Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(46.8682610909\) |
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: | \( x^{12} - 3 x^{11} - 4522 x^{10} + 11094 x^{9} + 7471016 x^{8} - 18339296 x^{7} - 5497728352 x^{6} + 13724467264 x^{5} + 1698856105344 x^{4} + \cdots + 170905444356096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(31.8951\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 29.8951 | 1.32119 | 0.660595 | − | 0.750743i | \(-0.270304\pi\) | ||||
0.660595 | + | 0.750743i | \(0.270304\pi\) | |||||||
\(3\) | −70.1432 | −0.499965 | −0.249983 | − | 0.968250i | \(-0.580425\pi\) | ||||
−0.249983 | + | 0.968250i | \(0.580425\pi\) | |||||||
\(4\) | 381.717 | 0.745541 | ||||||||
\(5\) | 1113.83 | 0.796991 | 0.398496 | − | 0.917170i | \(-0.369532\pi\) | ||||
0.398496 | + | 0.917170i | \(0.369532\pi\) | |||||||
\(6\) | −2096.94 | −0.660549 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | −3894.82 | −0.336188 | ||||||||
\(9\) | −14762.9 | −0.750035 | ||||||||
\(10\) | 33298.0 | 1.05298 | ||||||||
\(11\) | −33485.4 | −0.689585 | −0.344793 | − | 0.938679i | \(-0.612051\pi\) | ||||
−0.344793 | + | 0.938679i | \(0.612051\pi\) | |||||||
\(12\) | −26774.9 | −0.372745 | ||||||||
\(13\) | 28561.0 | 0.277350 | ||||||||
\(14\) | 71778.1 | 0.499363 | ||||||||
\(15\) | −78127.5 | −0.398468 | ||||||||
\(16\) | −311875. | −1.18971 | ||||||||
\(17\) | −157227. | −0.456569 | −0.228285 | − | 0.973594i | \(-0.573312\pi\) | ||||
−0.228285 | + | 0.973594i | \(0.573312\pi\) | |||||||
\(18\) | −441339. | −0.990938 | ||||||||
\(19\) | 309963. | 0.545655 | 0.272828 | − | 0.962063i | \(-0.412041\pi\) | ||||
0.272828 | + | 0.962063i | \(0.412041\pi\) | |||||||
\(20\) | 425168. | 0.594190 | ||||||||
\(21\) | −168414. | −0.188969 | ||||||||
\(22\) | −1.00105e6 | −0.911073 | ||||||||
\(23\) | −796674. | −0.593616 | −0.296808 | − | 0.954937i | \(-0.595922\pi\) | ||||
−0.296808 | + | 0.954937i | \(0.595922\pi\) | |||||||
\(24\) | 273195. | 0.168082 | ||||||||
\(25\) | −712510. | −0.364805 | ||||||||
\(26\) | 853834. | 0.366432 | ||||||||
\(27\) | 2.41615e6 | 0.874957 | ||||||||
\(28\) | 916503. | 0.281788 | ||||||||
\(29\) | −1.10860e6 | −0.291060 | −0.145530 | − | 0.989354i | \(-0.546489\pi\) | ||||
−0.145530 | + | 0.989354i | \(0.546489\pi\) | |||||||
\(30\) | −2.33563e6 | −0.526452 | ||||||||
\(31\) | −2.97639e6 | −0.578845 | −0.289423 | − | 0.957201i | \(-0.593463\pi\) | ||||
−0.289423 | + | 0.957201i | \(0.593463\pi\) | |||||||
\(32\) | −7.32939e6 | −1.23564 | ||||||||
\(33\) | 2.34877e6 | 0.344769 | ||||||||
\(34\) | −4.70031e6 | −0.603214 | ||||||||
\(35\) | 2.67430e6 | 0.301234 | ||||||||
\(36\) | −5.63526e6 | −0.559182 | ||||||||
\(37\) | 4.80851e6 | 0.421797 | 0.210898 | − | 0.977508i | \(-0.432361\pi\) | ||||
0.210898 | + | 0.977508i | \(0.432361\pi\) | |||||||
\(38\) | 9.26637e6 | 0.720914 | ||||||||
\(39\) | −2.00336e6 | −0.138665 | ||||||||
\(40\) | −4.33816e6 | −0.267939 | ||||||||
\(41\) | −2.00231e7 | −1.10664 | −0.553318 | − | 0.832970i | \(-0.686638\pi\) | ||||
−0.553318 | + | 0.832970i | \(0.686638\pi\) | |||||||
\(42\) | −5.03475e6 | −0.249664 | ||||||||
\(43\) | −3.06223e7 | −1.36593 | −0.682966 | − | 0.730450i | \(-0.739310\pi\) | ||||
−0.682966 | + | 0.730450i | \(0.739310\pi\) | |||||||
\(44\) | −1.27819e7 | −0.514114 | ||||||||
\(45\) | −1.64434e7 | −0.597771 | ||||||||
\(46\) | −2.38167e7 | −0.784279 | ||||||||
\(47\) | −6.06687e7 | −1.81353 | −0.906764 | − | 0.421638i | \(-0.861455\pi\) | ||||
−0.906764 | + | 0.421638i | \(0.861455\pi\) | |||||||
\(48\) | 2.18759e7 | 0.594814 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −2.13006e7 | −0.481977 | ||||||||
\(51\) | 1.10284e7 | 0.228269 | ||||||||
\(52\) | 1.09022e7 | 0.206776 | ||||||||
\(53\) | −4.36135e7 | −0.759241 | −0.379620 | − | 0.925142i | \(-0.623945\pi\) | ||||
−0.379620 | + | 0.925142i | \(0.623945\pi\) | |||||||
\(54\) | 7.22310e7 | 1.15598 | ||||||||
\(55\) | −3.72970e7 | −0.549593 | ||||||||
\(56\) | −9.35146e6 | −0.127067 | ||||||||
\(57\) | −2.17418e7 | −0.272809 | ||||||||
\(58\) | −3.31416e7 | −0.384545 | ||||||||
\(59\) | −3.11877e6 | −0.0335081 | −0.0167540 | − | 0.999860i | \(-0.505333\pi\) | ||||
−0.0167540 | + | 0.999860i | \(0.505333\pi\) | |||||||
\(60\) | −2.98226e7 | −0.297074 | ||||||||
\(61\) | 3.50947e6 | 0.0324532 | 0.0162266 | − | 0.999868i | \(-0.494835\pi\) | ||||
0.0162266 | + | 0.999868i | \(0.494835\pi\) | |||||||
\(62\) | −8.89795e7 | −0.764764 | ||||||||
\(63\) | −3.54458e7 | −0.283486 | ||||||||
\(64\) | −5.94328e7 | −0.442809 | ||||||||
\(65\) | 3.18121e7 | 0.221046 | ||||||||
\(66\) | 7.02168e7 | 0.455505 | ||||||||
\(67\) | 2.57742e8 | 1.56260 | 0.781302 | − | 0.624154i | \(-0.214556\pi\) | ||||
0.781302 | + | 0.624154i | \(0.214556\pi\) | |||||||
\(68\) | −6.00162e7 | −0.340391 | ||||||||
\(69\) | 5.58813e7 | 0.296787 | ||||||||
\(70\) | 7.99486e7 | 0.397988 | ||||||||
\(71\) | −1.34306e8 | −0.627237 | −0.313619 | − | 0.949549i | \(-0.601541\pi\) | ||||
−0.313619 | + | 0.949549i | \(0.601541\pi\) | |||||||
\(72\) | 5.74990e7 | 0.252153 | ||||||||
\(73\) | 2.83905e8 | 1.17009 | 0.585047 | − | 0.810999i | \(-0.301076\pi\) | ||||
0.585047 | + | 0.810999i | \(0.301076\pi\) | |||||||
\(74\) | 1.43751e8 | 0.557273 | ||||||||
\(75\) | 4.99777e7 | 0.182390 | ||||||||
\(76\) | 1.18318e8 | 0.406808 | ||||||||
\(77\) | −8.03984e7 | −0.260639 | ||||||||
\(78\) | −5.98906e7 | −0.183203 | ||||||||
\(79\) | 1.55074e7 | 0.0447936 | 0.0223968 | − | 0.999749i | \(-0.492870\pi\) | ||||
0.0223968 | + | 0.999749i | \(0.492870\pi\) | |||||||
\(80\) | −3.47376e8 | −0.948188 | ||||||||
\(81\) | 1.21102e8 | 0.312587 | ||||||||
\(82\) | −5.98593e8 | −1.46207 | ||||||||
\(83\) | 4.31445e8 | 0.997869 | 0.498935 | − | 0.866640i | \(-0.333725\pi\) | ||||
0.498935 | + | 0.866640i | \(0.333725\pi\) | |||||||
\(84\) | −6.42864e7 | −0.140884 | ||||||||
\(85\) | −1.75124e8 | −0.363881 | ||||||||
\(86\) | −9.15456e8 | −1.80466 | ||||||||
\(87\) | 7.77605e7 | 0.145520 | ||||||||
\(88\) | 1.30420e8 | 0.231831 | ||||||||
\(89\) | −5.70691e8 | −0.964153 | −0.482076 | − | 0.876129i | \(-0.660117\pi\) | ||||
−0.482076 | + | 0.876129i | \(0.660117\pi\) | |||||||
\(90\) | −4.91577e8 | −0.789769 | ||||||||
\(91\) | 6.85750e7 | 0.104828 | ||||||||
\(92\) | −3.04104e8 | −0.442565 | ||||||||
\(93\) | 2.08774e8 | 0.289403 | ||||||||
\(94\) | −1.81370e9 | −2.39601 | ||||||||
\(95\) | 3.45246e8 | 0.434882 | ||||||||
\(96\) | 5.14107e8 | 0.617779 | ||||||||
\(97\) | 2.89619e7 | 0.0332165 | 0.0166083 | − | 0.999862i | \(-0.494713\pi\) | ||||
0.0166083 | + | 0.999862i | \(0.494713\pi\) | |||||||
\(98\) | 1.72339e8 | 0.188741 | ||||||||
\(99\) | 4.94342e8 | 0.517213 | ||||||||
\(100\) | −2.71977e8 | −0.271977 | ||||||||
\(101\) | −4.10378e8 | −0.392408 | −0.196204 | − | 0.980563i | \(-0.562861\pi\) | ||||
−0.196204 | + | 0.980563i | \(0.562861\pi\) | |||||||
\(102\) | 3.29695e8 | 0.301586 | ||||||||
\(103\) | −4.17058e8 | −0.365114 | −0.182557 | − | 0.983195i | \(-0.558437\pi\) | ||||
−0.182557 | + | 0.983195i | \(0.558437\pi\) | |||||||
\(104\) | −1.11240e8 | −0.0932418 | ||||||||
\(105\) | −1.87584e8 | −0.150607 | ||||||||
\(106\) | −1.30383e9 | −1.00310 | ||||||||
\(107\) | −3.24207e7 | −0.0239108 | −0.0119554 | − | 0.999929i | \(-0.503806\pi\) | ||||
−0.0119554 | + | 0.999929i | \(0.503806\pi\) | |||||||
\(108\) | 9.22285e8 | 0.652316 | ||||||||
\(109\) | 2.58850e9 | 1.75642 | 0.878209 | − | 0.478276i | \(-0.158738\pi\) | ||||
0.878209 | + | 0.478276i | \(0.158738\pi\) | |||||||
