Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,36,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, 36, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 36);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
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: | \(7.75951306336\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 12422194x - 2645665785 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{3}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3412.77\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −26808.0 | −0.144624 | −0.0723119 | − | 0.997382i | \(-0.523038\pi\) | ||||
−0.0723119 | + | 0.997382i | \(0.523038\pi\) | |||||||
\(3\) | 3.95729e8 | 1.76920 | 0.884598 | − | 0.466355i | \(-0.154433\pi\) | ||||
0.884598 | + | 0.466355i | \(0.154433\pi\) | |||||||
\(4\) | −3.36411e10 | −0.979084 | ||||||||
\(5\) | 8.21401e11 | 0.481482 | 0.240741 | − | 0.970589i | \(-0.422610\pi\) | ||||
0.240741 | + | 0.970589i | \(0.422610\pi\) | |||||||
\(6\) | −1.06087e13 | −0.255868 | ||||||||
\(7\) | 6.06942e14 | 0.986124 | 0.493062 | − | 0.869994i | \(-0.335878\pi\) | ||||
0.493062 | + | 0.869994i | \(0.335878\pi\) | |||||||
\(8\) | 1.82297e15 | 0.286223 | ||||||||
\(9\) | 1.06570e17 | 2.13005 | ||||||||
\(10\) | −2.20201e16 | −0.0696337 | ||||||||
\(11\) | 1.23316e18 | 0.735607 | 0.367804 | − | 0.929904i | \(-0.380110\pi\) | ||||
0.367804 | + | 0.929904i | \(0.380110\pi\) | |||||||
\(12\) | −1.33127e19 | −1.73219 | ||||||||
\(13\) | −8.46079e17 | −0.0271270 | −0.0135635 | − | 0.999908i | \(-0.504318\pi\) | ||||
−0.0135635 | + | 0.999908i | \(0.504318\pi\) | |||||||
\(14\) | −1.62709e19 | −0.142617 | ||||||||
\(15\) | 3.25052e20 | 0.851836 | ||||||||
\(16\) | 1.10703e21 | 0.937689 | ||||||||
\(17\) | −3.92226e21 | −1.14995 | −0.574976 | − | 0.818170i | \(-0.694989\pi\) | ||||
−0.574976 | + | 0.818170i | \(0.694989\pi\) | |||||||
\(18\) | −2.85692e21 | −0.308056 | ||||||||
\(19\) | −3.52757e20 | −0.0147668 | −0.00738342 | − | 0.999973i | \(-0.502350\pi\) | ||||
−0.00738342 | + | 0.999973i | \(0.502350\pi\) | |||||||
\(20\) | −2.76328e22 | −0.471411 | ||||||||
\(21\) | 2.40184e23 | 1.74465 | ||||||||
\(22\) | −3.30584e22 | −0.106386 | ||||||||
\(23\) | −8.58137e23 | −1.26858 | −0.634292 | − | 0.773093i | \(-0.718708\pi\) | ||||
−0.634292 | + | 0.773093i | \(0.718708\pi\) | |||||||
\(24\) | 7.21400e23 | 0.506384 | ||||||||
\(25\) | −2.23568e24 | −0.768175 | ||||||||
\(26\) | 2.26817e22 | 0.00392321 | ||||||||
\(27\) | 2.23738e25 | 1.99928 | ||||||||
\(28\) | −2.04182e25 | −0.965498 | ||||||||
\(29\) | −1.38664e25 | −0.354812 | −0.177406 | − | 0.984138i | \(-0.556771\pi\) | ||||
−0.177406 | + | 0.984138i | \(0.556771\pi\) | |||||||
\(30\) | −8.71400e24 | −0.123196 | ||||||||
\(31\) | −3.33324e25 | −0.265483 | −0.132741 | − | 0.991151i | \(-0.542378\pi\) | ||||
−0.132741 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(32\) | −9.23139e25 | −0.421835 | ||||||||
\(33\) | 4.87995e26 | 1.30143 | ||||||||
\(34\) | 1.05148e26 | 0.166310 | ||||||||
\(35\) | 4.98543e26 | 0.474801 | ||||||||
\(36\) | −3.58512e27 | −2.08550 | ||||||||
\(37\) | 1.99674e27 | 0.719102 | 0.359551 | − | 0.933125i | \(-0.382930\pi\) | ||||
0.359551 | + | 0.933125i | \(0.382930\pi\) | |||||||
\(38\) | 9.45671e24 | 0.00213563 | ||||||||
\(39\) | −3.34818e26 | −0.0479930 | ||||||||
\(40\) | 1.49739e27 | 0.137811 | ||||||||
\(41\) | 2.10955e28 | 1.26029 | 0.630146 | − | 0.776476i | \(-0.282995\pi\) | ||||
0.630146 | + | 0.776476i | \(0.282995\pi\) | |||||||
\(42\) | −6.43887e27 | −0.252317 | ||||||||
\(43\) | −4.57475e28 | −1.18760 | −0.593799 | − | 0.804614i | \(-0.702372\pi\) | ||||
−0.593799 | + | 0.804614i | \(0.702372\pi\) | |||||||
\(44\) | −4.14847e28 | −0.720221 | ||||||||
\(45\) | 8.75365e28 | 1.02558 | ||||||||
\(46\) | 2.30049e28 | 0.183467 | ||||||||
\(47\) | −1.72608e29 | −0.944816 | −0.472408 | − | 0.881380i | \(-0.656615\pi\) | ||||
−0.472408 | + | 0.881380i | \(0.656615\pi\) | |||||||
\(48\) | 4.38083e29 | 1.65896 | ||||||||
\(49\) | −1.04400e28 | −0.0275593 | ||||||||
\(50\) | 5.99342e28 | 0.111096 | ||||||||
\(51\) | −1.55215e30 | −2.03449 | ||||||||
\(52\) | 2.84630e28 | 0.0265596 | ||||||||
\(53\) | 1.81145e30 | 1.21115 | 0.605577 | − | 0.795786i | \(-0.292942\pi\) | ||||
0.605577 | + | 0.795786i | \(0.292942\pi\) | |||||||
\(54\) | −5.99797e29 | −0.289144 | ||||||||
\(55\) | 1.01292e30 | 0.354182 | ||||||||
\(56\) | 1.10643e30 | 0.282251 | ||||||||
\(57\) | −1.39596e29 | −0.0261254 | ||||||||
\(58\) | 3.71730e29 | 0.0513143 | ||||||||
\(59\) | −5.02395e30 | −0.514204 | −0.257102 | − | 0.966384i | \(-0.582768\pi\) | ||||
−0.257102 | + | 0.966384i | \(0.582768\pi\) | |||||||
\(60\) | −1.09351e31 | −0.834019 | ||||||||
\(61\) | −3.25742e29 | −0.0186038 | −0.00930189 | − | 0.999957i | \(-0.502961\pi\) | ||||
−0.00930189 | + | 0.999957i | \(0.502961\pi\) | |||||||
\(62\) | 8.93574e29 | 0.0383951 | ||||||||
\(63\) | 6.46817e31 | 2.10050 | ||||||||
\(64\) | −3.55625e31 | −0.876682 | ||||||||
\(65\) | −6.94970e29 | −0.0130612 | ||||||||
\(66\) | −1.30822e31 | −0.188218 | ||||||||
\(67\) | −4.01253e31 | −0.443720 | −0.221860 | − | 0.975079i | \(-0.571213\pi\) | ||||
−0.221860 | + | 0.975079i | \(0.571213\pi\) | |||||||
\(68\) | 1.31949e32 | 1.12590 | ||||||||
\(69\) | −3.39589e32 | −2.24437 | ||||||||
\(70\) | −1.33649e31 | −0.0686675 | ||||||||
\(71\) | 3.85444e32 | 1.54504 | 0.772520 | − | 0.634990i | \(-0.218996\pi\) | ||||
0.772520 | + | 0.634990i | \(0.218996\pi\) | |||||||
\(72\) | 1.94273e32 | 0.609669 | ||||||||
\(73\) | 9.93637e31 | 0.244950 | 0.122475 | − | 0.992472i | \(-0.460917\pi\) | ||||
0.122475 | + | 0.992472i | \(0.460917\pi\) | |||||||
\(74\) | −5.35285e31 | −0.103999 | ||||||||
\(75\) | −8.84724e32 | −1.35905 | ||||||||
\(76\) | 1.18671e31 | 0.0144580 | ||||||||
\(77\) | 7.48454e32 | 0.725400 | ||||||||
\(78\) | 8.97580e30 | 0.00694093 | ||||||||
\(79\) | −2.62804e33 | −1.62614 | −0.813069 | − | 0.582167i | \(-0.802205\pi\) | ||||
−0.813069 | + | 0.582167i | \(0.802205\pi\) | |||||||
\(80\) | 9.09314e32 | 0.451481 | ||||||||
\(81\) | 3.52211e33 | 1.40707 | ||||||||
\(82\) | −5.65527e32 | −0.182268 | ||||||||
\(83\) | 6.17326e33 | 1.60934 | 0.804671 | − | 0.593722i | \(-0.202342\pi\) | ||||
0.804671 | + | 0.593722i | \(0.202342\pi\) | |||||||
\(84\) | −8.08006e33 | −1.70815 | ||||||||
\(85\) | −3.22175e33 | −0.553682 | ||||||||
\(86\) | 1.22640e33 | 0.171755 | ||||||||
\(87\) | −5.48733e33 | −0.627732 | ||||||||
\(88\) | 2.24800e33 | 0.210547 | ||||||||
\(89\) | 6.75031e33 | 0.518799 | 0.259399 | − | 0.965770i | \(-0.416475\pi\) | ||||
0.259399 | + | 0.965770i | \(0.416475\pi\) | |||||||
\(90\) | −2.34668e33 | −0.148323 | ||||||||
\(91\) | −5.13521e32 | −0.0267506 | ||||||||
\(92\) | 2.88686e34 | 1.24205 | ||||||||
\(93\) | −1.31906e34 | −0.469691 | ||||||||
\(94\) | 4.62727e33 | 0.136643 | ||||||||
\(95\) | −2.89755e32 | −0.00710997 | ||||||||
\(96\) | −3.65313e34 | −0.746308 | ||||||||
\(97\) | −8.10218e34 | −1.38069 | −0.690346 | − | 0.723480i | \(-0.742542\pi\) | ||||
−0.690346 | + | 0.723480i | \(0.742542\pi\) | |||||||
\(98\) | 2.79875e32 | 0.00398573 | ||||||||
\(99\) | 1.31417e35 | 1.56688 | ||||||||
\(100\) | 7.52108e34 | 0.752108 | ||||||||
\(101\) | −1.08776e35 | −0.913923 | −0.456962 | − | 0.889486i | \(-0.651062\pi\) | ||||
−0.456962 | + | 0.889486i | \(0.651062\pi\) | |||||||
\(102\) | 4.16101e34 | 0.294236 | ||||||||
\(103\) | −2.99910e33 | −0.0178788 | −0.00893941 | − | 0.999960i | \(-0.502846\pi\) | ||||
−0.00893941 | + | 0.999960i | \(0.502846\pi\) | |||||||
\(104\) | −1.54237e33 | −0.00776436 | ||||||||
\(105\) | 1.97288e35 | 0.840016 | ||||||||
\(106\) | −4.85615e34 | −0.175162 | ||||||||
\(107\) | −3.51492e35 | −1.07572 | −0.537860 | − | 0.843034i | \(-0.680767\pi\) | ||||
−0.537860 | + | 0.843034i | \(0.680767\pi\) | |||||||
\(108\) | −7.52679e35 | −1.95746 | ||||||||
\(109\) | 6.20112e35 | 1.37248 | 0.686240 | − | 0.727375i | \(-0.259260\pi\) | ||||
0.686240 | + | 0.727375i | \(0.259260\pi\) | |||||||
\(110\) | −2.71542e34 | −0.0512231 | ||||||||
\(111\) | 7.90166e35 | 1.27223 | ||||||||
\(112\) | 6.71902e35 | 0.924678 | ||||||||
\(113\) | −7.30280e35 | −0.860234 | −0.430117 | − | 0.902773i | \(-0.641528\pi\) | ||||
−0.430117 | + | 0.902773i | \(0.641528\pi\) | |||||||
\(114\) | 3.74229e33 | 0.00377835 | ||||||||
\(115\) | −7.04874e35 | −0.610801 | ||||||||
\(116\) | 4.66480e35 | 0.347391 | ||||||||
\(117\) | −9.01664e34 | −0.0577819 | ||||||||
\(118\) | 1.34682e35 | 0.0743661 | ||||||||
\(119\) | −2.38058e36 | −1.13400 | ||||||||
\(120\) | 5.92559e35 | 0.243815 | ||||||||
\(121\) | −1.28957e36 | −0.458882 | ||||||||
\(122\) | 8.73249e33 | 0.00269055 | ||||||||
\(123\) | 8.34808e36 | 2.22970 | ||||||||
\(124\) | 1.12134e36 | 0.259930 | ||||||||
\(125\) | −4.22698e36 | −0.851345 | ||||||||
\(126\) | −1.73399e36 | −0.303781 | ||||||||
\(127\) | 5.89251e35 | 0.0898949 | 0.0449475 | − | 0.998989i | \(-0.485688\pi\) | ||||
0.0449475 | + | 0.998989i | \(0.485688\pi\) | |||||||
\(128\) | 4.12524e36 | 0.548624 | ||||||||
\(129\) | −1.81036e37 | −2.10109 | ||||||||
\(130\) | 1.86308e34 | 0.00188896 | ||||||||
\(131\) | 2.10664e37 | 1.86785 | 0.933925 | − | 0.357468i | \(-0.116360\pi\) | ||||
0.933925 | + | 0.357468i | \(0.116360\pi\) | |||||||
\(132\) | −1.64167e37 | −1.27421 | ||||||||
\(133\) | −2.14103e35 | −0.0145619 | ||||||||
\(134\) | 1.07568e36 | 0.0641725 | ||||||||
\(135\) | 1.83779e37 | 0.962618 | ||||||||
\(136\) | −7.15014e36 | −0.329142 | ||||||||
\(137\) | 2.66291e37 | 1.07832 | 0.539158 | − | 0.842204i | \(-0.318742\pi\) | ||||
0.539158 | + | 0.842204i | \(0.318742\pi\) | |||||||
\(138\) | 9.10372e36 | 0.324590 | ||||||||
\(139\) | −1.89155e37 | −0.594374 | −0.297187 | − | 0.954819i | \(-0.596048\pi\) | ||||
−0.297187 | + | 0.954819i | \(0.596048\pi\) | |||||||
\(140\) | −1.67715e37 | −0.464870 | ||||||||
\(141\) | −6.83058e37 | −1.67156 | ||||||||
\(142\) | −1.03330e37 | −0.223449 | ||||||||
\(143\) | −1.04335e36 | −0.0199548 | ||||||||
\(144\) | 1.17976e38 | 1.99733 | ||||||||
\(145\) | −1.13899e37 | −0.170836 | ||||||||
\(146\) | −2.66374e36 | −0.0354256 | ||||||||
\(147\) | −4.13140e36 | −0.0487578 | ||||||||
\(148\) | −6.71723e37 | −0.704061 | ||||||||
\(149\) | 6.86254e37 | 0.639330 | 0.319665 | − | 0.947531i | \(-0.396430\pi\) | ||||
0.319665 | + | 0.947531i | \(0.396430\pi\) | |||||||
\(150\) | 2.37177e37 | 0.196551 | ||||||||
\(151\) | 1.75463e38 | 1.29446 | 0.647229 | − | 0.762295i | \(-0.275928\pi\) | ||||
0.647229 | + | 0.762295i | \(0.275928\pi\) | |||||||
\(152\) | −6.43064e35 | −0.00422660 | ||||||||
\(153\) | −4.17994e38 | −2.44946 | ||||||||
\(154\) | −2.00646e37 | −0.104910 | ||||||||
\(155\) | −2.73792e37 | −0.127825 | ||||||||
\(156\) | 1.12636e37 | 0.0469892 | ||||||||
\(157\) | −1.13686e36 | −0.00424096 | −0.00212048 | − | 0.999998i | \(-0.500675\pi\) | ||||
−0.00212048 | + | 0.999998i | \(0.500675\pi\) | |||||||
\(158\) | 7.04525e37 | 0.235178 | ||||||||
\(159\) | 7.16845e38 | 2.14277 | ||||||||
\(160\) | −7.58267e37 | −0.203106 | ||||||||
\(161\) | −5.20839e38 | −1.25098 | ||||||||
\(162\) | −9.44207e37 | −0.203495 | ||||||||
\(163\) | 7.96117e38 | 1.54061 | 0.770307 | − | 0.637673i | \(-0.220103\pi\) | ||||
0.770307 | + | 0.637673i | \(0.220103\pi\) | |||||||
\(164\) | −7.09674e38 | −1.23393 | ||||||||
\(165\) | 4.00840e38 | 0.626616 | ||||||||
\(166\) | −1.65493e38 | −0.232749 | ||||||||
\(167\) | −9.18990e38 | −1.16352 | −0.581758 | − | 0.813362i | \(-0.697635\pi\) | ||||
−0.581758 | + | 0.813362i | \(0.697635\pi\) | |||||||
\(168\) | 4.37848e38 | 0.499357 | ||||||||
\(169\) | −9.72070e38 | −0.999264 | ||||||||
\(170\) | 8.63686e37 | 0.0800755 | ||||||||
\(171\) | −3.75932e37 | −0.0314541 | ||||||||
\(172\) | 1.53899e39 | 1.16276 | ||||||||
\(173\) | 1.70459e39 | 1.16363 | 0.581813 | − | 0.813323i | \(-0.302344\pi\) | ||||
0.581813 | + | 0.813323i | \(0.302344\pi\) | |||||||
\(174\) | 1.47104e38 | 0.0907849 | ||||||||
\(175\) | −1.35693e39 | −0.757516 | ||||||||
\(176\) | 1.36514e39 | 0.689771 | ||||||||
\(177\) | −1.98812e39 | −0.909727 | ||||||||
\(178\) | −1.80962e38 | −0.0750306 | ||||||||
\(179\) | −9.48476e38 | −0.356532 | −0.178266 | − | 0.983982i | \(-0.557049\pi\) | ||||
−0.178266 | + | 0.983982i | \(0.557049\pi\) | |||||||
\(180\) | −2.94482e39 | −1.00413 | ||||||||
\(181\) | 3.12075e39 | 0.965791 | 0.482896 | − | 0.875678i | \(-0.339585\pi\) | ||||
0.482896 | + | 0.875678i | \(0.339585\pi\) | |||||||
\(182\) | 1.37665e37 | 0.00386877 | ||||||||
\(183\) | −1.28905e38 | −0.0329137 | ||||||||
\(184\) | −1.56435e39 | −0.363097 | ||||||||
\(185\) | 1.64012e39 | 0.346235 | ||||||||
\(186\) | 3.53613e38 | 0.0679285 | ||||||||
\(187\) | −4.83675e39 | −0.845913 | ||||||||
\(188\) | 5.80670e39 | 0.925054 | ||||||||
\(189\) | 1.35796e40 | 1.97154 | ||||||||
\(190\) | 7.76775e36 | 0.00102827 | ||||||||
\(191\) | −3.57216e38 | −0.0431367 | −0.0215683 | − | 0.999767i | \(-0.506866\pi\) | ||||
−0.0215683 | + | 0.999767i | \(0.506866\pi\) | |||||||
\(192\) | −1.40731e40 | −1.55102 | ||||||||
\(193\) | −1.46241e40 | −1.47169 | −0.735847 | − | 0.677148i | \(-0.763216\pi\) | ||||
−0.735847 | + | 0.677148i | \(0.763216\pi\) | |||||||
\(194\) | 2.17203e39 | 0.199681 | ||||||||
\(195\) | −2.75020e38 | −0.0231078 | ||||||||
\(196\) | 3.51212e38 | 0.0269829 | ||||||||
\(197\) | 1.11047e40 | 0.780453 | 0.390226 | − | 0.920719i | \(-0.372397\pi\) | ||||
0.390226 | + | 0.920719i | \(0.372397\pi\) | |||||||
\(198\) | −3.52303e39 | −0.226608 | ||||||||
\(199\) | 1.81867e40 | 1.07109 | 0.535545 | − | 0.844507i | \(-0.320106\pi\) | ||||
0.535545 | + | 0.844507i | \(0.320106\pi\) | |||||||
\(200\) | −4.07558e39 | −0.219869 | ||||||||
\(201\) | −1.58787e40 | −0.785027 | ||||||||
\(202\) | 2.91607e39 | 0.132175 | ||||||||
\(203\) | −8.41610e39 | −0.349889 | ||||||||
\(204\) | 5.22160e40 | 1.99194 | ||||||||
\(205\) | 1.73278e40 | 0.606808 | ||||||||
\(206\) | 8.03998e37 | 0.00258570 | ||||||||
\(207\) | −9.14514e40 | −2.70215 | ||||||||
\(208\) | −9.36633e38 | −0.0254367 | ||||||||
\(209\) | −4.35004e38 | −0.0108626 | ||||||||
\(210\) | −5.28889e39 | −0.121486 | ||||||||
\(211\) | −6.95408e39 | −0.146993 | −0.0734965 | − | 0.997295i | \(-0.523416\pi\) | ||||
−0.0734965 | + | 0.997295i | \(0.523416\pi\) | |||||||
\(212\) | −6.09393e40 | −1.18582 | ||||||||
\(213\) | 1.52531e41 | 2.73348 | ||||||||
\(214\) | 9.42280e39 | 0.155575 | ||||||||
\(215\) | −3.75770e40 | −0.571807 | ||||||||
\(216\) | 4.07867e40 | 0.572239 | ||||||||
\(217\) | −2.02308e40 | −0.261799 | ||||||||
\(218\) | −1.66240e40 | −0.198493 | ||||||||
\(219\) | 3.93211e40 | 0.433365 | ||||||||
\(220\) | −3.40756e40 | −0.346774 | ||||||||
\(221\) | 3.31854e39 | 0.0311948 | ||||||||
\(222\) | −2.11828e40 | −0.183995 | ||||||||
\(223\) | 7.64864e40 | 0.614115 | 0.307057 | − | 0.951691i | \(-0.400656\pi\) | ||||
0.307057 | + | 0.951691i | \(0.400656\pi\) | |||||||
\(224\) | −5.60292e40 | −0.415981 | ||||||||
\(225\) | −2.38256e41 | −1.63625 | ||||||||
\(226\) | 1.95773e40 | 0.124410 | ||||||||
\(227\) | −1.63339e40 | −0.0960808 | −0.0480404 | − | 0.998845i | \(-0.515298\pi\) | ||||
−0.0480404 | + | 0.998845i | \(0.515298\pi\) | |||||||
\(228\) | 4.69616e39 | 0.0255790 | ||||||||
\(229\) | 1.58770e41 | 0.801026 | 0.400513 | − | 0.916291i | \(-0.368832\pi\) | ||||
0.400513 | + | 0.916291i | \(0.368832\pi\) | |||||||
\(230\) | 1.88963e40 | 0.0883363 | ||||||||
\(231\) | 2.96185e41 | 1.28337 | ||||||||
\(232\) | −2.52780e40 | −0.101555 | ||||||||
\(233\) | 1.16673e41 | 0.434751 | 0.217375 | − | 0.976088i | \(-0.430250\pi\) | ||||
0.217375 | + | 0.976088i | \(0.430250\pi\) | |||||||
\(234\) | 2.41718e39 | 0.00835664 | ||||||||
\(235\) | −1.41780e41 | −0.454912 | ||||||||
\(236\) | 1.69011e41 | 0.503449 | ||||||||
\(237\) | −1.03999e42 | −2.87696 | ||||||||
\(238\) | 6.38187e40 | 0.164003 | ||||||||
\(239\) | 5.09777e41 | 1.21735 | 0.608677 | − | 0.793418i | \(-0.291701\pi\) | ||||
0.608677 | + | 0.793418i | \(0.291701\pi\) | |||||||
\(240\) | 3.59842e41 | 0.798757 | ||||||||
\(241\) | −7.27282e41 | −1.50108 | −0.750541 | − | 0.660824i | \(-0.770207\pi\) | ||||
−0.750541 | + | 0.660824i | \(0.770207\pi\) | |||||||
\(242\) | 3.45708e40 | 0.0663653 | ||||||||
\(243\) | 2.74404e41 | 0.490096 | ||||||||
\(244\) | 1.09583e40 | 0.0182147 | ||||||||
\(245\) | −8.57541e39 | −0.0132693 | ||||||||
\(246\) | −2.23795e41 | −0.322468 | ||||||||
\(247\) | 2.98460e38 | 0.000400580 0 | ||||||||
\(248\) | −6.07638e40 | −0.0759872 | ||||||||
\(249\) | 2.44294e42 | 2.84724 | ||||||||
\(250\) | 1.13317e41 | 0.123125 | ||||||||
\(251\) | 4.56359e40 | 0.0462399 | 0.0231199 | − | 0.999733i | \(-0.492640\pi\) | ||||
0.0231199 | + | 0.999733i | \(0.492640\pi\) | |||||||
\(252\) | −2.17596e42 | −2.05656 | ||||||||
\(253\) | −1.05822e42 | −0.933180 | ||||||||
\(254\) | −1.57966e40 | −0.0130009 | ||||||||
\(255\) | −1.27494e42 | −0.979571 | ||||||||
\(256\) | 1.11133e42 | 0.797338 | ||||||||
\(257\) | 2.36058e41 | 0.158194 | 0.0790968 | − | 0.996867i | \(-0.474796\pi\) | ||||
0.0790968 | + | 0.996867i | \(0.474796\pi\) | |||||||
\(258\) | 4.85321e41 | 0.303868 | ||||||||
\(259\) | 1.21190e42 | 0.709124 | ||||||||
\(260\) | 2.33795e40 | 0.0127880 | ||||||||
\(261\) | −1.47774e42 | −0.755768 | ||||||||
\(262\) | −5.64748e41 | −0.270136 | ||||||||
\(263\) | 7.96602e41 | 0.356464 | 0.178232 | − | 0.983988i | \(-0.442962\pi\) | ||||
0.178232 | + | 0.983988i | \(0.442962\pi\) | |||||||
\(264\) | 8.89599e41 | 0.372499 | ||||||||
\(265\) | 1.48793e42 | 0.583149 | ||||||||
\(266\) | 5.73967e39 | 0.00210600 | ||||||||
\(267\) | 2.67129e42 | 0.917856 | ||||||||
\(268\) | 1.34986e42 | 0.434439 | ||||||||
\(269\) | −4.82372e42 | −1.45451 | −0.727256 | − | 0.686366i | \(-0.759205\pi\) | ||||
−0.727256 | + | 0.686366i | \(0.759205\pi\) | |||||||
\(270\) | −4.92674e41 | −0.139217 | ||||||||
\(271\) | −2.22025e42 | −0.588083 | −0.294042 | − | 0.955793i | \(-0.595000\pi\) | ||||
−0.294042 | + | 0.955793i | \(0.595000\pi\) | |||||||
\(272\) | −4.34205e42 | −1.07830 | ||||||||
\(273\) | −2.03215e41 | −0.0473270 | ||||||||
\(274\) | −7.13873e41 | −0.155950 | ||||||||
\(275\) | −2.75695e42 | −0.565075 | ||||||||
\(276\) | 1.14242e43 | 2.19743 | ||||||||
\(277\) | 1.62622e42 | 0.293619 | 0.146809 | − | 0.989165i | \(-0.453100\pi\) | ||||
0.146809 | + | 0.989165i | \(0.453100\pi\) | |||||||
\(278\) | 5.07088e41 | 0.0859606 | ||||||||
\(279\) | −3.55222e42 | −0.565492 | ||||||||
\(280\) | 9.08827e41 | 0.135899 | ||||||||
\(281\) | 6.29076e42 | 0.883777 | 0.441888 | − | 0.897070i | \(-0.354309\pi\) | ||||
0.441888 | + | 0.897070i | \(0.354309\pi\) | |||||||
\(282\) | 1.83114e42 | 0.241748 | ||||||||
\(283\) | 4.07259e41 | 0.0505368 | 0.0252684 | − | 0.999681i | \(-0.491956\pi\) | ||||
0.0252684 | + | 0.999681i | \(0.491956\pi\) | |||||||
\(284\) | −1.29667e43 | −1.51272 | ||||||||
\(285\) | −1.14664e41 | −0.0125789 | ||||||||
\(286\) | 2.79700e40 | 0.00288594 | ||||||||
\(287\) | 1.28037e43 | 1.24281 | ||||||||
\(288\) | −9.83787e42 | −0.898530 | ||||||||
\(289\) | 3.75055e42 | 0.322391 | ||||||||
\(290\) | 3.05340e41 | 0.0247069 | ||||||||
\(291\) | −3.20627e43 | −2.44271 | ||||||||
\(292\) | −3.34270e42 | −0.239827 | ||||||||
\(293\) | 2.65171e43 | 1.79202 | 0.896010 | − | 0.444033i | \(-0.146453\pi\) | ||||
0.896010 | + | 0.444033i | \(0.146453\pi\) | |||||||
\(294\) | 1.10755e41 | 0.00705154 | ||||||||
\(295\) | −4.12668e42 | −0.247580 | ||||||||
\(296\) | 3.63998e42 | 0.205823 | ||||||||
\(297\) | 2.75904e43 | 1.47069 | ||||||||
\(298\) | −1.83971e42 | −0.0924623 | ||||||||
\(299\) | 7.26051e41 | 0.0344129 | ||||||||
\(300\) | 2.97631e43 | 1.33063 | ||||||||
\(301\) | −2.77661e43 | −1.17112 | ||||||||
\(302\) | −4.70380e42 | −0.187209 | ||||||||
\(303\) | −4.30459e43 | −1.61691 | ||||||||
\(304\) | −3.90512e41 | −0.0138467 | ||||||||
\(305\) | −2.67565e41 | −0.00895739 | ||||||||
\(306\) | 1.12056e43 | 0.354250 | ||||||||
\(307\) | 2.04163e43 | 0.609615 | 0.304808 | − | 0.952414i | \(-0.401408\pi\) | ||||
0.304808 | + | 0.952414i | \(0.401408\pi\) | |||||||
\(308\) | −2.51788e43 | −0.710227 | ||||||||
\(309\) | −1.18683e42 | −0.0316311 | ||||||||
\(310\) | 7.33983e41 | 0.0184866 | ||||||||
\(311\) | 1.35407e43 | 0.322355 | 0.161178 | − | 0.986925i | \(-0.448471\pi\) | ||||
0.161178 | + | 0.986925i | \(0.448471\pi\) | |||||||
\(312\) | −6.10361e41 | −0.0137367 | ||||||||
\(313\) | −6.11170e43 | −1.30058 | −0.650289 | − | 0.759687i | \(-0.725352\pi\) | ||||
−0.650289 | + | 0.759687i | \(0.725352\pi\) | |||||||
\(314\) | 3.04770e40 | 0.000613343 0 | ||||||||
\(315\) | 5.31296e43 | 1.01135 | ||||||||
\(316\) | 8.84100e43 | 1.59213 | ||||||||
\(317\) | 7.44500e43 | 1.26861 | 0.634305 | − | 0.773083i | \(-0.281286\pi\) | ||||
0.634305 | + | 0.773083i | \(0.281286\pi\) | |||||||
\(318\) | −1.92172e43 | −0.309895 | ||||||||
\(319\) | −1.70994e43 | −0.261002 | ||||||||
\(320\) | −2.92110e43 | −0.422107 | ||||||||
\(321\) | −1.39095e44 | −1.90316 | ||||||||
\(322\) | 1.39627e43 | 0.180922 | ||||||||
\(323\) | 1.38360e42 | 0.0169812 | ||||||||
\(324\) | −1.18488e44 | −1.37764 | ||||||||
\(325\) | 1.89156e42 | 0.0208383 | ||||||||
\(326\) | −2.13423e43 | −0.222809 | ||||||||
\(327\) | 2.45396e44 | 2.42819 | ||||||||
\(328\) | 3.84563e43 | 0.360724 | ||||||||
\(329\) | −1.04763e44 | −0.931706 | ||||||||
\(330\) | −1.07457e43 | −0.0906236 | ||||||||
\(331\) | 2.60186e43 | 0.208110 | 0.104055 | − | 0.994572i | \(-0.466818\pi\) | ||||
0.104055 | + | 0.994572i | \(0.466818\pi\) | |||||||
\(332\) | −2.07675e44 | −1.57568 | ||||||||
\(333\) | 2.12792e44 | 1.53172 | ||||||||
\(334\) | 2.46363e43 | 0.168272 | ||||||||
\(335\) | −3.29590e43 | −0.213643 | ||||||||
\(336\) | 2.65891e44 | 1.63594 | ||||||||
\(337\) | −3.62826e43 | −0.211921 | −0.105961 | − | 0.994370i | \(-0.533792\pi\) | ||||
−0.105961 | + | 0.994370i | \(0.533792\pi\) | |||||||
\(338\) | 2.60593e43 | 0.144517 | ||||||||
\(339\) | −2.88993e44 | −1.52192 | ||||||||
\(340\) | 1.08383e44 | 0.542101 | ||||||||
\(341\) | −4.11040e43 | −0.195291 | ||||||||
\(342\) | 1.00780e42 | 0.00454901 | ||||||||
\(343\) | −2.36257e44 | −1.01330 | ||||||||
\(344\) | −8.33961e43 | −0.339917 | ||||||||
\(345\) | −2.78939e44 | −1.08063 | ||||||||
\(346\) | −4.56967e43 | −0.168288 | ||||||||
\(347\) | 3.83287e44 | 1.34202 | 0.671009 | − | 0.741449i | \(-0.265861\pi\) | ||||
0.671009 | + | 0.741449i | \(0.265861\pi\) | |||||||
\(348\) | 1.84600e44 | 0.614602 | ||||||||
\(349\) | 1.99513e44 | 0.631723 | 0.315862 | − | 0.948805i | \(-0.397706\pi\) | ||||
0.315862 | + | 0.948805i | \(0.397706\pi\) | |||||||
\(350\) | 3.63766e43 | 0.109555 | ||||||||
\(351\) | −1.89300e43 | −0.0542345 | ||||||||
\(352\) | −1.13837e44 | −0.310305 | ||||||||
\(353\) | 2.67595e44 | 0.694098 | 0.347049 | − | 0.937847i | \(-0.387184\pi\) | ||||
0.347049 | + | 0.937847i | \(0.387184\pi\) | |||||||
\(354\) | 5.32976e43 | 0.131568 | ||||||||
\(355\) | 3.16604e44 | 0.743909 | ||||||||
\(356\) | −2.27088e44 | −0.507947 | ||||||||
\(357\) | −9.42065e44 | −2.00626 | ||||||||
