Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,106,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 106, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 106);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 106 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(69.8187388595\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.21371e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15346e16 | −1.81104 | −0.905521 | − | 0.424302i | \(-0.860519\pi\) | ||||
−0.905521 | + | 0.424302i | \(0.860519\pi\) | |||||||
\(3\) | 2.00325e25 | 1.79007 | 0.895033 | − | 0.446000i | \(-0.147152\pi\) | ||||
0.895033 | + | 0.446000i | \(0.147152\pi\) | |||||||
\(4\) | 9.24825e31 | 2.27987 | ||||||||
\(5\) | −4.02660e36 | −0.810987 | −0.405493 | − | 0.914098i | \(-0.632900\pi\) | ||||
−0.405493 | + | 0.914098i | \(0.632900\pi\) | |||||||
\(6\) | −2.31067e41 | −3.24188 | ||||||||
\(7\) | −1.49411e43 | −0.0640819 | −0.0320409 | − | 0.999487i | \(-0.510201\pi\) | ||||
−0.0320409 | + | 0.999487i | \(0.510201\pi\) | |||||||
\(8\) | −5.98851e47 | −2.31790 | ||||||||
\(9\) | 2.76064e50 | 2.20434 | ||||||||
\(10\) | 4.64453e52 | 1.46873 | ||||||||
\(11\) | −4.19278e54 | −0.889993 | −0.444996 | − | 0.895532i | \(-0.646795\pi\) | ||||
−0.444996 | + | 0.895532i | \(0.646795\pi\) | |||||||
\(12\) | 1.85266e57 | 4.08112 | ||||||||
\(13\) | 4.35724e58 | 1.43610 | 0.718052 | − | 0.695990i | \(-0.245034\pi\) | ||||
0.718052 | + | 0.695990i | \(0.245034\pi\) | |||||||
\(14\) | 1.72340e59 | 0.116055 | ||||||||
\(15\) | −8.06629e61 | −1.45172 | ||||||||
\(16\) | 3.15598e63 | 1.91794 | ||||||||
\(17\) | −5.45067e64 | −1.37367 | −0.686833 | − | 0.726815i | \(-0.741000\pi\) | ||||
−0.686833 | + | 0.726815i | \(0.741000\pi\) | |||||||
\(18\) | −3.18429e66 | −3.99214 | ||||||||
\(19\) | 5.82286e66 | 0.427142 | 0.213571 | − | 0.976928i | \(-0.431490\pi\) | ||||
0.213571 | + | 0.976928i | \(0.431490\pi\) | |||||||
\(20\) | −3.72391e68 | −1.84894 | ||||||||
\(21\) | −2.99307e68 | −0.114711 | ||||||||
\(22\) | 4.83621e70 | 1.61181 | ||||||||
\(23\) | −5.38565e70 | −0.173991 | −0.0869954 | − | 0.996209i | \(-0.527727\pi\) | ||||
−0.0869954 | + | 0.996209i | \(0.527727\pi\) | |||||||
\(24\) | −1.19965e73 | −4.14919 | ||||||||
\(25\) | −8.43836e72 | −0.342301 | ||||||||
\(26\) | −5.02591e74 | −2.60084 | ||||||||
\(27\) | 3.02144e75 | 2.15584 | ||||||||
\(28\) | −1.38179e75 | −0.146098 | ||||||||
\(29\) | −5.63591e76 | −0.944211 | −0.472106 | − | 0.881542i | \(-0.656506\pi\) | ||||
−0.472106 | + | 0.881542i | \(0.656506\pi\) | |||||||
\(30\) | 9.30415e77 | 2.62912 | ||||||||
\(31\) | 1.44648e78 | 0.730841 | 0.365421 | − | 0.930843i | \(-0.380925\pi\) | ||||
0.365421 | + | 0.930843i | \(0.380925\pi\) | |||||||
\(32\) | −1.21107e79 | −1.15557 | ||||||||
\(33\) | −8.39919e79 | −1.59315 | ||||||||
\(34\) | 6.28714e80 | 2.48777 | ||||||||
\(35\) | 6.01618e79 | 0.0519695 | ||||||||
\(36\) | 2.55311e82 | 5.02560 | ||||||||
\(37\) | −2.11238e81 | −0.0986693 | −0.0493347 | − | 0.998782i | \(-0.515710\pi\) | ||||
−0.0493347 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(38\) | −6.71645e82 | −0.773572 | ||||||||
\(39\) | 8.72864e83 | 2.57072 | ||||||||
\(40\) | 2.41134e84 | 1.87978 | ||||||||
\(41\) | −5.42415e84 | −1.15659 | −0.578295 | − | 0.815828i | \(-0.696282\pi\) | ||||
−0.578295 | + | 0.815828i | \(0.696282\pi\) | |||||||
\(42\) | 3.45239e84 | 0.207746 | ||||||||
\(43\) | −3.33535e85 | −0.583509 | −0.291755 | − | 0.956493i | \(-0.594239\pi\) | ||||
−0.291755 | + | 0.956493i | \(0.594239\pi\) | |||||||
\(44\) | −3.87759e86 | −2.02907 | ||||||||
\(45\) | −1.11160e87 | −1.78769 | ||||||||
\(46\) | 6.21214e86 | 0.315105 | ||||||||
\(47\) | 2.06871e87 | 0.339282 | 0.169641 | − | 0.985506i | \(-0.445739\pi\) | ||||
0.169641 | + | 0.985506i | \(0.445739\pi\) | |||||||
\(48\) | 6.32221e88 | 3.43324 | ||||||||
\(49\) | −5.41386e88 | −0.995894 | ||||||||
\(50\) | 9.73333e88 | 0.619921 | ||||||||
\(51\) | −1.09190e90 | −2.45895 | ||||||||
\(52\) | 4.02969e90 | 3.27413 | ||||||||
\(53\) | −1.52093e90 | −0.454596 | −0.227298 | − | 0.973825i | \(-0.572989\pi\) | ||||
−0.227298 | + | 0.973825i | \(0.572989\pi\) | |||||||
\(54\) | −3.48512e91 | −3.90432 | ||||||||
\(55\) | 1.68827e91 | 0.721772 | ||||||||
\(56\) | 8.94748e90 | 0.148535 | ||||||||
\(57\) | 1.16646e92 | 0.764613 | ||||||||
\(58\) | 6.50081e92 | 1.71001 | ||||||||
\(59\) | 1.70773e93 | 1.83100 | 0.915499 | − | 0.402320i | \(-0.131796\pi\) | ||||
0.915499 | + | 0.402320i | \(0.131796\pi\) | |||||||
\(60\) | −7.45991e93 | −3.30973 | ||||||||
\(61\) | 2.17269e93 | 0.404745 | 0.202372 | − | 0.979309i | \(-0.435135\pi\) | ||||
0.202372 | + | 0.979309i | \(0.435135\pi\) | |||||||
\(62\) | −1.66846e94 | −1.32358 | ||||||||
\(63\) | −4.12469e93 | −0.141258 | ||||||||
\(64\) | 1.16707e94 | 0.174843 | ||||||||
\(65\) | −1.75449e95 | −1.16466 | ||||||||
\(66\) | 9.68814e95 | 2.88525 | ||||||||
\(67\) | 8.39741e94 | 0.113558 | 0.0567791 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567791 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(68\) | −5.04092e96 | −3.13178 | ||||||||
\(69\) | −1.07888e96 | −0.311455 | ||||||||
\(70\) | −6.93944e95 | −0.0941190 | ||||||||
\(71\) | 1.45834e97 | 0.939278 | 0.469639 | − | 0.882859i | \(-0.344384\pi\) | ||||
0.469639 | + | 0.882859i | \(0.344384\pi\) | |||||||
\(72\) | −1.65321e98 | −5.10943 | ||||||||
\(73\) | 3.40172e97 | 0.509622 | 0.254811 | − | 0.966991i | \(-0.417987\pi\) | ||||
0.254811 | + | 0.966991i | \(0.417987\pi\) | |||||||
\(74\) | 2.43655e97 | 0.178694 | ||||||||
\(75\) | −1.69041e98 | −0.612741 | ||||||||
\(76\) | 5.38513e98 | 0.973829 | ||||||||
\(77\) | 6.26447e97 | 0.0570324 | ||||||||
\(78\) | −1.00682e100 | −4.65568 | ||||||||
\(79\) | −3.48037e99 | −0.824523 | −0.412261 | − | 0.911066i | \(-0.635261\pi\) | ||||
−0.412261 | + | 0.911066i | \(0.635261\pi\) | |||||||
\(80\) | −1.27079e100 | −1.55542 | ||||||||
\(81\) | 2.59537e100 | 1.65476 | ||||||||
\(82\) | 6.25655e100 | 2.09463 | ||||||||
\(83\) | −4.88553e100 | −0.865589 | −0.432795 | − | 0.901493i | \(-0.642472\pi\) | ||||
−0.432795 | + | 0.901493i | \(0.642472\pi\) | |||||||
\(84\) | −2.76807e100 | −0.261526 | ||||||||
\(85\) | 2.19477e101 | 1.11403 | ||||||||
\(86\) | 3.84720e101 | 1.05676 | ||||||||
\(87\) | −1.12901e102 | −1.69020 | ||||||||
\(88\) | 2.51085e102 | 2.06291 | ||||||||
\(89\) | −3.37399e102 | −1.53168 | −0.765841 | − | 0.643030i | \(-0.777677\pi\) | ||||
−0.765841 | + | 0.643030i | \(0.777677\pi\) | |||||||
\(90\) | 1.28219e103 | 3.23757 | ||||||||
\(91\) | −6.51020e101 | −0.0920282 | ||||||||
\(92\) | −4.98078e102 | −0.396677 | ||||||||
\(93\) | 2.89766e103 | 1.30825 | ||||||||
\(94\) | −2.38617e103 | −0.614454 | ||||||||
\(95\) | −2.34464e103 | −0.346407 | ||||||||
\(96\) | −2.42608e104 | −2.06854 | ||||||||
\(97\) | −3.41463e104 | −1.68977 | −0.844885 | − | 0.534948i | \(-0.820331\pi\) | ||||
−0.844885 | + | 0.534948i | \(0.820331\pi\) | |||||||
\(98\) | 6.24468e104 | 1.80360 | ||||||||
\(99\) | −1.15748e105 | −1.96184 | ||||||||
\(100\) | −7.80401e104 | −0.780401 | ||||||||
\(101\) | 9.40507e104 | 0.557814 | 0.278907 | − | 0.960318i | \(-0.410028\pi\) | ||||
0.278907 | + | 0.960318i | \(0.410028\pi\) | |||||||
\(102\) | 1.25947e106 | 4.45327 | ||||||||
\(103\) | −7.48693e105 | −1.58617 | −0.793084 | − | 0.609112i | \(-0.791526\pi\) | ||||
−0.793084 | + | 0.609112i | \(0.791526\pi\) | |||||||
\(104\) | −2.60934e106 | −3.32874 | ||||||||
\(105\) | 1.20519e105 | 0.0930289 | ||||||||
\(106\) | 1.75433e106 | 0.823291 | ||||||||
\(107\) | 1.11641e106 | 0.320020 | 0.160010 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160010 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(108\) | 2.79431e107 | 4.91504 | ||||||||
