Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [176,10,Mod(1,176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("176.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 176 = 2^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 176.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: | \(90.6463071648\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{889}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 222 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(15.4081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 176.1 |
$q$-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 | ||||||||
\(3\) | 144.672 | 1.03119 | 0.515597 | − | 0.856831i | \(-0.327570\pi\) | ||||
0.515597 | + | 0.856831i | \(0.327570\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1706.58 | −1.22113 | −0.610565 | − | 0.791966i | \(-0.709058\pi\) | ||||
−0.610565 | + | 0.791966i | \(0.709058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8664.66 | 1.36399 | 0.681993 | − | 0.731358i | \(-0.261113\pi\) | ||||
0.681993 | + | 0.731358i | \(0.261113\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1247.12 | 0.0633603 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14641.0 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 67852.1 | 0.658898 | 0.329449 | − | 0.944173i | \(-0.393137\pi\) | ||||
0.329449 | + | 0.944173i | \(0.393137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −246895. | −1.25922 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 249646. | 0.724943 | 0.362471 | − | 0.931995i | \(-0.381933\pi\) | ||||
0.362471 | + | 0.931995i | \(0.381933\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 293189. | 0.516127 | 0.258064 | − | 0.966128i | \(-0.416916\pi\) | ||||
0.258064 | + | 0.966128i | \(0.416916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.25354e6 | 1.40653 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.10315e6 | −0.821979 | −0.410990 | − | 0.911640i | \(-0.634817\pi\) | ||||
−0.410990 | + | 0.911640i | \(0.634817\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 959294. | 0.491158 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.66716e6 | −0.965857 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.23603e6 | −1.37471 | −0.687354 | − | 0.726322i | \(-0.741228\pi\) | ||||
−0.687354 | + | 0.726322i | \(0.741228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.38378e6 | 1.63047 | 0.815234 | − | 0.579131i | \(-0.196608\pi\) | ||||
0.815234 | + | 0.579131i | \(0.196608\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.11815e6 | −0.310917 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.47869e7 | −1.66561 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.34600e6 | 0.644382 | 0.322191 | − | 0.946675i | \(-0.395581\pi\) | ||||
0.322191 | + | 0.946675i | \(0.395581\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.81632e6 | 0.679451 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.01256e7 | 0.559623 | 0.279811 | − | 0.960055i | \(-0.409728\pi\) | ||||
0.279811 | + | 0.960055i | \(0.409728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.56347e7 | 1.14346 | 0.571730 | − | 0.820442i | \(-0.306273\pi\) | ||||
0.571730 | + | 0.820442i | \(0.306273\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.12831e6 | −0.0773712 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.88993e7 | −1.76064 | −0.880318 | − | 0.474385i | \(-0.842671\pi\) | ||||
−0.880318 | + | 0.474385i | \(0.842671\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47227e7 | 0.860460 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.61168e7 | 0.747556 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.68723e7 | 1.51231 | 0.756153 | − | 0.654395i | \(-0.227076\pi\) | ||||
0.756153 | + | 0.654395i | \(0.227076\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.49861e7 | 0.368185 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.24164e7 | 0.532227 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.82302e8 | 1.95865 | 0.979326 | − | 0.202289i | \(-0.0648379\pi\) | ||||
0.979326 | + | 0.202289i | \(0.0648379\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.22104e8 | 1.12914 | 0.564569 | − | 0.825386i | \(-0.309042\pi\) | ||||
0.564569 | + | 0.825386i | \(0.309042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.08059e7 | 0.0864227 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.15795e8 | −0.804600 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.80532e7 | 0.412584 | 0.206292 | − | 0.978491i | \(-0.433860\pi\) | ||||
0.206292 | + | 0.978491i | \(0.433860\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.59596e8 | −0.847620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.67349e8 | 0.781555 | 0.390777 | − | 0.920485i | \(-0.372206\pi\) | ||||
0.390777 | + | 0.920485i | \(0.372206\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.51799e8 | −0.625626 | −0.312813 | − | 0.949815i | \(-0.601271\pi\) | ||||
−0.312813 | + | 0.949815i | \(0.601271\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.38783e8 | 0.506479 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.26859e8 | −0.411258 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.95735e8 | −0.854241 | −0.427120 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427120 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.10412e8 | −1.05935 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.61094e8 | −1.06644 | −0.533222 | − | 0.845975i | \(-0.679019\pi\) | ||||
−0.533222 | + | 0.845975i | \(0.679019\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.26040e8 | −0.885249 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.57509e8 | −1.41759 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.63623e8 | 0.783267 | 0.391634 | − | 0.920121i | \(-0.371910\pi\) | ||||
0.391634 | + | 0.920121i | \(0.371910\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.87915e8 | 0.898728 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.21290e9 | 1.68133 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.00351e8 | −0.630258 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.06866e8 | 0.122565 | 0.0612825 | − | 0.998120i | \(-0.480481\pi\) | ||||
0.0612825 | + | 0.998120i | \(0.480481\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.82591e7 | −0.0191039 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.38561e9 | 1.32494 | 0.662470 | − | 0.749088i | \(-0.269508\pi\) | ||||
0.662470 | + | 0.749088i | \(0.269508\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.45242e9 | 1.27152 | 0.635760 | − | 0.771886i | \(-0.280687\pi\) | ||||