\(110\) | −1.11500e9 | −0.726117 | ||||||||
\(111\) | −3.37285e8 | −0.210884 | ||||||||
\(112\) | −7.48812e8 | −0.449668 | ||||||||
\(113\) | 9.93406e8 | 0.573157 | 0.286579 | − | 0.958057i | \(-0.407482\pi\) | ||||
0.286579 | + | 0.958057i | \(0.407482\pi\) | |||||||
\(114\) | −6.49973e8 | −0.360432 | ||||||||
\(115\) | −8.87359e8 | −0.473107 | ||||||||
\(116\) | −4.23170e8 | −0.216997 | ||||||||
\(117\) | −4.21644e8 | −0.208022 | ||||||||
\(118\) | −9.32359e7 | −0.0442705 | ||||||||
\(119\) | −3.77502e8 | −0.172567 | ||||||||
\(120\) | 3.04293e8 | 0.133960 | ||||||||
\(121\) | −1.23668e9 | −0.524472 | ||||||||
\(122\) | 1.04916e8 | 0.0428768 | ||||||||
\(123\) | 1.40449e9 | 0.553279 | ||||||||
\(124\) | −1.13614e9 | −0.431553 | ||||||||
\(125\) | −2.96906e9 | −1.08774 | ||||||||
\(126\) | −1.05966e9 | −0.374539 | ||||||||
\(127\) | −2.79338e8 | −0.0952824 | −0.0476412 | − | 0.998865i | \(-0.515170\pi\) | ||||
−0.0476412 | + | 0.998865i | \(0.515170\pi\) | |||||||
\(128\) | 1.97590e9 | 0.650609 | ||||||||
\(129\) | 2.14794e9 | 0.682919 | ||||||||
\(130\) | 9.51025e8 | 0.292043 | ||||||||
\(131\) | 3.52969e9 | 1.04717 | 0.523583 | − | 0.851975i | \(-0.324595\pi\) | ||||
0.523583 | + | 0.851975i | \(0.324595\pi\) | |||||||
\(132\) | 8.96566e8 | 0.257039 | ||||||||
\(133\) | 7.44221e8 | 0.206238 | ||||||||
\(134\) | 7.70523e9 | 2.06449 | ||||||||
\(135\) | 2.69118e9 | 0.697333 | ||||||||
\(136\) | 6.12370e8 | 0.153493 | ||||||||
\(137\) | −8.74657e7 | −0.0212127 | −0.0106063 | − | 0.999944i | \(-0.503376\pi\) | ||||
−0.0106063 | + | 0.999944i | \(0.503376\pi\) | |||||||
\(138\) | 1.67058e9 | 0.392112 | ||||||||
\(139\) | 2.64429e9 | 0.600818 | 0.300409 | − | 0.953811i | \(-0.402877\pi\) | ||||
0.300409 | + | 0.953811i | \(0.402877\pi\) | |||||||
\(140\) | 1.02083e9 | 0.224583 | ||||||||
\(141\) | 4.25550e9 | 0.906701 | ||||||||
\(142\) | −4.01508e9 | −0.828699 | ||||||||
\(143\) | −9.56376e8 | −0.191257 | ||||||||
\(144\) | 4.60419e9 | 0.892323 | ||||||||
\(145\) | −1.23479e9 | −0.231972 | ||||||||
\(146\) | 8.48738e9 | 1.54592 | ||||||||
\(147\) | −4.04362e8 | −0.0714236 | ||||||||
\(148\) | 1.83549e9 | 0.314467 | ||||||||
\(149\) | 5.42368e9 | 0.901480 | 0.450740 | − | 0.892655i | \(-0.351160\pi\) | ||||
0.450740 | + | 0.892655i | \(0.351160\pi\) | |||||||
\(150\) | 1.49409e9 | 0.240972 | ||||||||
\(151\) | 1.01732e9 | 0.159243 | 0.0796215 | − | 0.996825i | \(-0.474629\pi\) | ||||
0.0796215 | + | 0.996825i | \(0.474629\pi\) | |||||||
\(152\) | −1.20725e9 | −0.183443 | ||||||||
\(153\) | 2.32113e9 | 0.342443 | ||||||||
\(154\) | −2.40352e9 | −0.344353 | ||||||||
\(155\) | −3.31519e9 | −0.461334 | ||||||||
\(156\) | −7.64717e8 | −0.103381 | ||||||||
\(157\) | 9.64063e9 | 1.26636 | 0.633180 | − | 0.774005i | \(-0.281749\pi\) | ||||
0.633180 | + | 0.774005i | \(0.281749\pi\) | |||||||
\(158\) | 4.63594e8 | 0.0591808 | ||||||||
\(159\) | 3.05919e9 | 0.379594 | ||||||||
\(160\) | −8.16369e9 | −0.984797 | ||||||||
\(161\) | −1.91282e9 | −0.224366 | ||||||||
\(162\) | 3.62037e9 | 0.412986 | ||||||||
\(163\) | 3.18440e9 | 0.353332 | 0.176666 | − | 0.984271i | \(-0.443469\pi\) | ||||
0.176666 | + | 0.984271i | \(0.443469\pi\) | |||||||
\(164\) | −7.64317e9 | −0.825042 | ||||||||
\(165\) | 2.61613e9 | 0.274778 | ||||||||
\(166\) | 1.28981e10 | 1.31837 | ||||||||
\(167\) | −3.55621e9 | −0.353805 | −0.176902 | − | 0.984228i | \(-0.556608\pi\) | ||||
−0.176902 | + | 0.984228i | \(0.556608\pi\) | |||||||
\(168\) | 6.55942e8 | 0.0635292 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | −5.23534e9 | −0.480756 | ||||||||
\(171\) | −4.57596e9 | −0.409260 | ||||||||
\(172\) | −1.16890e10 | −1.01836 | ||||||||
\(173\) | −1.13899e10 | −0.966749 | −0.483375 | − | 0.875414i | \(-0.660589\pi\) | ||||
−0.483375 | + | 0.875414i | \(0.660589\pi\) | |||||||
\(174\) | 2.32466e9 | 0.192259 | ||||||||
\(175\) | −1.71074e9 | −0.137883 | ||||||||
\(176\) | 1.04433e10 | 0.820406 | ||||||||
\(177\) | 2.18760e8 | 0.0167529 | ||||||||
\(178\) | −1.70609e10 | −1.27383 | ||||||||
\(179\) | 7.23644e9 | 0.526849 | 0.263425 | − | 0.964680i | \(-0.415148\pi\) | ||||
0.263425 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(180\) | −6.27672e9 | −0.445663 | ||||||||
\(181\) | −5.99941e9 | −0.415484 | −0.207742 | − | 0.978184i | \(-0.566612\pi\) | ||||
−0.207742 | + | 0.978184i | \(0.566612\pi\) | |||||||
\(182\) | 2.05006e9 | 0.138498 | ||||||||
\(183\) | −2.46165e8 | −0.0162255 | ||||||||
\(184\) | 3.10290e9 | 0.199567 | ||||||||
\(185\) | 5.35586e9 | 0.336168 | ||||||||
\(186\) | 6.24131e9 | 0.382356 | ||||||||
\(187\) | 5.26480e9 | 0.314843 | ||||||||
\(188\) | −2.31583e10 | −1.35206 | ||||||||
\(189\) | 5.80117e9 | 0.330703 | ||||||||
\(190\) | 1.03211e10 | 0.574562 | ||||||||
\(191\) | −2.95421e10 | −1.60617 | −0.803084 | − | 0.595866i | \(-0.796809\pi\) | ||||
−0.803084 | + | 0.595866i | \(0.796809\pi\) | |||||||
\(192\) | 4.16881e9 | 0.221389 | ||||||||
\(193\) | −1.89971e9 | −0.0985552 | −0.0492776 | − | 0.998785i | \(-0.515692\pi\) | ||||
−0.0492776 | + | 0.998785i | \(0.515692\pi\) | |||||||
\(194\) | 8.65818e8 | 0.0438853 | ||||||||
\(195\) | −2.23140e9 | −0.110515 | ||||||||
\(196\) | 2.20052e9 | 0.106506 | ||||||||
\(197\) | −1.73402e10 | −0.820271 | −0.410135 | − | 0.912025i | \(-0.634519\pi\) | ||||
−0.410135 | + | 0.912025i | \(0.634519\pi\) | |||||||
\(198\) | 1.47784e10 | 0.683336 | ||||||||
\(199\) | −1.86147e10 | −0.841427 | −0.420714 | − | 0.907194i | \(-0.638220\pi\) | ||||
−0.420714 | + | 0.907194i | \(0.638220\pi\) | |||||||
\(200\) | 2.77510e9 | 0.122643 | ||||||||
\(201\) | −1.80789e10 | −0.781247 | ||||||||
\(202\) | −1.22683e10 | −0.518445 | ||||||||
\(203\) | −2.66174e9 | −0.110010 | ||||||||
\(204\) | 4.20973e9 | 0.170184 | ||||||||
\(205\) | −2.23023e10 | −0.881978 | ||||||||
\(206\) | −1.24680e10 | −0.482385 | ||||||||
\(207\) | 1.17613e10 | 0.445233 | ||||||||
\(208\) | −8.90747e9 | −0.329966 | ||||||||
\(209\) | −1.03792e10 | −0.376276 | ||||||||
\(210\) | −5.60785e9 | −0.198980 | ||||||||
\(211\) | 4.92241e10 | 1.70965 | 0.854823 | − | 0.518919i | \(-0.173665\pi\) | ||||
0.854823 | + | 0.518919i | \(0.173665\pi\) | |||||||
\(212\) | −1.66480e10 | −0.566045 | ||||||||
\(213\) | 9.42063e9 | 0.313597 | ||||||||
\(214\) | −9.69219e8 | −0.0315907 | ||||||||
\(215\) | −3.41080e10 | −1.08864 | ||||||||
\(216\) | −9.41046e9 | −0.294150 | ||||||||
\(217\) | −7.14632e9 | −0.218783 | ||||||||
\(218\) | 7.73833e10 | 2.32056 | ||||||||
\(219\) | −1.99140e10 | −0.585006 | ||||||||
\(220\) | −1.42369e10 | −0.409745 | ||||||||
\(221\) | −4.49056e9 | −0.126629 | ||||||||
\(222\) | −1.00832e10 | −0.278617 | ||||||||
\(223\) | −4.21527e10 | −1.14144 | −0.570721 | − | 0.821144i | \(-0.693336\pi\) | ||||
−0.570721 | + | 0.821144i | \(0.693336\pi\) | |||||||
\(224\) | −1.75979e10 | −0.467029 | ||||||||
\(225\) | 1.05187e10 | 0.273617 | ||||||||
\(226\) | 2.96980e10 | 0.757249 | ||||||||
\(227\) | 3.70523e10 | 0.926188 | 0.463094 | − | 0.886309i | \(-0.346739\pi\) | ||||
0.463094 | + | 0.886309i | \(0.346739\pi\) | |||||||
\(228\) | −8.29921e9 | −0.203390 | ||||||||
\(229\) | −5.49043e10 | −1.31931 | −0.659654 | − | 0.751569i | \(-0.729297\pi\) | ||||
−0.659654 | + | 0.751569i | \(0.729297\pi\) | |||||||
\(230\) | −2.65277e10 | −0.625063 | ||||||||
\(231\) | 5.63940e9 | 0.130310 | ||||||||
\(232\) | 4.31778e9 | 0.0978509 | ||||||||
\(233\) | −4.97221e10 | −1.10522 | −0.552609 | − | 0.833441i | \(-0.686368\pi\) | ||||
−0.552609 | + | 0.833441i | \(0.686368\pi\) | |||||||
\(234\) | −1.26051e10 | −0.274837 | ||||||||
\(235\) | −6.75746e10 | −1.44537 | ||||||||
\(236\) | −1.19049e9 | −0.0249816 | ||||||||
\(237\) | −1.08774e9 | −0.0223952 | ||||||||
\(238\) | −1.12854e10 | −0.227994 | ||||||||
\(239\) | 7.56250e10 | 1.49925 | 0.749627 | − | 0.661861i | \(-0.230233\pi\) | ||||
0.749627 | + | 0.661861i | \(0.230233\pi\) | |||||||
\(240\) | 2.43660e10 | 0.474061 | ||||||||
\(241\) | 1.96589e10 | 0.375389 | 0.187694 | − | 0.982227i | \(-0.439899\pi\) | ||||
0.187694 | + | 0.982227i | \(0.439899\pi\) | |||||||
\(242\) | −3.69706e10 | −0.692927 | ||||||||
\(243\) | −5.60516e10 | −1.03124 | ||||||||
\(244\) | 1.33962e9 | 0.0241952 | ||||||||
\(245\) | 6.42100e9 | 0.113856 | ||||||||
\(246\) | 4.19873e10 | 0.730987 | ||||||||
\(247\) | 8.85285e9 | 0.151338 | ||||||||
\(248\) | 1.15925e10 | 0.194601 | ||||||||
\(249\) | −3.02629e10 | −0.498900 | ||||||||
\(250\) | −8.87604e10 | −1.43711 | ||||||||
\(251\) | 8.25702e10 | 1.31308 | 0.656540 | − | 0.754291i | \(-0.272019\pi\) | ||||
0.656540 | + | 0.754291i | \(0.272019\pi\) | |||||||
\(252\) | −1.35303e10 | −0.211351 | ||||||||
\(253\) | 2.66769e10 | 0.409349 | ||||||||
\(254\) | −8.35083e9 | −0.125886 | ||||||||
\(255\) | 1.22837e10 | 0.181928 | ||||||||
\(256\) | 8.94993e10 | 1.30239 | ||||||||
\(257\) | −3.85626e10 | −0.551401 | −0.275700 | − | 0.961244i | \(-0.588910\pi\) | ||||
−0.275700 | + | 0.961244i | \(0.588910\pi\) | |||||||
\(258\) | 6.42130e10 | 0.902265 | ||||||||
\(259\) | 1.15452e10 | 0.159424 | ||||||||
\(260\) | 1.21432e10 | 0.164799 | ||||||||
\(261\) | 1.63661e10 | 0.218305 | ||||||||
\(262\) | 1.05520e11 | 1.38350 | ||||||||
\(263\) | 7.66052e10 | 0.987318 | 0.493659 | − | 0.869655i | \(-0.335659\pi\) | ||||
0.493659 | + | 0.869655i | \(0.335659\pi\) | |||||||
\(264\) | −9.14804e9 | −0.115907 | ||||||||
\(265\) | −4.85780e10 | −0.605108 | ||||||||
\(266\) | 2.22486e10 | 0.272480 | ||||||||
\(267\) | 4.00301e10 | 0.482043 | ||||||||
\(268\) | 9.83846e10 | 1.16499 | ||||||||
\(269\) | 1.41446e11 | 1.64705 | 0.823525 | − | 0.567280i | \(-0.192004\pi\) | ||||
0.823525 | + | 0.567280i | \(0.192004\pi\) | |||||||
\(270\) | 8.04530e10 | 0.921308 | ||||||||
\(271\) | −1.05413e11 | −1.18722 | −0.593612 | − | 0.804752i | \(-0.702298\pi\) | ||||
−0.593612 | + | 0.804752i | \(0.702298\pi\) | |||||||
\(272\) | 4.90351e10 | 0.543185 | ||||||||
\(273\) | −4.81007e9 | −0.0524106 | ||||||||
\(274\) | −2.61480e9 | −0.0280260 | ||||||||
\(275\) | 2.38587e10 | 0.251564 | ||||||||
\(276\) | 2.13308e10 | 0.221267 | ||||||||
\(277\) | −1.83792e11 | −1.87572 | −0.937861 | − | 0.347012i | \(-0.887196\pi\) | ||||
−0.937861 | + | 0.347012i | \(0.887196\pi\) | |||||||
\(278\) | 7.90514e10 | 0.793794 | ||||||||
\(279\) | 4.39403e10 | 0.434154 | ||||||||
\(280\) | −1.04159e10 | −0.101271 | ||||||||
\(281\) | −1.34769e11 | −1.28947 | −0.644734 | − | 0.764407i | \(-0.723032\pi\) | ||||
−0.644734 | + | 0.764407i | \(0.723032\pi\) | |||||||
\(282\) | 1.27219e11 | 1.19792 | ||||||||
\(283\) | 5.13736e10 | 0.476103 | 0.238052 | − | 0.971252i | \(-0.423491\pi\) | ||||
0.238052 | + | 0.971252i | \(0.423491\pi\) | |||||||
\(284\) | −5.12668e10 | −0.467631 | ||||||||
\(285\) | −2.42166e10 | −0.217426 | ||||||||
\(286\) | −2.85910e10 | −0.252686 | ||||||||
\(287\) | −4.80755e10 | −0.418269 | ||||||||
\(288\) | 1.08203e11 | 0.926775 | ||||||||
\(289\) | −9.38676e10 | −0.791545 | ||||||||
\(290\) | −3.69141e10 | −0.306479 | ||||||||
\(291\) | −2.03148e9 | −0.0166071 | ||||||||
\(292\) | 1.08372e11 | 0.872353 | ||||||||
\(293\) | −1.56721e11 | −1.24229 | −0.621147 | − | 0.783694i | \(-0.713333\pi\) | ||||
−0.621147 | + | 0.783694i | \(0.713333\pi\) | |||||||
\(294\) | −1.20884e10 | −0.0943641 | ||||||||
\(295\) | −3.47378e9 | −0.0267056 | ||||||||
\(296\) | −1.87283e10 | −0.141803 | ||||||||
\(297\) | −8.09056e10 | −0.603357 | ||||||||
\(298\) | 1.62142e11 | 1.19103 | ||||||||
\(299\) | −2.27538e10 | −0.164639 | ||||||||
\(300\) | 1.90774e10 | 0.135979 | ||||||||
\(301\) | −7.35240e10 | −0.516274 | ||||||||
\(302\) | 3.04128e10 | 0.210390 | ||||||||
\(303\) | 2.87852e10 | 0.196190 | ||||||||
\(304\) | −9.66697e10 | −0.649171 | ||||||||
\(305\) | 3.90895e9 | 0.0258649 | ||||||||
\(306\) | 6.93904e10 | 0.452432 | ||||||||
\(307\) | −1.92332e11 | −1.23574 | −0.617871 | − | 0.786279i | \(-0.712005\pi\) | ||||
−0.617871 | + | 0.786279i | \(0.712005\pi\) | |||||||
\(308\) | −3.06894e10 | −0.194317 | ||||||||
\(309\) | 2.92537e10 | 0.182544 | ||||||||
\(310\) | −9.91080e10 | −0.609510 | ||||||||
\(311\) | 1.48197e11 | 0.898290 | 0.449145 | − | 0.893459i | \(-0.351729\pi\) | ||||
0.449145 | + | 0.893459i | \(0.351729\pi\) | |||||||
\(312\) | 7.80273e9 | 0.0466177 | ||||||||
\(313\) | −8.52035e10 | −0.501774 | −0.250887 | − | 0.968016i | \(-0.580722\pi\) | ||||
−0.250887 | + | 0.968016i | \(0.580722\pi\) | |||||||
\(314\) | 2.88208e11 | 1.67310 | ||||||||
\(315\) | −3.94806e10 | −0.225936 | ||||||||
\(316\) | 5.91942e9 | 0.0333955 | ||||||||
\(317\) | −8.99689e10 | −0.500410 | −0.250205 | − | 0.968193i | \(-0.580498\pi\) | ||||
−0.250205 | + | 0.968193i | \(0.580498\pi\) | |||||||
\(318\) | 9.14548e10 | 0.501516 | ||||||||
\(319\) | 3.71218e10 | 0.200711 | ||||||||
\(320\) | −6.61980e10 | −0.352915 | ||||||||
\(321\) | 2.27409e9 | 0.0119546 | ||||||||
\(322\) | −5.71838e10 | −0.296430 | ||||||||
\(323\) | −4.87345e10 | −0.249129 | ||||||||
\(324\) | 4.62269e10 | 0.233046 | ||||||||
\(325\) | −2.03500e10 | −0.101179 | ||||||||
\(326\) | 9.51978e10 | 0.466818 | ||||||||
\(327\) | −1.81565e11 | −0.878149 | ||||||||
\(328\) | 7.79865e10 | 0.372038 | ||||||||
\(329\) | −1.45666e11 | −0.685449 | ||||||||
\(330\) | 7.82094e10 | 0.363033 | ||||||||
\(331\) | 8.80235e10 | 0.403063 | 0.201531 | − | 0.979482i | \(-0.435408\pi\) | ||||
0.201531 | + | 0.979482i | \(0.435408\pi\) | |||||||
\(332\) | 1.64690e11 | 0.743953 | ||||||||
\(333\) | −7.09878e10 | −0.316362 | ||||||||
\(334\) | −1.06313e11 | −0.467443 | ||||||||
\(335\) | 2.87081e11 | 1.24538 | ||||||||
\(336\) | 5.25241e10 | 0.224818 | ||||||||
\(337\) | 1.33487e11 | 0.563772 | 0.281886 | − | 0.959448i | \(-0.409040\pi\) | ||||
0.281886 | + | 0.959448i | \(0.409040\pi\) | |||||||
\(338\) | 2.43864e10 | 0.101630 | ||||||||
\(339\) | −6.96807e10 | −0.286559 | ||||||||
\(340\) | −6.68477e10 | −0.271289 | ||||||||
\(341\) | 9.96656e10 | 0.399163 | ||||||||
\(342\) | −1.36799e11 | −0.540710 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | 1.19268e11 | 0.459210 | ||||||||
\(345\) | 6.22422e10 | 0.236537 | ||||||||
\(346\) | −3.40503e11 | −1.27726 | ||||||||
\(347\) | −1.00900e11 | −0.373601 | −0.186801 | − | 0.982398i | \(-0.559812\pi\) | ||||
−0.186801 | + | 0.982398i | \(0.559812\pi\) | |||||||
\(348\) | 2.96825e10 | 0.108491 | ||||||||
\(349\) | −6.41636e10 | −0.231513 | −0.115756 | − | 0.993278i | \(-0.536929\pi\) | ||||
−0.115756 | + | 0.993278i | \(0.536929\pi\) | |||||||
\(350\) | −5.11427e10 | −0.182170 | ||||||||
\(351\) | 6.90076e10 | 0.242669 | ||||||||
\(352\) | 2.45427e11 | 0.852082 | ||||||||
\(353\) | −1.38158e11 | −0.473577 | −0.236788 | − | 0.971561i | \(-0.576095\pi\) | ||||
−0.236788 | + | 0.971561i | \(0.576095\pi\) | |||||||
\(354\) | 6.53987e9 | 0.0221337 | ||||||||
\(355\) | −1.49594e11 | −0.499902 | ||||||||
\(356\) | −2.17842e11 | −0.718816 | ||||||||
\(357\) | 2.64792e10 | 0.0862775 | ||||||||
\(358\) | 2.16334e11 | 0.696068 | ||||||||
\(359\) | −1.31907e10 | −0.0419125 | −0.0209563 | − | 0.999780i | \(-0.506671\pi\) | ||||
−0.0209563 | + | 0.999780i | \(0.506671\pi\) | |||||||
\(360\) | 6.40440e10 | 0.200964 | ||||||||
\(361\) | −2.26611e11 | −0.702260 | ||||||||
\(362\) | −1.79353e11 | −0.548934 | ||||||||
\(363\) | 8.67445e10 | 0.262218 | ||||||||
\(364\) | 2.61762e10 | 0.0781540 | ||||||||
\(365\) | 3.16222e11 | 0.932554 | ||||||||
\(366\) | −7.35914e9 | −0.0214369 | ||||||||
\(367\) | −5.69665e11 | −1.63916 | −0.819581 | − | 0.572963i | \(-0.805794\pi\) | ||||
−0.819581 | + | 0.572963i | \(0.805794\pi\) | |||||||
\(368\) | 2.48463e11 | 0.706231 | ||||||||
\(369\) | 2.95600e11 | 0.830015 | ||||||||
\(370\) | 1.60114e11 | 0.444142 | ||||||||
\(371\) | −1.04716e11 | −0.286966 | ||||||||
\(372\) | 7.96925e10 | 0.215762 | ||||||||
\(373\) | 4.96716e11 | 1.32867 | 0.664337 | − | 0.747433i | \(-0.268714\pi\) | ||||
0.664337 | + | 0.747433i | \(0.268714\pi\) | |||||||
\(374\) | 1.57392e11 | 0.415968 | ||||||||
\(375\) | 2.08259e11 | 0.543831 | ||||||||
\(376\) | 2.36294e11 | 0.609687 | ||||||||
\(377\) | −3.16626e10 | −0.0807255 | ||||||||
\(378\) | 1.73427e11 | 0.436921 | ||||||||
\(379\) | −7.50458e11 | −1.86832 | −0.934158 | − | 0.356861i | \(-0.883847\pi\) | ||||
−0.934158 | + | 0.356861i | \(0.883847\pi\) | |||||||
\(380\) | 1.31786e11 | 0.324223 | ||||||||
\(381\) | 1.95936e10 | 0.0476379 | ||||||||
\(382\) | −8.83164e11 | −2.12205 | ||||||||
\(383\) | 1.65558e11 | 0.393149 | 0.196574 | − | 0.980489i | \(-0.437018\pi\) | ||||
0.196574 | + | 0.980489i | \(0.437018\pi\) | |||||||
\(384\) | −1.38596e11 | −0.325282 | ||||||||
\(385\) | −8.95500e10 | −0.207727 | ||||||||
\(386\) | −5.67920e10 | −0.130210 | ||||||||
\(387\) | 4.52074e11 | 1.02450 | ||||||||
\(388\) | 1.10552e10 | 0.0247643 | ||||||||
\(389\) | 7.52301e11 | 1.66578 | 0.832891 | − | 0.553437i | \(-0.186684\pi\) | ||||
0.832891 | + | 0.553437i | \(0.186684\pi\) | |||||||
\(390\) | −6.67079e10 | −0.146011 | ||||||||
\(391\) | 1.25259e11 | 0.271027 | ||||||||
\(392\) | −2.24529e10 | −0.0480269 | ||||||||
\(393\) | −2.47583e11 | −0.523546 | ||||||||
\(394\) | −5.18388e11 | −1.08373 | ||||||||
\(395\) | 1.72725e10 | 0.0357001 | ||||||||
\(396\) | 1.88699e11 | 0.385604 | ||||||||
\(397\) | −5.82953e10 | −0.117781 | −0.0588906 | − | 0.998264i | \(-0.518756\pi\) | ||||
−0.0588906 | + | 0.998264i | \(0.518756\pi\) | |||||||
\(398\) | −5.56487e11 | −1.11168 | ||||||||
\(399\) | −5.22020e10 | −0.103112 | ||||||||
\(400\) | 2.22214e11 | 0.434012 | ||||||||
\(401\) | −1.84595e11 | −0.356508 | −0.178254 | − | 0.983984i | \(-0.557045\pi\) | ||||
−0.178254 | + | 0.983984i | \(0.557045\pi\) | |||||||
\(402\) | −5.40469e11 | −1.03218 | ||||||||
\(403\) | −8.50087e10 | −0.160543 | ||||||||
\(404\) | −1.56648e11 | −0.292556 | ||||||||
\(405\) | 1.34887e11 | 0.249129 | ||||||||
\(406\) | −7.95730e10 | −0.145344 | ||||||||
\(407\) | −1.61015e11 | −0.290865 | ||||||||
\(408\) | −4.29536e10 | −0.0767413 | ||||||||
\(409\) | −6.99412e11 | −1.23588 | −0.617942 | − | 0.786223i | \(-0.712034\pi\) | ||||
−0.617942 | + | 0.786223i | \(0.712034\pi\) | |||||||
\(410\) | −6.66731e11 | −1.16526 | ||||||||
\(411\) | 6.13512e9 | 0.0106056 | ||||||||
\(412\) | −1.59198e11 | −0.272208 | ||||||||
\(413\) | −7.48817e9 | −0.0126649 | ||||||||
\(414\) | 3.51604e11 | 0.588237 | ||||||||
\(415\) | 4.80555e11 | 0.795293 | ||||||||
\(416\) | −2.09335e11 | −0.342706 | ||||||||
\(417\) | −1.85479e11 | −0.300388 | ||||||||
\(418\) | −3.10288e11 | −0.497132 | ||||||||
\(419\) | −5.29034e11 | −0.838534 | −0.419267 | − | 0.907863i | \(-0.637713\pi\) | ||||
−0.419267 | + | 0.907863i | \(0.637713\pi\) | |||||||
\(420\) | −7.16041e10 | −0.112284 | ||||||||
\(421\) | −8.31929e11 | −1.29068 | −0.645338 | − | 0.763897i | \(-0.723283\pi\) | ||||
−0.645338 | + | 0.763897i | \(0.723283\pi\) | |||||||
\(422\) | 1.47156e12 | 2.25877 | ||||||||
\(423\) | 8.95648e11 | 1.36021 | ||||||||
\(424\) | 1.69867e11 | 0.255248 | ||||||||
\(425\) | 1.12026e11 | 0.166559 | ||||||||
\(426\) | 2.81631e11 | 0.414321 | ||||||||
\(427\) | 8.42624e9 | 0.0122662 | ||||||||
\(428\) | −1.23755e10 | −0.0178265 | ||||||||
\(429\) | 6.70833e10 | 0.0956217 | ||||||||
\(430\) | −1.01966e12 | −1.43829 | ||||||||
\(431\) | −6.35897e11 | −0.887645 | −0.443823 | − | 0.896115i | \(-0.646378\pi\) | ||||
−0.443823 | + | 0.896115i | \(0.646378\pi\) | |||||||
\(432\) | −7.53537e11 | −1.04094 | ||||||||
\(433\) | 9.71952e11 | 1.32877 | 0.664384 | − | 0.747392i | \(-0.268694\pi\) | ||||
0.664384 | + | 0.747392i | \(0.268694\pi\) | |||||||
\(434\) | −2.13640e11 | −0.289054 | ||||||||
\(435\) | 8.66119e10 | 0.115978 | ||||||||
\(436\) | 9.88073e11 | 1.30948 | ||||||||
\(437\) | −2.46939e11 | −0.323910 | ||||||||
\(438\) | −5.95332e11 | −0.772904 | ||||||||
\(439\) | 9.59753e11 | 1.23330 | 0.616651 | − | 0.787237i | \(-0.288489\pi\) | ||||
0.616651 | + | 0.787237i | \(0.288489\pi\) | |||||||
\(440\) | 1.45265e11 | 0.184767 | ||||||||
\(441\) | −8.51054e10 | −0.107148 | ||||||||
\(442\) | −1.34246e11 | −0.167302 | ||||||||
\(443\) | 4.97592e11 | 0.613842 | 0.306921 | − | 0.951735i | \(-0.400701\pi\) | ||||
0.306921 | + | 0.951735i | \(0.400701\pi\) | |||||||
\(444\) | −1.28747e11 | −0.157223 | ||||||||
\(445\) | −6.35652e11 | −0.768421 | ||||||||
\(446\) | −1.26016e12 | −1.50806 | ||||||||
\(447\) | −3.80434e11 | −0.450709 | ||||||||
\(448\) | −1.42698e11 | −0.167366 | ||||||||
\(449\) | −3.20380e11 | −0.372011 | −0.186006 | − | 0.982549i | \(-0.559554\pi\) | ||||
−0.186006 | + | 0.982549i | \(0.559554\pi\) | |||||||
\(450\) | 3.14459e11 | 0.361499 | ||||||||
\(451\) | 6.70482e11 | 0.763120 | ||||||||
\(452\) | 3.79200e11 | 0.427312 | ||||||||
\(453\) | −7.13579e10 | −0.0796160 | ||||||||
\(454\) | 1.10768e12 | 1.22367 | ||||||||
\(455\) | 7.63808e10 | 0.0835474 | ||||||||
\(456\) | 8.46803e10 | 0.0917151 | ||||||||
\(457\) | −1.61657e11 | −0.173370 | −0.0866848 | − | 0.996236i | \(-0.527627\pi\) | ||||
−0.0866848 | + | 0.996236i | \(0.527627\pi\) | |||||||
\(458\) | −1.64137e12 | −1.74306 | ||||||||
\(459\) | −3.79883e11 | −0.399478 | ||||||||
\(460\) | −3.38720e11 | −0.352721 | ||||||||
\(461\) | 8.13199e11 | 0.838576 | 0.419288 | − | 0.907853i | \(-0.362280\pi\) | ||||
0.419288 | + | 0.907853i | \(0.362280\pi\) | |||||||
\(462\) | 1.68590e11 | 0.172165 | ||||||||
\(463\) | 2.02415e11 | 0.204705 | 0.102353 | − | 0.994748i | \(-0.467363\pi\) | ||||
0.102353 | + | 0.994748i | \(0.467363\pi\) | |||||||
\(464\) | 3.45744e11 | 0.346277 | ||||||||
\(465\) | 2.32538e11 | 0.230651 | ||||||||
\(466\) | −1.48645e12 | −1.46020 | ||||||||
\(467\) | −3.73598e11 | −0.363478 | −0.181739 | − | 0.983347i | \(-0.558173\pi\) | ||||
−0.181739 | + | 0.983347i | \(0.558173\pi\) | |||||||
\(468\) | −1.60949e11 | −0.155089 | ||||||||
\(469\) | 6.18839e11 | 0.590608 | ||||||||
\(470\) | −2.02015e12 | −1.90960 | ||||||||
\(471\) | −6.76225e11 | −0.633136 | ||||||||
\(472\) | 1.21470e10 | 0.0112650 | ||||||||
\(473\) | 1.02540e12 | 0.941927 | ||||||||
\(474\) | −3.25180e10 | −0.0295883 | ||||||||
\(475\) | −2.20852e11 | −0.199058 | ||||||||
\(476\) | −1.44099e11 | −0.128656 | ||||||||
\(477\) | 6.43863e11 | 0.569457 | ||||||||
\(478\) | 2.26082e12 | 1.98080 | ||||||||
\(479\) | −1.12289e12 | −0.974600 | −0.487300 | − | 0.873235i | \(-0.662018\pi\) | ||||
−0.487300 | + | 0.873235i | \(0.662018\pi\) | |||||||
\(480\) | 5.72627e11 | 0.492364 | ||||||||
\(481\) | 1.37336e11 | 0.116985 | ||||||||
\(482\) | 5.87703e11 | 0.495960 | ||||||||
\(483\) | 1.34171e11 | 0.112175 | ||||||||
\(484\) | −4.72061e11 | −0.391015 | ||||||||
\(485\) | 3.22586e10 | 0.0264733 | ||||||||
\(486\) | −1.67567e12 | −1.36246 | ||||||||
