Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,10,Mod(1,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.9622935145\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 64.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 68.0000 | 0.484689 | 0.242345 | − | 0.970190i | \(-0.422084\pi\) | ||||
0.242345 | + | 0.970190i | \(0.422084\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1510.00 | −1.08047 | −0.540234 | − | 0.841515i | \(-0.681664\pi\) | ||||
−0.540234 | + | 0.841515i | \(0.681664\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10248.0 | −1.61324 | −0.806618 | − | 0.591073i | \(-0.798705\pi\) | ||||
−0.806618 | + | 0.591073i | \(0.798705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −15059.0 | −0.765076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3916.00 | 0.0806447 | 0.0403223 | − | 0.999187i | \(-0.487162\pi\) | ||||
0.0403223 | + | 0.999187i | \(0.487162\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 176594. | 1.71487 | 0.857434 | − | 0.514593i | \(-0.172057\pi\) | ||||
0.857434 | + | 0.514593i | \(0.172057\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −102680. | −0.523691 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 148370. | 0.430850 | 0.215425 | − | 0.976520i | \(-0.430886\pi\) | ||||
0.215425 | + | 0.976520i | \(0.430886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 499796. | 0.879836 | 0.439918 | − | 0.898038i | \(-0.355008\pi\) | ||||
0.439918 | + | 0.898038i | \(0.355008\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −696864. | −0.781918 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.88977e6 | 1.40810 | 0.704050 | − | 0.710151i | \(-0.251373\pi\) | ||||
0.704050 | + | 0.710151i | \(0.251373\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 326975. | 0.167411 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.36246e6 | −0.855513 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 920898. | 0.241780 | 0.120890 | − | 0.992666i | \(-0.461425\pi\) | ||||
0.120890 | + | 0.992666i | \(0.461425\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.37936e6 | −0.268256 | −0.134128 | − | 0.990964i | \(-0.542823\pi\) | ||||
−0.134128 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 266288. | 0.0390876 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.54745e7 | 1.74305 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.06497e6 | −0.444292 | −0.222146 | − | 0.975013i | \(-0.571306\pi\) | ||||
−0.222146 | + | 0.975013i | \(0.571306\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.20084e7 | 0.831178 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.41008e7 | −1.33200 | −0.665999 | − | 0.745953i | \(-0.731994\pi\) | ||||
−0.665999 | + | 0.745953i | \(0.731994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.57852e7 | 1.15017 | 0.575085 | − | 0.818093i | \(-0.304969\pi\) | ||||
0.575085 | + | 0.818093i | \(0.304969\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.27391e7 | 0.826641 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.07902e7 | 1.81716 | 0.908580 | − | 0.417710i | \(-0.137167\pi\) | ||||
0.908580 | + | 0.417710i | \(0.137167\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.46679e7 | 1.60253 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00892e7 | 0.208828 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.94962e7 | −0.513482 | −0.256741 | − | 0.966480i | \(-0.582649\pi\) | ||||
−0.256741 | + | 0.966480i | \(0.582649\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.91316e6 | −0.0871340 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.39861e7 | 0.426447 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.18194e7 | 0.556747 | 0.278374 | − | 0.960473i | \(-0.410205\pi\) | ||||
0.278374 | + | 0.960473i | \(0.410205\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.34269e7 | −0.309109 | −0.154555 | − | 0.987984i | \(-0.549394\pi\) | ||||
−0.154555 | + | 0.987984i | \(0.549394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.54325e8 | 1.23425 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.66657e8 | −1.85286 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.44856e8 | 0.878214 | 0.439107 | − | 0.898435i | \(-0.355295\pi\) | ||||
0.439107 | + | 0.898435i | \(0.355295\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.28504e8 | 0.682490 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.83971e7 | −0.319430 | −0.159715 | − | 0.987163i | \(-0.551057\pi\) | ||||
−0.159715 | + | 0.987163i | \(0.551057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.68216e8 | 0.693290 | 0.346645 | − | 0.937996i | \(-0.387321\pi\) | ||||
0.346645 | + | 0.937996i | \(0.387321\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.22343e7 | 0.0811424 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.01312e7 | −0.130099 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.35399e8 | −0.679958 | −0.339979 | − | 0.940433i | \(-0.610420\pi\) | ||||
−0.339979 | + | 0.940433i | \(0.610420\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.35759e8 | 0.350418 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.46399e7 | −0.149503 | −0.0747513 | − | 0.997202i | \(-0.523816\pi\) | ||||
−0.0747513 | + | 0.997202i | \(0.523816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.24039e8 | −0.465520 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.26211e7 | 0.117188 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.87827e7 | −0.133099 | −0.0665497 | − | 0.997783i | \(-0.521199\pi\) | ||||
−0.0665497 | + | 0.997783i | \(0.521199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.80974e9 | −2.76649 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.37965e7 | −0.130021 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.54692e8 | −0.950634 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.41136e7 | −0.0276560 | −0.0138280 | − | 0.999904i | \(-0.504402\pi\) | ||||
−0.0138280 | + | 0.999904i | \(0.504402\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.89710e7 | −0.0616993 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.25963e8 | 0.598553 | 0.299277 | − | 0.954166i | \(-0.403255\pi\) | ||||
0.299277 | + | 0.954166i | \(0.403255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00618e8 | −0.700902 | −0.350451 | − | 0.936581i | \(-0.613972\pi\) | ||||
−0.350451 | + | 0.936581i | \(0.613972\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.05226e9 | 0.844837 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.45358e9 | 1.80956 | 0.904781 | − | 0.425877i | \(-0.140034\pi\) | ||||
0.904781 | + | 0.425877i | \(0.140034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.29043e8 | 0.630400 | 0.315200 | − | 0.949025i | \(-0.397928\pi\) | ||||
0.315200 | + | 0.949025i | \(0.397928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.44418e8 | −0.215344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.65129e9 | −0.952731 | −0.476366 | − | 0.879247i | \(-0.658046\pi\) | ||||
−0.476366 | + | 0.879247i | \(0.658046\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.85355e9 | −1.52141 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.65933e9 | −1.31201 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.52050e9 | −0.695063 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.34261e9 | −0.993496 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.63885e9 | −0.645605 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.45549e9 | 0.899586 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.83042e9 | 0.624358 | 0.312179 | − | 0.950023i | \(-0.398941\pi\) | ||||
0.312179 | + | 0.950023i | \(0.398941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.75339e9 | 0.557475 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.60254e8 | 0.166213 | 0.0831064 | − | 0.996541i | \(-0.473516\pi\) | ||||
0.0831064 | + | 0.996541i | \(0.473516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.12191e9 | −1.41938 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.56731e9 | 0.924355 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.54232e9 | 1.58668 | 0.793340 | − | 0.608778i | \(-0.208340\pi\) | ||||
0.793340 | + | 0.608778i | \(0.208340\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.52722e9 | 1.25586 | 0.627929 | − | 0.778271i | \(-0.283903\pi\) | ||||
0.627929 | + | 0.778271i | \(0.283903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.13374e9 | 0.880758 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.91542e8 | 0.138295 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.39056e9 | −0.261236 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.39742e9 | 0.776729 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.25329e9 | 0.540734 | 0.270367 | − | 0.962757i | \(-0.412855\pi\) | ||||
0.270367 | + | 0.962757i | \(0.412855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.54419e9 | 1.33744 | 0.668721 | − | 0.743514i | \(-0.266842\pi\) | ||||
0.668721 | + | 0.743514i | \(0.266842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.23430e9 | −0.329633 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.08283e9 | 0.289842 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.69871e8 | 0.0354493 | 0.0177246 | − | 0.999843i | \(-0.494358\pi\) | ||||
0.0177246 | + | 0.999843i | \(0.494358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.00574e9 | −0.248879 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.93663e10 | −2.27160 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.02903e10 | 1.14178 | 0.570892 | − | 0.821025i | \(-0.306597\pi\) | ||||
0.570892 | + | 0.821025i | \(0.306597\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.02095e8 | −0.0422329 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.23946e8 | −0.0123313 | −0.00616565 | − | 0.999981i | \(-0.501963\pi\) | ||||
−0.00616565 | + | 0.999981i | \(0.501963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.05809e10 | 1.94077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.52643e9 | −0.673142 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.92770e9 | −0.418250 | −0.209125 | − | 0.977889i | \(-0.567062\pi\) | ||||
−0.209125 | + | 0.977889i | \(0.567062\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.35084e9 | −0.270074 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.52372e9 | 0.269849 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.54564e9 | −0.403751 | −0.201875 | − | 0.979411i | \(-0.564704\pi\) | ||||
−0.201875 | + | 0.979411i | \(0.564704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.16150e10 | −0.804391 | −0.402196 | − | 0.915554i | \(-0.631753\pi\) | ||||
−0.402196 | + | 0.915554i | \(0.631753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.27303e9 | −0.149822 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.64810e9 | 0.480044 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.81017e8 | 0.0347457 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.42104e10 | 1.38015 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.72404e10 | 1.48103 | 0.740514 | − | 0.672041i | \(-0.234582\pi\) | ||||
0.740514 | + | 0.672041i | \(0.234582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.88743e10 | −1.49797 | −0.748987 | − | 0.662585i | \(-0.769459\pi\) | ||||
−0.748987 | + | 0.662585i | \(0.769459\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.81327e10 | −0.898061 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.80169e10 | −1.79837 | −0.899184 | − | 0.437571i | \(-0.855839\pi\) | ||||
−0.899184 | + | 0.437571i | \(0.855839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.57386e10 | −1.16344 | −0.581722 | − | 0.813387i | \(-0.697621\pi\) | ||||
−0.581722 | + | 0.813387i | \(0.697621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.85022e9 | 0.425661 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.43736e9 | −0.390048 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.63921e10 | 1.43918 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.84580e10 | −1.07730 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.95720e9 | 0.0709540 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.50064e9 | 0.191048 | 0.0955239 | − | 0.995427i | \(-0.469547\pi\) | ||||
0.0955239 | + | 0.995427i | \(0.469547\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.65100e9 | −0.154824 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.89356e10 | −1.24272 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41357e10 | 0.432761 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.14387e10 | 0.336030 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.62013e10 | 0.738851 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.05983e10 | −0.557774 | −0.278887 | − | 0.960324i | \(-0.589966\pi\) | ||||
−0.278887 | + | 0.960324i | \(0.589966\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.92392e9 | −0.128082 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.46842e10 | −1.11696 | −0.558480 | − | 0.829518i | \(-0.688615\pi\) | ||||
−0.558480 | + | 0.829518i | \(0.688615\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.69323e9 | 0.136804 | 0.0684020 | − | 0.997658i | \(-0.478210\pi\) | ||||
0.0684020 | + | 0.997658i | \(0.478210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.72892e9 | −0.0630575 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.74032e10 | 0.386837 | 0.193419 | − | 0.981116i | \(-0.438042\pi\) | ||||
0.193419 | + | 0.981116i | \(0.438042\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.17932e10 | −1.96338 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.60071e10 | −0.329568 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.35988e10 | 0.666090 | 0.333045 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333045 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.08619e10 | −1.16217 | −0.581084 | − | 0.813844i | \(-0.697371\pi\) | ||||
−0.581084 | + | 0.813844i | \(0.697371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.57319e10 | 1.02536 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.76485e10 | −1.73148 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.82610e10 | 1.50880 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.39551e9 | −0.0724623 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.74389e10 | 1.39051 | 0.695253 | − | 0.718765i | \(-0.255292\pi\) | ||||
0.695253 | + | 0.718765i | \(0.255292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.40033e9 | 0.113556 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.52346e10 | −0.225632 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.11368e10 | 1.01717 | 0.508587 | − | 0.861011i | \(-0.330168\pi\) | ||||
0.508587 | + | 0.861011i | \(0.330168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.19058e10 | 0.716748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.38678e10 | −0.184980 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.24741e10 | 0.676308 | 0.338154 | − | 0.941091i | \(-0.390198\pi\) | ||||
0.338154 | + | 0.941091i | \(0.390198\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.45393e10 | 0.554800 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.35722e9 | −0.0645118 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.37810e11 | 1.60470 | 0.802350 | − | 0.596853i | \(-0.203583\pi\) | ||||
0.802350 | + | 0.596853i | \(0.203583\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.18786e11 | −1.33784 | −0.668921 | − | 0.743333i | \(-0.733244\pi\) | ||||
−0.668921 | + | 0.743333i | \(0.733244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.23062e11 | −1.34089 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.28043e9 | 0.0135008 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.20716e10 | 0.633481 | 0.316741 | − | 0.948512i | \(-0.397412\pi\) | ||||
0.316741 | + | 0.948512i | \(0.397412\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.07718e10 | 0.205237 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.20927e10 | 0.689784 | 0.344892 | − | 0.938642i | \(-0.387916\pi\) | ||||
0.344892 | + | 0.938642i | \(0.387916\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.90151e10 | 0.361571 | 0.180786 | − | 0.983523i | \(-0.442136\pi\) | ||||
0.180786 | + | 0.983523i | \(0.442136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.13191e10 | −0.460762 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.46985e11 | 2.14883 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.65742e10 | −0.814368 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.63972e9 | −0.0134045 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.37214e10 | 0.742907 | 0.371454 | − | 0.928451i | \(-0.378859\pi\) | ||||
0.371454 | + | 0.928451i | \(0.378859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.82473e10 | −0.601548 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.25138e9 | −0.0689926 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.33722e11 | 2.41471 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.64247e11 | −1.85550 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.25655e10 | 0.290112 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.04746e10 | 0.333983 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.63239e11 | −1.04882 | −0.524411 | − | 0.851465i | \(-0.675715\pi\) | ||||
−0.524411 | + | 0.851465i | \(0.675715\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.44420e10 | −0.339720 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.54012e10 | 0.335813 | 0.167906 | − | 0.985803i | \(-0.446299\pi\) | ||||
0.167906 | + | 0.985803i | \(0.446299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.35841e11 | 1.38889 | 0.694447 | − | 0.719544i | \(-0.255649\pi\) | ||||
0.694447 | + | 0.719544i | \(0.255649\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.33030e11 | −1.33357 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.74070e10 | 0.430540 | 0.215270 | − | 0.976555i | \(-0.430937\pi\) | ||||
0.215270 | + | 0.976555i | \(0.430937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.60624e9 | 0.0194983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.66844e11 | 0.877075 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.41547e10 | 0.379077 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.77418e10 | 0.287088 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.31749e10 | 0.305548 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.22978e11 | −2.93151 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.90091e10 | −0.361785 | −0.180893 | − | 0.983503i | \(-0.557899\pi\) | ||||
−0.180893 | + | 0.983503i | \(0.557899\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.62733e10 | 0.339918 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.18733e11 | −0.948882 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.15728e11 | 0.911114 | 0.455557 | − | 0.890207i | \(-0.349440\pi\) | ||||
0.455557 | + | 0.890207i | \(0.349440\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.12288e11 | −0.461778 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.40157e9 | −0.0216334 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.49173e11 | −0.972024 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.94041e11 | −0.737409 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.38976e11 | −0.884854 | −0.442427 | − | 0.896804i | \(-0.645882\pi\) | ||||
−0.442427 | + | 0.896804i | \(0.645882\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.14491e9 | −0.0185637 | −0.00928183 | − | 0.999957i | \(-0.502955\pi\) | ||||
−0.00928183 | + | 0.999957i | \(0.502955\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.17196e11 | −1.46709 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.71172e10 | 0.195786 | 0.0978928 | − | 0.995197i | \(-0.468790\pi\) | ||||
0.0978928 | + | 0.995197i | \(0.468790\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.03280e11 | 0.345134 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.03394e11 | −0.336889 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.89030e11 | −0.918371 | −0.459185 | − | 0.888340i | \(-0.651859\pi\) | ||||
−0.459185 | + | 0.888340i | \(0.651859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.28917e10 | −0.225889 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.59298e11 | −0.481537 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.54006e11 | −0.749078 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.68812e11 | 0.485742 | 0.242871 | − | 0.970059i | \(-0.421911\pi\) | ||||
0.242871 | + | 0.970059i | \(0.421911\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.62933e11 | 1.01908 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.02277e11 | 0.828367 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.06880e11 | 1.62335 | 0.811676 | − | 0.584108i | \(-0.198555\pi\) | ||||
0.811676 | + | 0.584108i | \(0.198555\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.66973e11 | 0.436019 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.62625e11 | 0.414621 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.67636e11 | −1.16421 | −0.582105 | − | 0.813114i | \(-0.697771\pi\) | ||||
−0.582105 | + | 0.813114i | \(0.697771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24468e11 | 0.302619 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.90199e11 | 0.926599 | 0.463300 | − | 0.886202i | \(-0.346665\pi\) | ||||
0.463300 | + | 0.886202i | \(0.346665\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.05981e10 | 0.140568 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.88299e11 | −0.879969 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.61508e11 | 0.357620 | 0.178810 | − | 0.983884i | \(-0.442775\pi\) | ||||
0.178810 | + | 0.983884i | \(0.442775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.80385e11 | 0.606679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.80973e10 | 0.0805615 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.55452e11 | 0.734673 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.18138e11 | −1.65299 | −0.826493 | − | 0.562947i | \(-0.809668\pi\) | ||||
−0.826493 | + | 0.562947i | \(0.809668\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.48290e11 | −0.687959 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.08197e11 | −0.208962 | −0.104481 | − | 0.994527i | \(-0.533318\pi\) | ||||
−0.104481 | + | 0.994527i | \(0.533318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.43587e11 | −0.460024 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.04997e11 | −0.378616 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.98344e10 | −0.0358298 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.56200e11 | −1.33623 | −0.668115 | − | 0.744058i | \(-0.732899\pi\) | ||||
−0.668115 | + | 0.744058i | \(0.732899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.44878e11 | 0.769047 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.31045e11 | −0.898165 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.76062e10 | 0.161533 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.75851e11 | 0.608701 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.64700e11 | 1.05357 | 0.526784 | − | 0.849999i | \(-0.323398\pi\) | ||||
0.526784 | + | 0.849999i | \(0.323398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.96689e11 | 1.08086 | 0.540430 | − | 0.841389i | \(-0.318261\pi\) | ||||
0.540430 | + | 0.841389i | \(0.318261\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.15440e11 | −1.39027 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.85133e10 | 0.0721291 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.42559e11 | 0.498666 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.70249e10 | 0.0670301 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.37728e12 | 1.92254 | 0.961268 | − | 0.275614i | \(-0.0888812\pi\) | ||||
0.961268 | + | 0.275614i | \(0.0888812\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.26719e11 | −0.309950 | −0.154975 | − | 0.987918i | \(-0.549530\pi\) | ||||
−0.154975 | + | 0.987918i | \(0.549530\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.45578e10 | −0.126618 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.44498e11 | 1.23890 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.03484e9 | −0.00518485 | −0.00259242 | − | 0.999997i | \(-0.500825\pi\) | ||||
−0.00259242 | + | 0.999997i | \(0.500825\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.73834e11 | −1.22606 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.08930e12 | 1.34379 | 0.671893 | − | 0.740649i | \(-0.265482\pi\) | ||||
0.671893 | + | 0.740649i | \(0.265482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.18962e11 | 0.143810 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.21223e11 | 0.262088 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.06107e12 | 1.23207 | 0.616035 | − | 0.787719i | \(-0.288738\pi\) | ||||
0.616035 | + | 0.787719i | \(0.288738\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.43786e10 | −0.107418 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.81005e11 | 0.648243 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.73270e12 | 2.98910 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.52127e11 | 0.806618 | 0.403309 | − | 0.915064i | \(-0.367860\pi\) | ||||
0.403309 | + | 0.915064i | \(0.367860\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.50518e11 | −0.368598 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.22335e12 | −1.26152 | −0.630761 | − | 0.775977i | \(-0.717257\pi\) | ||||
−0.630761 | + | 0.775977i | \(0.717257\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00710e12 | −1.01849 | −0.509246 | − | 0.860621i | \(-0.670076\pi\) | ||||
−0.509246 | + | 0.860621i | \(0.670076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.41633e11 | 0.140483 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.11362e12 | 1.08345 | 0.541725 | − | 0.840556i | \(-0.317771\pi\) | ||||
0.541725 | + | 0.840556i | \(0.317771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.48449e12 | −1.41677 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.83512e10 | 0.0171819 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.00975e11 | 0.0927551 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.63421e11 | 0.147294 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.44183e11 | 0.392853 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.94324e11 | −0.689426 | −0.344713 | − | 0.938708i | \(-0.612024\pi\) | ||||
−0.344713 | + | 0.938708i | \(0.612024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.94443e11 | −0.761903 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.31691e12 | −1.10102 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.64115e10 | 0.0298814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.75226e12 | −1.41162 | −0.705810 | − | 0.708401i | \(-0.749417\pi\) | ||||
−0.705810 | + | 0.708401i | \(0.749417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.99741e11 | 0.553411 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.49979e12 | −1.94105 | −0.970526 | − | 0.240997i | \(-0.922526\pi\) | ||||
−0.970526 | + | 0.240997i | \(0.922526\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.36634e11 | 0.104171 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.90463e10 | 0.0666642 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.00934e11 | 0.515316 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.03714e11 | −0.219286 | −0.109643 | − | 0.993971i | \(-0.534971\pi\) | ||||
−0.109643 | + | 0.993971i | \(0.534971\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.42834e9 | −0.00597685 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.56882e12 | 1.09274 | 0.546372 | − | 0.837543i | \(-0.316009\pi\) | ||||
0.546372 | + | 0.837543i | \(0.316009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.45204e11 | −0.646717 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.39950e12 | 0.940672 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.83572e12 | 1.87255 | 0.936274 | − | 0.351272i | \(-0.114251\pi\) | ||||
0.936274 | + | 0.351272i | \(0.114251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.72388e12 | −1.11844 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.18075e12 | −0.752711 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.20893e12 | 0.757303 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.38055e11 | 0.146544 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.35083e11 | −0.202721 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.43643e12 | −0.854111 | −0.427056 | − | 0.904225i | \(-0.640449\pi\) | ||||
−0.427056 | + | 0.904225i | \(0.640449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.78444e11 | −0.571845 | −0.285923 | − | 0.958253i | \(-0.592300\pi\) | ||||
−0.285923 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.27857e11 | −0.130902 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.04656e11 | −0.115578 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.77007e12 | 0.982743 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.80348e11 | −0.425954 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.25605e12 | −2.28420 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.70491e12 | −1.95517 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.77104e11 | −0.195694 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.53239e11 | 0.129236 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.85542e11 | 0.143312 | 0.0716560 | − | 0.997429i | \(-0.477172\pi\) | ||||
0.0716560 | + | 0.997429i | \(0.477172\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.89823e11 | −0.389880 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.40285e12 | −0.681127 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.87296e12 | −1.37210 | −0.686052 | − | 0.727552i | \(-0.740658\pi\) | ||||
−0.686052 | + | 0.727552i | \(0.740658\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.03376e11 | 0.236492 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.60261e11 | 0.212727 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.41237e12 | 1.09693 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.20071e11 | 0.232672 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.40595e12 | −0.618899 | −0.309450 | − | 0.950916i | \(-0.600145\pi\) | ||||
−0.309450 | + | 0.950916i | \(0.600145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.55351e12 | 1.97239 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.95092e10 | 0.0168409 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.50500e11 | −0.147028 | −0.0735139 | − | 0.997294i | \(-0.523421\pi\) | ||||
−0.0735139 | + | 0.997294i | \(0.523421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.49345e12 | 1.02940 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.39126e12 | −0.565308 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.17729e12 | 1.27073 | 0.635363 | − | 0.772214i | \(-0.280851\pi\) | ||||
0.635363 | + | 0.772214i | \(0.280851\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.02125e12 | −1.18939 | −0.594695 | − | 0.803951i | \(-0.702727\pi\) | ||||
−0.594695 | + | 0.803951i | \(0.702727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.85235e12 | 0.717838 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.17907e11 | 0.235732 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.01537e12 | −1.13253 | −0.566264 | − | 0.824224i | \(-0.691612\pi\) | ||||
−0.566264 | + | 0.824224i | \(0.691612\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.96345e12 | −0.726051 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.62429e11 | 0.241183 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.15507e11 | −0.0414095 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.01559e12 | 1.41758 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.76756e12 | 1.30975 | 0.654876 | − | 0.755736i | \(-0.272721\pi\) | ||||
0.654876 | + | 0.755736i | \(0.272721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.89399e11 | −0.236022 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.58515e12 | −0.871649 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.38478e12 | −1.45614 | −0.728068 | − | 0.685505i | \(-0.759581\pi\) | ||||
−0.728068 | + | 0.685505i | \(0.759581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.29595e12 | 0.750993 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.75022e12 | −0.563909 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.67903e11 | 0.0532890 | 0.0266445 | − | 0.999645i | \(-0.491518\pi\) | ||||
0.0266445 | + | 0.999645i | \(0.491518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.30729e12 | 0.721384 | 0.360692 | − | 0.932685i | \(-0.382541\pi\) | ||||
0.360692 | + | 0.932685i | \(0.382541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.18139e12 | −0.671901 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.53735e12 | 1.07344 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50248e12 | 0.449220 | 0.224610 | − | 0.974449i | \(-0.427889\pi\) | ||||
0.224610 | + | 0.974449i | \(0.427889\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.41741e11 | −0.189052 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.07352e13 | 3.11619 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.94077e12 | −1.12722 | −0.563610 | − | 0.826041i | \(-0.690588\pi\) | ||||
−0.563610 | + | 0.826041i | \(0.690588\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.47467e12 | 0.697555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.75098e12 | −1.04198 | −0.520992 | − | 0.853561i | \(-0.674438\pi\) | ||||
−0.520992 | + | 0.853561i | \(0.674438\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.29947e12 | 0.903308 | 0.451654 | − | 0.892193i | \(-0.350834\pi\) | ||||
0.451654 | + | 0.892193i | \(0.350834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.46449e12 | −1.20465 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.07365e11 | 0.214721 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.34641e12 | −1.13938 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.33090e11 | 0.0343907 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.51489e11 | −0.191423 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.22548e12 | 1.81441 | 0.907203 | − | 0.420693i | \(-0.138213\pi\) | ||||
0.907203 | + | 0.420693i | \(0.138213\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.74043e11 | 0.0925988 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.76393e12 | −0.674599 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.14200e13 | 2.74813 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.02999e12 | 0.244388 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.43842e12 | 1.03841 | 0.519203 | − | 0.854651i | \(-0.326229\pi\) | ||||
0.519203 | + | 0.854651i | \(0.326229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.95078e11 | −0.0680751 | −0.0340375 | − | 0.999421i | \(-0.510837\pi\) | ||||
−0.0340375 | + | 0.999421i | \(0.510837\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.64762e12 | −0.602334 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.07880e12 | −0.466383 | −0.233192 | − | 0.972431i | \(-0.574917\pi\) | ||||
−0.233192 | + | 0.972431i | \(0.574917\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.02925e11 | 0.0448987 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.61226e11 | 0.209754 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.80860e12 | 0.389254 | 0.194627 | − | 0.980877i | \(-0.437650\pi\) | ||||
0.194627 | + | 0.980877i | \(0.437650\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.45984e11 | −0.179588 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.53317e12 | −0.530420 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.58150e12 | −1.35938 | −0.679690 | − | 0.733500i | \(-0.737886\pi\) | ||||
−0.679690 | + | 0.733500i | \(0.737886\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.79747e12 | −1.58872 | −0.794360 | − | 0.607448i | \(-0.792193\pi\) | ||||
−0.794360 | + | 0.607448i | \(0.792193\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.78169e12 | 0.358113 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.73408e12 | 1.53360 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.74028e12 | 0.340450 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.40068e12 | −0.270347 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.30900e11 | −0.0249280 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.86129e12 | 1.47716 | 0.738578 | − | 0.674168i | \(-0.235498\pi\) | ||||
0.738578 | + | 0.674168i | \(0.235498\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.72464e11 | −0.143223 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.11388e12 | 1.11858 | 0.559291 | − | 0.828971i | \(-0.311073\pi\) | ||||
0.559291 | + | 0.828971i | \(0.311073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.47116e11 | 0.0446156 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.03852e12 | −0.541378 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.45133e11 | 0.0606867 | 0.0303434 | − | 0.999540i | \(-0.490340\pi\) | ||||
0.0303434 | + | 0.999540i | \(0.490340\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.87891e12 | −1.71436 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.87140e11 | 0.0663074 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.20885e12 | −0.880553 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.18228e12 | 0.864708 | 0.432354 | − | 0.901704i | \(-0.357683\pi\) | ||||
0.432354 | + | 0.901704i | \(0.357683\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.04335e11 | 0.0995356 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.34611e12 | −1.35691 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.57583e12 | −0.573891 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.18342e12 | 0.187496 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.33484e12 | 1.46008 | 0.730038 | − | 0.683406i | \(-0.239502\pi\) | ||||
0.730038 | + | 0.683406i | \(0.239502\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.53145e12 | −0.390904 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.24194e12 | −0.951631 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.41487e12 | −0.965607 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.63912e11 | 0.113536 | 0.0567682 | − | 0.998387i | \(-0.481920\pi\) | ||||
0.0567682 | + | 0.998387i | \(0.481920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.54487e12 | 0.520220 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.60667e12 | −0.377732 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.04423e12 | −0.149423 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.28472e12 | 0.322846 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.65176e12 | 0.509591 | 0.254796 | − | 0.966995i | \(-0.417992\pi\) | ||||
0.254796 | + | 0.966995i | \(0.417992\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.20473e12 | 1.13072 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.13861e12 | −0.563290 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.01111e11 | 0.0404767 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.06692e12 | −0.539959 | −0.269979 | − | 0.962866i | \(-0.587017\pi\) | ||||
−0.269979 | + | 0.962866i | \(0.587017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.11762e12 | 0.146561 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.82575e12 | 0.495551 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00125e13 | 1.28107 | 0.640537 | − | 0.767927i | \(-0.278712\pi\) | ||||
0.640537 | + | 0.767927i | \(0.278712\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.64010e12 | −0.839231 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.67257e11 | 0.0708233 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.95622e12 | −0.734634 | −0.367317 | − | 0.930096i | \(-0.619724\pi\) | ||||
−0.367317 | + | 0.930096i | \(0.619724\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00175e12 | 0.731300 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.85106e12 | −1.06548 | −0.532740 | − | 0.846279i | \(-0.678838\pi\) | ||||
−0.532740 | + | 0.846279i | \(0.678838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.91246e12 | −0.584246 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.73412e11 | 0.114381 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.51443e13 | −2.91925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.31039e13 | −1.50321 | −0.751606 | − | 0.659613i | \(-0.770720\pi\) | ||||
−0.751606 | + | 0.659613i | \(0.770720\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.94584e12 | 0.673963 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.29017e13 | −1.44506 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.31072e13 | −1.45071 | −0.725353 | − | 0.688378i | \(-0.758323\pi\) | ||||
−0.725353 | + | 0.688378i | \(0.758323\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.03223e11 | 0.0550392 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.34902e12 | 0.470068 | 0.235034 | − | 0.971987i | \(-0.424480\pi\) | ||||
0.235034 | + | 0.971987i | \(0.424480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.52083e12 | −1.01698 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.37380e12 | 0.356158 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.15099e12 | 0.954749 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.23095e12 | −0.951871 | −0.475935 | − | 0.879480i | \(-0.657890\pi\) | ||||
−0.475935 | + | 0.879480i | \(0.657890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.83730e12 | 0.493013 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.89415e12 | 0.493025 | 0.246513 | − | 0.969140i | \(-0.420715\pi\) | ||||
0.246513 | + | 0.969140i | \(0.420715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.51016e11 | −0.0449091 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.52959e12 | 0.347400 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.20455e13 | −1.17194 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.67843e11 | −0.0257603 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.17558e12 | −0.206846 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.07505e11 | −0.0383018 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.57772e13 | 1.46604 | 0.733018 | − | 0.680209i | \(-0.238111\pi\) | ||||
0.733018 | + | 0.680209i | \(0.238111\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.56824e12 | 0.327799 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.69224e13 | 1.53698 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.90299e12 | −0.530082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.02867e12 | 0.268906 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.39090e13 | −1.22105 | −0.610524 | − | 0.791998i | \(-0.709041\pi\) | ||||
−0.610524 | + | 0.791998i | \(0.709041\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.01945e12 | 0.782924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.18639e12 | 0.101831 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.58735e11 | 0.0559101 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.92432e13 | 2.45439 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.37105e12 | 0.777781 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.81208e11 | 0.0312891 | 0.0156446 | − | 0.999878i | \(-0.495020\pi\) | ||||
0.0156446 | + | 0.999878i | \(0.495020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.34915e12 | −0.758889 | −0.379445 | − | 0.925214i | \(-0.623885\pi\) | ||||
−0.379445 | + | 0.925214i | \(0.623885\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.07748e12 | −0.648438 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.55384e13 | −1.23366 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.28873e13 | 1.01196 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.72528e13 | 2.11657 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.17330e13 | 0.901290 | 0.450645 | − | 0.892703i | \(-0.351194\pi\) | ||||
0.450645 | + | 0.892703i | \(0.351194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.28533e12 | −0.477561 | −0.238781 | − | 0.971074i | \(-0.576748\pi\) | ||||
−0.238781 | + | 0.971074i | \(0.576748\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.70695e10 | 0.00654370 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.80738e13 | 1.34361 | 0.671806 | − | 0.740727i | \(-0.265519\pi\) | ||||
0.671806 | + | 0.740727i | \(0.265519\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.34766e13 | 0.991028 | 0.495514 | − | 0.868600i | \(-0.334980\pi\) | ||||
0.495514 | + | 0.868600i | \(0.334980\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.22087e12 | 0.307041 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.59478e12 | 0.690450 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.87159e11 | 0.0133236 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.25868e12 | 0.229497 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.14122e13 | −1.49188 | −0.745939 | − | 0.666014i | \(-0.767999\pi\) | ||||
−0.745939 | + | 0.666014i | \(0.767999\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.36591e13 | −0.941542 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.90231e12 | 0.334331 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.10772e13 | −2.09694 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.40071e13 | 1.60274 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.65303e12 | 0.175250 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.57161e12 | −0.625608 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.20087e13 | −0.776649 | −0.388324 | − | 0.921523i | \(-0.626946\pi\) | ||||
−0.388324 | + | 0.921523i | \(0.626946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.13649e13 | 0.727308 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.89490e13 | −1.83324 | −0.916620 | − | 0.399759i | \(-0.869094\pi\) | ||||
−0.916620 | + | 0.399759i | \(0.869094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.31413e13 | 1.45017 | 0.725083 | − | 0.688662i | \(-0.241801\pi\) | ||||
0.725083 | + | 0.688662i | \(0.241801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.67950e13 | 1.04151 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.84504e12 | 0.420075 | 0.210038 | − | 0.977693i | \(-0.432641\pi\) | ||||
0.210038 | + | 0.977693i | \(0.432641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.44082e12 | 0.451906 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.56705e12 | −0.394716 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.21821e11 | −0.0548350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.55807e13 | 1.50602 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.63126e11 | 0.0211589 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.51638e13 | −1.45124 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.24289e13 | −1.28029 | −0.640147 | − | 0.768253i | \(-0.721126\pi\) | ||||
−0.640147 | + | 0.768253i | \(0.721126\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.37306e12 | 0.360079 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.24212e13 | 0.694658 | 0.347329 | − | 0.937743i | \(-0.387089\pi\) | ||||
0.347329 | + | 0.937743i | \(0.387089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.52878e12 | −0.306060 | −0.153030 | − | 0.988222i | \(-0.548903\pi\) | ||||
−0.153030 | + | 0.988222i | \(0.548903\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.32081e12 | −0.291564 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.84924e13 | −1.00308 | −0.501542 | − | 0.865133i | \(-0.667234\pi\) | ||||
−0.501542 | + | 0.865133i | \(0.667234\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.87581e13 | −1.00724 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.31633e11 | 0.0282594 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.03827e13 | 1.59880 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.37392e12 | 0.436240 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.26931e13 | 1.17038 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.27025e12 | −0.0648590 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.37635e12 | −0.221233 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.79688e13 | −0.899339 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.75387e13 | 0.869119 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.72494e13 | 1.33698 | 0.668489 | − | 0.743722i | \(-0.266941\pi\) | ||||
0.668489 | + | 0.743722i | \(0.266941\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.42638e12 | −0.457939 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.31194e12 | 0.351722 | 0.175861 | − | 0.984415i | \(-0.443729\pi\) | ||||
0.175861 | + | 0.984415i | \(0.443729\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.53130e11 | −0.0120566 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.43228e12 | 0.161878 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.74148e12 | −0.268140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.17500e12 | 0.285573 | 0.142786 | − | 0.989754i | \(-0.454394\pi\) | ||||
0.142786 | + | 0.989754i | \(0.454394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.11003e13 | −0.508353 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.20785e13 | −0.547780 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.65612e12 | −0.0743795 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.20565e13 | 0.536244 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.90710e12 | 0.216149 | 0.108075 | − | 0.994143i | \(-0.465531\pi\) | ||||
0.108075 | + | 0.994143i | \(0.465531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.23208e13 | 1.40996 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.76728e12 | 0.162765 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.77336e11 | −0.0375417 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.66248e13 | 1.12839 | 0.564195 | − | 0.825642i | \(-0.309187\pi\) | ||||
0.564195 | + | 0.825642i | \(0.309187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.60372e13 | 0.673182 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.78799e11 | 0.0157491 | 0.00787454 | − | 0.999969i | \(-0.497493\pi\) | ||||
0.00787454 | + | 0.999969i | \(0.497493\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.55448e13 | −1.87558 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.65578e13 | −1.49120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.93752e13 | −1.59092 | −0.795460 | − | 0.606006i | \(-0.792771\pi\) | ||||
−0.795460 | + | 0.606006i | \(0.792771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.97060e13 | 1.18890 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.26368e12 | 0.208678 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.77122e13 | −1.48103 | −0.740514 | − | 0.672041i | \(-0.765418\pi\) | ||||
−0.740514 | + | 0.672041i | \(0.765418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.11330e13 | −1.60020 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.45224e11 | 0.00945060 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.70457e13 | −2.55969 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45370e13 | −0.928039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.69485e13 | −1.38445 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.36002e13 | 1.61851 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.28952e12 | 0.120980 | 0.0604900 | − | 0.998169i | \(-0.480734\pi\) | ||||
0.0604900 | + | 0.998169i | \(0.480734\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.04252e12 | 0.183735 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.68793e11 | 0.00970357 | 0.00485179 | − | 0.999988i | \(-0.498456\pi\) | ||||
0.00485179 | + | 0.999988i | \(0.498456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.66430e13 | −2.02599 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.92644e12 | 0.139149 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.44634e13 | 0.858998 | 0.429499 | − | 0.903067i | \(-0.358690\pi\) | ||||
0.429499 | + | 0.903067i | \(0.358690\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.08513e11 | −0.0107337 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.39905e13 | −0.482304 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.57199e13 | −0.536983 | −0.268491 | − | 0.963282i | \(-0.586525\pi\) | ||||
−0.268491 | + | 0.963282i | \(0.586525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.74055e13 | 1.94308 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.23625e13 | −1.42087 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.87280e13 | 1.61955 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.11195e13 | 0.366229 | 0.183114 | − | 0.983092i | \(-0.441382\pi\) | ||||
0.183114 | + | 0.983092i | \(0.441382\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.37262e12 | −0.175353 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.88652e13 | 1.25706 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50821e13 | −0.803962 | −0.401981 | − | 0.915648i | \(-0.631678\pi\) | ||||
−0.401981 | + | 0.915648i | \(0.631678\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.19658e13 | 0.380098 |
(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 | 64.10.a.g.1.1 | 1 | ||
4.3 | odd | 2 | 64.10.a.c.1.1 | 1 | |||
8.3 | odd | 2 | 8.10.a.b.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 16.10.a.b.1.1 | 1 | |||
16.3 | odd | 4 | 256.10.b.a.129.1 | 2 | |||
16.5 | even | 4 | 256.10.b.k.129.1 | 2 | |||
16.11 | odd | 4 | 256.10.b.a.129.2 | 2 | |||
16.13 | even | 4 | 256.10.b.k.129.2 | 2 | |||
24.5 | odd | 2 | 144.10.a.b.1.1 | 1 | |||
24.11 | even | 2 | 72.10.a.a.1.1 | 1 | |||
40.3 | even | 4 | 200.10.c.a.49.2 | 2 | |||
40.13 | odd | 4 | 400.10.c.f.49.1 | 2 | |||
40.19 | odd | 2 | 200.10.a.a.1.1 | 1 | |||
40.27 | even | 4 | 200.10.c.a.49.1 | 2 | |||
40.29 | even | 2 | 400.10.a.i.1.1 | 1 | |||
40.37 | odd | 4 | 400.10.c.f.49.2 | 2 | |||
56.27 | even | 2 | 392.10.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.10.a.b.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
16.10.a.b.1.1 | 1 | 8.5 | even | 2 | |||
64.10.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
64.10.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
72.10.a.a.1.1 | 1 | 24.11 | even | 2 | |||
144.10.a.b.1.1 | 1 | 24.5 | odd | 2 | |||
200.10.a.a.1.1 | 1 | 40.19 | odd | 2 | |||
200.10.c.a.49.1 | 2 | 40.27 | even | 4 | |||
200.10.c.a.49.2 | 2 | 40.3 | even | 4 | |||
256.10.b.a.129.1 | 2 | 16.3 | odd | 4 | |||
256.10.b.a.129.2 | 2 | 16.11 | odd | 4 | |||
256.10.b.k.129.1 | 2 | 16.5 | even | 4 | |||
256.10.b.k.129.2 | 2 | 16.13 | even | 4 | |||
392.10.a.a.1.1 | 1 | 56.27 | even | 2 | |||
400.10.a.i.1.1 | 1 | 40.29 | even | 2 | |||
400.10.c.f.49.1 | 2 | 40.13 | odd | 4 | |||
400.10.c.f.49.2 | 2 | 40.37 | odd | 4 |