Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(1,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.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: | \(134.149125258\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{537541}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 134385 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(367.086\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.1 |
$q$-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 | ||||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.80644e6 | −0.174314 | −0.0871572 | − | 0.996195i | \(-0.527778\pi\) | ||||
−0.0871572 | + | 0.996195i | \(0.527778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.01851e9 | 1.36281 | 0.681405 | − | 0.731907i | \(-0.261369\pi\) | ||||
0.681405 | + | 0.731907i | \(0.261369\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.06383e11 | −1.23665 | −0.618326 | − | 0.785922i | \(-0.712189\pi\) | ||||
−0.618326 | + | 0.785922i | \(0.712189\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.96922e11 | 0.798545 | 0.399273 | − | 0.916832i | \(-0.369263\pi\) | ||||
0.399273 | + | 0.916832i | \(0.369263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.24766e11 | 0.100640 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.67718e12 | −0.442386 | −0.221193 | − | 0.975230i | \(-0.570995\pi\) | ||||
−0.221193 | + | 0.975230i | \(0.570995\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.39341e12 | 0.276651 | 0.138325 | − | 0.990387i | \(-0.455828\pi\) | ||||
0.138325 | + | 0.990387i | \(0.455828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.01419e13 | −0.786819 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.08605e14 | −1.04998 | −0.524992 | − | 0.851107i | \(-0.675932\pi\) | ||||
−0.524992 | + | 0.851107i | \(0.675932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.62348e14 | −0.969614 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.10405e15 | −0.487314 | −0.243657 | − | 0.969862i | \(-0.578347\pi\) | ||||
−0.243657 | + | 0.969862i | \(0.578347\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.87819e15 | 1.72635 | 0.863175 | − | 0.504905i | \(-0.168472\pi\) | ||||
0.863175 | + | 0.504905i | \(0.168472\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.28179e15 | 0.713981 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.87689e15 | −0.237557 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.14668e16 | 0.392034 | 0.196017 | − | 0.980601i | \(-0.437199\pi\) | ||||
0.196017 | + | 0.980601i | \(0.437199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.34378e16 | −0.461040 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.57394e15 | 0.111394 | 0.0556968 | − | 0.998448i | \(-0.482262\pi\) | ||||
0.0556968 | + | 0.998448i | \(0.482262\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.54549e17 | 1.09056 | 0.545278 | − | 0.838255i | \(-0.316424\pi\) | ||||
0.545278 | + | 0.838255i | \(0.316424\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.32722e16 | −0.0581048 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.63961e17 | −0.732001 | −0.366001 | − | 0.930615i | \(-0.619273\pi\) | ||||
−0.366001 | + | 0.930615i | \(0.619273\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.78814e17 | 0.857250 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.17134e17 | 0.255412 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.43334e18 | −1.12577 | −0.562887 | − | 0.826534i | \(-0.690309\pi\) | ||||
−0.562887 | + | 0.826534i | \(0.690309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.04939e17 | 0.215566 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.36574e17 | −0.159725 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.89337e18 | 1.50113 | 0.750564 | − | 0.660798i | \(-0.229782\pi\) | ||||
0.750564 | + | 0.660798i | \(0.229782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.96513e18 | 0.532207 | 0.266104 | − | 0.963944i | \(-0.414264\pi\) | ||||
0.266104 | + | 0.963944i | \(0.414264\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.55132e18 | 0.454270 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.51086e18 | −0.139198 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.75878e19 | 1.17876 | 0.589380 | − | 0.807856i | \(-0.299372\pi\) | ||||
0.589380 | + | 0.807856i | \(0.299372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.23179e19 | 0.606208 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.35158e19 | −1.22190 | −0.610952 | − | 0.791668i | \(-0.709213\pi\) | ||||
−0.610952 | + | 0.791668i | \(0.709213\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.12183e19 | −1.66721 | −0.833607 | − | 0.552358i | \(-0.813728\pi\) | ||||
−0.833607 | + | 0.552358i | \(0.813728\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.73012e19 | 0.559807 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.08352e20 | −1.68532 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.83561e19 | 0.693429 | 0.346714 | − | 0.937971i | \(-0.387297\pi\) | ||||
0.346714 | + | 0.937971i | \(0.387297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.25379e20 | 0.886958 | 0.443479 | − | 0.896285i | \(-0.353744\pi\) | ||||
0.443479 | + | 0.896285i | \(0.353744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.39970e19 | 0.0771143 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.51929e19 | 0.281351 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.73528e20 | −1.60972 | −0.804860 | − | 0.593465i | \(-0.797760\pi\) | ||||
−0.804860 | + | 0.593465i | \(0.797760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.04268e20 | 1.08827 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.65200e20 | −0.996709 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.81426e19 | −0.0482243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.83797e20 | −0.390756 | −0.195378 | − | 0.980728i | \(-0.562593\pi\) | ||||
−0.195378 | + | 0.980728i | \(0.562593\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.70933e20 | −0.412217 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.60683e20 | 0.414980 | 0.207490 | − | 0.978237i | \(-0.433470\pi\) | ||||
0.207490 | + | 0.978237i | \(0.433470\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.01928e20 | −0.661273 | −0.330637 | − | 0.943758i | \(-0.607263\pi\) | ||||
−0.330637 | + | 0.943758i | \(0.607263\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.28926e20 | 0.137154 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.07173e21 | 1.01813 | 0.509065 | − | 0.860728i | \(-0.329991\pi\) | ||||
0.509065 | + | 0.860728i | \(0.329991\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.82773e21 | −0.739492 | −0.369746 | − | 0.929133i | \(-0.620555\pi\) | ||||
