Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} - 1751639 x^{18} + 15765036 x^{17} + 1288400424989 x^{16} - 10307560742020 x^{15} + \cdots + 51\!\cdots\!63 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{36}\cdot 3^{26}\cdot 7^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.10 | ||
Root | \(-589.770 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.73 |
Dual form | 252.9.z.e.145.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 885.405 | − | 511.189i | 1.41665 | − | 0.817902i | 0.420645 | − | 0.907225i | \(-0.361804\pi\) |
0.996003 | + | 0.0893233i | \(0.0284704\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 765.093 | + | 2275.84i | 0.318656 | + | 0.947870i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 89.3699 | − | 154.793i | 0.00610409 | − | 0.0105726i | −0.862957 | − | 0.505277i | \(-0.831390\pi\) |
0.869061 | + | 0.494704i | \(0.164724\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 19474.4i | − | 0.681854i | −0.940090 | − | 0.340927i | \(-0.889259\pi\) | ||
0.940090 | − | 0.340927i | \(-0.110741\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 64245.6 | + | 37092.2i | 0.769215 | + | 0.444107i | 0.832595 | − | 0.553883i | \(-0.186854\pi\) |
−0.0633793 | + | 0.997990i | \(0.520188\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4266.93 | − | 2463.51i | 0.0327417 | − | 0.0189034i | −0.483540 | − | 0.875322i | \(-0.660649\pi\) |
0.516281 | + | 0.856419i | \(0.327316\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 96237.7 | + | 166689.i | 0.343902 | + | 0.595655i | 0.985154 | − | 0.171675i | \(-0.0549180\pi\) |
−0.641252 | + | 0.767330i | \(0.721585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 327315. | − | 566927.i | 0.837927 | − | 1.45133i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.17929e6 | 1.66736 | 0.833682 | − | 0.552245i | \(-0.186229\pi\) | ||||
0.833682 | + | 0.552245i | \(0.186229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −950064. | − | 548520.i | −1.02874 | − | 0.593944i | −0.112118 | − | 0.993695i | \(-0.535763\pi\) |
−0.916624 | + | 0.399751i | \(0.869097\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.84080e6 | + | 1.62393e6i | 1.22669 | + | 1.08217i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.46795e6 | + | 2.54256e6i | 0.783256 | + | 1.35664i | 0.930035 | + | 0.367470i | \(0.119776\pi\) |
−0.146779 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 71941.4i | − | 0.0254591i | −0.999919 | − | 0.0127296i | \(-0.995948\pi\) | ||
0.999919 | − | 0.0127296i | \(-0.00405206\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 634388. | 0.185559 | 0.0927793 | − | 0.995687i | \(-0.470425\pi\) | ||||
0.0927793 | + | 0.995687i | \(0.470425\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 190090. | − | 109749.i | 0.0389554 | − | 0.0224909i | −0.480396 | − | 0.877052i | \(-0.659507\pi\) |
0.519351 | + | 0.854561i | \(0.326174\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.59407e6 | + | 3.48245e6i | −0.796917 | + | 0.604089i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −601096. | + | 1.04113e6i | −0.0761798 | + | 0.131947i | −0.901599 | − | 0.432573i | \(-0.857606\pi\) |
0.825419 | + | 0.564521i | \(0.190939\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 182740.i | − | 0.0199702i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.57841e6 | − | 4.95275e6i | −0.707944 | − | 0.408732i | 0.102355 | − | 0.994748i | \(-0.467362\pi\) |
−0.810299 | + | 0.586016i | \(0.800695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33423e7 | − | 7.70320e6i | 0.963635 | − | 0.556355i | 0.0663454 | − | 0.997797i | \(-0.478866\pi\) |
0.897290 | + | 0.441442i | \(0.145533\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.95511e6 | − | 1.72428e7i | −0.557690 | − | 0.965947i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 922496. | − | 1.59781e6i | 0.0457789 | − | 0.0792913i | −0.842228 | − | 0.539121i | \(-0.818756\pi\) |
0.888007 | + | 0.459830i | \(0.152090\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.59965e7 | −1.41654 | −0.708268 | − | 0.705944i | \(-0.750523\pi\) | ||||
−0.708268 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.11337e7 | + | 6.42804e6i | 0.392056 | + | 0.226354i | 0.683051 | − | 0.730371i | \(-0.260653\pi\) |
−0.290995 | + | 0.956725i | \(0.593986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 420661. | + | 84960.2i | 0.0119665 | + | 0.00241687i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.23201e7 | − | 3.86596e7i | −0.573045 | − | 0.992542i | −0.996251 | − | 0.0865090i | \(-0.972429\pi\) |
0.423207 | − | 0.906033i | \(-0.360904\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.52746e7i | 0.532564i | 0.963895 | + | 0.266282i | \(0.0857953\pi\) | ||||
−0.963895 | + | 0.266282i | \(0.914205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.58445e7 | 1.45294 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.07125e7 | − | 2.92789e7i | 0.808267 | − | 0.466653i | −0.0380869 | − | 0.999274i | \(-0.512126\pi\) |
0.846354 | + | 0.532621i | \(0.178793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.43206e7 | − | 1.48997e7i | 0.646309 | − | 0.217277i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.51864e6 | − | 4.36241e6i | 0.0309223 | − | 0.0535589i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.08177e8i | 1.22193i | 0.791657 | + | 0.610965i | \(0.209219\pi\) | ||||
−0.791657 | + | 0.610965i | \(0.790781\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.42918e8 | + | 8.25135e7i | 1.37341 | + | 0.792938i | 0.991356 | − | 0.131202i | \(-0.0418835\pi\) |
0.382054 | + | 0.924140i | \(0.375217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.72330e6 | + | 3.88170e6i | −0.0597356 | + | 0.0344884i | −0.529570 | − | 0.848266i | \(-0.677647\pi\) |
0.469835 | + | 0.882754i | \(0.344314\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.40986e7 | + | 4.17400e7i | 0.183847 | + | 0.318432i | 0.943187 | − | 0.332261i | \(-0.107812\pi\) |