\(109\) | −6.08327e106 | −0.659548 | −0.329774 | − | 0.944060i | \(-0.606973\pi\) | ||||
−0.329774 | + | 0.944060i | \(0.606973\pi\) | |||||||
\(110\) | −1.94735e107 | −1.30716 | ||||||||
\(111\) | −4.23163e106 | −0.176625 | ||||||||
\(112\) | −4.71537e106 | −0.122905 | ||||||||
\(113\) | −1.91150e107 | −0.312432 | −0.156216 | − | 0.987723i | \(-0.549930\pi\) | ||||
−0.156216 | + | 0.987723i | \(0.549930\pi\) | |||||||
\(114\) | −1.34547e108 | −1.38475 | ||||||||
\(115\) | 2.16859e107 | 0.141104 | ||||||||
\(116\) | −5.21223e108 | −2.15268 | ||||||||
\(117\) | 1.20288e109 | 3.16566 | ||||||||
\(118\) | −1.96980e109 | −3.31601 | ||||||||
\(119\) | 8.14389e107 | 0.0880271 | ||||||||
\(120\) | 4.83050e109 | 3.36494 | ||||||||
\(121\) | −4.61438e108 | −0.207913 | ||||||||
\(122\) | −2.50611e109 | −0.733009 | ||||||||
\(123\) | −1.08659e110 | −2.07037 | ||||||||
\(124\) | 1.33774e110 | 1.66622 | ||||||||
\(125\) | 1.33241e110 | 1.08859 | ||||||||
\(126\) | 4.75768e109 | 0.255824 | ||||||||
\(127\) | 7.03101e109 | 0.249645 | 0.124822 | − | 0.992179i | \(-0.460164\pi\) | ||||
0.124822 | + | 0.992179i | \(0.460164\pi\) | |||||||
\(128\) | 3.56652e110 | 0.838921 | ||||||||
\(129\) | −6.68154e110 | −1.04452 | ||||||||
\(130\) | 2.02374e111 | 2.10925 | ||||||||
\(131\) | −1.77240e111 | −1.23543 | −0.617717 | − | 0.786401i | \(-0.711942\pi\) | ||||
−0.617717 | + | 0.786401i | \(0.711942\pi\) | |||||||
\(132\) | −7.76778e111 | −3.63217 | ||||||||
\(133\) | −8.69999e109 | −0.0273721 | ||||||||
\(134\) | −9.68609e110 | −0.205658 | ||||||||
\(135\) | −1.21662e112 | −1.74836 | ||||||||
\(136\) | 3.26414e112 | 3.18402 | ||||||||
\(137\) | 1.65935e112 | 1.10181 | 0.550907 | − | 0.834567i | \(-0.314282\pi\) | ||||
0.550907 | + | 0.834567i | \(0.314282\pi\) | |||||||
\(138\) | 1.24445e112 | 0.564058 | ||||||||
\(139\) | −2.84779e112 | −0.883551 | −0.441775 | − | 0.897126i | \(-0.645651\pi\) | ||||
−0.441775 | + | 0.897126i | \(0.645651\pi\) | |||||||
\(140\) | 5.56392e111 | 0.118484 | ||||||||
\(141\) | 4.14413e112 | 0.607338 | ||||||||
\(142\) | −1.68213e113 | −1.70107 | ||||||||
\(143\) | −1.82690e113 | −1.27812 | ||||||||
\(144\) | 8.71251e113 | 4.22778 | ||||||||
\(145\) | 2.26936e113 | 0.765743 | ||||||||
\(146\) | −3.92375e113 | −0.922946 | ||||||||
\(147\) | −1.08453e114 | −1.78272 | ||||||||
\(148\) | −1.95359e113 | −0.224953 | ||||||||
\(149\) | −1.97570e114 | −1.59750 | −0.798752 | − | 0.601661i | \(-0.794506\pi\) | ||||
−0.798752 | + | 0.601661i | \(0.794506\pi\) | |||||||
\(150\) | 1.94983e114 | 1.10970 | ||||||||
\(151\) | 3.99582e114 | 1.60441 | 0.802207 | − | 0.597046i | \(-0.203659\pi\) | ||||
0.802207 | + | 0.597046i | \(0.203659\pi\) | |||||||
\(152\) | −3.48703e114 | −0.990072 | ||||||||
\(153\) | −1.50473e115 | −3.02802 | ||||||||
\(154\) | −7.22583e113 | −0.103288 | ||||||||
\(155\) | −5.82439e114 | −0.592702 | ||||||||
\(156\) | 8.07247e115 | 5.86091 | ||||||||
\(157\) | −3.24507e115 | −1.68458 | −0.842290 | − | 0.539024i | \(-0.818793\pi\) | ||||
−0.842290 | + | 0.539024i | \(0.818793\pi\) | |||||||
\(158\) | 4.01447e115 | 1.49325 | ||||||||
\(159\) | −3.04680e115 | −0.813756 | ||||||||
\(160\) | 4.87650e115 | 0.937150 | ||||||||
\(161\) | 8.04674e113 | 0.0111497 | ||||||||
\(162\) | −2.99366e116 | −2.99684 | ||||||||
\(163\) | 1.98748e116 | 1.44030 | 0.720150 | − | 0.693818i | \(-0.244073\pi\) | ||||
0.720150 | + | 0.693818i | \(0.244073\pi\) | |||||||
\(164\) | −5.01639e116 | −2.63687 | ||||||||
\(165\) | 3.38202e116 | 1.29202 | ||||||||
\(166\) | 5.63527e116 | 1.56762 | ||||||||
\(167\) | −6.79873e116 | −1.37979 | −0.689895 | − | 0.723910i | \(-0.742343\pi\) | ||||
−0.689895 | + | 0.723910i | \(0.742343\pi\) | |||||||
\(168\) | 1.79240e116 | 0.265888 | ||||||||
\(169\) | 9.77997e116 | 1.06239 | ||||||||
\(170\) | −2.53158e117 | −2.01755 | ||||||||
\(171\) | 1.60748e117 | 0.941565 | ||||||||
\(172\) | −3.08462e117 | −1.33033 | ||||||||
\(173\) | −3.33164e117 | −1.05983 | −0.529917 | − | 0.848049i | \(-0.677777\pi\) | ||||
−0.529917 | + | 0.848049i | \(0.677777\pi\) | |||||||
\(174\) | 1.30227e118 | 3.06102 | ||||||||
\(175\) | 1.26078e116 | 0.0219353 | ||||||||
\(176\) | −1.32323e118 | −1.70695 | ||||||||
\(177\) | 3.42100e118 | 3.27761 | ||||||||
\(178\) | 3.89177e118 | 2.77394 | ||||||||
\(179\) | −1.92920e118 | −1.02469 | −0.512345 | − | 0.858780i | \(-0.671223\pi\) | ||||
−0.512345 | + | 0.858780i | \(0.671223\pi\) | |||||||
\(180\) | −1.02804e119 | −4.07569 | ||||||||
\(181\) | −3.92801e118 | −1.16425 | −0.582126 | − | 0.813099i | \(-0.697779\pi\) | ||||
−0.582126 | + | 0.813099i | \(0.697779\pi\) | |||||||
\(182\) | 7.50926e117 | 0.166667 | ||||||||
\(183\) | 4.35244e118 | 0.724520 | ||||||||
\(184\) | 3.22520e118 | 0.403293 | ||||||||
\(185\) | 8.50573e117 | 0.0800195 | ||||||||
\(186\) | −3.34233e119 | −2.36930 | ||||||||
\(187\) | 2.28535e119 | 1.22255 | ||||||||
\(188\) | 1.91319e119 | 0.773520 | ||||||||
\(189\) | −4.51436e118 | −0.138150 | ||||||||
\(190\) | 2.70445e119 | 0.627357 | ||||||||
\(191\) | 5.36723e119 | 0.945145 | 0.472573 | − | 0.881292i | \(-0.343325\pi\) | ||||
0.472573 | + | 0.881292i | \(0.343325\pi\) | |||||||
\(192\) | 2.33793e119 | 0.312980 | ||||||||
\(193\) | −1.23058e120 | −1.25416 | −0.627079 | − | 0.778956i | \(-0.715750\pi\) | ||||
−0.627079 | + | 0.778956i | \(0.715750\pi\) | |||||||
\(194\) | 3.93865e120 | 3.06024 | ||||||||
\(195\) | −3.51468e120 | −2.08482 | ||||||||
\(196\) | −5.00688e120 | −2.27051 | ||||||||
\(197\) | −3.21266e120 | −1.11529 | −0.557644 | − | 0.830080i | \(-0.688295\pi\) | ||||
−0.557644 | + | 0.830080i | \(0.688295\pi\) | |||||||
\(198\) | 1.33510e121 | 3.55298 | ||||||||
\(199\) | −2.12151e120 | −0.433369 | −0.216685 | − | 0.976242i | \(-0.569524\pi\) | ||||
−0.216685 | + | 0.976242i | \(0.569524\pi\) | |||||||
\(200\) | 5.05332e120 | 0.793418 | ||||||||
\(201\) | 1.68221e120 | 0.203277 | ||||||||
\(202\) | −1.08484e121 | −1.01023 | ||||||||
\(203\) | 8.42066e119 | 0.0605068 | ||||||||
\(204\) | −1.00982e122 | −5.60610 | ||||||||
\(205\) | 2.18409e121 | 0.937979 | ||||||||
\(206\) | 8.63588e121 | 2.87262 | ||||||||
\(207\) | −1.48678e121 | −0.383534 | ||||||||
\(208\) | 1.37514e122 | 2.75436 | ||||||||
\(209\) | −2.44140e121 | −0.380153 | ||||||||
\(210\) | −1.39014e121 | −0.168479 | ||||||||
\(211\) | 1.16118e122 | 1.09665 | 0.548327 | − | 0.836264i | \(-0.315265\pi\) | ||||
0.548327 | + | 0.836264i | \(0.315265\pi\) | |||||||
\(212\) | −1.40659e122 | −1.03642 | ||||||||
\(213\) | 2.92141e122 | 1.68137 | ||||||||
\(214\) | −1.28774e122 | −0.579570 | ||||||||
\(215\) | 1.34301e122 | 0.473218 | ||||||||
\(216\) | −1.80939e123 | −4.99702 | ||||||||
\(217\) | −2.16120e121 | −0.0468336 | ||||||||
\(218\) | 7.01682e122 | 1.19447 | ||||||||
\(219\) | 6.81449e122 | 0.912257 | ||||||||
\(220\) | 1.56135e123 | 1.64555 | ||||||||
\(221\) | −2.37499e123 | −1.97273 | ||||||||
\(222\) | 4.88102e122 | 0.319874 | ||||||||
\(223\) | 7.24098e122 | 0.374793 | 0.187397 | − | 0.982284i | \(-0.439995\pi\) | ||||
0.187397 | + | 0.982284i | \(0.439995\pi\) | |||||||
\(224\) | 1.80947e122 | 0.0740510 | ||||||||
\(225\) | −2.32953e123 | −0.754546 | ||||||||
\(226\) | 2.20484e123 | 0.565828 | ||||||||
\(227\) | −2.60705e123 | −0.530630 | −0.265315 | − | 0.964162i | \(-0.585476\pi\) | ||||
−0.265315 | + | 0.964162i | \(0.585476\pi\) | |||||||
\(228\) | 1.07878e124 | 1.74322 | ||||||||
\(229\) | −3.82412e123 | −0.491098 | −0.245549 | − | 0.969384i | \(-0.578968\pi\) | ||||
−0.245549 | + | 0.969384i | \(0.578968\pi\) | |||||||
\(230\) | −2.50138e123 | −0.255546 | ||||||||