\(358\) | 2.54267e43 | 0.0515630 | ||||||||
\(359\) | 7.93674e44 | 1.53281 | 0.766407 | − | 0.642355i | \(-0.222043\pi\) | ||||
0.766407 | + | 0.642355i | \(0.222043\pi\) | |||||||
\(360\) | 1.59576e44 | 0.293545 | ||||||||
\(361\) | −5.70534e44 | −0.999782 | ||||||||
\(362\) | −8.36610e43 | −0.139676 | ||||||||
\(363\) | −5.10320e44 | −0.811852 | ||||||||
\(364\) | 1.72754e43 | 0.0261911 | ||||||||
\(365\) | 8.16175e43 | 0.117939 | ||||||||
\(366\) | 3.45570e42 | 0.00476011 | ||||||||
\(367\) | −4.95841e44 | −0.651158 | −0.325579 | − | 0.945515i | \(-0.605559\pi\) | ||||
−0.325579 | + | 0.945515i | \(0.605559\pi\) | |||||||
\(368\) | −9.49982e44 | −1.18954 | ||||||||
\(369\) | 2.24814e45 | 2.68449 | ||||||||
\(370\) | −4.39684e43 | −0.0500738 | ||||||||
\(371\) | 1.09945e45 | 1.19435 | ||||||||
\(372\) | 4.43745e44 | 0.459867 | ||||||||
\(373\) | 1.46949e44 | 0.145299 | 0.0726496 | − | 0.997358i | \(-0.476855\pi\) | ||||
0.0726496 | + | 0.997358i | \(0.476855\pi\) | |||||||
\(374\) | 1.29664e44 | 0.122339 | ||||||||
\(375\) | −1.67274e45 | −1.50619 | ||||||||
\(376\) | −3.14658e44 | −0.270428 | ||||||||
\(377\) | 1.17321e43 | 0.00962500 | ||||||||
\(378\) | −3.64042e44 | −0.285131 | ||||||||
\(379\) | −7.55442e44 | −0.564956 | −0.282478 | − | 0.959274i | \(-0.591156\pi\) | ||||
−0.282478 | + | 0.959274i | \(0.591156\pi\) | |||||||
\(380\) | 9.74766e42 | 0.00696125 | ||||||||
\(381\) | 2.33184e44 | 0.159042 | ||||||||
\(382\) | 9.57624e42 | 0.00623859 | ||||||||
\(383\) | −5.97753e44 | −0.372000 | −0.186000 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.186000 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(384\) | 1.63248e45 | 0.970622 | ||||||||
\(385\) | 6.14781e44 | 0.349267 | ||||||||
\(386\) | 3.92044e44 | 0.212842 | ||||||||
\(387\) | −4.87530e45 | −2.52964 | ||||||||
\(388\) | 2.72566e45 | 1.35181 | ||||||||
\(389\) | −2.41609e45 | −1.14550 | −0.572750 | − | 0.819730i | \(-0.694123\pi\) | ||||
−0.572750 | + | 0.819730i | \(0.694123\pi\) | |||||||
\(390\) | 7.37273e42 | 0.00334193 | ||||||||
\(391\) | 3.36583e45 | 1.45881 | ||||||||
\(392\) | −1.90317e43 | −0.00788810 | ||||||||
\(393\) | 8.33657e45 | 3.30459 | ||||||||
\(394\) | −2.97694e44 | −0.112872 | ||||||||
\(395\) | −2.15867e45 | −0.782957 | ||||||||
\(396\) | −4.42101e45 | −1.53411 | ||||||||
\(397\) | −1.25639e45 | −0.417148 | −0.208574 | − | 0.978007i | \(-0.566882\pi\) | ||||
−0.208574 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(398\) | −4.87550e44 | −0.154905 | ||||||||
\(399\) | −8.47267e43 | −0.0257629 | ||||||||
\(400\) | −2.47496e45 | −0.720310 | ||||||||
\(401\) | −3.77150e45 | −1.05072 | −0.525361 | − | 0.850880i | \(-0.676070\pi\) | ||||
−0.525361 | + | 0.850880i | \(0.676070\pi\) | |||||||
\(402\) | 4.25677e44 | 0.113534 | ||||||||
\(403\) | 2.82018e43 | 0.00720176 | ||||||||
\(404\) | 3.65935e45 | 0.894807 | ||||||||
\(405\) | 2.89306e45 | 0.677478 | ||||||||
\(406\) | 2.25619e44 | 0.0506022 | ||||||||
\(407\) | 2.46229e45 | 0.528977 | ||||||||
\(408\) | −2.82952e45 | −0.582317 | ||||||||
\(409\) | −5.28767e45 | −1.04257 | −0.521286 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521286 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(410\) | −4.64525e44 | −0.0877589 | ||||||||
\(411\) | 1.05379e46 | 1.90775 | ||||||||
\(412\) | 1.00893e44 | 0.0175049 | ||||||||
\(413\) | −3.04925e45 | −0.507069 | ||||||||
\(414\) | 2.45163e45 | 0.390795 | ||||||||
\(415\) | 5.07072e45 | 0.774869 | ||||||||
\(416\) | 7.81048e43 | 0.0114431 | ||||||||
\(417\) | −7.48542e45 | −1.05156 | ||||||||
\(418\) | 1.16616e43 | 0.00157099 | ||||||||
\(419\) | 3.73280e45 | 0.482270 | 0.241135 | − | 0.970492i | \(-0.422480\pi\) | ||||
0.241135 | + | 0.970492i | \(0.422480\pi\) | |||||||
\(420\) | −6.63697e45 | −0.822446 | ||||||||
\(421\) | −1.18084e45 | −0.140364 | −0.0701819 | − | 0.997534i | \(-0.522358\pi\) | ||||
−0.0701819 | + | 0.997534i | \(0.522358\pi\) | |||||||
\(422\) | 1.86425e44 | 0.0212587 | ||||||||
\(423\) | −1.83947e46 | −2.01251 | ||||||||
\(424\) | 3.30222e45 | 0.346660 | ||||||||
\(425\) | 8.76893e45 | 0.883365 | ||||||||
\(426\) | −4.08906e45 | −0.395326 | ||||||||
\(427\) | −1.97706e44 | −0.0183456 | ||||||||
\(428\) | 1.18246e46 | 1.05322 | ||||||||
\(429\) | −4.12882e44 | −0.0353040 | ||||||||
\(430\) | 1.00736e45 | 0.0826968 | ||||||||
\(431\) | 5.00269e45 | 0.394322 | 0.197161 | − | 0.980371i | \(-0.436828\pi\) | ||||
0.197161 | + | 0.980371i | \(0.436828\pi\) | |||||||
\(432\) | 2.47684e46 | 1.87471 | ||||||||
\(433\) | −1.22691e46 | −0.891817 | −0.445909 | − | 0.895079i | \(-0.647119\pi\) | ||||
−0.445909 | + | 0.895079i | \(0.647119\pi\) | |||||||
\(434\) | 5.42348e44 | 0.0378624 | ||||||||
\(435\) | −4.50730e45 | −0.302242 | ||||||||
\(436\) | −2.08612e46 | −1.34377 | ||||||||
\(437\) | 3.02714e44 | 0.0187330 | ||||||||
\(438\) | −1.05412e45 | −0.0626748 | ||||||||
\(439\) | 1.91016e46 | 1.09129 | 0.545645 | − | 0.838016i | \(-0.316285\pi\) | ||||
0.545645 | + | 0.838016i | \(0.316285\pi\) | |||||||
\(440\) | 1.84651e45 | 0.101375 | ||||||||
\(441\) | −1.11259e45 | −0.0587027 | ||||||||
\(442\) | −8.89634e43 | −0.00451151 | ||||||||
\(443\) | −1.54265e46 | −0.751973 | −0.375987 | − | 0.926625i | \(-0.622696\pi\) | ||||
−0.375987 | + | 0.926625i | \(0.622696\pi\) | |||||||
\(444\) | −2.65820e46 | −1.24562 | ||||||||
\(445\) | 5.54471e45 | 0.249792 | ||||||||
\(446\) | −2.05045e45 | −0.0888155 | ||||||||
\(447\) | 2.71570e46 | 1.13110 | ||||||||
\(448\) | −2.15843e46 | −0.864517 | ||||||||
\(449\) | −3.71387e46 | −1.43059 | −0.715296 | − | 0.698822i | \(-0.753708\pi\) | ||||
−0.715296 | + | 0.698822i | \(0.753708\pi\) | |||||||
\(450\) | 6.38718e45 | 0.236641 | ||||||||
\(451\) | 2.60140e46 | 0.927080 | ||||||||
\(452\) | 2.45674e46 | 0.842241 | ||||||||
\(453\) | 6.94356e46 | 2.29015 | ||||||||
\(454\) | 4.37878e44 | 0.0138956 | ||||||||
\(455\) | −4.21806e44 | −0.0128799 | ||||||||
\(456\) | −2.54479e44 | −0.00747768 | ||||||||
\(457\) | −1.10776e46 | −0.313266 | −0.156633 | − | 0.987657i | \(-0.550064\pi\) | ||||
−0.156633 | + | 0.987657i | \(0.550064\pi\) | |||||||
\(458\) | −4.25630e45 | −0.115847 | ||||||||
\(459\) | −8.77558e46 | −2.29908 | ||||||||
\(460\) | 2.37127e46 | 0.598025 | ||||||||
\(461\) | −3.91769e46 | −0.951183 | −0.475592 | − | 0.879666i | \(-0.657766\pi\) | ||||
−0.475592 | + | 0.879666i | \(0.657766\pi\) | |||||||
\(462\) | −7.94013e45 | −0.185606 | ||||||||
\(463\) | 5.50481e46 | 1.23901 | 0.619505 | − | 0.784992i | \(-0.287333\pi\) | ||||
0.619505 | + | 0.784992i | \(0.287333\pi\) | |||||||
\(464\) | −1.53505e46 | −0.332704 | ||||||||
\(465\) | −1.08348e46 | −0.226148 | ||||||||
\(466\) | −3.12776e45 | −0.0628753 | ||||||||
\(467\) | 2.96872e46 | 0.574808 | 0.287404 | − | 0.957809i | \(-0.407208\pi\) | ||||
0.287404 | + | 0.957809i | \(0.407208\pi\) | |||||||
\(468\) | 3.03329e45 | 0.0565734 | ||||||||
\(469\) | −2.43537e46 | −0.437563 | ||||||||
\(470\) | 3.80084e45 | 0.0657911 | ||||||||
\(471\) | −4.49889e44 | −0.00750308 | ||||||||
\(472\) | −9.15849e45 | −0.147177 | ||||||||
\(473\) | −5.64137e46 | −0.873605 | ||||||||
\(474\) | 2.78801e46 | 0.416076 | ||||||||
\(475\) | 7.88652e44 | 0.0113435 | ||||||||
\(476\) | 8.00854e46 | 1.11028 | ||||||||
\(477\) | 1.93046e47 | 2.57982 | ||||||||
\(478\) | −1.36661e46 | −0.176058 | ||||||||
\(479\) | −7.25716e46 | −0.901354 | −0.450677 | − | 0.892687i | \(-0.648817\pi\) | ||||
−0.450677 | + | 0.892687i | \(0.648817\pi\) | |||||||
\(480\) | −3.00068e46 | −0.359334 | ||||||||
\(481\) | −1.68940e45 | −0.0195071 | ||||||||
\(482\) | 1.94970e46 | 0.217092 | ||||||||
\(483\) | −2.06111e47 | −2.21323 | ||||||||
\(484\) | 4.33825e46 | 0.449284 | ||||||||
