Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(53,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bk (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.11 | ||
Character | \(\chi\) | \(=\) | 252.53 |
Dual form | 252.9.bk.a.233.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −23.4272 | + | 13.5257i | −0.0374835 | + | 0.0216411i | −0.518625 | − | 0.855002i | \(-0.673556\pi\) |
0.481141 | + | 0.876643i | \(0.340222\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2307.52 | + | 663.449i | −0.961065 | + | 0.276322i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6538.52 | + | 3775.02i | 0.446590 | + | 0.257839i | 0.706389 | − | 0.707824i | \(-0.250323\pi\) |
−0.259799 | + | 0.965663i | \(0.583656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10734.9 | 0.375860 | 0.187930 | − | 0.982182i | \(-0.439822\pi\) | ||||
0.187930 | + | 0.982182i | \(0.439822\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −48780.7 | − | 28163.5i | −0.584053 | − | 0.337203i | 0.178690 | − | 0.983906i | \(-0.442814\pi\) |
−0.762742 | + | 0.646702i | \(0.776148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 55457.2 | + | 96054.6i | 0.425543 | + | 0.737062i | 0.996471 | − | 0.0839383i | \(-0.0267499\pi\) |
−0.570928 | + | 0.821000i | \(0.693417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 409756. | − | 236573.i | 1.46425 | − | 0.845383i | 0.465043 | − | 0.885288i | \(-0.346039\pi\) |
0.999203 | + | 0.0399055i | \(0.0127057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −194947. | + | 337657.i | −0.499063 | + | 0.864403i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 386162.i | 0.545982i | 0.962017 | + | 0.272991i | \(0.0880128\pi\) | ||||
−0.962017 | + | 0.272991i | \(0.911987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 768340. | − | 1.33080e6i | 0.831968 | − | 1.44101i | −0.0645078 | − | 0.997917i | \(-0.520548\pi\) |
0.896476 | − | 0.443093i | \(-0.146119\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 45085.0 | − | 46753.5i | 0.0300441 | − | 0.0311560i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 792859. | + | 1.37327e6i | 0.423047 | + | 0.732739i | 0.996236 | − | 0.0866841i | \(-0.0276271\pi\) |
−0.573189 | + | 0.819424i | \(0.694294\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 794246.i | − | 0.281073i | −0.990075 | − | 0.140537i | \(-0.955117\pi\) | ||
0.990075 | − | 0.140537i | \(-0.0448828\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.19734e6 | −1.81272 | −0.906362 | − | 0.422502i | \(-0.861152\pi\) | ||||
−0.906362 | + | 0.422502i | \(0.861152\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.61379e6 | + | 3.81847e6i | −1.35537 | + | 0.782525i | −0.988996 | − | 0.147942i | \(-0.952735\pi\) |
−0.366377 | + | 0.930467i | \(0.619402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.88447e6 | − | 3.06184e6i | 0.847292 | − | 0.531127i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.25899e6 | − | 1.30423e6i | −0.286293 | − | 0.165291i | 0.349976 | − | 0.936759i | \(-0.386190\pi\) |
−0.636269 | + | 0.771467i | \(0.719523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −204239. | −0.0223197 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.13342e7 | + | 6.54383e6i | 0.935372 | + | 0.540037i | 0.888507 | − | 0.458864i | \(-0.151743\pi\) |
0.0468654 | + | 0.998901i | \(0.485077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.09062e6 | − | 3.62105e6i | −0.150992 | − | 0.261527i | 0.780600 | − | 0.625031i | \(-0.214914\pi\) |
−0.931593 | + | 0.363504i | \(0.881580\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −251489. | + | 145197.i | −0.0140885 | + | 0.00813401i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.05074e6 | + | 5.28404e6i | −0.151393 | + | 0.262221i | −0.931740 | − | 0.363126i | \(-0.881709\pi\) |
0.780347 | + | 0.625347i | \(0.215043\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.56254e7i | − | 1.00841i | −0.863584 | − | 0.504206i | \(-0.831785\pi\) | ||
0.863584 | − | 0.504206i | \(-0.168215\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 461382. | − | 799136.i | 0.0162468 | − | 0.0281403i | −0.857788 | − | 0.514004i | \(-0.828162\pi\) |
0.874035 | + | 0.485864i | \(0.161495\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.75923e7 | − | 4.37294e6i | −0.500449 | − | 0.124397i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −941806. | − | 1.63126e6i | −0.0241798 | − | 0.0418807i | 0.853682 | − | 0.520794i | \(-0.174364\pi\) |
−0.877862 | + | 0.478913i | \(0.841031\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.96877e7i | 1.88982i | 0.327330 | + | 0.944910i | \(0.393851\pi\) | ||||
−0.327330 | + | 0.944910i | \(0.606149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.52372e6 | 0.0291898 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.07346e7 | − | 1.19711e7i | 0.330473 | − | 0.190798i | −0.325578 | − | 0.945515i | \(-0.605559\pi\) |
0.656051 | + | 0.754717i | \(0.272226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.47710e7 | + | 7.12207e6i | −0.361225 | + | 0.103858i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.59841e6 | − | 1.50019e6i | −0.0319016 | − | 0.0184184i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.05576e7 | −0.119255 | −0.0596275 | − | 0.998221i | \(-0.518991\pi\) | ||||
−0.0596275 | + | 0.998221i | \(0.518991\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.14873e8 | − | 6.63218e7i | −1.10390 | − | 0.637339i | −0.166660 | − | 0.986014i | \(-0.553298\pi\) |
−0.937244 | + | 0.348675i | \(0.886632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.51652e7 | − | 1.64831e8i | −0.845530 | − | 1.46450i | −0.885160 | − | 0.465287i | \(-0.845951\pi\) |
0.0396300 | − | 0.999214i | \(-0.487382\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.13902e8 | + | 1.23496e8i | −1.63185 | + | 0.942147i | −0.648324 | + | 0.761365i | \(0.724530\pi\) |
−0.983523 | + | 0.180782i | \(0.942137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.32864e6 | − | 1.09615e7i | 0.0448337 | − | 0.0776542i | −0.842738 | − | 0.538324i | \(-0.819058\pi\) |