\(231\) | 1.25493e123 | 0.102092 | ||||||||
\(232\) | 3.37507e124 | 2.18859 | ||||||||
\(233\) | 2.49183e124 | 1.28923 | 0.644617 | − | 0.764505i | \(-0.277017\pi\) | ||||
0.644617 | + | 0.764505i | \(0.277017\pi\) | |||||||
\(234\) | −1.38747e125 | −5.73313 | ||||||||
\(235\) | −8.32986e123 | −0.275153 | ||||||||
\(236\) | 1.57935e125 | 4.17444 | ||||||||
\(237\) | −6.97204e124 | −1.47595 | ||||||||
\(238\) | −9.39366e123 | −0.159421 | ||||||||
\(239\) | −7.40706e123 | −0.100869 | −0.0504343 | − | 0.998727i | \(-0.516061\pi\) | ||||
−0.0504343 | + | 0.998727i | \(0.516061\pi\) | |||||||
\(240\) | −2.54570e125 | −2.78431 | ||||||||
\(241\) | −4.19382e124 | −0.368735 | −0.184368 | − | 0.982857i | \(-0.559024\pi\) | ||||
−0.184368 | + | 0.982857i | \(0.559024\pi\) | |||||||
\(242\) | 5.32251e124 | 0.376539 | ||||||||
\(243\) | 1.41521e125 | 0.806290 | ||||||||
\(244\) | 2.00936e125 | 0.922765 | ||||||||
\(245\) | 2.17995e125 | 0.807656 | ||||||||
\(246\) | 1.25334e126 | 3.74953 | ||||||||
\(247\) | 2.53716e125 | 0.613421 | ||||||||
\(248\) | −8.66225e125 | −1.69402 | ||||||||
\(249\) | −9.78693e125 | −1.54946 | ||||||||
\(250\) | −1.53689e126 | −1.97148 | ||||||||
\(251\) | 2.46814e125 | 0.256744 | 0.128372 | − | 0.991726i | \(-0.459025\pi\) | ||||
0.128372 | + | 0.991726i | \(0.459025\pi\) | |||||||
\(252\) | −3.81462e125 | −0.322050 | ||||||||
\(253\) | 2.25809e125 | 0.154851 | ||||||||
\(254\) | −8.10999e125 | −0.452117 | ||||||||
\(255\) | 4.39667e126 | 1.99418 | ||||||||
\(256\) | −4.58726e126 | −1.69416 | ||||||||
\(257\) | 1.85222e126 | 0.557448 | 0.278724 | − | 0.960371i | \(-0.410089\pi\) | ||||
0.278724 | + | 0.960371i | \(0.410089\pi\) | |||||||
\(258\) | 7.70690e126 | 1.89167 | ||||||||
\(259\) | 3.15613e124 | 0.00632291 | ||||||||
\(260\) | −1.62260e127 | −2.65528 | ||||||||
\(261\) | −1.55587e127 | −2.08136 | ||||||||
\(262\) | 2.04440e127 | 2.23742 | ||||||||
\(263\) | −1.47726e127 | −1.32367 | −0.661834 | − | 0.749650i | \(-0.730222\pi\) | ||||
−0.661834 | + | 0.749650i | \(0.730222\pi\) | |||||||
\(264\) | 5.02986e127 | 3.69275 | ||||||||
\(265\) | 6.12417e126 | 0.368671 | ||||||||
\(266\) | 1.00351e126 | 0.0495719 | ||||||||
\(267\) | −6.75894e127 | −2.74181 | ||||||||
\(268\) | 7.76614e126 | 0.258898 | ||||||||
\(269\) | 4.07814e127 | 1.11807 | 0.559033 | − | 0.829145i | \(-0.311172\pi\) | ||||
0.559033 | + | 0.829145i | \(0.311172\pi\) | |||||||
\(270\) | 1.40332e128 | 3.16635 | ||||||||
\(271\) | −2.10498e127 | −0.391165 | −0.195582 | − | 0.980687i | \(-0.562660\pi\) | ||||
−0.195582 | + | 0.980687i | \(0.562660\pi\) | |||||||
\(272\) | −1.72022e128 | −2.63461 | ||||||||
\(273\) | −1.30415e127 | −0.164737 | ||||||||
\(274\) | −1.91400e128 | −1.99543 | ||||||||
\(275\) | 3.53802e127 | 0.304645 | ||||||||
\(276\) | −9.97775e127 | −0.710077 | ||||||||
\(277\) | −1.88787e128 | −1.11118 | −0.555590 | − | 0.831456i | \(-0.687508\pi\) | ||||
−0.555590 | + | 0.831456i | \(0.687508\pi\) | |||||||
\(278\) | 3.28482e128 | 1.60015 | ||||||||
\(279\) | 3.99320e128 | 1.61102 | ||||||||
\(280\) | −3.60280e127 | −0.120460 | ||||||||
\(281\) | 1.51465e128 | 0.419982 | 0.209991 | − | 0.977703i | \(-0.432657\pi\) | ||||
0.209991 | + | 0.977703i | \(0.432657\pi\) | |||||||
\(282\) | −4.78010e128 | −1.09991 | ||||||||
\(283\) | −9.04953e127 | −0.172917 | −0.0864586 | − | 0.996255i | \(-0.527555\pi\) | ||||
−0.0864586 | + | 0.996255i | \(0.527555\pi\) | |||||||
\(284\) | 1.34871e129 | 2.14143 | ||||||||
\(285\) | −4.69689e128 | −0.620091 | ||||||||
\(286\) | 2.10726e129 | 2.31473 | ||||||||
\(287\) | 8.10427e127 | 0.0741164 | ||||||||
\(288\) | −3.34333e129 | −2.54726 | ||||||||
\(289\) | 1.39650e129 | 0.886960 | ||||||||
\(290\) | −2.61762e129 | −1.38679 | ||||||||
\(291\) | −6.84036e129 | −3.02480 | ||||||||
\(292\) | 3.14599e129 | 1.16187 | ||||||||
\(293\) | 6.96245e128 | 0.214888 | 0.107444 | − | 0.994211i | \(-0.465733\pi\) | ||||
0.107444 | + | 0.994211i | \(0.465733\pi\) | |||||||
\(294\) | 1.25096e130 | 3.22857 | ||||||||
\(295\) | −6.87634e129 | −1.48491 | ||||||||
\(296\) | 1.26500e129 | 0.228705 | ||||||||
\(297\) | −1.26683e130 | −1.91868 | ||||||||
\(298\) | 2.27889e130 | 2.89314 | ||||||||
\(299\) | −2.34666e129 | −0.249869 | ||||||||
\(300\) | −1.56334e130 | −1.39697 | ||||||||
\(301\) | 4.98338e128 | 0.0373923 | ||||||||
\(302\) | −4.60903e130 | −2.90566 | ||||||||
\(303\) | 1.88407e130 | 0.998525 | ||||||||
\(304\) | 1.83768e130 | 0.819233 | ||||||||
\(305\) | −8.74856e129 | −0.328243 | ||||||||
\(306\) | 1.73565e131 | 5.48387 | ||||||||
\(307\) | 4.13248e129 | 0.110014 | 0.0550068 | − | 0.998486i | \(-0.482482\pi\) | ||||
0.0550068 | + | 0.998486i | \(0.482482\pi\) | |||||||
\(308\) | 5.79354e129 | 0.130026 | ||||||||
\(309\) | −1.49982e131 | −2.83935 | ||||||||
\(310\) | 6.71821e130 | 1.07341 | ||||||||
\(311\) | −3.52591e130 | −0.475719 | −0.237859 | − | 0.971300i | \(-0.576446\pi\) | ||||
−0.237859 | + | 0.971300i | \(0.576446\pi\) | |||||||
\(312\) | −5.22716e131 | −5.95867 | ||||||||
\(313\) | 1.39264e131 | 1.34202 | 0.671011 | − | 0.741447i | \(-0.265860\pi\) | ||||
0.671011 | + | 0.741447i | \(0.265860\pi\) | |||||||
\(314\) | 3.74306e131 | 3.05084 | ||||||||
\(315\) | 1.66085e130 | 0.114558 | ||||||||
\(316\) | −3.21873e131 | −1.87981 | ||||||||
\(317\) | −2.13768e131 | −1.05762 | −0.528812 | − | 0.848739i | \(-0.677362\pi\) | ||||
−0.528812 | + | 0.848739i | \(0.677362\pi\) | |||||||
\(318\) | 3.51436e131 | 1.47375 | ||||||||
\(319\) | 2.36301e131 | 0.840341 | ||||||||
\(320\) | −4.69932e130 | −0.141795 | ||||||||
\(321\) | 2.23646e131 | 0.572857 | ||||||||
\(322\) | −9.28161e129 | −0.0201925 | ||||||||
\(323\) | −3.17385e131 | −0.586751 | ||||||||
\(324\) | 2.40026e132 | 3.77264 | ||||||||
\(325\) | −3.67680e131 | −0.491579 | ||||||||
\(326\) | −2.29248e132 | −2.60844 | ||||||||
\(327\) | −1.21863e132 | −1.18063 | ||||||||
\(328\) | 3.24826e132 | 2.68086 | ||||||||
\(329\) | −3.09087e130 | −0.0217418 | ||||||||
\(330\) | −3.90103e132 | −2.33990 | ||||||||
\(331\) | 1.84900e132 | 0.946166 | 0.473083 | − | 0.881018i | \(-0.343141\pi\) | ||||
0.473083 | + | 0.881018i | \(0.343141\pi\) | |||||||
\(332\) | −4.51826e132 | −1.97343 | ||||||||
\(333\) | −5.83153e131 | −0.217500 | ||||||||
\(334\) | 7.84207e132 | 2.49886 | ||||||||
\(335\) | −3.38130e131 | −0.0920941 | ||||||||
\(336\) | −9.44606e131 | −0.220008 | ||||||||
\(337\) | 1.77864e132 | 0.354421 | 0.177210 | − | 0.984173i | \(-0.443293\pi\) | ||||
0.177210 | + | 0.984173i | \(0.443293\pi\) | |||||||
\(338\) | −1.12808e133 | −1.92404 | ||||||||
\(339\) | −3.82921e132 | −0.559275 | ||||||||
\(340\) | 2.02978e133 | 2.53983 | ||||||||
\(341\) | −6.06477e132 | −0.650443 | ||||||||
\(342\) | −1.85417e133 | −1.70521 | ||||||||
\(343\) | 1.62111e132 | 0.127901 | ||||||||
\(344\) | 1.99738e133 | 1.35251 | ||||||||
\(345\) | 4.34422e132 | 0.252586 | ||||||||
\(346\) | 3.84292e133 | 1.91940 | ||||||||
\(347\) | 1.92289e133 | 0.825387 | 0.412694 | − | 0.910870i | \(-0.364588\pi\) | ||||
0.412694 | + | 0.910870i | \(0.364588\pi\) | |||||||
\(348\) | −1.04414e134 | −3.85344 | ||||||||
\(349\) | 2.67204e133 | 0.848220 | 0.424110 | − | 0.905611i | \(-0.360587\pi\) | ||||
0.424110 | + | 0.905611i | \(0.360587\pi\) | |||||||
\(350\) | −1.45427e132 | −0.0397257 | ||||||||
\(351\) | 1.31652e134 | 3.09601 | ||||||||
\(352\) | 5.07776e133 | 1.02845 | ||||||||
\(353\) | 7.63262e133 | 1.33199 | 0.665996 | − | 0.745955i | \(-0.268007\pi\) | ||||
0.665996 | + | 0.745955i | \(0.268007\pi\) | |||||||
\(354\) | −3.94599e134 | −5.93588 | ||||||||
\(355\) | −5.87214e133 | −0.761742 | ||||||||
\(356\) | −3.12035e134 | −3.49204 | ||||||||
