Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [54,10,Mod(1,54)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(54, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("54.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 54.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: | \(27.8119351528\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 54.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 435.000 | 0.311261 | 0.155630 | − | 0.987815i | \(-0.450259\pi\) | ||||
0.155630 | + | 0.987815i | \(0.450259\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2527.00 | −0.397799 | −0.198900 | − | 0.980020i | \(-0.563737\pi\) | ||||
−0.198900 | + | 0.980020i | \(0.563737\pi\) | |||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6960.00 | −0.220095 | ||||||||
\(11\) | 9123.00 | 0.187876 | 0.0939378 | − | 0.995578i | \(-0.470055\pi\) | ||||
0.0939378 | + | 0.995578i | \(0.470055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −79180.0 | −0.768901 | −0.384450 | − | 0.923146i | \(-0.625609\pi\) | ||||
−0.384450 | + | 0.923146i | \(0.625609\pi\) | |||||||
\(14\) | 40432.0 | 0.281287 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 437976. | 1.27183 | 0.635917 | − | 0.771758i | \(-0.280622\pi\) | ||||
0.635917 | + | 0.771758i | \(0.280622\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 116966. | 0.205906 | 0.102953 | − | 0.994686i | \(-0.467171\pi\) | ||||
0.102953 | + | 0.994686i | \(0.467171\pi\) | |||||||
\(20\) | 111360. | 0.155630 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −145968. | −0.132848 | ||||||||
\(23\) | 261102. | 0.194552 | 0.0972758 | − | 0.995257i | \(-0.468987\pi\) | ||||
0.0972758 | + | 0.995257i | \(0.468987\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76390e6 | −0.903117 | ||||||||
\(26\) | 1.26688e6 | 0.543695 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −646912. | −0.198900 | ||||||||
\(29\) | 396150. | 0.104008 | 0.0520042 | − | 0.998647i | \(-0.483439\pi\) | ||||
0.0520042 | + | 0.998647i | \(0.483439\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.88253e6 | −1.14403 | −0.572014 | − | 0.820244i | \(-0.693838\pi\) | ||||
−0.572014 | + | 0.820244i | \(0.693838\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.00762e6 | −0.899322 | ||||||||
\(35\) | −1.09924e6 | −0.123819 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.98625e6 | −0.788262 | −0.394131 | − | 0.919054i | \(-0.628954\pi\) | ||||
−0.394131 | + | 0.919054i | \(0.628954\pi\) | |||||||
\(38\) | −1.87146e6 | −0.145597 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.78176e6 | −0.110047 | ||||||||
\(41\) | −1.74496e7 | −0.964400 | −0.482200 | − | 0.876061i | \(-0.660162\pi\) | ||||
−0.482200 | + | 0.876061i | \(0.660162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.20946e7 | −1.43161 | −0.715805 | − | 0.698301i | \(-0.753940\pi\) | ||||
−0.715805 | + | 0.698301i | \(0.753940\pi\) | |||||||
\(44\) | 2.33549e6 | 0.0939378 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.17763e6 | −0.137569 | ||||||||
\(47\) | −2.09658e7 | −0.626716 | −0.313358 | − | 0.949635i | \(-0.601454\pi\) | ||||
−0.313358 | + | 0.949635i | \(0.601454\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.39679e7 | −0.841756 | ||||||||
\(50\) | 2.82224e7 | 0.638600 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.02701e7 | −0.384450 | ||||||||
\(53\) | −4.06690e7 | −0.707983 | −0.353991 | − | 0.935249i | \(-0.615176\pi\) | ||||
−0.353991 | + | 0.935249i | \(0.615176\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.96850e6 | 0.0584783 | ||||||||
\(56\) | 1.03506e7 | 0.140643 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.33840e6 | −0.0735451 | ||||||||
\(59\) | 8.43831e7 | 0.906612 | 0.453306 | − | 0.891355i | \(-0.350245\pi\) | ||||
0.453306 | + | 0.891355i | \(0.350245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.48038e8 | −1.36896 | −0.684479 | − | 0.729032i | \(-0.739970\pi\) | ||||
−0.684479 | + | 0.729032i | \(0.739970\pi\) | |||||||
\(62\) | 9.41205e7 | 0.808950 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −3.44433e7 | −0.239329 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.54939e8 | 0.939343 | 0.469672 | − | 0.882841i | \(-0.344372\pi\) | ||||
0.469672 | + | 0.882841i | \(0.344372\pi\) | |||||||
\(68\) | 1.12122e8 | 0.635917 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.75879e7 | 0.0875535 | ||||||||
\(71\) | −1.68344e8 | −0.786202 | −0.393101 | − | 0.919495i | \(-0.628598\pi\) | ||||
−0.393101 | + | 0.919495i | \(0.628598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.18698e8 | 1.72563 | 0.862816 | − | 0.505519i | \(-0.168699\pi\) | ||||
0.862816 | + | 0.505519i | \(0.168699\pi\) | |||||||
\(74\) | 1.43780e8 | 0.557385 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.99433e7 | 0.102953 | ||||||||
\(77\) | −2.30538e7 | −0.0747368 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.10598e8 | 0.608320 | 0.304160 | − | 0.952621i | \(-0.401624\pi\) | ||||
0.304160 | + | 0.952621i | \(0.401624\pi\) | |||||||
\(80\) | 2.85082e7 | 0.0778152 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.79193e8 | 0.681934 | ||||||||
\(83\) | −7.76395e8 | −1.79569 | −0.897844 | − | 0.440313i | \(-0.854867\pi\) | ||||
−0.897844 | + | 0.440313i | \(0.854867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.90520e8 | 0.395872 | ||||||||
\(86\) | 5.13514e8 | 1.01230 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.73678e7 | −0.0664241 | ||||||||
\(89\) | −3.70838e8 | −0.626511 | −0.313256 | − | 0.949669i | \(-0.601420\pi\) | ||||
−0.313256 | + | 0.949669i | \(0.601420\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00088e8 | 0.305868 | ||||||||
\(92\) | 6.68421e7 | 0.0972758 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.35453e8 | 0.443155 | ||||||||
\(95\) | 5.08802e7 | 0.0640904 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.09842e8 | 0.355359 | 0.177680 | − | 0.984088i | \(-0.443141\pi\) | ||||
0.177680 | + | 0.984088i | \(0.443141\pi\) | |||||||
\(98\) | 5.43486e8 | 0.595211 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.51558e8 | −0.451558 | ||||||||
\(101\) | −1.75966e9 | −1.68260 | −0.841301 | − | 0.540566i | \(-0.818210\pi\) | ||||
−0.841301 | + | 0.540566i | \(0.818210\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.33403e7 | −0.0116788 | −0.00583939 | − | 0.999983i | \(-0.501859\pi\) | ||||
−0.00583939 | + | 0.999983i | \(0.501859\pi\) | |||||||
\(104\) | 3.24321e8 | 0.271848 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.50705e8 | 0.500619 | ||||||||
\(107\) | 1.02477e8 | 0.0755787 | 0.0377894 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377894 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.48714e8 | −0.440184 | −0.220092 | − | 0.975479i | \(-0.570636\pi\) | ||||
−0.220092 | + | 0.975479i | \(0.570636\pi\) | |||||||
\(110\) | −6.34961e7 | −0.0413504 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.65609e8 | −0.0994498 | ||||||||
\(113\) | 3.07251e9 | 1.77272 | 0.886360 | − | 0.462996i | \(-0.153225\pi\) | ||||
0.886360 | + | 0.462996i | \(0.153225\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.13579e8 | 0.0605563 | ||||||||
\(116\) | 1.01414e8 | 0.0520042 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.35013e9 | −0.641071 | ||||||||
\(119\) | −1.10677e9 | −0.505934 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.27472e9 | −0.964703 | ||||||||
\(122\) | 2.36861e9 | 0.968000 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.50593e9 | −0.572014 | ||||||||
\(125\) | −1.61691e9 | −0.592365 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.34109e9 | −1.13965 | −0.569825 | − | 0.821766i | \(-0.692989\pi\) | ||||
−0.569825 | + | 0.821766i | \(0.692989\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.51093e8 | 0.169231 | ||||||||
\(131\) | 4.85065e9 | 1.43906 | 0.719530 | − | 0.694462i | \(-0.244357\pi\) | ||||
0.719530 | + | 0.694462i | \(0.244357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.95573e8 | −0.0819092 | ||||||||
\(134\) | −2.47903e9 | −0.664216 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.79395e9 | −0.449661 | ||||||||
\(137\) | −3.90021e9 | −0.945900 | −0.472950 | − | 0.881089i | \(-0.656811\pi\) | ||||
−0.472950 | + | 0.881089i | \(0.656811\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.34365e9 | −1.21415 | −0.607074 | − | 0.794646i | \(-0.707657\pi\) | ||||
−0.607074 | + | 0.794646i | \(0.707657\pi\) | |||||||
\(140\) | −2.81407e8 | −0.0619096 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.69350e9 | 0.555929 | ||||||||
\(143\) | −7.22359e8 | −0.144458 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.72325e8 | 0.0323737 | ||||||||
\(146\) | −6.69917e9 | −1.22021 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.30048e9 | −0.394131 | ||||||||
\(149\) | 5.94028e9 | 0.987344 | 0.493672 | − | 0.869648i | \(-0.335654\pi\) | ||||
0.493672 | + | 0.869648i | \(0.335654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.24779e9 | 0.195320 | 0.0976598 | − | 0.995220i | \(-0.468864\pi\) | ||||
0.0976598 | + | 0.995220i | \(0.468864\pi\) | |||||||
\(152\) | −4.79093e8 | −0.0727987 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.68861e8 | 0.0528469 | ||||||||
\(155\) | −2.55890e9 | −0.356091 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.12444e9 | 0.673129 | 0.336564 | − | 0.941660i | \(-0.390735\pi\) | ||||
0.336564 | + | 0.941660i | \(0.390735\pi\) | |||||||
\(158\) | −3.36957e9 | −0.430148 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.56131e8 | −0.0550236 | ||||||||
\(161\) | −6.59805e8 | −0.0773925 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.17910e10 | 1.30830 | 0.654151 | − | 0.756364i | \(-0.273026\pi\) | ||||
0.654151 | + | 0.756364i | \(0.273026\pi\) | |||||||
\(164\) | −4.46709e9 | −0.482200 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.24223e10 | 1.26974 | ||||||||
\(167\) | 1.04075e10 | 1.03544 | 0.517718 | − | 0.855551i | \(-0.326782\pi\) | ||||
0.517718 | + | 0.855551i | \(0.326782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.33503e9 | −0.408791 | ||||||||
\(170\) | −3.04831e9 | −0.279924 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.21623e9 | −0.715805 | ||||||||
\(173\) | 3.50370e9 | 0.297385 | 0.148693 | − | 0.988883i | \(-0.452494\pi\) | ||||
0.148693 | + | 0.988883i | \(0.452494\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.45738e9 | 0.359259 | ||||||||
\(176\) | 5.97885e8 | 0.0469689 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.93340e9 | 0.443010 | ||||||||
\(179\) | 1.89515e10 | 1.37976 | 0.689882 | − | 0.723922i | \(-0.257662\pi\) | ||||
0.689882 | + | 0.723922i | \(0.257662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.02932e10 | 1.40539 | 0.702695 | − | 0.711492i | \(-0.251980\pi\) | ||||
0.702695 | + | 0.711492i | \(0.251980\pi\) | |||||||
\(182\) | −3.20141e9 | −0.216282 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.06947e9 | −0.0687844 | ||||||||
\(185\) | −3.90902e9 | −0.245355 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.99566e9 | 0.238947 | ||||||||
\(188\) | −5.36724e9 | −0.313358 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.14083e8 | −0.0453187 | ||||||||
\(191\) | 1.19165e10 | 0.647887 | 0.323943 | − | 0.946076i | \(-0.394991\pi\) | ||||
0.323943 | + | 0.946076i | \(0.394991\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.02968e9 | −0.260935 | −0.130467 | − | 0.991453i | \(-0.541648\pi\) | ||||
−0.130467 | + | 0.991453i | \(0.541648\pi\) | |||||||
\(194\) | −4.95747e9 | −0.251277 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.69578e9 | −0.420878 | ||||||||
\(197\) | 5.95780e8 | 0.0281831 | 0.0140915 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140915 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.94694e10 | 0.880065 | 0.440032 | − | 0.897982i | \(-0.354967\pi\) | ||||
0.440032 | + | 0.897982i | \(0.354967\pi\) | |||||||
\(200\) | 7.22493e9 | 0.319300 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.81545e10 | 1.18978 | ||||||||
\(203\) | −1.00107e9 | −0.0413745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.59056e9 | −0.300180 | ||||||||
\(206\) | 2.13445e8 | 0.00825815 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.18914e9 | −0.192225 | ||||||||
\(209\) | 1.06708e9 | 0.0386847 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.09449e10 | −0.727457 | −0.363728 | − | 0.931505i | \(-0.618496\pi\) | ||||
−0.363728 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(212\) | −1.04113e10 | −0.353991 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.63963e9 | −0.0534422 | ||||||||
\(215\) | −1.39612e10 | −0.445604 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.48652e10 | 0.455094 | ||||||||
\(218\) | 1.03794e10 | 0.311257 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.01594e9 | 0.0292392 | ||||||||
\(221\) | −3.46789e10 | −0.977914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.74240e10 | −1.01339 | −0.506697 | − | 0.862124i | \(-0.669134\pi\) | ||||
−0.506697 | + | 0.862124i | \(0.669134\pi\) | |||||||
\(224\) | 2.64975e9 | 0.0703217 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.91602e10 | −1.25350 | ||||||||
\(227\) | 1.53871e10 | 0.384628 | 0.192314 | − | 0.981333i | \(-0.438401\pi\) | ||||
0.192314 | + | 0.981333i | \(0.438401\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.13954e10 | −1.71558 | −0.857789 | − | 0.514001i | \(-0.828163\pi\) | ||||
−0.857789 | + | 0.514001i | \(0.828163\pi\) | |||||||
\(230\) | −1.81727e9 | −0.0428198 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.62263e9 | −0.0367725 | ||||||||
\(233\) | −4.39177e10 | −0.976199 | −0.488099 | − | 0.872788i | \(-0.662310\pi\) | ||||
−0.488099 | + | 0.872788i | \(0.662310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.12012e9 | −0.195072 | ||||||||
\(236\) | 2.16021e10 | 0.453306 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.77082e10 | 0.357750 | ||||||||
\(239\) | −7.69544e10 | −1.52561 | −0.762804 | − | 0.646630i | \(-0.776178\pi\) | ||||
−0.762804 | + | 0.646630i | \(0.776178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.27096e10 | −0.433643 | −0.216822 | − | 0.976211i | \(-0.569569\pi\) | ||||
−0.216822 | + | 0.976211i | \(0.569569\pi\) | |||||||
\(242\) | 3.63955e10 | 0.682148 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.78978e10 | −0.684479 | ||||||||
\(245\) | −1.47760e10 | −0.262005 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.26137e9 | −0.158321 | ||||||||
\(248\) | 2.40949e10 | 0.404475 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.58705e10 | 0.418866 | ||||||||
\(251\) | 8.27276e10 | 1.31558 | 0.657792 | − | 0.753199i | \(-0.271490\pi\) | ||||
0.657792 | + | 0.753199i | \(0.271490\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.38203e9 | 0.0365515 | ||||||||
\(254\) | 5.34574e10 | 0.805854 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | −8.79790e10 | −1.25800 | −0.628999 | − | 0.777406i | \(-0.716535\pi\) | ||||
−0.628999 | + | 0.777406i | \(0.716535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.27082e10 | 0.313570 | ||||||||
\(260\) | −8.81748e9 | −0.119664 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.76103e10 | −1.01757 | ||||||||
\(263\) | 1.50737e11 | 1.94276 | 0.971381 | − | 0.237526i | \(-0.0763364\pi\) | ||||
0.971381 | + | 0.237526i | \(0.0763364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.76910e10 | −0.220367 | ||||||||
\(266\) | 4.72917e9 | 0.0579185 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.96644e10 | 0.469672 | ||||||||
\(269\) | −6.86181e10 | −0.799012 | −0.399506 | − | 0.916731i | \(-0.630818\pi\) | ||||
−0.399506 | + | 0.916731i | \(0.630818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.35686e10 | 0.265444 | 0.132722 | − | 0.991153i | \(-0.457628\pi\) | ||||
0.132722 | + | 0.991153i | \(0.457628\pi\) | |||||||
\(272\) | 2.87032e10 | 0.317958 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.24033e10 | 0.668852 | ||||||||
\(275\) | −1.60921e10 | −0.169674 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.22855e11 | 1.25381 | 0.626907 | − | 0.779094i | \(-0.284321\pi\) | ||||
0.626907 | + | 0.779094i | \(0.284321\pi\) | |||||||
\(278\) | 8.54984e10 | 0.858532 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.50251e9 | 0.0437767 | ||||||||
\(281\) | −3.49164e10 | −0.334080 | −0.167040 | − | 0.985950i | \(-0.553421\pi\) | ||||
−0.167040 | + | 0.985950i | \(0.553421\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.61645e10 | −0.705852 | −0.352926 | − | 0.935651i | \(-0.614813\pi\) | ||||
−0.352926 | + | 0.935651i | \(0.614813\pi\) | |||||||
\(284\) | −4.30960e10 | −0.393101 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.15577e10 | 0.102147 | ||||||||
\(287\) | 4.40951e10 | 0.383638 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.32351e10 | 0.617560 | ||||||||
\(290\) | −2.75720e9 | −0.0228917 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.07187e11 | 0.862816 | ||||||||
\(293\) | −1.77323e11 | −1.40560 | −0.702799 | − | 0.711388i | \(-0.748067\pi\) | ||||
−0.702799 | + | 0.711388i | \(0.748067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.67066e10 | 0.282193 | ||||||||
\(296\) | 3.68077e10 | 0.278693 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.50444e10 | −0.698158 | ||||||||
\(299\) | −2.06741e10 | −0.149591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.11032e10 | 0.569493 | ||||||||
\(302\) | −1.99647e10 | −0.138112 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.66548e9 | 0.0514764 | ||||||||
\(305\) | −6.43967e10 | −0.426103 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.91554e11 | 1.23075 | 0.615374 | − | 0.788235i | \(-0.289005\pi\) | ||||
0.615374 | + | 0.788235i | \(0.289005\pi\) | |||||||
\(308\) | −5.90178e9 | −0.0373684 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.09424e10 | 0.251794 | ||||||||
\(311\) | 1.52905e11 | 0.926827 | 0.463414 | − | 0.886142i | \(-0.346624\pi\) | ||||
0.463414 | + | 0.886142i | \(0.346624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.23800e10 | −0.0729076 | −0.0364538 | − | 0.999335i | \(-0.511606\pi\) | ||||
−0.0364538 | + | 0.999335i | \(0.511606\pi\) | |||||||
\(314\) | −8.19911e10 | −0.475974 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.39131e10 | 0.304160 | ||||||||
\(317\) | −6.02948e10 | −0.335361 | −0.167681 | − | 0.985841i | \(-0.553628\pi\) | ||||
−0.167681 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.61408e9 | 0.0195407 | ||||||||
\(320\) | 7.29809e9 | 0.0389076 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.05569e10 | 0.0547248 | ||||||||
\(323\) | 5.12283e10 | 0.261878 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.39666e11 | 0.694407 | ||||||||
\(326\) | −1.88657e11 | −0.925109 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.14734e10 | 0.340967 | ||||||||
\(329\) | 5.29805e10 | 0.249307 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.45035e10 | −0.341154 | −0.170577 | − | 0.985344i | \(-0.554563\pi\) | ||||
−0.170577 | + | 0.985344i | \(0.554563\pi\) | |||||||
\(332\) | −1.98757e11 | −0.897844 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.66520e11 | −0.732164 | ||||||||
\(335\) | 6.73985e10 | 0.292381 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.92661e11 | −0.813690 | −0.406845 | − | 0.913497i | \(-0.633371\pi\) | ||||
−0.406845 | + | 0.913497i | \(0.633371\pi\) | |||||||
\(338\) | 6.93604e10 | 0.289059 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.87730e10 | 0.197936 | ||||||||
\(341\) | −5.36663e10 | −0.214935 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.87810e11 | 0.732649 | ||||||||
\(344\) | 1.31460e11 | 0.506150 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.60592e10 | −0.210283 | ||||||||
\(347\) | 5.28835e11 | 1.95811 | 0.979056 | − | 0.203591i | \(-0.0652612\pi\) | ||||
0.979056 | + | 0.203591i | \(0.0652612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.94816e11 | −0.702927 | −0.351464 | − | 0.936202i | \(-0.614316\pi\) | ||||
−0.351464 | + | 0.936202i | \(0.614316\pi\) | |||||||
\(350\) | −7.13180e10 | −0.254035 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.56616e9 | −0.0332120 | ||||||||
\(353\) | −8.43923e10 | −0.289279 | −0.144639 | − | 0.989484i | \(-0.546202\pi\) | ||||
−0.144639 | + | 0.989484i | \(0.546202\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.32294e10 | −0.244714 | ||||||||
\(356\) | −9.49345e10 | −0.313256 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.03224e11 | −0.975641 | ||||||||
\(359\) | 2.49683e11 | 0.793347 | 0.396674 | − | 0.917960i | \(-0.370164\pi\) | ||||
0.396674 | + | 0.917960i | \(0.370164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.09007e11 | −0.957603 | ||||||||
\(362\) | −3.24691e11 | −0.993760 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.12225e10 | 0.152934 | ||||||||
