11i | 0.908237i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.45524e11 | 0.457484 | 0.228742 | − | 0.973487i | \(-0.426539\pi\) | ||||
0.228742 | + | 0.973487i | \(0.426539\pi\) | |||||||
\(752\) | 8.49726e10i | 0.265710i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.85477e10 | −0.212084 | ||||||||
\(755\) | − 6.82125e11i | − 2.09931i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.32953e11 | 0.709390 | 0.354695 | − | 0.934982i | \(-0.384585\pi\) | ||||
0.354695 | + | 0.934982i | \(0.384585\pi\) | |||||||
\(758\) | 5.06550e10i | 0.153442i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.66304e10 | −0.289641 | ||||||||
\(761\) | − 3.56275e11i | − 1.06230i | −0.847279 | − | 0.531149i | \(-0.821761\pi\) | ||||
0.847279 | − | 0.531149i | \(-0.178239\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.22815e11 | −0.362370 | ||||||||
\(764\) | − 1.47320e11i | − 0.432401i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.19873e10 | −0.0348182 | ||||||||
\(767\) | − 3.08558e11i | − 0.891570i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.68419e11 | 0.481599 | 0.240800 | − | 0.970575i | \(-0.422590\pi\) | ||||
0.240800 | + | 0.970575i | \(0.422590\pi\) | |||||||
\(770\) | 1.48034e11i | 0.421112i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.83135e8 | −0.00220479 | ||||||||
\(773\) | 3.15069e11i | 0.882444i | 0.897398 | + | 0.441222i | \(0.145455\pi\) | ||||
−0.897398 | + | 0.441222i | \(0.854545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.15230e11 | 0.319416 | ||||||||
\(776\) | − 5.12475e10i | − 0.141327i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.06781e11 | −0.291459 | ||||||||
\(779\) | − 3.29479e10i | − 0.0894700i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.34283e11 | −0.898485 | ||||||||
\(782\) | 2.11363e10i | 0.0565201i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.57966e11 | −0.418117 | ||||||||
\(785\) | − 4.33389e11i | − 1.14130i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.25510e11 | −1.63056 | −0.815278 | − | 0.579070i | \(-0.803416\pi\) | ||||
−0.815278 | + | 0.579070i | \(0.803416\pi\) | |||||||
\(788\) | − 1.08323e11i | − 0.280943i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.37391e11 | −0.352735 | ||||||||
\(791\) | 3.03258e11i | 0.774651i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.57272e11 | 1.15633 | ||||||||
\(794\) | − 9.45401e10i | − 0.237867i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.80636e10 | −0.119719 | ||||||||
\(797\) | − 5.74775e11i | − 1.42451i | −0.701922 | − | 0.712254i | \(-0.747675\pi\) | ||||
0.701922 | − | 0.712254i | \(-0.252325\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.47955e10 | −0.0608395 | ||||||||
\(800\) | − 4.44221e11i | − 1.08452i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.49298e10 | −0.0602589 | ||||||||
\(803\) | 1.90306e11i | 0.457710i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.35794e11 | 1.27589 | ||||||||
\(806\) | 2.18962e10i | 0.0518833i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.14112e11 | 0.502339 | ||||||||
\(809\) | 5.68847e11i | 1.32801i | 0.747728 | + | 0.664005i | \(0.231145\pi\) | ||||
−0.747728 | + | 0.664005i | \(0.768855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.39315e11 | −1.47785 | −0.738927 | − | 0.673785i | \(-0.764667\pi\) | ||||
−0.738927 | + | 0.673785i | \(0.764667\pi\) | |||||||
\(812\) | − 2.41797e11i | − 0.556194i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.55574e11 | 0.582129 | ||||||||
\(815\) | 1.19546e12i | 2.70959i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.03236e11 | −0.231709 | ||||||||
\(818\) | 1.74767e11i | 0.390343i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.66203e11 | 0.367606 | ||||||||