\(357\) | 1.63142e133 | 0.157574 | ||||||||
\(358\) | 2.22526e134 | 1.85576 | ||||||||
\(359\) | −3.74967e133 | −0.270106 | −0.135053 | − | 0.990838i | \(-0.543120\pi\) | ||||
−0.135053 | + | 0.990838i | \(0.543120\pi\) | |||||||
\(360\) | 6.65682e134 | 4.14368 | ||||||||
\(361\) | −1.51930e134 | −0.817549 | ||||||||
\(362\) | 4.53080e134 | 2.10851 | ||||||||
\(363\) | −9.24376e133 | −0.372178 | ||||||||
\(364\) | −6.02079e133 | −0.209812 | ||||||||
\(365\) | −1.36974e134 | −0.413297 | ||||||||
\(366\) | −5.02037e134 | −1.31213 | ||||||||
\(367\) | 8.36768e134 | 1.89512 | 0.947560 | − | 0.319578i | \(-0.103541\pi\) | ||||
0.947560 | + | 0.319578i | \(0.103541\pi\) | |||||||
\(368\) | −1.69970e134 | −0.333704 | ||||||||
\(369\) | −1.49741e135 | −2.54951 | ||||||||
\(370\) | −9.81103e133 | −0.144919 | ||||||||
\(371\) | 2.27243e133 | 0.0291313 | ||||||||
\(372\) | 2.67983e135 | 2.98265 | ||||||||
\(373\) | −3.45717e134 | −0.334200 | −0.167100 | − | 0.985940i | \(-0.553440\pi\) | ||||
−0.167100 | + | 0.985940i | \(0.553440\pi\) | |||||||
\(374\) | −2.63606e135 | −2.21409 | ||||||||
\(375\) | 2.66916e135 | 1.94864 | ||||||||
\(376\) | −1.23885e135 | −0.786422 | ||||||||
\(377\) | −2.45570e135 | −1.35599 | ||||||||
\(378\) | 5.20714e134 | 0.250196 | ||||||||
\(379\) | 8.50571e134 | 0.355756 | 0.177878 | − | 0.984053i | \(-0.443077\pi\) | ||||
0.177878 | + | 0.984053i | \(0.443077\pi\) | |||||||
\(380\) | −2.16838e135 | −0.789762 | ||||||||
\(381\) | 1.40849e135 | 0.446880 | ||||||||
\(382\) | −6.19090e135 | −1.71170 | ||||||||
\(383\) | 5.56925e135 | 1.34234 | 0.671168 | − | 0.741305i | \(-0.265793\pi\) | ||||
0.671168 | + | 0.741305i | \(0.265793\pi\) | |||||||
\(384\) | 7.14462e135 | 1.50172 | ||||||||
\(385\) | −2.52246e134 | −0.0462525 | ||||||||
\(386\) | 1.41943e136 | 2.27133 | ||||||||
\(387\) | −9.20770e135 | −1.28625 | ||||||||
\(388\) | −3.15794e136 | −3.85246 | ||||||||
\(389\) | −3.38533e135 | −0.360784 | −0.180392 | − | 0.983595i | \(-0.557737\pi\) | ||||
−0.180392 | + | 0.983595i | \(0.557737\pi\) | |||||||
\(390\) | 4.05405e136 | 3.77569 | ||||||||
\(391\) | 2.93554e135 | 0.239005 | ||||||||
\(392\) | 3.24210e136 | 2.30838 | ||||||||
\(393\) | −3.55056e136 | −2.21151 | ||||||||
\(394\) | 3.70568e136 | 2.01983 | ||||||||
\(395\) | 1.40141e136 | 0.668677 | ||||||||
\(396\) | −1.07046e137 | −4.47275 | ||||||||
\(397\) | −4.90612e136 | −1.79571 | −0.897856 | − | 0.440290i | \(-0.854876\pi\) | ||||
−0.897856 | + | 0.440290i | \(0.854876\pi\) | |||||||
\(398\) | 2.44708e136 | 0.784849 | ||||||||
\(399\) | −1.74282e135 | −0.0489978 | ||||||||
\(400\) | −2.66313e136 | −0.656512 | ||||||||
\(401\) | 1.98317e136 | 0.428826 | 0.214413 | − | 0.976743i | \(-0.431216\pi\) | ||||
0.214413 | + | 0.976743i | \(0.431216\pi\) | |||||||
\(402\) | −1.94036e136 | −0.368142 | ||||||||
\(403\) | 6.30266e136 | 1.04956 | ||||||||
\(404\) | 8.69804e136 | 1.27174 | ||||||||
\(405\) | −1.04505e137 | −1.34199 | ||||||||
\(406\) | −9.71291e135 | −0.109580 | ||||||||
\(407\) | 8.85677e135 | 0.0878150 | ||||||||
\(408\) | 6.53888e137 | 5.69960 | ||||||||
\(409\) | −1.84011e137 | −1.41049 | −0.705246 | − | 0.708963i | \(-0.749163\pi\) | ||||
−0.705246 | + | 0.708963i | \(0.749163\pi\) | |||||||
\(410\) | −2.51926e137 | −1.69872 | ||||||||
\(411\) | 3.32409e137 | 1.97232 | ||||||||
\(412\) | −6.92410e137 | −3.61626 | ||||||||
\(413\) | −2.55153e136 | −0.117334 | ||||||||
\(414\) | 1.71495e137 | 0.694597 | ||||||||
\(415\) | 1.96721e137 | 0.701981 | ||||||||
\(416\) | −5.27693e137 | −1.65952 | ||||||||
\(417\) | −5.70484e137 | −1.58161 | ||||||||
\(418\) | 2.81606e137 | 0.688474 | ||||||||
\(419\) | 4.70201e137 | 1.01402 | 0.507011 | − | 0.861940i | \(-0.330750\pi\) | ||||
0.507011 | + | 0.861940i | \(0.330750\pi\) | |||||||
\(420\) | 1.11459e137 | 0.212094 | ||||||||
\(421\) | 1.06651e138 | 1.79124 | 0.895622 | − | 0.444817i | \(-0.146731\pi\) | ||||
0.895622 | + | 0.444817i | \(0.146731\pi\) | |||||||
\(422\) | −1.33937e138 | −1.98609 | ||||||||
\(423\) | 5.71095e137 | 0.747892 | ||||||||
\(424\) | 9.10809e137 | 1.05371 | ||||||||
\(425\) | 4.59947e137 | 0.470207 | ||||||||
\(426\) | −3.36973e138 | −3.04503 | ||||||||
\(427\) | −3.24623e136 | −0.0259368 | ||||||||
\(428\) | 1.03249e138 | 0.729604 | ||||||||
\(429\) | −3.65973e138 | −2.28792 | ||||||||
\(430\) | −1.54911e138 | −0.857017 | ||||||||
\(431\) | 2.22553e138 | 1.08987 | 0.544937 | − | 0.838477i | \(-0.316554\pi\) | ||||
0.544937 | + | 0.838477i | \(0.316554\pi\) | |||||||
\(432\) | 9.53560e138 | 4.13477 | ||||||||
\(433\) | 2.56876e138 | 0.986525 | 0.493263 | − | 0.869880i | \(-0.335804\pi\) | ||||
0.493263 | + | 0.869880i | \(0.335804\pi\) | |||||||
\(434\) | 2.49286e137 | 0.0848177 | ||||||||
\(435\) | 4.54609e138 | 1.37073 | ||||||||
\(436\) | −5.62597e138 | −1.50368 | ||||||||
\(437\) | −3.13599e137 | −0.0743189 | ||||||||
\(438\) | −7.86025e138 | −1.65213 | ||||||||
\(439\) | −1.19025e138 | −0.221947 | −0.110973 | − | 0.993823i | \(-0.535397\pi\) | ||||
−0.110973 | + | 0.993823i | \(0.535397\pi\) | |||||||
\(440\) | −1.01102e139 | −1.67299 | ||||||||
\(441\) | −1.49457e139 | −2.19528 | ||||||||
\(442\) | 2.73946e139 | 3.57269 | ||||||||
\(443\) | −1.45385e138 | −0.168393 | −0.0841963 | − | 0.996449i | \(-0.526832\pi\) | ||||
−0.0841963 | + | 0.996449i | \(0.526832\pi\) | |||||||
\(444\) | −3.91352e138 | −0.402681 | ||||||||
\(445\) | 1.35857e139 | 1.24217 | ||||||||
\(446\) | −8.35219e138 | −0.678766 | ||||||||
\(447\) | −3.95782e139 | −2.85964 | ||||||||
\(448\) | −1.74373e137 | −0.0112042 | ||||||||
\(449\) | −1.37731e138 | −0.0787227 | −0.0393613 | − | 0.999225i | \(-0.512532\pi\) | ||||
−0.0393613 | + | 0.999225i | \(0.512532\pi\) | |||||||
\(450\) | 2.68702e139 | 1.36651 | ||||||||
\(451\) | 2.27423e139 | 1.02936 | ||||||||
\(452\) | −1.76780e139 | −0.712306 | ||||||||
\(453\) | 8.00463e139 | 2.87201 | ||||||||
\(454\) | 3.00713e139 | 0.960993 | ||||||||
\(455\) | 2.62140e138 | 0.0746336 | ||||||||
\(456\) | −6.98538e139 | −1.77229 | ||||||||
\(457\) | 3.38698e139 | 0.765970 | 0.382985 | − | 0.923755i | \(-0.374896\pi\) | ||||
0.382985 | + | 0.923755i | \(0.374896\pi\) | |||||||
\(458\) | 4.41097e139 | 0.889399 | ||||||||
\(459\) | −1.64689e140 | −2.96141 | ||||||||
\(460\) | 2.00556e139 | 0.321699 | ||||||||
\(461\) | 2.63171e139 | 0.376651 | 0.188325 | − | 0.982107i | \(-0.439694\pi\) | ||||
0.188325 | + | 0.982107i | \(0.439694\pi\) | |||||||
\(462\) | −1.44751e139 | −0.184892 | ||||||||
\(463\) | 1.79225e139 | 0.204360 | 0.102180 | − | 0.994766i | \(-0.467418\pi\) | ||||
0.102180 | + | 0.994766i | \(0.467418\pi\) | |||||||
\(464\) | −1.77868e140 | −1.81094 | ||||||||
\(465\) | −1.16677e140 | −1.06098 | ||||||||
\(466\) | −2.87423e140 | −2.33486 | ||||||||
\(467\) | 1.27444e140 | 0.925087 | 0.462543 | − | 0.886597i | \(-0.346937\pi\) | ||||
0.462543 | + | 0.886597i | \(0.346937\pi\) | |||||||
\(468\) | 1.11245e141 | 7.21728 | ||||||||
\(469\) | −1.25466e138 | −0.00727702 | ||||||||
\(470\) | 9.60817e139 | 0.498314 | ||||||||
\(471\) | −6.50067e140 | −3.01551 | ||||||||
\(472\) | −1.02267e141 | −4.24407 | ||||||||
\(473\) | 1.39844e140 | 0.519319 | ||||||||
\(474\) | 8.04198e140 | 2.67301 | ||||||||
\(475\) | −4.91354e139 | −0.146211 | ||||||||
\(476\) | 7.53168e139 | 0.200690 | ||||||||
\(477\) | −4.19873e140 | −1.00208 | ||||||||
\(478\) | 8.54375e139 | 0.182677 | ||||||||
\(479\) | 2.18412e140 | 0.418467 | 0.209233 | − | 0.977866i | \(-0.432903\pi\) | ||||
0.209233 | + | 0.977866i | \(0.432903\pi\) | |||||||
\(480\) | 9.76885e140 | 1.67756 | ||||||||
\(481\) | −9.20417e139 | −0.141699 | ||||||||
\(482\) | 4.83741e140 | 0.667795 | ||||||||
\(483\) | 1.61196e139 | 0.0199586 | ||||||||