0.635760 | + | 0.771886i | \(0.280687\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.13926e9 | −1.71756 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.44377e9 | −1.06481 | −0.532405 | − | 0.846490i | \(-0.678712\pi\) | ||||
−0.532405 | + | 0.846490i | \(0.678712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.58675e9 | 1.75524 | 0.877618 | − | 0.479361i | \(-0.159132\pi\) | ||||
0.877618 | + | 0.479361i | \(0.159132\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.06276e9 | 0.664482 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.13601e9 | 0.655433 | 0.327717 | − | 0.944776i | \(-0.393721\pi\) | ||||
0.327717 | + | 0.944776i | \(0.393721\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.88262e9 | 1.00374 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.46198e7 | 0.0417480 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.16309e9 | 0.988812 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.14359e8 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.46490e9 | 0.577079 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.69605e9 | 0.621362 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.27848e9 | 1.11829 | 0.559147 | − | 0.829068i | \(-0.311129\pi\) | ||||
0.559147 | + | 0.829068i | \(0.311129\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.70864e9 | 1.17913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.81056e9 | −0.537146 | −0.268573 | − | 0.963259i | \(-0.586552\pi\) | ||||
−0.268573 | + | 0.963259i | \(0.586552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.54038e9 | 0.703991 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.55173e9 | 1.17944 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.19317e9 | −0.774425 | −0.387213 | − | 0.921990i | \(-0.626562\pi\) | ||||
−0.387213 | + | 0.921990i | \(0.626562\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.30571e8 | 0.188717 | 0.0943583 | − | 0.995538i | \(-0.469920\pi\) | ||||
0.0943583 | + | 0.995538i | \(0.469920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.52110e9 | −1.81556 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.93422e8 | −0.198665 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.93570e9 | 1.67870 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.02341e9 | 0.887301 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.83876e9 | 1.46911 | 0.734553 | − | 0.678551i | \(-0.237392\pi\) | ||||
0.734553 | + | 0.678551i | \(0.237392\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.05461e9 | 0.947742 | 0.473871 | − | 0.880594i | \(-0.342856\pi\) | ||||
0.473871 | + | 0.880594i | \(0.342856\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.11338e8 | 0.0459326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.43076e10 | −1.99101 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.21421e9 | −0.422208 | −0.211104 | − | 0.977464i | \(-0.567706\pi\) | ||||
−0.211104 | + | 0.977464i | \(0.567706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.25680e10 | 1.55948 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.55845e9 | −1.12117 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.35516e9 | −0.372279 | −0.186140 | − | 0.982523i | \(-0.559598\pi\) | ||||
−0.186140 | + | 0.982523i | \(0.559598\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.61479e9 | 0.379670 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.13205e10 | −1.12627 | −0.563136 | − | 0.826364i | \(-0.690405\pi\) | ||||
−0.563136 | + | 0.826364i | \(0.690405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00060e9 | −0.565854 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.65643e8 | 0.0327020 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.24081e10 | 1.05317 | 0.526586 | − | 0.850122i | \(-0.323472\pi\) | ||||
0.526586 | + | 0.850122i | \(0.323472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.31195e9 | 0.669934 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.63741e10 | 2.01975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.78548e10 | 1.29992 | 0.649960 | − | 0.759968i | \(-0.274785\pi\) | ||||
0.649960 | + | 0.759968i | \(0.274785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.69794e10 | 1.86844 | 0.934220 | − | 0.356698i | \(-0.116098\pi\) | ||||
0.934220 | + | 0.356698i | \(0.116098\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.76652e10 | 1.16436 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.25365e10 | −0.786874 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.65506e9 | −0.218578 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.31101e10 | −1.31742 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.88704e10 | 1.02596 | 0.512980 | − | 0.858400i | \(-0.328541\pi\) | ||||
0.512980 | + | 0.858400i | \(0.328541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.63769e10 | −0.849618 | −0.424809 | − | 0.905283i | \(-0.639659\pi\) | ||||
−0.424809 | + | 0.905283i | \(0.639659\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.67524e10 | −0.829698 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.41377e10 | −1.14182 | −0.570909 | − | 0.821013i | \(-0.693409\pi\) | ||||
−0.570909 | + | 0.821013i | \(0.693409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.98474e7 | 0.00315727 | 0.00157863 | − | 0.999999i | \(-0.499498\pi\) | ||||
0.00157863 | + | 0.999999i | \(0.499498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.84543e9 | 0.425454 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.53684e10 | −1.87508 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.72802e10 | −0.683372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.37577e9 | −0.0520809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.29258e9 | −0.155618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.34436e10 | −1.16156 | −0.580780 | − | 0.814061i | \(-0.697252\pi\) | ||||
−0.580780 | + | 0.814061i | \(0.697252\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.42107e10 | 0.805935 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.37478e10 | −1.39631 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.26426e10 | 2.22394 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.19611e10 | −0.645141 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.69390e10 | 0.477663 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.74786e10 | 0.473299 | 0.236650 | − | 0.971595i | \(-0.423951\pi\) | ||||
0.236650 | + | 0.971595i | \(0.423951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.19636e9 | 0.0311200 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.99552e10 | 0.498816 | 0.249408 | − | 0.968398i | \(-0.419764\pi\) | ||||
0.249408 | + | 0.968398i | \(0.419764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.45741e10 | −1.79196 | −0.895980 | − | 0.444095i | \(-0.853525\pi\) | ||||