\(485\) | −6.65514e46 | −0.664778 | ||||||||
\(486\) | −7.35623e45 | −0.0708795 | ||||||||
\(487\) | −1.32479e47 | −1.23137 | −0.615686 | − | 0.787992i | \(-0.711121\pi\) | ||||
−0.615686 | + | 0.787992i | \(0.711121\pi\) | |||||||
\(488\) | −5.93816e44 | −0.00532482 | ||||||||
\(489\) | 3.15046e47 | 2.72565 | ||||||||
\(490\) | 2.29890e44 | 0.00191906 | ||||||||
\(491\) | 5.04170e46 | 0.406117 | 0.203058 | − | 0.979167i | \(-0.434912\pi\) | ||||
0.203058 | + | 0.979167i | \(0.434912\pi\) | |||||||
\(492\) | −2.80838e47 | −2.18307 | ||||||||
\(493\) | 5.43876e46 | 0.408017 | ||||||||
\(494\) | −8.00112e42 | −5.79334e−5 0 | ||||||||
\(495\) | 1.07946e47 | 0.754425 | ||||||||
\(496\) | −3.68999e46 | −0.248941 | ||||||||
\(497\) | 2.33942e47 | 1.52360 | ||||||||
\(498\) | −6.54903e46 | −0.411778 | ||||||||
\(499\) | 3.13288e46 | 0.190189 | 0.0950944 | − | 0.995468i | \(-0.469685\pi\) | ||||
0.0950944 | + | 0.995468i | \(0.469685\pi\) | |||||||
\(500\) | 1.42200e47 | 0.833538 | ||||||||
\(501\) | −3.63671e47 | −2.05849 | ||||||||
\(502\) | −1.22341e45 | −0.00668738 | ||||||||
\(503\) | 2.79560e47 | 1.47582 | 0.737912 | − | 0.674897i | \(-0.235812\pi\) | ||||
0.737912 | + | 0.674897i | \(0.235812\pi\) | |||||||
\(504\) | 1.17913e47 | 0.601209 | ||||||||
\(505\) | −8.93488e46 | −0.440038 | ||||||||
\(506\) | 2.83687e46 | 0.134960 | ||||||||
\(507\) | −3.84676e47 | −1.76789 | ||||||||
\(508\) | −1.98230e46 | −0.0880147 | ||||||||
\(509\) | −2.02483e47 | −0.868614 | −0.434307 | − | 0.900765i | \(-0.643007\pi\) | ||||
−0.434307 | + | 0.900765i | \(0.643007\pi\) | |||||||
\(510\) | 3.41785e46 | 0.141669 | ||||||||
\(511\) | 6.03080e46 | 0.241551 | ||||||||
\(512\) | −1.71535e47 | −0.663938 | ||||||||
\(513\) | −7.89251e45 | −0.0295231 | ||||||||
\(514\) | −6.32824e45 | −0.0228785 | ||||||||
\(515\) | −2.46346e45 | −0.00860833 | ||||||||
\(516\) | 6.09024e47 | 2.05714 | ||||||||
\(517\) | −2.12852e47 | −0.695014 | ||||||||
\(518\) | −3.24887e46 | −0.102556 | ||||||||
\(519\) | 6.74556e47 | 2.05868 | ||||||||
\(520\) | −1.26691e45 | −0.00373840 | ||||||||
\(521\) | −7.62521e46 | −0.217566 | −0.108783 | − | 0.994066i | \(-0.534695\pi\) | ||||
−0.108783 | + | 0.994066i | \(0.534695\pi\) | |||||||
\(522\) | 3.96152e46 | 0.109302 | ||||||||
\(523\) | 2.14532e47 | 0.572417 | 0.286208 | − | 0.958167i | \(-0.407605\pi\) | ||||
0.286208 | + | 0.958167i | \(0.407605\pi\) | |||||||
\(524\) | −7.08696e47 | −1.82878 | ||||||||
\(525\) | −5.36976e47 | −1.34019 | ||||||||
\(526\) | −2.13553e46 | −0.0515532 | ||||||||
\(527\) | 1.30738e47 | 0.305293 | ||||||||
\(528\) | 5.40225e47 | 1.22034 | ||||||||
\(529\) | 2.78811e47 | 0.609307 | ||||||||
\(530\) | −3.98884e46 | −0.0843372 | ||||||||
\(531\) | −5.35401e47 | −1.09528 | ||||||||
\(532\) | 7.20265e45 | 0.0142574 | ||||||||
\(533\) | −1.78484e46 | −0.0341880 | ||||||||
\(534\) | −7.16121e46 | −0.132744 | ||||||||
\(535\) | −2.88716e47 | −0.517940 | ||||||||
\(536\) | −7.31470e46 | −0.127003 | ||||||||
\(537\) | −3.75339e47 | −0.630774 | ||||||||
\(538\) | 1.29314e47 | 0.210357 | ||||||||
\(539\) | −1.28741e46 | −0.0202728 | ||||||||
\(540\) | −6.18251e47 | −0.942484 | ||||||||
\(541\) | 1.23166e48 | 1.81777 | 0.908884 | − | 0.417049i | \(-0.136936\pi\) | ||||
0.908884 | + | 0.417049i | \(0.136936\pi\) | |||||||
\(542\) | 5.95204e46 | 0.0850508 | ||||||||
\(543\) | 1.23497e48 | 1.70867 | ||||||||
\(544\) | 3.62079e47 | 0.485090 | ||||||||
\(545\) | 5.09360e47 | 0.660825 | ||||||||
\(546\) | 5.44779e45 | 0.00684461 | ||||||||
\(547\) | −7.20961e47 | −0.877271 | −0.438635 | − | 0.898665i | \(-0.644538\pi\) | ||||
−0.438635 | + | 0.898665i | \(0.644538\pi\) | |||||||
\(548\) | −8.95831e47 | −1.05576 | ||||||||
\(549\) | −3.47142e46 | −0.0396270 | ||||||||
\(550\) | 7.39082e46 | 0.0817233 | ||||||||
\(551\) | 4.89146e45 | 0.00523945 | ||||||||
\(552\) | −6.19060e47 | −0.642390 | ||||||||
\(553\) | −1.59507e48 | −1.60357 | ||||||||
\(554\) | −4.35958e46 | −0.0424642 | ||||||||
\(555\) | 6.49043e47 | 0.612557 | ||||||||
\(556\) | 6.36339e47 | 0.581942 | ||||||||
\(557\) | 5.88528e47 | 0.521556 | 0.260778 | − | 0.965399i | \(-0.416021\pi\) | ||||
0.260778 | + | 0.965399i | \(0.416021\pi\) | |||||||
\(558\) | 9.52280e46 | 0.0817836 | ||||||||
\(559\) | 3.87060e46 | 0.0322160 | ||||||||
\(560\) | 5.51901e47 | 0.445216 | ||||||||
\(561\) | −1.91404e48 | −1.49659 | ||||||||
\(562\) | −1.68643e47 | −0.127815 | ||||||||
\(563\) | −1.44205e48 | −1.05946 | −0.529730 | − | 0.848166i | \(-0.677707\pi\) | ||||
−0.529730 | + | 0.848166i | \(0.677707\pi\) | |||||||
\(564\) | 2.29788e48 | 1.63660 | ||||||||
\(565\) | −5.99852e47 | −0.414187 | ||||||||
\(566\) | −1.09178e46 | −0.00730882 | ||||||||
\(567\) | 2.13772e48 | 1.38754 | ||||||||
\(568\) | 7.02651e47 | 0.442225 | ||||||||
\(569\) | 1.87904e48 | 1.14676 | 0.573379 | − | 0.819290i | \(-0.305632\pi\) | ||||
0.573379 | + | 0.819290i | \(0.305632\pi\) | |||||||
\(570\) | 3.07392e45 | 0.00181921 | ||||||||
\(571\) | −1.57690e48 | −0.905050 | −0.452525 | − | 0.891752i | \(-0.649477\pi\) | ||||
−0.452525 | + | 0.891752i | \(0.649477\pi\) | |||||||
\(572\) | 3.50993e46 | 0.0195375 | ||||||||
\(573\) | −1.41361e47 | −0.0763172 | ||||||||
\(574\) | −3.43242e47 | −0.179739 | ||||||||
\(575\) | 1.91852e48 | 0.974495 | ||||||||
\(576\) | −3.78988e48 | −1.86738 | ||||||||
\(577\) | −7.02869e47 | −0.335968 | −0.167984 | − | 0.985790i | \(-0.553726\pi\) | ||||
−0.167984 | + | 0.985790i | \(0.553726\pi\) | |||||||
\(578\) | −1.00545e47 | −0.0466254 | ||||||||
\(579\) | −5.78720e48 | −2.60371 | ||||||||
\(580\) | 3.83167e47 | 0.167263 | ||||||||
\(581\) | 3.74681e48 | 1.58701 | ||||||||
\(582\) | 8.59536e47 | 0.353274 | ||||||||
\(583\) | 2.23381e48 | 0.890934 | ||||||||
\(584\) | 1.81137e47 | 0.0701103 | ||||||||
\(585\) | −7.40628e46 | −0.0278210 | ||||||||
\(586\) | −7.10871e47 | −0.259169 | ||||||||
\(587\) | −1.10752e48 | −0.391908 | −0.195954 | − | 0.980613i | \(-0.562780\pi\) | ||||
−0.195954 | + | 0.980613i | \(0.562780\pi\) | |||||||
\(588\) | 1.38985e47 | 0.0477380 | ||||||||
\(589\) | 1.17582e46 | 0.00392034 | ||||||||
\(590\) | 1.10628e47 | 0.0358059 | ||||||||
\(591\) | 4.39444e48 | 1.38077 | ||||||||
\(592\) | 2.21044e48 | 0.674294 | ||||||||
\(593\) | −2.15841e48 | −0.639258 | −0.319629 | − | 0.947543i | \(-0.603558\pi\) | ||||
−0.319629 | + | 0.947543i | \(0.603558\pi\) | |||||||
\(594\) | −7.39643e47 | −0.212696 | ||||||||
\(595\) | −1.95541e48 | −0.545999 | ||||||||
\(596\) | −2.30863e48 | −0.625958 | ||||||||
\(597\) | 7.19701e48 | 1.89497 | ||||||||
\(598\) | −1.94640e46 | −0.00497692 | ||||||||
\(599\) | −5.67895e48 | −1.41026 | −0.705129 | − | 0.709079i | \(-0.749111\pi\) | ||||
−0.705129 | + | 0.709079i | \(0.749111\pi\) | |||||||
\(600\) | −1.61282e48 | −0.388991 | ||||||||
\(601\) | 6.99029e48 | 1.63754 | 0.818770 | − | 0.574122i | \(-0.194656\pi\) | ||||
0.818770 | + | 0.574122i | \(0.194656\pi\) | |||||||
\(602\) | 7.44353e47 | 0.169371 | ||||||||
\(603\) | −4.27614e48 | −0.945147 | ||||||||
\(604\) | −5.90275e48 | −1.26738 | ||||||||
\(605\) | −1.05925e48 | −0.220944 | ||||||||
\(606\) | 1.15397e48 | 0.233843 | ||||||||
\(607\) | −4.92572e48 | −0.969768 | −0.484884 | − | 0.874578i | \(-0.661138\pi\) | ||||
−0.484884 | + | 0.874578i | \(0.661138\pi\) | |||||||
\(608\) | 3.25643e46 | 0.00622916 | ||||||||
\(609\) | −3.33049e48 | −0.619022 | ||||||||
\(610\) | 7.17287e45 | 0.00129545 | ||||||||
\(611\) | 1.46040e47 | 0.0256300 | ||||||||
\(612\) | 1.40618e49 | 2.39823 | ||||||||
\(613\) | 3.59765e48 | 0.596295 | 0.298148 | − | 0.954520i | \(-0.403631\pi\) | ||||
0.298148 | + | 0.954520i | \(0.403631\pi\) | |||||||
\(614\) | −5.47321e47 | −0.0881649 | ||||||||
\(615\) | 6.85712e48 | 1.07356 | ||||||||
\(616\) | 1.36441e48 | 0.207626 | ||||||||
\(617\) | −3.73363e48 | −0.552257 | −0.276128 | − | 0.961121i | \(-0.589051\pi\) | ||||
−0.276128 | + | 0.961121i | \(0.589051\pi\) | |||||||
\(618\) | 3.18165e46 | 0.00457461 | ||||||||
\(619\) | 2.84346e48 | 0.397430 | 0.198715 | − | 0.980057i | \(-0.436323\pi\) | ||||
0.198715 | + | 0.980057i | \(0.436323\pi\) | |||||||
\(620\) | 9.21067e47 | 0.125152 | ||||||||
\(621\) | −1.91998e49 | −2.53626 | ||||||||
\(622\) | −3.62999e47 | −0.0466202 | ||||||||
\(623\) | 4.09705e48 | 0.511600 | ||||||||
\(624\) | −3.70653e47 | −0.0450025 | ||||||||
\(625\) | 3.03465e48 | 0.358268 | ||||||||
\(626\) | 1.63843e48 | 0.188094 | ||||||||
\(627\) | −1.72144e47 | −0.0192180 | ||||||||
\(628\) | 3.82453e46 | 0.00415225 | ||||||||
\(629\) | −7.83171e48 | −0.826933 | ||||||||
\(630\) | −1.42430e48 | −0.146265 | ||||||||
\(631\) | 8.72640e48 | 0.871608 | 0.435804 | − | 0.900041i | \(-0.356464\pi\) | ||||
0.435804 | + | 0.900041i | \(0.356464\pi\) | |||||||
\(632\) | −4.79082e48 | −0.465438 | ||||||||
\(633\) | −2.75193e48 | −0.260059 | ||||||||
\(634\) | −1.99586e48 | −0.183471 | ||||||||
\(635\) | 4.84011e47 | 0.0432828 | ||||||||
\(636\) | −2.41154e49 | −2.09795 | ||||||||
\(637\) | 8.83305e45 | 0.000747602 0 | ||||||||
\(638\) | 4.58401e47 | 0.0377471 | ||||||||
\(639\) | 4.10766e49 | 3.29101 | ||||||||
\(640\) | 3.38848e48 | 0.264153 | ||||||||
\(641\) | 1.94871e49 | 1.47820 | 0.739098 | − | 0.673598i | \(-0.235252\pi\) | ||||
0.739098 | + | 0.673598i | \(0.235252\pi\) | |||||||
\(642\) | 3.72887e48 | 0.275242 | ||||||||
\(643\) | −2.20357e49 | −1.58283 | −0.791417 | − | 0.611277i | \(-0.790656\pi\) | ||||
−0.791417 | + | 0.611277i | \(0.790656\pi\) | |||||||
\(644\) | 1.75216e49 | 1.22482 | ||||||||
\(645\) | −1.48703e49 | −1.01164 | ||||||||
\(646\) | −3.70916e46 | −0.00245588 | ||||||||
\(647\) | −1.15002e49 | −0.741106 | −0.370553 | − | 0.928811i | \(-0.620832\pi\) | ||||
−0.370553 | + | 0.928811i | \(0.620832\pi\) | |||||||
\(648\) | 6.42069e48 | 0.402734 | ||||||||
\(649\) | −6.19531e48 | −0.378252 | ||||||||
\(650\) | −5.07091e46 | −0.00301371 | ||||||||
\(651\) | −8.00592e48 | −0.463174 | ||||||||
\(652\) | −2.67822e49 | −1.50839 | ||||||||
\(653\) | −3.36604e48 | −0.184560 | −0.0922801 | − | 0.995733i | \(-0.529416\pi\) | ||||
−0.0922801 | + | 0.995733i | \(0.529416\pi\) | |||||||
\(654\) | −6.57858e48 | −0.351173 | ||||||||
\(655\) | 1.73039e49 | 0.899337 | ||||||||
\(656\) | 2.33533e49 | 1.18176 | ||||||||
\(657\) | 1.05892e49 | 0.521757 | ||||||||
\(658\) | 2.80848e48 | 0.134747 | ||||||||
\(659\) | −1.07733e49 | −0.503334 | −0.251667 | − | 0.967814i | \(-0.580979\pi\) | ||||
−0.251667 | + | 0.967814i | \(0.580979\pi\) | |||||||
\(660\) | −1.34847e49 | −0.613510 | ||||||||
\(661\) | −1.67936e49 | −0.744079 | −0.372040 | − | 0.928217i | \(-0.621341\pi\) | ||||
−0.372040 | + | 0.928217i | \(0.621341\pi\) | |||||||
\(662\) | −6.97506e47 | −0.0300977 | ||||||||
\(663\) | 1.31324e48 | 0.0551897 | ||||||||
\(664\) | 1.12536e49 | 0.460630 | ||||||||
\(665\) | −1.75864e47 | −0.00701131 | ||||||||
\(666\) | −5.70452e48 | −0.221524 | ||||||||
\(667\) | 1.18993e49 | 0.450109 | ||||||||
\(668\) | 3.09158e49 | 1.13918 | ||||||||
\(669\) | 3.02679e49 | 1.08649 | ||||||||
\(670\) | 8.83564e47 | 0.0308979 | ||||||||
\(671\) | −4.01690e47 | −0.0136851 | ||||||||
\(672\) | −2.21724e49 | −0.735952 | ||||||||
\(673\) | 2.60356e49 | 0.841984 | 0.420992 | − | 0.907064i | \(-0.361682\pi\) | ||||
0.420992 | + | 0.907064i | \(0.361682\pi\) | |||||||
\(674\) | 9.72664e47 | 0.0306489 | ||||||||
\(675\) | −5.00207e49 | −1.53580 | ||||||||
\(676\) | 3.27015e49 | 0.978363 | ||||||||
\(677\) | −5.14137e49 | −1.49891 | −0.749457 | − | 0.662053i | \(-0.769685\pi\) | ||||
−0.749457 | + | 0.662053i | \(0.769685\pi\) | |||||||
\(678\) | 7.74732e48 | 0.220106 | ||||||||
\(679\) | −4.91756e49 | −1.36153 | ||||||||
\(680\) | −5.87313e48 | −0.158476 | ||||||||
\(681\) | −6.46378e48 | −0.169986 | ||||||||
\(682\) | 1.10192e48 | 0.0282437 | ||||||||
\(683\) | 3.66408e47 | 0.00915382 | 0.00457691 | − | 0.999990i | \(-0.498543\pi\) | ||||
0.00457691 | + | 0.999990i | \(0.498543\pi\) | |||||||
\(684\) | 1.26468e48 | 0.0307962 | ||||||||
\(685\) | 2.18732e49 | 0.519190 | ||||||||
\(686\) | 6.33359e48 | 0.146547 | ||||||||
\(687\) | 6.28298e49 | 1.41717 | ||||||||
\(688\) | −5.06437e49 | −1.11360 | ||||||||
\(689\) | −1.53263e48 | −0.0328550 | ||||||||
\(690\) | 7.47780e48 | 0.156284 | ||||||||
\(691\) | 8.07844e49 | 1.64612 | 0.823060 | − | 0.567954i | \(-0.192265\pi\) | ||||
0.823060 | + | 0.567954i | \(0.192265\pi\) | |||||||
\(692\) | −5.73443e49 | −1.13929 | ||||||||
\(693\) | 7.97626e49 | 1.54514 | ||||||||
\(694\) | −1.02752e49 | −0.194088 | ||||||||
\(695\) | −1.55372e49 | −0.286180 | ||||||||
\(696\) | −1.00032e49 | −0.179671 | ||||||||
\(697\) | −8.27418e49 | −1.44928 | ||||||||
\(698\) | −5.34856e48 | −0.0913622 | ||||||||
\(699\) | 4.61707e49 | 0.769159 | ||||||||
\(700\) | 4.56486e49 | 0.741672 | ||||||||
\(701\) | 1.36918e49 | 0.216968 | 0.108484 | − | 0.994098i | \(-0.465400\pi\) | ||||
0.108484 | + | 0.994098i | \(0.465400\pi\) | |||||||
\(702\) | 5.07476e47 | 0.00784360 | ||||||||
\(703\) | −7.04362e47 | −0.0106189 | ||||||||
\(704\) | −4.38540e49 | −0.644894 | ||||||||
\(705\) | −5.61065e49 | −0.804828 | ||||||||
\(706\) | −7.17369e48 | −0.100383 | ||||||||
\(707\) | −6.60208e49 | −0.901242 | ||||||||
\(708\) | 6.68826e49 | 0.890699 | ||||||||
\(709\) | 9.81931e49 | 1.27577 | 0.637884 | − | 0.770132i | \(-0.279810\pi\) | ||||
0.637884 | + | 0.770132i | \(0.279810\pi\) | |||||||
\(710\) | −8.48752e48 | −0.107587 | ||||||||
\(711\) | −2.80069e50 | −3.46376 | ||||||||
\(712\) | 1.23056e49 | 0.148492 | ||||||||
\(713\) | 2.86037e49 | 0.336787 | ||||||||
\(714\) | 2.52549e49 | 0.290153 | ||||||||
\(715\) | −8.57006e47 | −0.00960789 | ||||||||
\(716\) | 3.19077e49 | 0.349075 | ||||||||
\(717\) | 2.01733e50 | 2.15374 | ||||||||
\(718\) | −2.12768e49 | −0.221681 | ||||||||
\(719\) | 1.63037e50 | 1.65780 | 0.828899 | − | 0.559398i | \(-0.188968\pi\) | ||||
0.828899 | + | 0.559398i | \(0.188968\pi\) | |||||||
\(720\) | 9.69054e49 | 0.961677 | ||||||||
\(721\) | −1.82028e48 | −0.0176307 | ||||||||
\(722\) | 1.52949e49 | 0.144592 | ||||||||
\(723\) | −2.87806e50 | −2.65571 | ||||||||
\(724\) | −1.04985e50 | −0.945591 | ||||||||
\(725\) | 3.10009e49 | 0.272558 | ||||||||
\(726\) | 1.36807e49 | 0.117413 | ||||||||
\(727\) | 3.34890e49 | 0.280576 | 0.140288 | − | 0.990111i | \(-0.455197\pi\) | ||||
0.140288 | + | 0.990111i | \(0.455197\pi\) | |||||||
\(728\) | −9.36131e47 | −0.00765663 | ||||||||
\(729\) | −6.76269e49 | −0.539993 | ||||||||
\(730\) | −2.18800e48 | −0.0170568 | ||||||||
\(731\) | 1.79433e50 | 1.36568 | ||||||||
\(732\) | 4.33652e48 | 0.0322253 | ||||||||
\(733\) | −2.00965e50 | −1.45814 | −0.729071 | − | 0.684438i | \(-0.760048\pi\) | ||||
−0.729071 | + | 0.684438i | \(0.760048\pi\) | |||||||
\(734\) | 1.32925e49 | 0.0941729 | ||||||||
\(735\) | −3.39354e48 | −0.0234760 | ||||||||
\(736\) | 7.92179e49 | 0.535133 | ||||||||
\(737\) | −4.94807e49 | −0.326404 | ||||||||
\(738\) | −6.02681e49 | −0.388241 | ||||||||
\(739\) | −1.06372e50 | −0.669190 | −0.334595 | − | 0.942362i | \(-0.608599\pi\) | ||||
−0.334595 | + | 0.942362i | \(0.608599\pi\) | |||||||
\(740\) | −5.51754e49 | −0.338993 | ||||||||
\(741\) | 1.18109e47 | 0.000708704 0 | ||||||||
\(742\) | −2.94740e49 | −0.172731 | ||||||||
\(743\) | 7.25015e49 | 0.414995 | 0.207498 | − | 0.978236i | \(-0.433468\pi\) | ||||
0.207498 | + | 0.978236i | \(0.433468\pi\) | |||||||