−0.369746 | + | 0.929133i | \(0.620555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.77102e20 | −0.226341 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.45088e21 | 0.679201 | 0.339601 | − | 0.940570i | \(-0.389708\pi\) | ||||
0.339601 | + | 0.940570i | \(0.389708\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.94041e20 | 0.183027 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.38398e21 | 0.266182 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.74524e21 | −0.602888 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.91702e21 | 0.529309 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.65332e20 | −0.0643132 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.57495e21 | 0.343332 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.85246e22 | −1.50595 | −0.752976 | − | 0.658048i | \(-0.771382\pi\) | ||||
−0.752976 | + | 0.658048i | \(0.771382\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.12598e21 | −0.629633 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.23574e22 | −1.31242 | −0.656210 | − | 0.754579i | \(-0.727841\pi\) | ||||
−0.656210 | + | 0.754579i | \(0.727841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.53025e21 | 0.377023 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.83711e20 | 0.0335468 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.29591e22 | −0.842151 | −0.421075 | − | 0.907026i | \(-0.638347\pi\) | ||||
−0.421075 | + | 0.907026i | \(0.638347\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.16594e22 | −1.31237 | −0.656187 | − | 0.754598i | \(-0.727832\pi\) | ||||
−0.656187 | + | 0.754598i | \(0.727832\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.55866e22 | 0.422621 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.22256e22 | −0.987523 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.20248e21 | 0.0849458 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.82735e22 | −0.494934 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.33948e22 | −0.659147 | −0.329573 | − | 0.944130i | \(-0.606905\pi\) | ||||
−0.329573 | + | 0.944130i | \(0.606905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.01728e22 | 1.05869 | 0.529346 | − | 0.848406i | \(-0.322437\pi\) | ||||
0.529346 | + | 0.848406i | \(0.322437\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.28215e22 | −0.147462 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.99878e22 | −0.300928 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.91718e23 | −1.68157 | −0.840787 | − | 0.541366i | \(-0.817907\pi\) | ||||
−0.840787 | + | 0.541366i | \(0.817907\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.46370e22 | 0.649966 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.12466e23 | −1.43093 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.98873e23 | −1.17654 | −0.588269 | − | 0.808665i | \(-0.700191\pi\) | ||||
−0.588269 | + | 0.808665i | \(0.700191\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.39112e22 | −0.124457 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.01098e22 | −0.183962 | −0.0919808 | − | 0.995761i | \(-0.529320\pi\) | ||||
−0.0919808 | + | 0.995761i | \(0.529320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.95177e22 | −0.362325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.57792e22 | 0.0922170 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.87093e23 | −0.592344 | −0.296172 | − | 0.955135i | \(-0.595710\pi\) | ||||
−0.296172 | + | 0.955135i | \(0.595710\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.70906e23 | −1.32140 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.47998e23 | −0.866676 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.94050e23 | 1.75748 | 0.878742 | − | 0.477298i | \(-0.158384\pi\) | ||||
0.878742 | + | 0.477298i | \(0.158384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.89362e23 | −0.372964 | −0.186482 | − | 0.982458i | \(-0.559709\pi\) | ||||
−0.186482 | + | 0.982458i | \(0.559709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.75088e23 | −0.307270 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.36476e22 | −0.0683371 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.91189e23 | 0.547078 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.09702e23 | −0.262273 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.17670e24 | −1.31770 | −0.658848 | − | 0.752276i | \(-0.728956\pi\) | ||||
−0.658848 | + | 0.752276i | \(0.728956\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.30716e23 | 0.131213 | 0.0656064 | − | 0.997846i | \(-0.479102\pi\) | ||||
0.0656064 | + | 0.997846i | \(0.479102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.92146e22 | 0.0803660 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.43917e23 | −0.602045 | −0.301023 | − | 0.953617i | \(-0.597328\pi\) | ||||
−0.301023 | + | 0.953617i | \(0.597328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.02892e24 | −1.47675 | −0.738377 | − | 0.674388i | \(-0.764408\pi\) | ||||
−0.738377 | + | 0.674388i | \(0.764408\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.03854e24 | −0.680557 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.12448e24 | −0.664116 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.64426e22 | −0.0194175 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.27361e23 | −0.349994 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.86531e23 | −0.342121 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.73877e24 | −1.07793 | −0.538964 | − | 0.842329i | \(-0.681184\pi\) | ||||
−0.538964 | + | 0.842329i | \(0.681184\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.97907e24 | 0.705466 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.88281e23 | −0.190100 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.02401e24 | 2.35269 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.61488e24 | 0.962566 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.45955e24 | −0.353266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.35130e24 | −0.958116 | −0.479058 | − | 0.877783i | \(-0.659022\pi\) | ||||
−0.479058 | + | 0.877783i | \(0.659022\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.61211e24 | −0.323205 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.67094e23 | 0.140145 | 0.0700724 | − | 0.997542i | \(-0.477677\pi\) | ||||
0.0700724 | + | 0.997542i | \(0.477677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.54631e24 | 1.25737 | 0.628684 | − | 0.777661i | \(-0.283594\pi\) | ||||
0.628684 | + | 0.777661i | \(0.283594\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.39805e24 | 0.973021 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.10251e24 | 0.292079 | 0.146039 | − | 0.989279i | \(-0.453347\pi\) | ||||
0.146039 | + | 0.989279i | \(0.453347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.00475e24 | 0.127598 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.44587e24 | −0.400351 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.45098e25 | 1.54342 | 0.771709 | − | 0.635976i | \(-0.219402\pi\) | ||||
0.771709 | + | 0.635976i | \(0.219402\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.56087e24 | −0.347038 | −0.173519 | − | 0.984831i | \(-0.555514\pi\) | ||||
−0.173519 | + | 0.984831i | \(0.555514\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.82257e24 | −0.149431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.93461e24 | 0.220918 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.40348e24 | −0.512086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.01810e25 | 1.28342 | 0.641710 | − | 0.766948i | \(-0.278225\pi\) | ||||
0.641710 | + | 0.766948i | \(0.278225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.21920e25 | 1.29846 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.26507e23 | −0.0445220 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.05388e24 | 0.399675 | 0.199838 | − | 0.979829i | \(-0.435959\pi\) | ||||
0.199838 | + | 0.979829i | \(0.435959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.16790e25 | 0.534267 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.84957e24 | −0.162438 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.45231e25 | 0.565618 | 0.282809 | − | 0.959176i | \(-0.408734\pi\) | ||||
0.282809 | + | 0.959176i | \(0.408734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.45590e24 | 0.196239 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.79613e25 | 0.929372 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.59528e25 | −1.71958 | −0.859792 | − | 0.510645i | \(-0.829407\pi\) | ||||
−0.859792 | + | 0.510645i | \(0.829407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.65662e25 | −1.03969 | −0.519844 | − | 0.854261i | \(-0.674010\pi\) | ||||
−0.519844 | + | 0.854261i | \(0.674010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.38716e25 | −0.628310 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.91858e25 | 1.19908 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.21467e25 | 1.85589 | 0.927946 | − | 0.372715i | \(-0.121573\pi\) | ||||
0.927946 | + | 0.372715i | \(0.121573\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.74696e25 | 0.575450 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.16736e25 | 1.78167 | 0.890837 | − | 0.454324i | \(-0.150119\pi\) | ||||
0.890837 | + | 0.454324i | \(0.150119\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.45902e25 | −0.984821 | −0.492411 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492411 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.66179e24 | 0.0278423 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.75114e24 | 0.151808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.55702e25 | −0.804294 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.67580e25 | 0.225603 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.07858e26 | −1.35127 | −0.675635 | − | 0.737237i | \(-0.736130\pi\) | ||||
−0.675635 | + | 0.737237i | \(0.736130\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.24327e25 | −0.261668 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.19032e25 | 0.237994 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.27999e25 | −0.838460 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.57410e26 | 1.48622 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.72029e25 | −0.239589 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.12866e25 | −0.0927714 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.57928e25 | −0.121201 | −0.0606007 | − | 0.998162i | \(-0.519302\pi\) | ||||
−0.0606007 | + | 0.998162i | \(0.519302\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.32579e25 | 0.381786 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.16533e26 | −1.45057 | −0.725286 | − | 0.688447i | \(-0.758293\pi\) | ||||
−0.725286 | + | 0.688447i | \(0.758293\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.08285e26 | 1.30450 | 0.652249 | − | 0.758005i | \(-0.273826\pi\) | ||||
0.652249 | + | 0.758005i | \(0.273826\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.35179e25 | −0.0791858 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.51043e26 | 0.827900 | 0.413950 | − | 0.910300i | \(-0.364149\pi\) | ||||
0.413950 | + | 0.910300i | \(0.364149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.17451e26 | 0.602638 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.22333e26 | −0.587817 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.71869e25 | −0.122387 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.83516e26 | −0.774281 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.07925e26 | 0.426946 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.68846e26 | −0.997579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.02767e26 | −1.05418 | −0.527090 | − | 0.849809i | \(-0.676717\pi\) | ||||
−0.527090 | + | 0.849809i | \(0.676717\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.99822e25 | 0.130678 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.69467e25 | −0.205475 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.07259e26 | −1.46257 | −0.731284 | − | 0.682073i | \(-0.761079\pi\) | ||||
−0.731284 | + | 0.682073i | \(0.761079\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.44722e26 | −0.392137 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.38103e26 | −2.13489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.12080e25 | −0.194541 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.68873e25 | −0.105671 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.92246e26 | −0.407753 | −0.203876 | − | 0.978997i | \(-0.565354\pi\) | ||||
−0.203876 | + | 0.978997i | \(0.565354\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.69006e26 | −0.936507 | −0.468254 | − | 0.883594i | \(-0.655117\pi\) | ||||
−0.468254 | + | 0.883594i | \(0.655117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.17227e25 | −0.153680 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.16954e26 | 0.915836 | 0.457918 | − | 0.888994i | \(-0.348595\pi\) | ||||
0.457918 | + | 0.888994i | \(0.348595\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.27576e26 | 0.212995 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.21153e26 | 0.348078 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.26652e26 | 1.22696 | 0.613481 | − | 0.789710i | \(-0.289769\pi\) | ||||
0.613481 | + | 0.789710i | \(0.289769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.59547e26 | −0.923464 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.31296e26 | −0.305597 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.33023e26 | 0.290619 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.35866e27 | 1.59999 | 0.799995 | − | 0.600007i | \(-0.204835\pi\) | ||||
0.799995 | + | 0.600007i | \(0.204835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.33823e25 | 0.0371312 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.45986e27 | −1.53422 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.22128e27 | −1.21303 | −0.606517 | − | 0.795071i | \(-0.707434\pi\) | ||||
−0.606517 | + | 0.795071i | \(0.707434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.11097e26 | −0.198223 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.38220e26 | −0.389142 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.57479e26 | 0.552294 | 0.276147 | − | 0.961115i | \(-0.410942\pi\) | ||||
0.276147 | + | 0.961115i | \(0.410942\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.09386e27 | 0.869461 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.90325e27 | −1.43188 | −0.715942 | − | 0.698159i | \(-0.754003\pi\) | ||||
−0.715942 | + | 0.698159i | \(0.754003\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.12433e26 | 0.293776 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.38880e26 | 0.363519 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.12948e26 | 0.327795 | 0.163897 | − | 0.986477i | \(-0.447593\pi\) | ||||
0.163897 | + | 0.986477i | \(0.447593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.67079e26 | 0.464498 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.32018e27 | 0.757726 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.22129e26 | −0.120875 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.36102e27 | 1.21843 | 0.609213 | − | 0.793007i | \(-0.291485\pi\) | ||||
0.609213 | + | 0.793007i | \(0.291485\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.44654e26 | −0.217674 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.27592e27 | −1.52166 | −0.760829 | − | 0.648952i | \(-0.775208\pi\) | ||||
−0.760829 | + | 0.648952i | \(0.775208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.12703e27 | 1.37857 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.62774e25 | −0.0193683 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.21987e27 | −0.484809 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.16749e27 | 1.57318 | 0.786592 | − | 0.617473i | \(-0.211844\pi\) | ||||
0.786592 | + | 0.617473i | \(0.211844\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.35571e27 | 0.486216 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.00245e27 | 2.04575 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.77245e26 | −0.154610 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.45995e27 | 0.757700 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.60990e27 | −0.764497 | −0.382249 | − | 0.924060i | \(-0.624850\pi\) | ||||
−0.382249 | + | 0.924060i | \(0.624850\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.10137e27 | −0.585518 | −0.292759 | − | 0.956186i | \(-0.594573\pi\) | ||||
−0.292759 | + | 0.956186i | \(0.594573\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.20374e26 | −0.244000 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.70014e27 | 0.428944 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.02001e27 | 0.725297 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.49338e27 | 0.570147 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.31265e27 | −0.721380 | −0.360690 | − | 0.932686i | \(-0.617459\pi\) | ||||
−0.360690 | + | 0.932686i | \(0.617459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.60260e27 | −0.954730 | −0.477365 | − | 0.878705i | \(-0.658408\pi\) | ||||
−0.477365 | + | 0.878705i | \(0.658408\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.48152e26 | −0.0490435 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.54230e27 | −0.290479 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.40231e27 | 0.431273 | 0.215637 | − | 0.976474i | \(-0.430817\pi\) | ||||
0.215637 | + | 0.976474i | \(0.430817\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.66952e27 | 0.285750 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.24244e27 | 1.50851 | 0.754254 | − | 0.656583i | \(-0.227999\pi\) | ||||
0.754254 | + | 0.656583i | \(0.227999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.80245e27 | 0.280597 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.56242e27 | 0.380559 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.68141e27 | −0.946851 | −0.473426 | − | 0.880834i | \(-0.656983\pi\) | ||||
−0.473426 | + | 0.880834i | \(0.656983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.01850e27 | −0.137755 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.73413e27 | −0.611236 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.53882e27 | −0.189700 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.53406e27 | 0.180602 | 0.0903011 | − | 0.995915i | \(-0.471217\pi\) | ||||
0.0903011 | + | 0.995915i | \(0.471217\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.57100e26 | 0.0851373 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.04683e27 | −0.864500 | −0.432250 | − | 0.901754i | \(-0.642280\pi\) | ||||
−0.432250 | + | 0.901754i | \(0.642280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.43789e28 | 1.47613 | 0.738067 | − | 0.674727i | \(-0.235739\pi\) | ||||
0.738067 | + | 0.674727i | \(0.235739\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.77075e27 | 0.173741 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.22594e27 | −0.302573 | −0.151286 | − | 0.988490i | \(-0.548342\pi\) | ||||
−0.151286 | + | 0.988490i | \(0.548342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.79133e28 | 1.60642 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.13207e28 | 0.970857 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.64414e28 | −1.34864 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.41833e27 | −0.268245 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.99773e27 | −0.375258 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.52220e27 | 0.253099 | 0.126550 | − | 0.991960i | \(-0.459610\pi\) | ||||
0.126550 | + | 0.991960i | \(0.459610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.55141e27 | 0.313057 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.25459e28 | 0.826146 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.08026e27 | 0.0681143 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.18350e27 | −0.313018 | −0.156509 | − | 0.987677i | \(-0.550024\pi\) | ||||
−0.156509 | + | 0.987677i | \(0.550024\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.17433e28 | 0.679275 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.74020e28 | −1.51854 | −0.759270 | − | 0.650776i | \(-0.774444\pi\) | ||||
−0.759270 | + | 0.650776i | \(0.774444\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.05978e27 | 0.215581 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.41193e27 | 0.0718554 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.41361e28 | −1.66522 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.08162e28 | −0.505848 | −0.252924 | − | 0.967486i | \(-0.581392\pi\) | ||||
−0.252924 | + | 0.967486i | \(0.581392\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.36844e27 | 0.106210 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.89398e28 | −1.67467 | −0.837337 | − | 0.546687i | \(-0.815889\pi\) | ||||
−0.837337 | + | 0.546687i | \(0.815889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.75356e27 | −0.0723371 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.28593e27 | 0.209189 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.89861e28 | −1.10066 | −0.550329 | − | 0.834948i | \(-0.685498\pi\) | ||||
−0.550329 | + | 0.834948i | \(0.685498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.23514e28 | −2.27209 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.52224e27 | −0.0532415 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.43313e27 | 0.115269 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.80808e28 | 0.905231 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.10477e28 | 0.341990 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.41212e28 | −1.01444 | −0.507222 | − | 0.861816i | \(-0.669327\pi\) | ||||
−0.507222 | + | 0.861816i | \(0.669327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.37991e28 | 0.394078 | 0.197039 | − | 0.980396i | \(-0.436867\pi\) | ||||
0.197039 | + | 0.980396i | \(0.436867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.78065e28 | 0.762911 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.89696e28 | −0.763714 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.04446e27 | 0.102465 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.05489e28 | 0.500376 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.80011e27 | 0.0889529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.88589e27 | −0.177475 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.68879e28 | −1.01468 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.09375e28 | −1.06012 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.75791e28 | 1.15264 | 0.576320 | − | 0.817224i | \(-0.304488\pi\) | ||||
0.576320 | + | 0.817224i | \(0.304488\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.11816e28 | 0.215331 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.95713e27 | 0.128904 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.41040e28 | −1.32122 | −0.660609 | − | 0.750730i | \(-0.729702\pi\) | ||||
−0.660609 | + | 0.750730i | \(0.729702\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.03388e28 | 0.177402 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.16268e27 | −0.134816 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.94362e28 | 0.945012 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.57734e27 | 0.0394545 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.21534e28 | −1.06360 | −0.531799 | − | 0.846871i | \(-0.678484\pi\) | ||||
−0.531799 | + | 0.846871i | \(0.678484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.13439e28 | 0.870859 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.30993e28 | −0.315856 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.75204e27 | 0.102112 | 0.0510561 | − | 0.998696i | \(-0.483741\pi\) | ||||
0.0510561 | + | 0.998696i | \(0.483741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.32911e27 | −0.118395 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.23827e28 | 0.151423 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.42718e29 | −1.68190 | −0.840952 | − | 0.541109i | \(-0.818005\pi\) | ||||
−0.840952 | + | 0.541109i | \(0.818005\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.19587e29 | 1.35833 | 0.679165 | − | 0.733986i | \(-0.262342\pi\) | ||||
0.679165 | + | 0.733986i | \(0.262342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.94829e28 | 0.760772 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.64481e28 | 1.01808 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.02439e29 | −1.04261 | −0.521304 | − | 0.853371i | \(-0.674554\pi\) | ||||
−0.521304 | + | 0.853371i | \(0.674554\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.71864e27 | −0.0757557 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.27699e29 | 1.20876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.52482e29 | 1.39219 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.26803e27 | −0.0463993 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.48071e28 | −0.720663 | −0.360332 | − | 0.932824i | \(-0.617336\pi\) | ||||
−0.360332 | + | 0.932824i | \(0.617336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.82468e28 | 0.477597 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.39276e28 | 0.347591 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.14783e29 | 0.876601 | 0.438300 | − | 0.898829i | \(-0.355581\pi\) | ||||
0.438300 | + | 0.898829i | \(0.355581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.42560e28 | 0.105092 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.19806e29 | 0.852605 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.72380e29 | 1.18442 | 0.592208 | − | 0.805785i | \(-0.298256\pi\) | ||||
0.592208 | + | 0.805785i | \(0.298256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.73184e29 | −1.81248 | −0.906241 | − | 0.422761i | \(-0.861061\pi\) | ||||
−0.906241 | + | 0.422761i | \(0.861061\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.13247e28 | 0.392920 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.49099e28 | −0.0922662 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.31744e29 | 1.38525 | 0.692625 | − | 0.721298i | \(-0.256454\pi\) | ||||
0.692625 | + | 0.721298i | \(0.256454\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.63995e28 | 0.383427 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.04772e29 | −0.584536 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.48641e29 | 1.34041 | 0.670205 | − | 0.742176i | \(-0.266206\pi\) | ||||
0.670205 | + | 0.742176i | \(0.266206\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.15190e27 | 0.0112107 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.47882e29 | −1.24810 | −0.624052 | − | 0.781383i | \(-0.714514\pi\) | ||||
−0.624052 | + | 0.781383i | \(0.714514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.18780e28 | 0.252483 | 0.126241 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126241 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.29499e28 | 0.202069 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.82292e29 | −2.19374 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.06857e29 | 0.909767 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.64439e28 | 0.197524 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.21655e28 | −0.173430 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.91890e29 | −1.16121 | −0.580605 | − | 0.814186i | \(-0.697184\pi\) | ||||
−0.580605 | + | 0.814186i | \(0.697184\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.61722e29 | 0.622342 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.05129e28 | 0.262509 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.90051e29 | 0.684553 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.16862e29 | −0.407301 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.18026e29 | 1.07264 | 0.536319 | − | 0.844015i | \(-0.319814\pi\) | ||||
0.536319 | + | 0.844015i | \(0.319814\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.41840e29 | 1.44228 | 0.721140 | − | 0.692790i | \(-0.243619\pi\) | ||||
0.721140 | + | 0.692790i | \(0.243619\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.47374e28 | 0.109754 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.85233e28 | 0.178992 | 0.0894960 | − | 0.995987i | \(-0.471474\pi\) | ||||
0.0894960 | + | 0.995987i | \(0.471474\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.26952e29 | −1.85637 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.73810e29 | −1.35832 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.75541e29 | 1.87527 | 0.937634 | − | 0.347623i | \(-0.113011\pi\) | ||||
0.937634 | + | 0.347623i | \(0.113011\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.51020e28 | 0.228774 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.13455e29 | −0.555738 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.16262e28 | −0.130189 | −0.0650943 | − | 0.997879i | \(-0.520735\pi\) | ||||
−0.0650943 | + | 0.997879i | \(0.520735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.39834e29 | 0.341583 | 0.170792 | − | 0.985307i | \(-0.445367\pi\) | ||||
0.170792 | + | 0.985307i | \(0.445367\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.61852e28 | 0.203958 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.86634e28 | −0.0657205 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.30310e29 | 0.511671 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.56940e29 | 0.553169 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.15439e29 | −0.658155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.25080e29 | −1.66854 | −0.834272 | − | 0.551353i | \(-0.814112\pi\) | ||||
−0.834272 | + | 0.551353i | \(0.814112\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.51934e28 | 0.186602 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.97987e29 | 1.13635 | 0.568173 | − | 0.822909i | \(-0.307650\pi\) | ||||
0.568173 | + | 0.822909i | \(0.307650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.89050e29 | −0.532525 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.52962e28 | −0.0809127 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.71862e29 | 0.990545 | 0.495272 | − | 0.868738i | \(-0.335068\pi\) | ||||
0.495272 | + | 0.868738i | \(0.335068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.73925e28 | 0.146799 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.45602e29 | −0.725942 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.68922e29 | −0.898982 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.55681e29 | −1.46485 | −0.732426 | − | 0.680847i | \(-0.761612\pi\) | ||||
−0.732426 | + | 0.680847i | \(0.761612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.77799e29 | −0.561774 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.58574e29 | 0.228766 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.52052e28 | −0.0492790 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.24151e29 | −0.168632 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.42010e27 | 0.00846258 | 0.00423129 | − | 0.999991i | \(-0.498653\pi\) | ||||
0.00423129 | + | 0.999991i | \(0.498653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.47787e28 | 0.108457 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.93295e28 | −0.0736690 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.69209e29 | 0.565539 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.52437e29 | −0.763402 | −0.381701 | − | 0.924286i | \(-0.624662\pi\) | ||||
−0.381701 | + | 0.924286i | \(0.624662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.03475e29 | 0.231143 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.64343e30 | −1.81264 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.60729e29 | 0.172140 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.56789e29 | −0.891093 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.22078e29 | 0.123306 | 0.0616530 | − | 0.998098i | \(-0.480363\pi\) | ||||
0.0616530 | + | 0.998098i | \(0.480363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.18621e29 | −0.901189 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.10266e29 | 0.200362 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.10454e29 | 0.472506 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04525e30 | −0.939959 | −0.469980 | − | 0.882677i | \(-0.655739\pi\) | ||||
−0.469980 | + | 0.882677i | \(0.655739\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.68306e29 | −0.482447 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.69967e29 | 0.717647 | 0.358824 | − | 0.933405i | \(-0.383178\pi\) | ||||
0.358824 | + | 0.933405i | \(0.383178\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.07621e29 | 0.0862741 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.87103e30 | −1.45772 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.11587e29 | −0.0844980 | −0.0422490 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422490 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.73286e29 | −0.127547 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.69344e29 | 0.693578 | 0.346789 | − | 0.937943i | \(-0.387272\pi\) | ||||
0.346789 | + | 0.937943i | \(0.387272\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.65180e29 | 0.114899 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.37168e29 | 0.295653 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.11007e30 | 1.38752 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.68531e29 | 0.491408 | 0.245704 | − | 0.969345i | \(-0.420981\pi\) | ||||
0.245704 | + | 0.969345i | \(0.420981\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.19167e30 | −0.740982 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.05173e29 | −0.184545 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.16553e29 | −0.127367 | −0.0636836 | − | 0.997970i | \(-0.520285\pi\) | ||||
−0.0636836 | + | 0.997970i | \(0.520285\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.31041e30 | −0.749669 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.88897e28 | −0.0550316 | −0.0275158 | − | 0.999621i | \(-0.508760\pi\) | ||||
−0.0275158 | + | 0.999621i | \(0.508760\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.86156e30 | −1.00779 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.88044e28 | 0.0257048 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.33921e30 | 1.19872 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.21082e29 | 0.309686 | 0.154843 | − | 0.987939i | \(-0.450513\pi\) | ||||
0.154843 | + | 0.987939i | \(0.450513\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.75574e29 | −0.230753 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.43242e30 | 1.62075 | 0.810373 | − | 0.585914i | \(-0.199264\pi\) | ||||
0.810373 | + | 0.585914i | \(0.199264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.64247e30 | −1.67389 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.89634e29 | −0.308459 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.07841e28 | 0.0308172 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.56550e30 | 1.51107 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.27313e29 | 0.0937836 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.29761e29 | 0.293123 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.39619e30 | −1.32818 | −0.664091 | − | 0.747652i | \(-0.731181\pi\) | ||||
−0.664091 | + | 0.747652i | \(0.731181\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.57573e29 | −0.326560 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.49624e30 | 0.925622 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.17693e30 | 0.424992 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.22165e29 | −0.113298 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.15218e30 | 1.07969 | 0.539844 | − | 0.841765i | \(-0.318483\pi\) | ||||
0.539844 | + | 0.841765i | \(0.318483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.70633e29 | 0.323827 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.65109e30 | −0.536573 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.51256e30 | 2.06176 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.08738e29 | 0.249431 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.30396e30 | 0.992802 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.77781e30 | 1.69162 | 0.845811 | − | 0.533482i | \(-0.179117\pi\) | ||||
0.845811 | + | 0.533482i | \(0.179117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.71903e29 | 0.220213 | 0.110107 | − | 0.993920i | \(-0.464881\pi\) | ||||
0.110107 | + | 0.993920i | \(0.464881\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.15920e30 | 0.600264 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.56998e29 | 0.205088 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.14265e30 | 0.301703 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.40960e30 | 0.362755 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.63389e30 | −0.409845 | −0.204923 | − | 0.978778i | \(-0.565694\pi\) | ||||
−0.204923 | + | 0.978778i | \(0.565694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.56986e29 | −0.111739 | −0.0558695 | − | 0.998438i | \(-0.517793\pi\) | ||||
−0.0558695 | + | 0.998438i | \(0.517793\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.90437e30 | −0.692287 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.30833e30 | 0.536401 | 0.268201 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268201 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.52497e29 | −0.0798607 | −0.0399303 | − | 0.999202i | \(-0.512714\pi\) | ||||
−0.0399303 | + | 0.999202i | \(0.512714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.85068e30 | −1.07150 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.76069e30 | −0.379236 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.52675e29 | 0.0320672 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.62205e30 | −0.332236 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.70025e29 | 0.153817 | 0.0769084 | − | 0.997038i | \(-0.475495\pi\) | ||||
0.0769084 | + | 0.997038i | \(0.475495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.91392e30 | −0.762525 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.41324e30 | −1.02865 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.40743e29 | 0.0631585 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.98951e30 | 0.721347 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.22350e30 | 0.568587 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.39203e30 | −0.411629 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.31709e30 | −1.06060 | −0.530301 | − | 0.847810i | \(-0.677921\pi\) | ||||
−0.530301 | + | 0.847810i | \(0.677921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.81270e28 | −0.0160748 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.16894e30 | −0.506541 | −0.253271 | − | 0.967395i | \(-0.581506\pi\) | ||||
−0.253271 | + | 0.967395i | \(0.581506\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.21661e30 | 1.28164 | 0.640818 | − | 0.767693i | \(-0.278595\pi\) | ||||
0.640818 | + | 0.767693i | \(0.278595\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.75795e29 | −0.0876466 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.74681e30 | −0.705162 | −0.352581 | − | 0.935781i | \(-0.614696\pi\) | ||||
−0.352581 | + | 0.935781i | \(0.614696\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.12158e29 | 0.103254 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.28137e30 | 0.464360 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.20808e30 | −0.857530 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.98097e30 | 0.941293 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.89540e29 | −0.130252 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.64111e30 | 0.467897 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.72283e30 | 0.843444 | 0.421722 | − | 0.906725i | \(-0.361426\pi\) | ||||
0.421722 | + | 0.906725i | \(0.361426\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.36890e30 | 0.780156 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.20529e31 | 1.44160 | 0.720800 | − | 0.693143i | \(-0.243775\pi\) | ||||
0.720800 | + | 0.693143i | \(0.243775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.79063e30 | −0.325923 | −0.162962 | − | 0.986632i | \(-0.552105\pi\) | ||||
−0.162962 | + | 0.986632i | \(0.552105\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.32463e30 | 0.151074 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.22230e30 | 0.470274 | 0.235137 | − | 0.971962i | \(-0.424446\pi\) | ||||
0.235137 | + | 0.971962i | \(0.424446\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.88675e31 | −2.05232 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.29336e30 | −0.137406 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.95157e30 | −0.202509 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.02250e30 | −0.306355 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.88925e30 | 0.484085 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.69790e30 | −0.841274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.27064e30 | 0.498027 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.29488e30 | −0.858070 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.20793e29 | 0.0650130 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.17027e30 | −0.720045 | −0.360023 | − | 0.932944i | \(-0.617231\pi\) | ||||
−0.360023 | + | 0.932944i | \(0.617231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.60630e30 | 0.138327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.02621e30 | −0.675410 | −0.337705 | − | 0.941252i | \(-0.609651\pi\) | ||||
−0.337705 | + | 0.941252i | \(0.609651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.33381e31 | −1.09686 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.66462e29 | 0.0535616 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.27712e31 | −1.78858 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.31927e30 | 0.254818 | 0.127409 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127409 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.32552e29 | 0.0699756 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.33031e31 | −0.975746 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.30165e30 | −0.380122 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.14483e30 | −0.220424 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.23059e31 | 1.52846 | 0.764232 | − | 0.644941i | \(-0.223118\pi\) | ||||
0.764232 | + | 0.644941i | \(0.223118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.54007e30 | 0.237159 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.27860e31 | 0.837489 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.48903e30 | −0.0953636 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.24036e30 | 0.516037 | 0.258018 | − | 0.966140i | \(-0.416931\pi\) | ||||
0.258018 | + | 0.966140i | \(0.416931\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.22990e31 | −0.753152 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.13254e31 | 0.678208 | 0.339104 | − | 0.940749i | \(-0.389876\pi\) | ||||
0.339104 | + | 0.940749i | \(0.389876\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.99717e30 | −0.116961 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.98216e29 | 0.0457179 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.85285e31 | −1.59810 | −0.799050 | − | 0.601264i | \(-0.794664\pi\) | ||||
−0.799050 | + | 0.601264i | \(0.794664\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.42989e31 | −1.33135 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.91893e30 | −0.477988 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.28550e30 | −0.119814 | −0.0599068 | − | 0.998204i | \(-0.519080\pi\) | ||||
−0.0599068 | + | 0.998204i | \(0.519080\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.47903e30 | 0.229693 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.93539e30 | −0.347933 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.33841e31 | −1.14769 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.12404e31 | 1.98029 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.22366e30 | 0.339376 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.97561e29 | −0.0228723 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.86814e31 | −1.29010 | −0.645049 | − | 0.764141i | \(-0.723163\pi\) | ||||
−0.645049 | + | 0.764141i | \(0.723163\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.60536e30 | 0.0706600 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.70387e31 | 1.59534 | 0.797670 | − | 0.603094i | \(-0.206066\pi\) | ||||
0.797670 | + | 0.603094i | \(0.206066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.24305e31 | −1.78852 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.08364e31 | 0.447031 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.87685e31 | −0.757770 | −0.378885 | − | 0.925444i | \(-0.623692\pi\) | ||||
−0.378885 | + | 0.925444i | \(0.623692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.03751e31 | 1.99066 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.37289e30 | −0.246497 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.00084e31 | −0.757531 | −0.378766 | − | 0.925493i | \(-0.623651\pi\) | ||||
−0.378766 | + | 0.925493i | \(0.623651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.83167e30 | 0.104945 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.58751e31 | 0.575952 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.22397e31 | −1.14507 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.44667e31 | 0.503034 | 0.251517 | − | 0.967853i | \(-0.419071\pi\) | ||||
0.251517 | + | 0.967853i | \(0.419071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.78781e31 | 0.608631 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.72297e30 | 0.257420 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.92902e31 | 1.28229 | 0.641144 | − | 0.767421i | \(-0.278460\pi\) | ||||
0.641144 | + | 0.767421i | \(0.278460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.36091e30 | −0.0754469 |
(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 | 48.22.a.h.1.1 | 2 | ||
4.3 | odd | 2 | 24.22.a.a.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 72.22.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.22.a.a.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
48.22.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
72.22.a.a.1.2 | 2 | 12.11 | even | 2 |