−0.895980 | + | 0.444095i | \(0.853525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.83530e10 | −0.424086 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.84331e10 | −1.07657 | −0.538283 | − | 0.842764i | \(-0.680927\pi\) | ||||
−0.538283 | + | 0.842764i | \(0.680927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.00516e11 | 2.14996 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.27847e10 | −0.880888 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.76719e10 | 0.548591 | 0.274295 | − | 0.961645i | \(-0.411555\pi\) | ||||
0.274295 | + | 0.961645i | \(0.411555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.23953e10 | 1.00050 | 0.500248 | − | 0.865882i | \(-0.333242\pi\) | ||||
0.500248 | + | 0.865882i | \(0.333242\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.87757e9 | −0.126534 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.92571e10 | −1.05073 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.98935e10 | 0.340075 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.67076e10 | −1.09971 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.45608e10 | −0.867659 | −0.433829 | − | 0.900995i | \(-0.642838\pi\) | ||||
−0.433829 | + | 0.900995i | \(0.642838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.61513e10 | 0.247836 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.16363e10 | −0.912863 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.72020e10 | 0.245969 | 0.122985 | − | 0.992409i | \(-0.460753\pi\) | ||||
0.122985 | + | 0.992409i | \(0.460753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.36506e10 | 0.878928 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.52996e9 | −0.0871020 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.32552e10 | 0.299722 | 0.149861 | − | 0.988707i | \(-0.452117\pi\) | ||||
0.149861 | + | 0.988707i | \(0.452117\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.48255e11 | −1.84672 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.70735e10 | 0.807700 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.82157e10 | 0.328554 | 0.164277 | − | 0.986414i | \(-0.447471\pi\) | ||||
0.164277 | + | 0.986414i | \(0.447471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.37207e11 | −1.54530 | −0.772651 | − | 0.634831i | \(-0.781070\pi\) | ||||
−0.772651 | + | 0.634831i | \(0.781070\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.50551e10 | 0.926762 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.40450e10 | −0.148090 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.85402e11 | 1.89215 | 0.946074 | − | 0.323949i | \(-0.105011\pi\) | ||||
0.946074 | + | 0.323949i | \(0.105011\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.04556e10 | 0.103307 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.20765e10 | −0.498268 | −0.249134 | − | 0.968469i | \(-0.580146\pi\) | ||||
−0.249134 | + | 0.968469i | \(0.580146\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.03796e11 | −0.961925 | −0.480963 | − | 0.876741i | \(-0.659713\pi\) | ||||
−0.480963 | + | 0.876741i | \(0.659713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.23870e10 | −0.649918 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.77352e10 | 0.763318 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.62650e10 | −0.474458 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.54606e10 | 0.126388 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.51536e10 | −0.674992 | −0.337496 | − | 0.941327i | \(-0.609580\pi\) | ||||
−0.337496 | + | 0.941327i | \(0.609580\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.11113e11 | −2.39177 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.90499e10 | 0.291217 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.48513e10 | −0.541600 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.22116e11 | 1.55966 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00460e11 | 1.36627 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.08381e11 | −1.37882 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.79447e11 | −1.79547 | −0.897734 | − | 0.440539i | \(-0.854787\pi\) | ||||
−0.897734 | + | 0.440539i | \(0.854787\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.10125e11 | 1.31118 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.40111e11 | −1.45543 | −0.727714 | − | 0.685881i | \(-0.759417\pi\) | ||||
−0.727714 | + | 0.685881i | \(0.759417\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.68635e10 | 0.570441 | 0.285220 | − | 0.958462i | \(-0.407933\pi\) | ||||
0.285220 | + | 0.958462i | \(0.407933\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.84411e10 | −0.105533 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.70124e11 | −0.946237 | −0.473118 | − | 0.880999i | \(-0.656872\pi\) | ||||
−0.473118 | + | 0.880999i | \(0.656872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.66606e10 | 0.414490 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.08874e11 | −1.09803 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.31934e10 | 0.374163 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.50900e10 | 0.323623 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.74232e11 | 1.80999 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.10342e11 | −2.40148 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.45318e10 | −0.112332 | −0.0561661 | − | 0.998421i | \(-0.517888\pi\) | ||||
−0.0561661 | + | 0.998421i | \(0.517888\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.16136e9 | 0.0408282 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.16138e11 | −0.503818 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.64453e10 | 0.407330 | 0.203665 | − | 0.979041i | \(-0.434715\pi\) | ||||
0.203665 | + | 0.979041i | \(0.434715\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.64349e11 | 0.675879 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.22747e11 | −0.491605 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.87901e10 | −0.190330 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.72364e11 | 1.03505 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.02569e11 | 0.379783 | 0.189891 | − | 0.981805i | \(-0.439186\pi\) | ||||
0.189891 | + | 0.981805i | \(0.439186\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.59960e11 | −1.29879 | −0.649397 | − | 0.760450i | \(-0.724979\pi\) | ||||
−0.649397 | + | 0.760450i | \(0.724979\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.80973e11 | −0.636401 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.23410e10 | −0.213692 | −0.106846 | − | 0.994276i | \(-0.534075\pi\) | ||||
−0.106846 | + | 0.994276i | \(0.534075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.85594e11 | −0.954380 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.12940e11 | 1.01966 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.12478e11 | 0.357391 | 0.178696 | − | 0.983904i | \(-0.442812\pi\) | ||||
0.178696 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.36728e11 | −0.733613 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.10118e10 | 0.0937449 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.59056e11 | 0.763970 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.51938e11 | −0.437189 | −0.218594 | − | 0.975816i | \(-0.570147\pi\) | ||||
−0.218594 | + | 0.975816i | \(0.570147\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.26279e10 | 0.0354579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.52719e11 | 2.06277 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.79048e11 | 0.478938 | 0.239469 | − | 0.970904i | \(-0.423027\pi\) | ||||
0.239469 | + | 0.970904i | \(0.423027\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.45372e11 | 0.640744 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.55275e11 | −0.905792 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.31277e11 | −0.575780 | −0.287890 | − | 0.957663i | \(-0.592954\pi\) | ||||
−0.287890 | + | 0.957663i | \(0.592954\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.74306e11 | 1.15318 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.53920e11 | −0.840448 | −0.420224 | − | 0.907420i | \(-0.638049\pi\) | ||||
−0.420224 | + | 0.907420i | \(0.638049\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.16496e11 | 0.502199 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.19696e10 | 0.0724500 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.20470e11 | 0.931027 | 0.465513 | − | 0.885041i | \(-0.345870\pi\) | ||||
0.465513 | + | 0.885041i | \(0.345870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.75398e11 | −0.595888 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.61938e11 | −0.553901 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.04695e11 | 1.04314 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.43330e11 | −0.693672 | −0.346836 | − | 0.937926i | \(-0.612744\pi\) | ||||
−0.346836 | + | 0.937926i | \(0.612744\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.67524e11 | 0.725951 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.15897e11 | 0.996354 | 0.498177 | − | 0.867075i | \(-0.334003\pi\) | ||||
0.498177 | + | 0.867075i | \(0.334003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.68857e11 | 1.07431 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00402e11 | 1.29360 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.07553e11 | −0.194288 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.68357e11 | −0.827604 | −0.413802 | − | 0.910367i | \(-0.635799\pi\) | ||||
−0.413802 | + | 0.910367i | \(0.635799\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.61964e11 | −0.798582 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.57958e12 | 2.67158 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.86894e11 | 1.30227 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.20161e11 | 0.194603 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.15054e12 | 1.82364 | 0.911820 | − | 0.410590i | \(-0.134677\pi\) | ||||
0.911820 | + | 0.410590i | \(0.134677\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.49749e11 | −0.387467 | −0.193734 | − | 0.981054i | \(-0.562060\pi\) | ||||
−0.193734 | + | 0.981054i | \(0.562060\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.34545e10 | −0.111554 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.39483e11 | 0.356062 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.05799e12 | 1.54013 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.43721e11 | −0.204862 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.80621e11 | −0.391717 | −0.195858 | − | 0.980632i | \(-0.562749\pi\) | ||||
−0.195858 | + | 0.980632i | \(0.562749\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.07421e12 | 1.46857 | 0.734285 | − | 0.678841i | \(-0.237518\pi\) | ||||
0.734285 | + | 0.678841i | \(0.237518\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.29275e12 | 1.73106 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.23433e11 | −0.424246 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.45531e11 | −1.21503 | −0.607513 | − | 0.794310i | \(-0.707833\pi\) | ||||
−0.607513 | + | 0.794310i | \(0.707833\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.33034e10 | 0.0545191 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.41348e12 | −1.74370 | −0.871852 | − | 0.489769i | \(-0.837081\pi\) | ||||
−0.871852 | + | 0.489769i | \(0.837081\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.91210e11 | −0.956471 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.27873e12 | 1.51493 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.24374e11 | 0.376650 | 0.188325 | − | 0.982107i | \(-0.439694\pi\) | ||||
0.188325 | + | 0.982107i | \(0.439694\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.48250e11 | −0.168733 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.75936e11 | 0.977305 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00332e12 | −1.09746 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.44780e11 | −0.155269 | −0.0776344 | − | 0.996982i | \(-0.524737\pi\) | ||||
−0.0776344 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.65846e11 | −0.700191 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.94094e11 | 0.303271 | 0.151636 | − | 0.988436i | \(-0.451546\pi\) | ||||
0.151636 | + | 0.988436i | \(0.451546\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.78478e11 | −0.888416 | −0.444208 | − | 0.895924i | \(-0.646515\pi\) | ||||
−0.444208 | + | 0.895924i | \(0.646515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.06992e12 | −2.05312 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.31625e11 | −0.614516 | −0.307258 | − | 0.951626i | \(-0.599411\pi\) | ||||
−0.307258 | + | 0.951626i | \(0.599411\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.89658e11 | 0.562759 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.65008e11 | −0.435378 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.75318e11 | −0.344766 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.81255e11 | 0.253500 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.08340e11 | 0.0958203 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.70132e12 | 1.47664 | 0.738321 | − | 0.674449i | \(-0.235619\pi\) | ||||
0.738321 | + | 0.674449i | \(0.235619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.98441e11 | 0.424581 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.38284e12 | −1.15614 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.82375e11 | −0.149668 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.17815e11 | −0.175472 | −0.0877358 | − | 0.996144i | \(-0.527963\pi\) | ||||
−0.0877358 | + | 0.996144i | \(0.527963\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.85399e11 | −0.383892 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.45219e11 | −0.190409 | −0.0952045 | − | 0.995458i | \(-0.530351\pi\) | ||||
−0.0952045 | + | 0.995458i | \(0.530351\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.30715e12 | −0.996585 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.11606e10 | 0.0233283 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.45002e12 | 1.06603 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.14365e12 | 1.54775 | 0.773876 | − | 0.633337i | \(-0.218315\pi\) | ||||
0.773876 | + | 0.633337i | \(0.218315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.63777e12 | −1.16140 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.47725e11 | −0.520818 | −0.260409 | − | 0.965498i | \(-0.583857\pi\) | ||||
−0.260409 | + | 0.965498i | \(0.583857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.36466e12 | −1.61792 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.68121e11 | −0.583505 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.60539e11 | 0.238079 | 0.119040 | − | 0.992889i | \(-0.462018\pi\) | ||||
0.119040 | + | 0.992889i | \(0.462018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.31528e12 | −0.853345 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.81984e11 | −0.498505 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.47867e12 | −1.55269 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.62344e11 | 0.530852 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.79511e12 | 1.08602 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.98989e12 | −1.18320 | −0.591602 | − | 0.806230i | \(-0.701504\pi\) | ||||
−0.591602 | + | 0.806230i | \(0.701504\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.26127e12 | −0.737140 | −0.368570 | − | 0.929600i | \(-0.620153\pi\) | ||||
−0.368570 | + | 0.929600i | \(0.620153\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.20251e12 | 0.690831 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.09297e12 | 1.18200 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.84204e11 | −0.324350 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.27353e11 | 0.124101 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.87046e11 | 0.368734 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.46392e12 | 1.30027 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.58310e12 | 1.34047 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.08375e11 | −0.259439 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.48950e12 | 1.75136 | 0.875679 | − | 0.482893i | \(-0.160414\pi\) | ||||
0.875679 | + | 0.482893i | \(0.160414\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.90318e12 | 1.92672 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.41450e12 | −2.14337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.03037e12 | 0.969687 | 0.484844 | − | 0.874601i | \(-0.338877\pi\) | ||||
0.484844 | + | 0.874601i | \(0.338877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.52279e11 | 0.0715426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.53515e12 | −0.709525 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.56244e12 | −1.16517 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.81369e12 | −0.811419 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.94692e12 | 1.29724 | 0.648620 | − | 0.761112i | \(-0.275346\pi\) | ||||
0.648620 | + | 0.761112i | \(0.275346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.73937e12 | 0.753423 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.28787e11 | −0.225397 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.94805e11 | 0.333405 | 0.166703 | − | 0.986007i | \(-0.446688\pi\) | ||||
0.166703 | + | 0.986007i | \(0.446688\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.93869e12 | −0.800369 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.55608e12 | −1.44493 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.51857e12 | 0.607338 | 0.303669 | − | 0.952778i | \(-0.401788\pi\) | ||||
0.303669 | + | 0.952778i | \(0.401788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.97779e11 | 0.117228 | 0.0586140 | − | 0.998281i | \(-0.481332\pi\) | ||||
0.0586140 | + | 0.998281i | \(0.481332\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.73002e12 | 1.05796 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.05825e12 | −0.403722 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.81913e12 | 0.683241 | 0.341620 | − | 0.939838i | \(-0.389024\pi\) | ||||
0.341620 | + | 0.939838i | \(0.389024\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.36929e12 | −0.876121 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.99522e12 | −1.45462 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.27190e12 | −0.455978 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.44410e11 | −0.0509797 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.78354e12 | −0.967666 | −0.483833 | − | 0.875160i | \(-0.660756\pi\) | ||||
−0.483833 | + | 0.875160i | \(0.660756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.45803e12 | 0.841529 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.49205e12 | −1.17744 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.56438e11 | −0.184787 | −0.0923933 | − | 0.995723i | \(-0.529452\pi\) | ||||
−0.0923933 | + | 0.995723i | \(0.529452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.69149e12 | −1.20747 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.01050e10 | 0.00325576 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.73449e12 | 1.82001 | 0.910006 | − | 0.414595i | \(-0.136077\pi\) | ||||
0.910006 | + | 0.414595i | \(0.136077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50049e11 | 0.171975 | 0.0859877 | − | 0.996296i | \(-0.472595\pi\) | ||||
0.0859877 | + | 0.996296i | \(0.472595\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.48707e10 | 0.0261415 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.65821e11 | −0.111012 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.73380e12 | −1.11635 | −0.558177 | − | 0.829722i | \(-0.688499\pi\) | ||||
−0.558177 | + | 0.829722i | \(0.688499\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.56355e12 | −1.93358 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.99644e12 | −1.16008 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.83812e12 | 1.09786 | 0.548929 | − | 0.835869i | \(-0.315036\pi\) | ||||
0.548929 | + | 0.835869i | \(0.315036\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.49997e12 | −0.704689 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.53329e12 | −0.703723 | −0.351861 | − | 0.936052i | \(-0.614451\pi\) | ||||
−0.351861 | + | 0.936052i | \(0.614451\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.23255e12 | −0.884988 | −0.442494 | − | 0.896772i | \(-0.645906\pi\) | ||||
−0.442494 | + | 0.896772i | \(0.645906\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.94229e12 | 0.793914 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.01713e12 | 1.06837 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.76807e12 | −1.24992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.21019e11 | −0.160473 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.83390e12 | 0.467140 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.95011e11 | −0.0991921 | −0.0495961 | − | 0.998769i | \(-0.515793\pi\) | ||||
−0.0495961 | + | 0.998769i | \(0.515793\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.83836e12 | −1.19779 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.59500e12 | −1.36558 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.35600e12 | 0.566955 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.08704e11 | 0.0495196 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.96414e12 | −0.927444 | −0.463722 | − | 0.885981i | \(-0.653486\pi\) | ||||
−0.463722 | + | 0.885981i | \(0.653486\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.33426e12 | 1.69203 | 0.846013 | − | 0.533163i | \(-0.178997\pi\) | ||||
0.846013 | + | 0.533163i | \(0.178997\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.32910e12 | −1.43987 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.01763e12 | 0.228308 | 0.114154 | − | 0.993463i | \(-0.463584\pi\) | ||||
0.114154 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.66908e12 | −0.590556 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.05094e13 | 2.29331 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.78338e12 | 1.45995 | 0.729973 | − | 0.683476i | \(-0.239533\pi\) | ||||
0.729973 | + | 0.683476i | \(0.239533\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.08987e12 | 0.655925 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.89311e11 | −0.0396399 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.83983e12 | −0.380008 | −0.190004 | − | 0.981783i | \(-0.560850\pi\) | ||||
−0.190004 | + | 0.981783i | \(0.560850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.08220e12 | −0.627992 | −0.313996 | − | 0.949424i | \(-0.601668\pi\) | ||||
−0.313996 | + | 0.949424i | \(0.601668\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.45060e12 | 0.492563 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.33537e12 | −0.859664 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.77614e12 | 1.12998 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.52868e12 | 0.488063 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.78773e12 | −0.340448 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.07648e12 | −1.32969 | −0.664844 | − | 0.746983i | \(-0.731502\pi\) | ||||
−0.664844 | + | 0.746983i | \(0.731502\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.55859e12 | −0.474389 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.18522e11 | 0.0216846 | 0.0108423 | − | 0.999941i | \(-0.496549\pi\) | ||||
0.0108423 | + | 0.999941i | \(0.496549\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.25956e11 | 0.167177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.88697e12 | 0.514376 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.08882e12 | 0.718961 | 0.359480 | − | 0.933153i | \(-0.382954\pi\) | ||||
0.359480 | + | 0.933153i | \(0.382954\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.44940e12 | 0.945674 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.07888e13 | −1.84786 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.89446e12 | 0.996455 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.48976e12 | −0.415438 | −0.207719 | − | 0.978189i | \(-0.566604\pi\) | ||||
−0.207719 | + | 0.978189i | \(0.566604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.58209e11 | −0.0260574 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.41744e12 | −0.230447 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.52782e12 | 0.405694 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.00694e12 | −1.11015 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.94398e12 | 1.08612 | 0.543059 | − | 0.839694i | \(-0.317266\pi\) | ||||
0.543059 | + | 0.839694i | \(0.317266\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.15377e12 | 0.332583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.45419e13 | 2.21703 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.20059e13 | 1.80720 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00274e13 | −1.49032 | −0.745159 | − | 0.666887i | \(-0.767626\pi\) | ||||
−0.745159 | + | 0.666887i | \(0.767626\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.68817e11 | −0.0541250 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.24861e12 | −1.34021 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.69535e12 | 0.242596 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.00336e12 | 0.565703 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.41668e12 | −1.17452 | −0.587261 | − | 0.809398i | \(-0.699794\pi\) | ||||
−0.587261 | + | 0.809398i | \(0.699794\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.25847e13 | 1.73434 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.58015e12 | 1.03171 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.02289e12 | −0.675200 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.69707e10 | 0.00623622 | 0.00311811 | − | 0.999995i | \(-0.499007\pi\) | ||||
0.00311811 | + | 0.999995i | \(0.499007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.08315e12 | 0.928865 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.39960e12 | 0.828943 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.70015e12 | 0.857269 | 0.428634 | − | 0.903478i | \(-0.358995\pi\) | ||||
0.428634 | + | 0.903478i | \(0.358995\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.57286e12 | −1.08351 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.96367e11 | −0.124399 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.71079e11 | 0.0211007 | 0.0105503 | − | 0.999944i | \(-0.496642\pi\) | ||||
0.0105503 | + | 0.999944i | \(0.496642\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.87804e12 | 0.350683 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.82102e12 | −0.821106 | −0.410553 | − | 0.911837i | \(-0.634664\pi\) | ||||
−0.410553 | + | 0.911837i | \(0.634664\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.50841e13 | −1.79397 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.75040e11 | −0.0675702 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.25098e13 | −1.45239 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.72654e12 | −0.656920 | −0.328460 | − | 0.944518i | \(-0.606530\pi\) | ||||
−0.328460 | + | 0.944518i | \(0.606530\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.89345e12 | −0.894724 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.03327e13 | −1.15732 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.98205e12 | 0.330052 | 0.165026 | − | 0.986289i | \(-0.447229\pi\) | ||||
0.165026 | + | 0.986289i | \(0.447229\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.33665e12 | 0.255567 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.46525e12 | −0.914974 | −0.457487 | − | 0.889216i | \(-0.651250\pi\) | ||||
−0.457487 | + | 0.889216i | \(0.651250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.24133e13 | 2.39412 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.31324e11 | −0.0560897 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.23696e13 | 1.29055 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.77112e13 | 1.82633 | 0.913164 | − | 0.407592i | \(-0.133631\pi\) | ||||
0.913164 | + | 0.407592i | \(0.133631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.48866e12 | 0.253642 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.83204e12 | 0.990458 | 0.495229 | − | 0.868763i | \(-0.335084\pi\) | ||||
0.495229 | + | 0.868763i | \(0.335084\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.04251e12 | 0.800818 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.20848e12 | 0.906345 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.96873e12 | 0.288837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.45015e12 | −0.235648 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.39653e13 | 1.32777 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.48531e12 | 0.515570 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.78869e12 | 0.166207 | 0.0831036 | − | 0.996541i | \(-0.473517\pi\) | ||||
0.0831036 | + | 0.996541i | \(0.473517\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.36439e12 | 0.309072 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.84312e12 | 0.894002 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.28504e12 | 0.743987 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.14484e13 | −1.90433 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.04170e13 | 0.914496 | 0.457248 | − | 0.889339i | \(-0.348835\pi\) | ||||
0.457248 | + | 0.889339i | \(0.348835\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.47039e13 | −1.27636 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.78194e11 | 0.0496281 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.22248e12 | 0.188633 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.63123e13 | 1.36909 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.08204e12 | 0.338802 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.91008e10 | −0.00649251 | −0.00324625 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324625 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.52015e12 | −0.610425 | −0.305213 | − | 0.952284i | \(-0.598728\pi\) | ||||
−0.305213 | + | 0.952284i | \(0.598728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.98500e13 | −1.59351 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.72585e12 | 0.454601 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.51583e12 | 0.590171 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.33201e11 | 0.0569437 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.67347e12 | 0.359000 | 0.179500 | − | 0.983758i | \(-0.442552\pi\) | ||||
0.179500 | + | 0.983758i | \(0.442552\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.06045e12 | 0.308514 | 0.154257 | − | 0.988031i | \(-0.450702\pi\) | ||||
0.154257 | + | 0.988031i | \(0.450702\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.03193e12 | −0.152709 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.53074e12 | 0.188136 | 0.0940682 | − | 0.995566i | \(-0.470013\pi\) | ||||
0.0940682 | + | 0.995566i | \(0.470013\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.26450e12 | −0.166524 | −0.0832620 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832620 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.68226e13 | 1.95117 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.66836e12 | 0.623784 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.93194e13 | 1.37532 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.23609e13 | −1.57480 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.42242e12 | −0.517150 | −0.258575 | − | 0.965991i | \(-0.583253\pi\) | ||||
−0.258575 | + | 0.965991i | \(0.583253\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.29088e13 | 0.889825 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.53404e12 | −0.513811 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.02405e13 | 0.690981 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.85735e12 | 0.123999 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.50164e13 | −0.991931 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.10377e12 | −0.529668 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.60812e13 | 1.04004 | 0.520019 | − | 0.854155i | \(-0.325925\pi\) | ||||
0.520019 | + | 0.854155i | \(0.325925\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.23999e11 | −0.0399334 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.68029e11 | 0.0549693 | 0.0274847 | − | 0.999622i | \(-0.491250\pi\) | ||||
0.0274847 | + | 0.999622i | \(0.491250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.16610e13 | 0.730748 | 0.365374 | − | 0.930861i | \(-0.380941\pi\) | ||||
0.365374 | + | 0.930861i | \(0.380941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.26929e13 | 0.787129 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.04030e13 | −1.25212 | −0.626060 | − | 0.779775i | \(-0.715334\pi\) | ||||
−0.626060 | + | 0.779775i | \(0.715334\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.11755e13 | −1.28606 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.13999e12 | −0.489258 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.32985e12 | 0.257563 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.61755e12 | 0.271850 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.33275e11 | 0.00776576 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.46957e13 | 0.847529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.26576e13 | −1.86417 | −0.932085 | − | 0.362239i | \(-0.882012\pi\) | ||||
−0.932085 | + | 0.362239i | \(0.882012\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.23194e13 | −0.696048 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.89169e13 | 1.05793 | 0.528966 | − | 0.848643i | \(-0.322580\pi\) | ||||
0.528966 | + | 0.848643i | \(0.322580\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.52036e12 | 0.250236 | 0.125118 | − | 0.992142i | \(-0.460069\pi\) | ||||
0.125118 | + | 0.992142i | \(0.460069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.50095e13 | −2.46638 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.67209e13 | −0.906994 | −0.453497 | − | 0.891258i | \(-0.649824\pi\) | ||||
−0.453497 | + | 0.891258i | \(0.649824\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.84069e13 | 1.52534 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.00885e12 | 0.319405 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.72686e13 | −0.908712 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.04707e13 | −1.58737 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.08289e13 | −0.558495 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.38977e13 | −2.24142 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.16873e13 | 1.09634 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.21341e13 | 1.60832 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.60426e13 | −2.28161 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.68525e13 | 1.31751 | 0.658753 | − | 0.752359i | \(-0.271084\pi\) | ||||
0.658753 | + | 0.752359i | \(0.271084\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.72803e12 | 0.0839487 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.77113e12 | −0.421913 | −0.210957 | − | 0.977495i | \(-0.567658\pi\) | ||||
−0.210957 | + | 0.977495i | \(0.567658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.75088e12 | 0.321545 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.01470e13 | −1.42184 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.56879e13 | −0.732660 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.62159e11 | 0.0398720 | 0.0199360 | − | 0.999801i | \(-0.493654\pi\) | ||||
0.0199360 | + | 0.999801i | \(0.493654\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.04284e13 | −1.85147 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.13549e13 | 0.514965 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.04697e12 | 0.316493 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.81134e12 | 0.0805640 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.65304e12 | 0.0728138 | 0.0364069 | − | 0.999337i | \(-0.488409\pi\) | ||||
0.0364069 | + | 0.999337i | \(0.488409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.01803e13 | 0.444107 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.47375e13 | −1.50083 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.23766e12 | 0.266913 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.41842e13 | −1.02495 | −0.512476 | − | 0.858702i | \(-0.671272\pi\) | ||||
−0.512476 | + | 0.858702i | \(0.671272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.40135e13 | 0.588235 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.40036e13 | 1.41375 | 0.706874 | − | 0.707340i | \(-0.250105\pi\) | ||||
0.706874 | + | 0.707340i | \(0.250105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.11701e13 | −0.459998 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.94392e13 | 1.60874 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.65859e13 | −0.670138 | −0.335069 | − | 0.942194i | \(-0.608760\pi\) | ||||
−0.335069 | + | 0.942194i | \(0.608760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.02998e13 | −0.412223 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.46123e13 | −0.975753 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.57430e13 | −1.01098 | −0.505489 | − | 0.862833i | \(-0.668688\pi\) | ||||
−0.505489 | + | 0.862833i | \(0.668688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.22038e13 | −1.25283 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.10907e13 | 0.427420 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.76677e13 | −1.05631 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.38482e13 | 1.65843 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.80056e12 | −0.0674668 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.79485e13 | 1.03749 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.94862e12 | −0.181997 | −0.0909986 | − | 0.995851i | \(-0.529006\pi\) | ||||
−0.0909986 | + | 0.995851i | \(0.529006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.05891e13 | 0.385834 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.45094e13 | −0.523799 | −0.261899 | − | 0.965095i | \(-0.584349\pi\) | ||||
−0.261899 | + | 0.965095i | \(0.584349\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.19661e12 | 0.257407 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.41674e12 | 0.333718 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.00736e12 | −0.281167 | −0.140583 | − | 0.990069i | \(-0.544898\pi\) | ||||
−0.140583 | + | 0.990069i | \(0.544898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.78790e12 | −0.236164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.22599e12 | 0.111212 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.29697e13 | 1.12622 | 0.563111 | − | 0.826381i | \(-0.309604\pi\) | ||||
0.563111 | + | 0.826381i | \(0.309604\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.11929e13 | 1.39431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.38324e13 | −2.47639 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.82791e13 | −0.939900 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.22142e12 | −0.0402286 | −0.0201143 | − | 0.999798i | \(-0.506403\pi\) | ||||
−0.0201143 | + | 0.999798i | \(0.506403\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.54908e12 | −0.115836 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.19200e11 | −0.00385544 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.27455e13 | −1.04960 | −0.524800 | − | 0.851226i | \(-0.675860\pi\) | ||||
−0.524800 | + | 0.851226i | \(0.675860\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.95930e13 | −0.622380 |
(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 | 176.10.a.e.1.2 | 2 | ||
4.3 | odd | 2 | 22.10.a.d.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 198.10.a.n.1.2 | 2 | |||
44.43 | even | 2 | 242.10.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.10.a.d.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
176.10.a.e.1.2 | 2 | 1.1 | even | 1 | trivial | ||
198.10.a.n.1.2 | 2 | 12.11 | even | 2 | |||
242.10.a.e.1.1 | 2 | 44.43 | even | 2 |