\(744\) | −2.40460e49 | −0.134436 | ||||||||
\(745\) | 5.63690e49 | 0.307826 | ||||||||
\(746\) | −3.93942e48 | −0.0210137 | ||||||||
\(747\) | 6.57883e50 | 3.42798 | ||||||||
\(748\) | 1.62714e50 | 0.828220 | ||||||||
\(749\) | −2.13335e50 | −1.06079 | ||||||||
\(750\) | 4.48428e49 | 0.217832 | ||||||||
\(751\) | −4.51226e49 | −0.214139 | −0.107069 | − | 0.994252i | \(-0.534147\pi\) | ||||
−0.107069 | + | 0.994252i | \(0.534147\pi\) | |||||||
\(752\) | −1.91081e50 | −0.885944 | ||||||||
\(753\) | 1.80595e49 | 0.0818074 | ||||||||
\(754\) | −3.14513e47 | −0.00139200 | ||||||||
\(755\) | 1.44125e50 | 0.623259 | ||||||||
\(756\) | −4.56832e50 | −1.93030 | ||||||||
\(757\) | −1.21415e50 | −0.501296 | −0.250648 | − | 0.968078i | \(-0.580644\pi\) | ||||
−0.250648 | + | 0.968078i | \(0.580644\pi\) | |||||||
\(758\) | 2.02519e49 | 0.0817061 | ||||||||
\(759\) | −4.18767e50 | −1.65098 | ||||||||
\(760\) | −5.28213e47 | −0.00203503 | ||||||||
\(761\) | 3.14799e50 | 1.18523 | 0.592614 | − | 0.805486i | \(-0.298096\pi\) | ||||
0.592614 | + | 0.805486i | \(0.298096\pi\) | |||||||
\(762\) | −6.25119e48 | −0.0230012 | ||||||||
\(763\) | 3.76372e50 | 1.35344 | ||||||||
\(764\) | 1.20171e49 | 0.0422344 | ||||||||
\(765\) | −3.43341e50 | −1.17937 | ||||||||
\(766\) | 1.60246e49 | 0.0538000 | ||||||||
\(767\) | 4.25066e48 | 0.0139488 | ||||||||
\(768\) | 4.39784e50 | 1.41065 | ||||||||
\(769\) | −5.16540e50 | −1.61954 | −0.809772 | − | 0.586744i | \(-0.800409\pi\) | ||||
−0.809772 | + | 0.586744i | \(0.800409\pi\) | |||||||
\(770\) | −1.64811e49 | −0.0505123 | ||||||||
\(771\) | 9.34149e49 | 0.279875 | ||||||||
\(772\) | 4.91972e50 | 1.44091 | ||||||||
\(773\) | −4.51959e50 | −1.29407 | −0.647035 | − | 0.762460i | \(-0.723991\pi\) | ||||
−0.647035 | + | 0.762460i | \(0.723991\pi\) | |||||||
\(774\) | 1.30697e50 | 0.365846 | ||||||||
\(775\) | 7.45206e49 | 0.203937 | ||||||||
\(776\) | −1.47700e50 | −0.395185 | ||||||||
\(777\) | 4.79585e50 | 1.25458 | ||||||||
\(778\) | 6.47705e49 | 0.165666 | ||||||||
\(779\) | −7.44157e48 | −0.0186105 | ||||||||
\(780\) | 9.25195e48 | 0.0226244 | ||||||||
\(781\) | 4.75312e50 | 1.13654 | ||||||||
\(782\) | −9.02313e49 | −0.210979 | ||||||||
\(783\) | −3.10244e50 | −0.709369 | ||||||||
\(784\) | −1.15574e49 | −0.0258421 | ||||||||
\(785\) | −9.33820e47 | −0.00204195 | ||||||||
\(786\) | −2.23487e50 | −0.477923 | ||||||||
\(787\) | −7.76649e50 | −1.62430 | −0.812151 | − | 0.583447i | \(-0.801704\pi\) | ||||
−0.812151 | + | 0.583447i | \(0.801704\pi\) | |||||||
\(788\) | −3.73573e50 | −0.764129 | ||||||||
\(789\) | 3.15238e50 | 0.630655 | ||||||||
\(790\) | 5.78697e49 | 0.113234 | ||||||||
\(791\) | −4.43237e50 | −0.848297 | ||||||||
\(792\) | 2.39569e50 | 0.448477 | ||||||||
\(793\) | 2.75603e47 | 0.000504665 0 | ||||||||
\(794\) | 3.36813e49 | 0.0603295 | ||||||||
\(795\) | 5.88817e50 | 1.03171 | ||||||||
\(796\) | −6.11821e50 | −1.04869 | ||||||||
\(797\) | −7.96535e49 | −0.133562 | −0.0667812 | − | 0.997768i | \(-0.521273\pi\) | ||||
−0.0667812 | + | 0.997768i | \(0.521273\pi\) | |||||||
\(798\) | 2.27135e48 | 0.00372593 | ||||||||
\(799\) | 6.77011e50 | 1.08649 | ||||||||
\(800\) | 2.06385e50 | 0.324043 | ||||||||
\(801\) | 7.19379e50 | 1.10507 | ||||||||
\(802\) | 1.01106e50 | 0.151959 | ||||||||
\(803\) | 1.22531e50 | 0.180187 | ||||||||
\(804\) | 5.34178e50 | 0.768608 | ||||||||
\(805\) | −4.27818e50 | −0.602325 | ||||||||
\(806\) | −7.56034e47 | −0.00104155 | ||||||||
\(807\) | −1.90889e51 | −2.57332 | ||||||||
\(808\) | −1.98295e50 | −0.261585 | ||||||||
\(809\) | 8.80158e50 | 1.13622 | 0.568109 | − | 0.822954i | \(-0.307675\pi\) | ||||
0.568109 | + | 0.822954i | \(0.307675\pi\) | |||||||
\(810\) | −7.75573e49 | −0.0979794 | ||||||||
\(811\) | 1.29798e51 | 1.60473 | 0.802364 | − | 0.596835i | \(-0.203575\pi\) | ||||
0.802364 | + | 0.596835i | \(0.203575\pi\) | |||||||
\(812\) | 2.83126e50 | 0.342571 | ||||||||
\(813\) | −8.78616e50 | −1.04043 | ||||||||
\(814\) | −6.60090e49 | −0.0765026 | ||||||||
\(815\) | 6.53931e50 | 0.741778 | ||||||||
\(816\) | −1.71827e51 | −1.90772 | ||||||||
\(817\) | 1.61377e49 | 0.0175370 | ||||||||
\(818\) | 1.41752e50 | 0.150781 | ||||||||
\(819\) | −5.47258e49 | −0.0569802 | ||||||||
\(820\) | −5.82927e50 | −0.594116 | ||||||||
\(821\) | 8.37740e50 | 0.835804 | 0.417902 | − | 0.908492i | \(-0.362766\pi\) | ||||
0.417902 | + | 0.908492i | \(0.362766\pi\) | |||||||
\(822\) | −2.82500e50 | −0.275906 | ||||||||
\(823\) | −1.79490e51 | −1.71610 | −0.858051 | − | 0.513564i | \(-0.828325\pi\) | ||||
−0.858051 | + | 0.513564i | \(0.828325\pi\) | |||||||
\(824\) | −5.46725e48 | −0.00511732 | ||||||||
\(825\) | −1.09100e51 | −0.999728 | ||||||||
\(826\) | 8.17442e49 | 0.0733342 | ||||||||
\(827\) | 6.78828e50 | 0.596230 | 0.298115 | − | 0.954530i | \(-0.403642\pi\) | ||||
0.298115 | + | 0.954530i | \(0.403642\pi\) | |||||||
\(828\) | 3.07652e51 | 2.64563 | ||||||||
\(829\) | 1.62563e51 | 1.36873 | 0.684363 | − | 0.729141i | \(-0.260080\pi\) | ||||
0.684363 | + | 0.729141i | \(0.260080\pi\) | |||||||
\(830\) | −1.35936e50 | −0.112064 | ||||||||
\(831\) | 6.43543e50 | 0.519469 | ||||||||
\(832\) | 3.00886e49 | 0.0237818 | ||||||||
\(833\) | 4.09483e49 | 0.0316919 | ||||||||
\(834\) | 2.00669e50 | 0.152081 | ||||||||
\(835\) | −7.54860e50 | −0.560213 | ||||||||
\(836\) | 1.46340e49 | 0.0106354 | ||||||||
\(837\) | −7.45772e50 | −0.530775 | ||||||||
\(838\) | −1.00069e50 | −0.0697476 | ||||||||
\(839\) | −2.62276e51 | −1.79029 | −0.895147 | − | 0.445771i | \(-0.852930\pi\) | ||||
−0.895147 | + | 0.445771i | \(0.852930\pi\) | |||||||
\(840\) | 3.59649e50 | 0.240431 | ||||||||
\(841\) | −1.33504e51 | −0.874108 | ||||||||
\(842\) | 3.16560e49 | 0.0202999 | ||||||||
\(843\) | 2.48944e51 | 1.56357 | ||||||||
\(844\) | 2.33943e50 | 0.143918 | ||||||||
\(845\) | −7.98459e50 | −0.481128 | ||||||||
\(846\) | 4.93127e50 | 0.291056 | ||||||||
\(847\) | −7.82695e50 | −0.452515 | ||||||||
\(848\) | 2.00533e51 | 1.13569 | ||||||||
\(849\) | 1.61164e50 | 0.0894094 | ||||||||
\(850\) | −2.35077e50 | −0.127756 | ||||||||
\(851\) | −1.71347e51 | −0.912242 | ||||||||
\(852\) | −5.13131e51 | −2.67630 | ||||||||
\(853\) | 2.63497e51 | 1.34638 | 0.673191 | − | 0.739469i | \(-0.264923\pi\) | ||||
0.673191 | + | 0.739469i | \(0.264923\pi\) | |||||||
\(854\) | 5.30011e48 | 0.00265321 | ||||||||
\(855\) | −3.08791e49 | −0.0151446 | ||||||||
\(856\) | −6.40758e50 | −0.307895 | ||||||||
\(857\) | 1.21045e51 | 0.569880 | 0.284940 | − | 0.958545i | \(-0.408026\pi\) | ||||
0.284940 | + | 0.958545i | \(0.408026\pi\) | |||||||
\(858\) | 1.10686e49 | 0.00510579 | ||||||||
\(859\) | 1.22181e51 | 0.552234 | 0.276117 | − | 0.961124i | \(-0.410952\pi\) | ||||
0.276117 | + | 0.961124i | \(0.410952\pi\) | |||||||
\(860\) | 1.26413e51 | 0.559847 | ||||||||
\(861\) | 5.06680e51 | 2.19876 | ||||||||
\(862\) | −1.34112e50 | −0.0570283 | ||||||||
\(863\) | −1.06383e51 | −0.443284 | −0.221642 | − | 0.975128i | \(-0.571142\pi\) | ||||
−0.221642 | + | 0.975128i | \(0.571142\pi\) | |||||||
\(864\) | −2.06541e51 | −0.843366 | ||||||||
\(865\) | 1.40015e51 | 0.560265 | ||||||||
\(866\) | 3.28911e50 | 0.128978 | ||||||||
\(867\) | 1.48420e51 | 0.570373 | ||||||||
\(868\) | 6.80586e50 | 0.256323 | ||||||||
\(869\) | −3.24078e51 | −1.19620 | ||||||||
\(870\) | 1.20832e50 | 0.0437113 | ||||||||
\(871\) | 3.39491e49 | 0.0120368 | ||||||||
\(872\) | 1.13044e51 | 0.392835 | ||||||||
\(873\) | −8.63448e51 | −2.94094 | ||||||||
\(874\) | −8.11515e48 | −0.00270923 | ||||||||
\(875\) | −2.56553e51 | −0.839531 | ||||||||
\(876\) | −1.32280e51 | −0.424301 | ||||||||
\(877\) | 2.07831e51 | 0.653459 | 0.326729 | − | 0.945118i | \(-0.394053\pi\) | ||||
0.326729 | + | 0.945118i | \(0.394053\pi\) | |||||||
\(878\) | −5.12075e50 | −0.157826 | ||||||||
\(879\) | 1.04936e52 | 3.17043 | ||||||||
\(880\) | 1.12133e51 | 0.332112 | ||||||||
\(881\) | −5.23747e51 | −1.52070 | −0.760350 | − | 0.649514i | \(-0.774973\pi\) | ||||
−0.760350 | + | 0.649514i | \(0.774973\pi\) | |||||||
\(882\) | 2.98262e49 | 0.00848981 | ||||||||
\(883\) | −2.39426e51 | −0.668126 | −0.334063 | − | 0.942551i | \(-0.608420\pi\) | ||||
−0.334063 | + | 0.942551i | \(0.608420\pi\) | |||||||
\(884\) | −1.11639e50 | −0.0305423 | ||||||||
\(885\) | −1.63305e51 | −0.438017 | ||||||||
\(886\) | 4.13554e50 | 0.108753 | ||||||||
\(887\) | 4.11591e51 | 1.06121 | 0.530606 | − | 0.847618i | \(-0.321964\pi\) | ||||
0.530606 | + | 0.847618i | \(0.321964\pi\) | |||||||
\(888\) | 1.44045e51 | 0.364141 | ||||||||
\(889\) | 3.57641e50 | 0.0886476 | ||||||||
\(890\) | −1.48643e50 | −0.0361259 | ||||||||
\(891\) | 4.34331e51 | 1.03505 | ||||||||
\(892\) | −2.57309e51 | −0.601270 | ||||||||
\(893\) | 6.08885e49 | 0.0139519 | ||||||||
\(894\) | −7.28026e50 | −0.163584 | ||||||||
\(895\) | −7.79079e50 | −0.171664 | ||||||||
\(896\) | 2.50378e51 | 0.541011 | ||||||||
\(897\) | 2.87319e50 | 0.0608832 | ||||||||
\(898\) | 9.95614e50 | 0.206898 | ||||||||
\(899\) | 4.62200e50 | 0.0941966 | ||||||||
\(900\) | 8.01520e51 | 1.60203 | ||||||||
\(901\) | −7.10499e51 | −1.39277 | ||||||||
\(902\) | −6.97383e50 | −0.134078 | ||||||||
\(903\) | −1.09878e52 | −2.07194 | ||||||||
\(904\) | −1.33127e51 | −0.246218 | ||||||||
\(905\) | 2.56338e51 | 0.465011 | ||||||||
\(906\) | −1.86143e51 | −0.331210 | ||||||||
\(907\) | 1.27732e51 | 0.222932 | 0.111466 | − | 0.993768i | \(-0.464445\pi\) | ||||
0.111466 | + | 0.993768i | \(0.464445\pi\) | |||||||
\(908\) | 5.49489e50 | 0.0940712 | ||||||||
\(909\) | −1.15922e52 | −1.94670 | ||||||||
\(910\) | 1.13078e49 | 0.00186274 | ||||||||
\(911\) | 4.62833e51 | 0.747915 | 0.373958 | − | 0.927446i | \(-0.378001\pi\) | ||||
0.373958 | + | 0.927446i | \(0.378001\pi\) | |||||||
\(912\) | −1.54537e50 | −0.0244975 | ||||||||
\(913\) | 7.61259e51 | 1.18384 | ||||||||
\(914\) | 2.96970e50 | 0.0453058 | ||||||||
\(915\) | −1.05883e50 | −0.0158474 | ||||||||
\(916\) | −5.34118e51 | −0.784272 | ||||||||
\(917\) | 1.27861e52 | 1.84193 | ||||||||
\(918\) | 2.35256e51 | 0.332501 | ||||||||
\(919\) | 3.73013e50 | 0.0517253 | 0.0258626 | − | 0.999666i | \(-0.491767\pi\) | ||||
0.0258626 | + | 0.999666i | \(0.491767\pi\) | |||||||
\(920\) | −1.28496e51 | −0.174825 | ||||||||
\(921\) | 8.07933e51 | 1.07853 | ||||||||
\(922\) | 1.05026e51 | 0.137564 | ||||||||
\(923\) | −3.26116e50 | −0.0419123 | ||||||||
\(924\) | −9.96398e51 | −1.25653 | ||||||||
\(925\) | −4.46407e51 | −0.552396 | ||||||||
\(926\) | −1.47573e51 | −0.179190 | ||||||||
\(927\) | −3.19613e50 | −0.0380828 | ||||||||
\(928\) | 1.28006e51 | 0.149672 | ||||||||
\(929\) | 3.82307e51 | 0.438669 | 0.219334 | − | 0.975650i | \(-0.429611\pi\) | ||||
0.219334 | + | 0.975650i | \(0.429611\pi\) | |||||||
\(930\) | 2.90458e50 | 0.0327063 | ||||||||
\(931\) | 3.68277e48 | 0.000406964 0 | ||||||||
\(932\) | −3.92499e51 | −0.425658 | ||||||||
\(933\) | 5.35845e51 | 0.570309 | ||||||||
\(934\) | −7.95853e50 | −0.0831310 | ||||||||
\(935\) | −3.97291e51 | −0.407292 | ||||||||
\(936\) | −1.64370e50 | −0.0165385 | ||||||||
\(937\) | 1.21639e52 | 1.20124 | 0.600619 | − | 0.799536i | \(-0.294921\pi\) | ||||
0.600619 | + | 0.799536i | \(0.294921\pi\) | |||||||
\(938\) | 6.52875e50 | 0.0632820 | ||||||||
\(939\) | −2.41858e52 | −2.30098 | ||||||||
\(940\) | 4.76963e51 | 0.445397 | ||||||||
\(941\) | −1.11091e52 | −1.01827 | −0.509133 | − | 0.860688i | \(-0.670034\pi\) | ||||
−0.509133 | + | 0.860688i | \(0.670034\pi\) | |||||||
\(942\) | 1.20606e49 | 0.00108512 | ||||||||
\(943\) | −1.81028e52 | −1.59879 | ||||||||
\(944\) | −5.56166e51 | −0.482163 | ||||||||
\(945\) | 1.11543e52 | 0.949261 | ||||||||
\(946\) | 1.51234e51 | 0.126344 | ||||||||
\(947\) | 3.07714e51 | 0.252362 | 0.126181 | − | 0.992007i | \(-0.459728\pi\) | ||||
0.126181 | + | 0.992007i | \(0.459728\pi\) | |||||||
\(948\) | 3.49864e52 | 2.81678 | ||||||||
\(949\) | −8.40695e49 | −0.00664477 | ||||||||
\(950\) | −2.11422e49 | −0.00164054 | ||||||||
\(951\) | 2.94620e52 | 2.24442 | ||||||||
\(952\) | −4.33972e51 | −0.324575 | ||||||||
\(953\) | 4.41309e50 | 0.0324053 | 0.0162027 | − | 0.999869i | \(-0.494842\pi\) | ||||
0.0162027 | + | 0.999869i | \(0.494842\pi\) | |||||||
\(954\) | −5.17519e51 | −0.373104 | ||||||||
\(955\) | −2.93417e50 | −0.0207695 | ||||||||
\(956\) | −1.71494e52 | −1.19189 | ||||||||
\(957\) | −6.76673e51 | −0.461764 | ||||||||
\(958\) | 1.94550e51 | 0.130357 | ||||||||
\(959\) | 1.61623e52 | 1.06335 | ||||||||
\(960\) | −1.15596e52 | −0.746789 | ||||||||
\(961\) | −1.46527e52 | −0.929519 | ||||||||
\(962\) | 4.52893e49 | 0.00282119 | ||||||||
\(963\) | −3.74584e52 | −2.29134 | ||||||||
\(964\) | 2.44665e52 | 1.46969 | ||||||||
\(965\) | −1.20123e52 | −0.708594 | ||||||||
\(966\) | 5.52543e51 | 0.320086 | ||||||||
\(967\) | 2.95259e52 | 1.67973 | 0.839866 | − | 0.542795i | \(-0.182634\pi\) | ||||
0.839866 | + | 0.542795i | \(0.182634\pi\) | |||||||
\(968\) | −2.35084e51 | −0.131342 | ||||||||
\(969\) | 5.47532e50 | 0.0300430 | ||||||||
\(970\) | 1.78411e51 | 0.0961427 | ||||||||
\(971\) | −8.31094e51 | −0.439859 | −0.219930 | − | 0.975516i | \(-0.570583\pi\) | ||||
−0.219930 | + | 0.975516i | \(0.570583\pi\) | |||||||
\(972\) | −9.23125e51 | −0.479845 | ||||||||
\(973\) | −1.14806e52 | −0.586126 | ||||||||
\(974\) | 3.55149e51 | 0.178086 | ||||||||
\(975\) | 7.48546e50 | 0.0368670 | ||||||||
\(976\) | −3.60605e50 | −0.0174446 | ||||||||
\(977\) | −2.16398e52 | −1.02825 | −0.514125 | − | 0.857715i | \(-0.671883\pi\) | ||||
−0.514125 | + | 0.857715i | \(0.671883\pi\) | |||||||
\(978\) | −8.44577e51 | −0.394193 | ||||||||
\(979\) | 8.32419e51 | 0.381632 | ||||||||
\(980\) | 2.88486e50 | 0.0129918 | ||||||||
\(981\) | 6.60851e52 | 2.92345 | ||||||||
\(982\) | −1.35158e51 | −0.0587341 | ||||||||
\(983\) | 1.17980e51 | 0.0503643 | 0.0251822 | − | 0.999683i | \(-0.491983\pi\) | ||||
0.0251822 | + | 0.999683i | \(0.491983\pi\) | |||||||
\(984\) | 1.52183e52 | 0.638192 | ||||||||
\(985\) | 9.12139e51 | 0.375774 | ||||||||
\(986\) | −1.45802e51 | −0.0590090 | ||||||||
\(987\) | −4.14577e52 | −1.64837 | ||||||||
\(988\) | −1.00405e49 | −0.000392202 0 | ||||||||
\(989\) | 3.92576e52 | 1.50657 | ||||||||
\(990\) | −2.89382e51 | −0.109108 | ||||||||
\(991\) | −1.92041e52 | −0.711387 | −0.355694 | − | 0.934603i | \(-0.615755\pi\) | ||||
−0.355694 | + | 0.934603i | \(0.615755\pi\) | |||||||
\(992\) | 3.07704e51 | 0.111990 | ||||||||
\(993\) | 1.02963e52 | 0.368188 | ||||||||
\(994\) | −6.27152e51 | −0.220349 | ||||||||
\(995\) | 1.49386e52 | 0.515710 | ||||||||
\(996\) | −8.21830e52 | −2.78769 | ||||||||
\(997\) | −4.51709e52 | −1.50554 | −0.752772 | − | 0.658281i | \(-0.771284\pi\) | ||||
−0.752772 | + | 0.658281i | \(0.771284\pi\) | |||||||
\(998\) | −8.39864e50 | −0.0275058 | ||||||||
\(999\) | 4.46746e52 | 1.43769 |
(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 | 1.36.a.a.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 9.36.a.b.1.2 | 3 | |||
4.3 | odd | 2 | 16.36.a.d.1.1 | 3 | |||
5.2 | odd | 4 | 25.36.b.a.24.3 | 6 | |||
5.3 | odd | 4 | 25.36.b.a.24.4 | 6 | |||
5.4 | even | 2 | 25.36.a.a.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.36.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.36.a.b.1.2 | 3 | 3.2 | odd | 2 | |||
16.36.a.d.1.1 | 3 | 4.3 | odd | 2 | |||
25.36.a.a.1.2 | 3 | 5.4 | even | 2 | |||
25.36.b.a.24.3 | 6 | 5.2 | odd | 4 | |||
25.36.b.a.24.4 | 6 | 5.3 | odd | 4 |