\(821\) | 7.38100e10i | 0.162458i | 0.996695 | + | 0.0812292i | \(0.0258846\pi\) | ||||
−0.996695 | + | 0.0812292i | \(0.974115\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.34074e11 | 0.946159 | 0.473079 | − | 0.881020i | \(-0.343142\pi\) | ||||
0.473079 | + | 0.881020i | \(0.343142\pi\) | |||||||
\(824\) | 3.44264e11i | 0.746762i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.23171e10 | −0.176836 | ||||||||
\(827\) | − 1.01622e11i | − 0.217253i | −0.994083 | − | 0.108626i | \(-0.965355\pi\) | ||||
0.994083 | − | 0.108626i | \(-0.0346452\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.87841e10 | 0.187982 | 0.0939912 | − | 0.995573i | \(-0.470037\pi\) | ||||
0.0939912 | + | 0.995573i | \(0.470037\pi\) | |||||||
\(830\) | − 3.56863e11i | − 0.751949i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.65563e11 | −0.554210 | ||||||||
\(833\) | − 4.60953e10i | − 0.0957362i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.23335e12 | 2.53712 | ||||||||
\(836\) | − 2.37169e11i | − 0.485548i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.38864e10 | −0.0484368 | ||||||||
\(839\) | 3.88292e11i | 0.783628i | 0.920044 | + | 0.391814i | \(0.128152\pi\) | ||||
−0.920044 | + | 0.391814i | \(0.871848\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.22042e11 | 0.243963 | ||||||||
\(842\) | − 4.16933e10i | − 0.0829503i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.20376e11 | −1.41968 | ||||||||
\(845\) | − 1.24074e11i | − 0.243362i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.00023e11 | −0.777232 | ||||||||
\(848\) | 2.69998e11i | 0.522128i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.77885e10 | 0.0723908 | ||||||||
\(851\) | − 9.25027e11i | − 1.76375i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.37267e10 | 0.139261 | 0.0696304 | − | 0.997573i | \(-0.477818\pi\) | ||||
0.0696304 | + | 0.997573i | \(0.477818\pi\) | |||||||
\(854\) | − 1.21991e11i | − 0.229349i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.62643e11 | −0.675437 | ||||||||
\(857\) | 5.60118e11i | 1.03838i | 0.854659 | + | 0.519190i | \(0.173766\pi\) | ||||
−0.854659 | + | 0.519190i | \(0.826234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.95095e11 | 0.358322 | 0.179161 | − | 0.983820i | \(-0.442662\pi\) | ||||
0.179161 | + | 0.983820i | \(0.442662\pi\) | |||||||
\(860\) | − 5.20765e11i | − 0.952024i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.80908e11 | 0.508785 | ||||||||
\(863\) | 7.69232e11i | 1.38680i | 0.720552 | + | 0.693401i | \(0.243888\pi\) | ||||
−0.720552 | + | 0.693401i | \(0.756112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.54973e12 | −2.76816 | ||||||||
\(866\) | 8.58343e10i | 0.152612i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.72371e10 | −0.136065 | ||||||||
\(869\) | − 6.99923e11i | − 1.22736i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.76285e11 | 0.653799 | ||||||||
\(872\) | − 1.55813e11i | − 0.269487i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.49218e10 | 0.111261 | ||||||||
\(875\) | − 3.20001e11i | − 0.545908i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.58389e11 | −0.436793 | −0.218396 | − | 0.975860i | \(-0.570083\pi\) | ||||
−0.218396 | + | 0.975860i | \(0.570083\pi\) | |||||||
\(878\) | 1.19756e11i | 0.201520i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.09905e12 | 1.83268 | ||||||||
\(881\) | − 1.16798e12i | − 1.93879i | −0.245514 | − | 0.969393i | \(-0.578957\pi\) | ||||
0.245514 | − | 0.969393i | \(-0.421043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.16973e10 | −0.101490 | −0.0507450 | − | 0.998712i | \(-0.516160\pi\) | ||||
−0.0507450 | + | 0.998712i | \(0.516160\pi\) | |||||||