\(484\) | −4.26750e140 | −0.474015 | ||||||||
\(485\) | 1.37494e141 | 1.37038 | ||||||||
\(486\) | −1.63239e141 | −1.46023 | ||||||||
\(487\) | −6.62572e140 | −0.532062 | −0.266031 | − | 0.963964i | \(-0.585712\pi\) | ||||
−0.266031 | + | 0.963964i | \(0.585712\pi\) | |||||||
\(488\) | −1.30112e141 | −0.938157 | ||||||||
\(489\) | 3.98141e141 | 2.57823 | ||||||||
\(490\) | −2.51449e141 | −1.46270 | ||||||||
\(491\) | −1.37473e141 | −0.718518 | −0.359259 | − | 0.933238i | \(-0.616971\pi\) | ||||
−0.359259 | + | 0.933238i | \(0.616971\pi\) | |||||||
\(492\) | −1.00491e142 | −4.72018 | ||||||||
\(493\) | 3.07195e141 | 1.29703 | ||||||||
\(494\) | −2.92652e141 | −1.11093 | ||||||||
\(495\) | 4.66070e141 | 1.59103 | ||||||||
\(496\) | 4.56505e141 | 1.40171 | ||||||||
\(497\) | −2.17891e140 | −0.0601907 | ||||||||
\(498\) | 1.12888e142 | 2.80614 | ||||||||
\(499\) | 3.23152e141 | 0.722983 | 0.361491 | − | 0.932375i | \(-0.382268\pi\) | ||||
0.361491 | + | 0.932375i | \(0.382268\pi\) | |||||||
\(500\) | 1.23225e142 | 2.48184 | ||||||||
\(501\) | −1.36195e142 | −2.46991 | ||||||||
\(502\) | −2.84691e141 | −0.464974 | ||||||||
\(503\) | −9.98096e141 | −1.46843 | −0.734215 | − | 0.678917i | \(-0.762450\pi\) | ||||
−0.734215 | + | 0.678917i | \(0.762450\pi\) | |||||||
\(504\) | 2.47008e141 | 0.327422 | ||||||||
\(505\) | −3.78705e141 | −0.452380 | ||||||||
\(506\) | −2.60461e141 | −0.280441 | ||||||||
\(507\) | 1.95917e142 | 1.90176 | ||||||||
\(508\) | 6.50245e141 | 0.569157 | ||||||||
\(509\) | −9.19610e141 | −0.725972 | −0.362986 | − | 0.931795i | \(-0.618243\pi\) | ||||
−0.362986 | + | 0.931795i | \(0.618243\pi\) | |||||||
\(510\) | −5.07139e142 | −3.61154 | ||||||||
\(511\) | −5.08254e140 | −0.0326575 | ||||||||
\(512\) | 3.84448e142 | 2.22928 | ||||||||
\(513\) | 1.75934e142 | 0.920851 | ||||||||
\(514\) | −2.13647e142 | −1.00956 | ||||||||
\(515\) | 3.01469e142 | 1.28636 | ||||||||
\(516\) | −6.17925e142 | −2.38137 | ||||||||
\(517\) | −8.67363e141 | −0.301959 | ||||||||
\(518\) | −3.64047e140 | −0.0114511 | ||||||||
\(519\) | −6.67411e142 | −1.89717 | ||||||||
\(520\) | 1.05068e143 | 2.69957 | ||||||||
\(521\) | −3.87902e142 | −0.901034 | −0.450517 | − | 0.892768i | \(-0.648760\pi\) | ||||
−0.450517 | + | 0.892768i | \(0.648760\pi\) | |||||||
\(522\) | 1.79464e143 | 3.76943 | ||||||||
\(523\) | 3.97356e142 | 0.754815 | 0.377408 | − | 0.926047i | \(-0.376816\pi\) | ||||
0.377408 | + | 0.926047i | \(0.376816\pi\) | |||||||
\(524\) | −1.63916e143 | −2.81663 | ||||||||
\(525\) | 2.52566e141 | 0.0392656 | ||||||||
\(526\) | 1.70396e143 | 2.39722 | ||||||||
\(527\) | −7.88427e142 | −1.00393 | ||||||||
\(528\) | −2.65076e143 | −3.05556 | ||||||||
\(529\) | −9.29121e142 | −0.969727 | ||||||||
\(530\) | −7.06400e142 | −0.667678 | ||||||||
\(531\) | 4.71442e143 | 4.03613 | ||||||||
\(532\) | −8.04597e141 | −0.0624048 | ||||||||
\(533\) | −2.36343e143 | −1.66098 | ||||||||
\(534\) | 7.79618e143 | 4.96553 | ||||||||
\(535\) | −4.49536e142 | −0.259532 | ||||||||
\(536\) | −5.02880e142 | −0.263216 | ||||||||
\(537\) | −3.86466e143 | −1.83426 | ||||||||
\(538\) | −4.70398e143 | −2.02486 | ||||||||
\(539\) | 2.26991e143 | 0.886338 | ||||||||
\(540\) | −1.12516e144 | −3.98603 | ||||||||
\(541\) | 2.44851e143 | 0.787129 | 0.393564 | − | 0.919297i | \(-0.371242\pi\) | ||||
0.393564 | + | 0.919297i | \(0.371242\pi\) | |||||||
\(542\) | 2.42801e143 | 0.708416 | ||||||||
\(543\) | −7.86877e143 | −2.08409 | ||||||||
\(544\) | 6.60114e143 | 1.58737 | ||||||||
\(545\) | 2.44949e143 | 0.534884 | ||||||||
\(546\) | 1.50429e143 | 0.298345 | ||||||||
\(547\) | −3.00103e142 | −0.0540675 | −0.0270337 | − | 0.999635i | \(-0.508606\pi\) | ||||
−0.0270337 | + | 0.999635i | \(0.508606\pi\) | |||||||
\(548\) | 1.53461e144 | 2.51199 | ||||||||
\(549\) | 5.99801e143 | 0.892193 | ||||||||
\(550\) | −4.08097e143 | −0.551725 | ||||||||
\(551\) | −3.28171e143 | −0.403313 | ||||||||
\(552\) | 6.46088e143 | 0.721921 | ||||||||
\(553\) | 5.20005e142 | 0.0528370 | ||||||||
\(554\) | 2.17759e144 | 2.01239 | ||||||||
\(555\) | 1.70391e143 | 0.143240 | ||||||||
\(556\) | −2.63371e144 | −2.01438 | ||||||||
\(557\) | −5.76286e143 | −0.401089 | −0.200544 | − | 0.979685i | \(-0.564271\pi\) | ||||
−0.200544 | + | 0.979685i | \(0.564271\pi\) | |||||||
\(558\) | −4.60601e144 | −2.91762 | ||||||||
\(559\) | −1.45329e144 | −0.837980 | ||||||||
\(560\) | 1.89869e143 | 0.0996744 | ||||||||
\(561\) | 4.57812e144 | 2.18845 | ||||||||
\(562\) | −1.74709e144 | −0.760605 | ||||||||
\(563\) | −2.14485e144 | −0.850564 | −0.425282 | − | 0.905061i | \(-0.639825\pi\) | ||||
−0.425282 | + | 0.905061i | \(0.639825\pi\) | |||||||
\(564\) | 3.83260e144 | 1.38465 | ||||||||
\(565\) | 7.69686e143 | 0.253379 | ||||||||
\(566\) | 1.04383e144 | 0.313160 | ||||||||
\(567\) | −3.87776e143 | −0.106040 | ||||||||
\(568\) | −8.73325e144 | −2.17715 | ||||||||
\(569\) | 4.55830e144 | 1.03612 | 0.518059 | − | 0.855345i | \(-0.326655\pi\) | ||||
0.518059 | + | 0.855345i | \(0.326655\pi\) | |||||||
\(570\) | 5.41768e144 | 1.12301 | ||||||||
\(571\) | 8.13053e144 | 1.53717 | 0.768587 | − | 0.639745i | \(-0.220960\pi\) | ||||
0.768587 | + | 0.639745i | \(0.220960\pi\) | |||||||
\(572\) | −1.68956e145 | −2.91395 | ||||||||
\(573\) | 1.07519e145 | 1.69187 | ||||||||
\(574\) | −9.34796e143 | −0.134228 | ||||||||
\(575\) | 4.54461e143 | 0.0595572 | ||||||||
\(576\) | 3.22185e144 | 0.385412 | ||||||||
\(577\) | 6.19944e143 | 0.0677052 | 0.0338526 | − | 0.999427i | \(-0.489222\pi\) | ||||
0.0338526 | + | 0.999427i | \(0.489222\pi\) | |||||||
\(578\) | −1.61081e145 | −1.60632 | ||||||||
\(579\) | −2.46516e145 | −2.24503 | ||||||||
\(580\) | 2.09876e145 | 1.74579 | ||||||||
\(581\) | 7.29951e143 | 0.0554686 | ||||||||
\(582\) | 7.89009e145 | 5.47804 | ||||||||
\(583\) | 6.37692e144 | 0.404587 | ||||||||
\(584\) | −2.03712e145 | −1.18125 | ||||||||
\(585\) | −4.84351e145 | −2.56730 | ||||||||
\(586\) | −8.03092e144 | −0.389171 | ||||||||
\(587\) | 1.70804e145 | 0.756828 | 0.378414 | − | 0.925636i | \(-0.376470\pi\) | ||||
0.378414 | + | 0.925636i | \(0.376470\pi\) | |||||||
\(588\) | −1.00300e146 | −4.06436 | ||||||||
\(589\) | 8.42264e144 | 0.312173 | ||||||||
\(590\) | 7.93159e145 | 2.68924 | ||||||||
\(591\) | −6.43575e145 | −1.99644 | ||||||||
\(592\) | −6.66663e144 | −0.189242 | ||||||||
\(593\) | 2.00221e145 | 0.520160 | 0.260080 | − | 0.965587i | \(-0.416251\pi\) | ||||
0.260080 | + | 0.965587i | \(0.416251\pi\) | |||||||
\(594\) | 1.46123e146 | 3.47481 | ||||||||
\(595\) | −3.27922e144 | −0.0713888 | ||||||||
\(596\) | −1.82718e146 | −3.64210 | ||||||||
\(597\) | −4.24991e145 | −0.775759 | ||||||||
\(598\) | 2.70678e145 | 0.452523 | ||||||||
\(599\) | −7.83512e144 | −0.119988 | −0.0599940 | − | 0.998199i | \(-0.519108\pi\) | ||||
−0.0599940 | + | 0.998199i | \(0.519108\pi\) | |||||||
\(600\) | 1.01231e146 | 1.42027 | ||||||||
\(601\) | 7.00949e144 | 0.0901108 | 0.0450554 | − | 0.998984i | \(-0.485654\pi\) | ||||
0.0450554 | + | 0.998984i | \(0.485654\pi\) | |||||||
\(602\) | −5.74813e144 | −0.0677191 | ||||||||
\(603\) | 2.31822e145 | 0.250320 | ||||||||
\(604\) | 3.69544e146 | 3.65786 | ||||||||
\(605\) | 1.85803e145 | 0.168615 | ||||||||
\(606\) | −2.17320e146 | −1.80837 | ||||||||
\(607\) | 2.12280e146 | 1.61996 | 0.809978 | − | 0.586460i | \(-0.199479\pi\) | ||||
0.809978 | + | 0.586460i | \(0.199479\pi\) | |||||||
\(608\) | −7.05190e145 | −0.493592 | ||||||||
\(609\) | 1.68687e145 | 0.108311 | ||||||||
\(610\) | 1.00911e146 | 0.594461 | ||||||||
\(611\) | 9.01386e145 | 0.487245 | ||||||||
\(612\) | −1.39161e147 | −6.90350 | ||||||||
