Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + \cdots + 245077910606835 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.220633\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.779367 | 0.0344435 | 0.0172217 | − | 0.999852i | \(-0.494518\pi\) | ||||
0.0172217 | + | 0.999852i | \(0.494518\pi\) | |||||||
\(3\) | −32.1989 | −0.229507 | −0.114753 | − | 0.993394i | \(-0.536608\pi\) | ||||
−0.114753 | + | 0.993394i | \(0.536608\pi\) | |||||||
\(4\) | −511.393 | −0.998814 | ||||||||
\(5\) | 894.723 | 0.640212 | 0.320106 | − | 0.947382i | \(-0.396281\pi\) | ||||
0.320106 | + | 0.947382i | \(0.396281\pi\) | |||||||
\(6\) | −25.0947 | −0.00790501 | ||||||||
\(7\) | −2726.00 | −0.429126 | −0.214563 | − | 0.976710i | \(-0.568833\pi\) | ||||
−0.214563 | + | 0.976710i | \(0.568833\pi\) | |||||||
\(8\) | −797.598 | −0.0688461 | ||||||||
\(9\) | −18646.2 | −0.947327 | ||||||||
\(10\) | 697.318 | 0.0220511 | ||||||||
\(11\) | −18622.9 | −0.383513 | −0.191757 | − | 0.981442i | \(-0.561418\pi\) | ||||
−0.191757 | + | 0.981442i | \(0.561418\pi\) | |||||||
\(12\) | 16466.3 | 0.229234 | ||||||||
\(13\) | 50311.3 | 0.488563 | 0.244281 | − | 0.969704i | \(-0.421448\pi\) | ||||
0.244281 | + | 0.969704i | \(0.421448\pi\) | |||||||
\(14\) | −2124.55 | −0.0147806 | ||||||||
\(15\) | −28809.1 | −0.146933 | ||||||||
\(16\) | 261211. | 0.996442 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −14532.3 | −0.0326292 | ||||||||
\(19\) | −106811. | −0.188029 | −0.0940146 | − | 0.995571i | \(-0.529970\pi\) | ||||
−0.0940146 | + | 0.995571i | \(0.529970\pi\) | |||||||
\(20\) | −457555. | −0.639452 | ||||||||
\(21\) | 87774.1 | 0.0984872 | ||||||||
\(22\) | −14514.1 | −0.0132095 | ||||||||
\(23\) | 1.33151e6 | 0.992131 | 0.496066 | − | 0.868285i | \(-0.334778\pi\) | ||||
0.496066 | + | 0.868285i | \(0.334778\pi\) | |||||||
\(24\) | 25681.8 | 0.0158006 | ||||||||
\(25\) | −1.15260e6 | −0.590129 | ||||||||
\(26\) | 39211.0 | 0.0168278 | ||||||||
\(27\) | 1.23416e6 | 0.446924 | ||||||||
\(28\) | 1.39406e6 | 0.428617 | ||||||||
\(29\) | 3.99697e6 | 1.04940 | 0.524699 | − | 0.851288i | \(-0.324178\pi\) | ||||
0.524699 | + | 0.851288i | \(0.324178\pi\) | |||||||
\(30\) | −22452.9 | −0.00506088 | ||||||||
\(31\) | 1.47297e6 | 0.286461 | 0.143231 | − | 0.989689i | \(-0.454251\pi\) | ||||
0.143231 | + | 0.989689i | \(0.454251\pi\) | |||||||
\(32\) | 611950. | 0.103167 | ||||||||
\(33\) | 599637. | 0.0880189 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.43902e6 | −0.274731 | ||||||||
\(36\) | 9.53554e6 | 0.946203 | ||||||||
\(37\) | −7.90858e6 | −0.693730 | −0.346865 | − | 0.937915i | \(-0.612754\pi\) | ||||
−0.346865 | + | 0.937915i | \(0.612754\pi\) | |||||||
\(38\) | −83245.1 | −0.00647638 | ||||||||
\(39\) | −1.61997e6 | −0.112128 | ||||||||
\(40\) | −713630. | −0.0440761 | ||||||||
\(41\) | 2.29532e7 | 1.26857 | 0.634287 | − | 0.773098i | \(-0.281294\pi\) | ||||
0.634287 | + | 0.773098i | \(0.281294\pi\) | |||||||
\(42\) | 68408.3 | 0.00339224 | ||||||||
\(43\) | −1.21116e7 | −0.540249 | −0.270124 | − | 0.962825i | \(-0.587065\pi\) | ||||
−0.270124 | + | 0.962825i | \(0.587065\pi\) | |||||||
\(44\) | 9.52362e6 | 0.383058 | ||||||||
\(45\) | −1.66832e7 | −0.606490 | ||||||||
\(46\) | 1.03773e6 | 0.0341725 | ||||||||
\(47\) | −3.35639e7 | −1.00330 | −0.501651 | − | 0.865070i | \(-0.667274\pi\) | ||||
−0.501651 | + | 0.865070i | \(0.667274\pi\) | |||||||
\(48\) | −8.41072e6 | −0.228690 | ||||||||
\(49\) | −3.29225e7 | −0.815851 | ||||||||
\(50\) | −898295. | −0.0203261 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.57288e7 | −0.487983 | ||||||||
\(53\) | 9.30903e7 | 1.62055 | 0.810276 | − | 0.586049i | \(-0.199317\pi\) | ||||
0.810276 | + | 0.586049i | \(0.199317\pi\) | |||||||
\(54\) | 961862. | 0.0153936 | ||||||||
\(55\) | −1.66624e7 | −0.245530 | ||||||||
\(56\) | 2.17425e6 | 0.0295436 | ||||||||
\(57\) | 3.43920e6 | 0.0431540 | ||||||||
\(58\) | 3.11511e6 | 0.0361449 | ||||||||
\(59\) | 1.95305e7 | 0.209835 | 0.104918 | − | 0.994481i | \(-0.466542\pi\) | ||||
0.104918 | + | 0.994481i | \(0.466542\pi\) | |||||||
\(60\) | 1.47328e7 | 0.146759 | ||||||||
\(61\) | 1.21384e8 | 1.12248 | 0.561239 | − | 0.827654i | \(-0.310325\pi\) | ||||
0.561239 | + | 0.827654i | \(0.310325\pi\) | |||||||
\(62\) | 1.14798e6 | 0.00986673 | ||||||||
\(63\) | 5.08296e7 | 0.406522 | ||||||||
\(64\) | −1.33263e8 | −0.992889 | ||||||||
\(65\) | 4.50147e7 | 0.312784 | ||||||||
\(66\) | 467337. | 0.00303168 | ||||||||
\(67\) | 1.13597e8 | 0.688700 | 0.344350 | − | 0.938841i | \(-0.388099\pi\) | ||||
0.344350 | + | 0.938841i | \(0.388099\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.28731e7 | −0.227701 | ||||||||
\(70\) | −1.90089e6 | −0.00946270 | ||||||||
\(71\) | −1.11076e8 | −0.518749 | −0.259375 | − | 0.965777i | \(-0.583516\pi\) | ||||
−0.259375 | + | 0.965777i | \(0.583516\pi\) | |||||||
\(72\) | 1.48722e7 | 0.0652197 | ||||||||
\(73\) | 2.77779e8 | 1.14485 | 0.572423 | − | 0.819959i | \(-0.306004\pi\) | ||||
0.572423 | + | 0.819959i | \(0.306004\pi\) | |||||||
\(74\) | −6.16369e6 | −0.0238945 | ||||||||
\(75\) | 3.71123e7 | 0.135438 | ||||||||
\(76\) | 5.46224e7 | 0.187806 | ||||||||
\(77\) | 5.07661e7 | 0.164576 | ||||||||
\(78\) | −1.26255e6 | −0.00386209 | ||||||||
\(79\) | −1.52609e8 | −0.440818 | −0.220409 | − | 0.975408i | \(-0.570739\pi\) | ||||
−0.220409 | + | 0.975408i | \(0.570739\pi\) | |||||||
\(80\) | 2.33712e8 | 0.637934 | ||||||||
\(81\) | 3.27275e8 | 0.844755 | ||||||||
\(82\) | 1.78890e7 | 0.0436941 | ||||||||
\(83\) | 4.69638e7 | 0.108620 | 0.0543102 | − | 0.998524i | \(-0.482704\pi\) | ||||
0.0543102 | + | 0.998524i | \(0.482704\pi\) | |||||||
\(84\) | −4.48870e7 | −0.0983704 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.43939e6 | −0.0186080 | ||||||||
\(87\) | −1.28698e8 | −0.240844 | ||||||||
\(88\) | 1.48536e7 | 0.0264034 | ||||||||
\(89\) | 3.22965e8 | 0.545633 | 0.272816 | − | 0.962066i | \(-0.412045\pi\) | ||||
0.272816 | + | 0.962066i | \(0.412045\pi\) | |||||||
\(90\) | −1.30023e7 | −0.0208896 | ||||||||
\(91\) | −1.37149e8 | −0.209655 | ||||||||
\(92\) | −6.80924e8 | −0.990954 | ||||||||
\(93\) | −4.74280e7 | −0.0657448 | ||||||||
\(94\) | −2.61586e7 | −0.0345572 | ||||||||
\(95\) | −9.55664e7 | −0.120379 | ||||||||
\(96\) | −1.97041e7 | −0.0236775 | ||||||||
\(97\) | −9.17256e8 | −1.05201 | −0.526003 | − | 0.850483i | \(-0.676310\pi\) | ||||
−0.526003 | + | 0.850483i | \(0.676310\pi\) | |||||||
\(98\) | −2.56587e7 | −0.0281007 | ||||||||
\(99\) | 3.47247e8 | 0.363313 | ||||||||
\(100\) | 5.89429e8 | 0.589429 | ||||||||
\(101\) | −7.62747e8 | −0.729347 | −0.364673 | − | 0.931135i | \(-0.618819\pi\) | ||||
−0.364673 | + | 0.931135i | \(0.618819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.64466e9 | 1.43982 | 0.719912 | − | 0.694065i | \(-0.244182\pi\) | ||||
0.719912 | + | 0.694065i | \(0.244182\pi\) | |||||||
\(104\) | −4.01282e7 | −0.0336356 | ||||||||
\(105\) | 7.85336e7 | 0.0630527 | ||||||||
\(106\) | 7.25515e7 | 0.0558174 | ||||||||
\(107\) | −1.07132e9 | −0.790117 | −0.395059 | − | 0.918656i | \(-0.629276\pi\) | ||||
−0.395059 | + | 0.918656i | \(0.629276\pi\) | |||||||
\(108\) | −6.31140e8 | −0.446394 | ||||||||
\(109\) | −4.13878e8 | −0.280836 | −0.140418 | − | 0.990092i | \(-0.544845\pi\) | ||||
−0.140418 | + | 0.990092i | \(0.544845\pi\) | |||||||
\(110\) | −1.29861e7 | −0.00845690 | ||||||||
\(111\) | 2.54647e8 | 0.159216 | ||||||||
\(112\) | −7.12062e8 | −0.427599 | ||||||||