\(884\) | − 9.49441e10i | − 0.155474i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.72000e11 | −0.441401 | ||||||||
\(887\) | 1.45349e10i | 0.0234811i | 0.999931 | + | 0.0117405i | \(0.00373722\pi\) | ||||
−0.999931 | + | 0.0117405i | \(0.996263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.99683e11 | −0.639894 | ||||||||
\(890\) | 2.47178e11i | 0.393958i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.47817e11 | 0.233488 | ||||||||
\(893\) | 7.61612e10i | 0.119764i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.88869e11 | −0.294353 | ||||||||
\(896\) | 3.91123e11i | 0.606850i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.33532e11 | −0.205343 | ||||||||
\(899\) | 1.20810e11i | 0.184954i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.87870e10 | −0.119552 | ||||||||
\(902\) | − 6.40364e10i | − 0.0967388i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.84738e11 | −0.576091 | ||||||||
\(905\) | 1.51918e12i | 2.26473i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.00686e12 | 1.48778 | 0.743891 | − | 0.668301i | \(-0.232978\pi\) | ||||
0.743891 | + | 0.668301i | \(0.232978\pi\) | |||||||
\(908\) | 9.06996e11i | 1.33433i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.82025e11 | 0.265440 | ||||||||
\(911\) | − 2.55467e11i | − 0.370904i | −0.982653 | − | 0.185452i | \(-0.940625\pi\) | ||||
0.982653 | − | 0.185452i | \(-0.0593749\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.81800e12 | 2.61644 | ||||||||
\(914\) | − 2.75416e11i | − 0.394643i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.37174e11 | 0.336888 | ||||||||
\(917\) | − 6.21501e11i | − 0.878950i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.08241e11 | −0.291947 | −0.145973 | − | 0.989289i | \(-0.546631\pi\) | ||||
−0.145973 | + | 0.989289i | \(0.546631\pi\) | |||||||
\(920\) | 6.79753e11i | 0.948854i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.40449e10 | 0.0194355 | ||||||||
\(923\) | 4.11042e11i | 0.566342i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.65380e12 | −2.25900 | ||||||||
\(926\) | 1.69083e11i | 0.229962i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.65734e11 | 0.627980 | ||||||||
\(929\) | − 1.32373e12i | − 1.77720i | −0.458679 | − | 0.888602i | \(-0.651677\pi\) | ||||
0.458679 | − | 0.888602i | \(-0.348323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.41585e11 | −0.188460 | ||||||||
\(932\) | 1.73166e11i | 0.229508i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.04331e11 | 0.268501 | ||||||||
\(935\) | 3.20710e11i | 0.419629i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.83971e11 | −0.498127 | −0.249064 | − | 0.968487i | \(-0.580123\pi\) | ||||
−0.249064 | + | 0.968487i | \(0.580123\pi\) | |||||||
\(938\) | − 1.00385e11i | − 0.129676i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.84188e11 | −0.492077 | ||||||||
\(941\) | − 1.24371e11i | − 0.158621i | −0.996850 | − | 0.0793106i | \(-0.974728\pi\) | ||||
0.996850 | − | 0.0793106i | \(-0.0252719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.31774e11 | −0.293101 | ||||||||
\(944\) | 6.11150e11i | 0.769590i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.00646e11 | −0.250534 | ||||||||
\(947\) | 5.07114e11i | 0.630530i | 0.949004 | + | 0.315265i | \(0.102093\pi\) | ||||
−0.949004 | + | 0.315265i | \(0.897907\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.34004e11 | 0.288509 | ||||||||
\(950\) | − 1.16070e11i | − 0.142503i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.25740e10 | −0.0640064 | ||||||||
\(953\) | − 1.41309e12i | − 1.71316i | −0.516017 | − | 0.856578i | \(-0.672586\pi\) | ||||
0.516017 | − | 0.856578i | \(-0.327414\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.11893e11 | 0.735635 | ||||||||
\(956\) | − 9.48863e11i | − 1.13598i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.93901e11 | 0.230207 | ||||||||
\(959\) | − 5.44521e11i | − 0.643785i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.14301e11 | −0.954754 | ||||||||
\(962\) | − 3.14259e11i | − 0.366934i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.83726e11 | 1.02332 | ||||||||
\(965\) | − 3.25276e9i | − 0.00375096i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.85172e11 | −0.440503 | −0.220252 | − | 0.975443i | \(-0.570688\pi\) | ||||
−0.220252 | + | 0.975443i | \(0.570688\pi\) | |||||||
\(968\) | − 5.07502e11i | − 0.578011i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.02551e11 | 0.115838 | ||||||||
\(971\) | 4.39991e11i | 0.494957i | 0.968893 | + | 0.247478i | \(0.0796019\pi\) | ||||
−0.968893 | + | 0.247478i | \(0.920398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.65749e11 | −0.519637 | ||||||||
\(974\) | 1.55830e11i | 0.173147i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.05702e11 | −0.998128 | ||||||||
\(977\) | − 6.70267e10i | − 0.0735647i | −0.999323 | − | 0.0367823i | \(-0.988289\pi\) | ||||
0.999323 | − | 0.0367823i | \(-0.0117108\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.25922e12 | −1.37080 | ||||||||
\(980\) | − 7.14213e11i | − 0.774325i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.93168e10 | 0.0530333 | ||||||||
\(983\) | 1.28719e12i | 1.37857i | 0.724489 | + | 0.689287i | \(0.242076\pi\) | ||||
−0.724489 | + | 0.689287i | \(0.757924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.49922e11 | 0.477961 | ||||||||
\(986\) | 3.96185e10i | 0.0419170i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.91628e11 | −0.306056 | ||||||||
\(989\) | 7.26220e11i | 0.759072i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.01623e12 | 1.05365 | 0.526824 | − | 0.849974i | \(-0.323383\pi\) | ||||
0.526824 | + | 0.849974i | \(0.323383\pi\) | |||||||
\(992\) | − 1.48769e11i | − 0.153627i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.09658e11 | 0.112329 | ||||||||
\(995\) | − 1.99633e11i | − 0.203676i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.66136e12 | 1.68144 | 0.840721 | − | 0.541468i | \(-0.182131\pi\) | ||||
0.840721 | + | 0.541468i | \(0.182131\pi\) | |||||||
\(998\) | 1.46927e11i | 0.148109i | ||||||||
\(999\) | 0 | 0 |
(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 | 9.9.b.a.8.2 | yes | 2 | |
3.2 | odd | 2 | inner | 9.9.b.a.8.1 | ✓ | 2 | |
4.3 | odd | 2 | 144.9.e.a.17.2 | 2 | |||
5.2 | odd | 4 | 225.9.d.a.224.2 | 4 | |||
5.3 | odd | 4 | 225.9.d.a.224.3 | 4 | |||
5.4 | even | 2 | 225.9.c.a.26.1 | 2 | |||
9.2 | odd | 6 | 81.9.d.b.53.1 | 4 | |||
9.4 | even | 3 | 81.9.d.b.26.1 | 4 | |||
9.5 | odd | 6 | 81.9.d.b.26.2 | 4 | |||
9.7 | even | 3 | 81.9.d.b.53.2 | 4 | |||
12.11 | even | 2 | 144.9.e.a.17.1 | 2 | |||
15.2 | even | 4 | 225.9.d.a.224.4 | 4 | |||
15.8 | even | 4 | 225.9.d.a.224.1 | 4 | |||
15.14 | odd | 2 | 225.9.c.a.26.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.9.b.a.8.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
9.9.b.a.8.2 | yes | 2 | 1.1 | even | 1 | trivial | |
81.9.d.b.26.1 | 4 | 9.4 | even | 3 | |||
81.9.d.b.26.2 | 4 | 9.5 | odd | 6 | |||
81.9.d.b.53.1 | 4 | 9.2 | odd | 6 | |||
81.9.d.b.53.2 | 4 | 9.7 | even | 3 | |||
144.9.e.a.17.1 | 2 | 12.11 | even | 2 | |||
144.9.e.a.17.2 | 2 | 4.3 | odd | 2 | |||
225.9.c.a.26.1 | 2 | 5.4 | even | 2 | |||
225.9.c.a.26.2 | 2 | 15.14 | odd | 2 | |||
225.9.d.a.224.1 | 4 | 15.8 | even | 4 | |||
225.9.d.a.224.2 | 4 | 5.2 | odd | 4 | |||
225.9.d.a.224.3 | 4 | 5.3 | odd | 4 | |||
225.9.d.a.224.4 | 4 | 15.2 | even | 4 |