\(487\) | 3.09213e11 | 0.249102 | 0.124551 | − | 0.992213i | \(-0.460251\pi\) | ||||
0.124551 | + | 0.992213i | \(0.460251\pi\) | |||||||
\(488\) | −1.36688e10 | −0.0109104 | ||||||||
\(489\) | −2.23364e11 | −0.176654 | ||||||||
\(490\) | 1.91957e11 | 0.150425 | ||||||||
\(491\) | −7.16983e11 | −0.556727 | −0.278363 | − | 0.960476i | \(-0.589792\pi\) | ||||
−0.278363 | + | 0.960476i | \(0.589792\pi\) | |||||||
\(492\) | 5.36116e11 | 0.412493 | ||||||||
\(493\) | 1.74301e11 | 0.132889 | ||||||||
\(494\) | 2.64657e11 | 0.199946 | ||||||||
\(495\) | 5.50613e11 | 0.412214 | ||||||||
\(496\) | 9.28263e11 | 0.688658 | ||||||||
\(497\) | −3.22468e11 | −0.237073 | ||||||||
\(498\) | −9.04713e11 | −0.659141 | ||||||||
\(499\) | 1.84974e12 | 1.33554 | 0.667770 | − | 0.744367i | \(-0.267249\pi\) | ||||
0.667770 | + | 0.744367i | \(0.267249\pi\) | |||||||
\(500\) | −1.13334e12 | −0.810953 | ||||||||
\(501\) | 2.49444e11 | 0.176890 | ||||||||
\(502\) | 2.46844e12 | 1.73483 | ||||||||
\(503\) | 2.12992e12 | 1.48357 | 0.741784 | − | 0.670639i | \(-0.233980\pi\) | ||||
0.741784 | + | 0.670639i | \(0.233980\pi\) | |||||||
\(504\) | 1.38055e11 | 0.0953048 | ||||||||
\(505\) | −4.57091e11 | −0.312746 | ||||||||
\(506\) | 7.97510e11 | 0.540827 | ||||||||
\(507\) | −5.72180e10 | −0.0384589 | ||||||||
\(508\) | −1.06628e11 | −0.0710370 | ||||||||
\(509\) | −9.55257e11 | −0.630798 | −0.315399 | − | 0.948959i | \(-0.602138\pi\) | ||||
−0.315399 | + | 0.948959i | \(0.602138\pi\) | |||||||
\(510\) | 3.67224e11 | 0.240361 | ||||||||
\(511\) | 6.81657e11 | 0.442254 | ||||||||
\(512\) | 1.66393e12 | 1.07009 | ||||||||
\(513\) | 7.48916e11 | 0.477425 | ||||||||
\(514\) | −1.15283e12 | −0.728505 | ||||||||
\(515\) | −4.64531e11 | −0.290993 | ||||||||
\(516\) | 8.19907e11 | 0.509144 | ||||||||
\(517\) | 2.03151e12 | 1.25058 | ||||||||
\(518\) | 3.45146e11 | 0.210630 | ||||||||
\(519\) | 7.98927e11 | 0.483341 | ||||||||
\(520\) | −1.23902e11 | −0.0743129 | ||||||||
\(521\) | 1.31386e12 | 0.781230 | 0.390615 | − | 0.920554i | \(-0.372262\pi\) | ||||
0.390615 | + | 0.920554i | \(0.372262\pi\) | |||||||
\(522\) | 4.89267e11 | 0.288422 | ||||||||
\(523\) | −3.94633e11 | −0.230640 | −0.115320 | − | 0.993328i | \(-0.536789\pi\) | ||||
−0.115320 | + | 0.993328i | \(0.536789\pi\) | |||||||
\(524\) | 1.34734e12 | 0.780705 | ||||||||
\(525\) | 1.19997e11 | 0.0689369 | ||||||||
\(526\) | 2.29012e12 | 1.30443 | ||||||||
\(527\) | 4.67969e11 | 0.264283 | ||||||||
\(528\) | −7.32524e11 | −0.410175 | ||||||||
\(529\) | −1.16646e12 | −0.647620 | ||||||||
\(530\) | −1.45224e12 | −0.799462 | ||||||||
\(531\) | 4.60422e10 | 0.0251322 | ||||||||
\(532\) | 2.84082e11 | 0.153759 | ||||||||
\(533\) | −5.71881e11 | −0.306925 | ||||||||
\(534\) | 1.19670e12 | 0.636870 | ||||||||
\(535\) | −3.61111e10 | −0.0190567 | ||||||||
\(536\) | −1.00386e12 | −0.525329 | ||||||||
\(537\) | −5.07587e11 | −0.263406 | ||||||||
\(538\) | 4.22856e12 | 2.17607 | ||||||||
\(539\) | −1.93037e11 | −0.0985122 | ||||||||
\(540\) | 1.02727e12 | 0.519890 | ||||||||
\(541\) | 2.62837e12 | 1.31916 | 0.659582 | − | 0.751632i | \(-0.270733\pi\) | ||||
0.659582 | + | 0.751632i | \(0.270733\pi\) | |||||||
\(542\) | −3.15133e12 | −1.56855 | ||||||||
\(543\) | 4.20818e11 | 0.207728 | ||||||||
\(544\) | 1.15238e12 | 0.564156 | ||||||||
\(545\) | 2.88314e12 | 1.39985 | ||||||||
\(546\) | −1.43797e11 | −0.0692443 | ||||||||
\(547\) | 1.85373e12 | 0.885325 | 0.442663 | − | 0.896688i | \(-0.354034\pi\) | ||||
0.442663 | + | 0.896688i | \(0.354034\pi\) | |||||||
\(548\) | −3.33872e10 | −0.0158149 | ||||||||
\(549\) | −5.18101e10 | −0.0243410 | ||||||||
\(550\) | 7.13257e11 | 0.332364 | ||||||||
\(551\) | −3.43624e11 | −0.158818 | ||||||||
\(552\) | −2.17648e11 | −0.0997764 | ||||||||
\(553\) | 3.72332e10 | 0.0169304 | ||||||||
\(554\) | −5.49449e12 | −2.47818 | ||||||||
\(555\) | −3.75677e11 | −0.168072 | ||||||||
\(556\) | 1.00937e12 | 0.447934 | ||||||||
\(557\) | −4.50145e12 | −1.98155 | −0.990774 | − | 0.135527i | \(-0.956727\pi\) | ||||
−0.990774 | + | 0.135527i | \(0.956727\pi\) | |||||||
\(558\) | 1.31360e12 | 0.573600 | ||||||||
\(559\) | −8.74602e11 | −0.378841 | ||||||||
\(560\) | −8.34049e11 | −0.358381 | ||||||||
\(561\) | −3.69290e11 | −0.157411 | ||||||||
\(562\) | −4.02893e12 | −1.70363 | ||||||||
\(563\) | 4.31343e11 | 0.180940 | 0.0904700 | − | 0.995899i | \(-0.471163\pi\) | ||||
0.0904700 | + | 0.995899i | \(0.471163\pi\) | |||||||
\(564\) | 1.62440e12 | 0.675983 | ||||||||
\(565\) | 1.10648e12 | 0.456801 | ||||||||
\(566\) | 1.53582e12 | 0.629023 | ||||||||
\(567\) | 2.90767e11 | 0.118147 | ||||||||
\(568\) | 5.23096e11 | 0.210870 | ||||||||
\(569\) | −6.31363e11 | −0.252507 | −0.126254 | − | 0.991998i | \(-0.540295\pi\) | ||||
−0.126254 | + | 0.991998i | \(0.540295\pi\) | |||||||
\(570\) | −7.23958e11 | −0.287261 | ||||||||
\(571\) | 4.45553e12 | 1.75403 | 0.877015 | − | 0.480463i | \(-0.159531\pi\) | ||||
0.877015 | + | 0.480463i | \(0.159531\pi\) | |||||||
\(572\) | −3.65065e11 | −0.142590 | ||||||||
\(573\) | 2.07218e12 | 0.803028 | ||||||||
\(574\) | −1.43722e12 | −0.552612 | ||||||||
\(575\) | 5.67639e11 | 0.216554 | ||||||||
\(576\) | 8.77403e11 | 0.332122 | ||||||||
\(577\) | −7.52025e11 | −0.282450 | −0.141225 | − | 0.989978i | \(-0.545104\pi\) | ||||
−0.141225 | + | 0.989978i | \(0.545104\pi\) | |||||||
\(578\) | −2.80618e12 | −1.04578 | ||||||||
\(579\) | 1.33252e11 | 0.0492742 | ||||||||
\(580\) | −4.71339e11 | −0.172945 | ||||||||
\(581\) | 1.03590e12 | 0.377159 | ||||||||
\(582\) | −6.07313e10 | −0.0219411 | ||||||||
\(583\) | 1.46041e12 | 0.523561 | ||||||||
\(584\) | −1.10576e12 | −0.393372 | ||||||||
\(585\) | −4.69639e11 | −0.165792 | ||||||||
\(586\) | −4.68520e12 | −1.64130 | ||||||||
\(587\) | −3.19638e12 | −1.11119 | −0.555593 | − | 0.831454i | \(-0.687509\pi\) | ||||
−0.555593 | + | 0.831454i | \(0.687509\pi\) | |||||||
\(588\) | −1.54352e11 | −0.0532493 | ||||||||
\(589\) | −9.22571e11 | −0.315850 | ||||||||
\(590\) | −1.03849e11 | −0.0352832 | ||||||||
\(591\) | 1.21630e12 | 0.410107 | ||||||||
\(592\) | −1.49966e12 | −0.501816 | ||||||||
\(593\) | −4.40773e12 | −1.46376 | −0.731878 | − | 0.681436i | \(-0.761356\pi\) | ||||
−0.731878 | + | 0.681436i | \(0.761356\pi\) | |||||||
\(594\) | −2.41868e12 | −0.797149 | ||||||||
\(595\) | −4.20472e11 | −0.137534 | ||||||||
\(596\) | 2.07031e12 | 0.672090 | ||||||||
\(597\) | 1.30569e12 | 0.420684 | ||||||||
\(598\) | −6.80228e11 | −0.217520 | ||||||||
\(599\) | −5.68564e12 | −1.80451 | −0.902254 | − | 0.431205i | \(-0.858089\pi\) | ||||
−0.902254 | + | 0.431205i | \(0.858089\pi\) | |||||||
\(600\) | −1.94654e11 | −0.0613174 | ||||||||
\(601\) | −1.17360e12 | −0.366933 | −0.183466 | − | 0.983026i | \(-0.558732\pi\) | ||||
−0.183466 | + | 0.983026i | \(0.558732\pi\) | |||||||
\(602\) | −2.19801e12 | −0.682096 | ||||||||
\(603\) | −3.80503e12 | −1.17201 | ||||||||
\(604\) | 3.88328e11 | 0.118722 | ||||||||
\(605\) | −1.37745e12 | −0.417999 | ||||||||
\(606\) | 8.60537e11 | 0.259205 | ||||||||
\(607\) | −4.69756e11 | −0.140450 | −0.0702252 | − | 0.997531i | \(-0.522372\pi\) | ||||
−0.0702252 | + | 0.997531i | \(0.522372\pi\) | |||||||
\(608\) | −2.27184e12 | −0.674235 | ||||||||
\(609\) | 1.86703e11 | 0.0550013 | ||||||||
\(610\) | 1.16858e11 | 0.0341724 | ||||||||
\(611\) | −1.73276e12 | −0.502982 | ||||||||
\(612\) | 8.86015e11 | 0.255305 | ||||||||
\(613\) | −3.95664e12 | −1.13176 | −0.565880 | − | 0.824488i | \(-0.691463\pi\) | ||||
−0.565880 | + | 0.824488i | \(0.691463\pi\) | |||||||
\(614\) | −5.74977e12 | −1.63265 | ||||||||
\(615\) | 1.56436e12 | 0.440959 | ||||||||
\(616\) | 3.13137e11 | 0.0876237 | ||||||||
\(617\) | −3.22974e12 | −0.897189 | −0.448594 | − | 0.893735i | \(-0.648075\pi\) | ||||
−0.448594 | + | 0.893735i | \(0.648075\pi\) | |||||||
\(618\) | 8.74544e11 | 0.241176 | ||||||||
\(619\) | 2.67612e11 | 0.0732651 | 0.0366326 | − | 0.999329i | \(-0.488337\pi\) | ||||
0.0366326 | + | 0.999329i | \(0.488337\pi\) | |||||||
\(620\) | −1.26547e12 | −0.343944 | ||||||||
\(621\) | −1.92488e12 | −0.519388 | ||||||||
\(622\) | 4.43035e12 | 1.18681 | ||||||||
\(623\) | −1.37023e12 | −0.364416 | ||||||||
\(624\) | 6.24798e11 | 0.164972 | ||||||||
\(625\) | −1.91541e12 | −0.502112 | ||||||||
\(626\) | −2.54717e12 | −0.662938 | ||||||||
\(627\) | 7.28032e11 | 0.188125 | ||||||||
\(628\) | 3.67999e12 | 0.944123 | ||||||||
\(629\) | −7.56027e11 | −0.192579 | ||||||||
\(630\) | −1.18028e12 | −0.298504 | ||||||||
\(631\) | 3.92920e12 | 0.986670 | 0.493335 | − | 0.869839i | \(-0.335778\pi\) | ||||
0.493335 | + | 0.869839i | \(0.335778\pi\) | |||||||
\(632\) | −6.03984e10 | −0.0150591 | ||||||||
\(633\) | −3.45273e12 | −0.854764 | ||||||||
\(634\) | −2.68963e12 | −0.661136 | ||||||||
\(635\) | −3.11134e11 | −0.0759393 | ||||||||
\(636\) | 1.16774e12 | 0.283003 | ||||||||
\(637\) | 1.64648e11 | 0.0396214 | ||||||||
\(638\) | 1.10976e12 | 0.265177 | ||||||||
\(639\) | 1.98275e12 | 0.470450 | ||||||||
\(640\) | 2.20081e12 | 0.518529 | ||||||||
\(641\) | −8.01874e11 | −0.187605 | −0.0938026 | − | 0.995591i | \(-0.529902\pi\) | ||||
−0.0938026 | + | 0.995591i | \(0.529902\pi\) | |||||||
\(642\) | 6.79841e10 | 0.0157943 | ||||||||
\(643\) | −2.60093e12 | −0.600039 | −0.300019 | − | 0.953933i | \(-0.596993\pi\) | ||||
−0.300019 | + | 0.953933i | \(0.596993\pi\) | |||||||
\(644\) | −7.30154e11 | −0.167274 | ||||||||
\(645\) | 2.39244e12 | 0.544280 | ||||||||
\(646\) | −1.45692e12 | −0.329147 | ||||||||
\(647\) | 4.79153e12 | 1.07499 | 0.537496 | − | 0.843266i | \(-0.319370\pi\) | ||||
0.537496 | + | 0.843266i | \(0.319370\pi\) | |||||||
\(648\) | −4.71672e11 | −0.105088 | ||||||||
\(649\) | 1.04433e11 | 0.0231067 | ||||||||
\(650\) | −6.08365e11 | −0.133676 | ||||||||
\(651\) | 5.01265e11 | 0.109384 | ||||||||
\(652\) | 1.21554e12 | 0.263423 | ||||||||
\(653\) | 5.97413e12 | 1.28578 | 0.642888 | − | 0.765960i | \(-0.277736\pi\) | ||||
0.642888 | + | 0.765960i | \(0.277736\pi\) | |||||||
\(654\) | −5.42791e12 | −1.16020 | ||||||||
\(655\) | 3.93147e12 | 0.834581 | ||||||||
\(656\) | 6.24472e12 | 1.31657 | ||||||||
\(657\) | −4.19128e12 | −0.877611 | ||||||||
\(658\) | −4.35469e12 | −0.905608 | ||||||||
\(659\) | 7.35551e11 | 0.151925 | 0.0759624 | − | 0.997111i | \(-0.475797\pi\) | ||||
0.0759624 | + | 0.997111i | \(0.475797\pi\) | |||||||
\(660\) | 9.98621e11 | 0.204858 | ||||||||
\(661\) | 2.43174e12 | 0.495463 | 0.247731 | − | 0.968829i | \(-0.420315\pi\) | ||||
0.247731 | + | 0.968829i | \(0.420315\pi\) | |||||||
\(662\) | 2.63147e12 | 0.532522 | ||||||||
\(663\) | 3.14982e11 | 0.0633103 | ||||||||
\(664\) | −1.68040e12 | −0.335472 | ||||||||
\(665\) | 8.28934e11 | 0.164370 | ||||||||
\(666\) | −2.12219e12 | −0.417974 | ||||||||
\(667\) | 8.83190e11 | 0.172778 | ||||||||
\(668\) | −1.35747e12 | −0.263776 | ||||||||
\(669\) | 2.95673e12 | 0.570681 | ||||||||
\(670\) | 8.58230e12 | 1.64538 | ||||||||
\(671\) | −1.17516e11 | −0.0223792 | ||||||||
\(672\) | 1.23437e12 | 0.233498 | ||||||||
\(673\) | −2.68993e12 | −0.505445 | −0.252722 | − | 0.967539i | \(-0.581326\pi\) | ||||
−0.252722 | + | 0.967539i | \(0.581326\pi\) | |||||||
\(674\) | 3.99060e12 | 0.744849 | ||||||||
\(675\) | −1.72153e12 | −0.319189 | ||||||||
\(676\) | 3.11378e11 | 0.0573493 | ||||||||
\(677\) | −7.99672e12 | −1.46306 | −0.731531 | − | 0.681808i | \(-0.761194\pi\) | ||||
−0.731531 | + | 0.681808i | \(0.761194\pi\) | |||||||
\(678\) | −2.08311e12 | −0.378598 | ||||||||
\(679\) | 6.95375e10 | 0.0125547 | ||||||||
\(680\) | 6.82076e11 | 0.122333 | ||||||||
\(681\) | −2.59897e12 | −0.463062 | ||||||||
\(682\) | 2.97951e12 | 0.527370 | ||||||||
\(683\) | 3.73678e12 | 0.657060 | 0.328530 | − | 0.944494i | \(-0.393447\pi\) | ||||
0.328530 | + | 0.944494i | \(0.393447\pi\) | |||||||
\(684\) | −1.74672e12 | −0.305120 | ||||||||
\(685\) | −9.74218e10 | −0.0169063 | ||||||||
\(686\) | 4.13787e11 | 0.0713375 | ||||||||
\(687\) | 3.85116e12 | 0.659609 | ||||||||
\(688\) | 9.55032e12 | 1.62506 | ||||||||
\(689\) | −1.24564e12 | −0.210575 | ||||||||
\(690\) | 1.86074e12 | 0.312510 | ||||||||
\(691\) | −2.29823e11 | −0.0383479 | −0.0191740 | − | 0.999816i | \(-0.506104\pi\) | ||||
−0.0191740 | + | 0.999816i | \(0.506104\pi\) | |||||||
\(692\) | −4.34773e12 | −0.720752 | ||||||||
\(693\) | 1.18692e12 | 0.195488 | ||||||||
\(694\) | −3.01641e12 | −0.493598 | ||||||||
\(695\) | 2.94529e12 | 0.478846 | ||||||||
\(696\) | −3.02863e11 | −0.0489221 | ||||||||
\(697\) | 3.14817e12 | 0.505255 | ||||||||
\(698\) | −1.91818e12 | −0.305872 | ||||||||
\(699\) | 3.48767e12 | 0.552570 | ||||||||
\(700\) | −6.53018e11 | −0.102798 | ||||||||
\(701\) | 9.79164e12 | 1.53153 | 0.765763 | − | 0.643123i | \(-0.222362\pi\) | ||||
0.765763 | + | 0.643123i | \(0.222362\pi\) | |||||||
\(702\) | 2.06299e12 | 0.320612 | ||||||||
\(703\) | 1.49046e12 | 0.230156 | ||||||||
\(704\) | 1.99013e12 | 0.305355 | ||||||||
\(705\) | 4.73990e12 | 0.722633 | ||||||||
\(706\) | −4.13025e12 | −0.625685 | ||||||||
\(707\) | −9.85318e11 | −0.148316 | ||||||||
\(708\) | 8.35046e10 | 0.0124900 | ||||||||
\(709\) | 5.44585e12 | 0.809389 | 0.404695 | − | 0.914452i | \(-0.367378\pi\) | ||||
0.404695 | + | 0.914452i | \(0.367378\pi\) | |||||||
\(710\) | −4.47211e12 | −0.660466 | ||||||||
\(711\) | −2.28934e11 | −0.0335967 | ||||||||
\(712\) | 2.22274e12 | 0.324137 | ||||||||
\(713\) | 2.37122e12 | 0.343612 | ||||||||
\(714\) | 7.91597e11 | 0.113989 | ||||||||
\(715\) | −1.06524e12 | −0.152430 | ||||||||
\(716\) | 2.76227e12 | 0.392788 | ||||||||
\(717\) | −5.30458e12 | −0.749575 | ||||||||
\(718\) | −3.94338e11 | −0.0553744 | ||||||||
\(719\) | −7.91110e12 | −1.10397 | −0.551985 | − | 0.833854i | \(-0.686129\pi\) | ||||
−0.551985 | + | 0.833854i | \(0.686129\pi\) | |||||||
\(720\) | 5.12828e12 | 0.711174 | ||||||||
\(721\) | −1.00136e12 | −0.138000 | ||||||||
\(722\) | −6.77455e12 | −0.927819 | ||||||||
\(723\) | −1.37893e12 | −0.187681 | ||||||||
\(724\) | −2.29008e12 | −0.309761 | ||||||||
\(725\) | 7.89886e11 | 0.106180 | ||||||||
\(726\) | 2.59324e12 | 0.346439 | ||||||||
\(727\) | −7.47380e12 | −0.992286 | −0.496143 | − | 0.868241i | \(-0.665251\pi\) | ||||
−0.496143 | + | 0.868241i | \(0.665251\pi\) | |||||||
\(728\) | −2.67087e11 | −0.0352421 | ||||||||
\(729\) | 1.54797e12 | 0.202997 | ||||||||
\(730\) | 9.45349e12 | 1.23208 | ||||||||
\(731\) | 4.81464e12 | 0.623642 | ||||||||
\(732\) | −9.39656e10 | −0.0120968 | ||||||||
\(733\) | −2.41459e12 | −0.308941 | −0.154470 | − | 0.987997i | \(-0.549367\pi\) | ||||
−0.154470 | + | 0.987997i | \(0.549367\pi\) | |||||||
\(734\) | −1.70302e13 | −2.16564 | ||||||||
\(735\) | −4.50390e11 | −0.0569240 | ||||||||
\(736\) | 5.83914e12 | 0.733498 | ||||||||
\(737\) | −8.63059e12 | −1.07755 | ||||||||
\(738\) | 8.83699e12 | 1.09661 | ||||||||
\(739\) | −7.85537e12 | −0.968872 | −0.484436 | − | 0.874827i | \(-0.660975\pi\) | ||||
−0.484436 | + | 0.874827i | \(0.660975\pi\) | |||||||
\(740\) | 2.04442e12 | 0.250627 | ||||||||
\(741\) | −6.20967e11 | −0.0756635 | ||||||||
\(742\) | −3.13050e12 | −0.379136 | ||||||||
\(743\) | 9.59756e12 | 1.15534 | 0.577672 | − | 0.816269i | \(-0.303961\pi\) | ||||
0.577672 | + | 0.816269i | \(0.303961\pi\) | |||||||
\(744\) | −8.13136e11 | −0.0972937 | ||||||||
\(745\) | 6.04105e12 | 0.718471 | ||||||||
\(746\) | 1.48494e13 | 1.75543 | ||||||||
\(747\) | −6.36939e12 | −0.748437 | ||||||||
\(748\) | 2.00966e12 | 0.234729 | ||||||||
\(749\) | −7.78420e10 | −0.00903745 | ||||||||
\(750\) | 6.22594e12 | 0.718504 | ||||||||
\(751\) | −6.26106e12 | −0.718237 | −0.359119 | − | 0.933292i | \(-0.616923\pi\) | ||||
−0.359119 | + | 0.933292i | \(0.616923\pi\) | |||||||
\(752\) | 1.89211e13 | 2.15757 | ||||||||
\(753\) | −5.79174e12 | −0.656495 | ||||||||
\(754\) | −9.46557e11 | −0.106654 | ||||||||
\(755\) | 1.13312e12 | 0.126915 | ||||||||
\(756\) | 2.21441e12 | 0.246552 | ||||||||
\(757\) | 1.57603e12 | 0.174435 | 0.0872175 | − | 0.996189i | \(-0.472203\pi\) | ||||
0.0872175 | + | 0.996189i | \(0.472203\pi\) | |||||||
\(758\) | −2.24350e13 | −2.46840 | ||||||||
\(759\) | −1.87121e12 | −0.204660 | ||||||||
\(760\) | −1.34467e12 | −0.146202 | ||||||||
\(761\) | −2.47789e12 | −0.267825 | −0.133912 | − | 0.990993i | \(-0.542754\pi\) | ||||
−0.133912 | + | 0.990993i | \(0.542754\pi\) | |||||||
\(762\) | 5.85754e11 | 0.0629387 | ||||||||
\(763\) | 6.21498e12 | 0.663864 | ||||||||
\(764\) | −1.12767e13 | −1.19746 | ||||||||
\(765\) | 2.58534e12 | 0.272924 | ||||||||
\(766\) | 4.94938e12 | 0.519424 | ||||||||
\(767\) | −8.90752e10 | −0.00929346 | ||||||||
\(768\) | −6.27777e12 | −0.651148 | ||||||||
\(769\) | 8.56237e12 | 0.882929 | 0.441464 | − | 0.897279i | \(-0.354459\pi\) | ||||
0.441464 | + | 0.897279i | \(0.354459\pi\) | |||||||
\(770\) | −2.67711e12 | −0.274446 | ||||||||
\(771\) | 2.70490e12 | 0.275681 | ||||||||
\(772\) | −7.25152e11 | −0.0734770 | ||||||||
\(773\) | −1.18439e13 | −1.19313 | −0.596563 | − | 0.802567i | \(-0.703467\pi\) | ||||
−0.596563 | + | 0.802567i | \(0.703467\pi\) | |||||||
\(774\) | 1.35148e13 | 1.35355 | ||||||||
\(775\) | 2.12071e12 | 0.211166 | ||||||||
\(776\) | −1.12801e11 | −0.0111670 | ||||||||
\(777\) | −8.09820e11 | −0.0797066 | ||||||||
\(778\) | 2.24901e13 | 2.20081 | ||||||||
\(779\) | −6.20642e12 | −0.603841 | ||||||||
\(780\) | −8.51764e11 | −0.0823936 | ||||||||
\(781\) | 4.49728e12 | 0.432534 | ||||||||
\(782\) | 3.74462e12 | 0.358078 | ||||||||
\(783\) | −2.67853e12 | −0.254665 | ||||||||
\(784\) | −1.79790e12 | −0.169959 | ||||||||
\(785\) | 1.07380e13 | 1.00928 | ||||||||
\(786\) | −7.40153e12 | −0.691704 | ||||||||
\(787\) | 2.00273e13 | 1.86096 | 0.930479 | − | 0.366345i | \(-0.119391\pi\) | ||||
0.930479 | + | 0.366345i | \(0.119391\pi\) | |||||||
\(788\) | −6.61907e12 | −0.611546 | ||||||||
\(789\) | −5.37333e12 | −0.493625 | ||||||||
\(790\) | 5.16364e11 | 0.0471666 | ||||||||
\(791\) | 2.38517e12 | 0.216633 | ||||||||
\(792\) | −1.92537e12 | −0.173881 | ||||||||
\(793\) | 1.00234e11 | 0.00900089 | ||||||||
\(794\) | −1.74274e12 | −0.155611 | ||||||||
\(795\) | 3.40741e12 | 0.302533 | ||||||||
\(796\) | −7.10554e12 | −0.627319 | ||||||||
\(797\) | −1.83555e13 | −1.61140 | −0.805702 | − | 0.592321i | \(-0.798212\pi\) | ||||
−0.805702 | + | 0.592321i | \(0.798212\pi\) | |||||||
\(798\) | −1.56058e12 | −0.136230 | ||||||||
\(799\) | 9.53875e12 | 0.828001 | ||||||||
\(800\) | 5.22227e12 | 0.450769 | ||||||||
\(801\) | 8.42507e12 | 0.723148 | ||||||||
\(802\) | −5.51848e12 | −0.471015 | ||||||||
\(803\) | −9.50668e12 | −0.806880 | ||||||||
\(804\) | −6.90101e12 | −0.582452 | ||||||||
\(805\) | −2.13055e12 | −0.178818 | ||||||||
\(806\) | −2.54134e12 | −0.212107 | ||||||||
\(807\) | −9.92151e12 | −0.823468 | ||||||||
\(808\) | 1.59835e12 | 0.131923 | ||||||||
\(809\) | 3.82815e11 | 0.0314211 | 0.0157105 | − | 0.999877i | \(-0.494999\pi\) | ||||
0.0157105 | + | 0.999877i | \(0.494999\pi\) | |||||||
\(810\) | 4.03247e12 | 0.329146 | ||||||||
\(811\) | 1.28299e13 | 1.04143 | 0.520713 | − | 0.853732i | \(-0.325666\pi\) | ||||
0.520713 | + | 0.853732i | \(0.325666\pi\) | |||||||
\(812\) | −1.01603e12 | −0.0820172 | ||||||||
\(813\) | 7.39400e12 | 0.593570 | ||||||||
\(814\) | −4.81356e12 | −0.384288 | ||||||||
\(815\) | 3.54687e12 | 0.281602 | ||||||||
\(816\) | −3.43948e12 | −0.271573 | ||||||||
\(817\) | −9.49176e12 | −0.745328 | ||||||||
\(818\) | −2.09090e13 | −1.63284 | ||||||||
\(819\) | −1.01237e12 | −0.0786250 | ||||||||
\(820\) | −8.51318e12 | −0.657551 | ||||||||
\(821\) | 1.24894e13 | 0.959394 | 0.479697 | − | 0.877434i | \(-0.340747\pi\) | ||||
0.479697 | + | 0.877434i | \(0.340747\pi\) | |||||||
\(822\) | 1.83410e11 | 0.0140120 | ||||||||
\(823\) | −1.15679e13 | −0.878931 | −0.439465 | − | 0.898260i | \(-0.644832\pi\) | ||||
−0.439465 | + | 0.898260i | \(0.644832\pi\) | |||||||
\(824\) | 1.62436e12 | 0.122747 | ||||||||
\(825\) | −1.67352e12 | −0.125773 | ||||||||
\(826\) | −2.23859e11 | −0.0167327 | ||||||||
\(827\) | 7.47785e12 | 0.555907 | 0.277953 | − | 0.960595i | \(-0.410344\pi\) | ||||
0.277953 | + | 0.960595i | \(0.410344\pi\) | |||||||
\(828\) | 4.48947e12 | 0.331939 | ||||||||
\(829\) | −6.46169e12 | −0.475172 | −0.237586 | − | 0.971367i | \(-0.576356\pi\) | ||||
−0.237586 | + | 0.971367i | \(0.576356\pi\) | |||||||
\(830\) | 1.43663e13 | 1.05073 | ||||||||
\(831\) | 1.28918e13 | 0.937796 | ||||||||
\(832\) | −1.69746e12 | −0.122813 | ||||||||
\(833\) | −9.06381e11 | −0.0652242 | ||||||||
\(834\) | −5.54492e12 | −0.396870 | ||||||||
\(835\) | −3.96101e12 | −0.281979 | ||||||||
\(836\) | −3.96193e12 | −0.280529 | ||||||||
\(837\) | −7.19140e12 | −0.506465 | ||||||||
\(838\) | −1.58155e13 | −1.10786 | ||||||||
\(839\) | 4.80572e12 | 0.334834 | 0.167417 | − | 0.985886i | \(-0.446457\pi\) | ||||
0.167417 | + | 0.985886i | \(0.446457\pi\) | |||||||
\(840\) | 7.30607e11 | 0.0506322 | ||||||||
\(841\) | −1.32782e13 | −0.915284 | ||||||||
\(842\) | −2.48706e13 | −1.70523 | ||||||||
\(843\) | 9.45311e12 | 0.644690 | ||||||||
\(844\) | 1.87897e13 | 1.27461 | ||||||||
\(845\) | 9.08584e11 | 0.0613070 | ||||||||
\(846\) | 2.67755e13 | 1.79709 | ||||||||
\(847\) | −2.96926e12 | −0.198232 | ||||||||
\(848\) | 1.36020e13 | 0.903276 | ||||||||
\(849\) | −3.60351e12 | −0.238035 | ||||||||
\(850\) | 3.34902e12 | 0.220056 | ||||||||
\(851\) | −3.83082e12 | −0.250385 | ||||||||
\(852\) | 3.59601e12 | 0.233799 | ||||||||
\(853\) | 8.41348e12 | 0.544133 | 0.272066 | − | 0.962278i | \(-0.412293\pi\) | ||||
0.272066 | + | 0.962278i | \(0.412293\pi\) | |||||||
\(854\) | 2.51903e11 | 0.0162059 | ||||||||
\(855\) | −5.09684e12 | −0.326177 | ||||||||
\(856\) | 1.26273e11 | 0.00803854 | ||||||||
\(857\) | 3.95026e12 | 0.250157 | 0.125078 | − | 0.992147i | \(-0.460082\pi\) | ||||
0.125078 | + | 0.992147i | \(0.460082\pi\) | |||||||
\(858\) | 2.00546e12 | 0.126334 | ||||||||
\(859\) | 7.00057e12 | 0.438696 | 0.219348 | − | 0.975647i | \(-0.429607\pi\) | ||||
0.219348 | + | 0.975647i | \(0.429607\pi\) | |||||||
\(860\) | −1.30196e13 | −0.811623 | ||||||||
\(861\) | 3.37217e12 | 0.209120 | ||||||||
\(862\) | −1.90102e13 | −1.17275 | ||||||||
\(863\) | −2.02805e13 | −1.24460 | −0.622299 | − | 0.782780i | \(-0.713801\pi\) | ||||
−0.622299 | + | 0.782780i | \(0.713801\pi\) | |||||||
\(864\) | −1.77089e13 | −1.08113 | ||||||||
\(865\) | −1.26864e13 | −0.770491 | ||||||||
\(866\) | 2.90566e13 | 1.75555 | ||||||||
\(867\) | 6.58417e12 | 0.395745 | ||||||||
\(868\) | −2.72787e12 | −0.163112 | ||||||||
\(869\) | −5.19270e11 | −0.0308890 | ||||||||
\(870\) | 2.58927e12 | 0.153229 | ||||||||
\(871\) | 7.36137e12 | 0.433388 | ||||||||
\(872\) | −1.00817e13 | −0.590487 | ||||||||
\(873\) | −4.27562e11 | −0.0249135 | ||||||||
\(874\) | −7.38228e12 | −0.427946 | ||||||||
\(875\) | −7.12872e12 | −0.411126 | ||||||||
\(876\) | −7.60153e12 | −0.436146 | ||||||||
\(877\) | −5.14430e12 | −0.293649 | −0.146824 | − | 0.989163i | \(-0.546905\pi\) | ||||
−0.146824 | + | 0.989163i | \(0.546905\pi\) | |||||||
\(878\) | 2.86919e13 | 1.62942 | ||||||||
\(879\) | 1.09929e13 | 0.621104 | ||||||||
\(880\) | 1.16320e13 | 0.653857 | ||||||||
\(881\) | −1.26062e13 | −0.705004 | −0.352502 | − | 0.935811i | \(-0.614669\pi\) | ||||
−0.352502 | + | 0.935811i | \(0.614669\pi\) | |||||||
\(882\) | −2.54423e12 | −0.141563 | ||||||||
\(883\) | 1.72689e13 | 0.955963 | 0.477981 | − | 0.878370i | \(-0.341369\pi\) | ||||
0.477981 | + | 0.878370i | \(0.341369\pi\) | |||||||
\(884\) | −1.71412e12 | −0.0944075 | ||||||||
\(885\) | 2.43662e11 | 0.0133519 | ||||||||
\(886\) | 1.48756e13 | 0.811001 | ||||||||
\(887\) | −2.25561e12 | −0.122351 | −0.0611755 | − | 0.998127i | \(-0.519485\pi\) | ||||
−0.0611755 | + | 0.998127i | \(0.519485\pi\) | |||||||
\(888\) | 1.31366e12 | 0.0708966 | ||||||||
\(889\) | −6.70690e11 | −0.0360134 | ||||||||
\(890\) | −1.90029e13 | −1.01523 | ||||||||
\(891\) | −4.05516e12 | −0.215555 | ||||||||
\(892\) | −1.60904e13 | −0.850991 | ||||||||
\(893\) | −1.88050e13 | −0.989561 | ||||||||
\(894\) | −1.13731e13 | −0.595471 | ||||||||
\(895\) | 8.06016e12 | 0.419894 | ||||||||
\(896\) | 4.74413e12 | 0.245907 | ||||||||
\(897\) | 1.59603e12 | 0.0823140 | ||||||||
\(898\) | −9.57778e12 | −0.491498 | ||||||||
\(899\) | 3.29962e12 | 0.168479 | ||||||||
\(900\) | 4.01518e12 | 0.203992 | ||||||||
\(901\) | 6.85721e12 | 0.346646 | ||||||||
\(902\) | 2.00441e13 | 1.00823 | ||||||||
\(903\) | 5.15721e12 | 0.258119 | ||||||||
\(904\) | −3.86914e12 | −0.192689 | ||||||||
\(905\) | −6.68231e12 | −0.331137 | ||||||||
\(906\) | −2.13325e12 | −0.105188 | ||||||||
\(907\) | −1.98957e13 | −0.976172 | −0.488086 | − | 0.872796i | \(-0.662305\pi\) | ||||
−0.488086 | + | 0.872796i | \(0.662305\pi\) | |||||||
\(908\) | 1.41435e13 | 0.690511 | ||||||||
\(909\) | 6.05838e12 | 0.294320 | ||||||||
\(910\) | 2.28341e12 | 0.110382 | ||||||||
\(911\) | 1.23828e13 | 0.595643 | 0.297822 | − | 0.954622i | \(-0.403740\pi\) | ||||
0.297822 | + | 0.954622i | \(0.403740\pi\) | |||||||
\(912\) | 6.78072e12 | 0.324563 | ||||||||
\(913\) | −1.44471e13 | −0.688116 | ||||||||
\(914\) | −4.83276e12 | −0.229054 | ||||||||
\(915\) | −2.74186e11 | −0.0129316 | ||||||||
\(916\) | −2.09579e13 | −0.983599 | ||||||||
\(917\) | 8.47477e12 | 0.395791 | ||||||||
\(918\) | −1.13566e13 | −0.527786 | ||||||||
\(919\) | −3.21756e13 | −1.48801 | −0.744007 | − | 0.668172i | \(-0.767077\pi\) | ||||
−0.744007 | + | 0.668172i | \(0.767077\pi\) | |||||||
\(920\) | 3.45610e12 | 0.159053 | ||||||||
\(921\) | 1.34908e13 | 0.617828 | ||||||||
\(922\) | 2.43107e13 | 1.10792 | ||||||||
\(923\) | −3.83590e12 | −0.173964 | ||||||||
\(924\) | 2.15266e12 | 0.0971517 | ||||||||
\(925\) | −3.42612e12 | −0.153874 | ||||||||
\(926\) | 6.05123e12 | 0.270454 | ||||||||
\(927\) | 6.15699e12 | 0.273848 | ||||||||
\(928\) | 8.12534e12 | 0.359646 | ||||||||
\(929\) | −4.04390e13 | −1.78127 | −0.890634 | − | 0.454720i | \(-0.849739\pi\) | ||||
−0.890634 | + | 0.454720i | \(0.849739\pi\) | |||||||
\(930\) | 6.95175e12 | 0.304734 | ||||||||
\(931\) | 1.78687e12 | 0.0779508 | ||||||||
\(932\) | −1.89798e13 | −0.823985 | ||||||||
\(933\) | −1.03950e13 | −0.449114 | ||||||||
\(934\) | −1.11687e13 | −0.480223 | ||||||||
\(935\) | 5.86409e12 | 0.250927 | ||||||||
\(936\) | 1.64223e12 | 0.0699346 | ||||||||
\(937\) | 2.69594e13 | 1.14257 | 0.571284 | − | 0.820752i | \(-0.306445\pi\) | ||||
0.571284 | + | 0.820752i | \(0.306445\pi\) | |||||||
\(938\) | 1.85002e13 | 0.780306 | ||||||||
\(939\) | 5.97645e12 | 0.250869 | ||||||||
\(940\) | −2.57944e13 | −1.07758 | ||||||||
\(941\) | 1.75116e13 | 0.728068 | 0.364034 | − | 0.931386i | \(-0.381399\pi\) | ||||
0.364034 | + | 0.931386i | \(0.381399\pi\) | |||||||
\(942\) | −2.02158e13 | −0.836492 | ||||||||
\(943\) | 1.59519e13 | 0.656916 | ||||||||
\(944\) | 9.72667e11 | 0.0398649 | ||||||||
\(945\) | 6.46151e12 | 0.263567 | ||||||||
\(946\) | 3.06544e13 | 1.24446 | ||||||||
\(947\) | −2.17887e13 | −0.880353 | −0.440177 | − | 0.897911i | \(-0.645084\pi\) | ||||
−0.440177 | + | 0.897911i | \(0.645084\pi\) | |||||||
\(948\) | −4.15207e11 | −0.0166966 | ||||||||
\(949\) | 8.10862e12 | 0.324526 | ||||||||
\(950\) | −6.60238e12 | −0.262993 | ||||||||
\(951\) | 6.31071e12 | 0.250188 | ||||||||
\(952\) | 1.47030e12 | 0.0580150 | ||||||||
\(953\) | −3.37546e13 | −1.32561 | −0.662803 | − | 0.748794i | \(-0.730633\pi\) | ||||
−0.662803 | + | 0.748794i | \(0.730633\pi\) | |||||||
\(954\) | 1.92483e13 | 0.752360 | ||||||||
\(955\) | −3.29048e13 | −1.28010 | ||||||||
\(956\) | 2.88674e13 | 1.11776 | ||||||||
\(957\) | −2.60384e12 | −0.100348 | ||||||||
\(958\) | −3.35688e13 | −1.28763 | ||||||||
\(959\) | −2.10005e11 | −0.00801764 | ||||||||
\(960\) | 4.64334e12 | 0.176445 | ||||||||
\(961\) | −1.75807e13 | −0.664938 | ||||||||
\(962\) | 4.10567e12 | 0.154560 | ||||||||
\(963\) | 4.78624e11 | 0.0179340 | ||||||||
\(964\) | 7.50412e12 | 0.279868 | ||||||||
\(965\) | −2.11595e12 | −0.0785476 | ||||||||
\(966\) | 4.01105e12 | 0.148205 | ||||||||
\(967\) | −1.66009e13 | −0.610539 | −0.305270 | − | 0.952266i | \(-0.598747\pi\) | ||||
−0.305270 | + | 0.952266i | \(0.598747\pi\) | |||||||
\(968\) | 4.81664e12 | 0.176321 | ||||||||
\(969\) | 3.41839e12 | 0.124556 | ||||||||
\(970\) | 9.64374e11 | 0.0349762 | ||||||||
\(971\) | −6.48313e12 | −0.234045 | −0.117022 | − | 0.993129i | \(-0.537335\pi\) | ||||
−0.117022 | + | 0.993129i | \(0.537335\pi\) | |||||||
\(972\) | −2.13958e13 | −0.768831 | ||||||||
\(973\) | 6.34895e12 | 0.227088 | ||||||||
\(974\) | 9.24396e12 | 0.329111 | ||||||||
\(975\) | 1.42741e12 | 0.0505859 | ||||||||
\(976\) | −1.09452e12 | −0.0386099 | ||||||||
\(977\) | −1.49152e13 | −0.523725 | −0.261862 | − | 0.965105i | \(-0.584337\pi\) | ||||
−0.261862 | + | 0.965105i | \(0.584337\pi\) | |||||||
\(978\) | −6.67748e12 | −0.233393 | ||||||||
\(979\) | 1.91098e13 | 0.664866 | ||||||||
\(980\) | 2.45101e12 | 0.0848842 | ||||||||
\(981\) | −3.82138e13 | −1.31738 | ||||||||
\(982\) | −2.14343e13 | −0.735541 | ||||||||
\(983\) | −1.85671e12 | −0.0634239 | −0.0317119 | − | 0.999497i | \(-0.510096\pi\) | ||||
−0.0317119 | + | 0.999497i | \(0.510096\pi\) | |||||||
\(984\) | −5.47022e12 | −0.186006 | ||||||||
\(985\) | −1.93141e13 | −0.653748 | ||||||||
\(986\) | 5.21075e12 | 0.175571 | ||||||||
\(987\) | 1.02174e13 | 0.342701 | ||||||||
\(988\) | 3.37928e12 | 0.112828 | ||||||||
\(989\) | 2.43960e13 | 0.810839 | ||||||||
\(990\) | 1.64606e13 | 0.544613 | ||||||||
\(991\) | −5.77488e12 | −0.190200 | −0.0951002 | − | 0.995468i | \(-0.530317\pi\) | ||||
−0.0951002 | + | 0.995468i | \(0.530317\pi\) | |||||||
\(992\) | 2.18151e13 | 0.715246 | ||||||||
\(993\) | −6.17425e12 | −0.201517 | ||||||||
\(994\) | −9.64021e12 | −0.313219 | ||||||||
\(995\) | −2.07336e13 | −0.670610 | ||||||||
\(996\) | −1.15519e13 | −0.371951 | ||||||||
\(997\) | −2.38121e13 | −0.763256 | −0.381628 | − | 0.924316i | \(-0.624636\pi\) | ||||
−0.381628 | + | 0.924316i | \(0.624636\pi\) | |||||||
\(998\) | 5.52980e13 | 1.76450 | ||||||||
\(999\) | 1.16181e13 | 0.369054 |
(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 | 91.10.a.a.1.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.a.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial |