Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,110,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, 110, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 110);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 110 \) |
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: | \(75.2394221917\) |
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: | \( x^{8} - 2 x^{7} + \cdots + 46\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{118}\cdot 3^{40}\cdot 5^{14}\cdot 7^{6}\cdot 11^{3}\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.86979e14\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.56139e16 | −1.39793 | −0.698965 | − | 0.715156i | \(-0.746356\pi\) | ||||
−0.698965 | + | 0.715156i | \(0.746356\pi\) | |||||||
\(3\) | 1.00458e26 | 0.997418 | 0.498709 | − | 0.866770i | \(-0.333808\pi\) | ||||
0.498709 | + | 0.866770i | \(0.333808\pi\) | |||||||
\(4\) | 6.19316e32 | 0.954208 | ||||||||
\(5\) | −8.07110e36 | −0.0650231 | −0.0325116 | − | 0.999471i | \(-0.510351\pi\) | ||||
−0.0325116 | + | 0.999471i | \(0.510351\pi\) | |||||||
\(6\) | −3.57771e42 | −1.39432 | ||||||||
\(7\) | −7.18940e45 | −0.629288 | −0.314644 | − | 0.949210i | \(-0.601885\pi\) | ||||
−0.314644 | + | 0.949210i | \(0.601885\pi\) | |||||||
\(8\) | 1.05848e48 | 0.0640145 | ||||||||
\(9\) | −5.23267e49 | −0.00515830 | ||||||||
\(10\) | 2.87444e53 | 0.0908977 | ||||||||
\(11\) | 3.15771e56 | 0.553951 | 0.276976 | − | 0.960877i | \(-0.410668\pi\) | ||||
0.276976 | + | 0.960877i | \(0.410668\pi\) | |||||||
\(12\) | 6.22154e58 | 0.951743 | ||||||||
\(13\) | 3.96229e60 | 0.772740 | 0.386370 | − | 0.922344i | \(-0.373729\pi\) | ||||
0.386370 | + | 0.922344i | \(0.373729\pi\) | |||||||
\(14\) | 2.56043e62 | 0.879701 | ||||||||
\(15\) | −8.10809e62 | −0.0648552 | ||||||||
\(16\) | −4.39656e65 | −1.04370 | ||||||||
\(17\) | 7.90575e66 | 0.689409 | 0.344704 | − | 0.938711i | \(-0.387979\pi\) | ||||
0.344704 | + | 0.938711i | \(0.387979\pi\) | |||||||
\(18\) | 1.86356e66 | 0.00721094 | ||||||||
\(19\) | −8.36798e69 | −1.70039 | −0.850197 | − | 0.526465i | \(-0.823517\pi\) | ||||
−0.850197 | + | 0.526465i | \(0.823517\pi\) | |||||||
\(20\) | −4.99857e69 | −0.0620455 | ||||||||
\(21\) | −7.22234e71 | −0.627663 | ||||||||
\(22\) | −1.12459e73 | −0.774385 | ||||||||
\(23\) | 1.60412e74 | 0.979645 | 0.489823 | − | 0.871822i | \(-0.337062\pi\) | ||||
0.489823 | + | 0.871822i | \(0.337062\pi\) | |||||||
\(24\) | 1.06333e74 | 0.0638492 | ||||||||
\(25\) | −1.53423e76 | −0.995772 | ||||||||
\(26\) | −1.41113e77 | −1.08024 | ||||||||
\(27\) | −1.02432e78 | −1.00256 | ||||||||
\(28\) | −4.45251e78 | −0.600472 | ||||||||
\(29\) | 2.30631e79 | 0.459438 | 0.229719 | − | 0.973257i | \(-0.426219\pi\) | ||||
0.229719 | + | 0.973257i | \(0.426219\pi\) | |||||||
\(30\) | 2.88761e79 | 0.0906630 | ||||||||
\(31\) | −6.52163e80 | −0.342881 | −0.171441 | − | 0.985194i | \(-0.554842\pi\) | ||||
−0.171441 | + | 0.985194i | \(0.554842\pi\) | |||||||
\(32\) | 1.49709e82 | 1.39500 | ||||||||
\(33\) | 3.17218e82 | 0.552520 | ||||||||
\(34\) | −2.81555e83 | −0.963745 | ||||||||
\(35\) | 5.80264e82 | 0.0409183 | ||||||||
\(36\) | −3.24067e82 | −0.00492209 | ||||||||
\(37\) | 2.83538e85 | 0.967425 | 0.483713 | − | 0.875227i | \(-0.339288\pi\) | ||||
0.483713 | + | 0.875227i | \(0.339288\pi\) | |||||||
\(38\) | 2.98017e86 | 2.37703 | ||||||||
\(39\) | 3.98044e86 | 0.770744 | ||||||||
\(40\) | −8.54311e84 | −0.00416242 | ||||||||
\(41\) | 1.40024e88 | 1.77616 | 0.888082 | − | 0.459685i | \(-0.152038\pi\) | ||||
0.888082 | + | 0.459685i | \(0.152038\pi\) | |||||||
\(42\) | 2.57216e88 | 0.877429 | ||||||||
\(43\) | 4.04388e88 | 0.382619 | 0.191310 | − | 0.981530i | \(-0.438727\pi\) | ||||
0.191310 | + | 0.981530i | \(0.438727\pi\) | |||||||
\(44\) | 1.95562e89 | 0.528584 | ||||||||
\(45\) | 4.22334e86 | 0.000335408 0 | ||||||||
\(46\) | −5.71289e90 | −1.36948 | ||||||||
\(47\) | −1.37892e91 | −1.02378 | −0.511888 | − | 0.859052i | \(-0.671054\pi\) | ||||
−0.511888 | + | 0.859052i | \(0.671054\pi\) | |||||||
\(48\) | −4.41670e91 | −1.04100 | ||||||||
\(49\) | −7.88353e91 | −0.603996 | ||||||||
\(50\) | 5.46400e92 | 1.39202 | ||||||||
\(51\) | 7.94197e92 | 0.687628 | ||||||||
\(52\) | 2.45391e93 | 0.737354 | ||||||||
\(53\) | −9.81155e93 | −1.04401 | −0.522003 | − | 0.852944i | \(-0.674815\pi\) | ||||
−0.522003 | + | 0.852944i | \(0.674815\pi\) | |||||||
\(54\) | 3.64802e94 | 1.40151 | ||||||||
\(55\) | −2.54862e93 | −0.0360196 | ||||||||
\(56\) | −7.60984e93 | −0.0402836 | ||||||||
\(57\) | −8.40632e95 | −1.69600 | ||||||||
\(58\) | −8.21369e95 | −0.642263 | ||||||||
\(59\) | 4.69363e95 | 0.144569 | 0.0722844 | − | 0.997384i | \(-0.476971\pi\) | ||||
0.0722844 | + | 0.997384i | \(0.476971\pi\) | |||||||
\(60\) | −5.02147e95 | −0.0618853 | ||||||||
\(61\) | 3.61750e97 | 1.81106 | 0.905529 | − | 0.424284i | \(-0.139474\pi\) | ||||
0.905529 | + | 0.424284i | \(0.139474\pi\) | |||||||
\(62\) | 2.32261e97 | 0.479324 | ||||||||
\(63\) | 3.76197e95 | 0.00324606 | ||||||||
\(64\) | −2.47819e98 | −0.906414 | ||||||||
\(65\) | −3.19800e97 | −0.0502460 | ||||||||
\(66\) | −1.12974e99 | −0.772385 | ||||||||
\(67\) | −4.15119e99 | −1.25054 | −0.625268 | − | 0.780410i | \(-0.715010\pi\) | ||||
−0.625268 | + | 0.780410i | \(0.715010\pi\) | |||||||
\(68\) | 4.89616e99 | 0.657839 | ||||||||
\(69\) | 1.61147e100 | 0.977115 | ||||||||
\(70\) | −2.06655e99 | −0.0572009 | ||||||||
\(71\) | −6.22667e100 | −0.795566 | −0.397783 | − | 0.917480i | \(-0.630220\pi\) | ||||
−0.397783 | + | 0.917480i | \(0.630220\pi\) | |||||||
\(72\) | −5.53868e97 | −0.000330206 0 | ||||||||
\(73\) | 1.10474e101 | 0.310575 | 0.155287 | − | 0.987869i | \(-0.450370\pi\) | ||||
0.155287 | + | 0.987869i | \(0.450370\pi\) | |||||||
\(74\) | −1.00979e102 | −1.35239 | ||||||||
\(75\) | −1.54126e102 | −0.993200 | ||||||||
\(76\) | −5.18242e102 | −1.62253 | ||||||||
\(77\) | −2.27021e102 | −0.348595 | ||||||||
\(78\) | −1.41759e103 | −1.07745 | ||||||||
\(79\) | 2.39031e103 | 0.907357 | 0.453678 | − | 0.891165i | \(-0.350111\pi\) | ||||
0.453678 | + | 0.891165i | \(0.350111\pi\) | |||||||
\(80\) | 3.54851e102 | 0.0678643 | ||||||||
\(81\) | −1.02371e104 | −0.994815 | ||||||||
\(82\) | −4.98682e104 | −2.48295 | ||||||||
\(83\) | −6.41612e104 | −1.65012 | −0.825061 | − | 0.565043i | \(-0.808860\pi\) | ||||
−0.825061 | + | 0.565043i | \(0.808860\pi\) | |||||||
\(84\) | −4.47291e104 | −0.598921 | ||||||||
\(85\) | −6.38081e103 | −0.0448275 | ||||||||
\(86\) | −1.44018e105 | −0.534875 | ||||||||
\(87\) | 2.31688e105 | 0.458252 | ||||||||
\(88\) | 3.34238e104 | 0.0354609 | ||||||||
\(89\) | 1.35058e106 | 0.774045 | 0.387022 | − | 0.922070i | \(-0.373504\pi\) | ||||
0.387022 | + | 0.922070i | \(0.373504\pi\) | |||||||
\(90\) | −1.50410e103 | −0.000468877 0 | ||||||||
\(91\) | −2.84865e106 | −0.486276 | ||||||||
\(92\) | 9.93455e106 | 0.934785 | ||||||||
\(93\) | −6.55151e106 | −0.341996 | ||||||||
\(94\) | 4.91087e107 | 1.43117 | ||||||||
\(95\) | 6.75388e106 | 0.110565 | ||||||||
\(96\) | 1.50395e108 | 1.39140 | ||||||||
\(97\) | 1.03023e108 | 0.541847 | 0.270923 | − | 0.962601i | \(-0.412671\pi\) | ||||
0.270923 | + | 0.962601i | \(0.412671\pi\) | |||||||
\(98\) | 2.80764e108 | 0.844344 | ||||||||
\(99\) | −1.65233e106 | −0.00285744 | ||||||||
\(100\) | −9.50173e108 | −0.950173 | ||||||||
\(101\) | −3.45287e108 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(102\) | −2.82845e109 | −0.961256 | ||||||||
\(103\) | −9.34044e109 | −1.86526 | −0.932628 | − | 0.360840i | \(-0.882490\pi\) | ||||
−0.932628 | + | 0.360840i | \(0.882490\pi\) | |||||||
\(104\) | 4.19401e108 | 0.0494666 | ||||||||
\(105\) | 5.82923e108 | 0.0408126 | ||||||||
\(106\) | 3.49428e110 | 1.45945 | ||||||||