\(365\) | 1.82134e11 | 0.537121 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.53325e11 | −1.59215 | −0.796073 | − | 0.605201i | \(-0.793093\pi\) | ||||
−0.796073 | + | 0.605201i | \(0.793093\pi\) | |||||||
\(368\) | 1.71116e10 | 0.0486379 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.25443e10 | 0.173492 | ||||||||
\(371\) | 1.02771e11 | 0.281635 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.30552e11 | −0.349216 | −0.174608 | − | 0.984638i | \(-0.555866\pi\) | ||||
−0.174608 | + | 0.984638i | \(0.555866\pi\) | |||||||
\(374\) | −6.39305e10 | −0.168961 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.58758e10 | 0.221578 | ||||||||
\(377\) | −3.13672e10 | −0.0799722 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.21465e11 | −0.800307 | −0.400154 | − | 0.916448i | \(-0.631043\pi\) | ||||
−0.400154 | + | 0.916448i | \(0.631043\pi\) | |||||||
\(380\) | 1.30253e10 | 0.0320452 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.90664e11 | −0.458125 | ||||||||
\(383\) | 6.80223e11 | 1.61531 | 0.807656 | − | 0.589654i | \(-0.200736\pi\) | ||||
0.807656 | + | 0.589654i | \(0.200736\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00284e10 | −0.0232626 | ||||||||
\(386\) | 8.04748e10 | 0.184509 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.93195e10 | 0.177680 | ||||||||
\(389\) | −7.94587e11 | −1.75941 | −0.879707 | − | 0.475515i | \(-0.842262\pi\) | ||||
−0.879707 | + | 0.475515i | \(0.842262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.14356e11 | 0.247437 | ||||||||
\(392\) | 1.39132e11 | 0.297606 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.53249e9 | −0.0199284 | ||||||||
\(395\) | 9.16101e10 | 0.189346 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.97913e11 | 0.399868 | 0.199934 | − | 0.979809i | \(-0.435927\pi\) | ||||
0.199934 | + | 0.979809i | \(0.435927\pi\) | |||||||
\(398\) | −3.11511e11 | −0.622300 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.15599e11 | −0.225779 | ||||||||
\(401\) | −9.56475e10 | −0.184724 | −0.0923622 | − | 0.995725i | \(-0.529442\pi\) | ||||
−0.0923622 | + | 0.995725i | \(0.529442\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.65779e11 | 0.879644 | ||||||||
\(404\) | −4.50472e11 | −0.841301 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.60171e10 | 0.0292562 | ||||||||
\(407\) | −8.19815e10 | −0.148095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.82203e11 | 0.498663 | 0.249332 | − | 0.968418i | \(-0.419789\pi\) | ||||
0.249332 | + | 0.968418i | \(0.419789\pi\) | |||||||
\(410\) | 1.21449e11 | 0.212259 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.41511e9 | −0.00583939 | ||||||||
\(413\) | −2.13236e11 | −0.360650 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.37732e11 | −0.558927 | ||||||||
\(416\) | 8.30262e10 | 0.135924 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.70733e10 | −0.0273542 | ||||||||
\(419\) | −1.52503e11 | −0.241722 | −0.120861 | − | 0.992669i | \(-0.538565\pi\) | ||||
−0.120861 | + | 0.992669i | \(0.538565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.07657e11 | −0.167022 | −0.0835111 | − | 0.996507i | \(-0.526613\pi\) | ||||
−0.0835111 | + | 0.996507i | \(0.526613\pi\) | |||||||
\(422\) | 3.35118e11 | 0.514390 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.66580e11 | 0.250310 | ||||||||
\(425\) | −7.72546e11 | −1.14861 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.74093e11 | 0.544571 | ||||||||
\(428\) | 2.62341e10 | 0.0377894 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.23379e11 | 0.315089 | ||||||||
\(431\) | 7.77462e10 | 0.108525 | 0.0542627 | − | 0.998527i | \(-0.482719\pi\) | ||||
0.0542627 | + | 0.998527i | \(0.482719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.20952e11 | 0.165356 | 0.0826778 | − | 0.996576i | \(-0.473653\pi\) | ||||
0.0826778 | + | 0.996576i | \(0.473653\pi\) | |||||||
\(434\) | −2.37843e11 | −0.321800 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.66071e11 | −0.220092 | ||||||||
\(437\) | 3.05401e10 | 0.0400593 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.03193e12 | 1.32605 | 0.663026 | − | 0.748597i | \(-0.269272\pi\) | ||||
0.663026 | + | 0.748597i | \(0.269272\pi\) | |||||||
\(440\) | −1.62550e10 | −0.0206752 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.54863e11 | 0.691489 | ||||||||
\(443\) | 6.20515e11 | 0.765483 | 0.382742 | − | 0.923855i | \(-0.374980\pi\) | ||||
0.382742 | + | 0.923855i | \(0.374980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.61314e11 | −0.195008 | ||||||||
\(446\) | 5.98784e11 | 0.716578 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.23960e10 | −0.0497249 | ||||||||
\(449\) | −7.51040e11 | −0.872076 | −0.436038 | − | 0.899928i | \(-0.643619\pi\) | ||||
−0.436038 | + | 0.899928i | \(0.643619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.59192e11 | −0.181187 | ||||||||
\(452\) | 7.86563e11 | 0.886360 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.46194e11 | −0.271973 | ||||||||
\(455\) | 8.70382e10 | 0.0952048 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.33370e12 | 1.43033 | 0.715165 | − | 0.698955i | \(-0.246351\pi\) | ||||
0.715165 | + | 0.698955i | \(0.246351\pi\) | |||||||
\(458\) | 1.14233e12 | 1.21310 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.90763e10 | 0.0302781 | ||||||||
\(461\) | 5.27899e11 | 0.544373 | 0.272187 | − | 0.962244i | \(-0.412253\pi\) | ||||
0.272187 | + | 0.962244i | \(0.412253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.08746e12 | 1.09976 | 0.549879 | − | 0.835244i | \(-0.314674\pi\) | ||||
0.549879 | + | 0.835244i | \(0.314674\pi\) | |||||||
\(464\) | 2.59621e10 | 0.0260021 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.02684e11 | 0.690277 | ||||||||
\(467\) | −8.01186e11 | −0.779484 | −0.389742 | − | 0.920924i | \(-0.627436\pi\) | ||||
−0.389742 | + | 0.920924i | \(0.627436\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.91531e11 | −0.373670 | ||||||||
\(470\) | 1.45922e11 | 0.137937 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.45633e11 | −0.320536 | ||||||||
\(473\) | −2.92799e11 | −0.268965 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.06316e11 | −0.185957 | ||||||||
\(476\) | −2.83332e11 | −0.252967 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.23127e12 | 1.07877 | ||||||||
\(479\) | −3.89798e11 | −0.338322 | −0.169161 | − | 0.985588i | \(-0.554106\pi\) | ||||
−0.169161 | + | 0.985588i | \(0.554106\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.11531e11 | 0.606095 | ||||||||
\(482\) | 3.63353e11 | 0.306632 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.82328e11 | −0.482351 | ||||||||
\(485\) | 1.34781e11 | 0.110609 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.90992e12 | −1.53863 | −0.769317 | − | 0.638868i | \(-0.779403\pi\) | ||||
−0.769317 | + | 0.638868i | \(0.779403\pi\) | |||||||
\(488\) | 6.06365e11 | 0.484000 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.36416e11 | 0.185266 | ||||||||