−0.759340 | + | 0.650694i | \(0.774478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.30456e7 | − | 1.43839e8i | 0.588316 | − | 1.01899i | −0.406137 | − | 0.913812i | \(-0.633125\pi\) |
0.994453 | − | 0.105181i | \(-0.0335421\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.10120e8 | 0.675389 | 0.337694 | − | 0.941256i | \(-0.390353\pi\) | ||||
0.337694 | + | 0.941256i | \(0.390353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70419e8 | + | 9.83913e7i | 0.974375 | + | 0.562555i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.52620e7 | + | 1.74592e8i | −0.175841 | + | 0.870634i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.07163e8 | + | 1.85613e8i | 0.499925 | + | 0.865896i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.69913e8i | − | 1.10557i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.16647e8 | 1.60160 | 0.800798 | − | 0.598935i | \(-0.204409\pi\) | ||||
0.800798 | + | 0.598935i | \(0.204409\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.35188e8 | + | 2.51256e8i | −1.47772 | + | 0.853162i | −0.999683 | − | 0.0251777i | \(-0.991985\pi\) |
−0.478037 | + | 0.878340i | \(0.658652\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.87114e6 | + | 7.82601e6i | 0.0283513 | + | 0.0250112i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.63136e8 | − | 4.55764e8i | 0.746960 | − | 1.29377i | −0.202313 | − | 0.979321i | \(-0.564846\pi\) |
0.949273 | − | 0.314452i | \(-0.101821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.75267e8i | − | 1.27315i | −0.771216 | − | 0.636574i | \(-0.780351\pi\) | ||
0.771216 | − | 0.636574i | \(-0.219649\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.01451e6 | − | 1.74043e6i | −0.00720896 | − | 0.00416210i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.04415e9 | − | 6.02842e8i | 2.36207 | − | 1.36374i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.89018e8 | − | 3.27389e8i | −0.383494 | − | 0.664232i | 0.608065 | − | 0.793887i | \(-0.291946\pi\) |
−0.991559 | + | 0.129656i | \(0.958613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.48044e7 | − | 1.64206e8i | 0.182356 | − | 0.315850i | −0.760326 | − | 0.649541i | \(-0.774961\pi\) |
0.942682 | + | 0.333691i | \(0.108294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.12159e9 | −1.94315 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.56334e8 | + | 2.63464e8i | 0.751076 | + | 0.433634i | 0.826083 | − | 0.563549i | \(-0.190564\pi\) |
−0.0750066 | + | 0.997183i | \(0.523898\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.05725e8 | + | 3.46554e8i | −0.455017 | + | 0.515783i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.83633e8 | + | 6.64472e8i | 0.543457 | + | 0.941296i | 0.998702 | + | 0.0509295i | \(0.0162184\pi\) |
−0.455245 | + | 0.890366i | \(0.650448\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.12292e8i | 0.401508i | 0.979642 | + | 0.200754i | \(0.0643392\pi\) | ||||
−0.979642 | + | 0.200754i | \(0.935661\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.36477e8 | 0.535075 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.88275e7 | − | 4.55111e7i | 0.0880022 | − | 0.0508081i | −0.455353 | − | 0.890311i | \(-0.650487\pi\) |
0.543355 | + | 0.839503i | \(0.317154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.54066e9 | + | 3.11165e8i | 1.64269 | + | 0.331771i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.27225e8 | − | 1.60600e9i | 0.903177 | − | 1.56435i | 0.0798315 | − | 0.996808i | \(-0.474562\pi\) |
0.823346 | − | 0.567540i | \(-0.192105\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.07233e8i | 0.379428i | 0.981839 | + | 0.189714i | \(0.0607560\pi\) | ||||
−0.981839 | + | 0.189714i | \(0.939244\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.59946e9 | + | 1.50080e9i | 2.21920 | + | 1.28125i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.14833e7 | − | 6.62986e6i | 0.00939071 | − | 0.00542173i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.98416e7 | − | 1.03649e8i | −0.0449645 | − | 0.0778808i | 0.842667 | − | 0.538435i | \(-0.180984\pi\) |
−0.887632 | + | 0.460554i | \(0.847651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.84829e8 | − | 8.39749e8i | 0.349429 | − | 0.605230i | −0.636719 | − | 0.771096i | \(-0.719709\pi\) |
0.986148 | + | 0.165867i | \(0.0530421\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.18199e9 | −0.784784 | −0.392392 | − | 0.919798i | \(-0.628352\pi\) | ||||
−0.392392 | + | 0.919798i | \(0.628352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.76730e9 | + | 1.02035e9i | 1.12693 | + | 0.650633i | 0.943161 | − | 0.332336i | \(-0.107837\pi\) |
0.183769 | + | 0.982969i | \(0.441170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.02270e8 | + | 2.68388e9i | 0.531315 | + | 1.58044i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.67756e7 | − | 6.36973e7i | −0.0208231 | − | 0.0360666i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 880655.i | − | 0.000461552i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.10575e9 | 1.06237 | 0.531186 | − | 0.847255i | \(-0.321746\pi\) | ||||
0.531186 | + | 0.847255i | \(0.321746\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.61690e8 | − | 3.24292e8i | 0.262871 | − | 0.151769i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.21455e8 | − | 2.58186e9i | 0.235168 | − | 1.16438i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.22350e8 | − | 1.25115e9i | 0.302816 | − | 0.524493i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.37045e9i | − | 0.554172i | −0.960845 | − | 0.277086i | \(-0.910631\pi\) | ||
0.960845 | − | 0.277086i | \(-0.0893687\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.28035e9 | + | 1.89391e9i | 1.23543 | + | 0.713274i | 0.968156 | − | 0.250348i | \(-0.0805450\pi\) |
0.267270 | + | 0.963622i | \(0.413878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.41344e7 | − | 8.16050e6i | 0.00513967 | − | 0.00296739i | −0.497428 | − | 0.867505i | \(-0.665722\pi\) |
0.502568 | + | 0.864538i | \(0.332389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.88764e9 | − | 5.00154e9i | −0.979760 | − | 1.69699i | −0.663237 | − | 0.748409i | \(-0.730818\pi\) |
−0.316523 | − | 0.948585i | \(-0.602515\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.12204e8 | − | 1.94344e8i | 0.0367907 | − | 0.0637234i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.29837e9 | −1.31738 | −0.658692 | − | 0.752413i | \(-0.728890\pi\) | ||||
−0.658692 | + | 0.752413i | \(0.728890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.66397e8 | + | 3.84744e8i | 0.197544 | + | 0.114052i | 0.595510 | − | 0.803348i | \(-0.296950\pi\) |
−0.397965 | + | 0.917401i | \(0.630284\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.28742e9 | + | 5.43182e9i | −0.634865 | + | 1.50758i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.79755e7 | − | 8.30960e7i | −0.0128894 | − | 0.0223250i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.09715e9i | − | 1.78809i | −0.447979 | − | 0.894044i | \(-0.647856\pi\) | ||
0.447979 | − | 0.894044i | \(-0.352144\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.44030e7 | 0.00839682 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.26184e9 | + | 3.61527e9i | −1.43539 | + | 0.828721i | −0.997524 | − | 0.0703204i | \(-0.977598\pi\) |
−0.437863 | + | 0.899042i | \(0.644265\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.66334e9 | + | 5.28610e9i | −1.03633 | + | 1.17473i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.10490e9 | − | 5.37785e9i | 0.648971 | − | 1.12405i | −0.334398 | − | 0.942432i | \(-0.608533\pi\) |
0.983369 | − | 0.181619i | \(-0.0581336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.22909e9i | 0.249231i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.16864e9 | + | 6.74713e8i | 0.223188 | + | 0.128858i | 0.607426 | − | 0.794377i | \(-0.292202\pi\) |
−0.384238 | + | 0.923234i | \(0.625536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.80116e8 | − | 5.65870e8i | 0.181719 | − | 0.104916i | −0.406381 | − | 0.913704i | \(-0.633209\pi\) |
0.588100 | + | 0.808788i | \(0.299876\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.85043e7 | − | 1.01332e8i | −0.0102296 | − | 0.0177181i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.79327e9 | + | 3.10604e9i | −0.304599 | + | 0.527580i | −0.977172 | − | 0.212450i | \(-0.931856\pi\) |
0.672573 | + | 0.740030i | \(0.265189\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.75399e9 | −0.922877 | −0.461439 | − | 0.887172i | \(-0.652667\pi\) | ||||
−0.461439 | + | 0.887172i | \(0.652667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.95966e9 | − | 5.75021e9i | −1.55274 | − | 0.896475i | −0.997917 | − | 0.0645064i | \(-0.979453\pi\) |
−0.554823 | − | 0.831969i | \(-0.687214\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.63727e8 | − | 5.50419e7i | 0.0241320 | − | 0.00811270i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.36211e8 | − | 1.27515e9i | −0.105538 | − | 0.182798i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.07373e10i | 1.45688i | 0.685108 | + | 0.728442i | \(0.259755\pi\) | ||||
−0.685108 | + | 0.728442i | \(0.740245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.01272e10 | −1.33721 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.24617e9 | − | 1.87418e9i | 0.406150 | − | 0.234491i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.85366e8 | + | 1.44376e9i | 0.0591293 | + | 0.175886i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.87558e9 | − | 1.36409e10i | 0.910088 | − | 1.57632i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.74603e9i | 0.984595i | 0.870427 | + | 0.492297i | \(0.163843\pi\) | ||||
−0.870427 | + | 0.492297i | \(0.836157\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.53768e10 | + | 8.87781e9i | 1.64371 | + | 0.948996i | 0.979499 | + | 0.201449i | \(0.0645651\pi\) |
0.664210 | + | 0.747546i | \(0.268768\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.41291e9 | + | 3.70250e9i | −0.668156 | + | 0.385760i | −0.795378 | − | 0.606114i | \(-0.792727\pi\) |
0.127222 | + | 0.991874i | \(0.459394\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.94697e9 | + | 1.03005e10i | 0.588924 | + | 1.02005i | 0.994374 | + | 0.105928i | \(0.0337814\pi\) |
−0.405450 | + | 0.914117i | \(0.632885\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.05393e8 | − | 1.82547e8i | 0.0101777 | − | 0.0176283i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.65509e8 | 0.0335805 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.10406e10 | − | 6.37428e9i | −0.989597 | − | 0.571344i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.95206e8 | + | 3.48646e8i | 0.0337319 | + | 0.0297578i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.62889e9 | − | 1.14816e10i | −0.552241 | − | 0.956510i | −0.998112 | − | 0.0614129i | \(-0.980439\pi\) |
0.445871 | − | 0.895097i | \(-0.352894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.88628e9i | − | 0.149771i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.54131e8 | −0.0429628 | −0.0214814 | − | 0.999769i | \(-0.506838\pi\) | ||||
−0.0214814 | + | 0.999769i | \(0.506838\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.69814e8 | + | 9.80424e7i | −0.0125591 | + | 0.00725097i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.14404e10 | − | 7.79095e9i | −0.826540 | − | 0.562878i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.46399e9 | + | 1.29280e10i | −0.514818 | + | 0.891690i | 0.485035 | + | 0.874495i | \(0.338807\pi\) |
−0.999852 | + | 0.0171952i | \(0.994526\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.96683e10i | − | 1.32576i | −0.748724 | − | 0.662882i | \(-0.769333\pi\) | ||
0.748724 | − | 0.662882i | \(-0.230667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.25411e10 | − | 7.24064e9i | −0.807679 | − | 0.466313i | 0.0384705 | − | 0.999260i | \(-0.487751\pi\) |
−0.846149 | + | 0.532946i | \(0.821085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.18715e10 | + | 1.84010e10i | −2.00673 | + | 1.15859i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.20020e9 | − | 1.07391e10i | −0.373274 | − | 0.646530i | 0.616793 | − | 0.787126i | \(-0.288432\pi\) |
−0.990067 | + | 0.140595i | \(0.955098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.47964e9 | + | 1.46872e10i | −0.499285 | + | 0.864788i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.31438e10 | 0.740540 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.27624e10 | + | 1.31419e10i | 1.25474 | + | 0.724423i | 0.972047 | − | 0.234788i | \(-0.0754395\pi\) |
0.282691 | + | 0.959211i | \(0.408773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.82933e9 | − | 5.71436e8i | −0.149344 | − | 0.0301628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.39767e9 | − | 4.15288e9i | −0.123866 | − | 0.214543i | 0.797423 | − | 0.603421i | \(-0.206196\pi\) |
−0.921289 | + | 0.388878i | \(0.872863\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.29661e10i | − | 1.13690i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.55248e10 | −1.23710 | −0.618551 | − | 0.785744i | \(-0.712280\pi\) | ||||
−0.618551 | + | 0.785744i | \(0.712280\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.05386e10 | + | 6.08448e9i | −0.489767 | + | 0.282767i | −0.724478 | − | 0.689298i | \(-0.757919\pi\) |
0.234711 | + | 0.972065i | \(0.424586\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.15886e8 | − | 1.39813e8i | 0.0189291 | − | 0.00636361i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.13562e10 | + | 1.96696e10i | −0.495948 | + | 0.859008i | −0.999989 | − | 0.00467229i | \(-0.998513\pi\) |
0.504041 | + | 0.863680i | \(0.331846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.42787e10i | 0.610916i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.95247e10 | − | 2.28196e10i | −1.62360 | − | 0.937388i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.08354e8 | − | 2.93498e8i | 0.0204646 | − | 0.0118153i | −0.489733 | − | 0.871873i | \(-0.662906\pi\) |
0.510197 | + | 0.860057i | \(0.329572\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.10243e9 | − | 8.83767e9i | −0.197333 | − | 0.341791i | 0.750330 | − | 0.661064i | \(-0.229895\pi\) |
−0.947663 | + | 0.319273i | \(0.896561\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.06821e10 | + | 1.85020e10i | −0.404983 | + | 0.701452i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.24762e8 | 0.0191243 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.17938e10 | − | 2.41297e10i | −1.49355 | − | 0.862299i | −0.493573 | − | 0.869704i | \(-0.664309\pi\) |
−0.999973 | + | 0.00740547i | \(0.997643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.70837e9 | − | 2.33124e10i | 0.161834 | − | 0.801284i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.29201e10 | + | 2.23783e10i | 0.435585 | + | 0.754456i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.77178e10i | 0.899296i | 0.893206 | + | 0.449648i | \(0.148451\pi\) | ||||
−0.893206 | + | 0.449648i | \(0.851549\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.48421e10 | 0.472461 | 0.236231 | − | 0.971697i | \(-0.424088\pi\) | ||||
0.236231 | + | 0.971697i | \(0.424088\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.20572e10 | − | 2.42817e10i | 1.28909 | − | 0.744258i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.77394e10 | + | 2.44713e10i | 0.834421 | + | 0.736116i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.21503e10 | + | 5.56860e10i | −0.931700 | + | 1.61375i | −0.151285 | + | 0.988490i | \(0.548341\pi\) |
−0.780415 | + | 0.625262i | \(0.784992\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.96724e10i | − | 1.12859i | −0.825573 | − | 0.564296i | \(-0.809148\pi\) | ||
0.825573 | − | 0.564296i | \(-0.190852\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.21279e8 | + | 4.74165e8i | 0.0225198 | + | 0.0130018i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.43439e10 | − | 1.98284e10i | 0.924679 | − | 0.533864i | 0.0395542 | − | 0.999217i | \(-0.487406\pi\) |
0.885125 | + | 0.465354i | \(0.154073\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.44772e10 | + | 2.50752e10i | 0.375897 | + | 0.651072i | 0.990461 | − | 0.137795i | \(-0.0440015\pi\) |
−0.614564 | + | 0.788867i | \(0.710668\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.99340e10 | − | 5.18473e10i | 0.763353 | − | 1.32217i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.19948e10 | 1.52535 | 0.762675 | − | 0.646782i | \(-0.223885\pi\) | ||||
0.762675 | + | 0.646782i | \(0.223885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.11360e7 | − | 6.42940e6i | −0.000269169 | − | 0.000155405i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.16251e10 | − | 3.58485e10i | 0.737882 | − | 0.836422i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.46381e9 | − | 4.26744e9i | −0.0564861 | − | 0.0978368i | 0.836400 | − | 0.548120i | \(-0.184656\pi\) |
−0.892886 | + | 0.450283i | \(0.851323\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.17242e10i | 0.702404i | 0.936300 | + | 0.351202i | \(0.114227\pi\) | ||||
−0.936300 | + | 0.351202i | \(0.885773\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.40978e9 | 0.0959606 | 0.0479803 | − | 0.998848i | \(-0.484722\pi\) | ||||
0.0479803 | + | 0.998848i | \(0.484722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.65266e10 | − | 2.10887e10i | 0.767966 | − | 0.443386i | −0.0641824 | − | 0.997938i | \(-0.520444\pi\) |
0.832149 | + | 0.554553i | \(0.187111\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.34215e9 | + | 8.76978e8i | 0.0897456 | + | 0.0181258i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.66952e7 | − | 9.81990e7i | 0.00113267 | − | 0.00196183i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3.22538e9i | − | 0.0633587i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.82676e10 | − | 2.78673e10i | −0.916882 | − | 0.529362i | −0.0342429 | − | 0.999414i | \(-0.510902\pi\) |
−0.882639 | + | 0.470052i | \(0.844235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.95149e10 | − | 2.85875e10i | 0.925030 | − | 0.534066i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.52987e10 | + | 9.57802e10i | 0.999420 | + | 1.73105i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.30429e10 | + | 2.25910e10i | −0.231877 | + | 0.401623i | −0.958361 | − | 0.285561i | \(-0.907820\pi\) |
0.726483 | + | 0.687184i | \(0.241153\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.26082e10 | 0.561049 | 0.280525 | − | 0.959847i | \(-0.409492\pi\) | ||||
0.280525 | + | 0.959847i | \(0.409492\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.57645e10 | + | 4.37427e10i | 1.28256 | + | 0.740487i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.75407e10 | − | 8.19223e10i | −0.451387 | − | 1.34269i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.19192e10 | + | 3.79653e10i | 0.353528 | + | 0.612328i | 0.986865 | − | 0.161548i | \(-0.0516487\pi\) |
−0.633337 | + | 0.773876i | \(0.718315\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00135e10i | 0.937513i | 0.883327 | + | 0.468756i | \(0.155298\pi\) | ||||
−0.883327 | + | 0.468756i | \(0.844702\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.68720e11 | 2.59418 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.52781e10 | + | 3.76883e10i | −0.972514 | + | 0.561481i | −0.900002 | − | 0.435886i | \(-0.856435\pi\) |
−0.0725126 | + | 0.997367i | \(0.523102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.11087e9 | + | 3.02565e10i | −0.0896230 | + | 0.443747i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.96856e9 | + | 6.87375e9i | −0.0564162 | + | 0.0977158i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.92329e7i | − | 0.000549146i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.51950e10 | − | 4.91874e10i | −1.15628 | − | 0.667579i | −0.205871 | − | 0.978579i | \(-0.566003\pi\) |
−0.950410 | + | 0.311000i | \(0.899336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.50672e10 | + | 5.48871e10i | −1.27064 | + | 0.733607i | −0.975109 | − | 0.221725i | \(-0.928831\pi\) |
−0.295535 | + | 0.955332i | \(0.595498\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.06917e10 | − | 7.04800e10i | −0.527549 | − | 0.913742i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.06321e10 | − | 3.57358e10i | 0.263463 | − | 0.456332i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.40102e9 | −0.0173594 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.26740e10 | + | 2.46378e10i | 0.520893 | + | 0.300737i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.28489e8 | + | 1.02236e9i | 0.00152233 | + | 0.0121129i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.52106e10 | − | 6.09865e10i | −0.411040 | − | 0.711942i | 0.583964 | − | 0.811780i | \(-0.301501\pi\) |
−0.995004 | + | 0.0998378i | \(0.968168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.69808e11i | − | 1.92474i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.51267e11 | 1.68965 | 0.844823 | − | 0.535046i | \(-0.179706\pi\) | ||||
0.844823 | + | 0.535046i | \(0.179706\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.03196e9 | − | 2.90521e9i | 0.0545923 | − | 0.0315189i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.09060e10 | − | 8.03752e10i | 0.758198 | − | 0.859451i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.44814e10 | + | 1.29006e11i | −0.773797 | + | 1.34026i | 0.161671 | + | 0.986845i | \(0.448312\pi\) |
−0.935468 | + | 0.353411i | \(0.885022\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.23543e10i | − | 0.126524i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.90339e10 | − | 3.98568e10i | −0.687115 | − | 0.396706i | 0.115416 | − | 0.993317i | \(-0.463180\pi\) |
−0.802530 | + | 0.596612i | \(0.796513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.75011e10 | − | 5.62923e10i | 0.956788 | − | 0.552402i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.97355e9 | + | 1.55427e10i | 0.0856082 | + | 0.148278i | 0.905650 | − | 0.424026i | \(-0.139383\pi\) |
−0.820042 | + | 0.572303i | \(0.806050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.55428e9 | − | 1.30844e10i | 0.0710639 | − | 0.123086i | −0.828304 | − | 0.560279i | \(-0.810694\pi\) |
0.899368 | + | 0.437193i | \(0.144027\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.26000e11 | 1.15266 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.29450e10 | + | 2.47943e10i | 0.387444 | + | 0.223691i | 0.681052 | − | 0.732235i | \(-0.261523\pi\) |
−0.293608 | + | 0.955926i | \(0.594856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.75209e10 | + | 1.93374e10i | −0.504802 | + | 0.169705i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.07440e8 | + | 1.86091e8i | 0.000930017 | + | 0.00161084i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.84088e9i | − | 0.0744634i | −0.999307 | − | 0.0372317i | \(-0.988146\pi\) | ||
0.999307 | − | 0.0372317i | \(-0.0118540\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.40514e9 | −0.0449103 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.92824e10 | + | 5.73207e10i | −0.802885 | + | 0.463546i | −0.844479 | − | 0.535589i | \(-0.820090\pi\) |
0.0415939 | + | 0.999135i | \(0.486756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.80281e10 | + | 1.72610e11i | 0.462989 | + | 1.37720i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.15055e10 | − | 7.18897e10i | 0.322403 | − | 0.558418i | −0.658581 | − | 0.752510i | \(-0.728843\pi\) |
0.980983 | + | 0.194092i | \(0.0621761\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.02491e10i | − | 0.461799i | −0.972978 | − | 0.230899i | \(-0.925833\pi\) | ||
0.972978 | − | 0.230899i | \(-0.0741668\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.89766e11 | + | 1.09562e11i | 1.41644 | + | 0.817780i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.83559e10 | + | 1.63713e10i | −0.208876 | + | 0.120595i | −0.600789 | − | 0.799408i | \(-0.705147\pi\) |
0.391913 | + | 0.920002i | \(0.371813\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.13729e9 | − | 3.70190e9i | −0.0153355 | − | 0.0265619i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.89776e10 | − | 1.54114e11i | 0.630143 | − | 1.09144i | −0.357379 | − | 0.933959i | \(-0.616330\pi\) |
0.987522 | − | 0.157480i | \(-0.0503370\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.06150e11 | −0.732452 | −0.366226 | − | 0.930526i | \(-0.619350\pi\) | ||||
−0.366226 | + | 0.930526i | \(0.619350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.07518e11 | − | 1.19811e11i | −1.41349 | − | 0.816080i | −0.417777 | − | 0.908550i | \(-0.637191\pi\) |
−0.995716 | + | 0.0924692i | \(0.970524\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.05434e11 | + | 9.30123e10i | 0.699885 | + | 0.617430i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.01192e10 | − | 1.75269e10i | −0.0663169 | − | 0.114864i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.17798e11i | 1.39140i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.78175e10 | 0.238548 | 0.119274 | − | 0.992861i | \(-0.461943\pi\) | ||||
0.119274 | + | 0.992861i | \(0.461943\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.68901e11 | − | 2.12985e11i | 2.26890 | − | 1.30995i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.78188e10 | + | 8.94669e10i | 0.411901 | + | 0.543381i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.03428e11 | − | 1.79142e11i | 0.612638 | − | 1.06112i | −0.378155 | − | 0.925742i | \(-0.623442\pi\) |
0.990794 | − | 0.135379i | \(-0.0432252\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.87609e10i | − | 0.460752i | −0.973102 | − | 0.230376i | \(-0.926004\pi\) | ||
0.973102 | − | 0.230376i | \(-0.0739955\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.92434e11 | + | 1.11102e11i | 1.09816 | + | 0.634022i | 0.935737 | − | 0.352700i | \(-0.114736\pi\) |
0.162421 | + | 0.986721i | \(0.448070\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.53330e9 | + | 8.85254e8i | −0.00864270 | + | 0.00498987i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.38559e10 | + | 5.86402e10i | 0.186201 | + | 0.322510i | 0.943981 | − | 0.330001i | \(-0.107049\pi\) |
−0.757780 | + | 0.652511i | \(0.773716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.56879e11 | + | 4.44927e11i | −1.39561 | + | 2.41726i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.67964e11 | −1.42080 | −0.710402 | − | 0.703796i | \(-0.751487\pi\) | ||||
−0.710402 | + | 0.703796i | \(0.751487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.26106e10 | − | 4.19218e10i | −0.380360 | − | 0.219601i | 0.297615 | − | 0.954686i | \(-0.403809\pi\) |
−0.677975 | + | 0.735085i | \(0.737142\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.18551e10 | + | 2.39436e9i | 0.0606205 | + | 0.0122434i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.13493e11 | + | 1.96575e11i | 0.573409 | + | 0.993173i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.75374e9i | − | 0.0135842i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.88652e10 | −0.433183 | −0.216592 | − | 0.976262i | \(-0.569494\pi\) | ||||
−0.216592 | + | 0.976262i | \(0.569494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.38108e11 | + | 1.37471e11i | −1.13349 | + | 0.654422i | −0.944811 | − | 0.327616i | \(-0.893755\pi\) |
−0.188681 | + | 0.982038i | \(0.560421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.46192e11 | + | 8.27652e10i | −1.15823 | + | 0.389375i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.99131e10 | + | 8.64521e10i | −0.229368 | + | 0.397276i | −0.957621 | − | 0.288032i | \(-0.906999\pi\) |
0.728253 | + | 0.685308i | \(0.240332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 5.38048e11i | − | 2.44376i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.02754e10 | + | 1.17060e10i | 0.0899688 | + | 0.0519435i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.80607e11 | + | 2.19744e11i | −1.66942 | + | 0.963838i | −0.701463 | + | 0.712706i | \(0.747469\pi\) |
−0.967953 | + | 0.251132i | \(0.919197\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.42951e11 | − | 4.20804e11i | −1.04131 | − | 1.80360i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.66847e9 | − | 4.62192e9i | 0.0113066 | − | 0.0195836i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.37767e11 | −0.570524 | −0.285262 | − | 0.958450i | \(-0.592081\pi\) | ||||
−0.285262 | + | 0.958450i | \(0.592081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.25273e10 | + | 7.23261e9i | 0.0512902 | + | 0.0296124i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.84421e10 | + | 3.88388e11i | −0.313958 | + | 1.55449i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.01965e10 | − | 1.38904e11i | −0.317373 | − | 0.549707i | 0.662566 | − | 0.749004i | \(-0.269468\pi\) |
−0.979939 | + | 0.199297i | \(0.936134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.11153e11i | − | 0.817033i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.55875e9 | −0.0136167 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.30536e11 | + | 7.53649e10i | −0.488443 | + | 0.282003i | −0.723928 | − | 0.689875i | \(-0.757665\pi\) |
0.235485 | + | 0.971878i | \(0.424332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.39781e10 | − | 1.23313e10i | −0.0517256 | − | 0.0456317i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.86001e11 | − | 6.68574e11i | 1.39713 | − | 2.41990i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.37942e11i | 0.851793i | 0.904772 | + | 0.425896i | \(0.140041\pi\) | ||||
−0.904772 | + | 0.425896i | \(0.859959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.07567e10 | + | 2.35309e10i | 0.142735 | + | 0.0824078i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.06304e11 | + | 2.34580e11i | −1.40746 | + | 0.812597i | −0.995143 | − | 0.0984440i | \(-0.968613\pi\) |
−0.412316 | + | 0.911041i | \(0.635280\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.64887e8 | − | 2.85592e8i | −0.000558877 | − | 0.000968003i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.62346e10 | + | 6.27601e10i | −0.121491 | + | 0.210429i | −0.920356 | − | 0.391082i | \(-0.872101\pi\) |
0.798865 | + | 0.601511i | \(0.205434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.93093e11 | −1.61798 | −0.808990 | − | 0.587822i | \(-0.799985\pi\) | ||||
−0.808990 | + | 0.587822i | \(0.799985\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.34716e11 | − | 1.93248e11i | −1.08655 | − | 0.627322i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.65557e10 | + | 8.67794e10i | −0.243249 | + | 0.275733i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.51634e11 | − | 4.35842e11i | −0.791059 | − | 1.37015i | −0.925312 | − | 0.379207i | \(-0.876197\pi\) |
0.134253 | − | 0.990947i | \(-0.457137\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.93852e11i | − | 0.596598i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.55961e10 | 0.291110 | 0.145555 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145555 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.96935e11 | + | 2.29171e11i | −1.18354 | + | 0.683314i | −0.956830 | − | 0.290649i | \(-0.906129\pi\) |
−0.226705 | + | 0.973963i | \(0.572795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.90892e11 | + | 7.89479e10i | 1.15334 | + | 0.232939i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.64520e10 | + | 1.67060e11i | −0.278695 | + | 0.482715i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.23757e11i | − | 1.78365i | −0.452379 | − | 0.891826i | \(-0.649425\pi\) | ||
0.452379 | − | 0.891826i | \(-0.350575\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.37168e11 | + | 1.36929e11i | 0.664259 | + | 0.383510i | 0.793898 | − | 0.608051i | \(-0.208049\pi\) |
−0.129639 | + | 0.991561i | \(0.541382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.21941e11 | + | 3.59078e11i | −1.72402 | + | 0.995364i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.77228e8 | − | 3.06969e8i | −0.000481264 | − | 0.000833574i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.21701e9 | + | 5.57202e9i | −0.00864666 | + | 0.0149764i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.38720e11 | 1.41868 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.25601e11 | − | 1.87986e11i | −0.848764 | − | 0.490034i | 0.0114696 | − | 0.999934i | \(-0.496349\pi\) |
−0.860234 | + | 0.509900i | \(0.829682\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.42522e10 | + | 2.50616e11i | 0.215216 | + | 0.640181i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50016e11 | − | 2.59835e11i | −0.379353 | − | 0.657059i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.47010e11i | − | 0.364345i | −0.983267 | − | 0.182172i | \(-0.941687\pi\) | ||
0.983267 | − | 0.182172i | \(-0.0583129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.62833e10 | 0.0399535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.99004e9 | − | 1.14895e9i | 0.00478629 | − | 0.00276336i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.35365e10 | + | 4.63124e11i | −0.222740 | + | 1.10284i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.59804e11 | − | 6.23198e11i | 0.839985 | − | 1.45490i | −0.0499213 | − | 0.998753i | \(-0.515897\pi\) |
0.889906 | − | 0.456143i | \(-0.150770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.46899e11i | 1.03306i | 0.856269 | + | 0.516531i | \(0.172777\pi\) | ||||
−0.856269 | + | 0.516531i | \(0.827223\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.79341e11 | + | 3.92218e11i | 1.53978 | + | 0.888990i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.70689e9 | − | 1.56282e9i | 0.00607550 | − | 0.00350769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.82753e11 | + | 4.89743e11i | 0.622350 | + | 1.07794i | 0.989047 | + | 0.147602i | \(0.0471554\pi\) |
−0.366696 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.08180e11 | + | 7.06988e11i | −0.889718 | + | 1.54104i | −0.0495086 | + | 0.998774i | \(0.515766\pi\) |
−0.840209 | + | 0.542263i | \(0.817568\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.58275e11 | −0.338369 | −0.169185 | − | 0.985584i | \(-0.554113\pi\) | ||||
−0.169185 | + | 0.985584i | \(0.554113\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.94240e11 | − | 1.69880e11i | −0.622994 | − | 0.359686i | 0.155040 | − | 0.987908i | \(-0.450449\pi\) |
−0.778034 | + | 0.628223i | \(0.783783\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.24321e11 | + | 5.33281e10i | −0.881281 | + | 0.110758i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.59640e11 | + | 2.76504e11i | 0.328394 | + | 0.568796i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.17796e11i | 0.439543i | 0.975551 | + | 0.219772i | \(0.0705312\pi\) | ||||
−0.975551 | + | 0.219772i | \(0.929469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.90489e11 | 1.78010 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.86459e11 | − | 2.23122e11i | 0.758013 | − | 0.437639i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.40434e11 | + | 3.85897e11i | −0.661453 | + | 0.749788i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.82544e11 | + | 4.89381e11i | −0.538726 | + | 0.933101i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.85581e11i | − | 0.728315i | −0.931337 | − | 0.364158i | \(-0.881357\pi\) | ||
0.931337 | − | 0.364158i | \(-0.118643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.52464e11 | + | 2.61230e11i | 0.838804 | + | 0.484284i | 0.856857 | − | 0.515553i | \(-0.172414\pi\) |
−0.0180535 | + | 0.999837i | \(0.505747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.75889e10 | − | 1.01550e10i | 0.0323047 | − | 0.0186512i | −0.483761 | − | 0.875200i | \(-0.660729\pi\) |
0.516065 | + | 0.856549i | \(0.327396\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.35353e11 | − | 5.80848e11i | −0.604587 | − | 1.04718i | −0.992117 | − | 0.125319i | \(-0.960005\pi\) |
0.387529 | − | 0.921857i | \(-0.373329\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.65295e10 | − | 8.05915e10i | 0.0831121 | − | 0.143954i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.97899e9 | −0.0139917 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.11164e10 | − | 1.79651e10i | −0.0540651 | − | 0.0312145i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.14279e11 | − | 2.06509e11i | 1.04793 | − | 0.352295i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.78980e11 | − | 4.83207e11i | −0.471601 | − | 0.816837i | 0.527871 | − | 0.849324i | \(-0.322990\pi\) |
−0.999472 | + | 0.0324877i | \(0.989657\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.26303e11i | 0.209658i | 0.994490 | + | 0.104829i | \(0.0334295\pi\) | ||||
−0.994490 | + | 0.104829i | \(0.966571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.53162e11 | 0.580939 | 0.290470 | − | 0.956884i | \(-0.406188\pi\) | ||||
0.290470 | + | 0.956884i | \(0.406188\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.53648e11 | − | 2.04179e11i | 0.571317 | − | 0.329850i | −0.186358 | − | 0.982482i | \(-0.559668\pi\) |
0.757675 | + | 0.652632i | \(0.226335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.18773e11 | + | 9.48220e11i | 0.510358 | + | 1.51811i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.40733e8 | − | 9.36578e8i | 0.000850310 | − | 0.00147278i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.89595e12i | − | 2.95484i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.12041e12 | − | 6.46867e11i | −1.71529 | − | 0.990321i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.72355e10 | + | 4.45920e10i | −0.117197 | + | 0.0676640i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.08173e11 | + | 3.60566e11i | 0.310335 | + | 0.537515i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.15150e11 | − | 5.45855e11i | 0.465680 | − | 0.806581i | −0.533552 | − | 0.845767i | \(-0.679143\pi\) |
0.999232 | + | 0.0391859i | \(0.0124765\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.47406e11 | −1.37551 | −0.687753 | − | 0.725945i | \(-0.741403\pi\) | ||||
−0.687753 | + | 0.725945i | \(0.741403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.91234e9 | + | 2.25879e9i | 0.00563058 | + | 0.00325082i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.04778e11 | − | 7.98184e11i | −1.27957 | − | 1.12882i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.99492e11 | + | 6.91941e11i | 0.560075 | + | 0.970079i | 0.997489 | + | 0.0708185i | \(0.0225611\pi\) |
−0.437414 | + | 0.899260i | \(0.644106\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.01012e11i | 0.965871i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.92193e12 | 2.62525 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.54944e11 | + | 4.35867e11i | −1.01357 | + | 0.585182i | −0.912234 | − | 0.409670i | \(-0.865644\pi\) |
−0.101332 | + | 0.994853i | \(0.532310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.10235e10 | + | 2.61769e10i | −0.0146730 | + | 0.0348433i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.77822e9 | − | 1.17402e10i | 0.00886889 | − | 0.0153614i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.93757e11i | − | 0.381092i | −0.981678 | − | 0.190546i | \(-0.938974\pi\) | ||
0.981678 | − | 0.190546i | \(-0.0610258\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.62309e11 | − | 5.55589e11i | −1.22731 | − | 0.708590i | −0.260847 | − | 0.965380i | \(-0.584002\pi\) |
−0.966467 | + | 0.256790i | \(0.917335\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.19918e10 | − | 6.92348e9i | 0.0151649 | − | 0.00875543i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.58116e11 | − | 4.47070e11i | −0.320933 | − | 0.555873i | 0.659748 | − | 0.751487i | \(-0.270663\pi\) |
−0.980681 | + | 0.195614i | \(0.937330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.25183e11 | − | 2.16823e11i | 0.154340 | − | 0.267325i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.18648e11 | 0.750018 | 0.375009 | − | 0.927021i | \(-0.377640\pi\) | ||||
0.375009 | + | 0.927021i | \(0.377640\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.05968e11 | − | 6.11807e10i | −0.127398 | − | 0.0735531i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.23857e12 | + | 2.50152e11i | 1.46435 | + | 0.295753i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.75303e11 | + | 3.03633e11i | 0.205539 | + | 0.356004i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 9.91357e11i | − | 1.14320i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.14154e12 | 1.30552 | 0.652760 | − | 0.757565i | \(-0.273611\pi\) | ||||
0.652760 | + | 0.757565i | \(0.273611\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.03500e12 | − | 5.97555e11i | 1.16429 | − | 0.672204i | 0.211963 | − | 0.977278i | \(-0.432014\pi\) |
0.952329 | + | 0.305074i | \(0.0986811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.08163e12 | − | 3.63623e11i | 1.20678 | − | 0.405696i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.55277e11 | + | 1.48138e12i | −0.938703 | + | 1.62588i | −0.170810 | + | 0.985304i | \(0.554638\pi\) |
−0.767893 | + | 0.640578i | \(0.778695\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.04666e10i | − | 0.0113940i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.38729e11 | − | 5.41975e11i | −1.00537 | − | 0.580451i | −0.0955378 | − | 0.995426i | \(-0.530457\pi\) |
−0.909833 | + | 0.414975i | \(0.863790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.04654e12 | + | 6.04222e11i | −1.11176 | + | 0.641877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.10521e10 | + | 1.05745e11i | 0.0638139 | + | 0.110529i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.24842e11 | + | 2.16233e11i | −0.129439 | + | 0.224196i | −0.923460 | − | 0.383696i | \(-0.874651\pi\) |
0.794020 | + | 0.607891i | \(0.207984\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.08636e12 | 2.12862 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.78246e11 | + | 4.49320e11i | 0.787655 | + | 0.454753i | 0.839136 | − | 0.543921i | \(-0.183061\pi\) |
−0.0514813 | + | 0.998674i | \(0.516394\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.z.e.73.10 | yes | 20 | |
3.2 | odd | 2 | inner | 252.9.z.e.73.1 | ✓ | 20 | |
7.5 | odd | 6 | inner | 252.9.z.e.145.10 | yes | 20 | |
21.5 | even | 6 | inner | 252.9.z.e.145.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.z.e.73.1 | ✓ | 20 | 3.2 | odd | 2 | inner | |
252.9.z.e.73.10 | yes | 20 | 1.1 | even | 1 | trivial | |
252.9.z.e.145.1 | yes | 20 | 21.5 | even | 6 | inner | |
252.9.z.e.145.10 | yes | 20 | 7.5 | odd | 6 | inner |