\(107\) | −1.30188e110 | −0.325952 | −0.162976 | − | 0.986630i | \(-0.552109\pi\) | ||||
−0.162976 | + | 0.986630i | \(0.552109\pi\) | |||||||
\(108\) | −6.34379e110 | −0.956653 | ||||||||
\(109\) | −1.88543e111 | −1.72055 | −0.860274 | − | 0.509832i | \(-0.829708\pi\) | ||||
−0.860274 | + | 0.509832i | \(0.829708\pi\) | |||||||
\(110\) | 9.07665e109 | 0.0503529 | ||||||||
\(111\) | 2.84837e111 | 0.964927 | ||||||||
\(112\) | 3.16086e111 | 0.656785 | ||||||||
\(113\) | 1.04938e110 | 0.0134326 | 0.00671628 | − | 0.999977i | \(-0.497862\pi\) | ||||
0.00671628 | + | 0.999977i | \(0.497862\pi\) | |||||||
\(114\) | 2.99382e112 | 2.37089 | ||||||||
\(115\) | −1.29470e111 | −0.0636996 | ||||||||
\(116\) | 1.42834e112 | 0.438400 | ||||||||
\(117\) | −2.07333e110 | −0.00398602 | ||||||||
\(118\) | −1.67159e112 | −0.202097 | ||||||||
\(119\) | −5.68376e112 | −0.433837 | ||||||||
\(120\) | −8.58225e110 | −0.00415167 | ||||||||
\(121\) | −2.25228e113 | −0.693138 | ||||||||
\(122\) | −1.28833e114 | −2.53173 | ||||||||
\(123\) | 1.40666e114 | 1.77158 | ||||||||
\(124\) | −4.03895e113 | −0.327180 | ||||||||
\(125\) | 2.48184e113 | 0.129771 | ||||||||
\(126\) | −1.33979e112 | −0.00453776 | ||||||||
\(127\) | −3.59232e114 | −0.790810 | −0.395405 | − | 0.918507i | \(-0.629396\pi\) | ||||
−0.395405 | + | 0.918507i | \(0.629396\pi\) | |||||||
\(128\) | −8.90833e113 | −0.127895 | ||||||||
\(129\) | 4.06240e114 | 0.381631 | ||||||||
\(130\) | 1.13894e114 | 0.0702403 | ||||||||
\(131\) | −6.00882e113 | −0.0244064 | −0.0122032 | − | 0.999926i | \(-0.503884\pi\) | ||||
−0.0122032 | + | 0.999926i | \(0.503884\pi\) | |||||||
\(132\) | 1.96458e115 | 0.527219 | ||||||||
\(133\) | 6.01608e115 | 1.07004 | ||||||||
\(134\) | 1.47840e116 | 1.74816 | ||||||||
\(135\) | 8.26741e114 | 0.0651897 | ||||||||
\(136\) | 8.36808e114 | 0.0441322 | ||||||||
\(137\) | −2.53292e116 | −0.896086 | −0.448043 | − | 0.894012i | \(-0.647879\pi\) | ||||
−0.448043 | + | 0.894012i | \(0.647879\pi\) | |||||||
\(138\) | −5.73907e116 | −1.36594 | ||||||||
\(139\) | −7.24815e116 | −1.16391 | −0.581956 | − | 0.813220i | \(-0.697713\pi\) | ||||
−0.581956 | + | 0.813220i | \(0.697713\pi\) | |||||||
\(140\) | 3.59367e115 | 0.0390445 | ||||||||
\(141\) | −1.38524e117 | −1.02113 | ||||||||
\(142\) | 2.21756e117 | 1.11215 | ||||||||
\(143\) | 1.25118e117 | 0.428060 | ||||||||
\(144\) | 2.30057e115 | 0.00538369 | ||||||||
\(145\) | −1.86145e116 | −0.0298741 | ||||||||
\(146\) | −3.93443e117 | −0.434162 | ||||||||
\(147\) | −7.91965e117 | −0.602436 | ||||||||
\(148\) | 1.75600e118 | 0.923124 | ||||||||
\(149\) | 7.84968e117 | 0.285891 | 0.142945 | − | 0.989731i | \(-0.454343\pi\) | ||||
0.142945 | + | 0.989731i | \(0.454343\pi\) | |||||||
\(150\) | 5.48903e118 | 1.38842 | ||||||||
\(151\) | −1.39761e118 | −0.246117 | −0.123058 | − | 0.992399i | \(-0.539270\pi\) | ||||
−0.123058 | + | 0.992399i | \(0.539270\pi\) | |||||||
\(152\) | −8.85734e117 | −0.108850 | ||||||||
\(153\) | −4.13682e116 | −0.00355618 | ||||||||
\(154\) | 8.08511e118 | 0.487311 | ||||||||
\(155\) | 5.26367e117 | 0.0222952 | ||||||||
\(156\) | 2.46515e119 | 0.735450 | ||||||||
\(157\) | −7.03358e119 | −1.48131 | −0.740654 | − | 0.671887i | \(-0.765484\pi\) | ||||
−0.740654 | + | 0.671887i | \(0.765484\pi\) | |||||||
\(158\) | −8.51284e119 | −1.26842 | ||||||||
\(159\) | −9.85651e119 | −1.04131 | ||||||||
\(160\) | −1.20832e119 | −0.0907071 | ||||||||
\(161\) | −1.15326e120 | −0.616479 | ||||||||
\(162\) | 3.64583e120 | 1.39068 | ||||||||
\(163\) | −2.09789e120 | −0.572214 | −0.286107 | − | 0.958198i | \(-0.592361\pi\) | ||||
−0.286107 | + | 0.958198i | \(0.592361\pi\) | |||||||
\(164\) | 8.67193e120 | 1.69483 | ||||||||
\(165\) | −2.56030e119 | −0.0359266 | ||||||||
\(166\) | 2.28503e121 | 2.30676 | ||||||||
\(167\) | −2.23870e121 | −1.62910 | −0.814551 | − | 0.580092i | \(-0.803017\pi\) | ||||
−0.814551 | + | 0.580092i | \(0.803017\pi\) | |||||||
\(168\) | −7.64471e119 | −0.0401796 | ||||||||
\(169\) | −1.05924e121 | −0.402873 | ||||||||
\(170\) | 2.27246e120 | 0.0626657 | ||||||||
\(171\) | 4.37868e119 | 0.00877113 | ||||||||
\(172\) | 2.50444e121 | 0.365098 | ||||||||
\(173\) | 6.81871e120 | 0.0724753 | 0.0362376 | − | 0.999343i | \(-0.488463\pi\) | ||||
0.0362376 | + | 0.999343i | \(0.488463\pi\) | |||||||
\(174\) | −8.25132e121 | −0.640604 | ||||||||
\(175\) | 1.10302e122 | 0.626628 | ||||||||
\(176\) | −1.38831e122 | −0.578156 | ||||||||
\(177\) | 4.71514e121 | 0.144195 | ||||||||
\(178\) | −4.80996e122 | −1.08206 | ||||||||
\(179\) | −1.16550e123 | −1.93207 | −0.966035 | − | 0.258411i | \(-0.916801\pi\) | ||||
−0.966035 | + | 0.258411i | \(0.916801\pi\) | |||||||
\(180\) | 2.61558e119 | 0.000320049 0 | ||||||||
\(181\) | 1.18514e123 | 1.07223 | 0.536115 | − | 0.844145i | \(-0.319892\pi\) | ||||
0.536115 | + | 0.844145i | \(0.319892\pi\) | |||||||
\(182\) | 1.01452e123 | 0.679780 | ||||||||
\(183\) | 3.63408e123 | 1.80638 | ||||||||
\(184\) | 1.69793e122 | 0.0627115 | ||||||||
\(185\) | −2.28847e122 | −0.0629050 | ||||||||
\(186\) | 2.33325e123 | 0.478086 | ||||||||
\(187\) | 2.49641e123 | 0.381899 | ||||||||
\(188\) | −8.53986e123 | −0.976895 | ||||||||
\(189\) | 7.36427e123 | 0.630901 | ||||||||
\(190\) | −2.40532e123 | −0.154562 | ||||||||
\(191\) | −2.68673e124 | −1.29690 | −0.648449 | − | 0.761258i | \(-0.724582\pi\) | ||||
−0.648449 | + | 0.761258i | \(0.724582\pi\) | |||||||
\(192\) | −2.48955e124 | −0.904074 | ||||||||
\(193\) | 2.04325e124 | 0.559048 | 0.279524 | − | 0.960139i | \(-0.409823\pi\) | ||||
0.279524 | + | 0.960139i | \(0.409823\pi\) | |||||||
\(194\) | −3.66907e124 | −0.757463 | ||||||||
\(195\) | −3.21266e123 | −0.0501162 | ||||||||
\(196\) | −4.88240e124 | −0.576338 | ||||||||
\(197\) | 1.67102e125 | 1.49476 | 0.747381 | − | 0.664396i | \(-0.231311\pi\) | ||||
0.747381 | + | 0.664396i | \(0.231311\pi\) | |||||||
\(198\) | 5.88459e122 | 0.00399451 | ||||||||
\(199\) | 1.79326e125 | 0.925019 | 0.462509 | − | 0.886614i | \(-0.346949\pi\) | ||||
0.462509 | + | 0.886614i | \(0.346949\pi\) | |||||||
\(200\) | −1.62395e124 | −0.0637439 | ||||||||
\(201\) | −4.17022e125 | −1.24731 | ||||||||
\(202\) | 1.22970e125 | 0.280641 | ||||||||
\(203\) | −1.65810e125 | −0.289119 | ||||||||
\(204\) | 4.91859e125 | 0.656140 | ||||||||
\(205\) | −1.13015e125 | −0.115492 | ||||||||
\(206\) | 3.32650e126 | 2.60750 | ||||||||
\(207\) | −8.39381e123 | −0.00505330 | ||||||||
\(208\) | −1.74204e126 | −0.806505 | ||||||||
\(209\) | −2.64237e126 | −0.941935 | ||||||||
\(210\) | −2.07602e125 | −0.0570532 | ||||||||
\(211\) | −4.55403e126 | −0.966055 | −0.483027 | − | 0.875605i | \(-0.660463\pi\) | ||||
−0.483027 | + | 0.875605i | \(0.660463\pi\) | |||||||
\(212\) | −6.07645e126 | −0.996198 | ||||||||
\(213\) | −6.25520e126 | −0.793511 | ||||||||
\(214\) | 4.63650e126 | 0.455658 | ||||||||
\(215\) | −3.26385e125 | −0.0248791 | ||||||||
\(216\) | −1.08423e126 | −0.0641786 | ||||||||
\(217\) | 4.68866e126 | 0.215771 | ||||||||
\(218\) | 6.71477e127 | 2.40521 | ||||||||
\(219\) | 1.10981e127 | 0.309773 | ||||||||
\(220\) | −1.57840e126 | −0.0343702 | ||||||||
\(221\) | 3.13249e127 | 0.532734 | ||||||||
\(222\) | −1.01442e128 | −1.34890 | ||||||||
\(223\) | 7.56923e127 | 0.787838 | 0.393919 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393919 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(224\) | −1.07632e128 | −0.877856 | ||||||||
\(225\) | 8.02811e125 | 0.00513649 | ||||||||
\(226\) | −3.73727e126 | −0.0187778 | ||||||||
\(227\) | 1.83524e128 | 0.724910 | 0.362455 | − | 0.932001i | \(-0.381939\pi\) | ||||
0.362455 | + | 0.932001i | \(0.381939\pi\) | |||||||
\(228\) | −5.20617e128 | −1.61834 | ||||||||
\(229\) | 2.38042e128 | 0.582934 | 0.291467 | − | 0.956581i | \(-0.405857\pi\) | ||||
0.291467 | + | 0.956581i | \(0.405857\pi\) | |||||||
\(230\) | 4.61093e127 | 0.0890475 | ||||||||
\(231\) | −2.28061e128 | −0.347695 | ||||||||
\(232\) | 2.44119e127 | 0.0294107 | ||||||||
\(233\) | −9.64479e128 | −0.919168 | −0.459584 | − | 0.888134i | \(-0.652001\pi\) | ||||
−0.459584 | + | 0.888134i | \(0.652001\pi\) | |||||||
\(234\) | 7.38396e126 | 0.00557218 | ||||||||
\(235\) | 1.11294e128 | 0.0665691 | ||||||||
\(236\) | 2.90684e128 | 0.137949 | ||||||||
\(237\) | 2.40126e129 | 0.905014 | ||||||||
\(238\) | 2.02421e129 | 0.606474 | ||||||||
\(239\) | −2.75183e129 | −0.656049 | −0.328025 | − | 0.944669i | \(-0.606383\pi\) | ||||
−0.328025 | + | 0.944669i | \(0.606383\pi\) | |||||||
\(240\) | 3.56477e128 | 0.0676891 | ||||||||
\(241\) | 2.31148e129 | 0.349913 | 0.174957 | − | 0.984576i | \(-0.444021\pi\) | ||||
0.174957 | + | 0.984576i | \(0.444021\pi\) | |||||||
\(242\) | 8.02126e129 | 0.968959 | ||||||||
\(243\) | 1.06924e128 | 0.0103165 | ||||||||
\(244\) | 2.24038e130 | 1.72813 | ||||||||
\(245\) | 6.36288e128 | 0.0392737 | ||||||||
\(246\) | −5.00967e130 | −2.47654 | ||||||||
\(247\) | −3.31563e130 | −1.31396 | ||||||||
\(248\) | −6.90302e128 | −0.0219494 | ||||||||
\(249\) | −6.44552e130 | −1.64586 | ||||||||
\(250\) | −8.83882e129 | −0.181411 | ||||||||
\(251\) | 7.59986e130 | 1.25484 | 0.627419 | − | 0.778682i | \(-0.284111\pi\) | ||||
0.627419 | + | 0.778682i | \(0.284111\pi\) | |||||||
\(252\) | 2.32985e128 | 0.00309741 | ||||||||
\(253\) | 5.06534e130 | 0.542675 | ||||||||
\(254\) | 1.27937e131 | 1.10550 | ||||||||
\(255\) | −6.41005e129 | −0.0447117 | ||||||||
\(256\) | 1.92570e131 | 1.08520 | ||||||||
\(257\) | −2.73816e130 | −0.124768 | −0.0623840 | − | 0.998052i | \(-0.519870\pi\) | ||||
−0.0623840 | + | 0.998052i | \(0.519870\pi\) | |||||||
\(258\) | −1.44678e131 | −0.533494 | ||||||||
\(259\) | −2.03847e131 | −0.608789 | ||||||||
\(260\) | −1.98058e130 | −0.0479451 | ||||||||
\(261\) | −1.20682e129 | −0.00236992 | ||||||||
\(262\) | 2.13998e130 | 0.0341184 | ||||||||
\(263\) | 8.10061e131 | 1.04937 | 0.524686 | − | 0.851296i | \(-0.324183\pi\) | ||||
0.524686 | + | 0.851296i | \(0.324183\pi\) | |||||||
\(264\) | 3.35769e130 | 0.0353693 | ||||||||
\(265\) | 7.91901e130 | 0.0678845 | ||||||||
\(266\) | −2.14256e132 | −1.49584 | ||||||||
\(267\) | 1.35677e132 | 0.772046 | ||||||||
\(268\) | −2.57090e132 | −1.19327 | ||||||||
\(269\) | 1.10436e132 | 0.418420 | 0.209210 | − | 0.977871i | \(-0.432911\pi\) | ||||
0.209210 | + | 0.977871i | \(0.432911\pi\) | |||||||
\(270\) | −2.94435e131 | −0.0911307 | ||||||||
\(271\) | −1.79737e132 | −0.454790 | −0.227395 | − | 0.973803i | \(-0.573021\pi\) | ||||
−0.227395 | + | 0.973803i | \(0.573021\pi\) | |||||||
\(272\) | −3.47581e132 | −0.719533 | ||||||||
\(273\) | −2.86170e132 | −0.485020 | ||||||||
\(274\) | 9.02071e132 | 1.25267 | ||||||||
\(275\) | −4.84466e132 | −0.551609 | ||||||||
\(276\) | 9.98007e132 | 0.932371 | ||||||||
\(277\) | 9.56140e132 | 0.733456 | 0.366728 | − | 0.930328i | \(-0.380478\pi\) | ||||
0.366728 | + | 0.930328i | \(0.380478\pi\) | |||||||
\(278\) | 2.58135e133 | 1.62707 | ||||||||
\(279\) | 3.41255e130 | 0.00176868 | ||||||||
\(280\) | 6.14198e130 | 0.00261936 | ||||||||
\(281\) | −4.46085e133 | −1.56647 | −0.783236 | − | 0.621724i | \(-0.786433\pi\) | ||||
−0.783236 | + | 0.621724i | \(0.786433\pi\) | |||||||
\(282\) | 4.93337e133 | 1.42747 | ||||||||
\(283\) | −3.18805e133 | −0.760615 | −0.380308 | − | 0.924860i | \(-0.624182\pi\) | ||||
−0.380308 | + | 0.924860i | \(0.624182\pi\) | |||||||
\(284\) | −3.85628e133 | −0.759135 | ||||||||
\(285\) | 6.78483e132 | 0.110279 | ||||||||
\(286\) | −4.45594e133 | −0.598398 | ||||||||
\(287\) | −1.00669e134 | −1.11772 | ||||||||
\(288\) | −7.83377e131 | −0.00719582 | ||||||||
\(289\) | −6.90011e133 | −0.524715 | ||||||||
\(290\) | 6.62935e132 | 0.0417619 | ||||||||
\(291\) | 1.03495e134 | 0.540447 | ||||||||
\(292\) | 6.84186e133 | 0.296353 | ||||||||
\(293\) | 3.11001e134 | 1.11809 | 0.559045 | − | 0.829137i | \(-0.311168\pi\) | ||||
0.559045 | + | 0.829137i | \(0.311168\pi\) | |||||||
\(294\) | 2.82050e134 | 0.842164 | ||||||||
\(295\) | −3.78828e132 | −0.00940031 | ||||||||
\(296\) | 3.00120e133 | 0.0619293 | ||||||||
\(297\) | −3.23452e134 | −0.555371 | ||||||||
\(298\) | −2.79558e134 | −0.399655 | ||||||||
\(299\) | 6.35597e134 | 0.757011 | ||||||||
\(300\) | −9.54527e134 | −0.947719 | ||||||||
\(301\) | −2.90731e134 | −0.240778 | ||||||||
\(302\) | 4.97743e134 | 0.344054 | ||||||||
\(303\) | −3.46869e134 | −0.200236 | ||||||||
\(304\) | 3.67903e135 | 1.77469 | ||||||||
\(305\) | −2.91972e134 | −0.117761 | ||||||||
\(306\) | 1.47328e133 | 0.00497128 | ||||||||
\(307\) | −2.51941e135 | −0.711636 | −0.355818 | − | 0.934555i | \(-0.615798\pi\) | ||||
−0.355818 | + | 0.934555i | \(0.615798\pi\) | |||||||
\(308\) | −1.40598e135 | −0.332632 | ||||||||
\(309\) | −9.38323e135 | −1.86044 | ||||||||
\(310\) | −1.87460e134 | −0.0311671 | ||||||||
\(311\) | −1.03475e136 | −1.44342 | −0.721709 | − | 0.692196i | \(-0.756643\pi\) | ||||
−0.721709 | + | 0.692196i | \(0.756643\pi\) | |||||||
\(312\) | 4.21322e134 | 0.0493388 | ||||||||
\(313\) | 1.02153e136 | 1.00481 | 0.502405 | − | 0.864632i | \(-0.332449\pi\) | ||||
0.502405 | + | 0.864632i | \(0.332449\pi\) | |||||||
\(314\) | 2.50493e136 | 2.07076 | ||||||||
\(315\) | −3.03633e132 | −0.000211069 0 | ||||||||
\(316\) | 1.48036e136 | 0.865807 | ||||||||
\(317\) | −2.45989e136 | −1.21111 | −0.605557 | − | 0.795802i | \(-0.707050\pi\) | ||||
−0.605557 | + | 0.795802i | \(0.707050\pi\) | |||||||
\(318\) | 3.51029e136 | 1.45568 | ||||||||
\(319\) | 7.28267e135 | 0.254506 | ||||||||
\(320\) | 2.00018e135 | 0.0589379 | ||||||||
\(321\) | −1.30784e136 | −0.325111 | ||||||||
\(322\) | 4.10723e136 | 0.861795 | ||||||||
\(323\) | −6.61552e136 | −1.17227 | ||||||||
\(324\) | −6.33999e136 | −0.949260 | ||||||||
\(325\) | −6.07906e136 | −0.769473 | ||||||||
\(326\) | 7.47142e136 | 0.799915 | ||||||||
\(327\) | −1.89407e137 | −1.71610 | ||||||||
\(328\) | 1.48213e136 | 0.113700 | ||||||||
\(329\) | 9.91359e136 | 0.644250 | ||||||||
\(330\) | 9.11824e135 | 0.0502229 | ||||||||
\(331\) | 1.66846e137 | 0.779274 | 0.389637 | − | 0.920968i | \(-0.372600\pi\) | ||||
0.389637 | + | 0.920968i | \(0.372600\pi\) | |||||||
\(332\) | −3.97361e137 | −1.57456 | ||||||||
\(333\) | −1.48366e135 | −0.00499027 | ||||||||
\(334\) | 7.97289e137 | 2.27737 | ||||||||
\(335\) | 3.35047e136 | 0.0813138 | ||||||||
\(336\) | 3.17535e137 | 0.655089 | ||||||||
\(337\) | −9.18402e137 | −1.61140 | −0.805700 | − | 0.592324i | \(-0.798211\pi\) | ||||
−0.805700 | + | 0.592324i | \(0.798211\pi\) | |||||||
\(338\) | 3.77236e137 | 0.563188 | ||||||||
\(339\) | 1.05419e136 | 0.0133979 | ||||||||
\(340\) | −3.95174e136 | −0.0427747 | ||||||||
\(341\) | −2.05934e137 | −0.189939 | ||||||||
\(342\) | −1.55942e136 | −0.0122614 | ||||||||
\(343\) | 1.50516e138 | 1.00938 | ||||||||
\(344\) | 4.28036e136 | 0.0244932 | ||||||||
\(345\) | −1.30063e137 | −0.0635351 | ||||||||
\(346\) | −2.42841e137 | −0.101315 | ||||||||
\(347\) | −4.53577e138 | −1.61694 | −0.808472 | − | 0.588535i | \(-0.799705\pi\) | ||||
−0.808472 | + | 0.588535i | \(0.799705\pi\) | |||||||
\(348\) | 1.43488e138 | 0.437267 | ||||||||
\(349\) | 3.55561e138 | 0.926678 | 0.463339 | − | 0.886181i | \(-0.346651\pi\) | ||||
0.463339 | + | 0.886181i | \(0.346651\pi\) | |||||||
\(350\) | −3.92829e138 | −0.875981 | ||||||||
\(351\) | −4.05866e138 | −0.774720 | ||||||||
\(352\) | 4.72738e138 | 0.772761 | ||||||||
\(353\) | −1.37878e139 | −1.93096 | −0.965480 | − | 0.260476i | \(-0.916120\pi\) | ||||
−0.965480 | + | 0.260476i | \(0.916120\pi\) | |||||||
\(354\) | −1.67925e138 | −0.201575 | ||||||||
\(355\) | 5.02561e137 | 0.0517302 | ||||||||
\(356\) | 8.36438e138 | 0.738600 | ||||||||
\(357\) | −5.70980e138 | −0.432717 | ||||||||
\(358\) | 4.15081e139 | 2.70090 | ||||||||
\(359\) | 1.90732e139 | 1.06605 | 0.533023 | − | 0.846101i | \(-0.321056\pi\) | ||||
0.533023 | + | 0.846101i | \(0.321056\pi\) | |||||||
\(360\) | 4.47032e134 | 2.14710e−5 0 | ||||||||
\(361\) | 4.58048e139 | 1.89134 | ||||||||
\(362\) | −4.22075e139 | −1.49890 | ||||||||
\(363\) | −2.26260e139 | −0.691348 | ||||||||
\(364\) | −1.76421e139 | −0.464008 | ||||||||
\(365\) | −8.91651e137 | −0.0201945 | ||||||||
\(366\) | −1.29424e140 | −2.52519 | ||||||||
\(367\) | 7.10976e139 | 1.19551 | 0.597757 | − | 0.801678i | \(-0.296059\pi\) | ||||
0.597757 | + | 0.801678i | \(0.296059\pi\) | |||||||
\(368\) | −7.05259e139 | −1.02245 | ||||||||
\(369\) | −7.32700e137 | −0.00916198 | ||||||||
\(370\) | 8.15013e138 | 0.0879368 | ||||||||
\(371\) | 7.05392e139 | 0.656981 | ||||||||
\(372\) | −4.05746e139 | −0.326335 | ||||||||
\(373\) | 1.48848e140 | 1.03421 | 0.517107 | − | 0.855921i | \(-0.327009\pi\) | ||||
0.517107 | + | 0.855921i | \(0.327009\pi\) | |||||||
\(374\) | −8.89070e139 | −0.533868 | ||||||||
\(375\) | 2.49322e139 | 0.129436 | ||||||||
\(376\) | −1.45956e139 | −0.0655366 | ||||||||
\(377\) | 9.13828e139 | 0.355026 | ||||||||
\(378\) | −2.62271e140 | −0.881955 | ||||||||
\(379\) | 3.23786e140 | 0.942803 | 0.471402 | − | 0.881919i | \(-0.343748\pi\) | ||||
0.471402 | + | 0.881919i | \(0.343748\pi\) | |||||||
\(380\) | 4.18279e139 | 0.105502 | ||||||||
\(381\) | −3.60878e140 | −0.788768 | ||||||||
\(382\) | 9.56852e140 | 1.81297 | ||||||||
\(383\) | −2.90202e138 | −0.00476834 | −0.00238417 | − | 0.999997i | \(-0.500759\pi\) | ||||
−0.00238417 | + | 0.999997i | \(0.500759\pi\) | |||||||
\(384\) | −8.94915e139 | −0.127565 | ||||||||
\(385\) | 1.83231e139 | 0.0226667 | ||||||||
\(386\) | −7.27683e140 | −0.781509 | ||||||||
\(387\) | −2.11603e138 | −0.00197366 | ||||||||
\(388\) | 6.38040e140 | 0.517034 | ||||||||
\(389\) | −1.30244e141 | −0.917287 | −0.458644 | − | 0.888620i | \(-0.651665\pi\) | ||||
−0.458644 | + | 0.888620i | \(0.651665\pi\) | |||||||
\(390\) | 1.14415e140 | 0.0700589 | ||||||||
\(391\) | 1.26817e141 | 0.675376 | ||||||||
\(392\) | −8.34456e139 | −0.0386645 | ||||||||
\(393\) | −6.03636e139 | −0.0243434 | ||||||||
\(394\) | −5.95116e141 | −2.08957 | ||||||||
\(395\) | −1.92925e140 | −0.0589992 | ||||||||
\(396\) | −1.02331e139 | −0.00272659 | ||||||||
\(397\) | 4.65632e140 | 0.108134 | 0.0540668 | − | 0.998537i | \(-0.482782\pi\) | ||||
0.0540668 | + | 0.998537i | \(0.482782\pi\) | |||||||
\(398\) | −6.38651e141 | −1.29311 | ||||||||
\(399\) | 6.04364e141 | 1.06727 | ||||||||
\(400\) | 6.74533e141 | 1.03928 | ||||||||
\(401\) | 4.10237e141 | 0.551654 | 0.275827 | − | 0.961207i | \(-0.411048\pi\) | ||||
0.275827 | + | 0.961207i | \(0.411048\pi\) | |||||||
\(402\) | 1.48518e142 | 1.74365 | ||||||||
\(403\) | −2.58406e141 | −0.264958 | ||||||||
\(404\) | −2.13842e141 | −0.191561 | ||||||||
\(405\) | 8.26245e140 | 0.0646860 | ||||||||
\(406\) | 5.90515e141 | 0.404168 | ||||||||
\(407\) | 8.95332e141 | 0.535906 | ||||||||
\(408\) | 8.40643e140 | 0.0440182 | ||||||||
\(409\) | −3.31649e142 | −1.51970 | −0.759850 | − | 0.650098i | \(-0.774728\pi\) | ||||
−0.759850 | + | 0.650098i | \(0.774728\pi\) | |||||||
\(410\) | 4.02491e141 | 0.161449 | ||||||||
\(411\) | −2.54452e142 | −0.893772 | ||||||||
\(412\) | −5.78468e142 | −1.77984 | ||||||||
\(413\) | −3.37444e141 | −0.0909754 | ||||||||
\(414\) | 2.98937e140 | 0.00706416 | ||||||||
\(415\) | 5.17852e141 | 0.107296 | ||||||||
\(416\) | 5.93190e142 | 1.07797 | ||||||||
\(417\) | −7.28136e142 | −1.16091 | ||||||||
\(418\) | 9.41052e142 | 1.31676 | ||||||||
\(419\) | 1.21164e143 | 1.48837 | 0.744185 | − | 0.667973i | \(-0.232838\pi\) | ||||
0.744185 | + | 0.667973i | \(0.232838\pi\) | |||||||
\(420\) | 3.61014e141 | 0.0389437 | ||||||||
\(421\) | −1.96025e143 | −1.85754 | −0.928768 | − | 0.370661i | \(-0.879131\pi\) | ||||
−0.928768 | + | 0.370661i | \(0.879131\pi\) | |||||||
\(422\) | 1.62187e143 | 1.35048 | ||||||||
\(423\) | 7.21542e140 | 0.00528094 | ||||||||
\(424\) | −1.03853e142 | −0.0668315 | ||||||||
\(425\) | −1.21292e143 | −0.686494 | ||||||||
\(426\) | 2.22773e143 | 1.10927 | ||||||||
\(427\) | −2.60077e143 | −1.13968 | ||||||||
\(428\) | −8.06273e142 | −0.311026 | ||||||||
\(429\) | 1.25691e143 | 0.426955 | ||||||||
\(430\) | 1.16239e142 | 0.0347792 | ||||||||
\(431\) | 3.86754e143 | 1.01959 | 0.509793 | − | 0.860297i | \(-0.329722\pi\) | ||||
0.509793 | + | 0.860297i | \(0.329722\pi\) | |||||||
\(432\) | 4.50349e143 | 1.04637 | ||||||||
\(433\) | 7.82836e142 | 0.160354 | 0.0801771 | − | 0.996781i | \(-0.474451\pi\) | ||||
0.0801771 | + | 0.996781i | \(0.474451\pi\) | |||||||
\(434\) | −1.66982e143 | −0.301633 | ||||||||
\(435\) | −1.86998e142 | −0.0297970 | ||||||||
\(436\) | −1.16768e144 | −1.64176 | ||||||||
\(437\) | −1.34232e144 | −1.66578 | ||||||||
\(438\) | −3.95246e143 | −0.433040 | ||||||||
\(439\) | 3.98186e143 | 0.385274 | 0.192637 | − | 0.981270i | \(-0.438296\pi\) | ||||
0.192637 | + | 0.981270i | \(0.438296\pi\) | |||||||
\(440\) | −2.69767e141 | −0.00230578 | ||||||||
\(441\) | 4.12519e141 | 0.00311559 | ||||||||
\(442\) | −1.11560e144 | −0.744724 | ||||||||
\(443\) | 2.91682e144 | 1.72150 | 0.860750 | − | 0.509028i | \(-0.169995\pi\) | ||||
0.860750 | + | 0.509028i | \(0.169995\pi\) | |||||||
\(444\) | 1.76404e144 | 0.920741 | ||||||||
\(445\) | −1.09007e143 | −0.0503308 | ||||||||
\(446\) | −2.69570e144 | −1.10134 | ||||||||
\(447\) | 7.88564e143 | 0.285152 | ||||||||
\(448\) | 1.78167e144 | 0.570396 | ||||||||
\(449\) | 4.18120e144 | 1.18543 | 0.592715 | − | 0.805413i | \(-0.298056\pi\) | ||||
0.592715 | + | 0.805413i | \(0.298056\pi\) | |||||||
\(450\) | −2.85913e142 | −0.00718045 | ||||||||
\(451\) | 4.42157e144 | 0.983908 | ||||||||
\(452\) | 6.49900e142 | 0.0128175 | ||||||||
\(453\) | −1.40401e144 | −0.245481 | ||||||||
\(454\) | −6.53602e144 | −1.01337 | ||||||||
\(455\) | 2.29917e143 | 0.0316192 | ||||||||
\(456\) | −8.89793e143 | −0.108569 | ||||||||
\(457\) | −5.85132e144 | −0.633609 | −0.316804 | − | 0.948491i | \(-0.602610\pi\) | ||||
−0.316804 | + | 0.948491i | \(0.602610\pi\) | |||||||
\(458\) | −8.47761e144 | −0.814901 | ||||||||
\(459\) | −8.09804e144 | −0.691175 | ||||||||
\(460\) | −8.01828e143 | −0.0607826 | ||||||||
\(461\) | −1.72477e145 | −1.16153 | −0.580766 | − | 0.814071i | \(-0.697247\pi\) | ||||
−0.580766 | + | 0.814071i | \(0.697247\pi\) | |||||||
\(462\) | 8.12215e144 | 0.486053 | ||||||||
\(463\) | 2.23810e145 | 1.19046 | 0.595230 | − | 0.803555i | \(-0.297061\pi\) | ||||
0.595230 | + | 0.803555i | \(0.297061\pi\) | |||||||
\(464\) | −1.01398e145 | −0.479514 | ||||||||
\(465\) | 5.28779e143 | 0.0222376 | ||||||||
\(466\) | 3.43489e145 | 1.28493 | ||||||||
\(467\) | 2.29371e145 | 0.763428 | 0.381714 | − | 0.924280i | \(-0.375334\pi\) | ||||
0.381714 | + | 0.924280i | \(0.375334\pi\) | |||||||
\(468\) | −1.28405e143 | −0.00380349 | ||||||||
\(469\) | 2.98446e145 | 0.786948 | ||||||||
\(470\) | −3.96361e144 | −0.0930589 | ||||||||
\(471\) | −7.06580e145 | −1.47748 | ||||||||
\(472\) | 4.96812e143 | 0.00925450 | ||||||||
\(473\) | 1.27694e145 | 0.211952 | ||||||||
\(474\) | −8.55185e145 | −1.26515 | ||||||||
\(475\) | 1.28384e146 | 1.69320 | ||||||||
\(476\) | −3.52005e145 | −0.413970 | ||||||||
\(477\) | 5.13406e143 | 0.00538529 | ||||||||
\(478\) | 9.80036e145 | 0.917111 | ||||||||
\(479\) | −4.89548e145 | −0.408799 | −0.204400 | − | 0.978888i | \(-0.565524\pi\) | ||||
−0.204400 | + | 0.978888i | \(0.565524\pi\) | |||||||
\(480\) | −1.21385e145 | −0.0904729 | ||||||||
\(481\) | 1.12346e146 | 0.747568 | ||||||||
\(482\) | −8.23208e145 | −0.489154 | ||||||||
\(483\) | −1.15855e146 | −0.614887 | ||||||||
\(484\) | −1.39487e146 | −0.661398 | ||||||||
\(485\) | −8.31512e144 | −0.0352325 | ||||||||
\(486\) | −3.80797e144 | −0.0144217 | ||||||||
\(487\) | −1.96256e146 | −0.664500 | −0.332250 | − | 0.943191i | \(-0.607808\pi\) | ||||
−0.332250 | + | 0.943191i | \(0.607808\pi\) | |||||||
\(488\) | 3.82905e145 | 0.115934 | ||||||||
\(489\) | −2.10750e146 | −0.570736 | ||||||||
\(490\) | −2.26607e145 | −0.0549019 | ||||||||
\(491\) | −7.63740e146 | −1.65579 | −0.827893 | − | 0.560886i | \(-0.810461\pi\) | ||||
−0.827893 | + | 0.560886i | \(0.810461\pi\) | |||||||
\(492\) | 8.71166e146 | 1.69045 | ||||||||
\(493\) | 1.82331e146 | 0.316741 | ||||||||
\(494\) | 1.18083e147 | 1.83683 | ||||||||
\(495\) | 1.33361e143 | 0.000185800 0 | ||||||||
\(496\) | 2.86727e146 | 0.357864 | ||||||||
\(497\) | 4.47661e146 | 0.500640 | ||||||||
\(498\) | 2.29550e147 | 2.30080 | ||||||||
\(499\) | −1.09773e147 | −0.986314 | −0.493157 | − | 0.869940i | \(-0.664157\pi\) | ||||
−0.493157 | + | 0.869940i | \(0.664157\pi\) | |||||||
\(500\) | 1.53705e146 | 0.123829 | ||||||||
\(501\) | −2.24896e147 | −1.62489 | ||||||||
\(502\) | −2.70661e147 | −1.75418 | ||||||||
\(503\) | 7.26062e146 | 0.422200 | 0.211100 | − | 0.977464i | \(-0.432295\pi\) | ||||
0.211100 | + | 0.977464i | \(0.432295\pi\) | |||||||
\(504\) | 3.98198e143 | 0.000207795 0 | ||||||||
\(505\) | 2.78685e145 | 0.0130537 | ||||||||
\(506\) | −1.80397e147 | −0.758622 | ||||||||
\(507\) | −1.06409e147 | −0.401832 | ||||||||
\(508\) | −2.22478e147 | −0.754597 | ||||||||
\(509\) | 4.39329e147 | 1.33866 | 0.669331 | − | 0.742964i | \(-0.266581\pi\) | ||||
0.669331 | + | 0.742964i | \(0.266581\pi\) | |||||||
\(510\) | 2.28287e146 | 0.0625039 | ||||||||
\(511\) | −7.94246e146 | −0.195441 | ||||||||
\(512\) | −6.28000e147 | −1.38914 | ||||||||
\(513\) | 8.57151e147 | 1.70475 | ||||||||
\(514\) | 9.75166e146 | 0.174417 | ||||||||
\(515\) | 7.53876e146 | 0.121285 | ||||||||
\(516\) | 2.51591e147 | 0.364155 | ||||||||
\(517\) | −4.35423e147 | −0.567122 | ||||||||
\(518\) | 7.25979e147 | 0.851045 | ||||||||
\(519\) | 6.84996e146 | 0.0722881 | ||||||||
\(520\) | −3.38503e145 | −0.00321647 | ||||||||
\(521\) | 3.17006e147 | 0.271276 | 0.135638 | − | 0.990758i | \(-0.456692\pi\) | ||||
0.135638 | + | 0.990758i | \(0.456692\pi\) | |||||||
\(522\) | 4.29795e145 | 0.00331298 | ||||||||
\(523\) | 4.11162e147 | 0.285543 | 0.142771 | − | 0.989756i | \(-0.454399\pi\) | ||||
0.142771 | + | 0.989756i | \(0.454399\pi\) | |||||||
\(524\) | −3.72136e146 | −0.0232888 | ||||||||
\(525\) | 1.10807e148 | 0.625009 | ||||||||
\(526\) | −2.88495e148 | −1.46695 | ||||||||
\(527\) | −5.15584e147 | −0.236385 | ||||||||
\(528\) | −1.39467e148 | −0.576663 | ||||||||
\(529\) | −1.08041e147 | −0.0402954 | ||||||||
\(530\) | −2.82027e147 | −0.0948978 | ||||||||
\(531\) | −2.45602e145 | −0.000745729 0 | ||||||||
\(532\) | 3.72585e148 | 1.02104 | ||||||||
\(533\) | 5.54817e148 | 1.37251 | ||||||||
\(534\) | −4.83200e148 | −1.07927 | ||||||||
\(535\) | 1.05076e147 | 0.0211944 | ||||||||
\(536\) | −4.39396e147 | −0.0800525 | ||||||||
\(537\) | −1.17084e149 | −1.92708 | ||||||||
\(538\) | −3.93307e148 | −0.584922 | ||||||||
\(539\) | −2.48939e148 | −0.334584 | ||||||||
\(540\) | 5.12014e147 | 0.0622045 | ||||||||
\(541\) | −8.28104e146 | −0.00909565 | −0.00454783 | − | 0.999990i | \(-0.501448\pi\) | ||||
−0.00454783 | + | 0.999990i | \(0.501448\pi\) | |||||||
\(542\) | 6.40114e148 | 0.635764 | ||||||||
\(543\) | 1.19057e149 | 1.06946 | ||||||||
\(544\) | 1.18356e149 | 0.961724 | ||||||||
\(545\) | 1.52175e148 | 0.111875 | ||||||||
\(546\) | 1.01916e149 | 0.678024 | ||||||||
\(547\) | 2.33897e149 | 1.40837 | 0.704183 | − | 0.710019i | \(-0.251313\pi\) | ||||
0.704183 | + | 0.710019i | \(0.251313\pi\) | |||||||
\(548\) | −1.56868e149 | −0.855052 | ||||||||
\(549\) | −1.89292e147 | −0.00934198 | ||||||||
\(550\) | 1.72537e149 | 0.771111 | ||||||||
\(551\) | −1.92992e149 | −0.781226 | ||||||||
\(552\) | 1.70571e148 | 0.0625496 | ||||||||
\(553\) | −1.71849e149 | −0.570989 | ||||||||
\(554\) | −3.40519e149 | −1.02532 | ||||||||
\(555\) | −2.29895e148 | −0.0627425 | ||||||||
\(556\) | −4.48889e149 | −1.11061 | ||||||||
\(557\) | −6.72972e149 | −1.50969 | −0.754847 | − | 0.655901i | \(-0.772289\pi\) | ||||
−0.754847 | + | 0.655901i | \(0.772289\pi\) | |||||||
\(558\) | −1.21534e147 | −0.00247249 | ||||||||
\(559\) | 1.60230e149 | 0.295665 | ||||||||
\(560\) | −2.55117e148 | −0.0427062 | ||||||||
\(561\) | 2.50785e149 | 0.380913 | ||||||||
\(562\) | 1.58868e150 | 2.18982 | ||||||||
\(563\) | −1.56865e149 | −0.196254 | −0.0981270 | − | 0.995174i | \(-0.531285\pi\) | ||||
−0.0981270 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(564\) | −8.57899e149 | −0.974372 | ||||||||
\(565\) | −8.46968e146 | −0.000873427 0 | ||||||||
\(566\) | 1.13539e150 | 1.06329 | ||||||||
\(567\) | 7.35985e149 | 0.626025 | ||||||||
\(568\) | −6.59081e148 | −0.0509278 | ||||||||
\(569\) | 2.40146e149 | 0.168600 | 0.0842998 | − | 0.996440i | \(-0.473135\pi\) | ||||
0.0842998 | + | 0.996440i | \(0.473135\pi\) | |||||||
\(570\) | −2.41635e149 | −0.154163 | ||||||||
\(571\) | −2.97299e149 | −0.172395 | −0.0861975 | − | 0.996278i | \(-0.527472\pi\) | ||||
−0.0861975 | + | 0.996278i | \(0.527472\pi\) | |||||||
\(572\) | 7.74874e149 | 0.408458 | ||||||||
\(573\) | −2.69904e150 | −1.29355 | ||||||||
\(574\) | 3.58522e150 | 1.56249 | ||||||||
\(575\) | −2.46108e150 | −0.975503 | ||||||||
\(576\) | 1.29676e148 | 0.00467555 | ||||||||
\(577\) | −3.73020e150 | −1.22363 | −0.611816 | − | 0.791000i | \(-0.709561\pi\) | ||||
−0.611816 | + | 0.791000i | \(0.709561\pi\) | |||||||
\(578\) | 2.45740e150 | 0.733515 | ||||||||
\(579\) | 2.05261e150 | 0.557604 | ||||||||
\(580\) | −1.15283e149 | −0.0285061 | ||||||||
\(581\) | 4.61281e150 | 1.03840 | ||||||||
\(582\) | −3.68588e150 | −0.755507 | ||||||||
\(583\) | −3.09821e150 | −0.578328 | ||||||||
\(584\) | 1.16935e149 | 0.0198813 | ||||||||
\(585\) | 1.67341e147 | 0.000259184 0 | ||||||||
\(586\) | −1.10760e151 | −1.56301 | ||||||||
\(587\) | −2.27443e149 | −0.0292480 | −0.0146240 | − | 0.999893i | \(-0.504655\pi\) | ||||
−0.0146240 | + | 0.999893i | \(0.504655\pi\) | |||||||
\(588\) | −4.90477e150 | −0.574849 | ||||||||
\(589\) | 5.45728e150 | 0.583033 | ||||||||
\(590\) | 1.34916e149 | 0.0131410 | ||||||||
\(591\) | 1.67868e151 | 1.49090 | ||||||||
\(592\) | −1.24659e151 | −1.00970 | ||||||||
\(593\) | 2.75411e150 | 0.203470 | 0.101735 | − | 0.994812i | \(-0.467561\pi\) | ||||
0.101735 | + | 0.994812i | \(0.467561\pi\) | |||||||
\(594\) | 1.15194e151 | 0.776369 | ||||||||
\(595\) | 4.58742e149 | 0.0282094 | ||||||||
\(596\) | 4.86143e150 | 0.272799 | ||||||||
\(597\) | 1.80148e151 | 0.922630 | ||||||||
\(598\) | −2.26361e151 | −1.05825 | ||||||||
\(599\) | 2.69438e150 | 0.115000 | 0.0575000 | − | 0.998346i | \(-0.481687\pi\) | ||||
0.0575000 | + | 0.998346i | \(0.481687\pi\) | |||||||
\(600\) | −1.63139e150 | −0.0635793 | ||||||||
\(601\) | 3.99687e151 | 1.42253 | 0.711265 | − | 0.702924i | \(-0.248123\pi\) | ||||
0.711265 | + | 0.702924i | \(0.248123\pi\) | |||||||
\(602\) | 1.03541e151 | 0.336591 | ||||||||
\(603\) | 2.17218e149 | 0.00645064 | ||||||||
\(604\) | −8.65560e150 | −0.234847 | ||||||||
\(605\) | 1.81784e150 | 0.0450700 | ||||||||
\(606\) | 1.23534e151 | 0.279916 | ||||||||
\(607\) | −4.71998e151 | −0.977590 | −0.488795 | − | 0.872399i | \(-0.662563\pi\) | ||||
−0.488795 | + | 0.872399i | \(0.662563\pi\) | |||||||
\(608\) | −1.25276e152 | −2.37205 | ||||||||
\(609\) | −1.66570e151 | −0.288373 | ||||||||
\(610\) | 1.03983e151 | 0.164621 | ||||||||
\(611\) | −5.46367e151 | −0.791113 | ||||||||
\(612\) | −2.56200e149 | −0.00339333 | ||||||||
\(613\) | −6.97271e151 | −0.844901 | −0.422451 | − | 0.906386i | \(-0.638830\pi\) | ||||
−0.422451 | + | 0.906386i | \(0.638830\pi\) | |||||||
\(614\) | 8.97263e151 | 0.994817 | ||||||||
\(615\) | −1.13533e151 | −0.115193 | ||||||||
\(616\) | −2.40297e150 | −0.0223151 | ||||||||
\(617\) | 1.38408e152 | 1.17658 | 0.588289 | − | 0.808650i | \(-0.299802\pi\) | ||||
0.588289 | + | 0.808650i | \(0.299802\pi\) | |||||||
\(618\) | 3.34174e152 | 2.60076 | ||||||||
\(619\) | −2.77559e151 | −0.197794 | −0.0988972 | − | 0.995098i | \(-0.531532\pi\) | ||||
−0.0988972 | + | 0.995098i | \(0.531532\pi\) | |||||||
\(620\) | 3.25988e150 | 0.0212743 | ||||||||
\(621\) | −1.64313e152 | −0.982155 | ||||||||
\(622\) | 3.68514e152 | 2.01780 | ||||||||
\(623\) | −9.70989e151 | −0.487097 | ||||||||
\(624\) | −1.75003e152 | −0.804422 | ||||||||
\(625\) | 2.34382e152 | 0.987334 | ||||||||
\(626\) | −3.63807e152 | −1.40465 | ||||||||
\(627\) | −2.65448e152 | −0.939502 | ||||||||
\(628\) | −4.35601e152 | −1.41347 | ||||||||
\(629\) | 2.24158e152 | 0.666951 | ||||||||
\(630\) | 1.08136e149 | 0.000295059 0 | ||||||||
\(631\) | 5.40222e152 | 1.35199 | 0.675993 | − | 0.736908i | \(-0.263715\pi\) | ||||
0.675993 | + | 0.736908i | \(0.263715\pi\) | |||||||
\(632\) | 2.53010e151 | 0.0580840 | ||||||||
\(633\) | −4.57489e152 | −0.963560 | ||||||||
\(634\) | 8.76063e152 | 1.69305 | ||||||||
\(635\) | 2.89940e151 | 0.0514209 | ||||||||
\(636\) | −6.10430e152 | −0.993625 | ||||||||
\(637\) | −3.12368e152 | −0.466732 | ||||||||
\(638\) | −2.59365e152 | −0.355782 | ||||||||
\(639\) | 3.25821e150 | 0.00410376 | ||||||||
\(640\) | 7.19001e150 | 0.00831612 | ||||||||
\(641\) | −1.28863e153 | −1.36888 | −0.684441 | − | 0.729069i | \(-0.739954\pi\) | ||||
−0.684441 | + | 0.729069i | \(0.739954\pi\) | |||||||
\(642\) | 4.65774e152 | 0.454482 | ||||||||
\(643\) | 1.11168e153 | 0.996513 | 0.498256 | − | 0.867030i | \(-0.333974\pi\) | ||||
0.498256 | + | 0.867030i | \(0.333974\pi\) | |||||||
\(644\) | −7.14235e152 | −0.588249 | ||||||||
\(645\) | −3.27881e151 | −0.0248149 | ||||||||
\(646\) | 2.35605e153 | 1.63875 | ||||||||
\(647\) | −2.23161e153 | −1.42671 | −0.713354 | − | 0.700804i | \(-0.752825\pi\) | ||||
−0.713354 | + | 0.700804i | \(0.752825\pi\) | |||||||
\(648\) | −1.08357e152 | −0.0636826 | ||||||||
\(649\) | 1.48211e152 | 0.0800840 | ||||||||
\(650\) | 2.16499e153 | 1.07567 | ||||||||
\(651\) | 4.71014e152 | 0.215214 | ||||||||
\(652\) | −1.29926e153 | −0.546011 | ||||||||
\(653\) | 2.84275e153 | 1.09893 | 0.549466 | − | 0.835516i | \(-0.314831\pi\) | ||||
0.549466 | + | 0.835516i | \(0.314831\pi\) | |||||||
\(654\) | 6.74554e153 | 2.39899 | ||||||||
\(655\) | 4.84978e150 | 0.00158698 | ||||||||
\(656\) | −6.15625e153 | −1.85377 | ||||||||
\(657\) | −5.78076e150 | −0.00160204 | ||||||||
\(658\) | −3.53062e153 | −0.900617 | ||||||||
\(659\) | 2.20008e153 | 0.516635 | 0.258317 | − | 0.966060i | \(-0.416832\pi\) | ||||
0.258317 | + | 0.966060i | \(0.416832\pi\) | |||||||
\(660\) | −1.58564e152 | −0.0342814 | ||||||||
\(661\) | −8.61845e153 | −1.71573 | −0.857867 | − | 0.513872i | \(-0.828210\pi\) | ||||
−0.857867 | + | 0.513872i | \(0.828210\pi\) | |||||||
\(662\) | −5.94205e153 | −1.08937 | ||||||||
\(663\) | 3.14684e153 | 0.531358 | ||||||||
\(664\) | −6.79134e152 | −0.105632 | ||||||||
\(665\) | −4.85564e152 | −0.0695772 | ||||||||
\(666\) | 5.28390e151 | 0.00697604 | ||||||||
\(667\) | 3.69959e153 | 0.450087 | ||||||||
\(668\) | −1.38646e154 | −1.55450 | ||||||||
\(669\) | 7.60392e153 | 0.785803 | ||||||||
\(670\) | −1.19324e153 | −0.113671 | ||||||||
\(671\) | 1.14230e154 | 1.00324 | ||||||||
\(672\) | −1.08125e154 | −0.875589 | ||||||||
\(673\) | 6.72013e153 | 0.501830 | 0.250915 | − | 0.968009i | \(-0.419269\pi\) | ||||
0.250915 | + | 0.968009i | \(0.419269\pi\) | |||||||
\(674\) | 3.27079e154 | 2.25262 | ||||||||
\(675\) | 1.57155e154 | 0.998324 | ||||||||
\(676\) | −6.56003e153 | −0.384424 | ||||||||
\(677\) | −8.09368e153 | −0.437586 | −0.218793 | − | 0.975771i | \(-0.570212\pi\) | ||||
−0.218793 | + | 0.975771i | \(0.570212\pi\) | |||||||
\(678\) | −3.75439e152 | −0.0187293 | ||||||||
\(679\) | −7.40677e153 | −0.340978 | ||||||||
\(680\) | −6.75397e151 | −0.00286961 | ||||||||
\(681\) | 1.84365e154 | 0.723038 | ||||||||
\(682\) | 7.33413e153 | 0.265522 | ||||||||
\(683\) | −3.88180e154 | −1.29749 | −0.648746 | − | 0.761005i | \(-0.724706\pi\) | ||||
−0.648746 | + | 0.761005i | \(0.724706\pi\) | |||||||
\(684\) | 2.71179e152 | 0.00836948 | ||||||||
\(685\) | 2.04434e153 | 0.0582663 | ||||||||
\(686\) | −5.36047e154 | −1.41104 | ||||||||
\(687\) | 2.39133e154 | 0.581429 | ||||||||
\(688\) | −1.77791e154 | −0.399338 | ||||||||
\(689\) | −3.88762e154 | −0.806745 | ||||||||
\(690\) | 4.63206e153 | 0.0888176 | ||||||||
\(691\) | −3.61696e154 | −0.640900 | −0.320450 | − | 0.947265i | \(-0.603834\pi\) | ||||
−0.320450 | + | 0.947265i | \(0.603834\pi\) | |||||||
\(692\) | 4.22294e153 | 0.0691565 | ||||||||
\(693\) | 1.18792e152 | 0.00179816 | ||||||||
\(694\) | 1.61537e155 | 2.26037 | ||||||||
\(695\) | 5.85006e153 | 0.0756812 | ||||||||
\(696\) | 2.45237e153 | 0.0293348 | ||||||||
\(697\) | 1.10700e155 | 1.22450 | ||||||||
\(698\) | −1.26629e155 | −1.29543 | ||||||||
\(699\) | −9.68898e154 | −0.916794 | ||||||||
\(700\) | 6.83118e154 | 0.597933 | ||||||||
\(701\) | −1.75193e155 | −1.41868 | −0.709340 | − | 0.704867i | \(-0.751007\pi\) | ||||
−0.709340 | + | 0.704867i | \(0.751007\pi\) | |||||||
\(702\) | 1.44545e155 | 1.08300 | ||||||||
\(703\) | −2.37264e155 | −1.64500 | ||||||||
\(704\) | −7.82543e154 | −0.502109 | ||||||||
\(705\) | 1.11804e154 | 0.0663972 | ||||||||
\(706\) | 4.91038e155 | 2.69935 | ||||||||
\(707\) | 2.48241e154 | 0.126332 | ||||||||
\(708\) | 2.92016e154 | 0.137592 | ||||||||
\(709\) | 3.25375e155 | 1.41959 | 0.709796 | − | 0.704407i | \(-0.248787\pi\) | ||||
0.709796 | + | 0.704407i | \(0.248787\pi\) | |||||||
\(710\) | −1.78982e154 | −0.0723151 | ||||||||
\(711\) | −1.25077e153 | −0.00468042 | ||||||||
\(712\) | 1.42957e154 | 0.0495501 | ||||||||
\(713\) | −1.04614e155 | −0.335902 | ||||||||
\(714\) | 2.03349e155 | 0.604907 | ||||||||
\(715\) | −1.00984e154 | −0.0278338 | ||||||||
\(716\) | −7.21814e155 | −1.84360 | ||||||||
\(717\) | −2.76444e155 | −0.654355 | ||||||||
\(718\) | −6.79272e155 | −1.49026 | ||||||||
\(719\) | 2.80951e154 | 0.0571354 | 0.0285677 | − | 0.999592i | \(-0.490905\pi\) | ||||
0.0285677 | + | 0.999592i | \(0.490905\pi\) | |||||||
\(720\) | −1.85682e152 | −0.000350064 0 | ||||||||
\(721\) | 6.71522e155 | 1.17378 | ||||||||
\(722\) | −1.63129e156 | −2.64396 | ||||||||
\(723\) | 2.32207e155 | 0.349010 | ||||||||
\(724\) | 7.33977e155 | 1.02313 | ||||||||
\(725\) | −3.53841e155 | −0.457496 | ||||||||
\(726\) | 8.05801e155 | 0.966456 | ||||||||
\(727\) | 3.43575e155 | 0.382293 | 0.191147 | − | 0.981561i | \(-0.438779\pi\) | ||||
0.191147 | + | 0.981561i | \(0.438779\pi\) | |||||||
\(728\) | −3.01524e154 | −0.0311287 | ||||||||
\(729\) | 1.04921e156 | 1.00510 | ||||||||
\(730\) | 3.17552e154 | 0.0282305 | ||||||||
\(731\) | 3.19699e155 | 0.263781 | ||||||||
\(732\) | 2.25064e156 | 1.72366 | ||||||||
\(733\) | −5.00657e154 | −0.0355938 | −0.0177969 | − | 0.999842i | \(-0.505665\pi\) | ||||
−0.0177969 | + | 0.999842i | \(0.505665\pi\) | |||||||
\(734\) | −2.53207e156 | −1.67124 | ||||||||
\(735\) | 6.39203e154 | 0.0391723 | ||||||||
\(736\) | 2.40150e156 | 1.36660 | ||||||||
\(737\) | −1.31083e156 | −0.692736 | ||||||||
\(738\) | 2.60944e154 | 0.0128078 | ||||||||
\(739\) | 1.34210e156 | 0.611875 | 0.305937 | − | 0.952052i | \(-0.401030\pi\) | ||||
0.305937 | + | 0.952052i | \(0.401030\pi\) | |||||||
\(740\) | −1.41728e155 | −0.0600244 | ||||||||
\(741\) | −3.33083e156 | −1.31057 | ||||||||
\(742\) | −2.51218e156 | −0.918413 | ||||||||
\(743\) | 9.29385e155 | 0.315722 | 0.157861 | − | 0.987461i | \(-0.449540\pi\) | ||||
0.157861 | + | 0.987461i | \(0.449540\pi\) | |||||||
\(744\) | −6.93465e154 | −0.0218927 | ||||||||
\(745\) | −6.33555e154 | −0.0185895 | ||||||||
\(746\) | −5.30105e156 | −1.44576 | ||||||||
\(747\) | 3.35734e154 | 0.00851182 | ||||||||
\(748\) | 1.54607e156 | 0.364411 | ||||||||
\(749\) | 9.35972e155 | 0.205118 | ||||||||
\(750\) | −8.87932e155 | −0.180943 | ||||||||
\(751\) | −2.43545e156 | −0.461533 | −0.230766 | − | 0.973009i | \(-0.574123\pi\) | ||||
−0.230766 | + | 0.973009i | \(0.574123\pi\) | |||||||
\(752\) | 6.06249e156 | 1.06851 | ||||||||
\(753\) | 7.63468e156 | 1.25160 | ||||||||
\(754\) | −3.25450e156 | −0.496302 | ||||||||
\(755\) | 1.12802e155 | 0.0160033 | ||||||||
\(756\) | 4.56081e156 | 0.602010 | ||||||||
\(757\) | −5.10211e156 | −0.626649 | −0.313325 | − | 0.949646i | \(-0.601443\pi\) | ||||
−0.313325 | + | 0.949646i | \(0.601443\pi\) | |||||||
\(758\) | −1.15313e157 | −1.31797 | ||||||||
\(759\) | 5.08855e156 | 0.541274 | ||||||||
\(760\) | 7.14885e154 | 0.00707776 | ||||||||
\(761\) | 1.33251e156 | 0.122802 | 0.0614011 | − | 0.998113i | \(-0.480443\pi\) | ||||
0.0614011 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(762\) | 1.28523e157 | 1.10264 | ||||||||
\(763\) | 1.35551e157 | 1.08272 | ||||||||
\(764\) | −1.66394e157 | −1.23751 | ||||||||
\(765\) | 3.33887e153 | 0.000231234 0 | ||||||||
\(766\) | 1.03352e155 | 0.00666580 | ||||||||
\(767\) | 1.85975e156 | 0.111714 | ||||||||
\(768\) | 1.93452e157 | 1.08240 | ||||||||
\(769\) | −2.29704e157 | −1.19725 | −0.598623 | − | 0.801031i | \(-0.704285\pi\) | ||||
−0.598623 | + | 0.801031i | \(0.704285\pi\) | |||||||
\(770\) | −6.52557e155 | −0.0316865 | ||||||||
\(771\) | −2.75070e156 | −0.124446 | ||||||||
\(772\) | 1.26542e157 | 0.533447 | ||||||||
\(773\) | −3.91504e156 | −0.153799 | −0.0768995 | − | 0.997039i | \(-0.524502\pi\) | ||||
−0.0768995 | + | 0.997039i | \(0.524502\pi\) | |||||||
\(774\) | 7.53600e154 | 0.00275904 | ||||||||
\(775\) | 1.00057e157 | 0.341431 | ||||||||
\(776\) | 1.09048e156 | 0.0346861 | ||||||||
\(777\) | −2.04781e157 | −0.607217 | ||||||||
\(778\) | 4.63851e157 | 1.28230 | ||||||||
\(779\) | −1.17172e158 | −3.02018 | ||||||||
\(780\) | −1.98965e156 | −0.0478213 | ||||||||
\(781\) | −1.96621e157 | −0.440705 | ||||||||
\(782\) | −4.51647e157 | −0.944128 | ||||||||
\(783\) | −2.36241e157 | −0.460616 | ||||||||
\(784\) | 3.46604e157 | 0.630388 | ||||||||
\(785\) | 5.67687e156 | 0.0963192 | ||||||||
\(786\) | 2.14978e156 | 0.0340303 | ||||||||
\(787\) | 7.06698e157 | 1.04378 | 0.521892 | − | 0.853011i | \(-0.325226\pi\) | ||||
0.521892 | + | 0.853011i | \(0.325226\pi\) | |||||||
\(788\) | 1.03489e158 | 1.42631 | ||||||||
\(789\) | 8.13773e157 | 1.04666 | ||||||||
\(790\) | 6.87081e156 | 0.0824767 | ||||||||
\(791\) | −7.54444e155 | −0.00845296 | ||||||||
\(792\) | −1.74896e154 | −0.000182918 0 | ||||||||
\(793\) | 1.43336e158 | 1.39948 | ||||||||
\(794\) | −1.65830e157 | −0.151163 | ||||||||
\(795\) | 7.95529e156 | 0.0677092 | ||||||||
\(796\) | 1.11060e158 | 0.882660 | ||||||||
\(797\) | −3.65107e157 | −0.270982 | −0.135491 | − | 0.990779i | \(-0.543261\pi\) | ||||
−0.135491 | + | 0.990779i | \(0.543261\pi\) | |||||||
\(798\) | −2.15238e158 | −1.49197 | ||||||||
\(799\) | −1.09014e158 | −0.705800 | ||||||||
\(800\) | −2.29688e158 | −1.38910 | ||||||||
\(801\) | −7.06716e155 | −0.00399275 | ||||||||
\(802\) | −1.46102e158 | −0.771173 | ||||||||
\(803\) | 3.48847e157 | 0.172043 | ||||||||
\(804\) | −2.58268e158 | −1.19019 | ||||||||
\(805\) | 9.30811e156 | 0.0400854 | ||||||||
\(806\) | 9.20285e157 | 0.370393 | ||||||||
\(807\) | 1.10942e158 | 0.417340 | ||||||||
\(808\) | −3.65479e156 | −0.0128512 | ||||||||
\(809\) | 5.80414e158 | 1.90785 | 0.953923 | − | 0.300053i | \(-0.0970043\pi\) | ||||
0.953923 | + | 0.300053i | \(0.0970043\pi\) | |||||||
\(810\) | −2.94258e157 | −0.0904264 | ||||||||
\(811\) | 1.75473e158 | 0.504165 | 0.252083 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252083 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(812\) | −1.02689e158 | −0.275880 | ||||||||
\(813\) | −1.80560e158 | −0.453615 | ||||||||
\(814\) | −3.18863e158 | −0.749159 | ||||||||
\(815\) | 1.69323e157 | 0.0372071 | ||||||||
\(816\) | −3.49174e158 | −0.717675 | ||||||||
\(817\) | −3.38391e158 | −0.650603 | ||||||||
\(818\) | 1.18113e159 | 2.12443 | ||||||||
\(819\) | 1.49060e156 | 0.00250836 | ||||||||
\(820\) | −6.99921e157 | −0.110203 | ||||||||
\(821\) | 4.54576e158 | 0.669737 | 0.334869 | − | 0.942265i | \(-0.391308\pi\) | ||||
0.334869 | + | 0.942265i | \(0.391308\pi\) | |||||||
\(822\) | 9.06204e158 | 1.24943 | ||||||||
\(823\) | −6.60073e158 | −0.851728 | −0.425864 | − | 0.904787i | \(-0.640030\pi\) | ||||
−0.425864 | + | 0.904787i | \(0.640030\pi\) | |||||||
\(824\) | −9.88667e157 | −0.119403 | ||||||||
\(825\) | −4.86686e158 | −0.550184 | ||||||||
\(826\) | 1.20177e158 | 0.127177 | ||||||||
\(827\) | 3.88758e158 | 0.385149 | 0.192575 | − | 0.981282i | \(-0.438316\pi\) | ||||
0.192575 | + | 0.981282i | \(0.438316\pi\) | |||||||
\(828\) | −5.19842e156 | −0.00482190 | ||||||||
\(829\) | −9.56043e158 | −0.830339 | −0.415170 | − | 0.909744i | \(-0.636278\pi\) | ||||
−0.415170 | + | 0.909744i | \(0.636278\pi\) | |||||||
\(830\) | −1.84427e158 | −0.149992 | ||||||||
\(831\) | 9.60521e158 | 0.731562 | ||||||||
\(832\) | −9.81932e158 | −0.700423 | ||||||||
\(833\) | −6.23252e158 | −0.416400 | ||||||||
\(834\) | 2.59318e159 | 1.62287 | ||||||||
\(835\) | 1.80688e158 | 0.105929 | ||||||||
\(836\) | −1.63646e159 | −0.898801 | ||||||||
\(837\) | 6.68025e158 | 0.343760 | ||||||||
\(838\) | −4.31515e159 | −2.08064 | ||||||||
\(839\) | 1.42210e158 | 0.0642545 | 0.0321272 | − | 0.999484i | \(-0.489772\pi\) | ||||
0.0321272 | + | 0.999484i | \(0.489772\pi\) | |||||||
\(840\) | 6.17013e156 | 0.00261260 | ||||||||
\(841\) | −1.98798e159 | −0.788916 | ||||||||
\(842\) | 6.98123e159 | 2.59671 | ||||||||
\(843\) | −4.48129e159 | −1.56243 | ||||||||
\(844\) | −2.82038e159 | −0.921817 | ||||||||
\(845\) | 8.54922e157 | 0.0261960 | ||||||||
\(846\) | −2.56969e157 | −0.00738238 | ||||||||
\(847\) | 1.61926e159 | 0.436184 | ||||||||
\(848\) | 4.31371e159 | 1.08962 | ||||||||
\(849\) | −3.20266e159 | −0.758651 | ||||||||
\(850\) | 4.31970e159 | 0.959670 | ||||||||
\(851\) | 4.54828e159 | 0.947733 | ||||||||
\(852\) | −3.87395e159 | −0.757175 | ||||||||
\(853\) | 4.56241e159 | 0.836512 | 0.418256 | − | 0.908329i | \(-0.362642\pi\) | ||||
0.418256 | + | 0.908329i | \(0.362642\pi\) | |||||||
\(854\) | 9.26236e159 | 1.59319 | ||||||||
\(855\) | −3.53408e156 | −0.000570326 0 | ||||||||
\(856\) | −1.37801e158 | −0.0208657 | ||||||||
\(857\) | −4.25587e157 | −0.00604692 | −0.00302346 | − | 0.999995i | \(-0.500962\pi\) | ||||
−0.00302346 | + | 0.999995i | \(0.500962\pi\) | |||||||
\(858\) | −4.47635e159 | −0.596853 | ||||||||
\(859\) | 5.71553e159 | 0.715203 | 0.357601 | − | 0.933874i | \(-0.383595\pi\) | ||||
0.357601 | + | 0.933874i | \(0.383595\pi\) | |||||||
\(860\) | −2.02136e158 | −0.0237398 | ||||||||
\(861\) | −1.01130e160 | −1.11483 | ||||||||
\(862\) | −1.37738e160 | −1.42531 | ||||||||
\(863\) | 1.02491e159 | 0.0995632 | 0.0497816 | − | 0.998760i | \(-0.484147\pi\) | ||||
0.0497816 | + | 0.998760i | \(0.484147\pi\) | |||||||
\(864\) | −1.53350e160 | −1.39857 | ||||||||
\(865\) | −5.50345e157 | −0.00471257 | ||||||||
\(866\) | −2.78799e159 | −0.224164 | ||||||||
\(867\) | −6.93173e159 | −0.523360 | ||||||||
\(868\) | 2.90376e159 | 0.205890 | ||||||||
\(869\) | 7.54792e159 | 0.502631 | ||||||||
\(870\) | 6.65973e158 | 0.0416541 | ||||||||
\(871\) | −1.64482e160 | −0.966340 | ||||||||
\(872\) | −1.99569e159 | −0.110140 | ||||||||
\(873\) | −5.39087e157 | −0.00279501 | ||||||||
\(874\) | 4.78054e160 | 2.32865 | ||||||||
\(875\) | −1.78430e159 | −0.0816636 | ||||||||
\(876\) | 6.87321e159 | 0.295587 | ||||||||
\(877\) | 2.15553e160 | 0.871118 | 0.435559 | − | 0.900160i | \(-0.356551\pi\) | ||||
0.435559 | + | 0.900160i | \(0.356551\pi\) | |||||||
\(878\) | −1.41810e160 | −0.538586 | ||||||||
\(879\) | 3.12426e160 | 1.11520 | ||||||||
\(880\) | 1.12052e159 | 0.0375935 | ||||||||
\(881\) | −1.34416e160 | −0.423901 | −0.211950 | − | 0.977280i | \(-0.567981\pi\) | ||||
−0.211950 | + | 0.977280i | \(0.567981\pi\) | |||||||
\(882\) | −1.46914e158 | −0.00435538 | ||||||||
\(883\) | 7.25500e159 | 0.202199 | 0.101100 | − | 0.994876i | \(-0.467764\pi\) | ||||
0.101100 | + | 0.994876i | \(0.467764\pi\) | |||||||
\(884\) | 1.94000e160 | 0.508339 | ||||||||
\(885\) | −3.80564e158 | −0.00937603 | ||||||||
\(886\) | −1.03880e161 | −2.40654 | ||||||||
\(887\) | −2.66568e160 | −0.580725 | −0.290362 | − | 0.956917i | \(-0.593776\pi\) | ||||
−0.290362 | + | 0.956917i | \(0.593776\pi\) | |||||||
\(888\) | 3.01495e159 | 0.0617693 | ||||||||
\(889\) | 2.58266e160 | 0.497647 | ||||||||
\(890\) | 3.88217e159 | 0.0703589 | ||||||||
\(891\) | −3.23258e160 | −0.551079 | ||||||||
\(892\) | 4.68775e160 | 0.751761 | ||||||||
\(893\) | 1.15388e161 | 1.74082 | ||||||||
\(894\) | −2.80839e160 | −0.398623 | ||||||||
\(895\) | 9.40689e159 | 0.125629 | ||||||||
\(896\) | 6.40456e159 | 0.0804827 | ||||||||
\(897\) | 6.38509e160 | 0.755056 | ||||||||
\(898\) | −1.48909e161 | −1.65715 | ||||||||
\(899\) | −1.50409e160 | −0.157533 | ||||||||
\(900\) | 4.97194e158 | 0.00490128 | ||||||||
\(901\) | −7.75677e160 | −0.719747 | ||||||||
\(902\) | −1.57469e161 | −1.37543 | ||||||||
\(903\) | −2.92063e160 | −0.240156 | ||||||||
\(904\) | 1.11075e158 | 0.000859879 0 | ||||||||
\(905\) | −9.56539e159 | −0.0697197 | ||||||||
\(906\) | 5.00024e160 | 0.343166 | ||||||||
\(907\) | 4.81256e160 | 0.311013 | 0.155507 | − | 0.987835i | \(-0.450299\pi\) | ||||
0.155507 | + | 0.987835i | \(0.450299\pi\) | |||||||
\(908\) | 1.13660e161 | 0.691715 | ||||||||
\(909\) | 1.80677e158 | 0.00103555 | ||||||||
\(910\) | −8.18827e159 | −0.0442014 | ||||||||
\(911\) | 3.02239e160 | 0.153673 | 0.0768366 | − | 0.997044i | \(-0.475518\pi\) | ||||
0.0768366 | + | 0.997044i | \(0.475518\pi\) | |||||||
\(912\) | 3.69589e161 | 1.77011 | ||||||||
\(913\) | −2.02603e161 | −0.914087 | ||||||||
\(914\) | 2.08389e161 | 0.885740 | ||||||||
\(915\) | −2.93310e160 | −0.117457 | ||||||||
\(916\) | 1.47423e161 | 0.556240 | ||||||||
\(917\) | 4.31999e159 | 0.0153587 | ||||||||
\(918\) | 2.88403e161 | 0.966215 | ||||||||
\(919\) | −2.95847e161 | −0.934053 | −0.467027 | − | 0.884243i | \(-0.654675\pi\) | ||||
−0.467027 | + | 0.884243i | \(0.654675\pi\) | |||||||
\(920\) | −1.37041e159 | −0.00407770 | ||||||||
\(921\) | −2.53096e161 | −0.709798 | ||||||||
\(922\) | 6.14259e161 | 1.62374 | ||||||||
\(923\) | −2.46719e161 | −0.614766 | ||||||||
\(924\) | −1.41242e161 | −0.331773 | ||||||||
\(925\) | −4.35013e161 | −0.963335 | ||||||||
\(926\) | −7.97075e161 | −1.66418 | ||||||||
\(927\) | 4.88754e159 | 0.00962154 | ||||||||
\(928\) | 3.45275e161 | 0.640916 | ||||||||
\(929\) | −4.06546e160 | −0.0711629 | −0.0355815 | − | 0.999367i | \(-0.511328\pi\) | ||||
−0.0355815 | + | 0.999367i | \(0.511328\pi\) | |||||||
\(930\) | −1.88319e160 | −0.0310866 | ||||||||
\(931\) | 6.59692e161 | 1.02703 | ||||||||
\(932\) | −5.97317e161 | −0.877077 | ||||||||
\(933\) | −1.03949e162 | −1.43969 | ||||||||
\(934\) | −8.16880e161 | −1.06722 | ||||||||
\(935\) | −2.01488e160 | −0.0248322 | ||||||||
\(936\) | −2.19458e158 | −0.000255163 0 | ||||||||
\(937\) | 1.78882e162 | 1.96228 | 0.981138 | − | 0.193311i | \(-0.0619226\pi\) | ||||
0.981138 | + | 0.193311i | \(0.0619226\pi\) | |||||||
\(938\) | −1.06288e162 | −1.10010 | ||||||||
\(939\) | 1.02621e162 | 1.00222 | ||||||||
\(940\) | 6.89261e160 | 0.0635207 | ||||||||
\(941\) | 6.89283e160 | 0.0599464 | 0.0299732 | − | 0.999551i | \(-0.490458\pi\) | ||||
0.0299732 | + | 0.999551i | \(0.490458\pi\) | |||||||
\(942\) | 2.51641e162 | 2.06542 | ||||||||
\(943\) | 2.24615e162 | 1.74001 | ||||||||
\(944\) | −2.06358e161 | −0.150886 | ||||||||
\(945\) | −5.94378e160 | −0.0410231 | ||||||||
\(946\) | −4.54769e161 | −0.296295 | ||||||||
\(947\) | −1.13965e162 | −0.700965 | −0.350482 | − | 0.936569i | \(-0.613982\pi\) | ||||
−0.350482 | + | 0.936569i | \(0.613982\pi\) | |||||||
\(948\) | 1.48714e162 | 0.863571 | ||||||||
\(949\) | 4.37732e161 | 0.239993 | ||||||||
\(950\) | −4.57226e162 | −2.36698 | ||||||||
\(951\) | −2.47116e162 | −1.20799 | ||||||||
\(952\) | −6.01615e160 | −0.0277719 | ||||||||
\(953\) | 1.50922e162 | 0.657944 | 0.328972 | − | 0.944340i | \(-0.393298\pi\) | ||||
0.328972 | + | 0.944340i | \(0.393298\pi\) | |||||||
\(954\) | −1.82844e160 | −0.00752826 | ||||||||
\(955\) | 2.16849e161 | 0.0843284 | ||||||||
\(956\) | −1.70425e162 | −0.626007 | ||||||||
\(957\) | 7.31604e161 | 0.253849 | ||||||||
\(958\) | 1.74347e162 | 0.571473 | ||||||||
\(959\) | 1.82102e162 | 0.563897 | ||||||||
\(960\) | 2.00934e161 | 0.0587857 | ||||||||
\(961\) | −3.19232e162 | −0.882432 | ||||||||
\(962\) | −4.00108e162 | −1.04505 | ||||||||
\(963\) | 6.81229e159 | 0.00168136 | ||||||||
\(964\) | 1.43153e162 | 0.333890 | ||||||||
\(965\) | −1.64913e161 | −0.0363510 | ||||||||
\(966\) | 4.12605e162 | 0.859569 | ||||||||
\(967\) | 5.66771e162 | 1.11600 | 0.558000 | − | 0.829841i | \(-0.311569\pi\) | ||||
0.558000 | + | 0.829841i | \(0.311569\pi\) | |||||||
\(968\) | −2.38400e161 | −0.0443709 | ||||||||
\(969\) | −6.64583e162 | −1.16924 | ||||||||
\(970\) | 2.96134e161 | 0.0492526 | ||||||||
\(971\) | −8.55654e162 | −1.34540 | −0.672698 | − | 0.739917i | \(-0.734865\pi\) | ||||
−0.672698 | + | 0.739917i | \(0.734865\pi\) | |||||||
\(972\) | 6.62196e160 | 0.00984407 | ||||||||
\(973\) | 5.21099e162 | 0.732437 | ||||||||
\(974\) | 6.98945e162 | 0.928924 | ||||||||
\(975\) | −6.10691e162 | −0.767486 | ||||||||
\(976\) | −1.59046e163 | −1.89019 | ||||||||
\(977\) | 1.12692e163 | 1.26660 | 0.633300 | − | 0.773906i | \(-0.281700\pi\) | ||||
0.633300 | + | 0.773906i | \(0.281700\pi\) | |||||||
\(978\) | 7.50565e162 | 0.797849 | ||||||||
\(979\) | 4.26476e162 | 0.428783 | ||||||||
\(980\) | 3.94063e161 | 0.0374753 | ||||||||
\(981\) | 9.86584e160 | 0.00887510 | ||||||||
\(982\) | 2.71998e163 | 2.31467 | ||||||||
\(983\) | 2.66629e160 | 0.00214655 | 0.00107327 | − | 0.999999i | \(-0.499658\pi\) | ||||
0.00107327 | + | 0.999999i | \(0.499658\pi\) | |||||||
\(984\) | 1.48892e162 | 0.113407 | ||||||||
\(985\) | −1.34870e162 | −0.0971940 | ||||||||
\(986\) | −6.49354e162 | −0.442781 | ||||||||
\(987\) | 9.95902e162 | 0.642587 | ||||||||
\(988\) | −2.05343e163 | −1.25379 | ||||||||
\(989\) | 6.48685e162 | 0.374831 | ||||||||
\(990\) | −4.74951e159 | −0.000259735 0 | ||||||||
\(991\) | −3.68903e163 | −1.90940 | −0.954702 | − | 0.297562i | \(-0.903826\pi\) | ||||
−0.954702 | + | 0.297562i | \(0.903826\pi\) | |||||||
\(992\) | −9.76345e162 | −0.478319 | ||||||||
\(993\) | 1.67611e163 | 0.777262 | ||||||||
\(994\) | −1.59430e163 | −0.699860 | ||||||||
\(995\) | −1.44736e162 | −0.0601476 | ||||||||
\(996\) | −3.99181e163 | −1.57049 | ||||||||
\(997\) | −3.31436e163 | −1.23456 | −0.617282 | − | 0.786742i | \(-0.711766\pi\) | ||||
−0.617282 | + | 0.786742i | \(0.711766\pi\) | |||||||
\(998\) | 3.90944e163 | 1.37880 | ||||||||
\(999\) | −2.90434e163 | −0.969904 |
(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 | 1.110.a.a.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.110.a.a.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial |