Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 233.5 | ||
Character | \(\chi\) | \(=\) | 252.233 |
Dual form | 252.9.bk.a.53.5 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −674.478 | − | 389.410i | −1.07917 | − | 0.623056i | −0.148494 | − | 0.988913i | \(-0.547443\pi\) |
−0.930671 | + | 0.365857i | \(0.880776\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1634.98 | + | 1758.31i | −0.680956 | + | 0.732324i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 291.697 | − | 168.411i | 0.0199233 | − | 0.0115027i | −0.490005 | − | 0.871719i | \(-0.663005\pi\) |
0.509929 | + | 0.860217i | \(0.329672\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.7231 | 0.00163591 | 0.000817953 | − | 1.00000i | \(-0.499740\pi\) | ||||
0.000817953 | 1.00000i | \(0.499740\pi\) | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 98146.7 | − | 56665.0i | 1.17511 | − | 0.678453i | 0.220235 | − | 0.975447i | \(-0.429318\pi\) |
0.954879 | + | 0.296994i | \(0.0959842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 41181.7 | − | 71328.8i | 0.316002 | − | 0.547332i | −0.663648 | − | 0.748045i | \(-0.730993\pi\) |
0.979650 | + | 0.200713i | \(0.0643259\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 326470. | + | 188487.i | 1.16663 | + | 0.673552i | 0.952883 | − | 0.303338i | \(-0.0981011\pi\) |
0.213743 | + | 0.976890i | \(0.431434\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 107968. | + | 187006.i | 0.276399 | + | 0.478736i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 747068.i | − | 1.05625i | −0.849165 | − | 0.528127i | \(-0.822894\pi\) | ||
0.849165 | − | 0.528127i | \(-0.177106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −774022. | − | 1.34064e6i | −0.838120 | − | 1.45167i | −0.891464 | − | 0.453091i | \(-0.850321\pi\) |
0.0533442 | − | 0.998576i | \(-0.483012\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.78746e6 | − | 549266.i | 1.19114 | − | 0.366024i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 475345. | − | 823322.i | 0.253631 | − | 0.439302i | −0.710892 | − | 0.703301i | \(-0.751708\pi\) |
0.964523 | + | 0.264000i | \(0.0850418\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.98956e6i | 1.41185i | 0.708285 | + | 0.705927i | \(0.249469\pi\) | ||||
−0.708285 | + | 0.705927i | \(0.750531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −178869. | −0.0523193 | −0.0261596 | − | 0.999658i | \(-0.508328\pi\) | ||||
−0.0261596 | + | 0.999658i | \(0.508328\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.60967e6 | − | 2.66139e6i | −0.944666 | − | 0.545403i | −0.0532463 | − | 0.998581i | \(-0.516957\pi\) |
−0.891420 | + | 0.453178i | \(0.850290\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −418507. | − | 5.74959e6i | −0.0725969 | − | 0.997361i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −708441. | + | 409018.i | −0.0897842 | + | 0.0518369i | −0.544220 | − | 0.838943i | \(-0.683174\pi\) |
0.454436 | + | 0.890780i | \(0.349841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −262325. | −0.0286674 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.19042e6 | + | 4.72874e6i | −0.675925 | + | 0.390245i | −0.798318 | − | 0.602236i | \(-0.794276\pi\) |
0.122393 | + | 0.992482i | \(0.460943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.08168e7 | + | 1.87353e7i | −0.781234 | + | 1.35314i | 0.149989 | + | 0.988688i | \(0.452076\pi\) |
−0.931223 | + | 0.364450i | \(0.881257\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −31513.7 | − | 18194.5i | −0.00176541 | − | 0.00101926i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.78342e6 | + | 1.34813e7i | 0.386252 | + | 0.669009i | 0.991942 | − | 0.126692i | \(-0.0404361\pi\) |
−0.605690 | + | 0.795701i | \(0.707103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.95425e6i | 0.313015i | 0.987677 | + | 0.156508i | \(0.0500236\pi\) | ||||
−0.987677 | + | 0.156508i | \(0.949976\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.59210e7 | + | 2.75759e7i | 0.560632 | + | 0.971043i | 0.997441 | + | 0.0714887i | \(0.0227750\pi\) |
−0.436810 | + | 0.899554i | \(0.643892\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −180798. | + | 788243.i | −0.00514318 | + | 0.0224232i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44265e7 | − | 4.23079e7i | 0.627122 | − | 1.08621i | −0.361004 | − | 0.932564i | \(-0.617566\pi\) |
0.988126 | − | 0.153643i | \(-0.0491007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.26637e6i | 0.195253i | 0.995223 | + | 0.0976264i | \(0.0311250\pi\) | ||||
−0.995223 | + | 0.0976264i | \(0.968875\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.82638e7 | −1.69086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.56105e7 | + | 2.05597e7i | 0.567569 | + | 0.327686i | 0.756178 | − | 0.654366i | \(-0.227065\pi\) |
−0.188609 | + | 0.982052i | \(0.560398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −76391.2 | + | 82153.7i | −0.00111398 | + | 0.00119801i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.55524e7 | + | 3.20732e7i | −0.682037 | + | 0.393774i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.33379e7 | −0.715446 | −0.357723 | − | 0.933828i | \(-0.616447\pi\) | ||||
−0.357723 | + | 0.933828i | \(0.616447\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.64407e7 | + | 3.83595e7i | −0.638482 | + | 0.368628i | −0.784030 | − | 0.620724i | \(-0.786839\pi\) |
0.145548 | + | 0.989351i | \(0.453506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.07200e7 | − | 1.05170e8i | 0.539489 | − | 0.934423i | −0.459442 | − | 0.888208i | \(-0.651951\pi\) |
0.998932 | − | 0.0462153i | \(-0.0147160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.07115e7 | + | 4.65988e7i | 0.615744 | + | 0.355500i | 0.775210 | − | 0.631703i | \(-0.217644\pi\) |
−0.159466 | + | 0.987203i | \(0.550977\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.00369e8 | − | 1.73845e8i | −0.711042 | − | 1.23156i | −0.964466 | − | 0.264205i | \(-0.914890\pi\) |