\(613\) | −2.40584e146 | −1.09545 | −0.547725 | − | 0.836658i | \(-0.684506\pi\) | ||||
−0.547725 | + | 0.836658i | \(0.684506\pi\) | |||||||
\(614\) | −4.76666e145 | −0.199239 | ||||||||
\(615\) | 4.37528e146 | 1.67904 | ||||||||
\(616\) | −3.75149e145 | −0.132195 | ||||||||
\(617\) | −2.96563e146 | −0.959723 | −0.479861 | − | 0.877344i | \(-0.659313\pi\) | ||||
−0.479861 | + | 0.877344i | \(0.659313\pi\) | |||||||
\(618\) | 1.72998e147 | 5.14217 | ||||||||
\(619\) | −3.44019e146 | −0.939340 | −0.469670 | − | 0.882842i | \(-0.655627\pi\) | ||||
−0.469670 | + | 0.882842i | \(0.655627\pi\) | |||||||
\(620\) | −5.38655e146 | −1.35128 | ||||||||
\(621\) | −1.62724e146 | −0.375097 | ||||||||
\(622\) | 4.06700e146 | 0.861547 | ||||||||
\(623\) | 5.04111e145 | 0.0981530 | ||||||||
\(624\) | 2.75474e147 | 4.93048 | ||||||||
\(625\) | −3.28489e146 | −0.540530 | ||||||||
\(626\) | −1.60635e147 | −2.43046 | ||||||||
\(627\) | −4.89073e146 | −0.680500 | ||||||||
\(628\) | −3.00112e147 | −3.84062 | ||||||||
\(629\) | 1.15139e146 | 0.135539 | ||||||||
\(630\) | −1.91573e146 | −0.207470 | ||||||||
\(631\) | 8.24712e146 | 0.821790 | 0.410895 | − | 0.911683i | \(-0.365216\pi\) | ||||
0.410895 | + | 0.911683i | \(0.365216\pi\) | |||||||
\(632\) | 2.08422e147 | 1.91116 | ||||||||
\(633\) | 2.32613e147 | 1.96308 | ||||||||
\(634\) | 2.46573e147 | 1.91540 | ||||||||
\(635\) | −2.83111e146 | −0.202458 | ||||||||
\(636\) | −2.81775e147 | −1.85526 | ||||||||
\(637\) | −2.35895e147 | −1.43021 | ||||||||
\(638\) | −2.72565e147 | −1.52189 | ||||||||
\(639\) | 4.02594e147 | 2.07048 | ||||||||
\(640\) | −1.43610e147 | −0.680353 | ||||||||
\(641\) | 2.02276e147 | 0.882871 | 0.441436 | − | 0.897293i | \(-0.354469\pi\) | ||||
0.441436 | + | 0.897293i | \(0.354469\pi\) | |||||||
\(642\) | −2.57967e147 | −1.03747 | ||||||||
\(643\) | −2.37322e147 | −0.879553 | −0.439776 | − | 0.898107i | \(-0.644942\pi\) | ||||
−0.439776 | + | 0.898107i | \(0.644942\pi\) | |||||||
\(644\) | 7.44183e145 | 0.0254198 | ||||||||
\(645\) | 2.69039e147 | 0.847091 | ||||||||
\(646\) | 3.66091e147 | 1.06263 | ||||||||
\(647\) | 5.29062e146 | 0.141590 | 0.0707949 | − | 0.997491i | \(-0.477446\pi\) | ||||
0.0707949 | + | 0.997491i | \(0.477446\pi\) | |||||||
\(648\) | −1.55424e148 | −3.83557 | ||||||||
\(649\) | −7.16013e147 | −1.62957 | ||||||||
\(650\) | 4.24105e147 | 0.890271 | ||||||||
\(651\) | −4.32941e146 | −0.0838353 | ||||||||
\(652\) | 1.83807e148 | 3.28370 | ||||||||
\(653\) | −4.21757e146 | −0.0695218 | −0.0347609 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347609 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(654\) | 1.40564e148 | 2.13818 | ||||||||
\(655\) | 7.13677e147 | 1.00192 | ||||||||
\(656\) | −1.71185e148 | −2.21827 | ||||||||
\(657\) | 9.39091e147 | 1.12338 | ||||||||
\(658\) | 3.56520e146 | 0.0393754 | ||||||||
\(659\) | −1.62818e148 | −1.66042 | −0.830212 | − | 0.557448i | \(-0.811781\pi\) | ||||
−0.830212 | + | 0.557448i | \(0.811781\pi\) | |||||||
\(660\) | 3.12778e148 | 2.94564 | ||||||||
\(661\) | 6.87944e147 | 0.598380 | 0.299190 | − | 0.954194i | \(-0.403284\pi\) | ||||
0.299190 | + | 0.954194i | \(0.403284\pi\) | |||||||
\(662\) | −2.13275e148 | −1.71355 | ||||||||
\(663\) | −4.75769e148 | −3.53131 | ||||||||
\(664\) | 2.92570e148 | 2.00635 | ||||||||
\(665\) | 3.50314e146 | 0.0221984 | ||||||||
\(666\) | 6.72644e147 | 0.393902 | ||||||||
\(667\) | 3.03530e147 | 0.164284 | ||||||||
\(668\) | −6.28763e148 | −3.14574 | ||||||||
\(669\) | 1.45055e148 | 0.670905 | ||||||||
\(670\) | 3.90020e147 | 0.166786 | ||||||||
\(671\) | −9.10961e147 | −0.360220 | ||||||||
\(672\) | 3.62482e147 | 0.132556 | ||||||||
\(673\) | −4.65685e147 | −0.157508 | −0.0787538 | − | 0.996894i | \(-0.525094\pi\) | ||||
−0.0787538 | + | 0.996894i | \(0.525094\pi\) | |||||||
\(674\) | −2.05160e148 | −0.641871 | ||||||||
\(675\) | −2.54960e148 | −0.737946 | ||||||||
\(676\) | 9.04477e148 | 2.42212 | ||||||||
\(677\) | 6.98042e148 | 1.72972 | 0.864861 | − | 0.502012i | \(-0.167407\pi\) | ||||
0.864861 | + | 0.502012i | \(0.167407\pi\) | |||||||
\(678\) | 4.41685e148 | 1.01287 | ||||||||
\(679\) | 5.10183e147 | 0.108284 | ||||||||
\(680\) | −1.31434e149 | −2.58220 | ||||||||
\(681\) | −5.22257e148 | −0.949863 | ||||||||
\(682\) | 6.99548e148 | 1.17798 | ||||||||
\(683\) | 8.39022e148 | 1.30824 | 0.654118 | − | 0.756392i | \(-0.273040\pi\) | ||||
0.654118 | + | 0.756392i | \(0.273040\pi\) | |||||||
\(684\) | 1.48664e149 | 2.14665 | ||||||||
\(685\) | −6.68154e148 | −0.893556 | ||||||||
\(686\) | −1.86989e148 | −0.231633 | ||||||||
\(687\) | −7.66065e148 | −0.879098 | ||||||||
\(688\) | −1.05263e149 | −1.11913 | ||||||||
\(689\) | −6.62705e148 | −0.652847 | ||||||||
\(690\) | −5.01089e148 | −0.457444 | ||||||||
\(691\) | 1.77282e149 | 1.49992 | 0.749959 | − | 0.661484i | \(-0.230073\pi\) | ||||
0.749959 | + | 0.661484i | \(0.230073\pi\) | |||||||
\(692\) | −3.08119e149 | −2.41629 | ||||||||
\(693\) | 1.72939e148 | 0.125719 | ||||||||
\(694\) | −2.21798e149 | −1.49481 | ||||||||
\(695\) | 1.14669e149 | 0.716548 | ||||||||
\(696\) | 6.76110e149 | 3.91771 | ||||||||
\(697\) | 2.95652e149 | 1.58877 | ||||||||
\(698\) | −3.08210e149 | −1.53616 | ||||||||
\(699\) | 4.99175e149 | 2.30782 | ||||||||
\(700\) | 1.16600e148 | 0.0500096 | ||||||||
\(701\) | −2.47268e149 | −0.983948 | −0.491974 | − | 0.870610i | \(-0.663725\pi\) | ||||
−0.491974 | + | 0.870610i | \(0.663725\pi\) | |||||||
\(702\) | −1.51855e150 | −5.60700 | ||||||||
\(703\) | −1.23001e148 | −0.0421458 | ||||||||
\(704\) | −4.89326e148 | −0.155609 | ||||||||
\(705\) | −1.66868e149 | −0.492543 | ||||||||
\(706\) | −8.80394e149 | −2.41229 | ||||||||
\(707\) | −1.40522e148 | −0.0357458 | ||||||||
\(708\) | 3.16383e150 | 7.47252 | ||||||||
\(709\) | −6.59385e149 | −1.44614 | −0.723072 | − | 0.690772i | \(-0.757271\pi\) | ||||
−0.723072 | + | 0.690772i | \(0.757271\pi\) | |||||||
\(710\) | 6.77329e149 | 1.37955 | ||||||||
\(711\) | −9.60803e149 | −1.81753 | ||||||||
\(712\) | 2.02052e150 | 3.55028 | ||||||||
\(713\) | −7.79022e148 | −0.127160 | ||||||||
\(714\) | −1.88178e149 | −0.285374 | ||||||||
\(715\) | 7.35619e149 | 1.03654 | ||||||||
\(716\) | −1.78417e150 | −2.33616 | ||||||||
\(717\) | −1.48382e149 | −0.180561 | ||||||||
\(718\) | 4.32510e149 | 0.489173 | ||||||||
\(719\) | 6.21958e149 | 0.653875 | 0.326937 | − | 0.945046i | \(-0.393983\pi\) | ||||
0.326937 | + | 0.945046i | \(0.393983\pi\) | |||||||
\(720\) | −3.50818e150 | −3.42867 | ||||||||
\(721\) | 1.11863e149 | 0.101645 | ||||||||
\(722\) | 1.75245e150 | 1.48062 | ||||||||
\(723\) | −8.40126e149 | −0.660061 | ||||||||
\(724\) | −3.63272e150 | −2.65434 | ||||||||
\(725\) | 4.75579e149 | 0.323204 | ||||||||
\(726\) | 1.06623e150 | 0.674030 | ||||||||
\(727\) | −2.32064e149 | −0.136474 | −0.0682372 | − | 0.997669i | \(-0.521737\pi\) | ||||
−0.0682372 | + | 0.997669i | \(0.521737\pi\) | |||||||
\(728\) | 3.89864e149 | 0.213312 | ||||||||
\(729\) | −4.15335e149 | −0.211448 | ||||||||
\(730\) | 1.57994e150 | 0.748497 | ||||||||
\(731\) | 1.81799e150 | 0.801547 | ||||||||
\(732\) | 4.02524e150 | 1.65181 | ||||||||
\(733\) | −1.28759e150 | −0.491833 | −0.245917 | − | 0.969291i | \(-0.579089\pi\) | ||||
−0.245917 | + | 0.969291i | \(0.579089\pi\) | |||||||
\(734\) | −9.65180e150 | −3.43214 | ||||||||
\(735\) | 4.36698e150 | 1.44576 | ||||||||
\(736\) | 6.52240e149 | 0.201058 | ||||||||
\(737\) | −3.52085e149 | −0.101066 | ||||||||
\(738\) | 1.72721e151 | 4.61727 | ||||||||
\(739\) | −7.51915e150 | −1.87213 | −0.936064 | − | 0.351830i | \(-0.885559\pi\) | ||||
−0.936064 | + | 0.351830i | \(0.885559\pi\) | |||||||
\(740\) | 7.86632e149 | 0.182434 | ||||||||
\(741\) | 5.08257e150 | 1.09806 | ||||||||