\(113\) | 1.98843e8 | 0.114725 | 0.0573625 | − | 0.998353i | \(-0.481731\pi\) | ||||
0.0573625 | + | 0.998353i | \(0.481731\pi\) | |||||||
\(114\) | 2.68040e6 | 0.00148637 | ||||||||
\(115\) | 1.19133e9 | 0.635174 | ||||||||
\(116\) | −2.04402e9 | −1.04815 | ||||||||
\(117\) | −9.38116e8 | −0.462829 | ||||||||
\(118\) | 1.52214e7 | 0.00722745 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.29781e7 | 0.0101158 | ||||||||
\(121\) | −2.01113e9 | −0.852917 | ||||||||
\(122\) | 9.46027e7 | 0.0386620 | ||||||||
\(123\) | −7.39067e8 | −0.291146 | ||||||||
\(124\) | −7.53266e8 | −0.286122 | ||||||||
\(125\) | −2.77876e9 | −1.01802 | ||||||||
\(126\) | 3.96149e7 | 0.0140020 | ||||||||
\(127\) | −3.63691e9 | −1.24056 | −0.620278 | − | 0.784382i | \(-0.712980\pi\) | ||||
−0.620278 | + | 0.784382i | \(0.712980\pi\) | |||||||
\(128\) | −4.17179e8 | −0.137366 | ||||||||
\(129\) | 3.89980e8 | 0.123991 | ||||||||
\(130\) | 3.50830e7 | 0.0107734 | ||||||||
\(131\) | 9.54875e8 | 0.283287 | 0.141643 | − | 0.989918i | \(-0.454761\pi\) | ||||
0.141643 | + | 0.989918i | \(0.454761\pi\) | |||||||
\(132\) | −3.06650e8 | −0.0879145 | ||||||||
\(133\) | 2.91167e8 | 0.0806882 | ||||||||
\(134\) | 8.85337e7 | 0.0237212 | ||||||||
\(135\) | 1.10423e9 | 0.286126 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.40687e9 | 0.341203 | 0.170601 | − | 0.985340i | \(-0.445429\pi\) | ||||
0.170601 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(138\) | −3.34139e7 | −0.00784280 | ||||||||
\(139\) | −4.50608e9 | −1.02384 | −0.511920 | − | 0.859033i | \(-0.671066\pi\) | ||||
−0.511920 | + | 0.859033i | \(0.671066\pi\) | |||||||
\(140\) | 1.24729e9 | 0.274405 | ||||||||
\(141\) | 1.08072e9 | 0.230265 | ||||||||
\(142\) | −8.65690e7 | −0.0178675 | ||||||||
\(143\) | −9.36943e8 | −0.187370 | ||||||||
\(144\) | −4.87061e9 | −0.943956 | ||||||||
\(145\) | 3.57618e9 | 0.671837 | ||||||||
\(146\) | 2.16492e8 | 0.0394325 | ||||||||
\(147\) | 1.06007e9 | 0.187243 | ||||||||
\(148\) | 4.04439e9 | 0.692907 | ||||||||
\(149\) | −6.12301e9 | −1.01772 | −0.508858 | − | 0.860851i | \(-0.669932\pi\) | ||||
−0.508858 | + | 0.860851i | \(0.669932\pi\) | |||||||
\(150\) | 2.89241e7 | 0.00466497 | ||||||||
\(151\) | −7.02540e9 | −1.09970 | −0.549851 | − | 0.835263i | \(-0.685315\pi\) | ||||
−0.549851 | + | 0.835263i | \(0.685315\pi\) | |||||||
\(152\) | 8.51924e7 | 0.0129451 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.95654e7 | 0.00566855 | ||||||||
\(155\) | 1.31790e9 | 0.183396 | ||||||||
\(156\) | 8.28440e8 | 0.111995 | ||||||||
\(157\) | 8.92243e9 | 1.17202 | 0.586010 | − | 0.810304i | \(-0.300698\pi\) | ||||
0.586010 | + | 0.810304i | \(0.300698\pi\) | |||||||
\(158\) | −1.18939e8 | −0.0151833 | ||||||||
\(159\) | −2.99740e9 | −0.371927 | ||||||||
\(160\) | 5.47526e8 | 0.0660488 | ||||||||
\(161\) | −3.62970e9 | −0.425749 | ||||||||
\(162\) | 2.55067e8 | 0.0290963 | ||||||||
\(163\) | 1.41974e10 | 1.57530 | 0.787651 | − | 0.616122i | \(-0.211297\pi\) | ||||
0.787651 | + | 0.616122i | \(0.211297\pi\) | |||||||
\(164\) | −1.17381e10 | −1.26707 | ||||||||
\(165\) | 5.36509e8 | 0.0563507 | ||||||||
\(166\) | 3.66020e7 | 0.00374127 | ||||||||
\(167\) | −1.25753e10 | −1.25110 | −0.625552 | − | 0.780183i | \(-0.715126\pi\) | ||||
−0.625552 | + | 0.780183i | \(0.715126\pi\) | |||||||
\(168\) | −7.00085e7 | −0.00678046 | ||||||||
\(169\) | −8.07327e9 | −0.761306 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.99163e9 | 0.178125 | ||||||||
\(172\) | 6.19379e9 | 0.539608 | ||||||||
\(173\) | −1.25403e10 | −1.06439 | −0.532194 | − | 0.846622i | \(-0.678632\pi\) | ||||
−0.532194 | + | 0.846622i | \(0.678632\pi\) | |||||||
\(174\) | −1.00303e8 | −0.00829550 | ||||||||
\(175\) | 3.14197e9 | 0.253239 | ||||||||
\(176\) | −4.86452e9 | −0.382149 | ||||||||
\(177\) | −6.28859e8 | −0.0481586 | ||||||||
\(178\) | 2.51708e8 | 0.0187935 | ||||||||
\(179\) | 5.72919e9 | 0.417114 | 0.208557 | − | 0.978010i | \(-0.433123\pi\) | ||||
0.208557 | + | 0.978010i | \(0.433123\pi\) | |||||||
\(180\) | 8.53167e9 | 0.605770 | ||||||||
\(181\) | −2.19770e10 | −1.52200 | −0.760999 | − | 0.648753i | \(-0.775291\pi\) | ||||
−0.760999 | + | 0.648753i | \(0.775291\pi\) | |||||||
\(182\) | −1.06889e8 | −0.00722124 | ||||||||
\(183\) | −3.90843e9 | −0.257616 | ||||||||
\(184\) | −1.06201e9 | −0.0683044 | ||||||||
\(185\) | −7.07599e9 | −0.444134 | ||||||||
\(186\) | −3.69638e7 | −0.00226448 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.71643e10 | 1.00211 | ||||||||
\(189\) | −3.36432e9 | −0.191787 | ||||||||
\(190\) | −7.44813e7 | −0.00414626 | ||||||||
\(191\) | 2.60888e10 | 1.41841 | 0.709207 | − | 0.705000i | \(-0.249053\pi\) | ||||
0.709207 | + | 0.705000i | \(0.249053\pi\) | |||||||
\(192\) | 4.29093e9 | 0.227875 | ||||||||
\(193\) | −2.79178e10 | −1.44835 | −0.724174 | − | 0.689617i | \(-0.757779\pi\) | ||||
−0.724174 | + | 0.689617i | \(0.757779\pi\) | |||||||
\(194\) | −7.14879e8 | −0.0362347 | ||||||||
\(195\) | −1.44942e9 | −0.0717859 | ||||||||
\(196\) | 1.68363e10 | 0.814883 | ||||||||
\(197\) | 2.21064e10 | 1.04573 | 0.522866 | − | 0.852415i | \(-0.324863\pi\) | ||||
0.522866 | + | 0.852415i | \(0.324863\pi\) | |||||||
\(198\) | 2.70633e8 | 0.0125137 | ||||||||
\(199\) | 1.50851e10 | 0.681884 | 0.340942 | − | 0.940084i | \(-0.389254\pi\) | ||||
0.340942 | + | 0.940084i | \(0.389254\pi\) | |||||||
\(200\) | 9.19308e8 | 0.0406281 | ||||||||
\(201\) | −3.65769e9 | −0.158061 | ||||||||
\(202\) | −5.94460e8 | −0.0251212 | ||||||||
\(203\) | −1.08957e10 | −0.450324 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.05368e10 | 0.812156 | ||||||||
\(206\) | 1.28180e9 | 0.0495925 | ||||||||
\(207\) | −2.48276e10 | −0.939873 | ||||||||
\(208\) | 1.31419e10 | 0.486825 | ||||||||
\(209\) | 1.98914e9 | 0.0721118 | ||||||||
\(210\) | 6.12065e7 | 0.00217175 | ||||||||
\(211\) | −5.27406e10 | −1.83178 | −0.915891 | − | 0.401428i | \(-0.868514\pi\) | ||||
−0.915891 | + | 0.401428i | \(0.868514\pi\) | |||||||
\(212\) | −4.76057e10 | −1.61863 | ||||||||
\(213\) | 3.57652e9 | 0.119056 | ||||||||
\(214\) | −8.34950e8 | −0.0272144 | ||||||||
\(215\) | −1.08365e10 | −0.345874 | ||||||||
\(216\) | −9.84363e8 | −0.0307690 | ||||||||
\(217\) | −4.01531e9 | −0.122928 | ||||||||
\(218\) | −3.22563e8 | −0.00967297 | ||||||||
\(219\) | −8.94418e9 | −0.262750 | ||||||||
\(220\) | 8.52101e9 | 0.245239 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.98464e8 | 0.00548394 | ||||||||
\(223\) | −4.66541e10 | −1.26333 | −0.631666 | − | 0.775240i | \(-0.717629\pi\) | ||||
−0.631666 | + | 0.775240i | \(0.717629\pi\) | |||||||
\(224\) | −1.66817e9 | −0.0442716 | ||||||||
\(225\) | 2.14916e10 | 0.559045 | ||||||||
\(226\) | 1.54972e8 | 0.00395153 | ||||||||
\(227\) | −7.06458e10 | −1.76592 | −0.882958 | − | 0.469451i | \(-0.844452\pi\) | ||||
−0.882958 | + | 0.469451i | \(0.844452\pi\) | |||||||
\(228\) | −1.75878e9 | −0.0431028 | ||||||||
\(229\) | −6.05407e10 | −1.45475 | −0.727374 | − | 0.686241i | \(-0.759259\pi\) | ||||
−0.727374 | + | 0.686241i | \(0.759259\pi\) | |||||||
\(230\) | 9.28485e8 | 0.0218776 | ||||||||
\(231\) | −1.63461e9 | −0.0377712 | ||||||||
\(232\) | −3.18798e9 | −0.0722469 | ||||||||
\(233\) | 1.65324e10 | 0.367480 | 0.183740 | − | 0.982975i | \(-0.441180\pi\) | ||||
0.183740 | + | 0.982975i | \(0.441180\pi\) | |||||||
\(234\) | −7.31137e8 | −0.0159414 | ||||||||
\(235\) | −3.00304e10 | −0.642326 | ||||||||
\(236\) | −9.98773e9 | −0.209586 | ||||||||
\(237\) | 4.91385e9 | 0.101171 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.94845e10 | 1.77401 | 0.887007 | − | 0.461755i | \(-0.152780\pi\) | ||||
0.887007 | + | 0.461755i | \(0.152780\pi\) | |||||||
\(240\) | −7.52526e9 | −0.146410 | ||||||||
\(241\) | −5.87295e10 | −1.12145 | −0.560725 | − | 0.828002i | \(-0.689477\pi\) | ||||
−0.560725 | + | 0.828002i | \(0.689477\pi\) | |||||||
\(242\) | −1.56741e9 | −0.0293774 | ||||||||
\(243\) | −3.48298e10 | −0.640801 | ||||||||
\(244\) | −6.20749e10 | −1.12115 | ||||||||
\(245\) | −2.94566e10 | −0.522318 | ||||||||
\(246\) | −5.76005e8 | −0.0100281 | ||||||||
\(247\) | −5.37381e9 | −0.0918641 | ||||||||
\(248\) | −1.17484e9 | −0.0197217 | ||||||||
\(249\) | −1.51218e9 | −0.0249291 | ||||||||
\(250\) | −2.16567e9 | −0.0350641 | ||||||||
\(251\) | 2.89840e10 | 0.460920 | 0.230460 | − | 0.973082i | \(-0.425977\pi\) | ||||
0.230460 | + | 0.973082i | \(0.425977\pi\) | |||||||
\(252\) | −2.59939e10 | −0.406040 | ||||||||
\(253\) | −2.47966e10 | −0.380496 | ||||||||
\(254\) | −2.83449e9 | −0.0427290 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.79057e10 | 0.988158 | ||||||||
\(257\) | 2.53245e10 | 0.362111 | 0.181055 | − | 0.983473i | \(-0.442049\pi\) | ||||
0.181055 | + | 0.983473i | \(0.442049\pi\) | |||||||
\(258\) | 3.03938e8 | 0.00427067 | ||||||||
\(259\) | 2.15588e10 | 0.297698 | ||||||||
\(260\) | −2.30202e10 | −0.312413 | ||||||||
\(261\) | −7.45285e10 | −0.994123 | ||||||||
\(262\) | 7.44198e8 | 0.00975737 | ||||||||
\(263\) | −1.12966e11 | −1.45596 | −0.727978 | − | 0.685601i | \(-0.759540\pi\) | ||||
−0.727978 | + | 0.685601i | \(0.759540\pi\) | |||||||
\(264\) | −4.78270e8 | −0.00605976 | ||||||||
\(265\) | 8.32900e10 | 1.03750 | ||||||||
\(266\) | 2.26926e8 | 0.00277918 | ||||||||
\(267\) | −1.03991e10 | −0.125226 | ||||||||
\(268\) | −5.80926e10 | −0.687883 | ||||||||
\(269\) | −4.60210e10 | −0.535884 | −0.267942 | − | 0.963435i | \(-0.586344\pi\) | ||||
−0.267942 | + | 0.963435i | \(0.586344\pi\) | |||||||
\(270\) | 8.60601e8 | 0.00985518 | ||||||||
\(271\) | −9.91151e10 | −1.11629 | −0.558146 | − | 0.829743i | \(-0.688487\pi\) | ||||
−0.558146 | + | 0.829743i | \(0.688487\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.41603e9 | 0.0481172 | ||||||||
\(274\) | 1.09647e9 | 0.0117522 | ||||||||
\(275\) | 2.14647e10 | 0.226322 | ||||||||
\(276\) | 2.19250e10 | 0.227431 | ||||||||
\(277\) | −5.58341e10 | −0.569824 | −0.284912 | − | 0.958554i | \(-0.591964\pi\) | ||||
−0.284912 | + | 0.958554i | \(0.591964\pi\) | |||||||
\(278\) | −3.51189e9 | −0.0352646 | ||||||||
\(279\) | −2.74653e10 | −0.271373 | ||||||||
\(280\) | 1.94535e9 | 0.0189142 | ||||||||
\(281\) | 8.69561e10 | 0.831997 | 0.415998 | − | 0.909365i | \(-0.363432\pi\) | ||||
0.415998 | + | 0.909365i | \(0.363432\pi\) | |||||||
\(282\) | 8.42277e8 | 0.00793111 | ||||||||
\(283\) | −1.23295e11 | −1.14263 | −0.571314 | − | 0.820732i | \(-0.693566\pi\) | ||||
−0.571314 | + | 0.820732i | \(0.693566\pi\) | |||||||
\(284\) | 5.68034e10 | 0.518134 | ||||||||
\(285\) | 3.07713e9 | 0.0276277 | ||||||||
\(286\) | −7.30222e8 | −0.00645369 | ||||||||
\(287\) | −6.25704e10 | −0.544378 | ||||||||
\(288\) | −1.14106e10 | −0.0977329 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 2.78716e9 | 0.0231404 | ||||||||
\(291\) | 2.95346e10 | 0.241442 | ||||||||
\(292\) | −1.42054e11 | −1.14349 | ||||||||
\(293\) | 1.61705e11 | 1.28179 | 0.640896 | − | 0.767627i | \(-0.278563\pi\) | ||||
0.640896 | + | 0.767627i | \(0.278563\pi\) | |||||||
\(294\) | 8.26183e8 | 0.00644931 | ||||||||
\(295\) | 1.74744e10 | 0.134339 | ||||||||
\(296\) | 6.30787e9 | 0.0477606 | ||||||||
\(297\) | −2.29836e10 | −0.171402 | ||||||||
\(298\) | −4.77207e9 | −0.0350537 | ||||||||
\(299\) | 6.69900e10 | 0.484718 | ||||||||
\(300\) | −1.89789e10 | −0.135278 | ||||||||
\(301\) | 3.30162e10 | 0.231835 | ||||||||
\(302\) | −5.47536e9 | −0.0378775 | ||||||||
\(303\) | 2.45596e10 | 0.167390 | ||||||||
\(304\) | −2.79003e10 | −0.187360 | ||||||||
\(305\) | 1.08605e11 | 0.718623 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.09712e9 | 0.00704906 | 0.00352453 | − | 0.999994i | \(-0.498878\pi\) | ||||
0.00352453 | + | 0.999994i | \(0.498878\pi\) | |||||||
\(308\) | −2.59614e10 | −0.164380 | ||||||||
\(309\) | −5.29563e10 | −0.330449 | ||||||||
\(310\) | 1.02713e9 | 0.00631680 | ||||||||
\(311\) | 3.14000e11 | 1.90330 | 0.951650 | − | 0.307184i | \(-0.0993867\pi\) | ||||
0.951650 | + | 0.307184i | \(0.0993867\pi\) | |||||||
\(312\) | 1.29208e9 | 0.00771960 | ||||||||
\(313\) | 1.94805e10 | 0.114723 | 0.0573615 | − | 0.998353i | \(-0.481731\pi\) | ||||
0.0573615 | + | 0.998353i | \(0.481731\pi\) | |||||||
\(314\) | 6.95385e9 | 0.0403684 | ||||||||
\(315\) | 4.54784e10 | 0.260260 | ||||||||
\(316\) | 7.80432e10 | 0.440295 | ||||||||
\(317\) | −1.38120e11 | −0.768227 | −0.384113 | − | 0.923286i | \(-0.625493\pi\) | ||||
−0.384113 | + | 0.923286i | \(0.625493\pi\) | |||||||
\(318\) | −2.33608e9 | −0.0128105 | ||||||||
\(319\) | −7.44353e10 | −0.402458 | ||||||||
\(320\) | −1.19234e11 | −0.635659 | ||||||||
\(321\) | 3.44953e10 | 0.181337 | ||||||||
\(322\) | −2.82886e9 | −0.0146643 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.67366e11 | −0.843752 | ||||||||
\(325\) | −5.79886e10 | −0.288315 | ||||||||
\(326\) | 1.10650e10 | 0.0542589 | ||||||||
\(327\) | 1.33264e10 | 0.0644537 | ||||||||
\(328\) | −1.83074e10 | −0.0873364 | ||||||||
\(329\) | 9.14951e10 | 0.430543 | ||||||||
\(330\) | 4.18138e8 | 0.00194092 | ||||||||
\(331\) | 2.60047e10 | 0.119076 | 0.0595382 | − | 0.998226i | \(-0.481037\pi\) | ||||
0.0595382 | + | 0.998226i | \(0.481037\pi\) | |||||||
\(332\) | −2.40169e10 | −0.108492 | ||||||||
\(333\) | 1.47465e11 | 0.657189 | ||||||||
\(334\) | −9.80075e9 | −0.0430924 | ||||||||
\(335\) | 1.01638e11 | 0.440914 | ||||||||
\(336\) | 2.29276e10 | 0.0981368 | ||||||||
\(337\) | 1.17662e11 | 0.496939 | 0.248470 | − | 0.968640i | \(-0.420072\pi\) | ||||
0.248470 | + | 0.968640i | \(0.420072\pi\) | |||||||
\(338\) | −6.29204e9 | −0.0262220 | ||||||||
\(339\) | −6.40254e9 | −0.0263302 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.74310e10 | −0.109862 | ||||||||
\(342\) | 1.55221e9 | 0.00613525 | ||||||||
\(343\) | 1.99751e11 | 0.779228 | ||||||||
\(344\) | 9.66020e9 | 0.0371940 | ||||||||
\(345\) | −3.83596e10 | −0.145777 | ||||||||
\(346\) | −9.77349e9 | −0.0366612 | ||||||||
\(347\) | −4.51270e9 | −0.0167091 | −0.00835457 | − | 0.999965i | \(-0.502659\pi\) | ||||
−0.00835457 | + | 0.999965i | \(0.502659\pi\) | |||||||
\(348\) | 6.58152e10 | 0.240558 | ||||||||
\(349\) | 2.36847e11 | 0.854582 | 0.427291 | − | 0.904114i | \(-0.359468\pi\) | ||||
0.427291 | + | 0.904114i | \(0.359468\pi\) | |||||||
\(350\) | 2.44875e9 | 0.00872245 | ||||||||
\(351\) | 6.20921e10 | 0.218351 | ||||||||
\(352\) | −1.13963e10 | −0.0395659 | ||||||||
\(353\) | −7.38411e10 | −0.253112 | −0.126556 | − | 0.991959i | \(-0.540392\pi\) | ||||
−0.126556 | + | 0.991959i | \(0.540392\pi\) | |||||||
\(354\) | −4.90112e8 | −0.00165875 | ||||||||
\(355\) | −9.93823e10 | −0.332110 | ||||||||
\(356\) | −1.65162e11 | −0.544985 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.46514e9 | 0.0143669 | ||||||||
\(359\) | 1.36609e11 | 0.434064 | 0.217032 | − | 0.976165i | \(-0.430362\pi\) | ||||
0.217032 | + | 0.976165i | \(0.430362\pi\) | |||||||
\(360\) | 1.33065e10 | 0.0417544 | ||||||||
\(361\) | −3.11279e11 | −0.964645 | ||||||||
\(362\) | −1.71281e10 | −0.0524229 | ||||||||
\(363\) | 6.47563e10 | 0.195750 | ||||||||
\(364\) | 7.01368e10 | 0.209406 | ||||||||
\(365\) | 2.48536e11 | 0.732944 | ||||||||
\(366\) | −3.04610e9 | −0.00887319 | ||||||||
\(367\) | −4.84798e11 | −1.39497 | −0.697483 | − | 0.716601i | \(-0.745697\pi\) | ||||
−0.697483 | + | 0.716601i | \(0.745697\pi\) | |||||||
\(368\) | 3.47806e11 | 0.988602 | ||||||||
\(369\) | −4.27991e11 | −1.20175 | ||||||||
\(370\) | −5.51479e9 | −0.0152975 | ||||||||
\(371\) | −2.53764e11 | −0.695421 | ||||||||
\(372\) | 2.42543e10 | 0.0656668 | ||||||||
\(373\) | 1.66467e11 | 0.445285 | 0.222643 | − | 0.974900i | \(-0.428532\pi\) | ||||
0.222643 | + | 0.974900i | \(0.428532\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.94730e10 | 0.233642 | ||||||||
\(376\) | 2.67705e10 | 0.0690735 | ||||||||
\(377\) | 2.01093e11 | 0.512697 | ||||||||
\(378\) | −2.62204e9 | −0.00660580 | ||||||||
\(379\) | −3.25337e11 | −0.809949 | −0.404974 | − | 0.914328i | \(-0.632720\pi\) | ||||
−0.404974 | + | 0.914328i | \(0.632720\pi\) | |||||||
\(380\) | 4.88720e10 | 0.120236 | ||||||||
\(381\) | 1.17105e11 | 0.284716 | ||||||||
\(382\) | 2.03327e10 | 0.0488551 | ||||||||
\(383\) | −6.99081e11 | −1.66009 | −0.830047 | − | 0.557693i | \(-0.811687\pi\) | ||||
−0.830047 | + | 0.557693i | \(0.811687\pi\) | |||||||
\(384\) | 1.34327e10 | 0.0315263 | ||||||||
\(385\) | 4.54216e10 | 0.105363 | ||||||||
\(386\) | −2.17582e10 | −0.0498861 | ||||||||
\(387\) | 2.25836e11 | 0.511792 | ||||||||
\(388\) | 4.69078e11 | 1.05076 | ||||||||
\(389\) | 3.82012e11 | 0.845871 | 0.422936 | − | 0.906160i | \(-0.361000\pi\) | ||||
0.422936 | + | 0.906160i | \(0.361000\pi\) | |||||||
\(390\) | −1.12963e9 | −0.00247256 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.62590e10 | 0.0561682 | ||||||||
\(393\) | −3.07459e10 | −0.0650161 | ||||||||
\(394\) | 1.72290e10 | 0.0360187 | ||||||||
\(395\) | −1.36543e11 | −0.282217 | ||||||||
\(396\) | −1.77580e11 | −0.362882 | ||||||||
\(397\) | 1.90754e11 | 0.385405 | 0.192702 | − | 0.981257i | \(-0.438275\pi\) | ||||
0.192702 | + | 0.981257i | \(0.438275\pi\) | |||||||
\(398\) | 1.17569e10 | 0.0234864 | ||||||||
\(399\) | −9.37526e9 | −0.0185185 | ||||||||
\(400\) | −3.01071e11 | −0.588029 | ||||||||
\(401\) | −9.14970e11 | −1.76708 | −0.883542 | − | 0.468352i | \(-0.844848\pi\) | ||||
−0.883542 | + | 0.468352i | \(0.844848\pi\) | |||||||
\(402\) | −2.85069e9 | −0.00544418 | ||||||||
\(403\) | 7.41070e10 | 0.139954 | ||||||||
\(404\) | 3.90063e11 | 0.728482 | ||||||||
\(405\) | 2.92821e11 | 0.540822 | ||||||||
\(406\) | −8.49178e9 | −0.0155107 | ||||||||
\(407\) | 1.47281e11 | 0.266055 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.06321e11 | −1.07139 | −0.535695 | − | 0.844412i | \(-0.679950\pi\) | ||||
−0.535695 | + | 0.844412i | \(0.679950\pi\) | |||||||
\(410\) | 1.60057e10 | 0.0279735 | ||||||||
\(411\) | −4.52997e10 | −0.0783083 | ||||||||
\(412\) | −8.41068e11 | −1.43812 | ||||||||
\(413\) | −5.32400e10 | −0.0900457 | ||||||||
\(414\) | −1.93498e10 | −0.0323725 | ||||||||
\(415\) | 4.20196e10 | 0.0695401 | ||||||||
\(416\) | 3.07880e10 | 0.0504036 | ||||||||
\(417\) | 1.45091e11 | 0.234978 | ||||||||
\(418\) | 1.55027e9 | 0.00248378 | ||||||||
\(419\) | 1.12482e12 | 1.78287 | 0.891436 | − | 0.453146i | \(-0.149698\pi\) | ||||
0.891436 | + | 0.453146i | \(0.149698\pi\) | |||||||
\(420\) | −4.01615e10 | −0.0629779 | ||||||||
\(421\) | 1.60780e11 | 0.249439 | 0.124719 | − | 0.992192i | \(-0.460197\pi\) | ||||
0.124719 | + | 0.992192i | \(0.460197\pi\) | |||||||
\(422\) | −4.11042e10 | −0.0630929 | ||||||||
\(423\) | 6.25840e11 | 0.950455 | ||||||||
\(424\) | −7.42486e10 | −0.111569 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.78742e9 | 0.00410072 | ||||||||
\(427\) | −3.30893e11 | −0.481684 | ||||||||
\(428\) | 5.47864e11 | 0.789180 | ||||||||
\(429\) | 3.01685e10 | 0.0430028 | ||||||||
\(430\) | −8.44564e9 | −0.0119131 | ||||||||
\(431\) | 1.32759e12 | 1.85317 | 0.926584 | − | 0.376088i | \(-0.122731\pi\) | ||||
0.926584 | + | 0.376088i | \(0.122731\pi\) | |||||||
\(432\) | 3.22376e11 | 0.445334 | ||||||||
\(433\) | 6.87578e11 | 0.939998 | 0.469999 | − | 0.882667i | \(-0.344254\pi\) | ||||
0.469999 | + | 0.882667i | \(0.344254\pi\) | |||||||
\(434\) | −3.12940e9 | −0.00423407 | ||||||||
\(435\) | −1.15149e11 | −0.154191 | ||||||||
\(436\) | 2.11654e11 | 0.280503 | ||||||||
\(437\) | −1.42220e11 | −0.186550 | ||||||||
\(438\) | −6.97080e9 | −0.00905001 | ||||||||
\(439\) | 7.48155e11 | 0.961394 | 0.480697 | − | 0.876887i | \(-0.340384\pi\) | ||||
0.480697 | + | 0.876887i | \(0.340384\pi\) | |||||||
\(440\) | 1.32899e10 | 0.0169038 | ||||||||
\(441\) | 6.13881e11 | 0.772878 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.01469e9 | 0.0111207 | 0.00556037 | − | 0.999985i | \(-0.498230\pi\) | ||||
0.00556037 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(444\) | −1.30225e11 | −0.159027 | ||||||||
\(445\) | 2.88964e11 | 0.349320 | ||||||||
\(446\) | −3.63606e10 | −0.0435136 | ||||||||
\(447\) | 1.97154e11 | 0.233573 | ||||||||
\(448\) | 3.63276e11 | 0.426074 | ||||||||
\(449\) | 4.09134e10 | 0.0475069 | 0.0237535 | − | 0.999718i | \(-0.492438\pi\) | ||||
0.0237535 | + | 0.999718i | \(0.492438\pi\) | |||||||
\(450\) | 1.67498e10 | 0.0192554 | ||||||||
\(451\) | −4.27455e11 | −0.486515 | ||||||||
\(452\) | −1.01687e11 | −0.114589 | ||||||||
\(453\) | 2.26210e11 | 0.252389 | ||||||||
\(454\) | −5.50590e10 | −0.0608243 | ||||||||
\(455\) | −1.22710e11 | −0.134224 | ||||||||
\(456\) | −2.74310e9 | −0.00297098 | ||||||||
\(457\) | 4.94033e11 | 0.529826 | 0.264913 | − | 0.964272i | \(-0.414657\pi\) | ||||
0.264913 | + | 0.964272i | \(0.414657\pi\) | |||||||
\(458\) | −4.71834e10 | −0.0501066 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.09239e11 | −0.634421 | ||||||||
\(461\) | 1.00197e12 | 1.03324 | 0.516621 | − | 0.856214i | \(-0.327190\pi\) | ||||
0.516621 | + | 0.856214i | \(0.327190\pi\) | |||||||
\(462\) | −1.27396e9 | −0.00130097 | ||||||||
\(463\) | −9.11192e11 | −0.921500 | −0.460750 | − | 0.887530i | \(-0.652420\pi\) | ||||
−0.460750 | + | 0.887530i | \(0.652420\pi\) | |||||||
\(464\) | 1.04405e12 | 1.04566 | ||||||||
\(465\) | −4.24349e10 | −0.0420906 | ||||||||
\(466\) | 1.28848e10 | 0.0126573 | ||||||||
\(467\) | 2.03431e12 | 1.97921 | 0.989603 | − | 0.143826i | \(-0.0459404\pi\) | ||||
0.989603 | + | 0.143826i | \(0.0459404\pi\) | |||||||
\(468\) | 4.79746e11 | 0.462280 | ||||||||
\(469\) | −3.09665e11 | −0.295539 | ||||||||
\(470\) | −2.34047e10 | −0.0221239 | ||||||||
\(471\) | −2.87292e11 | −0.268986 | ||||||||
\(472\) | −1.55775e10 | −0.0144463 | ||||||||
\(473\) | 2.25554e11 | 0.207193 | ||||||||
\(474\) | 3.82969e9 | 0.00348467 | ||||||||
\(475\) | 1.23110e11 | 0.110961 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.73578e12 | −1.53519 | ||||||||
\(478\) | 6.97412e10 | 0.0611032 | ||||||||
\(479\) | 1.30117e12 | 1.12934 | 0.564670 | − | 0.825316i | \(-0.309003\pi\) | ||||
0.564670 | + | 0.825316i | \(0.309003\pi\) | |||||||
\(480\) | −1.76297e10 | −0.0151586 | ||||||||
\(481\) | −3.97891e11 | −0.338931 | ||||||||
\(482\) | −4.57718e10 | −0.0386266 | ||||||||
\(483\) | 1.16872e11 | 0.0977122 | ||||||||
\(484\) | 1.02848e12 | 0.851906 | ||||||||
\(485\) | −8.20691e11 | −0.673506 | ||||||||
\(486\) | −2.71452e10 | −0.0220714 | ||||||||
\(487\) | −1.49690e12 | −1.20591 | −0.602953 | − | 0.797777i | \(-0.706009\pi\) | ||||
−0.602953 | + | 0.797777i | \(0.706009\pi\) | |||||||
\(488\) | −9.68157e10 | −0.0772782 | ||||||||
\(489\) | −4.57140e11 | −0.361542 | ||||||||
\(490\) | −2.29575e10 | −0.0179904 | ||||||||
\(491\) | −1.75875e12 | −1.36564 | −0.682822 | − | 0.730585i | \(-0.739248\pi\) | ||||
−0.682822 | + | 0.730585i | \(0.739248\pi\) | |||||||
\(492\) | 3.77954e11 | 0.290801 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −4.18817e9 | −0.00316412 | ||||||||
\(495\) | 3.10690e11 | 0.232597 | ||||||||
\(496\) | 3.84756e11 | 0.285442 | ||||||||
\(497\) | 3.02793e11 | 0.222609 | ||||||||
\(498\) | −1.17854e9 | −0.000858645 0 | ||||||||
\(499\) | 2.16969e12 | 1.56655 | 0.783276 | − | 0.621674i | \(-0.213547\pi\) | ||||
0.783276 | + | 0.621674i | \(0.213547\pi\) | |||||||
\(500\) | 1.42104e12 | 1.01681 | ||||||||
\(501\) | 4.04910e11 | 0.287137 | ||||||||
\(502\) | 2.25891e10 | 0.0158757 | ||||||||
\(503\) | 4.58784e11 | 0.319560 | 0.159780 | − | 0.987153i | \(-0.448922\pi\) | ||||
0.159780 | + | 0.987153i | \(0.448922\pi\) | |||||||
\(504\) | −4.05416e10 | −0.0279875 | ||||||||
\(505\) | −6.82447e11 | −0.466937 | ||||||||
\(506\) | −1.93256e10 | −0.0131056 | ||||||||
\(507\) | 2.59950e11 | 0.174725 | ||||||||
\(508\) | 1.85989e12 | 1.23908 | ||||||||
\(509\) | −9.32948e11 | −0.616066 | −0.308033 | − | 0.951376i | \(-0.599671\pi\) | ||||
−0.308033 | + | 0.951376i | \(0.599671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.57226e11 | −0.491283 | ||||||||
\(512\) | 2.66519e11 | 0.171401 | ||||||||
\(513\) | −1.31822e11 | −0.0840349 | ||||||||
\(514\) | 1.97371e10 | 0.0124723 | ||||||||
\(515\) | 1.47152e12 | 0.921792 | ||||||||
\(516\) | −1.99433e11 | −0.123844 | ||||||||
\(517\) | 6.25058e11 | 0.384780 | ||||||||
\(518\) | 1.68022e10 | 0.0102537 | ||||||||
\(519\) | 4.03783e11 | 0.244284 | ||||||||
\(520\) | −3.59036e10 | −0.0215339 | ||||||||
\(521\) | 1.73581e12 | 1.03213 | 0.516064 | − | 0.856550i | \(-0.327397\pi\) | ||||
0.516064 | + | 0.856550i | \(0.327397\pi\) | |||||||
\(522\) | −5.80850e10 | −0.0342410 | ||||||||
\(523\) | −8.84542e11 | −0.516965 | −0.258482 | − | 0.966016i | \(-0.583222\pi\) | ||||
−0.258482 | + | 0.966016i | \(0.583222\pi\) | |||||||
\(524\) | −4.88316e11 | −0.282950 | ||||||||
\(525\) | −1.01168e11 | −0.0581201 | ||||||||
\(526\) | −8.80422e10 | −0.0501482 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.56632e11 | 0.0877057 | ||||||||
\(529\) | −2.82337e10 | −0.0156754 | ||||||||
\(530\) | 6.49135e10 | 0.0357350 | ||||||||
\(531\) | −3.64169e11 | −0.198783 | ||||||||
\(532\) | −1.48901e11 | −0.0805925 | ||||||||
\(533\) | 1.15481e12 | 0.619778 | ||||||||
\(534\) | −8.10472e9 | −0.00431323 | ||||||||
\(535\) | −9.58533e11 | −0.505842 | ||||||||
\(536\) | −9.06047e10 | −0.0474143 | ||||||||
\(537\) | −1.84474e11 | −0.0957304 | ||||||||
\(538\) | −3.58673e10 | −0.0184577 | ||||||||
\(539\) | 6.13114e11 | 0.312890 | ||||||||
\(540\) | −5.64695e11 | −0.285787 | ||||||||
\(541\) | 1.32655e12 | 0.665787 | 0.332893 | − | 0.942964i | \(-0.391975\pi\) | ||||
0.332893 | + | 0.942964i | \(0.391975\pi\) | |||||||
\(542\) | −7.72470e10 | −0.0384490 | ||||||||
\(543\) | 7.07634e11 | 0.349309 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.70306e11 | −0.179795 | ||||||||
\(546\) | 3.44171e9 | 0.00165732 | ||||||||
\(547\) | −9.98506e11 | −0.476879 | −0.238439 | − | 0.971157i | \(-0.576636\pi\) | ||||
−0.238439 | + | 0.971157i | \(0.576636\pi\) | |||||||
\(548\) | −7.19464e11 | −0.340798 | ||||||||
\(549\) | −2.26336e12 | −1.06335 | ||||||||
\(550\) | 1.67289e10 | 0.00779533 | ||||||||
\(551\) | −4.26921e11 | −0.197317 | ||||||||
\(552\) | 3.41955e10 | 0.0156763 | ||||||||
\(553\) | 4.16013e11 | 0.189166 | ||||||||
\(554\) | −4.35153e10 | −0.0196267 | ||||||||
\(555\) | 2.27839e11 | 0.101932 | ||||||||
\(556\) | 2.30438e12 | 1.02263 | ||||||||
\(557\) | 3.43127e12 | 1.51045 | 0.755226 | − | 0.655465i | \(-0.227527\pi\) | ||||
0.755226 | + | 0.655465i | \(0.227527\pi\) | |||||||
\(558\) | −2.14056e10 | −0.00934701 | ||||||||
\(559\) | −6.09351e11 | −0.263945 | ||||||||
\(560\) | −6.37099e11 | −0.273754 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.77707e10 | 0.0286569 | ||||||||
\(563\) | −5.19511e11 | −0.217925 | −0.108962 | − | 0.994046i | \(-0.534753\pi\) | ||||
−0.108962 | + | 0.994046i | \(0.534753\pi\) | |||||||
\(564\) | −5.52672e11 | −0.229991 | ||||||||
\(565\) | 1.77910e11 | 0.0734484 | ||||||||
\(566\) | −9.60917e10 | −0.0393561 | ||||||||
\(567\) | −8.92152e11 | −0.362506 | ||||||||
\(568\) | 8.85940e10 | 0.0357139 | ||||||||
\(569\) | −2.71055e12 | −1.08406 | −0.542029 | − | 0.840360i | \(-0.682344\pi\) | ||||
−0.542029 | + | 0.840360i | \(0.682344\pi\) | |||||||
\(570\) | 2.39822e9 | 0.000951593 0 | ||||||||
\(571\) | −5.10172e11 | −0.200842 | −0.100421 | − | 0.994945i | \(-0.532019\pi\) | ||||
−0.100421 | + | 0.994945i | \(0.532019\pi\) | |||||||
\(572\) | 4.79146e11 | 0.187148 | ||||||||
\(573\) | −8.40029e11 | −0.325536 | ||||||||
\(574\) | −4.87653e10 | −0.0187503 | ||||||||
\(575\) | −1.53469e12 | −0.585485 | ||||||||
\(576\) | 2.48486e12 | 0.940590 | ||||||||
\(577\) | 2.12813e12 | 0.799296 | 0.399648 | − | 0.916669i | \(-0.369132\pi\) | ||||
0.399648 | + | 0.916669i | \(0.369132\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.98921e11 | 0.332405 | ||||||||
\(580\) | −1.82883e12 | −0.671040 | ||||||||
\(581\) | −1.28023e11 | −0.0466118 | ||||||||
\(582\) | 2.30183e10 | 0.00831611 | ||||||||
\(583\) | −1.73361e12 | −0.621503 | ||||||||
\(584\) | −2.21556e11 | −0.0788181 | ||||||||
\(585\) | −8.39354e11 | −0.296308 | ||||||||
\(586\) | 1.26027e11 | 0.0441494 | ||||||||
\(587\) | −3.72613e12 | −1.29535 | −0.647675 | − | 0.761917i | \(-0.724258\pi\) | ||||
−0.647675 | + | 0.761917i | \(0.724258\pi\) | |||||||
\(588\) | −5.42111e11 | −0.187021 | ||||||||
\(589\) | −1.57330e11 | −0.0538631 | ||||||||
\(590\) | 1.36189e10 | 0.00462710 | ||||||||
\(591\) | −7.11802e11 | −0.240002 | ||||||||
\(592\) | −2.06581e12 | −0.691262 | ||||||||
\(593\) | −4.17129e12 | −1.38524 | −0.692619 | − | 0.721304i | \(-0.743543\pi\) | ||||
−0.692619 | + | 0.721304i | \(0.743543\pi\) | |||||||
\(594\) | −1.79127e10 | −0.00590366 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.13126e12 | 1.01651 | ||||||||
\(597\) | −4.85724e11 | −0.156497 | ||||||||
\(598\) | 5.22098e10 | 0.0166954 | ||||||||
\(599\) | 1.45781e12 | 0.462680 | 0.231340 | − | 0.972873i | \(-0.425689\pi\) | ||||
0.231340 | + | 0.972873i | \(0.425689\pi\) | |||||||
\(600\) | −2.96007e10 | −0.00932441 | ||||||||
\(601\) | −4.68500e12 | −1.46479 | −0.732393 | − | 0.680882i | \(-0.761596\pi\) | ||||
−0.732393 | + | 0.680882i | \(0.761596\pi\) | |||||||
\(602\) | 2.57318e10 | 0.00798519 | ||||||||
\(603\) | −2.11815e12 | −0.652424 | ||||||||
\(604\) | 3.59274e12 | 1.09840 | ||||||||
\(605\) | −1.79941e12 | −0.546048 | ||||||||
\(606\) | 1.91409e10 | 0.00576549 | ||||||||
\(607\) | −3.47157e12 | −1.03795 | −0.518976 | − | 0.854789i | \(-0.673686\pi\) | ||||
−0.518976 | + | 0.854789i | \(0.673686\pi\) | |||||||
\(608\) | −6.53631e10 | −0.0193984 | ||||||||
\(609\) | 3.50831e11 | 0.103352 | ||||||||
\(610\) | 8.46433e10 | 0.0247519 | ||||||||
\(611\) | −1.68864e12 | −0.490176 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.30507e12 | 0.659344 | 0.329672 | − | 0.944095i | \(-0.393062\pi\) | ||||
0.329672 | + | 0.944095i | \(0.393062\pi\) | |||||||
\(614\) | 8.55059e8 | 0.000242794 0 | ||||||||
\(615\) | −6.61261e11 | −0.186395 | ||||||||
\(616\) | −4.04909e10 | −0.0113304 | ||||||||
\(617\) | 8.72828e9 | 0.00242463 | 0.00121231 | − | 0.999999i | \(-0.499614\pi\) | ||||
0.00121231 | + | 0.999999i | \(0.499614\pi\) | |||||||
\(618\) | −4.12724e10 | −0.0113818 | ||||||||
\(619\) | −4.02662e12 | −1.10238 | −0.551192 | − | 0.834378i | \(-0.685827\pi\) | ||||
−0.551192 | + | 0.834378i | \(0.685827\pi\) | |||||||
\(620\) | −6.73964e11 | −0.183178 | ||||||||
\(621\) | 1.64329e12 | 0.443408 | ||||||||
\(622\) | 2.44721e11 | 0.0655563 | ||||||||
\(623\) | −8.80402e11 | −0.234145 | ||||||||
\(624\) | −4.23154e11 | −0.111729 | ||||||||
\(625\) | −2.35059e11 | −0.0616193 | ||||||||
\(626\) | 1.51825e10 | 0.00395146 | ||||||||
\(627\) | −6.40479e10 | −0.0165501 | ||||||||
\(628\) | −4.56286e12 | −1.17063 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 3.54444e10 | 0.00896427 | ||||||||
\(631\) | 2.15928e10 | 0.00542222 | 0.00271111 | − | 0.999996i | \(-0.499137\pi\) | ||||
0.00271111 | + | 0.999996i | \(0.499137\pi\) | |||||||
\(632\) | 1.21721e11 | 0.0303486 | ||||||||
\(633\) | 1.69819e12 | 0.420406 | ||||||||
\(634\) | −1.07646e11 | −0.0264604 | ||||||||
\(635\) | −3.25403e12 | −0.794218 | ||||||||
\(636\) | 1.53285e12 | 0.371486 | ||||||||
\(637\) | −1.65638e12 | −0.398595 | ||||||||
\(638\) | −5.80124e10 | −0.0138621 | ||||||||
\(639\) | 2.07115e12 | 0.491425 | ||||||||
\(640\) | −3.73260e11 | −0.0879431 | ||||||||
\(641\) | 3.19798e12 | 0.748195 | 0.374098 | − | 0.927389i | \(-0.377953\pi\) | ||||
0.374098 | + | 0.927389i | \(0.377953\pi\) | |||||||
\(642\) | 2.68845e10 | 0.00624588 | ||||||||
\(643\) | 3.65477e11 | 0.0843162 | 0.0421581 | − | 0.999111i | \(-0.486577\pi\) | ||||
0.0421581 | + | 0.999111i | \(0.486577\pi\) | |||||||
\(644\) | 1.85620e12 | 0.425244 | ||||||||
\(645\) | 3.48925e11 | 0.0793803 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.96485e12 | 0.889524 | 0.444762 | − | 0.895649i | \(-0.353288\pi\) | ||||
0.444762 | + | 0.895649i | \(0.353288\pi\) | |||||||
\(648\) | −2.61034e11 | −0.0581580 | ||||||||
\(649\) | −3.63714e11 | −0.0804746 | ||||||||
\(650\) | −4.51944e10 | −0.00993057 | ||||||||
\(651\) | 1.29289e11 | 0.0282128 | ||||||||
\(652\) | −7.26043e12 | −1.57343 | ||||||||
\(653\) | −6.94635e12 | −1.49502 | −0.747511 | − | 0.664249i | \(-0.768751\pi\) | ||||
−0.747511 | + | 0.664249i | \(0.768751\pi\) | |||||||
\(654\) | 1.03862e10 | 0.00222001 | ||||||||
\(655\) | 8.54349e11 | 0.181363 | ||||||||
\(656\) | 5.99564e12 | 1.26406 | ||||||||
\(657\) | −5.17954e12 | −1.08454 | ||||||||
\(658\) | 7.13083e10 | 0.0148294 | ||||||||
\(659\) | −4.54637e12 | −0.939032 | −0.469516 | − | 0.882924i | \(-0.655572\pi\) | ||||
−0.469516 | + | 0.882924i | \(0.655572\pi\) | |||||||
\(660\) | −2.74367e11 | −0.0562839 | ||||||||
\(661\) | −1.43628e12 | −0.292640 | −0.146320 | − | 0.989237i | \(-0.546743\pi\) | ||||
−0.146320 | + | 0.989237i | \(0.546743\pi\) | |||||||
\(662\) | 2.02672e10 | 0.00410140 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.74582e10 | −0.00747809 | ||||||||
\(665\) | 2.60514e11 | 0.0516575 | ||||||||
\(666\) | 1.14930e11 | 0.0226359 | ||||||||
\(667\) | 5.32201e12 | 1.04114 | ||||||||
\(668\) | 6.43090e12 | 1.24962 | ||||||||
\(669\) | 1.50221e12 | 0.289943 | ||||||||
\(670\) | 7.92131e10 | 0.0151866 | ||||||||
\(671\) | −2.26053e12 | −0.430485 | ||||||||
\(672\) | 5.37134e10 | 0.0101606 | ||||||||
\(673\) | 3.31284e12 | 0.622490 | 0.311245 | − | 0.950330i | \(-0.399254\pi\) | ||||
0.311245 | + | 0.950330i | \(0.399254\pi\) | |||||||
\(674\) | 9.17022e10 | 0.0171163 | ||||||||
\(675\) | −1.42249e12 | −0.263743 | ||||||||
\(676\) | 4.12861e12 | 0.760403 | ||||||||
\(677\) | −5.77140e12 | −1.05592 | −0.527961 | − | 0.849269i | \(-0.677043\pi\) | ||||
−0.527961 | + | 0.849269i | \(0.677043\pi\) | |||||||
\(678\) | −4.98993e9 | −0.000906902 0 | ||||||||
\(679\) | 2.50044e12 | 0.451443 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.27472e12 | 0.405290 | ||||||||
\(682\) | −2.13788e10 | −0.00378402 | ||||||||
\(683\) | −1.04373e13 | −1.83524 | −0.917620 | − | 0.397458i | \(-0.869893\pi\) | ||||
−0.917620 | + | 0.397458i | \(0.869893\pi\) | |||||||
\(684\) | −1.01850e12 | −0.177914 | ||||||||
\(685\) | 1.25876e12 | 0.218442 | ||||||||
\(686\) | 1.55679e11 | 0.0268393 | ||||||||
\(687\) | 1.94934e12 | 0.333874 | ||||||||
\(688\) | −3.16369e12 | −0.538327 | ||||||||
\(689\) | 4.68349e12 | 0.791741 | ||||||||
\(690\) | −2.98962e10 | −0.00502106 | ||||||||
\(691\) | −7.77913e12 | −1.29801 | −0.649007 | − | 0.760782i | \(-0.724816\pi\) | ||||
−0.649007 | + | 0.760782i | \(0.724816\pi\) | |||||||
\(692\) | 6.41301e12 | 1.06313 | ||||||||
\(693\) | −9.46596e11 | −0.155907 | ||||||||
\(694\) | −3.51705e9 | −0.000575521 0 | ||||||||
\(695\) | −4.03170e12 | −0.655475 | ||||||||
\(696\) | 1.02649e11 | 0.0165811 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.84591e11 | 0.0294348 | ||||||||
\(699\) | −5.32324e11 | −0.0843391 | ||||||||
\(700\) | −1.60678e12 | −0.252939 | ||||||||
\(701\) | 1.12758e13 | 1.76367 | 0.881836 | − | 0.471557i | \(-0.156308\pi\) | ||||
0.881836 | + | 0.471557i | \(0.156308\pi\) | |||||||
\(702\) | 4.83925e10 | 0.00752075 | ||||||||
\(703\) | 8.44725e11 | 0.130442 | ||||||||
\(704\) | 2.48175e12 | 0.380786 | ||||||||
\(705\) | 9.66945e11 | 0.147418 | ||||||||
\(706\) | −5.75493e10 | −0.00871804 | ||||||||
\(707\) | 2.07925e12 | 0.312982 | ||||||||
\(708\) | 3.21594e11 | 0.0481014 | ||||||||
\(709\) | 5.80955e12 | 0.863445 | 0.431722 | − | 0.902006i | \(-0.357906\pi\) | ||||
0.431722 | + | 0.902006i | \(0.357906\pi\) | |||||||
\(710\) | −7.74553e10 | −0.0114390 | ||||||||
\(711\) | 2.84559e12 | 0.417598 | ||||||||
\(712\) | −2.57596e11 | −0.0375647 | ||||||||
\(713\) | 1.96127e12 | 0.284207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.38305e11 | −0.119957 | ||||||||
\(716\) | −2.92987e12 | −0.416619 | ||||||||
\(717\) | −2.88130e12 | −0.407148 | ||||||||
\(718\) | 1.06468e11 | 0.0149507 | ||||||||
\(719\) | −3.73999e12 | −0.521904 | −0.260952 | − | 0.965352i | \(-0.584036\pi\) | ||||
−0.260952 | + | 0.965352i | \(0.584036\pi\) | |||||||
\(720\) | −4.35785e12 | −0.604332 | ||||||||
\(721\) | −4.48335e12 | −0.617866 | ||||||||
\(722\) | −2.42601e11 | −0.0332257 | ||||||||
\(723\) | 1.89102e12 | 0.257380 | ||||||||
\(724\) | 1.12389e13 | 1.52019 | ||||||||
\(725\) | −4.60689e12 | −0.619280 | ||||||||
\(726\) | 5.04689e10 | 0.00674232 | ||||||||
\(727\) | −4.47054e12 | −0.593547 | −0.296774 | − | 0.954948i | \(-0.595911\pi\) | ||||
−0.296774 | + | 0.954948i | \(0.595911\pi\) | |||||||
\(728\) | 1.09389e11 | 0.0144339 | ||||||||
\(729\) | −5.32028e12 | −0.697686 | ||||||||
\(730\) | 1.93700e11 | 0.0252451 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.99874e12 | 0.257310 | ||||||||
\(733\) | 1.27179e13 | 1.62722 | 0.813611 | − | 0.581410i | \(-0.197499\pi\) | ||||
0.813611 | + | 0.581410i | \(0.197499\pi\) | |||||||
\(734\) | −3.77836e11 | −0.0480475 | ||||||||
\(735\) | 9.48468e11 | 0.119875 | ||||||||
\(736\) | 8.14817e11 | 0.102355 | ||||||||
\(737\) | −2.11551e12 | −0.264126 | ||||||||
\(738\) | −3.33562e11 | −0.0413926 | ||||||||
\(739\) | −1.34347e13 | −1.65702 | −0.828509 | − | 0.559976i | \(-0.810810\pi\) | ||||
−0.828509 | + | 0.559976i | \(0.810810\pi\) | |||||||
\(740\) | 3.61861e12 | 0.443608 | ||||||||
\(741\) | 1.73031e11 | 0.0210834 | ||||||||
\(742\) | −1.97775e11 | −0.0239527 | ||||||||
\(743\) | −1.78979e12 | −0.215453 | −0.107727 | − | 0.994181i | \(-0.534357\pi\) | ||||
−0.107727 | + | 0.994181i | \(0.534357\pi\) | |||||||
\(744\) | 3.78285e10 | 0.00452627 | ||||||||
\(745\) | −5.47840e12 | −0.651554 | ||||||||
\(746\) | 1.29739e11 | 0.0153372 | ||||||||
\(747\) | −8.75698e11 | −0.102899 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.92041e12 | 0.339060 | ||||||||
\(750\) | 6.97323e10 | 0.00804745 | ||||||||
\(751\) | −1.33750e12 | −0.153431 | −0.0767156 | − | 0.997053i | \(-0.524443\pi\) | ||||
−0.0767156 | + | 0.997053i | \(0.524443\pi\) | |||||||
\(752\) | −8.76727e12 | −0.999733 | ||||||||
\(753\) | −9.33251e11 | −0.105784 | ||||||||
\(754\) | 1.56725e11 | 0.0176591 | ||||||||
\(755\) | −6.28579e12 | −0.704042 | ||||||||
\(756\) | 1.72049e12 | 0.191559 | ||||||||
\(757\) | −6.15593e12 | −0.681338 | −0.340669 | − | 0.940183i | \(-0.610654\pi\) | ||||
−0.340669 | + | 0.940183i | \(0.610654\pi\) | |||||||
\(758\) | −2.53557e11 | −0.0278974 | ||||||||
\(759\) | 7.98423e11 | 0.0873263 | ||||||||
\(760\) | 7.62236e10 | 0.00828759 | ||||||||
\(761\) | −6.40055e12 | −0.691810 | −0.345905 | − | 0.938270i | \(-0.612428\pi\) | ||||
−0.345905 | + | 0.938270i | \(0.612428\pi\) | |||||||
\(762\) | 9.12674e10 | 0.00980660 | ||||||||
\(763\) | 1.12823e12 | 0.120514 | ||||||||
\(764\) | −1.33416e13 | −1.41673 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.44840e11 | −0.0571794 | ||||||||
\(767\) | 9.82603e11 | 0.102518 | ||||||||
\(768\) | −2.18649e12 | −0.226789 | ||||||||
\(769\) | 1.07113e13 | 1.10452 | 0.552259 | − | 0.833673i | \(-0.313766\pi\) | ||||
0.552259 | + | 0.833673i | \(0.313766\pi\) | |||||||
\(770\) | 3.54001e10 | 0.00362907 | ||||||||
\(771\) | −8.15420e11 | −0.0831068 | ||||||||
\(772\) | 1.42769e13 | 1.44663 | ||||||||
\(773\) | −2.88044e12 | −0.290169 | −0.145084 | − | 0.989419i | \(-0.546345\pi\) | ||||
−0.145084 | + | 0.989419i | \(0.546345\pi\) | |||||||
\(774\) | 1.76009e11 | 0.0176279 | ||||||||
\(775\) | −1.69774e12 | −0.169049 | ||||||||
\(776\) | 7.31602e11 | 0.0724265 | ||||||||
\(777\) | −6.94169e11 | −0.0683236 | ||||||||
\(778\) | 2.97728e11 | 0.0291347 | ||||||||
\(779\) | −2.45166e12 | −0.238529 | ||||||||
\(780\) | 7.41224e11 | 0.0717008 | ||||||||
\(781\) | 2.06856e12 | 0.198947 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.93290e12 | 0.469001 | ||||||||
\(784\) | −8.59974e12 | −0.812949 | ||||||||
\(785\) | 7.98311e12 | 0.750341 | ||||||||
\(786\) | −2.39624e10 | −0.00223938 | ||||||||
\(787\) | −7.97631e12 | −0.741166 | −0.370583 | − | 0.928799i | \(-0.620842\pi\) | ||||
−0.370583 | + | 0.928799i | \(0.620842\pi\) | |||||||
\(788\) | −1.13051e13 | −1.04449 | ||||||||
\(789\) | 3.63739e12 | 0.334151 | ||||||||
\(790\) | −1.06417e11 | −0.00972052 | ||||||||
\(791\) | −5.42047e11 | −0.0492315 | ||||||||
\(792\) | −2.76964e11 | −0.0250126 | ||||||||
\(793\) | 6.10699e12 | 0.548401 | ||||||||
\(794\) | 1.48668e11 | 0.0132747 | ||||||||
\(795\) | −2.68185e12 | −0.238112 | ||||||||
\(796\) | −7.71442e12 | −0.681075 | ||||||||
\(797\) | −8.35103e12 | −0.733124 | −0.366562 | − | 0.930394i | \(-0.619465\pi\) | ||||
−0.366562 | + | 0.930394i | \(0.619465\pi\) | |||||||
\(798\) | −7.30677e9 | −0.000637841 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −7.05330e11 | −0.0608818 | ||||||||
\(801\) | −6.02208e12 | −0.516892 | ||||||||
\(802\) | −7.13097e11 | −0.0608645 | ||||||||
\(803\) | −5.17306e12 | −0.439064 | ||||||||
\(804\) | 1.87052e12 | 0.157874 | ||||||||
\(805\) | −3.24757e12 | −0.272570 | ||||||||
\(806\) | 5.77565e10 | 0.00482052 | ||||||||
\(807\) | 1.48183e12 | 0.122989 | ||||||||
\(808\) | 6.08365e11 | 0.0502127 | ||||||||
\(809\) | −1.72474e13 | −1.41565 | −0.707823 | − | 0.706390i | \(-0.750322\pi\) | ||||
−0.707823 | + | 0.706390i | \(0.750322\pi\) | |||||||
\(810\) | 2.28215e11 | 0.0186278 | ||||||||
\(811\) | −1.43590e13 | −1.16555 | −0.582776 | − | 0.812633i | \(-0.698034\pi\) | ||||
−0.582776 | + | 0.812633i | \(0.698034\pi\) | |||||||
\(812\) | 5.57200e12 | 0.449789 | ||||||||
\(813\) | 3.19139e12 | 0.256196 | ||||||||
\(814\) | 1.14786e11 | 0.00916386 | ||||||||
\(815\) | 1.27027e13 | 1.00853 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29366e12 | 0.101583 | ||||||||
\(818\) | −4.72546e11 | −0.0369024 | ||||||||
\(819\) | 2.55730e12 | 0.198612 | ||||||||
\(820\) | −1.05023e13 | −0.811193 | ||||||||
\(821\) | −5.55258e12 | −0.426531 | −0.213265 | − | 0.976994i | \(-0.568410\pi\) | ||||
−0.213265 | + | 0.976994i | \(0.568410\pi\) | |||||||
\(822\) | −3.53051e10 | −0.00269721 | ||||||||
\(823\) | −1.42535e13 | −1.08298 | −0.541491 | − | 0.840706i | \(-0.682140\pi\) | ||||
−0.541491 | + | 0.840706i | \(0.682140\pi\) | |||||||
\(824\) | −1.31178e12 | −0.0991263 | ||||||||
\(825\) | −6.91139e11 | −0.0519425 | ||||||||
\(826\) | −4.14935e10 | −0.00310149 | ||||||||
\(827\) | −1.26379e13 | −0.939505 | −0.469752 | − | 0.882798i | \(-0.655657\pi\) | ||||
−0.469752 | + | 0.882798i | \(0.655657\pi\) | |||||||
\(828\) | 1.26967e13 | 0.938758 | ||||||||
\(829\) | 1.04860e13 | 0.771104 | 0.385552 | − | 0.922686i | \(-0.374011\pi\) | ||||
0.385552 | + | 0.922686i | \(0.374011\pi\) | |||||||
\(830\) | 3.27487e10 | 0.00239520 | ||||||||
\(831\) | 1.79780e12 | 0.130778 | ||||||||
\(832\) | −6.70465e12 | −0.485089 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.13079e11 | 0.00809347 | ||||||||
\(835\) | −1.12514e13 | −0.800972 | ||||||||
\(836\) | −1.01723e12 | −0.0720262 | ||||||||
\(837\) | 1.81788e12 | 0.128027 | ||||||||
\(838\) | 8.76648e11 | 0.0614083 | ||||||||
\(839\) | 1.64507e13 | 1.14618 | 0.573092 | − | 0.819491i | \(-0.305744\pi\) | ||||
0.573092 | + | 0.819491i | \(0.305744\pi\) | |||||||
\(840\) | −6.26382e10 | −0.00434093 | ||||||||
\(841\) | 1.46864e12 | 0.101236 | ||||||||
\(842\) | 1.25307e11 | 0.00859153 | ||||||||
\(843\) | −2.79989e12 | −0.190949 | ||||||||
\(844\) | 2.69711e13 | 1.82961 | ||||||||
\(845\) | −7.22335e12 | −0.487397 | ||||||||
\(846\) | 4.87759e11 | 0.0327370 | ||||||||
\(847\) | 5.48235e12 | 0.366009 | ||||||||
\(848\) | 2.43162e13 | 1.61479 | ||||||||
\(849\) | 3.96995e12 | 0.262241 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.05304e13 | −0.688272 | ||||||||
\(852\) | −1.82901e12 | −0.118915 | ||||||||
\(853\) | 1.11182e13 | 0.719057 | 0.359528 | − | 0.933134i | \(-0.382938\pi\) | ||||
0.359528 | + | 0.933134i | \(0.382938\pi\) | |||||||
\(854\) | −2.57887e11 | −0.0165909 | ||||||||
\(855\) | 1.78195e12 | 0.114038 | ||||||||
\(856\) | 8.54482e11 | 0.0543965 | ||||||||
\(857\) | −7.82649e12 | −0.495625 | −0.247813 | − | 0.968808i | \(-0.579712\pi\) | ||||
−0.247813 | + | 0.968808i | \(0.579712\pi\) | |||||||
\(858\) | 2.35123e10 | 0.00148116 | ||||||||
\(859\) | −3.68708e12 | −0.231054 | −0.115527 | − | 0.993304i | \(-0.536856\pi\) | ||||
−0.115527 | + | 0.993304i | \(0.536856\pi\) | |||||||
\(860\) | 5.54173e12 | 0.345463 | ||||||||
\(861\) | 2.01470e12 | 0.124938 | ||||||||
\(862\) | 1.03468e12 | 0.0638295 | ||||||||
\(863\) | 1.56166e13 | 0.958380 | 0.479190 | − | 0.877711i | \(-0.340931\pi\) | ||||
0.479190 | + | 0.877711i | \(0.340931\pi\) | |||||||
\(864\) | 7.55243e11 | 0.0461079 | ||||||||
\(865\) | −1.12201e13 | −0.681434 | ||||||||
\(866\) | 5.35876e11 | 0.0323768 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.05340e12 | 0.122782 | ||||||||
\(869\) | 2.84203e12 | 0.169059 | ||||||||
\(870\) | −8.97434e10 | −0.00531087 | ||||||||
\(871\) | 5.71521e12 | 0.336473 | ||||||||
\(872\) | 3.30108e11 | 0.0193345 | ||||||||
\(873\) | 1.71034e13 | 0.996593 | ||||||||
\(874\) | −1.10842e11 | −0.00642542 | ||||||||
\(875\) | 7.57490e12 | 0.436858 | ||||||||
\(876\) | 4.57399e12 | 0.262438 | ||||||||
\(877\) | −1.84491e13 | −1.05312 | −0.526559 | − | 0.850139i | \(-0.676518\pi\) | ||||
−0.526559 | + | 0.850139i | \(0.676518\pi\) | |||||||
\(878\) | 5.83087e11 | 0.0331137 | ||||||||
\(879\) | −5.20671e12 | −0.294180 | ||||||||
\(880\) | −4.35240e12 | −0.244656 | ||||||||
\(881\) | 2.55028e13 | 1.42625 | 0.713125 | − | 0.701037i | \(-0.247279\pi\) | ||||
0.713125 | + | 0.701037i | \(0.247279\pi\) | |||||||
\(882\) | 4.78439e11 | 0.0266206 | ||||||||
\(883\) | 9.14795e12 | 0.506408 | 0.253204 | − | 0.967413i | \(-0.418516\pi\) | ||||
0.253204 | + | 0.967413i | \(0.418516\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.62655e11 | −0.0308317 | ||||||||
\(886\) | 7.02575e9 | 0.000383037 0 | ||||||||
\(887\) | 8.88742e12 | 0.482081 | 0.241040 | − | 0.970515i | \(-0.422511\pi\) | ||||
0.241040 | + | 0.970515i | \(0.422511\pi\) | |||||||
\(888\) | −2.03106e11 | −0.0109614 | ||||||||
\(889\) | 9.91422e12 | 0.532354 | ||||||||
\(890\) | 2.25209e11 | 0.0120318 | ||||||||
\(891\) | −6.09482e12 | −0.323975 | ||||||||
\(892\) | 2.38585e13 | 1.26183 | ||||||||
\(893\) | 3.58500e12 | 0.188650 | ||||||||
\(894\) | 1.53655e11 | 0.00804505 | ||||||||
\(895\) | 5.12604e12 | 0.267041 | ||||||||
\(896\) | 1.13723e12 | 0.0589471 | ||||||||
\(897\) | −2.15700e12 | −0.111246 | ||||||||
\(898\) | 3.18865e10 | 0.00163630 | ||||||||
\(899\) | 5.88742e12 | 0.300612 | ||||||||
\(900\) | −1.09906e13 | −0.558382 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −3.33145e11 | −0.0167573 | ||||||||
\(903\) | −1.06309e12 | −0.0532076 | ||||||||
\(904\) | −1.58597e11 | −0.00789837 | ||||||||
\(905\) | −1.96633e13 | −0.974401 | ||||||||
\(906\) | 1.76301e11 | 0.00869315 | ||||||||
\(907\) | 1.73486e13 | 0.851202 | 0.425601 | − | 0.904911i | \(-0.360063\pi\) | ||||
0.425601 | + | 0.904911i | \(0.360063\pi\) | |||||||
\(908\) | 3.61278e13 | 1.76382 | ||||||||
\(909\) | 1.42224e13 | 0.690930 | ||||||||
\(910\) | −9.56361e10 | −0.00462313 | ||||||||
\(911\) | −1.37894e12 | −0.0663302 | −0.0331651 | − | 0.999450i | \(-0.510559\pi\) | ||||
−0.0331651 | + | 0.999450i | \(0.510559\pi\) | |||||||
\(912\) | 8.98358e11 | 0.0430004 | ||||||||
\(913\) | −8.74603e11 | −0.0416574 | ||||||||
\(914\) | 3.85033e11 | 0.0182490 | ||||||||
\(915\) | −3.49697e12 | −0.164929 | ||||||||
\(916\) | 3.09601e13 | 1.45302 | ||||||||
\(917\) | −2.60299e12 | −0.121566 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.85500e13 | −1.32034 | −0.660170 | − | 0.751116i | \(-0.729516\pi\) | ||||
−0.660170 | + | 0.751116i | \(0.729516\pi\) | |||||||
\(920\) | −9.50205e11 | −0.0437293 | ||||||||
\(921\) | −3.53260e10 | −0.00161781 | ||||||||
\(922\) | 7.80905e11 | 0.0355884 | ||||||||
\(923\) | −5.58838e12 | −0.253442 | ||||||||
\(924\) | 8.35928e11 | 0.0377264 | ||||||||
\(925\) | 9.11539e12 | 0.409390 | ||||||||
\(926\) | −7.10153e11 | −0.0317397 | ||||||||
\(927\) | −3.06668e13 | −1.36398 | ||||||||
\(928\) | 2.44595e12 | 0.108263 | ||||||||
\(929\) | −1.97136e13 | −0.868351 | −0.434175 | − | 0.900828i | \(-0.642960\pi\) | ||||
−0.434175 | + | 0.900828i | \(0.642960\pi\) | |||||||
\(930\) | −3.30724e10 | −0.00144975 | ||||||||
\(931\) | 3.51649e12 | 0.153404 | ||||||||
\(932\) | −8.45454e12 | −0.367044 | ||||||||
\(933\) | −1.01104e13 | −0.436820 | ||||||||
\(934\) | 1.58547e12 | 0.0681707 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.48240e11 | 0.0318639 | ||||||||
\(937\) | 3.51151e13 | 1.48822 | 0.744108 | − | 0.668060i | \(-0.232875\pi\) | ||||
0.744108 | + | 0.668060i | \(0.232875\pi\) | |||||||
\(938\) | −2.41343e11 | −0.0101794 | ||||||||
\(939\) | −6.27250e11 | −0.0263297 | ||||||||
\(940\) | 1.53573e13 | 0.641564 | ||||||||
\(941\) | 2.11548e13 | 0.879540 | 0.439770 | − | 0.898110i | \(-0.355060\pi\) | ||||
0.439770 | + | 0.898110i | \(0.355060\pi\) | |||||||
\(942\) | −2.23906e11 | −0.00926482 | ||||||||
\(943\) | 3.05624e13 | 1.25859 | ||||||||
\(944\) | 5.10158e12 | 0.209089 | ||||||||
\(945\) | −3.01013e12 | −0.122784 | ||||||||
\(946\) | 1.75789e11 | 0.00713644 | ||||||||
\(947\) | −3.76128e13 | −1.51971 | −0.759854 | − | 0.650093i | \(-0.774730\pi\) | ||||
−0.759854 | + | 0.650093i | \(0.774730\pi\) | |||||||
\(948\) | −2.51291e12 | −0.101051 | ||||||||
\(949\) | 1.39754e13 | 0.559329 | ||||||||
\(950\) | 9.59479e10 | 0.00382190 | ||||||||
\(951\) | 4.44730e12 | 0.176313 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.31338e13 | −1.30123 | −0.650613 | − | 0.759410i | \(-0.725488\pi\) | ||||
−0.650613 | + | 0.759410i | \(0.725488\pi\) | |||||||
\(954\) | −1.35281e12 | −0.0528773 | ||||||||
\(955\) | 2.33422e13 | 0.908086 | ||||||||
\(956\) | −4.57617e13 | −1.77191 | ||||||||
\(957\) | 2.39673e12 | 0.0923668 | ||||||||
\(958\) | 1.01409e12 | 0.0388984 | ||||||||
\(959\) | −3.83514e12 | −0.146419 | ||||||||
\(960\) | 3.83919e12 | 0.145888 | ||||||||
\(961\) | −2.42700e13 | −0.917940 | ||||||||
\(962\) | −3.10103e11 | −0.0116740 | ||||||||
\(963\) | 1.99760e13 | 0.748499 | ||||||||
\(964\) | 3.00338e13 | 1.12012 | ||||||||
\(965\) | −2.49787e13 | −0.927250 | ||||||||
\(966\) | 9.10863e10 | 0.00336555 | ||||||||
\(967\) | −1.59894e13 | −0.588047 | −0.294023 | − | 0.955798i | \(-0.594994\pi\) | ||||
−0.294023 | + | 0.955798i | \(0.594994\pi\) | |||||||
\(968\) | 1.60408e12 | 0.0587200 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.39619e11 | −0.0231979 | ||||||||
\(971\) | 4.36090e13 | 1.57431 | 0.787154 | − | 0.616756i | \(-0.211554\pi\) | ||||
0.787154 | + | 0.616756i | \(0.211554\pi\) | |||||||
\(972\) | 1.78117e13 | 0.640041 | ||||||||
\(973\) | 1.22836e13 | 0.439356 | ||||||||
\(974\) | −1.16664e12 | −0.0415356 | ||||||||
\(975\) | 1.86717e12 | 0.0661702 | ||||||||
\(976\) | 3.17069e13 | 1.11848 | ||||||||
\(977\) | 2.51816e13 | 0.884213 | 0.442107 | − | 0.896962i | \(-0.354231\pi\) | ||||
0.442107 | + | 0.896962i | \(0.354231\pi\) | |||||||
\(978\) | −3.56279e11 | −0.0124528 | ||||||||
\(979\) | −6.01455e12 | −0.209257 | ||||||||
\(980\) | 1.50639e13 | 0.521698 | ||||||||
\(981\) | 7.71726e12 | 0.266044 | ||||||||
\(982\) | −1.37071e12 | −0.0470375 | ||||||||
\(983\) | 3.06207e13 | 1.04598 | 0.522992 | − | 0.852338i | \(-0.324816\pi\) | ||||
0.522992 | + | 0.852338i | \(0.324816\pi\) | |||||||
\(984\) | 5.89479e11 | 0.0200443 | ||||||||
\(985\) | 1.97791e13 | 0.669490 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.94604e12 | −0.0988125 | ||||||||
\(988\) | 2.74813e12 | 0.0917551 | ||||||||
\(989\) | −1.61267e13 | −0.535998 | ||||||||
\(990\) | 2.42142e11 | 0.00801145 | ||||||||
\(991\) | −3.59113e12 | −0.118277 | −0.0591385 | − | 0.998250i | \(-0.518835\pi\) | ||||
−0.0591385 | + | 0.998250i | \(0.518835\pi\) | |||||||
\(992\) | 9.01383e11 | 0.0295534 | ||||||||
\(993\) | −8.37322e11 | −0.0273288 | ||||||||
\(994\) | 2.35987e11 | 0.00766742 | ||||||||
\(995\) | 1.34970e13 | 0.436550 | ||||||||
\(996\) | 7.73318e11 | 0.0248995 | ||||||||
\(997\) | 1.79571e13 | 0.575582 | 0.287791 | − | 0.957693i | \(-0.407079\pi\) | ||||
0.287791 | + | 0.957693i | \(0.407079\pi\) | |||||||
\(998\) | 1.69098e12 | 0.0539575 | ||||||||
\(999\) | −9.76044e12 | −0.310045 |
(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 | 289.10.a.d.1.6 | ✓ | 12 | |
17.16 | even | 2 | 289.10.a.e.1.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.d.1.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
289.10.a.e.1.6 | yes | 12 | 17.16 | even | 2 |