0.887571 | + | 0.460670i | \(0.152391\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.79320e8i | 1.71312i | 0.516045 | + | 0.856561i | \(0.327404\pi\) | ||||
−0.516045 | + | 0.856561i | \(0.672596\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.39962e6 | + | 1.10845e7i | −0.0365900 | + | 0.0633758i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.31247e8 | + | 3.26244e7i | 0.654489 | + | 0.162688i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.86779e7 | − | 1.36274e8i | −0.367038 | − | 0.635729i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.11141e7i | − | 0.0864833i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.23251e8 | −0.473778 | −0.236889 | − | 0.971537i | \(-0.576128\pi\) | ||||
−0.236889 | + | 0.971537i | \(0.576128\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.20361e8 | + | 2.42695e8i | −1.42737 | + | 0.824093i | −0.996913 | − | 0.0785169i | \(-0.974982\pi\) |
−0.430459 | + | 0.902610i | \(0.641648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.91696e8 | − | 1.84855e8i | −0.612641 | − | 0.590778i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.51097e7 | − | 4.33646e7i | −0.213213 | − | 0.123099i | 0.389591 | − | 0.920988i | \(-0.372616\pi\) |
−0.602804 | + | 0.797889i | \(0.705950\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.81965e6 | 0.0155897 | 0.00779485 | − | 0.999970i | \(-0.497519\pi\) | ||||
0.00779485 | + | 0.999970i | \(0.497519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.01905e7 | + | 4.05245e7i | 0.167855 | + | 0.0969112i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.22311e6 | − | 9.04669e6i | −0.0118156 | − | 0.0204653i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.20908e8 | + | 6.98065e7i | −0.245308 | + | 0.141629i | −0.617614 | − | 0.786481i | \(-0.711901\pi\) |
0.372306 | + | 0.928110i | \(0.378567\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.96107e8 | + | 3.39667e8i | −0.377212 | + | 0.653350i | −0.990655 | − | 0.136389i | \(-0.956450\pi\) |
0.613444 | + | 0.789739i | \(0.289784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.15693e7i | 0.0720188i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.27122e8 | − | 2.20182e8i | 0.209229 | − | 0.362396i | −0.742243 | − | 0.670131i | \(-0.766238\pi\) |
0.951472 | + | 0.307735i | \(0.0995712\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.88565e8 | + | 8.17748e8i | −1.17364 | + | 1.21707i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.75798e8 | − | 8.24106e8i | −0.674019 | − | 1.16743i | −0.976755 | − | 0.214360i | \(-0.931233\pi\) |
0.302736 | − | 0.953074i | \(-0.402100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.84071e8i | 1.26520i | 0.774477 | + | 0.632602i | \(0.218013\pi\) | ||||
−0.774477 | + | 0.632602i | \(0.781987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00492e8 | −0.858730 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.96642e8 | + | 5.17677e8i | −1.00100 | + | 0.577929i | −0.908545 | − | 0.417788i | \(-0.862805\pi\) |
−0.0924573 | + | 0.995717i | \(0.529472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.25824e8 | − | 9.08488e8i | 0.240779 | − | 0.968650i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.97156e8 | − | 2.87033e8i | −0.484262 | − | 0.279589i | 0.237929 | − | 0.971283i | \(-0.423531\pi\) |
−0.722191 | + | 0.691694i | \(0.756865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.63207e9 | −1.52063 | −0.760315 | − | 0.649554i | \(-0.774956\pi\) | ||||
−0.760315 | + | 0.649554i | \(0.774956\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.71489e7 | − | 2.14479e7i | −0.0317146 | − | 0.0183104i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.12636e8 | − | 3.68296e8i | −0.173888 | − | 0.301183i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.57175e9 | + | 9.07449e8i | −1.18100 | + | 0.681850i | −0.956245 | − | 0.292566i | \(-0.905491\pi\) |
−0.224753 | + | 0.974416i | \(0.572158\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.04863e9 | − | 1.81629e9i | 0.755778 | − | 1.30905i | −0.189209 | − | 0.981937i | \(-0.560592\pi\) |
0.944987 | − | 0.327109i | \(-0.106074\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.93160e9i | 1.28248i | 0.767340 | + | 0.641241i | \(0.221580\pi\) | ||||
−0.767340 | + | 0.641241i | \(0.778420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.10563e8 | + | 3.64705e8i | −0.134267 | + | 0.232557i | −0.925317 | − | 0.379194i | \(-0.876201\pi\) |
0.791050 | + | 0.611751i | \(0.209535\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.56199e8 | − | 8.91076e8i | −0.150867 | − | 0.524724i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.07427e7 | + | 1.86069e7i | 0.00608274 | + | 0.0105356i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.37407e8i | 0.438886i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.78430e8 | −0.493628 | −0.246814 | − | 0.969063i | \(-0.579384\pi\) | ||||
−0.246814 | + | 0.969063i | \(0.579384\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.45186e8 | − | 8.38233e7i | 0.0679472 | − | 0.0392293i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.90037e8 | + | 3.58061e9i | −0.401392 | + | 1.61480i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.23657e8 | − | 3.02333e8i | −0.219522 | − | 0.126741i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.61547e8 | 0.307948 | 0.153974 | − | 0.988075i | \(-0.450793\pi\) | ||||
0.153974 | + | 0.988075i | \(0.450793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.50466e7 | + | 5.48752e7i | 0.0357959 | + | 0.0206668i | 0.517791 | − | 0.855507i | \(-0.326754\pi\) |
−0.481995 | + | 0.876174i | \(0.660088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.30437e9 | − | 2.25923e9i | −0.474305 | − | 0.821520i | 0.525262 | − | 0.850941i | \(-0.323967\pi\) |
−0.999567 | + | 0.0294201i | \(0.990634\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.63617e9 | − | 9.44645e8i | 0.555144 | − | 0.320513i | −0.196050 | − | 0.980594i | \(-0.562812\pi\) |
0.751194 | + | 0.660081i | \(0.229478\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.03295e8 | − | 1.78912e8i | 0.0338694 | − | 0.0586635i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.24465e8i | 0.130092i | 0.997882 | + | 0.0650460i | \(0.0207194\pi\) | ||||
−0.997882 | + | 0.0650460i | \(0.979281\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.12453e9 | − | 1.94775e9i | 0.333353 | − | 0.577385i | −0.649814 | − | 0.760093i | \(-0.725153\pi\) |
0.983167 | + | 0.182709i | \(0.0584865\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.30159e7 | + | 1.37796e8i | −0.0202653 | + | 0.0382448i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.95328e8 | + | 1.03114e9i | 0.159944 | + | 0.277032i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.27429e9i | − | 0.321050i | −0.987032 | − | 0.160525i | \(-0.948681\pi\) | ||
0.987032 | − | 0.160525i | \(-0.0513188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.57227e9 | 0.871890 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.93069e8 | + | 3.42409e8i | −0.135948 | + | 0.0784896i | −0.566431 | − | 0.824109i | \(-0.691676\pi\) |
0.430483 | + | 0.902598i | \(0.358343\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.74063e9 | − | 2.64283e9i | −0.609048 | − | 0.587313i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.99809e9 | + | 2.30830e9i | 0.835659 | + | 0.482468i | 0.855786 | − | 0.517329i | \(-0.173074\pi\) |
−0.0201272 | + | 0.999797i | \(0.506407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.05622e7 | 0.0143083 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.96006e9 | − | 1.13164e9i | −0.374335 | − | 0.216123i | 0.301015 | − | 0.953619i | \(-0.402674\pi\) |
−0.675351 | + | 0.737497i | \(0.736008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.08280e9 | + | 3.60752e9i | 0.386164 | + | 0.668855i | 0.991930 | − | 0.126788i | \(-0.0404667\pi\) |
−0.605766 | + | 0.795643i | \(0.707133\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.54933e9 | + | 1.47185e9i | −0.445753 | + | 0.257356i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.02982e9 | + | 5.24781e9i | −0.514634 | + | 0.891372i | 0.485222 | + | 0.874391i | \(0.338739\pi\) |
−0.999856 | + | 0.0169809i | \(0.994595\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.10028e9i | − | 1.13881i | −0.822058 | − | 0.569404i | \(-0.807174\pi\) | ||
0.822058 | − | 0.569404i | \(-0.192826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.76462e9 | + | 3.05642e9i | −0.275110 | + | 0.476504i | −0.970163 | − | 0.242454i | \(-0.922048\pi\) |
0.695053 | + | 0.718958i | \(0.255381\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.26942e8 | + | 1.83274e9i | 0.0776667 | + | 0.270130i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.90151e9 | − | 3.29351e9i | −0.272588 | − | 0.472137i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.26537e9i | − | 1.12148i | −0.827992 | − | 0.560740i | \(-0.810517\pi\) | ||
0.827992 | − | 0.560740i | \(-0.189483\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.54039e8 | −0.0467480 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.39870e9 | − | 2.53959e9i | 0.550351 | − | 0.317745i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.43005e10 | − | 4.11162e9i | 1.74215 | − | 0.500895i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.79545e7 | + | 5.65540e7i | 0.0113194 | + | 0.00653528i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.33317e9 | 0.712964 | 0.356482 | − | 0.934302i | \(-0.383976\pi\) | ||||
0.356482 | + | 0.934302i | \(0.383976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.27635e9 | + | 5.35571e9i | 0.991598 | + | 0.572500i | 0.905752 | − | 0.423809i | \(-0.139307\pi\) |
0.0858466 | + | 0.996308i | \(0.472640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.49028e9 | + | 9.50945e9i | 0.572028 | + | 0.990782i | 0.996358 | + | 0.0852740i | \(0.0271766\pi\) |
−0.424329 | + | 0.905508i | \(0.639490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.09639e10 | − | 6.33003e9i | 1.08575 | − | 0.626858i | 0.153308 | − | 0.988178i | \(-0.451007\pi\) |
0.932442 | + | 0.361321i | \(0.117674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.45777e9 | + | 2.52493e9i | −0.140775 | + | 0.243830i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 6.24748e9i | − | 0.573977i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.09274e9 | + | 3.62473e9i | −0.187578 | + | 0.324894i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.27281e10 | − | 1.31991e10i | 1.08637 | − | 1.12658i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.83211e9 | + | 6.63742e9i | 0.319247 | + | 0.552952i | 0.980331 | − | 0.197360i | \(-0.0632368\pi\) |
−0.661084 | + | 0.750312i | \(0.729903\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.65054e8i | − | 0.0131053i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.58097e9 | 0.200107 | 0.100054 | − | 0.994982i | \(-0.468099\pi\) | ||||
0.100054 | + | 0.994982i | \(0.468099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.00476e10 | − | 5.80099e9i | 0.743097 | − | 0.429027i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.23963e9 | + | 1.03058e10i | −0.667541 | + | 0.744573i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.85388e9 | − | 3.95709e9i | −0.472736 | − | 0.272934i | 0.244649 | − | 0.969612i | \(-0.421327\pi\) |
−0.717384 | + | 0.696678i | \(0.754661\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.58298e10 | 1.06702 | 0.533511 | − | 0.845793i | \(-0.320872\pi\) | ||||
0.533511 | + | 0.845793i | \(0.320872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.30037e9 | − | 4.21487e9i | −0.470160 | − | 0.271447i | 0.246146 | − | 0.969233i | \(-0.420836\pi\) |
−0.716307 | + | 0.697785i | \(0.754169\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.46601e8 | + | 6.00331e8i | 0.0218231 | + | 0.0377988i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.75753e10 | − | 1.01471e10i | 1.05810 | − | 0.610892i | 0.133191 | − | 0.991090i | \(-0.457478\pi\) |
0.924905 | + | 0.380199i | \(0.124144\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.34079e9 | − | 4.05436e9i | 0.137827 | − | 0.238723i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.49620e7i | 0.00140640i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.76794e9 | − | 4.79421e9i | 0.152578 | − | 0.264273i | −0.779596 | − | 0.626282i | \(-0.784576\pi\) |
0.932175 | + | 0.362009i | \(0.117909\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.07794e9 | + | 1.51080e9i | 0.320819 | + | 0.0797466i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.37790e10 | + | 2.38660e10i | 0.711841 | + | 1.23294i | 0.964165 | + | 0.265302i | \(0.0854717\pi\) |
−0.252324 | + | 0.967643i | \(0.581195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.14542e9i | 0.205212i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.52111e10 | 0.737233 | 0.368616 | − | 0.929582i | \(-0.379832\pi\) | ||||
0.368616 | + | 0.929582i | \(0.379832\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.72406e9 | − | 5.61419e9i | 0.451911 | − | 0.260911i | −0.256726 | − | 0.966484i | \(-0.582644\pi\) |
0.708637 | + | 0.705573i | \(0.249311\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.71285e8 | − | 1.35502e8i | 0.0214506 | − | 0.00616741i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.22888e10 | − | 7.09493e9i | −0.536674 | − | 0.309849i | 0.207056 | − | 0.978329i | \(-0.433612\pi\) |
−0.743730 | + | 0.668480i | \(0.766945\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.66509e10 | −1.14026 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.41277e7 | + | 2.54771e7i | 0.00181269 | + | 0.00104656i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.44616e10 | − | 2.50481e10i | −0.582174 | − | 1.00835i | −0.995221 | − | 0.0976454i | \(-0.968869\pi\) |
0.413047 | − | 0.910710i | \(-0.364464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.69181e10 | + | 9.76765e9i | −0.654294 | + | 0.377757i | −0.790100 | − | 0.612979i | \(-0.789971\pi\) |
0.135805 | + | 0.990736i | \(0.456638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.24807e9 | − | 1.42861e10i | 0.312703 | − | 0.541617i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.19722e10i | 0.436312i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.07739e10 | + | 1.86609e10i | −0.385016 | + | 0.666867i | −0.991771 | − | 0.128021i | \(-0.959137\pi\) |
0.606755 | + | 0.794889i | \(0.292471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.04954e10 | − | 7.58030e9i | −1.04818 | − | 0.260547i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.21309e9 | − | 2.10113e9i | −0.0408978 | − | 0.0708370i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 2.08301e10i | − | 0.675826i | −0.941177 | − | 0.337913i | \(-0.890279\pi\) | ||
0.941177 | − | 0.337913i | \(-0.109721\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.80612e10 | −0.574934 | −0.287467 | − | 0.957791i | \(-0.592813\pi\) | ||||
−0.287467 | + | 0.957791i | \(0.592813\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.90193e10 | − | 1.09808e10i | 0.582959 | − | 0.336571i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.22652e9 | + | 6.96863e9i | 0.217379 | + | 0.209622i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.37026e10 | + | 2.52317e10i | 1.26648 | + | 0.731202i | 0.974320 | − | 0.225167i | \(-0.0722929\pi\) |
0.292159 | + | 0.956370i | \(0.405626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.97105e10 | 1.41415 | 0.707076 | − | 0.707137i | \(-0.250014\pi\) | ||||
0.707076 | + | 0.707137i | \(0.250014\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.54478e10 | + | 2.62393e10i | 1.24620 | + | 0.719493i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.76507e10 | + | 3.05719e10i | 0.475230 | + | 0.823123i | 0.999598 | − | 0.0283692i | \(-0.00903140\pi\) |
−0.524367 | + | 0.851492i | \(0.675698\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.32356e10 | + | 1.91886e10i | −0.862955 | + | 0.498227i | −0.865001 | − | 0.501771i | \(-0.832682\pi\) |
0.00204575 | + | 0.999998i | \(0.499349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.23835e8 | + | 5.60899e8i | −0.00825817 | + | 0.0143036i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.18319e10i | − | 0.783209i | −0.920134 | − | 0.391604i | \(-0.871920\pi\) | ||
0.920134 | − | 0.391604i | \(-0.128080\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.99829e9 | − | 5.19320e9i | 0.0724716 | − | 0.125525i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.83984e8 | − | 5.01895e8i | 0.0112924 | − | 0.0117103i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.24032e10 | − | 5.61240e10i | −0.742887 | − | 1.28672i | −0.951175 | − | 0.308651i | \(-0.900123\pi\) |
0.208288 | − | 0.978068i | \(-0.433211\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.65098e10i | − | 0.586953i | −0.955966 | − | 0.293476i | \(-0.905188\pi\) | ||
0.955966 | − | 0.293476i | \(-0.0948122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.98576e10 | −0.649727 | −0.324864 | − | 0.945761i | \(-0.605318\pi\) | ||||
−0.324864 | + | 0.945761i | \(0.605318\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.64542e10 | + | 3.83673e10i | −1.39719 | + | 0.806667i | −0.994097 | − | 0.108493i | \(-0.965397\pi\) |
−0.403091 | + | 0.915160i | \(0.632064\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.53395e9 | − | 1.42170e10i | 0.0730414 | − | 0.293844i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.05215e10 | − | 2.33951e10i | −0.809544 | − | 0.467390i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.32447e10 | −0.849491 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.17717e9 | − | 4.14374e9i | −0.136336 | − | 0.0787137i | 0.430281 | − | 0.902695i | \(-0.358415\pi\) |
−0.566617 | + | 0.823981i | \(0.691748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.51128e9 | + | 1.47420e10i | 0.159006 | + | 0.275407i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.47334e8 | − | 1.42798e8i | 0.00447009 | − | 0.00258081i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.74730e10 | + | 4.75845e10i | −0.488416 | + | 0.845961i | −0.999911 | − | 0.0133253i | \(-0.995758\pi\) |
0.511496 | + | 0.859286i | \(0.329092\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.77959e10i | 1.68265i | 0.540527 | + | 0.841327i | \(0.318225\pi\) | ||||
−0.540527 | + | 0.841327i | \(0.681775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.08757e10 | − | 1.88373e10i | 0.184107 | − | 0.318882i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.70012e10 | + | 5.91311e10i | 0.278646 | + | 0.969149i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.63645e10 | − | 6.29852e10i | −0.586511 | − | 1.01587i | −0.994685 | − | 0.102962i | \(-0.967168\pi\) |
0.408175 | − | 0.912904i | \(-0.366165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.16837e10i | 0.963603i | 0.876280 | + | 0.481802i | \(0.160017\pi\) | ||||
−0.876280 | + | 0.481802i | \(0.839983\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.58819e9 | 0.0551709 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.53141e10 | + | 4.92561e10i | −1.27101 | + | 0.733820i | −0.975179 | − | 0.221420i | \(-0.928931\pi\) |
−0.295834 | + | 0.955239i | \(0.595598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.34460e8 | + | 2.15012e9i | −0.00783847 | + | 0.0315341i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.45890e9 | + | 2.57435e9i | 0.0633868 | + | 0.0365964i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.76592e10 | −0.807061 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.02652e11 | − | 5.92661e10i | −1.39321 | − | 0.804369i | −0.399540 | − | 0.916716i | \(-0.630830\pi\) |
−0.993669 | + | 0.112347i | \(0.964163\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.48450e10 | − | 9.49944e10i | −0.733045 | − | 1.26967i | −0.955576 | − | 0.294745i | \(-0.904765\pi\) |
0.222531 | − | 0.974926i | \(-0.428568\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.49603e10 | + | 4.32783e10i | −0.971826 | + | 0.561084i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.27779e10 | − | 1.26055e11i | 0.929344 | − | 1.60967i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.52617e9i | − | 0.105644i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.34074e9 | − | 5.78634e9i | 0.0407782 | − | 0.0706299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.34957e10 | − | 1.58094e9i | 0.515337 | − | 0.0187310i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.37169e10 | + | 2.37584e10i | 0.160128 | + | 0.277350i | 0.934915 | − | 0.354873i | \(-0.115476\pi\) |
−0.774786 | + | 0.632223i | \(0.782143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.42397e8i | 0.00388100i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.19133e10 | −1.02667 | −0.513333 | − | 0.858190i | \(-0.671589\pi\) | ||||
−0.513333 | + | 0.858190i | \(0.671589\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.70927e10 | + | 2.14155e10i | −0.402422 | + | 0.232339i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.25549e9 | + | 3.13931e9i | 0.0348109 | + | 0.0335687i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.13798e10 | − | 2.38907e10i | −0.429901 | − | 0.248203i | 0.269404 | − | 0.963027i | \(-0.413173\pi\) |
−0.699304 | + | 0.714824i | \(0.746507\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.65280e10 | −0.681329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.57197e11 | + | 9.07576e10i | 1.56462 | + | 0.903336i | 0.996779 | + | 0.0802008i | \(0.0255562\pi\) |
0.567845 | + | 0.823135i | \(0.307777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.77800e9 | − | 6.54368e9i | −0.0370738 | − | 0.0642138i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.35498e10 | + | 4.82375e10i | −0.797069 | + | 0.460188i | −0.842445 | − | 0.538782i | \(-0.818885\pi\) |
0.0453760 | + | 0.998970i | \(0.485551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.71303e10 | + | 6.43115e10i | −0.349288 | + | 0.604985i | −0.986123 | − | 0.166015i | \(-0.946910\pi\) |
0.636835 | + | 0.771000i | \(0.280243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.84476e11i | 1.68760i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.72547e10 | + | 8.18476e10i | −0.426326 | + | 0.738418i | −0.996543 | − | 0.0830756i | \(-0.973526\pi\) |
0.570217 | + | 0.821494i | \(0.306859\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.95032e10 | − | 2.06956e11i | −0.522199 | − | 1.81624i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.84696e9 | − | 1.70554e10i | −0.0852369 | − | 0.147635i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.97139e10i | 0.671401i | 0.941969 | + | 0.335700i | \(0.108973\pi\) | ||||
−0.941969 | + | 0.335700i | \(0.891027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.70440e11 | 1.41615 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.01085e11 | − | 5.83614e10i | 0.817463 | − | 0.471962i | −0.0320781 | − | 0.999485i | \(-0.510213\pi\) |
0.849541 | + | 0.527523i | \(0.176879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.51602e9 | + | 1.01091e9i | −0.0280533 | + | 0.00806577i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.28602e10 | − | 3.05189e10i | −0.410603 | − | 0.237062i | 0.280446 | − | 0.959870i | \(-0.409518\pi\) |
−0.691049 | + | 0.722808i | \(0.742851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.36720e11 | 1.04793 | 0.523967 | − | 0.851739i | \(-0.324452\pi\) | ||||
0.523967 | + | 0.851739i | \(0.324452\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.68640e9 | + | 2.12834e9i | 0.0275157 | + | 0.0158862i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.02143e10 | − | 1.21615e11i | −0.517215 | − | 0.895842i | −0.999800 | − | 0.0199934i | \(-0.993635\pi\) |
0.482585 | − | 0.875849i | \(-0.339698\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.09985e10 | + | 4.09910e10i | −0.509430 | + | 0.294119i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.09232e10 | − | 1.89195e10i | 0.0773585 | − | 0.133989i | −0.824751 | − | 0.565496i | \(-0.808685\pi\) |
0.902109 | + | 0.431507i | \(0.142018\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.01700e11i | − | 0.701749i | −0.936423 | − | 0.350874i | \(-0.885884\pi\) | ||
0.936423 | − | 0.350874i | \(-0.114116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.15225e11 | + | 1.99575e11i | −0.784844 | + | 1.35939i | 0.144248 | + | 0.989542i | \(0.453924\pi\) |
−0.929092 | + | 0.369849i | \(0.879409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.99032e10 | + | 4.13799e10i | −0.264884 | + | 0.274687i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.58654e10 | − | 1.31403e11i | −0.497192 | − | 0.861161i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8.93188e10i | − | 0.570611i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.70816e11 | −1.07748 | −0.538741 | − | 0.842471i | \(-0.681100\pi\) | ||||
−0.538741 | + | 0.842471i | \(0.681100\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.88742e9 | − | 1.66705e9i | 0.0177589 | − | 0.0102531i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.24344e10 | − | 3.28686e10i | 0.318463 | − | 0.199629i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.20728e10 | + | 4.73848e10i | 0.486146 | + | 0.280677i | 0.722974 | − | 0.690875i | \(-0.242774\pi\) |
−0.236828 | + | 0.971552i | \(0.576108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.13833e11 | 1.25093 | 0.625463 | − | 0.780254i | \(-0.284910\pi\) | ||||
0.625463 | + | 0.780254i | \(0.284910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.74854e11 | + | 1.00952e11i | 0.997834 | + | 0.576099i | 0.907607 | − | 0.419822i | \(-0.137907\pi\) |
0.0902270 | + | 0.995921i | \(0.471241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.94061e10 | + | 8.55739e10i | 0.278485 | + | 0.482350i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.24715e10 | − | 3.60680e10i | 0.343581 | − | 0.198367i | −0.318273 | − | 0.947999i | \(-0.603103\pi\) |
0.661855 | + | 0.749632i | \(0.269770\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.56524e9 | − | 1.13713e10i | 0.0356686 | − | 0.0617798i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 6.33845e10i | − | 0.336079i | −0.985780 | − | 0.168039i | \(-0.946256\pi\) | ||
0.985780 | − | 0.168039i | \(-0.0537436\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.25682e11 | − | 2.17687e11i | 0.658365 | − | 1.14032i | −0.322674 | − | 0.946510i | \(-0.604582\pi\) |
0.981039 | − | 0.193811i | \(-0.0620850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.99117e9 | + | 1.73781e9i | 0.0357490 | + | 0.00888618i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.13555e10 | + | 1.58232e11i | 0.461563 | + | 0.799451i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.15685e10i | − | 0.155727i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.56945e11 | −0.765043 | −0.382522 | − | 0.923947i | \(-0.624944\pi\) | ||||
−0.382522 | + | 0.923947i | \(0.624944\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.18203e11 | + | 6.82443e10i | −0.562694 | + | 0.324872i | −0.754226 | − | 0.656615i | \(-0.771988\pi\) |
0.191532 | + | 0.981486i | \(0.438654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.43617e10 | − | 7.00440e9i | 0.114612 | − | 0.0329528i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.12774e11 | − | 6.51104e10i | −0.518236 | − | 0.299204i | 0.217976 | − | 0.975954i | \(-0.430054\pi\) |
−0.736213 | + | 0.676750i | \(0.763388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.34614e9 | 0.0106560 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.42500e10 | − | 1.40008e10i | −0.107606 | − | 0.0621262i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.22049e10 | + | 3.84599e10i | 0.0973948 | + | 0.168693i | 0.910606 | − | 0.413277i | \(-0.135616\pi\) |
−0.813211 | + | 0.581969i | \(0.802282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.36338e8 | + | 7.87148e7i | −0.000584356 | + | 0.000337378i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.23688e10 | + | 3.87439e10i | −0.0947788 | + | 0.164162i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.01068e10i | − | 0.331740i | −0.986148 | − | 0.165870i | \(-0.946957\pi\) | ||
0.986148 | − | 0.165870i | \(-0.0530431\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.79394e10 | + | 1.52316e11i | −0.360049 | + | 0.623624i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.09072e11 | + | 7.68265e10i | 1.23703 | + | 0.307492i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.38242e10 | + | 1.10547e11i | 0.252581 | + | 0.437483i | 0.964236 | − | 0.265047i | \(-0.0853873\pi\) |
−0.711655 | + | 0.702529i | \(0.752054\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.27073e11i | − | 2.81333i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.19249e9 | −0.00838905 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.78418e11 | − | 1.60745e11i | 1.04179 | − | 0.601479i | 0.121452 | − | 0.992597i | \(-0.461245\pi\) |
0.920340 | + | 0.391118i | \(0.127912\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.28952e11 | + | 3.17213e11i | 1.21728 | + | 1.17384i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.30391e11 | − | 7.52810e10i | −0.471948 | − | 0.272479i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.63606e11 | 0.585682 | 0.292841 | − | 0.956161i | \(-0.405399\pi\) | ||||
0.292841 | + | 0.956161i | \(0.405399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.02311e11 | + | 1.74539e11i | 1.05873 | + | 0.611256i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.28002e11 | + | 2.21705e11i | 0.443404 | + | 0.767999i | 0.997940 | − | 0.0641615i | \(-0.0204373\pi\) |
−0.554535 | + | 0.832160i | \(0.687104\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.98947e10 | + | 2.30332e10i | −0.135221 | + | 0.0780701i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.79996e10 | + | 3.11762e10i | −0.0603510 | + | 0.104531i | −0.894622 | − | 0.446823i | \(-0.852555\pi\) |
0.834271 | + | 0.551354i | \(0.185889\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.01755e11i | 0.333888i | 0.985966 | + | 0.166944i | \(0.0533899\pi\) | ||||
−0.985966 | + | 0.166944i | \(0.946610\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.88836e9 | − | 3.27074e9i | 0.00612999 | − | 0.0106175i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.11649e11 | − | 4.26883e11i | 1.30798 | − | 1.35638i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.41349e11 | − | 4.18029e11i | −0.758727 | − | 1.31415i | −0.943500 | − | 0.331373i | \(-0.892488\pi\) |
0.184772 | − | 0.982781i | \(-0.440845\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.06099e10i | − | 0.0326531i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.09685e11 | 0.334013 | 0.167007 | − | 0.985956i | \(-0.446590\pi\) | ||||
0.167007 | + | 0.985956i | \(0.446590\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.65424e11 | − | 9.55079e10i | 0.493243 | − | 0.284774i | −0.232676 | − | 0.972554i | \(-0.574748\pi\) |
0.725919 | + | 0.687780i | \(0.241415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.33104e9 | + | 2.94926e10i | −0.0216305 | + | 0.0870193i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.21672e11 | + | 7.02475e10i | 0.351568 | + | 0.202978i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.65887e11 | 1.33222 | 0.666109 | − | 0.745855i | \(-0.267959\pi\) | ||||
0.666109 | + | 0.745855i | \(0.267959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.86382e11 | + | 2.23078e11i | 1.08218 | + | 0.624796i | 0.931483 | − | 0.363784i | \(-0.118515\pi\) |
0.150696 | + | 0.988580i | \(0.451849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.99570e11 | + | 5.18871e11i | 0.830409 | + | 1.43831i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.62910e10 | − | 4.40466e10i | 0.207168 | − | 0.119609i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.67364e10 | − | 1.67552e11i | 0.260008 | − | 0.450346i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.87765e9i | 0.0181118i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.20655e11 | + | 5.55390e11i | −0.835870 | + | 1.44777i | 0.0574510 | + | 0.998348i | \(0.481703\pi\) |
−0.893321 | + | 0.449420i | \(0.851631\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.85315e11 | − | 6.44536e11i | −0.473373 | − | 1.64642i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.24426e10 | − | 3.88717e10i | −0.0567519 | − | 0.0982972i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.23443e11i | − | 0.553776i | −0.960902 | − | 0.276888i | \(-0.910697\pi\) | ||
0.960902 | − | 0.276888i | \(-0.0893031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.30167e11 | 1.05548 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.03351e9 | − | 3.48345e9i | 0.0145113 | − | 0.00837813i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.41325e9 | − | 2.98234e10i | 0.0176533 | − | 0.0710189i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.18621e11 | − | 1.83956e11i | −0.743842 | − | 0.429457i | 0.0796224 | − | 0.996825i | \(-0.474629\pi\) |
−0.823465 | + | 0.567368i | \(0.807962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.14769e11 | −1.18995 | −0.594975 | − | 0.803744i | \(-0.702838\pi\) | ||||
−0.594975 | + | 0.803744i | \(0.702838\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.22932e10 | + | 1.28710e10i | 0.0505291 | + | 0.0291730i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.43687e11 | − | 5.95283e11i | −0.771391 | − | 1.33609i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.27822e11 | + | 1.89268e11i | −0.721549 | + | 0.416587i | −0.815323 | − | 0.579007i | \(-0.803440\pi\) |
0.0937735 | + | 0.995594i | \(0.470107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.44961e11 | − | 2.51080e11i | 0.315975 | − | 0.547284i | −0.663670 | − | 0.748026i | \(-0.731002\pi\) |
0.979644 | + | 0.200742i | \(0.0643352\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.65534e11i | 0.567673i | 0.958873 | + | 0.283836i | \(0.0916072\pi\) | ||||
−0.958873 | + | 0.283836i | \(0.908393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.06382e11 | + | 3.57463e11i | −0.436971 | + | 0.756856i | −0.997454 | − | 0.0713096i | \(-0.977282\pi\) |
0.560483 | + | 0.828166i | \(0.310615\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.24500e11 | + | 1.17946e10i | −0.673961 | + | 0.0244965i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.33102e10 | − | 2.30540e10i | −0.0273804 | − | 0.0474242i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.82771e10i | 0.157974i | 0.996876 | + | 0.0789872i | \(0.0251686\pi\) | ||||
−0.996876 | + | 0.0789872i | \(0.974831\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.51125e11 | 0.701904 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.64105e10 | − | 9.47463e9i | 0.0321882 | − | 0.0185838i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.71962e11 | + | 2.62256e11i | 0.528414 | + | 0.509556i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.49757e11 | + | 3.75138e11i | 1.23889 | + | 0.715274i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.71336e11 | 0.512521 | 0.256261 | − | 0.966608i | \(-0.417509\pi\) | ||||
0.256261 | + | 0.966608i | \(0.417509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.68531e11 | + | 2.12772e11i | 0.683205 | + | 0.394449i | 0.801061 | − | 0.598582i | \(-0.204269\pi\) |
−0.117857 | + | 0.993031i | \(0.537602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.66317e11 | − | 4.61275e11i | −0.489133 | − | 0.847203i | 0.510789 | − | 0.859706i | \(-0.329353\pi\) |
−0.999922 | + | 0.0125034i | \(0.996020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.35013e11 | + | 1.93420e11i | −0.603975 | + | 0.348705i | −0.770604 | − | 0.637315i | \(-0.780045\pi\) |
0.166629 | + | 0.986020i | \(0.446712\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.40039e10 | − | 2.42554e10i | 0.0250140 | − | 0.0433255i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.42213e10i | − | 0.0249380i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.27495e10 | + | 5.67238e10i | −0.0569026 | + | 0.0985582i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.40081e10 | + | 4.87211e10i | 0.0238972 | + | 0.0831161i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.55166e10 | + | 7.88371e10i | 0.0769435 | + | 0.133270i | 0.901930 | − | 0.431883i | \(-0.142151\pi\) |