\(742\) | −2.62116e149 | −0.0527580 | ||||||||
\(743\) | −8.03286e150 | −1.50646 | −0.753229 | − | 0.657758i | \(-0.771505\pi\) | ||||
−0.753229 | + | 0.657758i | \(0.771505\pi\) | |||||||
\(744\) | −1.73526e151 | −3.03240 | ||||||||
\(745\) | 7.95536e150 | 1.29555 | ||||||||
\(746\) | 3.98771e150 | 0.605250 | ||||||||
\(747\) | −1.34872e151 | −1.90805 | ||||||||
\(748\) | 2.11355e151 | 2.78726 | ||||||||
\(749\) | −1.66805e149 | −0.0205075 | ||||||||
\(750\) | −3.07877e151 | −3.52907 | ||||||||
\(751\) | 6.97978e150 | 0.746010 | 0.373005 | − | 0.927829i | \(-0.378327\pi\) | ||||
0.373005 | + | 0.927829i | \(0.378327\pi\) | |||||||
\(752\) | 6.52879e150 | 0.650723 | ||||||||
\(753\) | 4.94431e150 | 0.459589 | ||||||||
\(754\) | 2.83256e151 | 2.45575 | ||||||||
\(755\) | −1.60896e151 | −1.30116 | ||||||||
\(756\) | −4.17500e150 | −0.314965 | ||||||||
\(757\) | −1.00145e151 | −0.704851 | −0.352426 | − | 0.935840i | \(-0.614643\pi\) | ||||
−0.352426 | + | 0.935840i | \(0.614643\pi\) | |||||||
\(758\) | −9.81101e150 | −0.644288 | ||||||||
\(759\) | 4.52351e150 | 0.277193 | ||||||||
\(760\) | 1.40409e151 | 0.802935 | ||||||||
\(761\) | −3.09059e151 | −1.64948 | −0.824741 | − | 0.565511i | \(-0.808679\pi\) | ||||
−0.824741 | + | 0.565511i | \(0.808679\pi\) | |||||||
\(762\) | −1.62463e151 | −0.809318 | ||||||||
\(763\) | 9.08907e149 | 0.0422650 | ||||||||
\(764\) | 4.96375e151 | 2.15481 | ||||||||
\(765\) | 6.05896e151 | 2.45569 | ||||||||
\(766\) | −6.42392e151 | −2.43103 | ||||||||
\(767\) | 7.44098e151 | 2.62950 | ||||||||
\(768\) | −9.18942e151 | −3.03266 | ||||||||
\(769\) | 2.69582e150 | 0.0830917 | 0.0415459 | − | 0.999137i | \(-0.486772\pi\) | ||||
0.0415459 | + | 0.999137i | \(0.486772\pi\) | |||||||
\(770\) | 2.90956e150 | 0.0837652 | ||||||||
\(771\) | 3.71046e151 | 0.997869 | ||||||||
\(772\) | −1.13807e152 | −2.85932 | ||||||||
\(773\) | 3.50661e151 | 0.823122 | 0.411561 | − | 0.911382i | \(-0.364984\pi\) | ||||
0.411561 | + | 0.911382i | \(0.364984\pi\) | |||||||
\(774\) | 1.06207e152 | 2.32945 | ||||||||
\(775\) | −1.22059e151 | −0.250167 | ||||||||
\(776\) | 2.04485e152 | 3.91672 | ||||||||
\(777\) | 6.32251e149 | 0.0113184 | ||||||||
\(778\) | 3.90485e151 | 0.653394 | ||||||||
\(779\) | −3.15841e151 | −0.494028 | ||||||||
\(780\) | −3.25046e152 | −4.75312 | ||||||||
\(781\) | −6.11448e151 | −0.835951 | ||||||||
\(782\) | −3.38603e151 | −0.432849 | ||||||||
\(783\) | −1.70286e152 | −2.03557 | ||||||||
\(784\) | −1.70860e152 | −1.91006 | ||||||||
\(785\) | 1.30666e152 | 1.36617 | ||||||||
\(786\) | 4.09544e152 | 4.00513 | ||||||||
\(787\) | 1.02568e152 | 0.938289 | 0.469145 | − | 0.883121i | \(-0.344562\pi\) | ||||
0.469145 | + | 0.883121i | \(0.344562\pi\) | |||||||
\(788\) | −2.97115e152 | −2.54271 | ||||||||
\(789\) | −2.95931e152 | −2.36945 | ||||||||
\(790\) | −1.61647e152 | −1.21100 | ||||||||
\(791\) | 2.85599e150 | 0.0200213 | ||||||||
\(792\) | 6.93155e152 | 4.54735 | ||||||||
\(793\) | 9.46693e151 | 0.581255 | ||||||||
\(794\) | 5.65902e152 | 3.25211 | ||||||||
\(795\) | 1.22682e152 | 0.659945 | ||||||||
\(796\) | −1.96202e152 | −0.988025 | ||||||||
\(797\) | 6.06121e151 | 0.285757 | 0.142879 | − | 0.989740i | \(-0.454364\pi\) | ||||
0.142879 | + | 0.989740i | \(0.454364\pi\) | |||||||
\(798\) | 2.01028e151 | 0.0887371 | ||||||||
\(799\) | −1.12758e152 | −0.466061 | ||||||||
\(800\) | 1.02195e152 | 0.395552 | ||||||||
\(801\) | −9.31437e152 | −3.37634 | ||||||||
\(802\) | −2.28751e152 | −0.776621 | ||||||||
\(803\) | −1.42627e152 | −0.453560 | ||||||||
\(804\) | 1.55575e152 | 0.463444 | ||||||||
\(805\) | −3.24010e150 | −0.00904222 | ||||||||
\(806\) | −7.26987e152 | −1.90080 | ||||||||
\(807\) | 8.16953e152 | 2.00141 | ||||||||
\(808\) | −5.63223e152 | −1.29296 | ||||||||
\(809\) | 2.40237e152 | 0.516823 | 0.258412 | − | 0.966035i | \(-0.416801\pi\) | ||||
0.258412 | + | 0.966035i | \(0.416801\pi\) | |||||||
\(810\) | 1.20543e153 | 2.43040 | ||||||||
\(811\) | 8.16006e152 | 1.54205 | 0.771025 | − | 0.636805i | \(-0.219744\pi\) | ||||
0.771025 | + | 0.636805i | \(0.219744\pi\) | |||||||
\(812\) | 7.78764e151 | 0.137948 | ||||||||
\(813\) | −4.21680e152 | −0.700211 | ||||||||
\(814\) | −1.02159e152 | −0.159037 | ||||||||
\(815\) | −8.00278e152 | −1.16806 | ||||||||
\(816\) | −3.44603e153 | −4.71612 | ||||||||
\(817\) | −1.94213e152 | −0.249241 | ||||||||
\(818\) | 2.12250e153 | 2.55446 | ||||||||
\(819\) | −1.79723e152 | −0.202861 | ||||||||
\(820\) | 2.01990e153 | 2.13847 | ||||||||
\(821\) | 9.67277e152 | 0.960583 | 0.480292 | − | 0.877109i | \(-0.340531\pi\) | ||||
0.480292 | + | 0.877109i | \(0.340531\pi\) | |||||||
\(822\) | −3.83421e153 | −3.57195 | ||||||||
\(823\) | 6.39371e152 | 0.558807 | 0.279403 | − | 0.960174i | \(-0.409863\pi\) | ||||
0.279403 | + | 0.960174i | \(0.409863\pi\) | |||||||
\(824\) | 4.48355e153 | 3.67658 | ||||||||
\(825\) | 7.08754e152 | 0.545335 | ||||||||
\(826\) | 2.94309e152 | 0.212496 | ||||||||
\(827\) | −1.35582e153 | −0.918675 | −0.459338 | − | 0.888262i | \(-0.651913\pi\) | ||||
−0.459338 | + | 0.888262i | \(0.651913\pi\) | |||||||
\(828\) | −1.37501e153 | −0.874409 | ||||||||
\(829\) | −1.59964e151 | −0.00954791 | −0.00477396 | − | 0.999989i | \(-0.501520\pi\) | ||||
−0.00477396 | + | 0.999989i | \(0.501520\pi\) | |||||||
\(830\) | −2.26910e153 | −1.27132 | ||||||||
\(831\) | −3.78187e153 | −1.98909 | ||||||||
\(832\) | 5.08520e152 | 0.251092 | ||||||||
\(833\) | 2.95092e153 | 1.36803 | ||||||||
\(834\) | 6.58031e153 | 2.86437 | ||||||||
\(835\) | 2.73758e153 | 1.11899 | ||||||||
\(836\) | −2.25787e153 | −0.866701 | ||||||||
\(837\) | 4.37045e153 | 1.57558 | ||||||||
\(838\) | −5.42359e153 | −1.83644 | ||||||||
\(839\) | −2.91785e153 | −0.928025 | −0.464012 | − | 0.885829i | \(-0.653591\pi\) | ||||
−0.464012 | + | 0.885829i | \(0.653591\pi\) | |||||||
\(840\) | −7.21730e152 | −0.215631 | ||||||||
\(841\) | −3.86438e152 | −0.108465 | ||||||||
\(842\) | −1.23018e154 | −3.24402 | ||||||||
\(843\) | 3.03422e153 | 0.751795 | ||||||||
\(844\) | 1.07389e154 | 2.50023 | ||||||||
\(845\) | −3.93801e153 | −0.861588 | ||||||||
\(846\) | −6.58736e153 | −1.35446 | ||||||||
\(847\) | 6.89439e151 | 0.0133235 | ||||||||
\(848\) | −4.80001e153 | −0.871887 | ||||||||
\(849\) | −1.81285e153 | −0.309533 | ||||||||
\(850\) | −5.30531e153 | −0.851564 | ||||||||
\(851\) | 1.13766e152 | 0.0171676 | ||||||||
\(852\) | 2.70179e154 | 3.83330 | ||||||||
\(853\) | −1.89242e153 | −0.252460 | −0.126230 | − | 0.992001i | \(-0.540288\pi\) | ||||
−0.126230 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(854\) | 3.74440e152 | 0.0469726 | ||||||||
\(855\) | −6.47269e153 | −0.763597 | ||||||||
\(856\) | −6.68566e153 | −0.741774 | ||||||||
\(857\) | 1.69723e154 | 1.77111 | 0.885557 | − | 0.464531i | \(-0.153777\pi\) | ||||
0.885557 | + | 0.464531i | \(0.153777\pi\) | |||||||
\(858\) | 4.22136e154 | 4.14352 | ||||||||
\(859\) | −1.63155e154 | −1.50646 | −0.753232 | − | 0.657755i | \(-0.771506\pi\) | ||||
−0.753232 | + | 0.657755i | \(0.771506\pi\) | |||||||
\(860\) | 1.24205e154 | 1.07888 | ||||||||
\(861\) | 1.62349e153 | 0.132673 | ||||||||
\(862\) | −2.56706e154 | −1.97381 | ||||||||
\(863\) | −1.13157e153 | −0.0818682 | −0.0409341 | − | 0.999162i | \(-0.513033\pi\) | ||||
−0.0409341 | + | 0.999162i | \(0.513033\pi\) | |||||||
\(864\) | −3.65918e154 | −2.49122 | ||||||||
\(865\) | 1.34152e154 | 0.859512 | ||||||||
\(866\) | −2.96296e154 | −1.78664 | ||||||||
\(867\) | 2.79754e154 | 1.58772 | ||||||||
\(868\) | −1.99873e153 | −0.106775 | ||||||||
\(869\) | 1.45924e154 | 0.733819 | ||||||||
\(870\) | −5.24374e154 | −2.48245 | ||||||||
\(871\) | 3.65896e153 | 0.163081 | ||||||||
\(872\) | 3.64297e154 | 1.52876 | ||||||||
\(873\) | −9.42656e154 | −3.72482 | ||||||||
\(874\) | 3.61724e153 | 0.134595 | ||||||||
\(875\) | −1.99077e153 | −0.0697587 | ||||||||
\(876\) | 6.30221e154 | 2.07983 | ||||||||
\(877\) | 1.22909e154 | 0.382038 | 0.191019 | − | 0.981586i | \(-0.438821\pi\) | ||||
0.191019 | + | 0.981586i | \(0.438821\pi\) | |||||||
\(878\) | 1.37290e154 | 0.401955 | ||||||||
\(879\) | 1.39475e154 | 0.384663 | ||||||||
\(880\) | 5.32813e154 | 1.38431 | ||||||||
\(881\) | −7.81284e153 | −0.191238 | −0.0956189 | − | 0.995418i | \(-0.530483\pi\) | ||||
−0.0956189 | + | 0.995418i | \(0.530483\pi\) | |||||||
\(882\) | 1.72393e155 | 3.97575 | ||||||||
\(883\) | 1.14392e154 | 0.248575 | 0.124288 | − | 0.992246i | \(-0.460335\pi\) | ||||
0.124288 | + | 0.992246i | \(0.460335\pi\) | |||||||
\(884\) | −2.19645e155 | −4.49756 | ||||||||
\(885\) | −1.37750e155 | −2.65810 | ||||||||
\(886\) | 1.67696e154 | 0.304966 | ||||||||
\(887\) | 8.81345e154 | 1.51062 | 0.755311 | − | 0.655367i | \(-0.227486\pi\) | ||||
0.755311 | + | 0.655367i | \(0.227486\pi\) | |||||||
\(888\) | 2.53411e154 | 0.409398 | ||||||||
\(889\) | −1.05051e153 | −0.0159977 | ||||||||
\(890\) | −1.56706e155 | −2.24963 | ||||||||
\(891\) | −1.08818e155 | −1.47273 | ||||||||
\(892\) | 6.69664e154 | 0.854481 | ||||||||
\(893\) | 1.20458e154 | 0.144922 | ||||||||
\(894\) | 4.56519e155 | 5.17892 | ||||||||
\(895\) | 7.76812e154 | 0.831010 | ||||||||
\(896\) | −5.32876e153 | −0.0537596 | ||||||||
\(897\) | −4.70094e154 | −0.447282 | ||||||||
\(898\) | 1.58868e154 | 0.142570 | ||||||||
\(899\) | −8.15222e154 | −0.690068 | ||||||||
\(900\) | −2.15441e155 | −1.72027 | ||||||||
\(901\) | 8.29007e154 | 0.624463 | ||||||||
\(902\) | −2.62324e155 | −1.86421 | ||||||||
\(903\) | 9.98294e153 | 0.0669348 | ||||||||
\(904\) | 1.14470e155 | 0.724187 | ||||||||
\(905\) | 1.58165e155 | 0.944193 | ||||||||
\(906\) | −9.23303e155 | −5.20132 | ||||||||
\(907\) | 2.85448e155 | 1.51756 | 0.758778 | − | 0.651349i | \(-0.225797\pi\) | ||||
0.758778 | + | 0.651349i | \(0.225797\pi\) | |||||||
\(908\) | −2.41107e155 | −1.20977 | ||||||||
\(909\) | 2.59640e155 | 1.22961 | ||||||||
\(910\) | −3.02368e154 | −0.135165 | ||||||||
\(911\) | 3.07697e155 | 1.29840 | 0.649199 | − | 0.760619i | \(-0.275104\pi\) | ||||
0.649199 | + | 0.760619i | \(0.275104\pi\) | |||||||
\(912\) | 3.68133e155 | 1.46648 | ||||||||
\(913\) | 2.04840e155 | 0.770368 | ||||||||
\(914\) | −3.90675e155 | −1.38720 | ||||||||
\(915\) | −1.75255e155 | −0.587576 | ||||||||
\(916\) | −3.53664e155 | −1.11964 | ||||||||
\(917\) | 2.64816e154 | 0.0791689 | ||||||||
\(918\) | 1.89962e156 | 5.36323 | ||||||||
\(919\) | −6.63998e155 | −1.77053 | −0.885263 | − | 0.465092i | \(-0.846021\pi\) | ||||
−0.885263 | + | 0.465092i | \(0.846021\pi\) | |||||||
\(920\) | −1.29866e155 | −0.327065 | ||||||||
\(921\) | 8.27839e154 | 0.196932 | ||||||||
\(922\) | −3.03557e155 | −0.682130 | ||||||||
\(923\) | 6.35432e155 | 1.34890 | ||||||||
\(924\) | 1.16059e155 | 0.232756 | ||||||||
\(925\) | 1.78251e154 | 0.0337746 | ||||||||
\(926\) | −2.06729e155 | −0.370104 | ||||||||
\(927\) | −2.06687e156 | −3.49645 | ||||||||
\(928\) | 6.82548e155 | 1.09110 | ||||||||
\(929\) | 1.50933e155 | 0.228014 | 0.114007 | − | 0.993480i | \(-0.463631\pi\) | ||||
0.114007 | + | 0.993480i | \(0.463631\pi\) | |||||||
\(930\) | 1.34583e156 | 1.92147 | ||||||||
\(931\) | −3.15242e155 | −0.425388 | ||||||||
\(932\) | 2.30450e156 | 2.93929 | ||||||||
\(933\) | −7.06327e155 | −0.851568 | ||||||||
\(934\) | −1.47001e156 | −1.67537 | ||||||||
\(935\) | −9.20219e155 | −0.991474 | ||||||||
\(936\) | −7.20344e156 | −7.33767 | ||||||||
\(937\) | 1.05238e156 | 1.01355 | 0.506773 | − | 0.862079i | \(-0.330838\pi\) | ||||
0.506773 | + | 0.862079i | \(0.330838\pi\) | |||||||
\(938\) | 1.44721e154 | 0.0131790 | ||||||||
\(939\) | 2.78980e156 | 2.40231 | ||||||||
\(940\) | −7.70366e155 | −0.627314 | ||||||||
\(941\) | −2.16414e156 | −1.66660 | −0.833298 | − | 0.552825i | \(-0.813550\pi\) | ||||
−0.833298 | + | 0.552825i | \(0.813550\pi\) | |||||||
\(942\) | 7.49828e156 | 5.46121 | ||||||||
\(943\) | 2.92126e155 | 0.201236 | ||||||||
\(944\) | 5.38955e156 | 3.51174 | ||||||||
\(945\) | 1.81776e155 | 0.112038 | ||||||||
\(946\) | −1.61305e156 | −0.940508 | ||||||||
\(947\) | 1.62005e156 | 0.893625 | 0.446813 | − | 0.894628i | \(-0.352559\pi\) | ||||
0.446813 | + | 0.894628i | \(0.352559\pi\) | |||||||
\(948\) | −6.44792e156 | −3.36498 | ||||||||
\(949\) | 1.48221e156 | 0.731870 | ||||||||
\(950\) | 5.66758e155 | 0.264794 | ||||||||
\(951\) | −4.28230e156 | −1.89322 | ||||||||
\(952\) | −4.87698e155 | −0.204038 | ||||||||
\(953\) | −1.07207e156 | −0.424470 | −0.212235 | − | 0.977219i | \(-0.568074\pi\) | ||||
−0.212235 | + | 0.977219i | \(0.568074\pi\) | |||||||
\(954\) | 4.84307e156 | 1.81481 | ||||||||
\(955\) | −2.16117e156 | −0.766500 | ||||||||
\(956\) | −6.85023e155 | −0.229967 | ||||||||
\(957\) | 4.73371e156 | 1.50427 | ||||||||
\(958\) | −2.51929e156 | −0.757861 | ||||||||
\(959\) | −2.47925e155 | −0.0706062 | ||||||||
\(960\) | −9.41391e155 | −0.253823 | ||||||||
\(961\) | −1.82492e156 | −0.465871 | ||||||||
\(962\) | 1.06167e156 | 0.256623 | ||||||||
\(963\) | 3.08202e156 | 0.705432 | ||||||||
\(964\) | −3.87855e156 | −0.840669 | ||||||||
\(965\) | 4.95507e156 | 1.01711 | ||||||||
\(966\) | −1.85934e155 | −0.0361459 | ||||||||
\(967\) | 1.63853e156 | 0.301692 | 0.150846 | − | 0.988557i | \(-0.451800\pi\) | ||||
0.150846 | + | 0.988557i | \(0.451800\pi\) | |||||||
\(968\) | 2.76333e156 | 0.481921 | ||||||||
\(969\) | −6.35801e156 | −1.05032 | ||||||||
\(970\) | −1.58594e157 | −2.48182 | ||||||||
\(971\) | 1.42295e156 | 0.210951 | 0.105475 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105475 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(972\) | 1.30882e157 | 1.83824 | ||||||||
\(973\) | 4.25491e155 | 0.0566196 | ||||||||
\(974\) | 7.64251e156 | 0.963587 | ||||||||
\(975\) | −7.36555e156 | −0.879959 | ||||||||
\(976\) | 6.85696e156 | 0.776276 | ||||||||
\(977\) | −1.83385e157 | −1.96743 | −0.983715 | − | 0.179733i | \(-0.942477\pi\) | ||||
−0.983715 | + | 0.179733i | \(0.942477\pi\) | |||||||
\(978\) | −4.59241e157 | −4.66928 | ||||||||
\(979\) | 1.41464e157 | 1.36319 | ||||||||
\(980\) | 2.01607e157 | 1.84135 | ||||||||
\(981\) | −1.67937e157 | −1.45386 | ||||||||
\(982\) | 1.58569e157 | 1.30127 | ||||||||
\(983\) | 2.13639e157 | 1.66196 | 0.830980 | − | 0.556303i | \(-0.187780\pi\) | ||||
0.830980 | + | 0.556303i | \(0.187780\pi\) | |||||||
\(984\) | 6.50707e157 | 4.79891 | ||||||||
\(985\) | 1.29361e157 | 0.904484 | ||||||||
\(986\) | −3.54337e157 | −2.34898 | ||||||||
\(987\) | −6.19178e155 | −0.0389193 | ||||||||
\(988\) | 2.34643e157 | 1.39852 | ||||||||
\(989\) | 1.79630e156 | 0.101525 | ||||||||
\(990\) | −5.37593e157 | −2.88142 | ||||||||
\(991\) | 1.35147e157 | 0.686973 | 0.343487 | − | 0.939158i | \(-0.388392\pi\) | ||||
0.343487 | + | 0.939158i | \(0.388392\pi\) | |||||||
\(992\) | −1.75179e157 | −0.844537 | ||||||||
\(993\) | 3.70401e157 | 1.69370 | ||||||||
\(994\) | 2.51329e156 | 0.109008 | ||||||||
\(995\) | 8.54247e156 | 0.351457 | ||||||||
\(996\) | −9.05120e157 | −3.53257 | ||||||||
\(997\) | −4.76047e156 | −0.176260 | −0.0881301 | − | 0.996109i | \(-0.528089\pi\) | ||||
−0.0881301 | + | 0.996109i | \(0.528089\pi\) | |||||||
\(998\) | −3.72743e157 | −1.30935 | ||||||||
\(999\) | −6.38244e156 | −0.212715 |
(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 | 1.106.a.a.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.106.a.a.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial |