Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,8,Mod(1,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(23.7412619368\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5014x^{3} + 113222x^{2} - 625803x + 567036 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(57.9656\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.1 |
$q$-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 | ||||||||
\(3\) | −84.8970 | −1.81538 | −0.907690 | − | 0.419640i | \(-0.862156\pi\) | ||||
−0.907690 | + | 0.419640i | \(0.862156\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 72.4872 | 0.259338 | 0.129669 | − | 0.991557i | \(-0.458608\pi\) | ||||
0.129669 | + | 0.991557i | \(0.458608\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −210.006 | −0.231413 | −0.115707 | − | 0.993283i | \(-0.536913\pi\) | ||||
−0.115707 | + | 0.993283i | \(0.536913\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5020.49 | 2.29561 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2350.13 | 0.532375 | 0.266188 | − | 0.963921i | \(-0.414236\pi\) | ||||
0.266188 | + | 0.963921i | \(0.414236\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2219.57 | 0.280200 | 0.140100 | − | 0.990137i | \(-0.455258\pi\) | ||||
0.140100 | + | 0.990137i | \(0.455258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6153.94 | −0.470798 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22406.1 | 1.10610 | 0.553051 | − | 0.833147i | \(-0.313464\pi\) | ||||
0.553051 | + | 0.833147i | \(0.313464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6859.00 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17828.8 | 0.420103 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −33836.7 | −0.579883 | −0.289941 | − | 0.957044i | \(-0.593636\pi\) | ||||
−0.289941 | + | 0.957044i | \(0.593636\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −72870.6 | −0.932744 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −240555. | −2.35202 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −93654.9 | −0.713079 | −0.356539 | − | 0.934280i | \(-0.616043\pi\) | ||||
−0.356539 | + | 0.934280i | \(0.616043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −222646. | −1.34230 | −0.671150 | − | 0.741322i | \(-0.734199\pi\) | ||||
−0.671150 | + | 0.741322i | \(0.734199\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −199519. | −0.966464 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15222.7 | −0.0600142 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 228916. | 0.742968 | 0.371484 | − | 0.928439i | \(-0.378849\pi\) | ||||
0.371484 | + | 0.928439i | \(0.378849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −188435. | −0.508669 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 67353.8 | 0.152623 | 0.0763113 | − | 0.997084i | \(-0.475686\pi\) | ||||
0.0763113 | + | 0.997084i | \(0.475686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 162691. | 0.312049 | 0.156025 | − | 0.987753i | \(-0.450132\pi\) | ||||
0.156025 | + | 0.987753i | \(0.450132\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 363922. | 0.595339 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 81632.8 | 0.114689 | 0.0573445 | − | 0.998354i | \(-0.481737\pi\) | ||||
0.0573445 | + | 0.998354i | \(0.481737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −779441. | −0.946448 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.90221e6 | −2.00800 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 905874. | 0.835800 | 0.417900 | − | 0.908493i | \(-0.362766\pi\) | ||||
0.417900 | + | 0.908493i | \(0.362766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 170354. | 0.138065 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 582308. | 0.416477 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.42600e6 | −0.903934 | −0.451967 | − | 0.892035i | \(-0.649277\pi\) | ||||
−0.451967 | + | 0.892035i | \(0.649277\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.18670e6 | 1.23349 | 0.616745 | − | 0.787163i | \(-0.288451\pi\) | ||||
0.616745 | + | 0.787163i | \(0.288451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.05433e6 | −0.531234 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 160891. | 0.0726665 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.73974e6 | −1.92527 | −0.962636 | − | 0.270797i | \(-0.912713\pi\) | ||||
−0.962636 | + | 0.270797i | \(0.912713\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.87263e6 | 1.05271 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.58523e6 | −1.18881 | −0.594406 | − | 0.804165i | \(-0.702613\pi\) | ||||
−0.594406 | + | 0.804165i | \(0.702613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.22283e6 | −0.969632 | −0.484816 | − | 0.874616i | \(-0.661113\pi\) | ||||
−0.484816 | + | 0.874616i | \(0.661113\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.18649e6 | 1.69329 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −493541. | −0.123199 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 334481. | 0.0763268 | 0.0381634 | − | 0.999272i | \(-0.487849\pi\) | ||||
0.0381634 | + | 0.999272i | \(0.487849\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.44257e6 | 1.97421 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.68747e6 | 1.85967 | 0.929837 | − | 0.367972i | \(-0.119948\pi\) | ||||
0.929837 | + | 0.367972i | \(0.119948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.62416e6 | 0.286854 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.95102e6 | 1.29451 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.74280e6 | −1.01385 | −0.506927 | − | 0.861989i | \(-0.669219\pi\) | ||||
−0.506927 | + | 0.861989i | \(0.669219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −466123. | −0.0648419 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.89020e7 | 2.43679 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −497190. | −0.0594963 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −483068. | −0.0537412 | −0.0268706 | − | 0.999639i | \(-0.508554\pi\) | ||||
−0.0268706 | + | 0.999639i | \(0.508554\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.17988e7 | 1.22212 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.87119e7 | −1.80714 | −0.903571 | − | 0.428439i | \(-0.859064\pi\) | ||||
−0.903571 | + | 0.428439i | \(0.859064\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.79581e6 | 0.432446 | 0.216223 | − | 0.976344i | \(-0.430626\pi\) | ||||
0.216223 | + | 0.976344i | \(0.430626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.29236e6 | 0.108949 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.12089e6 | −0.719770 | −0.359885 | − | 0.932997i | \(-0.617184\pi\) | ||||
−0.359885 | + | 0.932997i | \(0.617184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.07583e7 | −0.795706 | −0.397853 | − | 0.917449i | \(-0.630245\pi\) | ||||
−0.397853 | + | 0.917449i | \(0.630245\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.94343e7 | −1.34877 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.08959e7 | 0.710378 | 0.355189 | − | 0.934795i | \(-0.384417\pi\) | ||||
0.355189 | + | 0.934795i | \(0.384417\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.45273e6 | −0.150386 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.11434e7 | 0.643229 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.70541e6 | −0.255966 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.39641e7 | −0.716577 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.71814e6 | −0.277068 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.09453e7 | −0.501234 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.16808e7 | −1.37241 | −0.686204 | − | 0.727409i | \(-0.740724\pi\) | ||||
−0.686204 | + | 0.727409i | \(0.740724\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.38119e7 | −0.566488 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.08202e7 | −1.58645 | −0.793223 | − | 0.608931i | \(-0.791598\pi\) | ||||
−0.793223 | + | 0.608931i | \(0.791598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.44043e6 | 0.0530898 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.74372e7 | −0.609969 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.17104e7 | 0.721351 | 0.360676 | − | 0.932691i | \(-0.382546\pi\) | ||||
0.360676 | + | 0.932691i | \(0.382546\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.68005e7 | 1.16226 | 0.581128 | − | 0.813812i | \(-0.302612\pi\) | ||||
0.581128 | + | 0.813812i | \(0.302612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.93037e6 | −0.208204 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.21629e6 | 0.149171 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.78878e6 | −0.184929 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.61721e7 | 1.71816 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.59158e6 | −0.188010 | −0.0940049 | − | 0.995572i | \(-0.529967\pi\) | ||||
−0.0940049 | + | 0.995572i | \(0.529967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51149e7 | −0.357260 | −0.178630 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178630 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.12490e8 | 2.53918 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.61390e7 | −0.348110 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.20106e7 | −0.660154 | −0.330077 | − | 0.943954i | \(-0.607075\pi\) | ||||
−0.330077 | + | 0.943954i | \(0.607075\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.69060e7 | −1.51730 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.10589e6 | 0.134192 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.86614e7 | 0.518372 | 0.259186 | − | 0.965827i | \(-0.416546\pi\) | ||||
0.259186 | + | 0.965827i | \(0.416546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.44626e7 | −0.250641 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00827e8 | −1.67522 | −0.837608 | − | 0.546271i | \(-0.816047\pi\) | ||||
−0.837608 | + | 0.546271i | \(0.816047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.78220e7 | −0.921488 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.44356e7 | −0.526648 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.62991e6 | −0.0533009 | −0.0266505 | − | 0.999645i | \(-0.508484\pi\) | ||||
−0.0266505 | + | 0.999645i | \(0.508484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.53032e7 | 0.215849 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.21063e8 | 1.64098 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.65481e7 | −0.867261 | −0.433630 | − | 0.901091i | \(-0.642768\pi\) | ||||
−0.433630 | + | 0.901091i | \(0.642768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41404e8 | 1.77250 | 0.886250 | − | 0.463207i | \(-0.153301\pi\) | ||||
0.886250 | + | 0.463207i | \(0.153301\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.85645e8 | −2.23925 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.65935e7 | 0.192680 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.26573e7 | 0.588861 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.05179e7 | 0.544288 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.12407e8 | 1.16728 | 0.583641 | − | 0.812012i | \(-0.301627\pi\) | ||||
0.583641 | + | 0.812012i | \(0.301627\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.05226e7 | 0.505866 | 0.252933 | − | 0.967484i | \(-0.418605\pi\) | ||||
0.252933 | + | 0.967484i | \(0.418605\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.36591e7 | −0.131917 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.40182e7 | −0.782964 | −0.391482 | − | 0.920186i | \(-0.628037\pi\) | ||||
−0.391482 | + | 0.920186i | \(0.628037\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.15328e8 | −1.03740 | −0.518701 | − | 0.854956i | \(-0.673584\pi\) | ||||
−0.518701 | + | 0.854956i | \(0.673584\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.02389e8 | 3.49510 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.96681e7 | 0.165016 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.88229e6 | 0.0395809 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.69877e8 | −1.33118 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.61196e7 | −0.122135 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.20711e6 | 0.0161747 | 0.00808733 | − | 0.999967i | \(-0.497426\pi\) | ||||
0.00808733 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.04375e8 | 2.15815 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.17930e7 | 0.0809262 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.67570e7 | 0.310626 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.73608e8 | 1.76025 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.97320e7 | 0.309929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.35844e8 | 0.820300 | 0.410150 | − | 0.912018i | \(-0.365476\pi\) | ||||
0.410150 | + | 0.912018i | \(0.365476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.65846e8 | −2.14121 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.40869e8 | 1.36675 | 0.683377 | − | 0.730066i | \(-0.260511\pi\) | ||||
0.683377 | + | 0.730066i | \(0.260511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.98261e8 | 1.64124 | 0.820621 | − | 0.571472i | \(-0.193628\pi\) | ||||
0.820621 | + | 0.571472i | \(0.193628\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.19001e7 | 0.223652 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.54139e8 | −0.798302 | −0.399151 | − | 0.916885i | \(-0.630695\pi\) | ||||
−0.399151 | + | 0.916885i | \(0.630695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.91733e6 | 0.0297433 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.83965e7 | −0.138562 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.87849e8 | −0.890054 | −0.445027 | − | 0.895517i | \(-0.646806\pi\) | ||||
−0.445027 | + | 0.895517i | \(0.646806\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.93989e8 | −1.81311 | −0.906555 | − | 0.422089i | \(-0.861297\pi\) | ||||
−0.906555 | + | 0.422089i | \(0.861297\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.75552e8 | −1.23192 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.64995e7 | −0.245450 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.52240e7 | −0.0642822 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.22436e8 | −3.37602 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.64401e8 | 1.45453 | 0.727263 | − | 0.686359i | \(-0.240792\pi\) | ||||
0.727263 | + | 0.686359i | \(0.240792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.95206e7 | −0.308715 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.37886e8 | −0.520750 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.31627e8 | −0.483702 | −0.241851 | − | 0.970313i | \(-0.577755\pi\) | ||||
−0.241851 | + | 0.970313i | \(0.577755\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.80737e7 | −0.171933 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.70194e8 | −1.63695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.06319e8 | −1.71625 | −0.858123 | − | 0.513445i | \(-0.828369\pi\) | ||||
−0.858123 | + | 0.513445i | \(0.828369\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.56643e7 | 0.216755 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.72443e8 | 1.84053 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.36604e7 | 0.105435 | 0.0527176 | − | 0.998609i | \(-0.483212\pi\) | ||||
0.0527176 | + | 0.998609i | \(0.483212\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.12274e8 | 1.56354 | 0.781772 | − | 0.623564i | \(-0.214316\pi\) | ||||
0.781772 | + | 0.623564i | \(0.214316\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.95724e7 | 0.117713 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.71255e8 | −0.496570 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.54393e8 | 1.84995 | 0.924974 | − | 0.380030i | \(-0.124086\pi\) | ||||
0.924974 | + | 0.380030i | \(0.124086\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.11779e9 | −3.08139 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.27528e8 | −0.342874 | −0.171437 | − | 0.985195i | \(-0.554841\pi\) | ||||
−0.171437 | + | 0.985195i | \(0.554841\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.21241e8 | 1.10479 | 0.552393 | − | 0.833584i | \(-0.313715\pi\) | ||||
0.552393 | + | 0.833584i | \(0.313715\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.22099e7 | 0.108008 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.41447e7 | −0.0353189 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.16947e7 | 0.223461 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.10110e7 | 0.0975608 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.75311e8 | −0.871675 | −0.435837 | − | 0.900025i | \(-0.643548\pi\) | ||||
−0.435837 | + | 0.900025i | \(0.643548\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.03367e8 | −0.234425 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.65336e8 | −1.25216 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.51030e7 | −0.162483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.41659e7 | −0.0722122 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.58858e9 | 3.28065 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.58508e8 | 0.319891 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.15576e7 | 0.0425223 | 0.0212611 | − | 0.999774i | \(-0.493232\pi\) | ||||
0.0212611 | + | 0.999774i | \(0.493232\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.07150e8 | −0.785054 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.96289e8 | 1.12408 | 0.562038 | − | 0.827111i | \(-0.310017\pi\) | ||||
0.562038 | + | 0.827111i | \(0.310017\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.04393e8 | 0.929746 | 0.464873 | − | 0.885377i | \(-0.346100\pi\) | ||||
0.464873 | + | 0.885377i | \(0.346100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.64256e7 | −0.137769 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.71147e8 | −1.35966 | −0.679829 | − | 0.733371i | \(-0.737946\pi\) | ||||
−0.679829 | + | 0.733371i | \(0.737946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.20101e8 | −0.379625 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.74336e8 | 1.30666 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.53683e8 | −0.253757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.61742e8 | −0.261354 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.13351e8 | 1.44451 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.71433e7 | −0.0265405 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.04843e8 | 0.462039 | 0.231020 | − | 0.972949i | \(-0.425794\pi\) | ||||
0.231020 | + | 0.972949i | \(0.425794\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.14927e9 | 1.70556 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.43570e8 | −0.499297 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.56300e8 | −1.07644 | −0.538219 | − | 0.842805i | \(-0.680903\pi\) | ||||
−0.538219 | + | 0.842805i | \(0.680903\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.25031e8 | −1.28961 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.23248e8 | −0.714607 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.36636e8 | 0.450433 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.08229e8 | 0.273007 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.93595e8 | 0.248737 | 0.124368 | − | 0.992236i | \(-0.460310\pi\) | ||||
0.124368 | + | 0.992236i | \(0.460310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.55673e8 | −0.951579 | −0.475790 | − | 0.879559i | \(-0.657838\pi\) | ||||
−0.475790 | + | 0.879559i | \(0.657838\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.33929e8 | −0.659036 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.97258e7 | −0.0480686 | −0.0240343 | − | 0.999711i | \(-0.507651\pi\) | ||||
−0.0240343 | + | 0.999711i | \(0.507651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.59884e8 | −0.308304 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.99475e8 | 0.464676 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.08901e9 | −1.24223 | −0.621113 | − | 0.783721i | \(-0.713319\pi\) | ||||
−0.621113 | + | 0.783721i | \(0.713319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.18551e9 | 1.30086 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.33614e8 | −0.251463 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47931e9 | 1.56216 | 0.781082 | − | 0.624428i | \(-0.214668\pi\) | ||||
0.781082 | + | 0.624428i | \(0.214668\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.38149e8 | 0.350362 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.90239e8 | −0.193415 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.36968e9 | 1.36659 | 0.683294 | − | 0.730144i | \(-0.260547\pi\) | ||||
0.683294 | + | 0.730144i | \(0.260547\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.29219e8 | 0.909931 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.07874e8 | −0.199804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.11167e7 | −0.0293600 | −0.0146800 | − | 0.999892i | \(-0.504673\pi\) | ||||
−0.0146800 | + | 0.999892i | \(0.504673\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.68961e9 | 2.49144 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.84422e8 | −0.804384 | −0.402192 | − | 0.915555i | \(-0.631752\pi\) | ||||
−0.402192 | + | 0.915555i | \(0.631752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.57754e7 | −0.0319501 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.16787e8 | 0.716342 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.48902e9 | −1.28256 | −0.641280 | − | 0.767307i | \(-0.721596\pi\) | ||||
−0.641280 | + | 0.767307i | \(0.721596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.58148e8 | −0.641409 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.46551e9 | 2.88000 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.42456e7 | 0.0197945 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12415e9 | −0.901692 | −0.450846 | − | 0.892602i | \(-0.648878\pi\) | ||||
−0.450846 | + | 0.892602i | \(0.648878\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.22288e8 | −0.0963782 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.49136e9 | −1.15499 | −0.577494 | − | 0.816395i | \(-0.695969\pi\) | ||||
−0.577494 | + | 0.816395i | \(0.695969\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.94180e8 | −0.376112 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.84466e8 | 0.511987 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.37983e8 | 0.395538 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.49909e9 | 1.08342 | 0.541710 | − | 0.840566i | \(-0.317777\pi\) | ||||
0.541710 | + | 0.840566i | \(0.317777\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.84315e9 | −1.30953 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.99467e8 | 0.209182 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.02217e8 | 0.482284 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.12425e9 | −2.10994 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.26383e9 | −1.50347 | −0.751735 | − | 0.659465i | \(-0.770783\pi\) | ||||
−0.751735 | + | 0.659465i | \(0.770783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.52298e8 | −0.491363 | −0.245682 | − | 0.969351i | \(-0.579012\pi\) | ||||
−0.245682 | + | 0.969351i | \(0.579012\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.09837e8 | 0.263281 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.63275e9 | −1.03171 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.59220e8 | −0.285446 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.42847e8 | −0.270803 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.07720e9 | 1.24970 | 0.624852 | − | 0.780743i | \(-0.285159\pi\) | ||||
0.624852 | + | 0.780743i | \(0.285159\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.52531e9 | −1.49488 | −0.747440 | − | 0.664329i | \(-0.768717\pi\) | ||||
−0.747440 | + | 0.664329i | \(0.768717\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.76347e8 | 0.335716 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.32086e8 | 0.133034 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.91118e9 | 1.07814 | 0.539071 | − | 0.842260i | \(-0.318775\pi\) | ||||
0.539071 | + | 0.842260i | \(0.318775\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.91318e9 | −2.17267 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.04554e7 | 0.0166438 | 0.00832188 | − | 0.999965i | \(-0.497351\pi\) | ||||
0.00832188 | + | 0.999965i | \(0.497351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.88767e8 | −0.262931 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.44502e8 | 0.341309 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.70483e9 | −1.93155 | −0.965775 | − | 0.259381i | \(-0.916481\pi\) | ||||
−0.965775 | + | 0.259381i | \(0.916481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.58290e8 | 0.0812525 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.28321e9 | 0.648564 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.37879e7 | −0.0168160 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.34064e9 | −0.657059 | −0.328529 | − | 0.944494i | \(-0.606553\pi\) | ||||
−0.328529 | + | 0.944494i | \(0.606553\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.38990e9 | −2.60157 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.91246e9 | −1.38454 | −0.692272 | − | 0.721637i | \(-0.743390\pi\) | ||||
−0.692272 | + | 0.721637i | \(0.743390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.56134e8 | 0.354051 | 0.177025 | − | 0.984206i | \(-0.443353\pi\) | ||||
0.177025 | + | 0.984206i | \(0.443353\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.37015e9 | 0.631951 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.01789e9 | −0.916831 | −0.458415 | − | 0.888738i | \(-0.651583\pi\) | ||||
−0.458415 | + | 0.888738i | \(0.651583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.95371e8 | 0.445533 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.71761e9 | 1.19843 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.82344e8 | 0.166127 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.99819e8 | 0.213986 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.54794e9 | 1.91867 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.39778e9 | −0.581118 | −0.290559 | − | 0.956857i | \(-0.593841\pi\) | ||||
−0.290559 | + | 0.956857i | \(0.593841\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.08096e8 | 0.208179 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.03269e8 | −0.243610 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.50163e7 | −0.0139371 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.34378e9 | 0.527203 | 0.263602 | − | 0.964632i | \(-0.415090\pi\) | ||||
0.263602 | + | 0.964632i | \(0.415090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.43327e9 | −0.941042 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.27643e8 | 0.353668 | 0.176834 | − | 0.984241i | \(-0.443414\pi\) | ||||
0.176834 | + | 0.984241i | \(0.443414\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.09844e9 | −0.788738 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.55264e8 | 0.316943 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.52919e8 | 0.275107 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.84992e9 | 1.02679 | 0.513394 | − | 0.858153i | \(-0.328388\pi\) | ||||
0.513394 | + | 0.858153i | \(0.328388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.55994e9 | 3.04116 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.38596e9 | 0.835940 | 0.417970 | − | 0.908461i | \(-0.362742\pi\) | ||||
0.417970 | + | 0.908461i | \(0.362742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.35637e9 | −0.468661 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.90891e9 | 1.67285 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.57715e9 | 1.87456 | 0.937282 | − | 0.348573i | \(-0.113333\pi\) | ||||
0.937282 | + | 0.348573i | \(0.113333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.76812e8 | 0.224385 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.64997e9 | 0.539591 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.47635e8 | 0.112150 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.91848e8 | 0.0610576 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.08168e8 | 0.0967615 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.55947e9 | 1.10269 | 0.551344 | − | 0.834278i | \(-0.314115\pi\) | ||||
0.551344 | + | 0.834278i | \(0.314115\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.38191e9 | −1.03373 | −0.516864 | − | 0.856067i | \(-0.672901\pi\) | ||||
−0.516864 | + | 0.856067i | \(0.672901\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.29920e9 | −0.391848 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.98864e9 | −1.48472 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.25990e9 | −0.663736 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.15921e9 | −2.07508 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.49497e8 | 0.0427648 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.61148e8 | −0.186664 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.64973e9 | 1.57441 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.83179e9 | −0.503865 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.48160e9 | 0.673817 | 0.336908 | − | 0.941537i | \(-0.390619\pi\) | ||||
0.336908 | + | 0.941537i | \(0.390619\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.20048e10 | −3.21776 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.79843e8 | −0.206357 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.17148e9 | 1.08977 | 0.544884 | − | 0.838511i | \(-0.316573\pi\) | ||||
0.544884 | + | 0.838511i | \(0.316573\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.09783e10 | 2.83161 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.42379e8 | 0.163591 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.02430e7 | −0.0176630 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.40874e9 | −0.349788 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.77249e9 | −0.434600 | −0.217300 | − | 0.976105i | \(-0.569725\pi\) | ||||
−0.217300 | + | 0.976105i | \(0.569725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.61104e8 | 0.0874360 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.47044e9 | −1.06901 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.96074e9 | 1.40774 | 0.703868 | − | 0.710331i | \(-0.251455\pi\) | ||||
0.703868 | + | 0.710331i | \(0.251455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.89815e8 | 0.184228 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.98299e9 | −0.456857 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.59626e9 | 0.590819 | 0.295410 | − | 0.955371i | \(-0.404544\pi\) | ||||
0.295410 | + | 0.955371i | \(0.404544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.53949e9 | −0.570848 | −0.285424 | − | 0.958401i | \(-0.592134\pi\) | ||||
−0.285424 | + | 0.958401i | \(0.592134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.54300e9 | −2.11906 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.46570e9 | 0.540882 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.51763e9 | 1.19574 | 0.597871 | − | 0.801592i | \(-0.296014\pi\) | ||||
0.597871 | + | 0.801592i | \(0.296014\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.28922e9 | −0.918339 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.03442e9 | −0.430353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.12892e9 | 0.444959 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.07751e8 | 0.166814 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.29754e9 | 1.28510 | 0.642550 | − | 0.766243i | \(-0.277876\pi\) | ||||
0.642550 | + | 0.766243i | \(0.277876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.52713e9 | 0.307945 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.13289e9 | 1.42138 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.02283e9 | −0.792209 | −0.396105 | − | 0.918205i | \(-0.629638\pi\) | ||||
−0.396105 | + | 0.918205i | \(0.629638\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.41082e8 | −0.0663819 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.79096e9 | 1.88328 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.25980e9 | 0.239502 | 0.119751 | − | 0.992804i | \(-0.461790\pi\) | ||||
0.119751 | + | 0.992804i | \(0.461790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.33022e9 | −0.437860 | −0.218930 | − | 0.975741i | \(-0.570257\pi\) | ||||
−0.218930 | + | 0.975741i | \(0.570257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.37958e10 | −4.41967 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.01222e9 | −0.185836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.72032e8 | −0.140112 | −0.0700559 | − | 0.997543i | \(-0.522318\pi\) | ||||
−0.0700559 | + | 0.997543i | \(0.522318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.66976e9 | −0.299566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.81190e8 | 0.0321358 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.24050e9 | 0.217514 | 0.108757 | − | 0.994068i | \(-0.465313\pi\) | ||||
0.108757 | + | 0.994068i | \(0.465313\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.14492e8 | −0.0718543 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.30230e8 | −0.0566003 | −0.0283002 | − | 0.999599i | \(-0.509009\pi\) | ||||
−0.0283002 | + | 0.999599i | \(0.509009\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.95644e9 | 1.00941 | 0.504707 | − | 0.863291i | \(-0.331600\pi\) | ||||
0.504707 | + | 0.863291i | \(0.331600\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.13958e9 | 1.36390 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.41603e9 | 0.234619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.89962e9 | 0.802755 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.36850e9 | 0.221722 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.12912e9 | 0.821798 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.68160e9 | −0.424905 | −0.212452 | − | 0.977171i | \(-0.568145\pi\) | ||||
−0.212452 | + | 0.977171i | \(0.568145\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.87377e8 | −0.0293632 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.29646e9 | −0.355918 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.73003e9 | −0.265194 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.79996e10 | −2.72905 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.85995e9 | 0.428899 | 0.214449 | − | 0.976735i | \(-0.431204\pi\) | ||||
0.214449 | + | 0.976735i | \(0.431204\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.77154e9 | 0.262792 | 0.131396 | − | 0.991330i | \(-0.458054\pi\) | ||||
0.131396 | + | 0.991330i | \(0.458054\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.00119e9 | −0.146912 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.32710e9 | 0.918416 | 0.459208 | − | 0.888329i | \(-0.348133\pi\) | ||||
0.459208 | + | 0.888329i | \(0.348133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.35128e9 | −0.481232 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.96953e9 | −0.563904 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.04854e10 | 1.47363 | 0.736817 | − | 0.676093i | \(-0.236328\pi\) | ||||
0.736817 | + | 0.676093i | \(0.236328\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.95894e9 | −0.411426 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.61802e10 | −2.22589 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.46117e8 | 0.0743339 | 0.0371669 | − | 0.999309i | \(-0.488167\pi\) | ||||
0.0371669 | + | 0.999309i | \(0.488167\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.98464e9 | −1.34471 | −0.672353 | − | 0.740231i | \(-0.734716\pi\) | ||||
−0.672353 | + | 0.740231i | \(0.734716\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.22209e9 | −0.562640 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.04413e8 | 0.0137682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.16897e9 | 0.413502 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.15327e10 | −1.48916 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.13904e9 | 0.656679 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.92194e9 | −0.495962 | −0.247981 | − | 0.968765i | \(-0.579767\pi\) | ||||
−0.247981 | + | 0.968765i | \(0.579767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.75294e10 | 2.19383 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.14925e9 | 0.142349 | 0.0711745 | − | 0.997464i | \(-0.477325\pi\) | ||||
0.0711745 | + | 0.997464i | \(0.477325\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.01447e8 | 0.0124364 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.04490e10 | −2.48118 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.45436e10 | −1.74662 | −0.873311 | − | 0.487164i | \(-0.838031\pi\) | ||||
−0.873311 | + | 0.487164i | \(0.838031\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.57373e9 | 0.187074 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.53215e10 | −2.97948 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.01065e9 | 0.234191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.07157e8 | −0.0930647 | −0.0465323 | − | 0.998917i | \(-0.514817\pi\) | ||||
−0.0465323 | + | 0.998917i | \(0.514817\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.47782e9 | −0.282816 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.66756e9 | 0.301417 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50914e9 | 0.168816 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.30859e10 | 1.44922 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.29139e10 | −1.41594 | −0.707970 | − | 0.706242i | \(-0.750389\pi\) | ||||
−0.707970 | + | 0.706242i | \(0.750389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.57014e9 | −0.170449 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.02364e8 | −0.0539953 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.92960e9 | 0.418196 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.99785e9 | 0.737399 | 0.368700 | − | 0.929549i | \(-0.379803\pi\) | ||||
0.368700 | + | 0.929549i | \(0.379803\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.67926e9 | 0.175216 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.53361e9 | 0.778377 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.78114e8 | 0.0386858 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.59478e10 | 1.61579 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.02312e10 | 1.02654 | 0.513271 | − | 0.858227i | \(-0.328434\pi\) | ||||
0.513271 | + | 0.858227i | \(0.328434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.00715e9 | −0.100074 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.34484e10 | 3.29148 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.82469e9 | 0.665120 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.55225e9 | −0.535918 | −0.267959 | − | 0.963430i | \(-0.586349\pi\) | ||||
−0.267959 | + | 0.963430i | \(0.586349\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.74259e9 | 0.262189 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.64526e9 | 0.345158 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.22155e10 | −1.14564 | −0.572818 | − | 0.819683i | \(-0.694150\pi\) | ||||
−0.572818 | + | 0.819683i | \(0.694150\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.79663e9 | 0.445585 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.11390e10 | −1.02497 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.14234e9 | −0.377564 | −0.188782 | − | 0.982019i | \(-0.560454\pi\) | ||||
−0.188782 | + | 0.982019i | \(0.560454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.29248e9 | 0.116697 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.49275e9 | −0.401839 | −0.200919 | − | 0.979608i | \(-0.564393\pi\) | ||||
−0.200919 | + | 0.979608i | \(0.564393\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.50293e8 | −0.0487581 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.86359e10 | 4.26908 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.91544e9 | 0.166564 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.17152e9 | 0.531683 | 0.265841 | − | 0.964017i | \(-0.414350\pi\) | ||||
0.265841 | + | 0.964017i | \(0.414350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.09365e10 | −2.64052 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.09563e9 | −0.0926513 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.23563e10 | −1.03527 | −0.517634 | − | 0.855602i | \(-0.673187\pi\) | ||||
−0.517634 | + | 0.855602i | \(0.673187\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.75106e9 | 0.560436 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.46973e10 | 1.20891 | 0.604453 | − | 0.796641i | \(-0.293392\pi\) | ||||
0.604453 | + | 0.796641i | \(0.293392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.25931e9 | 0.184137 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.15407e9 | 0.658505 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.16510e9 | −0.253282 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.99912e10 | −1.58525 | −0.792625 | − | 0.609710i | \(-0.791286\pi\) | ||||
−0.792625 | + | 0.609710i | \(0.791286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.11747e10 | 0.878104 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.87659e10 | 1.46130 | 0.730651 | − | 0.682751i | \(-0.239217\pi\) | ||||
0.730651 | + | 0.682751i | \(0.239217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.62244e10 | 1.25202 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.08131e9 | 0.312123 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.61980e8 | −0.0350140 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.42577e9 | −0.632894 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.25292e10 | 1.67718 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.32036e9 | −0.171203 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.33857e10 | −0.978877 | −0.489439 | − | 0.872038i | \(-0.662798\pi\) | ||||
−0.489439 | + | 0.872038i | \(0.662798\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.29850e10 | 3.11564 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.28821e9 | −0.164391 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.85355e9 | 0.345624 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.57470e9 | −0.393493 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.57977e10 | 1.80500 | 0.902498 | − | 0.430693i | \(-0.141731\pi\) | ||||
0.902498 | + | 0.430693i | \(0.141731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.82907e9 | 0.126858 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.38522e10 | −2.32741 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.57406e9 | −0.516208 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.15087e8 | 0.0348012 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.85766e9 | −0.191405 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.24018e10 | 0.823504 | 0.411752 | − | 0.911296i | \(-0.364917\pi\) | ||||
0.411752 | + | 0.911296i | \(0.364917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.28908e10 | −0.848607 | −0.424303 | − | 0.905520i | \(-0.639481\pi\) | ||||
−0.424303 | + | 0.905520i | \(0.639481\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.34905e10 | −2.83843 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.07759e9 | 0.134434 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.11589e9 | −0.0715890 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.34017e9 | −0.148851 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.73179e9 | −0.109218 | −0.0546089 | − | 0.998508i | \(-0.517391\pi\) | ||||
−0.0546089 | + | 0.998508i | \(0.517391\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.33148e10 | −0.832599 | −0.416299 | − | 0.909228i | \(-0.636673\pi\) | ||||
−0.416299 | + | 0.909228i | \(0.636673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.45391e10 | 0.901463 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.23050e9 | 0.444528 | 0.222264 | − | 0.974987i | \(-0.428655\pi\) | ||||
0.222264 | + | 0.974987i | \(0.428655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.85814e10 | −1.74238 | −0.871189 | − | 0.490947i | \(-0.836651\pi\) | ||||
−0.871189 | + | 0.490947i | \(0.836651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.55560e10 | −3.35836 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.74642e10 | −1.04687 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.30870e9 | −0.434448 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.35587e10 | 3.15712 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.31016e10 | −1.35044 | −0.675219 | − | 0.737618i | \(-0.735951\pi\) | ||||
−0.675219 | + | 0.737618i | \(0.735951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.47864e9 | −0.491519 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.08268e10 | 0.622447 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.19136e9 | −0.238977 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.93253e9 | 0.165825 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.57621e10 | −2.00561 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.74576e9 | −0.430834 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.69001e9 | 0.203566 | 0.101783 | − | 0.994807i | \(-0.467545\pi\) | ||||
0.101783 | + | 0.994807i | \(0.467545\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.49614e9 | −0.136580 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.27437e9 | 0.449057 | 0.224529 | − | 0.974467i | \(-0.427916\pi\) | ||||
0.224529 | + | 0.974467i | \(0.427916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.37678e10 | 1.81772 | 0.908859 | − | 0.417104i | \(-0.136955\pi\) | ||||
0.908859 | + | 0.417104i | \(0.136955\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.20084e9 | 0.0641172 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.31538e9 | −0.387435 | −0.193718 | − | 0.981057i | \(-0.562055\pi\) | ||||
−0.193718 | + | 0.981057i | \(0.562055\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.63122e8 | −0.0138230 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.78460e9 | −0.405667 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.86075e8 | 0.0406345 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.05202e10 | −0.539461 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.42524e9 | −0.123369 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.29856e9 | 0.115992 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.90785e10 | 1.45570 | 0.727852 | − | 0.685734i | \(-0.240519\pi\) | ||||
0.727852 | + | 0.685734i | \(0.240519\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.18628e10 | 1.58242 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.37853e10 | 0.679205 | 0.339602 | − | 0.940569i | \(-0.389708\pi\) | ||||
0.339602 | + | 0.940569i | \(0.389708\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.41202e10 | −0.690208 | −0.345104 | − | 0.938564i | \(-0.612156\pi\) | ||||
−0.345104 | + | 0.938564i | \(0.612156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.77551e9 | 0.425570 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.17818e10 | −1.52914 | −0.764568 | − | 0.644543i | \(-0.777048\pi\) | ||||
−0.764568 | + | 0.644543i | \(0.777048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.65315e9 | 0.317593 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.21913e10 | 1.05102 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.59919e8 | −0.0263115 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.82388e9 | −0.224914 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.37601e9 | 0.294969 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.08519e10 | 0.957166 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.02971e10 | 0.924480 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90058e9 | 0.131093 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.02500e10 | 0.459677 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.87339e10 | −1.72372 | −0.861858 | − | 0.507149i | \(-0.830699\pi\) | ||||
−0.861858 | + | 0.507149i | \(0.830699\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.39428e10 | −4.14849 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.43662e10 | 1.94419 | 0.972093 | − | 0.234597i | \(-0.0753772\pi\) | ||||
0.972093 | + | 0.234597i | \(0.0753772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.27668e10 | 0.990044 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.34569e10 | −0.580724 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.57247e9 | 0.367124 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.49991e10 | −0.637474 | −0.318737 | − | 0.947843i | \(-0.603259\pi\) | ||||
−0.318737 | + | 0.947843i | \(0.603259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.83018e9 | −0.0771941 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.95768e9 | −0.333105 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.66812e10 | −0.692999 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.40773e10 | 0.992726 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.26273e9 | −0.0925931 | −0.0462965 | − | 0.998928i | \(-0.514742\pi\) | ||||
−0.0462965 | + | 0.998928i | \(0.514742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.34618e9 | 0.217130 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.06232e10 | −2.04063 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.81698e9 | 0.152714 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.38459e10 | −0.549834 | −0.274917 | − | 0.961468i | \(-0.588650\pi\) | ||||
−0.274917 | + | 0.961468i | \(0.588650\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.28215e10 | −1.68784 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.00343e10 | −0.392574 | −0.196287 | − | 0.980547i | \(-0.562888\pi\) | ||||
−0.196287 | + | 0.980547i | \(0.562888\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.27903e9 | −0.0885032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.66190e9 | 0.141155 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.99331e10 | −0.762693 | −0.381347 | − | 0.924432i | \(-0.624540\pi\) | ||||
−0.381347 | + | 0.924432i | \(0.624540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.15330e9 | −0.271691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.54680e10 | 2.46830 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.95607e9 | 0.222913 | 0.111456 | − | 0.993769i | \(-0.464448\pi\) | ||||
0.111456 | + | 0.993769i | \(0.464448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.14806e9 | 0.302721 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.86859e10 | 0.689165 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.55932e9 | −0.166930 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.20588e10 | 0.801769 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.57914e10 | −1.65231 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.66225e9 | 0.131190 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.33084e10 | 0.473295 | 0.236648 | − | 0.971596i | \(-0.423951\pi\) | ||||
0.236648 | + | 0.971596i | \(0.423951\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.30473e10 | 0.460666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.00846e9 | 0.245672 | 0.122836 | − | 0.992427i | \(-0.460801\pi\) | ||||
0.122836 | + | 0.992427i | \(0.460801\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.72830e9 | −0.268961 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.37314e10 | 0.474458 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.45829e10 | 1.52946 | 0.764729 | − | 0.644352i | \(-0.222873\pi\) | ||||
0.764729 | + | 0.644352i | \(0.222873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.58465e10 | −0.539750 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.40122e10 | −1.82663 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.18845e10 | −0.399066 | −0.199533 | − | 0.979891i | \(-0.563943\pi\) | ||||
−0.199533 | + | 0.979891i | \(0.563943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.09025e9 | −0.203052 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.45542e9 | 0.0481812 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.50491e9 | −0.180952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.83738e9 | 0.288447 | 0.144223 | − | 0.989545i | \(-0.453932\pi\) | ||||
0.144223 | + | 0.989545i | \(0.453932\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.58803e10 | −0.838777 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.35977e9 | −0.269038 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.97053e10 | 1.58844 | 0.794219 | − | 0.607632i | \(-0.207880\pi\) | ||||
0.794219 | + | 0.607632i | \(0.207880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.50669e10 | −1.74748 |
(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 | 76.8.a.a.1.1 | ✓ | 5 | |
4.3 | odd | 2 | 304.8.a.g.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.8.a.a.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
304.8.a.g.1.5 | 5 | 4.3 | odd | 2 |