−0.824986 | + | 0.565153i | \(0.808817\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6.62395e11i | − | 1.09955i | −0.835314 | − | 0.549773i | \(-0.814714\pi\) | ||
0.835314 | − | 0.549773i | \(-0.185286\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.27751e11 | −1.52612 | −0.763060 | − | 0.646327i | \(-0.776304\pi\) | ||||
−0.763060 | + | 0.646327i | \(0.776304\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.74649e11 | + | 4.47244e11i | −1.25144 | + | 0.722520i | −0.971396 | − | 0.237467i | \(-0.923683\pi\) |
−0.280046 | + | 0.959987i | \(0.590350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.84404e11 | − | 8.17707e10i | 0.455332 | − | 0.130915i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.33564e11 | − | 4.23523e11i | −1.15354 | − | 0.665996i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.55293e10 | 0.0242024 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.13906e11 | + | 2.96704e11i | 0.786765 | + | 0.454239i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.34633e10 | + | 1.27242e11i | 0.111473 | + | 0.193078i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.82347e10 | − | 2.20748e10i | 0.0569985 | − | 0.0329081i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.21717e11 | − | 2.10820e11i | 0.179855 | − | 0.311518i | −0.761976 | − | 0.647606i | \(-0.775771\pi\) |
0.941831 | + | 0.336088i | \(0.109104\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.03684e11i | 0.731281i | 0.930756 | + | 0.365641i | \(0.119150\pi\) | ||||
−0.930756 | + | 0.365641i | \(0.880850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.38573e11 | + | 5.86425e11i | −0.487269 | + | 0.843975i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.08974e11 | − | 8.38912e11i | 1.14408 | − | 1.18642i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.56741e11 | − | 6.17893e11i | −0.500139 | − | 0.866266i | −1.00000 | 0.000160119i | \(-0.999949\pi\) | |
0.499861 | − | 0.866105i | \(-0.333384\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.75087e11i | − | 0.379021i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.18261e11 | −0.844510 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.03821e11 | + | 1.75411e11i | −0.407901 | + | 0.235502i | −0.689887 | − | 0.723917i | \(-0.742340\pi\) |
0.281987 | + | 0.959418i | \(0.409007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.64983e11 | + | 2.99375e11i | 0.752032 | + | 0.398490i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.96291e9 | + | 5.75209e9i | 0.0130359 | + | 0.00752626i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.13829e12 | 1.47671 | 0.738354 | − | 0.674413i | \(-0.235603\pi\) | ||||
0.738354 | + | 0.674413i | \(0.235603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.37867e11 | + | 3.10538e11i | 0.685988 | + | 0.396055i | 0.802107 | − | 0.597180i | \(-0.203712\pi\) |
−0.116119 | + | 0.993235i | \(0.537046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.87897e11 | − | 3.25447e11i | −0.237615 | − | 0.411561i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.54959e11 | + | 5.51346e11i | −1.18737 | + | 0.685526i | −0.957707 | − | 0.287745i | \(-0.907094\pi\) |
−0.229659 | + | 0.973271i | \(0.573761\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.95290e9 | − | 8.57867e9i | 0.00610653 | − | 0.0105768i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.30554e12i | 1.58277i | 0.611320 | + | 0.791384i | \(0.290639\pi\) | ||||
−0.611320 | + | 0.791384i | \(0.709361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.45477e10 | − | 4.25179e10i | 0.0295120 | − | 0.0511162i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.02087e11 | + | 5.02331e10i | 0.238927 | + | 0.0593904i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.54246e11 | − | 1.30639e12i | −0.884341 | − | 1.53172i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.67339e10i | 0.0654234i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.41138e12 | −1.61413 | −0.807066 | − | 0.590461i | \(-0.798946\pi\) | ||||
−0.807066 | + | 0.590461i | \(0.798946\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.73135e11 | + | 5.61840e11i | −1.09470 | + | 0.632027i | −0.934825 | − | 0.355110i | \(-0.884444\pi\) |
−0.159878 | + | 0.987137i | \(0.551110\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.34290e10 | + | 3.86104e9i | −0.0149827 | + | 0.00430778i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.06817e12 | − | 6.16708e11i | −1.17236 | − | 0.676864i | −0.218127 | − | 0.975920i | \(-0.569995\pi\) |
−0.954235 | + | 0.299056i | \(0.903328\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.80765e11 | 0.196781 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.24581e12 | + | 7.19268e11i | 1.33425 | + | 0.770330i | 0.985948 | − | 0.167052i | \(-0.0534249\pi\) |
0.348302 | + | 0.937382i | \(0.386758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.61261e10 | − | 4.52518e10i | −0.0277543 | − | 0.0480719i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.53940e12 | + | 1.46612e12i | −2.65427 | + | 1.53245i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.42784e11 | + | 5.93719e11i | −0.355407 | + | 0.615582i | −0.987187 | − | 0.159565i | \(-0.948991\pi\) |
0.631781 | + | 0.775147i | \(0.282324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.13920e10i | − | 0.0116227i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.31832e11 | − | 9.21160e11i | 0.538262 | − | 0.932298i | −0.460735 | − | 0.887538i | \(-0.652414\pi\) |
0.998998 | − | 0.0447602i | \(-0.0142524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.bk.a.53.11 | ✓ | 44 | |
3.2 | odd | 2 | inner | 252.9.bk.a.53.12 | yes | 44 | |
7.2 | even | 3 | inner | 252.9.bk.a.233.12 | yes | 44 | |
21.2 | odd | 6 | inner | 252.9.bk.a.233.11 | yes | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.bk.a.53.11 | ✓ | 44 | 1.1 | even | 1 | trivial | |
252.9.bk.a.53.12 | yes | 44 | 3.2 | odd | 2 | inner | |
252.9.bk.a.233.11 | yes | 44 | 21.2 | odd | 6 | inner | |
252.9.bk.a.233.12 | yes | 44 | 7.2 | even | 3 | inner |