\(491\) | −3.88418e11 | −0.301601 | −0.150800 | − | 0.988564i | \(-0.548185\pi\) | ||||
−0.150800 | + | 0.988564i | \(0.548185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.73504e11 | 0.132281 | ||||||||
\(494\) | 1.48182e11 | 0.111950 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.85518e11 | −0.286007 | ||||||||
\(497\) | 4.25404e11 | 0.312750 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.18044e10 | −0.0374037 | −0.0187018 | − | 0.999825i | \(-0.505953\pi\) | ||||
−0.0187018 | + | 0.999825i | \(0.505953\pi\) | |||||||
\(500\) | −4.13928e11 | −0.296183 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.32364e12 | −0.930259 | ||||||||
\(503\) | 9.91895e11 | 0.690891 | 0.345446 | − | 0.938439i | \(-0.387728\pi\) | ||||
0.345446 | + | 0.938439i | \(0.387728\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.65450e11 | −0.523728 | ||||||||
\(506\) | −3.81125e10 | −0.0258458 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.55319e11 | −0.569825 | ||||||||
\(509\) | −2.74642e12 | −1.81358 | −0.906792 | − | 0.421579i | \(-0.861476\pi\) | ||||
−0.906792 | + | 0.421579i | \(0.861476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.05805e12 | −0.686455 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.40766e12 | 0.889539 | ||||||||
\(515\) | −5.80302e9 | −0.00363515 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.91271e11 | −0.117745 | ||||||||
\(518\) | −3.63332e11 | −0.221728 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.41080e11 | 0.0846154 | ||||||||
\(521\) | 5.16949e11 | 0.307382 | 0.153691 | − | 0.988119i | \(-0.450884\pi\) | ||||
0.153691 | + | 0.988119i | \(0.450884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.12202e11 | −0.182464 | −0.0912322 | − | 0.995830i | \(-0.529081\pi\) | ||||
−0.0912322 | + | 0.995830i | \(0.529081\pi\) | |||||||
\(524\) | 1.24177e12 | 0.719530 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.41180e12 | −1.37374 | ||||||||
\(527\) | −2.57641e12 | −1.45501 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.73298e12 | −0.962150 | ||||||||
\(530\) | 2.83057e11 | 0.155823 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.56667e10 | −0.0409546 | ||||||||
\(533\) | 1.38166e12 | 0.741528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.45775e10 | 0.0235247 | ||||||||
\(536\) | −6.34631e11 | −0.332108 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.09789e12 | 0.564987 | ||||||||
\(539\) | −3.09889e11 | −0.158145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.35533e12 | −0.680234 | −0.340117 | − | 0.940383i | \(-0.610467\pi\) | ||||
−0.340117 | + | 0.940383i | \(0.610467\pi\) | |||||||
\(542\) | −3.77098e11 | −0.187697 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.59251e11 | −0.224830 | ||||||||
\(545\) | −2.82191e11 | −0.137012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.76918e12 | −1.32254 | −0.661269 | − | 0.750149i | \(-0.729982\pi\) | ||||
−0.661269 | + | 0.750149i | \(0.729982\pi\) | |||||||
\(548\) | −9.98453e11 | −0.472950 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.57473e11 | 0.119977 | ||||||||
\(551\) | 4.63361e10 | 0.0214159 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.32181e11 | −0.241989 | ||||||||
\(554\) | −1.96568e12 | −0.886580 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.36797e12 | −0.607074 | ||||||||
\(557\) | 8.90709e11 | 0.392091 | 0.196046 | − | 0.980595i | \(-0.437190\pi\) | ||||
0.196046 | + | 0.980595i | \(0.437190\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.54125e12 | 1.10077 | ||||||||
\(560\) | −7.20401e10 | −0.0309548 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.58662e11 | 0.236230 | ||||||||
\(563\) | 2.27487e10 | 0.00954264 | 0.00477132 | − | 0.999989i | \(-0.498481\pi\) | ||||
0.00477132 | + | 0.999989i | \(0.498481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.33654e12 | 0.551778 | ||||||||
\(566\) | 1.21863e12 | 0.499113 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.89535e11 | 0.277964 | ||||||||
\(569\) | 4.33772e12 | 1.73483 | 0.867415 | − | 0.497586i | \(-0.165780\pi\) | ||||
0.867415 | + | 0.497586i | \(0.165780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.48077e12 | 0.976617 | 0.488308 | − | 0.872671i | \(-0.337614\pi\) | ||||
0.488308 | + | 0.872671i | \(0.337614\pi\) | |||||||
\(572\) | −1.84924e11 | −0.0722289 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.05521e11 | −0.271273 | ||||||||
\(575\) | −4.60558e11 | −0.175703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.50387e12 | −0.564831 | −0.282415 | − | 0.959292i | \(-0.591136\pi\) | ||||
−0.282415 | + | 0.959292i | \(0.591136\pi\) | |||||||
\(578\) | −1.17176e12 | −0.436681 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.41153e10 | 0.0161869 | ||||||||
\(581\) | 1.96195e12 | 0.714324 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.71024e11 | −0.133013 | ||||||||
\(584\) | −1.71499e12 | −0.610103 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.83717e12 | 0.993908 | ||||||||
\(587\) | 1.80767e12 | 0.628416 | 0.314208 | − | 0.949354i | \(-0.398261\pi\) | ||||
0.314208 | + | 0.949354i | \(0.398261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.88056e11 | −0.235562 | ||||||||
\(590\) | −5.87306e11 | −0.199540 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.88923e11 | −0.197065 | ||||||||
\(593\) | 4.13005e12 | 1.37154 | 0.685771 | − | 0.727818i | \(-0.259465\pi\) | ||||
0.685771 | + | 0.727818i | \(0.259465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.81443e11 | −0.157477 | ||||||||
\(596\) | 1.52071e12 | 0.493672 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.30785e11 | 0.105777 | ||||||||
\(599\) | −1.62323e12 | −0.515182 | −0.257591 | − | 0.966254i | \(-0.582929\pi\) | ||||
−0.257591 | + | 0.966254i | \(0.582929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.87930e12 | 0.587573 | 0.293787 | − | 0.955871i | \(-0.405084\pi\) | ||||
0.293787 | + | 0.955871i | \(0.405084\pi\) | |||||||
\(602\) | −1.29765e12 | −0.402693 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.19435e11 | 0.0976598 | ||||||||
\(605\) | −9.89503e11 | −0.300274 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.43492e11 | 0.162497 | 0.0812483 | − | 0.996694i | \(-0.474109\pi\) | ||||
0.0812483 | + | 0.996694i | \(0.474109\pi\) | |||||||
\(608\) | −1.22648e11 | −0.0363993 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.03035e12 | 0.301300 | ||||||||
\(611\) | 1.66007e12 | 0.481882 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.90638e12 | 1.11738 | 0.558692 | − | 0.829375i | \(-0.311303\pi\) | ||||
0.558692 | + | 0.829375i | \(0.311303\pi\) | |||||||
\(614\) | −3.06487e12 | −0.870271 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.44285e10 | 0.0264235 | ||||||||
\(617\) | 4.16450e12 | 1.15686 | 0.578428 | − | 0.815733i | \(-0.303666\pi\) | ||||
0.578428 | + | 0.815733i | \(0.303666\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.42966e12 | 0.665177 | 0.332589 | − | 0.943072i | \(-0.392078\pi\) | ||||
0.332589 | + | 0.943072i | \(0.392078\pi\) | |||||||
\(620\) | −6.55079e11 | −0.178045 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.44647e12 | −0.655366 | ||||||||
\(623\) | 9.37107e11 | 0.249226 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.74176e12 | 0.718737 | ||||||||
\(626\) | 1.98081e11 | 0.0515534 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.31186e12 | 0.336564 | ||||||||
\(629\) | −3.93576e12 | −1.00254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.52098e12 | −0.381936 | −0.190968 | − | 0.981596i | \(-0.561163\pi\) | ||||
−0.190968 | + | 0.981596i | \(0.561163\pi\) | |||||||
\(632\) | −8.62610e11 | −0.215074 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.64717e11 | 0.237136 | ||||||||
\(635\) | −1.45337e12 | −0.354728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.68958e12 | 0.647227 | ||||||||
\(638\) | −5.78252e10 | −0.0138173 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.16769e11 | −0.0275118 | ||||||||
\(641\) | −6.09689e11 | −0.142642 | −0.0713210 | − | 0.997453i | \(-0.522721\pi\) | ||||
−0.0713210 | + | 0.997453i | \(0.522721\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.95241e12 | 1.14253 | 0.571265 | − | 0.820766i | \(-0.306453\pi\) | ||||
0.571265 | + | 0.820766i | \(0.306453\pi\) | |||||||
\(644\) | −1.68910e11 | −0.0386963 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.19653e11 | −0.185176 | ||||||||
\(647\) | −3.20285e12 | −0.718567 | −0.359284 | − | 0.933228i | \(-0.616979\pi\) | ||||
−0.359284 | + | 0.933228i | \(0.616979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.69827e11 | 0.170330 | ||||||||
\(650\) | −2.23465e12 | −0.491020 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.01851e12 | 0.654151 | ||||||||
\(653\) | 6.19750e12 | 1.33385 | 0.666925 | − | 0.745125i | \(-0.267610\pi\) | ||||
0.666925 | + | 0.745125i | \(0.267610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.11003e12 | 0.447923 | ||||||||
\(656\) | −1.14357e12 | −0.241100 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.47688e11 | −0.176287 | ||||||||
\(659\) | −8.01019e12 | −1.65447 | −0.827235 | − | 0.561857i | \(-0.810087\pi\) | ||||
−0.827235 | + | 0.561857i | \(0.810087\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.94817e12 | −1.82317 | −0.911586 | − | 0.411109i | \(-0.865141\pi\) | ||||
−0.911586 | + | 0.411109i | \(0.865141\pi\) | |||||||
\(662\) | 1.19206e12 | 0.241232 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.18011e12 | 0.634872 | ||||||||
\(665\) | −1.28574e11 | −0.0254951 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.03436e11 | 0.0202350 | ||||||||
\(668\) | 2.66433e12 | 0.517718 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.07838e12 | −0.206744 | ||||||||
\(671\) | −1.35055e12 | −0.257194 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.32555e12 | 1.00068 | 0.500341 | − | 0.865828i | \(-0.333208\pi\) | ||||
0.500341 | + | 0.865828i | \(0.333208\pi\) | |||||||
\(674\) | 3.08257e12 | 0.575366 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.10977e12 | −0.204396 | ||||||||
\(677\) | −1.10212e11 | −0.0201642 | −0.0100821 | − | 0.999949i | \(-0.503209\pi\) | ||||
−0.0100821 | + | 0.999949i | \(0.503209\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.82971e11 | −0.141362 | ||||||||
\(680\) | −7.80368e11 | −0.139962 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.58662e11 | 0.151982 | ||||||||
\(683\) | −3.48463e12 | −0.612722 | −0.306361 | − | 0.951915i | \(-0.599111\pi\) | ||||
−0.306361 | + | 0.951915i | \(0.599111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.69659e12 | −0.294421 | ||||||||
\(686\) | −3.00497e12 | −0.518061 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.10335e12 | −0.357902 | ||||||||
\(689\) | 3.22018e12 | 0.544369 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.10169e13 | −1.83827 | −0.919137 | − | 0.393939i | \(-0.871112\pi\) | ||||
−0.919137 | + | 0.393939i | \(0.871112\pi\) | |||||||
\(692\) | 8.96947e11 | 0.148693 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.46136e12 | −1.38459 | ||||||||
\(695\) | −2.32449e12 | −0.377916 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.64249e12 | −1.22656 | ||||||||
\(698\) | 3.11706e12 | 0.497045 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.14109e12 | 0.179630 | ||||||||
\(701\) | 8.81897e12 | 1.37939 | 0.689695 | − | 0.724100i | \(-0.257745\pi\) | ||||
0.689695 | + | 0.724100i | \(0.257745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.05109e12 | −0.162308 | ||||||||
\(704\) | 1.53059e11 | 0.0234845 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.35028e12 | 0.204551 | ||||||||
\(707\) | 4.44665e12 | 0.669338 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.84914e12 | −0.274829 | −0.137414 | − | 0.990514i | \(-0.543879\pi\) | ||||
−0.137414 | + | 0.990514i | \(0.543879\pi\) | |||||||
\(710\) | 1.17167e12 | 0.173039 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.51895e12 | 0.221505 | ||||||||
\(713\) | −1.53594e12 | −0.222573 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.14226e11 | −0.0449640 | ||||||||
\(716\) | 4.85158e12 | 0.689882 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.99492e12 | −0.560981 | ||||||||
\(719\) | −6.42135e12 | −0.896078 | −0.448039 | − | 0.894014i | \(-0.647878\pi\) | ||||
−0.448039 | + | 0.894014i | \(0.647878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.37109e10 | 0.00464581 | ||||||||
\(722\) | 4.94411e12 | 0.677127 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.19505e12 | 0.702695 | ||||||||
\(725\) | −6.98769e11 | −0.0939318 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.64920e12 | −0.750036 | −0.375018 | − | 0.927018i | \(-0.622363\pi\) | ||||
−0.375018 | + | 0.927018i | \(0.622363\pi\) | |||||||
\(728\) | −8.19560e11 | −0.108141 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.91414e12 | −0.379802 | ||||||||
\(731\) | −1.40567e13 | −1.82077 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.24309e12 | −0.159051 | −0.0795254 | − | 0.996833i | \(-0.525340\pi\) | ||||
−0.0795254 | + | 0.996833i | \(0.525340\pi\) | |||||||
\(734\) | 8.85319e12 | 1.12582 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.73785e11 | −0.0343922 | ||||||||
\(737\) | 1.41351e12 | 0.176480 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.20942e12 | −0.272507 | −0.136253 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136253 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(740\) | −1.00071e12 | −0.122677 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.64433e12 | −0.199146 | ||||||||
\(743\) | −1.66986e11 | −0.0201016 | −0.0100508 | − | 0.999949i | \(-0.503199\pi\) | ||||
−0.0100508 | + | 0.999949i | \(0.503199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.58402e12 | 0.307321 | ||||||||
\(746\) | 2.08884e12 | 0.246933 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.02289e12 | 0.119473 | ||||||||
\(749\) | −2.58959e11 | −0.0300652 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.97060e12 | −0.570202 | −0.285101 | − | 0.958497i | \(-0.592027\pi\) | ||||
−0.285101 | + | 0.958497i | \(0.592027\pi\) | |||||||
\(752\) | −1.37401e12 | −0.156679 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.01875e11 | 0.0565489 | ||||||||
\(755\) | 5.42790e11 | 0.0607953 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.48178e12 | 1.04944 | 0.524721 | − | 0.851274i | \(-0.324170\pi\) | ||||
0.524721 | + | 0.851274i | \(0.324170\pi\) | |||||||
\(758\) | 5.14343e12 | 0.565903 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.08405e11 | −0.0226594 | ||||||||
\(761\) | 9.47065e12 | 1.02364 | 0.511822 | − | 0.859092i | \(-0.328971\pi\) | ||||
0.511822 | + | 0.859092i | \(0.328971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.63930e12 | 0.175105 | ||||||||
\(764\) | 3.05063e12 | 0.323943 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.08836e13 | −1.14220 | ||||||||
\(767\) | −6.68145e12 | −0.697095 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.02727e13 | −1.05930 | −0.529649 | − | 0.848217i | \(-0.677676\pi\) | ||||
−0.529649 | + | 0.848217i | \(0.677676\pi\) | |||||||
\(770\) | 1.60455e11 | 0.0164492 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.28760e12 | −0.130467 | ||||||||
\(773\) | −1.13305e13 | −1.14141 | −0.570704 | − | 0.821156i | \(-0.693330\pi\) | ||||
−0.570704 | + | 0.821156i | \(0.693330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.03762e13 | 1.03319 | ||||||||
\(776\) | −1.26911e12 | −0.125638 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.27134e13 | 1.24409 | ||||||||
\(779\) | −2.04101e12 | −0.198576 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.53580e12 | −0.147708 | ||||||||
\(782\) | −1.82970e12 | −0.174965 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.22612e12 | −0.210439 | ||||||||
\(785\) | 2.22913e12 | 0.209518 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.86916e12 | 0.638289 | 0.319144 | − | 0.947706i | \(-0.396605\pi\) | ||||
0.319144 | + | 0.947706i | \(0.396605\pi\) | |||||||
\(788\) | 1.52520e11 | 0.0140915 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.46576e12 | −0.133888 | ||||||||
\(791\) | −7.76423e12 | −0.705187 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.17217e13 | 1.05259 | ||||||||
\(794\) | −3.16660e12 | −0.282749 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.98418e12 | 0.440032 | ||||||||
\(797\) | −8.35867e12 | −0.733795 | −0.366898 | − | 0.930261i | \(-0.619580\pi\) | ||||
−0.366898 | + | 0.930261i | \(0.619580\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.18251e12 | −0.797078 | ||||||||
\(800\) | 1.84958e12 | 0.159650 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.53036e12 | 0.130620 | ||||||||
\(803\) | 3.81978e12 | 0.324204 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.87015e11 | −0.0240892 | ||||||||
\(806\) | −7.45246e12 | −0.622003 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.20755e12 | 0.594890 | ||||||||
\(809\) | 5.37009e12 | 0.440771 | 0.220386 | − | 0.975413i | \(-0.429268\pi\) | ||||
0.220386 | + | 0.975413i | \(0.429268\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.15396e12 | 0.499529 | 0.249764 | − | 0.968307i | \(-0.419647\pi\) | ||||
0.249764 | + | 0.968307i | \(0.419647\pi\) | |||||||
\(812\) | −2.56274e11 | −0.0206872 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.31170e12 | 0.104719 | ||||||||
\(815\) | 5.12910e12 | 0.407223 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.75398e12 | −0.294777 | ||||||||
\(818\) | −4.51525e12 | −0.352608 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.94318e12 | −0.150090 | ||||||||
\(821\) | −7.73743e12 | −0.594364 | −0.297182 | − | 0.954821i | \(-0.596047\pi\) | ||||
−0.297182 | + | 0.954821i | \(0.596047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.19595e13 | 1.66849 | 0.834244 | − | 0.551395i | \(-0.185904\pi\) | ||||
0.834244 | + | 0.551395i | \(0.185904\pi\) | |||||||
\(824\) | 5.46418e10 | 0.00412907 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.41178e12 | 0.255018 | ||||||||
\(827\) | −1.89761e12 | −0.141069 | −0.0705346 | − | 0.997509i | \(-0.522471\pi\) | ||||
−0.0705346 | + | 0.997509i | \(0.522471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.14625e13 | 0.842912 | 0.421456 | − | 0.906849i | \(-0.361519\pi\) | ||||
0.421456 | + | 0.906849i | \(0.361519\pi\) | |||||||
\(830\) | 5.40371e12 | 0.395221 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.32842e12 | −0.0961126 | ||||||||
\(833\) | −1.48771e13 | −1.07057 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.52727e12 | 0.322290 | ||||||||
\(836\) | 2.73173e11 | 0.0193423 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.44005e12 | 0.170923 | ||||||||
\(839\) | 2.40490e13 | 1.67559 | 0.837794 | − | 0.545986i | \(-0.183845\pi\) | ||||
0.837794 | + | 0.545986i | \(0.183845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.43502e13 | −0.989182 | ||||||||
\(842\) | 1.72252e12 | 0.118103 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.36189e12 | −0.363728 | ||||||||
\(845\) | −1.88574e12 | −0.127241 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.74821e12 | 0.383758 | ||||||||
\(848\) | −2.66529e12 | −0.176996 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.23607e13 | 0.812193 | ||||||||
\(851\) | −2.34633e12 | −0.153358 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.28559e13 | 1.47818 | 0.739089 | − | 0.673608i | \(-0.235256\pi\) | ||||
0.739089 | + | 0.673608i | \(0.235256\pi\) | |||||||
\(854\) | −5.98549e12 | −0.385070 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.19746e11 | −0.0267211 | ||||||||
\(857\) | 2.61764e13 | 1.65766 | 0.828832 | − | 0.559497i | \(-0.189006\pi\) | ||||
0.828832 | + | 0.559497i | \(0.189006\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.56167e12 | −0.223195 | −0.111598 | − | 0.993753i | \(-0.535597\pi\) | ||||
−0.111598 | + | 0.993753i | \(0.535597\pi\) | |||||||
\(860\) | −3.57406e12 | −0.222802 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.24394e12 | −0.0767390 | ||||||||
\(863\) | 2.73564e13 | 1.67884 | 0.839421 | − | 0.543481i | \(-0.182894\pi\) | ||||
0.839421 | + | 0.543481i | \(0.182894\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.52411e12 | 0.0925643 | ||||||||
\(866\) | −1.93524e12 | −0.116924 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.80548e12 | 0.227547 | ||||||||
\(869\) | 1.92129e12 | 0.114289 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.22681e13 | −0.722262 | ||||||||
\(872\) | 2.65713e12 | 0.155629 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.88641e11 | −0.0283262 | ||||||||
\(875\) | 4.08592e12 | 0.235643 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.10519e13 | −0.630867 | −0.315434 | − | 0.948948i | \(-0.602150\pi\) | ||||
−0.315434 | + | 0.948948i | \(0.602150\pi\) | |||||||
\(878\) | −1.65109e13 | −0.937660 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.60080e11 | 0.0146196 | ||||||||
\(881\) | 2.76007e13 | 1.54358 | 0.771789 | − | 0.635879i | \(-0.219362\pi\) | ||||
0.771789 | + | 0.635879i | \(0.219362\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.98889e11 | 0.0165458 | 0.00827288 | − | 0.999966i | \(-0.497367\pi\) | ||||
0.00827288 | + | 0.999966i | \(0.497367\pi\) | |||||||
\(884\) | −8.87781e12 | −0.488957 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.92824e12 | −0.541278 | ||||||||
\(887\) | −3.08545e13 | −1.67364 | −0.836819 | − | 0.547479i | \(-0.815588\pi\) | ||||
−0.836819 | + | 0.547479i | \(0.815588\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.44293e12 | 0.453352 | ||||||||
\(890\) | 2.58103e12 | 0.137892 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.58055e12 | −0.506697 | ||||||||
\(893\) | −2.45228e12 | −0.129044 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.24390e12 | 0.429466 | ||||||||
\(896\) | 6.78336e11 | 0.0351608 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.20166e13 | 0.616651 | ||||||||
\(899\) | −2.33037e12 | −0.118989 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.78121e13 | −0.900436 | ||||||||
\(902\) | 2.54708e12 | 0.128119 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.25850e13 | −0.626752 | ||||||||
\(905\) | 8.82753e12 | 0.437442 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.33746e13 | −1.14686 | −0.573431 | − | 0.819254i | \(-0.694388\pi\) | ||||
−0.573431 | + | 0.819254i | \(0.694388\pi\) | |||||||
\(908\) | 3.93910e12 | 0.192314 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.39261e12 | −0.0673199 | ||||||||
\(911\) | 2.73111e13 | 1.31373 | 0.656865 | − | 0.754009i | \(-0.271882\pi\) | ||||
0.656865 | + | 0.754009i | \(0.271882\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.08305e12 | −0.337366 | ||||||||
\(914\) | −2.13393e13 | −1.01140 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.82772e13 | −0.857789 | ||||||||
\(917\) | −1.22576e13 | −0.572457 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.88513e13 | −1.33427 | −0.667137 | − | 0.744935i | \(-0.732481\pi\) | ||||
−0.667137 | + | 0.744935i | \(0.732481\pi\) | |||||||
\(920\) | −4.65221e11 | −0.0214099 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.44639e12 | −0.384930 | ||||||||
\(923\) | 1.33294e13 | 0.604511 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.58508e13 | 0.711893 | ||||||||
\(926\) | −1.73993e13 | −0.777647 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.15393e11 | −0.0183863 | ||||||||
\(929\) | −4.94460e12 | −0.217801 | −0.108901 | − | 0.994053i | \(-0.534733\pi\) | ||||
−0.108901 | + | 0.994053i | \(0.534733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.97309e12 | −0.173322 | ||||||||
\(932\) | −1.12429e13 | −0.488099 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.28190e13 | 0.551179 | ||||||||
\(935\) | 1.73811e12 | 0.0743747 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.28563e13 | −1.39248 | −0.696242 | − | 0.717807i | \(-0.745146\pi\) | ||||
−0.696242 | + | 0.717807i | \(0.745146\pi\) | |||||||
\(938\) | 6.26450e12 | 0.264225 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.33475e12 | −0.0975360 | ||||||||
\(941\) | −4.60517e13 | −1.91466 | −0.957332 | − | 0.288991i | \(-0.906680\pi\) | ||||
−0.957332 | + | 0.288991i | \(0.906680\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.55612e12 | −0.187626 | ||||||||
\(944\) | 5.53013e12 | 0.226653 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.68479e12 | 0.190187 | ||||||||
\(947\) | 2.89440e13 | 1.16946 | 0.584728 | − | 0.811229i | \(-0.301201\pi\) | ||||
0.584728 | + | 0.811229i | \(0.301201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.31525e13 | −1.32684 | ||||||||
\(950\) | 3.30106e12 | 0.131491 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.53331e12 | 0.178875 | ||||||||
\(953\) | −2.49105e13 | −0.978284 | −0.489142 | − | 0.872204i | \(-0.662690\pi\) | ||||
−0.489142 | + | 0.872204i | \(0.662690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.18369e12 | 0.201662 | ||||||||
\(956\) | −1.97003e13 | −0.762804 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.23677e12 | 0.239230 | ||||||||
\(959\) | 9.85583e12 | 0.376278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.16457e12 | 0.308801 | ||||||||
\(962\) | −1.13845e13 | −0.428574 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.81366e12 | −0.216822 | ||||||||
\(965\) | −2.18791e12 | −0.0812188 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.98414e13 | 1.46526 | 0.732632 | − | 0.680625i | \(-0.238292\pi\) | ||||
0.732632 | + | 0.680625i | \(0.238292\pi\) | |||||||
\(968\) | 9.31725e12 | 0.341074 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.15650e12 | −0.0782126 | ||||||||
\(971\) | 1.76953e13 | 0.638809 | 0.319405 | − | 0.947618i | \(-0.396517\pi\) | ||||
0.319405 | + | 0.947618i | \(0.396517\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.35034e13 | 0.482987 | ||||||||
\(974\) | 3.05587e13 | 1.08798 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.70185e12 | −0.342240 | ||||||||
\(977\) | 3.24515e12 | 0.113949 | 0.0569744 | − | 0.998376i | \(-0.481855\pi\) | ||||
0.0569744 | + | 0.998376i | \(0.481855\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.38315e12 | −0.117706 | ||||||||
\(980\) | −3.78266e12 | −0.131003 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.21469e12 | 0.213264 | ||||||||
\(983\) | −4.17615e13 | −1.42654 | −0.713272 | − | 0.700887i | \(-0.752788\pi\) | ||||
−0.713272 | + | 0.700887i | \(0.752788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.59164e11 | 0.00877228 | ||||||||
\(986\) | −2.77607e12 | −0.0935371 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.37091e12 | −0.0791606 | ||||||||
\(989\) | −8.37998e12 | −0.278522 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.72174e13 | −1.88450 | −0.942251 | − | 0.334907i | \(-0.891295\pi\) | ||||
−0.942251 | + | 0.334907i | \(0.891295\pi\) | |||||||
\(992\) | 6.16828e12 | 0.202238 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.80647e12 | −0.221148 | ||||||||
\(995\) | 8.46921e12 | 0.273930 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.42027e12 | −0.141684 | −0.0708420 | − | 0.997488i | \(-0.522569\pi\) | ||||
−0.0708420 | + | 0.997488i | \(0.522569\pi\) | |||||||
\(998\) | 8.28870e11 | 0.0264484 | ||||||||
\(999\) | 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 | 54.10.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 54.10.a.c.1.1 | yes | 1 | ||
9.2 | odd | 6 | 162.10.c.d.109.1 | 2 | |||
9.4 | even | 3 | 162.10.c.g.55.1 | 2 | |||
9.5 | odd | 6 | 162.10.c.d.55.1 | 2 | |||
9.7 | even | 3 | 162.10.c.g.109.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.10.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
54.10.a.c.1.1 | yes | 1 | 3.2 | odd | 2 | ||
162.10.c.d.55.1 | 2 | 9.5 | odd | 6 | |||
162.10.c.d.109.1 | 2 | 9.2 | odd | 6 | |||
162.10.c.g.55.1 | 2 | 9.4 | even | 3 | |||
162.10.c.g.109.1 | 2 | 9.7 | even | 3 |