0.253425 | − | 0.967355i | \(-0.418443\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.47043e7i | 0.396844i | 0.980117 | + | 0.198422i | \(0.0635816\pi\) | ||||
−0.980117 | + | 0.198422i | \(0.936418\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.46798e8 | − | 2.54261e8i | −0.839322 | − | 1.45375i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.08329e7 | + | 2.65218e8i | −0.303354 | + | 1.32256i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.07123e8 | + | 1.85542e8i | −0.499735 | + | 0.865567i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.36051e8i | 0.557265i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.72175e7 | 0.373706 | 0.186853 | − | 0.982388i | \(-0.440171\pi\) | ||||
0.186853 | + | 0.982388i | \(0.440171\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.80952e7 | − | 4.50883e7i | −0.265179 | − | 0.153101i | 0.361516 | − | 0.932366i | \(-0.382259\pi\) |
−0.626695 | + | 0.779265i | \(0.715593\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.80871e7 | + | 1.89031e8i | 0.185641 | + | 0.604125i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.80714e8 | + | 2.19806e8i | −1.08073 | + | 0.623959i | −0.931093 | − | 0.364782i | \(-0.881144\pi\) |
−0.149636 | + | 0.988741i | \(0.547810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.94059e8 | −1.59137 | −0.795683 | − | 0.605713i | \(-0.792888\pi\) | ||||
−0.795683 | + | 0.605713i | \(0.792888\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13629.0 | − | 7868.71i | 3.25927e−5 | − | 1.88174e-5i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.90916e8 | + | 5.03881e8i | −0.658106 | + | 1.13987i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.93167e8 | + | 1.11525e8i | 0.391912 | + | 0.226270i | 0.682988 | − | 0.730429i | \(-0.260680\pi\) |
−0.291076 | + | 0.956700i | \(0.594013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.98322e8 | + | 5.16710e8i | 0.573823 | + | 0.993891i | 0.996168 | + | 0.0874559i | \(0.0278737\pi\) |
−0.422345 | + | 0.906435i | \(0.638793\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.20565e9i | 2.08878i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.23899e8 | − | 5.61010e8i | −0.533103 | − | 0.923362i | −0.999253 | − | 0.0386560i | \(-0.987692\pi\) |
0.466149 | − | 0.884706i | \(-0.345641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.65190e8 | + | 2.65863e8i | −1.28768 | + | 0.395689i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.84999e8 | − | 8.40043e8i | 0.687054 | − | 1.19001i | −0.285733 | − | 0.958309i | \(-0.592237\pi\) |
0.972787 | − | 0.231702i | \(-0.0744296\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.10131e8i | 0.655868i | 0.944701 | + | 0.327934i | \(0.106352\pi\) | ||||
−0.944701 | + | 0.327934i | \(0.893648\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.15729e8 | −0.999997 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.78976e7 | − | 1.03332e7i | −0.0199807 | − | 0.0115358i | 0.489976 | − | 0.871736i | \(-0.337005\pi\) |
−0.509957 | + | 0.860200i | \(0.670339\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.05341e8 | − | 1.15909e8i | −0.538805 | − | 0.123585i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.33160e9 | + | 7.68801e8i | −1.29707 | + | 0.748862i | −0.979897 | − | 0.199507i | \(-0.936066\pi\) |
−0.317171 | + | 0.948369i | \(0.602733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.58836e9 | −1.47991 | −0.739954 | − | 0.672658i | \(-0.765153\pi\) | ||||
−0.739954 | + | 0.672658i | \(0.765153\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.41220e8 | + | 3.70209e8i | −0.547420 | + | 0.316053i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.90861e7 | − | 3.30581e7i | 0.0156081 | − | 0.0270340i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.16068e9 | + | 6.70118e8i | 0.872125 | + | 0.503521i | 0.868054 | − | 0.496470i | \(-0.165371\pi\) |
0.00407097 | + | 0.999992i | \(0.498704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.28612e8 | − | 1.08879e9i | −0.453058 | − | 0.784719i | 0.545516 | − | 0.838100i | \(-0.316334\pi\) |
−0.998574 | + | 0.0533809i | \(0.983000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.61383e8i | 0.306335i | 0.988200 | + | 0.153167i | \(0.0489474\pi\) | ||||
−0.988200 | + | 0.153167i | \(0.951053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.92807e8 | − | 1.02677e9i | −0.378008 | − | 0.654729i | 0.612764 | − | 0.790266i | \(-0.290057\pi\) |
−0.990772 | + | 0.135537i | \(0.956724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.31358e9 | + | 1.22144e9i | 0.773520 | + | 0.719263i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.55358e9 | − | 2.69087e9i | 0.879665 | − | 1.52362i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2.77419e7i | − | 0.0145396i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.99372e9 | −1.51037 | −0.755183 | − | 0.655514i | \(-0.772452\pi\) | ||||
−0.755183 | + | 0.655514i | \(0.772452\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.20643e8 | + | 6.96535e7i | 0.0564611 | + | 0.0325979i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.62278e9 | + | 8.30952e8i | 1.63381 | + | 0.374746i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.58572e6 | − | 2.64757e6i | 0.00192238 | − | 0.00110988i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.79107e9 | −1.12863 | −0.564314 | − | 0.825560i | \(-0.690859\pi\) | ||||
−0.564314 | + | 0.825560i | \(0.690859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.92916e9 | + | 1.11380e9i | −0.726549 | + | 0.419473i | −0.817158 | − | 0.576413i | \(-0.804452\pi\) |
0.0906092 | + | 0.995887i | \(0.471119\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29738e9 | + | 2.24713e9i | −0.471765 | + | 0.817122i | −0.999478 | − | 0.0323013i | \(-0.989716\pi\) |
0.527713 | + | 0.849423i | \(0.323050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.86548e9 | + | 1.65438e9i | 0.972239 | + | 0.561322i | 0.899918 | − | 0.436059i | \(-0.143626\pi\) |
0.0723208 | + | 0.997381i | \(0.476959\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.07275e9 | + | 3.59011e9i | 0.679634 | + | 1.17716i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.57435e9i | − | 1.70845i | −0.519902 | − | 0.854226i | \(-0.674032\pi\) | ||
0.519902 | − | 0.854226i | \(-0.325968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.64155e7 | + | 8.03940e7i | 0.0137592 | + | 0.0238317i | 0.872823 | − | 0.488037i | \(-0.162287\pi\) |
−0.859064 | + | 0.511869i | \(0.828953\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.95668e9 | + | 4.04094e9i | −0.543068 | + | 1.12155i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.92414e6 | − | 3.33271e6i | 0.000516950 | − | 0.000895384i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.50678e9i | − | 0.631571i | −0.948831 | − | 0.315785i | \(-0.897732\pi\) | ||
0.948831 | − | 0.315785i | \(-0.102268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.26974e8 | 0.0309907 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.74846e9 | − | 1.58683e9i | −0.630024 | − | 0.363745i | 0.150737 | − | 0.988574i | \(-0.451835\pi\) |
−0.780762 | + | 0.624829i | \(0.785169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.70478e8 | + | 2.18192e9i | 0.149000 | + | 0.484885i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.06026e9 | + | 3.49889e9i | −1.26668 | + | 0.731320i | −0.974359 | − | 0.224999i | \(-0.927762\pi\) |
−0.292325 | + | 0.956319i | \(0.594429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.37104e8 | 0.129189 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.42291e9 | − | 3.70827e9i | 1.22666 | − | 0.708210i | 0.260327 | − | 0.965521i | \(-0.416170\pi\) |
0.966329 | + | 0.257311i | \(0.0828364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.39114e8 | − | 1.62659e9i | 0.174117 | − | 0.301580i | −0.765738 | − | 0.643152i | \(-0.777626\pi\) |
0.939855 | + | 0.341573i | \(0.110960\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.29880e7 | + | 3.63662e7i | 0.0110135 | + | 0.00635867i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.49984e9 | + | 4.32985e9i | 0.424613 | + | 0.735450i | 0.996384 | − | 0.0849624i | \(-0.0270770\pi\) |
−0.571772 | + | 0.820413i | \(0.693744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.63815e9i | 1.22508i | 0.790441 | + | 0.612538i | \(0.209851\pi\) | ||||
−0.790441 | + | 0.612538i | \(0.790149\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.13228e9 | − | 1.96116e9i | −0.176525 | − | 0.305751i | 0.764163 | − | 0.645023i | \(-0.223152\pi\) |
−0.940688 | + | 0.339273i | \(0.889819\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.01489e9 | − | 6.52284e9i | −1.03393 | − | 0.961411i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.93398e9 | − | 5.08180e9i | 0.420596 | − | 0.728494i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.08056e10i | − | 1.46615i | −0.680148 | − | 0.733075i | \(-0.738084\pi\) | ||
0.680148 | − | 0.733075i | \(-0.261916\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.36568e9 | 0.972579 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.52537e7 | + | 8.80672e6i | 0.00190849 | + | 0.00110187i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.92447e8 | − | 3.14507e8i | 0.0356271 | − | 0.0383147i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.45915e10 | − | 8.42438e9i | 1.68616 | − | 0.973506i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.45717e9 | −0.164043 | −0.0820213 | − | 0.996631i | \(-0.526138\pi\) | ||||
−0.0820213 | + | 0.996631i | \(0.526138\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.11591e10 | − | 6.44270e9i | 1.19285 | − | 0.688694i | 0.233901 | − | 0.972260i | \(-0.424851\pi\) |
0.958953 | + | 0.283566i | \(0.0915175\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.96042e9 | + | 3.39554e9i | −0.204254 | + | 0.353779i | −0.949895 | − | 0.312570i | \(-0.898810\pi\) |
0.745641 | + | 0.666348i | \(0.232144\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.36309e9 | + | 2.51903e9i | 0.432073 | + | 0.249458i | 0.700229 | − | 0.713918i | \(-0.253081\pi\) |
−0.268156 | + | 0.963375i | \(0.586414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.25815e8 | − | 2.17918e8i | −0.0121498 | − | 0.0210441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9.33426e9i | − | 0.857570i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.04461e6 | + | 8.73752e6i | 0.000452162 | + | 0.000783167i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.22163e10 | − | 3.75391e9i | 1.04269 | − | 0.320406i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.79211e9 | − | 6.56813e9i | 0.315914 | − | 0.547180i | −0.663717 | − | 0.747984i | \(-0.731022\pi\) |
0.979631 | + | 0.200804i | \(0.0643554\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.21238e10i | − | 0.962628i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.10409e10 | 1.63134 | 0.815670 | − | 0.578517i | \(-0.196368\pi\) | ||||
0.815670 | + | 0.578517i | \(0.196368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.51560e8 | − | 2.60708e8i | −0.0333963 | − | 0.0192813i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.07938e10 | + | 8.66458e9i | 0.779827 | + | 0.625995i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.13881e9 | − | 1.81219e9i | 0.216495 | − | 0.124993i | −0.387832 | − | 0.921730i | \(-0.626776\pi\) |
0.604326 | + | 0.796737i | \(0.293442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00609e9 | 0.270034 | 0.135017 | − | 0.990843i | \(-0.456891\pi\) | ||||
0.135017 | + | 0.990843i | \(0.456891\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.38535e9 | + | 7.99830e8i | −0.0892194 | + | 0.0515108i | −0.543946 | − | 0.839120i | \(-0.683070\pi\) |
0.454727 | + | 0.890631i | \(0.349737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.09747e9 | − | 5.36497e9i | 0.195026 | − | 0.337795i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.59519e9 | − | 2.65303e9i | −0.276647 | − | 0.159722i | 0.355258 | − | 0.934768i | \(-0.384393\pi\) |
−0.631904 | + | 0.775046i | \(0.717726\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.09991e9 | + | 8.83331e9i | 0.300285 | + | 0.520109i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.47991e10i | − | 1.39722i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.07704e9 | + | 1.86549e9i | 0.0593700 | + | 0.102832i | 0.894183 | − | 0.447702i | \(-0.147757\pi\) |
−0.834813 | + | 0.550534i | \(0.814424\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.39102e8 | − | 1.91439e9i | 0.0231777 | − | 0.101050i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.54727e10 | + | 2.67995e10i | −0.799338 | + | 1.38449i | 0.120710 | + | 0.992688i | \(0.461483\pi\) |
−0.920048 | + | 0.391806i | \(0.871850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.49054e7i | − | 0.00172793i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.48874e10 | −1.20621 | −0.603105 | − | 0.797661i | \(-0.706070\pi\) | ||||
−0.603105 | + | 0.797661i | \(0.706070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.30297e8 | + | 3.06167e8i | 0.0246447 | + | 0.0142286i | 0.512272 | − | 0.858823i | \(-0.328804\pi\) |
−0.487627 | + | 0.873052i | \(0.662137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.28894e8 | − | 4.61248e8i | 0.0195212 | − | 0.0209938i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.98599e9 | + | 1.14661e9i | −0.0867320 | + | 0.0500747i | −0.542739 | − | 0.839902i | \(-0.682613\pi\) |
0.456007 | + | 0.889976i | \(0.349279\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.27226e10 | 1.82789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.29502e10 | + | 1.90238e10i | −1.35354 | + | 0.781465i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.26321e9 | − | 5.65204e9i | 0.131366 | − | 0.227532i | −0.792837 | − | 0.609433i | \(-0.791397\pi\) |
0.924203 | + | 0.381901i | \(0.124730\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.22563e10 | − | 1.86232e10i | −1.24749 | − | 0.720238i | −0.276881 | − | 0.960904i | \(-0.589301\pi\) |
−0.970608 | + | 0.240666i | \(0.922634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.61647e7 | − | 6.26391e7i | −0.00137109 | − | 0.00237479i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.20214e8i | − | 0.0116698i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.13828e10 | + | 3.70361e10i | 0.764138 | + | 1.32353i | 0.940701 | + | 0.339237i | \(0.110169\pi\) |
−0.176563 | + | 0.984289i | \(0.556498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.07655e9 | − | 2.21327e10i | 0.174489 | − | 0.760736i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.60842e9 | − | 6.24997e9i | 0.121653 | − | 0.210710i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.93333e10i | 1.27616i | 0.769971 | + | 0.638079i | \(0.220271\pi\) | ||||
−0.769971 | + | 0.638079i | \(0.779729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.12925e10 | −0.677795 | −0.338898 | − | 0.940823i | \(-0.610054\pi\) | ||||
−0.338898 | + | 0.940823i | \(0.610054\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.11934e10 | + | 1.22360e10i | 0.649600 | + | 0.375047i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.52572e10 | − | 4.96512e10i | −0.458949 | − | 1.49354i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.33185e10 | − | 1.92364e10i | 0.965553 | − | 0.557462i | 0.0676756 | − | 0.997707i | \(-0.478442\pi\) |
0.897878 | + | 0.440245i | \(0.145108\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.32573e9 | −0.0946097 | −0.0473048 | − | 0.998880i | \(-0.515063\pi\) | ||||
−0.0473048 | + | 0.998880i | \(0.515063\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.68892e10 | − | 1.55245e10i | 0.737313 | − | 0.425688i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.39336e8 | − | 9.34157e8i | 0.0145212 | − | 0.0251514i | −0.858674 | − | 0.512523i | \(-0.828711\pi\) |
0.873195 | + | 0.487372i | \(0.162044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.97276e10 | + | 1.71632e10i | 0.771870 | + | 0.445639i | 0.833541 | − | 0.552457i | \(-0.186310\pi\) |
−0.0616712 | + | 0.998097i | \(0.519643\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.60124e10 | − | 2.77342e10i | −0.408334 | − | 0.707254i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.67492e10i | 0.904195i | 0.891969 | + | 0.452098i | \(0.149324\pi\) | ||||
−0.891969 | + | 0.452098i | \(0.850676\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.71888e8 | + | 1.16374e9i | 0.0162402 | + | 0.0281288i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.35157e7 | − | 2.56634e7i | 0.00194860 | − | 0.000598782i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.21688e10 | + | 3.83974e10i | −0.508249 | + | 0.880314i | 0.491705 | + | 0.870762i | \(0.336374\pi\) |
−0.999954 | + | 0.00955198i | \(0.996959\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.39093e10i | − | 0.529374i | −0.964334 | − | 0.264687i | \(-0.914731\pi\) | ||
0.964334 | − | 0.264687i | \(-0.0852686\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.59365e10 | 0.346793 | 0.173396 | − | 0.984852i | \(-0.444526\pi\) | ||||
0.173396 | + | 0.984852i | \(0.444526\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.63380e10 | − | 2.09797e10i | −0.764000 | − | 0.441095i | 0.0667302 | − | 0.997771i | \(-0.478743\pi\) |
−0.830730 | + | 0.556676i | \(0.812077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.64300e10 | − | 8.35590e9i | −0.752952 | − | 0.172704i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.21756e7 | + | 3.01236e7i | −0.00104237 | + | 0.000601814i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.77853e10 | 0.349370 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.17379e10 | + | 2.98709e10i | −0.982803 | + | 0.567422i | −0.903115 | − | 0.429398i | \(-0.858726\pi\) |
−0.0796879 | + | 0.996820i | \(0.525392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.22096e7 | − | 3.84682e7i | 0.000414917 | − | 0.000718656i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.27201e10 | + | 2.46644e10i | 0.772085 | + | 0.445763i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.18299e10 | − | 8.97720e10i | −0.921434 | − | 1.59597i | −0.797197 | − | 0.603719i | \(-0.793685\pi\) |
−0.124237 | − | 0.992253i | \(-0.539648\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.00236e11i | 1.72464i | 0.506365 | + | 0.862319i | \(0.330989\pi\) | ||||
−0.506365 | + | 0.862319i | \(0.669011\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.23327e10 | − | 7.33223e10i | −0.716618 | − | 1.24122i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.39860e10 | − | 1.30050e10i | −0.229229 | − | 0.213150i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.28401e10 | + | 3.95601e10i | −0.368379 | + | 0.638051i | −0.989312 | − | 0.145812i | \(-0.953421\pi\) |
0.620933 | + | 0.783864i | \(0.286754\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.46334e10i | 1.00968i | 0.863212 | + | 0.504842i | \(0.168449\pi\) | ||||
−0.863212 | + | 0.504842i | \(0.831551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.97504e10 | 0.918703 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.11934e10 | + | 4.68770e10i | 1.20962 | + | 0.698375i | 0.962677 | − | 0.270654i | \(-0.0872400\pi\) |
0.246945 | + | 0.969029i | \(0.420573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.45174e10 | − | 1.70920e10i | −1.09288 | − | 0.250674i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.19086e10 | + | 4.72900e10i | −1.16440 | + | 0.672265i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.79284e9 | −0.0250945 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.63045e10 | + | 4.98279e10i | −1.17134 | + | 0.676272i | −0.953995 | − | 0.299823i | \(-0.903072\pi\) |
−0.217343 | + | 0.976095i | \(0.569739\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.25436e9 | − | 5.63672e9i | 0.0434969 | − | 0.0753389i | −0.843457 | − | 0.537196i | \(-0.819483\pi\) |
0.886954 | + | 0.461857i | \(0.152817\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.51935e11 | − | 8.77199e10i | −1.96977 | − | 1.13725i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.18995e10 | + | 5.52516e10i | 0.407344 | + | 0.705541i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.86405e8i | 0.00230966i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.62921e10 | − | 6.28598e10i | −0.442993 | − | 0.767287i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.09037e9 | − | 1.60666e9i | −0.0129187 | − | 0.0190357i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.36034e10 | + | 1.44805e11i | −0.975966 | + | 1.69042i | −0.299256 | + | 0.954173i | \(0.596738\pi\) |
−0.676710 | + | 0.736250i | \(0.736595\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.56339e11i | 1.77208i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.53766e10 | −0.953651 | −0.476826 | − | 0.878998i | \(-0.658213\pi\) | ||||
−0.476826 | + | 0.878998i | \(0.658213\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.32875e10 | − | 3.07656e10i | −0.578122 | − | 0.333779i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.44537e10 | + | 1.12122e11i | 0.368413 | + | 1.19892i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.84279e10 | − | 1.64129e10i | 0.295341 | − | 0.170515i | −0.345007 | − | 0.938600i | \(-0.612123\pi\) |
0.640348 | + | 0.768085i | \(0.278790\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.35732e6 | −8.55894e−5 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.16276e11 | + | 6.71317e10i | −1.15732 | + | 0.668181i | −0.950661 | − | 0.310231i | \(-0.899594\pi\) |
−0.206663 | + | 0.978412i | \(0.566260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.51965e10 | − | 4.36416e10i | 0.247256 | − | 0.428260i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.23300e11 | + | 7.11873e10i | 1.17629 | + | 0.679131i | 0.955153 | − | 0.296112i | \(-0.0956901\pi\) |
0.221136 | + | 0.975243i | \(0.429023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.17814e10 | − | 5.50470e10i | −0.298971 | − | 0.517833i | 0.676930 | − | 0.736047i | \(-0.263310\pi\) |
−0.975901 | + | 0.218215i | \(0.929977\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.14026e10i | 0.744675i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.97886e8 | + | 1.72839e9i | 0.00900281 | + | 0.0155933i | 0.870492 | − | 0.492183i | \(-0.163801\pi\) |
−0.861489 | + | 0.507776i | \(0.830468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.62931e10 | − | 1.51503e10i | −0.142988 | − | 0.132959i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.37767e8 | + | 2.38619e8i | −0.00119253 | + | 0.00206553i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.66874e11i | − | 1.40551i | −0.711430 | − | 0.702757i | \(-0.751952\pi\) | ||
0.711430 | − | 0.702757i | \(-0.248048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.27502e11 | −1.05939 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.57012e11 | + | 9.06509e10i | 1.26974 | + | 0.733084i | 0.974938 | − | 0.222475i | \(-0.0714137\pi\) |
0.294800 | + | 0.955559i | \(0.404747\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.44309e11 | − | 1.55195e11i | 1.15140 | − | 1.23826i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.12369e9 | + | 2.38081e9i | −0.0320316 | + | 0.0184935i | −0.515930 | − | 0.856631i | \(-0.672554\pi\) |
0.483899 | + | 0.875124i | \(0.339220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.35010e10 | 0.410075 | 0.205038 | − | 0.978754i | \(-0.434268\pi\) | ||||
0.205038 | + | 0.978754i | \(0.434268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.44504e11 | − | 8.34294e10i | 1.07859 | − | 0.622727i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.98245e10 | + | 6.89781e10i | −0.293357 | + | 0.508109i | −0.974601 | − | 0.223947i | \(-0.928106\pi\) |
0.681245 | + | 0.732056i | \(0.261439\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.15378e8 | − | 1.24349e8i | −0.00154539 | − | 0.000892229i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.46589e9 | + | 6.00309e9i | 0.0245455 | + | 0.0425141i | 0.878037 | − | 0.478592i | \(-0.158853\pi\) |
−0.853492 | + | 0.521106i | \(0.825519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.18082e11i | 0.814783i | 0.913254 | + | 0.407392i | \(0.133562\pi\) | ||||
−0.913254 | + | 0.407392i | \(0.866438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.23245e10 | + | 3.86672e10i | 0.152061 | + | 0.263378i | 0.931985 | − | 0.362496i | \(-0.118076\pi\) |
−0.779924 | + | 0.625875i | \(0.784742\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.43728e10 | + | 2.89996e10i | −0.626462 | + | 0.192504i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.51548e10 | − | 1.64813e11i | 0.623606 | − | 1.08012i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.07742e11i | − | 0.688307i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.91802e10 | −0.562537 | −0.281269 | − | 0.959629i | \(-0.590755\pi\) | ||||
−0.281269 | + | 0.959629i | \(0.590755\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.55711e10 | − | 3.78575e10i | −0.403290 | − | 0.232840i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.95539e7 | − | 2.68639e8i | −0.000118762 | − | 0.00163159i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.36113e11 | − | 1.36320e11i | 1.39858 | − | 0.807470i | 0.404336 | − | 0.914611i | \(-0.367503\pi\) |
0.994244 | + | 0.107140i | \(0.0341694\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.69153e11 | −1.57454 | −0.787272 | − | 0.616606i | \(-0.788507\pi\) | ||||
−0.787272 | + | 0.616606i | \(0.788507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.43221e11 | + | 1.40424e11i | −1.38798 | + | 0.801353i | −0.993088 | − | 0.117372i | \(-0.962553\pi\) |
−0.394896 | + | 0.918726i | \(0.629220\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.59275e9 | + | 2.75872e9i | −0.00897777 | + | 0.0155500i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.90008e11 | + | 1.09701e11i | 1.04501 | + | 0.603334i | 0.921247 | − | 0.388978i | \(-0.127172\pi\) |
0.123759 | + | 0.992312i | \(0.460505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.51157e10 | + | 6.08221e10i | 0.190781 | + | 0.330443i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.75082e11i | − | 1.45855i | −0.684223 | − | 0.729273i | \(-0.739858\pi\) | ||
0.684223 | − | 0.729273i | \(-0.260142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.90309e10 | − | 1.02245e11i | −0.309224 | − | 0.535592i | 0.668969 | − | 0.743291i | \(-0.266736\pi\) |
−0.978193 | + | 0.207698i | \(0.933403\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.44322e10 | − | 1.50117e11i | 0.176067 | − | 0.767616i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.40813e11 | − | 2.43895e11i | 0.711442 | − | 1.23225i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.28672e9i | 0.0359453i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.00170e11 | 0.488292 | 0.244146 | − | 0.969739i | \(-0.421492\pi\) | ||||
0.244146 | + | 0.969739i | \(0.421492\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.80353e11 | − | 1.04127e11i | −0.858558 | − | 0.495689i | 0.00497123 | − | 0.999988i | \(-0.498418\pi\) |
−0.863529 | + | 0.504299i | \(0.831751\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.03556e11 | − | 1.11368e11i | 0.487188 | − | 0.523938i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.75907e11 | + | 1.59295e11i | −1.26788 | + | 0.732013i | −0.974587 | − | 0.224008i | \(-0.928086\pi\) |
−0.293297 | + | 0.956021i | \(0.594753\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.42378e11 | 1.55505 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.31006e7 | + | 1.91106e7i | −0.000146879 | + | 8.48004e-5i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.42190e10 | + | 5.92691e10i | −0.150091 | + | 0.259966i | −0.931261 | − | 0.364353i | \(-0.881290\pi\) |
0.781170 | + | 0.624319i | \(0.214623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00680e11 | + | 2.31332e11i | 1.71735 | + | 0.991511i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.26069e11 | + | 3.91563e11i | 0.957876 | + | 1.65909i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.52825e10i | − | 0.187525i | −0.995595 | − | 0.0937624i | \(-0.970111\pi\) | ||
0.995595 | − | 0.0937624i | \(-0.0298894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.91511e10 | − | 6.78117e10i | −0.160296 | − | 0.277641i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.11810e10 | − | 1.79540e11i | 0.164823 | − | 0.718595i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.79001e11 | + | 3.10038e11i | −0.708385 | + | 1.22696i | 0.257071 | + | 0.966393i | \(0.417243\pi\) |
−0.965456 | + | 0.260566i | \(0.916091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.83573e11i | − | 2.25807i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.22566e7 | −4.68972e−5 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.08955e10 | − | 4.67051e10i | −0.302698 | − | 0.174763i | 0.340956 | − | 0.940079i | \(-0.389249\pi\) |
−0.643654 | + | 0.765317i | \(0.722582\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.56459e10 | + | 2.78715e11i | 0.316932 | + | 1.03138i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.39707e11 | − | 8.06596e10i | 0.505667 | − | 0.291947i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.36551e11 | 0.846811 | 0.423406 | − | 0.905940i | \(-0.360835\pi\) | ||||
0.423406 | + | 0.905940i | \(0.360835\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.75554e10 | + | 1.01356e10i | −0.0614811 | + | 0.0354962i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.17827e11 | + | 3.77288e11i | −0.754565 | + | 1.30694i | 0.191025 | + | 0.981585i | \(0.438819\pi\) |
−0.945590 | + | 0.325360i | \(0.894515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.54080e9 | + | 2.62163e9i | 0.0153908 | + | 0.00888591i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.87063e11 | + | 3.24003e11i | 0.627206 | + | 1.08635i | 0.988110 | + | 0.153750i | \(0.0491350\pi\) |
−0.360904 | + | 0.932603i | \(0.617532\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 3.22304e11i | − | 1.05757i | −0.848754 | − | 0.528787i | \(-0.822647\pi\) | ||
0.848754 | − | 0.528787i | \(-0.177353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.68581e10 | − | 1.50443e11i | −0.281958 | − | 0.488366i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.13897e11 | + | 6.57279e10i | −0.679636 | + | 0.208844i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.28833e10 | − | 5.69555e10i | 0.103375 | − | 0.179051i | −0.809698 | − | 0.586847i | \(-0.800369\pi\) |
0.913073 | + | 0.407796i | \(0.133703\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 4.64679e11i | − | 1.43010i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.18611e11 | 1.57928 | 0.789638 | − | 0.613573i | \(-0.210268\pi\) | ||||
0.789638 | + | 0.613573i | \(0.210268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.03805e11 | + | 5.99319e10i | 0.309514 | + | 0.178698i | 0.646709 | − | 0.762737i | \(-0.276145\pi\) |
−0.337195 | + | 0.941435i | \(0.609478\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.69775e11 | + | 1.07752e11i | 1.38609 | + | 0.317926i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.82682e8 | + | 2.20942e8i | −0.00110575 | + | 0.000638405i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.19093e11 | −0.912455 | −0.456227 | − | 0.889863i | \(-0.650800\pi\) | ||||
−0.456227 | + | 0.889863i | \(0.650800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.64540e11 | − | 3.25938e11i | 1.58116 | − | 0.912886i | 0.586475 | − | 0.809967i | \(-0.300515\pi\) |
0.994690 | − | 0.102918i | \(-0.0328181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.67139e11 | − | 2.89494e11i | 0.463310 | − | 0.802477i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.84571e11 | + | 1.64297e11i | 0.772753 | + | 0.446149i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.33959e9 | + | 2.32023e9i | 0.00360053 | + | 0.00623630i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.04519e11i | 1.32861i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.96638e11 | − | 3.40586e11i | −0.512587 | − | 0.887827i | −0.999893 | − | 0.0145960i | \(-0.995354\pi\) |
0.487306 | − | 0.873231i | \(-0.337980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.13770e11 | − | 1.05790e11i | −0.290618 | − | 0.270233i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.05397e8 | + | 8.75373e8i | −0.00127803 | + | 0.00221361i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.96733e11i | − | 1.72677i | −0.504550 | − | 0.863383i | \(-0.668341\pi\) | ||
0.504550 | − | 0.863383i | \(-0.331659\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.03232e11 | −1.48012 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.28820e9 | + | 5.36254e9i | 0.0223393 | + | 0.0128976i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.87081e11 | + | 1.57595e11i | 1.63616 | + | 0.375283i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.85430e11 | − | 3.37998e11i | 1.36672 | − | 0.789079i | 0.376216 | − | 0.926532i | \(-0.377225\pi\) |
0.990508 | + | 0.137453i | \(0.0438916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.84102e11 | 0.887897 | 0.443949 | − | 0.896052i | \(-0.353577\pi\) | ||||
0.443949 | + | 0.896052i | \(0.353577\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.54243e11 | + | 3.77727e11i | −1.48289 | + | 0.856146i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.36614e9 | + | 1.27585e10i | −0.0165330 | + | 0.0286360i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.20317e10 | − | 6.94653e9i | −0.0264823 | − | 0.0152896i | 0.486700 | − | 0.873569i | \(-0.338200\pi\) |
−0.513183 | + | 0.858279i | \(0.671534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.39268e10 | − | 1.28045e11i | −0.161140 | − | 0.279102i | 0.774138 | − | 0.633017i | \(-0.218184\pi\) |
−0.935278 | + | 0.353915i | \(0.884850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.04733e11i | 0.437689i | 0.975760 | + | 0.218845i | \(0.0702288\pi\) | ||||
−0.975760 | + | 0.218845i | \(0.929771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.99191e11 | − | 3.45009e11i | −0.421746 | − | 0.730486i | 0.574364 | − | 0.818600i | \(-0.305249\pi\) |
−0.996110 | + | 0.0881141i | \(0.971916\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.66876e11 | − | 5.40589e11i | −0.761972 | − | 1.12276i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.98650e11 | − | 3.44073e11i | 0.408643 | − | 0.707790i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.17098e11i | 0.438134i | 0.975710 | + | 0.219067i | \(0.0703014\pi\) | ||||
−0.975710 | + | 0.219067i | \(0.929699\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.78648e10 | −0.115673 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.50191e11 | + | 3.17653e11i | 1.07916 | + | 0.623055i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.51097e11 | − | 4.91712e11i | −0.293578 | − | 0.955382i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.10372e11 | − | 1.79193e11i | 0.591785 | − | 0.341667i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.80006e11 | −1.28445 | −0.642225 | − | 0.766517i | \(-0.721988\pi\) | ||||
−0.642225 | + | 0.766517i | \(0.721988\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.16628e11 | + | 1.82805e11i | −0.586984 | + | 0.338895i | −0.763904 | − | 0.645330i | \(-0.776720\pi\) |
0.176920 | + | 0.984225i | \(0.443387\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.66673e11 | − | 2.88687e11i | 0.306121 | − | 0.530217i | −0.671389 | − | 0.741105i | \(-0.734302\pi\) |
0.977510 | + | 0.210888i | \(0.0676354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.33254e10 | + | 4.23344e10i | 0.132194 | + | 0.0763221i | 0.564638 | − | 0.825338i | \(-0.309016\pi\) |
−0.432445 | + | 0.901660i | \(0.642349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.04769e9 | + | 1.39390e10i | 0.0143750 | + | 0.0248982i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.64548e10i | − | 0.0288545i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.63665e8 | + | 6.29887e8i | 0.000631872 | + | 0.00109444i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.39220e11 | − | 2.22440e11i | −0.408099 | − | 0.379473i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.79184e11 | + | 8.29972e11i | −0.810036 | + | 1.40302i | 0.102802 | + | 0.994702i | \(0.467219\pi\) |
−0.912838 | + | 0.408322i | \(0.866114\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.87605e11i | − | 0.311417i | −0.987803 | − | 0.155708i | \(-0.950234\pi\) | ||
0.987803 | − | 0.155708i | \(-0.0497660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.49167e11 | −0.574369 | −0.287184 | − | 0.957875i | \(-0.592719\pi\) | ||||
−0.287184 | + | 0.957875i | \(0.592719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.62160e10 | − | 2.66828e10i | −0.0746616 | − | 0.0431059i | 0.462204 | − | 0.886773i | \(-0.347059\pi\) |
−0.536866 | + | 0.843667i | \(0.680392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.58948e11 | + | 1.70939e11i | −0.254477 | + | 0.273674i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.79668e11 | + | 2.19202e11i | −0.597033 | + | 0.344697i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.19752e12 | 1.86633 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00155e12 | + | 5.78247e11i | −1.53333 | + | 0.885268i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.63541e10 | + | 8.02877e10i | −0.0703378 | + | 0.121829i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.07131e12 | + | 6.18524e11i | 1.59707 | + | 0.922066i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.30976e11 | + | 5.73267e11i | 0.489066 | + | 0.847087i | 0.999921 | − | 0.0125802i | \(-0.00400451\pi\) |
−0.510855 | + | 0.859667i | \(0.670671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.59034e11i | 0.230896i | 0.993314 | + | 0.115448i | \(0.0368304\pi\) | ||||
−0.993314 | + | 0.115448i | \(0.963170\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.56056e9 | + | 2.70297e9i | 0.00224594 | + | 0.00389008i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.06963e11 | − | 6.35973e10i | 0.292695 | − | 0.0899418i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.91908e10 | + | 8.52010e10i | −0.0689639 | + | 0.119449i | −0.898446 | − | 0.439085i | \(-0.855303\pi\) |
0.829482 | + | 0.558534i | \(0.188636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.71647e8i | 0.000512064i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.05289e11 | 0.280413 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.72137e10 | + | 4.45793e10i | 0.103665 | + | 0.0598509i | 0.550936 | − | 0.834547i | \(-0.314271\pi\) |
−0.447271 | + | 0.894398i | \(0.647604\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.27346e11 | − | 2.06926e11i | −0.568829 | − | 0.275434i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.57463e10 | + | 1.48646e10i | −0.0336875 | + | 0.0194495i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.04170e10 | 0.0783792 | 0.0391896 | − | 0.999232i | \(-0.487522\pi\) | ||||
0.0391896 | + | 0.999232i | \(0.487522\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.15284e12 | + | 6.65592e11i | −1.47031 | + | 0.848887i | −0.999445 | − | 0.0333161i | \(-0.989393\pi\) |
−0.470870 | + | 0.882203i | \(0.656060\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.51982e11 | + | 1.30247e12i | −0.950957 | + | 1.64711i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.29771e11 | + | 3.63598e11i | 0.783037 | + | 0.452087i | 0.837506 | − | 0.546429i | \(-0.184013\pi\) |
−0.0544683 | + | 0.998516i | \(0.517346\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.43876e8 | + | 1.28843e9i | 0.000917141 | + | 0.00158853i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.43625e11i | 1.02277i | 0.859352 | + | 0.511385i | \(0.170867\pi\) | ||||
−0.859352 | + | 0.511385i | \(0.829133\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.21902e11 | − | 9.03960e11i | −0.627444 | − | 1.08677i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.35973e11 | − | 1.02879e12i | 0.278989 | − | 1.21633i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.71773e11 | + | 1.33675e12i | −0.904891 | + | 1.56732i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.79153e11i | 1.12912i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.29950e12 | −1.48617 | −0.743087 | − | 0.669195i | \(-0.766639\pi\) | ||||
−0.743087 | + | 0.669195i | \(0.766639\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.21619e12 | − | 7.02169e11i | −1.36812 | − | 0.789887i | −0.377436 | − | 0.926036i | \(-0.623194\pi\) |
−0.990688 | + | 0.136149i | \(0.956527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.71272e11 | − | 1.04454e12i | 1.08365 | − | 1.16540i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.18792e11 | + | 1.26320e11i | −0.240134 | + | 0.138641i | −0.615238 | − | 0.788341i | \(-0.710940\pi\) |
0.375104 | + | 0.926983i | \(0.377607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.38500e10 | 0.0150771 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.51236e12 | + | 8.73163e11i | −1.61973 | + | 0.935150i | −0.632738 | + | 0.774366i | \(0.718069\pi\) |
−0.986990 | + | 0.160784i | \(0.948598\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.79667e11 | − | 3.11193e11i | 0.190864 | − | 0.330586i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.83954e10 | − | 3.37146e10i | −0.0610370 | − | 0.0352397i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.26050e11 | − | 7.37941e11i | −0.441740 | − | 0.765116i | 0.556079 | − | 0.831129i | \(-0.312305\pi\) |
−0.997819 | + | 0.0660138i | \(0.978972\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.23380e11i | 0.942081i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.18782e11 | − | 1.07176e12i | −0.626264 | − | 1.08472i | −0.988295 | − | 0.152554i | \(-0.951250\pi\) |
0.362032 | − | 0.932166i | \(-0.382083\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 252.9.bk.a.233.5 | yes | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.233.18 | yes | 44 | |
7.4 | even | 3 | inner | 252.9.bk.a.53.18 | yes | 44 | |
21.11 | odd | 6 | inner | 252.9.bk.a.53.5 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.5 | ✓ | 44 | 21.11 | odd | 6 | inner | |
252.9.bk.a.53.18 | yes | 44 | 7.4 | even | 3 | inner | |
252.9.bk.a.233.5 | yes | 44 | 1.1 | even | 1 | trivial | |
252.9.bk.a.233.18 | yes | 44 | 3.2 | odd | 2 | inner |